LMFDB - Embedded newform 322.2.g.b.45.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(45,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("322.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 $ x^16 + 12x^14 + 73x^12 + 312x^10 + 1045x^8 + 2808x^6 + 5913x^4 + 8748*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.3
Root			$-0.452119 - 1.67200i$ of defining polynomial
Character	$\chi$	$=$	322.45
Dual form			322.2.g.b.229.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.07743 - 0.622057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.668984 - 1.15871i) q^{5} -1.24411i q^{6} +(-2.09536 + 1.61539i) q^{7} -1.00000 q^{8} +(-0.726090 - 1.25762i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.07743 - 0.622057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.668984 - 1.15871i) q^{5} -1.24411i q^{6} +(-2.09536 + 1.61539i) q^{7} -1.00000 q^{8} +(-0.726090 - 1.25762i) q^{9} +(0.668984 - 1.15871i) q^{10} +(-5.22660 - 3.01758i) q^{11} +(1.07743 - 0.622057i) q^{12} +6.52207i q^{13} +(-2.44664 - 1.00694i) q^{14} +1.66459i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.568151 + 0.984066i) q^{17} +(0.726090 - 1.25762i) q^{18} +(-1.77489 - 3.07420i) q^{19} +1.33797 q^{20} +(3.26247 - 0.437039i) q^{21} -6.03516i q^{22} +(-1.35675 - 4.59992i) q^{23} +(1.07743 + 0.622057i) q^{24} +(1.60492 - 2.77980i) q^{25} +(-5.64828 + 3.26103i) q^{26} +5.53902i q^{27} +(-0.351285 - 2.62233i) q^{28} -3.18236 q^{29} +(-1.44157 + 0.832293i) q^{30} +(2.80352 + 1.61862i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.75422 + 6.50249i) q^{33} -1.13630 q^{34} +(3.27353 + 1.34726i) q^{35} +1.45218 q^{36} +(-5.10738 + 2.94875i) q^{37} +(1.77489 - 3.07420i) q^{38} +(4.05710 - 7.02710i) q^{39} +(0.668984 + 1.15871i) q^{40} -0.928266i q^{41} +(2.00972 + 2.60687i) q^{42} -0.303546i q^{43} +(5.22660 - 3.01758i) q^{44} +(-0.971485 + 1.68266i) q^{45} +(3.30527 - 3.47494i) q^{46} +(-0.243918 + 0.140826i) q^{47} +1.24411i q^{48} +(1.78106 - 6.76962i) q^{49} +3.20984 q^{50} +(1.22429 - 0.706844i) q^{51} +(-5.64828 - 3.26103i) q^{52} +(11.3667 + 6.56256i) q^{53} +(-4.79693 + 2.76951i) q^{54} +8.07486i q^{55} +(2.09536 - 1.61539i) q^{56} +4.41633i q^{57} +(-1.59118 - 2.75600i) q^{58} +(-1.10083 - 0.635567i) q^{59} +(-1.44157 - 0.832293i) q^{60} +(7.00107 + 12.1262i) q^{61} +3.23723i q^{62} +(3.55297 + 1.46226i) q^{63} +1.00000 q^{64} +(7.55722 - 4.36316i) q^{65} +(-3.75422 + 6.50249i) q^{66} +(-3.57337 - 2.06308i) q^{67} +(-0.568151 - 0.984066i) q^{68} +(-1.39960 + 5.80009i) q^{69} +(0.470008 + 3.50859i) q^{70} -4.02749 q^{71} +(0.726090 + 1.25762i) q^{72} +(-11.1001 - 6.40863i) q^{73} +(-5.10738 - 2.94875i) q^{74} +(-3.45839 + 1.99670i) q^{75} +3.54978 q^{76} +(15.8262 - 2.12006i) q^{77} +8.11420 q^{78} +(-10.6180 + 6.13032i) q^{79} +(-0.668984 + 1.15871i) q^{80} +(1.26732 - 2.19506i) q^{81} +(0.803902 - 0.464133i) q^{82} +5.99365 q^{83} +(-1.25275 + 3.04391i) q^{84} +1.52033 q^{85} +(0.262878 - 0.151773i) q^{86} +(3.42878 + 1.97961i) q^{87} +(5.22660 + 3.01758i) q^{88} +(-4.71966 - 8.17470i) q^{89} -1.94297 q^{90} +(-10.5357 - 13.6661i) q^{91} +(4.66202 + 1.12497i) q^{92} +(-2.01374 - 3.48790i) q^{93} +(-0.243918 - 0.140826i) q^{94} +(-2.37474 + 4.11318i) q^{95} +(-1.07743 + 0.622057i) q^{96} +14.1845 q^{97} +(6.75320 - 1.84237i) q^{98} +8.76414i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9	$ 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+O(q^{100}) $ 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9 + 6 * q^12 - 8 * q^16 - 10 * q^18 + 8 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^29 + 12 * q^31 + 8 * q^32 - 20 * q^36 - 2 * q^39 - 8 * q^46 - 6 * q^47 - 18 * q^49 + 4 * q^50 - 6 * q^52 + 18 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 12 * q^70 - 52 * q^71 - 10 * q^72 + 24 * q^73 + 30 * q^77 - 4 * q^78 - 20 * q^81 + 54 * q^82 + 80 * q^85 + 54 * q^87 - 16 * q^92 - 26 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.07743	−	0.622057i	−0.622057	−	0.359145i	0.155612	−	0.987818i	$-0.450265\pi$
$3$	−1.07743	−	0.622057i	−0.622057	−	0.359145i	−0.777670	+	0.628673i	$0.783598\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.668984	−	1.15871i	−0.299179	−	0.518193i	0.676769	−	0.736195i	$-0.263379\pi$
$5$	−0.668984	−	1.15871i	−0.299179	−	0.518193i	−0.975948	+	0.218002i	$0.930046\pi$
$6$		−	1.24411i		−	0.507908i
$7$	−2.09536	+	1.61539i	−0.791971	+	0.610558i
$7$	−2.09536	+	1.61539i	−0.791971	+	0.610558i
$8$	−1.00000			−0.353553
$9$	−0.726090	−	1.25762i	−0.242030	−	0.419208i
$10$	0.668984	−	1.15871i	0.211551	−	0.366418i
$11$	−5.22660	−	3.01758i	−1.57588	−	0.909835i	−0.995425	−	0.0955426i	$-0.969541\pi$
$11$	−5.22660	−	3.01758i	−1.57588	−	0.909835i	−0.580455	−	0.814292i	$-0.697125\pi$
$12$	1.07743	−	0.622057i	0.311029	−	0.179572i
$13$			6.52207i			1.80890i	0.426583	+	0.904448i	$0.359717\pi$
$13$			6.52207i			1.80890i	−0.426583	+	0.904448i	$0.640283\pi$
$14$	−2.44664	−	1.00694i	−0.653893	−	0.269117i
$15$			1.66459i			0.429794i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.568151	+	0.984066i	−0.137797	+	0.238671i	−0.926662	−	0.375895i	$-0.877335\pi$
$17$	−0.568151	+	0.984066i	−0.137797	+	0.238671i	0.788866	+	0.614566i	$0.210669\pi$
$18$	0.726090	−	1.25762i	0.171141	−	0.296425i
$19$	−1.77489	−	3.07420i	−0.407187	−	0.705269i	0.587386	−	0.809307i	$-0.300157\pi$
$19$	−1.77489	−	3.07420i	−0.407187	−	0.705269i	−0.994573	+	0.104038i	$0.966824\pi$
$20$	1.33797			0.299179
$21$	3.26247	−	0.437039i	0.711930	−	0.0953697i
$22$		−	6.03516i		−	1.28670i
$23$	−1.35675	−	4.59992i	−0.282903	−	0.959149i
$23$	−1.35675	−	4.59992i	−0.282903	−	0.959149i
$24$	1.07743	+	0.622057i	0.219930	+	0.126977i
$25$	1.60492	−	2.77980i	0.320984	−	0.555961i
$26$	−5.64828	+	3.26103i	−1.10772	+	0.639541i
$27$			5.53902i			1.06598i
$28$	−0.351285	−	2.62233i	−0.0663866	−	0.495573i
$29$	−3.18236			−0.590948			−0.295474	−	0.955351i	$-0.595478\pi$
$29$	−3.18236			−0.590948			−0.295474	+	0.955351i	$0.595478\pi$
$30$	−1.44157	+	0.832293i	−0.263194	+	0.151955i
$31$	2.80352	+	1.61862i	0.503528	+	0.290712i	0.730169	−	0.683266i	$-0.239441\pi$
$31$	2.80352	+	1.61862i	0.503528	+	0.290712i	−0.226641	+	0.973978i	$0.572775\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.75422	+	6.50249i	0.653525	+	1.13194i
$34$	−1.13630			−0.194874
$35$	3.27353	+	1.34726i	0.553328	+	0.227728i
$36$	1.45218			0.242030
$37$	−5.10738	+	2.94875i	−0.839649	+	0.484771i	−0.857145	−	0.515076i	$-0.827764\pi$
$37$	−5.10738	+	2.94875i	−0.839649	+	0.484771i	0.0174962	+	0.999847i	$0.494431\pi$
$38$	1.77489	−	3.07420i	0.287925	−	0.498701i
$39$	4.05710	−	7.02710i	0.649656	−	1.12524i
$40$	0.668984	+	1.15871i	0.105776	+	0.183209i
$41$		−	0.928266i		−	0.144971i	−0.997369	−	0.0724854i	$-0.976907\pi$
$41$		−	0.928266i		−	0.144971i	0.997369	−	0.0724854i	$-0.0230931\pi$
$42$	2.00972	+	2.60687i	0.310107	+	0.402248i
$43$		−	0.303546i		−	0.0462903i	−0.999732	−	0.0231451i	$-0.992632\pi$
$43$		−	0.303546i		−	0.0462903i	0.999732	−	0.0231451i	$-0.00736798\pi$
$44$	5.22660	−	3.01758i	0.787940	−	0.454917i
$45$	−0.971485	+	1.68266i	−0.144820	+	0.250836i
$46$	3.30527	−	3.47494i	0.487335	−	0.512352i
$47$	−0.243918	+	0.140826i	−0.0355792	+	0.0205416i	−0.517684	−	0.855572i	$-0.673206\pi$
$47$	−0.243918	+	0.140826i	−0.0355792	+	0.0205416i	0.482105	+	0.876113i	$0.339872\pi$
$48$			1.24411i			0.179572i
$49$	1.78106	−	6.76962i	0.254437	−	0.967089i
$50$	3.20984			0.453940
$51$	1.22429	−	0.706844i	0.171435	−	0.0989780i
$52$	−5.64828	−	3.26103i	−0.783275	−	0.452224i
$53$	11.3667	+	6.56256i	1.56133	+	0.901437i	0.997123	+	0.0758061i	$0.0241530\pi$
$53$	11.3667	+	6.56256i	1.56133	+	0.901437i	0.564211	+	0.825630i	$0.309180\pi$
$54$	−4.79693	+	2.76951i	−0.652780	+	0.376883i
$55$			8.07486i			1.08881i
$56$	2.09536	−	1.61539i	0.280004	−	0.215865i
$57$			4.41633i			0.584957i
$58$	−1.59118	−	2.75600i	−0.208932	−	0.361881i
$59$	−1.10083	−	0.635567i	−0.143316	−	0.0827438i	0.426627	−	0.904428i	$-0.359702\pi$
$59$	−1.10083	−	0.635567i	−0.143316	−	0.0827438i	−0.569944	+	0.821684i	$0.693035\pi$
$60$	−1.44157	−	0.832293i	−0.186106	−	0.107449i
$61$	7.00107	+	12.1262i	0.896396	+	1.55260i	0.832068	+	0.554674i	$0.187157\pi$
$61$	7.00107	+	12.1262i	0.896396	+	1.55260i	0.0643281	+	0.997929i	$0.479510\pi$
$62$			3.23723i			0.411129i
$63$	3.55297	+	1.46226i	0.447632	+	0.184227i
$64$	1.00000			0.125000
$65$	7.55722	−	4.36316i	0.937357	−	0.541183i
$66$	−3.75422	+	6.50249i	−0.462112	+	0.800402i
$67$	−3.57337	−	2.06308i	−0.436556	−	0.252046i	0.265580	−	0.964089i	$-0.414437\pi$
$67$	−3.57337	−	2.06308i	−0.436556	−	0.252046i	−0.702136	+	0.712043i	$0.747770\pi$
$68$	−0.568151	−	0.984066i	−0.0688984	−	0.119335i
$69$	−1.39960	+	5.80009i	−0.168492	+	0.698248i
$70$	0.470008	+	3.50859i	0.0561767	+	0.419357i
$71$	−4.02749			−0.477975			−0.238987	−	0.971023i	$-0.576815\pi$
$71$	−4.02749			−0.477975			−0.238987	+	0.971023i	$0.576815\pi$
$72$	0.726090	+	1.25762i	0.0855705	+	0.148212i
$73$	−11.1001	−	6.40863i	−1.29917	−	0.750074i	−0.318906	−	0.947786i	$-0.603315\pi$
$73$	−11.1001	−	6.40863i	−1.29917	−	0.750074i	−0.980260	+	0.197713i	$0.936649\pi$
$74$	−5.10738	−	2.94875i	−0.593721	−	0.342785i
$75$	−3.45839	+	1.99670i	−0.399341	+	0.230560i
$76$	3.54978			0.407187
$77$	15.8262	−	2.12006i	1.80356	−	0.241603i
$78$	8.11420			0.918752
$79$	−10.6180	+	6.13032i	−1.19462	+	0.689715i	−0.959351	−	0.282215i	$-0.908931\pi$
$79$	−10.6180	+	6.13032i	−1.19462	+	0.689715i	−0.235270	+	0.971930i	$0.575597\pi$
$80$	−0.668984	+	1.15871i	−0.0747947	+	0.129548i
$81$	1.26732	−	2.19506i	0.140813	−	0.243896i
$82$	0.803902	−	0.464133i	0.0887761	−	0.0512549i
$83$	5.99365			0.657889			0.328944	−	0.944349i	$-0.393307\pi$
$83$	5.99365			0.657889			0.328944	+	0.944349i	$0.393307\pi$
$84$	−1.25275	+	3.04391i	−0.136686	+	0.332117i
$85$	1.52033			0.164903
$86$	0.262878	−	0.151773i	0.0283469	−	0.0163661i
$87$	3.42878	+	1.97961i	0.367604	+	0.212236i
$88$	5.22660	+	3.01758i	0.557158	+	0.321675i
$89$	−4.71966	−	8.17470i	−0.500283	−	0.866516i	−1.00000		0.000327275i	$-0.999896\pi$
$89$	−4.71966	−	8.17470i	−0.500283	−	0.866516i	0.499717	−	0.866189i	$-0.333438\pi$
$90$	−1.94297			−0.204807
$91$	−10.5357	−	13.6661i	−1.10444	−	1.43259i
$92$	4.66202	+	1.12497i	0.486049	+	0.117287i
$93$	−2.01374	−	3.48790i	−0.208815	−	0.361679i
$94$	−0.243918	−	0.140826i	−0.0251583	−	0.0145251i
$95$	−2.37474	+	4.11318i	−0.243644	+	0.422003i
$96$	−1.07743	+	0.622057i	−0.109965	+	0.0634884i
$97$	14.1845			1.44022			0.720109	−	0.693861i	$-0.244092\pi$
$97$	14.1845			1.44022			0.720109	+	0.693861i	$0.244092\pi$
$98$	6.75320	−	1.84237i	0.682176	−	0.186107i
$99$			8.76414i			0.880829i
$100$	1.60492	+	2.77980i	0.160492	+	0.277980i
$101$	−8.86258	−	5.11681i	−0.881860	−	0.509142i	−0.0105887	−	0.999944i	$-0.503371\pi$
$101$	−8.86258	−	5.11681i	−0.881860	−	0.509142i	−0.871271	+	0.490802i	$0.836704\pi$
$102$	1.22429	+	0.706844i	0.121223	+	0.0699880i
$103$	−6.03001	−	10.4443i	−0.594154	−	1.02911i	−0.993666	−	0.112377i	$-0.964154\pi$
$103$	−6.03001	−	10.4443i	−0.594154	−	1.02911i	0.399511	−	0.916728i	$-0.369180\pi$
$104$		−	6.52207i		−	0.639541i
$105$	−2.68895	−	3.48790i	−0.262414	−	0.340385i
$106$			13.1251i			1.27482i
$107$	−7.66359	+	4.42458i	−0.740867	+	0.427740i	−0.822385	−	0.568932i	$-0.807357\pi$
$107$	−7.66359	+	4.42458i	−0.740867	+	0.427740i	0.0815172	+	0.996672i	$0.474023\pi$
$108$	−4.79693	−	2.76951i	−0.461585	−	0.266496i
$109$	−6.67380	−	3.85312i	−0.639234	−	0.369062i	0.145086	−	0.989419i	$-0.453654\pi$
$109$	−6.67380	−	3.85312i	−0.639234	−	0.369062i	−0.784319	+	0.620357i	$0.786988\pi$
$110$	−6.99303	+	4.03743i	−0.666759	+	0.384954i
$111$	7.33716			0.696413
$112$	2.44664	+	1.00694i	0.231186	+	0.0951471i
$113$		−	8.89491i		−	0.836762i	−0.908272	−	0.418381i	$-0.862598\pi$
$113$		−	8.89491i		−	0.836762i	0.908272	−	0.418381i	$-0.137402\pi$
$114$	−3.82465	+	2.20816i	−0.358212	+	0.206814i
$115$	−4.42234	+	4.64936i	−0.412386	+	0.433555i
$116$	1.59118	−	2.75600i	0.147737	−	0.255888i
$117$	8.20231	−	4.73561i	0.758304	−	0.437807i
$118$		−	1.27113i		−	0.117017i
$119$	−0.399166	−	2.97975i	−0.0365914	−	0.273154i
$120$		−	1.66459i		−	0.151955i
$121$	12.7116	+	22.0171i	1.15560	+	2.00156i
$122$	−7.00107	+	12.1262i	−0.633848	+	1.09786i
$123$	−0.577435	+	1.00015i	−0.0520655	+	0.0901801i
$124$	−2.80352	+	1.61862i	−0.251764	+	0.145356i
$125$	−10.9845			−0.982484
$126$	0.510129	+	3.80809i	0.0454459	+	0.339252i
$127$	−11.4514			−1.01615			−0.508075	−	0.861313i	$-0.669643\pi$
$127$	−11.4514			−1.01615			−0.508075	+	0.861313i	$0.669643\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.188823	+	0.327051i	−0.0166249	+	0.0287952i
$130$	7.55722	+	4.36316i	0.662812	+	0.382675i
$131$	−6.21988	+	3.59105i	−0.543433	+	0.313751i	−0.746469	−	0.665420i	$-0.768252\pi$
$131$	−6.21988	+	3.59105i	−0.543433	+	0.313751i	0.203036	+	0.979171i	$0.434919\pi$
$132$	−7.50843			−0.653525
$133$	8.68504	+	3.57442i	0.753089	+	0.309941i
$134$		−	4.12617i		−	0.356447i
$135$	6.41814	−	3.70552i	0.552386	−	0.318920i
$136$	0.568151	−	0.984066i	0.0487185	−	0.0843829i
$137$	−3.87856	−	2.23929i	−0.331368	−	0.191315i	0.325080	−	0.945686i	$-0.394609\pi$
$137$	−3.87856	−	2.23929i	−0.331368	−	0.191315i	−0.656448	+	0.754371i	$0.727942\pi$
$138$	−5.72282	+	1.68796i	−0.487159	+	0.143688i
$139$			9.07132i			0.769419i	0.923038	+	0.384709i	$0.125698\pi$
$139$			9.07132i			0.769419i	−0.923038	+	0.384709i	$0.874302\pi$
$140$	−2.80352	+	2.16133i	−0.236941	+	0.182666i
$141$	0.350408			0.0295097
$142$	−2.01374	−	3.48790i	−0.168990	−	0.292698i
$143$	19.6809	−	34.0883i	1.64580	−	2.85060i
$144$	−0.726090	+	1.25762i	−0.0605075	+	0.104802i
$145$	2.12895	+	3.68744i	0.176799	+	0.306225i
$146$		−	12.8173i		−	1.06076i
$147$	−6.13007	+	6.18591i	−0.505600	+	0.510205i
$148$		−	5.89750i		−	0.484771i
$149$	15.4017	−	8.89220i	1.26176	−	0.728478i	0.288345	−	0.957526i	$-0.406895\pi$
$149$	15.4017	−	8.89220i	1.26176	−	0.728478i	0.973415	+	0.229049i	$0.0735616\pi$
$150$	−3.45839	−	1.99670i	−0.282377	−	0.163030i
$151$	9.74158	−	16.8729i	0.792759	−	1.37310i	−0.131494	−	0.991317i	$-0.541977\pi$
$151$	9.74158	−	16.8729i	0.792759	−	1.37310i	0.924253	−	0.381782i	$-0.124689\pi$
$152$	1.77489	+	3.07420i	0.143962	+	0.249350i
$153$	1.65011			0.133404
$154$	9.74911	+	12.6458i	0.785606	+	1.01903i
$155$		−	4.33131i		−	0.347899i
$156$	4.05710	+	7.02710i	0.324828	+	0.562619i
$157$	−4.10550	+	7.11094i	−0.327655	+	0.567515i	−0.982046	−	0.188642i	$-0.939592\pi$
$157$	−4.10550	+	7.11094i	−0.327655	+	0.567515i	0.654391	+	0.756156i	$0.272925\pi$
$158$	−10.6180	−	6.13032i	−0.844725	−	0.487702i
$159$	−8.16457	−	14.1415i	−0.647493	−	1.12149i
$160$	−1.33797			−0.105776
$161$	10.2735	+	7.44680i	0.809667	+	0.586890i
$162$	2.53464			0.199140
$163$	−7.48801	−	12.9696i	−0.586506	−	1.01586i	−0.994686	−	0.102957i	$-0.967170\pi$
$163$	−7.48801	−	12.9696i	−0.586506	−	1.01586i	0.408180	−	0.912902i	$-0.366164\pi$
$164$	0.803902	+	0.464133i	0.0627742	+	0.0362427i
$165$	5.02302	−	8.70013i	0.391042	−	0.677304i
$166$	2.99683	+	5.19065i	0.232599	+	0.402873i
$167$		−	14.5565i		−	1.12642i	−0.826315	−	0.563208i	$-0.809567\pi$
$167$		−	14.5565i		−	1.12642i	0.826315	−	0.563208i	$-0.190433\pi$
$168$	−3.26247	+	0.437039i	−0.251705	+	0.0337183i
$169$	−29.5374			−2.27211
$170$	0.760167	+	1.31665i	0.0583022	+	0.100982i
$171$	−2.57746	+	4.46429i	−0.197103	+	0.341392i
$172$	0.262878	+	0.151773i	0.0200443	+	0.0115726i
$173$	0.143633	−	0.0829263i	0.0109202	−	0.00630477i	−0.494530	−	0.869161i	$-0.664660\pi$
$173$	0.143633	−	0.0829263i	0.0109202	−	0.00630477i	0.505450	+	0.862856i	$0.331326\pi$
$174$			3.95921i			0.300147i
$175$	1.12757	+	8.41725i	0.0852362	+	0.636284i
$176$			6.03516i			0.454917i
$177$	0.790718	+	1.36956i	0.0594340	+	0.102943i
$178$	4.71966	−	8.17470i	0.353754	−	0.612720i
$179$	−4.07122	+	7.05156i	−0.304297	+	0.527058i	−0.977105	−	0.212759i	$-0.931755\pi$
$179$	−4.07122	+	7.05156i	−0.304297	+	0.527058i	0.672807	+	0.739818i	$0.265088\pi$
$180$	−0.971485	−	1.68266i	−0.0724102	−	0.125418i
$181$	−16.7773			−1.24705			−0.623524	−	0.781804i	$-0.714300\pi$
$181$	−16.7773			−1.24705			−0.623524	+	0.781804i	$0.714300\pi$
$182$	6.56734	−	15.9572i	0.486804	−	1.18283i
$183$		−	17.4203i		−	1.28774i
$184$	1.35675	+	4.59992i	0.100021	+	0.339110i
$185$	6.83352	+	3.94533i	0.502410	+	0.290067i
$186$	2.01374	−	3.48790i	0.147655	−	0.255746i
$187$	5.93900	−	3.42888i	0.434302	−	0.250745i
$188$		−	0.281653i		−	0.0205416i
$189$	−8.94765	−	11.6062i	−0.650846	−	0.844230i
$190$	−4.74949			−0.344564
$191$	3.11889	−	1.80069i	0.225675	−	0.130294i	−0.382900	−	0.923790i	$-0.625075\pi$
$191$	3.11889	−	1.80069i	0.225675	−	0.130294i	0.608575	+	0.793496i	$0.291741\pi$
$192$	−1.07743	−	0.622057i	−0.0777571	−	0.0448931i
$193$	7.15236	−	12.3883i	0.514838	−	0.891726i	−0.485013	−	0.874507i	$-0.661185\pi$
$193$	7.15236	−	12.3883i	0.514838	−	0.891726i	0.999852	−	0.0172195i	$-0.00548140\pi$
$194$	7.09225	+	12.2841i	0.509194	+	0.881950i
$195$	−10.8565			−0.777453
$196$	4.97214	+	4.92726i	0.355153	+	0.351947i
$197$	−12.0468			−0.858299			−0.429149	−	0.903233i	$-0.641187\pi$
$197$	−12.0468			−0.858299			−0.429149	+	0.903233i	$0.641187\pi$
$198$	−7.58997	+	4.38207i	−0.539395	+	0.311420i
$199$	−9.74098	+	16.8719i	−0.690520	+	1.19602i	0.281148	+	0.959664i	$0.409285\pi$
$199$	−9.74098	+	16.8719i	−0.690520	+	1.19602i	−0.971668	+	0.236351i	$0.924048\pi$
$200$	−1.60492	+	2.77980i	−0.113485	+	0.196562i
$201$	2.56671	+	4.44568i	0.181042	+	0.313574i
$202$		−	10.2336i		−	0.720036i
$203$	6.66818	−	5.14073i	0.468014	−	0.360808i
$204$			1.41369i			0.0989780i
$205$	−1.07560	+	0.620995i	−0.0751229	+	0.0433722i
$206$	6.03001	−	10.4443i	0.420131	−	0.727687i
$207$	−4.79984	+	5.04624i	−0.333612	+	0.350738i
$208$	5.64828	−	3.26103i	0.391638	−	0.226112i
$209$			21.4235i			1.48189i
$210$	1.67614	−	4.07265i	0.115665	−	0.281039i
$211$	12.1866			0.838961			0.419480	−	0.907764i	$-0.362212\pi$
$211$	12.1866			0.838961			0.419480	+	0.907764i	$0.362212\pi$
$212$	−11.3667	+	6.56256i	−0.780667	+	0.450718i
$213$	4.33935	+	2.50533i	0.297328	+	0.171662i
$214$	−7.66359	−	4.42458i	−0.523872	−	0.302458i
$215$	−0.351723	+	0.203067i	−0.0239873	+	0.0138491i
$216$		−	5.53902i		−	0.376883i
$217$	−8.48908	+	1.13719i	−0.576276	+	0.0771975i
$218$		−	7.70624i		−	0.521932i
$219$	7.97307	+	13.8098i	0.538770	+	0.933178i
$220$	−6.99303	−	4.03743i	−0.471470	−	0.272203i
$221$	−6.41814	−	3.70552i	−0.431731	−	0.249260i
$222$	3.66858	+	6.35417i	0.246219	+	0.426464i
$223$			16.5496i			1.10824i	0.832436	+	0.554122i	$0.186946\pi$
$223$			16.5496i			1.10824i	−0.832436	+	0.554122i	$0.813054\pi$
$224$	0.351285	+	2.62233i	0.0234712	+	0.175212i
$225$	−4.66126			−0.310751
$226$	7.70322	−	4.44745i	0.512410	−	0.295840i
$227$	−8.69075	+	15.0528i	−0.576825	+	0.999090i	0.419016	+	0.907979i	$0.362375\pi$
$227$	−8.69075	+	15.0528i	−0.576825	+	0.999090i	−0.995841	+	0.0911113i	$0.970958\pi$
$228$	−3.82465	−	2.20816i	−0.253294	−	0.146239i
$229$	0.486122	+	0.841988i	0.0321239	+	0.0556402i	0.881640	−	0.471922i	$-0.156440\pi$
$229$	0.486122	+	0.841988i	0.0321239	+	0.0556402i	−0.849517	+	0.527562i	$0.823106\pi$
$230$	−6.23764	−	1.50518i	−0.411297	−	0.0992486i
$231$	−18.3705	−	7.56055i	−1.20869	−	0.497448i
$232$	3.18236			0.208932
$233$	3.41466	+	5.91436i	0.223702	+	0.387463i	0.955929	−	0.293597i	$-0.0948525\pi$
$233$	3.41466	+	5.91436i	0.223702	+	0.387463i	−0.732227	+	0.681060i	$0.761519\pi$
$234$	8.20231	+	4.73561i	0.536202	+	0.309576i
$235$	0.326355	+	0.188421i	0.0212891	+	0.0122912i
$236$	1.10083	−	0.635567i	0.0716582	−	0.0413719i
$237$	15.2536			0.990830
$238$	2.38096	−	1.83556i	0.154335	−	0.118982i
$239$	14.7894			0.956647			0.478324	−	0.878184i	$-0.341245\pi$
$239$	14.7894			0.956647			0.478324	+	0.878184i	$0.341245\pi$
$240$	1.44157	−	0.832293i	0.0930532	−	0.0537243i
$241$	−6.60378	+	11.4381i	−0.425387	+	0.736791i	−0.996456	−	0.0841102i	$-0.973195\pi$
$241$	−6.60378	+	11.4381i	−0.425387	+	0.736791i	0.571070	+	0.820902i	$0.306529\pi$
$242$	−12.7116	+	22.0171i	−0.817132	+	1.41531i
$243$	11.6599	−	6.73184i	0.747982	−	0.431848i
$244$	−14.0021			−0.896396
$245$	−9.03556	+	2.46503i	−0.577261	+	0.157485i
$246$	−1.15487			−0.0736318
$247$	20.0501	−	11.5759i	1.27576	−	0.736560i
$248$	−2.80352	−	1.61862i	−0.178024	−	0.102782i
$249$	−6.45777	−	3.72839i	−0.409244	−	0.236277i
$250$	−5.49225	−	9.51286i	−0.347361	−	0.601646i
$251$	−9.65778			−0.609593			−0.304797	−	0.952417i	$-0.598589\pi$
$251$	−9.65778			−0.609593			−0.304797	+	0.952417i	$0.598589\pi$
$252$	−3.04284	+	2.34583i	−0.191681	+	0.147773i
$253$	−6.78940	+	28.1360i	−0.426846	+	1.76890i
$254$	−5.72571	−	9.91722i	−0.359263	−	0.622262i
$255$	−1.63806	−	0.945735i	−0.102579	−	0.0592242i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.82152	+	3.36106i	−0.363137	+	0.209657i	−0.670456	−	0.741949i	$-0.733901\pi$
$257$	−5.82152	+	3.36106i	−0.363137	+	0.209657i	0.307319	+	0.951607i	$0.400568\pi$
$258$	−0.377645			−0.0235112
$259$	5.93844	−	14.4291i	0.368996	−	0.896579i
$260$			8.72632i			0.541183i
$261$	2.31068	+	4.00221i	0.143027	+	0.247730i
$262$	−6.21988	−	3.59105i	−0.384265	−	0.221856i
$263$	22.1864	+	12.8094i	1.36808	+	0.789859i	0.990682	−	0.136195i	$-0.0434873\pi$
$263$	22.1864	+	12.8094i	1.36808	+	0.789859i	0.377393	+	0.926053i	$0.376821\pi$
$264$	−3.75422	−	6.50249i	−0.231056	−	0.400201i
$265$		−	17.5610i		−	1.07876i
$266$	1.24698	+	9.30868i	0.0764575	+	0.570752i
$267$			11.7436i			0.718697i
$268$	3.57337	−	2.06308i	0.218278	−	0.126023i
$269$	−19.4220	−	11.2133i	−1.18418	−	0.683686i	−0.227201	−	0.973848i	$-0.572958\pi$
$269$	−19.4220	−	11.2133i	−1.18418	−	0.683686i	−0.956978	+	0.290162i	$0.906291\pi$
$270$	6.41814	+	3.70552i	0.390596	+	0.225511i
$271$	0.355990	−	0.205531i	0.0216248	−	0.0124851i	−0.489149	−	0.872200i	$-0.662692\pi$
$271$	0.355990	−	0.205531i	0.0216248	−	0.0124851i	0.510773	+	0.859715i	$0.329359\pi$
$272$	1.13630			0.0688984
$273$	2.85040	+	21.2781i	0.172514	+	1.28781i
$274$		−	4.47858i		−	0.270561i
$275$	−16.7766	+	9.68595i	−1.01166	+	0.584085i
$276$	−4.32322	−	4.11213i	−0.260227	−	0.247521i
$277$	−2.30603	+	3.99416i	−0.138556	+	0.239986i	−0.926950	−	0.375184i	$-0.877579\pi$
$277$	−2.30603	+	3.99416i	−0.138556	+	0.239986i	0.788394	+	0.615170i	$0.210913\pi$
$278$	−7.85599	+	4.53566i	−0.471171	+	0.272031i
$279$		−	4.70104i		−	0.281444i
$280$	−3.27353	−	1.34726i	−0.195631	−	0.0805140i
$281$		−	20.5915i		−	1.22839i	−0.789156	−	0.614193i	$-0.789482\pi$
$281$		−	20.5915i		−	1.22839i	0.789156	−	0.614193i	$-0.210518\pi$
$282$	0.175204	+	0.303462i	0.0104333	+	0.0180709i
$283$	−0.174471	+	0.302193i	−0.0103712	+	0.0179635i	−0.871164	−	0.490991i	$-0.836635\pi$
$283$	−0.174471	+	0.302193i	−0.0103712	+	0.0179635i	0.860793	+	0.508955i	$0.169968\pi$
$284$	2.01374	−	3.48790i	0.119494	−	0.206969i
$285$	5.11726	−	2.95445i	0.303121	−	0.175007i
$286$	39.3617			2.32751
$287$	1.49951	+	1.94505i	0.0885131	+	0.114813i
$288$	−1.45218			−0.0855705
$289$	7.85441	+	13.6042i	0.462024	+	0.800249i
$290$	−2.12895	+	3.68744i	−0.125016	+	0.216534i
$291$	−15.2829	−	8.82357i	−0.895898	−	0.517247i
$292$	11.1001	−	6.40863i	0.649583	−	0.375037i
$293$	25.1643			1.47011			0.735057	−	0.678005i	$-0.237155\pi$
$293$	25.1643			1.47011			0.735057	+	0.678005i	$0.237155\pi$
$294$	−8.42219	−	2.21584i	−0.491192	−	0.129231i
$295$			1.70074i			0.0990208i
$296$	5.10738	−	2.94875i	0.296861	−	0.171393i
$297$	16.7144	−	28.9503i	0.969870	−	1.67986i
$298$	15.4017	+	8.89220i	0.892199	+	0.515111i
$299$	30.0010	−	8.84884i	1.73500	−	0.511742i
$300$		−	3.99341i		−	0.230560i
$301$	0.490343	+	0.636037i	0.0282629	+	0.0366606i
$302$	19.4832			1.12113
$303$	6.36590	+	11.0261i	0.365712	+	0.633431i
$304$	−1.77489	+	3.07420i	−0.101797	+	0.176317i
$305$	9.36722	−	16.2245i	0.536365	−	0.929012i
$306$	0.825057	+	1.42904i	0.0471653	+	0.0816928i
$307$			12.9274i			0.737806i	0.929468	+	0.368903i	$0.120266\pi$
$307$			12.9274i			0.737806i	−0.929468	+	0.368903i	$0.879734\pi$
$308$	−6.07706	+	14.7659i	−0.346272	+	0.841365i
$309$			15.0040i			0.853550i
$310$	3.75103	−	2.16566i	0.213044	−	0.123001i
$311$	3.10046	+	1.79005i	0.175811	+	0.101504i	0.585323	−	0.810800i	$-0.300968\pi$
$311$	3.10046	+	1.79005i	0.175811	+	0.101504i	−0.409512	+	0.912305i	$0.634301\pi$
$312$	−4.05710	+	7.02710i	−0.229688	+	0.397831i
$313$	2.70313	+	4.68196i	0.152790	+	0.264640i	0.932252	−	0.361809i	$-0.117841\pi$
$313$	2.70313	+	4.68196i	0.152790	+	0.264640i	−0.779462	+	0.626449i	$0.784507\pi$
$314$	−8.21100			−0.463374
$315$	−0.682536	−	5.09510i	−0.0384566	−	0.287077i
$316$		−	12.2606i		−	0.689715i
$317$	−13.5155	−	23.4095i	−0.759106	−	1.31481i	−0.943307	−	0.331921i	$-0.892303\pi$
$317$	−13.5155	−	23.4095i	−0.759106	−	1.31481i	0.184201	−	0.982889i	$-0.441030\pi$
$318$	8.16457	−	14.1415i	0.457846	−	0.793013i
$319$	16.6329	+	9.60301i	0.931264	+	0.537666i
$320$	−0.668984	−	1.15871i	−0.0373974	−	0.0647741i
$321$	11.0094			0.614483
$322$	−1.31235	+	12.6205i	−0.0731346	+	0.703315i
$323$	4.03362			0.224436
$324$	1.26732	+	2.19506i	0.0704066	+	0.121948i
$325$	18.1301	+	10.4674i	1.00568	+	0.580627i
$326$	7.48801	−	12.9696i	0.414722	−	0.718320i
$327$	4.79372	+	8.30297i	0.265093	+	0.459155i
$328$			0.928266i			0.0512549i
$329$	0.283608	−	0.689104i	0.0156358	−	0.0379915i
$330$	10.0460			0.553017
$331$	3.64113	+	6.30662i	0.200134	+	0.346643i	0.948572	−	0.316563i	$-0.102529\pi$
$331$	3.64113	+	6.30662i	0.200134	+	0.346643i	−0.748437	+	0.663206i	$0.769195\pi$
$332$	−2.99683	+	5.19065i	−0.164472	+	0.284874i
$333$	7.41684	+	4.28211i	0.406440	+	0.234658i
$334$	12.6063	−	7.27825i	0.689786	−	0.398248i
$335$			5.52068i			0.301627i
$336$	−2.00972	−	2.60687i	−0.109639	−	0.142216i
$337$			19.2503i			1.04863i	0.851524	+	0.524316i	$0.175679\pi$
$337$			19.2503i			1.04863i	−0.851524	+	0.524316i	$0.824321\pi$
$338$	−14.7687	−	25.5801i	−0.803311	−	1.39138i
$339$	−5.53314	+	9.58368i	−0.300519	+	0.520514i
$340$	−0.760167	+	1.31665i	−0.0412259	+	0.0714053i
$341$	−9.76861	−	16.9197i	−0.529000	−	0.916254i
$342$	−5.15491			−0.278746
$343$	7.20359	+	17.0619i	0.388957	+	0.921256i
$344$			0.303546i			0.0163661i
$345$	7.65695	−	2.25843i	0.412236	−	0.121590i
$346$	0.143633	+	0.0829263i	0.00772173	+	0.00445814i
$347$	−14.4944	+	25.1050i	−0.778100	+	1.34771i	0.154935	+	0.987925i	$0.450483\pi$
$347$	−14.4944	+	25.1050i	−0.778100	+	1.34771i	−0.933035	+	0.359785i	$0.882850\pi$
$348$	−3.42878	+	1.97961i	−0.183802	+	0.106118i
$349$			12.4174i			0.664687i	0.943159	+	0.332343i	$0.107839\pi$
$349$			12.4174i			0.664687i	−0.943159	+	0.332343i	$0.892161\pi$
$350$	−6.72577	+	5.18513i	−0.359508	+	0.277157i
$351$	−36.1259			−1.92826
$352$	−5.22660	+	3.01758i	−0.278579	+	0.160838i
$353$	6.43499	+	3.71525i	0.342500	+	0.197743i	0.661377	−	0.750054i	$-0.269972\pi$
$353$	6.43499	+	3.71525i	0.342500	+	0.197743i	−0.318877	+	0.947796i	$0.603306\pi$
$354$	−0.790718	+	1.36956i	−0.0420262	+	0.0727915i
$355$	2.69432	+	4.66671i	0.143000	+	0.247683i
$356$	9.43933			0.500283
$357$	−1.42350	+	3.45879i	−0.0753397	+	0.183059i
$358$	−8.14244			−0.430341
$359$	−17.2194	+	9.94165i	−0.908808	+	0.524700i	−0.880047	−	0.474886i	$-0.842489\pi$
$359$	−17.2194	+	9.94165i	−0.908808	+	0.524700i	−0.0287603	+	0.999586i	$0.509156\pi$
$360$	0.971485	−	1.68266i	0.0512018	−	0.0886840i
$361$	3.19954	−	5.54177i	0.168397	−	0.291672i
$362$	−8.38866	−	14.5296i	−0.440898	−	0.763658i
$363$		−	31.6293i		−	1.66011i
$364$	17.1030	−	2.29110i	0.896441	−	0.120087i
$365$			17.1491i			0.897625i
$366$	15.0864	−	8.71014i	0.788579	−	0.455286i
$367$	10.8893	−	18.8608i	0.568416	−	0.984525i	−0.428307	−	0.903633i	$-0.640890\pi$
$367$	10.8893	−	18.8608i	0.568416	−	0.984525i	0.996723	−	0.0808918i	$-0.0257768\pi$
$368$	−3.30527	+	3.47494i	−0.172299	+	0.181144i
$369$	−1.16741	+	0.674005i	−0.0607729	+	0.0350873i
$370$			7.89066i			0.410216i
$371$	−34.4183	+	4.61066i	−1.78691	+	0.239373i
$372$	4.02749			0.208815
$373$	17.5547	−	10.1352i	0.908948	−	0.524781i	0.0288554	−	0.999584i	$-0.490814\pi$
$373$	17.5547	−	10.1352i	0.908948	−	0.524781i	0.880092	+	0.474802i	$0.157480\pi$
$374$	5.93900	+	3.42888i	0.307098	+	0.177303i
$375$	11.8351	+	6.83299i	0.611161	+	0.352854i
$376$	0.243918	−	0.140826i	0.0125791	−	0.00726257i
$377$		−	20.7555i		−	1.06896i
$378$	5.57747	−	13.5520i	0.286874	−	0.697040i
$379$		−	17.4861i		−	0.898200i	−0.893481	−	0.449100i	$-0.851745\pi$
$379$		−	17.4861i		−	0.898200i	0.893481	−	0.449100i	$-0.148255\pi$
$380$	−2.37474	−	4.11318i	−0.121822	−	0.211002i
$381$	12.3382	+	7.12344i	0.632103	+	0.364945i
$382$	3.11889	+	1.80069i	0.159576	+	0.0921315i
$383$	8.88242	+	15.3848i	0.453870	+	0.786126i	0.998622	−	0.0524707i	$-0.0167096\pi$
$383$	8.88242	+	15.3848i	0.453870	+	0.786126i	−0.544752	+	0.838597i	$0.683376\pi$
$384$		−	1.24411i		−	0.0634884i
$385$	−13.0440	−	16.9197i	−0.664784	−	0.862309i
$386$	14.3047			0.728091
$387$	−0.381746	+	0.220401i	−0.0194053	+	0.0112036i
$388$	−7.09225	+	12.2841i	−0.360055	+	0.623633i
$389$	−13.9506	−	8.05439i	−0.707324	−	0.408374i	0.102746	−	0.994708i	$-0.467237\pi$
$389$	−13.9506	−	8.05439i	−0.707324	−	0.408374i	−0.810069	+	0.586334i	$0.800571\pi$
$390$	−5.42827	−	9.40204i	−0.274871	−	0.476091i
$391$	5.29746	+	1.27831i	0.267904	+	0.0646469i
$392$	−1.78106	+	6.76962i	−0.0899572	+	0.341918i
$393$	8.93535			0.450729
$394$	−6.02340	−	10.4328i	−0.303454	−	0.525599i
$395$	14.2066	+	8.20217i	0.714811	+	0.412696i
$396$	−7.58997	−	4.38207i	−0.381410	−	0.220207i
$397$	−5.91641	+	3.41584i	−0.296936	+	0.171436i	−0.641066	−	0.767486i	$-0.721507\pi$
$397$	−5.91641	+	3.41584i	−0.296936	+	0.171436i	0.344130	+	0.938922i	$0.388174\pi$
$398$	−19.4820			−0.976543
$399$	−7.13407	−	9.25380i	−0.357150	−	0.463269i
$400$	−3.20984			−0.160492
$401$	−16.3143	+	9.41906i	−0.814697	+	0.470365i	−0.848584	−	0.529060i	$-0.822545\pi$
$401$	−16.3143	+	9.41906i	−0.814697	+	0.470365i	0.0338876	+	0.999426i	$0.489211\pi$
$402$	−2.56671	+	4.44568i	−0.128016	+	0.221730i
$403$	−10.5567	+	18.2848i	−0.525868	+	0.910830i
$404$	8.86258	−	5.11681i	0.440930	−	0.254571i
$405$	−3.39126			−0.168513
$406$	7.78609	+	3.20445i	0.386417	+	0.159034i
$407$	35.5924			1.76425
$408$	−1.22429	+	0.706844i	−0.0606114	+	0.0349940i
$409$	5.12526	+	2.95907i	0.253428	+	0.146316i	0.621333	−	0.783547i	$-0.286592\pi$
$409$	5.12526	+	2.95907i	0.253428	+	0.146316i	−0.367905	+	0.929863i	$0.619925\pi$
$410$	−1.07560	−	0.620995i	−0.0531199	−	0.0306688i
$411$	2.78593	+	4.82538i	0.137420	+	0.238018i
$412$	12.0600			0.594154
$413$	3.33333	−	0.446530i	0.164022	−	0.0219723i
$414$	−6.77009	−	1.63366i	−0.332732	−	0.0802902i
$415$	−4.00966	−	6.94493i	−0.196826	−	0.340913i
$416$	5.64828	+	3.26103i	0.276930	+	0.159885i
$417$	5.64288	−	9.77375i	0.276333	−	0.478623i
$418$	−18.5533	+	10.7117i	−0.907471	+	0.523928i
$419$	−4.13562			−0.202038			−0.101019	−	0.994884i	$-0.532210\pi$
$419$	−4.13562			−0.202038			−0.101019	+	0.994884i	$0.532210\pi$
$420$	4.36509	−	0.584744i	0.212994	−	0.0285326i
$421$		−	29.2892i		−	1.42747i	−0.700416	−	0.713735i	$-0.747002\pi$
$421$		−	29.2892i		−	1.42747i	0.700416	−	0.713735i	$-0.252998\pi$
$422$	6.09331	+	10.5539i	0.296617	+	0.513757i
$423$	0.354213	+	0.204505i	0.0172224	+	0.00994338i
$424$	−11.3667	−	6.56256i	−0.552015	−	0.318706i
$425$	1.82367	+	3.15869i	0.0884611	+	0.153219i
$426$			5.01065i			0.242767i
$427$	−34.2583	−	14.0993i	−1.65787	−	0.682315i
$428$		−	8.84915i		−	0.427740i
$429$	−42.4097	+	24.4853i	−2.04756	+	1.18216i
$430$	−0.351723	−	0.203067i	−0.0169616	−	0.00979277i
$431$	−4.57492	−	2.64133i	−0.220366	−	0.127228i	0.385754	−	0.922602i	$-0.373941\pi$
$431$	−4.57492	−	2.64133i	−0.220366	−	0.127228i	−0.606120	+	0.795373i	$0.707275\pi$
$432$	4.79693	−	2.76951i	0.230793	−	0.133248i
$433$	−29.0430			−1.39572			−0.697860	−	0.716235i	$-0.745864\pi$
$433$	−29.0430			−1.39572			−0.697860	+	0.716235i	$0.745864\pi$
$434$	−5.22938	−	6.78316i	−0.251018	−	0.325602i
$435$		−	5.29730i		−	0.253986i
$436$	6.67380	−	3.85312i	0.319617	−	0.184531i
$437$	−11.7330	+	12.3353i	−0.561264	+	0.590076i
$438$	−7.97307	+	13.8098i	−0.380968	+	0.659856i
$439$	29.6005	−	17.0899i	1.41276	−	0.815655i	0.417108	−	0.908857i	$-0.363044\pi$
$439$	29.6005	−	17.0899i	1.41276	−	0.815655i	0.995647	+	0.0932020i	$0.0297102\pi$
$440$		−	8.07486i		−	0.384954i
$441$	−9.80685	+	2.67545i	−0.466993	+	0.127402i
$442$		−	7.41103i		−	0.352507i
$443$	0.874186	+	1.51413i	0.0415338	+	0.0719387i	0.886045	−	0.463599i	$-0.153442\pi$
$443$	0.874186	+	1.51413i	0.0415338	+	0.0719387i	−0.844511	+	0.535538i	$0.820109\pi$
$444$	−3.66858	+	6.35417i	−0.174103	+	0.301555i
$445$	−6.31476	+	10.9375i	−0.299348	+	0.518487i
$446$	−14.3324	+	8.27481i	−0.678658	+	0.391823i
$447$	−22.1258			−1.04652
$448$	−2.09536	+	1.61539i	−0.0989964	+	0.0763198i
$449$	20.7363			0.978607			0.489303	−	0.872114i	$-0.337251\pi$
$449$	20.7363			0.978607			0.489303	+	0.872114i	$0.337251\pi$
$450$	−2.33063	−	4.03677i	−0.109867	−	0.190295i
$451$	−2.80112	+	4.85168i	−0.131900	+	0.228457i
$452$	7.70322	+	4.44745i	0.362329	+	0.209191i
$453$	−20.9918	+	12.1196i	−0.986283	+	0.569431i
$454$	−17.3815			−0.815754
$455$	−8.78690	+	21.3502i	−0.411936	+	1.00091i
$456$		−	4.41633i		−	0.206814i
$457$	−10.3635	+	5.98335i	−0.484782	+	0.279889i	−0.722407	−	0.691468i	$-0.756964\pi$
$457$	−10.3635	+	5.98335i	−0.484782	+	0.279889i	0.237625	+	0.971357i	$0.423631\pi$
$458$	−0.486122	+	0.841988i	−0.0227150	+	0.0393435i
$459$	−5.45076	−	3.14700i	−0.254420	−	0.146889i
$460$	−1.81529	−	6.15454i	−0.0846385	−	0.286957i
$461$		−	14.9676i		−	0.697109i	−0.937289	−	0.348554i	$-0.886673\pi$
$461$		−	14.9676i		−	0.697109i	0.937289	−	0.348554i	$-0.113327\pi$
$462$	−2.63760	−	19.6896i	−0.122712	−	0.916041i
$463$	8.01243			0.372369			0.186185	−	0.982515i	$-0.440388\pi$
$463$	8.01243			0.372369			0.186185	+	0.982515i	$0.440388\pi$
$464$	1.59118	+	2.75600i	0.0738686	+	0.127944i
$465$	−2.69432	+	4.66671i	−0.124946	+	0.216413i
$466$	−3.41466	+	5.91436i	−0.158181	+	0.273978i
$467$	0.207210	+	0.358899i	0.00958855	+	0.0166078i	0.870780	−	0.491673i	$-0.163614\pi$
$467$	0.207210	+	0.358899i	0.00958855	+	0.0166078i	−0.861191	+	0.508281i	$0.830281\pi$
$468$			9.47121i			0.437807i
$469$	10.8202	−	1.44946i	0.499629	−	0.0669299i
$470$			0.376843i			0.0173824i
$471$	8.84682	−	5.10771i	0.407640	−	0.235351i
$472$	1.10083	+	0.635567i	0.0506700	+	0.0292543i
$473$	−0.915973	+	1.58651i	−0.0421165	+	0.0729479i
$474$	7.62682	+	13.2100i	0.350311	+	0.606757i
$475$	−11.3942			−0.522803
$476$	2.78012	+	1.14419i	0.127427	+	0.0524438i
$477$		−	19.0600i		−	0.872698i
$478$	7.39470	+	12.8080i	0.338226	+	0.585824i
$479$	10.3395	−	17.9086i	0.472425	−	0.818264i	−0.527077	−	0.849818i	$-0.676712\pi$
$479$	10.3395	−	17.9086i	0.472425	−	0.818264i	0.999502	+	0.0315532i	$0.0100454\pi$
$480$	1.44157	+	0.832293i	0.0657985	+	0.0379888i
$481$	−19.2319	−	33.3107i	−0.876901	−	1.51884i
$482$	−13.2076			−0.601588
$483$	−6.43672	−	14.4142i	−0.292881	−	0.655867i
$484$	−25.4232			−1.15560
$485$	−9.48921	−	16.4358i	−0.430883	−	0.746311i
$486$	11.6599	+	6.73184i	0.528903	+	0.305363i
$487$	−3.26073	+	5.64774i	−0.147758	+	0.255924i	−0.930398	−	0.366550i	$-0.880539\pi$
$487$	−3.26073	+	5.64774i	−0.147758	+	0.255924i	0.782641	+	0.622474i	$0.213872\pi$
$488$	−7.00107	−	12.1262i	−0.316924	−	0.548928i
$489$			18.6319i			0.842563i
$490$	−6.65256	−	6.59251i	−0.300532	−	0.297819i
$491$	14.6314			0.660306			0.330153	−	0.943927i	$-0.392900\pi$
$491$	14.6314			0.660306			0.330153	+	0.943927i	$0.392900\pi$
$492$	−0.577435	−	1.00015i	−0.0260328	−	0.0450901i
$493$	1.80806	−	3.13165i	0.0814308	−	0.141042i
$494$	20.0501	+	11.5759i	0.902098	+	0.520826i
$495$	10.1551	−	5.86307i	0.456439	−	0.263525i
$496$		−	3.23723i		−	0.145356i
$497$	8.43903	−	6.50594i	0.378542	−	0.291831i
$498$		−	7.45679i		−	0.334147i
$499$	−8.69163	−	15.0544i	−0.389091	−	0.673925i	0.603237	−	0.797562i	$-0.293877\pi$
$499$	−8.69163	−	15.0544i	−0.389091	−	0.673925i	−0.992328	+	0.123637i	$0.960544\pi$
$500$	5.49225	−	9.51286i	0.245621	−	0.425428i
$501$	−9.05497	+	15.6837i	−0.404546	+	0.700695i
$502$	−4.82889	−	8.36388i	−0.215524	−	0.373298i
$503$	17.7000			0.789206			0.394603	−	0.918852i	$-0.370882\pi$
$503$	17.7000			0.789206			0.394603	+	0.918852i	$0.370882\pi$
$504$	−3.55297	−	1.46226i	−0.158262	−	0.0651342i
$505$			13.6923i			0.609298i
$506$	−27.7612	+	8.18823i	−1.23414	+	0.364011i
$507$	31.8246	+	18.3739i	1.41338	+	0.816015i
$508$	5.72571	−	9.91722i	0.254037	−	0.440006i
$509$	−24.1180	+	13.9245i	−1.06901	+	0.617193i	−0.927911	−	0.372802i	$-0.878397\pi$
$509$	−24.1180	+	13.9245i	−1.06901	+	0.617193i	−0.141099	+	0.989995i	$0.545064\pi$
$510$		−	1.89147i		−	0.0837557i
$511$	33.6111	−	4.50251i	1.48687	−	0.199179i
$512$	−1.00000			−0.0441942
$513$	17.0280	−	9.83114i	0.751806	−	0.434056i
$514$	−5.82152	−	3.36106i	−0.256776	−	0.148250i
$515$	−8.06796	+	13.9741i	−0.355517	+	0.615773i
$516$	−0.188823	−	0.327051i	−0.00831246	−	0.0143976i
$517$	1.69982			0.0747580
$518$	15.4652	−	2.07170i	0.679500	−	0.0910254i
$519$	−0.206340			−0.00905730
$520$	−7.55722	+	4.36316i	−0.331406	+	0.191337i
$521$	6.81914	−	11.8111i	0.298752	−	0.517453i	−0.677099	−	0.735892i	$-0.736763\pi$
$521$	6.81914	−	11.8111i	0.298752	−	0.517453i	0.975851	+	0.218439i	$0.0700964\pi$
$522$	−2.31068	+	4.00221i	−0.101136	+	0.175172i
$523$	−16.1015	−	27.8887i	−0.704071	−	1.21949i	−0.967026	−	0.254679i	$-0.918030\pi$
$523$	−16.1015	−	27.8887i	−0.704071	−	1.21949i	0.262954	−	0.964808i	$-0.415303\pi$
$524$		−	7.18209i		−	0.313751i
$525$	4.02113	−	9.77045i	0.175497	−	0.426417i
$526$			25.6187i			1.11703i
$527$	−3.18565	+	1.83923i	−0.138769	+	0.0801183i
$528$	3.75422	−	6.50249i	0.163381	−	0.282985i
$529$	−19.3184	+	12.4819i	−0.839932	+	0.542691i
$530$	15.2083	−	8.78049i	0.660605	−	0.381400i
$531$			1.84591i			0.0801059i
$532$	−7.43806	+	5.73426i	−0.322481	+	0.248612i
$533$	6.05422			0.262237
$534$	−10.1703	+	5.87180i	−0.440110	+	0.254098i
$535$	10.2536	+	5.91994i	0.443304	+	0.255942i
$536$	3.57337	+	2.06308i	0.154346	+	0.0891117i
$537$	8.77295	−	5.06506i	0.378581	−	0.218574i
$538$		−	22.4266i		−	0.966878i
$539$	−29.7368	+	30.0077i	−1.28085	+	1.29252i
$540$			7.41103i			0.318920i
$541$	−4.06544	−	7.04155i	−0.174787	−	0.302740i	0.765301	−	0.643673i	$-0.222590\pi$
$541$	−4.06544	−	7.04155i	−0.174787	−	0.302740i	−0.940088	+	0.340933i	$0.889257\pi$
$542$	0.355990	+	0.205531i	0.0152911	+	0.00882830i
$543$	18.0765	+	10.4365i	0.775736	+	0.447871i
$544$	0.568151	+	0.984066i	0.0243593	+	0.0421915i
$545$			10.3107i			0.441662i
$546$	−17.0022	+	13.1076i	−0.727625	+	0.560952i
$547$	23.6938			1.01307			0.506536	−	0.862219i	$-0.330926\pi$
$547$	23.6938			1.01307			0.506536	+	0.862219i	$0.330926\pi$
$548$	3.87856	−	2.23929i	0.165684	−	0.0956577i
$549$	10.1668	−	17.6094i	0.433909	−	0.751553i
$550$	−16.7766	−	9.68595i	−0.715355	−	0.413011i
$551$	5.64833	+	9.78319i	0.240627	+	0.416778i
$552$	1.39960	−	5.80009i	0.0595708	−	0.246868i
$553$	12.3457	−	29.9974i	0.524995	−	1.27562i
$554$	−4.61206			−0.195948
$555$	−4.90844	−	8.50168i	−0.208352	−	0.360876i
$556$	−7.85599	−	4.53566i	−0.333168	−	0.192355i
$557$	19.8469	+	11.4586i	0.840942	+	0.485518i	0.857584	−	0.514343i	$-0.171964\pi$
$557$	19.8469	+	11.4586i	0.840942	+	0.485518i	−0.0166424	+	0.999862i	$0.505298\pi$
$558$	4.07122	−	2.35052i	0.172349	−	0.0995055i
$559$	1.97975			0.0837343
$560$	−0.470008	−	3.50859i	−0.0198615	−	0.148265i
$561$	−8.53184			−0.360215
$562$	17.8328	−	10.2958i	0.752230	−	0.434300i
$563$	−11.0559	+	19.1493i	−0.465949	+	0.807048i	−0.999244	−	0.0388818i	$-0.987620\pi$
$563$	−11.0559	+	19.1493i	−0.465949	+	0.807048i	0.533295	+	0.845930i	$0.320954\pi$
$564$	−0.175204	+	0.303462i	−0.00737743	+	0.0127781i
$565$	−10.3067	+	5.95055i	−0.433604	+	0.250342i
$566$	−0.348943			−0.0146672
$567$	0.890380	+	6.64665i	0.0373924	+	0.279133i
$568$	4.02749			0.168990
$569$	11.4658	−	6.61980i	0.480673	−	0.277517i	−0.240024	−	0.970767i	$-0.577155\pi$
$569$	11.4658	−	6.61980i	0.480673	−	0.277517i	0.720697	+	0.693250i	$0.243822\pi$
$570$	5.11726	+	2.95445i	0.214339	+	0.123748i
$571$	−17.6182	−	10.1719i	−0.737298	−	0.425679i	0.0837883	−	0.996484i	$-0.473298\pi$
$571$	−17.6182	−	10.1719i	−0.737298	−	0.425679i	−0.821086	+	0.570805i	$0.806631\pi$
$572$	19.6809	+	34.0883i	0.822899	+	1.42530i
$573$	−4.48054			−0.187177
$574$	−0.934710	+	2.27114i	−0.0390140	+	0.0947954i
$575$	−14.9643	−	3.61099i	−0.624056	−	0.150589i
$576$	−0.726090	−	1.25762i	−0.0302537	−	0.0524010i
$577$	−14.5048	−	8.37436i	−0.603843	−	0.348629i	0.166709	−	0.986006i	$-0.446686\pi$
$577$	−14.5048	−	8.37436i	−0.603843	−	0.348629i	−0.770552	+	0.637377i	$0.780019\pi$
$578$	−7.85441	+	13.6042i	−0.326700	+	0.565862i
$579$	−15.4124	+	8.89836i	−0.640518	+	0.369803i
$580$	−4.25789			−0.176799
$581$	−12.5589	+	9.68205i	−0.521029	+	0.401679i
$582$		−	17.6471i		−	0.731498i
$583$	−39.6061	−	68.5998i	−1.64032	−	2.84111i
$584$	11.1001	+	6.40863i	0.459325	+	0.265191i
$585$	−10.9744	−	6.33609i	−0.453737	−	0.261965i
$586$	12.5822	+	21.7929i	0.519764	+	0.900258i
$587$		−	39.7788i		−	1.64185i	−0.571037	−	0.820924i	$-0.693459\pi$
$587$		−	39.7788i		−	1.64185i	0.571037	−	0.820924i	$-0.306541\pi$
$588$	−2.29212	−	8.40175i	−0.0945253	−	0.346482i
$589$		−	11.4914i		−	0.473497i
$590$	−1.47288	+	0.850369i	−0.0606376	+	0.0350091i
$591$	12.9796	+	7.49380i	0.533911	+	0.308254i
$592$	5.10738	+	2.94875i	0.209912	+	0.121193i
$593$	−10.8382	+	6.25742i	−0.445070	+	0.256961i	−0.705746	−	0.708465i	$-0.749388\pi$
$593$	−10.8382	+	6.25742i	−0.445070	+	0.256961i	0.260676	+	0.965426i	$0.416055\pi$
$594$	33.4289			1.37160
$595$	−3.18565	+	2.45593i	−0.130599	+	0.100683i
$596$			17.7844i			0.728478i
$597$	20.9905	−	12.1189i	0.859086	−	0.495993i
$598$	22.6638	+	21.5572i	0.926792	+	0.881539i
$599$	−19.3086	+	33.4435i	−0.788928	+	1.36646i	0.137696	+	0.990475i	$0.456030\pi$
$599$	−19.3086	+	33.4435i	−0.788928	+	1.36646i	−0.926624	+	0.375989i	$0.877303\pi$
$600$	3.45839	−	1.99670i	0.141188	−	0.0815151i
$601$			4.35612i			0.177690i	0.996045	+	0.0888449i	$0.0283176\pi$
$601$			4.35612i			0.177690i	−0.996045	+	0.0888449i	$0.971682\pi$
$602$	−0.305653	+	0.742668i	−0.0124575	+	0.0302689i
$603$			5.99194i			0.244011i
$604$	9.74158	+	16.8729i	0.396379	+	0.686549i
$605$	17.0077	−	29.4582i	0.691462	−	1.19765i
$606$	−6.36590	+	11.0261i	−0.258597	+	0.447903i
$607$	−36.2312	+	20.9181i	−1.47058	+	0.849039i	−0.999454	−	0.0330288i	$-0.989485\pi$
$607$	−36.2312	+	20.9181i	−1.47058	+	0.849039i	−0.471123	+	0.882067i	$0.656151\pi$
$608$	−3.54978			−0.143962
$609$	−10.3824	+	1.39081i	−0.420714	+	0.0563586i
$610$	18.7344			0.758535
$611$	−0.918479	−	1.59085i	−0.0371577	−	0.0643590i
$612$	−0.825057	+	1.42904i	−0.0333509	+	0.0577655i
$613$	−16.0219	−	9.25027i	−0.647120	−	0.373615i	0.140232	−	0.990119i	$-0.455215\pi$
$613$	−16.0219	−	9.25027i	−0.647120	−	0.373615i	−0.787352	+	0.616504i	$0.788548\pi$
$614$	−11.1955	+	6.46370i	−0.451812	+	0.260854i
$615$	1.54518			0.0623076
$616$	−15.8262	+	2.12006i	−0.637655	+	0.0854197i
$617$		−	10.0161i		−	0.403233i	−0.979465	−	0.201616i	$-0.935381\pi$
$617$		−	10.0161i		−	0.403233i	0.979465	−	0.201616i	$-0.0646194\pi$
$618$	−12.9939	+	7.50202i	−0.522690	+	0.301775i
$619$	9.18249	−	15.9045i	0.369075	−	0.639257i	−0.620346	−	0.784328i	$-0.713008\pi$
$619$	9.18249	−	15.9045i	0.369075	−	0.639257i	0.989421	+	0.145071i	$0.0463411\pi$
$620$	3.75103	+	2.16566i	0.150645	+	0.0869749i
$621$	25.4790	−	7.51509i	1.02244	−	0.301570i
$622$			3.58010i			0.143549i
$623$	23.0947	+	9.50485i	0.925269	+	0.380804i
$624$	−8.11420			−0.324828
$625$	−0.676141	−	1.17111i	−0.0270456	−	0.0468444i
$626$	−2.70313	+	4.68196i	−0.108039	+	0.187129i
$627$	13.3266	−	23.0824i	0.532214	−	0.921822i
$628$	−4.10550	−	7.11094i	−0.163827	−	0.283757i
$629$		−	6.70133i		−	0.267200i
$630$	4.07122	−	3.13865i	0.162201	−	0.125047i
$631$			3.02292i			0.120341i	0.998188	+	0.0601703i	$0.0191644\pi$
$631$			3.02292i			0.120341i	−0.998188	+	0.0601703i	$0.980836\pi$
$632$	10.6180	−	6.13032i	0.422362	−	0.243851i
$633$	−13.1303	−	7.58077i	−0.521882	−	0.301309i
$634$	13.5155	−	23.4095i	0.536769	−	0.929711i
$635$	7.66082	+	13.2689i	0.304010	+	0.526561i
$636$	16.3291			0.647493
$637$	44.1520	+	11.6162i	1.74936	+	0.460251i
$638$			19.2060i			0.760374i
$639$	2.92432	+	5.06506i	0.115684	+	0.200371i
$640$	0.668984	−	1.15871i	0.0264439	−	0.0458022i
$641$	0.850505	+	0.491039i	0.0335929	+	0.0193949i	0.516702	−	0.856165i	$-0.327159\pi$
$641$	0.850505	+	0.491039i	0.0335929	+	0.0193949i	−0.483109	+	0.875560i	$0.660493\pi$
$642$	5.50468	+	9.53439i	0.217252	+	0.376292i
$643$	42.9115			1.69227			0.846133	−	0.532972i	$-0.178925\pi$
$643$	42.9115			1.69227			0.846133	+	0.532972i	$0.178925\pi$
$644$	−11.5859	+	5.17373i	−0.456547	+	0.203874i
$645$	0.505278			0.0198953
$646$	2.01681	+	3.49321i	0.0793502	+	0.137439i
$647$	24.5410	+	14.1688i	0.964807	+	0.557032i	0.897649	−	0.440711i	$-0.145274\pi$
$647$	24.5410	+	14.1688i	0.964807	+	0.557032i	0.0671579	+	0.997742i	$0.478607\pi$
$648$	−1.26732	+	2.19506i	−0.0497850	+	0.0862301i
$649$	3.83575	+	6.64371i	0.150566	+	0.260789i
$650$			20.9348i			0.821131i
$651$	9.85382	+	4.05544i	0.386202	+	0.158945i
$652$	14.9760			0.586506
$653$	14.4667	+	25.0571i	0.566127	+	0.980561i	0.996944	+	0.0781215i	$0.0248922\pi$
$653$	14.4667	+	25.0571i	0.566127	+	0.980561i	−0.430817	+	0.902439i	$0.641774\pi$
$654$	−4.79372	+	8.30297i	−0.187449	+	0.324672i
$655$	8.32200	+	4.80471i	0.325167	+	0.187735i
$656$	−0.803902	+	0.464133i	−0.0313871	+	0.0181214i
$657$			18.6130i			0.726161i
$658$	0.738586	−	0.0989404i	0.0287931	−	0.00385710i
$659$			31.7305i			1.23605i	0.786160	+	0.618023i	$0.212066\pi$
$659$			31.7305i			1.23605i	−0.786160	+	0.618023i	$0.787934\pi$
$660$	5.02302	+	8.70013i	0.195521	+	0.338652i
$661$	13.8069	−	23.9142i	0.537025	−	0.930154i	−0.462038	−	0.886860i	$-0.652882\pi$
$661$	13.8069	−	23.9142i	0.537025	−	0.930154i	0.999062	−	0.0432937i	$-0.0137851\pi$
$662$	−3.64113	+	6.30662i	−0.141516	+	0.245114i
$663$	4.61009	+	7.98490i	0.179041	+	0.310108i
$664$	−5.99365			−0.232599
$665$	−1.66842	−	12.4547i	−0.0646987	−	0.482973i
$666$			8.56422i			0.331857i
$667$	4.31767	+	14.6386i	0.167181	+	0.566807i
$668$	12.6063	+	7.27825i	0.487752	+	0.281604i
$669$	10.2948	−	17.8311i	0.398020	−	0.689391i
$670$	−4.78105	+	2.76034i	−0.184708	+	0.106641i
$671$		−	84.5052i		−	3.26229i
$672$	1.25275	−	3.04391i	0.0483259	−	0.117421i
$673$	5.70731			0.220001			0.110000	−	0.993932i	$-0.464915\pi$
$673$	5.70731			0.220001			0.110000	+	0.993932i	$0.464915\pi$
$674$	−16.6713	+	9.62517i	−0.642154	+	0.370748i
$675$	15.3974	+	8.88969i	0.592646	+	0.342164i
$676$	14.7687	−	25.5801i	0.568027	−	0.983851i
$677$	−20.5855	−	35.6550i	−0.791163	−	1.37033i	−0.925247	−	0.379365i	$-0.876143\pi$
$677$	−20.5855	−	35.6550i	−0.791163	−	1.37033i	0.134084	−	0.990970i	$-0.457191\pi$
$678$	−11.0663			−0.424998
$679$	−29.7216	+	22.9134i	−1.14061	+	0.879337i
$680$	−1.52033			−0.0583022
$681$	18.7274	−	10.8123i	0.717636	−	0.414328i
$682$	9.76861	−	16.9197i	0.374059	−	0.647890i
$683$	−2.95142	+	5.11202i	−0.112933	+	0.195606i	−0.916952	−	0.398998i	$-0.869358\pi$
$683$	−2.95142	+	5.11202i	−0.112933	+	0.195606i	0.804019	+	0.594604i	$0.202691\pi$
$684$	−2.57746	−	4.46429i	−0.0985515	−	0.170696i
$685$			5.99220i			0.228950i
$686$	−11.1742	+	14.7694i	−0.426635	+	0.563900i
$687$		−	1.20958i		−	0.0461485i
$688$	−0.262878	+	0.151773i	−0.0100221	+	0.00578628i
$689$	−42.8014	+	74.1343i	−1.63061	+	2.82429i
$690$	5.78434	+	5.50190i	0.220206	+	0.209454i
$691$	12.6557	−	7.30676i	0.481445	−	0.277962i	−0.239574	−	0.970878i	$-0.577008\pi$
$691$	12.6557	−	7.30676i	0.481445	−	0.277962i	0.721018	+	0.692916i	$0.243674\pi$
$692$			0.165853i			0.00630477i
$693$	−14.1575	−	18.3640i	−0.537797	−	0.697591i
$694$	−28.9888			−1.10040
$695$	10.5111	−	6.06857i	0.398707	−	0.230194i
$696$	−3.42878	−	1.97961i	−0.129968	−	0.0750368i
$697$	0.913475	+	0.527395i	0.0346003	+	0.0199765i
$698$	−10.7538	+	6.20868i	−0.407036	+	0.235002i
$699$		−	8.49645i		−	0.321365i
$700$	−7.85334	−	3.23212i	−0.296828	−	0.122163i
$701$		−	15.3358i		−	0.579225i	−0.957144	−	0.289613i	$-0.906474\pi$
$701$		−	15.3358i		−	0.579225i	0.957144	−	0.289613i	$-0.0935265\pi$
$702$	−18.0629	−	31.2859i	−0.681742	−	1.18081i
$703$	18.1301	+	10.4674i	0.683789	+	0.394786i
$704$	−5.22660	−	3.01758i	−0.196985	−	0.113729i
$705$	−0.234418	−	0.406023i	−0.00882868	−	0.0152917i
$706$			7.43049i			0.279650i
$707$	26.8359	−	3.59492i	1.00927	−	0.135201i
$708$	−1.58144			−0.0594340
$709$	−6.16233	+	3.55782i	−0.231431	+	0.133617i	−0.611232	−	0.791451i	$-0.709326\pi$
$709$	−6.16233	+	3.55782i	−0.231431	+	0.133617i	0.379801	+	0.925068i	$0.375992\pi$
$710$	−2.69432	+	4.66671i	−0.101116	+	0.175138i
$711$	15.4193	+	8.90232i	0.578268	+	0.333863i
$712$	4.71966	+	8.17470i	0.176877	+	0.306360i
$713$	3.64180	−	15.0920i	0.136387	−	0.565201i
$714$	−3.70715	+	0.496608i	−0.138737	+	0.0185851i
$715$	−52.6648			−1.96955
$716$	−4.07122	−	7.05156i	−0.152149	−	0.263529i
$717$	−15.9346	−	9.19985i	−0.595089	−	0.343575i
$718$	−17.2194	−	9.94165i	−0.642624	−	0.371019i
$719$	−11.2974	+	6.52254i	−0.421321	+	0.243250i	−0.695642	−	0.718388i	$-0.744880\pi$
$719$	−11.2974	+	6.52254i	−0.421321	+	0.243250i	0.274321	+	0.961638i	$0.411547\pi$
$720$	1.94297			0.0724102
$721$	29.5066	+	12.1437i	1.09888	+	0.452256i
$722$	6.39908			0.238149
$723$	14.2303	−	8.21585i	0.529230	−	0.305551i
$724$	8.38866	−	14.5296i	0.311762	−	0.539988i
$725$	−5.10743	+	8.84632i	−0.189685	+	0.328544i
$726$	27.3918	−	15.8147i	1.01661	−	0.586938i
$727$	−10.9061			−0.404485			−0.202242	−	0.979336i	$-0.564823\pi$
$727$	−10.9061			−0.404485			−0.202242	+	0.979336i	$0.564823\pi$
$728$	10.5357	+	13.6661i	0.390477	+	0.506499i
$729$	−24.3543			−0.902010
$730$	−14.8516	+	8.57455i	−0.549681	+	0.317358i
$731$	0.298709	+	0.172460i	0.0110481	+	0.00637865i
$732$	15.0864	+	8.71014i	0.557609	+	0.321936i
$733$	20.8868	+	36.1769i	0.771470	+	1.33623i	0.936757	+	0.349980i	$0.113812\pi$
$733$	20.8868	+	36.1769i	0.771470	+	1.33623i	−0.165287	+	0.986246i	$0.552855\pi$
$734$	21.7786			0.803861
$735$	11.2686	+	2.96473i	0.415649	+	0.109356i
$736$	−4.66202	−	1.12497i	−0.171844	−	0.0414671i
$737$	12.4510	+	21.5658i	0.458640	+	0.794388i
$738$	−1.16741	−	0.674005i	−0.0429730	−	0.0248104i
$739$	−2.88980	+	5.00528i	−0.106303	+	0.184122i	−0.914270	−	0.405106i	$-0.867235\pi$
$739$	−2.88980	+	5.00528i	−0.106303	+	0.184122i	0.807967	+	0.589228i	$0.200568\pi$
$740$	−6.83352	+	3.94533i	−0.251205	+	0.145033i
$741$	−28.8036			−1.05813
$742$	−21.2021	−	27.5018i	−0.778354	−	1.00962i
$743$			2.74633i			0.100753i	0.998730	+	0.0503766i	$0.0160422\pi$
$743$			2.74633i			0.100753i	−0.998730	+	0.0503766i	$0.983958\pi$
$744$	2.01374	+	3.48790i	0.0738274	+	0.127873i
$745$	−20.6070	−	11.8975i	−0.754984	−	0.435890i
$746$	17.5547	+	10.1352i	0.642723	+	0.371076i
$747$	−4.35193	−	7.53776i	−0.159229	−	0.275792i
$748$			6.85776i			0.250745i
$749$	8.91058	−	21.6507i	0.325586	−	0.791101i
$750$			13.6660i			0.499011i
$751$	38.7452	−	22.3695i	1.41383	−	0.816275i	0.418084	−	0.908408i	$-0.362702\pi$
$751$	38.7452	−	22.3695i	1.41383	−	0.816275i	0.995747	+	0.0921329i	$0.0293685\pi$
$752$	0.243918	+	0.140826i	0.00889479	+	0.00513541i
$753$	10.4056	+	6.00769i	0.379202	+	0.218932i
$754$	17.9748	−	10.3778i	0.654604	−	0.377936i
$755$	−26.0679			−0.948707
$756$	14.5251	−	1.94577i	0.528274	−	0.0707671i
$757$		−	12.3037i		−	0.447185i	−0.974683	−	0.223593i	$-0.928222\pi$
$757$		−	12.3037i		−	0.447185i	0.974683	−	0.223593i	$-0.0717785\pi$
$758$	15.1434	−	8.74305i	0.550033	−	0.317562i
$759$	24.8174	−	26.0914i	0.900813	−	0.947056i
$760$	2.37474	−	4.11318i	0.0861410	−	0.149201i
$761$	19.1725	−	11.0692i	0.695002	−	0.401260i	−0.110481	−	0.993878i	$-0.535239\pi$
$761$	19.1725	−	11.0692i	0.695002	−	0.401260i	0.805483	+	0.592618i	$0.201906\pi$
$762$			14.2469i			0.516110i
$763$	20.2083	−	2.70709i	0.731589	−	0.0980031i
$764$			3.60139i			0.130294i
$765$	−1.10390	−	1.91201i	−0.0399116	−	0.0691289i
$766$	−8.88242	+	15.3848i	−0.320935	+	0.555875i
$767$	4.14521	−	7.17972i	0.149675	−	0.259245i
$768$	1.07743	−	0.622057i	0.0388786	−	0.0224466i
$769$	−0.436260			−0.0157320			−0.00786598	−	0.999969i	$-0.502504\pi$
$769$	−0.436260			−0.0157320			−0.00786598	+	0.999969i	$0.502504\pi$
$770$	8.13091	−	19.7563i	0.293018	−	0.711968i
$771$	8.36308			0.301189
$772$	7.15236	+	12.3883i	0.257419	+	0.445863i
$773$	−13.4233	+	23.2498i	−0.482801	+	0.836236i	−0.999805	−	0.0197472i	$-0.993714\pi$
$773$	−13.4233	+	23.2498i	−0.482801	+	0.836236i	0.517004	+	0.855983i	$0.327047\pi$
$774$	−0.381746	−	0.220401i	−0.0137216	−	0.00792216i
$775$	8.99887	−	5.19550i	0.323249	−	0.186628i
$776$	−14.1845			−0.509194
$777$	−15.3740	+	11.8523i	−0.551539	+	0.425200i
$778$		−	16.1088i		−	0.577527i
$779$	−2.85367	+	1.64757i	−0.102243	+	0.0590303i
$780$	5.42827	−	9.40204i	0.194363	−	0.336647i
$781$	21.0501	+	12.1533i	0.753231	+	0.434878i
$782$	1.54168	+	5.22689i	0.0551304	+	0.186913i
$783$		−	17.6271i		−	0.629942i
$784$	−6.75320	+	1.84237i	−0.241186	+	0.0657989i
$785$	10.9861			0.392109
$786$	4.46767	+	7.73824i	0.159357	+	0.276014i
$787$	10.3912	−	17.9982i	0.370408	−	0.641565i	−0.619221	−	0.785217i	$-0.712551\pi$
$787$	10.3912	−	17.9982i	0.370408	−	0.641565i	0.989628	+	0.143652i	$0.0458847\pi$
$788$	6.02340	−	10.4328i	0.214575	−	0.371654i
$789$	−15.9363	−	27.6025i	−0.567347	−	0.982674i
$790$			16.4043i			0.583640i
$791$	14.3687	+	18.6380i	0.510892	+	0.662692i
$792$		−	8.76414i		−	0.311420i
$793$	−79.0880	+	45.6615i	−2.80850	+	1.62149i
$794$	−5.91641	−	3.41584i	−0.209966	−	0.121224i
$795$	−10.9239	+	18.9208i	−0.387432	+	0.671052i
$796$	−9.74098	−	16.8719i	−0.345260	−	0.598008i
$797$	−15.7307			−0.557209			−0.278605	−	0.960406i	$-0.589872\pi$
$797$	−15.7307			−0.557209			−0.278605	+	0.960406i	$0.589872\pi$
$798$	4.44699	−	10.8052i	0.157422	−	0.382499i
$799$		−	0.320042i		−	0.0113223i
$800$	−1.60492	−	2.77980i	−0.0567425	−	0.0982809i
$801$	−6.85380	+	11.8711i	−0.242167	+	0.419446i
$802$	−16.3143	−	9.41906i	−0.576077	−	0.332598i
$803$	38.6771	+	66.9908i	1.36489	+	2.36405i
$804$	−5.13342			−0.181042
$805$	1.75589	−	16.8859i	0.0618869	−	0.595149i
$806$	−21.1134			−0.743689
$807$	13.9506	+	24.1632i	0.491085	+	0.850584i
$808$	8.86258	+	5.11681i	0.311785	+	0.180009i
$809$	−5.87066	+	10.1683i	−0.206401	+	0.357498i	−0.950578	−	0.310485i	$-0.899509\pi$
$809$	−5.87066	+	10.1683i	−0.206401	+	0.357498i	0.744177	+	0.667983i	$0.232842\pi$
$810$	−1.69563	−	2.93692i	−0.0595784	−	0.103193i
$811$			32.1592i			1.12926i	0.825343	+	0.564631i	$0.190982\pi$
$811$			32.1592i			1.12926i	−0.825343	+	0.564631i	$0.809018\pi$
$812$	1.11791	+	8.34518i	0.0392311	+	0.292858i
$813$	−0.511408			−0.0179358
$814$	17.7962	+	30.8239i	0.623756	+	1.08038i
$815$	−10.0187	+	17.3529i	−0.350940	+	0.607847i
$816$	−1.22429	−	0.706844i	−0.0428587	−	0.0247445i
$817$	−0.933159	+	0.538760i	−0.0326471	+	0.0188488i
$818$			5.91813i			0.206923i
$819$	−9.53696	+	23.1727i	−0.333248	+	0.809719i
$820$		−	1.24199i		−	0.0433722i
$821$	−1.84632	−	3.19792i	−0.0644371	−	0.111608i	0.832007	−	0.554765i	$-0.187192\pi$
$821$	−1.84632	−	3.19792i	−0.0644371	−	0.111608i	−0.896444	+	0.443157i	$0.853859\pi$
$822$	−2.78593	+	4.82538i	−0.0971705	+	0.168304i
$823$	−9.19610	+	15.9281i	−0.320556	+	0.555219i	−0.980603	−	0.196005i	$-0.937203\pi$
$823$	−9.19610	+	15.9281i	−0.320556	+	0.555219i	0.660047	+	0.751224i	$0.270536\pi$
$824$	6.03001	+	10.4443i	0.210065	+	0.363844i
$825$	24.1009			0.839085
$826$	2.05337	+	2.66348i	0.0714459	+	0.0926744i
$827$		−	2.41961i		−	0.0841382i	−0.999115	−	0.0420691i	$-0.986605\pi$
$827$		−	2.41961i		−	0.0841382i	0.999115	−	0.0420691i	$-0.0133950\pi$
$828$	−1.97025	−	6.67990i	−0.0684709	−	0.232143i
$829$	−9.79002	−	5.65227i	−0.340021	−	0.196311i	0.320260	−	0.947330i	$-0.396230\pi$
$829$	−9.79002	−	5.65227i	−0.340021	−	0.196311i	−0.660282	+	0.751018i	$0.729563\pi$
$830$	4.00966	−	6.94493i	0.139177	−	0.241062i
$831$	4.96919	−	2.86897i	0.172379	−	0.0995233i
$832$			6.52207i			0.226112i
$833$	5.64984	+	5.59885i	0.195755	+	0.193989i
$834$	11.2858			0.390794
$835$	−16.8668	+	9.73806i	−0.583700	+	0.337000i
$836$	−18.5533	−	10.7117i	−0.641679	−	0.370473i
$837$	−8.96554	+	15.5288i	−0.309895	+	0.536753i
$838$	−2.06781	−	3.58155i	−0.0714313	−	0.123723i
$839$	28.2187			0.974219			0.487110	−	0.873341i	$-0.338051\pi$
$839$	28.2187			0.974219			0.487110	+	0.873341i	$0.338051\pi$
$840$	2.68895	+	3.48790i	0.0927775	+	0.120344i
$841$	−18.8726			−0.650780
$842$	25.3652	−	14.6446i	0.874143	−	0.504687i
$843$	−12.8091	+	22.1860i	−0.441169	+	0.764126i
$844$	−6.09331	+	10.5539i	−0.209740	+	0.363281i
$845$	19.7600	+	34.2254i	0.679766	+	1.17739i
$846$			0.409010i			0.0140621i
$847$	−62.2015	−	25.5997i	−2.13727	−	0.879615i
$848$		−	13.1251i		−	0.450718i
$849$	0.375963	−	0.217062i	0.0129030	−	0.00744956i
$850$	−1.82367	+	3.15869i	−0.0625515	+	0.108342i
$851$	20.4935	+	19.4928i	0.702507	+	0.668205i
$852$	−4.33935	+	2.50533i	−0.148664	+	0.0858311i
$853$			44.0603i			1.50860i	0.656532	+	0.754298i	$0.272023\pi$
$853$			44.0603i			1.50860i	−0.656532	+	0.754298i	$0.727977\pi$
$854$	−4.91874	−	36.7182i	−0.168316	−	1.25647i
$855$	6.89711			0.235876
$856$	7.66359	−	4.42458i	0.261936	−	0.151229i
$857$	−47.2791	−	27.2966i	−1.61502	−	0.932434i	−0.988182	−	0.153287i	$-0.951014\pi$
$857$	−47.2791	−	27.2966i	−1.61502	−	0.932434i	−0.626842	−	0.779147i	$-0.715653\pi$
$858$	−42.4097	−	24.4853i	−1.44784	−	0.835913i
$859$	2.15309	−	1.24309i	0.0734626	−	0.0424136i	−0.462819	−	0.886453i	$-0.653162\pi$
$859$	2.15309	−	1.24309i	0.0734626	−	0.0424136i	0.536281	+	0.844039i	$0.319829\pi$
$860$		−	0.406134i		−	0.0138491i
$861$	−0.405688	−	3.02844i	−0.0138258	−	0.103209i
$862$		−	5.28266i		−	0.179928i
$863$	−21.9157	−	37.9590i	−0.746018	−	1.29214i	−0.949718	−	0.313107i	$-0.898630\pi$
$863$	−21.9157	−	37.9590i	−0.746018	−	1.29214i	0.203700	−	0.979033i	$-0.434703\pi$
$864$	4.79693	+	2.76951i	0.163195	+	0.0942207i
$865$	−0.192176	−	0.110953i	−0.00653417	−	0.00377251i
$866$	−14.5215	−	25.1520i	−0.493461	−	0.854700i
$867$		−	19.5436i		−	0.663734i
$868$	3.25970	−	7.92035i	0.110642	−	0.268834i
$869$	73.9949			2.51011
$870$	4.58760	−	2.64865i	0.155534	−	0.0897977i
$871$	13.4556	−	23.3057i	0.455925	−	0.789685i
$872$	6.67380	+	3.85312i	0.226003	+	0.130483i
$873$	−10.2992	−	17.8388i	−0.348576	−	0.603751i
$874$	−16.5491	−	3.99341i	−0.559783	−	0.135079i
$875$	23.0165	−	17.7442i	0.778099	−	0.599864i
$876$	−15.9461			−0.538770
$877$	2.75727	+	4.77574i	0.0931065	+	0.161265i	0.908817	−	0.417195i	$-0.136987\pi$
$877$	2.75727	+	4.77574i	0.0931065	+	0.161265i	−0.815710	+	0.578461i	$0.803654\pi$
$878$	29.6005	+	17.0899i	0.998969	+	0.576755i
$879$	−27.1129	−	15.6536i	−0.914495	−	0.527984i
$880$	6.99303	−	4.03743i	0.235735	−	0.136102i
$881$	−51.6788			−1.74110			−0.870552	−	0.492076i	$-0.836238\pi$
$881$	−51.6788			−1.74110			−0.870552	+	0.492076i	$0.836238\pi$
$882$	−7.22043	−	7.15526i	−0.243125	−	0.240930i
$883$	53.5374			1.80168			0.900838	−	0.434155i	$-0.142953\pi$
$883$	53.5374			1.80168			0.900838	+	0.434155i	$0.142953\pi$
$884$	6.41814	−	3.70552i	0.215866	−	0.124630i
$885$	1.05796	−	1.83243i	0.0355628	−	0.0615966i
$886$	−0.874186	+	1.51413i	−0.0293688	+	0.0508683i
$887$	23.7721	−	13.7248i	0.798190	−	0.460835i	−0.0446478	−	0.999003i	$-0.514217\pi$
$887$	23.7721	−	13.7248i	0.798190	−	0.460835i	0.842838	+	0.538167i	$0.180883\pi$
$888$	−7.33716			−0.246219
$889$	23.9948	−	18.4985i	0.804761	−	0.620418i
$890$	−12.6295			−0.423343
$891$	−13.2475	+	7.64847i	−0.443809	+	0.256233i
$892$	−14.3324	−	8.27481i	−0.479884	−	0.277061i
$893$	0.865856	+	0.499902i	0.0289748	+	0.0167286i
$894$	−11.0629	−	19.1615i	−0.369999	−	0.640858i
$895$	10.8943			0.364157
$896$	−2.44664	−	1.00694i	−0.0817366	−	0.0336396i
$897$	−37.8286	−	9.12827i	−1.26306	−	0.304784i
$898$	10.3682	+	17.9582i	0.345990	+	0.599272i
$899$	−8.92181	−	5.15101i	−0.297559	−	0.171796i
$900$	2.33063	−	4.03677i	0.0776877	−	0.134559i
$901$	−12.9160	+	7.45704i	−0.430293	+	0.248430i
$902$	−5.60224			−0.186534
$903$	−0.132661	−	0.990310i	−0.00441469	−	0.0329554i
$904$			8.89491i			0.295840i
$905$	11.2238	+	19.4401i	0.373091	+	0.646212i
$906$	−20.9918	−	12.1196i	−0.697407	−	0.402648i
$907$	−7.07108	−	4.08249i	−0.234791	−	0.135557i	0.377989	−	0.925810i	$-0.376616\pi$
$907$	−7.07108	−	4.08249i	−0.234791	−	0.135557i	−0.612781	+	0.790253i	$0.709949\pi$
$908$	−8.69075	−	15.0528i	−0.288413	−	0.499545i
$909$			14.8611i			0.492910i
$910$	−22.8833	+	3.06543i	−0.758573	+	0.101618i
$911$			5.20076i			0.172309i	0.996282	+	0.0861544i	$0.0274578\pi$
$911$			5.20076i			0.172309i	−0.996282	+	0.0861544i	$0.972542\pi$
$912$	3.82465	−	2.20816i	0.126647	−	0.0731196i
$913$	−31.3264	−	18.0863i	−1.03675	−	0.598570i
$914$	−10.3635	−	5.98335i	−0.342793	−	0.197912i
$915$	−20.1851	+	11.6539i	−0.667300	+	0.385266i
$916$	−0.972244			−0.0321239
$917$	7.23195	−	17.5720i	0.238820	−	0.580279i
$918$		−	6.29399i		−	0.207733i
$919$	13.2238	−	7.63479i	0.436214	−	0.251848i	−0.265776	−	0.964035i	$-0.585628\pi$
$919$	13.2238	−	7.63479i	0.436214	−	0.251848i	0.701990	+	0.712186i	$0.252295\pi$
$920$	4.42234	−	4.64936i	0.145800	−	0.153285i
$921$	8.04158	−	13.9284i	0.264979	−	0.458957i
$922$	12.9623	−	7.48378i	0.426890	−	0.246465i
$923$		−	26.2675i		−	0.864607i
$924$	15.7329	−	12.1290i	0.517573	−	0.399015i
$925$			18.9300i			0.622415i
$926$	4.00621	+	6.93897i	0.131652	+	0.228029i
$927$	−8.75665	+	15.1670i	−0.287606	+	0.498149i
$928$	−1.59118	+	2.75600i	−0.0522330	+	0.0904701i
$929$	−9.12023	+	5.26557i	−0.299225	+	0.172758i	−0.642095	−	0.766625i	$-0.721934\pi$
$929$	−9.12023	+	5.26557i	−0.299225	+	0.172758i	0.342870	+	0.939383i	$0.388601\pi$
$930$	−5.38865			−0.176701
$931$	−23.9723	+	6.54000i	−0.785662	+	0.214340i
$932$	−6.82932			−0.223702
$933$	−2.22703	−	3.85732i	−0.0729096	−	0.126283i
$934$	−0.207210	+	0.358899i	−0.00678013	+	0.0117435i
$935$	−7.94619	−	4.58773i	−0.259868	−	0.150035i
$936$	−8.20231	+	4.73561i	−0.268101	+	0.154788i
$937$	30.4361			0.994304			0.497152	−	0.867663i	$-0.334379\pi$
$937$	30.4361			0.994304			0.497152	+	0.867663i	$0.334379\pi$
$938$	6.66535	+	8.64580i	0.217631	+	0.282296i
$939$		−	6.72601i		−	0.219495i
$940$	−0.326355	+	0.188421i	−0.0106445	+	0.00614562i
$941$	−8.00849	+	13.8711i	−0.261069	+	0.452185i	−0.966526	−	0.256567i	$-0.917408\pi$
$941$	−8.00849	+	13.8711i	−0.261069	+	0.452185i	0.705457	+	0.708753i	$0.250742\pi$
$942$	8.84682	+	5.10771i	0.288245	+	0.166418i
$943$	−4.26995	+	1.25943i	−0.139049	+	0.0410126i
$944$			1.27113i			0.0413719i
$945$	−7.46248	+	18.1322i	−0.242754	+	0.589839i
$946$	−1.83195			−0.0595617
$947$	26.9028	+	46.5971i	0.874225	+	1.51420i	0.857586	+	0.514341i	$0.171963\pi$
$947$	26.9028	+	46.5971i	0.874225	+	1.51420i	0.0166392	+	0.999862i	$0.494703\pi$
$948$	−7.62682	+	13.2100i	−0.247708	+	0.429042i
$949$	41.7975	−	72.3955i	1.35681	−	2.35006i
$950$	−5.69711	−	9.86768i	−0.184839	−	0.320150i
$951$			33.6296i			1.09052i
$952$	0.399166	+	2.97975i	0.0129370	+	0.0965743i
$953$		−	21.2679i		−	0.688936i	−0.938798	−	0.344468i	$-0.888059\pi$
$953$		−	21.2679i		−	0.688936i	0.938798	−	0.344468i	$-0.111941\pi$
$954$	16.5065	−	9.53001i	0.534416	−	0.308545i
$955$	−4.17298	−	2.40927i	−0.135034	−	0.0779622i
$956$	−7.39470	+	12.8080i	−0.239162	+	0.414240i
$957$	−11.9472	−	20.6932i	−0.386200	−	0.668917i
$958$	20.6791			0.668110
$959$	11.7443	−	1.57326i	0.379243	−	0.0508031i
$960$			1.66459i			0.0537243i
$961$	−10.2602	−	17.7711i	−0.330973	−	0.573262i
$962$	19.2319	−	33.3107i	0.620063	−	1.07398i
$963$	11.1289	+	6.42528i	0.358624	+	0.207052i
$964$	−6.60378	−	11.4381i	−0.212693	−	0.368396i
$965$	−19.1393			−0.616115
$966$	9.26467	−	12.7814i	0.298086	−	0.411236i
$967$	−23.6682			−0.761116			−0.380558	−	0.924757i	$-0.624268\pi$
$967$	−23.6682			−0.761116			−0.380558	+	0.924757i	$0.624268\pi$
$968$	−12.7116	−	22.0171i	−0.408566	−	0.707657i
$969$	−4.34596	−	2.50914i	−0.139612	−	0.0806052i
$970$	9.48921	−	16.4358i	0.304680	−	0.527722i
$971$	−28.3288	−	49.0669i	−0.909114	−	1.57463i	−0.815297	−	0.579043i	$-0.803426\pi$
$971$	−28.3288	−	49.0669i	−0.909114	−	1.57463i	−0.0938170	−	0.995589i	$-0.529907\pi$
$972$			13.4637i			0.431848i
$973$	−14.6537	−	19.0077i	−0.469775	−	0.609358i
$974$	−6.52145			−0.208961
$975$	−13.0226	−	22.5559i	−0.417058	−	0.722366i
$976$	7.00107	−	12.1262i	0.224099	−	0.388151i
$977$	−31.5941	−	18.2409i	−1.01079	−	0.583577i	−0.0993638	−	0.995051i	$-0.531681\pi$
$977$	−31.5941	−	18.2409i	−1.01079	−	0.583577i	−0.911422	+	0.411474i	$0.865014\pi$
$978$	−16.1357	+	9.31594i	−0.515962	+	0.297891i
$979$			56.9679i			1.82070i
$980$	2.38300	−	9.05754i	0.0761223	−	0.289333i
$981$			11.1908i			0.357296i
$982$	7.31570	+	12.6712i	0.233453	+	0.404353i
$983$	−10.0238	+	17.3617i	−0.319708	+	0.553751i	−0.980427	−	0.196883i	$-0.936918\pi$
$983$	−10.0238	+	17.3617i	−0.319708	+	0.553751i	0.660719	+	0.750633i	$0.270252\pi$
$984$	0.577435	−	1.00015i	0.0184079	−	0.0318835i
$985$	8.05912	+	13.9588i	0.256785	+	0.444764i
$986$	3.61611			0.115161
$987$	−0.734231	+	0.566044i	−0.0233708	+	0.0180174i
$988$			23.1519i			0.736560i
$989$	−1.39628	+	0.411837i	−0.0443992	+	0.0130956i
$990$	10.1551	+	5.86307i	0.322751	+	0.186341i
$991$	2.86853	−	4.96844i	0.0911219	−	0.157828i	−0.816862	−	0.576834i	$-0.804288\pi$
$991$	2.86853	−	4.96844i	0.0911219	−	0.157828i	0.907983	+	0.419006i	$0.137621\pi$
$992$	2.80352	−	1.61862i	0.0890120	−	0.0513911i
$993$		−	9.05996i		−	0.287509i
$994$	9.85382	+	4.05544i	0.312544	+	0.128631i
$995$	26.0663			0.826356
$996$	6.45777	−	3.72839i	0.204622	−	0.118139i
$997$	2.57381	+	1.48599i	0.0815134	+	0.0470618i	0.540203	−	0.841535i	$-0.318348\pi$
$997$	2.57381	+	1.48599i	0.0815134	+	0.0470618i	−0.458689	+	0.888597i	$0.651681\pi$
$998$	8.69163	−	15.0544i	0.275129	−	0.476537i
$999$	−16.3332	−	28.2899i	−0.516759	−	0.895053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.b.45.3	✓	16
7.3	odd	6		2254.2.c.b.2253.5		16
7.4	even	3		2254.2.c.b.2253.12		16
7.5	odd	6	inner	322.2.g.b.229.4	yes	16
23.22	odd	2	inner	322.2.g.b.45.4	yes	16
161.45	even	6		2254.2.c.b.2253.6		16
161.68	even	6	inner	322.2.g.b.229.3	yes	16
161.137	odd	6		2254.2.c.b.2253.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.b.45.3	✓	16	1.1	even	1	trivial
322.2.g.b.45.4	yes	16	23.22	odd	2	inner
322.2.g.b.229.3	yes	16	161.68	even	6	inner
322.2.g.b.229.4	yes	16	7.5	odd	6	inner
2254.2.c.b.2253.5		16	7.3	odd	6
2254.2.c.b.2253.6		16	161.45	even	6
2254.2.c.b.2253.11		16	161.137	odd	6
2254.2.c.b.2253.12		16	7.4	even	3

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.07743 - 0.622057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.668984 - 1.15871i) q^{5} -1.24411i q^{6} +(-2.09536 + 1.61539i) q^{7} -1.00000 q^{8} +(-0.726090 - 1.25762i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.07743 - 0.622057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.668984 - 1.15871i) q^{5} -1.24411i q^{6} +(-2.09536 + 1.61539i) q^{7} -1.00000 q^{8} +(-0.726090 - 1.25762i) q^{9} +(0.668984 - 1.15871i) q^{10} +(-5.22660 - 3.01758i) q^{11} +(1.07743 - 0.622057i) q^{12} +6.52207i q^{13} +(-2.44664 - 1.00694i) q^{14} +1.66459i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.568151 + 0.984066i) q^{17} +(0.726090 - 1.25762i) q^{18} +(-1.77489 - 3.07420i) q^{19} +1.33797 q^{20} +(3.26247 - 0.437039i) q^{21} -6.03516i q^{22} +(-1.35675 - 4.59992i) q^{23} +(1.07743 + 0.622057i) q^{24} +(1.60492 - 2.77980i) q^{25} +(-5.64828 + 3.26103i) q^{26} +5.53902i q^{27} +(-0.351285 - 2.62233i) q^{28} -3.18236 q^{29} +(-1.44157 + 0.832293i) q^{30} +(2.80352 + 1.61862i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.75422 + 6.50249i) q^{33} -1.13630 q^{34} +(3.27353 + 1.34726i) q^{35} +1.45218 q^{36} +(-5.10738 + 2.94875i) q^{37} +(1.77489 - 3.07420i) q^{38} +(4.05710 - 7.02710i) q^{39} +(0.668984 + 1.15871i) q^{40} -0.928266i q^{41} +(2.00972 + 2.60687i) q^{42} -0.303546i q^{43} +(5.22660 - 3.01758i) q^{44} +(-0.971485 + 1.68266i) q^{45} +(3.30527 - 3.47494i) q^{46} +(-0.243918 + 0.140826i) q^{47} +1.24411i q^{48} +(1.78106 - 6.76962i) q^{49} +3.20984 q^{50} +(1.22429 - 0.706844i) q^{51} +(-5.64828 - 3.26103i) q^{52} +(11.3667 + 6.56256i) q^{53} +(-4.79693 + 2.76951i) q^{54} +8.07486i q^{55} +(2.09536 - 1.61539i) q^{56} +4.41633i q^{57} +(-1.59118 - 2.75600i) q^{58} +(-1.10083 - 0.635567i) q^{59} +(-1.44157 - 0.832293i) q^{60} +(7.00107 + 12.1262i) q^{61} +3.23723i q^{62} +(3.55297 + 1.46226i) q^{63} +1.00000 q^{64} +(7.55722 - 4.36316i) q^{65} +(-3.75422 + 6.50249i) q^{66} +(-3.57337 - 2.06308i) q^{67} +(-0.568151 - 0.984066i) q^{68} +(-1.39960 + 5.80009i) q^{69} +(0.470008 + 3.50859i) q^{70} -4.02749 q^{71} +(0.726090 + 1.25762i) q^{72} +(-11.1001 - 6.40863i) q^{73} +(-5.10738 - 2.94875i) q^{74} +(-3.45839 + 1.99670i) q^{75} +3.54978 q^{76} +(15.8262 - 2.12006i) q^{77} +8.11420 q^{78} +(-10.6180 + 6.13032i) q^{79} +(-0.668984 + 1.15871i) q^{80} +(1.26732 - 2.19506i) q^{81} +(0.803902 - 0.464133i) q^{82} +5.99365 q^{83} +(-1.25275 + 3.04391i) q^{84} +1.52033 q^{85} +(0.262878 - 0.151773i) q^{86} +(3.42878 + 1.97961i) q^{87} +(5.22660 + 3.01758i) q^{88} +(-4.71966 - 8.17470i) q^{89} -1.94297 q^{90} +(-10.5357 - 13.6661i) q^{91} +(4.66202 + 1.12497i) q^{92} +(-2.01374 - 3.48790i) q^{93} +(-0.243918 - 0.140826i) q^{94} +(-2.37474 + 4.11318i) q^{95} +(-1.07743 + 0.622057i) q^{96} +14.1845 q^{97} +(6.75320 - 1.84237i) q^{98} +8.76414i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9	\( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+O(q^{100}) \) 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9 + 6 * q^12 - 8 * q^16 - 10 * q^18 + 8 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^29 + 12 * q^31 + 8 * q^32 - 20 * q^36 - 2 * q^39 - 8 * q^46 - 6 * q^47 - 18 * q^49 + 4 * q^50 - 6 * q^52 + 18 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 12 * q^70 - 52 * q^71 - 10 * q^72 + 24 * q^73 + 30 * q^77 - 4 * q^78 - 20 * q^81 + 54 * q^82 + 80 * q^85 + 54 * q^87 - 16 * q^92 - 26 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96

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