LMFDB - Embedded newform 684.2.l.a.121.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(121,684)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("684.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.14
Character	$\chi$	$=$	684.121
Dual form			684.2.l.a.277.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.915791 - 1.47015i) q^{3} -1.49623 q^{5} +(-1.75655 - 3.04244i) q^{7} +(-1.32265 - 2.69269i) q^{9} +(0.434507 + 0.752587i) q^{11} +(0.568572 + 0.984796i) q^{13} +(-1.37024 + 2.19968i) q^{15} +(-0.621125 - 1.07582i) q^{17} +(-4.32633 - 0.531855i) q^{19} +(-6.08146 - 0.203851i) q^{21} +(2.37465 + 4.11302i) q^{23} -2.76129 q^{25} +(-5.16992 - 0.521451i) q^{27} -9.34648 q^{29} +(4.17123 - 7.22478i) q^{31} +(1.50433 + 0.0504252i) q^{33} +(2.62821 + 4.55219i) q^{35} -9.83760 q^{37} +(1.96849 + 0.0659838i) q^{39} +9.98097 q^{41} +(3.89011 - 6.73787i) q^{43} +(1.97900 + 4.02889i) q^{45} -5.09144 q^{47} +(-2.67095 + 4.62623i) q^{49} +(-2.15043 - 0.0720826i) q^{51} +(4.93311 - 8.54439i) q^{53} +(-0.650123 - 1.12605i) q^{55} +(-4.74392 + 5.87326i) q^{57} +13.5500 q^{59} +2.39838 q^{61} +(-5.86904 + 8.75395i) q^{63} +(-0.850716 - 1.47348i) q^{65} +(0.655524 + 1.13540i) q^{67} +(8.22142 + 0.275582i) q^{69} +(0.242447 + 0.419931i) q^{71} +(-5.07886 - 8.79685i) q^{73} +(-2.52877 + 4.05950i) q^{75} +(1.52647 - 2.64392i) q^{77} +(-3.14994 + 5.45585i) q^{79} +(-5.50118 + 7.12299i) q^{81} +(2.07977 + 3.60227i) q^{83} +(0.929347 + 1.60968i) q^{85} +(-8.55942 + 13.7407i) q^{87} +(-2.98670 + 5.17312i) q^{89} +(1.99745 - 3.45969i) q^{91} +(-6.80150 - 12.7487i) q^{93} +(6.47319 + 0.795778i) q^{95} +(6.97644 - 12.0835i) q^{97} +(1.45178 - 2.16540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{3} - q^{7} + q^{9} - q^{11} - q^{13} + 10 q^{15} + 5 q^{17} + q^{19} + 6 q^{21} - 4 q^{23} + 40 q^{25} + 7 q^{27} + 18 q^{29} + 2 q^{31} - 7 q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} + 50 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) $ 40 * q + q^3 - q^7 + q^9 - q^11 - q^13 + 10 * q^15 + 5 * q^17 + q^19 + 6 * q^21 - 4 * q^23 + 40 * q^25 + 7 * q^27 + 18 * q^29 + 2 * q^31 - 7 * q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 + 50 * q^41 + 8 * q^43 + 44 * q^45 + 20 * q^47 - 21 * q^49 - 17 * q^51 - 8 * q^53 + 15 * q^57 + 44 * q^59 + 14 * q^61 - 26 * q^63 - 6 * q^65 - 10 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 - q^79 + q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 + 46 * q^93 - 54 * q^95 - q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.915791	−	1.47015i	0.528732	−	0.848789i
$3$	0.915791	−	1.47015i	0.528732	−	0.848789i
$4$		0			0
$5$	−1.49623			−0.669135			−0.334568	−	0.942372i	$-0.608590\pi$
$5$	−1.49623			−0.669135			−0.334568	+	0.942372i	$0.608590\pi$
$6$		0			0
$7$	−1.75655	−	3.04244i	−0.663914	−	1.14993i	−0.979578	−	0.201063i	$-0.935561\pi$
$7$	−1.75655	−	3.04244i	−0.663914	−	1.14993i	0.315664	−	0.948871i	$-0.397773\pi$
$8$		0			0
$9$	−1.32265	−	2.69269i	−0.440884	−	0.897564i
$10$		0			0
$11$	0.434507	+	0.752587i	0.131009	+	0.226914i	0.924066	−	0.382234i	$-0.124845\pi$
$11$	0.434507	+	0.752587i	0.131009	+	0.226914i	−0.793057	+	0.609147i	$0.791512\pi$
$12$		0			0
$13$	0.568572	+	0.984796i	0.157694	+	0.273133i	0.934037	−	0.357177i	$-0.116261\pi$
$13$	0.568572	+	0.984796i	0.157694	+	0.273133i	−0.776343	+	0.630311i	$0.782928\pi$
$14$		0			0
$15$	−1.37024	+	2.19968i	−0.353793	+	0.567954i
$16$		0			0
$17$	−0.621125	−	1.07582i	−0.150645	−	0.260925i	0.780820	−	0.624756i	$-0.214802\pi$
$17$	−0.621125	−	1.07582i	−0.150645	−	0.260925i	−0.931465	+	0.363832i	$0.881468\pi$
$18$		0			0
$19$	−4.32633	−	0.531855i	−0.992528	−	0.122016i
$19$	−4.32633	−	0.531855i	−0.992528	−	0.122016i
$20$		0			0
$21$	−6.08146	−	0.203851i	−1.32708	−	0.0444839i
$22$		0			0
$23$	2.37465	+	4.11302i	0.495149	+	0.857623i	0.999984	−	0.00559238i	$-0.00178012\pi$
$23$	2.37465	+	4.11302i	0.495149	+	0.857623i	−0.504835	+	0.863216i	$0.668447\pi$
$24$		0			0
$25$	−2.76129			−0.552258
$26$		0			0
$27$	−5.16992	−	0.521451i	−0.994952	−	0.100353i
$28$		0			0
$29$	−9.34648			−1.73560			−0.867799	−	0.496916i	$-0.834466\pi$
$29$	−9.34648			−1.73560			−0.867799	+	0.496916i	$0.834466\pi$
$30$		0			0
$31$	4.17123	−	7.22478i	0.749175	−	1.29761i	−0.199044	−	0.979991i	$-0.563784\pi$
$31$	4.17123	−	7.22478i	0.749175	−	1.29761i	0.948219	−	0.317618i	$-0.102883\pi$
$32$		0			0
$33$	1.50433	+	0.0504252i	0.261870	+	0.00877790i
$34$		0			0
$35$	2.62821	+	4.55219i	0.444249	+	0.769461i
$36$		0			0
$37$	−9.83760			−1.61729			−0.808646	−	0.588296i	$-0.799799\pi$
$37$	−9.83760			−1.61729			−0.808646	+	0.588296i	$0.799799\pi$
$38$		0			0
$39$	1.96849	+	0.0659838i	0.315210	+	0.0105659i
$40$		0			0
$41$	9.98097			1.55877			0.779383	−	0.626548i	$-0.215533\pi$
$41$	9.98097			1.55877			0.779383	+	0.626548i	$0.215533\pi$
$42$		0			0
$43$	3.89011	−	6.73787i	0.593236	−	1.02752i	−0.400557	−	0.916272i	$-0.631183\pi$
$43$	3.89011	−	6.73787i	0.593236	−	1.02752i	0.993793	−	0.111243i	$-0.0354833\pi$
$44$		0			0
$45$	1.97900	+	4.02889i	0.295011	+	0.600592i
$46$		0			0
$47$	−5.09144			−0.742663			−0.371332	−	0.928500i	$-0.621099\pi$
$47$	−5.09144			−0.742663			−0.371332	+	0.928500i	$0.621099\pi$
$48$		0			0
$49$	−2.67095	+	4.62623i	−0.381565	+	0.660890i
$50$		0			0
$51$	−2.15043	−	0.0720826i	−0.301121	−	0.0100936i
$52$		0			0
$53$	4.93311	−	8.54439i	0.677614	−	1.17366i	−0.298083	−	0.954540i	$-0.596347\pi$
$53$	4.93311	−	8.54439i	0.677614	−	1.17366i	0.975697	−	0.219122i	$-0.0703194\pi$
$54$		0			0
$55$	−0.650123	−	1.12605i	−0.0876625	−	0.151836i
$56$		0			0
$57$	−4.74392	+	5.87326i	−0.628347	+	0.777933i
$58$		0			0
$59$	13.5500			1.76406			0.882028	−	0.471196i	$-0.156178\pi$
$59$	13.5500			1.76406			0.882028	+	0.471196i	$0.156178\pi$
$60$		0			0
$61$	2.39838			0.307082			0.153541	−	0.988142i	$-0.450932\pi$
$61$	2.39838			0.307082			0.153541	+	0.988142i	$0.450932\pi$
$62$		0			0
$63$	−5.86904	+	8.75395i	−0.739429	+	1.10289i
$64$		0			0
$65$	−0.850716	−	1.47348i	−0.105518	−	0.182763i
$66$		0			0
$67$	0.655524	+	1.13540i	0.0800850	+	0.138711i	0.903286	−	0.429038i	$-0.141147\pi$
$67$	0.655524	+	1.13540i	0.0800850	+	0.138711i	−0.823201	+	0.567750i	$0.807814\pi$
$68$		0			0
$69$	8.22142	+	0.275582i	0.989742	+	0.0331762i
$70$		0			0
$71$	0.242447	+	0.419931i	0.0287732	+	0.0498366i	0.880053	−	0.474875i	$-0.157507\pi$
$71$	0.242447	+	0.419931i	0.0287732	+	0.0498366i	−0.851280	+	0.524711i	$0.824173\pi$
$72$		0			0
$73$	−5.07886	−	8.79685i	−0.594436	−	1.02959i	−0.993626	−	0.112725i	$-0.964042\pi$
$73$	−5.07886	−	8.79685i	−0.594436	−	1.02959i	0.399190	−	0.916868i	$-0.369291\pi$
$74$		0			0
$75$	−2.52877	+	4.05950i	−0.291997	+	0.468750i
$76$		0			0
$77$	1.52647	−	2.64392i	0.173957	−	0.301303i
$78$		0			0
$79$	−3.14994	+	5.45585i	−0.354395	+	0.613831i	−0.987014	−	0.160632i	$-0.948647\pi$
$79$	−3.14994	+	5.45585i	−0.354395	+	0.613831i	0.632619	+	0.774463i	$0.281980\pi$
$80$		0			0
$81$	−5.50118	+	7.12299i	−0.611242	+	0.791444i
$82$		0			0
$83$	2.07977	+	3.60227i	0.228284	+	0.395400i	0.957300	−	0.289097i	$-0.0933550\pi$
$83$	2.07977	+	3.60227i	0.228284	+	0.395400i	−0.729015	+	0.684497i	$0.760022\pi$
$84$		0			0
$85$	0.929347	+	1.60968i	0.100802	+	0.174594i
$86$		0			0
$87$	−8.55942	+	13.7407i	−0.917666	+	1.47316i
$88$		0			0
$89$	−2.98670	+	5.17312i	−0.316590	+	0.548350i	−0.979774	−	0.200106i	$-0.935871\pi$
$89$	−2.98670	+	5.17312i	−0.316590	+	0.548350i	0.663184	+	0.748456i	$0.269205\pi$
$90$		0			0
$91$	1.99745	−	3.45969i	0.209390	−	0.362674i
$92$		0			0
$93$	−6.80150	−	12.7487i	−0.705283	−	1.32198i
$94$		0			0
$95$	6.47319	+	0.795778i	0.664136	+	0.0816451i
$96$		0			0
$97$	6.97644	−	12.0835i	0.708350	−	1.22690i	−0.257119	−	0.966380i	$-0.582773\pi$
$97$	6.97644	−	12.0835i	0.708350	−	1.22690i	0.965469	−	0.260518i	$-0.0838933\pi$
$98$		0			0
$99$	1.45178	−	2.16540i	0.145910	−	0.217631i
$100$		0			0
$101$	−0.355796			−0.0354030			−0.0177015	−	0.999843i	$-0.505635\pi$
$101$	−0.355796			−0.0354030			−0.0177015	+	0.999843i	$0.505635\pi$
$102$		0			0
$103$	0.824559	−	1.42818i	0.0812462	−	0.140723i	−0.822539	−	0.568708i	$-0.807443\pi$
$103$	0.824559	−	1.42818i	0.0812462	−	0.140723i	0.903785	+	0.427986i	$0.140777\pi$
$104$		0			0
$105$	9.09928	+	0.305008i	0.887998	+	0.0297658i
$106$		0			0
$107$	14.2854			1.38102			0.690510	−	0.723323i	$-0.257386\pi$
$107$	14.2854			1.38102			0.690510	+	0.723323i	$0.257386\pi$
$108$		0			0
$109$	−3.35900	−	5.81795i	−0.321734	−	0.557259i	0.659112	−	0.752045i	$-0.270932\pi$
$109$	−3.35900	−	5.81795i	−0.321734	−	0.557259i	−0.980846	+	0.194786i	$0.937599\pi$
$110$		0			0
$111$	−9.00918	+	14.4627i	−0.855114	+	1.37274i
$112$		0			0
$113$	4.03636	−	6.99118i	0.379709	−	0.657675i	−0.611311	−	0.791390i	$-0.709358\pi$
$113$	4.03636	−	6.99118i	0.379709	−	0.657675i	0.991020	+	0.133716i	$0.0426909\pi$
$114$		0			0
$115$	−3.55303	−	6.15403i	−0.331322	−	0.573866i
$116$		0			0
$117$	1.89973	−	2.83353i	0.175630	−	0.261960i
$118$		0			0
$119$	−2.18208	+	3.77947i	−0.200031	+	0.346463i
$120$		0			0
$121$	5.12241	−	8.87227i	0.465673	−	0.806570i
$122$		0			0
$123$	9.14048	−	14.6735i	0.824170	−	1.32306i
$124$		0			0
$125$	11.6127			1.03867
$126$		0			0
$127$	4.09331	−	7.08983i	0.363223	−	0.629121i	−0.625266	−	0.780411i	$-0.715010\pi$
$127$	4.09331	−	7.08983i	0.363223	−	0.629121i	0.988489	+	0.151291i	$0.0483430\pi$
$128$		0			0
$129$	−6.34312	−	11.8895i	−0.558480	−	1.04681i
$130$		0			0
$131$	−16.0622			−1.40336			−0.701682	−	0.712491i	$-0.747567\pi$
$131$	−16.0622			−1.40336			−0.701682	+	0.712491i	$0.747567\pi$
$132$		0			0
$133$	5.98129	+	14.0968i	0.518644	+	1.22235i
$134$		0			0
$135$	7.73540	+	0.780212i	0.665757	+	0.0671499i
$136$		0			0
$137$	4.95800			0.423590			0.211795	−	0.977314i	$-0.432069\pi$
$137$	4.95800			0.423590			0.211795	+	0.977314i	$0.432069\pi$
$138$		0			0
$139$	4.30548	+	7.45731i	0.365186	+	0.632521i	0.988806	−	0.149207i	$-0.0476720\pi$
$139$	4.30548	+	7.45731i	0.365186	+	0.632521i	−0.623620	+	0.781728i	$0.714339\pi$
$140$		0			0
$141$	−4.66270	+	7.48516i	−0.392670	+	0.630364i
$142$		0			0
$143$	−0.494097	+	0.855800i	−0.0413184	+	0.0715656i
$144$		0			0
$145$	13.9845			1.16135
$146$		0			0
$147$	4.35519	+	8.16335i	0.359210	+	0.673302i
$148$		0			0
$149$	−8.72144			−0.714488			−0.357244	−	0.934011i	$-0.616284\pi$
$149$	−8.72144			−0.714488			−0.357244	+	0.934011i	$0.616284\pi$
$150$		0			0
$151$	0.0114486	+	0.0198295i	0.000931673	+	0.00161371i	0.866491	−	0.499193i	$-0.166370\pi$
$151$	0.0114486	+	0.0198295i	0.000931673	+	0.00161371i	−0.865559	+	0.500807i	$0.833037\pi$
$152$		0			0
$153$	−2.07532	+	3.09543i	−0.167780	+	0.250251i
$154$		0			0
$155$	−6.24112	+	10.8099i	−0.501299	+	0.868276i
$156$		0			0
$157$	−11.6136			−0.926867			−0.463433	−	0.886132i	$-0.653383\pi$
$157$	−11.6136			−0.926867			−0.463433	+	0.886132i	$0.653383\pi$
$158$		0			0
$159$	−8.04380	−	15.0773i	−0.637915	−	1.19570i
$160$		0			0
$161$	8.34240	−	14.4495i	0.657473	−	1.13878i
$162$		0			0
$163$	19.2386			1.50689			0.753444	−	0.657513i	$-0.228391\pi$
$163$	19.2386			1.50689			0.753444	+	0.657513i	$0.228391\pi$
$164$		0			0
$165$	−2.25083	−	0.0754478i	−0.175227	−	0.00587361i
$166$		0			0
$167$	4.83444	+	8.37349i	0.374100	+	0.647960i	0.990192	−	0.139714i	$-0.0446184\pi$
$167$	4.83444	+	8.37349i	0.374100	+	0.647960i	−0.616092	+	0.787674i	$0.711285\pi$
$168$		0			0
$169$	5.85345	−	10.1385i	0.450266	−	0.779883i
$170$		0			0
$171$	4.29011	+	12.3529i	0.328073	+	0.944652i
$172$		0			0
$173$	−0.994425	+	1.72240i	−0.0756047	+	0.130951i	−0.901349	−	0.433093i	$-0.857422\pi$
$173$	−0.994425	+	1.72240i	−0.0756047	+	0.130951i	0.825744	+	0.564045i	$0.190755\pi$
$174$		0			0
$175$	4.85035	+	8.40106i	0.366652	+	0.635060i
$176$		0			0
$177$	12.4089	−	19.9204i	0.932714	−	1.49731i
$178$		0			0
$179$	−8.69114			−0.649607			−0.324803	−	0.945782i	$-0.605298\pi$
$179$	−8.69114			−0.649607			−0.324803	+	0.945782i	$0.605298\pi$
$180$		0			0
$181$	−9.29190	+	16.0940i	−0.690662	+	1.19626i	0.280960	+	0.959720i	$0.409347\pi$
$181$	−9.29190	+	16.0940i	−0.690662	+	1.19626i	−0.971621	+	0.236542i	$0.923986\pi$
$182$		0			0
$183$	2.19642	−	3.52597i	0.162364	−	0.260647i
$184$		0			0
$185$	14.7193			1.08219
$186$		0			0
$187$	0.539766	−	0.934902i	0.0394716	−	0.0683668i
$188$		0			0
$189$	7.49476	+	16.6451i	0.545163	+	1.21075i
$190$		0			0
$191$	11.0501	+	19.1393i	0.799554	+	1.38487i	0.919907	+	0.392137i	$0.128264\pi$
$191$	11.0501	+	19.1393i	0.799554	+	1.38487i	−0.120353	+	0.992731i	$0.538403\pi$
$192$		0			0
$193$	9.50968			0.684522			0.342261	−	0.939605i	$-0.388807\pi$
$193$	9.50968			0.684522			0.342261	+	0.939605i	$0.388807\pi$
$194$		0			0
$195$	−2.94531	−	0.0987270i	−0.210918	−	0.00706999i
$196$		0			0
$197$	2.30839			0.164466			0.0822329	−	0.996613i	$-0.473795\pi$
$197$	2.30839			0.164466			0.0822329	+	0.996613i	$0.473795\pi$
$198$		0			0
$199$	−4.27153	+	7.39850i	−0.302800	+	0.524466i	−0.976769	−	0.214294i	$-0.931255\pi$
$199$	−4.27153	+	7.39850i	−0.302800	+	0.524466i	0.673969	+	0.738760i	$0.264588\pi$
$200$		0			0
$201$	2.26953	+	0.0760746i	0.160080	+	0.00536589i
$202$		0			0
$203$	16.4176	+	28.4361i	1.15229	+	1.99582i
$204$		0			0
$205$	−14.9338			−1.04302
$206$		0			0
$207$	7.93425	−	11.8343i	0.551468	−	0.822541i
$208$		0			0
$209$	−1.47955	−	3.48704i	−0.102343	−	0.241203i
$210$		0			0
$211$	−18.0002			−1.23919			−0.619594	−	0.784923i	$-0.712703\pi$
$211$	−18.0002			−1.23919			−0.619594	+	0.784923i	$0.712703\pi$
$212$		0			0
$213$	0.839390	+	0.0281364i	0.0575141	+	0.00192788i
$214$		0			0
$215$	−5.82051	+	10.0814i	−0.396955	+	0.687547i
$216$		0			0
$217$	−29.3079			−1.98955
$218$		0			0
$219$	−17.5838	−	0.589411i	−1.18820	−	0.0398287i
$220$		0			0
$221$	0.706309	−	1.22336i	0.0475115	−	0.0822923i
$222$		0			0
$223$	8.07076	−	13.9790i	0.540458	−	0.936101i	−0.458419	−	0.888736i	$-0.651584\pi$
$223$	8.07076	−	13.9790i	0.540458	−	0.936101i	0.998878	−	0.0473651i	$-0.0150824\pi$
$224$		0			0
$225$	3.65223	+	7.43530i	0.243482	+	0.495687i
$226$		0			0
$227$	−4.82787	−	8.36211i	−0.320437	−	0.555013i	0.660141	−	0.751141i	$-0.270496\pi$
$227$	−4.82787	−	8.36211i	−0.320437	−	0.555013i	−0.980578	+	0.196128i	$0.937163\pi$
$228$		0			0
$229$	7.64050	−	13.2337i	0.504898	−	0.874510i	−0.495086	−	0.868844i	$-0.664863\pi$
$229$	7.64050	−	13.2337i	0.504898	−	0.874510i	0.999984	−	0.00566549i	$-0.00180339\pi$
$230$		0			0
$231$	−2.48902	−	4.66541i	−0.163765	−	0.306961i
$232$		0			0
$233$	7.75983	+	13.4404i	0.508363	+	0.880511i	0.999953	+	0.00968433i	$0.00308267\pi$
$233$	7.75983	+	13.4404i	0.508363	+	0.880511i	−0.491590	+	0.870827i	$0.663584\pi$
$234$		0			0
$235$	7.61798			0.496942
$236$		0			0
$237$	5.13621	+	9.62728i	0.333632	+	0.625359i
$238$		0			0
$239$	0.427593	−	0.740614i	0.0276587	−	0.0479063i	−0.851865	−	0.523762i	$-0.824528\pi$
$239$	0.427593	−	0.740614i	0.0276587	−	0.0479063i	0.879523	+	0.475856i	$0.157861\pi$
$240$		0			0
$241$	4.93166			0.317676			0.158838	−	0.987305i	$-0.449225\pi$
$241$	4.93166			0.317676			0.158838	+	0.987305i	$0.449225\pi$
$242$		0			0
$243$	5.43391	+	14.6107i	0.348585	+	0.937277i
$244$		0			0
$245$	3.99637	−	6.92191i	0.255319	−	0.442225i
$246$		0			0
$247$	−1.93606	−	4.56295i	−0.123189	−	0.290334i
$248$		0			0
$249$	7.20049	+	0.241361i	0.456313	+	0.0152956i
$250$		0			0
$251$	1.82902	−	3.16796i	0.115447	−	0.199960i	−0.802511	−	0.596637i	$-0.796503\pi$
$251$	1.82902	−	3.16796i	0.115447	−	0.199960i	0.917958	+	0.396677i	$0.129837\pi$
$252$		0			0
$253$	−2.06360	+	3.57427i	−0.129738	+	0.224712i
$254$		0			0
$255$	3.21755	+	0.107852i	0.201490	+	0.00675397i
$256$		0			0
$257$	−13.3148	−	23.0619i	−0.830553	−	1.43856i	−0.897601	−	0.440810i	$-0.854691\pi$
$257$	−13.3148	−	23.0619i	−0.830553	−	1.43856i	0.0670479	−	0.997750i	$-0.478642\pi$
$258$		0			0
$259$	17.2803	+	29.9303i	1.07374	+	1.85978i
$260$		0			0
$261$	12.3621	+	25.1672i	0.765198	+	1.55781i
$262$		0			0
$263$	9.70442	−	16.8086i	0.598400	−	1.03646i	−0.394657	−	0.918829i	$-0.629137\pi$
$263$	9.70442	−	16.8086i	0.598400	−	1.03646i	0.993057	−	0.117631i	$-0.0375301\pi$
$264$		0			0
$265$	−7.38107	+	12.7844i	−0.453416	+	0.785339i
$266$		0			0
$267$	4.87005	+	9.12839i	0.298042	+	0.558648i
$268$		0			0
$269$	−9.88560	−	17.1224i	−0.602736	−	1.04397i	−0.992405	−	0.123014i	$-0.960744\pi$
$269$	−9.88560	−	17.1224i	−0.602736	−	1.04397i	0.389669	−	0.920955i	$-0.372589\pi$
$270$		0			0
$271$	−0.144391	−	0.250093i	−0.00877114	−	0.0151921i	0.861607	−	0.507577i	$-0.169459\pi$
$271$	−0.144391	−	0.250093i	−0.00877114	−	0.0151921i	−0.870378	+	0.492385i	$0.836125\pi$
$272$		0			0
$273$	−3.25700	−	6.10490i	−0.197122	−	0.369485i
$274$		0			0
$275$	−1.19980	−	2.07811i	−0.0723506	−	0.125315i
$276$		0			0
$277$	−9.39174	−	16.2670i	−0.564295	−	0.977388i	−0.997115	−	0.0759072i	$-0.975815\pi$
$277$	−9.39174	−	16.2670i	−0.564295	−	0.977388i	0.432820	−	0.901480i	$-0.357519\pi$
$278$		0			0
$279$	−24.9712	−	1.67595i	−1.49499	−	0.100337i
$280$		0			0
$281$	−26.8843			−1.60379			−0.801893	−	0.597468i	$-0.796174\pi$
$281$	−26.8843			−1.60379			−0.801893	+	0.597468i	$0.796174\pi$
$282$		0			0
$283$	7.41143			0.440564			0.220282	−	0.975436i	$-0.429302\pi$
$283$	7.41143			0.440564			0.220282	+	0.975436i	$0.429302\pi$
$284$		0			0
$285$	7.09800	−	8.78777i	0.420449	−	0.520542i
$286$		0			0
$287$	−17.5321	−	30.3665i	−1.03489	−	1.79248i
$288$		0			0
$289$	7.72841	−	13.3860i	0.454612	−	0.787411i
$290$		0			0
$291$	−11.3756	−	21.3224i	−0.666850	−	1.24994i
$292$		0			0
$293$	−4.54267	+	7.86814i	−0.265386	+	0.459662i	−0.967665	−	0.252240i	$-0.918833\pi$
$293$	−4.54267	+	7.86814i	−0.265386	+	0.459662i	0.702279	+	0.711902i	$0.252166\pi$
$294$		0			0
$295$	−20.2739			−1.18039
$296$		0			0
$297$	−1.85393	−	4.11739i	−0.107576	−	0.238915i
$298$		0			0
$299$	−2.70032	+	4.67709i	−0.156164	+	0.270483i
$300$		0			0
$301$	−27.3327			−1.57543
$302$		0			0
$303$	−0.325835	+	0.523072i	−0.0187187	+	0.0300497i
$304$		0			0
$305$	−3.58854			−0.205479
$306$		0			0
$307$	7.30531	+	12.6532i	0.416936	+	0.722154i	0.995630	−	0.0933910i	$-0.0297707\pi$
$307$	7.30531	+	12.6532i	0.416936	+	0.722154i	−0.578694	+	0.815545i	$0.696437\pi$
$308$		0			0
$309$	−1.34450	−	2.52013i	−0.0764862	−	0.143365i
$310$		0			0
$311$	−1.37205	+	2.37646i	−0.0778019	+	0.134757i	−0.902301	−	0.431106i	$-0.858124\pi$
$311$	−1.37205	+	2.37646i	−0.0778019	+	0.134757i	0.824499	+	0.565863i	$0.191457\pi$
$312$		0			0
$313$	−11.0932			−0.627025			−0.313513	−	0.949584i	$-0.601506\pi$
$313$	−11.0932			−0.627025			−0.313513	+	0.949584i	$0.601506\pi$
$314$		0			0
$315$	8.78144	−	13.0979i	0.494778	−	0.737985i
$316$		0			0
$317$	−16.9245			−0.950575			−0.475288	−	0.879830i	$-0.657656\pi$
$317$	−16.9245			−0.950575			−0.475288	+	0.879830i	$0.657656\pi$
$318$		0			0
$319$	−4.06111	−	7.03404i	−0.227378	−	0.393831i
$320$		0			0
$321$	13.0824	−	21.0016i	0.730190	−	1.17219i
$322$		0			0
$323$	2.11501	+	4.98470i	0.117682	+	0.277356i
$324$		0			0
$325$	−1.56999	−	2.71931i	−0.0870875	−	0.150840i
$326$		0			0
$327$	−11.6294	−	0.389817i	−0.643106	−	0.0215569i
$328$		0			0
$329$	8.94339	+	15.4904i	0.493065	+	0.854014i
$330$		0			0
$331$	−2.56575	−	4.44401i	−0.141026	−	0.244265i	0.786857	−	0.617135i	$-0.211707\pi$
$331$	−2.56575	−	4.44401i	−0.141026	−	0.244265i	−0.927883	+	0.372871i	$0.878374\pi$
$332$		0			0
$333$	13.0117	+	26.4896i	0.713038	+	1.45162i
$334$		0			0
$335$	−0.980816	−	1.69882i	−0.0535877	−	0.0928166i
$336$		0			0
$337$	7.16701			0.390412			0.195206	−	0.980762i	$-0.437462\pi$
$337$	7.16701			0.390412			0.195206	+	0.980762i	$0.437462\pi$
$338$		0			0
$339$	−6.58158	−	12.3365i	−0.357463	−	0.670026i
$340$		0			0
$341$	7.24970			0.392593
$342$		0			0
$343$	−5.82505			−0.314523
$344$		0			0
$345$	−12.3011	−	0.412335i	−0.662271	−	0.0221994i
$346$		0			0
$347$	12.3314			0.661987			0.330993	−	0.943633i	$-0.392616\pi$
$347$	12.3314			0.661987			0.330993	+	0.943633i	$0.392616\pi$
$348$		0			0
$349$	7.48594	+	12.9660i	0.400713	+	0.694055i	0.993812	−	0.111074i	$-0.0354291\pi$
$349$	7.48594	+	12.9660i	0.400713	+	0.694055i	−0.593099	+	0.805129i	$0.702096\pi$
$350$		0			0
$351$	−2.42595	−	5.38780i	−0.129488	−	0.287579i
$352$		0			0
$353$	−2.39398	−	4.14650i	−0.127419	−	0.220696i	0.795257	−	0.606272i	$-0.207336\pi$
$353$	−2.39398	−	4.14650i	−0.127419	−	0.220696i	−0.922676	+	0.385577i	$0.874003\pi$
$354$		0			0
$355$	−0.362757	−	0.628314i	−0.0192532	−	0.0333474i
$356$		0			0
$357$	3.55804	+	6.66917i	0.188311	+	0.352970i
$358$		0			0
$359$	−15.7031	−	27.1985i	−0.828776	−	1.43548i	−0.898999	−	0.437951i	$-0.855704\pi$
$359$	−15.7031	−	27.1985i	−0.828776	−	1.43548i	0.0702230	−	0.997531i	$-0.477629\pi$
$360$		0			0
$361$	18.4343	+	4.60196i	0.970224	+	0.242208i
$362$		0			0
$363$	−8.35247	−	15.6558i	−0.438391	−	0.821718i
$364$		0			0
$365$	7.59916	+	13.1621i	0.397758	+	0.688937i
$366$		0			0
$367$	−11.1232			−0.580625			−0.290313	−	0.956932i	$-0.593759\pi$
$367$	−11.1232			−0.580625			−0.290313	+	0.956932i	$0.593759\pi$
$368$		0			0
$369$	−13.2014	−	26.8757i	−0.687235	−	1.39909i
$370$		0			0
$371$	−34.6610			−1.79951
$372$		0			0
$373$	−9.05268	+	15.6797i	−0.468730	+	0.811864i	−0.999361	−	0.0357386i	$-0.988622\pi$
$373$	−9.05268	+	15.6797i	−0.468730	+	0.811864i	0.530631	+	0.847603i	$0.321955\pi$
$374$		0			0
$375$	10.6348	−	17.0723i	0.549179	−	0.881612i
$376$		0			0
$377$	−5.31415	−	9.20437i	−0.273692	−	0.474049i
$378$		0			0
$379$	8.98835			0.461700			0.230850	−	0.972989i	$-0.425849\pi$
$379$	8.98835			0.461700			0.230850	+	0.972989i	$0.425849\pi$
$380$		0			0
$381$	−6.67446	−	12.5106i	−0.341943	−	0.640936i
$382$		0			0
$383$	−26.0050			−1.32879			−0.664397	−	0.747380i	$-0.731312\pi$
$383$	−26.0050			−1.32879			−0.664397	+	0.747380i	$0.731312\pi$
$384$		0			0
$385$	−2.28395	+	3.95592i	−0.116401	+	0.201612i
$386$		0			0
$387$	−23.2883	−	1.56300i	−1.18381	−	0.0794520i
$388$		0			0
$389$	−13.3965			−0.679228			−0.339614	−	0.940565i	$-0.610296\pi$
$389$	−13.3965			−0.679228			−0.339614	+	0.940565i	$0.610296\pi$
$390$		0			0
$391$	2.94991	−	5.10939i	0.149183	−	0.258393i
$392$		0			0
$393$	−14.7096	+	23.6138i	−0.742004	+	1.19116i
$394$		0			0
$395$	4.71303	−	8.16321i	0.237138	−	0.410736i
$396$		0			0
$397$	13.0282	+	22.5656i	0.653868	+	1.13253i	0.982176	+	0.187962i	$0.0601882\pi$
$397$	13.0282	+	22.5656i	0.653868	+	1.13253i	−0.328308	+	0.944571i	$0.606479\pi$
$398$		0			0
$399$	26.2020	+	4.11638i	1.31174	+	0.206077i
$400$		0			0
$401$	20.7232			1.03487			0.517435	−	0.855723i	$-0.326887\pi$
$401$	20.7232			1.03487			0.517435	+	0.855723i	$0.326887\pi$
$402$		0			0
$403$	9.48658			0.472560
$404$		0			0
$405$	8.23104	−	10.6577i	0.409003	−	0.529583i
$406$		0			0
$407$	−4.27450	−	7.40365i	−0.211879	−	0.366985i
$408$		0			0
$409$	16.5602	+	28.6831i	0.818849	+	1.41829i	0.906531	+	0.422140i	$0.138721\pi$
$409$	16.5602	+	28.6831i	0.818849	+	1.41829i	−0.0876817	+	0.996149i	$0.527946\pi$
$410$		0			0
$411$	4.54049	−	7.28898i	0.223966	−	0.359539i
$412$		0			0
$413$	−23.8012	−	41.2250i	−1.17118	−	2.02855i
$414$		0			0
$415$	−3.11182	−	5.38983i	−0.152753	−	0.264576i
$416$		0			0
$417$	14.9063	+	0.499658i	0.729962	+	0.0244684i
$418$		0			0
$419$	−16.4221	+	28.4440i	−0.802273	+	1.38958i	0.115843	+	0.993268i	$0.463043\pi$
$419$	−16.4221	+	28.4440i	−0.802273	+	1.38958i	−0.918117	+	0.396311i	$0.870290\pi$
$420$		0			0
$421$	−10.5090	+	18.2022i	−0.512179	+	0.887119i	0.487722	+	0.872999i	$0.337828\pi$
$421$	−10.5090	+	18.2022i	−0.512179	+	0.887119i	−0.999900	+	0.0141202i	$0.995505\pi$
$422$		0			0
$423$	6.73421	+	13.7097i	0.327429	+	0.666588i
$424$		0			0
$425$	1.71511	+	2.97065i	0.0831949	+	0.144098i
$426$		0			0
$427$	−4.21289	−	7.29693i	−0.203876	−	0.353123i
$428$		0			0
$429$	0.805662	+	1.51013i	0.0388977	+	0.0729097i
$430$		0			0
$431$	−1.35082	+	2.33969i	−0.0650668	+	0.112699i	−0.896724	−	0.442591i	$-0.854059\pi$
$431$	−1.35082	+	2.33969i	−0.0650668	+	0.112699i	0.831657	+	0.555290i	$0.187393\pi$
$432$		0			0
$433$	−11.1804	+	19.3651i	−0.537297	+	0.930626i	0.461751	+	0.887010i	$0.347221\pi$
$433$	−11.1804	+	19.3651i	−0.537297	+	0.930626i	−0.999048	+	0.0436167i	$0.986112\pi$
$434$		0			0
$435$	12.8069	−	20.5592i	0.614043	−	0.985740i
$436$		0			0
$437$	−8.08600	−	19.0572i	−0.386806	−	0.911631i
$438$		0			0
$439$	2.00081	−	3.46551i	0.0954935	−	0.165400i	−0.814321	−	0.580415i	$-0.802890\pi$
$439$	2.00081	−	3.46551i	0.0954935	−	0.165400i	0.909814	+	0.415015i	$0.136224\pi$
$440$		0			0
$441$	15.9898	+	1.07316i	0.761417	+	0.0511029i
$442$		0			0
$443$	−7.87826			−0.374307			−0.187154	−	0.982331i	$-0.559926\pi$
$443$	−7.87826			−0.374307			−0.187154	+	0.982331i	$0.559926\pi$
$444$		0			0
$445$	4.46880	−	7.74019i	0.211842	−	0.366920i
$446$		0			0
$447$	−7.98702	+	12.8218i	−0.377773	+	0.606450i
$448$		0			0
$449$	−23.4898			−1.10855			−0.554277	−	0.832332i	$-0.687005\pi$
$449$	−23.4898			−1.10855			−0.554277	+	0.832332i	$0.687005\pi$
$450$		0			0
$451$	4.33680	+	7.51155i	0.204212	+	0.353705i
$452$		0			0
$453$	0.0396368	+	0.00132863i	0.00186230	+	6.24244e-5i
$454$		0			0
$455$	−2.98865	+	5.17650i	−0.140110	+	0.242678i
$456$		0			0
$457$	8.23954	+	14.2713i	0.385430	+	0.667584i	0.991829	−	0.127577i	$-0.0407199\pi$
$457$	8.23954	+	14.2713i	0.385430	+	0.667584i	−0.606399	+	0.795160i	$0.707387\pi$
$458$		0			0
$459$	2.65018	+	5.88579i	0.123700	+	0.274725i
$460$		0			0
$461$	−20.6153	+	35.7068i	−0.960152	+	1.66303i	−0.238042	+	0.971255i	$0.576505\pi$
$461$	−20.6153	+	35.7068i	−0.960152	+	1.66303i	−0.722111	+	0.691778i	$0.756828\pi$
$462$		0			0
$463$	13.7198	−	23.7634i	0.637614	−	1.10438i	−0.348341	−	0.937368i	$-0.613255\pi$
$463$	13.7198	−	23.7634i	0.637614	−	1.10438i	0.985955	−	0.167012i	$-0.0534119\pi$
$464$		0			0
$465$	10.1766	+	19.0750i	0.471929	+	0.884582i
$466$		0			0
$467$	31.3504			1.45072			0.725361	−	0.688369i	$-0.241673\pi$
$467$	31.3504			1.45072			0.725361	+	0.688369i	$0.241673\pi$
$468$		0			0
$469$	2.30292	−	3.98878i	0.106339	−	0.184185i
$470$		0			0
$471$	−10.6356	+	17.0737i	−0.490064	+	0.786714i
$472$		0			0
$473$	6.76111			0.310876
$474$		0			0
$475$	11.9463	+	1.46861i	0.548132	+	0.0673842i
$476$		0			0
$477$	−29.5322	−	1.98207i	−1.35219	−	0.0907527i
$478$		0			0
$479$	26.8259			1.22570			0.612852	−	0.790197i	$-0.290022\pi$
$479$	26.8259			1.22570			0.612852	+	0.790197i	$0.290022\pi$
$480$		0			0
$481$	−5.59338	−	9.68802i	−0.255036	−	0.441736i
$482$		0			0
$483$	−13.6029	−	25.4972i	−0.618954	−	1.16016i
$484$		0			0
$485$	−10.4384	+	18.0798i	−0.473982	+	0.820960i
$486$		0			0
$487$	34.0195			1.54157			0.770785	−	0.637095i	$-0.219864\pi$
$487$	34.0195			1.54157			0.770785	+	0.637095i	$0.219864\pi$
$488$		0			0
$489$	17.6186	−	28.2836i	0.796740	−	1.27903i
$490$		0			0
$491$	−6.07072			−0.273968			−0.136984	−	0.990573i	$-0.543741\pi$
$491$	−6.07072			−0.273968			−0.136984	+	0.990573i	$0.543741\pi$
$492$		0			0
$493$	5.80533	+	10.0551i	0.261459	+	0.452860i
$494$		0			0
$495$	−2.17221	+	3.23995i	−0.0976334	+	0.145625i
$496$		0			0
$497$	0.851743	−	1.47526i	0.0382059	−	0.0661745i
$498$		0			0
$499$	15.9610			0.714512			0.357256	−	0.934006i	$-0.383712\pi$
$499$	15.9610			0.714512			0.357256	+	0.934006i	$0.383712\pi$
$500$		0			0
$501$	16.7376	+	0.561045i	0.747780	+	0.0250656i
$502$		0			0
$503$	0.880748	−	1.52550i	0.0392706	−	0.0680187i	−0.845722	−	0.533624i	$-0.820830\pi$
$503$	0.880748	−	1.52550i	0.0392706	−	0.0680187i	0.884993	+	0.465605i	$0.154163\pi$
$504$		0			0
$505$	0.532354			0.0236894
$506$		0			0
$507$	−9.54449	−	17.8901i	−0.423886	−	0.794529i
$508$		0			0
$509$	0.199953	+	0.346329i	0.00886276	+	0.0153507i	0.870423	−	0.492305i	$-0.163846\pi$
$509$	0.199953	+	0.346329i	0.00886276	+	0.0153507i	−0.861560	+	0.507656i	$0.830512\pi$
$510$		0			0
$511$	−17.8426	+	30.9043i	−0.789310	+	1.36712i
$512$		0			0
$513$	22.0895	+	5.00562i	0.975273	+	0.221003i
$514$		0			0
$515$	−1.23373	+	2.13688i	−0.0543647	+	0.0941624i
$516$		0			0
$517$	−2.21227	−	3.83176i	−0.0972953	−	0.168520i
$518$		0			0
$519$	1.62148	+	3.03930i	0.0711753	+	0.133411i
$520$		0			0
$521$	−14.1257			−0.618857			−0.309428	−	0.950923i	$-0.600138\pi$
$521$	−14.1257			−0.618857			−0.309428	+	0.950923i	$0.600138\pi$
$522$		0			0
$523$	−4.20355	+	7.28077i	−0.183809	+	0.318366i	−0.943174	−	0.332298i	$-0.892176\pi$
$523$	−4.20355	+	7.28077i	−0.183809	+	0.318366i	0.759366	+	0.650664i	$0.225509\pi$
$524$		0			0
$525$	16.7927	+	0.562892i	0.732893	+	0.0245666i
$526$		0			0
$527$	−10.3634			−0.451437
$528$		0			0
$529$	0.222062	−	0.384622i	0.00965486	−	0.0167227i
$530$		0			0
$531$	−17.9219	−	36.4859i	−0.777745	−	1.58335i
$532$		0			0
$533$	5.67490	+	9.82922i	0.245807	+	0.425751i
$534$		0			0
$535$	−21.3742			−0.924089
$536$		0			0
$537$	−7.95927	+	12.7772i	−0.343468	+	0.551379i
$538$		0			0
$539$	−4.64219			−0.199953
$540$		0			0
$541$	−8.74719	+	15.1506i	−0.376071	+	0.651374i	−0.990487	−	0.137608i	$-0.956058\pi$
$541$	−8.74719	+	15.1506i	−0.376071	+	0.651374i	0.614416	+	0.788982i	$0.289392\pi$
$542$		0			0
$543$	15.1511	+	28.3992i	0.650198	+	1.21873i
$544$		0			0
$545$	5.02584	+	8.70501i	0.215283	+	0.372882i
$546$		0			0
$547$	−19.2701			−0.823929			−0.411965	−	0.911200i	$-0.635157\pi$
$547$	−19.2701			−0.823929			−0.411965	+	0.911200i	$0.635157\pi$
$548$		0			0
$549$	−3.17223	−	6.45811i	−0.135387	−	0.275625i
$550$		0			0
$551$	40.4359	+	4.97097i	1.72263	+	0.211770i
$552$		0			0
$553$	22.1321			0.941153
$554$		0			0
$555$	13.4798	−	21.6395i	0.572187	−	0.918548i
$556$		0			0
$557$	8.95178	−	15.5049i	0.379299	−	0.656966i	−0.611661	−	0.791120i	$-0.709498\pi$
$557$	8.95178	−	15.5049i	0.379299	−	0.656966i	0.990960	+	0.134154i	$0.0428318\pi$
$558$		0			0
$559$	8.84723			0.374198
$560$		0			0
$561$	−0.880128	−	1.64971i	−0.0371591	−	0.0696508i
$562$		0			0
$563$	−19.6213	+	33.9851i	−0.826939	+	1.43230i	0.0734891	+	0.997296i	$0.476587\pi$
$563$	−19.6213	+	33.9851i	−0.826939	+	1.43230i	−0.900428	+	0.435005i	$0.856747\pi$
$564$		0			0
$565$	−6.03933	+	10.4604i	−0.254076	+	0.440073i
$566$		0			0
$567$	31.3344	+	4.22508i	1.31592	+	0.177437i
$568$		0			0
$569$	−22.3735	−	38.7520i	−0.937946	−	1.62457i	−0.769295	−	0.638894i	$-0.779392\pi$
$569$	−22.3735	−	38.7520i	−0.937946	−	1.62457i	−0.168651	−	0.985676i	$-0.553941\pi$
$570$		0			0
$571$	−8.96834	+	15.5336i	−0.375313	+	0.650062i	−0.990374	−	0.138418i	$-0.955798\pi$
$571$	−8.96834	+	15.5336i	−0.375313	+	0.650062i	0.615060	+	0.788480i	$0.289132\pi$
$572$		0			0
$573$	38.2570	+	1.28238i	1.59821	+	0.0535721i
$574$		0			0
$575$	−6.55710	−	11.3572i	−0.273450	−	0.473629i
$576$		0			0
$577$	−31.4029			−1.30732			−0.653659	−	0.756789i	$-0.726767\pi$
$577$	−31.4029			−1.30732			−0.653659	+	0.756789i	$0.726767\pi$
$578$		0			0
$579$	8.70889	−	13.9806i	0.361929	−	0.581015i
$580$		0			0
$581$	7.30645	−	12.6551i	0.303123	−	0.525024i
$582$		0			0
$583$	8.57387			0.355093
$584$		0			0
$585$	−2.84243	+	4.23962i	−0.117520	+	0.175287i
$586$		0			0
$587$	15.7460	−	27.2729i	0.649907	−	1.12567i	−0.333238	−	0.942843i	$-0.608141\pi$
$587$	15.7460	−	27.2729i	0.649907	−	1.12567i	0.983145	−	0.182829i	$-0.0585253\pi$
$588$		0			0
$589$	−21.8886	+	29.0383i	−0.901906	+	1.19650i
$590$		0			0
$591$	2.11400	−	3.39366i	0.0869583	−	0.139597i
$592$		0			0
$593$	−3.63034	+	6.28793i	−0.149080	+	0.258214i	−0.930888	−	0.365305i	$-0.880965\pi$
$593$	−3.63034	+	6.28793i	−0.149080	+	0.258214i	0.781808	+	0.623520i	$0.214298\pi$
$594$		0			0
$595$	3.26489	−	5.65496i	0.133848	−	0.231831i
$596$		0			0
$597$	6.96504	+	13.0552i	0.285060	+	0.534316i
$598$		0			0
$599$	−5.35440	−	9.27409i	−0.218775	−	0.378929i	0.735659	−	0.677352i	$-0.236873\pi$
$599$	−5.35440	−	9.27409i	−0.218775	−	0.378929i	−0.954434	+	0.298423i	$0.903539\pi$
$600$		0			0
$601$	4.56439	+	7.90576i	0.186185	+	0.322483i	0.943975	−	0.330016i	$-0.107054\pi$
$601$	4.56439	+	7.90576i	0.186185	+	0.322483i	−0.757790	+	0.652499i	$0.773721\pi$
$602$		0			0
$603$	2.19025	−	3.26686i	0.0891940	−	0.133037i
$604$		0			0
$605$	−7.66431	+	13.2750i	−0.311599	+	0.539704i
$606$		0			0
$607$	10.6643	−	18.4711i	0.432850	−	0.749719i	−0.564267	−	0.825592i	$-0.690841\pi$
$607$	10.6643	−	18.4711i	0.432850	−	0.749719i	0.997117	+	0.0758736i	$0.0241746\pi$
$608$		0			0
$609$	56.8402	+	1.90529i	2.30328	+	0.0772062i
$610$		0			0
$611$	−2.89485	−	5.01403i	−0.117113	−	0.202846i
$612$		0			0
$613$	−11.9515	−	20.7005i	−0.482715	−	0.836086i	0.517088	−	0.855932i	$-0.327016\pi$
$613$	−11.9515	−	20.7005i	−0.482715	−	0.836086i	−0.999803	+	0.0198457i	$0.993683\pi$
$614$		0			0
$615$	−13.6763	+	21.9549i	−0.551481	+	0.885308i
$616$		0			0
$617$	4.80312	+	8.31924i	0.193366	+	0.334920i	0.946364	−	0.323103i	$-0.104726\pi$
$617$	4.80312	+	8.31924i	0.193366	+	0.334920i	−0.752998	+	0.658023i	$0.771393\pi$
$618$		0			0
$619$	7.52398	+	13.0319i	0.302414	+	0.523797i	0.976682	−	0.214690i	$-0.0688741\pi$
$619$	7.52398	+	13.0319i	0.302414	+	0.523797i	−0.674268	+	0.738487i	$0.735541\pi$
$620$		0			0
$621$	−10.1320	−	22.5022i	−0.406584	−	0.902984i
$622$		0			0
$623$	20.9852			0.840755
$624$		0			0
$625$	−3.56883			−0.142753
$626$		0			0
$627$	−6.48141	−	1.01824i	−0.258843	−	0.0406646i
$628$		0			0
$629$	6.11038	+	10.5835i	0.243637	+	0.421991i
$630$		0			0
$631$	19.7730	−	34.2479i	0.787152	−	1.36339i	−0.140553	−	0.990073i	$-0.544888\pi$
$631$	19.7730	−	34.2479i	0.787152	−	1.36339i	0.927705	−	0.373314i	$-0.121779\pi$
$632$		0			0
$633$	−16.4845	+	26.4630i	−0.655198	+	1.05181i
$634$		0			0
$635$	−6.12455	+	10.6080i	−0.243045	+	0.420967i
$636$		0			0
$637$	−6.07452			−0.240681
$638$		0			0
$639$	0.810071	−	1.20826i	0.0320459	−	0.0477980i
$640$		0			0
$641$	−17.3288	+	30.0143i	−0.684445	+	1.18549i	0.289166	+	0.957279i	$0.406622\pi$
$641$	−17.3288	+	30.0143i	−0.684445	+	1.18549i	−0.973611	+	0.228214i	$0.926711\pi$
$642$		0			0
$643$	37.6021			1.48288			0.741442	−	0.671017i	$-0.234142\pi$
$643$	37.6021			1.48288			0.741442	+	0.671017i	$0.234142\pi$
$644$		0			0
$645$	9.49077	+	17.7895i	0.373699	+	0.700459i
$646$		0			0
$647$	32.2998			1.26984			0.634918	−	0.772579i	$-0.281034\pi$
$647$	32.2998			1.26984			0.634918	+	0.772579i	$0.281034\pi$
$648$		0			0
$649$	5.88755	+	10.1975i	0.231107	+	0.400289i
$650$		0			0
$651$	−26.8399	+	43.0869i	−1.05194	+	1.68871i
$652$		0			0
$653$	12.3179	−	21.3352i	0.482037	−	0.834913i	−0.517750	−	0.855532i	$-0.673230\pi$
$653$	12.3179	−	21.3352i	0.482037	−	0.834913i	0.999787	+	0.0206191i	$0.00656372\pi$
$654$		0			0
$655$	24.0328			0.939040
$656$		0			0
$657$	−16.9696	+	25.3110i	−0.662048	+	0.987476i
$658$		0			0
$659$	−11.7466			−0.457581			−0.228791	−	0.973476i	$-0.573477\pi$
$659$	−11.7466			−0.457581			−0.228791	+	0.973476i	$0.573477\pi$
$660$		0			0
$661$	13.8145	+	23.9275i	0.537323	+	0.930670i	0.999047	+	0.0436468i	$0.0138976\pi$
$661$	13.8145	+	23.9275i	0.537323	+	0.930670i	−0.461724	+	0.887023i	$0.652769\pi$
$662$		0			0
$663$	−1.15169	−	2.15872i	−0.0447279	−	0.0838378i
$664$		0			0
$665$	−8.94940	−	21.0921i	−0.347043	−	0.817917i
$666$		0			0
$667$	−22.1946	−	38.4422i	−0.859379	−	1.48849i
$668$		0			0
$669$	−13.1600	−	24.6670i	−0.508794	−	0.953682i
$670$		0			0
$671$	1.04211	+	1.80499i	0.0402303	+	0.0696810i
$672$		0			0
$673$	−10.7950	−	18.6975i	−0.416117	−	0.720735i	0.579428	−	0.815023i	$-0.303276\pi$
$673$	−10.7950	−	18.6975i	−0.416117	−	0.720735i	−0.995545	+	0.0942879i	$0.969943\pi$
$674$		0			0
$675$	14.2757	+	1.43988i	0.549470	+	0.0554209i
$676$		0			0
$677$	22.9415	+	39.7359i	0.881714	+	1.52717i	0.849434	+	0.527695i	$0.176944\pi$
$677$	22.9415	+	39.7359i	0.881714	+	1.52717i	0.0322806	+	0.999479i	$0.489723\pi$
$678$		0			0
$679$	−49.0179			−1.88113
$680$		0			0
$681$	−16.7148	−	0.560282i	−0.640514	−	0.0214701i
$682$		0			0
$683$	50.5559			1.93447			0.967234	−	0.253888i	$-0.0817094\pi$
$683$	50.5559			1.93447			0.967234	+	0.253888i	$0.0817094\pi$
$684$		0			0
$685$	−7.41832			−0.283439
$686$		0			0
$687$	−12.4584	−	23.3520i	−0.475318	−	0.890934i
$688$		0			0
$689$	11.2193			0.427422
$690$		0			0
$691$	−15.6877	−	27.1719i	−0.596788	−	1.03367i	−0.993292	−	0.115634i	$-0.963110\pi$
$691$	−15.6877	−	27.1719i	−0.596788	−	1.03367i	0.396504	−	0.918033i	$-0.370223\pi$
$692$		0			0
$693$	−9.13825	−	0.613318i	−0.347133	−	0.0232980i
$694$		0			0
$695$	−6.44200	−	11.1579i	−0.244359	−	0.423242i
$696$		0			0
$697$	−6.19943	−	10.7377i	−0.234820	−	0.406720i
$698$		0			0
$699$	26.8658	+	0.900542i	1.01616	+	0.0340616i
$700$		0			0
$701$	−24.2864	−	42.0653i	−0.917284	−	1.58878i	−0.803522	−	0.595275i	$-0.797043\pi$
$701$	−24.2864	−	42.0653i	−0.917284	−	1.58878i	−0.113762	−	0.993508i	$-0.536290\pi$
$702$		0			0
$703$	42.5607	+	5.23217i	1.60521	+	0.197335i
$704$		0			0
$705$	6.97648	−	11.1995i	0.262749	−	0.421799i
$706$		0			0
$707$	0.624975	+	1.08249i	0.0235046	+	0.0407112i
$708$		0			0
$709$	37.1523			1.39528			0.697641	−	0.716447i	$-0.254233\pi$
$709$	37.1523			1.39528			0.697641	+	0.716447i	$0.254233\pi$
$710$		0			0
$711$	18.8572	+	1.26561i	0.707200	+	0.0474641i
$712$		0			0
$713$	39.6209			1.48381
$714$		0			0
$715$	0.739283	−	1.28048i	0.0276476	−	0.0478871i
$716$		0			0
$717$	−0.697223	−	1.30687i	−0.0260383	−	0.0488060i
$718$		0			0
$719$	21.6419	+	37.4848i	0.807105	+	1.39795i	0.914860	+	0.403770i	$0.132300\pi$
$719$	21.6419	+	37.4848i	0.807105	+	1.39795i	−0.107755	+	0.994177i	$0.534366\pi$
$720$		0			0
$721$	−5.79352			−0.215762
$722$		0			0
$723$	4.51637	−	7.25025i	0.167966	−	0.269640i
$724$		0			0
$725$	25.8083			0.958498
$726$		0			0
$727$	−4.91137	+	8.50674i	−0.182153	+	0.315498i	−0.942613	−	0.333886i	$-0.891640\pi$
$727$	−4.91137	+	8.50674i	−0.182153	+	0.315498i	0.760461	+	0.649384i	$0.224973\pi$
$728$		0			0
$729$	26.4562	+	5.39172i	0.979858	+	0.199693i
$730$		0			0
$731$	−9.66498			−0.357472
$732$		0			0
$733$	−1.20996	+	2.09572i	−0.0446910	+	0.0774071i	−0.887506	−	0.460797i	$-0.847564\pi$
$733$	−1.20996	+	2.09572i	−0.0446910	+	0.0774071i	0.842815	+	0.538204i	$0.180897\pi$
$734$		0			0
$735$	−6.51638	−	12.2143i	−0.240360	−	0.450530i
$736$		0			0
$737$	−0.569659	+	0.986678i	−0.0209837	+	0.0363448i
$738$		0			0
$739$	−10.7192	−	18.5661i	−0.394311	−	0.682966i	0.598702	−	0.800972i	$-0.295683\pi$
$739$	−10.7192	−	18.5661i	−0.394311	−	0.682966i	−0.993013	+	0.118006i	$0.962350\pi$
$740$		0			0
$741$	−8.48123	−	1.33242i	−0.311566	−	0.0489475i
$742$		0			0
$743$	3.57145			0.131024			0.0655118	−	0.997852i	$-0.479132\pi$
$743$	3.57145			0.131024			0.0655118	+	0.997852i	$0.479132\pi$
$744$		0			0
$745$	13.0493			0.478089
$746$		0			0
$747$	6.94898	−	10.3647i	0.254250	−	0.379226i
$748$		0			0
$749$	−25.0930	−	43.4624i	−0.916879	−	1.58808i
$750$		0			0
$751$	−21.6450	−	37.4903i	−0.789838	−	1.36804i	−0.926066	−	0.377361i	$-0.876831\pi$
$751$	−21.6450	−	37.4903i	−0.789838	−	1.36804i	0.136229	−	0.990677i	$-0.456502\pi$
$752$		0			0
$753$	−2.98236	−	5.59012i	−0.108683	−	0.203715i
$754$		0			0
$755$	−0.0171298	−	0.0296696i	−0.000623416	−	0.00107979i
$756$		0			0
$757$	19.7129	+	34.1437i	0.716477	+	1.24097i	0.962387	+	0.271682i	$0.0875798\pi$
$757$	19.7129	+	34.1437i	0.716477	+	1.24097i	−0.245910	+	0.969293i	$0.579087\pi$
$758$		0			0
$759$	3.36486	+	6.30708i	0.122137	+	0.228932i
$760$		0			0
$761$	21.3008	−	36.8940i	0.772153	−	1.33741i	−0.164228	−	0.986422i	$-0.552513\pi$
$761$	21.3008	−	36.8940i	0.772153	−	1.33741i	0.936381	−	0.350986i	$-0.114153\pi$
$762$		0			0
$763$	−11.8005	+	20.4391i	−0.427207	+	0.739945i
$764$		0			0
$765$	3.10516	−	4.63149i	0.112267	−	0.167452i
$766$		0			0
$767$	7.70414	+	13.3440i	0.278180	+	0.481822i
$768$		0			0
$769$	−6.44920	−	11.1703i	−0.232564	−	0.402813i	0.725998	−	0.687697i	$-0.241378\pi$
$769$	−6.44920	−	11.1703i	−0.232564	−	0.402813i	−0.958562	+	0.284884i	$0.908045\pi$
$770$		0			0
$771$	−46.0978	−	1.54520i	−1.66017	−	0.0556491i
$772$		0			0
$773$	−22.3966	+	38.7921i	−0.805550	+	1.39525i	0.110370	+	0.993891i	$0.464797\pi$
$773$	−22.3966	+	38.7921i	−0.805550	+	1.39525i	−0.915919	+	0.401362i	$0.868537\pi$
$774$		0			0
$775$	−11.5180	+	19.9497i	−0.413738	+	0.716615i
$776$		0			0
$777$	59.8270	+	2.00540i	2.14628	+	0.0719434i
$778$		0			0
$779$	−43.1810	−	5.30842i	−1.54712	−	0.190194i
$780$		0			0
$781$	−0.210690	+	0.364926i	−0.00753908	+	0.0130581i
$782$		0			0
$783$	48.3206	+	4.87373i	1.72684	+	0.174173i
$784$		0			0
$785$	17.3766			0.620199
$786$		0			0
$787$	11.5847	−	20.0652i	0.412949	−	0.715249i	−0.582262	−	0.813001i	$-0.697832\pi$
$787$	11.5847	−	20.0652i	0.412949	−	0.715249i	0.995211	+	0.0977526i	$0.0311654\pi$
$788$		0			0
$789$	−15.8238	−	29.6600i	−0.563342	−	1.05593i
$790$		0			0
$791$	−28.3603			−1.00838
$792$		0			0
$793$	1.36365	+	2.36192i	0.0484248	+	0.0838742i
$794$		0			0
$795$	12.0354	+	22.5591i	0.426851	+	0.800088i
$796$		0			0
$797$	−18.3974	+	31.8653i	−0.651671	+	1.12873i	0.331047	+	0.943614i	$0.392598\pi$
$797$	−18.3974	+	31.8653i	−0.651671	+	1.12873i	−0.982717	+	0.185112i	$0.940735\pi$
$798$		0			0
$799$	3.16242	+	5.47748i	0.111878	+	0.193779i
$800$		0			0
$801$	17.8800	+	1.20003i	0.631759	+	0.0424008i
$802$		0			0
$803$	4.41360	−	7.64458i	0.155753	−	0.269771i
$804$		0			0
$805$	−12.4822	+	21.6197i	−0.439939	+	0.761996i
$806$		0			0
$807$	−34.2255	−	1.14724i	−1.20479	−	0.0403848i
$808$		0			0
$809$	43.2635			1.52107			0.760533	−	0.649300i	$-0.224938\pi$
$809$	43.2635			1.52107			0.760533	+	0.649300i	$0.224938\pi$
$810$		0			0
$811$	7.48664	−	12.9672i	0.262891	−	0.455341i	−0.704118	−	0.710083i	$-0.748657\pi$
$811$	7.48664	−	12.9672i	0.262891	−	0.455341i	0.967009	+	0.254742i	$0.0819905\pi$
$812$		0			0
$813$	−0.499905	−	0.0167568i	−0.0175324	−	0.000587688i
$814$		0			0
$815$	−28.7855			−1.00831
$816$		0			0
$817$	−20.4135	+	27.0813i	−0.714177	+	0.947454i
$818$		0			0
$819$	−11.9578	−	0.802555i	−0.417840	−	0.0280436i
$820$		0			0
$821$	25.7543			0.898832			0.449416	−	0.893323i	$-0.351632\pi$
$821$	25.7543			0.898832			0.449416	+	0.893323i	$0.351632\pi$
$822$		0			0
$823$	5.10194	+	8.83681i	0.177842	+	0.308032i	0.941141	−	0.338013i	$-0.109755\pi$
$823$	5.10194	+	8.83681i	0.177842	+	0.308032i	−0.763299	+	0.646045i	$0.776422\pi$
$824$		0			0
$825$	−4.15389	−	0.139239i	−0.144620	−	0.00484767i
$826$		0			0
$827$	−16.4527	+	28.4970i	−0.572118	+	0.990937i	0.424230	+	0.905554i	$0.360545\pi$
$827$	−16.4527	+	28.4970i	−0.572118	+	0.990937i	−0.996348	+	0.0853829i	$0.972789\pi$
$828$		0			0
$829$	19.2057			0.667043			0.333522	−	0.942742i	$-0.391763\pi$
$829$	19.2057			0.667043			0.333522	+	0.942742i	$0.391763\pi$
$830$		0			0
$831$	−32.5157	−	1.08993i	−1.12796	−	0.0378092i
$832$		0			0
$833$	6.63598			0.229923
$834$		0			0
$835$	−7.23344	−	12.5287i	−0.250323	−	0.433573i
$836$		0			0
$837$	−25.3323	+	35.1764i	−0.875612	+	1.21588i
$838$		0			0
$839$	6.91218	−	11.9722i	0.238635	−	0.413328i	−0.721688	−	0.692219i	$-0.756633\pi$
$839$	6.91218	−	11.9722i	0.238635	−	0.413328i	0.960323	+	0.278891i	$0.0899668\pi$
$840$		0			0
$841$	58.3567			2.01230
$842$		0			0
$843$	−24.6204	+	39.5239i	−0.847973	+	1.36128i
$844$		0			0
$845$	−8.75812	+	15.1695i	−0.301289	+	0.521847i
$846$		0			0
$847$	−35.9911			−1.23667
$848$		0			0
$849$	6.78733	−	10.8959i	0.232940	−	0.373946i
$850$		0			0
$851$	−23.3609	−	40.4622i	−0.800800	−	1.38703i
$852$		0			0
$853$	25.8241	−	44.7287i	0.884201	−	1.53148i	0.0375737	−	0.999294i	$-0.488037\pi$
$853$	25.8241	−	44.7287i	0.884201	−	1.53148i	0.846627	−	0.532187i	$-0.178630\pi$
$854$		0			0
$855$	−6.41900	−	18.4829i	−0.219525	−	0.632100i
$856$		0			0
$857$	−12.6600	+	21.9277i	−0.432457	+	0.749038i	−0.997084	−	0.0763085i	$-0.975687\pi$
$857$	−12.6600	+	21.9277i	−0.432457	+	0.749038i	0.564627	+	0.825346i	$0.309020\pi$
$858$		0			0
$859$	17.9727	+	31.1297i	0.613221	+	1.06213i	0.990694	+	0.136110i	$0.0434600\pi$
$859$	17.9727	+	31.1297i	0.613221	+	1.06213i	−0.377472	+	0.926021i	$0.623207\pi$
$860$		0			0
$861$	−60.6989	−	2.03463i	−2.06861	−	0.0693400i
$862$		0			0
$863$	51.9187			1.76733			0.883666	−	0.468118i	$-0.155068\pi$
$863$	51.9187			1.76733			0.883666	+	0.468118i	$0.155068\pi$
$864$		0			0
$865$	1.48789	−	2.57710i	0.0505898	−	0.0876241i
$866$		0			0
$867$	−12.6017	−	23.6207i	−0.427978	−	0.802200i
$868$		0			0
$869$	−5.47467			−0.185715
$870$		0			0
$871$	−0.745425	+	1.29111i	−0.0252578	+	0.0437477i
$872$		0			0
$873$	−41.7647	−	2.80306i	−1.41352	−	0.0948691i
$874$		0			0
$875$	−20.3983	−	35.3309i	−0.689588	−	1.19440i
$876$		0			0
$877$	13.9600			0.471395			0.235697	−	0.971827i	$-0.424263\pi$
$877$	13.9600			0.471395			0.235697	+	0.971827i	$0.424263\pi$
$878$		0			0
$879$	7.40717	+	13.8840i	0.249838	+	0.468294i
$880$		0			0
$881$	−30.4326			−1.02530			−0.512651	−	0.858597i	$-0.671336\pi$
$881$	−30.4326			−1.02530			−0.512651	+	0.858597i	$0.671336\pi$
$882$		0			0
$883$	−13.5617	+	23.4895i	−0.456387	+	0.790485i	−0.998767	−	0.0496480i	$-0.984190\pi$
$883$	−13.5617	+	23.4895i	−0.456387	+	0.790485i	0.542380	+	0.840133i	$0.317523\pi$
$884$		0			0
$885$	−18.5667	+	29.8056i	−0.624112	+	1.00190i
$886$		0			0
$887$	−8.46825	−	14.6674i	−0.284336	−	0.492484i	0.688112	−	0.725604i	$-0.258440\pi$
$887$	−8.46825	−	14.6674i	−0.284336	−	0.492484i	−0.972448	+	0.233120i	$0.925106\pi$
$888$		0			0
$889$	−28.7605			−0.964596
$890$		0			0
$891$	−7.75097	−	1.04513i	−0.259667	−	0.0350131i
$892$		0			0
$893$	22.0273	+	2.70791i	0.737114	+	0.0906167i
$894$		0			0
$895$	13.0040			0.434675
$896$		0			0
$897$	4.40308	+	8.25310i	0.147014	+	0.275563i
$898$		0			0
$899$	−38.9863	+	67.5262i	−1.30027	+	2.25213i
$900$		0			0
$901$	−12.2563			−0.408317
$902$		0			0
$903$	−25.0311	+	40.1831i	−0.832982	+	1.33721i
$904$		0			0
$905$	13.9028	−	24.0804i	0.462146	−	0.800461i
$906$		0			0
$907$	26.3318	−	45.6080i	0.874334	−	1.51439i	0.0168625	−	0.999858i	$-0.494632\pi$
$907$	26.3318	−	45.6080i	0.874334	−	1.51439i	0.857471	−	0.514532i	$-0.172034\pi$
$908$		0			0
$909$	0.470595	+	0.958050i	0.0156087	+	0.0317765i
$910$		0			0
$911$	12.8144	+	22.1952i	0.424561	+	0.735361i	0.996379	−	0.0850190i	$-0.0270951\pi$
$911$	12.8144	+	22.1952i	0.424561	+	0.735361i	−0.571818	+	0.820380i	$0.693762\pi$
$912$		0			0
$913$	−1.80735	+	3.13042i	−0.0598145	+	0.103602i
$914$		0			0
$915$	−3.28635	+	5.27567i	−0.108643	+	0.174408i
$916$		0			0
$917$	28.2142	+	48.8683i	0.931713	+	1.61377i
$918$		0			0
$919$	−39.5941			−1.30609			−0.653045	−	0.757319i	$-0.726509\pi$
$919$	−39.5941			−1.30609			−0.653045	+	0.757319i	$0.726509\pi$
$920$		0			0
$921$	25.2921	+	0.847793i	0.833404	+	0.0279357i
$922$		0			0
$923$	−0.275697	+	0.477522i	−0.00907469	+	0.0157178i
$924$		0			0
$925$	27.1645			0.893162
$926$		0			0
$927$	−4.93625	−	0.331299i	−0.162128	−	0.0108813i
$928$		0			0
$929$	−3.86465	+	6.69376i	−0.126795	+	0.219615i	−0.922433	−	0.386157i	$-0.873802\pi$
$929$	−3.86465	+	6.69376i	−0.126795	+	0.219615i	0.795638	+	0.605772i	$0.207136\pi$
$930$		0			0
$931$	14.0159	−	18.5940i	0.459353	−	0.609395i
$932$		0			0
$933$	2.23723	+	4.19346i	0.0732437	+	0.137288i
$934$		0			0
$935$	−0.807615	+	1.39883i	−0.0264118	+	0.0457466i
$936$		0			0
$937$	4.19831	−	7.27168i	0.137153	−	0.237556i	−0.789265	−	0.614053i	$-0.789538\pi$
$937$	4.19831	−	7.27168i	0.137153	−	0.237556i	0.926418	+	0.376497i	$0.122872\pi$
$938$		0			0
$939$	−10.1591	+	16.3086i	−0.331529	+	0.532212i
$940$		0			0
$941$	−3.59068	−	6.21923i	−0.117053	−	0.202741i	0.801546	−	0.597933i	$-0.204011\pi$
$941$	−3.59068	−	6.21923i	−0.117053	−	0.202741i	−0.918598	+	0.395192i	$0.870678\pi$
$942$		0			0
$943$	23.7013	+	41.0519i	0.771821	+	1.33683i
$944$		0			0
$945$	−11.2139	−	24.9050i	−0.364788	−	0.810159i
$946$		0			0
$947$	−3.70725	+	6.42115i	−0.120470	+	0.208659i	−0.919953	−	0.392029i	$-0.871773\pi$
$947$	−3.70725	+	6.42115i	−0.120470	+	0.208659i	0.799483	+	0.600688i	$0.205107\pi$
$948$		0			0
$949$	5.77540	−	10.0033i	0.187477	−	0.324720i
$950$		0			0
$951$	−15.4993	+	24.8815i	−0.502600	+	0.806838i
$952$		0			0
$953$	9.89456	+	17.1379i	0.320516	+	0.555150i	0.980595	−	0.196046i	$-0.0628103\pi$
$953$	9.89456	+	17.1379i	0.320516	+	0.555150i	−0.660078	+	0.751197i	$0.729477\pi$
$954$		0			0
$955$	−16.5334	−	28.6368i	−0.535010	−	0.926664i
$956$		0			0
$957$	−14.0602	−	0.471298i	−0.454501	−	0.0152349i
$958$		0			0
$959$	−8.70899	−	15.0844i	−0.281228	−	0.487101i
$960$		0			0
$961$	−19.2983	−	33.4256i	−0.622525	−	1.07825i
$962$		0			0
$963$	−18.8946	−	38.4661i	−0.608870	−	1.23955i
$964$		0			0
$965$	−14.2287			−0.458038
$966$		0			0
$967$	−36.9460			−1.18810			−0.594051	−	0.804427i	$-0.702472\pi$
$967$	−36.9460			−1.18810			−0.594051	+	0.804427i	$0.702472\pi$
$968$		0			0
$969$	9.26514	+	1.45557i	0.297639	+	0.0467597i
$970$		0			0
$971$	−8.39078	−	14.5333i	−0.269273	−	0.466394i	0.699401	−	0.714729i	$-0.253450\pi$
$971$	−8.39078	−	14.5333i	−0.269273	−	0.466394i	−0.968674	+	0.248335i	$0.920117\pi$
$972$		0			0
$973$	15.1256	−	26.1983i	0.484905	−	0.839880i
$974$		0			0
$975$	−5.43556	−	0.182200i	−0.174077	−	0.00583508i
$976$		0			0
$977$	9.59821	−	16.6246i	0.307074	−	0.531868i	−0.670647	−	0.741777i	$-0.733983\pi$
$977$	9.59821	−	16.6246i	0.307074	−	0.531868i	0.977721	+	0.209909i	$0.0673168\pi$
$978$		0			0
$979$	−5.19097			−0.165904
$980$		0			0
$981$	−11.2232	+	16.7399i	−0.358328	+	0.534463i
$982$		0			0
$983$	12.0122	−	20.8057i	0.383129	−	0.663599i	−0.608379	−	0.793647i	$-0.708180\pi$
$983$	12.0122	−	20.8057i	0.383129	−	0.663599i	0.991508	+	0.130048i	$0.0415131\pi$
$984$		0			0
$985$	−3.45388			−0.110050
$986$		0			0
$987$	30.9634	+	1.03790i	0.985577	+	0.0330366i
$988$		0			0
$989$	36.9506			1.17496
$990$		0			0
$991$	8.03491	+	13.9169i	0.255237	+	0.442084i	0.964960	−	0.262397i	$-0.0845131\pi$
$991$	8.03491	+	13.9169i	0.255237	+	0.442084i	−0.709723	+	0.704481i	$0.751180\pi$
$992$		0			0
$993$	−8.88302	−	0.297759i	−0.281894	−	0.00944911i
$994$		0			0
$995$	6.39119	−	11.0699i	0.202614	−	0.350939i
$996$		0			0
$997$	−35.5004			−1.12431			−0.562154	−	0.827033i	$-0.690027\pi$
$997$	−35.5004			−1.12431			−0.562154	+	0.827033i	$0.690027\pi$
$998$		0			0
$999$	50.8596	+	5.12983i	1.60913	+	0.162301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.l.a.121.14	yes	40
3.2	odd	2		2052.2.l.a.577.14		40
9.2	odd	6		2052.2.j.a.1261.7		40
9.7	even	3		684.2.j.a.349.2	yes	40
19.11	even	3		684.2.j.a.49.2	✓	40
57.11	odd	6		2052.2.j.a.1873.7		40
171.11	odd	6		2052.2.l.a.505.14		40
171.106	even	3	inner	684.2.l.a.277.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.j.a.49.2	✓	40	19.11	even	3
684.2.j.a.349.2	yes	40	9.7	even	3
684.2.l.a.121.14	yes	40	1.1	even	1	trivial
684.2.l.a.277.14	yes	40	171.106	even	3	inner
2052.2.j.a.1261.7		40	9.2	odd	6
2052.2.j.a.1873.7		40	57.11	odd	6
2052.2.l.a.505.14		40	171.11	odd	6
2052.2.l.a.577.14		40	3.2	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.915791 - 1.47015i) q^{3} -1.49623 q^{5} +(-1.75655 - 3.04244i) q^{7} +(-1.32265 - 2.69269i) q^{9} +(0.434507 + 0.752587i) q^{11} +(0.568572 + 0.984796i) q^{13} +(-1.37024 + 2.19968i) q^{15} +(-0.621125 - 1.07582i) q^{17} +(-4.32633 - 0.531855i) q^{19} +(-6.08146 - 0.203851i) q^{21} +(2.37465 + 4.11302i) q^{23} -2.76129 q^{25} +(-5.16992 - 0.521451i) q^{27} -9.34648 q^{29} +(4.17123 - 7.22478i) q^{31} +(1.50433 + 0.0504252i) q^{33} +(2.62821 + 4.55219i) q^{35} -9.83760 q^{37} +(1.96849 + 0.0659838i) q^{39} +9.98097 q^{41} +(3.89011 - 6.73787i) q^{43} +(1.97900 + 4.02889i) q^{45} -5.09144 q^{47} +(-2.67095 + 4.62623i) q^{49} +(-2.15043 - 0.0720826i) q^{51} +(4.93311 - 8.54439i) q^{53} +(-0.650123 - 1.12605i) q^{55} +(-4.74392 + 5.87326i) q^{57} +13.5500 q^{59} +2.39838 q^{61} +(-5.86904 + 8.75395i) q^{63} +(-0.850716 - 1.47348i) q^{65} +(0.655524 + 1.13540i) q^{67} +(8.22142 + 0.275582i) q^{69} +(0.242447 + 0.419931i) q^{71} +(-5.07886 - 8.79685i) q^{73} +(-2.52877 + 4.05950i) q^{75} +(1.52647 - 2.64392i) q^{77} +(-3.14994 + 5.45585i) q^{79} +(-5.50118 + 7.12299i) q^{81} +(2.07977 + 3.60227i) q^{83} +(0.929347 + 1.60968i) q^{85} +(-8.55942 + 13.7407i) q^{87} +(-2.98670 + 5.17312i) q^{89} +(1.99745 - 3.45969i) q^{91} +(-6.80150 - 12.7487i) q^{93} +(6.47319 + 0.795778i) q^{95} +(6.97644 - 12.0835i) q^{97} +(1.45178 - 2.16540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{3} - q^{7} + q^{9} - q^{11} - q^{13} + 10 q^{15} + 5 q^{17} + q^{19} + 6 q^{21} - 4 q^{23} + 40 q^{25} + 7 q^{27} + 18 q^{29} + 2 q^{31} - 7 q^{33} - 6 q^{35} + 2 q^{37} + 3 q^{39} + 50 q^{41}+ \cdots - 8 q^{99}+O(q^{100}) \) 40 * q + q^3 - q^7 + q^9 - q^11 - q^13 + 10 * q^15 + 5 * q^17 + q^19 + 6 * q^21 - 4 * q^23 + 40 * q^25 + 7 * q^27 + 18 * q^29 + 2 * q^31 - 7 * q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 + 50 * q^41 + 8 * q^43 + 44 * q^45 + 20 * q^47 - 21 * q^49 - 17 * q^51 - 8 * q^53 + 15 * q^57 + 44 * q^59 + 14 * q^61 - 26 * q^63 - 6 * q^65 - 10 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 - q^79 + q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 + 46 * q^93 - 54 * q^95 - q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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