LMFDB - Embedded newform 273.2.bz.b.229.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			229.9
Character	$\chi$	$=$	273.229
Dual form			273.2.bz.b.31.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11542 - 0.566824i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.42164 - 1.39814i) q^{4} +(0.169176 + 0.631372i) q^{5} +(1.54859 - 1.54859i) q^{6} +(-1.81137 - 1.92845i) q^{7} +(1.23310 - 1.23310i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(2.11542 - 0.566824i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.42164 - 1.39814i) q^{4} +(0.169176 + 0.631372i) q^{5} +(1.54859 - 1.54859i) q^{6} +(-1.81137 - 1.92845i) q^{7} +(1.23310 - 1.23310i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.715753 + 1.23972i) q^{10} +(-2.46032 - 0.659241i) q^{11} +(1.39814 - 2.42164i) q^{12} +(1.72632 + 3.16541i) q^{13} +(-4.92490 - 3.05275i) q^{14} +(0.462196 + 0.462196i) q^{15} +(-0.886704 + 1.53582i) q^{16} +(2.99130 + 5.18109i) q^{17} +(0.566824 - 2.11542i) q^{18} +(0.456716 + 1.70449i) q^{19} +(1.29243 + 1.29243i) q^{20} +(-2.53292 - 0.764403i) q^{21} -5.57827 q^{22} +(-4.55977 - 2.63259i) q^{23} +(0.451346 - 1.68444i) q^{24} +(3.96012 - 2.28637i) q^{25} +(5.44611 + 5.71764i) q^{26} -1.00000i q^{27} +(-7.08273 - 2.13748i) q^{28} -0.0763835 q^{29} +(1.23972 + 0.715753i) q^{30} +(-7.61556 - 2.04058i) q^{31} +(-1.90790 + 7.12039i) q^{32} +(-2.46032 + 0.659241i) q^{33} +(9.26461 + 9.26461i) q^{34} +(0.911131 - 1.46990i) q^{35} -2.79627i q^{36} +(-2.86365 - 10.6873i) q^{37} +(1.93229 + 3.34682i) q^{38} +(3.07774 + 1.87817i) q^{39} +(0.987154 + 0.569934i) q^{40} +(1.05558 - 1.05558i) q^{41} +(-5.79146 - 0.181311i) q^{42} -0.901426i q^{43} +(-6.87972 + 1.84342i) q^{44} +(0.631372 + 0.169176i) q^{45} +(-11.1380 - 2.98443i) q^{46} +(3.26758 - 0.875544i) q^{47} +1.77341i q^{48} +(-0.437863 + 6.98629i) q^{49} +(7.08132 - 7.08132i) q^{50} +(5.18109 + 2.99130i) q^{51} +(8.60620 + 5.25186i) q^{52} +(0.696069 + 1.20563i) q^{53} +(-0.566824 - 2.11542i) q^{54} -1.66490i q^{55} +(-4.61158 - 0.144373i) q^{56} +(1.24777 + 1.24777i) q^{57} +(-0.161583 + 0.0432960i) q^{58} +(-1.36632 + 5.09918i) q^{59} +(1.76549 + 0.473061i) q^{60} +(2.64864 + 1.52919i) q^{61} -17.2667 q^{62} +(-2.57578 + 0.604468i) q^{63} +12.5972i q^{64} +(-1.70650 + 1.62546i) q^{65} +(-4.83093 + 2.78914i) q^{66} +(0.940634 - 3.51049i) q^{67} +(14.4877 + 8.36449i) q^{68} -5.26517 q^{69} +(1.09425 - 3.62589i) q^{70} +(4.48225 + 4.48225i) q^{71} +(-0.451346 - 1.68444i) q^{72} +(4.00866 - 14.9605i) q^{73} +(-12.1156 - 20.9849i) q^{74} +(2.28637 - 3.96012i) q^{75} +(3.48911 + 3.48911i) q^{76} +(3.18524 + 5.93874i) q^{77} +(7.57529 + 2.22856i) q^{78} +(5.60217 - 9.70324i) q^{79} +(-1.11968 - 0.300017i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.63466 - 2.83131i) q^{82} +(-6.20423 + 6.20423i) q^{83} +(-7.20257 + 1.69026i) q^{84} +(-2.76514 + 2.76514i) q^{85} +(-0.510949 - 1.90689i) q^{86} +(-0.0661501 + 0.0381918i) q^{87} +(-3.84673 + 2.22091i) q^{88} +(8.92433 - 2.39127i) q^{89} +1.43151 q^{90} +(2.97734 - 9.06286i) q^{91} -14.7229 q^{92} +(-7.61556 + 2.04058i) q^{93} +(6.41600 - 3.70428i) q^{94} +(-0.998900 + 0.576715i) q^{95} +(1.90790 + 7.12039i) q^{96} +(-6.89422 + 6.89422i) q^{97} +(3.03374 + 15.0271i) q^{98} +(-1.80108 + 1.80108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 + 18 * q^9	$ 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.11542	−	0.566824i	1.49582	−	0.400805i	0.584125	−	0.811663i	$-0.301438\pi$
$2$	2.11542	−	0.566824i	1.49582	−	0.400805i	0.911699	+	0.410858i	$0.134771\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	2.42164	−	1.39814i	1.21082	−	0.699068i
$5$	0.169176	+	0.631372i	0.0756576	+	0.282358i	0.993382	−	0.114861i	$-0.0366421\pi$
$5$	0.169176	+	0.631372i	0.0756576	+	0.282358i	−0.917724	+	0.397219i	$0.869975\pi$
$6$	1.54859	−	1.54859i	0.632210	−	0.632210i
$7$	−1.81137	−	1.92845i	−0.684634	−	0.728887i
$7$	−1.81137	−	1.92845i	−0.684634	−	0.728887i
$8$	1.23310	−	1.23310i	0.435966	−	0.435966i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.715753	+	1.23972i	0.226341	+	0.392034i
$11$	−2.46032	−	0.659241i	−0.741815	−	0.198769i	−0.131930	−	0.991259i	$-0.542117\pi$
$11$	−2.46032	−	0.659241i	−0.741815	−	0.198769i	−0.609884	+	0.792490i	$0.708784\pi$
$12$	1.39814	−	2.42164i	0.403607	−	0.699068i
$13$	1.72632	+	3.16541i	0.478795	+	0.877927i
$13$	1.72632	+	3.16541i	0.478795	+	0.877927i
$14$	−4.92490	−	3.05275i	−1.31623	−	0.815882i
$15$	0.462196	+	0.462196i	0.119339	+	0.119339i
$16$	−0.886704	+	1.53582i	−0.221676	+	0.383954i
$17$	2.99130	+	5.18109i	0.725497	+	1.25660i	0.958769	+	0.284186i	$0.0917234\pi$
$17$	2.99130	+	5.18109i	0.725497	+	1.25660i	−0.233272	+	0.972412i	$0.574943\pi$
$18$	0.566824	−	2.11542i	0.133602	−	0.498608i
$19$	0.456716	+	1.70449i	0.104778	+	0.391036i	0.998320	−	0.0579434i	$-0.0184543\pi$
$19$	0.456716	+	1.70449i	0.104778	+	0.391036i	−0.893542	+	0.448980i	$0.851788\pi$
$20$	1.29243	+	1.29243i	0.288995	+	0.288995i
$21$	−2.53292	−	0.764403i	−0.552729	−	0.166806i
$22$	−5.57827			−1.18929
$23$	−4.55977	−	2.63259i	−0.950779	−	0.548932i	−0.0574559	−	0.998348i	$-0.518299\pi$
$23$	−4.55977	−	2.63259i	−0.950779	−	0.548932i	−0.893323	+	0.449416i	$0.851632\pi$
$24$	0.451346	−	1.68444i	0.0921305	−	0.343836i
$25$	3.96012	−	2.28637i	0.792023	−	0.457275i
$26$	5.44611	+	5.71764i	1.06807	+	1.12132i
$27$		−	1.00000i		−	0.192450i
$28$	−7.08273	−	2.13748i	−1.33851	−	0.403946i
$29$	−0.0763835			−0.0141841			−0.00709203	−	0.999975i	$-0.502257\pi$
$29$	−0.0763835			−0.0141841			−0.00709203	+	0.999975i	$0.502257\pi$
$30$	1.23972	+	0.715753i	0.226341	+	0.130678i
$31$	−7.61556	−	2.04058i	−1.36780	−	0.366500i	−0.501122	−	0.865377i	$-0.667079\pi$
$31$	−7.61556	−	2.04058i	−1.36780	−	0.366500i	−0.866673	+	0.498877i	$0.833746\pi$
$32$	−1.90790	+	7.12039i	−0.337273	+	1.25872i
$33$	−2.46032	+	0.659241i	−0.428287	+	0.114759i
$34$	9.26461	+	9.26461i	1.58887	+	1.58887i
$35$	0.911131	−	1.46990i	0.154009	−	0.248458i
$36$		−	2.79627i		−	0.466045i
$37$	−2.86365	−	10.6873i	−0.470781	−	1.75698i	−0.636974	−	0.770885i	$-0.719814\pi$
$37$	−2.86365	−	10.6873i	−0.470781	−	1.75698i	0.166193	−	0.986093i	$-0.446852\pi$
$38$	1.93229	+	3.34682i	0.313458	+	0.542926i
$39$	3.07774	+	1.87817i	0.492833	+	0.300747i
$40$	0.987154	+	0.569934i	0.156083	+	0.0901144i
$41$	1.05558	−	1.05558i	0.164853	−	0.164853i	−0.619860	−	0.784713i	$-0.712810\pi$
$41$	1.05558	−	1.05558i	0.164853	−	0.164853i	0.784713	+	0.619860i	$0.212810\pi$
$42$	−5.79146	−	0.181311i	−0.893642	−	0.0279768i
$43$		−	0.901426i		−	0.137466i	−0.997635	−	0.0687331i	$-0.978104\pi$
$43$		−	0.901426i		−	0.137466i	0.997635	−	0.0687331i	$-0.0218957\pi$
$44$	−6.87972	+	1.84342i	−1.03716	+	0.277905i
$45$	0.631372	+	0.169176i	0.0941193	+	0.0252192i
$46$	−11.1380	−	2.98443i	−1.64221	−	0.440030i
$47$	3.26758	−	0.875544i	0.476625	−	0.127711i	−0.0125057	−	0.999922i	$-0.503981\pi$
$47$	3.26758	−	0.875544i	0.476625	−	0.127711i	0.489131	+	0.872211i	$0.337314\pi$
$48$			1.77341i			0.255970i
$49$	−0.437863	+	6.98629i	−0.0625518	+	0.998042i
$50$	7.08132	−	7.08132i	1.00145	−	1.00145i
$51$	5.18109	+	2.99130i	0.725497	+	0.418866i
$52$	8.60620	+	5.25186i	1.19347	+	0.728302i
$53$	0.696069	+	1.20563i	0.0956124	+	0.165606i	0.909864	−	0.414907i	$-0.136186\pi$
$53$	0.696069	+	1.20563i	0.0956124	+	0.165606i	−0.814252	+	0.580512i	$0.802852\pi$
$54$	−0.566824	−	2.11542i	−0.0771350	−	0.287872i
$55$		−	1.66490i		−	0.224496i
$56$	−4.61158	−	0.144373i	−0.616248	−	0.0192926i
$57$	1.24777	+	1.24777i	0.165271	+	0.165271i
$58$	−0.161583	+	0.0432960i	−0.0212169	+	0.00568504i
$59$	−1.36632	+	5.09918i	−0.177880	+	0.663857i	0.818163	+	0.574986i	$0.194992\pi$
$59$	−1.36632	+	5.09918i	−0.177880	+	0.663857i	−0.996043	+	0.0888707i	$0.971674\pi$
$60$	1.76549	+	0.473061i	0.227923	+	0.0610719i
$61$	2.64864	+	1.52919i	0.339124	+	0.195793i	0.659884	−	0.751367i	$-0.270605\pi$
$61$	2.64864	+	1.52919i	0.339124	+	0.195793i	−0.320761	+	0.947160i	$0.603939\pi$
$62$	−17.2667			−2.19288
$63$	−2.57578	+	0.604468i	−0.324517	+	0.0761558i
$64$			12.5972i			1.57465i
$65$	−1.70650	+	1.62546i	−0.211665	+	0.201613i
$66$	−4.83093	+	2.78914i	−0.594646	+	0.343319i
$67$	0.940634	−	3.51049i	0.114917	−	0.428875i	−0.884364	−	0.466798i	$-0.845407\pi$
$67$	0.940634	−	3.51049i	0.114917	−	0.428875i	0.999281	+	0.0379229i	$0.0120741\pi$
$68$	14.4877	+	8.36449i	1.75689	+	1.01434i
$69$	−5.26517			−0.633852
$70$	1.09425	−	3.62589i	0.130788	−	0.433377i
$71$	4.48225	+	4.48225i	0.531946	+	0.531946i	0.921151	−	0.389205i	$-0.127250\pi$
$71$	4.48225	+	4.48225i	0.531946	+	0.531946i	−0.389205	+	0.921151i	$0.627250\pi$
$72$	−0.451346	−	1.68444i	−0.0531916	−	0.198514i
$73$	4.00866	−	14.9605i	0.469178	−	1.75100i	−0.173474	−	0.984839i	$-0.555499\pi$
$73$	4.00866	−	14.9605i	0.469178	−	1.75100i	0.642652	−	0.766158i	$-0.277834\pi$
$74$	−12.1156	−	20.9849i	−1.40841	−	2.43944i
$75$	2.28637	−	3.96012i	0.264008	−	0.457275i
$76$	3.48911	+	3.48911i	0.400228	+	0.400228i
$77$	3.18524	+	5.93874i	0.362992	+	0.676783i
$78$	7.57529	+	2.22856i	0.857733	+	0.252335i
$79$	5.60217	−	9.70324i	0.630293	−	1.09170i	−0.357198	−	0.934029i	$-0.616268\pi$
$79$	5.60217	−	9.70324i	0.630293	−	1.09170i	0.987492	−	0.157671i	$-0.0503987\pi$
$80$	−1.11968	−	0.300017i	−0.125184	−	0.0335430i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.63466	−	2.83131i	0.180518	−	0.312666i
$83$	−6.20423	+	6.20423i	−0.681002	+	0.681002i	−0.960226	−	0.279224i	$-0.909923\pi$
$83$	−6.20423	+	6.20423i	−0.681002	+	0.681002i	0.279224	+	0.960226i	$0.409923\pi$
$84$	−7.20257	+	1.69026i	−0.785865	+	0.184422i
$85$	−2.76514	+	2.76514i	−0.299921	+	0.299921i
$86$	−0.510949	−	1.90689i	−0.0550971	−	0.205625i
$87$	−0.0661501	+	0.0381918i	−0.00709203	+	0.00409459i
$88$	−3.84673	+	2.22091i	−0.410063	+	0.236750i
$89$	8.92433	−	2.39127i	0.945977	−	0.253474i	0.247323	−	0.968933i	$-0.420449\pi$
$89$	8.92433	−	2.39127i	0.945977	−	0.253474i	0.698654	+	0.715459i	$0.253783\pi$
$90$	1.43151			0.150894
$91$	2.97734	−	9.06286i	0.312110	−	0.950046i
$92$	−14.7229			−1.53496
$93$	−7.61556	+	2.04058i	−0.789697	+	0.211599i
$94$	6.41600	−	3.70428i	0.661760	−	0.382067i
$95$	−0.998900	+	0.576715i	−0.102485	+	0.0591697i
$96$	1.90790	+	7.12039i	0.194724	+	0.726721i
$97$	−6.89422	+	6.89422i	−0.700002	+	0.700002i	−0.964411	−	0.264409i	$-0.914823\pi$
$97$	−6.89422	+	6.89422i	−0.700002	+	0.700002i	0.264409	+	0.964411i	$0.414823\pi$
$98$	3.03374	+	15.0271i	0.306454	+	1.51797i
$99$	−1.80108	+	1.80108i	−0.181015	+	0.181015i
$100$	6.39332	−	11.0736i	0.639332	−	1.10736i
$101$	3.07469	+	5.32552i	0.305943	+	0.529909i	0.977471	−	0.211070i	$-0.0676949\pi$
$101$	3.07469	+	5.32552i	0.305943	+	0.529909i	−0.671528	+	0.740979i	$0.734362\pi$
$102$	12.6557	+	3.39108i	1.25310	+	0.335767i
$103$	8.10374	−	14.0361i	0.798485	−	1.38302i	−0.122118	−	0.992516i	$-0.538969\pi$
$103$	8.10374	−	14.0361i	0.798485	−	1.38302i	0.920603	−	0.390501i	$-0.127698\pi$
$104$	6.03199	+	1.77454i	0.591485	+	0.174008i
$105$	0.0541144	−	1.72853i	0.00528103	−	0.168688i
$106$	2.15585	+	2.15585i	0.209395	+	0.209395i
$107$	−8.76076	+	15.1741i	−0.846935	+	1.46693i	0.0369960	+	0.999315i	$0.488221\pi$
$107$	−8.76076	+	15.1741i	−0.846935	+	1.46693i	−0.883931	+	0.467618i	$0.845112\pi$
$108$	−1.39814	−	2.42164i	−0.134536	−	0.233023i
$109$	3.85998	−	14.4056i	0.369719	−	1.37981i	−0.491190	−	0.871052i	$-0.663438\pi$
$109$	3.85998	−	14.4056i	0.369719	−	1.37981i	0.860909	−	0.508758i	$-0.169895\pi$
$110$	−0.943707	−	3.52196i	−0.0899790	−	0.335806i
$111$	−7.82363	−	7.82363i	−0.742586	−	0.742586i
$112$	4.56790	−	1.07197i	0.431626	−	0.101291i
$113$	−0.944250			−0.0888276			−0.0444138	−	0.999013i	$-0.514142\pi$
$113$	−0.944250			−0.0888276			−0.0444138	+	0.999013i	$0.514142\pi$
$114$	3.34682	+	1.93229i	0.313458	+	0.180975i
$115$	0.890739	−	3.32428i	0.0830618	−	0.309991i
$116$	−0.184974	+	0.106795i	−0.0171744	+	0.00991562i
$117$	3.60449	+	0.0876680i	0.333235	+	0.00810491i
$118$			11.5613i			1.06431i
$119$	4.57312	−	15.1535i	0.419217	−	1.38912i
$120$	1.13987			0.104055
$121$	−3.90770	−	2.25611i	−0.355246	−	0.205101i
$122$	6.46976	+	1.73357i	0.585744	+	0.156950i
$123$	0.386368	−	1.44194i	0.0348376	−	0.130016i
$124$	−21.2952	+	5.70602i	−1.91236	+	0.512416i
$125$	4.42449	+	4.42449i	0.395738	+	0.395738i
$126$	−5.10621	+	2.73871i	−0.454897	+	0.243984i
$127$			15.9116i			1.41192i	0.708250	+	0.705962i	$0.249485\pi$
$127$			15.9116i			1.41192i	−0.708250	+	0.705962i	$0.750515\pi$
$128$	3.32459	+	12.4075i	0.293855	+	1.09668i
$129$	−0.450713	−	0.780657i	−0.0396830	−	0.0687331i
$130$	−2.68861	+	4.40581i	−0.235806	+	0.386415i
$131$	−12.6166	−	7.28421i	−1.10232	−	0.636424i	−0.165490	−	0.986212i	$-0.552920\pi$
$131$	−12.6166	−	7.28421i	−1.10232	−	0.636424i	−0.936829	+	0.349787i	$0.886254\pi$
$132$	−5.03631	+	5.03631i	−0.438354	+	0.438354i
$133$	2.45974	−	3.96822i	0.213287	−	0.344088i
$134$		−	7.95933i		−	0.687581i
$135$	0.631372	−	0.169176i	0.0543398	−	0.0145603i
$136$	10.0774	+	2.70022i	0.864127	+	0.231542i
$137$	−1.31441	−	0.352195i	−0.112297	−	0.0300900i	0.202233	−	0.979338i	$-0.435180\pi$
$137$	−1.31441	−	0.352195i	−0.112297	−	0.0300900i	−0.314530	+	0.949247i	$0.601847\pi$
$138$	−11.1380	+	2.98443i	−0.948132	+	0.254051i
$139$			10.4193i			0.883752i	0.897076	+	0.441876i	$0.145687\pi$
$139$			10.4193i			0.883752i	−0.897076	+	0.441876i	$0.854313\pi$
$140$	0.151319	−	4.83345i	0.0127888	−	0.408501i
$141$	2.39203	−	2.39203i	0.201445	−	0.201445i
$142$	12.0225	+	6.94118i	1.00890	+	0.582491i
$143$	−2.16053	−	8.92598i	−0.180673	−	0.746428i
$144$	0.886704	+	1.53582i	0.0738920	+	0.127985i
$145$	−0.0129222	−	0.0482264i	−0.00107313	−	0.00400498i
$146$		−	33.9199i		−	2.80723i
$147$	3.11395	+	6.26924i	0.256834	+	0.517078i
$148$	−21.8770	−	21.8770i	−1.79828	−	1.79828i
$149$	−4.37174	+	1.17141i	−0.358147	+	0.0959653i	−0.433406	−	0.901199i	$-0.642688\pi$
$149$	−4.37174	+	1.17141i	−0.358147	+	0.0959653i	0.0752588	+	0.997164i	$0.476022\pi$
$150$	2.59194	−	9.67326i	0.211631	−	0.789819i
$151$	4.19719	+	1.12463i	0.341563	+	0.0915214i	0.425523	−	0.904948i	$-0.360090\pi$
$151$	4.19719	+	1.12463i	0.341563	+	0.0915214i	−0.0839602	+	0.996469i	$0.526757\pi$
$152$	2.66498	+	1.53863i	0.216158	+	0.124799i
$153$	5.98260			0.483665
$154$	10.1043	+	10.7574i	0.814230	+	0.866859i
$155$		−	5.15347i		−	0.413936i
$156$	10.0791	+	0.245144i	0.806975	+	0.0196272i
$157$	−4.21329	+	2.43255i	−0.336257	+	0.194138i	−0.658616	−	0.752479i	$-0.728858\pi$
$157$	−4.21329	+	2.43255i	−0.336257	+	0.194138i	0.322358	+	0.946618i	$0.395524\pi$
$158$	6.35089	−	23.7018i	0.505249	−	1.88562i
$159$	1.20563	+	0.696069i	0.0956124	+	0.0552019i
$160$	−4.81838			−0.380926
$161$	3.18263	+	13.5619i	0.250826	+	1.06883i
$162$	−1.54859	−	1.54859i	−0.121669	−	0.121669i
$163$	0.0772829	+	0.288424i	0.00605326	+	0.0225911i	0.968886	−	0.247506i	$-0.0796109\pi$
$163$	0.0772829	+	0.288424i	0.00605326	+	0.0225911i	−0.962833	+	0.270097i	$0.912944\pi$
$164$	1.08039	−	4.03206i	0.0843642	−	0.314851i
$165$	−0.832452	−	1.44185i	−0.0648063	−	0.112248i
$166$	−9.60781	+	16.6412i	−0.745711	+	1.29161i
$167$	7.94164	+	7.94164i	0.614543	+	0.614543i	0.944126	−	0.329584i	$-0.106908\pi$
$167$	7.94164	+	7.94164i	0.614543	+	0.614543i	−0.329584	+	0.944126i	$0.606908\pi$
$168$	−4.06593	+	2.18076i	−0.313693	+	0.168249i
$169$	−7.03964	+	10.9290i	−0.541511	+	0.840694i
$170$	−4.28207	+	7.41676i	−0.328420	+	0.568839i
$171$	1.70449	+	0.456716i	0.130345	+	0.0349259i
$172$	−1.26032	−	2.18293i	−0.0960981	−	0.166447i
$173$	4.93150	−	8.54161i	0.374935	−	0.649407i	−0.615382	−	0.788229i	$-0.710998\pi$
$173$	4.93150	−	8.54161i	0.374935	−	0.649407i	0.990317	+	0.138822i	$0.0443316\pi$
$174$	−0.118287	+	0.118287i	−0.00896730	+	0.00896730i
$175$	−11.5824	−	3.49542i	−0.875548	−	0.264229i
$176$	3.19405	−	3.19405i	0.240761	−	0.240761i
$177$	1.36632	+	5.09918i	0.102699	+	0.383278i
$178$	17.5232	−	10.1170i	1.31342	−	0.758305i
$179$	20.7836	−	11.9994i	1.55344	−	0.896880i	0.555584	−	0.831460i	$-0.312495\pi$
$179$	20.7836	−	11.9994i	1.55344	−	0.896880i	0.997858	−	0.0654199i	$-0.0208387\pi$
$180$	1.76549	−	0.473061i	0.131592	−	0.0352599i
$181$	−6.83963			−0.508386			−0.254193	−	0.967154i	$-0.581810\pi$
$181$	−6.83963			−0.508386			−0.254193	+	0.967154i	$0.581810\pi$
$182$	1.16126	−	20.8593i	0.0860781	−	1.54620i
$183$	3.05839			0.226082
$184$	−8.86889	+	2.37641i	−0.653824	+	0.175192i
$185$	6.26319	−	3.61605i	0.460479	−	0.265858i
$186$	−14.9534	+	8.63336i	−1.09644	+	0.633029i
$187$	−3.94398	−	14.7191i	−0.288412	−	1.07637i
$188$	6.68877	−	6.68877i	0.487829	−	0.487829i
$189$	−1.92845	+	1.81137i	−0.140274	+	0.131758i
$190$	−1.78619	+	1.78619i	−0.129584	+	0.129584i
$191$	1.45631	−	2.52239i	0.105375	−	0.182514i	−0.808517	−	0.588473i	$-0.799729\pi$
$191$	1.45631	−	2.52239i	0.105375	−	0.182514i	0.913891	+	0.405959i	$0.133063\pi$
$192$	6.29860	+	10.9095i	0.454562	+	0.787325i
$193$	−6.37298	−	1.70763i	−0.458737	−	0.122918i	0.0220476	−	0.999757i	$-0.492981\pi$
$193$	−6.37298	−	1.70763i	−0.458737	−	0.122918i	−0.480785	+	0.876839i	$0.659648\pi$
$194$	−10.6763	+	18.4919i	−0.766515	+	1.32764i
$195$	−0.665142	+	2.26094i	−0.0476318	+	0.161909i
$196$	8.70744	+	17.5305i	0.621960	+	1.25218i
$197$	16.8890	+	16.8890i	1.20329	+	1.20329i	0.973160	+	0.230132i	$0.0739156\pi$
$197$	16.8890	+	16.8890i	1.20329	+	1.20329i	0.230132	+	0.973160i	$0.426084\pi$
$198$	−2.78914	+	4.83093i	−0.198215	+	0.343319i
$199$	0.402906	+	0.697854i	0.0285612	+	0.0494695i	0.879953	−	0.475061i	$-0.157574\pi$
$199$	0.402906	+	0.697854i	0.0285612	+	0.0494695i	−0.851391	+	0.524531i	$0.824241\pi$
$200$	2.06389	−	7.70254i	0.145939	−	0.544652i
$201$	−0.940634	−	3.51049i	−0.0663472	−	0.247611i
$202$	9.52288	+	9.52288i	0.670028	+	0.670028i
$203$	0.138359	+	0.147302i	0.00971089	+	0.0103386i
$204$	16.7290			1.17126
$205$	0.845038	+	0.487883i	0.0590200	+	0.0340752i
$206$	9.18678	−	34.2855i	0.640073	−	2.38879i
$207$	−4.55977	+	2.63259i	−0.316926	+	0.182977i
$208$	−6.39223	−	0.155471i	−0.443221	−	0.0107800i
$209$		−	4.49467i		−	0.310903i
$210$	−0.865299	−	3.68724i	−0.0597113	−	0.254444i
$211$	17.5503			1.20821			0.604106	−	0.796904i	$-0.293531\pi$
$211$	17.5503			1.20821			0.604106	+	0.796904i	$0.293531\pi$
$212$	3.37126	+	1.94640i	0.231539	+	0.133679i
$213$	6.12287	+	1.64062i	0.419532	+	0.112413i
$214$	−9.93161	+	37.0653i	−0.678911	+	2.53373i
$215$	0.569135	−	0.152499i	0.0388147	−	0.0104004i
$216$	−1.23310	−	1.23310i	−0.0839018	−	0.0839018i
$217$	9.85944	+	18.3825i	0.669303	+	1.24789i
$218$		−	32.6619i		−	2.21214i
$219$	−4.00866	−	14.9605i	−0.270880	−	1.01094i
$220$	−2.32776	−	4.03180i	−0.156938	−	0.271824i
$221$	−11.2363	+	18.4129i	−0.755836	+	1.23859i
$222$	−20.9849	−	12.1156i	−1.40841	−	0.813147i
$223$	2.56243	−	2.56243i	0.171593	−	0.171593i	−0.616086	−	0.787679i	$-0.711283\pi$
$223$	2.56243	−	2.56243i	0.171593	−	0.171593i	0.787679	+	0.616086i	$0.211283\pi$
$224$	17.1873	−	9.21837i	1.14837	−	0.615928i
$225$		−	4.57275i		−	0.304850i
$226$	−1.99748	+	0.535223i	−0.132870	+	0.0356025i
$227$	−12.5397	−	3.36001i	−0.832290	−	0.223011i	−0.182577	−	0.983191i	$-0.558444\pi$
$227$	−12.5397	−	3.36001i	−0.832290	−	0.223011i	−0.649712	+	0.760180i	$0.725111\pi$
$228$	4.76621	+	1.27710i	0.315650	+	0.0845781i
$229$	−11.2266	+	3.00815i	−0.741872	+	0.198784i	−0.609910	−	0.792471i	$-0.708794\pi$
$229$	−11.2266	+	3.00815i	−0.741872	+	0.198784i	−0.131962	+	0.991255i	$0.542128\pi$
$230$		−	7.53713i		−	0.496984i
$231$	5.72787	+	3.55048i	0.376866	+	0.233605i
$232$	−0.0941884	+	0.0941884i	−0.00618377	+	0.00618377i
$233$	22.4370	+	12.9540i	1.46990	+	0.848645i	0.999430	−	0.0337727i	$-0.0107522\pi$
$233$	22.4370	+	12.9540i	1.46990	+	0.848645i	0.470467	+	0.882418i	$0.344086\pi$
$234$	7.67468	−	1.85765i	0.501709	−	0.121439i
$235$	1.10559	+	1.91493i	0.0721206	+	0.124917i
$236$	3.82060	+	14.2587i	0.248700	+	0.928162i
$237$		−	11.2043i		−	0.727800i
$238$	1.08471	−	34.6480i	0.0703113	−	2.24590i
$239$	−10.8915	−	10.8915i	−0.704511	−	0.704511i	0.260864	−	0.965375i	$-0.415992\pi$
$239$	−10.8915	−	10.8915i	−0.704511	−	0.704511i	−0.965375	+	0.260864i	$0.915992\pi$
$240$	−1.11968	+	0.300017i	−0.0722751	+	0.0193660i
$241$	−3.02126	+	11.2755i	−0.194616	+	0.726318i	0.797749	+	0.602989i	$0.206024\pi$
$241$	−3.02126	+	11.2755i	−0.194616	+	0.726318i	−0.992366	+	0.123329i	$0.960643\pi$
$242$	−9.54523	−	2.55764i	−0.613591	−	0.164411i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	8.55208			0.547491
$245$	−4.48502	+	0.905456i	−0.286538	+	0.0578474i
$246$		−	3.26931i		−	0.208444i
$247$	−4.60696	+	4.38818i	−0.293134	+	0.279213i
$248$	−11.9070	+	6.87450i	−0.756094	+	0.436531i
$249$	−2.27090	+	8.47513i	−0.143913	+	0.537090i
$250$	11.8675	+	6.85173i	0.750569	+	0.433341i
$251$	3.55707			0.224520			0.112260	−	0.993679i	$-0.464191\pi$
$251$	3.55707			0.224520			0.112260	+	0.993679i	$0.464191\pi$
$252$	−5.39248	+	5.06509i	−0.339694	+	0.319071i
$253$	9.48300	+	9.48300i	0.596191	+	0.596191i
$254$	9.01906	+	33.6596i	0.565906	+	2.11199i
$255$	−1.01211	+	3.77725i	−0.0633808	+	0.236540i
$256$	1.46858	+	2.54365i	0.0917861	+	0.158978i
$257$	−7.55184	+	13.0802i	−0.471071	+	0.815918i	−0.999452	−	0.0330886i	$-0.989466\pi$
$257$	−7.55184	+	13.0802i	−0.471071	+	0.815918i	0.528382	+	0.849007i	$0.322799\pi$
$258$	−1.39594	−	1.39594i	−0.0869074	−	0.0869074i
$259$	−15.4228	+	24.8811i	−0.958325	+	1.54603i
$260$	−1.85992	+	6.32220i	−0.115347	+	0.392086i
$261$	−0.0381918	+	0.0661501i	−0.00236401	+	0.00409459i
$262$	−30.8182	−	8.25772i	−1.90396	−	0.510164i
$263$	−11.0113	−	19.0721i	−0.678984	−	1.17604i	−0.975287	−	0.220941i	$-0.929087\pi$
$263$	−11.0113	−	19.0721i	−0.678984	−	1.17604i	0.296303	−	0.955094i	$-0.404246\pi$
$264$	−2.22091	+	3.84673i	−0.136688	+	0.236750i
$265$	−0.643441	+	0.643441i	−0.0395263	+	0.0395263i
$266$	2.95409	−	9.78866i	0.181127	−	0.600181i
$267$	6.53306	−	6.53306i	0.399817	−	0.399817i
$268$	−2.63027	−	9.81630i	−0.160669	−	0.599626i
$269$	−26.0922	+	15.0643i	−1.59087	+	0.918488i	−0.597709	+	0.801713i	$0.703922\pi$
$269$	−26.0922	+	15.0643i	−1.59087	+	0.918488i	−0.993158	+	0.116775i	$0.962744\pi$
$270$	1.23972	−	0.715753i	0.0754470	−	0.0435593i
$271$	−25.9129	+	6.94335i	−1.57410	+	0.421779i	−0.937093	−	0.349080i	$-0.886494\pi$
$271$	−25.9129	+	6.94335i	−1.57410	+	0.421779i	−0.637007	+	0.770858i	$0.719828\pi$
$272$	−10.6096			−0.643302
$273$	−1.95298	−	9.33734i	−0.118200	−	0.565121i
$274$	−2.98015			−0.180038
$275$	−11.2504	+	3.01454i	−0.678426	+	0.181784i
$276$	−12.7504	+	7.36143i	−0.767482	+	0.443106i
$277$	−2.12102	+	1.22457i	−0.127440	+	0.0735775i	−0.562365	−	0.826889i	$-0.690108\pi$
$277$	−2.12102	+	1.22457i	−0.127440	+	0.0735775i	0.434925	+	0.900467i	$0.356775\pi$
$278$	5.90590	+	22.0411i	0.354212	+	1.32194i
$279$	−5.57498	+	5.57498i	−0.333765	+	0.333765i
$280$	−0.689013	−	2.93604i	−0.0411764	−	0.175462i
$281$	−20.1404	+	20.1404i	−1.20147	+	1.20147i	−0.227754	+	0.973719i	$0.573138\pi$
$281$	−20.1404	+	20.1404i	−1.20147	+	1.20147i	−0.973719	+	0.227754i	$0.926862\pi$
$282$	3.70428	−	6.41600i	0.220587	−	0.382067i
$283$	3.04663	+	5.27692i	0.181103	+	0.313680i	0.942257	−	0.334892i	$-0.108700\pi$
$283$	3.04663	+	5.27692i	0.181103	+	0.313680i	−0.761153	+	0.648572i	$0.775366\pi$
$284$	17.1212	+	4.58761i	1.01596	+	0.272225i
$285$	−0.576715	+	0.998900i	−0.0341617	+	0.0591697i
$286$	−9.62988	−	17.6575i	−0.569427	−	1.04411i
$287$	−3.94767	−	0.123588i	−0.233024	−	0.00729516i
$288$	5.21248	+	5.21248i	0.307149	+	0.307149i
$289$	−9.39577	+	16.2739i	−0.552692	+	0.957291i
$290$	−0.0546717	−	0.0946942i	−0.00321043	−	0.00556064i
$291$	−2.52346	+	9.41767i	−0.147928	+	0.552074i
$292$	−11.2093	−	41.8337i	−0.655975	−	2.44813i
$293$	−6.26592	−	6.26592i	−0.366059	−	0.366059i	0.499979	−	0.866038i	$-0.333341\pi$
$293$	−6.26592	−	6.26592i	−0.366059	−	0.366059i	−0.866038	+	0.499979i	$0.833341\pi$
$294$	10.1408	+	11.4970i	0.591426	+	0.670518i
$295$	−3.45063			−0.200903
$296$	−16.7096	−	9.64732i	−0.971228	−	0.560739i
$297$	−0.659241	+	2.46032i	−0.0382530	+	0.142762i
$298$	−8.58407	+	4.95602i	−0.497262	+	0.287094i
$299$	0.461587	−	18.9782i	0.0266943	−	1.09754i
$300$		−	12.7866i		−	0.738237i
$301$	−1.73836	+	1.63282i	−0.100197	+	0.0941140i
$302$	9.51627			0.547600
$303$	5.32552	+	3.07469i	0.305943	+	0.176636i
$304$	−3.02275	−	0.809944i	−0.173367	−	0.0464535i
$305$	−0.517404	+	1.93098i	−0.0296265	+	0.110568i
$306$	12.6557	−	3.39108i	0.723478	−	0.193855i
$307$	20.3624	+	20.3624i	1.16214	+	1.16214i	0.984006	+	0.178135i	$0.0570064\pi$
$307$	20.3624	+	20.3624i	1.16214	+	1.16214i	0.178135	+	0.984006i	$0.442994\pi$
$308$	16.0167	+	9.92811i	0.912635	+	0.565707i
$309$		−	16.2075i		−	0.922011i
$310$	−2.92111	−	10.9017i	−0.165908	−	0.619176i
$311$	1.47429	+	2.55354i	0.0835991	+	0.144798i	0.904793	−	0.425851i	$-0.140025\pi$
$311$	1.47429	+	2.55354i	0.0835991	+	0.144798i	−0.821194	+	0.570649i	$0.806692\pi$
$312$	6.11113	−	1.47920i	0.345974	−	0.0837430i
$313$	10.7571	+	6.21061i	0.608027	+	0.351044i	0.772193	−	0.635388i	$-0.219160\pi$
$313$	10.7571	+	6.21061i	0.608027	+	0.351044i	−0.164166	+	0.986433i	$0.552493\pi$
$314$	−7.53404	+	7.53404i	−0.425170	+	0.425170i
$315$	−0.817402	−	1.52401i	−0.0460554	−	0.0858683i
$316$		−	31.3304i		−	1.76247i
$317$	−14.7489	+	3.95195i	−0.828379	+	0.221964i	−0.648007	−	0.761635i	$-0.724397\pi$
$317$	−14.7489	+	3.95195i	−0.828379	+	0.221964i	−0.180373	+	0.983598i	$0.557730\pi$
$318$	2.94495	+	0.789097i	0.165145	+	0.0442504i
$319$	0.187928	+	0.0503551i	0.0105219	+	0.00281935i
$320$	−7.95352	+	2.13114i	−0.444615	+	0.119134i
$321$			17.5215i			0.977956i
$322$	14.4198	+	26.8851i	0.803583	+	1.49825i
$323$	−7.46492	+	7.46492i	−0.415359	+	0.415359i
$324$	−2.42164	−	1.39814i	−0.134536	−	0.0776742i
$325$	14.0737	+	8.58838i	0.780671	+	0.476398i
$326$	0.326971	+	0.566330i	0.0181092	+	0.0313661i
$327$	−3.85998	−	14.4056i	−0.213457	−	0.796634i
$328$		−	2.60326i		−	0.143741i
$329$	−7.60724	−	4.71543i	−0.419401	−	0.259970i
$330$	−2.57826	−	2.57826i	−0.141928	−	0.141928i
$331$	15.0781	−	4.04016i	0.828766	−	0.222067i	0.180591	−	0.983558i	$-0.442199\pi$
$331$	15.0781	−	4.04016i	0.828766	−	0.222067i	0.648175	+	0.761491i	$0.275532\pi$
$332$	−6.35006	+	23.6988i	−0.348505	+	1.30064i
$333$	−10.6873	−	2.86365i	−0.585659	−	0.156927i
$334$	21.3014	+	12.2984i	1.16556	+	0.672936i
$335$	2.37556			0.129791
$336$	3.41994	−	3.21230i	0.186573	−	0.175246i
$337$			1.81266i			0.0987418i	0.998781	+	0.0493709i	$0.0157216\pi$
$337$			1.81266i			0.0987418i	−0.998781	+	0.0493709i	$0.984278\pi$
$338$	−8.69693	+	27.1097i	−0.473051	+	1.47457i
$339$	−0.817745	+	0.472125i	−0.0444138	+	0.0256423i
$340$	−2.83013	+	10.5622i	−0.153486	+	0.572816i
$341$	17.3915	+	10.0410i	0.941802	+	0.543749i
$342$	3.86458			0.208972
$343$	14.2659	−	11.8104i	0.770284	−	0.637700i
$344$	−1.11155	−	1.11155i	−0.0599306	−	0.0599306i
$345$	−0.890739	−	3.32428i	−0.0479558	−	0.178973i
$346$	5.59059	−	20.8644i	0.300552	−	1.12167i
$347$	18.4617	+	31.9767i	0.991078	+	1.71660i	0.610968	+	0.791656i	$0.290781\pi$
$347$	18.4617	+	31.9767i	0.991078	+	1.71660i	0.380110	+	0.924941i	$0.375886\pi$
$348$	−0.106795	+	0.184974i	−0.00572479	+	0.00991562i
$349$	−19.8750	−	19.8750i	−1.06388	−	1.06388i	−0.997815	−	0.0660671i	$-0.978955\pi$
$349$	−19.8750	−	19.8750i	−1.06388	−	1.06388i	−0.0660671	−	0.997815i	$-0.521045\pi$
$350$	−26.4829	−	0.829088i	−1.41557	−	0.0443166i
$351$	3.16541	−	1.72632i	0.168957	−	0.0921441i
$352$	9.38810	−	16.2607i	0.500387	−	0.866696i
$353$	25.0131	+	6.70223i	1.33131	+	0.356724i	0.853204	−	0.521578i	$-0.174656\pi$
$353$	25.0131	+	6.70223i	1.33131	+	0.356724i	0.478107	+	0.878301i	$0.341323\pi$
$354$	5.78067	+	10.0124i	0.307239	+	0.532154i
$355$	−2.07168	+	3.58826i	−0.109953	+	0.190445i
$356$	18.2682	−	18.2682i	0.968214	−	0.968214i
$357$	−3.61629	−	15.4098i	−0.191394	−	0.815575i
$358$	37.1645	−	37.1645i	1.96420	−	1.96420i
$359$	−8.21137	−	30.6453i	−0.433380	−	1.61739i	−0.744914	−	0.667160i	$-0.767510\pi$
$359$	−8.21137	−	30.6453i	−0.433380	−	1.61739i	0.311535	−	0.950235i	$-0.399157\pi$
$360$	0.987154	−	0.569934i	0.0520276	−	0.0300381i
$361$	13.7578	−	7.94307i	0.724095	−	0.418056i
$362$	−14.4687	+	3.87686i	−0.760456	+	0.203763i
$363$	−4.51222			−0.236830
$364$	−5.46107	−	26.1097i	−0.286238	−	1.36852i
$365$	10.1238			0.529905
$366$	6.46976	−	1.73357i	0.338180	−	0.0906150i
$367$	−22.8752	+	13.2070i	−1.19408	+	0.689400i	−0.959229	−	0.282632i	$-0.908793\pi$
$367$	−22.8752	+	13.2070i	−1.19408	+	0.689400i	−0.234848	+	0.972032i	$0.575459\pi$
$368$	8.08634	−	4.66865i	0.421530	−	0.243370i
$369$	−0.386368	−	1.44194i	−0.0201135	−	0.0750646i
$370$	11.1996	−	11.1996i	0.582238	−	0.582238i
$371$	1.06415	−	3.52617i	0.0552482	−	0.183070i
$372$	−15.5891	+	15.5891i	−0.808260	+	0.808260i
$373$	1.37665	−	2.38442i	0.0712801	−	0.123461i	−0.828182	−	0.560459i	$-0.810625\pi$
$373$	1.37665	−	2.38442i	0.0712801	−	0.123461i	0.899463	+	0.436998i	$0.143958\pi$
$374$	−16.6863	−	28.9015i	−0.862828	−	1.49446i
$375$	6.04396	+	1.61948i	0.312109	+	0.0836293i
$376$	2.94961	−	5.10888i	0.152115	−	0.263470i
$377$	−0.131862	−	0.241785i	−0.00679126	−	0.0124526i
$378$	−3.05275	+	4.92490i	−0.157017	+	0.253309i
$379$	5.33831	+	5.33831i	0.274211	+	0.274211i	0.830793	−	0.556582i	$-0.187887\pi$
$379$	5.33831	+	5.33831i	0.274211	+	0.274211i	−0.556582	+	0.830793i	$0.687887\pi$
$380$	−1.61265	+	2.79319i	−0.0827273	+	0.143288i
$381$	7.95578	+	13.7798i	0.407587	+	0.705962i
$382$	1.65094	−	6.16138i	0.0844693	−	0.315244i
$383$	−6.84734	−	25.5546i	−0.349883	−	1.30578i	−0.886803	−	0.462147i	$-0.847079\pi$
$383$	−6.84734	−	25.5546i	−0.349883	−	1.30578i	0.536921	−	0.843633i	$-0.319587\pi$
$384$	9.08295	+	9.08295i	0.463512	+	0.463512i
$385$	−3.21069	+	3.01576i	−0.163632	+	0.153697i
$386$	−14.4494			−0.735456
$387$	−0.780657	−	0.450713i	−0.0396830	−	0.0229110i
$388$	−7.05627	+	26.3344i	−0.358228	+	1.33693i
$389$	5.09402	−	2.94103i	0.258277	−	0.149116i	−0.365271	−	0.930901i	$-0.619024\pi$
$389$	5.09402	−	2.94103i	0.258277	−	0.149116i	0.623548	+	0.781785i	$0.285690\pi$
$390$	−0.125497	+	5.15984i	−0.00635480	+	0.261279i
$391$		−	31.4994i		−	1.59300i
$392$	8.07486	+	9.15472i	0.407842	+	0.462383i
$393$	−14.5684			−0.734879
$394$	45.3003	+	26.1542i	2.28220	+	1.31763i
$395$	7.07410	+	1.89550i	0.355937	+	0.0953730i
$396$	−1.84342	+	6.87972i	−0.0926352	+	0.345719i
$397$	8.20055	−	2.19733i	0.411574	−	0.110281i	−0.0470903	−	0.998891i	$-0.514995\pi$
$397$	8.20055	−	2.19733i	0.411574	−	0.110281i	0.458664	+	0.888610i	$0.348328\pi$
$398$	1.24787	+	1.24787i	0.0625502	+	0.0625502i
$399$	0.146090	−	4.66645i	0.00731366	−	0.233614i
$400$			8.10935i			0.405468i
$401$	−10.1379	−	37.8352i	−0.506263	−	1.88940i	−0.454518	−	0.890737i	$-0.650189\pi$
$401$	−10.1379	−	37.8352i	−0.506263	−	1.88940i	−0.0517442	−	0.998660i	$-0.516478\pi$
$402$	−3.97966	−	6.89298i	−0.198488	−	0.343791i
$403$	−6.68761	−	27.6291i	−0.333134	−	1.37630i
$404$	14.8916	+	8.59767i	0.740885	+	0.427750i
$405$	0.462196	−	0.462196i	0.0229667	−	0.0229667i
$406$	0.376181	+	0.233180i	0.0186695	+	0.0115725i
$407$			28.1820i			1.39693i
$408$	10.0774	−	2.70022i	0.498904	−	0.133681i
$409$	1.85098	+	0.495968i	0.0915249	+	0.0245240i	0.304291	−	0.952579i	$-0.401581\pi$
$409$	1.85098	+	0.495968i	0.0915249	+	0.0245240i	−0.212766	+	0.977103i	$0.568247\pi$
$410$	2.06415	+	0.553088i	0.101941	+	0.0273150i
$411$	−1.31441	+	0.352195i	−0.0648350	+	0.0173725i
$412$		−	45.3205i		−	2.23278i
$413$	12.3084	−	6.60163i	0.605659	−	0.324845i
$414$	−8.15360	+	8.15360i	−0.400728	+	0.400728i
$415$	−4.96678	−	2.86757i	−0.243809	−	0.140763i
$416$	−25.8326	+	6.25277i	−1.26655	+	0.306567i
$417$	5.20964	+	9.02337i	0.255117	+	0.441876i
$418$	−2.54769	−	9.50809i	−0.124611	−	0.465056i
$419$			6.41207i			0.313250i	0.987658	+	0.156625i	$0.0500614\pi$
$419$			6.41207i			0.313250i	−0.987658	+	0.156625i	$0.949939\pi$
$420$	−2.28568	−	4.26155i	−0.111530	−	0.207942i
$421$	−5.78368	−	5.78368i	−0.281879	−	0.281879i	0.551979	−	0.833858i	$-0.313873\pi$
$421$	−5.78368	−	5.78368i	−0.281879	−	0.281879i	−0.833858	+	0.551979i	$0.813873\pi$
$422$	37.1261	−	9.94792i	1.80727	−	0.484257i
$423$	0.875544	−	3.26758i	0.0425704	−	0.158875i
$424$	2.34498	+	0.628335i	0.113882	+	0.0305147i
$425$	23.6918	+	13.6785i	1.14922	+	0.663503i
$426$	13.8824			0.672603
$427$	−1.84870	−	7.87772i	−0.0894647	−	0.381229i
$428$			48.9949i			2.36826i
$429$	−6.33407	−	6.64986i	−0.305812	−	0.321058i
$430$	1.11752	−	0.645198i	0.0538914	−	0.0311142i
$431$	−2.51954	+	9.40305i	−0.121362	+	0.452929i	−0.999684	−	0.0251405i	$-0.991997\pi$
$431$	−2.51954	+	9.40305i	−0.121362	+	0.452929i	0.878322	+	0.478070i	$0.158663\pi$
$432$	1.53582	+	0.886704i	0.0738920	+	0.0426616i
$433$	13.1342			0.631190			0.315595	−	0.948894i	$-0.397796\pi$
$433$	13.1342			0.631190			0.315595	+	0.948894i	$0.397796\pi$
$434$	31.2765	+	33.2981i	1.50132	+	1.59836i
$435$	−0.0353042	−	0.0353042i	−0.00169271	−	0.00169271i
$436$	−10.7936	−	40.2821i	−0.516918	−	1.92916i
$437$	2.40469	−	8.97442i	0.115032	−	0.429305i
$438$	−16.9600	−	29.3755i	−0.810378	−	1.40362i
$439$	3.44914	−	5.97409i	0.164619	−	0.285128i	−0.771901	−	0.635743i	$-0.780694\pi$
$439$	3.44914	−	5.97409i	0.164619	−	0.285128i	0.936520	+	0.350615i	$0.114027\pi$
$440$	−2.05299	−	2.05299i	−0.0978726	−	0.0978726i
$441$	5.83138	+	3.87235i	0.277685	+	0.184397i
$442$	−13.3326	+	45.3200i	−0.634167	+	2.15565i
$443$	−11.6463	+	20.1720i	−0.553332	+	0.958400i	0.444699	+	0.895680i	$0.353311\pi$
$443$	−11.6463	+	20.1720i	−0.553332	+	0.958400i	−0.998031	+	0.0627195i	$0.980023\pi$
$444$	−29.8845	−	8.00754i	−1.41826	−	0.380021i
$445$	3.01956	+	5.23003i	0.143141	+	0.247927i
$446$	3.96816	−	6.87306i	0.187898	−	0.325449i
$447$	−3.20034	+	3.20034i	−0.151371	+	0.151371i
$448$	24.2931	−	22.8182i	1.14774	−	1.07806i
$449$	−10.6650	+	10.6650i	−0.503312	+	0.503312i	−0.912465	−	0.409154i	$-0.865824\pi$
$449$	−10.6650	+	10.6650i	−0.503312	+	0.503312i	0.409154	+	0.912465i	$0.365824\pi$
$450$	−2.59194	−	9.67326i	−0.122185	−	0.456002i
$451$	−3.29293	+	1.90118i	−0.155058	+	0.0895229i
$452$	−2.28664	+	1.32019i	−0.107554	+	0.0620965i
$453$	4.19719	−	1.12463i	0.197201	−	0.0528399i
$454$	−28.4312			−1.33434
$455$	6.22573	+	0.346592i	0.291867	+	0.0162485i
$456$	3.07725			0.144105
$457$	12.0014	−	3.21576i	0.561401	−	0.150427i	0.0330510	−	0.999454i	$-0.489478\pi$
$457$	12.0014	−	3.21576i	0.561401	−	0.150427i	0.528350	+	0.849027i	$0.322811\pi$
$458$	−22.0437	+	12.7270i	−1.03004	+	0.594692i
$459$	5.18109	−	2.99130i	0.241832	−	0.139622i
$460$	−2.49075	−	9.29559i	−0.116132	−	0.433409i
$461$	16.0625	−	16.0625i	0.748103	−	0.748103i	−0.226019	−	0.974123i	$-0.572571\pi$
$461$	16.0625	−	16.0625i	0.748103	−	0.748103i	0.974123	+	0.226019i	$0.0725713\pi$
$462$	14.1293	+	4.26405i	0.657356	+	0.198382i
$463$	−4.57548	+	4.57548i	−0.212641	+	0.212641i	−0.805388	−	0.592748i	$-0.798043\pi$
$463$	−4.57548	+	4.57548i	−0.212641	+	0.212641i	0.592748	+	0.805388i	$0.298043\pi$
$464$	0.0677296	−	0.117311i	0.00314427	−	0.00544603i
$465$	−2.57673	−	4.46303i	−0.119493	−	0.206968i
$466$	54.8062	+	14.6853i	2.53885	+	0.680282i
$467$	15.0139	−	26.0049i	0.694762	−	1.20336i	−0.275499	−	0.961301i	$-0.588843\pi$
$467$	15.0139	−	26.0049i	0.694762	−	1.20336i	0.970261	−	0.242062i	$-0.0778236\pi$
$468$	8.85135	−	4.82726i	0.409154	−	0.223140i
$469$	−8.47366	+	4.54484i	−0.391277	+	0.209861i
$470$	3.42421	+	3.42421i	0.157947	+	0.157947i
$471$	−2.43255	+	4.21329i	−0.112086	+	0.194138i
$472$	4.60299	+	7.97260i	0.211870	+	0.366969i
$473$	−0.594257	+	2.21780i	−0.0273239	+	0.101974i
$474$	−6.35089	−	23.7018i	−0.291706	−	1.08866i
$475$	5.70574	+	5.70574i	0.261798	+	0.261798i
$476$	−10.1121	−	43.0901i	−0.463489	−	1.97503i
$477$	1.39214			0.0637416
$478$	−29.2135	−	16.8665i	−1.33620	−	0.771453i
$479$	9.77517	−	36.4814i	0.446639	−	1.66688i	−0.264933	−	0.964267i	$-0.585350\pi$
$479$	9.77517	−	36.4814i	0.446639	−	1.66688i	0.711572	−	0.702613i	$-0.247983\pi$
$480$	−4.17284	+	2.40919i	−0.190463	+	0.109964i
$481$	28.8861	−	27.5143i	1.31709	−	1.25454i
$482$			25.5649i			1.16445i
$483$	9.53719	+	10.1536i	0.433957	+	0.462007i
$484$	−12.6174			−0.573518
$485$	−5.51915	−	3.18648i	−0.250612	−	0.144691i
$486$	−2.11542	−	0.566824i	−0.0959572	−	0.0257117i
$487$	−5.28383	+	19.7195i	−0.239433	+	0.893577i	0.736667	+	0.676256i	$0.236399\pi$
$487$	−5.28383	+	19.7195i	−0.239433	+	0.893577i	−0.976100	+	0.217321i	$0.930268\pi$
$488$	5.15168	−	1.38039i	0.233206	−	0.0624873i
$489$	0.211141	+	0.211141i	0.00954812	+	0.00954812i
$490$	−8.97445	+	4.45763i	−0.405424	+	0.201375i
$491$		−	34.5398i		−	1.55876i	−0.626552	−	0.779380i	$-0.715534\pi$
$491$		−	34.5398i		−	1.55876i	0.626552	−	0.779380i	$-0.284466\pi$
$492$	−1.08039	−	4.03206i	−0.0487077	−	0.181780i
$493$	−0.228486	−	0.395750i	−0.0102905	−	0.0178237i
$494$	−7.25831	+	11.8942i	−0.326567	+	0.535144i
$495$	−1.44185	−	0.832452i	−0.0648063	−	0.0374159i
$496$	9.88671	−	9.88671i	0.443927	−	0.443927i
$497$	0.524787	−	16.7628i	0.0235399	−	0.751916i
$498$			19.2156i			0.861073i
$499$	1.61236	−	0.432031i	0.0721793	−	0.0193404i	−0.222549	−	0.974922i	$-0.571438\pi$
$499$	1.61236	−	0.432031i	0.0721793	−	0.0193404i	0.294728	+	0.955581i	$0.404771\pi$
$500$	16.9006	+	4.52849i	0.755816	+	0.202520i
$501$	10.8485	+	2.90684i	0.484675	+	0.129868i
$502$	7.52469	−	2.01623i	0.335843	−	0.0899889i
$503$			28.9670i			1.29157i	0.763518	+	0.645787i	$0.223470\pi$
$503$			28.9670i			1.29157i	−0.763518	+	0.645787i	$0.776530\pi$
$504$	−2.43082	+	3.92156i	−0.108277	+	0.174680i
$505$	−2.84222	+	2.84222i	−0.126477	+	0.126477i
$506$	25.4357	+	14.6853i	1.13075	+	0.652841i
$507$	−0.631996	+	12.9846i	−0.0280679	+	0.576668i
$508$	22.2465	+	38.5321i	0.987030	+	1.70959i
$509$	6.11751	+	22.8308i	0.271154	+	1.01196i	0.958375	+	0.285512i	$0.0921635\pi$
$509$	6.11751	+	22.8308i	0.271154	+	1.01196i	−0.687221	+	0.726448i	$0.741170\pi$
$510$			8.56413i			0.379226i
$511$	−36.1118	+	19.3686i	−1.59749	+	0.856815i
$512$	−13.6174	−	13.6174i	−0.601812	−	0.601812i
$513$	1.70449	−	0.456716i	0.0752549	−	0.0201645i
$514$	−8.56112	+	31.9505i	−0.377615	+	1.40928i
$515$	10.2329	+	2.74191i	0.450917	+	0.120823i
$516$	−2.18293	−	1.26032i	−0.0960981	−	0.0554823i
$517$	−8.61648			−0.378952
$518$	−18.5224	+	61.3758i	−0.813829	+	2.69670i
$519$		−	9.86301i		−	0.432938i
$520$	−0.0999299	+	4.10864i	−0.00438222	+	0.180176i
$521$	−8.01013	+	4.62465i	−0.350930	+	0.202610i	−0.665095	−	0.746759i	$-0.731609\pi$
$521$	−8.01013	+	4.62465i	−0.350930	+	0.202610i	0.314165	+	0.949369i	$0.398276\pi$
$522$	−0.0432960	+	0.161583i	−0.00189501	+	0.00707229i
$523$	23.8793	+	13.7867i	1.04417	+	0.602852i	0.921011	−	0.389536i	$-0.127364\pi$
$523$	23.8793	+	13.7867i	1.04417	+	0.602852i	0.123158	+	0.992387i	$0.460698\pi$
$524$	−40.7372			−1.77961
$525$	−11.7784	+	2.76408i	−0.514050	+	0.120634i
$526$	−34.1039	−	34.1039i	−1.48700	−	1.48700i
$527$	−12.2080	−	45.5609i	−0.531789	−	1.98466i
$528$	1.16910	−	4.36315i	0.0508787	−	0.189882i
$529$	2.36103	+	4.08942i	0.102653	+	0.177801i
$530$	−0.996427	+	1.72586i	−0.0432820	+	0.0749667i
$531$	3.73286	+	3.73286i	0.161992	+	0.161992i
$532$	0.408508	−	13.0486i	0.0177111	−	0.565731i
$533$	5.16359	+	1.51907i	0.223660	+	0.0657982i
$534$	10.1170	−	17.5232i	0.437807	−	0.758305i
$535$	−11.0626	−	2.96421i	−0.478278	−	0.128154i
$536$	−3.16889	−	5.48868i	−0.136875	−	0.237075i
$537$	11.9994	−	20.7836i	0.517814	−	0.896880i
$538$	−46.6570	+	46.6570i	−2.01152	+	2.01152i
$539$	5.68293	−	16.8999i	0.244781	−	0.727929i
$540$	1.29243	−	1.29243i	0.0556172	−	0.0556172i
$541$	2.21236	+	8.25664i	0.0951167	+	0.354981i	0.997037	−	0.0769218i	$-0.0245092\pi$
$541$	2.21236	+	8.25664i	0.0951167	+	0.354981i	−0.901920	+	0.431902i	$0.857843\pi$
$542$	−50.8810	+	29.3762i	−2.18553	+	1.26181i
$543$	−5.92329	+	3.41981i	−0.254193	+	0.146758i
$544$	−42.5984	+	11.4142i	−1.82639	+	0.489381i
$545$	9.74833			0.417573
$546$	−9.42399	−	18.6453i	−0.403310	−	0.797947i
$547$	40.4129			1.72793			0.863965	−	0.503552i	$-0.167974\pi$
$547$	40.4129			1.72793			0.863965	+	0.503552i	$0.167974\pi$
$548$	−3.67544	+	0.984832i	−0.157007	+	0.0420699i
$549$	2.64864	−	1.52919i	0.113041	−	0.0652644i
$550$	−22.0906	+	12.7540i	−0.941947	+	0.543833i
$551$	−0.0348856	−	0.130195i	−0.00148617	−	0.00554648i
$552$	−6.49248	+	6.49248i	−0.276338	+	0.276338i
$553$	−28.8599	+	6.77266i	−1.22725	+	0.288003i
$554$	−3.79273	+	3.79273i	−0.161138	+	0.161138i
$555$	3.61605	−	6.26319i	0.153493	−	0.265858i
$556$	14.5676	+	25.2318i	0.617803	+	1.07007i
$557$	−17.3133	−	4.63910i	−0.733590	−	0.196565i	−0.127362	−	0.991856i	$-0.540651\pi$
$557$	−17.3133	−	4.63910i	−0.733590	−	0.196565i	−0.606227	+	0.795291i	$0.707318\pi$
$558$	−8.63336	+	14.9534i	−0.365479	+	0.633029i
$559$	2.85338	−	1.55615i	0.120685	−	0.0658181i
$560$	1.44959	+	2.70269i	0.0612563	+	0.114210i
$561$	−10.7751	−	10.7751i	−0.454927	−	0.454927i
$562$	−31.1892	+	54.0213i	−1.31564	+	2.27875i
$563$	3.28323	+	5.68672i	0.138372	+	0.239667i	0.926880	−	0.375357i	$-0.122480\pi$
$563$	3.28323	+	5.68672i	0.138372	+	0.239667i	−0.788509	+	0.615024i	$0.789146\pi$
$564$	2.44826	−	9.13703i	0.103090	−	0.384738i
$565$	−0.159744	−	0.596173i	−0.00672048	−	0.0250812i
$566$	9.43598	+	9.43598i	0.396624	+	0.396624i
$567$	−0.764403	+	2.53292i	−0.0321019	+	0.106373i
$568$	11.0541			0.463821
$569$	−24.6318	−	14.2212i	−1.03262	−	0.596182i	−0.114884	−	0.993379i	$-0.536650\pi$
$569$	−24.6318	−	14.2212i	−1.03262	−	0.596182i	−0.917733	+	0.397197i	$0.869983\pi$
$570$	−0.653792	+	2.43998i	−0.0273843	+	0.102200i
$571$	19.7578	−	11.4072i	0.826839	−	0.477376i	−0.0259302	−	0.999664i	$-0.508255\pi$
$571$	19.7578	−	11.4072i	0.826839	−	0.477376i	0.852769	+	0.522288i	$0.174921\pi$
$572$	−17.7118	−	18.5948i	−0.740566	−	0.777488i
$573$		−	2.91261i		−	0.121676i
$574$	−8.42101	+	1.97619i	−0.351486	+	0.0824847i
$575$	−24.0763			−1.00405
$576$	10.9095	+	6.29860i	0.454562	+	0.262442i
$577$	−41.0315	−	10.9943i	−1.70816	−	0.457701i	−0.733189	−	0.680025i	$-0.761969\pi$
$577$	−41.0315	−	10.9943i	−1.70816	−	0.457701i	−0.974973	+	0.222324i	$0.928636\pi$
$578$	−10.6515	+	39.7519i	−0.443044	+	1.65346i
$579$	−6.37298	+	1.70763i	−0.264852	+	0.0709669i
$580$	−0.0987200	−	0.0987200i	−0.00409913	−	0.00409913i
$581$	23.2027	+	0.726397i	0.962611	+	0.0301360i
$582$			21.3527i			0.885096i
$583$	−0.917754	−	3.42511i	−0.0380095	−	0.141853i
$584$	−13.5047	−	23.3909i	−0.558830	−	0.967922i
$585$	0.554440	+	2.29060i	0.0229233	+	0.0947047i
$586$	−16.8067	−	9.70336i	−0.694279	−	0.400842i
$587$	−9.03045	+	9.03045i	−0.372727	+	0.372727i	−0.868469	−	0.495743i	$-0.834896\pi$
$587$	−9.03045	+	9.03045i	−0.372727	+	0.372727i	0.495743	+	0.868469i	$0.334896\pi$
$588$	16.3061	+	10.8281i	0.672453	+	0.446545i
$589$		−	13.9126i		−	0.573258i
$590$	−7.29951	+	1.95590i	−0.300516	+	0.0805230i
$591$	23.0708	+	6.18180i	0.949006	+	0.254285i
$592$	18.9529	+	5.07842i	0.778960	+	0.208722i
$593$	−21.4748	+	5.75416i	−0.881865	+	0.236295i	−0.671212	−	0.741266i	$-0.734226\pi$
$593$	−21.4748	+	5.75416i	−0.881865	+	0.236295i	−0.210654	+	0.977561i	$0.567559\pi$
$594$			5.57827i			0.228879i
$595$	10.3411	+	0.323745i	0.423945	+	0.0132723i
$596$	−8.94902	+	8.94902i	−0.366566	+	0.366566i
$597$	0.697854	+	0.402906i	0.0285612	+	0.0164898i
$598$	−9.78087	−	40.4085i	−0.399970	−	1.65243i
$599$	−13.9125	−	24.0971i	−0.568448	−	0.984581i	−0.996720	−	0.0809310i	$-0.974211\pi$
$599$	−13.9125	−	24.0971i	−0.568448	−	0.984581i	0.428272	−	0.903650i	$-0.359123\pi$
$600$	−2.06389	−	7.70254i	−0.0842580	−	0.314455i
$601$		−	17.9740i		−	0.733174i	−0.930384	−	0.366587i	$-0.880526\pi$
$601$		−	17.9740i		−	0.733174i	0.930384	−	0.366587i	$-0.119474\pi$
$602$	−2.75183	+	4.43943i	−0.112156	+	0.180938i
$603$	−2.56986	−	2.56986i	−0.104653	−	0.104653i
$604$	11.7365	−	3.14478i	0.477551	−	0.127959i
$605$	0.763358	−	2.84889i	0.0310349	−	0.115824i
$606$	13.0085	+	3.48562i	0.528434	+	0.141593i
$607$	11.4792	+	6.62754i	0.465928	+	0.269004i	0.714534	−	0.699601i	$-0.246639\pi$
$607$	11.4792	+	6.62754i	0.465928	+	0.269004i	−0.248606	+	0.968605i	$0.579972\pi$
$608$	−13.0080			−0.527543
$609$	0.193473	+	0.0583878i	0.00783994	+	0.00236599i
$610$			4.37810i			0.177264i
$611$	8.41234	+	8.83175i	0.340327	+	0.357294i
$612$	14.4877	−	8.36449i	0.585631	−	0.338114i
$613$	2.08722	−	7.78962i	0.0843021	−	0.314620i	−0.910879	−	0.412673i	$-0.864595\pi$
$613$	2.08722	−	7.78962i	0.0843021	−	0.314620i	0.995181	+	0.0980538i	$0.0312617\pi$
$614$	54.6167	+	31.5330i	2.20415	+	1.27257i
$615$	0.975766			0.0393467
$616$	11.2508	+	3.39534i	0.453307	+	0.136802i
$617$	−12.9666	−	12.9666i	−0.522016	−	0.522016i	0.396163	−	0.918180i	$-0.370341\pi$
$617$	−12.9666	−	12.9666i	−0.522016	−	0.522016i	−0.918180	+	0.396163i	$0.870341\pi$
$618$	−9.18678	−	34.2855i	−0.369547	−	1.37917i
$619$	−8.01277	+	29.9041i	−0.322061	+	1.20195i	0.595173	+	0.803597i	$0.297083\pi$
$619$	−8.01277	+	29.9041i	−0.322061	+	1.20195i	−0.917234	+	0.398349i	$0.869583\pi$
$620$	−7.20525	−	12.4799i	−0.289370	−	0.501203i
$621$	−2.63259	+	4.55977i	−0.105642	+	0.182977i
$622$	4.56613	+	4.56613i	0.183085	+	0.183085i
$623$	−20.7767	−	12.8787i	−0.832402	−	0.515973i
$624$	−5.61357	+	3.06147i	−0.224722	+	0.122557i
$625$	9.38689	−	16.2586i	0.375476	−	0.650343i
$626$	26.2760	+	7.04064i	1.05020	+	0.281401i
$627$	−2.24733	−	3.89250i	−0.0897499	−	0.155451i
$628$	−6.80206	+	11.7815i	−0.271432	+	0.470133i
$629$	46.8057	−	46.8057i	1.86626	−	1.86626i
$630$	−2.59299	−	2.76059i	−0.103307	−	0.109985i
$631$	25.6189	−	25.6189i	1.01987	−	1.01987i	0.0200749	−	0.999798i	$-0.493610\pi$
$631$	25.6189	−	25.6189i	1.01987	−	1.01987i	0.999798	−	0.0200749i	$-0.00639046\pi$
$632$	−5.05703	−	18.8731i	−0.201158	−	0.750731i
$633$	15.1990	−	8.77514i	0.604106	−	0.348780i
$634$	−28.9599	+	16.7200i	−1.15015	+	0.664037i
$635$	−10.0461	+	2.69185i	−0.398668	+	0.106823i
$636$	3.89280			0.154359
$637$	−22.8704	+	10.6746i	−0.906157	+	0.422941i
$638$	0.426088			0.0168690
$639$	6.12287	−	1.64062i	0.242217	−	0.0649019i
$640$	−7.27133	+	4.19810i	−0.287425	+	0.165945i
$641$	−33.3576	+	19.2590i	−1.31755	+	0.760687i	−0.983334	−	0.181811i	$-0.941804\pi$
$641$	−33.3576	+	19.2590i	−1.31755	+	0.760687i	−0.334214	+	0.942497i	$0.608471\pi$
$642$	9.93161	+	37.0653i	0.391970	+	1.46285i
$643$	−19.0170	+	19.0170i	−0.749958	+	0.749958i	−0.974471	−	0.224513i	$-0.927921\pi$
$643$	−19.0170	+	19.0170i	−0.749958	+	0.749958i	0.224513	+	0.974471i	$0.427921\pi$
$644$	26.6686	+	28.3923i	1.05089	+	1.11881i
$645$	0.416635	−	0.416635i	0.0164050	−	0.0164050i
$646$	−11.5601	+	20.0227i	−0.454826	+	0.787782i
$647$	24.4519	+	42.3520i	0.961305	+	1.66503i	0.719231	+	0.694771i	$0.244494\pi$
$647$	24.4519	+	42.3520i	0.961305	+	1.66503i	0.242074	+	0.970258i	$0.422172\pi$
$648$	−1.68444	−	0.451346i	−0.0661712	−	0.0177305i
$649$	6.72318	−	11.6449i	0.263908	−	0.457102i
$650$	34.6399	+	10.1907i	1.35869	+	0.399710i
$651$	17.7298	+	10.9900i	0.694885	+	0.430732i
$652$	0.590407	+	0.590407i	0.0231221	+	0.0231221i
$653$	19.4880	−	33.7542i	0.762625	−	1.32090i	−0.178868	−	0.983873i	$-0.557244\pi$
$653$	19.4880	−	33.7542i	0.762625	−	1.32090i	0.941493	−	0.337032i	$-0.109423\pi$
$654$	−16.3309	−	28.2860i	−0.638590	−	1.10607i
$655$	2.46462	−	9.19808i	0.0963006	−	0.359399i
$656$	0.685188	+	2.55715i	0.0267521	+	0.0998401i
$657$	−10.9519	−	10.9519i	−0.427273	−	0.427273i
$658$	−18.7653	−	5.66313i	−0.731547	−	0.220772i
$659$	−5.25399			−0.204666			−0.102333	−	0.994750i	$-0.532631\pi$
$659$	−5.25399			−0.204666			−0.102333	+	0.994750i	$0.532631\pi$
$660$	−4.03180	−	2.32776i	−0.156938	−	0.0906080i
$661$	−1.38916	+	5.18442i	−0.0540321	+	0.201650i	−0.987665	−	0.156580i	$-0.949953\pi$
$661$	−1.38916	+	5.18442i	−0.0540321	+	0.201650i	0.933633	+	0.358230i	$0.116620\pi$
$662$	29.6063	−	17.0932i	1.15068	−	0.664347i
$663$	−0.524483	+	21.5642i	−0.0203692	+	0.837484i
$664$			15.3009i			0.593788i
$665$	2.92155	+	0.881686i	0.113293	+	0.0341903i
$666$	−24.2312			−0.938941
$667$	0.348292	+	0.201086i	0.0134859	+	0.00778609i
$668$	30.3353	+	8.12832i	1.17371	+	0.314494i
$669$	0.937916	−	3.50035i	0.0362619	−	0.135331i
$670$	5.02530	−	1.34652i	0.194144	−	0.0520208i
$671$	−5.50840	−	5.50840i	−0.212649	−	0.212649i
$672$	10.2754	−	16.5770i	0.396383	−	0.639470i
$673$		−	40.2628i		−	1.55202i	−0.630722	−	0.776008i	$-0.717241\pi$
$673$		−	40.2628i		−	1.55202i	0.630722	−	0.776008i	$-0.282759\pi$
$674$	1.02746	+	3.83453i	0.0395762	+	0.147700i
$675$	−2.28637	−	3.96012i	−0.0880026	−	0.152425i
$676$	−1.76723	+	36.3085i	−0.0679705	+	1.39648i
$677$	23.1527	+	13.3672i	0.889832	+	0.513745i	0.873887	−	0.486128i	$-0.161591\pi$
$677$	23.1527	+	13.3672i	0.889832	+	0.513745i	0.0159443	+	0.999873i	$0.494925\pi$
$678$	−1.46226	+	1.46226i	−0.0561577	+	0.0561577i
$679$	25.7832	+	0.807182i	0.989467	+	0.0309768i
$680$			6.81937i			0.261511i
$681$	−12.5397	+	3.36001i	−0.480523	+	0.128756i
$682$	42.4817	+	11.3829i	1.62671	+	0.435875i
$683$	−31.8830	−	8.54301i	−1.21997	−	0.326889i	−0.409302	−	0.912399i	$-0.634228\pi$
$683$	−31.8830	−	8.54301i	−1.21997	−	0.326889i	−0.810665	+	0.585510i	$0.800894\pi$
$684$	4.76621	−	1.27710i	0.182241	−	0.0488312i
$685$		−	0.889463i		−	0.0339846i
$686$	23.4838	−	33.0701i	0.896617	−	1.26262i
$687$	−8.21841	+	8.21841i	−0.313552	+	0.313552i
$688$	1.38442	+	0.799298i	0.0527807	+	0.0304730i
$689$	−2.61467	+	4.28464i	−0.0996108	+	0.163232i
$690$	−3.76856	−	6.52735i	−0.143467	−	0.248492i
$691$	5.30765	+	19.8084i	0.201913	+	0.753548i	0.990369	+	0.138457i	$0.0442141\pi$
$691$	5.30765	+	19.8084i	0.201913	+	0.753548i	−0.788456	+	0.615091i	$0.789119\pi$
$692$		−	27.5796i		−	1.04842i
$693$	6.73572	+	0.210872i	0.255869	+	0.00801037i
$694$	57.1794	+	57.1794i	2.17050	+	2.17050i
$695$	−6.57844	+	1.76269i	−0.249535	+	0.0668626i
$696$	−0.0344754	+	0.128664i	−0.00130679	+	0.00487699i
$697$	8.62657	+	2.31148i	0.326755	+	0.0875537i
$698$	−53.3094	−	30.7782i	−2.01779	−	1.16497i
$699$	25.9080			0.979931
$700$	−32.9355	+	7.72912i	−1.24485	+	0.292133i
$701$		−	44.2019i		−	1.66948i	−0.550641	−	0.834742i	$-0.685617\pi$
$701$		−	44.2019i		−	1.66948i	0.550641	−	0.834742i	$-0.314383\pi$
$702$	5.71764	−	5.44611i	0.215798	−	0.205550i
$703$	16.9085	−	9.76210i	0.637715	−	0.368185i
$704$	8.30459	−	30.9932i	0.312991	−	1.16810i
$705$	1.91493	+	1.10559i	0.0721206	+	0.0416389i
$706$	56.7120			2.13438
$707$	4.70061	−	15.5759i	0.176785	−	0.585792i
$708$	10.4381	+	10.4381i	0.392287	+	0.392287i
$709$	10.6084	+	39.5912i	0.398408	+	1.48688i	0.815898	+	0.578196i	$0.196243\pi$
$709$	10.6084	+	39.5912i	0.398408	+	1.48688i	−0.417490	+	0.908681i	$0.637090\pi$
$710$	−2.34856	+	8.76493i	−0.0881397	+	0.328942i
$711$	−5.60217	−	9.70324i	−0.210098	−	0.363900i
$712$	8.05592	−	13.9533i	0.301908	−	0.522920i
$713$	29.3532	+	29.3532i	1.09929	+	1.09929i
$714$	−16.3846	−	30.5484i	−0.613179	−	1.14325i
$715$	5.27010	−	2.87416i	0.197091	−	0.107487i
$716$	33.5537	−	58.1167i	1.25396	−	2.17192i
$717$	−14.8780	−	3.98656i	−0.555630	−	0.148881i
$718$	−34.7409	−	60.1731i	−1.29652	−	2.24564i
$719$	−1.43809	+	2.49085i	−0.0536317	+	0.0928929i	−0.891595	−	0.452834i	$-0.850413\pi$
$719$	−1.43809	+	2.49085i	−0.0536317	+	0.0928929i	0.837963	+	0.545727i	$0.183746\pi$
$720$	−0.819663	+	0.819663i	−0.0305470	+	0.0305470i
$721$	−41.7468	+	9.79689i	−1.55473	+	0.364855i
$722$	24.6011	−	24.6011i	0.915559	−	0.915559i
$723$	3.02126	+	11.2755i	0.112362	+	0.419340i
$724$	−16.5631	+	9.56273i	−0.615564	+	0.355396i
$725$	−0.302488	+	0.174641i	−0.0112341	+	0.00648602i
$726$	−9.54523	+	2.55764i	−0.354257	+	0.0949228i
$727$	−26.3024			−0.975502			−0.487751	−	0.872983i	$-0.662183\pi$
$727$	−26.3024			−0.975502			−0.487751	+	0.872983i	$0.662183\pi$
$728$	−7.50406	−	14.8468i	−0.278119	−	0.550258i
$729$	−1.00000			−0.0370370
$730$	21.4161	−	5.73842i	0.792645	−	0.212389i
$731$	4.67036	−	2.69644i	0.172740	−	0.0997313i
$732$	7.40632	−	4.27604i	0.273745	−	0.158047i
$733$	10.5955	+	39.5431i	0.391355	+	1.46056i	0.827901	+	0.560875i	$0.189535\pi$
$733$	10.5955	+	39.5431i	0.391355	+	1.46056i	−0.436546	+	0.899682i	$0.643798\pi$
$734$	−40.9045	+	40.9045i	−1.50981	+	1.50981i
$735$	−3.43142	+	3.02666i	−0.126570	+	0.111640i
$736$	27.4446	−	27.4446i	1.01162	−	1.01162i
$737$	−4.62852	+	8.01684i	−0.170494	+	0.295304i
$738$	−1.63466	−	2.83131i	−0.0601725	−	0.104222i
$739$	27.4620	+	7.35841i	1.01020	+	0.270684i	0.725715	−	0.687995i	$-0.241509\pi$
$739$	27.4620	+	7.35841i	1.01020	+	0.270684i	0.284490	+	0.958679i	$0.408176\pi$
$740$	10.1115	−	17.5136i	0.371705	−	0.643812i
$741$	−1.79565	+	6.10376i	−0.0659650	+	0.224227i
$742$	0.252409	−	8.06251i	0.00926624	−	0.295984i
$743$	15.6997	+	15.6997i	0.575966	+	0.575966i	0.933789	−	0.357823i	$-0.116481\pi$
$743$	15.6997	+	15.6997i	0.575966	+	0.575966i	−0.357823	+	0.933789i	$0.616481\pi$
$744$	−6.87450	+	11.9070i	−0.252031	+	0.436531i
$745$	−1.47918	−	2.56202i	−0.0541931	−	0.0938653i
$746$	1.56063	−	5.82436i	0.0571388	−	0.213245i
$747$	2.27090	+	8.47513i	0.0830880	+	0.310089i
$748$	−30.1302	−	30.1302i	−1.10167	−	1.10167i
$749$	45.1315	−	10.5912i	1.64907	−	0.386994i
$750$	13.7035			0.500379
$751$	13.2341	+	7.64073i	0.482920	+	0.278814i	0.721633	−	0.692276i	$-0.243392\pi$
$751$	13.2341	+	7.64073i	0.482920	+	0.278814i	−0.238713	+	0.971090i	$0.576725\pi$
$752$	−1.55270	+	5.79475i	−0.0566211	+	0.211313i
$753$	3.08052	−	1.77854i	0.112260	−	0.0648135i
$754$	−0.415993	−	0.436733i	−0.0151496	−	0.0159049i
$755$			2.84025i			0.103367i
$756$	−2.13748	+	7.08273i	−0.0777394	+	0.257597i
$757$	−28.2653			−1.02732			−0.513660	−	0.857994i	$-0.671711\pi$
$757$	−28.2653			−1.02732			−0.513660	+	0.857994i	$0.671711\pi$
$758$	14.3186	+	8.26687i	0.520076	+	0.300266i
$759$	12.9540	+	3.47102i	0.470201	+	0.125990i
$760$	−0.520596	+	1.94289i	−0.0188840	+	0.0704760i
$761$	−23.5355	+	6.30631i	−0.853160	+	0.228603i	−0.658792	−	0.752325i	$-0.728932\pi$
$761$	−23.5355	+	6.30631i	−0.853160	+	0.228603i	−0.194368	+	0.980929i	$0.562266\pi$
$762$	24.6405	+	24.6405i	0.892632	+	0.892632i
$763$	−34.7725	+	18.6502i	−1.25885	+	0.675182i
$764$		−	8.14445i		−	0.294656i
$765$	1.01211	+	3.77725i	0.0365929	+	0.136567i
$766$	−28.9699	−	50.1774i	−1.04673	−	1.81298i
$767$	−18.4997	+	4.47785i	−0.667985	+	0.161686i
$768$	2.54365	+	1.46858i	0.0917861	+	0.0529927i
$769$	36.5890	−	36.5890i	1.31943	−	1.31943i	0.405206	−	0.914225i	$-0.367200\pi$
$769$	36.5890	−	36.5890i	1.31943	−	1.31943i	0.914225	−	0.405206i	$-0.132800\pi$
$770$	−5.08254	+	8.19948i	−0.183162	+	0.295489i
$771$			15.1037i			0.543946i
$772$	−17.8206	+	4.77501i	−0.641377	+	0.171856i
$773$	35.5939	+	9.53735i	1.28022	+	0.343035i	0.833939	−	0.551857i	$-0.186080\pi$
$773$	35.5939	+	9.53735i	1.28022	+	0.343035i	0.446284	+	0.894891i	$0.352747\pi$
$774$	−1.90689	−	0.510949i	−0.0685417	−	0.0183657i
$775$	−34.8240	+	9.33108i	−1.25092	+	0.335182i
$776$			17.0025i			0.610354i
$777$	−0.915999	+	29.2590i	−0.0328613	+	1.04966i
$778$	9.10892	−	9.10892i	0.326571	−	0.326571i
$779$	2.28131	+	1.31712i	0.0817365	+	0.0471906i
$780$	1.55036	+	6.40514i	0.0555119	+	0.229341i
$781$	−8.07290	−	13.9827i	−0.288871	−	0.500339i
$782$	−17.8546	−	66.6344i	−0.638480	−	2.38284i
$783$			0.0763835i			0.00272972i
$784$	−10.3414	−	6.86725i	−0.369336	−	0.245259i
$785$	−2.24863	−	2.24863i	−0.0802569	−	0.0802569i
$786$	−30.8182	+	8.25772i	−1.09925	+	0.294543i
$787$	1.46720	−	5.47568i	0.0523002	−	0.195187i	−0.934833	−	0.355088i	$-0.884451\pi$
$787$	1.46720	−	5.47568i	0.0523002	−	0.195187i	0.987133	+	0.159901i	$0.0511176\pi$
$788$	64.5122	+	17.2860i	2.29815	+	0.615788i
$789$	−19.0721	−	11.0113i	−0.678984	−	0.392012i
$790$	16.0391			0.570645
$791$	1.71039	+	1.82094i	0.0608144	+	0.0647452i
$792$			4.44182i			0.157833i
$793$	−0.268123	+	11.0239i	−0.00952132	+	0.391471i
$794$	16.1021	−	9.29653i	0.571441	−	0.329922i
$795$	−0.235516	+	0.878957i	−0.00835288	+	0.0311734i
$796$	1.95139	+	1.12663i	0.0691651	+	0.0399325i
$797$	4.66456			0.165227			0.0826136	−	0.996582i	$-0.473673\pi$
$797$	4.66456			0.165227			0.0826136	+	0.996582i	$0.473673\pi$
$798$	−2.33601	−	9.95428i	−0.0826939	−	0.352378i
$799$	14.3106	+	14.3106i	0.506272	+	0.506272i
$800$	8.72436	+	32.5597i	0.308453	+	1.15116i
$801$	2.39127	−	8.92433i	0.0844913	−	0.315326i
$802$	−42.8917	−	74.2907i	−1.51456	−	2.62329i
$803$	−19.7252	+	34.1650i	−0.696086	+	1.20566i
$804$	−7.18603	−	7.18603i	−0.253432	−	0.253432i
$805$	−8.02418	+	4.30376i	−0.282815	+	0.151688i
$806$	−29.8079	−	54.6563i	−1.04994	−	1.92518i
$807$	−15.0643	+	26.0922i	−0.530289	+	0.918488i
$808$	10.3583	+	2.77550i	0.364404	+	0.0976416i
$809$	−20.4024	−	35.3380i	−0.717310	−	1.24242i	−0.962062	−	0.272832i	$-0.912040\pi$
$809$	−20.4024	−	35.3380i	−0.717310	−	1.24242i	0.244751	−	0.969586i	$-0.421294\pi$
$810$	0.715753	−	1.23972i	0.0251490	−	0.0435593i
$811$	15.4548	−	15.4548i	0.542690	−	0.542690i	−0.381626	−	0.924317i	$-0.624636\pi$
$811$	15.4548	−	15.4548i	0.542690	−	0.542690i	0.924317	+	0.381626i	$0.124636\pi$
$812$	0.541004	+	0.163268i	0.0189855	+	0.00572959i
$813$	−18.9696	+	18.9696i	−0.665293	+	0.665293i
$814$	15.9742	+	59.6166i	0.559896	+	2.08956i
$815$	−0.169028	+	0.0975885i	−0.00592080	+	0.00341837i
$816$	−9.18818	+	5.30480i	−0.321651	+	0.185705i
$817$	1.53647	−	0.411695i	0.0537542	−	0.0144034i
$818$	4.19671			0.146735
$819$	−6.36000	−	7.10988i	−0.222236	−	0.248439i
$820$	2.72851			0.0952836
$821$	−8.62197	+	2.31025i	−0.300909	+	0.0806283i	−0.406114	−	0.913822i	$-0.633117\pi$
$821$	−8.62197	+	2.31025i	−0.300909	+	0.0806283i	0.105206	+	0.994450i	$0.466450\pi$
$822$	−2.58089	+	1.49008i	−0.0900188	+	0.0519724i
$823$	−15.7750	+	9.10768i	−0.549881	+	0.317474i	−0.749074	−	0.662487i	$-0.769501\pi$
$823$	−15.7750	+	9.10768i	−0.549881	+	0.317474i	0.199193	+	0.979960i	$0.436168\pi$
$824$	−7.31517	−	27.3006i	−0.254836	−	0.951061i
$825$	−8.23589	+	8.23589i	−0.286737	+	0.286737i
$826$	22.2955	−	20.9419i	0.775760	−	0.728662i
$827$	22.9060	−	22.9060i	0.796520	−	0.796520i	−0.186025	−	0.982545i	$-0.559561\pi$
$827$	22.9060	−	22.9060i	0.796520	−	0.796520i	0.982545	+	0.186025i	$0.0595605\pi$
$828$	−7.36143	+	12.7504i	−0.255827	+	0.443106i
$829$	−14.1448	−	24.4995i	−0.491268	−	0.850901i	0.508681	−	0.860955i	$-0.330133\pi$
$829$	−14.1448	−	24.4995i	−0.491268	−	0.850901i	−0.999949	+	0.0100536i	$0.996800\pi$
$830$	−12.1322	−	3.25081i	−0.421115	−	0.112837i
$831$	−1.22457	+	2.12102i	−0.0424800	+	0.0735775i
$832$	−39.8753	+	21.7468i	−1.38243	+	0.753935i
$833$	−37.5064	+	18.6295i	−1.29952	+	0.645474i
$834$	16.1352	+	16.1352i	0.558717	+	0.558717i
$835$	−3.67060	+	6.35766i	−0.127026	+	0.220016i
$836$	−6.28416	−	10.8845i	−0.217342	−	0.376448i
$837$	−2.04058	+	7.61556i	−0.0705329	+	0.263232i
$838$	3.63452	+	13.5642i	0.125552	+	0.468567i
$839$	−15.9512	−	15.9512i	−0.550698	−	0.550698i	0.375945	−	0.926642i	$-0.377318\pi$
$839$	−15.9512	−	15.9512i	−0.550698	−	0.550698i	−0.926642	+	0.375945i	$0.877318\pi$
$840$	−2.06472	−	2.19818i	−0.0712398	−	0.0758445i
$841$	−28.9942			−0.999799
$842$	−15.5132	−	8.95655i	−0.534620	−	0.308663i
$843$	−7.37188	+	27.5122i	−0.253901	+	0.947572i
$844$	42.5005	−	24.5377i	1.46293	−	0.844622i
$845$	−8.09121	−	2.59571i	−0.278346	−	0.0892950i
$846$		−	7.40856i		−	0.254712i
$847$	2.72749	+	11.6225i	0.0937178	+	0.399353i
$848$	−2.46883			−0.0847800
$849$	5.27692	+	3.04663i	0.181103	+	0.104560i
$850$	57.8713	+	15.5066i	1.98497	+	0.531871i
$851$	−15.0776	+	56.2704i	−0.516854	+	1.92892i
$852$	17.1212	−	4.58761i	0.586563	−	0.157169i
$853$	−22.1904	−	22.1904i	−0.759784	−	0.759784i	0.216499	−	0.976283i	$-0.430536\pi$
$853$	−22.1904	−	22.1904i	−0.759784	−	0.759784i	−0.976283	+	0.216499i	$0.930536\pi$
$854$	−8.37604	−	15.6168i	−0.286622	−	0.534395i
$855$			1.15343i			0.0394465i
$856$	7.90826	+	29.5140i	0.270299	+	1.00877i
$857$	−0.305420	−	0.529004i	−0.0104330	−	0.0180704i	0.860762	−	0.509008i	$-0.169988\pi$
$857$	−0.305420	−	0.529004i	−0.0104330	−	0.0180704i	−0.871195	+	0.490938i	$0.836654\pi$
$858$	−17.1685	−	10.4769i	−0.586122	−	0.357676i
$859$	−22.0653	−	12.7394i	−0.752858	−	0.434663i	0.0738678	−	0.997268i	$-0.476466\pi$
$859$	−22.0653	−	12.7394i	−0.752858	−	0.434663i	−0.826726	+	0.562605i	$0.809799\pi$
$860$	1.16503	−	1.16503i	0.0397271	−	0.0397271i
$861$	−3.48058	+	1.86680i	−0.118618	+	0.0636205i
$862$			21.3195i			0.726145i
$863$	7.02503	−	1.88235i	0.239135	−	0.0640760i	−0.137261	−	0.990535i	$-0.543830\pi$
$863$	7.02503	−	1.88235i	0.239135	−	0.0640760i	0.376396	+	0.926459i	$0.377163\pi$
$864$	7.12039	+	1.90790i	0.242240	+	0.0649081i
$865$	6.22722	+	1.66858i	0.211732	+	0.0567334i
$866$	27.7843	−	7.44479i	0.944150	−	0.252984i
$867$			18.7915i			0.638194i
$868$	49.5773	+	30.7310i	1.68276	+	1.04308i
$869$	−20.1799	+	20.1799i	−0.684556	+	0.684556i
$870$	−0.0946942	−	0.0546717i	−0.00321043	−	0.00185355i
$871$	12.7360	−	3.08274i	0.431543	−	0.104455i
$872$	−13.0039	−	22.5233i	−0.440366	−	0.762736i
$873$	2.52346	+	9.41767i	0.0854061	+	0.318740i
$874$		−	20.3477i		−	0.688270i
$875$	0.518024	−	16.5468i	0.0175124	−	0.559384i
$876$	−30.6244	−	30.6244i	−1.03470	−	1.03470i
$877$	−19.6745	+	5.27177i	−0.664361	+	0.178015i	−0.575214	−	0.818003i	$-0.695081\pi$
$877$	−19.6745	+	5.27177i	−0.664361	+	0.178015i	−0.0891479	+	0.996018i	$0.528414\pi$
$878$	3.91011	−	14.5927i	0.131960	−	0.492481i
$879$	−8.55941	−	2.29349i	−0.288702	−	0.0773574i
$880$	2.55699	+	1.47628i	0.0861961	+	0.0497653i
$881$	9.30783			0.313589			0.156794	−	0.987631i	$-0.449884\pi$
$881$	9.30783			0.313589			0.156794	+	0.987631i	$0.449884\pi$
$882$	14.5307	+	4.88626i	0.489275	+	0.164529i
$883$			20.6192i			0.693891i	0.937885	+	0.346945i	$0.112781\pi$
$883$			20.6192i			0.693891i	−0.937885	+	0.346945i	$0.887219\pi$
$884$	−1.46660	+	60.2994i	−0.0493270	+	2.02809i
$885$	−2.98833	+	1.72531i	−0.100452	+	0.0579958i
$886$	−13.2028	+	49.2735i	−0.443557	+	1.65538i
$887$	−16.2365	−	9.37414i	−0.545168	−	0.314753i	0.202003	−	0.979385i	$-0.435255\pi$
$887$	−16.2365	−	9.37414i	−0.545168	−	0.314753i	−0.747171	+	0.664632i	$0.768588\pi$
$888$	−19.2946			−0.647485
$889$	30.6847	−	28.8218i	1.02913	−	0.966651i
$890$	9.35212	+	9.35212i	0.313484	+	0.313484i
$891$	0.659241	+	2.46032i	0.0220854	+	0.0824238i
$892$	2.62267	−	9.78793i	0.0878134	−	0.327724i
$893$	2.98471	+	5.16967i	0.0998795	+	0.172996i
$894$	−4.95602	+	8.58407i	−0.165754	+	0.287094i
$895$	11.0922	+	11.0922i	0.370771	+	0.370771i
$896$	17.9053	−	28.8860i	0.598174	−	0.965013i
$897$	−9.08937	−	16.6664i	−0.303485	−	0.556476i
$898$	−16.5157	+	28.6060i	−0.551136	+	0.954596i
$899$	0.581703	+	0.155867i	0.0194009	+	0.00519845i
$900$	−6.39332	−	11.0736i	−0.213111	−	0.369119i
$901$	−4.16430	+	7.21279i	−0.138733	+	0.240293i
$902$	−5.88829	+	5.88829i	−0.196059	+	0.196059i
$903$	−0.689053	+	2.28324i	−0.0229302	+	0.0759815i
$904$	−1.16435	+	1.16435i	−0.0387258	+	0.0387258i
$905$	−1.15710	−	4.31835i	−0.0384632	−	0.143547i
$906$	8.24134	−	4.75814i	0.273800	−	0.158079i
$907$	8.16685	−	4.71513i	0.271176	−	0.156563i	−0.358246	−	0.933627i	$-0.616625\pi$
$907$	8.16685	−	4.71513i	0.271176	−	0.156563i	0.629422	+	0.777064i	$0.283292\pi$
$908$	−35.0644	+	9.39549i	−1.16365	+	0.311800i
$909$	6.14938			0.203962
$910$	13.3665	−	2.79571i	0.443094	−	0.0926767i
$911$	7.10474			0.235391			0.117695	−	0.993050i	$-0.462449\pi$
$911$	7.10474			0.235391			0.117695	+	0.993050i	$0.462449\pi$
$912$	−3.02275	+	0.809944i	−0.100093	+	0.0268199i
$913$	19.3545	−	11.1743i	0.640539	−	0.369815i
$914$	23.5651	−	13.6053i	0.779465	−	0.450025i
$915$	0.517404	+	1.93098i	0.0171049	+	0.0638362i
$916$	−22.9809	+	22.9809i	−0.759310	+	0.759310i
$917$	8.80613	+	37.5250i	0.290804	+	1.23918i
$918$	9.26461	−	9.26461i	0.305778	−	0.305778i
$919$	16.9808	−	29.4116i	0.560145	−	0.970199i	−0.437338	−	0.899297i	$-0.644079\pi$
$919$	16.9808	−	29.4116i	0.560145	−	0.970199i	0.997483	−	0.0709024i	$-0.0225879\pi$
$920$	−3.00080	−	5.19754i	−0.0989335	−	0.171358i
$921$	27.8155	+	7.45314i	0.916552	+	0.245589i
$922$	24.8742	−	43.0834i	0.819188	−	1.41887i
$923$	−6.45037	+	21.9260i	−0.212316	+	0.721702i
$924$	18.8349	+	0.589656i	0.619623	+	0.0193983i
$925$	−35.7755	−	35.7755i	−1.17629	−	1.17629i
$926$	−7.08555	+	12.2725i	−0.232846	+	0.403301i
$927$	−8.10374	−	14.0361i	−0.266162	−	0.461005i
$928$	0.145732	−	0.543880i	0.00478389	−	0.0178537i
$929$	−3.72954	−	13.9188i	−0.122362	−	0.456662i	0.877370	−	0.479815i	$-0.159296\pi$
$929$	−3.72954	−	13.9188i	−0.122362	−	0.456662i	−0.999732	+	0.0231532i	$0.992629\pi$
$930$	−7.98061	−	7.98061i	−0.261695	−	0.261695i
$931$	−12.1080	+	2.44442i	−0.396824	+	0.0801126i
$932$	72.4458			2.37304
$933$	2.55354	+	1.47429i	0.0835991	+	0.0482660i
$934$	17.0205	−	63.5214i	0.556928	−	2.07848i
$935$	8.62601	−	4.98023i	0.282101	−	0.162871i
$936$	4.55279	−	4.33658i	0.148813	−	0.141746i
$937$		−	5.67717i		−	0.185465i	−0.995691	−	0.0927325i	$-0.970440\pi$
$937$		−	5.67717i		−	0.185465i	0.995691	−	0.0927325i	$-0.0295601\pi$
$938$	−15.3492	+	14.4173i	−0.501169	+	0.470742i
$939$	12.4212			0.405351
$940$	5.35468	+	3.09152i	0.174650	+	0.100834i
$941$	−9.86113	−	2.64228i	−0.321464	−	0.0861360i	0.0944787	−	0.995527i	$-0.469882\pi$
$941$	−9.86113	−	2.64228i	−0.321464	−	0.0861360i	−0.415942	+	0.909391i	$0.636548\pi$
$942$	−2.75765	+	10.2917i	−0.0898491	+	0.335321i
$943$	−7.59208	+	2.03429i	−0.247232	+	0.0662457i
$944$	−6.61988	−	6.61988i	−0.215459	−	0.215459i
$945$	−1.46990	−	0.911131i	−0.0478157	−	0.0296391i
$946$			5.02840i			0.163487i
$947$	9.19324	+	34.3096i	0.298740	+	1.11491i	0.938201	+	0.346090i	$0.112491\pi$
$947$	9.19324	+	34.3096i	0.298740	+	1.11491i	−0.639461	+	0.768823i	$0.720843\pi$
$948$	−15.6652	−	27.1329i	−0.508782	−	0.881235i
$949$	54.2764	−	13.1376i	1.76189	−	0.426464i
$950$	15.3042	+	8.83587i	0.496533	+	0.286673i
$951$	−10.7969	+	10.7969i	−0.350114	+	0.350114i
$952$	−13.0466	−	24.3248i	−0.422843	−	0.788372i
$953$			24.3020i			0.787219i	0.919278	+	0.393609i	$0.128774\pi$
$953$			24.3020i			0.787219i	−0.919278	+	0.393609i	$0.871226\pi$
$954$	2.94495	−	0.789097i	0.0953463	−	0.0255480i
$955$	1.83894	+	0.492742i	0.0595067	+	0.0159448i
$956$	−41.6030	−	11.1475i	−1.34554	−	0.360536i
$957$	0.187928	−	0.0503551i	0.00607485	−	0.00162775i
$958$		−	82.7142i		−	2.67238i
$959$	1.70169	+	3.17273i	0.0549505	+	0.102453i
$960$	−5.82238	+	5.82238i	−0.187916	+	0.187916i
$961$	26.9860	+	15.5804i	0.870516	+	0.502593i
$962$	45.5102	−	74.5774i	1.46731	−	2.40447i
$963$	8.76076	+	15.1741i	0.282312	+	0.488978i
$964$	8.44826	+	31.5293i	0.272100	+	1.01549i
$965$		−	4.31261i		−	0.138828i
$966$	25.9304	+	16.0733i	0.834298	+	0.517149i
$967$	34.1587	+	34.1587i	1.09847	+	1.09847i	0.994590	+	0.103880i	$0.0331259\pi$
$967$	34.1587	+	34.1587i	1.09847	+	1.09847i	0.103880	+	0.994590i	$0.466874\pi$
$968$	−7.60059	+	2.03657i	−0.244292	+	0.0654579i
$969$	−2.73235	+	10.1973i	−0.0877757	+	0.327583i
$970$	−13.4815	−	3.61235i	−0.432864	−	0.115985i
$971$	−23.1545	−	13.3683i	−0.743064	−	0.429008i	0.0801184	−	0.996785i	$-0.474470\pi$
$971$	−23.1545	−	13.3683i	−0.743064	−	0.429008i	−0.823182	+	0.567777i	$0.807803\pi$
$972$	−2.79627			−0.0896904
$973$	20.0931	−	18.8732i	0.644155	−	0.605047i
$974$			44.7100i			1.43260i
$975$	16.4824	+	0.400884i	0.527860	+	0.0128386i
$976$	−4.69712	+	2.71189i	−0.150351	+	0.0868053i
$977$	6.37034	−	23.7744i	0.203805	−	0.760612i	−0.786005	−	0.618220i	$-0.787854\pi$
$977$	6.37034	−	23.7744i	0.203805	−	0.760612i	0.989810	−	0.142392i	$-0.0454792\pi$
$978$	0.566330	+	0.326971i	0.0181092	+	0.0104554i
$979$	−23.5331			−0.752122
$980$	−9.59517	+	8.46336i	−0.306506	+	0.270352i
$981$	−10.5457	−	10.5457i	−0.336697	−	0.336697i
$982$	−19.5780	−	73.0661i	−0.624759	−	2.33163i
$983$	0.321501	−	1.19986i	0.0102543	−	0.0382695i	−0.960609	−	0.277903i	$-0.910361\pi$
$983$	0.321501	−	1.19986i	0.0102543	−	0.0382695i	0.970863	+	0.239634i	$0.0770273\pi$
$984$	−1.30163	−	2.25449i	−0.0414944	−	0.0718705i
$985$	−7.80603	+	13.5204i	−0.248721	+	0.430797i
$986$	−0.707663	−	0.707663i	−0.0225366	−	0.0225366i
$987$	−8.94578	−	0.280062i	−0.284747	−	0.00891446i
$988$	−5.02114	+	17.0678i	−0.159744	+	0.542998i
$989$	−2.37308	+	4.11030i	−0.0754596	+	0.130700i
$990$	−3.52196	−	0.943707i	−0.111935	−	0.0299930i
$991$	−13.4870	−	23.3602i	−0.428429	−	0.742061i	0.568305	−	0.822818i	$-0.307600\pi$
$991$	−13.4870	−	23.3602i	−0.428429	−	0.742061i	−0.996734	+	0.0807570i	$0.974266\pi$
$992$	29.0595	−	50.3325i	0.922639	−	1.59806i
$993$	11.0379	−	11.0379i	0.350278	−	0.350278i
$994$	−8.39144	−	35.7578i	−0.266160	−	1.13417i
$995$	−0.372443	+	0.372443i	−0.0118072	+	0.0118072i
$996$	6.35006	+	23.6988i	0.201209	+	0.750924i
$997$	29.5536	−	17.0628i	0.935973	−	0.540384i	0.0472772	−	0.998882i	$-0.484946\pi$
$997$	29.5536	−	17.0628i	0.935973	−	0.540384i	0.888696	+	0.458498i	$0.151612\pi$
$998$	3.16593	−	1.82785i	0.100216	−	0.0578596i
$999$	−10.6873	+	2.86365i	−0.338131	+	0.0906018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.b.229.9	yes	36
3.2	odd	2		819.2.fn.g.775.1		36
7.3	odd	6		273.2.bz.a.73.1	✓	36
13.5	odd	4		273.2.bz.a.187.1	yes	36
21.17	even	6		819.2.fn.f.73.9		36
39.5	even	4		819.2.fn.f.460.9		36
91.31	even	12	inner	273.2.bz.b.31.9	yes	36
273.122	odd	12		819.2.fn.g.577.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.1	✓	36	7.3	odd	6
273.2.bz.a.187.1	yes	36	13.5	odd	4
273.2.bz.b.31.9	yes	36	91.31	even	12	inner
273.2.bz.b.229.9	yes	36	1.1	even	1	trivial
819.2.fn.f.73.9		36	21.17	even	6
819.2.fn.f.460.9		36	39.5	even	4
819.2.fn.g.577.1		36	273.122	odd	12
819.2.fn.g.775.1		36	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11542 - 0.566824i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.42164 - 1.39814i) q^{4} +(0.169176 + 0.631372i) q^{5} +(1.54859 - 1.54859i) q^{6} +(-1.81137 - 1.92845i) q^{7} +(1.23310 - 1.23310i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.11542 - 0.566824i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.42164 - 1.39814i) q^{4} +(0.169176 + 0.631372i) q^{5} +(1.54859 - 1.54859i) q^{6} +(-1.81137 - 1.92845i) q^{7} +(1.23310 - 1.23310i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.715753 + 1.23972i) q^{10} +(-2.46032 - 0.659241i) q^{11} +(1.39814 - 2.42164i) q^{12} +(1.72632 + 3.16541i) q^{13} +(-4.92490 - 3.05275i) q^{14} +(0.462196 + 0.462196i) q^{15} +(-0.886704 + 1.53582i) q^{16} +(2.99130 + 5.18109i) q^{17} +(0.566824 - 2.11542i) q^{18} +(0.456716 + 1.70449i) q^{19} +(1.29243 + 1.29243i) q^{20} +(-2.53292 - 0.764403i) q^{21} -5.57827 q^{22} +(-4.55977 - 2.63259i) q^{23} +(0.451346 - 1.68444i) q^{24} +(3.96012 - 2.28637i) q^{25} +(5.44611 + 5.71764i) q^{26} -1.00000i q^{27} +(-7.08273 - 2.13748i) q^{28} -0.0763835 q^{29} +(1.23972 + 0.715753i) q^{30} +(-7.61556 - 2.04058i) q^{31} +(-1.90790 + 7.12039i) q^{32} +(-2.46032 + 0.659241i) q^{33} +(9.26461 + 9.26461i) q^{34} +(0.911131 - 1.46990i) q^{35} -2.79627i q^{36} +(-2.86365 - 10.6873i) q^{37} +(1.93229 + 3.34682i) q^{38} +(3.07774 + 1.87817i) q^{39} +(0.987154 + 0.569934i) q^{40} +(1.05558 - 1.05558i) q^{41} +(-5.79146 - 0.181311i) q^{42} -0.901426i q^{43} +(-6.87972 + 1.84342i) q^{44} +(0.631372 + 0.169176i) q^{45} +(-11.1380 - 2.98443i) q^{46} +(3.26758 - 0.875544i) q^{47} +1.77341i q^{48} +(-0.437863 + 6.98629i) q^{49} +(7.08132 - 7.08132i) q^{50} +(5.18109 + 2.99130i) q^{51} +(8.60620 + 5.25186i) q^{52} +(0.696069 + 1.20563i) q^{53} +(-0.566824 - 2.11542i) q^{54} -1.66490i q^{55} +(-4.61158 - 0.144373i) q^{56} +(1.24777 + 1.24777i) q^{57} +(-0.161583 + 0.0432960i) q^{58} +(-1.36632 + 5.09918i) q^{59} +(1.76549 + 0.473061i) q^{60} +(2.64864 + 1.52919i) q^{61} -17.2667 q^{62} +(-2.57578 + 0.604468i) q^{63} +12.5972i q^{64} +(-1.70650 + 1.62546i) q^{65} +(-4.83093 + 2.78914i) q^{66} +(0.940634 - 3.51049i) q^{67} +(14.4877 + 8.36449i) q^{68} -5.26517 q^{69} +(1.09425 - 3.62589i) q^{70} +(4.48225 + 4.48225i) q^{71} +(-0.451346 - 1.68444i) q^{72} +(4.00866 - 14.9605i) q^{73} +(-12.1156 - 20.9849i) q^{74} +(2.28637 - 3.96012i) q^{75} +(3.48911 + 3.48911i) q^{76} +(3.18524 + 5.93874i) q^{77} +(7.57529 + 2.22856i) q^{78} +(5.60217 - 9.70324i) q^{79} +(-1.11968 - 0.300017i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.63466 - 2.83131i) q^{82} +(-6.20423 + 6.20423i) q^{83} +(-7.20257 + 1.69026i) q^{84} +(-2.76514 + 2.76514i) q^{85} +(-0.510949 - 1.90689i) q^{86} +(-0.0661501 + 0.0381918i) q^{87} +(-3.84673 + 2.22091i) q^{88} +(8.92433 - 2.39127i) q^{89} +1.43151 q^{90} +(2.97734 - 9.06286i) q^{91} -14.7229 q^{92} +(-7.61556 + 2.04058i) q^{93} +(6.41600 - 3.70428i) q^{94} +(-0.998900 + 0.576715i) q^{95} +(1.90790 + 7.12039i) q^{96} +(-6.89422 + 6.89422i) q^{97} +(3.03374 + 15.0271i) q^{98} +(-1.80108 + 1.80108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 + 18 * q^9	\( 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

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