LMFDB - Embedded newform 880.2.bo.k.641.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.1
Root			$-0.952275 - 2.93080i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.k.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.952275 - 2.93080i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0119064 + 0.0366440i) q^{7} +(-5.25571 + 3.81850i) q^{9} +O(q^{10})$	\(q+(-0.952275 - 2.93080i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0119064 + 0.0366440i) q^{7} +(-5.25571 + 3.81850i) q^{9} +(1.11209 - 3.12462i) q^{11} +(-2.79380 + 2.02981i) q^{13} +(-0.952275 + 2.93080i) q^{15} +(-0.726200 - 0.527615i) q^{17} +(-0.373056 - 1.14815i) q^{19} +0.118734 q^{21} -7.60421 q^{23} +(0.309017 + 0.951057i) q^{25} +(8.71688 + 6.33319i) q^{27} +(-2.33675 + 7.19177i) q^{29} +(-4.81829 + 3.50069i) q^{31} +(-10.2167 - 0.283805i) q^{33} +(0.0311712 - 0.0226472i) q^{35} +(3.31034 - 10.1882i) q^{37} +(8.60944 + 6.25512i) q^{39} +(0.954637 + 2.93807i) q^{41} +9.68676 q^{43} +6.49642 q^{45} +(0.403593 + 1.24213i) q^{47} +(5.66192 + 4.11362i) q^{49} +(-0.854793 + 2.63078i) q^{51} +(-1.64407 + 1.19449i) q^{53} +(-2.73630 + 1.87420i) q^{55} +(-3.00974 + 2.18671i) q^{57} +(0.0573598 - 0.176535i) q^{59} +(7.91147 + 5.74802i) q^{61} +(-0.0773487 - 0.238055i) q^{63} +3.45332 q^{65} -8.10586 q^{67} +(7.24130 + 22.2864i) q^{69} +(-5.81639 - 4.22586i) q^{71} +(3.92691 - 12.0858i) q^{73} +(2.49309 - 1.81133i) q^{75} +(0.101258 + 0.0779541i) q^{77} +(-10.2417 + 7.44102i) q^{79} +(4.23793 - 13.0430i) q^{81} +(-8.69073 - 6.31418i) q^{83} +(0.277384 + 0.853699i) q^{85} +23.3029 q^{87} -2.78161 q^{89} +(-0.0411165 - 0.126544i) q^{91} +(14.8482 + 10.7878i) q^{93} +(-0.373056 + 1.14815i) q^{95} +(-14.3301 + 10.4114i) q^{97} +(6.08656 + 20.6686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9}+O(q^{10}) $ 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9	$ 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37} - 3 q^{39} - 11 q^{41} + 16 q^{43} + 38 q^{45} + 10 q^{47} + 4 q^{49} - 26 q^{51} - 9 q^{53} - 3 q^{55} - 50 q^{57} + 60 q^{59} + 30 q^{61} - 52 q^{63} + 24 q^{65} + 4 q^{67} + 41 q^{69} + 10 q^{71} + q^{73} - 2 q^{75} - 4 q^{77} - 19 q^{79} - 31 q^{81} - 64 q^{83} - 11 q^{85} - 30 q^{87} + 24 q^{89} + 9 q^{91} + 45 q^{93} + 2 q^{95} - 3 q^{97} + 10 q^{99}+O(q^{100}) $ 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.952275	−	2.93080i	−0.549796	−	1.69210i	−0.709305	−	0.704902i	$-0.750991\pi$
$3$	−0.952275	−	2.93080i	−0.549796	−	1.69210i	0.159509	−	0.987197i	$-0.449009\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.0119064	+	0.0366440i	−0.00450018	+	0.0138501i	−0.953281	−	0.302084i	$-0.902318\pi$
$7$	−0.0119064	+	0.0366440i	−0.00450018	+	0.0138501i	0.948781	+	0.315934i	$0.102318\pi$
$8$		0			0
$9$	−5.25571	+	3.81850i	−1.75190	+	1.27283i
$10$		0			0
$11$	1.11209	−	3.12462i	0.335307	−	0.942109i
$11$	1.11209	−	3.12462i	0.335307	−	0.942109i
$12$		0			0
$13$	−2.79380	+	2.02981i	−0.774860	+	0.562969i	−0.903432	−	0.428731i	$-0.858961\pi$
$13$	−2.79380	+	2.02981i	−0.774860	+	0.562969i	0.128572	+	0.991700i	$0.458961\pi$
$14$		0			0
$15$	−0.952275	+	2.93080i	−0.245876	+	0.756729i
$16$		0			0
$17$	−0.726200	−	0.527615i	−0.176129	−	0.127965i	0.496228	−	0.868192i	$-0.334718\pi$
$17$	−0.726200	−	0.527615i	−0.176129	−	0.127965i	−0.672357	+	0.740227i	$0.734718\pi$
$18$		0			0
$19$	−0.373056	−	1.14815i	−0.0855850	−	0.263403i	0.899101	−	0.437741i	$-0.144221\pi$
$19$	−0.373056	−	1.14815i	−0.0855850	−	0.263403i	−0.984686	+	0.174338i	$0.944221\pi$
$20$		0			0
$21$	0.118734			0.0259100
$22$		0			0
$23$	−7.60421			−1.58559			−0.792794	−	0.609490i	$-0.791374\pi$
$23$	−7.60421			−1.58559			−0.792794	+	0.609490i	$0.791374\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	8.71688	+	6.33319i	1.67757	+	1.21882i
$28$		0			0
$29$	−2.33675	+	7.19177i	−0.433923	+	1.33548i	0.460263	+	0.887783i	$0.347755\pi$
$29$	−2.33675	+	7.19177i	−0.433923	+	1.33548i	−0.894186	+	0.447696i	$0.852245\pi$
$30$		0			0
$31$	−4.81829	+	3.50069i	−0.865391	+	0.628743i	−0.929346	−	0.369209i	$-0.879628\pi$
$31$	−4.81829	+	3.50069i	−0.865391	+	0.628743i	0.0639553	+	0.997953i	$0.479628\pi$
$32$		0			0
$33$	−10.2167	−	0.283805i	−1.77849	−	0.0494041i
$34$		0			0
$35$	0.0311712	−	0.0226472i	0.00526890	−	0.00382808i
$36$		0			0
$37$	3.31034	−	10.1882i	0.544216	−	1.67492i	−0.178631	−	0.983916i	$-0.557167\pi$
$37$	3.31034	−	10.1882i	0.544216	−	1.67492i	0.722847	−	0.691008i	$-0.242833\pi$
$38$		0			0
$39$	8.60944	+	6.25512i	1.37861	+	1.00162i
$40$		0			0
$41$	0.954637	+	2.93807i	0.149089	+	0.458849i	0.997514	−	0.0704663i	$-0.0224487\pi$
$41$	0.954637	+	2.93807i	0.149089	+	0.458849i	−0.848425	+	0.529316i	$0.822449\pi$
$42$		0			0
$43$	9.68676			1.47722			0.738609	−	0.674135i	$-0.235483\pi$
$43$	9.68676			1.47722			0.738609	+	0.674135i	$0.235483\pi$
$44$		0			0
$45$	6.49642			0.968429
$46$		0			0
$47$	0.403593	+	1.24213i	0.0588700	+	0.181183i	0.976167	−	0.217020i	$-0.0696338\pi$
$47$	0.403593	+	1.24213i	0.0588700	+	0.181183i	−0.917297	+	0.398204i	$0.869634\pi$
$48$		0			0
$49$	5.66192	+	4.11362i	0.808845	+	0.587661i
$50$		0			0
$51$	−0.854793	+	2.63078i	−0.119695	+	0.368383i
$52$		0			0
$53$	−1.64407	+	1.19449i	−0.225831	+	0.164075i	−0.694947	−	0.719061i	$-0.744572\pi$
$53$	−1.64407	+	1.19449i	−0.225831	+	0.164075i	0.469117	+	0.883136i	$0.344572\pi$
$54$		0			0
$55$	−2.73630	+	1.87420i	−0.368963	+	0.252718i
$56$		0			0
$57$	−3.00974	+	2.18671i	−0.398650	+	0.289636i
$58$		0			0
$59$	0.0573598	−	0.176535i	0.00746761	−	0.0229829i	−0.947253	−	0.320486i	$-0.896154\pi$
$59$	0.0573598	−	0.176535i	0.00746761	−	0.0229829i	0.954721	+	0.297503i	$0.0961538\pi$
$60$		0			0
$61$	7.91147	+	5.74802i	1.01296	+	0.735958i	0.964828	−	0.262883i	$-0.0846733\pi$
$61$	7.91147	+	5.74802i	1.01296	+	0.735958i	0.0481316	+	0.998841i	$0.484673\pi$
$62$		0			0
$63$	−0.0773487	−	0.238055i	−0.00974502	−	0.0299921i
$64$		0			0
$65$	3.45332			0.428332
$66$		0			0
$67$	−8.10586			−0.990288			−0.495144	−	0.868811i	$-0.664885\pi$
$67$	−8.10586			−0.990288			−0.495144	+	0.868811i	$0.664885\pi$
$68$		0			0
$69$	7.24130	+	22.2864i	0.871750	+	2.68297i
$70$		0			0
$71$	−5.81639	−	4.22586i	−0.690279	−	0.501517i	0.186473	−	0.982460i	$-0.440294\pi$
$71$	−5.81639	−	4.22586i	−0.690279	−	0.501517i	−0.876752	+	0.480943i	$0.840294\pi$
$72$		0			0
$73$	3.92691	−	12.0858i	0.459610	−	1.41453i	−0.406026	−	0.913861i	$-0.633086\pi$
$73$	3.92691	−	12.0858i	0.459610	−	1.41453i	0.865636	−	0.500673i	$-0.166914\pi$
$74$		0			0
$75$	2.49309	−	1.81133i	0.287877	−	0.209155i
$76$		0			0
$77$	0.101258	+	0.0779541i	0.0115394	+	0.00888370i
$78$		0			0
$79$	−10.2417	+	7.44102i	−1.15228	+	0.837181i	−0.988782	−	0.149363i	$-0.952278\pi$
$79$	−10.2417	+	7.44102i	−1.15228	+	0.837181i	−0.163498	+	0.986544i	$0.552278\pi$
$80$		0			0
$81$	4.23793	−	13.0430i	0.470881	−	1.44922i
$82$		0			0
$83$	−8.69073	−	6.31418i	−0.953931	−	0.693072i	−0.00219777	−	0.999998i	$-0.500700\pi$
$83$	−8.69073	−	6.31418i	−0.953931	−	0.693072i	−0.951733	+	0.306926i	$0.900700\pi$
$84$		0			0
$85$	0.277384	+	0.853699i	0.0300865	+	0.0925967i
$86$		0			0
$87$	23.3029			2.49833
$88$		0			0
$89$	−2.78161			−0.294850			−0.147425	−	0.989073i	$-0.547099\pi$
$89$	−2.78161			−0.294850			−0.147425	+	0.989073i	$0.547099\pi$
$90$		0			0
$91$	−0.0411165	−	0.126544i	−0.00431018	−	0.0132654i
$92$		0			0
$93$	14.8482	+	10.7878i	1.53968	+	1.11865i
$94$		0			0
$95$	−0.373056	+	1.14815i	−0.0382748	+	0.117798i
$96$		0			0
$97$	−14.3301	+	10.4114i	−1.45500	+	1.05712i	−0.470374	+	0.882467i	$0.655881\pi$
$97$	−14.3301	+	10.4114i	−1.45500	+	1.05712i	−0.984630	+	0.174655i	$0.944119\pi$
$98$		0			0
$99$	6.08656	+	20.6686i	0.611722	+	2.07727i
$100$		0			0
$101$	2.08495	−	1.51481i	0.207461	−	0.150729i	−0.479203	−	0.877704i	$-0.659074\pi$
$101$	2.08495	−	1.51481i	0.207461	−	0.150729i	0.686664	+	0.726975i	$0.259074\pi$
$102$		0			0
$103$	−1.14435	+	3.52196i	−0.112757	+	0.347029i	−0.991473	−	0.130316i	$-0.958401\pi$
$103$	−1.14435	+	3.52196i	−0.112757	+	0.347029i	0.878716	+	0.477345i	$0.158401\pi$
$104$		0			0
$105$	−0.0960581	−	0.0697903i	−0.00937431	−	0.00681084i
$106$		0			0
$107$	−5.93565	−	18.2681i	−0.573821	−	1.76604i	−0.640158	−	0.768243i	$-0.721131\pi$
$107$	−5.93565	−	18.2681i	−0.573821	−	1.76604i	0.0663370	−	0.997797i	$-0.478869\pi$
$108$		0			0
$109$	−6.51583			−0.624104			−0.312052	−	0.950065i	$-0.601016\pi$
$109$	−6.51583			−0.624104			−0.312052	+	0.950065i	$0.601016\pi$
$110$		0			0
$111$	−33.0118			−3.13334
$112$		0			0
$113$	−3.74482	−	11.5254i	−0.352283	−	1.08422i	−0.957568	−	0.288207i	$-0.906941\pi$
$113$	−3.74482	−	11.5254i	−0.352283	−	1.08422i	0.605285	−	0.796009i	$-0.293059\pi$
$114$		0			0
$115$	6.15194	+	4.46964i	0.573671	+	0.416796i
$116$		0			0
$117$	6.93256	−	21.3362i	0.640916	−	1.97254i
$118$		0			0
$119$	0.0279803	−	0.0203289i	0.00256495	−	0.00186355i
$120$		0			0
$121$	−8.52653	−	6.94970i	−0.775139	−	0.631791i
$122$		0			0
$123$	7.70182	−	5.59570i	0.694450	−	0.504547i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−2.33112	−	1.69366i	−0.206853	−	0.150288i	0.479536	−	0.877522i	$-0.340805\pi$
$127$	−2.33112	−	1.69366i	−0.206853	−	0.150288i	−0.686389	+	0.727235i	$0.740805\pi$
$128$		0			0
$129$	−9.22446	−	28.3900i	−0.812168	−	2.49960i
$130$		0			0
$131$	−3.67705			−0.321266			−0.160633	−	0.987014i	$-0.551353\pi$
$131$	−3.67705			−0.321266			−0.160633	+	0.987014i	$0.551353\pi$
$132$		0			0
$133$	0.0465145			0.00403332
$134$		0			0
$135$	−3.32955	−	10.2473i	−0.286562	−	0.881948i
$136$		0			0
$137$	5.18178	+	3.76478i	0.442709	+	0.321647i	0.786710	−	0.617322i	$-0.211783\pi$
$137$	5.18178	+	3.76478i	0.442709	+	0.321647i	−0.344001	+	0.938969i	$0.611783\pi$
$138$		0			0
$139$	−3.02495	+	9.30985i	−0.256573	+	0.789651i	0.736942	+	0.675956i	$0.236269\pi$
$139$	−3.02495	+	9.30985i	−0.256573	+	0.789651i	−0.993516	+	0.113696i	$0.963731\pi$
$140$		0			0
$141$	3.25611	−	2.36570i	0.274214	−	0.199228i
$142$		0			0
$143$	3.23545	+	10.9869i	0.270562	+	0.918770i
$144$		0			0
$145$	6.11769	−	4.44476i	0.508046	−	0.369117i
$146$		0			0
$147$	6.66451	−	20.5113i	0.549680	−	1.69174i
$148$		0			0
$149$	−15.7978	−	11.4778i	−1.29420	−	0.940295i	−0.294323	−	0.955706i	$-0.595094\pi$
$149$	−15.7978	−	11.4778i	−1.29420	−	0.940295i	−0.999881	+	0.0154112i	$0.995094\pi$
$150$		0			0
$151$	1.39409	+	4.29058i	0.113450	+	0.349162i	0.991621	−	0.129185i	$-0.0412361\pi$
$151$	1.39409	+	4.29058i	0.113450	+	0.349162i	−0.878171	+	0.478347i	$0.841236\pi$
$152$		0			0
$153$	5.83140			0.471440
$154$		0			0
$155$	5.95574			0.478376
$156$		0			0
$157$	1.40342	+	4.31927i	0.112005	+	0.344716i	0.991311	−	0.131542i	$-0.0419929\pi$
$157$	1.40342	+	4.31927i	0.112005	+	0.344716i	−0.879306	+	0.476258i	$0.841993\pi$
$158$		0			0
$159$	5.06641	+	3.68096i	0.401793	+	0.291919i
$160$		0			0
$161$	0.0905384	−	0.278649i	0.00713543	−	0.0219606i
$162$		0			0
$163$	−19.9540	+	14.4974i	−1.56292	+	1.13553i	−0.629352	+	0.777120i	$0.716680\pi$
$163$	−19.9540	+	14.4974i	−1.56292	+	1.13553i	−0.933566	+	0.358406i	$0.883320\pi$
$164$		0			0
$165$	8.09863	+	6.23480i	0.630478	+	0.485379i
$166$		0			0
$167$	13.4966	−	9.80583i	1.04440	−	0.758798i	0.0732569	−	0.997313i	$-0.476661\pi$
$167$	13.4966	−	9.80583i	1.04440	−	0.758798i	0.971139	+	0.238515i	$0.0766607\pi$
$168$		0			0
$169$	−0.332056	+	1.02196i	−0.0255427	+	0.0786125i
$170$		0			0
$171$	6.34488	+	4.60983i	0.485205	+	0.352522i
$172$		0			0
$173$	−4.08516	−	12.5728i	−0.310589	−	0.955895i	−0.977532	−	0.210787i	$-0.932398\pi$
$173$	−4.08516	−	12.5728i	−0.310589	−	0.955895i	0.666943	−	0.745109i	$-0.267602\pi$
$174$		0			0
$175$	−0.0385298			−0.00291258
$176$		0			0
$177$	−0.572012			−0.0429951
$178$		0			0
$179$	−6.38617	−	19.6546i	−0.477325	−	1.46905i	−0.842797	−	0.538232i	$-0.819092\pi$
$179$	−6.38617	−	19.6546i	−0.477325	−	1.46905i	0.365472	−	0.930822i	$-0.380908\pi$
$180$		0			0
$181$	3.04535	+	2.21257i	0.226359	+	0.164459i	0.695184	−	0.718832i	$-0.255323\pi$
$181$	3.04535	+	2.21257i	0.226359	+	0.164459i	−0.468826	+	0.883291i	$0.655323\pi$
$182$		0			0
$183$	9.31240	−	28.6606i	0.688392	−	2.11865i
$184$		0			0
$185$	−8.66657	+	6.29663i	−0.637179	+	0.462938i
$186$		0			0
$187$	−2.45619	+	1.68235i	−0.179615	+	0.123025i
$188$		0			0
$189$	−0.335860	+	0.244016i	−0.0244302	+	0.0177496i
$190$		0			0
$191$	2.92642	−	9.00661i	0.211749	−	0.651695i	−0.787620	−	0.616161i	$-0.788687\pi$
$191$	2.92642	−	9.00661i	0.211749	−	0.651695i	0.999368	−	0.0355338i	$-0.0113131\pi$
$192$		0			0
$193$	−13.2449	−	9.62296i	−0.953386	−	0.692676i	−0.00178079	−	0.999998i	$-0.500567\pi$
$193$	−13.2449	−	9.62296i	−0.953386	−	0.692676i	−0.951605	+	0.307323i	$0.900567\pi$
$194$		0			0
$195$	−3.28851	−	10.1210i	−0.235495	−	0.724780i
$196$		0			0
$197$	−15.1615			−1.08021			−0.540107	−	0.841596i	$-0.681616\pi$
$197$	−15.1615			−1.08021			−0.540107	+	0.841596i	$0.681616\pi$
$198$		0			0
$199$	−2.94883			−0.209037			−0.104519	−	0.994523i	$-0.533330\pi$
$199$	−2.94883			−0.209037			−0.104519	+	0.994523i	$0.533330\pi$
$200$		0			0
$201$	7.71901	+	23.7567i	0.544457	+	1.67567i
$202$		0			0
$203$	−0.235713	−	0.171256i	−0.0165438	−	0.0120198i
$204$		0			0
$205$	0.954637	−	2.93807i	0.0666747	−	0.205204i
$206$		0			0
$207$	39.9656	−	29.0367i	2.77780	−	2.01819i
$208$		0			0
$209$	−4.00240	−	0.111181i	−0.276852	−	0.00769058i
$210$		0			0
$211$	14.1094	−	10.2511i	0.971335	−	0.705716i	0.0155792	−	0.999879i	$-0.495041\pi$
$211$	14.1094	−	10.2511i	0.971335	−	0.705716i	0.955755	+	0.294163i	$0.0950408\pi$
$212$		0			0
$213$	−6.84634	+	21.0709i	−0.469103	+	1.44375i
$214$		0			0
$215$	−7.83675	−	5.69373i	−0.534462	−	0.388310i
$216$		0			0
$217$	−0.0709111	−	0.218242i	−0.00481376	−	0.0148152i
$218$		0			0
$219$	−39.1605			−2.64622
$220$		0			0
$221$	3.09981			0.208516
$222$		0			0
$223$	7.07077	+	21.7616i	0.473494	+	1.45726i	0.847978	+	0.530032i	$0.177820\pi$
$223$	7.07077	+	21.7616i	0.473494	+	1.45726i	−0.374484	+	0.927233i	$0.622180\pi$
$224$		0			0
$225$	−5.25571	−	3.81850i	−0.350381	−	0.254567i
$226$		0			0
$227$	−6.14352	+	18.9078i	−0.407760	+	1.25496i	0.510809	+	0.859694i	$0.329346\pi$
$227$	−6.14352	+	18.9078i	−0.407760	+	1.25496i	−0.918569	+	0.395261i	$0.870654\pi$
$228$		0			0
$229$	12.4562	−	9.04994i	0.823127	−	0.598037i	−0.0944794	−	0.995527i	$-0.530119\pi$
$229$	12.4562	−	9.04994i	0.823127	−	0.598037i	0.917607	+	0.397490i	$0.130119\pi$
$230$		0			0
$231$	0.132043	−	0.371000i	0.00868778	−	0.0244100i
$232$		0			0
$233$	−11.7463	+	8.53417i	−0.769525	+	0.559092i	−0.901817	−	0.432118i	$-0.857766\pi$
$233$	−11.7463	+	8.53417i	−0.769525	+	0.559092i	0.132292	+	0.991211i	$0.457766\pi$
$234$		0			0
$235$	0.403593	−	1.24213i	0.0263275	−	0.0810277i
$236$		0			0
$237$	31.5611	+	22.9305i	2.05011	+	1.48949i
$238$		0			0
$239$	−1.62621	−	5.00495i	−0.105191	−	0.323743i	0.884585	−	0.466380i	$-0.154442\pi$
$239$	−1.62621	−	5.00495i	−0.105191	−	0.323743i	−0.989775	+	0.142636i	$0.954442\pi$
$240$		0			0
$241$	10.2035			0.657265			0.328633	−	0.944458i	$-0.393412\pi$
$241$	10.2035			0.657265			0.328633	+	0.944458i	$0.393412\pi$
$242$		0			0
$243$	−9.93811			−0.637530
$244$		0			0
$245$	−2.16266	−	6.65598i	−0.138167	−	0.425235i
$246$		0			0
$247$	3.37277	+	2.45046i	0.214604	+	0.155919i
$248$		0			0
$249$	−10.2296	+	31.4836i	−0.648278	+	1.99519i
$250$		0			0
$251$	6.89285	−	5.00795i	0.435073	−	0.316099i	−0.348601	−	0.937271i	$-0.613343\pi$
$251$	6.89285	−	5.00795i	0.435073	−	0.316099i	0.783674	+	0.621172i	$0.213343\pi$
$252$		0			0
$253$	−8.45654	+	23.7603i	−0.531658	+	1.49380i
$254$		0			0
$255$	2.23788	−	1.62591i	0.140141	−	0.101819i
$256$		0			0
$257$	3.56962	−	10.9862i	0.222667	−	0.685298i	−0.775853	−	0.630913i	$-0.782680\pi$
$257$	3.56962	−	10.9862i	0.222667	−	0.685298i	0.998520	−	0.0543844i	$-0.0173196\pi$
$258$		0			0
$259$	0.333921	+	0.242608i	0.0207488	+	0.0150749i
$260$		0			0
$261$	−15.1805	−	46.7208i	−0.939649	−	2.89194i
$262$		0			0
$263$	2.91262			0.179600			0.0898000	−	0.995960i	$-0.471377\pi$
$263$	2.91262			0.179600			0.0898000	+	0.995960i	$0.471377\pi$
$264$		0			0
$265$	2.03218			0.124836
$266$		0			0
$267$	2.64886	+	8.15234i	0.162107	+	0.498915i
$268$		0			0
$269$	0.248336	+	0.180427i	0.0151413	+	0.0110008i	0.595330	−	0.803481i	$-0.297021\pi$
$269$	0.248336	+	0.180427i	0.0151413	+	0.0110008i	−0.580189	+	0.814482i	$0.697021\pi$
$270$		0			0
$271$	5.07375	−	15.6154i	0.308208	−	0.948567i	−0.670253	−	0.742133i	$-0.733814\pi$
$271$	5.07375	−	15.6154i	0.308208	−	0.948567i	0.978461	−	0.206434i	$-0.0661858\pi$
$272$		0			0
$273$	−0.331720	+	0.241008i	−0.0200766	+	0.0145865i
$274$		0			0
$275$	3.31535	+	0.0920959i	0.199923	+	0.00555359i
$276$		0			0
$277$	2.52061	−	1.83133i	0.151449	−	0.110034i	−0.509480	−	0.860482i	$-0.670162\pi$
$277$	2.52061	−	1.83133i	0.151449	−	0.110034i	0.660929	+	0.750448i	$0.270162\pi$
$278$		0			0
$279$	11.9562	−	36.7973i	0.715797	−	2.20300i
$280$		0			0
$281$	20.7508	+	15.0764i	1.23789	+	0.899380i	0.997456	−	0.0712855i	$-0.0227101\pi$
$281$	20.7508	+	15.0764i	1.23789	+	0.899380i	0.240434	+	0.970665i	$0.422710\pi$
$282$		0			0
$283$	6.27727	+	19.3195i	0.373145	+	1.14842i	0.944722	+	0.327874i	$0.106332\pi$
$283$	6.27727	+	19.3195i	0.373145	+	1.14842i	−0.571577	+	0.820549i	$0.693668\pi$
$284$		0			0
$285$	3.72025			0.220368
$286$		0			0
$287$	−0.119029			−0.00702605
$288$		0			0
$289$	−5.00430	−	15.4017i	−0.294371	−	0.905980i
$290$		0			0
$291$	44.1601	+	32.0842i	2.58871	+	1.88081i
$292$		0			0
$293$	9.30179	−	28.6280i	0.543416	−	1.67246i	−0.181310	−	0.983426i	$-0.558034\pi$
$293$	9.30179	−	28.6280i	0.543416	−	1.67246i	0.724726	−	0.689037i	$-0.241966\pi$
$294$		0			0
$295$	−0.150170	+	0.109105i	−0.00874323	+	0.00635233i
$296$		0			0
$297$	29.4827	−	20.1939i	1.71076	−	1.17177i
$298$		0			0
$299$	21.2446	−	15.4351i	1.22861	−	0.892636i
$300$		0			0
$301$	−0.115334	+	0.354962i	−0.00664774	+	0.0204596i
$302$		0			0
$303$	−6.42505	−	4.66807i	−0.369110	−	0.268174i
$304$		0			0
$305$	−3.02191	−	9.30049i	−0.173034	−	0.532544i
$306$		0			0
$307$	5.73211			0.327149			0.163574	−	0.986531i	$-0.447698\pi$
$307$	5.73211			0.327149			0.163574	+	0.986531i	$0.447698\pi$
$308$		0			0
$309$	11.4119			0.649200
$310$		0			0
$311$	8.12025	+	24.9916i	0.460457	+	1.41714i	0.864607	+	0.502449i	$0.167567\pi$
$311$	8.12025	+	24.9916i	0.460457	+	1.41714i	−0.404150	+	0.914693i	$0.632433\pi$
$312$		0			0
$313$	−8.17873	−	5.94220i	−0.462289	−	0.335873i	0.332139	−	0.943230i	$-0.392230\pi$
$313$	−8.17873	−	5.94220i	−0.462289	−	0.335873i	−0.794429	+	0.607357i	$0.792230\pi$
$314$		0			0
$315$	−0.0773487	+	0.238055i	−0.00435810	+	0.0134129i
$316$		0			0
$317$	−2.88667	+	2.09729i	−0.162132	+	0.117796i	−0.665893	−	0.746047i	$-0.731949\pi$
$317$	−2.88667	+	2.09729i	−0.162132	+	0.117796i	0.503761	+	0.863843i	$0.331949\pi$
$318$		0			0
$319$	19.8729	+	15.2993i	1.11267	+	0.856598i
$320$		0			0
$321$	−47.8877	+	34.7924i	−2.67283	+	1.94192i
$322$		0			0
$323$	−0.334867	+	1.03062i	−0.0186325	+	0.0573450i
$324$		0			0
$325$	−2.79380	−	2.02981i	−0.154972	−	0.112594i
$326$		0			0
$327$	6.20487	+	19.0966i	0.343130	+	1.05605i
$328$		0			0
$329$	−0.0503219			−0.00277434
$330$		0			0
$331$	−8.06105			−0.443075			−0.221538	−	0.975152i	$-0.571108\pi$
$331$	−8.06105			−0.443075			−0.221538	+	0.975152i	$0.571108\pi$
$332$		0			0
$333$	21.5053	+	66.1866i	1.17848	+	3.62700i
$334$		0			0
$335$	6.55778	+	4.76451i	0.358290	+	0.260313i
$336$		0			0
$337$	8.44928	−	26.0042i	0.460261	−	1.41654i	−0.404584	−	0.914501i	$-0.632584\pi$
$337$	8.44928	−	26.0042i	0.460261	−	1.41654i	0.864845	−	0.502038i	$-0.167416\pi$
$338$		0			0
$339$	−30.2125	+	21.9506i	−1.64092	+	1.19219i
$340$		0			0
$341$	5.57999	+	18.9484i	0.302173	+	1.02611i
$342$		0			0
$343$	−0.436351	+	0.317028i	−0.0235607	+	0.0171179i
$344$		0			0
$345$	7.24130	−	22.2864i	0.389858	−	1.19986i
$346$		0			0
$347$	−24.9457	−	18.1241i	−1.33915	−	0.972952i	−0.999475	−	0.0324105i	$-0.989682\pi$
$347$	−24.9457	−	18.1241i	−1.33915	−	0.972952i	−0.339679	−	0.940541i	$-0.610318\pi$
$348$		0			0
$349$	−7.35211	−	22.6275i	−0.393549	−	1.21122i	−0.930086	−	0.367343i	$-0.880268\pi$
$349$	−7.35211	−	22.6275i	−0.393549	−	1.21122i	0.536536	−	0.843877i	$-0.319732\pi$
$350$		0			0
$351$	−37.2084			−1.98604
$352$		0			0
$353$	2.87310			0.152920			0.0764598	−	0.997073i	$-0.475638\pi$
$353$	2.87310			0.152920			0.0764598	+	0.997073i	$0.475638\pi$
$354$		0			0
$355$	2.22166	+	6.83758i	0.117914	+	0.362901i
$356$		0			0
$357$	−0.0862249	−	0.0626460i	−0.00456350	−	0.00331558i
$358$		0			0
$359$	0.546690	−	1.68254i	0.0288532	−	0.0888009i	−0.935593	−	0.353081i	$-0.885134\pi$
$359$	0.546690	−	1.68254i	0.0288532	−	0.0888009i	0.964446	+	0.264280i	$0.0851342\pi$
$360$		0			0
$361$	14.1922	−	10.3113i	0.746960	−	0.542698i
$362$		0			0
$363$	−12.2486	+	31.6076i	−0.642884	+	1.65897i
$364$		0			0
$365$	−10.2808	+	7.46943i	−0.538121	+	0.390968i
$366$		0			0
$367$	−1.76698	+	5.43822i	−0.0922358	+	0.283873i	−0.986523	−	0.163620i	$-0.947683\pi$
$367$	−1.76698	+	5.43822i	−0.0922358	+	0.283873i	0.894288	+	0.447493i	$0.147683\pi$
$368$		0			0
$369$	−16.2363	−	11.7964i	−0.845229	−	0.614095i
$370$		0			0
$371$	−0.0241959	−	0.0744673i	−0.00125619	−	0.00386615i
$372$		0			0
$373$	18.1456			0.939543			0.469772	−	0.882788i	$-0.344336\pi$
$373$	18.1456			0.939543			0.469772	+	0.882788i	$0.344336\pi$
$374$		0			0
$375$	−3.08163			−0.159134
$376$		0			0
$377$	−8.06955	−	24.8355i	−0.415603	−	1.27909i
$378$		0			0
$379$	−25.4876	−	18.5178i	−1.30921	−	0.951196i	−1.00000		0.000202224i	$-0.999936\pi$
$379$	−25.4876	−	18.5178i	−1.30921	−	0.951196i	−0.309209	−	0.950994i	$-0.600064\pi$
$380$		0			0
$381$	−2.74390	+	8.44486i	−0.140574	+	0.432644i
$382$		0			0
$383$	2.33181	−	1.69416i	0.119150	−	0.0865673i	−0.526615	−	0.850104i	$-0.676539\pi$
$383$	2.33181	−	1.69416i	0.119150	−	0.0865673i	0.645764	+	0.763537i	$0.276539\pi$
$384$		0			0
$385$	−0.0360989	−	0.122584i	−0.00183977	−	0.00624746i
$386$		0			0
$387$	−50.9108	+	36.9889i	−2.58794	+	1.88025i
$388$		0			0
$389$	−10.5948	+	32.6075i	−0.537179	+	1.65327i	0.201713	+	0.979445i	$0.435349\pi$
$389$	−10.5948	+	32.6075i	−0.537179	+	1.65327i	−0.738892	+	0.673823i	$0.764651\pi$
$390$		0			0
$391$	5.52218	+	4.01210i	0.279268	+	0.202900i
$392$		0			0
$393$	3.50156	+	10.7767i	0.176631	+	0.543613i
$394$		0			0
$395$	12.6594			0.636965
$396$		0			0
$397$	−14.4405			−0.724746			−0.362373	−	0.932033i	$-0.618033\pi$
$397$	−14.4405			−0.724746			−0.362373	+	0.932033i	$0.618033\pi$
$398$		0			0
$399$	−0.0442946	−	0.136325i	−0.00221750	−	0.00682477i
$400$		0			0
$401$	−3.59985	−	2.61545i	−0.179768	−	0.130609i	0.494262	−	0.869313i	$-0.335438\pi$
$401$	−3.59985	−	2.61545i	−0.179768	−	0.130609i	−0.674030	+	0.738704i	$0.735438\pi$
$402$		0			0
$403$	6.35558	−	19.5605i	0.316594	−	0.974376i
$404$		0			0
$405$	−11.0950	+	8.06101i	−0.551317	+	0.400555i
$406$		0			0
$407$	−28.1528	−	21.6737i	−1.39548	−	1.07432i
$408$		0			0
$409$	−24.6453	+	17.9059i	−1.21863	+	0.885389i	−0.995986	−	0.0895101i	$-0.971470\pi$
$409$	−24.6453	+	17.9059i	−1.21863	+	0.885389i	−0.222647	+	0.974899i	$0.571470\pi$
$410$		0			0
$411$	6.09935	−	18.7719i	0.300859	−	0.925948i
$412$		0			0
$413$	0.00578601	+	0.00420378i	0.000284711	+	0.000206855i
$414$		0			0
$415$	3.31956	+	10.2166i	0.162951	+	0.501511i
$416$		0			0
$417$	30.1659			1.47723
$418$		0			0
$419$	14.5620			0.711402			0.355701	−	0.934600i	$-0.384242\pi$
$419$	14.5620			0.711402			0.355701	+	0.934600i	$0.384242\pi$
$420$		0			0
$421$	0.201378	+	0.619779i	0.00981459	+	0.0302062i	0.955844	−	0.293875i	$-0.0949449\pi$
$421$	0.201378	+	0.619779i	0.00981459	+	0.0302062i	−0.946029	+	0.324081i	$0.894945\pi$
$422$		0			0
$423$	−6.86424	−	4.98716i	−0.333751	−	0.242484i
$424$		0			0
$425$	0.277384	−	0.853699i	0.0134551	−	0.0414105i
$426$		0			0
$427$	−0.304827	+	0.221470i	−0.0147516	+	0.0107177i
$428$		0			0
$429$	29.1193	−	19.9450i	1.40590	−	0.962954i
$430$		0			0
$431$	−27.4797	+	19.9652i	−1.32365	+	0.961689i	−0.323773	+	0.946135i	$0.604951\pi$
$431$	−27.4797	+	19.9652i	−1.32365	+	0.961689i	−0.999879	+	0.0155542i	$0.995049\pi$
$432$		0			0
$433$	−9.83495	+	30.2689i	−0.472637	+	1.45463i	0.376480	+	0.926425i	$0.377134\pi$
$433$	−9.83495	+	30.2689i	−0.472637	+	1.45463i	−0.849118	+	0.528204i	$0.822866\pi$
$434$		0			0
$435$	−18.8524	−	13.6971i	−0.903905	−	0.656725i
$436$		0			0
$437$	2.83680	+	8.73077i	0.135702	+	0.417649i
$438$		0			0
$439$	1.74428			0.0832501			0.0416251	−	0.999133i	$-0.486747\pi$
$439$	1.74428			0.0832501			0.0416251	+	0.999133i	$0.486747\pi$
$440$		0			0
$441$	−45.4653			−2.16501
$442$		0			0
$443$	−0.284462	−	0.875485i	−0.0135152	−	0.0415955i	0.944071	−	0.329741i	$-0.106961\pi$
$443$	−0.284462	−	0.875485i	−0.0135152	−	0.0415955i	−0.957587	+	0.288145i	$0.906961\pi$
$444$		0			0
$445$	2.25037	+	1.63499i	0.106678	+	0.0775059i
$446$		0			0
$447$	−18.5952	+	57.2301i	−0.879523	+	2.70689i
$448$		0			0
$449$	−4.04783	+	2.94092i	−0.191029	+	0.138791i	−0.679189	−	0.733963i	$-0.737668\pi$
$449$	−4.04783	+	2.94092i	−0.191029	+	0.138791i	0.488160	+	0.872754i	$0.337668\pi$
$450$		0			0
$451$	10.2420	+	0.284509i	0.482277	+	0.0133970i
$452$		0			0
$453$	11.2473	−	8.17162i	0.528443	−	0.383936i
$454$		0			0
$455$	−0.0411165	+	0.126544i	−0.00192757	+	0.00593245i
$456$		0			0
$457$	8.88144	+	6.45275i	0.415456	+	0.301847i	0.775807	−	0.630970i	$-0.217343\pi$
$457$	8.88144	+	6.45275i	0.415456	+	0.301847i	−0.360351	+	0.932817i	$0.617343\pi$
$458$		0			0
$459$	−2.98871	−	9.19832i	−0.139501	−	0.429341i
$460$		0			0
$461$	−8.89371			−0.414221			−0.207111	−	0.978318i	$-0.566406\pi$
$461$	−8.89371			−0.414221			−0.207111	+	0.978318i	$0.566406\pi$
$462$		0			0
$463$	8.95007			0.415945			0.207972	−	0.978135i	$-0.433314\pi$
$463$	8.95007			0.415945			0.207972	+	0.978135i	$0.433314\pi$
$464$		0			0
$465$	−5.67150	−	17.4551i	−0.263009	−	0.809460i
$466$		0			0
$467$	9.86441	+	7.16691i	0.456470	+	0.331645i	0.792145	−	0.610333i	$-0.208964\pi$
$467$	9.86441	+	7.16691i	0.456470	+	0.331645i	−0.335675	+	0.941978i	$0.608964\pi$
$468$		0			0
$469$	0.0965112	−	0.297031i	0.00445647	−	0.0137156i
$470$		0			0
$471$	11.3225	−	8.22627i	0.521713	−	0.379047i
$472$		0			0
$473$	10.7725	−	30.2675i	0.495321	−	1.39170i
$474$		0			0
$475$	0.976674	−	0.709595i	0.0448129	−	0.0325585i
$476$		0			0
$477$	4.07962	−	12.5558i	0.186793	−	0.574889i
$478$		0			0
$479$	−34.5002	−	25.0659i	−1.57636	−	1.14529i	−0.920728	−	0.390205i	$-0.872404\pi$
$479$	−34.5002	−	25.0659i	−1.57636	−	1.14529i	−0.655627	−	0.755085i	$-0.727596\pi$
$480$		0			0
$481$	11.4317	+	35.1830i	0.521239	+	1.60421i
$482$		0			0
$483$	−0.902881			−0.0410825
$484$		0			0
$485$	17.7130			0.804306
$486$		0			0
$487$	−3.41885	−	10.5221i	−0.154923	−	0.476804i	0.843230	−	0.537553i	$-0.180651\pi$
$487$	−3.41885	−	10.5221i	−0.154923	−	0.476804i	−0.998153	+	0.0607488i	$0.980651\pi$
$488$		0			0
$489$	61.4908	+	44.6757i	2.78071	+	2.02030i
$490$		0			0
$491$	6.08215	−	18.7189i	0.274484	−	0.844774i	−0.714872	−	0.699256i	$-0.753515\pi$
$491$	6.08215	−	18.7189i	0.274484	−	0.844774i	0.989356	−	0.145519i	$-0.0464850\pi$
$492$		0			0
$493$	5.49143	−	3.98976i	0.247322	−	0.179690i
$494$		0			0
$495$	7.22458	−	20.2989i	0.324721	−	0.912366i
$496$		0			0
$497$	0.224104	−	0.162821i	0.0100524	−	0.00730353i
$498$		0			0
$499$	3.46256	−	10.6567i	0.155006	−	0.477058i	−0.843156	−	0.537669i	$-0.819305\pi$
$499$	3.46256	−	10.6567i	0.155006	−	0.477058i	0.998161	+	0.0606111i	$0.0193049\pi$
$500$		0			0
$501$	−41.5914	−	30.2179i	−1.85817	−	1.35004i
$502$		0			0
$503$	7.83954	+	24.1276i	0.349548	+	1.07580i	0.959104	+	0.283055i	$0.0913477\pi$
$503$	7.83954	+	24.1276i	0.349548	+	1.07580i	−0.609556	+	0.792743i	$0.708652\pi$
$504$		0			0
$505$	−2.57715			−0.114681
$506$		0			0
$507$	3.31138			0.147063
$508$		0			0
$509$	−11.5509	−	35.5501i	−0.511986	−	1.57573i	−0.788700	−	0.614778i	$-0.789246\pi$
$509$	−11.5509	−	35.5501i	−0.511986	−	1.57573i	0.276715	−	0.960952i	$-0.410754\pi$
$510$		0			0
$511$	0.396116	+	0.287795i	0.0175232	+	0.0127313i
$512$		0			0
$513$	4.01955	−	12.3709i	0.177468	−	0.546189i
$514$		0			0
$515$	2.99596	−	2.17669i	0.132018	−	0.0959165i
$516$		0			0
$517$	4.33002	+	0.120282i	0.190434	+	0.00529000i
$518$		0			0
$519$	−32.9583	+	23.9456i	−1.44671	+	1.05110i
$520$		0			0
$521$	8.19156	−	25.2110i	0.358879	−	1.10452i	−0.594847	−	0.803839i	$-0.702787\pi$
$521$	8.19156	−	25.2110i	0.358879	−	1.10452i	0.953726	−	0.300677i	$-0.0972126\pi$
$522$		0			0
$523$	14.8351	+	10.7783i	0.648692	+	0.471302i	0.862825	−	0.505502i	$-0.168693\pi$
$523$	14.8351	+	10.7783i	0.648692	+	0.471302i	−0.214134	+	0.976804i	$0.568693\pi$
$524$		0			0
$525$	0.0366909	+	0.112923i	0.00160132	+	0.00492837i
$526$		0			0
$527$	5.34606			0.232878
$528$		0			0
$529$	34.8240			1.51409
$530$		0			0
$531$	0.372633	+	1.14685i	0.0161709	+	0.0497689i
$532$		0			0
$533$	−8.63079	−	6.27064i	−0.373841	−	0.271611i
$534$		0			0
$535$	−5.93565	+	18.2681i	−0.256621	+	0.789797i
$536$		0			0
$537$	−51.5223	+	37.4332i	−2.22335	+	1.61536i
$538$		0			0
$539$	19.1501	−	13.1166i	0.824852	−	0.564974i
$540$		0			0
$541$	−4.61731	+	3.35467i	−0.198514	+	0.144229i	−0.682602	−	0.730791i	$-0.739152\pi$
$541$	−4.61731	+	3.35467i	−0.198514	+	0.144229i	0.484088	+	0.875019i	$0.339152\pi$
$542$		0			0
$543$	3.58460	−	11.0323i	0.153830	−	0.473440i
$544$		0			0
$545$	5.27142	+	3.82991i	0.225803	+	0.164055i
$546$		0			0
$547$	−4.22184	−	12.9935i	−0.180513	−	0.555562i	0.819329	−	0.573323i	$-0.194346\pi$
$547$	−4.22184	−	12.9935i	−0.180513	−	0.555562i	−0.999842	+	0.0177616i	$0.994346\pi$
$548$		0			0
$549$	−63.5292			−2.71136
$550$		0			0
$551$	9.12897			0.388907
$552$		0			0
$553$	−0.150728	−	0.463892i	−0.00640959	−	0.0197267i
$554$		0			0
$555$	26.7071	+	19.4039i	1.13365	+	0.823648i
$556$		0			0
$557$	4.35243	−	13.3954i	0.184418	−	0.567581i	−0.815520	−	0.578729i	$-0.803549\pi$
$557$	4.35243	−	13.3954i	0.184418	−	0.567581i	0.999938	+	0.0111484i	$0.00354872\pi$
$558$		0			0
$559$	−27.0628	+	19.6623i	−1.14464	+	0.831627i
$560$		0			0
$561$	7.26959	+	5.59656i	0.306923	+	0.236287i
$562$		0			0
$563$	−6.73373	+	4.89234i	−0.283793	+	0.206187i	−0.720570	−	0.693382i	$-0.756120\pi$
$563$	−6.73373	+	4.89234i	−0.283793	+	0.206187i	0.436777	+	0.899570i	$0.356120\pi$
$564$		0			0
$565$	−3.74482	+	11.5254i	−0.157546	+	0.484876i
$566$		0			0
$567$	0.427489	+	0.310589i	0.0179529	+	0.0130435i
$568$		0			0
$569$	5.29170	+	16.2862i	0.221840	+	0.682752i	0.998597	+	0.0529523i	$0.0168631\pi$
$569$	5.29170	+	16.2862i	0.221840	+	0.682752i	−0.776757	+	0.629800i	$0.783137\pi$
$570$		0			0
$571$	33.6964			1.41015			0.705076	−	0.709132i	$-0.250913\pi$
$571$	33.6964			1.41015			0.705076	+	0.709132i	$0.250913\pi$
$572$		0			0
$573$	−29.1833			−1.21915
$574$		0			0
$575$	−2.34983	−	7.23203i	−0.0979947	−	0.301597i
$576$		0			0
$577$	24.5965	+	17.8704i	1.02397	+	0.743955i	0.967092	−	0.254426i	$-0.0818865\pi$
$577$	24.5965	+	17.8704i	1.02397	+	0.743955i	0.0568745	+	0.998381i	$0.481886\pi$
$578$		0			0
$579$	−15.5902	+	47.9818i	−0.647907	+	1.99405i
$580$		0			0
$581$	0.334852	−	0.243284i	0.0138920	−	0.0100931i
$582$		0			0
$583$	1.90397	+	6.46547i	0.0788545	+	0.267773i
$584$		0			0
$585$	−18.1497	+	13.1865i	−0.750397	+	0.545195i
$586$		0			0
$587$	2.89912	−	8.92256i	0.119659	−	0.368273i	−0.873231	−	0.487306i	$-0.837979\pi$
$587$	2.89912	−	8.92256i	0.119659	−	0.368273i	0.992890	+	0.119033i	$0.0379795\pi$
$588$		0			0
$589$	5.81681	+	4.22616i	0.239678	+	0.174136i
$590$		0			0
$591$	14.4379	+	44.4354i	0.593898	+	1.82783i
$592$		0			0
$593$	30.1444			1.23788			0.618941	−	0.785437i	$-0.287562\pi$
$593$	30.1444			1.23788			0.618941	+	0.785437i	$0.287562\pi$
$594$		0			0
$595$	−0.0345856			−0.00141787
$596$		0			0
$597$	2.80810	+	8.64244i	0.114928	+	0.353711i
$598$		0			0
$599$	8.25456	+	5.99729i	0.337272	+	0.245043i	0.743510	−	0.668725i	$-0.233160\pi$
$599$	8.25456	+	5.99729i	0.337272	+	0.245043i	−0.406238	+	0.913767i	$0.633160\pi$
$600$		0			0
$601$	−5.41926	+	16.6788i	−0.221056	+	0.680341i	0.777612	+	0.628745i	$0.216431\pi$
$601$	−5.41926	+	16.6788i	−0.221056	+	0.680341i	−0.998668	+	0.0515962i	$0.983569\pi$
$602$		0			0
$603$	42.6021	−	30.9522i	1.73489	−	1.26047i
$604$		0			0
$605$	2.81317	+	10.6342i	0.114372	+	0.432341i
$606$		0			0
$607$	−3.49951	+	2.54254i	−0.142041	+	0.103198i	−0.656536	−	0.754294i	$-0.727979\pi$
$607$	−3.49951	+	2.54254i	−0.142041	+	0.103198i	0.514496	+	0.857493i	$0.327979\pi$
$608$		0			0
$609$	−0.277452	+	0.853910i	−0.0112429	+	0.0346022i
$610$		0			0
$611$	−3.64885	−	2.65104i	−0.147617	−	0.107250i
$612$		0			0
$613$	3.87702	+	11.9323i	0.156592	+	0.481939i	0.998319	−	0.0579639i	$-0.0184608\pi$
$613$	3.87702	+	11.9323i	0.156592	+	0.481939i	−0.841727	+	0.539903i	$0.818461\pi$
$614$		0			0
$615$	−9.51997			−0.383882
$616$		0			0
$617$	17.1256			0.689452			0.344726	−	0.938703i	$-0.387972\pi$
$617$	17.1256			0.689452			0.344726	+	0.938703i	$0.387972\pi$
$618$		0			0
$619$	2.25335	+	6.93510i	0.0905698	+	0.278745i	0.986074	−	0.166308i	$-0.0531847\pi$
$619$	2.25335	+	6.93510i	0.0905698	+	0.278745i	−0.895504	+	0.445053i	$0.853185\pi$
$620$		0			0
$621$	−66.2850	−	48.1589i	−2.65993	−	1.93255i
$622$		0			0
$623$	0.0331188	−	0.101929i	0.00132688	−	0.00408371i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	3.48554	+	11.8361i	0.139199	+	0.472689i
$628$		0			0
$629$	−7.77939	+	5.65206i	−0.310185	+	0.225362i
$630$		0			0
$631$	−8.52294	+	26.2309i	−0.339293	+	1.04424i	0.625276	+	0.780404i	$0.284986\pi$
$631$	−8.52294	+	26.2309i	−0.339293	+	1.04424i	−0.964569	+	0.263832i	$0.915014\pi$
$632$		0			0
$633$	−43.4801	−	31.5901i	−1.72818	−	1.25559i
$634$		0			0
$635$	0.890407	+	2.74039i	0.0353347	+	0.108749i
$636$		0			0
$637$	−24.1681			−0.957577
$638$		0			0
$639$	46.7057			1.84765
$640$		0			0
$641$	7.63135	+	23.4869i	0.301420	+	0.927676i	0.980989	+	0.194064i	$0.0621670\pi$
$641$	7.63135	+	23.4869i	0.301420	+	0.927676i	−0.679568	+	0.733612i	$0.737833\pi$
$642$		0			0
$643$	−20.8102	−	15.1195i	−0.820675	−	0.596255i	0.0962308	−	0.995359i	$-0.469321\pi$
$643$	−20.8102	−	15.1195i	−0.820675	−	0.596255i	−0.916906	+	0.399104i	$0.869321\pi$
$644$		0			0
$645$	−9.22446	+	28.3900i	−0.363213	+	1.11785i
$646$		0			0
$647$	7.41077	−	5.38424i	0.291348	−	0.211676i	−0.432504	−	0.901632i	$-0.642370\pi$
$647$	7.41077	−	5.38424i	0.291348	−	0.211676i	0.723852	+	0.689956i	$0.242370\pi$
$648$		0			0
$649$	−0.487817	−	0.375550i	−0.0191485	−	0.0147416i
$650$		0			0
$651$	−0.572097	+	0.415653i	−0.0224222	+	0.0162907i
$652$		0			0
$653$	6.16121	−	18.9623i	0.241107	−	0.742050i	−0.755146	−	0.655557i	$-0.772434\pi$
$653$	6.16121	−	18.9623i	0.241107	−	0.742050i	0.996252	−	0.0864933i	$-0.0275661\pi$
$654$		0			0
$655$	2.97480	+	2.16132i	0.116235	+	0.0844496i
$656$		0			0
$657$	25.5109	+	78.5144i	0.995274	+	3.06314i
$658$		0			0
$659$	21.8117			0.849662			0.424831	−	0.905273i	$-0.360333\pi$
$659$	21.8117			0.849662			0.424831	+	0.905273i	$0.360333\pi$
$660$		0			0
$661$	32.2443			1.25416			0.627079	−	0.778955i	$-0.284250\pi$
$661$	32.2443			1.25416			0.627079	+	0.778955i	$0.284250\pi$
$662$		0			0
$663$	−2.95188	−	9.08494i	−0.114641	−	0.352830i
$664$		0			0
$665$	−0.0376310	−	0.0273405i	−0.00145927	−	0.00106022i
$666$		0			0
$667$	17.7691	−	54.6877i	0.688023	−	2.11752i
$668$		0			0
$669$	57.0456	−	41.4461i	2.20551	−	1.60240i
$670$		0			0
$671$	26.7586	−	18.3280i	1.03300	−	0.707546i
$672$		0			0
$673$	1.41327	−	1.02680i	0.0544774	−	0.0395801i	−0.560213	−	0.828348i	$-0.689281\pi$
$673$	1.41327	−	1.02680i	0.0544774	−	0.0395801i	0.614691	+	0.788768i	$0.289281\pi$
$674$		0			0
$675$	−3.32955	+	10.2473i	−0.128155	+	0.394419i
$676$		0			0
$677$	−6.58002	−	4.78067i	−0.252891	−	0.183736i	0.454116	−	0.890942i	$-0.349955\pi$
$677$	−6.58002	−	4.78067i	−0.252891	−	0.183736i	−0.707007	+	0.707207i	$0.749955\pi$
$678$		0			0
$679$	−0.210897	−	0.649075i	−0.00809350	−	0.0249092i
$680$		0			0
$681$	61.2653			2.34769
$682$		0			0
$683$	−24.4004			−0.933655			−0.466827	−	0.884348i	$-0.654603\pi$
$683$	−24.4004			−0.933655			−0.466827	+	0.884348i	$0.654603\pi$
$684$		0			0
$685$	−1.97926	−	6.09154i	−0.0756237	−	0.232746i
$686$		0			0
$687$	−38.3853	−	27.8885i	−1.46449	−	1.06401i
$688$		0			0
$689$	2.16862	−	6.67431i	0.0826177	−	0.254271i
$690$		0			0
$691$	14.6212	−	10.6230i	0.556218	−	0.404116i	−0.273855	−	0.961771i	$-0.588299\pi$
$691$	14.6212	−	10.6230i	0.556218	−	0.404116i	0.830073	+	0.557655i	$0.188299\pi$
$692$		0			0
$693$	−0.829850	−	0.0230521i	−0.0315234	−	0.000875678i
$694$		0			0
$695$	7.91943	−	5.75380i	0.300401	−	0.218254i
$696$		0			0
$697$	0.856913	−	2.63731i	0.0324579	−	0.0998951i
$698$		0			0
$699$	36.1977	+	26.2991i	1.36912	+	0.994725i
$700$		0			0
$701$	5.03007	+	15.4810i	0.189983	+	0.584708i	0.999999	−	0.00170043i	$-0.000541262\pi$
$701$	5.03007	+	15.4810i	0.189983	+	0.584708i	−0.810015	+	0.586409i	$0.800541\pi$
$702$		0			0
$703$	−12.9325			−0.487758
$704$		0			0
$705$	−4.02477			−0.151582
$706$		0			0
$707$	0.0306844	+	0.0944369i	0.00115401	+	0.00355166i
$708$		0			0
$709$	27.3374	+	19.8618i	1.02668	+	0.745924i	0.967641	−	0.252332i	$-0.0811975\pi$
$709$	27.3374	+	19.8618i	1.02668	+	0.745924i	0.0590354	+	0.998256i	$0.481198\pi$
$710$		0			0
$711$	25.4138	−	78.2158i	0.953094	−	2.93332i
$712$		0			0
$713$	36.6393	−	26.6200i	1.37215	−	0.996927i
$714$		0			0
$715$	3.84040	−	10.7903i	0.143623	−	0.403536i
$716$		0			0
$717$	−13.1199	+	9.53218i	−0.489972	+	0.355986i
$718$		0			0
$719$	−7.26594	+	22.3623i	−0.270974	+	0.833972i	0.719283	+	0.694718i	$0.244471\pi$
$719$	−7.26594	+	22.3623i	−0.270974	+	0.833972i	−0.990257	+	0.139255i	$0.955529\pi$
$720$		0			0
$721$	−0.115434	−	0.0838674i	−0.00429897	−	0.00312339i
$722$		0			0
$723$	−9.71654	−	29.9044i	−0.361362	−	1.11216i
$724$		0			0
$725$	−7.56188			−0.280841
$726$		0			0
$727$	−2.84884			−0.105658			−0.0528288	−	0.998604i	$-0.516824\pi$
$727$	−2.84884			−0.105658			−0.0528288	+	0.998604i	$0.516824\pi$
$728$		0			0
$729$	−3.24997	−	10.0024i	−0.120369	−	0.370458i
$730$		0			0
$731$	−7.03452	−	5.11088i	−0.260181	−	0.189033i
$732$		0			0
$733$	−7.79223	+	23.9820i	−0.287813	+	0.885796i	0.697729	+	0.716362i	$0.254194\pi$
$733$	−7.79223	+	23.9820i	−0.287813	+	0.885796i	−0.985541	+	0.169434i	$0.945806\pi$
$734$		0			0
$735$	−17.4479	+	12.6767i	−0.643576	+	0.467585i
$736$		0			0
$737$	−9.01442	+	25.3278i	−0.332050	+	0.932960i
$738$		0			0
$739$	29.4358	−	21.3864i	1.08281	−	0.786710i	0.104643	−	0.994510i	$-0.466630\pi$
$739$	29.4358	−	21.3864i	1.08281	−	0.786710i	0.978171	+	0.207799i	$0.0666302\pi$
$740$		0			0
$741$	3.97001	−	12.2184i	0.145842	−	0.448855i
$742$		0			0
$743$	−19.9443	−	14.4904i	−0.731687	−	0.531601i	0.158410	−	0.987373i	$-0.449363\pi$
$743$	−19.9443	−	14.4904i	−0.731687	−	0.531601i	−0.890097	+	0.455772i	$0.849363\pi$
$744$		0			0
$745$	6.03422	+	18.5714i	0.221077	+	0.680404i
$746$		0			0
$747$	69.7867			2.55336
$748$		0			0
$749$	0.740087			0.0270422
$750$		0			0
$751$	−12.2040	−	37.5599i	−0.445328	−	1.37058i	−0.882123	−	0.471019i	$-0.843886\pi$
$751$	−12.2040	−	37.5599i	−0.445328	−	1.37058i	0.436795	−	0.899561i	$-0.356114\pi$
$752$		0			0
$753$	−21.2412	−	15.4326i	−0.774072	−	0.562396i
$754$		0			0
$755$	1.39409	−	4.29058i	0.0507362	−	0.156150i
$756$		0			0
$757$	7.53772	−	5.47647i	0.273963	−	0.199046i	−0.442317	−	0.896859i	$-0.645843\pi$
$757$	7.53772	−	5.47647i	0.273963	−	0.199046i	0.716280	+	0.697813i	$0.245843\pi$
$758$		0			0
$759$	77.6896	+	2.15811i	2.81995	+	0.0783346i
$760$		0			0
$761$	0.343853	−	0.249824i	0.0124647	−	0.00905611i	−0.581535	−	0.813521i	$-0.697548\pi$
$761$	0.343853	−	0.249824i	0.0124647	−	0.00905611i	0.594000	+	0.804465i	$0.297548\pi$
$762$		0			0
$763$	0.0775798	−	0.238766i	0.00280858	−	0.00864391i
$764$		0			0
$765$	−4.71770	−	3.42761i	−0.170569	−	0.123925i
$766$		0			0
$767$	0.198082	+	0.609634i	0.00715232	+	0.0220126i
$768$		0			0
$769$	5.37492			0.193825			0.0969123	−	0.995293i	$-0.469103\pi$
$769$	5.37492			0.193825			0.0969123	+	0.995293i	$0.469103\pi$
$770$		0			0
$771$	−35.5975			−1.28201
$772$		0			0
$773$	1.04627	+	3.22010i	0.0376318	+	0.115819i	0.968108	−	0.250534i	$-0.0806062\pi$
$773$	1.04627	+	3.22010i	0.0376318	+	0.115819i	−0.930476	+	0.366353i	$0.880606\pi$
$774$		0			0
$775$	−4.81829	−	3.50069i	−0.173078	−	0.125749i
$776$		0			0
$777$	0.393051	−	1.20969i	0.0141006	−	0.0433972i
$778$		0			0
$779$	3.01721	−	2.19213i	0.108103	−	0.0785412i
$780$		0			0
$781$	−19.6725	+	13.4745i	−0.703939	+	0.482156i
$782$		0			0
$783$	−65.9160	+	47.8908i	−2.35565	+	1.71148i
$784$		0			0
$785$	1.40342	−	4.31927i	0.0500901	−	0.154161i
$786$		0			0
$787$	−29.5871	−	21.4963i	−1.05467	−	0.766261i	−0.0815730	−	0.996667i	$-0.525994\pi$
$787$	−29.5871	−	21.4963i	−1.05467	−	0.766261i	−0.973094	+	0.230407i	$0.925994\pi$
$788$		0			0
$789$	−2.77362	−	8.53631i	−0.0987434	−	0.303901i
$790$		0			0
$791$	0.466923			0.0166019
$792$		0			0
$793$	−33.7704			−1.19922
$794$		0			0
$795$	−1.93520	−	5.95592i	−0.0686344	−	0.211235i
$796$		0			0
$797$	−21.4202	−	15.5627i	−0.758741	−	0.551257i	0.139783	−	0.990182i	$-0.455359\pi$
$797$	−21.4202	−	15.5627i	−0.758741	−	0.551257i	−0.898524	+	0.438925i	$0.855359\pi$
$798$		0			0
$799$	0.362278	−	1.11498i	0.0128165	−	0.0394450i
$800$		0			0
$801$	14.6193	−	10.6216i	0.516549	−	0.375295i
$802$		0			0
$803$	−33.3965	−	25.7106i	−1.17854	−	0.907306i
$804$		0			0
$805$	−0.237033	+	0.172214i	−0.00835430	+	0.00606976i
$806$		0			0
$807$	0.292310	−	0.899639i	0.0102898	−	0.0316688i
$808$		0			0
$809$	−9.25040	−	6.72081i	−0.325227	−	0.236291i	0.413176	−	0.910651i	$-0.364420\pi$
$809$	−9.25040	−	6.72081i	−0.325227	−	0.236291i	−0.738403	+	0.674360i	$0.764420\pi$
$810$		0			0
$811$	−1.37059	−	4.21825i	−0.0481281	−	0.148123i	0.924104	−	0.382140i	$-0.124813\pi$
$811$	−1.37059	−	4.21825i	−0.0481281	−	0.148123i	−0.972232	+	0.234017i	$0.924813\pi$
$812$		0			0
$813$	−50.5972			−1.77452
$814$		0			0
$815$	24.6645			0.863960
$816$		0			0
$817$	−3.61371	−	11.1218i	−0.126428	−	0.389104i
$818$		0			0
$819$	0.699303	+	0.508073i	0.0244356	+	0.0177535i
$820$		0			0
$821$	14.8994	−	45.8557i	0.519994	−	1.60038i	−0.254014	−	0.967200i	$-0.581751\pi$
$821$	14.8994	−	45.8557i	0.519994	−	1.60038i	0.774008	−	0.633176i	$-0.218249\pi$
$822$		0			0
$823$	34.0798	−	24.7604i	1.18795	−	0.863093i	0.194900	−	0.980823i	$-0.437562\pi$
$823$	34.0798	−	24.7604i	1.18795	−	0.863093i	0.993046	+	0.117730i	$0.0375616\pi$
$824$		0			0
$825$	−2.88721	−	9.80432i	−0.100520	−	0.341343i
$826$		0			0
$827$	−31.6315	+	22.9816i	−1.09993	+	0.799149i	−0.981049	−	0.193759i	$-0.937932\pi$
$827$	−31.6315	+	22.9816i	−1.09993	+	0.799149i	−0.118885	+	0.992908i	$0.537932\pi$
$828$		0			0
$829$	8.67245	−	26.6911i	0.301207	−	0.927019i	−0.679859	−	0.733343i	$-0.737959\pi$
$829$	8.67245	−	26.6911i	0.301207	−	0.927019i	0.981066	−	0.193676i	$-0.0620410\pi$
$830$		0			0
$831$	−7.76759	−	5.64349i	−0.269455	−	0.195770i
$832$		0			0
$833$	−1.94127	−	5.97463i	−0.0672611	−	0.207009i
$834$		0			0
$835$	−16.6827			−0.577328
$836$		0			0
$837$	−64.1710			−2.21808
$838$		0			0
$839$	10.6187	+	32.6810i	0.366598	+	1.12827i	0.948974	+	0.315353i	$0.102123\pi$
$839$	10.6187	+	32.6810i	0.366598	+	1.12827i	−0.582377	+	0.812919i	$0.697877\pi$
$840$		0			0
$841$	−22.7997	−	16.5650i	−0.786197	−	0.571205i
$842$		0			0
$843$	24.4253	−	75.1734i	0.841252	−	2.58911i
$844$		0			0
$845$	0.869333	−	0.631607i	0.0299060	−	0.0217280i
$846$		0			0
$847$	0.356185	−	0.229700i	0.0122386	−	0.00789260i
$848$		0			0
$849$	50.6438	−	36.7949i	1.73809	−	1.26280i
$850$		0			0
$851$	−25.1725	+	77.4730i	−0.862902	+	2.65574i
$852$		0			0
$853$	13.2635	+	9.63648i	0.454133	+	0.329947i	0.791225	−	0.611525i	$-0.209444\pi$
$853$	13.2635	+	9.63648i	0.454133	+	0.329947i	−0.337093	+	0.941472i	$0.609444\pi$
$854$		0			0
$855$	−2.42353	−	7.45886i	−0.0828830	−	0.255088i
$856$		0			0
$857$	−6.89777			−0.235623			−0.117812	−	0.993036i	$-0.537588\pi$
$857$	−6.89777			−0.235623			−0.117812	+	0.993036i	$0.537588\pi$
$858$		0			0
$859$	1.17514			0.0400954			0.0200477	−	0.999799i	$-0.493618\pi$
$859$	1.17514			0.0400954			0.0200477	+	0.999799i	$0.493618\pi$
$860$		0			0
$861$	0.113348	+	0.348850i	0.00386289	+	0.0118888i
$862$		0			0
$863$	−7.82191	−	5.68295i	−0.266261	−	0.193450i	0.446642	−	0.894713i	$-0.352620\pi$
$863$	−7.82191	−	5.68295i	−0.266261	−	0.193450i	−0.712903	+	0.701263i	$0.752620\pi$
$864$		0			0
$865$	−4.08516	+	12.5728i	−0.138900	+	0.427489i
$866$		0			0
$867$	−40.3737	+	29.3332i	−1.37116	+	0.996208i
$868$		0			0
$869$	11.8607	+	40.2765i	0.402348	+	1.36629i
$870$		0			0
$871$	22.6461	−	16.4534i	0.767335	−	0.557501i
$872$		0			0
$873$	35.5589	−	109.439i	1.20349	−	3.70396i
$874$		0			0
$875$	0.0311712	+	0.0226472i	0.00105378	+	0.000765616i
$876$		0			0
$877$	1.88197	+	5.79210i	0.0635495	+	0.195585i	0.977790	−	0.209586i	$-0.0672118\pi$
$877$	1.88197	+	5.79210i	0.0635495	+	0.195585i	−0.914241	+	0.405172i	$0.867212\pi$
$878$		0			0
$879$	−92.7607			−3.12874
$880$		0			0
$881$	55.4058			1.86667			0.933335	−	0.359008i	$-0.116885\pi$
$881$	55.4058			1.86667			0.933335	+	0.359008i	$0.116885\pi$
$882$		0			0
$883$	12.3879	+	38.1259i	0.416885	+	1.28304i	0.910554	+	0.413390i	$0.135655\pi$
$883$	12.3879	+	38.1259i	0.416885	+	1.28304i	−0.493669	+	0.869650i	$0.664345\pi$
$884$		0			0
$885$	0.462767	+	0.336220i	0.0155558	+	0.0113019i
$886$		0			0
$887$	−10.9929	+	33.8325i	−0.369104	+	1.13599i	0.578267	+	0.815848i	$0.303729\pi$
$887$	−10.9929	+	33.8325i	−0.369104	+	1.13599i	−0.947371	+	0.320138i	$0.896271\pi$
$888$		0			0
$889$	0.0898174	−	0.0652562i	0.00301238	−	0.00218862i
$890$		0			0
$891$	−36.0415	−	27.7469i	−1.20744	−	0.929555i
$892$		0			0
$893$	1.27559	−	0.926769i	0.0426859	−	0.0310131i
$894$		0			0
$895$	−6.38617	+	19.6546i	−0.213466	+	0.656981i
$896$		0			0
$897$	−65.4680	−	47.5653i	−2.18591	−	1.58816i
$898$		0			0
$899$	−13.9171	−	42.8323i	−0.464160	−	1.42854i
$900$		0			0
$901$	1.82415			0.0607714
$902$		0			0
$903$	1.15015			0.0382746
$904$		0			0
$905$	−1.16322	−	3.58002i	−0.0386667	−	0.119004i
$906$		0			0
$907$	9.88981	+	7.18537i	0.328386	+	0.238586i	0.739745	−	0.672887i	$-0.234946\pi$
$907$	9.88981	+	7.18537i	0.328386	+	0.238586i	−0.411360	+	0.911473i	$0.634946\pi$
$908$		0			0
$909$	−5.17363	+	15.9228i	−0.171599	+	0.528126i
$910$		0			0
$911$	−13.8505	+	10.0629i	−0.458886	+	0.333400i	−0.793094	−	0.609099i	$-0.791531\pi$
$911$	−13.8505	+	10.0629i	−0.458886	+	0.333400i	0.334208	+	0.942499i	$0.391531\pi$
$912$		0			0
$913$	−29.3943	+	20.1333i	−0.972808	+	0.666316i
$914$		0			0
$915$	−24.3802	+	17.7132i	−0.805984	+	0.585582i
$916$		0			0
$917$	0.0437803	−	0.134742i	0.00144575	−	0.00444957i
$918$		0			0
$919$	−24.9400	−	18.1200i	−0.822695	−	0.597723i	0.0947879	−	0.995497i	$-0.469783\pi$
$919$	−24.9400	−	18.1200i	−0.822695	−	0.597723i	−0.917483	+	0.397774i	$0.869783\pi$
$920$		0			0
$921$	−5.45854	−	16.7997i	−0.179865	−	0.553568i
$922$		0			0
$923$	24.8275			0.817208
$924$		0			0
$925$	10.7125			0.352224
$926$		0			0
$927$	−7.43421	−	22.8801i	−0.244171	−	0.751482i
$928$		0			0
$929$	−5.89944	−	4.28619i	−0.193554	−	0.140625i	0.486787	−	0.873520i	$-0.338169\pi$
$929$	−5.89944	−	4.28619i	−0.193554	−	0.140625i	−0.680342	+	0.732895i	$0.738169\pi$
$930$		0			0
$931$	2.61084	−	8.03534i	0.0855668	−	0.263348i
$932$		0			0
$933$	65.5126	−	47.5977i	2.14479	−	1.55828i
$934$		0			0
$935$	2.97596	+	0.0826683i	0.0973243	+	0.00270354i
$936$		0			0
$937$	−21.3696	+	15.5259i	−0.698114	+	0.507210i	−0.879318	−	0.476236i	$-0.842001\pi$
$937$	−21.3696	+	15.5259i	−0.698114	+	0.507210i	0.181203	+	0.983446i	$0.442001\pi$
$938$		0			0
$939$	−9.62699	+	29.6288i	−0.314165	+	0.966901i
$940$		0			0
$941$	−44.2292	−	32.1344i	−1.44183	−	1.04755i	−0.987656	−	0.156637i	$-0.949935\pi$
$941$	−44.2292	−	32.1344i	−1.44183	−	1.04755i	−0.454174	−	0.890913i	$-0.650065\pi$
$942$		0			0
$943$	−7.25926	−	22.3417i	−0.236394	−	0.727546i
$944$		0			0
$945$	0.415145			0.0135047
$946$		0			0
$947$	−6.86882			−0.223207			−0.111603	−	0.993753i	$-0.535599\pi$
$947$	−6.86882			−0.223207			−0.111603	+	0.993753i	$0.535599\pi$
$948$		0			0
$949$	13.5609	+	41.7361i	0.440205	+	1.35481i
$950$		0			0
$951$	8.89565	+	6.46307i	0.288461	+	0.209579i
$952$		0			0
$953$	13.4521	−	41.4013i	0.435756	−	1.34112i	−0.456554	−	0.889695i	$-0.650917\pi$
$953$	13.4521	−	41.4013i	0.435756	−	1.34112i	0.892310	−	0.451423i	$-0.149083\pi$
$954$		0			0
$955$	−7.66148	+	5.56639i	−0.247920	+	0.180124i
$956$		0			0
$957$	25.9148	−	72.8127i	0.837707	−	2.35370i
$958$		0			0
$959$	−0.199653	+	0.145056i	−0.00644712	+	0.00468411i
$960$		0			0
$961$	1.38156	−	4.25199i	0.0445663	−	0.137161i
$962$		0			0
$963$	100.953	+	73.3464i	3.25316	+	2.36356i
$964$		0			0
$965$	5.05909	+	15.5703i	0.162858	+	0.501225i
$966$		0			0
$967$	31.8547			1.02438			0.512188	−	0.858873i	$-0.328835\pi$
$967$	31.8547			1.02438			0.512188	+	0.858873i	$0.328835\pi$
$968$		0			0
$969$	3.33942			0.107277
$970$		0			0
$971$	5.93422	+	18.2637i	0.190438	+	0.586109i	1.00000		0.000926638i	$-0.000294958\pi$
$971$	5.93422	+	18.2637i	0.190438	+	0.586109i	−0.809561	+	0.587035i	$0.800295\pi$
$972$		0			0
$973$	−0.305134	−	0.221693i	−0.00978214	−	0.00710714i
$974$		0			0
$975$	−3.28851	+	10.1210i	−0.105317	+	0.324132i
$976$		0			0
$977$	−9.43960	+	6.85827i	−0.301999	+	0.219415i	−0.728456	−	0.685093i	$-0.759762\pi$
$977$	−9.43960	+	6.85827i	−0.301999	+	0.219415i	0.426457	+	0.904508i	$0.359762\pi$
$978$		0			0
$979$	−3.09339	+	8.69148i	−0.0988652	+	0.277781i
$980$		0			0
$981$	34.2454	−	24.8807i	1.09337	−	0.794380i
$982$		0			0
$983$	6.40976	−	19.7272i	0.204440	−	0.629201i	−0.795296	−	0.606221i	$-0.792685\pi$
$983$	6.40976	−	19.7272i	0.204440	−	0.629201i	0.999736	−	0.0229796i	$-0.00731529\pi$
$984$		0			0
$985$	12.2659	+	8.91173i	0.390825	+	0.283951i
$986$		0			0
$987$	0.0479203	+	0.147484i	0.00152532	+	0.00469445i
$988$		0			0
$989$	−73.6602			−2.34226
$990$		0			0
$991$	31.5161			1.00114			0.500572	−	0.865695i	$-0.333123\pi$
$991$	31.5161			1.00114			0.500572	+	0.865695i	$0.333123\pi$
$992$		0			0
$993$	7.67634	+	23.6253i	0.243601	+	0.749727i
$994$		0			0
$995$	2.38566	+	1.73328i	0.0756304	+	0.0549487i
$996$		0			0
$997$	7.19314	−	22.1382i	0.227809	−	0.701125i	−0.770185	−	0.637820i	$-0.779836\pi$
$997$	7.19314	−	22.1382i	0.227809	−	0.701125i	0.997994	−	0.0633041i	$-0.0201638\pi$
$998$		0			0
$999$	93.3794	−	67.8441i	2.95439	−	2.14649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.k.641.1		16
4.3	odd	2		440.2.y.d.201.4	yes	16
11.2	odd	10		9680.2.a.de.1.2		8
11.4	even	5	inner	880.2.bo.k.81.1		16
11.9	even	5		9680.2.a.df.1.2		8
44.15	odd	10		440.2.y.d.81.4	✓	16
44.31	odd	10		4840.2.a.bg.1.7		8
44.35	even	10		4840.2.a.bh.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.81.4	✓	16	44.15	odd	10
440.2.y.d.201.4	yes	16	4.3	odd	2
880.2.bo.k.81.1		16	11.4	even	5	inner
880.2.bo.k.641.1		16	1.1	even	1	trivial
4840.2.a.bg.1.7		8	44.31	odd	10
4840.2.a.bh.1.7		8	44.35	even	10
9680.2.a.de.1.2		8	11.2	odd	10
9680.2.a.df.1.2		8	11.9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.952275 - 2.93080i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0119064 + 0.0366440i) q^{7} +(-5.25571 + 3.81850i) q^{9} +O(q^{10})\)	\(q+(-0.952275 - 2.93080i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0119064 + 0.0366440i) q^{7} +(-5.25571 + 3.81850i) q^{9} +(1.11209 - 3.12462i) q^{11} +(-2.79380 + 2.02981i) q^{13} +(-0.952275 + 2.93080i) q^{15} +(-0.726200 - 0.527615i) q^{17} +(-0.373056 - 1.14815i) q^{19} +0.118734 q^{21} -7.60421 q^{23} +(0.309017 + 0.951057i) q^{25} +(8.71688 + 6.33319i) q^{27} +(-2.33675 + 7.19177i) q^{29} +(-4.81829 + 3.50069i) q^{31} +(-10.2167 - 0.283805i) q^{33} +(0.0311712 - 0.0226472i) q^{35} +(3.31034 - 10.1882i) q^{37} +(8.60944 + 6.25512i) q^{39} +(0.954637 + 2.93807i) q^{41} +9.68676 q^{43} +6.49642 q^{45} +(0.403593 + 1.24213i) q^{47} +(5.66192 + 4.11362i) q^{49} +(-0.854793 + 2.63078i) q^{51} +(-1.64407 + 1.19449i) q^{53} +(-2.73630 + 1.87420i) q^{55} +(-3.00974 + 2.18671i) q^{57} +(0.0573598 - 0.176535i) q^{59} +(7.91147 + 5.74802i) q^{61} +(-0.0773487 - 0.238055i) q^{63} +3.45332 q^{65} -8.10586 q^{67} +(7.24130 + 22.2864i) q^{69} +(-5.81639 - 4.22586i) q^{71} +(3.92691 - 12.0858i) q^{73} +(2.49309 - 1.81133i) q^{75} +(0.101258 + 0.0779541i) q^{77} +(-10.2417 + 7.44102i) q^{79} +(4.23793 - 13.0430i) q^{81} +(-8.69073 - 6.31418i) q^{83} +(0.277384 + 0.853699i) q^{85} +23.3029 q^{87} -2.78161 q^{89} +(-0.0411165 - 0.126544i) q^{91} +(14.8482 + 10.7878i) q^{93} +(-0.373056 + 1.14815i) q^{95} +(-14.3301 + 10.4114i) q^{97} +(6.08656 + 20.6686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9}+O(q^{10}) \) 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9	\( 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37} - 3 q^{39} - 11 q^{41} + 16 q^{43} + 38 q^{45} + 10 q^{47} + 4 q^{49} - 26 q^{51} - 9 q^{53} - 3 q^{55} - 50 q^{57} + 60 q^{59} + 30 q^{61} - 52 q^{63} + 24 q^{65} + 4 q^{67} + 41 q^{69} + 10 q^{71} + q^{73} - 2 q^{75} - 4 q^{77} - 19 q^{79} - 31 q^{81} - 64 q^{83} - 11 q^{85} - 30 q^{87} + 24 q^{89} + 9 q^{91} + 45 q^{93} + 2 q^{95} - 3 q^{97} + 10 q^{99}+O(q^{100}) \) 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more