LMFDB - Embedded newform 260.2.bk.c.197.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (of order $12$, degree $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.5
Root			$0.402430i$ of defining polynomial
Character	$\chi$	$=$	260.197
Dual form			260.2.bk.c.33.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.49316 + 0.668040i) q^{3} +(-0.380790 + 2.20341i) q^{5} +(-0.749297 - 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +O(q^{10})$	\(q+(2.49316 + 0.668040i) q^{3} +(-0.380790 + 2.20341i) q^{5} +(-0.749297 - 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +(0.417628 - 1.55861i) q^{11} +(1.32514 + 3.35321i) q^{13} +(-2.42134 + 5.23906i) q^{15} +(-1.33873 - 4.99621i) q^{17} +(-1.16619 + 0.312480i) q^{19} +(-1.57912 - 1.57912i) q^{21} +(0.704305 - 2.62850i) q^{23} +(-4.71000 - 1.67807i) q^{25} +(1.20845 + 1.20845i) q^{27} +(5.94138 - 3.43026i) q^{29} +(0.191663 - 0.191663i) q^{31} +(2.08243 - 3.60687i) q^{33} +(1.23853 - 1.48627i) q^{35} +(-8.22242 + 4.74722i) q^{37} +(1.06370 + 9.24533i) q^{39} +(0.417297 + 0.111814i) q^{41} +(11.5499 - 3.09480i) q^{43} +(-5.24225 + 6.29083i) q^{45} +1.52128i q^{47} +(-3.12570 - 5.41387i) q^{49} -13.3507i q^{51} +(-4.88398 + 4.88398i) q^{53} +(3.27522 + 1.51371i) q^{55} -3.11625 q^{57} +(-3.05172 - 11.3892i) q^{59} +(-2.94152 + 5.09486i) q^{61} +(-1.58426 - 2.74402i) q^{63} +(-7.89308 + 1.64294i) q^{65} +(6.76168 + 11.7116i) q^{67} +(3.51189 - 6.08277i) q^{69} +(-3.85102 - 14.3722i) q^{71} -10.9921 q^{73} +(-10.6218 - 7.33017i) q^{75} +(-0.987192 + 0.987192i) q^{77} +3.98168i q^{79} +(-3.28761 - 5.69431i) q^{81} +6.25583i q^{83} +(11.5185 - 1.04726i) q^{85} +(17.1044 - 4.58310i) q^{87} +(-9.80805 - 2.62806i) q^{89} +(0.457701 - 3.08581i) q^{91} +(0.605885 - 0.349808i) q^{93} +(-0.244446 - 2.68858i) q^{95} +(-0.728593 + 1.26196i) q^{97} +(4.17841 - 4.17841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.49316	+	0.668040i	1.43943	+	0.385693i	0.892333	−	0.451378i	$-0.149067\pi$
$3$	2.49316	+	0.668040i	1.43943	+	0.385693i	0.547094	+	0.837071i	$0.315734\pi$
$4$		0			0
$5$	−0.380790	+	2.20341i	−0.170295	+	0.985393i
$5$	−0.380790	+	2.20341i	−0.170295	+	0.985393i
$6$		0			0
$7$	−0.749297	−	0.432607i	−0.283208	−	0.163510i	0.351667	−	0.936125i	$-0.385615\pi$
$7$	−0.749297	−	0.432607i	−0.283208	−	0.163510i	−0.634875	+	0.772615i	$0.718948\pi$
$8$		0			0
$9$	3.17149	+	1.83106i	1.05716	+	0.610354i
$10$		0			0
$11$	0.417628	−	1.55861i	0.125920	−	0.469938i	−0.873951	−	0.486014i	$-0.838451\pi$
$11$	0.417628	−	1.55861i	0.125920	−	0.469938i	0.999871	+	0.0160756i	$0.00511723\pi$
$12$		0			0
$13$	1.32514	+	3.35321i	0.367527	+	0.930013i
$13$	1.32514	+	3.35321i	0.367527	+	0.930013i
$14$		0			0
$15$	−2.42134	+	5.23906i	−0.625186	+	1.35272i
$16$		0			0
$17$	−1.33873	−	4.99621i	−0.324690	−	1.21176i	−0.914623	−	0.404308i	$-0.867513\pi$
$17$	−1.33873	−	4.99621i	−0.324690	−	1.21176i	0.589933	−	0.807452i	$-0.299154\pi$
$18$		0			0
$19$	−1.16619	+	0.312480i	−0.267543	+	0.0716878i	−0.390096	−	0.920774i	$-0.627558\pi$
$19$	−1.16619	+	0.312480i	−0.267543	+	0.0716878i	0.122554	+	0.992462i	$0.460892\pi$
$20$		0			0
$21$	−1.57912	−	1.57912i	−0.344592	−	0.344592i
$22$		0			0
$23$	0.704305	−	2.62850i	0.146858	−	0.548080i	−0.852808	−	0.522225i	$-0.825102\pi$
$23$	0.704305	−	2.62850i	0.146858	−	0.548080i	0.999666	−	0.0258557i	$-0.00823103\pi$
$24$		0			0
$25$	−4.71000	−	1.67807i	−0.941999	−	0.335614i
$26$		0			0
$27$	1.20845	+	1.20845i	0.232567	+	0.232567i
$28$		0			0
$29$	5.94138	−	3.43026i	1.10329	−	0.636983i	0.166204	−	0.986091i	$-0.446849\pi$
$29$	5.94138	−	3.43026i	1.10329	−	0.636983i	0.937082	+	0.349109i	$0.113516\pi$
$30$		0			0
$31$	0.191663	−	0.191663i	0.0344237	−	0.0344237i	−0.689685	−	0.724109i	$-0.742251\pi$
$31$	0.191663	−	0.191663i	0.0344237	−	0.0344237i	0.724109	+	0.689685i	$0.242251\pi$
$32$		0			0
$33$	2.08243	−	3.60687i	0.362504	−	0.627875i
$34$		0			0
$35$	1.23853	−	1.48627i	0.209351	−	0.251226i
$36$		0			0
$37$	−8.22242	+	4.74722i	−1.35176	+	0.780438i	−0.988496	−	0.151249i	$-0.951670\pi$
$37$	−8.22242	+	4.74722i	−1.35176	+	0.780438i	−0.363262	+	0.931687i	$0.618337\pi$
$38$		0			0
$39$	1.06370	+	9.24533i	0.170328	+	1.48044i
$40$		0			0
$41$	0.417297	+	0.111814i	0.0651709	+	0.0174625i	0.291257	−	0.956645i	$-0.405926\pi$
$41$	0.417297	+	0.111814i	0.0651709	+	0.0174625i	−0.226086	+	0.974107i	$0.572593\pi$
$42$		0			0
$43$	11.5499	−	3.09480i	1.76135	−	0.471952i	0.774362	−	0.632743i	$-0.218071\pi$
$43$	11.5499	−	3.09480i	1.76135	−	0.471952i	0.986989	+	0.160791i	$0.0514044\pi$
$44$		0			0
$45$	−5.24225	+	6.29083i	−0.781468	+	0.937782i
$46$		0			0
$47$			1.52128i			0.221902i	0.993826	+	0.110951i	$0.0353897\pi$
$47$			1.52128i			0.221902i	−0.993826	+	0.110951i	$0.964610\pi$
$48$		0			0
$49$	−3.12570	−	5.41387i	−0.446529	−	0.773411i
$50$		0			0
$51$		−	13.3507i		−	1.86947i
$52$		0			0
$53$	−4.88398	+	4.88398i	−0.670867	+	0.670867i	−0.957916	−	0.287049i	$-0.907326\pi$
$53$	−4.88398	+	4.88398i	−0.670867	+	0.670867i	0.287049	+	0.957916i	$0.407326\pi$
$54$		0			0
$55$	3.27522	+	1.51371i	0.441630	+	0.204108i
$56$		0			0
$57$	−3.11625			−0.412757
$58$		0			0
$59$	−3.05172	−	11.3892i	−0.397300	−	1.48274i	−0.817828	−	0.575463i	$-0.804822\pi$
$59$	−3.05172	−	11.3892i	−0.397300	−	1.48274i	0.420528	−	0.907279i	$-0.361845\pi$
$60$		0			0
$61$	−2.94152	+	5.09486i	−0.376623	+	0.652330i	−0.990569	−	0.137018i	$-0.956248\pi$
$61$	−2.94152	+	5.09486i	−0.376623	+	0.652330i	0.613946	+	0.789348i	$0.289581\pi$
$62$		0			0
$63$	−1.58426	−	2.74402i	−0.199598	−	0.345714i
$64$		0			0
$65$	−7.89308	+	1.64294i	−0.979016	+	0.203782i
$66$		0			0
$67$	6.76168	+	11.7116i	0.826070	+	1.43080i	0.901099	+	0.433614i	$0.142762\pi$
$67$	6.76168	+	11.7116i	0.826070	+	1.43080i	−0.0750284	+	0.997181i	$0.523905\pi$
$68$		0			0
$69$	3.51189	−	6.08277i	0.422782	−	0.732279i
$70$		0			0
$71$	−3.85102	−	14.3722i	−0.457031	−	1.70566i	−0.682046	−	0.731309i	$-0.738910\pi$
$71$	−3.85102	−	14.3722i	−0.457031	−	1.70566i	0.225015	−	0.974355i	$-0.427757\pi$
$72$		0			0
$73$	−10.9921			−1.28653			−0.643266	−	0.765643i	$-0.722421\pi$
$73$	−10.9921			−1.28653			−0.643266	+	0.765643i	$0.722421\pi$
$74$		0			0
$75$	−10.6218	−	7.33017i	−1.22649	−	0.846415i
$76$		0			0
$77$	−0.987192	+	0.987192i	−0.112501	+	0.112501i
$78$		0			0
$79$			3.98168i			0.447974i	0.974592	+	0.223987i	$0.0719074\pi$
$79$			3.98168i			0.447974i	−0.974592	+	0.223987i	$0.928093\pi$
$80$		0			0
$81$	−3.28761	−	5.69431i	−0.365290	−	0.632701i
$82$		0			0
$83$			6.25583i			0.686667i	0.939214	+	0.343333i	$0.111556\pi$
$83$			6.25583i			0.686667i	−0.939214	+	0.343333i	$0.888444\pi$
$84$		0			0
$85$	11.5185	−	1.04726i	1.24935	−	0.113591i
$86$		0			0
$87$	17.1044	−	4.58310i	1.83378	−	0.491360i
$88$		0			0
$89$	−9.80805	−	2.62806i	−1.03965	−	0.278574i	−0.301683	−	0.953408i	$-0.597548\pi$
$89$	−9.80805	−	2.62806i	−1.03965	−	0.278574i	−0.737969	+	0.674835i	$0.764215\pi$
$90$		0			0
$91$	0.457701	−	3.08581i	0.0479801	−	0.323481i
$92$		0			0
$93$	0.605885	−	0.349808i	0.0628274	−	0.0362734i
$94$		0			0
$95$	−0.244446	−	2.68858i	−0.0250796	−	0.275843i
$96$		0			0
$97$	−0.728593	+	1.26196i	−0.0739774	+	0.128133i	−0.900641	−	0.434564i	$-0.856903\pi$
$97$	−0.728593	+	1.26196i	−0.0739774	+	0.128133i	0.826664	+	0.562696i	$0.190236\pi$
$98$		0			0
$99$	4.17841	−	4.17841i	0.419946	−	0.419946i
$100$		0			0
$101$	−10.0529	+	5.80403i	−1.00030	+	0.577523i	−0.908337	−	0.418240i	$-0.862647\pi$
$101$	−10.0529	+	5.80403i	−1.00030	+	0.577523i	−0.0919621	+	0.995763i	$0.529314\pi$
$102$		0			0
$103$	10.8660	+	10.8660i	1.07066	+	1.07066i	0.997306	+	0.0733504i	$0.0233691\pi$
$103$	10.8660	+	10.8660i	1.07066	+	1.07066i	0.0733504	+	0.997306i	$0.476631\pi$
$104$		0			0
$105$	4.08076	−	2.87813i	0.398241	−	0.280877i
$106$		0			0
$107$	−1.84601	+	6.88942i	−0.178461	+	0.666025i	0.817475	+	0.575964i	$0.195373\pi$
$107$	−1.84601	+	6.88942i	−0.178461	+	0.666025i	−0.995936	+	0.0900615i	$0.971294\pi$
$108$		0			0
$109$	4.56805	+	4.56805i	0.437540	+	0.437540i	0.891183	−	0.453643i	$-0.149876\pi$
$109$	4.56805	+	4.56805i	0.437540	+	0.437540i	−0.453643	+	0.891183i	$0.649876\pi$
$110$		0			0
$111$	−23.6711	+	6.34266i	−2.24677	+	0.602019i
$112$		0			0
$113$	2.23652	+	8.34679i	0.210394	+	0.785200i	0.987737	+	0.156124i	$0.0498999\pi$
$113$	2.23652	+	8.34679i	0.210394	+	0.785200i	−0.777344	+	0.629076i	$0.783433\pi$
$114$		0			0
$115$	5.52346	+	2.55278i	0.515065	+	0.238048i
$116$		0			0
$117$	−1.93727	+	13.0611i	−0.179101	+	1.20750i
$118$		0			0
$119$	−1.15829	+	4.32280i	−0.106180	+	0.396270i
$120$		0			0
$121$	7.27143	+	4.19816i	0.661039	+	0.381651i
$122$		0			0
$123$	0.965692	+	0.557543i	0.0870735	+	0.0502719i
$124$		0			0
$125$	5.49100	−	9.73904i	0.491130	−	0.871086i
$126$		0			0
$127$	−4.54494	−	1.21781i	−0.403299	−	0.108064i	0.0514670	−	0.998675i	$-0.483610\pi$
$127$	−4.54494	−	1.21781i	−0.403299	−	0.108064i	−0.454766	+	0.890611i	$0.650277\pi$
$128$		0			0
$129$	30.8633			2.71736
$130$		0			0
$131$	15.3255			1.33900			0.669498	−	0.742814i	$-0.266509\pi$
$131$	15.3255			1.33900			0.669498	+	0.742814i	$0.266509\pi$
$132$		0			0
$133$	1.00900	+	0.270362i	0.0874918	+	0.0234434i
$134$		0			0
$135$	−3.12288	+	2.20255i	−0.268775	+	0.189565i
$136$		0			0
$137$	14.6738	+	8.47191i	1.25367	+	0.723804i	0.971835	−	0.235661i	$-0.0757253\pi$
$137$	14.6738	+	8.47191i	1.25367	+	0.723804i	0.281830	+	0.959464i	$0.409059\pi$
$138$		0			0
$139$	−2.69425	−	1.55553i	−0.228524	−	0.131938i	0.381367	−	0.924424i	$-0.375453\pi$
$139$	−2.69425	−	1.55553i	−0.228524	−	0.131938i	−0.609891	+	0.792485i	$0.708787\pi$
$140$		0			0
$141$	−1.01628	+	3.79280i	−0.0855861	+	0.319412i
$142$		0			0
$143$	5.77975	−	0.664975i	0.483327	−	0.0556080i
$144$		0			0
$145$	5.29583	+	14.3975i	0.439795	+	1.19565i
$146$		0			0
$147$	−4.17619	−	15.5857i	−0.344446	−	1.28549i
$148$		0			0
$149$	15.9563	−	4.27549i	1.30719	−	0.350262i	0.463029	−	0.886343i	$-0.346763\pi$
$149$	15.9563	−	4.27549i	1.30719	−	0.350262i	0.844166	+	0.536082i	$0.180096\pi$
$150$		0			0
$151$	12.3067	+	12.3067i	1.00151	+	1.00151i	0.999999	+	0.00150662i	$0.000479574\pi$
$151$	12.3067	+	12.3067i	1.00151	+	1.00151i	0.00150662	+	0.999999i	$0.499520\pi$
$152$		0			0
$153$	4.90260	−	18.2968i	0.396352	−	1.47920i
$154$		0			0
$155$	0.349328	+	0.495295i	0.0280587	+	0.0397830i
$156$		0			0
$157$	−5.83463	−	5.83463i	−0.465654	−	0.465654i	0.434849	−	0.900503i	$-0.356802\pi$
$157$	−5.83463	−	5.83463i	−0.465654	−	0.465654i	−0.900503	+	0.434849i	$0.856802\pi$
$158$		0			0
$159$	−15.4392	+	8.91385i	−1.22441	+	0.706914i
$160$		0			0
$161$	−1.66484	+	1.66484i	−0.131208	+	0.131208i
$162$		0			0
$163$	−2.64140	+	4.57504i	−0.206890	+	0.358344i	−0.950733	−	0.310010i	$-0.899668\pi$
$163$	−2.64140	+	4.57504i	−0.206890	+	0.358344i	0.743843	+	0.668354i	$0.233001\pi$
$164$		0			0
$165$	7.15442	+	5.96189i	0.556971	+	0.464132i
$166$		0			0
$167$	−6.81358	+	3.93382i	−0.527251	+	0.304408i	−0.739896	−	0.672721i	$-0.765125\pi$
$167$	−6.81358	+	3.93382i	−0.527251	+	0.304408i	0.212645	+	0.977129i	$0.431792\pi$
$168$		0			0
$169$	−9.48803	+	8.88692i	−0.729848	+	0.683609i
$170$		0			0
$171$	−4.27073	−	1.14434i	−0.326591	−	0.0875098i
$172$		0			0
$173$	−19.2622	+	5.16129i	−1.46448	+	0.392406i	−0.901034	−	0.433749i	$-0.857191\pi$
$173$	−19.2622	+	5.16129i	−1.46448	+	0.392406i	−0.563444	+	0.826154i	$0.690524\pi$
$174$		0			0
$175$	2.80324	+	3.29495i	0.211905	+	0.249075i
$176$		0			0
$177$		−	30.4337i		−	2.28753i
$178$		0			0
$179$	−1.53139	−	2.65244i	−0.114461	−	0.198253i	0.803103	−	0.595840i	$-0.203181\pi$
$179$	−1.53139	−	2.65244i	−0.114461	−	0.198253i	−0.917564	+	0.397588i	$0.869847\pi$
$180$		0			0
$181$		−	23.3657i		−	1.73676i	−0.495901	−	0.868379i	$-0.665162\pi$
$181$		−	23.3657i		−	1.73676i	0.495901	−	0.868379i	$-0.334838\pi$
$182$		0			0
$183$	−10.7372	+	10.7372i	−0.793720	+	0.793720i
$184$		0			0
$185$	−7.32903	−	19.9250i	−0.538841	−	1.46492i
$186$		0			0
$187$	−8.34623			−0.610337
$188$		0			0
$189$	−0.382706	−	1.42828i	−0.0278377	−	0.103892i
$190$		0			0
$191$	3.73743	−	6.47341i	0.270431	−	0.468400i	−0.698541	−	0.715570i	$-0.746167\pi$
$191$	3.73743	−	6.47341i	0.270431	−	0.468400i	0.968972	+	0.247170i	$0.0795006\pi$
$192$		0			0
$193$	−1.00100	−	1.73378i	−0.0720536	−	0.124800i	0.827748	−	0.561101i	$-0.189622\pi$
$193$	−1.00100	−	1.73378i	−0.0720536	−	0.124800i	−0.899801	+	0.436300i	$0.856289\pi$
$194$		0			0
$195$	−20.7763	−	1.17678i	−1.48782	−	0.0842707i
$196$		0			0
$197$	1.59042	+	2.75469i	0.113313	+	0.196264i	0.917104	−	0.398648i	$-0.130520\pi$
$197$	1.59042	+	2.75469i	0.113313	+	0.196264i	−0.803791	+	0.594912i	$0.797187\pi$
$198$		0			0
$199$	−8.20225	+	14.2067i	−0.581442	+	1.00709i	0.413867	+	0.910337i	$0.364178\pi$
$199$	−8.20225	+	14.2067i	−0.581442	+	1.00709i	−0.995309	+	0.0967496i	$0.969155\pi$
$200$		0			0
$201$	9.03414	+	33.7159i	0.637219	+	2.37813i
$202$		0			0
$203$	−5.93581			−0.416612
$204$		0			0
$205$	−0.405275	+	0.876897i	−0.0283057	+	0.0612452i
$206$		0			0
$207$	7.04664	−	7.04664i	0.489775	−	0.489775i
$208$		0			0
$209$			1.94813i			0.134755i
$210$		0			0
$211$	5.66213	+	9.80710i	0.389797	+	0.675149i	0.992422	−	0.122876i	$-0.0392117\pi$
$211$	5.66213	+	9.80710i	0.389797	+	0.675149i	−0.602625	+	0.798025i	$0.705878\pi$
$212$		0			0
$213$		−	38.4048i		−	2.63145i
$214$		0			0
$215$	2.42099	+	26.6277i	0.165110	+	1.81599i
$216$		0			0
$217$	−0.226527	+	0.0606978i	−0.0153777	+	0.00412044i
$218$		0			0
$219$	−27.4051	−	7.34318i	−1.85187	−	0.496206i
$220$		0			0
$221$	14.9794	−	11.1097i	1.00762	−	0.747320i
$222$		0			0
$223$	8.74357	−	5.04810i	0.585513	−	0.338046i	−0.177808	−	0.984065i	$-0.556901\pi$
$223$	8.74357	−	5.04810i	0.585513	−	0.338046i	0.763321	+	0.646019i	$0.223567\pi$
$224$		0			0
$225$	−11.8651	−	13.9463i	−0.791004	−	0.929752i
$226$		0			0
$227$	6.86958	−	11.8985i	0.455950	−	0.789728i	−0.542792	−	0.839867i	$-0.682633\pi$
$227$	6.86958	−	11.8985i	0.455950	−	0.789728i	0.998742	+	0.0501387i	$0.0159663\pi$
$228$		0			0
$229$	−3.36743	+	3.36743i	−0.222526	+	0.222526i	−0.809561	−	0.587035i	$-0.800295\pi$
$229$	−3.36743	+	3.36743i	−0.222526	+	0.222526i	0.587035	+	0.809561i	$0.300295\pi$
$230$		0			0
$231$	−3.12071	+	1.80174i	−0.205328	+	0.118546i
$232$		0			0
$233$	19.1541	+	19.1541i	1.25482	+	1.25482i	0.953532	+	0.301293i	$0.0974181\pi$
$233$	19.1541	+	19.1541i	1.25482	+	1.25482i	0.301293	+	0.953532i	$0.402582\pi$
$234$		0			0
$235$	−3.35201	−	0.579291i	−0.218661	−	0.0377888i
$236$		0			0
$237$	−2.65992	+	9.92697i	−0.172781	+	0.644826i
$238$		0			0
$239$	−18.4667	−	18.4667i	−1.19451	−	1.19451i	−0.975786	−	0.218727i	$-0.929810\pi$
$239$	−18.4667	−	18.4667i	−1.19451	−	1.19451i	−0.218727	−	0.975786i	$-0.570190\pi$
$240$		0			0
$241$	0.850786	−	0.227967i	0.0548040	−	0.0146847i	−0.231313	−	0.972879i	$-0.574302\pi$
$241$	0.850786	−	0.227967i	0.0548040	−	0.0146847i	0.286117	+	0.958195i	$0.407635\pi$
$242$		0			0
$243$	−5.71949	−	21.3454i	−0.366905	−	1.36931i
$244$		0			0
$245$	13.1192	−	4.82564i	0.838155	−	0.308299i
$246$		0			0
$247$	−2.59317	−	3.49640i	−0.165000	−	0.222471i
$248$		0			0
$249$	−4.17915	+	15.5968i	−0.264843	+	0.988406i
$250$		0			0
$251$	5.62276	+	3.24630i	0.354905	+	0.204905i	0.666844	−	0.745198i	$-0.267645\pi$
$251$	5.62276	+	3.24630i	0.354905	+	0.204905i	−0.311938	+	0.950102i	$0.600978\pi$
$252$		0			0
$253$	−3.80266	−	2.19547i	−0.239071	−	0.138028i
$254$		0			0
$255$	29.4170	+	5.08381i	1.84216	+	0.318361i
$256$		0			0
$257$	−10.3489	−	2.77298i	−0.645547	−	0.172974i	−0.0788324	−	0.996888i	$-0.525119\pi$
$257$	−10.3489	−	2.77298i	−0.645547	−	0.172974i	−0.566715	+	0.823914i	$0.691786\pi$
$258$		0			0
$259$	8.21472			0.510438
$260$		0			0
$261$	25.1240			1.55514
$262$		0			0
$263$	−9.80873	−	2.62824i	−0.604832	−	0.162064i	−0.0566092	−	0.998396i	$-0.518029\pi$
$263$	−9.80873	−	2.62824i	−0.604832	−	0.162064i	−0.548223	+	0.836332i	$0.684696\pi$
$264$		0			0
$265$	−8.90162	−	12.6212i	−0.546822	−	0.775312i
$266$		0			0
$267$	−22.6974	−	13.1043i	−1.38906	−	0.801973i
$268$		0			0
$269$	−16.1943	−	9.34977i	−0.987383	−	0.570066i	−0.0828917	−	0.996559i	$-0.526416\pi$
$269$	−16.1943	−	9.34977i	−0.987383	−	0.570066i	−0.904491	+	0.426493i	$0.859749\pi$
$270$		0			0
$271$	−4.74484	+	17.7080i	−0.288228	+	1.07568i	0.658220	+	0.752826i	$0.271310\pi$
$271$	−4.74484	+	17.7080i	−0.288228	+	1.07568i	−0.946448	+	0.322856i	$0.895357\pi$
$272$		0			0
$273$	3.20257	−	7.38767i	0.193828	−	0.447122i
$274$		0			0
$275$	−4.58248	+	6.64023i	−0.276334	+	0.400421i
$276$		0			0
$277$	3.50958	+	13.0979i	0.210870	+	0.786979i	0.987580	+	0.157120i	$0.0502208\pi$
$277$	3.50958	+	13.0979i	0.210870	+	0.786979i	−0.776709	+	0.629859i	$0.783113\pi$
$278$		0			0
$279$	0.958804	−	0.256911i	0.0574021	−	0.0153809i
$280$		0			0
$281$	17.1478	+	17.1478i	1.02295	+	1.02295i	0.999730	+	0.0232200i	$0.00739181\pi$
$281$	17.1478	+	17.1478i	1.02295	+	1.02295i	0.0232200	+	0.999730i	$0.492608\pi$
$282$		0			0
$283$	2.37015	−	8.84554i	0.140891	−	0.525813i	−0.859013	−	0.511954i	$-0.828922\pi$
$283$	2.37015	−	8.84554i	0.140891	−	0.525813i	0.999904	−	0.0138586i	$-0.00441148\pi$
$284$		0			0
$285$	1.18664	−	6.86636i	0.0702904	−	0.406728i
$286$		0			0
$287$	−0.264308	−	0.264308i	−0.0156016	−	0.0156016i
$288$		0			0
$289$	−8.44752	+	4.87718i	−0.496913	+	0.286893i
$290$		0			0
$291$	−2.65954	+	2.65954i	−0.155905	+	0.155905i
$292$		0			0
$293$	9.09083	−	15.7458i	0.531092	−	0.919878i	−0.468250	−	0.883596i	$-0.655115\pi$
$293$	9.09083	−	15.7458i	0.531092	−	0.919878i	0.999342	−	0.0362820i	$-0.0115515\pi$
$294$		0			0
$295$	26.2570	−	2.38729i	1.52874	−	0.138993i
$296$		0			0
$297$	2.38819	−	1.37882i	0.138577	−	0.0800073i
$298$		0			0
$299$	9.74721	−	1.12144i	0.563696	−	0.0648546i
$300$		0			0
$301$	−9.99318	−	2.67766i	−0.575997	−	0.154338i
$302$		0			0
$303$	−28.9408	+	7.75465i	−1.66260	+	0.445493i
$304$		0			0
$305$	−10.1059	−	8.42144i	−0.578665	−	0.482210i
$306$		0			0
$307$		−	28.0356i		−	1.60008i	−0.599948	−	0.800039i	$-0.704812\pi$
$307$		−	28.0356i		−	1.60008i	0.599948	−	0.800039i	$-0.295188\pi$
$308$		0			0
$309$	19.8317	+	34.3495i	1.12819	+	1.95408i
$310$		0			0
$311$			11.5168i			0.653060i	0.945187	+	0.326530i	$0.105879\pi$
$311$			11.5168i			0.653060i	−0.945187	+	0.326530i	$0.894121\pi$
$312$		0			0
$313$	−10.3376	+	10.3376i	−0.584316	+	0.584316i	−0.936086	−	0.351771i	$-0.885580\pi$
$313$	−10.3376	+	10.3376i	−0.584316	+	0.584316i	0.351771	+	0.936086i	$0.385580\pi$
$314$		0			0
$315$	6.64946	−	2.44587i	0.374655	−	0.137809i
$316$		0			0
$317$	2.31106			0.129802			0.0649010	−	0.997892i	$-0.479327\pi$
$317$	2.31106			0.129802			0.0649010	+	0.997892i	$0.479327\pi$
$318$		0			0
$319$	−2.86514	−	10.6928i	−0.160417	−	0.598685i
$320$		0			0
$321$	−9.20481	+	15.9432i	−0.513763	+	0.889863i
$322$		0			0
$323$	3.12243	+	5.40821i	0.173737	+	0.300921i
$324$		0			0
$325$	−0.614460	−	18.0173i	−0.0340841	−	0.999419i
$326$		0			0
$327$	8.33724	+	14.4405i	0.461050	+	0.798563i
$328$		0			0
$329$	0.658118	−	1.13989i	0.0362832	−	0.0628444i
$330$		0			0
$331$	−9.10127	−	33.9664i	−0.500251	−	1.86696i	−0.498370	−	0.866965i	$-0.666068\pi$
$331$	−9.10127	−	33.9664i	−0.500251	−	1.86696i	−0.00188163	−	0.999998i	$-0.500599\pi$
$332$		0			0
$333$	−34.7698			−1.90537
$334$		0			0
$335$	−28.3801	+	10.4391i	−1.55057	+	0.570347i
$336$		0			0
$337$	−4.04414	+	4.04414i	−0.220298	+	0.220298i	−0.808624	−	0.588326i	$-0.799787\pi$
$337$	−4.04414	+	4.04414i	−0.220298	+	0.220298i	0.588326	+	0.808624i	$0.299787\pi$
$338$		0			0
$339$			22.3040i			1.21139i
$340$		0			0
$341$	−0.218684	−	0.378771i	−0.0118424	−	0.0205116i
$342$		0			0
$343$			11.4653i			0.619068i
$344$		0			0
$345$	12.0655	+	10.0544i	0.649585	+	0.541309i
$346$		0			0
$347$	−0.216132	+	0.0579124i	−0.0116026	+	0.00310890i	−0.264616	−	0.964354i	$-0.585245\pi$
$347$	−0.216132	+	0.0579124i	−0.0116026	+	0.00310890i	0.253013	+	0.967463i	$0.418578\pi$
$348$		0			0
$349$	−11.9175	−	3.19329i	−0.637930	−	0.170933i	−0.0746643	−	0.997209i	$-0.523789\pi$
$349$	−11.9175	−	3.19329i	−0.637930	−	0.170933i	−0.563266	+	0.826276i	$0.690455\pi$
$350$		0			0
$351$	−2.45083	+	5.65356i	−0.130816	+	0.301765i
$352$		0			0
$353$	−11.0318	+	6.36920i	−0.587162	+	0.338998i	−0.763975	−	0.645246i	$-0.776755\pi$
$353$	−11.0318	+	6.36920i	−0.587162	+	0.338998i	0.176812	+	0.984245i	$0.443421\pi$
$354$		0			0
$355$	33.1342	−	3.01256i	1.75858	−	0.159890i
$356$		0			0
$357$	−5.77560	+	10.0036i	−0.305677	+	0.529449i
$358$		0			0
$359$	18.8285	−	18.8285i	0.993730	−	0.993730i	−0.00625094	−	0.999980i	$-0.501990\pi$
$359$	18.8285	−	18.8285i	0.993730	−	0.993730i	0.999980	+	0.00625094i	$0.00198975\pi$
$360$		0			0
$361$	−15.1921	+	8.77118i	−0.799586	+	0.461641i
$362$		0			0
$363$	15.3243	+	15.3243i	0.804317	+	0.804317i
$364$		0			0
$365$	4.18570	−	24.2201i	0.219089	−	1.26774i
$366$		0			0
$367$	5.35985	−	20.0032i	0.279782	−	1.04416i	−0.672787	−	0.739837i	$-0.734903\pi$
$367$	5.35985	−	20.0032i	0.279782	−	1.04416i	0.952569	−	0.304324i	$-0.0984305\pi$
$368$		0			0
$369$	1.11872	+	1.11872i	0.0582380	+	0.0582380i
$370$		0			0
$371$	5.77240	−	1.54671i	0.299688	−	0.0803012i
$372$		0			0
$373$	1.10162	+	4.11130i	0.0570397	+	0.212875i	0.988563	−	0.150805i	$-0.0481867\pi$
$373$	1.10162	+	4.11130i	0.0570397	+	0.212875i	−0.931524	+	0.363680i	$0.881520\pi$
$374$		0			0
$375$	20.1960	−	20.6128i	1.04292	−	1.06444i
$376$		0			0
$377$	19.3755	+	15.3771i	0.997889	+	0.791962i
$378$		0			0
$379$	2.81310	−	10.4986i	0.144499	−	0.539278i	−0.855278	−	0.518169i	$-0.826614\pi$
$379$	2.81310	−	10.4986i	0.144499	−	0.539278i	0.999777	−	0.0211086i	$-0.00671957\pi$
$380$		0			0
$381$	−10.5177	−	6.07241i	−0.538839	−	0.311099i
$382$		0			0
$383$	−11.6937	−	6.75134i	−0.597518	−	0.344977i	0.170546	−	0.985350i	$-0.445447\pi$
$383$	−11.6937	−	6.75134i	−0.597518	−	0.344977i	−0.768065	+	0.640372i	$0.778780\pi$
$384$		0			0
$385$	−1.79927	−	2.55110i	−0.0916994	−	0.130016i
$386$		0			0
$387$	42.2973	+	11.3335i	2.15009	+	0.576116i
$388$		0			0
$389$	−7.82344			−0.396664			−0.198332	−	0.980135i	$-0.563552\pi$
$389$	−7.82344			−0.396664			−0.198332	+	0.980135i	$0.563552\pi$
$390$		0			0
$391$	−14.0754			−0.711825
$392$		0			0
$393$	38.2090	+	10.2381i	1.92739	+	0.516442i
$394$		0			0
$395$	−8.77327	−	1.51619i	−0.441431	−	0.0762877i
$396$		0			0
$397$	10.4670	+	6.04313i	0.525324	+	0.303296i	0.739110	−	0.673584i	$-0.235246\pi$
$397$	10.4670	+	6.04313i	0.525324	+	0.303296i	−0.213786	+	0.976881i	$0.568579\pi$
$398$		0			0
$399$	2.33500	+	1.34811i	0.116896	+	0.0674900i
$400$		0			0
$401$	−3.23948	+	12.0899i	−0.161772	+	0.603740i	0.836658	+	0.547725i	$0.184506\pi$
$401$	−3.23948	+	12.0899i	−0.161772	+	0.603740i	−0.998430	+	0.0560149i	$0.982161\pi$
$402$		0			0
$403$	0.896666	+	0.388707i	0.0446661	+	0.0193629i
$404$		0			0
$405$	13.7988	−	5.07561i	0.685666	−	0.252209i
$406$		0			0
$407$	3.96514	+	14.7981i	0.196545	+	0.733515i
$408$		0			0
$409$	12.0227	−	3.22147i	0.594484	−	0.159292i	0.0509825	−	0.998700i	$-0.483765\pi$
$409$	12.0227	−	3.22147i	0.594484	−	0.159292i	0.543502	+	0.839408i	$0.317098\pi$
$410$		0			0
$411$	30.9245	+	30.9245i	1.52539	+	1.52539i
$412$		0			0
$413$	−2.64039	+	9.85406i	−0.129925	+	0.484887i
$414$		0			0
$415$	−13.7841	−	2.38216i	−0.676637	−	0.116936i
$416$		0			0
$417$	−5.67805	−	5.67805i	−0.278055	−	0.278055i
$418$		0			0
$419$	−6.12710	+	3.53748i	−0.299328	+	0.172817i	−0.642141	−	0.766586i	$-0.721954\pi$
$419$	−6.12710	+	3.53748i	−0.299328	+	0.172817i	0.342813	+	0.939404i	$0.388620\pi$
$420$		0			0
$421$	−12.6378	+	12.6378i	−0.615930	+	0.615930i	−0.944485	−	0.328555i	$-0.893438\pi$
$421$	−12.6378	+	12.6378i	−0.615930	+	0.615930i	0.328555	+	0.944485i	$0.393438\pi$
$422$		0			0
$423$	−2.78557	+	4.82474i	−0.135439	+	0.234587i
$424$		0			0
$425$	−2.07859	+	25.7786i	−0.100826	+	1.25045i
$426$		0			0
$427$	4.40815	−	2.54504i	0.213325	−	0.123163i
$428$		0			0
$429$	14.8541	+	2.20322i	0.717162	+	0.106372i
$430$		0			0
$431$	1.66350	+	0.445735i	0.0801282	+	0.0214703i	0.298660	−	0.954359i	$-0.403460\pi$
$431$	1.66350	+	0.445735i	0.0801282	+	0.0214703i	−0.218532	+	0.975830i	$0.570127\pi$
$432$		0			0
$433$	15.5451	−	4.16531i	0.747052	−	0.200172i	0.134842	−	0.990867i	$-0.456947\pi$
$433$	15.5451	−	4.16531i	0.747052	−	0.200172i	0.612210	+	0.790695i	$0.290281\pi$
$434$		0			0
$435$	3.58525	+	39.4330i	0.171900	+	1.89067i
$436$		0			0
$437$			3.28541i			0.157163i
$438$		0			0
$439$	−7.54892	−	13.0751i	−0.360290	−	0.624041i	0.627718	−	0.778441i	$-0.283989\pi$
$439$	−7.54892	−	13.0751i	−0.360290	−	0.624041i	−0.988008	+	0.154400i	$0.950656\pi$
$440$		0			0
$441$		−	22.8934i		−	1.09016i
$442$		0			0
$443$	−13.3798	+	13.3798i	−0.635694	+	0.635694i	−0.949490	−	0.313797i	$-0.898399\pi$
$443$	−13.3798	+	13.3798i	−0.635694	+	0.635694i	0.313797	+	0.949490i	$0.398399\pi$
$444$		0			0
$445$	9.52550	−	20.6104i	0.451552	−	0.977026i
$446$		0			0
$447$	42.6379			2.01670
$448$		0			0
$449$	−4.77864	−	17.8341i	−0.225518	−	0.841645i	−0.982196	−	0.187858i	$-0.939846\pi$
$449$	−4.77864	−	17.8341i	−0.225518	−	0.841645i	0.756678	−	0.653788i	$-0.226821\pi$
$450$		0			0
$451$	0.348550	−	0.603706i	0.0164126	−	0.0284274i
$452$		0			0
$453$	22.4612	+	38.9040i	1.05532	+	1.82787i
$454$		0			0
$455$	6.62502	+	2.18355i	0.310585	+	0.102366i
$456$		0			0
$457$	−7.52390	−	13.0318i	−0.351953	−	0.609601i	0.634638	−	0.772809i	$-0.281149\pi$
$457$	−7.52390	−	13.0318i	−0.351953	−	0.609601i	−0.986592	+	0.163208i	$0.947816\pi$
$458$		0			0
$459$	4.41990	−	7.65549i	0.206303	−	0.357328i
$460$		0			0
$461$	3.12241	+	11.6530i	0.145425	+	0.542734i	0.999736	+	0.0229718i	$0.00731278\pi$
$461$	3.12241	+	11.6530i	0.145425	+	0.542734i	−0.854311	+	0.519762i	$0.826021\pi$
$462$		0			0
$463$	−32.5516			−1.51280			−0.756400	−	0.654109i	$-0.773044\pi$
$463$	−32.5516			−1.51280			−0.756400	+	0.654109i	$0.773044\pi$
$464$		0			0
$465$	0.540054	+	1.46821i	0.0250444	+	0.0680868i
$466$		0			0
$467$	−19.4091	+	19.4091i	−0.898145	+	0.898145i	−0.995272	−	0.0971268i	$-0.969035\pi$
$467$	−19.4091	+	19.4091i	−0.898145	+	0.898145i	0.0971268	+	0.995272i	$0.469035\pi$
$468$		0			0
$469$		−	11.7006i		−	0.540283i
$470$		0			0
$471$	−10.6489	−	18.4444i	−0.490675	−	0.849874i
$472$		0			0
$473$		−	19.2943i		−	0.887153i
$474$		0			0
$475$	6.01712	+	0.485173i	0.276084	+	0.0222613i
$476$		0			0
$477$	−24.4324	+	6.54664i	−1.11868	+	0.299750i
$478$		0			0
$479$	5.16289	+	1.38339i	0.235899	+	0.0632088i	0.374831	−	0.927093i	$-0.377701\pi$
$479$	5.16289	+	1.38339i	0.235899	+	0.0632088i	−0.138933	+	0.990302i	$0.544367\pi$
$480$		0			0
$481$	−26.8142	−	21.2808i	−1.22262	−	0.970321i
$482$		0			0
$483$	−5.26290	+	3.03853i	−0.239470	+	0.138258i
$484$		0			0
$485$	−2.50317	−	2.08593i	−0.113663	−	0.0947171i
$486$		0			0
$487$	5.93242	−	10.2752i	0.268823	−	0.465616i	−0.699735	−	0.714403i	$-0.746699\pi$
$487$	5.93242	−	10.2752i	0.268823	−	0.465616i	0.968558	+	0.248787i	$0.0800319\pi$
$488$		0			0
$489$	−9.64173	+	9.64173i	−0.436014	+	0.436014i
$490$		0			0
$491$	16.9915	−	9.81007i	0.766817	−	0.442722i	−0.0649209	−	0.997890i	$-0.520680\pi$
$491$	16.9915	−	9.81007i	0.766817	−	0.442722i	0.831738	+	0.555168i	$0.187346\pi$
$492$		0			0
$493$	−25.0922	−	25.0922i	−1.13010	−	1.13010i
$494$		0			0
$495$	7.61564	+	10.7978i	0.342297	+	0.485326i
$496$		0			0
$497$	−3.33195	+	12.4350i	−0.149459	+	0.557787i
$498$		0			0
$499$	25.2879	+	25.2879i	1.13204	+	1.13204i	0.989837	+	0.142203i	$0.0454187\pi$
$499$	25.2879	+	25.2879i	1.13204	+	1.13204i	0.142203	+	0.989837i	$0.454581\pi$
$500$		0			0
$501$	−19.6153	+	5.25591i	−0.876347	+	0.234817i
$502$		0			0
$503$	−3.69726	−	13.7984i	−0.164853	−	0.615239i	−0.998059	−	0.0622762i	$-0.980164\pi$
$503$	−3.69726	−	13.7984i	−0.164853	−	0.615239i	0.833206	−	0.552962i	$-0.186503\pi$
$504$		0			0
$505$	−8.96060	−	24.3607i	−0.398741	−	1.08404i
$506$		0			0
$507$	−29.5920	+	15.8181i	−1.31423	+	0.702508i
$508$		0			0
$509$	9.01986	−	33.6626i	0.399798	−	1.49207i	−0.413653	−	0.910435i	$-0.635747\pi$
$509$	9.01986	−	33.6626i	0.399798	−	1.49207i	0.813451	−	0.581633i	$-0.197586\pi$
$510$		0			0
$511$	8.23637	+	4.75527i	0.364356	+	0.210361i
$512$		0			0
$513$	−1.78690	−	1.03167i	−0.0788938	−	0.0455493i
$514$		0			0
$515$	−28.0798	+	19.8045i	−1.23734	+	0.872691i
$516$		0			0
$517$	2.37109	+	0.635331i	0.104280	+	0.0279418i
$518$		0			0
$519$	−51.4717			−2.25936
$520$		0			0
$521$	20.2982			0.889281			0.444641	−	0.895709i	$-0.353331\pi$
$521$	20.2982			0.889281			0.444641	+	0.895709i	$0.353331\pi$
$522$		0			0
$523$	18.2457	+	4.88891i	0.797827	+	0.213777i	0.634630	−	0.772816i	$-0.281153\pi$
$523$	18.2457	+	4.88891i	0.797827	+	0.213777i	0.163197	+	0.986593i	$0.447819\pi$
$524$		0			0
$525$	4.78777	+	10.0875i	0.208955	+	0.440256i
$526$		0			0
$527$	−1.21417	−	0.701004i	−0.0528903	−	0.0305362i
$528$		0			0
$529$	13.5056	+	7.79747i	0.587201	+	0.339020i
$530$		0			0
$531$	11.1758	−	41.7085i	0.484987	−	1.80999i
$532$		0			0
$533$	0.178038	+	1.54745i	0.00771170	+	0.0670277i
$534$		0			0
$535$	−14.4772	−	6.69094i	−0.625906	−	0.289275i
$536$		0			0
$537$	−2.04605	−	7.63598i	−0.0882938	−	0.329517i
$538$		0			0
$539$	−9.74349	+	2.61076i	−0.419682	+	0.112453i
$540$		0			0
$541$	−20.5158	−	20.5158i	−0.882042	−	0.882042i	0.111700	−	0.993742i	$-0.464371\pi$
$541$	−20.5158	−	20.5158i	−0.882042	−	0.882042i	−0.993742	+	0.111700i	$0.964371\pi$
$542$		0			0
$543$	15.6092	−	58.2544i	0.669856	−	2.49993i
$544$		0			0
$545$	−11.8047	+	8.32580i	−0.505660	+	0.356638i
$546$		0			0
$547$	−28.8176	−	28.8176i	−1.23215	−	1.23215i	−0.963135	−	0.269018i	$-0.913301\pi$
$547$	−28.8176	−	28.8176i	−1.23215	−	1.23215i	−0.269018	−	0.963135i	$-0.586699\pi$
$548$		0			0
$549$	−18.6580	+	10.7722i	−0.796304	+	0.459747i
$550$		0			0
$551$	−5.85689	+	5.85689i	−0.249512	+	0.249512i
$552$		0			0
$553$	1.72250	−	2.98347i	0.0732484	−	0.126870i
$554$		0			0
$555$	−4.96172	−	54.5724i	−0.210613	−	2.31647i
$556$		0			0
$557$	6.50881	−	3.75786i	0.275787	−	0.159226i	−0.355727	−	0.934590i	$-0.615767\pi$
$557$	6.50881	−	3.75786i	0.275787	−	0.159226i	0.631515	+	0.775364i	$0.282434\pi$
$558$		0			0
$559$	25.6828	+	34.6284i	1.08627	+	1.46462i
$560$		0			0
$561$	−20.8085	−	5.57562i	−0.878535	−	0.235403i
$562$		0			0
$563$	23.0668	−	6.18074i	0.972151	−	0.260487i	0.262415	−	0.964955i	$-0.415481\pi$
$563$	23.0668	−	6.18074i	0.972151	−	0.260487i	0.709736	+	0.704468i	$0.248814\pi$
$564$		0			0
$565$	−19.2430	+	1.74957i	−0.809560	+	0.0736051i
$566$		0			0
$567$			5.68898i			0.238915i
$568$		0			0
$569$	1.39258	+	2.41202i	0.0583801	+	0.101117i	0.893738	−	0.448589i	$-0.148073\pi$
$569$	1.39258	+	2.41202i	0.0583801	+	0.101117i	−0.835358	+	0.549706i	$0.814740\pi$
$570$		0			0
$571$		−	28.8794i		−	1.20857i	−0.796769	−	0.604284i	$-0.793459\pi$
$571$		−	28.8794i		−	1.20857i	0.796769	−	0.604284i	$-0.206541\pi$
$572$		0			0
$573$	13.6425	−	13.6425i	0.569924	−	0.569924i
$574$		0			0
$575$	−7.72809	+	11.1984i	−0.322283	+	0.467004i
$576$		0			0
$577$	4.20458			0.175039			0.0875196	−	0.996163i	$-0.472106\pi$
$577$	4.20458			0.175039			0.0875196	+	0.996163i	$0.472106\pi$
$578$		0			0
$579$	−1.33742	−	4.99131i	−0.0555811	−	0.207432i
$580$		0			0
$581$	2.70632	−	4.68748i	0.112277	−	0.194469i
$582$		0			0
$583$	5.57253	+	9.65190i	0.230790	+	0.399741i
$584$		0			0
$585$	−28.0412	−	9.24214i	−1.15936	−	0.382115i
$586$		0			0
$587$	2.71072	+	4.69510i	0.111883	+	0.193787i	0.916530	−	0.399967i	$-0.130978\pi$
$587$	2.71072	+	4.69510i	0.111883	+	0.193787i	−0.804646	+	0.593754i	$0.797645\pi$
$588$		0			0
$589$	−0.163625	+	0.283406i	−0.00674204	+	0.0116776i
$590$		0			0
$591$	2.12493	+	7.93036i	0.0874081	+	0.326211i
$592$		0			0
$593$	−15.8446			−0.650660			−0.325330	−	0.945601i	$-0.605475\pi$
$593$	−15.8446			−0.650660			−0.325330	+	0.945601i	$0.605475\pi$
$594$		0			0
$595$	−9.08381	−	4.19826i	−0.372400	−	0.172112i
$596$		0			0
$597$	−29.9402	+	29.9402i	−1.22537	+	1.22537i
$598$		0			0
$599$		−	34.8884i		−	1.42550i	−0.701418	−	0.712750i	$-0.747450\pi$
$599$		−	34.8884i		−	1.42550i	0.701418	−	0.712750i	$-0.252550\pi$
$600$		0			0
$601$	11.6867	+	20.2419i	0.476710	+	0.825686i	0.999644	−	0.0266875i	$-0.00849591\pi$
$601$	11.6867	+	20.2419i	0.476710	+	0.825686i	−0.522934	+	0.852373i	$0.675163\pi$
$602$		0			0
$603$			49.5242i			2.01678i
$604$		0			0
$605$	−12.0192	+	14.4233i	−0.488648	+	0.586391i
$606$		0			0
$607$	−31.2836	+	8.38242i	−1.26976	+	0.340232i	−0.829940	−	0.557853i	$-0.811625\pi$
$607$	−31.2836	+	8.38242i	−1.26976	+	0.340232i	−0.439823	+	0.898085i	$0.644959\pi$
$608$		0			0
$609$	−14.7989	−	3.96536i	−0.599683	−	0.160685i
$610$		0			0
$611$	−5.10118	+	2.01591i	−0.206372	+	0.0815549i
$612$		0			0
$613$	33.8649	−	19.5519i	1.36779	−	0.789695i	0.377146	−	0.926154i	$-0.376905\pi$
$613$	33.8649	−	19.5519i	1.36779	−	0.789695i	0.990646	+	0.136458i	$0.0435720\pi$
$614$		0			0
$615$	−1.59622	+	1.91550i	−0.0643658	+	0.0772406i
$616$		0			0
$617$	7.14533	−	12.3761i	0.287660	−	0.498242i	−0.685591	−	0.727987i	$-0.740456\pi$
$617$	7.14533	−	12.3761i	0.287660	−	0.498242i	0.973251	+	0.229745i	$0.0737893\pi$
$618$		0			0
$619$	−6.85038	+	6.85038i	−0.275340	+	0.275340i	−0.831245	−	0.555906i	$-0.812372\pi$
$619$	−6.85038	+	6.85038i	−0.275340	+	0.275340i	0.555906	+	0.831245i	$0.312372\pi$
$620$		0			0
$621$	4.02754	−	2.32530i	0.161620	−	0.0933111i
$622$		0			0
$623$	6.21223	+	6.21223i	0.248888	+	0.248888i
$624$		0			0
$625$	19.3681	+	15.8074i	0.774726	+	0.632297i
$626$		0			0
$627$	−1.30143	+	4.85701i	−0.0519742	+	0.193970i
$628$		0			0
$629$	34.7257	+	34.7257i	1.38461	+	1.38461i
$630$		0			0
$631$	37.2254	−	9.97452i	1.48192	−	0.397080i	0.574921	−	0.818209i	$-0.305033\pi$
$631$	37.2254	−	9.97452i	1.48192	−	0.397080i	0.907000	+	0.421130i	$0.138366\pi$
$632$		0			0
$633$	7.56506	+	28.2332i	0.300684	+	1.12217i
$634$		0			0
$635$	4.41401	−	9.55063i	0.175165	−	0.379005i
$636$		0			0
$637$	14.0119	−	17.6553i	0.555171	−	0.699527i
$638$		0			0
$639$	14.1029	−	52.6327i	0.557902	−	2.08212i
$640$		0			0
$641$	6.48111	+	3.74187i	0.255988	+	0.147795i	0.622503	−	0.782617i	$-0.286116\pi$
$641$	6.48111	+	3.74187i	0.255988	+	0.147795i	−0.366515	+	0.930412i	$0.619449\pi$
$642$		0			0
$643$	−20.7800	−	11.9973i	−0.819482	−	0.473128i	0.0307558	−	0.999527i	$-0.490209\pi$
$643$	−20.7800	−	11.9973i	−0.819482	−	0.473128i	−0.850238	+	0.526399i	$0.823542\pi$
$644$		0			0
$645$	−11.7525	+	68.0044i	−0.462752	+	2.67767i
$646$		0			0
$647$	22.5414	+	6.03995i	0.886195	+	0.237455i	0.673078	−	0.739572i	$-0.264972\pi$
$647$	22.5414	+	6.03995i	0.886195	+	0.237455i	0.213117	+	0.977027i	$0.431639\pi$
$648$		0			0
$649$	−19.0257			−0.746825
$650$		0			0
$651$	−0.605318			−0.0237243
$652$		0			0
$653$	20.3843	+	5.46196i	0.797700	+	0.213743i	0.634574	−	0.772862i	$-0.281176\pi$
$653$	20.3843	+	5.46196i	0.797700	+	0.213743i	0.163126	+	0.986605i	$0.447842\pi$
$654$		0			0
$655$	−5.83581	+	33.7683i	−0.228024	+	1.31944i
$656$		0			0
$657$	−34.8614	−	20.1273i	−1.36007	−	0.785239i
$658$		0			0
$659$	13.0042	+	7.50797i	0.506571	+	0.292469i	0.731423	−	0.681924i	$-0.238856\pi$
$659$	13.0042	+	7.50797i	0.506571	+	0.292469i	−0.224852	+	0.974393i	$0.572190\pi$
$660$		0			0
$661$	1.43378	−	5.35096i	0.0557677	−	0.208128i	−0.932420	−	0.361377i	$-0.882307\pi$
$661$	1.43378	−	5.35096i	0.0557677	−	0.208128i	0.988188	+	0.153249i	$0.0489735\pi$
$662$		0			0
$663$	44.7676	−	17.6915i	1.73863	−	0.687080i
$664$		0			0
$665$	−0.979937	+	2.12030i	−0.0380003	+	0.0822216i
$666$		0			0
$667$	−4.83189	−	18.0329i	−0.187092	−	0.698235i
$668$		0			0
$669$	25.1715	−	6.74467i	0.973185	−	0.260764i
$670$		0			0
$671$	6.71243	+	6.71243i	0.259130	+	0.259130i
$672$		0			0
$673$	8.14271	−	30.3890i	0.313878	−	1.17141i	−0.611151	−	0.791514i	$-0.709293\pi$
$673$	8.14271	−	30.3890i	0.313878	−	1.17141i	0.925029	−	0.379896i	$-0.124040\pi$
$674$		0			0
$675$	−3.66394	−	7.71969i	−0.141025	−	0.297131i
$676$		0			0
$677$	19.4080	+	19.4080i	0.745910	+	0.745910i	0.973708	−	0.227798i	$-0.0731527\pi$
$677$	19.4080	+	19.4080i	0.745910	+	0.745910i	−0.227798	+	0.973708i	$0.573153\pi$
$678$		0			0
$679$	1.09187	−	0.630389i	0.0419019	−	0.0241921i
$680$		0			0
$681$	25.0756	−	25.0756i	0.960899	−	0.960899i
$682$		0			0
$683$	−12.1706	+	21.0802i	−0.465697	+	0.806610i	−0.999233	−	0.0391672i	$-0.987530\pi$
$683$	−12.1706	+	21.0802i	−0.465697	+	0.806610i	0.533536	+	0.845777i	$0.320863\pi$
$684$		0			0
$685$	−24.2547	+	29.1063i	−0.926724	+	1.11209i
$686$		0			0
$687$	−10.6451	+	6.14597i	−0.406137	+	0.234483i
$688$		0			0
$689$	−22.8490	−	9.90507i	−0.870476	−	0.377353i
$690$		0			0
$691$	−11.5308	−	3.08967i	−0.438652	−	0.117537i	0.0327325	−	0.999464i	$-0.489579\pi$
$691$	−11.5308	−	3.08967i	−0.438652	−	0.117537i	−0.471385	+	0.881928i	$0.656246\pi$
$692$		0			0
$693$	−4.93848	+	1.32326i	−0.187597	+	0.0502666i
$694$		0			0
$695$	4.45341	−	5.34420i	0.168927	−	0.202717i
$696$		0			0
$697$		−	2.23460i		−	0.0846413i
$698$		0			0
$699$	34.9585	+	60.5498i	1.32225	+	2.29020i
$700$		0			0
$701$			21.2613i			0.803029i	0.915853	+	0.401515i	$0.131516\pi$
$701$			21.2613i			0.803029i	−0.915853	+	0.401515i	$0.868484\pi$
$702$		0			0
$703$	8.10550	−	8.10550i	0.305705	−	0.305705i
$704$		0			0
$705$	−7.97010	−	3.68354i	−0.300171	−	0.138730i
$706$		0			0
$707$	10.0435			0.377723
$708$		0			0
$709$	−5.58329	−	20.8371i	−0.209685	−	0.782555i	−0.987970	−	0.154644i	$-0.950577\pi$
$709$	−5.58329	−	20.8371i	−0.209685	−	0.782555i	0.778285	−	0.627911i	$-0.216090\pi$
$710$		0			0
$711$	−7.29071	+	12.6279i	−0.273423	+	0.473582i
$712$		0			0
$713$	−0.368797	−	0.638775i	−0.0138116	−	0.0239223i
$714$		0			0
$715$	−0.735666	+	12.9884i	−0.0275123	+	0.485737i
$716$		0			0
$717$	−33.7040	−	58.3770i	−1.25870	−	2.18013i
$718$		0			0
$719$	−4.13804	+	7.16730i	−0.154323	+	0.267295i	−0.932812	−	0.360363i	$-0.882653\pi$
$719$	−4.13804	+	7.16730i	−0.154323	+	0.267295i	0.778489	+	0.627658i	$0.215986\pi$
$720$		0			0
$721$	−3.44115	−	12.8425i	−0.128155	−	0.478282i
$722$		0			0
$723$	2.27344			0.0845500
$724$		0			0
$725$	−33.7401	+	6.18644i	−1.25308	+	0.229758i
$726$		0			0
$727$	−2.41639	+	2.41639i	−0.0896190	+	0.0896190i	−0.750495	−	0.660876i	$-0.770185\pi$
$727$	−2.41639	+	2.41639i	−0.0896190	+	0.0896190i	0.660876	+	0.750495i	$0.270185\pi$
$728$		0			0
$729$		−	37.3127i		−	1.38195i
$730$		0			0
$731$	−30.9246	−	53.5629i	−1.14379	−	1.98110i
$732$		0			0
$733$			32.4183i			1.19740i	0.800974	+	0.598699i	$0.204315\pi$
$733$			32.4183i			1.19740i	−0.800974	+	0.598699i	$0.795685\pi$
$734$		0			0
$735$	35.9320	−	3.26694i	1.32537	−	0.120503i
$736$		0			0
$737$	21.0776	−	5.64773i	0.776404	−	0.208037i
$738$		0			0
$739$	43.7773	+	11.7301i	1.61038	+	0.431499i	0.948154	−	0.317810i	$-0.102947\pi$
$739$	43.7773	+	11.7301i	1.61038	+	0.431499i	0.662221	+	0.749309i	$0.269614\pi$
$740$		0			0
$741$	−4.12945	−	10.4494i	−0.151699	−	0.383870i
$742$		0			0
$743$	13.1203	−	7.57500i	0.481336	−	0.277900i	−0.239637	−	0.970863i	$-0.577028\pi$
$743$	13.1203	−	7.57500i	0.481336	−	0.277900i	0.720973	+	0.692963i	$0.243695\pi$
$744$		0			0
$745$	3.34462	+	36.7864i	0.122537	+	1.34775i
$746$		0			0
$747$	−11.4548	+	19.8403i	−0.419110	+	0.725919i
$748$		0			0
$749$	4.36362	−	4.36362i	0.159443	−	0.159443i
$750$		0			0
$751$	−5.51200	+	3.18236i	−0.201136	+	0.116126i	−0.597185	−	0.802103i	$-0.703714\pi$
$751$	−5.51200	+	3.18236i	−0.201136	+	0.116126i	0.396049	+	0.918229i	$0.370381\pi$
$752$		0			0
$753$	11.8498	+	11.8498i	0.431830	+	0.431830i
$754$		0			0
$755$	−31.8029	+	22.4304i	−1.15743	+	0.816326i
$756$		0			0
$757$	−7.31666	+	27.3061i	−0.265928	+	0.992459i	0.695751	+	0.718283i	$0.255072\pi$
$757$	−7.31666	+	27.3061i	−0.265928	+	0.992459i	−0.961680	+	0.274176i	$0.911595\pi$
$758$		0			0
$759$	−8.01399	−	8.01399i	−0.290889	−	0.290889i
$760$		0			0
$761$	31.4842	−	8.43618i	1.14130	−	0.305811i	0.361828	−	0.932245i	$-0.382153\pi$
$761$	31.4842	−	8.43618i	1.14130	−	0.305811i	0.779475	+	0.626434i	$0.215486\pi$
$762$		0			0
$763$	−1.44666	−	5.39900i	−0.0523725	−	0.195457i
$764$		0			0
$765$	38.4483	+	17.7696i	1.39010	+	0.642463i
$766$		0			0
$767$	34.1463	−	25.3252i	1.23295	−	0.914441i
$768$		0			0
$769$	−10.7440	+	40.0972i	−0.387439	+	1.44594i	0.446848	+	0.894610i	$0.352547\pi$
$769$	−10.7440	+	40.0972i	−0.387439	+	1.44594i	−0.834286	+	0.551331i	$0.814120\pi$
$770$		0			0
$771$	−23.9490	−	13.8270i	−0.862503	−	0.497966i
$772$		0			0
$773$	−1.93793	−	1.11886i	−0.0697025	−	0.0402427i	0.464744	−	0.885445i	$-0.346146\pi$
$773$	−1.93793	−	1.11886i	−0.0697025	−	0.0402427i	−0.534446	+	0.845202i	$0.679480\pi$
$774$		0			0
$775$	−1.22436	+	0.581108i	−0.0439802	+	0.0208740i
$776$		0			0
$777$	20.4806	+	5.48776i	0.734738	+	0.196872i
$778$		0			0
$779$	−0.521588			−0.0186878
$780$		0			0
$781$	−24.0089			−0.859106
$782$		0			0
$783$	11.3252	+	3.03457i	0.404729	+	0.108447i
$784$		0			0
$785$	15.0778	−	10.6343i	0.538150	−	0.379554i
$786$		0			0
$787$	37.4425	+	21.6174i	1.33468	+	0.770577i	0.986013	−	0.166669i	$-0.0533013\pi$
$787$	37.4425	+	21.6174i	1.33468	+	0.770577i	0.348666	+	0.937247i	$0.386635\pi$
$788$		0			0
$789$	−22.6990	−	13.1053i	−0.808105	−	0.466559i
$790$		0			0
$791$	1.93507	−	7.22176i	0.0688030	−	0.256776i
$792$		0			0
$793$	−20.9820	−	3.11215i	−0.745094	−	0.110516i
$794$		0			0
$795$	−13.7617	−	37.4132i	−0.488078	−	1.32691i
$796$		0			0
$797$	5.89049	+	21.9836i	0.208652	+	0.778699i	0.988305	+	0.152488i	$0.0487286\pi$
$797$	5.89049	+	21.9836i	0.208652	+	0.778699i	−0.779653	+	0.626211i	$0.784605\pi$
$798$		0			0
$799$	7.60066	−	2.03659i	0.268892	−	0.0720494i
$800$		0			0
$801$	−26.2940	−	26.2940i	−0.929053	−	0.929053i
$802$		0			0
$803$	−4.59062	+	17.1324i	−0.161999	+	0.604590i
$804$		0			0
$805$	−3.03437	−	4.30228i	−0.106947	−	0.151635i
$806$		0			0
$807$	−34.1289	−	34.1289i	−1.20139	−	1.20139i
$808$		0			0
$809$	25.3301	−	14.6243i	0.890558	−	0.514164i	0.0164333	−	0.999865i	$-0.494769\pi$
$809$	25.3301	−	14.6243i	0.890558	−	0.514164i	0.874125	+	0.485701i	$0.161436\pi$
$810$		0			0
$811$	−16.1564	+	16.1564i	−0.567327	+	0.567327i	−0.931379	−	0.364052i	$-0.881393\pi$
$811$	−16.1564	+	16.1564i	−0.567327	+	0.567327i	0.364052	+	0.931379i	$0.381393\pi$
$812$		0			0
$813$	−23.6593	+	40.9790i	−0.829767	+	1.43720i
$814$		0			0
$815$	−9.07484	−	7.56220i	−0.317878	−	0.264892i
$816$		0			0
$817$	−12.5024	+	7.21825i	−0.437403	+	0.252535i
$818$		0			0
$819$	7.10191	−	8.94856i	0.248161	−	0.312688i
$820$		0			0
$821$	25.6639	+	6.87663i	0.895677	+	0.239996i	0.677159	−	0.735837i	$-0.263211\pi$
$821$	25.6639	+	6.87663i	0.895677	+	0.239996i	0.218518	+	0.975833i	$0.429878\pi$
$822$		0			0
$823$	40.5702	−	10.8708i	1.41419	−	0.378931i	0.530770	−	0.847516i	$-0.321903\pi$
$823$	40.5702	−	10.8708i	1.41419	−	0.378931i	0.883418	+	0.468585i	$0.155236\pi$
$824$		0			0
$825$	−15.8608	+	13.4939i	−0.552202	+	0.469796i
$826$		0			0
$827$			48.4948i			1.68633i	0.537655	+	0.843165i	$0.319310\pi$
$827$			48.4948i			1.68633i	−0.537655	+	0.843165i	$0.680690\pi$
$828$		0			0
$829$	20.4336	+	35.3921i	0.709689	+	1.22922i	0.964973	+	0.262351i	$0.0844978\pi$
$829$	20.4336	+	35.3921i	0.709689	+	1.22922i	−0.255284	+	0.966866i	$0.582169\pi$
$830$		0			0
$831$			34.9998i			1.21413i
$832$		0			0
$833$	−22.8644	+	22.8644i	−0.792205	+	0.792205i
$834$		0			0
$835$	−6.07327	−	16.5111i	−0.210174	−	0.571389i
$836$		0			0
$837$	0.463232			0.0160116
$838$		0			0
$839$	7.70239	+	28.7457i	0.265916	+	0.992412i	0.961687	+	0.274149i	$0.0883960\pi$
$839$	7.70239	+	28.7457i	0.265916	+	0.992412i	−0.695771	+	0.718263i	$0.744937\pi$
$840$		0			0
$841$	9.03332	−	15.6462i	0.311494	−	0.539523i
$842$		0			0
$843$	31.2967	+	54.2075i	1.07792	+	1.86701i
$844$		0			0
$845$	−15.9685	−	24.2900i	−0.549334	−	0.835603i
$846$		0			0
$847$	−3.63231	−	6.29135i	−0.124808	−	0.216173i
$848$		0			0
$849$	11.8183	−	20.4700i	0.405605	−	0.702528i
$850$		0			0
$851$	6.68697	+	24.9561i	0.229227	+	0.855485i
$852$		0			0
$853$	−8.67930			−0.297174			−0.148587	−	0.988899i	$-0.547472\pi$
$853$	−8.67930			−0.297174			−0.148587	+	0.988899i	$0.547472\pi$
$854$		0			0
$855$	4.14770	−	8.97441i	0.141848	−	0.306918i
$856$		0			0
$857$	−2.38807	+	2.38807i	−0.0815751	+	0.0815751i	−0.746717	−	0.665142i	$-0.768371\pi$
$857$	−2.38807	+	2.38807i	−0.0815751	+	0.0815751i	0.665142	+	0.746717i	$0.268371\pi$
$858$		0			0
$859$			0.237935i			0.00811823i	0.999992	+	0.00405912i	$0.00129206\pi$
$859$			0.237935i			0.00811823i	−0.999992	+	0.00405912i	$0.998708\pi$
$860$		0			0
$861$	−0.482394	−	0.835530i	−0.0164399	−	0.0284748i
$862$		0			0
$863$		−	48.8736i		−	1.66368i	−0.555017	−	0.831839i	$-0.687288\pi$
$863$		−	48.8736i		−	1.66368i	0.555017	−	0.831839i	$-0.312712\pi$
$864$		0			0
$865$	−4.03756	−	44.4078i	−0.137281	−	1.50991i
$866$		0			0
$867$	−24.3192	+	6.51630i	−0.825922	+	0.221305i
$868$		0			0
$869$	6.20588	+	1.66286i	0.210520	+	0.0564087i
$870$		0			0
$871$	−30.3112	+	38.1927i	−1.02706	+	1.29411i
$872$		0			0
$873$	−4.62145	+	2.66820i	−0.156412	+	0.0903048i
$874$		0			0
$875$	−8.32757	+	4.92200i	−0.281523	+	0.166394i
$876$		0			0
$877$	17.4333	−	30.1953i	0.588680	−	1.01962i	−0.405725	−	0.913995i	$-0.632981\pi$
$877$	17.4333	−	30.1953i	0.588680	−	1.01962i	0.994406	−	0.105629i	$-0.0336856\pi$
$878$		0			0
$879$	33.1837	−	33.1837i	1.11926	−	1.11926i
$880$		0			0
$881$	−24.6799	+	14.2489i	−0.831486	+	0.480058i	−0.854361	−	0.519680i	$-0.826051\pi$
$881$	−24.6799	+	14.2489i	−0.831486	+	0.480058i	0.0228755	+	0.999738i	$0.492718\pi$
$882$		0			0
$883$	−10.7320	−	10.7320i	−0.361160	−	0.361160i	0.503080	−	0.864240i	$-0.332200\pi$
$883$	−10.7320	−	10.7320i	−0.361160	−	0.361160i	−0.864240	+	0.503080i	$0.832200\pi$
$884$		0			0
$885$	67.0577	+	11.5888i	2.25412	+	0.389555i
$886$		0			0
$887$	−3.36490	+	12.5580i	−0.112982	+	0.421655i	−0.999128	−	0.0417512i	$-0.986706\pi$
$887$	−3.36490	+	12.5580i	−0.112982	+	0.421655i	0.886146	+	0.463406i	$0.153373\pi$
$888$		0			0
$889$	2.87868	+	2.87868i	0.0965478	+	0.0965478i
$890$		0			0
$891$	−10.2482	+	2.74600i	−0.343328	+	0.0919943i
$892$		0			0
$893$	−0.475371	−	1.77411i	−0.0159077	−	0.0593683i
$894$		0			0
$895$	6.42754	−	2.36424i	0.214849	−	0.0790279i
$896$		0			0
$897$	25.0505	+	3.71560i	0.836413	+	0.124060i
$898$		0			0
$899$	0.481289	−	1.79620i	0.0160519	−	0.0599065i
$900$		0			0
$901$	30.9398	+	17.8631i	1.03075	+	0.595105i
$902$		0			0
$903$	−23.1258	−	13.3517i	−0.769578	−	0.444316i
$904$		0			0
$905$	51.4841	+	8.89743i	1.71139	+	0.295761i
$906$		0			0
$907$	49.3926	+	13.2347i	1.64006	+	0.439451i	0.956804	−	0.290732i	$-0.0938990\pi$
$907$	49.3926	+	13.2347i	1.64006	+	0.439451i	0.683251	+	0.730184i	$0.260566\pi$
$908$		0			0
$909$	−42.5102			−1.40997
$910$		0			0
$911$	−45.3842			−1.50365			−0.751823	−	0.659365i	$-0.770825\pi$
$911$	−45.3842			−1.50365			−0.751823	+	0.659365i	$0.770825\pi$
$912$		0			0
$913$	9.75039	+	2.61261i	0.322691	+	0.0864647i
$914$		0			0
$915$	−19.5699	−	27.7472i	−0.646960	−	0.917293i
$916$		0			0
$917$	−11.4834	−	6.62993i	−0.379214	−	0.218940i
$918$		0			0
$919$	−26.3431	−	15.2092i	−0.868977	−	0.501704i	−0.00196918	−	0.999998i	$-0.500627\pi$
$919$	−26.3431	−	15.2092i	−0.868977	−	0.501704i	−0.867008	+	0.498294i	$0.833960\pi$
$920$		0			0
$921$	18.7289	−	69.8973i	0.617139	−	2.30319i
$922$		0			0
$923$	43.0898	−	31.9584i	1.41832	−	1.05192i
$924$		0			0
$925$	46.6938	−	8.56156i	1.53528	−	0.281503i
$926$		0			0
$927$	14.5651	+	54.3576i	0.478380	+	1.78534i
$928$		0			0
$929$	23.9374	−	6.41401i	0.785361	−	0.210437i	0.156214	−	0.987723i	$-0.450071\pi$
$929$	23.9374	−	6.41401i	0.785361	−	0.210437i	0.629147	+	0.777286i	$0.283404\pi$
$930$		0			0
$931$	5.33689	+	5.33689i	0.174910	+	0.174910i
$932$		0			0
$933$	−7.69371	+	28.7133i	−0.251881	+	0.940031i
$934$		0			0
$935$	3.17817	−	18.3901i	0.103937	−	0.601422i
$936$		0			0
$937$	25.3459	+	25.3459i	0.828014	+	0.828014i	0.987242	−	0.159228i	$-0.0509005\pi$
$937$	25.3459	+	25.3459i	0.828014	+	0.828014i	−0.159228	+	0.987242i	$0.550901\pi$
$938$		0			0
$939$	−32.6792	+	18.8674i	−1.06645	+	0.615713i
$940$		0			0
$941$	27.5969	−	27.5969i	0.899632	−	0.899632i	−0.0957715	−	0.995403i	$-0.530532\pi$
$941$	27.5969	−	27.5969i	0.899632	−	0.899632i	0.995403	+	0.0957715i	$0.0305318\pi$
$942$		0			0
$943$	0.587809	−	1.01811i	0.0191417	−	0.0331544i
$944$		0			0
$945$	3.29280	−	0.299382i	0.107115	−	0.00973889i
$946$		0			0
$947$	−45.7982	+	26.4416i	−1.48824	+	0.859237i	−0.999910	−	0.0134210i	$-0.995728\pi$
$947$	−45.7982	+	26.4416i	−1.48824	+	0.859237i	−0.488332	+	0.872658i	$0.662394\pi$
$948$		0			0
$949$	−14.5661	−	36.8589i	−0.472835	−	1.19649i
$950$		0			0
$951$	5.76184	+	1.54388i	0.186840	+	0.0500637i
$952$		0			0
$953$	−45.8852	+	12.2949i	−1.48637	+	0.398271i	−0.908509	−	0.417865i	$-0.862779\pi$
$953$	−45.8852	+	12.2949i	−1.48637	+	0.398271i	−0.577860	+	0.816136i	$0.696112\pi$
$954$		0			0
$955$	12.8404	+	10.7001i	0.415505	+	0.346247i
$956$		0			0
$957$		−	28.5730i		−	0.923634i
$958$		0			0
$959$	−7.33001	−	12.6960i	−0.236699	−	0.409974i
$960$		0			0
$961$			30.9265i			0.997630i
$962$		0			0
$963$	−18.4696	+	18.4696i	−0.595173	+	0.595173i
$964$		0			0
$965$	4.20140	−	1.54540i	0.135248	−	0.0497482i
$966$		0			0
$967$	−39.7754			−1.27909			−0.639546	−	0.768753i	$-0.720878\pi$
$967$	−39.7754			−1.27909			−0.639546	+	0.768753i	$0.720878\pi$
$968$		0			0
$969$	4.17182	+	15.5694i	0.134018	+	0.500163i
$970$		0			0
$971$	−0.597739	+	1.03531i	−0.0191824	+	0.0332248i	−0.875457	−	0.483296i	$-0.839440\pi$
$971$	−0.597739	+	1.03531i	−0.0191824	+	0.0332248i	0.856275	+	0.516520i	$0.172773\pi$
$972$		0			0
$973$	1.34586	+	2.33111i	0.0431464	+	0.0747318i
$974$		0			0
$975$	10.5043	−	45.3304i	0.336407	−	1.45174i
$976$		0			0
$977$	−8.23433	−	14.2623i	−0.263439	−	0.456291i	0.703714	−	0.710483i	$-0.251524\pi$
$977$	−8.23433	−	14.2623i	−0.263439	−	0.456291i	−0.967154	+	0.254193i	$0.918190\pi$
$978$		0			0
$979$	−8.19223	+	14.1894i	−0.261825	+	0.453494i
$980$		0			0
$981$	6.12315	+	22.8519i	0.195497	+	0.729605i
$982$		0			0
$983$	−1.80446			−0.0575534			−0.0287767	−	0.999586i	$-0.509161\pi$
$983$	−1.80446			−0.0575534			−0.0287767	+	0.999586i	$0.509161\pi$
$984$		0			0
$985$	−6.67533	+	2.45539i	−0.212694	+	0.0782351i
$986$		0			0
$987$	2.40229	−	2.40229i	0.0764657	−	0.0764657i
$988$		0			0
$989$		−	32.5387i		−	1.03467i
$990$		0			0
$991$	0.661562	+	1.14586i	0.0210152	+	0.0363994i	0.876342	−	0.481690i	$-0.159977\pi$
$991$	0.661562	+	1.14586i	0.0210152	+	0.0363994i	−0.855327	+	0.518089i	$0.826643\pi$
$992$		0			0
$993$		−	90.7637i		−	2.88030i
$994$		0			0
$995$	−28.1798	−	23.4827i	−0.893360	−	0.744451i
$996$		0			0
$997$	45.5416	−	12.2028i	1.44232	−	0.386467i	0.548972	−	0.835841i	$-0.315019\pi$
$997$	45.5416	−	12.2028i	1.44232	−	0.386467i	0.893344	+	0.449373i	$0.148353\pi$
$998$		0			0
$999$	−15.6732	−	4.19962i	−0.495878	−	0.132870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.c.197.5	yes	20
5.2	odd	4		1300.2.bn.d.93.5		20
5.3	odd	4		260.2.bf.c.93.1	✓	20
5.4	even	2		1300.2.bs.d.457.1		20
13.7	odd	12		260.2.bf.c.137.1	yes	20
65.7	even	12		1300.2.bs.d.293.1		20
65.33	even	12	inner	260.2.bk.c.33.5	yes	20
65.59	odd	12		1300.2.bn.d.657.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.1	✓	20	5.3	odd	4
260.2.bf.c.137.1	yes	20	13.7	odd	12
260.2.bk.c.33.5	yes	20	65.33	even	12	inner
260.2.bk.c.197.5	yes	20	1.1	even	1	trivial
1300.2.bn.d.93.5		20	5.2	odd	4
1300.2.bn.d.657.5		20	65.59	odd	12
1300.2.bs.d.293.1		20	65.7	even	12
1300.2.bs.d.457.1		20	5.4	even	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.49316 + 0.668040i) q^{3} +(-0.380790 + 2.20341i) q^{5} +(-0.749297 - 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +O(q^{10})\)	\(q+(2.49316 + 0.668040i) q^{3} +(-0.380790 + 2.20341i) q^{5} +(-0.749297 - 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +(0.417628 - 1.55861i) q^{11} +(1.32514 + 3.35321i) q^{13} +(-2.42134 + 5.23906i) q^{15} +(-1.33873 - 4.99621i) q^{17} +(-1.16619 + 0.312480i) q^{19} +(-1.57912 - 1.57912i) q^{21} +(0.704305 - 2.62850i) q^{23} +(-4.71000 - 1.67807i) q^{25} +(1.20845 + 1.20845i) q^{27} +(5.94138 - 3.43026i) q^{29} +(0.191663 - 0.191663i) q^{31} +(2.08243 - 3.60687i) q^{33} +(1.23853 - 1.48627i) q^{35} +(-8.22242 + 4.74722i) q^{37} +(1.06370 + 9.24533i) q^{39} +(0.417297 + 0.111814i) q^{41} +(11.5499 - 3.09480i) q^{43} +(-5.24225 + 6.29083i) q^{45} +1.52128i q^{47} +(-3.12570 - 5.41387i) q^{49} -13.3507i q^{51} +(-4.88398 + 4.88398i) q^{53} +(3.27522 + 1.51371i) q^{55} -3.11625 q^{57} +(-3.05172 - 11.3892i) q^{59} +(-2.94152 + 5.09486i) q^{61} +(-1.58426 - 2.74402i) q^{63} +(-7.89308 + 1.64294i) q^{65} +(6.76168 + 11.7116i) q^{67} +(3.51189 - 6.08277i) q^{69} +(-3.85102 - 14.3722i) q^{71} -10.9921 q^{73} +(-10.6218 - 7.33017i) q^{75} +(-0.987192 + 0.987192i) q^{77} +3.98168i q^{79} +(-3.28761 - 5.69431i) q^{81} +6.25583i q^{83} +(11.5185 - 1.04726i) q^{85} +(17.1044 - 4.58310i) q^{87} +(-9.80805 - 2.62806i) q^{89} +(0.457701 - 3.08581i) q^{91} +(0.605885 - 0.349808i) q^{93} +(-0.244446 - 2.68858i) q^{95} +(-0.728593 + 1.26196i) q^{97} +(4.17841 - 4.17841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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