LMFDB - Embedded newform 570.2.m.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$0.339574 - 0.339574i$ of defining polynomial
Character	$\chi$	$=$	570.37
Dual form			570.2.m.b.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.367533 - 2.20566i) q^{10} -4.80832 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.531491 - 0.531491i) q^{13} +1.03038 q^{14} +(-2.20566 + 0.367533i) q^{15} -1.00000 q^{16} +(-3.72984 - 3.72984i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.90517 + 3.24961i) q^{19} +(1.81952 + 1.29975i) q^{20} -1.03038i q^{21} +(3.39999 - 3.39999i) q^{22} +(-4.07973 + 4.07973i) q^{23} +1.00000i q^{24} +(-1.62130 - 4.72984i) q^{25} +0.751642 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.728588 + 0.728588i) q^{28} -0.494819 q^{29} +(1.29975 - 1.81952i) q^{30} -8.62312i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.39999 - 3.39999i) q^{33} +5.27479 q^{34} +(2.27266 - 0.378698i) q^{35} +1.00000 q^{36} +(-5.47836 + 5.47836i) q^{37} +(-4.35209 - 0.243552i) q^{38} -0.751642i q^{39} +(-2.20566 + 0.367533i) q^{40} +5.82553i q^{41} +(0.728588 + 0.728588i) q^{42} +(-3.04079 + 3.04079i) q^{43} +4.80832i q^{44} +(-1.81952 - 1.29975i) q^{45} -5.76961i q^{46} +(0.910451 + 0.910451i) q^{47} +(-0.707107 - 0.707107i) q^{48} -5.93832i q^{49} +(4.49094 + 2.19807i) q^{50} -5.27479i q^{51} +(-0.531491 + 0.531491i) q^{52} +(-3.53266 - 3.53266i) q^{53} -1.00000i q^{54} +(6.24961 - 8.74883i) q^{55} -1.03038i q^{56} +(-0.243552 + 4.35209i) q^{57} +(0.349890 - 0.349890i) q^{58} +12.1307 q^{59} +(0.367533 + 2.20566i) q^{60} -5.32419 q^{61} +(6.09747 + 6.09747i) q^{62} +(0.728588 - 0.728588i) q^{63} +1.00000i q^{64} +(1.65786 - 0.276253i) q^{65} +4.80832 q^{66} +(-9.19128 + 9.19128i) q^{67} +(-3.72984 + 3.72984i) q^{68} -5.76961 q^{69} +(-1.33924 + 1.87480i) q^{70} +2.06076i q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.31160 - 3.31160i) q^{73} -7.74758i q^{74} +(2.19807 - 4.49094i) q^{75} +(3.24961 - 2.90517i) q^{76} +(3.50328 + 3.50328i) q^{77} +(0.531491 + 0.531491i) q^{78} -2.77074 q^{79} +(1.29975 - 1.81952i) q^{80} -1.00000 q^{81} +(-4.11927 - 4.11927i) q^{82} +(-3.57770 + 3.57770i) q^{83} -1.03038 q^{84} +(11.6344 - 1.93866i) q^{85} -4.30033i q^{86} +(-0.349890 - 0.349890i) q^{87} +(-3.39999 - 3.39999i) q^{88} -1.08630 q^{89} +(2.20566 - 0.367533i) q^{90} +0.774476i q^{91} +(4.07973 + 4.07973i) q^{92} +(6.09747 - 6.09747i) q^{93} -1.28757 q^{94} +(-9.68873 + 1.06234i) q^{95} +1.00000 q^{96} +(-2.81665 + 2.81665i) q^{97} +(4.19903 + 4.19903i) q^{98} -4.80832i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−1.29975	+	1.81952i	−0.581266	+	0.813714i
$5$	−1.29975	+	1.81952i	−0.581266	+	0.813714i
$6$	−1.00000			−0.408248
$7$	−0.728588	−	0.728588i	−0.275380	−	0.275380i	0.555881	−	0.831262i	$-0.312381\pi$
$7$	−0.728588	−	0.728588i	−0.275380	−	0.275380i	−0.831262	+	0.555881i	$0.812381\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−0.367533	−	2.20566i	−0.116224	−	0.697490i
$11$	−4.80832			−1.44976			−0.724881	−	0.688874i	$-0.758105\pi$
$11$	−4.80832			−1.44976			−0.724881	+	0.688874i	$0.758105\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−0.531491	−	0.531491i	−0.147409	−	0.147409i	0.629550	−	0.776960i	$-0.283239\pi$
$13$	−0.531491	−	0.531491i	−0.147409	−	0.147409i	−0.776960	+	0.629550i	$0.783239\pi$
$14$	1.03038			0.275380
$15$	−2.20566	+	0.367533i	−0.569498	+	0.0948965i
$16$	−1.00000			−0.250000
$17$	−3.72984	−	3.72984i	−0.904619	−	0.904619i	0.0912125	−	0.995831i	$-0.470926\pi$
$17$	−3.72984	−	3.72984i	−0.904619	−	0.904619i	−0.995831	+	0.0912125i	$0.970926\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	2.90517	+	3.24961i	0.666493	+	0.745511i
$19$	2.90517	+	3.24961i	0.666493	+	0.745511i
$20$	1.81952	+	1.29975i	0.406857	+	0.290633i
$21$		−	1.03038i		−	0.224847i
$22$	3.39999	−	3.39999i	0.724881	−	0.724881i
$23$	−4.07973	+	4.07973i	−0.850682	+	0.850682i	−0.990217	−	0.139535i	$-0.955439\pi$
$23$	−4.07973	+	4.07973i	−0.850682	+	0.850682i	0.139535	+	0.990217i	$0.455439\pi$
$24$			1.00000i			0.204124i
$25$	−1.62130	−	4.72984i	−0.324260	−	0.945968i
$26$	0.751642			0.147409
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.728588	+	0.728588i	−0.137690	+	0.137690i
$29$	−0.494819			−0.0918856			−0.0459428	−	0.998944i	$-0.514629\pi$
$29$	−0.494819			−0.0918856			−0.0459428	+	0.998944i	$0.514629\pi$
$30$	1.29975	−	1.81952i	0.237301	−	0.332197i
$31$		−	8.62312i		−	1.54876i	−0.632722	−	0.774379i	$-0.718062\pi$
$31$		−	8.62312i		−	1.54876i	0.632722	−	0.774379i	$-0.281938\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.39999	−	3.39999i	−0.591863	−	0.591863i
$34$	5.27479			0.904619
$35$	2.27266	−	0.378698i	0.384150	−	0.0640117i
$36$	1.00000			0.166667
$37$	−5.47836	+	5.47836i	−0.900637	+	0.900637i	−0.995491	−	0.0948538i	$-0.969762\pi$
$37$	−5.47836	+	5.47836i	−0.900637	+	0.900637i	0.0948538	+	0.995491i	$0.469762\pi$
$38$	−4.35209	−	0.243552i	−0.706002	−	0.0395093i
$39$		−	0.751642i		−	0.120359i
$40$	−2.20566	+	0.367533i	−0.348745	+	0.0581120i
$41$			5.82553i			0.909794i	0.890544	+	0.454897i	$0.150324\pi$
$41$			5.82553i			0.909794i	−0.890544	+	0.454897i	$0.849676\pi$
$42$	0.728588	+	0.728588i	0.112424	+	0.112424i
$43$	−3.04079	+	3.04079i	−0.463716	+	0.463716i	−0.899871	−	0.436155i	$-0.856340\pi$
$43$	−3.04079	+	3.04079i	−0.463716	+	0.463716i	0.436155	+	0.899871i	$0.356340\pi$
$44$			4.80832i			0.724881i
$45$	−1.81952	−	1.29975i	−0.271238	−	0.193755i
$46$		−	5.76961i		−	0.850682i
$47$	0.910451	+	0.910451i	0.132803	+	0.132803i	0.770384	−	0.637581i	$-0.220065\pi$
$47$	0.910451	+	0.910451i	0.132803	+	0.132803i	−0.637581	+	0.770384i	$0.720065\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	5.93832i		−	0.848331i
$50$	4.49094	+	2.19807i	0.635114	+	0.310854i
$51$		−	5.27479i		−	0.738618i
$52$	−0.531491	+	0.531491i	−0.0737046	+	0.0737046i
$53$	−3.53266	−	3.53266i	−0.485248	−	0.485248i	0.421555	−	0.906803i	$-0.361484\pi$
$53$	−3.53266	−	3.53266i	−0.485248	−	0.485248i	−0.906803	+	0.421555i	$0.861484\pi$
$54$		−	1.00000i		−	0.136083i
$55$	6.24961	−	8.74883i	0.842697	−	1.17969i
$56$		−	1.03038i		−	0.137690i
$57$	−0.243552	+	4.35209i	−0.0322592	+	0.576448i
$58$	0.349890	−	0.349890i	0.0459428	−	0.0459428i
$59$	12.1307			1.57928			0.789641	−	0.613569i	$-0.210267\pi$
$59$	12.1307			1.57928			0.789641	+	0.613569i	$0.210267\pi$
$60$	0.367533	+	2.20566i	0.0474483	+	0.284749i
$61$	−5.32419			−0.681692			−0.340846	−	0.940119i	$-0.610713\pi$
$61$	−5.32419			−0.681692			−0.340846	+	0.940119i	$0.610713\pi$
$62$	6.09747	+	6.09747i	0.774379	+	0.774379i
$63$	0.728588	−	0.728588i	0.0917935	−	0.0917935i
$64$			1.00000i			0.125000i
$65$	1.65786	−	0.276253i	0.205633	−	0.0342650i
$66$	4.80832			0.591863
$67$	−9.19128	+	9.19128i	−1.12289	+	1.12289i	−0.131590	+	0.991304i	$0.542008\pi$
$67$	−9.19128	+	9.19128i	−1.12289	+	1.12289i	−0.991304	+	0.131590i	$0.957992\pi$
$68$	−3.72984	+	3.72984i	−0.452309	+	0.452309i
$69$	−5.76961			−0.694579
$70$	−1.33924	+	1.87480i	−0.160069	+	0.224081i
$71$			2.06076i			0.244567i	0.992495	+	0.122284i	$0.0390217\pi$
$71$			2.06076i			0.244567i	−0.992495	+	0.122284i	$0.960978\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	3.31160	−	3.31160i	0.387594	−	0.387594i	−0.486235	−	0.873828i	$-0.661630\pi$
$73$	3.31160	−	3.31160i	0.387594	−	0.387594i	0.873828	+	0.486235i	$0.161630\pi$
$74$		−	7.74758i		−	0.900637i
$75$	2.19807	−	4.49094i	0.253811	−	0.518569i
$76$	3.24961	−	2.90517i	0.372756	−	0.333246i
$77$	3.50328	+	3.50328i	0.399236	+	0.399236i
$78$	0.531491	+	0.531491i	0.0601795	+	0.0601795i
$79$	−2.77074			−0.311733			−0.155866	−	0.987778i	$-0.549817\pi$
$79$	−2.77074			−0.311733			−0.155866	+	0.987778i	$0.549817\pi$
$80$	1.29975	−	1.81952i	0.145316	−	0.203428i
$81$	−1.00000			−0.111111
$82$	−4.11927	−	4.11927i	−0.454897	−	0.454897i
$83$	−3.57770	+	3.57770i	−0.392703	+	0.392703i	−0.875650	−	0.482947i	$-0.839567\pi$
$83$	−3.57770	+	3.57770i	−0.392703	+	0.392703i	0.482947	+	0.875650i	$0.339567\pi$
$84$	−1.03038			−0.112424
$85$	11.6344	−	1.93866i	1.26192	−	0.210277i
$86$		−	4.30033i		−	0.463716i
$87$	−0.349890	−	0.349890i	−0.0375122	−	0.0375122i
$88$	−3.39999	−	3.39999i	−0.362441	−	0.362441i
$89$	−1.08630			−0.115147			−0.0575736	−	0.998341i	$-0.518336\pi$
$89$	−1.08630			−0.115147			−0.0575736	+	0.998341i	$0.518336\pi$
$90$	2.20566	−	0.367533i	0.232497	−	0.0387414i
$91$			0.774476i			0.0811872i
$92$	4.07973	+	4.07973i	0.425341	+	0.425341i
$93$	6.09747	−	6.09747i	0.632278	−	0.632278i
$94$	−1.28757			−0.132803
$95$	−9.68873	+	1.06234i	−0.994042	+	0.108994i
$96$	1.00000			0.102062
$97$	−2.81665	+	2.81665i	−0.285988	+	0.285988i	−0.835491	−	0.549503i	$-0.814817\pi$
$97$	−2.81665	+	2.81665i	−0.285988	+	0.285988i	0.549503	+	0.835491i	$0.314817\pi$
$98$	4.19903	+	4.19903i	0.424166	+	0.424166i
$99$		−	4.80832i		−	0.483254i
$100$	−4.72984	+	1.62130i	−0.472984	+	0.162130i
$101$	−14.0592			−1.39894			−0.699470	−	0.714662i	$-0.746581\pi$
$101$	−14.0592			−1.39894			−0.699470	+	0.714662i	$0.746581\pi$
$102$	3.72984	+	3.72984i	0.369309	+	0.369309i
$103$	6.63327	+	6.63327i	0.653596	+	0.653596i	0.953857	−	0.300261i	$-0.0970739\pi$
$103$	6.63327	+	6.63327i	0.653596	+	0.653596i	−0.300261	+	0.953857i	$0.597074\pi$
$104$		−	0.751642i		−	0.0737046i
$105$	1.87480	+	1.33924i	0.182961	+	0.130696i
$106$	4.99593			0.485248
$107$	−1.54262	+	1.54262i	−0.149131	+	0.149131i	−0.777730	−	0.628599i	$-0.783629\pi$
$107$	−1.54262	+	1.54262i	−0.149131	+	0.149131i	0.628599	+	0.777730i	$0.283629\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	18.4286			1.76514			0.882569	−	0.470183i	$-0.155812\pi$
$109$	18.4286			1.76514			0.882569	+	0.470183i	$0.155812\pi$
$110$	1.76721	+	10.6055i	0.168497	+	1.01119i
$111$	−7.74758			−0.735367
$112$	0.728588	+	0.728588i	0.0688451	+	0.0688451i
$113$	5.25913	+	5.25913i	0.494738	+	0.494738i	0.909795	−	0.415058i	$-0.136239\pi$
$113$	5.25913	+	5.25913i	0.494738	+	0.494738i	−0.415058	+	0.909795i	$0.636239\pi$
$114$	−2.90517	−	3.24961i	−0.272095	−	0.304354i
$115$	−2.12052	−	12.7258i	−0.197740	−	1.18668i
$116$			0.494819i			0.0459428i
$117$	0.531491	−	0.531491i	0.0491364	−	0.0491364i
$118$	−8.57770	+	8.57770i	−0.789641	+	0.789641i
$119$			5.43503i			0.498229i
$120$	−1.81952	−	1.29975i	−0.166099	−	0.118650i
$121$	12.1199			1.10181
$122$	3.76477	−	3.76477i	0.340846	−	0.340846i
$123$	−4.11927	+	4.11927i	−0.371422	+	0.371422i
$124$	−8.62312			−0.774379
$125$	10.7133	+	3.19762i	0.958229	+	0.286004i
$126$			1.03038i			0.0917935i
$127$	−9.35800	+	9.35800i	−0.830388	+	0.830388i	−0.987570	−	0.157181i	$-0.949759\pi$
$127$	−9.35800	+	9.35800i	−0.830388	+	0.830388i	0.157181	+	0.987570i	$0.449759\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−4.30033			−0.378623
$130$	−0.976946	+	1.36763i	−0.0856839	+	0.119949i
$131$	12.6267			1.10320			0.551601	−	0.834108i	$-0.314017\pi$
$131$	12.6267			1.10320			0.551601	+	0.834108i	$0.314017\pi$
$132$	−3.39999	+	3.39999i	−0.295931	+	0.295931i
$133$	0.250951	−	4.48430i	0.0217602	−	0.388838i
$134$		−	12.9984i		−	1.12289i
$135$	−0.367533	−	2.20566i	−0.0316322	−	0.189833i
$136$		−	5.27479i		−	0.452309i
$137$	0.378698	+	0.378698i	0.0323544	+	0.0323544i	0.723099	−	0.690745i	$-0.242717\pi$
$137$	0.378698	+	0.378698i	0.0323544	+	0.0323544i	−0.690745	+	0.723099i	$0.742717\pi$
$138$	4.07973	−	4.07973i	0.347290	−	0.347290i
$139$			22.7942i			1.93338i	0.255957	+	0.966688i	$0.417609\pi$
$139$			22.7942i			1.93338i	−0.255957	+	0.966688i	$0.582391\pi$
$140$	−0.378698	−	2.27266i	−0.0320058	−	0.192075i
$141$			1.28757i			0.108433i
$142$	−1.45718	−	1.45718i	−0.122284	−	0.122284i
$143$	2.55558	+	2.55558i	0.213708	+	0.213708i
$144$		−	1.00000i		−	0.0833333i
$145$	0.643141	−	0.900333i	0.0534100	−	0.0747686i
$146$			4.68331i			0.387594i
$147$	4.19903	−	4.19903i	0.346330	−	0.346330i
$148$	5.47836	+	5.47836i	0.450319	+	0.450319i
$149$			15.8801i			1.30095i	0.759529	+	0.650473i	$0.225429\pi$
$149$			15.8801i			1.30095i	−0.759529	+	0.650473i	$0.774571\pi$
$150$	1.62130	+	4.72984i	0.132379	+	0.386190i
$151$			13.3507i			1.08646i	0.839583	+	0.543231i	$0.182799\pi$
$151$			13.3507i			1.08646i	−0.839583	+	0.543231i	$0.817201\pi$
$152$	−0.243552	+	4.35209i	−0.0197547	+	0.353001i
$153$	3.72984	−	3.72984i	0.301540	−	0.301540i
$154$	−4.95439			−0.399236
$155$	15.6899	+	11.2079i	1.26025	+	0.900240i
$156$	−0.751642			−0.0601795
$157$	11.7372	+	11.7372i	0.936727	+	0.936727i	0.998114	−	0.0613870i	$-0.0195524\pi$
$157$	11.7372	+	11.7372i	0.936727	+	0.936727i	−0.0613870	+	0.998114i	$0.519552\pi$
$158$	1.95921	−	1.95921i	0.155866	−	0.155866i
$159$		−	4.99593i		−	0.396203i
$160$	0.367533	+	2.20566i	0.0290560	+	0.174372i
$161$	5.94489			0.468523
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−0.988668	+	0.988668i	−0.0774384	+	0.0774384i	−0.744765	−	0.667327i	$-0.767438\pi$
$163$	−0.988668	+	0.988668i	−0.0774384	+	0.0774384i	0.667327	+	0.744765i	$0.267438\pi$
$164$	5.82553			0.454897
$165$	10.6055	−	1.76721i	0.825637	−	0.137577i
$166$		−	5.05963i		−	0.392703i
$167$	−7.42584	+	7.42584i	−0.574629	+	0.574629i	−0.933418	−	0.358790i	$-0.883189\pi$
$167$	−7.42584	+	7.42584i	−0.574629	+	0.574629i	0.358790	+	0.933418i	$0.383189\pi$
$168$	0.728588	−	0.728588i	0.0562118	−	0.0562118i
$169$		−	12.4350i		−	0.956541i
$170$	−6.85591	+	9.59758i	−0.525824	+	0.736101i
$171$	−3.24961	+	2.90517i	−0.248504	+	0.222164i
$172$	3.04079	+	3.04079i	0.231858	+	0.231858i
$173$	−11.0462	−	11.0462i	−0.839825	−	0.839825i	0.149011	−	0.988836i	$-0.452391\pi$
$173$	−11.0462	−	11.0462i	−0.839825	−	0.839825i	−0.988836	+	0.149011i	$0.952391\pi$
$174$	0.494819			0.0375122
$175$	−2.26484	+	4.62737i	−0.171206	+	0.349796i
$176$	4.80832			0.362441
$177$	8.57770	+	8.57770i	0.644739	+	0.644739i
$178$	0.768128	−	0.768128i	0.0575736	−	0.0575736i
$179$	19.0425			1.42330			0.711652	−	0.702532i	$-0.247947\pi$
$179$	19.0425			1.42330			0.711652	+	0.702532i	$0.247947\pi$
$180$	−1.29975	+	1.81952i	−0.0968776	+	0.135619i
$181$		−	1.78110i		−	0.132388i	−0.997807	−	0.0661941i	$-0.978914\pi$
$181$		−	1.78110i		−	0.132388i	0.997807	−	0.0661941i	$-0.0210857\pi$
$182$	−0.547637	−	0.547637i	−0.0405936	−	0.0405936i
$183$	−3.76477	−	3.76477i	−0.278300	−	0.278300i
$184$	−5.76961			−0.425341
$185$	−2.84749	−	17.0885i	−0.209351	−	1.25637i
$186$			8.62312i			0.632278i
$187$	17.9343	+	17.9343i	1.31148	+	1.31148i
$188$	0.910451	−	0.910451i	0.0664014	−	0.0664014i
$189$	1.03038			0.0749491
$190$	6.09977	−	7.60215i	0.442524	−	0.551518i
$191$	−14.8650			−1.07559			−0.537797	−	0.843075i	$-0.680743\pi$
$191$	−14.8650			−1.07559			−0.537797	+	0.843075i	$0.680743\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−5.04632	−	5.04632i	−0.363242	−	0.363242i	0.501763	−	0.865005i	$-0.332685\pi$
$193$	−5.04632	−	5.04632i	−0.363242	−	0.363242i	−0.865005	+	0.501763i	$0.832685\pi$
$194$		−	3.98335i		−	0.285988i
$195$	1.36763	+	0.976946i	0.0979378	+	0.0699606i
$196$	−5.93832			−0.424166
$197$	−7.66209	−	7.66209i	−0.545901	−	0.545901i	0.379351	−	0.925253i	$-0.376147\pi$
$197$	−7.66209	−	7.66209i	−0.545901	−	0.545901i	−0.925253	+	0.379351i	$0.876147\pi$
$198$	3.39999	+	3.39999i	0.241627	+	0.241627i
$199$			20.9302i			1.48370i	0.670565	+	0.741851i	$0.266052\pi$
$199$			20.9302i			1.48370i	−0.670565	+	0.741851i	$0.733948\pi$
$200$	2.19807	−	4.49094i	0.155427	−	0.317557i
$201$	−12.9984			−0.916839
$202$	9.94134	−	9.94134i	0.699470	−	0.699470i
$203$	0.360520	+	0.360520i	0.0253035	+	0.0253035i
$204$	−5.27479			−0.369309
$205$	−10.5997	−	7.57173i	−0.740312	−	0.528832i
$206$	−9.38086			−0.653596
$207$	−4.07973	−	4.07973i	−0.283561	−	0.283561i
$208$	0.531491	+	0.531491i	0.0368523	+	0.0368523i
$209$	−13.9690	−	15.6252i	−0.966256	−	1.08081i
$210$	−2.27266	+	0.378698i	−0.156829	+	0.0261327i
$211$		−	27.6388i		−	1.90273i	−0.308062	−	0.951366i	$-0.599681\pi$
$211$		−	27.6388i		−	1.90273i	0.308062	−	0.951366i	$-0.400319\pi$
$212$	−3.53266	+	3.53266i	−0.242624	+	0.242624i
$213$	−1.45718	+	1.45718i	−0.0998441	+	0.0998441i
$214$		−	2.18160i		−	0.149131i
$215$	−1.58051	−	9.48504i	−0.107790	−	0.646875i
$216$	−1.00000			−0.0680414
$217$	−6.28270	+	6.28270i	−0.426498	+	0.426498i
$218$	−13.0310	+	13.0310i	−0.882569	+	0.882569i
$219$	4.68331			0.316469
$220$	−8.74883	−	6.24961i	−0.589846	−	0.421349i
$221$			3.96475i			0.266698i
$222$	5.47836	−	5.47836i	0.367684	−	0.367684i
$223$	8.04571	+	8.04571i	0.538781	+	0.538781i	0.923171	−	0.384390i	$-0.125588\pi$
$223$	8.04571	+	8.04571i	0.538781	+	0.538781i	−0.384390	+	0.923171i	$0.625588\pi$
$224$	−1.03038			−0.0688451
$225$	4.72984	−	1.62130i	0.315323	−	0.108087i
$226$	−7.43754			−0.494738
$227$	1.98330	−	1.98330i	0.131636	−	0.131636i	−0.638219	−	0.769855i	$-0.720329\pi$
$227$	1.98330	−	1.98330i	0.131636	−	0.131636i	0.769855	+	0.638219i	$0.220329\pi$
$228$	4.35209	+	0.243552i	0.288224	+	0.0161296i
$229$		−	19.6443i		−	1.29813i	−0.760732	−	0.649066i	$-0.775160\pi$
$229$		−	19.6443i		−	1.29813i	0.760732	−	0.649066i	$-0.224840\pi$
$230$	10.4979	+	7.49905i	0.692212	+	0.494473i
$231$			4.95439i			0.325975i
$232$	−0.349890	−	0.349890i	−0.0229714	−	0.0229714i
$233$	−4.73992	+	4.73992i	−0.310523	+	0.310523i	−0.845112	−	0.534589i	$-0.820466\pi$
$233$	−4.73992	+	4.73992i	−0.310523	+	0.310523i	0.534589	+	0.845112i	$0.320466\pi$
$234$			0.751642i			0.0491364i
$235$	−2.83994	+	0.473225i	−0.185257	+	0.0308698i
$236$		−	12.1307i		−	0.789641i
$237$	−1.95921	−	1.95921i	−0.127264	−	0.127264i
$238$	−3.84315	−	3.84315i	−0.249114	−	0.249114i
$239$		−	21.1851i		−	1.37035i	−0.728378	−	0.685176i	$-0.759725\pi$
$239$		−	21.1851i		−	1.37035i	0.728378	−	0.685176i	$-0.240275\pi$
$240$	2.20566	−	0.367533i	0.142375	−	0.0237241i
$241$		−	16.2784i		−	1.04859i	−0.851538	−	0.524293i	$-0.824329\pi$
$241$		−	16.2784i		−	1.04859i	0.851538	−	0.524293i	$-0.175671\pi$
$242$	−8.57008	+	8.57008i	−0.550905	+	0.550905i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$			5.32419i			0.340846i
$245$	10.8049	+	7.71833i	0.690299	+	0.493106i
$246$		−	5.82553i		−	0.371422i
$247$	0.183064	−	3.27121i	0.0116481	−	0.208142i
$248$	6.09747	−	6.09747i	0.387190	−	0.387190i
$249$	−5.05963			−0.320641
$250$	−9.83652	+	5.31441i	−0.622116	+	0.336113i
$251$	5.24992			0.331372			0.165686	−	0.986179i	$-0.447016\pi$
$251$	5.24992			0.331372			0.165686	+	0.986179i	$0.447016\pi$
$252$	−0.728588	−	0.728588i	−0.0458967	−	0.0458967i
$253$	19.6166	−	19.6166i	1.23329	−	1.23329i
$254$		−	13.2342i		−	0.830388i
$255$	9.59758	+	6.85591i	0.601024	+	0.429333i
$256$	1.00000			0.0625000
$257$	16.0320	−	16.0320i	1.00005	−	1.00005i	4.94079e−5	−	1.00000i	$-0.499984\pi$
$257$	16.0320	−	16.0320i	1.00005	−	1.00005i	1.00000		4.94079e-5i	$-1.57270e-5\pi$
$258$	3.04079	−	3.04079i	0.189311	−	0.189311i
$259$	7.98294			0.496036
$260$	−0.276253	−	1.65786i	−0.0171325	−	0.102816i
$261$		−	0.494819i		−	0.0306285i
$262$	−8.92844	+	8.92844i	−0.551601	+	0.551601i
$263$	−5.94999	+	5.94999i	−0.366892	+	0.366892i	−0.866342	−	0.499450i	$-0.833535\pi$
$263$	−5.94999	+	5.94999i	−0.366892	+	0.366892i	0.499450	+	0.866342i	$0.333535\pi$
$264$		−	4.80832i		−	0.295931i
$265$	11.0193	−	1.83617i	0.676911	−	0.112795i
$266$	2.99343	+	3.34833i	0.183539	+	0.205299i
$267$	−0.768128	−	0.768128i	−0.0470087	−	0.0470087i
$268$	9.19128	+	9.19128i	0.561447	+	0.561447i
$269$	−26.2880			−1.60281			−0.801404	−	0.598123i	$-0.795913\pi$
$269$	−26.2880			−1.60281			−0.801404	+	0.598123i	$0.795913\pi$
$270$	1.81952	+	1.29975i	0.110732	+	0.0791002i
$271$	−11.9318			−0.724802			−0.362401	−	0.932022i	$-0.618043\pi$
$271$	−11.9318			−0.724802			−0.362401	+	0.932022i	$0.618043\pi$
$272$	3.72984	+	3.72984i	0.226155	+	0.226155i
$273$	−0.547637	+	0.547637i	−0.0331445	+	0.0331445i
$274$	−0.535560			−0.0323544
$275$	7.79573	+	22.7426i	0.470100	+	1.37143i
$276$			5.76961i			0.347290i
$277$	−13.1943	−	13.1943i	−0.792771	−	0.792771i	0.189173	−	0.981944i	$-0.439419\pi$
$277$	−13.1943	−	13.1943i	−0.792771	−	0.792771i	−0.981944	+	0.189173i	$0.939419\pi$
$278$	−16.1179	−	16.1179i	−0.966688	−	0.966688i
$279$	8.62312			0.516253
$280$	1.87480	+	1.33924i	0.112040	+	0.0800346i
$281$		−	25.4814i		−	1.52009i	−0.649870	−	0.760045i	$-0.725177\pi$
$281$		−	25.4814i		−	1.52009i	0.649870	−	0.760045i	$-0.274823\pi$
$282$	−0.910451	−	0.910451i	−0.0542165	−	0.0542165i
$283$	−14.9451	+	14.9451i	−0.888392	+	0.888392i	−0.994369	−	0.105977i	$-0.966203\pi$
$283$	−14.9451	+	14.9451i	−0.888392	+	0.888392i	0.105977	+	0.994369i	$0.466203\pi$
$284$	2.06076			0.122284
$285$	−7.60215	−	6.09977i	−0.450313	−	0.361319i
$286$	−3.61413			−0.213708
$287$	4.24441	−	4.24441i	0.250540	−	0.250540i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			10.8234i			0.636671i
$290$	0.181862	+	1.09140i	0.0106793	+	0.0640893i
$291$	−3.98335			−0.233508
$292$	−3.31160	−	3.31160i	−0.193797	−	0.193797i
$293$	−19.3388	−	19.3388i	−1.12978	−	1.12978i	−0.990212	−	0.139570i	$-0.955428\pi$
$293$	−19.3388	−	19.3388i	−1.12978	−	1.12978i	−0.139570	−	0.990212i	$-0.544572\pi$
$294$			5.93832i			0.346330i
$295$	−15.7669	+	22.0720i	−0.917982	+	1.28508i
$296$	−7.74758			−0.450319
$297$	3.39999	−	3.39999i	0.197288	−	0.197288i
$298$	−11.2289	−	11.2289i	−0.650473	−	0.650473i
$299$	4.33668			0.250797
$300$	−4.49094	−	2.19807i	−0.259284	−	0.126906i
$301$	4.43097			0.255397
$302$	−9.44035	−	9.44035i	−0.543231	−	0.543231i
$303$	−9.94134	−	9.94134i	−0.571115	−	0.571115i
$304$	−2.90517	−	3.24961i	−0.166623	−	0.186378i
$305$	6.92011	−	9.68746i	0.396244	−	0.554702i
$306$			5.27479i			0.301540i
$307$	−0.00353863	+	0.00353863i	−0.000201960	+	0.000201960i	−0.707208	−	0.707006i	$-0.750045\pi$
$307$	−0.00353863	+	0.00353863i	−0.000201960	+	0.000201960i	0.707006	+	0.707208i	$0.250045\pi$
$308$	3.50328	−	3.50328i	0.199618	−	0.199618i
$309$			9.38086i			0.533659i
$310$	−19.0196	+	3.16928i	−1.08024	+	0.180003i
$311$	−11.6925			−0.663019			−0.331509	−	0.943452i	$-0.607558\pi$
$311$	−11.6925			−0.663019			−0.331509	+	0.943452i	$0.607558\pi$
$312$	0.531491	−	0.531491i	0.0300898	−	0.0300898i
$313$	−16.6688	+	16.6688i	−0.942174	+	0.942174i	−0.998417	−	0.0562432i	$-0.982088\pi$
$313$	−16.6688	+	16.6688i	−0.942174	+	0.942174i	0.0562432	+	0.998417i	$0.482088\pi$
$314$	−16.5988			−0.936727
$315$	0.378698	+	2.27266i	0.0213372	+	0.128050i
$316$			2.77074i			0.155866i
$317$	6.96737	−	6.96737i	0.391327	−	0.391327i	−0.483834	−	0.875160i	$-0.660756\pi$
$317$	6.96737	−	6.96737i	0.391327	−	0.391327i	0.875160	+	0.483834i	$0.160756\pi$
$318$	3.53266	+	3.53266i	0.198102	+	0.198102i
$319$	2.37925			0.133212
$320$	−1.81952	−	1.29975i	−0.101714	−	0.0726582i
$321$	−2.18160			−0.121765
$322$	−4.20367	+	4.20367i	−0.234261	+	0.234261i
$323$	1.28468	−	22.9564i	0.0714818	−	1.27733i
$324$			1.00000i			0.0555556i
$325$	−1.65216	+	3.37558i	−0.0916454	+	0.187243i
$326$		−	1.39819i		−	0.0774384i
$327$	13.0310	+	13.0310i	0.720614	+	0.720614i
$328$	−4.11927	+	4.11927i	−0.227449	+	0.227449i
$329$		−	1.32669i		−	0.0731426i
$330$	−6.24961	+	8.74883i	−0.344030	+	0.481607i
$331$			12.2381i			0.672669i	0.941743	+	0.336335i	$0.109187\pi$
$331$			12.2381i			0.672669i	−0.941743	+	0.336335i	$0.890813\pi$
$332$	3.57770	+	3.57770i	0.196352	+	0.196352i
$333$	−5.47836	−	5.47836i	−0.300212	−	0.300212i
$334$		−	10.5017i		−	0.574629i
$335$	−4.77735	−	28.6701i	−0.261015	−	1.56641i
$336$			1.03038i			0.0562118i
$337$	18.9918	−	18.9918i	1.03455	−	1.03455i	0.0351664	−	0.999381i	$-0.488804\pi$
$337$	18.9918	−	18.9918i	1.03455	−	1.03455i	0.999381	−	0.0351664i	$-0.0111961\pi$
$338$	8.79290	+	8.79290i	0.478271	+	0.478271i
$339$			7.43754i			0.403952i
$340$	−1.93866	−	11.6344i	−0.105138	−	0.630962i
$341$			41.4627i			2.24533i
$342$	0.243552	−	4.35209i	0.0131698	−	0.235334i
$343$	−9.42671	+	9.42671i	−0.508994	+	0.508994i
$344$	−4.30033			−0.231858
$345$	7.49905	−	10.4979i	0.403735	−	0.565189i
$346$	15.6216			0.839825
$347$	1.51527	+	1.51527i	0.0813438	+	0.0813438i	0.746608	−	0.665264i	$-0.231681\pi$
$347$	1.51527	+	1.51527i	0.0813438	+	0.0813438i	−0.665264	+	0.746608i	$0.731681\pi$
$348$	−0.349890	+	0.349890i	−0.0187561	+	0.0187561i
$349$			21.3136i			1.14089i	0.821336	+	0.570444i	$0.193229\pi$
$349$			21.3136i			1.14089i	−0.821336	+	0.570444i	$0.806771\pi$
$350$	−1.67056	−	4.87353i	−0.0892950	−	0.260501i
$351$	0.751642			0.0401197
$352$	−3.39999	+	3.39999i	−0.181220	+	0.181220i
$353$	9.37463	−	9.37463i	0.498961	−	0.498961i	−0.412153	−	0.911115i	$-0.635223\pi$
$353$	9.37463	−	9.37463i	0.498961	−	0.498961i	0.911115	+	0.412153i	$0.135223\pi$
$354$	−12.1307			−0.644739
$355$	−3.74959	−	2.67847i	−0.199008	−	0.142158i
$356$			1.08630i			0.0575736i
$357$	−3.84315	+	3.84315i	−0.203401	+	0.203401i
$358$	−13.4651	+	13.4651i	−0.711652	+	0.711652i
$359$		−	30.1209i		−	1.58972i	−0.606792	−	0.794861i	$-0.707544\pi$
$359$		−	30.1209i		−	1.58972i	0.606792	−	0.794861i	$-0.292456\pi$
$360$	−0.367533	−	2.20566i	−0.0193707	−	0.116248i
$361$	−2.11992	+	18.8814i	−0.111575	+	0.993756i
$362$	1.25943	+	1.25943i	0.0661941	+	0.0661941i
$363$	8.57008	+	8.57008i	0.449812	+	0.449812i
$364$	0.774476			0.0405936
$365$	1.72127	+	10.3298i	0.0900954	+	0.540685i
$366$	5.32419			0.278300
$367$	−10.0986	−	10.0986i	−0.527140	−	0.527140i	0.392578	−	0.919719i	$-0.371583\pi$
$367$	−10.0986	−	10.0986i	−0.527140	−	0.527140i	−0.919719	+	0.392578i	$0.871583\pi$
$368$	4.07973	−	4.07973i	0.212671	−	0.212671i
$369$	−5.82553			−0.303265
$370$	14.0969	+	10.0699i	0.732861	+	0.523510i
$371$			5.14771i			0.267256i
$372$	−6.09747	−	6.09747i	−0.316139	−	0.316139i
$373$	11.5759	+	11.5759i	0.599377	+	0.599377i	0.940147	−	0.340770i	$-0.110688\pi$
$373$	11.5759	+	11.5759i	0.599377	+	0.599377i	−0.340770	+	0.940147i	$0.610688\pi$
$374$	−25.3629			−1.31148
$375$	5.31441	+	9.83652i	0.274435	+	0.507956i
$376$			1.28757i			0.0664014i
$377$	0.262992	+	0.262992i	0.0135448	+	0.0135448i
$378$	−0.728588	+	0.728588i	−0.0374745	+	0.0374745i
$379$	30.6895			1.57641			0.788206	−	0.615412i	$-0.211010\pi$
$379$	30.6895			1.57641			0.788206	+	0.615412i	$0.211010\pi$
$380$	1.06234	+	9.68873i	0.0544971	+	0.497021i
$381$	−13.2342			−0.678009
$382$	10.5111	−	10.5111i	0.537797	−	0.537797i
$383$	−6.71232	−	6.71232i	−0.342983	−	0.342983i	0.514504	−	0.857488i	$-0.327976\pi$
$383$	−6.71232	−	6.71232i	−0.342983	−	0.342983i	−0.857488	+	0.514504i	$0.827976\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−10.9277	+	1.82090i	−0.556926	+	0.0928017i
$386$	7.13657			0.363242
$387$	−3.04079	−	3.04079i	−0.154572	−	0.154572i
$388$	2.81665	+	2.81665i	0.142994	+	0.142994i
$389$			1.69598i			0.0859894i	0.999075	+	0.0429947i	$0.0136899\pi$
$389$			1.69598i			0.0859894i	−0.999075	+	0.0429947i	$0.986310\pi$
$390$	−1.65786	+	0.276253i	−0.0839492	+	0.0139886i
$391$	30.4335			1.53909
$392$	4.19903	−	4.19903i	0.212083	−	0.212083i
$393$	8.92844	+	8.92844i	0.450380	+	0.450380i
$394$	10.8358			0.545901
$395$	3.60127	−	5.04142i	0.181199	−	0.253661i
$396$	−4.80832			−0.241627
$397$	−17.6346	−	17.6346i	−0.885057	−	0.885057i	0.108986	−	0.994043i	$-0.465240\pi$
$397$	−17.6346	−	17.6346i	−0.885057	−	0.885057i	−0.994043	+	0.108986i	$0.965240\pi$
$398$	−14.7999	−	14.7999i	−0.741851	−	0.741851i
$399$	3.34833	−	2.99343i	0.167626	−	0.149859i
$400$	1.62130	+	4.72984i	0.0810651	+	0.236492i
$401$		−	1.30146i		−	0.0649918i	−0.999472	−	0.0324959i	$-0.989654\pi$
$401$		−	1.30146i		−	0.0649918i	0.999472	−	0.0324959i	$-0.0103456\pi$
$402$	9.19128	−	9.19128i	0.458420	−	0.458420i
$403$	−4.58311	+	4.58311i	−0.228301	+	0.228301i
$404$			14.0592i			0.699470i
$405$	1.29975	−	1.81952i	0.0645851	−	0.0904126i
$406$	−0.509852			−0.0253035
$407$	26.3417	−	26.3417i	1.30571	−	1.30571i
$408$	3.72984	−	3.72984i	0.184655	−	0.184655i
$409$	18.8682			0.932971			0.466485	−	0.884529i	$-0.345520\pi$
$409$	18.8682			0.932971			0.466485	+	0.884529i	$0.345520\pi$
$410$	12.8491	−	2.14107i	0.634572	−	0.105740i
$411$			0.535560i			0.0264172i
$412$	6.63327	−	6.63327i	0.326798	−	0.326798i
$413$	−8.83828	−	8.83828i	−0.434903	−	0.434903i
$414$	5.76961			0.283561
$415$	−1.85958	−	11.1598i	−0.0912831	−	0.547813i
$416$	−0.751642			−0.0368523
$417$	−16.1179	+	16.1179i	−0.789298	+	0.789298i
$418$	20.9262	+	1.17107i	1.02354	+	0.0572791i
$419$			20.1568i			0.984725i	0.870390	+	0.492363i	$0.163867\pi$
$419$			20.1568i			0.984725i	−0.870390	+	0.492363i	$0.836133\pi$
$420$	1.33924	−	1.87480i	0.0653480	−	0.0914806i
$421$			8.85286i			0.431462i	0.976453	+	0.215731i	$0.0692134\pi$
$421$			8.85286i			0.431462i	−0.976453	+	0.215731i	$0.930787\pi$
$422$	19.5436	+	19.5436i	0.951366	+	0.951366i
$423$	−0.910451	+	0.910451i	−0.0442676	+	0.0442676i
$424$		−	4.99593i		−	0.242624i
$425$	−11.5943	+	23.6887i	−0.562408	+	1.14907i
$426$		−	2.06076i		−	0.0998441i
$427$	3.87914	+	3.87914i	0.187725	+	0.187725i
$428$	1.54262	+	1.54262i	0.0745656	+	0.0745656i
$429$			3.61413i			0.174492i
$430$	7.82453	+	5.58935i	0.377332	+	0.269542i
$431$			25.3047i			1.21889i	0.792830	+	0.609443i	$0.208607\pi$
$431$			25.3047i			1.21889i	−0.792830	+	0.609443i	$0.791393\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	6.00560	+	6.00560i	0.288611	+	0.288611i	0.836531	−	0.547920i	$-0.184580\pi$
$433$	6.00560	+	6.00560i	0.288611	+	0.288611i	−0.547920	+	0.836531i	$0.684580\pi$
$434$		−	8.88509i		−	0.426498i
$435$	1.09140	−	0.181862i	0.0523287	−	0.00871963i
$436$		−	18.4286i		−	0.882569i
$437$	−25.1099	−	1.40520i	−1.20117	−	0.0672198i
$438$	−3.31160	+	3.31160i	−0.158234	+	0.158234i
$439$	−38.4260			−1.83397			−0.916986	−	0.398919i	$-0.869386\pi$
$439$	−38.4260			−1.83397			−0.916986	+	0.398919i	$0.869386\pi$
$440$	10.6055	−	1.76721i	0.505597	−	0.0842486i
$441$	5.93832			0.282777
$442$	−2.80350	−	2.80350i	−0.133349	−	0.133349i
$443$	27.7457	−	27.7457i	1.31824	−	1.31824i	0.403066	−	0.915171i	$-0.367945\pi$
$443$	27.7457	−	27.7457i	1.31824	−	1.31824i	0.915171	−	0.403066i	$-0.132055\pi$
$444$			7.74758i			0.367684i
$445$	1.41191	−	1.97654i	0.0669311	−	0.0936969i
$446$	−11.3784			−0.538781
$447$	−11.2289	+	11.2289i	−0.531109	+	0.531109i
$448$	0.728588	−	0.728588i	0.0344226	−	0.0344226i
$449$	28.1598			1.32894			0.664472	−	0.747313i	$-0.268656\pi$
$449$	28.1598			1.32894			0.664472	+	0.747313i	$0.268656\pi$
$450$	−2.19807	+	4.49094i	−0.103618	+	0.211705i
$451$		−	28.0110i		−	1.31899i
$452$	5.25913	−	5.25913i	0.247369	−	0.247369i
$453$	−9.44035	+	9.44035i	−0.443546	+	0.443546i
$454$			2.80480i			0.131636i
$455$	−1.40917	−	1.00663i	−0.0660631	−	0.0471913i
$456$	−3.24961	+	2.90517i	−0.152177	+	0.136047i
$457$	−19.5575	−	19.5575i	−0.914859	−	0.914859i	0.0817904	−	0.996650i	$-0.473936\pi$
$457$	−19.5575	−	19.5575i	−0.914859	−	0.914859i	−0.996650	+	0.0817904i	$0.973936\pi$
$458$	13.8906	+	13.8906i	0.649066	+	0.649066i
$459$	5.27479			0.246206
$460$	−12.7258	+	2.12052i	−0.593342	+	0.0988698i
$461$	9.61570			0.447848			0.223924	−	0.974607i	$-0.428113\pi$
$461$	9.61570			0.447848			0.223924	+	0.974607i	$0.428113\pi$
$462$	−3.50328	−	3.50328i	−0.162988	−	0.162988i
$463$	16.6735	−	16.6735i	0.774882	−	0.774882i	−0.204074	−	0.978956i	$-0.565418\pi$
$463$	16.6735	−	16.6735i	0.774882	−	0.774882i	0.978956	+	0.204074i	$0.0654182\pi$
$464$	0.494819			0.0229714
$465$	3.16928	+	19.0196i	0.146972	+	0.882015i
$466$		−	6.70326i		−	0.310523i
$467$	−17.1190	−	17.1190i	−0.792171	−	0.792171i	0.189676	−	0.981847i	$-0.439256\pi$
$467$	−17.1190	−	17.1190i	−0.792171	−	0.792171i	−0.981847	+	0.189676i	$0.939256\pi$
$468$	−0.531491	−	0.531491i	−0.0245682	−	0.0245682i
$469$	13.3933			0.618446
$470$	1.67352	−	2.34276i	0.0771938	−	0.108064i
$471$			16.5988i			0.764834i
$472$	8.57770	+	8.57770i	0.394820	+	0.394820i
$473$	14.6211	−	14.6211i	0.672278	−	0.672278i
$474$	2.77074			0.127264
$475$	10.6600	−	19.0096i	0.489113	−	0.872221i
$476$	5.43503			0.249114
$477$	3.53266	−	3.53266i	0.161749	−	0.161749i
$478$	14.9801	+	14.9801i	0.685176	+	0.685176i
$479$			14.2801i			0.652474i	0.945288	+	0.326237i	$0.105781\pi$
$479$			14.2801i			0.652474i	−0.945288	+	0.326237i	$0.894219\pi$
$480$	−1.29975	+	1.81952i	−0.0593252	+	0.0830493i
$481$	5.82340			0.265524
$482$	11.5106	+	11.5106i	0.524293	+	0.524293i
$483$	4.20367	+	4.20367i	0.191274	+	0.191274i
$484$		−	12.1199i		−	0.550905i
$485$	−1.46401	−	8.78590i	−0.0664774	−	0.398947i
$486$	1.00000			0.0453609
$487$	−13.6790	+	13.6790i	−0.619856	+	0.619856i	−0.945494	−	0.325639i	$-0.894421\pi$
$487$	−13.6790	+	13.6790i	−0.619856	+	0.619856i	0.325639	+	0.945494i	$0.394421\pi$
$488$	−3.76477	−	3.76477i	−0.170423	−	0.170423i
$489$	−1.39819			−0.0632282
$490$	−13.0979	+	2.18253i	−0.591702	+	0.0985965i
$491$	6.60655			0.298150			0.149075	−	0.988826i	$-0.452370\pi$
$491$	6.60655			0.298150			0.149075	+	0.988826i	$0.452370\pi$
$492$	4.11927	+	4.11927i	0.185711	+	0.185711i
$493$	1.84560	+	1.84560i	0.0831215	+	0.0831215i
$494$	2.18365	+	2.44254i	0.0982471	+	0.109895i
$495$	8.74883	+	6.24961i	0.393231	+	0.280899i
$496$			8.62312i			0.387190i
$497$	1.50144	−	1.50144i	0.0673490	−	0.0673490i
$498$	3.57770	−	3.57770i	0.160320	−	0.160320i
$499$			35.7269i			1.59935i	0.600430	+	0.799677i	$0.294996\pi$
$499$			35.7269i			1.59935i	−0.600430	+	0.799677i	$0.705004\pi$
$500$	3.19762	−	10.7133i	0.143002	−	0.479114i
$501$	−10.5017			−0.469182
$502$	−3.71225	+	3.71225i	−0.165686	+	0.165686i
$503$	−8.52003	+	8.52003i	−0.379889	+	0.379889i	−0.871062	−	0.491173i	$-0.836568\pi$
$503$	−8.52003	+	8.52003i	−0.379889	+	0.379889i	0.491173	+	0.871062i	$0.336568\pi$
$504$	1.03038			0.0458967
$505$	18.2734	−	25.5809i	0.813156	−	1.13834i
$506$			27.7421i			1.23329i
$507$	8.79290	−	8.79290i	0.390506	−	0.390506i
$508$	9.35800	+	9.35800i	0.415194	+	0.415194i
$509$	−13.4408			−0.595753			−0.297877	−	0.954604i	$-0.596278\pi$
$509$	−13.4408			−0.595753			−0.297877	+	0.954604i	$0.596278\pi$
$510$	−11.6344	+	1.93866i	−0.515179	+	0.0858452i
$511$	−4.82559			−0.213471
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.35209	−	0.243552i	−0.192149	−	0.0107531i
$514$			22.6727i			1.00005i
$515$	−20.6910	+	3.44777i	−0.911752	+	0.151927i
$516$			4.30033i			0.189311i
$517$	−4.37774	−	4.37774i	−0.192533	−	0.192533i
$518$	−5.64479	+	5.64479i	−0.248018	+	0.248018i
$519$		−	15.6216i		−	0.685714i
$520$	1.36763	+	0.976946i	0.0599744	+	0.0428419i
$521$			13.5544i			0.593831i	0.954904	+	0.296916i	$0.0959580\pi$
$521$			13.5544i			0.593831i	−0.954904	+	0.296916i	$0.904042\pi$
$522$	0.349890	+	0.349890i	0.0153143	+	0.0153143i
$523$	5.40357	+	5.40357i	0.236282	+	0.236282i	0.815308	−	0.579027i	$-0.196567\pi$
$523$	5.40357	+	5.40357i	0.236282	+	0.236282i	−0.579027	+	0.815308i	$0.696567\pi$
$524$		−	12.6267i		−	0.551601i
$525$	−4.87353	+	1.67056i	−0.212698	+	0.0729090i
$526$		−	8.41456i		−	0.366892i
$527$	−32.1629	+	32.1629i	−1.40104	+	1.40104i
$528$	3.39999	+	3.39999i	0.147966	+	0.147966i
$529$		−	10.2884i		−	0.447321i
$530$	−6.49346	+	9.09020i	−0.282058	+	0.394853i
$531$			12.1307i			0.526427i
$532$	−4.48430	−	0.250951i	−0.194419	−	0.0108801i
$533$	3.09622	−	3.09622i	0.134112	−	0.134112i
$534$	1.08630			0.0470087
$535$	−0.801810	−	4.81186i	−0.0346653	−	0.208035i
$536$	−12.9984			−0.561447
$537$	13.4651	+	13.4651i	0.581062	+	0.581062i
$538$	18.5884	−	18.5884i	0.801404	−	0.801404i
$539$			28.5533i			1.22988i
$540$	−2.20566	+	0.367533i	−0.0949163	+	0.0158161i
$541$	7.68488			0.330399			0.165200	−	0.986260i	$-0.447173\pi$
$541$	7.68488			0.330399			0.165200	+	0.986260i	$0.447173\pi$
$542$	8.43702	−	8.43702i	0.362401	−	0.362401i
$543$	1.25943	−	1.25943i	0.0540473	−	0.0540473i
$544$	−5.27479			−0.226155
$545$	−23.9525	+	33.5312i	−1.02601	+	1.43632i
$546$		−	0.774476i		−	0.0331445i
$547$	−17.8604	+	17.8604i	−0.763656	+	0.763656i	−0.976981	−	0.213325i	$-0.931571\pi$
$547$	−17.8604	+	17.8604i	−0.763656	+	0.763656i	0.213325	+	0.976981i	$0.431571\pi$
$548$	0.378698	−	0.378698i	0.0161772	−	0.0161772i
$549$		−	5.32419i		−	0.227231i
$550$	−21.5938	−	10.5690i	−0.920765	−	0.450664i
$551$	−1.43754	−	1.60797i	−0.0612411	−	0.0685018i
$552$	−4.07973	−	4.07973i	−0.173645	−	0.173645i
$553$	2.01873	+	2.01873i	0.0858451	+	0.0858451i
$554$	18.6596			0.792771
$555$	10.0699	−	14.0969i	0.427444	−	0.598379i
$556$	22.7942			0.966688
$557$	12.5198	+	12.5198i	0.530480	+	0.530480i	0.920715	−	0.390235i	$-0.127606\pi$
$557$	12.5198	+	12.5198i	0.530480	+	0.530480i	−0.390235	+	0.920715i	$0.627606\pi$
$558$	−6.09747	+	6.09747i	−0.258126	+	0.258126i
$559$	3.23231			0.136712
$560$	−2.27266	+	0.378698i	−0.0960375	+	0.0160029i
$561$			25.3629i			1.07082i
$562$	18.0180	+	18.0180i	0.760045	+	0.760045i
$563$	11.0759	+	11.0759i	0.466791	+	0.466791i	0.900873	−	0.434082i	$-0.142927\pi$
$563$	11.0759	+	11.0759i	0.466791	+	0.466791i	−0.434082	+	0.900873i	$0.642927\pi$
$564$	1.28757			0.0542165
$565$	−16.4046	+	2.73354i	−0.690149	+	0.115001i
$566$		−	21.1355i		−	0.888392i
$567$	0.728588	+	0.728588i	0.0305978	+	0.0305978i
$568$	−1.45718	+	1.45718i	−0.0611418	+	0.0611418i
$569$	−43.4414			−1.82116			−0.910579	−	0.413336i	$-0.864364\pi$
$569$	−43.4414			−1.82116			−0.910579	+	0.413336i	$0.864364\pi$
$570$	9.68873	−	1.06234i	0.405816	−	0.0444967i
$571$	15.6768			0.656052			0.328026	−	0.944669i	$-0.393617\pi$
$571$	15.6768			0.656052			0.328026	+	0.944669i	$0.393617\pi$
$572$	2.55558	−	2.55558i	0.106854	−	0.106854i
$573$	−10.5111	−	10.5111i	−0.439109	−	0.439109i
$574$			6.00250i			0.250540i
$575$	25.9109	+	12.6820i	1.08056	+	0.528876i
$576$	−1.00000			−0.0416667
$577$	6.59569	+	6.59569i	0.274582	+	0.274582i	0.830942	−	0.556359i	$-0.187802\pi$
$577$	6.59569	+	6.59569i	0.274582	+	0.274582i	−0.556359	+	0.830942i	$0.687802\pi$
$578$	−7.65330	−	7.65330i	−0.318335	−	0.318335i
$579$		−	7.13657i		−	0.296586i
$580$	−0.900333	−	0.643141i	−0.0373843	−	0.0267050i
$581$	5.21334			0.216286
$582$	2.81665	−	2.81665i	0.116754	−	0.116754i
$583$	16.9861	+	16.9861i	0.703494	+	0.703494i
$584$	4.68331			0.193797
$585$	0.276253	+	1.65786i	0.0114217	+	0.0685442i
$586$	27.3491			1.12978
$587$	−23.8623	−	23.8623i	−0.984904	−	0.984904i	0.0149835	−	0.999888i	$-0.495230\pi$
$587$	−23.8623	−	23.8623i	−0.984904	−	0.984904i	−0.999888	+	0.0149835i	$0.995230\pi$
$588$	−4.19903	−	4.19903i	−0.173165	−	0.173165i
$589$	28.0218	−	25.0517i	1.15462	−	1.03224i
$590$	−4.45843	−	26.7561i	−0.183551	−	1.10153i
$591$		−	10.8358i		−	0.445727i
$592$	5.47836	−	5.47836i	0.225159	−	0.225159i
$593$	22.7988	−	22.7988i	0.936236	−	0.936236i	−0.0618495	−	0.998085i	$-0.519700\pi$
$593$	22.7988	−	22.7988i	0.936236	−	0.936236i	0.998085	+	0.0618495i	$0.0196999\pi$
$594$			4.80832i			0.197288i
$595$	−9.88915	−	7.06418i	−0.405416	−	0.289603i
$596$	15.8801			0.650473
$597$	−14.7999	+	14.7999i	−0.605719	+	0.605719i
$598$	−3.06650	+	3.06650i	−0.125398	+	0.125398i
$599$	−11.4248			−0.466805			−0.233402	−	0.972380i	$-0.574986\pi$
$599$	−11.4248			−0.466805			−0.233402	+	0.972380i	$0.574986\pi$
$600$	4.72984	−	1.62130i	0.193095	−	0.0661894i
$601$		−	7.14156i		−	0.291310i	−0.989335	−	0.145655i	$-0.953471\pi$
$601$		−	7.14156i		−	0.291310i	0.989335	−	0.145655i	$-0.0465290\pi$
$602$	−3.13317	+	3.13317i	−0.127698	+	0.127698i
$603$	−9.19128	−	9.19128i	−0.374298	−	0.374298i
$604$	13.3507			0.543231
$605$	−15.7529	+	22.0524i	−0.640445	+	0.896559i
$606$	14.0592			0.571115
$607$	6.44190	−	6.44190i	0.261469	−	0.261469i	−0.564182	−	0.825651i	$-0.690808\pi$
$607$	6.44190	−	6.44190i	0.261469	−	0.261469i	0.825651	+	0.564182i	$0.190808\pi$
$608$	4.35209	+	0.243552i	0.176501	+	0.00987733i
$609$			0.509852i			0.0206602i
$610$	1.95681	+	11.7433i	0.0792290	+	0.475473i
$611$		−	0.967793i		−	0.0391527i
$612$	−3.72984	−	3.72984i	−0.150770	−	0.150770i
$613$	−21.1379	+	21.1379i	−0.853752	+	0.853752i	−0.990593	−	0.136841i	$-0.956305\pi$
$613$	−21.1379	+	21.1379i	−0.853752	+	0.853752i	0.136841	+	0.990593i	$0.456305\pi$
$614$		−	0.00500438i		−	0.000201960i
$615$	−2.14107	−	12.8491i	−0.0863363	−	0.518126i
$616$			4.95439i			0.199618i
$617$	−9.52678	−	9.52678i	−0.383534	−	0.383534i	0.488840	−	0.872373i	$-0.337420\pi$
$617$	−9.52678	−	9.52678i	−0.383534	−	0.383534i	−0.872373	+	0.488840i	$0.837420\pi$
$618$	−6.63327	−	6.63327i	−0.266829	−	0.266829i
$619$		−	6.57762i		−	0.264377i	−0.991225	−	0.132188i	$-0.957800\pi$
$619$		−	6.57762i		−	0.264377i	0.991225	−	0.132188i	$-0.0422004\pi$
$620$	11.2079	−	15.6899i	0.450120	−	0.630123i
$621$		−	5.76961i		−	0.231526i
$622$	8.26782	−	8.26782i	0.331509	−	0.331509i
$623$	0.791463	+	0.791463i	0.0317093	+	0.0317093i
$624$			0.751642i			0.0300898i
$625$	−19.7428	+	15.3370i	−0.789710	+	0.613480i
$626$		−	23.5732i		−	0.942174i
$627$	1.17107	−	20.9262i	0.0467682	−	0.835713i
$628$	11.7372	−	11.7372i	0.468363	−	0.468363i
$629$	40.8668			1.62947
$630$	−1.87480	−	1.33924i	−0.0746936	−	0.0533564i
$631$	−17.0875			−0.680241			−0.340121	−	0.940382i	$-0.610468\pi$
$631$	−17.0875			−0.680241			−0.340121	+	0.940382i	$0.610468\pi$
$632$	−1.95921	−	1.95921i	−0.0779332	−	0.0779332i
$633$	19.5436	−	19.5436i	0.776787	−	0.776787i
$634$			9.85335i			0.391327i
$635$	−4.86401	−	29.1901i	−0.193022	−	1.15837i
$636$	−4.99593			−0.198102
$637$	−3.15616	+	3.15616i	−0.125052	+	0.125052i
$638$	−1.68238	+	1.68238i	−0.0666062	+	0.0666062i
$639$	−2.06076			−0.0815224
$640$	2.20566	−	0.367533i	0.0871862	−	0.0145280i
$641$			46.7376i			1.84602i	0.384773	+	0.923011i	$0.374280\pi$
$641$			46.7376i			1.84602i	−0.384773	+	0.923011i	$0.625720\pi$
$642$	1.54262	−	1.54262i	0.0608825	−	0.0608825i
$643$	−7.16897	+	7.16897i	−0.282717	+	0.282717i	−0.834191	−	0.551475i	$-0.814065\pi$
$643$	−7.16897	+	7.16897i	−0.282717	+	0.282717i	0.551475	+	0.834191i	$0.314065\pi$
$644$		−	5.94489i		−	0.234261i
$645$	5.58935	−	7.82453i	0.220080	−	0.308091i
$646$	15.3242	+	17.1410i	0.602922	+	0.674404i
$647$	−6.19558	−	6.19558i	−0.243574	−	0.243574i	0.574753	−	0.818327i	$-0.305098\pi$
$647$	−6.19558	−	6.19558i	−0.243574	−	0.243574i	−0.818327	+	0.574753i	$0.805098\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−58.3282			−2.28958
$650$	−1.21864	−	3.55515i	−0.0477989	−	0.139444i
$651$	−8.88509			−0.348234
$652$	0.988668	+	0.988668i	0.0387192	+	0.0387192i
$653$	17.2336	−	17.2336i	0.674401	−	0.674401i	−0.284326	−	0.958728i	$-0.591770\pi$
$653$	17.2336	−	17.2336i	0.674401	−	0.674401i	0.958728	+	0.284326i	$0.0917699\pi$
$654$	−18.4286			−0.720614
$655$	−16.4116	+	22.9746i	−0.641253	+	0.897690i
$656$		−	5.82553i		−	0.227449i
$657$	3.31160	+	3.31160i	0.129198	+	0.129198i
$658$	0.938110	+	0.938110i	0.0365713	+	0.0365713i
$659$	−21.6005			−0.841436			−0.420718	−	0.907191i	$-0.638222\pi$
$659$	−21.6005			−0.841436			−0.420718	+	0.907191i	$0.638222\pi$
$660$	−1.76721	−	10.6055i	−0.0687887	−	0.412818i
$661$		−	1.49297i		−	0.0580696i	−0.999578	−	0.0290348i	$-0.990757\pi$
$661$		−	1.49297i		−	0.0580696i	0.999578	−	0.0290348i	$-0.00924337\pi$
$662$	−8.65367	−	8.65367i	−0.336335	−	0.336335i
$663$	−2.80350	+	2.80350i	−0.108879	+	0.108879i
$664$	−5.05963			−0.196352
$665$	7.83310	+	6.28508i	0.303755	+	0.243725i
$666$	7.74758			0.300212
$667$	2.01873	−	2.01873i	0.0781655	−	0.0781655i
$668$	7.42584	+	7.42584i	0.287314	+	0.287314i
$669$			11.3784i			0.439913i
$670$	23.6509	+	16.8947i	0.913714	+	0.652700i
$671$	25.6004			0.988291
$672$	−0.728588	−	0.728588i	−0.0281059	−	0.0281059i
$673$	−8.49705	−	8.49705i	−0.327537	−	0.327537i	0.524112	−	0.851649i	$-0.324397\pi$
$673$	−8.49705	−	8.49705i	−0.327537	−	0.327537i	−0.851649	+	0.524112i	$0.824397\pi$
$674$			26.8584i			1.03455i
$675$	4.49094	+	2.19807i	0.172856	+	0.0846037i
$676$	−12.4350			−0.478271
$677$	−5.92660	+	5.92660i	−0.227778	+	0.227778i	−0.811764	−	0.583986i	$-0.801492\pi$
$677$	−5.92660	+	5.92660i	−0.227778	+	0.227778i	0.583986	+	0.811764i	$0.301492\pi$
$678$	−5.25913	−	5.25913i	−0.201976	−	0.201976i
$679$	4.10436			0.157511
$680$	9.59758	+	6.85591i	0.368050	+	0.262912i
$681$	2.80480			0.107480
$682$	−29.3186	−	29.3186i	−1.12267	−	1.12267i
$683$	26.3647	+	26.3647i	1.00882	+	1.00882i	0.999961	+	0.00885484i	$0.00281862\pi$
$683$	26.3647	+	26.3647i	1.00882	+	1.00882i	0.00885484	+	0.999961i	$0.497181\pi$
$684$	2.90517	+	3.24961i	0.111082	+	0.124252i
$685$	−1.18126	+	0.196836i	−0.0451337	+	0.00752071i
$686$		−	13.3314i		−	0.508994i
$687$	13.8906	−	13.8906i	0.529960	−	0.529960i
$688$	3.04079	−	3.04079i	0.115929	−	0.115929i
$689$			3.75515i			0.143060i
$690$	2.12052	+	12.7258i	0.0807268	+	0.484462i
$691$	19.3186			0.734913			0.367456	−	0.930041i	$-0.380229\pi$
$691$	19.3186			0.734913			0.367456	+	0.930041i	$0.380229\pi$
$692$	−11.0462	+	11.0462i	−0.419912	+	0.419912i
$693$	−3.50328	+	3.50328i	−0.133079	+	0.133079i
$694$	−2.14291			−0.0813438
$695$	−41.4744	−	29.6267i	−1.57322	−	1.12381i
$696$		−	0.494819i		−	0.0187561i
$697$	21.7283	−	21.7283i	0.823017	−	0.823017i
$698$	−15.0710	−	15.0710i	−0.570444	−	0.570444i
$699$	−6.70326			−0.253541
$700$	4.62737	+	2.26484i	0.174898	+	0.0856031i
$701$	8.82340			0.333255			0.166628	−	0.986020i	$-0.446712\pi$
$701$	8.82340			0.333255			0.166628	+	0.986020i	$0.446712\pi$
$702$	−0.531491	+	0.531491i	−0.0200598	+	0.0200598i
$703$	−33.7181	−	1.88694i	−1.27170	−	0.0711672i
$704$		−	4.80832i		−	0.181220i
$705$	−2.34276	−	1.67352i	−0.0882335	−	0.0630284i
$706$			13.2577i			0.498961i
$707$	10.2434	+	10.2434i	0.385241	+	0.385241i
$708$	8.57770	−	8.57770i	0.322370	−	0.322370i
$709$			1.20583i			0.0452859i	0.999744	+	0.0226429i	$0.00720808\pi$
$709$			1.20583i			0.0452859i	−0.999744	+	0.0226429i	$0.992792\pi$
$710$	4.54533	−	0.757396i	0.170583	−	0.0284246i
$711$		−	2.77074i		−	0.103911i
$712$	−0.768128	−	0.768128i	−0.0287868	−	0.0287868i
$713$	35.1800	+	35.1800i	1.31750	+	1.31750i
$714$		−	5.43503i		−	0.203401i
$715$	−7.97154	+	1.32831i	−0.298119	+	0.0496761i
$716$		−	19.0425i		−	0.711652i
$717$	14.9801	−	14.9801i	0.559443	−	0.559443i
$718$	21.2987	+	21.2987i	0.794861	+	0.794861i
$719$			9.38938i			0.350165i	0.984554	+	0.175082i	$0.0560192\pi$
$719$			9.38938i			0.350165i	−0.984554	+	0.175082i	$0.943981\pi$
$720$	1.81952	+	1.29975i	0.0678095	+	0.0484388i
$721$		−	9.66585i		−	0.359975i
$722$	−11.8521	−	14.8502i	−0.441091	−	0.552665i
$723$	11.5106	−	11.5106i	0.428084	−	0.428084i
$724$	−1.78110			−0.0661941
$725$	0.802251	+	2.34042i	0.0297949	+	0.0869209i
$726$	−12.1199			−0.449812
$727$	−17.4688	−	17.4688i	−0.647884	−	0.647884i	0.304597	−	0.952481i	$-0.401478\pi$
$727$	−17.4688	−	17.4688i	−0.647884	−	0.647884i	−0.952481	+	0.304597i	$0.901478\pi$
$728$	−0.547637	+	0.547637i	−0.0202968	+	0.0202968i
$729$		−	1.00000i		−	0.0370370i
$730$	−8.52138	−	6.08713i	−0.315390	−	0.225295i
$731$	22.6833			0.838973
$732$	−3.76477	+	3.76477i	−0.139150	+	0.139150i
$733$	13.1840	−	13.1840i	0.486963	−	0.486963i	−0.420383	−	0.907347i	$-0.638104\pi$
$733$	13.1840	−	13.1840i	0.486963	−	0.486963i	0.907347	+	0.420383i	$0.138104\pi$
$734$	14.2815			0.527140
$735$	2.18253	+	13.0979i	0.0805037	+	0.483123i
$736$			5.76961i			0.212671i
$737$	44.1946	−	44.1946i	1.62793	−	1.62793i
$738$	4.11927	−	4.11927i	0.151632	−	0.151632i
$739$		−	47.8710i		−	1.76096i	−0.474080	−	0.880482i	$-0.657219\pi$
$739$		−	47.8710i		−	1.76096i	0.474080	−	0.880482i	$-0.342781\pi$
$740$	−17.0885	+	2.84749i	−0.628185	+	0.104676i
$741$	2.44254	−	2.18365i	0.0897290	−	0.0802184i
$742$	−3.63998	−	3.63998i	−0.133628	−	0.133628i
$743$	19.4260	+	19.4260i	0.712670	+	0.712670i	0.967093	−	0.254423i	$-0.0818855\pi$
$743$	19.4260	+	19.4260i	0.712670	+	0.712670i	−0.254423	+	0.967093i	$0.581886\pi$
$744$	8.62312			0.316139
$745$	−28.8941	−	20.6401i	−1.05860	−	0.756196i
$746$	−16.3708			−0.599377
$747$	−3.57770	−	3.57770i	−0.130901	−	0.130901i
$748$	17.9343	−	17.9343i	0.655741	−	0.655741i
$749$	2.24788			0.0821356
$750$	−10.7133	−	3.19762i	−0.391195	−	0.116760i
$751$		−	23.5009i		−	0.857559i	−0.903409	−	0.428779i	$-0.858944\pi$
$751$		−	23.5009i		−	0.857559i	0.903409	−	0.428779i	$-0.141056\pi$
$752$	−0.910451	−	0.910451i	−0.0332007	−	0.0332007i
$753$	3.71225	+	3.71225i	0.135282	+	0.135282i
$754$	−0.371927			−0.0135448
$755$	−24.2918	−	17.3525i	−0.884069	−	0.631523i
$756$		−	1.03038i		−	0.0374745i
$757$	19.2062	+	19.2062i	0.698060	+	0.698060i	0.963992	−	0.265932i	$-0.0856796\pi$
$757$	19.2062	+	19.2062i	0.698060	+	0.698060i	−0.265932	+	0.963992i	$0.585680\pi$
$758$	−21.7007	+	21.7007i	−0.788206	+	0.788206i
$759$	27.7421			1.00697
$760$	−7.60215	−	6.09977i	−0.275759	−	0.221262i
$761$	−23.7982			−0.862685			−0.431343	−	0.902188i	$-0.641960\pi$
$761$	−23.7982			−0.862685			−0.431343	+	0.902188i	$0.641960\pi$
$762$	9.35800	−	9.35800i	0.339005	−	0.339005i
$763$	−13.4268	−	13.4268i	−0.486084	−	0.486084i
$764$			14.8650i			0.537797i
$765$	1.93866	+	11.6344i	0.0700923	+	0.420642i
$766$	9.49265			0.342983
$767$	−6.44736	−	6.44736i	−0.232801	−	0.232801i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$			28.9884i			1.04535i	0.852532	+	0.522675i	$0.175066\pi$
$769$			28.9884i			1.04535i	−0.852532	+	0.522675i	$0.824934\pi$
$770$	6.43947	−	9.01461i	0.232062	−	0.324864i
$771$	22.6727			0.816537
$772$	−5.04632	+	5.04632i	−0.181621	+	0.181621i
$773$	29.2365	+	29.2365i	1.05156	+	1.05156i	0.998596	+	0.0529667i	$0.0168677\pi$
$773$	29.2365	+	29.2365i	1.05156	+	1.05156i	0.0529667	+	0.998596i	$0.483132\pi$
$774$	4.30033			0.154572
$775$	−40.7860	+	13.9807i	−1.46508	+	0.502201i
$776$	−3.98335			−0.142994
$777$	5.64479	+	5.64479i	0.202506	+	0.202506i
$778$	−1.19924	−	1.19924i	−0.0429947	−	0.0429947i
$779$	−18.9307	+	16.9242i	−0.678262	+	0.606371i
$780$	0.976946	−	1.36763i	0.0349803	−	0.0489689i
$781$		−	9.90878i		−	0.354564i
$782$	−21.5197	+	21.5197i	−0.769543	+	0.769543i
$783$	0.349890	−	0.349890i	0.0125041	−	0.0125041i
$784$			5.93832i			0.212083i
$785$	−36.6113	+	6.10062i	−1.30671	+	0.217740i
$786$	−12.6267			−0.450380
$787$	12.6866	−	12.6866i	0.452228	−	0.452228i	−0.443866	−	0.896093i	$-0.646393\pi$
$787$	12.6866	−	12.6866i	0.452228	−	0.452228i	0.896093	+	0.443866i	$0.146393\pi$
$788$	−7.66209	+	7.66209i	−0.272951	+	0.272951i
$789$	−8.41456			−0.299566
$790$	1.01834	+	6.11130i	0.0362308	+	0.217430i
$791$		−	7.66348i		−	0.272482i
$792$	3.39999	−	3.39999i	0.120814	−	0.120814i
$793$	2.82976	+	2.82976i	0.100488	+	0.100488i
$794$	24.9391			0.885057
$795$	9.09020	+	6.49346i	0.322396	+	0.230299i
$796$	20.9302			0.741851
$797$	15.7202	−	15.7202i	0.556838	−	0.556838i	−0.371568	−	0.928406i	$-0.621180\pi$
$797$	15.7202	−	15.7202i	0.556838	−	0.556838i	0.928406	+	0.371568i	$0.121180\pi$
$798$	−0.250951	+	4.48430i	−0.00888356	+	0.158743i
$799$		−	6.79167i		−	0.240272i
$800$	−4.49094	−	2.19807i	−0.158779	−	0.0777134i
$801$		−	1.08630i		−	0.0383824i
$802$	0.920271	+	0.920271i	0.0324959	+	0.0324959i
$803$	−15.9232	+	15.9232i	−0.561919	+	0.561919i
$804$			12.9984i			0.458420i
$805$	−7.72686	+	10.8168i	−0.272336	+	0.381243i
$806$		−	6.48150i		−	0.228301i
$807$	−18.5884	−	18.5884i	−0.654344	−	0.654344i
$808$	−9.94134	−	9.94134i	−0.349735	−	0.349735i
$809$			11.4400i			0.402210i	0.979570	+	0.201105i	$0.0644533\pi$
$809$			11.4400i			0.402210i	−0.979570	+	0.201105i	$0.935547\pi$
$810$	0.367533	+	2.20566i	0.0129138	+	0.0774989i
$811$		−	17.5878i		−	0.617592i	−0.951128	−	0.308796i	$-0.900074\pi$
$811$		−	17.5878i		−	0.617592i	0.951128	−	0.308796i	$-0.0999260\pi$
$812$	0.360520	−	0.360520i	0.0126518	−	0.0126518i
$813$	−8.43702	−	8.43702i	−0.295899	−	0.295899i
$814$			37.2528i			1.30571i
$815$	−0.513880	−	3.08392i	−0.0180004	−	0.108025i
$816$			5.27479i			0.184655i
$817$	−18.7154	−	1.04735i	−0.654769	−	0.0366422i
$818$	−13.3418	+	13.3418i	−0.466485	+	0.466485i
$819$	−0.774476			−0.0270624
$820$	−7.57173	+	10.5997i	−0.264416	+	0.370156i
$821$	13.1354			0.458428			0.229214	−	0.973376i	$-0.426384\pi$
$821$	13.1354			0.458428			0.229214	+	0.973376i	$0.426384\pi$
$822$	−0.378698	−	0.378698i	−0.0132086	−	0.0132086i
$823$	−23.2779	+	23.2779i	−0.811417	+	0.811417i	−0.984846	−	0.173429i	$-0.944515\pi$
$823$	−23.2779	+	23.2779i	−0.811417	+	0.811417i	0.173429	+	0.984846i	$0.444515\pi$
$824$			9.38086i			0.326798i
$825$	−10.5690	+	21.5938i	−0.367966	+	0.751801i
$826$	12.4992			0.434903
$827$	33.6240	−	33.6240i	1.16922	−	1.16922i	0.186828	−	0.982393i	$-0.440179\pi$
$827$	33.6240	−	33.6240i	1.16922	−	1.16922i	0.982393	−	0.186828i	$-0.0598208\pi$
$828$	−4.07973	+	4.07973i	−0.141780	+	0.141780i
$829$	−22.3434			−0.776020			−0.388010	−	0.921655i	$-0.626837\pi$
$829$	−22.3434			−0.776020			−0.388010	+	0.921655i	$0.626837\pi$
$830$	9.20609	+	6.57625i	0.319548	+	0.228265i
$831$		−	18.6596i		−	0.647294i
$832$	0.531491	−	0.531491i	0.0184261	−	0.0184261i
$833$	−22.1490	+	22.1490i	−0.767416	+	0.767416i
$834$		−	22.7942i		−	0.789298i
$835$	−3.85973	−	23.1632i	−0.133571	−	0.801595i
$836$	−15.6252	+	13.9690i	−0.540407	+	0.483128i
$837$	6.09747	+	6.09747i	0.210759	+	0.210759i
$838$	−14.2530	−	14.2530i	−0.492363	−	0.492363i
$839$	−31.3884			−1.08365			−0.541824	−	0.840492i	$-0.682266\pi$
$839$	−31.3884			−1.08365			−0.541824	+	0.840492i	$0.682266\pi$
$840$	0.378698	+	2.27266i	0.0130663	+	0.0784143i
$841$	−28.7552			−0.991557
$842$	−6.25992	−	6.25992i	−0.215731	−	0.215731i
$843$	18.0180	−	18.0180i	0.620575	−	0.620575i
$844$	−27.6388			−0.951366
$845$	22.6258	+	16.1624i	0.778351	+	0.556005i
$846$		−	1.28757i		−	0.0442676i
$847$	−8.83043	−	8.83043i	−0.303417	−	0.303417i
$848$	3.53266	+	3.53266i	0.121312	+	0.121312i
$849$	−21.1355			−0.725369
$850$	−8.55203	−	24.9489i	−0.293332	−	0.855740i
$851$		−	44.7005i		−	1.53231i
$852$	1.45718	+	1.45718i	0.0499220	+	0.0499220i
$853$	−16.0193	+	16.0193i	−0.548490	+	0.548490i	−0.926004	−	0.377514i	$-0.876779\pi$
$853$	−16.0193	+	16.0193i	−0.548490	+	0.548490i	0.377514	+	0.926004i	$0.376779\pi$
$854$	−5.48593			−0.187725
$855$	−1.06234	−	9.68873i	−0.0363314	−	0.331347i
$856$	−2.18160			−0.0745656
$857$	−14.3582	+	14.3582i	−0.490467	+	0.490467i	−0.908453	−	0.417986i	$-0.862736\pi$
$857$	−14.3582	+	14.3582i	−0.490467	+	0.490467i	0.417986	+	0.908453i	$0.362736\pi$
$858$	−2.55558	−	2.55558i	−0.0872460	−	0.0872460i
$859$			23.5232i			0.802602i	0.915946	+	0.401301i	$0.131442\pi$
$859$			23.5232i			0.802602i	−0.915946	+	0.401301i	$0.868558\pi$
$860$	−9.48504	+	1.58051i	−0.323437	+	0.0538950i
$861$	6.00250			0.204565
$862$	−17.8931	−	17.8931i	−0.609443	−	0.609443i
$863$	34.2060	+	34.2060i	1.16439	+	1.16439i	0.983505	+	0.180881i	$0.0578950\pi$
$863$	34.2060	+	34.2060i	1.16439	+	1.16439i	0.180881	+	0.983505i	$0.442105\pi$
$864$			1.00000i			0.0340207i
$865$	34.4560	−	5.74146i	1.17154	−	0.195216i
$866$	−8.49320			−0.288611
$867$	−7.65330	+	7.65330i	−0.259920	+	0.259920i
$868$	6.28270	+	6.28270i	0.213249	+	0.213249i
$869$	13.3226			0.451938
$870$	−0.643141	+	0.900333i	−0.0218045	+	0.0305242i
$871$	9.77017			0.331050
$872$	13.0310	+	13.0310i	0.441284	+	0.441284i
$873$	−2.81665	−	2.81665i	−0.0953293	−	0.0953293i
$874$	18.7490	−	16.7617i	0.634193	−	0.566974i
$875$	−5.47585	−	10.1353i	−0.185118	−	0.342637i
$876$		−	4.68331i		−	0.158234i
$877$	34.2759	−	34.2759i	1.15742	−	1.15742i	0.172387	−	0.985029i	$-0.444852\pi$
$877$	34.2759	−	34.2759i	1.15742	−	1.15742i	0.985029	−	0.172387i	$-0.0551479\pi$
$878$	27.1713	−	27.1713i	0.916986	−	0.916986i
$879$		−	27.3491i		−	0.922463i
$880$	−6.24961	+	8.74883i	−0.210674	+	0.294923i
$881$	−16.2818			−0.548548			−0.274274	−	0.961652i	$-0.588438\pi$
$881$	−16.2818			−0.548548			−0.274274	+	0.961652i	$0.588438\pi$
$882$	−4.19903	+	4.19903i	−0.141389	+	0.141389i
$883$	−16.4556	+	16.4556i	−0.553774	+	0.553774i	−0.927528	−	0.373754i	$-0.878070\pi$
$883$	−16.4556	+	16.4556i	−0.553774	+	0.553774i	0.373754	+	0.927528i	$0.378070\pi$
$884$	3.96475			0.133349
$885$	−26.7561	+	4.45843i	−0.899398	+	0.149868i
$886$			39.2383i			1.31824i
$887$	−20.1627	+	20.1627i	−0.676997	+	0.676997i	−0.959320	−	0.282322i	$-0.908895\pi$
$887$	−20.1627	+	20.1627i	−0.676997	+	0.676997i	0.282322	+	0.959320i	$0.408895\pi$
$888$	−5.47836	−	5.47836i	−0.183842	−	0.183842i
$889$	13.6363			0.457345
$890$	0.399250	+	2.39600i	0.0133829	+	0.0803140i
$891$	4.80832			0.161085
$892$	8.04571	−	8.04571i	0.269390	−	0.269390i
$893$	−0.313590	+	5.60363i	−0.0104939	+	0.187518i
$894$		−	15.8801i		−	0.531109i
$895$	−24.7505	+	34.6482i	−0.827318	+	1.15816i
$896$			1.03038i			0.0344226i
$897$	3.06650	+	3.06650i	0.102387	+	0.102387i
$898$	−19.9120	+	19.9120i	−0.664472	+	0.664472i
$899$			4.26689i			0.142309i
$900$	−1.62130	−	4.72984i	−0.0540434	−	0.157661i
$901$			26.3525i			0.877929i
$902$	19.8068	+	19.8068i	0.659493	+	0.659493i
$903$	3.13317	+	3.13317i	0.104265	+	0.104265i
$904$			7.43754i			0.247369i
$905$	3.24075	+	2.31499i	0.107726	+	0.0769527i
$906$		−	13.3507i		−	0.443546i
$907$	−36.3346	+	36.3346i	−1.20647	+	1.20647i	−0.234309	+	0.972162i	$0.575283\pi$
$907$	−36.3346	+	36.3346i	−1.20647	+	1.20647i	−0.972162	+	0.234309i	$0.924717\pi$
$908$	−1.98330	−	1.98330i	−0.0658180	−	0.0658180i
$909$		−	14.0592i		−	0.466313i
$910$	1.70823	−	0.284645i	0.0566272	−	0.00943590i
$911$		−	9.50181i		−	0.314809i	−0.987534	−	0.157405i	$-0.949687\pi$
$911$		−	9.50181i		−	0.314809i	0.987534	−	0.157405i	$-0.0503127\pi$
$912$	0.243552	−	4.35209i	0.00806481	−	0.144112i
$913$	17.2027	−	17.2027i	0.569326	−	0.569326i
$914$	27.6584			0.914859
$915$	11.7433	−	1.95681i	0.388222	−	0.0646902i
$916$	−19.6443			−0.649066
$917$	−9.19968	−	9.19968i	−0.303800	−	0.303800i
$918$	−3.72984	+	3.72984i	−0.123103	+	0.123103i
$919$			3.20583i			0.105751i	0.998601	+	0.0528753i	$0.0168386\pi$
$919$			3.20583i			0.105751i	−0.998601	+	0.0528753i	$0.983161\pi$
$920$	7.49905	−	10.4979i	0.247236	−	0.346106i
$921$	−0.00500438			−0.000164900
$922$	−6.79932	+	6.79932i	−0.223924	+	0.223924i
$923$	1.09527	−	1.09527i	0.0360514	−	0.0360514i
$924$	4.95439			0.162988
$925$	34.7939	+	17.0297i	1.14402	+	0.559933i
$926$			23.5799i			0.774882i
$927$	−6.63327	+	6.63327i	−0.217865	+	0.217865i
$928$	−0.349890	+	0.349890i	−0.0114857	+	0.0114857i
$929$		−	0.680198i		−	0.0223166i	−0.999938	−	0.0111583i	$-0.996448\pi$
$929$		−	0.680198i		−	0.0223166i	0.999938	−	0.0111583i	$-0.00355187\pi$
$930$	−15.6899	−	11.2079i	−0.514493	−	0.367521i
$931$	19.2972	−	17.2519i	0.632441	−	0.565407i
$932$	4.73992	+	4.73992i	0.155261	+	0.155261i
$933$	−8.26782	−	8.26782i	−0.270676	−	0.270676i
$934$	24.2099			0.792171
$935$	−55.9418	+	9.32168i	−1.82949	+	0.304852i
$936$	0.751642			0.0245682
$937$	20.6037	+	20.6037i	0.673093	+	0.673093i	0.958428	−	0.285335i	$-0.0921048\pi$
$937$	20.6037	+	20.6037i	0.673093	+	0.673093i	−0.285335	+	0.958428i	$0.592105\pi$
$938$	−9.47051	+	9.47051i	−0.309223	+	0.309223i
$939$	−23.5732			−0.769282
$940$	0.473225	+	2.83994i	0.0154349	+	0.0926286i
$941$			16.5409i			0.539220i	0.962970	+	0.269610i	$0.0868947\pi$
$941$			16.5409i			0.539220i	−0.962970	+	0.269610i	$0.913105\pi$
$942$	−11.7372	−	11.7372i	−0.382417	−	0.382417i
$943$	−23.7666	−	23.7666i	−0.773946	−	0.773946i
$944$	−12.1307			−0.394820
$945$	−1.33924	+	1.87480i	−0.0435653	+	0.0609871i
$946$			20.6773i			0.672278i
$947$	21.1699	+	21.1699i	0.687929	+	0.687929i	0.961774	−	0.273845i	$-0.0882956\pi$
$947$	21.1699	+	21.1699i	0.687929	+	0.687929i	−0.273845	+	0.961774i	$0.588296\pi$
$948$	−1.95921	+	1.95921i	−0.0636322	+	0.0636322i
$949$	−3.52017			−0.114270
$950$	5.90409	+	20.9796i	0.191554	+	0.680667i
$951$	9.85335			0.319517
$952$	−3.84315	+	3.84315i	−0.124557	+	0.124557i
$953$	−28.1289	−	28.1289i	−0.911186	−	0.911186i	0.0851800	−	0.996366i	$-0.472853\pi$
$953$	−28.1289	−	28.1289i	−0.911186	−	0.911186i	−0.996366	+	0.0851800i	$0.972853\pi$
$954$			4.99593i			0.161749i
$955$	19.3208	−	27.0471i	0.625205	−	0.875225i
$956$	−21.1851			−0.685176
$957$	1.68238	+	1.68238i	0.0543837	+	0.0543837i
$958$	−10.0976	−	10.0976i	−0.326237	−	0.326237i
$959$		−	0.551830i		−	0.0178195i
$960$	−0.367533	−	2.20566i	−0.0118621	−	0.0711873i
$961$	−43.3582			−1.39865
$962$	−4.11777	+	4.11777i	−0.132762	+	0.132762i
$963$	−1.54262	−	1.54262i	−0.0497104	−	0.0497104i
$964$	−16.2784			−0.524293
$965$	15.7408	−	2.62292i	0.506715	−	0.0844349i
$966$	−5.94489			−0.191274
$967$	−2.96462	−	2.96462i	−0.0953359	−	0.0953359i	0.657830	−	0.753166i	$-0.271474\pi$
$967$	−2.96462	−	2.96462i	−0.0953359	−	0.0953359i	−0.753166	+	0.657830i	$0.771474\pi$
$968$	8.57008	+	8.57008i	0.275453	+	0.275453i
$969$	17.1410	−	15.3242i	0.550648	−	0.492284i
$970$	7.24778	+	5.17736i	0.232712	+	0.166235i
$971$		−	4.90480i		−	0.157403i	−0.996898	−	0.0787013i	$-0.974923\pi$
$971$		−	4.90480i		−	0.157403i	0.996898	−	0.0787013i	$-0.0250773\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	16.6076	−	16.6076i	0.532414	−	0.532414i
$974$		−	19.3451i		−	0.619856i
$975$	−3.55515	+	1.21864i	−0.113856	+	0.0390277i
$976$	5.32419			0.170423
$977$	11.6920	−	11.6920i	0.374061	−	0.374061i	−0.494893	−	0.868954i	$-0.664793\pi$
$977$	11.6920	−	11.6920i	0.374061	−	0.374061i	0.868954	+	0.494893i	$0.164793\pi$
$978$	0.988668	−	0.988668i	0.0316141	−	0.0316141i
$979$	5.22326			0.166936
$980$	7.71833	−	10.8049i	0.246553	−	0.345149i
$981$			18.4286i			0.588379i
$982$	−4.67154	+	4.67154i	−0.149075	+	0.149075i
$983$	24.4836	+	24.4836i	0.780907	+	0.780907i	0.979984	−	0.199077i	$-0.0637945\pi$
$983$	24.4836	+	24.4836i	0.780907	+	0.780907i	−0.199077	+	0.979984i	$0.563794\pi$
$984$	−5.82553			−0.185711
$985$	23.9001	−	3.98252i	0.761521	−	0.126894i
$986$	−2.61007			−0.0831215
$987$	0.938110	−	0.938110i	0.0298604	−	0.0298604i
$988$	−3.27121	−	0.183064i	−0.104071	−	0.00582404i
$989$		−	24.8112i		−	0.788950i
$990$	−10.6055	+	1.76721i	−0.337065	+	0.0561658i
$991$		−	56.2681i		−	1.78741i	−0.448650	−	0.893707i	$-0.648095\pi$
$991$		−	56.2681i		−	1.78741i	0.448650	−	0.893707i	$-0.351905\pi$
$992$	−6.09747	−	6.09747i	−0.193595	−	0.193595i
$993$	−8.65367	+	8.65367i	−0.274616	+	0.274616i
$994$			2.12336i			0.0673490i
$995$	−38.0829	−	27.2040i	−1.20731	−	0.862425i
$996$			5.05963i			0.160320i
$997$	−2.01280	−	2.01280i	−0.0637459	−	0.0637459i	0.674515	−	0.738261i	$-0.264353\pi$
$997$	−2.01280	−	2.01280i	−0.0637459	−	0.0637459i	−0.738261	+	0.674515i	$0.764353\pi$
$998$	−25.2627	−	25.2627i	−0.799677	−	0.799677i
$999$		−	7.74758i		−	0.245122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.b.37.1	✓	20
3.2	odd	2		1710.2.p.c.37.10		20
5.3	odd	4	inner	570.2.m.b.493.6	yes	20
15.8	even	4		1710.2.p.c.1063.5		20
19.18	odd	2	inner	570.2.m.b.37.6	yes	20
57.56	even	2		1710.2.p.c.37.5		20
95.18	even	4	inner	570.2.m.b.493.1	yes	20
285.113	odd	4		1710.2.p.c.1063.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.1	✓	20	1.1	even	1	trivial
570.2.m.b.37.6	yes	20	19.18	odd	2	inner
570.2.m.b.493.1	yes	20	95.18	even	4	inner
570.2.m.b.493.6	yes	20	5.3	odd	4	inner
1710.2.p.c.37.5		20	57.56	even	2
1710.2.p.c.37.10		20	3.2	odd	2
1710.2.p.c.1063.5		20	15.8	even	4
1710.2.p.c.1063.10		20	285.113	odd	4

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.367533 - 2.20566i) q^{10} -4.80832 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.531491 - 0.531491i) q^{13} +1.03038 q^{14} +(-2.20566 + 0.367533i) q^{15} -1.00000 q^{16} +(-3.72984 - 3.72984i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.90517 + 3.24961i) q^{19} +(1.81952 + 1.29975i) q^{20} -1.03038i q^{21} +(3.39999 - 3.39999i) q^{22} +(-4.07973 + 4.07973i) q^{23} +1.00000i q^{24} +(-1.62130 - 4.72984i) q^{25} +0.751642 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.728588 + 0.728588i) q^{28} -0.494819 q^{29} +(1.29975 - 1.81952i) q^{30} -8.62312i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.39999 - 3.39999i) q^{33} +5.27479 q^{34} +(2.27266 - 0.378698i) q^{35} +1.00000 q^{36} +(-5.47836 + 5.47836i) q^{37} +(-4.35209 - 0.243552i) q^{38} -0.751642i q^{39} +(-2.20566 + 0.367533i) q^{40} +5.82553i q^{41} +(0.728588 + 0.728588i) q^{42} +(-3.04079 + 3.04079i) q^{43} +4.80832i q^{44} +(-1.81952 - 1.29975i) q^{45} -5.76961i q^{46} +(0.910451 + 0.910451i) q^{47} +(-0.707107 - 0.707107i) q^{48} -5.93832i q^{49} +(4.49094 + 2.19807i) q^{50} -5.27479i q^{51} +(-0.531491 + 0.531491i) q^{52} +(-3.53266 - 3.53266i) q^{53} -1.00000i q^{54} +(6.24961 - 8.74883i) q^{55} -1.03038i q^{56} +(-0.243552 + 4.35209i) q^{57} +(0.349890 - 0.349890i) q^{58} +12.1307 q^{59} +(0.367533 + 2.20566i) q^{60} -5.32419 q^{61} +(6.09747 + 6.09747i) q^{62} +(0.728588 - 0.728588i) q^{63} +1.00000i q^{64} +(1.65786 - 0.276253i) q^{65} +4.80832 q^{66} +(-9.19128 + 9.19128i) q^{67} +(-3.72984 + 3.72984i) q^{68} -5.76961 q^{69} +(-1.33924 + 1.87480i) q^{70} +2.06076i q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.31160 - 3.31160i) q^{73} -7.74758i q^{74} +(2.19807 - 4.49094i) q^{75} +(3.24961 - 2.90517i) q^{76} +(3.50328 + 3.50328i) q^{77} +(0.531491 + 0.531491i) q^{78} -2.77074 q^{79} +(1.29975 - 1.81952i) q^{80} -1.00000 q^{81} +(-4.11927 - 4.11927i) q^{82} +(-3.57770 + 3.57770i) q^{83} -1.03038 q^{84} +(11.6344 - 1.93866i) q^{85} -4.30033i q^{86} +(-0.349890 - 0.349890i) q^{87} +(-3.39999 - 3.39999i) q^{88} -1.08630 q^{89} +(2.20566 - 0.367533i) q^{90} +0.774476i q^{91} +(4.07973 + 4.07973i) q^{92} +(6.09747 - 6.09747i) q^{93} -1.28757 q^{94} +(-9.68873 + 1.06234i) q^{95} +1.00000 q^{96} +(-2.81665 + 2.81665i) q^{97} +(4.19903 + 4.19903i) q^{98} -4.80832i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Introduction

L-functions

Modular forms

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