LMFDB - Embedded newform 45.2.l.a.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$45 = 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	45.l (of order $12$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1$ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.2
Root			$1.60599 - 0.430324i$ of defining polynomial
Character	$\chi$	$=$	45.32
Dual form			45.2.l.a.38.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60599 - 0.430324i) q^{2} +(-1.08121 - 1.35314i) q^{3} +(0.661975 + 0.382191i) q^{4} +(-1.24906 - 1.85468i) q^{5} +(1.15412 + 2.63840i) q^{6} +(0.465559 - 1.73749i) q^{7} +(1.45267 + 1.45267i) q^{8} +(-0.661975 + 2.92605i) q^{9} +(1.20786 + 3.51610i) q^{10} +(3.12636 - 1.80501i) q^{11} +(-0.198575 - 1.30897i) q^{12} +(0.342574 + 1.27850i) q^{13} +(-1.49537 + 2.59005i) q^{14} +(-1.15916 + 3.69545i) q^{15} +(-2.47224 - 4.28205i) q^{16} +(-0.277007 + 0.277007i) q^{17} +(2.32228 - 4.41435i) q^{18} -6.25273i q^{19} +(-0.118000 - 1.70513i) q^{20} +(-2.85443 + 1.24862i) q^{21} +(-5.79765 + 1.55348i) q^{22} +(2.16347 - 0.579699i) q^{23} +(0.395027 - 3.53631i) q^{24} +(-1.87971 + 4.63322i) q^{25} -2.20068i q^{26} +(4.67509 - 2.26793i) q^{27} +(0.972242 - 0.972242i) q^{28} +(1.56832 + 2.71642i) q^{29} +(3.45183 - 5.43605i) q^{30} +(-2.42605 + 4.20205i) q^{31} +(1.06430 + 3.97202i) q^{32} +(-5.82268 - 2.27882i) q^{33} +(0.564074 - 0.325668i) q^{34} +(-3.80401 + 1.30676i) q^{35} +(-1.55652 + 1.68397i) q^{36} +(5.55242 + 5.55242i) q^{37} +(-2.69070 + 10.0418i) q^{38} +(1.35960 - 1.84588i) q^{39} +(0.879778 - 4.50872i) q^{40} +(1.29036 + 0.744991i) q^{41} +(5.12150 - 0.776946i) q^{42} +(4.10976 + 1.10121i) q^{43} +2.75943 q^{44} +(6.25375 - 2.42705i) q^{45} -3.72396 q^{46} +(-3.82042 - 1.02368i) q^{47} +(-3.12120 + 7.97508i) q^{48} +(3.26005 + 1.88219i) q^{49} +(5.01258 - 6.63202i) q^{50} +(0.674332 + 0.0753268i) q^{51} +(-0.261857 + 0.977265i) q^{52} +(-7.48222 - 7.48222i) q^{53} +(-8.48410 + 1.63047i) q^{54} +(-7.25273 - 3.54386i) q^{55} +(3.20031 - 1.84770i) q^{56} +(-8.46082 + 6.76051i) q^{57} +(-1.34977 - 5.03742i) q^{58} +(-0.279377 + 0.483896i) q^{59} +(-2.17970 + 2.00328i) q^{60} +(-2.96237 - 5.13097i) q^{61} +(5.70446 - 5.70446i) q^{62} +(4.77580 + 2.51243i) q^{63} +3.05196i q^{64} +(1.94332 - 2.23229i) q^{65} +(8.37054 + 6.16540i) q^{66} +(10.8351 - 2.90325i) q^{67} +(-0.289242 + 0.0775020i) q^{68} +(-3.12357 - 2.30070i) q^{69} +(6.67153 - 0.461690i) q^{70} +8.01611i q^{71} +(-5.21223 + 3.28897i) q^{72} +(-1.29315 + 1.29315i) q^{73} +(-6.52779 - 11.3065i) q^{74} +(8.30175 - 2.46596i) q^{75} +(2.38974 - 4.13915i) q^{76} +(-1.68068 - 6.27237i) q^{77} +(-2.97783 + 2.37939i) q^{78} +(-6.96917 + 4.02365i) q^{79} +(-4.85388 + 9.93376i) q^{80} +(-8.12358 - 3.87395i) q^{81} +(-1.75172 - 1.75172i) q^{82} +(-0.150243 + 0.560714i) q^{83} +(-2.36678 - 0.264383i) q^{84} +(0.859759 + 0.167763i) q^{85} +(-6.12636 - 3.53706i) q^{86} +(1.98001 - 5.05917i) q^{87} +(7.16367 + 1.91950i) q^{88} +16.4343 q^{89} +(-11.0879 + 1.20669i) q^{90} +2.38087 q^{91} +(1.65372 + 0.443112i) q^{92} +(8.30903 - 1.26050i) q^{93} +(5.69504 + 3.28804i) q^{94} +(-11.5968 + 7.81002i) q^{95} +(4.22396 - 5.73472i) q^{96} +(-1.37786 + 5.14224i) q^{97} +(-4.42566 - 4.42566i) q^{98} +(3.21197 + 10.3428i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} - 8 q^{10} - 6 q^{12} - 2 q^{13} - 6 q^{15} - 8 q^{16} + 36 q^{18} + 18 q^{20} - 12 q^{21} - 10 q^{22} + 18 q^{23} + 4 q^{25} + 18 q^{27} - 16 q^{28} + 30 q^{30}+ \cdots + 28 q^{97}+O(q^{100})$ 16 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7 - 8 * q^10 - 6 * q^12 - 2 * q^13 - 6 * q^15 - 8 * q^16 + 36 * q^18 + 18 * q^20 - 12 * q^21 - 10 * q^22 + 18 * q^23 + 4 * q^25 + 18 * q^27 - 16 * q^28 + 30 * q^30 - 4 * q^31 + 30 * q^32 - 12 * q^33 - 48 * q^36 + 4 * q^37 - 30 * q^38 + 6 * q^40 - 24 * q^41 + 6 * q^42 - 2 * q^43 - 36 * q^45 + 32 * q^46 - 12 * q^47 - 30 * q^48 - 54 * q^50 + 36 * q^51 - 14 * q^52 - 16 * q^55 + 36 * q^56 - 6 * q^57 - 6 * q^58 + 18 * q^60 + 8 * q^61 + 36 * q^63 + 66 * q^65 + 36 * q^66 + 4 * q^67 + 42 * q^68 + 18 * q^70 + 18 * q^72 - 8 * q^73 + 42 * q^75 + 24 * q^76 - 6 * q^77 - 42 * q^78 - 48 * q^81 + 32 * q^82 - 66 * q^83 + 22 * q^85 - 48 * q^86 - 18 * q^87 + 18 * q^88 - 66 * q^90 - 40 * q^91 - 60 * q^92 - 18 * q^93 - 36 * q^95 - 24 * q^96 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$ .

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	−1.60599	−	0.430324i	−1.13561	−	0.304285i	−0.358423	−	0.933559i	$-0.616686\pi$
$2$	−1.60599	−	0.430324i	−1.13561	−	0.304285i	−0.777183	+	0.629274i	$0.783352\pi$
$3$	−1.08121	−	1.35314i	−0.624236	−	0.781236i
$3$	−1.08121	−	1.35314i	−0.624236	−	0.781236i
$4$	0.661975	+	0.382191i	0.330987	+	0.191096i
$5$	−1.24906	−	1.85468i	−0.558596	−	0.829440i
$5$	−1.24906	−	1.85468i	−0.558596	−	0.829440i
$6$	1.15412	+	2.63840i	0.471169	+	1.07712i
$7$	0.465559	−	1.73749i	0.175965	−	0.656710i	−0.820421	−	0.571761i	$-0.806261\pi$
$7$	0.465559	−	1.73749i	0.175965	−	0.656710i	0.996385	−	0.0849489i	$-0.0270727\pi$
$8$	1.45267	+	1.45267i	0.513598	+	0.513598i
$9$	−0.661975	+	2.92605i	−0.220658	+	0.975351i
$10$	1.20786	+	3.51610i	0.381959	+	1.11189i
$11$	3.12636	−	1.80501i	0.942634	−	0.544230i	0.0518493	−	0.998655i	$-0.483488\pi$
$11$	3.12636	−	1.80501i	0.942634	−	0.544230i	0.890785	+	0.454425i	$0.150155\pi$
$12$	−0.198575	−	1.30897i	−0.0573236	−	0.377868i
$13$	0.342574	+	1.27850i	0.0950128	+	0.354593i	0.997021	−	0.0771255i	$-0.0245742\pi$
$13$	0.342574	+	1.27850i	0.0950128	+	0.354593i	−0.902009	+	0.431718i	$0.857908\pi$
$14$	−1.49537	+	2.59005i	−0.399654	+	0.692220i
$15$	−1.15916	+	3.69545i	−0.299293	+	0.954161i
$16$	−2.47224	−	4.28205i	−0.618061	−	1.07051i
$17$	−0.277007	+	0.277007i	−0.0671841	+	0.0671841i	−0.739900	−	0.672716i	$-0.765127\pi$
$17$	−0.277007	+	0.277007i	−0.0671841	+	0.0671841i	0.672716	+	0.739900i	$0.265127\pi$
$18$	2.32228	−	4.41435i	0.547366	−	1.04047i
$19$		−	6.25273i		−	1.43447i	−0.696829	−	0.717237i	$-0.745406\pi$
$19$		−	6.25273i		−	1.43447i	0.696829	−	0.717237i	$-0.254594\pi$
$20$	−0.118000	−	1.70513i	−0.0263857	−	0.381280i
$21$	−2.85443	+	1.24862i	−0.622889	+	0.272472i
$22$	−5.79765	+	1.55348i	−1.23606	+	0.331202i
$23$	2.16347	−	0.579699i	0.451114	−	0.120876i	−0.0261067	−	0.999659i	$-0.508311\pi$
$23$	2.16347	−	0.579699i	0.451114	−	0.120876i	0.477221	+	0.878784i	$0.341644\pi$
$24$	0.395027	−	3.53631i	0.0806346	−	0.721847i
$25$	−1.87971	+	4.63322i	−0.375942	+	0.926643i
$26$		−	2.20068i		−	0.431589i
$27$	4.67509	−	2.26793i	0.899722	−	0.436463i
$28$	0.972242	−	0.972242i	0.183737	−	0.183737i
$29$	1.56832	+	2.71642i	0.291230	+	0.504426i	0.974101	−	0.226114i	$-0.0726021\pi$
$29$	1.56832	+	2.71642i	0.291230	+	0.504426i	−0.682871	+	0.730539i	$0.739269\pi$
$30$	3.45183	−	5.43605i	0.630216	−	0.992482i
$31$	−2.42605	+	4.20205i	−0.435732	+	0.754710i	−0.997355	−	0.0726832i	$-0.976844\pi$
$31$	−2.42605	+	4.20205i	−0.435732	+	0.754710i	0.561623	+	0.827393i	$0.310177\pi$
$32$	1.06430	+	3.97202i	0.188143	+	0.702160i
$33$	−5.82268	−	2.27882i	−1.01360	−	0.396691i
$34$	0.564074	−	0.325668i	0.0967378	−	0.0558516i
$35$	−3.80401	+	1.30676i	−0.642994	+	0.220883i
$36$	−1.55652	+	1.68397i	−0.259421	+	0.280662i
$37$	5.55242	+	5.55242i	0.912812	+	0.912812i	0.996493	−	0.0836807i	$-0.0266676\pi$
$37$	5.55242	+	5.55242i	0.912812	+	0.912812i	−0.0836807	+	0.996493i	$0.526668\pi$
$38$	−2.69070	+	10.0418i	−0.436489	+	1.62900i
$39$	1.35960	−	1.84588i	0.217710	−	0.295577i
$40$	0.879778	−	4.50872i	0.139105	−	0.712892i
$41$	1.29036	+	0.744991i	0.201521	+	0.116348i	0.597365	−	0.801970i	$-0.296215\pi$
$41$	1.29036	+	0.744991i	0.201521	+	0.116348i	−0.395844	+	0.918318i	$0.629548\pi$
$42$	5.12150	−	0.776946i	0.790265	−	0.119885i
$43$	4.10976	+	1.10121i	0.626733	+	0.167933i	0.558187	−	0.829715i	$-0.311497\pi$
$43$	4.10976	+	1.10121i	0.626733	+	0.167933i	0.0685463	+	0.997648i	$0.478164\pi$
$44$	2.75943			0.416000
$45$	6.25375	−	2.42705i	0.932254	−	0.361804i
$46$	−3.72396			−0.549069
$47$	−3.82042	−	1.02368i	−0.557266	−	0.149319i	−0.0308158	−	0.999525i	$-0.509811\pi$
$47$	−3.82042	−	1.02368i	−0.557266	−	0.149319i	−0.526450	+	0.850206i	$0.676477\pi$
$48$	−3.12120	+	7.97508i	−0.450507	+	1.15110i
$49$	3.26005	+	1.88219i	0.465722	+	0.268884i
$50$	5.01258	−	6.63202i	0.708886	−	0.937909i
$51$	0.674332	+	0.0753268i	0.0944254	+	0.0105479i
$52$	−0.261857	+	0.977265i	−0.0363131	+	0.135522i
$53$	−7.48222	−	7.48222i	−1.02776	−	1.02776i	−0.999603	−	0.0281581i	$-0.991036\pi$
$53$	−7.48222	−	7.48222i	−1.02776	−	1.02776i	−0.0281581	−	0.999603i	$-0.508964\pi$
$54$	−8.48410	+	1.63047i	−1.15454	+	0.221879i
$55$	−7.25273	−	3.54386i	−0.977958	−	0.477854i
$56$	3.20031	−	1.84770i	0.427660	−	0.246909i
$57$	−8.46082	+	6.76051i	−1.12066	+	0.895451i
$58$	−1.34977	−	5.03742i	−0.177234	−	0.661446i
$59$	−0.279377	+	0.483896i	−0.0363718	+	0.0629978i	−0.883638	−	0.468170i	$-0.844913\pi$
$59$	−0.279377	+	0.483896i	−0.0363718	+	0.0629978i	0.847266	+	0.531168i	$0.178247\pi$
$60$	−2.17970	+	2.00328i	−0.281398	+	0.258622i
$61$	−2.96237	−	5.13097i	−0.379292	−	0.656953i	0.611667	−	0.791115i	$-0.290499\pi$
$61$	−2.96237	−	5.13097i	−0.379292	−	0.656953i	−0.990959	+	0.134162i	$0.957166\pi$
$62$	5.70446	−	5.70446i	0.724467	−	0.724467i
$63$	4.77580	+	2.51243i	0.601694	+	0.316536i
$64$			3.05196i			0.381495i
$65$	1.94332	−	2.23229i	0.241040	−	0.276881i
$66$	8.37054	+	6.16540i	1.03034	+	0.758908i
$67$	10.8351	−	2.90325i	1.32371	−	0.354688i	0.473346	−	0.880876i	$-0.343046\pi$
$67$	10.8351	−	2.90325i	1.32371	−	0.354688i	0.850368	+	0.526188i	$0.176379\pi$
$68$	−0.289242	+	0.0775020i	−0.0350757	+	0.00939850i
$69$	−3.12357	−	2.30070i	−0.376034	−	0.276971i
$70$	6.67153	−	0.461690i	0.797400	−	0.0551825i
$71$			8.01611i			0.951338i	0.879624	+	0.475669i	$0.157794\pi$
$71$			8.01611i			0.951338i	−0.879624	+	0.475669i	$0.842206\pi$
$72$	−5.21223	+	3.28897i	−0.614268	+	0.387608i
$73$	−1.29315	+	1.29315i	−0.151352	+	0.151352i	−0.778721	−	0.627370i	$-0.784131\pi$
$73$	−1.29315	+	1.29315i	−0.151352	+	0.151352i	0.627370	+	0.778721i	$0.284131\pi$
$74$	−6.52779	−	11.3065i	−0.758840	−	1.31435i
$75$	8.30175	−	2.46596i	0.958603	−	0.284745i
$76$	2.38974	−	4.13915i	0.274122	−	0.474793i
$77$	−1.68068	−	6.27237i	−0.191531	−	0.714802i
$78$	−2.97783	+	2.37939i	−0.337172	+	0.269413i
$79$	−6.96917	+	4.02365i	−0.784093	+	0.452696i	−0.837879	−	0.545856i	$-0.816204\pi$
$79$	−6.96917	+	4.02365i	−0.784093	+	0.452696i	0.0537859	+	0.998552i	$0.482871\pi$
$80$	−4.85388	+	9.93376i	−0.542680	+	1.11063i
$81$	−8.12358	−	3.87395i	−0.902620	−	0.430439i
$82$	−1.75172	−	1.75172i	−0.193445	−	0.193445i
$83$	−0.150243	+	0.560714i	−0.0164913	+	0.0615463i	−0.973681	−	0.227914i	$-0.926809\pi$
$83$	−0.150243	+	0.560714i	−0.0164913	+	0.0615463i	0.957190	+	0.289461i	$0.0934760\pi$
$84$	−2.36678	−	0.264383i	−0.258237	−	0.0288465i
$85$	0.859759	+	0.167763i	0.0932539	+	0.0181965i
$86$	−6.12636	−	3.53706i	−0.660623	−	0.381411i
$87$	1.98001	−	5.05917i	0.212279	−	0.542400i
$88$	7.16367	+	1.91950i	0.763650	+	0.204619i
$89$	16.4343			1.74203			0.871016	−	0.491255i	$-0.163462\pi$
$89$	16.4343			1.74203			0.871016	+	0.491255i	$0.163462\pi$
$90$	−11.0879	+	1.20669i	−1.16877	+	0.127196i
$91$	2.38087			0.249583
$92$	1.65372	+	0.443112i	0.172412	+	0.0461976i
$93$	8.30903	−	1.26050i	0.861606	−	0.130708i
$94$	5.69504	+	3.28804i	0.587399	+	0.339135i
$95$	−11.5968	+	7.81002i	−1.18981	+	0.801291i
$96$	4.22396	−	5.73472i	0.431106	−	0.585298i
$97$	−1.37786	+	5.14224i	−0.139900	+	0.522116i	0.860029	+	0.510245i	$0.170445\pi$
$97$	−1.37786	+	5.14224i	−0.139900	+	0.522116i	−0.999930	+	0.0118706i	$0.996221\pi$
$98$	−4.42566	−	4.42566i	−0.447059	−	0.447059i
$99$	3.21197	+	10.3428i	0.322815	+	1.03949i
$100$	−3.01510	+	2.34866i	−0.301510	+	0.234866i
$101$	−4.73008	+	2.73092i	−0.470661	+	0.271736i	−0.716516	−	0.697570i	$-0.754265\pi$
$101$	−4.73008	+	2.73092i	−0.470661	+	0.271736i	0.245855	+	0.969307i	$0.420931\pi$
$102$	−1.05056	−	0.411155i	−0.104021	−	0.0407104i
$103$	−1.34888	−	5.03410i	−0.132909	−	0.496024i	0.867088	−	0.498154i	$-0.165989\pi$
$103$	−1.34888	−	5.03410i	−0.132909	−	0.496024i	−0.999998	+	0.00212995i	$0.999322\pi$
$104$	−1.35960	+	2.35489i	−0.133320	+	0.230916i
$105$	5.88115	+	3.73447i	0.573942	+	0.364447i
$106$	8.79659	+	15.2361i	0.854401	+	1.47987i
$107$	−4.07498	+	4.07498i	−0.393944	+	0.393944i	−0.876090	−	0.482147i	$-0.839857\pi$
$107$	−4.07498	+	4.07498i	−0.393944	+	0.393944i	0.482147	+	0.876090i	$0.339857\pi$
$108$	3.96158	+	0.285467i	0.381203	+	0.0274691i
$109$		−	1.10747i		−	0.106077i	−0.998592	−	0.0530384i	$-0.983109\pi$
$109$		−	1.10747i		−	0.106077i	0.998592	−	0.0530384i	$-0.0168906\pi$
$110$	10.1228	+	8.81243i	0.965171	+	0.840232i
$111$	1.50987	−	13.5165i	0.143311	−	1.28293i
$112$	−8.59099	+	2.30195i	−0.811773	+	0.217514i
$113$	8.06067	−	2.15985i	0.758284	−	0.203182i	0.141095	−	0.989996i	$-0.454938\pi$
$113$	8.06067	−	2.15985i	0.758284	−	0.203182i	0.617190	+	0.786815i	$0.288271\pi$
$114$	16.4972	−	7.21642i	1.54510	−	0.675879i
$115$	−3.77745	−	3.28847i	−0.352249	−	0.306651i
$116$			2.39760i			0.222611i
$117$	−3.96774	+	0.156052i	−0.366818	+	0.0144270i
$118$	0.656909	−	0.656909i	0.0604734	−	0.0604734i
$119$	0.352334	+	0.610260i	0.0322984	+	0.0559425i
$120$	−7.05216	+	3.68441i	−0.643771	+	0.336339i
$121$	1.01610	−	1.75994i	0.0923731	−	0.159995i
$122$	2.54955	+	9.51507i	0.230826	+	0.861454i
$123$	−0.387074	−	2.55153i	−0.0349013	−	0.230064i
$124$	−3.21197	+	1.85443i	−0.288444	+	0.166533i
$125$	10.9410	−	2.30088i	0.978595	−	0.205797i
$126$	−6.58873	−	6.09007i	−0.586971	−	0.542547i
$127$	−11.5887	−	11.5887i	−1.02833	−	1.02833i	−0.999587	−	0.0287470i	$-0.990848\pi$
$127$	−11.5887	−	11.5887i	−1.02833	−	1.02833i	−0.0287470	−	0.999587i	$-0.509152\pi$
$128$	3.44193	−	12.8454i	0.304226	−	1.13539i
$129$	−2.95342	−	6.75172i	−0.260035	−	0.594456i
$130$	−4.08157	+	2.74878i	−0.357977	+	0.241084i
$131$	4.34401	+	2.50802i	0.379538	+	0.219126i	0.677617	−	0.735415i	$-0.263013\pi$
$131$	4.34401	+	2.50802i	0.379538	+	0.219126i	−0.298079	+	0.954541i	$0.596346\pi$
$132$	−2.98352	−	3.73390i	−0.259682	−	0.324994i
$133$	−10.8641	−	2.91101i	−0.942033	−	0.252417i
$134$	−18.6504			−1.61115
$135$	−10.0458	−	5.83805i	−0.864601	−	0.502459i
$136$	−0.804802			−0.0690112
$137$	−0.440837	−	0.118122i	−0.0376632	−	0.0100918i	0.239938	−	0.970788i	$-0.422873\pi$
$137$	−0.440837	−	0.118122i	−0.0376632	−	0.0100918i	−0.277601	+	0.960696i	$0.589539\pi$
$138$	4.02638	+	5.03904i	0.342748	+	0.428952i
$139$	−13.8860	−	8.01711i	−1.17780	−	0.680003i	−0.222295	−	0.974980i	$-0.571355\pi$
$139$	−13.8860	−	8.01711i	−1.17780	−	0.680003i	−0.955504	+	0.294977i	$0.904688\pi$
$140$	−3.01759	−	0.588816i	−0.255033	−	0.0497640i
$141$	2.74549	+	6.27637i	0.231212	+	0.528566i
$142$	3.44952	−	12.8738i	0.289478	−	1.08035i
$143$	3.37872	+	3.37872i	0.282542	+	0.282542i
$144$	14.1661	−	4.39930i	1.18051	−	0.366609i
$145$	3.07917	−	6.30170i	0.255711	−	0.523328i
$146$	2.63326	−	1.52031i	0.217930	−	0.125822i
$147$	−0.977928	−	6.44635i	−0.0806581	−	0.531686i
$148$	1.55348	+	5.79765i	0.127695	+	0.476564i
$149$	−3.44153	+	5.96090i	−0.281941	+	0.488336i	−0.971863	−	0.235548i	$-0.924312\pi$
$149$	−3.44153	+	5.96090i	−0.281941	+	0.488336i	0.689922	+	0.723884i	$0.257645\pi$
$150$	−14.3937	+	0.387874i	−1.17524	+	0.0316698i
$151$	4.30647	+	7.45902i	0.350455	+	0.607006i	0.986329	−	0.164787i	$-0.0526935\pi$
$151$	4.30647	+	7.45902i	0.350455	+	0.607006i	−0.635874	+	0.771793i	$0.719360\pi$
$152$	9.08317	−	9.08317i	0.736743	−	0.736743i
$153$	−0.627166	−	0.993910i	−0.0507034	−	0.0803528i
$154$			10.7966i			0.870014i
$155$	10.8238	−	0.749036i	0.869385	−	0.0601640i
$156$	1.60550	−	0.702298i	0.128543	−	0.0562288i
$157$	−1.60930	+	0.431209i	−0.128436	+	0.0344142i	−0.322464	−	0.946582i	$-0.604511\pi$
$157$	−1.60930	+	0.431209i	−0.128436	+	0.0344142i	0.194029	+	0.980996i	$0.437845\pi$
$158$	12.9239	−	3.46295i	1.02817	−	0.275497i
$159$	−2.03465	+	18.2143i	−0.161358	+	1.44449i
$160$	6.03747	−	6.93521i	0.477304	−	0.548277i
$161$		−	4.02889i		−	0.317521i
$162$	11.3793	+	9.71729i	0.894045	+	0.763463i
$163$	−10.5120	+	10.5120i	−0.823363	+	0.823363i	−0.986589	−	0.163225i	$-0.947810\pi$
$163$	−10.5120	+	10.5120i	−0.823363	+	0.823363i	0.163225	+	0.986589i	$0.447810\pi$
$164$	0.569458	+	0.986331i	0.0444672	+	0.0770195i
$165$	3.04637	+	13.6456i	0.237160	+	1.06231i
$166$	0.482577	−	0.835848i	0.0374552	−	0.0648744i
$167$	2.51657	+	9.39195i	0.194738	+	0.726771i	0.992335	+	0.123580i	$0.0394376\pi$
$167$	2.51657	+	9.39195i	0.194738	+	0.726771i	−0.797597	+	0.603191i	$0.793896\pi$
$168$	−5.96040	−	2.33272i	−0.459855	−	0.179973i
$169$	9.74112	−	5.62404i	0.749317	−	0.432618i
$170$	−1.30857	−	0.639400i	−0.100363	−	0.0490398i
$171$	18.2958	+	4.13915i	1.39912	+	0.316529i
$172$	2.29969	+	2.29969i	0.175350	+	0.175350i
$173$	−3.88335	+	14.4929i	−0.295246	+	1.10187i	0.645776	+	0.763527i	$0.276534\pi$
$173$	−3.88335	+	14.4929i	−0.295246	+	1.10187i	−0.941022	+	0.338346i	$0.890133\pi$
$174$	−5.35695	+	7.27294i	−0.406109	+	0.551360i
$175$	7.17505	+	5.42301i	0.542383	+	0.409941i
$176$	−15.4583	−	8.92483i	−1.16521	−	0.672735i
$177$	0.956844	−	0.145156i	0.0719208	−	0.0109106i
$178$	−26.3933	−	7.07207i	−1.97826	−	0.530074i
$179$	−4.21995			−0.315414			−0.157707	−	0.987486i	$-0.550410\pi$
$179$	−4.21995			−0.315414			−0.157707	+	0.987486i	$0.550410\pi$
$180$	5.06743	+	0.783481i	0.377704	+	0.0583972i
$181$	23.7930			1.76852			0.884261	−	0.466993i	$-0.154663\pi$
$181$	23.7930			1.76852			0.884261	+	0.466993i	$0.154663\pi$
$182$	−3.82366	−	1.02455i	−0.283428	−	0.0759444i
$183$	−3.73998	+	9.55615i	−0.276468	+	0.706411i
$184$	3.98492	+	2.30070i	0.293772	+	0.169610i
$185$	3.36269	−	17.2333i	0.247230	−	1.26702i
$186$	−13.8866	−	1.55122i	−1.01822	−	0.113741i
$187$	−0.366025	+	1.36603i	−0.0267664	+	0.0998937i
$188$	−2.13778	−	2.13778i	−0.155914	−	0.155914i
$189$	−1.76397	−	9.17878i	−0.128310	−	0.667658i
$190$	21.9852	−	7.55242i	1.59498	−	0.547910i
$191$	−20.1545	+	11.6362i	−1.45833	+	0.841965i	−0.998929	−	0.0462661i	$-0.985268\pi$
$191$	−20.1545	+	11.6362i	−1.45833	+	0.841965i	−0.459397	+	0.888231i	$0.651934\pi$
$192$	4.12973	−	3.29980i	0.298037	−	0.238143i
$193$	5.36663	+	20.0285i	0.386299	+	1.44169i	0.836110	+	0.548562i	$0.184825\pi$
$193$	5.36663	+	20.0285i	0.386299	+	1.44169i	−0.449811	+	0.893124i	$0.648509\pi$
$194$	4.42566	−	7.66547i	0.317744	−	0.550348i
$195$	−5.12174	−	0.216019i	−0.366775	−	0.0154694i
$196$	1.43871	+	2.49193i	0.102765	+	0.177995i
$197$	−6.52613	+	6.52613i	−0.464968	+	0.464968i	−0.900280	−	0.435312i	$-0.856638\pi$
$197$	−6.52613	+	6.52613i	−0.464968	+	0.464968i	0.435312	+	0.900280i	$0.356638\pi$
$198$	−0.707653	−	17.9926i	−0.0502907	−	1.27868i
$199$			4.03778i			0.286231i	0.989706	+	0.143115i	$0.0457120\pi$
$199$			4.03778i			0.286231i	−0.989706	+	0.143115i	$0.954288\pi$
$200$	−9.46116	+	3.99995i	−0.669005	+	0.282839i
$201$	−15.6435	−	11.5223i	−1.10341	−	0.812724i
$202$	8.77165	−	2.35036i	0.617171	−	0.165370i
$203$	5.44989	−	1.46029i	0.382507	−	0.102493i
$204$	0.417602	+	0.307588i	0.0292380	+	0.0215355i
$205$	−0.230013	−	3.32375i	−0.0160648	−	0.232141i
$206$			8.66517i			0.603731i
$207$	0.264070	+	6.71416i	0.0183541	+	0.466667i
$208$	4.62768	−	4.62768i	0.320872	−	0.320872i
$209$	−11.2862	−	19.5483i	−0.780684	−	1.35219i
$210$	−7.83804	−	8.52833i	−0.540876	−	0.588510i
$211$	0.653114	−	1.13123i	0.0449623	−	0.0778769i	−0.842668	−	0.538433i	$-0.819017\pi$
$211$	0.653114	−	1.13123i	0.0449623	−	0.0778769i	0.887631	+	0.460556i	$0.152350\pi$
$212$	−2.09340	−	7.81268i	−0.143775	−	0.536577i
$213$	10.8469	−	8.66709i	0.743219	−	0.593859i
$214$	8.29795	−	4.79082i	0.567236	−	0.327494i
$215$	−3.09094	−	8.99779i	−0.210800	−	0.613644i
$216$	10.0859	+	3.49682i	0.686262	+	0.237929i
$217$	6.17155	+	6.17155i	0.418952	+	0.418952i
$218$	−0.476572	+	1.77859i	−0.0322776	+	0.120461i
$219$	3.14797	+	0.351647i	0.212720	+	0.0237621i
$220$	−3.44669	−	5.11788i	−0.232376	−	0.345047i
$221$	−0.449050	−	0.259259i	−0.0302063	−	0.0174396i
$222$	−8.24132	+	21.0577i	−0.553122	+	1.41330i
$223$	8.01142	+	2.14665i	0.536485	+	0.143751i	0.516881	−	0.856057i	$-0.327093\pi$
$223$	8.01142	+	2.14665i	0.536485	+	0.143751i	0.0196035	+	0.999808i	$0.493760\pi$
$224$	7.39683			0.494222
$225$	−12.3127	−	8.56720i	−0.820848	−	0.571147i
$226$	−13.8748			−0.922937
$227$	8.90739	+	2.38673i	0.591204	+	0.158413i	0.542003	−	0.840376i	$-0.317666\pi$
$227$	8.90739	+	2.38673i	0.591204	+	0.158413i	0.0492007	+	0.998789i	$0.484333\pi$
$228$	−8.18466	+	1.24163i	−0.542042	+	0.0822292i
$229$	−17.2032	−	9.93228i	−1.13682	−	0.656344i	−0.191179	−	0.981555i	$-0.561231\pi$
$229$	−17.2032	−	9.93228i	−1.13682	−	0.656344i	−0.945641	+	0.325211i	$0.894565\pi$
$230$	4.65145	+	6.90678i	0.306707	+	0.455419i
$231$	−6.67023	+	9.05593i	−0.438869	+	0.595836i
$232$	−1.66780	+	6.22433i	−0.109497	+	0.408647i
$233$	−5.45304	−	5.45304i	−0.357241	−	0.357241i	0.505554	−	0.862795i	$-0.331288\pi$
$233$	−5.45304	−	5.45304i	−0.357241	−	0.357241i	−0.862795	+	0.505554i	$0.831288\pi$
$234$	6.43930	+	1.45679i	0.420951	+	0.0952336i
$235$	2.87332	+	8.36431i	0.187435	+	0.545627i
$236$	−0.369882	+	0.213551i	−0.0240772	+	0.0139010i
$237$	12.9797	+	5.07985i	0.843122	+	0.329972i
$238$	−0.303235	−	1.13169i	−0.0196558	−	0.0733566i
$239$	3.48185	−	6.03074i	0.225222	−	0.390096i	−0.731164	−	0.682202i	$-0.761023\pi$
$239$	3.48185	−	6.03074i	0.225222	−	0.390096i	0.956386	+	0.292106i	$0.0943559\pi$
$240$	18.6898	−	4.17249i	1.20642	−	0.269333i
$241$	−11.7660	−	20.3794i	−0.757918	−	1.31275i	−0.943911	−	0.330201i	$-0.892883\pi$
$241$	−11.7660	−	20.3794i	−0.757918	−	1.31275i	0.185993	−	0.982551i	$-0.440450\pi$
$242$	−2.38920	+	2.38920i	−0.153584	+	0.153584i
$243$	3.54129	+	15.1809i	0.227174	+	0.973854i
$244$		−	4.52877i		−	0.289925i
$245$	−0.581120	−	8.39733i	−0.0371264	−	0.536486i
$246$	−0.476347	+	4.26430i	−0.0303708	+	0.271882i
$247$	7.99413	−	2.14202i	0.508654	−	0.136293i
$248$	−9.62847	+	2.57994i	−0.611408	+	0.163826i
$249$	0.921168	−	0.402949i	0.0583767	−	0.0255359i
$250$	−18.5613	−	1.01298i	−1.17392	−	0.0640667i
$251$		−	20.7941i		−	1.31251i	−0.754537	−	0.656257i	$-0.772139\pi$
$251$		−	20.7941i		−	1.31251i	0.754537	−	0.656257i	$-0.227861\pi$
$252$	2.20123	+	3.48843i	0.138665	+	0.219751i
$253$	5.71742	−	5.71742i	0.359451	−	0.359451i
$254$	13.6245	+	23.5983i	0.854876	+	1.48069i
$255$	−0.702572	−	1.34476i	−0.0439968	−	0.0842122i
$256$	−8.00344	+	13.8624i	−0.500215	+	0.866398i
$257$	2.72001	+	10.1512i	0.169670	+	0.633216i	0.997398	+	0.0720873i	$0.0229660\pi$
$257$	2.72001	+	10.1512i	0.169670	+	0.633216i	−0.827729	+	0.561129i	$0.810367\pi$
$258$	1.83774	+	12.1141i	0.114413	+	0.754193i
$259$	12.2323	−	7.06229i	0.760075	−	0.438830i
$260$	2.13959	−	0.734997i	0.132692	−	0.0455826i
$261$	−8.98657	+	2.79080i	−0.556255	+	0.172746i
$262$	−5.89718	−	5.89718i	−0.364329	−	0.364329i
$263$	3.86662	−	14.4304i	0.238426	−	0.889818i	−0.738148	−	0.674638i	$-0.764300\pi$
$263$	3.86662	−	14.4304i	0.238426	−	0.889818i	0.976574	−	0.215180i	$-0.0690338\pi$
$264$	−5.14807	−	11.7688i	−0.316842	−	0.724322i
$265$	−4.53143	+	23.2229i	−0.278364	+	1.42657i
$266$	16.1949	+	9.35012i	0.992972	+	0.573293i
$267$	−17.7689	−	22.2379i	−1.08744	−	1.36094i
$268$	8.28214	+	2.21919i	0.505912	+	0.135559i
$269$	0.781994			0.0476790			0.0238395	−	0.999716i	$-0.492411\pi$
$269$	0.781994			0.0476790			0.0238395	+	0.999716i	$0.492411\pi$
$270$	13.6211	+	13.6988i	0.828956	+	0.833681i
$271$	−12.4677			−0.757357			−0.378679	−	0.925528i	$-0.623621\pi$
$271$	−12.4677			−0.757357			−0.378679	+	0.925528i	$0.623621\pi$
$272$	1.87099	+	0.501329i	0.113445	+	0.0303976i
$273$	−2.57422	−	3.22165i	−0.155799	−	0.194983i
$274$	0.657149	+	0.379405i	0.0396998	+	0.0229207i
$275$	2.48633	+	17.8780i	0.149931	+	1.07808i
$276$	−1.18842	−	2.71681i	−0.0715345	−	0.163533i
$277$	−2.43120	+	9.07336i	−0.146077	+	0.545165i	0.853629	+	0.520882i	$0.174397\pi$
$277$	−2.43120	+	9.07336i	−0.146077	+	0.545165i	−0.999705	+	0.0242830i	$0.992270\pi$
$278$	18.8509	+	18.8509i	1.13060	+	1.13060i
$279$	−10.6894	−	9.88041i	−0.639959	−	0.591525i
$280$	−7.42428	−	3.62768i	−0.443685	−	0.216796i
$281$	26.6024	−	15.3589i	1.58697	−	0.916237i	0.593165	−	0.805081i	$-0.297878\pi$
$281$	26.6024	−	15.3589i	1.58697	−	0.916237i	0.993803	−	0.111156i	$-0.0354553\pi$
$282$	−1.70836	−	11.2612i	−0.101731	−	0.670597i
$283$	−4.86835	−	18.1689i	−0.289393	−	1.08003i	−0.945569	−	0.325423i	$-0.894493\pi$
$283$	−4.86835	−	18.1689i	−0.289393	−	1.08003i	0.656175	−	0.754609i	$-0.272173\pi$
$284$	−3.06369	+	5.30647i	−0.181797	+	0.314881i
$285$	23.1067	+	7.24789i	1.36872	+	0.429328i
$286$	−3.97224	−	6.88013i	−0.234884	−	0.406830i
$287$	1.89515	−	1.89515i	0.111867	−	0.111867i
$288$	−12.3269	+	0.484819i	−0.726368	+	0.0285682i
$289$			16.8465i			0.990973i
$290$	−7.65689	+	8.79544i	−0.449628	+	0.516486i
$291$	8.44793	−	3.69540i	0.495226	−	0.216628i
$292$	−1.35026	+	0.361802i	−0.0790181	+	0.0211728i
$293$	−32.6486	+	8.74817i	−1.90735	+	0.511074i	−0.912588	+	0.408880i	$0.865919\pi$
$293$	−32.6486	+	8.74817i	−1.90735	+	0.511074i	−0.994765	+	0.102194i	$0.967414\pi$
$294$	−1.20347	+	10.7736i	−0.0701880	+	0.628329i
$295$	1.24643	−	0.0862568i	0.0725701	−	0.00502207i
$296$			16.1317i			0.937636i
$297$	10.5224	−	15.5290i	0.610572	−	0.901081i
$298$	8.09218	−	8.09218i	0.468767	−	0.468767i
$299$	1.48229	+	2.56741i	0.0857232	+	0.148477i
$300$	6.43802	+	1.54045i	0.371699	+	0.0889380i
$301$	3.82668	−	6.62800i	0.220566	−	0.382031i
$302$	−3.70635	−	13.8323i	−0.213276	−	0.795959i
$303$	8.80952	+	3.44778i	0.506094	+	0.198070i
$304$	−26.7745	+	15.4583i	−1.53562	+	0.886592i
$305$	−5.81616	+	11.9031i	−0.333033	+	0.681572i
$306$	0.579519	+	1.86609i	0.0331289	+	0.106677i
$307$	−2.26728	−	2.26728i	−0.129400	−	0.129400i	0.639440	−	0.768841i	$-0.279166\pi$
$307$	−2.26728	−	2.26728i	−0.129400	−	0.129400i	−0.768841	+	0.639440i	$0.779166\pi$
$308$	1.28468	−	4.79449i	0.0732014	−	0.273191i
$309$	−5.35341	+	7.26814i	−0.304545	+	0.413470i
$310$	−17.7052	−	3.45477i	−1.00559	−	0.196218i
$311$	−1.86689	−	1.07785i	−0.105862	−	0.0611193i	0.446134	−	0.894966i	$-0.352800\pi$
$311$	−1.86689	−	1.07785i	−0.105862	−	0.0611193i	−0.551996	+	0.833847i	$0.686134\pi$
$312$	4.65651	−	0.706405i	0.263623	−	0.0399923i
$313$	20.9905	+	5.62439i	1.18645	+	0.317909i	0.797483	−	0.603341i	$-0.206164\pi$
$313$	20.9905	+	5.62439i	1.18645	+	0.317909i	0.388971	+	0.921250i	$0.372831\pi$
$314$	2.77007			0.156324
$315$	−1.30549	−	11.9958i	−0.0735562	−	0.675885i
$316$	−6.15122			−0.346033
$317$	4.47853	+	1.20002i	0.251539	+	0.0673997i	0.382385	−	0.924003i	$-0.375103\pi$
$317$	4.47853	+	1.20002i	0.251539	+	0.0673997i	−0.130846	+	0.991403i	$0.541769\pi$
$318$	11.1057	−	28.3765i	0.622776	−	1.59127i
$319$	9.80630	+	5.66167i	0.549047	+	0.316993i
$320$	5.66042	−	3.81207i	0.316427	−	0.213101i
$321$	9.91993	+	1.10811i	0.553677	+	0.0618489i
$322$	−1.73373	+	6.47035i	−0.0966167	+	0.360579i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$	−3.89702	−	5.66922i	−0.216501	−	0.314957i
$325$	−6.56751	−	0.815995i	−0.364300	−	0.0452633i
$326$	21.4057	−	12.3586i	1.18555	−	0.684480i
$327$	−1.49857	+	1.19741i	−0.0828709	+	0.0662170i
$328$	0.792246	+	2.95670i	0.0437445	+	0.163257i
$329$	−3.55726	+	6.16136i	−0.196118	+	0.339687i
$330$	0.979585	−	23.2256i	0.0539244	−	1.27853i
$331$	14.5549	+	25.2097i	0.800007	+	1.38565i	0.919611	+	0.392831i	$0.128504\pi$
$331$	14.5549	+	25.2097i	0.800007	+	1.38565i	−0.119604	+	0.992822i	$0.538162\pi$
$332$	−0.313757	+	0.313757i	−0.0172197	+	0.0172197i
$333$	−19.9222	+	12.5711i	−1.09173	+	0.688893i
$334$		−	16.1663i		−	0.884582i
$335$	−18.9182	−	16.4693i	−1.03361	−	0.899815i
$336$	12.4035	+	9.13593i	0.676667	+	0.498406i
$337$	−24.1823	+	6.47963i	−1.31729	+	0.352968i	−0.847963	−	0.530055i	$-0.822171\pi$
$337$	−24.1823	+	6.47963i	−1.31729	+	0.352968i	−0.469330	+	0.883023i	$0.655505\pi$
$338$	−18.0643	+	4.84031i	−0.982568	+	0.263278i
$339$	−11.6378	−	8.57197i	−0.632081	−	0.465565i
$340$	0.505021	+	0.439647i	0.0273886	+	0.0238432i
$341$			17.5162i			0.948554i
$342$	−27.6017	−	14.5206i	−1.49253	−	0.785182i
$343$	13.6916	−	13.6916i	0.739274	−	0.739274i
$344$	4.37045	+	7.56984i	0.235639	+	0.408138i
$345$	−0.365544	+	8.66695i	−0.0196802	+	0.466613i
$346$	12.4733	−	21.6043i	0.670566	−	1.16145i
$347$	−9.05260	−	33.7848i	−0.485969	−	1.81366i	−0.575657	−	0.817691i	$-0.695254\pi$
$347$	−9.05260	−	33.7848i	−0.485969	−	1.81366i	0.0896885	−	0.995970i	$-0.471413\pi$
$348$	3.24429	−	2.59231i	0.173912	−	0.138962i
$349$	17.0932	−	9.86876i	0.914978	−	0.528263i	0.0329483	−	0.999457i	$-0.489510\pi$
$349$	17.0932	−	9.86876i	0.914978	−	0.528263i	0.882029	+	0.471194i	$0.156177\pi$
$350$	−9.18941	−	11.7969i	−0.491195	−	0.630571i
$351$	4.50112	+	5.20018i	0.240252	+	0.277565i
$352$	10.4969	+	10.4969i	0.559487	+	0.559487i
$353$	−1.95875	+	7.31017i	−0.104254	+	0.389081i	−0.998259	−	0.0589749i	$-0.981217\pi$
$353$	−1.95875	+	7.31017i	−0.104254	+	0.389081i	0.894006	+	0.448056i	$0.147883\pi$
$354$	−1.59915	−	0.178634i	−0.0849936	−	0.00949429i
$355$	14.8674	−	10.0126i	0.789078	−	0.531413i
$356$	10.8791	+	6.28105i	0.576591	+	0.332895i
$357$	0.444821	−	1.13658i	0.0235424	−	0.0601540i
$358$	6.77720	+	1.81594i	0.358186	+	0.0959756i
$359$	8.47760			0.447430			0.223715	−	0.974655i	$-0.428181\pi$
$359$	8.47760			0.447430			0.223715	+	0.974655i	$0.428181\pi$
$360$	12.6104	+	5.55894i	0.664625	+	0.292982i
$361$	−20.0966			−1.05772
$362$	−38.2114	−	10.2387i	−2.00835	−	0.538135i
$363$	−3.48007	+	0.527936i	−0.182656	+	0.0277095i
$364$	1.57608	+	0.909949i	0.0826089	+	0.0476943i
$365$	4.01360	+	0.783166i	0.210081	+	0.0409928i
$366$	10.1186	−	13.7377i	0.528908	−	0.718080i
$367$	−2.12506	+	7.93083i	−0.110927	+	0.413986i	−0.998950	−	0.0458135i	$-0.985412\pi$
$367$	−2.12506	+	7.93083i	−0.110927	+	0.413986i	0.888023	+	0.459799i	$0.152079\pi$
$368$	−7.83091	−	7.83091i	−0.408215	−	0.408215i
$369$	−3.03407	+	3.28250i	−0.157947	+	0.170880i
$370$	−12.8163	+	26.2294i	−0.666290	+	1.36360i
$371$	−16.4837	+	9.51686i	−0.855791	+	0.494091i
$372$	5.98212	+	2.34122i	0.310159	+	0.121387i
$373$	−5.56939	−	20.7853i	−0.288372	−	1.07622i	−0.946340	−	0.323174i	$-0.895250\pi$
$373$	−5.56939	−	20.7853i	−0.288372	−	1.07622i	0.657967	−	0.753046i	$-0.271416\pi$
$374$	1.17567	−	2.03631i	0.0607923	−	0.105295i
$375$	−14.9429	−	12.3170i	−0.771650	−	0.636047i
$376$	−4.06275	−	7.03689i	−0.209520	−	0.362900i
$377$	−2.93568	+	2.93568i	−0.151195	+	0.151195i
$378$	−1.11692	+	15.5001i	−0.0574483	+	0.797240i
$379$			11.1614i			0.573325i	0.958032	+	0.286663i	$0.0925458\pi$
$379$			11.1614i			0.573325i	−0.958032	+	0.286663i	$0.907454\pi$
$380$	−10.6617	+	0.737824i	−0.546936	+	0.0378496i
$381$	−3.15134	+	28.2110i	−0.161448	+	1.44529i
$382$	37.3752	−	10.0147i	1.91228	−	0.512394i
$383$	14.6977	−	3.93824i	0.751018	−	0.201235i	0.137049	−	0.990564i	$-0.456238\pi$
$383$	14.6977	−	3.93824i	0.751018	−	0.201235i	0.613970	+	0.789330i	$0.289572\pi$
$384$	−21.1031	+	9.23120i	−1.07691	+	0.471078i
$385$	−9.53400	+	10.9517i	−0.485898	+	0.558149i
$386$		−	34.4750i		−	1.75473i
$387$	−5.94275	+	11.2964i	−0.302087	+	0.574229i
$388$	−2.87743	+	2.87743i	−0.146079	+	0.146079i
$389$	12.7395	+	22.0655i	0.645920	+	1.11877i	0.984088	+	0.177681i	$0.0568596\pi$
$389$	12.7395	+	22.0655i	0.645920	+	1.11877i	−0.338168	+	0.941086i	$0.609807\pi$
$390$	8.13250	+	2.55093i	0.411805	+	0.129171i
$391$	−0.438715	+	0.759876i	−0.0221868	+	0.0384286i
$392$	2.00158	+	7.47000i	0.101095	+	0.377292i
$393$	−1.30309	−	8.58974i	−0.0657320	−	0.433295i
$394$	13.2893	−	7.67255i	0.669503	−	0.386538i
$395$	16.1675	+	7.89984i	0.813475	+	0.397484i
$396$	−1.82668	+	8.07425i	−0.0917939	+	0.405746i
$397$	−5.96779	−	5.96779i	−0.299515	−	0.299515i	0.541309	−	0.840824i	$-0.317929\pi$
$397$	−5.96779	−	5.96779i	−0.299515	−	0.299515i	−0.840824	+	0.541309i	$0.817929\pi$
$398$	1.73755	−	6.48464i	0.0870957	−	0.325046i
$399$	7.80730	+	17.8480i	0.390854	+	0.893518i
$400$	24.4868	−	3.40542i	1.22434	−	0.170271i
$401$	23.6805	+	13.6719i	1.18255	+	0.682744i	0.956602	−	0.291396i	$-0.0941198\pi$
$401$	23.6805	+	13.6719i	1.18255	+	0.682744i	0.225945	+	0.974140i	$0.427453\pi$
$402$	20.1649	+	25.2365i	1.00574	+	1.25868i
$403$	−6.20343	−	1.66220i	−0.309015	−	0.0828003i
$404$	−4.17493			−0.207711
$405$	2.96187	+	19.9055i	0.147176	+	0.989110i
$406$	−9.38087			−0.465565
$407$	27.3810	+	7.33673i	1.35723	+	0.363668i
$408$	0.870159	+	1.08901i	0.0430793	+	0.0539140i
$409$	23.5441	+	13.5932i	1.16418	+	0.672140i	0.952302	−	0.305157i	$-0.0987088\pi$
$409$	23.5441	+	13.5932i	1.16418	+	0.672140i	0.211878	+	0.977296i	$0.432042\pi$
$410$	−1.06089	+	5.43689i	−0.0523936	+	0.268509i
$411$	0.316801	+	0.724228i	0.0156266	+	0.0357235i
$412$	1.03106	−	3.84798i	0.0507968	−	0.189576i
$413$	0.710697	+	0.710697i	0.0349711	+	0.0349711i
$414$	2.46517	−	10.8965i	0.121157	−	0.535535i
$415$	1.22761	−	0.421711i	0.0602610	−	0.0207010i
$416$	−4.71363	+	2.72142i	−0.231105	+	0.133428i
$417$	4.16544	+	27.4579i	0.203983	+	1.34462i
$418$	9.71346	+	36.2511i	0.475101	+	1.77310i
$419$	15.7018	−	27.1964i	0.767084	−	1.32863i	−0.172053	−	0.985088i	$-0.555040\pi$
$419$	15.7018	−	27.1964i	0.767084	−	1.32863i	0.939138	−	0.343541i	$-0.111627\pi$
$420$	2.46589	+	4.71985i	0.120323	+	0.230305i
$421$	−15.4328	−	26.7304i	−0.752150	−	1.30276i	−0.946779	−	0.321885i	$-0.895683\pi$
$421$	−15.4328	−	26.7304i	−0.752150	−	1.30276i	0.194629	−	0.980877i	$-0.437650\pi$
$422$	−1.53569	+	1.53569i	−0.0747562	+	0.0747562i
$423$	5.52436	−	10.5011i	0.268604	−	0.510581i
$424$		−	21.7384i		−	1.05571i
$425$	−0.762741	−	1.80413i	−0.0369984	−	0.0875130i
$426$	−21.1497	+	9.25158i	−1.02471	+	0.448240i
$427$	−10.2942	+	2.75831i	−0.498170	+	0.133484i
$428$	−4.25496	+	1.14011i	−0.205671	+	0.0551095i
$429$	0.918778	−	8.22497i	0.0443590	−	0.397105i
$430$	1.09206	+	15.7805i	0.0526636	+	0.761002i
$431$		−	32.6869i		−	1.57447i	−0.616652	−	0.787236i	$-0.711511\pi$
$431$		−	32.6869i		−	1.57447i	0.616652	−	0.787236i	$-0.288489\pi$
$432$	−21.2694	−	14.4121i	−1.02332	−	0.693403i
$433$	−7.25927	+	7.25927i	−0.348858	+	0.348858i	−0.859684	−	0.510826i	$-0.829340\pi$
$433$	−7.25927	+	7.25927i	−0.348858	+	0.348858i	0.510826	+	0.859684i	$0.329340\pi$
$434$	−7.25568	−	12.5672i	−0.348284	−	0.603245i
$435$	−11.8563	+	2.64691i	−0.568467	+	0.126910i
$436$	0.423267	−	0.733120i	0.0202708	−	0.0351101i
$437$	−3.62470	−	13.5276i	−0.173393	−	0.647111i
$438$	−4.90429	−	1.91939i	−0.234336	−	0.0917120i
$439$	−19.4684	+	11.2401i	−0.929175	+	0.536459i	−0.886550	−	0.462632i	$-0.846905\pi$
$439$	−19.4684	+	11.2401i	−0.929175	+	0.536459i	−0.0426241	+	0.999091i	$0.513572\pi$
$440$	−5.38777	−	15.6839i	−0.256852	−	0.747702i
$441$	−7.66547	+	8.29312i	−0.365022	+	0.394911i
$442$	0.609604	+	0.609604i	0.0289959	+	0.0289959i
$443$	−2.00030	+	7.46524i	−0.0950373	+	0.354684i	−0.997025	−	0.0770774i	$-0.975441\pi$
$443$	−2.00030	+	7.46524i	−0.0950373	+	0.354684i	0.901988	+	0.431762i	$0.142108\pi$
$444$	6.16540	−	8.37054i	0.292597	−	0.397248i
$445$	−20.5274	−	30.4804i	−0.973091	−	1.44491i
$446$	−11.9425	−	6.89501i	−0.565494	−	0.326488i
$447$	11.7869	−	1.78811i	0.557503	−	0.0845747i
$448$	5.30275	+	1.42087i	0.250531	+	0.0671297i
$449$	−38.1502			−1.80042			−0.900209	−	0.435458i	$-0.856586\pi$
$449$	−38.1502			−1.80042			−0.900209	+	0.435458i	$0.856586\pi$
$450$	16.0874	+	19.0573i	0.758369	+	0.898370i
$451$	5.37886			0.253280
$452$	6.16144	+	1.65095i	0.289810	+	0.0776543i
$453$	5.43691	−	13.8920i	0.255448	−	0.652703i
$454$	−13.2781	−	7.66612i	−0.623173	−	0.359789i
$455$	−2.97385	−	4.41577i	−0.139416	−	0.207014i
$456$	−22.1116	−	2.47000i	−1.03547	−	0.115668i
$457$	7.20855	−	26.9027i	0.337202	−	1.25845i	−0.564261	−	0.825596i	$-0.690839\pi$
$457$	7.20855	−	26.9027i	0.337202	−	1.25845i	0.901463	−	0.432857i	$-0.142495\pi$
$458$	23.3541	+	23.3541i	1.09127	+	1.09127i
$459$	−0.666801	+	1.92327i	−0.0311236	+	0.0897704i
$460$	−1.24375	−	3.62060i	−0.0579903	−	0.168811i
$461$	−21.2301	+	12.2572i	−0.988784	+	0.570874i	−0.904910	−	0.425602i	$-0.860062\pi$
$461$	−21.2301	+	12.2572i	−0.988784	+	0.570874i	−0.0838731	+	0.996476i	$0.526729\pi$
$462$	14.6093	−	11.6734i	0.679686	−	0.543094i
$463$	−4.62735	−	17.2695i	−0.215051	−	0.802582i	−0.986149	−	0.165865i	$-0.946958\pi$
$463$	−4.62735	−	17.2695i	−0.215051	−	0.802582i	0.771097	−	0.636717i	$-0.219708\pi$
$464$	7.75455	−	13.4313i	0.359996	−	0.623531i
$465$	−12.7163	−	13.8362i	−0.589704	−	0.641638i
$466$	6.41096	+	11.1041i	0.296982	+	0.514388i
$467$	−22.2894	+	22.2894i	−1.03143	+	1.03143i	−0.0319412	+	0.999490i	$0.510169\pi$
$467$	−22.2894	+	22.2894i	−1.03143	+	1.03143i	−0.999490	+	0.0319412i	$0.989831\pi$
$468$	−2.68619	−	1.41313i	−0.124169	−	0.0653221i
$469$		−	20.1775i		−	0.931709i
$470$	−1.01517	−	14.6695i	−0.0468263	−	0.676652i
$471$	2.32347	+	1.71137i	0.107060	+	0.0788559i
$472$	−1.10879	+	0.297098i	−0.0510360	+	0.0136751i
$473$	14.8363	−	3.97538i	0.682174	−	0.182788i
$474$	−18.6593	−	13.7437i	−0.857049	−	0.631267i
$475$	28.9702	+	11.7533i	1.32925	+	0.539279i
$476$			0.538636i			0.0246883i
$477$	26.8464	−	16.9403i	1.22921	−	0.775644i
$478$	−8.18699	+	8.18699i	−0.374464	+	0.374464i
$479$	6.76273	+	11.7134i	0.308997	+	0.535199i	0.978143	−	0.207932i	$-0.0666734\pi$
$479$	6.76273	+	11.7134i	0.308997	+	0.535199i	−0.669146	+	0.743131i	$0.733340\pi$
$480$	−15.9121	−	0.671121i	−0.726284	−	0.0306324i
$481$	−5.19667	+	9.00089i	−0.236948	+	0.410405i
$482$	10.1264	+	37.7923i	0.461246	+	1.72139i
$483$	−5.45165	+	4.35607i	−0.248058	+	0.198208i
$484$	1.34527	−	0.776693i	0.0611487	−	0.0353042i
$485$	11.2583	−	3.86746i	0.511211	−	0.175612i
$486$	0.845418	−	25.9043i	0.0383489	−	1.17504i
$487$	17.7890	+	17.7890i	0.806094	+	0.806094i	0.984040	−	0.177946i	$-0.0569452\pi$
$487$	17.7890	+	17.7890i	0.806094	+	0.806094i	−0.177946	+	0.984040i	$0.556945\pi$
$488$	3.15027	−	11.7570i	0.142606	−	0.532213i
$489$	25.5899	+	2.85854i	1.15721	+	0.129268i
$490$	−2.68030	+	13.7361i	−0.121084	+	0.620534i
$491$	−17.9785	−	10.3799i	−0.811359	−	0.468438i	0.0360688	−	0.999349i	$-0.488516\pi$
$491$	−17.9785	−	10.3799i	−0.811359	−	0.468438i	−0.847427	+	0.530911i	$0.821850\pi$
$492$	0.718940	−	1.83699i	0.0324123	−	0.0828177i
$493$	−1.18690	−	0.318030i	−0.0534554	−	0.0143233i
$494$	−13.7603			−0.619103
$495$	15.1707	−	18.8759i	0.681870	−	0.848410i
$496$	23.9912			1.07724
$497$	13.9279	+	3.73197i	0.624752	+	0.167402i
$498$	−1.65279	+	0.250732i	−0.0740631	+	0.0112356i
$499$	−8.56156	−	4.94302i	−0.383268	−	0.221280i	0.295971	−	0.955197i	$-0.404357\pi$
$499$	−8.56156	−	4.94302i	−0.383268	−	0.221280i	−0.679239	+	0.733917i	$0.737690\pi$
$500$	8.12206	+	2.65844i	0.363230	+	0.118889i
$501$	9.98769	−	13.5599i	0.446217	−	0.605813i
$502$	−8.94821	+	33.3952i	−0.399378	+	1.49050i
$503$	16.8084	+	16.8084i	0.749450	+	0.749450i	0.974376	−	0.224926i	$-0.0722140\pi$
$503$	16.8084	+	16.8084i	0.749450	+	0.749450i	−0.224926	+	0.974376i	$0.572214\pi$
$504$	3.28794	+	10.5874i	0.146457	+	0.471601i
$505$	10.9731	+	5.36174i	0.488298	+	0.238594i
$506$	−11.6425	+	6.72178i	−0.517571	+	0.298820i
$507$	−18.1423	−	7.10034i	−0.805728	−	0.315337i
$508$	−3.24234	−	12.1006i	−0.143855	−	0.536876i
$509$	−20.1795	+	34.9520i	−0.894442	+	1.54922i	−0.0599475	+	0.998202i	$0.519093\pi$
$509$	−20.1795	+	34.9520i	−0.894442	+	1.54922i	−0.834494	+	0.551017i	$0.814240\pi$
$510$	0.549641	+	2.46201i	0.0243385	+	0.109019i
$511$	1.64480	+	2.84887i	0.0727615	+	0.126027i
$512$	0.0117190	−	0.0117190i	0.000517913	−	0.000517913i
$513$	−14.1808	−	29.2321i	−0.626096	−	1.29063i
$514$		−	17.4733i		−	0.770712i
$515$	−7.65183	+	8.78963i	−0.337180	+	0.387317i
$516$	0.625357	−	5.59824i	0.0275298	−	0.246449i
$517$	−13.7918	+	3.69550i	−0.606562	+	0.162528i
$518$	−22.6839	+	6.07815i	−0.996675	+	0.267058i
$519$	23.8096	−	10.4151i	1.04513	−	0.457172i
$520$	6.06580	−	0.419772i	0.266003	−	0.0184082i
$521$			11.5144i			0.504456i	0.967668	+	0.252228i	$0.0811633\pi$
$521$			11.5144i			0.504456i	−0.967668	+	0.252228i	$0.918837\pi$
$522$	15.6333	−	0.614861i	0.684250	−	0.0269118i
$523$	−29.5457	+	29.5457i	−1.29194	+	1.29194i	−0.358358	+	0.933584i	$0.616663\pi$
$523$	−29.5457	+	29.5457i	−1.29194	+	1.29194i	−0.933584	+	0.358358i	$0.883337\pi$
$524$	1.91708	+	3.32049i	0.0837482	+	0.145056i
$525$	−0.419633	−	15.5723i	−0.0183143	−	0.679629i
$526$	−12.4195	+	21.5112i	−0.541517	+	0.937934i
$527$	−0.491963	−	1.83603i	−0.0214303	−	0.0799788i
$528$	4.63706	+	30.5668i	0.201802	+	1.33025i
$529$	−15.5740	+	8.99168i	−0.677133	+	0.390943i
$530$	17.2708	−	35.3457i	0.750195	−	1.53532i
$531$	−1.23096	−	1.13780i	−0.0534193	−	0.0493763i
$532$	−6.07917	−	6.07917i	−0.263565	−	0.263565i
$533$	−0.510428	+	1.90494i	−0.0221091	+	0.0825123i
$534$	18.9672	+	43.3602i	0.820791	+	1.87638i
$535$	12.6477	+	2.46792i	0.546808	+	0.106697i
$536$	19.9573	+	11.5223i	0.862024	+	0.497690i
$537$	4.56265	+	5.71018i	0.196893	+	0.246412i
$538$	−1.25587	−	0.336511i	−0.0541446	−	0.0145080i
$539$	13.5895			0.585340
$540$	−4.41879	−	7.70404i	−0.190154	−	0.331529i
$541$	6.30670			0.271146			0.135573	−	0.990767i	$-0.456712\pi$
$541$	6.30670			0.271146			0.135573	+	0.990767i	$0.456712\pi$
$542$	20.0230	+	5.36514i	0.860060	+	0.230452i
$543$	−25.7252	−	32.1953i	−1.10398	−	1.38163i
$544$	−1.39509	−	0.805458i	−0.0598142	−	0.0345337i
$545$	−2.05401	+	1.38330i	−0.0879843	+	0.0592540i
$546$	2.74782	+	6.28169i	0.117596	+	0.268832i
$547$	7.99863	−	29.8513i	0.341997	−	1.27635i	−0.554085	−	0.832460i	$-0.686932\pi$
$547$	7.99863	−	29.8513i	0.341997	−	1.27635i	0.896082	−	0.443889i	$-0.146401\pi$
$548$	−0.246678	−	0.246678i	−0.0105375	−	0.0105375i
$549$	16.9745	−	5.27147i	0.724454	−	0.224981i
$550$	3.70031	−	29.7818i	0.157782	−	1.26990i
$551$	16.9850	−	9.80630i	0.723586	−	0.417762i
$552$	−1.19537	−	7.87969i	−0.0508783	−	0.335382i
$553$	3.74650	+	13.9821i	0.159317	+	0.594580i
$554$	7.80896	−	13.5255i	0.331771	−	0.574644i
$555$	−26.9548	+	14.0826i	−1.14417	+	0.597772i
$556$	−6.12814	−	10.6143i	−0.259891	−	0.450145i
$557$	6.63181	−	6.63181i	0.280999	−	0.280999i	−0.552509	−	0.833507i	$-0.686329\pi$
$557$	6.63181	−	6.63181i	0.280999	−	0.280999i	0.833507	+	0.552509i	$0.186329\pi$
$558$	12.9153	+	20.4678i	0.546750	+	0.866469i
$559$			5.63159i			0.238191i
$560$	15.0000	+	13.0583i	0.633867	+	0.551815i
$561$	2.24417	−	0.981675i	0.0947491	−	0.0414464i
$562$	−49.3326	+	13.2186i	−2.08097	+	0.557594i
$563$	−18.2031	+	4.87751i	−0.767170	+	0.205563i	−0.621121	−	0.783715i	$-0.713322\pi$
$563$	−18.2031	+	4.87751i	−0.767170	+	0.205563i	−0.146049	+	0.989277i	$0.546656\pi$
$564$	−0.581329	+	5.20411i	−0.0244784	+	0.219132i
$565$	−14.0741	−	12.2522i	−0.592101	−	0.515455i
$566$			31.2741i			1.31455i
$567$	−10.5130	+	12.3111i	−0.441503	+	0.517017i
$568$	−11.6448	+	11.6448i	−0.488605	+	0.488605i
$569$	−10.4878	−	18.1654i	−0.439670	−	0.761531i	0.557994	−	0.829845i	$-0.311571\pi$
$569$	−10.4878	−	18.1654i	−0.439670	−	0.761531i	−0.997664	+	0.0683141i	$0.978238\pi$
$570$	−33.9901	−	21.5834i	−1.42369	−	0.904028i
$571$	−12.2406	+	21.2014i	−0.512254	+	0.887250i	0.487645	+	0.873042i	$0.337856\pi$
$571$	−12.2406	+	21.2014i	−0.512254	+	0.887250i	−0.999899	+	0.0142078i	$0.995477\pi$
$572$	0.945309	+	3.52794i	0.0395254	+	0.147511i
$573$	37.5366	+	14.6907i	1.56811	+	0.613711i
$574$	−3.85913	+	2.22807i	−0.161077	+	0.0929978i
$575$	−1.38082	+	11.1135i	−0.0575841	+	0.463464i
$576$	−8.93019	−	2.02032i	−0.372091	−	0.0841800i
$577$	−12.4198	−	12.4198i	−0.517041	−	0.517041i	0.399634	−	0.916675i	$-0.369137\pi$
$577$	−12.4198	−	12.4198i	−0.517041	−	0.517041i	−0.916675	+	0.399634i	$0.869137\pi$
$578$	7.24946	−	27.0554i	0.301538	−	1.12535i
$579$	21.2990	−	28.9168i	0.885155	−	1.20174i
$580$	4.44679	−	2.99474i	0.184643	−	0.124350i
$581$	0.904288	+	0.522091i	0.0375162	+	0.0216600i
$582$	−15.1575	+	2.29943i	−0.628299	+	0.0953146i
$583$	−36.8976	−	9.88668i	−1.52814	−	0.409465i
$584$	−3.75705			−0.155468
$585$	5.24536	+	7.16399i	0.216869	+	0.296194i
$586$	56.1979			2.32151
$587$	14.6173	+	3.91669i	0.603320	+	0.161659i	0.547534	−	0.836784i	$-0.315567\pi$
$587$	14.6173	+	3.91669i	0.603320	+	0.161659i	0.0557861	+	0.998443i	$0.482234\pi$
$588$	1.81637	−	4.64108i	0.0749060	−	0.191395i
$589$	26.2743	+	15.1695i	1.08261	+	0.625047i
$590$	−2.03888	−	0.397842i	−0.0839392	−	0.0163789i
$591$	15.8869	+	1.77466i	0.653499	+	0.0729997i
$592$	10.0488	−	37.5027i	0.413003	−	1.54135i
$593$	−12.8270	−	12.8270i	−0.526744	−	0.526744i	0.392856	−	0.919600i	$-0.371487\pi$
$593$	−12.8270	−	12.8270i	−0.526744	−	0.526744i	−0.919600	+	0.392856i	$0.871487\pi$
$594$	−23.5814	+	20.4113i	−0.967555	+	0.837486i
$595$	0.691755	−	1.41572i	0.0283592	−	0.0580388i
$596$	−4.55641	+	2.63064i	−0.186638	+	0.107755i
$597$	5.46368	−	4.36569i	0.223614	−	0.178676i
$598$	−1.27573	−	4.76109i	−0.0521685	−	0.194696i
$599$	−3.45057	+	5.97656i	−0.140987	+	0.244196i	−0.927868	−	0.372908i	$-0.878361\pi$
$599$	−3.45057	+	5.97656i	−0.140987	+	0.244196i	0.786882	+	0.617104i	$0.211694\pi$
$600$	15.6420	+	8.47749i	0.638581	+	0.346092i
$601$	6.29969	+	10.9114i	0.256970	+	0.445085i	0.965429	−	0.260667i	$-0.0839426\pi$
$601$	6.29969	+	10.9114i	0.256970	+	0.445085i	−0.708459	+	0.705752i	$0.750609\pi$
$602$	−8.99779	+	8.99779i	−0.366722	+	0.366722i
$603$	1.32251	+	33.6259i	0.0538570	+	1.36935i
$604$			6.58358i			0.267882i
$605$	−4.53331	+	0.313719i	−0.184305	+	0.0127545i
$606$	−12.6643	−	9.32804i	−0.514454	−	0.378926i
$607$	35.9453	−	9.63152i	1.45898	−	0.390931i	0.559839	−	0.828601i	$-0.310863\pi$
$607$	35.9453	−	9.63152i	1.45898	−	0.390931i	0.899136	+	0.437670i	$0.144196\pi$
$608$	24.8359	−	6.65477i	1.00723	−	0.269887i
$609$	−7.86845	−	5.79558i	−0.318846	−	0.234849i
$610$	14.4629	−	16.6135i	0.585586	−	0.672660i
$611$		−	5.23510i		−	0.211789i
$612$	−0.0353045	−	0.897641i	−0.00142710	−	0.0362850i
$613$	12.4072	−	12.4072i	0.501121	−	0.501121i	−0.410665	−	0.911786i	$-0.634704\pi$
$613$	12.4072	−	12.4072i	0.501121	−	0.501121i	0.911786	+	0.410665i	$0.134704\pi$
$614$	2.66556	+	4.61689i	0.107573	+	0.186322i
$615$	−4.24881	+	3.90491i	−0.171328	+	0.157461i
$616$	6.67023	−	11.5532i	0.268751	−	0.465491i
$617$	−2.65843	−	9.92141i	−0.107025	−	0.399421i	0.891542	−	0.452937i	$-0.149624\pi$
$617$	−2.65843	−	9.92141i	−0.107025	−	0.399421i	−0.998567	+	0.0535162i	$0.982957\pi$
$618$	11.7252	−	9.36885i	0.471656	−	0.376871i
$619$	−19.1639	+	11.0643i	−0.770264	+	0.444712i	−0.832969	−	0.553320i	$-0.813361\pi$
$619$	−19.1639	+	11.0643i	−0.770264	+	0.444712i	0.0627048	+	0.998032i	$0.480027\pi$
$620$	7.45133	+	3.64090i	0.299253	+	0.146222i
$621$	8.79969	−	7.61674i	0.353119	−	0.305649i
$622$	2.53439	+	2.53439i	0.101620	+	0.101620i
$623$	7.65114	−	28.5544i	0.306536	−	1.14401i
$624$	−11.2654	−	1.25841i	−0.450977	−	0.0503767i
$625$	−17.9334	−	17.4182i	−0.717335	−	0.696728i
$626$	−31.2902	−	18.0654i	−1.25061	−	0.722040i
$627$	−14.2488	+	36.4076i	−0.569044	+	1.45398i
$628$	−1.23012	−	0.329609i	−0.0490870	−	0.0131528i
$629$	−3.07612			−0.122653
$630$	−3.06546	+	19.8269i	−0.122131	+	0.789921i
$631$	8.15013			0.324451			0.162226	−	0.986754i	$-0.448133\pi$
$631$	8.15013			0.324451			0.162226	+	0.986754i	$0.448133\pi$
$632$	−15.9690	−	4.27888i	−0.635212	−	0.170205i
$633$	−2.23686	+	0.339338i	−0.0889073	+	0.0134875i
$634$	−6.67608	−	3.85443i	−0.265141	−	0.153079i
$635$	−7.01845	+	35.9684i	−0.278519	+	1.42736i
$636$	−8.30824	+	11.2798i	−0.329443	+	0.447273i
$637$	−1.28958	+	4.81277i	−0.0510949	+	0.190689i
$638$	−13.3125	−	13.3125i	−0.527046	−	0.527046i
$639$	−23.4556	−	5.30647i	−0.927888	−	0.209921i
$640$	−28.1234	+	9.66101i	−1.11168	+	0.381885i
$641$	−2.49058	+	1.43794i	−0.0983722	+	0.0567952i	−0.548379	−	0.836230i	$-0.684755\pi$
$641$	−2.49058	+	1.43794i	−0.0983722	+	0.0567952i	0.450007	+	0.893025i	$0.351422\pi$
$642$	−15.4545	−	6.04840i	−0.609939	−	0.238711i
$643$	2.54626	+	9.50279i	0.100415	+	0.374753i	0.997785	−	0.0665259i	$-0.0211915\pi$
$643$	2.54626	+	9.50279i	0.100415	+	0.374753i	−0.897370	+	0.441279i	$0.854525\pi$
$644$	1.53981	−	2.66702i	0.0606768	−	0.105095i
$645$	−8.83332	+	13.9110i	−0.347811	+	0.547744i
$646$	−2.03631	−	3.52700i	−0.0801177	−	0.138768i
$647$	14.2662	−	14.2662i	0.560862	−	0.560862i	−0.368691	−	0.929552i	$-0.620194\pi$
$647$	14.2662	−	14.2662i	0.560862	−	0.560862i	0.929552	+	0.368691i	$0.120194\pi$
$648$	−6.17332	−	17.4285i	−0.242511	−	0.684656i
$649$			2.01711i			0.0791786i
$650$	10.1962	+	4.13664i	0.399929	+	0.162252i
$651$	1.67823	−	15.0237i	0.0657752	−	0.588825i
$652$	−10.9763	+	2.94108i	−0.429864	+	0.115182i
$653$	38.3580	−	10.2780i	1.50106	−	0.402209i	0.587607	−	0.809146i	$-0.300070\pi$
$653$	38.3580	−	10.2780i	1.50106	−	0.402209i	0.913456	+	0.406937i	$0.133403\pi$
$654$	2.92196	−	1.27816i	0.114258	−	0.0499800i
$655$	−0.774342	−	11.1894i	−0.0302560	−	0.437207i
$656$		−	7.36719i		−	0.287641i
$657$	−2.92779	−	4.63985i	−0.114224	−	0.181018i
$658$	8.36431	−	8.36431i	0.326075	−	0.326075i
$659$	−23.3689	−	40.4762i	−0.910324	−	1.57673i	−0.813607	−	0.581415i	$-0.802499\pi$
$659$	−23.3689	−	40.4762i	−0.910324	−	1.57673i	−0.0967171	−	0.995312i	$-0.530834\pi$
$660$	−3.19861	+	10.1974i	−0.124506	+	0.396931i
$661$	−2.81433	+	4.87455i	−0.109465	+	0.189598i	−0.915553	−	0.402196i	$-0.868247\pi$
$661$	−2.81433	+	4.87455i	−0.109465	+	0.189598i	0.806089	+	0.591794i	$0.201580\pi$
$662$	−12.5266	−	46.7499i	−0.486860	−	1.81699i
$663$	0.134703	+	0.887940i	0.00523142	+	0.0344847i
$664$	−1.03279	+	0.596280i	−0.0400799	+	0.0231402i
$665$	8.17082	+	23.7854i	0.316851	+	0.922359i
$666$	37.4046	−	11.6161i	1.44940	−	0.450114i
$667$	4.96772	+	4.96772i	0.192351	+	0.192351i
$668$	−1.92362	+	7.17905i	−0.0744271	+	0.277766i
$669$	−5.75730	−	13.1616i	−0.222590	−	0.508855i
$670$	23.2954	+	34.5905i	0.899979	+	1.33635i
$671$	−18.5229	−	10.6942i	−0.715068	−	0.412845i
$672$	−7.99752	−	10.0089i	−0.308511	−	0.386104i
$673$	28.7938	+	7.71528i	1.10992	+	0.297402i	0.766798	−	0.641888i	$-0.221849\pi$
$673$	28.7938	+	7.71528i	1.10992	+	0.297402i	0.343122	+	0.939291i	$0.388515\pi$
$674$	41.6249			1.60333
$675$	1.71999	+	25.9238i	0.0662025	+	0.997806i
$676$	8.59784			0.330686
$677$	−48.2839	−	12.9376i	−1.85570	−	0.497234i	−0.855900	−	0.517141i	$-0.826996\pi$
$677$	−48.2839	−	12.9376i	−1.85570	−	0.497234i	−0.999802	+	0.0199076i	$0.993663\pi$
$678$	15.0015	+	18.7745i	0.576131	+	0.721032i
$679$	8.29312	+	4.78804i	0.318261	+	0.183748i
$680$	1.00524	+	1.49265i	0.0385493	+	0.0572407i
$681$	−6.40117	−	14.6335i	−0.245293	−	0.560757i
$682$	7.53763	−	28.1308i	0.288631	−	1.07718i
$683$	4.38271	+	4.38271i	0.167700	+	0.167700i	0.785968	−	0.618268i	$-0.212165\pi$
$683$	4.38271	+	4.38271i	0.167700	+	0.167700i	−0.618268	+	0.785968i	$0.712165\pi$
$684$	10.5294	+	9.73252i	0.402603	+	0.372132i
$685$	0.331552	+	0.965154i	0.0126679	+	0.0368766i
$686$	−27.8803	+	16.0967i	−1.06447	+	0.614575i
$687$	5.16050	+	34.0172i	0.196886	+	1.29784i
$688$	−5.44491	−	20.3207i	−0.207585	−	0.774718i
$689$	7.00282	−	12.1292i	0.266786	−	0.462087i
$690$	4.31665	−	13.7617i	0.164332	−	0.523900i
$691$	−0.346648	−	0.600412i	−0.0131871	−	0.0228407i	0.859357	−	0.511377i	$-0.170864\pi$
$691$	−0.346648	−	0.600412i	−0.0131871	−	0.0228407i	−0.872544	+	0.488536i	$0.837531\pi$
$692$	−8.10973	+	8.10973i	−0.308286	+	0.308286i
$693$	19.4658	−	0.765597i	0.739446	−	0.0290826i
$694$			58.1535i			2.20748i
$695$	2.47526	+	35.7681i	0.0938919	+	1.35676i
$696$	10.2256	−	4.47303i	0.387601	−	0.169550i
$697$	−0.563807	+	0.151072i	−0.0213557	+	0.00572225i
$698$	−31.6983	+	8.49352i	−1.19980	+	0.321485i
$699$	−1.48285	+	13.2746i	−0.0560866	+	0.502092i
$700$	2.67708	+	6.33214i	0.101184	+	0.239332i
$701$			8.36037i			0.315767i	0.987458	+	0.157883i	$0.0504670\pi$
$701$			8.36037i			0.315767i	−0.987458	+	0.157883i	$0.949533\pi$
$702$	−4.99099	−	10.2884i	−0.188373	−	0.388310i
$703$	34.7178	−	34.7178i	1.30941	−	1.30941i
$704$	5.50881	+	9.54154i	0.207621	+	0.359610i
$705$	8.21142	−	12.9316i	0.309260	−	0.487031i
$706$	6.29148	−	10.8972i	0.236783	−	0.410120i
$707$	2.54281	+	9.48988i	0.0956320	+	0.356904i
$708$	0.688884	+	0.269608i	0.0258898	+	0.0101325i
$709$	4.59399	−	2.65234i	0.172531	−	0.0996109i	−0.411248	−	0.911524i	$-0.634907\pi$
$709$	4.59399	−	2.65234i	0.172531	−	0.0996109i	0.583779	+	0.811913i	$0.301574\pi$
$710$	−28.1855	+	9.68234i	−1.05778	+	0.363372i
$711$	−7.16001	−	23.0557i	−0.268521	−	0.864657i
$712$	23.8737	+	23.8737i	0.894704	+	0.894704i
$713$	−2.81276	+	10.4974i	−0.105339	+	0.393130i
$714$	−1.20347	+	1.63391i	−0.0450389	+	0.0611477i
$715$	2.04624	−	10.4867i	0.0765251	−	0.392179i
$716$	−2.79350	−	1.61283i	−0.104398	−	0.0602742i
$717$	−11.9250	+	1.80906i	−0.445349	+	0.0675606i
$718$	−13.6149	−	3.64811i	−0.508105	−	0.136146i
$719$	−28.3121			−1.05586			−0.527932	−	0.849286i	$-0.677033\pi$
$719$	−28.3121			−1.05586			−0.527932	+	0.849286i	$0.677033\pi$
$720$	−25.8536	−	20.7786i	−0.963505	−	0.774373i
$721$	−9.37468			−0.349131
$722$	32.2750	+	8.64806i	1.20115	+	0.321847i
$723$	−14.8546	+	37.9555i	−0.552449	+	1.41158i
$724$	15.7504	+	9.09349i	0.585359	+	0.337957i
$725$	−15.5337	+	2.16031i	−0.576908	+	0.0802318i
$726$	5.81614	+	0.649697i	0.215857	+	0.0241125i
$727$	−11.6483	+	43.4720i	−0.432011	+	1.61229i	0.316108	+	0.948723i	$0.397624\pi$
$727$	−11.6483	+	43.4720i	−0.432011	+	1.61229i	−0.748119	+	0.663565i	$0.769043\pi$
$728$	3.45863	+	3.45863i	0.128185	+	0.128185i
$729$	16.7130	−	21.2056i	0.618999	−	0.785391i
$730$	−6.10879	−	2.98490i	−0.226096	−	0.110476i
$731$	−1.44348	+	0.833392i	−0.0533889	+	0.0308241i
$732$	−6.12805	+	4.89654i	−0.226499	+	0.180981i
$733$	6.25836	+	23.3565i	0.231158	+	0.862693i	0.979843	+	0.199768i	$0.0640187\pi$
$733$	6.25836	+	23.3565i	0.231158	+	0.862693i	−0.748685	+	0.662926i	$0.769315\pi$
$734$	6.82565	−	11.8224i	0.251939	−	0.436372i
$735$	−10.7345	+	9.86561i	−0.395946	+	0.363898i
$736$	4.60515	+	7.97635i	0.169748	+	0.294012i
$737$	28.6340	−	28.6340i	1.05475	−	1.05475i
$738$	6.28523	−	3.96604i	0.231362	−	0.145992i
$739$			5.60736i			0.206270i	0.994667	+	0.103135i	$0.0328874\pi$
$739$			5.60736i			0.206270i	−0.994667	+	0.103135i	$0.967113\pi$
$740$	8.81243	−	10.1228i	0.323951	−	0.372122i
$741$	−11.5418	−	8.50120i	−0.423998	−	0.312299i
$742$	30.5680	−	8.19067i	1.12219	−	0.300689i
$743$	−8.24852	+	2.21018i	−0.302609	+	0.0810838i	−0.406928	−	0.913460i	$-0.633400\pi$
$743$	−8.24852	+	2.21018i	−0.302609	+	0.0810838i	0.104320	+	0.994544i	$0.466733\pi$
$744$	13.9014	+	10.2392i	0.509650	+	0.375388i
$745$	15.3543	−	1.06256i	0.562536	−	0.0389292i
$746$			35.7776i			1.30991i
$747$	−1.54122	−	0.810797i	−0.0563903	−	0.0296655i
$748$	−0.764383	+	0.764383i	−0.0279486	+	0.0279486i
$749$	5.18310	+	8.97739i	0.189386	+	0.328027i
$750$	18.6979	+	26.2113i	0.682752	+	0.957100i
$751$	2.32268	−	4.02301i	0.0847560	−	0.146802i	−0.820531	−	0.571602i	$-0.806322\pi$
$751$	2.32268	−	4.02301i	0.0847560	−	0.146802i	0.905287	+	0.424800i	$0.139656\pi$
$752$	5.06156	+	18.8900i	0.184576	+	0.688848i
$753$	−28.1374	+	22.4828i	−1.02538	+	0.819319i
$754$	5.97796	−	3.45138i	0.217704	−	0.125692i
$755$	8.45510	−	17.3039i	0.307713	−	0.629753i
$756$	2.34035	−	6.75030i	0.0851175	−	0.245506i
$757$	−3.09830	−	3.09830i	−0.112609	−	0.112609i	0.648557	−	0.761166i	$-0.275373\pi$
$757$	−3.09830	−	3.09830i	−0.112609	−	0.112609i	−0.761166	+	0.648557i	$0.775373\pi$
$758$	4.80304	−	17.9252i	0.174454	−	0.651072i
$759$	−13.9182	−	1.55474i	−0.505199	−	0.0564337i
$760$	−28.1918	−	5.50102i	−1.02263	−	0.199543i
$761$	38.9876	+	22.5095i	1.41330	+	0.815968i	0.995698	−	0.0926625i	$-0.0295377\pi$
$761$	38.9876	+	22.5095i	1.41330	+	0.815968i	0.417601	+	0.908631i	$0.362871\pi$
$762$	17.2009	−	43.9505i	0.623122	−	1.59216i
$763$	−1.92422	−	0.515595i	−0.0696616	−	0.0186658i
$764$	−17.7890			−0.643584
$765$	−1.06002	+	2.40465i	−0.0383252	+	0.0869401i
$766$	−25.2991			−0.914094
$767$	−0.714369	−	0.191415i	−0.0257944	−	0.00691158i
$768$	27.4111	−	4.15834i	0.989114	−	0.150051i
$769$	−5.40503	−	3.12060i	−0.194910	−	0.112532i	0.399369	−	0.916790i	$-0.369229\pi$
$769$	−5.40503	−	3.12060i	−0.194910	−	0.112532i	−0.594279	+	0.804259i	$0.702563\pi$
$770$	20.0243	−	13.4856i	0.721625	−	0.485986i
$771$	10.7951	−	14.6561i	0.388777	−	0.527828i
$772$	−4.10216	+	15.3095i	−0.147640	+	0.551000i
$773$	−19.5366	−	19.5366i	−0.702681	−	0.702681i	0.262304	−	0.964985i	$-0.415518\pi$
$773$	−19.5366	−	19.5366i	−0.702681	−	0.702681i	−0.964985	+	0.262304i	$0.915518\pi$
$774$	14.4051	−	15.5846i	0.517781	−	0.560178i
$775$	−14.9087	−	19.1391i	−0.535537	−	0.687495i
$776$	−9.47158	+	5.46842i	−0.340010	+	0.196305i
$777$	−22.7819	−	8.91613i	−0.817296	−	0.319864i
$778$	−10.9643	−	40.9192i	−0.393088	−	1.46702i
$779$	4.65823	−	8.06829i	0.166898	−	0.289076i
$780$	−3.30790	−	2.10048i	−0.118442	−	0.0752094i
$781$	14.4691	+	25.0613i	0.517747	+	0.896764i
$782$	1.03156	−	1.03156i	0.0368887	−	0.0368887i
$783$	13.4927	+	9.14265i	0.482190	+	0.326732i
$784$		−	18.6129i		−	0.664748i
$785$	2.80986	+	2.44613i	0.100288	+	0.0873061i
$786$	−1.60363	+	14.3558i	−0.0571995	+	0.512054i
$787$	−28.3409	+	7.59393i	−1.01024	+	0.270694i	−0.725732	−	0.687978i	$-0.758499\pi$
$787$	−28.3409	+	7.59393i	−1.01024	+	0.270694i	−0.284513	+	0.958672i	$0.591832\pi$
$788$	−6.81437	+	1.82590i	−0.242752	+	0.0650451i
$789$	−23.7070	+	10.3702i	−0.843992	+	0.369190i
$790$	−22.5654	−	19.6443i	−0.802840	−	0.698914i
$791$		−	15.0109i		−	0.533725i
$792$	−10.3587	+	19.6906i	−0.368082	+	0.699676i
$793$	5.54513	−	5.54513i	0.196913	−	0.196913i
$794$	7.01613	+	12.1523i	0.248993	+	0.431269i
$795$	36.3232	−	18.9771i	1.28825	−	0.673049i
$796$	−1.54321	+	2.67291i	−0.0546975	+	0.0947388i
$797$	0.454070	+	1.69461i	0.0160840	+	0.0600263i	0.973501	−	0.228681i	$-0.0734413\pi$
$797$	0.454070	+	1.69461i	0.0160840	+	0.0600263i	−0.957417	+	0.288707i	$0.906775\pi$
$798$	−4.85803	−	32.0234i	−0.171972	−	1.13362i
$799$	1.34185	−	0.774718i	0.0474712	−	0.0274075i
$800$	−20.4038	−	2.53511i	−0.721382	−	0.0896298i
$801$	−10.8791	+	48.0876i	−0.384394	+	1.69909i
$802$	−32.1473	−	32.1473i	−1.13516	−	1.13516i
$803$	−1.70871	+	6.37700i	−0.0602991	+	0.225039i
$804$	−5.95185	−	13.6063i	−0.209905	−	0.479858i
$805$	−7.47231	+	5.03231i	−0.263364	+	0.177366i
$806$	9.24736	+	5.33897i	0.325724	+	0.188057i
$807$	−0.845499	−	1.05815i	−0.0297630	−	0.0372486i
$808$	−10.8384	−	2.90414i	−0.381294	−	0.102167i
$809$	27.5870			0.969908			0.484954	−	0.874540i	$-0.338836\pi$
$809$	27.5870			0.969908			0.484954	+	0.874540i	$0.338836\pi$
$810$	3.80907	−	33.2425i	0.133837	−	1.16802i
$811$	−44.5699			−1.56506			−0.782530	−	0.622613i	$-0.786071\pi$
$811$	−44.5699			−1.56506			−0.782530	+	0.622613i	$0.786071\pi$
$812$	4.16580	+	1.11622i	0.146191	+	0.0391718i
$813$	13.4802	+	16.8705i	0.472770	+	0.591675i
$814$	−40.8165	−	23.5654i	−1.43062	−	0.825968i
$815$	32.6265	+	6.36635i	1.14286	+	0.223004i
$816$	−1.34456	−	3.07375i	−0.0470690	−	0.107603i
$817$	6.88556	−	25.6972i	0.240895	−	0.899033i
$818$	−31.9621	−	31.9621i	−1.11753	−	1.11753i
$819$	−1.57608	+	6.96656i	−0.0550726	+	0.243431i
$820$	1.11805	−	2.28815i	0.0390439	−	0.0799056i
$821$	38.4678	−	22.2094i	1.34254	−	0.775114i	0.355357	−	0.934731i	$-0.384359\pi$
$821$	38.4678	−	22.2094i	1.34254	−	0.775114i	0.987179	+	0.159617i	$0.0510259\pi$
$822$	−0.197127	−	1.29943i	−0.00687559	−	0.0453228i
$823$	8.19082	+	30.5686i	0.285514	+	1.06555i	0.948463	+	0.316888i	$0.102638\pi$
$823$	8.19082	+	30.5686i	0.285514	+	1.06555i	−0.662949	+	0.748665i	$0.730695\pi$
$824$	5.35341	−	9.27239i	0.186495	−	0.323019i
$825$	21.5032	−	22.6942i	0.748646	−	0.790111i
$826$	−0.835543	−	1.44720i	−0.0290723	−	0.0503546i
$827$	−2.06846	+	2.06846i	−0.0719275	+	0.0719275i	−0.742155	−	0.670228i	$-0.766196\pi$
$827$	−2.06846	+	2.06846i	−0.0719275	+	0.0719275i	0.670228	+	0.742155i	$0.266196\pi$
$828$	−2.39129	+	4.54553i	−0.0831030	+	0.157968i
$829$		−	12.9618i		−	0.450182i	−0.974338	−	0.225091i	$-0.927732\pi$
$829$		−	12.9618i		−	0.450182i	0.974338	−	0.225091i	$-0.0722680\pi$
$830$	−2.15300	+	0.148994i	−0.0747317	+	0.00517166i
$831$	14.9062	−	6.52044i	0.517089	−	0.226192i
$832$	−3.90193	+	1.04552i	−0.135275	+	0.0362469i
$833$	−1.42444	+	0.381677i	−0.0493539	+	0.0132243i
$834$	5.12614	−	45.8897i	0.177504	−	1.58903i
$835$	14.2758	−	16.3985i	0.494033	−	0.567494i
$836$		−	17.2540i		−	0.596742i
$837$	−1.81207	+	25.1471i	−0.0626344	+	0.869210i
$838$	−36.9202	+	36.9202i	−1.27539	+	1.27539i
$839$	9.19525	+	15.9266i	0.317455	+	0.549849i	0.979956	−	0.199212i	$-0.0638383\pi$
$839$	9.19525	+	15.9266i	0.317455	+	0.549849i	−0.662501	+	0.749061i	$0.730505\pi$
$840$	3.11843	+	13.9684i	0.107596	+	0.481954i
$841$	9.58072	−	16.5943i	0.330370	−	0.572217i
$842$	13.2822	+	49.5699i	0.457736	+	1.70829i
$843$	−49.5456	−	19.3906i	−1.70644	−	0.667848i
$844$	0.864691	−	0.499230i	0.0297639	−	0.0171842i
$845$	−22.5980	−	11.0420i	−0.777396	−	0.379855i
$846$	−13.3909	+	14.4874i	−0.460390	+	0.498087i
$847$	−2.58483	−	2.58483i	−0.0888158	−	0.0888158i
$848$	−13.5414	+	50.5371i	−0.465013	+	1.73545i
$849$	−19.3214	+	26.2320i	−0.663109	+	0.900279i
$850$	0.448596	+	3.22564i	0.0153867	+	0.110638i
$851$	15.2312	+	8.79374i	0.522119	+	0.301445i
$852$	10.4929	−	1.59180i	0.359480	−	0.0545341i
$853$	−13.3437	−	3.57544i	−0.456880	−	0.122421i	0.0230366	−	0.999735i	$-0.492667\pi$
$853$	−13.3437	−	3.57544i	−0.456880	−	0.122421i	−0.479917	+	0.877314i	$0.659333\pi$
$854$	17.7193			0.606342
$855$	−15.1757	−	39.1030i	−0.518999	−	1.33729i
$856$	−11.8392			−0.404657
$857$	5.89302	+	1.57903i	0.201302	+	0.0539387i	0.358061	−	0.933698i	$-0.383438\pi$
$857$	5.89302	+	1.57903i	0.201302	+	0.0539387i	−0.156759	+	0.987637i	$0.550105\pi$
$858$	−5.01495	+	12.8139i	−0.171208	+	0.437458i
$859$	−16.1515	−	9.32505i	−0.551081	−	0.318166i	0.198477	−	0.980106i	$-0.436400\pi$
$859$	−16.1515	−	9.32505i	−0.551081	−	0.318166i	−0.749558	+	0.661939i	$0.769734\pi$
$860$	1.39275	−	7.13764i	0.0474925	−	0.243392i
$861$	−4.61347	−	0.515351i	−0.157226	−	0.0175631i
$862$	−14.0659	+	52.4948i	−0.479088	+	1.78798i
$863$	9.43441	+	9.43441i	0.321151	+	0.321151i	0.849209	−	0.528058i	$-0.177079\pi$
$863$	9.43441	+	9.43441i	0.321151	+	0.321151i	−0.528058	+	0.849209i	$0.677079\pi$
$864$	13.9839	+	16.1558i	0.475744	+	0.549631i
$865$	31.7302	−	10.9000i	1.07886	−	0.370612i
$866$	14.7822	−	8.53448i	0.502318	−	0.290013i
$867$	22.7957	−	18.2146i	0.774183	−	0.618601i
$868$	1.72670	+	6.44412i	0.0586079	+	0.218728i
$869$	−14.5254	+	25.1588i	−0.492742	+	0.853454i
$870$	20.1801	+	0.851135i	0.684171	+	0.0288562i
$871$	7.42362	+	12.8581i	0.251540	+	0.435680i
$872$	1.60880	−	1.60880i	0.0544808	−	0.0544808i
$873$	−14.1344	−	7.43573i	−0.478376	−	0.251661i
$874$			23.2849i			0.787625i
$875$	1.09593	−	20.0811i	0.0370491	−	0.678866i
$876$	1.94948	+	1.43591i	0.0658670	+	0.0485149i
$877$	47.4768	−	12.7214i	1.60318	−	0.429570i	0.657177	−	0.753736i	$-0.271750\pi$
$877$	47.4768	−	12.7214i	1.60318	−	0.429570i	0.946000	+	0.324166i	$0.105084\pi$
$878$	36.1029	−	9.67374i	1.21841	−	0.326473i
$879$	47.1375	+	34.7195i	1.58991	+	1.17106i
$880$	2.75551	+	39.8178i	0.0928883	+	1.34226i
$881$		−	17.7562i		−	0.598222i	−0.954218	−	0.299111i	$-0.903310\pi$
$881$		−	17.7562i		−	0.598222i	0.954218	−	0.299111i	$-0.0966901\pi$
$882$	15.8794	−	10.0200i	0.534687	−	0.337392i
$883$	8.09196	−	8.09196i	0.272316	−	0.272316i	−0.557716	−	0.830032i	$-0.688322\pi$
$883$	8.09196	−	8.09196i	0.272316	−	0.272316i	0.830032	+	0.557716i	$0.188322\pi$
$884$	−0.198173	−	0.343246i	−0.00666528	−	0.0115446i
$885$	−1.46437	−	1.59334i	−0.0492243	−	0.0535594i
$886$	6.42494	−	11.1283i	0.215850	−	0.373863i
$887$	2.74978	+	10.2623i	0.0923287	+	0.344575i	0.996601	−	0.0823810i	$-0.0262525\pi$
$887$	2.74978	+	10.2623i	0.0923287	+	0.344575i	−0.904272	+	0.426956i	$0.859586\pi$
$888$	21.8284	−	17.4417i	0.732515	−	0.585306i
$889$	−25.5305	+	14.7401i	−0.856267	+	0.494366i
$890$	19.8503	+	57.7847i	0.665384	+	1.93695i
$891$	−32.3898	+	2.55174i	−1.08510	+	0.0854867i
$892$	4.48293	+	4.48293i	0.150100	+	0.150100i
$893$	−6.40079	+	23.8881i	−0.214194	+	0.799383i
$894$	−19.6992	−	2.20051i	−0.658839	−	0.0735962i
$895$	5.27096	+	7.82667i	0.176189	+	0.261617i
$896$	−20.7164	−	11.9606i	−0.692087	−	0.399577i
$897$	1.87139	−	4.78165i	0.0624840	−	0.159655i
$898$	61.2688	+	16.4169i	2.04457	+	0.547840i
$899$	−15.2193			−0.507594
$900$	−4.87640	−	10.3771i	−0.162547	−	0.345903i
$901$	4.14526			0.138098
$902$	−8.63839	−	2.31465i	−0.287627	−	0.0770694i
$903$	−13.1060	+	1.98822i	−0.436142	+	0.0661639i
$904$	14.8471	+	8.57197i	0.493807	+	0.285099i
$905$	−29.7189	−	44.1286i	−0.987889	−	1.46688i
$906$	−14.7097	+	19.9708i	−0.488696	+	0.663485i
$907$	−2.00855	+	7.49600i	−0.0666927	+	0.248901i	−0.991222	−	0.132212i	$-0.957792\pi$
$907$	−2.00855	+	7.49600i	−0.0666927	+	0.248901i	0.924529	+	0.381112i	$0.124459\pi$
$908$	4.98428	+	4.98428i	0.165409	+	0.165409i
$909$	−4.85961	−	15.6483i	−0.161183	−	0.519021i
$910$	2.87576	+	8.37140i	0.0953305	+	0.277509i
$911$	−11.1341	+	6.42830i	−0.368890	+	0.212979i	−0.672974	−	0.739667i	$-0.734983\pi$
$911$	−11.1341	+	6.42830i	−0.368890	+	0.212979i	0.304083	+	0.952645i	$0.401650\pi$
$912$	49.8660	+	19.5160i	1.65123	+	0.646240i
$913$	0.542379	+	2.02419i	0.0179501	+	0.0669908i
$914$	−23.1537	+	40.1034i	−0.765857	+	1.32650i
$915$	22.3951	−	4.99969i	0.740359	−	0.165285i
$916$	−7.59207	−	13.1498i	−0.250849	−	0.434483i
$917$	6.38005	−	6.38005i	0.210688	−	0.210688i
$918$	1.89850	−	2.80181i	0.0626600	−	0.0924734i
$919$		−	30.7848i		−	1.01550i	−0.861505	−	0.507749i	$-0.830478\pi$
$919$		−	30.7848i		−	1.01550i	0.861505	−	0.507749i	$-0.169522\pi$
$920$	−0.710333	−	10.2645i	−0.0234190	−	0.338410i
$921$	−0.616543	+	5.51934i	−0.0203158	+	0.181869i
$922$	39.3699	−	10.5491i	1.29658	−	0.347417i
$923$	−10.2486	+	2.74611i	−0.337337	+	0.0903893i
$924$	−7.87662	+	3.44549i	−0.259122	+	0.113348i
$925$	−36.1625	+	15.2886i	−1.18902	+	0.502687i
$926$			29.7259i			0.976854i
$927$	15.6230	−	0.614455i	0.513125	−	0.0201814i
$928$	−9.12048	+	9.12048i	−0.299394	+	0.299394i
$929$	−12.1446	−	21.0351i	−0.398453	−	0.690141i	0.595082	−	0.803665i	$-0.297119\pi$
$929$	−12.1446	−	21.0351i	−0.398453	−	0.690141i	−0.993535	+	0.113524i	$0.963786\pi$
$930$	14.4682	+	27.6929i	0.474431	+	0.908086i
$931$	11.7688	−	20.3842i	0.385708	−	0.668066i
$932$	−1.52567	−	5.69388i	−0.0499750	−	0.186509i
$933$	0.560018	+	3.69155i	0.0183342	+	0.120856i
$934$	45.3882	−	26.2049i	1.48515	−	0.857451i
$935$	2.99073	−	1.02738i	0.0978074	−	0.0335990i
$936$	−5.99052	−	5.53714i	−0.195806	−	0.180987i
$937$	−18.4403	−	18.4403i	−0.602420	−	0.602420i	0.338534	−	0.940954i	$-0.390069\pi$
$937$	−18.4403	−	18.4403i	−0.602420	−	0.602420i	−0.940954	+	0.338534i	$0.890069\pi$
$938$	−8.68284	+	32.4048i	−0.283505	+	1.05805i
$939$	−15.0845	−	34.4842i	−0.492265	−	1.12535i
$940$	−1.29470	+	6.63512i	−0.0422284	+	0.216414i
$941$	−34.2802	−	19.7917i	−1.11750	−	0.645191i	−0.176741	−	0.984257i	$-0.556556\pi$
$941$	−34.2802	−	19.7917i	−1.11750	−	0.645191i	−0.940763	+	0.339066i	$0.889889\pi$
$942$	−2.99503	−	3.74829i	−0.0975832	−	0.122126i
$943$	3.22353	+	0.863741i	0.104972	+	0.0281273i
$944$	2.76275			0.0899200
$945$	−14.8204	+	14.7364i	−0.482109	+	0.479377i
$946$	−25.5377			−0.830301
$947$	−39.9850	−	10.7139i	−1.29934	−	0.348156i	−0.458138	−	0.888881i	$-0.651483\pi$
$947$	−39.9850	−	10.7139i	−1.29934	−	0.348156i	−0.841199	+	0.540725i	$0.818150\pi$
$948$	6.65076	+	8.32346i	0.216006	+	0.270334i
$949$	−2.09629	−	1.21029i	−0.0680485	−	0.0392878i
$950$	−41.4682	−	31.3423i	−1.34541	−	1.01688i
$951$	−3.21843	−	7.35754i	−0.104365	−	0.238585i
$952$	−0.374683	+	1.39834i	−0.0121435	+	0.0453203i
$953$	17.2048	+	17.2048i	0.557319	+	0.557319i	0.928543	−	0.371224i	$-0.121062\pi$
$953$	17.2048	+	17.2048i	0.557319	+	0.557319i	−0.371224	+	0.928543i	$0.621062\pi$
$954$	−50.4049	+	15.6534i	−1.63192	+	0.506796i
$955$	46.7556	+	22.8459i	1.51297	+	0.739276i
$956$	4.60979	−	2.66147i	0.149091	−	0.0860780i
$957$	−2.94163	−	19.3907i	−0.0950893	−	0.626814i
$958$	−5.82033	−	21.7218i	−0.188046	−	0.701798i
$959$	−0.410471	+	0.710957i	−0.0132548	+	0.0229580i
$960$	−11.2784	−	3.53769i	−0.364008	−	0.114179i
$961$	3.72853	+	6.45800i	0.120275	+	0.208323i
$962$	12.2191	−	12.2191i	0.393959	−	0.393959i
$963$	−9.22608	−	14.6212i	−0.297306	−	0.471160i
$964$		−	17.9875i		−	0.579339i
$965$	30.4434	−	34.9702i	0.980007	−	1.12573i
$966$	10.6298	−	4.64983i	0.342008	−	0.149606i
$967$	−21.3448	+	5.71932i	−0.686402	+	0.183921i	−0.585132	−	0.810938i	$-0.698957\pi$
$967$	−21.3448	+	5.71932i	−0.686402	+	0.183921i	−0.101270	+	0.994859i	$0.532291\pi$
$968$	4.03269	−	1.08056i	0.129616	−	0.0347304i
$969$	0.470998	−	4.21642i	0.0151306	−	0.135451i
$970$	−19.7449	+	1.36641i	−0.633971	+	0.0438727i
$971$			3.58038i			0.114900i	0.998348	+	0.0574499i	$0.0182969\pi$
$971$			3.58038i			0.114900i	−0.998348	+	0.0574499i	$0.981703\pi$
$972$	−3.45776	+	11.4028i	−0.110908	+	0.365746i
$973$	−20.3944	+	20.3944i	−0.653815	+	0.653815i
$974$	−20.9139	−	36.2239i	−0.670124	−	1.16069i
$975$	5.99670	+	9.76903i	0.192048	+	0.312859i
$976$	−14.6474	+	25.3700i	−0.468851	+	0.812074i
$977$	−5.33127	−	19.8966i	−0.170562	−	0.636548i	−0.997265	−	0.0739084i	$-0.976453\pi$
$977$	−5.33127	−	19.8966i	−0.170562	−	0.636548i	0.826703	−	0.562639i	$-0.190214\pi$
$978$	−39.8670	−	15.6027i	−1.27481	−	0.498920i
$979$	51.3796	−	29.6640i	1.64210	−	0.948067i
$980$	2.82470	−	5.78092i	0.0902318	−	0.184665i
$981$	3.24053	+	0.733120i	0.103462	+	0.0234067i
$982$	24.4066	+	24.4066i	0.778846	+	0.778846i
$983$	7.58120	−	28.2934i	0.241803	−	0.902420i	−0.733161	−	0.680055i	$-0.761956\pi$
$983$	7.58120	−	28.2934i	0.241803	−	0.902420i	0.974963	−	0.222365i	$-0.0713776\pi$
$984$	3.14425	−	4.26883i	0.100235	−	0.136085i
$985$	20.2554	+	3.95240i	0.645392	+	0.125934i
$986$	1.76930	+	1.02151i	0.0563460	+	0.0325314i
$987$	12.1833	−	1.84824i	0.387800	−	0.0588302i
$988$	6.11057	+	1.63732i	0.194403	+	0.0520902i
$989$	9.52971			0.303027
$990$	−32.4867	+	23.7863i	−1.03249	+	0.755977i
$991$	−21.0816			−0.669679			−0.334840	−	0.942275i	$-0.608682\pi$
$991$	−21.0816			−0.669679			−0.334840	+	0.942275i	$0.608682\pi$
$992$	−19.2726	−	5.16409i	−0.611907	−	0.163960i
$993$	18.3755	−	46.9518i	0.583128	−	1.48997i
$994$	−20.7621	−	11.9870i	−0.658535	−	0.380205i
$995$	7.48881	−	5.04342i	0.237411	−	0.159887i
$996$	0.763794	+	0.0853203i	0.0242017	+	0.00270348i
$997$	−13.3859	+	49.9569i	−0.423936	+	1.58215i	0.342300	+	0.939591i	$0.388794\pi$
$997$	−13.3859	+	49.9569i	−0.423936	+	1.58215i	−0.766236	+	0.642559i	$0.777873\pi$
$998$	11.6227	+	11.6227i	0.367909	+	0.367909i
$999$	38.5506	+	13.3656i	1.21969	+	0.422868i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.l.a.32.2	yes	16
3.2	odd	2		135.2.m.a.17.3		16
4.3	odd	2		720.2.cu.c.257.3		16
5.2	odd	4		225.2.p.b.68.3		16
5.3	odd	4	inner	45.2.l.a.23.2	yes	16
5.4	even	2		225.2.p.b.32.3		16
9.2	odd	6	inner	45.2.l.a.2.2	✓	16
9.4	even	3		405.2.f.a.242.7		16
9.5	odd	6		405.2.f.a.242.2		16
9.7	even	3		135.2.m.a.62.3		16
15.2	even	4		675.2.q.a.368.2		16
15.8	even	4		135.2.m.a.98.3		16
15.14	odd	2		675.2.q.a.557.2		16
20.3	even	4		720.2.cu.c.113.1		16
36.11	even	6		720.2.cu.c.497.1		16
45.2	even	12		225.2.p.b.218.3		16
45.7	odd	12		675.2.q.a.143.2		16
45.13	odd	12		405.2.f.a.323.2		16
45.23	even	12		405.2.f.a.323.7		16
45.29	odd	6		225.2.p.b.182.3		16
45.34	even	6		675.2.q.a.332.2		16
45.38	even	12	inner	45.2.l.a.38.2	yes	16
45.43	odd	12		135.2.m.a.8.3		16
180.83	odd	12		720.2.cu.c.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.2	✓	16	9.2	odd	6	inner
45.2.l.a.23.2	yes	16	5.3	odd	4	inner
45.2.l.a.32.2	yes	16	1.1	even	1	trivial
45.2.l.a.38.2	yes	16	45.38	even	12	inner
135.2.m.a.8.3		16	45.43	odd	12
135.2.m.a.17.3		16	3.2	odd	2
135.2.m.a.62.3		16	9.7	even	3
135.2.m.a.98.3		16	15.8	even	4
225.2.p.b.32.3		16	5.4	even	2
225.2.p.b.68.3		16	5.2	odd	4
225.2.p.b.182.3		16	45.29	odd	6
225.2.p.b.218.3		16	45.2	even	12
405.2.f.a.242.2		16	9.5	odd	6
405.2.f.a.242.7		16	9.4	even	3
405.2.f.a.323.2		16	45.13	odd	12
405.2.f.a.323.7		16	45.23	even	12
675.2.q.a.143.2		16	45.7	odd	12
675.2.q.a.332.2		16	45.34	even	6
675.2.q.a.368.2		16	15.2	even	4
675.2.q.a.557.2		16	15.14	odd	2
720.2.cu.c.113.1		16	20.3	even	4
720.2.cu.c.257.3		16	4.3	odd	2
720.2.cu.c.353.3		16	180.83	odd	12
720.2.cu.c.497.1		16	36.11	even	6

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	45.2.l.a.32.2

Level	$45$
Weight	$2$
Character	45.32
Analytic conductor	$0.359$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$