LMFDB - Embedded newform 425.2.j.d.149.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(149,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("425.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 364x^{6} + 519x^{4} + 278x^{2} + 1 $ x^12 + 18x^10 + 119x^8 + 364x^6 + 519x^4 + 278*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.5
Root			$-1.68228i$ of defining polynomial
Character	$\chi$	$=$	425.149
Dual form			425.2.j.d.174.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.68228 q^{2} +(-1.27457 + 1.27457i) q^{3} +0.830060 q^{4} +(-2.14419 + 2.14419i) q^{6} +(1.92759 + 1.92759i) q^{7} -1.96816 q^{8} -0.249077i q^{9} +(-0.0173960 + 0.0173960i) q^{11} +(-1.05797 + 1.05797i) q^{12} +3.62828i q^{13} +(3.24274 + 3.24274i) q^{14} -4.97112 q^{16} +(1.33255 + 3.90184i) q^{17} -0.419017i q^{18} -0.603141i q^{19} -4.91370 q^{21} +(-0.0292650 + 0.0292650i) q^{22} +(1.94875 + 1.94875i) q^{23} +(2.50857 - 2.50857i) q^{24} +6.10378i q^{26} +(-3.50625 - 3.50625i) q^{27} +(1.60001 + 1.60001i) q^{28} +(-3.01483 - 3.01483i) q^{29} +(-0.422356 - 0.422356i) q^{31} -4.42648 q^{32} -0.0443451i q^{33} +(2.24171 + 6.56397i) q^{34} -0.206749i q^{36} +(7.50498 - 7.50498i) q^{37} -1.01465i q^{38} +(-4.62452 - 4.62452i) q^{39} +(5.07178 - 5.07178i) q^{41} -8.26622 q^{42} +12.0321 q^{43} +(-0.0144398 + 0.0144398i) q^{44} +(3.27834 + 3.27834i) q^{46} +11.0911i q^{47} +(6.33606 - 6.33606i) q^{48} +0.431184i q^{49} +(-6.67161 - 3.27475i) q^{51} +3.01170i q^{52} -2.05698 q^{53} +(-5.89850 - 5.89850i) q^{54} +(-3.79381 - 3.79381i) q^{56} +(0.768748 + 0.768748i) q^{57} +(-5.07178 - 5.07178i) q^{58} +0.926819i q^{59} +(8.41435 - 8.41435i) q^{61} +(-0.710520 - 0.710520i) q^{62} +(0.480117 - 0.480117i) q^{63} +2.49567 q^{64} -0.0746007i q^{66} -5.79776i q^{67} +(1.10609 + 3.23876i) q^{68} -4.96765 q^{69} +(-3.84845 - 3.84845i) q^{71} +0.490224i q^{72} +(-2.88624 + 2.88624i) q^{73} +(12.6255 - 12.6255i) q^{74} -0.500644i q^{76} -0.0670647 q^{77} +(-7.77972 - 7.77972i) q^{78} +(-9.68618 + 9.68618i) q^{79} +9.68519 q^{81} +(8.53214 - 8.53214i) q^{82} -12.1804 q^{83} -4.07867 q^{84} +20.2414 q^{86} +7.68523 q^{87} +(0.0342382 - 0.0342382i) q^{88} +7.11750 q^{89} +(-6.99384 + 6.99384i) q^{91} +(1.61758 + 1.61758i) q^{92} +1.07665 q^{93} +18.6583i q^{94} +(5.64188 - 5.64188i) q^{96} +(5.01796 - 5.01796i) q^{97} +0.725372i q^{98} +(0.00433295 + 0.00433295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8} - 4 q^{11} - 4 q^{12} - 14 q^{14} + 4 q^{16} - 10 q^{17} + 8 q^{21} + 10 q^{22} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 34 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots - 30 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8 - 4 * q^11 - 4 * q^12 - 14 * q^14 + 4 * q^16 - 10 * q^17 + 8 * q^21 + 10 * q^22 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 34 * q^28 + 6 * q^29 - 6 * q^31 + 48 * q^32 - 30 * q^34 + 18 * q^37 - 16 * q^39 + 6 * q^41 - 56 * q^42 + 16 * q^43 - 32 * q^44 + 30 * q^46 + 10 * q^48 - 40 * q^51 - 48 * q^53 - 16 * q^54 - 56 * q^56 + 18 * q^57 - 6 * q^58 - 8 * q^61 + 22 * q^62 + 30 * q^63 + 44 * q^64 - 18 * q^68 + 72 * q^69 - 20 * q^71 + 18 * q^73 + 26 * q^74 - 24 * q^77 + 38 * q^78 + 14 * q^79 - 8 * q^81 - 10 * q^82 - 52 * q^83 - 36 * q^84 + 84 * q^86 + 48 * q^87 - 66 * q^88 + 24 * q^89 + 12 * q^91 + 32 * q^92 + 60 * q^93 + 22 * q^96 - 52 * q^97 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.68228			1.18955			0.594775	−	0.803892i	$-0.297241\pi$
$2$	1.68228			1.18955			0.594775	+	0.803892i	$0.297241\pi$
$3$	−1.27457	+	1.27457i	−0.735876	+	0.735876i	−0.971777	−	0.235901i	$-0.924196\pi$
$3$	−1.27457	+	1.27457i	−0.735876	+	0.735876i	0.235901	+	0.971777i	$0.424196\pi$
$4$	0.830060			0.415030
$5$		0			0
$5$		0			0
$6$	−2.14419	+	2.14419i	−0.875361	+	0.875361i
$7$	1.92759	+	1.92759i	0.728559	+	0.728559i	0.970333	−	0.241773i	$-0.0777290\pi$
$7$	1.92759	+	1.92759i	0.728559	+	0.728559i	−0.241773	+	0.970333i	$0.577729\pi$
$8$	−1.96816			−0.695851
$9$		−	0.249077i		−	0.0830256i
$10$		0			0
$11$	−0.0173960	+	0.0173960i	−0.00524510	+	0.00524510i	−0.709724	−	0.704479i	$-0.751181\pi$
$11$	−0.0173960	+	0.0173960i	−0.00524510	+	0.00524510i	0.704479	+	0.709724i	$0.251181\pi$
$12$	−1.05797	+	1.05797i	−0.305411	+	0.305411i
$13$			3.62828i			1.00631i	0.864198	+	0.503153i	$0.167827\pi$
$13$			3.62828i			1.00631i	−0.864198	+	0.503153i	$0.832173\pi$
$14$	3.24274	+	3.24274i	0.866658	+	0.866658i
$15$		0			0
$16$	−4.97112			−1.24278
$17$	1.33255	+	3.90184i	0.323190	+	0.946334i
$17$	1.33255	+	3.90184i	0.323190	+	0.946334i
$18$		−	0.419017i		−	0.0987632i
$19$		−	0.603141i		−	0.138370i	−0.997604	−	0.0691850i	$-0.977960\pi$
$19$		−	0.603141i		−	0.138370i	0.997604	−	0.0691850i	$-0.0220399\pi$
$20$		0			0
$21$	−4.91370			−1.07226
$22$	−0.0292650	+	0.0292650i	−0.00623931	+	0.00623931i
$23$	1.94875	+	1.94875i	0.406343	+	0.406343i	0.880461	−	0.474118i	$-0.157233\pi$
$23$	1.94875	+	1.94875i	0.406343	+	0.406343i	−0.474118	+	0.880461i	$0.657233\pi$
$24$	2.50857	−	2.50857i	0.512060	−	0.512060i
$25$		0			0
$26$			6.10378i			1.19705i
$27$	−3.50625	−	3.50625i	−0.674779	−	0.674779i
$28$	1.60001	+	1.60001i	0.302374	+	0.302374i
$29$	−3.01483	−	3.01483i	−0.559839	−	0.559839i	0.369423	−	0.929262i	$-0.379556\pi$
$29$	−3.01483	−	3.01483i	−0.559839	−	0.559839i	−0.929262	+	0.369423i	$0.879556\pi$
$30$		0			0
$31$	−0.422356	−	0.422356i	−0.0758573	−	0.0758573i	0.668160	−	0.744017i	$-0.267082\pi$
$31$	−0.422356	−	0.422356i	−0.0758573	−	0.0758573i	−0.744017	+	0.668160i	$0.767082\pi$
$32$	−4.42648			−0.782498
$33$		−	0.0443451i		−	0.00771948i
$34$	2.24171	+	6.56397i	0.384451	+	1.12571i
$35$		0			0
$36$		−	0.206749i		−	0.0344581i
$37$	7.50498	−	7.50498i	1.23381	−	1.23381i	0.271322	−	0.962489i	$-0.412539\pi$
$37$	7.50498	−	7.50498i	1.23381	−	1.23381i	0.962489	−	0.271322i	$-0.0874608\pi$
$38$		−	1.01465i		−	0.164598i
$39$	−4.62452	−	4.62452i	−0.740515	−	0.740515i
$40$		0			0
$41$	5.07178	−	5.07178i	0.792078	−	0.792078i	−0.189754	−	0.981832i	$-0.560769\pi$
$41$	5.07178	−	5.07178i	0.792078	−	0.792078i	0.981832	+	0.189754i	$0.0607689\pi$
$42$	−8.26622			−1.27551
$43$	12.0321			1.83488			0.917442	−	0.397869i	$-0.130250\pi$
$43$	12.0321			1.83488			0.917442	+	0.397869i	$0.130250\pi$
$44$	−0.0144398	+	0.0144398i	−0.00217688	+	0.00217688i
$45$		0			0
$46$	3.27834	+	3.27834i	0.483365	+	0.483365i
$47$			11.0911i			1.61780i	0.587943	+	0.808902i	$0.299938\pi$
$47$			11.0911i			1.61780i	−0.587943	+	0.808902i	$0.700062\pi$
$48$	6.33606	−	6.33606i	0.914531	−	0.914531i
$49$			0.431184i			0.0615978i
$50$		0			0
$51$	−6.67161	−	3.27475i	−0.934212	−	0.458556i
$52$			3.01170i			0.417647i
$53$	−2.05698			−0.282548			−0.141274	−	0.989971i	$-0.545120\pi$
$53$	−2.05698			−0.282548			−0.141274	+	0.989971i	$0.545120\pi$
$54$	−5.89850	−	5.89850i	−0.802684	−	0.802684i
$55$		0			0
$56$	−3.79381	−	3.79381i	−0.506969	−	0.506969i
$57$	0.768748	+	0.768748i	0.101823	+	0.101823i
$58$	−5.07178	−	5.07178i	−0.665957	−	0.665957i
$59$			0.926819i			0.120662i	0.998178	+	0.0603308i	$0.0192155\pi$
$59$			0.926819i			0.120662i	−0.998178	+	0.0603308i	$0.980784\pi$
$60$		0			0
$61$	8.41435	−	8.41435i	1.07735	−	1.07735i	0.0806003	−	0.996747i	$-0.474316\pi$
$61$	8.41435	−	8.41435i	1.07735	−	1.07735i	0.996747	−	0.0806003i	$-0.0256837\pi$
$62$	−0.710520	−	0.710520i	−0.0902361	−	0.0902361i
$63$	0.480117	−	0.480117i	0.0604891	−	0.0604891i
$64$	2.49567			0.311959
$65$		0			0
$66$		−	0.0746007i		−	0.00918271i
$67$		−	5.79776i		−	0.708309i	−0.935187	−	0.354154i	$-0.884769\pi$
$67$		−	5.79776i		−	0.708309i	0.935187	−	0.354154i	$-0.115231\pi$
$68$	1.10609	+	3.23876i	0.134134	+	0.392757i
$69$	−4.96765			−0.598035
$70$		0			0
$71$	−3.84845	−	3.84845i	−0.456727	−	0.456727i	0.440853	−	0.897580i	$-0.354676\pi$
$71$	−3.84845	−	3.84845i	−0.456727	−	0.456727i	−0.897580	+	0.440853i	$0.854676\pi$
$72$			0.490224i			0.0577735i
$73$	−2.88624	+	2.88624i	−0.337809	+	0.337809i	−0.855542	−	0.517733i	$-0.826776\pi$
$73$	−2.88624	+	2.88624i	−0.337809	+	0.337809i	0.517733	+	0.855542i	$0.326776\pi$
$74$	12.6255	−	12.6255i	1.46768	−	1.46768i
$75$		0			0
$76$		−	0.500644i		−	0.0574278i
$77$	−0.0670647			−0.00764274
$78$	−7.77972	−	7.77972i	−0.880880	−	0.880880i
$79$	−9.68618	+	9.68618i	−1.08978	+	1.08978i	−0.0942295	+	0.995550i	$0.530039\pi$
$79$	−9.68618	+	9.68618i	−1.08978	+	1.08978i	−0.995550	+	0.0942295i	$0.969961\pi$
$80$		0			0
$81$	9.68519			1.07613
$82$	8.53214	−	8.53214i	0.942217	−	0.942217i
$83$	−12.1804			−1.33697			−0.668486	−	0.743725i	$-0.733057\pi$
$83$	−12.1804			−1.33697			−0.668486	+	0.743725i	$0.733057\pi$
$84$	−4.07867			−0.445019
$85$		0			0
$86$	20.2414			2.18269
$87$	7.68523			0.823944
$88$	0.0342382	−	0.0342382i	0.00364981	−	0.00364981i
$89$	7.11750			0.754453			0.377227	−	0.926121i	$-0.376878\pi$
$89$	7.11750			0.754453			0.377227	+	0.926121i	$0.376878\pi$
$90$		0			0
$91$	−6.99384	+	6.99384i	−0.733153	+	0.733153i
$92$	1.61758	+	1.61758i	0.168644	+	0.168644i
$93$	1.07665			0.111643
$94$			18.6583i			1.92446i
$95$		0			0
$96$	5.64188	−	5.64188i	0.575821	−	0.575821i
$97$	5.01796	−	5.01796i	0.509496	−	0.509496i	−0.404876	−	0.914372i	$-0.632685\pi$
$97$	5.01796	−	5.01796i	0.509496	−	0.509496i	0.914372	+	0.404876i	$0.132685\pi$
$98$			0.725372i			0.0732737i
$99$	0.00433295	+	0.00433295i	0.000435478	+	0.000435478i
$100$		0			0
$101$	16.9936			1.69093			0.845464	−	0.534033i	$-0.179324\pi$
$101$	16.9936			1.69093			0.845464	+	0.534033i	$0.179324\pi$
$102$	−11.2235	−	5.50904i	−1.11129	−	0.545476i
$103$		−	2.34537i		−	0.231096i	−0.993302	−	0.115548i	$-0.963138\pi$
$103$		−	2.34537i		−	0.231096i	0.993302	−	0.115548i	$-0.0368624\pi$
$104$		−	7.14106i		−	0.700239i
$105$		0			0
$106$	−3.46041			−0.336105
$107$	−2.41794	+	2.41794i	−0.233751	+	0.233751i	−0.814257	−	0.580505i	$-0.802855\pi$
$107$	−2.41794	+	2.41794i	−0.233751	+	0.233751i	0.580505	+	0.814257i	$0.302855\pi$
$108$	−2.91040	−	2.91040i	−0.280054	−	0.280054i
$109$	4.01187	−	4.01187i	0.384267	−	0.384267i	−0.488370	−	0.872637i	$-0.662408\pi$
$109$	4.01187	−	4.01187i	0.384267	−	0.384267i	0.872637	+	0.488370i	$0.162408\pi$
$110$		0			0
$111$			19.1313i			1.81586i
$112$	−9.58227	−	9.58227i	−0.905439	−	0.905439i
$113$	−14.2494	−	14.2494i	−1.34047	−	1.34047i	−0.895591	−	0.444878i	$-0.853247\pi$
$113$	−14.2494	−	14.2494i	−1.34047	−	1.34047i	−0.444878	−	0.895591i	$-0.646753\pi$
$114$	1.29325	+	1.29325i	0.121124	+	0.121124i
$115$		0			0
$116$	−2.50249	−	2.50249i	−0.232350	−	0.232350i
$117$	0.903722			0.0835491
$118$			1.55917i			0.143533i
$119$	−4.95253	+	10.0897i	−0.453997	+	0.924924i
$120$		0			0
$121$			10.9994i			0.999945i
$122$	14.1553	−	14.1553i	1.28156	−	1.28156i
$123$			12.9287i			1.16574i
$124$	−0.350581	−	0.350581i	−0.0314831	−	0.0314831i
$125$		0			0
$126$	0.807691	−	0.807691i	0.0719548	−	0.0719548i
$127$	−19.9852			−1.77340			−0.886699	−	0.462347i	$-0.847007\pi$
$127$	−19.9852			−1.77340			−0.886699	+	0.462347i	$0.847007\pi$
$128$	13.0514			1.15359
$129$	−15.3359	+	15.3359i	−1.35025	+	1.35025i
$130$		0			0
$131$	7.54509	+	7.54509i	0.659217	+	0.659217i	0.955195	−	0.295978i	$-0.0956454\pi$
$131$	7.54509	+	7.54509i	0.659217	+	0.659217i	−0.295978	+	0.955195i	$0.595645\pi$
$132$		−	0.0368091i		−	0.00320382i
$133$	1.16261	−	1.16261i	0.100811	−	0.100811i
$134$		−	9.75344i		−	0.842569i
$135$		0			0
$136$	−2.62267	−	7.67945i	−0.224892	−	0.658508i
$137$			16.5098i			1.41053i	0.708946	+	0.705263i	$0.249171\pi$
$137$			16.5098i			1.41053i	−0.708946	+	0.705263i	$0.750829\pi$
$138$	−8.35698			−0.711393
$139$	7.41833	+	7.41833i	0.629214	+	0.629214i	0.947870	−	0.318656i	$-0.103232\pi$
$139$	7.41833	+	7.41833i	0.629214	+	0.629214i	−0.318656	+	0.947870i	$0.603232\pi$
$140$		0			0
$141$	−14.1364	−	14.1364i	−1.19050	−	1.19050i
$142$	−6.47416	−	6.47416i	−0.543300	−	0.543300i
$143$	−0.0631178	−	0.0631178i	−0.00527817	−	0.00527817i
$144$			1.23819i			0.103183i
$145$		0			0
$146$	−4.85547	+	4.85547i	−0.401841	+	0.401841i
$147$	−0.549576	−	0.549576i	−0.0453283	−	0.0453283i
$148$	6.22958	−	6.22958i	0.512069	−	0.512069i
$149$	−8.76888			−0.718375			−0.359187	−	0.933266i	$-0.616946\pi$
$149$	−8.76888			−0.718375			−0.359187	+	0.933266i	$0.616946\pi$
$150$		0			0
$151$		−	4.09736i		−	0.333438i	−0.986004	−	0.166719i	$-0.946683\pi$
$151$		−	4.09736i		−	0.333438i	0.986004	−	0.166719i	$-0.0533173\pi$
$152$			1.18708i			0.0962850i
$153$	0.971857	−	0.331907i	0.0785700	−	0.0268331i
$154$	−0.112822			−0.00909142
$155$		0			0
$156$	−3.83863	−	3.83863i	−0.307336	−	0.307336i
$157$			18.3271i			1.46266i	0.682022	+	0.731331i	$0.261101\pi$
$157$			18.3271i			1.46266i	−0.682022	+	0.731331i	$0.738899\pi$
$158$	−16.2948	+	16.2948i	−1.29635	+	1.29635i
$159$	2.62177	−	2.62177i	0.207920	−	0.207920i
$160$		0			0
$161$			7.51278i			0.592090i
$162$	16.2932			1.28011
$163$	9.33881	+	9.33881i	0.731472	+	0.731472i	0.970911	−	0.239439i	$-0.0769635\pi$
$163$	9.33881	+	9.33881i	0.731472	+	0.731472i	−0.239439	+	0.970911i	$0.576964\pi$
$164$	4.20988	−	4.20988i	0.328736	−	0.328736i
$165$		0			0
$166$	−20.4908			−1.59039
$167$	−3.01070	+	3.01070i	−0.232975	+	0.232975i	−0.813933	−	0.580958i	$-0.802678\pi$
$167$	−3.01070	+	3.01070i	−0.232975	+	0.232975i	0.580958	+	0.813933i	$0.302678\pi$
$168$	9.67098			0.746132
$169$	−0.164450			−0.0126500
$170$		0			0
$171$	−0.150229			−0.0114883
$172$	9.98740			0.761532
$173$	8.98548	−	8.98548i	0.683153	−	0.683153i	−0.277556	−	0.960709i	$-0.589524\pi$
$173$	8.98548	−	8.98548i	0.683153	−	0.683153i	0.960709	+	0.277556i	$0.0895244\pi$
$174$	12.9287			0.980122
$175$		0			0
$176$	0.0864778	−	0.0864778i	0.00651851	−	0.00651851i
$177$	−1.18130	−	1.18130i	−0.0887919	−	0.0887919i
$178$	11.9736			0.897460
$179$		−	11.0612i		−	0.826752i	−0.910560	−	0.413376i	$-0.864349\pi$
$179$		−	11.0612i		−	0.826752i	0.910560	−	0.413376i	$-0.135651\pi$
$180$		0			0
$181$	13.4949	−	13.4949i	1.00307	−	1.00307i	0.00306987	−	0.999995i	$-0.499023\pi$
$181$	13.4949	−	13.4949i	1.00307	−	1.00307i	0.999995	−	0.00306987i	$-0.000977172\pi$
$182$	−11.7656	+	11.7656i	−0.872123	+	0.872123i
$183$			21.4494i			1.58559i
$184$	−3.83546	−	3.83546i	−0.282754	−	0.282754i
$185$		0			0
$186$	1.81122			0.132805
$187$	−0.0910575	−	0.0446954i	−0.00665878	−	0.00326845i
$188$			9.20629i			0.671438i
$189$		−	13.5172i		−	0.983233i
$190$		0			0
$191$	−16.5896			−1.20038			−0.600190	−	0.799857i	$-0.704909\pi$
$191$	−16.5896			−1.20038			−0.600190	+	0.799857i	$0.704909\pi$
$192$	−3.18092	+	3.18092i	−0.229563	+	0.229563i
$193$	−5.95630	−	5.95630i	−0.428744	−	0.428744i	0.459457	−	0.888200i	$-0.348044\pi$
$193$	−5.95630	−	5.95630i	−0.428744	−	0.428744i	−0.888200	+	0.459457i	$0.848044\pi$
$194$	8.44160	−	8.44160i	0.606071	−	0.606071i
$195$		0			0
$196$			0.357909i			0.0255649i
$197$	−15.1996	−	15.1996i	−1.08292	−	1.08292i	−0.996235	−	0.0866884i	$-0.972372\pi$
$197$	−15.1996	−	15.1996i	−1.08292	−	1.08292i	−0.0866884	−	0.996235i	$-0.527628\pi$
$198$	0.00728923	+	0.00728923i	0.000518023	+	0.000518023i
$199$	6.39953	+	6.39953i	0.453651	+	0.453651i	0.896564	−	0.442914i	$-0.146055\pi$
$199$	6.39953	+	6.39953i	0.453651	+	0.453651i	−0.442914	+	0.896564i	$0.646055\pi$
$200$		0			0
$201$	7.38967	+	7.38967i	0.521227	+	0.521227i
$202$	28.5880			2.01144
$203$		−	11.6227i		−	0.815752i
$204$	−5.53784	−	2.71824i	−0.387726	−	0.190315i
$205$		0			0
$206$		−	3.94556i		−	0.274900i
$207$	0.485389	−	0.485389i	0.0337369	−	0.0337369i
$208$		−	18.0366i		−	1.25062i
$209$	0.0104923	+	0.0104923i	0.000725765	+	0.000725765i
$210$		0			0
$211$	−0.462382	+	0.462382i	−0.0318317	+	0.0318317i	−0.722843	−	0.691012i	$-0.757165\pi$
$211$	−0.462382	+	0.462382i	−0.0318317	+	0.0318317i	0.691012	+	0.722843i	$0.257165\pi$
$212$	−1.70742			−0.117266
$213$	9.81027			0.672188
$214$	−4.06765	+	4.06765i	−0.278059	+	0.278059i
$215$		0			0
$216$	6.90088	+	6.90088i	0.469546	+	0.469546i
$217$		−	1.62826i		−	0.110533i
$218$	6.74908	−	6.74908i	0.457105	−	0.457105i
$219$		−	7.35746i		−	0.497171i
$220$		0			0
$221$	−14.1570	+	4.83486i	−0.952301	+	0.325228i
$222$			32.1842i			2.16006i
$223$	23.6081			1.58092			0.790458	−	0.612516i	$-0.209843\pi$
$223$	23.6081			1.58092			0.790458	+	0.612516i	$0.209843\pi$
$224$	−8.53243	−	8.53243i	−0.570097	−	0.570097i
$225$		0			0
$226$	−23.9714	−	23.9714i	−1.59456	−	1.59456i
$227$	13.1516	+	13.1516i	0.872905	+	0.872905i	0.992788	−	0.119883i	$-0.0382519\pi$
$227$	13.1516	+	13.1516i	0.872905	+	0.872905i	−0.119883	+	0.992788i	$0.538252\pi$
$228$	0.638107	+	0.638107i	0.0422597	+	0.0422597i
$229$			1.08531i			0.0717195i	0.999357	+	0.0358598i	$0.0114170\pi$
$229$			1.08531i			0.0717195i	−0.999357	+	0.0358598i	$0.988583\pi$
$230$		0			0
$231$	0.0854790	−	0.0854790i	0.00562410	−	0.00562410i
$232$	5.93367	+	5.93367i	0.389565	+	0.389565i
$233$	7.35221	−	7.35221i	0.481660	−	0.481660i	−0.424002	−	0.905661i	$-0.639375\pi$
$233$	7.35221	−	7.35221i	0.481660	−	0.481660i	0.905661	+	0.424002i	$0.139375\pi$
$234$	1.52031			0.0993859
$235$		0			0
$236$			0.769315i			0.0500782i
$237$		−	24.6915i		−	1.60388i
$238$	−8.33153	+	16.9737i	−0.540053	+	1.10024i
$239$	12.9823			0.839758			0.419879	−	0.907580i	$-0.362072\pi$
$239$	12.9823			0.839758			0.419879	+	0.907580i	$0.362072\pi$
$240$		0			0
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	0.355091	−	0.934832i	$-0.384450\pi$
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	−0.934832	+	0.355091i	$0.884450\pi$
$242$			18.5040i			1.18948i
$243$	−1.82573	+	1.82573i	−0.117120	+	0.117120i
$244$	6.98442	−	6.98442i	0.447131	−	0.447131i
$245$		0			0
$246$			21.7497i			1.38671i
$247$	2.18837			0.139243
$248$	0.831266	+	0.831266i	0.0527854	+	0.0527854i
$249$	15.5248	−	15.5248i	0.983845	−	0.983845i
$250$		0			0
$251$	−24.0485			−1.51793			−0.758964	−	0.651133i	$-0.774294\pi$
$251$	−24.0485			−1.51793			−0.758964	+	0.651133i	$0.774294\pi$
$252$	0.398526	−	0.398526i	0.0251048	−	0.0251048i
$253$	−0.0678011			−0.00426262
$254$	−33.6206			−2.10955
$255$		0			0
$256$	16.9647			1.06029
$257$	−15.1812			−0.946978			−0.473489	−	0.880800i	$-0.657006\pi$
$257$	−15.1812			−0.946978			−0.473489	+	0.880800i	$0.657006\pi$
$258$	−25.7992	+	25.7992i	−1.60619	+	1.60619i
$259$	28.9330			1.79781
$260$		0			0
$261$	−0.750923	+	0.750923i	−0.0464810	+	0.0464810i
$262$	12.6929	+	12.6929i	0.784172	+	0.784172i
$263$	−12.3845			−0.763662			−0.381831	−	0.924232i	$-0.624706\pi$
$263$	−12.3845			−0.763662			−0.381831	+	0.924232i	$0.624706\pi$
$264$			0.0872783i			0.00537161i
$265$		0			0
$266$	1.95583	−	1.95583i	0.119920	−	0.119920i
$267$	−9.07178	+	9.07178i	−0.555184	+	0.555184i
$268$		−	4.81249i		−	0.293970i
$269$	6.97115	+	6.97115i	0.425039	+	0.425039i	0.886934	−	0.461896i	$-0.152831\pi$
$269$	6.97115	+	6.97115i	0.425039	+	0.425039i	−0.461896	+	0.886934i	$0.652831\pi$
$270$		0			0
$271$	−4.38049			−0.266096			−0.133048	−	0.991110i	$-0.542476\pi$
$271$	−4.38049			−0.266096			−0.133048	+	0.991110i	$0.542476\pi$
$272$	−6.62425	−	19.3965i	−0.401654	−	1.17609i
$273$		−	17.8283i		−	1.07902i
$274$			27.7740i			1.67789i
$275$		0			0
$276$	−4.12345			−0.248203
$277$	4.90350	−	4.90350i	0.294623	−	0.294623i	−0.544280	−	0.838903i	$-0.683197\pi$
$277$	4.90350	−	4.90350i	0.294623	−	0.294623i	0.838903	+	0.544280i	$0.183197\pi$
$278$	12.4797	+	12.4797i	0.748482	+	0.748482i
$279$	−0.105199	+	0.105199i	−0.00629810	+	0.00629810i
$280$		0			0
$281$		−	13.3453i		−	0.796113i	−0.917361	−	0.398056i	$-0.869685\pi$
$281$		−	13.3453i		−	0.796113i	0.917361	−	0.398056i	$-0.130315\pi$
$282$	−23.7814	−	23.7814i	−1.41616	−	1.41616i
$283$	4.23171	+	4.23171i	0.251549	+	0.251549i	0.821606	−	0.570056i	$-0.193079\pi$
$283$	4.23171	+	4.23171i	0.251549	+	0.251549i	−0.570056	+	0.821606i	$0.693079\pi$
$284$	−3.19445	−	3.19445i	−0.189555	−	0.189555i
$285$		0			0
$286$	−0.106182	−	0.106182i	−0.00627865	−	0.00627865i
$287$	19.5526			1.15415
$288$			1.10253i			0.0649674i
$289$	−13.4486	+	10.3988i	−0.791096	+	0.611692i
$290$		0			0
$291$			12.7915i			0.749852i
$292$	−2.39576	+	2.39576i	−0.140201	+	0.140201i
$293$			17.4231i			1.01787i	0.860806	+	0.508934i	$0.169960\pi$
$293$			17.4231i			1.01787i	−0.860806	+	0.508934i	$0.830040\pi$
$294$	−0.924540	−	0.924540i	−0.0539203	−	0.0539203i
$295$		0			0
$296$	−14.7710	+	14.7710i	−0.858548	+	0.858548i
$297$	0.121990			0.00707857
$298$	−14.7517			−0.854543
$299$	−7.07062	+	7.07062i	−0.408905	+	0.408905i
$300$		0			0
$301$	23.1930	+	23.1930i	1.33682	+	1.33682i
$302$		−	6.89289i		−	0.396641i
$303$	−21.6596	+	21.6596i	−1.24431	+	1.24431i
$304$			2.99829i			0.171964i
$305$		0			0
$306$	1.63493	−	0.558359i	0.0934629	−	0.0319193i
$307$			2.60778i			0.148834i	0.997227	+	0.0744169i	$0.0237096\pi$
$307$			2.60778i			0.148834i	−0.997227	+	0.0744169i	$0.976290\pi$
$308$	−0.0556678			−0.00317197
$309$	2.98935	+	2.98935i	0.170058	+	0.170058i
$310$		0			0
$311$	1.98182	+	1.98182i	0.112379	+	0.112379i	0.761060	−	0.648681i	$-0.224679\pi$
$311$	1.98182	+	1.98182i	0.112379	+	0.112379i	−0.648681	+	0.761060i	$0.724679\pi$
$312$	9.10181	+	9.10181i	0.515288	+	0.515288i
$313$	−8.06011	−	8.06011i	−0.455584	−	0.455584i	0.441619	−	0.897203i	$-0.354404\pi$
$313$	−8.06011	−	8.06011i	−0.455584	−	0.455584i	−0.897203	+	0.441619i	$0.854404\pi$
$314$			30.8313i			1.73991i
$315$		0			0
$316$	−8.04011	+	8.04011i	−0.452292	+	0.452292i
$317$	−15.0278	−	15.0278i	−0.844045	−	0.844045i	0.145337	−	0.989382i	$-0.453573\pi$
$317$	−15.0278	−	15.0278i	−0.844045	−	0.844045i	−0.989382	+	0.145337i	$0.953573\pi$
$318$	4.41055	−	4.41055i	0.247331	−	0.247331i
$319$	0.104892			0.00587282
$320$		0			0
$321$		−	6.16369i		−	0.344024i
$322$			12.6386i			0.704320i
$323$	2.35336	−	0.803714i	0.130944	−	0.0447198i
$324$	8.03929			0.446627
$325$		0			0
$326$	15.7105	+	15.7105i	0.870123	+	0.870123i
$327$			10.2268i			0.565546i
$328$	−9.98209	+	9.98209i	−0.551169	+	0.551169i
$329$	−21.3791	+	21.3791i	−1.17867	+	1.17867i
$330$		0			0
$331$			6.85020i			0.376521i	0.982119	+	0.188261i	$0.0602849\pi$
$331$			6.85020i			0.376521i	−0.982119	+	0.188261i	$0.939715\pi$
$332$	−10.1105			−0.554883
$333$	−1.86932	−	1.86932i	−0.102438	−	0.102438i
$334$	−5.06484	+	5.06484i	−0.277136	+	0.277136i
$335$		0			0
$336$	24.4266			1.33258
$337$	9.86609	−	9.86609i	0.537440	−	0.537440i	−0.385336	−	0.922776i	$-0.625914\pi$
$337$	9.86609	−	9.86609i	0.537440	−	0.537440i	0.922776	+	0.385336i	$0.125914\pi$
$338$	−0.276651			−0.0150478
$339$	36.3238			1.97284
$340$		0			0
$341$	0.0146946			0.000795759
$342$	−0.252726			−0.0136659
$343$	12.6620	−	12.6620i	0.683682	−	0.683682i
$344$	−23.6812			−1.27681
$345$		0			0
$346$	15.1161	−	15.1161i	0.812645	−	0.812645i
$347$	−9.99455	−	9.99455i	−0.536536	−	0.536536i	0.385974	−	0.922510i	$-0.373865\pi$
$347$	−9.99455	−	9.99455i	−0.536536	−	0.536536i	−0.922510	+	0.385974i	$0.873865\pi$
$348$	6.37921			0.341961
$349$		−	13.3019i		−	0.712036i	−0.934479	−	0.356018i	$-0.884134\pi$
$349$		−	13.3019i		−	0.712036i	0.934479	−	0.356018i	$-0.115866\pi$
$350$		0			0
$351$	12.7217	−	12.7217i	0.679034	−	0.679034i
$352$	0.0770032	−	0.0770032i	0.00410428	−	0.00410428i
$353$		−	6.86777i		−	0.365534i	−0.983156	−	0.182767i	$-0.941495\pi$
$353$		−	6.86777i		−	0.365534i	0.983156	−	0.182767i	$-0.0585054\pi$
$354$	−1.98727	−	1.98727i	−0.105622	−	0.105622i
$355$		0			0
$356$	5.90795			0.313121
$357$	−6.54774	−	19.1725i	−0.346543	−	1.01471i
$358$		−	18.6080i		−	0.983464i
$359$		−	30.8917i		−	1.63040i	−0.579178	−	0.815201i	$-0.696627\pi$
$359$		−	30.8917i		−	1.63040i	0.579178	−	0.815201i	$-0.303373\pi$
$360$		0			0
$361$	18.6362			0.980854
$362$	22.7021	−	22.7021i	1.19320	−	1.19320i
$363$	−14.0195	−	14.0195i	−0.735835	−	0.735835i
$364$	−5.80530	+	5.80530i	−0.304281	+	0.304281i
$365$		0			0
$366$			36.0839i			1.88613i
$367$	2.13492	+	2.13492i	0.111442	+	0.111442i	0.760629	−	0.649187i	$-0.224891\pi$
$367$	2.13492	+	2.13492i	0.111442	+	0.111442i	−0.649187	+	0.760629i	$0.724891\pi$
$368$	−9.68748	−	9.68748i	−0.504995	−	0.504995i
$369$	−1.26326	−	1.26326i	−0.0657628	−	0.0657628i
$370$		0			0
$371$	−3.96501	−	3.96501i	−0.205853	−	0.205853i
$372$	0.893682			0.0463353
$373$		−	6.62453i		−	0.343005i	−0.985184	−	0.171502i	$-0.945138\pi$
$373$		−	6.62453i		−	0.343005i	0.985184	−	0.171502i	$-0.0548622\pi$
$374$	−0.153184	−	0.0751901i	−0.00792096	−	0.00388799i
$375$		0			0
$376$		−	21.8291i		−	1.12575i
$377$	10.9386	−	10.9386i	0.563369	−	0.563369i
$378$		−	22.7397i		−	1.16961i
$379$	−9.47649	−	9.47649i	−0.486774	−	0.486774i	0.420512	−	0.907287i	$-0.361850\pi$
$379$	−9.47649	−	9.47649i	−0.486774	−	0.486774i	−0.907287	+	0.420512i	$0.861850\pi$
$380$		0			0
$381$	25.4726	−	25.4726i	1.30500	−	1.30500i
$382$	−27.9083			−1.42791
$383$	0.0616324			0.00314927			0.00157463	−	0.999999i	$-0.499499\pi$
$383$	0.0616324			0.00314927			0.00157463	+	0.999999i	$0.499499\pi$
$384$	−16.6349	+	16.6349i	−0.848898	+	0.848898i
$385$		0			0
$386$	−10.0201	−	10.0201i	−0.510012	−	0.510012i
$387$		−	2.99693i		−	0.152342i
$388$	4.16521	−	4.16521i	0.211456	−	0.211456i
$389$		−	2.20403i		−	0.111749i	−0.998438	−	0.0558743i	$-0.982205\pi$
$389$		−	2.20403i		−	0.111749i	0.998438	−	0.0558743i	$-0.0177946\pi$
$390$		0			0
$391$	−5.00690	+	10.2005i	−0.253210	+	0.515862i
$392$		−	0.848642i		−	0.0428629i
$393$	−19.2335			−0.970204
$394$	−25.5699	−	25.5699i	−1.28819	−	1.28819i
$395$		0			0
$396$	0.00359661	+	0.00359661i	0.000180736	+	0.000180736i
$397$	8.39588	+	8.39588i	0.421377	+	0.421377i	0.885678	−	0.464301i	$-0.153694\pi$
$397$	8.39588	+	8.39588i	0.421377	+	0.421377i	−0.464301	+	0.885678i	$0.653694\pi$
$398$	10.7658	+	10.7658i	0.539640	+	0.539640i
$399$			2.96366i			0.148368i
$400$		0			0
$401$	−3.05446	+	3.05446i	−0.152532	+	0.152532i	−0.779248	−	0.626716i	$-0.784399\pi$
$401$	−3.05446	+	3.05446i	−0.152532	+	0.152532i	0.626716	+	0.779248i	$0.284399\pi$
$402$	12.4315	+	12.4315i	0.620026	+	0.620026i
$403$	1.53243	−	1.53243i	0.0763356	−	0.0763356i
$404$	14.1057			0.701786
$405$		0			0
$406$		−	19.5526i		−	0.970378i
$407$			0.261114i			0.0129429i
$408$	13.1308	+	6.44524i	0.650072	+	0.319087i
$409$	39.0514			1.93097			0.965485	−	0.260459i	$-0.0838739\pi$
$409$	39.0514			1.93097			0.965485	+	0.260459i	$0.0838739\pi$
$410$		0			0
$411$	−21.0429	−	21.0429i	−1.03797	−	1.03797i
$412$		−	1.94680i		−	0.0959118i
$413$	−1.78652	+	1.78652i	−0.0879091	+	0.0879091i
$414$	0.816559	−	0.816559i	0.0401317	−	0.0401317i
$415$		0			0
$416$		−	16.0605i		−	0.787432i
$417$	−18.9104			−0.926047
$418$	0.0176509	+	0.0176509i	0.000863334	+	0.000863334i
$419$	1.36075	−	1.36075i	0.0664769	−	0.0664769i	−0.673087	−	0.739564i	$-0.735032\pi$
$419$	1.36075	−	1.36075i	0.0664769	−	0.0664769i	0.739564	+	0.673087i	$0.235032\pi$
$420$		0			0
$421$	−15.5179			−0.756297			−0.378148	−	0.925745i	$-0.623439\pi$
$421$	−15.5179			−0.756297			−0.378148	+	0.925745i	$0.623439\pi$
$422$	−0.777856	+	0.777856i	−0.0378654	+	0.0378654i
$423$	2.76254			0.134319
$424$	4.04847			0.196611
$425$		0			0
$426$	16.5036			0.799602
$427$	32.4388			1.56982
$428$	−2.00704	+	2.00704i	−0.0970138	+	0.0970138i
$429$	0.160896			0.00776816
$430$		0			0
$431$	5.44688	−	5.44688i	0.262367	−	0.262367i	−0.563648	−	0.826015i	$-0.690603\pi$
$431$	5.44688	−	5.44688i	0.262367	−	0.262367i	0.826015	+	0.563648i	$0.190603\pi$
$432$	17.4300	+	17.4300i	0.838602	+	0.838602i
$433$	2.45651			0.118052			0.0590262	−	0.998256i	$-0.481200\pi$
$433$	2.45651			0.118052			0.0590262	+	0.998256i	$0.481200\pi$
$434$		−	2.73918i		−	0.131485i
$435$		0			0
$436$	3.33009	−	3.33009i	0.159483	−	0.159483i
$437$	1.17537	−	1.17537i	0.0562257	−	0.0562257i
$438$		−	12.3773i		−	0.591410i
$439$	−28.2107	−	28.2107i	−1.34642	−	1.34642i	−0.889513	−	0.456910i	$-0.848956\pi$
$439$	−28.2107	−	28.2107i	−1.34642	−	1.34642i	−0.456910	−	0.889513i	$-0.651044\pi$
$440$		0			0
$441$	0.107398			0.00511419
$442$	−23.8160	+	8.13358i	−1.13281	+	0.386875i
$443$		−	29.7806i		−	1.41492i	−0.706754	−	0.707460i	$-0.749841\pi$
$443$		−	29.7806i		−	1.41492i	0.706754	−	0.707460i	$-0.250159\pi$
$444$			15.8801i			0.753637i
$445$		0			0
$446$	39.7154			1.88058
$447$	11.1766	−	11.1766i	0.528634	−	0.528634i
$448$	4.81062	+	4.81062i	0.227281	+	0.227281i
$449$	−7.26221	+	7.26221i	−0.342725	+	0.342725i	−0.857391	−	0.514666i	$-0.827916\pi$
$449$	−7.26221	+	7.26221i	−0.342725	+	0.342725i	0.514666	+	0.857391i	$0.327916\pi$
$450$		0			0
$451$			0.176458i			0.00830906i
$452$	−11.8278	−	11.8278i	−0.556335	−	0.556335i
$453$	5.22238	+	5.22238i	0.245369	+	0.245369i
$454$	22.1247	+	22.1247i	1.03836	+	1.03836i
$455$		0			0
$456$	−1.51302	−	1.51302i	−0.0708538	−	0.0708538i
$457$	−20.6404			−0.965519			−0.482760	−	0.875753i	$-0.660366\pi$
$457$	−20.6404			−0.965519			−0.482760	+	0.875753i	$0.660366\pi$
$458$			1.82580i			0.0853140i
$459$	9.00858	−	18.3531i	0.420484	−	0.856648i
$460$		0			0
$461$		−	9.20938i		−	0.428924i	−0.976732	−	0.214462i	$-0.931200\pi$
$461$		−	9.20938i		−	0.428924i	0.976732	−	0.214462i	$-0.0687998\pi$
$462$	0.143799	−	0.143799i	0.00669015	−	0.00669015i
$463$			19.1899i			0.891830i	0.895075	+	0.445915i	$0.147122\pi$
$463$			19.1899i			0.891830i	−0.895075	+	0.445915i	$0.852878\pi$
$464$	14.9871	+	14.9871i	0.695757	+	0.695757i
$465$		0			0
$466$	12.3685	−	12.3685i	0.572958	−	0.572958i
$467$	−12.8589			−0.595037			−0.297519	−	0.954716i	$-0.596159\pi$
$467$	−12.8589			−0.595037			−0.297519	+	0.954716i	$0.596159\pi$
$468$	0.750144			0.0346754
$469$	11.1757	−	11.1757i	0.516045	−	0.516045i
$470$		0			0
$471$	−23.3593	−	23.3593i	−1.07634	−	1.07634i
$472$		−	1.82413i		−	0.0839625i
$473$	−0.209312	+	0.209312i	−0.00962415	+	0.00962415i
$474$		−	41.5380i		−	1.90790i
$475$		0			0
$476$	−4.11090	+	8.37508i	−0.188423	+	0.383871i
$477$			0.512346i			0.0234587i
$478$	21.8399			0.998935
$479$	−14.9104	−	14.9104i	−0.681274	−	0.681274i	0.279013	−	0.960287i	$-0.409993\pi$
$479$	−14.9104	−	14.9104i	−0.681274	−	0.681274i	−0.960287	+	0.279013i	$0.909993\pi$
$480$		0			0
$481$	27.2302	+	27.2302i	1.24159	+	1.24159i
$482$	−15.1405	−	15.1405i	−0.689631	−	0.689631i
$483$	−9.57559	−	9.57559i	−0.435704	−	0.435704i
$484$			9.13016i			0.415007i
$485$		0			0
$486$	−3.07138	+	3.07138i	−0.139321	+	0.139321i
$487$	20.8708	+	20.8708i	0.945745	+	0.945745i	0.998602	−	0.0528575i	$-0.0168329\pi$
$487$	20.8708	+	20.8708i	0.945745	+	0.945745i	−0.0528575	+	0.998602i	$0.516833\pi$
$488$	−16.5608	+	16.5608i	−0.749673	+	0.749673i
$489$	−23.8060			−1.07655
$490$		0			0
$491$		−	8.36668i		−	0.377583i	−0.982017	−	0.188792i	$-0.939543\pi$
$491$		−	8.36668i		−	0.377583i	0.982017	−	0.188792i	$-0.0604571\pi$
$492$			10.7316i			0.483818i
$493$	7.74596	−	15.7807i	0.348860	−	0.710729i
$494$	3.68144			0.165636
$495$		0			0
$496$	2.09958	+	2.09958i	0.0942740	+	0.0942740i
$497$		−	14.8364i		−	0.665506i
$498$	26.1170	−	26.1170i	1.17033	−	1.17033i
$499$	−7.77797	+	7.77797i	−0.348190	+	0.348190i	−0.859435	−	0.511245i	$-0.829184\pi$
$499$	−7.77797	+	7.77797i	−0.348190	+	0.348190i	0.511245	+	0.859435i	$0.329184\pi$
$500$		0			0
$501$		−	7.67473i		−	0.342882i
$502$	−40.4563			−1.80565
$503$	8.55845	+	8.55845i	0.381603	+	0.381603i	0.871679	−	0.490077i	$-0.163031\pi$
$503$	8.55845	+	8.55845i	0.381603	+	0.381603i	−0.490077	+	0.871679i	$0.663031\pi$
$504$	−0.944950	+	0.944950i	−0.0420914	+	0.0420914i
$505$		0			0
$506$	−0.114060			−0.00507060
$507$	0.209604	−	0.209604i	0.00930884	−	0.00930884i
$508$	−16.5889			−0.736014
$509$	−10.2914			−0.456157			−0.228079	−	0.973643i	$-0.573244\pi$
$509$	−10.2914			−0.456157			−0.228079	+	0.973643i	$0.573244\pi$
$510$		0			0
$511$	−11.1270			−0.492228
$512$	2.43660			0.107684
$513$	−2.11477	+	2.11477i	−0.0933692	+	0.0933692i
$514$	−25.5390			−1.12648
$515$		0			0
$516$	−12.7297	+	12.7297i	−0.560393	+	0.560393i
$517$	−0.192941	−	0.192941i	−0.00848555	−	0.00848555i
$518$	48.6733			2.13858
$519$			22.9053i			1.00543i
$520$		0			0
$521$	−25.0222	+	25.0222i	−1.09624	+	1.09624i	−0.101396	+	0.994846i	$0.532331\pi$
$521$	−25.0222	+	25.0222i	−1.09624	+	1.09624i	−0.994846	+	0.101396i	$0.967669\pi$
$522$	−1.26326	+	1.26326i	−0.0552915	+	0.0552915i
$523$		−	41.9546i		−	1.83455i	−0.398259	−	0.917273i	$-0.630385\pi$
$523$		−	41.9546i		−	1.83455i	0.398259	−	0.917273i	$-0.369615\pi$
$524$	6.26288	+	6.26288i	0.273595	+	0.273595i
$525$		0			0
$526$	−20.8342			−0.908414
$527$	1.08515	−	2.21077i	0.0472700	−	0.0963027i
$528$			0.220445i			0.00959362i
$529$		−	15.4047i		−	0.669771i
$530$		0			0
$531$	0.230849			0.0100180
$532$	0.965034	−	0.965034i	0.0418395	−	0.0418395i
$533$	18.4018	+	18.4018i	0.797072	+	0.797072i
$534$	−15.2613	+	15.2613i	−0.660419	+	0.660419i
$535$		0			0
$536$			11.4109i			0.492878i
$537$	14.0983	+	14.0983i	0.608387	+	0.608387i
$538$	11.7274	+	11.7274i	0.505605	+	0.505605i
$539$	−0.00750090	−	0.00750090i	−0.000323087	−	0.000323087i
$540$		0			0
$541$	16.3343	+	16.3343i	0.702266	+	0.702266i	0.964897	−	0.262630i	$-0.0845899\pi$
$541$	16.3343	+	16.3343i	0.702266	+	0.702266i	−0.262630	+	0.964897i	$0.584590\pi$
$542$	−7.36920			−0.316534
$543$			34.4004i			1.47626i
$544$	−5.89849	−	17.2714i	−0.252896	−	0.740505i
$545$		0			0
$546$		−	29.9922i		−	1.28355i
$547$	22.5367	−	22.5367i	0.963600	−	0.963600i	−0.0357608	−	0.999360i	$-0.511385\pi$
$547$	22.5367	−	22.5367i	0.963600	−	0.963600i	0.999360	+	0.0357608i	$0.0113855\pi$
$548$			13.7041i			0.585411i
$549$	−2.09582	−	2.09582i	−0.0894474	−	0.0894474i
$550$		0			0
$551$	−1.81837	+	1.81837i	−0.0774650	+	0.0774650i
$552$	9.77716			0.416144
$553$	−37.3419			−1.58794
$554$	8.24906	−	8.24906i	0.350469	−	0.350469i
$555$		0			0
$556$	6.15766	+	6.15766i	0.261143	+	0.261143i
$557$			4.04822i			0.171528i	0.996315	+	0.0857642i	$0.0273332\pi$
$557$			4.04822i			0.171528i	−0.996315	+	0.0857642i	$0.972667\pi$
$558$	−0.176974	+	0.176974i	−0.00749191	+	0.00749191i
$559$			43.6560i			1.84645i
$560$		0			0
$561$	0.173027	−	0.0590919i	0.00730521	−	0.00249486i
$562$		−	22.4505i		−	0.947016i
$563$	−14.7608			−0.622095			−0.311047	−	0.950394i	$-0.600680\pi$
$563$	−14.7608			−0.622095			−0.311047	+	0.950394i	$0.600680\pi$
$564$	−11.7341	−	11.7341i	−0.494094	−	0.494094i
$565$		0			0
$566$	7.11891	+	7.11891i	0.299230	+	0.299230i
$567$	18.6691	+	18.6691i	0.784026	+	0.784026i
$568$	7.57438	+	7.57438i	0.317814	+	0.317814i
$569$			23.9741i			1.00505i	0.864563	+	0.502524i	$0.167595\pi$
$569$			23.9741i			1.00505i	−0.864563	+	0.502524i	$0.832405\pi$
$570$		0			0
$571$	−19.0184	+	19.0184i	−0.795894	+	0.795894i	−0.982445	−	0.186551i	$-0.940269\pi$
$571$	−19.0184	+	19.0184i	−0.795894	+	0.795894i	0.186551	+	0.982445i	$0.440269\pi$
$572$	−0.0523915	−	0.0523915i	−0.00219060	−	0.00219060i
$573$	21.1447	−	21.1447i	0.883331	−	0.883331i
$574$	32.8929			1.37292
$575$		0			0
$576$		−	0.621614i		−	0.0259006i
$577$		−	22.7542i		−	0.947271i	−0.880721	−	0.473635i	$-0.842941\pi$
$577$		−	22.7542i		−	0.947271i	0.880721	−	0.473635i	$-0.157059\pi$
$578$	−22.6244	+	17.4936i	−0.941049	+	0.727638i
$579$	15.1835			0.631004
$580$		0			0
$581$	−23.4788	−	23.4788i	−0.974063	−	0.974063i
$582$			21.5189i			0.891986i
$583$	0.0357833	−	0.0357833i	0.00148199	−	0.00148199i
$584$	5.68060	−	5.68060i	0.235065	−	0.235065i
$585$		0			0
$586$			29.3105i			1.21080i
$587$	−34.0841			−1.40680			−0.703401	−	0.710794i	$-0.748336\pi$
$587$	−34.0841			−1.40680			−0.703401	+	0.710794i	$0.748336\pi$
$588$	−0.456182	−	0.456182i	−0.0188126	−	0.0188126i
$589$	−0.254740	+	0.254740i	−0.0104964	+	0.0104964i
$590$		0			0
$591$	38.7459			1.59379
$592$	−37.3081	+	37.3081i	−1.53336	+	1.53336i
$593$	−45.2821			−1.85951			−0.929757	−	0.368174i	$-0.879983\pi$
$593$	−45.2821			−1.85951			−0.929757	+	0.368174i	$0.879983\pi$
$594$	0.205221			0.00842031
$595$		0			0
$596$	−7.27870			−0.298147
$597$	−16.3133			−0.667661
$598$	−11.8948	+	11.8948i	−0.486413	+	0.486413i
$599$	−13.2118			−0.539818			−0.269909	−	0.962886i	$-0.586994\pi$
$599$	−13.2118			−0.539818			−0.269909	+	0.962886i	$0.586994\pi$
$600$		0			0
$601$	−10.8424	+	10.8424i	−0.442271	+	0.442271i	−0.892774	−	0.450504i	$-0.851244\pi$
$601$	−10.8424	+	10.8424i	−0.442271	+	0.442271i	0.450504	+	0.892774i	$0.351244\pi$
$602$	39.0171	+	39.0171i	1.59022	+	1.59022i
$603$	−1.44409			−0.0588078
$604$		−	3.40105i		−	0.138387i
$605$		0			0
$606$	−36.4375	+	36.4375i	−1.48017	+	1.48017i
$607$	−6.57986	+	6.57986i	−0.267068	+	0.267068i	−0.827918	−	0.560849i	$-0.810475\pi$
$607$	−6.57986	+	6.57986i	−0.267068	+	0.267068i	0.560849	+	0.827918i	$0.310475\pi$
$608$			2.66979i			0.108274i
$609$	14.8140	+	14.8140i	0.600292	+	0.600292i
$610$		0			0
$611$	−40.2417			−1.62800
$612$	0.806700	−	0.275502i	0.0326089	−	0.0111365i
$613$			24.3891i			0.985065i	0.870294	+	0.492533i	$0.163929\pi$
$613$			24.3891i			0.985065i	−0.870294	+	0.492533i	$0.836071\pi$
$614$			4.38701i			0.177045i
$615$		0			0
$616$	0.131994			0.00531821
$617$	24.5305	−	24.5305i	0.987559	−	0.987559i	−0.0123641	−	0.999924i	$-0.503936\pi$
$617$	24.5305	−	24.5305i	0.987559	−	0.987559i	0.999924	+	0.0123641i	$0.00393572\pi$
$618$	5.02891	+	5.02891i	0.202292	+	0.202292i
$619$	31.0708	−	31.0708i	1.24884	−	1.24884i	0.292608	−	0.956232i	$-0.405477\pi$
$619$	31.0708	−	31.0708i	1.24884	−	1.24884i	0.956232	−	0.292608i	$-0.0945232\pi$
$620$		0			0
$621$		−	13.6656i		−	0.548383i
$622$	3.33398	+	3.33398i	0.133680	+	0.133680i
$623$	13.7196	+	13.7196i	0.549664	+	0.549664i
$624$	22.9890	+	22.9890i	0.920298	+	0.920298i
$625$		0			0
$626$	−13.5593	−	13.5593i	−0.541941	−	0.541941i
$627$	−0.0267463			−0.00106815
$628$			15.2126i			0.607049i
$629$	39.2839	+	19.2824i	1.56635	+	0.768842i
$630$		0			0
$631$			23.0280i			0.916728i	0.888764	+	0.458364i	$0.151564\pi$
$631$			23.0280i			0.916728i	−0.888764	+	0.458364i	$0.848436\pi$
$632$	19.0640	−	19.0640i	0.758325	−	0.758325i
$633$		−	1.17868i		−	0.0468484i
$634$	−25.2809	−	25.2809i	−1.00403	−	1.00403i
$635$		0			0
$636$	2.17623	−	2.17623i	0.0862931	−	0.0862931i
$637$	−1.56446			−0.0619862
$638$	0.176458			0.00698602
$639$	−0.958560	+	0.958560i	−0.0379200	+	0.0379200i
$640$		0			0
$641$	1.44987	+	1.44987i	0.0572664	+	0.0572664i	0.735160	−	0.677894i	$-0.237107\pi$
$641$	1.44987	+	1.44987i	0.0572664	+	0.0572664i	−0.677894	+	0.735160i	$0.737107\pi$
$642$		−	10.3690i		−	0.409233i
$643$	−29.5955	+	29.5955i	−1.16713	+	1.16713i	−0.184253	+	0.982879i	$0.558986\pi$
$643$	−29.5955	+	29.5955i	−1.16713	+	1.16713i	−0.982879	+	0.184253i	$0.941014\pi$
$644$			6.23606i			0.245735i
$645$		0			0
$646$	3.95900	−	1.35207i	0.155765	−	0.0531965i
$647$			23.1590i			0.910475i	0.890370	+	0.455238i	$0.150446\pi$
$647$			23.1590i			0.910475i	−0.890370	+	0.455238i	$0.849554\pi$
$648$	−19.0620			−0.748828
$649$	−0.0161230	−	0.0161230i	−0.000632882	−	0.000632882i
$650$		0			0
$651$	2.07533	+	2.07533i	0.0813387	+	0.0813387i
$652$	7.75178	+	7.75178i	0.303583	+	0.303583i
$653$	−12.0651	−	12.0651i	−0.472142	−	0.472142i	0.430465	−	0.902607i	$-0.358350\pi$
$653$	−12.0651	−	12.0651i	−0.472142	−	0.472142i	−0.902607	+	0.430465i	$0.858350\pi$
$654$			17.2044i			0.672745i
$655$		0			0
$656$	−25.2124	+	25.2124i	−0.984379	+	0.984379i
$657$	0.718897	+	0.718897i	0.0280468	+	0.0280468i
$658$	−35.9656	+	35.9656i	−1.40208	+	1.40208i
$659$	15.2346			0.593457			0.296728	−	0.954962i	$-0.404104\pi$
$659$	15.2346			0.593457			0.296728	+	0.954962i	$0.404104\pi$
$660$		0			0
$661$			19.2415i			0.748408i	0.927346	+	0.374204i	$0.122084\pi$
$661$			19.2415i			0.748408i	−0.927346	+	0.374204i	$0.877916\pi$
$662$			11.5239i			0.447891i
$663$	11.8817	−	24.2065i	0.461448	−	0.940102i
$664$	23.9730			0.930333
$665$		0			0
$666$	−3.14471	−	3.14471i	−0.121855	−	0.121855i
$667$		−	11.7503i		−	0.454973i
$668$	−2.49907	+	2.49907i	−0.0966918	+	0.0966918i
$669$	−30.0903	+	30.0903i	−1.16336	+	1.16336i
$670$		0			0
$671$			0.292753i			0.0113016i
$672$	21.7504			0.839040
$673$	32.2614	+	32.2614i	1.24358	+	1.24358i	0.958503	+	0.285082i	$0.0920207\pi$
$673$	32.2614	+	32.2614i	1.24358	+	1.24358i	0.285082	+	0.958503i	$0.407979\pi$
$674$	16.5975	−	16.5975i	0.639312	−	0.639312i
$675$		0			0
$676$	−0.136504			−0.00525014
$677$	−19.0624	+	19.0624i	−0.732627	+	0.732627i	−0.971139	−	0.238513i	$-0.923340\pi$
$677$	−19.0624	+	19.0624i	−0.732627	+	0.732627i	0.238513	+	0.971139i	$0.423340\pi$
$678$	61.1067			2.34679
$679$	19.3451			0.742397
$680$		0			0
$681$	−33.5255			−1.28470
$682$	0.0247205			0.000946595
$683$	−11.3404	+	11.3404i	−0.433929	+	0.433929i	−0.889963	−	0.456034i	$-0.849270\pi$
$683$	−11.3404	+	11.3404i	−0.433929	+	0.433929i	0.456034	+	0.889963i	$0.349270\pi$
$684$	−0.124699			−0.00476797
$685$		0			0
$686$	21.3009	−	21.3009i	0.813274	−	0.813274i
$687$	−1.38331	−	1.38331i	−0.0527766	−	0.0527766i
$688$	−59.8132			−2.28036
$689$		−	7.46331i		−	0.284329i
$690$		0			0
$691$	17.0042	−	17.0042i	0.646869	−	0.646869i	−0.305366	−	0.952235i	$-0.598779\pi$
$691$	17.0042	−	17.0042i	0.646869	−	0.646869i	0.952235	+	0.305366i	$0.0987789\pi$
$692$	7.45849	−	7.45849i	0.283529	−	0.283529i
$693$			0.0167043i			0.000634543i
$694$	−16.8136	−	16.8136i	−0.638236	−	0.638236i
$695$		0			0
$696$	−15.1258			−0.573342
$697$	26.5476	+	13.0309i	1.00556	+	0.493579i
$698$		−	22.3775i		−	0.847002i
$699$			18.7419i			0.708883i
$700$		0			0
$701$	36.8962			1.39355			0.696776	−	0.717289i	$-0.254617\pi$
$701$	36.8962			1.39355			0.696776	+	0.717289i	$0.254617\pi$
$702$	21.4014	−	21.4014i	0.807745	−	0.807745i
$703$	−4.52656	−	4.52656i	−0.170722	−	0.170722i
$704$	−0.0434148	+	0.0434148i	−0.00163626	+	0.00163626i
$705$		0			0
$706$		−	11.5535i		−	0.434821i
$707$	32.7567	+	32.7567i	1.23194	+	1.23194i
$708$	−0.980549	−	0.980549i	−0.0368513	−	0.0368513i
$709$	−25.6738	−	25.6738i	−0.964200	−	0.964200i	0.0351811	−	0.999381i	$-0.488799\pi$
$709$	−25.6738	−	25.6738i	−0.964200	−	0.964200i	−0.999381	+	0.0351811i	$0.988799\pi$
$710$		0			0
$711$	2.41260	+	2.41260i	0.0904797	+	0.0904797i
$712$	−14.0084			−0.524987
$713$		−	1.64613i		−	0.0616482i
$714$	−11.0151	−	32.2534i	−0.412231	−	1.20705i
$715$		0			0
$716$		−	9.18146i		−	0.343127i
$717$	−16.5470	+	16.5470i	−0.617958	+	0.617958i
$718$		−	51.9684i		−	1.93944i
$719$	4.81509	+	4.81509i	0.179573	+	0.179573i	0.791170	−	0.611597i	$-0.209473\pi$
$719$	4.81509	+	4.81509i	0.179573	+	0.179573i	−0.611597	+	0.791170i	$0.709473\pi$
$720$		0			0
$721$	4.52090	−	4.52090i	0.168367	−	0.168367i
$722$	31.3513			1.16677
$723$	22.9423			0.853234
$724$	11.2015	−	11.2015i	0.416302	−	0.416302i
$725$		0			0
$726$	−23.5848	−	23.5848i	−0.875313	−	0.875313i
$727$			12.6708i			0.469932i	0.972004	+	0.234966i	$0.0754980\pi$
$727$			12.6708i			0.469932i	−0.972004	+	0.234966i	$0.924502\pi$
$728$	13.7650	−	13.7650i	0.510165	−	0.510165i
$729$			24.4015i			0.903760i
$730$		0			0
$731$	16.0334	+	46.9474i	0.593016	+	1.73641i
$732$			17.8043i			0.658066i
$733$	−20.6418			−0.762422			−0.381211	−	0.924488i	$-0.624493\pi$
$733$	−20.6418			−0.762422			−0.381211	+	0.924488i	$0.624493\pi$
$734$	3.59154	+	3.59154i	0.132566	+	0.132566i
$735$		0			0
$736$	−8.62611	−	8.62611i	−0.317963	−	0.317963i
$737$	0.100858	+	0.100858i	0.00371515	+	0.00371515i
$738$	−2.12516	−	2.12516i	−0.0782281	−	0.0782281i
$739$		−	44.5263i		−	1.63793i	−0.573847	−	0.818963i	$-0.694550\pi$
$739$		−	44.5263i		−	1.63793i	0.573847	−	0.818963i	$-0.305450\pi$
$740$		0			0
$741$	−2.78924	+	2.78924i	−0.102465	+	0.102465i
$742$	−6.67025	−	6.67025i	−0.244872	−	0.244872i
$743$	15.6872	−	15.6872i	0.575506	−	0.575506i	−0.358156	−	0.933662i	$-0.616594\pi$
$743$	15.6872	−	15.6872i	0.575506	−	0.575506i	0.933662	+	0.358156i	$0.116594\pi$
$744$	−2.11902			−0.0776870
$745$		0			0
$746$		−	11.1443i		−	0.408022i
$747$			3.03385i			0.111003i
$748$	−0.0755832	−	0.0370999i	−0.00276360	−	0.00135651i
$749$	−9.32159			−0.340603
$750$		0			0
$751$	18.4987	+	18.4987i	0.675026	+	0.675026i	0.958870	−	0.283845i	$-0.0916100\pi$
$751$	18.4987	+	18.4987i	0.675026	+	0.675026i	−0.283845	+	0.958870i	$0.591610\pi$
$752$		−	55.1352i		−	2.01057i
$753$	30.6516	−	30.6516i	1.11701	−	1.11701i
$754$	18.4018	−	18.4018i	0.670156	−	0.670156i
$755$		0			0
$756$		−	11.2201i		−	0.408071i
$757$	−23.9905			−0.871949			−0.435974	−	0.899959i	$-0.643596\pi$
$757$	−23.9905			−0.871949			−0.435974	+	0.899959i	$0.643596\pi$
$758$	−15.9421	−	15.9421i	−0.579043	−	0.579043i
$759$	0.0864175	−	0.0864175i	0.00313676	−	0.00313676i
$760$		0			0
$761$	16.5206			0.598870			0.299435	−	0.954117i	$-0.403202\pi$
$761$	16.5206			0.598870			0.299435	+	0.954117i	$0.403202\pi$
$762$	42.8520	−	42.8520i	1.55236	−	1.55236i
$763$	15.4665			0.559923
$764$	−13.7704			−0.498194
$765$		0			0
$766$	0.103683			0.00374621
$767$	−3.36276			−0.121422
$768$	−21.6228	+	21.6228i	−0.780244	+	0.780244i
$769$	−48.8518			−1.76164			−0.880821	−	0.473450i	$-0.843009\pi$
$769$	−48.8518			−1.76164			−0.880821	+	0.473450i	$0.843009\pi$
$770$		0			0
$771$	19.3496	−	19.3496i	0.696858	−	0.696858i
$772$	−4.94408	−	4.94408i	−0.177941	−	0.177941i
$773$	35.5187			1.27752			0.638759	−	0.769407i	$-0.279448\pi$
$773$	35.5187			1.27752			0.638759	+	0.769407i	$0.279448\pi$
$774$		−	5.04167i		−	0.181219i
$775$		0			0
$776$	−9.87616	+	9.87616i	−0.354533	+	0.354533i
$777$	−36.8772	+	36.8772i	−1.32296	+	1.32296i
$778$		−	3.70778i		−	0.132930i
$779$	−3.05900	−	3.05900i	−0.109600	−	0.109600i
$780$		0			0
$781$	0.133896			0.00479116
$782$	−8.42301	+	17.1601i	−0.301206	+	0.613644i
$783$			21.1415i			0.755535i
$784$		−	2.14347i		−	0.0765525i
$785$		0			0
$786$	−32.3562			−1.15411
$787$	−13.3494	+	13.3494i	−0.475854	+	0.475854i	−0.903803	−	0.427949i	$-0.859236\pi$
$787$	−13.3494	+	13.3494i	−0.475854	+	0.475854i	0.427949	+	0.903803i	$0.359236\pi$
$788$	−12.6166	−	12.6166i	−0.449446	−	0.449446i
$789$	15.7850	−	15.7850i	0.561960	−	0.561960i
$790$		0			0
$791$		−	54.9338i		−	1.95322i
$792$	−0.00852795	−	0.00852795i	−0.000303028	−	0.000303028i
$793$	30.5296	+	30.5296i	1.08414	+	1.08414i
$794$	14.1242	+	14.1242i	0.501249	+	0.501249i
$795$		0			0
$796$	5.31200	+	5.31200i	0.188279	+	0.188279i
$797$	15.8796			0.562483			0.281242	−	0.959637i	$-0.409254\pi$
$797$	15.8796			0.562483			0.281242	+	0.959637i	$0.409254\pi$
$798$			4.98570i			0.176492i
$799$	−43.2757	+	14.7794i	−1.53098	+	0.522858i
$800$		0			0
$801$		−	1.77280i		−	0.0626389i
$802$	−5.13845	+	5.13845i	−0.181445	+	0.181445i
$803$		−	0.100418i		−	0.00354369i
$804$	6.13387	+	6.13387i	0.216325	+	0.216325i
$805$		0			0
$806$	2.57797	−	2.57797i	0.0908051	−	0.0908051i
$807$	−17.7705			−0.625551
$808$	−33.4462			−1.17663
$809$	−2.50314	+	2.50314i	−0.0880057	+	0.0880057i	−0.749739	−	0.661733i	$-0.769821\pi$
$809$	−2.50314	+	2.50314i	−0.0880057	+	0.0880057i	0.661733	+	0.749739i	$0.269821\pi$
$810$		0			0
$811$	−32.8175	−	32.8175i	−1.15238	−	1.15238i	−0.986075	−	0.166303i	$-0.946817\pi$
$811$	−32.8175	−	32.8175i	−1.15238	−	1.15238i	−0.166303	−	0.986075i	$-0.553183\pi$
$812$		−	9.64752i		−	0.338562i
$813$	5.58326	−	5.58326i	0.195813	−	0.195813i
$814$			0.439266i			0.0153963i
$815$		0			0
$816$	33.1654	+	16.2792i	1.16102	+	0.569885i
$817$		−	7.25708i		−	0.253893i
$818$	65.6954			2.29699
$819$	1.74200	+	1.74200i	0.0608705	+	0.0608705i
$820$		0			0
$821$	15.5572	+	15.5572i	0.542951	+	0.542951i	0.924393	−	0.381442i	$-0.124572\pi$
$821$	15.5572	+	15.5572i	0.542951	+	0.542951i	−0.381442	+	0.924393i	$0.624572\pi$
$822$	−35.4001	−	35.4001i	−1.23472	−	1.23472i
$823$	10.3745	+	10.3745i	0.361633	+	0.361633i	0.864414	−	0.502781i	$-0.167690\pi$
$823$	10.3745	+	10.3745i	0.361633	+	0.361633i	−0.502781	+	0.864414i	$0.667690\pi$
$824$			4.61607i			0.160808i
$825$		0			0
$826$	−3.00543	+	3.00543i	−0.104572	+	0.104572i
$827$	−18.5691	−	18.5691i	−0.645711	−	0.645711i	0.306242	−	0.951954i	$-0.400928\pi$
$827$	−18.5691	−	18.5691i	−0.645711	−	0.645711i	−0.951954	+	0.306242i	$0.900928\pi$
$828$	0.402902	−	0.402902i	0.0140018	−	0.0140018i
$829$	28.2971			0.982800			0.491400	−	0.870934i	$-0.336485\pi$
$829$	28.2971			0.982800			0.491400	+	0.870934i	$0.336485\pi$
$830$		0			0
$831$			12.4998i			0.433612i
$832$			9.05500i			0.313926i
$833$	−1.68241	+	0.574574i	−0.0582921	+	0.0199078i
$834$	−31.8126			−1.10158
$835$		0			0
$836$	0.00870921	+	0.00870921i	0.000301214	+	0.000301214i
$837$			2.96177i			0.102374i
$838$	2.28916	−	2.28916i	0.0790776	−	0.0790776i
$839$	−32.0977	+	32.0977i	−1.10814	+	1.10814i	−0.114740	+	0.993396i	$0.536603\pi$
$839$	−32.0977	+	32.0977i	−1.10814	+	1.10814i	−0.993396	+	0.114740i	$0.963397\pi$
$840$		0			0
$841$		−	10.8217i		−	0.373161i
$842$	−26.1054			−0.899653
$843$	17.0095	+	17.0095i	0.585840	+	0.585840i
$844$	−0.383805	+	0.383805i	−0.0132111	+	0.0132111i
$845$		0			0
$846$	4.64736			0.159779
$847$	−21.2023	+	21.2023i	−0.728519	+	0.728519i
$848$	10.2255			0.351145
$849$	−10.7873			−0.370218
$850$		0			0
$851$	29.2507			1.00270
$852$	8.14311			0.278978
$853$	9.97065	−	9.97065i	0.341389	−	0.341389i	−0.515501	−	0.856889i	$-0.672394\pi$
$853$	9.97065	−	9.97065i	0.341389	−	0.341389i	0.856889	+	0.515501i	$0.172394\pi$
$854$	54.5711			1.86738
$855$		0			0
$856$	4.75891	−	4.75891i	0.162656	−	0.162656i
$857$	5.00436	+	5.00436i	0.170946	+	0.170946i	0.787395	−	0.616449i	$-0.211429\pi$
$857$	5.00436	+	5.00436i	0.170946	+	0.170946i	−0.616449	+	0.787395i	$0.711429\pi$
$858$	0.270673			0.00924061
$859$			29.8876i			1.01975i	0.860248	+	0.509876i	$0.170309\pi$
$859$			29.8876i			1.01975i	−0.860248	+	0.509876i	$0.829691\pi$
$860$		0			0
$861$	−24.9212	+	24.9212i	−0.849312	+	0.849312i
$862$	9.16317	−	9.16317i	0.312099	−	0.312099i
$863$			37.7086i			1.28362i	0.766865	+	0.641808i	$0.221815\pi$
$863$			37.7086i			1.28362i	−0.766865	+	0.641808i	$0.778185\pi$
$864$	15.5204	+	15.5204i	0.528014	+	0.528014i
$865$		0			0
$866$	4.13254			0.140429
$867$	3.88730	−	30.3953i	0.132020	−	1.03228i
$868$		−	1.35155i		−	0.0458746i
$869$		−	0.337002i		−	0.0114320i
$870$		0			0
$871$	21.0359			0.712775
$872$	−7.89602	+	7.89602i	−0.267393	+	0.267393i
$873$	−1.24986	−	1.24986i	−0.0423012	−	0.0423012i
$874$	1.97730	−	1.97730i	0.0668833	−	0.0668833i
$875$		0			0
$876$		−	6.10714i		−	0.206341i
$877$	−25.5743	−	25.5743i	−0.863581	−	0.863581i	0.128171	−	0.991752i	$-0.459089\pi$
$877$	−25.5743	−	25.5743i	−0.863581	−	0.863581i	−0.991752	+	0.128171i	$0.959089\pi$
$878$	−47.4582	−	47.4582i	−1.60164	−	1.60164i
$879$	−22.2070	−	22.2070i	−0.749024	−	0.749024i
$880$		0			0
$881$	−19.4396	−	19.4396i	−0.654937	−	0.654937i	0.299241	−	0.954178i	$-0.403267\pi$
$881$	−19.4396	−	19.4396i	−0.654937	−	0.654937i	−0.954178	+	0.299241i	$0.903267\pi$
$882$	0.180673			0.00608359
$883$		−	45.3114i		−	1.52485i	−0.647076	−	0.762426i	$-0.724008\pi$
$883$		−	45.3114i		−	1.52485i	0.647076	−	0.762426i	$-0.275992\pi$
$884$	−11.7511	+	4.01322i	−0.395234	+	0.134979i
$885$		0			0
$886$		−	50.0993i		−	1.68312i
$887$	−27.7194	+	27.7194i	−0.930728	+	0.930728i	−0.997751	−	0.0670235i	$-0.978650\pi$
$887$	−27.7194	+	27.7194i	−0.930728	+	0.930728i	0.0670235	+	0.997751i	$0.478650\pi$
$888$		−	37.6535i		−	1.26357i
$889$	−38.5232	−	38.5232i	−1.29203	−	1.29203i
$890$		0			0
$891$	−0.168484	+	0.168484i	−0.00564442	+	0.00564442i
$892$	19.5962			0.656128
$893$	6.68950			0.223856
$894$	18.8021	−	18.8021i	0.628837	−	0.628837i
$895$		0			0
$896$	25.1577	+	25.1577i	0.840458	+	0.840458i
$897$		−	18.0241i		−	0.601806i
$898$	−12.2171	+	12.2171i	−0.407689	+	0.407689i
$899$			2.54666i			0.0849358i
$900$		0			0
$901$	−2.74102	−	8.02599i	−0.0913167	−	0.267385i
$902$			0.296851i			0.00988405i
$903$	−59.1224			−1.96747
$904$	28.0451	+	28.0451i	0.932767	+	0.932767i
$905$		0			0
$906$	8.78550	+	8.78550i	0.291879	+	0.291879i
$907$	−30.1151	−	30.1151i	−0.999955	−	0.999955i	4.45993e−5	−	1.00000i	$-0.499986\pi$
$907$	−30.1151	−	30.1151i	−0.999955	−	0.999955i	−1.00000		4.45993e-5i	$0.999986\pi$
$908$	10.9167	+	10.9167i	0.362282	+	0.362282i
$909$		−	4.23272i		−	0.140390i
$910$		0			0
$911$	7.35767	−	7.35767i	0.243771	−	0.243771i	−0.574637	−	0.818408i	$-0.694857\pi$
$911$	7.35767	−	7.35767i	0.243771	−	0.243771i	0.818408	+	0.574637i	$0.194857\pi$
$912$	−3.82154	−	3.82154i	−0.126544	−	0.126544i
$913$	0.211890	−	0.211890i	0.00701255	−	0.00701255i
$914$	−34.7230			−1.14853
$915$		0			0
$916$			0.900875i			0.0297658i
$917$			29.0876i			0.960558i
$918$	15.1549	−	30.8750i	0.500187	−	1.01903i
$919$	−8.24236			−0.271890			−0.135945	−	0.990716i	$-0.543407\pi$
$919$	−8.24236			−0.271890			−0.135945	+	0.990716i	$0.543407\pi$
$920$		0			0
$921$	−3.32381	−	3.32381i	−0.109523	−	0.109523i
$922$		−	15.4927i		−	0.510226i
$923$	13.9633	−	13.9633i	0.459607	−	0.459607i
$924$	0.0709527	−	0.0709527i	0.00233417	−	0.00233417i
$925$		0			0
$926$			32.2827i			1.06088i
$927$	−0.584177			−0.0191869
$928$	13.3451	+	13.3451i	0.438073	+	0.438073i
$929$	20.1421	−	20.1421i	0.660843	−	0.660843i	−0.294736	−	0.955579i	$-0.595232\pi$
$929$	20.1421	−	20.1421i	0.660843	−	0.660843i	0.955579	+	0.294736i	$0.0952318\pi$
$930$		0			0
$931$	0.260065			0.00852329
$932$	6.10278	−	6.10278i	0.199903	−	0.199903i
$933$	−5.05196			−0.165394
$934$	−21.6322			−0.707827
$935$		0			0
$936$	−1.77867			−0.0581377
$937$	−12.2683			−0.400786			−0.200393	−	0.979716i	$-0.564222\pi$
$937$	−12.2683			−0.400786			−0.200393	+	0.979716i	$0.564222\pi$
$938$	18.8006	−	18.8006i	0.613862	−	0.613862i
$939$	20.5464			0.670507
$940$		0			0
$941$	30.4772	−	30.4772i	0.993530	−	0.993530i	−0.00644964	−	0.999979i	$-0.502053\pi$
$941$	30.4772	−	30.4772i	0.993530	−	0.993530i	0.999979	+	0.00644964i	$0.00205300\pi$
$942$	−39.2968	−	39.2968i	−1.28036	−	1.28036i
$943$	19.7673			0.643710
$944$		−	4.60733i		−	0.149956i
$945$		0			0
$946$	−0.352120	+	0.352120i	−0.0114484	+	0.0114484i
$947$	18.8745	−	18.8745i	0.613338	−	0.613338i	−0.330476	−	0.943814i	$-0.607209\pi$
$947$	18.8745	−	18.8745i	0.613338	−	0.613338i	0.943814	+	0.330476i	$0.107209\pi$
$948$		−	20.4954i		−	0.665661i
$949$	−10.4721	−	10.4721i	−0.339939	−	0.339939i
$950$		0			0
$951$	38.3081			1.24222
$952$	9.74739	−	19.8582i	0.315915	−	0.643609i
$953$			37.6493i			1.21958i	0.792563	+	0.609790i	$0.208746\pi$
$953$			37.6493i			1.21958i	−0.792563	+	0.609790i	$0.791254\pi$
$954$			0.861908i			0.0279053i
$955$		0			0
$956$	10.7761			0.348525
$957$	−0.133693	+	0.133693i	−0.00432167	+	0.00432167i
$958$	−25.0835	−	25.0835i	−0.810410	−	0.810410i
$959$	−31.8240	+	31.8240i	−1.02765	+	1.02765i
$960$		0			0
$961$		−	30.6432i		−	0.988491i
$962$	45.8088	+	45.8088i	1.47693	+	1.47693i
$963$	0.602253	+	0.602253i	0.0194073	+	0.0194073i
$964$	−7.47054	−	7.47054i	−0.240610	−	0.240610i
$965$		0			0
$966$	−16.1088	−	16.1088i	−0.518292	−	0.518292i
$967$	47.6174			1.53127			0.765636	−	0.643274i	$-0.222425\pi$
$967$	47.6174			1.53127			0.765636	+	0.643274i	$0.222425\pi$
$968$		−	21.6486i		−	0.695813i
$969$	−1.97514	+	4.02392i	−0.0634505	+	0.129267i
$970$		0			0
$971$			30.9090i			0.991917i	0.868346	+	0.495958i	$0.165183\pi$
$971$			30.9090i			0.991917i	−0.868346	+	0.495958i	$0.834817\pi$
$972$	−1.51546	+	1.51546i	−0.0486085	+	0.0486085i
$973$			28.5989i			0.916840i
$974$	35.1104	+	35.1104i	1.12501	+	1.12501i
$975$		0			0
$976$	−41.8287	+	41.8287i	−1.33891	+	1.33891i
$977$	16.2675			0.520442			0.260221	−	0.965549i	$-0.416205\pi$
$977$	16.2675			0.520442			0.260221	+	0.965549i	$0.416205\pi$
$978$	−40.0483			−1.28060
$979$	−0.123816	+	0.123816i	−0.00395718	+	0.00395718i
$980$		0			0
$981$	−0.999264	−	0.999264i	−0.0319040	−	0.0319040i
$982$		−	14.0751i		−	0.449154i
$983$	18.8915	−	18.8915i	0.602544	−	0.602544i	−0.338443	−	0.940987i	$-0.609900\pi$
$983$	18.8915	−	18.8915i	0.602544	−	0.602544i	0.940987	+	0.338443i	$0.109900\pi$
$984$		−	25.4458i		−	0.811183i
$985$		0			0
$986$	13.0309	−	26.5476i	0.414987	−	0.845448i
$987$		−	54.4984i		−	1.73470i
$988$	1.81648			0.0577898
$989$	23.4476	+	23.4476i	0.745592	+	0.745592i
$990$		0			0
$991$	33.9667	+	33.9667i	1.07899	+	1.07899i	0.996600	+	0.0823867i	$0.0262542\pi$
$991$	33.9667	+	33.9667i	1.07899	+	1.07899i	0.0823867	+	0.996600i	$0.473746\pi$
$992$	1.86955	+	1.86955i	0.0593583	+	0.0593583i
$993$	−8.73109	−	8.73109i	−0.277073	−	0.277073i
$994$		−	24.9590i		−	0.791652i
$995$		0			0
$996$	12.8865	−	12.8865i	0.408325	−	0.408325i
$997$	30.5318	+	30.5318i	0.966951	+	0.966951i	0.999471	−	0.0325205i	$-0.0103534\pi$
$997$	30.5318	+	30.5318i	0.966951	+	0.966951i	−0.0325205	+	0.999471i	$0.510353\pi$
$998$	−13.0847	+	13.0847i	−0.414189	+	0.414189i
$999$	−52.6287			−1.66510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.j.d.149.5		12
5.2	odd	4		425.2.e.c.251.5	✓	12
5.3	odd	4		425.2.e.e.251.2	yes	12
5.4	even	2		425.2.j.a.149.2		12
17.4	even	4		425.2.j.a.174.2		12
85.2	odd	8		7225.2.a.bm.1.4		12
85.4	even	4	inner	425.2.j.d.174.5		12
85.32	odd	8		7225.2.a.bm.1.3		12
85.38	odd	4		425.2.e.e.276.5	yes	12
85.53	odd	8		7225.2.a.br.1.9		12
85.72	odd	4		425.2.e.c.276.2	yes	12
85.83	odd	8		7225.2.a.br.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.e.c.251.5	✓	12	5.2	odd	4
425.2.e.c.276.2	yes	12	85.72	odd	4
425.2.e.e.251.2	yes	12	5.3	odd	4
425.2.e.e.276.5	yes	12	85.38	odd	4
425.2.j.a.149.2		12	5.4	even	2
425.2.j.a.174.2		12	17.4	even	4
425.2.j.d.149.5		12	1.1	even	1	trivial
425.2.j.d.174.5		12	85.4	even	4	inner
7225.2.a.bm.1.3		12	85.32	odd	8
7225.2.a.bm.1.4		12	85.2	odd	8
7225.2.a.br.1.9		12	85.53	odd	8
7225.2.a.br.1.10		12	85.83	odd	8

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.68228 q^{2} +(-1.27457 + 1.27457i) q^{3} +0.830060 q^{4} +(-2.14419 + 2.14419i) q^{6} +(1.92759 + 1.92759i) q^{7} -1.96816 q^{8} -0.249077i q^{9} +(-0.0173960 + 0.0173960i) q^{11} +(-1.05797 + 1.05797i) q^{12} +3.62828i q^{13} +(3.24274 + 3.24274i) q^{14} -4.97112 q^{16} +(1.33255 + 3.90184i) q^{17} -0.419017i q^{18} -0.603141i q^{19} -4.91370 q^{21} +(-0.0292650 + 0.0292650i) q^{22} +(1.94875 + 1.94875i) q^{23} +(2.50857 - 2.50857i) q^{24} +6.10378i q^{26} +(-3.50625 - 3.50625i) q^{27} +(1.60001 + 1.60001i) q^{28} +(-3.01483 - 3.01483i) q^{29} +(-0.422356 - 0.422356i) q^{31} -4.42648 q^{32} -0.0443451i q^{33} +(2.24171 + 6.56397i) q^{34} -0.206749i q^{36} +(7.50498 - 7.50498i) q^{37} -1.01465i q^{38} +(-4.62452 - 4.62452i) q^{39} +(5.07178 - 5.07178i) q^{41} -8.26622 q^{42} +12.0321 q^{43} +(-0.0144398 + 0.0144398i) q^{44} +(3.27834 + 3.27834i) q^{46} +11.0911i q^{47} +(6.33606 - 6.33606i) q^{48} +0.431184i q^{49} +(-6.67161 - 3.27475i) q^{51} +3.01170i q^{52} -2.05698 q^{53} +(-5.89850 - 5.89850i) q^{54} +(-3.79381 - 3.79381i) q^{56} +(0.768748 + 0.768748i) q^{57} +(-5.07178 - 5.07178i) q^{58} +0.926819i q^{59} +(8.41435 - 8.41435i) q^{61} +(-0.710520 - 0.710520i) q^{62} +(0.480117 - 0.480117i) q^{63} +2.49567 q^{64} -0.0746007i q^{66} -5.79776i q^{67} +(1.10609 + 3.23876i) q^{68} -4.96765 q^{69} +(-3.84845 - 3.84845i) q^{71} +0.490224i q^{72} +(-2.88624 + 2.88624i) q^{73} +(12.6255 - 12.6255i) q^{74} -0.500644i q^{76} -0.0670647 q^{77} +(-7.77972 - 7.77972i) q^{78} +(-9.68618 + 9.68618i) q^{79} +9.68519 q^{81} +(8.53214 - 8.53214i) q^{82} -12.1804 q^{83} -4.07867 q^{84} +20.2414 q^{86} +7.68523 q^{87} +(0.0342382 - 0.0342382i) q^{88} +7.11750 q^{89} +(-6.99384 + 6.99384i) q^{91} +(1.61758 + 1.61758i) q^{92} +1.07665 q^{93} +18.6583i q^{94} +(5.64188 - 5.64188i) q^{96} +(5.01796 - 5.01796i) q^{97} +0.725372i q^{98} +(0.00433295 + 0.00433295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8} - 4 q^{11} - 4 q^{12} - 14 q^{14} + 4 q^{16} - 10 q^{17} + 8 q^{21} + 10 q^{22} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 34 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots - 30 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8 - 4 * q^11 - 4 * q^12 - 14 * q^14 + 4 * q^16 - 10 * q^17 + 8 * q^21 + 10 * q^22 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 34 * q^28 + 6 * q^29 - 6 * q^31 + 48 * q^32 - 30 * q^34 + 18 * q^37 - 16 * q^39 + 6 * q^41 - 56 * q^42 + 16 * q^43 - 32 * q^44 + 30 * q^46 + 10 * q^48 - 40 * q^51 - 48 * q^53 - 16 * q^54 - 56 * q^56 + 18 * q^57 - 6 * q^58 - 8 * q^61 + 22 * q^62 + 30 * q^63 + 44 * q^64 - 18 * q^68 + 72 * q^69 - 20 * q^71 + 18 * q^73 + 26 * q^74 - 24 * q^77 + 38 * q^78 + 14 * q^79 - 8 * q^81 - 10 * q^82 - 52 * q^83 - 36 * q^84 + 84 * q^86 + 48 * q^87 - 66 * q^88 + 24 * q^89 + 12 * q^91 + 32 * q^92 + 60 * q^93 + 22 * q^96 - 52 * q^97 - 30 * q^99

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