LMFDB - Embedded newform 875.2.bb.a.82.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			82.11
Character	$\chi$	$=$	875.82
Dual form			875.2.bb.a.843.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766047 + 0.294058i) q^{2} +(-0.140222 + 0.00734873i) q^{3} +(-0.985932 - 0.887737i) q^{4} +(-0.109578 - 0.0356039i) q^{6} +(1.23154 - 2.34165i) q^{7} +(-1.23927 - 2.43220i) q^{8} +(-2.96396 + 0.311524i) q^{9} +(-0.0483934 + 0.460432i) q^{11} +(0.144773 + 0.117235i) q^{12} +(-2.81849 - 0.446405i) q^{13} +(1.63200 - 1.43167i) q^{14} +(0.0432270 + 0.411277i) q^{16} +(-3.63317 + 5.59459i) q^{17} +(-2.36214 - 0.632933i) q^{18} +(-0.835637 - 0.928069i) q^{19} +(-0.155481 + 0.337401i) q^{21} +(-0.172465 + 0.338482i) q^{22} +(-1.88101 + 4.90021i) q^{23} +(0.191646 + 0.331940i) q^{24} +(-2.02783 - 1.17077i) q^{26} +(0.829380 - 0.131361i) q^{27} +(-3.29298 + 1.21542i) q^{28} +(-2.85581 + 0.927907i) q^{29} +(-2.24299 - 10.5524i) q^{31} +(-1.50083 + 5.60118i) q^{32} +(0.00340223 - 0.0649184i) q^{33} +(-4.42831 + 3.21736i) q^{34} +(3.19881 + 2.32407i) q^{36} +(-3.55947 + 4.39558i) q^{37} +(-0.367231 - 0.956670i) q^{38} +(0.398495 + 0.0418835i) q^{39} +(-1.91768 - 2.63945i) q^{41} +(-0.218321 + 0.212744i) q^{42} +(6.03422 - 6.03422i) q^{43} +(0.456455 - 0.410994i) q^{44} +(-2.88189 + 3.20066i) q^{46} +(1.38828 - 0.901557i) q^{47} +(-0.00908374 - 0.0573524i) q^{48} +(-3.96662 - 5.76766i) q^{49} +(0.468337 - 0.811184i) q^{51} +(2.38255 + 2.94221i) q^{52} +(-0.375223 - 7.15968i) q^{53} +(0.673972 + 0.143257i) q^{54} +(-7.22155 - 0.0934236i) q^{56} +(0.123995 + 0.123995i) q^{57} +(-2.46054 - 0.128951i) q^{58} +(-2.23160 - 0.993572i) q^{59} +(0.307313 + 0.690235i) q^{61} +(1.38479 - 8.74324i) q^{62} +(-2.92075 + 7.32420i) q^{63} +(-2.31063 + 3.18031i) q^{64} +(0.0216960 - 0.0487301i) q^{66} +(1.99402 + 1.29493i) q^{67} +(8.54858 - 2.29059i) q^{68} +(0.227749 - 0.700940i) q^{69} +(-2.47456 - 7.61592i) q^{71} +(4.43082 + 6.82286i) q^{72} +(-4.93803 + 3.99874i) q^{73} +(-4.01928 + 2.32053i) q^{74} +1.65684i q^{76} +(1.01857 + 0.680361i) q^{77} +(0.292950 + 0.149265i) q^{78} +(2.07461 - 9.76028i) q^{79} +(8.63014 - 1.83439i) q^{81} +(-0.692877 - 2.58585i) q^{82} +(-8.96119 + 4.56596i) q^{83} +(0.452817 - 0.194628i) q^{84} +(6.39691 - 2.84809i) q^{86} +(0.393628 - 0.151100i) q^{87} +(1.17983 - 0.452896i) q^{88} +(8.48635 - 3.77837i) q^{89} +(-4.51641 + 6.05015i) q^{91} +(6.20465 - 3.16143i) q^{92} +(0.392064 + 1.46320i) q^{93} +(1.32859 - 0.282401i) q^{94} +(0.169288 - 0.796437i) q^{96} +(-7.70801 - 3.92743i) q^{97} +(-1.34259 - 5.58472i) q^{98} -1.37978i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.766047	+	0.294058i	0.541677	+	0.207930i	0.613795	−	0.789466i	$-0.289642\pi$
$2$	0.766047	+	0.294058i	0.541677	+	0.207930i	−0.0721175	+	0.997396i	$0.522976\pi$
$3$	−0.140222	+	0.00734873i	−0.0809572	+	0.00424279i	−0.0927716	−	0.995687i	$-0.529573\pi$
$3$	−0.140222	+	0.00734873i	−0.0809572	+	0.00424279i	0.0118143	+	0.999930i	$0.496239\pi$
$4$	−0.985932	−	0.887737i	−0.492966	−	0.443868i
$5$		0			0
$5$		0			0
$6$	−0.109578	−	0.0356039i	−0.0447349	−	0.0145352i
$7$	1.23154	−	2.34165i	0.465478	−	0.885059i
$7$	1.23154	−	2.34165i	0.465478	−	0.885059i
$8$	−1.23927	−	2.43220i	−0.438146	−	0.859911i
$9$	−2.96396	+	0.311524i	−0.987986	+	0.103841i
$10$		0			0
$11$	−0.0483934	+	0.460432i	−0.0145912	+	0.138826i	−0.999392	−	0.0348608i	$-0.988901\pi$
$11$	−0.0483934	+	0.460432i	−0.0145912	+	0.138826i	0.984801	+	0.173686i	$0.0555679\pi$
$12$	0.144773	+	0.117235i	0.0417924	+	0.0338428i
$13$	−2.81849	−	0.446405i	−0.781709	−	0.123811i	−0.247190	−	0.968967i	$-0.579507\pi$
$13$	−2.81849	−	0.446405i	−0.781709	−	0.123811i	−0.534519	+	0.845156i	$0.679507\pi$
$14$	1.63200	−	1.43167i	0.436170	−	0.382629i
$15$		0			0
$16$	0.0432270	+	0.411277i	0.0108067	+	0.102819i
$17$	−3.63317	+	5.59459i	−0.881173	+	1.35689i	0.0524474	+	0.998624i	$0.483298\pi$
$17$	−3.63317	+	5.59459i	−0.881173	+	1.35689i	−0.933620	+	0.358264i	$0.883369\pi$
$18$	−2.36214	−	0.632933i	−0.556761	−	0.149184i
$19$	−0.835637	−	0.928069i	−0.191708	−	0.212914i	0.639626	−	0.768686i	$-0.279089\pi$
$19$	−0.835637	−	0.928069i	−0.191708	−	0.212914i	−0.831334	+	0.555773i	$0.812423\pi$
$20$		0			0
$21$	−0.155481	+	0.337401i	−0.0339287	+	0.0736269i
$22$	−0.172465	+	0.338482i	−0.0367697	+	0.0721647i
$23$	−1.88101	+	4.90021i	−0.392218	+	1.02176i	0.585282	+	0.810830i	$0.300984\pi$
$23$	−1.88101	+	4.90021i	−0.392218	+	1.02176i	−0.977500	+	0.210934i	$0.932349\pi$
$24$	0.191646	+	0.331940i	0.0391195	+	0.0677570i
$25$		0			0
$26$	−2.02783	−	1.17077i	−0.397690	−	0.229606i
$27$	0.829380	−	0.131361i	0.159614	−	0.0252804i
$28$	−3.29298	+	1.21542i	−0.622315	+	0.229693i
$29$	−2.85581	+	0.927907i	−0.530310	+	0.172308i	−0.561919	−	0.827192i	$-0.689937\pi$
$29$	−2.85581	+	0.927907i	−0.530310	+	0.172308i	0.0316093	+	0.999500i	$0.489937\pi$
$30$		0			0
$31$	−2.24299	−	10.5524i	−0.402853	−	1.89527i	−0.443824	−	0.896114i	$-0.646378\pi$
$31$	−2.24299	−	10.5524i	−0.402853	−	1.89527i	0.0409705	−	0.999160i	$-0.486955\pi$
$32$	−1.50083	+	5.60118i	−0.265312	+	0.990157i
$33$	0.00340223	−	0.0649184i	0.000592252	−	0.0113008i
$34$	−4.42831	+	3.21736i	−0.759449	+	0.551772i
$35$		0			0
$36$	3.19881	+	2.32407i	0.533135	+	0.387345i
$37$	−3.55947	+	4.39558i	−0.585173	+	0.722629i	−0.980633	−	0.195854i	$-0.937252\pi$
$37$	−3.55947	+	4.39558i	−0.585173	+	0.722629i	0.395460	+	0.918483i	$0.370585\pi$
$38$	−0.367231	−	0.956670i	−0.0595728	−	0.155192i
$39$	0.398495	+	0.0418835i	0.0638103	+	0.00670673i
$40$		0			0
$41$	−1.91768	−	2.63945i	−0.299491	−	0.412213i	0.632577	−	0.774497i	$-0.281997\pi$
$41$	−1.91768	−	2.63945i	−0.299491	−	0.412213i	−0.932068	+	0.362284i	$0.881997\pi$
$42$	−0.218321	+	0.212744i	−0.0336877	+	0.0328272i
$43$	6.03422	−	6.03422i	0.920211	−	0.920211i	−0.0768333	−	0.997044i	$-0.524481\pi$
$43$	6.03422	−	6.03422i	0.920211	−	0.920211i	0.997044	+	0.0768333i	$0.0244809\pi$
$44$	0.456455	−	0.410994i	0.0688132	−	0.0619597i
$45$		0			0
$46$	−2.88189	+	3.20066i	−0.424911	+	0.471912i
$47$	1.38828	−	0.901557i	0.202501	−	0.131506i	−0.439405	−	0.898289i	$-0.644811\pi$
$47$	1.38828	−	0.901557i	0.202501	−	0.131506i	0.641906	+	0.766784i	$0.278144\pi$
$48$	−0.00908374	−	0.0573524i	−0.00131112	−	0.00827811i
$49$	−3.96662	−	5.76766i	−0.566660	−	0.823952i
$50$		0			0
$51$	0.468337	−	0.811184i	0.0655803	−	0.113588i
$52$	2.38255	+	2.94221i	0.330400	+	0.408011i
$53$	−0.375223	−	7.15968i	−0.0515409	−	0.983458i	−0.894944	−	0.446178i	$-0.852785\pi$
$53$	−0.375223	−	7.15968i	−0.0515409	−	0.983458i	0.843404	−	0.537281i	$-0.180548\pi$
$54$	0.673972	+	0.143257i	0.0917159	+	0.0194948i
$55$		0			0
$56$	−7.22155	−	0.0934236i	−0.965020	−	0.0124842i
$57$	0.123995	+	0.123995i	0.0164235	+	0.0164235i
$58$	−2.46054	−	0.128951i	−0.323085	−	0.0169321i
$59$	−2.23160	−	0.993572i	−0.290529	−	0.129352i	0.256297	−	0.966598i	$-0.417498\pi$
$59$	−2.23160	−	0.993572i	−0.290529	−	0.129352i	−0.546826	+	0.837246i	$0.684164\pi$
$60$		0			0
$61$	0.307313	+	0.690235i	0.0393473	+	0.0883756i	0.932150	−	0.362073i	$-0.117931\pi$
$61$	0.307313	+	0.690235i	0.0393473	+	0.0883756i	−0.892802	+	0.450448i	$0.851264\pi$
$62$	1.38479	−	8.74324i	0.175869	−	1.11039i
$63$	−2.92075	+	7.32420i	−0.367980	+	0.922762i
$64$	−2.31063	+	3.18031i	−0.288829	+	0.397538i
$65$		0			0
$66$	0.0216960	−	0.0487301i	0.00267060	−	0.00599826i
$67$	1.99402	+	1.29493i	0.243608	+	0.158201i	0.660668	−	0.750678i	$-0.270273\pi$
$67$	1.99402	+	1.29493i	0.243608	+	0.158201i	−0.417060	+	0.908879i	$0.636940\pi$
$68$	8.54858	−	2.29059i	1.03667	−	0.277774i
$69$	0.227749	−	0.700940i	0.0274178	−	0.0843833i
$70$		0			0
$71$	−2.47456	−	7.61592i	−0.293676	−	0.903843i	−0.983663	−	0.180021i	$-0.942383\pi$
$71$	−2.47456	−	7.61592i	−0.293676	−	0.903843i	0.689986	−	0.723822i	$-0.257617\pi$
$72$	4.43082	+	6.82286i	0.522177	+	0.804082i
$73$	−4.93803	+	3.99874i	−0.577953	+	0.468017i	−0.873172	−	0.487413i	$-0.837941\pi$
$73$	−4.93803	+	3.99874i	−0.577953	+	0.468017i	0.295219	+	0.955430i	$0.404607\pi$
$74$	−4.01928	+	2.32053i	−0.467231	+	0.269756i
$75$		0			0
$76$			1.65684i			0.190052i
$77$	1.01857	+	0.680361i	0.116077	+	0.0775343i
$78$	0.292950	+	0.149265i	0.0331700	+	0.0169010i
$79$	2.07461	−	9.76028i	0.233412	−	1.09812i	−0.692805	−	0.721125i	$-0.743625\pi$
$79$	2.07461	−	9.76028i	0.233412	−	1.09812i	0.926217	−	0.376992i	$-0.123041\pi$
$80$		0			0
$81$	8.63014	−	1.83439i	0.958904	−	0.203821i
$82$	−0.692877	−	2.58585i	−0.0765155	−	0.285560i
$83$	−8.96119	+	4.56596i	−0.983619	+	0.501179i	−0.870375	−	0.492389i	$-0.836124\pi$
$83$	−8.96119	+	4.56596i	−0.983619	+	0.501179i	−0.113243	+	0.993567i	$0.536124\pi$
$84$	0.452817	−	0.194628i	0.0494063	−	0.0212357i
$85$		0			0
$86$	6.39691	−	2.84809i	0.689797	−	0.307117i
$87$	0.393628	−	0.151100i	0.0422013	−	0.0161996i
$88$	1.17983	−	0.452896i	0.125771	−	0.0482788i
$89$	8.48635	−	3.77837i	0.899551	−	0.400506i	0.0957511	−	0.995405i	$-0.469475\pi$
$89$	8.48635	−	3.77837i	0.899551	−	0.400506i	0.803800	+	0.594899i	$0.202808\pi$
$90$		0			0
$91$	−4.51641	+	6.05015i	−0.473448	+	0.634228i
$92$	6.20465	−	3.16143i	0.646879	−	0.329601i
$93$	0.392064	+	1.46320i	0.0406551	+	0.151727i
$94$	1.32859	−	0.282401i	0.137034	−	0.0291275i
$95$		0			0
$96$	0.169288	−	0.796437i	0.0172779	−	0.0812861i
$97$	−7.70801	−	3.92743i	−0.782630	−	0.398770i	0.0165492	−	0.999863i	$-0.494732\pi$
$97$	−7.70801	−	3.92743i	−0.782630	−	0.398770i	−0.799179	+	0.601093i	$0.794732\pi$
$98$	−1.34259	−	5.58472i	−0.135622	−	0.564141i
$99$		−	1.37978i		−	0.138673i
$100$		0			0
$101$	−15.3672	+	8.87223i	−1.52909	+	0.882820i	−0.529688	+	0.848192i	$0.677691\pi$
$101$	−15.3672	+	8.87223i	−1.52909	+	0.882820i	−0.999400	+	0.0346276i	$0.988975\pi$
$102$	0.597303	−	0.483687i	0.0591418	−	0.0478921i
$103$	6.05199	+	9.31925i	0.596320	+	0.918253i	0.999994	+	0.00334975i	$0.00106626\pi$
$103$	6.05199	+	9.31925i	0.596320	+	0.918253i	−0.403674	+	0.914903i	$0.632267\pi$
$104$	2.40712	+	7.40834i	0.236037	+	0.726448i
$105$		0			0
$106$	1.81792	−	5.59499i	0.176572	−	0.543434i
$107$	−2.32486	+	0.622945i	−0.224753	+	0.0602223i	−0.369438	−	0.929255i	$-0.620450\pi$
$107$	−2.32486	+	0.622945i	−0.224753	+	0.0602223i	0.144685	+	0.989478i	$0.453783\pi$
$108$	−0.934326	−	0.606758i	−0.0899056	−	0.0583854i
$109$	7.52976	−	16.9121i	0.721221	−	1.61989i	−0.0619487	−	0.998079i	$-0.519732\pi$
$109$	7.52976	−	16.9121i	0.721221	−	1.61989i	0.783169	−	0.621809i	$-0.213602\pi$
$110$		0			0
$111$	0.466814	−	0.642515i	0.0443081	−	0.0609848i
$112$	1.01630	+	0.405282i	0.0960315	+	0.0382955i
$113$	−1.54166	+	9.73363i	−0.145027	+	0.915663i	0.802654	+	0.596444i	$0.203420\pi$
$113$	−1.54166	+	9.73363i	−0.145027	+	0.915663i	−0.947681	+	0.319219i	$0.896580\pi$
$114$	0.0585242	+	0.131448i	0.00548130	+	0.0123112i
$115$		0			0
$116$	3.63937	+	1.62035i	0.337907	+	0.150446i
$117$	8.49296	+	0.445097i	0.785174	+	0.0411492i
$118$	−1.41734	−	1.41734i	−0.130477	−	0.130477i
$119$	8.62616	+	15.3976i	0.790759	+	1.41149i
$120$		0			0
$121$	10.5500	+	2.24246i	0.959088	+	0.203860i
$122$	0.0324467	+	0.619120i	0.00293759	+	0.0560525i
$123$	0.288297	+	0.356017i	0.0259949	+	0.0321010i
$124$	−7.15636	+	12.3952i	−0.642660	+	1.11312i
$125$		0			0
$126$	−4.39117	+	4.75181i	−0.391197	+	0.423325i
$127$	−1.02863	−	6.49451i	−0.0912761	−	0.576294i	−0.990360	−	0.138518i	$-0.955766\pi$
$127$	−1.02863	−	6.49451i	−0.0912761	−	0.576294i	0.899084	−	0.437776i	$-0.144234\pi$
$128$	7.02126	−	4.55966i	0.620598	−	0.403021i
$129$	−0.801787	+	0.890475i	−0.0705934	+	0.0784020i
$130$		0			0
$131$	8.20597	−	7.38869i	0.716959	−	0.645553i	−0.227653	−	0.973742i	$-0.573105\pi$
$131$	8.20597	−	7.38869i	0.716959	−	0.645553i	0.944612	+	0.328189i	$0.106438\pi$
$132$	−0.0609848	+	0.0609848i	−0.00530805	+	0.00530805i
$133$	−3.20233	+	0.813813i	−0.277677	+	0.0705666i
$134$	1.14673	+	1.57833i	0.0990621	+	0.136347i
$135$		0			0
$136$	18.1096	+	1.90340i	1.55289	+	0.163215i
$137$	0.492457	+	1.28289i	0.0420734	+	0.109605i	0.953007	−	0.302947i	$-0.0979707\pi$
$137$	0.492457	+	1.28289i	0.0420734	+	0.109605i	−0.910934	+	0.412552i	$0.864637\pi$
$138$	0.380584	−	0.469982i	0.0323974	−	0.0400075i
$139$	2.70776	+	1.96730i	0.229669	+	0.166865i	0.696668	−	0.717393i	$-0.254665\pi$
$139$	2.70776	+	1.96730i	0.229669	+	0.166865i	−0.466999	+	0.884258i	$0.654665\pi$
$140$		0			0
$141$	−0.188041	+	0.136620i	−0.0158360	+	0.0115055i
$142$	0.343890	−	6.56182i	0.0288586	−	0.550655i
$143$	0.341936	−	1.27612i	0.0285941	−	0.106715i
$144$	−0.256246	−	1.20554i	−0.0213538	−	0.100462i
$145$		0			0
$146$	−4.95862	+	1.61115i	−0.410378	+	0.133340i
$147$	0.598592	+	0.779604i	0.0493711	+	0.0643006i
$148$	7.41151	−	1.17387i	0.609223	−	0.0964914i
$149$	16.1916	+	9.34825i	1.32647	+	0.765838i	0.984752	−	0.173964i	$-0.0556577\pi$
$149$	16.1916	+	9.34825i	1.32647	+	0.765838i	0.341719	+	0.939802i	$0.388991\pi$
$150$		0			0
$151$	−5.55298	−	9.61804i	−0.451895	−	0.782705i	0.546609	−	0.837388i	$-0.315919\pi$
$151$	−5.55298	−	9.61804i	−0.451895	−	0.782705i	−0.998504	+	0.0546830i	$0.982585\pi$
$152$	−1.22167	+	3.18256i	−0.0990905	+	0.258139i
$153$	9.02571	−	17.7139i	0.729685	−	1.43209i
$154$	0.580208	+	0.820707i	0.0467545	+	0.0661345i
$155$		0			0
$156$	−0.355708	−	0.395053i	−0.0284794	−	0.0316296i
$157$	−0.753908	−	0.202009i	−0.0601684	−	0.0161221i	0.228609	−	0.973518i	$-0.426582\pi$
$157$	−0.753908	−	0.202009i	−0.0601684	−	0.0161221i	−0.288778	+	0.957396i	$0.593249\pi$
$158$	4.45934	−	6.86678i	0.354766	−	0.546291i
$159$	0.105229	+	1.00119i	0.00834521	+	0.0793994i
$160$		0			0
$161$	9.15801	+	10.4395i	0.721752	+	0.822745i
$162$	7.15051	+	1.13253i	0.561797	+	0.0889799i
$163$	16.8235	+	13.6234i	1.31772	+	1.06707i	0.992604	+	0.121396i	$0.0387370\pi$
$163$	16.8235	+	13.6234i	1.31772	+	1.06707i	0.325117	+	0.945674i	$0.394596\pi$
$164$	−0.452443	+	4.30471i	−0.0353299	+	0.336142i
$165$		0			0
$166$	−8.20735	+	0.862627i	−0.637014	+	0.0669528i
$167$	−4.06888	−	7.98564i	−0.314860	−	0.617947i	0.678290	−	0.734794i	$-0.262721\pi$
$167$	−4.06888	−	7.98564i	−0.314860	−	0.617947i	−0.993150	+	0.116847i	$0.962721\pi$
$168$	1.01331	−	0.0399691i	0.0781783	−	0.00308368i
$169$	−4.61911	−	1.50084i	−0.355316	−	0.115449i
$170$		0			0
$171$	2.76591	+	2.49044i	0.211514	+	0.190448i
$172$	−11.3061	+	0.592530i	−0.862085	+	0.0451800i
$173$	−13.5676	−	5.20812i	−1.03153	−	0.395966i	−0.217049	−	0.976161i	$-0.569643\pi$
$173$	−13.5676	−	5.20812i	−1.03153	−	0.395966i	−0.814478	+	0.580195i	$0.802976\pi$
$174$	0.345969			0.0262279
$175$		0			0
$176$	−0.191457			−0.0144316
$177$	0.320221	+	0.122921i	0.0240693	+	0.00923932i
$178$	7.61200	−	0.398928i	0.570544	−	0.0299009i
$179$	−7.18553	−	6.46988i	−0.537072	−	0.483582i	0.355382	−	0.934721i	$-0.384351\pi$
$179$	−7.18553	−	6.46988i	−0.537072	−	0.483582i	−0.892453	+	0.451140i	$0.851018\pi$
$180$		0			0
$181$	−19.1189	−	6.21211i	−1.42110	−	0.461742i	−0.505146	−	0.863034i	$-0.668561\pi$
$181$	−19.1189	−	6.21211i	−1.42110	−	0.461742i	−0.915950	+	0.401292i	$0.868561\pi$
$182$	−5.23888	+	3.30661i	−0.388331	+	0.245102i
$183$	−0.0481643	−	0.0945278i	−0.00356041	−	0.00698770i
$184$	14.2493	−	1.49767i	1.05047	−	0.110409i
$185$		0			0
$186$	−0.129927	+	1.23617i	−0.00952669	+	0.0906404i
$187$	−2.40011	−	1.94357i	−0.175513	−	0.142128i
$188$	−2.16909	−	0.343550i	−0.158197	−	0.0250560i
$189$	0.713814	−	2.10389i	0.0519223	−	0.153036i
$190$		0			0
$191$	2.59494	+	24.6892i	0.187763	+	1.78645i	0.531172	+	0.847264i	$0.321752\pi$
$191$	2.59494	+	24.6892i	0.187763	+	1.78645i	−0.343409	+	0.939186i	$0.611582\pi$
$192$	0.300630	−	0.462929i	0.0216961	−	0.0334090i
$193$	13.6684	+	3.66243i	0.983870	+	0.263627i	0.714674	−	0.699458i	$-0.246575\pi$
$193$	13.6684	+	3.66243i	0.983870	+	0.263627i	0.269196	+	0.963085i	$0.413242\pi$
$194$	−4.74981	−	5.27519i	−0.341016	−	0.378737i
$195$		0			0
$196$	−1.20935	+	9.20784i	−0.0863822	+	0.657703i
$197$	9.45216	−	18.5509i	0.673439	−	1.32170i	−0.260919	−	0.965361i	$-0.584025\pi$
$197$	9.45216	−	18.5509i	0.673439	−	1.32170i	0.934357	−	0.356337i	$-0.115975\pi$
$198$	0.405734	−	1.05697i	0.0288343	−	0.0751159i
$199$	−7.89655	−	13.6772i	−0.559772	−	0.969553i	−0.997515	−	0.0704529i	$-0.977556\pi$
$199$	−7.89655	−	13.6772i	−0.559772	−	0.969553i	0.437744	−	0.899100i	$-0.355778\pi$
$200$		0			0
$201$	−0.289121	−	0.166924i	−0.0203930	−	0.0117739i
$202$	−14.3809	+	2.27771i	−1.01184	+	0.160259i
$203$	−1.34421	+	7.83004i	−0.0943448	+	0.549561i
$204$	−1.18187	+	0.384012i	−0.0827472	+	0.0268862i
$205$		0			0
$206$	1.89571	+	8.91861i	0.132080	+	0.621389i
$207$	4.04871	−	15.1100i	0.281405	−	1.05022i
$208$	0.0617614	−	1.17848i	0.00428239	−	0.0817128i
$209$	0.467752	−	0.339842i	0.0323551	−	0.0235074i
$210$		0			0
$211$	3.76604	+	2.73619i	0.259265	+	0.188367i	0.709823	−	0.704380i	$-0.248775\pi$
$211$	3.76604	+	2.73619i	0.259265	+	0.188367i	−0.450558	+	0.892747i	$0.648775\pi$
$212$	−5.98597	+	7.39206i	−0.411118	+	0.507689i
$213$	0.402955	+	1.04973i	0.0276101	+	0.0719266i
$214$	−1.96413	−	0.206439i	−0.134265	−	0.0141119i
$215$		0			0
$216$	−1.34732	−	1.85442i	−0.0916733	−	0.126178i
$217$	−27.4724	−	7.74346i	−1.86495	−	0.525660i
$218$	10.7413	−	10.7413i	0.727492	−	0.727492i
$219$	0.663035	−	0.596999i	0.0448037	−	0.0403415i
$220$		0			0
$221$	12.7375	−	14.1464i	0.856818	−	0.951593i
$222$	0.546538	−	0.354926i	0.0366812	−	0.0238211i
$223$	−0.346137	−	2.18542i	−0.0231790	−	0.146347i	0.973385	−	0.229178i	$-0.0736038\pi$
$223$	−0.346137	−	2.18542i	−0.0231790	−	0.146347i	−0.996564	+	0.0828312i	$0.973604\pi$
$224$	11.2676	+	10.4125i	0.752851	+	0.695714i
$225$		0			0
$226$	−4.04323	+	7.00308i	−0.268952	+	0.465838i
$227$	−4.20139	−	5.18829i	−0.278856	−	0.344359i	0.618404	−	0.785860i	$-0.287779\pi$
$227$	−4.20139	−	5.18829i	−0.278856	−	0.344359i	−0.897261	+	0.441501i	$0.854446\pi$
$228$	−0.0121757	−	0.232325i	−0.000806353	−	0.0153861i
$229$	−11.0952	−	2.35835i	−0.733188	−	0.155844i	−0.173837	−	0.984774i	$-0.555616\pi$
$229$	−11.0952	−	2.35835i	−0.733188	−	0.155844i	−0.559352	+	0.828931i	$0.688950\pi$
$230$		0			0
$231$	−0.147826	−	0.0879164i	−0.00972623	−	0.00578447i
$232$	5.79595	+	5.79595i	0.380523	+	0.380523i
$233$	2.58663	+	0.135559i	0.169455	+	0.00888078i	0.136875	−	0.990588i	$-0.456294\pi$
$233$	2.58663	+	0.135559i	0.169455	+	0.00888078i	0.0325805	+	0.999469i	$0.489627\pi$
$234$	6.37512	+	2.83839i	0.416755	+	0.185551i
$235$		0			0
$236$	1.31817	+	2.96067i	0.0858058	+	0.192723i
$237$	−0.219181	+	1.38385i	−0.0142373	+	0.0898908i
$238$	2.08027	+	14.3318i	0.134844	+	0.928996i
$239$	−9.58977	+	13.1992i	−0.620311	+	0.853784i	−0.997375	−	0.0724026i	$-0.976933\pi$
$239$	−9.58977	+	13.1992i	−0.620311	+	0.853784i	0.377065	+	0.926187i	$0.376933\pi$
$240$		0			0
$241$	−3.22286	+	7.23866i	−0.207603	+	0.466283i	−0.987096	−	0.160127i	$-0.948810\pi$
$241$	−3.22286	+	7.23866i	−0.207603	+	0.466283i	0.779494	+	0.626410i	$0.215476\pi$
$242$	7.42236	+	4.82013i	0.477127	+	0.309850i
$243$	−3.62997	+	0.972648i	−0.232863	+	0.0623954i
$244$	0.309758	−	0.953338i	0.0198302	−	0.0610312i
$245$		0			0
$246$	0.116159	+	0.357502i	0.00740605	+	0.0227935i
$247$	1.94094	+	2.98879i	0.123499	+	0.190172i
$248$	−22.8859	+	18.5327i	−1.45326	+	1.17683i
$249$	1.22300	−	0.706101i	0.0775046	−	0.0447473i
$250$		0			0
$251$			13.1248i			0.828427i	0.910180	+	0.414214i	$0.135943\pi$
$251$			13.1248i			0.828427i	−0.910180	+	0.414214i	$0.864057\pi$
$252$	9.38162	−	4.62830i	0.590987	−	0.291555i
$253$	−2.16519	−	1.10322i	−0.136124	−	0.0693587i
$254$	1.12178	−	5.27757i	0.0703869	−	0.331144i
$255$		0			0
$256$	14.4098	−	3.06289i	0.900610	−	0.191431i
$257$	0.511448	+	1.90875i	0.0319033	+	0.119065i	0.980041	−	0.198795i	$-0.0637027\pi$
$257$	0.511448	+	1.90875i	0.0319033	+	0.119065i	−0.948138	+	0.317859i	$0.897036\pi$
$258$	−0.876058	+	0.446374i	−0.0545410	+	0.0277900i
$259$	5.90927	+	13.7484i	0.367184	+	0.854281i
$260$		0			0
$261$	8.17542	−	3.63993i	0.506046	−	0.225306i
$262$	8.45886	−	3.24705i	0.522590	−	0.200604i
$263$	−10.2674	+	3.94129i	−0.633116	+	0.243030i	−0.653695	−	0.756758i	$-0.726782\pi$
$263$	−10.2674	+	3.94129i	−0.633116	+	0.243030i	0.0205794	+	0.999788i	$0.493449\pi$
$264$	−0.162110	+	0.0721762i	−0.00997721	+	0.00444214i
$265$		0			0
$266$	−2.69244	−	0.318252i	−0.165084	−	0.0195133i
$267$	−1.16221	+	0.592174i	−0.0711259	+	0.0362405i
$268$	−0.816408	−	3.04688i	−0.0498700	−	0.186118i
$269$	5.51256	−	1.17173i	0.336107	−	0.0714417i	−0.0367668	−	0.999324i	$-0.511706\pi$
$269$	5.51256	−	1.17173i	0.336107	−	0.0714417i	0.372873	+	0.927882i	$0.378373\pi$
$270$		0			0
$271$	−5.70901	+	26.8588i	−0.346797	+	1.63155i	0.366306	+	0.930495i	$0.380622\pi$
$271$	−5.70901	+	26.8588i	−0.346797	+	1.63155i	−0.713103	+	0.701059i	$0.752711\pi$
$272$	−2.45798	−	1.25240i	−0.149037	−	0.0759380i
$273$	0.588839	−	0.881554i	0.0356382	−	0.0533541i
$274$			1.12757i			0.0681188i
$275$		0			0
$276$	−0.846796	+	0.488898i	−0.0509711	+	0.0294282i
$277$	−10.1358	+	8.20778i	−0.608999	+	0.493157i	−0.883501	−	0.468429i	$-0.844820\pi$
$277$	−10.1358	+	8.20778i	−0.608999	+	0.493157i	0.274502	+	0.961586i	$0.411487\pi$
$278$	1.49577	+	2.30329i	0.0897104	+	0.138142i
$279$	9.93547	+	30.5782i	0.594821	+	1.83067i
$280$		0			0
$281$	7.07687	−	21.7804i	0.422171	−	1.29931i	−0.483506	−	0.875341i	$-0.660637\pi$
$281$	7.07687	−	21.7804i	0.422171	−	1.29931i	0.905677	−	0.423968i	$-0.139363\pi$
$282$	−0.184223	+	0.0493624i	−0.0109703	+	0.00293949i
$283$	0.570558	+	0.370525i	0.0339162	+	0.0220254i	0.561486	−	0.827486i	$-0.310230\pi$
$283$	0.570558	+	0.370525i	0.0339162	+	0.0220254i	−0.527570	+	0.849512i	$0.676897\pi$
$284$	−4.32118	+	9.70554i	−0.256415	+	0.575918i
$285$		0			0
$286$	0.637193	−	0.877020i	0.0376780	−	0.0518593i
$287$	−8.54236	+	1.23993i	−0.504240	+	0.0731905i
$288$	2.70349	−	17.0692i	0.159305	−	1.00581i
$289$	−11.1850	−	25.1219i	−0.657941	−	1.47776i
$290$		0			0
$291$	1.10969	+	0.494068i	0.0650514	+	0.0289628i
$292$	8.41839	+	0.441189i	0.492649	+	0.0258186i
$293$	−17.9628	−	17.9628i	−1.04940	−	1.04940i	−0.998715	−	0.0506858i	$-0.983859\pi$
$293$	−17.9628	−	17.9628i	−1.04940	−	1.04940i	−0.0506858	−	0.998715i	$-0.516141\pi$
$294$	0.229301	+	0.773234i	0.0133731	+	0.0450959i
$295$		0			0
$296$	15.1020	+	3.21004i	0.877788	+	0.186580i
$297$	0.0203463	+	0.388230i	0.00118061	+	0.0225274i
$298$	9.65463	+	11.9225i	0.559278	+	0.690650i
$299$	7.48910	−	12.9715i	0.433106	−	0.750162i
$300$		0			0
$301$	−6.69863	−	21.5614i	−0.386103	−	1.24278i
$302$	−1.42558	−	9.00077i	−0.0820330	−	0.517936i
$303$	2.08961	−	1.35701i	0.120045	−	0.0779582i
$304$	0.345572	−	0.383796i	0.0198199	−	0.0220122i
$305$		0			0
$306$	12.1230	−	10.9156i	0.693028	−	0.624005i
$307$	10.5853	−	10.5853i	0.604135	−	0.604135i	−0.337272	−	0.941407i	$-0.609504\pi$
$307$	10.5853	−	10.5853i	0.604135	−	0.604135i	0.941407	+	0.337272i	$0.109504\pi$
$308$	−0.400260	−	1.57501i	−0.0228070	−	0.0897447i
$309$	−0.917107	−	1.26229i	−0.0521724	−	0.0718091i
$310$		0			0
$311$	0.410155	+	0.0431090i	0.0232577	+	0.00244449i	0.116150	−	0.993232i	$-0.462945\pi$
$311$	0.410155	+	0.0431090i	0.0232577	+	0.00244449i	−0.0928925	+	0.995676i	$0.529611\pi$
$312$	−0.391972	−	1.02112i	−0.0221911	−	0.0578097i
$313$	1.35166	−	1.66916i	0.0764003	−	0.0943465i	−0.737513	−	0.675333i	$-0.764000\pi$
$313$	1.35166	−	1.66916i	0.0764003	−	0.0943465i	0.813913	+	0.580987i	$0.197333\pi$
$314$	−0.518126	−	0.376441i	−0.0292396	−	0.0212438i
$315$		0			0
$316$	−10.7100	+	7.78126i	−0.602484	+	0.437730i
$317$	0.319105	−	6.08889i	0.0179227	−	0.341986i	−0.974920	−	0.222556i	$-0.928560\pi$
$317$	0.319105	−	6.08889i	0.0179227	−	0.341986i	0.992843	−	0.119430i	$-0.0381067\pi$
$318$	−0.213797	+	0.797901i	−0.0119891	+	0.0447440i
$319$	−0.289036	−	1.35981i	−0.0161829	−	0.0761347i
$320$		0			0
$321$	0.321419	−	0.104435i	0.0179399	−	0.00582901i
$322$	3.94566	+	10.6901i	0.219883	+	0.595737i
$323$	8.22818	−	1.30322i	0.457828	−	0.0725129i
$324$	−10.1372	−	5.85271i	−0.563177	−	0.325150i
$325$		0			0
$326$	8.88154	+	15.3833i	0.491903	+	0.852001i
$327$	−0.931556	+	2.42679i	−0.0515152	+	0.134202i
$328$	−4.04316	+	7.93514i	−0.223246	+	0.438145i
$329$	−0.401411	−	4.36115i	−0.0221305	−	0.240438i
$330$		0			0
$331$	−11.3685	−	12.6260i	−0.624869	−	0.693988i	0.344725	−	0.938704i	$-0.387972\pi$
$331$	−11.3685	−	12.6260i	−0.624869	−	0.693988i	−0.969595	+	0.244716i	$0.921305\pi$
$332$	12.8885	+	3.45346i	0.707348	+	0.189533i
$333$	9.18079	−	14.1372i	0.503104	−	0.774712i
$334$	−0.768718	−	7.31386i	−0.0420624	−	0.400197i
$335$		0			0
$336$	−0.145486	−	0.0493609i	−0.00793692	−	0.00269286i
$337$	19.0087	+	3.01068i	1.03547	+	0.164002i	0.650955	−	0.759116i	$-0.274369\pi$
$337$	19.0087	+	3.01068i	1.03547	+	0.164002i	0.384515	+	0.923119i	$0.374369\pi$
$338$	−3.09712	−	2.50800i	−0.168461	−	0.136417i
$339$	0.144644	−	1.37620i	0.00785600	−	0.0747449i
$340$		0			0
$341$	4.96723	−	0.522077i	0.268991	−	0.0282721i
$342$	1.38648	+	2.72113i	0.0749725	+	0.147142i
$343$	−18.3909	+	2.18531i	−0.993014	+	0.117996i
$344$	−22.1544	−	7.19841i	−1.19449	−	0.388112i
$345$		0			0
$346$	−8.86194	−	7.97933i	−0.476421	−	0.428971i
$347$	22.1420	−	1.16042i	1.18865	−	0.0622944i	0.552265	−	0.833668i	$-0.313764\pi$
$347$	22.1420	−	1.16042i	1.18865	−	0.0622944i	0.636382	+	0.771374i	$0.280430\pi$
$348$	−0.522227	−	0.200464i	−0.0279943	−	0.0107460i
$349$	17.0829			0.914426			0.457213	−	0.889357i	$-0.348848\pi$
$349$	17.0829			0.914426			0.457213	+	0.889357i	$0.348848\pi$
$350$		0			0
$351$	−2.39624			−0.127902
$352$	−2.50633	−	0.962091i	−0.133588	−	0.0512796i
$353$	17.7920	−	0.932442i	0.946975	−	0.0496289i	0.427408	−	0.904059i	$-0.359427\pi$
$353$	17.7920	−	0.932442i	0.946975	−	0.0496289i	0.519567	+	0.854430i	$0.326093\pi$
$354$	0.209158	+	0.188327i	0.0111166	+	0.0100095i
$355$		0			0
$356$	−11.7212	−	3.80844i	−0.621220	−	0.201847i
$357$	−1.32273	−	2.09569i	−0.0700063	−	0.110915i
$358$	−3.60193	−	7.06919i	−0.190368	−	0.373619i
$359$	−14.0809	+	1.47996i	−0.743159	+	0.0781092i	−0.468538	−	0.883443i	$-0.655219\pi$
$359$	−14.0809	+	1.47996i	−0.743159	+	0.0781092i	−0.274621	+	0.961553i	$0.588552\pi$
$360$		0			0
$361$	1.82302	−	17.3449i	0.0959483	−	0.912887i
$362$	−12.8193	−	10.3808i	−0.673765	−	0.545604i
$363$	−1.49582	−	0.236914i	−0.0785100	−	0.0124348i
$364$	9.82381	−	1.95565i	0.514908	−	0.102504i
$365$		0			0
$366$	−0.00909949	−	0.0865759i	−0.000475638	−	0.00452539i
$367$	−11.1432	+	17.1591i	−0.581672	+	0.895697i	−0.999920	−	0.0126360i	$-0.995978\pi$
$367$	−11.1432	+	17.1591i	−0.581672	+	0.895697i	0.418248	+	0.908333i	$0.362644\pi$
$368$	−2.09665	−	0.561797i	−0.109296	−	0.0292857i
$369$	6.50616	+	7.22582i	0.338697	+	0.376161i
$370$		0			0
$371$	−17.2276	−	7.93880i	−0.894410	−	0.412162i
$372$	0.912390	−	1.79067i	0.0473052	−	0.0928417i
$373$	−2.61067	+	6.80102i	−0.135175	+	0.352144i	−0.984414	−	0.175865i	$-0.943728\pi$
$373$	−2.61067	+	6.80102i	−0.135175	+	0.352144i	0.849239	+	0.528009i	$0.177061\pi$
$374$	−1.26707	−	2.19464i	−0.0655188	−	0.113482i
$375$		0			0
$376$	−3.91320	−	2.25929i	−0.201808	−	0.116514i
$377$	8.46329	−	1.34045i	0.435882	−	0.0690369i
$378$	1.16548	−	1.40178i	0.0599459	−	0.0720996i
$379$	−3.99729	+	1.29880i	−0.205327	+	0.0667147i	−0.409875	−	0.912142i	$-0.634428\pi$
$379$	−3.99729	+	1.29880i	−0.205327	+	0.0667147i	0.204548	+	0.978857i	$0.434428\pi$
$380$		0			0
$381$	0.191963	+	0.903114i	0.00983455	+	0.0462679i
$382$	−5.27221	+	19.6762i	−0.269750	+	1.00672i
$383$	1.16834	−	22.2933i	0.0596996	−	1.13914i	−0.790427	−	0.612557i	$-0.790141\pi$
$383$	1.16834	−	22.2933i	0.0596996	−	1.13914i	0.850126	−	0.526579i	$-0.176526\pi$
$384$	−0.951028	+	0.690962i	−0.0485319	+	0.0352605i
$385$		0			0
$386$	9.39364	+	6.82488i	0.478124	+	0.347377i
$387$	−16.0054	+	19.7650i	−0.813599	+	1.00471i
$388$	4.11305	+	10.7149i	0.208808	+	0.543965i
$389$	6.69321	+	0.703485i	0.339359	+	0.0356681i	0.272676	−	0.962106i	$-0.412091\pi$
$389$	6.69321	+	0.703485i	0.339359	+	0.0356681i	0.0666839	+	0.997774i	$0.478758\pi$
$390$		0			0
$391$	−20.5806	−	28.3268i	−1.04081	−	1.43255i
$392$	−9.11239	+	16.7953i	−0.460245	+	0.848289i
$393$	−1.09636	+	1.09636i	−0.0553041	+	0.0553041i
$394$	12.6958	−	11.4314i	0.639607	−	0.575905i
$395$		0			0
$396$	−1.22488	+	1.36037i	−0.0615525	+	0.0683610i
$397$	−13.7203	+	8.91007i	−0.688603	+	0.447184i	−0.840928	−	0.541147i	$-0.817990\pi$
$397$	−13.7203	+	8.91007i	−0.688603	+	0.447184i	0.152326	+	0.988330i	$0.451324\pi$
$398$	−2.02723	−	12.7994i	−0.101616	−	0.641578i
$399$	0.443057	−	0.137648i	0.0221806	−	0.00689100i
$400$		0			0
$401$	−3.19866	+	5.54023i	−0.159733	+	0.276666i	−0.934772	−	0.355247i	$-0.884397\pi$
$401$	−3.19866	+	5.54023i	−0.159733	+	0.276666i	0.775039	+	0.631913i	$0.217730\pi$
$402$	−0.172395	−	0.212890i	−0.00859828	−	0.0106180i
$403$	1.61119	+	30.7433i	0.0802589	+	1.53143i
$404$	23.0272	+	4.89458i	1.14564	+	0.243514i
$405$		0			0
$406$	−3.33221	+	5.60291i	−0.165375	+	0.278068i
$407$	−1.85161	−	1.85161i	−0.0917810	−	0.0917810i
$408$	−2.55335	−	0.133816i	−0.126410	−	0.00662485i
$409$	−4.31339	−	1.92044i	−0.213283	−	0.0949598i	0.297314	−	0.954780i	$-0.403909\pi$
$409$	−4.31339	−	1.92044i	−0.213283	−	0.0949598i	−0.510597	+	0.859820i	$0.670576\pi$
$410$		0			0
$411$	−0.0784809	−	0.176271i	−0.00387118	−	0.00869481i
$412$	2.30619	−	14.5607i	0.113618	−	0.717355i
$413$	−5.07490	+	4.00199i	−0.249719	+	0.196925i
$414$	7.54471	−	10.3844i	0.370802	−	0.510366i
$415$		0			0
$416$	6.73048	−	15.1169i	0.329989	−	0.741167i
$417$	−0.394145	−	0.255961i	−0.0193014	−	0.0125345i
$418$	0.458253	−	0.122789i	0.0224139	−	0.00600579i
$419$	−4.91344	+	15.1220i	−0.240037	+	0.738759i	0.756376	+	0.654137i	$0.226968\pi$
$419$	−4.91344	+	15.1220i	−0.240037	+	0.738759i	−0.996413	+	0.0846218i	$0.973032\pi$
$420$		0			0
$421$	−8.87472	−	27.3136i	−0.432527	−	1.33118i	−0.895599	−	0.444862i	$-0.853253\pi$
$421$	−8.87472	−	27.3136i	−0.432527	−	1.33118i	0.463072	−	0.886321i	$-0.346747\pi$
$422$	2.08037	+	3.20349i	0.101271	+	0.155943i
$423$	−3.83393	+	3.10466i	−0.186412	+	0.150954i
$424$	−16.9487	+	9.78537i	−0.823104	+	0.475219i
$425$		0			0
$426$			0.922638i			0.0447020i
$427$	1.99476	+	0.130435i	0.0965330	+	0.00631218i
$428$	2.84517	+	1.44968i	0.137526	+	0.0700731i
$429$	−0.0385691	+	0.181453i	−0.00186213	+	0.00876064i
$430$		0			0
$431$	−25.2825	+	5.37396i	−1.21782	+	0.258855i	−0.771622	−	0.636082i	$-0.780554\pi$
$431$	−25.2825	+	5.37396i	−1.21782	+	0.258855i	−0.446194	+	0.894936i	$0.647221\pi$
$432$	0.0898773	+	0.335427i	0.00432422	+	0.0161382i
$433$	−23.4750	+	11.9611i	−1.12814	+	0.574815i	−0.915501	−	0.402316i	$-0.868205\pi$
$433$	−23.4750	+	11.9611i	−1.12814	+	0.574815i	−0.212638	+	0.977131i	$0.568205\pi$
$434$	−18.7681	−	14.0103i	−0.900900	−	0.672518i
$435$		0			0
$436$	−22.4374	+	9.98975i	−1.07455	+	0.478422i
$437$	6.11958	−	2.34909i	0.292739	−	0.112372i
$438$	0.683468	−	0.262359i	0.0326574	−	0.0125360i
$439$	−33.2307	+	14.7952i	−1.58601	+	0.706138i	−0.994939	−	0.100479i	$-0.967962\pi$
$439$	−33.2307	+	14.7952i	−1.58601	+	0.706138i	−0.591074	+	0.806618i	$0.701296\pi$
$440$		0			0
$441$	13.5537	+	15.8594i	0.645412	+	0.755210i
$442$	13.9174	−	7.09128i	0.661984	−	0.337298i
$443$	4.61086	+	17.2080i	0.219069	+	0.817575i	0.984695	+	0.174289i	$0.0557627\pi$
$443$	4.61086	+	17.2080i	0.219069	+	0.817575i	−0.765626	+	0.643286i	$0.777571\pi$
$444$	−1.03063	+	0.219067i	−0.0489116	+	0.0103965i
$445$		0			0
$446$	0.377484	−	1.77592i	0.0178744	−	0.0840923i
$447$	−2.33912	−	1.19184i	−0.110637	−	0.0563722i
$448$	4.60152	+	9.32735i	0.217402	+	0.440676i
$449$		−	8.68138i		−	0.409699i	−0.978793	−	0.204850i	$-0.934329\pi$
$449$		−	8.68138i		−	0.409699i	0.978793	−	0.204850i	$-0.0656706\pi$
$450$		0			0
$451$	1.30809	−	0.755227i	0.0615957	−	0.0355623i
$452$	10.1609	−	8.22811i	0.477927	−	0.387018i
$453$	0.849330	+	1.30785i	0.0399050	+	0.0614483i
$454$	−1.69281	−	5.20992i	−0.0794473	−	0.244514i
$455$		0			0
$456$	0.147917	−	0.455242i	0.00692686	−	0.0213187i
$457$	−25.8197	+	6.91837i	−1.20780	+	0.323628i	−0.805896	−	0.592056i	$-0.798316\pi$
$457$	−25.8197	+	6.91837i	−1.20780	+	0.323628i	−0.401899	+	0.915684i	$0.631650\pi$
$458$	−7.80592	−	5.06922i	−0.364747	−	0.236869i
$459$	−2.27837	+	5.11730i	−0.106345	+	0.238855i
$460$		0			0
$461$	−0.325458	+	0.447954i	−0.0151581	+	0.0208633i	−0.816529	−	0.577305i	$-0.804104\pi$
$461$	−0.325458	+	0.447954i	−0.0151581	+	0.0208633i	0.801371	+	0.598168i	$0.204104\pi$
$462$	−0.0873891	−	0.110817i	−0.00406571	−	0.00515569i
$463$	5.44624	−	34.3862i	0.253108	−	1.59806i	−0.454030	−	0.890986i	$-0.650014\pi$
$463$	5.44624	−	34.3862i	0.253108	−	1.59806i	0.707138	−	0.707075i	$-0.249986\pi$
$464$	−0.505075	−	1.13442i	−0.0234475	−	0.0526640i
$465$		0			0
$466$	1.94161	+	0.864462i	0.0899435	+	0.0400454i
$467$	31.6053	+	1.65636i	1.46252	+	0.0766474i	0.766902	−	0.641765i	$-0.221797\pi$
$467$	31.6053	+	1.65636i	1.46252	+	0.0766474i	0.695618	+	0.718412i	$0.255131\pi$
$468$	−7.97835	−	7.97835i	−0.368799	−	0.368799i
$469$	5.48798	−	3.07453i	0.253411	−	0.141968i
$470$		0			0
$471$	0.107199	+	0.0227858i	0.00493947	+	0.00104992i
$472$	0.348982	+	6.65898i	0.0160632	+	0.306504i
$473$	2.48634	+	3.07037i	0.114322	+	0.141176i
$474$	−0.574835	+	0.995644i	−0.0264031	+	0.0457314i
$475$		0			0
$476$	5.16418	−	22.8387i	0.236700	−	1.04681i
$477$	3.34256	+	21.1041i	0.153045	+	0.966291i
$478$	−11.2275	+	7.29125i	−0.513536	+	0.333494i
$479$	14.4233	−	16.0187i	0.659019	−	0.731915i	−0.317282	−	0.948331i	$-0.602770\pi$
$479$	14.4233	−	16.0187i	0.659019	−	0.731915i	0.976301	+	0.216416i	$0.0694369\pi$
$480$		0			0
$481$	11.9946	−	10.7999i	0.546905	−	0.492435i
$482$	−4.59744	+	4.59744i	−0.209408	+	0.209408i
$483$	−1.36087	−	1.39654i	−0.0619218	−	0.0635449i
$484$	−8.41083	−	11.5765i	−0.382310	−	0.526205i
$485$		0			0
$486$	−3.06674	−	0.322328i	−0.139110	−	0.0146211i
$487$	6.36974	+	16.5937i	0.288640	+	0.751934i	0.998850	+	0.0479438i	$0.0152668\pi$
$487$	6.36974	+	16.5937i	0.288640	+	0.751934i	−0.710210	+	0.703990i	$0.751400\pi$
$488$	1.29795	−	1.60283i	0.0587552	−	0.0725567i
$489$	−2.45915	−	1.78667i	−0.111206	−	0.0807962i
$490$		0			0
$491$	16.3613	−	11.8872i	0.738374	−	0.536460i	−0.153828	−	0.988098i	$-0.549160\pi$
$491$	16.3613	−	11.8872i	0.738374	−	0.536460i	0.892201	+	0.451638i	$0.149160\pi$
$492$	0.0318084	−	0.606940i	0.00143403	−	0.0273630i
$493$	5.18436	−	19.3483i	0.233492	−	0.871404i
$494$	0.607976	+	2.86030i	0.0273541	+	0.128691i
$495$		0			0
$496$	4.24302	−	1.37864i	0.190517	−	0.0619028i
$497$	−20.8813	−	3.58476i	−0.936655	−	0.160798i
$498$	1.14451	−	0.181273i	0.0512868	−	0.00812303i
$499$	−20.1816	−	11.6518i	−0.903450	−	0.521607i	−0.0251324	−	0.999684i	$-0.508001\pi$
$499$	−20.1816	−	11.6518i	−0.903450	−	0.521607i	−0.878318	+	0.478077i	$0.841334\pi$
$500$		0			0
$501$	0.629232	+	1.08986i	0.0281120	+	0.0486914i
$502$	−3.85944	+	10.0542i	−0.172255	+	0.448740i
$503$	−12.9561	+	25.4278i	−0.577684	+	1.13377i	0.398569	+	0.917138i	$0.369507\pi$
$503$	−12.9561	+	25.4278i	−0.577684	+	1.13377i	−0.976254	+	0.216631i	$0.930493\pi$
$504$	21.4335	−	1.97279i	0.954722	−	0.0878748i
$505$		0			0
$506$	−1.33422	−	1.48181i	−0.0593135	−	0.0658743i
$507$	0.658730	+	0.176506i	0.0292552	+	0.00783892i
$508$	−4.75126	+	7.31629i	−0.210803	+	0.324608i
$509$	1.59286	+	15.1551i	0.0706025	+	0.671738i	0.971392	+	0.237482i	$0.0763220\pi$
$509$	1.59286	+	15.1551i	0.0706025	+	0.671738i	−0.900790	+	0.434256i	$0.857011\pi$
$510$		0			0
$511$	3.28225	+	16.4877i	0.145198	+	0.729374i
$512$	−4.59842	−	0.728319i	−0.203224	−	0.0321874i
$513$	−0.814973	−	0.659952i	−0.0359819	−	0.0291376i
$514$	−0.169490	+	1.61259i	−0.00747587	+	0.0711282i
$515$		0			0
$516$	1.58102	−	0.166171i	0.0696003	−	0.00731529i
$517$	0.347922	+	0.682836i	0.0153016	+	0.0300311i
$518$	0.483963	+	12.2696i	0.0212641	+	0.539093i
$519$	1.94075	+	0.630588i	0.0851895	+	0.0276798i
$520$		0			0
$521$	9.33285	+	8.40334i	0.408880	+	0.368157i	0.847752	−	0.530392i	$-0.177955\pi$
$521$	9.33285	+	8.40334i	0.408880	+	0.368157i	−0.438873	+	0.898549i	$0.644622\pi$
$522$	7.33311	−	0.384312i	0.320961	−	0.0168209i
$523$	−9.41934	−	3.61574i	−0.411879	−	0.158105i	0.143601	−	0.989636i	$-0.454132\pi$
$523$	−9.41934	−	3.61574i	−0.411879	−	0.158105i	−0.555479	+	0.831530i	$0.687465\pi$
$524$	−14.6497			−0.639977
$525$		0			0
$526$	−9.02429			−0.393478
$527$	67.1858	+	25.7902i	2.92666	+	1.12344i
$528$	0.0268465	−	0.00140697i	0.00116834	−	6.12303e-5i
$529$	−3.38149	−	3.04471i	−0.147021	−	0.132379i
$530$		0			0
$531$	6.92388	+	2.24971i	0.300471	+	0.0976289i
$532$	3.87973	+	2.04046i	0.168208	+	0.0884653i
$533$	4.22669	+	8.29534i	0.183078	+	0.359311i
$534$	−1.06444	+	0.111877i	−0.0460628	+	0.00484139i
$535$		0			0
$536$	0.678406	−	6.45460i	0.0293027	−	0.278796i
$537$	1.05512	+	0.854415i	0.0455316	+	0.0368707i
$538$	4.56744	+	0.723411i	0.196916	+	0.0311884i
$539$	2.84758	−	1.54724i	0.122654	−	0.0666445i
$540$		0			0
$541$	−0.767143	−	7.29888i	−0.0329821	−	0.313803i	−0.998558	−	0.0536823i	$-0.982904\pi$
$541$	−0.767143	−	7.29888i	−0.0329821	−	0.313803i	0.965576	−	0.260121i	$-0.0837625\pi$
$542$	−12.2714	+	18.8963i	−0.527102	+	0.811665i
$543$	2.72654	+	0.730575i	0.117007	+	0.0313520i
$544$	−25.8835	−	28.7466i	−1.10975	−	1.23250i
$545$		0			0
$546$	0.710306	−	0.502159i	0.0303983	−	0.0214904i
$547$	−14.3950	+	28.2518i	−0.615487	+	1.20796i	0.347314	+	0.937749i	$0.387094\pi$
$547$	−14.3950	+	28.2518i	−0.615487	+	1.20796i	−0.962801	+	0.270212i	$0.912906\pi$
$548$	0.653343	−	1.70202i	0.0279094	−	0.0727066i
$549$	−1.12589	−	1.95009i	−0.0480517	−	0.0832279i
$550$		0			0
$551$	3.24758	+	1.87499i	0.138352	+	0.0798773i
$552$	−1.98706	+	0.314720i	−0.0845751	+	0.0133954i
$553$	−20.3002	−	16.8782i	−0.863250	−	0.717733i
$554$	−10.1780	+	3.30704i	−0.432423	+	0.140503i
$555$		0			0
$556$	−0.923220	−	4.34341i	−0.0391532	−	0.184201i
$557$	4.81653	−	17.9755i	0.204083	−	0.761648i	−0.785644	−	0.618679i	$-0.787668\pi$
$557$	4.81653	−	17.9755i	0.204083	−	0.761648i	0.989727	−	0.142970i	$-0.0456651\pi$
$558$	−1.38073	+	26.3460i	−0.0584511	+	1.11531i
$559$	−19.7011	+	14.3137i	−0.833269	+	0.605405i
$560$		0			0
$561$	0.350831	+	0.254894i	0.0148121	+	0.0107616i
$562$	11.8259	−	14.6038i	0.498846	−	0.616023i
$563$	−6.39510	−	16.6598i	−0.269521	−	0.702127i	−0.999820	−	0.0189983i	$-0.993952\pi$
$563$	−6.39510	−	16.6598i	−0.269521	−	0.702127i	0.730298	−	0.683128i	$-0.239381\pi$
$564$	0.306679	+	0.0322332i	0.0129135	+	0.00135726i
$565$		0			0
$566$	0.328119	+	0.451617i	0.0137919	+	0.0189829i
$567$	6.33286	−	22.4679i	0.265955	−	0.943562i
$568$	−15.4568	+	15.4568i	−0.648551	+	0.648551i
$569$	−8.68699	+	7.82180i	−0.364177	+	0.327907i	−0.830822	−	0.556538i	$-0.812129\pi$
$569$	−8.68699	+	7.82180i	−0.364177	+	0.327907i	0.466645	+	0.884445i	$0.345463\pi$
$570$		0			0
$571$	−22.2630	+	24.7255i	−0.931676	+	1.03473i	0.0676381	+	0.997710i	$0.478454\pi$
$571$	−22.2630	+	24.7255i	−0.931676	+	1.03473i	−0.999314	+	0.0370215i	$0.988213\pi$
$572$	−1.46999	+	0.954620i	−0.0614632	+	0.0399147i
$573$	−0.545303	−	3.44290i	−0.0227803	−	0.143829i
$574$	−6.90846	−	1.56211i	−0.288354	−	0.0652011i
$575$		0			0
$576$	5.85786	−	10.1461i	0.244078	−	0.422755i
$577$	−26.5071	−	32.7336i	−1.10351	−	1.36272i	−0.925527	−	0.378682i	$-0.876378\pi$
$577$	−26.5071	−	32.7336i	−1.10351	−	1.36272i	−0.177979	−	0.984034i	$-0.556956\pi$
$578$	−1.18094	−	22.5336i	−0.0491205	−	0.937274i
$579$	−1.94352	−	0.413108i	−0.0807699	−	0.0171682i
$580$		0			0
$581$	−0.344210	+	26.6071i	−0.0142802	+	1.10385i
$582$	0.704793	+	0.704793i	0.0292146	+	0.0292146i
$583$	3.31471	+	0.173716i	0.137281	+	0.00719460i
$584$	15.8452	+	7.05475i	0.655681	+	0.291928i
$585$		0			0
$586$	−8.47827	−	19.0425i	−0.350234	−	0.786638i
$587$	1.86295	−	11.7622i	0.0768923	−	0.485479i	−0.918949	−	0.394376i	$-0.870961\pi$
$587$	1.86295	−	11.7622i	0.0768923	−	0.485479i	0.995841	−	0.0911028i	$-0.0290392\pi$
$588$	0.101912	−	1.30003i	0.00420277	−	0.0536123i
$589$	−7.91907	+	10.8997i	−0.326300	+	0.449113i
$590$		0			0
$591$	−1.18908	+	2.67071i	−0.0489121	+	0.109858i
$592$	−1.96167	−	1.27392i	−0.0806240	−	0.0523578i
$593$	8.14227	−	2.18171i	0.334363	−	0.0895922i	−0.0877316	−	0.996144i	$-0.527962\pi$
$593$	8.14227	−	2.18171i	0.334363	−	0.0895922i	0.422094	+	0.906552i	$0.361295\pi$
$594$	−0.0985760	+	0.303386i	−0.00404462	+	0.0124481i
$595$		0			0
$596$	−7.66507	−	23.5906i	−0.313973	−	0.966311i
$597$	1.20778	+	1.85982i	0.0494312	+	0.0761173i
$598$	9.55138	−	7.73455i	0.390585	−	0.316289i
$599$	31.0038	−	17.9000i	1.26678	−	0.731376i	0.292403	−	0.956295i	$-0.405545\pi$
$599$	31.0038	−	17.9000i	1.26678	−	0.731376i	0.974377	+	0.224919i	$0.0722118\pi$
$600$		0			0
$601$			12.5021i			0.509971i	0.966945	+	0.254985i	$0.0820706\pi$
$601$			12.5021i			0.509971i	−0.966945	+	0.254985i	$0.917929\pi$
$602$	1.20883	−	18.4868i	0.0492684	−	0.753467i
$603$	−6.31358	−	3.21693i	−0.257109	−	0.131004i
$604$	−3.06343	+	14.4123i	−0.124649	+	0.586429i
$605$		0			0
$606$	1.99978	−	0.425067i	0.0812356	−	0.0172672i
$607$	−8.04810	−	30.0359i	−0.326662	−	1.21912i	−0.912630	−	0.408786i	$-0.865952\pi$
$607$	−8.04810	−	30.0359i	−0.326662	−	1.21912i	0.585968	−	0.810334i	$-0.300715\pi$
$608$	6.45243	−	3.28768i	0.261681	−	0.133333i
$609$	0.130947	−	1.10782i	0.00530622	−	0.0448912i
$610$		0			0
$611$	−4.31530	+	1.92130i	−0.174579	+	0.0777274i
$612$	−24.6241	+	9.45229i	−0.995369	+	0.382086i
$613$	4.34940	−	1.66958i	0.175671	−	0.0674336i	−0.268943	−	0.963156i	$-0.586674\pi$
$613$	4.34940	−	1.66958i	0.175671	−	0.0674336i	0.444614	+	0.895722i	$0.353341\pi$
$614$	11.2215	−	4.99615i	0.452864	−	0.201628i
$615$		0			0
$616$	0.392490	−	3.32051i	0.0158139	−	0.133787i
$617$	−22.0504	+	11.2353i	−0.887717	+	0.452314i	−0.837508	−	0.546424i	$-0.815989\pi$
$617$	−22.0504	+	11.2353i	−0.887717	+	0.452314i	−0.0502084	+	0.998739i	$0.515989\pi$
$618$	−0.331361	−	1.23666i	−0.0133293	−	0.0497456i
$619$	−4.53636	+	0.964233i	−0.182332	+	0.0387558i	−0.298173	−	0.954512i	$-0.596377\pi$
$619$	−4.53636	+	0.964233i	−0.182332	+	0.0387558i	0.115841	+	0.993268i	$0.463044\pi$
$620$		0			0
$621$	−0.916379	+	4.31123i	−0.0367730	+	0.173004i
$622$	0.301521	+	0.153633i	0.0120899	+	0.00616011i
$623$	1.60368	−	24.5252i	0.0642500	−	0.982583i
$624$			0.165703i			0.00663341i
$625$		0			0
$626$	1.52626	−	0.881189i	0.0610018	−	0.0352194i
$627$	−0.0630918	+	0.0510907i	−0.00251964	+	0.00204037i
$628$	0.563971	+	0.868439i	0.0225049	+	0.0346545i
$629$	−11.6593	−	35.8837i	−0.464887	−	1.43078i
$630$		0			0
$631$	−8.92894	+	27.4805i	−0.355456	+	1.09398i	0.600289	+	0.799783i	$0.295052\pi$
$631$	−8.92894	+	27.4805i	−0.355456	+	1.09398i	−0.955745	+	0.294197i	$0.904948\pi$
$632$	−26.3099	+	7.04972i	−1.04655	+	0.280423i
$633$	−0.548190	−	0.355999i	−0.0217886	−	0.0141497i
$634$	2.03494	−	4.57054i	0.0808176	−	0.181519i
$635$		0			0
$636$	0.785043	−	1.08052i	0.0311290	−	0.0428454i
$637$	8.60517	+	18.0268i	0.340949	+	0.714249i
$638$	0.178447	−	1.12667i	0.00706479	−	0.0446053i
$639$	9.70704	+	21.8024i	0.384005	+	0.862489i
$640$		0			0
$641$	−12.1074	−	5.39056i	−0.478213	−	0.212914i	0.153451	−	0.988156i	$-0.450961\pi$
$641$	−12.1074	−	5.39056i	−0.478213	−	0.212914i	−0.631664	+	0.775242i	$0.717628\pi$
$642$	0.276932	+	0.0145134i	0.0109296	+	0.000572798i
$643$	11.0712	+	11.0712i	0.436605	+	0.436605i	0.890868	−	0.454263i	$-0.150097\pi$
$643$	11.0712	+	11.0712i	0.436605	+	0.436605i	−0.454263	+	0.890868i	$0.650097\pi$
$644$	0.238328	−	18.4225i	0.00939144	−	0.725949i
$645$		0			0
$646$	6.68639	+	1.42124i	0.263073	+	0.0559178i
$647$	−1.03247	−	19.7007i	−0.0405905	−	0.774514i	−0.940781	−	0.339016i	$-0.889906\pi$
$647$	−1.03247	−	19.7007i	−0.0405905	−	0.774514i	0.900190	−	0.435497i	$-0.143427\pi$
$648$	−15.1566	−	18.7169i	−0.595409	−	0.735269i
$649$	0.565467	−	0.979418i	0.0221965	−	0.0384455i
$650$		0			0
$651$	3.90914	+	0.883916i	0.153211	+	0.0346434i
$652$	−4.49284	−	28.3666i	−0.175953	−	1.11092i
$653$	−2.02366	+	1.31418i	−0.0791920	+	0.0514279i	−0.583628	−	0.812021i	$-0.698367\pi$
$653$	−2.02366	+	1.31418i	−0.0791920	+	0.0514279i	0.504436	+	0.863449i	$0.331701\pi$
$654$	−1.42723	+	1.58510i	−0.0558092	+	0.0619824i
$655$		0			0
$656$	1.00265	−	0.902791i	0.0391470	−	0.0352481i
$657$	13.3904	−	13.3904i	0.522409	−	0.522409i
$658$	0.974932	−	3.45889i	0.0380068	−	0.134841i
$659$	8.37171	+	11.5227i	0.326116	+	0.448859i	0.940322	−	0.340286i	$-0.110524\pi$
$659$	8.37171	+	11.5227i	0.326116	+	0.448859i	−0.614207	+	0.789145i	$0.710524\pi$
$660$		0			0
$661$	7.11319	+	0.747626i	0.276671	+	0.0290793i	0.241848	−	0.970314i	$-0.422247\pi$
$661$	7.11319	+	0.747626i	0.276671	+	0.0290793i	0.0348231	+	0.999393i	$0.488913\pi$
$662$	−4.99603	−	13.0151i	−0.194176	−	0.505847i
$663$	−1.68212	+	2.07725i	−0.0653282	+	0.0806736i
$664$	22.2106	+	16.1369i	0.861938	+	0.626235i
$665$		0			0
$666$	11.1901	−	8.13006i	0.433606	−	0.315033i
$667$	0.824869	−	15.7394i	0.0319391	−	0.609434i
$668$	−3.07750	+	11.4854i	−0.119072	+	0.444383i
$669$	0.0645961	+	0.303901i	0.00249743	+	0.0117495i
$670$		0			0
$671$	−0.332679	+	0.108094i	−0.0128429	+	0.00417292i
$672$	−1.65649	−	1.37726i	−0.0639005	−	0.0531289i
$673$	−11.9953	+	1.89988i	−0.462386	+	0.0732348i	−0.383282	−	0.923631i	$-0.625206\pi$
$673$	−11.9953	+	1.89988i	−0.462386	+	0.0732348i	−0.0791047	+	0.996866i	$0.525206\pi$
$674$	13.6762	+	7.89599i	0.526789	+	0.304142i
$675$		0			0
$676$	3.22178	+	5.58028i	0.123914	+	0.214626i
$677$	−18.2371	+	47.5094i	−0.700911	+	1.82593i	−0.155357	+	0.987858i	$0.549653\pi$
$677$	−18.2371	+	47.5094i	−0.700911	+	1.82593i	−0.545553	+	0.838076i	$0.683681\pi$
$678$	0.515486	−	1.01170i	0.0197971	−	0.0388541i
$679$	−18.6894	+	13.2127i	−0.717232	+	0.507055i
$680$		0			0
$681$	0.627255	+	0.696637i	0.0240365	+	0.0266952i
$682$	3.95865	+	1.06072i	0.151585	+	0.0406170i
$683$	5.01790	−	7.72689i	0.192005	−	0.295661i	−0.729536	−	0.683942i	$-0.760264\pi$
$683$	5.01790	−	7.72689i	0.192005	−	0.295661i	0.921541	+	0.388281i	$0.126931\pi$
$684$	−0.516146	−	4.91080i	−0.0197353	−	0.187769i
$685$		0			0
$686$	−14.7309	−	3.73393i	−0.562428	−	0.142562i
$687$	1.57312	+	0.249157i	0.0600181	+	0.00950593i
$688$	2.74258	+	2.22090i	0.104560	+	0.0846709i
$689$	−2.13856	+	20.3470i	−0.0814726	+	0.775160i
$690$		0			0
$691$	0.391533	−	0.0411518i	0.0148946	−	0.00156549i	−0.0970782	−	0.995277i	$-0.530950\pi$
$691$	0.391533	−	0.0411518i	0.0148946	−	0.00156549i	0.111973	+	0.993711i	$0.464283\pi$
$692$	8.75330	+	17.1793i	0.332751	+	0.653060i
$693$	−3.23095	−	1.69925i	−0.122734	−	0.0645492i
$694$	17.3031	+	5.62211i	0.656816	+	0.213412i
$695$		0			0
$696$	−0.855313	−	0.770127i	−0.0324206	−	0.0291916i
$697$	21.7339	−	1.13903i	0.823230	−	0.0431437i
$698$	13.0863	+	5.02336i	0.495324	+	0.190137i
$699$	−0.363698			−0.0137563
$700$		0			0
$701$	46.4699			1.75515			0.877573	−	0.479443i	$-0.159161\pi$
$701$	46.4699			1.75515			0.877573	+	0.479443i	$0.159161\pi$
$702$	−1.83563	−	0.704634i	−0.0692815	−	0.0265947i
$703$	7.05383	−	0.369676i	0.266040	−	0.0139426i
$704$	−1.35250	−	1.21779i	−0.0509741	−	0.0458973i
$705$		0			0
$706$	13.9037	+	4.51760i	0.523274	+	0.170022i
$707$	1.85037	+	46.9109i	0.0695902	+	1.76427i
$708$	−0.206594	−	0.405464i	−0.00776428	−	0.0152383i
$709$	34.4747	−	3.62344i	1.29473	−	0.136081i	0.568011	−	0.823021i	$-0.307713\pi$
$709$	34.4747	−	3.62344i	1.29473	−	0.136081i	0.726714	+	0.686940i	$0.241046\pi$
$710$		0			0
$711$	−3.10849	+	29.5753i	−0.116578	+	1.10916i
$712$	−19.7066	−	15.9581i	−0.738535	−	0.598054i
$713$	55.9283	+	8.85817i	2.09453	+	0.331741i
$714$	−0.397021	−	1.99435i	−0.0148581	−	0.0746368i
$715$		0			0
$716$	1.34089	+	12.7577i	0.0501114	+	0.476779i
$717$	1.24770	−	1.92129i	0.0465962	−	0.0717518i
$718$	−11.2218	−	3.00687i	−0.418793	−	0.112215i
$719$	24.4779	+	27.1854i	0.912870	+	1.01385i	0.999844	+	0.0176346i	$0.00561355\pi$
$719$	24.4779	+	27.1854i	0.912870	+	1.01385i	−0.0869742	+	0.996211i	$0.527720\pi$
$720$		0			0
$721$	29.2756	−	2.69460i	1.09028	−	0.100352i
$722$	6.49691	−	12.7509i	0.241790	−	0.474539i
$723$	0.398721	−	1.03870i	0.0148286	−	0.0386298i
$724$	13.3352	+	23.0973i	0.495599	+	0.858403i
$725$		0			0
$726$	−1.07620	−	0.621344i	−0.0399415	−	0.0230602i
$727$	−36.2364	+	5.73928i	−1.34393	+	0.212858i	−0.786616	−	0.617442i	$-0.788169\pi$
$727$	−36.2364	+	5.73928i	−1.34393	+	0.212858i	−0.557316	+	0.830300i	$0.688169\pi$
$728$	20.3122	+	3.48705i	0.752819	+	0.129239i
$729$	−24.6715	+	8.01626i	−0.913759	+	0.296898i
$730$		0			0
$731$	11.8357	+	55.6824i	0.437757	+	2.05949i
$732$	−0.0364291	+	0.135955i	−0.00134646	+	0.00502505i
$733$	0.886929	−	16.9236i	0.0327595	−	0.625088i	−0.932081	−	0.362251i	$-0.882008\pi$
$733$	0.886929	−	16.9236i	0.0327595	−	0.625088i	0.964840	−	0.262837i	$-0.0846583\pi$
$734$	−13.5820	+	9.86791i	−0.501321	+	0.364231i
$735$		0			0
$736$	−24.6238	−	17.8903i	−0.907647	−	0.659444i
$737$	−0.692725	+	0.855444i	−0.0255168	+	0.0315107i
$738$	2.85921	+	7.44851i	0.105249	+	0.274183i
$739$	9.14979	+	0.961682i	0.336580	+	0.0353760i	0.271311	−	0.962492i	$-0.412543\pi$
$739$	9.14979	+	0.961682i	0.336580	+	0.0353760i	0.0652692	+	0.997868i	$0.479209\pi$
$740$		0			0
$741$	−0.294127	−	0.404831i	−0.0108050	−	0.0148718i
$742$	−10.8626	−	11.1474i	−0.398780	−	0.409234i
$743$	−28.0230	+	28.0230i	−1.02806	+	1.02806i	−0.0284701	+	0.999595i	$0.509064\pi$
$743$	−28.0230	+	28.0230i	−1.02806	+	1.02806i	−0.999595	+	0.0284701i	$0.990936\pi$
$744$	3.07292	−	2.76687i	0.112659	−	0.101438i
$745$		0			0
$746$	−3.99979	+	4.44221i	−0.146443	+	0.162641i
$747$	25.1382	−	16.3249i	0.919758	−	0.597298i
$748$	0.640965	+	4.04689i	0.0234360	+	0.147969i
$749$	−1.40444	+	6.21119i	−0.0513172	+	0.226952i
$750$		0			0
$751$	21.1806	−	36.6859i	0.772892	−	1.33869i	−0.163080	−	0.986613i	$-0.552143\pi$
$751$	21.1806	−	36.6859i	0.772892	−	1.33869i	0.935972	−	0.352075i	$-0.114524\pi$
$752$	0.430800	+	0.531994i	0.0157097	+	0.0193998i
$753$	−0.0964502	−	1.84038i	−0.00351484	−	0.0670672i
$754$	6.87745	+	1.46185i	0.250462	+	0.0532373i
$755$		0			0
$756$	−2.57147	+	1.44061i	−0.0935236	+	0.0523946i
$757$	21.6112	+	21.6112i	0.785474	+	0.785474i	0.980749	−	0.195275i	$-0.0625599\pi$
$757$	21.6112	+	21.6112i	0.785474	+	0.785474i	−0.195275	+	0.980749i	$0.562560\pi$
$758$	−3.44403	−	0.180494i	−0.125093	−	0.00655583i
$759$	0.311714	+	0.138784i	0.0113145	+	0.00503754i
$760$		0			0
$761$	−16.0906	−	36.1400i	−0.583282	−	1.31007i	−0.928424	−	0.371523i	$-0.878836\pi$
$761$	−16.0906	−	36.1400i	−0.583282	−	1.31007i	0.345142	−	0.938551i	$-0.387831\pi$
$762$	−0.118515	+	0.748276i	−0.00429335	+	0.0271072i
$763$	−30.3290	−	38.4600i	−1.09798	−	1.39235i
$764$	19.3591	−	26.6455i	0.700388	−	0.964001i
$765$		0			0
$766$	7.45054	−	16.7342i	0.269199	−	0.604630i
$767$	5.84621	+	3.79657i	0.211094	+	0.137086i
$768$	−1.99806	+	0.535378i	−0.0720987	+	0.0193188i
$769$	0.678119	−	2.08704i	0.0244536	−	0.0752604i	−0.938085	−	0.346405i	$-0.887402\pi$
$769$	0.678119	−	2.08704i	0.0244536	−	0.0752604i	0.962539	+	0.271145i	$0.0874022\pi$
$770$		0			0
$771$	−0.0857432	−	0.263890i	−0.00308796	−	0.00950378i
$772$	−10.2248	−	15.7448i	−0.367998	−	0.566668i
$773$	36.3288	−	29.4185i	1.30666	−	1.05811i	0.312526	−	0.949909i	$-0.398825\pi$
$773$	36.3288	−	29.4185i	1.30666	−	1.05811i	0.994129	−	0.108199i	$-0.0345085\pi$
$774$	−18.0729	+	10.4344i	−0.649618	+	0.375057i
$775$		0			0
$776$			23.6145i			0.847711i
$777$	−0.929642	−	1.88440i	−0.0333507	−	0.0676024i
$778$	4.92045	+	2.50710i	0.176407	+	0.0898837i
$779$	−0.847115	+	3.98536i	−0.0303510	+	0.142790i
$780$		0			0
$781$	3.62637	−	0.770808i	0.129762	−	0.0275817i
$782$	−7.43600	−	27.7515i	−0.265911	−	0.992393i
$783$	−2.24666	+	1.14473i	−0.0802890	+	0.0409093i
$784$	2.20064	−	1.88070i	0.0785944	−	0.0671678i
$785$		0			0
$786$	−1.16226	+	0.517470i	−0.0414563	+	0.0184576i
$787$	35.8960	−	13.7792i	1.27955	−	0.491174i	0.378789	−	0.925483i	$-0.376341\pi$
$787$	35.8960	−	13.7792i	1.27955	−	0.491174i	0.900764	+	0.434309i	$0.143007\pi$
$788$	−25.7875	+	9.89890i	−0.918643	+	0.352634i
$789$	1.41075	−	0.628108i	0.0502242	−	0.0223613i
$790$		0			0
$791$	20.8941	+	15.5974i	0.742909	+	0.554579i
$792$	−3.35589	+	1.70991i	−0.119246	+	0.0607590i
$793$	−0.558034	−	2.08261i	−0.0198164	−	0.0739556i
$794$	−13.1305	+	2.79097i	−0.465983	+	0.0990478i
$795$		0			0
$796$	−4.35632	+	20.4949i	−0.154406	+	0.726421i
$797$	−8.48456	−	4.32310i	−0.300539	−	0.153132i	0.297218	−	0.954810i	$-0.403941\pi$
$797$	−8.48456	−	4.32310i	−0.300539	−	0.153132i	−0.597757	+	0.801678i	$0.703941\pi$
$798$	0.379879	+	0.0248398i	0.0134476	+	0.000879321i
$799$			11.0423i			0.390650i
$800$		0			0
$801$	−23.9761	+	13.8426i	−0.847155	+	0.489105i
$802$	−4.07947	+	3.30349i	−0.144051	+	0.116650i
$803$	−1.60218	−	2.46714i	−0.0565397	−	0.0870635i
$804$	0.136869	+	0.421239i	0.00482700	+	0.0148560i
$805$		0			0
$806$	−7.80606	+	24.0246i	−0.274957	+	0.846229i
$807$	−0.764371	+	0.204813i	−0.0269071	+	0.00720975i
$808$	40.6230	+	26.3809i	1.42911	+	0.928076i
$809$	−4.19545	+	9.42313i	−0.147504	+	0.331300i	−0.972154	−	0.234344i	$-0.924706\pi$
$809$	−4.19545	+	9.42313i	−0.147504	+	0.331300i	0.824650	+	0.565644i	$0.191372\pi$
$810$		0			0
$811$	−2.44836	+	3.36987i	−0.0859734	+	0.118332i	−0.849837	−	0.527045i	$-0.823300\pi$
$811$	−2.44836	+	3.36987i	−0.0859734	+	0.118332i	0.763864	+	0.645377i	$0.223300\pi$
$812$	8.27631	−	6.52659i	0.290442	−	0.229038i
$813$	0.603151	−	3.80814i	0.0211534	−	0.133557i
$814$	−0.873941	−	1.96290i	−0.0306316	−	0.0687997i
$815$		0			0
$816$	0.353866	+	0.157551i	0.0123878	+	0.00551540i
$817$	−10.6426	−	0.557755i	−0.372338	−	0.0195134i
$818$	−2.73953	−	2.73953i	−0.0957856	−	0.0957856i
$819$	11.5017	−	19.3394i	0.401901	−	0.675772i
$820$		0			0
$821$	31.7211	+	6.74254i	1.10708	+	0.235316i	0.724955	−	0.688796i	$-0.241861\pi$
$821$	31.7211	+	6.74254i	1.10708	+	0.235316i	0.382121	+	0.924112i	$0.375194\pi$
$822$	−0.00828618	−	0.158110i	−0.000289014	−	0.00551471i
$823$	27.2112	+	33.6031i	0.948523	+	1.17133i	0.985097	+	0.171998i	$0.0550223\pi$
$823$	27.2112	+	33.6031i	0.948523	+	1.17133i	−0.0365738	+	0.999331i	$0.511644\pi$
$824$	15.1662	−	26.2686i	0.528340	−	0.915111i
$825$		0			0
$826$	−5.06443	+	1.57340i	−0.176214	+	0.0547456i
$827$	−0.940691	−	5.93929i	−0.0327110	−	0.206529i	0.965920	−	0.258842i	$-0.0833408\pi$
$827$	−0.940691	−	5.93929i	−0.0327110	−	0.206529i	−0.998631	+	0.0523125i	$0.983341\pi$
$828$	−17.4054	+	11.3032i	−0.604881	+	0.392814i
$829$	6.44654	−	7.15960i	0.223897	−	0.248663i	−0.620722	−	0.784031i	$-0.713160\pi$
$829$	6.44654	−	7.15960i	0.223897	−	0.248663i	0.844619	+	0.535368i	$0.179827\pi$
$830$		0			0
$831$	1.36094	−	1.22540i	0.0472105	−	0.0425085i
$832$	7.93220	−	7.93220i	0.274999	−	0.274999i
$833$	46.6791	−	1.23671i	1.61734	−	0.0428496i
$834$	−0.226666	−	0.311979i	−0.00784881	−	0.0108030i
$835$		0			0
$836$	−0.762862	−	0.0801801i	−0.0263841	−	0.00277309i
$837$	−3.24647	−	8.45734i	−0.112214	−	0.292329i
$838$	−8.21068	+	10.1393i	−0.283633	+	0.350258i
$839$	−32.1825	−	23.3819i	−1.11106	−	0.807234i	−0.128232	−	0.991744i	$-0.540930\pi$
$839$	−32.1825	−	23.3819i	−1.11106	−	0.807234i	−0.982831	+	0.184510i	$0.940930\pi$
$840$		0			0
$841$	−16.1669	+	11.7459i	−0.557479	+	0.405032i
$842$	1.23332	−	23.5332i	0.0425031	−	0.811007i
$843$	−0.832276	+	3.10610i	−0.0286651	+	0.106980i
$844$	−1.28404	−	6.04095i	−0.0441986	−	0.207938i
$845$		0			0
$846$	−3.84992	+	1.25092i	−0.132363	+	0.0430073i
$847$	18.2438	−	21.9426i	0.626863	−	0.753957i
$848$	2.92839	−	0.463812i	0.100561	−	0.0159274i
$849$	−0.0827277	−	0.0477629i	−0.00283921	−	0.00163922i
$850$		0			0
$851$	−14.8438	−	25.7103i	−0.508840	−	0.881337i
$852$	0.534602	−	1.39269i	0.0183152	−	0.0477126i
$853$	11.8947	−	23.3447i	0.407267	−	0.799307i	−0.592714	−	0.805413i	$-0.701944\pi$
$853$	11.8947	−	23.3447i	0.407267	−	0.799307i	0.999981	+	0.00610592i	$0.00194359\pi$
$854$	1.48972	+	0.686493i	0.0509772	+	0.0234913i
$855$		0			0
$856$	4.39624	+	4.88252i	0.150261	+	0.166881i
$857$	8.06662	+	2.16145i	0.275551	+	0.0738336i	0.393948	−	0.919133i	$-0.371109\pi$
$857$	8.06662	+	2.16145i	0.275551	+	0.0738336i	−0.118397	+	0.992966i	$0.537776\pi$
$858$	−0.0829035	+	0.127660i	−0.00283028	+	0.00435825i
$859$	−0.536493	−	5.10439i	−0.0183049	−	0.174160i	0.981550	−	0.191207i	$-0.0612401\pi$
$859$	−0.536493	−	5.10439i	−0.0183049	−	0.174160i	−0.999855	+	0.0170472i	$0.994573\pi$
$860$		0			0
$861$	1.18872	−	0.236640i	0.0405113	−	0.00806468i
$862$	−20.9478	−	3.31781i	−0.713486	−	0.113005i
$863$	−1.31908	−	1.06817i	−0.0449021	−	0.0363610i	0.606607	−	0.795002i	$-0.292530\pi$
$863$	−1.31908	−	1.06817i	−0.0449021	−	0.0363610i	−0.651509	+	0.758641i	$0.725864\pi$
$864$	−0.508983	+	4.84265i	−0.0173160	+	0.164750i
$865$		0			0
$866$	−21.5003	+	2.25977i	−0.730608	+	0.0767900i
$867$	1.75300	+	3.44045i	0.0595349	+	0.116844i
$868$	20.2118	+	32.0228i	0.686033	+	1.08693i
$869$	4.39355	+	1.42755i	0.149041	+	0.0484263i
$870$		0			0
$871$	−5.04206	−	4.53989i	−0.170844	−	0.153828i
$872$	−50.4650	+	2.64476i	−1.70896	+	0.0895628i
$873$	24.0697	+	9.23949i	0.814636	+	0.312709i
$874$	5.37865			0.181936
$875$		0			0
$876$	−1.18369			−0.0399930
$877$	10.4385	+	4.00698i	0.352484	+	0.135306i	0.528166	−	0.849141i	$-0.322880\pi$
$877$	10.4385	+	4.00698i	0.352484	+	0.135306i	−0.175682	+	0.984447i	$0.556213\pi$
$878$	−29.8069	+	1.56211i	−1.00593	+	0.0527188i
$879$	2.65079	+	2.38678i	0.0894089	+	0.0805042i
$880$		0			0
$881$	19.9227	+	6.47328i	0.671213	+	0.218090i	0.624744	−	0.780829i	$-0.285203\pi$
$881$	19.9227	+	6.47328i	0.671213	+	0.218090i	0.0464689	+	0.998920i	$0.485203\pi$
$882$	5.71916	+	16.1346i	0.192574	+	0.543281i
$883$	20.5259	+	40.2843i	0.690751	+	1.35567i	0.923674	+	0.383180i	$0.125171\pi$
$883$	20.5259	+	40.2843i	0.690751	+	1.35567i	−0.232923	+	0.972495i	$0.574829\pi$
$884$	−25.1166	+	2.63987i	−0.844764	+	0.0887883i
$885$		0			0
$886$	−1.52800	+	14.5380i	−0.0513342	+	0.488413i
$887$	27.2474	+	22.0645i	0.914879	+	0.740855i	0.966191	−	0.257828i	$-0.0830068\pi$
$887$	27.2474	+	22.0645i	0.914879	+	0.740855i	−0.0513114	+	0.998683i	$0.516340\pi$
$888$	−2.14123	−	0.339137i	−0.0718549	−	0.0113807i
$889$	−16.4746	−	5.58956i	−0.552542	−	0.187468i
$890$		0			0
$891$	0.426972	+	4.06237i	0.0143041	+	0.136094i
$892$	−1.59881	+	2.46196i	−0.0535322	+	0.0824324i
$893$	−1.99680	−	0.535041i	−0.0668204	−	0.0179045i
$894$	−1.44141	−	1.60084i	−0.0482079	−	0.0535402i
$895$		0			0
$896$	−2.03015	−	22.0567i	−0.0678226	−	0.736863i
$897$	−0.954813	+	1.87393i	−0.0318803	+	0.0625686i
$898$	2.55283	−	6.65034i	0.0851889	−	0.221925i
$899$	16.1972	+	28.0544i	0.540208	+	0.935668i
$900$		0			0
$901$	41.4188	+	23.9131i	1.37986	+	0.796662i
$902$	1.22414	−	0.193885i	0.0407594	−	0.00645566i
$903$	1.09775	+	2.97416i	0.0365307	+	0.0989738i
$904$	25.5846	−	8.31294i	0.850932	−	0.276484i
$905$		0			0
$906$	0.266042	+	1.25163i	0.00883866	+	0.0415826i
$907$	4.55651	−	17.0051i	0.151296	−	0.564646i	−0.848098	−	0.529840i	$-0.822252\pi$
$907$	4.55651	−	17.0051i	0.151296	−	0.564646i	0.999394	−	0.0348060i	$-0.0110813\pi$
$908$	−0.463548	+	8.84503i	−0.0153834	+	0.293532i
$909$	42.7837	−	31.0842i	1.41904	−	1.03100i
$910$		0			0
$911$	−17.7761	−	12.9151i	−0.588949	−	0.427897i	0.252990	−	0.967469i	$-0.418586\pi$
$911$	−17.7761	−	12.9151i	−0.588949	−	0.427897i	−0.841939	+	0.539572i	$0.818586\pi$
$912$	−0.0456363	+	0.0563562i	−0.00151117	+	0.00186614i
$913$	−1.66865	−	4.34698i	−0.0552243	−	0.143864i
$914$	−21.8135	−	2.29269i	−0.721527	−	0.0758355i
$915$		0			0
$916$	8.84547	+	12.1747i	0.292263	+	0.402265i
$917$	−7.19572	−	28.3150i	−0.237624	−	0.935042i
$918$	−3.25012	+	3.25012i	−0.107270	+	0.107270i
$919$	12.0720	−	10.8697i	0.398219	−	0.358558i	−0.445557	−	0.895254i	$-0.646994\pi$
$919$	12.0720	−	10.8697i	0.398219	−	0.358558i	0.843776	+	0.536695i	$0.180328\pi$
$920$		0			0
$921$	−1.40650	+	1.56208i	−0.0463459	+	0.0514723i
$922$	−0.381040	+	0.247450i	−0.0125489	+	0.00814935i
$923$	3.57475	+	22.5701i	0.117664	+	0.742903i
$924$	0.0676997	+	0.217910i	0.00222716	+	0.00716872i
$925$		0			0
$926$	14.2836	−	24.7399i	0.469388	−	0.813004i
$927$	−20.8410	−	25.7365i	−0.684509	−	0.845298i
$928$	−0.911293	−	17.3885i	−0.0299147	−	0.570806i
$929$	−18.4656	−	3.92499i	−0.605837	−	0.128775i	−0.105228	−	0.994448i	$-0.533557\pi$
$929$	−18.4656	−	3.92499i	−0.605837	−	0.128775i	−0.500609	+	0.865673i	$0.666891\pi$
$930$		0			0
$931$	−2.03814	+	8.50097i	−0.0667972	+	0.278608i
$932$	−2.42989	−	2.42989i	−0.0795939	−	0.0795939i
$933$	−0.0578295	−	0.00303072i	−0.00189325	−	9.92212e-5i
$934$	23.7241	+	10.5626i	0.776276	+	0.345620i
$935$		0			0
$936$	−9.44247	−	21.2081i	−0.308637	−	0.693209i
$937$	−5.52877	+	34.9073i	−0.180617	+	1.14037i	0.716175	+	0.697920i	$0.245891\pi$
$937$	−5.52877	+	34.9073i	−0.180617	+	1.14037i	−0.896792	+	0.442451i	$0.854109\pi$
$938$	5.10814	−	0.741448i	0.166787	−	0.0242091i
$939$	−0.177266	+	0.243986i	−0.00578486	+	0.00796218i
$940$		0			0
$941$	17.0291	−	38.2479i	0.555131	−	1.24685i	−0.390199	−	0.920731i	$-0.627594\pi$
$941$	17.0291	−	38.2479i	0.555131	−	1.24685i	0.945330	−	0.326115i	$-0.105740\pi$
$942$	0.0754191	+	0.0489777i	0.00245729	+	0.00159578i
$943$	16.5410	−	4.43216i	0.538650	−	0.144331i
$944$	0.312168	−	0.960754i	0.0101602	−	0.0312699i
$945$		0			0
$946$	1.00178	+	3.08317i	0.0325708	+	0.100243i
$947$	0.388606	+	0.598401i	0.0126280	+	0.0194454i	0.844928	−	0.534880i	$-0.179643\pi$
$947$	0.388606	+	0.598401i	0.0126280	+	0.0194454i	−0.832300	+	0.554325i	$0.812976\pi$
$948$	1.44459	−	1.16981i	0.0469182	−	0.0379936i
$949$	15.7029	−	9.06605i	0.509736	−	0.294296i
$950$		0			0
$951$			0.856142i			0.0277623i
$952$	26.7598	−	40.0622i	0.867289	−	1.29842i
$953$	−19.8369	−	10.1074i	−0.642581	−	0.327411i	0.102157	−	0.994768i	$-0.467426\pi$
$953$	−19.8369	−	10.1074i	−0.642581	−	0.327411i	−0.744738	+	0.667357i	$0.767426\pi$
$954$	−3.64527	+	17.1496i	−0.118020	+	0.555240i
$955$		0			0
$956$	21.1723	−	4.50030i	0.684760	−	0.145550i
$957$	0.0505221	+	0.188551i	0.00163315	+	0.00609500i
$958$	15.7594	−	8.02981i	0.509163	−	0.259431i
$959$	3.61056	+	0.426775i	0.116591	+	0.0137813i
$960$		0			0
$961$	−78.0031	+	34.7292i	−2.51623	+	1.12030i
$962$	12.3642	−	4.74617i	0.398638	−	0.153023i
$963$	6.69673	−	2.57063i	0.215799	−	0.0828375i
$964$	9.60354	−	4.27577i	0.309309	−	0.137713i
$965$		0			0
$966$	−0.631827	−	1.46999i	−0.0203287	−	0.0472963i
$967$	−24.2914	+	12.3771i	−0.781158	+	0.398020i	−0.798626	−	0.601828i	$-0.794439\pi$
$967$	−24.2914	+	12.3771i	−0.781158	+	0.398020i	0.0174683	+	0.999847i	$0.494439\pi$
$968$	−7.62010	−	28.4386i	−0.244919	−	0.914051i
$969$	−1.14420	+	0.243206i	−0.0367568	+	0.00781291i
$970$		0			0
$971$	−5.21228	+	24.5219i	−0.167270	+	0.786944i	0.811883	+	0.583820i	$0.198443\pi$
$971$	−5.21228	+	24.5219i	−0.167270	+	0.786944i	−0.979153	+	0.203124i	$0.934891\pi$
$972$	4.44236	+	2.26350i	0.142489	+	0.0726017i
$973$	7.94145	−	3.91781i	0.254591	−	0.125599i
$974$			14.5847i			0.467322i
$975$		0			0
$976$	−0.270594	+	0.156227i	−0.00866150	+	0.00500072i
$977$	−13.0377	+	10.5578i	−0.417114	+	0.337772i	−0.814793	−	0.579752i	$-0.803149\pi$
$977$	−13.0377	+	10.5578i	−0.417114	+	0.337772i	0.397679	+	0.917525i	$0.369816\pi$
$978$	−1.35844	−	2.09181i	−0.0434380	−	0.0668886i
$979$	1.32900	+	4.09024i	0.0424750	+	0.130725i
$980$		0			0
$981$	−17.0494	+	52.4725i	−0.544344	+	1.67532i
$982$	16.0290	−	4.29496i	0.511506	−	0.137058i
$983$	13.4200	+	8.71505i	0.428032	+	0.277967i	0.740623	−	0.671921i	$-0.234530\pi$
$983$	13.4200	+	8.71505i	0.428032	+	0.277967i	−0.312591	+	0.949888i	$0.601197\pi$
$984$	0.508627	−	1.14239i	0.0162144	−	0.0364182i
$985$		0			0
$986$	9.66099	−	13.2972i	0.307669	−	0.423469i
$987$	0.0883355	+	0.608580i	0.00281175	+	0.0193713i
$988$	0.739622	−	4.66979i	0.0235305	−	0.148566i
$989$	18.2185	+	40.9194i	0.579314	+	1.30116i
$990$		0			0
$991$	24.1634	+	10.7582i	0.767575	+	0.341746i	0.752890	−	0.658146i	$-0.228659\pi$
$991$	24.1634	+	10.7582i	0.767575	+	0.341746i	0.0146843	+	0.999892i	$0.495326\pi$
$992$	62.4724	+	3.27404i	1.98350	+	0.103951i
$993$	1.68690	+	1.68690i	0.0535321	+	0.0535321i
$994$	−14.9419	−	8.88641i	−0.473930	−	0.281860i
$995$		0			0
$996$	−1.83263	−	0.389537i	−0.0580691	−	0.0123430i
$997$	−0.484111	−	9.23739i	−0.0153320	−	0.292551i	−0.995524	−	0.0945041i	$-0.969873\pi$
$997$	−0.484111	−	9.23739i	−0.0153320	−	0.292551i	0.980193	−	0.198047i	$-0.0634599\pi$
$998$	−12.0337	−	14.8604i	−0.380920	−	0.470397i
$999$	−2.37475	+	4.11318i	−0.0751337	+	0.130135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.82.11		288
5.2	odd	4		175.2.x.a.138.8	yes	288
5.3	odd	4		875.2.bb.c.418.11		288
5.4	even	2		875.2.bb.b.82.8		288
7.3	odd	6	inner	875.2.bb.a.332.8		288
25.2	odd	20		875.2.bb.b.593.11		288
25.11	even	5		875.2.bb.c.782.11		288
25.14	even	10		175.2.x.a.152.8	yes	288
25.23	odd	20	inner	875.2.bb.a.593.8		288
35.3	even	12		875.2.bb.c.668.11		288
35.17	even	12		175.2.x.a.38.8	✓	288
35.24	odd	6		875.2.bb.b.332.11		288
175.52	even	60		875.2.bb.b.843.8		288
175.73	even	60	inner	875.2.bb.a.843.11		288
175.136	odd	30		875.2.bb.c.157.11		288
175.164	odd	30		175.2.x.a.52.8	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.8	✓	288	35.17	even	12
175.2.x.a.52.8	yes	288	175.164	odd	30
175.2.x.a.138.8	yes	288	5.2	odd	4
175.2.x.a.152.8	yes	288	25.14	even	10
875.2.bb.a.82.11		288	1.1	even	1	trivial
875.2.bb.a.332.8		288	7.3	odd	6	inner
875.2.bb.a.593.8		288	25.23	odd	20	inner
875.2.bb.a.843.11		288	175.73	even	60	inner
875.2.bb.b.82.8		288	5.4	even	2
875.2.bb.b.332.11		288	35.24	odd	6
875.2.bb.b.593.11		288	25.2	odd	20
875.2.bb.b.843.8		288	175.52	even	60
875.2.bb.c.157.11		288	175.136	odd	30
875.2.bb.c.418.11		288	5.3	odd	4
875.2.bb.c.668.11		288	35.3	even	12
875.2.bb.c.782.11		288	25.11	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766047 + 0.294058i) q^{2} +(-0.140222 + 0.00734873i) q^{3} +(-0.985932 - 0.887737i) q^{4} +(-0.109578 - 0.0356039i) q^{6} +(1.23154 - 2.34165i) q^{7} +(-1.23927 - 2.43220i) q^{8} +(-2.96396 + 0.311524i) q^{9} +(-0.0483934 + 0.460432i) q^{11} +(0.144773 + 0.117235i) q^{12} +(-2.81849 - 0.446405i) q^{13} +(1.63200 - 1.43167i) q^{14} +(0.0432270 + 0.411277i) q^{16} +(-3.63317 + 5.59459i) q^{17} +(-2.36214 - 0.632933i) q^{18} +(-0.835637 - 0.928069i) q^{19} +(-0.155481 + 0.337401i) q^{21} +(-0.172465 + 0.338482i) q^{22} +(-1.88101 + 4.90021i) q^{23} +(0.191646 + 0.331940i) q^{24} +(-2.02783 - 1.17077i) q^{26} +(0.829380 - 0.131361i) q^{27} +(-3.29298 + 1.21542i) q^{28} +(-2.85581 + 0.927907i) q^{29} +(-2.24299 - 10.5524i) q^{31} +(-1.50083 + 5.60118i) q^{32} +(0.00340223 - 0.0649184i) q^{33} +(-4.42831 + 3.21736i) q^{34} +(3.19881 + 2.32407i) q^{36} +(-3.55947 + 4.39558i) q^{37} +(-0.367231 - 0.956670i) q^{38} +(0.398495 + 0.0418835i) q^{39} +(-1.91768 - 2.63945i) q^{41} +(-0.218321 + 0.212744i) q^{42} +(6.03422 - 6.03422i) q^{43} +(0.456455 - 0.410994i) q^{44} +(-2.88189 + 3.20066i) q^{46} +(1.38828 - 0.901557i) q^{47} +(-0.00908374 - 0.0573524i) q^{48} +(-3.96662 - 5.76766i) q^{49} +(0.468337 - 0.811184i) q^{51} +(2.38255 + 2.94221i) q^{52} +(-0.375223 - 7.15968i) q^{53} +(0.673972 + 0.143257i) q^{54} +(-7.22155 - 0.0934236i) q^{56} +(0.123995 + 0.123995i) q^{57} +(-2.46054 - 0.128951i) q^{58} +(-2.23160 - 0.993572i) q^{59} +(0.307313 + 0.690235i) q^{61} +(1.38479 - 8.74324i) q^{62} +(-2.92075 + 7.32420i) q^{63} +(-2.31063 + 3.18031i) q^{64} +(0.0216960 - 0.0487301i) q^{66} +(1.99402 + 1.29493i) q^{67} +(8.54858 - 2.29059i) q^{68} +(0.227749 - 0.700940i) q^{69} +(-2.47456 - 7.61592i) q^{71} +(4.43082 + 6.82286i) q^{72} +(-4.93803 + 3.99874i) q^{73} +(-4.01928 + 2.32053i) q^{74} +1.65684i q^{76} +(1.01857 + 0.680361i) q^{77} +(0.292950 + 0.149265i) q^{78} +(2.07461 - 9.76028i) q^{79} +(8.63014 - 1.83439i) q^{81} +(-0.692877 - 2.58585i) q^{82} +(-8.96119 + 4.56596i) q^{83} +(0.452817 - 0.194628i) q^{84} +(6.39691 - 2.84809i) q^{86} +(0.393628 - 0.151100i) q^{87} +(1.17983 - 0.452896i) q^{88} +(8.48635 - 3.77837i) q^{89} +(-4.51641 + 6.05015i) q^{91} +(6.20465 - 3.16143i) q^{92} +(0.392064 + 1.46320i) q^{93} +(1.32859 - 0.282401i) q^{94} +(0.169288 - 0.796437i) q^{96} +(-7.70801 - 3.92743i) q^{97} +(-1.34259 - 5.58472i) q^{98} -1.37978i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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