LMFDB - Embedded newform 1240.2.bm.a.129.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1240,2,Mod(129,1240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1240.129"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1240, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1240 = 2^{3} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1240.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.90144985064$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.4
Character	$\chi$	$=$	1240.129
Dual form			1240.2.bm.a.769.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.37824 - 1.37308i) q^{3} +(2.12977 + 0.681248i) q^{5} +(-3.56474 - 2.05811i) q^{7} +(2.27069 + 3.93295i) q^{9} +(1.14204 + 1.97808i) q^{11} +(-2.92397 + 1.68816i) q^{13} +(-4.12969 - 4.54451i) q^{15} +(2.40398 + 1.38794i) q^{17} +(2.28213 - 3.95276i) q^{19} +(5.65188 + 9.78934i) q^{21} +4.87944i q^{23} +(4.07180 + 2.90180i) q^{25} -4.23286i q^{27} -7.30900 q^{29} +(5.56400 - 0.204788i) q^{31} -6.27246i q^{33} +(-6.18999 - 6.81176i) q^{35} +(5.61746 + 3.24324i) q^{37} +9.27189 q^{39} +(-4.54906 - 7.87921i) q^{41} +(2.32676 + 1.34336i) q^{43} +(2.15672 + 9.92315i) q^{45} +2.34003i q^{47} +(4.97160 + 8.61106i) q^{49} +(-3.81150 - 6.60171i) q^{51} +(2.33560 - 1.34846i) q^{53} +(1.08472 + 4.99086i) q^{55} +(-10.8549 + 6.26708i) q^{57} +(-2.56422 + 4.44136i) q^{59} +15.1066 q^{61} -18.6933i q^{63} +(-7.37743 + 1.60343i) q^{65} +(3.02299 - 1.74532i) q^{67} +(6.69986 - 11.6045i) q^{69} +(-0.560430 - 0.970694i) q^{71} +(12.7125 - 7.33957i) q^{73} +(-5.69933 - 12.4921i) q^{75} -9.40178i q^{77} +(-0.334371 + 0.579148i) q^{79} +(1.00002 - 1.73208i) q^{81} +(6.52565 - 3.76759i) q^{83} +(4.17439 + 4.59369i) q^{85} +(17.3826 + 10.0358i) q^{87} +1.68677 q^{89} +13.8976 q^{91} +(-13.5137 - 7.15277i) q^{93} +(7.55321 - 6.86376i) q^{95} -9.64115i q^{97} +(-5.18645 + 8.98319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{9} + 12 q^{11} - 20 q^{15} - 8 q^{21} + 8 q^{25} - 24 q^{29} - 12 q^{31} + 4 q^{35} + 16 q^{39} + 60 q^{49} + 12 q^{51} + 2 q^{55} - 8 q^{59} + 24 q^{61} - 4 q^{69} + 8 q^{71} + 10 q^{75} + 84 q^{79}+ \cdots - 56 q^{99}+O(q^{100}) $ 96 * q + 48 * q^9 + 12 * q^11 - 20 * q^15 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 12 * q^31 + 4 * q^35 + 16 * q^39 + 60 * q^49 + 12 * q^51 + 2 * q^55 - 8 * q^59 + 24 * q^61 - 4 * q^69 + 8 * q^71 + 10 * q^75 + 84 * q^79 - 56 * q^81 - 40 * q^85 - 56 * q^89 - 96 * q^91 + 4 * q^95 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1240\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$	$621$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.37824	−	1.37308i	−1.37308	−	0.792747i	−0.381764	−	0.924260i	$-0.624683\pi$
$3$	−2.37824	−	1.37308i	−1.37308	−	0.792747i	−0.991314	+	0.131513i	$0.958017\pi$
$4$		0			0
$5$	2.12977	+	0.681248i	0.952460	+	0.304663i
$5$	2.12977	+	0.681248i	0.952460	+	0.304663i
$6$		0			0
$7$	−3.56474	−	2.05811i	−1.34735	−	0.777891i	−0.359473	−	0.933155i	$-0.617044\pi$
$7$	−3.56474	−	2.05811i	−1.34735	−	0.777891i	−0.987873	+	0.155265i	$0.950377\pi$
$8$		0			0
$9$	2.27069	+	3.93295i	0.756896	+	1.31098i
$10$		0			0
$11$	1.14204	+	1.97808i	0.344339	+	0.596413i	0.985233	−	0.171216i	$-0.0547697\pi$
$11$	1.14204	+	1.97808i	0.344339	+	0.596413i	−0.640894	+	0.767629i	$0.721436\pi$
$12$		0			0
$13$	−2.92397	+	1.68816i	−0.810965	+	0.468211i	−0.847291	−	0.531129i	$-0.821768\pi$
$13$	−2.92397	+	1.68816i	−0.810965	+	0.468211i	0.0363261	+	0.999340i	$0.488435\pi$
$14$		0			0
$15$	−4.12969	−	4.54451i	−1.06628	−	1.17339i
$16$		0			0
$17$	2.40398	+	1.38794i	0.583051	+	0.336625i	0.762345	−	0.647171i	$-0.224048\pi$
$17$	2.40398	+	1.38794i	0.583051	+	0.336625i	−0.179294	+	0.983796i	$0.557381\pi$
$18$		0			0
$19$	2.28213	−	3.95276i	0.523556	−	0.906826i	−0.476068	−	0.879408i	$-0.657938\pi$
$19$	2.28213	−	3.95276i	0.523556	−	0.906826i	0.999624	−	0.0274172i	$-0.00872825\pi$
$20$		0			0
$21$	5.65188	+	9.78934i	1.23334	+	2.13621i
$22$		0			0
$23$			4.87944i			1.01743i	0.860934	+	0.508717i	$0.169880\pi$
$23$			4.87944i			1.01743i	−0.860934	+	0.508717i	$0.830120\pi$
$24$		0			0
$25$	4.07180	+	2.90180i	0.814360	+	0.580359i
$26$		0			0
$27$		−	4.23286i		−	0.814614i
$28$		0			0
$29$	−7.30900			−1.35725			−0.678624	−	0.734486i	$-0.737423\pi$
$29$	−7.30900			−1.35725			−0.678624	+	0.734486i	$0.737423\pi$
$30$		0			0
$31$	5.56400	−	0.204788i	0.999323	−	0.0367809i
$31$	5.56400	−	0.204788i	0.999323	−	0.0367809i
$32$		0			0
$33$		−	6.27246i		−	1.09190i
$34$		0			0
$35$	−6.18999	−	6.81176i	−1.04630	−	1.15140i
$36$		0			0
$37$	5.61746	+	3.24324i	0.923504	+	0.533185i	0.884751	−	0.466064i	$-0.154328\pi$
$37$	5.61746	+	3.24324i	0.923504	+	0.533185i	0.0387527	+	0.999249i	$0.487662\pi$
$38$		0			0
$39$	9.27189			1.48469
$40$		0			0
$41$	−4.54906	−	7.87921i	−0.710445	−	1.23053i	−0.964690	−	0.263386i	$-0.915161\pi$
$41$	−4.54906	−	7.87921i	−0.710445	−	1.23053i	0.254246	−	0.967140i	$-0.418173\pi$
$42$		0			0
$43$	2.32676	+	1.34336i	0.354828	+	0.204860i	0.666809	−	0.745228i	$-0.267659\pi$
$43$	2.32676	+	1.34336i	0.354828	+	0.204860i	−0.311982	+	0.950088i	$0.600993\pi$
$44$		0			0
$45$	2.15672	+	9.92315i	0.321505	+	1.47926i
$46$		0			0
$47$			2.34003i			0.341328i	0.985329	+	0.170664i	$0.0545912\pi$
$47$			2.34003i			0.341328i	−0.985329	+	0.170664i	$0.945409\pi$
$48$		0			0
$49$	4.97160	+	8.61106i	0.710228	+	1.23015i
$50$		0			0
$51$	−3.81150	−	6.60171i	−0.533717	−	0.924424i
$52$		0			0
$53$	2.33560	−	1.34846i	0.320820	−	0.185225i	−0.330938	−	0.943652i	$-0.607365\pi$
$53$	2.33560	−	1.34846i	0.320820	−	0.185225i	0.651758	+	0.758427i	$0.274032\pi$
$54$		0			0
$55$	1.08472	+	4.99086i	0.146264	+	0.672967i
$56$		0			0
$57$	−10.8549	+	6.26708i	−1.43777	+	0.830095i
$58$		0			0
$59$	−2.56422	+	4.44136i	−0.333833	+	0.578216i	−0.983260	−	0.182208i	$-0.941676\pi$
$59$	−2.56422	+	4.44136i	−0.333833	+	0.578216i	0.649427	+	0.760424i	$0.275009\pi$
$60$		0			0
$61$	15.1066			1.93421			0.967103	−	0.254386i	$-0.0818733\pi$
$61$	15.1066			1.93421			0.967103	+	0.254386i	$0.0818733\pi$
$62$		0			0
$63$		−	18.6933i		−	2.35513i
$64$		0			0
$65$	−7.37743	+	1.60343i	−0.915058	+	0.198881i
$66$		0			0
$67$	3.02299	−	1.74532i	0.369317	−	0.213225i	−0.303843	−	0.952722i	$-0.598270\pi$
$67$	3.02299	−	1.74532i	0.369317	−	0.213225i	0.673160	+	0.739497i	$0.264937\pi$
$68$		0			0
$69$	6.69986	−	11.6045i	0.806568	−	1.39702i
$70$		0			0
$71$	−0.560430	−	0.970694i	−0.0665108	−	0.115200i	0.830852	−	0.556493i	$-0.187853\pi$
$71$	−0.560430	−	0.970694i	−0.0665108	−	0.115200i	−0.897363	+	0.441293i	$0.854520\pi$
$72$		0			0
$73$	12.7125	−	7.33957i	1.48789	−	0.859032i	0.487982	−	0.872854i	$-0.337733\pi$
$73$	12.7125	−	7.33957i	1.48789	−	0.859032i	0.999904	+	0.0138219i	$0.00439980\pi$
$74$		0			0
$75$	−5.69933	−	12.4921i	−0.658102	−	1.44246i
$76$		0			0
$77$		−	9.40178i		−	1.07143i
$78$		0			0
$79$	−0.334371	+	0.579148i	−0.0376197	+	0.0651593i	−0.884222	−	0.467066i	$-0.845311\pi$
$79$	−0.334371	+	0.579148i	−0.0376197	+	0.0651593i	0.846603	+	0.532226i	$0.178644\pi$
$80$		0			0
$81$	1.00002	−	1.73208i	0.111113	−	0.192454i
$82$		0			0
$83$	6.52565	−	3.76759i	0.716283	−	0.413546i	−0.0970999	−	0.995275i	$-0.530957\pi$
$83$	6.52565	−	3.76759i	0.716283	−	0.413546i	0.813383	+	0.581728i	$0.197623\pi$
$84$		0			0
$85$	4.17439	+	4.59369i	0.452776	+	0.498256i
$86$		0			0
$87$	17.3826	+	10.0358i	1.86361	+	1.07595i
$88$		0			0
$89$	1.68677			0.178798			0.0893988	−	0.995996i	$-0.471505\pi$
$89$	1.68677			0.178798			0.0893988	+	0.995996i	$0.471505\pi$
$90$		0			0
$91$	13.8976			1.45687
$92$		0			0
$93$	−13.5137	−	7.15277i	−1.40131	−	0.741708i
$94$		0			0
$95$	7.55321	−	6.86376i	0.774943	−	0.704207i
$96$		0			0
$97$		−	9.64115i		−	0.978910i	−0.872028	−	0.489455i	$-0.837196\pi$
$97$		−	9.64115i		−	0.978910i	0.872028	−	0.489455i	$-0.162804\pi$
$98$		0			0
$99$	−5.18645	+	8.98319i	−0.521258	+	0.902845i
$100$		0			0
$101$	16.3044			1.62235			0.811176	−	0.584802i	$-0.198828\pi$
$101$	16.3044			1.62235			0.811176	+	0.584802i	$0.198828\pi$
$102$		0			0
$103$	−6.70436	+	3.87076i	−0.660600	+	0.381397i	−0.792505	−	0.609865i	$-0.791224\pi$
$103$	−6.70436	+	3.87076i	−0.660600	+	0.381397i	0.131906	+	0.991262i	$0.457890\pi$
$104$		0			0
$105$	5.36821	+	24.6993i	0.523883	+	2.41041i
$106$		0			0
$107$	17.6370	+	10.1827i	1.70504	+	0.984403i	0.940482	+	0.339845i	$0.110374\pi$
$107$	17.6370	+	10.1827i	1.70504	+	0.984403i	0.764555	+	0.644559i	$0.222959\pi$
$108$		0			0
$109$	−5.70260			−0.546210			−0.273105	−	0.961984i	$-0.588051\pi$
$109$	−5.70260			−0.546210			−0.273105	+	0.961984i	$0.588051\pi$
$110$		0			0
$111$	−8.90644	−	15.4264i	−0.845362	−	1.46421i
$112$		0			0
$113$	−12.6208	+	7.28663i	−1.18727	+	0.685468i	−0.957684	−	0.287821i	$-0.907069\pi$
$113$	−12.6208	+	7.28663i	−1.18727	+	0.685468i	−0.229582	+	0.973289i	$0.573736\pi$
$114$		0			0
$115$	−3.32411	+	10.3921i	−0.309975	+	0.969066i
$116$		0			0
$117$	−13.2789	−	7.66656i	−1.22763	−	0.708773i
$118$		0			0
$119$	−5.71305	−	9.89530i	−0.523715	−	0.907100i
$120$		0			0
$121$	2.89147	−	5.00818i	0.262861	−	0.455289i
$122$		0			0
$123$			24.9849i			2.25281i
$124$		0			0
$125$	6.69514	+	8.95405i	0.598832	+	0.800875i
$126$		0			0
$127$	12.0599	+	6.96277i	1.07014	+	0.617846i	0.928220	−	0.372032i	$-0.121339\pi$
$127$	12.0599	+	6.96277i	1.07014	+	0.617846i	0.141921	+	0.989878i	$0.454672\pi$
$128$		0			0
$129$	−3.68906	−	6.38965i	−0.324804	−	0.562577i
$130$		0			0
$131$	−8.72379	+	15.1100i	−0.762201	+	1.32017i	0.179513	+	0.983756i	$0.442548\pi$
$131$	−8.72379	+	15.1100i	−0.762201	+	1.32017i	−0.941714	+	0.336415i	$0.890785\pi$
$132$		0			0
$133$	−16.2704	+	9.39372i	−1.41082	+	0.814539i
$134$		0			0
$135$	2.88363	−	9.01499i	0.248183	−	0.775887i
$136$		0			0
$137$	19.2667	−	11.1236i	1.64606	−	0.950355i	0.667447	−	0.744658i	$-0.267387\pi$
$137$	19.2667	−	11.1236i	1.64606	−	0.950355i	0.978616	−	0.205697i	$-0.0659461\pi$
$138$		0			0
$139$	7.06107			0.598912			0.299456	−	0.954110i	$-0.403195\pi$
$139$	7.06107			0.598912			0.299456	+	0.954110i	$0.403195\pi$
$140$		0			0
$141$	3.21304	−	5.56514i	0.270587	−	0.468670i
$142$		0			0
$143$	−6.67861	−	3.85590i	−0.558494	−	0.322446i
$144$		0			0
$145$	−15.5665	−	4.97924i	−1.29272	−	0.413504i
$146$		0			0
$147$		−	27.3056i		−	2.25213i
$148$		0			0
$149$	−2.33400	+	4.04261i	−0.191209	+	0.331183i	−0.945651	−	0.325183i	$-0.894574\pi$
$149$	−2.33400	+	4.04261i	−0.191209	+	0.331183i	0.754442	+	0.656366i	$0.227907\pi$
$150$		0			0
$151$	−8.67244			−0.705753			−0.352877	−	0.935670i	$-0.614796\pi$
$151$	−8.67244			−0.705753			−0.352877	+	0.935670i	$0.614796\pi$
$152$		0			0
$153$			12.6063i			1.01916i
$154$		0			0
$155$	11.9895	+	3.35431i	0.963021	+	0.269425i
$156$		0			0
$157$			8.45888i			0.675092i	0.941309	+	0.337546i	$0.109597\pi$
$157$			8.45888i			0.675092i	−0.941309	+	0.337546i	$0.890403\pi$
$158$		0			0
$159$	−7.40617			−0.587348
$160$		0			0
$161$	10.0424	−	17.3940i	0.791453	−	1.37084i
$162$		0			0
$163$		−	15.7378i		−	1.23268i	−0.787481	−	0.616339i	$-0.788615\pi$
$163$		−	15.7378i		−	1.23268i	0.787481	−	0.616339i	$-0.211385\pi$
$164$		0			0
$165$	4.27310	−	13.3589i	0.332660	−	1.03999i
$166$		0			0
$167$	−4.96540	−	2.86677i	−0.384234	−	0.221838i	0.295425	−	0.955366i	$-0.404539\pi$
$167$	−4.96540	−	2.86677i	−0.384234	−	0.221838i	−0.679659	+	0.733528i	$0.737872\pi$
$168$		0			0
$169$	−0.800248	+	1.38607i	−0.0615575	+	0.106621i
$170$		0			0
$171$	20.7280			1.58511
$172$		0			0
$173$	−6.27230	+	3.62131i	−0.476874	+	0.275323i	−0.719113	−	0.694893i	$-0.755452\pi$
$173$	−6.27230	+	3.62131i	−0.476874	+	0.275323i	0.242239	+	0.970217i	$0.422118\pi$
$174$		0			0
$175$	−8.54272	−	18.7244i	−0.645769	−	1.41543i
$176$		0			0
$177$	12.1967	−	7.04176i	0.916759	−	0.529291i
$178$		0			0
$179$	−6.00032	+	10.3929i	−0.448485	+	0.776799i	−0.998288	−	0.0584958i	$-0.981370\pi$
$179$	−6.00032	+	10.3929i	−0.448485	+	0.776799i	0.549803	+	0.835295i	$0.314703\pi$
$180$		0			0
$181$	10.2741	+	17.7952i	0.763665	+	1.32271i	0.940949	+	0.338547i	$0.109936\pi$
$181$	10.2741	+	17.7952i	0.763665	+	1.32271i	−0.177284	+	0.984160i	$0.556731\pi$
$182$		0			0
$183$	−35.9272	−	20.7426i	−2.65582	−	1.53334i
$184$		0			0
$185$	9.75441	+	10.7342i	0.717159	+	0.789196i
$186$		0			0
$187$			6.34035i			0.463652i
$188$		0			0
$189$	−8.71167	+	15.0890i	−0.633681	+	1.09757i
$190$		0			0
$191$	1.45995	+	2.52870i	0.105638	+	0.182970i	0.913999	−	0.405717i	$-0.132978\pi$
$191$	1.45995	+	2.52870i	0.105638	+	0.182970i	−0.808361	+	0.588688i	$0.799645\pi$
$192$		0			0
$193$	−8.09980	−	4.67642i	−0.583036	−	0.336616i	0.179303	−	0.983794i	$-0.442616\pi$
$193$	−8.09980	−	4.67642i	−0.583036	−	0.336616i	−0.762339	+	0.647178i	$0.775949\pi$
$194$		0			0
$195$	19.7470	+	6.31646i	1.41411	+	0.452331i
$196$		0			0
$197$	−10.8554	+	6.26734i	−0.773412	+	0.446530i	−0.834090	−	0.551628i	$-0.814007\pi$
$197$	−10.8554	+	6.26734i	−0.773412	+	0.446530i	0.0606784	+	0.998157i	$0.480674\pi$
$198$		0			0
$199$	−7.40594	−	12.8275i	−0.524993	−	0.909315i	−0.999576	−	0.0291042i	$-0.990735\pi$
$199$	−7.40594	−	12.8275i	−0.524993	−	0.909315i	0.474583	−	0.880211i	$-0.342599\pi$
$200$		0			0
$201$	−9.58586			−0.676134
$202$		0			0
$203$	26.0547	+	15.0427i	1.82868	+	1.05579i
$204$		0			0
$205$	−4.32074	−	19.8799i	−0.301774	−	1.38847i
$206$		0			0
$207$	−19.1906	+	11.0797i	−1.33384	+	0.770092i
$208$		0			0
$209$	10.4252			0.721123
$210$		0			0
$211$	1.57531	−	2.72852i	0.108449	−	0.187839i	−0.806693	−	0.590971i	$-0.798745\pi$
$211$	1.57531	−	2.72852i	0.108449	−	0.187839i	0.915142	+	0.403131i	$0.132078\pi$
$212$		0			0
$213$			3.07806i			0.210905i
$214$		0			0
$215$	4.04029	+	4.44613i	0.275546	+	0.303224i
$216$		0			0
$217$	−20.2557	−	10.7213i	−1.37505	−	0.727808i
$218$		0			0
$219$	−40.3112			−2.72398
$220$		0			0
$221$	−9.37224			−0.630445
$222$		0			0
$223$	−5.35828	−	3.09360i	−0.358817	−	0.207163i	0.309745	−	0.950820i	$-0.399756\pi$
$223$	−5.35828	−	3.09360i	−0.358817	−	0.207163i	−0.668562	+	0.743657i	$0.733090\pi$
$224$		0			0
$225$	−2.16682	+	22.6033i	−0.144455	+	1.50688i
$226$		0			0
$227$	−9.20130	+	5.31238i	−0.610712	+	0.352595i	−0.773244	−	0.634109i	$-0.781367\pi$
$227$	−9.20130	+	5.31238i	−0.610712	+	0.352595i	0.162532	+	0.986703i	$0.448034\pi$
$228$		0			0
$229$	−11.8063	+	20.4490i	−0.780180	+	1.35131i	0.151657	+	0.988433i	$0.451539\pi$
$229$	−11.8063	+	20.4490i	−0.780180	+	1.35131i	−0.931837	+	0.362878i	$0.881794\pi$
$230$		0			0
$231$	−12.9094	+	22.3597i	−0.849375	+	1.47116i
$232$		0			0
$233$			16.5643i			1.08516i	0.840003	+	0.542581i	$0.182553\pi$
$233$			16.5643i			1.08516i	−0.840003	+	0.542581i	$0.817447\pi$
$234$		0			0
$235$	−1.59414	+	4.98371i	−0.103990	+	0.325101i
$236$		0			0
$237$	1.59043	−	0.918236i	0.103310	−	0.0596458i
$238$		0			0
$239$	1.35855	+	2.35307i	0.0878771	+	0.152208i	0.906614	−	0.421962i	$-0.138658\pi$
$239$	1.35855	+	2.35307i	0.0878771	+	0.152208i	−0.818736	+	0.574169i	$0.805325\pi$
$240$		0			0
$241$	0.0644726	−	0.111670i	0.00415304	−	0.00719328i	−0.863941	−	0.503592i	$-0.832011\pi$
$241$	0.0644726	−	0.111670i	0.00415304	−	0.00719328i	0.868094	+	0.496399i	$0.165345\pi$
$242$		0			0
$243$	−15.7539	+	9.09549i	−1.01061	+	0.583476i
$244$		0			0
$245$	4.72207	+	21.7264i	0.301682	+	1.38805i
$246$		0			0
$247$			15.4104i			0.980538i
$248$		0			0
$249$	−20.6928			−1.31135
$250$		0			0
$251$	−4.17415	+	7.22985i	−0.263470	+	0.456344i	−0.967162	−	0.254162i	$-0.918200\pi$
$251$	−4.17415	+	7.22985i	−0.263470	+	0.456344i	0.703691	+	0.710506i	$0.251534\pi$
$252$		0			0
$253$	−9.65192	+	5.57254i	−0.606811	+	0.350342i
$254$		0			0
$255$	−3.62020	−	16.6567i	−0.226706	−	1.04308i
$256$		0			0
$257$	−10.7111	+	6.18406i	−0.668141	+	0.385751i	−0.795372	−	0.606122i	$-0.792724\pi$
$257$	−10.7111	+	6.18406i	−0.668141	+	0.385751i	0.127231	+	0.991873i	$0.459391\pi$
$258$		0			0
$259$	−13.3499	−	23.1226i	−0.829520	−	1.43677i
$260$		0			0
$261$	−16.5965	−	28.7459i	−1.02729	−	1.77933i
$262$		0			0
$263$		−	10.5188i		−	0.648619i	−0.945951	−	0.324309i	$-0.894868\pi$
$263$		−	10.5188i		−	0.648619i	0.945951	−	0.324309i	$-0.105132\pi$
$264$		0			0
$265$	5.89292	−	1.28078i	0.361999	−	0.0786777i
$266$		0			0
$267$	−4.01155	−	2.31607i	−0.245503	−	0.141741i
$268$		0			0
$269$	13.2899	+	23.0187i	0.810297	+	1.40348i	0.912656	+	0.408728i	$0.134028\pi$
$269$	13.2899	+	23.0187i	0.810297	+	1.40348i	−0.102359	+	0.994748i	$0.532639\pi$
$270$		0			0
$271$	21.1898			1.28719			0.643596	−	0.765366i	$-0.277442\pi$
$271$	21.1898			1.28719			0.643596	+	0.765366i	$0.277442\pi$
$272$		0			0
$273$	−33.0519	−	19.0825i	−2.00039	−	1.15493i
$274$		0			0
$275$	−1.08980	+	11.3683i	−0.0657177	+	0.685535i
$276$		0			0
$277$		−	19.8454i		−	1.19240i	−0.802838	−	0.596198i	$-0.796677\pi$
$277$		−	19.8454i		−	1.19240i	0.802838	−	0.596198i	$-0.203323\pi$
$278$		0			0
$279$	13.4395	+	21.4179i	0.804603	+	1.28226i
$280$		0			0
$281$	−16.6305			−0.992093			−0.496047	−	0.868296i	$-0.665215\pi$
$281$	−16.6305			−0.992093			−0.496047	+	0.868296i	$0.665215\pi$
$282$		0			0
$283$			1.18974i			0.0707230i	0.999375	+	0.0353615i	$0.0112583\pi$
$283$			1.18974i			0.0707230i	−0.999375	+	0.0353615i	$0.988742\pi$
$284$		0			0
$285$	−27.3878	+	5.95253i	−1.62231	+	0.352597i
$286$		0			0
$287$			37.4498i			2.21059i
$288$		0			0
$289$	−4.64725	−	8.04927i	−0.273368	−	0.473486i
$290$		0			0
$291$	−13.2381	+	22.9290i	−0.776028	+	1.34412i
$292$		0			0
$293$	−15.5495	−	8.97749i	−0.908409	−	0.524470i	−0.0284904	−	0.999594i	$-0.509070\pi$
$293$	−15.5495	−	8.97749i	−0.908409	−	0.524470i	−0.879919	+	0.475124i	$0.842403\pi$
$294$		0			0
$295$	−8.48686	+	7.71219i	−0.494124	+	0.449021i
$296$		0			0
$297$	8.37292	−	4.83411i	0.485846	−	0.280503i
$298$		0			0
$299$	−8.23727	−	14.2674i	−0.476374	−	0.825103i
$300$		0			0
$301$	−5.52953	−	9.57744i	−0.318717	−	0.552034i
$302$		0			0
$303$	−38.7759	−	22.3873i	−2.22762	−	1.28612i
$304$		0			0
$305$	32.1736	+	10.2914i	1.84225	+	0.589282i
$306$		0			0
$307$	27.7860	+	16.0423i	1.58583	+	0.915580i	0.993984	+	0.109529i	$0.0349344\pi$
$307$	27.7860	+	16.0423i	1.58583	+	0.915580i	0.591847	+	0.806050i	$0.298399\pi$
$308$		0			0
$309$	21.2594			1.20941
$310$		0			0
$311$	0.874226			0.0495728			0.0247864	−	0.999693i	$-0.492109\pi$
$311$	0.874226			0.0495728			0.0247864	+	0.999693i	$0.492109\pi$
$312$		0			0
$313$	18.7417	+	10.8205i	1.05934	+	0.611613i	0.925251	−	0.379356i	$-0.123854\pi$
$313$	18.7417	+	10.8205i	1.05934	+	0.611613i	0.134094	+	0.990969i	$0.457188\pi$
$314$		0			0
$315$	12.7347	−	39.8123i	0.717522	−	2.24317i
$316$		0			0
$317$	10.7548	+	6.20930i	0.604051	+	0.348749i	0.770634	−	0.637278i	$-0.219940\pi$
$317$	10.7548	+	6.20930i	0.604051	+	0.348749i	−0.166582	+	0.986028i	$0.553273\pi$
$318$		0			0
$319$	−8.34720	−	14.4578i	−0.467353	−	0.809480i
$320$		0			0
$321$	−27.9634	−	48.4341i	−1.56077	−	2.70333i
$322$		0			0
$323$	10.9724	−	6.33491i	0.610520	−	0.352484i
$324$		0			0
$325$	−16.8045	−	1.61094i	−0.932148	−	0.0893588i
$326$		0			0
$327$	13.5621	+	7.83011i	0.749989	+	0.433006i
$328$		0			0
$329$	4.81602	−	8.34159i	0.265516	−	0.459887i
$330$		0			0
$331$	12.4357	+	21.5392i	0.683527	+	1.18390i	0.973897	+	0.226989i	$0.0728880\pi$
$331$	12.4357	+	21.5392i	0.683527	+	1.18390i	−0.290371	+	0.956914i	$0.593779\pi$
$332$		0			0
$333$			29.4575i			1.61426i
$334$		0			0
$335$	7.62725	−	1.65772i	0.416721	−	0.0905711i
$336$		0			0
$337$			21.0328i			1.14573i	0.819650	+	0.572864i	$0.194168\pi$
$337$			21.0328i			1.14573i	−0.819650	+	0.572864i	$0.805832\pi$
$338$		0			0
$339$	40.0204			2.17361
$340$		0			0
$341$	6.75941	+	10.7721i	0.366043	+	0.583344i
$342$		0			0
$343$		−	12.1148i		−	0.654138i
$344$		0			0
$345$	22.1747	−	20.1506i	1.19384	−	1.08487i
$346$		0			0
$347$	−2.11196	−	1.21934i	−0.113376	−	0.0654575i	0.442240	−	0.896897i	$-0.354184\pi$
$347$	−2.11196	−	1.21934i	−0.113376	−	0.0654575i	−0.555616	+	0.831439i	$0.687517\pi$
$348$		0			0
$349$	−1.10585			−0.0591950			−0.0295975	−	0.999562i	$-0.509423\pi$
$349$	−1.10585			−0.0591950			−0.0295975	+	0.999562i	$0.509423\pi$
$350$		0			0
$351$	7.14573	+	12.3768i	0.381411	+	0.660623i
$352$		0			0
$353$	−7.17865	−	4.14459i	−0.382081	−	0.220594i	0.296642	−	0.954989i	$-0.404133\pi$
$353$	−7.17865	−	4.14459i	−0.382081	−	0.220594i	−0.678723	+	0.734394i	$0.737466\pi$
$354$		0			0
$355$	−0.532302	−	2.44914i	−0.0282516	−	0.129987i
$356$		0			0
$357$			31.3779i			1.66069i
$358$		0			0
$359$	−11.2797	−	19.5371i	−0.595322	−	1.03113i	−0.993501	−	0.113820i	$-0.963691\pi$
$359$	−11.2797	−	19.5371i	−0.595322	−	1.03113i	0.398179	−	0.917308i	$-0.369642\pi$
$360$		0			0
$361$	−0.916214	−	1.58693i	−0.0482218	−	0.0835226i
$362$		0			0
$363$	−13.7532	+	7.94044i	−0.721858	+	0.416765i
$364$		0			0
$365$	32.0747	−	6.97119i	1.67887	−	0.364889i
$366$		0			0
$367$	11.6575	−	6.73044i	0.608514	−	0.351326i	−0.163869	−	0.986482i	$-0.552398\pi$
$367$	11.6575	−	6.73044i	0.608514	−	0.351326i	0.772384	+	0.635156i	$0.219064\pi$
$368$		0			0
$369$	20.6590	−	35.7825i	1.07547	−	1.86276i
$370$		0			0
$371$	−11.1011			−0.576340
$372$		0			0
$373$			37.6534i			1.94962i	0.223038	+	0.974810i	$0.428403\pi$
$373$			37.6534i			1.94962i	−0.223038	+	0.974810i	$0.571597\pi$
$374$		0			0
$375$	−3.62804	−	30.4879i	−0.187351	−	1.57439i
$376$		0			0
$377$	21.3713	−	12.3387i	1.10068	−	0.635478i
$378$		0			0
$379$	12.6062	−	21.8346i	0.647538	−	1.12157i	−0.336171	−	0.941801i	$-0.609132\pi$
$379$	12.6062	−	21.8346i	0.647538	−	1.12157i	0.983709	−	0.179768i	$-0.0575348\pi$
$380$		0			0
$381$	−19.1209	−	33.1183i	−0.979591	−	1.69670i
$382$		0			0
$383$	16.0646	−	9.27492i	0.820865	−	0.473926i	−0.0298498	−	0.999554i	$-0.509503\pi$
$383$	16.0646	−	9.27492i	0.820865	−	0.473926i	0.850715	+	0.525628i	$0.176170\pi$
$384$		0			0
$385$	6.40495	−	20.0236i	0.326426	−	1.02050i
$386$		0			0
$387$			12.2014i			0.620230i
$388$		0			0
$389$	15.5210	−	26.8831i	0.786946	−	1.36303i	−0.140884	−	0.990026i	$-0.544995\pi$
$389$	15.5210	−	26.8831i	0.786946	−	1.36303i	0.927830	−	0.373004i	$-0.121672\pi$
$390$		0			0
$391$	−6.77237	+	11.7301i	−0.342494	+	0.593216i
$392$		0			0
$393$	41.4945	−	23.9569i	2.09312	−	1.20847i
$394$		0			0
$395$	−1.10668	+	1.00566i	−0.0556829	+	0.0506003i
$396$		0			0
$397$	−12.7056	−	7.33559i	−0.637677	−	0.368163i	0.146042	−	0.989278i	$-0.453346\pi$
$397$	−12.7056	−	7.33559i	−0.637677	−	0.368163i	−0.783719	+	0.621115i	$0.786680\pi$
$398$		0			0
$399$	51.5932			2.58289
$400$		0			0
$401$	−14.2916			−0.713686			−0.356843	−	0.934164i	$-0.616147\pi$
$401$	−14.2916			−0.713686			−0.356843	+	0.934164i	$0.616147\pi$
$402$		0			0
$403$	−15.9233	+	9.99170i	−0.793195	+	0.497722i
$404$		0			0
$405$	3.30978	−	3.00767i	0.164464	−	0.149452i
$406$		0			0
$407$			14.8157i			0.734386i
$408$		0			0
$409$	4.75939	−	8.24351i	0.235337	−	0.407615i	−0.724034	−	0.689765i	$-0.757714\pi$
$409$	4.75939	−	8.24351i	0.235337	−	0.407615i	0.959370	+	0.282149i	$0.0910474\pi$
$410$		0			0
$411$	−61.0944			−3.01356
$412$		0			0
$413$	18.2816	−	10.5549i	0.899578	−	0.519372i
$414$		0			0
$415$	16.4648	−	3.57849i	0.808224	−	0.175661i
$416$		0			0
$417$	−16.7929	−	9.69540i	−0.822353	−	0.474786i
$418$		0			0
$419$	26.7952			1.30903			0.654517	−	0.756048i	$-0.272872\pi$
$419$	26.7952			1.30903			0.654517	+	0.756048i	$0.272872\pi$
$420$		0			0
$421$	8.63288	+	14.9526i	0.420741	+	0.728745i	0.996012	−	0.0892181i	$-0.0284368\pi$
$421$	8.63288	+	14.9526i	0.420741	+	0.728745i	−0.575271	+	0.817963i	$0.695103\pi$
$422$		0			0
$423$	−9.20319	+	5.31347i	−0.447475	+	0.258350i
$424$		0			0
$425$	5.76102	+	12.6273i	0.279450	+	0.612513i
$426$		0			0
$427$	−53.8513	−	31.0910i	−2.60604	−	1.50460i
$428$		0			0
$429$	10.5889	+	18.3405i	0.511237	+	0.885488i
$430$		0			0
$431$	0.275374	−	0.476962i	0.0132643	−	0.0229745i	−0.859317	−	0.511443i	$-0.829111\pi$
$431$	0.275374	−	0.476962i	0.0132643	−	0.0229745i	0.872581	+	0.488469i	$0.162444\pi$
$432$		0			0
$433$		−	31.8286i		−	1.52959i	−0.644276	−	0.764793i	$-0.722841\pi$
$433$		−	31.8286i		−	1.52959i	0.644276	−	0.764793i	$-0.277159\pi$
$434$		0			0
$435$	30.1839	+	33.2158i	1.44721	+	1.59258i
$436$		0			0
$437$	19.2873	+	11.1355i	0.922635	+	0.532684i
$438$		0			0
$439$	−9.28131	−	16.0757i	−0.442973	−	0.767251i	0.554936	−	0.831893i	$-0.312743\pi$
$439$	−9.28131	−	16.0757i	−0.442973	−	0.767251i	−0.997909	+	0.0646420i	$0.979409\pi$
$440$		0			0
$441$	−22.5779	+	39.1060i	−1.07514	+	1.86219i
$442$		0			0
$443$	−12.4649	+	7.19660i	−0.592224	+	0.341921i	−0.765976	−	0.642869i	$-0.777744\pi$
$443$	−12.4649	+	7.19660i	−0.592224	+	0.341921i	0.173752	+	0.984789i	$0.444411\pi$
$444$		0			0
$445$	3.59243	+	1.14911i	0.170298	+	0.0544731i
$446$		0			0
$447$	11.1016	−	6.40953i	0.525089	−	0.303160i
$448$		0			0
$449$	−18.6994			−0.882478			−0.441239	−	0.897390i	$-0.645461\pi$
$449$	−18.6994			−0.882478			−0.441239	+	0.897390i	$0.645461\pi$
$450$		0			0
$451$	10.3905	−	17.9968i	0.489268	−	0.847436i
$452$		0			0
$453$	20.6252	+	11.9079i	0.969054	+	0.559484i
$454$		0			0
$455$	29.5987	+	9.46773i	1.38761	+	0.443854i
$456$		0			0
$457$		−	33.9720i		−	1.58914i	−0.607171	−	0.794571i	$-0.707696\pi$
$457$		−	33.9720i		−	1.58914i	0.607171	−	0.794571i	$-0.292304\pi$
$458$		0			0
$459$	5.87495	−	10.1757i	0.274219	−	0.474961i
$460$		0			0
$461$	35.2728			1.64282			0.821409	−	0.570339i	$-0.193188\pi$
$461$	35.2728			1.64282			0.821409	+	0.570339i	$0.193188\pi$
$462$		0			0
$463$			14.1689i			0.658485i	0.944245	+	0.329243i	$0.106793\pi$
$463$			14.1689i			0.658485i	−0.944245	+	0.329243i	$0.893207\pi$
$464$		0			0
$465$	−23.9082	−	24.4399i	−1.10872	−	1.13337i
$466$		0			0
$467$		−	26.4262i		−	1.22286i	−0.791298	−	0.611430i	$-0.790594\pi$
$467$		−	26.4262i		−	1.22286i	0.791298	−	0.611430i	$-0.209406\pi$
$468$		0			0
$469$	−14.3682			−0.663463
$470$		0			0
$471$	11.6147	−	20.1172i	0.535177	−	0.926954i
$472$		0			0
$473$			6.13668i			0.282165i
$474$		0			0
$475$	20.7625	−	9.47259i	0.952648	−	0.434632i
$476$		0			0
$477$	10.6069	+	6.12387i	0.485654	+	0.280393i
$478$		0			0
$479$	−6.19232	+	10.7254i	−0.282935	+	0.490057i	−0.972106	−	0.234541i	$-0.924641\pi$
$479$	−6.19232	+	10.7254i	−0.282935	+	0.490057i	0.689172	+	0.724598i	$0.257975\pi$
$480$		0			0
$481$	−21.9004			−0.998572
$482$		0			0
$483$	−47.7665	+	27.5780i	−2.17345	+	1.25484i
$484$		0			0
$485$	6.56801	−	20.5334i	0.298238	−	0.932373i
$486$		0			0
$487$	−18.0165	+	10.4018i	−0.816407	+	0.471353i	−0.849176	−	0.528110i	$-0.822901\pi$
$487$	−18.0165	+	10.4018i	−0.816407	+	0.471353i	0.0327692	+	0.999463i	$0.489567\pi$
$488$		0			0
$489$	−21.6092	+	37.4282i	−0.977202	+	1.69256i
$490$		0			0
$491$	1.24918	+	2.16364i	0.0563747	+	0.0976438i	0.892835	−	0.450383i	$-0.148713\pi$
$491$	1.24918	+	2.16364i	0.0563747	+	0.0976438i	−0.836461	+	0.548027i	$0.815379\pi$
$492$		0			0
$493$	−17.5707	−	10.1444i	−0.791345	−	0.456883i
$494$		0			0
$495$	−17.1657	+	15.5988i	−0.771541	+	0.701115i
$496$		0			0
$497$			4.61370i			0.206953i
$498$		0			0
$499$	−6.48139	+	11.2261i	−0.290147	+	0.502549i	−0.973844	−	0.227216i	$-0.927038\pi$
$499$	−6.48139	+	11.2261i	−0.290147	+	0.502549i	0.683697	+	0.729766i	$0.260371\pi$
$500$		0			0
$501$	7.87261	+	13.6358i	0.351722	+	0.609201i
$502$		0			0
$503$	8.11146	+	4.68315i	0.361672	+	0.208811i	0.669814	−	0.742529i	$-0.266374\pi$
$503$	8.11146	+	4.68315i	0.361672	+	0.208811i	−0.308142	+	0.951340i	$0.599707\pi$
$504$		0			0
$505$	34.7246	+	11.1074i	1.54523	+	0.494271i
$506$		0			0
$507$	3.80636	−	2.19761i	0.169047	−	0.0975991i
$508$		0			0
$509$	13.6793	+	23.6932i	0.606324	+	1.05018i	0.991841	+	0.127483i	$0.0406900\pi$
$509$	13.6793	+	23.6932i	0.606324	+	1.05018i	−0.385516	+	0.922701i	$0.625977\pi$
$510$		0			0
$511$	−60.4224			−2.67293
$512$		0			0
$513$	−16.7315	−	9.65992i	−0.738713	−	0.426496i
$514$		0			0
$515$	−16.9157	+	3.67649i	−0.745393	+	0.162005i
$516$		0			0
$517$	−4.62875	+	2.67241i	−0.203572	+	0.117532i
$518$		0			0
$519$	19.8894			0.873047
$520$		0			0
$521$	−13.4354	+	23.2708i	−0.588617	+	1.01951i	0.405797	+	0.913963i	$0.366994\pi$
$521$	−13.4354	+	23.2708i	−0.588617	+	1.01951i	−0.994414	+	0.105551i	$0.966339\pi$
$522$		0			0
$523$		−	1.01543i		−	0.0444018i	−0.999754	−	0.0222009i	$-0.992933\pi$
$523$		−	1.01543i		−	0.0444018i	0.999754	−	0.0222009i	$-0.00706735\pi$
$524$		0			0
$525$	−5.39335	+	56.2609i	−0.235385	+	2.45543i
$526$		0			0
$527$	13.6600	+	7.23019i	0.595038	+	0.314952i
$528$		0			0
$529$	−0.808969			−0.0351725
$530$		0			0
$531$	−23.2902			−1.01071
$532$		0			0
$533$	26.6027	+	15.3591i	1.15229	+	0.665275i
$534$		0			0
$535$	30.6258	+	33.7021i	1.32407	+	1.45707i
$536$		0			0
$537$	28.5404	−	16.4778i	1.23161	−	0.711070i
$538$		0			0
$539$	−11.3556	+	19.6684i	−0.489119	+	0.847178i
$540$		0			0
$541$	7.01355	−	12.1478i	0.301536	−	0.522275i	−0.674948	−	0.737865i	$-0.735834\pi$
$541$	7.01355	−	12.1478i	0.301536	−	0.522275i	0.976484	+	0.215590i	$0.0691674\pi$
$542$		0			0
$543$		−	56.4284i		−	2.42157i
$544$		0			0
$545$	−12.1452	−	3.88488i	−0.520243	−	0.166410i
$546$		0			0
$547$	22.9681	−	13.2606i	0.982045	−	0.566984i	0.0791583	−	0.996862i	$-0.474777\pi$
$547$	22.9681	−	13.2606i	0.982045	−	0.566984i	0.902887	+	0.429878i	$0.141443\pi$
$548$		0			0
$549$	34.3024	+	59.4136i	1.46399	+	2.53571i
$550$		0			0
$551$	−16.6801	+	28.8907i	−0.710595	+	1.23079i
$552$		0			0
$553$	2.38390	−	1.37634i	0.101374	−	0.0585281i
$554$		0			0
$555$	−8.45942	−	38.9221i	−0.359082	−	1.65215i
$556$		0			0
$557$		−	22.2445i		−	0.942530i	−0.881992	−	0.471265i	$-0.843798\pi$
$557$		−	22.2445i		−	0.942530i	0.881992	−	0.471265i	$-0.156202\pi$
$558$		0			0
$559$	−9.07118			−0.383670
$560$		0			0
$561$	8.70579	−	15.0789i	0.367559	−	0.636631i
$562$		0			0
$563$	1.67777	−	0.968664i	0.0707098	−	0.0408243i	−0.464228	−	0.885716i	$-0.653668\pi$
$563$	1.67777	−	0.968664i	0.0707098	−	0.0408243i	0.534938	+	0.844891i	$0.320335\pi$
$564$		0			0
$565$	−31.8434	+	6.92091i	−1.33966	+	0.291165i
$566$		0			0
$567$	−7.12962	+	4.11629i	−0.299416	+	0.172868i
$568$		0			0
$569$	−9.16048	−	15.8664i	−0.384027	−	0.665155i	0.607606	−	0.794238i	$-0.292130\pi$
$569$	−9.16048	−	15.8664i	−0.384027	−	0.665155i	−0.991634	+	0.129083i	$0.958797\pi$
$570$		0			0
$571$	15.6373	+	27.0847i	0.654402	+	1.13346i	0.982043	+	0.188655i	$0.0604129\pi$
$571$	15.6373	+	27.0847i	0.654402	+	1.13346i	−0.327641	+	0.944802i	$0.606254\pi$
$572$		0			0
$573$		−	8.01849i		−	0.334977i
$574$		0			0
$575$	−14.1592	+	19.8681i	−0.590478	+	0.828558i
$576$		0			0
$577$	−18.0965	−	10.4480i	−0.753365	−	0.434956i	0.0735433	−	0.997292i	$-0.476569\pi$
$577$	−18.0965	−	10.4480i	−0.753365	−	0.434956i	−0.826909	+	0.562336i	$0.809903\pi$
$578$		0			0
$579$	12.8422	+	22.2433i	0.533703	+	0.924400i
$580$		0			0
$581$	−31.0164			−1.28678
$582$		0			0
$583$	5.33472	+	3.08000i	0.220942	+	0.127561i
$584$		0			0
$585$	−23.0580	−	25.3742i	−0.953333	−	1.04909i
$586$		0			0
$587$			0.785367i			0.0324156i	0.999869	+	0.0162078i	$0.00515932\pi$
$587$			0.785367i			0.0324156i	−0.999869	+	0.0162078i	$0.994841\pi$
$588$		0			0
$589$	11.8883	−	22.4605i	0.489848	−	0.925469i
$590$		0			0
$591$	34.4222			1.41594
$592$		0			0
$593$		−	30.8993i		−	1.26888i	−0.772972	−	0.634440i	$-0.781231\pi$
$593$		−	30.8993i		−	1.26888i	0.772972	−	0.634440i	$-0.218769\pi$
$594$		0			0
$595$	−5.42631	−	24.9667i	−0.222457	−	1.02353i
$596$		0			0
$597$			40.6757i			1.66475i
$598$		0			0
$599$	11.9294	+	20.6624i	0.487423	+	0.844241i	0.999895	−	0.0144625i	$-0.00460371\pi$
$599$	11.9294	+	20.6624i	0.487423	+	0.844241i	−0.512473	+	0.858704i	$0.671270\pi$
$600$		0			0
$601$	2.02090	−	3.50030i	0.0824342	−	0.142780i	−0.821861	−	0.569688i	$-0.807064\pi$
$601$	2.02090	−	3.50030i	0.0824342	−	0.142780i	0.904295	+	0.426908i	$0.140397\pi$
$602$		0			0
$603$	13.7285	+	7.92616i	0.559069	+	0.322778i
$604$		0			0
$605$	9.56997	−	8.69644i	0.389075	−	0.353560i
$606$		0			0
$607$	9.14269	−	5.27853i	0.371090	−	0.214249i	−0.302844	−	0.953040i	$-0.597936\pi$
$607$	9.14269	−	5.27853i	0.371090	−	0.214249i	0.673935	+	0.738791i	$0.264603\pi$
$608$		0			0
$609$	−41.3096	−	71.5503i	−1.67395	−	2.89936i
$610$		0			0
$611$	−3.95033	−	6.84217i	−0.159813	−	0.276805i
$612$		0			0
$613$	−41.7375	−	24.0971i	−1.68576	−	0.973274i	−0.957704	−	0.287757i	$-0.907091\pi$
$613$	−41.7375	−	24.0971i	−1.68576	−	0.973274i	−0.728056	−	0.685517i	$-0.759576\pi$
$614$		0			0
$615$	−17.0209	+	53.2119i	−0.686349	+	2.14571i
$616$		0			0
$617$	0.110124	+	0.0635803i	0.00443344	+	0.00255965i	0.502215	−	0.864743i	$-0.332519\pi$
$617$	0.110124	+	0.0635803i	0.00443344	+	0.00255965i	−0.497782	+	0.867302i	$0.665852\pi$
$618$		0			0
$619$	17.3115			0.695810			0.347905	−	0.937530i	$-0.386893\pi$
$619$	17.3115			0.695810			0.347905	+	0.937530i	$0.386893\pi$
$620$		0			0
$621$	20.6540			0.828816
$622$		0			0
$623$	−6.01291	−	3.47156i	−0.240902	−	0.139085i
$624$		0			0
$625$	8.15915	+	23.6311i	0.326366	+	0.945244i
$626$		0			0
$627$	−24.7935	−	14.3146i	−0.990158	−	0.571668i
$628$		0			0
$629$	9.00284	+	15.5934i	0.358967	+	0.621749i
$630$		0			0
$631$	10.7298	+	18.5845i	0.427146	+	0.739839i	0.996618	−	0.0821720i	$-0.0261857\pi$
$631$	10.7298	+	18.5845i	0.427146	+	0.739839i	−0.569472	+	0.822011i	$0.692852\pi$
$632$		0			0
$633$	−7.49295	+	4.32606i	−0.297818	+	0.171945i
$634$		0			0
$635$	20.9413	+	23.0448i	0.831031	+	0.914506i
$636$		0			0
$637$	−29.0736	−	16.7857i	−1.15194	−	0.665073i
$638$		0			0
$639$	2.54512	−	4.40828i	0.100684	−	0.174389i
$640$		0			0
$641$	−10.5859	−	18.3353i	−0.418117	−	0.724201i	0.577633	−	0.816297i	$-0.303977\pi$
$641$	−10.5859	−	18.3353i	−0.418117	−	0.724201i	−0.995750	+	0.0920961i	$0.970643\pi$
$642$		0			0
$643$			32.0238i			1.26289i	0.775419	+	0.631447i	$0.217539\pi$
$643$			32.0238i			1.26289i	−0.775419	+	0.631447i	$0.782461\pi$
$644$		0			0
$645$	−3.50391	−	16.1216i	−0.137966	−	0.634788i
$646$		0			0
$647$			35.5581i			1.39793i	0.715154	+	0.698967i	$0.246356\pi$
$647$			35.5581i			1.39793i	−0.715154	+	0.698967i	$0.753644\pi$
$648$		0			0
$649$	−11.7138			−0.459807
$650$		0			0
$651$	33.4518	+	53.3104i	1.31108	+	2.08940i
$652$		0			0
$653$		−	28.1902i		−	1.10317i	−0.834119	−	0.551584i	$-0.814024\pi$
$653$		−	28.1902i		−	1.10317i	0.834119	−	0.551584i	$-0.185976\pi$
$654$		0			0
$655$	−28.8733	+	26.2378i	−1.12817	+	1.02520i
$656$		0			0
$657$	57.7323	+	33.3317i	2.25235	+	1.30040i
$658$		0			0
$659$	47.6941			1.85790			0.928950	−	0.370206i	$-0.120713\pi$
$659$	47.6941			1.85790			0.928950	+	0.370206i	$0.120713\pi$
$660$		0			0
$661$	2.17917	+	3.77443i	0.0847599	+	0.146808i	0.905289	−	0.424796i	$-0.139654\pi$
$661$	2.17917	+	3.77443i	0.0847599	+	0.146808i	−0.820529	+	0.571605i	$0.806321\pi$
$662$		0			0
$663$	22.2895	+	12.8688i	0.865651	+	0.499784i
$664$		0			0
$665$	−41.0516	+	8.92224i	−1.59191	+	0.345990i
$666$		0			0
$667$		−	35.6639i		−	1.38091i
$668$		0			0
$669$	8.49552	+	14.7147i	0.328456	+	0.568902i
$670$		0			0
$671$	17.2524	+	29.8821i	0.666023	+	1.15358i
$672$		0			0
$673$	−4.69122	+	2.70848i	−0.180833	+	0.104404i	−0.587684	−	0.809090i	$-0.699960\pi$
$673$	−4.69122	+	2.70848i	−0.180833	+	0.104404i	0.406851	+	0.913495i	$0.366627\pi$
$674$		0			0
$675$	12.2829	−	17.2354i	0.472769	−	0.663389i
$676$		0			0
$677$	32.1760	−	18.5768i	1.23663	−	0.713966i	0.268223	−	0.963357i	$-0.413564\pi$
$677$	32.1760	−	18.5768i	1.23663	−	0.713966i	0.968403	+	0.249391i	$0.0802303\pi$
$678$		0			0
$679$	−19.8425	+	34.3682i	−0.761485	+	1.31893i
$680$		0			0
$681$	29.1772			1.11807
$682$		0			0
$683$		−	33.3681i		−	1.27680i	−0.769706	−	0.638398i	$-0.779597\pi$
$683$		−	33.3681i		−	1.27680i	0.769706	−	0.638398i	$-0.220403\pi$
$684$		0			0
$685$	48.6114	−	10.5653i	1.85735	−	0.403680i
$686$		0			0
$687$	56.1563	−	32.4218i	2.14250	−	1.23697i
$688$		0			0
$689$	−4.55283	+	7.88573i	−0.173449	+	0.300422i
$690$		0			0
$691$	−26.0189	−	45.0661i	−0.989806	−	1.71439i	−0.618242	−	0.785988i	$-0.712155\pi$
$691$	−26.0189	−	45.0661i	−0.989806	−	1.71439i	−0.371564	−	0.928407i	$-0.621178\pi$
$692$		0			0
$693$	36.9767	−	21.3485i	1.40463	−	0.810963i
$694$		0			0
$695$	15.0384	+	4.81034i	0.570440	+	0.182467i
$696$		0			0
$697$		−	25.2553i		−	0.956613i
$698$		0			0
$699$	22.7441	−	39.3939i	0.860260	−	1.49001i
$700$		0			0
$701$	−22.3461	+	38.7045i	−0.843999	+	1.46185i	0.0424891	+	0.999097i	$0.486471\pi$
$701$	−22.3461	+	38.7045i	−0.843999	+	1.46185i	−0.886488	+	0.462752i	$0.846862\pi$
$702$		0			0
$703$	25.6395	−	14.8030i	0.967012	−	0.558305i
$704$		0			0
$705$	10.6343	−	9.66358i	0.400509	−	0.363951i
$706$		0			0
$707$	−58.1212	−	33.5563i	−2.18587	−	1.26201i
$708$		0			0
$709$	−42.9707			−1.61380			−0.806899	−	0.590690i	$-0.798856\pi$
$709$	−42.9707			−1.61380			−0.806899	+	0.590690i	$0.798856\pi$
$710$		0			0
$711$	−3.03701			−0.113897
$712$		0			0
$713$	0.999249	+	27.1492i	0.0374222	+	1.01675i
$714$		0			0
$715$	−11.5971	−	12.7620i	−0.433705	−	0.477270i
$716$		0			0
$717$		−	7.46157i		−	0.278657i
$718$		0			0
$719$	−24.0650	+	41.6817i	−0.897472	+	1.55447i	−0.0667560	+	0.997769i	$0.521265\pi$
$719$	−24.0650	+	41.6817i	−0.897472	+	1.55447i	−0.830716	+	0.556697i	$0.812068\pi$
$720$		0			0
$721$	31.8657			1.18674
$722$		0			0
$723$	−0.306663	+	0.177052i	−0.0114049	+	0.00658463i
$724$		0			0
$725$	−29.7608	−	21.2092i	−1.10529	−	0.787691i
$726$		0			0
$727$	22.5946	+	13.0450i	0.837986	+	0.483812i	0.856579	−	0.516015i	$-0.172585\pi$
$727$	22.5946	+	13.0450i	0.837986	+	0.483812i	−0.0185929	+	0.999827i	$0.505919\pi$
$728$		0			0
$729$	43.9552			1.62797
$730$		0			0
$731$	3.72899	+	6.45880i	0.137922	+	0.238887i
$732$		0			0
$733$	7.46755	−	4.31139i	0.275820	−	0.159245i	−0.355709	−	0.934597i	$-0.615761\pi$
$733$	7.46755	−	4.31139i	0.275820	−	0.159245i	0.631530	+	0.775352i	$0.282427\pi$
$734$		0			0
$735$	18.6019	−	58.1545i	0.686140	−	2.14506i
$736$		0			0
$737$	6.90477	+	3.98647i	0.254340	+	0.146843i
$738$		0			0
$739$	−12.6306	−	21.8769i	−0.464625	−	0.804754i	0.534560	−	0.845131i	$-0.320477\pi$
$739$	−12.6306	−	21.8769i	−0.464625	−	0.804754i	−0.999185	+	0.0403769i	$0.987144\pi$
$740$		0			0
$741$	21.1596	−	36.6496i	0.777319	−	1.34636i
$742$		0			0
$743$		−	41.0899i		−	1.50744i	−0.657195	−	0.753720i	$-0.728257\pi$
$743$		−	41.0899i		−	1.50744i	0.657195	−	0.753720i	$-0.271743\pi$
$744$		0			0
$745$	−7.72489	+	7.01977i	−0.283018	+	0.257185i
$746$		0			0
$747$	29.6354	+	17.1100i	1.08430	+	0.626023i
$748$		0			0
$749$	−41.9143	−	72.5978i	−1.53152	−	2.65266i
$750$		0			0
$751$	−5.21354	+	9.03012i	−0.190245	+	0.329514i	−0.945331	−	0.326112i	$-0.894262\pi$
$751$	−5.21354	+	9.03012i	−0.190245	+	0.329514i	0.755087	+	0.655625i	$0.227595\pi$
$752$		0			0
$753$	19.8543	−	11.4629i	0.723531	−	0.417731i
$754$		0			0
$755$	−18.4703	−	5.90808i	−0.672202	−	0.215017i
$756$		0			0
$757$	2.05850	−	1.18848i	0.0748175	−	0.0431959i	−0.462125	−	0.886815i	$-0.652913\pi$
$757$	2.05850	−	1.18848i	0.0748175	−	0.0431959i	0.536942	+	0.843619i	$0.319579\pi$
$758$		0			0
$759$	30.6061			1.11093
$760$		0			0
$761$	19.7792	−	34.2585i	0.716994	−	1.24187i	−0.245191	−	0.969475i	$-0.578851\pi$
$761$	19.7792	−	34.2585i	0.716994	−	1.24187i	0.962185	−	0.272395i	$-0.0878159\pi$
$762$		0			0
$763$	20.3283	+	11.7365i	0.735934	+	0.424891i
$764$		0			0
$765$	−8.58802	+	26.8485i	−0.310501	+	0.970709i
$766$		0			0
$767$		−	17.3152i		−	0.625217i
$768$		0			0
$769$	9.89681	−	17.1418i	0.356888	−	0.618148i	−0.630551	−	0.776148i	$-0.717171\pi$
$769$	9.89681	−	17.1418i	0.356888	−	0.618148i	0.987439	+	0.157999i	$0.0505044\pi$
$770$		0			0
$771$	33.9648			1.22321
$772$		0			0
$773$			12.2441i			0.440388i	0.975456	+	0.220194i	$0.0706691\pi$
$773$			12.2441i			0.440388i	−0.975456	+	0.220194i	$0.929331\pi$
$774$		0			0
$775$	23.2497	+	15.3117i	0.835156	+	0.550014i
$776$		0			0
$777$			73.3216i			2.63040i
$778$		0			0
$779$	−41.5262			−1.48783
$780$		0			0
$781$	1.28007	−	2.21715i	0.0458046	−	0.0793358i
$782$		0			0
$783$			30.9380i			1.10563i
$784$		0			0
$785$	−5.76259	+	18.0154i	−0.205676	+	0.642998i
$786$		0			0
$787$	−23.9476	−	13.8262i	−0.853640	−	0.492849i	0.00823762	−	0.999966i	$-0.497378\pi$
$787$	−23.9476	−	13.8262i	−0.853640	−	0.492849i	−0.861877	+	0.507117i	$0.830711\pi$
$788$		0			0
$789$	−14.4432	+	25.0163i	−0.514190	+	0.890604i
$790$		0			0
$791$	59.9866			2.13288
$792$		0			0
$793$	−44.1714	+	25.5024i	−1.56857	+	0.905616i
$794$		0			0
$795$	−15.7734	−	5.04544i	−0.559425	−	0.178943i
$796$		0			0
$797$	−40.3412	+	23.2910i	−1.42896	+	0.825009i	−0.997039	−	0.0769033i	$-0.975497\pi$
$797$	−40.3412	+	23.2910i	−1.42896	+	0.825009i	−0.431919	+	0.901912i	$0.642163\pi$
$798$		0			0
$799$	−3.24781	+	5.62538i	−0.114899	+	0.199012i
$800$		0			0
$801$	3.83013	+	6.63399i	0.135331	+	0.234400i
$802$		0			0
$803$	29.0365	+	16.7642i	1.02467	+	0.591596i
$804$		0			0
$805$	33.2376	−	30.2037i	1.17147	−	1.06454i
$806$		0			0
$807$		−	72.9921i		−	2.56944i
$808$		0			0
$809$	−8.62179	+	14.9334i	−0.303126	+	0.525030i	−0.976842	−	0.213960i	$-0.931364\pi$
$809$	−8.62179	+	14.9334i	−0.303126	+	0.525030i	0.673716	+	0.738990i	$0.264697\pi$
$810$		0			0
$811$	−6.00444	−	10.4000i	−0.210844	−	0.365193i	0.741135	−	0.671356i	$-0.234288\pi$
$811$	−6.00444	−	10.4000i	−0.210844	−	0.365193i	−0.951979	+	0.306163i	$0.900955\pi$
$812$		0			0
$813$	−50.3946	−	29.0953i	−1.76741	−	1.02042i
$814$		0			0
$815$	10.7213	−	33.5178i	0.375552	−	1.17408i
$816$		0			0
$817$	10.6199	−	6.13142i	0.371544	−	0.214511i
$818$		0			0
$819$	31.5572	+	54.6586i	1.10270	+	1.90993i
$820$		0			0
$821$	−36.1816			−1.26275			−0.631373	−	0.775479i	$-0.717508\pi$
$821$	−36.1816			−1.26275			−0.631373	+	0.775479i	$0.717508\pi$
$822$		0			0
$823$	16.6892	+	9.63551i	0.581749	+	0.335873i	0.761828	−	0.647779i	$-0.224302\pi$
$823$	16.6892	+	9.63551i	0.581749	+	0.335873i	−0.180079	+	0.983652i	$0.557635\pi$
$824$		0			0
$825$	18.2014	−	25.5402i	0.633692	−	0.889196i
$826$		0			0
$827$	−28.5214	+	16.4668i	−0.991785	+	0.572607i	−0.905807	−	0.423690i	$-0.860735\pi$
$827$	−28.5214	+	16.4668i	−0.991785	+	0.572607i	−0.0859777	+	0.996297i	$0.527401\pi$
$828$		0			0
$829$	14.6470			0.508710			0.254355	−	0.967111i	$-0.418137\pi$
$829$	14.6470			0.508710			0.254355	+	0.967111i	$0.418137\pi$
$830$		0			0
$831$	−27.2493	+	47.1972i	−0.945268	+	1.63725i
$832$		0			0
$833$			27.6011i			0.956321i
$834$		0			0
$835$	−8.62215	−	9.48822i	−0.298382	−	0.328353i
$836$		0			0
$837$	−0.866837	−	23.5516i	−0.0299623	−	0.814063i
$838$		0			0
$839$	−29.6507			−1.02365			−0.511827	−	0.859088i	$-0.671031\pi$
$839$	−29.6507			−1.02365			−0.511827	+	0.859088i	$0.671031\pi$
$840$		0			0
$841$	24.4215			0.842120
$842$		0			0
$843$	39.5514	+	22.8350i	1.36222	+	0.786479i
$844$		0			0
$845$	−2.64860	+	2.40684i	−0.0911145	+	0.0827977i
$846$		0			0
$847$	−20.6147	+	11.9019i	−0.708330	+	0.408955i
$848$		0			0
$849$	1.63361	−	2.82950i	0.0560654	−	0.0971082i
$850$		0			0
$851$	−15.8252	+	27.4101i	−0.542481	+	0.939605i
$852$		0			0
$853$			23.0040i			0.787643i	0.919187	+	0.393822i	$0.128847\pi$
$853$			23.0040i			0.787643i	−0.919187	+	0.393822i	$0.871153\pi$
$854$		0			0
$855$	44.1458	+	14.1209i	1.50975	+	0.482925i
$856$		0			0
$857$	12.9021	−	7.44906i	0.440729	−	0.254455i	−0.263178	−	0.964747i	$-0.584771\pi$
$857$	12.9021	−	7.44906i	0.440729	−	0.254455i	0.703907	+	0.710292i	$0.251437\pi$
$858$		0			0
$859$	−10.2471	−	17.7485i	−0.349627	−	0.605572i	0.636556	−	0.771230i	$-0.280358\pi$
$859$	−10.2471	−	17.7485i	−0.349627	−	0.605572i	−0.986183	+	0.165659i	$0.947025\pi$
$860$		0			0
$861$	51.4215	−	89.0647i	1.75244	−	3.03532i
$862$		0			0
$863$	−30.6824	+	17.7145i	−1.04444	+	0.603009i	−0.921088	−	0.389354i	$-0.872698\pi$
$863$	−30.6824	+	17.7145i	−1.04444	+	0.603009i	−0.123354	+	0.992363i	$0.539365\pi$
$864$		0			0
$865$	−15.8255	+	3.43956i	−0.538084	+	0.116948i
$866$		0			0
$867$			25.5241i			0.866845i
$868$		0			0
$869$	−1.52747			−0.0518158
$870$		0			0
$871$	−5.89276	+	10.2066i	−0.199669	+	0.345836i
$872$		0			0
$873$	37.9181	−	21.8920i	1.28333	−	0.740933i
$874$		0			0
$875$	−5.43807	−	45.6982i	−0.183840	−	1.54488i
$876$		0			0
$877$	−41.6559	+	24.0500i	−1.40662	+	0.812112i	−0.995060	−	0.0992719i	$-0.968349\pi$
$877$	−41.6559	+	24.0500i	−1.40662	+	0.812112i	−0.411558	+	0.911383i	$0.635015\pi$
$878$		0			0
$879$	24.6536	+	42.7013i	0.831545	+	1.44028i
$880$		0			0
$881$	16.9746	+	29.4008i	0.571887	+	0.990538i	0.996372	+	0.0851026i	$0.0271218\pi$
$881$	16.9746	+	29.4008i	0.571887	+	0.990538i	−0.424485	+	0.905435i	$0.639545\pi$
$882$		0			0
$883$			20.4406i			0.687881i	0.938991	+	0.343941i	$0.111762\pi$
$883$			20.4406i			0.687881i	−0.938991	+	0.343941i	$0.888238\pi$
$884$		0			0
$885$	30.7733	−	6.68833i	1.03443	−	0.224826i
$886$		0			0
$887$	22.5353	+	13.0107i	0.756660	+	0.436858i	0.828095	−	0.560587i	$-0.189425\pi$
$887$	22.5353	+	13.0107i	0.756660	+	0.436858i	−0.0714351	+	0.997445i	$0.522758\pi$
$888$		0			0
$889$	−28.6602	−	49.6410i	−0.961233	−	1.66491i
$890$		0			0
$891$	4.56826			0.153042
$892$		0			0
$893$	9.24956	+	5.34024i	0.309525	+	0.178704i
$894$		0			0
$895$	−19.8594	+	18.0466i	−0.663826	+	0.603233i
$896$		0			0
$897$			45.2417i			1.51058i
$898$		0			0
$899$	−40.6673	+	1.49679i	−1.35633	+	0.0499208i
$900$		0			0
$901$	7.48633			0.249406
$902$		0			0
$903$			30.3699i			1.01065i
$904$		0			0
$905$	9.75840	+	44.8988i	0.324380	+	1.49249i
$906$		0			0
$907$		−	42.7134i		−	1.41827i	−0.705071	−	0.709137i	$-0.749085\pi$
$907$		−	42.7134i		−	1.41827i	0.705071	−	0.709137i	$-0.250915\pi$
$908$		0			0
$909$	37.0223	+	64.1245i	1.22795	+	2.12688i
$910$		0			0
$911$	−8.60589	+	14.9058i	−0.285126	+	0.493852i	−0.972640	−	0.232319i	$-0.925369\pi$
$911$	−8.60589	+	14.9058i	−0.285126	+	0.493852i	0.687514	+	0.726171i	$0.258702\pi$
$912$		0			0
$913$	14.9052	+	8.60550i	0.493289	+	0.284800i
$914$		0			0
$915$	−62.3857	−	68.6522i	−2.06241	−	2.26957i
$916$		0			0
$917$	62.1961	−	35.9090i	2.05390	−	1.18582i
$918$		0			0
$919$	−21.4764	−	37.1982i	−0.708440	−	1.22705i	−0.965436	−	0.260641i	$-0.916066\pi$
$919$	−21.4764	−	37.1982i	−0.708440	−	1.22705i	0.256996	−	0.966413i	$-0.417267\pi$
$920$		0			0
$921$	−44.0545	−	76.3047i	−1.45165	−	2.51433i
$922$		0			0
$923$	3.27737	+	1.89219i	0.107876	+	0.0622822i
$924$		0			0
$925$	13.4619	+	29.5065i	0.442626	+	0.970169i
$926$		0			0
$927$	−30.4470	−	17.5786i	−1.00001	−	0.577356i
$928$		0			0
$929$	7.04620			0.231178			0.115589	−	0.993297i	$-0.463124\pi$
$929$	7.04620			0.231178			0.115589	+	0.993297i	$0.463124\pi$
$930$		0			0
$931$	45.3833			1.48738
$932$		0			0
$933$	−2.07912	−	1.20038i	−0.0680673	−	0.0392987i
$934$		0			0
$935$	−4.31935	+	13.5035i	−0.141258	+	0.441610i
$936$		0			0
$937$	−13.0279	−	7.52169i	−0.425604	−	0.245723i	0.271868	−	0.962335i	$-0.412359\pi$
$937$	−13.0279	−	7.52169i	−0.425604	−	0.245723i	−0.697472	+	0.716612i	$0.745692\pi$
$938$		0			0
$939$	−29.7149	−	51.4677i	−0.969709	−	1.67958i
$940$		0			0
$941$	−9.13033	−	15.8142i	−0.297640	−	0.515528i	0.677955	−	0.735103i	$-0.262866\pi$
$941$	−9.13033	−	15.8142i	−0.297640	−	0.515528i	−0.975596	+	0.219575i	$0.929533\pi$
$942$		0			0
$943$	38.4462	−	22.1969i	1.25198	−	0.722831i
$944$		0			0
$945$	−28.8332	+	26.2013i	−0.937944	+	0.852329i
$946$		0			0
$947$	31.5546	+	18.2180i	1.02539	+	0.592007i	0.915659	−	0.401955i	$-0.131669\pi$
$947$	31.5546	+	18.2180i	1.02539	+	0.592007i	0.109727	+	0.993962i	$0.465002\pi$
$948$		0			0
$949$	−24.7807	+	42.9214i	−0.804416	+	1.39329i
$950$		0			0
$951$	−17.0517	−	29.5344i	−0.552940	−	0.957720i
$952$		0			0
$953$			5.88586i			0.190662i	0.995446	+	0.0953309i	$0.0303909\pi$
$953$			5.88586i			0.190662i	−0.995446	+	0.0953309i	$0.969609\pi$
$954$		0			0
$955$	1.38667	+	6.38013i	0.0448716	+	0.206456i
$956$		0			0
$957$			45.8454i			1.48197i
$958$		0			0
$959$	−91.5743			−2.95709
$960$		0			0
$961$	30.9161	−	2.27887i	0.997294	−	0.0735121i
$962$		0			0
$963$			92.4873i			2.98036i
$964$		0			0
$965$	−14.0649	−	15.4777i	−0.452764	−	0.498243i
$966$		0			0
$967$	−23.8388	−	13.7634i	−0.766606	−	0.442600i	0.0650568	−	0.997882i	$-0.479277\pi$
$967$	−23.8388	−	13.7634i	−0.766606	−	0.442600i	−0.831662	+	0.555282i	$0.812610\pi$
$968$		0			0
$969$	−34.7933			−1.11772
$970$		0			0
$971$	−17.6390	−	30.5516i	−0.566061	−	0.980447i	−0.996950	−	0.0780417i	$-0.975133\pi$
$971$	−17.6390	−	30.5516i	−0.566061	−	0.980447i	0.430889	−	0.902405i	$-0.358200\pi$
$972$		0			0
$973$	−25.1709	−	14.5324i	−0.806942	−	0.465888i
$974$		0			0
$975$	37.7533	+	26.9051i	1.20907	+	0.861654i
$976$		0			0
$977$		−	6.29430i		−	0.201373i	−0.994918	−	0.100686i	$-0.967896\pi$
$977$		−	6.29430i		−	0.201373i	0.994918	−	0.100686i	$-0.0321038\pi$
$978$		0			0
$979$	1.92637	+	3.33657i	0.0615670	+	0.106637i
$980$		0			0
$981$	−12.9488	−	22.4280i	−0.413424	−	0.716071i
$982$		0			0
$983$	−21.9695	+	12.6841i	−0.700717	+	0.404559i	−0.807614	−	0.589711i	$-0.799242\pi$
$983$	−21.9695	+	12.6841i	−0.700717	+	0.404559i	0.106898	+	0.994270i	$0.465908\pi$
$984$		0			0
$985$	−27.3890	+	5.95278i	−0.872685	+	0.189671i
$986$		0			0
$987$	−22.9073	+	13.2255i	−0.729148	+	0.420974i
$988$		0			0
$989$	−6.55483	+	11.3533i	−0.208431	+	0.361014i
$990$		0			0
$991$	−30.6952			−0.975065			−0.487532	−	0.873105i	$-0.662103\pi$
$991$	−30.6952			−0.975065			−0.487532	+	0.873105i	$0.662103\pi$
$992$		0			0
$993$		−	68.3006i		−	2.16745i
$994$		0			0
$995$	−7.03423	−	32.3648i	−0.223000	−	1.02603i
$996$		0			0
$997$	−26.9592	+	15.5649i	−0.853805	+	0.492945i	−0.861933	−	0.507022i	$-0.830746\pi$
$997$	−26.9592	+	15.5649i	−0.853805	+	0.492945i	0.00812764	+	0.999967i	$0.497413\pi$
$998$		0			0
$999$	13.7282	−	23.7779i	0.434340	−	0.752299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1240.2.bm.a.129.4	✓	96
5.4	even	2	inner	1240.2.bm.a.129.45	yes	96
31.25	even	3	inner	1240.2.bm.a.769.45	yes	96
155.149	even	6	inner	1240.2.bm.a.769.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1240.2.bm.a.129.4	✓	96	1.1	even	1	trivial
1240.2.bm.a.129.45	yes	96	5.4	even	2	inner
1240.2.bm.a.769.4	yes	96	155.149	even	6	inner
1240.2.bm.a.769.45	yes	96	31.25	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1240 = 2^{3} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1240.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37824 - 1.37308i) q^{3} +(2.12977 + 0.681248i) q^{5} +(-3.56474 - 2.05811i) q^{7} +(2.27069 + 3.93295i) q^{9} +(1.14204 + 1.97808i) q^{11} +(-2.92397 + 1.68816i) q^{13} +(-4.12969 - 4.54451i) q^{15} +(2.40398 + 1.38794i) q^{17} +(2.28213 - 3.95276i) q^{19} +(5.65188 + 9.78934i) q^{21} +4.87944i q^{23} +(4.07180 + 2.90180i) q^{25} -4.23286i q^{27} -7.30900 q^{29} +(5.56400 - 0.204788i) q^{31} -6.27246i q^{33} +(-6.18999 - 6.81176i) q^{35} +(5.61746 + 3.24324i) q^{37} +9.27189 q^{39} +(-4.54906 - 7.87921i) q^{41} +(2.32676 + 1.34336i) q^{43} +(2.15672 + 9.92315i) q^{45} +2.34003i q^{47} +(4.97160 + 8.61106i) q^{49} +(-3.81150 - 6.60171i) q^{51} +(2.33560 - 1.34846i) q^{53} +(1.08472 + 4.99086i) q^{55} +(-10.8549 + 6.26708i) q^{57} +(-2.56422 + 4.44136i) q^{59} +15.1066 q^{61} -18.6933i q^{63} +(-7.37743 + 1.60343i) q^{65} +(3.02299 - 1.74532i) q^{67} +(6.69986 - 11.6045i) q^{69} +(-0.560430 - 0.970694i) q^{71} +(12.7125 - 7.33957i) q^{73} +(-5.69933 - 12.4921i) q^{75} -9.40178i q^{77} +(-0.334371 + 0.579148i) q^{79} +(1.00002 - 1.73208i) q^{81} +(6.52565 - 3.76759i) q^{83} +(4.17439 + 4.59369i) q^{85} +(17.3826 + 10.0358i) q^{87} +1.68677 q^{89} +13.8976 q^{91} +(-13.5137 - 7.15277i) q^{93} +(7.55321 - 6.86376i) q^{95} -9.64115i q^{97} +(-5.18645 + 8.98319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{9} + 12 q^{11} - 20 q^{15} - 8 q^{21} + 8 q^{25} - 24 q^{29} - 12 q^{31} + 4 q^{35} + 16 q^{39} + 60 q^{49} + 12 q^{51} + 2 q^{55} - 8 q^{59} + 24 q^{61} - 4 q^{69} + 8 q^{71} + 10 q^{75} + 84 q^{79}+ \cdots - 56 q^{99}+O(q^{100}) \) 96 * q + 48 * q^9 + 12 * q^11 - 20 * q^15 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 12 * q^31 + 4 * q^35 + 16 * q^39 + 60 * q^49 + 12 * q^51 + 2 * q^55 - 8 * q^59 + 24 * q^61 - 4 * q^69 + 8 * q^71 + 10 * q^75 + 84 * q^79 - 56 * q^81 - 40 * q^85 - 56 * q^89 - 96 * q^91 + 4 * q^95 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more