LMFDB - Embedded newform 765.2.be.b.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(406,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("765.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			451.1
Character	$\chi$	$=$	765.451
Dual form			765.2.be.b.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66305 + 1.66305i) q^{2} -3.53144i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.37082 + 3.30945i) q^{7} +(2.54686 + 2.54686i) q^{8} +O(q^{10})$	\(q+(-1.66305 + 1.66305i) q^{2} -3.53144i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.37082 + 3.30945i) q^{7} +(2.54686 + 2.54686i) q^{8} +(0.900034 + 2.17287i) q^{10} +(-2.29362 + 0.950048i) q^{11} -1.25948i q^{13} +(-7.78350 - 3.22403i) q^{14} -1.40821 q^{16} +(3.84535 - 1.48772i) q^{17} +(-2.56985 + 2.56985i) q^{19} +(-3.26263 - 1.35142i) q^{20} +(2.23442 - 5.39437i) q^{22} +(8.16056 - 3.38021i) q^{23} +(-0.707107 - 0.707107i) q^{25} +(2.09458 + 2.09458i) q^{26} +(11.6871 - 4.84097i) q^{28} +(-3.35200 + 8.09244i) q^{29} +(2.25799 + 0.935290i) q^{31} +(-2.75181 + 2.75181i) q^{32} +(-3.92084 + 8.86913i) q^{34} +3.58212 q^{35} +(-4.25128 - 1.76094i) q^{37} -8.54755i q^{38} +(3.32763 - 1.37835i) q^{40} +(1.65510 + 3.99575i) q^{41} +(5.33668 + 5.33668i) q^{43} +(3.35504 + 8.09978i) q^{44} +(-7.94993 + 19.1928i) q^{46} +11.3322i q^{47} +(-4.12357 + 4.12357i) q^{49} +2.35190 q^{50} -4.44779 q^{52} +(-4.02442 + 4.02442i) q^{53} +2.48259i q^{55} +(-4.93742 + 11.9200i) q^{56} +(-7.88357 - 19.0326i) q^{58} +(-3.16077 - 3.16077i) q^{59} +(0.0929426 + 0.224383i) q^{61} +(-5.31057 + 2.19971i) q^{62} -11.9692i q^{64} +(-1.16361 - 0.481983i) q^{65} +7.23278 q^{67} +(-5.25380 - 13.5796i) q^{68} +(-5.95724 + 5.95724i) q^{70} +(1.69789 + 0.703290i) q^{71} +(-2.09426 + 5.05599i) q^{73} +(9.99859 - 4.14155i) q^{74} +(9.07527 + 9.07527i) q^{76} +(-6.28827 - 6.28827i) q^{77} +(-8.34789 + 3.45781i) q^{79} +(-0.538897 + 1.30101i) q^{80} +(-9.39762 - 3.89262i) q^{82} +(5.17302 - 5.17302i) q^{83} +(0.0970771 - 4.12196i) q^{85} -17.7503 q^{86} +(-8.26117 - 3.42189i) q^{88} -2.19350i q^{89} +(4.16819 - 1.72652i) q^{91} +(-11.9370 - 28.8186i) q^{92} +(-18.8459 - 18.8459i) q^{94} +(1.39079 + 3.35767i) q^{95} +(-3.75810 + 9.07286i) q^{97} -13.7154i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	−1.66305	+	1.66305i	−1.17595	+	1.17595i	−0.195185	+	0.980767i	$0.562531\pi$
$2$	−1.66305	+	1.66305i	−1.17595	+	1.17595i	−0.980767	+	0.195185i	$0.937469\pi$
$3$		0			0
$3$		0			0
$4$		−	3.53144i		−	1.76572i
$5$	0.382683	−	0.923880i	0.171141	−	0.413171i
$5$	0.382683	−	0.923880i	0.171141	−	0.413171i
$6$		0			0
$7$	1.37082	+	3.30945i	0.518121	+	1.25085i	0.939056	+	0.343764i	$0.111702\pi$
$7$	1.37082	+	3.30945i	0.518121	+	1.25085i	−0.420935	+	0.907091i	$0.638298\pi$
$8$	2.54686	+	2.54686i	0.900451	+	0.900451i
$9$		0			0
$10$	0.900034	+	2.17287i	0.284616	+	0.687123i
$11$	−2.29362	+	0.950048i	−0.691552	+	0.286450i	−0.700647	−	0.713508i	$-0.747105\pi$
$11$	−2.29362	+	0.950048i	−0.691552	+	0.286450i	0.00909468	+	0.999959i	$0.497105\pi$
$12$		0			0
$13$		−	1.25948i		−	0.349317i	−0.984629	−	0.174659i	$-0.944118\pi$
$13$		−	1.25948i		−	0.349317i	0.984629	−	0.174659i	$-0.0558822\pi$
$14$	−7.78350	−	3.22403i	−2.08023	−	0.861659i
$15$		0			0
$16$	−1.40821			−0.352052
$17$	3.84535	−	1.48772i	0.932634	−	0.360825i
$17$	3.84535	−	1.48772i	0.932634	−	0.360825i
$18$		0			0
$19$	−2.56985	+	2.56985i	−0.589563	+	0.589563i	−0.937513	−	0.347950i	$-0.886878\pi$
$19$	−2.56985	+	2.56985i	−0.589563	+	0.589563i	0.347950	+	0.937513i	$0.386878\pi$
$20$	−3.26263	−	1.35142i	−0.729546	−	0.302188i
$21$		0			0
$22$	2.23442	−	5.39437i	0.476380	−	1.15008i
$23$	8.16056	−	3.38021i	1.70159	−	0.704823i	0.701624	−	0.712547i	$-0.252459\pi$
$23$	8.16056	−	3.38021i	1.70159	−	0.704823i	0.999970	+	0.00772401i	$0.00245865\pi$
$24$		0			0
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	2.09458	+	2.09458i	0.410780	+	0.410780i
$27$		0			0
$28$	11.6871	−	4.84097i	2.20866	−	0.914857i
$29$	−3.35200	+	8.09244i	−0.622451	+	1.50273i	0.226367	+	0.974042i	$0.427315\pi$
$29$	−3.35200	+	8.09244i	−0.622451	+	1.50273i	−0.848817	+	0.528686i	$0.822685\pi$
$30$		0			0
$31$	2.25799	+	0.935290i	0.405547	+	0.167983i	0.576126	−	0.817361i	$-0.304564\pi$
$31$	2.25799	+	0.935290i	0.405547	+	0.167983i	−0.170579	+	0.985344i	$0.554564\pi$
$32$	−2.75181	+	2.75181i	−0.486456	+	0.486456i
$33$		0			0
$34$	−3.92084	+	8.86913i	−0.672419	+	1.52104i
$35$	3.58212			0.605489
$36$		0			0
$37$	−4.25128	−	1.76094i	−0.698906	−	0.289496i	0.00479925	−	0.999988i	$-0.498472\pi$
$37$	−4.25128	−	1.76094i	−0.698906	−	0.289496i	−0.703705	+	0.710492i	$0.748472\pi$
$38$		−	8.54755i		−	1.38660i
$39$		0			0
$40$	3.32763	−	1.37835i	0.526145	−	0.217936i
$41$	1.65510	+	3.99575i	0.258483	+	0.624032i	0.998839	−	0.0481830i	$-0.0153431\pi$
$41$	1.65510	+	3.99575i	0.258483	+	0.624032i	−0.740356	+	0.672215i	$0.765343\pi$
$42$		0			0
$43$	5.33668	+	5.33668i	0.813836	+	0.813836i	0.985207	−	0.171371i	$-0.0548196\pi$
$43$	5.33668	+	5.33668i	0.813836	+	0.813836i	−0.171371	+	0.985207i	$0.554820\pi$
$44$	3.35504	+	8.09978i	0.505791	+	1.22109i
$45$		0			0
$46$	−7.94993	+	19.1928i	−1.17215	+	2.82983i
$47$			11.3322i			1.65297i	0.562961	+	0.826484i	$0.309662\pi$
$47$			11.3322i			1.65297i	−0.562961	+	0.826484i	$0.690338\pi$
$48$		0			0
$49$	−4.12357	+	4.12357i	−0.589081	+	0.589081i
$50$	2.35190			0.332609
$51$		0			0
$52$	−4.44779			−0.616797
$53$	−4.02442	+	4.02442i	−0.552797	+	0.552797i	−0.927247	−	0.374450i	$-0.877831\pi$
$53$	−4.02442	+	4.02442i	−0.552797	+	0.552797i	0.374450	+	0.927247i	$0.377831\pi$
$54$		0			0
$55$			2.48259i			0.334753i
$56$	−4.93742	+	11.9200i	−0.659791	+	1.59288i
$57$		0			0
$58$	−7.88357	−	19.0326i	−1.03516	−	2.49911i
$59$	−3.16077	−	3.16077i	−0.411497	−	0.411497i	0.470763	−	0.882260i	$-0.343979\pi$
$59$	−3.16077	−	3.16077i	−0.411497	−	0.411497i	−0.882260	+	0.470763i	$0.843979\pi$
$60$		0			0
$61$	0.0929426	+	0.224383i	0.0119001	+	0.0287293i	0.929718	−	0.368273i	$-0.120051\pi$
$61$	0.0929426	+	0.224383i	0.0119001	+	0.0287293i	−0.917818	+	0.397002i	$0.870051\pi$
$62$	−5.31057	+	2.19971i	−0.674443	+	0.279364i
$63$		0			0
$64$		−	11.9692i		−	1.49615i
$65$	−1.16361	−	0.481983i	−0.144328	−	0.0597826i
$66$		0			0
$67$	7.23278			0.883625			0.441812	−	0.897108i	$-0.354336\pi$
$67$	7.23278			0.883625			0.441812	+	0.897108i	$0.354336\pi$
$68$	−5.25380	−	13.5796i	−0.637116	−	1.64677i
$69$		0			0
$70$	−5.95724	+	5.95724i	−0.712026	+	0.712026i
$71$	1.69789	+	0.703290i	0.201503	+	0.0834651i	0.481152	−	0.876637i	$-0.340218\pi$
$71$	1.69789	+	0.703290i	0.201503	+	0.0834651i	−0.279650	+	0.960102i	$0.590218\pi$
$72$		0			0
$73$	−2.09426	+	5.05599i	−0.245114	+	0.591758i	−0.997777	−	0.0666485i	$-0.978769\pi$
$73$	−2.09426	+	5.05599i	−0.245114	+	0.591758i	0.752662	+	0.658407i	$0.228769\pi$
$74$	9.99859	−	4.14155i	1.16231	−	0.481446i
$75$		0			0
$76$	9.07527	+	9.07527i	1.04100	+	1.04100i
$77$	−6.28827	−	6.28827i	−0.716615	−	0.716615i
$78$		0			0
$79$	−8.34789	+	3.45781i	−0.939211	+	0.389034i	−0.799166	−	0.601111i	$-0.794725\pi$
$79$	−8.34789	+	3.45781i	−0.939211	+	0.389034i	−0.140046	+	0.990145i	$0.544725\pi$
$80$	−0.538897	+	1.30101i	−0.0602505	+	0.145458i
$81$		0			0
$82$	−9.39762	−	3.89262i	−1.03779	−	0.429868i
$83$	5.17302	−	5.17302i	0.567812	−	0.567812i	−0.363703	−	0.931515i	$-0.618488\pi$
$83$	5.17302	−	5.17302i	0.567812	−	0.567812i	0.931515	+	0.363703i	$0.118488\pi$
$84$		0			0
$85$	0.0970771	−	4.12196i	0.0105295	−	0.447090i
$86$	−17.7503			−1.91406
$87$		0			0
$88$	−8.26117	−	3.42189i	−0.880643	−	0.364774i
$89$		−	2.19350i		−	0.232510i	−0.993219	−	0.116255i	$-0.962911\pi$
$89$		−	2.19350i		−	0.232510i	0.993219	−	0.116255i	$-0.0370890\pi$
$90$		0			0
$91$	4.16819	−	1.72652i	0.436945	−	0.180989i
$92$	−11.9370	−	28.8186i	−1.24452	−	3.00454i
$93$		0			0
$94$	−18.8459	−	18.8459i	−1.94381	−	1.94381i
$95$	1.39079	+	3.35767i	0.142692	+	0.344489i
$96$		0			0
$97$	−3.75810	+	9.07286i	−0.381577	+	0.921209i	0.610084	+	0.792337i	$0.291136\pi$
$97$	−3.75810	+	9.07286i	−0.381577	+	0.921209i	−0.991661	+	0.128872i	$0.958864\pi$
$98$		−	13.7154i		−	1.38546i
$99$		0			0
$100$	−2.49711	+	2.49711i	−0.249711	+	0.249711i
$101$	−5.46415			−0.543704			−0.271852	−	0.962339i	$-0.587636\pi$
$101$	−5.46415			−0.543704			−0.271852	+	0.962339i	$0.587636\pi$
$102$		0			0
$103$	7.16074			0.705568			0.352784	−	0.935705i	$-0.385235\pi$
$103$	7.16074			0.705568			0.352784	+	0.935705i	$0.385235\pi$
$104$	3.20773	−	3.20773i	0.314543	−	0.314543i
$105$		0			0
$106$		−	13.3856i		−	1.30012i
$107$	0.238471	−	0.575721i	0.0230539	−	0.0556570i	−0.911933	−	0.410338i	$-0.865411\pi$
$107$	0.238471	−	0.575721i	0.0230539	−	0.0556570i	0.934987	+	0.354681i	$0.115411\pi$
$108$		0			0
$109$	2.36863	+	5.71837i	0.226873	+	0.547720i	0.995794	−	0.0916242i	$-0.0292058\pi$
$109$	2.36863	+	5.71837i	0.226873	+	0.547720i	−0.768921	+	0.639344i	$0.779206\pi$
$110$	−4.12867	−	4.12867i	−0.393653	−	0.393653i
$111$		0			0
$112$	−1.93040	−	4.66039i	−0.182405	−	0.440365i
$113$	−14.8371	+	6.14574i	−1.39576	+	0.578143i	−0.948648	−	0.316335i	$-0.897548\pi$
$113$	−14.8371	+	6.14574i	−1.39576	+	0.578143i	−0.447113	+	0.894478i	$0.647548\pi$
$114$		0			0
$115$		−	8.83293i		−	0.823675i
$116$	28.5780	+	11.8374i	2.65340	+	1.09907i
$117$		0			0
$118$	10.5130			0.967801
$119$	10.1948	+	10.6866i	0.934557	+	0.979638i
$120$		0			0
$121$	−3.42008	+	3.42008i	−0.310916	+	0.310916i
$122$	−0.527727	−	0.218592i	−0.0477782	−	0.0197904i
$123$		0			0
$124$	3.30292	−	7.97396i	0.296611	−	0.716083i
$125$	−0.923880	+	0.382683i	−0.0826343	+	0.0342282i
$126$		0			0
$127$	4.18456	+	4.18456i	0.371320	+	0.371320i	0.867958	−	0.496638i	$-0.165432\pi$
$127$	4.18456	+	4.18456i	0.371320	+	0.371320i	−0.496638	+	0.867958i	$0.665432\pi$
$128$	14.4017	+	14.4017i	1.27294	+	1.27294i
$129$		0			0
$130$	2.73670	−	1.13358i	0.240024	−	0.0994213i
$131$	−6.16914	+	14.8936i	−0.539000	+	1.30126i	0.386421	+	0.922322i	$0.373711\pi$
$131$	−6.16914	+	14.8936i	−0.539000	+	1.30126i	−0.925422	+	0.378939i	$0.876289\pi$
$132$		0			0
$133$	−12.0276	−	4.98198i	−1.04292	−	0.431993i
$134$	−12.0284	+	12.0284i	−1.03910	+	1.03910i
$135$		0			0
$136$	13.5826	+	6.00455i	1.16470	+	0.514886i
$137$	17.1320			1.46369			0.731843	−	0.681473i	$-0.238661\pi$
$137$	17.1320			1.46369			0.731843	+	0.681473i	$0.238661\pi$
$138$		0			0
$139$	1.97070	+	0.816292i	0.167153	+	0.0692369i	0.464691	−	0.885473i	$-0.346165\pi$
$139$	1.97070	+	0.816292i	0.167153	+	0.0692369i	−0.297538	+	0.954710i	$0.596165\pi$
$140$		−	12.6501i		−	1.06913i
$141$		0			0
$142$	−3.99327	+	1.65407i	−0.335108	+	0.138806i
$143$	1.19657	+	2.88877i	0.100062	+	0.241571i
$144$		0			0
$145$	6.19369	+	6.19369i	0.514358	+	0.514358i
$146$	−4.92549	−	11.8912i	−0.407636	−	0.984121i
$147$		0			0
$148$	−6.21865	+	15.0131i	−0.511170	+	1.23407i
$149$		−	18.5384i		−	1.51872i	−0.650669	−	0.759362i	$-0.725511\pi$
$149$		−	18.5384i		−	1.51872i	0.650669	−	0.759362i	$-0.274489\pi$
$150$		0			0
$151$	−6.30217	+	6.30217i	−0.512863	+	0.512863i	−0.915403	−	0.402539i	$-0.868128\pi$
$151$	−6.30217	+	6.30217i	−0.512863	+	0.512863i	0.402539	+	0.915403i	$0.368128\pi$
$152$	−13.0901			−1.06175
$153$		0			0
$154$	20.9154			1.68541
$155$	1.72819	−	1.72819i	0.138812	−	0.138812i
$156$		0			0
$157$		−	18.2426i		−	1.45592i	−0.685620	−	0.727960i	$-0.740469\pi$
$157$		−	18.2426i		−	1.45592i	0.685620	−	0.727960i	$-0.259531\pi$
$158$	8.13243	−	19.6334i	0.646982	−	1.56195i
$159$		0			0
$160$	1.48927	+	3.59541i	0.117737	+	0.284242i
$161$	22.3733	+	22.3733i	1.76326	+	1.76326i
$162$		0			0
$163$	−3.58387	−	8.65222i	−0.280710	−	0.677694i	0.719142	−	0.694863i	$-0.244535\pi$
$163$	−3.58387	−	8.65222i	−0.280710	−	0.677694i	−0.999853	+	0.0171684i	$0.994535\pi$
$164$	14.1108	−	5.84488i	1.10187	−	0.456408i
$165$		0			0
$166$			17.2059i			1.33544i
$167$	8.57484	+	3.55181i	0.663541	+	0.274848i	0.688928	−	0.724830i	$-0.258082\pi$
$167$	8.57484	+	3.55181i	0.663541	+	0.274848i	−0.0253869	+	0.999678i	$0.508082\pi$
$168$		0			0
$169$	11.4137			0.877977
$170$	6.69357	+	7.01646i	0.513373	+	0.538138i
$171$		0			0
$172$	18.8462	−	18.8462i	1.43701	−	1.43701i
$173$	3.97248	+	1.64545i	0.302022	+	0.125102i	0.528548	−	0.848904i	$-0.322737\pi$
$173$	3.97248	+	1.64545i	0.302022	+	0.125102i	−0.226526	+	0.974005i	$0.572737\pi$
$174$		0			0
$175$	1.37082	−	3.30945i	0.103624	−	0.250171i
$176$	3.22989	−	1.33786i	0.243462	−	0.100845i
$177$		0			0
$178$	3.64789	+	3.64789i	0.273421	+	0.273421i
$179$	0.0832109	+	0.0832109i	0.00621948	+	0.00621948i	0.710210	−	0.703990i	$-0.248600\pi$
$179$	0.0832109	+	0.0832109i	0.00621948	+	0.00621948i	−0.703990	+	0.710210i	$0.748600\pi$
$180$		0			0
$181$	−2.14676	+	0.889218i	−0.159568	+	0.0660951i	−0.461038	−	0.887381i	$-0.652523\pi$
$181$	−2.14676	+	0.889218i	−0.159568	+	0.0660951i	0.301470	+	0.953476i	$0.402523\pi$
$182$	−4.06061	+	9.80318i	−0.300993	+	0.726660i
$183$		0			0
$184$	29.3927	+	12.1749i	2.16686	+	0.897544i
$185$	−3.25379	+	3.25379i	−0.239223	+	0.239223i
$186$		0			0
$187$	−7.40635	+	7.06552i	−0.541606	+	0.516682i
$188$	40.0189			2.91868
$189$		0			0
$190$	−7.89690	−	3.27100i	−0.572902	−	0.237304i
$191$		−	14.6622i		−	1.06092i	−0.847710	−	0.530461i	$-0.822019\pi$
$191$		−	14.6622i		−	1.06092i	0.847710	−	0.530461i	$-0.177981\pi$
$192$		0			0
$193$	7.75695	−	3.21303i	0.558357	−	0.231279i	−0.0856146	−	0.996328i	$-0.527285\pi$
$193$	7.75695	−	3.21303i	0.558357	−	0.231279i	0.643972	+	0.765049i	$0.277285\pi$
$194$	−8.83869	−	21.3385i	−0.634581	−	1.53201i
$195$		0			0
$196$	14.5622	+	14.5622i	1.04015	+	1.04015i
$197$	2.55690	+	6.17290i	0.182171	+	0.439801i	0.988414	−	0.151785i	$-0.0485021\pi$
$197$	2.55690	+	6.17290i	0.182171	+	0.439801i	−0.806242	+	0.591586i	$0.798502\pi$
$198$		0			0
$199$	7.22192	−	17.4353i	0.511949	−	1.23595i	−0.430800	−	0.902448i	$-0.641768\pi$
$199$	7.22192	−	17.4353i	0.511949	−	1.23595i	0.942748	−	0.333506i	$-0.108232\pi$
$200$		−	3.60181i		−	0.254686i
$201$		0			0
$202$	9.08714	−	9.08714i	0.639369	−	0.639369i
$203$	−31.3765			−2.20220
$204$		0			0
$205$	4.32497			0.302069
$206$	−11.9086	+	11.9086i	−0.829714	+	0.829714i
$207$		0			0
$208$			1.77361i			0.122978i
$209$	3.45277	−	8.33572i	0.238833	−	0.576594i
$210$		0			0
$211$	2.53326	+	6.11583i	0.174397	+	0.421031i	0.986774	−	0.162101i	$-0.0518270\pi$
$211$	2.53326	+	6.11583i	0.174397	+	0.421031i	−0.812377	+	0.583132i	$0.801827\pi$
$212$	14.2120	+	14.2120i	0.976085	+	0.976085i
$213$		0			0
$214$	0.560861	+	1.35404i	0.0383397	+	0.0925602i
$215$	6.97271	−	2.88819i	0.475535	−	0.196973i
$216$		0			0
$217$			8.75482i			0.594316i
$218$	−13.4490	−	5.57077i	−0.910884	−	0.377300i
$219$		0			0
$220$	8.76714			0.591081
$221$	−1.87376	−	4.84315i	−0.126042	−	0.325785i
$222$		0			0
$223$	2.08077	−	2.08077i	0.139339	−	0.139339i	−0.633997	−	0.773336i	$-0.718587\pi$
$223$	2.08077	−	2.08077i	0.139339	−	0.139339i	0.773336	+	0.633997i	$0.218587\pi$
$224$	−12.8792	−	5.33474i	−0.860529	−	0.356443i
$225$		0			0
$226$	14.4542	−	34.8955i	0.961478	−	2.32121i
$227$	19.8871	−	8.23750i	1.31995	−	0.546742i	0.392180	−	0.919889i	$-0.371721\pi$
$227$	19.8871	−	8.23750i	1.31995	−	0.546742i	0.927772	+	0.373147i	$0.121721\pi$
$228$		0			0
$229$	8.44347	+	8.44347i	0.557960	+	0.557960i	0.928726	−	0.370766i	$-0.120905\pi$
$229$	8.44347	+	8.44347i	0.557960	+	0.557960i	−0.370766	+	0.928726i	$0.620905\pi$
$230$	14.6896	+	14.6896i	0.968601	+	0.968601i
$231$		0			0
$232$	−29.1474	+	12.0732i	−1.91362	+	0.792647i
$233$	3.85313	−	9.30228i	0.252427	−	0.609412i	−0.745972	−	0.665977i	$-0.768015\pi$
$233$	3.85313	−	9.30228i	0.252427	−	0.609412i	0.998399	+	0.0565648i	$0.0180148\pi$
$234$		0			0
$235$	10.4696	+	4.33664i	0.682959	+	0.282891i
$236$	−11.1621	+	11.1621i	−0.726590	+	0.726590i
$237$		0			0
$238$	−34.7267	−	0.817856i	−2.25100	−	0.0530137i
$239$	16.6253			1.07540			0.537701	−	0.843135i	$-0.319293\pi$
$239$	16.6253			1.07540			0.537701	+	0.843135i	$0.319293\pi$
$240$		0			0
$241$	5.47122	+	2.26625i	0.352432	+	0.145982i	0.551874	−	0.833928i	$-0.313913\pi$
$241$	5.47122	+	2.26625i	0.352432	+	0.145982i	−0.199442	+	0.979910i	$0.563913\pi$
$242$		−	11.3755i		−	0.731245i
$243$		0			0
$244$	0.792397	−	0.328221i	0.0507280	−	0.0210122i
$245$	2.23166	+	5.38770i	0.142575	+	0.344208i
$246$		0			0
$247$	3.23668	+	3.23668i	0.205945	+	0.205945i
$248$	3.36873	+	8.13284i	0.213915	+	0.516436i
$249$		0			0
$250$	0.900034	−	2.17287i	0.0569231	−	0.137425i
$251$		−	7.77270i		−	0.490608i	−0.969446	−	0.245304i	$-0.921112\pi$
$251$		−	7.77270i		−	0.490608i	0.969446	−	0.245304i	$-0.0788878\pi$
$252$		0			0
$253$	−15.5058	+	15.5058i	−0.974844	+	0.974844i
$254$	−13.9182			−0.873307
$255$		0			0
$256$	−23.9630			−1.49768
$257$	5.70344	−	5.70344i	0.355771	−	0.355771i	−0.506481	−	0.862251i	$-0.669054\pi$
$257$	5.70344	−	5.70344i	0.355771	−	0.355771i	0.862251	+	0.506481i	$0.169054\pi$
$258$		0			0
$259$		−	16.4833i		−	1.02422i
$260$	−1.70210	+	4.10922i	−0.105559	+	0.254843i
$261$		0			0
$262$	−14.5092	−	35.0283i	−0.896382	−	2.16406i
$263$	−15.0792	−	15.0792i	−0.929822	−	0.929822i	0.0678724	−	0.997694i	$-0.478379\pi$
$263$	−15.0792	−	15.0792i	−0.929822	−	0.929822i	−0.997694	+	0.0678724i	$0.978379\pi$
$264$		0			0
$265$	2.17800	+	5.25816i	0.133794	+	0.323006i
$266$	28.2877	−	11.7171i	1.73443	−	0.718424i
$267$		0			0
$268$		−	25.5422i		−	1.56024i
$269$	−3.88200	−	1.60798i	−0.236690	−	0.0980401i	0.261186	−	0.965289i	$-0.415886\pi$
$269$	−3.88200	−	1.60798i	−0.236690	−	0.0980401i	−0.497876	+	0.867248i	$0.665886\pi$
$270$		0			0
$271$	−24.7136			−1.50124			−0.750621	−	0.660733i	$-0.770245\pi$
$271$	−24.7136			−1.50124			−0.750621	+	0.660733i	$0.770245\pi$
$272$	−5.41504	+	2.09502i	−0.328335	+	0.127029i
$273$		0			0
$274$	−28.4913	+	28.4913i	−1.72122	+	1.72122i
$275$	2.29362	+	0.950048i	0.138310	+	0.0572900i
$276$		0			0
$277$	7.67765	−	18.5355i	0.461305	−	1.11369i	−0.506556	−	0.862207i	$-0.669082\pi$
$277$	7.67765	−	18.5355i	0.461305	−	1.11369i	0.967862	−	0.251483i	$-0.0809182\pi$
$278$	−4.63490	+	1.91984i	−0.277983	+	0.115144i
$279$		0			0
$280$	9.12317	+	9.12317i	0.545214	+	0.545214i
$281$	−17.8053	−	17.8053i	−1.06218	−	1.06218i	−0.997934	−	0.0642430i	$-0.979537\pi$
$281$	−17.8053	−	17.8053i	−1.06218	−	1.06218i	−0.0642430	−	0.997934i	$-0.520463\pi$
$282$		0			0
$283$	7.84059	−	3.24768i	0.466075	−	0.193054i	−0.137272	−	0.990533i	$-0.543833\pi$
$283$	7.84059	−	3.24768i	0.466075	−	0.193054i	0.603347	+	0.797479i	$0.293833\pi$
$284$	2.48363	−	5.99601i	0.147376	−	0.355798i
$285$		0			0
$286$	−6.79411	−	2.81421i	−0.401744	−	0.166408i
$287$	−10.9549	+	10.9549i	−0.646648	+	0.646648i
$288$		0			0
$289$	12.5734	−	11.4416i	0.739611	−	0.673035i
$290$	−20.6008			−1.20972
$291$		0			0
$292$	17.8549	+	7.39575i	1.04488	+	0.432804i
$293$			25.9873i			1.51820i	0.650977	+	0.759098i	$0.274360\pi$
$293$			25.9873i			1.51820i	−0.650977	+	0.759098i	$0.725640\pi$
$294$		0			0
$295$	−4.12975	+	1.71060i	−0.240443	+	0.0995948i
$296$	−6.34255	−	15.3123i	−0.368653	−	0.890008i
$297$		0			0
$298$	30.8302	+	30.8302i	1.78594	+	1.78594i
$299$	−4.25732	−	10.2781i	−0.246207	−	0.594397i
$300$		0			0
$301$	−10.3458	+	24.9771i	−0.596325	+	1.43966i
$302$		−	20.9616i		−	1.20620i
$303$		0			0
$304$	3.61887	−	3.61887i	0.207557	−	0.207557i
$305$	0.242871			0.0139067
$306$		0			0
$307$	16.9475			0.967245			0.483622	−	0.875277i	$-0.339321\pi$
$307$	16.9475			0.967245			0.483622	+	0.875277i	$0.339321\pi$
$308$	−22.2067	+	22.2067i	−1.26534	+	1.26534i
$309$		0			0
$310$			5.74812i			0.326471i
$311$	6.57851	−	15.8819i	0.373033	−	0.900581i	−0.620200	−	0.784444i	$-0.712949\pi$
$311$	6.57851	−	15.8819i	0.373033	−	0.900581i	0.993233	−	0.116138i	$-0.0370513\pi$
$312$		0			0
$313$	−2.26352	−	5.46463i	−0.127942	−	0.308879i	0.846909	−	0.531738i	$-0.178461\pi$
$313$	−2.26352	−	5.46463i	−0.127942	−	0.308879i	−0.974851	+	0.222859i	$0.928461\pi$
$314$	30.3383	+	30.3383i	1.71209	+	1.71209i
$315$		0			0
$316$	12.2111	+	29.4801i	0.686926	+	1.65839i
$317$	0.591813	−	0.245137i	0.0332395	−	0.0137683i	−0.366002	−	0.930614i	$-0.619274\pi$
$317$	0.591813	−	0.245137i	0.0332395	−	0.0137683i	0.399241	+	0.916846i	$0.369274\pi$
$318$		0			0
$319$		−	21.7455i		−	1.21752i
$320$	−11.0581	−	4.58041i	−0.618166	−	0.256053i
$321$		0			0
$322$	−74.4157			−4.14702
$323$	−6.05874	+	13.7052i	−0.337117	+	0.762576i
$324$		0			0
$325$	−0.890588	+	0.890588i	−0.0494010	+	0.0494010i
$326$	20.3492	+	8.42891i	1.12704	+	0.466834i
$327$		0			0
$328$	−5.96133	+	14.3919i	−0.329160	+	0.794661i
$329$	−37.5033	+	15.5344i	−2.06762	+	0.856437i
$330$		0			0
$331$	−8.24547	−	8.24547i	−0.453212	−	0.453212i	0.443207	−	0.896419i	$-0.353841\pi$
$331$	−8.24547	−	8.24547i	−0.453212	−	0.453212i	−0.896419	+	0.443207i	$0.853841\pi$
$332$	−18.2682	−	18.2682i	−1.00260	−	1.00260i
$333$		0			0
$334$	−20.1672	+	8.35352i	−1.10350	+	0.457084i
$335$	2.76786	−	6.68222i	0.151225	−	0.365088i
$336$		0			0
$337$	28.5300	+	11.8175i	1.55413	+	0.643740i	0.984056	−	0.177856i	$-0.0569162\pi$
$337$	28.5300	+	11.8175i	1.55413	+	0.643740i	0.570070	+	0.821596i	$0.306916\pi$
$338$	−18.9815	+	18.9815i	−1.03246	+	1.03246i
$339$		0			0
$340$	−14.5565	−	0.342822i	−0.789436	−	0.0185922i
$341$	−6.06754			−0.328576
$342$		0			0
$343$	3.86674	+	1.60166i	0.208784	+	0.0864813i
$344$			27.1836i			1.46564i
$345$		0			0
$346$	−9.34288	+	3.86995i	−0.502276	+	0.208050i
$347$	0.00573993	+	0.0138574i	0.000308135	+	0.000743905i	0.924034	−	0.382311i	$-0.124872\pi$
$347$	0.00573993	+	0.0138574i	0.000308135	+	0.000743905i	−0.923725	+	0.383055i	$0.874872\pi$
$348$		0			0
$349$	−2.58441	−	2.58441i	−0.138340	−	0.138340i	0.634545	−	0.772886i	$-0.281187\pi$
$349$	−2.58441	−	2.58441i	−0.138340	−	0.138340i	−0.772886	+	0.634545i	$0.781187\pi$
$350$	3.22403	+	7.78350i	0.172332	+	0.416046i
$351$		0			0
$352$	3.69725	−	8.92595i	0.197064	−	0.475755i
$353$		−	3.82333i		−	0.203495i	−0.994810	−	0.101748i	$-0.967557\pi$
$353$		−	3.82333i		−	0.203495i	0.994810	−	0.101748i	$-0.0324434\pi$
$354$		0			0
$355$	1.29951	−	1.29951i	0.0689708	−	0.0689708i
$356$	−7.74622			−0.410549
$357$		0			0
$358$	−0.276767			−0.0146276
$359$	4.73532	−	4.73532i	0.249921	−	0.249921i	−0.571017	−	0.820938i	$-0.693451\pi$
$359$	4.73532	−	4.73532i	0.249921	−	0.249921i	0.820938	+	0.571017i	$0.193451\pi$
$360$		0			0
$361$			5.79178i			0.304830i
$362$	2.09135	−	5.04897i	0.109919	−	0.265368i
$363$		0			0
$364$	−6.09712	−	14.7197i	−0.319576	−	0.771524i
$365$	3.86968	+	3.86968i	0.202549	+	0.202549i
$366$		0			0
$367$	−8.81227	−	21.2747i	−0.459997	−	1.11053i	−0.968398	−	0.249410i	$-0.919763\pi$
$367$	−8.81227	−	21.2747i	−0.459997	−	1.11053i	0.508401	−	0.861120i	$-0.330237\pi$
$368$	−11.4917	+	4.76004i	−0.599049	+	0.248134i
$369$		0			0
$370$		−	10.8224i		−	0.562630i
$371$	−18.8354	−	7.80187i	−0.977884	−	0.405053i
$372$		0			0
$373$	−23.7303			−1.22871			−0.614355	−	0.789030i	$-0.710584\pi$
$373$	−23.7303			−1.22871			−0.614355	+	0.789030i	$0.710584\pi$
$374$	0.566816	−	24.0674i	0.0293094	−	1.24450i
$375$		0			0
$376$	−28.8615	+	28.8615i	−1.48842	+	1.48842i
$377$	10.1923	+	4.22178i	0.524929	+	0.217433i
$378$		0			0
$379$	1.13970	−	2.75149i	0.0585427	−	0.141335i	−0.891902	−	0.452230i	$-0.850629\pi$
$379$	1.13970	−	2.75149i	0.0585427	−	0.141335i	0.950444	+	0.310895i	$0.100629\pi$
$380$	11.8574	−	4.91150i	0.608272	−	0.251955i
$381$		0			0
$382$	24.3839	+	24.3839i	1.24759	+	1.24759i
$383$	17.2691	+	17.2691i	0.882408	+	0.882408i	0.993779	−	0.111371i	$-0.0355241\pi$
$383$	17.2691	+	17.2691i	0.882408	+	0.882408i	−0.111371	+	0.993779i	$0.535524\pi$
$384$		0			0
$385$	−8.21602	+	3.40319i	−0.418727	+	0.173443i
$386$	−7.55674	+	18.2436i	−0.384628	+	0.928574i
$387$		0			0
$388$	32.0403	+	13.2715i	1.62660	+	0.673759i
$389$	1.19407	−	1.19407i	0.0605418	−	0.0605418i	−0.676188	−	0.736729i	$-0.736369\pi$
$389$	1.19407	−	1.19407i	0.0605418	−	0.0605418i	0.736729	+	0.676188i	$0.236369\pi$
$390$		0			0
$391$	26.3514	−	25.1387i	1.33265	−	1.27132i
$392$	−21.0043			−1.06088
$393$		0			0
$394$	−14.5181	−	6.01357i	−0.731409	−	0.302960i
$395$			9.03570i			0.454635i
$396$		0			0
$397$	−29.1259	+	12.0643i	−1.46178	+	0.605491i	−0.964969	−	0.262365i	$-0.915498\pi$
$397$	−29.1259	+	12.0643i	−1.46178	+	0.605491i	−0.496816	+	0.867856i	$0.665498\pi$
$398$	16.9853	+	41.0060i	0.851394	+	2.05545i
$399$		0			0
$400$	0.995752	+	0.995752i	0.0497876	+	0.0497876i
$401$	−1.93870	−	4.68044i	−0.0968141	−	0.233730i	0.868051	−	0.496474i	$-0.165372\pi$
$401$	−1.93870	−	4.68044i	−0.0968141	−	0.233730i	−0.964865	+	0.262745i	$0.915372\pi$
$402$		0			0
$403$	1.17798	−	2.84390i	0.0586794	−	0.141665i
$404$			19.2964i			0.960029i
$405$		0			0
$406$	52.1806	−	52.1806i	2.58968	−	2.58968i
$407$	11.4238			0.566256
$408$		0			0
$409$	−26.1178			−1.29144			−0.645722	−	0.763573i	$-0.723443\pi$
$409$	−26.1178			−1.29144			−0.645722	+	0.763573i	$0.723443\pi$
$410$	−7.19263	+	7.19263i	−0.355219	+	0.355219i
$411$		0			0
$412$		−	25.2877i		−	1.24584i
$413$	6.12757	−	14.7933i	0.301518	−	0.727929i
$414$		0			0
$415$	−2.79962	−	6.75887i	−0.137428	−	0.331780i
$416$	3.46586	+	3.46586i	0.169928	+	0.169928i
$417$		0			0
$418$	8.12058	+	19.6048i	0.397190	+	0.958903i
$419$	−6.74298	+	2.79303i	−0.329416	+	0.136449i	−0.541261	−	0.840855i	$-0.682053\pi$
$419$	−6.74298	+	2.79303i	−0.329416	+	0.136449i	0.211845	+	0.977303i	$0.432053\pi$
$420$		0			0
$421$		−	21.0644i		−	1.02662i	−0.858204	−	0.513309i	$-0.828420\pi$
$421$		−	21.0644i		−	1.02662i	0.858204	−	0.513309i	$-0.171580\pi$
$422$	−14.3838	−	5.95798i	−0.700194	−	0.290030i
$423$		0			0
$424$	−20.4993			−0.995533
$425$	−3.77105	−	1.66709i	−0.182923	−	0.0808660i
$426$		0			0
$427$	−0.615178	+	0.615178i	−0.0297705	+	0.0297705i
$428$	−2.03313	−	0.842148i	−0.0982749	−	0.0407068i
$429$		0			0
$430$	−6.79274	+	16.3991i	−0.327575	+	0.790836i
$431$	19.4414	−	8.05290i	0.936460	−	0.387894i	0.138334	−	0.990386i	$-0.455825\pi$
$431$	19.4414	−	8.05290i	0.936460	−	0.387894i	0.798126	+	0.602491i	$0.205825\pi$
$432$		0			0
$433$	−26.2522	−	26.2522i	−1.26160	−	1.26160i	−0.950318	−	0.311280i	$-0.899242\pi$
$433$	−26.2522	−	26.2522i	−1.26160	−	1.26160i	−0.311280	−	0.950318i	$-0.600758\pi$
$434$	−14.5597	−	14.5597i	−0.698886	−	0.698886i
$435$		0			0
$436$	20.1941	−	8.36467i	0.967121	−	0.400595i
$437$	−12.2848	+	29.6580i	−0.587659	+	1.41874i
$438$		0			0
$439$	0.435448	+	0.180369i	0.0207828	+	0.00860852i	0.393051	−	0.919517i	$-0.371420\pi$
$439$	0.435448	+	0.180369i	0.0207828	+	0.00860852i	−0.372268	+	0.928125i	$0.621420\pi$
$440$	−6.32282	+	6.32282i	−0.301429	+	0.301429i
$441$		0			0
$442$	11.1705	+	4.93823i	0.531327	+	0.234888i
$443$	11.0249			0.523808			0.261904	−	0.965094i	$-0.415650\pi$
$443$	11.0249			0.523808			0.261904	+	0.965094i	$0.415650\pi$
$444$		0			0
$445$	−2.02653	−	0.839416i	−0.0960667	−	0.0397921i
$446$			6.92084i			0.327711i
$447$		0			0
$448$	39.6114	−	16.4076i	1.87146	−	0.775186i
$449$	−6.60636	−	15.9492i	−0.311773	−	0.752688i	−0.999639	−	0.0268500i	$-0.991452\pi$
$449$	−6.60636	−	15.9492i	−0.311773	−	0.752688i	0.687866	−	0.725838i	$-0.258548\pi$
$450$		0			0
$451$	−7.59232	−	7.59232i	−0.357508	−	0.357508i
$452$	21.7033	+	52.3965i	1.02084	+	2.46452i
$453$		0			0
$454$	−19.3738	+	46.7725i	−0.909257	+	2.19514i
$455$		−	4.51162i		−	0.211508i
$456$		0			0
$457$	−7.96742	+	7.96742i	−0.372700	+	0.372700i	−0.868460	−	0.495760i	$-0.834890\pi$
$457$	−7.96742	+	7.96742i	−0.372700	+	0.372700i	0.495760	+	0.868460i	$0.334890\pi$
$458$	−28.0837			−1.31227
$459$		0			0
$460$	−31.1930			−1.45438
$461$	−21.2185	+	21.2185i	−0.988244	+	0.988244i	−0.999932	−	0.0116873i	$-0.996280\pi$
$461$	−21.2185	+	21.2185i	−0.988244	+	0.988244i	0.0116873	+	0.999932i	$0.496280\pi$
$462$		0			0
$463$			17.1592i			0.797457i	0.917069	+	0.398728i	$0.130548\pi$
$463$			17.1592i			0.797457i	−0.917069	+	0.398728i	$0.869452\pi$
$464$	4.72031	−	11.3958i	0.219135	−	0.529038i
$465$		0			0
$466$	9.06218	+	21.8780i	0.419798	+	1.01348i
$467$	−18.8030	−	18.8030i	−0.870099	−	0.870099i	0.122384	−	0.992483i	$-0.460946\pi$
$467$	−18.8030	−	18.8030i	−0.870099	−	0.870099i	−0.992483	+	0.122384i	$0.960946\pi$
$468$		0			0
$469$	9.91483	+	23.9365i	0.457824	+	1.10529i
$470$	−24.6234	+	10.1993i	−1.13579	+	0.470461i
$471$		0			0
$472$		−	16.1001i		−	0.741066i
$473$	−17.3104	−	7.17020i	−0.795933	−	0.329686i
$474$		0			0
$475$	3.63431			0.166754
$476$	37.7391	−	36.0024i	1.72977	−	1.65017i
$477$		0			0
$478$	−27.6487	+	27.6487i	−1.26462	+	1.26462i
$479$	21.1662	+	8.76732i	0.967107	+	0.400589i	0.809635	−	0.586934i	$-0.199665\pi$
$479$	21.1662	+	8.76732i	0.967107	+	0.400589i	0.157473	+	0.987523i	$0.449665\pi$
$480$		0			0
$481$	−2.21787	+	5.35441i	−0.101126	+	0.244140i
$482$	−12.8678	+	5.33000i	−0.586111	+	0.242775i
$483$		0			0
$484$	12.0778	+	12.0778i	0.548992	+	0.548992i
$485$	6.94407	+	6.94407i	0.315314	+	0.315314i
$486$		0			0
$487$	14.5174	−	6.01330i	0.657846	−	0.272489i	−0.0286857	−	0.999588i	$-0.509132\pi$
$487$	14.5174	−	6.01330i	0.657846	−	0.272489i	0.686532	+	0.727100i	$0.259132\pi$
$488$	−0.334761	+	0.808185i	−0.0151539	+	0.0365848i
$489$		0			0
$490$	−12.6713	−	5.24864i	−0.572433	−	0.237110i
$491$	−0.607534	+	0.607534i	−0.0274176	+	0.0274176i	−0.720683	−	0.693265i	$-0.756172\pi$
$491$	−0.607534	+	0.607534i	−0.0274176	+	0.0274176i	0.693265	+	0.720683i	$0.256172\pi$
$492$		0			0
$493$	−0.850318	+	36.1051i	−0.0382964	+	1.62609i
$494$	−10.7655			−0.484362
$495$		0			0
$496$	−3.17972	−	1.31708i	−0.142773	−	0.0591387i
$497$			6.58317i			0.295296i
$498$		0			0
$499$	−20.9163	+	8.66380i	−0.936340	+	0.387845i	−0.798080	−	0.602551i	$-0.794151\pi$
$499$	−20.9163	+	8.66380i	−0.936340	+	0.387845i	−0.138260	+	0.990396i	$0.544151\pi$
$500$	1.35142	+	3.26263i	0.0604376	+	0.145909i
$501$		0			0
$502$	12.9264	+	12.9264i	0.576931	+	0.576931i
$503$	−6.54963	−	15.8122i	−0.292034	−	0.705032i	0.707966	−	0.706247i	$-0.249613\pi$
$503$	−6.54963	−	15.8122i	−0.292034	−	0.705032i	−0.999999	+	0.00121517i	$0.999613\pi$
$504$		0			0
$505$	−2.09104	+	5.04822i	−0.0930501	+	0.224643i
$506$		−	51.5739i		−	2.29274i
$507$		0			0
$508$	14.7775	−	14.7775i	0.655647	−	0.655647i
$509$	−29.7081			−1.31679			−0.658393	−	0.752674i	$-0.728764\pi$
$509$	−29.7081			−1.31679			−0.658393	+	0.752674i	$0.728764\pi$
$510$		0			0
$511$	−19.6034			−0.867203
$512$	11.0481	−	11.0481i	0.488263	−	0.488263i
$513$		0			0
$514$			18.9701i			0.836737i
$515$	2.74030	−	6.61566i	0.120752	−	0.291521i
$516$		0			0
$517$	−10.7661	−	25.9917i	−0.473493	−	1.14311i
$518$	27.4125	+	27.4125i	1.20444	+	1.20444i
$519$		0			0
$520$	−1.73601	−	4.19110i	−0.0761290	−	0.183792i
$521$	35.7139	−	14.7932i	1.56465	−	0.648101i	0.578764	−	0.815495i	$-0.303535\pi$
$521$	35.7139	−	14.7932i	1.56465	−	0.648101i	0.985890	+	0.167395i	$0.0535354\pi$
$522$		0			0
$523$			0.599508i			0.0262147i	0.999914	+	0.0131073i	$0.00417231\pi$
$523$			0.599508i			0.0262147i	−0.999914	+	0.0131073i	$0.995828\pi$
$524$	52.5960	+	21.7860i	2.29767	+	0.951724i
$525$		0			0
$526$	50.1547			2.18685
$527$	10.0742	+	0.237259i	0.438839	+	0.0103352i
$528$		0			0
$529$	38.9054	−	38.9054i	1.69154	−	1.69154i
$530$	−12.3667	−	5.12244i	−0.537174	−	0.222505i
$531$		0			0
$532$	−17.5936	+	42.4747i	−0.762779	+	1.84151i
$533$	5.03258	−	2.08456i	0.217985	−	0.0902925i
$534$		0			0
$535$	−0.440638	−	0.440638i	−0.0190504	−	0.0190504i
$536$	18.4209	+	18.4209i	0.795661	+	0.795661i
$537$		0			0
$538$	9.13009	−	3.78181i	0.393626	−	0.163045i
$539$	5.54031	−	13.3755i	0.238638	−	0.576123i
$540$		0			0
$541$	36.6847	+	15.1953i	1.57720	+	0.653297i	0.987966	−	0.154668i	$-0.0494308\pi$
$541$	36.6847	+	15.1953i	1.57720	+	0.653297i	0.589231	+	0.807965i	$0.299431\pi$
$542$	41.0998	−	41.0998i	1.76539	−	1.76539i
$543$		0			0
$544$	−6.48774	+	14.6756i	−0.278160	+	0.629211i
$545$	6.18952			0.265130
$546$		0			0
$547$	−3.73035	−	1.54516i	−0.159498	−	0.0660663i	0.301506	−	0.953464i	$-0.402511\pi$
$547$	−3.73035	−	1.54516i	−0.159498	−	0.0660663i	−0.461004	+	0.887398i	$0.652511\pi$
$548$		−	60.5007i		−	2.58446i
$549$		0			0
$550$	−5.39437	+	2.23442i	−0.230017	+	0.0952760i
$551$	−12.1822	−	29.4105i	−0.518980	−	1.25293i
$552$		0			0
$553$	−22.8869	−	22.8869i	−0.973250	−	0.973250i
$554$	18.0571	+	43.5937i	0.767172	+	1.85212i
$555$		0			0
$556$	2.88269	−	6.95942i	0.122253	−	0.295145i
$557$		−	5.42781i		−	0.229984i	−0.993366	−	0.114992i	$-0.963316\pi$
$557$		−	5.42781i		−	0.229984i	0.993366	−	0.114992i	$-0.0366842\pi$
$558$		0			0
$559$	6.72145	−	6.72145i	0.284287	−	0.284287i
$560$	−5.04437			−0.213163
$561$		0			0
$562$	59.2222			2.49814
$563$	3.66888	−	3.66888i	0.154625	−	0.154625i	−0.625555	−	0.780180i	$-0.715127\pi$
$563$	3.66888	−	3.66888i	0.154625	−	0.154625i	0.780180	+	0.625555i	$0.215127\pi$
$564$		0			0
$565$			16.0596i			0.675632i
$566$	−7.63822	+	18.4403i	−0.321058	+	0.775104i
$567$		0			0
$568$	2.53311	+	6.11547i	0.106287	+	0.256600i
$569$	−8.48266	−	8.48266i	−0.355611	−	0.355611i	0.506581	−	0.862192i	$-0.330909\pi$
$569$	−8.48266	−	8.48266i	−0.355611	−	0.355611i	−0.862192	+	0.506581i	$0.830909\pi$
$570$		0			0
$571$	−16.6512	−	40.1996i	−0.696833	−	1.68230i	−0.730539	−	0.682871i	$-0.760731\pi$
$571$	−16.6512	−	40.1996i	−0.696833	−	1.68230i	0.0337061	−	0.999432i	$-0.489269\pi$
$572$	10.2015	−	4.22561i	0.426548	−	0.176682i
$573$		0			0
$574$		−	36.4371i		−	1.52085i
$575$	−8.16056	−	3.38021i	−0.340319	−	0.140965i
$576$		0			0
$577$	27.7097			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$577$	27.7097			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$578$	−1.88222	+	39.9380i	−0.0782900	+	1.66120i
$579$		0			0
$580$	21.8727	−	21.8727i	0.908212	−	0.908212i
$581$	24.2111	+	10.0286i	1.00445	+	0.416055i
$582$		0			0
$583$	5.40709	−	13.0539i	0.223939	−	0.540636i
$584$	−18.2107	+	7.54311i	−0.753563	+	0.312136i
$585$		0			0
$586$	−43.2181	−	43.2181i	−1.78532	−	1.78532i
$587$	−3.09653	−	3.09653i	−0.127808	−	0.127808i	0.640309	−	0.768117i	$-0.278806\pi$
$587$	−3.09653	−	3.09653i	−0.127808	−	0.127808i	−0.768117	+	0.640309i	$0.778806\pi$
$588$		0			0
$589$	−8.20624	+	3.39914i	−0.338132	+	0.140059i
$590$	4.02316	−	9.71276i	0.165631	−	0.399868i
$591$		0			0
$592$	5.98668	+	2.47976i	0.246051	+	0.101918i
$593$	−25.3698	+	25.3698i	−1.04181	+	1.04181i	−0.0427255	+	0.999087i	$0.513604\pi$
$593$	−25.3698	+	25.3698i	−1.04181	+	1.04181i	−0.999087	+	0.0427255i	$0.986396\pi$
$594$		0			0
$595$	13.7745	−	5.32919i	0.564700	−	0.218476i
$596$	−65.4673			−2.68164
$597$		0			0
$598$	24.1730	+	10.0128i	0.988509	+	0.409454i
$599$			11.1415i			0.455230i	0.973751	+	0.227615i	$0.0730928\pi$
$599$			11.1415i			0.455230i	−0.973751	+	0.227615i	$0.926907\pi$
$600$		0			0
$601$	18.8938	−	7.82606i	0.770693	−	0.319232i	0.0375402	−	0.999295i	$-0.488048\pi$
$601$	18.8938	−	7.82606i	0.770693	−	0.319232i	0.733153	+	0.680063i	$0.238048\pi$
$602$	−24.3324	−	58.7437i	−0.991716	−	2.39421i
$603$		0			0
$604$	22.2558	+	22.2558i	0.905574	+	0.905574i
$605$	1.85093	+	4.46855i	0.0752512	+	0.181672i
$606$		0			0
$607$	0.602934	−	1.45561i	0.0244723	−	0.0590814i	−0.911171	−	0.412028i	$-0.864820\pi$
$607$	0.602934	−	1.45561i	0.0244723	−	0.0590814i	0.935643	+	0.352947i	$0.114820\pi$
$608$		−	14.1435i		−	0.573593i
$609$		0			0
$610$	−0.403905	+	0.403905i	−0.0163536	+	0.0163536i
$611$	14.2727			0.577410
$612$		0			0
$613$	−22.4800			−0.907959			−0.453980	−	0.891012i	$-0.649996\pi$
$613$	−22.4800			−0.907959			−0.453980	+	0.891012i	$0.649996\pi$
$614$	−28.1845	+	28.1845i	−1.13743	+	1.13743i
$615$		0			0
$616$		−	32.0307i		−	1.29055i
$617$	−10.4081	+	25.1273i	−0.419013	+	1.01159i	0.563621	+	0.826034i	$0.309408\pi$
$617$	−10.4081	+	25.1273i	−0.419013	+	1.01159i	−0.982634	+	0.185554i	$0.940592\pi$
$618$		0			0
$619$	5.49924	+	13.2763i	0.221033	+	0.533621i	0.995031	−	0.0995671i	$-0.0317458\pi$
$619$	5.49924	+	13.2763i	0.221033	+	0.533621i	−0.773998	+	0.633188i	$0.781746\pi$
$620$	−6.10301	−	6.10301i	−0.245103	−	0.245103i
$621$		0			0
$622$	15.4720	+	37.3527i	0.620371	+	1.49771i
$623$	7.25927	−	3.00689i	0.290837	−	0.120469i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$	12.8523	+	5.32358i	0.513680	+	0.212773i
$627$		0			0
$628$	−64.4228			−2.57075
$629$	−18.9674	−	0.446705i	−0.756280	−	0.0178113i
$630$		0			0
$631$	−16.4538	+	16.4538i	−0.655014	+	0.655014i	−0.954196	−	0.299182i	$-0.903286\pi$
$631$	−16.4538	+	16.4538i	−0.655014	+	0.655014i	0.299182	+	0.954196i	$0.403286\pi$
$632$	−30.0675	−	12.4544i	−1.19602	−	0.495408i
$633$		0			0
$634$	−0.576538	+	1.39189i	−0.0228972	+	0.0552788i
$635$	5.46739	−	2.26467i	0.216967	−	0.0898706i
$636$		0			0
$637$	5.19356	+	5.19356i	0.205776	+	0.205776i
$638$	36.1638	+	36.1638i	1.43174	+	1.43174i
$639$		0			0
$640$	18.8167	−	7.79414i	0.743796	−	0.308090i
$641$	2.06038	−	4.97419i	0.0813800	−	0.196469i	−0.877952	−	0.478748i	$-0.841091\pi$
$641$	2.06038	−	4.97419i	0.0813800	−	0.196469i	0.959332	+	0.282280i	$0.0910906\pi$
$642$		0			0
$643$	14.9568	+	6.19532i	0.589839	+	0.244319i	0.657582	−	0.753383i	$-0.271580\pi$
$643$	14.9568	+	6.19532i	0.589839	+	0.244319i	−0.0677421	+	0.997703i	$0.521580\pi$
$644$	79.0101	−	79.0101i	3.11343	−	3.11343i
$645$		0			0
$646$	−12.7163	−	32.8683i	−0.500318	−	1.29319i
$647$	25.8383			1.01581			0.507904	−	0.861413i	$-0.330420\pi$
$647$	25.8383			1.01581			0.507904	+	0.861413i	$0.330420\pi$
$648$		0			0
$649$	10.2525	+	4.24672i	0.402445	+	0.166698i
$650$		−	2.96218i		−	0.116186i
$651$		0			0
$652$	−30.5548	+	12.6562i	−1.19662	+	0.495656i
$653$	4.77529	+	11.5286i	0.186872	+	0.451148i	0.989354	−	0.145528i	$-0.0464880\pi$
$653$	4.77529	+	11.5286i	0.186872	+	0.451148i	−0.802483	+	0.596675i	$0.796488\pi$
$654$		0			0
$655$	11.3991	+	11.3991i	0.445399	+	0.445399i
$656$	−2.33072	−	5.62685i	−0.0909992	−	0.219691i
$657$		0			0
$658$	36.5353	−	88.2040i	1.42429	−	3.43855i
$659$		−	41.7109i		−	1.62483i	−0.583082	−	0.812413i	$-0.698153\pi$
$659$		−	41.7109i		−	1.62483i	0.583082	−	0.812413i	$-0.301847\pi$
$660$		0			0
$661$	−12.8495	+	12.8495i	−0.499789	+	0.499789i	−0.911372	−	0.411583i	$-0.864976\pi$
$661$	−12.8495	+	12.8495i	−0.499789	+	0.499789i	0.411583	+	0.911372i	$0.364976\pi$
$662$	27.4252			1.06591
$663$		0			0
$664$	26.3499			1.02257
$665$	−9.20551	+	9.20551i	−0.356974	+	0.356974i
$666$		0			0
$667$			77.3693i			2.99575i
$668$	12.5430	−	30.2815i	0.485304	−	1.17163i
$669$		0			0
$670$	6.50975	+	15.7159i	0.251493	+	0.607159i
$671$	−0.426350	−	0.426350i	−0.0164590	−	0.0164590i
$672$		0			0
$673$	2.44794	+	5.90984i	0.0943610	+	0.227808i	0.964012	−	0.265860i	$-0.0856559\pi$
$673$	2.44794	+	5.90984i	0.0943610	+	0.227808i	−0.869651	+	0.493668i	$0.835656\pi$
$674$	−67.0997	+	27.7936i	−2.58458	+	1.07057i
$675$		0			0
$676$		−	40.3069i		−	1.55026i
$677$	38.7001	+	16.0301i	1.48737	+	0.616087i	0.970742	−	0.240125i	$-0.0771886\pi$
$677$	38.7001	+	16.0301i	1.48737	+	0.616087i	0.516624	+	0.856212i	$0.327189\pi$
$678$		0			0
$679$	−35.1779			−1.35000
$680$	10.7453	−	10.2508i	0.412064	−	0.393101i
$681$		0			0
$682$	10.0906	−	10.0906i	0.386389	−	0.386389i
$683$	−27.9994	−	11.5977i	−1.07137	−	0.443775i	−0.223895	−	0.974613i	$-0.571877\pi$
$683$	−27.9994	−	11.5977i	−1.07137	−	0.443775i	−0.847473	+	0.530838i	$0.821877\pi$
$684$		0			0
$685$	6.55613	−	15.8279i	0.250497	−	0.604753i
$686$	−9.09419	+	3.76694i	−0.347218	+	0.143822i
$687$		0			0
$688$	−7.51514	−	7.51514i	−0.286512	−	0.286512i
$689$	5.06869	+	5.06869i	0.193102	+	0.193102i
$690$		0			0
$691$	5.35185	−	2.21681i	0.203594	−	0.0843314i	−0.278556	−	0.960420i	$-0.589856\pi$
$691$	5.35185	−	2.21681i	0.203594	−	0.0843314i	0.482150	+	0.876088i	$0.339856\pi$
$692$	5.81083	−	14.0286i	0.220895	−	0.533287i
$693$		0			0
$694$	−0.0325913	−	0.0134997i	−0.00123715	−	0.000512443i
$695$	1.50831	−	1.50831i	0.0572135	−	0.0572135i
$696$		0			0
$697$	12.3090	+	12.9027i	0.466236	+	0.488726i
$698$	8.59600			0.325363
$699$		0			0
$700$	−11.6871	−	4.84097i	−0.441732	−	0.182971i
$701$			5.24783i			0.198208i	0.995077	+	0.0991039i	$0.0315976\pi$
$701$			5.24783i			0.198208i	−0.995077	+	0.0991039i	$0.968402\pi$
$702$		0			0
$703$	15.4505	−	6.39979i	0.582726	−	0.241373i
$704$	11.3713	+	27.4527i	0.428572	+	1.03466i
$705$		0			0
$706$	6.35837	+	6.35837i	0.239300	+	0.239300i
$707$	−7.49037	−	18.0833i	−0.281704	−	0.680094i
$708$		0			0
$709$	15.9798	−	38.5786i	0.600134	−	1.44885i	−0.273310	−	0.961926i	$-0.588118\pi$
$709$	15.9798	−	38.5786i	0.600134	−	1.44885i	0.873444	−	0.486925i	$-0.161882\pi$
$710$			4.32229i			0.162213i
$711$		0			0
$712$	5.58654	−	5.58654i	0.209364	−	0.209364i
$713$	21.5879			0.808475
$714$		0			0
$715$	3.12678			0.116935
$716$	0.293855	−	0.293855i	0.0109819	−	0.0109819i
$717$		0			0
$718$			15.7501i			0.587789i
$719$	−3.89643	+	9.40681i	−0.145312	+	0.350815i	−0.979731	−	0.200316i	$-0.935803\pi$
$719$	−3.89643	+	9.40681i	−0.145312	+	0.350815i	0.834419	+	0.551130i	$0.185803\pi$
$720$		0			0
$721$	9.81608	+	23.6981i	0.365570	+	0.882564i
$722$	−9.63199	−	9.63199i	−0.358465	−	0.358465i
$723$		0			0
$724$	3.14022	+	7.58117i	0.116705	+	0.281752i
$725$	8.09244	−	3.35200i	0.300546	−	0.124490i
$726$		0			0
$727$			46.0182i			1.70672i	0.521321	+	0.853361i	$0.325439\pi$
$727$			46.0182i			1.70672i	−0.521321	+	0.853361i	$0.674561\pi$
$728$	15.0130	+	6.21860i	0.556420	+	0.230477i
$729$		0			0
$730$	−12.8709			−0.476374
$731$	28.4609	+	12.5819i	1.05266	+	0.465358i
$732$		0			0
$733$	−1.80962	+	1.80962i	−0.0668398	+	0.0668398i	−0.739736	−	0.672897i	$-0.765050\pi$
$733$	−1.80962	+	1.80962i	−0.0668398	+	0.0668398i	0.672897	+	0.739736i	$0.265050\pi$
$734$	50.0360	+	20.7256i	1.84686	+	0.764996i
$735$		0			0
$736$	−13.1546	+	31.7580i	−0.484885	+	1.17062i
$737$	−16.5892	+	6.87149i	−0.611072	+	0.253114i
$738$		0			0
$739$	1.75127	+	1.75127i	0.0644215	+	0.0644215i	0.738583	−	0.674162i	$-0.235495\pi$
$739$	1.75127	+	1.75127i	0.0644215	+	0.0644215i	−0.674162	+	0.738583i	$0.735495\pi$
$740$	11.4906	+	11.4906i	0.422402	+	0.422402i
$741$		0			0
$742$	44.2989	−	18.3492i	1.62627	−	0.673621i
$743$	−0.610291	+	1.47337i	−0.0223894	+	0.0540528i	−0.934679	−	0.355493i	$-0.884313\pi$
$743$	−0.610291	+	1.47337i	−0.0223894	+	0.0540528i	0.912289	+	0.409546i	$0.134313\pi$
$744$		0			0
$745$	−17.1272	−	7.09433i	−0.627493	−	0.259916i
$746$	39.4646	−	39.4646i	1.44490	−	1.44490i
$747$		0			0
$748$	24.9515	+	26.1551i	0.912317	+	0.956326i
$749$	2.23222			0.0815636
$750$		0			0
$751$	11.7741	+	4.87697i	0.429641	+	0.177963i	0.587015	−	0.809576i	$-0.300303\pi$
$751$	11.7741	+	4.87697i	0.429641	+	0.177963i	−0.157374	+	0.987539i	$0.550303\pi$
$752$		−	15.9580i		−	0.581930i
$753$		0			0
$754$	−23.9713	+	9.92922i	−0.872982	+	0.361601i
$755$	3.41071	+	8.23418i	0.124128	+	0.299672i
$756$		0			0
$757$	−32.5674	−	32.5674i	−1.18368	−	1.18368i	−0.978783	−	0.204901i	$-0.934313\pi$
$757$	−32.5674	−	32.5674i	−1.18368	−	1.18368i	−0.204901	−	0.978783i	$-0.565687\pi$
$758$	2.68047	+	6.47123i	0.0973592	+	0.235046i
$759$		0			0
$760$	−5.00936	+	12.0937i	−0.181709	+	0.438683i
$761$			29.7003i			1.07664i	0.842742	+	0.538318i	$0.180940\pi$
$761$			29.7003i			1.07664i	−0.842742	+	0.538318i	$0.819060\pi$
$762$		0			0
$763$	−15.6777	+	15.6777i	−0.567571	+	0.567571i
$764$	−51.7788			−1.87329
$765$		0			0
$766$	−57.4385			−2.07534
$767$	−3.98093	+	3.98093i	−0.143743	+	0.143743i
$768$		0			0
$769$		−	43.8299i		−	1.58055i	−0.612755	−	0.790273i	$-0.709939\pi$
$769$		−	43.8299i		−	1.58055i	0.612755	−	0.790273i	$-0.290061\pi$
$770$	8.00397	−	19.3233i	0.288443	−	0.696363i
$771$		0			0
$772$	−11.3466	−	27.3932i	−0.408375	−	0.985904i
$773$	−19.7369	−	19.7369i	−0.709887	−	0.709887i	0.256624	−	0.966511i	$-0.417390\pi$
$773$	−19.7369	−	19.7369i	−0.709887	−	0.709887i	−0.966511	+	0.256624i	$0.917390\pi$
$774$		0			0
$775$	−0.935290	−	2.25799i	−0.0335966	−	0.0811094i
$776$	−32.6787	+	13.5359i	−1.17310	+	0.485912i
$777$		0			0
$778$			3.97159i			0.142388i
$779$	−14.5218	−	6.01513i	−0.520298	−	0.215515i
$780$		0			0
$781$	−4.56247			−0.163258
$782$	−2.01670	+	85.6304i	−0.0721170	+	3.06214i
$783$		0			0
$784$	5.80684	−	5.80684i	0.207387	−	0.207387i
$785$	−16.8540	−	6.98115i	−0.601545	−	0.249168i
$786$		0			0
$787$	11.4892	−	27.7373i	0.409544	−	0.988728i	−0.575713	−	0.817652i	$-0.695276\pi$
$787$	11.4892	−	27.7373i	0.409544	−	0.988728i	0.985258	−	0.171076i	$-0.0547244\pi$
$788$	21.7992	−	9.02954i	0.776566	−	0.321664i
$789$		0			0
$790$	−15.0268	−	15.0268i	−0.534629	−	0.534629i
$791$	−40.6781	−	40.6781i	−1.44635	−	1.44635i
$792$		0			0
$793$	0.282607	−	0.117060i	0.0100357	−	0.00415691i
$794$	28.3741	−	68.5012i	1.00696	−	2.43102i
$795$		0			0
$796$	−61.5717	−	25.5038i	−2.18235	−	0.903959i
$797$	−3.65013	+	3.65013i	−0.129294	+	0.129294i	−0.768793	−	0.639498i	$-0.779142\pi$
$797$	−3.65013	+	3.65013i	−0.129294	+	0.129294i	0.639498	+	0.768793i	$0.279142\pi$
$798$		0			0
$799$	16.8591	+	43.5761i	0.596432	+	1.54161i
$800$	3.89165			0.137591
$801$		0			0
$802$	11.0079	+	4.55963i	0.388704	+	0.161006i
$803$		−	13.5861i		−	0.479445i
$804$		0			0
$805$	29.2321	−	12.1083i	1.03030	−	0.426763i
$806$	2.77050	+	6.68857i	0.0975866	+	0.235595i
$807$		0			0
$808$	−13.9164	−	13.9164i	−0.489579	−	0.489579i
$809$	−8.50871	−	20.5418i	−0.299150	−	0.722213i	−0.999961	−	0.00886509i	$-0.997178\pi$
$809$	−8.50871	−	20.5418i	−0.299150	−	0.722213i	0.700810	−	0.713348i	$-0.252822\pi$
$810$		0			0
$811$	−5.99450	+	14.4720i	−0.210495	+	0.508181i	−0.993500	−	0.113836i	$-0.963686\pi$
$811$	−5.99450	+	14.4720i	−0.210495	+	0.508181i	0.783004	+	0.622016i	$0.213686\pi$
$812$			110.804i			3.88847i
$813$		0			0
$814$	−18.9983	+	18.9983i	−0.665889	+	0.665889i
$815$	−9.36510			−0.328045
$816$		0			0
$817$	−27.4289			−0.959615
$818$	43.4351	−	43.4351i	1.51867	−	1.51867i
$819$		0			0
$820$		−	15.2734i		−	0.533370i
$821$	−13.3707	+	32.2797i	−0.466640	+	1.12657i	0.498981	+	0.866613i	$0.333708\pi$
$821$	−13.3707	+	32.2797i	−0.466640	+	1.12657i	−0.965621	+	0.259955i	$0.916292\pi$
$822$		0			0
$823$	0.935339	+	2.25811i	0.0326039	+	0.0787127i	0.939343	−	0.342980i	$-0.111436\pi$
$823$	0.935339	+	2.25811i	0.0326039	+	0.0787127i	−0.906739	+	0.421692i	$0.861436\pi$
$824$	18.2374	+	18.2374i	0.635330	+	0.635330i
$825$		0			0
$826$	14.4114	+	34.7923i	0.501438	+	1.21058i
$827$	46.9533	−	19.4487i	1.63273	−	0.676298i	0.637194	−	0.770703i	$-0.280095\pi$
$827$	46.9533	−	19.4487i	1.63273	−	0.676298i	0.995534	+	0.0944054i	$0.0300950\pi$
$828$		0			0
$829$			41.5846i			1.44429i	0.691740	+	0.722147i	$0.256844\pi$
$829$			41.5846i			1.44429i	−0.691740	+	0.722147i	$0.743156\pi$
$830$	15.8962	+	6.58442i	0.551765	+	0.228549i
$831$		0			0
$832$	−15.0750			−0.522631
$833$	−9.72184	+	21.9913i	−0.336842	+	0.761952i
$834$		0			0
$835$	6.56289	−	6.56289i	0.227118	−	0.227118i
$836$	−29.4371	−	12.1933i	−1.01810	−	0.421713i
$837$		0			0
$838$	6.56894	−	15.8588i	0.226920	−	0.547834i
$839$	−4.10912	+	1.70205i	−0.141863	+	0.0587614i	−0.452485	−	0.891772i	$-0.649462\pi$
$839$	−4.10912	+	1.70205i	−0.141863	+	0.0587614i	0.310623	+	0.950533i	$0.399462\pi$
$840$		0			0
$841$	−33.7456	−	33.7456i	−1.16364	−	1.16364i
$842$	35.0311	+	35.0311i	1.20725	+	1.20725i
$843$		0			0
$844$	21.5977	−	8.94607i	0.743424	−	0.307936i
$845$	4.36784	−	10.5449i	0.150258	−	0.362755i
$846$		0			0
$847$	−16.0069	−	6.63027i	−0.550004	−	0.227819i
$848$	5.66721	−	5.66721i	0.194613	−	0.194613i
$849$		0			0
$850$	9.04388	−	3.49897i	0.310202	−	0.120014i
$851$	−40.6451			−1.39330
$852$		0			0
$853$	16.5251	+	6.84491i	0.565808	+	0.234365i	0.647204	−	0.762317i	$-0.275938\pi$
$853$	16.5251	+	6.84491i	0.565808	+	0.234365i	−0.0813967	+	0.996682i	$0.525938\pi$
$854$		−	2.04614i		−	0.0700174i
$855$		0			0
$856$	2.07363	−	0.858928i	0.0708754	−	0.0293575i
$857$	−14.7557	−	35.6234i	−0.504045	−	1.21687i	−0.947263	−	0.320458i	$-0.896163\pi$
$857$	−14.7557	−	35.6234i	−0.504045	−	1.21687i	0.443218	−	0.896414i	$-0.353837\pi$
$858$		0			0
$859$	2.48184	+	2.48184i	0.0846792	+	0.0846792i	0.748178	−	0.663498i	$-0.230929\pi$
$859$	2.48184	+	2.48184i	0.0846792	+	0.0846792i	−0.663498	+	0.748178i	$0.730929\pi$
$860$	−10.1995	−	24.6237i	−0.347799	−	0.839662i
$861$		0			0
$862$	−18.9396	+	45.7243i	−0.645086	+	1.55738i
$863$			21.9552i			0.747365i	0.927557	+	0.373683i	$0.121905\pi$
$863$			21.9552i			0.747365i	−0.927557	+	0.373683i	$0.878095\pi$
$864$		0			0
$865$	3.04040	−	3.04040i	0.103377	−	0.103377i
$866$	87.3171			2.96715
$867$		0			0
$868$	30.9171			1.04940
$869$	15.8618	−	15.8618i	0.538075	−	0.538075i
$870$		0			0
$871$		−	9.10956i		−	0.308666i
$872$	−8.53133	+	20.5964i	−0.288907	+	0.697484i
$873$		0			0
$874$	−28.8925	−	69.7528i	−0.977305	−	2.35942i
$875$	−2.53294	−	2.53294i	−0.0856291	−	0.0856291i
$876$		0			0
$877$	2.16444	+	5.22542i	0.0730879	+	0.176450i	0.956201	−	0.292710i	$-0.0945569\pi$
$877$	2.16444	+	5.22542i	0.0730879	+	0.176450i	−0.883113	+	0.469159i	$0.844557\pi$
$878$	−1.02413	+	0.424209i	−0.0345628	+	0.0143164i
$879$		0			0
$880$		−	3.49601i		−	0.117850i
$881$	−31.7736	−	13.1611i	−1.07048	−	0.443407i	−0.223320	−	0.974745i	$-0.571689\pi$
$881$	−31.7736	−	13.1611i	−1.07048	−	0.443407i	−0.847160	+	0.531338i	$0.821689\pi$
$882$		0			0
$883$	−58.3115			−1.96234			−0.981170	−	0.193148i	$-0.938130\pi$
$883$	−58.3115			−1.96234			−0.981170	+	0.193148i	$0.938130\pi$
$884$	−17.1033	+	6.61706i	−0.575246	+	0.222556i
$885$		0			0
$886$	−18.3349	+	18.3349i	−0.615973	+	0.615973i
$887$	−41.1137	−	17.0299i	−1.38046	−	0.571807i	−0.435859	−	0.900015i	$-0.643555\pi$
$887$	−41.1137	−	17.0299i	−1.38046	−	0.571807i	−0.944605	+	0.328208i	$0.893555\pi$
$888$		0			0
$889$	−8.11232	+	19.5849i	−0.272078	+	0.656855i
$890$	4.76620	−	1.97422i	0.159763	−	0.0661761i
$891$		0			0
$892$	−7.34813	−	7.34813i	−0.246034	−	0.246034i
$893$	−29.1220	−	29.1220i	−0.974529	−	0.974529i
$894$		0			0
$895$	0.108720	−	0.0450334i	0.00363412	−	0.00150530i
$896$	−27.9196	+	67.4038i	−0.932727	+	2.25180i
$897$		0			0
$898$	37.5109	+	15.5375i	1.25175	+	0.518494i
$899$	−15.1376	+	15.1376i	−0.504866	+	0.504866i
$900$		0			0
$901$	−9.48808	+	21.4625i	−0.316094	+	0.715019i
$902$	25.2527			0.840824
$903$		0			0
$904$	−53.4405	−	22.1358i	−1.77740	−	0.736225i
$905$			2.32364i			0.0772404i
$906$		0			0
$907$	−32.6800	+	13.5365i	−1.08512	+	0.449472i	−0.852303	−	0.523048i	$-0.824795\pi$
$907$	−32.6800	+	13.5365i	−1.08512	+	0.449472i	−0.232819	+	0.972520i	$0.574795\pi$
$908$	−29.0903	−	70.2301i	−0.965394	−	2.33067i
$909$		0			0
$910$	7.50303	+	7.50303i	0.248723	+	0.248723i
$911$	18.8207	+	45.4373i	0.623559	+	1.50540i	0.847496	+	0.530801i	$0.178109\pi$
$911$	18.8207	+	45.4373i	0.623559	+	1.50540i	−0.223937	+	0.974604i	$0.571891\pi$
$912$		0			0
$913$	−6.95031	+	16.7795i	−0.230022	+	0.555322i
$914$		−	26.5004i		−	0.876554i
$915$		0			0
$916$	29.8176	−	29.8176i	0.985202	−	0.985202i
$917$	−57.7465			−1.90696
$918$		0			0
$919$	49.6635			1.63825			0.819123	−	0.573618i	$-0.194460\pi$
$919$	49.6635			1.63825			0.819123	+	0.573618i	$0.194460\pi$
$920$	22.4962	−	22.4962i	0.741679	−	0.741679i
$921$		0			0
$922$		−	70.5747i		−	2.32425i
$923$	0.885781	−	2.13846i	0.0291558	−	0.0703884i
$924$		0			0
$925$	1.76094	+	4.25128i	0.0578993	+	0.139781i
$926$	−28.5366	−	28.5366i	−0.937770	−	0.937770i
$927$		0			0
$928$	−13.0448	−	31.4929i	−0.428216	−	1.03381i
$929$	31.5196	−	13.0558i	1.03412	−	0.428348i	0.199924	−	0.979811i	$-0.435930\pi$
$929$	31.5196	−	13.0558i	1.03412	−	0.428348i	0.834199	+	0.551463i	$0.185930\pi$
$930$		0			0
$931$		−	21.1939i		−	0.694601i
$932$	−32.8505	−	13.6071i	−1.07605	−	0.445716i
$933$		0			0
$934$	62.5405			2.04639
$935$	3.69340	+	9.54644i	0.120787	+	0.312202i
$936$		0			0
$937$	−27.2430	+	27.2430i	−0.889991	+	0.889991i	−0.994522	−	0.104530i	$-0.966666\pi$
$937$	−27.2430	+	27.2430i	−0.889991	+	0.889991i	0.104530	+	0.994522i	$0.466666\pi$
$938$	−56.2964	−	23.3187i	−1.83814	−	0.761383i
$939$		0			0
$940$	15.3146	−	36.9727i	0.499507	−	1.20592i
$941$	−34.3095	+	14.2115i	−1.11846	+	0.463280i	−0.863842	−	0.503762i	$-0.831949\pi$
$941$	−34.3095	+	14.2115i	−1.11846	+	0.463280i	−0.254615	+	0.967043i	$0.581949\pi$
$942$		0			0
$943$	27.0130	+	27.0130i	0.879665	+	0.879665i
$944$	4.45102	+	4.45102i	0.144868	+	0.144868i
$945$		0			0
$946$	40.7124	−	16.8636i	1.32367	−	0.548283i
$947$	0.853817	−	2.06130i	0.0277453	−	0.0669832i	−0.909400	−	0.415923i	$-0.863458\pi$
$947$	0.853817	−	2.06130i	0.0277453	−	0.0669832i	0.937145	+	0.348940i	$0.113458\pi$
$948$		0			0
$949$	6.36792	+	2.63768i	0.206712	+	0.0856227i
$950$	−6.04403	+	6.04403i	−0.196094	+	0.196094i
$951$		0			0
$952$	−1.25250	+	53.1820i	−0.0405938	+	1.72364i
$953$	−25.8280			−0.836651			−0.418326	−	0.908297i	$-0.637383\pi$
$953$	−25.8280			−0.836651			−0.418326	+	0.908297i	$0.637383\pi$
$954$		0			0
$955$	−13.5461	−	5.61099i	−0.438342	−	0.181567i
$956$		−	58.7114i		−	1.89886i
$957$		0			0
$958$	−49.7808	+	20.6199i	−1.60834	+	0.666198i
$959$	23.4849	+	56.6975i	0.758366	+	1.83086i
$960$		0			0
$961$	−17.6966	−	17.6966i	−0.570857	−	0.570857i
$962$	−5.21621	−	12.5930i	−0.168177	−	0.406016i
$963$		0			0
$964$	8.00314	−	19.3213i	0.257764	−	0.622297i
$965$		−	8.39606i		−	0.270279i
$966$		0			0
$967$	22.2041	−	22.2041i	0.714035	−	0.714035i	−0.253341	−	0.967377i	$-0.581530\pi$
$967$	22.2041	−	22.2041i	0.714035	−	0.714035i	0.967377	+	0.253341i	$0.0815296\pi$
$968$	−17.4209			−0.559930
$969$		0			0
$970$	−23.0966			−0.741587
$971$	−29.0808	+	29.0808i	−0.933248	+	0.933248i	−0.997907	−	0.0646590i	$-0.979404\pi$
$971$	−29.0808	+	29.0808i	−0.933248	+	0.933248i	0.0646590	+	0.997907i	$0.479404\pi$
$972$		0			0
$973$			7.64093i			0.244957i
$974$	−14.1427	+	34.1435i	−0.453161	+	1.09403i
$975$		0			0
$976$	−0.130882	−	0.315978i	−0.00418944	−	0.0101142i
$977$	19.7205	+	19.7205i	0.630916	+	0.630916i	0.948298	−	0.317382i	$-0.102804\pi$
$977$	19.7205	+	19.7205i	0.630916	+	0.630916i	−0.317382	+	0.948298i	$0.602804\pi$
$978$		0			0
$979$	2.08393	+	5.03105i	0.0666026	+	0.160793i
$980$	19.0264	−	7.88098i	0.607775	−	0.251749i
$981$		0			0
$982$		−	2.02071i		−	0.0644836i
$983$	52.3778	+	21.6956i	1.67059	+	0.691982i	0.998810	−	0.0487673i	$-0.0155293\pi$
$983$	52.3778	+	21.6956i	1.67059	+	0.691982i	0.671782	+	0.740749i	$0.265529\pi$
$984$		0			0
$985$	6.68150			0.212890
$986$	−58.6303	−	61.4585i	−1.86717	−	1.95724i
$987$		0			0
$988$	11.4301	−	11.4301i	0.363641	−	0.363641i
$989$	61.5894	+	25.5112i	1.95843	+	0.811208i
$990$		0			0
$991$	−13.7333	+	33.1551i	−0.436252	+	1.05321i	0.540980	+	0.841035i	$0.318053\pi$
$991$	−13.7333	+	33.1551i	−0.436252	+	1.05321i	−0.977233	+	0.212171i	$0.931947\pi$
$992$	−8.78730	+	3.63982i	−0.278997	+	0.115564i
$993$		0			0
$994$	−10.9481	−	10.9481i	−0.347253	−	0.347253i
$995$	−13.3444	−	13.3444i	−0.423045	−	0.423045i
$996$		0			0
$997$	30.4465	−	12.6113i	0.964249	−	0.399405i	0.155681	−	0.987807i	$-0.450243\pi$
$997$	30.4465	−	12.6113i	0.964249	−	0.399405i	0.808568	+	0.588402i	$0.200243\pi$
$998$	20.3764	−	49.1930i	0.645004	−	1.55718i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.451.1		24
3.2	odd	2		85.2.l.a.26.6	✓	24
15.2	even	4		425.2.n.f.349.6		24
15.8	even	4		425.2.n.c.349.1		24
15.14	odd	2		425.2.m.b.26.1		24
17.2	even	8	inner	765.2.be.b.631.1		24
51.2	odd	8		85.2.l.a.36.6	yes	24
51.11	even	16		1445.2.a.q.1.12		12
51.23	even	16		1445.2.a.p.1.12		12
51.41	even	16		1445.2.d.j.866.1		24
51.44	even	16		1445.2.d.j.866.2		24
255.2	even	8		425.2.n.c.274.1		24
255.53	even	8		425.2.n.f.274.6		24
255.74	even	16		7225.2.a.bs.1.1		12
255.104	odd	8		425.2.m.b.376.1		24
255.164	even	16		7225.2.a.bq.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.6	✓	24	3.2	odd	2
85.2.l.a.36.6	yes	24	51.2	odd	8
425.2.m.b.26.1		24	15.14	odd	2
425.2.m.b.376.1		24	255.104	odd	8
425.2.n.c.274.1		24	255.2	even	8
425.2.n.c.349.1		24	15.8	even	4
425.2.n.f.274.6		24	255.53	even	8
425.2.n.f.349.6		24	15.2	even	4
765.2.be.b.451.1		24	1.1	even	1	trivial
765.2.be.b.631.1		24	17.2	even	8	inner
1445.2.a.p.1.12		12	51.23	even	16
1445.2.a.q.1.12		12	51.11	even	16
1445.2.d.j.866.1		24	51.41	even	16
1445.2.d.j.866.2		24	51.44	even	16
7225.2.a.bq.1.1		12	255.164	even	16
7225.2.a.bs.1.1		12	255.74	even	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66305 + 1.66305i) q^{2} -3.53144i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.37082 + 3.30945i) q^{7} +(2.54686 + 2.54686i) q^{8} +O(q^{10})\)	\(q+(-1.66305 + 1.66305i) q^{2} -3.53144i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.37082 + 3.30945i) q^{7} +(2.54686 + 2.54686i) q^{8} +(0.900034 + 2.17287i) q^{10} +(-2.29362 + 0.950048i) q^{11} -1.25948i q^{13} +(-7.78350 - 3.22403i) q^{14} -1.40821 q^{16} +(3.84535 - 1.48772i) q^{17} +(-2.56985 + 2.56985i) q^{19} +(-3.26263 - 1.35142i) q^{20} +(2.23442 - 5.39437i) q^{22} +(8.16056 - 3.38021i) q^{23} +(-0.707107 - 0.707107i) q^{25} +(2.09458 + 2.09458i) q^{26} +(11.6871 - 4.84097i) q^{28} +(-3.35200 + 8.09244i) q^{29} +(2.25799 + 0.935290i) q^{31} +(-2.75181 + 2.75181i) q^{32} +(-3.92084 + 8.86913i) q^{34} +3.58212 q^{35} +(-4.25128 - 1.76094i) q^{37} -8.54755i q^{38} +(3.32763 - 1.37835i) q^{40} +(1.65510 + 3.99575i) q^{41} +(5.33668 + 5.33668i) q^{43} +(3.35504 + 8.09978i) q^{44} +(-7.94993 + 19.1928i) q^{46} +11.3322i q^{47} +(-4.12357 + 4.12357i) q^{49} +2.35190 q^{50} -4.44779 q^{52} +(-4.02442 + 4.02442i) q^{53} +2.48259i q^{55} +(-4.93742 + 11.9200i) q^{56} +(-7.88357 - 19.0326i) q^{58} +(-3.16077 - 3.16077i) q^{59} +(0.0929426 + 0.224383i) q^{61} +(-5.31057 + 2.19971i) q^{62} -11.9692i q^{64} +(-1.16361 - 0.481983i) q^{65} +7.23278 q^{67} +(-5.25380 - 13.5796i) q^{68} +(-5.95724 + 5.95724i) q^{70} +(1.69789 + 0.703290i) q^{71} +(-2.09426 + 5.05599i) q^{73} +(9.99859 - 4.14155i) q^{74} +(9.07527 + 9.07527i) q^{76} +(-6.28827 - 6.28827i) q^{77} +(-8.34789 + 3.45781i) q^{79} +(-0.538897 + 1.30101i) q^{80} +(-9.39762 - 3.89262i) q^{82} +(5.17302 - 5.17302i) q^{83} +(0.0970771 - 4.12196i) q^{85} -17.7503 q^{86} +(-8.26117 - 3.42189i) q^{88} -2.19350i q^{89} +(4.16819 - 1.72652i) q^{91} +(-11.9370 - 28.8186i) q^{92} +(-18.8459 - 18.8459i) q^{94} +(1.39079 + 3.35767i) q^{95} +(-3.75810 + 9.07286i) q^{97} -13.7154i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

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