LMFDB - Embedded newform 1456.2.cc.g.225.7

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)

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);

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")

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			225.7
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.g.673.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.266360 - 0.461349i) q^{3} +3.61008i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.35810 + 2.35231i) q^{9} +(-0.788493 - 0.455237i) q^{11} +(-2.94171 + 2.08479i) q^{13} +(1.66551 + 0.961580i) q^{15} +(-1.46831 - 2.54318i) q^{17} +(0.223125 - 0.128821i) q^{19} +0.532720i q^{21} +(-2.40672 + 4.16856i) q^{23} -8.03267 q^{25} +3.04514 q^{27} +(-1.09793 + 1.90166i) q^{29} -7.13553i q^{31} +(-0.420046 + 0.242514i) q^{33} +(-1.80504 - 3.12642i) q^{35} +(3.59529 + 2.07574i) q^{37} +(0.178264 + 1.91246i) q^{39} +(-6.85301 - 3.95658i) q^{41} +(-0.906650 - 1.57036i) q^{43} +(-8.49201 + 4.90287i) q^{45} -0.764866i q^{47} +(0.500000 - 0.866025i) q^{49} -1.56439 q^{51} -7.04212 q^{53} +(1.64344 - 2.84652i) q^{55} -0.137251i q^{57} +(6.34092 - 3.66093i) q^{59} +(4.99008 + 8.64307i) q^{61} +(-2.35231 - 1.35810i) q^{63} +(-7.52626 - 10.6198i) q^{65} +(-12.3936 - 7.15546i) q^{67} +(1.28211 + 2.22068i) q^{69} +(-7.36565 + 4.25256i) q^{71} -1.78944i q^{73} +(-2.13958 + 3.70586i) q^{75} +0.910474 q^{77} -4.79045 q^{79} +(-3.26321 + 5.65205i) q^{81} +14.1237i q^{83} +(9.18108 - 5.30070i) q^{85} +(0.584886 + 1.01305i) q^{87} +(10.0457 + 5.79987i) q^{89} +(1.50520 - 3.27634i) q^{91} +(-3.29197 - 1.90062i) q^{93} +(0.465055 + 0.805499i) q^{95} +(3.96317 - 2.28814i) q^{97} -2.47304i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

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

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
$3$	0.266360	−	0.461349i	0.153783	−	0.266360i	−0.778832	−	0.627232i	$-0.784188\pi$
$3$	0.266360	−	0.461349i	0.153783	−	0.266360i	0.932615	+	0.360872i	$0.117521\pi$
$4$		0			0
$5$			3.61008i			1.61448i	0.590226	+	0.807238i	$0.299039\pi$
$5$			3.61008i			1.61448i	−0.590226	+	0.807238i	$0.700961\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		0			0
$9$	1.35810	+	2.35231i	0.452702	+	0.784102i
$10$		0			0
$11$	−0.788493	−	0.455237i	−0.237740	−	0.137259i	0.376398	−	0.926458i	$-0.377163\pi$
$11$	−0.788493	−	0.455237i	−0.237740	−	0.137259i	−0.614137	+	0.789199i	$0.710496\pi$
$12$		0			0
$13$	−2.94171	+	2.08479i	−0.815883	+	0.578217i
$13$	−2.94171	+	2.08479i	−0.815883	+	0.578217i
$14$		0			0
$15$	1.66551	+	0.961580i	0.430032	+	0.248279i
$16$		0			0
$17$	−1.46831	−	2.54318i	−0.356116	−	0.616812i	0.631192	−	0.775627i	$-0.282566\pi$
$17$	−1.46831	−	2.54318i	−0.356116	−	0.616812i	−0.987308	+	0.158815i	$0.949233\pi$
$18$		0			0
$19$	0.223125	−	0.128821i	0.0511884	−	0.0295536i	−0.474187	−	0.880424i	$-0.657258\pi$
$19$	0.223125	−	0.128821i	0.0511884	−	0.0295536i	0.525376	+	0.850870i	$0.323925\pi$
$20$		0			0
$21$			0.532720i			0.116249i
$22$		0			0
$23$	−2.40672	+	4.16856i	−0.501836	+	0.869206i	0.498162	+	0.867084i	$0.334009\pi$
$23$	−2.40672	+	4.16856i	−0.501836	+	0.869206i	−0.999998	+	0.00212145i	$0.999325\pi$
$24$		0			0
$25$	−8.03267			−1.60653
$26$		0			0
$27$	3.04514			0.586037
$28$		0			0
$29$	−1.09793	+	1.90166i	−0.203880	+	0.353130i	−0.949775	−	0.312933i	$-0.898688\pi$
$29$	−1.09793	+	1.90166i	−0.203880	+	0.353130i	0.745896	+	0.666063i	$0.232022\pi$
$30$		0			0
$31$		−	7.13553i		−	1.28158i	−0.767716	−	0.640790i	$-0.778607\pi$
$31$		−	7.13553i		−	1.28158i	0.767716	−	0.640790i	$-0.221393\pi$
$32$		0			0
$33$	−0.420046	+	0.242514i	−0.0731206	+	0.0422162i
$34$		0			0
$35$	−1.80504	−	3.12642i	−0.305107	−	0.528461i
$36$		0			0
$37$	3.59529	+	2.07574i	0.591062	+	0.341250i	0.765517	−	0.643415i	$-0.222483\pi$
$37$	3.59529	+	2.07574i	0.591062	+	0.341250i	−0.174455	+	0.984665i	$0.555816\pi$
$38$		0			0
$39$	0.178264	+	1.91246i	0.0285450	+	0.306238i
$40$		0			0
$41$	−6.85301	−	3.95658i	−1.07026	−	0.617915i	−0.142007	−	0.989866i	$-0.545356\pi$
$41$	−6.85301	−	3.95658i	−1.07026	−	0.617915i	−0.928252	+	0.371951i	$0.878689\pi$
$42$		0			0
$43$	−0.906650	−	1.57036i	−0.138263	−	0.239478i	0.788576	−	0.614937i	$-0.210819\pi$
$43$	−0.906650	−	1.57036i	−0.138263	−	0.239478i	−0.926839	+	0.375459i	$0.877485\pi$
$44$		0			0
$45$	−8.49201	+	4.90287i	−1.26591	+	0.730876i
$46$		0			0
$47$		−	0.764866i		−	0.111567i	−0.998443	−	0.0557836i	$-0.982234\pi$
$47$		−	0.764866i		−	0.111567i	0.998443	−	0.0557836i	$-0.0177657\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−1.56439			−0.219058
$52$		0			0
$53$	−7.04212			−0.967309			−0.483655	−	0.875259i	$-0.660691\pi$
$53$	−7.04212			−0.967309			−0.483655	+	0.875259i	$0.660691\pi$
$54$		0			0
$55$	1.64344	−	2.84652i	0.221602	−	0.383825i
$56$		0			0
$57$		−	0.137251i		−	0.0181794i
$58$		0			0
$59$	6.34092	−	3.66093i	0.825517	−	0.476613i	−0.0267980	−	0.999641i	$-0.508531\pi$
$59$	6.34092	−	3.66093i	0.825517	−	0.476613i	0.852315	+	0.523028i	$0.175198\pi$
$60$		0			0
$61$	4.99008	+	8.64307i	0.638914	+	1.10663i	0.985671	+	0.168677i	$0.0539494\pi$
$61$	4.99008	+	8.64307i	0.638914	+	1.10663i	−0.346757	+	0.937955i	$0.612717\pi$
$62$		0			0
$63$	−2.35231	−	1.35810i	−0.296363	−	0.171105i
$64$		0			0
$65$	−7.52626	−	10.6198i	−0.933518	−	1.31722i
$66$		0			0
$67$	−12.3936	−	7.15546i	−1.51412	−	0.874178i	−0.999863	−	0.0165424i	$-0.994734\pi$
$67$	−12.3936	−	7.15546i	−1.51412	−	0.874178i	−0.514258	−	0.857636i	$-0.671933\pi$
$68$		0			0
$69$	1.28211	+	2.22068i	0.154348	+	0.267338i
$70$		0			0
$71$	−7.36565	+	4.25256i	−0.874142	+	0.504686i	−0.868722	−	0.495299i	$-0.835058\pi$
$71$	−7.36565	+	4.25256i	−0.874142	+	0.504686i	−0.00541939	+	0.999985i	$0.501725\pi$
$72$		0			0
$73$		−	1.78944i		−	0.209438i	−0.994502	−	0.104719i	$-0.966606\pi$
$73$		−	1.78944i		−	0.209438i	0.994502	−	0.104719i	$-0.0333944\pi$
$74$		0			0
$75$	−2.13958	+	3.70586i	−0.247058	+	0.427916i
$76$		0			0
$77$	0.910474			0.103758
$78$		0			0
$79$	−4.79045			−0.538967			−0.269484	−	0.963005i	$-0.586853\pi$
$79$	−4.79045			−0.538967			−0.269484	+	0.963005i	$0.586853\pi$
$80$		0			0
$81$	−3.26321	+	5.65205i	−0.362579	+	0.628005i
$82$		0			0
$83$			14.1237i			1.55027i	0.631794	+	0.775137i	$0.282319\pi$
$83$			14.1237i			1.55027i	−0.631794	+	0.775137i	$0.717681\pi$
$84$		0			0
$85$	9.18108	−	5.30070i	0.995828	−	0.574941i
$86$		0			0
$87$	0.584886	+	1.01305i	0.0627064	+	0.108611i
$88$		0			0
$89$	10.0457	+	5.79987i	1.06484	+	0.614785i	0.926767	−	0.375637i	$-0.122576\pi$
$89$	10.0457	+	5.79987i	1.06484	+	0.614785i	0.138072	+	0.990422i	$0.455909\pi$
$90$		0			0
$91$	1.50520	−	3.27634i	0.157788	−	0.343453i
$92$		0			0
$93$	−3.29197	−	1.90062i	−0.341361	−	0.197085i
$94$		0			0
$95$	0.465055	+	0.805499i	0.0477136	+	0.0826424i
$96$		0			0
$97$	3.96317	−	2.28814i	0.402399	−	0.232325i	−0.285120	−	0.958492i	$-0.592033\pi$
$97$	3.96317	−	2.28814i	0.402399	−	0.232325i	0.687519	+	0.726167i	$0.258700\pi$
$98$		0			0
$99$		−	2.47304i		−	0.248550i
$100$		0			0
$101$	−0.954236	+	1.65279i	−0.0949501	+	0.164458i	−0.909588	−	0.415512i	$-0.863602\pi$
$101$	−0.954236	+	1.65279i	−0.0949501	+	0.164458i	0.814638	+	0.579970i	$0.196936\pi$
$102$		0			0
$103$	9.65209			0.951048			0.475524	−	0.879703i	$-0.342258\pi$
$103$	9.65209			0.951048			0.475524	+	0.879703i	$0.342258\pi$
$104$		0			0
$105$	−1.92316			−0.187681
$106$		0			0
$107$	−4.02416	+	6.97005i	−0.389030	+	0.673820i	−0.992319	−	0.123702i	$-0.960523\pi$
$107$	−4.02416	+	6.97005i	−0.389030	+	0.673820i	0.603289	+	0.797523i	$0.293857\pi$
$108$		0			0
$109$			10.9962i			1.05324i	0.850101	+	0.526620i	$0.176541\pi$
$109$			10.9962i			1.05324i	−0.850101	+	0.526620i	$0.823459\pi$
$110$		0			0
$111$	1.91528	−	1.10579i	0.181790	−	0.104957i
$112$		0			0
$113$	5.19941	+	9.00565i	0.489120	+	0.847180i	0.999922	−	0.0125184i	$-0.00398484\pi$
$113$	5.19941	+	9.00565i	0.489120	+	0.847180i	−0.510802	+	0.859698i	$0.670652\pi$
$114$		0			0
$115$	−15.0488	−	8.68845i	−1.40331	−	0.810203i
$116$		0			0
$117$	−8.89922	−	4.08843i	−0.822733	−	0.377976i
$118$		0			0
$119$	2.54318	+	1.46831i	0.233133	+	0.134599i
$120$		0			0
$121$	−5.08552	−	8.80838i	−0.462320	−	0.800762i
$122$		0			0
$123$	−3.65073	+	2.10775i	−0.329175	+	0.190049i
$124$		0			0
$125$		−	10.9482i		−	0.979235i
$126$		0			0
$127$	−10.8413	+	18.7777i	−0.962009	+	1.66625i	−0.244564	+	0.969633i	$0.578645\pi$
$127$	−10.8413	+	18.7777i	−0.962009	+	1.66625i	−0.717445	+	0.696615i	$0.754689\pi$
$128$		0			0
$129$	−0.965981			−0.0850499
$130$		0			0
$131$	3.47007			0.303182			0.151591	−	0.988443i	$-0.451560\pi$
$131$	3.47007			0.303182			0.151591	+	0.988443i	$0.451560\pi$
$132$		0			0
$133$	−0.128821	+	0.223125i	−0.0111702	+	0.0193474i
$134$		0			0
$135$			10.9932i			0.946143i
$136$		0			0
$137$	4.52594	−	2.61305i	0.386677	−	0.223248i	−0.294042	−	0.955792i	$-0.595001\pi$
$137$	4.52594	−	2.61305i	0.386677	−	0.223248i	0.680719	+	0.732544i	$0.261667\pi$
$138$		0			0
$139$	6.43826	+	11.1514i	0.546086	+	0.945848i	0.998538	+	0.0540595i	$0.0172161\pi$
$139$	6.43826	+	11.1514i	0.546086	+	0.945848i	−0.452452	+	0.891789i	$0.649451\pi$
$140$		0			0
$141$	−0.352870	−	0.203730i	−0.0297170	−	0.0171571i
$142$		0			0
$143$	3.26859	−	0.304671i	0.273333	−	0.0254779i
$144$		0			0
$145$	−6.86515	−	3.96360i	−0.570120	−	0.329159i
$146$		0			0
$147$	−0.266360	−	0.461349i	−0.0219690	−	0.0380514i
$148$		0			0
$149$	0.349996	−	0.202070i	0.0286728	−	0.0165542i	−0.485595	−	0.874184i	$-0.661397\pi$
$149$	0.349996	−	0.202070i	0.0286728	−	0.0165542i	0.514268	+	0.857630i	$0.328064\pi$
$150$		0			0
$151$		−	0.690599i		−	0.0562001i	−0.999605	−	0.0281001i	$-0.991054\pi$
$151$		−	0.690599i		−	0.0562001i	0.999605	−	0.0281001i	$-0.00894571\pi$
$152$		0			0
$153$	3.98823	−	6.90781i	0.322429	−	0.558463i
$154$		0			0
$155$	25.7598			2.06908
$156$		0			0
$157$	15.0585			1.20180			0.600900	−	0.799324i	$-0.294809\pi$
$157$	15.0585			1.20180			0.600900	+	0.799324i	$0.294809\pi$
$158$		0			0
$159$	−1.87574	+	3.24887i	−0.148756	+	0.257652i
$160$		0			0
$161$		−	4.81344i		−	0.379352i
$162$		0			0
$163$	−4.74129	+	2.73739i	−0.371367	+	0.214409i	−0.674055	−	0.738681i	$-0.735449\pi$
$163$	−4.74129	+	2.73739i	−0.371367	+	0.214409i	0.302689	+	0.953090i	$0.402116\pi$
$164$		0			0
$165$	−0.875493	−	1.51640i	−0.0681571	−	0.118052i
$166$		0			0
$167$	−11.3759	−	6.56788i	−0.880294	−	0.508238i	−0.00953843	−	0.999955i	$-0.503036\pi$
$167$	−11.3759	−	6.56788i	−0.880294	−	0.508238i	−0.870755	+	0.491717i	$0.836370\pi$
$168$		0			0
$169$	4.30728	−	12.2657i	0.331329	−	0.943515i
$170$		0			0
$171$	0.606054	+	0.349905i	0.0463461	+	0.0267579i
$172$		0			0
$173$	12.4954	+	21.6426i	0.950006	+	1.64546i	0.745403	+	0.666614i	$0.232257\pi$
$173$	12.4954	+	21.6426i	0.950006	+	1.64546i	0.204603	+	0.978845i	$0.434410\pi$
$174$		0			0
$175$	6.95650	−	4.01634i	0.525862	−	0.303606i
$176$		0			0
$177$		−	3.90050i		−	0.293180i
$178$		0			0
$179$	−8.27646	+	14.3353i	−0.618612	+	1.07147i	0.371127	+	0.928582i	$0.378971\pi$
$179$	−8.27646	+	14.3353i	−0.618612	+	1.07147i	−0.989739	+	0.142885i	$0.954362\pi$
$180$		0			0
$181$	20.7503			1.54236			0.771179	−	0.636619i	$-0.219667\pi$
$181$	20.7503			1.54236			0.771179	+	0.636619i	$0.219667\pi$
$182$		0			0
$183$	5.31663			0.393016
$184$		0			0
$185$	−7.49359	+	12.9793i	−0.550940	+	0.954256i
$186$		0			0
$187$			2.67371i			0.195521i
$188$		0			0
$189$	−2.63717	+	1.52257i	−0.191826	+	0.110751i
$190$		0			0
$191$	9.43337	+	16.3391i	0.682575	+	1.18225i	0.974192	+	0.225719i	$0.0724732\pi$
$191$	9.43337	+	16.3391i	0.682575	+	1.18225i	−0.291618	+	0.956535i	$0.594193\pi$
$192$		0			0
$193$	−7.66632	−	4.42615i	−0.551833	−	0.318601i	0.198028	−	0.980196i	$-0.436546\pi$
$193$	−7.66632	−	4.42615i	−0.551833	−	0.318601i	−0.749861	+	0.661595i	$0.769880\pi$
$194$		0			0
$195$	−6.90412	+	0.643546i	−0.494415	+	0.0460853i
$196$		0			0
$197$	4.46069	+	2.57538i	0.317811	+	0.183488i	0.650417	−	0.759578i	$-0.274594\pi$
$197$	4.46069	+	2.57538i	0.317811	+	0.183488i	−0.332605	+	0.943066i	$0.607928\pi$
$198$		0			0
$199$	−4.30884	−	7.46312i	−0.305445	−	0.529047i	0.671915	−	0.740628i	$-0.265472\pi$
$199$	−4.30884	−	7.46312i	−0.305445	−	0.529047i	−0.977360	+	0.211581i	$0.932139\pi$
$200$		0			0
$201$	−6.60232	+	3.81185i	−0.465692	+	0.268867i
$202$		0			0
$203$		−	2.19585i		−	0.154119i
$204$		0			0
$205$	14.2836	−	24.7399i	0.997609	−	1.72791i
$206$		0			0
$207$	−13.0743			−0.908728
$208$		0			0
$209$	−0.234577			−0.0162260
$210$		0			0
$211$	11.0490	−	19.1374i	0.760642	−	1.31747i	−0.181877	−	0.983321i	$-0.558217\pi$
$211$	11.0490	−	19.1374i	0.760642	−	1.31747i	0.942520	−	0.334150i	$-0.108449\pi$
$212$		0			0
$213$			4.53084i			0.310448i
$214$		0			0
$215$	5.66914	−	3.27308i	0.386632	−	0.223222i
$216$		0			0
$217$	3.56777	+	6.17955i	0.242196	+	0.419495i
$218$		0			0
$219$	−0.825557	−	0.476636i	−0.0557860	−	0.0322081i
$220$		0			0
$221$	9.62133	+	4.42018i	0.647200	+	0.297333i
$222$		0			0
$223$	−22.0108	−	12.7079i	−1.47395	−	0.850986i	−0.474382	−	0.880319i	$-0.657328\pi$
$223$	−22.0108	−	12.7079i	−1.47395	−	0.850986i	−0.999570	+	0.0293327i	$0.990662\pi$
$224$		0			0
$225$	−10.9092	−	18.8953i	−0.727281	−	1.25969i
$226$		0			0
$227$	−4.55590	+	2.63035i	−0.302385	+	0.174582i	−0.643514	−	0.765434i	$-0.722524\pi$
$227$	−4.55590	+	2.63035i	−0.302385	+	0.174582i	0.341129	+	0.940017i	$0.389191\pi$
$228$		0			0
$229$		−	7.43362i		−	0.491228i	−0.969368	−	0.245614i	$-0.921011\pi$
$229$		−	7.43362i		−	0.491228i	0.969368	−	0.245614i	$-0.0789895\pi$
$230$		0			0
$231$	0.242514	−	0.420046i	0.0159562	−	0.0276370i
$232$		0			0
$233$	−11.4030			−0.747033			−0.373517	−	0.927623i	$-0.621848\pi$
$233$	−11.4030			−0.747033			−0.373517	+	0.927623i	$0.621848\pi$
$234$		0			0
$235$	2.76123			0.180123
$236$		0			0
$237$	−1.27598	+	2.21007i	−0.0828840	+	0.143559i
$238$		0			0
$239$		−	16.3733i		−	1.05910i	−0.848278	−	0.529551i	$-0.822361\pi$
$239$		−	16.3733i		−	1.05910i	0.848278	−	0.529551i	$-0.177639\pi$
$240$		0			0
$241$	4.51905	−	2.60907i	0.291098	−	0.168065i	−0.347339	−	0.937740i	$-0.612915\pi$
$241$	4.51905	−	2.60907i	0.291098	−	0.168065i	0.638437	+	0.769674i	$0.279581\pi$
$242$		0			0
$243$	6.30608	+	10.9225i	0.404535	+	0.700676i
$244$		0			0
$245$	3.12642	+	1.80504i	0.199740	+	0.115320i
$246$		0			0
$247$	−0.387803	+	0.844123i	−0.0246753	+	0.0537103i
$248$		0			0
$249$	6.51593	+	3.76198i	0.412931	+	0.238406i
$250$		0			0
$251$	−5.51020	−	9.54395i	−0.347801	−	0.602408i	0.638058	−	0.769988i	$-0.279738\pi$
$251$	−5.51020	−	9.54395i	−0.347801	−	0.602408i	−0.985858	+	0.167580i	$0.946405\pi$
$252$		0			0
$253$	3.79537	−	2.19126i	0.238613	−	0.137763i
$254$		0			0
$255$		−	5.64757i		−	0.353665i
$256$		0			0
$257$	−13.6609	+	23.6613i	−0.852143	+	1.47595i	0.0271283	+	0.999632i	$0.491364\pi$
$257$	−13.6609	+	23.6613i	−0.852143	+	1.47595i	−0.879271	+	0.476322i	$0.841970\pi$
$258$		0			0
$259$	−4.15148			−0.257961
$260$		0			0
$261$	−5.96439			−0.369187
$262$		0			0
$263$	2.54175	−	4.40244i	0.156731	−	0.271466i	−0.776957	−	0.629554i	$-0.783238\pi$
$263$	2.54175	−	4.40244i	0.156731	−	0.271466i	0.933688	+	0.358088i	$0.116571\pi$
$264$		0			0
$265$		−	25.4226i		−	1.56170i
$266$		0			0
$267$	5.35153	−	3.08971i	0.327508	−	0.189087i
$268$		0			0
$269$	−5.38662	−	9.32990i	−0.328428	−	0.568854i	0.653772	−	0.756692i	$-0.273186\pi$
$269$	−5.38662	−	9.32990i	−0.328428	−	0.568854i	−0.982200	+	0.187837i	$0.939852\pi$
$270$		0			0
$271$	−17.2208	−	9.94243i	−1.04609	−	0.603960i	−0.124537	−	0.992215i	$-0.539745\pi$
$271$	−17.2208	−	9.94243i	−1.04609	−	0.603960i	−0.921552	+	0.388255i	$0.873078\pi$
$272$		0			0
$273$	−1.11061	−	1.56711i	−0.0672172	−	0.0948455i
$274$		0			0
$275$	6.33371	+	3.65677i	0.381937	+	0.220511i
$276$		0			0
$277$	10.4609	+	18.1188i	0.628533	+	1.08865i	0.987846	+	0.155434i	$0.0496775\pi$
$277$	10.4609	+	18.1188i	0.628533	+	1.08865i	−0.359314	+	0.933217i	$0.616989\pi$
$278$		0			0
$279$	16.7850	−	9.69080i	1.00489	−	0.580173i
$280$		0			0
$281$		−	9.93537i		−	0.592695i	−0.955080	−	0.296347i	$-0.904231\pi$
$281$		−	9.93537i		−	0.592695i	0.955080	−	0.296347i	$-0.0957686\pi$
$282$		0			0
$283$	5.59308	−	9.68751i	0.332474	−	0.575862i	−0.650522	−	0.759487i	$-0.725450\pi$
$283$	5.59308	−	9.68751i	0.332474	−	0.575862i	0.982996	+	0.183625i	$0.0587832\pi$
$284$		0			0
$285$	0.495488			0.0293502
$286$		0			0
$287$	7.91317			0.467100
$288$		0			0
$289$	4.18816	−	7.25410i	0.246362	−	0.426712i
$290$		0			0
$291$		−	2.43787i		−	0.142911i
$292$		0			0
$293$	26.2472	−	15.1538i	1.53338	−	0.885297i	0.534177	−	0.845373i	$-0.320622\pi$
$293$	26.2472	−	15.1538i	1.53338	−	0.885297i	0.999203	−	0.0399244i	$-0.0127117\pi$
$294$		0			0
$295$	13.2163	+	22.8912i	0.769480	+	1.33278i
$296$		0			0
$297$	−2.40107	−	1.38626i	−0.139324	−	0.0804389i
$298$		0			0
$299$	−1.61072	−	17.2802i	−0.0931503	−	0.999340i
$300$		0			0
$301$	1.57036	+	0.906650i	0.0905143	+	0.0522585i
$302$		0			0
$303$	0.508341	+	0.880472i	0.0292034	+	0.0505818i
$304$		0			0
$305$	−31.2022	+	18.0146i	−1.78663	+	1.03151i
$306$		0			0
$307$			34.3173i			1.95859i	0.202428	+	0.979297i	$0.435117\pi$
$307$			34.3173i			1.95859i	−0.202428	+	0.979297i	$0.564883\pi$
$308$		0			0
$309$	2.57093	−	4.45298i	0.146255	−	0.253321i
$310$		0			0
$311$	29.9417			1.69784			0.848918	−	0.528525i	$-0.177255\pi$
$311$	29.9417			1.69784			0.848918	+	0.528525i	$0.177255\pi$
$312$		0			0
$313$	−15.3150			−0.865657			−0.432828	−	0.901476i	$-0.642484\pi$
$313$	−15.3150			−0.865657			−0.432828	+	0.901476i	$0.642484\pi$
$314$		0			0
$315$	4.90287	−	8.49201i	0.276245	−	0.478471i
$316$		0			0
$317$		−	18.3548i		−	1.03091i	−0.856917	−	0.515455i	$-0.827623\pi$
$317$		−	18.3548i		−	1.03091i	0.856917	−	0.515455i	$-0.172377\pi$
$318$		0			0
$319$	1.73141	−	0.999632i	0.0969406	−	0.0559687i
$320$		0			0
$321$	2.14375	+	3.71308i	0.119652	+	0.207244i
$322$		0			0
$323$	−0.655231	−	0.378298i	−0.0364580	−	0.0210491i
$324$		0			0
$325$	23.6298	−	16.7464i	1.31074	−	0.928926i
$326$		0			0
$327$	5.07306	+	2.92893i	0.280541	+	0.161970i
$328$		0			0
$329$	0.382433	+	0.662393i	0.0210842	+	0.0365189i
$330$		0			0
$331$	23.5096	−	13.5733i	1.29220	−	0.746054i	0.313159	−	0.949701i	$-0.398613\pi$
$331$	23.5096	−	13.5733i	1.29220	−	0.746054i	0.979044	+	0.203647i	$0.0652793\pi$
$332$		0			0
$333$			11.2763i			0.617937i
$334$		0			0
$335$	25.8318	−	44.7419i	1.41134	−	2.44451i
$336$		0			0
$337$	−32.0948			−1.74832			−0.874158	−	0.485641i	$-0.838586\pi$
$337$	−32.0948			−1.74832			−0.874158	+	0.485641i	$0.838586\pi$
$338$		0			0
$339$	5.53966			0.300873
$340$		0			0
$341$	−3.24836	+	5.62632i	−0.175908	+	0.304682i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−8.01682	+	4.62851i	−0.431611	+	0.249191i
$346$		0			0
$347$	9.08991	+	15.7442i	0.487972	+	0.845193i	0.999904	−	0.0138333i	$-0.00440343\pi$
$347$	9.08991	+	15.7442i	0.487972	+	0.845193i	−0.511932	+	0.859026i	$0.671070\pi$
$348$		0			0
$349$	−0.316993	−	0.183016i	−0.0169683	−	0.00979664i	0.491492	−	0.870882i	$-0.336452\pi$
$349$	−0.316993	−	0.183016i	−0.0169683	−	0.00979664i	−0.508460	+	0.861086i	$0.669785\pi$
$350$		0			0
$351$	−8.95790	+	6.34848i	−0.478137	+	0.338857i
$352$		0			0
$353$	28.4201	+	16.4083i	1.51265	+	0.873327i	0.999891	+	0.0147935i	$0.00470910\pi$
$353$	28.4201	+	16.4083i	1.51265	+	0.873327i	0.512757	+	0.858534i	$0.328624\pi$
$354$		0			0
$355$	−15.3521	−	26.5906i	−0.814804	−	1.41128i
$356$		0			0
$357$	1.35480	−	0.782195i	0.0717037	−	0.0413982i
$358$		0			0
$359$			33.2979i			1.75740i	0.477378	+	0.878698i	$0.341587\pi$
$359$			33.2979i			1.75740i	−0.477378	+	0.878698i	$0.658413\pi$
$360$		0			0
$361$	−9.46681	+	16.3970i	−0.498253	+	0.863000i
$362$		0			0
$363$	−5.41831			−0.284388
$364$		0			0
$365$	6.46003			0.338133
$366$		0			0
$367$	14.6032	−	25.2935i	0.762281	−	1.32031i	−0.179392	−	0.983778i	$-0.557413\pi$
$367$	14.6032	−	25.2935i	0.762281	−	1.32031i	0.941672	−	0.336531i	$-0.109254\pi$
$368$		0			0
$369$		−	21.4938i		−	1.11892i
$370$		0			0
$371$	6.09865	−	3.52106i	0.316626	−	0.182804i
$372$		0			0
$373$	7.05484	+	12.2193i	0.365286	+	0.632693i	0.988822	−	0.149101i	$-0.0476380\pi$
$373$	7.05484	+	12.2193i	0.365286	+	0.632693i	−0.623536	+	0.781794i	$0.714305\pi$
$374$		0			0
$375$	−5.05093	−	2.91616i	−0.260829	−	0.150590i
$376$		0			0
$377$	−0.734796	−	7.88308i	−0.0378439	−	0.405999i
$378$		0			0
$379$	−19.5621	−	11.2942i	−1.00484	−	0.580144i	−0.0951629	−	0.995462i	$-0.530337\pi$
$379$	−19.5621	−	11.2942i	−1.00484	−	0.580144i	−0.909677	+	0.415317i	$0.863671\pi$
$380$		0			0
$381$	5.77537	+	10.0032i	0.295881	+	0.512481i
$382$		0			0
$383$	−3.14983	+	1.81856i	−0.160949	+	0.0929239i	−0.578311	−	0.815816i	$-0.696288\pi$
$383$	−3.14983	+	1.81856i	−0.160949	+	0.0929239i	0.417362	+	0.908740i	$0.362955\pi$
$384$		0			0
$385$			3.28688i			0.167515i
$386$		0			0
$387$	2.46265	−	4.26544i	0.125184	−	0.216824i
$388$		0			0
$389$	9.36399			0.474773			0.237387	−	0.971415i	$-0.423709\pi$
$389$	9.36399			0.474773			0.237387	+	0.971415i	$0.423709\pi$
$390$		0			0
$391$	14.1352			0.714848
$392$		0			0
$393$	0.924288	−	1.60091i	0.0466242	−	0.0807555i
$394$		0			0
$395$		−	17.2939i		−	0.870150i
$396$		0			0
$397$	18.2814	−	10.5548i	0.917517	−	0.529729i	0.0346751	−	0.999399i	$-0.488960\pi$
$397$	18.2814	−	10.5548i	0.917517	−	0.529729i	0.882842	+	0.469670i	$0.155627\pi$
$398$		0			0
$399$	0.0686256	+	0.118863i	0.00343558	+	0.00595059i
$400$		0			0
$401$	31.2841	+	18.0619i	1.56225	+	0.901966i	0.997029	+	0.0770278i	$0.0245430\pi$
$401$	31.2841	+	18.0619i	1.56225	+	0.901966i	0.565223	+	0.824938i	$0.308790\pi$
$402$		0			0
$403$	14.8761	+	20.9906i	0.741032	+	1.04562i
$404$		0			0
$405$	−20.4043	−	11.7805i	−1.01390	−	0.585375i
$406$		0			0
$407$	−1.88991	−	3.27342i	−0.0936793	−	0.162257i
$408$		0			0
$409$	−3.83742	+	2.21554i	−0.189748	+	0.109551i	−0.591865	−	0.806037i	$-0.701608\pi$
$409$	−3.83742	+	2.21554i	−0.189748	+	0.109551i	0.402116	+	0.915589i	$0.368275\pi$
$410$		0			0
$411$		−	2.78405i		−	0.137327i
$412$		0			0
$413$	−3.66093	+	6.34092i	−0.180143	+	0.312016i
$414$		0			0
$415$	−50.9875			−2.50288
$416$		0			0
$417$	6.85957			0.335915
$418$		0			0
$419$	3.63831	−	6.30174i	0.177743	−	0.307860i	−0.763364	−	0.645969i	$-0.776454\pi$
$419$	3.63831	−	6.30174i	0.177743	−	0.307860i	0.941107	+	0.338108i	$0.109787\pi$
$420$		0			0
$421$			34.6205i			1.68730i	0.536893	+	0.843650i	$0.319598\pi$
$421$			34.6205i			1.68730i	−0.536893	+	0.843650i	$0.680402\pi$
$422$		0			0
$423$	1.79920	−	1.03877i	0.0874801	−	0.0505066i
$424$		0			0
$425$	11.7944	+	20.4285i	0.572113	+	0.990929i
$426$		0			0
$427$	−8.64307	−	4.99008i	−0.418267	−	0.241487i
$428$		0			0
$429$	0.730062	−	1.58911i	0.0352477	−	0.0767231i
$430$		0			0
$431$	8.99073	+	5.19080i	0.433068	+	0.250032i	0.700653	−	0.713502i	$-0.252892\pi$
$431$	8.99073	+	5.19080i	0.433068	+	0.250032i	−0.267585	+	0.963534i	$0.586226\pi$
$432$		0			0
$433$	0.0473814	+	0.0820669i	0.00227700	+	0.00394388i	0.867162	−	0.498027i	$-0.165942\pi$
$433$	0.0473814	+	0.0820669i	0.00227700	+	0.00394388i	−0.864885	+	0.501971i	$0.832609\pi$
$434$		0			0
$435$	−3.65720	+	2.11149i	−0.175349	+	0.101238i
$436$		0			0
$437$			1.24015i			0.0593243i
$438$		0			0
$439$	−6.93900	+	12.0187i	−0.331180	+	0.573621i	−0.982744	−	0.184973i	$-0.940780\pi$
$439$	−6.93900	+	12.0187i	−0.331180	+	0.573621i	0.651563	+	0.758594i	$0.274113\pi$
$440$		0			0
$441$	2.71621			0.129343
$442$		0			0
$443$	34.0718			1.61880			0.809400	−	0.587257i	$-0.199792\pi$
$443$	34.0718			1.61880			0.809400	+	0.587257i	$0.199792\pi$
$444$		0			0
$445$	−20.9380	+	36.2657i	−0.992556	+	1.71916i
$446$		0			0
$447$		−	0.215294i		−	0.0101830i
$448$		0			0
$449$	15.4470	−	8.91833i	0.728989	−	0.420882i	−0.0890634	−	0.996026i	$-0.528387\pi$
$449$	15.4470	−	8.91833i	0.728989	−	0.420882i	0.818052	+	0.575144i	$0.195054\pi$
$450$		0			0
$451$	3.60237	+	6.23948i	0.169629	+	0.293806i
$452$		0			0
$453$	−0.318607	−	0.183948i	−0.0149695	−	0.00864262i
$454$		0			0
$455$	11.8278	+	5.43388i	0.554497	+	0.254744i
$456$		0			0
$457$	3.82457	+	2.20812i	0.178906	+	0.103291i	0.586778	−	0.809748i	$-0.300396\pi$
$457$	3.82457	+	2.20812i	0.178906	+	0.103291i	−0.407873	+	0.913039i	$0.633729\pi$
$458$		0			0
$459$	−4.47119	−	7.74433i	−0.208697	−	0.361474i
$460$		0			0
$461$	−21.9618	+	12.6796i	−1.02286	+	0.590550i	−0.914932	−	0.403609i	$-0.867756\pi$
$461$	−21.9618	+	12.6796i	−1.02286	+	0.590550i	−0.107930	+	0.994158i	$0.534422\pi$
$462$		0			0
$463$		−	3.38088i		−	0.157123i	−0.996909	−	0.0785615i	$-0.974967\pi$
$463$		−	3.38088i		−	0.157123i	0.996909	−	0.0785615i	$-0.0250327\pi$
$464$		0			0
$465$	6.86139	−	11.8843i	0.318189	−	0.551120i
$466$		0			0
$467$	−11.8096			−0.546485			−0.273242	−	0.961945i	$-0.588096\pi$
$467$	−11.8096			−0.546485			−0.273242	+	0.961945i	$0.588096\pi$
$468$		0			0
$469$	14.3109			0.660817
$470$		0			0
$471$	4.01099	−	6.94723i	0.184816	−	0.320111i
$472$		0			0
$473$			1.65096i			0.0759113i
$474$		0			0
$475$	−1.79229	+	1.03478i	−0.0822359	+	0.0474789i
$476$		0			0
$477$	−9.56393	−	16.5652i	−0.437902	−	0.758469i
$478$		0			0
$479$	20.9061	+	12.0702i	0.955225	+	0.551499i	0.894700	−	0.446667i	$-0.147389\pi$
$479$	20.9061	+	12.0702i	0.955225	+	0.551499i	0.0605249	+	0.998167i	$0.480723\pi$
$480$		0			0
$481$	−14.9038	+	1.38921i	−0.679554	+	0.0633425i
$482$		0			0
$483$	−2.22068	−	1.28211i	−0.101044	−	0.0583379i
$484$		0			0
$485$	8.26036	+	14.3074i	0.375084	+	0.649664i
$486$		0			0
$487$	−5.47359	+	3.16018i	−0.248032	+	0.143201i	−0.618863	−	0.785499i	$-0.712406\pi$
$487$	−5.47359	+	3.16018i	−0.248032	+	0.143201i	0.370831	+	0.928700i	$0.379073\pi$
$488$		0			0
$489$			2.91652i			0.131890i
$490$		0			0
$491$	10.1159	−	17.5213i	0.456525	−	0.790724i	−0.542250	−	0.840217i	$-0.682427\pi$
$491$	10.1159	−	17.5213i	0.456525	−	0.790724i	0.998774	+	0.0494933i	$0.0157606\pi$
$492$		0			0
$493$	6.44836			0.290419
$494$		0			0
$495$	8.92786			0.401278
$496$		0			0
$497$	4.25256	−	7.36565i	0.190753	−	0.330395i
$498$		0			0
$499$			23.5570i			1.05456i	0.849692	+	0.527279i	$0.176788\pi$
$499$			23.5570i			1.05456i	−0.849692	+	0.527279i	$0.823212\pi$
$500$		0			0
$501$	−6.06017	+	3.49884i	−0.270748	+	0.156317i
$502$		0			0
$503$	5.51750	+	9.55659i	0.246013	+	0.426107i	0.962416	−	0.271579i	$-0.0875460\pi$
$503$	5.51750	+	9.55659i	0.246013	+	0.426107i	−0.716403	+	0.697687i	$0.754213\pi$
$504$		0			0
$505$	−5.96669	−	3.44487i	−0.265514	−	0.153295i
$506$		0			0
$507$	−4.51148	−	5.25425i	−0.200362	−	0.233349i
$508$		0			0
$509$	−21.5792	−	12.4587i	−0.956480	−	0.552224i	−0.0613918	−	0.998114i	$-0.519554\pi$
$509$	−21.5792	−	12.4587i	−0.956480	−	0.552224i	−0.895088	+	0.445890i	$0.852887\pi$
$510$		0			0
$511$	0.894721	+	1.54970i	0.0395801	+	0.0685548i
$512$		0			0
$513$	0.679446	−	0.392278i	0.0299983	−	0.0173195i
$514$		0			0
$515$			34.8448i			1.53545i
$516$		0			0
$517$	−0.348195	+	0.603092i	−0.0153136	+	0.0265239i
$518$		0			0
$519$	13.3131			0.584379
$520$		0			0
$521$	−17.3560			−0.760382			−0.380191	−	0.924908i	$-0.624142\pi$
$521$	−17.3560			−0.760382			−0.380191	+	0.924908i	$0.624142\pi$
$522$		0			0
$523$	−9.93362	+	17.2055i	−0.434367	+	0.752346i	−0.997244	−	0.0741952i	$-0.976361\pi$
$523$	−9.93362	+	17.2055i	−0.434367	+	0.752346i	0.562877	+	0.826541i	$0.309695\pi$
$524$		0			0
$525$		−	4.27916i		−	0.186758i
$526$		0			0
$527$	−18.1469	+	10.4771i	−0.790493	+	0.456391i
$528$		0			0
$529$	−0.0846157	−	0.146559i	−0.00367894	−	0.00637212i
$530$		0			0
$531$	17.2233	+	9.94386i	0.747426	+	0.431527i
$532$		0			0
$533$	28.4082	−	2.64798i	1.23050	−	0.114697i
$534$		0			0
$535$	−25.1624	−	14.5275i	−1.08787	−	0.628080i
$536$		0			0
$537$	4.40903	+	7.63667i	0.190264	+	0.329547i
$538$		0			0
$539$	−0.788493	+	0.455237i	−0.0339628	+	0.0196084i
$540$		0			0
$541$			21.4083i			0.920416i	0.887811	+	0.460208i	$0.152225\pi$
$541$			21.4083i			0.920416i	−0.887811	+	0.460208i	$0.847775\pi$
$542$		0			0
$543$	5.52705	−	9.57312i	0.237188	−	0.410822i
$544$		0			0
$545$	−39.6970			−1.70043
$546$		0			0
$547$	−45.7522			−1.95622			−0.978112	−	0.208078i	$-0.933279\pi$
$547$	−45.7522			−1.95622			−0.978112	+	0.208078i	$0.933279\pi$
$548$		0			0
$549$	−13.5541	+	23.4764i	−0.578475	+	1.00195i
$550$		0			0
$551$			0.565744i			0.0241015i
$552$		0			0
$553$	4.14865	−	2.39522i	0.176418	−	0.101855i
$554$		0			0
$555$	3.99198	+	6.91432i	0.169450	+	0.293496i
$556$		0			0
$557$	−15.8153	−	9.13097i	−0.670116	−	0.386892i	0.126005	−	0.992030i	$-0.459785\pi$
$557$	−15.8153	−	9.13097i	−0.670116	−	0.386892i	−0.796121	+	0.605138i	$0.793118\pi$
$558$		0			0
$559$	5.94098	+	2.72938i	0.251277	+	0.115440i
$560$		0			0
$561$	1.23351	+	0.712168i	0.0520789	+	0.0300678i
$562$		0			0
$563$	17.6905	+	30.6408i	0.745564	+	1.29135i	0.949931	+	0.312460i	$0.101153\pi$
$563$	17.6905	+	30.6408i	0.745564	+	1.29135i	−0.204367	+	0.978894i	$0.565514\pi$
$564$		0			0
$565$	−32.5111	+	18.7703i	−1.36775	+	0.789672i
$566$		0			0
$567$		−	6.52642i		−	0.274084i
$568$		0			0
$569$	10.0459	−	17.4000i	0.421145	−	0.729444i	−0.574907	−	0.818219i	$-0.694962\pi$
$569$	10.0459	−	17.4000i	0.421145	−	0.729444i	0.996052	+	0.0887746i	$0.0282951\pi$
$570$		0			0
$571$	−12.7624			−0.534088			−0.267044	−	0.963684i	$-0.586047\pi$
$571$	−12.7624			−0.534088			−0.267044	+	0.963684i	$0.586047\pi$
$572$		0			0
$573$	10.0507			0.419873
$574$		0			0
$575$	19.3324	−	33.4847i	0.806217	−	1.39641i
$576$		0			0
$577$		−	29.6469i		−	1.23422i	−0.786878	−	0.617109i	$-0.788304\pi$
$577$		−	29.6469i		−	1.23422i	0.786878	−	0.617109i	$-0.211696\pi$
$578$		0			0
$579$	−4.08400	+	2.35790i	−0.169725	+	0.0979909i
$580$		0			0
$581$	−7.06183	−	12.2315i	−0.292974	−	0.507446i
$582$		0			0
$583$	5.55266	+	3.20583i	0.229968	+	0.132772i
$584$		0			0
$585$	14.7596	−	32.1269i	0.610233	−	1.32828i
$586$		0			0
$587$	29.2832	+	16.9067i	1.20865	+	0.697812i	0.962463	−	0.271411i	$-0.0874903\pi$
$587$	29.2832	+	16.9067i	1.20865	+	0.697812i	0.246183	+	0.969223i	$0.420824\pi$
$588$		0			0
$589$	−0.919208	−	1.59212i	−0.0378753	−	0.0656020i
$590$		0			0
$591$	2.37630	−	1.37196i	0.0977479	−	0.0564348i
$592$		0			0
$593$		−	36.8255i		−	1.51224i	−0.654433	−	0.756120i	$-0.727093\pi$
$593$		−	36.8255i		−	1.51224i	0.654433	−	0.756120i	$-0.272907\pi$
$594$		0			0
$595$	−5.30070	+	9.18108i	−0.217307	+	0.376388i
$596$		0			0
$597$	−4.59080			−0.187889
$598$		0			0
$599$	9.49676			0.388027			0.194014	−	0.980999i	$-0.437849\pi$
$599$	9.49676			0.388027			0.194014	+	0.980999i	$0.437849\pi$
$600$		0			0
$601$	12.7832	−	22.1412i	0.521438	−	0.903157i	−0.478251	−	0.878223i	$-0.658729\pi$
$601$	12.7832	−	22.1412i	0.521438	−	0.903157i	0.999689	−	0.0249337i	$-0.00793746\pi$
$602$		0			0
$603$		−	38.8714i		−	1.58297i
$604$		0			0
$605$	31.7989	−	18.3591i	1.29281	−	0.746405i
$606$		0			0
$607$	−1.09834	−	1.90238i	−0.0445803	−	0.0772153i	0.842874	−	0.538111i	$-0.180862\pi$
$607$	−1.09834	−	1.90238i	−0.0445803	−	0.0772153i	−0.887455	+	0.460895i	$0.847528\pi$
$608$		0			0
$609$	−1.01305	−	0.584886i	−0.0410510	−	0.0237008i
$610$		0			0
$611$	1.59459	+	2.25001i	0.0645101	+	0.0910257i
$612$		0			0
$613$	−1.02232	−	0.590239i	−0.0412913	−	0.0238395i	0.479212	−	0.877699i	$-0.340922\pi$
$613$	−1.02232	−	0.590239i	−0.0412913	−	0.0238395i	−0.520504	+	0.853860i	$0.674256\pi$
$614$		0			0
$615$	−7.60915	−	13.1794i	−0.306830	−	0.531446i
$616$		0			0
$617$	30.1687	−	17.4179i	1.21455	−	0.701218i	0.250799	−	0.968039i	$-0.419307\pi$
$617$	30.1687	−	17.4179i	1.21455	−	0.701218i	0.963746	+	0.266821i	$0.0859733\pi$
$618$		0			0
$619$		−	23.1480i		−	0.930398i	−0.885206	−	0.465199i	$-0.845983\pi$
$619$		−	23.1480i		−	0.930398i	0.885206	−	0.465199i	$-0.154017\pi$
$620$		0			0
$621$	−7.32880	+	12.6938i	−0.294095	+	0.509387i
$622$		0			0
$623$	−11.5997			−0.464734
$624$		0			0
$625$	−0.639556			−0.0255823
$626$		0			0
$627$	−0.0624818	+	0.108222i	−0.00249528	+	0.00432196i
$628$		0			0
$629$		−	12.1913i		−	0.486099i
$630$		0			0
$631$	−40.1591	+	23.1859i	−1.59871	+	0.923014i	−0.606971	+	0.794724i	$0.707616\pi$
$631$	−40.1591	+	23.1859i	−1.59871	+	0.923014i	−0.991737	+	0.128290i	$0.959051\pi$
$632$		0			0
$633$	−5.88600	−	10.1949i	−0.233948	−	0.405209i
$634$		0			0
$635$	−67.7889	−	39.1379i	−2.69012	−	1.55314i
$636$		0			0
$637$	0.334629	+	3.58999i	0.0132585	+	0.142241i
$638$		0			0
$639$	−20.0066	−	11.5508i	−0.791451	−	0.456944i
$640$		0			0
$641$	3.77661	+	6.54128i	0.149167	+	0.258365i	0.930920	−	0.365223i	$-0.119007\pi$
$641$	3.77661	+	6.54128i	0.149167	+	0.258365i	−0.781753	+	0.623589i	$0.785674\pi$
$642$		0			0
$643$	22.0811	−	12.7485i	0.870795	−	0.502754i	0.00318261	−	0.999995i	$-0.498987\pi$
$643$	22.0811	−	12.7485i	0.870795	−	0.502754i	0.867612	+	0.497241i	$0.165654\pi$
$644$		0			0
$645$		−	3.48727i		−	0.137311i
$646$		0			0
$647$	−16.5563	+	28.6763i	−0.650894	+	1.12738i	0.332012	+	0.943275i	$0.392273\pi$
$647$	−16.5563	+	28.6763i	−0.650894	+	1.12738i	−0.982906	+	0.184107i	$0.941061\pi$
$648$		0			0
$649$	−6.66636			−0.261678
$650$		0			0
$651$	3.80124			0.148982
$652$		0			0
$653$	−3.94442	+	6.83194i	−0.154357	+	0.267355i	−0.932825	−	0.360330i	$-0.882664\pi$
$653$	−3.94442	+	6.83194i	−0.154357	+	0.267355i	0.778468	+	0.627685i	$0.215997\pi$
$654$		0			0
$655$			12.5272i			0.489480i
$656$		0			0
$657$	4.20932	−	2.43025i	0.164221	−	0.0948131i
$658$		0			0
$659$	14.3089	+	24.7837i	0.557394	+	0.965435i	0.997713	+	0.0675937i	$0.0215322\pi$
$659$	14.3089	+	24.7837i	0.557394	+	0.965435i	−0.440319	+	0.897842i	$0.645134\pi$
$660$		0			0
$661$	−28.0320	−	16.1843i	−1.09032	−	0.629495i	−0.156656	−	0.987653i	$-0.550071\pi$
$661$	−28.0320	−	16.1843i	−1.09032	−	0.629495i	−0.933661	+	0.358158i	$0.883405\pi$
$662$		0			0
$663$	4.60198	−	3.26143i	0.178726	−	0.126663i
$664$		0			0
$665$	−0.805499	−	0.465055i	−0.0312359	−	0.0180341i
$666$		0			0
$667$	−5.28480	−	9.15354i	−0.204628	−	0.354427i
$668$		0			0
$669$	−11.7256	+	6.76977i	−0.453337	+	0.261734i
$670$		0			0
$671$		−	9.08667i		−	0.350787i
$672$		0			0
$673$	9.24041	−	16.0049i	0.356192	−	0.616942i	−0.631130	−	0.775677i	$-0.717408\pi$
$673$	9.24041	−	16.0049i	0.356192	−	0.616942i	0.987321	+	0.158736i	$0.0507417\pi$
$674$		0			0
$675$	−24.4606			−0.941488
$676$		0			0
$677$	−14.2876			−0.549119			−0.274559	−	0.961570i	$-0.588532\pi$
$677$	−14.2876			−0.549119			−0.274559	+	0.961570i	$0.588532\pi$
$678$		0			0
$679$	−2.28814	+	3.96317i	−0.0878107	+	0.152093i
$680$		0			0
$681$			2.80248i			0.107391i
$682$		0			0
$683$	−24.5575	+	14.1783i	−0.939665	+	0.542516i	−0.889855	−	0.456243i	$-0.849195\pi$
$683$	−24.5575	+	14.1783i	−0.939665	+	0.542516i	−0.0498098	+	0.998759i	$0.515862\pi$
$684$		0			0
$685$	9.43332	+	16.3390i	0.360429	+	0.624281i
$686$		0			0
$687$	−3.42949	−	1.98002i	−0.130843	−	0.0755424i
$688$		0			0
$689$	20.7158	−	14.6813i	0.789211	−	0.559315i
$690$		0			0
$691$	5.84731	+	3.37595i	0.222442	+	0.128427i	0.607081	−	0.794640i	$-0.292341\pi$
$691$	5.84731	+	3.37595i	0.222442	+	0.128427i	−0.384638	+	0.923067i	$0.625674\pi$
$692$		0			0
$693$	1.23652	+	2.14171i	0.0469715	+	0.0813570i
$694$		0			0
$695$	−40.2574	+	23.2426i	−1.52705	+	0.881643i
$696$		0			0
$697$			23.2379i			0.880198i
$698$		0			0
$699$	−3.03729	+	5.26075i	−0.114881	+	0.198980i
$700$		0			0
$701$	−35.7504			−1.35028			−0.675138	−	0.737692i	$-0.735916\pi$
$701$	−35.7504			−1.35028			−0.675138	+	0.737692i	$0.735916\pi$
$702$		0			0
$703$	1.06960			0.0403407
$704$		0			0
$705$	0.735480	−	1.27389i	0.0276998	−	0.0479774i
$706$		0			0
$707$		−	1.90847i		−	0.0717755i
$708$		0			0
$709$	−31.4534	+	18.1597i	−1.18126	+	0.682000i	−0.956305	−	0.292369i	$-0.905556\pi$
$709$	−31.4534	+	18.1597i	−1.18126	+	0.682000i	−0.224954	+	0.974369i	$0.572223\pi$
$710$		0			0
$711$	−6.50593	−	11.2686i	−0.243991	−	0.422605i
$712$		0			0
$713$	29.7449	+	17.1732i	1.11396	+	0.643143i
$714$		0			0
$715$	1.09989	+	11.7999i	0.0411335	+	0.441290i
$716$		0			0
$717$	−7.55380	−	4.36119i	−0.282102	−	0.162872i
$718$		0			0
$719$	10.6885	+	18.5130i	0.398612	+	0.690417i	0.993555	−	0.113351i	$-0.0361585\pi$
$719$	10.6885	+	18.5130i	0.398612	+	0.690417i	−0.594942	+	0.803768i	$0.702825\pi$
$720$		0			0
$721$	−8.35895	+	4.82604i	−0.311304	+	0.179731i
$722$		0			0
$723$		−	2.77981i		−	0.103382i
$724$		0			0
$725$	8.81927	−	15.2754i	0.327540	−	0.567315i
$726$		0			0
$727$	−29.3652			−1.08909			−0.544547	−	0.838730i	$-0.683299\pi$
$727$	−29.3652			−1.08909			−0.544547	+	0.838730i	$0.683299\pi$
$728$		0			0
$729$	−12.8605			−0.476316
$730$		0			0
$731$	−2.66248	+	4.61155i	−0.0984754	+	0.170564i
$732$		0			0
$733$		−	29.0055i		−	1.07134i	−0.844426	−	0.535672i	$-0.820058\pi$
$733$		−	29.0055i		−	1.07134i	0.844426	−	0.535672i	$-0.179942\pi$
$734$		0			0
$735$	1.66551	−	0.961580i	0.0614331	−	0.0354684i
$736$		0			0
$737$	6.51485	+	11.2841i	0.239978	+	0.415654i
$738$		0			0
$739$	−12.7973	−	7.38854i	−0.470757	−	0.271792i	0.245800	−	0.969321i	$-0.420950\pi$
$739$	−12.7973	−	7.38854i	−0.470757	−	0.271792i	−0.716557	+	0.697529i	$0.754283\pi$
$740$		0			0
$741$	0.286140	+	0.403753i	0.0105116	+	0.0148322i
$742$		0			0
$743$	−15.4881	−	8.94208i	−0.568205	−	0.328053i	0.188227	−	0.982126i	$-0.439726\pi$
$743$	−15.4881	−	8.94208i	−0.568205	−	0.328053i	−0.756432	+	0.654072i	$0.773059\pi$
$744$		0			0
$745$	0.729490	+	1.26351i	0.0267264	+	0.0462915i
$746$		0			0
$747$	−33.2232	+	19.1814i	−1.21557	+	0.701811i
$748$		0			0
$749$		−	8.04832i		−	0.294079i
$750$		0			0
$751$	13.0547	−	22.6115i	0.476374	−	0.825104i	−0.523259	−	0.852173i	$-0.675284\pi$
$751$	13.0547	−	22.6115i	0.476374	−	0.825104i	0.999634	+	0.0270692i	$0.00861745\pi$
$752$		0			0
$753$	−5.87078			−0.213943
$754$		0			0
$755$	2.49312			0.0907338
$756$		0			0
$757$	7.59547	−	13.1557i	0.276062	−	0.478154i	−0.694340	−	0.719647i	$-0.744304\pi$
$757$	7.59547	−	13.1557i	0.276062	−	0.478154i	0.970403	+	0.241493i	$0.0776371\pi$
$758$		0			0
$759$		−	2.33465i		−	0.0847425i
$760$		0			0
$761$	7.17839	−	4.14445i	0.260216	−	0.150236i	−0.364217	−	0.931314i	$-0.618663\pi$
$761$	7.17839	−	4.14445i	0.260216	−	0.150236i	0.624433	+	0.781078i	$0.285330\pi$
$762$		0			0
$763$	−5.49808	−	9.52295i	−0.199044	−	0.344754i
$764$		0			0
$765$	24.9377	+	14.3978i	0.901626	+	0.520554i
$766$		0			0
$767$	−11.0208	+	23.9889i	−0.397940	+	0.866189i
$768$		0			0
$769$	20.0965	+	11.6027i	0.724699	+	0.418405i	0.816480	−	0.577374i	$-0.195923\pi$
$769$	20.0965	+	11.6027i	0.724699	+	0.418405i	−0.0917808	+	0.995779i	$0.529256\pi$
$770$		0			0
$771$	7.27742	+	12.6049i	0.262090	+	0.453953i
$772$		0			0
$773$	−30.8325	+	17.8012i	−1.10897	+	0.640263i	−0.938562	−	0.345111i	$-0.887841\pi$
$773$	−30.8325	+	17.8012i	−1.10897	+	0.640263i	−0.170407	+	0.985374i	$0.554508\pi$
$774$		0			0
$775$			57.3174i			2.05890i
$776$		0			0
$777$	−1.10579	+	1.91528i	−0.0396699	+	0.0687103i
$778$		0			0
$779$	−2.03877			−0.0730464
$780$		0			0
$781$	7.74369			0.277091
$782$		0			0
$783$	−3.34333	+	5.79082i	−0.119481	+	0.206947i
$784$		0			0
$785$			54.3624i			1.94028i
$786$		0			0
$787$	−11.3347	+	6.54411i	−0.404039	+	0.233272i	−0.688225	−	0.725497i	$-0.741610\pi$
$787$	−11.3347	+	6.54411i	−0.404039	+	0.233272i	0.284186	+	0.958769i	$0.408277\pi$
$788$		0			0
$789$	−1.35404	−	2.34526i	−0.0482051	−	0.0834936i
$790$		0			0
$791$	−9.00565	−	5.19941i	−0.320204	−	0.184870i
$792$		0			0
$793$	−32.6984	−	15.0221i	−1.16115	−	0.533450i
$794$		0			0
$795$	−11.7287	−	6.77156i	−0.415974	−	0.240162i
$796$		0			0
$797$	13.5036	+	23.3889i	0.478322	+	0.828478i	0.999691	−	0.0248533i	$-0.00791185\pi$
$797$	13.5036	+	23.3889i	0.478322	+	0.828478i	−0.521369	+	0.853331i	$0.674579\pi$
$798$		0			0
$799$	−1.94519	+	1.12306i	−0.0688159	+	0.0397309i
$800$		0			0
$801$			31.5073i			1.11326i
$802$		0			0
$803$	−0.814620	+	1.41096i	−0.0287473	+	0.0497918i
$804$		0			0
$805$	17.3769			0.612456
$806$		0			0
$807$	−5.73912			−0.202027
$808$		0			0
$809$	20.0830	−	34.7847i	0.706080	−	1.22297i	−0.260221	−	0.965549i	$-0.583795\pi$
$809$	20.0830	−	34.7847i	0.706080	−	1.22297i	0.966300	−	0.257417i	$-0.0828713\pi$
$810$		0			0
$811$		−	2.28814i		−	0.0803475i	−0.999193	−	0.0401738i	$-0.987209\pi$
$811$		−	2.28814i		−	0.0803475i	0.999193	−	0.0401738i	$-0.0127911\pi$
$812$		0			0
$813$	−9.17386	+	5.29653i	−0.321741	+	0.185757i
$814$		0			0
$815$	−9.88219	−	17.1164i	−0.346158	−	0.599563i
$816$		0			0
$817$	−0.404593	−	0.233592i	−0.0141549	−	0.00817234i
$818$		0			0
$819$	9.75116	−	0.908924i	0.340733	−	0.0317604i
$820$		0			0
$821$	−32.1548	−	18.5646i	−1.12221	−	0.647907i	−0.180245	−	0.983622i	$-0.557689\pi$
$821$	−32.1548	−	18.5646i	−1.12221	−	0.647907i	−0.941964	+	0.335714i	$0.891022\pi$
$822$		0			0
$823$	21.6549	+	37.5074i	0.754842	+	1.30743i	0.945453	+	0.325760i	$0.105620\pi$
$823$	21.6549	+	37.5074i	0.754842	+	1.30743i	−0.190610	+	0.981666i	$0.561047\pi$
$824$		0			0
$825$	3.37409	−	1.94803i	0.117471	−	0.0678218i
$826$		0			0
$827$			42.5097i			1.47821i	0.673591	+	0.739104i	$0.264751\pi$
$827$			42.5097i			1.47821i	−0.673591	+	0.739104i	$0.735249\pi$
$828$		0			0
$829$	13.2928	−	23.0238i	0.461678	−	0.799649i	−0.537367	−	0.843348i	$-0.680581\pi$
$829$	13.2928	−	23.0238i	0.461678	−	0.799649i	0.999045	+	0.0436993i	$0.0139143\pi$
$830$		0			0
$831$	11.1454			0.386630
$832$		0			0
$833$	−2.93661			−0.101748
$834$		0			0
$835$	23.7106	−	41.0679i	0.820538	−	1.42121i
$836$		0			0
$837$		−	21.7287i		−	0.751053i
$838$		0			0
$839$	−12.9346	+	7.46781i	−0.446553	+	0.257817i	−0.706373	−	0.707840i	$-0.749670\pi$
$839$	−12.9346	+	7.46781i	−0.446553	+	0.257817i	0.259820	+	0.965657i	$0.416337\pi$
$840$		0			0
$841$	12.0891	+	20.9390i	0.416866	+	0.722033i
$842$		0			0
$843$	−4.58367	−	2.64638i	−0.157870	−	0.0911463i
$844$		0			0
$845$	44.2801	+	15.5496i	1.52328	+	0.534924i
$846$		0			0
$847$	8.80838	+	5.08552i	0.302659	+	0.174740i
$848$		0			0
$849$	−2.97955	−	5.16073i	−0.102258	−	0.177116i
$850$		0			0
$851$	−17.3057	+	9.99146i	−0.593232	+	0.342503i
$852$		0			0
$853$		−	7.37904i		−	0.252653i	−0.991989	−	0.126327i	$-0.959681\pi$
$853$		−	7.37904i		−	0.252653i	0.991989	−	0.126327i	$-0.0403188\pi$
$854$		0			0
$855$	−1.26319	+	2.18790i	−0.0432001	+	0.0748247i
$856$		0			0
$857$	−43.4305			−1.48356			−0.741779	−	0.670644i	$-0.766018\pi$
$857$	−43.4305			−1.48356			−0.741779	+	0.670644i	$0.766018\pi$
$858$		0			0
$859$	57.0429			1.94628			0.973139	−	0.230220i	$-0.0739445\pi$
$859$	57.0429			1.94628			0.973139	+	0.230220i	$0.0739445\pi$
$860$		0			0
$861$	2.10775	−	3.65073i	0.0718319	−	0.124417i
$862$		0			0
$863$		−	15.2795i		−	0.520121i	−0.965592	−	0.260060i	$-0.916257\pi$
$863$		−	15.2795i		−	0.520121i	0.965592	−	0.260060i	$-0.0837425\pi$
$864$		0			0
$865$	−78.1316	+	45.1093i	−2.65655	+	1.53376i
$866$		0			0
$867$	−2.23111	−	3.86440i	−0.0757726	−	0.131242i
$868$		0			0
$869$	3.77723	+	2.18079i	0.128134	+	0.0739781i
$870$		0			0
$871$	51.3760	−	4.78885i	1.74081	−	0.162264i
$872$		0			0
$873$	10.7648	+	6.21506i	0.364333	+	0.210348i
$874$		0			0
$875$	5.47409	+	9.48140i	0.185058	+	0.320530i
$876$		0			0
$877$	−37.4073	+	21.5971i	−1.26315	+	0.729282i	−0.973684	−	0.227904i	$-0.926813\pi$
$877$	−37.4073	+	21.5971i	−1.26315	+	0.729282i	−0.289471	+	0.957187i	$0.593479\pi$
$878$		0			0
$879$		−	16.1455i		−	0.544574i
$880$		0			0
$881$	3.84139	−	6.65348i	0.129420	−	0.224161i	−0.794032	−	0.607876i	$-0.792022\pi$
$881$	3.84139	−	6.65348i	0.129420	−	0.224161i	0.923452	+	0.383714i	$0.125355\pi$
$882$		0			0
$883$	37.5753			1.26451			0.632254	−	0.774761i	$-0.282130\pi$
$883$	37.5753			1.26451			0.632254	+	0.774761i	$0.282130\pi$
$884$		0			0
$885$	14.0811			0.473332
$886$		0			0
$887$	−21.7098	+	37.6024i	−0.728943	+	1.26257i	0.228387	+	0.973570i	$0.426655\pi$
$887$	−21.7098	+	37.6024i	−0.728943	+	1.26257i	−0.957330	+	0.288996i	$0.906679\pi$
$888$		0			0
$889$		−	21.6826i		−	0.727210i
$890$		0			0
$891$	5.14604	−	2.97107i	0.172399	−	0.0995346i
$892$		0			0
$893$	−0.0985310	−	0.170661i	−0.00329721	−	0.00571094i
$894$		0			0
$895$	−51.7514	−	29.8787i	−1.72986	−	0.998734i
$896$		0			0
$897$	−8.40123	−	3.85965i	−0.280509	−	0.128870i
$898$		0			0
$899$	13.5694	+	7.83428i	0.452564	+	0.261288i
$900$		0			0
$901$	10.3400	+	17.9094i	0.344475	+	0.596647i
$902$		0			0
$903$	0.836564	−	0.482991i	0.0278391	−	0.0160729i
$904$		0			0
$905$			74.9102i			2.49010i
$906$		0			0
$907$	−27.4248	+	47.5011i	−0.910625	+	1.57725i	−0.0974426	+	0.995241i	$0.531066\pi$
$907$	−27.4248	+	47.5011i	−0.910625	+	1.57725i	−0.813183	+	0.582008i	$0.802267\pi$
$908$		0			0
$909$	−5.18381			−0.171936
$910$		0			0
$911$	52.4156			1.73660			0.868302	−	0.496035i	$-0.165211\pi$
$911$	52.4156			1.73660			0.868302	+	0.496035i	$0.165211\pi$
$912$		0			0
$913$	6.42961	−	11.1364i	0.212789	−	0.368561i
$914$		0			0
$915$			19.1934i			0.634516i
$916$		0			0
$917$	−3.00517	+	1.73504i	−0.0992395	+	0.0572960i
$918$		0			0
$919$	−9.59839	−	16.6249i	−0.316622	−	0.548405i	0.663159	−	0.748478i	$-0.269215\pi$
$919$	−9.59839	−	16.6249i	−0.316622	−	0.548405i	−0.979781	+	0.200074i	$0.935882\pi$
$920$		0			0
$921$	15.8323	+	9.14076i	0.521691	+	0.301198i
$922$		0			0
$923$	12.8019	−	27.8656i	0.421379	−	0.917209i
$924$		0			0
$925$	−28.8798	−	16.6737i	−0.949561	−	0.548229i
$926$		0			0
$927$	13.1085	+	22.7047i	0.430541	+	0.745719i
$928$		0			0
$929$	11.0196	−	6.36218i	0.361542	−	0.208736i	−0.308215	−	0.951317i	$-0.599732\pi$
$929$	11.0196	−	6.36218i	0.361542	−	0.208736i	0.669757	+	0.742580i	$0.266398\pi$
$930$		0			0
$931$		−	0.257642i		−	0.00844389i
$932$		0			0
$933$	7.97526	−	13.8136i	0.261098	−	0.452235i
$934$		0			0
$935$	−9.65229			−0.315664
$936$		0			0
$937$	0.0926021			0.00302518			0.00151259	−	0.999999i	$-0.499519\pi$
$937$	0.0926021			0.00302518			0.00151259	+	0.999999i	$0.499519\pi$
$938$		0			0
$939$	−4.07931	+	7.06557i	−0.133123	+	0.230576i
$940$		0			0
$941$		−	5.26900i		−	0.171765i	−0.996305	−	0.0858823i	$-0.972629\pi$
$941$		−	5.26900i		−	0.171765i	0.996305	−	0.0858823i	$-0.0273709\pi$
$942$		0			0
$943$	32.9865	−	19.0448i	1.07419	−	0.620184i
$944$		0			0
$945$	−5.49659	−	9.52038i	−0.178804	−	0.309698i
$946$		0			0
$947$	35.2974	+	20.3790i	1.14701	+	0.662228i	0.948158	−	0.317801i	$-0.102944\pi$
$947$	35.2974	+	20.3790i	1.14701	+	0.662228i	0.198855	+	0.980029i	$0.436278\pi$
$948$		0			0
$949$	3.73062	+	5.26402i	0.121101	+	0.170877i
$950$		0			0
$951$	−8.46797	−	4.88899i	−0.274593	−	0.158536i
$952$		0			0
$953$	−8.14075	−	14.1002i	−0.263705	−	0.456750i	0.703519	−	0.710677i	$-0.251611\pi$
$953$	−8.14075	−	14.1002i	−0.263705	−	0.456750i	−0.967223	+	0.253927i	$0.918278\pi$
$954$		0			0
$955$	−58.9854	+	34.0552i	−1.90872	+	1.10200i
$956$		0			0
$957$		−	1.06505i		−	0.0344281i
$958$		0			0
$959$	−2.61305	+	4.52594i	−0.0843799	+	0.146150i
$960$		0			0
$961$	−19.9158			−0.642446
$962$		0			0
$963$	−21.8609			−0.704459
$964$		0			0
$965$	15.9787	−	27.6760i	0.514374	−	0.890922i
$966$		0			0
$967$			8.98682i			0.288997i	0.989505	+	0.144498i	$0.0461568\pi$
$967$			8.98682i			0.288997i	−0.989505	+	0.144498i	$0.953843\pi$
$968$		0			0
$969$	−0.349054	+	0.201527i	−0.0112132	+	0.00647397i
$970$		0			0
$971$	−16.7196	−	28.9592i	−0.536557	−	0.929345i	−0.999086	−	0.0427404i	$-0.986391\pi$
$971$	−16.7196	−	28.9592i	−0.536557	−	0.929345i	0.462529	−	0.886604i	$-0.346942\pi$
$972$		0			0
$973$	−11.1514	−	6.43826i	−0.357497	−	0.206401i
$974$		0			0
$975$	−1.43193	−	15.3621i	−0.0458586	−	0.491982i
$976$		0			0
$977$	3.81934	+	2.20510i	0.122192	+	0.0705473i	0.559850	−	0.828594i	$-0.310859\pi$
$977$	3.81934	+	2.20510i	0.122192	+	0.0705473i	−0.437658	+	0.899141i	$0.644192\pi$
$978$		0			0
$979$	−5.28063	−	9.14632i	−0.168770	−	0.292318i
$980$		0			0
$981$	−25.8663	+	14.9339i	−0.825848	+	0.476804i
$982$		0			0
$983$			9.75675i			0.311192i	0.987821	+	0.155596i	$0.0497298\pi$
$983$			9.75675i			0.311192i	−0.987821	+	0.155596i	$0.950270\pi$
$984$		0			0
$985$	−9.29733	+	16.1035i	−0.296238	+	0.513099i
$986$		0			0
$987$	0.407459			0.0129696
$988$		0			0
$989$	8.72822			0.277541
$990$		0			0
$991$	26.2747	−	45.5091i	0.834643	−	1.44564i	−0.0596771	−	0.998218i	$-0.519007\pi$
$991$	26.2747	−	45.5091i	0.834643	−	1.44564i	0.894320	−	0.447427i	$-0.147660\pi$
$992$		0			0
$993$		−	14.4615i		−	0.458922i
$994$		0			0
$995$	26.9425	−	15.5552i	0.854133	−	0.493134i
$996$		0			0
$997$	−23.3898	−	40.5123i	−0.740761	−	1.28304i	−0.952149	−	0.305634i	$-0.901132\pi$
$997$	−23.3898	−	40.5123i	−0.740761	−	1.28304i	0.211388	−	0.977402i	$-0.432202\pi$
$998$		0			0
$999$	10.9482	+	6.32092i	0.346384	+	0.199985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.g.225.7		24
4.3	odd	2		728.2.bm.c.225.6	✓	24
13.10	even	6	inner	1456.2.cc.g.673.7		24
52.7	even	12		9464.2.a.bm.1.7		12
52.19	even	12		9464.2.a.bl.1.7		12
52.23	odd	6		728.2.bm.c.673.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.6	✓	24	4.3	odd	2
728.2.bm.c.673.6	yes	24	52.23	odd	6
1456.2.cc.g.225.7		24	1.1	even	1	trivial
1456.2.cc.g.673.7		24	13.10	even	6	inner
9464.2.a.bl.1.7		12	52.19	even	12
9464.2.a.bm.1.7		12	52.7	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)

\(f(q)\)	\(=\)	\(q+(0.266360 - 0.461349i) q^{3} +3.61008i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.35810 + 2.35231i) q^{9} +(-0.788493 - 0.455237i) q^{11} +(-2.94171 + 2.08479i) q^{13} +(1.66551 + 0.961580i) q^{15} +(-1.46831 - 2.54318i) q^{17} +(0.223125 - 0.128821i) q^{19} +0.532720i q^{21} +(-2.40672 + 4.16856i) q^{23} -8.03267 q^{25} +3.04514 q^{27} +(-1.09793 + 1.90166i) q^{29} -7.13553i q^{31} +(-0.420046 + 0.242514i) q^{33} +(-1.80504 - 3.12642i) q^{35} +(3.59529 + 2.07574i) q^{37} +(0.178264 + 1.91246i) q^{39} +(-6.85301 - 3.95658i) q^{41} +(-0.906650 - 1.57036i) q^{43} +(-8.49201 + 4.90287i) q^{45} -0.764866i q^{47} +(0.500000 - 0.866025i) q^{49} -1.56439 q^{51} -7.04212 q^{53} +(1.64344 - 2.84652i) q^{55} -0.137251i q^{57} +(6.34092 - 3.66093i) q^{59} +(4.99008 + 8.64307i) q^{61} +(-2.35231 - 1.35810i) q^{63} +(-7.52626 - 10.6198i) q^{65} +(-12.3936 - 7.15546i) q^{67} +(1.28211 + 2.22068i) q^{69} +(-7.36565 + 4.25256i) q^{71} -1.78944i q^{73} +(-2.13958 + 3.70586i) q^{75} +0.910474 q^{77} -4.79045 q^{79} +(-3.26321 + 5.65205i) q^{81} +14.1237i q^{83} +(9.18108 - 5.30070i) q^{85} +(0.584886 + 1.01305i) q^{87} +(10.0457 + 5.79987i) q^{89} +(1.50520 - 3.27634i) q^{91} +(-3.29197 - 1.90062i) q^{93} +(0.465055 + 0.805499i) q^{95} +(3.96317 - 2.28814i) q^{97} -2.47304i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) \) 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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