LMFDB - Embedded newform 208.2.w.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, degree $2$, not 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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$-1.58726 - 0.693255i$ of defining polynomial
Character	$\chi$	$=$	208.49
Dual form			208.2.w.c.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.193255 + 0.334727i) q^{3} -3.17452i q^{5} +(-2.98127 - 1.72124i) q^{7} +(1.42531 - 2.46870i) q^{9} +O(q^{10})$	\(q+(0.193255 + 0.334727i) q^{3} -3.17452i q^{5} +(-2.98127 - 1.72124i) q^{7} +(1.42531 - 2.46870i) q^{9} +(2.98127 - 1.72124i) q^{11} +(-0.362708 + 3.58726i) q^{13} +(1.06260 - 0.613491i) q^{15} +(-0.886509 + 1.53548i) q^{17} +(2.88434 + 1.66527i) q^{19} -1.33055i q^{21} +(0.193255 + 0.334727i) q^{23} -5.07759 q^{25} +2.26131 q^{27} +(2.28801 + 3.96296i) q^{29} -11.0401i q^{31} +(1.15229 + 0.665273i) q^{33} +(-5.46410 + 9.46410i) q^{35} +(-1.40307 + 0.810063i) q^{37} +(-1.27085 + 0.571847i) q^{39} +(-1.96410 + 1.13397i) q^{41} +(-5.36778 + 9.29726i) q^{43} +(-7.83695 - 4.52466i) q^{45} +8.11192i q^{47} +(2.42531 + 4.20075i) q^{49} -0.685288 q^{51} +11.6536 q^{53} +(-5.46410 - 9.46410i) q^{55} +1.28729i q^{57} +(5.47970 + 3.16371i) q^{59} +(-1.21042 + 2.09651i) q^{61} +(-8.49843 + 4.90657i) q^{63} +(11.3878 + 1.15142i) q^{65} +(7.91867 - 4.57185i) q^{67} +(-0.0746946 + 0.129375i) q^{69} +(8.88434 + 5.12937i) q^{71} -8.40150i q^{73} +(-0.981268 - 1.69961i) q^{75} -11.8506 q^{77} -8.22385 q^{79} +(-3.83891 - 6.64918i) q^{81} -1.11506i q^{83} +(4.87441 + 2.81424i) q^{85} +(-0.884338 + 1.53172i) q^{87} +(-15.4339 + 8.91075i) q^{89} +(7.25585 - 10.0703i) q^{91} +(3.69543 - 2.13356i) q^{93} +(5.28645 - 9.15640i) q^{95} +(3.88205 + 2.24130i) q^{97} -9.81315i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9	$ 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{13} + 6 q^{19} - 2 q^{23} - 20 q^{25} + 28 q^{27} - 8 q^{29} + 6 q^{33} - 16 q^{35} - 24 q^{37} + 14 q^{39} + 12 q^{41} - 6 q^{43} + 30 q^{45} + 2 q^{49} - 68 q^{51} + 20 q^{53} - 16 q^{55} - 18 q^{59} - 4 q^{61} - 36 q^{63} + 14 q^{65} + 42 q^{67} - 18 q^{69} + 54 q^{71} + 22 q^{75} - 60 q^{77} - 16 q^{79} - 20 q^{81} + 6 q^{85} + 10 q^{87} - 18 q^{89} + 46 q^{91} + 36 q^{93} - 16 q^{95} + 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^13 + 6 * q^19 - 2 * q^23 - 20 * q^25 + 28 * q^27 - 8 * q^29 + 6 * q^33 - 16 * q^35 - 24 * q^37 + 14 * q^39 + 12 * q^41 - 6 * q^43 + 30 * q^45 + 2 * q^49 - 68 * q^51 + 20 * q^53 - 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 14 * q^65 + 42 * q^67 - 18 * q^69 + 54 * q^71 + 22 * q^75 - 60 * q^77 - 16 * q^79 - 20 * q^81 + 6 * q^85 + 10 * q^87 - 18 * q^89 + 46 * q^91 + 36 * q^93 - 16 * q^95 + 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.193255	+	0.334727i	0.111576	+	0.193255i	0.916406	−	0.400251i	$-0.131077\pi$
$3$	0.193255	+	0.334727i	0.111576	+	0.193255i	−0.804830	+	0.593505i	$0.797744\pi$
$4$		0			0
$5$		−	3.17452i		−	1.41969i	−0.704358	−	0.709845i	$-0.748765\pi$
$5$		−	3.17452i		−	1.41969i	0.704358	−	0.709845i	$-0.251235\pi$
$6$		0			0
$7$	−2.98127	−	1.72124i	−1.12681	−	0.650566i	−0.183682	−	0.982986i	$-0.558802\pi$
$7$	−2.98127	−	1.72124i	−1.12681	−	0.650566i	−0.943132	+	0.332420i	$0.892135\pi$
$8$		0			0
$9$	1.42531	−	2.46870i	0.475102	−	0.822900i
$10$		0			0
$11$	2.98127	−	1.72124i	0.898886	−	0.518972i	0.0220475	−	0.999757i	$-0.492982\pi$
$11$	2.98127	−	1.72124i	0.898886	−	0.518972i	0.876839	+	0.480785i	$0.159648\pi$
$12$		0			0
$13$	−0.362708	+	3.58726i	−0.100597	+	0.994927i
$13$	−0.362708	+	3.58726i	−0.100597	+	0.994927i
$14$		0			0
$15$	1.06260	−	0.613491i	0.274361	−	0.158403i
$16$		0			0
$17$	−0.886509	+	1.53548i	−0.215010	+	0.372408i	−0.953276	−	0.302102i	$-0.902312\pi$
$17$	−0.886509	+	1.53548i	−0.215010	+	0.372408i	0.738266	+	0.674510i	$0.235645\pi$
$18$		0			0
$19$	2.88434	+	1.66527i	0.661713	+	0.382040i	0.792929	−	0.609314i	$-0.208555\pi$
$19$	2.88434	+	1.66527i	0.661713	+	0.382040i	−0.131217	+	0.991354i	$0.541888\pi$
$20$		0			0
$21$		−	1.33055i		−	0.290349i
$22$		0			0
$23$	0.193255	+	0.334727i	0.0402964	+	0.0697953i	0.885470	−	0.464696i	$-0.153836\pi$
$23$	0.193255	+	0.334727i	0.0402964	+	0.0697953i	−0.845174	+	0.534492i	$0.820503\pi$
$24$		0			0
$25$	−5.07759			−1.01552
$26$		0			0
$27$	2.26131			0.435190
$28$		0			0
$29$	2.28801	+	3.96296i	0.424873	+	0.735902i	0.996409	−	0.0846752i	$-0.0269853\pi$
$29$	2.28801	+	3.96296i	0.424873	+	0.735902i	−0.571535	+	0.820578i	$0.693652\pi$
$30$		0			0
$31$		−	11.0401i		−	1.98287i	−0.130618	−	0.991433i	$-0.541696\pi$
$31$		−	11.0401i		−	1.98287i	0.130618	−	0.991433i	$-0.458304\pi$
$32$		0			0
$33$	1.15229	+	0.665273i	0.200587	+	0.115809i
$34$		0			0
$35$	−5.46410	+	9.46410i	−0.923602	+	1.59973i
$36$		0			0
$37$	−1.40307	+	0.810063i	−0.230663	+	0.133174i	−0.610878	−	0.791725i	$-0.709183\pi$
$37$	−1.40307	+	0.810063i	−0.230663	+	0.133174i	0.380215	+	0.924898i	$0.375850\pi$
$38$		0			0
$39$	−1.27085	+	0.571847i	−0.203498	+	0.0915687i
$40$		0			0
$41$	−1.96410	+	1.13397i	−0.306741	+	0.177097i	−0.645467	−	0.763788i	$-0.723337\pi$
$41$	−1.96410	+	1.13397i	−0.306741	+	0.177097i	0.338726	+	0.940885i	$0.390004\pi$
$42$		0			0
$43$	−5.36778	+	9.29726i	−0.818578	+	1.41782i	0.0881515	+	0.996107i	$0.471904\pi$
$43$	−5.36778	+	9.29726i	−0.818578	+	1.41782i	−0.906730	+	0.421712i	$0.861429\pi$
$44$		0			0
$45$	−7.83695	−	4.52466i	−1.16826	−	0.674497i
$46$		0			0
$47$			8.11192i			1.18325i	0.806215	+	0.591623i	$0.201513\pi$
$47$			8.11192i			1.18325i	−0.806215	+	0.591623i	$0.798487\pi$
$48$		0			0
$49$	2.42531	+	4.20075i	0.346472	+	0.600107i
$50$		0			0
$51$	−0.685288			−0.0959595
$52$		0			0
$53$	11.6536			1.60075			0.800374	−	0.599501i	$-0.204634\pi$
$53$	11.6536			1.60075			0.800374	+	0.599501i	$0.204634\pi$
$54$		0			0
$55$	−5.46410	−	9.46410i	−0.736779	−	1.27614i
$56$		0			0
$57$			1.28729i			0.170505i
$58$		0			0
$59$	5.47970	+	3.16371i	0.713396	+	0.411880i	0.812317	−	0.583216i	$-0.198206\pi$
$59$	5.47970	+	3.16371i	0.713396	+	0.411880i	−0.0989209	+	0.995095i	$0.531539\pi$
$60$		0			0
$61$	−1.21042	+	2.09651i	−0.154979	+	0.268431i	−0.933051	−	0.359744i	$-0.882864\pi$
$61$	−1.21042	+	2.09651i	−0.154979	+	0.268431i	0.778073	+	0.628174i	$0.216197\pi$
$62$		0			0
$63$	−8.49843	+	4.90657i	−1.07070	+	0.618170i
$64$		0			0
$65$	11.3878	+	1.15142i	1.41249	+	0.142817i
$66$		0			0
$67$	7.91867	−	4.57185i	0.967420	−	0.558540i	0.0689710	−	0.997619i	$-0.478028\pi$
$67$	7.91867	−	4.57185i	0.967420	−	0.558540i	0.898449	+	0.439079i	$0.144695\pi$
$68$		0			0
$69$	−0.0746946	+	0.129375i	−0.00899218	+	0.0155749i
$70$		0			0
$71$	8.88434	+	5.12937i	1.05438	+	0.608745i	0.923872	−	0.382703i	$-0.125007\pi$
$71$	8.88434	+	5.12937i	1.05438	+	0.608745i	0.130505	+	0.991448i	$0.458340\pi$
$72$		0			0
$73$		−	8.40150i		−	0.983322i	−0.870787	−	0.491661i	$-0.836390\pi$
$73$		−	8.40150i		−	0.983322i	0.870787	−	0.491661i	$-0.163610\pi$
$74$		0			0
$75$	−0.981268	−	1.69961i	−0.113307	−	0.196254i
$76$		0			0
$77$	−11.8506			−1.35050
$78$		0			0
$79$	−8.22385			−0.925255			−0.462628	−	0.886553i	$-0.653093\pi$
$79$	−8.22385			−0.925255			−0.462628	+	0.886553i	$0.653093\pi$
$80$		0			0
$81$	−3.83891	−	6.64918i	−0.426545	−	0.738798i
$82$		0			0
$83$		−	1.11506i		−	0.122393i	−0.998126	−	0.0611967i	$-0.980508\pi$
$83$		−	1.11506i		−	0.122393i	0.998126	−	0.0611967i	$-0.0194917\pi$
$84$		0			0
$85$	4.87441	+	2.81424i	0.528704	+	0.305248i
$86$		0			0
$87$	−0.884338	+	1.53172i	−0.0948110	+	0.164217i
$88$		0			0
$89$	−15.4339	+	8.91075i	−1.63599	+	0.944538i	−0.653793	+	0.756674i	$0.726823\pi$
$89$	−15.4339	+	8.91075i	−1.63599	+	0.944538i	−0.982195	+	0.187864i	$0.939843\pi$
$90$		0			0
$91$	7.25585	−	10.0703i	0.760620	−	1.05565i
$92$		0			0
$93$	3.69543	−	2.13356i	0.383198	−	0.221239i
$94$		0			0
$95$	5.28645	−	9.15640i	0.542378	−	0.939426i
$96$		0			0
$97$	3.88205	+	2.24130i	0.394162	+	0.227570i	0.683962	−	0.729518i	$-0.260255\pi$
$97$	3.88205	+	2.24130i	0.394162	+	0.227570i	−0.289800	+	0.957087i	$0.593589\pi$
$98$		0			0
$99$		−	9.81315i		−	0.986258i
$100$		0			0
$101$	0.0984958	+	0.170600i	0.00980070	+	0.0169753i	0.870884	−	0.491488i	$-0.163547\pi$
$101$	0.0984958	+	0.170600i	0.00980070	+	0.0169753i	−0.861083	+	0.508464i	$0.830214\pi$
$102$		0			0
$103$	6.34904			0.625590			0.312795	−	0.949821i	$-0.398735\pi$
$103$	6.34904			0.625590			0.312795	+	0.949821i	$0.398735\pi$
$104$		0			0
$105$	−4.22385			−0.412206
$106$		0			0
$107$	−2.57976	−	4.46828i	−0.249395	−	0.431965i	0.713963	−	0.700183i	$-0.246898\pi$
$107$	−2.57976	−	4.46828i	−0.249395	−	0.431965i	−0.963358	+	0.268218i	$0.913565\pi$
$108$		0			0
$109$		−	10.9282i		−	1.04673i	−0.852108	−	0.523366i	$-0.824676\pi$
$109$		−	10.9282i		−	1.04673i	0.852108	−	0.523366i	$-0.175324\pi$
$110$		0			0
$111$	−0.542299	−	0.313097i	−0.0514728	−	0.0297178i
$112$		0			0
$113$	5.46254	−	9.46139i	0.513872	−	0.890053i	−0.485998	−	0.873960i	$-0.661544\pi$
$113$	5.46254	−	9.46139i	0.513872	−	0.890053i	0.999871	−	0.0160929i	$-0.00512276\pi$
$114$		0			0
$115$	1.06260	−	0.613491i	0.0990877	−	0.0572083i
$116$		0			0
$117$	8.33891	+	6.00836i	0.770932	+	0.555473i
$118$		0			0
$119$	5.28584	−	3.05178i	0.484552	−	0.279756i
$120$		0			0
$121$	0.425305	−	0.736650i	0.0386641	−	0.0669682i
$122$		0			0
$123$	−0.759143	−	0.438292i	−0.0684496	−	0.0395194i
$124$		0			0
$125$			0.246319i			0.0220315i
$126$		0			0
$127$	4.30518	+	7.45679i	0.382023	+	0.661683i	0.991351	−	0.131235i	$-0.0418942\pi$
$127$	4.30518	+	7.45679i	0.382023	+	0.661683i	−0.609328	+	0.792918i	$0.708561\pi$
$128$		0			0
$129$	−4.14939			−0.365333
$130$		0			0
$131$	3.19699			0.279322			0.139661	−	0.990199i	$-0.455399\pi$
$131$	3.19699			0.279322			0.139661	+	0.990199i	$0.455399\pi$
$132$		0			0
$133$	−5.73266	−	9.92925i	−0.497084	−	0.860975i
$134$		0			0
$135$		−	7.17859i		−	0.617835i
$136$		0			0
$137$	6.99843	+	4.04055i	0.597917	+	0.345207i	0.768222	−	0.640184i	$-0.221142\pi$
$137$	6.99843	+	4.04055i	0.597917	+	0.345207i	−0.170305	+	0.985391i	$0.554475\pi$
$138$		0			0
$139$	−5.90368	+	10.2255i	−0.500743	+	0.867313i	0.499256	+	0.866454i	$0.333607\pi$
$139$	−5.90368	+	10.2255i	−0.500743	+	0.867313i	−1.00000		0.000858394i	$0.999727\pi$
$140$		0			0
$141$	−2.71528	+	1.56767i	−0.228668	+	0.132021i
$142$		0			0
$143$	5.09319	+	11.3189i	0.425914	+	0.946533i
$144$		0			0
$145$	12.5805	−	7.26335i	1.04475	−	0.603188i
$146$		0			0
$147$	−0.937403	+	1.62363i	−0.0773157	+	0.133915i
$148$		0			0
$149$	14.9892	+	8.65404i	1.22797	+	0.708966i	0.966604	−	0.256274i	$-0.0824951\pi$
$149$	14.9892	+	8.65404i	1.22797	+	0.708966i	0.261362	+	0.965241i	$0.415828\pi$
$150$		0			0
$151$			2.81628i			0.229185i	0.993413	+	0.114593i	$0.0365563\pi$
$151$			2.81628i			0.229185i	−0.993413	+	0.114593i	$0.963444\pi$
$152$		0			0
$153$	2.52709	+	4.37705i	0.204303	+	0.353864i
$154$		0			0
$155$	−35.0471			−2.81505
$156$		0			0
$157$	−13.1997			−1.05345			−0.526724	−	0.850037i	$-0.676580\pi$
$157$	−13.1997			−1.05345			−0.526724	+	0.850037i	$0.676580\pi$
$158$		0			0
$159$	2.25211	+	3.90078i	0.178604	+	0.309352i
$160$		0			0
$161$		−	1.33055i		−	0.104862i
$162$		0			0
$163$	−15.9095	−	9.18534i	−1.24613	−	0.719451i	−0.275791	−	0.961217i	$-0.588940\pi$
$163$	−15.9095	−	9.18534i	−1.24613	−	0.719451i	−0.970334	+	0.241766i	$0.922273\pi$
$164$		0			0
$165$	2.11192	−	3.65796i	0.164413	−	0.284772i
$166$		0			0
$167$	−9.01873	+	5.20697i	−0.697890	+	0.402927i	−0.806561	−	0.591151i	$-0.798674\pi$
$167$	−9.01873	+	5.20697i	−0.697890	+	0.402927i	0.108671	+	0.994078i	$0.465341\pi$
$168$		0			0
$169$	−12.7369	−	2.60226i	−0.979760	−	0.200174i
$170$		0			0
$171$	8.22212	−	4.74705i	0.628762	−	0.363016i
$172$		0			0
$173$	−3.22988	+	5.59432i	−0.245563	+	0.425328i	−0.962290	−	0.272026i	$-0.912306\pi$
$173$	−3.22988	+	5.59432i	−0.245563	+	0.425328i	0.716727	+	0.697354i	$0.245640\pi$
$174$		0			0
$175$	15.1377	+	8.73973i	1.14430	+	0.660662i
$176$		0			0
$177$			2.44560i			0.183823i
$178$		0			0
$179$	4.59476	+	7.95836i	0.343428	+	0.594835i	0.985067	−	0.172172i	$-0.0550784\pi$
$179$	4.59476	+	7.95836i	0.343428	+	0.594835i	−0.641639	+	0.767007i	$0.721745\pi$
$180$		0			0
$181$	1.95240			0.145121			0.0725603	−	0.997364i	$-0.476883\pi$
$181$	1.95240			0.145121			0.0725603	+	0.997364i	$0.476883\pi$
$182$		0			0
$183$	−0.935677			−0.0691673
$184$		0			0
$185$	2.57156	+	4.45408i	0.189065	+	0.327470i
$186$		0			0
$187$			6.10356i			0.446337i
$188$		0			0
$189$	−6.74158	−	3.89226i	−0.490378	−	0.283120i
$190$		0			0
$191$	8.60975	−	14.9125i	0.622980	−	1.07903i	−0.365948	−	0.930635i	$-0.619255\pi$
$191$	8.60975	−	14.9125i	0.622980	−	1.07903i	0.988928	−	0.148398i	$-0.0474115\pi$
$192$		0			0
$193$	7.64192	−	4.41206i	0.550077	−	0.317587i	−0.199076	−	0.979984i	$-0.563794\pi$
$193$	7.64192	−	4.41206i	0.550077	−	0.317587i	0.749153	+	0.662397i	$0.230461\pi$
$194$		0			0
$195$	1.81534	+	4.03433i	0.129999	+	0.288905i
$196$		0			0
$197$	−11.9698	+	6.91075i	−0.852811	+	0.492371i	−0.861598	−	0.507591i	$-0.830536\pi$
$197$	−11.9698	+	6.91075i	−0.852811	+	0.492371i	0.00878717	+	0.999961i	$0.497203\pi$
$198$		0			0
$199$	−12.4604	+	21.5820i	−0.883292	+	1.52991i	−0.0356328	+	0.999365i	$0.511345\pi$
$199$	−12.4604	+	21.5820i	−0.883292	+	1.52991i	−0.847659	+	0.530541i	$0.821989\pi$
$200$		0			0
$201$	3.06064	+	1.76706i	0.215881	+	0.124639i
$202$		0			0
$203$		−	15.7528i		−	1.10563i
$204$		0			0
$205$	3.59983	+	6.23508i	0.251423	+	0.435477i
$206$		0			0
$207$	1.10179			0.0765795
$208$		0			0
$209$	11.4653			0.793072
$210$		0			0
$211$	−3.38277	−	5.85913i	−0.232880	−	0.403359i	0.725775	−	0.687932i	$-0.241481\pi$
$211$	−3.38277	−	5.85913i	−0.232880	−	0.403359i	−0.958654	+	0.284573i	$0.908148\pi$
$212$		0			0
$213$			3.96510i			0.271684i
$214$		0			0
$215$	29.5144	+	17.0401i	2.01286	+	1.16213i
$216$		0			0
$217$	−19.0027	+	32.9136i	−1.28998	+	2.23432i
$218$		0			0
$219$	2.81221	−	1.62363i	0.190031	−	0.109715i
$220$		0			0
$221$	−5.18662	−	3.73707i	−0.348890	−	0.251383i
$222$		0			0
$223$	−20.3987	+	11.7772i	−1.36600	+	0.788660i	−0.990414	−	0.138129i	$-0.955891\pi$
$223$	−20.3987	+	11.7772i	−1.36600	+	0.788660i	−0.375584	+	0.926788i	$0.622558\pi$
$224$		0			0
$225$	−7.23712	+	12.5351i	−0.482475	+	0.835671i
$226$		0			0
$227$	−10.9721	−	6.33473i	−0.728242	−	0.420451i	0.0895368	−	0.995984i	$-0.471461\pi$
$227$	−10.9721	−	6.33473i	−0.728242	−	0.420451i	−0.817779	+	0.575533i	$0.804795\pi$
$228$		0			0
$229$			2.92820i			0.193501i	0.995309	+	0.0967506i	$0.0308449\pi$
$229$			2.92820i			0.193501i	−0.995309	+	0.0967506i	$0.969155\pi$
$230$		0			0
$231$	−2.29018	−	3.96672i	−0.150683	−	0.260991i
$232$		0			0
$233$	−6.22385			−0.407738			−0.203869	−	0.978998i	$-0.565352\pi$
$233$	−6.22385			−0.407738			−0.203869	+	0.978998i	$0.565352\pi$
$234$		0			0
$235$	25.7515			1.67984
$236$		0			0
$237$	−1.58930	−	2.75274i	−0.103236	−	0.178810i
$238$		0			0
$239$		−	16.4910i		−	1.06671i	−0.845891	−	0.533356i	$-0.820931\pi$
$239$		−	16.4910i		−	1.06671i	0.845891	−	0.533356i	$-0.179069\pi$
$240$		0			0
$241$	−13.6564	−	7.88452i	−0.879686	−	0.507887i	−0.00913098	−	0.999958i	$-0.502907\pi$
$241$	−13.6564	−	7.88452i	−0.879686	−	0.507887i	−0.870555	+	0.492071i	$0.836240\pi$
$242$		0			0
$243$	4.87574	−	8.44504i	0.312779	−	0.541749i
$244$		0			0
$245$	13.3354	−	7.69919i	0.851966	−	0.491883i
$246$		0			0
$247$	−7.01994	+	9.74287i	−0.446668	+	0.619924i
$248$		0			0
$249$	0.373239	−	0.215490i	0.0236531	−	0.0136561i
$250$		0			0
$251$	7.93194	−	13.7385i	0.500660	−	0.867168i	−0.499340	−	0.866406i	$-0.666424\pi$
$251$	7.93194	−	13.7385i	0.500660	−	0.867168i	1.00000		0.000761843i	$-0.000242502\pi$
$252$		0			0
$253$	1.15229	+	0.665273i	0.0724437	+	0.0418254i
$254$		0			0
$255$			2.17546i			0.136233i
$256$		0			0
$257$	−7.61192	−	13.1842i	−0.474819	−	0.822410i	0.524765	−	0.851247i	$-0.324153\pi$
$257$	−7.61192	−	13.1842i	−0.474819	−	0.822410i	−0.999584	+	0.0288366i	$0.990820\pi$
$258$		0			0
$259$	5.57724			0.346553
$260$		0			0
$261$	13.0445			0.807432
$262$		0			0
$263$	2.71995	+	4.71110i	0.167720	+	0.290499i	0.937618	−	0.347668i	$-0.113026\pi$
$263$	2.71995	+	4.71110i	0.167720	+	0.290499i	−0.769898	+	0.638167i	$0.779693\pi$
$264$		0			0
$265$		−	36.9947i		−	2.27256i
$266$		0			0
$267$	−5.96533	−	3.44409i	−0.365073	−	0.210775i
$268$		0			0
$269$	−8.88784	+	15.3942i	−0.541901	+	0.938600i	0.456894	+	0.889521i	$0.348962\pi$
$269$	−8.88784	+	15.3942i	−0.541901	+	0.938600i	−0.998795	+	0.0490791i	$0.984371\pi$
$270$		0			0
$271$	0.856073	−	0.494254i	0.0520027	−	0.0300238i	−0.473773	−	0.880647i	$-0.657108\pi$
$271$	0.856073	−	0.494254i	0.0520027	−	0.0300238i	0.525776	+	0.850623i	$0.323775\pi$
$272$		0			0
$273$	4.77302	+	0.482600i	0.288876	+	0.0292083i
$274$		0			0
$275$	−15.1377	+	8.73973i	−0.912835	+	0.527026i
$276$		0			0
$277$	1.02670	−	1.77829i	0.0616884	−	0.106847i	−0.833532	−	0.552471i	$-0.813685\pi$
$277$	1.02670	−	1.77829i	0.0616884	−	0.106847i	0.895220	+	0.445624i	$0.147018\pi$
$278$		0			0
$279$	−27.2548	−	15.7356i	−1.63170	−	0.942063i
$280$		0			0
$281$		−	1.20451i		−	0.0718552i	−0.999354	−	0.0359276i	$-0.988561\pi$
$281$		−	1.20451i		−	0.0718552i	0.999354	−	0.0359276i	$-0.0114386\pi$
$282$		0			0
$283$	−0.856073	−	1.48276i	−0.0508883	−	0.0881411i	0.839459	−	0.543423i	$-0.182872\pi$
$283$	−0.856073	−	1.48276i	−0.0508883	−	0.0881411i	−0.890347	+	0.455282i	$0.849539\pi$
$284$		0			0
$285$	4.08652			0.242065
$286$		0			0
$287$	7.80735			0.460853
$288$		0			0
$289$	6.92820	+	12.0000i	0.407541	+	0.705882i
$290$		0			0
$291$			1.73257i			0.101565i
$292$		0			0
$293$	−2.24041	−	1.29350i	−0.130886	−	0.0755672i	0.433127	−	0.901333i	$-0.357410\pi$
$293$	−2.24041	−	1.29350i	−0.130886	−	0.0755672i	−0.564013	+	0.825766i	$0.690743\pi$
$294$		0			0
$295$	10.0433	−	17.3954i	0.584741	−	1.01280i
$296$		0			0
$297$	6.74158	−	3.89226i	0.391186	−	0.225852i
$298$		0			0
$299$	−1.27085	+	0.571847i	−0.0734950	+	0.0330707i
$300$		0			0
$301$	32.0056	−	18.4784i	1.84477	−	1.06508i
$302$		0			0
$303$	−0.0380695	+	0.0659383i	−0.00218704	+	0.00378806i
$304$		0			0
$305$	6.65542	+	3.84251i	0.381088	+	0.220021i
$306$		0			0
$307$			12.3358i			0.704040i	0.935993	+	0.352020i	$0.114505\pi$
$307$			12.3358i			0.704040i	−0.935993	+	0.352020i	$0.885495\pi$
$308$		0			0
$309$	1.22698	+	2.12519i	0.0698006	+	0.120898i
$310$		0			0
$311$	4.74303			0.268952			0.134476	−	0.990917i	$-0.457065\pi$
$311$	4.74303			0.268952			0.134476	+	0.990917i	$0.457065\pi$
$312$		0			0
$313$	−0.230114			−0.0130068			−0.00650339	−	0.999979i	$-0.502070\pi$
$313$	−0.230114			−0.0130068			−0.00650339	+	0.999979i	$0.502070\pi$
$314$		0			0
$315$	15.5760	+	26.9785i	0.877610	+	1.52006i
$316$		0			0
$317$			5.87888i			0.330191i	0.986278	+	0.165095i	$0.0527932\pi$
$317$			5.87888i			0.330191i	−0.986278	+	0.165095i	$0.947207\pi$
$318$		0			0
$319$	13.6424	+	7.87642i	0.763826	+	0.440995i
$320$		0			0
$321$	0.997102	−	1.72703i	0.0556528	−	0.0963935i
$322$		0			0
$323$	−5.11398	+	2.95256i	−0.284550	+	0.164285i
$324$		0			0
$325$	1.84168	−	18.2147i	0.102158	−	1.01037i
$326$		0			0
$327$	3.65796	−	2.11192i	0.202286	−	0.116790i
$328$		0			0
$329$	13.9625	−	24.1838i	0.769780	−	1.33330i
$330$		0			0
$331$	−11.1065	−	6.41232i	−0.610466	−	0.352453i	0.162682	−	0.986679i	$-0.447986\pi$
$331$	−11.1065	−	6.41232i	−0.610466	−	0.352453i	−0.773148	+	0.634226i	$0.781319\pi$
$332$		0			0
$333$			4.61835i			0.253084i
$334$		0			0
$335$	−14.5134	−	25.1380i	−0.792953	−	1.37344i
$336$		0			0
$337$	30.5456			1.66392			0.831962	−	0.554833i	$-0.187218\pi$
$337$	30.5456			1.66392			0.831962	+	0.554833i	$0.187218\pi$
$338$		0			0
$339$	4.22264			0.229342
$340$		0			0
$341$	−19.0027	−	32.9136i	−1.02905	−	1.78237i
$342$		0			0
$343$			7.39921i			0.399520i
$344$		0			0
$345$	0.410704	+	0.237120i	0.0221115	+	0.0127661i
$346$		0			0
$347$	−6.19325	+	10.7270i	−0.332471	+	0.575857i	−0.982996	−	0.183628i	$-0.941216\pi$
$347$	−6.19325	+	10.7270i	−0.332471	+	0.575857i	0.650524	+	0.759485i	$0.274549\pi$
$348$		0			0
$349$	−15.1651	+	8.75557i	−0.811769	+	0.468675i	−0.847570	−	0.530684i	$-0.821935\pi$
$349$	−15.1651	+	8.75557i	−0.811769	+	0.468675i	0.0358011	+	0.999359i	$0.488602\pi$
$350$		0			0
$351$	−0.820197	+	8.11192i	−0.0437789	+	0.432983i
$352$		0			0
$353$	−19.7983	+	11.4306i	−1.05376	+	0.608387i	−0.923699	−	0.383119i	$-0.874850\pi$
$353$	−19.7983	+	11.4306i	−1.05376	+	0.608387i	−0.130059	+	0.991506i	$0.541517\pi$
$354$		0			0
$355$	16.2833	−	28.2035i	0.864229	−	1.49689i
$356$		0			0
$357$	2.04303	+	1.17954i	0.108128	+	0.0624280i
$358$		0			0
$359$		−	20.4310i		−	1.07831i	−0.842208	−	0.539153i	$-0.818744\pi$
$359$		−	20.4310i		−	1.07831i	0.842208	−	0.539153i	$-0.181256\pi$
$360$		0			0
$361$	−3.95373	−	6.84806i	−0.208091	−	0.360424i
$362$		0			0
$363$	0.328769			0.0172559
$364$		0			0
$365$	−26.6708			−1.39601
$366$		0			0
$367$	−12.2810	−	21.2713i	−0.641062	−	1.11035i	−0.985196	−	0.171432i	$-0.945161\pi$
$367$	−12.2810	−	21.2713i	−0.641062	−	1.11035i	0.344134	−	0.938921i	$-0.388173\pi$
$368$		0			0
$369$			6.46504i			0.336557i
$370$		0			0
$371$	−34.7426	−	20.0586i	−1.80374	−	1.04139i
$372$		0			0
$373$	−2.52826	+	4.37908i	−0.130909	+	0.226740i	−0.924027	−	0.382327i	$-0.875123\pi$
$373$	−2.52826	+	4.37908i	−0.130909	+	0.226740i	0.793118	+	0.609067i	$0.208456\pi$
$374$		0			0
$375$	−0.0824496	+	0.0476023i	−0.00425768	+	0.00245817i
$376$		0			0
$377$	−15.0460	+	6.77031i	−0.774910	+	0.348688i
$378$		0			0
$379$	3.45144	−	1.99269i	0.177288	−	0.102358i	−0.408730	−	0.912656i	$-0.634028\pi$
$379$	3.45144	−	1.99269i	0.177288	−	0.102358i	0.586018	+	0.810298i	$0.300695\pi$
$380$		0			0
$381$	−1.66399	+	2.88212i	−0.0852488	+	0.147655i
$382$		0			0
$383$	−1.97814	−	1.14208i	−0.101078	−	0.0583574i	0.448609	−	0.893728i	$-0.351920\pi$
$383$	−1.97814	−	1.14208i	−0.101078	−	0.0583574i	−0.549687	+	0.835371i	$0.685253\pi$
$384$		0			0
$385$			37.6200i			1.91729i
$386$		0			0
$387$	15.3014	+	26.5029i	0.777816	+	1.34722i
$388$		0			0
$389$	19.9727			1.01265			0.506327	−	0.862341i	$-0.331003\pi$
$389$	19.9727			1.01265			0.506327	+	0.862341i	$0.331003\pi$
$390$		0			0
$391$	−0.685288			−0.0346565
$392$		0			0
$393$	0.617833	+	1.07012i	0.0311656	+	0.0539803i
$394$		0			0
$395$			26.1068i			1.31358i
$396$		0			0
$397$	12.8605	+	7.42502i	0.645451	+	0.372651i	0.786711	−	0.617321i	$-0.211782\pi$
$397$	12.8605	+	7.42502i	0.645451	+	0.372651i	−0.141260	+	0.989972i	$0.545115\pi$
$398$		0			0
$399$	2.21572	−	3.83775i	0.110925	−	0.192128i
$400$		0			0
$401$	12.5877	−	7.26753i	0.628601	−	0.362923i	−0.151609	−	0.988441i	$-0.548445\pi$
$401$	12.5877	−	7.26753i	0.628601	−	0.362923i	0.780210	+	0.625517i	$0.215112\pi$
$402$		0			0
$403$	39.6038	+	4.00434i	1.97281	+	0.199470i
$404$		0			0
$405$	−21.1080	+	12.1867i	−1.04886	+	0.605562i
$406$		0			0
$407$	−2.78862	+	4.83003i	−0.138227	+	0.239416i
$408$		0			0
$409$	−15.3550	−	8.86519i	−0.759254	−	0.438355i	0.0697741	−	0.997563i	$-0.477772\pi$
$409$	−15.3550	−	8.86519i	−0.759254	−	0.438355i	−0.829028	+	0.559208i	$0.811105\pi$
$410$		0			0
$411$			3.12342i			0.154067i
$412$		0			0
$413$	−10.8910	−	18.8637i	−0.535910	−	0.928223i
$414$		0			0
$415$	−3.53977			−0.173761
$416$		0			0
$417$	−4.56365			−0.223483
$418$		0			0
$419$	17.5824	+	30.4537i	0.858958	+	1.48776i	0.872924	+	0.487856i	$0.162221\pi$
$419$	17.5824	+	30.4537i	0.858958	+	1.48776i	−0.0139663	+	0.999902i	$0.504446\pi$
$420$		0			0
$421$			21.4186i			1.04388i	0.852982	+	0.521941i	$0.174792\pi$
$421$			21.4186i			1.04388i	−0.852982	+	0.521941i	$0.825208\pi$
$422$		0			0
$423$	20.0259	+	11.5620i	0.973694	+	0.562162i
$424$		0			0
$425$	4.50133	−	7.79654i	0.218347	−	0.378188i
$426$		0			0
$427$	7.21718	−	4.16684i	0.349264	−	0.201647i
$428$		0			0
$429$	−2.80445	+	3.89226i	−0.135400	+	0.187920i
$430$		0			0
$431$	7.56743	−	4.36906i	0.364510	−	0.210450i	−0.306547	−	0.951855i	$-0.599174\pi$
$431$	7.56743	−	4.36906i	0.364510	−	0.210450i	0.671057	+	0.741405i	$0.265840\pi$
$432$		0			0
$433$	−13.9610	+	24.1811i	−0.670921	+	1.16207i	0.306722	+	0.951799i	$0.400768\pi$
$433$	−13.9610	+	24.1811i	−0.670921	+	1.16207i	−0.977643	+	0.210271i	$0.932565\pi$
$434$		0			0
$435$	4.86247	+	2.80735i	0.233138	+	0.134602i
$436$		0			0
$437$			1.28729i			0.0615793i
$438$		0			0
$439$	−9.79755	−	16.9698i	−0.467611	−	0.809927i	0.531704	−	0.846930i	$-0.321552\pi$
$439$	−9.79755	−	16.9698i	−0.467611	−	0.809927i	−0.999315	+	0.0370038i	$0.988219\pi$
$440$		0			0
$441$	13.8272			0.658438
$442$		0			0
$443$	−19.1521			−0.909942			−0.454971	−	0.890506i	$-0.650350\pi$
$443$	−19.1521			−0.909942			−0.454971	+	0.890506i	$0.650350\pi$
$444$		0			0
$445$	28.2874	+	48.9952i	1.34095	+	2.32259i
$446$		0			0
$447$			6.68973i			0.316413i
$448$		0			0
$449$	−16.3851	−	9.45992i	−0.773259	−	0.446441i	0.0607770	−	0.998151i	$-0.480642\pi$
$449$	−16.3851	−	9.45992i	−0.773259	−	0.446441i	−0.834036	+	0.551710i	$0.813975\pi$
$450$		0			0
$451$	−3.90368	+	6.76136i	−0.183817	+	0.318380i
$452$		0			0
$453$	−0.942684	+	0.544259i	−0.0442911	+	0.0255715i
$454$		0			0
$455$	−31.9683	−	23.0339i	−1.49870	−	1.07984i
$456$		0			0
$457$	9.55027	−	5.51385i	0.446743	−	0.257927i	−0.259711	−	0.965686i	$-0.583627\pi$
$457$	9.55027	−	5.51385i	0.446743	−	0.257927i	0.706454	+	0.707759i	$0.250294\pi$
$458$		0			0
$459$	−2.00468	+	3.47220i	−0.0935702	+	0.162068i
$460$		0			0
$461$	8.27788	+	4.77923i	0.385539	+	0.222591i	0.680225	−	0.733003i	$-0.261882\pi$
$461$	8.27788	+	4.77923i	0.385539	+	0.222591i	−0.294686	+	0.955594i	$0.595215\pi$
$462$		0			0
$463$			17.1151i			0.795404i	0.917515	+	0.397702i	$0.130192\pi$
$463$			17.1151i			0.795404i	−0.917515	+	0.397702i	$0.869808\pi$
$464$		0			0
$465$	−6.77302	−	11.7312i	−0.314091	−	0.544022i
$466$		0			0
$467$	4.86196			0.224985			0.112492	−	0.993653i	$-0.464117\pi$
$467$	4.86196			0.224985			0.112492	+	0.993653i	$0.464117\pi$
$468$		0			0
$469$	−31.4769			−1.45347
$470$		0			0
$471$	−2.55089	−	4.41828i	−0.117539	−	0.203583i
$472$		0			0
$473$			36.9568i			1.69928i
$474$		0			0
$475$	−14.6455	−	8.45558i	−0.671981	−	0.387969i
$476$		0			0
$477$	16.6100	−	28.7693i	0.760518	−	1.31726i
$478$		0			0
$479$	−16.2003	+	9.35322i	−0.740209	+	0.427360i	−0.822145	−	0.569278i	$-0.807223\pi$
$479$	−16.2003	+	9.35322i	−0.740209	+	0.427360i	0.0819364	+	0.996638i	$0.473890\pi$
$480$		0			0
$481$	−2.39700	−	5.32700i	−0.109294	−	0.242890i
$482$		0			0
$483$	0.445369	−	0.257134i	0.0202650	−	0.0117000i
$484$		0			0
$485$	7.11506	−	12.3236i	0.323078	−	0.559588i
$486$		0			0
$487$	−3.03321	−	1.75123i	−0.137448	−	0.0793556i	0.429699	−	0.902972i	$-0.358620\pi$
$487$	−3.03321	−	1.75123i	−0.137448	−	0.0793556i	−0.567147	+	0.823616i	$0.691953\pi$
$488$		0			0
$489$		−	7.10043i		−	0.321093i
$490$		0			0
$491$	10.9005	+	18.8803i	0.491935	+	0.852056i	0.999957	−	0.00928817i	$-0.00295656\pi$
$491$	10.9005	+	18.8803i	0.491935	+	0.852056i	−0.508022	+	0.861344i	$0.669623\pi$
$492$		0			0
$493$	−8.11338			−0.365408
$494$		0			0
$495$	−31.1521			−1.40018
$496$		0			0
$497$	−17.6577	−	30.5841i	−0.792057	−	1.37188i
$498$		0			0
$499$			35.3505i			1.58251i	0.611489	+	0.791253i	$0.290571\pi$
$499$			35.3505i			1.58251i	−0.611489	+	0.791253i	$0.709429\pi$
$500$		0			0
$501$	−3.48582	−	2.01254i	−0.155735	−	0.0899137i
$502$		0			0
$503$	11.3003	−	19.5727i	0.503856	−	0.872705i	−0.496134	−	0.868246i	$-0.665247\pi$
$503$	11.3003	−	19.5727i	0.503856	−	0.872705i	0.999990	−	0.00445881i	$-0.00141929\pi$
$504$		0			0
$505$	0.541573	−	0.312677i	0.0240997	−	0.0139139i
$506$		0			0
$507$	−1.59042	−	4.76627i	−0.0706329	−	0.211678i
$508$		0			0
$509$	12.9670	−	7.48652i	0.574754	−	0.331834i	−0.184292	−	0.982872i	$-0.558999\pi$
$509$	12.9670	−	7.48652i	0.574754	−	0.331834i	0.759046	+	0.651037i	$0.225666\pi$
$510$		0			0
$511$	−14.4610	+	25.0471i	−0.639716	+	1.10802i
$512$		0			0
$513$	6.52239	+	3.76571i	0.287971	+	0.166260i
$514$		0			0
$515$		−	20.1552i		−	0.888144i
$516$		0			0
$517$	13.9625	+	24.1838i	0.614072	+	1.06360i
$518$		0			0
$519$	−2.49676			−0.109595
$520$		0			0
$521$	17.7101			0.775896			0.387948	−	0.921681i	$-0.373184\pi$
$521$	17.7101			0.775896			0.387948	+	0.921681i	$0.373184\pi$
$522$		0			0
$523$	−4.79441	−	8.30417i	−0.209645	−	0.363116i	0.741958	−	0.670447i	$-0.233898\pi$
$523$	−4.79441	−	8.30417i	−0.209645	−	0.363116i	−0.951603	+	0.307331i	$0.900564\pi$
$524$		0			0
$525$			6.75597i			0.294855i
$526$		0			0
$527$	16.9519	+	9.78717i	0.738436	+	0.426336i
$528$		0			0
$529$	11.4253	−	19.7892i	0.496752	−	0.860400i
$530$		0			0
$531$	15.6205	−	9.01850i	0.677872	−	0.391369i
$532$		0			0
$533$	−3.35547	−	7.45705i	−0.145341	−	0.323001i
$534$		0			0
$535$	−14.1847	+	8.18952i	−0.613256	+	0.354064i
$536$		0			0
$537$	−1.77592	+	3.07598i	−0.0766364	+	0.132738i
$538$		0			0
$539$	14.4610	+	8.34904i	0.622878	+	0.359619i
$540$		0			0
$541$		−	24.1149i		−	1.03678i	−0.855145	−	0.518389i	$-0.826532\pi$
$541$		−	24.1149i		−	1.03678i	0.855145	−	0.518389i	$-0.173468\pi$
$542$		0			0
$543$	0.377310	+	0.653520i	0.0161919	+	0.0280452i
$544$		0			0
$545$	−34.6918			−1.48603
$546$		0			0
$547$	−26.1392			−1.11763			−0.558816	−	0.829292i	$-0.688744\pi$
$547$	−26.1392			−1.11763			−0.558816	+	0.829292i	$0.688744\pi$
$548$		0			0
$549$	3.45044	+	5.97633i	0.147261	+	0.255064i
$550$		0			0
$551$			15.2407i			0.649274i
$552$		0			0
$553$	24.5175	+	14.1552i	1.04259	+	0.601940i
$554$		0			0
$555$	−0.993932	+	1.72154i	−0.0421901	+	0.0730754i
$556$		0			0
$557$	15.2220	−	8.78843i	0.644977	−	0.372378i	−0.141552	−	0.989931i	$-0.545209\pi$
$557$	15.2220	−	8.78843i	0.644977	−	0.372378i	0.786529	+	0.617553i	$0.211876\pi$
$558$		0			0
$559$	−31.4048	−	22.6278i	−1.32828	−	0.957054i
$560$		0			0
$561$	−2.04303	+	1.17954i	−0.0862566	+	0.0498003i
$562$		0			0
$563$	16.8693	−	29.2186i	0.710958	−	1.23142i	−0.253540	−	0.967325i	$-0.581595\pi$
$563$	16.8693	−	29.2186i	0.710958	−	1.23142i	0.964498	−	0.264091i	$-0.0850718\pi$
$564$		0			0
$565$	−30.0354	−	17.3409i	−1.26360	−	0.729539i
$566$		0			0
$567$			26.4307i			1.10998i
$568$		0			0
$569$	22.5083	+	38.9856i	0.943599	+	1.63436i	0.758533	+	0.651635i	$0.225916\pi$
$569$	22.5083	+	38.9856i	0.943599	+	1.63436i	0.185066	+	0.982726i	$0.440750\pi$
$570$		0			0
$571$	35.4624			1.48406			0.742028	−	0.670369i	$-0.233864\pi$
$571$	35.4624			1.48406			0.742028	+	0.670369i	$0.233864\pi$
$572$		0			0
$573$	6.65550			0.278037
$574$		0			0
$575$	−0.981268	−	1.69961i	−0.0409217	−	0.0708785i
$576$		0			0
$577$			26.1530i			1.08876i	0.838838	+	0.544382i	$0.183236\pi$
$577$			26.1530i			1.08876i	−0.838838	+	0.544382i	$0.816764\pi$
$578$		0			0
$579$	2.95367	+	1.70530i	0.122750	+	0.0708699i
$580$		0			0
$581$	−1.91928	+	3.32428i	−0.0796250	+	0.137914i
$582$		0			0
$583$	34.7426	−	20.0586i	1.43889	−	0.830743i
$584$		0			0
$585$	19.0737	−	26.4720i	0.788599	−	1.09448i
$586$		0			0
$587$	−9.35451	+	5.40083i	−0.386102	+	0.222916i	−0.680470	−	0.732776i	$-0.738224\pi$
$587$	−9.35451	+	5.40083i	−0.386102	+	0.222916i	0.294368	+	0.955692i	$0.404891\pi$
$588$		0			0
$589$	18.3848	−	31.8435i	0.757534	−	1.31209i
$590$		0			0
$591$	−4.62643	−	2.67107i	−0.190306	−	0.109873i
$592$		0			0
$593$		−	44.4421i		−	1.82502i	−0.409058	−	0.912508i	$-0.634143\pi$
$593$		−	44.4421i		−	1.82502i	0.409058	−	0.912508i	$-0.365857\pi$
$594$		0			0
$595$	−9.68795	−	16.7800i	−0.397167	−	0.687914i
$596$		0			0
$597$	−9.63209			−0.394215
$598$		0			0
$599$	15.7312			0.642760			0.321380	−	0.946950i	$-0.395853\pi$
$599$	15.7312			0.642760			0.321380	+	0.946950i	$0.395853\pi$
$600$		0			0
$601$	14.8447	+	25.7118i	0.605528	+	1.04881i	0.991968	+	0.126491i	$0.0403714\pi$
$601$	14.8447	+	25.7118i	0.605528	+	1.04881i	−0.386440	+	0.922315i	$0.626295\pi$
$602$		0			0
$603$		−	26.0651i		−	1.06145i
$604$		0			0
$605$	−2.33851	−	1.35014i	−0.0950741	−	0.0548911i
$606$		0			0
$607$	18.2677	−	31.6406i	0.741464	−	1.28425i	−0.210365	−	0.977623i	$-0.567465\pi$
$607$	18.2677	−	31.6406i	0.741464	−	1.28425i	0.951829	−	0.306630i	$-0.0992014\pi$
$608$		0			0
$609$	5.27290	−	3.04431i	0.213669	−	0.123362i
$610$		0			0
$611$	−29.0996	−	2.94226i	−1.17724	−	0.119031i
$612$		0			0
$613$	−29.0380	+	16.7651i	−1.17284	+	0.677137i	−0.954346	−	0.298702i	$-0.903446\pi$
$613$	−29.0380	+	16.7651i	−1.17284	+	0.677137i	−0.218489	+	0.975839i	$0.570113\pi$
$614$		0			0
$615$	−1.39137	+	2.40992i	−0.0561053	+	0.0971772i
$616$		0			0
$617$	−18.9769	−	10.9563i	−0.763981	−	0.441085i	0.0667420	−	0.997770i	$-0.478740\pi$
$617$	−18.9769	−	10.9563i	−0.763981	−	0.441085i	−0.830723	+	0.556685i	$0.812073\pi$
$618$		0			0
$619$			3.13533i			0.126020i	0.998013	+	0.0630098i	$0.0200699\pi$
$619$			3.13533i			0.126020i	−0.998013	+	0.0630098i	$0.979930\pi$
$620$		0			0
$621$	0.437009	+	0.756922i	0.0175366	+	0.0303742i
$622$		0			0
$623$	61.3500			2.45794
$624$		0			0
$625$	−24.6060			−0.984241
$626$		0			0
$627$	2.21572	+	3.83775i	0.0884875	+	0.153265i
$628$		0			0
$629$		−	2.87251i		−	0.114535i
$630$		0			0
$631$	−0.251510	−	0.145209i	−0.0100124	−	0.00578069i	0.494985	−	0.868901i	$-0.335173\pi$
$631$	−0.251510	−	0.145209i	−0.0100124	−	0.00578069i	−0.504998	+	0.863121i	$0.668507\pi$
$632$		0			0
$633$	1.30747	−	2.26461i	0.0519674	−	0.0900101i
$634$		0			0
$635$	23.6717	−	13.6669i	0.939385	−	0.542354i
$636$		0			0
$637$	−15.9489	+	7.17656i	−0.631917	+	0.284346i
$638$		0			0
$639$	25.3258	−	14.6219i	1.00187	−	0.578431i
$640$		0			0
$641$	7.43255	−	12.8735i	0.293568	−	0.508475i	−0.681083	−	0.732206i	$-0.738491\pi$
$641$	7.43255	−	12.8735i	0.293568	−	0.508475i	0.974651	+	0.223732i	$0.0718240\pi$
$642$		0			0
$643$	0.806474	+	0.465618i	0.0318042	+	0.0183622i	0.515818	−	0.856698i	$-0.327488\pi$
$643$	0.806474	+	0.465618i	0.0318042	+	0.0183622i	−0.484014	+	0.875060i	$0.660821\pi$
$644$		0			0
$645$			13.1723i			0.518660i
$646$		0			0
$647$	−7.76349	−	13.4468i	−0.305214	−	0.528646i	0.672095	−	0.740465i	$-0.265395\pi$
$647$	−7.76349	−	13.4468i	−0.305214	−	0.528646i	−0.977309	+	0.211819i	$0.932061\pi$
$648$		0			0
$649$	21.7819			0.855016
$650$		0			0
$651$	−14.6894			−0.575723
$652$		0			0
$653$	4.10903	+	7.11704i	0.160799	+	0.278511i	0.935155	−	0.354238i	$-0.115260\pi$
$653$	4.10903	+	7.11704i	0.160799	+	0.278511i	−0.774357	+	0.632749i	$0.781926\pi$
$654$		0			0
$655$		−	10.1489i		−	0.396551i
$656$		0			0
$657$	−20.7408	−	11.9747i	−0.809176	−	0.467178i
$658$		0			0
$659$	−16.8751	+	29.2286i	−0.657362	+	1.13858i	0.323934	+	0.946080i	$0.394994\pi$
$659$	−16.8751	+	29.2286i	−0.657362	+	1.13858i	−0.981296	+	0.192505i	$0.938339\pi$
$660$		0			0
$661$	−5.20295	+	3.00392i	−0.202371	+	0.116839i	−0.597761	−	0.801674i	$-0.703943\pi$
$661$	−5.20295	+	3.00392i	−0.202371	+	0.116839i	0.395390	+	0.918513i	$0.370610\pi$
$662$		0			0
$663$	0.248559	−	2.45831i	0.00965324	−	0.0954727i
$664$		0			0
$665$	−31.5206	+	18.1984i	−1.22232	+	0.705705i
$666$		0			0
$667$	−0.884338	+	1.53172i	−0.0342417	+	0.0593084i
$668$		0			0
$669$	−7.88429	−	4.55199i	−0.304824	−	0.175990i
$670$		0			0
$671$			8.33368i			0.321718i
$672$		0			0
$673$	−11.5476	−	20.0010i	−0.445127	−	0.770983i	0.552934	−	0.833225i	$-0.313508\pi$
$673$	−11.5476	−	20.0010i	−0.445127	−	0.770983i	−0.998061	+	0.0622420i	$0.980175\pi$
$674$		0			0
$675$	−11.4820			−0.441944
$676$		0			0
$677$	47.1723			1.81298			0.906490	−	0.422227i	$-0.138752\pi$
$677$	47.1723			1.81298			0.906490	+	0.422227i	$0.138752\pi$
$678$		0			0
$679$	−7.71561	−	13.3638i	−0.296098	−	0.512857i
$680$		0			0
$681$		−	4.89686i		−	0.187648i
$682$		0			0
$683$	−36.3780	−	21.0028i	−1.39196	−	0.803651i	−0.398431	−	0.917198i	$-0.630445\pi$
$683$	−36.3780	−	21.0028i	−1.39196	−	0.803651i	−0.993533	+	0.113547i	$0.963779\pi$
$684$		0			0
$685$	12.8268	−	22.2167i	0.490087	−	0.848856i
$686$		0			0
$687$	−0.980148	+	0.565889i	−0.0373950	+	0.0215900i
$688$		0			0
$689$	−4.22686	+	41.8046i	−0.161031	+	1.59263i
$690$		0			0
$691$	−22.7253	+	13.1204i	−0.864510	+	0.499125i	−0.865520	−	0.500874i	$-0.833012\pi$
$691$	−22.7253	+	13.1204i	−0.864510	+	0.499125i	0.00100968	+	0.999999i	$0.499679\pi$
$692$		0			0
$693$	−16.8907	+	29.2556i	−0.641626	+	1.11133i
$694$		0			0
$695$	32.4610	+	18.7413i	1.23131	+	0.710900i
$696$		0			0
$697$		−	4.02112i		−	0.152311i
$698$		0			0
$699$	−1.20279	−	2.08329i	−0.0454936	−	0.0787972i
$700$		0			0
$701$	23.6200			0.892116			0.446058	−	0.895004i	$-0.352827\pi$
$701$	23.6200			0.892116			0.446058	+	0.895004i	$0.352827\pi$
$702$		0			0
$703$	−5.39590			−0.203510
$704$		0			0
$705$	4.97659	+	8.61971i	0.187429	+	0.324637i
$706$		0			0
$707$		−	0.678138i		−	0.0255040i
$708$		0			0
$709$	−3.72212	−	2.14897i	−0.139787	−	0.0807063i	0.428475	−	0.903553i	$-0.359051\pi$
$709$	−3.72212	−	2.14897i	−0.139787	−	0.0807063i	−0.568263	+	0.822847i	$0.692384\pi$
$710$		0			0
$711$	−11.7215	+	20.3022i	−0.439590	+	0.761393i
$712$		0			0
$713$	3.69543	−	2.13356i	0.138395	−	0.0799023i
$714$		0			0
$715$	35.9321	−	16.1685i	1.34378	−	0.604666i
$716$		0			0
$717$	5.51996	−	3.18695i	0.206147	−	0.119019i
$718$		0			0
$719$	0.0530646	−	0.0919106i	0.00197898	−	0.00342769i	−0.865034	−	0.501713i	$-0.832703\pi$
$719$	0.0530646	−	0.0919106i	0.00197898	−	0.00342769i	0.867013	+	0.498285i	$0.166037\pi$
$720$		0			0
$721$	−18.9282	−	10.9282i	−0.704923	−	0.406988i
$722$		0			0
$723$		−	6.09488i		−	0.226671i
$724$		0			0
$725$	−11.6176	−	20.1223i	−0.431467	−	0.747322i
$726$		0			0
$727$	9.79643			0.363329			0.181665	−	0.983361i	$-0.441851\pi$
$727$	9.79643			0.363329			0.181665	+	0.983361i	$0.441851\pi$
$728$		0			0
$729$	−19.2644			−0.713496
$730$		0			0
$731$	−9.51717	−	16.4842i	−0.352005	−	0.609691i
$732$		0			0
$733$			1.98379i			0.0732731i	0.999329	+	0.0366366i	$0.0116644\pi$
$733$			1.98379i			0.0732731i	−0.999329	+	0.0366366i	$0.988336\pi$
$734$		0			0
$735$	5.15425	+	2.97581i	0.190117	+	0.109764i
$736$		0			0
$737$	15.7385	−	27.2598i	0.579733	−	1.00413i
$738$		0			0
$739$	4.50190	−	2.59917i	0.165605	−	0.0956121i	−0.414907	−	0.909864i	$-0.636186\pi$
$739$	4.50190	−	2.59917i	0.165605	−	0.0956121i	0.580512	+	0.814252i	$0.302852\pi$
$740$		0			0
$741$	−4.61783	−	0.466909i	−0.169640	−	0.0171523i
$742$		0			0
$743$	−15.9989	+	9.23696i	−0.586942	+	0.338871i	−0.763887	−	0.645350i	$-0.776712\pi$
$743$	−15.9989	+	9.23696i	−0.586942	+	0.338871i	0.176945	+	0.984221i	$0.443378\pi$
$744$		0			0
$745$	27.4724	−	47.5837i	1.00651	−	1.74333i
$746$		0			0
$747$	−2.75274	−	1.58930i	−0.100718	−	0.0581493i
$748$		0			0
$749$			17.7615i			0.648992i
$750$		0			0
$751$	18.3646	+	31.8085i	0.670135	+	1.16071i	0.977865	+	0.209235i	$0.0670973\pi$
$751$	18.3646	+	31.8085i	0.670135	+	1.16071i	−0.307730	+	0.951474i	$0.599569\pi$
$752$		0			0
$753$	6.13153			0.223446
$754$		0			0
$755$	8.94034			0.325372
$756$		0			0
$757$	12.7385	+	22.0636i	0.462987	+	0.801917i	0.999108	−	0.0422241i	$-0.0134444\pi$
$757$	12.7385	+	22.0636i	0.462987	+	0.801917i	−0.536121	+	0.844141i	$0.680111\pi$
$758$		0			0
$759$			0.514268i			0.0186668i
$760$		0			0
$761$	28.6834	+	16.5604i	1.03977	+	0.600312i	0.919769	−	0.392461i	$-0.128376\pi$
$761$	28.6834	+	16.5604i	1.03977	+	0.600312i	0.120003	+	0.992774i	$0.461710\pi$
$762$		0			0
$763$	−18.8100	+	32.5799i	−0.680968	+	1.17947i
$764$		0			0
$765$	13.8951	−	8.02231i	0.502377	−	0.290047i
$766$		0			0
$767$	−13.3366	+	18.5096i	−0.481556	+	0.668344i
$768$		0			0
$769$	2.15542	−	1.24443i	0.0777264	−	0.0448754i	−0.460633	−	0.887591i	$-0.652378\pi$
$769$	2.15542	−	1.24443i	0.0777264	−	0.0448754i	0.538359	+	0.842715i	$0.319044\pi$
$770$		0			0
$771$	2.94208	−	5.09583i	0.105956	−	0.183522i
$772$		0			0
$773$	−13.8492	−	7.99582i	−0.498120	−	0.287590i	0.229817	−	0.973234i	$-0.426187\pi$
$773$	−13.8492	−	7.99582i	−0.498120	−	0.287590i	−0.727937	+	0.685644i	$0.759521\pi$
$774$		0			0
$775$			56.0573i			2.01364i
$776$		0			0
$777$	1.07783	+	1.86685i	0.0386668	+	0.0669729i
$778$		0			0
$779$	−7.55351			−0.270633
$780$		0			0
$781$	35.3155			1.26369
$782$		0			0
$783$	5.17392	+	8.96149i	0.184901	+	0.320257i
$784$		0			0
$785$			41.9026i			1.49557i
$786$		0			0
$787$	−25.0453	−	14.4599i	−0.892769	−	0.515441i	−0.0179219	−	0.999839i	$-0.505705\pi$
$787$	−25.0453	−	14.4599i	−0.892769	−	0.515441i	−0.874847	+	0.484399i	$0.839038\pi$
$788$		0			0
$789$	−1.05129	+	1.82088i	−0.0374268	+	0.0648251i
$790$		0			0
$791$	−32.5706	+	18.8046i	−1.15808	+	0.668615i
$792$		0			0
$793$	−7.08170	−	5.10252i	−0.251479	−	0.181196i
$794$		0			0
$795$	12.3831	−	7.14939i	0.439183	−	0.253563i
$796$		0			0
$797$	−3.54893	+	6.14693i	−0.125710	+	0.217736i	−0.922010	−	0.387166i	$-0.873454\pi$
$797$	−3.54893	+	6.14693i	−0.125710	+	0.217736i	0.796300	+	0.604901i	$0.206787\pi$
$798$		0			0
$799$	−12.4557	−	7.19130i	−0.440651	−	0.254410i
$800$		0			0
$801$			50.8022i			1.79501i
$802$		0			0
$803$	−14.4610	−	25.0471i	−0.510317	−	0.883894i
$804$		0			0
$805$	−4.22385			−0.148871
$806$		0			0
$807$	−6.87046			−0.241852
$808$		0			0
$809$	3.26868	+	5.66151i	0.114921	+	0.199048i	0.917748	−	0.397163i	$-0.130005\pi$
$809$	3.26868	+	5.66151i	0.114921	+	0.199048i	−0.802827	+	0.596211i	$0.796672\pi$
$810$		0			0
$811$			16.3358i			0.573627i	0.957986	+	0.286813i	$0.0925959\pi$
$811$			16.3358i			0.573627i	−0.957986	+	0.286813i	$0.907404\pi$
$812$		0			0
$813$	0.330880	+	0.191034i	0.0116045	+	0.00669984i
$814$		0			0
$815$	−29.1591	+	50.5050i	−1.02140	+	1.76911i
$816$		0			0
$817$	−30.9650	+	17.8776i	−1.08333	+	0.625459i
$818$		0			0
$819$	−14.5187	−	32.2658i	−0.507325	−	1.12746i
$820$		0			0
$821$	−35.9698	+	20.7672i	−1.25535	+	0.724779i	−0.972168	−	0.234286i	$-0.924725\pi$
$821$	−35.9698	+	20.7672i	−1.25535	+	0.724779i	−0.283186	+	0.959065i	$0.591391\pi$
$822$		0			0
$823$	2.66922	−	4.62322i	0.0930431	−	0.161155i	−0.815747	−	0.578409i	$-0.803674\pi$
$823$	2.66922	−	4.62322i	0.0930431	−	0.161155i	0.908790	+	0.417253i	$0.137007\pi$
$824$		0			0
$825$	−5.85084	−	3.37799i	−0.203700	−	0.117606i
$826$		0			0
$827$		−	22.2608i		−	0.774085i	−0.922062	−	0.387043i	$-0.873497\pi$
$827$		−	22.2608i		−	0.774085i	0.922062	−	0.387043i	$-0.126503\pi$
$828$		0			0
$829$	−20.2276	−	35.0352i	−0.702532	−	1.21682i	−0.967575	−	0.252585i	$-0.918719\pi$
$829$	−20.2276	−	35.0352i	−0.702532	−	1.21682i	0.265042	−	0.964237i	$-0.414614\pi$
$830$		0			0
$831$	0.793657			0.0275317
$832$		0			0
$833$	−8.60022			−0.297980
$834$		0			0
$835$	16.5296	+	28.6302i	0.572032	+	0.990788i
$836$		0			0
$837$		−	24.9652i		−	0.862924i
$838$		0			0
$839$	3.42482	+	1.97732i	0.118238	+	0.0682647i	0.557953	−	0.829873i	$-0.311587\pi$
$839$	3.42482	+	1.97732i	0.118238	+	0.0682647i	−0.439715	+	0.898138i	$0.644920\pi$
$840$		0			0
$841$	4.02999	−	6.98015i	0.138965	−	0.240695i
$842$		0			0
$843$	0.403183	−	0.232778i	0.0138863	−	0.00801728i
$844$		0			0
$845$	−8.26092	+	40.4335i	−0.284184	+	1.39096i
$846$		0			0
$847$	−2.53590	+	1.46410i	−0.0871345	+	0.0503071i
$848$		0			0
$849$	0.330880	−	0.573101i	0.0113558	−	0.0196688i
$850$		0			0
$851$	−0.542299	−	0.313097i	−0.0185898	−	0.0107328i
$852$		0			0
$853$		−	27.7953i		−	0.951692i	−0.879529	−	0.475846i	$-0.842142\pi$
$853$		−	27.7953i		−	0.951692i	0.879529	−	0.475846i	$-0.157858\pi$
$854$		0			0
$855$	−15.0696	−	26.1013i	−0.515370	−	0.892646i
$856$		0			0
$857$	16.5940			0.566839			0.283419	−	0.958996i	$-0.408531\pi$
$857$	16.5940			0.566839			0.283419	+	0.958996i	$0.408531\pi$
$858$		0			0
$859$	36.5932			1.24854			0.624271	−	0.781208i	$-0.285396\pi$
$859$	36.5932			1.24854			0.624271	+	0.781208i	$0.285396\pi$
$860$		0			0
$861$	1.50881	+	2.61333i	0.0514200	+	0.0890620i
$862$		0			0
$863$			10.4107i			0.354384i	0.984176	+	0.177192i	$0.0567014\pi$
$863$			10.4107i			0.354384i	−0.984176	+	0.177192i	$0.943299\pi$
$864$		0			0
$865$	17.7593	+	10.2533i	0.603834	+	0.348624i
$866$		0			0
$867$	−2.67781	+	4.63811i	−0.0909433	+	0.157518i
$868$		0			0
$869$	−24.5175	+	14.1552i	−0.831699	+	0.480182i
$870$		0			0
$871$	13.5282	+	30.0646i	0.458387	+	1.01870i
$872$		0			0
$873$	11.0662	−	6.38907i	0.374534	−	0.216237i
$874$		0			0
$875$	0.423973	−	0.734343i	0.0143329	−	0.0248253i
$876$		0			0
$877$	−5.92136	−	3.41870i	−0.199950	−	0.115441i	0.396682	−	0.917956i	$-0.370162\pi$
$877$	−5.92136	−	3.41870i	−0.199950	−	0.115441i	−0.596632	+	0.802515i	$0.703495\pi$
$878$		0			0
$879$		−	0.999901i		−	0.0337258i
$880$		0			0
$881$	−8.77024	−	15.1905i	−0.295477	−	0.511781i	0.679619	−	0.733565i	$-0.262145\pi$
$881$	−8.77024	−	15.1905i	−0.295477	−	0.511781i	−0.975096	+	0.221784i	$0.928812\pi$
$882$		0			0
$883$	−3.95506			−0.133098			−0.0665492	−	0.997783i	$-0.521199\pi$
$883$	−3.95506			−0.133098			−0.0665492	+	0.997783i	$0.521199\pi$
$884$		0			0
$885$	7.76362			0.260971
$886$		0			0
$887$	10.0889	+	17.4744i	0.338750	+	0.586733i	0.984198	−	0.177072i	$-0.0566624\pi$
$887$	10.0889	+	17.4744i	0.338750	+	0.586733i	−0.645448	+	0.763805i	$0.723329\pi$
$888$		0			0
$889$		−	29.6409i		−	0.994124i
$890$		0			0
$891$	−22.8896	−	13.2153i	−0.766831	−	0.442730i
$892$		0			0
$893$	−13.5086	+	23.3975i	−0.452047	+	0.782969i
$894$		0			0
$895$	25.2640	−	14.5862i	0.844482	−	0.487562i
$896$		0			0
$897$	−0.437009	−	0.314875i	−0.0145913	−	0.0105134i
$898$		0			0
$899$	43.7515	−	25.2600i	1.45920	−	0.842467i
$900$		0			0
$901$	−10.3310	+	17.8939i	−0.344177	+	0.596132i
$902$		0			0
$903$	12.3704	+	7.14208i	0.411662	+	0.237673i
$904$		0			0
$905$		−	6.19793i		−	0.206026i
$906$		0			0
$907$	−15.5242	−	26.8887i	−0.515472	−	0.892823i	−0.999839	−	0.0179583i	$-0.994283\pi$
$907$	−15.5242	−	26.8887i	−0.515472	−	0.892823i	0.484367	−	0.874865i	$-0.339050\pi$
$908$		0			0
$909$	0.561546			0.0186253
$910$		0			0
$911$	25.2956			0.838082			0.419041	−	0.907967i	$-0.362366\pi$
$911$	25.2956			0.838082			0.419041	+	0.907967i	$0.362366\pi$
$912$		0			0
$913$	−1.91928	−	3.32428i	−0.0635188	−	0.110018i
$914$		0			0
$915$			2.97033i			0.0981960i
$916$		0			0
$917$	−9.53109	−	5.50278i	−0.314744	−	0.181718i
$918$		0			0
$919$	24.2447	−	41.9931i	0.799760	−	1.38522i	−0.120012	−	0.992772i	$-0.538293\pi$
$919$	24.2447	−	41.9931i	0.799760	−	1.38522i	0.919772	−	0.392452i	$-0.128373\pi$
$920$		0			0
$921$	−4.12911	+	2.38394i	−0.136059	+	0.0785536i
$922$		0			0
$923$	−21.6228	+	30.0100i	−0.711724	+	0.987790i
$924$		0			0
$925$	7.12422	−	4.11317i	0.234243	−	0.135240i
$926$		0			0
$927$	9.04933	−	15.6739i	0.297219	−	0.514798i
$928$		0			0
$929$	35.8923	+	20.7224i	1.17759	+	0.679881i	0.955455	−	0.295135i	$-0.0953648\pi$
$929$	35.8923	+	20.7224i	1.17759	+	0.679881i	0.222133	+	0.975016i	$0.428698\pi$
$930$		0			0
$931$			16.1552i			0.529465i
$932$		0			0
$933$	0.916612	+	1.58762i	0.0300085	+	0.0519763i
$934$		0			0
$935$	19.3759			0.633660
$936$		0			0
$937$	14.5402			0.475009			0.237504	−	0.971386i	$-0.423671\pi$
$937$	14.5402			0.475009			0.237504	+	0.971386i	$0.423671\pi$
$938$		0			0
$939$	−0.0444705	−	0.0770252i	−0.00145124	−	0.00251362i
$940$		0			0
$941$			38.0803i			1.24138i	0.784056	+	0.620690i	$0.213148\pi$
$941$			38.0803i			1.24138i	−0.784056	+	0.620690i	$0.786852\pi$
$942$		0			0
$943$	−0.759143	−	0.438292i	−0.0247211	−	0.0142727i
$944$		0			0
$945$	−12.3561	+	21.4013i	−0.401942	+	0.696185i
$946$		0			0
$947$	39.5704	−	22.8460i	1.28586	−	0.742394i	0.307950	−	0.951402i	$-0.400357\pi$
$947$	39.5704	−	22.8460i	1.28586	−	0.742394i	0.977914	+	0.209008i	$0.0670236\pi$
$948$		0			0
$949$	30.1384	+	3.04729i	0.978334	+	0.0989193i
$950$		0			0
$951$	−1.96782	+	1.13612i	−0.0638108	+	0.0368412i
$952$		0			0
$953$	−17.9712	+	31.1271i	−0.582145	+	1.00831i	0.413080	+	0.910695i	$0.364453\pi$
$953$	−17.9712	+	31.1271i	−0.582145	+	1.00831i	−0.995225	+	0.0976101i	$0.968880\pi$
$954$		0			0
$955$	−47.3402	−	27.3319i	−1.53189	−	0.884438i
$956$		0			0
$957$			6.08862i			0.196817i
$958$		0			0
$959$	−13.9095	−	24.0919i	−0.449160	−	0.777968i
$960$		0			0
$961$	−90.8844			−2.93176
$962$		0			0
$963$	−14.7078			−0.473952
$964$		0			0
$965$	−14.0062	−	24.2594i	−0.450875	−	0.780939i
$966$		0			0
$967$		−	40.3763i		−	1.29842i	−0.760611	−	0.649208i	$-0.775101\pi$
$967$		−	40.3763i		−	1.29842i	0.760611	−	0.649208i	$-0.224899\pi$
$968$		0			0
$969$	−1.97660	−	1.14119i	−0.0634976	−	0.0366603i
$970$		0			0
$971$	4.89013	−	8.46996i	0.156932	−	0.271814i	−0.776829	−	0.629712i	$-0.783173\pi$
$971$	4.89013	−	8.46996i	0.156932	−	0.271814i	0.933761	+	0.357898i	$0.116506\pi$
$972$		0			0
$973$	35.2009	−	20.3232i	1.12849	−	0.651533i
$974$		0			0
$975$	6.45284	−	2.90360i	0.206656	−	0.0929897i
$976$		0			0
$977$	48.6158	−	28.0683i	1.55536	−	0.897986i	0.557667	−	0.830065i	$-0.311697\pi$
$977$	48.6158	−	28.0683i	1.55536	−	0.897986i	0.997691	−	0.0679208i	$-0.0216365\pi$
$978$		0			0
$979$	−30.6750	+	53.1307i	−0.980378	+	1.69806i
$980$		0			0
$981$	−26.9785	−	15.5760i	−0.861356	−	0.497304i
$982$		0			0
$983$		−	18.9028i		−	0.602906i	−0.953481	−	0.301453i	$-0.902528\pi$
$983$		−	18.9028i		−	0.602906i	0.953481	−	0.301453i	$-0.0974716\pi$
$984$		0			0
$985$	21.9383	+	37.9983i	0.699014	+	1.21073i
$986$		0			0
$987$	10.7933			0.343554
$988$		0			0
$989$	−4.14939			−0.131943
$990$		0			0
$991$	−1.82002	−	3.15236i	−0.0578147	−	0.100138i	0.835669	−	0.549233i	$-0.185080\pi$
$991$	−1.82002	−	3.15236i	−0.0578147	−	0.100138i	−0.893484	+	0.449095i	$0.851747\pi$
$992$		0			0
$993$		−	4.95684i		−	0.157301i
$994$		0			0
$995$	68.5125	+	39.5557i	2.17199	+	1.25400i
$996$		0			0
$997$	5.20729	−	9.01929i	0.164916	−	0.285644i	−0.771709	−	0.635976i	$-0.780598\pi$
$997$	5.20729	−	9.01929i	0.164916	−	0.285644i	0.936626	+	0.350332i	$0.113931\pi$
$998$		0			0
$999$	−3.17278	+	1.83181i	−0.100382	+	0.0579558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.w.c.49.3		8
3.2	odd	2		1872.2.by.n.1297.4		8
4.3	odd	2		104.2.o.a.49.2	yes	8
8.3	odd	2		832.2.w.g.257.3		8
8.5	even	2		832.2.w.i.257.2		8
12.11	even	2		936.2.bi.b.361.4		8
13.2	odd	12		2704.2.a.be.1.2		4
13.3	even	3		2704.2.f.q.337.3		8
13.4	even	6	inner	208.2.w.c.17.3		8
13.10	even	6		2704.2.f.q.337.4		8
13.11	odd	12		2704.2.a.bd.1.2		4
39.17	odd	6		1872.2.by.n.433.1		8
52.3	odd	6		1352.2.f.f.337.5		8
52.7	even	12		1352.2.i.k.529.2		8
52.11	even	12		1352.2.a.k.1.3		4
52.15	even	12		1352.2.a.l.1.3		4
52.19	even	12		1352.2.i.l.529.2		8
52.23	odd	6		1352.2.f.f.337.6		8
52.31	even	4		1352.2.i.l.1329.2		8
52.35	odd	6		1352.2.o.f.1161.2		8
52.43	odd	6		104.2.o.a.17.2	✓	8
52.47	even	4		1352.2.i.k.1329.2		8
52.51	odd	2		1352.2.o.f.361.2		8
104.43	odd	6		832.2.w.g.641.3		8
104.69	even	6		832.2.w.i.641.2		8
156.95	even	6		936.2.bi.b.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.2	✓	8	52.43	odd	6
104.2.o.a.49.2	yes	8	4.3	odd	2
208.2.w.c.17.3		8	13.4	even	6	inner
208.2.w.c.49.3		8	1.1	even	1	trivial
832.2.w.g.257.3		8	8.3	odd	2
832.2.w.g.641.3		8	104.43	odd	6
832.2.w.i.257.2		8	8.5	even	2
832.2.w.i.641.2		8	104.69	even	6
936.2.bi.b.361.4		8	12.11	even	2
936.2.bi.b.433.1		8	156.95	even	6
1352.2.a.k.1.3		4	52.11	even	12
1352.2.a.l.1.3		4	52.15	even	12
1352.2.f.f.337.5		8	52.3	odd	6
1352.2.f.f.337.6		8	52.23	odd	6
1352.2.i.k.529.2		8	52.7	even	12
1352.2.i.k.1329.2		8	52.47	even	4
1352.2.i.l.529.2		8	52.19	even	12
1352.2.i.l.1329.2		8	52.31	even	4
1352.2.o.f.361.2		8	52.51	odd	2
1352.2.o.f.1161.2		8	52.35	odd	6
1872.2.by.n.433.1		8	39.17	odd	6
1872.2.by.n.1297.4		8	3.2	odd	2
2704.2.a.bd.1.2		4	13.11	odd	12
2704.2.a.be.1.2		4	13.2	odd	12
2704.2.f.q.337.3		8	13.3	even	3
2704.2.f.q.337.4		8	13.10	even	6

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.193255 + 0.334727i) q^{3} -3.17452i q^{5} +(-2.98127 - 1.72124i) q^{7} +(1.42531 - 2.46870i) q^{9} +O(q^{10})\)	\(q+(0.193255 + 0.334727i) q^{3} -3.17452i q^{5} +(-2.98127 - 1.72124i) q^{7} +(1.42531 - 2.46870i) q^{9} +(2.98127 - 1.72124i) q^{11} +(-0.362708 + 3.58726i) q^{13} +(1.06260 - 0.613491i) q^{15} +(-0.886509 + 1.53548i) q^{17} +(2.88434 + 1.66527i) q^{19} -1.33055i q^{21} +(0.193255 + 0.334727i) q^{23} -5.07759 q^{25} +2.26131 q^{27} +(2.28801 + 3.96296i) q^{29} -11.0401i q^{31} +(1.15229 + 0.665273i) q^{33} +(-5.46410 + 9.46410i) q^{35} +(-1.40307 + 0.810063i) q^{37} +(-1.27085 + 0.571847i) q^{39} +(-1.96410 + 1.13397i) q^{41} +(-5.36778 + 9.29726i) q^{43} +(-7.83695 - 4.52466i) q^{45} +8.11192i q^{47} +(2.42531 + 4.20075i) q^{49} -0.685288 q^{51} +11.6536 q^{53} +(-5.46410 - 9.46410i) q^{55} +1.28729i q^{57} +(5.47970 + 3.16371i) q^{59} +(-1.21042 + 2.09651i) q^{61} +(-8.49843 + 4.90657i) q^{63} +(11.3878 + 1.15142i) q^{65} +(7.91867 - 4.57185i) q^{67} +(-0.0746946 + 0.129375i) q^{69} +(8.88434 + 5.12937i) q^{71} -8.40150i q^{73} +(-0.981268 - 1.69961i) q^{75} -11.8506 q^{77} -8.22385 q^{79} +(-3.83891 - 6.64918i) q^{81} -1.11506i q^{83} +(4.87441 + 2.81424i) q^{85} +(-0.884338 + 1.53172i) q^{87} +(-15.4339 + 8.91075i) q^{89} +(7.25585 - 10.0703i) q^{91} +(3.69543 - 2.13356i) q^{93} +(5.28645 - 9.15640i) q^{95} +(3.88205 + 2.24130i) q^{97} -9.81315i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9	\( 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{13} + 6 q^{19} - 2 q^{23} - 20 q^{25} + 28 q^{27} - 8 q^{29} + 6 q^{33} - 16 q^{35} - 24 q^{37} + 14 q^{39} + 12 q^{41} - 6 q^{43} + 30 q^{45} + 2 q^{49} - 68 q^{51} + 20 q^{53} - 16 q^{55} - 18 q^{59} - 4 q^{61} - 36 q^{63} + 14 q^{65} + 42 q^{67} - 18 q^{69} + 54 q^{71} + 22 q^{75} - 60 q^{77} - 16 q^{79} - 20 q^{81} + 6 q^{85} + 10 q^{87} - 18 q^{89} + 46 q^{91} + 36 q^{93} - 16 q^{95} + 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^13 + 6 * q^19 - 2 * q^23 - 20 * q^25 + 28 * q^27 - 8 * q^29 + 6 * q^33 - 16 * q^35 - 24 * q^37 + 14 * q^39 + 12 * q^41 - 6 * q^43 + 30 * q^45 + 2 * q^49 - 68 * q^51 + 20 * q^53 - 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 14 * q^65 + 42 * q^67 - 18 * q^69 + 54 * q^71 + 22 * q^75 - 60 * q^77 - 16 * q^79 - 20 * q^81 + 6 * q^85 + 10 * q^87 - 18 * q^89 + 46 * q^91 + 36 * q^93 - 16 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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