LMFDB - Embedded newform 325.2.k.d.268.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(57,325)]

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([1, 3]))

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

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

chi := DirichletCharacter("325.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.k (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			268.3
Root			$-0.881421 + 0.881421i$ of defining polynomial
Character	$\chi$	$=$	325.268
Dual form			325.2.k.d.57.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.13453 q^{2} +(1.59157 + 1.59157i) q^{3} -0.712838 q^{4} +(-1.80569 - 1.80569i) q^{6} +1.13453i q^{7} +3.07780 q^{8} +2.06618i q^{9} +O(q^{10})$	\(q-1.13453 q^{2} +(1.59157 + 1.59157i) q^{3} -0.712838 q^{4} +(-1.80569 - 1.80569i) q^{6} +1.13453i q^{7} +3.07780 q^{8} +2.06618i q^{9} +(-2.76952 + 2.76952i) q^{11} +(-1.13453 - 1.13453i) q^{12} +(3.09292 + 1.85306i) q^{13} -1.28716i q^{14} -2.06618 q^{16} +(1.39602 + 1.39602i) q^{17} -2.34415i q^{18} +(-2.89853 + 2.89853i) q^{19} +(-1.80569 + 1.80569i) q^{21} +(3.14211 - 3.14211i) q^{22} +(-5.28093 + 5.28093i) q^{23} +(4.89853 + 4.89853i) q^{24} +(-3.50902 - 2.10235i) q^{26} +(1.48623 - 1.48623i) q^{27} -0.808738i q^{28} -7.39039i q^{29} +(-2.10235 - 2.10235i) q^{31} -3.81145 q^{32} -8.81577 q^{33} +(-1.58383 - 1.58383i) q^{34} -1.47286i q^{36} +8.61859i q^{37} +(3.28848 - 3.28848i) q^{38} +(1.97334 + 7.87187i) q^{39} +(5.58471 + 5.58471i) q^{41} +(2.04861 - 2.04861i) q^{42} +(4.04106 - 4.04106i) q^{43} +(1.97422 - 1.97422i) q^{44} +(5.99138 - 5.99138i) q^{46} +0.447884i q^{47} +(-3.28848 - 3.28848i) q^{48} +5.71284 q^{49} +4.44372i q^{51} +(-2.20476 - 1.32093i) q^{52} +(0.997317 + 0.997317i) q^{53} +(-1.68618 + 1.68618i) q^{54} +3.49186i q^{56} -9.22643 q^{57} +8.38463i q^{58} +(-5.35423 - 5.35423i) q^{59} +15.1151 q^{61} +(2.38518 + 2.38518i) q^{62} -2.34415 q^{63} +8.45658 q^{64} +10.0018 q^{66} +5.68941 q^{67} +(-0.995135 - 0.995135i) q^{68} -16.8099 q^{69} +(-7.70422 - 7.70422i) q^{71} +6.35930i q^{72} +3.52724 q^{73} -9.77806i q^{74} +(2.06618 - 2.06618i) q^{76} +(-3.14211 - 3.14211i) q^{77} +(-2.23881 - 8.93088i) q^{78} -8.54519i q^{79} +10.9294 q^{81} +(-6.33603 - 6.33603i) q^{82} -11.9752i q^{83} +(1.28716 - 1.28716i) q^{84} +(-4.58471 + 4.58471i) q^{86} +(11.7623 - 11.7623i) q^{87} +(-8.52403 + 8.52403i) q^{88} +(-3.34473 - 3.34473i) q^{89} +(-2.10235 + 3.50902i) q^{91} +(3.76445 - 3.76445i) q^{92} -6.69207i q^{93} -0.508138i q^{94} +(-6.06618 - 6.06618i) q^{96} +15.2972 q^{97} -6.48139 q^{98} +(-5.72234 - 5.72234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.13453			−0.802235			−0.401117	−	0.916027i	$-0.631378\pi$
$2$	−1.13453			−0.802235			−0.401117	+	0.916027i	$0.631378\pi$
$3$	1.59157	+	1.59157i	0.918893	+	0.918893i	0.996949	−	0.0780561i	$-0.0248713\pi$
$3$	1.59157	+	1.59157i	0.918893	+	0.918893i	−0.0780561	+	0.996949i	$0.524871\pi$
$4$	−0.712838			−0.356419
$5$		0			0
$5$		0			0
$6$	−1.80569	−	1.80569i	−0.737168	−	0.737168i
$7$			1.13453i			0.428813i	0.976745	+	0.214406i	$0.0687817\pi$
$7$			1.13453i			0.428813i	−0.976745	+	0.214406i	$0.931218\pi$
$8$	3.07780			1.08817
$9$			2.06618i			0.688728i
$10$		0			0
$11$	−2.76952	+	2.76952i	−0.835042	+	0.835042i	−0.988201	−	0.153160i	$-0.951055\pi$
$11$	−2.76952	+	2.76952i	−0.835042	+	0.835042i	0.153160	+	0.988201i	$0.451055\pi$
$12$	−1.13453	−	1.13453i	−0.327511	−	0.327511i
$13$	3.09292	+	1.85306i	0.857823	+	0.513945i
$13$	3.09292	+	1.85306i	0.857823	+	0.513945i
$14$		−	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	$0.673044\pi$
$18$		−	2.34415i		−	0.552522i
$19$	−2.89853	+	2.89853i	−0.664969	+	0.664969i	−0.956547	−	0.291578i	$-0.905820\pi$
$19$	−2.89853	+	2.89853i	−0.664969	+	0.664969i	0.291578	+	0.956547i	$0.405820\pi$
$20$		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
$28$		−	0.808738i		−	0.152837i
$29$		−	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	0.492640	−	0.870233i	$-0.336032\pi$
$31$	−2.10235	−	2.10235i	−0.377593	−	0.377593i	−0.870233	+	0.492640i	$0.836032\pi$
$32$	−3.81145			−0.673775
$33$	−8.81577			−1.53463
$34$	−1.58383	−	1.58383i	−0.271624	−	0.271624i
$35$		0			0
$36$		−	1.47286i		−	0.245476i
$37$			8.61859i			1.41689i	0.705767	+	0.708444i	$0.250602\pi$
$37$			8.61859i			1.41689i	−0.705767	+	0.708444i	$0.749398\pi$
$38$	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	0.992710	−	0.120525i	$-0.0384579\pi$
$41$	5.58471	+	5.58471i	0.872185	+	0.872185i	−0.120525	+	0.992710i	$0.538458\pi$
$42$	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
$47$			0.447884i			0.0653306i	0.999466	+	0.0326653i	$0.0103995\pi$
$47$			0.447884i			0.0653306i	−0.999466	+	0.0326653i	$0.989600\pi$
$48$	−3.28848	−	3.28848i	−0.474651	−	0.474651i
$49$	5.71284			0.816120
$50$		0			0
$51$			4.44372i			0.622245i
$52$	−2.20476	−	1.32093i	−0.305745	−	0.183180i
$53$	0.997317	+	0.997317i	0.136992	+	0.136992i	0.772277	−	0.635285i	$-0.219118\pi$
$53$	0.997317	+	0.997317i	0.136992	+	0.136992i	−0.635285	+	0.772277i	$0.719118\pi$
$54$	−1.68618	+	1.68618i	−0.229460	+	0.229460i
$55$		0			0
$56$			3.49186i			0.466620i
$57$	−9.22643			−1.22207
$58$			8.38463i			1.10096i
$59$	−5.35423	−	5.35423i	−0.697061	−	0.697061i	0.266714	−	0.963776i	$-0.414062\pi$
$59$	−5.35423	−	5.35423i	−0.697061	−	0.697061i	−0.963776	+	0.266714i	$0.914062\pi$
$60$		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
$63$	−2.34415			−0.295335
$64$	8.45658			1.05707
$65$		0			0
$66$	10.0018			1.23113
$67$	5.68941			0.695072			0.347536	−	0.937667i	$-0.387018\pi$
$67$	5.68941			0.695072			0.347536	+	0.937667i	$0.387018\pi$
$68$	−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	0.0822863	−	0.996609i	$-0.473778\pi$
$71$	−7.70422	−	7.70422i	−0.914322	−	0.914322i	−0.996609	+	0.0822863i	$0.973778\pi$
$72$			6.35930i			0.749451i
$73$	3.52724			0.412832			0.206416	−	0.978464i	$-0.433820\pi$
$73$	3.52724			0.412832			0.206416	+	0.978464i	$0.433820\pi$
$74$		−	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
$78$	−2.23881	−	8.93088i	−0.253496	−	1.01122i
$79$		−	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
$83$		−	11.9752i		−	1.31445i	−0.753696	−	0.657223i	$-0.771731\pi$
$83$		−	11.9752i		−	1.31445i	0.753696	−	0.657223i	$-0.228269\pi$
$84$	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	$-0.330660\pi$
$89$	−3.34473	−	3.34473i	−0.354540	−	0.354540i	−0.861796	+	0.507255i	$0.830660\pi$
$90$		0			0
$91$	−2.10235	+	3.50902i	−0.220386	+	0.367845i
$92$	3.76445	−	3.76445i	0.392471	−	0.392471i
$93$		−	6.69207i		−	0.693935i
$94$		−	0.508138i		−	0.0524105i
$95$		0			0
$96$	−6.06618	−	6.06618i	−0.619127	−	0.619127i
$97$	15.2972			1.55319			0.776596	−	0.629999i	$-0.216945\pi$
$97$	15.2972			1.55319			0.776596	+	0.629999i	$0.216945\pi$
$98$	−6.48139			−0.654720
$99$	−5.72234	−	5.72234i	−0.575117	−	0.575117i
$100$		0			0
$101$		−	8.74374i		−	0.870035i	−0.900422	−	0.435017i	$-0.856742\pi$
$101$		−	8.74374i		−	0.870035i	0.900422	−	0.435017i	$-0.143258\pi$
$102$		−	5.04154i		−	0.499187i
$103$	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	−0.876539	−	0.481331i	$-0.840153\pi$
$107$	−4.08806	+	4.08806i	−0.395208	+	0.395208i	0.481331	+	0.876539i	$0.340153\pi$
$108$	−1.05944	+	1.05944i	−0.101945	+	0.101945i
$109$	−9.83235	+	9.83235i	−0.941768	+	0.941768i	−0.998395	−	0.0566273i	$-0.981965\pi$
$109$	−9.83235	+	9.83235i	−0.941768	+	0.941768i	0.0566273	+	0.998395i	$0.481965\pi$
$110$		0			0
$111$	−13.7171	+	13.7171i	−1.30197	+	1.30197i
$112$		−	2.34415i		−	0.221502i
$113$	1.99245	+	1.99245i	0.187434	+	0.187434i	0.794586	−	0.607152i	$-0.207688\pi$
$113$	1.99245	+	1.99245i	0.187434	+	0.187434i	−0.607152	+	0.794586i	$0.707688\pi$
$114$	10.4677			0.980388
$115$		0			0
$116$			5.26816i			0.489136i
$117$	−3.82876	+	6.39055i	−0.353969	+	0.590807i
$118$	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
$122$	−17.1486			−1.55256
$123$			17.7769i			1.60289i
$124$	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	$0.894421\pi$
$128$	−1.97136			−0.174245
$129$	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	$0.632466\pi$
$132$	6.28422			0.546971
$133$	−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
$137$			5.56732i			0.475648i	0.971308	+	0.237824i	$0.0764342\pi$
$137$			5.56732i			0.475648i	−0.971308	+	0.237824i	$0.923566\pi$
$138$	19.0714			1.62346
$139$			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
$143$	−13.6980	+	3.43384i	−1.14548	+	0.287152i
$144$		−	4.26912i		−	0.355760i
$145$		0			0
$146$	−4.00176			−0.331188
$147$	9.09238	+	9.09238i	0.749927	+	0.749927i
$148$		−	6.14366i		−	0.505006i
$149$	6.23136	−	6.23136i	0.510493	−	0.510493i	−0.404184	−	0.914678i	$-0.632445\pi$
$149$	6.23136	−	6.23136i	0.510493	−	0.510493i	0.914678	+	0.404184i	$0.132445\pi$
$150$		0			0
$151$	4.52803	−	4.52803i	0.368486	−	0.368486i	−0.498439	−	0.866925i	$-0.666093\pi$
$151$	4.52803	−	4.52803i	0.368486	−	0.368486i	0.866925	+	0.498439i	$0.166093\pi$
$152$	−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	−0.640809	−	0.767700i	$-0.721401\pi$
$157$	1.58994	−	1.58994i	0.126891	−	0.126891i	0.767700	+	0.640809i	$0.221401\pi$
$158$			9.69478i			0.771275i
$159$			3.17460i			0.251762i
$160$		0			0
$161$	−5.99138	−	5.99138i	−0.472187	−	0.472187i
$162$	−12.3998			−0.974219
$163$	−1.14587			−0.0897512			−0.0448756	−	0.998993i	$-0.514289\pi$
$163$	−1.14587			−0.0897512			−0.0448756	+	0.998993i	$0.514289\pi$
$164$	−3.98099	−	3.98099i	−0.310863	−	0.310863i
$165$		0			0
$166$			13.5862i			1.05450i
$167$			17.6483i			1.36567i	0.730575	+	0.682833i	$0.239252\pi$
$167$			17.6483i			1.36567i	−0.730575	+	0.682833i	$0.760748\pi$
$168$	−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
$177$		−	17.0433i		−	1.28105i
$178$	3.79470	+	3.79470i	0.284425	+	0.284425i
$179$	14.5452			1.08716			0.543579	−	0.839358i	$-0.317069\pi$
$179$	14.5452			1.08716			0.543579	+	0.839358i	$0.317069\pi$
$180$		0			0
$181$		−	3.34049i		−	0.248296i	−0.992264	−	0.124148i	$-0.960380\pi$
$181$		−	3.34049i		−	0.248296i	0.992264	−	0.124148i	$-0.0396198\pi$
$182$	2.38518	−	3.98109i	0.176801	−	0.295098i
$183$	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
$187$	−7.73260			−0.565464
$188$		−	0.319269i		−	0.0232851i
$189$	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
$193$	−10.4495			−0.752175			−0.376087	−	0.926584i	$-0.622731\pi$
$193$	−10.4495			−0.752175			−0.376087	+	0.926584i	$0.622731\pi$
$194$	−17.3551			−1.24602
$195$		0			0
$196$	−4.07233			−0.290881
$197$	−11.8050			−0.841070			−0.420535	−	0.907276i	$-0.638158\pi$
$197$	−11.8050			−0.841070			−0.420535	+	0.907276i	$0.638158\pi$
$198$	6.49218	+	6.49218i	0.461379	+	0.461379i
$199$	17.9413			1.27183			0.635914	−	0.771760i	$-0.280623\pi$
$199$	17.9413			1.27183			0.635914	+	0.771760i	$0.280623\pi$
$200$		0			0
$201$	9.05509	+	9.05509i	0.638697	+	0.638697i
$202$			9.92005i			0.697972i
$203$	8.38463			0.588486
$204$		−	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
$208$	−6.39055	−	3.82876i	−0.443105	−	0.265476i
$209$		−	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
$213$		−	24.5236i		−	1.68033i
$214$	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
$223$		−	5.73099i		−	0.383776i	−0.981417	−	0.191888i	$-0.938539\pi$
$223$		−	5.73099i		−	0.383776i	0.981417	−	0.191888i	$-0.0614610\pi$
$224$		−	4.32421i		−	0.288923i
$225$		0			0
$226$	−2.26050	−	2.26050i	−0.150366	−	0.150366i
$227$	12.9243			0.857817			0.428908	−	0.903348i	$-0.358898\pi$
$227$	12.9243			0.857817			0.428908	+	0.903348i	$0.358898\pi$
$228$	6.57695			0.435569
$229$	−13.8719	−	13.8719i	−0.916679	−	0.916679i	0.0801073	−	0.996786i	$-0.474474\pi$
$229$	−13.8719	−	13.8719i	−0.916679	−	0.916679i	−0.996786	+	0.0801073i	$0.974474\pi$
$230$		0			0
$231$		−	10.0018i		−	0.658068i
$232$		−	22.7462i		−	1.49336i
$233$	−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	$-0.780872\pi$
$239$	−2.11712	+	2.11712i	−0.136945	+	0.136945i	0.635311	+	0.772256i	$0.280872\pi$
$240$		0			0
$241$	−8.61752	+	8.61752i	−0.555103	+	0.555103i	−0.927909	−	0.372806i	$-0.878396\pi$
$241$	−8.61752	+	8.61752i	−0.555103	+	0.555103i	0.372806	+	0.927909i	$0.378396\pi$
$242$			4.92442i			0.316554i
$243$	12.9363	+	12.9363i	0.829861	+	0.829861i
$244$	−10.7746			−0.689776
$245$		0			0
$246$		−	20.1685i		−	1.28589i
$247$	−14.3361	+	3.59380i	−0.912183	+	0.228668i
$248$	−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	$-0.871909\pi$
$251$		−	12.4094i		−	0.783274i	0.920120	−	0.391637i	$-0.128091\pi$
$252$	1.67100			0.105263
$253$		−	29.2513i		−	1.83901i
$254$	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	$0.632723\pi$
$258$	−14.5938			−0.908568
$259$	−9.77806			−0.607579
$260$		0			0
$261$	15.2699			0.945184
$262$	10.4986			0.648603
$263$	4.36623	+	4.36623i	0.269233	+	0.269233i	0.828791	−	0.559558i	$-0.189029\pi$
$263$	4.36623	+	4.36623i	0.269233	+	0.269233i	−0.559558	+	0.828791i	$0.689029\pi$
$264$	−27.1332			−1.66993
$265$		0			0
$266$	3.73088	+	3.73088i	0.228755	+	0.228755i
$267$		−	10.6467i		−	0.651569i
$268$	−4.05563			−0.247737
$269$			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	−0.395261	−	0.918569i	$-0.629346\pi$
$271$	8.61473	−	8.61473i	0.523307	−	0.523307i	0.918569	+	0.395261i	$0.129346\pi$
$272$	−2.88443	−	2.88443i	−0.174894	−	0.174894i
$273$	−8.93088	+	2.23881i	−0.540522	+	0.135499i
$274$		−	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	$0.947961\pi$
$278$		−	20.3766i		−	1.22211i
$279$	4.34384	−	4.34384i	0.260059	−	0.260059i
$280$		0			0
$281$	18.2450	−	18.2450i	1.08841	−	1.08841i	0.0927140	−	0.995693i	$-0.470446\pi$
$281$	18.2450	−	18.2450i	1.08841	−	1.08841i	0.995693	−	0.0927140i	$-0.0295542\pi$
$282$	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
$288$		−	7.87516i		−	0.464048i
$289$		−	13.1023i		−	0.770722i
$290$		0			0
$291$	24.3465	+	24.3465i	1.42722	+	1.42722i
$292$	−2.51435			−0.147141
$293$	6.10379			0.356587			0.178294	−	0.983977i	$-0.442942\pi$
$293$	6.10379			0.356587			0.178294	+	0.983977i	$0.442942\pi$
$294$	−10.3156	−	10.3156i	−0.601617	−	0.601617i
$295$		0			0
$296$			26.5263i			1.54181i
$297$			8.23230i			0.477686i
$298$	−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
$307$		−	0.391103i		−	0.0223214i	−0.999938	−	0.0111607i	$-0.996447\pi$
$307$		−	0.391103i		−	0.0223214i	0.999938	−	0.0111607i	$-0.00355264\pi$
$308$	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	$-0.796423\pi$
$311$		−	21.0507i		−	1.19368i	0.802362	−	0.596838i	$-0.203577\pi$
$312$	6.07354	+	24.2280i	0.343847	+	1.37164i
$313$	−12.1529	−	12.1529i	−0.686921	−	0.686921i	0.274629	−	0.961550i	$-0.411445\pi$
$313$	−12.1529	−	12.1529i	−0.686921	−	0.686921i	−0.961550	+	0.274629i	$0.911445\pi$
$314$	−1.80384	+	1.80384i	−0.101797	+	0.101797i
$315$		0			0
$316$			6.09134i			0.342664i
$317$	1.23831			0.0695506			0.0347753	−	0.999395i	$-0.488928\pi$
$317$	1.23831			0.0695506			0.0347753	+	0.999395i	$0.488928\pi$
$318$		−	3.60168i		−	0.201972i
$319$	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
$323$	−8.09281			−0.450296
$324$	−7.79092			−0.432829
$325$		0			0
$326$	1.30002			0.0720016
$327$	−31.2977			−1.73077
$328$	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	0.958001	+	0.286764i	$0.0925794\pi$
$331$	22.6465	+	22.6465i	1.24476	+	1.24476i	0.286764	+	0.958001i	$0.407421\pi$
$332$			8.53637i			0.468494i
$333$	−17.8076			−0.975850
$334$		−	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	$0.637257\pi$
$338$	−6.95737	−	13.0048i	−0.378431	−	0.707369i
$339$			6.34225i			0.344464i
$340$		0			0
$341$	11.6450			0.630612
$342$	6.79460	+	6.79460i	0.367410	+	0.367410i
$343$			14.4231i			0.778775i
$344$	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	−0.945333	−	0.326107i	$-0.894263\pi$
$347$	−11.5349	+	11.5349i	−0.619226	+	0.619226i	0.326107	+	0.945333i	$0.394263\pi$
$348$	−8.38463	+	8.38463i	−0.449464	+	0.449464i
$349$	−6.76426	−	6.76426i	−0.362082	−	0.362082i	0.502497	−	0.864579i	$-0.332415\pi$
$349$	−6.76426	−	6.76426i	−0.362082	−	0.362082i	−0.864579	+	0.502497i	$0.832415\pi$
$350$		0			0
$351$	7.35087	−	1.84273i	0.392360	−	0.0983578i
$352$	10.5559	−	10.5559i	0.562631	−	0.562631i
$353$			7.57745i			0.403307i	0.979457	+	0.201654i	$0.0646315\pi$
$353$			7.57745i			0.403307i	−0.979457	+	0.201654i	$0.935368\pi$
$354$			19.3361i			1.02770i
$355$		0			0
$356$	2.38425	+	2.38425i	0.126365	+	0.126365i
$357$	−5.04154			−0.266826
$358$	−16.5020			−0.872156
$359$	13.8246	+	13.8246i	0.729635	+	0.729635i	0.970547	−	0.240912i	$-0.0774465\pi$
$359$	13.8246	+	13.8246i	0.729635	+	0.729635i	−0.240912	+	0.970547i	$0.577447\pi$
$360$		0			0
$361$			2.19702i			0.115633i
$362$			3.78989i			0.199192i
$363$	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	−0.469820	−	0.882762i	$-0.655681\pi$
$367$	7.91084	−	7.91084i	0.412943	−	0.412943i	0.882762	+	0.469820i	$0.155681\pi$
$368$	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
$372$			4.77036i			0.247332i
$373$	11.3372	+	11.3372i	0.587016	+	0.587016i	0.936822	−	0.349806i	$-0.113753\pi$
$373$	11.3372	+	11.3372i	0.587016	+	0.587016i	−0.349806	+	0.936822i	$0.613753\pi$
$374$	8.77288			0.453635
$375$		0			0
$376$			1.37850i			0.0710906i
$377$	13.6948	−	22.8579i	0.705319	−	1.17724i
$378$	−1.91302	−	1.91302i	−0.0983951	−	0.0983951i
$379$	−3.42232	+	3.42232i	−0.175793	+	0.175793i	−0.789519	−	0.613726i	$-0.789670\pi$
$379$	−3.42232	+	3.42232i	−0.175793	+	0.175793i	0.613726	+	0.789519i	$0.289670\pi$
$380$		0			0
$381$		−	22.2356i		−	1.13916i
$382$	6.97086			0.356660
$383$		−	16.8644i		−	0.861730i	−0.902416	−	0.430865i	$-0.858209\pi$
$383$		−	16.8644i		−	0.861730i	0.902416	−	0.430865i	$-0.141791\pi$
$384$	−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
$388$	−10.9044			−0.553587
$389$	−12.3803			−0.627704			−0.313852	−	0.949472i	$-0.601620\pi$
$389$	−12.3803			−0.627704			−0.313852	+	0.949472i	$0.601620\pi$
$390$		0			0
$391$	−14.7445			−0.745663
$392$	17.5830			0.888074
$393$	−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
$397$		−	28.3464i		−	1.42266i	−0.702856	−	0.711332i	$-0.748092\pi$
$397$		−	28.3464i		−	1.42266i	0.702856	−	0.711332i	$-0.251908\pi$
$398$	−20.3550			−1.02030
$399$		−	10.4677i		−	0.524039i
$400$		0			0
$401$	−8.12989	+	8.12989i	−0.405988	+	0.405988i	−0.880337	−	0.474349i	$-0.842683\pi$
$401$	−8.12989	+	8.12989i	−0.405988	+	0.405988i	0.474349	+	0.880337i	$0.342683\pi$
$402$	−10.2733	−	10.2733i	−0.512385	−	0.512385i
$403$	−2.60664	−	10.3982i	−0.129846	−	0.517970i
$404$			6.23287i			0.310097i
$405$		0			0
$406$	−9.51263			−0.472104
$407$	−23.8694	−	23.8694i	−1.18316	−	1.18316i
$408$			13.6769i			0.677106i
$409$	2.92001	−	2.92001i	0.144385	−	0.144385i	−0.631219	−	0.775605i	$-0.717445\pi$
$409$	2.92001	−	2.92001i	0.144385	−	0.144385i	0.775605	+	0.631219i	$0.217445\pi$
$410$		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
$418$			18.2150i			0.890925i
$419$		−	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	0.411971	−	0.911197i	$-0.364840\pi$
$421$	−10.2433	−	10.2433i	−0.499226	−	0.499226i	−0.911197	+	0.411971i	$0.864840\pi$
$422$	24.3567			1.18566
$423$	−0.925411			−0.0449950
$424$	3.06954	+	3.06954i	0.149070	+	0.149070i
$425$		0			0
$426$			27.8228i			1.34802i
$427$			17.1486i			0.829878i
$428$	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	0.793055	−	0.609150i	$-0.208489\pi$
$431$	3.81798	+	3.81798i	0.183905	+	0.183905i	−0.609150	+	0.793055i	$0.708489\pi$
$432$	−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
$437$		−	30.6139i		−	1.46446i
$438$	−6.36909	−	6.36909i	−0.304327	−	0.304327i
$439$	−18.5418			−0.884950			−0.442475	−	0.896781i	$-0.645900\pi$
$439$	−18.5418			−0.884950			−0.442475	+	0.896781i	$0.645900\pi$
$440$		0			0
$441$			11.8038i			0.562085i
$442$	−1.96374	−	7.83357i	−0.0934055	−	0.372605i
$443$	26.8649	+	26.8649i	1.27639	+	1.27639i	0.942673	+	0.333719i	$0.108304\pi$
$443$	26.8649	+	26.8649i	1.27639	+	1.27639i	0.333719	+	0.942673i	$0.391696\pi$
$444$	9.77806	−	9.77806i	0.464046	−	0.464046i
$445$		0			0
$446$			6.50199i			0.307878i
$447$	19.8353			0.938177
$448$			9.59425i			0.453286i
$449$	22.4994	+	22.4994i	1.06181	+	1.06181i	0.997959	+	0.0638519i	$0.0203385\pi$
$449$	22.4994	+	22.4994i	1.06181	+	1.06181i	0.0638519	+	0.997959i	$0.479661\pi$
$450$		0			0
$451$	−30.9339			−1.45662
$452$	−1.42030	−	1.42030i	−0.0668051	−	0.0668051i
$453$	14.4133			0.677198
$454$	−14.6630			−0.688171
$455$		0			0
$456$	−28.3971			−1.32982
$457$	−0.339291			−0.0158714			−0.00793568	−	0.999969i	$-0.502526\pi$
$457$	−0.339291			−0.0158714			−0.00793568	+	0.999969i	$0.502526\pi$
$458$	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	−0.996148	−	0.0876849i	$-0.972053\pi$
$461$	−23.2709	−	23.2709i	−1.08383	−	1.08383i	−0.0876849	−	0.996148i	$-0.527947\pi$
$462$			11.3473i			0.527925i
$463$	28.5246			1.32565			0.662825	−	0.748774i	$-0.269357\pi$
$463$	28.5246			1.32565			0.662825	+	0.748774i	$0.269357\pi$
$464$			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	$0.590887\pi$
$468$	2.72928	−	4.55543i	0.126161	−	0.210575i
$469$			6.45481i			0.298056i
$470$		0			0
$471$	5.06100			0.233199
$472$	−16.4792	−	16.4792i	−0.758519	−	0.758519i
$473$			22.3836i			1.02920i
$474$	−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	$-0.305163\pi$
$479$	−5.33713	−	5.33713i	−0.243860	−	0.243860i	−0.818445	+	0.574585i	$0.805163\pi$
$480$		0			0
$481$	−15.9707	+	26.6566i	−0.728202	+	1.21544i
$482$	9.77684	−	9.77684i	0.445323	−	0.445323i
$483$		−	19.0714i		−	0.867778i
$484$			3.09406i			0.140639i
$485$		0			0
$486$	−14.6766	−	14.6766i	−0.665744	−	0.665744i
$487$	−10.2793			−0.465802			−0.232901	−	0.972500i	$-0.574822\pi$
$487$	−10.2793			−0.465802			−0.232901	+	0.972500i	$0.574822\pi$
$488$	46.5214			2.10592
$489$	−1.82373	−	1.82373i	−0.0824718	−	0.0824718i
$490$		0			0
$491$		−	26.3973i		−	1.19130i	−0.803246	−	0.595648i	$-0.796895\pi$
$491$		−	26.3973i		−	1.19130i	0.803246	−	0.595648i	$-0.203105\pi$
$492$		−	12.6721i		−	0.571300i
$493$	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	$-0.837959\pi$
$499$	−8.61897	+	8.61897i	−0.385838	+	0.385838i	0.487362	+	0.873200i	$0.337959\pi$
$500$		0			0
$501$	−28.0885	+	28.0885i	−1.25490	+	1.25490i
$502$			14.0789i			0.628370i
$503$	0.0659351	+	0.0659351i	0.00293990	+	0.00293990i	0.708575	−	0.705635i	$-0.249338\pi$
$503$	0.0659351	+	0.0659351i	0.00293990	+	0.00293990i	−0.705635	+	0.708575i	$0.749338\pi$
$504$	−7.21483			−0.321374
$505$		0			0
$506$			33.1865i			1.47532i
$507$	−8.48363	+	28.0038i	−0.376771	+	1.24369i
$508$	4.97948	+	4.97948i	0.220929	+	0.220929i
$509$	−5.54846	+	5.54846i	−0.245931	+	0.245931i	−0.819298	−	0.573367i	$-0.805637\pi$
$509$	−5.54846	+	5.54846i	−0.245931	+	0.245931i	0.573367	+	0.819298i	$0.305637\pi$
$510$		0			0
$511$			4.00176i			0.177028i
$512$	20.5938			0.910125
$513$			8.61578i			0.380396i
$514$	−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
$518$	11.0935			0.487421
$519$	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	$0.262979\pi$
$522$	−17.3242			−0.758260
$523$	−0.897323	−	0.897323i	−0.0392372	−	0.0392372i	0.687216	−	0.726453i	$-0.258833\pi$
$523$	−0.897323	−	0.897323i	−0.0392372	−	0.0392372i	−0.726453	+	0.687216i	$0.758833\pi$
$524$	6.59635			0.288163
$525$		0			0
$526$	−4.95362	−	4.95362i	−0.215988	−	0.215988i
$527$		−	5.86984i		−	0.255694i
$528$	18.2150			0.792706
$529$		−	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
$533$	6.92431	+	27.6219i	0.299925	+	1.19644i
$534$			12.0790i			0.522711i
$535$		0			0
$536$	17.5109			0.756354
$537$	23.1497	+	23.1497i	0.998982	+	0.998982i
$538$		−	5.37430i		−	0.231703i
$539$	−15.8218	+	15.8218i	−0.681494	+	0.681494i
$540$		0			0
$541$	20.7351	−	20.7351i	0.891472	−	0.891472i	−0.103189	−	0.994662i	$-0.532905\pi$
$541$	20.7351	−	20.7351i	0.891472	−	0.891472i	0.994662	+	0.103189i	$0.0329047\pi$
$542$	−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	−0.916391	−	0.400284i	$-0.868912\pi$
$547$	−12.0707	+	12.0707i	−0.516108	+	0.516108i	0.400284	+	0.916391i	$0.368912\pi$
$548$		−	3.96860i		−	0.169530i
$549$			31.2307i			1.33289i
$550$		0			0
$551$	21.4213	+	21.4213i	0.912578	+	0.912578i
$552$	−51.7376			−2.20210
$553$	9.69478			0.412264
$554$	15.5573	+	15.5573i	0.660968	+	0.660968i
$555$		0			0
$556$		−	12.8028i		−	0.542960i
$557$		−	17.4025i		−	0.737370i	−0.929554	−	0.368685i	$-0.879808\pi$
$557$		−	17.4025i		−	0.737370i	0.929554	−	0.368685i	$-0.120192\pi$
$558$	−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
$567$			12.3998i			0.520742i
$568$	−23.7120	−	23.7120i	−0.994935	−	0.994935i
$569$	−32.2263			−1.35100			−0.675498	−	0.737362i	$-0.736071\pi$
$569$	−32.2263			−1.35100			−0.675498	+	0.737362i	$0.736071\pi$
$570$		0			0
$571$			8.19417i			0.342916i	0.985191	+	0.171458i	$0.0548477\pi$
$571$			8.19417i			0.342916i	−0.985191	+	0.171458i	$0.945152\pi$
$572$	9.76445	−	2.44778i	0.408272	−	0.102347i
$573$	−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
$577$	−14.2517			−0.593304			−0.296652	−	0.954986i	$-0.595870\pi$
$577$	−14.2517			−0.593304			−0.296652	+	0.954986i	$0.595870\pi$
$578$			14.8649i			0.618300i
$579$	−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
$583$	−5.52418			−0.228788
$584$	10.8561			0.449230
$585$		0			0
$586$	−6.92494			−0.286067
$587$	−2.55919			−0.105629			−0.0528146	−	0.998604i	$-0.516819\pi$
$587$	−2.55919			−0.105629			−0.0528146	+	0.998604i	$0.516819\pi$
$588$	−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
$592$		−	17.8076i		−	0.731888i
$593$	−17.4690			−0.717364			−0.358682	−	0.933460i	$-0.616774\pi$
$593$	−17.4690			−0.717364			−0.358682	+	0.933460i	$0.616774\pi$
$594$		−	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
$598$	29.6332	−	7.42853i	1.21179	−	0.303775i
$599$			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
$603$			11.7554i			0.478716i
$604$	−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	−0.616974	−	0.786984i	$-0.711641\pi$
$607$	4.18861	−	4.18861i	0.170010	−	0.170010i	0.786984	+	0.616974i	$0.211641\pi$
$608$	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
$613$			14.2756i			0.576586i	0.957542	+	0.288293i	$0.0930876\pi$
$613$			14.2756i			0.576586i	−0.957542	+	0.288293i	$0.906912\pi$
$614$			0.443718i			0.0179070i
$615$		0			0
$616$	−9.67078	−	9.67078i	−0.389647	−	0.389647i
$617$	47.3133			1.90476			0.952382	−	0.304909i	$-0.0986259\pi$
$617$	47.3133			1.90476			0.952382	+	0.304909i	$0.0986259\pi$
$618$	−35.7919			−1.43976
$619$	10.3491	+	10.3491i	0.415966	+	0.415966i	0.883811	−	0.467845i	$-0.154969\pi$
$619$	10.3491	+	10.3491i	0.415966	+	0.415966i	−0.467845	+	0.883811i	$0.654969\pi$
$620$		0			0
$621$			15.6974i			0.629913i
$622$			23.8827i			0.957609i
$623$	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	−0.446210	−	0.894928i	$-0.647226\pi$
$631$	11.2717	−	11.2717i	0.448719	−	0.448719i	0.894928	+	0.446210i	$0.147226\pi$
$632$		−	26.3004i		−	1.04617i
$633$	−34.1686	−	34.1686i	−1.35808	−	1.35808i
$634$	−1.40491			−0.0557960
$635$		0			0
$636$		−	2.26298i		−	0.0897328i
$637$	17.6694	+	10.5862i	0.700086	+	0.419441i
$638$	−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	$-0.794161\pi$
$641$		−	30.5095i		−	1.20505i	0.798099	−	0.602527i	$-0.205839\pi$
$642$	14.7635			0.582669
$643$		−	5.60519i		−	0.221047i	−0.993874	−	0.110524i	$-0.964747\pi$
$643$		−	5.60519i		−	0.221047i	0.993874	−	0.110524i	$-0.0352527\pi$
$644$	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	$0.793234\pi$
$648$	33.6386			1.32145
$649$	29.6573			1.16415
$650$		0			0
$651$	7.59236			0.297568
$652$	0.816818			0.0319891
$653$	−33.8017	−	33.8017i	−1.32276	−	1.32276i	−0.911529	−	0.411235i	$-0.865098\pi$
$653$	−33.8017	−	33.8017i	−1.32276	−	1.32276i	−0.411235	−	0.911529i	$-0.634902\pi$
$654$	35.5083			1.38848
$655$		0			0
$656$	−11.5390	−	11.5390i	−0.450524	−	0.450524i
$657$			7.28793i			0.284329i
$658$	0.576499			0.0224743
$659$			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	−0.954191	−	0.299197i	$-0.903281\pi$
$661$	−16.8399	+	16.8399i	−0.654995	+	0.654995i	0.299197	+	0.954191i	$0.403281\pi$
$662$	−25.6932	−	25.6932i	−0.998594	−	0.998594i
$663$	−8.23446	+	13.7441i	−0.319800	+	0.533776i
$664$		−	36.8572i		−	1.43034i
$665$		0			0
$666$	20.2033			0.782861
$667$	39.0281	+	39.0281i	1.51118	+	1.51118i
$668$		−	12.5804i		−	0.486749i
$669$	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	−0.593168	−	0.805079i	$-0.702123\pi$
$677$	5.51377	−	5.51377i	0.211911	−	0.211911i	0.805079	+	0.593168i	$0.202123\pi$
$678$		−	7.19548i		−	0.276341i
$679$			17.3551i			0.666028i
$680$		0			0
$681$	20.5699	+	20.5699i	0.788242	+	0.788242i
$682$	−13.2116			−0.505899
$683$	−29.6709			−1.13533			−0.567663	−	0.823261i	$-0.692152\pi$
$683$	−29.6709			−1.13533			−0.567663	+	0.823261i	$0.692152\pi$
$684$	4.26912	+	4.26912i	0.163234	+	0.163234i
$685$		0			0
$686$		−	16.3635i		−	0.624761i
$687$		−	44.1561i		−	1.68466i
$688$	−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	0.990178	+	0.139816i	$0.0446510\pi$
$691$	29.7040	+	29.7040i	1.12999	+	1.12999i	0.139816	+	0.990178i	$0.455349\pi$
$692$	−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
$697$			15.5927i			0.590616i
$698$	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	$0.195519\pi$
$701$			30.5188i			1.15268i	−0.817211	+	0.576339i	$0.804481\pi$
$702$	−8.33979	+	2.09064i	−0.314765	+	0.0789061i
$703$	−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
$707$	9.92005			0.373082
$708$			12.1491i			0.456590i
$709$	−35.3379	−	35.3379i	−1.32714	−	1.32714i	−0.907853	−	0.419289i	$-0.862280\pi$
$709$	−35.3379	−	35.3379i	−1.32714	−	1.32714i	−0.419289	−	0.907853i	$-0.637720\pi$
$710$		0			0
$711$	17.6559			0.662149
$712$	−10.2944	−	10.2944i	−0.385799	−	0.385799i
$713$	22.2047			0.831573
$714$	5.71978			0.214058
$715$		0			0
$716$	−10.3684			−0.387484
$717$	−6.73907			−0.251675
$718$	−15.6845	−	15.6845i	−0.585339	−	0.585339i
$719$	35.2659			1.31520			0.657599	−	0.753368i	$-0.271572\pi$
$719$	35.2659			1.31520			0.657599	+	0.753368i	$0.271572\pi$
$720$		0			0
$721$	11.2442	+	11.2442i	0.418757	+	0.418757i
$722$		−	2.49259i		−	0.0927645i
$723$	−27.4307			−1.02016
$724$			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	$0.623360\pi$
$728$	−6.47061	+	10.8001i	−0.239817	+	0.400277i
$729$			8.38959i			0.310726i
$730$		0			0
$731$	11.2828			0.417309
$732$	−17.1486	−	17.1486i	−0.633830	−	0.633830i
$733$			43.4921i			1.60642i	0.595698	+	0.803209i	$0.296876\pi$
$733$			43.4921i			1.60642i	−0.595698	+	0.803209i	$0.703124\pi$
$734$	−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	−0.886148	−	0.463402i	$-0.846629\pi$
$739$	−36.6869	−	36.6869i	−1.34955	−	1.34955i	−0.463402	−	0.886148i	$-0.653371\pi$
$740$		0			0
$741$	−28.5367	−	17.0971i	−1.04832	−	0.628077i
$742$	1.28371	−	1.28371i	0.0471264	−	0.0471264i
$743$		−	2.24579i		−	0.0823899i	−0.999151	−	0.0411949i	$-0.986884\pi$
$743$		−	2.24579i		−	0.0823899i	0.999151	−	0.0411949i	$-0.0131165\pi$
$744$		−	20.5969i		−	0.755117i
$745$		0			0
$746$	−12.8624	−	12.8624i	−0.470925	−	0.470925i
$747$	24.7429			0.905297
$748$	5.51209			0.201542
$749$	−4.63803	−	4.63803i	−0.169470	−	0.169470i
$750$		0			0
$751$		−	50.7239i		−	1.85094i	−0.378820	−	0.925470i	$-0.623670\pi$
$751$		−	50.7239i		−	1.85094i	0.378820	−	0.925470i	$-0.376330\pi$
$752$		−	0.925411i		−	0.0337463i
$753$	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	$0.598618\pi$
$757$	−34.5922	+	34.5922i	−1.25727	+	1.25727i	−0.952389	+	0.304884i	$0.901382\pi$
$758$	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	−0.00800445	−	0.999968i	$-0.502548\pi$
$761$	27.3645	−	27.3645i	0.991964	−	0.991964i	0.999968	+	0.00800445i	$0.00254792\pi$
$762$			25.2270i			0.913877i
$763$	−11.1551	−	11.1551i	−0.403842	−	0.403842i
$764$	4.37987			0.158458
$765$		0			0
$766$			19.1332i			0.691310i
$767$	−6.63854	−	26.4819i	−0.239704	−	0.956206i
$768$	−23.3588	−	23.3588i	−0.842888	−	0.842888i
$769$	6.10912	−	6.10912i	0.220301	−	0.220301i	−0.588324	−	0.808625i	$-0.700212\pi$
$769$	6.10912	−	6.10912i	0.220301	−	0.220301i	0.808625	+	0.588324i	$0.200212\pi$
$770$		0			0
$771$			25.9915i			0.936060i
$772$	7.44884			0.268090
$773$			14.6511i			0.526965i	0.964664	+	0.263483i	$0.0848712\pi$
$773$			14.6511i			0.526965i	−0.964664	+	0.263483i	$0.915129\pi$
$774$	−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
$778$	14.0458			0.503566
$779$	−32.3749			−1.15995
$780$		0			0
$781$	42.6740			1.52699
$782$	16.7281			0.598197
$783$	−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
$787$		−	34.9849i		−	1.24708i	−0.781792	−	0.623539i	$-0.785694\pi$
$787$		−	34.9849i		−	1.24708i	0.781792	−	0.623539i	$-0.214306\pi$
$788$	8.41504			0.299773
$789$			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
$793$	46.7500	+	28.0092i	1.66014	+	0.994635i
$794$			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	$0.708316\pi$
$798$			11.8759i			0.420403i
$799$	−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
$808$		−	26.9115i		−	0.946743i
$809$			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	0.922376	−	0.386294i	$-0.126245\pi$
$811$	15.2666	+	15.2666i	0.536082	+	0.536082i	−0.386294	+	0.922376i	$0.626245\pi$
$812$	−5.97689			−0.209748
$813$	27.4219			0.961727
$814$	27.0805	+	27.0805i	0.949172	+	0.949172i
$815$		0			0
$816$		−	9.18154i		−	0.321418i
$817$			23.4263i			0.819582i
$818$	−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	0.979975	−	0.199122i	$-0.0638089\pi$
$821$	22.3739	+	22.3739i	0.780853	+	0.780853i	−0.199122	+	0.979975i	$0.563809\pi$
$822$	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
$827$			27.2891i			0.948935i	0.880273	+	0.474467i	$0.157359\pi$
$827$			27.2891i			0.948935i	−0.880273	+	0.474467i	$0.842641\pi$
$828$	7.77805	+	7.77805i	0.270306	+	0.270306i
$829$	−0.831547			−0.0288808			−0.0144404	−	0.999896i	$-0.504597\pi$
$829$	−0.831547			−0.0288808			−0.0144404	+	0.999896i	$0.504597\pi$
$830$		0			0
$831$		−	43.6490i		−	1.51417i
$832$	26.1556	+	15.6705i	0.906781	+	0.543277i
$833$	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
$837$	−6.24916			−0.216002
$838$			22.8237i			0.788431i
$839$	−11.1299	−	11.1299i	−0.384247	−	0.384247i	0.488383	−	0.872629i	$-0.337587\pi$
$839$	−11.1299	−	11.1299i	−0.384247	−	0.384247i	−0.872629	+	0.488383i	$0.837587\pi$
$840$		0			0
$841$	−25.6179			−0.883377
$842$	11.6213	+	11.6213i	0.400496	+	0.400496i
$843$	58.0764			2.00026
$844$	15.3036			0.526770
$845$		0			0
$846$	1.04991			0.0360966
$847$	4.92442			0.169205
$848$	−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
$852$			17.4814i			0.598901i
$853$	−15.7213			−0.538288			−0.269144	−	0.963100i	$-0.586741\pi$
$853$	−15.7213			−0.538288			−0.269144	+	0.963100i	$0.586741\pi$
$854$		−	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	$0.958220\pi$
$858$	30.9347	+	18.5338i	1.05609	+	0.632734i
$859$			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
$863$		−	20.2303i		−	0.688646i	−0.938851	−	0.344323i	$-0.888109\pi$
$863$		−	20.2303i		−	0.688646i	0.938851	−	0.344323i	$-0.111891\pi$
$864$	−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
$873$			31.6068i			1.06973i
$874$			34.7324i			1.17484i
$875$		0			0
$876$	−4.00176	−	4.00176i	−0.135207	−	0.135207i
$877$	−50.8477			−1.71701			−0.858503	−	0.512809i	$-0.828605\pi$
$877$	−50.8477			−1.71701			−0.858503	+	0.512809i	$0.828605\pi$
$878$	21.0362			0.709938
$879$	9.71460	+	9.71460i	0.327665	+	0.327665i
$880$		0			0
$881$			20.8619i			0.702855i	0.936215	+	0.351427i	$0.114304\pi$
$881$			20.8619i			0.702855i	−0.936215	+	0.351427i	$0.885696\pi$
$882$		−	13.3918i		−	0.450924i
$883$	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	−0.715330	−	0.698786i	$-0.753724\pi$
$887$	−0.492724	+	0.492724i	−0.0165440	+	0.0165440i	0.698786	+	0.715330i	$0.253724\pi$
$888$	−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
$892$			4.08527i			0.136785i
$893$	−1.29821	−	1.29821i	−0.0434428	−	0.0434428i
$894$	−22.5038			−0.752638
$895$		0			0
$896$		−	2.23657i		−	0.0747184i
$897$	−51.9918	−	31.1497i	−1.73596	−	1.04006i
$898$	−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
$902$	35.0955			1.16855
$903$			14.5938i			0.485650i
$904$	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	$0.774954\pi$
$908$	−9.21295			−0.305742
$909$	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	$0.517573\pi$
$912$	19.0635			0.631256
$913$	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
$917$		−	10.4986i		−	0.346693i
$918$	−4.70786			−0.155383
$919$			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
$923$	−9.55222	−	38.1049i	−0.314415	−	1.25424i
$924$			7.12964i			0.234548i
$925$		0			0
$926$	−32.3621			−1.06348
$927$	20.4777	+	20.4777i	0.672577	+	0.672577i
$928$			28.1681i			0.924664i
$929$	−22.0097	+	22.0097i	−0.722114	+	0.722114i	−0.969035	−	0.246921i	$-0.920581\pi$
$929$	−22.0097	+	22.0097i	−0.722114	+	0.722114i	0.246921	+	0.969035i	$0.420581\pi$
$930$		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	−0.692656	−	0.721268i	$-0.743560\pi$
$937$	0.875833	−	0.875833i	0.0286122	−	0.0286122i	0.721268	+	0.692656i	$0.243560\pi$
$938$		−	7.32319i		−	0.239111i
$939$		−	38.6843i		−	1.26241i
$940$		0			0
$941$	−12.8932	−	12.8932i	−0.420306	−	0.420306i	0.465003	−	0.885309i	$-0.346053\pi$
$941$	−12.8932	−	12.8932i	−0.420306	−	0.420306i	−0.885309	+	0.465003i	$0.846053\pi$
$942$	−5.74187			−0.187080
$943$	−58.9849			−1.92081
$944$	11.0628	+	11.0628i	0.360064	+	0.360064i
$945$		0			0
$946$		−	25.3949i		−	0.825659i
$947$		−	46.6408i		−	1.51562i	−0.652473	−	0.757812i	$-0.726269\pi$
$947$		−	46.6408i		−	1.51562i	0.652473	−	0.757812i	$-0.273731\pi$
$948$	−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
$957$			65.1520i			2.10606i
$958$	6.05514	+	6.05514i	0.195633	+	0.195633i
$959$	−6.31630			−0.203964
$960$		0			0
$961$		−	22.1602i		−	0.714847i
$962$	18.1193	−	30.2428i	0.584189	−	0.975067i
$963$	−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
$967$	−27.7289			−0.891701			−0.445851	−	0.895107i	$-0.647099\pi$
$967$	−27.7289			−0.891701			−0.445851	+	0.895107i	$0.647099\pi$
$968$		−	13.3591i		−	0.429379i
$969$	−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
$973$	−20.3766			−0.653243
$974$	11.6622			0.373682
$975$		0			0
$976$	−31.2307			−0.999669
$977$	40.5165			1.29624			0.648119	−	0.761539i	$-0.275556\pi$
$977$	40.5165			1.29624			0.648119	+	0.761539i	$0.275556\pi$
$978$	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
$982$			29.9486i			0.955699i
$983$	−22.9573			−0.732225			−0.366112	−	0.930571i	$-0.619311\pi$
$983$	−22.9573			−0.732225			−0.366112	+	0.930571i	$0.619311\pi$
$984$			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
$988$	10.2193	−	2.56180i	0.325120	−	0.0815017i
$989$			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
$993$			72.0870i			2.28761i
$994$	−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	−0.706823	−	0.707391i	$-0.749872\pi$
$997$	0.0179330	−	0.0179330i	0.000567945	−	0.000567945i	0.707391	+	0.706823i	$0.249872\pi$
$998$	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.k.d.268.3	yes	16
5.2	odd	4		325.2.f.d.307.3	yes	16
5.3	odd	4		325.2.f.d.307.6	yes	16
5.4	even	2	inner	325.2.k.d.268.6	yes	16
13.5	odd	4		325.2.f.d.18.6	yes	16
65.18	even	4	inner	325.2.k.d.57.6	yes	16
65.44	odd	4		325.2.f.d.18.3	✓	16
65.57	even	4	inner	325.2.k.d.57.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.f.d.18.3	✓	16	65.44	odd	4
325.2.f.d.18.6	yes	16	13.5	odd	4
325.2.f.d.307.3	yes	16	5.2	odd	4
325.2.f.d.307.6	yes	16	5.3	odd	4
325.2.k.d.57.3	yes	16	65.57	even	4	inner
325.2.k.d.57.6	yes	16	65.18	even	4	inner
325.2.k.d.268.3	yes	16	1.1	even	1	trivial
325.2.k.d.268.6	yes	16	5.4	even	2	inner

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.k (of order \(4\), degree \(2\), minimal)

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