LMFDB - Embedded newform 1008.2.cz.g.607.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.2
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.g.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62154 + 0.608772i) q^{3} +(1.53539 - 0.886460i) q^{5} +(2.64391 + 0.0987102i) q^{7} +(2.25879 - 1.97430i) q^{9} +O(q^{10})$	\(q+(-1.62154 + 0.608772i) q^{3} +(1.53539 - 0.886460i) q^{5} +(2.64391 + 0.0987102i) q^{7} +(2.25879 - 1.97430i) q^{9} +(-5.33976 - 3.08291i) q^{11} +(-4.60307 - 2.65758i) q^{13} +(-1.95005 + 2.37214i) q^{15} +(4.69663 - 2.71160i) q^{17} +(-0.935544 + 1.62041i) q^{19} +(-4.34730 + 1.44947i) q^{21} +(0.562751 - 0.324904i) q^{23} +(-0.928378 + 1.60800i) q^{25} +(-2.46083 + 4.57649i) q^{27} +(-1.14874 - 1.98967i) q^{29} -10.2138 q^{31} +(10.5354 + 1.74837i) q^{33} +(4.14694 - 2.19216i) q^{35} +(1.09566 - 1.89773i) q^{37} +(9.08193 + 1.50716i) q^{39} +(-6.64391 - 3.83586i) q^{41} +(1.07492 - 0.620607i) q^{43} +(1.71800 - 5.03365i) q^{45} +0.468259 q^{47} +(6.98051 + 0.521962i) q^{49} +(-5.96504 + 7.25615i) q^{51} +(-0.941715 - 1.63110i) q^{53} -10.9315 q^{55} +(0.530564 - 3.19709i) q^{57} +9.24765 q^{59} -6.33056i q^{61} +(6.16693 - 4.99690i) q^{63} -9.42337 q^{65} -9.93473i q^{67} +(-0.714731 + 0.869433i) q^{69} -11.1497i q^{71} +(-4.77625 + 2.75757i) q^{73} +(0.526500 - 3.17261i) q^{75} +(-13.8135 - 8.67802i) q^{77} -10.5842i q^{79} +(1.20430 - 8.91906i) q^{81} +(-4.06061 - 7.03319i) q^{83} +(4.80745 - 8.32675i) q^{85} +(3.07398 + 2.52701i) q^{87} +(-0.228674 - 0.132025i) q^{89} +(-11.9078 - 7.48078i) q^{91} +(16.5622 - 6.21790i) q^{93} +3.31729i q^{95} +(-12.5762 + 7.26089i) q^{97} +(-18.1480 + 3.57861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.62154	+	0.608772i	−0.936197	+	0.351474i
$3$	−1.62154	+	0.608772i	−0.936197	+	0.351474i
$4$		0			0
$5$	1.53539	−	0.886460i	0.686649	−	0.396437i	−0.115707	−	0.993283i	$-0.536913\pi$
$5$	1.53539	−	0.886460i	0.686649	−	0.396437i	0.802355	+	0.596847i	$0.203580\pi$
$6$		0			0
$7$	2.64391	+	0.0987102i	0.999304	+	0.0373090i
$7$	2.64391	+	0.0987102i	0.999304	+	0.0373090i
$8$		0			0
$9$	2.25879	−	1.97430i	0.752931	−	0.658099i
$10$		0			0
$11$	−5.33976	−	3.08291i	−1.61000	−	0.929532i	−0.989369	−	0.145427i	$-0.953544\pi$
$11$	−5.33976	−	3.08291i	−1.61000	−	0.929532i	−0.620628	−	0.784105i	$-0.713122\pi$
$12$		0			0
$13$	−4.60307	−	2.65758i	−1.27666	−	0.737081i	−0.300429	−	0.953804i	$-0.597130\pi$
$13$	−4.60307	−	2.65758i	−1.27666	−	0.737081i	−0.976233	+	0.216723i	$0.930463\pi$
$14$		0			0
$15$	−1.95005	+	2.37214i	−0.503501	+	0.612483i
$16$		0			0
$17$	4.69663	−	2.71160i	1.13910	−	0.657660i	0.192893	−	0.981220i	$-0.438213\pi$
$17$	4.69663	−	2.71160i	1.13910	−	0.657660i	0.946208	+	0.323560i	$0.104880\pi$
$18$		0			0
$19$	−0.935544	+	1.62041i	−0.214629	+	0.371748i	−0.953158	−	0.302474i	$-0.902187\pi$
$19$	−0.935544	+	1.62041i	−0.214629	+	0.371748i	0.738529	+	0.674222i	$0.235521\pi$
$20$		0			0
$21$	−4.34730	+	1.44947i	−0.948659	+	0.316301i
$22$		0			0
$23$	0.562751	−	0.324904i	0.117342	−	0.0677472i	−0.440180	−	0.897909i	$-0.645086\pi$
$23$	0.562751	−	0.324904i	0.117342	−	0.0677472i	0.557522	+	0.830162i	$0.311752\pi$
$24$		0			0
$25$	−0.928378	+	1.60800i	−0.185676	+	0.321600i
$26$		0			0
$27$	−2.46083	+	4.57649i	−0.473587	+	0.880747i
$28$		0			0
$29$	−1.14874	−	1.98967i	−0.213315	−	0.369472i	0.739435	−	0.673228i	$-0.235093\pi$
$29$	−1.14874	−	1.98967i	−0.213315	−	0.369472i	−0.952750	+	0.303756i	$0.901759\pi$
$30$		0			0
$31$	−10.2138			−1.83446			−0.917230	−	0.398358i	$-0.869580\pi$
$31$	−10.2138			−1.83446			−0.917230	+	0.398358i	$0.869580\pi$
$32$		0			0
$33$	10.5354	+	1.74837i	1.83398	+	0.304353i
$34$		0			0
$35$	4.14694	−	2.19216i	0.700961	−	0.370543i
$36$		0			0
$37$	1.09566	−	1.89773i	0.180125	−	0.311985i	−0.761798	−	0.647815i	$-0.775683\pi$
$37$	1.09566	−	1.89773i	0.180125	−	0.311985i	0.941923	+	0.335829i	$0.109017\pi$
$38$		0			0
$39$	9.08193	+	1.50716i	1.45427	+	0.241339i
$40$		0			0
$41$	−6.64391	−	3.83586i	−1.03760	−	0.599061i	−0.118450	−	0.992960i	$-0.537793\pi$
$41$	−6.64391	−	3.83586i	−1.03760	−	0.599061i	−0.919154	+	0.393899i	$0.871126\pi$
$42$		0			0
$43$	1.07492	−	0.620607i	0.163924	−	0.0946416i	−0.415794	−	0.909459i	$-0.636496\pi$
$43$	1.07492	−	0.620607i	0.163924	−	0.0946416i	0.579718	+	0.814817i	$0.303163\pi$
$44$		0			0
$45$	1.71800	−	5.03365i	0.256105	−	0.750373i
$46$		0			0
$47$	0.468259			0.0683026			0.0341513	−	0.999417i	$-0.489127\pi$
$47$	0.468259			0.0683026			0.0341513	+	0.999417i	$0.489127\pi$
$48$		0			0
$49$	6.98051	+	0.521962i	0.997216	+	0.0745660i
$50$		0			0
$51$	−5.96504	+	7.25615i	−0.835272	+	1.01606i
$52$		0			0
$53$	−0.941715	−	1.63110i	−0.129354	−	0.224048i	0.794072	−	0.607823i	$-0.207957\pi$
$53$	−0.941715	−	1.63110i	−0.129354	−	0.224048i	−0.923427	+	0.383775i	$0.874624\pi$
$54$		0			0
$55$	−10.9315			−1.47400
$56$		0			0
$57$	0.530564	−	3.19709i	0.0702749	−	0.423466i
$58$		0			0
$59$	9.24765			1.20394			0.601971	−	0.798518i	$-0.294382\pi$
$59$	9.24765			1.20394			0.601971	+	0.798518i	$0.294382\pi$
$60$		0			0
$61$		−	6.33056i		−	0.810545i	−0.914196	−	0.405273i	$-0.867177\pi$
$61$		−	6.33056i		−	0.810545i	0.914196	−	0.405273i	$-0.132823\pi$
$62$		0			0
$63$	6.16693	−	4.99690i	0.776960	−	0.629550i
$64$		0			0
$65$	−9.42337			−1.16882
$66$		0			0
$67$		−	9.93473i		−	1.21372i	−0.794808	−	0.606860i	$-0.792429\pi$
$67$		−	9.93473i		−	1.21372i	0.794808	−	0.606860i	$-0.207571\pi$
$68$		0			0
$69$	−0.714731	+	0.869433i	−0.0860435	+	0.104667i
$70$		0			0
$71$		−	11.1497i		−	1.32322i	−0.749847	−	0.661612i	$-0.769873\pi$
$71$		−	11.1497i		−	1.32322i	0.749847	−	0.661612i	$-0.230127\pi$
$72$		0			0
$73$	−4.77625	+	2.75757i	−0.559018	+	0.322749i	−0.752751	−	0.658305i	$-0.771274\pi$
$73$	−4.77625	+	2.75757i	−0.559018	+	0.322749i	0.193733	+	0.981054i	$0.437940\pi$
$74$		0			0
$75$	0.526500	−	3.17261i	0.0607950	−	0.366341i
$76$		0			0
$77$	−13.8135	−	8.67802i	−1.57420	−	0.988952i
$78$		0			0
$79$		−	10.5842i		−	1.19081i	−0.803425	−	0.595406i	$-0.796991\pi$
$79$		−	10.5842i		−	1.19081i	0.803425	−	0.595406i	$-0.203009\pi$
$80$		0			0
$81$	1.20430	−	8.91906i	0.133811	−	0.991007i
$82$		0			0
$83$	−4.06061	−	7.03319i	−0.445710	−	0.771992i	0.552391	−	0.833585i	$-0.313715\pi$
$83$	−4.06061	−	7.03319i	−0.445710	−	0.771992i	−0.998101	+	0.0615925i	$0.980382\pi$
$84$		0			0
$85$	4.80745	−	8.32675i	0.521441	−	0.903163i
$86$		0			0
$87$	3.07398	+	2.52701i	0.329565	+	0.270924i
$88$		0			0
$89$	−0.228674	−	0.132025i	−0.0242394	−	0.0139946i	0.487831	−	0.872938i	$-0.337788\pi$
$89$	−0.228674	−	0.132025i	−0.0242394	−	0.0139946i	−0.512071	+	0.858943i	$0.671121\pi$
$90$		0			0
$91$	−11.9078	−	7.48078i	−1.24827	−	0.784199i
$92$		0			0
$93$	16.5622	−	6.21790i	1.71742	−	0.644766i
$94$		0			0
$95$			3.31729i			0.340347i
$96$		0			0
$97$	−12.5762	+	7.26089i	−1.27692	+	0.737231i	−0.976281	−	0.216506i	$-0.930534\pi$
$97$	−12.5762	+	7.26089i	−1.27692	+	0.737231i	−0.300641	+	0.953737i	$0.597201\pi$
$98$		0			0
$99$	−18.1480	+	3.57861i	−1.82394	+	0.359663i
$100$		0			0
$101$	11.2127	+	6.47364i	1.11570	+	0.644151i	0.940300	−	0.340346i	$-0.110544\pi$
$101$	11.2127	+	6.47364i	1.11570	+	0.644151i	0.175402	+	0.984497i	$0.443877\pi$
$102$		0			0
$103$	6.24550	+	10.8175i	0.615387	+	1.06588i	0.990316	+	0.138829i	$0.0443337\pi$
$103$	6.24550	+	10.8175i	0.615387	+	1.06588i	−0.374929	+	0.927053i	$0.622333\pi$
$104$		0			0
$105$	−5.38992	+	6.07922i	−0.526002	+	0.593271i
$106$		0			0
$107$	9.00119	+	5.19684i	0.870178	+	0.502398i	0.867407	−	0.497599i	$-0.165785\pi$
$107$	9.00119	+	5.19684i	0.870178	+	0.502398i	0.00277074	+	0.999996i	$0.499118\pi$
$108$		0			0
$109$	1.34449	+	2.32873i	0.128779	+	0.223051i	0.923204	−	0.384311i	$-0.125561\pi$
$109$	1.34449	+	2.32873i	0.128779	+	0.223051i	−0.794425	+	0.607362i	$0.792228\pi$
$110$		0			0
$111$	−0.621367	+	3.74426i	−0.0589775	+	0.355389i
$112$		0			0
$113$	6.39791	−	11.0815i	0.601864	−	1.04246i	−0.390674	−	0.920529i	$-0.627758\pi$
$113$	6.39791	−	11.0815i	0.601864	−	1.04246i	0.992539	−	0.121931i	$-0.0389086\pi$
$114$		0			0
$115$	0.576029	−	0.997712i	0.0537150	−	0.0930371i
$116$		0			0
$117$	−15.6443	+	3.08489i	−1.44631	+	0.285198i
$118$		0			0
$119$	12.6851	−	6.70562i	1.16284	−	0.614703i
$120$		0			0
$121$	13.5087	+	23.3977i	1.22806	+	2.12706i
$122$		0			0
$123$	13.1085	+	2.17539i	1.18196	+	0.196148i
$124$		0			0
$125$			12.1565i			1.08731i
$126$		0			0
$127$		−	3.34509i		−	0.296829i	−0.988925	−	0.148414i	$-0.952583\pi$
$127$		−	3.34509i		−	0.296829i	0.988925	−	0.148414i	$-0.0474170\pi$
$128$		0			0
$129$	−1.36522	+	1.66072i	−0.120201	+	0.146218i
$130$		0			0
$131$	−1.52532	−	2.64194i	−0.133268	−	0.230827i	0.791666	−	0.610954i	$-0.209214\pi$
$131$	−1.52532	−	2.64194i	−0.133268	−	0.230827i	−0.924935	+	0.380126i	$0.875880\pi$
$132$		0			0
$133$	−2.63344	+	4.19187i	−0.228349	+	0.363481i
$134$		0			0
$135$	0.278532	+	9.20815i	0.0239722	+	0.792511i
$136$		0			0
$137$	6.58747	−	11.4098i	0.562806	−	0.974808i	−0.434444	−	0.900699i	$-0.643055\pi$
$137$	6.58747	−	11.4098i	0.562806	−	0.974808i	0.997250	−	0.0741094i	$-0.0236114\pi$
$138$		0			0
$139$	−5.78263	+	10.0158i	−0.490476	+	0.849529i	−0.999940	−	0.0109626i	$-0.996510\pi$
$139$	−5.78263	+	10.0158i	−0.490476	+	0.849529i	0.509464	+	0.860492i	$0.329844\pi$
$140$		0			0
$141$	−0.759302	+	0.285063i	−0.0639447	+	0.0240066i
$142$		0			0
$143$	16.3862	+	28.3817i	1.37028	+	2.37340i
$144$		0			0
$145$	−3.52752	−	2.03662i	−0.292945	−	0.169132i
$146$		0			0
$147$	−11.6369	+	3.40316i	−0.959799	+	0.280688i
$148$		0			0
$149$	4.15048	+	7.18885i	0.340021	+	0.588933i	0.984436	−	0.175742i	$-0.0562325\pi$
$149$	4.15048	+	7.18885i	0.340021	+	0.588933i	−0.644415	+	0.764676i	$0.722899\pi$
$150$		0			0
$151$	7.77662	+	4.48983i	0.632852	+	0.365377i	0.781856	−	0.623459i	$-0.214273\pi$
$151$	7.77662	+	4.48983i	0.632852	+	0.365377i	−0.149004	+	0.988837i	$0.547607\pi$
$152$		0			0
$153$	5.25522	−	15.3975i	0.424859	−	1.24481i
$154$		0			0
$155$	−15.6823	+	9.05416i	−1.25963	+	0.727247i
$156$		0			0
$157$		−	0.436812i		−	0.0348614i	−0.999848	−	0.0174307i	$-0.994451\pi$
$157$		−	0.436812i		−	0.0348614i	0.999848	−	0.0174307i	$-0.00554865\pi$
$158$		0			0
$159$	2.52000	+	2.07160i	0.199849	+	0.164289i
$160$		0			0
$161$	1.51993	−	0.803468i	0.119788	−	0.0633222i
$162$		0			0
$163$	−15.7966	−	9.12015i	−1.23728	−	0.714345i	−0.268744	−	0.963212i	$-0.586609\pi$
$163$	−15.7966	−	9.12015i	−1.23728	−	0.714345i	−0.968538	+	0.248867i	$0.919942\pi$
$164$		0			0
$165$	17.7259	−	6.65479i	1.37996	−	0.518075i
$166$		0			0
$167$	7.51273	−	13.0124i	0.581352	−	1.00693i	−0.413967	−	0.910292i	$-0.635857\pi$
$167$	7.51273	−	13.0124i	0.581352	−	1.00693i	0.995319	−	0.0966400i	$-0.0308096\pi$
$168$		0			0
$169$	7.62551	+	13.2078i	0.586578	+	1.01598i
$170$		0			0
$171$	1.08597	+	5.50721i	0.0830461	+	0.421147i
$172$		0			0
$173$			2.83455i			0.215507i	0.994178	+	0.107753i	$0.0343657\pi$
$173$			2.83455i			0.215507i	−0.994178	+	0.107753i	$0.965634\pi$
$174$		0			0
$175$	−2.61327	+	4.15976i	−0.197545	+	0.314448i
$176$		0			0
$177$	−14.9955	+	5.62971i	−1.12713	+	0.423155i
$178$		0			0
$179$	13.0126	−	7.51284i	0.972609	−	0.561536i	0.0725782	−	0.997363i	$-0.476877\pi$
$179$	13.0126	−	7.51284i	0.972609	−	0.561536i	0.900031	+	0.435827i	$0.143544\pi$
$180$		0			0
$181$			24.8091i			1.84404i	0.387137	+	0.922022i	$0.373464\pi$
$181$			24.8091i			1.84404i	−0.387137	+	0.922022i	$0.626536\pi$
$182$		0			0
$183$	3.85387	+	10.2653i	0.284886	+	0.758830i
$184$		0			0
$185$		−	3.88502i		−	0.285632i
$186$		0			0
$187$	−33.4385			−2.44526
$188$		0			0
$189$	−6.95797	+	11.8569i	−0.506118	+	0.862465i
$190$		0			0
$191$		−	25.2415i		−	1.82641i	−0.407498	−	0.913206i	$-0.633599\pi$
$191$		−	25.2415i		−	1.82641i	0.407498	−	0.913206i	$-0.366401\pi$
$192$		0			0
$193$	−15.1601			−1.09125			−0.545623	−	0.838030i	$-0.683707\pi$
$193$	−15.1601			−1.09125			−0.545623	+	0.838030i	$0.683707\pi$
$194$		0			0
$195$	15.2804	−	5.73668i	1.09425	−	0.410812i
$196$		0			0
$197$	−1.89234			−0.134823			−0.0674117	−	0.997725i	$-0.521474\pi$
$197$	−1.89234			−0.134823			−0.0674117	+	0.997725i	$0.521474\pi$
$198$		0			0
$199$	6.63078	+	11.4849i	0.470044	+	0.814140i	0.999413	−	0.0342518i	$-0.0109048\pi$
$199$	6.63078	+	11.4849i	0.470044	+	0.814140i	−0.529370	+	0.848391i	$0.677571\pi$
$200$		0			0
$201$	6.04798	+	16.1096i	0.426592	+	1.13628i
$202$		0			0
$203$	−2.84075	−	5.37389i	−0.199382	−	0.377173i
$204$		0			0
$205$	−13.6013			−0.949959
$206$		0			0
$207$	0.629681	−	1.84493i	0.0437658	−	0.128231i
$208$		0			0
$209$	9.99116	−	5.76840i	0.691103	−	0.399008i
$210$		0			0
$211$	7.44279	+	4.29710i	0.512383	+	0.295824i	0.733813	−	0.679352i	$-0.237739\pi$
$211$	7.44279	+	4.29710i	0.512383	+	0.295824i	−0.221430	+	0.975176i	$0.571072\pi$
$212$		0			0
$213$	6.78761	+	18.0797i	0.465079	+	1.23880i
$214$		0			0
$215$	1.10029	−	1.90575i	0.0750389	−	0.129971i
$216$		0			0
$217$	−27.0045	−	1.00821i	−1.83318	−	0.0684418i
$218$		0			0
$219$	6.06616	−	7.37916i	0.409913	−	0.498637i
$220$		0			0
$221$	−28.8252			−1.93900
$222$		0			0
$223$	−3.34744	−	5.79794i	−0.224161	−	0.388259i	0.731906	−	0.681405i	$-0.238631\pi$
$223$	−3.34744	−	5.79794i	−0.224161	−	0.388259i	−0.956068	+	0.293147i	$0.905298\pi$
$224$		0			0
$225$	1.07765	+	5.46503i	0.0718434	+	0.364336i
$226$		0			0
$227$	1.10565	−	1.91504i	0.0733843	−	0.127105i	−0.826998	−	0.562205i	$-0.809953\pi$
$227$	1.10565	−	1.91504i	0.0733843	−	0.127105i	0.900383	+	0.435099i	$0.143287\pi$
$228$		0			0
$229$	8.64408	−	4.99066i	0.571217	−	0.329792i	−0.186418	−	0.982470i	$-0.559688\pi$
$229$	8.64408	−	4.99066i	0.571217	−	0.329792i	0.757635	+	0.652678i	$0.226355\pi$
$230$		0			0
$231$	27.6821	+	5.66250i	1.82135	+	0.372565i
$232$		0			0
$233$	−11.2371	+	19.4633i	−0.736169	+	1.27508i	0.218040	+	0.975940i	$0.430034\pi$
$233$	−11.2371	+	19.4633i	−0.736169	+	1.27508i	−0.954209	+	0.299142i	$0.903300\pi$
$234$		0			0
$235$	0.718962	−	0.415093i	0.0468999	−	0.0270777i
$236$		0			0
$237$	6.44334	+	17.1627i	0.418540	+	1.11483i
$238$		0			0
$239$	18.6203	+	10.7504i	1.20445	+	0.695387i	0.961541	−	0.274663i	$-0.0885662\pi$
$239$	18.6203	+	10.7504i	1.20445	+	0.695387i	0.242906	+	0.970050i	$0.421899\pi$
$240$		0			0
$241$	16.8420	+	9.72375i	1.08489	+	0.626362i	0.932211	−	0.361914i	$-0.117877\pi$
$241$	16.8420	+	9.72375i	1.08489	+	0.626362i	0.152679	+	0.988276i	$0.451210\pi$
$242$		0			0
$243$	3.47684	+	15.1958i	0.223040	+	0.974809i
$244$		0			0
$245$	11.1805	−	5.38653i	0.714298	−	0.344133i
$246$		0			0
$247$	8.61275	−	4.97257i	0.548016	−	0.316397i
$248$		0			0
$249$	10.8661	+	8.93262i	0.688608	+	0.566082i
$250$		0			0
$251$	−11.3542			−0.716674			−0.358337	−	0.933592i	$-0.616656\pi$
$251$	−11.3542			−0.716674			−0.358337	+	0.933592i	$0.616656\pi$
$252$		0			0
$253$	−4.00660			−0.251893
$254$		0			0
$255$	−2.72639	+	16.4288i	−0.170733	+	1.02881i
$256$		0			0
$257$	−17.7865	+	10.2691i	−1.10949	+	0.640566i	−0.938698	−	0.344741i	$-0.887967\pi$
$257$	−17.7865	+	10.2691i	−1.10949	+	0.640566i	−0.170795	+	0.985307i	$0.554634\pi$
$258$		0			0
$259$	3.08414	−	4.90928i	0.191639	−	0.305048i
$260$		0			0
$261$	−6.52295	−	2.22631i	−0.403761	−	0.137805i
$262$		0			0
$263$	9.36552	+	5.40719i	0.577503	+	0.333422i	0.760140	−	0.649759i	$-0.225130\pi$
$263$	9.36552	+	5.40719i	0.577503	+	0.333422i	−0.182637	+	0.983180i	$0.558463\pi$
$264$		0			0
$265$	−2.89180	−	1.66958i	−0.177642	−	0.102562i
$266$		0			0
$267$	0.451178	+	0.0748739i	0.0276116	+	0.00458221i
$268$		0			0
$269$	−11.8170	+	6.82255i	−0.720495	+	0.415978i	−0.814935	−	0.579553i	$-0.803227\pi$
$269$	−11.8170	+	6.82255i	−0.720495	+	0.415978i	0.0944398	+	0.995531i	$0.469894\pi$
$270$		0			0
$271$	5.49515	−	9.51788i	0.333807	−	0.578170i	−0.649448	−	0.760406i	$-0.725000\pi$
$271$	5.49515	−	9.51788i	0.333807	−	0.578170i	0.983255	+	0.182236i	$0.0583334\pi$
$272$		0			0
$273$	23.8630	+	4.88129i	1.44426	+	0.295429i
$274$		0			0
$275$	9.91463	−	5.72421i	0.597875	−	0.345183i
$276$		0			0
$277$	10.6221	−	18.3980i	0.638219	−	1.10543i	−0.347605	−	0.937641i	$-0.613005\pi$
$277$	10.6221	−	18.3980i	0.638219	−	1.10543i	0.985823	−	0.167786i	$-0.0536618\pi$
$278$		0			0
$279$	−23.0710	+	20.1652i	−1.38122	+	1.20726i
$280$		0			0
$281$	−5.38885	−	9.33375i	−0.321472	−	0.556805i	0.659320	−	0.751862i	$-0.270844\pi$
$281$	−5.38885	−	9.33375i	−0.321472	−	0.556805i	−0.980792	+	0.195057i	$0.937511\pi$
$282$		0			0
$283$	−1.61290			−0.0958769			−0.0479385	−	0.998850i	$-0.515265\pi$
$283$	−1.61290			−0.0958769			−0.0479385	+	0.998850i	$0.515265\pi$
$284$		0			0
$285$	−2.01947	−	5.37912i	−0.119623	−	0.318632i
$286$		0			0
$287$	−17.1872	−	10.7975i	−1.01453	−	0.637356i
$288$		0			0
$289$	6.20556	−	10.7484i	0.365033	−	0.632256i
$290$		0			0
$291$	15.9727	−	19.4299i	0.936333	−	1.13900i
$292$		0			0
$293$	−5.09618	−	2.94228i	−0.297722	−	0.171890i	0.343697	−	0.939081i	$-0.388321\pi$
$293$	−5.09618	−	2.94228i	−0.297722	−	0.171890i	−0.641419	+	0.767191i	$0.721654\pi$
$294$		0			0
$295$	14.1988	−	8.19767i	0.826685	−	0.477287i
$296$		0			0
$297$	27.2492	−	16.8508i	1.58116	−	0.977785i
$298$		0			0
$299$	−3.45384			−0.199741
$300$		0			0
$301$	2.90326	−	1.53472i	0.167341	−	0.0884599i
$302$		0			0
$303$	−22.1228	−	3.67132i	−1.27092	−	0.210912i
$304$		0			0
$305$	−5.61179	−	9.71990i	−0.321330	−	0.556560i
$306$		0			0
$307$	4.93775			0.281812			0.140906	−	0.990023i	$-0.454998\pi$
$307$	4.93775			0.281812			0.140906	+	0.990023i	$0.454998\pi$
$308$		0			0
$309$	−16.7127	−	13.7390i	−0.950754	−	0.781583i
$310$		0			0
$311$	−15.7060			−0.890607			−0.445303	−	0.895380i	$-0.646904\pi$
$311$	−15.7060			−0.890607			−0.445303	+	0.895380i	$0.646904\pi$
$312$		0			0
$313$		−	33.9317i		−	1.91794i	−0.283515	−	0.958968i	$-0.591501\pi$
$313$		−	33.9317i		−	1.91794i	0.283515	−	0.958968i	$-0.408499\pi$
$314$		0			0
$315$	5.03912	−	13.1389i	0.283922	−	0.740295i
$316$		0			0
$317$	16.4578			0.924364			0.462182	−	0.886785i	$-0.347067\pi$
$317$	16.4578			0.924364			0.462182	+	0.886785i	$0.347067\pi$
$318$		0			0
$319$			14.1658i			0.793132i
$320$		0			0
$321$	−17.7595	−	2.94722i	−0.991239	−	0.164498i
$322$		0			0
$323$			10.1473i			0.564610i
$324$		0			0
$325$	8.54678	−	4.93449i	0.474090	−	0.273716i
$326$		0			0
$327$	−3.59781	−	2.95764i	−0.198959	−	0.163558i
$328$		0			0
$329$	1.23803	+	0.0462220i	0.0682550	+	0.00254830i
$330$		0			0
$331$			3.92749i			0.215875i	0.994158	+	0.107937i	$0.0344246\pi$
$331$			3.92749i			0.215875i	−0.994158	+	0.107937i	$0.965575\pi$
$332$		0			0
$333$	−1.27183	−	6.44974i	−0.0696956	−	0.353444i
$334$		0			0
$335$	−8.80674	−	15.2537i	−0.481164	−	0.833400i
$336$		0			0
$337$	−17.4006	+	30.1387i	−0.947870	+	1.64176i	−0.197969	+	0.980208i	$0.563435\pi$
$337$	−17.4006	+	30.1387i	−0.947870	+	1.64176i	−0.749900	+	0.661551i	$0.769899\pi$
$338$		0			0
$339$	−3.62837	+	21.8640i	−0.197066	+	1.18749i
$340$		0			0
$341$	54.5394	+	31.4883i	2.95347	+	1.70519i
$342$		0			0
$343$	18.4043	+	2.06907i	0.993740	+	0.111719i
$344$		0			0
$345$	−0.326677	+	1.96850i	−0.0175877	+	0.105981i
$346$		0			0
$347$		−	2.41593i		−	0.129694i	−0.997895	−	0.0648470i	$-0.979344\pi$
$347$		−	2.41593i		−	0.129694i	0.997895	−	0.0648470i	$-0.0206559\pi$
$348$		0			0
$349$	3.23522	−	1.86785i	0.173177	−	0.0999840i	−0.410906	−	0.911678i	$-0.634788\pi$
$349$	3.23522	−	1.86785i	0.173177	−	0.0999840i	0.584083	+	0.811694i	$0.301454\pi$
$350$		0			0
$351$	23.4898	−	14.5261i	1.25379	−	0.775344i
$352$		0			0
$353$	−26.5648	−	15.3372i	−1.41390	−	0.816316i	−0.418148	−	0.908379i	$-0.637321\pi$
$353$	−26.5648	−	15.3372i	−1.41390	−	0.816316i	−0.995753	+	0.0920629i	$0.970654\pi$
$354$		0			0
$355$	−9.88374	−	17.1191i	−0.524575	−	0.908590i
$356$		0			0
$357$	−16.4873	+	18.5958i	−0.872599	+	0.984194i
$358$		0			0
$359$	23.0928	+	13.3326i	1.21879	+	0.703669i	0.964659	−	0.263500i	$-0.0848770\pi$
$359$	23.0928	+	13.3326i	1.21879	+	0.703669i	0.254132	+	0.967170i	$0.418210\pi$
$360$		0			0
$361$	7.74951	+	13.4226i	0.407869	+	0.706450i
$362$		0			0
$363$	−36.1487	−	29.7166i	−1.89732	−	1.55972i
$364$		0			0
$365$	−4.88895	+	8.46790i	−0.255899	+	0.443230i
$366$		0			0
$367$	5.56943	−	9.64654i	0.290722	−	0.503545i	−0.683259	−	0.730176i	$-0.739438\pi$
$367$	5.56943	−	9.64654i	0.290722	−	0.503545i	0.973981	+	0.226631i	$0.0727712\pi$
$368$		0			0
$369$	−22.5803	+	4.45262i	−1.17549	+	0.231794i
$370$		0			0
$371$	−2.32880	−	4.40543i	−0.120905	−	0.228719i
$372$		0			0
$373$	−9.31048	−	16.1262i	−0.482079	−	0.834985i	0.517710	−	0.855556i	$-0.326785\pi$
$373$	−9.31048	−	16.1262i	−0.482079	−	0.834985i	−0.999788	+	0.0205717i	$0.993451\pi$
$374$		0			0
$375$	−7.40052	−	19.7122i	−0.382161	−	1.01794i
$376$		0			0
$377$			12.2114i			0.628921i
$378$		0			0
$379$		−	2.95154i		−	0.151610i	−0.997123	−	0.0758051i	$-0.975847\pi$
$379$		−	2.95154i		−	0.151610i	0.997123	−	0.0758051i	$-0.0241527\pi$
$380$		0			0
$381$	2.03640	+	5.42421i	0.104328	+	0.277891i
$382$		0			0
$383$	3.74662	+	6.48933i	0.191443	+	0.331589i	0.945729	−	0.324957i	$-0.105350\pi$
$383$	3.74662	+	6.48933i	0.191443	+	0.331589i	−0.754285	+	0.656547i	$0.772017\pi$
$384$		0			0
$385$	−28.9019	−	1.07905i	−1.47298	−	0.0549935i
$386$		0			0
$387$	1.20277	−	3.52404i	0.0611401	−	0.179137i
$388$		0			0
$389$	8.01874	−	13.8889i	0.406566	−	0.704193i	−0.587936	−	0.808907i	$-0.700059\pi$
$389$	8.01874	−	13.8889i	0.406566	−	0.704193i	0.994502	+	0.104714i	$0.0333928\pi$
$390$		0			0
$391$	1.76202	−	3.05191i	0.0891093	−	0.154342i
$392$		0			0
$393$	4.08171	+	3.35544i	0.205895	+	0.169259i
$394$		0			0
$395$	−9.38243	−	16.2509i	−0.472081	−	0.817669i
$396$		0			0
$397$	24.7118	+	14.2673i	1.24025	+	0.716057i	0.969145	−	0.246493i	$-0.0792783\pi$
$397$	24.7118	+	14.2673i	1.24025	+	0.716057i	0.271103	+	0.962550i	$0.412612\pi$
$398$		0			0
$399$	1.71835	−	8.40046i	0.0860251	−	0.420549i
$400$		0			0
$401$	−9.25499	−	16.0301i	−0.462172	−	0.800506i	0.536897	−	0.843648i	$-0.319597\pi$
$401$	−9.25499	−	16.0301i	−0.462172	−	0.800506i	−0.999069	+	0.0431421i	$0.986263\pi$
$402$		0			0
$403$	47.0150	+	27.1441i	2.34199	+	1.35215i
$404$		0			0
$405$	−6.05731	−	14.7618i	−0.300990	−	0.733521i
$406$		0			0
$407$	−11.7011	+	6.75562i	−0.580001	+	0.334864i
$408$		0			0
$409$		−	10.1232i		−	0.500560i	−0.968174	−	0.250280i	$-0.919477\pi$
$409$		−	10.1232i		−	0.500560i	0.968174	−	0.250280i	$-0.0805227\pi$
$410$		0			0
$411$	−3.73588	+	22.5118i	−0.184277	+	1.11042i
$412$		0			0
$413$	24.4500	+	0.912838i	1.20310	+	0.0449178i
$414$		0			0
$415$	−12.4693	−	7.19914i	−0.612092	−	0.353392i
$416$		0			0
$417$	3.27943	−	19.7613i	0.160595	−	0.967717i
$418$		0			0
$419$	−17.3083	+	29.9789i	−0.845566	+	1.46456i	0.0395630	+	0.999217i	$0.487403\pi$
$419$	−17.3083	+	29.9789i	−0.845566	+	1.46456i	−0.885129	+	0.465346i	$0.845930\pi$
$420$		0			0
$421$	8.91746	+	15.4455i	0.434610	+	0.752767i	0.997264	−	0.0739258i	$-0.0235528\pi$
$421$	8.91746	+	15.4455i	0.434610	+	0.752767i	−0.562654	+	0.826693i	$0.690219\pi$
$422$		0			0
$423$	1.05770	−	0.924482i	0.0514272	−	0.0449499i
$424$		0			0
$425$			10.0696i			0.488446i
$426$		0			0
$427$	0.624891	−	16.7374i	0.0302406	−	0.809981i
$428$		0			0
$429$	−43.8489	−	36.0467i	−2.11704	−	1.74035i
$430$		0			0
$431$	12.6343	−	7.29439i	0.608571	−	0.351359i	−0.163835	−	0.986488i	$-0.552386\pi$
$431$	12.6343	−	7.29439i	0.608571	−	0.351359i	0.772406	+	0.635129i	$0.219053\pi$
$432$		0			0
$433$			10.2683i			0.493463i	0.969084	+	0.246731i	$0.0793565\pi$
$433$			10.2683i			0.493463i	−0.969084	+	0.246731i	$0.920643\pi$
$434$		0			0
$435$	6.95986	+	1.15500i	0.333700	+	0.0553781i
$436$		0			0
$437$			1.21585i			0.0581620i
$438$		0			0
$439$	−25.0851			−1.19725			−0.598623	−	0.801031i	$-0.704285\pi$
$439$	−25.0851			−1.19725			−0.598623	+	0.801031i	$0.704285\pi$
$440$		0			0
$441$	16.7980	−	12.6026i	0.799907	−	0.600124i
$442$		0			0
$443$			11.9393i			0.567255i	0.958934	+	0.283628i	$0.0915380\pi$
$443$			11.9393i			0.567255i	−0.958934	+	0.283628i	$0.908462\pi$
$444$		0			0
$445$	−0.468140			−0.0221920
$446$		0			0
$447$	−11.1065	−	9.13032i	−0.525322	−	0.431849i
$448$		0			0
$449$	−13.2652			−0.626026			−0.313013	−	0.949749i	$-0.601338\pi$
$449$	−13.2652			−0.626026			−0.313013	+	0.949749i	$0.601338\pi$
$450$		0			0
$451$	23.6512	+	40.9651i	1.11369	+	1.92897i
$452$		0			0
$453$	−15.3434	−	2.54627i	−0.720896	−	0.119634i
$454$		0			0
$455$	−24.9145	−	0.930183i	−1.16801	−	0.0436076i
$456$		0			0
$457$	31.1413			1.45673			0.728364	−	0.685190i	$-0.240281\pi$
$457$	31.1413			1.45673			0.728364	+	0.685190i	$0.240281\pi$
$458$		0			0
$459$	0.852005	+	28.1669i	0.0397682	+	1.31472i
$460$		0			0
$461$	13.4565	−	7.76913i	0.626733	−	0.361845i	−0.152753	−	0.988264i	$-0.548814\pi$
$461$	13.4565	−	7.76913i	0.626733	−	0.361845i	0.779486	+	0.626420i	$0.215480\pi$
$462$		0			0
$463$	−17.3249	−	10.0026i	−0.805158	−	0.464858i	0.0401133	−	0.999195i	$-0.487228\pi$
$463$	−17.3249	−	10.0026i	−0.805158	−	0.464858i	−0.845272	+	0.534337i	$0.820561\pi$
$464$		0			0
$465$	19.9175	−	24.2286i	0.923653	−	1.12357i
$466$		0			0
$467$	4.56009	−	7.89831i	0.211016	−	0.365490i	−0.741017	−	0.671486i	$-0.765656\pi$
$467$	4.56009	−	7.89831i	0.211016	−	0.365490i	0.952033	+	0.305996i	$0.0989895\pi$
$468$		0			0
$469$	0.980660	−	26.2665i	0.0452827	−	1.21288i
$470$		0			0
$471$	0.265919	+	0.708309i	0.0122529	+	0.0326372i
$472$		0			0
$473$	−7.65310			−0.351890
$474$		0			0
$475$	−1.73708	−	3.00871i	−0.0797026	−	0.138049i
$476$		0			0
$477$	−5.34741	−	1.82509i	−0.244841	−	0.0835651i
$478$		0			0
$479$	−7.22232	+	12.5094i	−0.329996	+	0.571570i	−0.982511	−	0.186206i	$-0.940381\pi$
$479$	−7.22232	+	12.5094i	−0.329996	+	0.571570i	0.652514	+	0.757776i	$0.273714\pi$
$480$		0			0
$481$	−10.0868	+	5.82360i	−0.459917	+	0.265533i
$482$		0			0
$483$	−1.97551	+	2.22815i	−0.0898887	+	0.101384i
$484$		0			0
$485$	−12.8730	+	22.2966i	−0.584531	+	1.01244i
$486$		0			0
$487$	7.70646	−	4.44933i	0.349213	−	0.201618i	−0.315126	−	0.949050i	$-0.602047\pi$
$487$	7.70646	−	4.44933i	0.349213	−	0.201618i	0.664339	+	0.747432i	$0.268713\pi$
$488$		0			0
$489$	31.1669	+	5.17220i	1.40941	+	0.233895i
$490$		0			0
$491$	6.76842	+	3.90775i	0.305455	+	0.176354i	0.644891	−	0.764275i	$-0.276903\pi$
$491$	6.76842	+	3.90775i	0.305455	+	0.176354i	−0.339436	+	0.940629i	$0.610236\pi$
$492$		0			0
$493$	−10.7904	−	6.22982i	−0.485974	−	0.280577i
$494$		0			0
$495$	−24.6920	+	21.5820i	−1.10982	+	0.970040i
$496$		0			0
$497$	1.10059	−	29.4787i	0.0493681	−	1.32230i
$498$		0			0
$499$	−2.29721	+	1.32629i	−0.102837	+	0.0593730i	−0.550536	−	0.834811i	$-0.685577\pi$
$499$	−2.29721	+	1.32629i	−0.102837	+	0.0593730i	0.447699	+	0.894184i	$0.352243\pi$
$500$		0			0
$501$	−4.26061	+	25.6737i	−0.190350	+	1.14702i
$502$		0			0
$503$	12.8732			0.573986			0.286993	−	0.957933i	$-0.407344\pi$
$503$	12.8732			0.573986			0.286993	+	0.957933i	$0.407344\pi$
$504$		0			0
$505$	22.9545			1.02146
$506$		0			0
$507$	−20.4056	−	16.7748i	−0.906244	−	0.744993i
$508$		0			0
$509$	9.02324	−	5.20957i	0.399948	−	0.230910i	−0.286514	−	0.958076i	$-0.592496\pi$
$509$	9.02324	−	5.20957i	0.399948	−	0.230910i	0.686462	+	0.727166i	$0.259163\pi$
$510$		0			0
$511$	−12.9002	+	6.81930i	−0.570670	+	0.301668i
$512$		0			0
$513$	−5.11358	−	8.26907i	−0.225770	−	0.365088i
$514$		0			0
$515$	19.1786	+	11.0728i	0.845110	+	0.487924i
$516$		0			0
$517$	−2.50039	−	1.44360i	−0.109967	−	0.0634895i
$518$		0			0
$519$	−1.72559	−	4.59634i	−0.0757451	−	0.201757i
$520$		0			0
$521$	1.91461	−	1.10540i	0.0838807	−	0.0484285i	−0.457473	−	0.889224i	$-0.651245\pi$
$521$	1.91461	−	1.10540i	0.0838807	−	0.0484285i	0.541354	+	0.840795i	$0.317912\pi$
$522$		0			0
$523$	−12.8836	+	22.3151i	−0.563361	+	0.975770i	0.433839	+	0.900990i	$0.357159\pi$
$523$	−12.8836	+	22.3151i	−0.563361	+	0.975770i	−0.997200	+	0.0747794i	$0.976175\pi$
$524$		0			0
$525$	1.70519	−	8.33611i	0.0744205	−	0.363818i
$526$		0			0
$527$	−47.9706	+	27.6959i	−2.08963	+	1.20645i
$528$		0			0
$529$	−11.2889	+	19.5529i	−0.490821	+	0.850126i
$530$		0			0
$531$	20.8885	−	18.2576i	0.906486	−	0.792313i
$532$		0			0
$533$	20.3882	+	35.3135i	0.883113	+	1.52960i
$534$		0			0
$535$	18.4272			0.796676
$536$		0			0
$537$	−16.5269	+	20.1041i	−0.713188	+	0.867556i
$538$		0			0
$539$	−35.6651	−	24.3074i	−1.53620	−	1.04700i
$540$		0			0
$541$	18.0878	−	31.3289i	0.777653	−	1.34694i	−0.155638	−	0.987814i	$-0.549743\pi$
$541$	18.0878	−	31.3289i	0.777653	−	1.34694i	0.933291	−	0.359121i	$-0.116923\pi$
$542$		0			0
$543$	−15.1031	−	40.2289i	−0.648134	−	1.72639i
$544$		0			0
$545$	4.12864	+	2.38367i	0.176852	+	0.102105i
$546$		0			0
$547$	−29.1084	+	16.8057i	−1.24458	+	0.718561i	−0.970024	−	0.243009i	$-0.921865\pi$
$547$	−29.1084	+	16.8057i	−1.24458	+	0.718561i	−0.274560	+	0.961570i	$0.588532\pi$
$548$		0			0
$549$	−12.4984	−	14.2994i	−0.533419	−	0.610285i
$550$		0			0
$551$	4.29877			0.183134
$552$		0			0
$553$	1.04477	−	27.9836i	0.0444279	−	1.18998i
$554$		0			0
$555$	2.36509	+	6.29972i	0.100393	+	0.267408i
$556$		0			0
$557$	−20.2862	−	35.1367i	−0.859552	−	1.48879i	−0.872357	−	0.488870i	$-0.837409\pi$
$557$	−20.2862	−	35.1367i	−0.859552	−	1.48879i	0.0128047	−	0.999918i	$-0.495924\pi$
$558$		0			0
$559$	−6.59726			−0.279034
$560$		0			0
$561$	54.2219	−	20.3564i	2.28925	−	0.859448i
$562$		0			0
$563$	−17.5148			−0.738159			−0.369080	−	0.929398i	$-0.620327\pi$
$563$	−17.5148			−0.738159			−0.369080	+	0.929398i	$0.620327\pi$
$564$		0			0
$565$		−	22.6859i		−	0.954405i
$566$		0			0
$567$	4.06447	−	23.4623i	0.170692	−	0.985324i
$568$		0			0
$569$	−3.93338			−0.164896			−0.0824480	−	0.996595i	$-0.526274\pi$
$569$	−3.93338			−0.164896			−0.0824480	+	0.996595i	$0.526274\pi$
$570$		0			0
$571$			3.65160i			0.152815i	0.997077	+	0.0764074i	$0.0243449\pi$
$571$			3.65160i			0.152815i	−0.997077	+	0.0764074i	$0.975655\pi$
$572$		0			0
$573$	15.3663	+	40.9302i	0.641937	+	1.70988i
$574$		0			0
$575$			1.20654i			0.0503161i
$576$		0			0
$577$	19.6944	−	11.3706i	0.819889	−	0.473363i	−0.0304894	−	0.999535i	$-0.509707\pi$
$577$	19.6944	−	11.3706i	0.819889	−	0.473363i	0.850378	+	0.526172i	$0.176373\pi$
$578$		0			0
$579$	24.5827	−	9.22903i	1.02162	−	0.383545i
$580$		0			0
$581$	−10.0416	−	18.9959i	−0.416597	−	0.788084i
$582$		0			0
$583$			11.6129i			0.480957i
$584$		0			0
$585$	−21.2854	+	18.6045i	−0.880045	+	0.769202i
$586$		0			0
$587$	−5.83767	−	10.1111i	−0.240947	−	0.417332i	0.720038	−	0.693935i	$-0.244125\pi$
$587$	−5.83767	−	10.1111i	−0.240947	−	0.417332i	−0.960984	+	0.276603i	$0.910791\pi$
$588$		0			0
$589$	9.55550	−	16.5506i	0.393727	−	0.681956i
$590$		0			0
$591$	3.06850	−	1.15200i	0.126221	−	0.0473870i
$592$		0			0
$593$	14.8178	+	8.55508i	0.608496	+	0.351315i	0.772376	−	0.635165i	$-0.219068\pi$
$593$	14.8178	+	8.55508i	0.608496	+	0.351315i	−0.163881	+	0.986480i	$0.552401\pi$
$594$		0			0
$595$	13.5324	−	21.5406i	0.554774	−	0.883079i
$596$		0			0
$597$	−17.7437	−	14.5865i	−0.726203	−	0.596987i
$598$		0			0
$599$			34.0410i			1.39088i	0.718584	+	0.695440i	$0.244790\pi$
$599$			34.0410i			1.39088i	−0.718584	+	0.695440i	$0.755210\pi$
$600$		0			0
$601$	15.9273	−	9.19561i	0.649686	−	0.375097i	−0.138650	−	0.990341i	$-0.544276\pi$
$601$	15.9273	−	9.19561i	0.649686	−	0.375097i	0.788336	+	0.615245i	$0.210943\pi$
$602$		0			0
$603$	−19.6141	−	22.4405i	−0.798749	−	0.913849i
$604$		0			0
$605$	41.4822	+	23.9498i	1.68649	+	0.973697i
$606$		0			0
$607$	3.78485	+	6.55555i	0.153622	+	0.266082i	0.932557	−	0.361024i	$-0.117573\pi$
$607$	3.78485	+	6.55555i	0.153622	+	0.266082i	−0.778934	+	0.627106i	$0.784239\pi$
$608$		0			0
$609$	7.87787	+	6.98462i	0.319227	+	0.283031i
$610$		0			0
$611$	−2.15543	−	1.24444i	−0.0871994	−	0.0503446i
$612$		0			0
$613$	−3.18881	−	5.52319i	−0.128795	−	0.223080i	0.794415	−	0.607375i	$-0.207778\pi$
$613$	−3.18881	−	5.52319i	−0.128795	−	0.223080i	−0.923210	+	0.384296i	$0.874444\pi$
$614$		0			0
$615$	22.0551	−	8.28011i	0.889349	−	0.333886i
$616$		0			0
$617$	7.53848	−	13.0570i	0.303488	−	0.525656i	−0.673436	−	0.739246i	$-0.735182\pi$
$617$	7.53848	−	13.0570i	0.303488	−	0.525656i	0.976924	+	0.213589i	$0.0685155\pi$
$618$		0			0
$619$	3.70692	−	6.42058i	0.148994	−	0.258065i	−0.781862	−	0.623451i	$-0.785730\pi$
$619$	3.70692	−	6.42058i	0.148994	−	0.258065i	0.930856	+	0.365387i	$0.119063\pi$
$620$		0			0
$621$	0.102087	+	3.37496i	0.00409662	+	0.135433i
$622$		0			0
$623$	−0.591562	−	0.371635i	−0.0237004	−	0.0148892i
$624$		0			0
$625$	6.13433	+	10.6250i	0.245373	+	0.424999i
$626$		0			0
$627$	−12.6894	+	15.4360i	−0.506767	+	0.616455i
$628$		0			0
$629$		−	11.8839i		−	0.473843i
$630$		0			0
$631$		−	4.50590i		−	0.179377i	−0.995970	−	0.0896885i	$-0.971413\pi$
$631$		−	4.50590i		−	0.179377i	0.995970	−	0.0896885i	$-0.0285872\pi$
$632$		0			0
$633$	−14.6847	−	2.43696i	−0.583666	−	0.0968606i
$634$		0			0
$635$	−2.96529	−	5.13603i	−0.117674	−	0.203817i
$636$		0			0
$637$	−30.7446	−	20.9539i	−1.21815	−	0.830225i
$638$		0			0
$639$	−22.0128	−	25.1848i	−0.870812	−	0.996297i
$640$		0			0
$641$	22.2663	−	38.5664i	0.879467	−	1.52328i	0.0275404	−	0.999621i	$-0.491233\pi$
$641$	22.2663	−	38.5664i	0.879467	−	1.52328i	0.851927	−	0.523661i	$-0.175434\pi$
$642$		0			0
$643$	5.01024	−	8.67799i	0.197585	−	0.342227i	−0.750160	−	0.661256i	$-0.770024\pi$
$643$	5.01024	−	8.67799i	0.197585	−	0.342227i	0.947745	+	0.319030i	$0.103357\pi$
$644$		0			0
$645$	−0.623992	+	3.76008i	−0.0245697	+	0.148053i
$646$		0			0
$647$	7.17309	+	12.4242i	0.282003	+	0.488444i	0.971878	−	0.235485i	$-0.0756677\pi$
$647$	7.17309	+	12.4242i	0.282003	+	0.488444i	−0.689875	+	0.723929i	$0.742334\pi$
$648$		0			0
$649$	−49.3802	−	28.5097i	−1.93834	−	1.11910i
$650$		0			0
$651$	44.4026	−	14.8047i	1.74028	−	0.580242i
$652$		0			0
$653$	5.09260	+	8.82064i	0.199289	+	0.345178i	0.948298	−	0.317381i	$-0.102804\pi$
$653$	5.09260	+	8.82064i	0.199289	+	0.345178i	−0.749009	+	0.662559i	$0.769470\pi$
$654$		0			0
$655$	−4.68394	−	2.70428i	−0.183017	−	0.105665i
$656$		0			0
$657$	−5.34430	+	15.6585i	−0.208501	+	0.610897i
$658$		0			0
$659$	−13.1154	+	7.57216i	−0.510902	+	0.294970i	−0.733205	−	0.680008i	$-0.761976\pi$
$659$	−13.1154	+	7.57216i	−0.510902	+	0.294970i	0.222302	+	0.974978i	$0.428643\pi$
$660$		0			0
$661$		−	7.28596i		−	0.283391i	−0.989910	−	0.141695i	$-0.954745\pi$
$661$		−	7.28596i		−	0.283391i	0.989910	−	0.141695i	$-0.0452554\pi$
$662$		0			0
$663$	46.7413	−	17.5480i	1.81528	−	0.681507i
$664$		0			0
$665$	−0.327450	+	8.77061i	−0.0126980	+	0.340110i
$666$		0			0
$667$	−1.29290	−	0.746458i	−0.0500614	−	0.0289030i
$668$		0			0
$669$	8.95764	+	7.36378i	0.346322	+	0.284700i
$670$		0			0
$671$	−19.5165	+	33.8037i	−0.753428	+	1.30498i
$672$		0			0
$673$	9.14049	+	15.8318i	0.352340	+	0.610271i	0.986659	−	0.162801i	$-0.0520528\pi$
$673$	9.14049	+	15.8318i	0.352340	+	0.610271i	−0.634319	+	0.773071i	$0.718719\pi$
$674$		0			0
$675$	−5.07441	−	8.20573i	−0.195314	−	0.315839i
$676$		0			0
$677$		−	6.06704i		−	0.233175i	−0.993180	−	0.116588i	$-0.962804\pi$
$677$		−	6.06704i		−	0.233175i	0.993180	−	0.116588i	$-0.0371956\pi$
$678$		0			0
$679$	−33.9671	+	17.9557i	−1.30354	+	0.689078i
$680$		0			0
$681$	−0.627032	+	3.77840i	−0.0240279	+	0.144788i
$682$		0			0
$683$	−19.2524	+	11.1154i	−0.736672	+	0.425318i	−0.820858	−	0.571132i	$-0.806504\pi$
$683$	−19.2524	+	11.1154i	−0.736672	+	0.425318i	0.0841862	+	0.996450i	$0.473171\pi$
$684$		0			0
$685$		−	23.3581i		−	0.892468i
$686$		0			0
$687$	−10.9786	+	13.3548i	−0.418858	+	0.509519i
$688$		0			0
$689$			10.0107i			0.381379i
$690$		0			0
$691$	29.0317			1.10442			0.552209	−	0.833706i	$-0.313785\pi$
$691$	29.0317			1.10442			0.552209	+	0.833706i	$0.313785\pi$
$692$		0			0
$693$	−48.3349	+	7.67012i	−1.83609	+	0.291364i
$694$		0			0
$695$			20.5043i			0.777771i
$696$		0			0
$697$	−41.6053			−1.57591
$698$		0			0
$699$	6.37278	−	38.4014i	0.241041	−	1.45247i
$700$		0			0
$701$	−26.6798			−1.00768			−0.503841	−	0.863796i	$-0.668080\pi$
$701$	−26.6798			−1.00768			−0.503841	+	0.863796i	$0.668080\pi$
$702$		0			0
$703$	2.05007	+	3.55083i	0.0773198	+	0.133922i
$704$		0			0
$705$	−0.913130	+	1.11077i	−0.0343905	+	0.0418342i
$706$		0			0
$707$	29.0063	+	18.2225i	1.09089	+	0.685328i
$708$		0			0
$709$	40.8942			1.53581			0.767907	−	0.640561i	$-0.221298\pi$
$709$	40.8942			1.53581			0.767907	+	0.640561i	$0.221298\pi$
$710$		0			0
$711$	−20.8963	−	23.9074i	−0.783672	−	0.896599i
$712$		0			0
$713$	−5.74785	+	3.31852i	−0.215259	+	0.124280i
$714$		0			0
$715$	50.3185	+	29.0514i	1.88180	+	1.08646i
$716$		0			0
$717$	−36.7381	−	6.09676i	−1.37201	−	0.227688i
$718$		0			0
$719$	3.01395	−	5.22031i	0.112401	−	0.194685i	−0.804337	−	0.594174i	$-0.797479\pi$
$719$	3.01395	−	5.22031i	0.112401	−	0.194685i	0.916738	+	0.399489i	$0.130812\pi$
$720$		0			0
$721$	15.4447	+	29.2170i	0.575192	+	1.08810i
$722$		0			0
$723$	−33.2296	−	5.51452i	−1.23582	−	0.205087i
$724$		0			0
$725$	4.26584			0.158429
$726$		0			0
$727$	9.28363	+	16.0797i	0.344311	+	0.596364i	0.985228	−	0.171246i	$-0.0547793\pi$
$727$	9.28363	+	16.0797i	0.344311	+	0.596364i	−0.640918	+	0.767610i	$0.721446\pi$
$728$		0			0
$729$	−14.8886	−	22.5240i	−0.551430	−	0.834221i
$730$		0			0
$731$	3.36568	−	5.82952i	0.124484	−	0.215613i
$732$		0			0
$733$	24.2957	−	14.0272i	0.897384	−	0.518105i	0.0210332	−	0.999779i	$-0.493304\pi$
$733$	24.2957	−	14.0272i	0.897384	−	0.518105i	0.876350	+	0.481674i	$0.159971\pi$
$734$		0			0
$735$	−14.8505	+	15.5409i	−0.547770	+	0.573233i
$736$		0			0
$737$	−30.6279	+	53.0491i	−1.12819	+	1.95409i
$738$		0			0
$739$	41.9757	−	24.2347i	1.54410	−	0.891488i	0.545529	−	0.838092i	$-0.316329\pi$
$739$	41.9757	−	24.2347i	1.54410	−	0.891488i	0.998573	−	0.0533962i	$-0.0170046\pi$
$740$		0			0
$741$	−10.9388	+	13.3064i	−0.401846	+	0.488824i
$742$		0			0
$743$	−0.173090	−	0.0999335i	−0.00635005	−	0.00366620i	0.496822	−	0.867853i	$-0.334500\pi$
$743$	−0.173090	−	0.0999335i	−0.00635005	−	0.00366620i	−0.503172	+	0.864186i	$0.667834\pi$
$744$		0			0
$745$	12.7452	+	7.35847i	0.466950	+	0.269594i
$746$		0			0
$747$	−23.0577	−	7.86967i	−0.843637	−	0.287936i
$748$		0			0
$749$	23.2854	+	14.6285i	0.850828	+	0.534513i
$750$		0			0
$751$	30.6319	−	17.6853i	1.11777	−	0.645347i	0.176942	−	0.984221i	$-0.443379\pi$
$751$	30.6319	−	17.6853i	1.11777	−	0.645347i	0.940832	+	0.338874i	$0.110046\pi$
$752$		0			0
$753$	18.4114	−	6.91214i	0.670948	−	0.251893i
$754$		0			0
$755$	15.9202			0.579396
$756$		0			0
$757$	−32.7804			−1.19142			−0.595712	−	0.803198i	$-0.703130\pi$
$757$	−32.7804			−1.19142			−0.595712	+	0.803198i	$0.703130\pi$
$758$		0			0
$759$	6.49687	−	2.43911i	0.235822	−	0.0885339i
$760$		0			0
$761$	20.7302	−	11.9686i	0.751470	−	0.433861i	−0.0747551	−	0.997202i	$-0.523818\pi$
$761$	20.7302	−	11.9686i	0.751470	−	0.433861i	0.826225	+	0.563341i	$0.190484\pi$
$762$		0			0
$763$	3.32484	+	6.28965i	0.120367	+	0.227701i
$764$		0			0
$765$	−5.58043	−	28.2997i	−0.201761	−	1.02318i
$766$		0			0
$767$	−42.5676	−	24.5764i	−1.53703	−	0.887403i
$768$		0			0
$769$	−3.09015	−	1.78410i	−0.111434	−	0.0643363i	0.443247	−	0.896399i	$-0.353826\pi$
$769$	−3.09015	−	1.78410i	−0.111434	−	0.0643363i	−0.554681	+	0.832063i	$0.687160\pi$
$770$		0			0
$771$	22.5901	−	27.4796i	0.813562	−	0.989655i
$772$		0			0
$773$	7.21515	−	4.16567i	0.259511	−	0.149829i	−0.364600	−	0.931164i	$-0.618794\pi$
$773$	7.21515	−	4.16567i	0.259511	−	0.149829i	0.624111	+	0.781335i	$0.285461\pi$
$774$		0			0
$775$	9.48231	−	16.4238i	0.340615	−	0.589962i
$776$		0			0
$777$	−2.01243	+	9.83814i	−0.0721957	+	0.352941i
$778$		0			0
$779$	12.4313	−	7.17723i	0.445399	−	0.257151i
$780$		0			0
$781$	−34.3735	+	59.5366i	−1.22998	+	2.13039i
$782$		0			0
$783$	11.9326	−	0.360941i	0.426435	−	0.0128990i
$784$		0			0
$785$	−0.387217	−	0.670679i	−0.0138204	−	0.0239376i
$786$		0			0
$787$	−11.6617			−0.415693			−0.207847	−	0.978161i	$-0.566645\pi$
$787$	−11.6617			−0.415693			−0.207847	+	0.978161i	$0.566645\pi$
$788$		0			0
$789$	−18.4783	−	3.06651i	−0.657846	−	0.109171i
$790$		0			0
$791$	18.0093	−	28.6669i	0.640338	−	1.01928i
$792$		0			0
$793$	−16.8240	+	29.1400i	−0.597438	+	1.03479i
$794$		0			0
$795$	5.70558	+	0.946852i	0.202356	+	0.0335814i
$796$		0			0
$797$	7.96836	+	4.60053i	0.282254	+	0.162959i	0.634443	−	0.772969i	$-0.281229\pi$
$797$	7.96836	+	4.60053i	0.282254	+	0.162959i	−0.352190	+	0.935929i	$0.614563\pi$
$798$		0			0
$799$	2.19924	−	1.26973i	0.0778035	−	0.0449199i
$800$		0			0
$801$	−0.777185	+	0.153253i	−0.0274605	+	0.00541494i
$802$		0			0
$803$	34.0053			1.20002
$804$		0			0
$805$	1.62145	−	2.58100i	0.0571487	−	0.0909683i
$806$		0			0
$807$	15.0084	−	18.2569i	0.528320	−	0.642673i
$808$		0			0
$809$	12.5382	+	21.7168i	0.440820	+	0.763523i	0.997751	−	0.0670362i	$-0.0213543\pi$
$809$	12.5382	+	21.7168i	0.440820	+	0.763523i	−0.556930	+	0.830559i	$0.688021\pi$
$810$		0			0
$811$	28.4265			0.998191			0.499095	−	0.866547i	$-0.333666\pi$
$811$	28.4265			0.998191			0.499095	+	0.866547i	$0.333666\pi$
$812$		0			0
$813$	−3.11640	+	18.7789i	−0.109297	+	0.658606i
$814$		0			0
$815$	−32.3386			−1.13277
$816$		0			0
$817$			2.32242i			0.0812512i
$818$		0			0
$819$	−41.6665	+	6.61193i	−1.45595	+	0.231040i
$820$		0			0
$821$	−43.1755			−1.50684			−0.753418	−	0.657542i	$-0.771596\pi$
$821$	−43.1755			−1.50684			−0.753418	+	0.657542i	$0.771596\pi$
$822$		0			0
$823$		−	31.1928i		−	1.08731i	−0.839308	−	0.543656i	$-0.817040\pi$
$823$		−	31.1928i		−	1.08731i	0.839308	−	0.543656i	$-0.182960\pi$
$824$		0			0
$825$	−12.5922	+	15.3178i	−0.438406	+	0.533297i
$826$		0			0
$827$		−	28.5280i		−	0.992015i	−0.868318	−	0.496008i	$-0.834799\pi$
$827$		−	28.5280i		−	0.992015i	0.868318	−	0.496008i	$-0.165201\pi$
$828$		0			0
$829$	11.4834	−	6.62996i	0.398836	−	0.230268i	−0.287146	−	0.957887i	$-0.592706\pi$
$829$	11.4834	−	6.62996i	0.398836	−	0.230268i	0.685982	+	0.727619i	$0.259373\pi$
$830$		0			0
$831$	−6.02397	+	36.2995i	−0.208969	+	1.25922i
$832$		0			0
$833$	34.2002	−	16.4769i	1.18497	−	0.570891i
$834$		0			0
$835$		−	26.6389i		−	0.921878i
$836$		0			0
$837$	25.1346	−	46.7436i	0.868777	−	1.61569i
$838$		0			0
$839$	−25.8498	−	44.7732i	−0.892434	−	1.54574i	−0.836949	−	0.547281i	$-0.815663\pi$
$839$	−25.8498	−	44.7732i	−0.892434	−	1.54574i	−0.0554852	−	0.998460i	$-0.517671\pi$
$840$		0			0
$841$	11.8608	−	20.5435i	0.408994	−	0.708398i
$842$		0			0
$843$	14.4204	+	11.8545i	0.496664	+	0.408290i
$844$		0			0
$845$	23.4163	+	13.5194i	0.805546	+	0.465082i
$846$		0			0
$847$	33.4061	+	63.1948i	1.14785	+	2.17140i
$848$		0			0
$849$	2.61538	−	0.981888i	0.0897598	−	0.0336983i
$850$		0			0
$851$		−	1.42393i		−	0.0488118i
$852$		0			0
$853$	−7.05764	+	4.07473i	−0.241649	+	0.139516i	−0.615934	−	0.787798i	$-0.711221\pi$
$853$	−7.05764	+	4.07473i	−0.241649	+	0.139516i	0.374285	+	0.927314i	$0.377888\pi$
$854$		0			0
$855$	6.54931	+	7.49307i	0.223982	+	0.256258i
$856$		0			0
$857$	−10.1744	−	5.87421i	−0.347552	−	0.200659i	0.316055	−	0.948741i	$-0.397642\pi$
$857$	−10.1744	−	5.87421i	−0.347552	−	0.200659i	−0.663606	+	0.748082i	$0.730975\pi$
$858$		0			0
$859$	5.47139	+	9.47672i	0.186681	+	0.323342i	0.944142	−	0.329539i	$-0.106893\pi$
$859$	5.47139	+	9.47672i	0.186681	+	0.323342i	−0.757460	+	0.652881i	$0.773560\pi$
$860$		0			0
$861$	34.4430	+	7.04547i	1.17382	+	0.240109i
$862$		0			0
$863$	2.81866	+	1.62735i	0.0959482	+	0.0553957i	0.547206	−	0.836998i	$-0.315691\pi$
$863$	2.81866	+	1.62735i	0.0959482	+	0.0553957i	−0.451258	+	0.892393i	$0.649025\pi$
$864$		0			0
$865$	2.51271	+	4.35215i	0.0854348	+	0.147977i
$866$		0			0
$867$	−3.51929	+	21.2067i	−0.119521	+	0.720216i
$868$		0			0
$869$	−32.6300	+	56.5168i	−1.10690	+	1.91720i
$870$		0			0
$871$	−26.4024	+	45.7303i	−0.894611	+	1.54951i
$872$		0			0
$873$	−14.0720	+	41.2301i	−0.476264	+	1.39543i
$874$		0			0
$875$	−1.19997	+	32.1406i	−0.0405664	+	1.08655i
$876$		0			0
$877$	6.94971	+	12.0373i	0.234675	+	0.406469i	0.959178	−	0.282802i	$-0.0912641\pi$
$877$	6.94971	+	12.0373i	0.234675	+	0.406469i	−0.724503	+	0.689271i	$0.757931\pi$
$878$		0			0
$879$	10.0549	+	1.66862i	0.339142	+	0.0562812i
$880$		0			0
$881$		−	18.1825i		−	0.612583i	−0.951938	−	0.306292i	$-0.900912\pi$
$881$		−	18.1825i		−	0.612583i	0.951938	−	0.306292i	$-0.0990882\pi$
$882$		0			0
$883$		−	8.80976i		−	0.296472i	−0.988952	−	0.148236i	$-0.952640\pi$
$883$		−	8.80976i		−	0.296472i	0.988952	−	0.148236i	$-0.0473595\pi$
$884$		0			0
$885$	−18.0334	+	21.9367i	−0.606186	+	0.737394i
$886$		0			0
$887$	−21.8229	−	37.7984i	−0.732742	−	1.26915i	−0.955707	−	0.294320i	$-0.904907\pi$
$887$	−21.8229	−	37.7984i	−0.732742	−	1.26915i	0.222964	−	0.974827i	$-0.428427\pi$
$888$		0			0
$889$	0.330195	−	8.84412i	0.0110744	−	0.296622i
$890$		0			0
$891$	−33.9273	+	43.9129i	−1.13661	+	1.47114i
$892$		0			0
$893$	−0.438077	+	0.758772i	−0.0146597	+	0.0253913i
$894$		0			0
$895$	13.3197	−	23.0703i	0.445227	−	0.771156i
$896$		0			0
$897$	5.60055	−	2.10260i	0.186997	−	0.0702038i
$898$		0			0
$899$	11.7330	+	20.3222i	0.391317	+	0.677782i
$900$		0			0
$901$	−8.84577	−	5.10711i	−0.294695	−	0.170142i
$902$		0			0
$903$	−3.77346	+	4.25604i	−0.125573	+	0.141632i
$904$		0			0
$905$	21.9922	+	38.0917i	0.731047	+	1.26621i
$906$		0			0
$907$	−0.424560	−	0.245120i	−0.0140973	−	0.00813907i	0.492935	−	0.870066i	$-0.335924\pi$
$907$	−0.424560	−	0.245120i	−0.0140973	−	0.00813907i	−0.507032	+	0.861927i	$0.669257\pi$
$908$		0			0
$909$	38.1080	−	7.51453i	1.26396	−	0.249241i
$910$		0			0
$911$	27.7336	−	16.0120i	0.918857	−	0.530502i	0.0355865	−	0.999367i	$-0.488670\pi$
$911$	27.7336	−	16.0120i	0.918857	−	0.530502i	0.883270	+	0.468864i	$0.155337\pi$
$912$		0			0
$913$			50.0740i			1.65721i
$914$		0			0
$915$	15.0169	+	12.3449i	0.496445	+	0.408111i
$916$		0			0
$917$	−3.77203	−	7.13561i	−0.124563	−	0.235639i
$918$		0			0
$919$	37.3319	+	21.5536i	1.23146	+	0.710986i	0.967335	−	0.253501i	$-0.0815821\pi$
$919$	37.3319	+	21.5536i	1.23146	+	0.710986i	0.264129	+	0.964487i	$0.414915\pi$
$920$		0			0
$921$	−8.00677	+	3.00596i	−0.263832	+	0.0990498i
$922$		0			0
$923$	−29.6312	+	51.3228i	−0.975323	+	1.68931i
$924$		0			0
$925$	2.03437	+	3.52363i	0.0668896	+	0.115856i
$926$		0			0
$927$	35.4643	+	12.1041i	1.16480	+	0.397550i
$928$		0			0
$929$		−	26.4825i		−	0.868863i	−0.900705	−	0.434432i	$-0.856949\pi$
$929$		−	26.4825i		−	0.868863i	0.900705	−	0.434432i	$-0.143051\pi$
$930$		0			0
$931$	−7.37637	+	10.8230i	−0.241751	+	0.354709i
$932$		0			0
$933$	25.4680	−	9.56138i	0.833784	−	0.313026i
$934$		0			0
$935$	−51.3412	+	29.6419i	−1.67904	+	0.969393i
$936$		0			0
$937$		−	42.2140i		−	1.37907i	−0.724252	−	0.689535i	$-0.757815\pi$
$937$		−	42.2140i		−	1.37907i	0.724252	−	0.689535i	$-0.242185\pi$
$938$		0			0
$939$	20.6567	+	55.0217i	0.674105	+	1.79557i
$940$		0			0
$941$			32.9583i			1.07441i	0.843452	+	0.537204i	$0.180520\pi$
$941$			32.9583i			1.07441i	−0.843452	+	0.537204i	$0.819480\pi$
$942$		0			0
$943$	−4.98515			−0.162339
$944$		0			0
$945$	−0.172525	+	24.3730i	−0.00561225	+	0.792854i
$946$		0			0
$947$			47.1913i			1.53351i	0.641939	+	0.766755i	$0.278130\pi$
$947$			47.1913i			1.53351i	−0.641939	+	0.766755i	$0.721870\pi$
$948$		0			0
$949$	29.3139			0.951569
$950$		0			0
$951$	−26.6871	+	10.0191i	−0.865387	+	0.324890i
$952$		0			0
$953$	−51.1369			−1.65649			−0.828244	−	0.560368i	$-0.810660\pi$
$953$	−51.1369			−1.65649			−0.828244	+	0.560368i	$0.810660\pi$
$954$		0			0
$955$	−22.3756	−	38.7556i	−0.724057	−	1.25410i
$956$		0			0
$957$	−8.62373	−	22.9704i	−0.278766	−	0.742528i
$958$		0			0
$959$	18.5429	−	29.5163i	0.598783	−	0.953132i
$960$		0			0
$961$	73.3225			2.36524
$962$		0			0
$963$	30.5920	−	6.03243i	0.985812	−	0.194392i
$964$		0			0
$965$	−23.2767	+	13.4388i	−0.749303	+	0.432610i
$966$		0			0
$967$	8.10631	+	4.68018i	0.260681	+	0.150504i	0.624645	−	0.780909i	$-0.285244\pi$
$967$	8.10631	+	4.68018i	0.260681	+	0.150504i	−0.363964	+	0.931413i	$0.618577\pi$
$968$		0			0
$969$	−6.17738	−	16.4543i	−0.198446	−	0.528587i
$970$		0			0
$971$	11.1378	−	19.2913i	0.357429	−	0.619086i	−0.630101	−	0.776513i	$-0.716987\pi$
$971$	11.1378	−	19.2913i	0.357429	−	0.619086i	0.987531	+	0.157427i	$0.0503200\pi$
$972$		0			0
$973$	−16.2774	+	25.9101i	−0.521830	+	0.830639i
$974$		0			0
$975$	−10.8550	+	13.2045i	−0.347638	+	0.422883i
$976$		0			0
$977$	−57.7424			−1.84734			−0.923671	−	0.383186i	$-0.874827\pi$
$977$	−57.7424			−1.84734			−0.923671	+	0.383186i	$0.874827\pi$
$978$		0			0
$979$	0.814043	+	1.40996i	0.0260169	+	0.0450627i
$980$		0			0
$981$	7.63452	+	2.60569i	0.243752	+	0.0831932i
$982$		0			0
$983$	0.946409	−	1.63923i	0.0301858	−	0.0522833i	−0.850538	−	0.525914i	$-0.823723\pi$
$983$	0.946409	−	1.63923i	0.0301858	−	0.0522833i	0.880724	+	0.473631i	$0.157057\pi$
$984$		0			0
$985$	−2.90548	+	1.67748i	−0.0925763	+	0.0534490i
$986$		0			0
$987$	−2.03566	+	0.678729i	−0.0647959	+	0.0216042i
$988$		0			0
$989$	0.403276	−	0.698494i	0.0128234	−	0.0222108i
$990$		0			0
$991$	−13.3910	+	7.73132i	−0.425380	+	0.245594i	−0.697377	−	0.716705i	$-0.745650\pi$
$991$	−13.3910	+	7.73132i	−0.425380	+	0.245594i	0.271996	+	0.962298i	$0.412316\pi$
$992$		0			0
$993$	−2.39095	−	6.36860i	−0.0758744	−	0.202101i
$994$		0			0
$995$	20.3617	+	11.7558i	0.645510	+	0.372685i
$996$		0			0
$997$	7.70115	+	4.44626i	0.243898	+	0.140815i	0.616967	−	0.786989i	$-0.288361\pi$
$997$	7.70115	+	4.44626i	0.243898	+	0.140815i	−0.373069	+	0.927804i	$0.621695\pi$
$998$		0			0
$999$	5.98874	+	9.68427i	0.189475	+	0.306397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.607.2	yes	24
3.2	odd	2		3024.2.cz.h.1279.5		24
4.3	odd	2		1008.2.cz.h.607.11	yes	24
7.3	odd	6		1008.2.bf.g.31.4	✓	24
9.2	odd	6		3024.2.bf.g.2287.5		24
9.7	even	3		1008.2.bf.h.943.9	yes	24
12.11	even	2		3024.2.cz.g.1279.5		24
21.17	even	6		3024.2.bf.h.1711.8		24
28.3	even	6		1008.2.bf.h.31.9	yes	24
36.7	odd	6		1008.2.bf.g.943.4	yes	24
36.11	even	6		3024.2.bf.h.2287.5		24
63.38	even	6		3024.2.cz.g.2719.5		24
63.52	odd	6		1008.2.cz.h.367.11	yes	24
84.59	odd	6		3024.2.bf.g.1711.8		24
252.115	even	6	inner	1008.2.cz.g.367.2	yes	24
252.227	odd	6		3024.2.cz.h.2719.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.4	✓	24	7.3	odd	6
1008.2.bf.g.943.4	yes	24	36.7	odd	6
1008.2.bf.h.31.9	yes	24	28.3	even	6
1008.2.bf.h.943.9	yes	24	9.7	even	3
1008.2.cz.g.367.2	yes	24	252.115	even	6	inner
1008.2.cz.g.607.2	yes	24	1.1	even	1	trivial
1008.2.cz.h.367.11	yes	24	63.52	odd	6
1008.2.cz.h.607.11	yes	24	4.3	odd	2
3024.2.bf.g.1711.8		24	84.59	odd	6
3024.2.bf.g.2287.5		24	9.2	odd	6
3024.2.bf.h.1711.8		24	21.17	even	6
3024.2.bf.h.2287.5		24	36.11	even	6
3024.2.cz.g.1279.5		24	12.11	even	2
3024.2.cz.g.2719.5		24	63.38	even	6
3024.2.cz.h.1279.5		24	3.2	odd	2
3024.2.cz.h.2719.5		24	252.227	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62154 + 0.608772i) q^{3} +(1.53539 - 0.886460i) q^{5} +(2.64391 + 0.0987102i) q^{7} +(2.25879 - 1.97430i) q^{9} +O(q^{10})\)	\(q+(-1.62154 + 0.608772i) q^{3} +(1.53539 - 0.886460i) q^{5} +(2.64391 + 0.0987102i) q^{7} +(2.25879 - 1.97430i) q^{9} +(-5.33976 - 3.08291i) q^{11} +(-4.60307 - 2.65758i) q^{13} +(-1.95005 + 2.37214i) q^{15} +(4.69663 - 2.71160i) q^{17} +(-0.935544 + 1.62041i) q^{19} +(-4.34730 + 1.44947i) q^{21} +(0.562751 - 0.324904i) q^{23} +(-0.928378 + 1.60800i) q^{25} +(-2.46083 + 4.57649i) q^{27} +(-1.14874 - 1.98967i) q^{29} -10.2138 q^{31} +(10.5354 + 1.74837i) q^{33} +(4.14694 - 2.19216i) q^{35} +(1.09566 - 1.89773i) q^{37} +(9.08193 + 1.50716i) q^{39} +(-6.64391 - 3.83586i) q^{41} +(1.07492 - 0.620607i) q^{43} +(1.71800 - 5.03365i) q^{45} +0.468259 q^{47} +(6.98051 + 0.521962i) q^{49} +(-5.96504 + 7.25615i) q^{51} +(-0.941715 - 1.63110i) q^{53} -10.9315 q^{55} +(0.530564 - 3.19709i) q^{57} +9.24765 q^{59} -6.33056i q^{61} +(6.16693 - 4.99690i) q^{63} -9.42337 q^{65} -9.93473i q^{67} +(-0.714731 + 0.869433i) q^{69} -11.1497i q^{71} +(-4.77625 + 2.75757i) q^{73} +(0.526500 - 3.17261i) q^{75} +(-13.8135 - 8.67802i) q^{77} -10.5842i q^{79} +(1.20430 - 8.91906i) q^{81} +(-4.06061 - 7.03319i) q^{83} +(4.80745 - 8.32675i) q^{85} +(3.07398 + 2.52701i) q^{87} +(-0.228674 - 0.132025i) q^{89} +(-11.9078 - 7.48078i) q^{91} +(16.5622 - 6.21790i) q^{93} +3.31729i q^{95} +(-12.5762 + 7.26089i) q^{97} +(-18.1480 + 3.57861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

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