LMFDB - Embedded newform 728.2.bm.c.673.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(225,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.225"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.7
Character	$\chi$	$=$	728.673
Dual form			728.2.bm.c.225.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.223973 - 0.387932i) q^{3} +0.513505i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.39967 - 2.42430i) q^{9} +(-1.05084 + 0.606703i) q^{11} +(-0.600562 + 3.55518i) q^{13} +(0.199205 - 0.115011i) q^{15} +(3.32783 - 5.76397i) q^{17} +(5.39324 + 3.11379i) q^{19} -0.447945i q^{21} +(-0.100432 - 0.173953i) q^{23} +4.73631 q^{25} -2.59779 q^{27} +(-0.904563 - 1.56675i) q^{29} +0.945010i q^{31} +(0.470719 + 0.271770i) q^{33} +(-0.256753 + 0.444709i) q^{35} +(0.151323 - 0.0873661i) q^{37} +(1.51368 - 0.563287i) q^{39} +(5.45396 - 3.14885i) q^{41} +(1.13760 - 1.97038i) q^{43} +(1.24489 + 0.718739i) q^{45} +3.38387i q^{47} +(0.500000 + 0.866025i) q^{49} -2.98137 q^{51} +9.32989 q^{53} +(-0.311545 - 0.539612i) q^{55} -2.78962i q^{57} +(12.8019 + 7.39117i) q^{59} +(4.46098 - 7.72665i) q^{61} +(2.42430 - 1.39967i) q^{63} +(-1.82561 - 0.308392i) q^{65} +(-6.09270 + 3.51762i) q^{67} +(-0.0449879 + 0.0779214i) q^{69} +(-9.82460 - 5.67224i) q^{71} +2.60456i q^{73} +(-1.06080 - 1.83737i) q^{75} -1.21341 q^{77} -11.0720 q^{79} +(-3.61718 - 6.26515i) q^{81} -0.866273i q^{83} +(2.95983 + 1.70886i) q^{85} +(-0.405195 + 0.701818i) q^{87} +(6.67370 - 3.85306i) q^{89} +(-2.29769 + 2.77860i) q^{91} +(0.366600 - 0.211656i) q^{93} +(-1.59895 + 2.76946i) q^{95} +(-13.3489 - 7.70701i) q^{97} +3.39674i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} - 18 q^{9} + 12 q^{11} + 8 q^{17} - 12 q^{19} + 2 q^{23} - 28 q^{25} - 20 q^{27} + 2 q^{29} - 18 q^{33} - 8 q^{35} + 60 q^{37} + 18 q^{39} - 6 q^{41} + 24 q^{43} - 72 q^{45} + 12 q^{49} - 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 - 18 * q^9 + 12 * q^11 + 8 * q^17 - 12 * q^19 + 2 * q^23 - 28 * q^25 - 20 * q^27 + 2 * q^29 - 18 * q^33 - 8 * q^35 + 60 * q^37 + 18 * q^39 - 6 * q^41 + 24 * q^43 - 72 * q^45 + 12 * q^49 - 72 * q^51 - 48 * q^53 - 44 * q^55 - 12 * q^59 - 30 * q^61 + 12 * q^63 + 10 * q^65 + 78 * q^67 + 36 * q^69 - 36 * q^71 + 22 * q^75 + 4 * q^77 + 20 * q^79 - 40 * q^81 - 6 * q^85 - 20 * q^87 + 108 * q^89 + 6 * q^91 + 30 * q^93 + 18 * q^95 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.223973	−	0.387932i	−0.129311	−	0.223973i	0.794099	−	0.607788i	$-0.207943\pi$
$3$	−0.223973	−	0.387932i	−0.129311	−	0.223973i	−0.923410	+	0.383816i	$0.874610\pi$
$4$		0			0
$5$			0.513505i			0.229647i	0.993386	+	0.114823i	$0.0366302\pi$
$5$			0.513505i			0.229647i	−0.993386	+	0.114823i	$0.963370\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	1.39967	−	2.42430i	0.466557	−	0.808101i
$10$		0			0
$11$	−1.05084	+	0.606703i	−0.316840	+	0.182928i	−0.649983	−	0.759948i	$-0.725224\pi$
$11$	−1.05084	+	0.606703i	−0.316840	+	0.182928i	0.333143	+	0.942876i	$0.391891\pi$
$12$		0			0
$13$	−0.600562	+	3.55518i	−0.166566	+	0.986030i
$13$	−0.600562	+	3.55518i	−0.166566	+	0.986030i
$14$		0			0
$15$	0.199205	−	0.115011i	0.0514346	−	0.0296958i
$16$		0			0
$17$	3.32783	−	5.76397i	0.807117	−	1.39797i	−0.107735	−	0.994180i	$-0.534360\pi$
$17$	3.32783	−	5.76397i	0.807117	−	1.39797i	0.914852	−	0.403788i	$-0.132307\pi$
$18$		0			0
$19$	5.39324	+	3.11379i	1.23729	+	0.714352i	0.968540	−	0.248856i	$-0.0800547\pi$
$19$	5.39324	+	3.11379i	1.23729	+	0.714352i	0.268754	+	0.963209i	$0.413388\pi$
$20$		0			0
$21$		−	0.447945i		−	0.0977497i
$22$		0			0
$23$	−0.100432	−	0.173953i	−0.0209415	−	0.0362717i	0.855365	−	0.518026i	$-0.173333\pi$
$23$	−0.100432	−	0.173953i	−0.0209415	−	0.0362717i	−0.876306	+	0.481755i	$0.840000\pi$
$24$		0			0
$25$	4.73631			0.947262
$26$		0			0
$27$	−2.59779			−0.499945
$28$		0			0
$29$	−0.904563	−	1.56675i	−0.167973	−	0.290938i	0.769734	−	0.638365i	$-0.220389\pi$
$29$	−0.904563	−	1.56675i	−0.167973	−	0.290938i	−0.937707	+	0.347427i	$0.887056\pi$
$30$		0			0
$31$			0.945010i			0.169729i	0.996393	+	0.0848644i	$0.0270457\pi$
$31$			0.945010i			0.169729i	−0.996393	+	0.0848644i	$0.972954\pi$
$32$		0			0
$33$	0.470719	+	0.271770i	0.0819417	+	0.0473091i
$34$		0			0
$35$	−0.256753	+	0.444709i	−0.0433991	+	0.0751695i
$36$		0			0
$37$	0.151323	−	0.0873661i	0.0248773	−	0.0143629i	−0.487510	−	0.873118i	$-0.662095\pi$
$37$	0.151323	−	0.0873661i	0.0248773	−	0.0143629i	0.512387	+	0.858755i	$0.328761\pi$
$38$		0			0
$39$	1.51368	−	0.563287i	0.242383	−	0.0901980i
$40$		0			0
$41$	5.45396	−	3.14885i	0.851766	−	0.491767i	−0.00948045	−	0.999955i	$-0.503018\pi$
$41$	5.45396	−	3.14885i	0.851766	−	0.491767i	0.861246	+	0.508188i	$0.169684\pi$
$42$		0			0
$43$	1.13760	−	1.97038i	0.173483	−	0.300481i	−0.766153	−	0.642659i	$-0.777831\pi$
$43$	1.13760	−	1.97038i	0.173483	−	0.300481i	0.939635	+	0.342178i	$0.111165\pi$
$44$		0			0
$45$	1.24489	+	0.718739i	0.185578	+	0.107143i
$46$		0			0
$47$			3.38387i			0.493588i	0.969068	+	0.246794i	$0.0793770\pi$
$47$			3.38387i			0.493588i	−0.969068	+	0.246794i	$0.920623\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−2.98137			−0.417475
$52$		0			0
$53$	9.32989			1.28156			0.640779	−	0.767725i	$-0.278611\pi$
$53$	9.32989			1.28156			0.640779	+	0.767725i	$0.278611\pi$
$54$		0			0
$55$	−0.311545	−	0.539612i	−0.0420088	−	0.0727613i
$56$		0			0
$57$		−	2.78962i		−	0.369494i
$58$		0			0
$59$	12.8019	+	7.39117i	1.66666	+	0.962249i	0.969418	+	0.245417i	$0.0789250\pi$
$59$	12.8019	+	7.39117i	1.66666	+	0.962249i	0.697246	+	0.716832i	$0.254408\pi$
$60$		0			0
$61$	4.46098	−	7.72665i	0.571170	−	0.989296i	−0.425276	−	0.905064i	$-0.639823\pi$
$61$	4.46098	−	7.72665i	0.571170	−	0.989296i	0.996446	−	0.0842321i	$-0.0268437\pi$
$62$		0			0
$63$	2.42430	−	1.39967i	0.305434	−	0.176342i
$64$		0			0
$65$	−1.82561	−	0.308392i	−0.226439	−	0.0382513i
$66$		0			0
$67$	−6.09270	+	3.51762i	−0.744341	+	0.429746i	−0.823646	−	0.567105i	$-0.808063\pi$
$67$	−6.09270	+	3.51762i	−0.744341	+	0.429746i	0.0793044	+	0.996850i	$0.474730\pi$
$68$		0			0
$69$	−0.0449879	+	0.0779214i	−0.00541591	+	0.00938063i
$70$		0			0
$71$	−9.82460	−	5.67224i	−1.16597	−	0.673171i	−0.213239	−	0.977000i	$-0.568401\pi$
$71$	−9.82460	−	5.67224i	−1.16597	−	0.673171i	−0.952726	+	0.303829i	$0.901735\pi$
$72$		0			0
$73$			2.60456i			0.304840i	0.988316	+	0.152420i	$0.0487067\pi$
$73$			2.60456i			0.304840i	−0.988316	+	0.152420i	$0.951293\pi$
$74$		0			0
$75$	−1.06080	−	1.83737i	−0.122491	−	0.212161i
$76$		0			0
$77$	−1.21341			−0.138281
$78$		0			0
$79$	−11.0720			−1.24570			−0.622850	−	0.782341i	$-0.714025\pi$
$79$	−11.0720			−1.24570			−0.622850	+	0.782341i	$0.714025\pi$
$80$		0			0
$81$	−3.61718	−	6.26515i	−0.401909	−	0.696127i
$82$		0			0
$83$		−	0.866273i		−	0.0950858i	−0.998869	−	0.0475429i	$-0.984861\pi$
$83$		−	0.866273i		−	0.0950858i	0.998869	−	0.0475429i	$-0.0151391\pi$
$84$		0			0
$85$	2.95983	+	1.70886i	0.321039	+	0.185352i
$86$		0			0
$87$	−0.405195	+	0.701818i	−0.0434414	+	0.0752428i
$88$		0			0
$89$	6.67370	−	3.85306i	0.707411	−	0.408424i	−0.102691	−	0.994713i	$-0.532745\pi$
$89$	6.67370	−	3.85306i	0.707411	−	0.408424i	0.810102	+	0.586289i	$0.199412\pi$
$90$		0			0
$91$	−2.29769	+	2.77860i	−0.240864	+	0.291276i
$92$		0			0
$93$	0.366600	−	0.211656i	0.0380146	−	0.0219477i
$94$		0			0
$95$	−1.59895	+	2.76946i	−0.164049	+	0.284140i
$96$		0			0
$97$	−13.3489	−	7.70701i	−1.35538	−	0.782529i	−0.366383	−	0.930464i	$-0.619404\pi$
$97$	−13.3489	−	7.70701i	−1.35538	−	0.782529i	−0.988997	+	0.147936i	$0.952737\pi$
$98$		0			0
$99$			3.39674i			0.341386i
$100$		0			0
$101$	3.41786	+	5.91991i	0.340090	+	0.589053i	0.984449	−	0.175670i	$-0.0562091\pi$
$101$	3.41786	+	5.91991i	0.340090	+	0.589053i	−0.644359	+	0.764723i	$0.722876\pi$
$102$		0			0
$103$	−6.83815			−0.673783			−0.336892	−	0.941543i	$-0.609376\pi$
$103$	−6.83815			−0.673783			−0.336892	+	0.941543i	$0.609376\pi$
$104$		0			0
$105$	0.230022			0.0224479
$106$		0			0
$107$	−6.78090	−	11.7449i	−0.655535	−	1.13542i	−0.981759	−	0.190127i	$-0.939110\pi$
$107$	−6.78090	−	11.7449i	−0.655535	−	1.13542i	0.326225	−	0.945292i	$-0.394223\pi$
$108$		0			0
$109$			8.70702i			0.833981i	0.908911	+	0.416991i	$0.136915\pi$
$109$			8.70702i			0.833981i	−0.908911	+	0.416991i	$0.863085\pi$
$110$		0			0
$111$	−0.0677842	−	0.0391352i	−0.00643379	−	0.00371455i
$112$		0			0
$113$	−4.48306	+	7.76489i	−0.421731	+	0.730459i	−0.996109	−	0.0881309i	$-0.971911\pi$
$113$	−4.48306	+	7.76489i	−0.421731	+	0.730459i	0.574378	+	0.818590i	$0.305244\pi$
$114$		0			0
$115$	0.0893257	−	0.0515722i	0.00832967	−	0.00480914i
$116$		0			0
$117$	7.77825	+	6.43204i	0.719100	+	0.594642i
$118$		0			0
$119$	5.76397	−	3.32783i	0.528382	−	0.305062i
$120$		0			0
$121$	−4.76382	+	8.25118i	−0.433075	+	0.750107i
$122$		0			0
$123$	−2.44308	−	1.41051i	−0.220285	−	0.127182i
$124$		0			0
$125$			4.99965i			0.447182i
$126$		0			0
$127$	7.82328	+	13.5503i	0.694204	+	1.20240i	0.970448	+	0.241309i	$0.0775766\pi$
$127$	7.82328	+	13.5503i	0.694204	+	1.20240i	−0.276245	+	0.961087i	$0.589090\pi$
$128$		0			0
$129$	−1.01917			−0.0897326
$130$		0			0
$131$	−0.441531			−0.0385768			−0.0192884	−	0.999814i	$-0.506140\pi$
$131$	−0.441531			−0.0385768			−0.0192884	+	0.999814i	$0.506140\pi$
$132$		0			0
$133$	3.11379	+	5.39324i	0.270000	+	0.467653i
$134$		0			0
$135$		−	1.33398i		−	0.114811i
$136$		0			0
$137$	−3.23799	−	1.86945i	−0.276640	−	0.159718i	0.355261	−	0.934767i	$-0.384392\pi$
$137$	−3.23799	−	1.86945i	−0.276640	−	0.159718i	−0.631901	+	0.775049i	$0.717725\pi$
$138$		0			0
$139$	−6.98667	+	12.1013i	−0.592602	+	1.02642i	0.401279	+	0.915956i	$0.368566\pi$
$139$	−6.98667	+	12.1013i	−0.592602	+	1.02642i	−0.993881	+	0.110460i	$0.964767\pi$
$140$		0			0
$141$	1.31271	−	0.757893i	0.110550	−	0.0638261i
$142$		0			0
$143$	−1.52585	−	4.10029i	−0.127598	−	0.342884i
$144$		0			0
$145$	0.804534	−	0.464498i	0.0668129	−	0.0385744i
$146$		0			0
$147$	0.223973	−	0.387932i	0.0184730	−	0.0319961i
$148$		0			0
$149$	−15.4642	−	8.92825i	−1.26688	−	0.731431i	−0.292480	−	0.956272i	$-0.594480\pi$
$149$	−15.4642	−	8.92825i	−1.26688	−	0.731431i	−0.974396	+	0.224841i	$0.927814\pi$
$150$		0			0
$151$			14.7033i			1.19654i	0.801295	+	0.598269i	$0.204145\pi$
$151$			14.7033i			1.19654i	−0.801295	+	0.598269i	$0.795855\pi$
$152$		0			0
$153$	−9.31574	−	16.1353i	−0.753133	−	1.30446i
$154$		0			0
$155$	−0.485268			−0.0389776
$156$		0			0
$157$	−2.87043			−0.229085			−0.114543	−	0.993418i	$-0.536540\pi$
$157$	−2.87043			−0.229085			−0.114543	+	0.993418i	$0.536540\pi$
$158$		0			0
$159$	−2.08964	−	3.61936i	−0.165719	−	0.287034i
$160$		0			0
$161$		−	0.200863i		−	0.0158303i
$162$		0			0
$163$	−16.8356	−	9.72004i	−1.31867	−	0.761332i	−0.335152	−	0.942164i	$-0.608788\pi$
$163$	−16.8356	−	9.72004i	−1.31867	−	0.761332i	−0.983514	+	0.180832i	$0.942121\pi$
$164$		0			0
$165$	−0.139555	+	0.241717i	−0.0108644	+	0.0188176i
$166$		0			0
$167$	−5.33374	+	3.07944i	−0.412737	+	0.238294i	−0.691965	−	0.721931i	$-0.743255\pi$
$167$	−5.33374	+	3.07944i	−0.412737	+	0.238294i	0.279228	+	0.960225i	$0.409922\pi$
$168$		0			0
$169$	−12.2787	−	4.27021i	−0.944512	−	0.328478i
$170$		0			0
$171$	15.0975	−	8.71657i	1.15454	−	0.666573i
$172$		0			0
$173$	2.00237	−	3.46820i	0.152237	−	0.263682i	−0.779813	−	0.626013i	$-0.784686\pi$
$173$	2.00237	−	3.46820i	0.152237	−	0.263682i	0.932050	+	0.362331i	$0.118019\pi$
$174$		0			0
$175$	4.10177	+	2.36816i	0.310064	+	0.179016i
$176$		0			0
$177$		−	6.62168i		−	0.497716i
$178$		0			0
$179$	−1.06309	−	1.84132i	−0.0794590	−	0.137627i	0.823558	−	0.567233i	$-0.191986\pi$
$179$	−1.06309	−	1.84132i	−0.0794590	−	0.137627i	−0.903017	+	0.429606i	$0.858653\pi$
$180$		0			0
$181$	−17.4412			−1.29640			−0.648198	−	0.761472i	$-0.724477\pi$
$181$	−17.4412			−1.29640			−0.648198	+	0.761472i	$0.724477\pi$
$182$		0			0
$183$	−3.99655			−0.295434
$184$		0			0
$185$	0.0448630	+	0.0777049i	0.00329839	+	0.00571298i
$186$		0			0
$187$			8.07602i			0.590577i
$188$		0			0
$189$	−2.24975	−	1.29889i	−0.163645	−	0.0944807i
$190$		0			0
$191$	0.337550	−	0.584655i	0.0244243	−	0.0423041i	−0.853555	−	0.521003i	$-0.825558\pi$
$191$	0.337550	−	0.584655i	0.0244243	−	0.0423041i	0.877979	+	0.478699i	$0.158891\pi$
$192$		0			0
$193$	19.4940	−	11.2549i	1.40321	−	0.810143i	0.408488	−	0.912764i	$-0.366056\pi$
$193$	19.4940	−	11.2549i	1.40321	−	0.810143i	0.994721	+	0.102621i	$0.0327227\pi$
$194$		0			0
$195$	0.289251	+	0.777282i	0.0207137	+	0.0556623i
$196$		0			0
$197$	−22.2018	+	12.8182i	−1.58182	+	0.913262i	−0.587222	+	0.809426i	$0.699778\pi$
$197$	−22.2018	+	12.8182i	−1.58182	+	0.913262i	−0.994594	+	0.103836i	$0.966888\pi$
$198$		0			0
$199$	−0.343787	+	0.595457i	−0.0243704	+	0.0422108i	−0.877953	−	0.478746i	$-0.841091\pi$
$199$	−0.343787	+	0.595457i	−0.0243704	+	0.0422108i	0.853583	+	0.520957i	$0.174425\pi$
$200$		0			0
$201$	2.72919	+	1.57570i	0.192503	+	0.111141i
$202$		0			0
$203$		−	1.80913i		−	0.126976i
$204$		0			0
$205$	1.61695	+	2.80064i	0.112933	+	0.195605i
$206$		0			0
$207$	−0.562286			−0.0390816
$208$		0			0
$209$	−7.55659			−0.522700
$210$		0			0
$211$	0.970272	+	1.68056i	0.0667963	+	0.115695i	0.897489	−	0.441036i	$-0.145389\pi$
$211$	0.970272	+	1.68056i	0.0667963	+	0.115695i	−0.830693	+	0.556731i	$0.812056\pi$
$212$		0			0
$213$			5.08170i			0.348193i
$214$		0			0
$215$	1.01180	+	0.584164i	0.0690044	+	0.0398397i
$216$		0			0
$217$	−0.472505	+	0.818402i	−0.0320757	+	0.0555568i
$218$		0			0
$219$	1.01039	−	0.583349i	0.0682759	−	0.0394191i
$220$		0			0
$221$	18.4934	+	15.2927i	1.24400	+	1.02870i
$222$		0			0
$223$	11.6208	−	6.70928i	0.778188	−	0.449287i	−0.0575999	−	0.998340i	$-0.518345\pi$
$223$	11.6208	−	6.70928i	0.778188	−	0.449287i	0.835788	+	0.549053i	$0.185011\pi$
$224$		0			0
$225$	6.62929	−	11.4823i	0.441952	−	0.765484i
$226$		0			0
$227$	−4.33583	−	2.50329i	−0.287779	−	0.166149i	0.349161	−	0.937063i	$-0.386467\pi$
$227$	−4.33583	−	2.50329i	−0.287779	−	0.166149i	−0.636940	+	0.770914i	$0.719800\pi$
$228$		0			0
$229$			23.9222i			1.58082i	0.612576	+	0.790411i	$0.290133\pi$
$229$			23.9222i			1.58082i	−0.612576	+	0.790411i	$0.709867\pi$
$230$		0			0
$231$	0.271770	+	0.470719i	0.0178811	+	0.0309711i
$232$		0			0
$233$	−18.3427			−1.20167			−0.600836	−	0.799373i	$-0.705165\pi$
$233$	−18.3427			−1.20167			−0.600836	+	0.799373i	$0.705165\pi$
$234$		0			0
$235$	−1.73763			−0.113351
$236$		0			0
$237$	2.47983	+	4.29519i	0.161082	+	0.279003i
$238$		0			0
$239$		−	15.9907i		−	1.03435i	−0.855878	−	0.517177i	$-0.826983\pi$
$239$		−	15.9907i		−	1.03435i	0.855878	−	0.517177i	$-0.173017\pi$
$240$		0			0
$241$	8.09282	+	4.67239i	0.521305	+	0.300975i	0.737468	−	0.675382i	$-0.236021\pi$
$241$	8.09282	+	4.67239i	0.521305	+	0.300975i	−0.216164	+	0.976357i	$0.569354\pi$
$242$		0			0
$243$	−5.51698	+	9.55570i	−0.353915	+	0.612998i
$244$		0			0
$245$	−0.444709	+	0.256753i	−0.0284114	+	0.0164033i
$246$		0			0
$247$	−14.3091	+	17.3039i	−0.910464	+	1.10102i
$248$		0			0
$249$	−0.336055	+	0.194021i	−0.0212966	+	0.0122956i
$250$		0			0
$251$	14.9750	−	25.9374i	0.945212	−	1.63715i	0.189885	−	0.981806i	$-0.439189\pi$
$251$	14.9750	−	25.9374i	0.945212	−	1.63715i	0.755327	−	0.655348i	$-0.227478\pi$
$252$		0			0
$253$	0.211076	+	0.121865i	0.0132702	+	0.00766156i
$254$		0			0
$255$		−	1.53095i		−	0.0958718i
$256$		0			0
$257$	8.23979	+	14.2717i	0.513984	+	0.890246i	0.999868	+	0.0162232i	$0.00516424\pi$
$257$	8.23979	+	14.2717i	0.513984	+	0.890246i	−0.485884	+	0.874023i	$0.661502\pi$
$258$		0			0
$259$	0.174732			0.0108573
$260$		0			0
$261$	−5.06437			−0.313476
$262$		0			0
$263$	−14.2331	−	24.6525i	−0.877651	−	1.52014i	−0.853912	−	0.520417i	$-0.825776\pi$
$263$	−14.2331	−	24.6525i	−0.877651	−	1.52014i	−0.0237383	−	0.999718i	$-0.507557\pi$
$264$		0			0
$265$			4.79095i			0.294306i
$266$		0			0
$267$	−2.98945	−	1.72596i	−0.182952	−	0.105627i
$268$		0			0
$269$	−2.39771	+	4.15295i	−0.146191	+	0.253210i	−0.929817	−	0.368023i	$-0.880035\pi$
$269$	−2.39771	+	4.15295i	−0.146191	+	0.253210i	0.783626	+	0.621233i	$0.213368\pi$
$270$		0			0
$271$	23.0244	−	13.2932i	1.39863	−	0.807502i	0.404384	−	0.914589i	$-0.367486\pi$
$271$	23.0244	−	13.2932i	1.39863	−	0.807502i	0.994250	+	0.107088i	$0.0341525\pi$
$272$		0			0
$273$	1.59253	+	0.269019i	0.0963841	+	0.0162818i
$274$		0			0
$275$	−4.97711	+	2.87354i	−0.300131	+	0.173281i
$276$		0			0
$277$	11.5438	−	19.9945i	0.693602	−	1.20135i	−0.277047	−	0.960856i	$-0.589356\pi$
$277$	11.5438	−	19.9945i	0.693602	−	1.20135i	0.970650	−	0.240498i	$-0.0773108\pi$
$278$		0			0
$279$	2.29099	+	1.32270i	0.137158	+	0.0791882i
$280$		0			0
$281$		−	15.7355i		−	0.938701i	−0.883012	−	0.469350i	$-0.844488\pi$
$281$		−	15.7355i		−	0.938701i	0.883012	−	0.469350i	$-0.155512\pi$
$282$		0			0
$283$	7.21744	+	12.5010i	0.429032	+	0.743105i	0.996787	−	0.0800919i	$-0.0255214\pi$
$283$	7.21744	+	12.5010i	0.429032	+	0.743105i	−0.567755	+	0.823197i	$0.692188\pi$
$284$		0			0
$285$	1.43248			0.0848529
$286$		0			0
$287$	6.29769			0.371741
$288$		0			0
$289$	−13.6489	−	23.6406i	−0.802876	−	1.39062i
$290$		0			0
$291$			6.90464i			0.404757i
$292$		0			0
$293$	2.14887	+	1.24065i	0.125538	+	0.0724795i	0.561454	−	0.827508i	$-0.310242\pi$
$293$	2.14887	+	1.24065i	0.125538	+	0.0724795i	−0.435916	+	0.899987i	$0.643575\pi$
$294$		0			0
$295$	−3.79541	+	6.57384i	−0.220977	+	0.382744i
$296$		0			0
$297$	2.72986	−	1.57609i	0.158403	−	0.0914539i
$298$		0			0
$299$	0.678750	−	0.252584i	0.0392531	−	0.0146073i
$300$		0			0
$301$	1.97038	−	1.13760i	0.113571	−	0.0655703i
$302$		0			0
$303$	1.53102	−	2.65180i	0.0879545	−	0.152342i
$304$		0			0
$305$	3.96768	+	2.29074i	0.227188	+	0.131167i
$306$		0			0
$307$			3.02698i			0.172759i	0.996262	+	0.0863793i	$0.0275297\pi$
$307$			3.02698i			0.172759i	−0.996262	+	0.0863793i	$0.972470\pi$
$308$		0			0
$309$	1.53156	+	2.65274i	0.0871273	+	0.150909i
$310$		0			0
$311$	33.8272			1.91816			0.959082	−	0.283130i	$-0.0913728\pi$
$311$	33.8272			1.91816			0.959082	+	0.283130i	$0.0913728\pi$
$312$		0			0
$313$	−2.92903			−0.165559			−0.0827794	−	0.996568i	$-0.526380\pi$
$313$	−2.92903			−0.165559			−0.0827794	+	0.996568i	$0.526380\pi$
$314$		0			0
$315$	0.718739	+	1.24489i	0.0404964	+	0.0701418i
$316$		0			0
$317$			14.1111i			0.792556i	0.918131	+	0.396278i	$0.129698\pi$
$317$			14.1111i			0.792556i	−0.918131	+	0.396278i	$0.870302\pi$
$318$		0			0
$319$	1.90110	+	1.09760i	0.106441	+	0.0614539i
$320$		0			0
$321$	−3.03747	+	5.26106i	−0.169535	+	0.293644i
$322$		0			0
$323$	35.8956	−	20.7243i	1.99728	−	1.15313i
$324$		0			0
$325$	−2.84445	+	16.8385i	−0.157782	+	0.934029i
$326$		0			0
$327$	3.37773	−	1.95013i	0.186789	−	0.107843i
$328$		0			0
$329$	−1.69193	+	2.93051i	−0.0932793	+	0.161564i
$330$		0			0
$331$	13.2496	+	7.64968i	0.728266	+	0.420464i	0.817787	−	0.575521i	$-0.195201\pi$
$331$	13.2496	+	7.64968i	0.728266	+	0.420464i	−0.0895218	+	0.995985i	$0.528534\pi$
$332$		0			0
$333$		−	0.489136i		−	0.0268045i
$334$		0			0
$335$	−1.80632	−	3.12863i	−0.0986896	−	0.170935i
$336$		0			0
$337$	−27.7862			−1.51361			−0.756806	−	0.653639i	$-0.773241\pi$
$337$	−27.7862			−1.51361			−0.756806	+	0.653639i	$0.773241\pi$
$338$		0			0
$339$	4.01633			0.218137
$340$		0			0
$341$	−0.573341	−	0.993055i	−0.0310481	−	0.0537769i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−0.0400130	−	0.0231015i	−0.00215423	−	0.00124375i
$346$		0			0
$347$	−7.66358	+	13.2737i	−0.411402	+	0.712570i	−0.995043	−	0.0994420i	$-0.968294\pi$
$347$	−7.66358	+	13.2737i	−0.411402	+	0.712570i	0.583641	+	0.812012i	$0.301628\pi$
$348$		0			0
$349$	−12.5885	+	7.26799i	−0.673849	+	0.389047i	−0.797533	−	0.603275i	$-0.793862\pi$
$349$	−12.5885	+	7.26799i	−0.673849	+	0.389047i	0.123685	+	0.992322i	$0.460529\pi$
$350$		0			0
$351$	1.56013	−	9.23562i	0.0832737	−	0.492961i
$352$		0			0
$353$	−5.27079	+	3.04309i	−0.280536	+	0.161967i	−0.633666	−	0.773607i	$-0.718451\pi$
$353$	−5.27079	+	3.04309i	−0.280536	+	0.161967i	0.353130	+	0.935574i	$0.385117\pi$
$354$		0			0
$355$	2.91272	−	5.04499i	0.154591	−	0.267760i
$356$		0			0
$357$	−2.58194	−	1.49069i	−0.136651	−	0.0788954i
$358$		0			0
$359$			1.05654i			0.0557621i	0.999611	+	0.0278811i	$0.00887597\pi$
$359$			1.05654i			0.0557621i	−0.999611	+	0.0278811i	$0.991124\pi$
$360$		0			0
$361$	9.89137	+	17.1324i	0.520599	+	0.901703i
$362$		0			0
$363$	4.26786			0.224005
$364$		0			0
$365$	−1.33745			−0.0700055
$366$		0			0
$367$	−0.958906	−	1.66087i	−0.0500545	−	0.0866969i	0.839913	−	0.542722i	$-0.182606\pi$
$367$	−0.958906	−	1.66087i	−0.0500545	−	0.0866969i	−0.889967	+	0.456025i	$0.849273\pi$
$368$		0			0
$369$		−	17.6294i		−	0.917751i
$370$		0			0
$371$	8.07992	+	4.66494i	0.419489	+	0.242192i
$372$		0			0
$373$	−3.20525	+	5.55165i	−0.165962	+	0.287454i	−0.936996	−	0.349339i	$-0.886406\pi$
$373$	−3.20525	+	5.55165i	−0.165962	+	0.287454i	0.771035	+	0.636793i	$0.219739\pi$
$374$		0			0
$375$	1.93952	−	1.11978i	0.100157	−	0.0578254i
$376$		0			0
$377$	6.11332	−	2.27496i	0.314852	−	0.117166i
$378$		0			0
$379$	17.6014	−	10.1622i	0.904123	−	0.521996i	0.0255874	−	0.999673i	$-0.491854\pi$
$379$	17.6014	−	10.1622i	0.904123	−	0.521996i	0.878536	+	0.477677i	$0.158521\pi$
$380$		0			0
$381$	3.50440	−	6.06980i	0.179536	−	0.310965i
$382$		0			0
$383$	8.52361	+	4.92111i	0.435536	+	0.251457i	0.701702	−	0.712470i	$-0.252424\pi$
$383$	8.52361	+	4.92111i	0.435536	+	0.251457i	−0.266166	+	0.963927i	$0.585757\pi$
$384$		0			0
$385$		−	0.623091i		−	0.0317556i
$386$		0			0
$387$	−3.18454	−	5.51578i	−0.161879	−	0.280383i
$388$		0			0
$389$	18.6688			0.946546			0.473273	−	0.880916i	$-0.343072\pi$
$389$	18.6688			0.946546			0.473273	+	0.880916i	$0.343072\pi$
$390$		0			0
$391$	−1.33688			−0.0676089
$392$		0			0
$393$	0.0988910	+	0.171284i	0.00498839	+	0.00864014i
$394$		0			0
$395$		−	5.68555i		−	0.286071i
$396$		0			0
$397$	22.7952	+	13.1608i	1.14406	+	0.660521i	0.947432	−	0.319958i	$-0.103669\pi$
$397$	22.7952	+	13.1608i	1.14406	+	0.660521i	0.196625	+	0.980479i	$0.437002\pi$
$398$		0			0
$399$	1.39481	−	2.41588i	0.0698277	−	0.120945i
$400$		0			0
$401$	18.1917	−	10.5030i	0.908450	−	0.524494i	0.0285176	−	0.999593i	$-0.490921\pi$
$401$	18.1917	−	10.5030i	0.908450	−	0.524494i	0.879932	+	0.475100i	$0.157588\pi$
$402$		0			0
$403$	−3.35968	−	0.567537i	−0.167358	−	0.0282710i
$404$		0			0
$405$	3.21719	−	1.85744i	0.159863	−	0.0922971i
$406$		0			0
$407$	−0.106011	+	0.183616i	−0.00525475	+	0.00910149i
$408$		0			0
$409$	−17.7218	−	10.2317i	−0.876289	−	0.505926i	−0.00685600	−	0.999976i	$-0.502182\pi$
$409$	−17.7218	−	10.2317i	−0.876289	−	0.505926i	−0.869433	+	0.494051i	$0.835516\pi$
$410$		0			0
$411$			1.67483i			0.0826131i
$412$		0			0
$413$	7.39117	+	12.8019i	0.363696	+	0.629940i
$414$		0			0
$415$	0.444836			0.0218361
$416$		0			0
$417$	6.25929			0.306519
$418$		0			0
$419$	−14.1991	−	24.5935i	−0.693669	−	1.20147i	−0.970627	−	0.240588i	$-0.922660\pi$
$419$	−14.1991	−	24.5935i	−0.693669	−	1.20147i	0.276958	−	0.960882i	$-0.410674\pi$
$420$		0			0
$421$			25.0074i			1.21879i	0.792868	+	0.609393i	$0.208587\pi$
$421$			25.0074i			1.21879i	−0.792868	+	0.609393i	$0.791413\pi$
$422$		0			0
$423$	8.20352	+	4.73630i	0.398869	+	0.230287i
$424$		0			0
$425$	15.7616	−	27.3000i	0.764552	−	1.32424i
$426$		0			0
$427$	7.72665	−	4.46098i	0.373919	−	0.215882i
$428$		0			0
$429$	−1.24889	+	1.51028i	−0.0602969	+	0.0729169i
$430$		0			0
$431$	12.1959	−	7.04133i	0.587458	−	0.339169i	−0.176634	−	0.984277i	$-0.556521\pi$
$431$	12.1959	−	7.04133i	0.587458	−	0.339169i	0.764092	+	0.645108i	$0.223187\pi$
$432$		0			0
$433$	−8.66959	+	15.0162i	−0.416634	+	0.721631i	−0.995598	−	0.0937214i	$-0.970124\pi$
$433$	−8.66959	+	15.0162i	−0.416634	+	0.721631i	0.578964	+	0.815353i	$0.303457\pi$
$434$		0			0
$435$	−0.360387	−	0.208070i	−0.0172792	−	0.00997617i
$436$		0			0
$437$		−	1.25089i		−	0.0598383i
$438$		0			0
$439$	−3.48416	−	6.03474i	−0.166290	−	0.288023i	0.770823	−	0.637050i	$-0.219845\pi$
$439$	−3.48416	−	6.03474i	−0.166290	−	0.288023i	−0.937113	+	0.349027i	$0.886512\pi$
$440$		0			0
$441$	2.79934			0.133302
$442$		0			0
$443$	−15.4247			−0.732851			−0.366425	−	0.930447i	$-0.619419\pi$
$443$	−15.4247			−0.732851			−0.366425	+	0.930447i	$0.619419\pi$
$444$		0			0
$445$	1.97857	+	3.42698i	0.0937932	+	0.162455i
$446$		0			0
$447$			7.99874i			0.378327i
$448$		0			0
$449$	20.8297	+	12.0260i	0.983015	+	0.567544i	0.903179	−	0.429264i	$-0.141227\pi$
$449$	20.8297	+	12.0260i	0.983015	+	0.567544i	0.0798362	+	0.996808i	$0.474560\pi$
$450$		0			0
$451$	−3.82083	+	6.61787i	−0.179916	+	0.311623i
$452$		0			0
$453$	5.70388	−	3.29314i	0.267992	−	0.154725i
$454$		0			0
$455$	−1.42682	−	1.17988i	−0.0668906	−	0.0553135i
$456$		0			0
$457$	0.836738	−	0.483091i	0.0391410	−	0.0225980i	−0.480302	−	0.877103i	$-0.659473\pi$
$457$	0.836738	−	0.483091i	0.0391410	−	0.0225980i	0.519443	+	0.854505i	$0.326140\pi$
$458$		0			0
$459$	−8.64500	+	14.9736i	−0.403514	+	0.698907i
$460$		0			0
$461$	−18.5401	−	10.7041i	−0.863497	−	0.498540i	0.00168489	−	0.999999i	$-0.499464\pi$
$461$	−18.5401	−	10.7041i	−0.863497	−	0.498540i	−0.865182	+	0.501458i	$0.832797\pi$
$462$		0			0
$463$			31.8588i			1.48060i	0.672275	+	0.740301i	$0.265317\pi$
$463$			31.8588i			1.48060i	−0.672275	+	0.740301i	$0.734683\pi$
$464$		0			0
$465$	0.108687	+	0.188251i	0.00504022	+	0.00872992i
$466$		0			0
$467$	−34.3765			−1.59075			−0.795376	−	0.606116i	$-0.792727\pi$
$467$	−34.3765			−1.59075			−0.795376	+	0.606116i	$0.792727\pi$
$468$		0			0
$469$	−7.03524			−0.324857
$470$		0			0
$471$	0.642897	+	1.11353i	0.0296231	+	0.0513088i
$472$		0			0
$473$			2.76075i			0.126939i
$474$		0			0
$475$	25.5441	+	14.7479i	1.17204	+	0.676679i
$476$		0			0
$477$	13.0588	−	22.6185i	0.597921	−	1.03563i
$478$		0			0
$479$	20.7680	−	11.9904i	0.948916	−	0.547857i	0.0561718	−	0.998421i	$-0.482111\pi$
$479$	20.7680	−	11.9904i	0.948916	−	0.547857i	0.892744	+	0.450564i	$0.148777\pi$
$480$		0			0
$481$	0.219724	+	0.590448i	0.0100185	+	0.0269221i
$482$		0			0
$483$	−0.0779214	+	0.0449879i	−0.00354554	+	0.00204702i
$484$		0			0
$485$	3.95759	−	6.85475i	0.179705	−	0.311258i
$486$		0			0
$487$	−19.7517	−	11.4037i	−0.895037	−	0.516750i	−0.0194500	−	0.999811i	$-0.506192\pi$
$487$	−19.7517	−	11.4037i	−0.895037	−	0.516750i	−0.875587	+	0.483061i	$0.839525\pi$
$488$		0			0
$489$			8.70809i			0.393794i
$490$		0			0
$491$	−6.44981	−	11.1714i	−0.291076	−	0.504158i	0.682989	−	0.730429i	$-0.260680\pi$
$491$	−6.44981	−	11.1714i	−0.291076	−	0.504158i	−0.974064	+	0.226271i	$0.927347\pi$
$492$		0			0
$493$	−12.0409			−0.542296
$494$		0			0
$495$	−1.74425			−0.0783980
$496$		0			0
$497$	−5.67224	−	9.82460i	−0.254435	−	0.440694i
$498$		0			0
$499$		−	43.2772i		−	1.93735i	−0.248326	−	0.968677i	$-0.579880\pi$
$499$		−	43.2772i		−	1.93735i	0.248326	−	0.968677i	$-0.420120\pi$
$500$		0			0
$501$	2.38922	+	1.37942i	0.106743	+	0.0616279i
$502$		0			0
$503$	−4.29338	+	7.43636i	−0.191433	+	0.331571i	−0.945725	−	0.324967i	$-0.894647\pi$
$503$	−4.29338	+	7.43636i	−0.191433	+	0.331571i	0.754293	+	0.656538i	$0.227980\pi$
$504$		0			0
$505$	−3.03991	+	1.75509i	−0.135274	+	0.0781005i
$506$		0			0
$507$	1.09353	+	5.71969i	0.0485653	+	0.254020i
$508$		0			0
$509$	−0.925062	+	0.534085i	−0.0410026	+	0.0236729i	−0.520361	−	0.853946i	$-0.674203\pi$
$509$	−0.925062	+	0.534085i	−0.0410026	+	0.0236729i	0.479359	+	0.877619i	$0.340869\pi$
$510$		0			0
$511$	−1.30228	+	2.25561i	−0.0576094	+	0.0997824i
$512$		0			0
$513$	−14.0105	−	8.08897i	−0.618579	−	0.357137i
$514$		0			0
$515$		−	3.51143i		−	0.154732i
$516$		0			0
$517$	−2.05300	−	3.55590i	−0.0902909	−	0.156389i
$518$		0			0
$519$	−1.79390			−0.0787435
$520$		0			0
$521$	1.01764			0.0445834			0.0222917	−	0.999752i	$-0.492904\pi$
$521$	1.01764			0.0445834			0.0222917	+	0.999752i	$0.492904\pi$
$522$		0			0
$523$	9.79632	+	16.9677i	0.428363	+	0.741947i	0.996728	−	0.0808300i	$-0.0257571\pi$
$523$	9.79632	+	16.9677i	0.428363	+	0.741947i	−0.568365	+	0.822777i	$0.692424\pi$
$524$		0			0
$525$		−	2.12161i		−	0.0925946i
$526$		0			0
$527$	5.44701	+	3.14483i	0.237275	+	0.136991i
$528$		0			0
$529$	11.4798	−	19.8836i	0.499123	−	0.864506i
$530$		0			0
$531$	35.8369	−	20.6904i	1.55519	−	0.897889i
$532$		0			0
$533$	7.91928	+	21.2809i	0.343022	+	0.921779i
$534$		0			0
$535$	6.03105	−	3.48203i	0.260745	−	0.150541i
$536$		0			0
$537$	−0.476205	+	0.824812i	−0.0205498	+	0.0355933i
$538$		0			0
$539$	−1.05084	−	0.606703i	−0.0452629	−	0.0261326i
$540$		0			0
$541$		−	5.02635i		−	0.216100i	−0.994145	−	0.108050i	$-0.965539\pi$
$541$		−	5.02635i		−	0.216100i	0.994145	−	0.108050i	$-0.0344606\pi$
$542$		0			0
$543$	3.90636	+	6.76601i	0.167638	+	0.290357i
$544$		0			0
$545$	−4.47110			−0.191521
$546$		0			0
$547$	−34.2286			−1.46351			−0.731755	−	0.681568i	$-0.761298\pi$
$547$	−34.2286			−1.46351			−0.731755	+	0.681568i	$0.761298\pi$
$548$		0			0
$549$	−12.4878	−	21.6296i	−0.532967	−	0.923127i
$550$		0			0
$551$		−	11.2665i		−	0.479968i
$552$		0			0
$553$	−9.58866	−	5.53601i	−0.407751	−	0.235415i
$554$		0			0
$555$	0.0200962	−	0.0348076i	0.000853034	−	0.00147750i
$556$		0			0
$557$	−23.1413	+	13.3606i	−0.980527	+	0.566108i	−0.902429	−	0.430838i	$-0.858218\pi$
$557$	−23.1413	+	13.3606i	−0.980527	+	0.566108i	−0.0780978	+	0.996946i	$0.524885\pi$
$558$		0			0
$559$	6.32187	+	5.22772i	0.267387	+	0.221109i
$560$		0			0
$561$	3.13295	−	1.80881i	0.132273	−	0.0763679i
$562$		0			0
$563$	−9.19952	+	15.9340i	−0.387713	+	0.671539i	−0.992142	−	0.125120i	$-0.960068\pi$
$563$	−9.19952	+	15.9340i	−0.387713	+	0.671539i	0.604428	+	0.796660i	$0.293402\pi$
$564$		0			0
$565$	−3.98731	−	2.30208i	−0.167747	−	0.0968491i
$566$		0			0
$567$		−	7.23437i		−	0.303815i
$568$		0			0
$569$	14.8539	+	25.7278i	0.622710	+	1.07857i	0.988979	+	0.148056i	$0.0473016\pi$
$569$	14.8539	+	25.7278i	0.622710	+	1.07857i	−0.366269	+	0.930509i	$0.619365\pi$
$570$		0			0
$571$	24.0391			1.00600			0.503002	−	0.864285i	$-0.332229\pi$
$571$	24.0391			1.00600			0.503002	+	0.864285i	$0.332229\pi$
$572$		0			0
$573$	−0.302408			−0.0126333
$574$		0			0
$575$	−0.475676	−	0.823895i	−0.0198371	−	0.0343588i
$576$		0			0
$577$			19.4579i			0.810041i	0.914308	+	0.405021i	$0.132736\pi$
$577$			19.4579i			0.810041i	−0.914308	+	0.405021i	$0.867264\pi$
$578$		0			0
$579$	−8.73225	−	5.04156i	−0.362900	−	0.209520i
$580$		0			0
$581$	0.433136	−	0.750214i	0.0179695	−	0.0311241i
$582$		0			0
$583$	−9.80423	+	5.66047i	−0.406050	+	0.234433i
$584$		0			0
$585$	−3.30289	+	3.99418i	−0.136558	+	0.165139i
$586$		0			0
$587$	−7.96443	+	4.59827i	−0.328727	+	0.189791i	−0.655276	−	0.755390i	$-0.727448\pi$
$587$	−7.96443	+	4.59827i	−0.328727	+	0.189791i	0.326549	+	0.945180i	$0.394114\pi$
$588$		0			0
$589$	−2.94256	+	5.09667i	−0.121246	+	0.210004i
$590$		0			0
$591$	9.94521	+	5.74187i	0.409091	+	0.236189i
$592$		0			0
$593$			9.79698i			0.402314i	0.979559	+	0.201157i	$0.0644701\pi$
$593$			9.79698i			0.402314i	−0.979559	+	0.201157i	$0.935530\pi$
$594$		0			0
$595$	1.70886	+	2.95983i	0.0700564	+	0.121341i
$596$		0			0
$597$	0.307996			0.0126054
$598$		0			0
$599$	−45.6442			−1.86497			−0.932487	−	0.361205i	$-0.882366\pi$
$599$	−45.6442			−1.86497			−0.932487	+	0.361205i	$0.882366\pi$
$600$		0			0
$601$	−9.93424	−	17.2066i	−0.405226	−	0.701872i	0.589122	−	0.808044i	$-0.299474\pi$
$601$	−9.93424	−	17.2066i	−0.405226	−	0.701872i	−0.994348	+	0.106172i	$0.966141\pi$
$602$		0			0
$603$			19.6941i			0.802004i
$604$		0			0
$605$	−4.23703	−	2.44625i	−0.172260	−	0.0994541i
$606$		0			0
$607$	−15.5948	+	27.0110i	−0.632974	+	1.09634i	0.353967	+	0.935258i	$0.384833\pi$
$607$	−15.5948	+	27.0110i	−0.632974	+	1.09634i	−0.986941	+	0.161085i	$0.948501\pi$
$608$		0			0
$609$	−0.701818	+	0.405195i	−0.0284391	+	0.0164193i
$610$		0			0
$611$	−12.0303	−	2.03222i	−0.486692	−	0.0822148i
$612$		0			0
$613$	24.6358	−	14.2235i	0.995031	−	0.574481i	0.0882564	−	0.996098i	$-0.471871\pi$
$613$	24.6358	−	14.2235i	0.995031	−	0.574481i	0.906774	+	0.421617i	$0.138537\pi$
$614$		0			0
$615$	0.724305	−	1.25453i	0.0292068	−	0.0505877i
$616$		0			0
$617$	−4.12564	−	2.38194i	−0.166092	−	0.0958932i	0.414650	−	0.909981i	$-0.363904\pi$
$617$	−4.12564	−	2.38194i	−0.166092	−	0.0958932i	−0.580742	+	0.814088i	$0.697237\pi$
$618$		0			0
$619$			38.6156i			1.55209i	0.630676	+	0.776046i	$0.282778\pi$
$619$			38.6156i			1.55209i	−0.630676	+	0.776046i	$0.717222\pi$
$620$		0			0
$621$	0.260900	+	0.451893i	0.0104696	+	0.0181338i
$622$		0			0
$623$	7.70613			0.308739
$624$		0			0
$625$	21.1142			0.844569
$626$		0			0
$627$	1.69247	+	2.93144i	0.0675907	+	0.117070i
$628$		0			0
$629$		−	1.16296i		−	0.0463702i
$630$		0			0
$631$	−9.05840	−	5.22987i	−0.360609	−	0.208198i	0.308739	−	0.951147i	$-0.400093\pi$
$631$	−9.05840	−	5.22987i	−0.360609	−	0.208198i	−0.669348	+	0.742949i	$0.733426\pi$
$632$		0			0
$633$	0.434629	−	0.752799i	0.0172749	−	0.0299211i
$634$		0			0
$635$	−6.95816	+	4.01729i	−0.276126	+	0.159421i
$636$		0			0
$637$	−3.37916	+	1.25749i	−0.133887	+	0.0498236i
$638$		0			0
$639$	−27.5025	+	15.8785i	−1.08798	+	0.628146i
$640$		0			0
$641$	4.56383	−	7.90479i	0.180261	−	0.312220i	−0.761709	−	0.647920i	$-0.775639\pi$
$641$	4.56383	−	7.90479i	0.180261	−	0.312220i	0.941969	+	0.335699i	$0.108973\pi$
$642$		0			0
$643$	−2.15211	−	1.24252i	−0.0848709	−	0.0490002i	0.456964	−	0.889485i	$-0.348937\pi$
$643$	−2.15211	−	1.24252i	−0.0848709	−	0.0490002i	−0.541835	+	0.840485i	$0.682270\pi$
$644$		0			0
$645$		−	0.523347i		−	0.0206068i
$646$		0			0
$647$	−20.7448	−	35.9310i	−0.815561	−	1.41259i	−0.908924	−	0.416962i	$-0.863095\pi$
$647$	−20.7448	−	35.9310i	−0.815561	−	1.41259i	0.0933626	−	0.995632i	$-0.470238\pi$
$648$		0			0
$649$	−17.9370			−0.704089
$650$		0			0
$651$	0.423313			0.0165909
$652$		0			0
$653$	6.58656	+	11.4083i	0.257752	+	0.446440i	0.965639	−	0.259886i	$-0.0836849\pi$
$653$	6.58656	+	11.4083i	0.257752	+	0.446440i	−0.707887	+	0.706325i	$0.750352\pi$
$654$		0			0
$655$		−	0.226729i		−	0.00885903i
$656$		0			0
$657$	6.31423	+	3.64552i	0.246342	+	0.142225i
$658$		0			0
$659$	−0.306784	+	0.531366i	−0.0119506	+	0.0206991i	−0.871939	−	0.489615i	$-0.837137\pi$
$659$	−0.306784	+	0.531366i	−0.0119506	+	0.0206991i	0.859988	+	0.510314i	$0.170471\pi$
$660$		0			0
$661$	8.42874	−	4.86634i	0.327840	−	0.189279i	−0.327042	−	0.945010i	$-0.606052\pi$
$661$	8.42874	−	4.86634i	0.327840	−	0.189279i	0.654882	+	0.755731i	$0.272718\pi$
$662$		0			0
$663$	1.79050	−	10.5993i	0.0695372	−	0.411643i
$664$		0			0
$665$	−2.76946	+	1.59895i	−0.107395	+	0.0620045i
$666$		0			0
$667$	−0.181694	+	0.314703i	−0.00703520	+	0.0121853i
$668$		0			0
$669$	−5.20549	−	3.00539i	−0.201256	−	0.116195i
$670$		0			0
$671$			10.8260i			0.417932i
$672$		0			0
$673$	−7.42529	−	12.8610i	−0.286224	−	0.495754i	0.686681	−	0.726958i	$-0.259067\pi$
$673$	−7.42529	−	12.8610i	−0.286224	−	0.495754i	−0.972905	+	0.231204i	$0.925733\pi$
$674$		0			0
$675$	−12.3039			−0.473579
$676$		0			0
$677$	−20.3971			−0.783925			−0.391962	−	0.919981i	$-0.628204\pi$
$677$	−20.3971			−0.783925			−0.391962	+	0.919981i	$0.628204\pi$
$678$		0			0
$679$	−7.70701	−	13.3489i	−0.295768	−	0.512285i
$680$		0			0
$681$			2.24267i			0.0859395i
$682$		0			0
$683$	−13.7360	−	7.93047i	−0.525593	−	0.303451i	0.213627	−	0.976915i	$-0.431472\pi$
$683$	−13.7360	−	7.93047i	−0.525593	−	0.303451i	−0.739220	+	0.673464i	$0.764806\pi$
$684$		0			0
$685$	0.959975	−	1.66273i	0.0366788	−	0.0635295i
$686$		0			0
$687$	9.28018	−	5.35792i	0.354061	−	0.204417i
$688$		0			0
$689$	−5.60317	+	33.1695i	−0.213464	+	1.26366i
$690$		0			0
$691$	−29.6870	+	17.1398i	−1.12935	+	0.652029i	−0.943771	−	0.330601i	$-0.892749\pi$
$691$	−29.6870	+	17.1398i	−1.12935	+	0.652029i	−0.185577	+	0.982630i	$0.559415\pi$
$692$		0			0
$693$	−1.69837	+	2.94167i	−0.0645158	+	0.111745i
$694$		0			0
$695$	−6.21407	−	3.58769i	−0.235713	−	0.136089i
$696$		0			0
$697$		−	41.9153i		−	1.58766i
$698$		0			0
$699$	4.10827	+	7.11573i	0.155389	+	0.269141i
$700$		0			0
$701$	−2.97957			−0.112537			−0.0562685	−	0.998416i	$-0.517920\pi$
$701$	−2.97957			−0.112537			−0.0562685	+	0.998416i	$0.517920\pi$
$702$		0			0
$703$	1.08816			0.0410407
$704$		0			0
$705$	0.389182	+	0.674084i	0.0146575	+	0.0253875i
$706$		0			0
$707$			6.83572i			0.257084i
$708$		0			0
$709$	13.9577	+	8.05850i	0.524194	+	0.302643i	0.738649	−	0.674091i	$-0.235464\pi$
$709$	13.9577	+	8.05850i	0.524194	+	0.302643i	−0.214455	+	0.976734i	$0.568798\pi$
$710$		0			0
$711$	−15.4972	+	26.8420i	−0.581191	+	1.00665i
$712$		0			0
$713$	0.164387	−	0.0949090i	0.00615635	−	0.00355437i
$714$		0			0
$715$	2.10552	−	0.783530i	0.0787421	−	0.0293024i
$716$		0			0
$717$	−6.20331	+	3.58149i	−0.231667	+	0.133753i
$718$		0			0
$719$	9.10556	−	15.7713i	0.339580	−	0.588170i	−0.644774	−	0.764374i	$-0.723048\pi$
$719$	9.10556	−	15.7713i	0.339580	−	0.588170i	0.984354	+	0.176203i	$0.0563817\pi$
$720$		0			0
$721$	−5.92201	−	3.41908i	−0.220547	−	0.127333i
$722$		0			0
$723$		−	4.18595i		−	0.155677i
$724$		0			0
$725$	−4.28429	−	7.42061i	−0.159115	−	0.275595i
$726$		0			0
$727$	−20.9527			−0.777094			−0.388547	−	0.921429i	$-0.627023\pi$
$727$	−20.9527			−0.777094			−0.388547	+	0.921429i	$0.627023\pi$
$728$		0			0
$729$	−16.7605			−0.620759
$730$		0			0
$731$	−7.57149	−	13.1142i	−0.280042	−	0.485046i
$732$		0			0
$733$		−	33.6472i		−	1.24279i	−0.783498	−	0.621394i	$-0.786566\pi$
$733$		−	33.6472i		−	1.24279i	0.783498	−	0.621394i	$-0.213434\pi$
$734$		0			0
$735$	0.199205	+	0.115011i	0.00734779	+	0.00424225i
$736$		0			0
$737$	4.26830	−	7.39292i	0.157225	−	0.272322i
$738$		0			0
$739$	−27.5487	+	15.9053i	−1.01340	+	0.585085i	−0.912184	−	0.409780i	$-0.865606\pi$
$739$	−27.5487	+	15.9053i	−1.01340	+	0.585085i	−0.101212	+	0.994865i	$0.532272\pi$
$740$		0			0
$741$	9.91759	+	1.67534i	0.364332	+	0.0615450i
$742$		0			0
$743$	3.98668	−	2.30171i	0.146257	−	0.0844417i	−0.425086	−	0.905153i	$-0.639756\pi$
$743$	3.98668	−	2.30171i	0.146257	−	0.0844417i	0.571343	+	0.820712i	$0.306423\pi$
$744$		0			0
$745$	4.58471	−	7.94094i	0.167971	−	0.290934i
$746$		0			0
$747$	−2.10011	−	1.21250i	−0.0768390	−	0.0443630i
$748$		0			0
$749$		−	13.5618i		−	0.495538i
$750$		0			0
$751$	18.6203	+	32.2513i	0.679465	+	1.17687i	0.975142	+	0.221580i	$0.0711214\pi$
$751$	18.6203	+	32.2513i	0.679465	+	1.17687i	−0.295677	+	0.955288i	$0.595545\pi$
$752$		0			0
$753$	−13.4159			−0.488904
$754$		0			0
$755$	−7.55023			−0.274781
$756$		0			0
$757$	−11.3213	−	19.6092i	−0.411481	−	0.712707i	0.583571	−	0.812062i	$-0.301655\pi$
$757$	−11.3213	−	19.6092i	−0.411481	−	0.712707i	−0.995052	+	0.0993557i	$0.968322\pi$
$758$		0			0
$759$		−	0.109177i		−	0.00396288i
$760$		0			0
$761$	34.2062	+	19.7489i	1.23997	+	0.715899i	0.969089	−	0.246713i	$-0.0793506\pi$
$761$	34.2062	+	19.7489i	1.23997	+	0.715899i	0.270884	+	0.962612i	$0.412684\pi$
$762$		0			0
$763$	−4.35351	+	7.54050i	−0.157608	+	0.272984i
$764$		0			0
$765$	8.28558	−	4.78368i	0.299566	−	0.172954i
$766$		0			0
$767$	−33.9653	+	41.0742i	−1.22642	+	1.48310i
$768$		0			0
$769$	−39.8354	+	22.9990i	−1.43650	+	0.829363i	−0.997605	−	0.0691750i	$-0.977963\pi$
$769$	−39.8354	+	22.9990i	−1.43650	+	0.829363i	−0.438895	+	0.898538i	$0.644630\pi$
$770$		0			0
$771$	3.69097	−	6.39296i	0.132927	−	0.230237i
$772$		0			0
$773$	−20.1887	−	11.6559i	−0.726136	−	0.419235i	0.0908712	−	0.995863i	$-0.471035\pi$
$773$	−20.1887	−	11.6559i	−0.726136	−	0.419235i	−0.817007	+	0.576628i	$0.804368\pi$
$774$		0			0
$775$			4.47586i			0.160778i
$776$		0			0
$777$	−0.0391352	−	0.0677842i	−0.00140397	−	0.00243174i
$778$		0			0
$779$	39.2194			1.40518
$780$		0			0
$781$	13.7655			0.492567
$782$		0			0
$783$	2.34986	+	4.07008i	0.0839773	+	0.145453i
$784$		0			0
$785$		−	1.47398i		−	0.0526086i
$786$		0			0
$787$	−26.1282	−	15.0851i	−0.931370	−	0.537727i	−0.0441253	−	0.999026i	$-0.514050\pi$
$787$	−26.1282	−	15.0851i	−0.931370	−	0.537727i	−0.887245	+	0.461299i	$0.847383\pi$
$788$		0			0
$789$	−6.37565	+	11.0430i	−0.226979	+	0.393139i
$790$		0			0
$791$	−7.76489	+	4.48306i	−0.276088	+	0.159399i
$792$		0			0
$793$	24.7905	+	20.4999i	0.880338	+	0.727974i
$794$		0			0
$795$	1.85856	−	1.07304i	0.0659164	−	0.0380569i
$796$		0			0
$797$	3.50723	−	6.07471i	0.124233	−	0.215177i	−0.797200	−	0.603715i	$-0.793686\pi$
$797$	3.50723	−	6.07471i	0.124233	−	0.215177i	0.921433	+	0.388538i	$0.127020\pi$
$798$		0			0
$799$	19.5045	+	11.2609i	0.690020	+	0.398383i
$800$		0			0
$801$		−	21.5721i		−	0.762213i
$802$		0			0
$803$	−1.58019	−	2.73697i	−0.0557638	−	0.0965857i
$804$		0			0
$805$	0.103144			0.00363536
$806$		0			0
$807$	2.14808			0.0756161
$808$		0			0
$809$	21.8194	+	37.7924i	0.767131	+	1.32871i	0.939113	+	0.343609i	$0.111650\pi$
$809$	21.8194	+	37.7924i	0.767131	+	1.32871i	−0.171982	+	0.985100i	$0.555017\pi$
$810$		0			0
$811$		−	6.77674i		−	0.237964i	−0.992896	−	0.118982i	$-0.962037\pi$
$811$		−	6.77674i		−	0.237964i	0.992896	−	0.118982i	$-0.0379630\pi$
$812$		0			0
$813$	−10.3137	−	5.95461i	−0.361717	−	0.208837i
$814$		0			0
$815$	4.99129	−	8.64517i	0.174837	−	0.302827i
$816$		0			0
$817$	12.2707	−	7.08450i	0.429298	−	0.247855i
$818$		0			0
$819$	3.52015	+	9.45943i	0.123004	+	0.330539i
$820$		0			0
$821$	29.9561	−	17.2951i	1.04547	−	0.603605i	0.124095	−	0.992270i	$-0.460397\pi$
$821$	29.9561	−	17.2951i	1.04547	−	0.603605i	0.921379	+	0.388666i	$0.127064\pi$
$822$		0			0
$823$	22.8633	−	39.6004i	0.796965	−	1.38038i	−0.124618	−	0.992205i	$-0.539771\pi$
$823$	22.8633	−	39.6004i	0.796965	−	1.38038i	0.921584	−	0.388180i	$-0.126896\pi$
$824$		0			0
$825$	2.22947	+	1.28719i	0.0776203	+	0.0448141i
$826$		0			0
$827$			19.0625i			0.662869i	0.943478	+	0.331434i	$0.107533\pi$
$827$			19.0625i			0.662869i	−0.943478	+	0.331434i	$0.892467\pi$
$828$		0			0
$829$	−8.56856	−	14.8412i	−0.297598	−	0.515455i	0.677988	−	0.735073i	$-0.262852\pi$
$829$	−8.56856	−	14.8412i	−0.297598	−	0.515455i	−0.975586	+	0.219618i	$0.929519\pi$
$830$		0			0
$831$	−10.3420			−0.358761
$832$		0			0
$833$	6.65566			0.230605
$834$		0			0
$835$	−1.58131	−	2.73891i	−0.0547234	−	0.0947837i
$836$		0			0
$837$		−	2.45494i		−	0.0848550i
$838$		0			0
$839$	−4.60791	−	2.66038i	−0.159083	−	0.0918464i	0.418345	−	0.908288i	$-0.362610\pi$
$839$	−4.60791	−	2.66038i	−0.159083	−	0.0918464i	−0.577428	+	0.816442i	$0.695944\pi$
$840$		0			0
$841$	12.8635	−	22.2803i	0.443570	−	0.768286i
$842$		0			0
$843$	−6.10430	+	3.52432i	−0.210243	+	0.121384i
$844$		0			0
$845$	2.19278	−	6.30515i	0.0754339	−	0.216904i
$846$		0			0
$847$	−8.25118	+	4.76382i	−0.283514	+	0.163687i
$848$		0			0
$849$	3.23302	−	5.59975i	0.110957	−	0.192183i
$850$		0			0
$851$	−0.0303952	−	0.0175487i	−0.00104193	−	0.000601560i
$852$		0			0
$853$			14.4810i			0.495821i	0.968783	+	0.247910i	$0.0797438\pi$
$853$			14.4810i			0.495821i	−0.968783	+	0.247910i	$0.920256\pi$
$854$		0			0
$855$	4.47601	+	7.75267i	0.153076	+	0.265136i
$856$		0			0
$857$	−15.5998			−0.532878			−0.266439	−	0.963852i	$-0.585847\pi$
$857$	−15.5998			−0.532878			−0.266439	+	0.963852i	$0.585847\pi$
$858$		0			0
$859$	−1.56167			−0.0532835			−0.0266417	−	0.999645i	$-0.508481\pi$
$859$	−1.56167			−0.0532835			−0.0266417	+	0.999645i	$0.508481\pi$
$860$		0			0
$861$	−1.41051	−	2.44308i	−0.0480701	−	0.0832598i
$862$		0			0
$863$			42.2076i			1.43676i	0.695649	+	0.718382i	$0.255117\pi$
$863$			42.2076i			1.43676i	−0.695649	+	0.718382i	$0.744883\pi$
$864$		0			0
$865$	1.78094	+	1.02823i	0.0605537	+	0.0349607i
$866$		0			0
$867$	−6.11396	+	10.5897i	−0.207641	+	0.359645i
$868$		0			0
$869$	11.6349	−	6.71744i	0.394688	−	0.227873i
$870$		0			0
$871$	−8.84674	−	23.7732i	−0.299760	−	0.805524i
$872$		0			0
$873$	−37.3683	+	21.5746i	−1.26472	+	0.730189i
$874$		0			0
$875$	−2.49982	+	4.32982i	−0.0845095	+	0.146375i
$876$		0			0
$877$	−6.91336	−	3.99143i	−0.233448	−	0.134781i	0.378714	−	0.925514i	$-0.376366\pi$
$877$	−6.91336	−	3.99143i	−0.233448	−	0.134781i	−0.612162	+	0.790733i	$0.709700\pi$
$878$		0			0
$879$		−	1.11149i		−	0.0374895i
$880$		0			0
$881$	10.9285	+	18.9288i	0.368192	+	0.637727i	0.989283	−	0.146011i	$-0.0466436\pi$
$881$	10.9285	+	18.9288i	0.368192	+	0.637727i	−0.621091	+	0.783739i	$0.713310\pi$
$882$		0			0
$883$	−23.5213			−0.791555			−0.395778	−	0.918346i	$-0.629525\pi$
$883$	−23.5213			−0.791555			−0.395778	+	0.918346i	$0.629525\pi$
$884$		0			0
$885$	3.40027			0.114299
$886$		0			0
$887$	−7.39357	−	12.8060i	−0.248252	−	0.429985i	0.714789	−	0.699340i	$-0.246523\pi$
$887$	−7.39357	−	12.8060i	−0.248252	−	0.429985i	−0.963041	+	0.269355i	$0.913189\pi$
$888$		0			0
$889$			15.6466i			0.524769i
$890$		0			0
$891$	7.60217	+	4.38911i	0.254682	+	0.147041i
$892$		0			0
$893$	−10.5366	+	18.2500i	−0.352595	+	0.610713i
$894$		0			0
$895$	0.945529	−	0.545902i	0.0316056	−	0.0182475i
$896$		0			0
$897$	−0.250007	−	0.206737i	−0.00834748	−	0.00690274i
$898$		0			0
$899$	1.48059	−	0.854821i	0.0493805	−	0.0285099i
$900$		0			0
$901$	31.0483	−	53.7772i	1.03437	−	1.79158i
$902$		0			0
$903$	−0.882624	−	0.509583i	−0.0293719	−	0.0169579i
$904$		0			0
$905$		−	8.95616i		−	0.297713i
$906$		0			0
$907$	4.26305	+	7.38382i	0.141552	+	0.245176i	0.928081	−	0.372377i	$-0.121457\pi$
$907$	4.26305	+	7.38382i	0.141552	+	0.245176i	−0.786529	+	0.617553i	$0.788124\pi$
$908$		0			0
$909$	19.1356			0.634686
$910$		0			0
$911$	43.5745			1.44369			0.721843	−	0.692057i	$-0.243295\pi$
$911$	43.5745			1.44369			0.721843	+	0.692057i	$0.243295\pi$
$912$		0			0
$913$	0.525571	+	0.910315i	0.0173938	+	0.0301270i
$914$		0			0
$915$		−	2.05225i		−	0.0678453i
$916$		0			0
$917$	−0.382377	−	0.220766i	−0.0126272	−	0.00729033i
$918$		0			0
$919$	−20.1129	+	34.8365i	−0.663462	+	1.14915i	0.316237	+	0.948680i	$0.397580\pi$
$919$	−20.1129	+	34.8365i	−0.663462	+	1.14915i	−0.979700	+	0.200470i	$0.935753\pi$
$920$		0			0
$921$	1.17426	−	0.677960i	0.0386932	−	0.0223395i
$922$		0			0
$923$	26.0661	−	31.5217i	0.857977	−	1.03755i
$924$		0			0
$925$	0.716711	−	0.413793i	0.0235653	−	0.0136054i
$926$		0			0
$927$	−9.57117	+	16.5778i	−0.314359	+	0.544485i
$928$		0			0
$929$	−4.47945	−	2.58621i	−0.146966	−	0.0848508i	0.424714	−	0.905328i	$-0.360375\pi$
$929$	−4.47945	−	2.58621i	−0.146966	−	0.0848508i	−0.571680	+	0.820477i	$0.693708\pi$
$930$		0			0
$931$			6.22758i			0.204101i
$932$		0			0
$933$	−7.57636	−	13.1226i	−0.248039	−	0.429616i
$934$		0			0
$935$	−4.14708			−0.135624
$936$		0			0
$937$	54.0084			1.76438			0.882188	−	0.470897i	$-0.156070\pi$
$937$	54.0084			1.76438			0.882188	+	0.470897i	$0.156070\pi$
$938$		0			0
$939$	0.656023	+	1.13627i	0.0214085	+	0.0370806i
$940$		0			0
$941$			6.99115i			0.227905i	0.993486	+	0.113953i	$0.0363512\pi$
$941$			6.99115i			0.227905i	−0.993486	+	0.113953i	$0.963649\pi$
$942$		0			0
$943$	−1.09550	−	0.632488i	−0.0356744	−	0.0205967i
$944$		0			0
$945$	0.666989	−	1.15526i	0.0216972	−	0.0375806i
$946$		0			0
$947$	18.0291	−	10.4091i	0.585867	−	0.338250i	−0.177595	−	0.984104i	$-0.556832\pi$
$947$	18.0291	−	10.4091i	0.585867	−	0.338250i	0.763462	+	0.645853i	$0.223498\pi$
$948$		0			0
$949$	−9.25967	−	1.56420i	−0.300582	−	0.0507760i
$950$		0			0
$951$	5.47413	−	3.16049i	0.177511	−	0.102486i
$952$		0			0
$953$	−8.03096	+	13.9100i	−0.260148	+	0.450590i	−0.966281	−	0.257489i	$-0.917105\pi$
$953$	−8.03096	+	13.9100i	−0.260148	+	0.450590i	0.706133	+	0.708079i	$0.250438\pi$
$954$		0			0
$955$	0.300223	+	0.173334i	0.00971500	+	0.00560896i
$956$		0			0
$957$		−	0.983332i		−	0.0317866i
$958$		0			0
$959$	−1.86945	−	3.23799i	−0.0603678	−	0.104560i
$960$		0			0
$961$	30.1070			0.971192
$962$		0			0
$963$	−37.9642			−1.22338
$964$		0			0
$965$	5.77943	+	10.0103i	0.186047	+	0.322242i
$966$		0			0
$967$			13.7691i			0.442786i	0.975185	+	0.221393i	$0.0710603\pi$
$967$			13.7691i			0.442786i	−0.975185	+	0.221393i	$0.928940\pi$
$968$		0			0
$969$	−16.0793	−	9.28336i	−0.516540	−	0.298225i
$970$		0			0
$971$	−15.6658	+	27.1340i	−0.502740	+	0.870771i	0.497255	+	0.867605i	$0.334341\pi$
$971$	−15.6658	+	27.1340i	−0.502740	+	0.870771i	−0.999995	+	0.00316696i	$0.998992\pi$
$972$		0			0
$973$	−12.1013	+	6.98667i	−0.387949	+	0.223982i
$974$		0			0
$975$	7.16925	−	2.66790i	0.229600	−	0.0854412i
$976$		0			0
$977$	6.84904	−	3.95430i	0.219120	−	0.126509i	−0.386423	−	0.922322i	$-0.626289\pi$
$977$	6.84904	−	3.95430i	0.219120	−	0.126509i	0.605543	+	0.795813i	$0.292956\pi$
$978$		0			0
$979$	−4.67533	+	8.09791i	−0.149424	+	0.258810i
$980$		0			0
$981$	21.1085	+	12.1870i	0.673941	+	0.389100i
$982$		0			0
$983$		−	56.2452i		−	1.79394i	−0.442087	−	0.896972i	$-0.645762\pi$
$983$		−	56.2452i		−	1.79394i	0.442087	−	0.896972i	$-0.354238\pi$
$984$		0			0
$985$	−6.58224	−	11.4008i	−0.209728	−	0.363259i
$986$		0			0
$987$	1.51579			0.0482480
$988$		0			0
$989$	−0.457005			−0.0145319
$990$		0			0
$991$	−24.6073	−	42.6210i	−0.781676	−	1.35390i	−0.930965	−	0.365109i	$-0.881032\pi$
$991$	−24.6073	−	42.6210i	−0.781676	−	1.35390i	0.149289	−	0.988794i	$-0.452301\pi$
$992$		0			0
$993$		−	6.85327i		−	0.217482i
$994$		0			0
$995$	−0.305771	−	0.176537i	−0.00969358	−	0.00559659i
$996$		0			0
$997$	1.36350	−	2.36165i	0.0431824	−	0.0747942i	−0.843626	−	0.536931i	$-0.819584\pi$
$997$	1.36350	−	2.36165i	0.0431824	−	0.0747942i	0.886809	+	0.462137i	$0.152917\pi$
$998$		0			0
$999$	−0.393104	+	0.226959i	−0.0124373	+	0.00718066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.bm.c.673.7	yes	24
4.3	odd	2		1456.2.cc.g.673.6		24
13.2	odd	12		9464.2.a.bm.1.6		12
13.4	even	6	inner	728.2.bm.c.225.7	✓	24
13.11	odd	12		9464.2.a.bl.1.6		12
52.43	odd	6		1456.2.cc.g.225.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.7	✓	24	13.4	even	6	inner
728.2.bm.c.673.7	yes	24	1.1	even	1	trivial
1456.2.cc.g.225.6		24	52.43	odd	6
1456.2.cc.g.673.6		24	4.3	odd	2
9464.2.a.bl.1.6		12	13.11	odd	12
9464.2.a.bm.1.6		12	13.2	odd	12

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.223973 - 0.387932i) q^{3} +0.513505i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.39967 - 2.42430i) q^{9} +(-1.05084 + 0.606703i) q^{11} +(-0.600562 + 3.55518i) q^{13} +(0.199205 - 0.115011i) q^{15} +(3.32783 - 5.76397i) q^{17} +(5.39324 + 3.11379i) q^{19} -0.447945i q^{21} +(-0.100432 - 0.173953i) q^{23} +4.73631 q^{25} -2.59779 q^{27} +(-0.904563 - 1.56675i) q^{29} +0.945010i q^{31} +(0.470719 + 0.271770i) q^{33} +(-0.256753 + 0.444709i) q^{35} +(0.151323 - 0.0873661i) q^{37} +(1.51368 - 0.563287i) q^{39} +(5.45396 - 3.14885i) q^{41} +(1.13760 - 1.97038i) q^{43} +(1.24489 + 0.718739i) q^{45} +3.38387i q^{47} +(0.500000 + 0.866025i) q^{49} -2.98137 q^{51} +9.32989 q^{53} +(-0.311545 - 0.539612i) q^{55} -2.78962i q^{57} +(12.8019 + 7.39117i) q^{59} +(4.46098 - 7.72665i) q^{61} +(2.42430 - 1.39967i) q^{63} +(-1.82561 - 0.308392i) q^{65} +(-6.09270 + 3.51762i) q^{67} +(-0.0449879 + 0.0779214i) q^{69} +(-9.82460 - 5.67224i) q^{71} +2.60456i q^{73} +(-1.06080 - 1.83737i) q^{75} -1.21341 q^{77} -11.0720 q^{79} +(-3.61718 - 6.26515i) q^{81} -0.866273i q^{83} +(2.95983 + 1.70886i) q^{85} +(-0.405195 + 0.701818i) q^{87} +(6.67370 - 3.85306i) q^{89} +(-2.29769 + 2.77860i) q^{91} +(0.366600 - 0.211656i) q^{93} +(-1.59895 + 2.76946i) q^{95} +(-13.3489 - 7.70701i) q^{97} +3.39674i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} - 18 q^{9} + 12 q^{11} + 8 q^{17} - 12 q^{19} + 2 q^{23} - 28 q^{25} - 20 q^{27} + 2 q^{29} - 18 q^{33} - 8 q^{35} + 60 q^{37} + 18 q^{39} - 6 q^{41} + 24 q^{43} - 72 q^{45} + 12 q^{49} - 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 - 18 * q^9 + 12 * q^11 + 8 * q^17 - 12 * q^19 + 2 * q^23 - 28 * q^25 - 20 * q^27 + 2 * q^29 - 18 * q^33 - 8 * q^35 + 60 * q^37 + 18 * q^39 - 6 * q^41 + 24 * q^43 - 72 * q^45 + 12 * q^49 - 72 * q^51 - 48 * q^53 - 44 * q^55 - 12 * q^59 - 30 * q^61 + 12 * q^63 + 10 * q^65 + 78 * q^67 + 36 * q^69 - 36 * q^71 + 22 * q^75 + 4 * q^77 + 20 * q^79 - 40 * q^81 - 6 * q^85 - 20 * q^87 + 108 * q^89 + 6 * q^91 + 30 * q^93 + 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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