LMFDB - Embedded newform 280.2.bo.a.33.10

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			33.10
Character	$\chi$	$=$	280.33
Dual form			280.2.bo.a.17.10

$q$-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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.19810	+	0.588978i	1.26907	+	0.340047i	0.829675	−	0.558247i	$-0.188526\pi$
$3$	2.19810	+	0.588978i	1.26907	+	0.340047i	0.439396	+	0.898293i	$0.355192\pi$
$4$		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	0.998942	+	0.0459913i	$0.0146447\pi$
$11$	1.78866	+	3.09805i	0.539301	+	0.934096i	−0.459641	+	0.888105i	$0.652022\pi$
$12$		0			0
$13$	3.13432	−	3.13432i	0.869305	−	0.869305i	−0.123090	−	0.992395i	$-0.539280\pi$
$13$	3.13432	−	3.13432i	0.869305	−	0.869305i	0.992395	+	0.123090i	$0.0392804\pi$
$14$		0			0
$15$	−3.74681	+	3.44296i	−0.967422	+	0.888970i
$16$		0			0
$17$	−1.34033	+	5.00217i	−0.325077	+	1.21320i	0.589157	+	0.808019i	$0.299460\pi$
$17$	−1.34033	+	5.00217i	−0.325077	+	1.21320i	−0.914234	+	0.405186i	$0.867207\pi$
$18$		0			0
$19$	−0.687063	+	1.19003i	−0.157623	+	0.273011i	−0.934011	−	0.357244i	$-0.883716\pi$
$19$	−0.687063	+	1.19003i	−0.157623	+	0.273011i	0.776388	+	0.630255i	$0.217050\pi$
$20$		0			0
$21$	4.40706	−	4.10213i	0.961700	−	0.895157i
$22$		0			0
$23$	−4.00784	+	1.07390i	−0.835692	+	0.223923i	−0.651195	−	0.758910i	$-0.725732\pi$
$23$	−4.00784	+	1.07390i	−0.835692	+	0.223923i	−0.184497	+	0.982833i	$0.559065\pi$
$24$		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	$-0.662565\pi$
$29$		−	9.39599i		−	1.74479i	0.488800	−	0.872396i	$-0.337435\pi$
$30$		0			0
$31$	−6.08064	+	3.51066i	−1.09212	+	0.630533i	−0.934139	−	0.356910i	$-0.883830\pi$
$31$	−6.08064	+	3.51066i	−1.09212	+	0.630533i	−0.157976	+	0.987443i	$0.550497\pi$
$32$		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	−0.954334	−	0.298743i	$-0.903433\pi$
$37$	−1.68631	−	6.29340i	−0.277228	−	1.03463i	0.677105	−	0.735886i	$-0.263234\pi$
$38$		0			0
$39$	8.73559	−	5.04350i	1.39881	−	0.807606i
$40$		0			0
$41$		−	4.63297i		−	0.723549i	−0.932266	−	0.361774i	$-0.882171\pi$
$41$		−	4.63297i		−	0.723549i	0.932266	−	0.361774i	$-0.117829\pi$
$42$		0			0
$43$	2.51561	+	2.51561i	0.383626	+	0.383626i	0.872407	−	0.488780i	$-0.162558\pi$
$43$	2.51561	+	2.51561i	0.383626	+	0.383626i	−0.488780	+	0.872407i	$0.662558\pi$
$44$		0			0
$45$	−4.31776	+	2.25536i	−0.643654	+	0.336209i
$46$		0			0
$47$	8.76422	−	2.34837i	1.27839	−	0.342544i	0.445153	−	0.895455i	$-0.353149\pi$
$47$	8.76422	−	2.34837i	1.27839	−	0.342544i	0.833241	+	0.552910i	$0.186483\pi$
$48$		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	−0.990692	−	0.136120i	$-0.956537\pi$
$53$	−0.470788	+	1.75701i	−0.0646678	+	0.241343i	0.926025	+	0.377463i	$0.123203\pi$
$54$		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	0.758525	−	0.651644i	$-0.225920\pi$
$59$	−1.42161	−	2.46230i	−0.185078	−	0.320565i	−0.943603	+	0.331080i	$0.892587\pi$
$60$		0			0
$61$	1.91951	+	1.10823i	0.245769	+	0.141895i	0.617825	−	0.786315i	$-0.288014\pi$
$61$	1.91951	+	1.10823i	0.245769	+	0.141895i	−0.372057	+	0.928210i	$0.621347\pi$
$62$		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	−0.0188425	−	0.999822i	$-0.505998\pi$
$67$	−4.37975	−	1.17355i	−0.535072	−	0.143372i	−0.516229	+	0.856450i	$0.672665\pi$
$68$		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	0.398939	−	0.916977i	$-0.369378\pi$
$73$	2.44309	+	0.654624i	0.285942	+	0.0766179i	−0.112997	+	0.993595i	$0.536045\pi$
$74$		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	0.203446	−	0.979086i	$-0.434786\pi$
$79$	−4.82403	−	2.78515i	−0.542745	−	0.313354i	−0.746191	+	0.665732i	$0.768119\pi$
$80$		0			0
$81$	−5.39481	−	9.34408i	−0.599423	−	1.03823i
$82$		0			0
$83$	0.863341	−	0.863341i	0.0947640	−	0.0947640i	−0.658136	−	0.752899i	$-0.728655\pi$
$83$	0.863341	−	0.863341i	0.0947640	−	0.0947640i	0.752899	+	0.658136i	$0.228655\pi$
$84$		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	−0.842316	−	0.538985i	$-0.818808\pi$
$89$	0.430347	−	0.745382i	0.0456167	−	0.0790104i	0.887932	+	0.459974i	$0.152141\pi$
$90$		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	0.939193	+	0.343390i	$0.111575\pi$
$97$	12.6320	+	12.6320i	1.28258	+	1.28258i	0.343390	+	0.939193i	$0.388425\pi$
$98$		0			0
$99$			7.79325i			0.783251i
$100$		0			0
$101$	−10.2545	+	5.92042i	−1.02036	+	0.589103i	−0.914207	−	0.405247i	$-0.867186\pi$
$101$	−10.2545	+	5.92042i	−1.02036	+	0.589103i	−0.106150	+	0.994350i	$0.533852\pi$
$102$		0			0
$103$	4.95903	+	18.5073i	0.488627	+	1.82358i	0.563139	+	0.826362i	$0.309594\pi$
$103$	4.95903	+	18.5073i	0.488627	+	1.82358i	−0.0745114	+	0.997220i	$0.523740\pi$
$104$		0			0
$105$	2.45980	+	13.2362i	0.240052	+	1.29172i
$106$		0			0
$107$	1.91825	+	7.15899i	0.185444	+	0.692086i	0.994535	+	0.104403i	$0.0332931\pi$
$107$	1.91825	+	7.15899i	0.185444	+	0.692086i	−0.809091	+	0.587683i	$0.800040\pi$
$108$		0			0
$109$	−3.66475	+	2.11584i	−0.351019	+	0.202661i	−0.665134	−	0.746724i	$-0.731626\pi$
$109$	−3.66475	+	2.11584i	−0.351019	+	0.202661i	0.314115	+	0.949385i	$0.398292\pi$
$110$		0			0
$111$		−	14.8267i		−	1.40729i
$112$		0			0
$113$	8.21616	+	8.21616i	0.772911	+	0.772911i	0.978614	−	0.205703i	$-0.0659481\pi$
$113$	8.21616	+	8.21616i	0.772911	+	0.772911i	−0.205703	+	0.978614i	$0.565948\pi$
$114$		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	−0.999754	−	0.0221820i	$-0.992939\pi$
$127$	−11.0167	+	11.0167i	−0.977572	+	0.977572i	0.0221820	+	0.999754i	$0.492939\pi$
$128$		0			0
$129$	4.04791	+	7.01118i	0.356398	+	0.617300i
$130$		0			0
$131$	11.4510	+	6.61125i	1.00048	+	0.577628i	0.908391	−	0.418123i	$-0.137312\pi$
$131$	11.4510	+	6.61125i	1.00048	+	0.577628i	0.0920903	+	0.995751i	$0.470645\pi$
$132$		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	−0.634383	−	0.773019i	$-0.718746\pi$
$137$	−18.3797	−	4.92483i	−1.57028	−	0.420756i	−0.935901	+	0.352263i	$0.885412\pi$
$138$		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	0.571874	−	0.820341i	$-0.306217\pi$
$149$	1.79894	+	1.03862i	0.147375	+	0.0850868i	−0.424499	+	0.905428i	$0.639550\pi$
$150$		0			0
$151$	2.97729	+	5.15681i	0.242288	+	0.419655i	0.961366	−	0.275274i	$-0.0887687\pi$
$151$	2.97729	+	5.15681i	0.242288	+	0.419655i	−0.719078	+	0.694930i	$0.755435\pi$
$152$		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	−0.873646	−	0.486562i	$-0.838251\pi$
$157$	1.58172	−	5.90304i	0.126235	−	0.471114i	0.999881	+	0.0154480i	$0.00491745\pi$
$158$		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	0.378536	−	0.925587i	$-0.376428\pi$
$163$	14.9267	−	3.99960i	1.16915	−	0.313273i	0.790615	+	0.612313i	$0.209761\pi$
$164$		0			0
$165$	−17.3682	−	5.44951i	−1.35211	−	0.424243i
$166$		0			0
$167$	17.3840	+	17.3840i	1.34521	+	1.34521i	0.890783	+	0.454428i	$0.150156\pi$
$167$	17.3840	+	17.3840i	1.34521	+	1.34521i	0.454428	+	0.890783i	$0.349844\pi$
$168$		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	0.914230	−	0.405196i	$-0.132797\pi$
$173$	−1.05374	−	3.93262i	−0.0801146	−	0.298992i	−0.994344	+	0.106205i	$0.966130\pi$
$174$		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	−0.289348	−	0.957224i	$-0.593439\pi$
$179$	5.28417	−	3.05082i	0.394958	−	0.228029i	0.684306	+	0.729195i	$0.260105\pi$
$180$		0			0
$181$		−	23.2896i		−	1.73110i	−0.500820	−	0.865552i	$-0.666968\pi$
$181$		−	23.2896i		−	1.73110i	0.500820	−	0.865552i	$-0.333032\pi$
$182$		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	0.433666	+	0.901074i	$0.357220\pi$
$191$	−7.78800	+	13.4892i	−0.563520	+	0.976045i	−0.997186	+	0.0749713i	$0.976113\pi$
$192$		0			0
$193$	5.61718	−	20.9636i	0.404333	−	1.50899i	−0.400949	−	0.916100i	$-0.631320\pi$
$193$	5.61718	−	20.9636i	0.404333	−	1.50899i	0.805282	−	0.592892i	$-0.202014\pi$
$194$		0			0
$195$	−0.952351	+	22.5351i	−0.0681993	+	1.61377i
$196$		0			0
$197$	−3.09635	+	3.09635i	−0.220606	+	0.220606i	−0.808753	−	0.588148i	$-0.799857\pi$
$197$	−3.09635	+	3.09635i	−0.220606	+	0.220606i	0.588148	+	0.808753i	$0.299857\pi$
$198$		0			0
$199$	−0.426614	−	0.738916i	−0.0302418	−	0.0523804i	0.850508	−	0.525962i	$-0.176294\pi$
$199$	−0.426614	−	0.738916i	−0.0302418	−	0.0523804i	−0.880750	+	0.473581i	$0.842961\pi$
$200$		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	−0.443851	−	0.896101i	$-0.646388\pi$
$223$	6.75353	−	6.75353i	0.452250	−	0.452250i	0.896101	+	0.443851i	$0.146388\pi$
$224$		0			0
$225$	0.919019	−	10.8538i	0.0612679	−	0.723584i
$226$		0			0
$227$	−1.21237	+	4.52464i	−0.0804680	+	0.300311i	−0.994417	−	0.105517i	$-0.966350\pi$
$227$	−1.21237	+	4.52464i	−0.0804680	+	0.300311i	0.913949	+	0.405828i	$0.133017\pi$
$228$		0			0
$229$	6.17273	−	10.6915i	0.407905	−	0.706513i	−0.586750	−	0.809768i	$-0.699593\pi$
$229$	6.17273	−	10.6915i	0.407905	−	0.706513i	0.994655	+	0.103256i	$0.0329260\pi$
$230$		0			0
$231$	20.5913	+	6.31598i	1.35481	+	0.415561i
$232$		0			0
$233$	−20.2083	+	5.41480i	−1.32389	+	0.354735i	−0.850433	−	0.526083i	$-0.823660\pi$
$233$	−20.2083	+	5.41480i	−1.32389	+	0.354735i	−0.473456	+	0.880818i	$0.656994\pi$
$234$		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	$-0.781924\pi$
$239$		−	19.5643i		−	1.26551i	0.774352	−	0.632755i	$-0.218076\pi$
$240$		0			0
$241$	−0.432477	+	0.249691i	−0.0278583	+	0.0160840i	−0.513864	−	0.857871i	$-0.671787\pi$
$241$	−0.432477	+	0.249691i	−0.0278583	+	0.0160840i	0.486006	+	0.873955i	$0.338453\pi$
$242$		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	$-0.927647\pi$
$251$		−	7.14052i		−	0.450705i	0.974277	−	0.225353i	$-0.0723535\pi$
$252$		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	−0.497928	−	0.867218i	$-0.665906\pi$
$257$	−7.94408	+	2.12861i	−0.495538	+	0.132779i	0.00239046	+	0.999997i	$0.499239\pi$
$258$		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	−0.996109	−	0.0881258i	$-0.971912\pi$
$263$	−1.44967	+	5.41024i	−0.0893905	+	0.333610i	0.906719	+	0.421736i	$0.138579\pi$
$264$		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	0.729403	+	0.684084i	$0.239798\pi$
$269$	15.6982	+	27.1901i	0.957136	+	1.65781i	0.227732	+	0.973724i	$0.426869\pi$
$270$		0			0
$271$	5.04530	+	2.91290i	0.306480	+	0.176946i	0.645350	−	0.763887i	$-0.276711\pi$
$271$	5.04530	+	2.91290i	0.306480	+	0.176946i	−0.338870	+	0.940833i	$0.610045\pi$
$272$		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	0.661425	−	0.750011i	$-0.269952\pi$
$277$	14.3005	+	3.83179i	0.859231	+	0.230230i	0.197806	+	0.980241i	$0.436619\pi$
$278$		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	0.117168	−	0.993112i	$-0.462619\pi$
$283$	−4.67531	−	1.25275i	−0.277918	−	0.0744680i	−0.395086	+	0.918644i	$0.629285\pi$
$284$		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	−0.740643	−	0.671899i	$-0.765479\pi$
$293$	−1.17671	+	1.17671i	−0.0687440	+	0.0687440i	0.671899	+	0.740643i	$0.265479\pi$
$294$		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	0.960784	−	0.277299i	$-0.0894393\pi$
$307$	11.9756	+	11.9756i	0.683485	+	0.683485i	−0.277299	+	0.960784i	$0.589439\pi$
$308$		0			0
$309$			43.6017i			2.48041i
$310$		0			0
$311$	−4.47627	+	2.58438i	−0.253826	+	0.146547i	−0.621515	−	0.783402i	$-0.713482\pi$
$311$	−4.47627	+	2.58438i	−0.253826	+	0.146547i	0.367689	+	0.929949i	$0.380149\pi$
$312$		0			0
$313$	−1.64135	−	6.12562i	−0.0927748	−	0.346240i	0.903898	−	0.427748i	$-0.140693\pi$
$313$	−1.64135	−	6.12562i	−0.0927748	−	0.346240i	−0.996673	+	0.0815080i	$0.974026\pi$
$314$		0			0
$315$	−1.00499	+	12.8490i	−0.0566250	+	0.723962i
$316$		0			0
$317$	−5.34333	−	19.9416i	−0.300112	−	1.12003i	−0.937072	−	0.349135i	$-0.886475\pi$
$317$	−5.34333	−	19.9416i	−0.300112	−	1.12003i	0.636961	−	0.770896i	$-0.280191\pi$
$318$		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	−0.517820	−	0.855490i	$-0.673256\pi$
$331$	8.76860	−	15.1877i	0.481966	−	0.834790i	0.999786	+	0.0207000i	$0.00658950\pi$
$332$		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	−0.827984	−	0.560752i	$-0.810512\pi$
$337$	−4.90571	+	4.90571i	−0.267231	+	0.267231i	0.560752	+	0.827984i	$0.310512\pi$
$338$		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	−0.0464585	−	0.998920i	$-0.514794\pi$
$347$	−10.9188	−	2.92569i	−0.586153	−	0.157059i	−0.539694	+	0.841861i	$0.681460\pi$
$348$		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	0.662803	−	0.748794i	$-0.269367\pi$
$353$	16.2032	+	4.34163i	0.862409	+	0.231082i	0.199607	+	0.979876i	$0.436034\pi$
$354$		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	0.339814	−	0.940493i	$-0.389636\pi$
$359$	−5.77457	−	3.33395i	−0.304770	−	0.175959i	−0.644584	+	0.764534i	$0.722969\pi$
$360$		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	0.516006	+	0.856585i	$0.327418\pi$
$367$	−6.88053	+	25.6785i	−0.359161	+	1.34041i	−0.875167	+	0.483821i	$0.839248\pi$
$368$		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	0.857714	−	0.514127i	$-0.171884\pi$
$373$	35.8758	−	9.61290i	1.85758	−	0.497737i	0.999866	+	0.0163896i	$0.00521720\pi$
$374$		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	$0.235827\pi$
$379$			26.2790i			1.34986i	−0.737881	+	0.674931i	$0.764173\pi$
$380$		0			0
$381$	−30.7043	+	17.7271i	−1.57303	+	0.908188i
$382$		0			0
$383$	−3.94516	−	14.7235i	−0.201588	−	0.752337i	−0.990463	−	0.137783i	$-0.956002\pi$
$383$	−3.94516	−	14.7235i	−0.201588	−	0.752337i	0.788874	−	0.614554i	$-0.210664\pi$
$384$		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	−0.782518	−	0.622628i	$-0.786065\pi$
$389$	−12.5156	+	7.22588i	−0.634566	+	0.366367i	0.147952	+	0.988994i	$0.452732\pi$
$390$		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	−0.498755	−	0.866743i	$-0.666209\pi$
$397$	−9.90897	+	2.65510i	−0.497317	+	0.133256i	0.00143754	+	0.999999i	$0.499542\pi$
$398$		0			0
$399$	1.85372	+	8.06295i	0.0928018	+	0.403652i
$400$		0			0
$401$	16.9889	−	29.4256i	0.848384	−	1.46944i	−0.0342665	−	0.999413i	$-0.510910\pi$
$401$	16.9889	−	29.4256i	0.848384	−	1.46944i	0.882650	−	0.470031i	$-0.155757\pi$
$402$		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	0.591330	−	0.806430i	$-0.298603\pi$
$409$	−8.14459	−	14.1068i	−0.402724	−	0.697538i	−0.994054	+	0.108892i	$0.965270\pi$
$410$		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	0.752938	−	0.658092i	$-0.228636\pi$
$431$	−4.01624	−	6.95633i	−0.193456	−	0.335075i	−0.946393	+	0.323017i	$0.895303\pi$
$432$		0			0
$433$	−18.7693	+	18.7693i	−0.901994	+	0.901994i	−0.995608	−	0.0936149i	$-0.970158\pi$
$433$	−18.7693	+	18.7693i	−0.901994	+	0.901994i	0.0936149	+	0.995608i	$0.470158\pi$
$434$		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	0.0634849	+	0.997983i	$0.479779\pi$
$439$	−17.4436	+	30.2131i	−0.832536	+	1.44199i	−0.896021	+	0.444012i	$0.853555\pi$
$440$		0			0
$441$	1.09158	−	15.2105i	0.0519798	−	0.724310i
$442$		0			0
$443$	30.0869	−	8.06175i	1.42947	−	0.383025i	0.540637	−	0.841256i	$-0.318183\pi$
$443$	30.0869	−	8.06175i	1.42947	−	0.383025i	0.888833	+	0.458231i	$0.151517\pi$
$444$		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	$-0.832690\pi$
$449$		−	21.2638i		−	1.00350i	0.865013	−	0.501750i	$-0.167310\pi$
$450$		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	0.925003	+	0.379959i	$0.124062\pi$
$457$	6.71055	+	25.0441i	0.313906	+	1.17151i	−0.611097	+	0.791556i	$0.709272\pi$
$458$		0			0
$459$	8.38390	−	4.84044i	0.391327	−	0.225933i
$460$		0			0
$461$		−	1.24276i		−	0.0578811i	−0.999581	−	0.0289405i	$-0.990787\pi$
$461$		−	1.24276i		−	0.0578811i	0.999581	−	0.0289405i	$-0.00921335\pi$
$462$		0			0
$463$	−13.6086	−	13.6086i	−0.632448	−	0.632448i	0.316234	−	0.948681i	$-0.397582\pi$
$463$	−13.6086	−	13.6086i	−0.632448	−	0.632448i	−0.948681	+	0.316234i	$0.897582\pi$
$464$		0			0
$465$	10.6959	−	34.0892i	0.496012	−	1.58085i
$466$		0			0
$467$	23.7974	−	6.37649i	1.10121	−	0.295069i	0.337954	−	0.941163i	$-0.390265\pi$
$467$	23.7974	−	6.37649i	1.10121	−	0.295069i	0.763258	+	0.646094i	$0.223599\pi$
$468$		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	0.918953	−	0.394367i	$-0.129036\pi$
$479$	2.58135	+	4.47103i	0.117945	+	0.204287i	−0.801008	+	0.598653i	$0.795703\pi$
$480$		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	0.421048	−	0.907039i	$-0.361663\pi$
$487$	7.33027	+	1.96414i	0.332166	+	0.0890037i	−0.0888813	+	0.996042i	$0.528329\pi$
$488$		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	−0.0556434	−	0.998451i	$-0.517721\pi$
$499$	−21.1800	−	12.2283i	−0.948149	−	0.547414i	−0.892505	+	0.451037i	$0.851054\pi$
$500$		0			0
$501$	27.9728	+	48.4504i	1.24973	+	2.16460i
$502$		0			0
$503$	−15.4661	+	15.4661i	−0.689600	+	0.689600i	−0.962143	−	0.272544i	$-0.912135\pi$
$503$	−15.4661	+	15.4661i	−0.689600	+	0.689600i	0.272544	+	0.962143i	$0.412135\pi$
$504$		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	0.186079	+	0.982535i	$0.440422\pi$
$509$	−17.0981	+	29.6148i	−0.757861	+	1.31265i	−0.943940	+	0.330118i	$0.892911\pi$
$510$		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	−0.913322	−	0.407238i	$-0.866492\pi$
$521$	−23.2204	+	13.4063i	−1.01730	+	0.587341i	−0.103983	+	0.994579i	$0.533159\pi$
$522$		0			0
$523$	−1.52679	−	5.69806i	−0.0667619	−	0.249159i	0.924477	−	0.381237i	$-0.124502\pi$
$523$	−1.52679	−	5.69806i	−0.0667619	−	0.249159i	−0.991239	+	0.132078i	$0.957835\pi$
$524$		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	−0.999159	−	0.0410039i	$-0.986944\pi$
$541$	−10.7940	+	18.6957i	−0.464069	+	0.803791i	0.535090	+	0.844795i	$0.320278\pi$
$542$		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	−0.398947	−	0.916974i	$-0.630624\pi$
$547$	12.1156	−	12.1156i	0.518027	−	0.518027i	0.916974	+	0.398947i	$0.130624\pi$
$548$		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	0.107695	−	0.994184i	$-0.465653\pi$
$557$	−6.98891	−	1.87267i	−0.296130	−	0.0793477i	−0.403825	+	0.914836i	$0.632320\pi$
$558$		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	0.226652	−	0.973976i	$-0.427222\pi$
$563$	−1.51972	−	0.407209i	−0.0640487	−	0.0171618i	−0.290701	+	0.956814i	$0.593889\pi$
$564$		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	0.384190	−	0.923254i	$-0.374481\pi$
$569$	−5.32597	−	3.07495i	−0.223276	−	0.128909i	−0.607466	+	0.794345i	$0.707814\pi$
$570$		0			0
$571$	−7.60099	−	13.1653i	−0.318092	−	0.550951i	0.661998	−	0.749505i	$-0.269709\pi$
$571$	−7.60099	−	13.1653i	−0.318092	−	0.550951i	−0.980090	+	0.198555i	$0.936375\pi$
$572$		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	−0.797016	−	0.603959i	$-0.793589\pi$
$577$	4.68885	−	17.4990i	0.195199	−	0.728494i	0.992215	−	0.124536i	$-0.0397441\pi$
$578$		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	0.509666	−	0.860373i	$-0.329769\pi$
$587$	−8.49695	−	8.49695i	−0.350707	−	0.350707i	−0.860373	+	0.509666i	$0.829769\pi$
$588$		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	0.892550	−	0.450948i	$-0.148914\pi$
$593$	−2.57872	−	9.62390i	−0.105895	−	0.395206i	−0.998445	+	0.0557423i	$0.982247\pi$
$594$		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	−0.536164	+	0.844114i	$0.680127\pi$
$599$	−37.5749	+	21.6939i	−1.53527	+	0.886388i	−0.999106	+	0.0422744i	$0.986540\pi$
$600$		0			0
$601$			46.7450i			1.90677i	0.301757	+	0.953385i	$0.402427\pi$
$601$			46.7450i			1.90677i	−0.301757	+	0.953385i	$0.597573\pi$
$602$		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	−0.264209	−	0.964465i	$-0.585111\pi$
$607$	−0.265783	+	0.0712163i	−0.0107878	+	0.00289058i	0.253421	+	0.967356i	$0.418444\pi$
$608$		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	−0.623500	−	0.781823i	$-0.714290\pi$
$613$	7.61033	−	28.4021i	0.307378	−	1.14715i	0.930879	−	0.365328i	$-0.119043\pi$
$614$		0			0
$615$	15.9512	+	17.3589i	0.643213	+	0.699977i
$616$		0			0
$617$	18.4708	−	18.4708i	0.743606	−	0.743606i	−0.229664	−	0.973270i	$-0.573763\pi$
$617$	18.4708	−	18.4708i	0.743606	−	0.743606i	0.973270	+	0.229664i	$0.0737626\pi$
$618$		0			0
$619$	−17.4488	−	30.2222i	−0.701325	−	1.21473i	−0.968001	−	0.250945i	$-0.919259\pi$
$619$	−17.4488	−	30.2222i	−0.701325	−	1.21473i	0.266676	−	0.963786i	$-0.414075\pi$
$620$		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	−0.995172	−	0.0981437i	$-0.968710\pi$
$641$	−14.7498	−	25.5474i	−0.582581	−	1.00906i	0.412591	−	0.910916i	$-0.364624\pi$
$642$		0			0
$643$	7.54699	−	7.54699i	0.297624	−	0.297624i	−0.542458	−	0.840083i	$-0.682506\pi$
$643$	7.54699	−	7.54699i	0.297624	−	0.297624i	0.840083	+	0.542458i	$0.182506\pi$
$644$		0			0
$645$	−18.0866	−	0.764356i	−0.712161	−	0.0300965i
$646$		0			0
$647$	−0.0666143	+	0.248608i	−0.00261888	+	0.00977379i	−0.967223	−	0.253929i	$-0.918277\pi$
$647$	−0.0666143	+	0.248608i	−0.00261888	+	0.00977379i	0.964604	+	0.263703i	$0.0849438\pi$
$648$		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	−0.234093	−	0.972214i	$-0.575212\pi$
$653$	1.25937	−	0.337448i	0.0492830	−	0.0132054i	0.283376	+	0.959009i	$0.408545\pi$
$654$		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	$-0.982188\pi$
$659$		−	2.87148i		−	0.111857i	0.998435	−	0.0559286i	$-0.0178119\pi$
$660$		0			0
$661$	21.1356	−	12.2026i	0.822078	−	0.474627i	−0.0290547	−	0.999578i	$-0.509250\pi$
$661$	21.1356	−	12.2026i	0.822078	−	0.474627i	0.851132	+	0.524951i	$0.175916\pi$
$662$		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	0.996135	+	0.0878369i	$0.0279954\pi$
$673$	28.1207	+	28.1207i	1.08397	+	1.08397i	0.0878369	+	0.996135i	$0.472005\pi$
$674$		0			0
$675$	−3.17229	+	8.79217i	−0.122101	+	0.338411i
$676$		0			0
$677$	20.8842	−	5.59591i	0.802646	−	0.215068i	0.165901	−	0.986142i	$-0.446947\pi$
$677$	20.8842	−	5.59591i	0.802646	−	0.215068i	0.636745	+	0.771074i	$0.280280\pi$
$678$		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	0.497034	+	0.867731i	$0.334423\pi$
$683$	−9.59848	+	35.8220i	−0.367276	+	1.37069i	−0.864309	+	0.502961i	$0.832244\pi$
$684$		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	0.753807	−	0.657096i	$-0.228215\pi$
$691$	14.7640	+	8.52400i	0.561649	+	0.324268i	−0.192158	+	0.981364i	$0.561549\pi$
$692$		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	0.646654	−	0.762784i	$-0.276168\pi$
$709$	8.23815	+	4.75630i	0.309390	+	0.178627i	−0.337263	+	0.941410i	$0.609501\pi$
$710$		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	−0.843977	−	0.536379i	$-0.819792\pi$
$719$	1.14039	−	1.97522i	0.0425295	−	0.0736632i	0.886507	+	0.462716i	$0.153125\pi$
$720$		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	0.814782	−	0.579768i	$-0.196857\pi$
$727$	6.33666	+	6.33666i	0.235014	+	0.235014i	−0.579768	+	0.814782i	$0.696857\pi$
$728$		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	−0.971182	−	0.238341i	$-0.923396\pi$
$733$	−6.74911	−	25.1880i	−0.249284	−	0.930341i	0.721897	−	0.692000i	$-0.243270\pi$
$734$		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	0.278846	−	0.960336i	$-0.410048\pi$
$739$	33.9792	−	19.6179i	1.24994	−	0.721656i	0.971098	+	0.238680i	$0.0767148\pi$
$740$		0			0
$741$			13.8608i			0.509189i
$742$		0			0
$743$	−9.29603	−	9.29603i	−0.341038	−	0.341038i	0.515719	−	0.856758i	$-0.327525\pi$
$743$	−9.29603	−	9.29603i	−0.341038	−	0.341038i	−0.856758	+	0.515719i	$0.827525\pi$
$744$		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	−0.789561	−	0.613673i	$-0.789692\pi$
$751$	3.74551	−	6.48742i	0.136676	−	0.236729i	0.926236	+	0.376943i	$0.123025\pi$
$752$		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	−0.817853	−	0.575427i	$-0.804836\pi$
$757$	−6.67005	+	6.67005i	−0.242427	+	0.242427i	0.575427	+	0.817853i	$0.304836\pi$
$758$		0			0
$759$	−16.8887	−	29.2521i	−0.613021	−	1.06178i
$760$		0			0
$761$	−13.0745	−	7.54859i	−0.473952	−	0.273636i	0.243941	−	0.969790i	$-0.421560\pi$
$761$	−13.0745	−	7.54859i	−0.473952	−	0.273636i	−0.717893	+	0.696154i	$0.754893\pi$
$762$		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	0.672579	−	0.740026i	$-0.265187\pi$
$773$	24.6065	+	6.59331i	0.885036	+	0.237145i	0.212457	+	0.977170i	$0.431853\pi$
$774$		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	0.810603	+	0.585596i	$0.199139\pi$
$787$	−5.16739	+	19.2850i	−0.184198	+	0.687435i	−0.994801	+	0.101839i	$0.967527\pi$
$788$		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	0.0592654	−	0.998242i	$-0.481124\pi$
$797$	−26.5084	−	26.5084i	−0.938977	−	0.938977i	−0.998242	+	0.0592654i	$0.981124\pi$
$798$		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	0.0958027	−	0.995400i	$-0.469458\pi$
$809$	28.6064	−	16.5159i	1.00575	−	0.580668i	0.909943	+	0.414733i	$0.136125\pi$
$810$		0			0
$811$		−	40.2650i		−	1.41390i	−0.707265	−	0.706948i	$-0.750071\pi$
$811$		−	40.2650i		−	1.41390i	0.707265	−	0.706948i	$-0.249929\pi$
$812$		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	0.386233	+	0.922401i	$0.373776\pi$
$821$	−17.3554	+	30.0604i	−0.605707	+	1.04911i	−0.991939	+	0.126713i	$0.959557\pi$
$822$		0			0
$823$	10.8152	−	40.3629i	0.376995	−	1.40696i	−0.473414	−	0.880840i	$-0.656978\pi$
$823$	10.8152	−	40.3629i	0.376995	−	1.40696i	0.850408	−	0.526123i	$-0.176355\pi$
$824$		0			0
$825$	31.1073	−	26.2507i	1.08302	−	0.913930i
$826$		0			0
$827$	25.2377	−	25.2377i	0.877600	−	0.877600i	−0.115686	−	0.993286i	$-0.536907\pi$
$827$	25.2377	−	25.2377i	0.877600	−	0.877600i	0.993286	+	0.115686i	$0.0369067\pi$
$828$		0			0
$829$	10.2989	+	17.8381i	0.357694	+	0.619544i	0.987575	−	0.157147i	$-0.0502297\pi$
$829$	10.2989	+	17.8381i	0.357694	+	0.619544i	−0.629881	+	0.776692i	$0.716896\pi$
$830$		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	−0.936387	−	0.350970i	$-0.885852\pi$
$853$	−17.0978	+	17.0978i	−0.585417	+	0.585417i	0.350970	+	0.936387i	$0.385852\pi$
$854$		0			0
$855$	0.282633	−	6.68783i	0.00966586	−	0.228719i
$856$		0			0
$857$	1.82672	−	6.81740i	0.0623995	−	0.232878i	−0.927682	−	0.373371i	$-0.878202\pi$
$857$	1.82672	−	6.81740i	0.0623995	−	0.232878i	0.990082	+	0.140493i	$0.0448686\pi$
$858$		0			0
$859$	15.4580	−	26.7741i	0.527422	−	0.913521i	−0.472068	−	0.881562i	$-0.656492\pi$
$859$	15.4580	−	26.7741i	0.527422	−	0.913521i	0.999489	−	0.0319586i	$-0.0101745\pi$
$860$		0			0
$861$	−19.0050	−	20.4178i	−0.647690	−	0.695837i
$862$		0			0
$863$	−0.835836	+	0.223962i	−0.0284522	+	0.00762374i	−0.273017	−	0.962009i	$-0.588022\pi$
$863$	−0.835836	+	0.223962i	−0.0284522	+	0.00762374i	0.244565	+	0.969633i	$0.421355\pi$
$864$		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	0.995783	+	0.0917391i	$0.0292426\pi$
$877$	5.30921	+	19.8142i	0.179279	+	0.669079i	−0.816504	+	0.577340i	$0.804091\pi$
$878$		0			0
$879$	−3.27957	+	1.89346i	−0.110617	+	0.0638649i
$880$		0			0
$881$		−	7.65158i		−	0.257788i	−0.991658	−	0.128894i	$-0.958857\pi$
$881$		−	7.65158i		−	0.257788i	0.991658	−	0.128894i	$-0.0411428\pi$
$882$		0			0
$883$	39.4562	+	39.4562i	1.32781	+	1.32781i	0.907279	+	0.420528i	$0.138155\pi$
$883$	39.4562	+	39.4562i	1.32781	+	1.32781i	0.420528	+	0.907279i	$0.361845\pi$
$884$		0			0
$885$	13.8041	+	4.33122i	0.464021	+	0.145593i
$886$		0			0
$887$	−14.6259	+	3.91901i	−0.491091	+	0.131587i	−0.495862	−	0.868401i	$-0.665148\pi$
$887$	−14.6259	+	3.91901i	−0.491091	+	0.131587i	0.00477122	+	0.999989i	$0.498481\pi$
$888$		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	0.495943	−	0.868355i	$-0.334823\pi$
$907$	14.7951	+	3.96434i	0.491264	+	0.131634i	−0.00467871	+	0.999989i	$0.501489\pi$
$908$		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	−0.222348	−	0.974967i	$-0.571372\pi$
$919$	−35.7071	−	20.6155i	−1.17787	−	0.680043i	−0.955520	+	0.294925i	$0.904705\pi$
$920$		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	−0.808530	−	0.588455i	$-0.799736\pi$
$929$	3.21108	−	5.56175i	0.105352	−	0.182475i	0.913882	+	0.405980i	$0.133070\pi$
$930$		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	−0.957620	−	0.288034i	$-0.906998\pi$
$937$	−38.1300	−	38.1300i	−1.24565	−	1.24565i	−0.288034	−	0.957620i	$-0.593002\pi$
$938$		0			0
$939$		−	14.4314i		−	0.470951i
$940$		0			0
$941$	5.07275	−	2.92875i	0.165367	−	0.0954746i	−0.415032	−	0.909807i	$-0.636230\pi$
$941$	5.07275	−	2.92875i	0.165367	−	0.0954746i	0.580399	+	0.814332i	$0.302896\pi$
$942$		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	−0.999097	−	0.0424864i	$-0.986472\pi$
$947$	−4.77285	−	17.8125i	−0.155097	−	0.578829i	0.844000	−	0.536343i	$-0.180195\pi$
$948$		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	0.627537	−	0.778587i	$-0.284063\pi$
$953$	−4.66301	−	4.66301i	−0.151050	−	0.151050i	−0.778587	+	0.627537i	$0.784063\pi$
$954$		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	0.104247	−	0.994551i	$-0.466757\pi$
$967$	34.1689	−	34.1689i	1.09880	−	1.09880i	0.994551	−	0.104247i	$-0.0332432\pi$
$968$		0			0
$969$	−8.09682	−	14.0241i	−0.260107	−	0.450519i
$970$		0			0
$971$	31.8954	+	18.4148i	1.02357	+	0.590959i	0.915136	−	0.403145i	$-0.132083\pi$
$971$	31.8954	+	18.4148i	1.02357	+	0.590959i	0.108435	+	0.994104i	$0.465416\pi$
$972$		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	0.745800	−	0.666170i	$-0.232067\pi$
$977$	33.0886	+	8.86606i	1.05860	+	0.283650i	0.312797	+	0.949820i	$0.398734\pi$
$978$		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	−0.100960	−	0.994891i	$-0.532191\pi$
$983$	−21.5030	−	5.76170i	−0.685838	−	0.183770i	−0.584879	+	0.811121i	$0.698858\pi$
$984$		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	0.958847	−	0.283925i	$-0.0916366\pi$
$991$	7.35178	+	12.7337i	0.233537	+	0.404498i	−0.725309	+	0.688423i	$0.758303\pi$
$992$		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	−0.797794	−	0.602930i	$-0.794000\pi$
$997$	6.14395	−	22.9296i	0.194581	−	0.726186i	0.992375	−	0.123256i	$-0.0393336\pi$
$998$		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.33.10	yes	48
4.3	odd	2		560.2.ci.e.33.3		48
5.2	odd	4	inner	280.2.bo.a.257.10	yes	48
7.3	odd	6	inner	280.2.bo.a.73.10	yes	48
20.7	even	4		560.2.ci.e.257.3		48
28.3	even	6		560.2.ci.e.353.3		48
35.17	even	12	inner	280.2.bo.a.17.10	✓	48
140.87	odd	12		560.2.ci.e.17.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.10	✓	48	35.17	even	12	inner
280.2.bo.a.33.10	yes	48	1.1	even	1	trivial
280.2.bo.a.73.10	yes	48	7.3	odd	6	inner
280.2.bo.a.257.10	yes	48	5.2	odd	4	inner
560.2.ci.e.17.3		48	140.87	odd	12
560.2.ci.e.33.3		48	4.3	odd	2
560.2.ci.e.257.3		48	20.7	even	4
560.2.ci.e.353.3		48	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
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

Related objects

Downloads

Learn more