LMFDB - Embedded newform 273.2.bz.b.31.9

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			31.9
Character	$\chi$	$=$	273.31
Dual form			273.2.bz.b.229.9

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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	0.911699	−	0.410858i	$-0.134771\pi$
$2$	2.11542	+	0.566824i	1.49582	+	0.400805i	0.584125	+	0.811663i	$0.301438\pi$
$3$	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	−0.917724	−	0.397219i	$-0.869975\pi$
$5$	0.169176	−	0.631372i	0.0756576	−	0.282358i	0.993382	+	0.114861i	$0.0366421\pi$
$6$	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	−0.609884	−	0.792490i	$-0.708784\pi$
$11$	−2.46032	+	0.659241i	−0.741815	+	0.198769i	−0.131930	+	0.991259i	$0.542117\pi$
$12$	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	−0.233272	−	0.972412i	$-0.574943\pi$
$17$	2.99130	−	5.18109i	0.725497	−	1.25660i	0.958769	−	0.284186i	$-0.0917234\pi$
$18$	0.566824	+	2.11542i	0.133602	+	0.498608i
$19$	0.456716	−	1.70449i	0.104778	−	0.391036i	−0.893542	−	0.448980i	$-0.851788\pi$
$19$	0.456716	−	1.70449i	0.104778	−	0.391036i	0.998320	+	0.0579434i	$0.0184543\pi$
$20$	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	−0.893323	−	0.449416i	$-0.851632\pi$
$23$	−4.55977	+	2.63259i	−0.950779	+	0.548932i	−0.0574559	+	0.998348i	$0.518299\pi$
$24$	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	−0.866673	−	0.498877i	$-0.833746\pi$
$31$	−7.61556	+	2.04058i	−1.36780	+	0.366500i	−0.501122	+	0.865377i	$0.667079\pi$
$32$	−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	0.166193	+	0.986093i	$0.446852\pi$
$37$	−2.86365	+	10.6873i	−0.470781	+	1.75698i	−0.636974	+	0.770885i	$0.719814\pi$
$38$	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	0.784713	−	0.619860i	$-0.212810\pi$
$41$	1.05558	+	1.05558i	0.164853	+	0.164853i	−0.619860	+	0.784713i	$0.712810\pi$
$42$	−5.79146	+	0.181311i	−0.893642	+	0.0279768i
$43$			0.901426i			0.137466i	0.997635	+	0.0687331i	$0.0218957\pi$
$43$			0.901426i			0.137466i	−0.997635	+	0.0687331i	$0.978104\pi$
$44$	−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	0.489131	−	0.872211i	$-0.337314\pi$
$47$	3.26758	+	0.875544i	0.476625	+	0.127711i	−0.0125057	+	0.999922i	$0.503981\pi$
$48$		−	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	−0.814252	−	0.580512i	$-0.802852\pi$
$53$	0.696069	−	1.20563i	0.0956124	−	0.165606i	0.909864	+	0.414907i	$0.136186\pi$
$54$	−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	−0.996043	−	0.0888707i	$-0.971674\pi$
$59$	−1.36632	−	5.09918i	−0.177880	−	0.663857i	0.818163	−	0.574986i	$-0.194992\pi$
$60$	1.76549	−	0.473061i	0.227923	−	0.0610719i
$61$	2.64864	−	1.52919i	0.339124	−	0.195793i	−0.320761	−	0.947160i	$-0.603939\pi$
$61$	2.64864	−	1.52919i	0.339124	−	0.195793i	0.659884	+	0.751367i	$0.270605\pi$
$62$	−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	0.999281	−	0.0379229i	$-0.0120741\pi$
$67$	0.940634	+	3.51049i	0.114917	+	0.428875i	−0.884364	+	0.466798i	$0.845407\pi$
$68$	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	−0.389205	−	0.921151i	$-0.627250\pi$
$71$	4.48225	−	4.48225i	0.531946	−	0.531946i	0.921151	+	0.389205i	$0.127250\pi$
$72$	−0.451346	+	1.68444i	−0.0531916	+	0.198514i
$73$	4.00866	+	14.9605i	0.469178	+	1.75100i	0.642652	+	0.766158i	$0.277834\pi$
$73$	4.00866	+	14.9605i	0.469178	+	1.75100i	−0.173474	+	0.984839i	$0.555499\pi$
$74$	−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	0.987492	+	0.157671i	$0.0503987\pi$
$79$	5.60217	+	9.70324i	0.630293	+	1.09170i	−0.357198	+	0.934029i	$0.616268\pi$
$80$	−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	0.279224	−	0.960226i	$-0.409923\pi$
$83$	−6.20423	−	6.20423i	−0.681002	−	0.681002i	−0.960226	+	0.279224i	$0.909923\pi$
$84$	−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	0.698654	−	0.715459i	$-0.253783\pi$
$89$	8.92433	+	2.39127i	0.945977	+	0.253474i	0.247323	+	0.968933i	$0.420449\pi$
$90$	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	0.264409	−	0.964411i	$-0.414823\pi$
$97$	−6.89422	−	6.89422i	−0.700002	−	0.700002i	−0.964411	+	0.264409i	$0.914823\pi$
$98$	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	−0.671528	−	0.740979i	$-0.734362\pi$
$101$	3.07469	−	5.32552i	0.305943	−	0.529909i	0.977471	+	0.211070i	$0.0676949\pi$
$102$	12.6557	−	3.39108i	1.25310	−	0.335767i
$103$	8.10374	+	14.0361i	0.798485	+	1.38302i	0.920603	+	0.390501i	$0.127698\pi$
$103$	8.10374	+	14.0361i	0.798485	+	1.38302i	−0.122118	+	0.992516i	$0.538969\pi$
$104$	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	−0.883931	−	0.467618i	$-0.845112\pi$
$107$	−8.76076	−	15.1741i	−0.846935	−	1.46693i	0.0369960	−	0.999315i	$-0.488221\pi$
$108$	−1.39814	+	2.42164i	−0.134536	+	0.233023i
$109$	3.85998	+	14.4056i	0.369719	+	1.37981i	0.860909	+	0.508758i	$0.169895\pi$
$109$	3.85998	+	14.4056i	0.369719	+	1.37981i	−0.491190	+	0.871052i	$0.663438\pi$
$110$	−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	$-0.750515\pi$
$127$		−	15.9116i		−	1.41192i	0.708250	−	0.705962i	$-0.249485\pi$
$128$	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	−0.936829	−	0.349787i	$-0.886254\pi$
$131$	−12.6166	+	7.28421i	−1.10232	+	0.636424i	−0.165490	+	0.986212i	$0.552920\pi$
$132$	−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	−0.314530	−	0.949247i	$-0.601847\pi$
$137$	−1.31441	+	0.352195i	−0.112297	+	0.0300900i	0.202233	+	0.979338i	$0.435180\pi$
$138$	−11.1380	−	2.98443i	−0.948132	−	0.254051i
$139$		−	10.4193i		−	0.883752i	−0.897076	−	0.441876i	$-0.854313\pi$
$139$		−	10.4193i		−	0.883752i	0.897076	−	0.441876i	$-0.145687\pi$
$140$	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	0.0752588	−	0.997164i	$-0.476022\pi$
$149$	−4.37174	−	1.17141i	−0.358147	−	0.0959653i	−0.433406	+	0.901199i	$0.642688\pi$
$150$	2.59194	+	9.67326i	0.211631	+	0.789819i
$151$	4.19719	−	1.12463i	0.341563	−	0.0915214i	−0.0839602	−	0.996469i	$-0.526757\pi$
$151$	4.19719	−	1.12463i	0.341563	−	0.0915214i	0.425523	+	0.904948i	$0.360090\pi$
$152$	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	0.322358	−	0.946618i	$-0.395524\pi$
$157$	−4.21329	−	2.43255i	−0.336257	−	0.194138i	−0.658616	+	0.752479i	$0.728858\pi$
$158$	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	−0.962833	−	0.270097i	$-0.912944\pi$
$163$	0.0772829	−	0.288424i	0.00605326	−	0.0225911i	0.968886	+	0.247506i	$0.0796109\pi$
$164$	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	−0.329584	−	0.944126i	$-0.606908\pi$
$167$	7.94164	−	7.94164i	0.614543	−	0.614543i	0.944126	+	0.329584i	$0.106908\pi$
$168$	−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	0.990317	−	0.138822i	$-0.0443316\pi$
$173$	4.93150	+	8.54161i	0.374935	+	0.649407i	−0.615382	+	0.788229i	$0.710998\pi$
$174$	−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	0.997858	+	0.0654199i	$0.0208387\pi$
$179$	20.7836	+	11.9994i	1.55344	+	0.896880i	0.555584	+	0.831460i	$0.312495\pi$
$180$	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	0.913891	−	0.405959i	$-0.133063\pi$
$191$	1.45631	+	2.52239i	0.105375	+	0.182514i	−0.808517	+	0.588473i	$0.799729\pi$
$192$	6.29860	−	10.9095i	0.454562	−	0.787325i
$193$	−6.37298	+	1.70763i	−0.458737	+	0.122918i	−0.480785	−	0.876839i	$-0.659648\pi$
$193$	−6.37298	+	1.70763i	−0.458737	+	0.122918i	0.0220476	+	0.999757i	$0.492981\pi$
$194$	−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	0.230132	−	0.973160i	$-0.426084\pi$
$197$	16.8890	−	16.8890i	1.20329	−	1.20329i	0.973160	−	0.230132i	$-0.0739156\pi$
$198$	−2.78914	−	4.83093i	−0.198215	−	0.343319i
$199$	0.402906	−	0.697854i	0.0285612	−	0.0494695i	−0.851391	−	0.524531i	$-0.824241\pi$
$199$	0.402906	−	0.697854i	0.0285612	−	0.0494695i	0.879953	+	0.475061i	$0.157574\pi$
$200$	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	0.787679	−	0.616086i	$-0.211283\pi$
$223$	2.56243	+	2.56243i	0.171593	+	0.171593i	−0.616086	+	0.787679i	$0.711283\pi$
$224$	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	−0.649712	−	0.760180i	$-0.725111\pi$
$227$	−12.5397	+	3.36001i	−0.832290	+	0.223011i	−0.182577	+	0.983191i	$0.558444\pi$
$228$	4.76621	−	1.27710i	0.315650	−	0.0845781i
$229$	−11.2266	−	3.00815i	−0.741872	−	0.198784i	−0.131962	−	0.991255i	$-0.542128\pi$
$229$	−11.2266	−	3.00815i	−0.741872	−	0.198784i	−0.609910	+	0.792471i	$0.708794\pi$
$230$			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	0.470467	−	0.882418i	$-0.344086\pi$
$233$	22.4370	−	12.9540i	1.46990	−	0.848645i	0.999430	+	0.0337727i	$0.0107522\pi$
$234$	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	−0.965375	−	0.260864i	$-0.915992\pi$
$239$	−10.8915	+	10.8915i	−0.704511	+	0.704511i	0.260864	+	0.965375i	$0.415992\pi$
$240$	−1.11968	−	0.300017i	−0.0722751	−	0.0193660i
$241$	−3.02126	−	11.2755i	−0.194616	−	0.726318i	−0.992366	−	0.123329i	$-0.960643\pi$
$241$	−3.02126	−	11.2755i	−0.194616	−	0.726318i	0.797749	−	0.602989i	$-0.206024\pi$
$242$	−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	0.528382	−	0.849007i	$-0.322799\pi$
$257$	−7.55184	−	13.0802i	−0.471071	−	0.815918i	−0.999452	+	0.0330886i	$0.989466\pi$
$258$	−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	0.296303	+	0.955094i	$0.404246\pi$
$263$	−11.0113	+	19.0721i	−0.678984	+	1.17604i	−0.975287	+	0.220941i	$0.929087\pi$
$264$	−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	−0.993158	−	0.116775i	$-0.962744\pi$
$269$	−26.0922	−	15.0643i	−1.59087	−	0.918488i	−0.597709	−	0.801713i	$-0.703922\pi$
$270$	1.23972	+	0.715753i	0.0754470	+	0.0435593i
$271$	−25.9129	−	6.94335i	−1.57410	−	0.421779i	−0.637007	−	0.770858i	$-0.719828\pi$
$271$	−25.9129	−	6.94335i	−1.57410	−	0.421779i	−0.937093	+	0.349080i	$0.886494\pi$
$272$	−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	0.434925	−	0.900467i	$-0.356775\pi$
$277$	−2.12102	−	1.22457i	−0.127440	−	0.0735775i	−0.562365	+	0.826889i	$0.690108\pi$
$278$	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	−0.973719	−	0.227754i	$-0.926862\pi$
$281$	−20.1404	−	20.1404i	−1.20147	−	1.20147i	−0.227754	−	0.973719i	$-0.573138\pi$
$282$	3.70428	+	6.41600i	0.220587	+	0.382067i
$283$	3.04663	−	5.27692i	0.181103	−	0.313680i	−0.761153	−	0.648572i	$-0.775366\pi$
$283$	3.04663	−	5.27692i	0.181103	−	0.313680i	0.942257	+	0.334892i	$0.108700\pi$
$284$	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	−0.866038	−	0.499979i	$-0.833341\pi$
$293$	−6.26592	+	6.26592i	−0.366059	+	0.366059i	0.499979	+	0.866038i	$0.333341\pi$
$294$	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	0.178135	−	0.984006i	$-0.442994\pi$
$307$	20.3624	−	20.3624i	1.16214	−	1.16214i	0.984006	−	0.178135i	$-0.0570064\pi$
$308$	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	−0.821194	−	0.570649i	$-0.806692\pi$
$311$	1.47429	−	2.55354i	0.0835991	−	0.144798i	0.904793	+	0.425851i	$0.140025\pi$
$312$	6.11113	+	1.47920i	0.345974	+	0.0837430i
$313$	10.7571	−	6.21061i	0.608027	−	0.351044i	−0.164166	−	0.986433i	$-0.552493\pi$
$313$	10.7571	−	6.21061i	0.608027	−	0.351044i	0.772193	+	0.635388i	$0.219160\pi$
$314$	−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	−0.180373	−	0.983598i	$-0.557730\pi$
$317$	−14.7489	−	3.95195i	−0.828379	−	0.221964i	−0.648007	+	0.761635i	$0.724397\pi$
$318$	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	0.648175	−	0.761491i	$-0.275532\pi$
$331$	15.0781	+	4.04016i	0.828766	+	0.222067i	0.180591	+	0.983558i	$0.442199\pi$
$332$	−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	$-0.984278\pi$
$337$		−	1.81266i		−	0.0987418i	0.998781	−	0.0493709i	$-0.0157216\pi$
$338$	−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	0.380110	−	0.924941i	$-0.375886\pi$
$347$	18.4617	−	31.9767i	0.991078	−	1.71660i	0.610968	−	0.791656i	$-0.290781\pi$
$348$	−0.106795	−	0.184974i	−0.00572479	−	0.00991562i
$349$	−19.8750	+	19.8750i	−1.06388	+	1.06388i	−0.0660671	+	0.997815i	$0.521045\pi$
$349$	−19.8750	+	19.8750i	−1.06388	+	1.06388i	−0.997815	+	0.0660671i	$0.978955\pi$
$350$	−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	0.478107	−	0.878301i	$-0.341323\pi$
$353$	25.0131	−	6.70223i	1.33131	−	0.356724i	0.853204	+	0.521578i	$0.174656\pi$
$354$	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	0.311535	+	0.950235i	$0.399157\pi$
$359$	−8.21137	+	30.6453i	−0.433380	+	1.61739i	−0.744914	+	0.667160i	$0.767510\pi$
$360$	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	−0.234848	−	0.972032i	$-0.575459\pi$
$367$	−22.8752	−	13.2070i	−1.19408	−	0.689400i	−0.959229	+	0.282632i	$0.908793\pi$
$368$	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	0.899463	−	0.436998i	$-0.143958\pi$
$373$	1.37665	+	2.38442i	0.0712801	+	0.123461i	−0.828182	+	0.560459i	$0.810625\pi$
$374$	−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	−0.556582	−	0.830793i	$-0.687887\pi$
$379$	5.33831	−	5.33831i	0.274211	−	0.274211i	0.830793	+	0.556582i	$0.187887\pi$
$380$	−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	0.536921	+	0.843633i	$0.319587\pi$
$383$	−6.84734	+	25.5546i	−0.349883	+	1.30578i	−0.886803	+	0.462147i	$0.847079\pi$
$384$	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	0.623548	−	0.781785i	$-0.285690\pi$
$389$	5.09402	+	2.94103i	0.258277	+	0.149116i	−0.365271	+	0.930901i	$0.619024\pi$
$390$	−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	0.458664	−	0.888610i	$-0.348328\pi$
$397$	8.20055	+	2.19733i	0.411574	+	0.110281i	−0.0470903	+	0.998891i	$0.514995\pi$
$398$	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	−0.0517442	+	0.998660i	$0.516478\pi$
$401$	−10.1379	+	37.8352i	−0.506263	+	1.88940i	−0.454518	+	0.890737i	$0.650189\pi$
$402$	−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	−0.212766	−	0.977103i	$-0.568247\pi$
$409$	1.85098	−	0.495968i	0.0915249	−	0.0245240i	0.304291	+	0.952579i	$0.401581\pi$
$410$	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	$-0.949939\pi$
$419$		−	6.41207i		−	0.313250i	0.987658	−	0.156625i	$-0.0500614\pi$
$420$	−2.28568	+	4.26155i	−0.111530	+	0.207942i
$421$	−5.78368	+	5.78368i	−0.281879	+	0.281879i	−0.833858	−	0.551979i	$-0.813873\pi$
$421$	−5.78368	+	5.78368i	−0.281879	+	0.281879i	0.551979	+	0.833858i	$0.313873\pi$
$422$	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	0.878322	−	0.478070i	$-0.158663\pi$
$431$	−2.51954	−	9.40305i	−0.121362	−	0.452929i	−0.999684	+	0.0251405i	$0.991997\pi$
$432$	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	0.936520	−	0.350615i	$-0.114027\pi$
$439$	3.44914	+	5.97409i	0.164619	+	0.285128i	−0.771901	+	0.635743i	$0.780694\pi$
$440$	−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	−0.998031	−	0.0627195i	$-0.980023\pi$
$443$	−11.6463	−	20.1720i	−0.553332	−	0.958400i	0.444699	−	0.895680i	$-0.353311\pi$
$444$	−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	0.409154	−	0.912465i	$-0.365824\pi$
$449$	−10.6650	−	10.6650i	−0.503312	−	0.503312i	−0.912465	+	0.409154i	$0.865824\pi$
$450$	−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	0.528350	−	0.849027i	$-0.322811\pi$
$457$	12.0014	+	3.21576i	0.561401	+	0.150427i	0.0330510	+	0.999454i	$0.489478\pi$
$458$	−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	0.974123	−	0.226019i	$-0.0725713\pi$
$461$	16.0625	+	16.0625i	0.748103	+	0.748103i	−0.226019	+	0.974123i	$0.572571\pi$
$462$	14.1293	−	4.26405i	0.657356	−	0.198382i
$463$	−4.57548	−	4.57548i	−0.212641	−	0.212641i	0.592748	−	0.805388i	$-0.298043\pi$
$463$	−4.57548	−	4.57548i	−0.212641	−	0.212641i	−0.805388	+	0.592748i	$0.798043\pi$
$464$	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	0.970261	+	0.242062i	$0.0778236\pi$
$467$	15.0139	+	26.0049i	0.694762	+	1.20336i	−0.275499	+	0.961301i	$0.588843\pi$
$468$	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	0.711572	+	0.702613i	$0.247983\pi$
$479$	9.77517	+	36.4814i	0.446639	+	1.66688i	−0.264933	+	0.964267i	$0.585350\pi$
$480$	−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	−0.976100	−	0.217321i	$-0.930268\pi$
$487$	−5.28383	−	19.7195i	−0.239433	−	0.893577i	0.736667	−	0.676256i	$-0.236399\pi$
$488$	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	$0.284466\pi$
$491$			34.5398i			1.55876i	−0.626552	+	0.779380i	$0.715534\pi$
$492$	−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	0.294728	−	0.955581i	$-0.404771\pi$
$499$	1.61236	+	0.432031i	0.0721793	+	0.0193404i	−0.222549	+	0.974922i	$0.571438\pi$
$500$	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	$-0.776530\pi$
$503$		−	28.9670i		−	1.29157i	0.763518	−	0.645787i	$-0.223470\pi$
$504$	−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	−0.687221	−	0.726448i	$-0.741170\pi$
$509$	6.11751	−	22.8308i	0.271154	−	1.01196i	0.958375	−	0.285512i	$-0.0921635\pi$
$510$		−	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	0.314165	−	0.949369i	$-0.398276\pi$
$521$	−8.01013	−	4.62465i	−0.350930	−	0.202610i	−0.665095	+	0.746759i	$0.731609\pi$
$522$	−0.0432960	−	0.161583i	−0.00189501	−	0.00707229i
$523$	23.8793	−	13.7867i	1.04417	−	0.602852i	0.123158	−	0.992387i	$-0.460698\pi$
$523$	23.8793	−	13.7867i	1.04417	−	0.602852i	0.921011	+	0.389536i	$0.127364\pi$
$524$	−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	−0.901920	−	0.431902i	$-0.857843\pi$
$541$	2.21236	−	8.25664i	0.0951167	−	0.354981i	0.997037	+	0.0769218i	$0.0245092\pi$
$542$	−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	−0.606227	−	0.795291i	$-0.707318\pi$
$557$	−17.3133	+	4.63910i	−0.733590	+	0.196565i	−0.127362	+	0.991856i	$0.540651\pi$
$558$	−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	−0.788509	−	0.615024i	$-0.789146\pi$
$563$	3.28323	−	5.68672i	0.138372	−	0.239667i	0.926880	+	0.375357i	$0.122480\pi$
$564$	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	−0.917733	−	0.397197i	$-0.869983\pi$
$569$	−24.6318	+	14.2212i	−1.03262	+	0.596182i	−0.114884	+	0.993379i	$0.536650\pi$
$570$	−0.653792	−	2.43998i	−0.0273843	−	0.102200i
$571$	19.7578	+	11.4072i	0.826839	+	0.477376i	0.852769	−	0.522288i	$-0.174921\pi$
$571$	19.7578	+	11.4072i	0.826839	+	0.477376i	−0.0259302	+	0.999664i	$0.508255\pi$
$572$	−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	−0.974973	−	0.222324i	$-0.928636\pi$
$577$	−41.0315	+	10.9943i	−1.70816	+	0.457701i	−0.733189	+	0.680025i	$0.761969\pi$
$578$	−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	0.495743	−	0.868469i	$-0.334896\pi$
$587$	−9.03045	−	9.03045i	−0.372727	−	0.372727i	−0.868469	+	0.495743i	$0.834896\pi$
$588$	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	−0.210654	−	0.977561i	$-0.567559\pi$
$593$	−21.4748	−	5.75416i	−0.881865	−	0.236295i	−0.671212	+	0.741266i	$0.734226\pi$
$594$		−	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	0.428272	+	0.903650i	$0.359123\pi$
$599$	−13.9125	+	24.0971i	−0.568448	+	0.984581i	−0.996720	+	0.0809310i	$0.974211\pi$
$600$	−2.06389	+	7.70254i	−0.0842580	+	0.314455i
$601$			17.9740i			0.733174i	0.930384	+	0.366587i	$0.119474\pi$
$601$			17.9740i			0.733174i	−0.930384	+	0.366587i	$0.880526\pi$
$602$	−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	−0.248606	−	0.968605i	$-0.579972\pi$
$607$	11.4792	−	6.62754i	0.465928	−	0.269004i	0.714534	+	0.699601i	$0.246639\pi$
$608$	−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	0.995181	−	0.0980538i	$-0.0312617\pi$
$613$	2.08722	+	7.78962i	0.0843021	+	0.314620i	−0.910879	+	0.412673i	$0.864595\pi$
$614$	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	−0.918180	−	0.396163i	$-0.870341\pi$
$617$	−12.9666	+	12.9666i	−0.522016	+	0.522016i	0.396163	+	0.918180i	$0.370341\pi$
$618$	−9.18678	+	34.2855i	−0.369547	+	1.37917i
$619$	−8.01277	−	29.9041i	−0.322061	−	1.20195i	−0.917234	−	0.398349i	$-0.869583\pi$
$619$	−8.01277	−	29.9041i	−0.322061	−	1.20195i	0.595173	−	0.803597i	$-0.297083\pi$
$620$	−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	0.999798	+	0.0200749i	$0.00639046\pi$
$631$	25.6189	+	25.6189i	1.01987	+	1.01987i	0.0200749	+	0.999798i	$0.493610\pi$
$632$	−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	−0.334214	−	0.942497i	$-0.608471\pi$
$641$	−33.3576	−	19.2590i	−1.31755	−	0.760687i	−0.983334	+	0.181811i	$0.941804\pi$
$642$	9.93161	−	37.0653i	0.391970	−	1.46285i
$643$	−19.0170	−	19.0170i	−0.749958	−	0.749958i	0.224513	−	0.974471i	$-0.427921\pi$
$643$	−19.0170	−	19.0170i	−0.749958	−	0.749958i	−0.974471	+	0.224513i	$0.927921\pi$
$644$	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	0.242074	−	0.970258i	$-0.422172\pi$
$647$	24.4519	−	42.3520i	0.961305	−	1.66503i	0.719231	−	0.694771i	$-0.244494\pi$
$648$	−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	0.941493	+	0.337032i	$0.109423\pi$
$653$	19.4880	+	33.7542i	0.762625	+	1.32090i	−0.178868	+	0.983873i	$0.557244\pi$
$654$	−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	0.933633	−	0.358230i	$-0.116620\pi$
$661$	−1.38916	−	5.18442i	−0.0540321	−	0.201650i	−0.987665	+	0.156580i	$0.949953\pi$
$662$	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	$0.282759\pi$
$673$			40.2628i			1.55202i	−0.630722	+	0.776008i	$0.717241\pi$
$674$	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	0.0159443	−	0.999873i	$-0.494925\pi$
$677$	23.1527	−	13.3672i	0.889832	−	0.513745i	0.873887	+	0.486128i	$0.161591\pi$
$678$	−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	−0.810665	−	0.585510i	$-0.800894\pi$
$683$	−31.8830	+	8.54301i	−1.21997	+	0.326889i	−0.409302	+	0.912399i	$0.634228\pi$
$684$	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	−0.788456	−	0.615091i	$-0.789119\pi$
$691$	5.30765	−	19.8084i	0.201913	−	0.753548i	0.990369	−	0.138457i	$-0.0442141\pi$
$692$			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	$0.314383\pi$
$701$			44.2019i			1.66948i	−0.550641	+	0.834742i	$0.685617\pi$
$702$	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	−0.417490	−	0.908681i	$-0.637090\pi$
$709$	10.6084	−	39.5912i	0.398408	−	1.48688i	0.815898	−	0.578196i	$-0.196243\pi$
$710$	−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	0.837963	−	0.545727i	$-0.183746\pi$
$719$	−1.43809	−	2.49085i	−0.0536317	−	0.0928929i	−0.891595	+	0.452834i	$0.850413\pi$
$720$	−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	−0.436546	−	0.899682i	$-0.643798\pi$
$733$	10.5955	−	39.5431i	0.391355	−	1.46056i	0.827901	−	0.560875i	$-0.189535\pi$
$734$	−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	0.284490	−	0.958679i	$-0.408176\pi$
$739$	27.4620	−	7.35841i	1.01020	−	0.270684i	0.725715	+	0.687995i	$0.241509\pi$
$740$	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	−0.357823	−	0.933789i	$-0.616481\pi$
$743$	15.6997	−	15.6997i	0.575966	−	0.575966i	0.933789	+	0.357823i	$0.116481\pi$
$744$	−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	−0.238713	−	0.971090i	$-0.576725\pi$
$751$	13.2341	−	7.64073i	0.482920	−	0.278814i	0.721633	+	0.692276i	$0.243392\pi$
$752$	−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	−0.194368	−	0.980929i	$-0.562266\pi$
$761$	−23.5355	−	6.30631i	−0.853160	−	0.228603i	−0.658792	+	0.752325i	$0.728932\pi$
$762$	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	0.914225	+	0.405206i	$0.132800\pi$
$769$	36.5890	+	36.5890i	1.31943	+	1.31943i	0.405206	+	0.914225i	$0.367200\pi$
$770$	−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	0.446284	−	0.894891i	$-0.352747\pi$
$773$	35.5939	−	9.53735i	1.28022	−	0.343035i	0.833939	+	0.551857i	$0.186080\pi$
$774$	−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	0.987133	−	0.159901i	$-0.0511176\pi$
$787$	1.46720	+	5.47568i	0.0523002	+	0.195187i	−0.934833	+	0.355088i	$0.884451\pi$
$788$	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	0.244751	+	0.969586i	$0.421294\pi$
$809$	−20.4024	+	35.3380i	−0.717310	+	1.24242i	−0.962062	+	0.272832i	$0.912040\pi$
$810$	0.715753	+	1.23972i	0.0251490	+	0.0435593i
$811$	15.4548	+	15.4548i	0.542690	+	0.542690i	0.924317	−	0.381626i	$-0.124636\pi$
$811$	15.4548	+	15.4548i	0.542690	+	0.542690i	−0.381626	+	0.924317i	$0.624636\pi$
$812$	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	0.105206	−	0.994450i	$-0.466450\pi$
$821$	−8.62197	−	2.31025i	−0.300909	−	0.0806283i	−0.406114	+	0.913822i	$0.633117\pi$
$822$	−2.58089	−	1.49008i	−0.0900188	−	0.0519724i
$823$	−15.7750	−	9.10768i	−0.549881	−	0.317474i	0.199193	−	0.979960i	$-0.436168\pi$
$823$	−15.7750	−	9.10768i	−0.549881	−	0.317474i	−0.749074	+	0.662487i	$0.769501\pi$
$824$	−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	0.982545	−	0.186025i	$-0.0595605\pi$
$827$	22.9060	+	22.9060i	0.796520	+	0.796520i	−0.186025	+	0.982545i	$0.559561\pi$
$828$	−7.36143	−	12.7504i	−0.255827	−	0.443106i
$829$	−14.1448	+	24.4995i	−0.491268	+	0.850901i	−0.999949	−	0.0100536i	$-0.996800\pi$
$829$	−14.1448	+	24.4995i	−0.491268	+	0.850901i	0.508681	+	0.860955i	$0.330133\pi$
$830$	−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	−0.926642	−	0.375945i	$-0.877318\pi$
$839$	−15.9512	+	15.9512i	−0.550698	+	0.550698i	0.375945	+	0.926642i	$0.377318\pi$
$840$	−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	−0.976283	−	0.216499i	$-0.930536\pi$
$853$	−22.1904	+	22.1904i	−0.759784	+	0.759784i	0.216499	+	0.976283i	$0.430536\pi$
$854$	−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	−0.871195	−	0.490938i	$-0.836654\pi$
$857$	−0.305420	+	0.529004i	−0.0104330	+	0.0180704i	0.860762	+	0.509008i	$0.169988\pi$
$858$	−17.1685	+	10.4769i	−0.586122	+	0.357676i
$859$	−22.0653	+	12.7394i	−0.752858	+	0.434663i	−0.826726	−	0.562605i	$-0.809799\pi$
$859$	−22.0653	+	12.7394i	−0.752858	+	0.434663i	0.0738678	+	0.997268i	$0.476466\pi$
$860$	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	0.376396	−	0.926459i	$-0.377163\pi$
$863$	7.02503	+	1.88235i	0.239135	+	0.0640760i	−0.137261	+	0.990535i	$0.543830\pi$
$864$	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	−0.0891479	−	0.996018i	$-0.528414\pi$
$877$	−19.6745	−	5.27177i	−0.664361	−	0.178015i	−0.575214	+	0.818003i	$0.695081\pi$
$878$	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	$-0.887219\pi$
$883$		−	20.6192i		−	0.693891i	0.937885	−	0.346945i	$-0.112781\pi$
$884$	−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	−0.747171	−	0.664632i	$-0.768588\pi$
$887$	−16.2365	+	9.37414i	−0.545168	+	0.314753i	0.202003	+	0.979385i	$0.435255\pi$
$888$	−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	0.629422	−	0.777064i	$-0.283292\pi$
$907$	8.16685	+	4.71513i	0.271176	+	0.156563i	−0.358246	+	0.933627i	$0.616625\pi$
$908$	−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	0.997483	+	0.0709024i	$0.0225879\pi$
$919$	16.9808	+	29.4116i	0.560145	+	0.970199i	−0.437338	+	0.899297i	$0.644079\pi$
$920$	−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	−0.999732	−	0.0231532i	$-0.992629\pi$
$929$	−3.72954	+	13.9188i	−0.122362	+	0.456662i	0.877370	+	0.479815i	$0.159296\pi$
$930$	−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	$0.0295601\pi$
$937$			5.67717i			0.185465i	−0.995691	+	0.0927325i	$0.970440\pi$
$938$	−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	−0.415942	−	0.909391i	$-0.636548\pi$
$941$	−9.86113	+	2.64228i	−0.321464	+	0.0861360i	0.0944787	+	0.995527i	$0.469882\pi$
$942$	−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	−0.639461	−	0.768823i	$-0.720843\pi$
$947$	9.19324	−	34.3096i	0.298740	−	1.11491i	0.938201	−	0.346090i	$-0.112491\pi$
$948$	−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	$-0.871226\pi$
$953$		−	24.3020i		−	0.787219i	0.919278	−	0.393609i	$-0.128774\pi$
$954$	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	0.103880	−	0.994590i	$-0.466874\pi$
$967$	34.1587	−	34.1587i	1.09847	−	1.09847i	0.994590	−	0.103880i	$-0.0331259\pi$
$968$	−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	−0.823182	−	0.567777i	$-0.807803\pi$
$971$	−23.1545	+	13.3683i	−0.743064	+	0.429008i	0.0801184	+	0.996785i	$0.474470\pi$
$972$	−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	0.989810	+	0.142392i	$0.0454792\pi$
$977$	6.37034	+	23.7744i	0.203805	+	0.760612i	−0.786005	+	0.618220i	$0.787854\pi$
$978$	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	0.970863	−	0.239634i	$-0.0770273\pi$
$983$	0.321501	+	1.19986i	0.0102543	+	0.0382695i	−0.960609	+	0.277903i	$0.910361\pi$
$984$	−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	−0.996734	−	0.0807570i	$-0.974266\pi$
$991$	−13.4870	+	23.3602i	−0.428429	+	0.742061i	0.568305	+	0.822818i	$0.307600\pi$
$992$	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	0.888696	−	0.458498i	$-0.151612\pi$
$997$	29.5536	+	17.0628i	0.935973	+	0.540384i	0.0472772	+	0.998882i	$0.484946\pi$
$998$	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.31.9	yes	36
3.2	odd	2		819.2.fn.g.577.1		36
7.5	odd	6		273.2.bz.a.187.1	yes	36
13.8	odd	4		273.2.bz.a.73.1	✓	36
21.5	even	6		819.2.fn.f.460.9		36
39.8	even	4		819.2.fn.f.73.9		36
91.47	even	12	inner	273.2.bz.b.229.9	yes	36
273.47	odd	12		819.2.fn.g.775.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.1	✓	36	13.8	odd	4
273.2.bz.a.187.1	yes	36	7.5	odd	6
273.2.bz.b.31.9	yes	36	1.1	even	1	trivial
273.2.bz.b.229.9	yes	36	91.47	even	12	inner
819.2.fn.f.73.9		36	39.8	even	4
819.2.fn.f.460.9		36	21.5	even	6
819.2.fn.g.577.1		36	3.2	odd	2
819.2.fn.g.775.1		36	273.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.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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