LMFDB - Embedded newform 945.2.be.b.206.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(206,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("945.206");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.be (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			206.3
Character	$\chi$	$=$	945.206
Dual form			945.2.be.b.656.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87276 - 1.08124i) q^{2} +(1.33817 + 2.31777i) q^{4} -1.00000 q^{5} +(-1.75124 - 1.98322i) q^{7} -1.46255i q^{8} +O(q^{10})$	\(q+(-1.87276 - 1.08124i) q^{2} +(1.33817 + 2.31777i) q^{4} -1.00000 q^{5} +(-1.75124 - 1.98322i) q^{7} -1.46255i q^{8} +(1.87276 + 1.08124i) q^{10} -1.72665i q^{11} +(-2.89037 - 1.66875i) q^{13} +(1.13533 + 5.60762i) q^{14} +(1.09496 - 1.89652i) q^{16} +(-2.47597 + 4.28850i) q^{17} +(2.88684 - 1.66672i) q^{19} +(-1.33817 - 2.31777i) q^{20} +(-1.86692 + 3.23361i) q^{22} -2.67531i q^{23} +1.00000 q^{25} +(3.60865 + 6.25037i) q^{26} +(2.25319 - 6.71285i) q^{28} +(4.72502 - 2.72799i) q^{29} +(-6.73911 + 3.89083i) q^{31} +(-6.63441 + 3.83038i) q^{32} +(9.27381 - 5.35423i) q^{34} +(1.75124 + 1.98322i) q^{35} +(-1.70041 - 2.94520i) q^{37} -7.20850 q^{38} +1.46255i q^{40} +(0.394491 - 0.683278i) q^{41} +(5.82305 + 10.0858i) q^{43} +(4.00198 - 2.31054i) q^{44} +(-2.89265 + 5.01022i) q^{46} +(-5.76865 + 9.99159i) q^{47} +(-0.866300 + 6.94619i) q^{49} +(-1.87276 - 1.08124i) q^{50} -8.93228i q^{52} +(-5.69516 - 3.28810i) q^{53} +1.72665i q^{55} +(-2.90056 + 2.56129i) q^{56} -11.7985 q^{58} +(5.45596 + 9.45000i) q^{59} +(-5.58942 - 3.22705i) q^{61} +16.8277 q^{62} +12.1864 q^{64} +(2.89037 + 1.66875i) q^{65} +(1.06208 + 1.83958i) q^{67} -13.2530 q^{68} +(-1.13533 - 5.60762i) q^{70} +1.34885i q^{71} +(2.68498 + 1.55018i) q^{73} +7.35423i q^{74} +(7.72615 + 4.46069i) q^{76} +(-3.42432 + 3.02378i) q^{77} +(-6.80923 + 11.7939i) q^{79} +(-1.09496 + 1.89652i) q^{80} +(-1.47758 + 0.853079i) q^{82} +(-4.95763 - 8.58686i) q^{83} +(2.47597 - 4.28850i) q^{85} -25.1845i q^{86} -2.52532 q^{88} +(5.36098 + 9.28549i) q^{89} +(1.75223 + 8.65462i) q^{91} +(6.20075 - 3.58001i) q^{92} +(21.6066 - 12.4746i) q^{94} +(-2.88684 + 1.66672i) q^{95} +(2.88709 - 1.66686i) q^{97} +(9.13288 - 12.0719i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 15 q^{4} - 30 q^{5} + 6 q^{7}+O(q^{10}) $ 30 * q - 3 * q^2 + 15 * q^4 - 30 * q^5 + 6 * q^7	$ 30 q - 3 q^{2} + 15 q^{4} - 30 q^{5} + 6 q^{7} + 3 q^{10} + 12 q^{13} + 9 q^{14} - 21 q^{16} - 3 q^{17} - 15 q^{20} + 15 q^{22} + 30 q^{25} + 24 q^{26} + 27 q^{28} + 6 q^{31} - 9 q^{32} - 48 q^{34} - 6 q^{35} - 3 q^{37} + 60 q^{38} - 18 q^{41} + 12 q^{43} + 15 q^{44} + 9 q^{46} + 30 q^{47} - 24 q^{49} - 3 q^{50} - 30 q^{53} - 72 q^{56} - 15 q^{59} - 30 q^{61} + 12 q^{62} - 138 q^{64} - 12 q^{65} - 6 q^{67} + 42 q^{68} - 9 q^{70} + 6 q^{73} + 54 q^{76} + 21 q^{77} - 12 q^{79} + 21 q^{80} + 6 q^{82} - 6 q^{83} + 3 q^{85} + 96 q^{88} - 3 q^{89} + 15 q^{91} + 3 q^{92} + 3 q^{94} - 36 q^{97} + 24 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 15 * q^4 - 30 * q^5 + 6 * q^7 + 3 * q^10 + 12 * q^13 + 9 * q^14 - 21 * q^16 - 3 * q^17 - 15 * q^20 + 15 * q^22 + 30 * q^25 + 24 * q^26 + 27 * q^28 + 6 * q^31 - 9 * q^32 - 48 * q^34 - 6 * q^35 - 3 * q^37 + 60 * q^38 - 18 * q^41 + 12 * q^43 + 15 * q^44 + 9 * q^46 + 30 * q^47 - 24 * q^49 - 3 * q^50 - 30 * q^53 - 72 * q^56 - 15 * q^59 - 30 * q^61 + 12 * q^62 - 138 * q^64 - 12 * q^65 - 6 * q^67 + 42 * q^68 - 9 * q^70 + 6 * q^73 + 54 * q^76 + 21 * q^77 - 12 * q^79 + 21 * q^80 + 6 * q^82 - 6 * q^83 + 3 * q^85 + 96 * q^88 - 3 * q^89 + 15 * q^91 + 3 * q^92 + 3 * q^94 - 36 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.87276	−	1.08124i	−1.32424	−	0.764553i	−0.339842	−	0.940483i	$-0.610374\pi$
$2$	−1.87276	−	1.08124i	−1.32424	−	0.764553i	−0.984403	+	0.175929i	$0.943707\pi$
$3$		0			0
$3$		0			0
$4$	1.33817	+	2.31777i	0.669083	+	1.15889i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.75124	−	1.98322i	−0.661907	−	0.749586i
$7$	−1.75124	−	1.98322i	−0.661907	−	0.749586i
$8$		−	1.46255i		−	0.517091i
$9$		0			0
$10$	1.87276	+	1.08124i	0.592220	+	0.341919i
$11$		−	1.72665i		−	0.520604i	−0.965527	−	0.260302i	$-0.916178\pi$
$11$		−	1.72665i		−	0.520604i	0.965527	−	0.260302i	$-0.0838222\pi$
$12$		0			0
$13$	−2.89037	−	1.66875i	−0.801643	−	0.462829i	0.0424021	−	0.999101i	$-0.486499\pi$
$13$	−2.89037	−	1.66875i	−0.801643	−	0.462829i	−0.844045	+	0.536272i	$0.819832\pi$
$14$	1.13533	+	5.60762i	0.303429	+	1.49870i
$15$		0			0
$16$	1.09496	−	1.89652i	0.273739	−	0.474130i
$17$	−2.47597	+	4.28850i	−0.600510	+	1.04011i	0.392234	+	0.919866i	$0.371702\pi$
$17$	−2.47597	+	4.28850i	−0.600510	+	1.04011i	−0.992744	+	0.120248i	$0.961631\pi$
$18$		0			0
$19$	2.88684	−	1.66672i	0.662287	−	0.382372i	−0.130861	−	0.991401i	$-0.541774\pi$
$19$	2.88684	−	1.66672i	0.662287	−	0.382372i	0.793148	+	0.609029i	$0.208441\pi$
$20$	−1.33817	−	2.31777i	−0.299223	−	0.518269i
$21$		0			0
$22$	−1.86692	+	3.23361i	−0.398030	+	0.689408i
$23$		−	2.67531i		−	0.557840i	−0.960314	−	0.278920i	$-0.910024\pi$
$23$		−	2.67531i		−	0.557840i	0.960314	−	0.278920i	$-0.0899765\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	3.60865	+	6.25037i	0.707715	+	1.22580i
$27$		0			0
$28$	2.25319	−	6.71285i	0.425813	−	1.26861i
$29$	4.72502	−	2.72799i	0.877414	−	0.506575i	0.00760893	−	0.999971i	$-0.497578\pi$
$29$	4.72502	−	2.72799i	0.877414	−	0.506575i	0.869805	+	0.493396i	$0.164245\pi$
$30$		0			0
$31$	−6.73911	+	3.89083i	−1.21038	+	0.698813i	−0.962842	−	0.270065i	$-0.912955\pi$
$31$	−6.73911	+	3.89083i	−1.21038	+	0.698813i	−0.247538	+	0.968878i	$0.579622\pi$
$32$	−6.63441	+	3.83038i	−1.17281	+	0.677122i
$33$		0			0
$34$	9.27381	−	5.35423i	1.59044	−	0.918244i
$35$	1.75124	+	1.98322i	0.296014	+	0.335225i
$36$		0			0
$37$	−1.70041	−	2.94520i	−0.279546	−	0.484189i	0.691726	−	0.722160i	$-0.256851\pi$
$37$	−1.70041	−	2.94520i	−0.279546	−	0.484189i	−0.971272	+	0.237972i	$0.923517\pi$
$38$	−7.20850			−1.16937
$39$		0			0
$40$			1.46255i			0.231250i
$41$	0.394491	−	0.683278i	0.0616091	−	0.106710i	−0.833576	−	0.552405i	$-0.813710\pi$
$41$	0.394491	−	0.683278i	0.0616091	−	0.106710i	0.895185	+	0.445695i	$0.147043\pi$
$42$		0			0
$43$	5.82305	+	10.0858i	0.888006	+	1.53807i	0.842229	+	0.539120i	$0.181243\pi$
$43$	5.82305	+	10.0858i	0.888006	+	1.53807i	0.0457776	+	0.998952i	$0.485423\pi$
$44$	4.00198	−	2.31054i	0.603321	−	0.348327i
$45$		0			0
$46$	−2.89265	+	5.01022i	−0.426498	+	0.738717i
$47$	−5.76865	+	9.99159i	−0.841444	+	1.45742i	0.0472307	+	0.998884i	$0.484960\pi$
$47$	−5.76865	+	9.99159i	−0.841444	+	1.45742i	−0.888674	+	0.458539i	$0.848373\pi$
$48$		0			0
$49$	−0.866300	+	6.94619i	−0.123757	+	0.992313i
$50$	−1.87276	−	1.08124i	−0.264849	−	0.152911i
$51$		0			0
$52$		−	8.93228i		−	1.23868i
$53$	−5.69516	−	3.28810i	−0.782290	−	0.451656i	0.0549510	−	0.998489i	$-0.482500\pi$
$53$	−5.69516	−	3.28810i	−0.782290	−	0.451656i	−0.837241	+	0.546833i	$0.815833\pi$
$54$		0			0
$55$			1.72665i			0.232821i
$56$	−2.90056	+	2.56129i	−0.387604	+	0.342267i
$57$		0			0
$58$	−11.7985			−1.54921
$59$	5.45596	+	9.45000i	0.710306	+	1.23029i	0.964742	+	0.263196i	$0.0847767\pi$
$59$	5.45596	+	9.45000i	0.710306	+	1.23029i	−0.254437	+	0.967089i	$0.581890\pi$
$60$		0			0
$61$	−5.58942	−	3.22705i	−0.715651	−	0.413182i	0.0974987	−	0.995236i	$-0.468916\pi$
$61$	−5.58942	−	3.22705i	−0.715651	−	0.413182i	−0.813150	+	0.582054i	$0.802249\pi$
$62$	16.8277			2.13712
$63$		0			0
$64$	12.1864			1.52330
$65$	2.89037	+	1.66875i	0.358506	+	0.206983i
$66$		0			0
$67$	1.06208	+	1.83958i	0.129754	+	0.224741i	0.923581	−	0.383403i	$-0.125248\pi$
$67$	1.06208	+	1.83958i	0.129754	+	0.224741i	−0.793827	+	0.608143i	$0.791915\pi$
$68$	−13.2530			−1.60716
$69$		0			0
$70$	−1.13533	−	5.60762i	−0.135698	−	0.670238i
$71$			1.34885i			0.160079i	0.996792	+	0.0800395i	$0.0255047\pi$
$71$			1.34885i			0.160079i	−0.996792	+	0.0800395i	$0.974495\pi$
$72$		0			0
$73$	2.68498	+	1.55018i	0.314254	+	0.181434i	0.648828	−	0.760935i	$-0.275259\pi$
$73$	2.68498	+	1.55018i	0.314254	+	0.181434i	−0.334575	+	0.942369i	$0.608593\pi$
$74$			7.35423i			0.854912i
$75$		0			0
$76$	7.72615	+	4.46069i	0.886250	+	0.511677i
$77$	−3.42432	+	3.02378i	−0.390238	+	0.344592i
$78$		0			0
$79$	−6.80923	+	11.7939i	−0.766098	+	1.32692i	0.173566	+	0.984822i	$0.444471\pi$
$79$	−6.80923	+	11.7939i	−0.766098	+	1.32692i	−0.939664	+	0.342098i	$0.888862\pi$
$80$	−1.09496	+	1.89652i	−0.122420	+	0.212037i
$81$		0			0
$82$	−1.47758	+	0.853079i	−0.163171	+	0.0942069i
$83$	−4.95763	−	8.58686i	−0.544170	−	0.942531i	−0.998659	−	0.0517780i	$-0.983511\pi$
$83$	−4.95763	−	8.58686i	−0.544170	−	0.942531i	0.454488	−	0.890753i	$-0.349822\pi$
$84$		0			0
$85$	2.47597	−	4.28850i	0.268556	−	0.465153i
$86$		−	25.1845i		−	2.71571i
$87$		0			0
$88$	−2.52532			−0.269200
$89$	5.36098	+	9.28549i	0.568263	+	0.984260i	0.996738	+	0.0807066i	$0.0257177\pi$
$89$	5.36098	+	9.28549i	0.568263	+	0.984260i	−0.428475	+	0.903554i	$0.640949\pi$
$90$		0			0
$91$	1.75223	+	8.65462i	0.183684	+	0.907250i
$92$	6.20075	−	3.58001i	0.646473	−	0.373241i
$93$		0			0
$94$	21.6066	−	12.4746i	2.22855	−	1.28666i
$95$	−2.88684	+	1.66672i	−0.296184	+	0.171002i
$96$		0			0
$97$	2.88709	−	1.66686i	0.293139	−	0.169244i	−0.346217	−	0.938154i	$-0.612534\pi$
$97$	2.88709	−	1.66686i	0.293139	−	0.169244i	0.639357	+	0.768910i	$0.279201\pi$
$98$	9.13288	−	12.0719i	0.922560	−	1.21945i
$99$		0			0
$100$	1.33817	+	2.31777i	0.133817	+	0.231777i
$101$	10.8489			1.07950			0.539751	−	0.841825i	$-0.318519\pi$
$101$	10.8489			1.07950			0.539751	+	0.841825i	$0.318519\pi$
$102$		0			0
$103$			11.6206i			1.14501i	0.819901	+	0.572505i	$0.194028\pi$
$103$			11.6206i			1.14501i	−0.819901	+	0.572505i	$0.805972\pi$
$104$	−2.44064	+	4.22732i	−0.239325	+	0.414523i
$105$		0			0
$106$	7.11046	+	12.3157i	0.690629	+	1.19621i
$107$	3.90865	−	2.25666i	0.377863	−	0.218159i	−0.299025	−	0.954245i	$-0.596661\pi$
$107$	3.90865	−	2.25666i	0.377863	−	0.218159i	0.676888	+	0.736086i	$0.263328\pi$
$108$		0			0
$109$	−3.20833	+	5.55699i	−0.307302	+	0.532263i	−0.977771	−	0.209674i	$-0.932760\pi$
$109$	−3.20833	+	5.55699i	−0.307302	+	0.532263i	0.670469	+	0.741938i	$0.266093\pi$
$110$	1.86692	−	3.23361i	0.178004	−	0.308312i
$111$		0			0
$112$	−5.67875	+	1.14973i	−0.536591	+	0.108639i
$113$	9.22896	+	5.32834i	0.868188	+	0.501248i	0.866746	−	0.498751i	$-0.166208\pi$
$113$	9.22896	+	5.32834i	0.868188	+	0.501248i	0.00144211	+	0.999999i	$0.499541\pi$
$114$		0			0
$115$			2.67531i			0.249474i
$116$	12.6457	+	7.30101i	1.17412	+	0.677881i
$117$		0			0
$118$		−	23.5968i		−	2.17227i
$119$	12.8410	−	2.59982i	1.17714	−	0.238325i
$120$		0			0
$121$	8.01868			0.728971
$122$	6.97844	+	12.0870i	0.631798	+	1.09431i
$123$		0			0
$124$	−18.0361	−	10.4131i	−1.61969	−	0.935128i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.18737			0.815247			0.407623	−	0.913150i	$-0.366358\pi$
$127$	9.18737			0.815247			0.407623	+	0.913150i	$0.366358\pi$
$128$	−9.55350	−	5.51572i	−0.844418	−	0.487525i
$129$		0			0
$130$	−3.60865	−	6.25037i	−0.316500	−	0.548193i
$131$	−8.96780			−0.783521			−0.391760	−	0.920067i	$-0.628134\pi$
$131$	−8.96780			−0.783521			−0.391760	+	0.920067i	$0.628134\pi$
$132$		0			0
$133$	−8.36103	−	2.80641i	−0.724993	−	0.243346i
$134$		−	4.59347i		−	0.396816i
$135$		0			0
$136$	6.27217	+	3.62124i	0.537834	+	0.310518i
$137$			4.53858i			0.387757i	0.981026	+	0.193878i	$0.0621067\pi$
$137$			4.53858i			0.387757i	−0.981026	+	0.193878i	$0.937893\pi$
$138$		0			0
$139$	17.8922	+	10.3300i	1.51759	+	0.876182i	0.999786	+	0.0206846i	$0.00658457\pi$
$139$	17.8922	+	10.3300i	1.51759	+	0.876182i	0.517806	+	0.855498i	$0.326749\pi$
$140$	−2.25319	+	6.71285i	−0.190429	+	0.567340i
$141$		0			0
$142$	1.45843	−	2.52608i	0.122389	−	0.211984i
$143$	−2.88135	+	4.99065i	−0.240951	+	0.417339i
$144$		0			0
$145$	−4.72502	+	2.72799i	−0.392391	+	0.226547i
$146$	−3.35223	−	5.80623i	−0.277432	−	0.480527i
$147$		0			0
$148$	4.55087	−	7.88234i	0.374079	−	0.647925i
$149$			13.5187i			1.10749i	0.832685	+	0.553747i	$0.186802\pi$
$149$			13.5187i			1.10749i	−0.832685	+	0.553747i	$0.813198\pi$
$150$		0			0
$151$	−19.7465			−1.60695			−0.803475	−	0.595339i	$-0.797018\pi$
$151$	−19.7465			−1.60695			−0.803475	+	0.595339i	$0.797018\pi$
$152$	−2.43767	−	4.22217i	−0.197721	−	0.342463i
$153$		0			0
$154$	9.68238	−	1.96032i	0.780229	−	0.157967i
$155$	6.73911	−	3.89083i	0.541299	−	0.312519i
$156$		0			0
$157$	−4.92641	+	2.84427i	−0.393171	+	0.226997i	−0.683533	−	0.729920i	$-0.739557\pi$
$157$	−4.92641	+	2.84427i	−0.393171	+	0.226997i	0.290362	+	0.956917i	$0.406224\pi$
$158$	25.5042	−	14.7248i	2.02900	−	1.17145i
$159$		0			0
$160$	6.63441	−	3.83038i	0.524496	−	0.302818i
$161$	−5.30572	+	4.68511i	−0.418149	+	0.369239i
$162$		0			0
$163$	−7.27331	−	12.5977i	−0.569689	−	0.986731i	−0.996596	−	0.0824356i	$-0.973730\pi$
$163$	−7.27331	−	12.5977i	−0.569689	−	0.986731i	0.426907	−	0.904296i	$-0.359603\pi$
$164$	2.11158			0.164886
$165$		0			0
$166$			21.4416i			1.66419i
$167$	7.00178	−	12.1274i	0.541814	−	0.938450i	−0.456986	−	0.889474i	$-0.651071\pi$
$167$	7.00178	−	12.1274i	0.541814	−	0.938450i	0.998800	−	0.0489756i	$-0.0155956\pi$
$168$		0			0
$169$	−0.930521	−	1.61171i	−0.0715785	−	0.123978i
$170$	−9.27381	+	5.35423i	−0.711268	+	0.410651i
$171$		0			0
$172$	−15.5844	+	26.9930i	−1.18830	+	2.05820i
$173$	0.208244	−	0.360690i	0.0158325	−	0.0274227i	−0.858001	−	0.513649i	$-0.828293\pi$
$173$	0.208244	−	0.360690i	0.0158325	−	0.0274227i	0.873833	+	0.486226i	$0.161627\pi$
$174$		0			0
$175$	−1.75124	−	1.98322i	−0.132381	−	0.149917i
$176$	−3.27463	−	1.89061i	−0.246834	−	0.142510i
$177$		0			0
$178$		−	23.1861i		−	1.73787i
$179$	−18.9614	−	10.9474i	−1.41724	−	0.818246i	−0.421188	−	0.906973i	$-0.638387\pi$
$179$	−18.9614	−	10.9474i	−1.41724	−	0.818246i	−0.996056	+	0.0887272i	$0.971720\pi$
$180$		0			0
$181$			4.86189i			0.361382i	0.983540	+	0.180691i	$0.0578333\pi$
$181$			4.86189i			0.361382i	−0.983540	+	0.180691i	$0.942167\pi$
$182$	6.07621	−	18.1026i	0.450399	−	1.34186i
$183$		0			0
$184$	−3.91278			−0.288454
$185$	1.70041	+	2.94520i	0.125017	+	0.216536i
$186$		0			0
$187$	7.40473	+	4.27513i	0.541488	+	0.312628i
$188$	−30.8776			−2.25198
$189$		0			0
$190$	7.20850			0.522960
$191$	0.931482	+	0.537791i	0.0673997	+	0.0389132i	0.533321	−	0.845913i	$-0.320944\pi$
$191$	0.931482	+	0.537791i	0.0673997	+	0.0389132i	−0.465921	+	0.884826i	$0.654277\pi$
$192$		0			0
$193$	−4.32095	−	7.48411i	−0.311029	−	0.538718i	0.667556	−	0.744559i	$-0.267340\pi$
$193$	−4.32095	−	7.48411i	−0.311029	−	0.538718i	−0.978585	+	0.205841i	$0.934007\pi$
$194$	−7.20911			−0.517584
$195$		0			0
$196$	−17.2589	+	7.28727i	−1.23278	+	0.520519i
$197$		−	2.66589i		−	0.189937i	−0.995480	−	0.0949685i	$-0.969725\pi$
$197$		−	2.66589i		−	0.189937i	0.995480	−	0.0949685i	$-0.0302750\pi$
$198$		0			0
$199$	−17.1929	−	9.92633i	−1.21877	−	0.703659i	−0.254117	−	0.967173i	$-0.581785\pi$
$199$	−17.1929	−	9.92633i	−1.21877	−	0.703659i	−0.964655	+	0.263515i	$0.915118\pi$
$200$		−	1.46255i		−	0.103418i
$201$		0			0
$202$	−20.3174	−	11.7302i	−1.42952	−	0.825336i
$203$	−13.6848	−	4.59336i	−0.960488	−	0.322391i
$204$		0			0
$205$	−0.394491	+	0.683278i	−0.0275524	+	0.0477222i
$206$	12.5647	−	21.7626i	0.875421	−	1.51627i
$207$		0			0
$208$	−6.32965	+	3.65443i	−0.438882	+	0.253389i
$209$	−2.87784	−	4.98457i	−0.199064	−	0.344790i
$210$		0			0
$211$	−4.78399	+	8.28611i	−0.329343	+	0.570439i	−0.982382	−	0.186886i	$-0.940161\pi$
$211$	−4.78399	+	8.28611i	−0.329343	+	0.570439i	0.653039	+	0.757325i	$0.273494\pi$
$212$		−	17.6001i		−	1.20878i
$213$		0			0
$214$	−9.75997			−0.667178
$215$	−5.82305	−	10.0858i	−0.397129	−	0.687847i
$216$		0			0
$217$	19.5182	+	6.55134i	1.32498	+	0.444734i
$218$	12.0169	−	6.93796i	0.813887	−	0.469898i
$219$		0			0
$220$	−4.00198	+	2.31054i	−0.269813	+	0.155777i
$221$	14.3129	−	8.26356i	0.962790	−	0.555867i
$222$		0			0
$223$	−11.9147	+	6.87897i	−0.797870	+	0.460650i	−0.842726	−	0.538343i	$-0.819050\pi$
$223$	−11.9147	+	6.87897i	−0.797870	+	0.460650i	0.0448561	+	0.998993i	$0.485717\pi$
$224$	19.2149	+	6.44956i	1.28385	+	0.430929i
$225$		0			0
$226$	−11.5225	−	19.9575i	−0.766462	−	1.32755i
$227$	−28.8798			−1.91682			−0.958409	−	0.285397i	$-0.907874\pi$
$227$	−28.8798			−1.91682			−0.958409	+	0.285397i	$0.907874\pi$
$228$		0			0
$229$			6.54173i			0.432289i	0.976361	+	0.216145i	$0.0693483\pi$
$229$			6.54173i			0.432289i	−0.976361	+	0.216145i	$0.930652\pi$
$230$	2.89265	−	5.01022i	0.190736	−	0.330364i
$231$		0			0
$232$	−3.98984	−	6.91060i	−0.261946	−	0.453703i
$233$	−18.1428	+	10.4747i	−1.18857	+	0.686222i	−0.957982	−	0.286829i	$-0.907399\pi$
$233$	−18.1428	+	10.4747i	−1.18857	+	0.686222i	−0.230589	+	0.973051i	$0.574065\pi$
$234$		0			0
$235$	5.76865	−	9.99159i	0.376305	−	0.651779i
$236$	−14.6020	+	25.2913i	−0.950507	+	1.64633i
$237$		0			0
$238$	−26.8593	−	9.01541i	−1.74103	−	0.584382i
$239$	−25.6748	−	14.8234i	−1.66077	−	0.958844i	−0.972350	−	0.233528i	$-0.924973\pi$
$239$	−25.6748	−	14.8234i	−1.66077	−	0.958844i	−0.688417	−	0.725316i	$-0.741694\pi$
$240$		0			0
$241$		−	4.30710i		−	0.277445i	−0.990331	−	0.138722i	$-0.955700\pi$
$241$		−	4.30710i		−	0.277445i	0.990331	−	0.138722i	$-0.0442996\pi$
$242$	−15.0171	−	8.67013i	−0.965336	−	0.557337i
$243$		0			0
$244$		−	17.2733i		−	1.10581i
$245$	0.866300	−	6.94619i	0.0553459	−	0.443776i
$246$		0			0
$247$	−11.1254			−0.707891
$248$	5.69055	+	9.85632i	0.361350	+	0.625877i
$249$		0			0
$250$	1.87276	+	1.08124i	0.118444	+	0.0683837i
$251$	−13.7433			−0.867471			−0.433735	−	0.901040i	$-0.642805\pi$
$251$	−13.7433			−0.867471			−0.433735	+	0.901040i	$0.642805\pi$
$252$		0			0
$253$	−4.61932			−0.290414
$254$	−17.2058	−	9.93376i	−1.07959	−	0.623300i
$255$		0			0
$256$	−0.258793	−	0.448242i	−0.0161746	−	0.0280152i
$257$	−2.82020			−0.175919			−0.0879597	−	0.996124i	$-0.528035\pi$
$257$	−2.82020			−0.175919			−0.0879597	+	0.996124i	$0.528035\pi$
$258$		0			0
$259$	−2.86314	+	8.53006i	−0.177907	+	0.530032i
$260$			8.93228i			0.553956i
$261$		0			0
$262$	16.7946	+	9.69636i	1.03757	+	0.599043i
$263$			18.4774i			1.13937i	0.821864	+	0.569683i	$0.192934\pi$
$263$			18.4774i			1.13937i	−0.821864	+	0.569683i	$0.807066\pi$
$264$		0			0
$265$	5.69516	+	3.28810i	0.349851	+	0.201987i
$266$	12.6238	+	14.2960i	0.774017	+	0.876546i
$267$		0			0
$268$	−2.84249	+	4.92333i	−0.173633	+	0.300740i
$269$	−9.72956	+	16.8521i	−0.593222	+	1.02749i	0.400573	+	0.916265i	$0.368811\pi$
$269$	−9.72956	+	16.8521i	−0.593222	+	1.02749i	−0.993795	+	0.111225i	$0.964522\pi$
$270$		0			0
$271$	16.5777	−	9.57111i	1.00702	−	0.581404i	0.0967028	−	0.995313i	$-0.469170\pi$
$271$	16.5777	−	9.57111i	1.00702	−	0.581404i	0.910318	+	0.413910i	$0.135837\pi$
$272$	5.42215	+	9.39144i	0.328766	+	0.569440i
$273$		0			0
$274$	4.90730	−	8.49969i	0.296461	−	0.513485i
$275$		−	1.72665i		−	0.104121i
$276$		0			0
$277$	26.0217			1.56349			0.781745	−	0.623599i	$-0.214330\pi$
$277$	26.0217			1.56349			0.781745	+	0.623599i	$0.214330\pi$
$278$	−22.3385	−	38.6915i	−1.33978	−	2.32056i
$279$		0			0
$280$	2.90056	−	2.56129i	0.173342	−	0.153066i
$281$	19.5500	−	11.2872i	1.16626	−	0.673338i	0.213460	−	0.976952i	$-0.431527\pi$
$281$	19.5500	−	11.2872i	1.16626	−	0.673338i	0.952795	+	0.303614i	$0.0981932\pi$
$282$		0			0
$283$	9.24160	−	5.33564i	0.549356	−	0.317171i	−0.199506	−	0.979897i	$-0.563934\pi$
$283$	9.24160	−	5.33564i	0.549356	−	0.317171i	0.748862	+	0.662726i	$0.230600\pi$
$284$	−3.12633	+	1.80499i	−0.185513	+	0.107106i
$285$		0			0
$286$	10.7922	−	6.23088i	0.638156	−	0.368439i
$287$	−2.04594	+	0.414225i	−0.120768	+	0.0244509i
$288$		0			0
$289$	−3.76082	−	6.51393i	−0.221225	−	0.383172i
$290$	11.7985			0.692830
$291$		0			0
$292$			8.29757i			0.485578i
$293$	−0.0874653	+	0.151494i	−0.00510978	+	0.00885040i	−0.868569	−	0.495568i	$-0.834960\pi$
$293$	−0.0874653	+	0.151494i	−0.00510978	+	0.00885040i	0.863459	+	0.504419i	$0.168293\pi$
$294$		0			0
$295$	−5.45596	−	9.45000i	−0.317658	−	0.550200i
$296$	−4.30752	+	2.48695i	−0.250370	+	0.144551i
$297$		0			0
$298$	14.6170	−	25.3173i	0.846737	−	1.46659i
$299$	−4.46443	+	7.73262i	−0.258185	+	0.447189i
$300$		0			0
$301$	9.80479	−	29.2111i	0.565139	−	1.68370i
$302$	36.9806	+	21.3508i	2.12799	+	1.22860i
$303$		0			0
$304$		−	7.29994i		−	0.418680i
$305$	5.58942	+	3.22705i	0.320049	+	0.184780i
$306$		0			0
$307$			29.6519i			1.69232i	0.532928	+	0.846161i	$0.321092\pi$
$307$			29.6519i			1.69232i	−0.532928	+	0.846161i	$0.678908\pi$
$308$	−11.5907	−	3.89047i	−0.660444	−	0.221680i
$309$		0			0
$310$	−16.8277			−0.955749
$311$	1.11042	+	1.92330i	0.0629660	+	0.109060i	0.895790	−	0.444478i	$-0.146611\pi$
$311$	1.11042	+	1.92330i	0.0629660	+	0.109060i	−0.832824	+	0.553538i	$0.813277\pi$
$312$		0			0
$313$	−23.6459	−	13.6519i	−1.33654	−	0.771653i	−0.350250	−	0.936656i	$-0.613903\pi$
$313$	−23.6459	−	13.6519i	−1.33654	−	0.771653i	−0.986293	+	0.165003i	$0.947237\pi$
$314$	12.3014			0.694205
$315$		0			0
$316$	−36.4475			−2.05033
$317$	13.1016	+	7.56423i	0.735861	+	0.424849i	0.820562	−	0.571557i	$-0.193660\pi$
$317$	13.1016	+	7.56423i	0.735861	+	0.424849i	−0.0847018	+	0.996406i	$0.526994\pi$
$318$		0			0
$319$	−4.71028	−	8.15845i	−0.263725	−	0.456785i
$320$	−12.1864			−0.681242
$321$		0			0
$322$	15.0021	−	3.03735i	0.836034	−	0.169265i
$323$			16.5070i			0.918472i
$324$		0			0
$325$	−2.89037	−	1.66875i	−0.160329	−	0.0925658i
$326$			31.4568i			1.74223i
$327$		0			0
$328$	−0.999332	−	0.576964i	−0.0551789	−	0.0318575i
$329$	29.9178	−	6.05722i	1.64942	−	0.333945i
$330$		0			0
$331$	11.3803	−	19.7113i	0.625518	−	1.08343i	−0.362922	−	0.931819i	$-0.618221\pi$
$331$	11.3803	−	19.7113i	0.625518	−	1.08343i	0.988440	−	0.151610i	$-0.0484457\pi$
$332$	13.2683	−	22.9813i	0.728190	−	1.26126i
$333$		0			0
$334$	−26.2254	+	15.1412i	−1.43499	+	0.828491i
$335$	−1.06208	−	1.83958i	−0.0580278	−	0.100507i
$336$		0			0
$337$	9.02581	−	15.6332i	0.491667	−	0.851592i	−0.508287	−	0.861188i	$-0.669721\pi$
$337$	9.02581	−	15.6332i	0.491667	−	0.851592i	0.999954	+	0.00959554i	$0.00305440\pi$
$338$			4.02447i			0.218902i
$339$		0			0
$340$	13.2530			0.718746
$341$	6.71810	+	11.6361i	0.363805	+	0.630129i
$342$		0			0
$343$	15.2929	−	10.4464i	0.825739	−	0.564052i
$344$	14.7511	−	8.51653i	0.795324	−	0.459180i
$345$		0			0
$346$	−0.779985	+	0.450325i	−0.0419323	+	0.0242096i
$347$	6.73424	−	3.88802i	0.361513	−	0.208720i	−0.308231	−	0.951311i	$-0.599737\pi$
$347$	6.73424	−	3.88802i	0.361513	−	0.208720i	0.669744	+	0.742592i	$0.266404\pi$
$348$		0			0
$349$	−23.4206	+	13.5219i	−1.25368	+	0.723810i	−0.971838	−	0.235652i	$-0.924277\pi$
$349$	−23.4206	+	13.5219i	−1.25368	+	0.723810i	−0.281838	+	0.959462i	$0.590944\pi$
$350$	1.13533	+	5.60762i	0.0606859	+	0.299740i
$351$		0			0
$352$	6.61372	+	11.4553i	0.352513	+	0.610570i
$353$	−6.01892			−0.320355			−0.160177	−	0.987088i	$-0.551207\pi$
$353$	−6.01892			−0.320355			−0.160177	+	0.987088i	$0.551207\pi$
$354$		0			0
$355$		−	1.34885i		−	0.0715895i
$356$	−14.3478	+	24.8511i	−0.760430	+	1.31710i
$357$		0			0
$358$	23.6735	+	41.0038i	1.25119	+	2.16712i
$359$	6.21974	−	3.59097i	0.328265	−	0.189524i	−0.326805	−	0.945092i	$-0.605972\pi$
$359$	6.21974	−	3.59097i	0.328265	−	0.189524i	0.655071	+	0.755568i	$0.272639\pi$
$360$		0			0
$361$	−3.94409	+	6.83137i	−0.207584	+	0.359546i
$362$	5.25688	−	9.10518i	0.276295	−	0.478558i
$363$		0			0
$364$	−17.7146	+	15.6426i	−0.928500	+	0.819894i
$365$	−2.68498	−	1.55018i	−0.140538	−	0.0811399i
$366$		0			0
$367$		−	21.9618i		−	1.14640i	−0.819416	−	0.573199i	$-0.805702\pi$
$367$		−	21.9618i		−	1.14640i	0.819416	−	0.573199i	$-0.194298\pi$
$368$	−5.07378	−	2.92935i	−0.264489	−	0.152703i
$369$		0			0
$370$		−	7.35423i		−	0.382328i
$371$	3.45259	+	17.0530i	0.179249	+	0.885348i
$372$		0			0
$373$	36.8807			1.90961			0.954806	−	0.297229i	$-0.0960625\pi$
$373$	36.8807			1.90961			0.954806	+	0.297229i	$0.0960625\pi$
$374$	−9.24488	−	16.0126i	−0.478042	−	0.827992i
$375$		0			0
$376$	14.6132	+	8.43696i	0.753621	+	0.435103i
$377$	−18.2094			−0.937831
$378$		0			0
$379$	7.89653			0.405618			0.202809	−	0.979218i	$-0.434993\pi$
$379$	7.89653			0.405618			0.202809	+	0.979218i	$0.434993\pi$
$380$	−7.72615	−	4.46069i	−0.396343	−	0.228829i
$381$		0			0
$382$	−1.16296	−	2.01431i	−0.0595024	−	0.103061i
$383$	−22.1516			−1.13189			−0.565946	−	0.824443i	$-0.691489\pi$
$383$	−22.1516			−1.13189			−0.565946	+	0.824443i	$0.691489\pi$
$384$		0			0
$385$	3.42432	−	3.02378i	0.174520	−	0.154106i
$386$			18.6880i			0.951193i
$387$		0			0
$388$	7.72680	+	4.46107i	0.392269	+	0.226477i
$389$			13.4670i			0.682805i	0.939917	+	0.341402i	$0.110902\pi$
$389$			13.4670i			0.682805i	−0.939917	+	0.341402i	$0.889098\pi$
$390$		0			0
$391$	11.4731	+	6.62397i	0.580217	+	0.334989i
$392$	10.1592	+	1.26701i	0.513116	+	0.0639937i
$393$		0			0
$394$	−2.88247	+	4.99259i	−0.145217	+	0.251523i
$395$	6.80923	−	11.7939i	0.342609	−	0.593417i
$396$		0			0
$397$	2.97013	−	1.71481i	0.149067	−	0.0860637i	−0.423611	−	0.905844i	$-0.639238\pi$
$397$	2.97013	−	1.71481i	0.149067	−	0.0860637i	0.572678	+	0.819780i	$0.305904\pi$
$398$	21.4655	+	37.1794i	1.07597	+	1.86363i
$399$		0			0
$400$	1.09496	−	1.89652i	0.0547478	−	0.0948260i
$401$		−	10.6402i		−	0.531346i	−0.964063	−	0.265673i	$-0.914406\pi$
$401$		−	10.6402i		−	0.531346i	0.964063	−	0.265673i	$-0.0855941\pi$
$402$		0			0
$403$	25.9713			1.29372
$404$	14.5176	+	25.1452i	0.722276	+	1.25102i
$405$		0			0
$406$	20.6620	+	23.3989i	1.02544	+	1.16127i
$407$	−5.08533	+	2.93602i	−0.252071	+	0.145533i
$408$		0			0
$409$	−7.51434	+	4.33841i	−0.371560	+	0.214520i	−0.674140	−	0.738604i	$-0.735485\pi$
$409$	−7.51434	+	4.33841i	−0.371560	+	0.214520i	0.302580	+	0.953124i	$0.402152\pi$
$410$	1.47758	−	0.853079i	0.0729723	−	0.0421306i
$411$		0			0
$412$	−26.9339	+	15.5503i	−1.32694	+	0.766107i
$413$	9.18670	−	27.3696i	0.452048	−	1.34677i
$414$		0			0
$415$	4.95763	+	8.58686i	0.243360	+	0.421513i
$416$	25.5678			1.25357
$417$		0			0
$418$			12.4466i			0.608781i
$419$	9.02520	−	15.6321i	0.440910	−	0.763678i	−0.556848	−	0.830615i	$-0.687989\pi$
$419$	9.02520	−	15.6321i	0.440910	−	0.763678i	0.997757	+	0.0669367i	$0.0213226\pi$
$420$		0			0
$421$	−14.6491	−	25.3730i	−0.713953	−	1.23660i	−0.963362	−	0.268204i	$-0.913570\pi$
$421$	−14.6491	−	25.3730i	−0.713953	−	1.23660i	0.249409	−	0.968398i	$-0.419764\pi$
$422$	17.9186	−	10.3453i	0.872262	−	0.503601i
$423$		0			0
$424$	−4.80903	+	8.32948i	−0.233547	+	0.404515i
$425$	−2.47597	+	4.28850i	−0.120102	+	0.208023i
$426$		0			0
$427$	3.38848	+	16.7364i	0.163980	+	0.809930i
$428$	10.4608	+	6.03957i	0.505644	+	0.291934i
$429$		0			0
$430$			25.1845i			1.21450i
$431$	−28.5071	−	16.4586i	−1.37314	−	0.792783i	−0.381818	−	0.924238i	$-0.624702\pi$
$431$	−28.5071	−	16.4586i	−1.37314	−	0.792783i	−0.991322	+	0.131455i	$0.958035\pi$
$432$		0			0
$433$			7.13725i			0.342994i	0.985185	+	0.171497i	$0.0548604\pi$
$433$			7.13725i			0.342994i	−0.985185	+	0.171497i	$0.945140\pi$
$434$	−29.4694	−	33.3730i	−1.41458	−	1.60195i
$435$		0			0
$436$	−17.1731			−0.822443
$437$	−4.45899	−	7.72319i	−0.213302	−	0.369450i
$438$		0			0
$439$	19.6537	+	11.3471i	0.938020	+	0.541566i	0.889339	−	0.457248i	$-0.151165\pi$
$439$	19.6537	+	11.3471i	0.938020	+	0.541566i	0.0486809	+	0.998814i	$0.484498\pi$
$440$	2.52532			0.120390
$441$		0			0
$442$	−35.7396			−1.69996
$443$	−2.04657	−	1.18159i	−0.0972356	−	0.0561390i	0.450594	−	0.892729i	$-0.351212\pi$
$443$	−2.04657	−	1.18159i	−0.0972356	−	0.0561390i	−0.547829	+	0.836590i	$0.684546\pi$
$444$		0			0
$445$	−5.36098	−	9.28549i	−0.254135	−	0.440175i
$446$	29.7513			1.40877
$447$		0			0
$448$	−21.3414	−	24.1683i	−1.00829	−	1.14185i
$449$		−	2.75417i		−	0.129978i	−0.997886	−	0.0649888i	$-0.979299\pi$
$449$		−	2.75417i		−	0.129978i	0.997886	−	0.0649888i	$-0.0207012\pi$
$450$		0			0
$451$	−1.17978	−	0.681147i	−0.0555537	−	0.0320740i
$452$			28.5208i			1.34151i
$453$		0			0
$454$	54.0850	+	31.2260i	2.53834	+	1.46551i
$455$	−1.75223	−	8.65462i	−0.0821459	−	0.405735i
$456$		0			0
$457$	−4.45984	+	7.72468i	−0.208623	+	0.361345i	−0.951281	−	0.308326i	$-0.900231\pi$
$457$	−4.45984	+	7.72468i	−0.208623	+	0.361345i	0.742658	+	0.669671i	$0.233565\pi$
$458$	7.07319	−	12.2511i	0.330508	−	0.572457i
$459$		0			0
$460$	−6.20075	+	3.58001i	−0.289111	+	0.166919i
$461$	4.13030	+	7.15390i	0.192367	+	0.333190i	0.946034	−	0.324066i	$-0.105050\pi$
$461$	4.13030	+	7.15390i	0.192367	+	0.333190i	−0.753667	+	0.657257i	$0.771717\pi$
$462$		0			0
$463$	1.50983	−	2.61509i	0.0701675	−	0.121534i	−0.828807	−	0.559534i	$-0.810980\pi$
$463$	1.50983	−	2.61509i	0.0701675	−	0.121534i	0.898975	+	0.438001i	$0.144313\pi$
$464$		−	11.9481i		−	0.554678i
$465$		0			0
$466$	45.3028			2.09861
$467$	14.6749	+	25.4177i	0.679074	+	1.17619i	0.975260	+	0.221061i	$0.0709518\pi$
$467$	14.6749	+	25.4177i	0.679074	+	1.17619i	−0.296186	+	0.955130i	$0.595715\pi$
$468$		0			0
$469$	1.78833	−	5.32790i	0.0825772	−	0.246019i
$470$	−21.6066	+	12.4746i	−0.996640	+	0.575410i
$471$		0			0
$472$	13.8211	−	7.97964i	0.636170	−	0.367293i
$473$	17.4147	−	10.0544i	0.800727	−	0.462300i
$474$		0			0
$475$	2.88684	−	1.66672i	0.132457	−	0.0764743i
$476$	23.2092	+	26.2836i	1.06379	+	1.20471i
$477$		0			0
$478$	32.0553	+	55.5214i	1.46617	+	2.53949i
$479$	−0.796214			−0.0363800			−0.0181900	−	0.999835i	$-0.505790\pi$
$479$	−0.796214			−0.0363800			−0.0181900	+	0.999835i	$0.505790\pi$
$480$		0			0
$481$			11.3503i			0.517529i
$482$	−4.65702	+	8.06619i	−0.212121	+	0.367405i
$483$		0			0
$484$	10.7303	+	18.5855i	0.487742	+	0.844794i
$485$	−2.88709	+	1.66686i	−0.131096	+	0.0756882i
$486$		0			0
$487$	−4.82550	+	8.35802i	−0.218664	+	0.378738i	−0.954400	−	0.298531i	$-0.903503\pi$
$487$	−4.82550	+	8.35802i	−0.218664	+	0.378738i	0.735736	+	0.677269i	$0.236837\pi$
$488$	−4.71974	+	8.17483i	−0.213653	+	0.370057i
$489$		0			0
$490$	−9.13288	+	12.0719i	−0.412582	+	0.545353i
$491$	−11.0595	−	6.38522i	−0.499110	−	0.288161i	0.229236	−	0.973371i	$-0.426377\pi$
$491$	−11.0595	−	6.38522i	−0.499110	−	0.288161i	−0.728346	+	0.685210i	$0.759711\pi$
$492$		0			0
$493$			27.0176i			1.21681i
$494$	20.8352	+	12.0292i	0.937421	+	0.541220i
$495$		0			0
$496$			17.0412i			0.765170i
$497$	2.67506	−	2.36216i	0.119993	−	0.105958i
$498$		0			0
$499$	−33.6786			−1.50766			−0.753831	−	0.657068i	$-0.771796\pi$
$499$	−33.6786			−1.50766			−0.753831	+	0.657068i	$0.771796\pi$
$500$	−1.33817	−	2.31777i	−0.0598446	−	0.103654i
$501$		0			0
$502$	25.7380	+	14.8598i	1.14874	+	0.663227i
$503$	9.90713			0.441737			0.220869	−	0.975304i	$-0.429111\pi$
$503$	9.90713			0.441737			0.220869	+	0.975304i	$0.429111\pi$
$504$		0			0
$505$	−10.8489			−0.482768
$506$	8.65090	+	4.99460i	0.384579	+	0.222037i
$507$		0			0
$508$	12.2942	+	21.2942i	0.545468	+	0.944778i
$509$	−35.6778			−1.58139			−0.790695	−	0.612210i	$-0.790281\pi$
$509$	−35.6778			−1.58139			−0.790695	+	0.612210i	$0.790281\pi$
$510$		0			0
$511$	−1.62772	−	8.03964i	−0.0720062	−	0.355653i
$512$			23.1821i			1.02452i
$513$		0			0
$514$	5.28158	+	3.04932i	0.232960	+	0.134500i
$515$		−	11.6206i		−	0.512064i
$516$		0			0
$517$	17.2520	+	9.96043i	0.758741	+	0.438059i
$518$	14.5850	−	12.8790i	0.640830	−	0.565873i
$519$		0			0
$520$	2.44064	−	4.22732i	0.107029	−	0.185380i
$521$	9.14291	−	15.8360i	0.400558	−	0.693787i	−0.593235	−	0.805029i	$-0.702150\pi$
$521$	9.14291	−	15.8360i	0.400558	−	0.693787i	0.993793	+	0.111242i	$0.0354829\pi$
$522$		0			0
$523$	−17.6652	+	10.1990i	−0.772446	+	0.445972i	−0.833746	−	0.552147i	$-0.813809\pi$
$523$	−17.6652	+	10.1990i	−0.772446	+	0.445972i	0.0613005	+	0.998119i	$0.480475\pi$
$524$	−12.0004	−	20.7853i	−0.524240	−	0.908011i
$525$		0			0
$526$	19.9786	−	34.6039i	0.871106	−	1.50880i
$527$		−	38.5342i		−	1.67858i
$528$		0			0
$529$	15.8427			0.688814
$530$	−7.11046	−	12.3157i	−0.308859	−	0.534959i
$531$		0			0
$532$	−4.68383	−	23.1344i	−0.203070	−	1.00300i
$533$	−2.28045	+	1.31662i	−0.0987771	+	0.0570290i
$534$		0			0
$535$	−3.90865	+	2.25666i	−0.168986	+	0.0975639i
$536$	2.69049	−	1.55336i	0.116211	−	0.0670947i
$537$		0			0
$538$	36.4424	−	21.0400i	1.57114	−	0.907099i
$539$	11.9936	+	1.49580i	0.516602	+	0.0644285i
$540$		0			0
$541$	−3.98849	−	6.90827i	−0.171479	−	0.297010i	0.767458	−	0.641099i	$-0.221521\pi$
$541$	−3.98849	−	6.90827i	−0.171479	−	0.297010i	−0.938937	+	0.344089i	$0.888188\pi$
$542$	−41.3947			−1.77806
$543$		0			0
$544$		−	37.9356i		−	1.62647i
$545$	3.20833	−	5.55699i	0.137430	−	0.238035i
$546$		0			0
$547$	−8.04726	−	13.9383i	−0.344076	−	0.595957i	0.641109	−	0.767449i	$-0.278474\pi$
$547$	−8.04726	−	13.9383i	−0.344076	−	0.595957i	−0.985185	+	0.171492i	$0.945141\pi$
$548$	−10.5194	+	6.07337i	−0.449366	+	0.259442i
$549$		0			0
$550$	−1.86692	+	3.23361i	−0.0796059	+	0.137882i
$551$	9.09359	−	15.7506i	0.387400	−	0.670996i
$552$		0			0
$553$	35.3145	−	7.14985i	1.50173	−	0.304043i
$554$	−48.7324	−	28.1357i	−2.07044	−	1.19537i
$555$		0			0
$556$			55.2932i			2.34495i
$557$	−4.36517	−	2.52023i	−0.184958	−	0.106786i	0.404662	−	0.914466i	$-0.367389\pi$
$557$	−4.36517	−	2.52023i	−0.184958	−	0.106786i	−0.589620	+	0.807681i	$0.700723\pi$
$558$		0			0
$559$		−	38.8689i		−	1.64398i
$560$	5.67875	−	1.14973i	0.239971	−	0.0485850i
$561$		0			0
$562$	−48.8168			−2.05921
$563$	12.7290	+	22.0473i	0.536465	+	0.929185i	0.999091	+	0.0426311i	$0.0135740\pi$
$563$	12.7290	+	22.0473i	0.536465	+	0.929185i	−0.462626	+	0.886554i	$0.653093\pi$
$564$		0			0
$565$	−9.22896	−	5.32834i	−0.388265	−	0.224165i
$566$	−23.0765			−0.969976
$567$		0			0
$568$	1.97277			0.0827755
$569$	13.5116	+	7.80094i	0.566437	+	0.327032i	0.755725	−	0.654889i	$-0.227285\pi$
$569$	13.5116	+	7.80094i	0.566437	+	0.327032i	−0.189288	+	0.981922i	$0.560618\pi$
$570$		0			0
$571$	6.01702	+	10.4218i	0.251804	+	0.436138i	0.964023	−	0.265820i	$-0.0856427\pi$
$571$	6.01702	+	10.4218i	0.251804	+	0.436138i	−0.712218	+	0.701958i	$0.752309\pi$
$572$	−15.4229			−0.644864
$573$		0			0
$574$	4.27944	+	1.43641i	0.178620	+	0.0599545i
$575$		−	2.67531i		−	0.111568i
$576$		0			0
$577$	−2.90129	−	1.67506i	−0.120782	−	0.0697337i	0.438392	−	0.898784i	$-0.355548\pi$
$577$	−2.90129	−	1.67506i	−0.120782	−	0.0697337i	−0.559174	+	0.829050i	$0.688882\pi$
$578$			16.2654i			0.676552i
$579$		0			0
$580$	−12.6457	−	7.30101i	−0.525085	−	0.303158i
$581$	−8.34761	+	24.8697i	−0.346317	+	1.03177i
$582$		0			0
$583$	−5.67740	+	9.83354i	−0.235134	+	0.407264i
$584$	2.26722	−	3.92694i	0.0938181	−	0.162498i
$585$		0			0
$586$	0.327604	−	0.189142i	0.0135332	−	0.00781340i
$587$	21.0363	+	36.4359i	0.868260	+	1.50387i	0.863773	+	0.503881i	$0.168095\pi$
$587$	21.0363	+	36.4359i	0.868260	+	1.50387i	0.00448747	+	0.999990i	$0.498572\pi$
$588$		0			0
$589$	−12.9698	+	22.4644i	−0.534413	+	0.925630i
$590$			23.5968i			0.971467i
$591$		0			0
$592$	−7.44752			−0.306091
$593$	13.5045	+	23.3905i	0.554564	+	0.960534i	0.997937	+	0.0641964i	$0.0204484\pi$
$593$	13.5045	+	23.3905i	0.554564	+	0.960534i	−0.443373	+	0.896337i	$0.646218\pi$
$594$		0			0
$595$	−12.8410	+	2.59982i	−0.526431	+	0.106582i
$596$	−31.3332	+	18.0902i	−1.28346	+	0.741005i
$597$		0			0
$598$	16.7217	−	9.65425i	0.683799	−	0.394792i
$599$	−19.3762	+	11.1869i	−0.791690	+	0.457082i	−0.840557	−	0.541723i	$-0.817772\pi$
$599$	−19.3762	+	11.1869i	−0.791690	+	0.457082i	0.0488672	+	0.998805i	$0.484439\pi$
$600$		0			0
$601$	−33.0130	+	19.0601i	−1.34663	+	0.777476i	−0.987770	−	0.155916i	$-0.950167\pi$
$601$	−33.0130	+	19.0601i	−1.34663	+	0.777476i	−0.358858	+	0.933392i	$0.616834\pi$
$602$	−49.9463	+	44.1041i	−2.03566	+	1.79755i
$603$		0			0
$604$	−26.4241	−	45.7679i	−1.07518	−	1.86227i
$605$	−8.01868			−0.326006
$606$		0			0
$607$			3.05245i			0.123895i	0.998079	+	0.0619476i	$0.0197312\pi$
$607$			3.05245i			0.123895i	−0.998079	+	0.0619476i	$0.980269\pi$
$608$	−12.7683	+	22.1154i	−0.517824	+	0.896898i
$609$		0			0
$610$	−6.97844	−	12.0870i	−0.282549	−	0.489389i
$611$	33.3470	−	19.2529i	1.34908	−	0.778889i
$612$		0			0
$613$	19.9401	−	34.5372i	0.805372	−	1.39495i	−0.110668	−	0.993857i	$-0.535299\pi$
$613$	19.9401	−	34.5372i	0.805372	−	1.39495i	0.916040	−	0.401088i	$-0.131368\pi$
$614$	32.0608	−	55.5310i	1.29387	−	2.24105i
$615$		0			0
$616$	4.42245	+	5.00826i	0.178185	+	0.201788i
$617$	−9.69826	−	5.59929i	−0.390437	−	0.225419i	0.291912	−	0.956445i	$-0.405708\pi$
$617$	−9.69826	−	5.59929i	−0.390437	−	0.225419i	−0.682350	+	0.731026i	$0.739042\pi$
$618$		0			0
$619$			39.5580i			1.58997i	0.606628	+	0.794986i	$0.292522\pi$
$619$			39.5580i			1.58997i	−0.606628	+	0.794986i	$0.707478\pi$
$620$	18.0361	+	10.4131i	0.724347	+	0.418202i
$621$		0			0
$622$		−	4.80252i		−	0.192563i
$623$	9.02677	−	26.8931i	0.361650	−	1.07745i
$624$		0			0
$625$	1.00000			0.0400000
$626$	29.5221	+	51.1337i	1.17994	+	2.04372i
$627$		0			0
$628$	−13.1847	−	7.61220i	−0.526127	−	0.303760i
$629$	16.8407			0.671482
$630$		0			0
$631$	−31.1354			−1.23948			−0.619740	−	0.784807i	$-0.712762\pi$
$631$	−31.1354			−1.23948			−0.619740	+	0.784807i	$0.712762\pi$
$632$	17.2493	+	9.95887i	0.686139	+	0.396143i
$633$		0			0
$634$	−16.3575	−	28.3320i	−0.649640	−	1.12521i
$635$	−9.18737			−0.364590
$636$		0			0
$637$	14.0954	−	18.6314i	0.558480	−	0.738202i
$638$			20.3718i			0.806528i
$639$		0			0
$640$	9.55350	+	5.51572i	0.377635	+	0.218028i
$641$		−	42.9406i		−	1.69605i	−0.529955	−	0.848026i	$-0.677791\pi$
$641$		−	42.9406i		−	1.69605i	0.529955	−	0.848026i	$-0.322209\pi$
$642$		0			0
$643$	−25.1028	−	14.4931i	−0.989959	−	0.571553i	−0.0846970	−	0.996407i	$-0.526992\pi$
$643$	−25.1028	−	14.4931i	−0.989959	−	0.571553i	−0.905262	+	0.424854i	$0.860326\pi$
$644$	−17.9589	−	6.02798i	−0.707682	−	0.237536i
$645$		0			0
$646$	17.8480	−	30.9137i	0.702221	−	1.21628i
$647$	14.4462	−	25.0215i	0.567937	−	0.983696i	−0.428833	−	0.903384i	$-0.641075\pi$
$647$	14.4462	−	25.0215i	0.567937	−	0.983696i	0.996770	−	0.0803122i	$-0.0255917\pi$
$648$		0			0
$649$	16.3168	−	9.42053i	0.640492	−	0.369788i
$650$	3.60865	+	6.25037i	0.141543	+	0.245160i
$651$		0			0
$652$	19.4658	−	33.7157i	0.762339	−	1.32041i
$653$			44.1588i			1.72807i	0.503435	+	0.864033i	$0.332069\pi$
$653$			44.1588i			1.72807i	−0.503435	+	0.864033i	$0.667931\pi$
$654$		0			0
$655$	8.96780			0.350401
$656$	−0.863900	−	1.49632i	−0.0337296	−	0.0584215i
$657$		0			0
$658$	−62.5783	−	21.0046i	−2.43956	−	0.818845i
$659$	11.1900	−	6.46056i	0.435901	−	0.251668i	−0.265956	−	0.963985i	$-0.585688\pi$
$659$	11.1900	−	6.46056i	0.435901	−	0.251668i	0.701858	+	0.712317i	$0.252354\pi$
$660$		0			0
$661$	16.7305	−	9.65938i	0.650743	−	0.375706i	−0.137998	−	0.990432i	$-0.544067\pi$
$661$	16.7305	−	9.65938i	0.650743	−	0.375706i	0.788741	+	0.614726i	$0.210733\pi$
$662$	−42.6253	+	24.6097i	−1.65668	+	0.956484i
$663$		0			0
$664$	−12.5588	+	7.25080i	−0.487374	+	0.281386i
$665$	8.36103	+	2.80641i	0.324227	+	0.108828i
$666$		0			0
$667$	−7.29821	−	12.6409i	−0.282588	−	0.489457i
$668$	37.4782			1.45007
$669$		0			0
$670$			4.59347i			0.177461i
$671$	−5.57199	+	9.65096i	−0.215104	+	0.372571i
$672$		0			0
$673$	13.1315	+	22.7444i	0.506180	+	0.876730i	0.999974	+	0.00715136i	$0.00227637\pi$
$673$	13.1315	+	22.7444i	0.506180	+	0.876730i	−0.493794	+	0.869579i	$0.664390\pi$
$674$	−33.8064	+	19.5181i	−1.30217	+	0.751811i
$675$		0			0
$676$	2.49038	−	4.31347i	0.0957839	−	0.165903i
$677$	3.26374	−	5.65296i	0.125436	−	0.217261i	−0.796468	−	0.604681i	$-0.793300\pi$
$677$	3.26374	−	5.65296i	0.125436	−	0.217261i	0.921903	+	0.387420i	$0.126634\pi$
$678$		0			0
$679$	−8.36173	−	2.80664i	−0.320894	−	0.107709i
$680$	−6.27217	−	3.62124i	−0.240527	−	0.138868i
$681$		0			0
$682$		−	29.0555i		−	1.11259i
$683$	4.15228	+	2.39732i	0.158883	+	0.0917309i	0.577333	−	0.816509i	$-0.304093\pi$
$683$	4.15228	+	2.39732i	0.158883	+	0.0917309i	−0.418451	+	0.908240i	$0.637427\pi$
$684$		0			0
$685$		−	4.53858i		−	0.173410i
$686$	−39.9351	+	3.02833i	−1.52473	+	0.115622i
$687$		0			0
$688$	25.5039			0.972328
$689$	10.9741	+	19.0076i	0.418079	+	0.724133i
$690$		0			0
$691$	9.76593	+	5.63836i	0.371513	+	0.214493i	0.674119	−	0.738622i	$-0.264523\pi$
$691$	9.76593	+	5.63836i	0.371513	+	0.214493i	−0.302606	+	0.953116i	$0.597857\pi$
$692$	1.11466			0.0423731
$693$		0			0
$694$	−16.8155			−0.638309
$695$	−17.8922	−	10.3300i	−0.678688	−	0.391841i
$696$		0			0
$697$	1.95349	+	3.38355i	0.0739938	+	0.128161i
$698$	58.4817			2.21356
$699$		0			0
$700$	2.25319	−	6.71285i	0.0851626	−	0.253722i
$701$		−	25.1208i		−	0.948799i	−0.880310	−	0.474399i	$-0.842665\pi$
$701$		−	25.1208i		−	0.948799i	0.880310	−	0.474399i	$-0.157335\pi$
$702$		0			0
$703$	−9.81766	−	5.66823i	−0.370280	−	0.213781i
$704$		−	21.0417i		−	0.793039i
$705$		0			0
$706$	11.2720	+	6.50790i	0.424228	+	0.244928i
$707$	−18.9990	−	21.5156i	−0.714530	−	0.809179i
$708$		0			0
$709$	−10.5485	+	18.2706i	−0.396159	+	0.686168i	−0.993248	−	0.116007i	$-0.962990\pi$
$709$	−10.5485	+	18.2706i	−0.396159	+	0.686168i	0.597089	+	0.802175i	$0.296324\pi$
$710$	−1.45843	+	2.52608i	−0.0547340	+	0.0948021i
$711$		0			0
$712$	13.5805	−	7.84073i	0.508952	−	0.293844i
$713$	10.4092	+	18.0292i	0.389826	+	0.675199i
$714$		0			0
$715$	2.88135	−	4.99065i	0.107756	−	0.186640i
$716$		−	58.5977i		−	2.18990i
$717$		0			0
$718$	−15.5308			−0.579605
$719$	18.8427	+	32.6366i	0.702716	+	1.21714i	0.967510	+	0.252835i	$0.0813629\pi$
$719$	18.8427	+	32.6366i	0.702716	+	1.21714i	−0.264794	+	0.964305i	$0.585304\pi$
$720$		0			0
$721$	23.0461	−	20.3505i	0.858283	−	0.757891i
$722$	14.7727	−	8.52903i	0.549784	−	0.317418i
$723$		0			0
$724$	−11.2688	+	6.50602i	−0.418800	+	0.241794i
$725$	4.72502	−	2.72799i	0.175483	−	0.101315i
$726$		0			0
$727$	−13.1307	+	7.58102i	−0.486991	+	0.281165i	−0.723325	−	0.690507i	$-0.757387\pi$
$727$	−13.1307	+	7.58102i	−0.486991	+	0.281165i	0.236334	+	0.971672i	$0.424054\pi$
$728$	12.6579	−	2.56273i	0.469131	−	0.0949813i
$729$		0			0
$730$	3.35223	+	5.80623i	0.124072	+	0.214898i
$731$	−57.6707			−2.13303
$732$		0			0
$733$		−	9.72729i		−	0.359286i	−0.983732	−	0.179643i	$-0.942506\pi$
$733$		−	9.72729i		−	0.359286i	0.983732	−	0.179643i	$-0.0574942\pi$
$734$	−23.7460	+	41.1293i	−0.876482	+	1.51811i
$735$		0			0
$736$	10.2474	+	17.7491i	0.377726	+	0.654240i
$737$	3.17631	−	1.83385i	0.117001	−	0.0675506i
$738$		0			0
$739$	1.17078	−	2.02785i	0.0430678	−	0.0745956i	−0.843688	−	0.536834i	$-0.819620\pi$
$739$	1.17078	−	2.02785i	0.0430678	−	0.0745956i	0.886756	+	0.462238i	$0.152954\pi$
$740$	−4.55087	+	7.88234i	−0.167293	+	0.289761i
$741$		0			0
$742$	11.9725	−	35.6693i	0.439525	−	1.30946i
$743$	22.8122	+	13.1707i	0.836900	+	0.483185i	0.856209	−	0.516629i	$-0.172813\pi$
$743$	22.8122	+	13.1707i	0.836900	+	0.483185i	−0.0193092	+	0.999814i	$0.506147\pi$
$744$		0			0
$745$		−	13.5187i		−	0.495286i
$746$	−69.0690	−	39.8770i	−2.52879	−	1.46000i
$747$		0			0
$748$			22.8833i			0.836697i
$749$	−11.3204	−	3.79974i	−0.413640	−	0.138840i
$750$		0			0
$751$	−46.6505			−1.70230			−0.851151	−	0.524921i	$-0.824095\pi$
$751$	−46.6505			−1.70230			−0.851151	+	0.524921i	$0.824095\pi$
$752$	12.6328	+	21.8807i	0.460672	+	0.797907i
$753$		0			0
$754$	34.1019	+	19.6887i	1.24192	+	0.717021i
$755$	19.7465			0.718650
$756$		0			0
$757$	4.42659			0.160887			0.0804435	−	0.996759i	$-0.474366\pi$
$757$	4.42659			0.160887			0.0804435	+	0.996759i	$0.474366\pi$
$758$	−14.7883	−	8.53806i	−0.537137	−	0.310116i
$759$		0			0
$760$	2.43767	+	4.22217i	0.0884235	+	0.153154i
$761$	45.3737			1.64480			0.822398	−	0.568913i	$-0.192636\pi$
$761$	45.3737			1.64480			0.822398	+	0.568913i	$0.192636\pi$
$762$		0			0
$763$	16.6393	−	3.36882i	0.602382	−	0.121960i
$764$			2.87862i			0.104145i
$765$		0			0
$766$	41.4846	+	23.9512i	1.49890	+	0.865391i
$767$		−	36.4186i		−	1.31500i
$768$		0			0
$769$	−9.23372	−	5.33109i	−0.332976	−	0.192244i	0.324185	−	0.945994i	$-0.394910\pi$
$769$	−9.23372	−	5.33109i	−0.332976	−	0.192244i	−0.657162	+	0.753750i	$0.728243\pi$
$770$	−9.68238	+	1.96032i	−0.348929	+	0.0706449i
$771$		0			0
$772$	11.5643	−	20.0300i	0.416208	−	0.720894i
$773$	−7.19154	+	12.4561i	−0.258662	+	0.448015i	−0.965884	−	0.258976i	$-0.916615\pi$
$773$	−7.19154	+	12.4561i	−0.258662	+	0.448015i	0.707222	+	0.706992i	$0.249948\pi$
$774$		0			0
$775$	−6.73911	+	3.89083i	−0.242076	+	0.139763i
$776$	−2.43787	−	4.22252i	−0.0875146	−	0.151580i
$777$		0			0
$778$	14.5611	−	25.2205i	0.522040	−	0.904200i
$779$		−	2.63002i		−	0.0942303i
$780$		0			0
$781$	2.32899			0.0833379
$782$	−14.3242	−	24.8103i	−0.512233	−	0.887214i
$783$		0			0
$784$	12.2250	+	9.24873i	0.436608	+	0.330312i
$785$	4.92641	−	2.84427i	0.175831	−	0.101516i
$786$		0			0
$787$	−18.5423	+	10.7054i	−0.660961	+	0.381606i	−0.792643	−	0.609686i	$-0.791295\pi$
$787$	−18.5423	+	10.7054i	−0.660961	+	0.381606i	0.131682	+	0.991292i	$0.457962\pi$
$788$	6.17893	−	3.56741i	0.220115	−	0.127084i
$789$		0			0
$790$	−25.5042	+	14.7248i	−0.907398	+	0.523886i
$791$	−5.59489	−	27.6343i	−0.198931	−	0.982561i
$792$		0			0
$793$	10.7703	+	18.6547i	0.382465	+	0.662448i
$794$	−7.41648			−0.263201
$795$		0			0
$796$		−	53.1323i		−	1.88322i
$797$	8.94216	−	15.4883i	0.316748	−	0.548623i	−0.663060	−	0.748566i	$-0.730743\pi$
$797$	8.94216	−	15.4883i	0.316748	−	0.548623i	0.979807	+	0.199944i	$0.0640759\pi$
$798$		0			0
$799$	−28.5659	−	49.4777i	−1.01059	−	1.75039i
$800$	−6.63441	+	3.83038i	−0.234562	+	0.135424i
$801$		0			0
$802$	−11.5046	+	19.9266i	−0.406242	+	0.703632i
$803$	2.67661	−	4.63602i	0.0944555	−	0.163602i
$804$		0			0
$805$	5.30572	−	4.68511i	0.187002	−	0.165129i
$806$	−48.6382	−	28.0813i	−1.71321	−	0.989121i
$807$		0			0
$808$		−	15.8670i		−	0.558201i
$809$	−28.6232	−	16.5256i	−1.00634	−	0.581010i	−0.0962218	−	0.995360i	$-0.530676\pi$
$809$	−28.6232	−	16.5256i	−1.00634	−	0.581010i	−0.910118	+	0.414349i	$0.864009\pi$
$810$		0			0
$811$		−	35.2859i		−	1.23905i	−0.784975	−	0.619527i	$-0.787324\pi$
$811$		−	35.2859i		−	1.23905i	0.784975	−	0.619527i	$-0.212676\pi$
$812$	−7.66623	−	37.8650i	−0.269032	−	1.32880i
$813$		0			0
$814$	12.6982			0.445071
$815$	7.27331	+	12.5977i	0.254773	+	0.441280i
$816$		0			0
$817$	33.6204	+	19.4108i	1.17623	+	0.679097i
$818$	18.7635			0.656049
$819$		0			0
$820$	−2.11158			−0.0737394
$821$	−4.35529	−	2.51453i	−0.152001	−	0.0877576i	0.422071	−	0.906563i	$-0.361303\pi$
$821$	−4.35529	−	2.51453i	−0.152001	−	0.0877576i	−0.574071	+	0.818805i	$0.694637\pi$
$822$		0			0
$823$	1.34511	+	2.32979i	0.0468875	+	0.0812115i	0.888517	−	0.458844i	$-0.151736\pi$
$823$	1.34511	+	2.32979i	0.0468875	+	0.0812115i	−0.841629	+	0.540056i	$0.818403\pi$
$824$	16.9957			0.592075
$825$		0			0
$826$	−46.7977	+	41.3238i	−1.62830	+	1.43784i
$827$			18.8965i			0.657097i	0.944487	+	0.328548i	$0.106559\pi$
$827$			18.8965i			0.657097i	−0.944487	+	0.328548i	$0.893441\pi$
$828$		0			0
$829$	−15.3012	−	8.83413i	−0.531432	−	0.306822i	0.210168	−	0.977665i	$-0.432599\pi$
$829$	−15.3012	−	8.83413i	−0.531432	−	0.306822i	−0.741599	+	0.670843i	$0.765932\pi$
$830$		−	21.4416i		−	0.744248i
$831$		0			0
$832$	−35.2233	−	20.3362i	−1.22115	−	0.705029i
$833$	−27.6438	−	20.9137i	−0.957801	−	0.724615i
$834$		0			0
$835$	−7.00178	+	12.1274i	−0.242307	+	0.419687i
$836$	7.70205	−	13.3403i	0.266381	−	0.461386i
$837$		0			0
$838$	−33.8041	+	19.5168i	−1.16774	+	0.674198i
$839$	−6.02682	−	10.4388i	−0.208069	−	0.360386i	0.743037	−	0.669250i	$-0.233384\pi$
$839$	−6.02682	−	10.4388i	−0.208069	−	0.360386i	−0.951106	+	0.308864i	$0.900051\pi$
$840$		0			0
$841$	0.383861	−	0.664866i	0.0132366	−	0.0229264i
$842$			63.3568i			2.18342i
$843$		0			0
$844$	−25.6071			−0.881431
$845$	0.930521	+	1.61171i	0.0320109	+	0.0554445i
$846$		0			0
$847$	−14.0427	−	15.9028i	−0.482511	−	0.546426i
$848$	−12.4719	+	7.20066i	−0.428287	+	0.247272i
$849$		0			0
$850$	9.27381	−	5.35423i	0.318089	−	0.183649i
$851$	−7.87933	+	4.54913i	−0.270100	+	0.155942i
$852$		0			0
$853$	−10.5988	+	6.11923i	−0.362896	+	0.209518i	−0.670351	−	0.742045i	$-0.733856\pi$
$853$	−10.5988	+	6.11923i	−0.362896	+	0.209518i	0.307454	+	0.951563i	$0.400523\pi$
$854$	11.7502	−	35.0071i	0.402085	−	1.19792i
$855$		0			0
$856$	−3.30049	−	5.71661i	−0.112808	−	0.195390i
$857$	−0.591040			−0.0201896			−0.0100948	−	0.999949i	$-0.503213\pi$
$857$	−0.591040			−0.0201896			−0.0100948	+	0.999949i	$0.503213\pi$
$858$		0			0
$859$			12.3165i			0.420235i	0.977676	+	0.210117i	$0.0673846\pi$
$859$			12.3165i			0.420235i	−0.977676	+	0.210117i	$0.932615\pi$
$860$	15.5844	−	26.9930i	0.531424	−	0.920453i
$861$		0			0
$862$	35.5914	+	61.6462i	1.21225	+	2.09968i
$863$	−7.47167	+	4.31377i	−0.254339	+	0.146843i	−0.621749	−	0.783216i	$-0.713578\pi$
$863$	−7.47167	+	4.31377i	−0.254339	+	0.146843i	0.367411	+	0.930059i	$0.380244\pi$
$864$		0			0
$865$	−0.208244	+	0.360690i	−0.00708052	+	0.0122638i
$866$	7.71708	−	13.3664i	0.262237	−	0.454208i
$867$		0			0
$868$	10.9341	+	54.0054i	0.371126	+	1.83306i
$869$	20.3640	+	11.7571i	0.690801	+	0.398834i
$870$		0			0
$871$		−	7.08942i		−	0.240216i
$872$	8.12740	+	4.69236i	0.275229	+	0.158903i
$873$		0			0
$874$			19.2850i			0.652324i
$875$	1.75124	+	1.98322i	0.0592028	+	0.0670450i
$876$		0			0
$877$	19.4720			0.657521			0.328761	−	0.944413i	$-0.393369\pi$
$877$	19.4720			0.657521			0.328761	+	0.944413i	$0.393369\pi$
$878$	−24.5378	−	42.5008i	−0.828112	−	1.43433i
$879$		0			0
$880$	3.27463	+	1.89061i	0.110388	+	0.0637323i
$881$	35.4636			1.19480			0.597400	−	0.801944i	$-0.296201\pi$
$881$	35.4636			1.19480			0.597400	+	0.801944i	$0.296201\pi$
$882$		0			0
$883$	−45.6972			−1.53783			−0.768916	−	0.639350i	$-0.779204\pi$
$883$	−45.6972			−1.53783			−0.768916	+	0.639350i	$0.779204\pi$
$884$	38.3061	+	22.1160i	1.28837	+	0.743842i
$885$		0			0
$886$	2.55517	+	4.42568i	0.0858425	+	0.148684i
$887$	5.43400			0.182456			0.0912280	−	0.995830i	$-0.470921\pi$
$887$	5.43400			0.182456			0.0912280	+	0.995830i	$0.470921\pi$
$888$		0			0
$889$	−16.0893	−	18.2205i	−0.539618	−	0.611097i
$890$			23.1861i			0.777198i
$891$		0			0
$892$	−31.8878	−	18.4104i	−1.06768	−	0.616426i
$893$			38.4589i			1.28698i
$894$		0			0
$895$	18.9614	+	10.9474i	0.633811	+	0.365931i
$896$	5.79163	+	28.6060i	0.193485	+	0.955660i
$897$		0			0
$898$	−2.97793	+	5.15792i	−0.0993747	+	0.172122i
$899$	−21.2283	+	36.7685i	−0.708003	+	1.22630i
$900$		0			0
$901$	28.2020	−	16.2825i	0.939546	−	0.542447i
$902$	1.47297	+	2.55126i	0.0490445	+	0.0849476i
$903$		0			0
$904$	7.79299	−	13.4979i	0.259191	−	0.448932i
$905$		−	4.86189i		−	0.161615i
$906$		0			0
$907$	−54.0819			−1.79576			−0.897880	−	0.440241i	$-0.854893\pi$
$907$	−54.0819			−1.79576			−0.897880	+	0.440241i	$0.854893\pi$
$908$	−38.6459	−	66.9367i	−1.28251	−	2.22137i
$909$		0			0
$910$	−6.07621	+	18.1026i	−0.201424	+	0.600097i
$911$	−25.6198	+	14.7916i	−0.848822	+	0.490068i	−0.860253	−	0.509867i	$-0.829695\pi$
$911$	−25.6198	+	14.7916i	−0.848822	+	0.490068i	0.0114310	+	0.999935i	$0.496361\pi$
$912$		0			0
$913$	−14.8265	+	8.56008i	−0.490686	+	0.283297i
$914$	16.7045	−	9.64433i	0.552535	−	0.319006i
$915$		0			0
$916$	−15.1622	+	8.75391i	−0.500974	+	0.289237i
$917$	15.7048	+	17.7851i	0.518618	+	0.587316i
$918$		0			0
$919$	26.3746	+	45.6822i	0.870019	+	1.50692i	0.861976	+	0.506949i	$0.169227\pi$
$919$	26.3746	+	45.6822i	0.870019	+	1.50692i	0.00804249	+	0.999968i	$0.497440\pi$
$920$	3.91278			0.129001
$921$		0			0
$922$		−	17.8634i		−	0.588300i
$923$	2.25090	−	3.89867i	0.0740892	−	0.128326i
$924$		0			0
$925$	−1.70041	−	2.94520i	−0.0559093	−	0.0968377i
$926$	−5.65510	+	3.26497i	−0.185838	+	0.107294i
$927$		0			0
$928$	−20.8985	+	36.1972i	−0.686026	+	1.18823i
$929$	5.00434	−	8.66777i	0.164187	−	0.284380i	−0.772179	−	0.635405i	$-0.780833\pi$
$929$	5.00434	−	8.66777i	0.164187	−	0.284380i	0.936366	+	0.351024i	$0.114167\pi$
$930$		0			0
$931$	9.07647	+	21.4964i	0.297469	+	0.704517i
$932$	−48.5560	−	28.0338i	−1.59051	−	0.918279i
$933$		0			0
$934$		−	63.4685i		−	2.07675i
$935$	−7.40473	−	4.27513i	−0.242161	−	0.139812i
$936$		0			0
$937$			11.9255i			0.389590i	0.980844	+	0.194795i	$0.0624042\pi$
$937$			11.9255i			0.389590i	−0.980844	+	0.194795i	$0.937596\pi$
$938$	−9.10986	+	8.04429i	−0.297447	+	0.262655i
$939$		0			0
$940$	30.8776			1.00712
$941$	12.5261	+	21.6959i	0.408339	+	0.707265i	0.994704	−	0.102783i	$-0.0327746\pi$
$941$	12.5261	+	21.6959i	0.408339	+	0.707265i	−0.586364	+	0.810047i	$0.699441\pi$
$942$		0			0
$943$	−1.82798	−	1.05538i	−0.0595272	−	0.0343680i
$944$	23.8962			0.777754
$945$		0			0
$946$	−43.4848			−1.41381
$947$	−8.37805	−	4.83707i	−0.272250	−	0.157184i	0.357660	−	0.933852i	$-0.383575\pi$
$947$	−8.37805	−	4.83707i	−0.272250	−	0.157184i	−0.629910	+	0.776668i	$0.716908\pi$
$948$		0			0
$949$	−5.17372	−	8.96115i	−0.167946	−	0.290891i
$950$	−7.20850			−0.233875
$951$		0			0
$952$	−3.80238	−	18.7807i	−0.123236	−	0.608687i
$953$		−	26.6999i		−	0.864895i	−0.901659	−	0.432447i	$-0.857650\pi$
$953$		−	26.6999i		−	0.864895i	0.901659	−	0.432447i	$-0.142350\pi$
$954$		0			0
$955$	−0.931482	−	0.537791i	−0.0301421	−	0.0174025i
$956$		−	79.3445i		−	2.56618i
$957$		0			0
$958$	1.49112	+	0.860900i	0.0481760	+	0.0278144i
$959$	9.00099	−	7.94815i	0.290657	−	0.256659i
$960$		0			0
$961$	14.7771	−	25.5947i	0.476680	−	0.825635i
$962$	12.2724	−	21.2564i	0.395678	−	0.685335i
$963$		0			0
$964$	9.98288	−	5.76362i	0.321527	−	0.185634i
$965$	4.32095	+	7.48411i	0.139096	+	0.240922i
$966$		0			0
$967$	−1.97863	+	3.42710i	−0.0636286	+	0.110208i	−0.896085	−	0.443883i	$-0.853601\pi$
$967$	−1.97863	+	3.42710i	−0.0636286	+	0.110208i	0.832456	+	0.554091i	$0.186934\pi$
$968$		−	11.7278i		−	0.376945i
$969$		0			0
$970$	7.20911			0.231471
$971$	15.7464	+	27.2736i	0.505327	+	0.875251i	0.999981	+	0.00616165i	$0.00196133\pi$
$971$	15.7464	+	27.2736i	0.505327	+	0.875251i	−0.494654	+	0.869090i	$0.664705\pi$
$972$		0			0
$973$	−10.8468	−	53.5744i	−0.347732	−	1.71752i
$974$	18.0741	−	10.4351i	0.579130	−	0.334361i
$975$		0			0
$976$	−12.2403	+	7.06696i	−0.391804	+	0.226208i
$977$	−12.1168	+	6.99563i	−0.387650	+	0.223810i	−0.681142	−	0.732152i	$-0.738516\pi$
$977$	−12.1168	+	6.99563i	−0.387650	+	0.223810i	0.293491	+	0.955962i	$0.405183\pi$
$978$		0			0
$979$	16.0328	−	9.25654i	0.512410	−	0.295840i
$980$	17.2589	−	7.28727i	0.551316	−	0.232783i
$981$		0			0
$982$	13.8079	+	23.9161i	0.440629	+	0.763192i
$983$	2.02425			0.0645635			0.0322818	−	0.999479i	$-0.489723\pi$
$983$	2.02425			0.0645635			0.0322818	+	0.999479i	$0.489723\pi$
$984$		0			0
$985$			2.66589i			0.0849424i
$986$	29.2126	−	50.5977i	0.930319	−	1.61136i
$987$		0			0
$988$	−14.8876	−	25.7861i	−0.473638	−	0.820364i
$989$	26.9827	−	15.5784i	0.857999	−	0.495366i
$990$		0			0
$991$	−12.3884	+	21.4573i	−0.393529	+	0.681612i	−0.992912	−	0.118850i	$-0.962079\pi$
$991$	−12.3884	+	21.4573i	−0.393529	+	0.681612i	0.599383	+	0.800462i	$0.295413\pi$
$992$	29.8067	−	51.6267i	0.946364	−	1.63915i
$993$		0			0
$994$	−7.56383	+	1.53139i	−0.239910	+	0.0485727i
$995$	17.1929	+	9.92633i	0.545052	+	0.314686i
$996$		0			0
$997$			12.2634i			0.388387i	0.980963	+	0.194193i	$0.0622089\pi$
$997$			12.2634i			0.388387i	−0.980963	+	0.194193i	$0.937791\pi$
$998$	63.0721	+	36.4147i	1.99651	+	1.15269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.be.b.206.3		30
3.2	odd	2		315.2.be.b.311.13	yes	30
7.5	odd	6		945.2.t.b.341.13		30
9.2	odd	6		945.2.t.b.521.3		30
9.7	even	3		315.2.t.b.101.13	✓	30
21.5	even	6		315.2.t.b.131.3	yes	30
63.47	even	6	inner	945.2.be.b.656.3		30
63.61	odd	6		315.2.be.b.236.13	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.13	✓	30	9.7	even	3
315.2.t.b.131.3	yes	30	21.5	even	6
315.2.be.b.236.13	yes	30	63.61	odd	6
315.2.be.b.311.13	yes	30	3.2	odd	2
945.2.t.b.341.13		30	7.5	odd	6
945.2.t.b.521.3		30	9.2	odd	6
945.2.be.b.206.3		30	1.1	even	1	trivial
945.2.be.b.656.3		30	63.47	even	6	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87276 - 1.08124i) q^{2} +(1.33817 + 2.31777i) q^{4} -1.00000 q^{5} +(-1.75124 - 1.98322i) q^{7} -1.46255i q^{8} +O(q^{10})\)	\(q+(-1.87276 - 1.08124i) q^{2} +(1.33817 + 2.31777i) q^{4} -1.00000 q^{5} +(-1.75124 - 1.98322i) q^{7} -1.46255i q^{8} +(1.87276 + 1.08124i) q^{10} -1.72665i q^{11} +(-2.89037 - 1.66875i) q^{13} +(1.13533 + 5.60762i) q^{14} +(1.09496 - 1.89652i) q^{16} +(-2.47597 + 4.28850i) q^{17} +(2.88684 - 1.66672i) q^{19} +(-1.33817 - 2.31777i) q^{20} +(-1.86692 + 3.23361i) q^{22} -2.67531i q^{23} +1.00000 q^{25} +(3.60865 + 6.25037i) q^{26} +(2.25319 - 6.71285i) q^{28} +(4.72502 - 2.72799i) q^{29} +(-6.73911 + 3.89083i) q^{31} +(-6.63441 + 3.83038i) q^{32} +(9.27381 - 5.35423i) q^{34} +(1.75124 + 1.98322i) q^{35} +(-1.70041 - 2.94520i) q^{37} -7.20850 q^{38} +1.46255i q^{40} +(0.394491 - 0.683278i) q^{41} +(5.82305 + 10.0858i) q^{43} +(4.00198 - 2.31054i) q^{44} +(-2.89265 + 5.01022i) q^{46} +(-5.76865 + 9.99159i) q^{47} +(-0.866300 + 6.94619i) q^{49} +(-1.87276 - 1.08124i) q^{50} -8.93228i q^{52} +(-5.69516 - 3.28810i) q^{53} +1.72665i q^{55} +(-2.90056 + 2.56129i) q^{56} -11.7985 q^{58} +(5.45596 + 9.45000i) q^{59} +(-5.58942 - 3.22705i) q^{61} +16.8277 q^{62} +12.1864 q^{64} +(2.89037 + 1.66875i) q^{65} +(1.06208 + 1.83958i) q^{67} -13.2530 q^{68} +(-1.13533 - 5.60762i) q^{70} +1.34885i q^{71} +(2.68498 + 1.55018i) q^{73} +7.35423i q^{74} +(7.72615 + 4.46069i) q^{76} +(-3.42432 + 3.02378i) q^{77} +(-6.80923 + 11.7939i) q^{79} +(-1.09496 + 1.89652i) q^{80} +(-1.47758 + 0.853079i) q^{82} +(-4.95763 - 8.58686i) q^{83} +(2.47597 - 4.28850i) q^{85} -25.1845i q^{86} -2.52532 q^{88} +(5.36098 + 9.28549i) q^{89} +(1.75223 + 8.65462i) q^{91} +(6.20075 - 3.58001i) q^{92} +(21.6066 - 12.4746i) q^{94} +(-2.88684 + 1.66672i) q^{95} +(2.88709 - 1.66686i) q^{97} +(9.13288 - 12.0719i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 15 q^{4} - 30 q^{5} + 6 q^{7}+O(q^{10}) \) 30 * q - 3 * q^2 + 15 * q^4 - 30 * q^5 + 6 * q^7	\( 30 q - 3 q^{2} + 15 q^{4} - 30 q^{5} + 6 q^{7} + 3 q^{10} + 12 q^{13} + 9 q^{14} - 21 q^{16} - 3 q^{17} - 15 q^{20} + 15 q^{22} + 30 q^{25} + 24 q^{26} + 27 q^{28} + 6 q^{31} - 9 q^{32} - 48 q^{34} - 6 q^{35} - 3 q^{37} + 60 q^{38} - 18 q^{41} + 12 q^{43} + 15 q^{44} + 9 q^{46} + 30 q^{47} - 24 q^{49} - 3 q^{50} - 30 q^{53} - 72 q^{56} - 15 q^{59} - 30 q^{61} + 12 q^{62} - 138 q^{64} - 12 q^{65} - 6 q^{67} + 42 q^{68} - 9 q^{70} + 6 q^{73} + 54 q^{76} + 21 q^{77} - 12 q^{79} + 21 q^{80} + 6 q^{82} - 6 q^{83} + 3 q^{85} + 96 q^{88} - 3 q^{89} + 15 q^{91} + 3 q^{92} + 3 q^{94} - 36 q^{97} + 24 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 15 * q^4 - 30 * q^5 + 6 * q^7 + 3 * q^10 + 12 * q^13 + 9 * q^14 - 21 * q^16 - 3 * q^17 - 15 * q^20 + 15 * q^22 + 30 * q^25 + 24 * q^26 + 27 * q^28 + 6 * q^31 - 9 * q^32 - 48 * q^34 - 6 * q^35 - 3 * q^37 + 60 * q^38 - 18 * q^41 + 12 * q^43 + 15 * q^44 + 9 * q^46 + 30 * q^47 - 24 * q^49 - 3 * q^50 - 30 * q^53 - 72 * q^56 - 15 * q^59 - 30 * q^61 + 12 * q^62 - 138 * q^64 - 12 * q^65 - 6 * q^67 + 42 * q^68 - 9 * q^70 + 6 * q^73 + 54 * q^76 + 21 * q^77 - 12 * q^79 + 21 * q^80 + 6 * q^82 - 6 * q^83 + 3 * q^85 + 96 * q^88 - 3 * q^89 + 15 * q^91 + 3 * q^92 + 3 * q^94 - 36 * q^97 + 24 * q^98

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