LMFDB - Embedded newform 930.2.k.b.247.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.9
Character	$\chi$	$=$	930.247
Dual form			930.2.k.b.433.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.96413 - 1.06873i) q^{5} +1.00000i q^{6} +(-1.95397 - 1.95397i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.96413 - 1.06873i) q^{5} +1.00000i q^{6} +(-1.95397 - 1.95397i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.633142 - 2.14456i) q^{10} -0.865384i q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.63683 - 3.63683i) q^{13} -2.76332i q^{14} +(-0.633142 - 2.14456i) q^{15} -1.00000 q^{16} +(2.10331 - 2.10331i) q^{17} +(-0.707107 + 0.707107i) q^{18} +0.565832i q^{19} +(1.06873 - 1.96413i) q^{20} -2.76332i q^{21} +(0.611919 - 0.611919i) q^{22} +(-6.50377 - 6.50377i) q^{23} -1.00000 q^{24} +(2.71562 + 4.19826i) q^{25} -5.14326i q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.95397 - 1.95397i) q^{28} +0.232261 q^{29} +(1.06873 - 1.96413i) q^{30} +(5.55877 - 0.316406i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.611919 - 0.611919i) q^{33} +2.97453 q^{34} +(1.74958 + 5.92611i) q^{35} -1.00000 q^{36} +(2.57063 - 2.57063i) q^{37} +(-0.400104 + 0.400104i) q^{38} -5.14326i q^{39} +(2.14456 - 0.633142i) q^{40} -11.3710 q^{41} +(1.95397 - 1.95397i) q^{42} +(-4.95147 - 4.95147i) q^{43} +0.865384 q^{44} +(1.06873 - 1.96413i) q^{45} -9.19772i q^{46} +(4.14227 + 4.14227i) q^{47} +(-0.707107 - 0.707107i) q^{48} +0.635959i q^{49} +(-1.04839 + 4.88885i) q^{50} +2.97453 q^{51} +(3.63683 - 3.63683i) q^{52} +(-0.513226 - 0.513226i) q^{53} -1.00000 q^{54} +(-0.924865 + 1.69973i) q^{55} +2.76332 q^{56} +(-0.400104 + 0.400104i) q^{57} +(0.164233 + 0.164233i) q^{58} +4.60876i q^{59} +(2.14456 - 0.633142i) q^{60} +2.89347i q^{61} +(4.15437 + 3.70691i) q^{62} +(1.95397 - 1.95397i) q^{63} -1.00000i q^{64} +(3.25641 + 11.0300i) q^{65} +0.865384 q^{66} +(-1.09903 - 1.09903i) q^{67} +(2.10331 + 2.10331i) q^{68} -9.19772i q^{69} +(-2.95326 + 5.42753i) q^{70} -9.81816 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-0.542153 - 0.542153i) q^{73} +3.63541 q^{74} +(-1.04839 + 4.88885i) q^{75} -0.565832 q^{76} +(-1.69093 + 1.69093i) q^{77} +(3.63683 - 3.63683i) q^{78} +9.17904 q^{79} +(1.96413 + 1.06873i) q^{80} -1.00000 q^{81} +(-8.04052 - 8.04052i) q^{82} +(-0.433367 - 0.433367i) q^{83} +2.76332 q^{84} +(-6.37906 + 1.88330i) q^{85} -7.00244i q^{86} +(0.164233 + 0.164233i) q^{87} +(0.611919 + 0.611919i) q^{88} -3.35210 q^{89} +(2.14456 - 0.633142i) q^{90} +14.2125i q^{91} +(6.50377 - 6.50377i) q^{92} +(4.15437 + 3.70691i) q^{93} +5.85805i q^{94} +(0.604723 - 1.11137i) q^{95} -1.00000i q^{96} +(6.46801 + 6.46801i) q^{97} +(-0.449691 + 0.449691i) q^{98} +0.865384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} + 4 q^{15} - 32 q^{16} + 8 q^{17} - 4 q^{22} - 32 q^{24} + 8 q^{25} + 4 q^{28} + 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} + 4 q^{37} + 16 q^{38} - 16 q^{41} + 4 q^{42} - 16 q^{43} - 8 q^{44} - 8 q^{47} - 16 q^{50} - 24 q^{53} - 32 q^{54} - 28 q^{55} + 16 q^{57} + 20 q^{58} - 8 q^{62} + 4 q^{63} + 56 q^{65} - 8 q^{66} + 32 q^{67} + 8 q^{68} - 28 q^{70} + 16 q^{71} - 20 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 40 q^{77} - 56 q^{79} - 32 q^{81} + 16 q^{82} + 72 q^{83} - 32 q^{85} + 20 q^{87} - 4 q^{88} - 64 q^{89} - 8 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 + 4 * q^15 - 32 * q^16 + 8 * q^17 - 4 * q^22 - 32 * q^24 + 8 * q^25 + 4 * q^28 + 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 + 4 * q^37 + 16 * q^38 - 16 * q^41 + 4 * q^42 - 16 * q^43 - 8 * q^44 - 8 * q^47 - 16 * q^50 - 24 * q^53 - 32 * q^54 - 28 * q^55 + 16 * q^57 + 20 * q^58 - 8 * q^62 + 4 * q^63 + 56 * q^65 - 8 * q^66 + 32 * q^67 + 8 * q^68 - 28 * q^70 + 16 * q^71 - 20 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 40 * q^77 - 56 * q^79 - 32 * q^81 + 16 * q^82 + 72 * q^83 - 32 * q^85 + 20 * q^87 - 4 * q^88 - 64 * q^89 - 8 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	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
$5$	−1.96413	−	1.06873i	−0.878386	−	0.477952i
$5$	−1.96413	−	1.06873i	−0.878386	−	0.477952i
$6$			1.00000i			0.408248i
$7$	−1.95397	−	1.95397i	−0.738529	−	0.738529i	0.233764	−	0.972293i	$-0.424896\pi$
$7$	−1.95397	−	1.95397i	−0.738529	−	0.738529i	−0.972293	+	0.233764i	$0.924896\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−0.633142	−	2.14456i	−0.200217	−	0.678169i
$11$		−	0.865384i		−	0.260923i	−0.991453	−	0.130462i	$-0.958354\pi$
$11$		−	0.865384i		−	0.260923i	0.991453	−	0.130462i	$-0.0416459\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−3.63683	−	3.63683i	−1.00868	−	1.00868i	−0.999962	−	0.00871385i	$-0.997226\pi$
$13$	−3.63683	−	3.63683i	−1.00868	−	1.00868i	−0.00871385	−	0.999962i	$-0.502774\pi$
$14$		−	2.76332i		−	0.738529i
$15$	−0.633142	−	2.14456i	−0.163477	−	0.553723i
$16$	−1.00000			−0.250000
$17$	2.10331	−	2.10331i	0.510128	−	0.510128i	−0.404438	−	0.914566i	$-0.632533\pi$
$17$	2.10331	−	2.10331i	0.510128	−	0.510128i	0.914566	+	0.404438i	$0.132533\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$			0.565832i			0.129811i	0.997891	+	0.0649054i	$0.0206746\pi$
$19$			0.565832i			0.129811i	−0.997891	+	0.0649054i	$0.979325\pi$
$20$	1.06873	−	1.96413i	0.238976	−	0.439193i
$21$		−	2.76332i		−	0.603007i
$22$	0.611919	−	0.611919i	0.130462	−	0.130462i
$23$	−6.50377	−	6.50377i	−1.35613	−	1.35613i	−0.878634	−	0.477496i	$-0.841544\pi$
$23$	−6.50377	−	6.50377i	−1.35613	−	1.35613i	−0.477496	−	0.878634i	$-0.658456\pi$
$24$	−1.00000			−0.204124
$25$	2.71562	+	4.19826i	0.543124	+	0.839653i
$26$		−	5.14326i		−	1.00868i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.95397	−	1.95397i	0.369265	−	0.369265i
$29$	0.232261			0.0431298			0.0215649	−	0.999767i	$-0.493135\pi$
$29$	0.232261			0.0431298			0.0215649	+	0.999767i	$0.493135\pi$
$30$	1.06873	−	1.96413i	0.195123	−	0.358600i
$31$	5.55877	−	0.316406i	0.998384	−	0.0568282i
$31$	5.55877	−	0.316406i	0.998384	−	0.0568282i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.611919	−	0.611919i	0.106521	−	0.106521i
$34$	2.97453			0.510128
$35$	1.74958	+	5.92611i	0.295732	+	1.00170i
$36$	−1.00000			−0.166667
$37$	2.57063	−	2.57063i	0.422608	−	0.422608i	−0.463492	−	0.886101i	$-0.653404\pi$
$37$	2.57063	−	2.57063i	0.422608	−	0.422608i	0.886101	+	0.463492i	$0.153404\pi$
$38$	−0.400104	+	0.400104i	−0.0649054	+	0.0649054i
$39$		−	5.14326i		−	0.823580i
$40$	2.14456	−	0.633142i	0.339084	−	0.100109i
$41$	−11.3710			−1.77585			−0.887927	−	0.459985i	$-0.847855\pi$
$41$	−11.3710			−1.77585			−0.887927	+	0.459985i	$0.847855\pi$
$42$	1.95397	−	1.95397i	0.301503	−	0.301503i
$43$	−4.95147	−	4.95147i	−0.755092	−	0.755092i	0.220332	−	0.975425i	$-0.429286\pi$
$43$	−4.95147	−	4.95147i	−0.755092	−	0.755092i	−0.975425	+	0.220332i	$0.929286\pi$
$44$	0.865384			0.130462
$45$	1.06873	−	1.96413i	0.159317	−	0.292795i
$46$		−	9.19772i		−	1.35613i
$47$	4.14227	+	4.14227i	0.604212	+	0.604212i	0.941428	−	0.337215i	$-0.109485\pi$
$47$	4.14227	+	4.14227i	0.604212	+	0.604212i	−0.337215	+	0.941428i	$0.609485\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			0.635959i			0.0908512i
$50$	−1.04839	+	4.88885i	−0.148264	+	0.691388i
$51$	2.97453			0.416518
$52$	3.63683	−	3.63683i	0.504338	−	0.504338i
$53$	−0.513226	−	0.513226i	−0.0704970	−	0.0704970i	0.670979	−	0.741476i	$-0.265874\pi$
$53$	−0.513226	−	0.513226i	−0.0704970	−	0.0704970i	−0.741476	+	0.670979i	$0.765874\pi$
$54$	−1.00000			−0.136083
$55$	−0.924865	+	1.69973i	−0.124709	+	0.229191i
$56$	2.76332			0.369265
$57$	−0.400104	+	0.400104i	−0.0529950	+	0.0529950i
$58$	0.164233	+	0.164233i	0.0215649	+	0.0215649i
$59$			4.60876i			0.600009i	0.953938	+	0.300005i	$0.0969883\pi$
$59$			4.60876i			0.600009i	−0.953938	+	0.300005i	$0.903012\pi$
$60$	2.14456	−	0.633142i	0.276861	−	0.0817383i
$61$			2.89347i			0.370471i	0.982694	+	0.185236i	$0.0593048\pi$
$61$			2.89347i			0.370471i	−0.982694	+	0.185236i	$0.940695\pi$
$62$	4.15437	+	3.70691i	0.527606	+	0.470778i
$63$	1.95397	−	1.95397i	0.246176	−	0.246176i
$64$		−	1.00000i		−	0.125000i
$65$	3.25641	+	11.0300i	0.403908	+	1.36811i
$66$	0.865384			0.106521
$67$	−1.09903	−	1.09903i	−0.134268	−	0.134268i	0.636779	−	0.771047i	$-0.280267\pi$
$67$	−1.09903	−	1.09903i	−0.134268	−	0.134268i	−0.771047	+	0.636779i	$0.780267\pi$
$68$	2.10331	+	2.10331i	0.255064	+	0.255064i
$69$		−	9.19772i		−	1.10728i
$70$	−2.95326	+	5.42753i	−0.352982	+	0.648714i
$71$	−9.81816			−1.16520			−0.582601	−	0.812758i	$-0.697965\pi$
$71$	−9.81816			−1.16520			−0.582601	+	0.812758i	$0.697965\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−0.542153	−	0.542153i	−0.0634542	−	0.0634542i	0.674668	−	0.738122i	$-0.264287\pi$
$73$	−0.542153	−	0.542153i	−0.0634542	−	0.0634542i	−0.738122	+	0.674668i	$0.764287\pi$
$74$	3.63541			0.422608
$75$	−1.04839	+	4.88885i	−0.121057	+	0.564516i
$76$	−0.565832			−0.0649054
$77$	−1.69093	+	1.69093i	−0.192699	+	0.192699i
$78$	3.63683	−	3.63683i	0.411790	−	0.411790i
$79$	9.17904			1.03272			0.516361	−	0.856371i	$-0.327286\pi$
$79$	9.17904			1.03272			0.516361	+	0.856371i	$0.327286\pi$
$80$	1.96413	+	1.06873i	0.219596	+	0.119488i
$81$	−1.00000			−0.111111
$82$	−8.04052	−	8.04052i	−0.887927	−	0.887927i
$83$	−0.433367	−	0.433367i	−0.0475682	−	0.0475682i	0.682923	−	0.730491i	$-0.260709\pi$
$83$	−0.433367	−	0.433367i	−0.0475682	−	0.0475682i	−0.730491	+	0.682923i	$0.760709\pi$
$84$	2.76332			0.301503
$85$	−6.37906	+	1.88330i	−0.691906	+	0.204273i
$86$		−	7.00244i		−	0.755092i
$87$	0.164233	+	0.164233i	0.0176077	+	0.0176077i
$88$	0.611919	+	0.611919i	0.0652308	+	0.0652308i
$89$	−3.35210			−0.355322			−0.177661	−	0.984092i	$-0.556853\pi$
$89$	−3.35210			−0.355322			−0.177661	+	0.984092i	$0.556853\pi$
$90$	2.14456	−	0.633142i	0.226056	−	0.0667390i
$91$			14.2125i			1.48987i
$92$	6.50377	−	6.50377i	0.678065	−	0.678065i
$93$	4.15437	+	3.70691i	0.430789	+	0.384389i
$94$			5.85805i			0.604212i
$95$	0.604723	−	1.11137i	0.0620433	−	0.114024i
$96$		−	1.00000i		−	0.102062i
$97$	6.46801	+	6.46801i	0.656727	+	0.656727i	0.954604	−	0.297877i	$-0.0962785\pi$
$97$	6.46801	+	6.46801i	0.656727	+	0.656727i	−0.297877	+	0.954604i	$0.596278\pi$
$98$	−0.449691	+	0.449691i	−0.0454256	+	0.0454256i
$99$	0.865384			0.0869744
$100$	−4.19826	+	2.71562i	−0.419826	+	0.271562i
$101$	−3.84714			−0.382804			−0.191402	−	0.981512i	$-0.561303\pi$
$101$	−3.84714			−0.382804			−0.191402	+	0.981512i	$0.561303\pi$
$102$	2.10331	+	2.10331i	0.208259	+	0.208259i
$103$	8.28550	−	8.28550i	0.816395	−	0.816395i	−0.169189	−	0.985584i	$-0.554115\pi$
$103$	8.28550	−	8.28550i	0.816395	−	0.816395i	0.985584	+	0.169189i	$0.0541148\pi$
$104$	5.14326			0.504338
$105$	−2.95326	+	5.42753i	−0.288208	+	0.529673i
$106$		−	0.725811i		−	0.0704970i
$107$	5.16276	+	5.16276i	0.499103	+	0.499103i	0.911159	−	0.412056i	$-0.135189\pi$
$107$	5.16276	+	5.16276i	0.499103	+	0.499103i	−0.412056	+	0.911159i	$0.635189\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			4.48999i			0.430063i	0.976607	+	0.215031i	$0.0689854\pi$
$109$			4.48999i			0.430063i	−0.976607	+	0.215031i	$0.931015\pi$
$110$	−1.85587	+	0.547911i	−0.176950	+	0.0522413i
$111$	3.63541			0.345058
$112$	1.95397	+	1.95397i	0.184632	+	0.184632i
$113$	−11.0258	+	11.0258i	−1.03722	+	1.03722i	−0.0379406	+	0.999280i	$0.512080\pi$
$113$	−11.0258	+	11.0258i	−1.03722	+	1.03722i	−0.999280	+	0.0379406i	$0.987920\pi$
$114$	−0.565832			−0.0529950
$115$	5.82346	+	19.7251i	0.543041	+	1.83937i
$116$			0.232261i			0.0215649i
$117$	3.63683	−	3.63683i	0.336225	−	0.336225i
$118$	−3.25889	+	3.25889i	−0.300005	+	0.300005i
$119$	−8.21959			−0.753489
$120$	1.96413	+	1.06873i	0.179300	+	0.0975615i
$121$	10.2511			0.931919
$122$	−2.04599	+	2.04599i	−0.185236	+	0.185236i
$123$	−8.04052	−	8.04052i	−0.724989	−	0.724989i
$124$	0.316406	+	5.55877i	0.0284141	+	0.499192i
$125$	−0.847009	−	11.1482i	−0.0757588	−	0.997126i
$126$	2.76332			0.246176
$127$	7.69192	−	7.69192i	0.682547	−	0.682547i	−0.278026	−	0.960574i	$-0.589680\pi$
$127$	7.69192	−	7.69192i	0.682547	−	0.682547i	0.960574	+	0.278026i	$0.0896802\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		−	7.00244i		−	0.616530i
$130$	−5.49677	+	10.1020i	−0.482099	+	0.886007i
$131$	−12.8922			−1.12640			−0.563199	−	0.826321i	$-0.690430\pi$
$131$	−12.8922			−1.12640			−0.563199	+	0.826321i	$0.690430\pi$
$132$	0.611919	+	0.611919i	0.0532607	+	0.0532607i
$133$	1.10562	−	1.10562i	0.0958690	−	0.0958690i
$134$		−	1.55426i		−	0.134268i
$135$	2.14456	−	0.633142i	0.184574	−	0.0544922i
$136$			2.97453i			0.255064i
$137$	2.75114	−	2.75114i	0.235046	−	0.235046i	−0.579749	−	0.814795i	$-0.696849\pi$
$137$	2.75114	−	2.75114i	0.235046	−	0.235046i	0.814795	+	0.579749i	$0.196849\pi$
$138$	6.50377	−	6.50377i	0.553638	−	0.553638i
$139$	−18.0454			−1.53059			−0.765295	−	0.643680i	$-0.777407\pi$
$139$	−18.0454			−1.53059			−0.765295	+	0.643680i	$0.777407\pi$
$140$	−5.92611	+	1.74958i	−0.500848	+	0.147866i
$141$			5.85805i			0.493337i
$142$	−6.94249	−	6.94249i	−0.582601	−	0.582601i
$143$	−3.14726	+	3.14726i	−0.263187	+	0.263187i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.456191	−	0.248225i	−0.0378846	−	0.0206140i
$146$		−	0.766720i		−	0.0634542i
$147$	−0.449691	+	0.449691i	−0.0370899	+	0.0370899i
$148$	2.57063	+	2.57063i	0.211304	+	0.211304i
$149$		−	12.2319i		−	1.00208i	−0.865425	−	0.501038i	$-0.832952\pi$
$149$		−	12.2319i		−	1.00208i	0.865425	−	0.501038i	$-0.167048\pi$
$150$	−4.19826	+	2.71562i	−0.342787	+	0.221729i
$151$		−	23.6478i		−	1.92443i	−0.272288	−	0.962216i	$-0.587780\pi$
$151$		−	23.6478i		−	1.92443i	0.272288	−	0.962216i	$-0.412220\pi$
$152$	−0.400104	−	0.400104i	−0.0324527	−	0.0324527i
$153$	2.10331	+	2.10331i	0.170043	+	0.170043i
$154$	−2.39134			−0.192699
$155$	−11.2563	−	5.31937i	−0.904128	−	0.427262i
$156$	5.14326			0.411790
$157$	−1.49742	−	1.49742i	−0.119507	−	0.119507i	0.644824	−	0.764331i	$-0.276931\pi$
$157$	−1.49742	−	1.49742i	−0.119507	−	0.119507i	−0.764331	+	0.644824i	$0.776931\pi$
$158$	6.49056	+	6.49056i	0.516361	+	0.516361i
$159$		−	0.725811i		−	0.0575606i
$160$	0.633142	+	2.14456i	0.0500543	+	0.169542i
$161$			25.4163i			2.00308i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	5.47538	−	5.47538i	0.428865	−	0.428865i	−0.459377	−	0.888242i	$-0.651927\pi$
$163$	5.47538	−	5.47538i	0.428865	−	0.428865i	0.888242	+	0.459377i	$0.151927\pi$
$164$		−	11.3710i		−	0.887927i
$165$	−1.85587	+	0.547911i	−0.144479	+	0.0426548i
$166$		−	0.612873i		−	0.0475682i
$167$	2.73932	−	2.73932i	0.211975	−	0.211975i	−0.593131	−	0.805106i	$-0.702108\pi$
$167$	2.73932	−	2.73932i	0.211975	−	0.211975i	0.805106	+	0.593131i	$0.202108\pi$
$168$	1.95397	+	1.95397i	0.150752	+	0.150752i
$169$			13.4531i			1.03485i
$170$	−5.84237	−	3.17898i	−0.448089	−	0.243817i
$171$	−0.565832			−0.0432702
$172$	4.95147	−	4.95147i	0.377546	−	0.377546i
$173$	−4.69909	+	4.69909i	−0.357265	+	0.357265i	−0.862804	−	0.505539i	$-0.831294\pi$
$173$	−4.69909	+	4.69909i	−0.357265	+	0.357265i	0.505539	+	0.862804i	$0.331294\pi$
$174$			0.232261i			0.0176077i
$175$	2.89703	−	13.5095i	0.218995	−	1.02122i
$176$			0.865384i			0.0652308i
$177$	−3.25889	+	3.25889i	−0.244953	+	0.244953i
$178$	−2.37030	−	2.37030i	−0.177661	−	0.177661i
$179$	−9.22382			−0.689421			−0.344710	−	0.938709i	$-0.612023\pi$
$179$	−9.22382			−0.689421			−0.344710	+	0.938709i	$0.612023\pi$
$180$	1.96413	+	1.06873i	0.146398	+	0.0796587i
$181$			18.1679i			1.35041i	0.737629	+	0.675206i	$0.235945\pi$
$181$			18.1679i			1.35041i	−0.737629	+	0.675206i	$0.764055\pi$
$182$	−10.0497	+	10.0497i	−0.744937	+	0.744937i
$183$	−2.04599	+	2.04599i	−0.151244	+	0.151244i
$184$	9.19772			0.678065
$185$	−7.79636	+	2.30173i	−0.573200	+	0.169227i
$186$	0.316406	+	5.55877i	0.0232000	+	0.407589i
$187$	−1.82017	−	1.82017i	−0.133104	−	0.133104i
$188$	−4.14227	+	4.14227i	−0.302106	+	0.302106i
$189$	2.76332			0.201002
$190$	1.21346	−	0.358252i	0.0880336	−	0.0259903i
$191$	2.29216			0.165855			0.0829275	−	0.996556i	$-0.473573\pi$
$191$	2.29216			0.165855			0.0829275	+	0.996556i	$0.473573\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	5.16906	−	5.16906i	0.372077	−	0.372077i	−0.496156	−	0.868233i	$-0.665256\pi$
$193$	5.16906	−	5.16906i	0.372077	−	0.372077i	0.868233	+	0.496156i	$0.165256\pi$
$194$			9.14715i			0.656727i
$195$	−5.49677	+	10.1020i	−0.393632	+	0.723421i
$196$	−0.635959			−0.0454256
$197$	15.6594	−	15.6594i	1.11569	−	1.11569i	0.123321	−	0.992367i	$-0.460645\pi$
$197$	15.6594	−	15.6594i	1.11569	−	1.11569i	0.992367	−	0.123321i	$-0.0393546\pi$
$198$	0.611919	+	0.611919i	0.0434872	+	0.0434872i
$199$	−13.9435			−0.988432			−0.494216	−	0.869339i	$-0.664545\pi$
$199$	−13.9435			−0.988432			−0.494216	+	0.869339i	$0.664545\pi$
$200$	−4.88885	−	1.04839i	−0.345694	−	0.0741322i
$201$		−	1.55426i		−	0.109629i
$202$	−2.72034	−	2.72034i	−0.191402	−	0.191402i
$203$	−0.453830	−	0.453830i	−0.0318526	−	0.0318526i
$204$			2.97453i			0.208259i
$205$	22.3341	+	12.1526i	1.55988	+	0.848772i
$206$	11.7175			0.816395
$207$	6.50377	−	6.50377i	0.452043	−	0.452043i
$208$	3.63683	+	3.63683i	0.252169	+	0.252169i
$209$	0.489662			0.0338706
$210$	−5.92611	+	1.74958i	−0.408940	+	0.120732i
$211$	9.69550			0.667466			0.333733	−	0.942668i	$-0.391692\pi$
$211$	9.69550			0.667466			0.333733	+	0.942668i	$0.391692\pi$
$212$	0.513226	−	0.513226i	0.0352485	−	0.0352485i
$213$	−6.94249	−	6.94249i	−0.475692	−	0.475692i
$214$			7.30124i			0.499103i
$215$	4.43354	+	15.0171i	0.302365	+	1.02416i
$216$		−	1.00000i		−	0.0680414i
$217$	−11.4799	−	10.2434i	−0.779305	−	0.695367i
$218$	−3.17490	+	3.17490i	−0.215031	+	0.215031i
$219$		−	0.766720i		−	0.0518102i
$220$	−1.69973	−	0.924865i	−0.114596	−	0.0623544i
$221$	−15.2988			−1.02911
$222$	2.57063	+	2.57063i	0.172529	+	0.172529i
$223$	0.509124	+	0.509124i	0.0340934	+	0.0340934i	0.723948	−	0.689855i	$-0.242326\pi$
$223$	0.509124	+	0.509124i	0.0340934	+	0.0340934i	−0.689855	+	0.723948i	$0.742326\pi$
$224$			2.76332i			0.184632i
$225$	−4.19826	+	2.71562i	−0.279884	+	0.181041i
$226$	−15.5928			−1.03722
$227$	9.01025	+	9.01025i	0.598031	+	0.598031i	0.939788	−	0.341757i	$-0.111022\pi$
$227$	9.01025	+	9.01025i	0.598031	+	0.598031i	−0.341757	+	0.939788i	$0.611022\pi$
$228$	−0.400104	−	0.400104i	−0.0264975	−	0.0264975i
$229$	24.6303			1.62762			0.813808	−	0.581133i	$-0.197391\pi$
$229$	24.6303			1.62762			0.813808	+	0.581133i	$0.197391\pi$
$230$	−9.82991	+	18.0655i	−0.648165	+	1.19121i
$231$	−2.39134			−0.157338
$232$	−0.164233	+	0.164233i	−0.0107824	+	0.0107824i
$233$	4.90717	−	4.90717i	0.321479	−	0.321479i	−0.527855	−	0.849334i	$-0.677004\pi$
$233$	4.90717	−	4.90717i	0.321479	−	0.321479i	0.849334	+	0.527855i	$0.177004\pi$
$234$	5.14326			0.336225
$235$	−3.70898	−	12.5629i	−0.241947	−	0.819516i
$236$	−4.60876			−0.300005
$237$	6.49056	+	6.49056i	0.421607	+	0.421607i
$238$	−5.81213	−	5.81213i	−0.376744	−	0.376744i
$239$	24.3120			1.57261			0.786305	−	0.617838i	$-0.211991\pi$
$239$	24.3120			1.57261			0.786305	+	0.617838i	$0.211991\pi$
$240$	0.633142	+	2.14456i	0.0408691	+	0.138431i
$241$			24.3869i			1.57090i	0.618926	+	0.785449i	$0.287568\pi$
$241$			24.3869i			1.57090i	−0.618926	+	0.785449i	$0.712432\pi$
$242$	7.24863	+	7.24863i	0.465960	+	0.465960i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−2.89347			−0.185236
$245$	0.679670	−	1.24911i	0.0434225	−	0.0798024i
$246$		−	11.3710i		−	0.724989i
$247$	2.05784	−	2.05784i	0.130937	−	0.130937i
$248$	−3.70691	+	4.15437i	−0.235389	+	0.263803i
$249$		−	0.612873i		−	0.0388393i
$250$	7.28405	−	8.48190i	0.460684	−	0.536442i
$251$			13.3413i			0.842093i	0.907039	+	0.421047i	$0.138337\pi$
$251$			13.3413i			0.842093i	−0.907039	+	0.421047i	$0.861663\pi$
$252$	1.95397	+	1.95397i	0.123088	+	0.123088i
$253$	−5.62826	+	5.62826i	−0.353846	+	0.353846i
$254$	10.8780			0.682547
$255$	−5.84237	−	3.17898i	−0.365863	−	0.199075i
$256$	1.00000			0.0625000
$257$	−19.8661	−	19.8661i	−1.23921	−	1.23921i	−0.960323	−	0.278889i	$-0.910034\pi$
$257$	−19.8661	−	19.8661i	−1.23921	−	1.23921i	−0.278889	−	0.960323i	$-0.589966\pi$
$258$	4.95147	−	4.95147i	0.308265	−	0.308265i
$259$	−10.0458			−0.624217
$260$	−11.0300	+	3.25641i	−0.684053	+	0.201954i
$261$			0.232261i			0.0143766i
$262$	−9.11618	−	9.11618i	−0.563199	−	0.563199i
$263$	−21.6463	−	21.6463i	−1.33477	−	1.33477i	−0.901049	−	0.433718i	$-0.857201\pi$
$263$	−21.6463	−	21.6463i	−1.33477	−	1.33477i	−0.433718	−	0.901049i	$-0.642799\pi$
$264$			0.865384i			0.0532607i
$265$	0.459541	+	1.55654i	0.0282294	+	0.0956178i
$266$	1.56358			0.0958690
$267$	−2.37030	−	2.37030i	−0.145060	−	0.145060i
$268$	1.09903	−	1.09903i	0.0671340	−	0.0671340i
$269$	−5.89906			−0.359672			−0.179836	−	0.983697i	$-0.557557\pi$
$269$	−5.89906			−0.359672			−0.179836	+	0.983697i	$0.557557\pi$
$270$	1.96413	+	1.06873i	0.119533	+	0.0650410i
$271$		−	12.1796i		−	0.739860i	−0.929060	−	0.369930i	$-0.879382\pi$
$271$		−	12.1796i		−	0.739860i	0.929060	−	0.369930i	$-0.120618\pi$
$272$	−2.10331	+	2.10331i	−0.127532	+	0.127532i
$273$	−10.0497	+	10.0497i	−0.608238	+	0.608238i
$274$	3.89070			0.235046
$275$	3.63311	−	2.35005i	0.219085	−	0.141714i
$276$	9.19772			0.553638
$277$	−19.0870	+	19.0870i	−1.14683	+	1.14683i	−0.159654	+	0.987173i	$0.551038\pi$
$277$	−19.0870	+	19.0870i	−1.14683	+	1.14683i	−0.987173	+	0.159654i	$0.948962\pi$
$278$	−12.7600	−	12.7600i	−0.765295	−	0.765295i
$279$	0.316406	+	5.55877i	0.0189427	+	0.332795i
$280$	−5.42753	−	2.95326i	−0.324357	−	0.176491i
$281$	19.1984			1.14528			0.572640	−	0.819807i	$-0.305919\pi$
$281$	19.1984			1.14528			0.572640	+	0.819807i	$0.305919\pi$
$282$	−4.14227	+	4.14227i	−0.246669	+	0.246669i
$283$	21.3401	−	21.3401i	1.26854	−	1.26854i	0.321693	−	0.946844i	$-0.395748\pi$
$283$	21.3401	−	21.3401i	1.26854	−	1.26854i	0.946844	−	0.321693i	$-0.104252\pi$
$284$		−	9.81816i		−	0.582601i
$285$	1.21346	−	0.358252i	0.0718791	−	0.0212210i
$286$	−4.45089			−0.263187
$287$	22.2186	+	22.2186i	1.31152	+	1.31152i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			8.15216i			0.479539i
$290$	−0.147054	−	0.498097i	−0.00863531	−	0.0292493i
$291$			9.14715i			0.536216i
$292$	0.542153	−	0.542153i	0.0317271	−	0.0317271i
$293$	−13.0475	+	13.0475i	−0.762242	+	0.762242i	−0.976727	−	0.214486i	$-0.931193\pi$
$293$	−13.0475	+	13.0475i	−0.762242	+	0.762242i	0.214486	+	0.976727i	$0.431193\pi$
$294$	−0.635959			−0.0370899
$295$	4.92553	−	9.05221i	0.286776	−	0.527040i
$296$			3.63541i			0.211304i
$297$	0.611919	+	0.611919i	0.0355071	+	0.0355071i
$298$	8.64926	−	8.64926i	0.501038	−	0.501038i
$299$			47.3063i			2.73579i
$300$	−4.88885	−	1.04839i	−0.282258	−	0.0605287i
$301$			19.3500i			1.11532i
$302$	16.7215	−	16.7215i	0.962216	−	0.962216i
$303$	−2.72034	−	2.72034i	−0.156279	−	0.156279i
$304$		−	0.565832i		−	0.0324527i
$305$	3.09235	−	5.68316i	0.177067	−	0.325417i
$306$			2.97453i			0.170043i
$307$	−12.1191	−	12.1191i	−0.691676	−	0.691676i	0.270925	−	0.962601i	$-0.412671\pi$
$307$	−12.1191	−	12.1191i	−0.691676	−	0.691676i	−0.962601	+	0.270925i	$0.912671\pi$
$308$	−1.69093	−	1.69093i	−0.0963497	−	0.0963497i
$309$	11.7175			0.666584
$310$	−4.19804	−	11.7208i	−0.238433	−	0.665695i
$311$	2.96205			0.167963			0.0839813	−	0.996467i	$-0.473236\pi$
$311$	2.96205			0.167963			0.0839813	+	0.996467i	$0.473236\pi$
$312$	3.63683	+	3.63683i	0.205895	+	0.205895i
$313$	8.15492	+	8.15492i	0.460943	+	0.460943i	0.898965	−	0.438021i	$-0.144321\pi$
$313$	8.15492	+	8.15492i	0.460943	+	0.460943i	−0.438021	+	0.898965i	$0.644321\pi$
$314$		−	2.11767i		−	0.119507i
$315$	−5.92611	+	1.74958i	−0.333898	+	0.0985774i
$316$			9.17904i			0.516361i
$317$	14.6933	+	14.6933i	0.825256	+	0.825256i	0.986856	−	0.161601i	$-0.0516657\pi$
$317$	14.6933	+	14.6933i	0.825256	+	0.825256i	−0.161601	+	0.986856i	$0.551666\pi$
$318$	0.513226	−	0.513226i	0.0287803	−	0.0287803i
$319$		−	0.200995i		−	0.0112536i
$320$	−1.06873	+	1.96413i	−0.0597440	+	0.109798i
$321$			7.30124i			0.407516i
$322$	−17.9720	+	17.9720i	−1.00154	+	1.00154i
$323$	1.19012	+	1.19012i	0.0662201	+	0.0662201i
$324$		−	1.00000i		−	0.0555556i
$325$	5.39213	−	25.1446i	0.299101	−	1.39477i
$326$	7.74336			0.428865
$327$	−3.17490	+	3.17490i	−0.175572	+	0.175572i
$328$	8.04052	−	8.04052i	0.443963	−	0.443963i
$329$		−	16.1877i		−	0.892457i
$330$	−1.69973	−	0.924865i	−0.0935669	−	0.0509121i
$331$		−	27.0762i		−	1.48824i	−0.668046	−	0.744120i	$-0.732869\pi$
$331$		−	27.0762i		−	1.48824i	0.668046	−	0.744120i	$-0.267131\pi$
$332$	0.433367	−	0.433367i	0.0237841	−	0.0237841i
$333$	2.57063	+	2.57063i	0.140869	+	0.140869i
$334$	3.87398			0.211975
$335$	0.984070	+	3.33321i	0.0537655	+	0.182113i
$336$			2.76332i			0.150752i
$337$	16.9852	−	16.9852i	0.925244	−	0.925244i	−0.0721495	−	0.997394i	$-0.522986\pi$
$337$	16.9852	−	16.9852i	0.925244	−	0.925244i	0.997394	+	0.0721495i	$0.0229859\pi$
$338$	−9.51278	+	9.51278i	−0.517427	+	0.517427i
$339$	−15.5928			−0.846887
$340$	−1.88330	−	6.37906i	−0.102136	−	0.345953i
$341$	−0.273813	−	4.81047i	−0.0148278	−	0.260501i
$342$	−0.400104	−	0.400104i	−0.0216351	−	0.0216351i
$343$	−12.4351	+	12.4351i	−0.671433	+	0.671433i
$344$	7.00244			0.377546
$345$	−9.82991	+	18.0655i	−0.529225	+	0.972615i
$346$	−6.64551			−0.357265
$347$	−5.05088	+	5.05088i	−0.271145	+	0.271145i	−0.829561	−	0.558416i	$-0.811409\pi$
$347$	−5.05088	+	5.05088i	−0.271145	+	0.271145i	0.558416	+	0.829561i	$0.311409\pi$
$348$	−0.164233	+	0.164233i	−0.00880383	+	0.00880383i
$349$		−	13.0089i		−	0.696353i	−0.937429	−	0.348176i	$-0.886801\pi$
$349$		−	13.0089i		−	0.696353i	0.937429	−	0.348176i	$-0.113199\pi$
$350$	11.6012	−	7.50414i	0.620108	−	0.401113i
$351$	5.14326			0.274527
$352$	−0.611919	+	0.611919i	−0.0326154	+	0.0326154i
$353$	−3.59121	−	3.59121i	−0.191141	−	0.191141i	0.605048	−	0.796189i	$-0.293154\pi$
$353$	−3.59121	−	3.59121i	−0.191141	−	0.191141i	−0.796189	+	0.605048i	$0.793154\pi$
$354$	−4.60876			−0.244953
$355$	19.2842	+	10.4930i	1.02350	+	0.556910i
$356$		−	3.35210i		−	0.177661i
$357$	−5.81213	−	5.81213i	−0.307611	−	0.307611i
$358$	−6.52223	−	6.52223i	−0.344710	−	0.344710i
$359$			6.59790i			0.348224i	0.984726	+	0.174112i	$0.0557054\pi$
$359$			6.59790i			0.348224i	−0.984726	+	0.174112i	$0.944295\pi$
$360$	0.633142	+	2.14456i	0.0333695	+	0.113028i
$361$	18.6798			0.983149
$362$	−12.8467	+	12.8467i	−0.675206	+	0.675206i
$363$	7.24863	+	7.24863i	0.380454	+	0.380454i
$364$	−14.2125			−0.744937
$365$	0.485443	+	1.64428i	0.0254092	+	0.0860654i
$366$	−2.89347			−0.151244
$367$	4.35399	−	4.35399i	0.227276	−	0.227276i	−0.584278	−	0.811554i	$-0.698622\pi$
$367$	4.35399	−	4.35399i	0.227276	−	0.227276i	0.811554	+	0.584278i	$0.198622\pi$
$368$	6.50377	+	6.50377i	0.339033	+	0.339033i
$369$		−	11.3710i		−	0.591951i
$370$	−7.14043	−	3.88529i	−0.371213	−	0.201987i
$371$			2.00565i			0.104128i
$372$	−3.70691	+	4.15437i	−0.192194	+	0.215394i
$373$	−11.2114	+	11.2114i	−0.580507	+	0.580507i	−0.935042	−	0.354536i	$-0.884639\pi$
$373$	−11.2114	+	11.2114i	−0.580507	+	0.580507i	0.354536	+	0.935042i	$0.384639\pi$
$374$		−	2.57411i		−	0.133104i
$375$	7.28405	−	8.48190i	0.376147	−	0.438003i
$376$	−5.85805			−0.302106
$377$	−0.844694	−	0.844694i	−0.0435039	−	0.0435039i
$378$	1.95397	+	1.95397i	0.100501	+	0.100501i
$379$		−	26.7895i		−	1.37609i	−0.725670	−	0.688043i	$-0.758470\pi$
$379$		−	26.7895i		−	1.37609i	0.725670	−	0.688043i	$-0.241530\pi$
$380$	1.11137	+	0.604723i	0.0570120	+	0.0310216i
$381$	10.8780			0.557298
$382$	1.62080	+	1.62080i	0.0829275	+	0.0829275i
$383$	−20.9508	−	20.9508i	−1.07054	−	1.07054i	−0.997316	−	0.0732223i	$-0.976672\pi$
$383$	−20.9508	−	20.9508i	−1.07054	−	1.07054i	−0.0732223	−	0.997316i	$-0.523328\pi$
$384$	1.00000			0.0510310
$385$	5.12836	−	1.51406i	0.261365	−	0.0771634i
$386$	7.31016			0.372077
$387$	4.95147	−	4.95147i	0.251697	−	0.251697i
$388$	−6.46801	+	6.46801i	−0.328364	+	0.328364i
$389$	20.9227			1.06082			0.530411	−	0.847740i	$-0.322038\pi$
$389$	20.9227			1.06082			0.530411	+	0.847740i	$0.322038\pi$
$390$	−11.0300	+	3.25641i	−0.558527	+	0.164895i
$391$	−27.3589			−1.38360
$392$	−0.449691	−	0.449691i	−0.0227128	−	0.0227128i
$393$	−9.11618	−	9.11618i	−0.459850	−	0.459850i
$394$	22.1458			1.11569
$395$	−18.0288	−	9.80994i	−0.907129	−	0.493592i
$396$			0.865384i			0.0434872i
$397$	−0.178340	−	0.178340i	−0.00895061	−	0.00895061i	0.702617	−	0.711568i	$-0.252015\pi$
$397$	−0.178340	−	0.178340i	−0.00895061	−	0.00895061i	−0.711568	+	0.702617i	$0.752015\pi$
$398$	−9.85958	−	9.85958i	−0.494216	−	0.494216i
$399$	1.56358			0.0782767
$400$	−2.71562	−	4.19826i	−0.135781	−	0.209913i
$401$			31.1047i			1.55329i	0.629936	+	0.776647i	$0.283081\pi$
$401$			31.1047i			1.55329i	−0.629936	+	0.776647i	$0.716919\pi$
$402$	1.09903	−	1.09903i	0.0548147	−	0.0548147i
$403$	−21.3670	−	19.0656i	−1.06437	−	0.949725i
$404$		−	3.84714i		−	0.191402i
$405$	1.96413	+	1.06873i	0.0975984	+	0.0531058i
$406$		−	0.641812i		−	0.0318526i
$407$	−2.22458	−	2.22458i	−0.110268	−	0.110268i
$408$	−2.10331	+	2.10331i	−0.104129	+	0.104129i
$409$	32.7175			1.61778			0.808889	−	0.587961i	$-0.200069\pi$
$409$	32.7175			1.61778			0.808889	+	0.587961i	$0.200069\pi$
$410$	7.19946	+	24.3858i	0.355556	+	1.20433i
$411$	3.89070			0.191914
$412$	8.28550	+	8.28550i	0.408197	+	0.408197i
$413$	9.00535	−	9.00535i	0.443125	−	0.443125i
$414$	9.19772			0.452043
$415$	0.388036	+	1.31434i	0.0190479	+	0.0645186i
$416$			5.14326i			0.252169i
$417$	−12.7600	−	12.7600i	−0.624861	−	0.624861i
$418$	0.346243	+	0.346243i	0.0169353	+	0.0169353i
$419$		−	32.8329i		−	1.60399i	−0.597330	−	0.801996i	$-0.703772\pi$
$419$		−	32.8329i		−	1.60399i	0.597330	−	0.801996i	$-0.296228\pi$
$420$	−5.42753	−	2.95326i	−0.264836	−	0.144104i
$421$	5.01129			0.244235			0.122118	−	0.992516i	$-0.461031\pi$
$421$	5.01129			0.244235			0.122118	+	0.992516i	$0.461031\pi$
$422$	6.85575	+	6.85575i	0.333733	+	0.333733i
$423$	−4.14227	+	4.14227i	−0.201404	+	0.201404i
$424$	0.725811			0.0352485
$425$	14.5420	+	3.11846i	0.705393	+	0.151268i
$426$		−	9.81816i		−	0.475692i
$427$	5.65374	−	5.65374i	0.273604	−	0.273604i
$428$	−5.16276	+	5.16276i	−0.249551	+	0.249551i
$429$	−4.45089			−0.214891
$430$	−7.48374	+	13.7537i	−0.360898	+	0.663263i
$431$	−9.98295			−0.480862			−0.240431	−	0.970666i	$-0.577289\pi$
$431$	−9.98295			−0.480862			−0.240431	+	0.970666i	$0.577289\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−1.48979	−	1.48979i	−0.0715947	−	0.0715947i	0.670403	−	0.741997i	$-0.266121\pi$
$433$	−1.48979	−	1.48979i	−0.0715947	−	0.0715947i	−0.741997	+	0.670403i	$0.766121\pi$
$434$	−0.874333	−	15.3607i	−0.0419693	−	0.737336i
$435$	−0.147054	−	0.498097i	−0.00705070	−	0.0238819i
$436$	−4.48999			−0.215031
$437$	3.68004	−	3.68004i	0.176040	−	0.176040i
$438$	0.542153	−	0.542153i	0.0259051	−	0.0259051i
$439$			32.3910i			1.54594i	0.634444	+	0.772969i	$0.281229\pi$
$439$			32.3910i			1.54594i	−0.634444	+	0.772969i	$0.718771\pi$
$440$	−0.547911	−	1.85587i	−0.0261206	−	0.0884750i
$441$	−0.635959			−0.0302837
$442$	−10.8179	−	10.8179i	−0.514554	−	0.514554i
$443$	18.2845	−	18.2845i	0.868725	−	0.868725i	−0.123607	−	0.992331i	$-0.539446\pi$
$443$	18.2845	−	18.2845i	0.868725	−	0.868725i	0.992331	+	0.123607i	$0.0394461\pi$
$444$			3.63541i			0.172529i
$445$	6.58397	+	3.58250i	0.312110	+	0.169827i
$446$			0.720010i			0.0340934i
$447$	8.64926	−	8.64926i	0.409096	−	0.409096i
$448$	−1.95397	+	1.95397i	−0.0923162	+	0.0923162i
$449$	39.1054			1.84550			0.922750	−	0.385400i	$-0.125936\pi$
$449$	39.1054			1.84550			0.922750	+	0.385400i	$0.125936\pi$
$450$	−4.88885	−	1.04839i	−0.230463	−	0.0494215i
$451$			9.84029i			0.463361i
$452$	−11.0258	−	11.0258i	−0.518610	−	0.518610i
$453$	16.7215	−	16.7215i	0.785646	−	0.785646i
$454$			12.7424i			0.598031i
$455$	15.1894	−	27.9152i	0.712088	−	1.30868i
$456$		−	0.565832i		−	0.0264975i
$457$	20.9451	−	20.9451i	0.979771	−	0.979771i	−0.0200279	−	0.999799i	$-0.506376\pi$
$457$	20.9451	−	20.9451i	0.979771	−	0.979771i	0.999799	+	0.0200279i	$0.00637552\pi$
$458$	17.4163	+	17.4163i	0.813808	+	0.813808i
$459$			2.97453i			0.138839i
$460$	−19.7251	+	5.82346i	−0.919685	+	0.271520i
$461$		−	40.2010i		−	1.87235i	−0.351538	−	0.936174i	$-0.614341\pi$
$461$		−	40.2010i		−	1.87235i	0.351538	−	0.936174i	$-0.385659\pi$
$462$	−1.69093	−	1.69093i	−0.0786692	−	0.0786692i
$463$	−8.48915	−	8.48915i	−0.394524	−	0.394524i	0.481772	−	0.876296i	$-0.339993\pi$
$463$	−8.48915	−	8.48915i	−0.394524	−	0.394524i	−0.876296	+	0.481772i	$0.839993\pi$
$464$	−0.232261			−0.0107824
$465$	−4.19804	−	11.7208i	−0.194679	−	0.543538i
$466$	6.93978			0.321479
$467$	−13.9488	−	13.9488i	−0.645475	−	0.645475i	0.306421	−	0.951896i	$-0.400868\pi$
$467$	−13.9488	−	13.9488i	−0.645475	−	0.645475i	−0.951896	+	0.306421i	$0.900868\pi$
$468$	3.63683	+	3.63683i	0.168113	+	0.168113i
$469$			4.29494i			0.198322i
$470$	6.26069	−	11.5060i	0.288784	−	0.530731i
$471$		−	2.11767i		−	0.0975771i
$472$	−3.25889	−	3.25889i	−0.150002	−	0.150002i
$473$	−4.28493	+	4.28493i	−0.197021	+	0.197021i
$474$			9.17904i			0.421607i
$475$	−2.37551	+	1.53658i	−0.108996	+	0.0705033i
$476$		−	8.21959i		−	0.376744i
$477$	0.513226	−	0.513226i	0.0234990	−	0.0234990i
$478$	17.1912	+	17.1912i	0.786305	+	0.786305i
$479$		−	26.3184i		−	1.20252i	−0.799053	−	0.601260i	$-0.794666\pi$
$479$		−	26.3184i		−	1.20252i	0.799053	−	0.601260i	$-0.205334\pi$
$480$	−1.06873	+	1.96413i	−0.0487808	+	0.0896499i
$481$	−18.6979			−0.852550
$482$	−17.2441	+	17.2441i	−0.785449	+	0.785449i
$483$	−17.9720	+	17.9720i	−0.817755	+	0.817755i
$484$			10.2511i			0.465960i
$485$	−5.79145	−	19.6166i	−0.262976	−	0.890744i
$486$		−	1.00000i		−	0.0453609i
$487$	11.0727	−	11.0727i	0.501753	−	0.501753i	−0.410230	−	0.911982i	$-0.634551\pi$
$487$	11.0727	−	11.0727i	0.501753	−	0.501753i	0.911982	+	0.410230i	$0.134551\pi$
$488$	−2.04599	−	2.04599i	−0.0926178	−	0.0926178i
$489$	7.74336			0.350167
$490$	1.36385	−	0.402652i	0.0616125	−	0.0181900i
$491$		−	1.09460i		−	0.0493985i	−0.999695	−	0.0246993i	$-0.992137\pi$
$491$		−	1.09460i		−	0.0493985i	0.999695	−	0.0246993i	$-0.00786282\pi$
$492$	8.04052	−	8.04052i	0.362495	−	0.362495i
$493$	0.488517	−	0.488517i	0.0220017	−	0.0220017i
$494$	2.91022			0.130937
$495$	−1.69973	−	0.924865i	−0.0763971	−	0.0415696i
$496$	−5.55877	+	0.316406i	−0.249596	+	0.0142071i
$497$	19.1843	+	19.1843i	0.860536	+	0.860536i
$498$	0.433367	−	0.433367i	0.0194196	−	0.0194196i
$499$	−5.94903			−0.266315			−0.133158	−	0.991095i	$-0.542512\pi$
$499$	−5.94903			−0.266315			−0.133158	+	0.991095i	$0.542512\pi$
$500$	11.1482	−	0.847009i	0.498563	−	0.0378794i
$501$	3.87398			0.173077
$502$	−9.43370	+	9.43370i	−0.421047	+	0.421047i
$503$	−9.60835	+	9.60835i	−0.428415	+	0.428415i	−0.888088	−	0.459673i	$-0.847967\pi$
$503$	−9.60835	+	9.60835i	−0.428415	+	0.428415i	0.459673	+	0.888088i	$0.347967\pi$
$504$			2.76332i			0.123088i
$505$	7.55628	+	4.11156i	0.336250	+	0.182962i
$506$	−7.95956			−0.353846
$507$	−9.51278	+	9.51278i	−0.422477	+	0.422477i
$508$	7.69192	+	7.69192i	0.341274	+	0.341274i
$509$	−14.9921			−0.664515			−0.332258	−	0.943189i	$-0.607810\pi$
$509$	−14.9921			−0.664515			−0.332258	+	0.943189i	$0.607810\pi$
$510$	−1.88330	−	6.37906i	−0.0833939	−	0.282469i
$511$			2.11870i			0.0937256i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.400104	−	0.400104i	−0.0176650	−	0.0176650i
$514$		−	28.0949i		−	1.23921i
$515$	−25.1288	+	7.41882i	−1.10731	+	0.326912i
$516$	7.00244			0.308265
$517$	3.58465	−	3.58465i	0.157653	−	0.157653i
$518$	−7.10347	−	7.10347i	−0.312109	−	0.312109i
$519$	−6.64551			−0.291706
$520$	−10.1020	−	5.49677i	−0.443003	−	0.241049i
$521$	45.0097			1.97191			0.985954	−	0.167015i	$-0.0534129\pi$
$521$	45.0097			1.97191			0.985954	+	0.167015i	$0.0534129\pi$
$522$	−0.164233	+	0.164233i	−0.00718829	+	0.00718829i
$523$	−19.7796	−	19.7796i	−0.864902	−	0.864902i	0.127000	−	0.991903i	$-0.459465\pi$
$523$	−19.7796	−	19.7796i	−0.864902	−	0.864902i	−0.991903	+	0.127000i	$0.959465\pi$
$524$		−	12.8922i		−	0.563199i
$525$	11.6012	−	7.50414i	0.506316	−	0.327507i
$526$		−	30.6125i		−	1.33477i
$527$	11.0263	−	12.3573i	0.480314	−	0.538293i
$528$	−0.611919	+	0.611919i	−0.0266304	+	0.0266304i
$529$			61.5981i			2.67818i
$530$	−0.775698	+	1.42559i	−0.0336942	+	0.0619236i
$531$	−4.60876			−0.200003
$532$	1.10562	+	1.10562i	0.0479345	+	0.0479345i
$533$	41.3545	+	41.3545i	1.79126	+	1.79126i
$534$		−	3.35210i		−	0.145060i
$535$	−4.62272	−	15.6579i	−0.199858	−	0.676952i
$536$	1.55426			0.0671340
$537$	−6.52223	−	6.52223i	−0.281455	−	0.281455i
$538$	−4.17126	−	4.17126i	−0.179836	−	0.179836i
$539$	0.550348			0.0237052
$540$	0.633142	+	2.14456i	0.0272461	+	0.0922871i
$541$	−16.5894			−0.713233			−0.356616	−	0.934251i	$-0.616070\pi$
$541$	−16.5894			−0.713233			−0.356616	+	0.934251i	$0.616070\pi$
$542$	8.61231	−	8.61231i	0.369930	−	0.369930i
$543$	−12.8467	+	12.8467i	−0.551304	+	0.551304i
$544$	−2.97453			−0.127532
$545$	4.79860	−	8.81892i	0.205549	−	0.377761i
$546$	−14.2125			−0.608238
$547$	−9.95577	−	9.95577i	−0.425678	−	0.425678i	0.461475	−	0.887153i	$-0.347320\pi$
$547$	−9.95577	−	9.95577i	−0.425678	−	0.425678i	−0.887153	+	0.461475i	$0.847320\pi$
$548$	2.75114	+	2.75114i	0.117523	+	0.117523i
$549$	−2.89347			−0.123490
$550$	4.23074	+	0.907258i	0.180399	+	0.0386856i
$551$			0.131421i			0.00559870i
$552$	6.50377	+	6.50377i	0.276819	+	0.276819i
$553$	−17.9355	−	17.9355i	−0.762696	−	0.762696i
$554$	−26.9931			−1.14683
$555$	−7.14043	−	3.88529i	−0.303094	−	0.164921i
$556$		−	18.0454i		−	0.765295i
$557$	−3.86165	+	3.86165i	−0.163623	+	0.163623i	−0.784170	−	0.620546i	$-0.786911\pi$
$557$	−3.86165	+	3.86165i	−0.163623	+	0.163623i	0.620546	+	0.784170i	$0.286911\pi$
$558$	−3.70691	+	4.15437i	−0.156926	+	0.175869i
$559$			36.0154i			1.52329i
$560$	−1.74958	−	5.92611i	−0.0739331	−	0.250424i
$561$		−	2.57411i		−	0.108679i
$562$	13.5753	+	13.5753i	0.572640	+	0.572640i
$563$	19.8783	−	19.8783i	0.837771	−	0.837771i	−0.150795	−	0.988565i	$-0.548183\pi$
$563$	19.8783	−	19.8783i	0.837771	−	0.837771i	0.988565	+	0.150795i	$0.0481832\pi$
$564$	−5.85805			−0.246669
$565$	33.4398	−	9.87248i	1.40682	−	0.415338i
$566$	30.1795			1.26854
$567$	1.95397	+	1.95397i	0.0820588	+	0.0820588i
$568$	6.94249	−	6.94249i	0.291300	−	0.291300i
$569$	−13.5683			−0.568814			−0.284407	−	0.958704i	$-0.591797\pi$
$569$	−13.5683			−0.568814			−0.284407	+	0.958704i	$0.591797\pi$
$570$	1.11137	+	0.604723i	0.0465501	+	0.0253291i
$571$			30.0322i			1.25681i	0.777886	+	0.628405i	$0.216292\pi$
$571$			30.0322i			1.25681i	−0.777886	+	0.628405i	$0.783708\pi$
$572$	−3.14726	−	3.14726i	−0.131593	−	0.131593i
$573$	1.62080	+	1.62080i	0.0677100	+	0.0677100i
$574$			31.4218i			1.31152i
$575$	9.64277	−	44.9663i	0.402131	−	1.87522i
$576$	1.00000			0.0416667
$577$	9.57476	+	9.57476i	0.398602	+	0.398602i	0.877740	−	0.479137i	$-0.159050\pi$
$577$	9.57476	+	9.57476i	0.398602	+	0.398602i	−0.479137	+	0.877740i	$0.659050\pi$
$578$	−5.76445	+	5.76445i	−0.239770	+	0.239770i
$579$	7.31016			0.303800
$580$	0.248225	−	0.456191i	0.0103070	−	0.0189423i
$581$			1.69357i			0.0702610i
$582$	−6.46801	+	6.46801i	−0.268108	+	0.268108i
$583$	−0.444138	+	0.444138i	−0.0183943	+	0.0183943i
$584$	0.766720			0.0317271
$585$	−11.0300	+	3.25641i	−0.456035	+	0.134636i
$586$	−18.4519			−0.762242
$587$	−32.7649	+	32.7649i	−1.35235	+	1.35235i	−0.469326	+	0.883025i	$0.655503\pi$
$587$	−32.7649	+	32.7649i	−1.35235	+	1.35235i	−0.883025	+	0.469326i	$0.844497\pi$
$588$	−0.449691	−	0.449691i	−0.0185449	−	0.0185449i
$589$	0.179033	+	3.14533i	0.00737691	+	0.129601i
$590$	9.88375	−	2.91800i	0.406908	−	0.120132i
$591$	22.1458			0.910956
$592$	−2.57063	+	2.57063i	−0.105652	+	0.105652i
$593$	23.6993	−	23.6993i	0.973213	−	0.973213i	−0.0264375	−	0.999650i	$-0.508416\pi$
$593$	23.6993	−	23.6993i	0.973213	−	0.973213i	0.999650	+	0.0264375i	$0.00841631\pi$
$594$			0.865384i			0.0355071i
$595$	16.1444	+	8.78455i	0.661854	+	0.360131i
$596$	12.2319			0.501038
$597$	−9.85958	−	9.85958i	−0.403526	−	0.403526i
$598$	−33.4506	+	33.4506i	−1.36790	+	1.36790i
$599$		−	30.9277i		−	1.26367i	−0.775102	−	0.631836i	$-0.782302\pi$
$599$		−	30.9277i		−	1.26367i	0.775102	−	0.631836i	$-0.217698\pi$
$600$	−2.71562	−	4.19826i	−0.110865	−	0.171393i
$601$			17.8861i			0.729591i	0.931088	+	0.364795i	$0.118861\pi$
$601$			17.8861i			0.729591i	−0.931088	+	0.364795i	$0.881139\pi$
$602$	−13.6825	+	13.6825i	−0.557658	+	0.557658i
$603$	1.09903	−	1.09903i	0.0447560	−	0.0447560i
$604$	23.6478			0.962216
$605$	−20.1345	−	10.9557i	−0.818585	−	0.445413i
$606$		−	3.84714i		−	0.156279i
$607$	−20.8214	−	20.8214i	−0.845115	−	0.845115i	0.144404	−	0.989519i	$-0.453874\pi$
$607$	−20.8214	−	20.8214i	−0.845115	−	0.845115i	−0.989519	+	0.144404i	$0.953874\pi$
$608$	0.400104	−	0.400104i	0.0162263	−	0.0162263i
$609$		−	0.641812i		−	0.0260075i
$610$	6.20522	−	1.83198i	0.251242	−	0.0741746i
$611$		−	30.1295i		−	1.21891i
$612$	−2.10331	+	2.10331i	−0.0850213	+	0.0850213i
$613$	−4.24526	−	4.24526i	−0.171464	−	0.171464i	0.616158	−	0.787622i	$-0.288688\pi$
$613$	−4.24526	−	4.24526i	−0.171464	−	0.171464i	−0.787622	+	0.616158i	$0.788688\pi$
$614$		−	17.1391i		−	0.691676i
$615$	7.19946	+	24.3858i	0.290310	+	0.983330i
$616$		−	2.39134i		−	0.0963497i
$617$	3.07757	+	3.07757i	0.123898	+	0.123898i	0.766337	−	0.642439i	$-0.222077\pi$
$617$	3.07757	+	3.07757i	0.123898	+	0.123898i	−0.642439	+	0.766337i	$0.722077\pi$
$618$	8.28550	+	8.28550i	0.333292	+	0.333292i
$619$	−11.7104			−0.470679			−0.235339	−	0.971913i	$-0.575620\pi$
$619$	−11.7104			−0.470679			−0.235339	+	0.971913i	$0.575620\pi$
$620$	5.31937	−	11.2563i	0.213631	−	0.452064i
$621$	9.19772			0.369092
$622$	2.09449	+	2.09449i	0.0839813	+	0.0839813i
$623$	6.54989	+	6.54989i	0.262416	+	0.262416i
$624$			5.14326i			0.205895i
$625$	−10.2508	+	22.8018i	−0.410033	+	0.912071i
$626$			11.5328i			0.460943i
$627$	0.346243	+	0.346243i	0.0138276	+	0.0138276i
$628$	1.49742	−	1.49742i	0.0597535	−	0.0597535i
$629$		−	10.8137i		−	0.431169i
$630$	−5.42753	−	2.95326i	−0.216238	−	0.117661i
$631$		−	23.9602i		−	0.953839i	−0.878947	−	0.476920i	$-0.841753\pi$
$631$		−	23.9602i		−	0.953839i	0.878947	−	0.476920i	$-0.158247\pi$
$632$	−6.49056	+	6.49056i	−0.258181	+	0.258181i
$633$	6.85575	+	6.85575i	0.272492	+	0.272492i
$634$			20.7794i			0.825256i
$635$	−23.3285	+	6.88733i	−0.925765	+	0.273315i
$636$	0.725811			0.0287803
$637$	2.31287	−	2.31287i	0.0916394	−	0.0916394i
$638$	0.142125	−	0.142125i	0.00562678	−	0.00562678i
$639$		−	9.81816i		−	0.388401i
$640$	−2.14456	+	0.633142i	−0.0847711	+	0.0250271i
$641$		−	29.1991i		−	1.15329i	−0.816993	−	0.576647i	$-0.804361\pi$
$641$		−	29.1991i		−	1.15329i	0.816993	−	0.576647i	$-0.195639\pi$
$642$	−5.16276	+	5.16276i	−0.203758	+	0.203758i
$643$	19.1243	+	19.1243i	0.754187	+	0.754187i	0.975258	−	0.221071i	$-0.0709552\pi$
$643$	19.1243	+	19.1243i	0.754187	+	0.754187i	−0.221071	+	0.975258i	$0.570955\pi$
$644$	−25.4163			−1.00154
$645$	−7.48374	+	13.7537i	−0.294672	+	0.541552i
$646$			1.68308i			0.0662201i
$647$	26.4181	−	26.4181i	1.03860	−	1.03860i	0.0393764	−	0.999224i	$-0.487463\pi$
$647$	26.4181	−	26.4181i	1.03860	−	1.03860i	0.999224	−	0.0393764i	$-0.0125371\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	3.98835			0.156556
$650$	21.5927	−	13.9671i	0.846937	−	0.547836i
$651$	−0.874333	−	15.3607i	−0.0342678	−	0.602032i
$652$	5.47538	+	5.47538i	0.214432	+	0.214432i
$653$	10.9167	−	10.9167i	0.427205	−	0.427205i	−0.460470	−	0.887675i	$-0.652319\pi$
$653$	10.9167	−	10.9167i	0.427205	−	0.427205i	0.887675	+	0.460470i	$0.152319\pi$
$654$	−4.48999			−0.175572
$655$	25.3220	+	13.7783i	0.989413	+	0.538364i
$656$	11.3710			0.443963
$657$	0.542153	−	0.542153i	0.0211514	−	0.0211514i
$658$	11.4464	−	11.4464i	0.446228	−	0.446228i
$659$			20.6425i			0.804117i	0.915614	+	0.402058i	$0.131705\pi$
$659$			20.6425i			0.804117i	−0.915614	+	0.402058i	$0.868295\pi$
$660$	−0.547911	−	1.85587i	−0.0213274	−	0.0722395i
$661$	−33.6607			−1.30925			−0.654624	−	0.755955i	$-0.727173\pi$
$661$	−33.6607			−1.30925			−0.654624	+	0.755955i	$0.727173\pi$
$662$	19.1457	−	19.1457i	0.744120	−	0.744120i
$663$	−10.8179	−	10.8179i	−0.420131	−	0.420131i
$664$	0.612873			0.0237841
$665$	−3.35318	+	0.989966i	−0.130031	+	0.0383892i
$666$			3.63541i			0.140869i
$667$	−1.51057	−	1.51057i	−0.0584896	−	0.0584896i
$668$	2.73932	+	2.73932i	0.105987	+	0.105987i
$669$			0.720010i			0.0278372i
$670$	−1.66109	+	3.05278i	−0.0641736	+	0.117939i
$671$	2.50396			0.0966645
$672$	−1.95397	+	1.95397i	−0.0753758	+	0.0753758i
$673$	−11.3998	−	11.3998i	−0.439428	−	0.439428i	0.452391	−	0.891820i	$-0.350571\pi$
$673$	−11.3998	−	11.3998i	−0.439428	−	0.439428i	−0.891820	+	0.452391i	$0.850571\pi$
$674$	24.0207			0.925244
$675$	−4.88885	−	1.04839i	−0.188172	−	0.0403524i
$676$	−13.4531			−0.517427
$677$	−19.9935	+	19.9935i	−0.768411	+	0.768411i	−0.977827	−	0.209416i	$-0.932844\pi$
$677$	−19.9935	+	19.9935i	−0.768411	+	0.768411i	0.209416	+	0.977827i	$0.432844\pi$
$678$	−11.0258	−	11.0258i	−0.423444	−	0.423444i
$679$		−	25.2765i		−	0.970025i
$680$	3.17898	−	5.84237i	0.121908	−	0.224045i
$681$			12.7424i			0.488290i
$682$	3.20790	−	3.59513i	0.122837	−	0.137665i
$683$	7.18248	−	7.18248i	0.274830	−	0.274830i	−0.556211	−	0.831041i	$-0.687745\pi$
$683$	7.18248	−	7.18248i	0.274830	−	0.274830i	0.831041	+	0.556211i	$0.187745\pi$
$684$		−	0.565832i		−	0.0216351i
$685$	−8.34384	+	2.46337i	−0.318802	+	0.0941204i
$686$	−17.5859			−0.671433
$687$	17.4163	+	17.4163i	0.664472	+	0.664472i
$688$	4.95147	+	4.95147i	0.188773	+	0.188773i
$689$			3.73303i			0.142217i
$690$	−19.7251	+	5.82346i	−0.750920	+	0.221695i
$691$	34.2312			1.30222			0.651108	−	0.758985i	$-0.274304\pi$
$691$	34.2312			1.30222			0.651108	+	0.758985i	$0.274304\pi$
$692$	−4.69909	−	4.69909i	−0.178632	−	0.178632i
$693$	−1.69093	−	1.69093i	−0.0642331	−	0.0642331i
$694$	−7.14302			−0.271145
$695$	35.4435	+	19.2857i	1.34445	+	0.731548i
$696$	−0.232261			−0.00880383
$697$	−23.9168	+	23.9168i	−0.905912	+	0.905912i
$698$	9.19871	−	9.19871i	0.348176	−	0.348176i
$699$	6.93978			0.262487
$700$	13.5095	+	2.89703i	0.510611	+	0.109498i
$701$	−0.374888			−0.0141593			−0.00707967	−	0.999975i	$-0.502254\pi$
$701$	−0.374888			−0.0141593			−0.00707967	+	0.999975i	$0.502254\pi$
$702$	3.63683	+	3.63683i	0.137263	+	0.137263i
$703$	1.45454	+	1.45454i	0.0548591	+	0.0548591i
$704$	−0.865384			−0.0326154
$705$	6.26069	−	11.5060i	0.235791	−	0.433340i
$706$		−	5.07874i		−	0.191141i
$707$	7.51717	+	7.51717i	0.282712	+	0.282712i
$708$	−3.25889	−	3.25889i	−0.122476	−	0.122476i
$709$	−0.480309			−0.0180384			−0.00901919	−	0.999959i	$-0.502871\pi$
$709$	−0.480309			−0.0180384			−0.00901919	+	0.999959i	$0.502871\pi$
$710$	6.21629	+	21.0556i	0.233293	+	0.790204i
$711$			9.17904i			0.344241i
$712$	2.37030	−	2.37030i	0.0888306	−	0.0888306i
$713$	−38.2108	−	34.0951i	−1.43100	−	1.27687i
$714$		−	8.21959i		−	0.307611i
$715$	9.54520	−	2.81805i	0.356970	−	0.105389i
$716$		−	9.22382i		−	0.344710i
$717$	17.1912	+	17.1912i	0.642015	+	0.642015i
$718$	−4.66542	+	4.66542i	−0.174112	+	0.174112i
$719$	−35.7704			−1.33401			−0.667005	−	0.745053i	$-0.732424\pi$
$719$	−35.7704			−1.33401			−0.667005	+	0.745053i	$0.732424\pi$
$720$	−1.06873	+	1.96413i	−0.0398293	+	0.0731988i
$721$	−32.3792			−1.20586
$722$	13.2086	+	13.2086i	0.491575	+	0.491575i
$723$	−17.2441	+	17.2441i	−0.641317	+	0.641317i
$724$	−18.1679			−0.675206
$725$	0.630732	+	0.975092i	0.0234248	+	0.0362140i
$726$			10.2511i			0.380454i
$727$	14.0731	+	14.0731i	0.521944	+	0.521944i	0.918158	−	0.396214i	$-0.129676\pi$
$727$	14.0731	+	14.0731i	0.521944	+	0.521944i	−0.396214	+	0.918158i	$0.629676\pi$
$728$	−10.0497	−	10.0497i	−0.372468	−	0.372468i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.819419	+	1.50594i	−0.0303281	+	0.0557373i
$731$	−20.8290			−0.770387
$732$	−2.04599	−	2.04599i	−0.0756221	−	0.0756221i
$733$	19.2656	−	19.2656i	0.711592	−	0.711592i	−0.255277	−	0.966868i	$-0.582167\pi$
$733$	19.2656	−	19.2656i	0.711592	−	0.711592i	0.966868	+	0.255277i	$0.0821665\pi$
$734$	6.15747			0.227276
$735$	1.36385	−	0.402652i	0.0503064	−	0.0148520i
$736$			9.19772i			0.339033i
$737$	−0.951084	+	0.951084i	−0.0350336	+	0.0350336i
$738$	8.04052	−	8.04052i	0.295976	−	0.295976i
$739$	−6.03181			−0.221884			−0.110942	−	0.993827i	$-0.535387\pi$
$739$	−6.03181			−0.221884			−0.110942	+	0.993827i	$0.535387\pi$
$740$	−2.30173	−	7.79636i	−0.0846134	−	0.286600i
$741$	2.91022			0.106910
$742$	−1.41821	+	1.41821i	−0.0520641	+	0.0520641i
$743$	16.3906	+	16.3906i	0.601313	+	0.601313i	0.940661	−	0.339348i	$-0.110206\pi$
$743$	16.3906	+	16.3906i	0.601313	+	0.601313i	−0.339348	+	0.940661i	$0.610206\pi$
$744$	−5.55877	+	0.316406i	−0.203794	+	0.0116000i
$745$	−13.0726	+	24.0251i	−0.478944	+	0.880210i
$746$	−15.8554			−0.580507
$747$	0.433367	−	0.433367i	0.0158561	−	0.0158561i
$748$	1.82017	−	1.82017i	0.0665521	−	0.0665521i
$749$		−	20.1757i		−	0.737204i
$750$	11.1482	−	0.847009i	0.407075	−	0.0309284i
$751$	−36.7092			−1.33954			−0.669769	−	0.742570i	$-0.733607\pi$
$751$	−36.7092			−1.33954			−0.669769	+	0.742570i	$0.733607\pi$
$752$	−4.14227	−	4.14227i	−0.151053	−	0.151053i
$753$	−9.43370	+	9.43370i	−0.343783	+	0.343783i
$754$		−	1.19458i		−	0.0435039i
$755$	−25.2732	+	46.4474i	−0.919786	+	1.69039i
$756$			2.76332i			0.100501i
$757$	−28.1852	+	28.1852i	−1.02441	+	1.02441i	−0.0247136	+	0.999695i	$0.507867\pi$
$757$	−28.1852	+	28.1852i	−1.02441	+	1.02441i	−0.999695	+	0.0247136i	$0.992133\pi$
$758$	18.9430	−	18.9430i	0.688043	−	0.688043i
$759$	−7.95956			−0.288914
$760$	0.358252	+	1.21346i	0.0129952	+	0.0440168i
$761$			3.78919i			0.137358i	0.997639	+	0.0686790i	$0.0218784\pi$
$761$			3.78919i			0.137358i	−0.997639	+	0.0686790i	$0.978122\pi$
$762$	7.69192	+	7.69192i	0.278649	+	0.278649i
$763$	8.77328	−	8.77328i	0.317614	−	0.317614i
$764$			2.29216i			0.0829275i
$765$	−1.88330	−	6.37906i	−0.0680909	−	0.230635i
$766$		−	29.6290i		−	1.07054i
$767$	16.7613	−	16.7613i	0.605215	−	0.605215i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$			16.5298i			0.596080i	0.954553	+	0.298040i	$0.0963329\pi$
$769$			16.5298i			0.596080i	−0.954553	+	0.298040i	$0.903667\pi$
$770$	4.69690	+	2.55570i	0.169264	+	0.0921010i
$771$		−	28.0949i		−	1.01181i
$772$	5.16906	+	5.16906i	0.186039	+	0.186039i
$773$	−2.43384	−	2.43384i	−0.0875391	−	0.0875391i	0.661981	−	0.749520i	$-0.269716\pi$
$773$	−2.43384	−	2.43384i	−0.0875391	−	0.0875391i	−0.749520	+	0.661981i	$0.769716\pi$
$774$	7.00244			0.251697
$775$	16.4239	+	22.4779i	0.589962	+	0.807431i
$776$	−9.14715			−0.328364
$777$	−7.10347	−	7.10347i	−0.254836	−	0.254836i
$778$	14.7946	+	14.7946i	0.530411	+	0.530411i
$779$		−	6.43408i		−	0.230525i
$780$	−10.1020	−	5.49677i	−0.361711	−	0.196816i
$781$			8.49648i			0.304028i
$782$	−19.3457	−	19.3457i	−0.691800	−	0.691800i
$783$	−0.164233	+	0.164233i	−0.00586922	+	0.00586922i
$784$		−	0.635959i		−	0.0227128i
$785$	1.34079	+	4.54147i	0.0478547	+	0.162092i
$786$		−	12.8922i		−	0.459850i
$787$	−21.6303	+	21.6303i	−0.771036	+	0.771036i	−0.978288	−	0.207251i	$-0.933548\pi$
$787$	−21.6303	+	21.6303i	−0.771036	+	0.771036i	0.207251	+	0.978288i	$0.433548\pi$
$788$	15.6594	+	15.6594i	0.557844	+	0.557844i
$789$		−	30.6125i		−	1.08983i
$790$	−5.81163	−	19.6850i	−0.206769	−	0.700360i
$791$	43.0881			1.53204
$792$	−0.611919	+	0.611919i	−0.0217436	+	0.0217436i
$793$	10.5231	−	10.5231i	0.373685	−	0.373685i
$794$		−	0.252210i		−	0.00895061i
$795$	−0.775698	+	1.42559i	−0.0275112	+	0.0505604i
$796$		−	13.9435i		−	0.494216i
$797$	−25.9492	+	25.9492i	−0.919168	+	0.919168i	−0.996969	−	0.0778011i	$-0.975210\pi$
$797$	−25.9492	+	25.9492i	−0.919168	+	0.919168i	0.0778011	+	0.996969i	$0.475210\pi$
$798$	1.10562	+	1.10562i	0.0391384	+	0.0391384i
$799$	17.4250			0.616451
$800$	1.04839	−	4.88885i	0.0370661	−	0.172847i
$801$		−	3.35210i		−	0.118441i
$802$	−21.9943	+	21.9943i	−0.776647	+	0.776647i
$803$	−0.469171	+	0.469171i	−0.0165567	+	0.0165567i
$804$	1.55426			0.0548147
$805$	27.1632	−	49.9209i	0.957378	−	1.75948i
$806$	−1.62736	−	28.5902i	−0.0573213	−	1.00705i
$807$	−4.17126	−	4.17126i	−0.146835	−	0.146835i
$808$	2.72034	−	2.72034i	0.0957011	−	0.0957011i
$809$	−47.2394			−1.66085			−0.830425	−	0.557131i	$-0.811902\pi$
$809$	−47.2394			−1.66085			−0.830425	+	0.557131i	$0.811902\pi$
$810$	0.633142	+	2.14456i	0.0222463	+	0.0753521i
$811$	−6.06747			−0.213058			−0.106529	−	0.994310i	$-0.533974\pi$
$811$	−6.06747			−0.213058			−0.106529	+	0.994310i	$0.533974\pi$
$812$	0.453830	−	0.453830i	0.0159263	−	0.0159263i
$813$	8.61231	−	8.61231i	0.302047	−	0.302047i
$814$		−	3.14603i		−	0.110268i
$815$	−16.6061	+	4.90264i	−0.581686	+	0.171732i
$816$	−2.97453			−0.104129
$817$	2.80170	−	2.80170i	0.0980191	−	0.0980191i
$818$	23.1348	+	23.1348i	0.808889	+	0.808889i
$819$	−14.2125			−0.496624
$820$	−12.1526	+	22.3341i	−0.424386	+	0.779942i
$821$			37.6348i			1.31346i	0.754124	+	0.656732i	$0.228062\pi$
$821$			37.6348i			1.31346i	−0.754124	+	0.656732i	$0.771938\pi$
$822$	2.75114	+	2.75114i	0.0959572	+	0.0959572i
$823$	−22.2818	−	22.2818i	−0.776695	−	0.776695i	0.202572	−	0.979267i	$-0.435070\pi$
$823$	−22.2818	−	22.2818i	−0.776695	−	0.776695i	−0.979267	+	0.202572i	$0.935070\pi$
$824$			11.7175i			0.408197i
$825$	4.23074	+	0.907258i	0.147295	+	0.0315867i
$826$	12.7355			0.443125
$827$	−7.21832	+	7.21832i	−0.251006	+	0.251006i	−0.821383	−	0.570377i	$-0.806797\pi$
$827$	−7.21832	+	7.21832i	−0.251006	+	0.251006i	0.570377	+	0.821383i	$0.306797\pi$
$828$	6.50377	+	6.50377i	0.226022	+	0.226022i
$829$	−37.4701			−1.30139			−0.650695	−	0.759339i	$-0.725523\pi$
$829$	−37.4701			−1.30139			−0.650695	+	0.759339i	$0.725523\pi$
$830$	−0.654998	+	1.20376i	−0.0227353	+	0.0417832i
$831$	−26.9931			−0.936381
$832$	−3.63683	+	3.63683i	−0.126084	+	0.126084i
$833$	1.33762	+	1.33762i	0.0463457	+	0.0463457i
$834$		−	18.0454i		−	0.624861i
$835$	−8.30797	+	2.45278i	−0.287509	+	0.0848819i
$836$			0.489662i			0.0169353i
$837$	−3.70691	+	4.15437i	−0.128130	+	0.143596i
$838$	23.2164	−	23.2164i	0.801996	−	0.801996i
$839$		−	15.9390i		−	0.550274i	−0.961405	−	0.275137i	$-0.911277\pi$
$839$		−	15.9390i		−	0.550274i	0.961405	−	0.275137i	$-0.0887233\pi$
$840$	−1.74958	−	5.92611i	−0.0603661	−	0.204470i
$841$	−28.9461			−0.998140
$842$	3.54352	+	3.54352i	0.122118	+	0.122118i
$843$	13.5753	+	13.5753i	0.467559	+	0.467559i
$844$			9.69550i			0.333733i
$845$	14.3778	−	26.4237i	0.494611	−	0.909001i
$846$	−5.85805			−0.201404
$847$	−20.0303	−	20.0303i	−0.688250	−	0.688250i
$848$	0.513226	+	0.513226i	0.0176243	+	0.0176243i
$849$	30.1795			1.03576
$850$	8.07769	+	12.4879i	0.277063	+	0.428330i
$851$	−33.4375			−1.14622
$852$	6.94249	−	6.94249i	0.237846	−	0.237846i
$853$	−23.3870	+	23.3870i	−0.800754	+	0.800754i	−0.983213	−	0.182459i	$-0.941594\pi$
$853$	−23.3870	+	23.3870i	−0.800754	+	0.800754i	0.182459	+	0.983213i	$0.441594\pi$
$854$	7.99560			0.273604
$855$	1.11137	+	0.604723i	0.0380080	+	0.0206811i
$856$	−7.30124			−0.249551
$857$	21.3687	+	21.3687i	0.729939	+	0.729939i	0.970607	−	0.240668i	$-0.0773665\pi$
$857$	21.3687	+	21.3687i	0.729939	+	0.729939i	−0.240668	+	0.970607i	$0.577367\pi$
$858$	−3.14726	−	3.14726i	−0.107446	−	0.107446i
$859$	−22.3465			−0.762454			−0.381227	−	0.924481i	$-0.624498\pi$
$859$	−22.3465			−0.762454			−0.381227	+	0.924481i	$0.624498\pi$
$860$	−15.0171	+	4.43354i	−0.512080	+	0.151182i
$861$			31.4218i			1.07085i
$862$	−7.05901	−	7.05901i	−0.240431	−	0.240431i
$863$	21.4455	+	21.4455i	0.730012	+	0.730012i	0.970622	−	0.240610i	$-0.0773475\pi$
$863$	21.4455	+	21.4455i	0.730012	+	0.730012i	−0.240610	+	0.970622i	$0.577347\pi$
$864$	1.00000			0.0340207
$865$	14.2517	−	4.20755i	0.484572	−	0.143061i
$866$		−	2.10688i		−	0.0715947i
$867$	−5.76445	+	5.76445i	−0.195771	+	0.195771i
$868$	10.2434	−	11.4799i	0.347683	−	0.389653i
$869$		−	7.94339i		−	0.269461i
$870$	0.248225	−	0.456191i	0.00841561	−	0.0154663i
$871$			7.99398i			0.270866i
$872$	−3.17490	−	3.17490i	−0.107516	−	0.107516i
$873$	−6.46801	+	6.46801i	−0.218909	+	0.218909i
$874$	5.20436			0.176040
$875$	−20.1282	+	23.4382i	−0.680457	+	0.792357i
$876$	0.766720			0.0259051
$877$	−28.0878	−	28.0878i	−0.948456	−	0.948456i	0.0502791	−	0.998735i	$-0.483989\pi$
$877$	−28.0878	−	28.0878i	−0.948456	−	0.948456i	−0.998735	+	0.0502791i	$0.983989\pi$
$878$	−22.9039	+	22.9039i	−0.772969	+	0.772969i
$879$	−18.4519			−0.622368
$880$	0.924865	−	1.69973i	0.0311772	−	0.0572978i
$881$			45.7175i			1.54026i	0.637885	+	0.770131i	$0.279809\pi$
$881$			45.7175i			1.54026i	−0.637885	+	0.770131i	$0.720191\pi$
$882$	−0.449691	−	0.449691i	−0.0151419	−	0.0151419i
$883$	37.4628	+	37.4628i	1.26072	+	1.26072i	0.950744	+	0.309978i	$0.100322\pi$
$883$	37.4628	+	37.4628i	1.26072	+	1.26072i	0.309978	+	0.950744i	$0.399678\pi$
$884$		−	15.2988i		−	0.514554i
$885$	9.88375	−	2.91800i	0.332239	−	0.0980874i
$886$	25.8582			0.868725
$887$	13.0190	+	13.0190i	0.437134	+	0.437134i	0.891046	−	0.453912i	$-0.149972\pi$
$887$	13.0190	+	13.0190i	0.437134	+	0.437134i	−0.453912	+	0.891046i	$0.649972\pi$
$888$	−2.57063	+	2.57063i	−0.0862646	+	0.0862646i
$889$	−30.0595			−1.00816
$890$	2.12236	+	7.18878i	0.0711416	+	0.240969i
$891$			0.865384i			0.0289915i
$892$	−0.509124	+	0.509124i	−0.0170467	+	0.0170467i
$893$	−2.34383	+	2.34383i	−0.0784332	+	0.0784332i
$894$	12.2319			0.409096
$895$	18.1168	+	9.85780i	0.605577	+	0.329510i
$896$	−2.76332			−0.0923162
$897$	−33.4506	+	33.4506i	−1.11688	+	1.11688i
$898$	27.6517	+	27.6517i	0.922750	+	0.922750i
$899$	1.29108	−	0.0734888i	0.0430601	−	0.00245099i
$900$	−2.71562	−	4.19826i	−0.0905206	−	0.139942i
$901$	−2.15895			−0.0719250
$902$	−6.95814	+	6.95814i	−0.231681	+	0.231681i
$903$	−13.6825	+	13.6825i	−0.455326	+	0.455326i
$904$		−	15.5928i		−	0.518610i
$905$	19.4167	−	35.6842i	0.645432	−	1.18618i
$906$	23.6478			0.785646
$907$	20.9352	+	20.9352i	0.695141	+	0.695141i	0.963358	−	0.268218i	$-0.0864347\pi$
$907$	20.9352	+	20.9352i	0.695141	+	0.695141i	−0.268218	+	0.963358i	$0.586435\pi$
$908$	−9.01025	+	9.01025i	−0.299015	+	0.299015i
$909$		−	3.84714i		−	0.127601i
$910$	30.4795	−	8.99852i	1.01039	−	0.298298i
$911$			49.0468i			1.62499i	0.582965	+	0.812497i	$0.301892\pi$
$911$			49.0468i			1.62499i	−0.582965	+	0.812497i	$0.698108\pi$
$912$	0.400104	−	0.400104i	0.0132488	−	0.0132488i
$913$	−0.375029	+	0.375029i	−0.0124116	+	0.0124116i
$914$	29.6209			0.979771
$915$	6.20522	−	1.83198i	0.205138	−	0.0605633i
$916$			24.6303i			0.813808i
$917$	25.1909	+	25.1909i	0.831878	+	0.831878i
$918$	−2.10331	+	2.10331i	−0.0694196	+	0.0694196i
$919$		−	41.1510i		−	1.35745i	−0.734394	−	0.678724i	$-0.762533\pi$
$919$		−	41.1510i		−	1.35745i	0.734394	−	0.678724i	$-0.237467\pi$
$920$	−18.0655	−	9.82991i	−0.595603	−	0.324082i
$921$		−	17.1391i		−	0.564751i
$922$	28.4264	−	28.4264i	0.936174	−	0.936174i
$923$	35.7070	+	35.7070i	1.17531	+	1.17531i
$924$		−	2.39134i		−	0.0786692i
$925$	17.7730	+	3.81132i	0.584373	+	0.125316i
$926$		−	12.0055i		−	0.394524i
$927$	8.28550	+	8.28550i	0.272132	+	0.272132i
$928$	−0.164233	−	0.164233i	−0.00539122	−	0.00539122i
$929$	42.4243			1.39190			0.695949	−	0.718092i	$-0.254984\pi$
$929$	42.4243			1.39190			0.695949	+	0.718092i	$0.254984\pi$
$930$	5.31937	−	11.2563i	0.174429	−	0.369109i
$931$	−0.359846			−0.0117935
$932$	4.90717	+	4.90717i	0.160740	+	0.160740i
$933$	2.09449	+	2.09449i	0.0685705	+	0.0685705i
$934$		−	19.7266i		−	0.645475i
$935$	1.62978	+	5.52033i	0.0532994	+	0.180534i
$936$			5.14326i			0.168113i
$937$	−17.6875	−	17.6875i	−0.577826	−	0.577826i	0.356478	−	0.934304i	$-0.383978\pi$
$937$	−17.6875	−	17.6875i	−0.577826	−	0.577826i	−0.934304	+	0.356478i	$0.883978\pi$
$938$	−3.03698	+	3.03698i	−0.0991609	+	0.0991609i
$939$			11.5328i			0.376359i
$940$	12.5629	−	3.70898i	0.409758	−	0.120974i
$941$			32.9359i			1.07368i	0.843684	+	0.536841i	$0.180382\pi$
$941$			32.9359i			1.07368i	−0.843684	+	0.536841i	$0.819618\pi$
$942$	1.49742	−	1.49742i	0.0487885	−	0.0487885i
$943$	73.9544	+	73.9544i	2.40829	+	2.40829i
$944$		−	4.60876i		−	0.150002i
$945$	−5.42753	−	2.95326i	−0.176558	−	0.0960694i
$946$	−6.05980			−0.197021
$947$	0.610184	−	0.610184i	0.0198283	−	0.0198283i	−0.697123	−	0.716951i	$-0.745537\pi$
$947$	0.610184	−	0.610184i	0.0198283	−	0.0198283i	0.716951	+	0.697123i	$0.245537\pi$
$948$	−6.49056	+	6.49056i	−0.210804	+	0.210804i
$949$			3.94344i			0.128009i
$950$	−2.76627	−	0.593211i	−0.0897496	−	0.0192463i
$951$			20.7794i			0.673818i
$952$	5.81213	−	5.81213i	0.188372	−	0.188372i
$953$	−16.5381	−	16.5381i	−0.535722	−	0.535722i	0.386547	−	0.922270i	$-0.373668\pi$
$953$	−16.5381	−	16.5381i	−0.535722	−	0.535722i	−0.922270	+	0.386547i	$0.873668\pi$
$954$	0.725811			0.0234990
$955$	−4.50211	−	2.44971i	−0.145685	−	0.0792708i
$956$			24.3120i			0.786305i
$957$	0.142125	−	0.142125i	0.00459424	−	0.00459424i
$958$	18.6099	−	18.6099i	0.601260	−	0.601260i
$959$	−10.7513			−0.347177
$960$	−2.14456	+	0.633142i	−0.0692153	+	0.0204346i
$961$	30.7998	−	3.51766i	0.993541	−	0.113473i
$962$	−13.2214	−	13.2214i	−0.426275	−	0.426275i
$963$	−5.16276	+	5.16276i	−0.166368	+	0.166368i
$964$	−24.3869			−0.785449
$965$	−15.6771	+	4.62837i	−0.504663	+	0.148992i
$966$	−25.4163			−0.817755
$967$	−4.15927	+	4.15927i	−0.133753	+	0.133753i	−0.770814	−	0.637061i	$-0.780150\pi$
$967$	−4.15927	+	4.15927i	−0.133753	+	0.133753i	0.637061	+	0.770814i	$0.280150\pi$
$968$	−7.24863	+	7.24863i	−0.232980	+	0.232980i
$969$			1.68308i			0.0540685i
$970$	9.77587	−	17.9662i	0.313884	−	0.576860i
$971$	30.7058			0.985396			0.492698	−	0.870200i	$-0.336011\pi$
$971$	30.7058			0.985396			0.492698	+	0.870200i	$0.336011\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	35.2601	+	35.2601i	1.13039	+	1.13039i
$974$	15.6592			0.501753
$975$	21.5927	−	13.9671i	0.691521	−	0.447306i
$976$		−	2.89347i		−	0.0926178i
$977$	−9.40403	−	9.40403i	−0.300862	−	0.300862i	0.540489	−	0.841351i	$-0.318239\pi$
$977$	−9.40403	−	9.40403i	−0.300862	−	0.300862i	−0.841351	+	0.540489i	$0.818239\pi$
$978$	5.47538	+	5.47538i	0.175083	+	0.175083i
$979$			2.90086i			0.0927118i
$980$	1.24911	+	0.679670i	0.0399012	+	0.0217113i
$981$	−4.48999			−0.143354
$982$	0.773998	−	0.773998i	0.0246993	−	0.0246993i
$983$	7.54187	+	7.54187i	0.240548	+	0.240548i	0.817077	−	0.576529i	$-0.195593\pi$
$983$	7.54187	+	7.54187i	0.240548	+	0.240548i	−0.576529	+	0.817077i	$0.695593\pi$
$984$	11.3710			0.362495
$985$	−47.4929	+	14.0214i	−1.51325	+	0.446760i
$986$	0.690867			0.0220017
$987$	11.4464	−	11.4464i	0.364344	−	0.364344i
$988$	2.05784	+	2.05784i	0.0654685	+	0.0654685i
$989$			64.4065i			2.04801i
$990$	−0.547911	−	1.85587i	−0.0174138	−	0.0589833i
$991$			9.57170i			0.304055i	0.988376	+	0.152028i	$0.0485803\pi$
$991$			9.57170i			0.304055i	−0.988376	+	0.152028i	$0.951420\pi$
$992$	−4.15437	−	3.70691i	−0.131902	−	0.117694i
$993$	19.1457	−	19.1457i	0.607572	−	0.607572i
$994$			27.1308i			0.860536i
$995$	27.3869	+	14.9019i	0.868225	+	0.472423i
$996$	0.612873			0.0194196
$997$	−15.2890	−	15.2890i	−0.484209	−	0.484209i	0.422264	−	0.906473i	$-0.361236\pi$
$997$	−15.2890	−	15.2890i	−0.484209	−	0.484209i	−0.906473	+	0.422264i	$0.861236\pi$
$998$	−4.20660	−	4.20660i	−0.133158	−	0.133158i
$999$			3.63541i			0.115019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.b.247.9	yes	32
5.3	odd	4		930.2.k.a.433.9	yes	32
31.30	odd	2		930.2.k.a.247.9	✓	32
155.123	even	4	inner	930.2.k.b.433.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.9	✓	32	31.30	odd	2
930.2.k.a.433.9	yes	32	5.3	odd	4
930.2.k.b.247.9	yes	32	1.1	even	1	trivial
930.2.k.b.433.9	yes	32	155.123	even	4	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.96413 - 1.06873i) q^{5} +1.00000i q^{6} +(-1.95397 - 1.95397i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.96413 - 1.06873i) q^{5} +1.00000i q^{6} +(-1.95397 - 1.95397i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.633142 - 2.14456i) q^{10} -0.865384i q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.63683 - 3.63683i) q^{13} -2.76332i q^{14} +(-0.633142 - 2.14456i) q^{15} -1.00000 q^{16} +(2.10331 - 2.10331i) q^{17} +(-0.707107 + 0.707107i) q^{18} +0.565832i q^{19} +(1.06873 - 1.96413i) q^{20} -2.76332i q^{21} +(0.611919 - 0.611919i) q^{22} +(-6.50377 - 6.50377i) q^{23} -1.00000 q^{24} +(2.71562 + 4.19826i) q^{25} -5.14326i q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.95397 - 1.95397i) q^{28} +0.232261 q^{29} +(1.06873 - 1.96413i) q^{30} +(5.55877 - 0.316406i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.611919 - 0.611919i) q^{33} +2.97453 q^{34} +(1.74958 + 5.92611i) q^{35} -1.00000 q^{36} +(2.57063 - 2.57063i) q^{37} +(-0.400104 + 0.400104i) q^{38} -5.14326i q^{39} +(2.14456 - 0.633142i) q^{40} -11.3710 q^{41} +(1.95397 - 1.95397i) q^{42} +(-4.95147 - 4.95147i) q^{43} +0.865384 q^{44} +(1.06873 - 1.96413i) q^{45} -9.19772i q^{46} +(4.14227 + 4.14227i) q^{47} +(-0.707107 - 0.707107i) q^{48} +0.635959i q^{49} +(-1.04839 + 4.88885i) q^{50} +2.97453 q^{51} +(3.63683 - 3.63683i) q^{52} +(-0.513226 - 0.513226i) q^{53} -1.00000 q^{54} +(-0.924865 + 1.69973i) q^{55} +2.76332 q^{56} +(-0.400104 + 0.400104i) q^{57} +(0.164233 + 0.164233i) q^{58} +4.60876i q^{59} +(2.14456 - 0.633142i) q^{60} +2.89347i q^{61} +(4.15437 + 3.70691i) q^{62} +(1.95397 - 1.95397i) q^{63} -1.00000i q^{64} +(3.25641 + 11.0300i) q^{65} +0.865384 q^{66} +(-1.09903 - 1.09903i) q^{67} +(2.10331 + 2.10331i) q^{68} -9.19772i q^{69} +(-2.95326 + 5.42753i) q^{70} -9.81816 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-0.542153 - 0.542153i) q^{73} +3.63541 q^{74} +(-1.04839 + 4.88885i) q^{75} -0.565832 q^{76} +(-1.69093 + 1.69093i) q^{77} +(3.63683 - 3.63683i) q^{78} +9.17904 q^{79} +(1.96413 + 1.06873i) q^{80} -1.00000 q^{81} +(-8.04052 - 8.04052i) q^{82} +(-0.433367 - 0.433367i) q^{83} +2.76332 q^{84} +(-6.37906 + 1.88330i) q^{85} -7.00244i q^{86} +(0.164233 + 0.164233i) q^{87} +(0.611919 + 0.611919i) q^{88} -3.35210 q^{89} +(2.14456 - 0.633142i) q^{90} +14.2125i q^{91} +(6.50377 - 6.50377i) q^{92} +(4.15437 + 3.70691i) q^{93} +5.85805i q^{94} +(0.604723 - 1.11137i) q^{95} -1.00000i q^{96} +(6.46801 + 6.46801i) q^{97} +(-0.449691 + 0.449691i) q^{98} +0.865384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} + 4 q^{15} - 32 q^{16} + 8 q^{17} - 4 q^{22} - 32 q^{24} + 8 q^{25} + 4 q^{28} + 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} + 4 q^{37} + 16 q^{38} - 16 q^{41} + 4 q^{42} - 16 q^{43} - 8 q^{44} - 8 q^{47} - 16 q^{50} - 24 q^{53} - 32 q^{54} - 28 q^{55} + 16 q^{57} + 20 q^{58} - 8 q^{62} + 4 q^{63} + 56 q^{65} - 8 q^{66} + 32 q^{67} + 8 q^{68} - 28 q^{70} + 16 q^{71} - 20 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 40 q^{77} - 56 q^{79} - 32 q^{81} + 16 q^{82} + 72 q^{83} - 32 q^{85} + 20 q^{87} - 4 q^{88} - 64 q^{89} - 8 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 + 4 * q^15 - 32 * q^16 + 8 * q^17 - 4 * q^22 - 32 * q^24 + 8 * q^25 + 4 * q^28 + 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 + 4 * q^37 + 16 * q^38 - 16 * q^41 + 4 * q^42 - 16 * q^43 - 8 * q^44 - 8 * q^47 - 16 * q^50 - 24 * q^53 - 32 * q^54 - 28 * q^55 + 16 * q^57 + 20 * q^58 - 8 * q^62 + 4 * q^63 + 56 * q^65 - 8 * q^66 + 32 * q^67 + 8 * q^68 - 28 * q^70 + 16 * q^71 - 20 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 40 * q^77 - 56 * q^79 - 32 * q^81 + 16 * q^82 + 72 * q^83 - 32 * q^85 + 20 * q^87 - 4 * q^88 - 64 * q^89 - 8 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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