LMFDB - Embedded newform 504.2.t.c.457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Character	$\chi$	$=$	504.457
Dual form			504.2.t.c.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72692 - 0.133195i) q^{3} -4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} +(2.96452 + 0.460034i) q^{9} +O(q^{10})$	\(q+(-1.72692 - 0.133195i) q^{3} -4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} +(2.96452 + 0.460034i) q^{9} +1.92915 q^{11} +(-0.291529 - 0.504943i) q^{13} +(7.29273 + 0.562477i) q^{15} +(3.61082 + 6.25412i) q^{17} +(2.10268 - 3.64194i) q^{19} +(3.95219 + 2.31953i) q^{21} +1.27988 q^{23} +12.8334 q^{25} +(-5.05822 - 1.18930i) q^{27} +(-4.20305 + 7.27990i) q^{29} +(0.476061 - 0.824561i) q^{31} +(-3.33149 - 0.256953i) q^{33} +(10.0423 + 4.89755i) q^{35} +(3.03329 - 5.25381i) q^{37} +(0.436192 + 0.910828i) q^{39} +(1.31299 + 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} +(-12.5191 - 1.94271i) q^{45} +(-2.88201 - 4.99178i) q^{47} +(4.30999 + 5.51579i) q^{49} +(-5.40259 - 11.2813i) q^{51} +(-0.962456 - 1.66702i) q^{53} -8.14673 q^{55} +(-4.11625 + 6.00929i) q^{57} +(2.27614 - 3.94240i) q^{59} +(5.29008 + 9.16268i) q^{61} +(-6.51617 - 4.53205i) q^{63} +(1.23112 + 2.13236i) q^{65} +(2.43191 - 4.21220i) q^{67} +(-2.21025 - 0.170473i) q^{69} +11.5443 q^{71} +(0.446138 + 0.772734i) q^{73} +(-22.1623 - 1.70934i) q^{75} +(-4.58756 - 2.23732i) q^{77} +(5.93520 + 10.2801i) q^{79} +(8.57674 + 2.72756i) q^{81} +(-5.24250 + 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(8.22798 - 12.0120i) q^{87} +(3.87906 - 6.71874i) q^{89} +(0.107659 + 1.53887i) q^{91} +(-0.931947 + 1.36054i) q^{93} +(-8.87953 + 15.3798i) q^{95} +(-1.98651 + 3.44073i) q^{97} +(5.71900 + 0.887474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.72692	−	0.133195i	−0.997039	−	0.0769000i
$3$	−1.72692	−	0.133195i	−0.997039	−	0.0769000i
$4$		0			0
$5$	−4.22296			−1.88857			−0.944283	−	0.329134i	$-0.893243\pi$
$5$	−4.22296			−1.88857			−0.944283	+	0.329134i	$0.893243\pi$
$6$		0			0
$7$	−2.37802	−	1.15974i	−0.898809	−	0.438341i
$7$	−2.37802	−	1.15974i	−0.898809	−	0.438341i
$8$		0			0
$9$	2.96452	+	0.460034i	0.988173	+	0.153345i
$10$		0			0
$11$	1.92915			0.581660			0.290830	−	0.956775i	$-0.406069\pi$
$11$	1.92915			0.581660			0.290830	+	0.956775i	$0.406069\pi$
$12$		0			0
$13$	−0.291529	−	0.504943i	−0.0808557	−	0.140046i	0.822762	−	0.568386i	$-0.192432\pi$
$13$	−0.291529	−	0.504943i	−0.0808557	−	0.140046i	−0.903618	+	0.428340i	$0.859099\pi$
$14$		0			0
$15$	7.29273	+	0.562477i	1.88297	+	0.145231i
$16$		0			0
$17$	3.61082	+	6.25412i	0.875753	+	1.51685i	0.855959	+	0.517044i	$0.172968\pi$
$17$	3.61082	+	6.25412i	0.875753	+	1.51685i	0.0197936	+	0.999804i	$0.493699\pi$
$18$		0			0
$19$	2.10268	−	3.64194i	0.482387	−	0.835519i	−0.517408	−	0.855739i	$-0.673103\pi$
$19$	2.10268	−	3.64194i	0.482387	−	0.835519i	0.999796	+	0.0202194i	$0.00643646\pi$
$20$		0			0
$21$	3.95219	+	2.31953i	0.862438	+	0.506162i
$22$		0			0
$23$	1.27988			0.266873			0.133437	−	0.991057i	$-0.457399\pi$
$23$	1.27988			0.266873			0.133437	+	0.991057i	$0.457399\pi$
$24$		0			0
$25$	12.8334			2.56668
$26$		0			0
$27$	−5.05822	−	1.18930i	−0.973454	−	0.228881i
$28$		0			0
$29$	−4.20305	+	7.27990i	−0.780487	+	1.35184i	0.151171	+	0.988508i	$0.451695\pi$
$29$	−4.20305	+	7.27990i	−0.780487	+	1.35184i	−0.931658	+	0.363335i	$0.881638\pi$
$30$		0			0
$31$	0.476061	−	0.824561i	0.0855030	−	0.148096i	−0.820102	−	0.572217i	$-0.806084\pi$
$31$	0.476061	−	0.824561i	0.0855030	−	0.148096i	0.905605	+	0.424121i	$0.139417\pi$
$32$		0			0
$33$	−3.33149	−	0.256953i	−0.579938	−	0.0447297i
$34$		0			0
$35$	10.0423	+	4.89755i	1.69746	+	0.827837i
$36$		0			0
$37$	3.03329	−	5.25381i	0.498669	−	0.863721i	−0.501330	−	0.865256i	$-0.667156\pi$
$37$	3.03329	−	5.25381i	0.498669	−	0.863721i	0.999999	+	0.00153588i	$0.000488885\pi$
$38$		0			0
$39$	0.436192	+	0.910828i	0.0698467	+	0.145849i
$40$		0			0
$41$	1.31299	+	2.27416i	0.205054	+	0.355164i	0.950150	−	0.311794i	$-0.100930\pi$
$41$	1.31299	+	2.27416i	0.205054	+	0.355164i	−0.745096	+	0.666957i	$0.767596\pi$
$42$		0			0
$43$	0.442349	−	0.766171i	0.0674576	−	0.116840i	−0.830324	−	0.557281i	$-0.811845\pi$
$43$	0.442349	−	0.766171i	0.0674576	−	0.116840i	0.897782	+	0.440441i	$0.145178\pi$
$44$		0			0
$45$	−12.5191	−	1.94271i	−1.86623	−	0.289602i
$46$		0			0
$47$	−2.88201	−	4.99178i	−0.420384	−	0.728126i	0.575593	−	0.817736i	$-0.304771\pi$
$47$	−2.88201	−	4.99178i	−0.420384	−	0.728126i	−0.995977	+	0.0896103i	$0.971438\pi$
$48$		0			0
$49$	4.30999	+	5.51579i	0.615713	+	0.787970i
$50$		0			0
$51$	−5.40259	−	11.2813i	−0.756514	−	1.57970i
$52$		0			0
$53$	−0.962456	−	1.66702i	−0.132204	−	0.228983i	0.792322	−	0.610103i	$-0.208872\pi$
$53$	−0.962456	−	1.66702i	−0.132204	−	0.228983i	−0.924526	+	0.381120i	$0.875539\pi$
$54$		0			0
$55$	−8.14673			−1.09850
$56$		0			0
$57$	−4.11625	+	6.00929i	−0.545210	+	0.795950i
$58$		0			0
$59$	2.27614	−	3.94240i	0.296329	−	0.513256i	−0.678964	−	0.734171i	$-0.737571\pi$
$59$	2.27614	−	3.94240i	0.296329	−	0.513256i	0.975293	+	0.220915i	$0.0709043\pi$
$60$		0			0
$61$	5.29008	+	9.16268i	0.677325	+	1.17316i	0.975783	+	0.218739i	$0.0701943\pi$
$61$	5.29008	+	9.16268i	0.677325	+	1.17316i	−0.298458	+	0.954423i	$0.596472\pi$
$62$		0			0
$63$	−6.51617	−	4.53205i	−0.820961	−	0.570985i
$64$		0			0
$65$	1.23112	+	2.13236i	0.152701	+	0.264486i
$66$		0			0
$67$	2.43191	−	4.21220i	0.297106	−	0.514602i	−0.678367	−	0.734723i	$-0.737312\pi$
$67$	2.43191	−	4.21220i	0.297106	−	0.514602i	0.975473	+	0.220121i	$0.0706453\pi$
$68$		0			0
$69$	−2.21025	−	0.170473i	−0.266083	−	0.0205226i
$70$		0			0
$71$	11.5443			1.37005			0.685027	−	0.728518i	$-0.259791\pi$
$71$	11.5443			1.37005			0.685027	+	0.728518i	$0.259791\pi$
$72$		0			0
$73$	0.446138	+	0.772734i	0.0522165	+	0.0904417i	0.890952	−	0.454097i	$-0.150038\pi$
$73$	0.446138	+	0.772734i	0.0522165	+	0.0904417i	−0.838736	+	0.544539i	$0.816705\pi$
$74$		0			0
$75$	−22.1623	−	1.70934i	−2.55908	−	0.197378i
$76$		0			0
$77$	−4.58756	−	2.23732i	−0.522801	−	0.254966i
$78$		0			0
$79$	5.93520	+	10.2801i	0.667763	+	1.15660i	0.978528	+	0.206112i	$0.0660812\pi$
$79$	5.93520	+	10.2801i	0.667763	+	1.15660i	−0.310766	+	0.950487i	$0.600585\pi$
$80$		0			0
$81$	8.57674	+	2.72756i	0.952971	+	0.303062i
$82$		0			0
$83$	−5.24250	+	9.08028i	−0.575439	+	0.996690i	0.420555	+	0.907267i	$0.361836\pi$
$83$	−5.24250	+	9.08028i	−0.575439	+	0.996690i	−0.995994	+	0.0894227i	$0.971498\pi$
$84$		0			0
$85$	−15.2484	−	26.4109i	−1.65392	−	2.86467i
$86$		0			0
$87$	8.22798	−	12.0120i	0.882133	−	1.28782i
$88$		0			0
$89$	3.87906	−	6.71874i	0.411180	−	0.712185i	−0.583839	−	0.811869i	$-0.698450\pi$
$89$	3.87906	−	6.71874i	0.411180	−	0.712185i	0.995019	+	0.0996849i	$0.0317835\pi$
$90$		0			0
$91$	0.107659	+	1.53887i	0.0112857	+	0.161317i
$92$		0			0
$93$	−0.931947	+	1.36054i	−0.0966384	+	0.141082i
$94$		0			0
$95$	−8.87953	+	15.3798i	−0.911020	+	1.57793i
$96$		0			0
$97$	−1.98651	+	3.44073i	−0.201699	+	0.349353i	−0.949076	−	0.315047i	$-0.897980\pi$
$97$	−1.98651	+	3.44073i	−0.201699	+	0.349353i	0.747377	+	0.664400i	$0.231313\pi$
$98$		0			0
$99$	5.71900	+	0.887474i	0.574781	+	0.0891945i
$100$		0			0
$101$	16.7707			1.66874			0.834372	−	0.551202i	$-0.185831\pi$
$101$	16.7707			1.66874			0.834372	+	0.551202i	$0.185831\pi$
$102$		0			0
$103$	11.6114			1.14410			0.572052	−	0.820218i	$-0.306148\pi$
$103$	11.6114			1.14410			0.572052	+	0.820218i	$0.306148\pi$
$104$		0			0
$105$	−16.6900	−	9.79527i	−1.62877	−	0.955920i
$106$		0			0
$107$	−10.2454	+	17.7455i	−0.990460	+	1.71553i	−0.375890	+	0.926664i	$0.622663\pi$
$107$	−10.2454	+	17.7455i	−0.990460	+	1.71553i	−0.614570	+	0.788862i	$0.710671\pi$
$108$		0			0
$109$	2.46965	+	4.27756i	0.236550	+	0.409716i	0.959722	−	0.280951i	$-0.0906500\pi$
$109$	2.46965	+	4.27756i	0.236550	+	0.409716i	−0.723172	+	0.690668i	$0.757317\pi$
$110$		0			0
$111$	−5.93803	+	8.66890i	−0.563613	+	0.822815i
$112$		0			0
$113$	−7.42131	−	12.8541i	−0.698138	−	1.20921i	−0.969111	−	0.246623i	$-0.920679\pi$
$113$	−7.42131	−	12.8541i	−0.698138	−	1.20921i	0.270974	−	0.962587i	$-0.412654\pi$
$114$		0			0
$115$	−5.40488			−0.504008
$116$		0			0
$117$	−0.631953	−	1.63103i	−0.0584240	−	0.150789i
$118$		0			0
$119$	−1.33344	−	19.0601i	−0.122236	−	1.74723i
$120$		0			0
$121$	−7.27838			−0.661671
$122$		0			0
$123$	−1.96452	−	4.10217i	−0.177135	−	0.369881i
$124$		0			0
$125$	−33.0802			−2.95879
$126$		0			0
$127$	−8.53648			−0.757490			−0.378745	−	0.925501i	$-0.623644\pi$
$127$	−8.53648			−0.757490			−0.378745	+	0.925501i	$0.623644\pi$
$128$		0			0
$129$	−0.865953	+	1.26420i	−0.0762429	+	0.111307i
$130$		0			0
$131$	−2.34684			−0.205045			−0.102522	−	0.994731i	$-0.532691\pi$
$131$	−2.34684			−0.205045			−0.102522	+	0.994731i	$0.532691\pi$
$132$		0			0
$133$	−9.22393	+	6.22207i	−0.799817	+	0.539522i
$134$		0			0
$135$	21.3607	+	5.02237i	1.83843	+	0.432257i
$136$		0			0
$137$	1.28363			0.109668			0.0548340	−	0.998495i	$-0.482537\pi$
$137$	1.28363			0.109668			0.0548340	+	0.998495i	$0.482537\pi$
$138$		0			0
$139$	0.610553	+	1.05751i	0.0517865	+	0.0896968i	0.890757	−	0.454481i	$-0.150175\pi$
$139$	0.610553	+	1.05751i	0.0517865	+	0.0896968i	−0.838970	+	0.544177i	$0.816842\pi$
$140$		0			0
$141$	4.31212	+	9.00428i	0.363146	+	0.758297i
$142$		0			0
$143$	−0.562403	−	0.974111i	−0.0470305	−	0.0814593i
$144$		0			0
$145$	17.7493	−	30.7427i	1.47400	−	2.55305i
$146$		0			0
$147$	−6.70835	−	10.0994i	−0.553295	−	0.832985i
$148$		0			0
$149$	6.29459			0.515673			0.257836	−	0.966189i	$-0.416990\pi$
$149$	6.29459			0.515673			0.257836	+	0.966189i	$0.416990\pi$
$150$		0			0
$151$	2.35453			0.191609			0.0958044	−	0.995400i	$-0.469458\pi$
$151$	2.35453			0.191609			0.0958044	+	0.995400i	$0.469458\pi$
$152$		0			0
$153$	7.82723	+	20.2016i	0.632794	+	1.63320i
$154$		0			0
$155$	−2.01039	+	3.48209i	−0.161478	+	0.279688i
$156$		0			0
$157$	1.44437	−	2.50172i	0.115273	−	0.199659i	−0.802616	−	0.596496i	$-0.796559\pi$
$157$	1.44437	−	2.50172i	0.115273	−	0.199659i	0.917889	+	0.396838i	$0.129892\pi$
$158$		0			0
$159$	1.44005	+	3.00701i	0.114203	+	0.238472i
$160$		0			0
$161$	−3.04358	−	1.48433i	−0.239868	−	0.116982i
$162$		0			0
$163$	2.60538	−	4.51265i	0.204069	−	0.353458i	−0.745767	−	0.666207i	$-0.767917\pi$
$163$	2.60538	−	4.51265i	0.204069	−	0.353458i	0.949836	+	0.312749i	$0.101250\pi$
$164$		0			0
$165$	14.0688	+	1.08510i	1.09525	+	0.0844750i
$166$		0			0
$167$	10.5400	+	18.2558i	0.815610	+	1.41268i	0.908889	+	0.417039i	$0.136932\pi$
$167$	10.5400	+	18.2558i	0.815610	+	1.41268i	−0.0932784	+	0.995640i	$0.529735\pi$
$168$		0			0
$169$	6.33002	−	10.9639i	0.486925	−	0.843378i
$170$		0			0
$171$	7.90884	−	9.82931i	0.604804	−	0.751666i
$172$		0			0
$173$	2.03653	+	3.52737i	0.154834	+	0.268181i	0.932999	−	0.359880i	$-0.117182\pi$
$173$	2.03653	+	3.52737i	0.154834	+	0.268181i	−0.778164	+	0.628061i	$0.783849\pi$
$174$		0			0
$175$	−30.5182	−	14.8835i	−2.30696	−	1.12508i
$176$		0			0
$177$	−4.45583	+	6.50504i	−0.334921	+	0.488949i
$178$		0			0
$179$	−3.11088	−	5.38821i	−0.232518	−	0.402733i	0.726030	−	0.687663i	$-0.241363\pi$
$179$	−3.11088	−	5.38821i	−0.232518	−	0.402733i	−0.958549	+	0.284929i	$0.908030\pi$
$180$		0			0
$181$	18.2396			1.35574			0.677868	−	0.735184i	$-0.262904\pi$
$181$	18.2396			1.35574			0.677868	+	0.735184i	$0.262904\pi$
$182$		0			0
$183$	−7.91513	−	16.5279i	−0.585103	−	1.22177i
$184$		0			0
$185$	−12.8095	+	22.1866i	−0.941770	+	1.63119i
$186$		0			0
$187$	6.96581	+	12.0651i	0.509391	+	0.882290i
$188$		0			0
$189$	10.6493	+	8.69442i	0.774621	+	0.632426i
$190$		0			0
$191$	3.69298	+	6.39644i	0.267215	+	0.462830i	0.968142	−	0.250404i	$-0.0805633\pi$
$191$	3.69298	+	6.39644i	0.267215	+	0.462830i	−0.700927	+	0.713233i	$0.747230\pi$
$192$		0			0
$193$	−9.75908	+	16.9032i	−0.702474	+	1.21672i	0.265121	+	0.964215i	$0.414588\pi$
$193$	−9.75908	+	16.9032i	−0.702474	+	1.21672i	−0.967595	+	0.252506i	$0.918745\pi$
$194$		0			0
$195$	−1.84202	−	3.84639i	−0.131910	−	0.275446i
$196$		0			0
$197$	7.77564			0.553992			0.276996	−	0.960871i	$-0.410661\pi$
$197$	7.77564			0.553992			0.276996	+	0.960871i	$0.410661\pi$
$198$		0			0
$199$	−3.85734	−	6.68110i	−0.273439	−	0.473611i	0.696301	−	0.717750i	$-0.254828\pi$
$199$	−3.85734	−	6.68110i	−0.273439	−	0.473611i	−0.969740	+	0.244139i	$0.921495\pi$
$200$		0			0
$201$	−4.76077	+	6.95022i	−0.335799	+	0.490231i
$202$		0			0
$203$	18.4378	−	12.4373i	1.29408	−	0.872928i
$204$		0			0
$205$	−5.54469	−	9.60368i	−0.387258	−	0.670750i
$206$		0			0
$207$	3.79422	+	0.588788i	0.263717	+	0.0409236i
$208$		0			0
$209$	4.05638	−	7.02585i	0.280586	−	0.485989i
$210$		0			0
$211$	11.7645	+	20.3767i	0.809899	+	1.40279i	0.912933	+	0.408109i	$0.133812\pi$
$211$	11.7645	+	20.3767i	0.809899	+	1.40279i	−0.103034	+	0.994678i	$0.532855\pi$
$212$		0			0
$213$	−19.9361	−	1.53764i	−1.36600	−	0.105357i
$214$		0			0
$215$	−1.86802	+	3.23551i	−0.127398	+	0.220660i
$216$		0			0
$217$	−2.08836	+	1.40872i	−0.141767	+	0.0956301i
$218$		0			0
$219$	−0.667522	−	1.39387i	−0.0451069	−	0.0941893i
$220$		0			0
$221$	2.10532	−	3.64652i	0.141619	−	0.245291i
$222$		0			0
$223$	−4.83093	+	8.36742i	−0.323503	+	0.560324i	−0.981208	−	0.192952i	$-0.938194\pi$
$223$	−4.83093	+	8.36742i	−0.323503	+	0.560324i	0.657705	+	0.753275i	$0.271527\pi$
$224$		0			0
$225$	38.0449	+	5.90381i	2.53633	+	0.393587i
$226$		0			0
$227$	17.9718			1.19283			0.596417	−	0.802675i	$-0.296591\pi$
$227$	17.9718			1.19283			0.596417	+	0.802675i	$0.296591\pi$
$228$		0			0
$229$	−7.91668			−0.523149			−0.261574	−	0.965183i	$-0.584242\pi$
$229$	−7.91668			−0.523149			−0.261574	+	0.965183i	$0.584242\pi$
$230$		0			0
$231$	7.62436	+	4.47471i	0.501646	+	0.294414i
$232$		0			0
$233$	3.27796	−	5.67759i	0.214746	−	0.371951i	−0.738448	−	0.674311i	$-0.764441\pi$
$233$	3.27796	−	5.67759i	0.214746	−	0.371951i	0.953194	+	0.302359i	$0.0977742\pi$
$234$		0			0
$235$	12.1706	+	21.0801i	0.793922	+	1.37511i
$236$		0			0
$237$	−8.88038	−	18.5434i	−0.576843	−	1.20452i
$238$		0			0
$239$	−8.01922	−	13.8897i	−0.518720	−	0.898450i	−0.999763	−	0.0217529i	$-0.993075\pi$
$239$	−8.01922	−	13.8897i	−0.518720	−	0.898450i	0.481043	−	0.876697i	$-0.340258\pi$
$240$		0			0
$241$	11.1791			0.720112			0.360056	−	0.932931i	$-0.382758\pi$
$241$	11.1791			0.720112			0.360056	+	0.932931i	$0.382758\pi$
$242$		0			0
$243$	−14.4481	−	5.85266i	−0.926843	−	0.375448i
$244$		0			0
$245$	−18.2009	−	23.2930i	−1.16282	−	1.48813i
$246$		0			0
$247$	−2.45197			−0.156015
$248$		0			0
$249$	10.2628	−	14.9827i	0.650381	−	0.949487i
$250$		0			0
$251$	14.6169			0.922613			0.461307	−	0.887241i	$-0.347381\pi$
$251$	14.6169			0.922613			0.461307	+	0.887241i	$0.347381\pi$
$252$		0			0
$253$	2.46908			0.155230
$254$		0			0
$255$	22.8149	+	47.6406i	1.42873	+	2.98337i
$256$		0			0
$257$	14.9187			0.930605			0.465302	−	0.885152i	$-0.345946\pi$
$257$	14.9187			0.930605			0.465302	+	0.885152i	$0.345946\pi$
$258$		0			0
$259$	−13.3063	+	8.97585i	−0.826813	+	0.557732i
$260$		0			0
$261$	−15.8090	+	19.6478i	−0.978554	+	1.21617i
$262$		0			0
$263$	−22.2114			−1.36962			−0.684808	−	0.728724i	$-0.740114\pi$
$263$	−22.2114			−1.36962			−0.684808	+	0.728724i	$0.740114\pi$
$264$		0			0
$265$	4.06442	+	7.03978i	0.249675	+	0.432450i
$266$		0			0
$267$	−7.59374	+	11.0861i	−0.464729	+	0.678456i
$268$		0			0
$269$	−4.73590	−	8.20281i	−0.288753	−	0.500134i	0.684760	−	0.728769i	$-0.259907\pi$
$269$	−4.73590	−	8.20281i	−0.288753	−	0.500134i	−0.973512	+	0.228635i	$0.926574\pi$
$270$		0			0
$271$	8.78188	−	15.2107i	0.533461	−	0.923982i	−0.465775	−	0.884903i	$-0.654224\pi$
$271$	8.78188	−	15.2107i	0.533461	−	0.923982i	0.999236	−	0.0390786i	$-0.0124423\pi$
$272$		0			0
$273$	0.0190502	−	2.67184i	0.00115297	−	0.161707i
$274$		0			0
$275$	24.7576			1.49294
$276$		0			0
$277$	13.5530			0.814322			0.407161	−	0.913356i	$-0.366519\pi$
$277$	13.5530			0.814322			0.407161	+	0.913356i	$0.366519\pi$
$278$		0			0
$279$	1.79062	−	2.22542i	0.107201	−	0.133233i
$280$		0			0
$281$	6.14196	−	10.6382i	0.366398	−	0.634621i	−0.622601	−	0.782539i	$-0.713924\pi$
$281$	6.14196	−	10.6382i	0.366398	−	0.634621i	0.989000	+	0.147919i	$0.0472574\pi$
$282$		0			0
$283$	−7.02415	+	12.1662i	−0.417542	+	0.723204i	−0.995692	−	0.0927267i	$-0.970442\pi$
$283$	−7.02415	+	12.1662i	−0.417542	+	0.723204i	0.578149	+	0.815931i	$0.303775\pi$
$284$		0			0
$285$	17.3828	−	25.3770i	1.02967	−	1.50320i
$286$		0			0
$287$	−0.484873	−	6.93072i	−0.0286212	−	0.409108i
$288$		0			0
$289$	−17.5760	+	30.4426i	−1.03388	+	1.79074i
$290$		0			0
$291$	3.88883	−	5.67728i	0.227967	−	0.332808i
$292$		0			0
$293$	4.05863	+	7.02975i	0.237108	+	0.410682i	0.959883	−	0.280401i	$-0.0904673\pi$
$293$	4.05863	+	7.02975i	0.237108	+	0.410682i	−0.722776	+	0.691083i	$0.757134\pi$
$294$		0			0
$295$	−9.61207	+	16.6486i	−0.559636	+	0.969319i
$296$		0			0
$297$	−9.75806	−	2.29434i	−0.566220	−	0.133131i
$298$		0			0
$299$	−0.373122	−	0.646266i	−0.0215782	−	0.0373746i
$300$		0			0
$301$	−1.94048	+	1.30896i	−0.111847	+	0.0754473i
$302$		0			0
$303$	−28.9616	−	2.23377i	−1.66380	−	0.128326i
$304$		0			0
$305$	−22.3398	−	38.6937i	−1.27917	−	2.21559i
$306$		0			0
$307$	6.61556			0.377570			0.188785	−	0.982018i	$-0.439545\pi$
$307$	6.61556			0.377570			0.188785	+	0.982018i	$0.439545\pi$
$308$		0			0
$309$	−20.0519	−	1.54658i	−1.14072	−	0.0879816i
$310$		0			0
$311$	4.17980	−	7.23963i	0.237015	−	0.410522i	−0.722841	−	0.691014i	$-0.757164\pi$
$311$	4.17980	−	7.23963i	0.237015	−	0.410522i	0.959856	+	0.280492i	$0.0904976\pi$
$312$		0			0
$313$	−13.0542	−	22.6105i	−0.737864	−	1.27802i	−0.953455	−	0.301535i	$-0.902501\pi$
$313$	−13.0542	−	22.6105i	−0.737864	−	1.27802i	0.215591	−	0.976484i	$-0.430832\pi$
$314$		0			0
$315$	27.5176	+	19.1387i	1.55044	+	1.07834i
$316$		0			0
$317$	−5.60741	−	9.71231i	−0.314943	−	0.545498i	0.664482	−	0.747304i	$-0.268652\pi$
$317$	−5.60741	−	9.71231i	−0.314943	−	0.545498i	−0.979425	+	0.201806i	$0.935319\pi$
$318$		0			0
$319$	−8.10831	+	14.0440i	−0.453978	+	0.786314i
$320$		0			0
$321$	20.0566	−	29.2805i	1.11945	−	1.63428i
$322$		0			0
$323$	30.3696			1.68981
$324$		0			0
$325$	−3.74132	−	6.48015i	−0.207531	−	0.359454i
$326$		0			0
$327$	−3.69515	−	7.71597i	−0.204342	−	0.426694i
$328$		0			0
$329$	1.06430	+	15.2130i	0.0586766	+	0.838717i
$330$		0			0
$331$	9.11645	+	15.7902i	0.501086	+	0.867906i	0.999999	+	0.00125391i	$0.000399132\pi$
$331$	9.11645	+	15.7902i	0.501086	+	0.867906i	−0.498914	+	0.866652i	$0.666268\pi$
$332$		0			0
$333$	11.4092	−	14.1796i	0.625218	−	0.777037i
$334$		0			0
$335$	−10.2699	+	17.7880i	−0.561104	+	0.971860i
$336$		0			0
$337$	4.62148	+	8.00465i	0.251748	+	0.436041i	0.964007	−	0.265876i	$-0.0856612\pi$
$337$	4.62148	+	8.00465i	0.251748	+	0.436041i	−0.712259	+	0.701917i	$0.752328\pi$
$338$		0			0
$339$	11.1039	+	23.1865i	0.603082	+	1.25932i
$340$		0			0
$341$	0.918392	−	1.59070i	0.0497337	−	0.0861413i
$342$		0			0
$343$	−3.85237	−	18.1152i	−0.208009	−	0.978127i
$344$		0			0
$345$	9.33381	+	0.719902i	0.502515	+	0.0387582i
$346$		0			0
$347$	15.8325	−	27.4226i	0.849931	−	1.47212i	−0.0313384	−	0.999509i	$-0.509977\pi$
$347$	15.8325	−	27.4226i	0.849931	−	1.47212i	0.881269	−	0.472615i	$-0.156690\pi$
$348$		0			0
$349$	−18.2112	+	31.5427i	−0.974821	+	1.68844i	−0.294296	+	0.955714i	$0.595085\pi$
$349$	−18.2112	+	31.5427i	−0.974821	+	1.68844i	−0.680525	+	0.732725i	$0.738248\pi$
$350$		0			0
$351$	0.874088	+	2.90083i	0.0466554	+	0.154835i
$352$		0			0
$353$	7.19777			0.383098			0.191549	−	0.981483i	$-0.438649\pi$
$353$	7.19777			0.383098			0.191549	+	0.981483i	$0.438649\pi$
$354$		0			0
$355$	−48.7510			−2.58744
$356$		0			0
$357$	−0.235952	+	33.0929i	−0.0124879	+	1.75146i
$358$		0			0
$359$	−7.39891	+	12.8153i	−0.390499	+	0.676365i	−0.992515	−	0.122119i	$-0.961031\pi$
$359$	−7.39891	+	12.8153i	−0.390499	+	0.676365i	0.602016	+	0.798484i	$0.294364\pi$
$360$		0			0
$361$	0.657495	+	1.13881i	0.0346050	+	0.0599376i
$362$		0			0
$363$	12.5692	+	0.969442i	0.659712	+	0.0508825i
$364$		0			0
$365$	−1.88402	−	3.26323i	−0.0986144	−	0.170805i
$366$		0			0
$367$	4.19100			0.218768			0.109384	−	0.994000i	$-0.465112\pi$
$367$	4.19100			0.218768			0.109384	+	0.994000i	$0.465112\pi$
$368$		0			0
$369$	2.84618	+	7.34580i	0.148166	+	0.382407i
$370$		0			0
$371$	0.355426	+	5.08042i	0.0184528	+	0.263762i
$372$		0			0
$373$	17.4175			0.901844			0.450922	−	0.892563i	$-0.351095\pi$
$373$	17.4175			0.901844			0.450922	+	0.892563i	$0.351095\pi$
$374$		0			0
$375$	57.1270	+	4.40611i	2.95002	+	0.227531i
$376$		0			0
$377$	4.90125			0.252427
$378$		0			0
$379$	−11.1732			−0.573927			−0.286964	−	0.957941i	$-0.592646\pi$
$379$	−11.1732			−0.573927			−0.286964	+	0.957941i	$0.592646\pi$
$380$		0			0
$381$	14.7418	+	1.13701i	0.755247	+	0.0582510i
$382$		0			0
$383$	−25.1016			−1.28263			−0.641316	−	0.767276i	$-0.721611\pi$
$383$	−25.1016			−1.28263			−0.641316	+	0.767276i	$0.721611\pi$
$384$		0			0
$385$	19.3731	+	9.44811i	0.987345	+	0.481520i
$386$		0			0
$387$	1.66382	−	2.06783i	0.0845766	−	0.105114i
$388$		0			0
$389$	1.46402			0.0742289			0.0371144	−	0.999311i	$-0.488183\pi$
$389$	1.46402			0.0742289			0.0371144	+	0.999311i	$0.488183\pi$
$390$		0			0
$391$	4.62141	+	8.00452i	0.233715	+	0.404806i
$392$		0			0
$393$	4.05282	+	0.312587i	0.204438	+	0.0157679i
$394$		0			0
$395$	−25.0641	−	43.4124i	−1.26111	−	2.18431i
$396$		0			0
$397$	−1.49591	+	2.59100i	−0.0750778	+	0.130039i	−0.901120	−	0.433570i	$-0.857254\pi$
$397$	−1.49591	+	2.59100i	−0.0750778	+	0.130039i	0.826042	+	0.563608i	$0.190587\pi$
$398$		0			0
$399$	16.7578	−	9.51644i	0.838937	−	0.476418i
$400$		0			0
$401$	−26.3371			−1.31521			−0.657605	−	0.753363i	$-0.728430\pi$
$401$	−26.3371			−1.31521			−0.657605	+	0.753363i	$0.728430\pi$
$402$		0			0
$403$	−0.555142			−0.0276536
$404$		0			0
$405$	−36.2192	−	11.5184i	−1.79975	−	0.572353i
$406$		0			0
$407$	5.85166	−	10.1354i	0.290056	−	0.502392i
$408$		0			0
$409$	−1.50392	+	2.60487i	−0.0743642	+	0.128803i	−0.900810	−	0.434214i	$-0.857026\pi$
$409$	−1.50392	+	2.60487i	−0.0743642	+	0.128803i	0.826445	+	0.563017i	$0.190359\pi$
$410$		0			0
$411$	−2.21673	−	0.170973i	−0.109343	−	0.00843347i
$412$		0			0
$413$	−9.98489	+	6.73537i	−0.491324	+	0.331426i
$414$		0			0
$415$	22.1389	−	38.3457i	1.08676	−	1.88232i
$416$		0			0
$417$	−0.913523	−	1.90756i	−0.0447354	−	0.0934136i
$418$		0			0
$419$	−17.2414	−	29.8630i	−0.842297	−	1.45890i	−0.887948	−	0.459944i	$-0.847869\pi$
$419$	−17.2414	−	29.8630i	−0.842297	−	1.45890i	0.0456508	−	0.998957i	$-0.485464\pi$
$420$		0			0
$421$	9.86151	−	17.0806i	0.480620	−	0.832459i	−0.519132	−	0.854694i	$-0.673745\pi$
$421$	9.86151	−	17.0806i	0.480620	−	0.832459i	0.999753	+	0.0222349i	$0.00707818\pi$
$422$		0			0
$423$	−6.24737	−	16.1240i	−0.303757	−	0.783978i
$424$		0			0
$425$	46.3392	+	80.2618i	2.24778	+	3.89327i
$426$		0			0
$427$	−1.95358	−	27.9242i	−0.0945402	−	1.35135i
$428$		0			0
$429$	0.841480	+	1.75712i	0.0406270	+	0.0848347i
$430$		0			0
$431$	10.4257	+	18.0578i	0.502188	+	0.869816i	0.999997	+	0.00252883i	$0.000804953\pi$
$431$	10.4257	+	18.0578i	0.502188	+	0.869816i	−0.497808	+	0.867287i	$0.665862\pi$
$432$		0			0
$433$	15.6324			0.751247			0.375624	−	0.926772i	$-0.377429\pi$
$433$	15.6324			0.751247			0.375624	+	0.926772i	$0.377429\pi$
$434$		0			0
$435$	−34.7465	+	50.7262i	−1.66597	+	2.43213i
$436$		0			0
$437$	2.69117	−	4.66125i	0.128736	−	0.222978i
$438$		0			0
$439$	−17.8495	−	30.9162i	−0.851909	−	1.47555i	−0.879483	−	0.475930i	$-0.842112\pi$
$439$	−17.8495	−	30.9162i	−0.851909	−	1.47555i	0.0275746	−	0.999620i	$-0.491222\pi$
$440$		0			0
$441$	10.2396	+	18.3344i	0.487600	+	0.873067i
$442$		0			0
$443$	−9.05787	−	15.6887i	−0.430352	−	0.745392i	0.566551	−	0.824027i	$-0.308277\pi$
$443$	−9.05787	−	15.6887i	−0.430352	−	0.745392i	−0.996904	+	0.0786344i	$0.974944\pi$
$444$		0			0
$445$	−16.3811	+	28.3730i	−0.776541	+	1.34501i
$446$		0			0
$447$	−10.8703	−	0.838406i	−0.514146	−	0.0396552i
$448$		0			0
$449$	17.4189			0.822051			0.411025	−	0.911624i	$-0.365171\pi$
$449$	17.4189			0.822051			0.411025	+	0.911624i	$0.365171\pi$
$450$		0			0
$451$	2.53294	+	4.38719i	0.119272	+	0.206585i
$452$		0			0
$453$	−4.06609	−	0.313611i	−0.191041	−	0.0147347i
$454$		0			0
$455$	−0.454640	−	6.49858i	−0.0213139	−	0.304658i
$456$		0			0
$457$	−7.67918	−	13.3007i	−0.359217	−	0.622182i	0.628613	−	0.777718i	$-0.283623\pi$
$457$	−7.67918	−	13.3007i	−0.359217	−	0.622182i	−0.987830	+	0.155536i	$0.950290\pi$
$458$		0			0
$459$	−10.8263	−	35.9291i	−0.505327	−	1.67703i
$460$		0			0
$461$	−6.15140	+	10.6545i	−0.286499	+	0.496231i	−0.972972	−	0.230924i	$-0.925825\pi$
$461$	−6.15140	+	10.6545i	−0.286499	+	0.496231i	0.686472	+	0.727156i	$0.259158\pi$
$462$		0			0
$463$	9.18922	+	15.9162i	0.427059	+	0.739688i	0.996610	−	0.0822677i	$-0.0262162\pi$
$463$	9.18922	+	15.9162i	0.427059	+	0.739688i	−0.569551	+	0.821956i	$0.692883\pi$
$464$		0			0
$465$	3.93558	−	5.74553i	0.182508	−	0.266442i
$466$		0			0
$467$	−11.1020	+	19.2292i	−0.513738	+	0.889820i	0.486135	+	0.873884i	$0.338406\pi$
$467$	−11.1020	+	19.2292i	−0.513738	+	0.889820i	−0.999873	+	0.0159363i	$0.994927\pi$
$468$		0			0
$469$	−10.6682	+	7.19631i	−0.492612	+	0.332295i
$470$		0			0
$471$	−2.82752	+	4.12789i	−0.130285	+	0.190203i
$472$		0			0
$473$	0.853358	−	1.47806i	0.0392374	−	0.0679612i
$474$		0			0
$475$	26.9845	−	46.7386i	1.23814	−	2.14451i
$476$		0			0
$477$	−2.08633	−	5.38468i	−0.0955266	−	0.246548i
$478$		0			0
$479$	−34.5938			−1.58063			−0.790317	−	0.612699i	$-0.790084\pi$
$479$	−34.5938			−1.58063			−0.790317	+	0.612699i	$0.790084\pi$
$480$		0			0
$481$	−3.53717			−0.161281
$482$		0			0
$483$	5.05832	+	2.96871i	0.230162	+	0.135081i
$484$		0			0
$485$	8.38895	−	14.5301i	0.380922	−	0.659777i
$486$		0			0
$487$	6.79789	+	11.7743i	0.308042	+	0.533544i	0.977934	−	0.208915i	$-0.0669931\pi$
$487$	6.79789	+	11.7743i	0.308042	+	0.533544i	−0.669892	+	0.742458i	$0.733660\pi$
$488$		0			0
$489$	−5.10035	+	7.44597i	−0.230646	+	0.336718i
$490$		0			0
$491$	−7.01841	−	12.1563i	−0.316737	−	0.548604i	0.663069	−	0.748559i	$-0.269254\pi$
$491$	−7.01841	−	12.1563i	−0.316737	−	0.548604i	−0.979805	+	0.199955i	$0.935920\pi$
$492$		0			0
$493$	−60.7058			−2.73405
$494$		0			0
$495$	−24.1511	−	3.74777i	−1.08551	−	0.168450i
$496$		0			0
$497$	−27.4526	−	13.3884i	−1.23142	−	0.600551i
$498$		0			0
$499$	−30.2816			−1.35559			−0.677794	−	0.735251i	$-0.737064\pi$
$499$	−30.2816			−1.35559			−0.677794	+	0.735251i	$0.737064\pi$
$500$		0			0
$501$	−15.7702	−	32.9303i	−0.704560	−	1.47122i
$502$		0			0
$503$	−35.5942			−1.58707			−0.793533	−	0.608527i	$-0.791761\pi$
$503$	−35.5942			−1.58707			−0.793533	+	0.608527i	$0.791761\pi$
$504$		0			0
$505$	−70.8219			−3.15153
$506$		0			0
$507$	−12.3918	+	18.0907i	−0.550339	+	0.803436i
$508$		0			0
$509$	−6.47349			−0.286932			−0.143466	−	0.989655i	$-0.545825\pi$
$509$	−6.47349			−0.286932			−0.143466	+	0.989655i	$0.545825\pi$
$510$		0			0
$511$	−0.164755	−	2.35499i	−0.00728832	−	0.104178i
$512$		0			0
$513$	−14.9672	+	15.9210i	−0.660817	+	0.702931i
$514$		0			0
$515$	−49.0344			−2.16072
$516$		0			0
$517$	−5.55982	−	9.62989i	−0.244521	−	0.423522i
$518$		0			0
$519$	−3.04710	−	6.36274i	−0.133753	−	0.279293i
$520$		0			0
$521$	6.18988	+	10.7212i	0.271184	+	0.469704i	0.969165	−	0.246412i	$-0.0792516\pi$
$521$	6.18988	+	10.7212i	0.271184	+	0.469704i	−0.697982	+	0.716116i	$0.745918\pi$
$522$		0			0
$523$	11.0290	−	19.1028i	0.482265	−	0.835308i	−0.517527	−	0.855667i	$-0.673147\pi$
$523$	11.0290	−	19.1028i	0.482265	−	0.835308i	0.999793	+	0.0203585i	$0.00648074\pi$
$524$		0			0
$525$	50.7201	+	29.7674i	2.21361	+	1.29916i
$526$		0			0
$527$	6.87588			0.299518
$528$		0			0
$529$	−21.3619			−0.928779
$530$		0			0
$531$	8.56131	−	10.6402i	0.371529	−	0.461746i
$532$		0			0
$533$	0.765547	−	1.32597i	0.0331595	−	0.0574340i
$534$		0			0
$535$	43.2659	−	74.9388i	1.87055	−	3.23989i
$536$		0			0
$537$	4.65457	+	9.71936i	0.200860	+	0.419422i
$538$		0			0
$539$	8.31462	+	10.6408i	0.358136	+	0.458331i
$540$		0			0
$541$	7.24989	−	12.5572i	0.311697	−	0.539875i	−0.667033	−	0.745028i	$-0.732436\pi$
$541$	7.24989	−	12.5572i	0.311697	−	0.539875i	0.978730	+	0.205153i	$0.0657693\pi$
$542$		0			0
$543$	−31.4983	−	2.42941i	−1.35172	−	0.104256i
$544$		0			0
$545$	−10.4293	−	18.0640i	−0.446740	−	0.773777i
$546$		0			0
$547$	−12.4034	+	21.4834i	−0.530332	+	0.918562i	0.469042	+	0.883176i	$0.344599\pi$
$547$	−12.4034	+	21.4834i	−0.530332	+	0.918562i	−0.999374	+	0.0353858i	$0.988734\pi$
$548$		0			0
$549$	11.4674	+	29.5966i	0.489416	+	1.26315i
$550$		0			0
$551$	17.6753	+	30.6146i	0.752994	+	1.30422i
$552$		0			0
$553$	−2.19182	−	31.3296i	−0.0932055	−	1.33227i
$554$		0			0
$555$	25.0761	−	36.6084i	1.06442	−	1.55394i
$556$		0			0
$557$	9.02336	+	15.6289i	0.382332	+	0.662219i	0.991395	−	0.130903i	$-0.0417877\pi$
$557$	9.02336	+	15.6289i	0.382332	+	0.662219i	−0.609063	+	0.793122i	$0.708454\pi$
$558$		0			0
$559$	−0.515831			−0.0218173
$560$		0			0
$561$	−10.4224	−	21.7634i	−0.440034	−	0.918850i
$562$		0			0
$563$	−9.51748	+	16.4848i	−0.401114	+	0.694749i	−0.993861	−	0.110639i	$-0.964710\pi$
$563$	−9.51748	+	16.4848i	−0.401114	+	0.694749i	0.592747	+	0.805389i	$0.298043\pi$
$564$		0			0
$565$	31.3399	+	54.2823i	1.31848	+	2.28367i
$566$		0			0
$567$	−17.2324	−	16.4330i	−0.723694	−	0.690121i
$568$		0			0
$569$	−4.68018	−	8.10631i	−0.196203	−	0.339834i	0.751091	−	0.660199i	$-0.229528\pi$
$569$	−4.68018	−	8.10631i	−0.196203	−	0.339834i	−0.947294	+	0.320364i	$0.896195\pi$
$570$		0			0
$571$	−17.6805	+	30.6236i	−0.739907	+	1.28156i	0.212630	+	0.977133i	$0.431797\pi$
$571$	−17.6805	+	30.6236i	−0.739907	+	1.28156i	−0.952537	+	0.304424i	$0.901536\pi$
$572$		0			0
$573$	−5.52552	−	11.5380i	−0.230832	−	0.482008i
$574$		0			0
$575$	16.4252			0.684979
$576$		0			0
$577$	14.0160	+	24.2764i	0.583493	+	1.01064i	0.995061	+	0.0992610i	$0.0316479\pi$
$577$	14.0160	+	24.2764i	0.583493	+	1.01064i	−0.411568	+	0.911379i	$0.635019\pi$
$578$		0			0
$579$	19.1046	−	27.8907i	0.793960	−	1.15910i
$580$		0			0
$581$	22.9976	−	15.5132i	0.954100	−	0.643595i
$582$		0			0
$583$	−1.85672	−	3.21594i	−0.0768976	−	0.133190i
$584$		0			0
$585$	2.66871	+	6.88777i	0.110338	+	0.284774i
$586$		0			0
$587$	13.7305	−	23.7819i	0.566718	−	0.981585i	−0.430169	−	0.902748i	$-0.641546\pi$
$587$	13.7305	−	23.7819i	0.566718	−	0.981585i	0.996888	−	0.0788364i	$-0.0251205\pi$
$588$		0			0
$589$	−2.00200	−	3.46757i	−0.0824912	−	0.142879i
$590$		0			0
$591$	−13.4279	−	1.03568i	−0.552351	−	0.0426020i
$592$		0			0
$593$	−11.1267	+	19.2719i	−0.456917	+	0.791404i	−0.998796	−	0.0490525i	$-0.984380\pi$
$593$	−11.1267	+	19.2719i	−0.456917	+	0.791404i	0.541879	+	0.840457i	$0.317713\pi$
$594$		0			0
$595$	5.63108	+	80.4900i	0.230852	+	3.29977i
$596$		0			0
$597$	5.77143	+	12.0515i	0.236209	+	0.493236i
$598$		0			0
$599$	−3.37059	+	5.83804i	−0.137719	+	0.238536i	−0.926633	−	0.375968i	$-0.877310\pi$
$599$	−3.37059	+	5.83804i	−0.137719	+	0.238536i	0.788914	+	0.614504i	$0.210644\pi$
$600$		0			0
$601$	4.04153	−	7.00013i	0.164857	−	0.285541i	−0.771747	−	0.635929i	$-0.780617\pi$
$601$	4.04153	−	7.00013i	0.164857	−	0.285541i	0.936605	+	0.350388i	$0.113950\pi$
$602$		0			0
$603$	9.14721	−	11.3684i	0.372503	−	0.462956i
$604$		0			0
$605$	30.7363			1.24961
$606$		0			0
$607$	31.6039			1.28276			0.641382	−	0.767222i	$-0.278361\pi$
$607$	31.6039			1.28276			0.641382	+	0.767222i	$0.278361\pi$
$608$		0			0
$609$	−33.4972	+	19.0225i	−1.35737	+	0.770829i
$610$		0			0
$611$	−1.68038	+	2.91050i	−0.0679808	+	0.117746i
$612$		0			0
$613$	−3.10601	−	5.37977i	−0.125451	−	0.217287i	0.796458	−	0.604693i	$-0.206704\pi$
$613$	−3.10601	−	5.37977i	−0.125451	−	0.217287i	−0.921909	+	0.387407i	$0.873371\pi$
$614$		0			0
$615$	8.29608	+	17.3233i	0.334530	+	0.698544i
$616$		0			0
$617$	−0.309009	−	0.535218i	−0.0124402	−	0.0215471i	0.859738	−	0.510735i	$-0.170627\pi$
$617$	−0.309009	−	0.535218i	−0.0124402	−	0.0215471i	−0.872178	+	0.489188i	$0.837293\pi$
$618$		0			0
$619$	40.0206			1.60857			0.804283	−	0.594247i	$-0.202550\pi$
$619$	40.0206			1.60857			0.804283	+	0.594247i	$0.202550\pi$
$620$		0			0
$621$	−6.47391	−	1.52216i	−0.259789	−	0.0610822i
$622$		0			0
$623$	−17.0165	+	11.4786i	−0.681752	+	0.459880i
$624$		0			0
$625$	75.5295			3.02118
$626$		0			0
$627$	−7.94086	+	11.5928i	−0.317127	+	0.462972i
$628$		0			0
$629$	43.8106			1.74684
$630$		0			0
$631$	5.20154			0.207070			0.103535	−	0.994626i	$-0.466985\pi$
$631$	5.20154			0.207070			0.103535	+	0.994626i	$0.466985\pi$
$632$		0			0
$633$	−17.6023	−	36.7559i	−0.699627	−	1.46091i
$634$		0			0
$635$	36.0492			1.43057
$636$		0			0
$637$	1.52867	−	3.78432i	0.0605682	−	0.149940i
$638$		0			0
$639$	34.2232	+	5.31076i	1.35385	+	0.210090i
$640$		0			0
$641$	−0.274587			−0.0108455			−0.00542277	−	0.999985i	$-0.501726\pi$
$641$	−0.274587			−0.0108455			−0.00542277	+	0.999985i	$0.501726\pi$
$642$		0			0
$643$	11.2657	+	19.5128i	0.444277	+	0.769510i	0.998002	−	0.0631900i	$-0.0201274\pi$
$643$	11.2657	+	19.5128i	0.444277	+	0.769510i	−0.553725	+	0.832700i	$0.686794\pi$
$644$		0			0
$645$	3.65689	−	5.33867i	0.143990	−	0.210210i
$646$		0			0
$647$	12.2737	+	21.2586i	0.482528	+	0.835763i	0.999799	−	0.0200588i	$-0.00638534\pi$
$647$	12.2737	+	21.2586i	0.482528	+	0.835763i	−0.517271	+	0.855822i	$0.673052\pi$
$648$		0			0
$649$	4.39102	−	7.60547i	0.172363	−	0.298541i
$650$		0			0
$651$	3.79407	−	2.15459i	0.148701	−	0.0844450i
$652$		0			0
$653$	33.0308			1.29260			0.646298	−	0.763085i	$-0.276316\pi$
$653$	33.0308			1.29260			0.646298	+	0.763085i	$0.276316\pi$
$654$		0			0
$655$	9.91064			0.387241
$656$		0			0
$657$	0.967101	+	2.49602i	0.0377302	+	0.0973791i
$658$		0			0
$659$	21.3813	−	37.0335i	0.832897	−	1.44262i	−0.0628336	−	0.998024i	$-0.520014\pi$
$659$	21.3813	−	37.0335i	0.832897	−	1.44262i	0.895731	−	0.444596i	$-0.146653\pi$
$660$		0			0
$661$	9.55416	−	16.5483i	0.371614	−	0.643654i	−0.618200	−	0.786021i	$-0.712138\pi$
$661$	9.55416	−	16.5483i	0.371614	−	0.643654i	0.989814	+	0.142367i	$0.0454713\pi$
$662$		0			0
$663$	−4.12142	+	6.01684i	−0.160063	+	0.233675i
$664$		0			0
$665$	38.9523	−	26.2756i	1.51051	−	1.01892i
$666$		0			0
$667$	−5.37940	+	9.31739i	−0.208291	+	0.360771i
$668$		0			0
$669$	9.45714	−	13.8064i	0.365634	−	0.533787i
$670$		0			0
$671$	10.2054	+	17.6762i	0.393973	+	0.682382i
$672$		0			0
$673$	−12.9345	+	22.4032i	−0.498588	+	0.863579i	−0.999999	−	0.00162995i	$-0.999481\pi$
$673$	−12.9345	+	22.4032i	−0.498588	+	0.863579i	0.501411	+	0.865209i	$0.332815\pi$
$674$		0			0
$675$	−64.9142	−	15.2628i	−2.49855	−	0.587465i
$676$		0			0
$677$	−0.946686	−	1.63971i	−0.0363841	−	0.0630191i	0.847260	−	0.531178i	$-0.178251\pi$
$677$	−0.946686	−	1.63971i	−0.0363841	−	0.0630191i	−0.883644	+	0.468159i	$0.844917\pi$
$678$		0			0
$679$	8.71432	−	5.87830i	0.334425	−	0.225589i
$680$		0			0
$681$	−31.0360	−	2.39376i	−1.18930	−	0.0917289i
$682$		0			0
$683$	−6.39573	−	11.0777i	−0.244726	−	0.423878i	0.717329	−	0.696735i	$-0.245365\pi$
$683$	−6.39573	−	11.0777i	−0.244726	−	0.423878i	−0.962055	+	0.272857i	$0.912031\pi$
$684$		0			0
$685$	−5.42072			−0.207115
$686$		0			0
$687$	13.6715	+	1.05446i	0.521599	+	0.0402301i
$688$		0			0
$689$	−0.561168	+	0.971972i	−0.0213788	+	0.0370292i
$690$		0			0
$691$	18.0349	+	31.2373i	0.686079	+	1.18832i	0.973096	+	0.230399i	$0.0740030\pi$
$691$	18.0349	+	31.2373i	0.686079	+	1.18832i	−0.287017	+	0.957925i	$0.592664\pi$
$692$		0			0
$693$	−12.5707	−	8.74300i	−0.477520	−	0.332119i
$694$		0			0
$695$	−2.57834	−	4.46582i	−0.0978022	−	0.169398i
$696$		0			0
$697$	−9.48191	+	16.4231i	−0.359153	+	0.622071i
$698$		0			0
$699$	−6.41700	+	9.36815i	−0.242713	+	0.354336i
$700$		0			0
$701$	−20.2524			−0.764922			−0.382461	−	0.923972i	$-0.624923\pi$
$701$	−20.2524			−0.764922			−0.382461	+	0.923972i	$0.624923\pi$
$702$		0			0
$703$	−12.7560	−	22.0941i	−0.481103	−	0.833296i
$704$		0			0
$705$	−18.2099	−	38.0247i	−0.685825	−	1.43209i
$706$		0			0
$707$	−39.8811	−	19.4497i	−1.49988	−	0.731480i
$708$		0			0
$709$	3.38318	+	5.85984i	0.127058	+	0.220071i	0.922536	−	0.385912i	$-0.126113\pi$
$709$	3.38318	+	5.85984i	0.127058	+	0.220071i	−0.795478	+	0.605983i	$0.792780\pi$
$710$		0			0
$711$	12.8658	+	33.2059i	0.482507	+	1.24532i
$712$		0			0
$713$	0.609300	−	1.05534i	0.0228185	−	0.0395227i
$714$		0			0
$715$	2.37501	+	4.11364i	0.0888203	+	0.153841i
$716$		0			0
$717$	11.9985	+	25.0545i	0.448093	+	0.935679i
$718$		0			0
$719$	6.43767	−	11.1504i	0.240084	−	0.415839i	−0.720654	−	0.693295i	$-0.756158\pi$
$719$	6.43767	−	11.1504i	0.240084	−	0.415839i	0.960738	+	0.277457i	$0.0894915\pi$
$720$		0			0
$721$	−27.6121	−	13.4662i	−1.02833	−	0.501508i
$722$		0			0
$723$	−19.3055	−	1.48900i	−0.717979	−	0.0553766i
$724$		0			0
$725$	−53.9395	+	93.4260i	−2.00326	+	3.46975i
$726$		0			0
$727$	14.3621	−	24.8758i	0.532659	−	0.922593i	−0.466613	−	0.884461i	$-0.654526\pi$
$727$	14.3621	−	24.8758i	0.532659	−	0.922593i	0.999273	−	0.0381316i	$-0.0121406\pi$
$728$		0			0
$729$	24.1711	+	12.0315i	0.895227	+	0.445611i
$730$		0			0
$731$	6.38897			0.236305
$732$		0			0
$733$	4.66050			0.172139			0.0860697	−	0.996289i	$-0.472569\pi$
$733$	4.66050			0.172139			0.0860697	+	0.996289i	$0.472569\pi$
$734$		0			0
$735$	28.3291	+	42.6494i	1.04493	+	1.57315i
$736$		0			0
$737$	4.69153	−	8.12596i	0.172815	−	0.299324i
$738$		0			0
$739$	9.46395	+	16.3920i	0.348137	+	0.602991i	0.985919	−	0.167227i	$-0.0534811\pi$
$739$	9.46395	+	16.3920i	0.348137	+	0.602991i	−0.637782	+	0.770217i	$0.720148\pi$
$740$		0			0
$741$	4.23436	+	0.326589i	0.155553	+	0.0119976i
$742$		0			0
$743$	6.64732	+	11.5135i	0.243867	+	0.422389i	0.961812	−	0.273710i	$-0.0882507\pi$
$743$	6.64732	+	11.5135i	0.243867	+	0.422389i	−0.717946	+	0.696099i	$0.754917\pi$
$744$		0			0
$745$	−26.5818			−0.973882
$746$		0			0
$747$	−19.7187	+	24.5069i	−0.721470	+	0.896661i
$748$		0			0
$749$	44.9441	−	30.3173i	1.64222	−	1.10777i
$750$		0			0
$751$	−15.2353			−0.555945			−0.277972	−	0.960589i	$-0.589662\pi$
$751$	−15.2353			−0.555945			−0.277972	+	0.960589i	$0.589662\pi$
$752$		0			0
$753$	−25.2423	−	1.94690i	−0.919881	−	0.0709490i
$754$		0			0
$755$	−9.94308			−0.361866
$756$		0			0
$757$	15.6279			0.568004			0.284002	−	0.958824i	$-0.408338\pi$
$757$	15.6279			0.568004			0.284002	+	0.958824i	$0.408338\pi$
$758$		0			0
$759$	−4.26390	−	0.328868i	−0.154770	−	0.0119372i
$760$		0			0
$761$	7.09595			0.257228			0.128614	−	0.991695i	$-0.458947\pi$
$761$	7.09595			0.257228			0.128614	+	0.991695i	$0.458947\pi$
$762$		0			0
$763$	−0.912020	−	13.0363i	−0.0330173	−	0.471946i
$764$		0			0
$765$	−33.0541	−	85.3105i	−1.19507	−	3.08441i
$766$		0			0
$767$	−2.65425			−0.0958394
$768$		0			0
$769$	5.71618	+	9.90071i	0.206131	+	0.357029i	0.950492	−	0.310748i	$-0.100579\pi$
$769$	5.71618	+	9.90071i	0.206131	+	0.357029i	−0.744362	+	0.667777i	$0.767246\pi$
$770$		0			0
$771$	−25.7635	−	1.98710i	−0.927849	−	0.0715635i
$772$		0			0
$773$	7.40125	+	12.8193i	0.266204	+	0.461080i	0.967878	−	0.251418i	$-0.0808970\pi$
$773$	7.40125	+	12.8193i	0.266204	+	0.461080i	−0.701674	+	0.712498i	$0.747564\pi$
$774$		0			0
$775$	6.10949	−	10.5819i	0.219459	−	0.380114i
$776$		0			0
$777$	24.1745	−	13.7283i	0.867254	−	0.492498i
$778$		0			0
$779$	11.0431			0.395661
$780$		0			0
$781$	22.2706			0.796906
$782$		0			0
$783$	29.9179	−	31.8246i	1.06918	−	1.13732i
$784$		0			0
$785$	−6.09951	+	10.5647i	−0.217701	+	0.377069i
$786$		0			0
$787$	9.85887	−	17.0761i	0.351431	−	0.608696i	−0.635070	−	0.772455i	$-0.719029\pi$
$787$	9.85887	−	17.0761i	0.351431	−	0.608696i	0.986500	+	0.163759i	$0.0523619\pi$
$788$		0			0
$789$	38.3574	+	2.95845i	1.36556	+	0.105324i
$790$		0			0
$791$	2.74062	+	39.1741i	0.0974452	+	1.39287i
$792$		0			0
$793$	3.08442	−	5.34238i	0.109531	−	0.189713i
$794$		0			0
$795$	−6.08127	−	12.6985i	−0.215680	−	0.450369i
$796$		0			0
$797$	22.2215	+	38.4887i	0.787125	+	1.36334i	0.927722	+	0.373273i	$0.121764\pi$
$797$	22.2215	+	38.4887i	0.787125	+	1.36334i	−0.140597	+	0.990067i	$0.544902\pi$
$798$		0			0
$799$	20.8128	−	36.0488i	0.736304	−	1.27532i
$800$		0			0
$801$	14.5904	−	18.1333i	0.515526	−	0.640709i
$802$		0			0
$803$	0.860667	+	1.49072i	0.0303723	+	0.0526063i
$804$		0			0
$805$	12.8529	+	6.26827i	0.453007	+	0.220928i
$806$		0			0
$807$	7.08595	+	14.7964i	0.249437	+	0.520858i
$808$		0			0
$809$	−5.34657	−	9.26053i	−0.187975	−	0.325583i	0.756600	−	0.653878i	$-0.226859\pi$
$809$	−5.34657	−	9.26053i	−0.187975	−	0.325583i	−0.944575	+	0.328296i	$0.893526\pi$
$810$		0			0
$811$	−13.1292			−0.461030			−0.230515	−	0.973069i	$-0.574041\pi$
$811$	−13.1292			−0.461030			−0.230515	+	0.973069i	$0.574041\pi$
$812$		0			0
$813$	−17.1916	+	25.0979i	−0.602936	+	0.880222i
$814$		0			0
$815$	−11.0024	+	19.0567i	−0.385398	+	0.667529i
$816$		0			0
$817$	−1.86024	−	3.22202i	−0.0650814	−	0.112724i
$818$		0			0
$819$	−0.388773	+	4.61152i	−0.0135848	+	0.161140i
$820$		0			0
$821$	−1.31404	−	2.27598i	−0.0458602	−	0.0794323i	0.842184	−	0.539190i	$-0.181270\pi$
$821$	−1.31404	−	2.27598i	−0.0458602	−	0.0794323i	−0.888044	+	0.459758i	$0.847936\pi$
$822$		0			0
$823$	23.1960	−	40.1767i	0.808563	−	1.40047i	−0.105296	−	0.994441i	$-0.533579\pi$
$823$	23.1960	−	40.1767i	0.808563	−	1.40047i	0.913859	−	0.406031i	$-0.133088\pi$
$824$		0			0
$825$	−42.7544	−	3.29758i	−1.48852	−	0.114807i
$826$		0			0
$827$	−15.2072			−0.528807			−0.264404	−	0.964412i	$-0.585175\pi$
$827$	−15.2072			−0.528807			−0.264404	+	0.964412i	$0.585175\pi$
$828$		0			0
$829$	19.0782	+	33.0445i	0.662615	+	1.14768i	0.979926	+	0.199361i	$0.0638867\pi$
$829$	19.0782	+	33.0445i	0.662615	+	1.14768i	−0.317311	+	0.948322i	$0.602780\pi$
$830$		0			0
$831$	−23.4050	−	1.80519i	−0.811911	−	0.0626214i
$832$		0			0
$833$	−18.9338	+	46.8718i	−0.656018	+	1.62401i
$834$		0			0
$835$	−44.5101	−	77.0937i	−1.54033	−	2.66794i
$836$		0			0
$837$	−3.38867	+	3.60463i	−0.117130	+	0.124594i
$838$		0			0
$839$	−5.52298	+	9.56608i	−0.190674	+	0.330258i	−0.945474	−	0.325698i	$-0.894401\pi$
$839$	−5.52298	+	9.56608i	−0.190674	+	0.330258i	0.754800	+	0.655955i	$0.227734\pi$
$840$		0			0
$841$	−20.8313	−	36.0808i	−0.718320	−	1.24417i
$842$		0			0
$843$	−12.0236	+	17.5532i	−0.414116	+	0.604565i
$844$		0			0
$845$	−26.7314	+	46.3002i	−0.919590	+	1.59278i
$846$		0			0
$847$	17.3082	+	8.44105i	0.594716	+	0.290038i
$848$		0			0
$849$	13.7506	−	20.0745i	0.471920	−	0.688954i
$850$		0			0
$851$	3.88224	−	6.72424i	0.133081	−	0.230504i
$852$		0			0
$853$	22.4259	−	38.8428i	0.767847	−	1.32995i	−0.170881	−	0.985292i	$-0.554661\pi$
$853$	22.4259	−	38.8428i	0.767847	−	1.32995i	0.938728	−	0.344659i	$-0.112005\pi$
$854$		0			0
$855$	−33.3988	+	41.5088i	−1.14221	+	1.41957i
$856$		0			0
$857$	6.09527			0.208211			0.104105	−	0.994566i	$-0.466802\pi$
$857$	6.09527			0.208211			0.104105	+	0.994566i	$0.466802\pi$
$858$		0			0
$859$	30.2137			1.03088			0.515438	−	0.856927i	$-0.327629\pi$
$859$	30.2137			1.03088			0.515438	+	0.856927i	$0.327629\pi$
$860$		0			0
$861$	−0.0857979	+	12.0334i	−0.00292399	+	0.410097i
$862$		0			0
$863$	−21.3315	+	36.9472i	−0.726131	+	1.25770i	0.232375	+	0.972626i	$0.425350\pi$
$863$	−21.3315	+	36.9472i	−0.726131	+	1.25770i	−0.958507	+	0.285070i	$0.907983\pi$
$864$		0			0
$865$	−8.60018	−	14.8959i	−0.292415	−	0.506477i
$866$		0			0
$867$	34.4073	−	50.2310i	1.16853	−	1.70593i
$868$		0			0
$869$	11.4499	+	19.8318i	0.388411	+	0.672748i
$870$		0			0
$871$	−2.83590			−0.0960907
$872$		0			0
$873$	−7.47189	+	9.28625i	−0.252885	+	0.314292i
$874$		0			0
$875$	78.6656	+	38.3645i	2.65938	+	1.29696i
$876$		0			0
$877$	20.6751			0.698147			0.349074	−	0.937095i	$-0.386496\pi$
$877$	20.6751			0.698147			0.349074	+	0.937095i	$0.386496\pi$
$878$		0			0
$879$	−6.07261	−	12.6804i	−0.204824	−	0.427700i
$880$		0			0
$881$	5.40674			0.182158			0.0910789	−	0.995844i	$-0.470968\pi$
$881$	5.40674			0.182158			0.0910789	+	0.995844i	$0.470968\pi$
$882$		0			0
$883$	−3.16348			−0.106460			−0.0532299	−	0.998582i	$-0.516952\pi$
$883$	−3.16348			−0.106460			−0.0532299	+	0.998582i	$0.516952\pi$
$884$		0			0
$885$	18.8168	−	27.4705i	0.632520	−	0.923412i
$886$		0			0
$887$	−10.0863			−0.338666			−0.169333	−	0.985559i	$-0.554161\pi$
$887$	−10.0863			−0.338666			−0.169333	+	0.985559i	$0.554161\pi$
$888$		0			0
$889$	20.3000	+	9.90012i	0.680839	+	0.332039i
$890$		0			0
$891$	16.5458	+	5.26187i	0.554305	+	0.176279i
$892$		0			0
$893$	−24.2397			−0.811151
$894$		0			0
$895$	13.1371	+	22.7542i	0.439126	+	0.760589i
$896$		0			0
$897$	0.558273	+	1.16575i	0.0186402	+	0.0389232i
$898$		0			0
$899$	4.00181	+	6.93135i	0.133468	+	0.231173i
$900$		0			0
$901$	6.95051	−	12.0386i	0.231555	−	0.401065i
$902$		0			0
$903$	3.52540	−	2.00201i	0.117318	−	0.0666229i
$904$		0			0
$905$	−77.0249			−2.56040
$906$		0			0
$907$	−23.8637			−0.792380			−0.396190	−	0.918169i	$-0.629668\pi$
$907$	−23.8637			−0.792380			−0.396190	+	0.918169i	$0.629668\pi$
$908$		0			0
$909$	49.7170	+	7.71508i	1.64901	+	0.255893i
$910$		0			0
$911$	9.67946	−	16.7653i	0.320695	−	0.555460i	−0.659937	−	0.751321i	$-0.729417\pi$
$911$	9.67946	−	16.7653i	0.320695	−	0.555460i	0.980632	+	0.195862i	$0.0627503\pi$
$912$		0			0
$913$	−10.1136	+	17.5172i	−0.334710	+	0.579735i
$914$		0			0
$915$	33.4253	+	69.7965i	1.10501	+	2.30740i
$916$		0			0
$917$	5.58085	+	2.72174i	0.184296	+	0.0898796i
$918$		0			0
$919$	−25.2052	+	43.6567i	−0.831444	+	1.44010i	0.0654498	+	0.997856i	$0.479152\pi$
$919$	−25.2052	+	43.6567i	−0.831444	+	1.44010i	−0.896893	+	0.442247i	$0.854182\pi$
$920$		0			0
$921$	−11.4245	−	0.881158i	−0.376452	−	0.0290351i
$922$		0			0
$923$	−3.36549	−	5.82920i	−0.110777	−	0.191871i
$924$		0			0
$925$	38.9274	−	67.4243i	1.27993	−	2.21690i
$926$		0			0
$927$	34.4222	+	5.34163i	1.13057	+	0.175442i
$928$		0			0
$929$	−21.1465	−	36.6267i	−0.693793	−	1.20168i	−0.970586	−	0.240755i	$-0.922605\pi$
$929$	−21.1465	−	36.6267i	−0.693793	−	1.20168i	0.276793	−	0.960930i	$-0.410728\pi$
$930$		0			0
$931$	29.1507	−	4.09883i	0.955377	−	0.134334i
$932$		0			0
$933$	−8.18248	+	11.9456i	−0.267882	+	0.391080i
$934$		0			0
$935$	−29.4164	−	50.9506i	−0.962018	−	1.66626i
$936$		0			0
$937$	20.6771			0.675490			0.337745	−	0.941238i	$-0.390336\pi$
$937$	20.6771			0.675490			0.337745	+	0.941238i	$0.390336\pi$
$938$		0			0
$939$	19.5319	+	40.7852i	0.637400	+	1.33098i
$940$		0			0
$941$	17.1646	−	29.7300i	0.559550	−	0.969170i	−0.437983	−	0.898983i	$-0.644307\pi$
$941$	17.1646	−	29.7300i	0.559550	−	0.969170i	0.997534	−	0.0701867i	$-0.0223595\pi$
$942$		0			0
$943$	1.68046	+	2.91065i	0.0547234	+	0.0947837i
$944$		0			0
$945$	−44.9715	−	36.7162i	−1.46292	−	1.19438i
$946$		0			0
$947$	13.8650	+	24.0149i	0.450551	+	0.780378i	0.998420	−	0.0561863i	$-0.0178941\pi$
$947$	13.8650	+	24.0149i	0.450551	+	0.780378i	−0.547869	+	0.836564i	$0.684561\pi$
$948$		0			0
$949$	0.260125	−	0.450549i	0.00844400	−	0.0146254i
$950$		0			0
$951$	8.38992	+	17.5193i	0.272062	+	0.568102i
$952$		0			0
$953$	−22.8102			−0.738894			−0.369447	−	0.929252i	$-0.620453\pi$
$953$	−22.8102			−0.738894			−0.369447	+	0.929252i	$0.620453\pi$
$954$		0			0
$955$	−15.5953	−	27.0119i	−0.504653	−	0.874085i
$956$		0			0
$957$	15.8730	−	23.1729i	0.513102	−	0.749074i
$958$		0			0
$959$	−3.05250	−	1.48868i	−0.0985705	−	0.0480720i
$960$		0			0
$961$	15.0467	+	26.0617i	0.485378	+	0.840700i
$962$		0			0
$963$	−38.5362	+	47.8938i	−1.24181	+	1.54336i
$964$		0			0
$965$	41.2123	−	71.3817i	1.32667	−	2.29786i
$966$		0			0
$967$	10.8697	+	18.8269i	0.349546	+	0.605432i	0.986169	−	0.165744i	$-0.0530024\pi$
$967$	10.8697	+	18.8269i	0.349546	+	0.605432i	−0.636623	+	0.771175i	$0.719669\pi$
$968$		0			0
$969$	−52.4459	−	4.04507i	−1.68480	−	0.129946i
$970$		0			0
$971$	−19.7959	+	34.2875i	−0.635281	+	1.10034i	0.351174	+	0.936310i	$0.385782\pi$
$971$	−19.7959	+	34.2875i	−0.635281	+	1.10034i	−0.986455	+	0.164029i	$0.947551\pi$
$972$		0			0
$973$	−0.225472	−	3.22287i	−0.00722829	−	0.103320i
$974$		0			0
$975$	5.59784	+	11.6890i	0.179274	+	0.374349i
$976$		0			0
$977$	22.8724	−	39.6161i	0.731752	−	1.26743i	−0.224382	−	0.974501i	$-0.572036\pi$
$977$	22.8724	−	39.6161i	0.731752	−	1.26743i	0.956134	−	0.292930i	$-0.0946303\pi$
$978$		0			0
$979$	7.48329	−	12.9614i	0.239167	−	0.414250i
$980$		0			0
$981$	5.35351	+	13.8170i	0.170924	+	0.441144i
$982$		0			0
$983$	15.0498			0.480014			0.240007	−	0.970771i	$-0.422850\pi$
$983$	15.0498			0.480014			0.240007	+	0.970771i	$0.422850\pi$
$984$		0			0
$985$	−32.8363			−1.04625
$986$		0			0
$987$	0.188327	−	26.4133i	0.00599450	−	0.840746i
$988$		0			0
$989$	0.566154	−	0.980607i	0.0180026	−	0.0311815i
$990$		0			0
$991$	−11.3516	−	19.6616i	−0.360596	−	0.624570i	0.627463	−	0.778646i	$-0.284093\pi$
$991$	−11.3516	−	19.6616i	−0.360596	−	0.624570i	−0.988059	+	0.154076i	$0.950760\pi$
$992$		0			0
$993$	−13.6402	−	28.4826i	−0.432860	−	0.903869i
$994$		0			0
$995$	16.2894	+	28.2140i	0.516408	+	0.894445i
$996$		0			0
$997$	−55.5352			−1.75882			−0.879408	−	0.476069i	$-0.842061\pi$
$997$	−55.5352			−1.75882			−0.879408	+	0.476069i	$0.842061\pi$
$998$		0			0
$999$	−21.5914	+	22.9674i	−0.683121	+	0.726657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.457.1	yes	22
3.2	odd	2		1512.2.t.c.289.11		22
4.3	odd	2		1008.2.t.l.961.11		22
7.4	even	3		504.2.q.c.25.7	✓	22
9.4	even	3		504.2.q.c.121.7	yes	22
9.5	odd	6		1512.2.q.d.793.1		22
12.11	even	2		3024.2.t.k.289.11		22
21.11	odd	6		1512.2.q.d.1369.1		22
28.11	odd	6		1008.2.q.l.529.5		22
36.23	even	6		3024.2.q.l.2305.1		22
36.31	odd	6		1008.2.q.l.625.5		22
63.4	even	3	inner	504.2.t.c.193.1	yes	22
63.32	odd	6		1512.2.t.c.361.11		22
84.11	even	6		3024.2.q.l.2881.1		22
252.67	odd	6		1008.2.t.l.193.11		22
252.95	even	6		3024.2.t.k.1873.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.7	✓	22	7.4	even	3
504.2.q.c.121.7	yes	22	9.4	even	3
504.2.t.c.193.1	yes	22	63.4	even	3	inner
504.2.t.c.457.1	yes	22	1.1	even	1	trivial
1008.2.q.l.529.5		22	28.11	odd	6
1008.2.q.l.625.5		22	36.31	odd	6
1008.2.t.l.193.11		22	252.67	odd	6
1008.2.t.l.961.11		22	4.3	odd	2
1512.2.q.d.793.1		22	9.5	odd	6
1512.2.q.d.1369.1		22	21.11	odd	6
1512.2.t.c.289.11		22	3.2	odd	2
1512.2.t.c.361.11		22	63.32	odd	6
3024.2.q.l.2305.1		22	36.23	even	6
3024.2.q.l.2881.1		22	84.11	even	6
3024.2.t.k.289.11		22	12.11	even	2
3024.2.t.k.1873.11		22	252.95	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72692 - 0.133195i) q^{3} -4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} +(2.96452 + 0.460034i) q^{9} +O(q^{10})\)	\(q+(-1.72692 - 0.133195i) q^{3} -4.22296 q^{5} +(-2.37802 - 1.15974i) q^{7} +(2.96452 + 0.460034i) q^{9} +1.92915 q^{11} +(-0.291529 - 0.504943i) q^{13} +(7.29273 + 0.562477i) q^{15} +(3.61082 + 6.25412i) q^{17} +(2.10268 - 3.64194i) q^{19} +(3.95219 + 2.31953i) q^{21} +1.27988 q^{23} +12.8334 q^{25} +(-5.05822 - 1.18930i) q^{27} +(-4.20305 + 7.27990i) q^{29} +(0.476061 - 0.824561i) q^{31} +(-3.33149 - 0.256953i) q^{33} +(10.0423 + 4.89755i) q^{35} +(3.03329 - 5.25381i) q^{37} +(0.436192 + 0.910828i) q^{39} +(1.31299 + 2.27416i) q^{41} +(0.442349 - 0.766171i) q^{43} +(-12.5191 - 1.94271i) q^{45} +(-2.88201 - 4.99178i) q^{47} +(4.30999 + 5.51579i) q^{49} +(-5.40259 - 11.2813i) q^{51} +(-0.962456 - 1.66702i) q^{53} -8.14673 q^{55} +(-4.11625 + 6.00929i) q^{57} +(2.27614 - 3.94240i) q^{59} +(5.29008 + 9.16268i) q^{61} +(-6.51617 - 4.53205i) q^{63} +(1.23112 + 2.13236i) q^{65} +(2.43191 - 4.21220i) q^{67} +(-2.21025 - 0.170473i) q^{69} +11.5443 q^{71} +(0.446138 + 0.772734i) q^{73} +(-22.1623 - 1.70934i) q^{75} +(-4.58756 - 2.23732i) q^{77} +(5.93520 + 10.2801i) q^{79} +(8.57674 + 2.72756i) q^{81} +(-5.24250 + 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(8.22798 - 12.0120i) q^{87} +(3.87906 - 6.71874i) q^{89} +(0.107659 + 1.53887i) q^{91} +(-0.931947 + 1.36054i) q^{93} +(-8.87953 + 15.3798i) q^{95} +(-1.98651 + 3.44073i) q^{97} +(5.71900 + 0.887474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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