LMFDB - Embedded newform 273.2.l.c.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Root			$0.328258 + 0.568560i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.c.256.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.656517 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.56899 q^{4} +(-0.0109774 + 0.0190133i) q^{5} +(-0.328258 + 0.568560i) q^{6} +(-1.55912 + 2.13756i) q^{7} -2.34310 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+0.656517 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.56899 q^{4} +(-0.0109774 + 0.0190133i) q^{5} +(-0.328258 + 0.568560i) q^{6} +(-1.55912 + 2.13756i) q^{7} -2.34310 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.00720682 + 0.0124826i) q^{10} +(-1.69615 + 2.93782i) q^{11} +(0.784493 - 1.35878i) q^{12} +(-2.82607 + 2.23905i) q^{13} +(-1.02359 + 1.40334i) q^{14} +(-0.0109774 - 0.0190133i) q^{15} +1.59969 q^{16} +3.32836 q^{17} +(-0.328258 - 0.568560i) q^{18} +(-1.66694 - 2.88722i) q^{19} +(0.0172233 - 0.0298316i) q^{20} +(-1.07162 - 2.41901i) q^{21} +(-1.11355 + 1.92873i) q^{22} -5.50172 q^{23} +(1.17155 - 2.02918i) q^{24} +(2.49976 + 4.32971i) q^{25} +(-1.85536 + 1.46998i) q^{26} +1.00000 q^{27} +(2.44623 - 3.35380i) q^{28} +(3.52603 + 6.10726i) q^{29} +(-0.00720682 - 0.0124826i) q^{30} +(-3.13349 - 5.42737i) q^{31} +5.73642 q^{32} +(-1.69615 - 2.93782i) q^{33} +2.18512 q^{34} +(-0.0235271 - 0.0531087i) q^{35} +(0.784493 + 1.35878i) q^{36} +4.90882 q^{37} +(-1.09437 - 1.89551i) q^{38} +(-0.526042 - 3.56697i) q^{39} +(0.0257210 - 0.0445501i) q^{40} +(1.27443 + 2.20738i) q^{41} +(-0.703538 - 1.58812i) q^{42} +(4.49157 - 7.77963i) q^{43} +(2.66124 - 4.60940i) q^{44} +0.0219547 q^{45} -3.61197 q^{46} +(-4.08171 + 7.06973i) q^{47} +(-0.799843 + 1.38537i) q^{48} +(-2.13831 - 6.66540i) q^{49} +(1.64113 + 2.84253i) q^{50} +(-1.66418 + 2.88244i) q^{51} +(4.43406 - 3.51304i) q^{52} +(5.68199 + 9.84149i) q^{53} +0.656517 q^{54} +(-0.0372385 - 0.0644990i) q^{55} +(3.65316 - 5.00851i) q^{56} +3.33387 q^{57} +(2.31490 + 4.00952i) q^{58} +12.1859 q^{59} +(0.0172233 + 0.0298316i) q^{60} +(-5.23676 - 9.07034i) q^{61} +(-2.05719 - 3.56316i) q^{62} +(2.63074 + 0.281455i) q^{63} +0.566683 q^{64} +(-0.0115491 - 0.0783118i) q^{65} +(-1.11355 - 1.92873i) q^{66} +(-5.35554 + 9.27608i) q^{67} -5.22215 q^{68} +(2.75086 - 4.76463i) q^{69} +(-0.0154460 - 0.0348668i) q^{70} +(-3.57850 + 6.19814i) q^{71} +(1.17155 + 2.02918i) q^{72} +(0.102129 + 0.176893i) q^{73} +3.22272 q^{74} -4.99952 q^{75} +(2.61540 + 4.53000i) q^{76} +(-3.63526 - 8.20602i) q^{77} +(-0.345356 - 2.34178i) q^{78} +(-3.42085 + 5.92509i) q^{79} +(-0.0175603 + 0.0304154i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.836686 + 1.44918i) q^{82} -14.4458 q^{83} +(1.68136 + 3.79540i) q^{84} +(-0.0365366 + 0.0632832i) q^{85} +(2.94879 - 5.10746i) q^{86} -7.05206 q^{87} +(3.97425 - 6.88360i) q^{88} -5.45516 q^{89} +0.0144136 q^{90} +(-0.379938 - 9.53182i) q^{91} +8.63212 q^{92} +6.26699 q^{93} +(-2.67971 + 4.64140i) q^{94} +0.0731942 q^{95} +(-2.86821 + 4.96789i) q^{96} +(4.71678 - 8.16970i) q^{97} +(-1.40384 - 4.37595i) q^{98} +3.39230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.656517			0.464228			0.232114	−	0.972689i	$-0.425436\pi$
$2$	0.656517			0.464228			0.232114	+	0.972689i	$0.425436\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.56899			−0.784493
$5$	−0.0109774	+	0.0190133i	−0.00490922	+	0.00850302i	−0.868470	−	0.495742i	$-0.834896\pi$
$5$	−0.0109774	+	0.0190133i	−0.00490922	+	0.00850302i	0.863560	+	0.504245i	$0.168229\pi$
$6$	−0.328258	+	0.568560i	−0.134011	+	0.232114i
$7$	−1.55912	+	2.13756i	−0.589291	+	0.807921i
$7$	−1.55912	+	2.13756i	−0.589291	+	0.807921i
$8$	−2.34310			−0.828411
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.00720682	+	0.0124826i	−0.00227900	+	0.00394734i
$11$	−1.69615	+	2.93782i	−0.511409	+	0.885786i	0.488504	+	0.872562i	$0.337543\pi$
$11$	−1.69615	+	2.93782i	−0.511409	+	0.885786i	−0.999913	+	0.0132240i	$0.995791\pi$
$12$	0.784493	−	1.35878i	0.226464	−	0.392246i
$13$	−2.82607	+	2.23905i	−0.783810	+	0.621001i
$13$	−2.82607	+	2.23905i	−0.783810	+	0.621001i
$14$	−1.02359	+	1.40334i	−0.273565	+	0.375059i
$15$	−0.0109774	−	0.0190133i	−0.00283434	−	0.00490922i
$16$	1.59969			0.399922
$17$	3.32836			0.807246			0.403623	−	0.914925i	$-0.367751\pi$
$17$	3.32836			0.807246			0.403623	+	0.914925i	$0.367751\pi$
$18$	−0.328258	−	0.568560i	−0.0773713	−	0.134011i
$19$	−1.66694	−	2.88722i	−0.382421	−	0.662373i	0.608987	−	0.793181i	$-0.291576\pi$
$19$	−1.66694	−	2.88722i	−0.382421	−	0.662373i	−0.991408	+	0.130808i	$0.958243\pi$
$20$	0.0172233	−	0.0298316i	0.00385125	−	0.00667056i
$21$	−1.07162	−	2.41901i	−0.233847	−	0.527872i
$22$	−1.11355	+	1.92873i	−0.237410	+	0.411206i
$23$	−5.50172			−1.14719			−0.573594	−	0.819140i	$-0.694451\pi$
$23$	−5.50172			−1.14719			−0.573594	+	0.819140i	$0.694451\pi$
$24$	1.17155	−	2.02918i	0.239142	−	0.414205i
$25$	2.49976	+	4.32971i	0.499952	+	0.865942i
$26$	−1.85536	+	1.46998i	−0.363866	+	0.288286i
$27$	1.00000			0.192450
$28$	2.44623	−	3.35380i	0.462294	−	0.633808i
$29$	3.52603	+	6.10726i	0.654767	+	1.13409i	0.981952	+	0.189130i	$0.0605668\pi$
$29$	3.52603	+	6.10726i	0.654767	+	1.13409i	−0.327185	+	0.944960i	$0.606100\pi$
$30$	−0.00720682	−	0.0124826i	−0.00131578	−	0.00227900i
$31$	−3.13349	−	5.42737i	−0.562792	−	0.974785i	−0.997251	−	0.0740931i	$-0.976394\pi$
$31$	−3.13349	−	5.42737i	−0.562792	−	0.974785i	0.434459	−	0.900692i	$-0.356940\pi$
$32$	5.73642			1.01407
$33$	−1.69615	−	2.93782i	−0.295262	−	0.511409i
$34$	2.18512			0.374746
$35$	−0.0235271	−	0.0531087i	−0.00397681	−	0.00897702i
$36$	0.784493	+	1.35878i	0.130749	+	0.226464i
$37$	4.90882			0.807005			0.403502	−	0.914979i	$-0.367793\pi$
$37$	4.90882			0.807005			0.403502	+	0.914979i	$0.367793\pi$
$38$	−1.09437	−	1.89551i	−0.177530	−	0.307492i
$39$	−0.526042	−	3.56697i	−0.0842342	−	0.571172i
$40$	0.0257210	−	0.0445501i	0.00406685	−	0.00704399i
$41$	1.27443	+	2.20738i	0.199033	+	0.344735i	0.948215	−	0.317629i	$-0.102887\pi$
$41$	1.27443	+	2.20738i	0.199033	+	0.344735i	−0.749182	+	0.662364i	$0.769553\pi$
$42$	−0.703538	−	1.58812i	−0.108558	−	0.245053i
$43$	4.49157	−	7.77963i	0.684958	−	1.18638i	−0.288492	−	0.957482i	$-0.593154\pi$
$43$	4.49157	−	7.77963i	0.684958	−	1.18638i	0.973450	−	0.228900i	$-0.0735128\pi$
$44$	2.66124	−	4.60940i	0.401196	−	0.694892i
$45$	0.0219547			0.00327281
$46$	−3.61197			−0.532556
$47$	−4.08171	+	7.06973i	−0.595379	+	1.03123i	0.398115	+	0.917336i	$0.369665\pi$
$47$	−4.08171	+	7.06973i	−0.595379	+	1.03123i	−0.993493	+	0.113890i	$0.963669\pi$
$48$	−0.799843	+	1.38537i	−0.115447	+	0.199961i
$49$	−2.13831	−	6.66540i	−0.305473	−	0.952201i
$50$	1.64113	+	2.84253i	0.232091	+	0.401994i
$51$	−1.66418	+	2.88244i	−0.233032	+	0.403623i
$52$	4.43406	−	3.51304i	0.614893	−	0.487171i
$53$	5.68199	+	9.84149i	0.780481	+	1.35183i	0.931662	+	0.363327i	$0.118359\pi$
$53$	5.68199	+	9.84149i	0.780481	+	1.35183i	−0.151181	+	0.988506i	$0.548308\pi$
$54$	0.656517			0.0893406
$55$	−0.0372385	−	0.0644990i	−0.00502124	−	0.00869704i
$56$	3.65316	−	5.00851i	0.488175	−	0.669291i
$57$	3.33387			0.441582
$58$	2.31490	+	4.00952i	0.303961	+	0.526476i
$59$	12.1859			1.58647			0.793236	−	0.608914i	$-0.208395\pi$
$59$	12.1859			1.58647			0.793236	+	0.608914i	$0.208395\pi$
$60$	0.0172233	+	0.0298316i	0.00222352	+	0.00385125i
$61$	−5.23676	−	9.07034i	−0.670499	−	1.16134i	−0.977763	−	0.209714i	$-0.932747\pi$
$61$	−5.23676	−	9.07034i	−0.670499	−	1.16134i	0.307264	−	0.951624i	$-0.400587\pi$
$62$	−2.05719	−	3.56316i	−0.261264	−	0.452522i
$63$	2.63074	+	0.281455i	0.331442	+	0.0354600i
$64$	0.566683			0.0708354
$65$	−0.0115491	−	0.0783118i	−0.00143249	−	0.00971338i
$66$	−1.11355	−	1.92873i	−0.137069	−	0.237410i
$67$	−5.35554	+	9.27608i	−0.654284	+	1.13325i	0.327789	+	0.944751i	$0.393697\pi$
$67$	−5.35554	+	9.27608i	−0.654284	+	1.13325i	−0.982073	+	0.188502i	$0.939637\pi$
$68$	−5.22215			−0.633278
$69$	2.75086	−	4.76463i	0.331165	−	0.573594i
$70$	−0.0154460	−	0.0348668i	−0.00184615	−	0.00416738i
$71$	−3.57850	+	6.19814i	−0.424690	+	0.735584i	−0.996391	−	0.0848774i	$-0.972950\pi$
$71$	−3.57850	+	6.19814i	−0.424690	+	0.735584i	0.571702	+	0.820462i	$0.306283\pi$
$72$	1.17155	+	2.02918i	0.138068	+	0.239142i
$73$	0.102129	+	0.176893i	0.0119533	+	0.0207038i	0.871940	−	0.489612i	$-0.162862\pi$
$73$	0.102129	+	0.176893i	0.0119533	+	0.0207038i	−0.859987	+	0.510316i	$0.829528\pi$
$74$	3.22272			0.374634
$75$	−4.99952			−0.577295
$76$	2.61540	+	4.53000i	0.300007	+	0.519627i
$77$	−3.63526	−	8.20602i	−0.414277	−	0.935163i
$78$	−0.345356	−	2.34178i	−0.0391038	−	0.265154i
$79$	−3.42085	+	5.92509i	−0.384876	+	0.666625i	−0.991752	−	0.128172i	$-0.959089\pi$
$79$	−3.42085	+	5.92509i	−0.384876	+	0.666625i	0.606876	+	0.794797i	$0.292422\pi$
$80$	−0.0175603	+	0.0304154i	−0.00196330	+	0.00340054i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.836686	+	1.44918i	0.0923965	+	0.160035i
$83$	−14.4458			−1.58563			−0.792815	−	0.609462i	$-0.791385\pi$
$83$	−14.4458			−1.58563			−0.792815	+	0.609462i	$0.791385\pi$
$84$	1.68136	+	3.79540i	0.183451	+	0.414112i
$85$	−0.0365366	+	0.0632832i	−0.00396295	+	0.00686403i
$86$	2.94879	−	5.10746i	0.317976	−	0.550751i
$87$	−7.05206			−0.756060
$88$	3.97425	−	6.88360i	0.423656	−	0.733794i
$89$	−5.45516			−0.578246			−0.289123	−	0.957292i	$-0.593364\pi$
$89$	−5.45516			−0.578246			−0.289123	+	0.957292i	$0.593364\pi$
$90$	0.0144136			0.00151933
$91$	−0.379938	−	9.53182i	−0.0398283	−	0.999207i
$92$	8.63212			0.899961
$93$	6.26699			0.649856
$94$	−2.67971	+	4.64140i	−0.276391	+	0.478724i
$95$	0.0731942			0.00750956
$96$	−2.86821	+	4.96789i	−0.292735	+	0.507033i
$97$	4.71678	−	8.16970i	0.478916	−	0.829507i	−0.520792	−	0.853684i	$-0.674363\pi$
$97$	4.71678	−	8.16970i	0.478916	−	0.829507i	0.999708	+	0.0241767i	$0.00769644\pi$
$98$	−1.40384	−	4.37595i	−0.141809	−	0.442038i
$99$	3.39230			0.340939
$100$	−3.92209	−	6.79325i	−0.392209	−	0.679325i
$101$	0.106547	−	0.184545i	0.0106018	−	0.0183629i	−0.860676	−	0.509153i	$-0.829959\pi$
$101$	0.106547	−	0.184545i	0.0106018	−	0.0183629i	0.871278	+	0.490790i	$0.163292\pi$
$102$	−1.09256	+	1.89237i	−0.108180	+	0.187373i
$103$	−2.39085	+	4.14107i	−0.235577	+	0.408032i	−0.959440	−	0.281912i	$-0.909031\pi$
$103$	−2.39085	+	4.14107i	−0.235577	+	0.408032i	0.723863	+	0.689944i	$0.242365\pi$
$104$	6.62175	−	5.24632i	0.649316	−	0.514444i
$105$	0.0577571	+	0.00617927i	0.00563651	+	0.000603035i
$106$	3.73032	+	6.46111i	0.362321	+	0.627558i
$107$	13.4883			1.30396			0.651981	−	0.758236i	$-0.273938\pi$
$107$	13.4883			1.30396			0.651981	+	0.758236i	$0.273938\pi$
$108$	−1.56899			−0.150976
$109$	−2.39198	−	4.14303i	−0.229110	−	0.396830i	0.728435	−	0.685115i	$-0.240248\pi$
$109$	−2.39198	−	4.14303i	−0.229110	−	0.396830i	−0.957545	+	0.288285i	$0.906915\pi$
$110$	−0.0244477	−	0.0423447i	−0.00233100	−	0.00403740i
$111$	−2.45441	+	4.25116i	−0.232962	+	0.403502i
$112$	−2.49410	+	3.41942i	−0.235670	+	0.323105i
$113$	−6.01904	+	10.4253i	−0.566224	+	0.980729i	0.430711	+	0.902490i	$0.358263\pi$
$113$	−6.01904	+	10.4253i	−0.566224	+	0.980729i	−0.996935	+	0.0782387i	$0.975070\pi$
$114$	2.18874			0.204994
$115$	0.0603943	−	0.104606i	0.00563180	−	0.00975456i
$116$	−5.53229	−	9.58221i	−0.513660	−	0.889686i
$117$	3.35211	+	1.32792i	0.309903	+	0.122766i
$118$	8.00026			0.736484
$119$	−5.18930	+	7.11456i	−0.475702	+	0.652191i
$120$	0.0257210	+	0.0445501i	0.00234800	+	0.00406685i
$121$	−0.253853	−	0.439686i	−0.0230775	−	0.0399715i
$122$	−3.43802	−	5.95483i	−0.311264	−	0.539125i
$123$	−2.54886			−0.229823
$124$	4.91641	+	8.51547i	0.441506	+	0.764711i
$125$	−0.219537			−0.0196359
$126$	1.72712	+	0.184780i	0.153864	+	0.0164615i
$127$	5.03649	+	8.72345i	0.446916	+	0.774081i	0.998183	−	0.0602474i	$-0.0191890\pi$
$127$	5.03649	+	8.72345i	0.446916	+	0.774081i	−0.551268	+	0.834329i	$0.685856\pi$
$128$	−11.1008			−0.981182
$129$	4.49157	+	7.77963i	0.395461	+	0.684958i
$130$	−0.00758219	−	0.0514130i	−0.000665002	−	0.00450922i
$131$	2.07849	−	3.60006i	0.181599	−	0.314538i	−0.760826	−	0.648955i	$-0.775206\pi$
$131$	2.07849	−	3.60006i	0.181599	−	0.314538i	0.942425	+	0.334417i	$0.108539\pi$
$132$	2.66124	+	4.60940i	0.231631	+	0.401196i
$133$	8.77054	+	0.938335i	0.760502	+	0.0813640i
$134$	−3.51601	+	6.08990i	−0.303737	+	0.526087i
$135$	−0.0109774	+	0.0190133i	−0.000944780	+	0.00163641i
$136$	−7.79867			−0.668731
$137$	−10.3770			−0.886570			−0.443285	−	0.896381i	$-0.646187\pi$
$137$	−10.3770			−0.886570			−0.443285	+	0.896381i	$0.646187\pi$
$138$	1.80599	−	3.12806i	0.153736	−	0.266278i
$139$	−9.72065	+	16.8367i	−0.824495	+	1.42807i	0.0778096	+	0.996968i	$0.475207\pi$
$139$	−9.72065	+	16.8367i	−0.824495	+	1.42807i	−0.902305	+	0.431099i	$0.858126\pi$
$140$	0.0369137	+	0.0833268i	0.00311978	+	0.00704240i
$141$	−4.08171	−	7.06973i	−0.343742	−	0.595379i
$142$	−2.34935	+	4.06919i	−0.197153	+	0.341478i
$143$	−1.78449	−	12.1002i	−0.149227	−	1.01187i
$144$	−0.799843	−	1.38537i	−0.0666536	−	0.115447i
$145$	−0.154826			−0.0128576
$146$	0.0670496	+	0.116133i	0.00554907	+	0.00961126i
$147$	6.84157	+	1.48087i	0.564283	+	0.122140i
$148$	−7.70186			−0.633089
$149$	1.42870	+	2.47458i	0.117044	+	0.202726i	0.918595	−	0.395201i	$-0.129325\pi$
$149$	1.42870	+	2.47458i	0.117044	+	0.202726i	−0.801551	+	0.597926i	$0.795992\pi$
$150$	−3.28227			−0.267996
$151$	−1.15655	−	2.00321i	−0.0941191	−	0.163019i	0.815122	−	0.579290i	$-0.196670\pi$
$151$	−1.15655	−	2.00321i	−0.0941191	−	0.163019i	−0.909241	+	0.416271i	$0.863337\pi$
$152$	3.90579	+	6.76504i	0.316802	+	0.548717i
$153$	−1.66418	−	2.88244i	−0.134541	−	0.233032i
$154$	−2.38661	−	5.38739i	−0.192319	−	0.434128i
$155$	0.137590			0.0110515
$156$	0.825353	+	5.59653i	0.0660811	+	0.448081i
$157$	−1.49849	−	2.59547i	−0.119593	−	0.207141i	0.800014	−	0.599982i	$-0.204826\pi$
$157$	−1.49849	−	2.59547i	−0.119593	−	0.207141i	−0.919606	+	0.392841i	$0.871492\pi$
$158$	−2.24585	+	3.88992i	−0.178670	+	0.309466i
$159$	−11.3640			−0.901222
$160$	−0.0629707	+	0.109068i	−0.00497827	+	0.00862262i
$161$	8.57782	−	11.7602i	0.676027	−	0.926837i
$162$	−0.328258	+	0.568560i	−0.0257904	+	0.0446703i
$163$	1.92198	+	3.32896i	0.150541	+	0.260744i	0.931426	−	0.363930i	$-0.118565\pi$
$163$	1.92198	+	3.32896i	0.150541	+	0.260744i	−0.780886	+	0.624674i	$0.785232\pi$
$164$	−1.99956	−	3.46335i	−0.156140	−	0.270442i
$165$	0.0744770			0.00579803
$166$	−9.48390			−0.736093
$167$	4.63931	+	8.03553i	0.359001	+	0.621808i	0.987794	−	0.155765i	$-0.0497841\pi$
$167$	4.63931	+	8.03553i	0.359001	+	0.621808i	−0.628793	+	0.777573i	$0.716451\pi$
$168$	2.51092	+	5.66799i	0.193721	+	0.437295i
$169$	2.97330	−	12.6554i	0.228715	−	0.973493i
$170$	−0.0239869	+	0.0415465i	−0.00183971	+	0.00318647i
$171$	−1.66694	+	2.88722i	−0.127474	+	0.220791i
$172$	−7.04721	+	12.2061i	−0.537345	+	0.930708i
$173$	1.90987	+	3.30799i	0.145205	+	0.251502i	0.929449	−	0.368950i	$-0.120283\pi$
$173$	1.90987	+	3.30799i	0.145205	+	0.251502i	−0.784245	+	0.620452i	$0.786949\pi$
$174$	−4.62980			−0.350984
$175$	−13.1524	−	1.40714i	−0.994230	−	0.106370i
$176$	−2.71331	+	4.69959i	−0.204523	+	0.354245i
$177$	−6.09296	+	10.5533i	−0.457975	+	0.793236i
$178$	−3.58140			−0.268438
$179$	7.50978	−	13.0073i	0.561307	−	0.972213i	−0.436075	−	0.899910i	$-0.643632\pi$
$179$	7.50978	−	13.0073i	0.561307	−	0.972213i	0.997383	−	0.0723028i	$-0.0230348\pi$
$180$	−0.0344466			−0.00256750
$181$	0.904121			0.0672028			0.0336014	−	0.999435i	$-0.489302\pi$
$181$	0.904121			0.0672028			0.0336014	+	0.999435i	$0.489302\pi$
$182$	−0.249435	−	6.25780i	−0.0184894	−	0.463859i
$183$	10.4735			0.774225
$184$	12.8911			0.950343
$185$	−0.0538858	+	0.0933330i	−0.00396177	+	0.00686198i
$186$	4.11438			0.301681
$187$	−5.64540	+	9.77811i	−0.412832	+	0.715047i
$188$	6.40414	−	11.0923i	0.467070	−	0.808989i
$189$	−1.55912	+	2.13756i	−0.113409	+	0.155484i
$190$	0.0480532			0.00348615
$191$	−7.78910	−	13.4911i	−0.563600	−	0.976183i	−0.997178	−	0.0750675i	$-0.976083\pi$
$191$	−7.78910	−	13.4911i	−0.563600	−	0.976183i	0.433579	−	0.901116i	$-0.357251\pi$
$192$	−0.283341	+	0.490762i	−0.0204484	+	0.0354177i
$193$	−4.39731	+	7.61636i	−0.316525	+	0.548238i	−0.979761	−	0.200173i	$-0.935850\pi$
$193$	−4.39731	+	7.61636i	−0.316525	+	0.548238i	0.663235	+	0.748411i	$0.269183\pi$
$194$	3.09664	−	5.36354i	0.222326	−	0.385080i
$195$	0.0735946	+	0.0291541i	0.00527022	+	0.00208777i
$196$	3.35498	+	10.4579i	0.239641	+	0.746995i
$197$	7.19616	+	12.4641i	0.512705	+	0.888032i	0.999891	+	0.0147334i	$0.00468997\pi$
$197$	7.19616	+	12.4641i	0.512705	+	0.888032i	−0.487186	+	0.873298i	$0.661977\pi$
$198$	2.22710			0.158273
$199$	23.7861			1.68615			0.843074	−	0.537797i	$-0.180743\pi$
$199$	23.7861			1.68615			0.843074	+	0.537797i	$0.180743\pi$
$200$	−5.85718	−	10.1449i	−0.414165	−	0.717356i
$201$	−5.35554	−	9.27608i	−0.377751	−	0.654284i
$202$	0.0699499	−	0.121157i	0.00492166	−	0.00852456i
$203$	−18.5521	−	1.98484i	−1.30210	−	0.139308i
$204$	2.61107	−	4.52251i	0.182812	−	0.316639i
$205$	−0.0559596			−0.00390838
$206$	−1.56963	+	2.71868i	−0.109362	+	0.189420i
$207$	2.75086	+	4.76463i	0.191198	+	0.331165i
$208$	−4.52082	+	3.58178i	−0.313463	+	0.248352i
$209$	11.3095			0.782294
$210$	0.0379185	+	0.00405679i	0.00261663	+	0.000279945i
$211$	3.11236	+	5.39077i	0.214264	+	0.371116i	0.953045	−	0.302830i	$-0.0979314\pi$
$211$	3.11236	+	5.39077i	0.214264	+	0.371116i	−0.738781	+	0.673946i	$0.764598\pi$
$212$	−8.91496	−	15.4412i	−0.612282	−	1.06050i
$213$	−3.57850	−	6.19814i	−0.245195	−	0.424690i
$214$	8.85529			0.605335
$215$	0.0986111	+	0.170799i	0.00672522	+	0.0116484i
$216$	−2.34310			−0.159428
$217$	16.4868	+	1.76388i	1.11920	+	0.119740i
$218$	−1.57037	−	2.71997i	−0.106359	−	0.184219i
$219$	−0.204259			−0.0138025
$220$	0.0584267	+	0.101198i	0.00393912	+	0.00682276i
$221$	−9.40616	+	7.45237i	−0.632727	+	0.501300i
$222$	−1.61136	+	2.79096i	−0.108147	+	0.187317i
$223$	−7.49534	−	12.9823i	−0.501925	−	0.869359i	−0.999998	−	0.00222396i	$-0.999292\pi$
$223$	−7.49534	−	12.9823i	−0.501925	−	0.869359i	0.498073	−	0.867135i	$-0.334041\pi$
$224$	−8.94375	+	12.2619i	−0.597579	+	0.819285i
$225$	2.49976	−	4.32971i	0.166651	−	0.288647i
$226$	−3.95160	+	6.84438i	−0.262857	+	0.455281i
$227$	29.7041			1.97153			0.985766	−	0.168125i	$-0.0537711\pi$
$227$	29.7041			1.97153			0.985766	+	0.168125i	$0.0537711\pi$
$228$	−5.23079			−0.346418
$229$	6.58433	−	11.4044i	0.435105	−	0.753623i	−0.562199	−	0.827002i	$-0.690045\pi$
$229$	6.58433	−	11.4044i	0.435105	−	0.753623i	0.997304	+	0.0733782i	$0.0233780\pi$
$230$	0.0396499	−	0.0686756i	0.00261444	−	0.00452834i
$231$	8.92426	+	0.954781i	0.587173	+	0.0628200i
$232$	−8.26184	−	14.3099i	−0.542416	−	0.939493i
$233$	7.62363	−	13.2045i	0.499441	−	0.865057i	−0.500559	−	0.865703i	$-0.666872\pi$
$233$	7.62363	−	13.2045i	0.499441	−	0.865057i	1.00000		0.000645444i	$0.000205451\pi$
$234$	2.20072	+	0.871801i	0.143865	+	0.0569914i
$235$	−0.0896128	−	0.155214i	−0.00584569	−	0.0101250i
$236$	−19.1195			−1.24458
$237$	−3.42085	−	5.92509i	−0.222208	−	0.384876i
$238$	−3.40686	+	4.67083i	−0.220834	+	0.302765i
$239$	−18.7827			−1.21495			−0.607475	−	0.794339i	$-0.707818\pi$
$239$	−18.7827			−1.21495			−0.607475	+	0.794339i	$0.707818\pi$
$240$	−0.0175603	−	0.0304154i	−0.00113351	−	0.00196330i
$241$	−8.42630			−0.542786			−0.271393	−	0.962469i	$-0.587484\pi$
$241$	−8.42630			−0.542786			−0.271393	+	0.962469i	$0.587484\pi$
$242$	−0.166659	−	0.288662i	−0.0107132	−	0.0185559i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	8.21641	+	14.2312i	0.526002	+	0.911061i
$245$	0.150205	+	0.0325121i	0.00959622	+	0.00207712i
$246$	−1.67337			−0.106690
$247$	11.1755	+	4.42711i	0.711080	+	0.281690i
$248$	7.34209	+	12.7169i	0.466223	+	0.807522i
$249$	7.22289	−	12.5104i	0.457732	−	0.792815i
$250$	−0.144129			−0.00911555
$251$	5.31695	−	9.20923i	0.335603	−	0.581281i	−0.647998	−	0.761642i	$-0.724393\pi$
$251$	5.31695	−	9.20923i	0.335603	−	0.581281i	0.983600	+	0.180361i	$0.0577267\pi$
$252$	−4.12759	−	0.441599i	−0.260014	−	0.0278181i
$253$	9.33174	−	16.1631i	0.586682	−	1.01616i
$254$	3.30654	+	5.72709i	0.207471	+	0.359350i
$255$	−0.0365366	−	0.0632832i	−0.00228801	−	0.00396295i
$256$	−8.42123			−0.526327
$257$	24.8849			1.55228			0.776138	−	0.630563i	$-0.217176\pi$
$257$	24.8849			1.55228			0.776138	+	0.630563i	$0.217176\pi$
$258$	2.94879	+	5.10746i	0.183584	+	0.317976i
$259$	−7.65342	+	10.4929i	−0.475560	+	0.651996i
$260$	0.0181204	+	0.122870i	0.00112378	+	0.00762008i
$261$	3.52603	−	6.10726i	0.218256	−	0.378030i
$262$	1.36457	−	2.36350i	0.0843031	−	0.146017i
$263$	7.82375	−	13.5511i	0.482433	−	0.835599i	−0.517363	−	0.855766i	$-0.673086\pi$
$263$	7.82375	−	13.5511i	0.482433	−	0.835599i	0.999797	+	0.0201669i	$0.00641974\pi$
$264$	3.97425	+	6.88360i	0.244598	+	0.423656i
$265$	−0.249493			−0.0153262
$266$	5.75801	+	0.616033i	0.353046	+	0.0377714i
$267$	2.72758	−	4.72431i	0.166925	−	0.289123i
$268$	8.40277	−	14.5540i	0.513281	−	0.889029i
$269$	5.52900			0.337109			0.168555	−	0.985692i	$-0.446090\pi$
$269$	5.52900			0.337109			0.168555	+	0.985692i	$0.446090\pi$
$270$	−0.00720682	+	0.0124826i	−0.000438593	+	0.000759665i
$271$	13.1181			0.796869			0.398434	−	0.917197i	$-0.369554\pi$
$271$	13.1181			0.796869			0.398434	+	0.917197i	$0.369554\pi$
$272$	5.32433			0.322835
$273$	8.44477	+	4.43688i	0.511101	+	0.268532i
$274$	−6.81270			−0.411570
$275$	−16.9599			−1.02272
$276$	−4.31606	+	7.47563i	−0.259796	+	0.449980i
$277$	27.3934			1.64591			0.822955	−	0.568106i	$-0.192324\pi$
$277$	27.3934			1.64591			0.822955	+	0.568106i	$0.192324\pi$
$278$	−6.38177	+	11.0536i	−0.382753	+	0.662948i
$279$	−3.13349	+	5.42737i	−0.187597	+	0.324928i
$280$	0.0551264	+	0.124439i	0.00329443	+	0.00743666i
$281$	5.08316			0.303236			0.151618	−	0.988439i	$-0.451552\pi$
$281$	5.08316			0.303236			0.151618	+	0.988439i	$0.451552\pi$
$282$	−2.67971	−	4.64140i	−0.159575	−	0.276391i
$283$	−3.06193	+	5.30341i	−0.182013	+	0.315255i	−0.942566	−	0.334021i	$-0.891595\pi$
$283$	−3.06193	+	5.30341i	−0.182013	+	0.315255i	0.760553	+	0.649276i	$0.224928\pi$
$284$	5.61461	−	9.72480i	0.333166	−	0.577061i
$285$	−0.0365971	+	0.0633880i	−0.00216782	+	0.00375478i
$286$	−1.17155	−	7.94401i	−0.0692752	−	0.469739i
$287$	−6.70539	−	0.717391i	−0.395807	−	0.0423462i
$288$	−2.86821	−	4.96789i	−0.169011	−	0.292735i
$289$	−5.92203			−0.348355
$290$	−0.101646			−0.00596885
$291$	4.71678	+	8.16970i	0.276502	+	0.478916i
$292$	−0.160239	−	0.277543i	−0.00937730	−	0.0162420i
$293$	1.05051	−	1.81953i	0.0613712	−	0.106298i	−0.833707	−	0.552207i	$-0.813786\pi$
$293$	1.05051	−	1.81953i	0.0613712	−	0.106298i	0.895079	+	0.445908i	$0.147119\pi$
$294$	4.49160	+	0.972216i	0.261956	+	0.0567008i
$295$	−0.133769	+	0.231695i	−0.00778834	+	0.0134898i
$296$	−11.5018			−0.668531
$297$	−1.69615	+	2.93782i	−0.0984206	+	0.170470i
$298$	0.937966	+	1.62460i	0.0543349	+	0.0941108i
$299$	15.5482	−	12.3186i	0.899177	−	0.712405i
$300$	7.84417			0.452883
$301$	9.62653	+	21.7303i	0.554864	+	1.25252i
$302$	−0.759298	−	1.31514i	−0.0436927	−	0.0756779i
$303$	0.106547	+	0.184545i	0.00612097	+	0.0106018i
$304$	−2.66657	−	4.61864i	−0.152939	−	0.264897i
$305$	0.229943			0.0131665
$306$	−1.09256	−	1.89237i	−0.0624576	−	0.108180i
$307$	−9.82908			−0.560975			−0.280488	−	0.959858i	$-0.590496\pi$
$307$	−9.82908			−0.560975			−0.280488	+	0.959858i	$0.590496\pi$
$308$	5.70368	+	12.8751i	0.324997	+	0.733629i
$309$	−2.39085	−	4.14107i	−0.136011	−	0.235577i
$310$	0.0903301			0.00513040
$311$	−1.34993	−	2.33815i	−0.0765475	−	0.132584i	0.825211	−	0.564825i	$-0.191056\pi$
$311$	−1.34993	−	2.33815i	−0.0765475	−	0.132584i	−0.901758	+	0.432241i	$0.857723\pi$
$312$	1.23257	+	8.35777i	0.0697805	+	0.473165i
$313$	11.8486	−	20.5223i	0.669721	−	1.15999i	−0.308261	−	0.951302i	$-0.599747\pi$
$313$	11.8486	−	20.5223i	0.669721	−	1.15999i	0.977982	−	0.208689i	$-0.0669196\pi$
$314$	−0.983786	−	1.70397i	−0.0555183	−	0.0961604i
$315$	−0.0342299	+	0.0469295i	−0.00192864	+	0.00264418i
$316$	5.36727	−	9.29638i	0.301932	−	0.522962i
$317$	−3.51073	+	6.08076i	−0.197182	+	0.341529i	−0.947614	−	0.319419i	$-0.896512\pi$
$317$	−3.51073	+	6.08076i	−0.197182	+	0.341529i	0.750432	+	0.660948i	$0.229846\pi$
$318$	−7.46064			−0.418372
$319$	−23.9227			−1.33941
$320$	−0.00622068	+	0.0107745i	−0.000347747	+	0.000602315i
$321$	−6.74414	+	11.6812i	−0.376421	+	0.651981i
$322$	5.63148	−	7.72080i	0.313830	−	0.430263i
$323$	−5.54816	−	9.60969i	−0.308708	−	0.534698i
$324$	0.784493	−	1.35878i	0.0435829	−	0.0754879i
$325$	−16.7589	−	6.63896i	−0.929618	−	0.368263i
$326$	1.26181	+	2.18552i	0.0698852	+	0.121045i
$327$	4.78396			0.264553
$328$	−2.98612	−	5.17211i	−0.164881	−	0.285582i
$329$	−8.74810	−	19.7474i	−0.482298	−	1.08871i
$330$	0.0488954			0.00269160
$331$	−7.20552	−	12.4803i	−0.396051	−	0.685981i	0.597184	−	0.802105i	$-0.296286\pi$
$331$	−7.20552	−	12.4803i	−0.396051	−	0.685981i	−0.993235	+	0.116124i	$0.962953\pi$
$332$	22.6652			1.24392
$333$	−2.45441	−	4.25116i	−0.134501	−	0.232962i
$334$	3.04579	+	5.27546i	0.166658	+	0.288660i
$335$	−0.117579	−	0.203654i	−0.00642405	−	0.0111268i
$336$	−1.71426	−	3.86966i	−0.0935205	−	0.211107i
$337$	−13.6190			−0.741876			−0.370938	−	0.928658i	$-0.620964\pi$
$337$	−13.6190			−0.741876			−0.370938	+	0.928658i	$0.620964\pi$
$338$	1.95202	−	8.30849i	0.106176	−	0.451922i
$339$	−6.01904	−	10.4253i	−0.326910	−	0.566224i
$340$	0.0573254	−	0.0992904i	0.00310890	−	0.00538478i
$341$	21.2595			1.15127
$342$	−1.09437	+	1.89551i	−0.0591768	+	0.102497i
$343$	17.5816	+	5.82138i	0.949316	+	0.314325i
$344$	−10.5242	+	18.2284i	−0.567427	+	0.982812i
$345$	0.0603943	+	0.104606i	0.00325152	+	0.00563180i
$346$	1.25386	+	2.17175i	0.0674081	+	0.116754i
$347$	26.6123			1.42862			0.714311	−	0.699828i	$-0.246740\pi$
$347$	26.6123			1.42862			0.714311	+	0.699828i	$0.246740\pi$
$348$	11.0646			0.593124
$349$	4.88358	+	8.45861i	0.261412	+	0.452779i	0.966617	−	0.256224i	$-0.0824785\pi$
$349$	4.88358	+	8.45861i	0.261412	+	0.452779i	−0.705205	+	0.709003i	$0.749145\pi$
$350$	−8.63479	−	0.923811i	−0.461549	−	0.0493798i
$351$	−2.82607	+	2.23905i	−0.150844	+	0.119512i
$352$	−9.72983	+	16.8526i	−0.518602	+	0.898245i
$353$	−9.45200	+	16.3713i	−0.503079	+	0.871359i	0.496914	+	0.867800i	$0.334466\pi$
$353$	−9.45200	+	16.3713i	−0.503079	+	0.871359i	−0.999994	+	0.00355939i	$0.998867\pi$
$354$	−4.00013	+	6.92843i	−0.212605	+	0.368242i
$355$	−0.0785649	−	0.136078i	−0.00416979	−	0.00722229i
$356$	8.55907			0.453630
$357$	−3.56674	−	8.05134i	−0.188772	−	0.426122i
$358$	4.93030	−	8.53953i	0.260574	−	0.451328i
$359$	−16.2594	+	28.1622i	−0.858140	+	1.48634i	0.0155607	+	0.999879i	$0.495047\pi$
$359$	−16.2594	+	28.1622i	−0.858140	+	1.48634i	−0.873701	+	0.486463i	$0.838287\pi$
$360$	−0.0514421			−0.00271123
$361$	3.94265	−	6.82888i	0.207508	−	0.359415i
$362$	0.593570			0.0311974
$363$	0.507706			0.0266477
$364$	0.596117	+	14.9553i	0.0312450	+	0.783870i
$365$	−0.00448444			−0.000234726
$366$	6.87605			0.359417
$367$	−7.37603	+	12.7757i	−0.385026	+	0.666884i	−0.991773	−	0.128011i	$-0.959141\pi$
$367$	−7.37603	+	12.7757i	−0.385026	+	0.666884i	0.606747	+	0.794895i	$0.292474\pi$
$368$	−8.80103			−0.458785
$369$	1.27443	−	2.20738i	0.0663443	−	0.114912i
$370$	−0.0353770	+	0.0612747i	−0.00183916	+	0.00318552i
$371$	−29.8956	−	3.19845i	−1.55210	−	0.166055i
$372$	−9.83281			−0.509808
$373$	−6.60573	−	11.4415i	−0.342032	−	0.592416i	0.642778	−	0.766052i	$-0.277782\pi$
$373$	−6.60573	−	11.4415i	−0.342032	−	0.592416i	−0.984810	+	0.173636i	$0.944448\pi$
$374$	−3.70630	+	6.41950i	−0.191648	+	0.331944i
$375$	0.109768	−	0.190124i	0.00566841	−	0.00981797i
$376$	9.56385	−	16.5651i	0.493218	−	0.854279i
$377$	−23.6393	−	9.36457i	−1.21748	−	0.482300i
$378$	−1.02359	+	1.40334i	−0.0526476	+	0.0721802i
$379$	−12.5482	−	21.7340i	−0.644556	−	1.11640i	−0.984404	−	0.175923i	$-0.943709\pi$
$379$	−12.5482	−	21.7340i	−0.644556	−	1.11640i	0.339848	−	0.940480i	$-0.389624\pi$
$380$	−0.114841			−0.00589120
$381$	−10.0730			−0.516054
$382$	−5.11368	−	8.85715i	−0.261638	−	0.453171i
$383$	13.0132	+	22.5395i	0.664944	+	1.15172i	0.979301	+	0.202411i	$0.0648778\pi$
$383$	13.0132	+	22.5395i	0.664944	+	1.15172i	−0.314357	+	0.949305i	$0.601789\pi$
$384$	5.55040	−	9.61358i	0.283243	−	0.490591i
$385$	0.195929	+	0.0209619i	0.00998549	+	0.00106832i
$386$	−2.88691	+	5.00027i	−0.146940	+	0.254507i
$387$	−8.98314			−0.456639
$388$	−7.40056	+	12.8181i	−0.375706	+	0.650742i
$389$	7.00812	+	12.1384i	0.355326	+	0.615442i	0.987174	−	0.159650i	$-0.0510366\pi$
$389$	7.00812	+	12.1384i	0.355326	+	0.615442i	−0.631848	+	0.775092i	$0.717703\pi$
$390$	0.0483161	+	0.0191401i	0.00244658	+	0.000969199i
$391$	−18.3117			−0.926062
$392$	5.01028	+	15.6177i	0.253057	+	0.788813i
$393$	2.07849	+	3.60006i	0.104846	+	0.181599i
$394$	4.72440	+	8.18290i	0.238012	+	0.412249i
$395$	−0.0751038	−	0.130084i	−0.00377888	−	0.00654522i
$396$	−5.32247			−0.267464
$397$	−3.30711	−	5.72808i	−0.165979	−	0.287484i	0.771023	−	0.636807i	$-0.219745\pi$
$397$	−3.30711	−	5.72808i	−0.165979	−	0.287484i	−0.937003	+	0.349323i	$0.886412\pi$
$398$	15.6159			0.782757
$399$	−5.19789	+	7.12634i	−0.260220	+	0.356763i
$400$	3.99883	+	6.92618i	0.199942	+	0.346309i
$401$	2.88574			0.144107			0.0720536	−	0.997401i	$-0.477045\pi$
$401$	2.88574			0.144107			0.0720536	+	0.997401i	$0.477045\pi$
$402$	−3.51601	−	6.08990i	−0.175362	−	0.303737i
$403$	21.0076	+	8.32205i	1.04646	+	0.414551i
$404$	−0.167171	+	0.289548i	−0.00831705	+	0.0144056i
$405$	−0.0109774	−	0.0190133i	−0.000545469	−	0.000944780i
$406$	−12.1798	−	1.30308i	−0.604473	−	0.0646708i
$407$	−8.32609	+	14.4212i	−0.412709	+	0.714833i
$408$	3.89934	−	6.75385i	0.193046	−	0.334365i
$409$	−30.3948			−1.50293			−0.751464	−	0.659775i	$-0.770652\pi$
$409$	−30.3948			−1.50293			−0.751464	+	0.659775i	$0.770652\pi$
$410$	−0.0367384			−0.00181438
$411$	5.18852	−	8.98678i	0.255931	−	0.443285i
$412$	3.75121	−	6.49728i	0.184809	−	0.320098i
$413$	−18.9993	+	26.0481i	−0.934893	+	1.28174i
$414$	1.80599	+	3.12806i	0.0887594	+	0.153736i
$415$	0.158576	−	0.274662i	0.00778421	−	0.0134826i
$416$	−16.2115	+	12.8441i	−0.794834	+	0.629736i
$417$	−9.72065	−	16.8367i	−0.476022	−	0.824495i
$418$	7.42487			0.363162
$419$	−0.393507	−	0.681574i	−0.0192241	−	0.0332971i	0.856253	−	0.516556i	$-0.172786\pi$
$419$	−0.393507	−	0.681574i	−0.0192241	−	0.0332971i	−0.875477	+	0.483259i	$0.839453\pi$
$420$	−0.0906200	−	0.00969518i	−0.00442181	−	0.000473076i
$421$	−14.2626			−0.695115			−0.347557	−	0.937659i	$-0.612989\pi$
$421$	−14.2626			−0.695115			−0.347557	+	0.937659i	$0.612989\pi$
$422$	2.04332	+	3.53913i	0.0994672	+	0.172282i
$423$	8.16342			0.396919
$424$	−13.3135	−	23.0596i	−0.646559	−	1.11987i
$425$	8.32009	+	14.4108i	0.403584	+	0.699028i
$426$	−2.34935	−	4.06919i	−0.113826	−	0.197153i
$427$	27.5531	+	2.94783i	1.33339	+	0.142655i
$428$	−21.1629			−1.02295
$429$	11.3714	+	4.50470i	0.549014	+	0.217489i
$430$	0.0647399	+	0.112133i	0.00312203	+	0.00540752i
$431$	−19.1336	+	33.1403i	−0.921632	+	1.59631i	−0.124741	+	0.992189i	$0.539810\pi$
$431$	−19.1336	+	33.1403i	−0.921632	+	1.59631i	−0.796891	+	0.604124i	$0.793523\pi$
$432$	1.59969			0.0769650
$433$	−12.7987	+	22.1679i	−0.615064	+	1.06532i	0.375309	+	0.926900i	$0.377537\pi$
$433$	−12.7987	+	22.1679i	−0.615064	+	1.06532i	−0.990373	+	0.138423i	$0.955797\pi$
$434$	10.8239	+	1.15801i	0.519562	+	0.0555865i
$435$	0.0774130	−	0.134083i	0.00371167	−	0.00642880i
$436$	3.75298	+	6.50035i	0.179735	+	0.311310i
$437$	9.17101	+	15.8847i	0.438709	+	0.759866i
$438$	−0.134099			−0.00640751
$439$	−14.4323			−0.688816			−0.344408	−	0.938820i	$-0.611920\pi$
$439$	−14.4323			−0.688816			−0.344408	+	0.938820i	$0.611920\pi$
$440$	0.0872535	+	0.151127i	0.00415965	+	0.00720472i
$441$	−4.70325	+	5.18453i	−0.223964	+	0.246883i
$442$	−6.17530	+	4.89260i	−0.293729	+	0.232717i
$443$	−17.8704	+	30.9525i	−0.849050	+	1.47060i	0.0330077	+	0.999455i	$0.489491\pi$
$443$	−17.8704	+	30.9525i	−0.849050	+	1.47060i	−0.882057	+	0.471142i	$0.843842\pi$
$444$	3.85093	−	6.67001i	0.182757	−	0.316545i
$445$	0.0598832	−	0.103721i	0.00283874	−	0.00491684i
$446$	−4.92081	−	8.52310i	−0.233007	−	0.403580i
$447$	−2.85740			−0.135150
$448$	−0.883525	+	1.21132i	−0.0417426	+	0.0572294i
$449$	8.14402	−	14.1059i	0.384340	−	0.665697i	−0.607337	−	0.794444i	$-0.707762\pi$
$449$	8.14402	−	14.1059i	0.384340	−	0.665697i	0.991677	+	0.128747i	$0.0410956\pi$
$450$	1.64113	−	2.84253i	0.0773638	−	0.133998i
$451$	−8.64651			−0.407148
$452$	9.44379	−	16.3571i	0.444199	−	0.769375i
$453$	2.31311			0.108679
$454$	19.5013			0.915239
$455$	0.185402	+	0.0974103i	0.00869180	+	0.00456667i
$456$	−7.81159			−0.365811
$457$	26.7852			1.25296			0.626480	−	0.779438i	$-0.284495\pi$
$457$	26.7852			1.25296			0.626480	+	0.779438i	$0.284495\pi$
$458$	4.32272	−	7.48718i	0.201988	−	0.349853i
$459$	3.32836			0.155354
$460$	−0.0947578	+	0.164125i	−0.00441811	+	0.00765238i
$461$	2.53171	−	4.38505i	0.117914	−	0.204232i	−0.801027	−	0.598628i	$-0.795713\pi$
$461$	2.53171	−	4.38505i	0.117914	−	0.204232i	0.918941	+	0.394396i	$0.129046\pi$
$462$	5.85892	+	0.626830i	0.272582	+	0.0291628i
$463$	20.6813			0.961140			0.480570	−	0.876956i	$-0.340430\pi$
$463$	20.6813			0.961140			0.480570	+	0.876956i	$0.340430\pi$
$464$	5.64054	+	9.76971i	0.261856	+	0.453547i
$465$	−0.0687950	+	0.119156i	−0.00319029	+	0.00552574i
$466$	5.00505	−	8.66899i	0.231854	−	0.401583i
$467$	19.3668	−	33.5443i	0.896190	−	1.55225i	0.0638661	−	0.997958i	$-0.479657\pi$
$467$	19.3668	−	33.5443i	0.896190	−	1.55225i	0.832324	−	0.554289i	$-0.187010\pi$
$468$	−5.25941	−	2.08349i	−0.243116	−	0.0963092i
$469$	−11.4782	−	25.9103i	−0.530016	−	1.19643i
$470$	−0.0588323	−	0.101901i	−0.00271373	−	0.00470032i
$471$	2.99699			0.138094
$472$	−28.5528			−1.31425
$473$	15.2368	+	26.3908i	0.700587	+	1.21345i
$474$	−2.24585	−	3.88992i	−0.103155	−	0.178670i
$475$	8.33387	−	14.4347i	0.382384	−	0.662309i
$476$	8.14193	−	11.1626i	0.373185	−	0.511639i
$477$	5.68199	−	9.84149i	0.260160	−	0.450611i
$478$	−12.3311			−0.564013
$479$	0.176991	−	0.306558i	0.00808693	−	0.0140070i	−0.861954	−	0.506987i	$-0.830759\pi$
$479$	0.176991	−	0.306558i	0.00808693	−	0.0140070i	0.870041	+	0.492980i	$0.164092\pi$
$480$	−0.0629707	−	0.109068i	−0.00287421	−	0.00497827i
$481$	−13.8726	+	10.9911i	−0.632538	+	0.501151i
$482$	−5.53201			−0.251976
$483$	5.89576	+	13.3087i	0.268266	+	0.605568i
$484$	0.398292	+	0.689862i	0.0181042	+	0.0313573i
$485$	0.103555	+	0.179363i	0.00470221	+	0.00814447i
$486$	−0.328258	−	0.568560i	−0.0148901	−	0.0257904i
$487$	4.54182			0.205809			0.102905	−	0.994691i	$-0.467186\pi$
$487$	4.54182			0.205809			0.102905	+	0.994691i	$0.467186\pi$
$488$	12.2703	+	21.2527i	0.555448	+	0.962065i
$489$	−3.84395			−0.173830
$490$	0.0986119	+	0.0213447i	0.00445483	+	0.000964256i
$491$	0.408747	+	0.707971i	0.0184465	+	0.0319503i	0.875101	−	0.483940i	$-0.160795\pi$
$491$	0.408747	+	0.707971i	0.0184465	+	0.0319503i	−0.856655	+	0.515890i	$0.827461\pi$
$492$	3.99913			0.180295
$493$	11.7359	+	20.3272i	0.528558	+	0.915489i
$494$	7.33690	+	2.90647i	0.330103	+	0.130768i
$495$	−0.0372385	+	0.0644990i	−0.00167375	+	0.00289901i
$496$	−5.01261	−	8.68209i	−0.225073	−	0.389838i
$497$	−7.66960	−	17.3129i	−0.344028	−	0.776589i
$498$	4.74195	−	8.21330i	0.212492	−	0.368047i
$499$	8.72832	−	15.1179i	0.390733	−	0.676770i	−0.601813	−	0.798637i	$-0.705555\pi$
$499$	8.72832	−	15.1179i	0.390733	−	0.676770i	0.992546	+	0.121867i	$0.0388881\pi$
$500$	0.344450			0.0154043
$501$	−9.27863			−0.414539
$502$	3.49067	−	6.04601i	0.155796	−	0.269847i
$503$	−14.8475	+	25.7166i	−0.662017	+	1.14665i	0.318068	+	0.948068i	$0.396966\pi$
$503$	−14.8475	+	25.7166i	−0.662017	+	1.14665i	−0.980085	+	0.198579i	$0.936367\pi$
$504$	−6.16408	−	0.659478i	−0.274570	−	0.0293755i
$505$	0.00233921	+	0.00405163i	0.000104093	+	0.000180295i
$506$	6.12645	−	10.6113i	0.272354	−	0.471731i
$507$	9.47326	+	8.90266i	0.420722	+	0.395381i
$508$	−7.90217	−	13.6870i	−0.350602	−	0.607261i
$509$	−31.6284			−1.40191			−0.700953	−	0.713208i	$-0.747242\pi$
$509$	−31.6284			−1.40191			−0.700953	+	0.713208i	$0.747242\pi$
$510$	−0.0239869	−	0.0415465i	−0.00106216	−	0.00183971i
$511$	−0.537351	−	0.0574897i	−0.0237710	−	0.00254319i
$512$	16.6729			0.736846
$513$	−1.66694	−	2.88722i	−0.0735970	−	0.127474i
$514$	16.3373			0.720610
$515$	−0.0524904	−	0.0909160i	−0.00231300	−	0.00400624i
$516$	−7.04721	−	12.2061i	−0.310236	−	0.537345i
$517$	−13.8464	−	23.9827i	−0.608964	−	1.05476i
$518$	−5.02460	+	6.88876i	−0.220768	+	0.302675i
$519$	−3.81974			−0.167668
$520$	0.0270607	+	0.183492i	0.00118669	+	0.00804667i
$521$	0.792401	+	1.37248i	0.0347157	+	0.0601294i	0.882861	−	0.469634i	$-0.155614\pi$
$521$	0.792401	+	1.37248i	0.0347157	+	0.0601294i	−0.848146	+	0.529763i	$0.822281\pi$
$522$	2.31490	−	4.00952i	0.101320	−	0.175492i
$523$	25.6592			1.12200			0.561000	−	0.827816i	$-0.310417\pi$
$523$	25.6592			1.12200			0.561000	+	0.827816i	$0.310417\pi$
$524$	−3.26113	+	5.64843i	−0.142463	+	0.246753i
$525$	7.79483	−	10.6868i	0.340194	−	0.466409i
$526$	5.13643	−	8.89655i	0.223959	−	0.387908i
$527$	−10.4294	−	18.0642i	−0.454311	−	0.786891i
$528$	−2.71331	−	4.69959i	−0.118082	−	0.204523i
$529$	7.26892			0.316040
$530$	−0.163796			−0.00711485
$531$	−6.09296	−	10.5533i	−0.264412	−	0.457975i
$532$	−13.7609	−	1.47223i	−0.596609	−	0.0638295i
$533$	−8.54407	−	3.38468i	−0.370085	−	0.146607i
$534$	1.79070	−	3.10159i	0.0774913	−	0.134219i
$535$	−0.148066	+	0.256457i	−0.00640144	+	0.0110876i
$536$	12.5486	−	21.7348i	0.542016	−	0.938799i
$537$	7.50978	+	13.0073i	0.324071	+	0.561307i
$538$	3.62988			0.156495
$539$	23.2087	+	5.02356i	0.999667	+	0.216380i
$540$	0.0172233	−	0.0298316i	0.000741173	−	0.00128375i
$541$	−16.4754	+	28.5362i	−0.708333	+	1.22687i	0.257143	+	0.966373i	$0.417219\pi$
$541$	−16.4754	+	28.5362i	−0.708333	+	1.22687i	−0.965475	+	0.260495i	$0.916114\pi$
$542$	8.61227			0.369929
$543$	−0.452060	+	0.782991i	−0.0193998	+	0.0336014i
$544$	19.0929			0.818600
$545$	0.105030			0.00449901
$546$	5.54413	+	2.91288i	0.237267	+	0.124660i
$547$	28.0763			1.20046			0.600229	−	0.799828i	$-0.295076\pi$
$547$	28.0763			1.20046			0.600229	+	0.799828i	$0.295076\pi$
$548$	16.2814			0.695508
$549$	−5.23676	+	9.07034i	−0.223500	+	0.387113i
$550$	−11.1344			−0.474774
$551$	11.7553	−	20.3608i	0.500794	−	0.867400i
$552$	−6.44554	+	11.1640i	−0.274340	+	0.475171i
$553$	−7.33172	−	16.5502i	−0.311776	−	0.703785i
$554$	17.9842			0.764077
$555$	−0.0538858	−	0.0933330i	−0.00228733	−	0.00396177i
$556$	15.2516	−	26.4165i	0.646810	−	1.12031i
$557$	−3.45502	+	5.98427i	−0.146394	+	0.253562i	−0.929892	−	0.367832i	$-0.880100\pi$
$557$	−3.45502	+	5.98427i	−0.146394	+	0.253562i	0.783498	+	0.621394i	$0.213433\pi$
$558$	−2.05719	+	3.56316i	−0.0870879	+	0.150841i
$559$	4.72551	+	32.0426i	0.199868	+	1.35526i
$560$	−0.0376361	−	0.0849574i	−0.00159041	−	0.00359010i
$561$	−5.64540	−	9.77811i	−0.238349	−	0.412832i
$562$	3.33718			0.140770
$563$	14.9048			0.628163			0.314082	−	0.949396i	$-0.398303\pi$
$563$	14.9048			0.628163			0.314082	+	0.949396i	$0.398303\pi$
$564$	6.40414	+	11.0923i	0.269663	+	0.467070i
$565$	−0.132146	−	0.228884i	−0.00555944	−	0.00962923i
$566$	−2.01021	+	3.48178i	−0.0844953	+	0.146350i
$567$	−1.07162	−	2.41901i	−0.0450039	−	0.101589i
$568$	8.38478	−	14.5229i	0.351818	−	0.609366i
$569$	−2.85464			−0.119673			−0.0598364	−	0.998208i	$-0.519058\pi$
$569$	−2.85464			−0.119673			−0.0598364	+	0.998208i	$0.519058\pi$
$570$	−0.0240266	+	0.0416153i	−0.00100636	+	0.00174307i
$571$	7.35674	+	12.7422i	0.307870	+	0.533246i	0.977896	−	0.209091i	$-0.0670505\pi$
$571$	7.35674	+	12.7422i	0.307870	+	0.533246i	−0.670026	+	0.742337i	$0.733717\pi$
$572$	2.79985	+	18.9851i	0.117067	+	0.793807i
$573$	15.5782			0.650789
$574$	−4.40220	−	0.470979i	−0.183744	−	0.0196583i
$575$	−13.7530	−	23.8208i	−0.573539	−	0.993398i
$576$	−0.283341	−	0.490762i	−0.0118059	−	0.0204484i
$577$	11.3488	+	19.6566i	0.472455	+	0.818316i	0.999503	−	0.0315196i	$-0.0100347\pi$
$577$	11.3488	+	19.6566i	0.472455	+	0.818316i	−0.527048	+	0.849835i	$0.676701\pi$
$578$	−3.88791			−0.161716
$579$	−4.39731	−	7.61636i	−0.182746	−	0.316525i
$580$	0.242920			0.0100867
$581$	22.5227	−	30.8787i	0.934397	−	1.28106i
$582$	3.09664	+	5.36354i	0.128360	+	0.222326i
$583$	−38.5500			−1.59658
$584$	−0.239299	−	0.414478i	−0.00990227	−	0.0171512i
$585$	−0.0620455	+	0.0491577i	−0.00256526	+	0.00203242i
$586$	0.689675	−	1.19455i	0.0284902	−	0.0493465i
$587$	−22.6020	−	39.1478i	−0.932884	−	1.61580i	−0.778364	−	0.627813i	$-0.783950\pi$
$587$	−22.6020	−	39.1478i	−0.932884	−	1.61580i	−0.154520	−	0.987990i	$-0.549383\pi$
$588$	−10.7343	−	2.32346i	−0.442676	−	0.0958180i
$589$	−10.4467	+	18.0942i	−0.430447	+	0.745557i
$590$	−0.0878217	+	0.152112i	−0.00361556	+	0.00626234i
$591$	−14.3923			−0.592021
$592$	7.85257			0.322739
$593$	−9.80704	+	16.9863i	−0.402727	+	0.697543i	−0.994054	−	0.108888i	$-0.965271\pi$
$593$	−9.80704	+	16.9863i	−0.402727	+	0.697543i	0.591327	+	0.806432i	$0.298604\pi$
$594$	−1.11355	+	1.92873i	−0.0456896	+	0.0791367i
$595$	−0.0783068	−	0.176765i	−0.00321026	−	0.00724666i
$596$	−2.24161	−	3.88258i	−0.0918199	−	0.159037i
$597$	−11.8930	+	20.5993i	−0.486749	+	0.843074i
$598$	10.2077	−	8.08739i	0.417423	−	0.330718i
$599$	−16.1525	−	27.9769i	−0.659972	−	1.14311i	−0.980622	−	0.195908i	$-0.937235\pi$
$599$	−16.1525	−	27.9769i	−0.659972	−	1.14311i	0.320650	−	0.947198i	$-0.396099\pi$
$600$	11.7144			0.478237
$601$	−12.0669	−	20.9005i	−0.492220	−	0.852549i	0.507740	−	0.861510i	$-0.330481\pi$
$601$	−12.0669	−	20.9005i	−0.492220	−	0.852549i	−0.999960	+	0.00896092i	$0.997148\pi$
$602$	6.31998	+	14.2663i	0.257583	+	0.581452i
$603$	10.7111			0.436189
$604$	1.81462	+	3.14301i	0.0738357	+	0.127887i
$605$	0.0111465			0.000453171
$606$	0.0699499	+	0.121157i	0.00284152	+	0.00492166i
$607$	−0.413375	−	0.715987i	−0.0167784	−	0.0290610i	0.857514	−	0.514460i	$-0.172008\pi$
$607$	−0.413375	−	0.715987i	−0.0167784	−	0.0290610i	−0.874293	+	0.485399i	$0.838674\pi$
$608$	−9.56224	−	16.5623i	−0.387800	−	0.671689i
$609$	10.9950	−	15.0742i	0.445539	−	0.610837i
$610$	0.150962			0.00611226
$611$	−4.29431	−	29.1187i	−0.173729	−	1.17802i
$612$	2.61107	+	4.52251i	0.105546	+	0.182812i
$613$	22.0403	−	38.1750i	0.890200	−	1.54187i	0.0505659	−	0.998721i	$-0.483898\pi$
$613$	22.0403	−	38.1750i	0.890200	−	1.54187i	0.839635	−	0.543152i	$-0.182769\pi$
$614$	−6.45296			−0.260420
$615$	0.0279798	−	0.0484624i	0.00112825	−	0.00195419i
$616$	8.51778	+	19.2275i	0.343191	+	0.774699i
$617$	−6.58199	+	11.4003i	−0.264981	+	0.458960i	−0.967559	−	0.252647i	$-0.918699\pi$
$617$	−6.58199	+	11.4003i	−0.264981	+	0.458960i	0.702578	+	0.711607i	$0.252032\pi$
$618$	−1.56963	−	2.71868i	−0.0631399	−	0.109362i
$619$	12.0529	+	20.8762i	0.484447	+	0.839087i	0.999840	−	0.0178669i	$-0.00568751\pi$
$619$	12.0529	+	20.8762i	0.484447	+	0.839087i	−0.515393	+	0.856954i	$0.672354\pi$
$620$	−0.215877			−0.00866981
$621$	−5.50172			−0.220776
$622$	−0.886251	−	1.53503i	−0.0355354	−	0.0615492i
$623$	8.50523	−	11.6607i	0.340755	−	0.467177i
$624$	−0.841503	−	5.70604i	−0.0336871	−	0.228424i
$625$	−12.4964	+	21.6444i	−0.499855	+	0.865775i
$626$	7.77879	−	13.4733i	0.310903	−	0.538500i
$627$	−5.65475	+	9.79431i	−0.225829	+	0.391147i
$628$	2.35111	+	4.07225i	0.0938197	+	0.162500i
$629$	16.3383			0.651451
$630$	−0.0224725	+	0.0308100i	−0.000895327	+	0.00122750i
$631$	−15.7381	+	27.2591i	−0.626522	+	1.08517i	0.361722	+	0.932286i	$0.382189\pi$
$631$	−15.7381	+	27.2591i	−0.626522	+	1.08517i	−0.988244	+	0.152882i	$0.951145\pi$
$632$	8.01540	−	13.8831i	0.318835	−	0.552239i
$633$	−6.22472			−0.247411
$634$	−2.30485	+	3.99212i	−0.0915373	+	0.158547i
$635$	−0.221149			−0.00877604
$636$	17.8299			0.707002
$637$	20.9672	+	14.0491i	0.830751	+	0.556645i
$638$	−15.7057			−0.621793
$639$	7.15700			0.283126
$640$	0.121857	−	0.211063i	0.00481684	−	0.00834301i
$641$	−2.89641			−0.114401			−0.0572006	−	0.998363i	$-0.518217\pi$
$641$	−2.89641			−0.114401			−0.0572006	+	0.998363i	$0.518217\pi$
$642$	−4.42764	+	7.66890i	−0.174745	+	0.302667i
$643$	−13.7090	+	23.7446i	−0.540629	+	0.936398i	0.458239	+	0.888829i	$0.348481\pi$
$643$	−13.7090	+	23.7446i	−0.540629	+	0.936398i	−0.998868	+	0.0475683i	$0.984853\pi$
$644$	−13.4585	+	18.4517i	−0.530338	+	0.727097i
$645$	−0.197222			−0.00776562
$646$	−3.64246	−	6.30893i	−0.143311	−	0.248221i
$647$	−9.20333	+	15.9406i	−0.361820	+	0.626691i	−0.988260	−	0.152778i	$-0.951178\pi$
$647$	−9.20333	+	15.9406i	−0.361820	+	0.626691i	0.626440	+	0.779470i	$0.284511\pi$
$648$	1.17155	−	2.02918i	0.0460228	−	0.0797139i
$649$	−20.6692	+	35.8000i	−0.811335	+	1.40527i
$650$	−11.0025	−	4.35859i	−0.431554	−	0.170958i
$651$	−9.77096	+	13.3961i	−0.382954	+	0.525033i
$652$	−3.01555	−	5.22309i	−0.118098	−	0.204552i
$653$	35.8399			1.40252			0.701261	−	0.712905i	$-0.252621\pi$
$653$	35.8399			1.40252			0.701261	+	0.712905i	$0.252621\pi$
$654$	3.14075			0.122813
$655$	0.0456327	+	0.0790382i	0.00178302	+	0.00308828i
$656$	2.03869	+	3.53112i	0.0795975	+	0.137867i
$657$	0.102129	−	0.176893i	0.00398444	−	0.00690126i
$658$	−5.74327	−	12.9645i	−0.223896	−	0.505410i
$659$	20.9973	−	36.3684i	0.817939	−	1.41671i	−0.0892591	−	0.996008i	$-0.528450\pi$
$659$	20.9973	−	36.3684i	0.817939	−	1.41671i	0.907198	−	0.420704i	$-0.138217\pi$
$660$	−0.116853			−0.00454851
$661$	4.16701	−	7.21747i	0.162078	−	0.280727i	−0.773536	−	0.633752i	$-0.781514\pi$
$661$	4.16701	−	7.21747i	0.162078	−	0.280727i	0.935614	+	0.353026i	$0.114847\pi$
$662$	−4.73055	−	8.19354i	−0.183858	−	0.318451i
$663$	−1.75086	−	11.8722i	−0.0679977	−	0.461076i
$664$	33.8479			1.31355
$665$	−0.114118	+	0.156457i	−0.00442531	+	0.00606713i
$666$	−1.61136	−	2.79096i	−0.0624390	−	0.108147i
$667$	−19.3992	−	33.6005i	−0.751141	−	1.30101i
$668$	−7.27902	−	12.6076i	−0.281634	−	0.487804i
$669$	14.9907			0.579573
$670$	−0.0771929	−	0.133702i	−0.00298222	−	0.00516536i
$671$	35.5294			1.37160
$672$	−6.14727	−	13.8765i	−0.237136	−	0.535297i
$673$	11.9621	+	20.7189i	0.461104	+	0.798655i	0.999016	−	0.0443458i	$-0.0141203\pi$
$673$	11.9621	+	20.7189i	0.461104	+	0.798655i	−0.537913	+	0.843001i	$0.680787\pi$
$674$	−8.94113			−0.344399
$675$	2.49976	+	4.32971i	0.0962158	+	0.166651i
$676$	−4.66506	+	19.8562i	−0.179425	+	0.763699i
$677$	12.7371	−	22.0614i	0.489528	−	0.847887i	−0.510399	−	0.859937i	$-0.670502\pi$
$677$	12.7371	−	22.0614i	0.489528	−	0.847887i	0.999927	+	0.0120501i	$0.00383577\pi$
$678$	−3.95160	−	6.84438i	−0.151760	−	0.262857i
$679$	10.1092	+	22.8199i	0.387956	+	0.875747i
$680$	0.0856088	−	0.148279i	0.00328295	−	0.00568623i
$681$	−14.8521	+	25.7245i	−0.569132	+	0.985766i
$682$	13.9572			0.534450
$683$	3.73235			0.142814			0.0714072	−	0.997447i	$-0.477251\pi$
$683$	3.73235			0.142814			0.0714072	+	0.997447i	$0.477251\pi$
$684$	2.61540	−	4.53000i	0.100002	−	0.173209i
$685$	0.113912	−	0.197302i	0.00435237	−	0.00753852i
$686$	11.5426	+	3.82183i	0.440698	+	0.145918i
$687$	6.58433	+	11.4044i	0.251208	+	0.435105i
$688$	7.18511	−	12.4450i	0.273930	−	0.474460i
$689$	−38.0933	−	15.0904i	−1.45124	−	0.574900i
$690$	0.0396499	+	0.0686756i	0.00150945	+	0.00261444i
$691$	−25.7815			−0.980775			−0.490388	−	0.871504i	$-0.663145\pi$
$691$	−25.7815			−0.980775			−0.490388	+	0.871504i	$0.663145\pi$
$692$	−2.99656	−	5.19019i	−0.113912	−	0.197302i
$693$	−5.28899	+	7.25124i	−0.200912	+	0.275452i
$694$	17.4714			0.663206
$695$	−0.213414	−	0.369644i	−0.00809526	−	0.0140214i
$696$	16.5237			0.626328
$697$	4.24177	+	7.34695i	0.160668	+	0.278286i
$698$	3.20615	+	5.55322i	0.121355	+	0.210192i
$699$	7.62363	+	13.2045i	0.288352	+	0.499441i
$700$	20.6360	+	2.20778i	0.779966	+	0.0834464i
$701$	7.96930			0.300996			0.150498	−	0.988610i	$-0.451912\pi$
$701$	7.96930			0.300996			0.150498	+	0.988610i	$0.451912\pi$
$702$	−1.85536	+	1.46998i	−0.0700261	+	0.0554806i
$703$	−8.18268	−	14.1728i	−0.308616	−	0.534538i
$704$	−0.961180	+	1.66481i	−0.0362258	+	0.0627450i
$705$	0.179226			0.00675002
$706$	−6.20540	+	10.7481i	−0.233543	+	0.404509i
$707$	0.228356	+	0.515477i	0.00858822	+	0.0193865i
$708$	9.55977	−	16.5580i	0.359278	−	0.622288i
$709$	11.6944	+	20.2552i	0.439191	+	0.760702i	0.997627	−	0.0688459i	$-0.0219317\pi$
$709$	11.6944	+	20.2552i	0.439191	+	0.760702i	−0.558436	+	0.829548i	$0.688598\pi$
$710$	−0.0515792	−	0.0893378i	−0.00193573	−	0.00335279i
$711$	6.84171			0.256584
$712$	12.7820			0.479025
$713$	17.2396	+	29.8599i	0.645628	+	1.11826i
$714$	−2.34163	−	5.28584i	−0.0876331	−	0.197818i
$715$	0.249655	+	0.0988994i	0.00933656	+	0.00369863i
$716$	−11.7827	+	20.4083i	−0.440342	+	0.762694i
$717$	9.39134	−	16.2663i	0.350726	−	0.607475i
$718$	−10.6746	+	18.4889i	−0.398372	+	0.690001i
$719$	−4.65833	−	8.06846i	−0.173726	−	0.300903i	0.765993	−	0.642848i	$-0.222248\pi$
$719$	−4.65833	−	8.06846i	−0.173726	−	0.300903i	−0.939720	+	0.341946i	$0.888914\pi$
$720$	0.0351207			0.00130887
$721$	−5.12417	−	11.5670i	−0.190834	−	0.430777i
$722$	2.58842	−	4.48327i	0.0963310	−	0.166850i
$723$	4.21315	−	7.29739i	0.156689	−	0.271393i
$724$	−1.41855			−0.0527201
$725$	−17.6285	+	30.5334i	−0.654704	+	1.13398i
$726$	0.333318			0.0123706
$727$	−31.8742			−1.18215			−0.591075	−	0.806617i	$-0.701296\pi$
$727$	−31.8742			−1.18215			−0.591075	+	0.806617i	$0.701296\pi$
$728$	0.890231	+	22.3340i	0.0329942	+	0.827753i
$729$	1.00000			0.0370370
$730$	−0.00294411			−0.000108966
$731$	14.9496	−	25.8934i	0.552929	−	0.957702i
$732$	−16.4328			−0.607374
$733$	−2.46025	+	4.26128i	−0.0908715	+	0.157394i	−0.907878	−	0.419234i	$-0.862299\pi$
$733$	−2.46025	+	4.26128i	−0.0908715	+	0.157394i	0.817007	+	0.576628i	$0.195632\pi$
$734$	−4.84249	+	8.38744i	−0.178740	+	0.309586i
$735$	−0.103259	+	0.113825i	−0.00380875	+	0.00419850i
$736$	−31.5602			−1.16332
$737$	−18.1676	−	31.4672i	−0.669213	−	1.15911i
$738$	0.836686	−	1.44918i	0.0307988	−	0.0533451i
$739$	10.3617	−	17.9469i	0.381160	−	0.660188i	−0.610069	−	0.792349i	$-0.708858\pi$
$739$	10.3617	−	17.9469i	0.381160	−	0.660188i	0.991228	+	0.132161i	$0.0421915\pi$
$740$	0.0845461	−	0.146438i	0.00310798	−	0.00538317i
$741$	−9.42174	+	7.46471i	−0.346116	+	0.274223i
$742$	−19.6270	−	2.09984i	−0.720530	−	0.0770874i
$743$	−6.82937	−	11.8288i	−0.250545	−	0.433957i	0.713131	−	0.701031i	$-0.247277\pi$
$743$	−6.82937	−	11.8288i	−0.250545	−	0.433957i	−0.963676	+	0.267074i	$0.913943\pi$
$744$	−14.6842			−0.538348
$745$	−0.0627334			−0.00229837
$746$	−4.33677	−	7.51151i	−0.158780	−	0.275016i
$747$	7.22289	+	12.5104i	0.264272	+	0.457732i
$748$	8.85755	−	15.3417i	0.323864	−	0.560949i
$749$	−21.0298	+	28.8320i	−0.768412	+	1.05350i
$750$	0.0720647	−	0.124820i	0.00263143	−	0.00455777i
$751$	23.3132			0.850710			0.425355	−	0.905027i	$-0.360149\pi$
$751$	23.3132			0.850710			0.425355	+	0.905027i	$0.360149\pi$
$752$	−6.52946	+	11.3094i	−0.238105	+	0.412410i
$753$	5.31695	+	9.20923i	0.193760	+	0.335603i
$754$	−15.5196	−	6.14800i	−0.565190	−	0.223897i
$755$	0.0507836			0.00184821
$756$	2.44623	−	3.35380i	0.0889686	−	0.121976i
$757$	−10.0104	−	17.3385i	−0.363834	−	0.630179i	0.624754	−	0.780821i	$-0.285199\pi$
$757$	−10.0104	−	17.3385i	−0.363834	−	0.630179i	−0.988588	+	0.150642i	$0.951866\pi$
$758$	−8.23808	−	14.2688i	−0.299220	−	0.518265i
$759$	9.33174	+	16.1631i	0.338721	+	0.586682i
$760$	−0.171501			−0.00622100
$761$	−7.72957	−	13.3880i	−0.280197	−	0.485315i	0.691236	−	0.722629i	$-0.257066\pi$
$761$	−7.72957	−	13.3880i	−0.280197	−	0.485315i	−0.971433	+	0.237314i	$0.923733\pi$
$762$	−6.61308			−0.239567
$763$	12.5853	+	1.34647i	0.455620	+	0.0487455i
$764$	12.2210	+	21.1674i	0.442140	+	0.765809i
$765$	0.0730731			0.00264197
$766$	8.54339	+	14.7976i	0.308685	+	0.534658i
$767$	−34.4382	+	27.2849i	−1.24349	+	0.985201i
$768$	4.21062	−	7.29300i	0.151937	−	0.263163i
$769$	−19.1476	−	33.1646i	−0.690480	−	1.19595i	−0.971681	−	0.236298i	$-0.924066\pi$
$769$	−19.1476	−	33.1646i	−0.690480	−	1.19595i	0.281200	−	0.959649i	$-0.409267\pi$
$770$	0.128631	+	0.0137619i	0.00463554	+	0.000495943i
$771$	−12.4424	+	21.5509i	−0.448104	+	0.776138i
$772$	6.89932	−	11.9500i	0.248312	−	0.430089i
$773$	−30.0649			−1.08136			−0.540680	−	0.841228i	$-0.681833\pi$
$773$	−30.0649			−1.08136			−0.540680	+	0.841228i	$0.681833\pi$
$774$	−5.89758			−0.211984
$775$	15.6660	−	27.1342i	0.562738	−	0.974691i
$776$	−11.0519	+	19.1424i	−0.396739	+	0.687173i
$777$	−5.26040	−	11.8745i	−0.188716	−	0.425995i
$778$	4.60095	+	7.96908i	0.164952	+	0.285705i
$779$	4.24879	−	7.35912i	0.152229	−	0.263668i
$780$	−0.115469	−	0.0457423i	−0.00413445	−	0.00163784i
$781$	−12.1393	−	21.0260i	−0.434380	−	0.752368i
$782$	−12.0219			−0.429904
$783$	3.52603	+	6.10726i	0.126010	+	0.218256i
$784$	−3.42063	−	10.6626i	−0.122165	−	0.380806i
$785$	0.0657980			0.00234843
$786$	1.36457	+	2.36350i	0.0486724	+	0.0843031i
$787$	29.8058			1.06246			0.531231	−	0.847227i	$-0.321729\pi$
$787$	29.8058			1.06246			0.531231	+	0.847227i	$0.321729\pi$
$788$	−11.2907	−	19.5560i	−0.402214	−	0.696654i
$789$	7.82375	+	13.5511i	0.278533	+	0.482433i
$790$	−0.0493069	−	0.0854021i	−0.00175426	−	0.00303847i
$791$	−12.9003	−	29.1203i	−0.458681	−	1.03540i
$792$	−7.94850			−0.282438
$793$	35.1084	+	13.9080i	1.24674	+	0.493887i
$794$	−2.17117	−	3.76058i	−0.0770521	−	0.133458i
$795$	0.124746	−	0.216067i	0.00442430	−	0.00766311i
$796$	−37.3200			−1.32277
$797$	−21.1950	+	36.7109i	−0.750766	+	1.30037i	0.196685	+	0.980467i	$0.436982\pi$
$797$	−21.1950	+	36.7109i	−0.750766	+	1.30037i	−0.947452	+	0.319899i	$0.896351\pi$
$798$	−3.41250	+	4.67856i	−0.120801	+	0.165619i
$799$	−13.5854	+	23.5306i	−0.480617	+	0.832453i
$800$	14.3397	+	24.8370i	0.506984	+	0.878122i
$801$	2.72758	+	4.72431i	0.0963743	+	0.166925i
$802$	1.89454			0.0668985
$803$	−0.692907			−0.0244521
$804$	8.40277	+	14.5540i	0.296343	+	0.513281i
$805$	0.129440	+	0.292189i	0.00456215	+	0.0102983i
$806$	13.7919	+	5.46357i	0.485798	+	0.192446i
$807$	−2.76450	+	4.78826i	−0.0973151	+	0.168555i
$808$	−0.249650	+	0.432407i	−0.00878266	+	0.0152120i
$809$	13.4663	−	23.3244i	0.473452	−	0.820042i	−0.526087	−	0.850431i	$-0.676341\pi$
$809$	13.4663	−	23.3244i	0.473452	−	0.820042i	0.999538	+	0.0303888i	$0.00967453\pi$
$810$	−0.00720682	−	0.0124826i	−0.000253222	−	0.000438593i
$811$	35.6985			1.25354			0.626772	−	0.779203i	$-0.284376\pi$
$811$	35.6985			1.25354			0.626772	+	0.779203i	$0.284376\pi$
$812$	29.1080	+	3.11418i	1.02149	+	0.109286i
$813$	−6.55906	+	11.3606i	−0.230036	+	0.398434i
$814$	−5.46622	+	9.46777i	−0.191591	+	0.331845i
$815$	−0.0843928			−0.00295615
$816$	−2.66217	+	4.61101i	−0.0931944	+	0.161418i
$817$	−29.9486			−1.04777
$818$	−19.9547			−0.697700
$819$	−8.06483	+	5.09495i	−0.281808	+	0.178032i
$820$	0.0877997			0.00306610
$821$	50.2811			1.75482			0.877411	−	0.479739i	$-0.159269\pi$
$821$	50.2811			1.75482			0.877411	+	0.479739i	$0.159269\pi$
$822$	3.40635	−	5.89997i	0.118810	−	0.205785i
$823$	−18.1058			−0.631127			−0.315563	−	0.948904i	$-0.602194\pi$
$823$	−18.1058			−0.631127			−0.315563	+	0.948904i	$0.602194\pi$
$824$	5.60200	−	9.70294i	0.195155	−	0.338018i
$825$	8.47993	−	14.6877i	0.295233	−	0.511359i
$826$	−12.4733	+	17.1010i	−0.434003	+	0.595021i
$827$	12.0733			0.419830			0.209915	−	0.977720i	$-0.432681\pi$
$827$	12.0733			0.419830			0.209915	+	0.977720i	$0.432681\pi$
$828$	−4.31606	−	7.47563i	−0.149993	−	0.259796i
$829$	−18.3030	+	31.7016i	−0.635688	+	1.10104i	0.350681	+	0.936495i	$0.385950\pi$
$829$	−18.3030	+	31.7016i	−0.635688	+	1.10104i	−0.986369	+	0.164549i	$0.947383\pi$
$830$	0.104108	−	0.180321i	0.00361365	−	0.00625902i
$831$	−13.6967	+	23.7234i	−0.475133	+	0.822955i
$832$	−1.60148	+	1.26883i	−0.0555214	+	0.0439888i
$833$	−7.11707	−	22.1849i	−0.246592	−	0.768660i
$834$	−6.38177	−	11.0536i	−0.220983	−	0.382753i
$835$	−0.203710			−0.00704966
$836$	−17.7444			−0.613704
$837$	−3.13349	−	5.42737i	−0.108309	−	0.187597i
$838$	−0.258344	−	0.447465i	−0.00892434	−	0.0154574i
$839$	−5.93703	+	10.2832i	−0.204969	+	0.355017i	−0.950123	−	0.311876i	$-0.899043\pi$
$839$	−5.93703	+	10.2832i	−0.204969	+	0.355017i	0.745154	+	0.666893i	$0.232376\pi$
$840$	−0.135331	−	0.0144786i	−0.00466935	−	0.000499560i
$841$	−10.3658	+	17.9541i	−0.357441	+	0.619106i
$842$	−9.36361			−0.322691
$843$	−2.54158	+	4.40215i	−0.0875367	+	0.151618i
$844$	−4.88325	−	8.45804i	−0.168088	−	0.291138i
$845$	0.207983	+	0.195455i	0.00715482	+	0.00672387i
$846$	5.35942			0.184261
$847$	1.33564	+	0.142897i	0.0458932	+	0.00490998i
$848$	9.08940	+	15.7433i	0.312131	+	0.540627i
$849$	−3.06193	−	5.30341i	−0.105085	−	0.182013i
$850$	5.46228	+	9.46095i	0.187355	+	0.324508i
$851$	−27.0069			−0.925786
$852$	5.61461	+	9.72480i	0.192354	+	0.333166i
$853$	18.8037			0.643826			0.321913	−	0.946769i	$-0.395674\pi$
$853$	18.8037			0.643826			0.321913	+	0.946769i	$0.395674\pi$
$854$	18.0891	+	1.93530i	0.618996	+	0.0662246i
$855$	−0.0365971	−	0.0633880i	−0.00125159	−	0.00216782i
$856$	−31.6044			−1.08022
$857$	−23.9503	−	41.4831i	−0.818127	−	1.41704i	−0.907061	−	0.421000i	$-0.861679\pi$
$857$	−23.9503	−	41.4831i	−0.818127	−	1.41704i	0.0889340	−	0.996038i	$-0.471654\pi$
$858$	7.46549	+	2.95741i	0.254868	+	0.100964i
$859$	−12.3001	+	21.3044i	−0.419675	+	0.726898i	−0.995907	−	0.0903881i	$-0.971189\pi$
$859$	−12.3001	+	21.3044i	−0.419675	+	0.726898i	0.576232	+	0.817286i	$0.304523\pi$
$860$	−0.154719	−	0.267982i	−0.00527589	−	0.00913811i
$861$	3.97397	−	5.44834i	0.135433	−	0.185679i
$862$	−12.5615	+	21.7572i	−0.427847	+	0.741052i
$863$	13.6634	−	23.6657i	0.465108	−	0.805590i	−0.534099	−	0.845422i	$-0.679349\pi$
$863$	13.6634	−	23.6657i	0.465108	−	0.805590i	0.999206	+	0.0398319i	$0.0126823\pi$
$864$	5.73642			0.195157
$865$	−0.0838613			−0.00285137
$866$	−8.40253	+	14.5536i	−0.285530	+	0.494552i
$867$	2.96101	−	5.12863i	0.100561	−	0.174177i
$868$	−25.8676	−	2.76750i	−0.878002	−	0.0939350i
$869$	−11.6046	−	20.0997i	−0.393658	−	0.681835i
$870$	0.0508229	−	0.0880279i	0.00172306	−	0.00298443i
$871$	−5.63449	−	38.2061i	−0.190917	−	1.29457i
$872$	5.60464	+	9.70752i	0.189797	+	0.328738i
$873$	−9.43355			−0.319277
$874$	6.02092	+	10.4285i	0.203661	+	0.352751i
$875$	0.342283	−	0.469272i	0.0115713	−	0.0158643i
$876$	0.320479			0.0108280
$877$	0.916805	+	1.58795i	0.0309583	+	0.0536213i	0.881089	−	0.472950i	$-0.156811\pi$
$877$	0.916805	+	1.58795i	0.0309583	+	0.0536213i	−0.850131	+	0.526571i	$0.823477\pi$
$878$	−9.47504			−0.319767
$879$	1.05051	+	1.81953i	0.0354327	+	0.0613712i
$880$	−0.0595699	−	0.103178i	−0.00200810	−	0.00347813i
$881$	18.1675	+	31.4671i	0.612080	+	1.06015i	0.990889	+	0.134679i	$0.0430003\pi$
$881$	18.1675	+	31.4671i	0.612080	+	1.06015i	−0.378809	+	0.925475i	$0.623666\pi$
$882$	−3.08777	+	3.40373i	−0.103970	+	0.114610i
$883$	29.4585			0.991356			0.495678	−	0.868506i	$-0.334920\pi$
$883$	29.4585			0.991356			0.495678	+	0.868506i	$0.334920\pi$
$884$	14.7581	−	11.6927i	0.496370	−	0.393267i
$885$	−0.133769	−	0.231695i	−0.00449660	−	0.00778834i
$886$	−11.7322	+	20.3208i	−0.394152	+	0.682692i
$887$	2.64572			0.0888346			0.0444173	−	0.999013i	$-0.485857\pi$
$887$	2.64572			0.0888346			0.0444173	+	0.999013i	$0.485857\pi$
$888$	5.75092	−	9.96089i	0.192988	−	0.334266i
$889$	−26.4994	−	2.83509i	−0.888760	−	0.0950859i
$890$	0.0393143	−	0.0680944i	0.00131782	−	0.00228253i
$891$	−1.69615	−	2.93782i	−0.0568232	−	0.0984206i
$892$	11.7601	+	20.3690i	0.393756	+	0.682006i
$893$	27.2158			0.910742
$894$	−1.87593			−0.0627405
$895$	0.164875	+	0.285572i	0.00551117	+	0.00954562i
$896$	17.3074	−	23.7286i	0.578201	−	0.792717i
$897$	2.89414	+	19.6245i	0.0966325	+	0.655242i
$898$	5.34669	−	9.26074i	0.178421	−	0.309035i
$899$	22.0976	−	38.2742i	0.736996	−	1.27651i
$900$	−3.92209	+	6.79325i	−0.130736	+	0.226442i
$901$	18.9117	+	32.7560i	0.630040	+	1.09126i
$902$	−5.67658			−0.189009
$903$	−23.6323	−	2.52835i	−0.786433	−	0.0841383i
$904$	14.1032	−	24.4275i	0.469066	−	0.812446i
$905$	−0.00992485	+	0.0171903i	−0.000329913	+	0.000571427i
$906$	1.51860			0.0504519
$907$	−8.57995	+	14.8609i	−0.284893	+	0.493449i	−0.972583	−	0.232555i	$-0.925291\pi$
$907$	−8.57995	+	14.8609i	−0.284893	+	0.493449i	0.687690	+	0.726004i	$0.258625\pi$
$908$	−46.6053			−1.54665
$909$	−0.213094			−0.00706788
$910$	0.121720	+	0.0639515i	0.00403497	+	0.00211997i
$911$	22.4706			0.744483			0.372241	−	0.928136i	$-0.378589\pi$
$911$	22.4706			0.744483			0.372241	+	0.928136i	$0.378589\pi$
$912$	5.33315			0.176598
$913$	24.5022	−	42.4391i	0.810905	−	1.40453i
$914$	17.5849			0.581658
$915$	−0.114972	+	0.199137i	−0.00380084	+	0.00658326i
$916$	−10.3307	+	17.8933i	−0.341337	+	0.591212i
$917$	4.45472	+	10.0558i	0.147108	+	0.332072i
$918$	2.18512			0.0721198
$919$	−21.9814	−	38.0729i	−0.725100	−	1.25591i	−0.958933	−	0.283633i	$-0.908460\pi$
$919$	−21.9814	−	38.0729i	−0.725100	−	1.25591i	0.233833	−	0.972277i	$-0.424873\pi$
$920$	−0.141510	+	0.245102i	−0.00466544	+	0.00808078i
$921$	4.91454	−	8.51223i	0.161940	−	0.280488i
$922$	1.66211	−	2.87886i	0.0547387	−	0.0948103i
$923$	−3.76489	−	25.5288i	−0.123923	−	0.840291i
$924$	−14.0020	−	1.49804i	−0.460633	−	0.0492818i
$925$	12.2709	+	21.2538i	0.403463	+	0.698819i
$926$	13.5776			0.446188
$927$	4.78170			0.157052
$928$	20.2268	+	35.0338i	0.663977	+	1.15004i
$929$	−10.0841	−	17.4661i	−0.330848	−	0.573045i	0.651831	−	0.758365i	$-0.274001\pi$
$929$	−10.0841	−	17.4661i	−0.330848	−	0.573045i	−0.982678	+	0.185320i	$0.940668\pi$
$930$	−0.0451650	+	0.0782282i	−0.00148102	+	0.00256520i
$931$	−15.6800	+	17.2846i	−0.513893	+	0.566479i
$932$	−11.9614	+	20.7177i	−0.391808	+	0.678631i
$933$	2.69986			0.0883894
$934$	12.7147	−	22.0224i	0.416036	−	0.720596i
$935$	−0.123943	−	0.214676i	−0.00405337	−	0.00702064i
$936$	−7.85432	−	3.11145i	−0.256727	−	0.101701i
$937$	25.2750			0.825699			0.412849	−	0.910799i	$-0.364534\pi$
$937$	25.2750			0.825699			0.412849	+	0.910799i	$0.364534\pi$
$938$	−7.53566	−	17.0105i	−0.246048	−	0.555414i
$939$	11.8486	+	20.5223i	0.386664	+	0.669721i
$940$	0.140601	+	0.243528i	0.00458590	+	0.00794302i
$941$	14.0439	+	24.3247i	0.457818	+	0.792963i	0.998845	−	0.0480414i	$-0.0152979\pi$
$941$	14.0439	+	24.3247i	0.457818	+	0.792963i	−0.541028	+	0.841005i	$0.681965\pi$
$942$	1.96757			0.0641070
$943$	−7.01157	−	12.1444i	−0.228328	−	0.395476i
$944$	19.4937			0.634465
$945$	−0.0235271	−	0.0531087i	−0.000765338	−	0.00172763i
$946$	10.0032	+	17.3260i	0.325232	+	0.563318i
$947$	5.27460			0.171401			0.0857007	−	0.996321i	$-0.472687\pi$
$947$	5.27460			0.171401			0.0857007	+	0.996321i	$0.472687\pi$
$948$	5.36727	+	9.29638i	0.174321	+	0.301932i
$949$	−0.684697	−	0.271239i	−0.0222262	−	0.00880479i
$950$	5.47133	−	9.47662i	0.177513	−	0.307462i
$951$	−3.51073	−	6.08076i	−0.113843	−	0.197182i
$952$	12.1590	−	16.6701i	0.394077	−	0.540282i
$953$	−19.9525	+	34.5587i	−0.646323	+	1.11946i	0.337671	+	0.941264i	$0.390361\pi$
$953$	−19.9525	+	34.5587i	−0.646323	+	1.11946i	−0.983994	+	0.178201i	$0.942972\pi$
$954$	3.73032	−	6.46111i	0.120774	−	0.209186i
$955$	0.342015			0.0110673
$956$	29.4697			0.953120
$957$	11.9614	−	20.7177i	0.386656	−	0.669707i
$958$	0.116198	−	0.201260i	0.00375418	−	0.00650243i
$959$	16.1790	−	22.1815i	0.522447	−	0.716279i
$960$	−0.00622068	−	0.0107745i	−0.000200772	−	0.000347747i
$961$	−4.13757	+	7.16648i	−0.133470	+	0.231177i
$962$	−9.10762	+	7.21584i	−0.293642	+	0.232648i
$963$	−6.74414	−	11.6812i	−0.217327	−	0.376421i
$964$	13.2207			0.425812
$965$	−0.0965417	−	0.167215i	−0.00310779	−	0.00538284i
$966$	3.87067	+	8.73741i	0.124537	+	0.281122i
$967$	17.2394			0.554383			0.277192	−	0.960815i	$-0.410596\pi$
$967$	17.2394			0.554383			0.277192	+	0.960815i	$0.410596\pi$
$968$	0.594803	+	1.03023i	0.0191177	+	0.0331128i
$969$	11.0963			0.356465
$970$	0.0679859	+	0.117755i	0.00218290	+	0.00378089i
$971$	−7.83132	−	13.5642i	−0.251319	−	0.435297i	0.712570	−	0.701601i	$-0.247531\pi$
$971$	−7.83132	−	13.5642i	−0.251319	−	0.435297i	−0.963889	+	0.266304i	$0.914198\pi$
$972$	0.784493	+	1.35878i	0.0251626	+	0.0435829i
$973$	−20.8337	−	47.0288i	−0.667899	−	1.50767i
$974$	2.98178			0.0955424
$975$	14.1290	−	11.1942i	0.452489	−	0.358501i
$976$	−8.37718	−	14.5097i	−0.268147	−	0.464444i
$977$	−26.6395	+	46.1410i	−0.852273	+	1.47618i	0.0268786	+	0.999639i	$0.491443\pi$
$977$	−26.6395	+	46.1410i	−0.852273	+	1.47618i	−0.879152	+	0.476542i	$0.841890\pi$
$978$	−2.52362			−0.0806964
$979$	9.25277	−	16.0263i	0.295720	−	0.512202i
$980$	−0.235669	−	0.0510110i	−0.00752816	−	0.00162949i
$981$	−2.39198	+	4.14303i	−0.0763700	+	0.132277i
$982$	0.268350	+	0.464795i	0.00856338	+	0.0148322i
$983$	−18.4519	−	31.9596i	−0.588524	−	1.01935i	−0.994426	−	0.105437i	$-0.966376\pi$
$983$	−18.4519	−	31.9596i	−0.588524	−	1.01935i	0.405902	−	0.913917i	$-0.366958\pi$
$984$	5.97224			0.190388
$985$	−0.315979			−0.0100679
$986$	7.70481	+	13.3451i	0.245371	+	0.424995i
$987$	21.4758	+	2.29764i	0.683583	+	0.0731346i
$988$	−17.5342	−	6.94607i	−0.557837	−	0.220984i
$989$	−24.7114	+	42.8013i	−0.785776	+	1.36100i
$990$	−0.0244477	+	0.0423447i	−0.000776999	+	0.00134580i
$991$	6.24775	−	10.8214i	0.198466	−	0.343754i	−0.749565	−	0.661931i	$-0.769737\pi$
$991$	6.24775	−	10.8214i	0.198466	−	0.343754i	0.948031	+	0.318177i	$0.103071\pi$
$992$	−17.9750	−	31.1337i	−0.570708	−	0.988495i
$993$	14.4110			0.457321
$994$	−5.03522	−	11.3662i	−0.159707	−	0.360514i
$995$	−0.261108	+	0.452252i	−0.00827768	+	0.0143374i
$996$	−11.3326	+	19.6287i	−0.359087	+	0.621958i
$997$	−38.3521			−1.21462			−0.607312	−	0.794464i	$-0.707752\pi$
$997$	−38.3521			−1.21462			−0.607312	+	0.794464i	$0.707752\pi$
$998$	5.73029	−	9.92516i	0.181389	−	0.314175i
$999$	4.90882			0.155308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.16.6	yes	20
3.2	odd	2		819.2.s.f.289.5		20
7.4	even	3		273.2.j.c.172.5	yes	20
13.9	even	3		273.2.j.c.100.5	✓	20
21.11	odd	6		819.2.n.f.172.6		20
39.35	odd	6		819.2.n.f.100.6		20
91.74	even	3	inner	273.2.l.c.256.6	yes	20
273.74	odd	6		819.2.s.f.802.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.5	✓	20	13.9	even	3
273.2.j.c.172.5	yes	20	7.4	even	3
273.2.l.c.16.6	yes	20	1.1	even	1	trivial
273.2.l.c.256.6	yes	20	91.74	even	3	inner
819.2.n.f.100.6		20	39.35	odd	6
819.2.n.f.172.6		20	21.11	odd	6
819.2.s.f.289.5		20	3.2	odd	2
819.2.s.f.802.5		20	273.74	odd	6

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

\(f(q)\)	\(=\)	\(q+0.656517 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.56899 q^{4} +(-0.0109774 + 0.0190133i) q^{5} +(-0.328258 + 0.568560i) q^{6} +(-1.55912 + 2.13756i) q^{7} -2.34310 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+0.656517 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.56899 q^{4} +(-0.0109774 + 0.0190133i) q^{5} +(-0.328258 + 0.568560i) q^{6} +(-1.55912 + 2.13756i) q^{7} -2.34310 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.00720682 + 0.0124826i) q^{10} +(-1.69615 + 2.93782i) q^{11} +(0.784493 - 1.35878i) q^{12} +(-2.82607 + 2.23905i) q^{13} +(-1.02359 + 1.40334i) q^{14} +(-0.0109774 - 0.0190133i) q^{15} +1.59969 q^{16} +3.32836 q^{17} +(-0.328258 - 0.568560i) q^{18} +(-1.66694 - 2.88722i) q^{19} +(0.0172233 - 0.0298316i) q^{20} +(-1.07162 - 2.41901i) q^{21} +(-1.11355 + 1.92873i) q^{22} -5.50172 q^{23} +(1.17155 - 2.02918i) q^{24} +(2.49976 + 4.32971i) q^{25} +(-1.85536 + 1.46998i) q^{26} +1.00000 q^{27} +(2.44623 - 3.35380i) q^{28} +(3.52603 + 6.10726i) q^{29} +(-0.00720682 - 0.0124826i) q^{30} +(-3.13349 - 5.42737i) q^{31} +5.73642 q^{32} +(-1.69615 - 2.93782i) q^{33} +2.18512 q^{34} +(-0.0235271 - 0.0531087i) q^{35} +(0.784493 + 1.35878i) q^{36} +4.90882 q^{37} +(-1.09437 - 1.89551i) q^{38} +(-0.526042 - 3.56697i) q^{39} +(0.0257210 - 0.0445501i) q^{40} +(1.27443 + 2.20738i) q^{41} +(-0.703538 - 1.58812i) q^{42} +(4.49157 - 7.77963i) q^{43} +(2.66124 - 4.60940i) q^{44} +0.0219547 q^{45} -3.61197 q^{46} +(-4.08171 + 7.06973i) q^{47} +(-0.799843 + 1.38537i) q^{48} +(-2.13831 - 6.66540i) q^{49} +(1.64113 + 2.84253i) q^{50} +(-1.66418 + 2.88244i) q^{51} +(4.43406 - 3.51304i) q^{52} +(5.68199 + 9.84149i) q^{53} +0.656517 q^{54} +(-0.0372385 - 0.0644990i) q^{55} +(3.65316 - 5.00851i) q^{56} +3.33387 q^{57} +(2.31490 + 4.00952i) q^{58} +12.1859 q^{59} +(0.0172233 + 0.0298316i) q^{60} +(-5.23676 - 9.07034i) q^{61} +(-2.05719 - 3.56316i) q^{62} +(2.63074 + 0.281455i) q^{63} +0.566683 q^{64} +(-0.0115491 - 0.0783118i) q^{65} +(-1.11355 - 1.92873i) q^{66} +(-5.35554 + 9.27608i) q^{67} -5.22215 q^{68} +(2.75086 - 4.76463i) q^{69} +(-0.0154460 - 0.0348668i) q^{70} +(-3.57850 + 6.19814i) q^{71} +(1.17155 + 2.02918i) q^{72} +(0.102129 + 0.176893i) q^{73} +3.22272 q^{74} -4.99952 q^{75} +(2.61540 + 4.53000i) q^{76} +(-3.63526 - 8.20602i) q^{77} +(-0.345356 - 2.34178i) q^{78} +(-3.42085 + 5.92509i) q^{79} +(-0.0175603 + 0.0304154i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.836686 + 1.44918i) q^{82} -14.4458 q^{83} +(1.68136 + 3.79540i) q^{84} +(-0.0365366 + 0.0632832i) q^{85} +(2.94879 - 5.10746i) q^{86} -7.05206 q^{87} +(3.97425 - 6.88360i) q^{88} -5.45516 q^{89} +0.0144136 q^{90} +(-0.379938 - 9.53182i) q^{91} +8.63212 q^{92} +6.26699 q^{93} +(-2.67971 + 4.64140i) q^{94} +0.0731942 q^{95} +(-2.86821 + 4.96789i) q^{96} +(4.71678 - 8.16970i) q^{97} +(-1.40384 - 4.37595i) q^{98} +3.39230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

L-functions

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