LMFDB - Embedded newform 560.2.bd.a.141.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.5
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16029 + 0.808533i) q^{2} +(0.925827 + 0.925827i) q^{3} +(0.692549 - 1.87627i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.82279 - 0.325667i) q^{6} -1.00000i q^{7} +(0.713464 + 2.73696i) q^{8} -1.28569i q^{9} +O(q^{10})$	\(q+(-1.16029 + 0.808533i) q^{2} +(0.925827 + 0.925827i) q^{3} +(0.692549 - 1.87627i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.82279 - 0.325667i) q^{6} -1.00000i q^{7} +(0.713464 + 2.73696i) q^{8} -1.28569i q^{9} +(0.248730 - 1.39217i) q^{10} +(3.01204 - 3.01204i) q^{11} +(2.37828 - 1.09592i) q^{12} +(-0.350216 - 0.350216i) q^{13} +(0.808533 + 1.16029i) q^{14} -1.30932 q^{15} +(-3.04075 - 2.59881i) q^{16} +5.90144 q^{17} +(1.03952 + 1.49177i) q^{18} +(0.223515 + 0.223515i) q^{19} +(0.837014 + 1.81643i) q^{20} +(0.925827 - 0.925827i) q^{21} +(-1.05951 + 5.93017i) q^{22} +2.20486i q^{23} +(-1.87341 + 3.19450i) q^{24} -1.00000i q^{25} +(0.689514 + 0.123191i) q^{26} +(3.96781 - 3.96781i) q^{27} +(-1.87627 - 0.692549i) q^{28} +(1.25462 + 1.25462i) q^{29} +(1.51919 - 1.05863i) q^{30} +2.03846 q^{31} +(5.62938 + 0.556833i) q^{32} +5.57725 q^{33} +(-6.84738 + 4.77150i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-2.41230 - 0.890403i) q^{36} +(-1.71551 + 1.71551i) q^{37} +(-0.440062 - 0.0786233i) q^{38} -0.648479i q^{39} +(-2.43982 - 1.43083i) q^{40} -8.96038i q^{41} +(-0.325667 + 1.82279i) q^{42} +(-5.64543 + 5.64543i) q^{43} +(-3.56540 - 7.73737i) q^{44} +(0.909119 + 0.909119i) q^{45} +(-1.78270 - 2.55828i) q^{46} +10.6249 q^{47} +(-0.409157 - 5.22126i) q^{48} -1.00000 q^{49} +(0.808533 + 1.16029i) q^{50} +(5.46371 + 5.46371i) q^{51} +(-0.899641 + 0.414557i) q^{52} +(-1.26828 + 1.26828i) q^{53} +(-1.39571 + 7.81191i) q^{54} +4.25966i q^{55} +(2.73696 - 0.713464i) q^{56} +0.413873i q^{57} +(-2.47013 - 0.441324i) q^{58} +(-3.11416 + 3.11416i) q^{59} +(-0.906767 + 2.45663i) q^{60} +(2.39463 + 2.39463i) q^{61} +(-2.36521 + 1.64817i) q^{62} -1.28569 q^{63} +(-6.98194 + 3.90545i) q^{64} +0.495280 q^{65} +(-6.47123 + 4.50939i) q^{66} +(4.05417 + 4.05417i) q^{67} +(4.08703 - 11.0727i) q^{68} +(-2.04132 + 2.04132i) q^{69} +(-1.39217 - 0.248730i) q^{70} +9.47994i q^{71} +(3.51888 - 0.917293i) q^{72} -6.05800i q^{73} +(0.603444 - 3.37754i) q^{74} +(0.925827 - 0.925827i) q^{75} +(0.574170 - 0.264579i) q^{76} +(-3.01204 - 3.01204i) q^{77} +(0.524317 + 0.752424i) q^{78} -1.37345 q^{79} +(3.98777 - 0.312497i) q^{80} +3.48994 q^{81} +(7.24476 + 10.3966i) q^{82} +(8.19539 + 8.19539i) q^{83} +(-1.09592 - 2.37828i) q^{84} +(-4.17295 + 4.17295i) q^{85} +(1.98583 - 11.1149i) q^{86} +2.32313i q^{87} +(10.3928 + 6.09485i) q^{88} -9.38882i q^{89} +(-1.78990 - 0.319790i) q^{90} +(-0.350216 + 0.350216i) q^{91} +(4.13690 + 1.52697i) q^{92} +(1.88726 + 1.88726i) q^{93} +(-12.3280 + 8.59061i) q^{94} -0.316098 q^{95} +(4.69630 + 5.72736i) q^{96} -6.87272 q^{97} +(1.16029 - 0.808533i) q^{98} +(-3.87254 - 3.87254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.16029	+	0.808533i	−0.820449	+	0.571719i
$2$	−1.16029	+	0.808533i	−0.820449	+	0.571719i
$3$	0.925827	+	0.925827i	0.534526	+	0.534526i	0.921916	−	0.387390i	$-0.126623\pi$
$3$	0.925827	+	0.925827i	0.534526	+	0.534526i	−0.387390	+	0.921916i	$0.626623\pi$
$4$	0.692549	−	1.87627i	0.346275	−	0.938133i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−1.82279	−	0.325667i	−0.744151	−	0.132953i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.713464	+	2.73696i	0.252248	+	0.967663i
$9$		−	1.28569i		−	0.428563i
$10$	0.248730	−	1.39217i	0.0786555	−	0.440242i
$11$	3.01204	−	3.01204i	0.908163	−	0.908163i	−0.0879605	−	0.996124i	$-0.528035\pi$
$11$	3.01204	−	3.01204i	0.908163	−	0.908163i	0.996124	+	0.0879605i	$0.0280349\pi$
$12$	2.37828	−	1.09592i	0.686550	−	0.316364i
$13$	−0.350216	−	0.350216i	−0.0971325	−	0.0971325i	0.656871	−	0.754003i	$-0.271880\pi$
$13$	−0.350216	−	0.350216i	−0.0971325	−	0.0971325i	−0.754003	+	0.656871i	$0.771880\pi$
$14$	0.808533	+	1.16029i	0.216089	+	0.310101i
$15$	−1.30932			−0.338064
$16$	−3.04075	−	2.59881i	−0.760188	−	0.649703i
$17$	5.90144			1.43131			0.715654	−	0.698455i	$-0.246129\pi$
$17$	5.90144			1.43131			0.715654	+	0.698455i	$0.246129\pi$
$18$	1.03952	+	1.49177i	0.245018	+	0.351614i
$19$	0.223515	+	0.223515i	0.0512779	+	0.0512779i	0.732281	−	0.681003i	$-0.238456\pi$
$19$	0.223515	+	0.223515i	0.0512779	+	0.0512779i	−0.681003	+	0.732281i	$0.738456\pi$
$20$	0.837014	+	1.81643i	0.187162	+	0.406165i
$21$	0.925827	−	0.925827i	0.202032	−	0.202032i
$22$	−1.05951	+	5.93017i	−0.225888	+	1.26432i
$23$			2.20486i			0.459745i	0.973221	+	0.229873i	$0.0738309\pi$
$23$			2.20486i			0.459745i	−0.973221	+	0.229873i	$0.926169\pi$
$24$	−1.87341	+	3.19450i	−0.382408	+	0.652074i
$25$		−	1.00000i		−	0.200000i
$26$	0.689514	+	0.123191i	0.135225	+	0.0241598i
$27$	3.96781	−	3.96781i	0.763605	−	0.763605i
$28$	−1.87627	−	0.692549i	−0.354581	−	0.130880i
$29$	1.25462	+	1.25462i	0.232978	+	0.232978i	0.813935	−	0.580957i	$-0.197321\pi$
$29$	1.25462	+	1.25462i	0.232978	+	0.232978i	−0.580957	+	0.813935i	$0.697321\pi$
$30$	1.51919	−	1.05863i	0.277365	−	0.193278i
$31$	2.03846			0.366119			0.183059	−	0.983102i	$-0.441400\pi$
$31$	2.03846			0.366119			0.183059	+	0.983102i	$0.441400\pi$
$32$	5.62938	+	0.556833i	0.995143	+	0.0984350i
$33$	5.57725			0.970875
$34$	−6.84738	+	4.77150i	−1.17432	+	0.818306i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	−2.41230	−	0.890403i	−0.402049	−	0.148400i
$37$	−1.71551	+	1.71551i	−0.282028	+	0.282028i	−0.833917	−	0.551889i	$-0.813907\pi$
$37$	−1.71551	+	1.71551i	−0.282028	+	0.282028i	0.551889	+	0.833917i	$0.313907\pi$
$38$	−0.440062	−	0.0786233i	−0.0713875	−	0.0127544i
$39$		−	0.648479i		−	0.103840i
$40$	−2.43982	−	1.43083i	−0.385770	−	0.226234i
$41$		−	8.96038i		−	1.39938i	−0.714449	−	0.699688i	$-0.753322\pi$
$41$		−	8.96038i		−	1.39938i	0.714449	−	0.699688i	$-0.246678\pi$
$42$	−0.325667	+	1.82279i	−0.0502515	+	0.281263i
$43$	−5.64543	+	5.64543i	−0.860920	+	0.860920i	−0.991445	−	0.130525i	$-0.958334\pi$
$43$	−5.64543	+	5.64543i	−0.860920	+	0.860920i	0.130525	+	0.991445i	$0.458334\pi$
$44$	−3.56540	−	7.73737i	−0.537504	−	1.16645i
$45$	0.909119	+	0.909119i	0.135524	+	0.135524i
$46$	−1.78270	−	2.55828i	−0.262845	−	0.377198i
$47$	10.6249			1.54981			0.774903	−	0.632080i	$-0.217798\pi$
$47$	10.6249			1.54981			0.774903	+	0.632080i	$0.217798\pi$
$48$	−0.409157	−	5.22126i	−0.0590568	−	0.753624i
$49$	−1.00000			−0.142857
$50$	0.808533	+	1.16029i	0.114344	+	0.164090i
$51$	5.46371	+	5.46371i	0.765072	+	0.765072i
$52$	−0.899641	+	0.414557i	−0.124758	+	0.0574887i
$53$	−1.26828	+	1.26828i	−0.174211	+	0.174211i	−0.788827	−	0.614616i	$-0.789311\pi$
$53$	−1.26828	+	1.26828i	−0.174211	+	0.174211i	0.614616	+	0.788827i	$0.289311\pi$
$54$	−1.39571	+	7.81191i	−0.189932	+	1.06307i
$55$			4.25966i			0.574373i
$56$	2.73696	−	0.713464i	0.365742	−	0.0953407i
$57$			0.413873i			0.0548188i
$58$	−2.47013	−	0.441324i	−0.324345	−	0.0579487i
$59$	−3.11416	+	3.11416i	−0.405429	+	0.405429i	−0.880141	−	0.474712i	$-0.842552\pi$
$59$	−3.11416	+	3.11416i	−0.405429	+	0.405429i	0.474712	+	0.880141i	$0.342552\pi$
$60$	−0.906767	+	2.45663i	−0.117063	+	0.317149i
$61$	2.39463	+	2.39463i	0.306601	+	0.306601i	0.843590	−	0.536988i	$-0.180438\pi$
$61$	2.39463	+	2.39463i	0.306601	+	0.306601i	−0.536988	+	0.843590i	$0.680438\pi$
$62$	−2.36521	+	1.64817i	−0.300382	+	0.209317i
$63$	−1.28569			−0.161982
$64$	−6.98194	+	3.90545i	−0.872742	+	0.488182i
$65$	0.495280			0.0614320
$66$	−6.47123	+	4.50939i	−0.796554	+	0.555068i
$67$	4.05417	+	4.05417i	0.495296	+	0.495296i	0.909970	−	0.414674i	$-0.136104\pi$
$67$	4.05417	+	4.05417i	0.495296	+	0.495296i	−0.414674	+	0.909970i	$0.636104\pi$
$68$	4.08703	−	11.0727i	0.495626	−	1.34276i
$69$	−2.04132	+	2.04132i	−0.245746	+	0.245746i
$70$	−1.39217	−	0.248730i	−0.166396	−	0.0297290i
$71$			9.47994i			1.12506i	0.826776	+	0.562531i	$0.190172\pi$
$71$			9.47994i			1.12506i	−0.826776	+	0.562531i	$0.809828\pi$
$72$	3.51888	−	0.917293i	0.414704	−	0.108104i
$73$		−	6.05800i		−	0.709035i	−0.935049	−	0.354518i	$-0.884645\pi$
$73$		−	6.05800i		−	0.709035i	0.935049	−	0.354518i	$-0.115355\pi$
$74$	0.603444	−	3.37754i	0.0701490	−	0.392631i
$75$	0.925827	−	0.925827i	0.106905	−	0.106905i
$76$	0.574170	−	0.264579i	0.0658618	−	0.0303493i
$77$	−3.01204	−	3.01204i	−0.343254	−	0.343254i
$78$	0.524317	+	0.752424i	0.0593672	+	0.0851953i
$79$	−1.37345			−0.154525			−0.0772624	−	0.997011i	$-0.524618\pi$
$79$	−1.37345			−0.154525			−0.0772624	+	0.997011i	$0.524618\pi$
$80$	3.98777	−	0.312497i	0.445847	−	0.0349382i
$81$	3.48994			0.387771
$82$	7.24476	+	10.3966i	0.800050	+	1.14812i
$83$	8.19539	+	8.19539i	0.899561	+	0.899561i	0.995397	−	0.0958357i	$-0.0305523\pi$
$83$	8.19539	+	8.19539i	0.899561	+	0.899561i	−0.0958357	+	0.995397i	$0.530552\pi$
$84$	−1.09592	−	2.37828i	−0.119574	−	0.259491i
$85$	−4.17295	+	4.17295i	−0.452619	+	0.452619i
$86$	1.98583	−	11.1149i	0.214137	−	1.19855i
$87$			2.32313i			0.249066i
$88$	10.3928	+	6.09485i	1.10788	+	0.649714i
$89$		−	9.38882i		−	0.995213i	−0.867403	−	0.497607i	$-0.834212\pi$
$89$		−	9.38882i		−	0.995213i	0.867403	−	0.497607i	$-0.165788\pi$
$90$	−1.78990	−	0.319790i	−0.188672	−	0.0337088i
$91$	−0.350216	+	0.350216i	−0.0367126	+	0.0367126i
$92$	4.13690	+	1.52697i	0.431302	+	0.159198i
$93$	1.88726	+	1.88726i	0.195700	+	0.195700i
$94$	−12.3280	+	8.59061i	−1.27154	+	0.886054i
$95$	−0.316098			−0.0324310
$96$	4.69630	+	5.72736i	0.479314	+	0.584547i
$97$	−6.87272			−0.697819			−0.348909	−	0.937156i	$-0.613448\pi$
$97$	−6.87272			−0.697819			−0.348909	+	0.937156i	$0.613448\pi$
$98$	1.16029	−	0.808533i	0.117207	−	0.0816742i
$99$	−3.87254	−	3.87254i	−0.389205	−	0.389205i
$100$	−1.87627	−	0.692549i	−0.187627	−	0.0692549i
$101$	−0.783172	+	0.783172i	−0.0779285	+	0.0779285i	−0.744997	−	0.667068i	$-0.767549\pi$
$101$	−0.783172	+	0.783172i	−0.0779285	+	0.0779285i	0.667068	+	0.744997i	$0.267549\pi$
$102$	−10.7571	−	1.92190i	−1.06511	−	0.190297i
$103$		−	2.79038i		−	0.274944i	−0.990506	−	0.137472i	$-0.956102\pi$
$103$		−	2.79038i		−	0.274944i	0.990506	−	0.137472i	$-0.0438977\pi$
$104$	0.708662	−	1.20840i	0.0694900	−	0.118493i
$105$			1.30932i			0.127776i
$106$	0.446126	−	2.49701i	0.0433316	−	0.242531i
$107$	13.3613	−	13.3613i	1.29169	−	1.29169i	0.357948	−	0.933742i	$-0.383477\pi$
$107$	13.3613	−	13.3613i	1.29169	−	1.29169i	0.933742	−	0.357948i	$-0.116523\pi$
$108$	−4.69676	−	10.1926i	−0.451946	−	0.980780i
$109$	−8.93723	−	8.93723i	−0.856031	−	0.856031i	0.134837	−	0.990868i	$-0.456949\pi$
$109$	−8.93723	−	8.93723i	−0.856031	−	0.856031i	−0.990868	+	0.134837i	$0.956949\pi$
$110$	−3.44408	−	4.94245i	−0.328380	−	0.471244i
$111$	−3.17653			−0.301503
$112$	−2.59881	+	3.04075i	−0.245565	+	0.287324i
$113$	−7.38782			−0.694988			−0.347494	−	0.937682i	$-0.612967\pi$
$113$	−7.38782			−0.694988			−0.347494	+	0.937682i	$0.612967\pi$
$114$	−0.334630	−	0.480213i	−0.0313410	−	0.0449761i
$115$	−1.55907	−	1.55907i	−0.145384	−	0.145384i
$116$	3.22290	−	1.48512i	0.299239	−	0.137890i
$117$	−0.450269	+	0.450269i	−0.0416274	+	0.0416274i
$118$	1.09543	−	6.13123i	0.100843	−	0.564425i
$119$		−	5.90144i		−	0.540984i
$120$	−0.934151	−	3.58355i	−0.0852759	−	0.327132i
$121$		−	7.14474i		−	0.649522i
$122$	−4.71461	−	0.842331i	−0.426841	−	0.0762611i
$123$	8.29576	−	8.29576i	0.748003	−	0.748003i
$124$	1.41174	−	3.82470i	0.126778	−	0.343468i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	1.49177	−	1.03952i	0.132898	−	0.0926080i
$127$	−12.8149			−1.13714			−0.568571	−	0.822634i	$-0.692503\pi$
$127$	−12.8149			−1.13714			−0.568571	+	0.822634i	$0.692503\pi$
$128$	4.94339	−	10.1766i	0.436938	−	0.899492i
$129$	−10.4534			−0.920369
$130$	−0.574669	+	0.400451i	−0.0504018	+	0.0351218i
$131$	−4.93512	−	4.93512i	−0.431183	−	0.431183i	0.457847	−	0.889031i	$-0.348621\pi$
$131$	−4.93512	−	4.93512i	−0.431183	−	0.431183i	−0.889031	+	0.457847i	$0.848621\pi$
$132$	3.86252	−	10.4644i	0.336189	−	0.910810i
$133$	0.223515	−	0.223515i	0.0193812	−	0.0193812i
$134$	−7.98194	−	1.42609i	−0.689535	−	0.123195i
$135$			5.61133i			0.482946i
$136$	4.21046	+	16.1520i	0.361044	+	1.38502i
$137$		−	14.2127i		−	1.21427i	−0.794598	−	0.607136i	$-0.792318\pi$
$137$		−	14.2127i		−	1.21427i	0.794598	−	0.607136i	$-0.207682\pi$
$138$	0.718050	−	4.01900i	0.0611245	−	0.342120i
$139$	−13.0180	+	13.0180i	−1.10417	+	1.10417i	−0.110267	+	0.993902i	$0.535171\pi$
$139$	−13.0180	+	13.0180i	−1.10417	+	1.10417i	−0.993902	+	0.110267i	$0.964829\pi$
$140$	1.81643	−	0.837014i	0.153516	−	0.0707406i
$141$	9.83686	+	9.83686i	0.828413	+	0.828413i
$142$	−7.66484	−	10.9995i	−0.643219	−	0.923056i
$143$	−2.10973			−0.176424
$144$	−3.34127	+	3.90946i	−0.278439	+	0.325788i
$145$	−1.77431			−0.147348
$146$	4.89809	+	7.02904i	0.405369	+	0.581728i
$147$	−0.925827	−	0.925827i	−0.0763609	−	0.0763609i
$148$	2.03068	+	4.40683i	0.166921	+	0.362239i
$149$	−13.8454	+	13.8454i	−1.13426	+	1.13426i	−0.144794	+	0.989462i	$0.546252\pi$
$149$	−13.8454	+	13.8454i	−1.13426	+	1.13426i	−0.989462	+	0.144794i	$0.953748\pi$
$150$	−0.325667	+	1.82279i	−0.0265906	+	0.148830i
$151$		−	16.5472i		−	1.34659i	−0.739373	−	0.673297i	$-0.764878\pi$
$151$		−	16.5472i		−	1.34659i	0.739373	−	0.673297i	$-0.235122\pi$
$152$	−0.452283	+	0.771224i	−0.0366850	+	0.0625545i
$153$		−	7.58741i		−	0.613406i
$154$	5.93017	+	1.05951i	0.477867	+	0.0853776i
$155$	−1.44141	+	1.44141i	−0.115777	+	0.115777i
$156$	−1.21672	−	0.449104i	−0.0974155	−	0.0359571i
$157$	−8.40414	−	8.40414i	−0.670723	−	0.670723i	0.287159	−	0.957883i	$-0.407289\pi$
$157$	−8.40414	−	8.40414i	−0.670723	−	0.670723i	−0.957883	+	0.287159i	$0.907289\pi$
$158$	1.59360	−	1.11048i	0.126780	−	0.0883447i
$159$	−2.34841			−0.186241
$160$	−4.37431	+	3.58683i	−0.345820	+	0.283564i
$161$	2.20486			0.173767
$162$	−4.04934	+	2.82173i	−0.318146	+	0.221696i
$163$	15.0181	+	15.0181i	1.17631	+	1.17631i	0.980677	+	0.195633i	$0.0626761\pi$
$163$	15.0181	+	15.0181i	1.17631	+	1.17631i	0.195633	+	0.980677i	$0.437324\pi$
$164$	−16.8121	−	6.20550i	−1.31280	−	0.484568i
$165$	−3.94371	+	3.94371i	−0.307018	+	0.307018i
$166$	−16.1353	−	2.88279i	−1.25234	−	0.223748i
$167$			9.58846i			0.741977i	0.928637	+	0.370989i	$0.120981\pi$
$167$			9.58846i			0.741977i	−0.928637	+	0.370989i	$0.879019\pi$
$168$	3.19450	+	1.87341i	0.246461	+	0.144537i
$169$		−	12.7547i		−	0.981131i
$170$	1.46787	−	8.21579i	0.112580	−	0.630123i
$171$	0.287371	−	0.287371i	0.0219758	−	0.0219758i
$172$	6.68259	+	14.5021i	0.509543	+	1.10577i
$173$	−13.1389	−	13.1389i	−0.998930	−	0.998930i	0.00106946	−	0.999999i	$-0.499660\pi$
$173$	−13.1389	−	13.1389i	−0.998930	−	0.998930i	−0.999999	+	0.00106946i	$0.999660\pi$
$174$	−1.87833	−	2.69551i	−0.142396	−	0.204346i
$175$	−1.00000			−0.0755929
$176$	−16.9866	+	1.33113i	−1.28041	+	0.100338i
$177$	−5.76634			−0.433425
$178$	7.59117	+	10.8938i	0.568982	+	0.816522i
$179$	8.51372	+	8.51372i	0.636345	+	0.636345i	0.949652	−	0.313307i	$-0.101437\pi$
$179$	8.51372	+	8.51372i	0.636345	+	0.636345i	−0.313307	+	0.949652i	$0.601437\pi$
$180$	2.33536	−	1.07614i	0.174067	−	0.0802108i
$181$	14.9294	−	14.9294i	1.10969	−	1.10969i	0.116500	−	0.993191i	$-0.462833\pi$
$181$	14.9294	−	14.9294i	1.10969	−	1.10969i	0.993191	−	0.116500i	$-0.0371675\pi$
$182$	0.123191	−	0.689514i	0.00913155	−	0.0511102i
$183$			4.43403i			0.327773i
$184$	−6.03462	+	1.57309i	−0.444878	+	0.115970i
$185$		−	2.42610i		−	0.178370i
$186$	−3.71569	−	0.663860i	−0.272448	−	0.0486766i
$187$	17.7753	−	17.7753i	1.29986	−	1.29986i
$188$	7.35829	−	19.9352i	0.536659	−	1.45393i
$189$	−3.96781	−	3.96781i	−0.288615	−	0.288615i
$190$	0.366766	−	0.255576i	0.0266080	−	0.0185414i
$191$	−8.81514			−0.637841			−0.318921	−	0.947781i	$-0.603320\pi$
$191$	−8.81514			−0.637841			−0.318921	+	0.947781i	$0.603320\pi$
$192$	−10.0798	−	2.84829i	−0.727450	−	0.205558i
$193$	−8.97061			−0.645718			−0.322859	−	0.946447i	$-0.604644\pi$
$193$	−8.97061			−0.645718			−0.322859	+	0.946447i	$0.604644\pi$
$194$	7.97435	−	5.55682i	0.572525	−	0.398956i
$195$	0.458544	+	0.458544i	0.0328370	+	0.0328370i
$196$	−0.692549	+	1.87627i	−0.0494678	+	0.134019i
$197$	−15.4975	+	15.4975i	−1.10415	+	1.10415i	−0.110250	+	0.993904i	$0.535165\pi$
$197$	−15.4975	+	15.4975i	−1.10415	+	1.10415i	−0.993904	+	0.110250i	$0.964835\pi$
$198$	7.62435	+	1.36220i	0.541839	+	0.0968072i
$199$			15.7328i			1.11527i	0.830086	+	0.557636i	$0.188291\pi$
$199$			15.7328i			1.11527i	−0.830086	+	0.557636i	$0.811709\pi$
$200$	2.73696	−	0.713464i	0.193533	−	0.0504496i
$201$			7.50692i			0.529497i
$202$	0.275487	−	1.54193i	0.0193832	−	0.108490i
$203$	1.25462	−	1.25462i	0.0880574	−	0.0880574i
$204$	14.0353	−	6.46748i	0.982665	−	0.452814i
$205$	6.33594	+	6.33594i	0.442521	+	0.442521i
$206$	2.25611	+	3.23765i	0.157191	+	0.225578i
$207$	2.83476			0.197030
$208$	0.154774	+	1.97507i	0.0107316	+	0.136946i
$209$	1.34647			0.0931375
$210$	−1.05863	−	1.51919i	−0.0730521	−	0.104834i
$211$	3.38251	+	3.38251i	0.232861	+	0.232861i	0.813886	−	0.581025i	$-0.197348\pi$
$211$	3.38251	+	3.38251i	0.232861	+	0.232861i	−0.581025	+	0.813886i	$0.697348\pi$
$212$	1.50128	+	3.25797i	0.103108	+	0.223758i
$213$	−8.77678	+	8.77678i	−0.601375	+	0.601375i
$214$	−4.69996	+	26.3061i	−0.321282	+	1.79825i
$215$		−	7.98385i		−	0.544494i
$216$	13.6906	+	8.02885i	0.931529	+	0.546294i
$217$		−	2.03846i		−	0.138380i
$218$	17.5958	+	3.14374i	1.19174	+	0.212921i
$219$	5.60866	−	5.60866i	0.378998	−	0.378998i
$220$	7.99226	+	2.95003i	0.538838	+	0.198891i
$221$	−2.06678	−	2.06678i	−0.139027	−	0.139027i
$222$	3.68570	−	2.56833i	0.247368	−	0.172375i
$223$	−19.0977			−1.27888			−0.639439	−	0.768842i	$-0.720833\pi$
$223$	−19.0977			−1.27888			−0.639439	+	0.768842i	$0.720833\pi$
$224$	0.556833	−	5.62938i	0.0372050	−	0.376129i
$225$	−1.28569			−0.0857126
$226$	8.57202	−	5.97330i	0.570202	−	0.397338i
$227$	10.9840	+	10.9840i	0.729037	+	0.729037i	0.970428	−	0.241391i	$-0.0776037\pi$
$227$	10.9840	+	10.9840i	0.729037	+	0.729037i	−0.241391	+	0.970428i	$0.577604\pi$
$228$	0.776536	+	0.286628i	0.0514274	+	0.0189824i
$229$	11.2684	−	11.2684i	0.744634	−	0.744634i	−0.228832	−	0.973466i	$-0.573491\pi$
$229$	11.2684	−	11.2684i	0.744634	−	0.744634i	0.973466	+	0.228832i	$0.0734905\pi$
$230$	3.06954	+	0.548416i	0.202399	+	0.0361615i
$231$		−	5.57725i		−	0.366956i
$232$	−2.53873	+	4.32899i	−0.166676	+	0.284212i
$233$			26.6523i			1.74605i	0.487678	+	0.873024i	$0.337844\pi$
$233$			26.6523i			1.74605i	−0.487678	+	0.873024i	$0.662156\pi$
$234$	0.158386	−	0.886500i	0.0103540	−	0.0579523i
$235$	−7.51297	+	7.51297i	−0.490092	+	0.490092i
$236$	3.68628	+	7.99970i	0.239957	+	0.520736i
$237$	−1.27157	−	1.27157i	−0.0825976	−	0.0825976i
$238$	4.77150	+	6.84738i	0.309291	+	0.443850i
$239$	17.9375			1.16028			0.580139	−	0.814517i	$-0.302998\pi$
$239$	17.9375			1.16028			0.580139	+	0.814517i	$0.302998\pi$
$240$	3.98131	+	3.40267i	0.256992	+	0.219641i
$241$	14.1243			0.909825			0.454913	−	0.890536i	$-0.349670\pi$
$241$	14.1243			0.909825			0.454913	+	0.890536i	$0.349670\pi$
$242$	5.77676	+	8.28997i	0.371344	+	0.532900i
$243$	−8.67234	−	8.67234i	−0.556331	−	0.556331i
$244$	6.15137	−	2.83457i	0.393801	−	0.181465i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	−2.91810	+	16.3329i	−0.186051	+	1.04135i
$247$		−	0.156557i		−	0.00996151i
$248$	1.45437	+	5.57920i	0.0923527	+	0.354280i
$249$			15.1750i			0.961679i
$250$	−1.39217	−	0.248730i	−0.0880485	−	0.0157311i
$251$	−4.35614	+	4.35614i	−0.274957	+	0.274957i	−0.831092	−	0.556135i	$-0.812284\pi$
$251$	−4.35614	+	4.35614i	−0.274957	+	0.274957i	0.556135	+	0.831092i	$0.312284\pi$
$252$	−0.890403	+	2.41230i	−0.0560901	+	0.151960i
$253$	6.64112	+	6.64112i	0.417524	+	0.417524i
$254$	14.8690	−	10.3613i	0.932967	−	0.650125i
$255$	−7.72685			−0.483874
$256$	2.49233	+	15.8047i	0.155771	+	0.987793i
$257$	−16.3679			−1.02100			−0.510501	−	0.859877i	$-0.670540\pi$
$257$	−16.3679			−1.02100			−0.510501	+	0.859877i	$0.670540\pi$
$258$	12.1290	−	8.45190i	0.755116	−	0.526193i
$259$	1.71551	+	1.71551i	0.106597	+	0.106597i
$260$	0.343006	−	0.929278i	0.0212723	−	0.0576314i
$261$	1.61306	−	1.61306i	0.0998457	−	0.0998457i
$262$	9.71638	+	1.73597i	0.600280	+	0.107248i
$263$			4.48665i			0.276659i	0.990386	+	0.138329i	$0.0441732\pi$
$263$			4.48665i			0.276659i	−0.990386	+	0.138329i	$0.955827\pi$
$264$	3.97917	+	15.2647i	0.244901	+	0.939479i
$265$		−	1.79361i		−	0.110181i
$266$	−0.0786233	+	0.440062i	−0.00482070	+	0.0269820i
$267$	8.69243	−	8.69243i	0.531968	−	0.531968i
$268$	10.4144	−	4.79899i	0.636162	−	0.293145i
$269$	9.44999	+	9.44999i	0.576176	+	0.576176i	0.933847	−	0.357671i	$-0.116429\pi$
$269$	9.44999	+	9.44999i	0.576176	+	0.576176i	−0.357671	+	0.933847i	$0.616429\pi$
$270$	−4.53694	−	6.51077i	−0.276109	−	0.396233i
$271$	−13.2073			−0.802284			−0.401142	−	0.916016i	$-0.631387\pi$
$271$	−13.2073			−0.802284			−0.401142	+	0.916016i	$0.631387\pi$
$272$	−17.9448	−	15.3367i	−1.08806	−	0.929926i
$273$	−0.648479			−0.0392477
$274$	11.4914	+	16.4908i	0.694222	+	0.996248i
$275$	−3.01204	−	3.01204i	−0.181633	−	0.181633i
$276$	2.41634	+	5.24377i	0.145447	+	0.315638i
$277$	−12.6596	+	12.6596i	−0.760639	+	0.760639i	−0.976438	−	0.215799i	$-0.930764\pi$
$277$	−12.6596	+	12.6596i	−0.760639	+	0.760639i	0.215799	+	0.976438i	$0.430764\pi$
$278$	4.57917	−	25.6301i	0.274640	−	1.53719i
$279$		−	2.62083i		−	0.156905i
$280$	−1.43083	+	2.43982i	−0.0855084	+	0.145807i
$281$			11.9602i			0.713484i	0.934203	+	0.356742i	$0.116113\pi$
$281$			11.9602i			0.713484i	−0.934203	+	0.356742i	$0.883887\pi$
$282$	−19.3670	−	3.46019i	−1.15329	−	0.206051i
$283$	−14.2431	+	14.2431i	−0.846664	+	0.846664i	−0.989715	−	0.143051i	$-0.954309\pi$
$283$	−14.2431	+	14.2431i	−0.846664	+	0.846664i	0.143051	+	0.989715i	$0.454309\pi$
$284$	17.7869	+	6.56533i	1.05546	+	0.389580i
$285$	−0.292652	−	0.292652i	−0.0173352	−	0.0173352i
$286$	2.44790	−	1.70578i	0.144747	−	0.100865i
$287$	−8.96038			−0.528914
$288$	0.715914	−	7.23763i	0.0421856	−	0.426482i
$289$	17.8269			1.04864
$290$	2.05871	−	1.43459i	0.120892	−	0.0842418i
$291$	−6.36295	−	6.36295i	−0.373003	−	0.373003i
$292$	−11.3664	−	4.19546i	−0.665169	−	0.245521i
$293$	10.2406	−	10.2406i	0.598265	−	0.598265i	−0.341586	−	0.939851i	$-0.610964\pi$
$293$	10.2406	−	10.2406i	0.598265	−	0.598265i	0.939851	+	0.341586i	$0.110964\pi$
$294$	1.82279	+	0.325667i	0.106307	+	0.0189933i
$295$		−	4.40409i		−	0.256416i
$296$	−5.91924	−	3.47133i	−0.344049	−	0.201767i
$297$		−	23.9024i		−	1.38696i
$298$	4.87021	−	27.2591i	0.282124	−	1.57908i
$299$	0.772178	−	0.772178i	0.0446562	−	0.0446562i
$300$	−1.09592	−	2.37828i	−0.0632728	−	0.137310i
$301$	5.64543	+	5.64543i	0.325397	+	0.325397i
$302$	13.3790	+	19.1996i	0.769873	+	1.10481i
$303$	−1.45016			−0.0833097
$304$	−0.0987797	−	1.26053i	−0.00566541	−	0.0722963i
$305$	−3.38652			−0.193912
$306$	6.13467	+	8.80360i	0.350696	+	0.503268i
$307$	12.9956	+	12.9956i	0.741699	+	0.741699i	0.972905	−	0.231206i	$-0.0742670\pi$
$307$	12.9956	+	12.9956i	0.741699	+	0.741699i	−0.231206	+	0.972905i	$0.574267\pi$
$308$	−7.73737	+	3.56540i	−0.440877	+	0.203158i
$309$	2.58340	−	2.58340i	0.146965	−	0.146965i
$310$	0.507028	−	2.83789i	0.0287973	−	0.161181i
$311$		−	25.8999i		−	1.46865i	−0.678800	−	0.734323i	$-0.737500\pi$
$311$		−	25.8999i		−	1.46865i	0.678800	−	0.734323i	$-0.262500\pi$
$312$	1.77486	−	0.462667i	0.100482	−	0.0261934i
$313$			21.9356i			1.23987i	0.784653	+	0.619936i	$0.212841\pi$
$313$			21.9356i			1.23987i	−0.784653	+	0.619936i	$0.787159\pi$
$314$	16.5463	+	2.95622i	0.933760	+	0.166829i
$315$	0.909119	−	0.909119i	0.0512231	−	0.0512231i
$316$	−0.951179	+	2.57695i	−0.0535080	+	0.144965i
$317$	22.9623	+	22.9623i	1.28969	+	1.28969i	0.934973	+	0.354719i	$0.115424\pi$
$317$	22.9623	+	22.9623i	1.28969	+	1.28969i	0.354719	+	0.934973i	$0.384576\pi$
$318$	2.72484	−	1.89876i	0.152801	−	0.106477i
$319$	7.55795			0.423164
$320$	2.17540	−	7.69855i	0.121609	−	0.430362i
$321$	24.7406			1.38088
$322$	−2.55828	+	1.78270i	−0.142567	+	0.0993461i
$323$	1.31906	+	1.31906i	0.0733945	+	0.0733945i
$324$	2.41695	−	6.54805i	0.134275	−	0.363781i
$325$	−0.350216	+	0.350216i	−0.0194265	+	0.0194265i
$326$	−29.5680	−	5.28274i	−1.63762	−	0.292584i
$327$		−	16.5487i		−	0.915143i
$328$	24.5242	−	6.39291i	1.35412	−	0.352989i
$329$		−	10.6249i		−	0.585772i
$330$	1.38723	−	7.76447i	0.0763646	−	0.427420i
$331$	−7.66581	+	7.66581i	−0.421351	+	0.421351i	−0.885669	−	0.464318i	$-0.846300\pi$
$331$	−7.66581	+	7.66581i	−0.421351	+	0.421351i	0.464318	+	0.885669i	$0.346300\pi$
$332$	21.0525	−	9.70103i	1.15540	−	0.532413i
$333$	2.20561	+	2.20561i	0.120867	+	0.120867i
$334$	−7.75259	−	11.1254i	−0.424203	−	0.608755i
$335$	−5.73346			−0.313252
$336$	−5.22126	+	0.409157i	−0.284843	+	0.0223214i
$337$	−30.7171			−1.67327			−0.836633	−	0.547764i	$-0.815479\pi$
$337$	−30.7171			−1.67327			−0.836633	+	0.547764i	$0.815479\pi$
$338$	10.3126	+	14.7992i	0.560931	+	0.804968i
$339$	−6.83985	−	6.83985i	−0.371489	−	0.371489i
$340$	4.93959	+	10.7195i	0.267887	+	0.581348i
$341$	6.13993	−	6.13993i	0.332496	−	0.332496i
$342$	−0.101085	+	0.565783i	−0.00546606	+	0.0305941i
$343$			1.00000i			0.0539949i
$344$	−19.4792	−	11.4235i	−1.05025	−	0.615915i
$345$		−	2.88686i		−	0.155423i
$346$	25.8681	+	4.62170i	1.39068	+	0.248464i
$347$	−6.78909	+	6.78909i	−0.364458	+	0.364458i	−0.865451	−	0.500993i	$-0.832968\pi$
$347$	−6.78909	+	6.78909i	−0.364458	+	0.364458i	0.500993	+	0.865451i	$0.332968\pi$
$348$	4.35881	+	1.60888i	0.233657	+	0.0862452i
$349$	3.28153	+	3.28153i	0.175656	+	0.175656i	0.789459	−	0.613803i	$-0.210361\pi$
$349$	3.28153	+	3.28153i	0.175656	+	0.175656i	−0.613803	+	0.789459i	$0.710361\pi$
$350$	1.16029	−	0.808533i	0.0620201	−	0.0432179i
$351$	−2.77918			−0.148342
$352$	18.6331	−	15.2787i	0.993148	−	0.814358i
$353$	24.7321			1.31636			0.658179	−	0.752862i	$-0.271327\pi$
$353$	24.7321			1.31636			0.658179	+	0.752862i	$0.271327\pi$
$354$	6.69064	−	4.66228i	0.355603	−	0.247797i
$355$	−6.70333	−	6.70333i	−0.355776	−	0.355776i
$356$	−17.6159	−	6.50222i	−0.933643	−	0.344617i
$357$	5.46371	−	5.46371i	0.289170	−	0.289170i
$358$	−16.7620	−	2.99477i	−0.885899	−	0.158278i
$359$		−	7.24666i		−	0.382464i	−0.981545	−	0.191232i	$-0.938752\pi$
$359$		−	7.24666i		−	0.382464i	0.981545	−	0.191232i	$-0.0612483\pi$
$360$	−1.83960	+	3.13685i	−0.0969555	+	0.165327i
$361$		−	18.9001i		−	0.994741i
$362$	−5.25152	+	29.3933i	−0.276014	+	1.54488i
$363$	6.61479	−	6.61479i	0.347186	−	0.347186i
$364$	0.414557	+	0.899641i	0.0217287	+	0.0471540i
$365$	4.28365	+	4.28365i	0.224217	+	0.224217i
$366$	−3.58506	−	5.14476i	−0.187394	−	0.268921i
$367$	−4.69566			−0.245111			−0.122556	−	0.992462i	$-0.539109\pi$
$367$	−4.69566			−0.245111			−0.122556	+	0.992462i	$0.539109\pi$
$368$	5.73002	−	6.70443i	0.298698	−	0.349493i
$369$	−11.5203			−0.599721
$370$	1.96158	+	2.81498i	0.101978	+	0.146344i
$371$	1.26828	+	1.26828i	0.0658456	+	0.0658456i
$372$	4.84804	−	2.23399i	0.251359	−	0.115827i
$373$	−20.1544	+	20.1544i	−1.04356	+	1.04356i	−0.0445499	+	0.999007i	$0.514185\pi$
$373$	−20.1544	+	20.1544i	−1.04356	+	1.04356i	−0.999007	+	0.0445499i	$0.985815\pi$
$374$	−6.25262	+	34.9965i	−0.323315	+	1.80963i
$375$			1.30932i			0.0676128i
$376$	7.58052	+	29.0801i	0.390935	+	1.49969i
$377$		−	0.878780i		−	0.0452595i
$378$	7.81191	+	1.39571i	0.401801	+	0.0717874i
$379$	−22.0924	+	22.0924i	−1.13481	+	1.13481i	−0.145441	+	0.989367i	$0.546460\pi$
$379$	−22.0924	+	22.0924i	−1.13481	+	1.13481i	−0.989367	+	0.145441i	$0.953540\pi$
$380$	−0.218914	+	0.593085i	−0.0112300	+	0.0304246i
$381$	−11.8644	−	11.8644i	−0.607832	−	0.607832i
$382$	10.2281	−	7.12733i	0.523317	−	0.364666i
$383$	−28.5460			−1.45863			−0.729315	−	0.684178i	$-0.760161\pi$
$383$	−28.5460			−1.45863			−0.729315	+	0.684178i	$0.760161\pi$
$384$	13.9985	−	4.84503i	0.714357	−	0.247247i
$385$	4.25966			0.217093
$386$	10.4085	−	7.25303i	0.529779	−	0.369169i
$387$	7.25827	+	7.25827i	0.368959	+	0.368959i
$388$	−4.75970	+	12.8950i	−0.241637	+	0.654647i
$389$	−25.3326	+	25.3326i	−1.28441	+	1.28441i	−0.346281	+	0.938131i	$0.612556\pi$
$389$	−25.3326	+	25.3326i	−1.28441	+	1.28441i	−0.938131	+	0.346281i	$0.887444\pi$
$390$	−0.902792	−	0.161296i	−0.0457147	−	0.00816756i
$391$			13.0118i			0.658037i
$392$	−0.713464	−	2.73696i	−0.0360354	−	0.138238i
$393$		−	9.13813i		−	0.460958i
$394$	5.45138	−	30.5119i	0.274637	−	1.53717i
$395$	0.971173	−	0.971173i	0.0488650	−	0.0488650i
$396$	−9.94785	+	4.58400i	−0.499898	+	0.230354i
$397$	17.2976	+	17.2976i	0.868144	+	0.868144i	0.992267	−	0.124123i	$-0.0396118\pi$
$397$	17.2976	+	17.2976i	0.868144	+	0.868144i	−0.124123	+	0.992267i	$0.539612\pi$
$398$	−12.7205	−	18.2547i	−0.637622	−	0.915024i
$399$	0.413873			0.0207196
$400$	−2.59881	+	3.04075i	−0.129941	+	0.152038i
$401$	2.09676			0.104707			0.0523536	−	0.998629i	$-0.483328\pi$
$401$	2.09676			0.104707			0.0523536	+	0.998629i	$0.483328\pi$
$402$	−6.06959	−	8.71021i	−0.302724	−	0.434426i
$403$	−0.713903	−	0.713903i	−0.0355620	−	0.0355620i
$404$	0.927054	+	2.01182i	0.0461227	+	0.100092i
$405$	−2.46776	+	2.46776i	−0.122624	+	0.122624i
$406$	−0.441324	+	2.47013i	−0.0219026	+	0.122591i
$407$			10.3344i			0.512255i
$408$	−11.0558	+	18.8521i	−0.547344	+	0.933319i
$409$		−	21.8100i		−	1.07843i	−0.842167	−	0.539217i	$-0.818720\pi$
$409$		−	21.8100i		−	1.07843i	0.842167	−	0.539217i	$-0.181280\pi$
$410$	−12.4744	−	2.22872i	−0.616064	−	0.110069i
$411$	13.1585	−	13.1585i	0.649060	−	0.649060i
$412$	−5.23549	−	1.93247i	−0.257934	−	0.0952061i
$413$	3.11416	+	3.11416i	0.153238	+	0.153238i
$414$	−3.28915	+	2.29200i	−0.161653	+	0.112646i
$415$	−11.5900			−0.568933
$416$	−1.77649	−	2.16651i	−0.0870995	−	0.106222i
$417$	−24.1048			−1.18042
$418$	−1.56230	+	1.08867i	−0.0764146	+	0.0532485i
$419$	3.25943	+	3.25943i	0.159234	+	0.159234i	0.782227	−	0.622993i	$-0.214084\pi$
$419$	3.25943	+	3.25943i	0.159234	+	0.159234i	−0.622993	+	0.782227i	$0.714084\pi$
$420$	2.45663	+	0.906767i	0.119871	+	0.0442457i
$421$	14.9763	−	14.9763i	0.729902	−	0.729902i	−0.240698	−	0.970600i	$-0.577376\pi$
$421$	14.9763	−	14.9763i	0.729902	−	0.729902i	0.970600	+	0.240698i	$0.0773764\pi$
$422$	−6.65956	−	1.18982i	−0.324182	−	0.0579197i
$423$		−	13.6604i		−	0.664190i
$424$	−4.37609	−	2.56635i	−0.212522	−	0.124633i
$425$		−	5.90144i		−	0.286262i
$426$	3.08730	−	17.2799i	0.149580	−	0.837216i
$427$	2.39463	−	2.39463i	0.115884	−	0.115884i
$428$	−15.8160	−	34.3228i	−0.764497	−	1.65906i
$429$	−1.95324	−	1.95324i	−0.0943035	−	0.0943035i
$430$	6.45520	+	9.26358i	0.311297	+	0.446730i
$431$	−16.4430			−0.792032			−0.396016	−	0.918244i	$-0.629607\pi$
$431$	−16.4430			−0.792032			−0.396016	+	0.918244i	$0.629607\pi$
$432$	−22.3767	+	1.75352i	−1.07660	+	0.0843663i
$433$	−10.2249			−0.491380			−0.245690	−	0.969348i	$-0.579014\pi$
$433$	−10.2249			−0.491380			−0.245690	+	0.969348i	$0.579014\pi$
$434$	1.64817	+	2.36521i	0.0791145	+	0.113534i
$435$	−1.64270	−	1.64270i	−0.0787615	−	0.0787615i
$436$	−22.9581	+	10.5791i	−1.09949	+	0.506649i
$437$	−0.492820	+	0.492820i	−0.0235748	+	0.0235748i
$438$	−1.97289	+	11.0425i	−0.0942683	+	0.527629i
$439$			11.5135i			0.549509i	0.961514	+	0.274754i	$0.0885965\pi$
$439$			11.5135i			0.549509i	−0.961514	+	0.274754i	$0.911403\pi$
$440$	−11.6585	+	3.03912i	−0.555799	+	0.144884i
$441$			1.28569i			0.0612233i
$442$	4.06912	+	0.727006i	0.193548	+	0.0345801i
$443$	−23.3868	+	23.3868i	−1.11114	+	1.11114i	−0.118146	+	0.992996i	$0.537695\pi$
$443$	−23.3868	+	23.3868i	−1.11114	+	1.11114i	−0.992996	+	0.118146i	$0.962305\pi$
$444$	−2.19990	+	5.96002i	−0.104403	+	0.282850i
$445$	6.63890	+	6.63890i	0.314714	+	0.314714i
$446$	22.1589	−	15.4411i	1.04925	−	0.731159i
$447$	−25.6368			−1.21258
$448$	3.90545	+	6.98194i	0.184515	+	0.329866i
$449$	41.7134			1.96858			0.984288	−	0.176573i	$-0.0565011\pi$
$449$	41.7134			1.96858			0.984288	+	0.176573i	$0.0565011\pi$
$450$	1.49177	−	1.03952i	0.0703229	−	0.0490035i
$451$	−26.9890	−	26.9890i	−1.27086	−	1.27086i
$452$	−5.11643	+	13.8615i	−0.240657	+	0.651991i
$453$	15.3199	−	15.3199i	0.719790	−	0.719790i
$454$	−21.6256	−	3.86373i	−1.01494	−	0.181334i
$455$		−	0.495280i		−	0.0232191i
$456$	−1.13276	+	0.295284i	−0.0530461	+	0.0138279i
$457$		−	1.58487i		−	0.0741370i	−0.999313	−	0.0370685i	$-0.988198\pi$
$457$		−	1.58487i		−	0.0741370i	0.999313	−	0.0370685i	$-0.0118020\pi$
$458$	−3.96374	+	22.1854i	−0.185213	+	1.03666i
$459$	23.4158	−	23.4158i	1.09295	−	1.09295i
$460$	−4.00497	+	1.84550i	−0.186733	+	0.0860468i
$461$	6.86533	+	6.86533i	0.319750	+	0.319750i	0.848671	−	0.528921i	$-0.177403\pi$
$461$	6.86533	+	6.86533i	0.319750	+	0.319750i	−0.528921	+	0.848671i	$0.677403\pi$
$462$	4.50939	+	6.47123i	0.209796	+	0.301069i
$463$	10.1268			0.470634			0.235317	−	0.971919i	$-0.424387\pi$
$463$	10.1268			0.470634			0.235317	+	0.971919i	$0.424387\pi$
$464$	−0.554465	−	7.07554i	−0.0257404	−	0.328474i
$465$	−2.66900			−0.123772
$466$	−21.5492	−	30.9244i	−0.998248	−	1.43254i
$467$	16.1318	+	16.1318i	0.746490	+	0.746490i	0.973818	−	0.227328i	$-0.0729990\pi$
$467$	16.1318	+	16.1318i	0.746490	+	0.746490i	−0.227328	+	0.973818i	$0.572999\pi$
$468$	0.532991	+	1.15666i	0.0246375	+	0.0534665i
$469$	4.05417	−	4.05417i	0.187204	−	0.187204i
$470$	2.64275	−	14.7917i	0.121901	−	0.682291i
$471$		−	15.5616i		−	0.717039i
$472$	−10.7452	−	6.30150i	−0.494587	−	0.290050i
$473$			34.0085i			1.56371i
$474$	2.50350	+	0.447286i	0.114990	+	0.0205445i
$475$	0.223515	−	0.223515i	0.0102556	−	0.0102556i
$476$	−11.0727	−	4.08703i	−0.507515	−	0.187329i
$477$	1.63061	+	1.63061i	0.0746604	+	0.0746604i
$478$	−20.8127	+	14.5030i	−0.951950	+	0.663353i
$479$	27.2044			1.24300			0.621499	−	0.783415i	$-0.286524\pi$
$479$	27.2044			1.24300			0.621499	+	0.783415i	$0.286524\pi$
$480$	−7.37065	−	0.729071i	−0.336422	−	0.0332774i
$481$	1.20160			0.0547882
$482$	−16.3883	+	11.4200i	−0.746466	+	0.520164i
$483$	2.04132	+	2.04132i	0.0928832	+	0.0928832i
$484$	−13.4054	−	4.94808i	−0.609338	−	0.224913i
$485$	4.85974	−	4.85974i	0.220670	−	0.220670i
$486$	17.0743	+	3.05056i	0.774506	+	0.138376i
$487$		−	24.4779i		−	1.10920i	−0.832118	−	0.554599i	$-0.812872\pi$
$487$		−	24.4779i		−	1.10920i	0.832118	−	0.554599i	$-0.187128\pi$
$488$	−4.84554	+	8.26251i	−0.219347	+	0.374026i
$489$			27.8084i			1.25754i
$490$	−0.248730	+	1.39217i	−0.0112365	+	0.0628918i
$491$	−10.5824	+	10.5824i	−0.477578	+	0.477578i	−0.904356	−	0.426779i	$-0.859648\pi$
$491$	−10.5824	+	10.5824i	−0.477578	+	0.477578i	0.426779	+	0.904356i	$0.359648\pi$
$492$	−9.81983	−	21.3103i	−0.442712	−	0.960741i
$493$	7.40409	+	7.40409i	0.333463	+	0.333463i
$494$	0.126582	+	0.181652i	0.00569518	+	0.00817291i
$495$	5.47660			0.246155
$496$	−6.19846	−	5.29759i	−0.278319	−	0.237869i
$497$	9.47994			0.425233
$498$	−12.2695	−	17.6075i	−0.549810	−	0.789009i
$499$	−9.57472	−	9.57472i	−0.428624	−	0.428624i	0.459536	−	0.888159i	$-0.348016\pi$
$499$	−9.57472	−	9.57472i	−0.428624	−	0.428624i	−0.888159	+	0.459536i	$0.848016\pi$
$500$	1.81643	−	0.837014i	0.0812331	−	0.0374324i
$501$	−8.87726	+	8.87726i	−0.396607	+	0.396607i
$502$	1.53231	−	8.57647i	0.0683902	−	0.382786i
$503$		−	3.04019i		−	0.135556i	−0.997700	−	0.0677778i	$-0.978409\pi$
$503$		−	3.04019i		−	0.135556i	0.997700	−	0.0677778i	$-0.0215909\pi$
$504$	−0.917293	−	3.51888i	−0.0408595	−	0.156744i
$505$		−	1.10757i		−	0.0492863i
$506$	−13.0752	−	2.33607i	−0.581263	−	0.103851i
$507$	11.8086	−	11.8086i	0.524440	−	0.524440i
$508$	−8.87497	+	24.0442i	−0.393763	+	1.06679i
$509$	−17.7897	−	17.7897i	−0.788514	−	0.788514i	0.192736	−	0.981251i	$-0.438264\pi$
$509$	−17.7897	−	17.7897i	−0.788514	−	0.788514i	−0.981251	+	0.192736i	$0.938264\pi$
$510$	8.96539	−	6.24741i	0.396994	−	0.276640i
$511$	−6.05800			−0.267990
$512$	−15.6704	−	16.3229i	−0.692542	−	0.721377i
$513$	1.77373			0.0783122
$514$	18.9915	−	13.2340i	0.837681	−	0.583727i
$515$	1.97309	+	1.97309i	0.0869449	+	0.0869449i
$516$	−7.23948	+	19.6133i	−0.318701	+	0.863429i
$517$	32.0027	−	32.0027i	1.40748	−	1.40748i
$518$	−3.37754	−	0.603444i	−0.148400	−	0.0265138i
$519$		−	24.3286i		−	1.06791i
$520$	0.353365	+	1.35556i	0.0154961	+	0.0594454i
$521$		−	40.8555i		−	1.78991i	−0.446154	−	0.894956i	$-0.647207\pi$
$521$		−	40.8555i		−	1.78991i	0.446154	−	0.894956i	$-0.352793\pi$
$522$	−0.567406	+	3.17583i	−0.0248347	+	0.139002i
$523$	12.3834	−	12.3834i	0.541490	−	0.541490i	−0.382476	−	0.923966i	$-0.624928\pi$
$523$	12.3834	−	12.3834i	0.541490	−	0.541490i	0.923966	+	0.382476i	$0.124928\pi$
$524$	−12.6774	+	5.84179i	−0.553815	+	0.255200i
$525$	−0.925827	−	0.925827i	−0.0404064	−	0.0404064i
$526$	−3.62760	−	5.20582i	−0.158171	−	0.226984i
$527$	12.0299			0.524029
$528$	−16.9590	−	14.4942i	−0.738047	−	0.630781i
$529$	18.1386			0.788634
$530$	1.45019	+	2.08111i	0.0629924	+	0.0903978i
$531$	4.00384	+	4.00384i	0.173752	+	0.173752i
$532$	−0.264579	−	0.574170i	−0.0114710	−	0.0248934i
$533$	−3.13807	+	3.13807i	−0.135925	+	0.135925i
$534$	−3.05763	+	17.1139i	−0.132317	+	0.740589i
$535$			18.8958i			0.816936i
$536$	−8.20361	+	13.9886i	−0.354342	+	0.604216i
$537$			15.7645i			0.680286i
$538$	−18.6054	−	3.32411i	−0.802134	−	0.143313i
$539$	−3.01204	+	3.01204i	−0.129738	+	0.129738i
$540$	10.5283	+	3.88612i	0.453068	+	0.167232i
$541$	−14.3807	−	14.3807i	−0.618275	−	0.618275i	0.326814	−	0.945089i	$-0.394025\pi$
$541$	−14.3807	−	14.3807i	−0.618275	−	0.618275i	−0.945089	+	0.326814i	$0.894025\pi$
$542$	15.3243	−	10.6785i	0.658233	−	0.458681i
$543$	27.6440			1.18632
$544$	33.2214	+	3.28611i	1.42436	+	0.140891i
$545$	12.6391			0.541402
$546$	0.752424	−	0.524317i	0.0322008	−	0.0224387i
$547$	−24.3063	−	24.3063i	−1.03926	−	1.03926i	−0.999197	−	0.0400647i	$-0.987244\pi$
$547$	−24.3063	−	24.3063i	−1.03926	−	1.03926i	−0.0400647	−	0.999197i	$-0.512756\pi$
$548$	−26.6668	−	9.84298i	−1.13915	−	0.420471i
$549$	3.07875	−	3.07875i	0.131398	−	0.131398i
$550$	5.93017	+	1.05951i	0.252863	+	0.0451776i
$551$			0.560856i			0.0238933i
$552$	−7.04342	−	4.13061i	−0.299788	−	0.175810i
$553$			1.37345i			0.0584049i
$554$	4.45310	−	24.9244i	0.189194	−	1.05894i
$555$	2.24615	−	2.24615i	0.0953436	−	0.0953436i
$556$	15.4096	+	33.4407i	0.653512	+	1.41820i
$557$	15.1118	+	15.1118i	0.640309	+	0.640309i	0.950631	−	0.310322i	$-0.100437\pi$
$557$	15.1118	+	15.1118i	0.640309	+	0.640309i	−0.310322	+	0.950631i	$0.600437\pi$
$558$	2.11903	+	3.04093i	0.0897056	+	0.128733i
$559$	3.95424			0.167247
$560$	−0.312497	−	3.98777i	−0.0132054	−	0.168514i
$561$	32.9138			1.38962
$562$	−9.67020	−	13.8773i	−0.407913	−	0.585378i
$563$	−3.23080	−	3.23080i	−0.136162	−	0.136162i	0.635741	−	0.771903i	$-0.280695\pi$
$563$	−3.23080	−	3.23080i	−0.136162	−	0.136162i	−0.771903	+	0.635741i	$0.780695\pi$
$564$	25.2691	−	11.6441i	1.06402	−	0.490303i
$565$	5.22398	−	5.22398i	0.219774	−	0.219774i
$566$	5.01012	−	28.0421i	0.210591	−	1.17870i
$567$		−	3.48994i		−	0.146564i
$568$	−25.9462	+	6.76360i	−1.08868	+	0.283794i
$569$			42.8630i			1.79691i	0.439064	+	0.898456i	$0.355310\pi$
$569$			42.8630i			1.79691i	−0.439064	+	0.898456i	$0.644690\pi$
$570$	0.576181	+	0.102943i	0.0241336	+	0.00431180i
$571$	14.9285	−	14.9285i	0.624739	−	0.624739i	−0.322000	−	0.946740i	$-0.604355\pi$
$571$	14.9285	−	14.9285i	0.624739	−	0.624739i	0.946740	+	0.322000i	$0.104355\pi$
$572$	−1.46109	+	3.95841i	−0.0610913	+	0.165510i
$573$	−8.16130	−	8.16130i	−0.340943	−	0.340943i
$574$	10.3966	−	7.24476i	0.433947	−	0.302390i
$575$	2.20486			0.0919490
$576$	5.02120	+	8.97660i	0.209217	+	0.374025i
$577$	7.81792			0.325464			0.162732	−	0.986670i	$-0.447969\pi$
$577$	7.81792			0.325464			0.162732	+	0.986670i	$0.447969\pi$
$578$	−20.6844	+	14.4137i	−0.860359	+	0.599529i
$579$	−8.30523	−	8.30523i	−0.345153	−	0.345153i
$580$	−1.22880	+	3.32907i	−0.0510229	+	0.138232i
$581$	8.19539	−	8.19539i	0.340002	−	0.340002i
$582$	12.5275	+	2.23822i	0.519282	+	0.0927771i
$583$			7.64019i			0.316424i
$584$	16.5805	−	4.32217i	0.686107	−	0.178853i
$585$		−	0.636777i		−	0.0263275i
$586$	−3.60223	+	20.1620i	−0.148807	+	0.832885i
$587$	4.65241	−	4.65241i	0.192026	−	0.192026i	−0.604545	−	0.796571i	$-0.706645\pi$
$587$	4.65241	−	4.65241i	0.192026	−	0.192026i	0.796571	+	0.604545i	$0.206645\pi$
$588$	−2.37828	+	1.09592i	−0.0980786	+	0.0451949i
$589$	0.455628	+	0.455628i	0.0187738	+	0.0187738i
$590$	3.56085	+	5.11002i	0.146598	+	0.210376i
$591$	−28.6961			−1.18040
$592$	9.67473	−	0.758148i	0.397629	−	0.0311597i
$593$	−36.1078			−1.48277			−0.741385	−	0.671080i	$-0.765831\pi$
$593$	−36.1078			−1.48277			−0.741385	+	0.671080i	$0.765831\pi$
$594$	19.3258	+	27.7337i	0.792949	+	1.13793i
$595$	4.17295	+	4.17295i	0.171074	+	0.171074i
$596$	16.3890	+	35.5662i	0.671319	+	1.45685i
$597$	−14.5659	+	14.5659i	−0.596142	+	0.596142i
$598$	−0.271620	+	1.52028i	−0.0111074	+	0.0621689i
$599$		−	39.9771i		−	1.63342i	−0.577048	−	0.816710i	$-0.695796\pi$
$599$		−	39.9771i		−	1.63342i	0.577048	−	0.816710i	$-0.304204\pi$
$600$	3.19450	+	1.87341i	0.130415	+	0.0764816i
$601$			41.8677i			1.70782i	0.520421	+	0.853910i	$0.325775\pi$
$601$			41.8677i			1.70782i	−0.520421	+	0.853910i	$0.674225\pi$
$602$	−11.1149	−	1.98583i	−0.453008	−	0.0809362i
$603$	5.21240	−	5.21240i	0.212265	−	0.212265i
$604$	−31.0470	−	11.4598i	−1.26328	−	0.466291i
$605$	5.05209	+	5.05209i	0.205397	+	0.205397i
$606$	1.68261	−	1.17250i	0.0683514	−	0.0476297i
$607$	12.8994			0.523572			0.261786	−	0.965126i	$-0.415689\pi$
$607$	12.8994			0.523572			0.261786	+	0.965126i	$0.415689\pi$
$608$	1.13379	+	1.38271i	0.0459814	+	0.0560765i
$609$	2.32313			0.0941380
$610$	3.92935	−	2.73811i	0.159095	−	0.110863i
$611$	−3.72103	−	3.72103i	−0.150537	−	0.150537i
$612$	−14.2360	−	5.25466i	−0.575456	−	0.212407i
$613$	−3.38419	+	3.38419i	−0.136686	+	0.136686i	−0.772139	−	0.635453i	$-0.780813\pi$
$613$	−3.38419	+	3.38419i	−0.136686	+	0.136686i	0.635453	+	0.772139i	$0.280813\pi$
$614$	−25.5861	−	4.57131i	−1.03257	−	0.184483i
$615$			11.7320i			0.473079i
$616$	6.09485	−	10.3928i	0.245569	−	0.418739i
$617$		−	0.239954i		−	0.00966017i	−0.999988	−	0.00483009i	$-0.998463\pi$
$617$		−	0.239954i		−	0.00966017i	0.999988	−	0.00483009i	$-0.00153747\pi$
$618$	−0.908733	+	5.08627i	−0.0365546	+	0.204600i
$619$	15.6188	−	15.6188i	0.627773	−	0.627773i	−0.319734	−	0.947507i	$-0.603594\pi$
$619$	15.6188	−	15.6188i	0.627773	−	0.627773i	0.947507	+	0.319734i	$0.103594\pi$
$620$	1.70622	+	3.70272i	0.0685236	+	0.148705i
$621$	8.74846	+	8.74846i	0.351063	+	0.351063i
$622$	20.9409	+	30.0514i	0.839653	+	1.20495i
$623$	−9.38882			−0.376155
$624$	−1.68528	+	1.97186i	−0.0674651	+	0.0789377i
$625$	−1.00000			−0.0400000
$626$	−17.7356	−	25.4516i	−0.708858	−	1.01725i
$627$	1.24660	+	1.24660i	0.0497845	+	0.0497845i
$628$	−21.5887	+	9.94812i	−0.861482	+	0.396973i
$629$	−10.1240	+	10.1240i	−0.403669	+	0.403669i
$630$	−0.319790	+	1.78990i	−0.0127407	+	0.0713112i
$631$			19.7185i			0.784980i	0.919756	+	0.392490i	$0.128386\pi$
$631$			19.7185i			0.784980i	−0.919756	+	0.392490i	$0.871614\pi$
$632$	−0.979905	−	3.75907i	−0.0389785	−	0.149528i
$633$			6.26323i			0.248941i
$634$	−45.2088	−	8.07718i	−1.79547	−	0.320786i
$635$	9.06153	−	9.06153i	0.359596	−	0.359596i
$636$	−1.62639	+	4.40624i	−0.0644905	+	0.174719i
$637$	0.350216	+	0.350216i	0.0138761	+	0.0138761i
$638$	−8.76942	+	6.11085i	−0.347185	+	0.241931i
$639$	12.1883			0.482160
$640$	3.70043	+	10.6914i	0.146272	+	0.422616i
$641$	1.18448			0.0467842			0.0233921	−	0.999726i	$-0.492553\pi$
$641$	1.18448			0.0467842			0.0233921	+	0.999726i	$0.492553\pi$
$642$	−28.7063	+	20.0036i	−1.13295	+	0.789478i
$643$	−15.4791	−	15.4791i	−0.610435	−	0.610435i	0.332624	−	0.943059i	$-0.392066\pi$
$643$	−15.4791	−	15.4791i	−0.610435	−	0.610435i	−0.943059	+	0.332624i	$0.892066\pi$
$644$	1.52697	−	4.13690i	0.0601712	−	0.163017i
$645$	7.39166	−	7.39166i	0.291046	−	0.291046i
$646$	−2.59700	−	0.463990i	−0.102178	−	0.0182555i
$647$			14.4135i			0.566654i	0.959023	+	0.283327i	$0.0914381\pi$
$647$			14.4135i			0.566654i	−0.959023	+	0.283327i	$0.908562\pi$
$648$	2.48995	+	9.55183i	0.0978143	+	0.375231i
$649$			18.7599i			0.736392i
$650$	0.123191	−	0.689514i	0.00483196	−	0.0270450i
$651$	1.88726	−	1.88726i	0.0739677	−	0.0739677i
$652$	38.5788	−	17.7772i	1.51086	−	0.696209i
$653$	−24.8909	−	24.8909i	−0.974056	−	0.974056i	0.0256155	−	0.999672i	$-0.491845\pi$
$653$	−24.8909	−	24.8909i	−0.974056	−	0.974056i	−0.999672	+	0.0256155i	$0.991845\pi$
$654$	13.3801	+	19.2012i	0.523204	+	0.750828i
$655$	6.97931			0.272704
$656$	−23.2863	+	27.2463i	−0.909179	+	1.06379i
$657$	−7.78870			−0.303866
$658$	8.59061	+	12.3280i	0.334897	+	0.480596i
$659$	−7.83523	−	7.83523i	−0.305217	−	0.305217i	0.537834	−	0.843051i	$-0.319243\pi$
$659$	−7.83523	−	7.83523i	−0.305217	−	0.305217i	−0.843051	+	0.537834i	$0.819243\pi$
$660$	4.66824	+	10.1307i	0.181711	+	0.394336i
$661$	11.9212	−	11.9212i	0.463680	−	0.463680i	−0.436180	−	0.899860i	$-0.643669\pi$
$661$	11.9212	−	11.9212i	0.463680	−	0.463680i	0.899860	+	0.436180i	$0.143669\pi$
$662$	2.69651	−	15.0926i	0.104803	−	0.586592i
$663$		−	3.82696i		−	0.148627i
$664$	−16.5834	+	28.2776i	−0.643560	+	1.09738i
$665$			0.316098i			0.0122578i
$666$	−4.34246	−	0.775842i	−0.168267	−	0.0300633i
$667$	−2.76627	+	2.76627i	−0.107110	+	0.107110i
$668$	17.9905	+	6.64048i	0.696074	+	0.256928i
$669$	−17.6812	−	17.6812i	−0.683594	−	0.683594i
$670$	6.65248	−	4.63569i	0.257008	−	0.179092i
$671$	14.4254			0.556888
$672$	5.72736	−	4.69630i	0.220938	−	0.181164i
$673$	8.96341			0.345514			0.172757	−	0.984964i	$-0.444732\pi$
$673$	8.96341			0.345514			0.172757	+	0.984964i	$0.444732\pi$
$674$	35.6407	−	24.8358i	1.37283	−	0.956638i
$675$	−3.96781	−	3.96781i	−0.152721	−	0.152721i
$676$	−23.9312	−	8.83326i	−0.920431	−	0.339741i
$677$	−19.6106	+	19.6106i	−0.753697	+	0.753697i	−0.975167	−	0.221470i	$-0.928914\pi$
$677$	−19.6106	+	19.6106i	−0.753697	+	0.753697i	0.221470	+	0.975167i	$0.428914\pi$
$678$	13.4664	+	2.40597i	0.517176	+	0.0924007i
$679$			6.87272i			0.263751i
$680$	−14.3984	−	8.44395i	−0.552155	−	0.323811i
$681$			20.3387i			0.779379i
$682$	−2.15977	+	12.0884i	−0.0827018	+	0.462890i
$683$	0.421800	−	0.421800i	0.0161397	−	0.0161397i	−0.698991	−	0.715131i	$-0.746367\pi$
$683$	0.421800	−	0.421800i	0.0161397	−	0.0161397i	0.715131	+	0.698991i	$0.246367\pi$
$684$	−0.340166	−	0.738204i	−0.0130066	−	0.0282259i
$685$	10.0499	+	10.0499i	0.383986	+	0.383986i
$686$	−0.808533	−	1.16029i	−0.0308699	−	0.0443001i
$687$	20.8651			0.796054
$688$	31.8378	−	2.49493i	1.21380	−	0.0951181i
$689$	0.888341			0.0338431
$690$	2.33412	+	3.34960i	0.0888585	+	0.127517i
$691$	18.9466	+	18.9466i	0.720762	+	0.720762i	0.968761	−	0.247998i	$-0.0797727\pi$
$691$	18.9466	+	18.9466i	0.720762	+	0.720762i	−0.247998	+	0.968761i	$0.579773\pi$
$692$	−33.7513	+	15.5527i	−1.28303	+	0.591225i
$693$	−3.87254	+	3.87254i	−0.147106	+	0.147106i
$694$	2.38812	−	13.3665i	0.0906517	−	0.507386i
$695$		−	18.4102i		−	0.698338i
$696$	−6.35832	+	1.65747i	−0.241012	+	0.0628263i
$697$		−	52.8791i		−	2.00294i
$698$	−6.46076	−	1.15431i	−0.244543	−	0.0436911i
$699$	−24.6754	+	24.6754i	−0.933308	+	0.933308i
$700$	−0.692549	+	1.87627i	−0.0261759	+	0.0709162i
$701$	21.3358	+	21.3358i	0.805843	+	0.805843i	0.984002	−	0.178159i	$-0.0570141\pi$
$701$	21.3358	+	21.3358i	0.805843	+	0.805843i	−0.178159	+	0.984002i	$0.557014\pi$
$702$	3.22466	−	2.24706i	0.121707	−	0.0848097i
$703$	−0.766886			−0.0289236
$704$	−9.26649	+	32.7932i	−0.349244	+	1.23594i
$705$	−13.9114			−0.523934
$706$	−28.6964	+	19.9967i	−1.08000	+	0.752587i
$707$	0.783172	+	0.783172i	0.0294542	+	0.0294542i
$708$	−3.99348	+	10.8192i	−0.150084	+	0.406610i
$709$	29.0466	−	29.0466i	1.09087	−	1.09087i	0.0954328	−	0.995436i	$-0.469576\pi$
$709$	29.0466	−	29.0466i	1.09087	−	1.09087i	0.995436	−	0.0954328i	$-0.0304235\pi$
$710$	13.1977	+	2.35795i	0.495300	+	0.0884923i
$711$			1.76582i			0.0662236i
$712$	25.6969	−	6.69859i	0.963031	−	0.251040i
$713$			4.49453i			0.168321i
$714$	−1.92190	+	10.7571i	−0.0719254	+	0.402573i
$715$	1.49180	−	1.49180i	0.0557903	−	0.0557903i
$716$	21.8702	−	10.0778i	0.817326	−	0.376626i
$717$	16.6070	+	16.6070i	0.620200	+	0.620200i
$718$	5.85917	+	8.40824i	0.218662	+	0.313793i
$719$	45.4791			1.69608			0.848042	−	0.529929i	$-0.177782\pi$
$719$	45.4791			1.69608			0.848042	+	0.529929i	$0.177782\pi$
$720$	−0.401774	−	5.12704i	−0.0149732	−	0.191073i
$721$	−2.79038			−0.103919
$722$	15.2813	+	21.9296i	0.568712	+	0.816135i
$723$	13.0766	+	13.0766i	0.486326	+	0.486326i
$724$	−17.6721	−	38.3508i	−0.656780	−	1.42530i
$725$	1.25462	−	1.25462i	0.0465956	−	0.0465956i
$726$	−2.32681	+	13.0234i	−0.0863558	+	0.483342i
$727$			32.4376i			1.20305i	0.798856	+	0.601523i	$0.205439\pi$
$727$			32.4376i			1.20305i	−0.798856	+	0.601523i	$0.794561\pi$
$728$	−1.20840	−	0.708662i	−0.0447861	−	0.0262648i
$729$		−	26.5280i		−	0.982518i
$730$	−8.43376	−	1.50681i	−0.312147	−	0.0557695i
$731$	−33.3161	+	33.3161i	−1.23224	+	1.23224i
$732$	8.31942	+	3.07078i	0.307495	+	0.113499i
$733$	−24.2373	−	24.2373i	−0.895226	−	0.895226i	0.0997835	−	0.995009i	$-0.468185\pi$
$733$	−24.2373	−	24.2373i	−0.895226	−	0.895226i	−0.995009	+	0.0997835i	$0.968185\pi$
$734$	5.44833	−	3.79659i	0.201102	−	0.140135i
$735$	1.30932			0.0482949
$736$	−1.22774	+	12.4120i	−0.0452550	+	0.457512i
$737$	24.4226			0.899619
$738$	13.3668	−	9.31451i	0.492040	−	0.342872i
$739$	−1.99226	−	1.99226i	−0.0732865	−	0.0732865i	0.669513	−	0.742800i	$-0.266503\pi$
$739$	−1.99226	−	1.99226i	−0.0732865	−	0.0732865i	−0.742800	+	0.669513i	$0.766503\pi$
$740$	−4.55201	−	1.68019i	−0.167335	−	0.0617651i
$741$	0.144945	−	0.144945i	0.00532469	−	0.00532469i
$742$	−2.49701	−	0.446126i	−0.0916682	−	0.0163778i
$743$			32.9553i			1.20901i	0.796600	+	0.604507i	$0.206630\pi$
$743$			32.9553i			1.20901i	−0.796600	+	0.604507i	$0.793370\pi$
$744$	−3.81888	+	6.51187i	−0.140007	+	0.238737i
$745$		−	19.5803i		−	0.717366i
$746$	7.08948	−	39.6805i	0.259564	−	1.45281i
$747$	10.5367	−	10.5367i	0.385519	−	0.385519i
$748$	−21.0410	−	45.6616i	−0.769334	−	1.66955i
$749$	−13.3613	−	13.3613i	−0.488213	−	0.488213i
$750$	−1.05863	−	1.51919i	−0.0386555	−	0.0554729i
$751$	−24.2542			−0.885049			−0.442525	−	0.896756i	$-0.645917\pi$
$751$	−24.2542			−0.885049			−0.442525	+	0.896756i	$0.645917\pi$
$752$	−32.3078	−	27.6122i	−1.17814	−	1.00691i
$753$	−8.06606			−0.293944
$754$	0.710522	+	1.01964i	0.0258757	+	0.0371331i
$755$	11.7006	+	11.7006i	0.425830	+	0.425830i
$756$	−10.1926	+	4.69676i	−0.370700	+	0.170820i
$757$	−7.66050	+	7.66050i	−0.278426	+	0.278426i	−0.832480	−	0.554055i	$-0.813080\pi$
$757$	−7.66050	+	7.66050i	−0.278426	+	0.278426i	0.554055	+	0.832480i	$0.313080\pi$
$758$	7.77116	−	43.4960i	0.282261	−	1.57984i
$759$			12.2971i			0.446355i
$760$	−0.225525	−	0.865150i	−0.00818065	−	0.0313823i
$761$			42.8028i			1.55160i	0.630978	+	0.775800i	$0.282654\pi$
$761$			42.8028i			1.55160i	−0.630978	+	0.775800i	$0.717346\pi$
$762$	23.3589	+	4.17340i	0.846205	+	0.151186i
$763$	−8.93723	+	8.93723i	−0.323549	+	0.323549i
$764$	−6.10492	+	16.5396i	−0.220868	+	0.598380i
$765$	5.36511	+	5.36511i	0.193976	+	0.193976i
$766$	33.1216	−	23.0803i	1.19673	−	0.833927i
$767$	2.18126			0.0787607
$768$	−12.3249	+	16.9399i	−0.444738	+	0.611265i
$769$	6.59350			0.237768			0.118884	−	0.992908i	$-0.462068\pi$
$769$	6.59350			0.237768			0.118884	+	0.992908i	$0.462068\pi$
$770$	−4.94245	+	3.44408i	−0.178113	+	0.124116i
$771$	−15.1539	−	15.1539i	−0.545753	−	0.545753i
$772$	−6.21259	+	16.8312i	−0.223596	+	0.605770i
$773$	1.02422	−	1.02422i	0.0368386	−	0.0368386i	−0.688448	−	0.725286i	$-0.741707\pi$
$773$	1.02422	−	1.02422i	0.0368386	−	0.0368386i	0.725286	+	0.688448i	$0.241707\pi$
$774$	−14.2903	−	2.55315i	−0.513652	−	0.0917712i
$775$		−	2.03846i		−	0.0732238i
$776$	−4.90344	−	18.8104i	−0.176023	−	0.675253i
$777$			3.17653i			0.113957i
$778$	8.91093	−	49.8753i	0.319472	−	1.78812i
$779$	2.00278	−	2.00278i	0.0717571	−	0.0717571i
$780$	1.17792	−	0.542786i	0.0421761	−	0.0194349i
$781$	28.5539	+	28.5539i	1.02174	+	1.02174i
$782$	−10.5205	−	15.0975i	−0.376212	−	0.539886i
$783$	9.95622			0.355806
$784$	3.04075	+	2.59881i	0.108598	+	0.0928148i
$785$	11.8852			0.424203
$786$	7.38848	+	10.6029i	0.263538	+	0.378193i
$787$	−16.6417	−	16.6417i	−0.593214	−	0.593214i	0.345284	−	0.938498i	$-0.387783\pi$
$787$	−16.6417	−	16.6417i	−0.593214	−	0.593214i	−0.938498	+	0.345284i	$0.887783\pi$
$788$	18.3447	+	39.8103i	0.653503	+	1.41818i
$789$	−4.15386	+	4.15386i	−0.147881	+	0.147881i
$790$	−0.341618	+	1.91207i	−0.0121542	+	0.0680283i
$791$			7.38782i			0.262681i
$792$	7.83609	−	13.3619i	0.278443	−	0.474796i
$793$		−	1.67728i		−	0.0595619i
$794$	−34.0560	−	6.08458i	−1.20860	−	0.215934i
$795$	1.66058	−	1.66058i	0.0588945	−	0.0588945i
$796$	29.5190	+	10.8958i	1.04627	+	0.386190i
$797$	−27.8403	−	27.8403i	−0.986155	−	0.986155i	0.0137505	−	0.999905i	$-0.495623\pi$
$797$	−27.8403	−	27.8403i	−0.986155	−	0.986155i	−0.999905	+	0.0137505i	$0.995623\pi$
$798$	−0.480213	+	0.334630i	−0.0169994	+	0.0118458i
$799$	62.7024			2.21825
$800$	0.556833	−	5.62938i	0.0196870	−	0.199029i
$801$	−12.0711			−0.426512
$802$	−2.43285	+	1.69530i	−0.0859070	+	0.0598631i
$803$	−18.2469	−	18.2469i	−0.643920	−	0.643920i
$804$	14.0850	+	5.19891i	0.496739	+	0.183351i
$805$	−1.55907	+	1.55907i	−0.0549500	+	0.0549500i
$806$	1.40555	+	0.251121i	0.0495084	+	0.00884536i
$807$			17.4981i			0.615963i
$808$	−2.70228	−	1.58475i	−0.0950658	−	0.0557512i
$809$			21.4768i			0.755084i	0.925992	+	0.377542i	$0.123231\pi$
$809$			21.4768i			0.755084i	−0.925992	+	0.377542i	$0.876769\pi$
$810$	0.868053	−	4.85858i	0.0305003	−	0.170713i
$811$	−5.40500	+	5.40500i	−0.189795	+	0.189795i	−0.795608	−	0.605812i	$-0.792848\pi$
$811$	−5.40500	+	5.40500i	−0.189795	+	0.189795i	0.605812	+	0.795608i	$0.292848\pi$
$812$	−1.48512	−	3.22290i	−0.0521175	−	0.113102i
$813$	−12.2276	−	12.2276i	−0.428842	−	0.428842i
$814$	−8.35567	−	11.9909i	−0.292866	−	0.420280i
$815$	−21.2388			−0.743964
$816$	−2.41462	−	30.8129i	−0.0845284	−	1.07867i
$817$	−2.52368			−0.0882924
$818$	17.6341	+	25.3059i	0.616561	+	0.884800i
$819$	0.450269	+	0.450269i	0.0157337	+	0.0157337i
$820$	16.2759	−	7.49996i	0.568378	−	0.261910i
$821$	−13.9346	+	13.9346i	−0.486322	+	0.486322i	−0.907143	−	0.420822i	$-0.861742\pi$
$821$	−13.9346	+	13.9346i	−0.486322	+	0.486322i	0.420822	+	0.907143i	$0.361742\pi$
$822$	−4.62860	+	25.9067i	−0.161441	+	0.903601i
$823$		−	30.9856i		−	1.08009i	−0.841636	−	0.540045i	$-0.818407\pi$
$823$		−	30.9856i		−	1.08009i	0.841636	−	0.540045i	$-0.181593\pi$
$824$	7.63715	−	1.99083i	0.266053	−	0.0693540i
$825$		−	5.57725i		−	0.194175i
$826$	−6.13123	−	1.09543i	−0.213333	−	0.0381149i
$827$	−9.23130	+	9.23130i	−0.321004	+	0.321004i	−0.849152	−	0.528148i	$-0.822886\pi$
$827$	−9.23130	+	9.23130i	−0.321004	+	0.321004i	0.528148	+	0.849152i	$0.322886\pi$
$828$	1.96321	−	5.31877i	0.0682264	−	0.184840i
$829$	−7.51172	−	7.51172i	−0.260893	−	0.260893i	0.564524	−	0.825417i	$-0.309060\pi$
$829$	−7.51172	−	7.51172i	−0.260893	−	0.260893i	−0.825417	+	0.564524i	$0.809060\pi$
$830$	13.4478	−	9.37093i	0.466780	−	0.325270i
$831$	−23.4411			−0.813163
$832$	3.81294	+	1.07743i	0.132190	+	0.0373533i
$833$	−5.90144			−0.204473
$834$	27.9685	−	19.4895i	0.968471	−	0.674866i
$835$	−6.78007	−	6.78007i	−0.234634	−	0.234634i
$836$	0.932499	−	2.52634i	0.0322512	−	0.0873754i
$837$	8.08823	−	8.08823i	0.279570	−	0.279570i
$838$	−6.41725	−	1.14653i	−0.221680	−	0.0396063i
$839$		−	37.0240i		−	1.27821i	−0.769120	−	0.639105i	$-0.779305\pi$
$839$		−	37.0240i		−	1.27821i	0.769120	−	0.639105i	$-0.220695\pi$
$840$	−3.58355	+	0.934151i	−0.123644	+	0.0322313i
$841$		−	25.8518i		−	0.891443i
$842$	−5.26804	+	29.4858i	−0.181549	+	1.01615i
$843$	−11.0731	+	11.0731i	−0.381376	+	0.381376i
$844$	8.68904	−	4.00393i	0.299089	−	0.137821i
$845$	9.01893	+	9.01893i	0.310261	+	0.310261i
$846$	11.0449	+	15.8500i	0.379730	+	0.544934i
$847$	−7.14474			−0.245496
$848$	7.15252	−	0.560498i	0.245619	−	0.0192476i
$849$	−26.3733			−0.905128
$850$	4.77150	+	6.84738i	0.163661	+	0.234863i
$851$	−3.78246	−	3.78246i	−0.129661	−	0.129661i
$852$	10.3892	+	22.5459i	0.355929	+	0.772411i
$853$	5.54644	−	5.54644i	0.189906	−	0.189906i	−0.605749	−	0.795656i	$-0.707127\pi$
$853$	5.54644	−	5.54644i	0.189906	−	0.189906i	0.795656	+	0.605749i	$0.207127\pi$
$854$	−0.842331	+	4.71461i	−0.0288240	+	0.161331i
$855$			0.406404i			0.0138987i
$856$	46.1023	+	27.0367i	1.57575	+	0.924094i
$857$			16.2268i			0.554296i	0.960827	+	0.277148i	$0.0893892\pi$
$857$			16.2268i			0.554296i	−0.960827	+	0.277148i	$0.910611\pi$
$858$	3.84559	+	0.687069i	0.131286	+	0.0234561i
$859$	−10.3439	+	10.3439i	−0.352928	+	0.352928i	−0.861198	−	0.508270i	$-0.830285\pi$
$859$	−10.3439	+	10.3439i	−0.352928	+	0.352928i	0.508270	+	0.861198i	$0.330285\pi$
$860$	−14.9798	−	5.52921i	−0.510808	−	0.188544i
$861$	−8.29576	−	8.29576i	−0.282719	−	0.282719i
$862$	19.0787	−	13.2947i	0.649822	−	0.452820i
$863$	46.3673			1.57836			0.789181	−	0.614161i	$-0.210505\pi$
$863$	46.3673			1.57836			0.789181	+	0.614161i	$0.210505\pi$
$864$	24.5457	−	20.1269i	0.835062	−	0.684731i
$865$	18.5812			0.631779
$866$	11.8639	−	8.26721i	0.403152	−	0.280931i
$867$	16.5047	+	16.5047i	0.560528	+	0.560528i
$868$	−3.82470	−	1.41174i	−0.129819	−	0.0479175i
$869$	−4.13687	+	4.13687i	−0.140334	+	0.140334i
$870$	3.23419	+	0.577833i	0.109649	+	0.0195904i
$871$		−	2.83967i		−	0.0962186i
$872$	18.0845	−	30.8373i	0.612417	−	1.04428i
$873$			8.83618i			0.299059i
$874$	0.173353	−	0.970276i	0.00586376	−	0.0328201i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−6.63907	−	14.4076i	−0.224313	−	0.486788i
$877$	−19.8494	−	19.8494i	−0.670267	−	0.670267i	0.287510	−	0.957778i	$-0.407173\pi$
$877$	−19.8494	−	19.8494i	−0.670267	−	0.670267i	−0.957778	+	0.287510i	$0.907173\pi$
$878$	−9.30903	−	13.3590i	−0.314165	−	0.450844i
$879$	18.9621			0.639576
$880$	11.0701	−	12.9526i	0.373172	−	0.436631i
$881$	8.12466			0.273727			0.136863	−	0.990590i	$-0.456298\pi$
$881$	8.12466			0.273727			0.136863	+	0.990590i	$0.456298\pi$
$882$	−1.03952	−	1.49177i	−0.0350025	−	0.0502306i
$883$	−27.0170	−	27.0170i	−0.909194	−	0.909194i	0.0870136	−	0.996207i	$-0.472268\pi$
$883$	−27.0170	−	27.0170i	−0.909194	−	0.909194i	−0.996207	+	0.0870136i	$0.972268\pi$
$884$	−5.30917	+	2.44648i	−0.178567	+	0.0822840i
$885$	4.07742	−	4.07742i	0.137061	−	0.137061i
$886$	8.22651	−	46.0446i	0.276375	−	1.54690i
$887$			38.7464i			1.30098i	0.759516	+	0.650489i	$0.225436\pi$
$887$			38.7464i			1.30098i	−0.759516	+	0.650489i	$0.774564\pi$
$888$	−2.26634	−	8.69405i	−0.0760535	−	0.291753i
$889$			12.8149i			0.429799i
$890$	−13.0708	−	2.33529i	−0.438135	−	0.0782790i
$891$	10.5118	−	10.5118i	0.352159	−	0.352159i
$892$	−13.2261	+	35.8324i	−0.442843	+	1.19976i
$893$	2.37484	+	2.37484i	0.0794709	+	0.0794709i
$894$	29.7461	−	20.7282i	0.994860	−	0.693255i
$895$	−12.0402			−0.402460
$896$	−10.1766	−	4.94339i	−0.339976	−	0.165147i
$897$	1.42981			0.0477398
$898$	−48.3996	+	33.7266i	−1.61512	+	1.12547i
$899$	2.55751	+	2.55751i	0.0852976	+	0.0852976i
$900$	−0.890403	+	2.41230i	−0.0296801	+	0.0804098i
$901$	−7.48465	+	7.48465i	−0.249350	+	0.249350i
$902$	53.1366	+	9.49359i	1.76925	+	0.316102i
$903$			10.4534i			0.347867i
$904$	−5.27095	−	20.2202i	−0.175309	−	0.672514i
$905$			21.1133i			0.701830i
$906$	−5.38888	+	30.1621i	−0.179034	+	1.00207i
$907$	32.1206	−	32.1206i	1.06655	−	1.06655i	0.0689235	−	0.997622i	$-0.478044\pi$
$907$	32.1206	−	32.1206i	1.06655	−	1.06655i	0.997622	−	0.0689235i	$-0.0219564\pi$
$908$	28.2160	−	13.0020i	0.936381	−	0.431487i
$909$	1.00692	+	1.00692i	0.0333973	+	0.0333973i
$910$	0.400451	+	0.574669i	0.0132748	+	0.0190501i
$911$	48.8815			1.61951			0.809757	−	0.586765i	$-0.199599\pi$
$911$	48.8815			1.61951			0.809757	+	0.586765i	$0.199599\pi$
$912$	1.07558	−	1.25849i	0.0356160	−	0.0416726i
$913$	49.3697			1.63390
$914$	1.28142	+	1.83891i	0.0423855	+	0.0608257i
$915$	−3.13533	−	3.13533i	−0.103651	−	0.103651i
$916$	−13.3386	−	28.9464i	−0.440718	−	0.956414i
$917$	−4.93512	+	4.93512i	−0.162972	+	0.162972i
$918$	−8.23668	+	46.1015i	−0.271851	+	1.52158i
$919$			11.8821i			0.391954i	0.980608	+	0.195977i	$0.0627878\pi$
$919$			11.8821i			0.391954i	−0.980608	+	0.195977i	$0.937212\pi$
$920$	3.15478	−	5.37946i	0.104010	−	0.177356i
$921$			24.0634i			0.792916i
$922$	−13.5166	−	2.41493i	−0.445146	−	0.0795316i
$923$	3.32003	−	3.32003i	0.109280	−	0.109280i
$924$	−10.4644	−	3.86252i	−0.344254	−	0.127068i
$925$	1.71551	+	1.71551i	0.0564056	+	0.0564056i
$926$	−11.7501	+	8.18788i	−0.386132	+	0.269070i
$927$	−3.58755			−0.117831
$928$	6.36415	+	7.76138i	0.208913	+	0.254780i
$929$	−42.1834			−1.38399			−0.691996	−	0.721901i	$-0.743268\pi$
$929$	−42.1834			−1.38399			−0.691996	+	0.721901i	$0.743268\pi$
$930$	3.09681	−	2.15797i	0.101548	−	0.0707626i
$931$	−0.223515	−	0.223515i	−0.00732542	−	0.00732542i
$932$	50.0067	+	18.4580i	1.63802	+	0.604612i
$933$	23.9788	−	23.9788i	0.785030	−	0.785030i
$934$	−31.7606	−	5.67448i	−1.03924	−	0.185675i
$935$			25.1381i			0.822105i
$936$	−1.55362	−	0.911119i	−0.0507817	−	0.0297809i
$937$		−	36.3205i		−	1.18654i	−0.805003	−	0.593270i	$-0.797837\pi$
$937$		−	36.3205i		−	1.18654i	0.805003	−	0.593270i	$-0.202163\pi$
$938$	−1.42609	+	7.98194i	−0.0465634	+	0.260620i
$939$	−20.3085	+	20.3085i	−0.662744	+	0.662744i
$940$	8.89323	+	19.2994i	0.290065	+	0.629478i
$941$	−20.9066	−	20.9066i	−0.681536	−	0.681536i	0.278810	−	0.960346i	$-0.410060\pi$
$941$	−20.9066	−	20.9066i	−0.681536	−	0.681536i	−0.960346	+	0.278810i	$0.910060\pi$
$942$	12.5820	+	18.0559i	0.409945	+	0.588294i
$943$	19.7564			0.643356
$944$	17.5625	−	1.37626i	0.571611	−	0.0447935i
$945$	5.61133			0.182536
$946$	−27.4970	−	39.4597i	−0.894004	−	1.28295i
$947$	30.8926	+	30.8926i	1.00388	+	1.00388i	0.999992	+	0.00388357i	$0.00123618\pi$
$947$	30.8926	+	30.8926i	1.00388	+	1.00388i	0.00388357	+	0.999992i	$0.498764\pi$
$948$	−3.26644	+	1.50518i	−0.106089	+	0.0488861i
$949$	−2.12161	+	2.12161i	−0.0688704	+	0.0688704i
$950$	−0.0786233	+	0.440062i	−0.00255088	+	0.0142775i
$951$			42.5183i			1.37875i
$952$	16.1520	−	4.21046i	0.523490	−	0.136462i
$953$		−	48.5176i		−	1.57164i	−0.618456	−	0.785819i	$-0.712242\pi$
$953$		−	48.5176i		−	1.57164i	0.618456	−	0.785819i	$-0.287758\pi$
$954$	−3.21038	−	0.573579i	−0.103940	−	0.0185703i
$955$	6.23325	−	6.23325i	0.201703	−	0.201703i
$956$	12.4226	−	33.6555i	0.401775	−	1.08850i
$957$	6.99736	+	6.99736i	0.226192	+	0.226192i
$958$	−31.5650	+	21.9956i	−1.01982	+	0.710646i
$959$	−14.2127			−0.458951
$960$	9.14157	−	5.11347i	0.295043	−	0.165037i
$961$	−26.8447			−0.865957
$962$	−1.39420	+	0.971532i	−0.0449509	+	0.0313235i
$963$	−17.1785	−	17.1785i	−0.553570	−	0.553570i
$964$	9.78177	−	26.5009i	0.315049	−	0.853537i
$965$	6.34318	−	6.34318i	0.204194	−	0.204194i
$966$	−4.01900	−	0.718050i	−0.129309	−	0.0231029i
$967$			25.8083i			0.829939i	0.909835	+	0.414970i	$0.136208\pi$
$967$			25.8083i			0.829939i	−0.909835	+	0.414970i	$0.863792\pi$
$968$	19.5549	−	5.09752i	0.628518	−	0.163840i
$969$			2.44245i			0.0784626i
$970$	−1.70945	+	9.56798i	−0.0548873	+	0.307209i
$971$	−26.2389	+	26.2389i	−0.842047	+	0.842047i	−0.989125	−	0.147078i	$-0.953013\pi$
$971$	−26.2389	+	26.2389i	−0.842047	+	0.842047i	0.147078	+	0.989125i	$0.453013\pi$
$972$	−22.2776	+	10.2656i	−0.714556	+	0.329269i
$973$	13.0180	+	13.0180i	0.417337	+	0.417337i
$974$	19.7912	+	28.4014i	0.634150	+	0.910041i
$975$	−0.648479			−0.0207680
$976$	−1.05828	−	13.5047i	−0.0338746	−	0.432274i
$977$	−47.2771			−1.51253			−0.756265	−	0.654265i	$-0.772978\pi$
$977$	−47.2771			−1.51253			−0.756265	+	0.654265i	$0.772978\pi$
$978$	−22.4840	−	32.2658i	−0.718958	−	1.03175i
$979$	−28.2795	−	28.2795i	−0.903816	−	0.903816i
$980$	−0.837014	−	1.81643i	−0.0267374	−	0.0580236i
$981$	−11.4905	+	11.4905i	−0.366863	+	0.366863i
$982$	3.72245	−	20.8349i	0.118788	−	0.664869i
$983$		−	44.2099i		−	1.41008i	−0.709169	−	0.705039i	$-0.750930\pi$
$983$		−	44.2099i		−	1.41008i	0.709169	−	0.705039i	$-0.249070\pi$
$984$	28.6239	+	16.7865i	0.912497	+	0.535133i
$985$		−	21.9168i		−	0.698328i
$986$	−14.5773	−	2.60445i	−0.464237	−	0.0829425i
$987$	9.83686	−	9.83686i	0.313111	−	0.313111i
$988$	−0.293743	−	0.108424i	−0.00934522	−	0.00344942i
$989$	−12.4474	−	12.4474i	−0.395804	−	0.395804i
$990$	−6.35445	+	4.42801i	−0.201958	+	0.140732i
$991$	26.8105			0.851664			0.425832	−	0.904802i	$-0.359981\pi$
$991$	26.8105			0.851664			0.425832	+	0.904802i	$0.359981\pi$
$992$	11.4753	+	1.13508i	0.364341	+	0.0360389i
$993$	−14.1944			−0.450447
$994$	−10.9995	+	7.66484i	−0.348883	+	0.243114i
$995$	−11.1248	−	11.1248i	−0.352680	−	0.352680i
$996$	28.4724	+	10.5095i	0.902183	+	0.333005i
$997$	8.49269	−	8.49269i	0.268966	−	0.268966i	−0.559717	−	0.828684i	$-0.689090\pi$
$997$	8.49269	−	8.49269i	0.268966	−	0.268966i	0.828684	+	0.559717i	$0.189090\pi$
$998$	18.8509	+	3.36799i	0.596716	+	0.106612i
$999$			13.6136i			0.430716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.5	✓	44
4.3	odd	2		2240.2.bd.a.1681.7		44
16.5	even	4	inner	560.2.bd.a.421.5	yes	44
16.11	odd	4		2240.2.bd.a.561.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.5	✓	44	1.1	even	1	trivial
560.2.bd.a.421.5	yes	44	16.5	even	4	inner
2240.2.bd.a.561.7		44	16.11	odd	4
2240.2.bd.a.1681.7		44	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16029 + 0.808533i) q^{2} +(0.925827 + 0.925827i) q^{3} +(0.692549 - 1.87627i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.82279 - 0.325667i) q^{6} -1.00000i q^{7} +(0.713464 + 2.73696i) q^{8} -1.28569i q^{9} +O(q^{10})\)	\(q+(-1.16029 + 0.808533i) q^{2} +(0.925827 + 0.925827i) q^{3} +(0.692549 - 1.87627i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.82279 - 0.325667i) q^{6} -1.00000i q^{7} +(0.713464 + 2.73696i) q^{8} -1.28569i q^{9} +(0.248730 - 1.39217i) q^{10} +(3.01204 - 3.01204i) q^{11} +(2.37828 - 1.09592i) q^{12} +(-0.350216 - 0.350216i) q^{13} +(0.808533 + 1.16029i) q^{14} -1.30932 q^{15} +(-3.04075 - 2.59881i) q^{16} +5.90144 q^{17} +(1.03952 + 1.49177i) q^{18} +(0.223515 + 0.223515i) q^{19} +(0.837014 + 1.81643i) q^{20} +(0.925827 - 0.925827i) q^{21} +(-1.05951 + 5.93017i) q^{22} +2.20486i q^{23} +(-1.87341 + 3.19450i) q^{24} -1.00000i q^{25} +(0.689514 + 0.123191i) q^{26} +(3.96781 - 3.96781i) q^{27} +(-1.87627 - 0.692549i) q^{28} +(1.25462 + 1.25462i) q^{29} +(1.51919 - 1.05863i) q^{30} +2.03846 q^{31} +(5.62938 + 0.556833i) q^{32} +5.57725 q^{33} +(-6.84738 + 4.77150i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-2.41230 - 0.890403i) q^{36} +(-1.71551 + 1.71551i) q^{37} +(-0.440062 - 0.0786233i) q^{38} -0.648479i q^{39} +(-2.43982 - 1.43083i) q^{40} -8.96038i q^{41} +(-0.325667 + 1.82279i) q^{42} +(-5.64543 + 5.64543i) q^{43} +(-3.56540 - 7.73737i) q^{44} +(0.909119 + 0.909119i) q^{45} +(-1.78270 - 2.55828i) q^{46} +10.6249 q^{47} +(-0.409157 - 5.22126i) q^{48} -1.00000 q^{49} +(0.808533 + 1.16029i) q^{50} +(5.46371 + 5.46371i) q^{51} +(-0.899641 + 0.414557i) q^{52} +(-1.26828 + 1.26828i) q^{53} +(-1.39571 + 7.81191i) q^{54} +4.25966i q^{55} +(2.73696 - 0.713464i) q^{56} +0.413873i q^{57} +(-2.47013 - 0.441324i) q^{58} +(-3.11416 + 3.11416i) q^{59} +(-0.906767 + 2.45663i) q^{60} +(2.39463 + 2.39463i) q^{61} +(-2.36521 + 1.64817i) q^{62} -1.28569 q^{63} +(-6.98194 + 3.90545i) q^{64} +0.495280 q^{65} +(-6.47123 + 4.50939i) q^{66} +(4.05417 + 4.05417i) q^{67} +(4.08703 - 11.0727i) q^{68} +(-2.04132 + 2.04132i) q^{69} +(-1.39217 - 0.248730i) q^{70} +9.47994i q^{71} +(3.51888 - 0.917293i) q^{72} -6.05800i q^{73} +(0.603444 - 3.37754i) q^{74} +(0.925827 - 0.925827i) q^{75} +(0.574170 - 0.264579i) q^{76} +(-3.01204 - 3.01204i) q^{77} +(0.524317 + 0.752424i) q^{78} -1.37345 q^{79} +(3.98777 - 0.312497i) q^{80} +3.48994 q^{81} +(7.24476 + 10.3966i) q^{82} +(8.19539 + 8.19539i) q^{83} +(-1.09592 - 2.37828i) q^{84} +(-4.17295 + 4.17295i) q^{85} +(1.98583 - 11.1149i) q^{86} +2.32313i q^{87} +(10.3928 + 6.09485i) q^{88} -9.38882i q^{89} +(-1.78990 - 0.319790i) q^{90} +(-0.350216 + 0.350216i) q^{91} +(4.13690 + 1.52697i) q^{92} +(1.88726 + 1.88726i) q^{93} +(-12.3280 + 8.59061i) q^{94} -0.316098 q^{95} +(4.69630 + 5.72736i) q^{96} -6.87272 q^{97} +(1.16029 - 0.808533i) q^{98} +(-3.87254 - 3.87254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Introduction

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