LMFDB - Embedded newform 882.2.l.b.509.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.8
Root			$1.71298 - 0.256290i$ of defining polynomial
Character	$\chi$	$=$	882.509
Dual form			882.2.l.b.227.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.56012 + 0.752355i) q^{3} -1.00000 q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 + 1.56012i) q^{6} -1.00000i q^{8} +(1.86792 + 2.34752i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.56012 + 0.752355i) q^{3} -1.00000 q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 + 1.56012i) q^{6} -1.00000i q^{8} +(1.86792 + 2.34752i) q^{9} +(-3.13442 + 1.80966i) q^{10} +(-1.73534 - 1.00190i) q^{11} +(-1.56012 - 0.752355i) q^{12} +(-2.95206 - 1.70437i) q^{13} +(0.465079 + 6.25156i) q^{15} +1.00000 q^{16} +(3.08709 + 5.34700i) q^{17} +(-2.34752 + 1.86792i) q^{18} +(-0.877353 - 0.506540i) q^{19} +(-1.80966 - 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} +(-2.62232 + 1.51400i) q^{23} +(0.752355 - 1.56012i) q^{24} +(-4.04972 + 7.01433i) q^{25} +(1.70437 - 2.95206i) q^{26} +(1.14800 + 5.06775i) q^{27} +(5.04560 - 2.91308i) q^{29} +(-6.25156 + 0.465079i) q^{30} +0.909687i q^{31} +1.00000i q^{32} +(-1.95354 - 2.86867i) q^{33} +(-5.34700 + 3.08709i) q^{34} +(-1.86792 - 2.34752i) q^{36} +(3.66825 - 6.35359i) q^{37} +(0.506540 - 0.877353i) q^{38} +(-3.32326 - 4.88001i) q^{39} +(3.13442 - 1.80966i) q^{40} +(2.85045 - 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +(1.73534 + 1.00190i) q^{44} +(-3.97782 + 10.1031i) q^{45} +(-1.51400 - 2.62232i) q^{46} +2.23022 q^{47} +(1.56012 + 0.752355i) q^{48} +(-7.01433 - 4.04972i) q^{50} +(0.793376 + 10.6645i) q^{51} +(2.95206 + 1.70437i) q^{52} +(7.58088 - 4.37683i) q^{53} +(-5.06775 + 1.14800i) q^{54} -7.25237i q^{55} +(-0.987674 - 1.45034i) q^{57} +(2.91308 + 5.04560i) q^{58} -8.98627 q^{59} +(-0.465079 - 6.25156i) q^{60} +14.7121i q^{61} -0.909687 q^{62} -1.00000 q^{64} -12.3373i q^{65} +(2.86867 - 1.95354i) q^{66} -8.31641 q^{67} +(-3.08709 - 5.34700i) q^{68} +(-5.23019 + 0.389094i) q^{69} +0.466287i q^{71} +(2.34752 - 1.86792i) q^{72} +(3.65022 - 2.10746i) q^{73} +(6.35359 + 3.66825i) q^{74} +(-11.5953 + 7.89633i) q^{75} +(0.877353 + 0.506540i) q^{76} +(4.88001 - 3.32326i) q^{78} +3.82533 q^{79} +(1.80966 + 3.13442i) q^{80} +(-2.02173 + 8.76998i) q^{81} +(4.93712 + 2.85045i) q^{82} +(4.00481 + 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(4.15605 - 2.39949i) q^{86} +(10.0634 - 0.748656i) q^{87} +(-1.00190 + 1.73534i) q^{88} +(2.39324 - 4.14521i) q^{89} +(-10.1031 - 3.97782i) q^{90} +(2.62232 - 1.51400i) q^{92} +(-0.684408 + 1.41922i) q^{93} +2.23022i q^{94} -3.66666i q^{95} +(-0.752355 + 1.56012i) q^{96} +(10.1835 - 5.87944i) q^{97} +(-0.889499 - 5.94521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 12 q^{11} - 6 q^{13} - 18 q^{15} + 16 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 36 q^{27} + 6 q^{29} - 2 q^{37} - 12 q^{39} + 6 q^{41} - 2 q^{43} - 12 q^{44} + 30 q^{45} + 6 q^{46} + 36 q^{47} - 12 q^{50} + 6 q^{51} + 6 q^{52} - 36 q^{53} - 18 q^{54} + 6 q^{57} + 6 q^{58} - 60 q^{59} + 18 q^{60} - 36 q^{62} - 16 q^{64} - 24 q^{66} - 28 q^{67} - 18 q^{68} + 42 q^{69} + 12 q^{72} + 18 q^{74} - 60 q^{75} + 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{86} + 24 q^{87} + 24 q^{89} - 18 q^{90} + 6 q^{92} - 42 q^{93} - 6 q^{97} + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 12 * q^11 - 6 * q^13 - 18 * q^15 + 16 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 36 * q^27 + 6 * q^29 - 2 * q^37 - 12 * q^39 + 6 * q^41 - 2 * q^43 - 12 * q^44 + 30 * q^45 + 6 * q^46 + 36 * q^47 - 12 * q^50 + 6 * q^51 + 6 * q^52 - 36 * q^53 - 18 * q^54 + 6 * q^57 + 6 * q^58 - 60 * q^59 + 18 * q^60 - 36 * q^62 - 16 * q^64 - 24 * q^66 - 28 * q^67 - 18 * q^68 + 42 * q^69 + 12 * q^72 + 18 * q^74 - 60 * q^75 + 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^86 + 24 * q^87 + 24 * q^89 - 18 * q^90 + 6 * q^92 - 42 * q^93 - 6 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.56012	+	0.752355i	0.900733	+	0.434373i
$3$	1.56012	+	0.752355i	0.900733	+	0.434373i
$4$	−1.00000			−0.500000
$5$	1.80966	+	3.13442i	0.809304	+	1.40175i	0.913347	+	0.407182i	$0.133489\pi$
$5$	1.80966	+	3.13442i	0.809304	+	1.40175i	−0.104043	+	0.994573i	$0.533178\pi$
$6$	−0.752355	+	1.56012i	−0.307148	+	0.636915i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.86792	+	2.34752i	0.622641	+	0.782508i
$10$	−3.13442	+	1.80966i	−0.991190	+	0.572264i
$11$	−1.73534	−	1.00190i	−0.523224	−	0.302083i	0.215029	−	0.976608i	$-0.431015\pi$
$11$	−1.73534	−	1.00190i	−0.523224	−	0.302083i	−0.738253	+	0.674524i	$0.764349\pi$
$12$	−1.56012	−	0.752355i	−0.450367	−	0.217186i
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	0.0312328	−	0.999512i	$-0.490057\pi$
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	−0.849987	+	0.526804i	$0.823390\pi$
$14$		0			0
$15$	0.465079	+	6.25156i	0.120083	+	1.61415i
$16$	1.00000			0.250000
$17$	3.08709	+	5.34700i	0.748730	+	1.29684i	0.948432	+	0.316981i	$0.102669\pi$
$17$	3.08709	+	5.34700i	0.748730	+	1.29684i	−0.199702	+	0.979857i	$0.563998\pi$
$18$	−2.34752	+	1.86792i	−0.553316	+	0.440274i
$19$	−0.877353	−	0.506540i	−0.201279	−	0.116208i	0.395973	−	0.918262i	$-0.370407\pi$
$19$	−0.877353	−	0.506540i	−0.201279	−	0.116208i	−0.597252	+	0.802054i	$0.703741\pi$
$20$	−1.80966	−	3.13442i	−0.404652	−	0.700877i
$21$		0			0
$22$	1.00190	−	1.73534i	0.213605	−	0.369975i
$23$	−2.62232	+	1.51400i	−0.546791	+	0.315690i	−0.747827	−	0.663894i	$-0.768903\pi$
$23$	−2.62232	+	1.51400i	−0.546791	+	0.315690i	0.201035	+	0.979584i	$0.435569\pi$
$24$	0.752355	−	1.56012i	0.153574	−	0.318457i
$25$	−4.04972	+	7.01433i	−0.809945	+	1.40287i
$26$	1.70437	−	2.95206i	0.334255	−	0.578946i
$27$	1.14800	+	5.06775i	0.220934	+	0.975289i
$28$		0			0
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.0479434	−	0.998850i	$-0.484733\pi$
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.889001	+	0.457905i	$0.151400\pi$
$30$	−6.25156	+	0.465079i	−1.14137	+	0.0849113i
$31$			0.909687i			0.163385i	0.996658	+	0.0816923i	$0.0260325\pi$
$31$			0.909687i			0.163385i	−0.996658	+	0.0816923i	$0.973968\pi$
$32$			1.00000i			0.176777i
$33$	−1.95354	−	2.86867i	−0.340068	−	0.499371i
$34$	−5.34700	+	3.08709i	−0.917003	+	0.529432i
$35$		0			0
$36$	−1.86792	−	2.34752i	−0.311320	−	0.391254i
$37$	3.66825	−	6.35359i	0.603056	−	1.04452i	−0.389299	−	0.921111i	$-0.627283\pi$
$37$	3.66825	−	6.35359i	0.603056	−	1.04452i	0.992355	−	0.123413i	$-0.0393839\pi$
$38$	0.506540	−	0.877353i	0.0821717	−	0.142325i
$39$	−3.32326	−	4.88001i	−0.532148	−	0.781428i
$40$	3.13442	−	1.80966i	0.495595	−	0.286132i
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	0.998064	+	0.0622002i	$0.0198117\pi$
$42$		0			0
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	0.623004	−	0.782219i	$-0.285912\pi$
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	−0.988923	+	0.148428i	$0.952579\pi$
$44$	1.73534	+	1.00190i	0.261612	+	0.151042i
$45$	−3.97782	+	10.1031i	−0.592978	+	1.50608i
$46$	−1.51400	−	2.62232i	−0.223227	−	0.386640i
$47$	2.23022			0.325311			0.162655	−	0.986683i	$-0.447994\pi$
$47$	2.23022			0.325311			0.162655	+	0.986683i	$0.447994\pi$
$48$	1.56012	+	0.752355i	0.225183	+	0.108593i
$49$		0			0
$50$	−7.01433	−	4.04972i	−0.991975	−	0.572717i
$51$	0.793376	+	10.6645i	0.111095	+	1.49333i
$52$	2.95206	+	1.70437i	0.409377	+	0.236354i
$53$	7.58088	−	4.37683i	1.04131	−	0.601203i	0.121109	−	0.992639i	$-0.461355\pi$
$53$	7.58088	−	4.37683i	1.04131	−	0.601203i	0.920205	+	0.391436i	$0.128022\pi$
$54$	−5.06775	+	1.14800i	−0.689633	+	0.156224i
$55$		−	7.25237i		−	0.977909i
$56$		0			0
$57$	−0.987674	−	1.45034i	−0.130821	−	0.192103i
$58$	2.91308	+	5.04560i	0.382506	+	0.662520i
$59$	−8.98627			−1.16991			−0.584956	−	0.811065i	$-0.698888\pi$
$59$	−8.98627			−1.16991			−0.584956	+	0.811065i	$0.698888\pi$
$60$	−0.465079	−	6.25156i	−0.0600414	−	0.807073i
$61$			14.7121i			1.88369i	0.336053	+	0.941843i	$0.390908\pi$
$61$			14.7121i			1.88369i	−0.336053	+	0.941843i	$0.609092\pi$
$62$	−0.909687			−0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	12.3373i		−	1.53026i
$66$	2.86867	−	1.95354i	0.353108	−	0.240465i
$67$	−8.31641			−1.01601			−0.508006	−	0.861354i	$-0.669617\pi$
$67$	−8.31641			−1.01601			−0.508006	+	0.861354i	$0.669617\pi$
$68$	−3.08709	−	5.34700i	−0.374365	−	0.648419i
$69$	−5.23019	+	0.389094i	−0.629640	+	0.0468415i
$70$		0			0
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$	2.34752	−	1.86792i	0.276658	−	0.220137i
$73$	3.65022	−	2.10746i	0.427226	−	0.246659i	−0.270938	−	0.962597i	$-0.587334\pi$
$73$	3.65022	−	2.10746i	0.427226	−	0.246659i	0.698164	+	0.715938i	$0.254000\pi$
$74$	6.35359	+	3.66825i	0.738590	+	0.426425i
$75$	−11.5953	+	7.89633i	−1.33891	+	0.911790i
$76$	0.877353	+	0.506540i	0.100639	+	0.0581041i
$77$		0			0
$78$	4.88001	−	3.32326i	0.552553	−	0.376285i
$79$	3.82533			0.430384			0.215192	−	0.976572i	$-0.430962\pi$
$79$	3.82533			0.430384			0.215192	+	0.976572i	$0.430962\pi$
$80$	1.80966	+	3.13442i	0.202326	+	0.350439i
$81$	−2.02173	+	8.76998i	−0.224637	+	0.974443i
$82$	4.93712	+	2.85045i	0.545213	+	0.314779i
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	0.997657	−	0.0684084i	$-0.0217921\pi$
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	−0.558072	+	0.829792i	$0.688459\pi$
$84$		0			0
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$	4.15605	−	2.39949i	0.448158	−	0.258744i
$87$	10.0634	−	0.748656i	1.07891	−	0.0802643i
$88$	−1.00190	+	1.73534i	−0.106803	+	0.184988i
$89$	2.39324	−	4.14521i	0.253683	−	0.439391i	−0.710854	−	0.703339i	$-0.751691\pi$
$89$	2.39324	−	4.14521i	0.253683	−	0.439391i	0.964537	+	0.263948i	$0.0850248\pi$
$90$	−10.1031	−	3.97782i	−1.06496	−	0.419299i
$91$		0			0
$92$	2.62232	−	1.51400i	0.273396	−	0.157845i
$93$	−0.684408	+	1.41922i	−0.0709698	+	0.147166i
$94$			2.23022i			0.230029i
$95$		−	3.66666i		−	0.376191i
$96$	−0.752355	+	1.56012i	−0.0767869	+	0.159229i
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.115856	−	0.993266i	$-0.463039\pi$
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.918121	+	0.396299i	$0.129706\pi$
$98$		0			0
$99$	−0.889499	−	5.94521i	−0.0893980	−	0.597516i
$100$	4.04972	−	7.01433i	0.404972	−	0.701433i
$101$	6.44610	−	11.1650i	0.641411	−	1.11096i	−0.343707	−	0.939077i	$-0.611683\pi$
$101$	6.44610	−	11.1650i	0.641411	−	1.11096i	0.985118	−	0.171879i	$-0.0549840\pi$
$102$	−10.6645	+	0.793376i	−1.05595	+	0.0785560i
$103$	−9.31740	+	5.37940i	−0.918070	+	0.530048i	−0.883019	−	0.469337i	$-0.844493\pi$
$103$	−9.31740	+	5.37940i	−0.918070	+	0.530048i	−0.0350515	+	0.999386i	$0.511160\pi$
$104$	−1.70437	+	2.95206i	−0.167127	+	0.289473i
$105$		0			0
$106$	4.37683	+	7.58088i	0.425115	+	0.736321i
$107$	−2.28602	−	1.31983i	−0.220998	−	0.127593i	0.385414	−	0.922744i	$-0.374058\pi$
$107$	−2.28602	−	1.31983i	−0.220998	−	0.127593i	−0.606412	+	0.795151i	$0.707392\pi$
$108$	−1.14800	−	5.06775i	−0.110467	−	0.487644i
$109$	4.51768	+	7.82484i	0.432715	+	0.749484i	0.997106	−	0.0760233i	$-0.0242224\pi$
$109$	4.51768	+	7.82484i	0.432715	+	0.749484i	−0.564391	+	0.825507i	$0.690889\pi$
$110$	7.25237			0.691486
$111$	10.5031	−	7.15251i	0.996905	−	0.678886i
$112$		0			0
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	0.429551	−	0.903043i	$-0.358672\pi$
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	−0.567283	+	0.823523i	$0.692005\pi$
$114$	1.45034	−	0.987674i	0.135837	−	0.0925042i
$115$	−9.49100	−	5.47963i	−0.885041	−	0.510978i
$116$	−5.04560	+	2.91308i	−0.468472	+	0.270473i
$117$	−1.51317	−	10.1137i	−0.139892	−	0.935008i
$118$		−	8.98627i		−	0.827253i
$119$		0			0
$120$	6.25156	−	0.465079i	0.570687	−	0.0424557i
$121$	−3.49240	−	6.04902i	−0.317491	−	0.549911i
$122$	−14.7121			−1.33197
$123$	8.16149	−	5.55793i	0.735897	−	0.501141i
$124$		−	0.909687i		−	0.0816923i
$125$	−11.2179			−1.00336
$126$		0			0
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.616665	−	8.28919i	−0.0542944	−	0.729822i
$130$	12.3373			1.08205
$131$	−8.66567	−	15.0094i	−0.757123	−	1.31138i	−0.944312	−	0.329052i	$-0.893271\pi$
$131$	−8.66567	−	15.0094i	−0.757123	−	1.31138i	0.187188	−	0.982324i	$-0.440062\pi$
$132$	1.95354	+	2.86867i	0.170034	+	0.249685i
$133$		0			0
$134$		−	8.31641i		−	0.718429i
$135$	−13.8070	+	12.7692i	−1.18831	+	1.09900i
$136$	5.34700	−	3.08709i	0.458501	−	0.264716i
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	0.500024	−	0.866012i	$-0.333325\pi$
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	−0.499976	+	0.866039i	$0.666658\pi$
$138$	−0.389094	−	5.23019i	−0.0331219	−	0.445223i
$139$	8.73273	+	5.04185i	0.740701	+	0.427644i	0.822324	−	0.569019i	$-0.192677\pi$
$139$	8.73273	+	5.04185i	0.740701	+	0.427644i	−0.0816233	+	0.996663i	$0.526010\pi$
$140$		0			0
$141$	3.47940	+	1.67792i	0.293018	+	0.141306i
$142$	−0.466287			−0.0391300
$143$	3.41521	+	5.91532i	0.285594	+	0.494664i
$144$	1.86792	+	2.34752i	0.155660	+	0.195627i
$145$	18.2616	+	10.5434i	1.51655	+	0.875578i
$146$	2.10746	+	3.65022i	0.174414	+	0.302095i
$147$		0			0
$148$	−3.66825	+	6.35359i	−0.301528	+	0.522262i
$149$	−9.74064	+	5.62376i	−0.797984	+	0.460716i	−0.842766	−	0.538280i	$-0.819074\pi$
$149$	−9.74064	+	5.62376i	−0.797984	+	0.460716i	0.0447816	+	0.998997i	$0.485741\pi$
$150$	−7.89633	−	11.5953i	−0.644733	−	0.946752i
$151$	2.36189	−	4.09092i	0.192208	−	0.332914i	−0.753774	−	0.657134i	$-0.771768\pi$
$151$	2.36189	−	4.09092i	0.192208	−	0.332914i	0.945982	+	0.324220i	$0.105102\pi$
$152$	−0.506540	+	0.877353i	−0.0410858	+	0.0711627i
$153$	−6.78575	+	17.2348i	−0.548596	+	1.39335i
$154$		0			0
$155$	−2.85134	+	1.64622i	−0.229025	+	0.132228i
$156$	3.32326	+	4.88001i	0.266074	+	0.390714i
$157$			3.06972i			0.244990i	0.992469	+	0.122495i	$0.0390895\pi$
$157$			3.06972i			0.244990i	−0.992469	+	0.122495i	$0.960910\pi$
$158$			3.82533i			0.304327i
$159$	15.1200	−	1.12484i	1.19909	−	0.0892053i
$160$	−3.13442	+	1.80966i	−0.247798	+	0.143066i
$161$		0			0
$162$	−8.76998	−	2.02173i	−0.689035	−	0.158842i
$163$	−1.43687	+	2.48873i	−0.112544	+	0.194932i	−0.916795	−	0.399357i	$-0.869233\pi$
$163$	−1.43687	+	2.48873i	−0.112544	+	0.194932i	0.804251	+	0.594289i	$0.202567\pi$
$164$	−2.85045	+	4.93712i	−0.222582	+	0.385524i
$165$	5.45636	−	11.3145i	0.424777	−	0.880835i
$166$	−6.93654	+	4.00481i	−0.538380	+	0.310834i
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	−0.892905	−	0.450245i	$-0.851337\pi$
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	0.836376	+	0.548156i	$0.184670\pi$
$168$		0			0
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$	−19.3525	−	11.1732i	−1.48427	−	0.856942i
$171$	−0.449713	−	3.00578i	−0.0343904	−	0.229858i
$172$	2.39949	+	4.15605i	0.182960	+	0.316896i
$173$	3.07081			0.233470			0.116735	−	0.993163i	$-0.462757\pi$
$173$	3.07081			0.233470			0.116735	+	0.993163i	$0.462757\pi$
$174$	0.748656	+	10.0634i	0.0567554	+	0.762904i
$175$		0			0
$176$	−1.73534	−	1.00190i	−0.130806	−	0.0755209i
$177$	−14.0196	−	6.76087i	−1.05378	−	0.508178i
$178$	4.14521	+	2.39324i	0.310696	+	0.179381i
$179$	16.7310	−	9.65966i	1.25054	−	0.721997i	0.279320	−	0.960198i	$-0.409891\pi$
$179$	16.7310	−	9.65966i	1.25054	−	0.721997i	0.971216	+	0.238201i	$0.0765578\pi$
$180$	3.97782	−	10.1031i	0.296489	−	0.753038i
$181$			7.89318i			0.586695i	0.956006	+	0.293348i	$0.0947693\pi$
$181$			7.89318i			0.586695i	−0.956006	+	0.293348i	$0.905231\pi$
$182$		0			0
$183$	−11.0687	+	22.9525i	−0.818222	+	1.69670i
$184$	1.51400	+	2.62232i	0.111613	+	0.193320i
$185$	26.5531			1.95222
$186$	−1.41922	−	0.684408i	−0.104062	−	0.0501832i
$187$		−	12.3718i		−	0.904715i
$188$	−2.23022			−0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$		−	13.3042i		−	0.962660i	−0.876540	−	0.481330i	$-0.840154\pi$
$191$		−	13.3042i		−	0.962660i	0.876540	−	0.481330i	$-0.159846\pi$
$192$	−1.56012	−	0.752355i	−0.112592	−	0.0542966i
$193$	6.53573			0.470452			0.235226	−	0.971941i	$-0.424417\pi$
$193$	6.53573			0.470452			0.235226	+	0.971941i	$0.424417\pi$
$194$	5.87944	+	10.1835i	0.422119	+	0.731132i
$195$	9.28205	−	19.2476i	0.664701	−	1.37835i
$196$		0			0
$197$		−	4.44250i		−	0.316515i	−0.987398	−	0.158258i	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$	5.94521	−	0.889499i	0.422508	−	0.0632139i
$199$	−9.96868	+	5.75542i	−0.706661	+	0.407991i	−0.809823	−	0.586674i	$-0.800437\pi$
$199$	−9.96868	+	5.75542i	−0.706661	+	0.407991i	0.103163	+	0.994665i	$0.467104\pi$
$200$	7.01433	+	4.04972i	0.495988	+	0.286359i
$201$	−12.9746	−	6.25690i	−0.915155	−	0.441328i
$202$	11.1650	+	6.44610i	0.785565	+	0.453546i
$203$		0			0
$204$	−0.793376	−	10.6645i	−0.0555475	−	0.746666i
$205$	20.6333			1.44109
$206$	−5.37940	−	9.31740i	−0.374801	−	0.649174i
$207$	−8.45243	−	3.32793i	−0.587485	−	0.231307i
$208$	−2.95206	−	1.70437i	−0.204688	−	0.118177i
$209$	1.01500	+	1.75804i	0.0702092	+	0.121606i
$210$		0			0
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	−0.155155	−	0.987890i	$-0.549588\pi$
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	0.933115	−	0.359577i	$-0.117079\pi$
$212$	−7.58088	+	4.37683i	−0.520657	+	0.300602i
$213$	−0.350814	+	0.727462i	−0.0240374	+	0.0498449i
$214$	1.31983	−	2.28602i	0.0902219	−	0.156269i
$215$	8.68453	−	15.0420i	0.592280	−	1.02586i
$216$	5.06775	−	1.14800i	0.344817	−	0.0781118i
$217$		0			0
$218$	−7.82484	+	4.51768i	−0.529965	+	0.305976i
$219$	7.28033	−	0.541613i	0.491959	−	0.0365988i
$220$			7.25237i			0.488954i
$221$		−	21.0462i		−	1.41572i
$222$	7.15251	+	10.5031i	0.480045	+	0.704919i
$223$	−16.2994	+	9.41045i	−1.09149	+	0.630170i	−0.933972	−	0.357346i	$-0.883682\pi$
$223$	−16.2994	+	9.41045i	−1.09149	+	0.630170i	−0.157515	+	0.987517i	$0.550348\pi$
$224$		0			0
$225$	−24.0309	+	3.59540i	−1.60206	+	0.239693i
$226$	0.845306	−	1.46411i	0.0562289	−	0.0973914i
$227$	7.30665	−	12.6555i	0.484960	−	0.839975i	−0.514891	−	0.857256i	$-0.672168\pi$
$227$	7.30665	−	12.6555i	0.484960	−	0.839975i	0.999851	+	0.0172809i	$0.00550095\pi$
$228$	0.987674	+	1.45034i	0.0654103	+	0.0960513i
$229$	−2.06044	+	1.18959i	−0.136158	+	0.0786106i	−0.566531	−	0.824040i	$-0.691715\pi$
$229$	−2.06044	+	1.18959i	−0.136158	+	0.0786106i	0.430374	+	0.902651i	$0.358382\pi$
$230$	5.47963	−	9.49100i	0.361316	−	0.625818i
$231$		0			0
$232$	−2.91308	−	5.04560i	−0.191253	−	0.331260i
$233$	9.03470	+	5.21619i	0.591883	+	0.341724i	0.765842	−	0.643029i	$-0.222323\pi$
$233$	9.03470	+	5.21619i	0.591883	+	0.341724i	−0.173959	+	0.984753i	$0.555656\pi$
$234$	10.1137	−	1.51317i	0.661151	−	0.0989187i
$235$	4.03593	+	6.99044i	0.263275	+	0.456006i
$236$	8.98627			0.584956
$237$	5.96796	+	2.87801i	0.387661	+	0.186947i
$238$		0			0
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.985654	−	0.168777i	$-0.0539818\pi$
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.346662	+	0.937990i	$0.387315\pi$
$240$	0.465079	+	6.25156i	0.0300207	+	0.403537i
$241$	−24.8105	−	14.3243i	−1.59818	−	0.922712i	−0.991837	−	0.127513i	$-0.959301\pi$
$241$	−24.8105	−	14.3243i	−1.59818	−	0.922712i	−0.606348	−	0.795200i	$-0.707366\pi$
$242$	6.04902	−	3.49240i	0.388846	−	0.224500i
$243$	−9.75228	+	12.1611i	−0.625609	+	0.780137i
$244$		−	14.7121i		−	0.941843i
$245$		0			0
$246$	5.55793	+	8.16149i	0.354360	+	0.520358i
$247$	1.72667	+	2.99067i	0.109865	+	0.190292i
$248$	0.909687			0.0577652
$249$	1.02923	+	13.8348i	0.0652248	+	0.876748i
$250$		−	11.2179i		−	0.709481i
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$			17.9292i			1.12498i
$255$	−31.9914	+	21.7859i	−2.00338	+	1.36429i
$256$	1.00000			0.0625000
$257$	7.54890	+	13.0751i	0.470888	+	0.815601i	0.999446	−	0.0332960i	$-0.0106004\pi$
$257$	7.54890	+	13.0751i	0.470888	+	0.815601i	−0.528558	+	0.848897i	$0.677267\pi$
$258$	8.28919	−	0.616665i	0.516062	−	0.0383919i
$259$		0			0
$260$			12.3373i			0.765128i
$261$	16.2633	+	6.40326i	1.00667	+	0.396352i
$262$	15.0094	−	8.66567i	0.927283	−	0.535367i
$263$	17.0075	+	9.81926i	1.04873	+	0.605482i	0.922292	−	0.386493i	$-0.126314\pi$
$263$	17.0075	+	9.81926i	1.04873	+	0.605482i	0.126433	+	0.991975i	$0.459647\pi$
$264$	−2.86867	+	1.95354i	−0.176554	+	0.120232i
$265$	27.4376	+	15.8411i	1.68548	+	0.973112i
$266$		0			0
$267$	6.85240	−	4.66644i	0.419360	−	0.285581i
$268$	8.31641			0.508006
$269$	−0.245503	−	0.425223i	−0.0149686	−	0.0259263i	0.858444	−	0.512907i	$-0.171431\pi$
$269$	−0.245503	−	0.425223i	−0.0149686	−	0.0259263i	−0.873413	+	0.486981i	$0.838098\pi$
$270$	−12.7692	−	13.8070i	−0.777110	−	0.840265i
$271$	12.1927	+	7.03945i	0.740653	+	0.427616i	0.822307	−	0.569045i	$-0.192687\pi$
$271$	12.1927	+	7.03945i	0.740653	+	0.427616i	−0.0816537	+	0.996661i	$0.526020\pi$
$272$	3.08709	+	5.34700i	0.187182	+	0.324209i
$273$		0			0
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$	14.0553	−	8.11481i	0.847565	−	0.489342i
$276$	5.23019	−	0.389094i	0.314820	−	0.0234207i
$277$	−15.3600	+	26.6043i	−0.922894	+	1.59850i	−0.127981	+	0.991777i	$0.540850\pi$
$277$	−15.3600	+	26.6043i	−0.922894	+	1.59850i	−0.794913	+	0.606723i	$0.792484\pi$
$278$	−5.04185	+	8.73273i	−0.302390	+	0.523755i
$279$	−2.13551	+	1.69923i	−0.127850	+	0.101730i
$280$		0			0
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	−0.281130	−	0.959670i	$-0.590709\pi$
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	0.690534	+	0.723300i	$0.257376\pi$
$282$	−1.67792	+	3.47940i	−0.0999185	+	0.207195i
$283$		−	11.5159i		−	0.684547i	−0.939600	−	0.342273i	$-0.888803\pi$
$283$		−	11.5159i		−	0.684547i	0.939600	−	0.342273i	$-0.111197\pi$
$284$		−	0.466287i		−	0.0276691i
$285$	2.75863	−	5.72041i	0.163407	−	0.338848i
$286$	−5.91532	+	3.41521i	−0.349780	+	0.201946i
$287$		0			0
$288$	−2.34752	+	1.86792i	−0.138329	+	0.110068i
$289$	−10.5603	+	18.2909i	−0.621192	+	1.07594i
$290$	−10.5434	+	18.2616i	−0.619127	+	1.07236i
$291$	20.3109	−	1.51101i	1.19064	−	0.0885767i
$292$	−3.65022	+	2.10746i	−0.213613	+	0.123330i
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	−0.783369	−	0.621557i	$-0.786501\pi$
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	0.929968	+	0.367639i	$0.119834\pi$
$294$		0			0
$295$	−16.2621	−	28.1667i	−0.946814	−	1.63993i
$296$	−6.35359	−	3.66825i	−0.369295	−	0.213213i
$297$	3.08519	−	9.94444i	0.179021	−	0.577035i
$298$	−5.62376	−	9.74064i	−0.325776	−	0.564260i
$299$	10.3217			0.596917
$300$	11.5953	−	7.89633i	0.669455	−	0.455895i
$301$		0			0
$302$	4.09092	+	2.36189i	0.235406	+	0.135912i
$303$	18.4567	−	12.5689i	1.06031	−	0.722064i
$304$	−0.877353	−	0.506540i	−0.0503197	−	0.0290521i
$305$	−46.1138	+	26.6238i	−2.64047	+	1.52447i
$306$	−17.2348	−	6.78575i	−0.985248	−	0.387916i
$307$		−	17.5309i		−	1.00054i	−0.865869	−	0.500271i	$-0.833234\pi$
$307$		−	17.5309i		−	1.00054i	0.865869	−	0.500271i	$-0.166766\pi$
$308$		0			0
$309$	−18.5834	+	1.38250i	−1.05717	+	0.0786474i
$310$	−1.64622	−	2.85134i	−0.0934992	−	0.161945i
$311$	−17.2952			−0.980720			−0.490360	−	0.871520i	$-0.663135\pi$
$311$	−17.2952			−0.980720			−0.490360	+	0.871520i	$0.663135\pi$
$312$	−4.88001	+	3.32326i	−0.276276	+	0.188143i
$313$		−	8.99498i		−	0.508426i	−0.967148	−	0.254213i	$-0.918184\pi$
$313$		−	8.99498i		−	0.508426i	0.967148	−	0.254213i	$-0.0818165\pi$
$314$	−3.06972			−0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$			6.72038i			0.377454i	0.982030	+	0.188727i	$0.0604362\pi$
$317$			6.72038i			0.377454i	−0.982030	+	0.188727i	$0.939564\pi$
$318$	1.12484	+	15.1200i	0.0630777	+	0.847887i
$319$	−11.6744			−0.653642
$320$	−1.80966	−	3.13442i	−0.101163	−	0.175219i
$321$	−2.57347	−	3.77899i	−0.143637	−	0.210923i
$322$		0			0
$323$		−	6.25494i		−	0.348034i
$324$	2.02173	−	8.76998i	0.112318	−	0.487221i
$325$	23.9100	−	13.8045i	1.32629	−	0.765734i
$326$	−2.48873	−	1.43687i	−0.137838	−	0.0795807i
$327$	1.16103	+	15.6066i	0.0642053	+	0.863045i
$328$	−4.93712	−	2.85045i	−0.272607	−	0.157390i
$329$		0			0
$330$	11.3145	+	5.45636i	0.622844	+	0.300363i
$331$	−18.7745			−1.03194			−0.515970	−	0.856607i	$-0.672568\pi$
$331$	−18.7745			−1.03194			−0.515970	+	0.856607i	$0.672568\pi$
$332$	−4.00481	−	6.93654i	−0.219793	−	0.380692i
$333$	21.7672	−	3.25672i	1.19284	−	0.178467i
$334$	−1.26529	−	0.730517i	−0.0692338	−	0.0399721i
$335$	−15.0499	−	26.0671i	−0.822262	−	1.42420i
$336$		0			0
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$	1.19552	−	0.690233i	0.0650276	−	0.0375437i
$339$	−1.64822	−	2.42031i	−0.0895188	−	0.131453i
$340$	11.1732	−	19.3525i	0.605949	−	1.04954i
$341$	0.911413	−	1.57861i	0.0493558	−	0.0854868i
$342$	3.00578	−	0.449713i	0.162534	−	0.0243177i
$343$		0			0
$344$	−4.15605	+	2.39949i	−0.224079	+	0.129372i
$345$	−10.6844	−	15.6895i	−0.575230	−	0.844693i
$346$			3.07081i			0.165088i
$347$		−	17.4712i		−	0.937902i	−0.883224	−	0.468951i	$-0.844632\pi$
$347$		−	17.4712i		−	0.937902i	0.883224	−	0.468951i	$-0.155368\pi$
$348$	−10.0634	+	0.748656i	−0.539454	+	0.0401322i
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.937399	−	0.348257i	$-0.886774\pi$
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.167101	+	0.985940i	$0.553440\pi$
$350$		0			0
$351$	5.24835	−	16.9169i	0.280136	−	0.902958i
$352$	1.00190	−	1.73534i	0.0534013	−	0.0924938i
$353$	−5.02061	+	8.69596i	−0.267220	+	0.462839i	−0.968143	−	0.250398i	$-0.919438\pi$
$353$	−5.02061	+	8.69596i	−0.267220	+	0.462839i	0.700923	+	0.713237i	$0.252772\pi$
$354$	6.76087	−	14.0196i	0.359336	−	0.745134i
$355$	−1.46154	+	0.843820i	−0.0775705	+	0.0447853i
$356$	−2.39324	+	4.14521i	−0.126841	+	0.219696i
$357$		0			0
$358$	9.65966	+	16.7310i	0.510529	+	0.884262i
$359$	−10.5353	−	6.08254i	−0.556030	−	0.321024i	0.195521	−	0.980700i	$-0.437360\pi$
$359$	−10.5353	−	6.08254i	−0.556030	−	0.321024i	−0.751550	+	0.659676i	$0.770694\pi$
$360$	10.1031	+	3.97782i	0.532478	+	0.209650i
$361$	−8.98683	−	15.5657i	−0.472991	−	0.819245i
$362$	−7.89318			−0.414856
$363$	−0.897541	−	12.0647i	−0.0471087	−	0.633233i
$364$		0			0
$365$	13.2113	+	7.62756i	0.691512	+	0.399245i
$366$	−22.9525	−	11.0687i	−1.19975	−	0.578570i
$367$	−3.14420	−	1.81531i	−0.164126	−	0.0947582i	0.415687	−	0.909508i	$-0.363541\pi$
$367$	−3.14420	−	1.81531i	−0.164126	−	0.0947582i	−0.579813	+	0.814749i	$0.696874\pi$
$368$	−2.62232	+	1.51400i	−0.136698	+	0.0789225i
$369$	16.9144	−	2.53067i	0.880529	−	0.131741i
$370$			26.5531i			1.38043i
$371$		0			0
$372$	0.684408	−	1.41922i	0.0354849	−	0.0735830i
$373$	−2.74616	−	4.75648i	−0.142191	−	0.246281i	0.786131	−	0.618060i	$-0.212081\pi$
$373$	−2.74616	−	4.75648i	−0.142191	−	0.246281i	−0.928321	+	0.371779i	$0.878748\pi$
$374$	12.3718			0.639730
$375$	−17.5012	−	8.43983i	−0.903757	−	0.435831i
$376$		−	2.23022i		−	0.115015i
$377$	−19.8599			−1.02284
$378$		0			0
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$			3.66666i			0.188096i
$381$	27.9716	+	13.4891i	1.43303	+	0.691067i
$382$	13.3042			0.680703
$383$	−4.71534	−	8.16720i	−0.240942	−	0.417324i	0.720041	−	0.693932i	$-0.244123\pi$
$383$	−4.71534	−	8.16720i	−0.240942	−	0.417324i	−0.960983	+	0.276607i	$0.910790\pi$
$384$	0.752355	−	1.56012i	0.0383935	−	0.0796143i
$385$		0			0
$386$			6.53573i			0.332660i
$387$	5.27434	−	13.3960i	0.268110	−	0.680959i
$388$	−10.1835	+	5.87944i	−0.516989	+	0.298483i
$389$	5.56142	+	3.21089i	0.281975	+	0.162798i	0.634317	−	0.773073i	$-0.281281\pi$
$389$	5.56142	+	3.21089i	0.281975	+	0.162798i	−0.352342	+	0.935871i	$0.614615\pi$
$390$	19.2476	+	9.28205i	0.974643	+	0.470015i
$391$	−16.1907	−	9.34769i	−0.818798	−	0.472733i
$392$		0			0
$393$	−2.22706	−	29.9360i	−0.112340	−	1.51007i
$394$	4.44250			0.223810
$395$	6.92255	+	11.9902i	0.348311	+	0.603293i
$396$	0.889499	+	5.94521i	0.0446990	+	0.298758i
$397$	−5.99750	−	3.46266i	−0.301006	−	0.173786i	0.341889	−	0.939740i	$-0.388933\pi$
$397$	−5.99750	−	3.46266i	−0.301006	−	0.173786i	−0.642895	+	0.765955i	$0.722267\pi$
$398$	−5.75542	−	9.96868i	−0.288493	−	0.499685i
$399$		0			0
$400$	−4.04972	+	7.01433i	−0.202486	+	0.350716i
$401$	−9.16848	+	5.29343i	−0.457852	+	0.264341i	−0.711141	−	0.703050i	$-0.751821\pi$
$401$	−9.16848	+	5.29343i	−0.457852	+	0.264341i	0.253289	+	0.967391i	$0.418488\pi$
$402$	6.25690	−	12.9746i	0.312066	−	0.647113i
$403$	1.55045	−	2.68545i	0.0772332	−	0.133772i
$404$	−6.44610	+	11.1650i	−0.320705	+	0.555478i
$405$	−31.1474	+	9.53372i	−1.54773	+	0.473735i
$406$		0			0
$407$	−12.7313	+	7.35042i	−0.631067	+	0.364347i
$408$	10.6645	−	0.793376i	0.527973	−	0.0392780i
$409$			8.92343i			0.441235i	0.975360	+	0.220618i	$0.0708073\pi$
$409$			8.92343i			0.441235i	−0.975360	+	0.220618i	$0.929193\pi$
$410$			20.6333i			1.01901i
$411$	0.000628945	0	0.000923569i	3.10236e−5	0	4.55563e-5i
$412$	9.31740	−	5.37940i	0.459035	−	0.265024i
$413$		0			0
$414$	3.32793	−	8.45243i	0.163559	−	0.415414i
$415$	−14.4947	+	25.1055i	−0.711516	+	1.23238i
$416$	1.70437	−	2.95206i	0.0835637	−	0.144737i
$417$	9.83082	+	14.4360i	0.481417	+	0.706933i
$418$	−1.75804	+	1.01500i	−0.0859883	+	0.0496454i
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	0.0500724	+	0.998746i	$0.484055\pi$
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	−0.889975	+	0.456009i	$0.849279\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$	19.5731	+	11.3005i	0.952803	+	0.550101i
$423$	4.16587	+	5.23549i	0.202552	+	0.254558i
$424$	−4.37683	−	7.58088i	−0.212557	−	0.368160i
$425$	−50.0075			−2.42572
$426$	−0.727462	−	0.350814i	−0.0352457	−	0.0169970i
$427$		0			0
$428$	2.28602	+	1.31983i	0.110499	+	0.0637965i
$429$	0.877703	+	11.7980i	0.0423759	+	0.569615i
$430$	15.0420	+	8.68453i	0.725392	+	0.418805i
$431$	−26.7338	+	15.4348i	−1.28772	+	0.743466i	−0.978247	−	0.207442i	$-0.933486\pi$
$431$	−26.7338	+	15.4348i	−1.28772	+	0.743466i	−0.309474	+	0.950908i	$0.600153\pi$
$432$	1.14800	+	5.06775i	0.0552334	+	0.243822i
$433$		−	23.2463i		−	1.11715i	−0.829455	−	0.558574i	$-0.811349\pi$
$433$		−	23.2463i		−	1.11715i	0.829455	−	0.558574i	$-0.188651\pi$
$434$		0			0
$435$	20.5579	+	30.1881i	0.985676	+	1.44741i
$436$	−4.51768	−	7.82484i	−0.216357	−	0.374742i
$437$	3.06760			0.146743
$438$	0.541613	+	7.28033i	0.0258793	+	0.347868i
$439$		−	22.2727i		−	1.06302i	−0.847052	−	0.531509i	$-0.821625\pi$
$439$		−	22.2727i		−	1.06302i	0.847052	−	0.531509i	$-0.178375\pi$
$440$	−7.25237			−0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$		−	17.9852i		−	0.854501i	−0.904133	−	0.427251i	$-0.859482\pi$
$443$		−	17.9852i		−	0.854501i	0.904133	−	0.427251i	$-0.140518\pi$
$444$	−10.5031	+	7.15251i	−0.498453	+	0.339443i
$445$	17.3238			0.821225
$446$	−9.41045	−	16.2994i	−0.445598	−	0.771798i
$447$	−19.4276	+	1.44530i	−0.918894	+	0.0683601i
$448$		0			0
$449$			9.44363i			0.445673i	0.974856	+	0.222836i	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$	−3.59540	−	24.0309i	−0.169489	−	1.13283i
$451$	−9.89297	+	5.71171i	−0.465842	+	0.268954i
$452$	1.46411	+	0.845306i	0.0688661	+	0.0397599i
$453$	6.76266	−	4.60533i	0.317737	−	0.216377i
$454$	12.6555	+	7.30665i	0.593952	+	0.342918i
$455$		0			0
$456$	−1.45034	+	0.987674i	−0.0679185	+	0.0462521i
$457$	−1.84450			−0.0862821			−0.0431411	−	0.999069i	$-0.513736\pi$
$457$	−1.84450			−0.0862821			−0.0431411	+	0.999069i	$0.513736\pi$
$458$	−1.18959	−	2.06044i	−0.0555861	−	0.0962779i
$459$	−23.5533	+	21.7830i	−1.09937	+	1.01674i
$460$	9.49100	+	5.47963i	0.442520	+	0.255489i
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	0.883829	+	0.467810i	$0.154957\pi$
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	−0.0367790	+	0.999323i	$0.511710\pi$
$462$		0			0
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	0.208425	+	0.978038i	$0.433166\pi$
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	−0.951219	+	0.308518i	$0.900167\pi$
$464$	5.04560	−	2.91308i	0.234236	−	0.135236i
$465$	−5.68697	+	0.423076i	−0.263727	+	0.0196197i
$466$	−5.21619	+	9.03470i	−0.241635	+	0.418525i
$467$	−12.2206	+	21.1666i	−0.565500	+	0.979475i	0.431503	+	0.902112i	$0.357983\pi$
$467$	−12.2206	+	21.1666i	−0.565500	+	0.979475i	−0.997003	+	0.0773632i	$0.975350\pi$
$468$	1.51317	+	10.1137i	0.0699461	+	0.467504i
$469$		0			0
$470$	−6.99044	+	4.03593i	−0.322445	+	0.186164i
$471$	−2.30952	+	4.78911i	−0.106417	+	0.220671i
$472$			8.98627i			0.413626i
$473$			9.61619i			0.442153i
$474$	−2.87801	+	5.96796i	−0.132191	+	0.274118i
$475$	7.10607	−	4.10269i	0.326049	−	0.188245i
$476$		0			0
$477$	24.4352	+	9.62073i	1.11881	+	0.440503i
$478$	−11.8917	+	20.5971i	−0.543916	+	0.942090i
$479$	−5.48032	+	9.49220i	−0.250402	+	0.433710i	−0.963637	−	0.267216i	$-0.913896\pi$
$479$	−5.48032	+	9.49220i	−0.250402	+	0.433710i	0.713234	+	0.700926i	$0.247230\pi$
$480$	−6.25156	+	0.465079i	−0.285344	+	0.0212278i
$481$	−21.6578	+	12.5041i	−0.987509	+	0.570139i
$482$	14.3243	−	24.8105i	0.652456	−	1.13009i
$483$		0			0
$484$	3.49240	+	6.04902i	0.158746	+	0.274955i
$485$	36.8573	+	21.2796i	1.67360	+	0.966255i
$486$	−12.1611	−	9.75228i	−0.551640	−	0.442372i
$487$	−16.8087	−	29.1136i	−0.761677	−	1.31926i	−0.941986	−	0.335653i	$-0.891043\pi$
$487$	−16.8087	−	29.1136i	−0.761677	−	1.31926i	0.180309	−	0.983610i	$-0.442290\pi$
$488$	14.7121			0.665984
$489$	−4.11408	+	2.80167i	−0.186045	+	0.126696i
$490$		0			0
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.0150939	−	0.999886i	$-0.504805\pi$
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.873474	+	0.486871i	$0.838138\pi$
$492$	−8.16149	+	5.55793i	−0.367949	+	0.250571i
$493$	31.1525	+	17.9859i	1.40304	+	0.810043i
$494$	−2.99067	+	1.72667i	−0.134557	+	0.0776863i
$495$	17.0251	−	13.5469i	0.765221	−	0.608886i
$496$			0.909687i			0.0408462i
$497$		0			0
$498$	−13.8348	+	1.02923i	−0.619954	+	0.0461209i
$499$	−9.76175	−	16.9079i	−0.436996	−	0.756899i	0.560460	−	0.828181i	$-0.310624\pi$
$499$	−9.76175	−	16.9079i	−0.436996	−	0.756899i	−0.997456	+	0.0712820i	$0.977291\pi$
$500$	11.2179			0.501679
$501$	−2.09164	+	1.42440i	−0.0934477	+	0.0636373i
$502$			11.0301i			0.492299i
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$			6.06748i			0.269732i
$507$	−0.177389	−	2.38445i	−0.00787810	−	0.105897i
$508$	−17.9292			−0.795478
$509$	1.14583	+	1.98464i	0.0507881	+	0.0879675i	0.890302	−	0.455371i	$-0.150493\pi$
$509$	1.14583	+	1.98464i	0.0507881	+	0.0879675i	−0.839514	+	0.543338i	$0.817160\pi$
$510$	−21.7859	−	31.9914i	−0.964697	−	1.41660i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	1.55981	−	5.02772i	0.0688674	−	0.221979i
$514$	−13.0751	+	7.54890i	−0.576717	+	0.332968i
$515$	−33.7226	−	19.4698i	−1.48600	−	0.857940i
$516$	0.616665	+	8.28919i	0.0271472	+	0.364911i
$517$	−3.87018	−	2.23445i	−0.170210	−	0.0982710i
$518$		0			0
$519$	4.79082	+	2.31034i	0.210294	+	0.101413i
$520$	−12.3373			−0.541027
$521$	−8.54102	−	14.7935i	−0.374189	−	0.648114i	0.616017	−	0.787733i	$-0.288745\pi$
$521$	−8.54102	−	14.7935i	−0.374189	−	0.648114i	−0.990205	+	0.139619i	$0.955412\pi$
$522$	−6.40326	+	16.2633i	−0.280263	+	0.711826i
$523$	−35.7462	−	20.6381i	−1.56307	−	0.902440i	−0.996944	−	0.0781229i	$-0.975107\pi$
$523$	−35.7462	−	20.6381i	−1.56307	−	0.902440i	−0.566128	−	0.824317i	$-0.691559\pi$
$524$	8.66567	+	15.0094i	0.378562	+	0.655688i
$525$		0			0
$526$	−9.81926	+	17.0075i	−0.428140	+	0.741561i
$527$	−4.86410	+	2.80829i	−0.211883	+	0.122331i
$528$	−1.95354	−	2.86867i	−0.0850171	−	0.124843i
$529$	−6.91563	+	11.9782i	−0.300679	+	0.520792i
$530$	−15.8411	+	27.4376i	−0.688094	+	1.19181i
$531$	−16.7857	−	21.0955i	−0.728435	−	0.915465i
$532$		0			0
$533$	−16.8294	+	9.71644i	−0.728961	+	0.420866i
$534$	4.66644	+	6.85240i	0.201937	+	0.296532i
$535$		−	9.55378i		−	0.413046i
$536$			8.31641i			0.359214i
$537$	33.3698	−	2.48251i	1.44001	−	0.107128i
$538$	0.425223	−	0.245503i	0.0183327	−	0.0105844i
$539$		0			0
$540$	13.8070	−	12.7692i	0.594157	−	0.549500i
$541$	22.7197	−	39.3516i	0.976795	−	1.69186i	0.302915	−	0.953018i	$-0.402040\pi$
$541$	22.7197	−	39.3516i	0.976795	−	1.69186i	0.673880	−	0.738841i	$-0.264627\pi$
$542$	−7.03945	+	12.1927i	−0.302370	+	0.523721i
$543$	−5.93847	+	12.3143i	−0.254844	+	0.528456i
$544$	−5.34700	+	3.08709i	−0.229251	+	0.132358i
$545$	−16.3509	+	28.3206i	−0.700395	+	1.21312i
$546$		0			0
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	0.984061	+	0.177832i	$0.0569082\pi$
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	−0.338024	+	0.941138i	$0.609758\pi$
$548$	−0.000558693	0	0.000322562i	−2.38662e−5	0	1.37791e-5i
$549$	−34.5369	+	27.4810i	−1.47400	+	1.17286i
$550$	8.11481	+	14.0553i	0.346017	+	0.599319i
$551$	−5.90237			−0.251449
$552$	0.389094	+	5.23019i	0.0165610	+	0.222612i
$553$		0			0
$554$	−26.6043	−	15.3600i	−1.13031	−	0.652585i
$555$	41.4259	+	19.9774i	1.75843	+	0.847992i
$556$	−8.73273	−	5.04185i	−0.370350	−	0.213822i
$557$	22.0154	−	12.7106i	0.932822	−	0.538565i	0.0451189	−	0.998982i	$-0.485633\pi$
$557$	22.0154	−	12.7106i	0.932822	−	0.538565i	0.887703	+	0.460417i	$0.152300\pi$
$558$	−1.69923	−	2.13551i	−0.0719340	−	0.0904034i
$559$			16.3585i			0.691892i
$560$		0			0
$561$	9.30799	−	19.3014i	0.392983	−	0.814907i
$562$	3.96227	+	6.86286i	0.167138	+	0.289492i
$563$	−2.88692			−0.121669			−0.0608346	−	0.998148i	$-0.519376\pi$
$563$	−2.88692			−0.121669			−0.0608346	+	0.998148i	$0.519376\pi$
$564$	−3.47940	−	1.67792i	−0.146509	−	0.0706530i
$565$		−	6.11886i		−	0.257422i
$566$	11.5159			0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$			44.5651i			1.86827i	0.356922	+	0.934134i	$0.383826\pi$
$569$			44.5651i			1.86827i	−0.356922	+	0.934134i	$0.616174\pi$
$570$	5.72041	+	2.75863i	0.239602	+	0.115546i
$571$	−6.52939			−0.273247			−0.136623	−	0.990623i	$-0.543625\pi$
$571$	−6.52939			−0.273247			−0.136623	+	0.990623i	$0.543625\pi$
$572$	−3.41521	−	5.91532i	−0.142797	−	0.247332i
$573$	10.0095	−	20.7561i	0.418153	−	0.867100i
$574$		0			0
$575$		−	24.5251i		−	1.02277i
$576$	−1.86792	−	2.34752i	−0.0778301	−	0.0978135i
$577$	−1.17720	+	0.679658i	−0.0490076	+	0.0282945i	−0.524304	−	0.851531i	$-0.675674\pi$
$577$	−1.17720	+	0.679658i	−0.0490076	+	0.0282945i	0.475296	+	0.879826i	$0.342341\pi$
$578$	−18.2909	−	10.5603i	−0.760802	−	0.439249i
$579$	10.1965	+	4.91719i	0.423752	+	0.204352i
$580$	−18.2616	−	10.5434i	−0.758273	−	0.437789i
$581$		0			0
$582$	1.51101	+	20.3109i	0.0626332	+	0.841912i
$583$	−17.5405			−0.726454
$584$	−2.10746	−	3.65022i	−0.0872072	−	0.151047i
$585$	28.9621	−	23.0452i	1.19744	−	0.952800i
$586$	4.34636	+	2.50937i	0.179547	+	0.103661i
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.804843	−	0.593488i	$-0.797750\pi$
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.111555	−	0.993758i	$-0.535583\pi$
$588$		0			0
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$	28.1667	−	16.2621i	1.15961	−	0.669499i
$591$	3.34234	−	6.93082i	0.137485	−	0.285096i
$592$	3.66825	−	6.35359i	0.150764	−	0.261131i
$593$	−7.17564	+	12.4286i	−0.294668	+	0.510380i	−0.974908	−	0.222610i	$-0.928542\pi$
$593$	−7.17564	+	12.4286i	−0.294668	+	0.510380i	0.680240	+	0.732990i	$0.261876\pi$
$594$	9.94444	+	3.08519i	0.408025	+	0.126587i
$595$		0			0
$596$	9.74064	−	5.62376i	0.398992	−	0.230358i
$597$	−19.8824	+	1.47913i	−0.813733	+	0.0605368i
$598$			10.3217i			0.422084i
$599$		−	3.50277i		−	0.143119i	−0.997436	−	0.0715597i	$-0.977202\pi$
$599$		−	3.50277i		−	0.143119i	0.997436	−	0.0715597i	$-0.0227977\pi$
$600$	7.89633	+	11.5953i	0.322366	+	0.473376i
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	−0.776633	−	0.629953i	$-0.783074\pi$
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	0.157239	+	0.987561i	$0.449741\pi$
$602$		0			0
$603$	−15.5344	−	19.5230i	−0.632610	−	0.795037i
$604$	−2.36189	+	4.09092i	−0.0961041	+	0.166457i
$605$	12.6401	−	21.8933i	0.513894	−	0.890090i
$606$	12.5689	+	18.4567i	0.510576	+	0.749752i
$607$	−0.0755923	+	0.0436432i	−0.00306820	+	0.00177142i	−0.501533	−	0.865138i	$-0.667231\pi$
$607$	−0.0755923	+	0.0436432i	−0.00306820	+	0.00177142i	0.498465	+	0.866910i	$0.333897\pi$
$608$	0.506540	−	0.877353i	0.0205429	−	0.0355814i
$609$		0			0
$610$	−26.6238	−	46.1138i	−1.07797	−	1.86709i
$611$	−6.58373	−	3.80112i	−0.266349	−	0.153777i
$612$	6.78575	−	17.2348i	0.274298	−	0.696675i
$613$	12.5352	+	21.7116i	0.506292	+	0.876924i	0.999973	+	0.00728071i	$0.00231754\pi$
$613$	12.5352	+	21.7116i	0.506292	+	0.876924i	−0.493681	+	0.869643i	$0.664349\pi$
$614$	17.5309			0.707490
$615$	32.1904	+	15.5236i	1.29804	+	0.625972i
$616$		0			0
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	0.270373	−	0.962756i	$-0.412853\pi$
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	−0.698584	+	0.715528i	$0.746186\pi$
$618$	−1.38250	−	18.5834i	−0.0556121	−	0.747536i
$619$	17.5869	+	10.1538i	0.706875	+	0.408115i	0.809903	−	0.586564i	$-0.199520\pi$
$619$	17.5869	+	10.1538i	0.706875	+	0.408115i	−0.103028	+	0.994678i	$0.532853\pi$
$620$	2.85134	−	1.64622i	0.114513	−	0.0661139i
$621$	−10.6830	−	11.5512i	−0.428694	−	0.463533i
$622$		−	17.2952i		−	0.693474i
$623$		0			0
$624$	−3.32326	−	4.88001i	−0.133037	−	0.195357i
$625$	−0.0518970	−	0.0898882i	−0.00207588	−	0.00359553i
$626$	8.99498			0.359512
$627$	0.260854	+	3.50638i	0.0104175	+	0.140031i
$628$		−	3.06972i		−	0.122495i
$629$	45.2969			1.80610
$630$		0			0
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$		−	3.82533i		−	0.152164i
$633$	32.3561	−	22.0343i	1.28604	−	0.875784i
$634$	−6.72038			−0.266901
$635$	32.4456	+	56.1975i	1.28757	+	2.23013i
$636$	−15.1200	+	1.12484i	−0.599546	+	0.0446026i
$637$		0			0
$638$		−	11.6744i		−	0.462195i
$639$	−1.09462	+	0.870989i	−0.0433025	+	0.0344558i
$640$	3.13442	−	1.80966i	0.123899	−	0.0715330i
$641$	−27.4104	−	15.8254i	−1.08265	−	0.625067i	−0.151038	−	0.988528i	$-0.548262\pi$
$641$	−27.4104	−	15.8254i	−1.08265	−	0.625067i	−0.931609	+	0.363461i	$0.881595\pi$
$642$	3.77899	−	2.57347i	0.149145	−	0.101567i
$643$	10.0106	+	5.77960i	0.394778	+	0.227925i	0.684228	−	0.729268i	$-0.260139\pi$
$643$	10.0106	+	5.77960i	0.394778	+	0.227925i	−0.289450	+	0.957193i	$0.593472\pi$
$644$		0			0
$645$	24.8658	−	16.9335i	0.979091	−	0.666755i
$646$	6.25494			0.246097
$647$	13.0365	+	22.5799i	0.512519	+	0.887708i	0.999895	+	0.0145160i	$0.00462076\pi$
$647$	13.0365	+	22.5799i	0.512519	+	0.887708i	−0.487376	+	0.873192i	$0.662046\pi$
$648$	8.76998	+	2.02173i	0.344517	+	0.0794210i
$649$	15.5942	+	9.00332i	0.612126	+	0.353411i
$650$	13.8045	+	23.9100i	0.541456	+	0.937829i
$651$		0			0
$652$	1.43687	−	2.48873i	0.0562720	−	0.0974660i
$653$	16.3952	−	9.46576i	0.641593	−	0.370424i	−0.143635	−	0.989631i	$-0.545879\pi$
$653$	16.3952	−	9.46576i	0.641593	−	0.370424i	0.785228	+	0.619207i	$0.212546\pi$
$654$	−15.6066	+	1.16103i	−0.610265	+	0.0454000i
$655$	31.3638	−	54.3237i	1.22549	−	2.12260i
$656$	2.85045	−	4.93712i	0.111291	−	0.192762i
$657$	11.7656	+	4.63242i	0.459021	+	0.180728i
$658$		0			0
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.0293098	−	0.999570i	$-0.490669\pi$
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.880308	+	0.474402i	$0.157336\pi$
$660$	−5.45636	+	11.3145i	−0.212388	+	0.440418i
$661$			25.7730i			1.00245i	0.865316	+	0.501227i	$0.167118\pi$
$661$			25.7730i			1.00245i	−0.865316	+	0.501227i	$0.832882\pi$
$662$		−	18.7745i		−	0.729691i
$663$	15.8342	−	32.8345i	0.614950	−	1.27519i
$664$	6.93654	−	4.00481i	0.269190	−	0.155417i
$665$		0			0
$666$	3.25672	+	21.7672i	0.126195	+	0.843462i
$667$	−8.82079	+	15.2780i	−0.341542	+	0.591568i
$668$	0.730517	−	1.26529i	0.0282646	−	0.0489557i
$669$	−32.5089	+	2.41847i	−1.25687	+	0.0935034i
$670$	26.0671	−	15.0499i	1.00706	−	0.581427i
$671$	14.7400	−	25.5304i	0.569030	−	0.985590i
$672$		0			0
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$	4.19654	+	2.42287i	0.161645	+	0.0933256i
$675$	−40.1959	−	12.4705i	−1.54714	−	0.479990i
$676$	0.690233	+	1.19552i	0.0265474	+	0.0459815i
$677$	−13.1076			−0.503767			−0.251884	−	0.967758i	$-0.581050\pi$
$677$	−13.1076			−0.503767			−0.251884	+	0.967758i	$0.581050\pi$
$678$	2.42031	−	1.64822i	0.0929514	−	0.0632993i
$679$		0			0
$680$	19.3525	+	11.1732i	0.742134	+	0.428471i
$681$	20.9207	−	14.2468i	0.801681	−	0.545940i
$682$	1.57861	+	0.911413i	0.0604483	+	0.0348998i
$683$	25.6910	−	14.8327i	0.983038	−	0.567557i	0.0798523	−	0.996807i	$-0.474555\pi$
$683$	25.6910	−	14.8327i	0.983038	−	0.567557i	0.903186	+	0.429249i	$0.141222\pi$
$684$	0.449713	+	3.00578i	0.0171952	+	0.114929i
$685$			0.00233490i			8.92121e-5i
$686$		0			0
$687$	−4.10952	+	0.305723i	−0.156788	+	0.0116641i
$688$	−2.39949	−	4.15605i	−0.0914799	−	0.158448i
$689$	−29.8390			−1.13677
$690$	15.6895	−	10.6844i	0.597288	−	0.406749i
$691$		−	47.3159i		−	1.79998i	−0.435910	−	0.899990i	$-0.643573\pi$
$691$		−	47.3159i		−	1.79998i	0.435910	−	0.899990i	$-0.356427\pi$
$692$	−3.07081			−0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$			36.4961i			1.38437i
$696$	−0.748656	−	10.0634i	−0.0283777	−	0.381452i
$697$	35.1983			1.33323
$698$	−11.9129	−	20.6338i	−0.450910	−	0.780999i
$699$	10.1708	+	14.9352i	0.384693	+	0.564900i
$700$		0			0
$701$			13.7742i			0.520244i	0.965576	+	0.260122i	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$	16.9169	+	5.24835i	0.638488	+	0.198086i
$703$	−6.43670	+	3.71623i	−0.242765	+	0.140160i
$704$	1.73534	+	1.00190i	0.0654030	+	0.0377604i
$705$	1.03723	+	13.9423i	0.0390642	+	0.525099i
$706$	−8.69596	−	5.02061i	−0.327277	−	0.188953i
$707$		0			0
$708$	14.0196	+	6.76087i	0.526889	+	0.254089i
$709$	−43.9383			−1.65014			−0.825069	−	0.565032i	$-0.808864\pi$
$709$	−43.9383			−1.65014			−0.825069	+	0.565032i	$0.808864\pi$
$710$	−0.843820	−	1.46154i	−0.0316680	−	0.0548506i
$711$	7.14543	+	8.98006i	0.267975	+	0.336779i
$712$	−4.14521	−	2.39324i	−0.155348	−	0.0896903i
$713$	−1.37726	−	2.38549i	−0.0515789	−	0.0893373i
$714$		0			0
$715$	−12.3607	+	21.4094i	−0.462265	+	0.800667i
$716$	−16.7310	+	9.65966i	−0.625268	+	0.360998i
$717$	23.1871	+	34.0488i	0.865936	+	1.27158i
$718$	6.08254	−	10.5353i	0.226998	−	0.393173i
$719$	14.7930	−	25.6223i	0.551687	−	0.955549i	−0.446466	−	0.894800i	$-0.647318\pi$
$719$	14.7930	−	25.6223i	0.551687	−	0.955549i	0.998153	−	0.0607489i	$-0.0193489\pi$
$720$	−3.97782	+	10.1031i	−0.148245	+	0.376519i
$721$		0			0
$722$	15.5657	−	8.98683i	0.579294	−	0.334455i
$723$	−27.9303	−	41.0140i	−1.03874	−	1.52533i
$724$		−	7.89318i		−	0.293348i
$725$			47.1887i			1.75254i
$726$	12.0647	−	0.897541i	0.447763	−	0.0333109i
$727$	−10.1244	+	5.84534i	−0.375494	+	0.216792i	−0.675856	−	0.737034i	$-0.736226\pi$
$727$	−10.1244	+	5.84534i	−0.375494	+	0.216792i	0.300362	+	0.953825i	$0.402893\pi$
$728$		0			0
$729$	−24.3642	+	11.6356i	−0.902377	+	0.430948i
$730$	−7.62756	+	13.2113i	−0.282308	+	0.488973i
$731$	14.8149	−	25.6602i	0.547949	−	0.949076i
$732$	11.0687	−	22.9525i	0.409111	−	0.848350i
$733$	28.6423	−	16.5366i	1.05793	−	0.610795i	0.133070	−	0.991107i	$-0.457517\pi$
$733$	28.6423	−	16.5366i	1.05793	−	0.610795i	0.924858	+	0.380312i	$0.124183\pi$
$734$	1.81531	−	3.14420i	0.0670042	−	0.116055i
$735$		0			0
$736$	−1.51400	−	2.62232i	−0.0558067	−	0.0966600i
$737$	14.4318	+	8.33219i	0.531601	+	0.306920i
$738$	2.53067	+	16.9144i	0.0931551	+	0.622628i
$739$	−21.7528	−	37.6770i	−0.800190	−	1.38597i	−0.919491	−	0.393111i	$-0.871399\pi$
$739$	−21.7528	−	37.6770i	−0.800190	−	1.38597i	0.119301	−	0.992858i	$-0.461935\pi$
$740$	−26.5531			−0.976111
$741$	0.443750	+	5.96486i	0.0163016	+	0.219125i
$742$		0			0
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	0.792701	−	0.609611i	$-0.208674\pi$
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	−0.131589	+	0.991304i	$0.542008\pi$
$744$	1.41922	+	0.684408i	0.0520310	+	0.0250916i
$745$	−35.2544	−	20.3542i	−1.29162	−	0.745719i
$746$	4.75648	−	2.74616i	0.174147	−	0.100544i
$747$	−8.80300	+	22.3583i	−0.322085	+	0.818048i
$748$			12.3718i			0.452358i
$749$		0			0
$750$	8.43983	−	17.5012i	0.308179	−	0.639053i
$751$	19.9492	+	34.5531i	0.727957	+	1.26086i	0.957745	+	0.287618i	$0.0928634\pi$
$751$	19.9492	+	34.5531i	0.727957	+	1.26086i	−0.229788	+	0.973241i	$0.573803\pi$
$752$	2.23022			0.0813277
$753$	17.2083	+	8.29858i	0.627105	+	0.302417i
$754$		−	19.8599i		−	0.723254i
$755$	17.0969			0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$		−	15.5960i		−	0.566472i
$759$	9.46597	+	4.56490i	0.343593	+	0.165695i
$760$	−3.66666			−0.133004
$761$	4.32462	+	7.49046i	0.156767	+	0.271529i	0.933701	−	0.358053i	$-0.116559\pi$
$761$	4.32462	+	7.49046i	0.156767	+	0.271529i	−0.776934	+	0.629582i	$0.783226\pi$
$762$	−13.4891	+	27.9716i	−0.488658	+	1.01330i
$763$		0			0
$764$			13.3042i			0.481330i
$765$	−66.3010	+	9.91969i	−2.39712	+	0.358647i
$766$	8.16720	−	4.71534i	0.295093	−	0.170372i
$767$	26.5280	+	15.3159i	0.957870	+	0.553026i
$768$	1.56012	+	0.752355i	0.0562958	+	0.0271483i
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	0.0829652	−	0.996552i	$-0.473561\pi$
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	−0.821557	+	0.570126i	$0.806894\pi$
$770$		0			0
$771$	1.94005	+	26.0781i	0.0698693	+	0.939180i
$772$	−6.53573			−0.235226
$773$	−23.2849	−	40.3307i	−0.837501	−	1.45059i	−0.891978	−	0.452079i	$-0.850683\pi$
$773$	−23.2849	−	40.3307i	−0.837501	−	1.45059i	0.0544774	−	0.998515i	$-0.482651\pi$
$774$	13.3960	+	5.27434i	0.481511	+	0.189582i
$775$	−6.38084	−	3.68398i	−0.229207	−	0.132333i
$776$	−5.87944	−	10.1835i	−0.211060	−	0.365566i
$777$		0			0
$778$	−3.21089	+	5.56142i	−0.115116	+	0.199387i
$779$	−5.00170	+	2.88773i	−0.179204	+	0.103464i
$780$	−9.28205	+	19.2476i	−0.332351	+	0.689176i
$781$	0.467172	−	0.809166i	0.0167167	−	0.0289542i
$782$	9.34769	−	16.1907i	0.334273	−	0.578977i
$783$	20.5551	+	22.2256i	0.734580	+	0.794279i
$784$		0			0
$785$	−9.62178	+	5.55513i	−0.343416	+	0.198271i
$786$	29.9360	−	2.22706i	1.06778	−	0.0794366i
$787$		−	24.4400i		−	0.871192i	−0.900142	−	0.435596i	$-0.856538\pi$
$787$		−	24.4400i		−	0.871192i	0.900142	−	0.435596i	$-0.143462\pi$
$788$			4.44250i			0.158258i
$789$	19.1460	+	28.1148i	0.681617	+	1.00091i
$790$	−11.9902	+	6.92255i	−0.426592	+	0.246293i
$791$		0			0
$792$	−5.94521	+	0.889499i	−0.211254	+	0.0316070i
$793$	25.0748	−	43.4309i	0.890433	−	1.54228i
$794$	3.46266	−	5.99750i	0.122885	−	0.212843i
$795$	30.8877	+	45.3568i	1.09547	+	1.60864i
$796$	9.96868	−	5.75542i	0.353330	−	0.203995i
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.0344128	−	0.999408i	$-0.489044\pi$
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.848306	−	0.529506i	$-0.177623\pi$
$798$		0			0
$799$	6.88489	+	11.9250i	0.243570	+	0.421875i
$800$	−7.01433	−	4.04972i	−0.247994	−	0.143179i
$801$	14.2014	−	2.12475i	0.501780	−	0.0750743i
$802$	−5.29343	−	9.16848i	−0.186917	−	0.323750i
$803$	−8.44583			−0.298047
$804$	12.9746	+	6.25690i	0.457578	+	0.220664i
$805$		0			0
$806$	2.68545	+	1.55045i	0.0945910	+	0.0546121i
$807$	−0.0630937	−	0.848103i	−0.00222100	−	0.0298546i
$808$	−11.1650	−	6.44610i	−0.392782	−	0.226773i
$809$	−10.6735	+	6.16237i	−0.375262	+	0.216657i	−0.675755	−	0.737127i	$-0.736182\pi$
$809$	−10.6735	+	6.16237i	−0.375262	+	0.216657i	0.300493	+	0.953784i	$0.402849\pi$
$810$	−9.53372	−	31.1474i	−0.334981	−	1.09441i
$811$		−	24.8017i		−	0.870906i	−0.900212	−	0.435453i	$-0.856588\pi$
$811$		−	24.8017i		−	0.870906i	0.900212	−	0.435453i	$-0.143412\pi$
$812$		0			0
$813$	13.7258	+	20.1556i	0.481386	+	0.706888i
$814$	−7.35042	−	12.7313i	−0.257632	−	0.446232i
$815$	−10.4009			−0.364329
$816$	0.793376	+	10.6645i	0.0277737	+	0.373333i
$817$			4.86176i			0.170091i
$818$	−8.92343			−0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$		−	36.2083i		−	1.26368i	−0.775100	−	0.631839i	$-0.782300\pi$
$821$		−	36.2083i		−	1.26368i	0.775100	−	0.631839i	$-0.217700\pi$
$822$	−0.000923569	0	0.000628945i	−3.22132e−5	0	2.19370e-5i
$823$	−19.0819			−0.665152			−0.332576	−	0.943076i	$-0.607918\pi$
$823$	−19.0819			−0.665152			−0.332576	+	0.943076i	$0.607918\pi$
$824$	5.37940	+	9.31740i	0.187400	+	0.324587i
$825$	28.0331	−	2.08549i	0.975986	−	0.0726075i
$826$		0			0
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$	8.45243	+	3.32793i	0.293742	+	0.115653i
$829$	−13.0645	+	7.54278i	−0.453748	+	0.261971i	−0.709412	−	0.704794i	$-0.751039\pi$
$829$	−13.0645	+	7.54278i	−0.453748	+	0.261971i	0.255664	+	0.966766i	$0.417706\pi$
$830$	−25.1055	−	14.4947i	−0.871425	−	0.503118i
$831$	−43.9793	+	29.9497i	−1.52563	+	1.03894i
$832$	2.95206	+	1.70437i	0.102344	+	0.0590885i
$833$		0			0
$834$	−14.4360	+	9.83082i	−0.499877	+	0.340413i
$835$	−5.28795			−0.182997
$836$	−1.01500	−	1.75804i	−0.0351046	−	0.0608029i
$837$	−4.61007	+	1.04432i	−0.159347	+	0.0360972i
$838$	−29.7781	−	17.1924i	−1.02867	−	0.593901i
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	0.972134	−	0.234427i	$-0.0753214\pi$
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	−0.689087	+	0.724679i	$0.741988\pi$
$840$		0			0
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$	30.8028	−	17.7840i	1.06153	−	0.612877i
$843$	13.6879	−	1.01830i	0.471436	−	0.0350720i
$844$	−11.3005	+	19.5731i	−0.388980	+	0.673734i
$845$	2.49817	−	4.32696i	0.0859397	−	0.148852i
$846$	−5.23549	+	4.16587i	−0.180000	+	0.143226i
$847$		0			0
$848$	7.58088	−	4.37683i	0.260329	−	0.150301i
$849$	8.66402	−	17.9661i	0.297348	−	0.616594i
$850$		−	50.0075i		−	1.71524i
$851$			22.2149i			0.761516i
$852$	0.350814	−	0.727462i	0.0120187	−	0.0249224i
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	−0.756411	−	0.654096i	$-0.773049\pi$
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	0.188258	+	0.982120i	$0.439716\pi$
$854$		0			0
$855$	8.60756	−	6.84903i	0.294372	−	0.234232i
$856$	−1.31983	+	2.28602i	−0.0451110	+	0.0781345i
$857$	−8.05723	+	13.9555i	−0.275230	+	0.476712i	−0.970193	−	0.242333i	$-0.922087\pi$
$857$	−8.05723	+	13.9555i	−0.275230	+	0.476712i	0.694963	+	0.719045i	$0.255421\pi$
$858$	−11.7980	+	0.877703i	−0.402778	+	0.0299643i
$859$	−10.4830	+	6.05238i	−0.357677	+	0.206505i	−0.668061	−	0.744106i	$-0.732876\pi$
$859$	−10.4830	+	6.05238i	−0.357677	+	0.206505i	0.310384	+	0.950611i	$0.399542\pi$
$860$	−8.68453	+	15.0420i	−0.296140	+	0.512929i
$861$		0			0
$862$	−15.4348	−	26.7338i	−0.525710	−	0.910556i
$863$	32.2728	+	18.6327i	1.09858	+	0.634265i	0.935848	−	0.352405i	$-0.114636\pi$
$863$	32.2728	+	18.6327i	1.09858	+	0.634265i	0.162732	+	0.986670i	$0.447969\pi$
$864$	−5.06775	+	1.14800i	−0.172408	+	0.0390559i
$865$	5.55712	+	9.62522i	0.188948	+	0.327267i
$866$	23.2463			0.789942
$867$	−30.2365	+	20.5909i	−1.02689	+	0.699303i
$868$		0			0
$869$	−6.63824	−	3.83259i	−0.225187	−	0.130012i
$870$	−30.1881	+	20.5579i	−1.02347	+	0.696978i
$871$	24.5505	+	14.1743i	0.831863	+	0.480276i
$872$	7.82484	−	4.51768i	0.264983	−	0.152988i
$873$	32.8241	+	12.9236i	1.11093	+	0.437399i
$874$			3.06760i			0.103763i
$875$		0			0
$876$	−7.28033	+	0.541613i	−0.245980	+	0.0182994i
$877$	4.85474	+	8.40866i	0.163933	+	0.283940i	0.936276	−	0.351266i	$-0.114249\pi$
$877$	4.85474	+	8.40866i	0.163933	+	0.283940i	−0.772343	+	0.635206i	$0.780915\pi$
$878$	22.2727			0.751668
$879$	7.18493	−	4.89289i	0.242342	−	0.165033i
$880$		−	7.25237i		−	0.244477i
$881$	2.63241			0.0886881			0.0443440	−	0.999016i	$-0.485880\pi$
$881$	2.63241			0.0886881			0.0443440	+	0.999016i	$0.485880\pi$
$882$		0			0
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$			21.0462i			0.707860i
$885$	−4.17932	−	56.1782i	−0.140486	−	1.88841i
$886$	17.9852			0.604224
$887$	8.18209	+	14.1718i	0.274728	+	0.475842i	0.970066	−	0.242840i	$-0.0780790\pi$
$887$	8.18209	+	14.1718i	0.274728	+	0.475842i	−0.695339	+	0.718682i	$0.744746\pi$
$888$	−7.15251	−	10.5031i	−0.240023	−	0.352459i
$889$		0			0
$890$			17.3238i			0.580694i
$891$	12.2950	−	13.1933i	0.411898	−	0.441993i
$892$	16.2994	−	9.41045i	0.545744	−	0.315085i
$893$	−1.95669	−	1.12969i	−0.0654781	−	0.0378038i
$894$	−1.44530	−	19.4276i	−0.0483379	−	0.649756i
$895$	60.5549	+	34.9614i	2.02413	+	1.16863i
$896$		0			0
$897$	16.1030	+	7.76555i	0.537663	+	0.259284i
$898$	−9.44363			−0.315138
$899$	2.64999	+	4.58992i	0.0883822	+	0.153082i
$900$	24.0309	−	3.59540i	0.801029	−	0.119847i
$901$	46.8058	+	27.0233i	1.55933	+	0.900277i
$902$	−5.71171	−	9.89297i	−0.190179	−	0.329400i
$903$		0			0
$904$	−0.845306	+	1.46411i	−0.0281145	+	0.0486957i
$905$	−24.7405	+	14.2839i	−0.822403	+	0.474814i
$906$	4.60533	+	6.76266i	0.153002	+	0.224674i
$907$	−5.41666	+	9.38192i	−0.179857	+	0.311522i	−0.941831	−	0.336086i	$-0.890897\pi$
$907$	−5.41666	+	9.38192i	−0.179857	+	0.311522i	0.761974	+	0.647607i	$0.224230\pi$
$908$	−7.30665	+	12.6555i	−0.242480	+	0.419987i
$909$	38.2509	−	5.72294i	1.26870	−	0.189818i
$910$		0			0
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.255817	−	0.966725i	$-0.417655\pi$
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.965117	+	0.261818i	$0.0843221\pi$
$912$	−0.987674	−	1.45034i	−0.0327052	−	0.0480256i
$913$		−	16.0496i		−	0.531166i
$914$		−	1.84450i		−	0.0610107i
$915$	−91.9734	+	6.84227i	−3.04055	+	0.226198i
$916$	2.06044	−	1.18959i	0.0680788	−	0.0393053i
$917$		0			0
$918$	−21.7830	−	23.5533i	−0.718946	−	0.777373i
$919$	−12.9697	+	22.4641i	−0.427829	+	0.741022i	−0.996680	−	0.0814187i	$-0.974055\pi$
$919$	−12.9697	+	22.4641i	−0.427829	+	0.741022i	0.568851	+	0.822441i	$0.307388\pi$
$920$	−5.47963	+	9.49100i	−0.180658	+	0.312909i
$921$	13.1895	−	27.3502i	0.434608	−	0.901221i
$922$	−31.5007	+	18.1869i	−1.03742	+	0.598955i
$923$	0.794727	−	1.37651i	0.0261588	−	0.0453083i
$924$		0			0
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$	−27.6834	−	15.9830i	−0.909733	−	0.525234i
$927$	−30.0324	−	11.8245i	−0.986395	−	0.388367i
$928$	2.91308	+	5.04560i	0.0956265	+	0.165630i
$929$	−46.8911			−1.53845			−0.769224	−	0.638979i	$-0.779357\pi$
$929$	−46.8911			−1.53845			−0.769224	+	0.638979i	$0.779357\pi$
$930$	−0.423076	−	5.68697i	−0.0138732	−	0.186483i
$931$		0			0
$932$	−9.03470	−	5.21619i	−0.295942	−	0.170862i
$933$	−26.9825	−	13.0121i	−0.883367	−	0.425998i
$934$	−21.1666	−	12.2206i	−0.692593	−	0.399869i
$935$	38.7784	−	22.3887i	1.26819	−	0.732189i
$936$	−10.1137	+	1.51317i	−0.330575	+	0.0494594i
$937$		−	0.209357i		−	0.00683939i	−0.999994	−	0.00341969i	$-0.998911\pi$
$937$		−	0.209357i		−	0.00683939i	0.999994	−	0.00341969i	$-0.00108852\pi$
$938$		0			0
$939$	6.76742	−	14.0332i	0.220846	−	0.457956i
$940$	−4.03593	−	6.99044i	−0.131638	−	0.228003i
$941$	0.777130			0.0253337			0.0126669	−	0.999920i	$-0.495968\pi$
$941$	0.777130			0.0253337			0.0126669	+	0.999920i	$0.495968\pi$
$942$	−4.78911	−	2.30952i	−0.156038	−	0.0752481i
$943$			17.2623i			0.562137i
$944$	−8.98627			−0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$		−	49.7945i		−	1.61810i	−0.587737	−	0.809052i	$-0.699981\pi$
$947$		−	49.7945i		−	1.61810i	0.587737	−	0.809052i	$-0.300019\pi$
$948$	−5.96796	−	2.87801i	−0.193830	−	0.0934734i
$949$	−14.3676			−0.466391
$950$	4.10269	+	7.10607i	0.133109	+	0.230552i
$951$	−5.05612	+	10.4846i	−0.163956	+	0.339986i
$952$		0			0
$953$			41.4104i			1.34141i	0.741722	+	0.670707i	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$	−9.62073	+	24.4352i	−0.311483	+	0.791119i
$955$	41.7010	−	24.0761i	1.34941	−	0.779084i
$956$	−20.5971	−	11.8917i	−0.666158	−	0.384607i
$957$	−18.2135	−	8.78332i	−0.588757	−	0.283924i
$958$	−9.49220	−	5.48032i	−0.306679	−	0.177061i
$959$		0			0
$960$	−0.465079	−	6.25156i	−0.0150103	−	0.201768i
$961$	30.1725			0.973305
$962$	−12.5041	−	21.6578i	−0.403149	−	0.698274i
$963$	−1.17177	−	7.83183i	−0.0377596	−	0.252377i
$964$	24.8105	+	14.3243i	0.799092	+	0.461356i
$965$	11.8274	+	20.4857i	0.380739	+	0.659459i
$966$		0			0
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	−0.222181	−	0.975005i	$-0.571318\pi$
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	0.955470	−	0.295088i	$-0.0953491\pi$
$968$	−6.04902	+	3.49240i	−0.194423	+	0.112250i
$969$	4.70594	−	9.75843i	0.151177	−	0.313486i
$970$	−21.2796	+	36.8573i	−0.683245	+	1.18342i
$971$	4.36733	−	7.56444i	0.140154	−	0.242754i	−0.787400	−	0.616442i	$-0.788573\pi$
$971$	4.36733	−	7.56444i	0.140154	−	0.242754i	0.927555	+	0.373688i	$0.121907\pi$
$972$	9.75228	−	12.1611i	0.312804	−	0.390068i
$973$		0			0
$974$	29.1136	−	16.8087i	0.932860	−	0.538587i
$975$	47.6883	−	3.54772i	1.52725	−	0.113618i
$976$			14.7121i			0.470922i
$977$		−	14.9023i		−	0.476766i	−0.971171	−	0.238383i	$-0.923383\pi$
$977$		−	14.9023i		−	0.476766i	0.971171	−	0.238383i	$-0.0766174\pi$
$978$	−2.80167	−	4.11408i	−0.0895874	−	0.131554i
$979$	−8.30615	+	4.79556i	−0.265466	+	0.153267i
$980$		0			0
$981$	−9.93033	+	25.2216i	−0.317051	+	0.805262i
$982$	11.3676	−	19.6893i	0.362756	−	0.628312i
$983$	1.53458	−	2.65798i	0.0489456	−	0.0847763i	−0.840515	−	0.541789i	$-0.817747\pi$
$983$	1.53458	−	2.65798i	0.0489456	−	0.0847763i	0.889460	+	0.457013i	$0.151081\pi$
$984$	−5.55793	−	8.16149i	−0.177180	−	0.260179i
$985$	13.9247	−	8.03941i	0.443677	−	0.256157i
$986$	−17.9859	+	31.1525i	−0.572787	+	0.992096i
$987$		0			0
$988$	−1.72667	−	2.99067i	−0.0549325	−	0.0951460i
$989$	12.5845	+	7.26565i	0.400163	+	0.231034i
$990$	13.5469	+	17.0251i	0.430547	+	0.541093i
$991$	27.9075	+	48.3372i	0.886510	+	1.53548i	0.843973	+	0.536386i	$0.180211\pi$
$991$	27.9075	+	48.3372i	0.886510	+	1.53548i	0.0425375	+	0.999095i	$0.486456\pi$
$992$	−0.909687			−0.0288826
$993$	−29.2904	−	14.1251i	−0.929502	−	0.448246i
$994$		0			0
$995$	−36.0798	−	20.8307i	−1.14381	−	0.660377i
$996$	−1.02923	−	13.8348i	−0.0326124	−	0.438374i
$997$	−5.30607	−	3.06346i	−0.168045	−	0.0970208i	0.413619	−	0.910450i	$-0.364265\pi$
$997$	−5.30607	−	3.06346i	−0.168045	−	0.0970208i	−0.581664	+	0.813429i	$0.697598\pi$
$998$	16.9079	−	9.76175i	0.535209	−	0.309003i
$999$	36.4096	+	11.2958i	1.15195	+	0.357384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.b.509.8		16
3.2	odd	2		2646.2.l.a.1097.1		16
7.2	even	3		882.2.m.a.293.6		16
7.3	odd	6		882.2.t.a.815.3		16
7.4	even	3		126.2.t.a.59.2	yes	16
7.5	odd	6		882.2.m.b.293.7		16
7.6	odd	2		126.2.l.a.5.5	✓	16
9.2	odd	6		882.2.t.a.803.3		16
9.7	even	3		2646.2.t.b.1979.5		16
21.2	odd	6		2646.2.m.a.881.1		16
21.5	even	6		2646.2.m.b.881.4		16
21.11	odd	6		378.2.t.a.17.8		16
21.17	even	6		2646.2.t.b.2285.5		16
21.20	even	2		378.2.l.a.341.4		16
28.11	odd	6		1008.2.df.c.689.5		16
28.27	even	2		1008.2.ca.c.257.8		16
63.2	odd	6		882.2.m.b.587.7		16
63.4	even	3		1134.2.k.b.647.8		16
63.11	odd	6		126.2.l.a.101.1	yes	16
63.13	odd	6		1134.2.k.a.971.1		16
63.16	even	3		2646.2.m.b.1763.4		16
63.20	even	6		126.2.t.a.47.2	yes	16
63.25	even	3		378.2.l.a.143.8		16
63.32	odd	6		1134.2.k.a.647.1		16
63.34	odd	6		378.2.t.a.89.8		16
63.38	even	6	inner	882.2.l.b.227.4		16
63.41	even	6		1134.2.k.b.971.8		16
63.47	even	6		882.2.m.a.587.6		16
63.52	odd	6		2646.2.l.a.521.5		16
63.61	odd	6		2646.2.m.a.1763.1		16
84.11	even	6		3024.2.df.c.17.7		16
84.83	odd	2		3024.2.ca.c.2609.7		16
252.11	even	6		1008.2.ca.c.353.8		16
252.83	odd	6		1008.2.df.c.929.5		16
252.151	odd	6		3024.2.ca.c.2033.7		16
252.223	even	6		3024.2.df.c.1601.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	7.6	odd	2
126.2.l.a.101.1	yes	16	63.11	odd	6
126.2.t.a.47.2	yes	16	63.20	even	6
126.2.t.a.59.2	yes	16	7.4	even	3
378.2.l.a.143.8		16	63.25	even	3
378.2.l.a.341.4		16	21.20	even	2
378.2.t.a.17.8		16	21.11	odd	6
378.2.t.a.89.8		16	63.34	odd	6
882.2.l.b.227.4		16	63.38	even	6	inner
882.2.l.b.509.8		16	1.1	even	1	trivial
882.2.m.a.293.6		16	7.2	even	3
882.2.m.a.587.6		16	63.47	even	6
882.2.m.b.293.7		16	7.5	odd	6
882.2.m.b.587.7		16	63.2	odd	6
882.2.t.a.803.3		16	9.2	odd	6
882.2.t.a.815.3		16	7.3	odd	6
1008.2.ca.c.257.8		16	28.27	even	2
1008.2.ca.c.353.8		16	252.11	even	6
1008.2.df.c.689.5		16	28.11	odd	6
1008.2.df.c.929.5		16	252.83	odd	6
1134.2.k.a.647.1		16	63.32	odd	6
1134.2.k.a.971.1		16	63.13	odd	6
1134.2.k.b.647.8		16	63.4	even	3
1134.2.k.b.971.8		16	63.41	even	6
2646.2.l.a.521.5		16	63.52	odd	6
2646.2.l.a.1097.1		16	3.2	odd	2
2646.2.m.a.881.1		16	21.2	odd	6
2646.2.m.a.1763.1		16	63.61	odd	6
2646.2.m.b.881.4		16	21.5	even	6
2646.2.m.b.1763.4		16	63.16	even	3
2646.2.t.b.1979.5		16	9.7	even	3
2646.2.t.b.2285.5		16	21.17	even	6
3024.2.ca.c.2033.7		16	252.151	odd	6
3024.2.ca.c.2609.7		16	84.83	odd	2
3024.2.df.c.17.7		16	84.11	even	6
3024.2.df.c.1601.7		16	252.223	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.56012 + 0.752355i) q^{3} -1.00000 q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 + 1.56012i) q^{6} -1.00000i q^{8} +(1.86792 + 2.34752i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.56012 + 0.752355i) q^{3} -1.00000 q^{4} +(1.80966 + 3.13442i) q^{5} +(-0.752355 + 1.56012i) q^{6} -1.00000i q^{8} +(1.86792 + 2.34752i) q^{9} +(-3.13442 + 1.80966i) q^{10} +(-1.73534 - 1.00190i) q^{11} +(-1.56012 - 0.752355i) q^{12} +(-2.95206 - 1.70437i) q^{13} +(0.465079 + 6.25156i) q^{15} +1.00000 q^{16} +(3.08709 + 5.34700i) q^{17} +(-2.34752 + 1.86792i) q^{18} +(-0.877353 - 0.506540i) q^{19} +(-1.80966 - 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} +(-2.62232 + 1.51400i) q^{23} +(0.752355 - 1.56012i) q^{24} +(-4.04972 + 7.01433i) q^{25} +(1.70437 - 2.95206i) q^{26} +(1.14800 + 5.06775i) q^{27} +(5.04560 - 2.91308i) q^{29} +(-6.25156 + 0.465079i) q^{30} +0.909687i q^{31} +1.00000i q^{32} +(-1.95354 - 2.86867i) q^{33} +(-5.34700 + 3.08709i) q^{34} +(-1.86792 - 2.34752i) q^{36} +(3.66825 - 6.35359i) q^{37} +(0.506540 - 0.877353i) q^{38} +(-3.32326 - 4.88001i) q^{39} +(3.13442 - 1.80966i) q^{40} +(2.85045 - 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +(1.73534 + 1.00190i) q^{44} +(-3.97782 + 10.1031i) q^{45} +(-1.51400 - 2.62232i) q^{46} +2.23022 q^{47} +(1.56012 + 0.752355i) q^{48} +(-7.01433 - 4.04972i) q^{50} +(0.793376 + 10.6645i) q^{51} +(2.95206 + 1.70437i) q^{52} +(7.58088 - 4.37683i) q^{53} +(-5.06775 + 1.14800i) q^{54} -7.25237i q^{55} +(-0.987674 - 1.45034i) q^{57} +(2.91308 + 5.04560i) q^{58} -8.98627 q^{59} +(-0.465079 - 6.25156i) q^{60} +14.7121i q^{61} -0.909687 q^{62} -1.00000 q^{64} -12.3373i q^{65} +(2.86867 - 1.95354i) q^{66} -8.31641 q^{67} +(-3.08709 - 5.34700i) q^{68} +(-5.23019 + 0.389094i) q^{69} +0.466287i q^{71} +(2.34752 - 1.86792i) q^{72} +(3.65022 - 2.10746i) q^{73} +(6.35359 + 3.66825i) q^{74} +(-11.5953 + 7.89633i) q^{75} +(0.877353 + 0.506540i) q^{76} +(4.88001 - 3.32326i) q^{78} +3.82533 q^{79} +(1.80966 + 3.13442i) q^{80} +(-2.02173 + 8.76998i) q^{81} +(4.93712 + 2.85045i) q^{82} +(4.00481 + 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(4.15605 - 2.39949i) q^{86} +(10.0634 - 0.748656i) q^{87} +(-1.00190 + 1.73534i) q^{88} +(2.39324 - 4.14521i) q^{89} +(-10.1031 - 3.97782i) q^{90} +(2.62232 - 1.51400i) q^{92} +(-0.684408 + 1.41922i) q^{93} +2.23022i q^{94} -3.66666i q^{95} +(-0.752355 + 1.56012i) q^{96} +(10.1835 - 5.87944i) q^{97} +(-0.889499 - 5.94521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 12 q^{11} - 6 q^{13} - 18 q^{15} + 16 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 36 q^{27} + 6 q^{29} - 2 q^{37} - 12 q^{39} + 6 q^{41} - 2 q^{43} - 12 q^{44} + 30 q^{45} + 6 q^{46} + 36 q^{47} - 12 q^{50} + 6 q^{51} + 6 q^{52} - 36 q^{53} - 18 q^{54} + 6 q^{57} + 6 q^{58} - 60 q^{59} + 18 q^{60} - 36 q^{62} - 16 q^{64} - 24 q^{66} - 28 q^{67} - 18 q^{68} + 42 q^{69} + 12 q^{72} + 18 q^{74} - 60 q^{75} + 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{86} + 24 q^{87} + 24 q^{89} - 18 q^{90} + 6 q^{92} - 42 q^{93} - 6 q^{97} + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 12 * q^11 - 6 * q^13 - 18 * q^15 + 16 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 36 * q^27 + 6 * q^29 - 2 * q^37 - 12 * q^39 + 6 * q^41 - 2 * q^43 - 12 * q^44 + 30 * q^45 + 6 * q^46 + 36 * q^47 - 12 * q^50 + 6 * q^51 + 6 * q^52 - 36 * q^53 - 18 * q^54 + 6 * q^57 + 6 * q^58 - 60 * q^59 + 18 * q^60 - 36 * q^62 - 16 * q^64 - 24 * q^66 - 28 * q^67 - 18 * q^68 + 42 * q^69 + 12 * q^72 + 18 * q^74 - 60 * q^75 + 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^86 + 24 * q^87 + 24 * q^89 - 18 * q^90 + 6 * q^92 - 42 * q^93 - 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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