LMFDB - Embedded newform 1008.2.t.l.193.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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([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("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.11
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.l.961.11

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.72692	−	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	$-0.593931\pi$
$11$	−1.92915			−0.581660			−0.290830	+	0.956775i	$0.593931\pi$
$12$		0			0
$13$	−0.291529	+	0.504943i	−0.0808557	+	0.140046i	−0.903618	−	0.428340i	$-0.859099\pi$
$13$	−0.291529	+	0.504943i	−0.0808557	+	0.140046i	0.822762	+	0.568386i	$0.192432\pi$
$14$		0			0
$15$	−7.29273	+	0.562477i	−1.88297	+	0.145231i
$16$		0			0
$17$	3.61082	−	6.25412i	0.875753	−	1.51685i	0.0197936	−	0.999804i	$-0.493699\pi$
$17$	3.61082	−	6.25412i	0.875753	−	1.51685i	0.855959	−	0.517044i	$-0.172968\pi$
$18$		0			0
$19$	−2.10268	−	3.64194i	−0.482387	−	0.835519i	0.517408	−	0.855739i	$-0.326897\pi$
$19$	−2.10268	−	3.64194i	−0.482387	−	0.835519i	−0.999796	+	0.0202194i	$0.993564\pi$
$20$		0			0
$21$	3.95219	−	2.31953i	0.862438	−	0.506162i
$22$		0			0
$23$	−1.27988			−0.266873			−0.133437	−	0.991057i	$-0.542601\pi$
$23$	−1.27988			−0.266873			−0.133437	+	0.991057i	$0.542601\pi$
$24$		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	−0.931658	−	0.363335i	$-0.881638\pi$
$29$	−4.20305	−	7.27990i	−0.780487	−	1.35184i	0.151171	−	0.988508i	$-0.451695\pi$
$30$		0			0
$31$	−0.476061	−	0.824561i	−0.0855030	−	0.148096i	0.820102	−	0.572217i	$-0.193916\pi$
$31$	−0.476061	−	0.824561i	−0.0855030	−	0.148096i	−0.905605	+	0.424121i	$0.860583\pi$
$32$		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	0.999999	−	0.00153588i	$-0.000488885\pi$
$37$	3.03329	+	5.25381i	0.498669	+	0.863721i	−0.501330	+	0.865256i	$0.667156\pi$
$38$		0			0
$39$	−0.436192	+	0.910828i	−0.0698467	+	0.145849i
$40$		0			0
$41$	1.31299	−	2.27416i	0.205054	−	0.355164i	−0.745096	−	0.666957i	$-0.767596\pi$
$41$	1.31299	−	2.27416i	0.205054	−	0.355164i	0.950150	+	0.311794i	$0.100930\pi$
$42$		0			0
$43$	−0.442349	−	0.766171i	−0.0674576	−	0.116840i	0.830324	−	0.557281i	$-0.188155\pi$
$43$	−0.442349	−	0.766171i	−0.0674576	−	0.116840i	−0.897782	+	0.440441i	$0.854822\pi$
$44$		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	$-0.695229\pi$
$47$	2.88201	−	4.99178i	0.420384	−	0.728126i	0.995977	+	0.0896103i	$0.0285622\pi$
$48$		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	−0.924526	−	0.381120i	$-0.875539\pi$
$53$	−0.962456	+	1.66702i	−0.132204	+	0.228983i	0.792322	+	0.610103i	$0.208872\pi$
$54$		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	$-0.262429\pi$
$59$	−2.27614	−	3.94240i	−0.296329	−	0.513256i	−0.975293	+	0.220915i	$0.929096\pi$
$60$		0			0
$61$	5.29008	−	9.16268i	0.677325	−	1.17316i	−0.298458	−	0.954423i	$-0.596472\pi$
$61$	5.29008	−	9.16268i	0.677325	−	1.17316i	0.975783	−	0.218739i	$-0.0701943\pi$
$62$		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	$-0.262688\pi$
$67$	−2.43191	−	4.21220i	−0.297106	−	0.514602i	−0.975473	+	0.220121i	$0.929355\pi$
$68$		0			0
$69$	−2.21025	+	0.170473i	−0.266083	+	0.0205226i
$70$		0			0
$71$	−11.5443			−1.37005			−0.685027	−	0.728518i	$-0.740209\pi$
$71$	−11.5443			−1.37005			−0.685027	+	0.728518i	$0.740209\pi$
$72$		0			0
$73$	0.446138	−	0.772734i	0.0522165	−	0.0904417i	−0.838736	−	0.544539i	$-0.816705\pi$
$73$	0.446138	−	0.772734i	0.0522165	−	0.0904417i	0.890952	+	0.454097i	$0.150038\pi$
$74$		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	0.310766	+	0.950487i	$0.399415\pi$
$79$	−5.93520	+	10.2801i	−0.667763	+	1.15660i	−0.978528	+	0.206112i	$0.933919\pi$
$80$		0			0
$81$	8.57674	−	2.72756i	0.952971	−	0.303062i
$82$		0			0
$83$	5.24250	+	9.08028i	0.575439	+	0.996690i	0.995994	+	0.0894227i	$0.0285022\pi$
$83$	5.24250	+	9.08028i	0.575439	+	0.996690i	−0.420555	+	0.907267i	$0.638164\pi$
$84$		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	0.995019	−	0.0996849i	$-0.0317835\pi$
$89$	3.87906	+	6.71874i	0.411180	+	0.712185i	−0.583839	+	0.811869i	$0.698450\pi$
$90$		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	0.747377	−	0.664400i	$-0.231313\pi$
$97$	−1.98651	−	3.44073i	−0.201699	−	0.349353i	−0.949076	+	0.315047i	$0.897980\pi$
$98$		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	$-0.693852\pi$
$103$	−11.6114			−1.14410			−0.572052	+	0.820218i	$0.693852\pi$
$104$		0			0
$105$	−16.6900	+	9.79527i	−1.62877	+	0.955920i
$106$		0			0
$107$	10.2454	+	17.7455i	0.990460	+	1.71553i	0.614570	+	0.788862i	$0.289329\pi$
$107$	10.2454	+	17.7455i	0.990460	+	1.71553i	0.375890	+	0.926664i	$0.377337\pi$
$108$		0			0
$109$	2.46965	−	4.27756i	0.236550	−	0.409716i	−0.723172	−	0.690668i	$-0.757317\pi$
$109$	2.46965	−	4.27756i	0.236550	−	0.409716i	0.959722	+	0.280951i	$0.0906500\pi$
$110$		0			0
$111$	5.93803	+	8.66890i	0.563613	+	0.822815i
$112$		0			0
$113$	−7.42131	+	12.8541i	−0.698138	+	1.20921i	0.270974	+	0.962587i	$0.412654\pi$
$113$	−7.42131	+	12.8541i	−0.698138	+	1.20921i	−0.969111	+	0.246623i	$0.920679\pi$
$114$		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	$-0.376356\pi$
$127$	8.53648			0.757490			0.378745	+	0.925501i	$0.376356\pi$
$128$		0			0
$129$	−0.865953	−	1.26420i	−0.0762429	−	0.111307i
$130$		0			0
$131$	2.34684			0.205045			0.102522	−	0.994731i	$-0.467309\pi$
$131$	2.34684			0.205045			0.102522	+	0.994731i	$0.467309\pi$
$132$		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	$-0.849825\pi$
$139$	−0.610553	+	1.05751i	−0.0517865	+	0.0896968i	0.838970	+	0.544177i	$0.183158\pi$
$140$		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	$-0.530542\pi$
$151$	−2.35453			−0.191609			−0.0958044	+	0.995400i	$0.530542\pi$
$152$		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	0.917889	−	0.396838i	$-0.129892\pi$
$157$	1.44437	+	2.50172i	0.115273	+	0.199659i	−0.802616	+	0.596496i	$0.796559\pi$
$158$		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	$-0.232083\pi$
$163$	−2.60538	−	4.51265i	−0.204069	−	0.353458i	−0.949836	+	0.312749i	$0.898750\pi$
$164$		0			0
$165$	14.0688	−	1.08510i	1.09525	−	0.0844750i
$166$		0			0
$167$	−10.5400	+	18.2558i	−0.815610	+	1.41268i	0.0932784	+	0.995640i	$0.470265\pi$
$167$	−10.5400	+	18.2558i	−0.815610	+	1.41268i	−0.908889	+	0.417039i	$0.863068\pi$
$168$		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	−0.778164	−	0.628061i	$-0.783849\pi$
$173$	2.03653	−	3.52737i	0.154834	−	0.268181i	0.932999	+	0.359880i	$0.117182\pi$
$174$		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	$-0.758637\pi$
$179$	3.11088	−	5.38821i	0.232518	−	0.402733i	0.958549	+	0.284929i	$0.0919701\pi$
$180$		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	$-0.919437\pi$
$191$	−3.69298	+	6.39644i	−0.267215	+	0.462830i	0.700927	+	0.713233i	$0.252770\pi$
$192$		0			0
$193$	−9.75908	−	16.9032i	−0.702474	−	1.21672i	−0.967595	−	0.252506i	$-0.918745\pi$
$193$	−9.75908	−	16.9032i	−0.702474	−	1.21672i	0.265121	−	0.964215i	$-0.414588\pi$
$194$		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	$-0.745172\pi$
$199$	3.85734	−	6.68110i	0.273439	−	0.473611i	0.969740	+	0.244139i	$0.0785054\pi$
$200$		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	0.103034	+	0.994678i	$0.467145\pi$
$211$	−11.7645	+	20.3767i	−0.809899	+	1.40279i	−0.912933	+	0.408109i	$0.866188\pi$
$212$		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	$-0.0618061\pi$
$223$	4.83093	+	8.36742i	0.323503	+	0.560324i	−0.657705	+	0.753275i	$0.728473\pi$
$224$		0			0
$225$	38.0449	−	5.90381i	2.53633	−	0.393587i
$226$		0			0
$227$	−17.9718			−1.19283			−0.596417	−	0.802675i	$-0.703409\pi$
$227$	−17.9718			−1.19283			−0.596417	+	0.802675i	$0.703409\pi$
$228$		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	0.953194	−	0.302359i	$-0.0977742\pi$
$233$	3.27796	+	5.67759i	0.214746	+	0.371951i	−0.738448	+	0.674311i	$0.764441\pi$
$234$		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	−0.481043	−	0.876697i	$-0.659742\pi$
$239$	8.01922	−	13.8897i	0.518720	−	0.898450i	0.999763	−	0.0217529i	$-0.00692470\pi$
$240$		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	$-0.652619\pi$
$251$	−14.6169			−0.922613			−0.461307	+	0.887241i	$0.652619\pi$
$252$		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	$-0.259886\pi$
$263$	22.2114			1.36962			0.684808	+	0.728724i	$0.259886\pi$
$264$		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	−0.973512	−	0.228635i	$-0.926574\pi$
$269$	−4.73590	+	8.20281i	−0.288753	+	0.500134i	0.684760	+	0.728769i	$0.259907\pi$
$270$		0			0
$271$	−8.78188	−	15.2107i	−0.533461	−	0.923982i	−0.999236	−	0.0390786i	$-0.987558\pi$
$271$	−8.78188	−	15.2107i	−0.533461	−	0.923982i	0.465775	−	0.884903i	$-0.345776\pi$
$272$		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	0.989000	−	0.147919i	$-0.0472574\pi$
$281$	6.14196	+	10.6382i	0.366398	+	0.634621i	−0.622601	+	0.782539i	$0.713924\pi$
$282$		0			0
$283$	7.02415	+	12.1662i	0.417542	+	0.723204i	0.995692	−	0.0927267i	$-0.0295583\pi$
$283$	7.02415	+	12.1662i	0.417542	+	0.723204i	−0.578149	+	0.815931i	$0.696225\pi$
$284$		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	−0.722776	−	0.691083i	$-0.757134\pi$
$293$	4.05863	−	7.02975i	0.237108	−	0.410682i	0.959883	+	0.280401i	$0.0904673\pi$
$294$		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	$-0.560455\pi$
$307$	−6.61556			−0.377570			−0.188785	+	0.982018i	$0.560455\pi$
$308$		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	$-0.242836\pi$
$311$	−4.17980	−	7.23963i	−0.237015	−	0.410522i	−0.959856	+	0.280492i	$0.909502\pi$
$312$		0			0
$313$	−13.0542	+	22.6105i	−0.737864	+	1.27802i	0.215591	+	0.976484i	$0.430832\pi$
$313$	−13.0542	+	22.6105i	−0.737864	+	1.27802i	−0.953455	+	0.301535i	$0.902501\pi$
$314$		0			0
$315$	−27.5176	+	19.1387i	−1.55044	+	1.07834i
$316$		0			0
$317$	−5.60741	+	9.71231i	−0.314943	+	0.545498i	−0.979425	−	0.201806i	$-0.935319\pi$
$317$	−5.60741	+	9.71231i	−0.314943	+	0.545498i	0.664482	+	0.747304i	$0.268652\pi$
$318$		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	0.498914	+	0.866652i	$0.333732\pi$
$331$	−9.11645	+	15.7902i	−0.501086	+	0.867906i	−0.999999	+	0.00125391i	$0.999601\pi$
$332$		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	−0.712259	−	0.701917i	$-0.752328\pi$
$337$	4.62148	−	8.00465i	0.251748	−	0.436041i	0.964007	+	0.265876i	$0.0856612\pi$
$338$		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	−0.881269	−	0.472615i	$-0.843310\pi$
$347$	−15.8325	−	27.4226i	−0.849931	−	1.47212i	0.0313384	−	0.999509i	$-0.490023\pi$
$348$		0			0
$349$	−18.2112	−	31.5427i	−0.974821	−	1.68844i	−0.680525	−	0.732725i	$-0.738248\pi$
$349$	−18.2112	−	31.5427i	−0.974821	−	1.68844i	−0.294296	−	0.955714i	$-0.595085\pi$
$350$		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	$-0.0389690\pi$
$359$	7.39891	+	12.8153i	0.390499	+	0.676365i	−0.602016	+	0.798484i	$0.705636\pi$
$360$		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	$-0.534888\pi$
$367$	−4.19100			−0.218768			−0.109384	+	0.994000i	$0.534888\pi$
$368$		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	$-0.407354\pi$
$379$	11.1732			0.573927			0.286964	+	0.957941i	$0.407354\pi$
$380$		0			0
$381$	14.7418	−	1.13701i	0.755247	−	0.0582510i
$382$		0			0
$383$	25.1016			1.28263			0.641316	−	0.767276i	$-0.278389\pi$
$383$	25.1016			1.28263			0.641316	+	0.767276i	$0.278389\pi$
$384$		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	0.826042	−	0.563608i	$-0.190587\pi$
$397$	−1.49591	−	2.59100i	−0.0750778	−	0.130039i	−0.901120	+	0.433570i	$0.857254\pi$
$398$		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	0.826445	−	0.563017i	$-0.190359\pi$
$409$	−1.50392	−	2.60487i	−0.0743642	−	0.128803i	−0.900810	+	0.434214i	$0.857026\pi$
$410$		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	−0.0456508	−	0.998957i	$-0.514536\pi$
$419$	17.2414	−	29.8630i	0.842297	−	1.45890i	0.887948	−	0.459944i	$-0.152131\pi$
$420$		0			0
$421$	9.86151	+	17.0806i	0.480620	+	0.832459i	0.999753	−	0.0222349i	$-0.00707818\pi$
$421$	9.86151	+	17.0806i	0.480620	+	0.832459i	−0.519132	+	0.854694i	$0.673745\pi$
$422$		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	0.497808	+	0.867287i	$0.334138\pi$
$431$	−10.4257	+	18.0578i	−0.502188	+	0.869816i	−0.999997	+	0.00252883i	$0.999195\pi$
$432$		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	−0.0275746	−	0.999620i	$-0.508778\pi$
$439$	17.8495	−	30.9162i	0.851909	−	1.47555i	0.879483	−	0.475930i	$-0.157888\pi$
$440$		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	$-0.691723\pi$
$443$	9.05787	−	15.6887i	0.430352	−	0.745392i	0.996904	+	0.0786344i	$0.0250560\pi$
$444$		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	−0.987830	−	0.155536i	$-0.950290\pi$
$457$	−7.67918	+	13.3007i	−0.359217	+	0.622182i	0.628613	+	0.777718i	$0.283623\pi$
$458$		0			0
$459$	10.8263	−	35.9291i	0.505327	−	1.67703i
$460$		0			0
$461$	−6.15140	−	10.6545i	−0.286499	−	0.496231i	0.686472	−	0.727156i	$-0.259158\pi$
$461$	−6.15140	−	10.6545i	−0.286499	−	0.496231i	−0.972972	+	0.230924i	$0.925825\pi$
$462$		0			0
$463$	−9.18922	+	15.9162i	−0.427059	+	0.739688i	−0.996610	−	0.0822677i	$-0.973784\pi$
$463$	−9.18922	+	15.9162i	−0.427059	+	0.739688i	0.569551	+	0.821956i	$0.307117\pi$
$464$		0			0
$465$	3.93558	+	5.74553i	0.182508	+	0.266442i
$466$		0			0
$467$	11.1020	+	19.2292i	0.513738	+	0.889820i	0.999873	+	0.0159363i	$0.00507290\pi$
$467$	11.1020	+	19.2292i	0.513738	+	0.889820i	−0.486135	+	0.873884i	$0.661594\pi$
$468$		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	$-0.209916\pi$
$479$	34.5938			1.58063			0.790317	+	0.612699i	$0.209916\pi$
$480$		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	$-0.933007\pi$
$487$	−6.79789	+	11.7743i	−0.308042	+	0.533544i	0.669892	+	0.742458i	$0.266340\pi$
$488$		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	$-0.730746\pi$
$491$	7.01841	−	12.1563i	0.316737	−	0.548604i	0.979805	+	0.199955i	$0.0640795\pi$
$492$		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	$-0.262936\pi$
$499$	30.2816			1.35559			0.677794	+	0.735251i	$0.262936\pi$
$500$		0			0
$501$	−15.7702	+	32.9303i	−0.704560	+	1.47122i
$502$		0			0
$503$	35.5942			1.58707			0.793533	−	0.608527i	$-0.208239\pi$
$503$	35.5942			1.58707			0.793533	+	0.608527i	$0.208239\pi$
$504$		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	−0.697982	−	0.716116i	$-0.745918\pi$
$521$	6.18988	−	10.7212i	0.271184	−	0.469704i	0.969165	+	0.246412i	$0.0792516\pi$
$522$		0			0
$523$	−11.0290	−	19.1028i	−0.482265	−	0.835308i	0.517527	−	0.855667i	$-0.326853\pi$
$523$	−11.0290	−	19.1028i	−0.482265	−	0.835308i	−0.999793	+	0.0203585i	$0.993519\pi$
$524$		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	0.978730	−	0.205153i	$-0.0657693\pi$
$541$	7.24989	+	12.5572i	0.311697	+	0.539875i	−0.667033	+	0.745028i	$0.732436\pi$
$542$		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	0.999374	+	0.0353858i	$0.0112660\pi$
$547$	12.4034	+	21.4834i	0.530332	+	0.918562i	−0.469042	+	0.883176i	$0.655401\pi$
$548$		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	−0.609063	−	0.793122i	$-0.708454\pi$
$557$	9.02336	−	15.6289i	0.382332	−	0.662219i	0.991395	+	0.130903i	$0.0417877\pi$
$558$		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	$-0.0352899\pi$
$563$	9.51748	+	16.4848i	0.401114	+	0.694749i	−0.592747	+	0.805389i	$0.701957\pi$
$564$		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	−0.947294	−	0.320364i	$-0.896195\pi$
$569$	−4.68018	+	8.10631i	−0.196203	+	0.339834i	0.751091	+	0.660199i	$0.229528\pi$
$570$		0			0
$571$	17.6805	+	30.6236i	0.739907	+	1.28156i	0.952537	+	0.304424i	$0.0984638\pi$
$571$	17.6805	+	30.6236i	0.739907	+	1.28156i	−0.212630	+	0.977133i	$0.568203\pi$
$572$		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	−0.411568	−	0.911379i	$-0.635019\pi$
$577$	14.0160	−	24.2764i	0.583493	−	1.01064i	0.995061	−	0.0992610i	$-0.0316479\pi$
$578$		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	−0.996888	−	0.0788364i	$-0.974880\pi$
$587$	−13.7305	−	23.7819i	−0.566718	−	0.981585i	0.430169	−	0.902748i	$-0.358454\pi$
$588$		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	0.541879	−	0.840457i	$-0.317713\pi$
$593$	−11.1267	−	19.2719i	−0.456917	−	0.791404i	−0.998796	+	0.0490525i	$0.984380\pi$
$594$		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	$-0.122690\pi$
$599$	3.37059	+	5.83804i	0.137719	+	0.238536i	−0.788914	+	0.614504i	$0.789356\pi$
$600$		0			0
$601$	4.04153	+	7.00013i	0.164857	+	0.285541i	0.936605	−	0.350388i	$-0.113950\pi$
$601$	4.04153	+	7.00013i	0.164857	+	0.285541i	−0.771747	+	0.635929i	$0.780617\pi$
$602$		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	$-0.721639\pi$
$607$	−31.6039			−1.28276			−0.641382	+	0.767222i	$0.721639\pi$
$608$		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	−0.921909	−	0.387407i	$-0.873371\pi$
$613$	−3.10601	+	5.37977i	−0.125451	+	0.217287i	0.796458	+	0.604693i	$0.206704\pi$
$614$		0			0
$615$	−8.29608	+	17.3233i	−0.334530	+	0.698544i
$616$		0			0
$617$	−0.309009	+	0.535218i	−0.0124402	+	0.0215471i	−0.872178	−	0.489188i	$-0.837293\pi$
$617$	−0.309009	+	0.535218i	−0.0124402	+	0.0215471i	0.859738	+	0.510735i	$0.170627\pi$
$618$		0			0
$619$	−40.0206			−1.60857			−0.804283	−	0.594247i	$-0.797450\pi$
$619$	−40.0206			−1.60857			−0.804283	+	0.594247i	$0.797450\pi$
$620$		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	$-0.533015\pi$
$631$	−5.20154			−0.207070			−0.103535	+	0.994626i	$0.533015\pi$
$632$		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	$-0.979873\pi$
$643$	−11.2657	+	19.5128i	−0.444277	+	0.769510i	0.553725	+	0.832700i	$0.313206\pi$
$644$		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	$-0.993615\pi$
$647$	−12.2737	+	21.2586i	−0.482528	+	0.835763i	0.517271	+	0.855822i	$0.326948\pi$
$648$		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	−0.895731	−	0.444596i	$-0.853347\pi$
$659$	−21.3813	−	37.0335i	−0.832897	−	1.44262i	0.0628336	−	0.998024i	$-0.479986\pi$
$660$		0			0
$661$	9.55416	+	16.5483i	0.371614	+	0.643654i	0.989814	−	0.142367i	$-0.0454713\pi$
$661$	9.55416	+	16.5483i	0.371614	+	0.643654i	−0.618200	+	0.786021i	$0.712138\pi$
$662$		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	0.501411	−	0.865209i	$-0.332815\pi$
$673$	−12.9345	−	22.4032i	−0.498588	−	0.863579i	−0.999999	+	0.00162995i	$0.999481\pi$
$674$		0			0
$675$	64.9142	−	15.2628i	2.49855	−	0.587465i
$676$		0			0
$677$	−0.946686	+	1.63971i	−0.0363841	+	0.0630191i	−0.883644	−	0.468159i	$-0.844917\pi$
$677$	−0.946686	+	1.63971i	−0.0363841	+	0.0630191i	0.847260	+	0.531178i	$0.178251\pi$
$678$		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	$-0.754635\pi$
$683$	6.39573	−	11.0777i	0.244726	−	0.423878i	0.962055	+	0.272857i	$0.0879687\pi$
$684$		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	0.287017	+	0.957925i	$0.407336\pi$
$691$	−18.0349	+	31.2373i	−0.686079	+	1.18832i	−0.973096	+	0.230399i	$0.925997\pi$
$692$		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	−0.795478	−	0.605983i	$-0.792780\pi$
$709$	3.38318	−	5.85984i	0.127058	−	0.220071i	0.922536	+	0.385912i	$0.126113\pi$
$710$		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	$-0.243842\pi$
$719$	−6.43767	−	11.1504i	−0.240084	−	0.415839i	−0.960738	+	0.277457i	$0.910508\pi$
$720$		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	−0.999273	−	0.0381316i	$-0.987859\pi$
$727$	−14.3621	−	24.8758i	−0.532659	−	0.922593i	0.466613	−	0.884461i	$-0.345474\pi$
$728$		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	$-0.946519\pi$
$739$	−9.46395	+	16.3920i	−0.348137	+	0.602991i	0.637782	+	0.770217i	$0.279852\pi$
$740$		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	$-0.911749\pi$
$743$	−6.64732	+	11.5135i	−0.243867	+	0.422389i	0.717946	+	0.696099i	$0.245083\pi$
$744$		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	$-0.410338\pi$
$751$	15.2353			0.555945			0.277972	+	0.960589i	$0.410338\pi$
$752$		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	−0.744362	−	0.667777i	$-0.767246\pi$
$769$	5.71618	−	9.90071i	0.206131	−	0.357029i	0.950492	+	0.310748i	$0.100579\pi$
$770$		0			0
$771$	25.7635	−	1.98710i	0.927849	−	0.0715635i
$772$		0			0
$773$	7.40125	−	12.8193i	0.266204	−	0.461080i	−0.701674	−	0.712498i	$-0.747564\pi$
$773$	7.40125	−	12.8193i	0.266204	−	0.461080i	0.967878	+	0.251418i	$0.0808970\pi$
$774$		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	$-0.280971\pi$
$787$	−9.85887	−	17.0761i	−0.351431	−	0.608696i	−0.986500	+	0.163759i	$0.947638\pi$
$788$		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	−0.140597	−	0.990067i	$-0.544902\pi$
$797$	22.2215	−	38.4887i	0.787125	−	1.36334i	0.927722	−	0.373273i	$-0.121764\pi$
$798$		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	−0.944575	−	0.328296i	$-0.893526\pi$
$809$	−5.34657	+	9.26053i	−0.187975	+	0.325583i	0.756600	+	0.653878i	$0.226859\pi$
$810$		0			0
$811$	13.1292			0.461030			0.230515	−	0.973069i	$-0.425959\pi$
$811$	13.1292			0.461030			0.230515	+	0.973069i	$0.425959\pi$
$812$		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	−0.888044	−	0.459758i	$-0.847936\pi$
$821$	−1.31404	+	2.27598i	−0.0458602	+	0.0794323i	0.842184	+	0.539190i	$0.181270\pi$
$822$		0			0
$823$	−23.1960	−	40.1767i	−0.808563	−	1.40047i	−0.913859	−	0.406031i	$-0.866912\pi$
$823$	−23.1960	−	40.1767i	−0.808563	−	1.40047i	0.105296	−	0.994441i	$-0.466421\pi$
$824$		0			0
$825$	−42.7544	+	3.29758i	−1.48852	+	0.114807i
$826$		0			0
$827$	15.2072			0.528807			0.264404	−	0.964412i	$-0.414825\pi$
$827$	15.2072			0.528807			0.264404	+	0.964412i	$0.414825\pi$
$828$		0			0
$829$	19.0782	−	33.0445i	0.662615	−	1.14768i	−0.317311	−	0.948322i	$-0.602780\pi$
$829$	19.0782	−	33.0445i	0.662615	−	1.14768i	0.979926	−	0.199361i	$-0.0638867\pi$
$830$		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	$-0.105599\pi$
$839$	5.52298	+	9.56608i	0.190674	+	0.330258i	−0.754800	+	0.655955i	$0.772266\pi$
$840$		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	0.938728	+	0.344659i	$0.112005\pi$
$853$	22.4259	+	38.8428i	0.767847	+	1.32995i	−0.170881	+	0.985292i	$0.554661\pi$
$854$		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	$-0.672371\pi$
$859$	−30.2137			−1.03088			−0.515438	+	0.856927i	$0.672371\pi$
$860$		0			0
$861$	−0.0857979	−	12.0334i	−0.00292399	−	0.410097i
$862$		0			0
$863$	21.3315	+	36.9472i	0.726131	+	1.25770i	0.958507	+	0.285070i	$0.0920169\pi$
$863$	21.3315	+	36.9472i	0.726131	+	1.25770i	−0.232375	+	0.972626i	$0.574650\pi$
$864$		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	$-0.483048\pi$
$883$	3.16348			0.106460			0.0532299	+	0.998582i	$0.483048\pi$
$884$		0			0
$885$	18.8168	+	27.4705i	0.632520	+	0.923412i
$886$		0			0
$887$	10.0863			0.338666			0.169333	−	0.985559i	$-0.445839\pi$
$887$	10.0863			0.338666			0.169333	+	0.985559i	$0.445839\pi$
$888$		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	$-0.370332\pi$
$907$	23.8637			0.792380			0.396190	+	0.918169i	$0.370332\pi$
$908$		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	$-0.270583\pi$
$911$	−9.67946	−	16.7653i	−0.320695	−	0.555460i	−0.980632	+	0.195862i	$0.937250\pi$
$912$		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	0.896893	+	0.442247i	$0.145818\pi$
$919$	25.2052	+	43.6567i	0.831444	+	1.44010i	−0.0654498	+	0.997856i	$0.520848\pi$
$920$		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	0.276793	+	0.960930i	$0.410728\pi$
$929$	−21.1465	+	36.6267i	−0.693793	+	1.20168i	−0.970586	+	0.240755i	$0.922605\pi$
$930$		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	0.997534	+	0.0701867i	$0.0223595\pi$
$941$	17.1646	+	29.7300i	0.559550	+	0.969170i	−0.437983	+	0.898983i	$0.644307\pi$
$942$		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	$-0.982106\pi$
$947$	−13.8650	+	24.0149i	−0.450551	+	0.780378i	0.547869	+	0.836564i	$0.315439\pi$
$948$		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	$-0.946998\pi$
$967$	−10.8697	+	18.8269i	−0.349546	+	0.605432i	0.636623	+	0.771175i	$0.280331\pi$
$968$		0			0
$969$	−52.4459	+	4.04507i	−1.68480	+	0.129946i
$970$		0			0
$971$	19.7959	+	34.2875i	0.635281	+	1.10034i	0.986455	+	0.164029i	$0.0524491\pi$
$971$	19.7959	+	34.2875i	0.635281	+	1.10034i	−0.351174	+	0.936310i	$0.614218\pi$
$972$		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	0.956134	+	0.292930i	$0.0946303\pi$
$977$	22.8724	+	39.6161i	0.731752	+	1.26743i	−0.224382	+	0.974501i	$0.572036\pi$
$978$		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	$-0.577150\pi$
$983$	−15.0498			−0.480014			−0.240007	+	0.970771i	$0.577150\pi$
$984$		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	$-0.715907\pi$
$991$	11.3516	−	19.6616i	0.360596	−	0.624570i	0.988059	+	0.154076i	$0.0492400\pi$
$992$		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	1008.2.t.l.193.11		22
3.2	odd	2		3024.2.t.k.1873.11		22
4.3	odd	2		504.2.t.c.193.1	yes	22
7.2	even	3		1008.2.q.l.625.5		22
9.2	odd	6		3024.2.q.l.2881.1		22
9.7	even	3		1008.2.q.l.529.5		22
12.11	even	2		1512.2.t.c.361.11		22
21.2	odd	6		3024.2.q.l.2305.1		22
28.23	odd	6		504.2.q.c.121.7	yes	22
36.7	odd	6		504.2.q.c.25.7	✓	22
36.11	even	6		1512.2.q.d.1369.1		22
63.2	odd	6		3024.2.t.k.289.11		22
63.16	even	3	inner	1008.2.t.l.961.11		22
84.23	even	6		1512.2.q.d.793.1		22
252.79	odd	6		504.2.t.c.457.1	yes	22
252.191	even	6		1512.2.t.c.289.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.7	✓	22	36.7	odd	6
504.2.q.c.121.7	yes	22	28.23	odd	6
504.2.t.c.193.1	yes	22	4.3	odd	2
504.2.t.c.457.1	yes	22	252.79	odd	6
1008.2.q.l.529.5		22	9.7	even	3
1008.2.q.l.625.5		22	7.2	even	3
1008.2.t.l.193.11		22	1.1	even	1	trivial
1008.2.t.l.961.11		22	63.16	even	3	inner
1512.2.q.d.793.1		22	84.23	even	6
1512.2.q.d.1369.1		22	36.11	even	6
1512.2.t.c.289.11		22	252.191	even	6
1512.2.t.c.361.11		22	12.11	even	2
3024.2.q.l.2305.1		22	21.2	odd	6
3024.2.q.l.2881.1		22	9.2	odd	6
3024.2.t.k.289.11		22	63.2	odd	6
3024.2.t.k.1873.11		22	3.2	odd	2

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.t (of order \(3\), degree \(2\), not 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

L-functions

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