LMFDB - Embedded newform 280.2.bo.a.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	280.17
Dual form			280.2.bo.a.33.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.19810 - 0.588978i) q^{3} +(-1.19880 - 1.88756i) q^{5} +(1.40409 + 2.24244i) q^{7} +(1.88665 - 1.08926i) q^{9} +O(q^{10})$	\(q+(2.19810 - 0.588978i) q^{3} +(-1.19880 - 1.88756i) q^{5} +(1.40409 + 2.24244i) q^{7} +(1.88665 - 1.08926i) q^{9} +(1.78866 - 3.09805i) q^{11} +(3.13432 + 3.13432i) q^{13} +(-3.74681 - 3.44296i) q^{15} +(-1.34033 - 5.00217i) q^{17} +(-0.687063 - 1.19003i) q^{19} +(4.40706 + 4.10213i) q^{21} +(-4.00784 - 1.07390i) q^{23} +(-2.12575 + 4.52561i) q^{25} +(-1.32186 + 1.32186i) q^{27} +9.39599i q^{29} +(-6.08064 - 3.51066i) q^{31} +(2.10696 - 7.86328i) q^{33} +(2.54952 - 5.33854i) q^{35} +(-1.68631 + 6.29340i) q^{37} +(8.73559 + 5.04350i) q^{39} +4.63297i q^{41} +(2.51561 - 2.51561i) q^{43} +(-4.31776 - 2.25536i) q^{45} +(8.76422 + 2.34837i) q^{47} +(-3.05709 + 6.29716i) q^{49} +(-5.89234 - 10.2058i) q^{51} +(-0.470788 - 1.75701i) q^{53} +(-7.99199 + 0.337748i) q^{55} +(-2.21113 - 2.21113i) q^{57} +(-1.42161 + 2.46230i) q^{59} +(1.91951 - 1.10823i) q^{61} +(5.09162 + 2.70129i) q^{63} +(2.15879 - 9.67365i) q^{65} +(-4.37975 + 1.17355i) q^{67} -9.44211 q^{69} -10.5787 q^{71} +(2.44309 - 0.654624i) q^{73} +(-2.00711 + 11.1998i) q^{75} +(9.45862 - 0.338961i) q^{77} +(-4.82403 + 2.78515i) q^{79} +(-5.39481 + 9.34408i) q^{81} +(0.863341 + 0.863341i) q^{83} +(-7.83510 + 8.52656i) q^{85} +(5.53403 + 20.6533i) q^{87} +(0.430347 + 0.745382i) q^{89} +(-2.62768 + 11.4294i) q^{91} +(-15.4335 - 4.13540i) q^{93} +(-1.42259 + 2.72348i) q^{95} +(12.6320 - 12.6320i) q^{97} -7.79325i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	2.19810	−	0.588978i	1.26907	−	0.340047i	0.439396	−	0.898293i	$-0.355192\pi$
$3$	2.19810	−	0.588978i	1.26907	−	0.340047i	0.829675	+	0.558247i	$0.188526\pi$
$4$		0			0
$5$	−1.19880	−	1.88756i	−0.536120	−	0.844142i
$5$	−1.19880	−	1.88756i	−0.536120	−	0.844142i
$6$		0			0
$7$	1.40409	+	2.24244i	0.530694	+	0.847563i
$7$	1.40409	+	2.24244i	0.530694	+	0.847563i
$8$		0			0
$9$	1.88665	−	1.08926i	0.628884	−	0.363086i
$10$		0			0
$11$	1.78866	−	3.09805i	0.539301	−	0.934096i	−0.459641	−	0.888105i	$-0.652022\pi$
$11$	1.78866	−	3.09805i	0.539301	−	0.934096i	0.998942	−	0.0459913i	$-0.0146447\pi$
$12$		0			0
$13$	3.13432	+	3.13432i	0.869305	+	0.869305i	0.992395	−	0.123090i	$-0.0392804\pi$
$13$	3.13432	+	3.13432i	0.869305	+	0.869305i	−0.123090	+	0.992395i	$0.539280\pi$
$14$		0			0
$15$	−3.74681	−	3.44296i	−0.967422	−	0.888970i
$16$		0			0
$17$	−1.34033	−	5.00217i	−0.325077	−	1.21320i	−0.914234	−	0.405186i	$-0.867207\pi$
$17$	−1.34033	−	5.00217i	−0.325077	−	1.21320i	0.589157	−	0.808019i	$-0.299460\pi$
$18$		0			0
$19$	−0.687063	−	1.19003i	−0.157623	−	0.273011i	0.776388	−	0.630255i	$-0.217050\pi$
$19$	−0.687063	−	1.19003i	−0.157623	−	0.273011i	−0.934011	+	0.357244i	$0.883716\pi$
$20$		0			0
$21$	4.40706	+	4.10213i	0.961700	+	0.895157i
$22$		0			0
$23$	−4.00784	−	1.07390i	−0.835692	−	0.223923i	−0.184497	−	0.982833i	$-0.559065\pi$
$23$	−4.00784	−	1.07390i	−0.835692	−	0.223923i	−0.651195	+	0.758910i	$0.725732\pi$
$24$		0			0
$25$	−2.12575	+	4.52561i	−0.425150	+	0.905123i
$26$		0			0
$27$	−1.32186	+	1.32186i	−0.254392	+	0.254392i
$28$		0			0
$29$			9.39599i			1.74479i	0.488800	+	0.872396i	$0.337435\pi$
$29$			9.39599i			1.74479i	−0.488800	+	0.872396i	$0.662565\pi$
$30$		0			0
$31$	−6.08064	−	3.51066i	−1.09212	−	0.630533i	−0.157976	−	0.987443i	$-0.550497\pi$
$31$	−6.08064	−	3.51066i	−1.09212	−	0.630533i	−0.934139	+	0.356910i	$0.883830\pi$
$32$		0			0
$33$	2.10696	−	7.86328i	0.366775	−	1.36882i
$34$		0			0
$35$	2.54952	−	5.33854i	0.430947	−	0.902377i
$36$		0			0
$37$	−1.68631	+	6.29340i	−0.277228	+	1.03463i	0.677105	+	0.735886i	$0.263234\pi$
$37$	−1.68631	+	6.29340i	−0.277228	+	1.03463i	−0.954334	+	0.298743i	$0.903433\pi$
$38$		0			0
$39$	8.73559	+	5.04350i	1.39881	+	0.807606i
$40$		0			0
$41$			4.63297i			0.723549i	0.932266	+	0.361774i	$0.117829\pi$
$41$			4.63297i			0.723549i	−0.932266	+	0.361774i	$0.882171\pi$
$42$		0			0
$43$	2.51561	−	2.51561i	0.383626	−	0.383626i	−0.488780	−	0.872407i	$-0.662558\pi$
$43$	2.51561	−	2.51561i	0.383626	−	0.383626i	0.872407	+	0.488780i	$0.162558\pi$
$44$		0			0
$45$	−4.31776	−	2.25536i	−0.643654	−	0.336209i
$46$		0			0
$47$	8.76422	+	2.34837i	1.27839	+	0.342544i	0.833241	−	0.552910i	$-0.186483\pi$
$47$	8.76422	+	2.34837i	1.27839	+	0.342544i	0.445153	+	0.895455i	$0.353149\pi$
$48$		0			0
$49$	−3.05709	+	6.29716i	−0.436727	+	0.899594i
$50$		0			0
$51$	−5.89234	−	10.2058i	−0.825092	−	1.42910i
$52$		0			0
$53$	−0.470788	−	1.75701i	−0.0646678	−	0.241343i	0.926025	−	0.377463i	$-0.123203\pi$
$53$	−0.470788	−	1.75701i	−0.0646678	−	0.241343i	−0.990692	+	0.136120i	$0.956537\pi$
$54$		0			0
$55$	−7.99199	+	0.337748i	−1.07764	+	0.0455419i
$56$		0			0
$57$	−2.21113	−	2.21113i	−0.292871	−	0.292871i
$58$		0			0
$59$	−1.42161	+	2.46230i	−0.185078	+	0.320565i	−0.943603	−	0.331080i	$-0.892587\pi$
$59$	−1.42161	+	2.46230i	−0.185078	+	0.320565i	0.758525	+	0.651644i	$0.225920\pi$
$60$		0			0
$61$	1.91951	−	1.10823i	0.245769	−	0.141895i	−0.372057	−	0.928210i	$-0.621347\pi$
$61$	1.91951	−	1.10823i	0.245769	−	0.141895i	0.617825	+	0.786315i	$0.288014\pi$
$62$		0			0
$63$	5.09162	+	2.70129i	0.641484	+	0.340331i
$64$		0			0
$65$	2.15879	−	9.67365i	0.267764	−	1.19987i
$66$		0			0
$67$	−4.37975	+	1.17355i	−0.535072	+	0.143372i	−0.516229	−	0.856450i	$-0.672665\pi$
$67$	−4.37975	+	1.17355i	−0.535072	+	0.143372i	−0.0188425	+	0.999822i	$0.505998\pi$
$68$		0			0
$69$	−9.44211			−1.13670
$70$		0			0
$71$	−10.5787			−1.25546			−0.627731	−	0.778430i	$-0.716016\pi$
$71$	−10.5787			−1.25546			−0.627731	+	0.778430i	$0.716016\pi$
$72$		0			0
$73$	2.44309	−	0.654624i	0.285942	−	0.0766179i	−0.112997	−	0.993595i	$-0.536045\pi$
$73$	2.44309	−	0.654624i	0.285942	−	0.0766179i	0.398939	+	0.916977i	$0.369378\pi$
$74$		0			0
$75$	−2.00711	+	11.1998i	−0.231761	+	1.29324i
$76$		0			0
$77$	9.45862	−	0.338961i	1.07791	−	0.0386282i
$78$		0			0
$79$	−4.82403	+	2.78515i	−0.542745	+	0.313354i	−0.746191	−	0.665732i	$-0.768119\pi$
$79$	−4.82403	+	2.78515i	−0.542745	+	0.313354i	0.203446	+	0.979086i	$0.434786\pi$
$80$		0			0
$81$	−5.39481	+	9.34408i	−0.599423	+	1.03823i
$82$		0			0
$83$	0.863341	+	0.863341i	0.0947640	+	0.0947640i	0.752899	−	0.658136i	$-0.228655\pi$
$83$	0.863341	+	0.863341i	0.0947640	+	0.0947640i	−0.658136	+	0.752899i	$0.728655\pi$
$84$		0			0
$85$	−7.83510	+	8.52656i	−0.849836	+	0.924835i
$86$		0			0
$87$	5.53403	+	20.6533i	0.593311	+	2.21427i
$88$		0			0
$89$	0.430347	+	0.745382i	0.0456167	+	0.0790104i	0.887932	−	0.459974i	$-0.152141\pi$
$89$	0.430347	+	0.745382i	0.0456167	+	0.0790104i	−0.842316	+	0.538985i	$0.818808\pi$
$90$		0			0
$91$	−2.62768	+	11.4294i	−0.275456	+	1.19813i
$92$		0			0
$93$	−15.4335	−	4.13540i	−1.60038	−	0.428821i
$94$		0			0
$95$	−1.42259	+	2.72348i	−0.145955	+	0.279423i
$96$		0			0
$97$	12.6320	−	12.6320i	1.28258	−	1.28258i	0.343390	−	0.939193i	$-0.388425\pi$
$97$	12.6320	−	12.6320i	1.28258	−	1.28258i	0.939193	−	0.343390i	$-0.111575\pi$
$98$		0			0
$99$		−	7.79325i		−	0.783251i
$100$		0			0
$101$	−10.2545	−	5.92042i	−1.02036	−	0.589103i	−0.106150	−	0.994350i	$-0.533852\pi$
$101$	−10.2545	−	5.92042i	−1.02036	−	0.589103i	−0.914207	+	0.405247i	$0.867186\pi$
$102$		0			0
$103$	4.95903	−	18.5073i	0.488627	−	1.82358i	−0.0745114	−	0.997220i	$-0.523740\pi$
$103$	4.95903	−	18.5073i	0.488627	−	1.82358i	0.563139	−	0.826362i	$-0.309594\pi$
$104$		0			0
$105$	2.45980	−	13.2362i	0.240052	−	1.29172i
$106$		0			0
$107$	1.91825	−	7.15899i	0.185444	−	0.692086i	−0.809091	−	0.587683i	$-0.800040\pi$
$107$	1.91825	−	7.15899i	0.185444	−	0.692086i	0.994535	−	0.104403i	$-0.0332931\pi$
$108$		0			0
$109$	−3.66475	−	2.11584i	−0.351019	−	0.202661i	0.314115	−	0.949385i	$-0.398292\pi$
$109$	−3.66475	−	2.11584i	−0.351019	−	0.202661i	−0.665134	+	0.746724i	$0.731626\pi$
$110$		0			0
$111$			14.8267i			1.40729i
$112$		0			0
$113$	8.21616	−	8.21616i	0.772911	−	0.772911i	−0.205703	−	0.978614i	$-0.565948\pi$
$113$	8.21616	−	8.21616i	0.772911	−	0.772911i	0.978614	+	0.205703i	$0.0659481\pi$
$114$		0			0
$115$	2.77756	+	8.85242i	0.259009	+	0.825492i
$116$		0			0
$117$	9.32747	+	2.49929i	0.862325	+	0.231059i
$118$		0			0
$119$	9.33514	−	10.0291i	0.855751	−	0.919364i
$120$		0			0
$121$	−0.898593	−	1.55641i	−0.0816903	−	0.141492i
$122$		0			0
$123$	2.72872	+	10.1837i	0.246040	+	0.918235i
$124$		0			0
$125$	11.0907	−	1.41284i	0.991983	−	0.126368i
$126$		0			0
$127$	−11.0167	−	11.0167i	−0.977572	−	0.977572i	0.0221820	−	0.999754i	$-0.492939\pi$
$127$	−11.0167	−	11.0167i	−0.977572	−	0.977572i	−0.999754	+	0.0221820i	$0.992939\pi$
$128$		0			0
$129$	4.04791	−	7.01118i	0.356398	−	0.617300i
$130$		0			0
$131$	11.4510	−	6.61125i	1.00048	−	0.577628i	0.0920903	−	0.995751i	$-0.470645\pi$
$131$	11.4510	−	6.61125i	1.00048	−	0.577628i	0.908391	+	0.418123i	$0.137312\pi$
$132$		0			0
$133$	1.70387	−	3.21160i	0.147745	−	0.278481i
$134$		0			0
$135$	4.07974	+	0.910439i	0.351128	+	0.0783581i
$136$		0			0
$137$	−18.3797	+	4.92483i	−1.57028	+	0.420756i	−0.935901	−	0.352263i	$-0.885412\pi$
$137$	−18.3797	+	4.92483i	−1.57028	+	0.420756i	−0.634383	+	0.773019i	$0.718746\pi$
$138$		0			0
$139$	2.17884			0.184807			0.0924034	−	0.995722i	$-0.470545\pi$
$139$	2.17884			0.184807			0.0924034	+	0.995722i	$0.470545\pi$
$140$		0			0
$141$	20.6477			1.73885
$142$		0			0
$143$	15.3165	−	4.10405i	1.28083	−	0.343198i
$144$		0			0
$145$	17.7355	−	11.2639i	1.47285	−	0.935419i
$146$		0			0
$147$	−3.01088	+	15.6423i	−0.248333	+	1.29016i
$148$		0			0
$149$	1.79894	−	1.03862i	0.147375	−	0.0850868i	−0.424499	−	0.905428i	$-0.639550\pi$
$149$	1.79894	−	1.03862i	0.147375	−	0.0850868i	0.571874	+	0.820341i	$0.306217\pi$
$150$		0			0
$151$	2.97729	−	5.15681i	0.242288	−	0.419655i	−0.719078	−	0.694930i	$-0.755435\pi$
$151$	2.97729	−	5.15681i	0.242288	−	0.419655i	0.961366	+	0.275274i	$0.0887687\pi$
$152$		0			0
$153$	−7.97739	−	7.97739i	−0.644934	−	0.644934i
$154$		0			0
$155$	0.662909	+	15.6861i	0.0532462	+	1.25994i
$156$		0			0
$157$	1.58172	+	5.90304i	0.126235	+	0.471114i	0.999881	−	0.0154480i	$-0.00491745\pi$
$157$	1.58172	+	5.90304i	0.126235	+	0.471114i	−0.873646	+	0.486562i	$0.838251\pi$
$158$		0			0
$159$	−2.06968	−	3.58478i	−0.164136	−	0.284292i
$160$		0			0
$161$	−3.21920	−	10.4952i	−0.253708	−	0.827137i
$162$		0			0
$163$	14.9267	+	3.99960i	1.16915	+	0.313273i	0.790615	−	0.612313i	$-0.209761\pi$
$163$	14.9267	+	3.99960i	1.16915	+	0.313273i	0.378536	+	0.925587i	$0.376428\pi$
$164$		0			0
$165$	−17.3682	+	5.44951i	−1.35211	+	0.424243i
$166$		0			0
$167$	17.3840	−	17.3840i	1.34521	−	1.34521i	0.454428	−	0.890783i	$-0.349844\pi$
$167$	17.3840	−	17.3840i	1.34521	−	1.34521i	0.890783	−	0.454428i	$-0.150156\pi$
$168$		0			0
$169$			6.64798i			0.511383i
$170$		0			0
$171$	−2.59250	−	1.49678i	−0.198253	−	0.114462i
$172$		0			0
$173$	−1.05374	+	3.93262i	−0.0801146	+	0.298992i	−0.994344	−	0.106205i	$-0.966130\pi$
$173$	−1.05374	+	3.93262i	−0.0801146	+	0.298992i	0.914230	+	0.405196i	$0.132797\pi$
$174$		0			0
$175$	−13.1332	+	1.58748i	−0.992774	+	0.120002i
$176$		0			0
$177$	−1.67460	+	6.24967i	−0.125870	+	0.469754i
$178$		0			0
$179$	5.28417	+	3.05082i	0.394958	+	0.228029i	0.684306	−	0.729195i	$-0.260105\pi$
$179$	5.28417	+	3.05082i	0.394958	+	0.228029i	−0.289348	+	0.957224i	$0.593439\pi$
$180$		0			0
$181$			23.2896i			1.73110i	0.500820	+	0.865552i	$0.333032\pi$
$181$			23.2896i			1.73110i	−0.500820	+	0.865552i	$0.666968\pi$
$182$		0			0
$183$	3.56655	−	3.56655i	0.263647	−	0.263647i
$184$		0			0
$185$	13.9007	−	4.36153i	1.02200	−	0.320666i
$186$		0			0
$187$	−17.8943	−	4.79477i	−1.30856	−	0.350629i
$188$		0			0
$189$	−4.82020	−	1.10819i	−0.350618	−	0.0806089i
$190$		0			0
$191$	−7.78800	−	13.4892i	−0.563520	−	0.976045i	−0.997186	−	0.0749713i	$-0.976113\pi$
$191$	−7.78800	−	13.4892i	−0.563520	−	0.976045i	0.433666	−	0.901074i	$-0.357220\pi$
$192$		0			0
$193$	5.61718	+	20.9636i	0.404333	+	1.50899i	0.805282	+	0.592892i	$0.202014\pi$
$193$	5.61718	+	20.9636i	0.404333	+	1.50899i	−0.400949	+	0.916100i	$0.631320\pi$
$194$		0			0
$195$	−0.952351	−	22.5351i	−0.0681993	−	1.61377i
$196$		0			0
$197$	−3.09635	−	3.09635i	−0.220606	−	0.220606i	0.588148	−	0.808753i	$-0.299857\pi$
$197$	−3.09635	−	3.09635i	−0.220606	−	0.220606i	−0.808753	+	0.588148i	$0.799857\pi$
$198$		0			0
$199$	−0.426614	+	0.738916i	−0.0302418	+	0.0523804i	−0.880750	−	0.473581i	$-0.842961\pi$
$199$	−0.426614	+	0.738916i	−0.0302418	+	0.0523804i	0.850508	+	0.525962i	$0.176294\pi$
$200$		0			0
$201$	−8.93592	+	5.15915i	−0.630291	+	0.363899i
$202$		0			0
$203$	−21.0700	+	13.1928i	−1.47882	+	0.925951i
$204$		0			0
$205$	8.74501	−	5.55402i	0.610778	−	0.387909i
$206$		0			0
$207$	−8.73115	+	2.33950i	−0.606857	+	0.162607i
$208$		0			0
$209$	−4.91568			−0.340025
$210$		0			0
$211$	−5.15723			−0.355038			−0.177519	−	0.984117i	$-0.556807\pi$
$211$	−5.15723			−0.355038			−0.177519	+	0.984117i	$0.556807\pi$
$212$		0			0
$213$	−23.2530	+	6.23063i	−1.59327	+	0.426915i
$214$		0			0
$215$	−7.76406	−	1.73264i	−0.529505	−	0.118165i
$216$		0			0
$217$	−0.665290	−	18.5647i	−0.0451629	−	1.26026i
$218$		0			0
$219$	4.98459	−	2.87785i	0.336827	−	0.194467i
$220$		0			0
$221$	11.4774	−	19.8795i	0.772054	−	1.33724i
$222$		0			0
$223$	6.75353	+	6.75353i	0.452250	+	0.452250i	0.896101	−	0.443851i	$-0.146388\pi$
$223$	6.75353	+	6.75353i	0.452250	+	0.452250i	−0.443851	+	0.896101i	$0.646388\pi$
$224$		0			0
$225$	0.919019	+	10.8538i	0.0612679	+	0.723584i
$226$		0			0
$227$	−1.21237	−	4.52464i	−0.0804680	−	0.300311i	0.913949	−	0.405828i	$-0.133017\pi$
$227$	−1.21237	−	4.52464i	−0.0804680	−	0.300311i	−0.994417	+	0.105517i	$0.966350\pi$
$228$		0			0
$229$	6.17273	+	10.6915i	0.407905	+	0.706513i	0.994655	−	0.103256i	$-0.0329260\pi$
$229$	6.17273	+	10.6915i	0.407905	+	0.706513i	−0.586750	+	0.809768i	$0.699593\pi$
$230$		0			0
$231$	20.5913	−	6.31598i	1.35481	−	0.415561i
$232$		0			0
$233$	−20.2083	−	5.41480i	−1.32389	−	0.354735i	−0.473456	−	0.880818i	$-0.656994\pi$
$233$	−20.2083	−	5.41480i	−1.32389	−	0.354735i	−0.850433	+	0.526083i	$0.823660\pi$
$234$		0			0
$235$	−6.07389	−	19.3582i	−0.396217	−	1.26279i
$236$		0			0
$237$	−8.96328	+	8.96328i	−0.582227	+	0.582227i
$238$		0			0
$239$			19.5643i			1.26551i	0.774352	+	0.632755i	$0.218076\pi$
$239$			19.5643i			1.26551i	−0.774352	+	0.632755i	$0.781924\pi$
$240$		0			0
$241$	−0.432477	−	0.249691i	−0.0278583	−	0.0160840i	0.486006	−	0.873955i	$-0.338453\pi$
$241$	−0.432477	−	0.249691i	−0.0278583	−	0.0160840i	−0.513864	+	0.857871i	$0.671787\pi$
$242$		0			0
$243$	−4.90334	+	18.2995i	−0.314549	+	1.17391i
$244$		0			0
$245$	15.5511	−	1.77861i	0.993523	−	0.113632i
$246$		0			0
$247$	1.57646	−	5.88342i	0.100308	−	0.374353i
$248$		0			0
$249$	2.40619	+	1.38922i	0.152486	+	0.0880380i
$250$		0			0
$251$			7.14052i			0.450705i	0.974277	+	0.225353i	$0.0723535\pi$
$251$			7.14052i			0.450705i	−0.974277	+	0.225353i	$0.927647\pi$
$252$		0			0
$253$	−10.4956	+	10.4956i	−0.659855	+	0.659855i
$254$		0			0
$255$	−12.2003	+	23.3569i	−0.764015	+	1.46266i
$256$		0			0
$257$	−7.94408	−	2.12861i	−0.495538	−	0.132779i	0.00239046	−	0.999997i	$-0.499239\pi$
$257$	−7.94408	−	2.12861i	−0.495538	−	0.132779i	−0.497928	+	0.867218i	$0.665906\pi$
$258$		0			0
$259$	−16.4803	+	5.05502i	−1.02404	+	0.314104i
$260$		0			0
$261$	10.2347	+	17.7270i	0.633510	+	1.09727i
$262$		0			0
$263$	−1.44967	−	5.41024i	−0.0893905	−	0.333610i	0.906719	−	0.421736i	$-0.138579\pi$
$263$	−1.44967	−	5.41024i	−0.0893905	−	0.333610i	−0.996109	+	0.0881258i	$0.971912\pi$
$264$		0			0
$265$	−2.75207	+	2.99494i	−0.169058	+	0.183978i
$266$		0			0
$267$	1.38496	+	1.38496i	0.0847580	+	0.0847580i
$268$		0			0
$269$	15.6982	−	27.1901i	0.957136	−	1.65781i	0.227732	−	0.973724i	$-0.426869\pi$
$269$	15.6982	−	27.1901i	0.957136	−	1.65781i	0.729403	−	0.684084i	$-0.239798\pi$
$270$		0			0
$271$	5.04530	−	2.91290i	0.306480	−	0.176946i	−0.338870	−	0.940833i	$-0.610045\pi$
$271$	5.04530	−	2.91290i	0.306480	−	0.176946i	0.645350	+	0.763887i	$0.276711\pi$
$272$		0			0
$273$	0.955772	+	26.6706i	0.0578460	+	1.61418i
$274$		0			0
$275$	10.2183	+	14.6804i	0.616188	+	0.885264i
$276$		0			0
$277$	14.3005	−	3.83179i	0.859231	−	0.230230i	0.197806	−	0.980241i	$-0.436619\pi$
$277$	14.3005	−	3.83179i	0.859231	−	0.230230i	0.661425	+	0.750011i	$0.269952\pi$
$278$		0			0
$279$	−15.2961			−0.915752
$280$		0			0
$281$	4.04511			0.241311			0.120656	−	0.992694i	$-0.461500\pi$
$281$	4.04511			0.241311			0.120656	+	0.992694i	$0.461500\pi$
$282$		0			0
$283$	−4.67531	+	1.25275i	−0.277918	+	0.0744680i	−0.395086	−	0.918644i	$-0.629285\pi$
$283$	−4.67531	+	1.25275i	−0.277918	+	0.0744680i	0.117168	+	0.993112i	$0.462619\pi$
$284$		0			0
$285$	−1.52293	+	6.82435i	−0.0902106	+	0.404239i
$286$		0			0
$287$	−10.3892	+	6.50509i	−0.613253	+	0.383983i
$288$		0			0
$289$	−8.50280	+	4.90910i	−0.500165	+	0.288770i
$290$		0			0
$291$	20.3263	−	35.2062i	1.19155	−	2.06383i
$292$		0			0
$293$	−1.17671	−	1.17671i	−0.0687440	−	0.0687440i	0.671899	−	0.740643i	$-0.265479\pi$
$293$	−1.17671	−	1.17671i	−0.0687440	−	0.0687440i	−0.740643	+	0.671899i	$0.765479\pi$
$294$		0			0
$295$	6.35197	−	0.268439i	0.369826	−	0.0156291i
$296$		0			0
$297$	1.73083	+	6.45954i	0.100433	+	0.374820i
$298$		0			0
$299$	−9.19592	−	15.9278i	−0.531814	−	0.921129i
$300$		0			0
$301$	9.17323	+	2.10897i	0.528736	+	0.121559i
$302$		0			0
$303$	−26.0273	−	6.97399i	−1.49523	−	0.400645i
$304$		0			0
$305$	−4.39297	−	2.29464i	−0.251541	−	0.131391i
$306$		0			0
$307$	11.9756	−	11.9756i	0.683485	−	0.683485i	−0.277299	−	0.960784i	$-0.589439\pi$
$307$	11.9756	−	11.9756i	0.683485	−	0.683485i	0.960784	+	0.277299i	$0.0894393\pi$
$308$		0			0
$309$		−	43.6017i		−	2.48041i
$310$		0			0
$311$	−4.47627	−	2.58438i	−0.253826	−	0.146547i	0.367689	−	0.929949i	$-0.380149\pi$
$311$	−4.47627	−	2.58438i	−0.253826	−	0.146547i	−0.621515	+	0.783402i	$0.713482\pi$
$312$		0			0
$313$	−1.64135	+	6.12562i	−0.0927748	+	0.346240i	−0.996673	−	0.0815080i	$-0.974026\pi$
$313$	−1.64135	+	6.12562i	−0.0927748	+	0.346240i	0.903898	+	0.427748i	$0.140693\pi$
$314$		0			0
$315$	−1.00499	−	12.8490i	−0.0566250	−	0.723962i
$316$		0			0
$317$	−5.34333	+	19.9416i	−0.300112	+	1.12003i	0.636961	+	0.770896i	$0.280191\pi$
$317$	−5.34333	+	19.9416i	−0.300112	+	1.12003i	−0.937072	+	0.349135i	$0.886475\pi$
$318$		0			0
$319$	29.1092	+	16.8062i	1.62980	+	0.940967i
$320$		0			0
$321$		−	16.8659i		−	0.941365i
$322$		0			0
$323$	−5.03184	+	5.03184i	−0.279979	+	0.279979i
$324$		0			0
$325$	−20.8475	+	7.52196i	−1.15641	+	0.417243i
$326$		0			0
$327$	−9.30165	−	2.49237i	−0.514383	−	0.137828i
$328$		0			0
$329$	7.03964	+	22.9506i	0.388108	+	1.26531i
$330$		0			0
$331$	8.76860	+	15.1877i	0.481966	+	0.834790i	0.999786	−	0.0207000i	$-0.00658950\pi$
$331$	8.76860	+	15.1877i	0.481966	+	0.834790i	−0.517820	+	0.855490i	$0.673256\pi$
$332$		0			0
$333$	3.67366	+	13.7103i	0.201316	+	0.751320i
$334$		0			0
$335$	7.46560	+	6.86018i	0.407889	+	0.374812i
$336$		0			0
$337$	−4.90571	−	4.90571i	−0.267231	−	0.267231i	0.560752	−	0.827984i	$-0.310512\pi$
$337$	−4.90571	−	4.90571i	−0.267231	−	0.267231i	−0.827984	+	0.560752i	$0.810512\pi$
$338$		0			0
$339$	13.2208	−	22.8990i	0.718053	−	1.24371i
$340$		0			0
$341$	−21.7524	+	12.5587i	−1.17796	+	0.680094i
$342$		0			0
$343$	−18.4134	+	1.98641i	−0.994231	+	0.107256i
$344$		0			0
$345$	11.3192	+	17.8225i	0.609406	+	0.959533i
$346$		0			0
$347$	−10.9188	+	2.92569i	−0.586153	+	0.157059i	−0.539694	−	0.841861i	$-0.681460\pi$
$347$	−10.9188	+	2.92569i	−0.586153	+	0.157059i	−0.0464585	+	0.998920i	$0.514794\pi$
$348$		0			0
$349$	−22.2886			−1.19308			−0.596541	−	0.802582i	$-0.703459\pi$
$349$	−22.2886			−1.19308			−0.596541	+	0.802582i	$0.703459\pi$
$350$		0			0
$351$	−8.28628			−0.442289
$352$		0			0
$353$	16.2032	−	4.34163i	0.862409	−	0.231082i	0.199607	−	0.979876i	$-0.436034\pi$
$353$	16.2032	−	4.34163i	0.862409	−	0.231082i	0.662803	+	0.748794i	$0.269367\pi$
$354$		0			0
$355$	12.6818	+	19.9679i	0.673079	+	1.05979i
$356$		0			0
$357$	14.6126	−	27.5431i	0.773382	−	1.45773i
$358$		0			0
$359$	−5.77457	+	3.33395i	−0.304770	+	0.175959i	−0.644584	−	0.764534i	$-0.722969\pi$
$359$	−5.77457	+	3.33395i	−0.304770	+	0.175959i	0.339814	+	0.940493i	$0.389636\pi$
$360$		0			0
$361$	8.55589	−	14.8192i	0.450310	−	0.779960i
$362$		0			0
$363$	−2.89188	−	2.89188i	−0.151785	−	0.151785i
$364$		0			0
$365$	−4.16442	−	3.82671i	−0.217976	−	0.200299i
$366$		0			0
$367$	−6.88053	−	25.6785i	−0.359161	−	1.34041i	−0.875167	−	0.483821i	$-0.839248\pi$
$367$	−6.88053	−	25.6785i	−0.359161	−	1.34041i	0.516006	−	0.856585i	$-0.327418\pi$
$368$		0			0
$369$	5.04651	+	8.74081i	0.262711	+	0.455028i
$370$		0			0
$371$	3.27896	−	3.52270i	0.170235	−	0.182890i
$372$		0			0
$373$	35.8758	+	9.61290i	1.85758	+	0.497737i	0.999866	−	0.0163896i	$-0.00521720\pi$
$373$	35.8758	+	9.61290i	1.85758	+	0.497737i	0.857714	+	0.514127i	$0.171884\pi$
$374$		0			0
$375$	23.5463	−	9.63774i	1.21593	−	0.497691i
$376$		0			0
$377$	−29.4501	+	29.4501i	−1.51676	+	1.51676i
$378$		0			0
$379$		−	26.2790i		−	1.34986i	−0.737881	−	0.674931i	$-0.764173\pi$
$379$		−	26.2790i		−	1.34986i	0.737881	−	0.674931i	$-0.235827\pi$
$380$		0			0
$381$	−30.7043	−	17.7271i	−1.57303	−	0.908188i
$382$		0			0
$383$	−3.94516	+	14.7235i	−0.201588	+	0.752337i	0.788874	+	0.614554i	$0.210664\pi$
$383$	−3.94516	+	14.7235i	−0.201588	+	0.752337i	−0.990463	+	0.137783i	$0.956002\pi$
$384$		0			0
$385$	−11.9788	−	17.4473i	−0.610497	−	0.889199i
$386$		0			0
$387$	2.00593	−	7.48622i	0.101967	−	0.380546i
$388$		0			0
$389$	−12.5156	−	7.22588i	−0.634566	−	0.366367i	0.147952	−	0.988994i	$-0.452732\pi$
$389$	−12.5156	−	7.22588i	−0.634566	−	0.366367i	−0.782518	+	0.622628i	$0.786065\pi$
$390$		0			0
$391$			21.4873i			1.08666i
$392$		0			0
$393$	21.2766	−	21.2766i	1.07326	−	1.07326i
$394$		0			0
$395$	11.0402	+	5.76678i	0.555492	+	0.290158i
$396$		0			0
$397$	−9.90897	−	2.65510i	−0.497317	−	0.133256i	0.00143754	−	0.999999i	$-0.499542\pi$
$397$	−9.90897	−	2.65510i	−0.497317	−	0.133256i	−0.498755	+	0.866743i	$0.666209\pi$
$398$		0			0
$399$	1.85372	−	8.06295i	0.0928018	−	0.403652i
$400$		0			0
$401$	16.9889	+	29.4256i	0.848384	+	1.46944i	0.882650	+	0.470031i	$0.155757\pi$
$401$	16.9889	+	29.4256i	0.848384	+	1.46944i	−0.0342665	+	0.999413i	$0.510910\pi$
$402$		0			0
$403$	−8.05515	−	30.0622i	−0.401256	−	1.49751i
$404$		0			0
$405$	24.1048	−	1.01869i	1.19778	−	0.0506190i
$406$		0			0
$407$	16.4810	+	16.4810i	0.816934	+	0.816934i
$408$		0			0
$409$	−8.14459	+	14.1068i	−0.402724	+	0.697538i	−0.994054	−	0.108892i	$-0.965270\pi$
$409$	−8.14459	+	14.1068i	−0.402724	+	0.697538i	0.591330	+	0.806430i	$0.298603\pi$
$410$		0			0
$411$	−37.4997	+	21.6505i	−1.84973	+	1.06794i
$412$		0			0
$413$	−7.51763	+	0.269404i	−0.369919	+	0.0132565i
$414$		0			0
$415$	0.594631	−	2.66458i	0.0291893	−	0.130799i
$416$		0			0
$417$	4.78930	−	1.28329i	0.234533	−	0.0628429i
$418$		0			0
$419$	−14.3954			−0.703261			−0.351631	−	0.936139i	$-0.614373\pi$
$419$	−14.3954			−0.703261			−0.351631	+	0.936139i	$0.614373\pi$
$420$		0			0
$421$	26.0871			1.27141			0.635705	−	0.771932i	$-0.280710\pi$
$421$	26.0871			1.27141			0.635705	+	0.771932i	$0.280710\pi$
$422$		0			0
$423$	19.0930	−	5.11596i	0.928335	−	0.248747i
$424$		0			0
$425$	25.4871	+	4.56755i	1.23631	+	0.221559i
$426$		0			0
$427$	5.18031	+	2.74835i	0.250693	+	0.133002i
$428$		0			0
$429$	31.2500	−	18.0422i	1.50876	−	0.871085i
$430$		0			0
$431$	−4.01624	+	6.95633i	−0.193456	+	0.335075i	−0.946393	−	0.323017i	$-0.895303\pi$
$431$	−4.01624	+	6.95633i	−0.193456	+	0.335075i	0.752938	+	0.658092i	$0.228636\pi$
$432$		0			0
$433$	−18.7693	−	18.7693i	−0.901994	−	0.901994i	0.0936149	−	0.995608i	$-0.470158\pi$
$433$	−18.7693	−	18.7693i	−0.901994	−	0.901994i	−0.995608	+	0.0936149i	$0.970158\pi$
$434$		0			0
$435$	32.3501	−	35.2050i	1.55107	−	1.68795i
$436$		0			0
$437$	1.47567	+	5.50728i	0.0705909	+	0.263449i
$438$		0			0
$439$	−17.4436	−	30.2131i	−0.832536	−	1.44199i	−0.896021	−	0.444012i	$-0.853555\pi$
$439$	−17.4436	−	30.2131i	−0.832536	−	1.44199i	0.0634849	−	0.997983i	$-0.479779\pi$
$440$		0			0
$441$	1.09158	+	15.2105i	0.0519798	+	0.724310i
$442$		0			0
$443$	30.0869	+	8.06175i	1.42947	+	0.383025i	0.888833	−	0.458231i	$-0.151517\pi$
$443$	30.0869	+	8.06175i	1.42947	+	0.383025i	0.540637	+	0.841256i	$0.318183\pi$
$444$		0			0
$445$	0.891052	−	1.70587i	0.0422399	−	0.0808660i
$446$		0			0
$447$	3.34251	−	3.34251i	0.158095	−	0.158095i
$448$		0			0
$449$			21.2638i			1.00350i	0.865013	+	0.501750i	$0.167310\pi$
$449$			21.2638i			1.00350i	−0.865013	+	0.501750i	$0.832690\pi$
$450$		0			0
$451$	14.3532	+	8.28680i	0.675864	+	0.390210i
$452$		0			0
$453$	3.50711	−	13.0887i	0.164778	−	0.614962i
$454$		0			0
$455$	24.7237	−	8.74169i	1.15907	−	0.409817i
$456$		0			0
$457$	6.71055	−	25.0441i	0.313906	−	1.17151i	−0.611097	−	0.791556i	$-0.709272\pi$
$457$	6.71055	−	25.0441i	0.313906	−	1.17151i	0.925003	−	0.379959i	$-0.124062\pi$
$458$		0			0
$459$	8.38390	+	4.84044i	0.391327	+	0.225933i
$460$		0			0
$461$			1.24276i			0.0578811i	0.999581	+	0.0289405i	$0.00921335\pi$
$461$			1.24276i			0.0578811i	−0.999581	+	0.0289405i	$0.990787\pi$
$462$		0			0
$463$	−13.6086	+	13.6086i	−0.632448	+	0.632448i	−0.948681	−	0.316234i	$-0.897582\pi$
$463$	−13.6086	+	13.6086i	−0.632448	+	0.632448i	0.316234	+	0.948681i	$0.397582\pi$
$464$		0			0
$465$	10.6959	+	34.0892i	0.496012	+	1.58085i
$466$		0			0
$467$	23.7974	+	6.37649i	1.10121	+	0.295069i	0.763258	−	0.646094i	$-0.223599\pi$
$467$	23.7974	+	6.37649i	1.10121	+	0.295069i	0.337954	+	0.941163i	$0.390265\pi$
$468$		0			0
$469$	−8.78116	−	8.17357i	−0.405476	−	0.377420i
$470$		0			0
$471$	6.95352	+	12.0439i	0.320401	+	0.554951i
$472$		0			0
$473$	−3.29391	−	12.2930i	−0.151454	−	0.565234i
$474$		0			0
$475$	6.84613	−	0.579682i	0.314122	−	0.0265976i
$476$		0			0
$477$	−2.80205	−	2.80205i	−0.128297	−	0.128297i
$478$		0			0
$479$	2.58135	−	4.47103i	0.117945	−	0.204287i	−0.801008	−	0.598653i	$-0.795703\pi$
$479$	2.58135	−	4.47103i	0.117945	−	0.204287i	0.918953	+	0.394367i	$0.129036\pi$
$480$		0			0
$481$	−25.0110	+	14.4401i	−1.14040	+	0.658413i
$482$		0			0
$483$	−13.2575	−	21.1734i	−0.603239	−	0.963422i
$484$		0			0
$485$	−38.9868	−	8.70035i	−1.77030	−	0.395063i
$486$		0			0
$487$	7.33027	−	1.96414i	0.332166	−	0.0890037i	−0.0888813	−	0.996042i	$-0.528329\pi$
$487$	7.33027	−	1.96414i	0.332166	−	0.0890037i	0.421048	+	0.907039i	$0.361663\pi$
$488$		0			0
$489$	35.1660			1.59026
$490$		0			0
$491$	−12.2484			−0.552763			−0.276382	−	0.961048i	$-0.589135\pi$
$491$	−12.2484			−0.552763			−0.276382	+	0.961048i	$0.589135\pi$
$492$		0			0
$493$	47.0004	−	12.5937i	2.11679	−	0.567192i
$494$		0			0
$495$	−14.7102	+	9.34256i	−0.661175	+	0.419917i
$496$		0			0
$497$	−14.8534	−	23.7221i	−0.666267	−	1.06408i
$498$		0			0
$499$	−21.1800	+	12.2283i	−0.948149	+	0.547414i	−0.892505	−	0.451037i	$-0.851054\pi$
$499$	−21.1800	+	12.2283i	−0.948149	+	0.547414i	−0.0556434	+	0.998451i	$0.517721\pi$
$500$		0			0
$501$	27.9728	−	48.4504i	1.24973	−	2.16460i
$502$		0			0
$503$	−15.4661	−	15.4661i	−0.689600	−	0.689600i	0.272544	−	0.962143i	$-0.412135\pi$
$503$	−15.4661	−	15.4661i	−0.689600	−	0.689600i	−0.962143	+	0.272544i	$0.912135\pi$
$504$		0			0
$505$	1.11794	+	26.4533i	0.0497476	+	1.17716i
$506$		0			0
$507$	3.91552	+	14.6129i	0.173894	+	0.648982i
$508$		0			0
$509$	−17.0981	−	29.6148i	−0.757861	−	1.31265i	−0.943940	−	0.330118i	$-0.892911\pi$
$509$	−17.0981	−	29.6148i	−0.757861	−	1.31265i	0.186079	−	0.982535i	$-0.440422\pi$
$510$		0			0
$511$	4.89826	+	4.55934i	0.216686	+	0.201693i
$512$		0			0
$513$	2.48125	+	0.664850i	0.109550	+	0.0293538i
$514$		0			0
$515$	−40.8786	+	12.8262i	−1.80132	+	0.565189i
$516$		0			0
$517$	22.9515	−	22.9515i	1.00941	−	1.00941i
$518$		0			0
$519$			9.26491i			0.406684i
$520$		0			0
$521$	−23.2204	−	13.4063i	−1.01730	−	0.587341i	−0.103983	−	0.994579i	$-0.533159\pi$
$521$	−23.2204	−	13.4063i	−1.01730	−	0.587341i	−0.913322	+	0.407238i	$0.866492\pi$
$522$		0			0
$523$	−1.52679	+	5.69806i	−0.0667619	+	0.249159i	−0.991239	−	0.132078i	$-0.957835\pi$
$523$	−1.52679	+	5.69806i	−0.0667619	+	0.249159i	0.924477	+	0.381237i	$0.124502\pi$
$524$		0			0
$525$	−27.9329	+	11.2246i	−1.21909	+	0.489881i
$526$		0			0
$527$	−9.41087	+	35.1218i	−0.409944	+	1.52993i
$528$		0			0
$529$	−5.00907	−	2.89199i	−0.217786	−	0.125739i
$530$		0			0
$531$			6.19401i			0.268797i
$532$		0			0
$533$	−14.5212	+	14.5212i	−0.628985	+	0.628985i
$534$		0			0
$535$	−15.8126	+	4.96141i	−0.683638	+	0.214500i
$536$		0			0
$537$	13.4120	+	3.59373i	0.578770	+	0.155081i
$538$		0			0
$539$	14.0408	+	20.7345i	0.604780	+	0.893096i
$540$		0			0
$541$	−10.7940	−	18.6957i	−0.464069	−	0.803791i	0.535090	−	0.844795i	$-0.320278\pi$
$541$	−10.7940	−	18.6957i	−0.464069	−	0.803791i	−0.999159	+	0.0410039i	$0.986944\pi$
$542$		0			0
$543$	13.7171	+	51.1928i	0.588656	+	2.19689i
$544$		0			0
$545$	0.399530	+	9.45390i	0.0171140	+	0.404961i
$546$		0			0
$547$	12.1156	+	12.1156i	0.518027	+	0.518027i	0.916974	−	0.398947i	$-0.130624\pi$
$547$	12.1156	+	12.1156i	0.518027	+	0.518027i	−0.398947	+	0.916974i	$0.630624\pi$
$548$		0			0
$549$	2.41430	−	4.18170i	0.103040	−	0.178471i
$550$		0			0
$551$	11.1815	−	6.45564i	0.476348	−	0.275020i
$552$		0			0
$553$	−13.0189	−	6.90700i	−0.553619	−	0.293716i
$554$		0			0
$555$	27.9863	−	17.7743i	1.18795	−	0.754476i
$556$		0			0
$557$	−6.98891	+	1.87267i	−0.296130	+	0.0793477i	−0.403825	−	0.914836i	$-0.632320\pi$
$557$	−6.98891	+	1.87267i	−0.296130	+	0.0793477i	0.107695	+	0.994184i	$0.465653\pi$
$558$		0			0
$559$	15.7695			0.666977
$560$		0			0
$561$	−42.1575			−1.77989
$562$		0			0
$563$	−1.51972	+	0.407209i	−0.0640487	+	0.0171618i	−0.290701	−	0.956814i	$-0.593889\pi$
$563$	−1.51972	+	0.407209i	−0.0640487	+	0.0171618i	0.226652	+	0.973976i	$0.427222\pi$
$564$		0			0
$565$	−25.3580	−	5.65893i	−1.06682	−	0.238073i
$566$		0			0
$567$	−28.5283	+	1.02235i	−1.19808	+	0.0429346i
$568$		0			0
$569$	−5.32597	+	3.07495i	−0.223276	+	0.128909i	−0.607466	−	0.794345i	$-0.707814\pi$
$569$	−5.32597	+	3.07495i	−0.223276	+	0.128909i	0.384190	+	0.923254i	$0.374481\pi$
$570$		0			0
$571$	−7.60099	+	13.1653i	−0.318092	+	0.550951i	−0.980090	−	0.198555i	$-0.936375\pi$
$571$	−7.60099	+	13.1653i	−0.318092	+	0.550951i	0.661998	+	0.749505i	$0.269709\pi$
$572$		0			0
$573$	−25.0636	−	25.0636i	−1.04705	−	1.04705i
$574$		0			0
$575$	13.3797	−	15.8551i	0.557972	−	0.661203i
$576$		0			0
$577$	4.68885	+	17.4990i	0.195199	+	0.728494i	0.992215	+	0.124536i	$0.0397441\pi$
$577$	4.68885	+	17.4990i	0.195199	+	0.728494i	−0.797016	+	0.603959i	$0.793589\pi$
$578$		0			0
$579$	24.6942	+	42.7716i	1.02626	+	1.77753i
$580$		0			0
$581$	−0.723787	+	3.14820i	−0.0300277	+	0.130609i
$582$		0			0
$583$	−6.28537	−	1.68416i	−0.260313	−	0.0697507i
$584$		0			0
$585$	−6.46424	−	20.6023i	−0.267263	−	0.851800i
$586$		0			0
$587$	−8.49695	+	8.49695i	−0.350707	+	0.350707i	−0.860373	−	0.509666i	$-0.829769\pi$
$587$	−8.49695	+	8.49695i	−0.350707	+	0.350707i	0.509666	+	0.860373i	$0.329769\pi$
$588$		0			0
$589$			9.64818i			0.397546i
$590$		0			0
$591$	−8.62975	−	4.98239i	−0.354980	−	0.204948i
$592$		0			0
$593$	−2.57872	+	9.62390i	−0.105895	+	0.395206i	−0.998445	−	0.0557423i	$-0.982247\pi$
$593$	−2.57872	+	9.62390i	−0.105895	+	0.395206i	0.892550	+	0.450948i	$0.148914\pi$
$594$		0			0
$595$	−30.1215	−	5.59774i	−1.23486	−	0.229485i
$596$		0			0
$597$	−0.502532	+	1.87547i	−0.0205673	+	0.0767581i
$598$		0			0
$599$	−37.5749	−	21.6939i	−1.53527	−	0.886388i	−0.999106	−	0.0422744i	$-0.986540\pi$
$599$	−37.5749	−	21.6939i	−1.53527	−	0.886388i	−0.536164	−	0.844114i	$-0.680127\pi$
$600$		0			0
$601$		−	46.7450i		−	1.90677i	−0.301757	−	0.953385i	$-0.597573\pi$
$601$		−	46.7450i		−	1.90677i	0.301757	−	0.953385i	$-0.402427\pi$
$602$		0			0
$603$	−6.98477	+	6.98477i	−0.284442	+	0.284442i
$604$		0			0
$605$	−1.86058	+	3.56197i	−0.0756432	+	0.144815i
$606$		0			0
$607$	−0.265783	−	0.0712163i	−0.0107878	−	0.00289058i	0.253421	−	0.967356i	$-0.418444\pi$
$607$	−0.265783	−	0.0712163i	−0.0107878	−	0.00289058i	−0.264209	+	0.964465i	$0.585111\pi$
$608$		0			0
$609$	−38.5435	+	41.4087i	−1.56186	+	1.67797i
$610$		0			0
$611$	20.1094	+	34.8305i	0.813538	+	1.40909i
$612$		0			0
$613$	7.61033	+	28.4021i	0.307378	+	1.14715i	0.930879	+	0.365328i	$0.119043\pi$
$613$	7.61033	+	28.4021i	0.307378	+	1.14715i	−0.623500	+	0.781823i	$0.714290\pi$
$614$		0			0
$615$	15.9512	−	17.3589i	0.643213	−	0.699977i
$616$		0			0
$617$	18.4708	+	18.4708i	0.743606	+	0.743606i	0.973270	−	0.229664i	$-0.0737626\pi$
$617$	18.4708	+	18.4708i	0.743606	+	0.743606i	−0.229664	+	0.973270i	$0.573763\pi$
$618$		0			0
$619$	−17.4488	+	30.2222i	−0.701325	+	1.21473i	0.266676	+	0.963786i	$0.414075\pi$
$619$	−17.4488	+	30.2222i	−0.701325	+	1.21473i	−0.968001	+	0.250945i	$0.919259\pi$
$620$		0			0
$621$	6.71734	−	3.87826i	0.269558	−	0.155629i
$622$		0			0
$623$	−1.06723	+	2.01161i	−0.0427578	+	0.0805934i
$624$		0			0
$625$	−15.9624	−	19.2406i	−0.638495	−	0.769626i
$626$		0			0
$627$	−10.8051	+	2.89523i	−0.431516	+	0.115624i
$628$		0			0
$629$	33.7409			1.34534
$630$		0			0
$631$	15.9645			0.635537			0.317768	−	0.948168i	$-0.397067\pi$
$631$	15.9645			0.635537			0.317768	+	0.948168i	$0.397067\pi$
$632$		0			0
$633$	−11.3361	+	3.03749i	−0.450569	+	0.120729i
$634$		0			0
$635$	−7.58780	+	34.0014i	−0.301113	+	1.34931i
$636$		0			0
$637$	−29.3192	+	10.1554i	−1.16167	+	0.402373i
$638$		0			0
$639$	−19.9583	+	11.5230i	−0.789540	+	0.455841i
$640$		0			0
$641$	−14.7498	+	25.5474i	−0.582581	+	1.00906i	0.412591	+	0.910916i	$0.364624\pi$
$641$	−14.7498	+	25.5474i	−0.582581	+	1.00906i	−0.995172	+	0.0981437i	$0.968710\pi$
$642$		0			0
$643$	7.54699	+	7.54699i	0.297624	+	0.297624i	0.840083	−	0.542458i	$-0.182506\pi$
$643$	7.54699	+	7.54699i	0.297624	+	0.297624i	−0.542458	+	0.840083i	$0.682506\pi$
$644$		0			0
$645$	−18.0866	+	0.764356i	−0.712161	+	0.0300965i
$646$		0			0
$647$	−0.0666143	−	0.248608i	−0.00261888	−	0.00977379i	0.964604	−	0.263703i	$-0.0849438\pi$
$647$	−0.0666143	−	0.248608i	−0.00261888	−	0.00977379i	−0.967223	+	0.253929i	$0.918277\pi$
$648$		0			0
$649$	5.08555	+	8.80843i	0.199625	+	0.345761i
$650$		0			0
$651$	−12.3966	−	40.4152i	−0.485861	−	1.58400i
$652$		0			0
$653$	1.25937	+	0.337448i	0.0492830	+	0.0132054i	0.283376	−	0.959009i	$-0.408545\pi$
$653$	1.25937	+	0.337448i	0.0492830	+	0.0132054i	−0.234093	+	0.972214i	$0.575212\pi$
$654$		0			0
$655$	−26.2066	−	13.6889i	−1.02398	−	0.534869i
$656$		0			0
$657$	3.89621	−	3.89621i	0.152005	−	0.152005i
$658$		0			0
$659$			2.87148i			0.111857i	0.998435	+	0.0559286i	$0.0178119\pi$
$659$			2.87148i			0.111857i	−0.998435	+	0.0559286i	$0.982188\pi$
$660$		0			0
$661$	21.1356	+	12.2026i	0.822078	+	0.474627i	0.851132	−	0.524951i	$-0.175916\pi$
$661$	21.1356	+	12.2026i	0.822078	+	0.474627i	−0.0290547	+	0.999578i	$0.509250\pi$
$662$		0			0
$663$	13.5199	−	50.4569i	0.525069	−	1.95958i
$664$		0			0
$665$	−8.10469	+	0.633912i	−0.314286	+	0.0245821i
$666$		0			0
$667$	10.0903	−	37.6576i	0.390699	−	1.45811i
$668$		0			0
$669$	18.8226	+	10.8672i	0.727723	+	0.420151i
$670$		0			0
$671$		−	7.92899i		−	0.306095i
$672$		0			0
$673$	28.1207	−	28.1207i	1.08397	−	1.08397i	0.0878369	−	0.996135i	$-0.472005\pi$
$673$	28.1207	−	28.1207i	1.08397	−	1.08397i	0.996135	−	0.0878369i	$-0.0279954\pi$
$674$		0			0
$675$	−3.17229	−	8.79217i	−0.122101	−	0.338411i
$676$		0			0
$677$	20.8842	+	5.59591i	0.802646	+	0.215068i	0.636745	−	0.771074i	$-0.280280\pi$
$677$	20.8842	+	5.59591i	0.802646	+	0.215068i	0.165901	+	0.986142i	$0.446947\pi$
$678$		0			0
$679$	46.0628	+	10.5901i	1.76773	+	0.406410i
$680$		0			0
$681$	−5.32982	−	9.23152i	−0.204239	−	0.353753i
$682$		0			0
$683$	−9.59848	−	35.8220i	−0.367276	−	1.37069i	−0.864309	−	0.502961i	$-0.832244\pi$
$683$	−9.59848	−	35.8220i	−0.367276	−	1.37069i	0.497034	−	0.867731i	$-0.334423\pi$
$684$		0			0
$685$	31.3295	+	28.7889i	1.19704	+	1.09997i
$686$		0			0
$687$	19.8653	+	19.8653i	0.757908	+	0.757908i
$688$		0			0
$689$	4.03142	−	6.98263i	0.153585	−	0.266017i
$690$		0			0
$691$	14.7640	−	8.52400i	0.561649	−	0.324268i	−0.192158	−	0.981364i	$-0.561549\pi$
$691$	14.7640	−	8.52400i	0.561649	−	0.324268i	0.753807	+	0.657096i	$0.228215\pi$
$692$		0			0
$693$	17.4759	−	10.9424i	0.663855	−	0.415667i
$694$		0			0
$695$	−2.61200	−	4.11269i	−0.0990787	−	0.156003i
$696$		0			0
$697$	23.1749	−	6.20970i	0.877813	−	0.235209i
$698$		0			0
$699$	−47.6089			−1.80074
$700$		0			0
$701$	10.9087			0.412017			0.206009	−	0.978550i	$-0.433953\pi$
$701$	10.9087			0.412017			0.206009	+	0.978550i	$0.433953\pi$
$702$		0			0
$703$	8.64793	−	2.31721i	0.326163	−	0.0873951i
$704$		0			0
$705$	−24.7525	−	38.9738i	−0.932235	−	1.46784i
$706$		0			0
$707$	−1.12195	−	31.3078i	−0.0421954	−	1.17745i
$708$		0			0
$709$	8.23815	−	4.75630i	0.309390	−	0.178627i	−0.337263	−	0.941410i	$-0.609501\pi$
$709$	8.23815	−	4.75630i	0.309390	−	0.178627i	0.646654	+	0.762784i	$0.276168\pi$
$710$		0			0
$711$	−6.06751	+	10.5092i	−0.227549	+	0.394127i
$712$		0			0
$713$	20.6001	+	20.6001i	0.771481	+	0.771481i
$714$		0			0
$715$	−26.1081	−	23.9909i	−0.976387	−	0.897208i
$716$		0			0
$717$	11.5229	+	43.0042i	0.430332	+	1.60602i
$718$		0			0
$719$	1.14039	+	1.97522i	0.0425295	+	0.0736632i	0.886507	−	0.462716i	$-0.153125\pi$
$719$	1.14039	+	1.97522i	0.0425295	+	0.0736632i	−0.843977	+	0.536379i	$0.819792\pi$
$720$		0			0
$721$	48.4645	−	14.8656i	1.80491	−	0.553622i
$722$		0			0
$723$	−1.09769	−	0.294125i	−0.0408234	−	0.0109386i
$724$		0			0
$725$	−42.5226	−	19.9735i	−1.57925	−	0.741798i
$726$		0			0
$727$	6.33666	−	6.33666i	0.235014	−	0.235014i	−0.579768	−	0.814782i	$-0.696857\pi$
$727$	6.33666	−	6.33666i	0.235014	−	0.235014i	0.814782	+	0.579768i	$0.196857\pi$
$728$		0			0
$729$			10.7432i			0.397896i
$730$		0			0
$731$	−15.9552	−	9.21176i	−0.590125	−	0.340709i
$732$		0			0
$733$	−6.74911	+	25.1880i	−0.249284	+	0.930341i	0.721897	+	0.692000i	$0.243270\pi$
$733$	−6.74911	+	25.1880i	−0.249284	+	0.930341i	−0.971182	+	0.238341i	$0.923396\pi$
$734$		0			0
$735$	33.1352	−	13.0688i	1.22221	−	0.482051i
$736$		0			0
$737$	−4.19816	+	15.6678i	−0.154641	+	0.577129i
$738$		0			0
$739$	33.9792	+	19.6179i	1.24994	+	0.721656i	0.971098	−	0.238680i	$-0.0767148\pi$
$739$	33.9792	+	19.6179i	1.24994	+	0.721656i	0.278846	+	0.960336i	$0.410048\pi$
$740$		0			0
$741$		−	13.8608i		−	0.509189i
$742$		0			0
$743$	−9.29603	+	9.29603i	−0.341038	+	0.341038i	−0.856758	−	0.515719i	$-0.827525\pi$
$743$	−9.29603	+	9.29603i	−0.341038	+	0.341038i	0.515719	+	0.856758i	$0.327525\pi$
$744$		0			0
$745$	−4.11702	−	2.15050i	−0.150836	−	0.0787883i
$746$		0			0
$747$	2.56923	+	0.688422i	0.0940031	+	0.0251880i
$748$		0			0
$749$	18.7470	−	5.75028i	0.685000	−	0.210111i
$750$		0			0
$751$	3.74551	+	6.48742i	0.136676	+	0.236729i	0.926236	−	0.376943i	$-0.123025\pi$
$751$	3.74551	+	6.48742i	0.136676	+	0.236729i	−0.789561	+	0.613673i	$0.789692\pi$
$752$		0			0
$753$	4.20561	+	15.6955i	0.153261	+	0.571977i
$754$		0			0
$755$	−13.3030	+	0.562194i	−0.484144	+	0.0204603i
$756$		0			0
$757$	−6.67005	−	6.67005i	−0.242427	−	0.242427i	0.575427	−	0.817853i	$-0.304836\pi$
$757$	−6.67005	−	6.67005i	−0.242427	−	0.242427i	−0.817853	+	0.575427i	$0.804836\pi$
$758$		0			0
$759$	−16.8887	+	29.2521i	−0.613021	+	1.06178i
$760$		0			0
$761$	−13.0745	+	7.54859i	−0.473952	+	0.273636i	−0.717893	−	0.696154i	$-0.754893\pi$
$761$	−13.0745	+	7.54859i	−0.473952	+	0.273636i	0.243941	+	0.969790i	$0.421560\pi$
$762$		0			0
$763$	−0.400965	−	11.1888i	−0.0145159	−	0.405062i
$764$		0			0
$765$	−5.49448	+	24.6211i	−0.198653	+	0.890178i
$766$		0			0
$767$	−12.1734	+	3.26187i	−0.439558	+	0.117779i
$768$		0			0
$769$	−3.50495			−0.126392			−0.0631959	−	0.998001i	$-0.520129\pi$
$769$	−3.50495			−0.126392			−0.0631959	+	0.998001i	$0.520129\pi$
$770$		0			0
$771$	−18.7155			−0.674024
$772$		0			0
$773$	24.6065	−	6.59331i	0.885036	−	0.237145i	0.212457	−	0.977170i	$-0.431853\pi$
$773$	24.6065	−	6.59331i	0.885036	−	0.237145i	0.672579	+	0.740026i	$0.265187\pi$
$774$		0			0
$775$	28.8138	−	20.0559i	1.03502	−	0.720428i
$776$		0			0
$777$	−33.2480	+	20.8180i	−1.19277	+	0.746840i
$778$		0			0
$779$	5.51337	−	3.18315i	0.197537	−	0.114048i
$780$		0			0
$781$	−18.9217	+	32.7733i	−0.677071	+	1.17272i
$782$		0			0
$783$	−12.4202	−	12.4202i	−0.443861	−	0.443861i
$784$		0			0
$785$	9.24617	−	10.0622i	0.330010	−	0.359134i
$786$		0			0
$787$	−5.16739	−	19.2850i	−0.184198	−	0.687435i	−0.994801	−	0.101839i	$-0.967527\pi$
$787$	−5.16739	−	19.2850i	−0.184198	−	0.687435i	0.810603	−	0.585596i	$-0.199139\pi$
$788$		0			0
$789$	−6.37302	−	11.0384i	−0.226886	−	0.392978i
$790$		0			0
$791$	29.9604	+	6.88807i	1.06527	+	0.244911i
$792$		0			0
$793$	9.48994	+	2.54282i	0.336998	+	0.0902983i
$794$		0			0
$795$	−4.28536	+	8.20408i	−0.151986	+	0.290969i
$796$		0			0
$797$	−26.5084	+	26.5084i	−0.938977	+	0.938977i	−0.998242	−	0.0592654i	$-0.981124\pi$
$797$	−26.5084	+	26.5084i	−0.938977	+	0.938977i	0.0592654	+	0.998242i	$0.481124\pi$
$798$		0			0
$799$		−	46.9877i		−	1.66231i
$800$		0			0
$801$	1.62383	+	0.937518i	0.0573752	+	0.0331256i
$802$		0			0
$803$	2.34180	−	8.73970i	0.0826402	−	0.308417i
$804$		0			0
$805$	−15.9511	+	18.6581i	−0.562202	+	0.657610i
$806$		0			0
$807$	18.4918	−	69.0123i	0.650941	−	2.42935i
$808$		0			0
$809$	28.6064	+	16.5159i	1.00575	+	0.580668i	0.909943	−	0.414733i	$-0.136125\pi$
$809$	28.6064	+	16.5159i	1.00575	+	0.580668i	0.0958027	+	0.995400i	$0.469458\pi$
$810$		0			0
$811$			40.2650i			1.41390i	0.707265	+	0.706948i	$0.249929\pi$
$811$			40.2650i			1.41390i	−0.707265	+	0.706948i	$0.750071\pi$
$812$		0			0
$813$	9.37441	−	9.37441i	0.328775	−	0.328775i
$814$		0			0
$815$	−10.3447	−	32.9698i	−0.362359	−	1.15488i
$816$		0			0
$817$	−4.72202	−	1.26526i	−0.165203	−	0.0442659i
$818$		0			0
$819$	7.49206	+	24.4255i	0.261794	+	0.853497i
$820$		0			0
$821$	−17.3554	−	30.0604i	−0.605707	−	1.04911i	−0.991939	−	0.126713i	$-0.959557\pi$
$821$	−17.3554	−	30.0604i	−0.605707	−	1.04911i	0.386233	−	0.922401i	$-0.373776\pi$
$822$		0			0
$823$	10.8152	+	40.3629i	0.376995	+	1.40696i	0.850408	+	0.526123i	$0.176355\pi$
$823$	10.8152	+	40.3629i	0.376995	+	1.40696i	−0.473414	+	0.880840i	$0.656978\pi$
$824$		0			0
$825$	31.1073	+	26.2507i	1.08302	+	0.913930i
$826$		0			0
$827$	25.2377	+	25.2377i	0.877600	+	0.877600i	0.993286	−	0.115686i	$-0.0369067\pi$
$827$	25.2377	+	25.2377i	0.877600	+	0.877600i	−0.115686	+	0.993286i	$0.536907\pi$
$828$		0			0
$829$	10.2989	−	17.8381i	0.357694	−	0.619544i	−0.629881	−	0.776692i	$-0.716896\pi$
$829$	10.2989	−	17.8381i	0.357694	−	0.619544i	0.987575	+	0.157147i	$0.0502297\pi$
$830$		0			0
$831$	29.1769	−	16.8453i	1.01214	−	0.584357i
$832$		0			0
$833$	35.5970	+	6.85182i	1.23336	+	0.237401i
$834$		0			0
$835$	−53.6532	−	11.9733i	−1.85674	−	0.414354i
$836$		0			0
$837$	12.6784	−	3.39715i	0.438228	−	0.117423i
$838$		0			0
$839$	−8.88062			−0.306593			−0.153297	−	0.988180i	$-0.548989\pi$
$839$	−8.88062			−0.306593			−0.153297	+	0.988180i	$0.548989\pi$
$840$		0			0
$841$	−59.2847			−2.04430
$842$		0			0
$843$	8.89154	−	2.38248i	0.306241	−	0.0820570i
$844$		0			0
$845$	12.5485	−	7.96961i	0.431680	−	0.274163i
$846$		0			0
$847$	2.22845	−	4.20037i	0.0765706	−	0.144327i
$848$		0			0
$849$	−9.53894	+	5.50731i	−0.327376	+	0.189010i
$850$		0			0
$851$	13.5169	−	23.4120i	0.463355	−	0.802554i
$852$		0			0
$853$	−17.0978	−	17.0978i	−0.585417	−	0.585417i	0.350970	−	0.936387i	$-0.385852\pi$
$853$	−17.0978	−	17.0978i	−0.585417	−	0.585417i	−0.936387	+	0.350970i	$0.885852\pi$
$854$		0			0
$855$	0.282633	+	6.68783i	0.00966586	+	0.228719i
$856$		0			0
$857$	1.82672	+	6.81740i	0.0623995	+	0.232878i	0.990082	−	0.140493i	$-0.0448686\pi$
$857$	1.82672	+	6.81740i	0.0623995	+	0.232878i	−0.927682	+	0.373371i	$0.878202\pi$
$858$		0			0
$859$	15.4580	+	26.7741i	0.527422	+	0.913521i	0.999489	+	0.0319586i	$0.0101745\pi$
$859$	15.4580	+	26.7741i	0.527422	+	0.913521i	−0.472068	+	0.881562i	$0.656492\pi$
$860$		0			0
$861$	−19.0050	+	20.4178i	−0.647690	+	0.695837i
$862$		0			0
$863$	−0.835836	−	0.223962i	−0.0284522	−	0.00762374i	0.244565	−	0.969633i	$-0.421355\pi$
$863$	−0.835836	−	0.223962i	−0.0284522	−	0.00762374i	−0.273017	+	0.962009i	$0.588022\pi$
$864$		0			0
$865$	8.68628	−	2.72543i	0.295342	−	0.0926675i
$866$		0			0
$867$	−15.7986	+	15.7986i	−0.536549	+	0.536549i
$868$		0			0
$869$			19.9267i			0.675968i
$870$		0			0
$871$	−17.4059	−	10.0493i	−0.589775	−	0.340507i
$872$		0			0
$873$	10.0726	−	37.5916i	0.340908	−	1.27228i
$874$		0			0
$875$	18.7405	+	22.8865i	0.633545	+	0.773706i
$876$		0			0
$877$	5.30921	−	19.8142i	0.179279	−	0.669079i	−0.816504	−	0.577340i	$-0.804091\pi$
$877$	5.30921	−	19.8142i	0.179279	−	0.669079i	0.995783	−	0.0917391i	$-0.0292426\pi$
$878$		0			0
$879$	−3.27957	−	1.89346i	−0.110617	−	0.0638649i
$880$		0			0
$881$			7.65158i			0.257788i	0.991658	+	0.128894i	$0.0411428\pi$
$881$			7.65158i			0.257788i	−0.991658	+	0.128894i	$0.958857\pi$
$882$		0			0
$883$	39.4562	−	39.4562i	1.32781	−	1.32781i	0.420528	−	0.907279i	$-0.361845\pi$
$883$	39.4562	−	39.4562i	1.32781	−	1.32781i	0.907279	−	0.420528i	$-0.138155\pi$
$884$		0			0
$885$	13.8041	−	4.33122i	0.464021	−	0.145593i
$886$		0			0
$887$	−14.6259	−	3.91901i	−0.491091	−	0.131587i	0.00477122	−	0.999989i	$-0.498481\pi$
$887$	−14.6259	−	3.91901i	−0.491091	−	0.131587i	−0.495862	+	0.868401i	$0.665148\pi$
$888$		0			0
$889$	9.23590	−	40.1726i	0.309762	−	1.34735i
$890$		0			0
$891$	19.2989	+	33.4267i	0.646538	+	1.11984i
$892$		0			0
$893$	−3.22695	−	12.0432i	−0.107986	−	0.403009i
$894$		0			0
$895$	−0.576079	−	13.6315i	−0.0192562	−	0.455651i
$896$		0			0
$897$	−29.5946	−	29.5946i	−0.988137	−	0.988137i
$898$		0			0
$899$	32.9861	−	57.1336i	1.10015	−	1.90551i
$900$		0			0
$901$	−8.15784	+	4.70993i	−0.271777	+	0.156910i
$902$		0			0
$903$	21.4058	−	0.767102i	0.712339	−	0.0255276i
$904$		0			0
$905$	43.9605	−	27.9196i	1.46130	−	0.928080i
$906$		0			0
$907$	14.7951	−	3.96434i	0.491264	−	0.131634i	−0.00467871	−	0.999989i	$-0.501489\pi$
$907$	14.7951	−	3.96434i	0.491264	−	0.131634i	0.495943	+	0.868355i	$0.334823\pi$
$908$		0			0
$909$	−25.7955			−0.855582
$910$		0			0
$911$	−32.8204			−1.08739			−0.543694	−	0.839284i	$-0.682975\pi$
$911$	−32.8204			−1.08739			−0.543694	+	0.839284i	$0.682975\pi$
$912$		0			0
$913$	4.21889	−	1.13045i	0.139625	−	0.0374124i
$914$		0			0
$915$	−11.0077	−	2.45648i	−0.363902	−	0.0812089i
$916$		0			0
$917$	30.9036	+	16.3955i	1.02053	+	0.541427i
$918$		0			0
$919$	−35.7071	+	20.6155i	−1.17787	+	0.680043i	−0.955520	−	0.294925i	$-0.904705\pi$
$919$	−35.7071	+	20.6155i	−1.17787	+	0.680043i	−0.222348	+	0.974967i	$0.571372\pi$
$920$		0			0
$921$	19.2702	−	33.3769i	0.634974	−	1.09981i
$922$		0			0
$923$	−33.1571	−	33.1571i	−1.09138	−	1.09138i
$924$		0			0
$925$	−24.8968	−	21.0098i	−0.818603	−	0.690798i
$926$		0			0
$927$	−10.8033	−	40.3186i	−0.354828	−	1.32424i
$928$		0			0
$929$	3.21108	+	5.56175i	0.105352	+	0.182475i	0.913882	−	0.405980i	$-0.133070\pi$
$929$	3.21108	+	5.56175i	0.105352	+	0.182475i	−0.808530	+	0.588455i	$0.799736\pi$
$930$		0			0
$931$	9.59421	−	0.688525i	0.314438	−	0.0225655i
$932$		0			0
$933$	−11.3614	−	3.04428i	−0.371956	−	0.0996653i
$934$		0			0
$935$	12.4014	+	39.5246i	0.405568	+	1.29259i
$936$		0			0
$937$	−38.1300	+	38.1300i	−1.24565	+	1.24565i	−0.288034	+	0.957620i	$0.593002\pi$
$937$	−38.1300	+	38.1300i	−1.24565	+	1.24565i	−0.957620	+	0.288034i	$0.906998\pi$
$938$		0			0
$939$			14.4314i			0.470951i
$940$		0			0
$941$	5.07275	+	2.92875i	0.165367	+	0.0954746i	0.580399	−	0.814332i	$-0.302896\pi$
$941$	5.07275	+	2.92875i	0.165367	+	0.0954746i	−0.415032	+	0.909807i	$0.636230\pi$
$942$		0			0
$943$	4.97534	−	18.5682i	0.162019	−	0.604664i
$944$		0			0
$945$	3.68669	+	10.4269i	0.119928	+	0.339187i
$946$		0			0
$947$	−4.77285	+	17.8125i	−0.155097	+	0.578829i	0.844000	+	0.536343i	$0.180195\pi$
$947$	−4.77285	+	17.8125i	−0.155097	+	0.578829i	−0.999097	+	0.0424864i	$0.986472\pi$
$948$		0			0
$949$	9.70924	+	5.60563i	0.315175	+	0.181967i
$950$		0			0
$951$			46.9806i			1.52345i
$952$		0			0
$953$	−4.66301	+	4.66301i	−0.151050	+	0.151050i	−0.778587	−	0.627537i	$-0.784063\pi$
$953$	−4.66301	+	4.66301i	−0.151050	+	0.151050i	0.627537	+	0.778587i	$0.284063\pi$
$954$		0			0
$955$	−16.1254	+	30.8712i	−0.521806	+	0.998968i
$956$		0			0
$957$	73.8833	+	19.7970i	2.38831	+	0.639945i
$958$		0			0
$959$	−36.8503	−	34.3005i	−1.18996	−	1.10762i
$960$		0			0
$961$	9.14945	+	15.8473i	0.295144	+	0.511204i
$962$		0			0
$963$	−4.17893	−	15.5960i	−0.134664	−	0.502574i
$964$		0			0
$965$	32.8361	−	35.7339i	1.05703	−	1.15032i
$966$		0			0
$967$	34.1689	+	34.1689i	1.09880	+	1.09880i	0.994551	+	0.104247i	$0.0332432\pi$
$967$	34.1689	+	34.1689i	1.09880	+	1.09880i	0.104247	+	0.994551i	$0.466757\pi$
$968$		0			0
$969$	−8.09682	+	14.0241i	−0.260107	+	0.450519i
$970$		0			0
$971$	31.8954	−	18.4148i	1.02357	−	0.590959i	0.108435	−	0.994104i	$-0.465416\pi$
$971$	31.8954	−	18.4148i	1.02357	−	0.590959i	0.915136	+	0.403145i	$0.132083\pi$
$972$		0			0
$973$	3.05928	+	4.88592i	0.0980760	+	0.156635i
$974$		0			0
$975$	−41.3946	+	28.8127i	−1.32569	+	0.922746i
$976$		0			0
$977$	33.0886	−	8.86606i	1.05860	−	0.283650i	0.312797	−	0.949820i	$-0.398734\pi$
$977$	33.0886	−	8.86606i	1.05860	−	0.283650i	0.745800	+	0.666170i	$0.232067\pi$
$978$		0			0
$979$	3.07897			0.0984044
$980$		0			0
$981$	−9.21881			−0.294334
$982$		0			0
$983$	−21.5030	+	5.76170i	−0.685838	+	0.183770i	−0.584879	−	0.811121i	$-0.698858\pi$
$983$	−21.5030	+	5.76170i	−0.685838	+	0.183770i	−0.100960	+	0.994891i	$0.532191\pi$
$984$		0			0
$985$	−2.13263	+	9.55644i	−0.0679512	+	0.304494i
$986$		0			0
$987$	28.9912	+	46.3013i	0.922800	+	1.47379i
$988$		0			0
$989$	−12.7836	+	7.38064i	−0.406496	+	0.234691i
$990$		0			0
$991$	7.35178	−	12.7337i	0.233537	−	0.404498i	−0.725309	−	0.688423i	$-0.758303\pi$
$991$	7.35178	−	12.7337i	0.233537	−	0.404498i	0.958847	+	0.283925i	$0.0916366\pi$
$992$		0			0
$993$	28.2194	+	28.2194i	0.895517	+	0.895517i
$994$		0			0
$995$	1.90617	−	0.0805564i	0.0604297	−	0.00255381i
$996$		0			0
$997$	6.14395	+	22.9296i	0.194581	+	0.726186i	0.992375	+	0.123256i	$0.0393336\pi$
$997$	6.14395	+	22.9296i	0.194581	+	0.726186i	−0.797794	+	0.602930i	$0.794000\pi$
$998$		0			0
$999$	−6.08993	−	10.5481i	−0.192677	−	0.333726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.17.10	✓	48
4.3	odd	2		560.2.ci.e.17.3		48
5.3	odd	4	inner	280.2.bo.a.73.10	yes	48
7.5	odd	6	inner	280.2.bo.a.257.10	yes	48
20.3	even	4		560.2.ci.e.353.3		48
28.19	even	6		560.2.ci.e.257.3		48
35.33	even	12	inner	280.2.bo.a.33.10	yes	48
140.103	odd	12		560.2.ci.e.33.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.10	✓	48	1.1	even	1	trivial
280.2.bo.a.33.10	yes	48	35.33	even	12	inner
280.2.bo.a.73.10	yes	48	5.3	odd	4	inner
280.2.bo.a.257.10	yes	48	7.5	odd	6	inner
560.2.ci.e.17.3		48	4.3	odd	2
560.2.ci.e.33.3		48	140.103	odd	12
560.2.ci.e.257.3		48	28.19	even	6
560.2.ci.e.353.3		48	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19810 - 0.588978i) q^{3} +(-1.19880 - 1.88756i) q^{5} +(1.40409 + 2.24244i) q^{7} +(1.88665 - 1.08926i) q^{9} +O(q^{10})\)	\(q+(2.19810 - 0.588978i) q^{3} +(-1.19880 - 1.88756i) q^{5} +(1.40409 + 2.24244i) q^{7} +(1.88665 - 1.08926i) q^{9} +(1.78866 - 3.09805i) q^{11} +(3.13432 + 3.13432i) q^{13} +(-3.74681 - 3.44296i) q^{15} +(-1.34033 - 5.00217i) q^{17} +(-0.687063 - 1.19003i) q^{19} +(4.40706 + 4.10213i) q^{21} +(-4.00784 - 1.07390i) q^{23} +(-2.12575 + 4.52561i) q^{25} +(-1.32186 + 1.32186i) q^{27} +9.39599i q^{29} +(-6.08064 - 3.51066i) q^{31} +(2.10696 - 7.86328i) q^{33} +(2.54952 - 5.33854i) q^{35} +(-1.68631 + 6.29340i) q^{37} +(8.73559 + 5.04350i) q^{39} +4.63297i q^{41} +(2.51561 - 2.51561i) q^{43} +(-4.31776 - 2.25536i) q^{45} +(8.76422 + 2.34837i) q^{47} +(-3.05709 + 6.29716i) q^{49} +(-5.89234 - 10.2058i) q^{51} +(-0.470788 - 1.75701i) q^{53} +(-7.99199 + 0.337748i) q^{55} +(-2.21113 - 2.21113i) q^{57} +(-1.42161 + 2.46230i) q^{59} +(1.91951 - 1.10823i) q^{61} +(5.09162 + 2.70129i) q^{63} +(2.15879 - 9.67365i) q^{65} +(-4.37975 + 1.17355i) q^{67} -9.44211 q^{69} -10.5787 q^{71} +(2.44309 - 0.654624i) q^{73} +(-2.00711 + 11.1998i) q^{75} +(9.45862 - 0.338961i) q^{77} +(-4.82403 + 2.78515i) q^{79} +(-5.39481 + 9.34408i) q^{81} +(0.863341 + 0.863341i) q^{83} +(-7.83510 + 8.52656i) q^{85} +(5.53403 + 20.6533i) q^{87} +(0.430347 + 0.745382i) q^{89} +(-2.62768 + 11.4294i) q^{91} +(-15.4335 - 4.13540i) q^{93} +(-1.42259 + 2.72348i) q^{95} +(12.6320 - 12.6320i) q^{97} -7.79325i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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