LMFDB - Embedded newform 1456.2.cc.g.673.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(225,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, 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("1456.225"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,2,0,0,0,0,0,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.6
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.g.225.6

$q$-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 $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.223973	+	0.387932i	0.129311	+	0.223973i	0.923410	−	0.383816i	$-0.125390\pi$
$3$	0.223973	+	0.387932i	0.129311	+	0.223973i	−0.794099	+	0.607788i	$0.792057\pi$
$4$		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	−0.333143	−	0.942876i	$-0.608109\pi$
$11$	1.05084	−	0.606703i	0.316840	−	0.182928i	0.649983	+	0.759948i	$0.274776\pi$
$12$		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	−0.268754	−	0.963209i	$-0.586612\pi$
$19$	−5.39324	−	3.11379i	−1.23729	−	0.714352i	−0.968540	+	0.248856i	$0.919945\pi$
$20$		0			0
$21$		−	0.447945i		−	0.0977497i
$22$		0			0
$23$	0.100432	+	0.173953i	0.0209415	+	0.0362717i	0.876306	−	0.481755i	$-0.160000\pi$
$23$	0.100432	+	0.173953i	0.0209415	+	0.0362717i	−0.855365	+	0.518026i	$0.826667\pi$
$24$		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	$-0.972954\pi$
$31$		−	0.945010i		−	0.169729i	0.996393	−	0.0848644i	$-0.0270457\pi$
$32$		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	−0.939635	−	0.342178i	$-0.888835\pi$
$43$	−1.13760	+	1.97038i	−0.173483	+	0.300481i	0.766153	+	0.642659i	$0.222169\pi$
$44$		0			0
$45$	1.24489	+	0.718739i	0.185578	+	0.107143i
$46$		0			0
$47$		−	3.38387i		−	0.493588i	−0.969068	−	0.246794i	$-0.920623\pi$
$47$		−	3.38387i		−	0.493588i	0.969068	−	0.246794i	$-0.0793770\pi$
$48$		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	$-0.921075\pi$
$59$	−12.8019	−	7.39117i	−1.66666	−	0.962249i	−0.697246	−	0.716832i	$-0.745592\pi$
$60$		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	−0.0793044	−	0.996850i	$-0.525270\pi$
$67$	6.09270	−	3.51762i	0.744341	−	0.429746i	0.823646	+	0.567105i	$0.191937\pi$
$68$		0			0
$69$	−0.0449879	+	0.0779214i	−0.00541591	+	0.00938063i
$70$		0			0
$71$	9.82460	+	5.67224i	1.16597	+	0.673171i	0.952726	−	0.303829i	$-0.0982653\pi$
$71$	9.82460	+	5.67224i	1.16597	+	0.673171i	0.213239	+	0.977000i	$0.431599\pi$
$72$		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	$-0.285975\pi$
$79$	11.0720			1.24570			0.622850	+	0.782341i	$0.285975\pi$
$80$		0			0
$81$	−3.61718	−	6.26515i	−0.401909	−	0.696127i
$82$		0			0
$83$			0.866273i			0.0950858i	0.998869	+	0.0475429i	$0.0151391\pi$
$83$			0.866273i			0.0950858i	−0.998869	+	0.0475429i	$0.984861\pi$
$84$		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	$-0.390624\pi$
$103$	6.83815			0.673783			0.336892	+	0.941543i	$0.390624\pi$
$104$		0			0
$105$	0.230022			0.0224479
$106$		0			0
$107$	6.78090	+	11.7449i	0.655535	+	1.13542i	0.981759	+	0.190127i	$0.0608900\pi$
$107$	6.78090	+	11.7449i	0.655535	+	1.13542i	−0.326225	+	0.945292i	$0.605777\pi$
$108$		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	$-0.922423\pi$
$127$	−7.82328	−	13.5503i	−0.694204	−	1.20240i	0.276245	−	0.961087i	$-0.410910\pi$
$128$		0			0
$129$	−1.01917			−0.0897326
$130$		0			0
$131$	0.441531			0.0385768			0.0192884	−	0.999814i	$-0.493860\pi$
$131$	0.441531			0.0385768			0.0192884	+	0.999814i	$0.493860\pi$
$132$		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	$-0.631434\pi$
$139$	6.98667	−	12.1013i	0.592602	−	1.02642i	0.993881	−	0.110460i	$-0.0352325\pi$
$140$		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	$-0.795855\pi$
$151$		−	14.7033i		−	1.19654i	0.801295	−	0.598269i	$-0.204145\pi$
$152$		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	0.983514	−	0.180832i	$-0.0578790\pi$
$163$	16.8356	+	9.72004i	1.31867	+	0.761332i	0.335152	+	0.942164i	$0.391212\pi$
$164$		0			0
$165$	−0.139555	+	0.241717i	−0.0108644	+	0.0188176i
$166$		0			0
$167$	5.33374	−	3.07944i	0.412737	−	0.238294i	−0.279228	−	0.960225i	$-0.590078\pi$
$167$	5.33374	−	3.07944i	0.412737	−	0.238294i	0.691965	+	0.721931i	$0.256745\pi$
$168$		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	0.903017	−	0.429606i	$-0.141347\pi$
$179$	1.06309	+	1.84132i	0.0794590	+	0.137627i	−0.823558	+	0.567233i	$0.808014\pi$
$180$		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	−0.877979	−	0.478699i	$-0.841109\pi$
$191$	−0.337550	+	0.584655i	−0.0244243	+	0.0423041i	0.853555	+	0.521003i	$0.174442\pi$
$192$		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	−0.853583	−	0.520957i	$-0.825575\pi$
$199$	0.343787	−	0.595457i	0.0243704	−	0.0422108i	0.877953	+	0.478746i	$0.158909\pi$
$200$		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	0.830693	−	0.556731i	$-0.187944\pi$
$211$	−0.970272	−	1.68056i	−0.0667963	−	0.115695i	−0.897489	+	0.441036i	$0.854611\pi$
$212$		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	−0.835788	−	0.549053i	$-0.814989\pi$
$223$	−11.6208	+	6.70928i	−0.778188	+	0.449287i	0.0575999	+	0.998340i	$0.481655\pi$
$224$		0			0
$225$	6.62929	−	11.4823i	0.441952	−	0.765484i
$226$		0			0
$227$	4.33583	+	2.50329i	0.287779	+	0.166149i	0.636940	−	0.770914i	$-0.280200\pi$
$227$	4.33583	+	2.50329i	0.287779	+	0.166149i	−0.349161	+	0.937063i	$0.613533\pi$
$228$		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	$0.173017\pi$
$239$			15.9907i			1.03435i	−0.855878	+	0.517177i	$0.826983\pi$
$240$		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	$0.560811\pi$
$251$	−14.9750	+	25.9374i	−0.945212	+	1.63715i	−0.755327	+	0.655348i	$0.772522\pi$
$252$		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	$0.174224\pi$
$263$	14.2331	+	24.6525i	0.877651	+	1.52014i	0.0237383	+	0.999718i	$0.492443\pi$
$264$		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	−0.994250	−	0.107088i	$-0.965848\pi$
$271$	−23.0244	+	13.2932i	−1.39863	+	0.807502i	−0.404384	+	0.914589i	$0.632514\pi$
$272$		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	0.567755	−	0.823197i	$-0.307812\pi$
$283$	−7.21744	−	12.5010i	−0.429032	−	0.743105i	−0.996787	+	0.0800919i	$0.974479\pi$
$284$		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	$-0.972470\pi$
$307$		−	3.02698i		−	0.172759i	0.996262	−	0.0863793i	$-0.0275297\pi$
$308$		0			0
$309$	1.53156	+	2.65274i	0.0871273	+	0.150909i
$310$		0			0
$311$	−33.8272			−1.91816			−0.959082	−	0.283130i	$-0.908627\pi$
$311$	−33.8272			−1.91816			−0.959082	+	0.283130i	$0.908627\pi$
$312$		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	0.0895218	−	0.995985i	$-0.471466\pi$
$331$	−13.2496	−	7.64968i	−0.728266	−	0.420464i	−0.817787	+	0.575521i	$0.804799\pi$
$332$		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	−0.583641	−	0.812012i	$-0.698372\pi$
$347$	7.66358	−	13.2737i	0.411402	−	0.712570i	0.995043	+	0.0994420i	$0.0317058\pi$
$348$		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	$-0.991124\pi$
$359$		−	1.05654i		−	0.0557621i	0.999611	−	0.0278811i	$-0.00887597\pi$
$360$		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	0.889967	−	0.456025i	$-0.150727\pi$
$367$	0.958906	+	1.66087i	0.0500545	+	0.0866969i	−0.839913	+	0.542722i	$0.817394\pi$
$368$		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	−0.878536	−	0.477677i	$-0.841479\pi$
$379$	−17.6014	+	10.1622i	−0.904123	+	0.521996i	−0.0255874	+	0.999673i	$0.508146\pi$
$380$		0			0
$381$	3.50440	−	6.06980i	0.179536	−	0.310965i
$382$		0			0
$383$	−8.52361	−	4.92111i	−0.435536	−	0.251457i	0.266166	−	0.963927i	$-0.414243\pi$
$383$	−8.52361	−	4.92111i	−0.435536	−	0.251457i	−0.701702	+	0.712470i	$0.747576\pi$
$384$		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	$0.0773404\pi$
$419$	14.1991	+	24.5935i	0.693669	+	1.20147i	−0.276958	+	0.960882i	$0.589326\pi$
$420$		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	−0.764092	−	0.645108i	$-0.776813\pi$
$431$	−12.1959	+	7.04133i	−0.587458	+	0.339169i	0.176634	+	0.984277i	$0.443479\pi$
$432$		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	0.937113	−	0.349027i	$-0.113488\pi$
$439$	3.48416	+	6.03474i	0.166290	+	0.288023i	−0.770823	+	0.637050i	$0.780155\pi$
$440$		0			0
$441$	2.79934			0.133302
$442$		0			0
$443$	15.4247			0.732851			0.366425	−	0.930447i	$-0.380581\pi$
$443$	15.4247			0.732851			0.366425	+	0.930447i	$0.380581\pi$
$444$		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	$-0.734683\pi$
$463$		−	31.8588i		−	1.48060i	0.672275	−	0.740301i	$-0.265317\pi$
$464$		0			0
$465$	0.108687	+	0.188251i	0.00504022	+	0.00872992i
$466$		0			0
$467$	34.3765			1.59075			0.795376	−	0.606116i	$-0.207273\pi$
$467$	34.3765			1.59075			0.795376	+	0.606116i	$0.207273\pi$
$468$		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	−0.892744	−	0.450564i	$-0.851223\pi$
$479$	−20.7680	+	11.9904i	−0.948916	+	0.547857i	−0.0561718	+	0.998421i	$0.517889\pi$
$480$		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	0.875587	−	0.483061i	$-0.160475\pi$
$487$	19.7517	+	11.4037i	0.895037	+	0.516750i	0.0194500	+	0.999811i	$0.493808\pi$
$488$		0			0
$489$			8.70809i			0.393794i
$490$		0			0
$491$	6.44981	+	11.1714i	0.291076	+	0.504158i	0.974064	−	0.226271i	$-0.0726535\pi$
$491$	6.44981	+	11.1714i	0.291076	+	0.504158i	−0.682989	+	0.730429i	$0.739320\pi$
$492$		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	$0.420120\pi$
$499$			43.2772i			1.93735i	−0.248326	+	0.968677i	$0.579880\pi$
$500$		0			0
$501$	2.38922	+	1.37942i	0.106743	+	0.0616279i
$502$		0			0
$503$	4.29338	−	7.43636i	0.191433	−	0.331571i	−0.754293	−	0.656538i	$-0.772020\pi$
$503$	4.29338	−	7.43636i	0.191433	−	0.331571i	0.945725	+	0.324967i	$0.105353\pi$
$504$		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	0.568365	−	0.822777i	$-0.307576\pi$
$523$	−9.79632	−	16.9677i	−0.428363	−	0.741947i	−0.996728	+	0.0808300i	$0.974243\pi$
$524$		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	$-0.238702\pi$
$547$	34.2286			1.46351			0.731755	+	0.681568i	$0.238702\pi$
$548$		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	−0.604428	−	0.796660i	$-0.706598\pi$
$563$	9.19952	−	15.9340i	0.387713	−	0.671539i	0.992142	+	0.125120i	$0.0399317\pi$
$564$		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	$-0.667771\pi$
$571$	−24.0391			−1.00600			−0.503002	+	0.864285i	$0.667771\pi$
$572$		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	−0.326549	−	0.945180i	$-0.605886\pi$
$587$	7.96443	−	4.59827i	0.328727	−	0.189791i	0.655276	+	0.755390i	$0.272552\pi$
$588$		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	$-0.117634\pi$
$599$	45.6442			1.86497			0.932487	+	0.361205i	$0.117634\pi$
$600$		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	$-0.615167\pi$
$607$	15.5948	−	27.0110i	0.632974	−	1.09634i	0.986941	−	0.161085i	$-0.0514992\pi$
$608$		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	$-0.717222\pi$
$619$		−	38.6156i		−	1.55209i	0.630676	−	0.776046i	$-0.282778\pi$
$620$		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	0.669348	−	0.742949i	$-0.266574\pi$
$631$	9.05840	+	5.22987i	0.360609	+	0.208198i	−0.308739	+	0.951147i	$0.599907\pi$
$632$		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	0.541835	−	0.840485i	$-0.317730\pi$
$643$	2.15211	+	1.24252i	0.0848709	+	0.0490002i	−0.456964	+	0.889485i	$0.651063\pi$
$644$		0			0
$645$		−	0.523347i		−	0.0206068i
$646$		0			0
$647$	20.7448	+	35.9310i	0.815561	+	1.41259i	0.908924	+	0.416962i	$0.136905\pi$
$647$	20.7448	+	35.9310i	0.815561	+	1.41259i	−0.0933626	+	0.995632i	$0.529762\pi$
$648$		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	−0.859988	−	0.510314i	$-0.829529\pi$
$659$	0.306784	−	0.531366i	0.0119506	−	0.0206991i	0.871939	+	0.489615i	$0.162863\pi$
$660$		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	0.739220	−	0.673464i	$-0.235194\pi$
$683$	13.7360	+	7.93047i	0.525593	+	0.303451i	−0.213627	+	0.976915i	$0.568528\pi$
$684$		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	0.185577	−	0.982630i	$-0.440585\pi$
$691$	29.6870	−	17.1398i	1.12935	−	0.652029i	0.943771	+	0.330601i	$0.107251\pi$
$692$		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	−0.984354	−	0.176203i	$-0.943618\pi$
$719$	−9.10556	+	15.7713i	−0.339580	+	0.588170i	0.644774	+	0.764374i	$0.276952\pi$
$720$		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	$-0.372977\pi$
$727$	20.9527			0.777094			0.388547	+	0.921429i	$0.372977\pi$
$728$		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	0.101212	−	0.994865i	$-0.467728\pi$
$739$	27.5487	−	15.9053i	1.01340	−	0.585085i	0.912184	+	0.409780i	$0.134394\pi$
$740$		0			0
$741$	9.91759	+	1.67534i	0.364332	+	0.0615450i
$742$		0			0
$743$	−3.98668	+	2.30171i	−0.146257	+	0.0844417i	−0.571343	−	0.820712i	$-0.693577\pi$
$743$	−3.98668	+	2.30171i	−0.146257	+	0.0844417i	0.425086	+	0.905153i	$0.360244\pi$
$744$		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	$-0.928879\pi$
$751$	−18.6203	−	32.2513i	−0.679465	−	1.17687i	0.295677	−	0.955288i	$-0.404455\pi$
$752$		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	0.887245	−	0.461299i	$-0.152617\pi$
$787$	26.1282	+	15.0851i	0.931370	+	0.537727i	0.0441253	+	0.999026i	$0.485950\pi$
$788$		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	$0.0379630\pi$
$811$			6.77674i			0.237964i	−0.992896	+	0.118982i	$0.962037\pi$
$812$		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	$0.460229\pi$
$823$	−22.8633	+	39.6004i	−0.796965	+	1.38038i	−0.921584	+	0.388180i	$0.873104\pi$
$824$		0			0
$825$	2.22947	+	1.28719i	0.0776203	+	0.0448141i
$826$		0			0
$827$		−	19.0625i		−	0.662869i	−0.943478	−	0.331434i	$-0.892467\pi$
$827$		−	19.0625i		−	0.662869i	0.943478	−	0.331434i	$-0.107533\pi$
$828$		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	0.577428	−	0.816442i	$-0.304056\pi$
$839$	4.60791	+	2.66038i	0.159083	+	0.0918464i	−0.418345	+	0.908288i	$0.637390\pi$
$840$		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	$-0.491519\pi$
$859$	1.56167			0.0532835			0.0266417	+	0.999645i	$0.491519\pi$
$860$		0			0
$861$	−1.41051	−	2.44308i	−0.0480701	−	0.0832598i
$862$		0			0
$863$		−	42.2076i		−	1.43676i	−0.695649	−	0.718382i	$-0.744883\pi$
$863$		−	42.2076i		−	1.43676i	0.695649	−	0.718382i	$-0.255117\pi$
$864$		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	$-0.370475\pi$
$883$	23.5213			0.791555			0.395778	+	0.918346i	$0.370475\pi$
$884$		0			0
$885$	3.40027			0.114299
$886$		0			0
$887$	7.39357	+	12.8060i	0.248252	+	0.429985i	0.963041	−	0.269355i	$-0.0868106\pi$
$887$	7.39357	+	12.8060i	0.248252	+	0.429985i	−0.714789	+	0.699340i	$0.753477\pi$
$888$		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	0.786529	−	0.617553i	$-0.211876\pi$
$907$	−4.26305	−	7.38382i	−0.141552	−	0.245176i	−0.928081	+	0.372377i	$0.878543\pi$
$908$		0			0
$909$	19.1356			0.634686
$910$		0			0
$911$	−43.5745			−1.44369			−0.721843	−	0.692057i	$-0.756705\pi$
$911$	−43.5745			−1.44369			−0.721843	+	0.692057i	$0.756705\pi$
$912$		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	$-0.602420\pi$
$919$	20.1129	−	34.8365i	0.663462	−	1.14915i	0.979700	−	0.200470i	$-0.0642470\pi$
$920$		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	−0.763462	−	0.645853i	$-0.776502\pi$
$947$	−18.0291	+	10.4091i	−0.585867	+	0.338250i	0.177595	+	0.984104i	$0.443168\pi$
$948$		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	$-0.928940\pi$
$967$		−	13.7691i		−	0.442786i	0.975185	−	0.221393i	$-0.0710603\pi$
$968$		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	$-0.665659\pi$
$971$	15.6658	−	27.1340i	0.502740	−	0.870771i	0.999995	−	0.00316696i	$-0.00100808\pi$
$972$		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	$0.354238\pi$
$983$			56.2452i			1.79394i	−0.442087	+	0.896972i	$0.645762\pi$
$984$		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	$0.118968\pi$
$991$	24.6073	+	42.6210i	0.781676	+	1.35390i	−0.149289	+	0.988794i	$0.547699\pi$
$992$		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	1456.2.cc.g.673.6		24
4.3	odd	2		728.2.bm.c.673.7	yes	24
13.4	even	6	inner	1456.2.cc.g.225.6		24
52.11	even	12		9464.2.a.bl.1.6		12
52.15	even	12		9464.2.a.bm.1.6		12
52.43	odd	6		728.2.bm.c.225.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.7	✓	24	52.43	odd	6
728.2.bm.c.673.7	yes	24	4.3	odd	2
1456.2.cc.g.225.6		24	13.4	even	6	inner
1456.2.cc.g.673.6		24	1.1	even	1	trivial
9464.2.a.bl.1.6		12	52.11	even	12
9464.2.a.bm.1.6		12	52.15	even	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not 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

Related objects

Downloads

Learn more