LMFDB - Embedded newform 460.2.m.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	460.101
Dual form			460.2.m.b.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10811 + 1.27883i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.08165 + 2.36848i) q^{7} +(0.0194536 - 0.135303i) q^{9} +O(q^{10})$	\(q+(1.10811 + 1.27883i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.08165 + 2.36848i) q^{7} +(0.0194536 - 0.135303i) q^{9} +(2.24629 + 0.659569i) q^{11} +(-0.0828187 - 0.181348i) q^{13} +(-1.10811 + 1.27883i) q^{15} +(4.73736 + 3.04452i) q^{17} +(-6.46583 + 4.15533i) q^{19} +(-4.22747 + 1.24130i) q^{21} +(-3.17241 + 3.59664i) q^{23} +(-0.959493 + 0.281733i) q^{25} +(4.46512 - 2.86956i) q^{27} +(-2.94239 - 1.89096i) q^{29} +(5.81264 - 6.70814i) q^{31} +(1.64566 + 3.60349i) q^{33} +(-2.49831 - 0.733570i) q^{35} +(0.334267 - 2.32488i) q^{37} +(0.140140 - 0.306864i) q^{39} +(-0.441676 - 3.07192i) q^{41} +(4.84355 + 5.58976i) q^{43} +0.136694 q^{45} -7.38769 q^{47} +(0.144279 + 0.166507i) q^{49} +(1.35611 + 9.43193i) q^{51} +(2.03449 - 4.45492i) q^{53} +(-0.333176 + 2.31729i) q^{55} +(-12.4788 - 3.66411i) q^{57} +(0.971960 + 2.12830i) q^{59} +(8.18748 - 9.44886i) q^{61} +(0.299420 + 0.192426i) q^{63} +(0.167716 - 0.107784i) q^{65} +(15.5896 - 4.57753i) q^{67} +(-8.11486 - 0.0714895i) q^{69} +(-4.37919 + 1.28585i) q^{71} +(0.560221 - 0.360032i) q^{73} +(-1.42351 - 0.914835i) q^{75} +(-3.99187 + 4.60687i) q^{77} +(2.95253 + 6.46514i) q^{79} +(8.22404 + 2.41480i) q^{81} +(1.68937 - 11.7498i) q^{83} +(-2.33933 + 5.12243i) q^{85} +(-0.842281 - 5.85819i) q^{87} +(-6.64231 - 7.66564i) q^{89} +0.519100 q^{91} +15.0196 q^{93} +(-5.03322 - 5.80865i) q^{95} +(-0.0541899 - 0.376899i) q^{97} +(0.132940 - 0.291097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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
$3$	1.10811	+	1.27883i	0.639768	+	0.738331i	0.979334	−	0.202251i	$-0.0648257\pi$
$3$	1.10811	+	1.27883i	0.639768	+	0.738331i	−0.339566	+	0.940582i	$0.610280\pi$
$4$		0			0
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$		0			0
$7$	−1.08165	+	2.36848i	−0.408825	+	0.895202i	0.587473	+	0.809243i	$0.300123\pi$
$7$	−1.08165	+	2.36848i	−0.408825	+	0.895202i	−0.996299	+	0.0859590i	$0.972605\pi$
$8$		0			0
$9$	0.0194536	−	0.135303i	0.00648452	−	0.0451009i
$10$		0			0
$11$	2.24629	+	0.659569i	0.677281	+	0.198868i	0.602243	−	0.798313i	$-0.294274\pi$
$11$	2.24629	+	0.659569i	0.677281	+	0.198868i	0.0750382	+	0.997181i	$0.476092\pi$
$12$		0			0
$13$	−0.0828187	−	0.181348i	−0.0229698	−	0.0502968i	0.897799	−	0.440405i	$-0.145165\pi$
$13$	−0.0828187	−	0.181348i	−0.0229698	−	0.0502968i	−0.920769	+	0.390108i	$0.872438\pi$
$14$		0			0
$15$	−1.10811	+	1.27883i	−0.286113	+	0.330192i
$16$		0			0
$17$	4.73736	+	3.04452i	1.14898	+	0.738404i	0.969436	−	0.245345i	$-0.0789014\pi$
$17$	4.73736	+	3.04452i	1.14898	+	0.738404i	0.179544	+	0.983750i	$0.442538\pi$
$18$		0			0
$19$	−6.46583	+	4.15533i	−1.48336	+	0.953299i	−0.486539	+	0.873659i	$0.661741\pi$
$19$	−6.46583	+	4.15533i	−1.48336	+	0.953299i	−0.996824	+	0.0796402i	$0.974623\pi$
$20$		0			0
$21$	−4.22747	+	1.24130i	−0.922509	+	0.270873i
$22$		0			0
$23$	−3.17241	+	3.59664i	−0.661493	+	0.749951i
$23$	−3.17241	+	3.59664i	−0.661493	+	0.749951i
$24$		0			0
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$		0			0
$27$	4.46512	−	2.86956i	0.859312	−	0.552247i
$28$		0			0
$29$	−2.94239	−	1.89096i	−0.546388	−	0.351142i	0.238145	−	0.971230i	$-0.423461\pi$
$29$	−2.94239	−	1.89096i	−0.546388	−	0.351142i	−0.784533	+	0.620088i	$0.787097\pi$
$30$		0			0
$31$	5.81264	−	6.70814i	1.04398	−	1.20482i	0.0656341	−	0.997844i	$-0.479093\pi$
$31$	5.81264	−	6.70814i	1.04398	−	1.20482i	0.978346	−	0.206974i	$-0.0663616\pi$
$32$		0			0
$33$	1.64566	+	3.60349i	0.286472	+	0.627287i
$34$		0			0
$35$	−2.49831	−	0.733570i	−0.422292	−	0.123996i
$36$		0			0
$37$	0.334267	−	2.32488i	0.0549531	−	0.382208i	−0.943722	−	0.330741i	$-0.892701\pi$
$37$	0.334267	−	2.32488i	0.0549531	−	0.382208i	0.998675	−	0.0514666i	$-0.0163896\pi$
$38$		0			0
$39$	0.140140	−	0.306864i	0.0224404	−	0.0491376i
$40$		0			0
$41$	−0.441676	−	3.07192i	−0.0689782	−	0.479754i	−0.994804	−	0.101804i	$-0.967538\pi$
$41$	−0.441676	−	3.07192i	−0.0689782	−	0.479754i	0.925826	−	0.377949i	$-0.123371\pi$
$42$		0			0
$43$	4.84355	+	5.58976i	0.738635	+	0.852430i	0.993415	−	0.114569i	$-0.0365486\pi$
$43$	4.84355	+	5.58976i	0.738635	+	0.852430i	−0.254780	+	0.966999i	$0.582003\pi$
$44$		0			0
$45$	0.136694			0.0203771
$46$		0			0
$47$	−7.38769			−1.07761			−0.538803	−	0.842432i	$-0.681123\pi$
$47$	−7.38769			−1.07761			−0.538803	+	0.842432i	$0.681123\pi$
$48$		0			0
$49$	0.144279	+	0.166507i	0.0206113	+	0.0237868i
$50$		0			0
$51$	1.35611	+	9.43193i	0.189893	+	1.32073i
$52$		0			0
$53$	2.03449	−	4.45492i	0.279459	−	0.611930i	−0.716901	−	0.697175i	$-0.754440\pi$
$53$	2.03449	−	4.45492i	0.279459	−	0.611930i	0.996360	+	0.0852449i	$0.0271673\pi$
$54$		0			0
$55$	−0.333176	+	2.31729i	−0.0449254	+	0.312463i
$56$		0			0
$57$	−12.4788	−	3.66411i	−1.65286	−	0.485323i
$58$		0			0
$59$	0.971960	+	2.12830i	0.126538	+	0.277081i	0.962289	−	0.272028i	$-0.0876945\pi$
$59$	0.971960	+	2.12830i	0.126538	+	0.277081i	−0.835751	+	0.549109i	$0.814967\pi$
$60$		0			0
$61$	8.18748	−	9.44886i	1.04830	−	1.20980i	0.0711024	−	0.997469i	$-0.477348\pi$
$61$	8.18748	−	9.44886i	1.04830	−	1.20980i	0.977197	−	0.212333i	$-0.0681063\pi$
$62$		0			0
$63$	0.299420	+	0.192426i	0.0377234	+	0.0242433i
$64$		0			0
$65$	0.167716	−	0.107784i	0.0208026	−	0.0133690i
$66$		0			0
$67$	15.5896	−	4.57753i	1.90458	−	0.559235i	0.917830	−	0.396974i	$-0.129940\pi$
$67$	15.5896	−	4.57753i	1.90458	−	0.559235i	0.986748	−	0.162261i	$-0.0518787\pi$
$68$		0			0
$69$	−8.11486	−	0.0714895i	−0.976914	−	0.00860633i
$70$		0			0
$71$	−4.37919	+	1.28585i	−0.519714	+	0.152602i	−0.531061	−	0.847334i	$-0.678206\pi$
$71$	−4.37919	+	1.28585i	−0.519714	+	0.152602i	0.0113465	+	0.999936i	$0.496388\pi$
$72$		0			0
$73$	0.560221	−	0.360032i	0.0655690	−	0.0421386i	−0.507446	−	0.861684i	$-0.669410\pi$
$73$	0.560221	−	0.360032i	0.0655690	−	0.0421386i	0.573015	+	0.819545i	$0.305774\pi$
$74$		0			0
$75$	−1.42351	−	0.914835i	−0.164373	−	0.105636i
$76$		0			0
$77$	−3.99187	+	4.60687i	−0.454916	+	0.525001i
$78$		0			0
$79$	2.95253	+	6.46514i	0.332186	+	0.727385i	0.999854	−	0.0170734i	$-0.00543489\pi$
$79$	2.95253	+	6.46514i	0.332186	+	0.727385i	−0.667668	+	0.744459i	$0.732708\pi$
$80$		0			0
$81$	8.22404	+	2.41480i	0.913782	+	0.268311i
$82$		0			0
$83$	1.68937	−	11.7498i	0.185433	−	1.28971i	−0.658221	−	0.752825i	$-0.728691\pi$
$83$	1.68937	−	11.7498i	0.185433	−	1.28971i	0.843653	−	0.536888i	$-0.180400\pi$
$84$		0			0
$85$	−2.33933	+	5.12243i	−0.253736	+	0.555605i
$86$		0			0
$87$	−0.842281	−	5.85819i	−0.0903020	−	0.628064i
$88$		0			0
$89$	−6.64231	−	7.66564i	−0.704084	−	0.812556i	0.285215	−	0.958464i	$-0.407935\pi$
$89$	−6.64231	−	7.66564i	−0.704084	−	0.812556i	−0.989298	+	0.145908i	$0.953390\pi$
$90$		0			0
$91$	0.519100			0.0544165
$92$		0			0
$93$	15.0196			1.55746
$94$		0			0
$95$	−5.03322	−	5.80865i	−0.516398	−	0.595955i
$96$		0			0
$97$	−0.0541899	−	0.376899i	−0.00550215	−	0.0382683i	0.986885	−	0.161422i	$-0.0516082\pi$
$97$	−0.0541899	−	0.376899i	−0.00550215	−	0.0382683i	−0.992388	+	0.123154i	$0.960699\pi$
$98$		0			0
$99$	0.132940	−	0.291097i	0.0133609	−	0.0292564i
$100$		0			0
$101$	1.32330	−	9.20375i	0.131673	−	0.915807i	−0.811700	−	0.584074i	$-0.801458\pi$
$101$	1.32330	−	9.20375i	0.131673	−	0.915807i	0.943373	−	0.331733i	$-0.107633\pi$
$102$		0			0
$103$	6.81119	+	1.99995i	0.671127	+	0.197061i	0.599505	−	0.800371i	$-0.295364\pi$
$103$	6.81119	+	1.99995i	0.671127	+	0.197061i	0.0716221	+	0.997432i	$0.477182\pi$
$104$		0			0
$105$	−1.83029	−	4.00778i	−0.178618	−	0.391120i
$106$		0			0
$107$	4.50448	−	5.19844i	0.435464	−	0.502552i	−0.495022	−	0.868881i	$-0.664840\pi$
$107$	4.50448	−	5.19844i	0.435464	−	0.502552i	0.930486	+	0.366328i	$0.119385\pi$
$108$		0			0
$109$	−15.7820	−	10.1425i	−1.51164	−	0.971471i	−0.993208	−	0.116352i	$-0.962880\pi$
$109$	−15.7820	−	10.1425i	−1.51164	−	0.971471i	−0.518431	−	0.855120i	$-0.673484\pi$
$110$		0			0
$111$	3.34352	−	2.14875i	0.317353	−	0.203950i
$112$		0			0
$113$	9.69936	−	2.84799i	0.912439	−	0.267916i	0.208372	−	0.978050i	$-0.433184\pi$
$113$	9.69936	−	2.84799i	0.912439	−	0.267916i	0.704067	+	0.710133i	$0.251365\pi$
$114$		0			0
$115$	−4.01151	−	2.62826i	−0.374075	−	0.245087i
$116$		0			0
$117$	−0.0261479	+	0.00767773i	−0.00241738	+	0.000709806i
$118$		0			0
$119$	−12.3351	+	7.92726i	−1.13075	+	0.726691i
$120$		0			0
$121$	−4.64302	−	2.98389i	−0.422092	−	0.271262i
$122$		0			0
$123$	3.43903	−	3.96886i	0.310087	−	0.357860i
$124$		0			0
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$		0			0
$127$	9.01293	+	2.64644i	0.799769	+	0.234833i	0.655983	−	0.754776i	$-0.272254\pi$
$127$	9.01293	+	2.64644i	0.799769	+	0.234833i	0.143786	+	0.989609i	$0.454072\pi$
$128$		0			0
$129$	−1.78114	+	12.3881i	−0.156821	+	1.09071i
$130$		0			0
$131$	−6.67779	+	14.6223i	−0.583441	+	1.27756i	0.355884	+	0.934530i	$0.384180\pi$
$131$	−6.67779	+	14.6223i	−0.583441	+	1.27756i	−0.939325	+	0.343028i	$0.888547\pi$
$132$		0			0
$133$	−2.84808	−	19.8088i	−0.246960	−	1.71764i
$134$		0			0
$135$	3.47580	+	4.01129i	0.299149	+	0.345237i
$136$		0			0
$137$	4.91048			0.419531			0.209765	−	0.977752i	$-0.432730\pi$
$137$	4.91048			0.419531			0.209765	+	0.977752i	$0.432730\pi$
$138$		0			0
$139$	−0.895703			−0.0759725			−0.0379863	−	0.999278i	$-0.512094\pi$
$139$	−0.895703			−0.0759725			−0.0379863	+	0.999278i	$0.512094\pi$
$140$		0			0
$141$	−8.18638	−	9.44758i	−0.689417	−	0.795630i
$142$		0			0
$143$	−0.0664232	−	0.461984i	−0.00555459	−	0.0386330i
$144$		0			0
$145$	1.45296	−	3.18155i	0.120662	−	0.264213i
$146$		0			0
$147$	−0.0530566	+	0.369017i	−0.00437604	+	0.0304360i
$148$		0			0
$149$	−14.7346	−	4.32648i	−1.20711	−	0.354439i	−0.384542	−	0.923108i	$-0.625641\pi$
$149$	−14.7346	−	4.32648i	−1.20711	−	0.354439i	−0.822567	+	0.568668i	$0.807459\pi$
$150$		0			0
$151$	4.04645	+	8.86048i	0.329295	+	0.721056i	0.999782	−	0.0208654i	$-0.00664214\pi$
$151$	4.04645	+	8.86048i	0.329295	+	0.721056i	−0.670487	+	0.741921i	$0.733915\pi$
$152$		0			0
$153$	0.504090	−	0.581751i	0.0407533	−	0.0470318i
$154$		0			0
$155$	7.46709	+	4.79881i	0.599771	+	0.385449i
$156$		0			0
$157$	−13.9041	+	8.93559i	−1.10966	+	0.713138i	−0.961220	−	0.275783i	$-0.911063\pi$
$157$	−13.9041	+	8.93559i	−1.10966	+	0.713138i	−0.148444	+	0.988921i	$0.547427\pi$
$158$		0			0
$159$	7.95151	−	2.33478i	0.630596	−	0.185160i
$160$		0			0
$161$	−5.08715	−	11.4041i	−0.400923	−	0.898769i
$162$		0			0
$163$	0.948713	−	0.278567i	0.0743090	−	0.0218191i	−0.244367	−	0.969683i	$-0.578580\pi$
$163$	0.948713	−	0.278567i	0.0743090	−	0.0218191i	0.318676	+	0.947864i	$0.396762\pi$
$164$		0			0
$165$	−3.33261	+	2.14174i	−0.259443	+	0.166734i
$166$		0			0
$167$	−12.1537	−	7.81069i	−0.940480	−	0.604410i	−0.0219490	−	0.999759i	$-0.506987\pi$
$167$	−12.1537	−	7.81069i	−0.940480	−	0.604410i	−0.918531	+	0.395349i	$0.870624\pi$
$168$		0			0
$169$	8.48716	−	9.79471i	0.652859	−	0.753439i
$170$		0			0
$171$	0.436444	+	0.955679i	0.0333757	+	0.0730826i
$172$		0			0
$173$	−16.2191	−	4.76235i	−1.23311	−	0.362075i	−0.400690	−	0.916214i	$-0.631229\pi$
$173$	−16.2191	−	4.76235i	−1.23311	−	0.362075i	−0.832424	+	0.554139i	$0.813048\pi$
$174$		0			0
$175$	0.370557	−	2.57728i	0.0280115	−	0.194824i
$176$		0			0
$177$	−1.64468	+	3.60135i	−0.123622	+	0.270694i
$178$		0			0
$179$	−2.45633	−	17.0841i	−0.183594	−	1.27693i	−0.848177	−	0.529713i	$-0.822300\pi$
$179$	−2.45633	−	17.0841i	−0.183594	−	1.27693i	0.664583	−	0.747215i	$-0.268609\pi$
$180$		0			0
$181$	7.02669	+	8.10924i	0.522290	+	0.602755i	0.954203	−	0.299161i	$-0.0967066\pi$
$181$	7.02669	+	8.10924i	0.522290	+	0.602755i	−0.431913	+	0.901915i	$0.642161\pi$
$182$		0			0
$183$	21.1561			1.56390
$184$		0			0
$185$	2.34878			0.172686
$186$		0			0
$187$	8.63341	+	9.96348i	0.631337	+	0.728602i
$188$		0			0
$189$	1.96680	+	13.6794i	0.143064	+	0.995031i
$190$		0			0
$191$	−8.26311	+	18.0937i	−0.597898	+	1.30921i	0.332653	+	0.943049i	$0.392056\pi$
$191$	−8.26311	+	18.0937i	−0.597898	+	1.30921i	−0.930550	+	0.366164i	$0.880671\pi$
$192$		0			0
$193$	−1.31286	+	9.13113i	−0.0945016	+	0.657273i	0.886422	+	0.462878i	$0.153183\pi$
$193$	−1.31286	+	9.13113i	−0.0945016	+	0.657273i	−0.980923	+	0.194395i	$0.937726\pi$
$194$		0			0
$195$	0.323685	+	0.0950424i	0.0231795	+	0.00680613i
$196$		0			0
$197$	5.93449	+	12.9947i	0.422815	+	0.925835i	0.994438	+	0.105319i	$0.0335864\pi$
$197$	5.93449	+	12.9947i	0.422815	+	0.925835i	−0.571624	+	0.820516i	$0.693686\pi$
$198$		0			0
$199$	−3.30993	+	3.81986i	−0.234635	+	0.270783i	−0.860840	−	0.508875i	$-0.830062\pi$
$199$	−3.30993	+	3.81986i	−0.234635	+	0.270783i	0.626206	+	0.779658i	$0.284607\pi$
$200$		0			0
$201$	23.1289	+	14.8640i	1.63139	+	1.04843i
$202$		0			0
$203$	7.66133	−	4.92364i	0.537720	−	0.345572i
$204$		0			0
$205$	2.97780	−	0.874361i	0.207979	−	0.0610680i
$206$		0			0
$207$	0.424920	+	0.499203i	0.0295340	+	0.0346970i
$208$		0			0
$209$	−17.2648	+	5.06941i	−1.19423	+	0.350659i
$210$		0			0
$211$	−1.19683	+	0.769153i	−0.0823929	+	0.0529507i	−0.581189	−	0.813769i	$-0.697412\pi$
$211$	−1.19683	+	0.769153i	−0.0823929	+	0.0529507i	0.498796	+	0.866720i	$0.333776\pi$
$212$		0			0
$213$	−6.49700	−	4.17537i	−0.445167	−	0.286091i
$214$		0			0
$215$	−4.84355	+	5.58976i	−0.330328	+	0.381218i
$216$		0			0
$217$	9.60088	+	21.0230i	0.651750	+	1.42713i
$218$		0			0
$219$	1.08121	+	0.317471i	0.0730611	+	0.0214527i
$220$		0			0
$221$	0.159774	−	1.11125i	0.0107476	−	0.0747510i
$222$		0			0
$223$	2.12299	−	4.64871i	0.142166	−	0.311300i	−0.825133	−	0.564938i	$-0.808900\pi$
$223$	2.12299	−	4.64871i	0.142166	−	0.311300i	0.967299	+	0.253638i	$0.0816272\pi$
$224$		0			0
$225$	0.0194536	+	0.135303i	0.00129690	+	0.00902017i
$226$		0			0
$227$	−7.80344	−	9.00565i	−0.517933	−	0.597726i	0.435180	−	0.900344i	$-0.356685\pi$
$227$	−7.80344	−	9.00565i	−0.517933	−	0.597726i	−0.953112	+	0.302618i	$0.902139\pi$
$228$		0			0
$229$	15.4444			1.02060			0.510298	−	0.859998i	$-0.329535\pi$
$229$	15.4444			1.02060			0.510298	+	0.859998i	$0.329535\pi$
$230$		0			0
$231$	−10.3148			−0.678666
$232$		0			0
$233$	10.8904	+	12.5682i	0.713456	+	0.823372i	0.990504	−	0.137484i	$-0.0439015\pi$
$233$	10.8904	+	12.5682i	0.713456	+	0.823372i	−0.277048	+	0.960856i	$0.589356\pi$
$234$		0			0
$235$	−1.05138	−	7.31250i	−0.0685844	−	0.477015i
$236$		0			0
$237$	−4.99607	+	10.9399i	−0.324530	+	0.710621i
$238$		0			0
$239$	−2.76071	+	19.2012i	−0.178576	+	1.24202i	0.681486	+	0.731831i	$0.261334\pi$
$239$	−2.76071	+	19.2012i	−0.178576	+	1.24202i	−0.860062	+	0.510190i	$0.829575\pi$
$240$		0			0
$241$	9.16055	+	2.68978i	0.590083	+	0.173264i	0.563124	−	0.826373i	$-0.309599\pi$
$241$	9.16055	+	2.68978i	0.590083	+	0.173264i	0.0269590	+	0.999637i	$0.491418\pi$
$242$		0			0
$243$	−0.589657	−	1.29117i	−0.0378265	−	0.0828286i
$244$		0			0
$245$	−0.144279	+	0.166507i	−0.00921767	+	0.0106378i
$246$		0			0
$247$	1.28905	+	0.828424i	0.0820204	+	0.0527113i
$248$		0			0
$249$	16.8980	−	10.8597i	1.07087	−	0.688206i
$250$		0			0
$251$	−10.6191	+	3.11805i	−0.670272	+	0.196810i	−0.599124	−	0.800656i	$-0.704484\pi$
$251$	−10.6191	+	3.11805i	−0.670272	+	0.196810i	−0.0711479	+	0.997466i	$0.522666\pi$
$252$		0			0
$253$	−9.49837	+	5.98666i	−0.597158	+	0.376378i
$254$		0			0
$255$	−9.14293	+	2.68461i	−0.572553	+	0.168117i
$256$		0			0
$257$	−3.45113	+	2.21790i	−0.215275	+	0.138349i	−0.643835	−	0.765164i	$-0.722658\pi$
$257$	−3.45113	+	2.21790i	−0.215275	+	0.138349i	0.428559	+	0.903514i	$0.359021\pi$
$258$		0			0
$259$	5.14487	+	3.30641i	0.319687	+	0.205450i
$260$		0			0
$261$	−0.313091	+	0.361327i	−0.0193799	+	0.0223656i
$262$		0			0
$263$	8.24902	+	18.0628i	0.508657	+	1.11380i	0.973558	+	0.228440i	$0.0733625\pi$
$263$	8.24902	+	18.0628i	0.508657	+	1.11380i	−0.464901	+	0.885363i	$0.653910\pi$
$264$		0			0
$265$	4.69911	+	1.37978i	0.288664	+	0.0847595i
$266$		0			0
$267$	2.44261	−	16.9887i	0.149485	−	1.03969i
$268$		0			0
$269$	−7.43692	+	16.2846i	−0.453437	+	0.992889i	0.535497	+	0.844537i	$0.320124\pi$
$269$	−7.43692	+	16.2846i	−0.453437	+	0.992889i	−0.988935	+	0.148352i	$0.952603\pi$
$270$		0			0
$271$	−2.91222	−	20.2550i	−0.176905	−	1.23040i	−0.863872	−	0.503712i	$-0.831967\pi$
$271$	−2.91222	−	20.2550i	−0.176905	−	1.23040i	0.686967	−	0.726689i	$-0.258942\pi$
$272$		0			0
$273$	0.575220	+	0.663839i	0.0348139	+	0.0401774i
$274$		0			0
$275$	−2.34112			−0.141175
$276$		0			0
$277$	−5.07429			−0.304885			−0.152442	−	0.988312i	$-0.548714\pi$
$277$	−5.07429			−0.304885			−0.152442	+	0.988312i	$0.548714\pi$
$278$		0			0
$279$	−0.794552	−	0.916962i	−0.0475686	−	0.0548971i
$280$		0			0
$281$	2.43267	+	16.9196i	0.145121	+	1.00934i	0.924062	+	0.382242i	$0.124848\pi$
$281$	2.43267	+	16.9196i	0.145121	+	1.00934i	−0.778942	+	0.627097i	$0.784243\pi$
$282$		0			0
$283$	−10.6238	+	23.2628i	−0.631518	+	1.38283i	0.275320	+	0.961353i	$0.411216\pi$
$283$	−10.6238	+	23.2628i	−0.631518	+	1.38283i	−0.906838	+	0.421479i	$0.861511\pi$
$284$		0			0
$285$	1.85089	−	12.8732i	0.109637	−	0.762545i
$286$		0			0
$287$	7.75354	+	2.27664i	0.457677	+	0.134386i
$288$		0			0
$289$	6.11147	+	13.3823i	0.359498	+	0.787192i
$290$		0			0
$291$	0.421940	−	0.486945i	0.0247346	−	0.0285452i
$292$		0			0
$293$	−2.51292	−	1.61496i	−0.146807	−	0.0943468i	0.465176	−	0.885218i	$-0.345991\pi$
$293$	−2.51292	−	1.61496i	−0.146807	−	0.0943468i	−0.611982	+	0.790872i	$0.709628\pi$
$294$		0			0
$295$	−1.96831	+	1.26496i	−0.114599	+	0.0736485i
$296$		0			0
$297$	11.9226	−	3.50079i	0.691820	−	0.203137i
$298$		0			0
$299$	0.914978	+	0.277440i	0.0529145	+	0.0160448i
$300$		0			0
$301$	−18.4783	+	5.42571i	−1.06507	+	0.312733i
$302$		0			0
$303$	13.2364	−	8.50649i	0.760409	−	0.488685i
$304$		0			0
$305$	10.5179	+	6.75943i	0.602252	+	0.387044i
$306$		0			0
$307$	10.0835	−	11.6370i	0.575497	−	0.664159i	−0.391133	−	0.920334i	$-0.627917\pi$
$307$	10.0835	−	11.6370i	0.575497	−	0.664159i	0.966631	+	0.256175i	$0.0824622\pi$
$308$		0			0
$309$	4.98997	+	10.9265i	0.283869	+	0.621587i
$310$		0			0
$311$	−18.5008	−	5.43232i	−1.04908	−	0.308039i	−0.288637	−	0.957439i	$-0.593202\pi$
$311$	−18.5008	−	5.43232i	−1.04908	−	0.308039i	−0.760447	+	0.649400i	$0.775020\pi$
$312$		0			0
$313$	1.57363	−	10.9448i	0.0889468	−	0.618639i	−0.895775	−	0.444507i	$-0.853379\pi$
$313$	1.57363	−	10.9448i	0.0889468	−	0.618639i	0.984722	−	0.174132i	$-0.0557120\pi$
$314$		0			0
$315$	−0.147855	+	0.323757i	−0.00833069	+	0.0182417i
$316$		0			0
$317$	−2.03471	−	14.1517i	−0.114281	−	0.794839i	−0.963674	−	0.267080i	$-0.913941\pi$
$317$	−2.03471	−	14.1517i	−0.114281	−	0.794839i	0.849394	−	0.527760i	$-0.176968\pi$
$318$		0			0
$319$	−5.36223	−	6.18834i	−0.300227	−	0.346481i
$320$		0			0
$321$	11.6394			0.649646
$322$		0			0
$323$	−43.2820			−2.40827
$324$		0			0
$325$	0.130556	+	0.150669i	0.00724192	+	0.00835762i
$326$		0			0
$327$	−4.51771	−	31.4214i	−0.249830	−	1.73761i
$328$		0			0
$329$	7.99090	−	17.4976i	0.440552	−	0.964675i
$330$		0			0
$331$	2.05848	−	14.3170i	0.113144	−	0.786935i	−0.851684	−	0.524055i	$-0.824419\pi$
$331$	2.05848	−	14.3170i	0.113144	−	0.786935i	0.964829	−	0.262880i	$-0.0846722\pi$
$332$		0			0
$333$	−0.308059	−	0.0904544i	−0.0168815	−	0.00495687i
$334$		0			0
$335$	6.74958	+	14.7795i	0.368769	+	0.807491i
$336$		0			0
$337$	−12.6829	+	14.6369i	−0.690883	+	0.797321i	−0.987491	−	0.157678i	$-0.949599\pi$
$337$	−12.6829	+	14.6369i	−0.690883	+	0.797321i	0.296608	+	0.954999i	$0.404145\pi$
$338$		0			0
$339$	14.3900	+	9.24792i	0.781560	+	0.502278i
$340$		0			0
$341$	17.4813	−	11.2346i	0.946667	−	0.608386i
$342$		0			0
$343$	−18.0386	+	5.29661i	−0.973993	+	0.285990i
$344$		0			0
$345$	−1.08410	−	8.04243i	−0.0583661	−	0.432990i
$346$		0			0
$347$	−5.29642	+	1.55517i	−0.284327	+	0.0834858i	−0.420786	−	0.907160i	$-0.638246\pi$
$347$	−5.29642	+	1.55517i	−0.284327	+	0.0834858i	0.136460	+	0.990646i	$0.456428\pi$
$348$		0			0
$349$	6.19680	−	3.98244i	0.331707	−	0.213175i	−0.364176	−	0.931330i	$-0.618649\pi$
$349$	6.19680	−	3.98244i	0.331707	−	0.213175i	0.695883	+	0.718155i	$0.255013\pi$
$350$		0			0
$351$	−0.890183	−	0.572086i	−0.0475145	−	0.0305357i
$352$		0			0
$353$	2.24659	−	2.59271i	0.119574	−	0.137996i	−0.692806	−	0.721124i	$-0.743626\pi$
$353$	2.24659	−	2.59271i	0.119574	−	0.137996i	0.812380	+	0.583128i	$0.198171\pi$
$354$		0			0
$355$	−1.89598	−	4.15162i	−0.100628	−	0.220345i
$356$		0			0
$357$	−23.8062	−	6.99013i	−1.25996	−	0.369957i
$358$		0			0
$359$	2.24244	−	15.5965i	0.118351	−	0.823152i	−0.841020	−	0.541004i	$-0.818044\pi$
$359$	2.24244	−	15.5965i	0.118351	−	0.823152i	0.959371	−	0.282147i	$-0.0910467\pi$
$360$		0			0
$361$	16.6472	−	36.4523i	0.876170	−	1.91854i
$362$		0			0
$363$	−1.32910	−	9.24409i	−0.0697596	−	0.485189i
$364$		0			0
$365$	0.436096	+	0.503281i	0.0228263	+	0.0263429i
$366$		0			0
$367$	−13.2711			−0.692748			−0.346374	−	0.938097i	$-0.612587\pi$
$367$	−13.2711			−0.692748			−0.346374	+	0.938097i	$0.612587\pi$
$368$		0			0
$369$	−0.424231			−0.0220846
$370$		0			0
$371$	8.35079	+	9.63733i	0.433552	+	0.500345i
$372$		0			0
$373$	3.45507	+	24.0305i	0.178897	+	1.24425i	0.859322	+	0.511435i	$0.170886\pi$
$373$	3.45507	+	24.0305i	0.178897	+	1.24425i	−0.680425	+	0.732818i	$0.738205\pi$
$374$		0			0
$375$	0.702936	−	1.53922i	0.0362995	−	0.0794848i
$376$		0			0
$377$	−0.0992361	+	0.690202i	−0.00511092	+	0.0355472i
$378$		0			0
$379$	−30.1545	−	8.85417i	−1.54893	−	0.454808i	−0.608152	−	0.793820i	$-0.708089\pi$
$379$	−30.1545	−	8.85417i	−1.54893	−	0.454808i	−0.940782	+	0.339012i	$0.889907\pi$
$380$		0			0
$381$	6.60299	+	14.4585i	0.338281	+	0.740733i
$382$		0			0
$383$	−4.97646	+	5.74314i	−0.254285	+	0.293461i	−0.868511	−	0.495669i	$-0.834923\pi$
$383$	−4.97646	+	5.74314i	−0.254285	+	0.293461i	0.614226	+	0.789130i	$0.289468\pi$
$384$		0			0
$385$	−5.12808	−	3.29562i	−0.261351	−	0.167960i
$386$		0			0
$387$	0.850533	−	0.546605i	0.0432350	−	0.0277855i
$388$		0			0
$389$	16.9810	−	4.98608i	0.860973	−	0.252804i	0.178701	−	0.983903i	$-0.442810\pi$
$389$	16.9810	−	4.98608i	0.860973	−	0.252804i	0.682271	+	0.731099i	$0.260992\pi$
$390$		0			0
$391$	−25.9789	+	7.38014i	−1.31381	+	0.373230i
$392$		0			0
$393$	−26.0991	+	7.66340i	−1.31653	+	0.386567i
$394$		0			0
$395$	−5.97915	+	3.84256i	−0.300844	+	0.193340i
$396$		0			0
$397$	9.05037	+	5.81632i	0.454225	+	0.291913i	0.747679	−	0.664061i	$-0.231168\pi$
$397$	9.05037	+	5.81632i	0.454225	+	0.291913i	−0.293454	+	0.955973i	$0.594805\pi$
$398$		0			0
$399$	22.1761	−	25.5925i	1.11019	−	1.28123i
$400$		0			0
$401$	0.464661	+	1.01747i	0.0232041	+	0.0508098i	0.920879	−	0.389848i	$-0.127472\pi$
$401$	0.464661	+	1.01747i	0.0232041	+	0.0508098i	−0.897675	+	0.440658i	$0.854745\pi$
$402$		0			0
$403$	−1.69790	−	0.498549i	−0.0845785	−	0.0248345i
$404$		0			0
$405$	−1.21981	+	8.48399i	−0.0606130	+	0.421573i
$406$		0			0
$407$	2.28428	−	5.00187i	0.113227	−	0.247933i
$408$		0			0
$409$	−0.533583	−	3.71115i	−0.0263840	−	0.183505i	0.972368	−	0.233454i	$-0.0750030\pi$
$409$	−0.533583	−	3.71115i	−0.0263840	−	0.183505i	−0.998752	+	0.0499497i	$0.984094\pi$
$410$		0			0
$411$	5.44135	+	6.27966i	0.268402	+	0.309753i
$412$		0			0
$413$	−6.09215			−0.299775
$414$		0			0
$415$	11.8707			0.582708
$416$		0			0
$417$	−0.992537	−	1.14545i	−0.0486048	−	0.0560929i
$418$		0			0
$419$	−2.51237	−	17.4739i	−0.122737	−	0.853658i	−0.954433	−	0.298426i	$-0.903539\pi$
$419$	−2.51237	−	17.4739i	−0.122737	−	0.853658i	0.831695	−	0.555232i	$-0.187371\pi$
$420$		0			0
$421$	14.1461	−	30.9756i	0.689438	−	1.50966i	−0.162887	−	0.986645i	$-0.552080\pi$
$421$	14.1461	−	30.9756i	0.689438	−	1.50966i	0.852324	−	0.523013i	$-0.175192\pi$
$422$		0			0
$423$	−0.143717	+	0.999574i	−0.00698776	+	0.0486009i
$424$		0			0
$425$	−5.40321	−	1.58653i	−0.262094	−	0.0769578i
$426$		0			0
$427$	13.5235	+	29.6123i	0.654447	+	1.43304i
$428$		0			0
$429$	0.517193	−	0.596873i	0.0249703	−	0.0288173i
$430$		0			0
$431$	−18.5009	−	11.8898i	−0.891158	−	0.572713i	0.0129975	−	0.999916i	$-0.495863\pi$
$431$	−18.5009	−	11.8898i	−0.891158	−	0.572713i	−0.904156	+	0.427203i	$0.859499\pi$
$432$		0			0
$433$	7.18622	−	4.61830i	0.345348	−	0.221941i	−0.356456	−	0.934312i	$-0.616015\pi$
$433$	7.18622	−	4.61830i	0.345348	−	0.221941i	0.701803	+	0.712371i	$0.252379\pi$
$434$		0			0
$435$	5.67870	−	1.66742i	0.272273	−	0.0799465i
$436$		0			0
$437$	5.56700	−	36.4377i	0.266306	−	1.74305i
$438$		0			0
$439$	31.7804	−	9.33157i	1.51680	−	0.445371i	0.585817	−	0.810444i	$-0.300774\pi$
$439$	31.7804	−	9.33157i	1.51680	−	0.445371i	0.930979	+	0.365072i	$0.118956\pi$
$440$		0			0
$441$	0.0253356	−	0.0162822i	0.00120646	−	0.000775344i
$442$		0			0
$443$	−29.1613	−	18.7409i	−1.38550	−	0.890405i	−0.386012	−	0.922494i	$-0.626148\pi$
$443$	−29.1613	−	18.7409i	−1.38550	−	0.890405i	−0.999485	+	0.0320889i	$0.989784\pi$
$444$		0			0
$445$	6.64231	−	7.66564i	0.314876	−	0.363386i
$446$		0			0
$447$	−10.7948	−	23.6373i	−0.510576	−	1.11800i
$448$		0			0
$449$	38.2267	+	11.2244i	1.80403	+	0.529710i	0.998061	−	0.0622499i	$-0.0198276\pi$
$449$	38.2267	+	11.2244i	1.80403	+	0.529710i	0.805967	+	0.591960i	$0.201646\pi$
$450$		0			0
$451$	1.03402	−	7.19174i	0.0486899	−	0.338646i
$452$		0			0
$453$	−6.84712	+	14.9931i	−0.321706	+	0.704437i
$454$		0			0
$455$	0.0738756	+	0.513816i	0.00346334	+	0.0240881i
$456$		0			0
$457$	27.2211	+	31.4148i	1.27335	+	1.46952i	0.813546	+	0.581501i	$0.197534\pi$
$457$	27.2211	+	31.4148i	1.27335	+	1.46952i	0.459802	+	0.888021i	$0.347920\pi$
$458$		0			0
$459$	29.8893			1.39511
$460$		0			0
$461$	3.28790			0.153133			0.0765664	−	0.997064i	$-0.475604\pi$
$461$	3.28790			0.153133			0.0765664	+	0.997064i	$0.475604\pi$
$462$		0			0
$463$	−5.64323	−	6.51264i	−0.262263	−	0.302668i	0.609311	−	0.792931i	$-0.291446\pi$
$463$	−5.64323	−	6.51264i	−0.262263	−	0.302668i	−0.871574	+	0.490263i	$0.836901\pi$
$464$		0			0
$465$	2.13751	+	14.8667i	0.0991247	+	0.689427i
$466$		0			0
$467$	−12.8170	+	28.0654i	−0.593102	+	1.29871i	0.340448	+	0.940263i	$0.389421\pi$
$467$	−12.8170	+	28.0654i	−0.593102	+	1.29871i	−0.933550	+	0.358448i	$0.883306\pi$
$468$		0			0
$469$	−6.02073	+	41.8751i	−0.278011	+	1.93361i
$470$		0			0
$471$	−26.8343	−	7.87926i	−1.23646	−	0.363057i
$472$		0			0
$473$	7.19318	+	15.7509i	0.330743	+	0.724225i
$474$		0			0
$475$	5.03322	−	5.80865i	0.230940	−	0.266519i
$476$		0			0
$477$	−0.563184	−	0.361936i	−0.0257864	−	0.0165719i
$478$		0			0
$479$	28.7095	−	18.4505i	1.31177	−	0.843025i	0.317331	−	0.948315i	$-0.397213\pi$
$479$	28.7095	−	18.4505i	1.31177	−	0.843025i	0.994442	+	0.105290i	$0.0335770\pi$
$480$		0			0
$481$	−0.449295	+	0.131925i	−0.0204861	+	0.00601526i
$482$		0			0
$483$	8.94676	−	19.1426i	0.407092	−	0.871018i
$484$		0			0
$485$	0.365351	−	0.107277i	0.0165897	−	0.00487118i
$486$		0			0
$487$	7.40852	−	4.76117i	0.335712	−	0.215749i	−0.361913	−	0.932212i	$-0.617876\pi$
$487$	7.40852	−	4.76117i	0.335712	−	0.215749i	0.697625	+	0.716463i	$0.254240\pi$
$488$		0			0
$489$	1.40752	+	0.904557i	0.0636502	+	0.0409055i
$490$		0			0
$491$	−14.2720	+	16.4707i	−0.644085	+	0.743314i	−0.980092	−	0.198546i	$-0.936378\pi$
$491$	−14.2720	+	16.4707i	−0.644085	+	0.743314i	0.336007	+	0.941860i	$0.390924\pi$
$492$		0			0
$493$	−8.18210	−	17.9163i	−0.368503	−	0.806910i
$494$		0			0
$495$	0.307054	+	0.0901591i	0.0138010	+	0.00405235i
$496$		0			0
$497$	1.69125	−	11.7629i	0.0758627	−	0.527637i
$498$		0			0
$499$	−4.27590	+	9.36292i	−0.191416	+	0.419142i	−0.980869	−	0.194669i	$-0.937637\pi$
$499$	−4.27590	+	9.36292i	−0.191416	+	0.419142i	0.789453	+	0.613811i	$0.210364\pi$
$500$		0			0
$501$	−3.47908	−	24.1976i	−0.155434	−	1.08107i
$502$		0			0
$503$	−1.28717	−	1.48547i	−0.0573921	−	0.0662340i	0.726328	−	0.687349i	$-0.241226\pi$
$503$	−1.28717	−	1.48547i	−0.0573921	−	0.0662340i	−0.783720	+	0.621115i	$0.786680\pi$
$504$		0			0
$505$	9.29839			0.413773
$506$		0			0
$507$	21.9304			0.973965
$508$		0			0
$509$	−27.7588	−	32.0353i	−1.23039	−	1.41994i	−0.874228	−	0.485515i	$-0.838632\pi$
$509$	−27.7588	−	32.0353i	−1.23039	−	1.41994i	−0.356158	−	0.934426i	$-0.615913\pi$
$510$		0			0
$511$	0.246767	+	1.71630i	0.0109163	+	0.0759248i
$512$		0			0
$513$	−16.9467	+	37.1081i	−0.748216	+	1.63836i
$514$		0			0
$515$	−1.01026	+	7.02649i	−0.0445172	+	0.309624i
$516$		0			0
$517$	−16.5949	−	4.87270i	−0.729842	−	0.214301i
$518$		0			0
$519$	−11.8823	−	26.0186i	−0.521575	−	1.14209i
$520$		0			0
$521$	−7.16119	+	8.26445i	−0.313737	+	0.362072i	−0.890615	−	0.454758i	$-0.849726\pi$
$521$	−7.16119	+	8.26445i	−0.313737	+	0.362072i	0.576877	+	0.816831i	$0.304271\pi$
$522$		0			0
$523$	0.319343	+	0.205229i	0.0139639	+	0.00897404i	0.547604	−	0.836738i	$-0.315540\pi$
$523$	0.319343	+	0.205229i	0.0139639	+	0.00897404i	−0.533640	+	0.845712i	$0.679176\pi$
$524$		0			0
$525$	3.70651	−	2.38203i	0.161765	−	0.103960i
$526$		0			0
$527$	47.9597	−	14.0822i	2.08916	−	0.613431i
$528$		0			0
$529$	−2.87164	−	22.8200i	−0.124854	−	0.992175i
$530$		0			0
$531$	0.306872	−	0.0901058i	0.0133171	−	0.00391026i
$532$		0			0
$533$	−0.520507	+	0.334510i	−0.0225457	+	0.0144892i
$534$		0			0
$535$	5.78658	+	3.71881i	0.250176	+	0.160778i
$536$		0			0
$537$	19.1258	−	22.0723i	0.825337	−	0.952490i
$538$		0			0
$539$	0.214270	+	0.469185i	0.00922925	+	0.0202092i
$540$		0			0
$541$	−39.2338	−	11.5201i	−1.68679	−	0.495287i	−0.709060	−	0.705148i	$-0.750881\pi$
$541$	−39.2338	−	11.5201i	−1.68679	−	0.495287i	−0.977731	+	0.209861i	$0.932699\pi$
$542$		0			0
$543$	−2.58396	+	17.9719i	−0.110888	+	0.771246i
$544$		0			0
$545$	7.79321	−	17.0648i	0.333825	−	0.730974i
$546$		0			0
$547$	1.00520	+	6.99134i	0.0429794	+	0.298928i	0.999961	+	0.00878105i	$0.00279513\pi$
$547$	1.00520	+	6.99134i	0.0429794	+	0.298928i	−0.956982	+	0.290147i	$0.906296\pi$
$548$		0			0
$549$	−1.11918	−	1.29160i	−0.0477654	−	0.0551242i
$550$		0			0
$551$	26.8825			1.14523
$552$		0			0
$553$	−18.5062			−0.786963
$554$		0			0
$555$	2.60271	+	3.00369i	0.110479	+	0.127500i
$556$		0			0
$557$	2.53877	+	17.6575i	0.107571	+	0.748173i	0.970195	+	0.242327i	$0.0779106\pi$
$557$	2.53877	+	17.6575i	0.107571	+	0.748173i	−0.862624	+	0.505846i	$0.831180\pi$
$558$		0			0
$559$	0.612553	−	1.34130i	0.0259082	−	0.0567311i
$560$		0			0
$561$	−3.17481	+	22.0813i	−0.134040	+	0.932272i
$562$		0			0
$563$	−28.5341	−	8.37836i	−1.20257	−	0.353106i	−0.381734	−	0.924272i	$-0.624673\pi$
$563$	−28.5341	−	8.37836i	−1.20257	−	0.353106i	−0.820834	+	0.571166i	$0.806491\pi$
$564$		0			0
$565$	4.19936	+	9.19532i	0.176669	+	0.386850i
$566$		0			0
$567$	−14.6149	+	16.8665i	−0.613769	+	0.708328i
$568$		0			0
$569$	−7.07603	−	4.54749i	−0.296643	−	0.190641i	0.383850	−	0.923395i	$-0.374598\pi$
$569$	−7.07603	−	4.54749i	−0.296643	−	0.190641i	−0.680493	+	0.732755i	$0.738234\pi$
$570$		0			0
$571$	15.9857	−	10.2734i	0.668979	−	0.429927i	−0.161578	−	0.986860i	$-0.551658\pi$
$571$	15.9857	−	10.2734i	0.668979	−	0.429927i	0.830557	+	0.556933i	$0.188022\pi$
$572$		0			0
$573$	−32.2951	+	9.48270i	−1.34915	+	0.396146i
$574$		0			0
$575$	2.03061	−	4.34472i	0.0846824	−	0.181187i
$576$		0			0
$577$	−45.9117	+	13.4809i	−1.91133	+	0.561216i	−0.930518	+	0.366246i	$0.880643\pi$
$577$	−45.9117	+	13.4809i	−1.91133	+	0.561216i	−0.980809	+	0.194970i	$0.937539\pi$
$578$		0			0
$579$	−13.1319	+	8.43938i	−0.545744	+	0.350729i
$580$		0			0
$581$	26.0020	+	16.7105i	1.07875	+	0.693267i
$582$		0			0
$583$	7.50838	−	8.66514i	0.310965	−	0.358873i
$584$		0			0
$585$	−0.0113208	−	0.0247891i	−0.000468058	−	0.00102490i
$586$		0			0
$587$	−40.1871	−	11.8000i	−1.65870	−	0.487038i	−0.687676	−	0.726018i	$-0.741369\pi$
$587$	−40.1871	−	11.8000i	−1.65870	−	0.487038i	−0.971025	+	0.238980i	$0.923187\pi$
$588$		0			0
$589$	−9.70894	+	67.5271i	−0.400050	+	2.78241i
$590$		0			0
$591$	−10.0419	+	21.9888i	−0.413070	+	0.904496i
$592$		0			0
$593$	−0.710815	−	4.94382i	−0.0291897	−	0.203019i	0.970008	−	0.243074i	$-0.0781557\pi$
$593$	−0.710815	−	4.94382i	−0.0291897	−	0.203019i	−0.999197	+	0.0400552i	$0.987247\pi$
$594$		0			0
$595$	−9.60204	−	11.0813i	−0.393645	−	0.454291i
$596$		0			0
$597$	−8.55271			−0.350039
$598$		0			0
$599$	21.4500			0.876422			0.438211	−	0.898872i	$-0.355612\pi$
$599$	21.4500			0.876422			0.438211	+	0.898872i	$0.355612\pi$
$600$		0			0
$601$	−14.2482	−	16.4433i	−0.581196	−	0.670736i	0.386666	−	0.922220i	$-0.373627\pi$
$601$	−14.2482	−	16.4433i	−0.581196	−	0.670736i	−0.967861	+	0.251484i	$0.919081\pi$
$602$		0			0
$603$	−0.316078	−	2.19837i	−0.0128717	−	0.0895245i
$604$		0			0
$605$	2.29274	−	5.02041i	0.0932133	−	0.204109i
$606$		0			0
$607$	−0.801196	+	5.57244i	−0.0325195	+	0.226178i	−0.999600	−	0.0282938i	$-0.990993\pi$
$607$	−0.801196	+	5.57244i	−0.0325195	+	0.226178i	0.967080	+	0.254472i	$0.0819017\pi$
$608$		0			0
$609$	14.7861	+	4.34159i	0.599162	+	0.175930i
$610$		0			0
$611$	0.611839	+	1.33974i	0.0247524	+	0.0542001i
$612$		0			0
$613$	27.7501	−	32.0253i	1.12082	−	1.29349i	0.169413	−	0.985545i	$-0.445813\pi$
$613$	27.7501	−	32.0253i	1.12082	−	1.29349i	0.951404	−	0.307946i	$-0.0996417\pi$
$614$		0			0
$615$	4.41788	+	2.83920i	0.178146	+	0.114488i
$616$		0			0
$617$	−26.1711	+	16.8191i	−1.05361	+	0.677113i	−0.948316	−	0.317328i	$-0.897214\pi$
$617$	−26.1711	+	16.8191i	−1.05361	+	0.677113i	−0.105293	+	0.994441i	$0.533578\pi$
$618$		0			0
$619$	31.9525	−	9.38211i	1.28428	−	0.377099i	0.432802	−	0.901489i	$-0.357525\pi$
$619$	31.9525	−	9.38211i	1.28428	−	0.377099i	0.851478	+	0.524390i	$0.175707\pi$
$620$		0			0
$621$	−3.84442	+	25.1628i	−0.154271	+	1.00975i
$622$		0			0
$623$	25.3406	−	7.44067i	1.01525	−	0.298104i
$624$		0			0
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$		0			0
$627$	−25.6142	−	16.4613i	−1.02293	−	0.657400i
$628$		0			0
$629$	8.66168	−	9.99611i	0.345364	−	0.398571i
$630$		0			0
$631$	5.49910	+	12.0413i	0.218916	+	0.479358i	0.986945	−	0.161056i	$-0.0514899\pi$
$631$	5.49910	+	12.0413i	0.218916	+	0.479358i	−0.768030	+	0.640414i	$0.778763\pi$
$632$		0			0
$633$	−2.30983	−	0.678227i	−0.0918075	−	0.0269571i
$634$		0			0
$635$	−1.33683	+	9.29782i	−0.0530503	+	0.368973i
$636$		0			0
$637$	0.0182467	−	0.0399547i	0.000722960	−	0.00158306i
$638$		0			0
$639$	0.0887874	+	0.617530i	0.00351238	+	0.0244291i
$640$		0			0
$641$	20.5288	+	23.6915i	0.810840	+	0.935759i	0.998923	−	0.0463941i	$-0.0147730\pi$
$641$	20.5288	+	23.6915i	0.810840	+	0.935759i	−0.188083	+	0.982153i	$0.560228\pi$
$642$		0			0
$643$	−15.4669			−0.609954			−0.304977	−	0.952360i	$-0.598649\pi$
$643$	−15.4669			−0.609954			−0.304977	+	0.952360i	$0.598649\pi$
$644$		0			0
$645$	−12.5155			−0.492798
$646$		0			0
$647$	14.7374	+	17.0078i	0.579386	+	0.668647i	0.967473	−	0.252976i	$-0.0814093\pi$
$647$	14.7374	+	17.0078i	0.579386	+	0.668647i	−0.388087	+	0.921623i	$0.626864\pi$
$648$		0			0
$649$	0.779543	+	5.42184i	0.0305997	+	0.212826i
$650$		0			0
$651$	−16.2459	+	35.5737i	−0.636729	+	1.39424i
$652$		0			0
$653$	2.63752	−	18.3443i	0.103214	−	0.717870i	−0.870842	−	0.491563i	$-0.836426\pi$
$653$	2.63752	−	18.3443i	0.103214	−	0.717870i	0.974056	−	0.226307i	$-0.0726652\pi$
$654$		0			0
$655$	−15.4238	−	4.52885i	−0.602659	−	0.176957i
$656$		0			0
$657$	−0.0378150	−	0.0828033i	−0.00147530	−	0.00323047i
$658$		0			0
$659$	−13.6221	+	15.7207i	−0.530640	+	0.612391i	−0.956263	−	0.292510i	$-0.905510\pi$
$659$	−13.6221	+	15.7207i	−0.530640	+	0.612391i	0.425623	+	0.904901i	$0.360055\pi$
$660$		0			0
$661$	−21.3773	−	13.7383i	−0.831479	−	0.534359i	0.0542688	−	0.998526i	$-0.482717\pi$
$661$	−21.3773	−	13.7383i	−0.831479	−	0.534359i	−0.885747	+	0.464167i	$0.846354\pi$
$662$		0			0
$663$	1.59815	−	1.02707i	0.0620670	−	0.0398880i
$664$		0			0
$665$	19.2019	−	5.63818i	0.744617	−	0.218639i
$666$		0			0
$667$	16.1355	−	4.58382i	0.624771	−	0.177486i
$668$		0			0
$669$	8.29740	−	2.43634i	0.320796	−	0.0941942i
$670$		0			0
$671$	24.6236	−	15.8246i	0.950584	−	0.610903i
$672$		0			0
$673$	24.1297	+	15.5072i	0.930130	+	0.597758i	0.915580	−	0.402136i	$-0.131732\pi$
$673$	24.1297	+	15.5072i	0.930130	+	0.597758i	0.0145502	+	0.999894i	$0.495368\pi$
$674$		0			0
$675$	−3.47580	+	4.01129i	−0.133784	+	0.154395i
$676$		0			0
$677$	−4.96598	−	10.8740i	−0.190858	−	0.417921i	0.789876	−	0.613266i	$-0.210145\pi$
$677$	−4.96598	−	10.8740i	−0.190858	−	0.417921i	−0.980735	+	0.195345i	$0.937417\pi$
$678$		0			0
$679$	0.951294	+	0.279325i	0.0365073	+	0.0107195i
$680$		0			0
$681$	2.86960	−	19.9585i	0.109963	−	0.764811i
$682$		0			0
$683$	15.6880	−	34.3520i	0.600286	−	1.31444i	−0.328737	−	0.944421i	$-0.606623\pi$
$683$	15.6880	−	34.3520i	0.600286	−	1.31444i	0.929023	−	0.370022i	$-0.120650\pi$
$684$		0			0
$685$	0.698834	+	4.86050i	0.0267011	+	0.185710i
$686$		0			0
$687$	17.1141	+	19.7507i	0.652944	+	0.753537i
$688$		0			0
$689$	−0.976384			−0.0371973
$690$		0			0
$691$	−33.4709			−1.27329			−0.636646	−	0.771156i	$-0.719679\pi$
$691$	−33.4709			−1.27329			−0.636646	+	0.771156i	$0.719679\pi$
$692$		0			0
$693$	0.545665	+	0.629731i	0.0207281	+	0.0239215i
$694$		0			0
$695$	−0.127472	−	0.886586i	−0.00483528	−	0.0336301i
$696$		0			0
$697$	7.26015	−	15.8975i	0.274998	−	0.602161i
$698$		0			0
$699$	−4.00480	+	27.8540i	−0.151475	+	1.05353i
$700$		0			0
$701$	−1.99992	−	0.587228i	−0.0755358	−	0.0221793i	0.243746	−	0.969839i	$-0.421624\pi$
$701$	−1.99992	−	0.587228i	−0.0755358	−	0.0221793i	−0.319282	+	0.947660i	$0.603442\pi$
$702$		0			0
$703$	7.49933	+	16.4212i	0.282843	+	0.619339i
$704$		0			0
$705$	8.18638	−	9.44758i	0.308317	−	0.355816i
$706$		0			0
$707$	20.3676	+	13.0894i	0.766001	+	0.492279i
$708$		0			0
$709$	0.871848	−	0.560302i	0.0327429	−	0.0210426i	−0.524167	−	0.851616i	$-0.675623\pi$
$709$	0.871848	−	0.560302i	0.0327429	−	0.0210426i	0.556910	+	0.830573i	$0.311987\pi$
$710$		0			0
$711$	0.932188	−	0.273715i	0.0349598	−	0.0102651i
$712$		0			0
$713$	5.68671	+	42.1869i	0.212969	+	1.57991i
$714$		0			0
$715$	0.447828	−	0.131494i	0.0167478	−	0.00491761i
$716$		0			0
$717$	−27.6142	+	17.7465i	−1.03127	+	0.662757i
$718$		0			0
$719$	38.6160	+	24.8170i	1.44013	+	0.925518i	0.999614	+	0.0277750i	$0.00884219\pi$
$719$	38.6160	+	24.8170i	1.44013	+	0.925518i	0.440520	+	0.897743i	$0.354794\pi$
$720$		0			0
$721$	−12.1042	+	13.9690i	−0.450783	+	0.520231i
$722$		0			0
$723$	6.71113	+	14.6953i	0.249590	+	0.546525i
$724$		0			0
$725$	3.35594	+	0.985394i	0.124637	+	0.0365966i
$726$		0			0
$727$	−0.645510	+	4.48962i	−0.0239406	+	0.166511i	−0.998284	−	0.0585552i	$-0.981351\pi$
$727$	−0.645510	+	4.48962i	−0.0239406	+	0.166511i	0.974344	+	0.225066i	$0.0722597\pi$
$728$		0			0
$729$	11.6796	−	25.5748i	0.432579	−	0.947216i
$730$		0			0
$731$	5.92755	+	41.2270i	0.219238	+	1.52484i
$732$		0			0
$733$	16.9580	+	19.5706i	0.626357	+	0.722855i	0.976901	−	0.213691i	$-0.0685487\pi$
$733$	16.9580	+	19.5706i	0.626357	+	0.722855i	−0.350544	+	0.936546i	$0.614003\pi$
$734$		0			0
$735$	−0.372811			−0.0137514
$736$		0			0
$737$	38.0380			1.40115
$738$		0			0
$739$	−9.43763	−	10.8916i	−0.347169	−	0.400654i	0.555131	−	0.831763i	$-0.312668\pi$
$739$	−9.43763	−	10.8916i	−0.347169	−	0.400654i	−0.902300	+	0.431109i	$0.858123\pi$
$740$		0			0
$741$	0.369001	+	2.56646i	0.0135556	+	0.0942812i
$742$		0			0
$743$	−21.9683	+	48.1040i	−0.805940	+	1.76476i	−0.181987	+	0.983301i	$0.558253\pi$
$743$	−21.9683	+	48.1040i	−0.805940	+	1.76476i	−0.623953	+	0.781462i	$0.714474\pi$
$744$		0			0
$745$	2.18549	−	15.2004i	0.0800700	−	0.556899i
$746$		0			0
$747$	−1.55692	−	0.457153i	−0.0569647	−	0.0167264i
$748$		0			0
$749$	7.44016	+	16.2917i	0.271857	+	0.595285i
$750$		0			0
$751$	2.04273	−	2.35744i	0.0745404	−	0.0860242i	−0.717254	−	0.696811i	$-0.754601\pi$
$751$	2.04273	−	2.35744i	0.0745404	−	0.0860242i	0.791795	+	0.610787i	$0.209147\pi$
$752$		0			0
$753$	−15.7546	−	10.1249i	−0.574129	−	0.368970i
$754$		0			0
$755$	−8.19442	+	5.26624i	−0.298226	+	0.191658i
$756$		0			0
$757$	−20.5639	+	6.03811i	−0.747408	+	0.219459i	−0.633189	−	0.773997i	$-0.718255\pi$
$757$	−20.5639	+	6.03811i	−0.747408	+	0.219459i	−0.114218	+	0.993456i	$0.536436\pi$
$758$		0			0
$759$	−18.1811	−	5.51290i	−0.659934	−	0.200106i
$760$		0			0
$761$	−21.8145	+	6.40533i	−0.790777	+	0.232193i	−0.652088	−	0.758143i	$-0.726107\pi$
$761$	−21.8145	+	6.40533i	−0.790777	+	0.232193i	−0.138688	+	0.990336i	$0.544289\pi$
$762$		0			0
$763$	41.0928	−	26.4087i	1.48766	−	0.956061i
$764$		0			0
$765$	0.647569	+	0.416167i	0.0234129	+	0.0150466i
$766$		0			0
$767$	0.305465	−	0.352526i	0.0110297	−	0.0127290i
$768$		0			0
$769$	9.80845	+	21.4775i	0.353702	+	0.774498i	0.999935	+	0.0113591i	$0.00361578\pi$
$769$	9.80845	+	21.4775i	0.353702	+	0.774498i	−0.646234	+	0.763139i	$0.723657\pi$
$770$		0			0
$771$	−6.66054	−	1.95571i	−0.239874	−	0.0704333i
$772$		0			0
$773$	3.05022	−	21.2147i	0.109709	−	0.763040i	−0.858485	−	0.512839i	$-0.828594\pi$
$773$	3.05022	−	21.2147i	0.109709	−	0.763040i	0.968194	−	0.250202i	$-0.0804970\pi$
$774$		0			0
$775$	−3.68728	+	8.07402i	−0.132451	+	0.290028i
$776$		0			0
$777$	1.47276	+	10.2433i	0.0528350	+	0.367475i
$778$		0			0
$779$	15.6207	+	18.0272i	0.559669	+	0.645892i
$780$		0			0
$781$	−10.6850			−0.382340
$782$		0			0
$783$	−18.5643			−0.663435
$784$		0			0
$785$	−10.8234	−	12.4909i	−0.386304	−	0.445818i
$786$		0			0
$787$	5.68359	+	39.5303i	0.202598	+	1.40910i	0.796536	+	0.604591i	$0.206663\pi$
$787$	5.68359	+	39.5303i	0.202598	+	1.40910i	−0.593938	+	0.804511i	$0.702428\pi$
$788$		0			0
$789$	−13.9584	+	30.5647i	−0.496933	+	1.08813i
$790$		0			0
$791$	−3.74590	+	26.0533i	−0.133189	+	0.926348i
$792$		0			0
$793$	−2.39161	−	0.702239i	−0.0849284	−	0.0249372i
$794$		0			0
$795$	3.44263	+	7.53831i	0.122097	+	0.267356i
$796$		0			0
$797$	20.3637	−	23.5009i	0.721318	−	0.832445i	−0.270147	−	0.962819i	$-0.587072\pi$
$797$	20.3637	−	23.5009i	0.721318	−	0.832445i	0.991465	+	0.130374i	$0.0416179\pi$
$798$		0			0
$799$	−34.9982	−	22.4920i	−1.23815	−	0.795709i
$800$		0			0
$801$	−1.16640	+	0.749598i	−0.0412126	+	0.0264857i
$802$		0			0
$803$	1.49588	−	0.439231i	0.0527886	−	0.0155001i
$804$		0			0
$805$	10.5640	−	6.65834i	0.372334	−	0.234676i
$806$		0			0
$807$	−29.0661	+	8.53458i	−1.02318	+	0.300431i
$808$		0			0
$809$	31.7897	−	20.4300i	1.11767	−	0.718280i	0.154715	−	0.987959i	$-0.450554\pi$
$809$	31.7897	−	20.4300i	1.11767	−	0.718280i	0.962950	+	0.269679i	$0.0869176\pi$
$810$		0			0
$811$	10.4868	+	6.73948i	0.368243	+	0.236655i	0.711654	−	0.702530i	$-0.247946\pi$
$811$	10.4868	+	6.73948i	0.368243	+	0.236655i	−0.343412	+	0.939185i	$0.611583\pi$
$812$		0			0
$813$	22.6755	−	26.1690i	0.795265	−	0.917785i
$814$		0			0
$815$	0.410748	+	0.899413i	0.0143879	+	0.0315050i
$816$		0			0
$817$	−54.5449	−	16.0158i	−1.90828	−	0.560323i
$818$		0			0
$819$	0.0100984	−	0.0702356i	0.000352865	−	0.00245423i
$820$		0			0
$821$	15.9328	−	34.8880i	0.556060	−	1.21760i	−0.397834	−	0.917457i	$-0.630238\pi$
$821$	15.9328	−	34.8880i	0.556060	−	1.21760i	0.953894	−	0.300144i	$-0.0970347\pi$
$822$		0			0
$823$	−3.81064	−	26.5036i	−0.132830	−	0.923856i	−0.941840	−	0.336061i	$-0.890905\pi$
$823$	−3.81064	−	26.5036i	−0.132830	−	0.923856i	0.809010	−	0.587795i	$-0.200004\pi$
$824$		0			0
$825$	−2.59422	−	2.99389i	−0.0903190	−	0.104234i
$826$		0			0
$827$	41.5456			1.44468			0.722341	−	0.691537i	$-0.243066\pi$
$827$	41.5456			1.44468			0.722341	+	0.691537i	$0.243066\pi$
$828$		0			0
$829$	20.2897			0.704691			0.352346	−	0.935870i	$-0.385384\pi$
$829$	20.2897			0.704691			0.352346	+	0.935870i	$0.385384\pi$
$830$		0			0
$831$	−5.62287	−	6.48914i	−0.195055	−	0.225106i
$832$		0			0
$833$	0.176569	+	1.22807i	0.00611777	+	0.0425500i
$834$		0			0
$835$	6.00154	−	13.1415i	0.207692	−	0.454782i
$836$		0			0
$837$	6.70472	−	46.6323i	0.231749	−	1.61185i
$838$		0			0
$839$	−44.2738	−	13.0000i	−1.52850	−	0.448809i	−0.593910	−	0.804531i	$-0.702417\pi$
$839$	−44.2738	−	13.0000i	−1.52850	−	0.448809i	−0.934592	+	0.355723i	$0.884235\pi$
$840$		0			0
$841$	−6.96511	−	15.2515i	−0.240176	−	0.525913i
$842$		0			0
$843$	−18.9416	+	21.8597i	−0.652382	+	0.752889i
$844$		0			0
$845$	10.9029	+	7.00684i	0.375070	+	0.241043i
$846$		0			0
$847$	12.0894	−	7.76939i	0.415397	−	0.266959i
$848$		0			0
$849$	−41.5214	+	12.1918i	−1.42501	+	0.418421i
$850$		0			0
$851$	7.30132	+	8.57770i	0.250286	+	0.294040i
$852$		0			0
$853$	−37.0059	+	10.8659i	−1.26706	+	0.372042i	−0.845117	−	0.534581i	$-0.820469\pi$
$853$	−37.0059	+	10.8659i	−1.26706	+	0.372042i	−0.421941	+	0.906623i	$0.638651\pi$
$854$		0			0
$855$	−0.883839	+	0.568009i	−0.0302267	+	0.0194255i
$856$		0			0
$857$	−10.1876	−	6.54717i	−0.348001	−	0.223647i	0.354949	−	0.934886i	$-0.384498\pi$
$857$	−10.1876	−	6.54717i	−0.348001	−	0.223647i	−0.702951	+	0.711239i	$0.748135\pi$
$858$		0			0
$859$	20.3735	−	23.5123i	0.695135	−	0.802228i	−0.292952	−	0.956127i	$-0.594638\pi$
$859$	20.3735	−	23.5123i	0.695135	−	0.802228i	0.988087	+	0.153899i	$0.0491831\pi$
$860$		0			0
$861$	5.68034	+	12.4382i	0.193585	+	0.423893i
$862$		0			0
$863$	−0.222969	−	0.0654695i	−0.00758994	−	0.00222861i	0.277935	−	0.960600i	$-0.410350\pi$
$863$	−0.222969	−	0.0654695i	−0.00758994	−	0.00222861i	−0.285525	+	0.958371i	$0.592168\pi$
$864$		0			0
$865$	2.40566	−	16.7317i	0.0817950	−	0.568896i
$866$		0			0
$867$	−10.3414	+	22.6445i	−0.351213	+	0.769048i
$868$		0			0
$869$	2.36802	+	16.4700i	0.0803297	+	0.558705i
$870$		0			0
$871$	−2.12124	−	2.44804i	−0.0718755	−	0.0829487i
$872$		0			0
$873$	−0.0520496			−0.00176161
$874$		0			0
$875$	2.60378			0.0880239
$876$		0			0
$877$	38.1226	+	43.9959i	1.28731	+	1.48564i	0.782865	+	0.622191i	$0.213757\pi$
$877$	38.1226	+	43.9959i	1.28731	+	1.48564i	0.504445	+	0.863444i	$0.331697\pi$
$878$		0			0
$879$	−0.719343	−	5.00314i	−0.0242629	−	0.168752i
$880$		0			0
$881$	−18.9074	+	41.4014i	−0.637007	+	1.39485i	0.265473	+	0.964118i	$0.414472\pi$
$881$	−18.9074	+	41.4014i	−0.637007	+	1.39485i	−0.902480	+	0.430732i	$0.858255\pi$
$882$		0			0
$883$	0.912476	−	6.34641i	0.0307073	−	0.213574i	−0.968691	−	0.248271i	$-0.920138\pi$
$883$	0.912476	−	6.34641i	0.0307073	−	0.213574i	0.999398	+	0.0346973i	$0.0110467\pi$
$884$		0			0
$885$	−3.79876	−	1.11542i	−0.127694	−	0.0374943i
$886$		0			0
$887$	−9.66152	−	21.1558i	−0.324402	−	0.710342i	0.675226	−	0.737611i	$-0.264046\pi$
$887$	−9.66152	−	21.1558i	−0.324402	−	0.710342i	−0.999628	+	0.0272693i	$0.991319\pi$
$888$		0			0
$889$	−16.0169	+	18.4845i	−0.537189	+	0.619949i
$890$		0			0
$891$	16.8808	+	10.8486i	0.565529	+	0.363443i
$892$		0			0
$893$	47.7675	−	30.6983i	1.59848	−	1.02728i
$894$		0			0
$895$	16.5607	−	4.86265i	0.553562	−	0.162540i
$896$		0			0
$897$	0.659098	+	1.47753i	0.0220066	+	0.0493334i
$898$		0			0
$899$	−29.7878	+	8.74650i	−0.993480	+	0.291712i
$900$		0			0
$901$	23.2012	−	14.9105i	0.772945	−	0.496742i
$902$		0			0
$903$	−27.4145	−	17.6182i	−0.912298	−	0.586298i
$904$		0			0
$905$	−7.02669	+	8.10924i	−0.233575	+	0.269560i
$906$		0			0
$907$	−21.9150	−	47.9872i	−0.727677	−	1.59339i	−0.802823	−	0.596218i	$-0.796669\pi$
$907$	−21.9150	−	47.9872i	−0.727677	−	1.59339i	0.0751457	−	0.997173i	$-0.476058\pi$
$908$		0			0
$909$	−1.21955	−	0.358092i	−0.0404498	−	0.0118771i
$910$		0			0
$911$	3.66707	−	25.5050i	0.121495	−	0.845019i	−0.834368	−	0.551208i	$-0.814167\pi$
$911$	3.66707	−	25.5050i	0.121495	−	0.845019i	0.955864	−	0.293811i	$-0.0949237\pi$
$912$		0			0
$913$	11.5447	−	25.2793i	0.382072	−	0.836622i
$914$		0			0
$915$	3.01082	+	20.9407i	0.0995348	+	0.692280i
$916$		0			0
$917$	−27.4097	−	31.6325i	−0.905148	−	1.04460i
$918$		0			0
$919$	6.92575			0.228459			0.114230	−	0.993454i	$-0.463560\pi$
$919$	6.92575			0.228459			0.114230	+	0.993454i	$0.463560\pi$
$920$		0			0
$921$	26.0554			0.858554
$922$		0			0
$923$	0.595864	+	0.687664i	0.0196131	+	0.0226347i
$924$		0			0
$925$	0.334267	+	2.32488i	0.0109906	+	0.0764415i
$926$		0			0
$927$	0.403100	−	0.882666i	0.0132395	−	0.0289906i
$928$		0			0
$929$	7.31024	−	50.8438i	0.239841	−	1.66813i	−0.413072	−	0.910699i	$-0.635544\pi$
$929$	7.31024	−	50.8438i	0.239841	−	1.66813i	0.652913	−	0.757433i	$-0.273547\pi$
$930$		0			0
$931$	−1.62478	−	0.477078i	−0.0532500	−	0.0156356i
$932$		0			0
$933$	−13.5539	−	29.6789i	−0.443735	−	0.971645i
$934$		0			0
$935$	−8.63341	+	9.96348i	−0.282343	+	0.325841i
$936$		0			0
$937$	36.5895	+	23.5147i	1.19533	+	0.768191i	0.978142	−	0.207939i	$-0.0666757\pi$
$937$	36.5895	+	23.5147i	1.19533	+	0.768191i	0.217186	+	0.976130i	$0.430312\pi$
$938$		0			0
$939$	15.7403	−	10.1157i	0.513666	−	0.330113i
$940$		0			0
$941$	32.1318	−	9.43474i	1.04747	−	0.307564i	0.287673	−	0.957729i	$-0.407118\pi$
$941$	32.1318	−	9.43474i	1.04747	−	0.307564i	0.759793	+	0.650165i	$0.225300\pi$
$942$		0			0
$943$	12.4498	+	8.15685i	0.405421	+	0.265624i
$944$		0			0
$945$	−13.2603	+	3.89357i	−0.431357	+	0.126658i
$946$		0			0
$947$	0.901818	−	0.579563i	0.0293051	−	0.0188333i	−0.525906	−	0.850543i	$-0.676274\pi$
$947$	0.901818	−	0.579563i	0.0293051	−	0.0188333i	0.555211	+	0.831709i	$0.312637\pi$
$948$		0			0
$949$	−0.111688	−	0.0717775i	−0.00362554	−	0.00232999i
$950$		0			0
$951$	15.8429	−	18.2837i	0.513742	−	0.592889i
$952$		0			0
$953$	4.49030	+	9.83239i	0.145455	+	0.318502i	0.968311	−	0.249748i	$-0.0803478\pi$
$953$	4.49030	+	9.83239i	0.145455	+	0.318502i	−0.822856	+	0.568250i	$0.807620\pi$
$954$		0			0
$955$	−19.0855	−	5.60400i	−0.617592	−	0.181341i
$956$		0			0
$957$	1.97188	−	13.7147i	0.0637418	−	0.443334i
$958$		0			0
$959$	−5.31142	+	11.6304i	−0.171515	+	0.375565i
$960$		0			0
$961$	−6.80065	−	47.2995i	−0.219376	−	1.52579i
$962$		0			0
$963$	−0.615735	−	0.710596i	−0.0198418	−	0.0228986i
$964$		0			0
$965$	−9.22503			−0.296964
$966$		0			0
$967$	−18.5042			−0.595054			−0.297527	−	0.954713i	$-0.596162\pi$
$967$	−18.5042			−0.595054			−0.297527	+	0.954713i	$0.596162\pi$
$968$		0			0
$969$	−47.9612	−	55.3502i	−1.54074	−	1.77810i
$970$		0			0
$971$	−5.13949	−	35.7460i	−0.164934	−	1.14714i	−0.889166	−	0.457585i	$-0.848714\pi$
$971$	−5.13949	−	35.7460i	−0.164934	−	1.14714i	0.724232	−	0.689557i	$-0.242195\pi$
$972$		0			0
$973$	0.968837	−	2.12146i	0.0310595	−	0.0680108i
$974$		0			0
$975$	−0.0480099	+	0.333916i	−0.00153755	+	0.0106939i
$976$		0			0
$977$	−11.9236	−	3.50108i	−0.381469	−	0.112009i	0.0853754	−	0.996349i	$-0.472791\pi$
$977$	−11.9236	−	3.50108i	−0.381469	−	0.112009i	−0.466844	+	0.884339i	$0.654609\pi$
$978$		0			0
$979$	−9.86452	−	21.6003i	−0.315271	−	0.690348i
$980$		0			0
$981$	−1.67932	+	1.93803i	−0.0536165	+	0.0618767i
$982$		0			0
$983$	18.4731	+	11.8719i	0.589200	+	0.378656i	0.801006	−	0.598656i	$-0.204298\pi$
$983$	18.4731	+	11.8719i	0.589200	+	0.378656i	−0.211806	+	0.977312i	$0.567935\pi$
$984$		0			0
$985$	−12.0179	+	7.72342i	−0.382922	+	0.246089i
$986$		0			0
$987$	31.2312	−	9.17032i	0.994101	−	0.291894i
$988$		0			0
$989$	−35.4701	−	0.312481i	−1.12788	−	0.00993632i
$990$		0			0
$991$	8.73337	−	2.56435i	0.277425	−	0.0814592i	−0.140061	−	0.990143i	$-0.544730\pi$
$991$	8.73337	−	2.56435i	0.277425	−	0.0814592i	0.417485	+	0.908684i	$0.362912\pi$
$992$		0			0
$993$	20.5900	−	13.2324i	0.653404	−	0.419917i
$994$		0			0
$995$	−4.25203	−	2.73262i	−0.134798	−	0.0866297i
$996$		0			0
$997$	−30.4558	+	35.1479i	−0.964546	+	1.11315i	0.0289846	+	0.999580i	$0.490773\pi$
$997$	−30.4558	+	35.1479i	−0.964546	+	1.11315i	−0.993531	+	0.113565i	$0.963773\pi$
$998$		0			0
$999$	−5.17883	−	11.3401i	−0.163851	−	0.358783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.101.4	yes	50
23.18	even	11	inner	460.2.m.b.41.4	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.41.4	✓	50	23.18	even	11	inner
460.2.m.b.101.4	yes	50	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10811 + 1.27883i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.08165 + 2.36848i) q^{7} +(0.0194536 - 0.135303i) q^{9} +O(q^{10})\)	\(q+(1.10811 + 1.27883i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.08165 + 2.36848i) q^{7} +(0.0194536 - 0.135303i) q^{9} +(2.24629 + 0.659569i) q^{11} +(-0.0828187 - 0.181348i) q^{13} +(-1.10811 + 1.27883i) q^{15} +(4.73736 + 3.04452i) q^{17} +(-6.46583 + 4.15533i) q^{19} +(-4.22747 + 1.24130i) q^{21} +(-3.17241 + 3.59664i) q^{23} +(-0.959493 + 0.281733i) q^{25} +(4.46512 - 2.86956i) q^{27} +(-2.94239 - 1.89096i) q^{29} +(5.81264 - 6.70814i) q^{31} +(1.64566 + 3.60349i) q^{33} +(-2.49831 - 0.733570i) q^{35} +(0.334267 - 2.32488i) q^{37} +(0.140140 - 0.306864i) q^{39} +(-0.441676 - 3.07192i) q^{41} +(4.84355 + 5.58976i) q^{43} +0.136694 q^{45} -7.38769 q^{47} +(0.144279 + 0.166507i) q^{49} +(1.35611 + 9.43193i) q^{51} +(2.03449 - 4.45492i) q^{53} +(-0.333176 + 2.31729i) q^{55} +(-12.4788 - 3.66411i) q^{57} +(0.971960 + 2.12830i) q^{59} +(8.18748 - 9.44886i) q^{61} +(0.299420 + 0.192426i) q^{63} +(0.167716 - 0.107784i) q^{65} +(15.5896 - 4.57753i) q^{67} +(-8.11486 - 0.0714895i) q^{69} +(-4.37919 + 1.28585i) q^{71} +(0.560221 - 0.360032i) q^{73} +(-1.42351 - 0.914835i) q^{75} +(-3.99187 + 4.60687i) q^{77} +(2.95253 + 6.46514i) q^{79} +(8.22404 + 2.41480i) q^{81} +(1.68937 - 11.7498i) q^{83} +(-2.33933 + 5.12243i) q^{85} +(-0.842281 - 5.85819i) q^{87} +(-6.64231 - 7.66564i) q^{89} +0.519100 q^{91} +15.0196 q^{93} +(-5.03322 - 5.80865i) q^{95} +(-0.0541899 - 0.376899i) q^{97} +(0.132940 - 0.291097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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