LMFDB - Embedded newform 1680.2.bl.c.127.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(127,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$1.41127 - 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	1680.127
Dual form			1680.2.bl.c.463.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(1.32001 - 1.80487i) q^{5} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{9} +2.82843i q^{11} +(3.12489 - 3.12489i) q^{13} +(-2.20963 + 0.342849i) q^{15} +(-5.76491 - 5.76491i) q^{17} +5.83347 q^{19} -1.00000 q^{21} +(4.87182 + 4.87182i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(0.707107 - 0.707107i) q^{27} +1.03028i q^{29} -1.63365i q^{31} +(2.00000 - 2.00000i) q^{33} +(-0.342849 - 2.20963i) q^{35} +(1.00000 + 1.00000i) q^{37} -4.41926 q^{39} +4.57947 q^{41} +(-6.56198 - 6.56198i) q^{43} +(1.80487 + 1.32001i) q^{45} +(3.73356 - 3.73356i) q^{47} -1.00000i q^{49} +8.15281i q^{51} +(-0.155162 + 0.155162i) q^{53} +(5.10495 + 3.73356i) q^{55} +(-4.12489 - 4.12489i) q^{57} +1.45703 q^{59} -6.31032 q^{61} +(0.707107 + 0.707107i) q^{63} +(-1.51514 - 9.76491i) q^{65} +(-3.73356 + 3.73356i) q^{67} -6.88979i q^{69} +8.01901i q^{71} +(8.09461 - 8.09461i) q^{73} +(-2.29793 + 4.44066i) q^{75} +(2.00000 + 2.00000i) q^{77} -1.45703 q^{79} -1.00000 q^{81} +(-7.93338 - 7.93338i) q^{83} +(-18.0147 + 2.79518i) q^{85} +(0.728515 - 0.728515i) q^{87} -3.92007i q^{89} -4.41926i q^{91} +(-1.15516 + 1.15516i) q^{93} +(7.70025 - 10.5287i) q^{95} +(-0.155162 - 0.155162i) q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{13} - 4 q^{17} - 12 q^{21} - 20 q^{25} + 24 q^{33} + 12 q^{37} + 16 q^{41} + 4 q^{45} + 28 q^{53} - 16 q^{57} - 16 q^{61} - 20 q^{65} + 60 q^{73} + 24 q^{77} - 12 q^{81} - 84 q^{85} + 16 q^{93}+ \cdots + 28 q^{97}+O(q^{100}) $ 12 * q + 4 * q^13 - 4 * q^17 - 12 * q^21 - 20 * q^25 + 24 * q^33 + 12 * q^37 + 16 * q^41 + 4 * q^45 + 28 * q^53 - 16 * q^57 - 16 * q^61 - 20 * q^65 + 60 * q^73 + 24 * q^77 - 12 * q^81 - 84 * q^85 + 16 * q^93 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.32001	−	1.80487i	0.590327	−	0.807164i
$5$	1.32001	−	1.80487i	0.590327	−	0.807164i
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	−0.125417	−	0.992104i	$-0.540027\pi$
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	0.992104	+	0.125417i	$0.0400268\pi$
$14$		0			0
$15$	−2.20963	+	0.342849i	−0.570523	+	0.0885233i
$16$		0			0
$17$	−5.76491	−	5.76491i	−1.39820	−	1.39820i	−0.805221	−	0.592975i	$-0.797953\pi$
$17$	−5.76491	−	5.76491i	−1.39820	−	1.39820i	−0.592975	−	0.805221i	$-0.702047\pi$
$18$		0			0
$19$	5.83347			1.33829			0.669145	−	0.743132i	$-0.266661\pi$
$19$	5.83347			1.33829			0.669145	+	0.743132i	$0.266661\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	4.87182	+	4.87182i	1.01584	+	1.01584i	0.999872	+	0.0159723i	$0.00508436\pi$
$23$	4.87182	+	4.87182i	1.01584	+	1.01584i	0.0159723	+	0.999872i	$0.494916\pi$
$24$		0			0
$25$	−1.51514	−	4.76491i	−0.303028	−	0.952982i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			1.03028i			0.191317i	0.995414	+	0.0956587i	$0.0304958\pi$
$29$			1.03028i			0.191317i	−0.995414	+	0.0956587i	$0.969504\pi$
$30$		0			0
$31$		−	1.63365i		−	0.293411i	−0.989180	−	0.146706i	$-0.953133\pi$
$31$		−	1.63365i		−	0.293411i	0.989180	−	0.146706i	$-0.0468670\pi$
$32$		0			0
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		0			0
$35$	−0.342849	−	2.20963i	−0.0579521	−	0.373495i
$36$		0			0
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	0.784512	−	0.620113i	$-0.212913\pi$
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	−0.620113	+	0.784512i	$0.712913\pi$
$38$		0			0
$39$	−4.41926			−0.707647
$40$		0			0
$41$	4.57947			0.715193			0.357597	−	0.933876i	$-0.383596\pi$
$41$	4.57947			0.715193			0.357597	+	0.933876i	$0.383596\pi$
$42$		0			0
$43$	−6.56198	−	6.56198i	−1.00069	−	1.00069i	−1.00000		0.000693437i	$-0.999779\pi$
$43$	−6.56198	−	6.56198i	−1.00069	−	1.00069i	−0.000693437	−	1.00000i	$-0.500221\pi$
$44$		0			0
$45$	1.80487	+	1.32001i	0.269055	+	0.196776i
$46$		0			0
$47$	3.73356	−	3.73356i	0.544595	−	0.544595i	−0.380277	−	0.924873i	$-0.624171\pi$
$47$	3.73356	−	3.73356i	0.544595	−	0.544595i	0.924873	+	0.380277i	$0.124171\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$			8.15281i			1.14162i
$52$		0			0
$53$	−0.155162	+	0.155162i	−0.0213131	+	0.0213131i	−0.717683	−	0.696370i	$-0.754797\pi$
$53$	−0.155162	+	0.155162i	−0.0213131	+	0.0213131i	0.696370	+	0.717683i	$0.254797\pi$
$54$		0			0
$55$	5.10495	+	3.73356i	0.688352	+	0.503433i
$56$		0			0
$57$	−4.12489	−	4.12489i	−0.546354	−	0.546354i
$58$		0			0
$59$	1.45703			0.189689			0.0948446	−	0.995492i	$-0.469765\pi$
$59$	1.45703			0.189689			0.0948446	+	0.995492i	$0.469765\pi$
$60$		0			0
$61$	−6.31032			−0.807954			−0.403977	−	0.914769i	$-0.632372\pi$
$61$	−6.31032			−0.807954			−0.403977	+	0.914769i	$0.632372\pi$
$62$		0			0
$63$	0.707107	+	0.707107i	0.0890871	+	0.0890871i
$64$		0			0
$65$	−1.51514	−	9.76491i	−0.187930	−	1.21119i
$66$		0			0
$67$	−3.73356	+	3.73356i	−0.456127	+	0.456127i	−0.897382	−	0.441255i	$-0.854533\pi$
$67$	−3.73356	+	3.73356i	−0.456127	+	0.456127i	0.441255	+	0.897382i	$0.354533\pi$
$68$		0			0
$69$		−	6.88979i		−	0.829434i
$70$		0			0
$71$			8.01901i			0.951682i	0.879531	+	0.475841i	$0.157856\pi$
$71$			8.01901i			0.951682i	−0.879531	+	0.475841i	$0.842144\pi$
$72$		0			0
$73$	8.09461	−	8.09461i	0.947402	−	0.947402i	−0.0512819	−	0.998684i	$-0.516331\pi$
$73$	8.09461	−	8.09461i	0.947402	−	0.947402i	0.998684	+	0.0512819i	$0.0163307\pi$
$74$		0			0
$75$	−2.29793	+	4.44066i	−0.265343	+	0.512764i
$76$		0			0
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$	−1.45703			−0.163929			−0.0819644	−	0.996635i	$-0.526119\pi$
$79$	−1.45703			−0.163929			−0.0819644	+	0.996635i	$0.526119\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.93338	−	7.93338i	−0.870802	−	0.870802i	0.121758	−	0.992560i	$-0.461147\pi$
$83$	−7.93338	−	7.93338i	−0.870802	−	0.870802i	−0.992560	+	0.121758i	$0.961147\pi$
$84$		0			0
$85$	−18.0147	+	2.79518i	−1.95397	+	0.303180i
$86$		0			0
$87$	0.728515	−	0.728515i	0.0781050	−	0.0781050i
$88$		0			0
$89$		−	3.92007i		−	0.415527i	−0.978179	−	0.207763i	$-0.933382\pi$
$89$		−	3.92007i		−	0.415527i	0.978179	−	0.207763i	$-0.0666184\pi$
$90$		0			0
$91$		−	4.41926i		−	0.463264i
$92$		0			0
$93$	−1.15516	+	1.15516i	−0.119785	+	0.119785i
$94$		0			0
$95$	7.70025	−	10.5287i	0.790029	−	1.08022i
$96$		0			0
$97$	−0.155162	−	0.155162i	−0.0157543	−	0.0157543i	0.699186	−	0.714940i	$-0.253546\pi$
$97$	−0.155162	−	0.155162i	−0.0157543	−	0.0157543i	−0.714940	+	0.699186i	$0.753546\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$		0			0
$101$	−11.6097			−1.15521			−0.577607	−	0.816315i	$-0.696013\pi$
$101$	−11.6097			−1.15521			−0.577607	+	0.816315i	$0.696013\pi$
$102$		0			0
$103$	−10.4722	−	10.4722i	−1.03185	−	1.03185i	−0.999476	−	0.0323764i	$-0.989692\pi$
$103$	−10.4722	−	10.4722i	−1.03185	−	1.03185i	−0.0323764	−	0.999476i	$-0.510308\pi$
$104$		0			0
$105$	−1.32001	+	1.80487i	−0.128820	+	0.176138i
$106$		0			0
$107$	−10.5287	+	10.5287i	−1.01785	+	1.01785i	−0.0180075	+	0.999838i	$0.505732\pi$
$107$	−10.5287	+	10.5287i	−1.01785	+	1.01785i	−0.999838	+	0.0180075i	$0.994268\pi$
$108$		0			0
$109$		−	13.4693i		−	1.29012i	−0.764131	−	0.645061i	$-0.776832\pi$
$109$		−	13.4693i		−	1.29012i	0.764131	−	0.645061i	$-0.223168\pi$
$110$		0			0
$111$		−	1.41421i		−	0.134231i
$112$		0			0
$113$	7.12489	−	7.12489i	0.670253	−	0.670253i	−0.287521	−	0.957774i	$-0.592831\pi$
$113$	7.12489	−	7.12489i	0.670253	−	0.670253i	0.957774	+	0.287521i	$0.0928312\pi$
$114$		0			0
$115$	15.2239	−	2.36216i	1.41963	−	0.220273i
$116$		0			0
$117$	3.12489	+	3.12489i	0.288896	+	0.288896i
$118$		0			0
$119$	−8.15281			−0.747367
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$	−3.23818	−	3.23818i	−0.291976	−	0.291976i
$124$		0			0
$125$	−10.6001	−	3.55510i	−0.948098	−	0.317978i
$126$		0			0
$127$	13.0383	−	13.0383i	1.15697	−	1.15697i	0.171840	−	0.985125i	$-0.445029\pi$
$127$	13.0383	−	13.0383i	1.15697	−	1.15697i	0.985125	−	0.171840i	$-0.0549713\pi$
$128$		0			0
$129$			9.28005i			0.817063i
$130$		0			0
$131$			4.19982i			0.366940i	0.983025	+	0.183470i	$0.0587331\pi$
$131$			4.19982i			0.366940i	−0.983025	+	0.183470i	$0.941267\pi$
$132$		0			0
$133$	4.12489	−	4.12489i	0.357673	−	0.357673i
$134$		0			0
$135$	−0.342849	−	2.20963i	−0.0295078	−	0.190174i
$136$		0			0
$137$	13.3747	+	13.3747i	1.14267	+	1.14267i	0.987959	+	0.154715i	$0.0494459\pi$
$137$	13.3747	+	13.3747i	1.14267	+	1.14267i	0.154715	+	0.987959i	$0.450554\pi$
$138$		0			0
$139$	−1.28042			−0.108603			−0.0543017	−	0.998525i	$-0.517293\pi$
$139$	−1.28042			−0.108603			−0.0543017	+	0.998525i	$0.517293\pi$
$140$		0			0
$141$	−5.28005			−0.444660
$142$		0			0
$143$	8.83851	+	8.83851i	0.739113	+	0.739113i
$144$		0			0
$145$	1.85952	+	1.35998i	0.154425	+	0.112940i
$146$		0			0
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$		0			0
$149$		−	2.49954i		−	0.204770i	−0.994745	−	0.102385i	$-0.967353\pi$
$149$		−	2.49954i		−	0.204770i	0.994745	−	0.102385i	$-0.0326474\pi$
$150$		0			0
$151$		−	23.6871i		−	1.92763i	−0.266573	−	0.963815i	$-0.585891\pi$
$151$		−	23.6871i		−	1.92763i	0.266573	−	0.963815i	$-0.414109\pi$
$152$		0			0
$153$	5.76491	−	5.76491i	0.466065	−	0.466065i
$154$		0			0
$155$	−2.94852	−	2.15643i	−0.236831	−	0.173209i
$156$		0			0
$157$	3.90539	+	3.90539i	0.311684	+	0.311684i	0.845562	−	0.533878i	$-0.179266\pi$
$157$	3.90539	+	3.90539i	0.311684	+	0.311684i	−0.533878	+	0.845562i	$0.679266\pi$
$158$		0			0
$159$	0.219432			0.0174021
$160$		0			0
$161$	6.88979			0.542992
$162$		0			0
$163$	14.8486	+	14.8486i	1.16303	+	1.16303i	0.983808	+	0.179223i	$0.0573584\pi$
$163$	14.8486	+	14.8486i	1.16303	+	1.16303i	0.179223	+	0.983808i	$0.442642\pi$
$164$		0			0
$165$	−0.969724	−	6.24977i	−0.0754929	−	0.486544i
$166$		0			0
$167$	−16.3056	+	16.3056i	−1.26177	+	1.26177i	−0.311531	+	0.950236i	$0.600842\pi$
$167$	−16.3056	+	16.3056i	−1.26177	+	1.26177i	−0.950236	+	0.311531i	$0.899158\pi$
$168$		0			0
$169$		−	6.52982i		−	0.502294i
$170$		0			0
$171$			5.83347i			0.446097i
$172$		0			0
$173$	13.7649	−	13.7649i	1.04653	−	1.04653i	0.0476632	−	0.998863i	$-0.484823\pi$
$173$	13.7649	−	13.7649i	1.04653	−	1.04653i	0.998863	−	0.0476632i	$-0.0151774\pi$
$174$		0			0
$175$	−4.44066	−	2.29793i	−0.335683	−	0.173708i
$176$		0			0
$177$	−1.03028	−	1.03028i	−0.0774403	−	0.0774403i
$178$		0			0
$179$	−6.91521			−0.516867			−0.258434	−	0.966029i	$-0.583206\pi$
$179$	−6.91521			−0.516867			−0.258434	+	0.966029i	$0.583206\pi$
$180$		0			0
$181$	5.34060			0.396964			0.198482	−	0.980105i	$-0.436399\pi$
$181$	5.34060			0.396964			0.198482	+	0.980105i	$0.436399\pi$
$182$		0			0
$183$	4.46207	+	4.46207i	0.329846	+	0.329846i
$184$		0			0
$185$	3.12489	−	0.484862i	0.229746	−	0.0356478i
$186$		0			0
$187$	16.3056	−	16.3056i	1.19239	−	1.19239i
$188$		0			0
$189$		−	1.00000i		−	0.0727393i
$190$		0			0
$191$			7.38148i			0.534105i	0.963682	+	0.267053i	$0.0860497\pi$
$191$			7.38148i			0.534105i	−0.963682	+	0.267053i	$0.913950\pi$
$192$		0			0
$193$	−0.219495	+	0.219495i	−0.0157996	+	0.0157996i	−0.714962	−	0.699163i	$-0.753556\pi$
$193$	−0.219495	+	0.219495i	−0.0157996	+	0.0157996i	0.699163	+	0.714962i	$0.253556\pi$
$194$		0			0
$195$	−5.83347	+	7.97620i	−0.417743	+	0.571187i
$196$		0			0
$197$	−2.34438	−	2.34438i	−0.167030	−	0.167030i	0.618642	−	0.785673i	$-0.287683\pi$
$197$	−2.34438	−	2.34438i	−0.167030	−	0.167030i	−0.785673	+	0.618642i	$0.787683\pi$
$198$		0			0
$199$	12.1968			0.864607			0.432303	−	0.901728i	$-0.357701\pi$
$199$	12.1968			0.864607			0.432303	+	0.901728i	$0.357701\pi$
$200$		0			0
$201$	5.28005			0.372426
$202$		0			0
$203$	0.728515	+	0.728515i	0.0511317	+	0.0511317i
$204$		0			0
$205$	6.04496	−	8.26537i	0.422198	−	0.577278i
$206$		0			0
$207$	−4.87182	+	4.87182i	−0.338615	+	0.338615i
$208$		0			0
$209$			16.4995i			1.14130i
$210$		0			0
$211$			5.65685i			0.389434i	0.980859	+	0.194717i	$0.0623788\pi$
$211$			5.65685i			0.389434i	−0.980859	+	0.194717i	$0.937621\pi$
$212$		0			0
$213$	5.67030	−	5.67030i	0.388523	−	0.388523i
$214$		0			0
$215$	−20.5054	+	3.18166i	−1.39846	+	0.216987i
$216$		0			0
$217$	−1.15516	−	1.15516i	−0.0784175	−	0.0784175i
$218$		0			0
$219$	−11.4475			−0.773551
$220$		0			0
$221$	−36.0294			−2.42360
$222$		0			0
$223$	−1.98687	−	1.98687i	−0.133051	−	0.133051i	0.637445	−	0.770496i	$-0.279991\pi$
$223$	−1.98687	−	1.98687i	−0.133051	−	0.133051i	−0.770496	+	0.637445i	$0.779991\pi$
$224$		0			0
$225$	4.76491	−	1.51514i	0.317661	−	0.101009i
$226$		0			0
$227$	−2.74279	+	2.74279i	−0.182046	+	0.182046i	−0.792247	−	0.610201i	$-0.791089\pi$
$227$	−2.74279	+	2.74279i	−0.182046	+	0.182046i	0.610201	+	0.792247i	$0.291089\pi$
$228$		0			0
$229$			17.5298i			1.15840i	0.815184	+	0.579201i	$0.196636\pi$
$229$			17.5298i			1.15840i	−0.815184	+	0.579201i	$0.803364\pi$
$230$		0			0
$231$		−	2.82843i		−	0.186097i
$232$		0			0
$233$	12.6547	−	12.6547i	0.829037	−	0.829037i	−0.158346	−	0.987384i	$-0.550616\pi$
$233$	12.6547	−	12.6547i	0.829037	−	0.829037i	0.987384	+	0.158346i	$0.0506163\pi$
$234$		0			0
$235$	−1.81026	−	11.6669i	−0.118088	−	0.761067i
$236$		0			0
$237$	1.03028	+	1.03028i	0.0669236	+	0.0669236i
$238$		0			0
$239$	−18.6952			−1.20929			−0.604646	−	0.796495i	$-0.706685\pi$
$239$	−18.6952			−1.20929			−0.604646	+	0.796495i	$0.706685\pi$
$240$		0			0
$241$	−13.0303			−0.839354			−0.419677	−	0.907674i	$-0.637857\pi$
$241$	−13.0303			−0.839354			−0.419677	+	0.907674i	$0.637857\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.80487	−	1.32001i	−0.115309	−	0.0843325i
$246$		0			0
$247$	18.2289	−	18.2289i	1.15988	−	1.15988i
$248$		0			0
$249$			11.2195i			0.711007i
$250$		0			0
$251$		−	8.75288i		−	0.552477i	−0.961089	−	0.276238i	$-0.910912\pi$
$251$		−	8.75288i		−	0.552477i	0.961089	−	0.276238i	$-0.0890879\pi$
$252$		0			0
$253$	−13.7796	+	13.7796i	−0.866315	+	0.866315i
$254$		0			0
$255$	14.7148	+	10.7618i	0.921476	+	0.673931i
$256$		0			0
$257$	9.37466	+	9.37466i	0.584775	+	0.584775i	0.936212	−	0.351437i	$-0.114307\pi$
$257$	9.37466	+	9.37466i	0.584775	+	0.584775i	−0.351437	+	0.936212i	$0.614307\pi$
$258$		0			0
$259$	1.41421			0.0878750
$260$		0			0
$261$	−1.03028			−0.0637725
$262$		0			0
$263$	−13.3571	−	13.3571i	−0.823634	−	0.823634i	0.162993	−	0.986627i	$-0.447885\pi$
$263$	−13.3571	−	13.3571i	−0.823634	−	0.823634i	−0.986627	+	0.162993i	$0.947885\pi$
$264$		0			0
$265$	0.0752319	+	0.484862i	0.00462146	+	0.0297848i
$266$		0			0
$267$	−2.77191	+	2.77191i	−0.169638	+	0.169638i
$268$		0			0
$269$			22.6694i			1.38218i	0.722770	+	0.691088i	$0.242868\pi$
$269$			22.6694i			1.38218i	−0.722770	+	0.691088i	$0.757132\pi$
$270$		0			0
$271$			19.6639i			1.19450i	0.802056	+	0.597248i	$0.203739\pi$
$271$			19.6639i			1.19450i	−0.802056	+	0.597248i	$0.796261\pi$
$272$		0			0
$273$	−3.12489	+	3.12489i	−0.189127	+	0.189127i
$274$		0			0
$275$	13.4772	−	4.28546i	0.812706	−	0.258423i
$276$		0			0
$277$	8.03028	+	8.03028i	0.482493	+	0.482493i	0.905927	−	0.423434i	$-0.139176\pi$
$277$	8.03028	+	8.03028i	0.482493	+	0.482493i	−0.423434	+	0.905927i	$0.639176\pi$
$278$		0			0
$279$	1.63365			0.0978038
$280$		0			0
$281$	−2.96972			−0.177159			−0.0885794	−	0.996069i	$-0.528233\pi$
$281$	−2.96972			−0.177159			−0.0885794	+	0.996069i	$0.528233\pi$
$282$		0			0
$283$	22.0535	+	22.0535i	1.31094	+	1.31094i	0.920721	+	0.390221i	$0.127601\pi$
$283$	22.0535	+	22.0535i	1.31094	+	1.31094i	0.390221	+	0.920721i	$0.372399\pi$
$284$		0			0
$285$	−12.8898	+	2.00000i	−0.763526	+	0.118470i
$286$		0			0
$287$	3.23818	−	3.23818i	0.191143	−	0.191143i
$288$		0			0
$289$			49.4683i			2.90990i
$290$		0			0
$291$			0.219432i			0.0128633i
$292$		0			0
$293$	−12.9045	+	12.9045i	−0.753887	+	0.753887i	−0.975202	−	0.221315i	$-0.928965\pi$
$293$	−12.9045	+	12.9045i	−0.753887	+	0.753887i	0.221315	+	0.975202i	$0.428965\pi$
$294$		0			0
$295$	1.92330	−	2.62976i	0.111979	−	0.153110i
$296$		0			0
$297$	2.00000	+	2.00000i	0.116052	+	0.116052i
$298$		0			0
$299$	30.4478			1.76084
$300$		0			0
$301$	−9.28005			−0.534893
$302$		0			0
$303$	8.20933	+	8.20933i	0.471614	+	0.471614i
$304$		0			0
$305$	−8.32970	+	11.3893i	−0.476957	+	0.652151i
$306$		0			0
$307$	6.01008	−	6.01008i	0.343014	−	0.343014i	−0.514485	−	0.857499i	$-0.672017\pi$
$307$	6.01008	−	6.01008i	0.343014	−	0.343014i	0.857499	+	0.514485i	$0.172017\pi$
$308$		0			0
$309$			14.8099i			0.842504i
$310$		0			0
$311$			30.2765i			1.71682i	0.512962	+	0.858411i	$0.328548\pi$
$311$			30.2765i			1.71682i	−0.512962	+	0.858411i	$0.671452\pi$
$312$		0			0
$313$	19.1249	−	19.1249i	1.08100	−	1.08100i	0.0845863	−	0.996416i	$-0.473043\pi$
$313$	19.1249	−	19.1249i	1.08100	−	1.08100i	0.996416	−	0.0845863i	$-0.0269569\pi$
$314$		0			0
$315$	2.20963	−	0.342849i	0.124498	−	0.0193174i
$316$		0			0
$317$	6.87511	+	6.87511i	0.386145	+	0.386145i	0.873310	−	0.487165i	$-0.161969\pi$
$317$	6.87511	+	6.87511i	0.386145	+	0.386145i	−0.487165	+	0.873310i	$0.661969\pi$
$318$		0			0
$319$	−2.91406			−0.163156
$320$		0			0
$321$	14.8898			0.831067
$322$		0			0
$323$	−33.6294	−	33.6294i	−1.87119	−	1.87119i
$324$		0			0
$325$	−19.6244	−	10.1552i	−1.08857	−	0.563307i
$326$		0			0
$327$	−9.52421	+	9.52421i	−0.526690	+	0.526690i
$328$		0			0
$329$		−	5.28005i		−	0.291098i
$330$		0			0
$331$			0.932534i			0.0512567i	0.999672	+	0.0256283i	$0.00815865\pi$
$331$			0.932534i			0.0512567i	−0.999672	+	0.0256283i	$0.991841\pi$
$332$		0			0
$333$	−1.00000	+	1.00000i	−0.0547997	+	0.0547997i
$334$		0			0
$335$	1.81026	+	11.6669i	0.0989051	+	0.637433i
$336$		0			0
$337$	19.0294	+	19.0294i	1.03660	+	1.03660i	0.999304	+	0.0372908i	$0.0118728\pi$
$337$	19.0294	+	19.0294i	1.03660	+	1.03660i	0.0372908	+	0.999304i	$0.488127\pi$
$338$		0			0
$339$	−10.0761			−0.547259
$340$		0			0
$341$	4.62065			0.250222
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	−12.4352	−	9.09461i	−0.669489	−	0.489637i
$346$		0			0
$347$	−5.42372	+	5.42372i	−0.291161	+	0.291161i	−0.837539	−	0.546378i	$-0.816006\pi$
$347$	−5.42372	+	5.42372i	−0.291161	+	0.291161i	0.546378	+	0.837539i	$0.316006\pi$
$348$		0			0
$349$			36.7493i			1.96715i	0.180512	+	0.983573i	$0.442225\pi$
$349$			36.7493i			1.96715i	−0.180512	+	0.983573i	$0.557775\pi$
$350$		0			0
$351$		−	4.41926i		−	0.235882i
$352$		0			0
$353$	−8.59415	+	8.59415i	−0.457421	+	0.457421i	−0.897808	−	0.440387i	$-0.854841\pi$
$353$	−8.59415	+	8.59415i	−0.457421	+	0.457421i	0.440387	+	0.897808i	$0.354841\pi$
$354$		0			0
$355$	14.4733	+	10.5852i	0.768163	+	0.561804i
$356$		0			0
$357$	5.76491	+	5.76491i	0.305111	+	0.305111i
$358$		0			0
$359$	27.2661			1.43905			0.719525	−	0.694467i	$-0.244360\pi$
$359$	27.2661			1.43905			0.719525	+	0.694467i	$0.244360\pi$
$360$		0			0
$361$	15.0294			0.791019
$362$		0			0
$363$	−2.12132	−	2.12132i	−0.111340	−	0.111340i
$364$		0			0
$365$	−3.92477	−	25.2947i	−0.205432	−	1.32399i
$366$		0			0
$367$	8.74753	−	8.74753i	0.456617	−	0.456617i	−0.440926	−	0.897543i	$-0.645350\pi$
$367$	8.74753	−	8.74753i	0.456617	−	0.456617i	0.897543	+	0.440926i	$0.145350\pi$
$368$		0			0
$369$			4.57947i			0.238398i
$370$		0			0
$371$			0.219432i			0.0113923i
$372$		0			0
$373$	−12.4087	+	12.4087i	−0.642499	+	0.642499i	−0.951169	−	0.308670i	$-0.900116\pi$
$373$	−12.4087	+	12.4087i	−0.642499	+	0.642499i	0.308670	+	0.951169i	$0.400116\pi$
$374$		0			0
$375$	4.98154	+	10.0092i	0.257245	+	0.516873i
$376$		0			0
$377$	3.21949	+	3.21949i	0.165812	+	0.165812i
$378$		0			0
$379$	−29.5152			−1.51610			−0.758048	−	0.652199i	$-0.773847\pi$
$379$	−29.5152			−1.51610			−0.758048	+	0.652199i	$0.773847\pi$
$380$		0			0
$381$	−18.4390			−0.944658
$382$		0			0
$383$	20.0392	+	20.0392i	1.02395	+	1.02395i	0.999706	+	0.0242484i	$0.00771926\pi$
$383$	20.0392	+	20.0392i	1.02395	+	1.02395i	0.0242484	+	0.999706i	$0.492281\pi$
$384$		0			0
$385$	6.24977	−	0.969724i	0.318518	−	0.0494217i
$386$		0			0
$387$	6.56198	−	6.56198i	0.333564	−	0.333564i
$388$		0			0
$389$			5.21949i			0.264639i	0.991207	+	0.132319i	$0.0422425\pi$
$389$			5.21949i			0.264639i	−0.991207	+	0.132319i	$0.957758\pi$
$390$		0			0
$391$		−	56.1712i		−	2.84070i
$392$		0			0
$393$	2.96972	−	2.96972i	0.149803	−	0.149803i
$394$		0			0
$395$	−1.92330	+	2.62976i	−0.0967716	+	0.132317i
$396$		0			0
$397$	−21.9348	−	21.9348i	−1.10087	−	1.10087i	−0.994305	−	0.106568i	$-0.966014\pi$
$397$	−21.9348	−	21.9348i	−1.10087	−	1.10087i	−0.106568	−	0.994305i	$-0.533986\pi$
$398$		0			0
$399$	−5.83347			−0.292039
$400$		0			0
$401$	15.2800			0.763049			0.381525	−	0.924359i	$-0.375399\pi$
$401$	15.2800			0.763049			0.381525	+	0.924359i	$0.375399\pi$
$402$		0			0
$403$	−5.10495	−	5.10495i	−0.254296	−	0.254296i
$404$		0			0
$405$	−1.32001	+	1.80487i	−0.0655919	+	0.0896849i
$406$		0			0
$407$	−2.82843	+	2.82843i	−0.140200	+	0.140200i
$408$		0			0
$409$		−	30.8392i		−	1.52490i	−0.647046	−	0.762451i	$-0.723996\pi$
$409$		−	30.8392i		−	1.52490i	0.647046	−	0.762451i	$-0.276004\pi$
$410$		0			0
$411$		−	18.9146i		−	0.932989i
$412$		0			0
$413$	1.03028	−	1.03028i	0.0506966	−	0.0506966i
$414$		0			0
$415$	−24.7909	+	3.84659i	−1.21694	+	0.188822i
$416$		0			0
$417$	0.905391	+	0.905391i	0.0443372	+	0.0443372i
$418$		0			0
$419$	20.8172			1.01698			0.508492	−	0.861067i	$-0.330203\pi$
$419$	20.8172			1.01698			0.508492	+	0.861067i	$0.330203\pi$
$420$		0			0
$421$	9.65092			0.470357			0.235179	−	0.971952i	$-0.424433\pi$
$421$	9.65092			0.470357			0.235179	+	0.971952i	$0.424433\pi$
$422$		0			0
$423$	3.73356	+	3.73356i	0.181532	+	0.181532i
$424$		0			0
$425$	−18.7346	+	36.2039i	−0.908763	+	1.75615i
$426$		0			0
$427$	−4.46207	+	4.46207i	−0.215935	+	0.215935i
$428$		0			0
$429$		−	12.4995i		−	0.603484i
$430$		0			0
$431$			16.5899i			0.799109i	0.916709	+	0.399554i	$0.130835\pi$
$431$			16.5899i			0.799109i	−0.916709	+	0.399554i	$0.869165\pi$
$432$		0			0
$433$	24.7153	−	24.7153i	1.18774	−	1.18774i	0.210048	−	0.977691i	$-0.432638\pi$
$433$	24.7153	−	24.7153i	1.18774	−	1.18774i	0.977691	−	0.210048i	$-0.0673622\pi$
$434$		0			0
$435$	−0.353229	−	2.27653i	−0.0169360	−	0.109151i
$436$		0			0
$437$	28.4196	+	28.4196i	1.35949	+	1.35949i
$438$		0			0
$439$	−6.18670			−0.295275			−0.147637	−	0.989042i	$-0.547167\pi$
$439$	−6.18670			−0.295275			−0.147637	+	0.989042i	$0.547167\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	−4.31992	−	4.31992i	−0.205246	−	0.205246i	0.596998	−	0.802243i	$-0.296360\pi$
$443$	−4.31992	−	4.31992i	−0.205246	−	0.205246i	−0.802243	+	0.596998i	$0.796360\pi$
$444$		0			0
$445$	−7.07523	−	5.17454i	−0.335398	−	0.245297i
$446$		0			0
$447$	−1.76744	+	1.76744i	−0.0835972	+	0.0835972i
$448$		0			0
$449$			38.4995i			1.81691i	0.417987	+	0.908453i	$0.362736\pi$
$449$			38.4995i			1.81691i	−0.417987	+	0.908453i	$0.637264\pi$
$450$		0			0
$451$			12.9527i			0.609919i
$452$		0			0
$453$	−16.7493	+	16.7493i	−0.786951	+	0.786951i
$454$		0			0
$455$	−7.97620	−	5.83347i	−0.373930	−	0.273477i
$456$		0			0
$457$	18.8401	+	18.8401i	0.881305	+	0.881305i	0.993667	−	0.112363i	$-0.0358418\pi$
$457$	18.8401	+	18.8401i	0.881305	+	0.881305i	−0.112363	+	0.993667i	$0.535842\pi$
$458$		0			0
$459$	−8.15281			−0.380541
$460$		0			0
$461$	−13.6703			−0.636689			−0.318345	−	0.947975i	$-0.603127\pi$
$461$	−13.6703			−0.636689			−0.318345	+	0.947975i	$0.603127\pi$
$462$		0			0
$463$	−17.2382	−	17.2382i	−0.801125	−	0.801125i	0.182146	−	0.983271i	$-0.441696\pi$
$463$	−17.2382	−	17.2382i	−0.801125	−	0.801125i	−0.983271	+	0.182146i	$0.941696\pi$
$464$		0			0
$465$	0.560094	+	3.60975i	0.0259737	+	0.167398i
$466$		0			0
$467$	−20.2379	+	20.2379i	−0.936496	+	0.936496i	−0.998101	−	0.0616045i	$-0.980378\pi$
$467$	−20.2379	+	20.2379i	−0.936496	+	0.936496i	0.0616045	+	0.998101i	$0.480378\pi$
$468$		0			0
$469$			5.28005i			0.243810i
$470$		0			0
$471$		−	5.52306i		−	0.254489i
$472$		0			0
$473$	18.5601	−	18.5601i	0.853394	−	0.853394i
$474$		0			0
$475$	−8.83851	−	27.7959i	−0.405539	−	1.27537i
$476$		0			0
$477$	−0.155162	−	0.155162i	−0.00710436	−	0.00710436i
$478$		0			0
$479$	38.6213			1.76465			0.882327	−	0.470637i	$-0.155976\pi$
$479$	38.6213			1.76465			0.882327	+	0.470637i	$0.155976\pi$
$480$		0			0
$481$	6.24977			0.284965
$482$		0			0
$483$	−4.87182	−	4.87182i	−0.221675	−	0.221675i
$484$		0			0
$485$	−0.484862	+	0.0752319i	−0.0220164	+	0.00341611i
$486$		0			0
$487$	−3.81919	+	3.81919i	−0.173064	+	0.173064i	−0.788324	−	0.615260i	$-0.789051\pi$
$487$	−3.81919	+	3.81919i	−0.173064	+	0.173064i	0.615260	+	0.788324i	$0.289051\pi$
$488$		0			0
$489$		−	20.9991i		−	0.949611i
$490$		0			0
$491$		−	5.81141i		−	0.262265i	−0.991365	−	0.131133i	$-0.958139\pi$
$491$		−	5.81141i		−	0.262265i	0.991365	−	0.131133i	$-0.0418614\pi$
$492$		0			0
$493$	5.93945	−	5.93945i	0.267499	−	0.267499i
$494$		0			0
$495$	−3.73356	+	5.10495i	−0.167811	+	0.229451i
$496$		0			0
$497$	5.67030	+	5.67030i	0.254348	+	0.254348i
$498$		0			0
$499$	35.1721			1.57452			0.787259	−	0.616622i	$-0.211499\pi$
$499$	35.1721			1.57452			0.787259	+	0.616622i	$0.211499\pi$
$500$		0			0
$501$	23.0596			1.03023
$502$		0			0
$503$	−16.7719	−	16.7719i	−0.747822	−	0.747822i	0.226248	−	0.974070i	$-0.427354\pi$
$503$	−16.7719	−	16.7719i	−0.747822	−	0.747822i	−0.974070	+	0.226248i	$0.927354\pi$
$504$		0			0
$505$	−15.3250	+	20.9541i	−0.681954	+	0.932446i
$506$		0			0
$507$	−4.61728	+	4.61728i	−0.205061	+	0.205061i
$508$		0			0
$509$			12.7006i			0.562943i	0.959570	+	0.281472i	$0.0908225\pi$
$509$			12.7006i			0.562943i	−0.959570	+	0.281472i	$0.909177\pi$
$510$		0			0
$511$		−	11.4475i		−	0.506408i
$512$		0			0
$513$	4.12489	−	4.12489i	0.182118	−	0.182118i
$514$		0			0
$515$	−32.7243	+	5.07755i	−1.44200	+	0.223744i
$516$		0			0
$517$	10.5601	+	10.5601i	0.464432	+	0.464432i
$518$		0			0
$519$	−19.4665			−0.854485
$520$		0			0
$521$	28.1093			1.23149			0.615745	−	0.787945i	$-0.288855\pi$
$521$	28.1093			1.23149			0.615745	+	0.787945i	$0.288855\pi$
$522$		0			0
$523$	18.8718	+	18.8718i	0.825206	+	0.825206i	0.986849	−	0.161643i	$-0.0516793\pi$
$523$	18.8718	+	18.8718i	0.825206	+	0.825206i	−0.161643	+	0.986849i	$0.551679\pi$
$524$		0			0
$525$	1.51514	+	4.76491i	0.0661260	+	0.207958i
$526$		0			0
$527$	−9.41782	+	9.41782i	−0.410246	+	0.410246i
$528$		0			0
$529$			24.4693i			1.06388i
$530$		0			0
$531$			1.45703i			0.0632297i
$532$		0			0
$533$	14.3103	−	14.3103i	0.619849	−	0.619849i
$534$		0			0
$535$	5.10495	+	32.9009i	0.220706	+	1.42243i
$536$		0			0
$537$	4.88979	+	4.88979i	0.211010	+	0.211010i
$538$		0			0
$539$	2.82843			0.121829
$540$		0			0
$541$	−35.4087			−1.52234			−0.761170	−	0.648553i	$-0.775375\pi$
$541$	−35.4087			−1.52234			−0.761170	+	0.648553i	$0.775375\pi$
$542$		0			0
$543$	−3.77637	−	3.77637i	−0.162060	−	0.162060i
$544$		0			0
$545$	−24.3103	−	17.7796i	−1.04134	−	0.761594i
$546$		0			0
$547$	13.2370	−	13.2370i	0.565973	−	0.565973i	−0.365024	−	0.930998i	$-0.618939\pi$
$547$	13.2370	−	13.2370i	0.565973	−	0.565973i	0.930998	+	0.365024i	$0.118939\pi$
$548$		0			0
$549$		−	6.31032i		−	0.269318i
$550$		0			0
$551$			6.01008i			0.256038i
$552$		0			0
$553$	−1.03028	+	1.03028i	−0.0438118	+	0.0438118i
$554$		0			0
$555$	−2.55248	−	1.86678i	−0.108347	−	0.0792403i
$556$		0			0
$557$	−0.654703	−	0.654703i	−0.0277407	−	0.0277407i	0.693100	−	0.720841i	$-0.256244\pi$
$557$	−0.654703	−	0.654703i	−0.0277407	−	0.0277407i	−0.720841	+	0.693100i	$0.756244\pi$
$558$		0			0
$559$	−41.0109			−1.73458
$560$		0			0
$561$	−23.0596			−0.973579
$562$		0			0
$563$	23.1352	+	23.1352i	0.975033	+	0.975033i	0.999696	−	0.0246632i	$-0.00785134\pi$
$563$	23.1352	+	23.1352i	0.975033	+	0.975033i	−0.0246632	+	0.999696i	$0.507851\pi$
$564$		0			0
$565$	−3.45459	−	22.2645i	−0.145336	−	0.936672i
$566$		0			0
$567$	−0.707107	+	0.707107i	−0.0296957	+	0.0296957i
$568$		0			0
$569$		−	40.2791i		−	1.68859i	−0.535879	−	0.844294i	$-0.680020\pi$
$569$		−	40.2791i		−	1.68859i	0.535879	−	0.844294i	$-0.319980\pi$
$570$		0			0
$571$			1.81026i			0.0757570i	0.999282	+	0.0378785i	$0.0120600\pi$
$571$			1.81026i			0.0757570i	−0.999282	+	0.0378785i	$0.987940\pi$
$572$		0			0
$573$	5.21949	−	5.21949i	0.218048	−	0.218048i
$574$		0			0
$575$	15.8323	−	30.5953i	0.660253	−	1.27591i
$576$		0			0
$577$	14.3444	+	14.3444i	0.597164	+	0.597164i	0.939557	−	0.342393i	$-0.111237\pi$
$577$	14.3444	+	14.3444i	0.597164	+	0.597164i	−0.342393	+	0.939557i	$0.611237\pi$
$578$		0			0
$579$	0.310412			0.0129003
$580$		0			0
$581$	−11.2195			−0.465463
$582$		0			0
$583$	−0.438863	−	0.438863i	−0.0181758	−	0.0181758i
$584$		0			0
$585$	9.76491	−	1.51514i	0.403729	−	0.0626432i
$586$		0			0
$587$	7.26844	−	7.26844i	0.300001	−	0.300001i	−0.541013	−	0.841014i	$-0.681959\pi$
$587$	7.26844	−	7.26844i	0.300001	−	0.300001i	0.841014	+	0.541013i	$0.181959\pi$
$588$		0			0
$589$		−	9.52982i		−	0.392669i
$590$		0			0
$591$			3.31545i			0.136380i
$592$		0			0
$593$	1.26537	−	1.26537i	0.0519624	−	0.0519624i	−0.680648	−	0.732611i	$-0.738302\pi$
$593$	1.26537	−	1.26537i	0.0519624	−	0.0519624i	0.732611	+	0.680648i	$0.238302\pi$
$594$		0			0
$595$	−10.7618	+	14.7148i	−0.441191	+	0.603248i
$596$		0			0
$597$	−8.62443	−	8.62443i	−0.352974	−	0.352974i
$598$		0			0
$599$	12.3319			0.503867			0.251933	−	0.967745i	$-0.418934\pi$
$599$	12.3319			0.503867			0.251933	+	0.967745i	$0.418934\pi$
$600$		0			0
$601$	−35.8089			−1.46068			−0.730339	−	0.683085i	$-0.760638\pi$
$601$	−35.8089			−1.46068			−0.730339	+	0.683085i	$0.760638\pi$
$602$		0			0
$603$	−3.73356	−	3.73356i	−0.152042	−	0.152042i
$604$		0			0
$605$	3.96004	−	5.41462i	0.160998	−	0.220136i
$606$		0			0
$607$	−24.9675	+	24.9675i	−1.01340	+	1.01340i	−0.0134914	+	0.999909i	$0.504295\pi$
$607$	−24.9675	+	24.9675i	−1.01340	+	1.01340i	−0.999909	+	0.0134914i	$0.995705\pi$
$608$		0			0
$609$		−	1.03028i		−	0.0417489i
$610$		0			0
$611$		−	23.3339i		−	0.943988i
$612$		0			0
$613$	9.68876	−	9.68876i	0.391325	−	0.391325i	−0.483834	−	0.875160i	$-0.660756\pi$
$613$	9.68876	−	9.68876i	0.391325	−	0.391325i	0.875160	+	0.483834i	$0.160756\pi$
$614$		0			0
$615$	−10.1189	+	1.57007i	−0.408034	+	0.0633113i
$616$		0			0
$617$	−27.6850	−	27.6850i	−1.11456	−	1.11456i	−0.992527	−	0.122029i	$-0.961060\pi$
$617$	−27.6850	−	27.6850i	−1.11456	−	1.11456i	−0.122029	−	0.992527i	$-0.538940\pi$
$618$		0			0
$619$	16.9211			0.680117			0.340058	−	0.940404i	$-0.389553\pi$
$619$	16.9211			0.680117			0.340058	+	0.940404i	$0.389553\pi$
$620$		0			0
$621$	6.88979			0.276478
$622$		0			0
$623$	−2.77191	−	2.77191i	−0.111054	−	0.111054i
$624$		0			0
$625$	−20.4087	+	14.4390i	−0.816349	+	0.577560i
$626$		0			0
$627$	11.6669	−	11.6669i	0.465933	−	0.465933i
$628$		0			0
$629$		−	11.5298i		−	0.459724i
$630$		0			0
$631$		−	0.181962i		−	0.00724379i	−0.999993	−	0.00362189i	$-0.998847\pi$
$631$		−	0.181962i		−	0.00724379i	0.999993	−	0.00362189i	$-0.00115289\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	−6.32179	−	40.7433i	−0.250873	−	1.61685i
$636$		0			0
$637$	−3.12489	−	3.12489i	−0.123812	−	0.123812i
$638$		0			0
$639$	−8.01901			−0.317227
$640$		0			0
$641$	−10.9697			−0.433278			−0.216639	−	0.976252i	$-0.569509\pi$
$641$	−10.9697			−0.433278			−0.216639	+	0.976252i	$0.569509\pi$
$642$		0			0
$643$	24.0844	+	24.0844i	0.949798	+	0.949798i	0.998799	−	0.0490008i	$-0.0156037\pi$
$643$	24.0844	+	24.0844i	0.949798	+	0.949798i	−0.0490008	+	0.998799i	$0.515604\pi$
$644$		0			0
$645$	16.7493	+	12.2498i	0.659504	+	0.482334i
$646$		0			0
$647$	22.3157	−	22.3157i	0.877321	−	0.877321i	−0.115936	−	0.993257i	$-0.536987\pi$
$647$	22.3157	−	22.3157i	0.877321	−	0.877321i	0.993257	+	0.115936i	$0.0369867\pi$
$648$		0			0
$649$			4.12110i			0.161767i
$650$		0			0
$651$			1.63365i			0.0640276i
$652$		0			0
$653$	−0.276266	+	0.276266i	−0.0108111	+	0.0108111i	−0.712492	−	0.701681i	$-0.752433\pi$
$653$	−0.276266	+	0.276266i	−0.0108111	+	0.0108111i	0.701681	+	0.712492i	$0.252433\pi$
$654$		0			0
$655$	7.58015	+	5.54382i	0.296181	+	0.216615i
$656$		0			0
$657$	8.09461	+	8.09461i	0.315801	+	0.315801i
$658$		0			0
$659$	24.8183			0.966784			0.483392	−	0.875404i	$-0.339405\pi$
$659$	24.8183			0.966784			0.483392	+	0.875404i	$0.339405\pi$
$660$		0			0
$661$	−8.37088			−0.325589			−0.162795	−	0.986660i	$-0.552051\pi$
$661$	−8.37088			−0.325589			−0.162795	+	0.986660i	$0.552051\pi$
$662$		0			0
$663$	25.4766	+	25.4766i	0.989429	+	0.989429i
$664$		0			0
$665$	−2.00000	−	12.8898i	−0.0775567	−	0.499845i
$666$		0			0
$667$	−5.01932	+	5.01932i	−0.194349	+	0.194349i
$668$		0			0
$669$			2.80986i			0.108636i
$670$		0			0
$671$		−	17.8483i		−	0.689026i
$672$		0			0
$673$	27.5601	−	27.5601i	1.06236	−	1.06236i	0.0644421	−	0.997921i	$-0.479473\pi$
$673$	27.5601	−	27.5601i	1.06236	−	1.06236i	0.997921	−	0.0644421i	$-0.0205268\pi$
$674$		0			0
$675$	−4.44066	−	2.29793i	−0.170921	−	0.0884476i
$676$		0			0
$677$	−0.174539	−	0.174539i	−0.00670808	−	0.00670808i	0.703745	−	0.710453i	$-0.251510\pi$
$677$	−0.174539	−	0.174539i	−0.00670808	−	0.00670808i	−0.710453	+	0.703745i	$0.751510\pi$
$678$		0			0
$679$	−0.219432			−0.00842101
$680$		0			0
$681$	3.87890			0.148640
$682$		0			0
$683$	−28.1201	−	28.1201i	−1.07598	−	1.07598i	−0.996865	−	0.0791191i	$-0.974789\pi$
$683$	−28.1201	−	28.1201i	−1.07598	−	1.07598i	−0.0791191	−	0.996865i	$-0.525211\pi$
$684$		0			0
$685$	41.7943	−	6.48486i	1.59688	−	0.247774i
$686$		0			0
$687$	12.3955	−	12.3955i	0.472916	−	0.472916i
$688$		0			0
$689$			0.969724i			0.0369435i
$690$		0			0
$691$		−	39.1953i		−	1.49106i	−0.666473	−	0.745530i	$-0.732197\pi$
$691$		−	39.1953i		−	1.49106i	0.666473	−	0.745530i	$-0.267803\pi$
$692$		0			0
$693$	−2.00000	+	2.00000i	−0.0759737	+	0.0759737i
$694$		0			0
$695$	−1.69016	+	2.31099i	−0.0641116	+	0.0876608i
$696$		0			0
$697$	−26.4002	−	26.4002i	−0.999980	−	0.999980i
$698$		0			0
$699$	−17.8965			−0.676906
$700$		0			0
$701$	10.8486			0.409747			0.204873	−	0.978788i	$-0.434322\pi$
$701$	10.8486			0.409747			0.204873	+	0.978788i	$0.434322\pi$
$702$		0			0
$703$	5.83347	+	5.83347i	0.220013	+	0.220013i
$704$		0			0
$705$	−6.96972	+	9.52982i	−0.262495	+	0.358914i
$706$		0			0
$707$	−8.20933	+	8.20933i	−0.308744	+	0.308744i
$708$		0			0
$709$			31.5592i			1.18523i	0.805486	+	0.592615i	$0.201904\pi$
$709$			31.5592i			1.18523i	−0.805486	+	0.592615i	$0.798096\pi$
$710$		0			0
$711$		−	1.45703i		−	0.0546429i
$712$		0			0
$713$	7.95883	−	7.95883i	0.298060	−	0.298060i
$714$		0			0
$715$	27.6193	−	4.28546i	1.03290	−	0.160267i
$716$		0			0
$717$	13.2195	+	13.2195i	0.493691	+	0.493691i
$718$		0			0
$719$	−19.8405			−0.739926			−0.369963	−	0.929046i	$-0.620630\pi$
$719$	−19.8405			−0.739926			−0.369963	+	0.929046i	$0.620630\pi$
$720$		0			0
$721$	−14.8099			−0.551548
$722$		0			0
$723$	9.21380	+	9.21380i	0.342665	+	0.342665i
$724$		0			0
$725$	4.90917	−	1.56101i	0.182322	−	0.0579745i
$726$		0			0
$727$	−24.8765	+	24.8765i	−0.922620	+	0.922620i	−0.997214	−	0.0745942i	$-0.976234\pi$
$727$	−24.8765	+	24.8765i	−0.922620	+	0.922620i	0.0745942	+	0.997214i	$0.476234\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			75.6585i			2.79833i
$732$		0			0
$733$	29.7531	−	29.7531i	1.09896	−	1.09896i	0.104423	−	0.994533i	$-0.466701\pi$
$733$	29.7531	−	29.7531i	1.09896	−	1.09896i	0.994533	−	0.104423i	$-0.0332994\pi$
$734$		0			0
$735$	0.342849	+	2.20963i	0.0126462	+	0.0815033i
$736$		0			0
$737$	−10.5601	−	10.5601i	−0.388986	−	0.388986i
$738$		0			0
$739$	−31.0271			−1.14135			−0.570675	−	0.821176i	$-0.693318\pi$
$739$	−31.0271			−1.14135			−0.570675	+	0.821176i	$0.693318\pi$
$740$		0			0
$741$	−25.7796			−0.947037
$742$		0			0
$743$	19.2541	+	19.2541i	0.706366	+	0.706366i	0.965769	−	0.259403i	$-0.0835258\pi$
$743$	19.2541	+	19.2541i	0.706366	+	0.706366i	−0.259403	+	0.965769i	$0.583526\pi$
$744$		0			0
$745$	−4.51136	−	3.29942i	−0.165283	−	0.120882i
$746$		0			0
$747$	7.93338	−	7.93338i	0.290267	−	0.290267i
$748$		0			0
$749$			14.8898i			0.544061i
$750$		0			0
$751$		−	15.1603i		−	0.553207i	−0.960984	−	0.276604i	$-0.910791\pi$
$751$		−	15.1603i		−	0.553207i	0.960984	−	0.276604i	$-0.0892089\pi$
$752$		0			0
$753$	−6.18922	+	6.18922i	−0.225548	+	0.225548i
$754$		0			0
$755$	−42.7522	−	31.2673i	−1.55591	−	1.13793i
$756$		0			0
$757$	12.5298	+	12.5298i	0.455404	+	0.455404i	0.897143	−	0.441739i	$-0.145638\pi$
$757$	12.5298	+	12.5298i	0.455404	+	0.455404i	−0.441739	+	0.897143i	$0.645638\pi$
$758$		0			0
$759$	19.4873			0.707343
$760$		0			0
$761$	1.33062			0.0482348			0.0241174	−	0.999709i	$-0.492322\pi$
$761$	1.33062			0.0482348			0.0241174	+	0.999709i	$0.492322\pi$
$762$		0			0
$763$	−9.52421	−	9.52421i	−0.344800	−	0.344800i
$764$		0			0
$765$	−2.79518	−	18.0147i	−0.101060	−	0.651322i
$766$		0			0
$767$	4.55305	−	4.55305i	0.164401	−	0.164401i
$768$		0			0
$769$			2.31032i			0.0833124i	0.999132	+	0.0416562i	$0.0132634\pi$
$769$			2.31032i			0.0833124i	−0.999132	+	0.0416562i	$0.986737\pi$
$770$		0			0
$771$		−	13.2578i		−	0.477467i
$772$		0			0
$773$	−21.8448	+	21.8448i	−0.785704	+	0.785704i	−0.980787	−	0.195083i	$-0.937503\pi$
$773$	−21.8448	+	21.8448i	−0.785704	+	0.785704i	0.195083	+	0.980787i	$0.437503\pi$
$774$		0			0
$775$	−7.78417	+	2.47520i	−0.279616	+	0.0889117i
$776$		0			0
$777$	−1.00000	−	1.00000i	−0.0358748	−	0.0358748i
$778$		0			0
$779$	26.7142			0.957136
$780$		0			0
$781$	−22.6812			−0.811597
$782$		0			0
$783$	0.728515	+	0.728515i	0.0260350	+	0.0260350i
$784$		0			0
$785$	12.2039	−	1.89358i	0.435576	−	0.0675846i
$786$		0			0
$787$	−21.6146	+	21.6146i	−0.770477	+	0.770477i	−0.978190	−	0.207713i	$-0.933398\pi$
$787$	−21.6146	+	21.6146i	−0.770477	+	0.770477i	0.207713	+	0.978190i	$0.433398\pi$
$788$		0			0
$789$			18.8898i			0.672494i
$790$		0			0
$791$		−	10.0761i		−	0.358265i
$792$		0			0
$793$	−19.7190	+	19.7190i	−0.700244	+	0.700244i
$794$		0			0
$795$	0.289652	−	0.396046i	0.0102729	−	0.0140463i
$796$		0			0
$797$	−14.2645	−	14.2645i	−0.505273	−	0.505273i	0.407799	−	0.913072i	$-0.366296\pi$
$797$	−14.2645	−	14.2645i	−0.505273	−	0.505273i	−0.913072	+	0.407799i	$0.866296\pi$
$798$		0			0
$799$	−43.0472			−1.52290
$800$		0			0
$801$	3.92007			0.138509
$802$		0			0
$803$	22.8950	+	22.8950i	0.807947	+	0.807947i
$804$		0			0
$805$	9.09461	−	12.4352i	0.320543	−	0.438284i
$806$		0			0
$807$	16.0297	−	16.0297i	0.564271	−	0.564271i
$808$		0			0
$809$			20.3709i			0.716202i	0.933683	+	0.358101i	$0.116576\pi$
$809$			20.3709i			0.716202i	−0.933683	+	0.358101i	$0.883424\pi$
$810$		0			0
$811$			43.3510i			1.52226i	0.648600	+	0.761130i	$0.275355\pi$
$811$			43.3510i			1.52226i	−0.648600	+	0.761130i	$0.724645\pi$
$812$		0			0
$813$	13.9045	−	13.9045i	0.487651	−	0.487651i
$814$		0			0
$815$	46.4002	−	7.19952i	1.62533	−	0.252188i
$816$		0			0
$817$	−38.2791	−	38.2791i	−1.33922	−	1.33922i
$818$		0			0
$819$	4.41926			0.154421
$820$		0			0
$821$	−15.8713			−0.553913			−0.276957	−	0.960882i	$-0.589326\pi$
$821$	−15.8713			−0.553913			−0.276957	+	0.960882i	$0.589326\pi$
$822$		0			0
$823$	−9.19174	−	9.19174i	−0.320404	−	0.320404i	0.528518	−	0.848922i	$-0.322748\pi$
$823$	−9.19174	−	9.19174i	−0.320404	−	0.320404i	−0.848922	+	0.528518i	$0.822748\pi$
$824$		0			0
$825$	−12.5601	−	6.49954i	−0.437286	−	0.226285i
$826$		0			0
$827$	−20.4436	+	20.4436i	−0.710893	+	0.710893i	−0.966722	−	0.255829i	$-0.917652\pi$
$827$	−20.4436	+	20.4436i	−0.710893	+	0.710893i	0.255829	+	0.966722i	$0.417652\pi$
$828$		0			0
$829$		−	52.6576i		−	1.82887i	−0.404729	−	0.914436i	$-0.632634\pi$
$829$		−	52.6576i		−	1.82887i	0.404729	−	0.914436i	$-0.367366\pi$
$830$		0			0
$831$		−	11.3565i		−	0.393954i
$832$		0			0
$833$	−5.76491	+	5.76491i	−0.199742	+	0.199742i
$834$		0			0
$835$	7.90598	+	50.9532i	0.273598	+	1.76331i
$836$		0			0
$837$	−1.15516	−	1.15516i	−0.0399282	−	0.0399282i
$838$		0			0
$839$	22.6274			0.781185			0.390593	−	0.920564i	$-0.372270\pi$
$839$	22.6274			0.781185			0.390593	+	0.920564i	$0.372270\pi$
$840$		0			0
$841$	27.9385			0.963398
$842$		0			0
$843$	2.09991	+	2.09991i	0.0723248	+	0.0723248i
$844$		0			0
$845$	−11.7855	−	8.61944i	−0.405433	−	0.296518i
$846$		0			0
$847$	2.12132	−	2.12132i	0.0728894	−	0.0728894i
$848$		0			0
$849$		−	31.1883i		−	1.07038i
$850$		0			0
$851$			9.74364i			0.334008i
$852$		0			0
$853$	−34.7834	+	34.7834i	−1.19096	+	1.19096i	−0.214162	+	0.976798i	$0.568702\pi$
$853$	−34.7834	+	34.7834i	−1.19096	+	1.19096i	−0.976798	+	0.214162i	$0.931298\pi$
$854$		0			0
$855$	10.5287	+	7.70025i	0.360073	+	0.263343i
$856$		0			0
$857$	−35.9348	−	35.9348i	−1.22751	−	1.22751i	−0.964904	−	0.262604i	$-0.915419\pi$
$857$	−35.9348	−	35.9348i	−1.22751	−	1.22751i	−0.262604	−	0.964904i	$-0.584581\pi$
$858$		0			0
$859$	19.8900			0.678637			0.339319	−	0.940672i	$-0.389804\pi$
$859$	19.8900			0.678637			0.339319	+	0.940672i	$0.389804\pi$
$860$		0			0
$861$	−4.57947			−0.156068
$862$		0			0
$863$	−7.78588	−	7.78588i	−0.265034	−	0.265034i	0.562061	−	0.827096i	$-0.310009\pi$
$863$	−7.78588	−	7.78588i	−0.265034	−	0.265034i	−0.827096	+	0.562061i	$0.810009\pi$
$864$		0			0
$865$	−6.67408	−	43.0138i	−0.226926	−	1.46251i
$866$		0			0
$867$	34.9794	−	34.9794i	1.18796	−	1.18796i
$868$		0			0
$869$		−	4.12110i		−	0.139799i
$870$		0			0
$871$			23.3339i			0.790638i
$872$		0			0
$873$	0.155162	−	0.155162i	0.00525142	−	0.00525142i
$874$		0			0
$875$	−10.0092	+	4.98154i	−0.338373	+	0.168407i
$876$		0			0
$877$	33.1892	+	33.1892i	1.12072	+	1.12072i	0.991633	+	0.129087i	$0.0412047\pi$
$877$	33.1892	+	33.1892i	1.12072	+	1.12072i	0.129087	+	0.991633i	$0.458795\pi$
$878$		0			0
$879$	18.2497			0.615547
$880$		0			0
$881$	23.1396			0.779592			0.389796	−	0.920901i	$-0.372546\pi$
$881$	23.1396			0.779592			0.389796	+	0.920901i	$0.372546\pi$
$882$		0			0
$883$	−36.1046	−	36.1046i	−1.21502	−	1.21502i	−0.969356	−	0.245661i	$-0.920995\pi$
$883$	−36.1046	−	36.1046i	−1.21502	−	1.21502i	−0.245661	−	0.969356i	$-0.579005\pi$
$884$		0			0
$885$	−3.21949	+	0.499542i	−0.108222	+	0.0167919i
$886$		0			0
$887$	−14.8760	+	14.8760i	−0.499487	+	0.499487i	−0.911278	−	0.411791i	$-0.864903\pi$
$887$	−14.8760	+	14.8760i	−0.499487	+	0.499487i	0.411791	+	0.911278i	$0.364903\pi$
$888$		0			0
$889$		−	18.4390i		−	0.618424i
$890$		0			0
$891$		−	2.82843i		−	0.0947559i
$892$		0			0
$893$	21.7796	−	21.7796i	0.728826	−	0.728826i
$894$		0			0
$895$	−9.12816	+	12.4811i	−0.305121	+	0.417197i
$896$		0			0
$897$	−21.5298	−	21.5298i	−0.718860	−	0.718860i
$898$		0			0
$899$	1.68311			0.0561347
$900$		0			0
$901$	1.78898			0.0595997
$902$		0			0
$903$	6.56198	+	6.56198i	0.218369	+	0.218369i
$904$		0			0
$905$	7.04965	−	9.63911i	0.234338	−	0.320415i
$906$		0			0
$907$	16.0380	−	16.0380i	0.532534	−	0.532534i	−0.388792	−	0.921326i	$-0.627107\pi$
$907$	16.0380	−	16.0380i	0.532534	−	0.532534i	0.921326	+	0.388792i	$0.127107\pi$
$908$		0			0
$909$		−	11.6097i		−	0.385071i
$910$		0			0
$911$			17.2823i			0.572587i	0.958142	+	0.286294i	$0.0924233\pi$
$911$			17.2823i			0.572587i	−0.958142	+	0.286294i	$0.907577\pi$
$912$		0			0
$913$	22.4390	−	22.4390i	0.742622	−	0.742622i
$914$		0			0
$915$	13.9435	−	2.16349i	0.460957	−	0.0715227i
$916$		0			0
$917$	2.96972	+	2.96972i	0.0980689	+	0.0980689i
$918$		0			0
$919$	17.6770			0.583111			0.291556	−	0.956554i	$-0.405827\pi$
$919$	17.6770			0.583111			0.291556	+	0.956554i	$0.405827\pi$
$920$		0			0
$921$	−8.49954			−0.280069
$922$		0			0
$923$	25.0585	+	25.0585i	0.824811	+	0.824811i
$924$		0			0
$925$	3.24977	−	6.28005i	0.106852	−	0.206487i
$926$		0			0
$927$	10.4722	−	10.4722i	0.343951	−	0.343951i
$928$		0			0
$929$		−	16.2304i		−	0.532502i	−0.963904	−	0.266251i	$-0.914215\pi$
$929$		−	16.2304i		−	0.532502i	0.963904	−	0.266251i	$-0.0857850\pi$
$930$		0			0
$931$		−	5.83347i		−	0.191184i
$932$		0			0
$933$	21.4087	−	21.4087i	0.700890	−	0.700890i
$934$		0			0
$935$	−7.90598	−	50.9532i	−0.258553	−	1.66635i
$936$		0			0
$937$	−13.0038	−	13.0038i	−0.424815	−	0.424815i	0.462043	−	0.886858i	$-0.347117\pi$
$937$	−13.0038	−	13.0038i	−0.424815	−	0.424815i	−0.886858	+	0.462043i	$0.847117\pi$
$938$		0			0
$939$	−27.0467			−0.882635
$940$		0			0
$941$	19.4499			0.634048			0.317024	−	0.948417i	$-0.397316\pi$
$941$	19.4499			0.634048			0.317024	+	0.948417i	$0.397316\pi$
$942$		0			0
$943$	22.3104	+	22.3104i	0.726525	+	0.726525i
$944$		0			0
$945$	−1.80487	−	1.32001i	−0.0587125	−	0.0429400i
$946$		0			0
$947$	−28.7576	+	28.7576i	−0.934496	+	0.934496i	−0.997983	−	0.0634864i	$-0.979778\pi$
$947$	−28.7576	+	28.7576i	−0.934496	+	0.934496i	0.0634864	+	0.997983i	$0.479778\pi$
$948$		0			0
$949$		−	50.5895i		−	1.64220i
$950$		0			0
$951$		−	9.72288i		−	0.315286i
$952$		0			0
$953$	24.2838	−	24.2838i	0.786630	−	0.786630i	−0.194310	−	0.980940i	$-0.562247\pi$
$953$	24.2838	−	24.2838i	0.786630	−	0.786630i	0.980940	+	0.194310i	$0.0622467\pi$
$954$		0			0
$955$	13.3226	+	9.74364i	0.431110	+	0.315297i
$956$		0			0
$957$	2.06055	+	2.06055i	0.0666082	+	0.0666082i
$958$		0			0
$959$	18.9146			0.610785
$960$		0			0
$961$	28.3312			0.913910
$962$		0			0
$963$	−10.5287	−	10.5287i	−0.339282	−	0.339282i
$964$		0			0
$965$	0.106425	+	0.685896i	0.00342593	+	0.0220798i
$966$		0			0
$967$	−27.7739	+	27.7739i	−0.893148	+	0.893148i	−0.994818	−	0.101670i	$-0.967581\pi$
$967$	−27.7739	+	27.7739i	−0.893148	+	0.893148i	0.101670	+	0.994818i	$0.467581\pi$
$968$		0			0
$969$			47.5592i			1.52782i
$970$		0			0
$971$		−	57.9815i		−	1.86071i	−0.366655	−	0.930357i	$-0.619497\pi$
$971$		−	57.9815i		−	1.86071i	0.366655	−	0.930357i	$-0.380503\pi$
$972$		0			0
$973$	−0.905391	+	0.905391i	−0.0290255	+	0.0290255i
$974$		0			0
$975$	6.69578	+	21.0573i	0.214437	+	0.674375i
$976$		0			0
$977$	22.2451	+	22.2451i	0.711683	+	0.711683i	0.966887	−	0.255204i	$-0.0821427\pi$
$977$	22.2451	+	22.2451i	0.711683	+	0.711683i	−0.255204	+	0.966887i	$0.582143\pi$
$978$		0			0
$979$	11.0876			0.354362
$980$		0			0
$981$	13.4693			0.430041
$982$		0			0
$983$	−34.8189	−	34.8189i	−1.11055	−	1.11055i	−0.993076	−	0.117473i	$-0.962521\pi$
$983$	−34.8189	−	34.8189i	−1.11055	−	1.11055i	−0.117473	−	0.993076i	$-0.537479\pi$
$984$		0			0
$985$	−7.32592	+	1.13670i	−0.233423	+	0.0362183i
$986$		0			0
$987$	−3.73356	+	3.73356i	−0.118840	+	0.118840i
$988$		0			0
$989$		−	63.9376i		−	2.03310i
$990$		0			0
$991$		−	10.2099i		−	0.324328i	−0.986764	−	0.162164i	$-0.948153\pi$
$991$		−	10.2099i		−	0.324328i	0.986764	−	0.162164i	$-0.0518474\pi$
$992$		0			0
$993$	0.659401	−	0.659401i	0.0209255	−	0.0209255i
$994$		0			0
$995$	16.0999	−	22.0137i	0.510401	−	0.697880i
$996$		0			0
$997$	−4.96503	−	4.96503i	−0.157244	−	0.157244i	0.624100	−	0.781344i	$-0.285466\pi$
$997$	−4.96503	−	4.96503i	−0.157244	−	0.157244i	−0.781344	+	0.624100i	$0.785466\pi$
$998$		0			0
$999$	1.41421			0.0447437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bl.c.127.3	✓	12
4.3	odd	2	inner	1680.2.bl.c.127.6	yes	12
5.3	odd	4	inner	1680.2.bl.c.463.6	yes	12
20.3	even	4	inner	1680.2.bl.c.463.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.bl.c.127.3	✓	12	1.1	even	1	trivial
1680.2.bl.c.127.6	yes	12	4.3	odd	2	inner
1680.2.bl.c.463.3	yes	12	20.3	even	4	inner
1680.2.bl.c.463.6	yes	12	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.32001 - 1.80487i) q^{5} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{9} +2.82843i q^{11} +(3.12489 - 3.12489i) q^{13} +(-2.20963 + 0.342849i) q^{15} +(-5.76491 - 5.76491i) q^{17} +5.83347 q^{19} -1.00000 q^{21} +(4.87182 + 4.87182i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(0.707107 - 0.707107i) q^{27} +1.03028i q^{29} -1.63365i q^{31} +(2.00000 - 2.00000i) q^{33} +(-0.342849 - 2.20963i) q^{35} +(1.00000 + 1.00000i) q^{37} -4.41926 q^{39} +4.57947 q^{41} +(-6.56198 - 6.56198i) q^{43} +(1.80487 + 1.32001i) q^{45} +(3.73356 - 3.73356i) q^{47} -1.00000i q^{49} +8.15281i q^{51} +(-0.155162 + 0.155162i) q^{53} +(5.10495 + 3.73356i) q^{55} +(-4.12489 - 4.12489i) q^{57} +1.45703 q^{59} -6.31032 q^{61} +(0.707107 + 0.707107i) q^{63} +(-1.51514 - 9.76491i) q^{65} +(-3.73356 + 3.73356i) q^{67} -6.88979i q^{69} +8.01901i q^{71} +(8.09461 - 8.09461i) q^{73} +(-2.29793 + 4.44066i) q^{75} +(2.00000 + 2.00000i) q^{77} -1.45703 q^{79} -1.00000 q^{81} +(-7.93338 - 7.93338i) q^{83} +(-18.0147 + 2.79518i) q^{85} +(0.728515 - 0.728515i) q^{87} -3.92007i q^{89} -4.41926i q^{91} +(-1.15516 + 1.15516i) q^{93} +(7.70025 - 10.5287i) q^{95} +(-0.155162 - 0.155162i) q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{13} - 4 q^{17} - 12 q^{21} - 20 q^{25} + 24 q^{33} + 12 q^{37} + 16 q^{41} + 4 q^{45} + 28 q^{53} - 16 q^{57} - 16 q^{61} - 20 q^{65} + 60 q^{73} + 24 q^{77} - 12 q^{81} - 84 q^{85} + 16 q^{93}+ \cdots + 28 q^{97}+O(q^{100}) \) 12 * q + 4 * q^13 - 4 * q^17 - 12 * q^21 - 20 * q^25 + 24 * q^33 + 12 * q^37 + 16 * q^41 + 4 * q^45 + 28 * q^53 - 16 * q^57 - 16 * q^61 - 20 * q^65 + 60 * q^73 + 24 * q^77 - 12 * q^81 - 84 * q^85 + 16 * q^93 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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