LMFDB - Embedded newform 225.2.p.b.218.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.p (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:	$1.79663404548$
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:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			218.3
Root			$1.60599 + 0.430324i$ of defining polynomial
Character	$\chi$	$=$	225.218
Dual form			225.2.p.b.32.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60599 - 0.430324i) q^{2} +(1.08121 - 1.35314i) q^{3} +(0.661975 - 0.382191i) q^{4} +(1.15412 - 2.63840i) q^{6} +(-0.465559 - 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +(-0.661975 - 2.92605i) q^{9} +O(q^{10})$	\(q+(1.60599 - 0.430324i) q^{2} +(1.08121 - 1.35314i) q^{3} +(0.661975 - 0.382191i) q^{4} +(1.15412 - 2.63840i) q^{6} +(-0.465559 - 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +(-0.661975 - 2.92605i) q^{9} +(3.12636 + 1.80501i) q^{11} +(0.198575 - 1.30897i) q^{12} +(-0.342574 + 1.27850i) q^{13} +(-1.49537 - 2.59005i) q^{14} +(-2.47224 + 4.28205i) q^{16} +(0.277007 + 0.277007i) q^{17} +(-2.32228 - 4.41435i) q^{18} +6.25273i q^{19} +(-2.85443 - 1.24862i) q^{21} +(5.79765 + 1.55348i) q^{22} +(-2.16347 - 0.579699i) q^{23} +(0.395027 + 3.53631i) q^{24} +2.20068i q^{26} +(-4.67509 - 2.26793i) q^{27} +(-0.972242 - 0.972242i) q^{28} +(1.56832 - 2.71642i) q^{29} +(-2.42605 - 4.20205i) q^{31} +(-1.06430 + 3.97202i) q^{32} +(5.82268 - 2.27882i) q^{33} +(0.564074 + 0.325668i) q^{34} +(-1.55652 - 1.68397i) q^{36} +(-5.55242 + 5.55242i) q^{37} +(2.69070 + 10.0418i) q^{38} +(1.35960 + 1.84588i) q^{39} +(1.29036 - 0.744991i) q^{41} +(-5.12150 - 0.776946i) q^{42} +(-4.10976 + 1.10121i) q^{43} +2.75943 q^{44} -3.72396 q^{46} +(3.82042 - 1.02368i) q^{47} +(3.12120 + 7.97508i) q^{48} +(3.26005 - 1.88219i) q^{49} +(0.674332 - 0.0753268i) q^{51} +(0.261857 + 0.977265i) q^{52} +(7.48222 - 7.48222i) q^{53} +(-8.48410 - 1.63047i) q^{54} +(3.20031 + 1.84770i) q^{56} +(8.46082 + 6.76051i) q^{57} +(1.34977 - 5.03742i) q^{58} +(-0.279377 - 0.483896i) q^{59} +(-2.96237 + 5.13097i) q^{61} +(-5.70446 - 5.70446i) q^{62} +(-4.77580 + 2.51243i) q^{63} -3.05196i q^{64} +(8.37054 - 6.16540i) q^{66} +(-10.8351 - 2.90325i) q^{67} +(0.289242 + 0.0775020i) q^{68} +(-3.12357 + 2.30070i) q^{69} -8.01611i q^{71} +(5.21223 + 3.28897i) q^{72} +(1.29315 + 1.29315i) q^{73} +(-6.52779 + 11.3065i) q^{74} +(2.38974 + 4.13915i) q^{76} +(1.68068 - 6.27237i) q^{77} +(2.97783 + 2.37939i) q^{78} +(-6.96917 - 4.02365i) q^{79} +(-8.12358 + 3.87395i) q^{81} +(1.75172 - 1.75172i) q^{82} +(0.150243 + 0.560714i) q^{83} +(-2.36678 + 0.264383i) q^{84} +(-6.12636 + 3.53706i) q^{86} +(-1.98001 - 5.05917i) q^{87} +(-7.16367 + 1.91950i) q^{88} +16.4343 q^{89} +2.38087 q^{91} +(-1.65372 + 0.443112i) q^{92} +(-8.30903 - 1.26050i) q^{93} +(5.69504 - 3.28804i) q^{94} +(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} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.60599	−	0.430324i	1.13561	−	0.304285i	0.358423	−	0.933559i	$-0.383314\pi$
$2$	1.60599	−	0.430324i	1.13561	−	0.304285i	0.777183	+	0.629274i	$0.216648\pi$
$3$	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
$5$		0			0
$5$		0			0
$6$	1.15412	−	2.63840i	0.471169	−	1.07712i
$7$	−0.465559	−	1.73749i	−0.175965	−	0.656710i	−0.996385	−	0.0849489i	$-0.972927\pi$
$7$	−0.465559	−	1.73749i	−0.175965	−	0.656710i	0.820421	−	0.571761i	$-0.193739\pi$
$8$	−1.45267	+	1.45267i	−0.513598	+	0.513598i
$9$	−0.661975	−	2.92605i	−0.220658	−	0.975351i
$10$		0			0
$11$	3.12636	+	1.80501i	0.942634	+	0.544230i	0.890785	−	0.454425i	$-0.150155\pi$
$11$	3.12636	+	1.80501i	0.942634	+	0.544230i	0.0518493	+	0.998655i	$0.483488\pi$
$12$	0.198575	−	1.30897i	0.0573236	−	0.377868i
$13$	−0.342574	+	1.27850i	−0.0950128	+	0.354593i	−0.997021	−	0.0771255i	$-0.975426\pi$
$13$	−0.342574	+	1.27850i	−0.0950128	+	0.354593i	0.902009	+	0.431718i	$0.142092\pi$
$14$	−1.49537	−	2.59005i	−0.399654	−	0.692220i
$15$		0			0
$16$	−2.47224	+	4.28205i	−0.618061	+	1.07051i
$17$	0.277007	+	0.277007i	0.0671841	+	0.0671841i	0.739900	−	0.672716i	$-0.234873\pi$
$17$	0.277007	+	0.277007i	0.0671841	+	0.0671841i	−0.672716	+	0.739900i	$0.734873\pi$
$18$	−2.32228	−	4.41435i	−0.547366	−	1.04047i
$19$			6.25273i			1.43447i	0.696829	+	0.717237i	$0.254594\pi$
$19$			6.25273i			1.43447i	−0.696829	+	0.717237i	$0.745406\pi$
$20$		0			0
$21$	−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	$-0.491689\pi$
$23$	−2.16347	−	0.579699i	−0.451114	−	0.120876i	−0.477221	+	0.878784i	$0.658356\pi$
$24$	0.395027	+	3.53631i	0.0806346	+	0.721847i
$25$		0			0
$26$			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	−0.682871	−	0.730539i	$-0.739269\pi$
$29$	1.56832	−	2.71642i	0.291230	−	0.504426i	0.974101	+	0.226114i	$0.0726021\pi$
$30$		0			0
$31$	−2.42605	−	4.20205i	−0.435732	−	0.754710i	0.561623	−	0.827393i	$-0.310177\pi$
$31$	−2.42605	−	4.20205i	−0.435732	−	0.754710i	−0.997355	+	0.0726832i	$0.976844\pi$
$32$	−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
$35$		0			0
$36$	−1.55652	−	1.68397i	−0.259421	−	0.280662i
$37$	−5.55242	+	5.55242i	−0.912812	+	0.912812i	−0.996493	−	0.0836807i	$-0.973332\pi$
$37$	−5.55242	+	5.55242i	−0.912812	+	0.912812i	0.0836807	+	0.996493i	$0.473332\pi$
$38$	2.69070	+	10.0418i	0.436489	+	1.62900i
$39$	1.35960	+	1.84588i	0.217710	+	0.295577i
$40$		0			0
$41$	1.29036	−	0.744991i	0.201521	−	0.116348i	−0.395844	−	0.918318i	$-0.629548\pi$
$41$	1.29036	−	0.744991i	0.201521	−	0.116348i	0.597365	+	0.801970i	$0.296215\pi$
$42$	−5.12150	−	0.776946i	−0.790265	−	0.119885i
$43$	−4.10976	+	1.10121i	−0.626733	+	0.167933i	−0.558187	−	0.829715i	$-0.688503\pi$
$43$	−4.10976	+	1.10121i	−0.626733	+	0.167933i	−0.0685463	+	0.997648i	$0.521836\pi$
$44$	2.75943			0.416000
$45$		0			0
$46$	−3.72396			−0.549069
$47$	3.82042	−	1.02368i	0.557266	−	0.149319i	0.0308158	−	0.999525i	$-0.490189\pi$
$47$	3.82042	−	1.02368i	0.557266	−	0.149319i	0.526450	+	0.850206i	$0.323523\pi$
$48$	3.12120	+	7.97508i	0.450507	+	1.15110i
$49$	3.26005	−	1.88219i	0.465722	−	0.268884i
$50$		0			0
$51$	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	0.0281581	−	0.999603i	$-0.491036\pi$
$53$	7.48222	−	7.48222i	1.02776	−	1.02776i	0.999603	−	0.0281581i	$-0.00896420\pi$
$54$	−8.48410	−	1.63047i	−1.15454	−	0.221879i
$55$		0			0
$56$	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	0.847266	−	0.531168i	$-0.178247\pi$
$59$	−0.279377	−	0.483896i	−0.0363718	−	0.0629978i	−0.883638	+	0.468170i	$0.844913\pi$
$60$		0			0
$61$	−2.96237	+	5.13097i	−0.379292	+	0.656953i	−0.990959	−	0.134162i	$-0.957166\pi$
$61$	−2.96237	+	5.13097i	−0.379292	+	0.656953i	0.611667	+	0.791115i	$0.290499\pi$
$62$	−5.70446	−	5.70446i	−0.724467	−	0.724467i
$63$	−4.77580	+	2.51243i	−0.601694	+	0.316536i
$64$		−	3.05196i		−	0.381495i
$65$		0			0
$66$	8.37054	−	6.16540i	1.03034	−	0.758908i
$67$	−10.8351	−	2.90325i	−1.32371	−	0.354688i	−0.473346	−	0.880876i	$-0.656954\pi$
$67$	−10.8351	−	2.90325i	−1.32371	−	0.354688i	−0.850368	+	0.526188i	$0.823621\pi$
$68$	0.289242	+	0.0775020i	0.0350757	+	0.00939850i
$69$	−3.12357	+	2.30070i	−0.376034	+	0.276971i
$70$		0			0
$71$		−	8.01611i		−	0.951338i	−0.879624	−	0.475669i	$-0.842206\pi$
$71$		−	8.01611i		−	0.951338i	0.879624	−	0.475669i	$-0.157794\pi$
$72$	5.21223	+	3.28897i	0.614268	+	0.387608i
$73$	1.29315	+	1.29315i	0.151352	+	0.151352i	0.778721	−	0.627370i	$-0.215869\pi$
$73$	1.29315	+	1.29315i	0.151352	+	0.151352i	−0.627370	+	0.778721i	$0.715869\pi$
$74$	−6.52779	+	11.3065i	−0.758840	+	1.31435i
$75$		0			0
$76$	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	0.0537859	−	0.998552i	$-0.482871\pi$
$79$	−6.96917	−	4.02365i	−0.784093	−	0.452696i	−0.837879	+	0.545856i	$0.816204\pi$
$80$		0			0
$81$	−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	$-0.0731907\pi$
$83$	0.150243	+	0.560714i	0.0164913	+	0.0615463i	−0.957190	+	0.289461i	$0.906524\pi$
$84$	−2.36678	+	0.264383i	−0.258237	+	0.0288465i
$85$		0			0
$86$	−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	$0.163462\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	4.22396	+	5.73472i	0.431106	+	0.585298i
$97$	1.37786	+	5.14224i	0.139900	+	0.522116i	0.999930	+	0.0118706i	$0.00377862\pi$
$97$	1.37786	+	5.14224i	0.139900	+	0.522116i	−0.860029	+	0.510245i	$0.829555\pi$
$98$	4.42566	−	4.42566i	0.447059	−	0.447059i
$99$	3.21197	−	10.3428i	0.322815	−	1.03949i
$100$		0			0
$101$	−4.73008	−	2.73092i	−0.470661	−	0.271736i	0.245855	−	0.969307i	$-0.420931\pi$
$101$	−4.73008	−	2.73092i	−0.470661	−	0.271736i	−0.716516	+	0.697570i	$0.754265\pi$
$102$	1.05056	−	0.411155i	0.104021	−	0.0407104i
$103$	1.34888	−	5.03410i	0.132909	−	0.496024i	−0.867088	−	0.498154i	$-0.834011\pi$
$103$	1.34888	−	5.03410i	0.132909	−	0.496024i	0.999998	+	0.00212995i	$0.000677984\pi$
$104$	−1.35960	−	2.35489i	−0.133320	−	0.230916i
$105$		0			0
$106$	8.79659	−	15.2361i	0.854401	−	1.47987i
$107$	4.07498	+	4.07498i	0.393944	+	0.393944i	0.876090	−	0.482147i	$-0.160143\pi$
$107$	4.07498	+	4.07498i	0.393944	+	0.393944i	−0.482147	+	0.876090i	$0.660143\pi$
$108$	−3.96158	+	0.285467i	−0.381203	+	0.0274691i
$109$			1.10747i			0.106077i	0.998592	+	0.0530384i	$0.0168906\pi$
$109$			1.10747i			0.106077i	−0.998592	+	0.0530384i	$0.983109\pi$
$110$		0			0
$111$	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	$-0.545062\pi$
$113$	−8.06067	−	2.15985i	−0.758284	−	0.203182i	−0.617190	+	0.786815i	$0.711729\pi$
$114$	16.4972	+	7.21642i	1.54510	+	0.675879i
$115$		0			0
$116$		−	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
$120$		0			0
$121$	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
$125$		0			0
$126$	−6.58873	+	6.09007i	−0.586971	+	0.542547i
$127$	11.5887	−	11.5887i	1.02833	−	1.02833i	0.0287470	−	0.999587i	$-0.490848\pi$
$127$	11.5887	−	11.5887i	1.02833	−	1.02833i	0.999587	−	0.0287470i	$-0.00915171\pi$
$128$	−3.44193	−	12.8454i	−0.304226	−	1.13539i
$129$	−2.95342	+	6.75172i	−0.260035	+	0.594456i
$130$		0			0
$131$	4.34401	−	2.50802i	0.379538	−	0.219126i	−0.298079	−	0.954541i	$-0.596346\pi$
$131$	4.34401	−	2.50802i	0.379538	−	0.219126i	0.677617	+	0.735415i	$0.263013\pi$
$132$	2.98352	−	3.73390i	0.259682	−	0.324994i
$133$	10.8641	−	2.91101i	0.942033	−	0.252417i
$134$	−18.6504			−1.61115
$135$		0			0
$136$	−0.804802			−0.0690112
$137$	0.440837	−	0.118122i	0.0376632	−	0.0100918i	−0.239938	−	0.970788i	$-0.577127\pi$
$137$	0.440837	−	0.118122i	0.0376632	−	0.0100918i	0.277601	+	0.960696i	$0.410461\pi$
$138$	−4.02638	+	5.03904i	−0.342748	+	0.428952i
$139$	−13.8860	+	8.01711i	−1.17780	+	0.680003i	−0.955504	−	0.294977i	$-0.904688\pi$
$139$	−13.8860	+	8.01711i	−1.17780	+	0.680003i	−0.222295	+	0.974980i	$0.571355\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	0.689922	−	0.723884i	$-0.257645\pi$
$149$	−3.44153	−	5.96090i	−0.281941	−	0.488336i	−0.971863	+	0.235548i	$0.924312\pi$
$150$		0			0
$151$	4.30647	−	7.45902i	0.350455	−	0.607006i	−0.635874	−	0.771793i	$-0.719360\pi$
$151$	4.30647	−	7.45902i	0.350455	−	0.607006i	0.986329	+	0.164787i	$0.0526935\pi$
$152$	−9.08317	−	9.08317i	−0.736743	−	0.736743i
$153$	0.627166	−	0.993910i	0.0507034	−	0.0803528i
$154$		−	10.7966i		−	0.870014i
$155$		0			0
$156$	1.60550	+	0.702298i	0.128543	+	0.0562288i
$157$	1.60930	+	0.431209i	0.128436	+	0.0344142i	0.322464	−	0.946582i	$-0.395489\pi$
$157$	1.60930	+	0.431209i	0.128436	+	0.0344142i	−0.194029	+	0.980996i	$0.562155\pi$
$158$	−12.9239	−	3.46295i	−1.02817	−	0.275497i
$159$	−2.03465	−	18.2143i	−0.161358	−	1.44449i
$160$		0			0
$161$			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	$-0.0521898\pi$
$163$	10.5120	+	10.5120i	0.823363	+	0.823363i	−0.163225	+	0.986589i	$0.552190\pi$
$164$	0.569458	−	0.986331i	0.0444672	−	0.0770195i
$165$		0			0
$166$	0.482577	+	0.835848i	0.0374552	+	0.0648744i
$167$	−2.51657	+	9.39195i	−0.194738	+	0.726771i	0.797597	+	0.603191i	$0.206104\pi$
$167$	−2.51657	+	9.39195i	−0.194738	+	0.726771i	−0.992335	+	0.123580i	$0.960562\pi$
$168$	5.96040	−	2.33272i	0.459855	−	0.179973i
$169$	9.74112	+	5.62404i	0.749317	+	0.432618i
$170$		0			0
$171$	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	0.941022	+	0.338346i	$0.109867\pi$
$173$	3.88335	+	14.4929i	0.295246	+	1.10187i	−0.645776	+	0.763527i	$0.723466\pi$
$174$	−5.35695	−	7.27294i	−0.406109	−	0.551360i
$175$		0			0
$176$	−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	$0.550410\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$	−20.1545	−	11.6362i	−1.45833	−	0.841965i	−0.459397	−	0.888231i	$-0.651934\pi$
$191$	−20.1545	−	11.6362i	−1.45833	−	0.841965i	−0.998929	+	0.0462661i	$0.985268\pi$
$192$	−4.12973	−	3.29980i	−0.298037	−	0.238143i
$193$	−5.36663	+	20.0285i	−0.386299	+	1.44169i	0.449811	+	0.893124i	$0.351491\pi$
$193$	−5.36663	+	20.0285i	−0.386299	+	1.44169i	−0.836110	+	0.548562i	$0.815175\pi$
$194$	4.42566	+	7.66547i	0.317744	+	0.550348i
$195$		0			0
$196$	1.43871	−	2.49193i	0.102765	−	0.177995i
$197$	6.52613	+	6.52613i	0.464968	+	0.464968i	0.900280	−	0.435312i	$-0.143362\pi$
$197$	6.52613	+	6.52613i	0.464968	+	0.464968i	−0.435312	+	0.900280i	$0.643362\pi$
$198$	0.707653	−	17.9926i	0.0502907	−	1.27868i
$199$		−	4.03778i		−	0.286231i	−0.989706	−	0.143115i	$-0.954288\pi$
$199$		−	4.03778i		−	0.286231i	0.989706	−	0.143115i	$-0.0457120\pi$
$200$		0			0
$201$	−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			0
$206$		−	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
$210$		0			0
$211$	0.653114	+	1.13123i	0.0449623	+	0.0778769i	0.887631	−	0.460556i	$-0.152350\pi$
$211$	0.653114	+	1.13123i	0.0449623	+	0.0778769i	−0.842668	+	0.538433i	$0.819017\pi$
$212$	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
$215$		0			0
$216$	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
$220$		0			0
$221$	−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	$-0.672907\pi$
$223$	−8.01142	+	2.14665i	−0.536485	+	0.143751i	−0.0196035	+	0.999808i	$0.506240\pi$
$224$	7.39683			0.494222
$225$		0			0
$226$	−13.8748			−0.922937
$227$	−8.90739	+	2.38673i	−0.591204	+	0.158413i	−0.542003	−	0.840376i	$-0.682334\pi$
$227$	−8.90739	+	2.38673i	−0.591204	+	0.158413i	−0.0492007	+	0.998789i	$0.515667\pi$
$228$	8.18466	+	1.24163i	0.542042	+	0.0822292i
$229$	−17.2032	+	9.93228i	−1.13682	+	0.656344i	−0.945641	−	0.325211i	$-0.894565\pi$
$229$	−17.2032	+	9.93228i	−1.13682	+	0.656344i	−0.191179	+	0.981555i	$0.561231\pi$
$230$		0			0
$231$	−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	$-0.668712\pi$
$233$	5.45304	−	5.45304i	0.357241	−	0.357241i	0.862795	+	0.505554i	$0.168712\pi$
$234$	6.43930	−	1.45679i	0.420951	−	0.0952336i
$235$		0			0
$236$	−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	0.956386	−	0.292106i	$-0.0943559\pi$
$239$	3.48185	+	6.03074i	0.225222	+	0.390096i	−0.731164	+	0.682202i	$0.761023\pi$
$240$		0			0
$241$	−11.7660	+	20.3794i	−0.757918	+	1.31275i	0.185993	+	0.982551i	$0.440450\pi$
$241$	−11.7660	+	20.3794i	−0.757918	+	1.31275i	−0.943911	+	0.330201i	$0.892883\pi$
$242$	2.38920	+	2.38920i	0.153584	+	0.153584i
$243$	−3.54129	+	15.1809i	−0.227174	+	0.973854i
$244$			4.52877i			0.289925i
$245$		0			0
$246$	−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
$250$		0			0
$251$			20.7941i			1.31251i	0.754537	+	0.656257i	$0.227861\pi$
$251$			20.7941i			1.31251i	−0.754537	+	0.656257i	$0.772139\pi$
$252$	−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			0
$256$	−8.00344	−	13.8624i	−0.500215	−	0.866398i
$257$	−2.72001	+	10.1512i	−0.169670	+	0.633216i	0.827729	+	0.561129i	$0.189633\pi$
$257$	−2.72001	+	10.1512i	−0.169670	+	0.633216i	−0.997398	+	0.0720873i	$0.977034\pi$
$258$	−1.83774	+	12.1141i	−0.114413	+	0.754193i
$259$	12.2323	+	7.06229i	0.760075	+	0.438830i
$260$		0			0
$261$	−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	−0.976574	−	0.215180i	$-0.930966\pi$
$263$	−3.86662	−	14.4304i	−0.238426	−	0.889818i	0.738148	−	0.674638i	$-0.235700\pi$
$264$	−5.14807	+	11.7688i	−0.316842	+	0.724322i
$265$		0			0
$266$	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	$0.492411\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	−1.18842	+	2.71681i	−0.0715345	+	0.163533i
$277$	2.43120	+	9.07336i	0.146077	+	0.545165i	0.999705	+	0.0242830i	$0.00773027\pi$
$277$	2.43120	+	9.07336i	0.146077	+	0.545165i	−0.853629	+	0.520882i	$0.825603\pi$
$278$	−18.8509	+	18.8509i	−1.13060	+	1.13060i
$279$	−10.6894	+	9.88041i	−0.639959	+	0.591525i
$280$		0			0
$281$	26.6024	+	15.3589i	1.58697	+	0.916237i	0.993803	+	0.111156i	$0.0354553\pi$
$281$	26.6024	+	15.3589i	1.58697	+	0.916237i	0.593165	+	0.805081i	$0.297878\pi$
$282$	1.70836	−	11.2612i	0.101731	−	0.670597i
$283$	4.86835	−	18.1689i	0.289393	−	1.08003i	−0.656175	−	0.754609i	$-0.727827\pi$
$283$	4.86835	−	18.1689i	0.289393	−	1.08003i	0.945569	−	0.325423i	$-0.105507\pi$
$284$	−3.06369	−	5.30647i	−0.181797	−	0.314881i
$285$		0			0
$286$	−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
$290$		0			0
$291$	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	0.994765	+	0.102194i	$0.0325861\pi$
$293$	32.6486	+	8.74817i	1.90735	+	0.511074i	0.912588	+	0.408880i	$0.134081\pi$
$294$	−1.20347	−	10.7736i	−0.0701880	−	0.628329i
$295$		0			0
$296$		−	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
$300$		0			0
$301$	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
$305$		0			0
$306$	0.579519	−	1.86609i	0.0331289	−	0.106677i
$307$	2.26728	−	2.26728i	0.129400	−	0.129400i	−0.639440	−	0.768841i	$-0.720834\pi$
$307$	2.26728	−	2.26728i	0.129400	−	0.129400i	0.768841	+	0.639440i	$0.220834\pi$
$308$	−1.28468	−	4.79449i	−0.0732014	−	0.273191i
$309$	−5.35341	−	7.26814i	−0.304545	−	0.413470i
$310$		0			0
$311$	−1.86689	+	1.07785i	−0.105862	+	0.0611193i	−0.551996	−	0.833847i	$-0.686134\pi$
$311$	−1.86689	+	1.07785i	−0.105862	+	0.0611193i	0.446134	+	0.894966i	$0.352800\pi$
$312$	−4.65651	−	0.706405i	−0.263623	−	0.0399923i
$313$	−20.9905	+	5.62439i	−1.18645	+	0.317909i	−0.797483	−	0.603341i	$-0.793836\pi$
$313$	−20.9905	+	5.62439i	−1.18645	+	0.317909i	−0.388971	+	0.921250i	$0.627169\pi$
$314$	2.77007			0.156324
$315$		0			0
$316$	−6.15122			−0.346033
$317$	−4.47853	+	1.20002i	−0.251539	+	0.0673997i	−0.382385	−	0.924003i	$-0.624897\pi$
$317$	−4.47853	+	1.20002i	−0.251539	+	0.0673997i	0.130846	+	0.991403i	$0.458231\pi$
$318$	−11.1057	−	28.3765i	−0.622776	−	1.59127i
$319$	9.80630	−	5.66167i	0.549047	−	0.316993i
$320$		0			0
$321$	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
$325$		0			0
$326$	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			0
$331$	14.5549	−	25.2097i	0.800007	−	1.38565i	−0.119604	−	0.992822i	$-0.538162\pi$
$331$	14.5549	−	25.2097i	0.800007	−	1.38565i	0.919611	−	0.392831i	$-0.128504\pi$
$332$	0.313757	+	0.313757i	0.0172197	+	0.0172197i
$333$	19.9222	+	12.5711i	1.09173	+	0.688893i
$334$			16.1663i			0.884582i
$335$		0			0
$336$	12.4035	−	9.13593i	0.676667	−	0.498406i
$337$	24.1823	+	6.47963i	1.31729	+	0.352968i	0.847963	−	0.530055i	$-0.177829\pi$
$337$	24.1823	+	6.47963i	1.31729	+	0.352968i	0.469330	+	0.883023i	$0.344495\pi$
$338$	18.0643	+	4.84031i	0.982568	+	0.263278i
$339$	−11.6378	+	8.57197i	−0.632081	+	0.465565i
$340$		0			0
$341$		−	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			0
$346$	12.4733	+	21.6043i	0.670566	+	1.16145i
$347$	9.05260	−	33.7848i	0.485969	−	1.81366i	−0.0896885	−	0.995970i	$-0.528587\pi$
$347$	9.05260	−	33.7848i	0.485969	−	1.81366i	0.575657	−	0.817691i	$-0.304746\pi$
$348$	−3.24429	−	2.59231i	−0.173912	−	0.138962i
$349$	17.0932	+	9.86876i	0.914978	+	0.528263i	0.882029	−	0.471194i	$-0.156177\pi$
$349$	17.0932	+	9.86876i	0.914978	+	0.528263i	0.0329483	+	0.999457i	$0.489510\pi$
$350$		0			0
$351$	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	$-0.0187832\pi$
$353$	1.95875	+	7.31017i	0.104254	+	0.389081i	−0.894006	+	0.448056i	$0.852117\pi$
$354$	−1.59915	+	0.178634i	−0.0849936	+	0.00949429i
$355$		0			0
$356$	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	$0.428181\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	10.1186	+	13.7377i	0.528908	+	0.718080i
$367$	2.12506	+	7.93083i	0.110927	+	0.413986i	0.998950	−	0.0458135i	$-0.0145880\pi$
$367$	2.12506	+	7.93083i	0.110927	+	0.413986i	−0.888023	+	0.459799i	$0.847921\pi$
$368$	7.83091	−	7.83091i	0.408215	−	0.408215i
$369$	−3.03407	−	3.28250i	−0.157947	−	0.170880i
$370$		0			0
$371$	−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	−0.657967	−	0.753046i	$-0.728584\pi$
$373$	5.56939	−	20.7853i	0.288372	−	1.07622i	0.946340	−	0.323174i	$-0.104750\pi$
$374$	1.17567	+	2.03631i	0.0607923	+	0.105295i
$375$		0			0
$376$	−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	$-0.907454\pi$
$379$		−	11.1614i		−	0.573325i	0.958032	−	0.286663i	$-0.0925458\pi$
$380$		0			0
$381$	−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	$-0.543762\pi$
$383$	−14.6977	−	3.93824i	−0.751018	−	0.201235i	−0.613970	+	0.789330i	$0.710428\pi$
$384$	−21.1031	−	9.23120i	−1.07691	−	0.471078i
$385$		0			0
$386$			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	−0.338168	−	0.941086i	$-0.609807\pi$
$389$	12.7395	−	22.0655i	0.645920	−	1.11877i	0.984088	−	0.177681i	$-0.0568596\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	−1.82668	−	8.07425i	−0.0917939	−	0.405746i
$397$	5.96779	−	5.96779i	0.299515	−	0.299515i	−0.541309	−	0.840824i	$-0.682071\pi$
$397$	5.96779	−	5.96779i	0.299515	−	0.299515i	0.840824	+	0.541309i	$0.182071\pi$
$398$	−1.73755	−	6.48464i	−0.0870957	−	0.325046i
$399$	7.80730	−	17.8480i	0.390854	−	0.893518i
$400$		0			0
$401$	23.6805	−	13.6719i	1.18255	−	0.682744i	0.225945	−	0.974140i	$-0.427453\pi$
$401$	23.6805	−	13.6719i	1.18255	−	0.682744i	0.956602	+	0.291396i	$0.0941198\pi$
$402$	−20.1649	+	25.2365i	−1.00574	+	1.25868i
$403$	6.20343	−	1.66220i	0.309015	−	0.0828003i
$404$	−4.17493			−0.207711
$405$		0			0
$406$	−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	0.211878	−	0.977296i	$-0.432042\pi$
$409$	23.5441	−	13.5932i	1.16418	−	0.672140i	0.952302	+	0.305157i	$0.0987088\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	−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	0.939138	+	0.343541i	$0.111627\pi$
$419$	15.7018	+	27.1964i	0.767084	+	1.32863i	−0.172053	+	0.985088i	$0.555040\pi$
$420$		0			0
$421$	−15.4328	+	26.7304i	−0.752150	+	1.30276i	0.194629	+	0.980877i	$0.437650\pi$
$421$	−15.4328	+	26.7304i	−0.752150	+	1.30276i	−0.946779	+	0.321885i	$0.895683\pi$
$422$	1.53569	+	1.53569i	0.0747562	+	0.0747562i
$423$	−5.52436	−	10.5011i	−0.268604	−	0.510581i
$424$			21.7384i			1.05571i
$425$		0			0
$426$	−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
$430$		0			0
$431$			32.6869i			1.57447i	0.616652	+	0.787236i	$0.288489\pi$
$431$			32.6869i			1.57447i	−0.616652	+	0.787236i	$0.711511\pi$
$432$	21.2694	−	14.4121i	1.02332	−	0.693403i
$433$	7.25927	+	7.25927i	0.348858	+	0.348858i	0.859684	−	0.510826i	$-0.170660\pi$
$433$	7.25927	+	7.25927i	0.348858	+	0.348858i	−0.510826	+	0.859684i	$0.670660\pi$
$434$	−7.25568	+	12.5672i	−0.348284	+	0.603245i
$435$		0			0
$436$	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	−0.0426241	−	0.999091i	$-0.513572\pi$
$439$	−19.4684	−	11.2401i	−0.929175	−	0.536459i	−0.886550	+	0.462632i	$0.846905\pi$
$440$		0			0
$441$	−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	$-0.0245589\pi$
$443$	2.00030	+	7.46524i	0.0950373	+	0.354684i	−0.901988	+	0.431762i	$0.857892\pi$
$444$	6.16540	+	8.37054i	0.292597	+	0.397248i
$445$		0			0
$446$	−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	$0.856586\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	−22.1116	+	2.47000i	−1.03547	+	0.115668i
$457$	−7.20855	−	26.9027i	−0.337202	−	1.25845i	−0.901463	−	0.432857i	$-0.857505\pi$
$457$	−7.20855	−	26.9027i	−0.337202	−	1.25845i	0.564261	−	0.825596i	$-0.309161\pi$
$458$	−23.3541	+	23.3541i	−1.09127	+	1.09127i
$459$	−0.666801	−	1.92327i	−0.0311236	−	0.0897704i
$460$		0			0
$461$	−21.2301	−	12.2572i	−0.988784	−	0.570874i	−0.0838731	−	0.996476i	$-0.526729\pi$
$461$	−21.2301	−	12.2572i	−0.988784	−	0.570874i	−0.904910	+	0.425602i	$0.860062\pi$
$462$	−14.6093	−	11.6734i	−0.679686	−	0.543094i
$463$	4.62735	−	17.2695i	0.215051	−	0.802582i	−0.771097	−	0.636717i	$-0.780292\pi$
$463$	4.62735	−	17.2695i	0.215051	−	0.802582i	0.986149	−	0.165865i	$-0.0530415\pi$
$464$	7.75455	+	13.4313i	0.359996	+	0.623531i
$465$		0			0
$466$	6.41096	−	11.1041i	0.296982	−	0.514388i
$467$	22.2894	+	22.2894i	1.03143	+	1.03143i	0.999490	+	0.0319412i	$0.0101689\pi$
$467$	22.2894	+	22.2894i	1.03143	+	1.03143i	0.0319412	+	0.999490i	$0.489831\pi$
$468$	2.68619	−	1.41313i	0.124169	−	0.0653221i
$469$			20.1775i			0.931709i
$470$		0			0
$471$	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
$475$		0			0
$476$		−	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	−0.669146	−	0.743131i	$-0.733340\pi$
$479$	6.76273	−	11.7134i	0.308997	−	0.535199i	0.978143	+	0.207932i	$0.0666734\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	0.845418	+	25.9043i	0.0383489	+	1.17504i
$487$	−17.7890	+	17.7890i	−0.806094	+	0.806094i	−0.984040	−	0.177946i	$-0.943055\pi$
$487$	−17.7890	+	17.7890i	−0.806094	+	0.806094i	0.177946	+	0.984040i	$0.443055\pi$
$488$	−3.15027	−	11.7570i	−0.142606	−	0.532213i
$489$	25.5899	−	2.85854i	1.15721	−	0.129268i
$490$		0			0
$491$	−17.9785	+	10.3799i	−0.811359	+	0.468438i	−0.847427	−	0.530911i	$-0.821850\pi$
$491$	−17.9785	+	10.3799i	−0.811359	+	0.468438i	0.0360688	+	0.999349i	$0.488516\pi$
$492$	−0.718940	−	1.83699i	−0.0324123	−	0.0828177i
$493$	1.18690	−	0.318030i	0.0534554	−	0.0143233i
$494$	−13.7603			−0.619103
$495$		0			0
$496$	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	−0.679239	−	0.733917i	$-0.737690\pi$
$499$	−8.56156	+	4.94302i	−0.383268	+	0.221280i	0.295971	+	0.955197i	$0.404357\pi$
$500$		0			0
$501$	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	$-0.927786\pi$
$503$	−16.8084	+	16.8084i	−0.749450	+	0.749450i	0.224926	+	0.974376i	$0.427786\pi$
$504$	3.28794	−	10.5874i	0.146457	−	0.471601i
$505$		0			0
$506$	−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	−0.834494	−	0.551017i	$-0.814240\pi$
$509$	−20.1795	−	34.9520i	−0.894442	−	1.54922i	−0.0599475	−	0.998202i	$-0.519093\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$		−	11.5144i		−	0.504456i	−0.967668	−	0.252228i	$-0.918837\pi$
$521$		−	11.5144i		−	0.504456i	0.967668	−	0.252228i	$-0.0811633\pi$
$522$	−15.6333	−	0.614861i	−0.684250	−	0.0269118i
$523$	29.5457	+	29.5457i	1.29194	+	1.29194i	0.933584	+	0.358358i	$0.116663\pi$
$523$	29.5457	+	29.5457i	1.29194	+	1.29194i	0.358358	+	0.933584i	$0.383337\pi$
$524$	1.91708	−	3.32049i	0.0837482	−	0.145056i
$525$		0			0
$526$	−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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		0			0
$541$	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
$545$		0			0
$546$	2.74782	−	6.28169i	0.117596	−	0.268832i
$547$	−7.99863	−	29.8513i	−0.341997	−	1.27635i	−0.896082	−	0.443889i	$-0.853599\pi$
$547$	−7.99863	−	29.8513i	−0.341997	−	1.27635i	0.554085	−	0.832460i	$-0.313068\pi$
$548$	0.246678	−	0.246678i	0.0105375	−	0.0105375i
$549$	16.9745	+	5.27147i	0.724454	+	0.224981i
$550$		0			0
$551$	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
$555$		0			0
$556$	−6.12814	+	10.6143i	−0.259891	+	0.450145i
$557$	−6.63181	−	6.63181i	−0.280999	−	0.280999i	0.552509	−	0.833507i	$-0.313671\pi$
$557$	−6.63181	−	6.63181i	−0.280999	−	0.280999i	−0.833507	+	0.552509i	$0.813671\pi$
$558$	−12.9153	+	20.4678i	−0.546750	+	0.866469i
$559$		−	5.63159i		−	0.238191i
$560$		0			0
$561$	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	$-0.286678\pi$
$563$	18.2031	+	4.87751i	0.767170	+	0.205563i	0.146049	+	0.989277i	$0.453344\pi$
$564$	−0.581329	−	5.20411i	−0.0244784	−	0.219132i
$565$		0			0
$566$		−	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	−0.997664	−	0.0683141i	$-0.978238\pi$
$569$	−10.4878	+	18.1654i	−0.439670	+	0.761531i	0.557994	+	0.829845i	$0.311571\pi$
$570$		0			0
$571$	−12.2406	−	21.2014i	−0.512254	−	0.887250i	−0.999899	−	0.0142078i	$-0.995477\pi$
$571$	−12.2406	−	21.2014i	−0.512254	−	0.887250i	0.487645	−	0.873042i	$-0.337856\pi$
$572$	−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
$575$		0			0
$576$	−8.93019	+	2.02032i	−0.372091	+	0.0841800i
$577$	12.4198	−	12.4198i	0.517041	−	0.517041i	−0.399634	−	0.916675i	$-0.630863\pi$
$577$	12.4198	−	12.4198i	0.517041	−	0.517041i	0.916675	+	0.399634i	$0.130863\pi$
$578$	−7.24946	−	27.0554i	−0.301538	−	1.12535i
$579$	21.2990	+	28.9168i	0.885155	+	1.20174i
$580$		0			0
$581$	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
$585$		0			0
$586$	56.1979			2.32151
$587$	−14.6173	+	3.91669i	−0.603320	+	0.161659i	−0.547534	−	0.836784i	$-0.684433\pi$
$587$	−14.6173	+	3.91669i	−0.603320	+	0.161659i	−0.0557861	+	0.998443i	$0.517766\pi$
$588$	−1.81637	−	4.64108i	−0.0749060	−	0.191395i
$589$	26.2743	−	15.1695i	1.08261	−	0.625047i
$590$		0			0
$591$	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	$-0.628513\pi$
$593$	12.8270	−	12.8270i	0.526744	−	0.526744i	0.919600	+	0.392856i	$0.128513\pi$
$594$	−23.5814	−	20.4113i	−0.967555	−	0.837486i
$595$		0			0
$596$	−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	0.786882	−	0.617104i	$-0.211694\pi$
$599$	−3.45057	−	5.97656i	−0.140987	−	0.244196i	−0.927868	+	0.372908i	$0.878361\pi$
$600$		0			0
$601$	6.29969	−	10.9114i	0.256970	−	0.445085i	−0.708459	−	0.705752i	$-0.750609\pi$
$601$	6.29969	−	10.9114i	0.256970	−	0.445085i	0.965429	+	0.260667i	$0.0839426\pi$
$602$	8.99779	+	8.99779i	0.366722	+	0.366722i
$603$	−1.32251	+	33.6259i	−0.0538570	+	1.36935i
$604$		−	6.58358i		−	0.267882i
$605$		0			0
$606$	−12.6643	+	9.32804i	−0.514454	+	0.378926i
$607$	−35.9453	−	9.63152i	−1.45898	−	0.390931i	−0.559839	−	0.828601i	$-0.689137\pi$
$607$	−35.9453	−	9.63152i	−1.45898	−	0.390931i	−0.899136	+	0.437670i	$0.855804\pi$
$608$	−24.8359	−	6.65477i	−1.00723	−	0.269887i
$609$	−7.86845	+	5.79558i	−0.318846	+	0.234849i
$610$		0			0
$611$			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	$-0.365296\pi$
$613$	−12.4072	−	12.4072i	−0.501121	−	0.501121i	−0.911786	+	0.410665i	$0.865296\pi$
$614$	2.66556	−	4.61689i	0.107573	−	0.186322i
$615$		0			0
$616$	6.67023	+	11.5532i	0.268751	+	0.465491i
$617$	2.65843	−	9.92141i	0.107025	−	0.399421i	−0.891542	−	0.452937i	$-0.850376\pi$
$617$	2.65843	−	9.92141i	0.107025	−	0.399421i	0.998567	+	0.0535162i	$0.0170429\pi$
$618$	−11.7252	−	9.36885i	−0.471656	−	0.376871i
$619$	−19.1639	−	11.0643i	−0.770264	−	0.444712i	0.0627048	−	0.998032i	$-0.480027\pi$
$619$	−19.1639	−	11.0643i	−0.770264	−	0.444712i	−0.832969	+	0.553320i	$0.813361\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	−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
$630$		0			0
$631$	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
$635$		0			0
$636$	−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
$640$		0			0
$641$	−2.49058	−	1.43794i	−0.0983722	−	0.0567952i	0.450007	−	0.893025i	$-0.351422\pi$
$641$	−2.49058	−	1.43794i	−0.0983722	−	0.0567952i	−0.548379	+	0.836230i	$0.684755\pi$
$642$	15.4545	−	6.04840i	0.609939	−	0.238711i
$643$	−2.54626	+	9.50279i	−0.100415	+	0.374753i	−0.997785	−	0.0665259i	$-0.978809\pi$
$643$	−2.54626	+	9.50279i	−0.100415	+	0.374753i	0.897370	+	0.441279i	$0.145475\pi$
$644$	1.53981	+	2.66702i	0.0606768	+	0.105095i
$645$		0			0
$646$	−2.03631	+	3.52700i	−0.0801177	+	0.138768i
$647$	−14.2662	−	14.2662i	−0.560862	−	0.560862i	0.368691	−	0.929552i	$-0.379806\pi$
$647$	−14.2662	−	14.2662i	−0.560862	−	0.560862i	−0.929552	+	0.368691i	$0.879806\pi$
$648$	6.17332	−	17.4285i	0.242511	−	0.684656i
$649$		−	2.01711i		−	0.0791786i
$650$		0			0
$651$	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	$-0.699930\pi$
$653$	−38.3580	−	10.2780i	−1.50106	−	0.402209i	−0.913456	+	0.406937i	$0.866597\pi$
$654$	2.92196	+	1.27816i	0.114258	+	0.0499800i
$655$		0			0
$656$			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	−0.0967171	+	0.995312i	$0.530834\pi$
$659$	−23.3689	+	40.4762i	−0.910324	+	1.57673i	−0.813607	+	0.581415i	$0.802499\pi$
$660$		0			0
$661$	−2.81433	−	4.87455i	−0.109465	−	0.189598i	0.806089	−	0.591794i	$-0.201580\pi$
$661$	−2.81433	−	4.87455i	−0.109465	−	0.189598i	−0.915553	+	0.402196i	$0.868247\pi$
$662$	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
$665$		0			0
$666$	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
$670$		0			0
$671$	−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	$-0.778151\pi$
$673$	−28.7938	+	7.71528i	−1.10992	+	0.297402i	−0.343122	+	0.939291i	$0.611485\pi$
$674$	41.6249			1.60333
$675$		0			0
$676$	8.59784			0.330686
$677$	48.2839	−	12.9376i	1.85570	−	0.497234i	0.855900	−	0.517141i	$-0.173004\pi$
$677$	48.2839	−	12.9376i	1.85570	−	0.497234i	0.999802	+	0.0199076i	$0.00633719\pi$
$678$	−15.0015	+	18.7745i	−0.576131	+	0.721032i
$679$	8.29312	−	4.78804i	0.318261	−	0.183748i
$680$		0			0
$681$	−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	$-0.787835\pi$
$683$	−4.38271	+	4.38271i	−0.167700	+	0.167700i	0.618268	+	0.785968i	$0.287835\pi$
$684$	10.5294	−	9.73252i	0.402603	−	0.372132i
$685$		0			0
$686$	−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
$690$		0			0
$691$	−0.346648	+	0.600412i	−0.0131871	+	0.0228407i	−0.872544	−	0.488536i	$-0.837531\pi$
$691$	−0.346648	+	0.600412i	−0.0131871	+	0.0228407i	0.859357	+	0.511377i	$0.170864\pi$
$692$	8.10973	+	8.10973i	0.308286	+	0.308286i
$693$	−19.4658	−	0.765597i	−0.739446	−	0.0290826i
$694$		−	58.1535i		−	2.20748i
$695$		0			0
$696$	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
$700$		0			0
$701$		−	8.36037i		−	0.315767i	−0.987458	−	0.157883i	$-0.949533\pi$
$701$		−	8.36037i		−	0.315767i	0.987458	−	0.157883i	$-0.0504670\pi$
$702$	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
$705$		0			0
$706$	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	0.583779	−	0.811913i	$-0.301574\pi$
$709$	4.59399	+	2.65234i	0.172531	+	0.0996109i	−0.411248	+	0.911524i	$0.634907\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	−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	$0.677033\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	5.81614	−	0.649697i	0.215857	−	0.0241125i
$727$	11.6483	+	43.4720i	0.432011	+	1.61229i	0.748119	+	0.663565i	$0.230957\pi$
$727$	11.6483	+	43.4720i	0.432011	+	1.61229i	−0.316108	+	0.948723i	$0.602376\pi$
$728$	−3.45863	+	3.45863i	−0.128185	+	0.128185i
$729$	16.7130	+	21.2056i	0.618999	+	0.785391i
$730$		0			0
$731$	−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	0.748685	+	0.662926i	$0.230685\pi$
$733$	−6.25836	+	23.3565i	−0.231158	+	0.862693i	−0.979843	+	0.199768i	$0.935981\pi$
$734$	6.82565	+	11.8224i	0.251939	+	0.436372i
$735$		0			0
$736$	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	$-0.967113\pi$
$739$		−	5.60736i		−	0.206270i	0.994667	−	0.103135i	$-0.0328874\pi$
$740$		0			0
$741$	−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	$-0.366600\pi$
$743$	8.24852	+	2.21018i	0.302609	+	0.0810838i	−0.104320	+	0.994544i	$0.533267\pi$
$744$	13.9014	−	10.2392i	0.509650	−	0.375388i
$745$		0			0
$746$		−	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
$750$		0			0
$751$	2.32268	+	4.02301i	0.0847560	+	0.146802i	0.905287	−	0.424800i	$-0.139656\pi$
$751$	2.32268	+	4.02301i	0.0847560	+	0.146802i	−0.820531	+	0.571602i	$0.806322\pi$
$752$	−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
$755$		0			0
$756$	2.34035	+	6.75030i	0.0851175	+	0.245506i
$757$	3.09830	−	3.09830i	0.112609	−	0.112609i	−0.648557	−	0.761166i	$-0.724627\pi$
$757$	3.09830	−	3.09830i	0.112609	−	0.112609i	0.761166	+	0.648557i	$0.224627\pi$
$758$	−4.80304	−	17.9252i	−0.174454	−	0.651072i
$759$	−13.9182	+	1.55474i	−0.505199	+	0.0564337i
$760$		0			0
$761$	38.9876	−	22.5095i	1.41330	−	0.815968i	0.417601	−	0.908631i	$-0.362871\pi$
$761$	38.9876	−	22.5095i	1.41330	−	0.815968i	0.995698	+	0.0926625i	$0.0295377\pi$
$762$	−17.2009	−	43.9505i	−0.623122	−	1.59216i
$763$	1.92422	−	0.515595i	0.0696616	−	0.0186658i
$764$	−17.7890			−0.643584
$765$		0			0
$766$	−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	−0.594279	−	0.804259i	$-0.702563\pi$
$769$	−5.40503	+	3.12060i	−0.194910	+	0.112532i	0.399369	+	0.916790i	$0.369229\pi$
$770$		0			0
$771$	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	$-0.584482\pi$
$773$	19.5366	−	19.5366i	0.702681	−	0.702681i	0.964985	+	0.262304i	$0.0844823\pi$
$774$	14.4051	+	15.5846i	0.517781	+	0.560178i
$775$		0			0
$776$	−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
$780$		0			0
$781$	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
$785$		0			0
$786$	−1.60363	−	14.3558i	−0.0571995	−	0.512054i
$787$	28.3409	+	7.59393i	1.01024	+	0.270694i	0.725732	−	0.687978i	$-0.241501\pi$
$787$	28.3409	+	7.59393i	1.01024	+	0.270694i	0.284513	+	0.958672i	$0.408168\pi$
$788$	6.81437	+	1.82590i	0.242752	+	0.0650451i
$789$	−23.7070	−	10.3702i	−0.843992	−	0.369190i
$790$		0			0
$791$			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
$795$		0			0
$796$	−1.54321	−	2.67291i	−0.0546975	−	0.0947388i
$797$	−0.454070	+	1.69461i	−0.0160840	+	0.0600263i	−0.973501	−	0.228681i	$-0.926559\pi$
$797$	−0.454070	+	1.69461i	−0.0160840	+	0.0600263i	0.957417	+	0.288707i	$0.0932254\pi$
$798$	4.85803	−	32.0234i	0.171972	−	1.13362i
$799$	1.34185	+	0.774718i	0.0474712	+	0.0274075i
$800$		0			0
$801$	−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
$805$		0			0
$806$	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	$0.338836\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$	−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
$820$		0			0
$821$	38.4678	+	22.2094i	1.34254	+	0.775114i	0.987179	−	0.159617i	$-0.0510259\pi$
$821$	38.4678	+	22.2094i	1.34254	+	0.775114i	0.355357	+	0.934731i	$0.384359\pi$
$822$	0.197127	−	1.29943i	0.00687559	−	0.0453228i
$823$	−8.19082	+	30.5686i	−0.285514	+	1.06555i	0.662949	+	0.748665i	$0.269305\pi$
$823$	−8.19082	+	30.5686i	−0.285514	+	1.06555i	−0.948463	+	0.316888i	$0.897362\pi$
$824$	5.35341	+	9.27239i	0.186495	+	0.323019i
$825$		0			0
$826$	−0.835543	+	1.44720i	−0.0290723	+	0.0503546i
$827$	2.06846	+	2.06846i	0.0719275	+	0.0719275i	0.742155	−	0.670228i	$-0.233804\pi$
$827$	2.06846	+	2.06846i	0.0719275	+	0.0719275i	−0.670228	+	0.742155i	$0.733804\pi$
$828$	2.39129	+	4.54553i	0.0831030	+	0.157968i
$829$			12.9618i			0.450182i	0.974338	+	0.225091i	$0.0722680\pi$
$829$			12.9618i			0.450182i	−0.974338	+	0.225091i	$0.927732\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$			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	−0.662501	−	0.749061i	$-0.730505\pi$
$839$	9.19525	−	15.9266i	0.317455	−	0.549849i	0.979956	+	0.199212i	$0.0638383\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−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			0
$851$	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	$-0.507333\pi$
$853$	13.3437	−	3.57544i	0.456880	−	0.122421i	0.479917	+	0.877314i	$0.340667\pi$
$854$	17.7193			0.606342
$855$		0			0
$856$	−11.8392			−0.404657
$857$	−5.89302	+	1.57903i	−0.201302	+	0.0539387i	−0.358061	−	0.933698i	$-0.616562\pi$
$857$	−5.89302	+	1.57903i	−0.201302	+	0.0539387i	0.156759	+	0.987637i	$0.449895\pi$
$858$	5.01495	+	12.8139i	0.171208	+	0.437458i
$859$	−16.1515	+	9.32505i	−0.551081	+	0.318166i	−0.749558	−	0.661939i	$-0.769734\pi$
$859$	−16.1515	+	9.32505i	−0.551081	+	0.318166i	0.198477	+	0.980106i	$0.436400\pi$
$860$		0			0
$861$	−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	$-0.822921\pi$
$863$	−9.43441	+	9.43441i	−0.321151	+	0.321151i	0.528058	+	0.849209i	$0.322921\pi$
$864$	13.9839	−	16.1558i	0.475744	−	0.549631i
$865$		0			0
$866$	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
$870$		0			0
$871$	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
$875$		0			0
$876$	1.94948	−	1.43591i	0.0658670	−	0.0485149i
$877$	−47.4768	−	12.7214i	−1.60318	−	0.429570i	−0.657177	−	0.753736i	$-0.728250\pi$
$877$	−47.4768	−	12.7214i	−1.60318	−	0.429570i	−0.946000	+	0.324166i	$0.894916\pi$
$878$	−36.1029	−	9.67374i	−1.21841	−	0.326473i
$879$	47.1375	−	34.7195i	1.58991	−	1.17106i
$880$		0			0
$881$			17.7562i			0.598222i	0.954218	+	0.299111i	$0.0966901\pi$
$881$			17.7562i			0.598222i	−0.954218	+	0.299111i	$0.903310\pi$
$882$	−15.8794	−	10.0200i	−0.534687	−	0.337392i
$883$	−8.09196	−	8.09196i	−0.272316	−	0.272316i	0.557716	−	0.830032i	$-0.311678\pi$
$883$	−8.09196	−	8.09196i	−0.272316	−	0.272316i	−0.830032	+	0.557716i	$0.811678\pi$
$884$	−0.198173	+	0.343246i	−0.00666528	+	0.0115446i
$885$		0			0
$886$	6.42494	+	11.1283i	0.215850	+	0.373863i
$887$	−2.74978	+	10.2623i	−0.0923287	+	0.344575i	−0.996601	−	0.0823810i	$-0.973748\pi$
$887$	−2.74978	+	10.2623i	−0.0923287	+	0.344575i	0.904272	+	0.426956i	$0.140414\pi$
$888$	−21.8284	−	17.4417i	−0.732515	−	0.585306i
$889$	−25.5305	−	14.7401i	−0.856267	−	0.494366i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−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
$900$		0			0
$901$	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
$905$		0			0
$906$	−14.7097	−	19.9708i	−0.488696	−	0.663485i
$907$	2.00855	+	7.49600i	0.0666927	+	0.248901i	0.991222	−	0.132212i	$-0.0422078\pi$
$907$	2.00855	+	7.49600i	0.0666927	+	0.248901i	−0.924529	+	0.381112i	$0.875541\pi$
$908$	−4.98428	+	4.98428i	−0.165409	+	0.165409i
$909$	−4.85961	+	15.6483i	−0.161183	+	0.519021i
$910$		0			0
$911$	−11.1341	−	6.42830i	−0.368890	−	0.212979i	0.304083	−	0.952645i	$-0.401650\pi$
$911$	−11.1341	−	6.42830i	−0.368890	−	0.212979i	−0.672974	+	0.739667i	$0.734983\pi$
$912$	−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
$915$		0			0
$916$	−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	$0.169522\pi$
$919$			30.7848i			1.01550i	−0.861505	+	0.507749i	$0.830478\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$		−	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	−0.993535	−	0.113524i	$-0.963786\pi$
$929$	−12.1446	+	21.0351i	−0.398453	+	0.690141i	0.595082	+	0.803665i	$0.297119\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	−5.99052	+	5.53714i	−0.195806	+	0.180987i
$937$	18.4403	−	18.4403i	0.602420	−	0.602420i	−0.338534	−	0.940954i	$-0.609931\pi$
$937$	18.4403	−	18.4403i	0.602420	−	0.602420i	0.940954	+	0.338534i	$0.109931\pi$
$938$	8.68284	+	32.4048i	0.283505	+	1.05805i
$939$	−15.0845	+	34.4842i	−0.492265	+	1.12535i
$940$		0			0
$941$	−34.2802	+	19.7917i	−1.11750	+	0.645191i	−0.940763	−	0.339066i	$-0.889889\pi$
$941$	−34.2802	+	19.7917i	−1.11750	+	0.645191i	−0.176741	+	0.984257i	$0.556556\pi$
$942$	2.99503	−	3.74829i	0.0975832	−	0.122126i
$943$	−3.22353	+	0.863741i	−0.104972	+	0.0281273i
$944$	2.76275			0.0899200
$945$		0			0
$946$	−25.5377			−0.830301
$947$	39.9850	−	10.7139i	1.29934	−	0.348156i	0.458138	−	0.888881i	$-0.348517\pi$
$947$	39.9850	−	10.7139i	1.29934	−	0.348156i	0.841199	+	0.540725i	$0.181850\pi$
$948$	−6.65076	+	8.32346i	−0.216006	+	0.270334i
$949$	−2.09629	+	1.21029i	−0.0680485	+	0.0392878i
$950$		0			0
$951$	−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	$-0.878938\pi$
$953$	−17.2048	+	17.2048i	−0.557319	+	0.557319i	0.371224	+	0.928543i	$0.378938\pi$
$954$	−50.4049	−	15.6534i	−1.63192	−	0.506796i
$955$		0			0
$956$	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
$960$		0			0
$961$	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
$965$		0			0
$966$	10.6298	+	4.64983i	0.342008	+	0.149606i
$967$	21.3448	+	5.71932i	0.686402	+	0.183921i	0.585132	−	0.810938i	$-0.301043\pi$
$967$	21.3448	+	5.71932i	0.686402	+	0.183921i	0.101270	+	0.994859i	$0.467709\pi$
$968$	−4.03269	−	1.08056i	−0.129616	−	0.0347304i
$969$	0.470998	+	4.21642i	0.0151306	+	0.135451i
$970$		0			0
$971$		−	3.58038i		−	0.114900i	−0.998348	−	0.0574499i	$-0.981703\pi$
$971$		−	3.58038i		−	0.114900i	0.998348	−	0.0574499i	$-0.0182969\pi$
$972$	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
$975$		0			0
$976$	−14.6474	−	25.3700i	−0.468851	−	0.812074i
$977$	5.33127	−	19.8966i	0.170562	−	0.636548i	−0.826703	−	0.562639i	$-0.809786\pi$
$977$	5.33127	−	19.8966i	0.170562	−	0.636548i	0.997265	−	0.0739084i	$-0.0235473\pi$
$978$	39.8670	−	15.6027i	1.27481	−	0.498920i
$979$	51.3796	+	29.6640i	1.64210	+	0.948067i
$980$		0			0
$981$	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	−0.974963	−	0.222365i	$-0.928622\pi$
$983$	−7.58120	−	28.2934i	−0.241803	−	0.902420i	0.733161	−	0.680055i	$-0.238044\pi$
$984$	3.14425	+	4.26883i	0.100235	+	0.136085i
$985$		0			0
$986$	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
$990$		0			0
$991$	−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
$995$		0			0
$996$	0.763794	−	0.0853203i	0.0242017	−	0.00270348i
$997$	13.3859	+	49.9569i	0.423936	+	1.58215i	0.766236	+	0.642559i	$0.222127\pi$
$997$	13.3859	+	49.9569i	0.423936	+	1.58215i	−0.342300	+	0.939591i	$0.611206\pi$
$998$	−11.6227	+	11.6227i	−0.367909	+	0.367909i
$999$	38.5506	−	13.3656i	1.21969	−	0.422868i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.2	✓	16	5.3	odd	4
45.2.l.a.23.2	yes	16	45.14	odd	6
45.2.l.a.32.2	yes	16	45.23	even	12
45.2.l.a.38.2	yes	16	5.4	even	2
135.2.m.a.8.3		16	15.14	odd	2
135.2.m.a.17.3		16	45.13	odd	12
135.2.m.a.62.3		16	15.8	even	4
135.2.m.a.98.3		16	45.4	even	6
225.2.p.b.32.3		16	45.32	even	12	inner
225.2.p.b.68.3		16	9.5	odd	6	inner
225.2.p.b.182.3		16	5.2	odd	4	inner
225.2.p.b.218.3		16	1.1	even	1	trivial
405.2.f.a.242.2		16	45.43	odd	12
405.2.f.a.242.7		16	45.38	even	12
405.2.f.a.323.2		16	45.29	odd	6
405.2.f.a.323.7		16	45.34	even	6
675.2.q.a.143.2		16	3.2	odd	2
675.2.q.a.332.2		16	15.2	even	4
675.2.q.a.368.2		16	9.4	even	3
675.2.q.a.557.2		16	45.22	odd	12
720.2.cu.c.113.1		16	180.59	even	6
720.2.cu.c.257.3		16	180.23	odd	12
720.2.cu.c.353.3		16	20.19	odd	2
720.2.cu.c.497.1		16	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60599 - 0.430324i) q^{2} +(1.08121 - 1.35314i) q^{3} +(0.661975 - 0.382191i) q^{4} +(1.15412 - 2.63840i) q^{6} +(-0.465559 - 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +(-0.661975 - 2.92605i) q^{9} +O(q^{10})\)	\(q+(1.60599 - 0.430324i) q^{2} +(1.08121 - 1.35314i) q^{3} +(0.661975 - 0.382191i) q^{4} +(1.15412 - 2.63840i) q^{6} +(-0.465559 - 1.73749i) q^{7} +(-1.45267 + 1.45267i) q^{8} +(-0.661975 - 2.92605i) q^{9} +(3.12636 + 1.80501i) q^{11} +(0.198575 - 1.30897i) q^{12} +(-0.342574 + 1.27850i) q^{13} +(-1.49537 - 2.59005i) q^{14} +(-2.47224 + 4.28205i) q^{16} +(0.277007 + 0.277007i) q^{17} +(-2.32228 - 4.41435i) q^{18} +6.25273i q^{19} +(-2.85443 - 1.24862i) q^{21} +(5.79765 + 1.55348i) q^{22} +(-2.16347 - 0.579699i) q^{23} +(0.395027 + 3.53631i) q^{24} +2.20068i q^{26} +(-4.67509 - 2.26793i) q^{27} +(-0.972242 - 0.972242i) q^{28} +(1.56832 - 2.71642i) q^{29} +(-2.42605 - 4.20205i) q^{31} +(-1.06430 + 3.97202i) q^{32} +(5.82268 - 2.27882i) q^{33} +(0.564074 + 0.325668i) q^{34} +(-1.55652 - 1.68397i) q^{36} +(-5.55242 + 5.55242i) q^{37} +(2.69070 + 10.0418i) q^{38} +(1.35960 + 1.84588i) q^{39} +(1.29036 - 0.744991i) q^{41} +(-5.12150 - 0.776946i) q^{42} +(-4.10976 + 1.10121i) q^{43} +2.75943 q^{44} -3.72396 q^{46} +(3.82042 - 1.02368i) q^{47} +(3.12120 + 7.97508i) q^{48} +(3.26005 - 1.88219i) q^{49} +(0.674332 - 0.0753268i) q^{51} +(0.261857 + 0.977265i) q^{52} +(7.48222 - 7.48222i) q^{53} +(-8.48410 - 1.63047i) q^{54} +(3.20031 + 1.84770i) q^{56} +(8.46082 + 6.76051i) q^{57} +(1.34977 - 5.03742i) q^{58} +(-0.279377 - 0.483896i) q^{59} +(-2.96237 + 5.13097i) q^{61} +(-5.70446 - 5.70446i) q^{62} +(-4.77580 + 2.51243i) q^{63} -3.05196i q^{64} +(8.37054 - 6.16540i) q^{66} +(-10.8351 - 2.90325i) q^{67} +(0.289242 + 0.0775020i) q^{68} +(-3.12357 + 2.30070i) q^{69} -8.01611i q^{71} +(5.21223 + 3.28897i) q^{72} +(1.29315 + 1.29315i) q^{73} +(-6.52779 + 11.3065i) q^{74} +(2.38974 + 4.13915i) q^{76} +(1.68068 - 6.27237i) q^{77} +(2.97783 + 2.37939i) q^{78} +(-6.96917 - 4.02365i) q^{79} +(-8.12358 + 3.87395i) q^{81} +(1.75172 - 1.75172i) q^{82} +(0.150243 + 0.560714i) q^{83} +(-2.36678 + 0.264383i) q^{84} +(-6.12636 + 3.53706i) q^{86} +(-1.98001 - 5.05917i) q^{87} +(-7.16367 + 1.91950i) q^{88} +16.4343 q^{89} +2.38087 q^{91} +(-1.65372 + 0.443112i) q^{92} +(-8.30903 - 1.26050i) q^{93} +(5.69504 - 3.28804i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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