LMFDB - Embedded newform 325.2.f.d.18.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(18,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("325.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 111x^{12} + 329x^{8} + 168x^{4} + 16 $ x^16 + 111x^12 + 329x^8 + 168*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.3
Root			$0.881421 - 0.881421i$ of defining polynomial
Character	$\chi$	$=$	325.18
Dual form			325.2.f.d.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.13453i q^{2} +(-1.59157 - 1.59157i) q^{3} +0.712838 q^{4} +(-1.80569 + 1.80569i) q^{6} +1.13453 q^{7} -3.07780i q^{8} +2.06618i q^{9} +O(q^{10})$	\(q-1.13453i q^{2} +(-1.59157 - 1.59157i) q^{3} +0.712838 q^{4} +(-1.80569 + 1.80569i) q^{6} +1.13453 q^{7} -3.07780i q^{8} +2.06618i q^{9} +(-2.76952 - 2.76952i) q^{11} +(-1.13453 - 1.13453i) q^{12} +(-1.85306 - 3.09292i) q^{13} -1.28716i q^{14} -2.06618 q^{16} +(1.39602 + 1.39602i) q^{17} +2.34415 q^{18} +(2.89853 + 2.89853i) q^{19} +(-1.80569 - 1.80569i) q^{21} +(-3.14211 + 3.14211i) q^{22} +(-5.28093 + 5.28093i) q^{23} +(-4.89853 + 4.89853i) q^{24} +(-3.50902 + 2.10235i) q^{26} +(-1.48623 + 1.48623i) q^{27} +0.808738 q^{28} -7.39039i q^{29} +(-2.10235 + 2.10235i) q^{31} -3.81145i q^{32} +8.81577i q^{33} +(1.58383 - 1.58383i) q^{34} +1.47286i q^{36} +8.61859 q^{37} +(3.28848 - 3.28848i) q^{38} +(-1.97334 + 7.87187i) q^{39} +(5.58471 - 5.58471i) q^{41} +(-2.04861 + 2.04861i) q^{42} +(4.04106 - 4.04106i) q^{43} +(-1.97422 - 1.97422i) q^{44} +(5.99138 + 5.99138i) q^{46} +0.447884 q^{47} +(3.28848 + 3.28848i) q^{48} -5.71284 q^{49} -4.44372i q^{51} +(-1.32093 - 2.20476i) q^{52} +(-0.997317 - 0.997317i) q^{53} +(1.68618 + 1.68618i) q^{54} -3.49186i q^{56} -9.22643i q^{57} -8.38463 q^{58} +(5.35423 - 5.35423i) q^{59} +15.1151 q^{61} +(2.38518 + 2.38518i) q^{62} +2.34415i q^{63} -8.45658 q^{64} +10.0018 q^{66} +5.68941i q^{67} +(0.995135 + 0.995135i) q^{68} +16.8099 q^{69} +(-7.70422 + 7.70422i) q^{71} +6.35930 q^{72} -3.52724i q^{73} -9.77806i q^{74} +(2.06618 + 2.06618i) q^{76} +(-3.14211 - 3.14211i) q^{77} +(8.93088 + 2.23881i) q^{78} -8.54519i q^{79} +10.9294 q^{81} +(-6.33603 - 6.33603i) q^{82} +11.9752 q^{83} +(-1.28716 - 1.28716i) q^{84} +(-4.58471 - 4.58471i) q^{86} +(-11.7623 + 11.7623i) q^{87} +(-8.52403 + 8.52403i) q^{88} +(3.34473 - 3.34473i) q^{89} +(-2.10235 - 3.50902i) q^{91} +(-3.76445 + 3.76445i) q^{92} +6.69207 q^{93} -0.508138i q^{94} +(-6.06618 + 6.06618i) q^{96} +15.2972i q^{97} +6.48139i q^{98} +(5.72234 - 5.72234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 16 * q - 8 * q^4 + 12 * q^6	$ 16 q - 8 q^{4} + 12 q^{6} - 20 q^{11} - 8 q^{16} - 16 q^{19} + 12 q^{21} - 16 q^{24} - 16 q^{26} + 8 q^{31} + 44 q^{34} - 28 q^{39} + 4 q^{41} + 76 q^{44} + 12 q^{46} - 72 q^{49} + 4 q^{54} - 24 q^{59} + 24 q^{61} + 16 q^{64} - 48 q^{66} + 112 q^{69} - 20 q^{71} + 8 q^{76} - 40 q^{84} + 12 q^{86} - 36 q^{89} + 8 q^{91} - 72 q^{96} + 52 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 12 * q^6 - 20 * q^11 - 8 * q^16 - 16 * q^19 + 12 * q^21 - 16 * q^24 - 16 * q^26 + 8 * q^31 + 44 * q^34 - 28 * q^39 + 4 * q^41 + 76 * q^44 + 12 * q^46 - 72 * q^49 + 4 * q^54 - 24 * q^59 + 24 * q^61 + 16 * q^64 - 48 * q^66 + 112 * q^69 - 20 * q^71 + 8 * q^76 - 40 * q^84 + 12 * q^86 - 36 * q^89 + 8 * q^91 - 72 * q^96 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.13453i		−	0.802235i	−0.916027	−	0.401117i	$-0.868622\pi$
$2$		−	1.13453i		−	0.802235i	0.916027	−	0.401117i	$-0.131378\pi$
$3$	−1.59157	−	1.59157i	−0.918893	−	0.918893i	0.0780561	−	0.996949i	$-0.475129\pi$
$3$	−1.59157	−	1.59157i	−0.918893	−	0.918893i	−0.996949	+	0.0780561i	$0.975129\pi$
$4$	0.712838			0.356419
$5$		0			0
$5$		0			0
$6$	−1.80569	+	1.80569i	−0.737168	+	0.737168i
$7$	1.13453			0.428813			0.214406	−	0.976745i	$-0.431218\pi$
$7$	1.13453			0.428813			0.214406	+	0.976745i	$0.431218\pi$
$8$		−	3.07780i		−	1.08817i
$9$			2.06618i			0.688728i
$10$		0			0
$11$	−2.76952	−	2.76952i	−0.835042	−	0.835042i	0.153160	−	0.988201i	$-0.451055\pi$
$11$	−2.76952	−	2.76952i	−0.835042	−	0.835042i	−0.988201	+	0.153160i	$0.951055\pi$
$12$	−1.13453	−	1.13453i	−0.327511	−	0.327511i
$13$	−1.85306	−	3.09292i	−0.513945	−	0.857823i
$13$	−1.85306	−	3.09292i	−0.513945	−	0.857823i
$14$		−	1.28716i		−	0.344008i
$15$		0			0
$16$	−2.06618			−0.516546
$17$	1.39602	+	1.39602i	0.338584	+	0.338584i	0.855834	−	0.517250i	$-0.173044\pi$
$17$	1.39602	+	1.39602i	0.338584	+	0.338584i	−0.517250	+	0.855834i	$0.673044\pi$
$18$	2.34415			0.552522
$19$	2.89853	+	2.89853i	0.664969	+	0.664969i	0.956547	−	0.291578i	$-0.0941803\pi$
$19$	2.89853	+	2.89853i	0.664969	+	0.664969i	−0.291578	+	0.956547i	$0.594180\pi$
$20$		0			0
$21$	−1.80569	−	1.80569i	−0.394033	−	0.394033i
$22$	−3.14211	+	3.14211i	−0.669900	+	0.669900i
$23$	−5.28093	+	5.28093i	−1.10115	+	1.10115i	−0.106877	+	0.994272i	$0.534085\pi$
$23$	−5.28093	+	5.28093i	−1.10115	+	1.10115i	−0.994272	+	0.106877i	$0.965915\pi$
$24$	−4.89853	+	4.89853i	−0.999909	+	0.999909i
$25$		0			0
$26$	−3.50902	+	2.10235i	−0.688176	+	0.412305i
$27$	−1.48623	+	1.48623i	−0.286025	+	0.286025i
$28$	0.808738			0.152837
$29$		−	7.39039i		−	1.37236i	−0.727431	−	0.686181i	$-0.759286\pi$
$29$		−	7.39039i		−	1.37236i	0.727431	−	0.686181i	$-0.240714\pi$
$30$		0			0
$31$	−2.10235	+	2.10235i	−0.377593	+	0.377593i	−0.870233	−	0.492640i	$-0.836032\pi$
$31$	−2.10235	+	2.10235i	−0.377593	+	0.377593i	0.492640	+	0.870233i	$0.336032\pi$
$32$		−	3.81145i		−	0.673775i
$33$			8.81577i			1.53463i
$34$	1.58383	−	1.58383i	0.271624	−	0.271624i
$35$		0			0
$36$			1.47286i			0.245476i
$37$	8.61859			1.41689			0.708444	−	0.705767i	$-0.249398\pi$
$37$	8.61859			1.41689			0.708444	+	0.705767i	$0.249398\pi$
$38$	3.28848	−	3.28848i	0.533461	−	0.533461i
$39$	−1.97334	+	7.87187i	−0.315987	+	1.26051i
$40$		0			0
$41$	5.58471	−	5.58471i	0.872185	−	0.872185i	−0.120525	−	0.992710i	$-0.538458\pi$
$41$	5.58471	−	5.58471i	0.872185	−	0.872185i	0.992710	+	0.120525i	$0.0384579\pi$
$42$	−2.04861	+	2.04861i	−0.316107	+	0.316107i
$43$	4.04106	−	4.04106i	0.616256	−	0.616256i	−0.328313	−	0.944569i	$-0.606480\pi$
$43$	4.04106	−	4.04106i	0.616256	−	0.616256i	0.944569	+	0.328313i	$0.106480\pi$
$44$	−1.97422	−	1.97422i	−0.297625	−	0.297625i
$45$		0			0
$46$	5.99138	+	5.99138i	0.883381	+	0.883381i
$47$	0.447884			0.0653306			0.0326653	−	0.999466i	$-0.489600\pi$
$47$	0.447884			0.0653306			0.0326653	+	0.999466i	$0.489600\pi$
$48$	3.28848	+	3.28848i	0.474651	+	0.474651i
$49$	−5.71284			−0.816120
$50$		0			0
$51$		−	4.44372i		−	0.622245i
$52$	−1.32093	−	2.20476i	−0.183180	−	0.305745i
$53$	−0.997317	−	0.997317i	−0.136992	−	0.136992i	0.635285	−	0.772277i	$-0.280882\pi$
$53$	−0.997317	−	0.997317i	−0.136992	−	0.136992i	−0.772277	+	0.635285i	$0.780882\pi$
$54$	1.68618	+	1.68618i	0.229460	+	0.229460i
$55$		0			0
$56$		−	3.49186i		−	0.466620i
$57$		−	9.22643i		−	1.22207i
$58$	−8.38463			−1.10096
$59$	5.35423	−	5.35423i	0.697061	−	0.697061i	−0.266714	−	0.963776i	$-0.585938\pi$
$59$	5.35423	−	5.35423i	0.697061	−	0.697061i	0.963776	+	0.266714i	$0.0859380\pi$
$60$		0			0
$61$	15.1151			1.93529			0.967647	−	0.252308i	$-0.0811896\pi$
$61$	15.1151			1.93529			0.967647	+	0.252308i	$0.0811896\pi$
$62$	2.38518	+	2.38518i	0.302918	+	0.302918i
$63$			2.34415i			0.295335i
$64$	−8.45658			−1.05707
$65$		0			0
$66$	10.0018			1.23113
$67$			5.68941i			0.695072i	0.937667	+	0.347536i	$0.112982\pi$
$67$			5.68941i			0.695072i	−0.937667	+	0.347536i	$0.887018\pi$
$68$	0.995135	+	0.995135i	0.120678	+	0.120678i
$69$	16.8099			2.02368
$70$		0			0
$71$	−7.70422	+	7.70422i	−0.914322	+	0.914322i	−0.996609	−	0.0822863i	$-0.973778\pi$
$71$	−7.70422	+	7.70422i	−0.914322	+	0.914322i	0.0822863	+	0.996609i	$0.473778\pi$
$72$	6.35930			0.749451
$73$		−	3.52724i		−	0.412832i	−0.978464	−	0.206416i	$-0.933820\pi$
$73$		−	3.52724i		−	0.412832i	0.978464	−	0.206416i	$-0.0661800\pi$
$74$		−	9.77806i		−	1.13668i
$75$		0			0
$76$	2.06618	+	2.06618i	0.237008	+	0.237008i
$77$	−3.14211	−	3.14211i	−0.358076	−	0.358076i
$78$	8.93088	+	2.23881i	1.01122	+	0.253496i
$79$		−	8.54519i		−	0.961409i	−0.876883	−	0.480704i	$-0.840381\pi$
$79$		−	8.54519i		−	0.961409i	0.876883	−	0.480704i	$-0.159619\pi$
$80$		0			0
$81$	10.9294			1.21438
$82$	−6.33603	−	6.33603i	−0.699697	−	0.699697i
$83$	11.9752			1.31445			0.657223	−	0.753696i	$-0.271731\pi$
$83$	11.9752			1.31445			0.657223	+	0.753696i	$0.271731\pi$
$84$	−1.28716	−	1.28716i	−0.140441	−	0.140441i
$85$		0			0
$86$	−4.58471	−	4.58471i	−0.494382	−	0.494382i
$87$	−11.7623	+	11.7623i	−1.26105	+	1.26105i
$88$	−8.52403	+	8.52403i	−0.908665	+	0.908665i
$89$	3.34473	−	3.34473i	0.354540	−	0.354540i	−0.507255	−	0.861796i	$-0.669340\pi$
$89$	3.34473	−	3.34473i	0.354540	−	0.354540i	0.861796	+	0.507255i	$0.169340\pi$
$90$		0			0
$91$	−2.10235	−	3.50902i	−0.220386	−	0.367845i
$92$	−3.76445	+	3.76445i	−0.392471	+	0.392471i
$93$	6.69207			0.693935
$94$		−	0.508138i		−	0.0524105i
$95$		0			0
$96$	−6.06618	+	6.06618i	−0.619127	+	0.619127i
$97$			15.2972i			1.55319i	0.629999	+	0.776596i	$0.283055\pi$
$97$			15.2972i			1.55319i	−0.629999	+	0.776596i	$0.716945\pi$
$98$			6.48139i			0.654720i
$99$	5.72234	−	5.72234i	0.575117	−	0.575117i
$100$		0			0
$101$			8.74374i			0.870035i	0.900422	+	0.435017i	$0.143258\pi$
$101$			8.74374i			0.870035i	−0.900422	+	0.435017i	$0.856742\pi$
$102$	−5.04154			−0.499187
$103$	9.91090	−	9.91090i	0.976550	−	0.976550i	−0.0231817	−	0.999731i	$-0.507380\pi$
$103$	9.91090	−	9.91090i	0.976550	−	0.976550i	0.999731	+	0.0231817i	$0.00737964\pi$
$104$	−9.51941	+	5.70334i	−0.933455	+	0.559258i
$105$		0			0
$106$	−1.13149	+	1.13149i	−0.109900	+	0.109900i
$107$	4.08806	−	4.08806i	0.395208	−	0.395208i	−0.481331	−	0.876539i	$-0.659847\pi$
$107$	4.08806	−	4.08806i	0.395208	−	0.395208i	0.876539	+	0.481331i	$0.159847\pi$
$108$	−1.05944	+	1.05944i	−0.101945	+	0.101945i
$109$	9.83235	+	9.83235i	0.941768	+	0.941768i	0.998395	−	0.0566273i	$-0.0180347\pi$
$109$	9.83235	+	9.83235i	0.941768	+	0.941768i	−0.0566273	+	0.998395i	$0.518035\pi$
$110$		0			0
$111$	−13.7171	−	13.7171i	−1.30197	−	1.30197i
$112$	−2.34415			−0.221502
$113$	−1.99245	−	1.99245i	−0.187434	−	0.187434i	0.607152	−	0.794586i	$-0.292312\pi$
$113$	−1.99245	−	1.99245i	−0.187434	−	0.187434i	−0.794586	+	0.607152i	$0.792312\pi$
$114$	−10.4677			−0.980388
$115$		0			0
$116$		−	5.26816i		−	0.489136i
$117$	6.39055	−	3.82876i	0.590807	−	0.353969i
$118$	−6.07454	−	6.07454i	−0.559207	−	0.559207i
$119$	1.58383	+	1.58383i	0.145189	+	0.145189i
$120$		0			0
$121$			4.34049i			0.394590i
$122$		−	17.1486i		−	1.55256i
$123$	−17.7769			−1.60289
$124$	−1.49864	+	1.49864i	−0.134581	+	0.134581i
$125$		0			0
$126$	2.65951			0.236928
$127$	−6.98543	−	6.98543i	−0.619857	−	0.619857i	0.325638	−	0.945495i	$-0.394421\pi$
$127$	−6.98543	−	6.98543i	−0.619857	−	0.619857i	−0.945495	+	0.325638i	$0.894421\pi$
$128$			1.97136i			0.174245i
$129$	−12.8632			−1.13255
$130$		0			0
$131$	−9.25364			−0.808495			−0.404247	−	0.914650i	$-0.632466\pi$
$131$	−9.25364			−0.808495			−0.404247	+	0.914650i	$0.632466\pi$
$132$			6.28422i			0.546971i
$133$	3.28848	+	3.28848i	0.285147	+	0.285147i
$134$	6.45481			0.557611
$135$		0			0
$136$	4.29666	−	4.29666i	0.368436	−	0.368436i
$137$	5.56732			0.475648			0.237824	−	0.971308i	$-0.423566\pi$
$137$	5.56732			0.475648			0.237824	+	0.971308i	$0.423566\pi$
$138$		−	19.0714i		−	1.62346i
$139$			17.9603i			1.52338i	0.647944	+	0.761688i	$0.275629\pi$
$139$			17.9603i			1.52338i	−0.647944	+	0.761688i	$0.724371\pi$
$140$		0			0
$141$	−0.712838	−	0.712838i	−0.0600318	−	0.0600318i
$142$	8.74068	+	8.74068i	0.733501	+	0.733501i
$143$	−3.43384	+	13.6980i	−0.287152	+	1.14548i
$144$		−	4.26912i		−	0.355760i
$145$		0			0
$146$	−4.00176			−0.331188
$147$	9.09238	+	9.09238i	0.749927	+	0.749927i
$148$	6.14366			0.505006
$149$	−6.23136	−	6.23136i	−0.510493	−	0.510493i	0.404184	−	0.914678i	$-0.367555\pi$
$149$	−6.23136	−	6.23136i	−0.510493	−	0.510493i	−0.914678	+	0.404184i	$0.867555\pi$
$150$		0			0
$151$	4.52803	+	4.52803i	0.368486	+	0.368486i	0.866925	−	0.498439i	$-0.166093\pi$
$151$	4.52803	+	4.52803i	0.368486	+	0.368486i	−0.498439	+	0.866925i	$0.666093\pi$
$152$	8.92110	−	8.92110i	0.723597	−	0.723597i
$153$	−2.88443	+	2.88443i	−0.233192	+	0.233192i
$154$	−3.56482	+	3.56482i	−0.287261	+	0.287261i
$155$		0			0
$156$	−1.40667	+	5.61137i	−0.112624	+	0.449269i
$157$	−1.58994	+	1.58994i	−0.126891	+	0.126891i	−0.767700	−	0.640809i	$-0.778599\pi$
$157$	−1.58994	+	1.58994i	−0.126891	+	0.126891i	0.640809	+	0.767700i	$0.278599\pi$
$158$	−9.69478			−0.771275
$159$			3.17460i			0.251762i
$160$		0			0
$161$	−5.99138	+	5.99138i	−0.472187	+	0.472187i
$162$		−	12.3998i		−	0.974219i
$163$			1.14587i			0.0897512i	0.998993	+	0.0448756i	$0.0142892\pi$
$163$			1.14587i			0.0897512i	−0.998993	+	0.0448756i	$0.985711\pi$
$164$	3.98099	−	3.98099i	0.310863	−	0.310863i
$165$		0			0
$166$		−	13.5862i		−	1.05450i
$167$	17.6483			1.36567			0.682833	−	0.730575i	$-0.260748\pi$
$167$	17.6483			1.36567			0.682833	+	0.730575i	$0.260748\pi$
$168$	−5.55754	+	5.55754i	−0.428773	+	0.428773i
$169$	−6.13237	+	11.4627i	−0.471721	+	0.881748i
$170$		0			0
$171$	−5.98890	+	5.98890i	−0.457983	+	0.457983i
$172$	2.88062	−	2.88062i	0.219645	−	0.219645i
$173$	4.41007	−	4.41007i	0.335291	−	0.335291i	−0.519301	−	0.854592i	$-0.673807\pi$
$173$	4.41007	−	4.41007i	0.335291	−	0.335291i	0.854592	+	0.519301i	$0.173807\pi$
$174$	13.3447	+	13.3447i	1.01166	+	1.01166i
$175$		0			0
$176$	5.72234	+	5.72234i	0.431338	+	0.431338i
$177$	−17.0433			−1.28105
$178$	−3.79470	−	3.79470i	−0.284425	−	0.284425i
$179$	−14.5452			−1.08716			−0.543579	−	0.839358i	$-0.682931\pi$
$179$	−14.5452			−1.08716			−0.543579	+	0.839358i	$0.682931\pi$
$180$		0			0
$181$			3.34049i			0.248296i	0.992264	+	0.124148i	$0.0396198\pi$
$181$			3.34049i			0.248296i	−0.992264	+	0.124148i	$0.960380\pi$
$182$	−3.98109	+	2.38518i	−0.295098	+	0.176801i
$183$	−24.0568	−	24.0568i	−1.77833	−	1.77833i
$184$	16.2536	+	16.2536i	1.19823	+	1.19823i
$185$		0			0
$186$		−	7.59236i		−	0.556699i
$187$		−	7.73260i		−	0.565464i
$188$	0.319269			0.0232851
$189$	−1.68618	+	1.68618i	−0.122651	+	0.122651i
$190$		0			0
$191$	−6.14427			−0.444584			−0.222292	−	0.974980i	$-0.571354\pi$
$191$	−6.14427			−0.444584			−0.222292	+	0.974980i	$0.571354\pi$
$192$	13.4592	+	13.4592i	0.971336	+	0.971336i
$193$			10.4495i			0.752175i	0.926584	+	0.376087i	$0.122731\pi$
$193$			10.4495i			0.752175i	−0.926584	+	0.376087i	$0.877269\pi$
$194$	17.3551			1.24602
$195$		0			0
$196$	−4.07233			−0.290881
$197$		−	11.8050i		−	0.841070i	−0.907276	−	0.420535i	$-0.861842\pi$
$197$		−	11.8050i		−	0.841070i	0.907276	−	0.420535i	$-0.138158\pi$
$198$	−6.49218	−	6.49218i	−0.461379	−	0.461379i
$199$	−17.9413			−1.27183			−0.635914	−	0.771760i	$-0.719377\pi$
$199$	−17.9413			−1.27183			−0.635914	+	0.771760i	$0.719377\pi$
$200$		0			0
$201$	9.05509	−	9.05509i	0.638697	−	0.638697i
$202$	9.92005			0.697972
$203$		−	8.38463i		−	0.588486i
$204$		−	3.16765i		−	0.221780i
$205$		0			0
$206$	−11.2442	−	11.2442i	−0.783422	−	0.783422i
$207$	−10.9114	−	10.9114i	−0.758393	−	0.758393i
$208$	3.82876	+	6.39055i	0.265476	+	0.443105i
$209$		−	16.0551i		−	1.11055i
$210$		0			0
$211$	−21.4685			−1.47795			−0.738975	−	0.673732i	$-0.764690\pi$
$211$	−21.4685			−1.47795			−0.738975	+	0.673732i	$0.764690\pi$
$212$	−0.710926	−	0.710926i	−0.0488266	−	0.0488266i
$213$	24.5236			1.68033
$214$	−4.63803	−	4.63803i	−0.317049	−	0.317049i
$215$		0			0
$216$	4.57432	+	4.57432i	0.311243	+	0.311243i
$217$	−2.38518	+	2.38518i	−0.161917	+	0.161917i
$218$	11.1551	−	11.1551i	0.755519	−	0.755519i
$219$	−5.61385	+	5.61385i	−0.379349	+	0.379349i
$220$		0			0
$221$	1.73088	−	6.90468i	0.116432	−	0.464459i
$222$	−15.5625	+	15.5625i	−1.04448	+	1.04448i
$223$	5.73099			0.383776			0.191888	−	0.981417i	$-0.438539\pi$
$223$	5.73099			0.383776			0.191888	+	0.981417i	$0.438539\pi$
$224$		−	4.32421i		−	0.288923i
$225$		0			0
$226$	−2.26050	+	2.26050i	−0.150366	+	0.150366i
$227$			12.9243i			0.857817i	0.903348	+	0.428908i	$0.141102\pi$
$227$			12.9243i			0.857817i	−0.903348	+	0.428908i	$0.858898\pi$
$228$		−	6.57695i		−	0.435569i
$229$	13.8719	−	13.8719i	0.916679	−	0.916679i	−0.0801073	−	0.996786i	$-0.525526\pi$
$229$	13.8719	−	13.8719i	0.916679	−	0.916679i	0.996786	+	0.0801073i	$0.0255263\pi$
$230$		0			0
$231$			10.0018i			0.658068i
$232$	−22.7462			−1.49336
$233$	−18.7434	+	18.7434i	−1.22792	+	1.22792i	−0.263173	+	0.964749i	$0.584769\pi$
$233$	−18.7434	+	18.7434i	−1.22792	+	1.22792i	−0.964749	+	0.263173i	$0.915231\pi$
$234$	−4.34384	−	7.25029i	−0.283966	−	0.473966i
$235$		0			0
$236$	3.81670	−	3.81670i	0.248446	−	0.248446i
$237$	−13.6003	+	13.6003i	−0.883431	+	0.883431i
$238$	1.79690	−	1.79690i	0.116476	−	0.116476i
$239$	2.11712	+	2.11712i	0.136945	+	0.136945i	0.772256	−	0.635311i	$-0.219128\pi$
$239$	2.11712	+	2.11712i	0.136945	+	0.136945i	−0.635311	+	0.772256i	$0.719128\pi$
$240$		0			0
$241$	−8.61752	−	8.61752i	−0.555103	−	0.555103i	0.372806	−	0.927909i	$-0.378396\pi$
$241$	−8.61752	−	8.61752i	−0.555103	−	0.555103i	−0.927909	+	0.372806i	$0.878396\pi$
$242$	4.92442			0.316554
$243$	−12.9363	−	12.9363i	−0.829861	−	0.829861i
$244$	10.7746			0.689776
$245$		0			0
$246$			20.1685i			1.28589i
$247$	3.59380	−	14.3361i	0.228668	−	0.912183i
$248$	6.47061	+	6.47061i	0.410884	+	0.410884i
$249$	−19.0593	−	19.0593i	−1.20784	−	1.20784i
$250$		0			0
$251$			12.4094i			0.783274i	0.920120	+	0.391637i	$0.128091\pi$
$251$			12.4094i			0.783274i	−0.920120	+	0.391637i	$0.871909\pi$
$252$			1.67100i			0.105263i
$253$	29.2513			1.83901
$254$	−7.92519	+	7.92519i	−0.497271	+	0.497271i
$255$		0			0
$256$	−14.6766			−0.917287
$257$	8.16536	+	8.16536i	0.509341	+	0.509341i	0.914324	−	0.404983i	$-0.132723\pi$
$257$	8.16536	+	8.16536i	0.509341	+	0.509341i	−0.404983	+	0.914324i	$0.632723\pi$
$258$			14.5938i			0.908568i
$259$	9.77806			0.607579
$260$		0			0
$261$	15.2699			0.945184
$262$			10.4986i			0.648603i
$263$	−4.36623	−	4.36623i	−0.269233	−	0.269233i	0.559558	−	0.828791i	$-0.310971\pi$
$263$	−4.36623	−	4.36623i	−0.269233	−	0.269233i	−0.828791	+	0.559558i	$0.810971\pi$
$264$	27.1332			1.66993
$265$		0			0
$266$	3.73088	−	3.73088i	0.228755	−	0.228755i
$267$	−10.6467			−0.651569
$268$			4.05563i			0.247737i
$269$			4.73702i			0.288822i	0.989518	+	0.144411i	$0.0461287\pi$
$269$			4.73702i			0.288822i	−0.989518	+	0.144411i	$0.953871\pi$
$270$		0			0
$271$	8.61473	+	8.61473i	0.523307	+	0.523307i	0.918569	−	0.395261i	$-0.129346\pi$
$271$	8.61473	+	8.61473i	0.523307	+	0.523307i	−0.395261	+	0.918569i	$0.629346\pi$
$272$	−2.88443	−	2.88443i	−0.174894	−	0.174894i
$273$	−2.23881	+	8.93088i	−0.135499	+	0.540522i
$274$		−	6.31630i		−	0.381582i
$275$		0			0
$276$	11.9828			0.721277
$277$	−13.7126	−	13.7126i	−0.823908	−	0.823908i	0.162758	−	0.986666i	$-0.447961\pi$
$277$	−13.7126	−	13.7126i	−0.823908	−	0.823908i	−0.986666	+	0.162758i	$0.947961\pi$
$278$	20.3766			1.22211
$279$	−4.34384	−	4.34384i	−0.260059	−	0.260059i
$280$		0			0
$281$	18.2450	+	18.2450i	1.08841	+	1.08841i	0.995693	+	0.0927140i	$0.0295542\pi$
$281$	18.2450	+	18.2450i	1.08841	+	1.08841i	0.0927140	+	0.995693i	$0.470446\pi$
$282$	−0.808738	+	0.808738i	−0.0481596	+	0.0481596i
$283$	−16.3496	+	16.3496i	−0.971885	+	0.971885i	−0.999615	−	0.0277307i	$-0.991172\pi$
$283$	−16.3496	+	16.3496i	−0.971885	+	0.971885i	0.0277307	+	0.999615i	$0.491172\pi$
$284$	−5.49186	+	5.49186i	−0.325882	+	0.325882i
$285$		0			0
$286$	15.5408	+	3.89580i	0.918947	+	0.230364i
$287$	6.33603	−	6.33603i	0.374004	−	0.374004i
$288$	7.87516			0.464048
$289$		−	13.1023i		−	0.770722i
$290$		0			0
$291$	24.3465	−	24.3465i	1.42722	−	1.42722i
$292$		−	2.51435i		−	0.147141i
$293$		−	6.10379i		−	0.356587i	−0.983977	−	0.178294i	$-0.942942\pi$
$293$		−	6.10379i		−	0.356587i	0.983977	−	0.178294i	$-0.0570577\pi$
$294$	10.3156	−	10.3156i	0.601617	−	0.601617i
$295$		0			0
$296$		−	26.5263i		−	1.54181i
$297$	8.23230			0.477686
$298$	−7.06968	+	7.06968i	−0.409535	+	0.409535i
$299$	26.1194	+	6.54766i	1.51052	+	0.378661i
$300$		0			0
$301$	4.58471	−	4.58471i	0.264258	−	0.264258i
$302$	5.13719	−	5.13719i	0.295612	−	0.295612i
$303$	13.9163	−	13.9163i	0.799469	−	0.799469i
$304$	−5.98890	−	5.98890i	−0.343487	−	0.343487i
$305$		0			0
$306$	3.27248	+	3.27248i	0.187075	+	0.187075i
$307$	−0.391103			−0.0223214			−0.0111607	−	0.999938i	$-0.503553\pi$
$307$	−0.391103			−0.0223214			−0.0111607	+	0.999938i	$0.503553\pi$
$308$	−2.23981	−	2.23981i	−0.127625	−	0.127625i
$309$	−31.5478			−1.79469
$310$		0			0
$311$			21.0507i			1.19368i	0.802362	+	0.596838i	$0.203577\pi$
$311$			21.0507i			1.19368i	−0.802362	+	0.596838i	$0.796423\pi$
$312$	24.2280	+	6.07354i	1.37164	+	0.343847i
$313$	12.1529	+	12.1529i	0.686921	+	0.686921i	0.961550	−	0.274629i	$-0.0885551\pi$
$313$	12.1529	+	12.1529i	0.686921	+	0.686921i	−0.274629	+	0.961550i	$0.588555\pi$
$314$	1.80384	+	1.80384i	0.101797	+	0.101797i
$315$		0			0
$316$		−	6.09134i		−	0.342664i
$317$			1.23831i			0.0695506i	0.999395	+	0.0347753i	$0.0110716\pi$
$317$			1.23831i			0.0695506i	−0.999395	+	0.0347753i	$0.988928\pi$
$318$	3.60168			0.201972
$319$	−20.4678	+	20.4678i	−1.14598	+	1.14598i
$320$		0			0
$321$	−13.0129			−0.726307
$322$	6.79741	+	6.79741i	0.378805	+	0.378805i
$323$			8.09281i			0.450296i
$324$	7.79092			0.432829
$325$		0			0
$326$	1.30002			0.0720016
$327$		−	31.2977i		−	1.73077i
$328$	−17.1886	−	17.1886i	−0.949083	−	0.949083i
$329$	0.508138			0.0280146
$330$		0			0
$331$	22.6465	−	22.6465i	1.24476	−	1.24476i	0.286764	−	0.958001i	$-0.407421\pi$
$331$	22.6465	−	22.6465i	1.24476	−	1.24476i	0.958001	−	0.286764i	$-0.0925794\pi$
$332$	8.53637			0.468494
$333$			17.8076i			0.975850i
$334$		−	20.0225i		−	1.09558i
$335$		0			0
$336$	3.73088	+	3.73088i	0.203536	+	0.203536i
$337$	9.00435	+	9.00435i	0.490498	+	0.490498i	0.908463	−	0.417965i	$-0.137257\pi$
$337$	9.00435	+	9.00435i	0.490498	+	0.490498i	−0.417965	+	0.908463i	$0.637257\pi$
$338$	13.0048	+	6.95737i	0.707369	+	0.378431i
$339$			6.34225i			0.344464i
$340$		0			0
$341$	11.6450			0.630612
$342$	6.79460	+	6.79460i	0.367410	+	0.367410i
$343$	−14.4231			−0.778775
$344$	−12.4376	−	12.4376i	−0.670589	−	0.670589i
$345$		0			0
$346$	−5.00336	−	5.00336i	−0.268982	−	0.268982i
$347$	11.5349	−	11.5349i	0.619226	−	0.619226i	−0.326107	−	0.945333i	$-0.605737\pi$
$347$	11.5349	−	11.5349i	0.619226	−	0.619226i	0.945333	+	0.326107i	$0.105737\pi$
$348$	−8.38463	+	8.38463i	−0.449464	+	0.449464i
$349$	6.76426	−	6.76426i	0.362082	−	0.362082i	−0.502497	−	0.864579i	$-0.667585\pi$
$349$	6.76426	−	6.76426i	0.362082	−	0.362082i	0.864579	+	0.502497i	$0.167585\pi$
$350$		0			0
$351$	7.35087	+	1.84273i	0.392360	+	0.0983578i
$352$	−10.5559	+	10.5559i	−0.562631	+	0.562631i
$353$	−7.57745			−0.403307			−0.201654	−	0.979457i	$-0.564632\pi$
$353$	−7.57745			−0.403307			−0.201654	+	0.979457i	$0.564632\pi$
$354$			19.3361i			1.02770i
$355$		0			0
$356$	2.38425	−	2.38425i	0.126365	−	0.126365i
$357$		−	5.04154i		−	0.266826i
$358$			16.5020i			0.872156i
$359$	−13.8246	+	13.8246i	−0.729635	+	0.729635i	−0.970547	−	0.240912i	$-0.922553\pi$
$359$	−13.8246	+	13.8246i	−0.729635	+	0.729635i	0.240912	+	0.970547i	$0.422553\pi$
$360$		0			0
$361$		−	2.19702i		−	0.115633i
$362$	3.78989			0.199192
$363$	6.90818	−	6.90818i	0.362586	−	0.362586i
$364$	−1.49864	−	2.50136i	−0.0785498	−	0.131107i
$365$		0			0
$366$	−27.2932	+	27.2932i	−1.42664	+	1.42664i
$367$	−7.91084	+	7.91084i	−0.412943	+	0.412943i	−0.882762	−	0.469820i	$-0.844319\pi$
$367$	−7.91084	+	7.91084i	−0.412943	+	0.412943i	0.469820	+	0.882762i	$0.344319\pi$
$368$	10.9114	−	10.9114i	0.568795	−	0.568795i
$369$	11.5390	+	11.5390i	0.600698	+	0.600698i
$370$		0			0
$371$	−1.13149	−	1.13149i	−0.0587439	−	0.0587439i
$372$	4.77036			0.247332
$373$	−11.3372	−	11.3372i	−0.587016	−	0.587016i	0.349806	−	0.936822i	$-0.386247\pi$
$373$	−11.3372	−	11.3372i	−0.587016	−	0.587016i	−0.936822	+	0.349806i	$0.886247\pi$
$374$	−8.77288			−0.453635
$375$		0			0
$376$		−	1.37850i		−	0.0710906i
$377$	−22.8579	+	13.6948i	−1.17724	+	0.705319i
$378$	1.91302	+	1.91302i	0.0983951	+	0.0983951i
$379$	3.42232	+	3.42232i	0.175793	+	0.175793i	0.789519	−	0.613726i	$-0.210330\pi$
$379$	3.42232	+	3.42232i	0.175793	+	0.175793i	−0.613726	+	0.789519i	$0.710330\pi$
$380$		0			0
$381$			22.2356i			1.13916i
$382$			6.97086i			0.356660i
$383$	16.8644			0.861730			0.430865	−	0.902416i	$-0.358209\pi$
$383$	16.8644			0.861730			0.430865	+	0.902416i	$0.358209\pi$
$384$	3.13755	−	3.13755i	0.160112	−	0.160112i
$385$		0			0
$386$	11.8553			0.603421
$387$	8.34958	+	8.34958i	0.424433	+	0.424433i
$388$			10.9044i			0.553587i
$389$	12.3803			0.627704			0.313852	−	0.949472i	$-0.398380\pi$
$389$	12.3803			0.627704			0.313852	+	0.949472i	$0.398380\pi$
$390$		0			0
$391$	−14.7445			−0.745663
$392$			17.5830i			0.888074i
$393$	14.7278	+	14.7278i	0.742920	+	0.742920i
$394$	−13.3931			−0.674736
$395$		0			0
$396$	4.07910	−	4.07910i	0.204983	−	0.204983i
$397$	−28.3464			−1.42266			−0.711332	−	0.702856i	$-0.751908\pi$
$397$	−28.3464			−1.42266			−0.711332	+	0.702856i	$0.751908\pi$
$398$			20.3550i			1.02030i
$399$		−	10.4677i		−	0.524039i
$400$		0			0
$401$	−8.12989	−	8.12989i	−0.405988	−	0.405988i	0.474349	−	0.880337i	$-0.342683\pi$
$401$	−8.12989	−	8.12989i	−0.405988	−	0.405988i	−0.880337	+	0.474349i	$0.842683\pi$
$402$	−10.2733	−	10.2733i	−0.512385	−	0.512385i
$403$	10.3982	+	2.60664i	0.517970	+	0.129846i
$404$			6.23287i			0.310097i
$405$		0			0
$406$	−9.51263			−0.472104
$407$	−23.8694	−	23.8694i	−1.18316	−	1.18316i
$408$	−13.6769			−0.677106
$409$	−2.92001	−	2.92001i	−0.144385	−	0.144385i	0.631219	−	0.775605i	$-0.282555\pi$
$409$	−2.92001	−	2.92001i	−0.144385	−	0.144385i	−0.775605	+	0.631219i	$0.782555\pi$
$410$		0			0
$411$	−8.86077	−	8.86077i	−0.437070	−	0.437070i
$412$	7.06487	−	7.06487i	0.348061	−	0.348061i
$413$	6.07454	−	6.07454i	0.298909	−	0.298909i
$414$	−12.3793	+	12.3793i	−0.608409	+	0.608409i
$415$		0			0
$416$	−11.7885	+	7.06283i	−0.577980	+	0.346284i
$417$	28.5851	−	28.5851i	1.39982	−	1.39982i
$418$	−18.2150			−0.890925
$419$		−	20.1173i		−	0.982794i	−0.870936	−	0.491397i	$-0.836486\pi$
$419$		−	20.1173i		−	0.982794i	0.870936	−	0.491397i	$-0.163514\pi$
$420$		0			0
$421$	−10.2433	+	10.2433i	−0.499226	+	0.499226i	−0.911197	−	0.411971i	$-0.864840\pi$
$421$	−10.2433	+	10.2433i	−0.499226	+	0.499226i	0.411971	+	0.911197i	$0.364840\pi$
$422$			24.3567i			1.18566i
$423$			0.925411i			0.0449950i
$424$	−3.06954	+	3.06954i	−0.149070	+	0.149070i
$425$		0			0
$426$		−	27.8228i		−	1.34802i
$427$	17.1486			0.829878
$428$	2.91413	−	2.91413i	0.140860	−	0.140860i
$429$	27.2665	−	16.3361i	1.31644	−	0.788715i
$430$		0			0
$431$	3.81798	−	3.81798i	0.183905	−	0.183905i	−0.609150	−	0.793055i	$-0.708489\pi$
$431$	3.81798	−	3.81798i	0.183905	−	0.183905i	0.793055	+	0.609150i	$0.208489\pi$
$432$	3.07083	−	3.07083i	0.147745	−	0.147745i
$433$	6.56564	−	6.56564i	0.315524	−	0.315524i	−0.531521	−	0.847045i	$-0.678379\pi$
$433$	6.56564	−	6.56564i	0.315524	−	0.315524i	0.847045	+	0.531521i	$0.178379\pi$
$434$	2.70606	+	2.70606i	0.129895	+	0.129895i
$435$		0			0
$436$	7.00887	+	7.00887i	0.335664	+	0.335664i
$437$	−30.6139			−1.46446
$438$	6.36909	+	6.36909i	0.304327	+	0.304327i
$439$	18.5418			0.884950			0.442475	−	0.896781i	$-0.354100\pi$
$439$	18.5418			0.884950			0.442475	+	0.896781i	$0.354100\pi$
$440$		0			0
$441$		−	11.8038i		−	0.562085i
$442$	−7.83357	−	1.96374i	−0.372605	−	0.0934055i
$443$	−26.8649	−	26.8649i	−1.27639	−	1.27639i	−0.942673	−	0.333719i	$-0.891696\pi$
$443$	−26.8649	−	26.8649i	−1.27639	−	1.27639i	−0.333719	−	0.942673i	$-0.608304\pi$
$444$	−9.77806	−	9.77806i	−0.464046	−	0.464046i
$445$		0			0
$446$		−	6.50199i		−	0.307878i
$447$			19.8353i			0.938177i
$448$	−9.59425			−0.453286
$449$	−22.4994	+	22.4994i	−1.06181	+	1.06181i	−0.0638519	+	0.997959i	$0.520339\pi$
$449$	−22.4994	+	22.4994i	−1.06181	+	1.06181i	−0.997959	+	0.0638519i	$0.979661\pi$
$450$		0			0
$451$	−30.9339			−1.45662
$452$	−1.42030	−	1.42030i	−0.0668051	−	0.0668051i
$453$		−	14.4133i		−	0.677198i
$454$	14.6630			0.688171
$455$		0			0
$456$	−28.3971			−1.32982
$457$		−	0.339291i		−	0.0158714i	−0.999969	−	0.00793568i	$-0.997474\pi$
$457$		−	0.339291i		−	0.0158714i	0.999969	−	0.00793568i	$-0.00252603\pi$
$458$	−15.7381	−	15.7381i	−0.735392	−	0.735392i
$459$	−4.14961			−0.193687
$460$		0			0
$461$	−23.2709	+	23.2709i	−1.08383	+	1.08383i	−0.0876849	+	0.996148i	$0.527947\pi$
$461$	−23.2709	+	23.2709i	−1.08383	+	1.08383i	−0.996148	+	0.0876849i	$0.972053\pi$
$462$	11.3473			0.527925
$463$		−	28.5246i		−	1.32565i	−0.748774	−	0.662825i	$-0.769357\pi$
$463$		−	28.5246i		−	1.32565i	0.748774	−	0.662825i	$-0.230643\pi$
$464$			15.2699i			0.708888i
$465$		0			0
$466$	21.2650	+	21.2650i	0.985082	+	0.985082i
$467$	14.6484	+	14.6484i	0.677845	+	0.677845i	0.959512	−	0.281667i	$-0.0908873\pi$
$467$	14.6484	+	14.6484i	0.677845	+	0.677845i	−0.281667	+	0.959512i	$0.590887\pi$
$468$	4.55543	−	2.72928i	0.210575	−	0.126161i
$469$			6.45481i			0.298056i
$470$		0			0
$471$	5.06100			0.233199
$472$	−16.4792	−	16.4792i	−0.758519	−	0.758519i
$473$	−22.3836			−1.02920
$474$	15.4299	+	15.4299i	0.708720	+	0.708720i
$475$		0			0
$476$	1.12901	+	1.12901i	0.0517482	+	0.0517482i
$477$	2.06064	−	2.06064i	0.0943503	−	0.0943503i
$478$	2.40193	−	2.40193i	0.109862	−	0.109862i
$479$	5.33713	−	5.33713i	0.243860	−	0.243860i	−0.574585	−	0.818445i	$-0.694837\pi$
$479$	5.33713	−	5.33713i	0.243860	−	0.243860i	0.818445	+	0.574585i	$0.194837\pi$
$480$		0			0
$481$	−15.9707	−	26.6566i	−0.728202	−	1.21544i
$482$	−9.77684	+	9.77684i	−0.445323	+	0.445323i
$483$	19.0714			0.867778
$484$			3.09406i			0.140639i
$485$		0			0
$486$	−14.6766	+	14.6766i	−0.665744	+	0.665744i
$487$		−	10.2793i		−	0.465802i	−0.972500	−	0.232901i	$-0.925178\pi$
$487$		−	10.2793i		−	0.465802i	0.972500	−	0.232901i	$-0.0748218\pi$
$488$		−	46.5214i		−	2.10592i
$489$	1.82373	−	1.82373i	0.0824718	−	0.0824718i
$490$		0			0
$491$			26.3973i			1.19130i	0.803246	+	0.595648i	$0.203105\pi$
$491$			26.3973i			1.19130i	−0.803246	+	0.595648i	$0.796895\pi$
$492$	−12.6721			−0.571300
$493$	10.3171	−	10.3171i	0.464660	−	0.464660i
$494$	−16.2647	−	4.07728i	−0.731785	−	0.183446i
$495$		0			0
$496$	4.34384	−	4.34384i	0.195044	−	0.195044i
$497$	−8.74068	+	8.74068i	−0.392073	+	0.392073i
$498$	−21.6234	+	21.6234i	−0.968968	+	0.968968i
$499$	8.61897	+	8.61897i	0.385838	+	0.385838i	0.873200	−	0.487362i	$-0.162041\pi$
$499$	8.61897	+	8.61897i	0.385838	+	0.385838i	−0.487362	+	0.873200i	$0.662041\pi$
$500$		0			0
$501$	−28.0885	−	28.0885i	−1.25490	−	1.25490i
$502$	14.0789			0.628370
$503$	−0.0659351	−	0.0659351i	−0.00293990	−	0.00293990i	0.705635	−	0.708575i	$-0.250662\pi$
$503$	−0.0659351	−	0.0659351i	−0.00293990	−	0.00293990i	−0.708575	+	0.705635i	$0.750662\pi$
$504$	7.21483			0.321374
$505$		0			0
$506$		−	33.1865i		−	1.47532i
$507$	28.0038	−	8.48363i	1.24369	−	0.376771i
$508$	−4.97948	−	4.97948i	−0.220929	−	0.220929i
$509$	5.54846	+	5.54846i	0.245931	+	0.245931i	0.819298	−	0.573367i	$-0.194363\pi$
$509$	5.54846	+	5.54846i	0.245931	+	0.245931i	−0.573367	+	0.819298i	$0.694363\pi$
$510$		0			0
$511$		−	4.00176i		−	0.177028i
$512$			20.5938i			0.910125i
$513$	−8.61578			−0.380396
$514$	9.26386	−	9.26386i	0.408611	−	0.408611i
$515$		0			0
$516$	−9.16942			−0.403661
$517$	−1.24042	−	1.24042i	−0.0545538	−	0.0545538i
$518$		−	11.0935i		−	0.487421i
$519$	−14.0378			−0.616193
$520$		0			0
$521$	30.9373			1.35539			0.677695	−	0.735343i	$-0.262979\pi$
$521$	30.9373			1.35539			0.677695	+	0.735343i	$0.262979\pi$
$522$		−	17.3242i		−	0.758260i
$523$	0.897323	+	0.897323i	0.0392372	+	0.0392372i	0.726453	−	0.687216i	$-0.241167\pi$
$523$	0.897323	+	0.897323i	0.0392372	+	0.0392372i	−0.687216	+	0.726453i	$0.741167\pi$
$524$	−6.59635			−0.288163
$525$		0			0
$526$	−4.95362	+	4.95362i	−0.215988	+	0.215988i
$527$	−5.86984			−0.255694
$528$		−	18.2150i		−	0.792706i
$529$		−	32.7764i		−	1.42506i
$530$		0			0
$531$	11.0628	+	11.0628i	0.480086	+	0.480086i
$532$	2.34415	+	2.34415i	0.101632	+	0.101632i
$533$	−27.6219	−	6.92431i	−1.19644	−	0.299925i
$534$			12.0790i			0.522711i
$535$		0			0
$536$	17.5109			0.756354
$537$	23.1497	+	23.1497i	0.998982	+	0.998982i
$538$	5.37430			0.231703
$539$	15.8218	+	15.8218i	0.681494	+	0.681494i
$540$		0			0
$541$	20.7351	+	20.7351i	0.891472	+	0.891472i	0.994662	−	0.103189i	$-0.0329047\pi$
$541$	20.7351	+	20.7351i	0.891472	+	0.891472i	−0.103189	+	0.994662i	$0.532905\pi$
$542$	9.77368	−	9.77368i	0.419816	−	0.419816i
$543$	5.31661	−	5.31661i	0.228158	−	0.228158i
$544$	5.32085	−	5.32085i	0.228130	−	0.228130i
$545$		0			0
$546$	10.1324	+	2.54000i	0.433625	+	0.108702i
$547$	12.0707	−	12.0707i	0.516108	−	0.516108i	−0.400284	−	0.916391i	$-0.631088\pi$
$547$	12.0707	−	12.0707i	0.516108	−	0.516108i	0.916391	+	0.400284i	$0.131088\pi$
$548$	3.96860			0.169530
$549$			31.2307i			1.33289i
$550$		0			0
$551$	21.4213	−	21.4213i	0.912578	−	0.912578i
$552$		−	51.7376i		−	2.20210i
$553$		−	9.69478i		−	0.412264i
$554$	−15.5573	+	15.5573i	−0.660968	+	0.660968i
$555$		0			0
$556$			12.8028i			0.542960i
$557$	−17.4025			−0.737370			−0.368685	−	0.929554i	$-0.620192\pi$
$557$	−17.4025			−0.737370			−0.368685	+	0.929554i	$0.620192\pi$
$558$	−4.92823	+	4.92823i	−0.208629	+	0.208629i
$559$	−19.9870	−	5.01039i	−0.845360	−	0.211917i
$560$		0			0
$561$	−12.3070	+	12.3070i	−0.519601	+	0.519601i
$562$	20.6996	−	20.6996i	0.873158	−	0.873158i
$563$	−30.4631	+	30.4631i	−1.28387	+	1.28387i	−0.345416	+	0.938450i	$0.612262\pi$
$563$	−30.4631	+	30.4631i	−1.28387	+	1.28387i	−0.938450	+	0.345416i	$0.887738\pi$
$564$	−0.508138	−	0.508138i	−0.0213965	−	0.0213965i
$565$		0			0
$566$	18.5492	+	18.5492i	0.779680	+	0.779680i
$567$	12.3998			0.520742
$568$	23.7120	+	23.7120i	0.994935	+	0.994935i
$569$	32.2263			1.35100			0.675498	−	0.737362i	$-0.263929\pi$
$569$	32.2263			1.35100			0.675498	+	0.737362i	$0.263929\pi$
$570$		0			0
$571$		−	8.19417i		−	0.342916i	−0.985191	−	0.171458i	$-0.945152\pi$
$571$		−	8.19417i		−	0.342916i	0.985191	−	0.171458i	$-0.0548477\pi$
$572$	−2.44778	+	9.76445i	−0.102347	+	0.408272i
$573$	9.77902	+	9.77902i	0.408525	+	0.408525i
$574$	−7.18842	−	7.18842i	−0.300039	−	0.300039i
$575$		0			0
$576$		−	17.4729i		−	0.728036i
$577$		−	14.2517i		−	0.593304i	−0.954986	−	0.296652i	$-0.904130\pi$
$577$		−	14.2517i		−	0.593304i	0.954986	−	0.296652i	$-0.0958702\pi$
$578$	−14.8649			−0.618300
$579$	16.6312	−	16.6312i	0.691168	−	0.691168i
$580$		0			0
$581$	13.5862			0.563651
$582$	−27.6219	−	27.6219i	−1.14496	−	1.14496i
$583$			5.52418i			0.228788i
$584$	−10.8561			−0.449230
$585$		0			0
$586$	−6.92494			−0.286067
$587$		−	2.55919i		−	0.105629i	−0.998604	−	0.0528146i	$-0.983181\pi$
$587$		−	2.55919i		−	0.105629i	0.998604	−	0.0528146i	$-0.0168192\pi$
$588$	6.48139	+	6.48139i	0.267288	+	0.267288i
$589$	−12.1875			−0.502175
$590$		0			0
$591$	−18.7884	+	18.7884i	−0.772853	+	0.772853i
$592$	−17.8076			−0.731888
$593$			17.4690i			0.717364i	0.933460	+	0.358682i	$0.116774\pi$
$593$			17.4690i			0.717364i	−0.933460	+	0.358682i	$0.883226\pi$
$594$		−	9.33980i		−	0.383217i
$595$		0			0
$596$	−4.44195	−	4.44195i	−0.181950	−	0.181950i
$597$	28.5549	+	28.5549i	1.16867	+	1.16867i
$598$	7.42853	−	29.6332i	0.303775	−	1.21179i
$599$			2.29945i			0.0939531i	0.998896	+	0.0469765i	$0.0149586\pi$
$599$			2.29945i			0.0939531i	−0.998896	+	0.0469765i	$0.985041\pi$
$600$		0			0
$601$	−22.6684			−0.924663			−0.462331	−	0.886707i	$-0.652987\pi$
$601$	−22.6684			−0.924663			−0.462331	+	0.886707i	$0.652987\pi$
$602$	−5.20150	−	5.20150i	−0.211997	−	0.211997i
$603$	−11.7554			−0.478716
$604$	3.22775	+	3.22775i	0.131335	+	0.131335i
$605$		0			0
$606$	−15.7884	−	15.7884i	−0.641362	−	0.641362i
$607$	−4.18861	+	4.18861i	−0.170010	+	0.170010i	−0.786984	−	0.616974i	$-0.788359\pi$
$607$	−4.18861	+	4.18861i	−0.170010	+	0.170010i	0.616974	+	0.786984i	$0.288359\pi$
$608$	11.0476	−	11.0476i	0.448040	−	0.448040i
$609$	−13.3447	+	13.3447i	−0.540756	+	0.540756i
$610$		0			0
$611$	−0.829954	−	1.38527i	−0.0335763	−	0.0560421i
$612$	−2.05613	+	2.05613i	−0.0831143	+	0.0831143i
$613$	−14.2756			−0.576586			−0.288293	−	0.957542i	$-0.593088\pi$
$613$	−14.2756			−0.576586			−0.288293	+	0.957542i	$0.593088\pi$
$614$			0.443718i			0.0179070i
$615$		0			0
$616$	−9.67078	+	9.67078i	−0.389647	+	0.389647i
$617$			47.3133i			1.90476i	0.304909	+	0.952382i	$0.401374\pi$
$617$			47.3133i			1.90476i	−0.304909	+	0.952382i	$0.598626\pi$
$618$			35.7919i			1.43976i
$619$	−10.3491	+	10.3491i	−0.415966	+	0.415966i	−0.883811	−	0.467845i	$-0.845031\pi$
$619$	−10.3491	+	10.3491i	−0.415966	+	0.415966i	0.467845	+	0.883811i	$0.345031\pi$
$620$		0			0
$621$		−	15.6974i		−	0.629913i
$622$	23.8827			0.957609
$623$	3.79470	−	3.79470i	0.152031	−	0.152031i
$624$	4.07728	−	16.2647i	0.163222	−	0.651111i
$625$		0			0
$626$	13.7878	−	13.7878i	0.551072	−	0.551072i
$627$	−25.5528	+	25.5528i	−1.02048	+	1.02048i
$628$	−1.13337	+	1.13337i	−0.0452264	+	0.0452264i
$629$	12.0317	+	12.0317i	0.479735	+	0.479735i
$630$		0			0
$631$	11.2717	+	11.2717i	0.448719	+	0.448719i	0.894928	−	0.446210i	$-0.147226\pi$
$631$	11.2717	+	11.2717i	0.448719	+	0.448719i	−0.446210	+	0.894928i	$0.647226\pi$
$632$	−26.3004			−1.04617
$633$	34.1686	+	34.1686i	1.35808	+	1.35808i
$634$	1.40491			0.0557960
$635$		0			0
$636$			2.26298i			0.0897328i
$637$	10.5862	+	17.6694i	0.419441	+	0.700086i
$638$	23.2214	+	23.2214i	0.919345	+	0.919345i
$639$	−15.9183	−	15.9183i	−0.629720	−	0.629720i
$640$		0			0
$641$			30.5095i			1.20505i	0.798099	+	0.602527i	$0.205839\pi$
$641$			30.5095i			1.20505i	−0.798099	+	0.602527i	$0.794161\pi$
$642$			14.7635i			0.582669i
$643$	5.60519			0.221047			0.110524	−	0.993874i	$-0.464747\pi$
$643$	5.60519			0.221047			0.110524	+	0.993874i	$0.464747\pi$
$644$	−4.27088	+	4.27088i	−0.168296	+	0.168296i
$645$		0			0
$646$	9.18154			0.361243
$647$	−4.87089	−	4.87089i	−0.191495	−	0.191495i	0.604847	−	0.796342i	$-0.293234\pi$
$647$	−4.87089	−	4.87089i	−0.191495	−	0.191495i	−0.796342	+	0.604847i	$0.793234\pi$
$648$		−	33.6386i		−	1.32145i
$649$	−29.6573			−1.16415
$650$		0			0
$651$	7.59236			0.297568
$652$			0.816818i			0.0319891i
$653$	33.8017	+	33.8017i	1.32276	+	1.32276i	0.911529	+	0.411235i	$0.134902\pi$
$653$	33.8017	+	33.8017i	1.32276	+	1.32276i	0.411235	+	0.911529i	$0.365098\pi$
$654$	−35.5083			−1.38848
$655$		0			0
$656$	−11.5390	+	11.5390i	−0.450524	+	0.450524i
$657$	7.28793			0.284329
$658$		−	0.576499i		−	0.0224743i
$659$			3.84344i			0.149719i	0.997194	+	0.0748597i	$0.0238509\pi$
$659$			3.84344i			0.149719i	−0.997194	+	0.0748597i	$0.976149\pi$
$660$		0			0
$661$	−16.8399	−	16.8399i	−0.654995	−	0.654995i	0.299197	−	0.954191i	$-0.403281\pi$
$661$	−16.8399	−	16.8399i	−0.654995	−	0.654995i	−0.954191	+	0.299197i	$0.903281\pi$
$662$	−25.6932	−	25.6932i	−0.998594	−	0.998594i
$663$	−13.7441	+	8.23446i	−0.533776	+	0.319800i
$664$		−	36.8572i		−	1.43034i
$665$		0			0
$666$	20.2033			0.782861
$667$	39.0281	+	39.0281i	1.51118	+	1.51118i
$668$	12.5804			0.486749
$669$	−9.12127	−	9.12127i	−0.352649	−	0.352649i
$670$		0			0
$671$	−41.8617	−	41.8617i	−1.61605	−	1.61605i
$672$	−6.88228	+	6.88228i	−0.265490	+	0.265490i
$673$	3.22572	−	3.22572i	0.124343	−	0.124343i	−0.642197	−	0.766540i	$-0.721977\pi$
$673$	3.22572	−	3.22572i	0.124343	−	0.124343i	0.766540	+	0.642197i	$0.221977\pi$
$674$	10.2157	−	10.2157i	0.393495	−	0.393495i
$675$		0			0
$676$	−4.37139	+	8.17107i	−0.168130	+	0.314272i
$677$	−5.51377	+	5.51377i	−0.211911	+	0.211911i	−0.805079	−	0.593168i	$-0.797877\pi$
$677$	−5.51377	+	5.51377i	−0.211911	+	0.211911i	0.593168	+	0.805079i	$0.297877\pi$
$678$	7.19548			0.276341
$679$			17.3551i			0.666028i
$680$		0			0
$681$	20.5699	−	20.5699i	0.788242	−	0.788242i
$682$		−	13.2116i		−	0.505899i
$683$			29.6709i			1.13533i	0.823261	+	0.567663i	$0.192152\pi$
$683$			29.6709i			1.13533i	−0.823261	+	0.567663i	$0.807848\pi$
$684$	−4.26912	+	4.26912i	−0.163234	+	0.163234i
$685$		0			0
$686$			16.3635i			0.624761i
$687$	−44.1561			−1.68466
$688$	−8.34958	+	8.34958i	−0.318325	+	0.318325i
$689$	−1.23654	+	4.93271i	−0.0471085	+	0.187921i
$690$		0			0
$691$	29.7040	−	29.7040i	1.12999	−	1.12999i	0.139816	−	0.990178i	$-0.455349\pi$
$691$	29.7040	−	29.7040i	1.12999	−	1.12999i	0.990178	−	0.139816i	$-0.0446510\pi$
$692$	3.14366	−	3.14366i	0.119504	−	0.119504i
$693$	6.49218	−	6.49218i	0.246617	−	0.246617i
$694$	−13.0867	−	13.0867i	−0.496764	−	0.496764i
$695$		0			0
$696$	36.2021	+	36.2021i	1.37224	+	1.37224i
$697$	15.5927			0.590616
$698$	−7.67426	−	7.67426i	−0.290475	−	0.290475i
$699$	59.6629			2.25666
$700$		0			0
$701$		−	30.5188i		−	1.15268i	−0.817211	−	0.576339i	$-0.804481\pi$
$701$		−	30.5188i		−	1.15268i	0.817211	−	0.576339i	$-0.195519\pi$
$702$	2.09064	−	8.33979i	0.0789061	−	0.314765i
$703$	24.9813	+	24.9813i	0.942186	+	0.942186i
$704$	23.4207	+	23.4207i	0.882700	+	0.882700i
$705$		0			0
$706$			8.59686i			0.323547i
$707$			9.92005i			0.373082i
$708$	−12.1491			−0.456590
$709$	35.3379	−	35.3379i	1.32714	−	1.32714i	0.419289	−	0.907853i	$-0.362280\pi$
$709$	35.3379	−	35.3379i	1.32714	−	1.32714i	0.907853	−	0.419289i	$-0.137720\pi$
$710$		0			0
$711$	17.6559			0.662149
$712$	−10.2944	−	10.2944i	−0.385799	−	0.385799i
$713$		−	22.2047i		−	0.831573i
$714$	−5.71978			−0.214058
$715$		0			0
$716$	−10.3684			−0.387484
$717$		−	6.73907i		−	0.251675i
$718$	15.6845	+	15.6845i	0.585339	+	0.585339i
$719$	−35.2659			−1.31520			−0.657599	−	0.753368i	$-0.728428\pi$
$719$	−35.2659			−1.31520			−0.657599	+	0.753368i	$0.728428\pi$
$720$		0			0
$721$	11.2442	−	11.2442i	0.418757	−	0.418757i
$722$	−2.49259			−0.0927645
$723$			27.4307i			1.02016i
$724$			2.38123i			0.0884976i
$725$		0			0
$726$	−7.83755	−	7.83755i	−0.290879	−	0.290879i
$727$	14.7736	+	14.7736i	0.547921	+	0.547921i	0.925839	−	0.377918i	$-0.123360\pi$
$727$	14.7736	+	14.7736i	0.547921	+	0.547921i	−0.377918	+	0.925839i	$0.623360\pi$
$728$	−10.8001	+	6.47061i	−0.400277	+	0.239817i
$729$			8.38959i			0.310726i
$730$		0			0
$731$	11.2828			0.417309
$732$	−17.1486	−	17.1486i	−0.633830	−	0.633830i
$733$	−43.4921			−1.60642			−0.803209	−	0.595698i	$-0.796876\pi$
$733$	−43.4921			−1.60642			−0.803209	+	0.595698i	$0.796876\pi$
$734$	8.97510	+	8.97510i	0.331277	+	0.331277i
$735$		0			0
$736$	20.1280	+	20.1280i	0.741928	+	0.741928i
$737$	15.7569	−	15.7569i	0.580414	−	0.580414i
$738$	13.0914	−	13.0914i	0.481901	−	0.481901i
$739$	36.6869	−	36.6869i	1.34955	−	1.34955i	0.463402	−	0.886148i	$-0.346629\pi$
$739$	36.6869	−	36.6869i	1.34955	−	1.34955i	0.886148	−	0.463402i	$-0.153371\pi$
$740$		0			0
$741$	−28.5367	+	17.0971i	−1.04832	+	0.628077i
$742$	−1.28371	+	1.28371i	−0.0471264	+	0.0471264i
$743$	2.24579			0.0823899			0.0411949	−	0.999151i	$-0.486884\pi$
$743$	2.24579			0.0823899			0.0411949	+	0.999151i	$0.486884\pi$
$744$		−	20.5969i		−	0.755117i
$745$		0			0
$746$	−12.8624	+	12.8624i	−0.470925	+	0.470925i
$747$			24.7429i			0.905297i
$748$		−	5.51209i		−	0.201542i
$749$	4.63803	−	4.63803i	0.169470	−	0.169470i
$750$		0			0
$751$			50.7239i			1.85094i	0.378820	+	0.925470i	$0.376330\pi$
$751$			50.7239i			1.85094i	−0.378820	+	0.925470i	$0.623670\pi$
$752$	−0.925411			−0.0337463
$753$	19.7504	−	19.7504i	0.719745	−	0.719745i
$754$	15.5372	+	25.9330i	0.565831	+	0.944426i
$755$		0			0
$756$	−1.20197	+	1.20197i	−0.0437153	+	0.0437153i
$757$	34.5922	−	34.5922i	1.25727	−	1.25727i	0.304884	−	0.952389i	$-0.401382\pi$
$757$	34.5922	−	34.5922i	1.25727	−	1.25727i	0.952389	−	0.304884i	$-0.0986178\pi$
$758$	3.88273	−	3.88273i	0.141027	−	0.141027i
$759$	−46.5554	−	46.5554i	−1.68986	−	1.68986i
$760$		0			0
$761$	27.3645	+	27.3645i	0.991964	+	0.991964i	0.999968	−	0.00800445i	$-0.00254792\pi$
$761$	27.3645	+	27.3645i	0.991964	+	0.991964i	−0.00800445	+	0.999968i	$0.502548\pi$
$762$	25.2270			0.913877
$763$	11.1551	+	11.1551i	0.403842	+	0.403842i
$764$	−4.37987			−0.158458
$765$		0			0
$766$		−	19.1332i		−	0.691310i
$767$	−26.4819	−	6.63854i	−0.956206	−	0.239704i
$768$	23.3588	+	23.3588i	0.842888	+	0.842888i
$769$	−6.10912	−	6.10912i	−0.220301	−	0.220301i	0.588324	−	0.808625i	$-0.299788\pi$
$769$	−6.10912	−	6.10912i	−0.220301	−	0.220301i	−0.808625	+	0.588324i	$0.799788\pi$
$770$		0			0
$771$		−	25.9915i		−	0.936060i
$772$			7.44884i			0.268090i
$773$	−14.6511			−0.526965			−0.263483	−	0.964664i	$-0.584871\pi$
$773$	−14.6511			−0.526965			−0.263483	+	0.964664i	$0.584871\pi$
$774$	9.47286	−	9.47286i	0.340495	−	0.340495i
$775$		0			0
$776$	47.0816			1.69013
$777$	−15.5625	−	15.5625i	−0.558300	−	0.558300i
$778$		−	14.0458i		−	0.503566i
$779$	32.3749			1.15995
$780$		0			0
$781$	42.6740			1.52699
$782$			16.7281i			0.598197i
$783$	10.9838	+	10.9838i	0.392530	+	0.392530i
$784$	11.8038			0.421564
$785$		0			0
$786$	16.7092	−	16.7092i	0.595996	−	0.595996i
$787$	−34.9849			−1.24708			−0.623539	−	0.781792i	$-0.714306\pi$
$787$	−34.9849			−1.24708			−0.623539	+	0.781792i	$0.714306\pi$
$788$		−	8.41504i		−	0.299773i
$789$			13.8983i			0.494793i
$790$		0			0
$791$	−2.26050	−	2.26050i	−0.0803741	−	0.0803741i
$792$	−17.6122	−	17.6122i	−0.625823	−	0.625823i
$793$	−28.0092	−	46.7500i	−0.994635	−	1.66014i
$794$			32.1599i			1.14131i
$795$		0			0
$796$	−12.7893			−0.453304
$797$	5.21337	+	5.21337i	0.184667	+	0.184667i	0.793386	−	0.608719i	$-0.208316\pi$
$797$	5.21337	+	5.21337i	0.184667	+	0.184667i	−0.608719	+	0.793386i	$0.708316\pi$
$798$	−11.8759			−0.420403
$799$	0.625254	+	0.625254i	0.0221199	+	0.0221199i
$800$		0			0
$801$	6.91082	+	6.91082i	0.244182	+	0.244182i
$802$	−9.22362	+	9.22362i	−0.325697	+	0.325697i
$803$	−9.76876	+	9.76876i	−0.344732	+	0.344732i
$804$	6.45481	−	6.45481i	0.227644	−	0.227644i
$805$		0			0
$806$	2.95731	−	11.7971i	0.104167	−	0.415534i
$807$	7.53930	−	7.53930i	0.265396	−	0.265396i
$808$	26.9115			0.946743
$809$			14.2390i			0.500617i	0.968166	+	0.250309i	$0.0805321\pi$
$809$			14.2390i			0.500617i	−0.968166	+	0.250309i	$0.919468\pi$
$810$		0			0
$811$	15.2666	−	15.2666i	0.536082	−	0.536082i	−0.386294	−	0.922376i	$-0.626245\pi$
$811$	15.2666	−	15.2666i	0.536082	−	0.536082i	0.922376	+	0.386294i	$0.126245\pi$
$812$		−	5.97689i		−	0.209748i
$813$		−	27.4219i		−	0.961727i
$814$	−27.0805	+	27.0805i	−0.949172	+	0.949172i
$815$		0			0
$816$			9.18154i			0.321418i
$817$	23.4263			0.819582
$818$	−3.31285	+	3.31285i	−0.115831	+	0.115831i
$819$	7.25029	−	4.34384i	0.253345	−	0.151786i
$820$		0			0
$821$	22.3739	−	22.3739i	0.780853	−	0.780853i	−0.199122	−	0.979975i	$-0.563809\pi$
$821$	22.3739	−	22.3739i	0.780853	−	0.780853i	0.979975	+	0.199122i	$0.0638089\pi$
$822$	−10.0528	+	10.0528i	−0.350633	+	0.350633i
$823$	11.9980	−	11.9980i	0.418223	−	0.418223i	−0.466368	−	0.884591i	$-0.654438\pi$
$823$	11.9980	−	11.9980i	0.418223	−	0.418223i	0.884591	+	0.466368i	$0.154438\pi$
$824$	−30.5038	−	30.5038i	−1.06265	−	1.06265i
$825$		0			0
$826$	−6.89176	−	6.89176i	−0.239795	−	0.239795i
$827$	27.2891			0.948935			0.474467	−	0.880273i	$-0.342641\pi$
$827$	27.2891			0.948935			0.474467	+	0.880273i	$0.342641\pi$
$828$	−7.77805	−	7.77805i	−0.270306	−	0.270306i
$829$	0.831547			0.0288808			0.0144404	−	0.999896i	$-0.495403\pi$
$829$	0.831547			0.0288808			0.0144404	+	0.999896i	$0.495403\pi$
$830$		0			0
$831$			43.6490i			1.51417i
$832$	15.6705	+	26.1556i	0.543277	+	0.906781i
$833$	−7.97522	−	7.97522i	−0.276325	−	0.276325i
$834$	−32.4307	−	32.4307i	−1.12298	−	1.12298i
$835$		0			0
$836$		−	11.4447i		−	0.395823i
$837$		−	6.24916i		−	0.216002i
$838$	−22.8237			−0.788431
$839$	11.1299	−	11.1299i	0.384247	−	0.384247i	−0.488383	−	0.872629i	$-0.662413\pi$
$839$	11.1299	−	11.1299i	0.384247	−	0.384247i	0.872629	+	0.488383i	$0.162413\pi$
$840$		0			0
$841$	−25.6179			−0.883377
$842$	11.6213	+	11.6213i	0.400496	+	0.400496i
$843$		−	58.0764i		−	2.00026i
$844$	−15.3036			−0.526770
$845$		0			0
$846$	1.04991			0.0360966
$847$			4.92442i			0.169205i
$848$	2.06064	+	2.06064i	0.0707627	+	0.0707627i
$849$	52.0431			1.78612
$850$		0			0
$851$	−45.5141	+	45.5141i	−1.56020	+	1.56020i
$852$	17.4814			0.598901
$853$			15.7213i			0.538288i	0.963100	+	0.269144i	$0.0867407\pi$
$853$			15.7213i			0.538288i	−0.963100	+	0.269144i	$0.913259\pi$
$854$		−	19.4556i		−	0.665757i
$855$		0			0
$856$	−12.5822	−	12.5822i	−0.430052	−	0.430052i
$857$	−25.1913	−	25.1913i	−0.860519	−	0.860519i	0.130880	−	0.991398i	$-0.458220\pi$
$857$	−25.1913	−	25.1913i	−0.860519	−	0.860519i	−0.991398	+	0.130880i	$0.958220\pi$
$858$	−18.5338	−	30.9347i	−0.632734	−	1.05609i
$859$			27.9104i			0.952292i	0.879366	+	0.476146i	$0.157967\pi$
$859$			27.9104i			0.952292i	−0.879366	+	0.476146i	$0.842033\pi$
$860$		0			0
$861$	−20.1685			−0.687339
$862$	−4.33161	−	4.33161i	−0.147535	−	0.147535i
$863$	20.2303			0.688646			0.344323	−	0.938851i	$-0.388109\pi$
$863$	20.2303			0.688646			0.344323	+	0.938851i	$0.388109\pi$
$864$	5.66469	+	5.66469i	0.192717	+	0.192717i
$865$		0			0
$866$	−7.44892	−	7.44892i	−0.253125	−	0.253125i
$867$	−20.8532	+	20.8532i	−0.708211	+	0.708211i
$868$	−1.70025	+	1.70025i	−0.0577102	+	0.0577102i
$869$	−23.6661	+	23.6661i	−0.802816	+	0.802816i
$870$		0			0
$871$	17.5969	−	10.5428i	0.596249	−	0.357229i
$872$	30.2620	−	30.2620i	1.02480	−	1.02480i
$873$	−31.6068			−1.06973
$874$			34.7324i			1.17484i
$875$		0			0
$876$	−4.00176	+	4.00176i	−0.135207	+	0.135207i
$877$		−	50.8477i		−	1.71701i	−0.512809	−	0.858503i	$-0.671395\pi$
$877$		−	50.8477i		−	1.71701i	0.512809	−	0.858503i	$-0.328605\pi$
$878$		−	21.0362i		−	0.709938i
$879$	−9.71460	+	9.71460i	−0.327665	+	0.327665i
$880$		0			0
$881$		−	20.8619i		−	0.702855i	−0.936215	−	0.351427i	$-0.885696\pi$
$881$		−	20.8619i		−	0.702855i	0.936215	−	0.351427i	$-0.114304\pi$
$882$	−13.3918			−0.450924
$883$	19.1508	−	19.1508i	0.644476	−	0.644476i	−0.307176	−	0.951653i	$-0.599384\pi$
$883$	19.1508	−	19.1508i	0.644476	−	0.644476i	0.951653	+	0.307176i	$0.0993841\pi$
$884$	1.23384	−	4.92192i	0.0414984	−	0.165542i
$885$		0			0
$886$	−30.4791	+	30.4791i	−1.02397	+	1.02397i
$887$	0.492724	−	0.492724i	0.0165440	−	0.0165440i	−0.698786	−	0.715330i	$-0.746276\pi$
$887$	0.492724	−	0.492724i	0.0165440	−	0.0165440i	0.715330	+	0.698786i	$0.246276\pi$
$888$	−42.2184	+	42.2184i	−1.41676	+	1.41676i
$889$	−7.92519	−	7.92519i	−0.265802	−	0.265802i
$890$		0			0
$891$	−30.2693	−	30.2693i	−1.01406	−	1.01406i
$892$	4.08527			0.136785
$893$	1.29821	+	1.29821i	0.0434428	+	0.0434428i
$894$	22.5038			0.752638
$895$		0			0
$896$			2.23657i			0.0747184i
$897$	−31.1497	−	51.9918i	−1.04006	−	1.73596i
$898$	25.5263	+	25.5263i	0.851822	+	0.851822i
$899$	15.5372	+	15.5372i	0.518194	+	0.518194i
$900$		0			0
$901$		−	2.78454i		−	0.0927666i
$902$			35.0955i			1.16855i
$903$	−14.5938			−0.485650
$904$	−6.13237	+	6.13237i	−0.203960	+	0.203960i
$905$		0			0
$906$	−16.3524			−0.543272
$907$	−3.33550	−	3.33550i	−0.110753	−	0.110753i	0.649558	−	0.760312i	$-0.274954\pi$
$907$	−3.33550	−	3.33550i	−0.110753	−	0.110753i	−0.760312	+	0.649558i	$0.774954\pi$
$908$			9.21295i			0.305742i
$909$	−18.0662			−0.599218
$910$		0			0
$911$	−3.33092			−0.110358			−0.0551792	−	0.998476i	$-0.517573\pi$
$911$	−3.33092			−0.110358			−0.0551792	+	0.998476i	$0.517573\pi$
$912$			19.0635i			0.631256i
$913$	−33.1655	−	33.1655i	−1.09762	−	1.09762i
$914$	−0.384936			−0.0127326
$915$		0			0
$916$	9.88840	−	9.88840i	0.326722	−	0.326722i
$917$	−10.4986			−0.346693
$918$			4.70786i			0.155383i
$919$			12.2978i			0.405667i	0.979213	+	0.202833i	$0.0650150\pi$
$919$			12.2978i			0.405667i	−0.979213	+	0.202833i	$0.934985\pi$
$920$		0			0
$921$	0.622467	+	0.622467i	0.0205110	+	0.0205110i
$922$	26.4016	+	26.4016i	0.869489	+	0.869489i
$923$	38.1049	+	9.55222i	1.25424	+	0.314415i
$924$			7.12964i			0.234548i
$925$		0			0
$926$	−32.3621			−1.06348
$927$	20.4777	+	20.4777i	0.672577	+	0.672577i
$928$	−28.1681			−0.924664
$929$	22.0097	+	22.0097i	0.722114	+	0.722114i	0.969035	−	0.246921i	$-0.0794190\pi$
$929$	22.0097	+	22.0097i	0.722114	+	0.722114i	−0.246921	+	0.969035i	$0.579419\pi$
$930$		0			0
$931$	−16.5588	−	16.5588i	−0.542694	−	0.542694i
$932$	−13.3610	+	13.3610i	−0.437655	+	0.437655i
$933$	33.5037	−	33.5037i	1.09686	−	1.09686i
$934$	16.6190	−	16.6190i	0.543791	−	0.543791i
$935$		0			0
$936$	−11.7841	−	19.6689i	−0.385177	−	0.642897i
$937$	−0.875833	+	0.875833i	−0.0286122	+	0.0286122i	−0.721268	−	0.692656i	$-0.756440\pi$
$937$	−0.875833	+	0.875833i	−0.0286122	+	0.0286122i	0.692656	+	0.721268i	$0.256440\pi$
$938$	7.32319			0.239111
$939$		−	38.6843i		−	1.26241i
$940$		0			0
$941$	−12.8932	+	12.8932i	−0.420306	+	0.420306i	−0.885309	−	0.465003i	$-0.846053\pi$
$941$	−12.8932	+	12.8932i	−0.420306	+	0.420306i	0.465003	+	0.885309i	$0.346053\pi$
$942$		−	5.74187i		−	0.187080i
$943$			58.9849i			1.92081i
$944$	−11.0628	+	11.0628i	−0.360064	+	0.360064i
$945$		0			0
$946$			25.3949i			0.825659i
$947$	−46.6408			−1.51562			−0.757812	−	0.652473i	$-0.773731\pi$
$947$	−46.6408			−1.51562			−0.757812	+	0.652473i	$0.773731\pi$
$948$	−9.69478	+	9.69478i	−0.314872	+	0.314872i
$949$	−10.9095	+	6.53617i	−0.354137	+	0.212173i
$950$		0			0
$951$	1.97086	−	1.97086i	0.0639096	−	0.0639096i
$952$	4.87470	−	4.87470i	0.157990	−	0.157990i
$953$	−4.59962	+	4.59962i	−0.148996	+	0.148996i	−0.777670	−	0.628673i	$-0.783598\pi$
$953$	−4.59962	+	4.59962i	−0.148996	+	0.148996i	0.628673	+	0.777670i	$0.283598\pi$
$954$	−2.33786	−	2.33786i	−0.0756911	−	0.0756911i
$955$		0			0
$956$	1.50916	+	1.50916i	0.0488098	+	0.0488098i
$957$	65.1520			2.10606
$958$	−6.05514	−	6.05514i	−0.195633	−	0.195633i
$959$	6.31630			0.203964
$960$		0			0
$961$			22.1602i			0.714847i
$962$	−30.2428	+	18.1193i	−0.975067	+	0.584189i
$963$	8.44669	+	8.44669i	0.272191	+	0.272191i
$964$	−6.14290	−	6.14290i	−0.197849	−	0.197849i
$965$		0			0
$966$		−	21.6371i		−	0.696162i
$967$		−	27.7289i		−	0.891701i	−0.895107	−	0.445851i	$-0.852901\pi$
$967$		−	27.7289i		−	0.891701i	0.895107	−	0.445851i	$-0.147099\pi$
$968$	13.3591			0.429379
$969$	12.8803	−	12.8803i	0.413774	−	0.413774i
$970$		0			0
$971$	29.9865			0.962311			0.481156	−	0.876635i	$-0.340217\pi$
$971$	29.9865			0.962311			0.481156	+	0.876635i	$0.340217\pi$
$972$	−9.22146	−	9.22146i	−0.295778	−	0.295778i
$973$			20.3766i			0.653243i
$974$	−11.6622			−0.373682
$975$		0			0
$976$	−31.2307			−0.999669
$977$			40.5165i			1.29624i	0.761539	+	0.648119i	$0.224444\pi$
$977$			40.5165i			1.29624i	−0.761539	+	0.648119i	$0.775556\pi$
$978$	−2.06908	−	2.06908i	−0.0661617	−	0.0661617i
$979$	−18.5266			−0.592112
$980$		0			0
$981$	−20.3154	+	20.3154i	−0.648622	+	0.648622i
$982$	29.9486			0.955699
$983$			22.9573i			0.732225i	0.930571	+	0.366112i	$0.119311\pi$
$983$			22.9573i			0.732225i	−0.930571	+	0.366112i	$0.880689\pi$
$984$			54.7138i			1.74421i
$985$		0			0
$986$	−11.7051	−	11.7051i	−0.372766	−	0.372766i
$987$	−0.808738	−	0.808738i	−0.0257424	−	0.0257424i
$988$	2.56180	−	10.2193i	0.0815017	−	0.325120i
$989$			42.6811i			1.35718i
$990$		0			0
$991$	−6.19775			−0.196878			−0.0984391	−	0.995143i	$-0.531385\pi$
$991$	−6.19775			−0.196878			−0.0984391	+	0.995143i	$0.531385\pi$
$992$	8.01300	+	8.01300i	0.254413	+	0.254413i
$993$	−72.0870			−2.28761
$994$	9.91657	+	9.91657i	0.314535	+	0.314535i
$995$		0			0
$996$	−13.5862	−	13.5862i	−0.430496	−	0.430496i
$997$	−0.0179330	+	0.0179330i	−0.000567945	+	0.000567945i	−0.707391	−	0.706823i	$-0.750128\pi$
$997$	−0.0179330	+	0.0179330i	−0.000567945	+	0.000567945i	0.706823	+	0.707391i	$0.250128\pi$
$998$	9.77849	−	9.77849i	0.309533	−	0.309533i
$999$	−12.8092	+	12.8092i	−0.405266	+	0.405266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.f.d.18.3	✓	16
5.2	odd	4		325.2.k.d.57.6	yes	16
5.3	odd	4		325.2.k.d.57.3	yes	16
5.4	even	2	inner	325.2.f.d.18.6	yes	16
13.8	odd	4		325.2.k.d.268.6	yes	16
65.8	even	4	inner	325.2.f.d.307.3	yes	16
65.34	odd	4		325.2.k.d.268.3	yes	16
65.47	even	4	inner	325.2.f.d.307.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.f.d.18.3	✓	16	1.1	even	1	trivial
325.2.f.d.18.6	yes	16	5.4	even	2	inner
325.2.f.d.307.3	yes	16	65.8	even	4	inner
325.2.f.d.307.6	yes	16	65.47	even	4	inner
325.2.k.d.57.3	yes	16	5.3	odd	4
325.2.k.d.57.6	yes	16	5.2	odd	4
325.2.k.d.268.3	yes	16	65.34	odd	4
325.2.k.d.268.6	yes	16	13.8	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.13453i q^{2} +(-1.59157 - 1.59157i) q^{3} +0.712838 q^{4} +(-1.80569 + 1.80569i) q^{6} +1.13453 q^{7} -3.07780i q^{8} +2.06618i q^{9} +O(q^{10})\)	\(q-1.13453i q^{2} +(-1.59157 - 1.59157i) q^{3} +0.712838 q^{4} +(-1.80569 + 1.80569i) q^{6} +1.13453 q^{7} -3.07780i q^{8} +2.06618i q^{9} +(-2.76952 - 2.76952i) q^{11} +(-1.13453 - 1.13453i) q^{12} +(-1.85306 - 3.09292i) q^{13} -1.28716i q^{14} -2.06618 q^{16} +(1.39602 + 1.39602i) q^{17} +2.34415 q^{18} +(2.89853 + 2.89853i) q^{19} +(-1.80569 - 1.80569i) q^{21} +(-3.14211 + 3.14211i) q^{22} +(-5.28093 + 5.28093i) q^{23} +(-4.89853 + 4.89853i) q^{24} +(-3.50902 + 2.10235i) q^{26} +(-1.48623 + 1.48623i) q^{27} +0.808738 q^{28} -7.39039i q^{29} +(-2.10235 + 2.10235i) q^{31} -3.81145i q^{32} +8.81577i q^{33} +(1.58383 - 1.58383i) q^{34} +1.47286i q^{36} +8.61859 q^{37} +(3.28848 - 3.28848i) q^{38} +(-1.97334 + 7.87187i) q^{39} +(5.58471 - 5.58471i) q^{41} +(-2.04861 + 2.04861i) q^{42} +(4.04106 - 4.04106i) q^{43} +(-1.97422 - 1.97422i) q^{44} +(5.99138 + 5.99138i) q^{46} +0.447884 q^{47} +(3.28848 + 3.28848i) q^{48} -5.71284 q^{49} -4.44372i q^{51} +(-1.32093 - 2.20476i) q^{52} +(-0.997317 - 0.997317i) q^{53} +(1.68618 + 1.68618i) q^{54} -3.49186i q^{56} -9.22643i q^{57} -8.38463 q^{58} +(5.35423 - 5.35423i) q^{59} +15.1151 q^{61} +(2.38518 + 2.38518i) q^{62} +2.34415i q^{63} -8.45658 q^{64} +10.0018 q^{66} +5.68941i q^{67} +(0.995135 + 0.995135i) q^{68} +16.8099 q^{69} +(-7.70422 + 7.70422i) q^{71} +6.35930 q^{72} -3.52724i q^{73} -9.77806i q^{74} +(2.06618 + 2.06618i) q^{76} +(-3.14211 - 3.14211i) q^{77} +(8.93088 + 2.23881i) q^{78} -8.54519i q^{79} +10.9294 q^{81} +(-6.33603 - 6.33603i) q^{82} +11.9752 q^{83} +(-1.28716 - 1.28716i) q^{84} +(-4.58471 - 4.58471i) q^{86} +(-11.7623 + 11.7623i) q^{87} +(-8.52403 + 8.52403i) q^{88} +(3.34473 - 3.34473i) q^{89} +(-2.10235 - 3.50902i) q^{91} +(-3.76445 + 3.76445i) q^{92} +6.69207 q^{93} -0.508138i q^{94} +(-6.06618 + 6.06618i) q^{96} +15.2972i q^{97} +6.48139i q^{98} +(5.72234 - 5.72234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 16 * q - 8 * q^4 + 12 * q^6	\( 16 q - 8 q^{4} + 12 q^{6} - 20 q^{11} - 8 q^{16} - 16 q^{19} + 12 q^{21} - 16 q^{24} - 16 q^{26} + 8 q^{31} + 44 q^{34} - 28 q^{39} + 4 q^{41} + 76 q^{44} + 12 q^{46} - 72 q^{49} + 4 q^{54} - 24 q^{59} + 24 q^{61} + 16 q^{64} - 48 q^{66} + 112 q^{69} - 20 q^{71} + 8 q^{76} - 40 q^{84} + 12 q^{86} - 36 q^{89} + 8 q^{91} - 72 q^{96} + 52 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 12 * q^6 - 20 * q^11 - 8 * q^16 - 16 * q^19 + 12 * q^21 - 16 * q^24 - 16 * q^26 + 8 * q^31 + 44 * q^34 - 28 * q^39 + 4 * q^41 + 76 * q^44 + 12 * q^46 - 72 * q^49 + 4 * q^54 - 24 * q^59 + 24 * q^61 + 16 * q^64 - 48 * q^66 + 112 * q^69 - 20 * q^71 + 8 * q^76 - 40 * q^84 + 12 * q^86 - 36 * q^89 + 8 * q^91 - 72 * q^96 + 52 * q^99

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