LMFDB - Embedded newform 504.2.t.c.457.7

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			457.7
Character	$\chi$	$=$	504.457
Dual form			504.2.t.c.193.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.666060 - 1.59886i) q^{3} -0.468169 q^{5} +(-2.39007 + 1.13471i) q^{7} +(-2.11273 - 2.12988i) q^{9} +O(q^{10})$	\(q+(0.666060 - 1.59886i) q^{3} -0.468169 q^{5} +(-2.39007 + 1.13471i) q^{7} +(-2.11273 - 2.12988i) q^{9} -1.34859 q^{11} +(-3.16486 - 5.48171i) q^{13} +(-0.311829 + 0.748538i) q^{15} +(-2.47120 - 4.28024i) q^{17} +(2.38910 - 4.13804i) q^{19} +(0.222319 + 4.57718i) q^{21} +7.62799 q^{23} -4.78082 q^{25} +(-4.81259 + 1.95934i) q^{27} +(-1.80565 + 3.12747i) q^{29} +(-3.24939 + 5.62810i) q^{31} +(-0.898239 + 2.15620i) q^{33} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(-10.8725 + 1.40904i) q^{39} +(-0.0251630 - 0.0435837i) q^{41} +(-0.431869 + 0.748019i) q^{43} +(0.989114 + 0.997143i) q^{45} +(5.49417 + 9.51619i) q^{47} +(4.42486 - 5.42408i) q^{49} +(-8.48948 + 1.10021i) q^{51} +(5.84976 + 10.1321i) q^{53} +0.631366 q^{55} +(-5.02488 - 6.57603i) q^{57} +(1.93892 - 3.35831i) q^{59} +(-1.87231 - 3.24294i) q^{61} +(7.46636 + 2.69322i) q^{63} +(1.48169 + 2.56637i) q^{65} +(1.32436 - 2.29385i) q^{67} +(5.08070 - 12.1961i) q^{69} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(-3.18431 + 7.64387i) q^{75} +(3.22321 - 1.53026i) q^{77} +(-1.58951 - 2.75311i) q^{79} +(-0.0727634 + 8.99971i) q^{81} +(4.90272 - 8.49176i) q^{83} +(1.15694 + 2.00388i) q^{85} +(3.79773 + 4.97007i) q^{87} +(5.30709 - 9.19214i) q^{89} +(13.7844 + 9.51045i) q^{91} +(6.83428 + 8.94398i) q^{93} +(-1.11850 + 1.93730i) q^{95} +(6.97792 - 12.0861i) q^{97} +(2.84919 + 2.87232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.666060	−	1.59886i	0.384550	−	0.923104i
$3$	0.666060	−	1.59886i	0.384550	−	0.923104i
$4$		0			0
$5$	−0.468169			−0.209372			−0.104686	−	0.994505i	$-0.533384\pi$
$5$	−0.468169			−0.209372			−0.104686	+	0.994505i	$0.533384\pi$
$6$		0			0
$7$	−2.39007	+	1.13471i	−0.903361	+	0.428881i
$7$	−2.39007	+	1.13471i	−0.903361	+	0.428881i
$8$		0			0
$9$	−2.11273	−	2.12988i	−0.704243	−	0.709959i
$10$		0			0
$11$	−1.34859			−0.406614			−0.203307	−	0.979115i	$-0.565169\pi$
$11$	−1.34859			−0.406614			−0.203307	+	0.979115i	$0.565169\pi$
$12$		0			0
$13$	−3.16486	−	5.48171i	−0.877775	−	1.52035i	−0.853777	−	0.520640i	$-0.825694\pi$
$13$	−3.16486	−	5.48171i	−0.877775	−	1.52035i	−0.0239988	−	0.999712i	$-0.507640\pi$
$14$		0			0
$15$	−0.311829	+	0.748538i	−0.0805139	+	0.193272i
$16$		0			0
$17$	−2.47120	−	4.28024i	−0.599353	−	1.03811i	−0.992917	−	0.118813i	$-0.962091\pi$
$17$	−2.47120	−	4.28024i	−0.599353	−	1.03811i	0.393563	−	0.919298i	$-0.371242\pi$
$18$		0			0
$19$	2.38910	−	4.13804i	0.548097	−	0.949332i	−0.450308	−	0.892873i	$-0.648686\pi$
$19$	2.38910	−	4.13804i	0.548097	−	0.949332i	0.998405	−	0.0564585i	$-0.0179809\pi$
$20$		0			0
$21$	0.222319	+	4.57718i	0.0485140	+	0.998823i
$22$		0			0
$23$	7.62799			1.59055			0.795273	−	0.606252i	$-0.207328\pi$
$23$	7.62799			1.59055			0.795273	+	0.606252i	$0.207328\pi$
$24$		0			0
$25$	−4.78082			−0.956164
$26$		0			0
$27$	−4.81259	+	1.95934i	−0.926183	+	0.377074i
$28$		0			0
$29$	−1.80565	+	3.12747i	−0.335300	+	0.580757i	−0.983542	−	0.180677i	$-0.942171\pi$
$29$	−1.80565	+	3.12747i	−0.335300	+	0.580757i	0.648242	+	0.761434i	$0.275504\pi$
$30$		0			0
$31$	−3.24939	+	5.62810i	−0.583607	+	1.01084i	0.411440	+	0.911437i	$0.365026\pi$
$31$	−3.24939	+	5.62810i	−0.583607	+	1.01084i	−0.995047	+	0.0994007i	$0.968307\pi$
$32$		0			0
$33$	−0.898239	+	2.15620i	−0.156363	+	0.375347i
$34$		0			0
$35$	1.11896	−	0.531237i	0.189138	−	0.0897954i
$36$		0			0
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	−0.00838383	−	0.999965i	$-0.502669\pi$
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	0.870187	−	0.492722i	$-0.163998\pi$
$38$		0			0
$39$	−10.8725	+	1.40904i	−1.74099	+	0.225627i
$40$		0			0
$41$	−0.0251630	−	0.0435837i	−0.00392981	−	0.00680662i	0.864054	−	0.503399i	$-0.167918\pi$
$41$	−0.0251630	−	0.0435837i	−0.00392981	−	0.00680662i	−0.867984	+	0.496593i	$0.834584\pi$
$42$		0			0
$43$	−0.431869	+	0.748019i	−0.0658594	+	0.114072i	−0.897075	−	0.441879i	$-0.854312\pi$
$43$	−0.431869	+	0.748019i	−0.0658594	+	0.114072i	0.831215	+	0.555950i	$0.187646\pi$
$44$		0			0
$45$	0.989114	+	0.997143i	0.147448	+	0.148645i
$46$		0			0
$47$	5.49417	+	9.51619i	0.801408	+	1.38808i	0.918690	+	0.394980i	$0.129249\pi$
$47$	5.49417	+	9.51619i	0.801408	+	1.38808i	−0.117282	+	0.993099i	$0.537418\pi$
$48$		0			0
$49$	4.42486	−	5.42408i	0.632123	−	0.774868i
$50$		0			0
$51$	−8.48948	+	1.10021i	−1.18877	+	0.154060i
$52$		0			0
$53$	5.84976	+	10.1321i	0.803526	+	1.39175i	0.917282	+	0.398239i	$0.130378\pi$
$53$	5.84976	+	10.1321i	0.803526	+	1.39175i	−0.113756	+	0.993509i	$0.536288\pi$
$54$		0			0
$55$	0.631366			0.0851334
$56$		0			0
$57$	−5.02488	−	6.57603i	−0.665561	−	0.871016i
$58$		0			0
$59$	1.93892	−	3.35831i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$59$	1.93892	−	3.35831i	0.252426	−	0.437215i	0.964193	+	0.265201i	$0.0854382\pi$
$60$		0			0
$61$	−1.87231	−	3.24294i	−0.239725	−	0.415216i	0.720910	−	0.693028i	$-0.243724\pi$
$61$	−1.87231	−	3.24294i	−0.239725	−	0.415216i	−0.960635	+	0.277813i	$0.910391\pi$
$62$		0			0
$63$	7.46636	+	2.69322i	0.940673	+	0.339314i
$64$		0			0
$65$	1.48169	+	2.56637i	0.183781	+	0.318318i
$66$		0			0
$67$	1.32436	−	2.29385i	0.161796	−	0.280239i	−0.773717	−	0.633532i	$-0.781605\pi$
$67$	1.32436	−	2.29385i	0.161796	−	0.280239i	0.935513	+	0.353293i	$0.114938\pi$
$68$		0			0
$69$	5.08070	−	12.1961i	0.611644	−	1.46824i
$70$		0			0
$71$	−7.04562			−0.836161			−0.418081	−	0.908410i	$-0.637297\pi$
$71$	−7.04562			−0.836161			−0.418081	+	0.908410i	$0.637297\pi$
$72$		0			0
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	0.605586	−	0.795780i	$-0.292939\pi$
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	−0.991959	+	0.126563i	$0.959605\pi$
$74$		0			0
$75$	−3.18431	+	7.64387i	−0.367693	+	0.882639i
$76$		0			0
$77$	3.22321	−	1.53026i	0.367319	−	0.174389i
$78$		0			0
$79$	−1.58951	−	2.75311i	−0.178834	−	0.309749i	0.762648	−	0.646814i	$-0.223899\pi$
$79$	−1.58951	−	2.75311i	−0.178834	−	0.309749i	−0.941481	+	0.337065i	$0.890566\pi$
$80$		0			0
$81$	−0.0727634	+	8.99971i	−0.00808482	+	0.999967i
$82$		0			0
$83$	4.90272	−	8.49176i	0.538143	−	0.932092i	−0.460861	−	0.887472i	$-0.652459\pi$
$83$	4.90272	−	8.49176i	0.538143	−	0.932092i	0.999004	−	0.0446192i	$-0.0142074\pi$
$84$		0			0
$85$	1.15694	+	2.00388i	0.125488	+	0.217351i
$86$		0			0
$87$	3.79773	+	4.97007i	0.407159	+	0.532847i
$88$		0			0
$89$	5.30709	−	9.19214i	0.562550	−	0.974365i	−0.434723	−	0.900564i	$-0.643154\pi$
$89$	5.30709	−	9.19214i	0.562550	−	0.974365i	0.997273	−	0.0738011i	$-0.0235130\pi$
$90$		0			0
$91$	13.7844	+	9.51045i	1.44500	+	0.996966i
$92$		0			0
$93$	6.83428	+	8.94398i	0.708682	+	0.927448i
$94$		0			0
$95$	−1.11850	+	1.93730i	−0.114756	+	0.198763i
$96$		0			0
$97$	6.97792	−	12.0861i	0.708500	−	1.22716i	−0.256913	−	0.966434i	$-0.582706\pi$
$97$	6.97792	−	12.0861i	0.708500	−	1.22716i	0.965413	−	0.260724i	$-0.0839611\pi$
$98$		0			0
$99$	2.84919	+	2.87232i	0.286355	+	0.288679i
$100$		0			0
$101$	4.24945			0.422836			0.211418	−	0.977396i	$-0.432192\pi$
$101$	4.24945			0.422836			0.211418	+	0.977396i	$0.432192\pi$
$102$		0			0
$103$	−8.95640			−0.882501			−0.441250	−	0.897384i	$-0.645465\pi$
$103$	−8.95640			−0.882501			−0.441250	+	0.897384i	$0.645465\pi$
$104$		0			0
$105$	−0.104083	−	2.14289i	−0.0101574	−	0.209125i
$106$		0			0
$107$	−0.810731	+	1.40423i	−0.0783763	+	0.135752i	−0.902550	−	0.430586i	$-0.858307\pi$
$107$	−0.810731	+	1.40423i	−0.0783763	+	0.135752i	0.824173	+	0.566338i	$0.191640\pi$
$108$		0			0
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	0.972631	−	0.232354i	$-0.0746428\pi$
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	−0.687540	+	0.726146i	$0.741309\pi$
$110$		0			0
$111$	−11.0255	−	14.4291i	−1.04650	−	1.36955i
$112$		0			0
$113$	4.14346	+	7.17669i	0.389784	+	0.675126i	0.992420	−	0.122890i	$-0.0392162\pi$
$113$	4.14346	+	7.17669i	0.389784	+	0.675126i	−0.602636	+	0.798016i	$0.705883\pi$
$114$		0			0
$115$	−3.57119			−0.333015
$116$		0			0
$117$	−4.98887	+	18.3221i	−0.461221	+	1.69388i
$118$		0			0
$119$	10.7632	+	7.42597i	0.986658	+	0.680738i
$120$		0			0
$121$	−9.18132			−0.834665
$122$		0			0
$123$	−0.0864444	+	0.0112029i	−0.00779443	+	0.00101013i
$124$		0			0
$125$	4.57908			0.409565
$126$		0			0
$127$	8.12368			0.720860			0.360430	−	0.932786i	$-0.382630\pi$
$127$	8.12368			0.720860			0.360430	+	0.932786i	$0.382630\pi$
$128$		0			0
$129$	0.908330	+	1.18873i	0.0799740	+	0.104661i
$130$		0			0
$131$	19.4965			1.70341			0.851707	−	0.524018i	$-0.175568\pi$
$131$	19.4965			1.70341			0.851707	+	0.524018i	$0.175568\pi$
$132$		0			0
$133$	−1.01463	+	12.6011i	−0.0879795	+	1.09266i
$134$		0			0
$135$	2.25311	−	0.917300i	0.193916	−	0.0789487i
$136$		0			0
$137$	−15.1035			−1.29038			−0.645189	−	0.764023i	$-0.723221\pi$
$137$	−15.1035			−1.29038			−0.645189	+	0.764023i	$0.723221\pi$
$138$		0			0
$139$	−2.18826	−	3.79017i	−0.185605	−	0.321478i	0.758175	−	0.652051i	$-0.226091\pi$
$139$	−2.18826	−	3.79017i	−0.185605	−	0.321478i	−0.943780	+	0.330573i	$0.892758\pi$
$140$		0			0
$141$	18.8745	−	2.44608i	1.58952	−	0.205997i
$142$		0			0
$143$	4.26809	+	7.39255i	0.356916	+	0.618196i
$144$		0			0
$145$	0.845348	−	1.46419i	0.0702023	−	0.121594i
$146$		0			0
$147$	−5.72514	−	10.6875i	−0.472201	−	0.881491i
$148$		0			0
$149$	−11.7564			−0.963121			−0.481561	−	0.876413i	$-0.659930\pi$
$149$	−11.7564			−0.963121			−0.481561	+	0.876413i	$0.659930\pi$
$150$		0			0
$151$	−5.14305			−0.418536			−0.209268	−	0.977858i	$-0.567108\pi$
$151$	−5.14305			−0.418536			−0.209268	+	0.977858i	$0.567108\pi$
$152$		0			0
$153$	−3.89542	+	14.3063i	−0.314926	+	1.15660i
$154$		0			0
$155$	1.52126	−	2.63490i	0.122191	−	0.211641i
$156$		0			0
$157$	6.04447	−	10.4693i	0.482401	−	0.835544i	−0.517395	−	0.855747i	$-0.673098\pi$
$157$	6.04447	−	10.4693i	0.482401	−	0.835544i	0.999796	+	0.0202033i	$0.00643136\pi$
$158$		0			0
$159$	20.0961	−	2.60439i	1.59372	−	0.206541i
$160$		0			0
$161$	−18.2314	+	8.65557i	−1.43684	+	0.682154i
$162$		0			0
$163$	−2.74663	+	4.75730i	−0.215133	+	0.372621i	−0.953314	−	0.301982i	$-0.902352\pi$
$163$	−2.74663	+	4.75730i	−0.215133	+	0.372621i	0.738181	+	0.674603i	$0.235685\pi$
$164$		0			0
$165$	0.420528	−	1.00947i	0.0327380	−	0.0785870i
$166$		0			0
$167$	−3.59378	−	6.22461i	−0.278095	−	0.481675i	0.692816	−	0.721114i	$-0.256370\pi$
$167$	−3.59378	−	6.22461i	−0.278095	−	0.481675i	−0.970911	+	0.239440i	$0.923036\pi$
$168$		0			0
$169$	−13.5327	+	23.4394i	−1.04098	+	1.80303i
$170$		0			0
$171$	−13.8610	+	3.65406i	−1.05998	+	0.279433i
$172$		0			0
$173$	3.97951	+	6.89271i	0.302557	+	0.524043i	0.976714	−	0.214544i	$-0.0688266\pi$
$173$	3.97951	+	6.89271i	0.302557	+	0.524043i	−0.674158	+	0.738587i	$0.735493\pi$
$174$		0			0
$175$	11.4265	−	5.42485i	0.863761	−	0.410080i
$176$		0			0
$177$	−4.07804	−	5.33691i	−0.306524	−	0.401147i
$178$		0			0
$179$	0.168821	+	0.292406i	0.0126182	+	0.0218554i	0.872266	−	0.489032i	$-0.162650\pi$
$179$	0.168821	+	0.292406i	0.0126182	+	0.0218554i	−0.859647	+	0.510888i	$0.829317\pi$
$180$		0			0
$181$	7.05801			0.524618			0.262309	−	0.964984i	$-0.415516\pi$
$181$	7.05801			0.524618			0.262309	+	0.964984i	$0.415516\pi$
$182$		0			0
$183$	−6.43209	+	0.833578i	−0.475474	+	0.0616198i
$184$		0			0
$185$	−2.45421	+	4.25082i	−0.180437	+	0.312526i
$186$		0			0
$187$	3.33262	+	5.77227i	0.243705	+	0.422110i
$188$		0			0
$189$	9.27914	−	10.1438i	0.674958	−	0.737856i
$190$		0			0
$191$	−8.85934	−	15.3448i	−0.641039	−	1.11031i	−0.985201	−	0.171402i	$-0.945170\pi$
$191$	−8.85934	−	15.3448i	−0.641039	−	1.11031i	0.344162	−	0.938910i	$-0.388163\pi$
$192$		0			0
$193$	8.40121	−	14.5513i	0.604732	−	1.04743i	−0.387362	−	0.921928i	$-0.626614\pi$
$193$	8.40121	−	14.5513i	0.604732	−	1.04743i	0.992094	−	0.125499i	$-0.0400531\pi$
$194$		0			0
$195$	5.09016	−	0.659669i	0.364514	−	0.0472399i
$196$		0			0
$197$	5.97545			0.425733			0.212867	−	0.977081i	$-0.431720\pi$
$197$	5.97545			0.425733			0.212867	+	0.977081i	$0.431720\pi$
$198$		0			0
$199$	6.26093	+	10.8443i	0.443826	+	0.768729i	0.997970	−	0.0636923i	$-0.0202876\pi$
$199$	6.26093	+	10.8443i	0.443826	+	0.768729i	−0.554144	+	0.832421i	$0.686954\pi$
$200$		0			0
$201$	−2.78546	−	3.64531i	−0.196471	−	0.257120i
$202$		0			0
$203$	0.766842	−	9.52376i	0.0538217	−	0.668437i
$204$		0			0
$205$	0.0117806	+	0.0204045i	0.000822790	+	0.00142511i
$206$		0			0
$207$	−16.1159	−	16.2467i	−1.12013	−	1.12922i
$208$		0			0
$209$	−3.22190	+	5.58050i	−0.222864	+	0.386011i
$210$		0			0
$211$	1.17688	+	2.03842i	0.0810198	+	0.140330i	0.903688	−	0.428191i	$-0.140849\pi$
$211$	1.17688	+	2.03842i	0.0810198	+	0.140330i	−0.822668	+	0.568521i	$0.807516\pi$
$212$		0			0
$213$	−4.69281	+	11.2650i	−0.321546	+	0.771864i
$214$		0			0
$215$	0.202188	−	0.350199i	0.0137891	−	0.0238834i
$216$		0			0
$217$	1.37999	−	17.1387i	0.0936795	−	1.16345i
$218$		0			0
$219$	−11.3407	+	1.46972i	−0.766336	+	0.0993147i
$220$		0			0
$221$	−15.6420	+	27.0928i	−1.05220	+	1.82246i
$222$		0			0
$223$	5.30709	−	9.19215i	0.355389	−	0.615552i	−0.631795	−	0.775135i	$-0.717682\pi$
$223$	5.30709	−	9.19215i	0.355389	−	0.615552i	0.987184	+	0.159583i	$0.0510150\pi$
$224$		0			0
$225$	10.1006	+	10.1826i	0.673371	+	0.678837i
$226$		0			0
$227$	1.27550			0.0846578			0.0423289	−	0.999104i	$-0.486522\pi$
$227$	1.27550			0.0846578			0.0423289	+	0.999104i	$0.486522\pi$
$228$		0			0
$229$	−13.4663			−0.889876			−0.444938	−	0.895561i	$-0.646774\pi$
$229$	−13.4663			−0.889876			−0.444938	+	0.895561i	$0.646774\pi$
$230$		0			0
$231$	−0.299816	−	6.17272i	−0.0197264	−	0.406135i
$232$		0			0
$233$	9.98509	−	17.2947i	0.654145	−	1.13301i	−0.327963	−	0.944691i	$-0.606362\pi$
$233$	9.98509	−	17.2947i	0.654145	−	1.13301i	0.982107	−	0.188321i	$-0.0603047\pi$
$234$		0			0
$235$	−2.57220	−	4.45519i	−0.167792	−	0.290624i
$236$		0			0
$237$	−5.46055	+	0.707670i	−0.354701	+	0.0459681i
$238$		0			0
$239$	−14.1092	−	24.4379i	−0.912650	−	1.58076i	−0.810305	−	0.586008i	$-0.800699\pi$
$239$	−14.1092	−	24.4379i	−0.912650	−	1.58076i	−0.102345	−	0.994749i	$-0.532635\pi$
$240$		0			0
$241$	−17.3524			−1.11777			−0.558884	−	0.829246i	$-0.688770\pi$
$241$	−17.3524			−1.11777			−0.558884	+	0.829246i	$0.688770\pi$
$242$		0			0
$243$	14.3408	+	6.11068i	0.919965	+	0.392001i
$244$		0			0
$245$	−2.07158	+	2.53939i	−0.132349	+	0.162235i
$246$		0			0
$247$	−30.2447			−1.92442
$248$		0			0
$249$	−10.3117	−	13.4948i	−0.653475	−	0.855198i
$250$		0			0
$251$	6.29051			0.397054			0.198527	−	0.980095i	$-0.436384\pi$
$251$	6.29051			0.397054			0.198527	+	0.980095i	$0.436384\pi$
$252$		0			0
$253$	−10.2870			−0.646738
$254$		0			0
$255$	3.97451	−	0.515084i	0.248894	−	0.0322558i
$256$		0			0
$257$	−6.13637			−0.382777			−0.191388	−	0.981514i	$-0.561299\pi$
$257$	−6.13637			−0.382777			−0.191388	+	0.981514i	$0.561299\pi$
$258$		0			0
$259$	−2.22629	+	27.6493i	−0.138335	+	1.71805i
$260$		0			0
$261$	10.4760	−	2.76169i	0.648446	−	0.170944i
$262$		0			0
$263$	5.87914			0.362523			0.181262	−	0.983435i	$-0.441982\pi$
$263$	5.87914			0.362523			0.181262	+	0.983435i	$0.441982\pi$
$264$		0			0
$265$	−2.73868	−	4.74352i	−0.168235	−	0.291392i
$266$		0			0
$267$	−11.1621	−	14.6078i	−0.683112	−	0.893985i
$268$		0			0
$269$	−15.4633	−	26.7832i	−0.942812	−	1.63300i	−0.760074	−	0.649837i	$-0.774837\pi$
$269$	−15.4633	−	26.7832i	−0.942812	−	1.63300i	−0.182738	−	0.983162i	$-0.558496\pi$
$270$		0			0
$271$	5.44528	−	9.43150i	0.330777	−	0.572923i	−0.651887	−	0.758316i	$-0.726022\pi$
$271$	5.44528	−	9.43150i	0.330777	−	0.572923i	0.982664	+	0.185393i	$0.0593558\pi$
$272$		0			0
$273$	24.3871	−	15.7048i	1.47598	−	0.950500i
$274$		0			0
$275$	6.44734			0.388789
$276$		0			0
$277$	19.5900			1.17705			0.588524	−	0.808480i	$-0.299709\pi$
$277$	19.5900			1.17705			0.588524	+	0.808480i	$0.299709\pi$
$278$		0			0
$279$	18.8522	−	4.96985i	1.12865	−	0.297537i
$280$		0			0
$281$	−0.142477	+	0.246777i	−0.00849944	+	0.0147215i	−0.870244	−	0.492621i	$-0.836039\pi$
$281$	−0.142477	+	0.246777i	−0.00849944	+	0.0147215i	0.861744	+	0.507343i	$0.169372\pi$
$282$		0			0
$283$	−1.42135	+	2.46185i	−0.0844903	+	0.146342i	−0.905174	−	0.425041i	$-0.860260\pi$
$283$	−1.42135	+	2.46185i	−0.0844903	+	0.146342i	0.820684	+	0.571383i	$0.193593\pi$
$284$		0			0
$285$	2.35249	+	3.07869i	0.139350	+	0.182366i
$286$		0			0
$287$	0.109596	+	0.0756152i	0.00646926	+	0.00446342i
$288$		0			0
$289$	−3.71364	+	6.43221i	−0.218449	+	0.378365i
$290$		0			0
$291$	−14.6763	−	19.2068i	−0.860341	−	1.12592i
$292$		0			0
$293$	−1.45979	−	2.52842i	−0.0852816	−	0.147712i	0.820230	−	0.572034i	$-0.193846\pi$
$293$	−1.45979	−	2.52842i	−0.0852816	−	0.147712i	−0.905511	+	0.424322i	$0.860512\pi$
$294$		0			0
$295$	−0.907743	+	1.57226i	−0.0528509	+	0.0915404i
$296$		0			0
$297$	6.49019	−	2.64233i	0.376599	−	0.153324i
$298$		0			0
$299$	−24.1415	−	41.8144i	−1.39614	−	2.41819i
$300$		0			0
$301$	0.183411	−	2.27786i	0.0105716	−	0.131294i
$302$		0			0
$303$	2.83039	−	6.79429i	0.162602	−	0.390322i
$304$		0			0
$305$	0.876558	+	1.51824i	0.0501916	+	0.0869344i
$306$		0			0
$307$	−4.12553			−0.235457			−0.117728	−	0.993046i	$-0.537561\pi$
$307$	−4.12553			−0.235457			−0.117728	+	0.993046i	$0.537561\pi$
$308$		0			0
$309$	−5.96550	+	14.3201i	−0.339366	+	0.814640i
$310$		0			0
$311$	−7.69583	+	13.3296i	−0.436390	+	0.755850i	−0.997408	−	0.0719535i	$-0.977077\pi$
$311$	−7.69583	+	13.3296i	−0.436390	+	0.755850i	0.561018	+	0.827804i	$0.310410\pi$
$312$		0			0
$313$	10.3620	+	17.9475i	0.585694	+	1.01445i	0.994789	+	0.101959i	$0.0325112\pi$
$313$	10.3620	+	17.9475i	0.585694	+	1.01445i	−0.409095	+	0.912492i	$0.634156\pi$
$314$		0			0
$315$	−3.49552	−	1.26088i	−0.196950	−	0.0710427i
$316$		0			0
$317$	0.244146	+	0.422873i	0.0137126	+	0.0237509i	0.872800	−	0.488078i	$-0.162302\pi$
$317$	0.244146	+	0.422873i	0.0137126	+	0.0237509i	−0.859088	+	0.511828i	$0.828968\pi$
$318$		0			0
$319$	2.43507	−	4.21766i	0.136338	−	0.236144i
$320$		0			0
$321$	1.70517	+	2.23155i	0.0951734	+	0.124553i
$322$		0			0
$323$	−23.6157			−1.31402
$324$		0			0
$325$	15.1306	+	26.2070i	0.839297	+	1.45370i
$326$		0			0
$327$	10.2252	−	1.32515i	0.565454	−	0.0732810i
$328$		0			0
$329$	−23.9296	−	16.5100i	−1.31928	−	0.910228i
$330$		0			0
$331$	9.47864	+	16.4175i	0.520993	+	0.902387i	0.999702	+	0.0244131i	$0.00777169\pi$
$331$	9.47864	+	16.4175i	0.520993	+	0.902387i	−0.478709	+	0.877974i	$0.658895\pi$
$332$		0			0
$333$	−30.4138	+	8.01772i	−1.66667	+	0.439368i
$334$		0			0
$335$	−0.620023	+	1.07391i	−0.0338755	+	0.0586740i
$336$		0			0
$337$	11.6202	+	20.1268i	0.632993	+	1.09638i	0.986937	+	0.161109i	$0.0515071\pi$
$337$	11.6202	+	20.1268i	0.632993	+	1.09638i	−0.353944	+	0.935267i	$0.615160\pi$
$338$		0			0
$339$	14.2343	−	1.84473i	0.773104	−	0.100192i
$340$		0			0
$341$	4.38208	−	7.58998i	0.237303	−	0.411020i
$342$		0			0
$343$	−4.42096	+	17.9849i	−0.238709	+	0.971091i
$344$		0			0
$345$	−2.37863	+	5.70984i	−0.128061	+	0.307408i
$346$		0			0
$347$	−9.09439	+	15.7519i	−0.488212	+	0.845609i	−0.999908	−	0.0135582i	$-0.995684\pi$
$347$	−9.09439	+	15.7519i	−0.488212	+	0.845609i	0.511696	+	0.859167i	$0.329018\pi$
$348$		0			0
$349$	−9.40155	+	16.2840i	−0.503253	+	0.871661i	0.496740	+	0.867900i	$0.334530\pi$
$349$	−9.40155	+	16.2840i	−0.503253	+	0.871661i	−0.999993	+	0.00376081i	$0.998803\pi$
$350$		0			0
$351$	25.9717	+	20.1802i	1.38627	+	1.07714i
$352$		0			0
$353$	−11.9199			−0.634435			−0.317217	−	0.948353i	$-0.602748\pi$
$353$	−11.9199			−0.634435			−0.317217	+	0.948353i	$0.602748\pi$
$354$		0			0
$355$	3.29854			0.175068
$356$		0			0
$357$	19.0420	−	12.2627i	1.00781	−	0.649011i
$358$		0			0
$359$	−17.3849	+	30.1115i	−0.917540	+	1.58923i	−0.114400	+	0.993435i	$0.536495\pi$
$359$	−17.3849	+	30.1115i	−0.917540	+	1.58923i	−0.803140	+	0.595791i	$0.796839\pi$
$360$		0			0
$361$	−1.91559	−	3.31790i	−0.100821	−	0.174626i
$362$		0			0
$363$	−6.11531	+	14.6797i	−0.320971	+	0.770483i
$364$		0			0
$365$	1.54551	+	2.67689i	0.0808954	+	0.140115i
$366$		0			0
$367$	−28.8861			−1.50784			−0.753922	−	0.656964i	$-0.771840\pi$
$367$	−28.8861			−1.50784			−0.753922	+	0.656964i	$0.771840\pi$
$368$		0			0
$369$	−0.0396652	+	0.145675i	−0.00206489	+	0.00758352i
$370$		0			0
$371$	−25.4783	−	17.5786i	−1.32277	−	0.912634i
$372$		0			0
$373$	14.3094			0.740915			0.370457	−	0.928849i	$-0.379201\pi$
$373$	14.3094			0.740915			0.370457	+	0.928849i	$0.379201\pi$
$374$		0			0
$375$	3.04994	−	7.32132i	0.157498	−	0.378071i
$376$		0			0
$377$	22.8585			1.17727
$378$		0			0
$379$	1.15511			0.0593340			0.0296670	−	0.999560i	$-0.490555\pi$
$379$	1.15511			0.0593340			0.0296670	+	0.999560i	$0.490555\pi$
$380$		0			0
$381$	5.41086	−	12.9887i	0.277207	−	0.665429i
$382$		0			0
$383$	33.8262			1.72844			0.864219	−	0.503115i	$-0.167813\pi$
$383$	33.8262			1.72844			0.864219	+	0.503115i	$0.167813\pi$
$384$		0			0
$385$	−1.50901	+	0.716418i	−0.0769062	+	0.0365121i
$386$		0			0
$387$	2.50561	−	0.660532i	0.127367	−	0.0335767i
$388$		0			0
$389$	19.3216			0.979644			0.489822	−	0.871822i	$-0.337062\pi$
$389$	19.3216			0.979644			0.489822	+	0.871822i	$0.337062\pi$
$390$		0			0
$391$	−18.8503	−	32.6496i	−0.953299	−	1.65116i
$392$		0			0
$393$	12.9858	−	31.1722i	0.655048	−	1.57243i
$394$		0			0
$395$	0.744159	+	1.28892i	0.0374427	+	0.0648526i
$396$		0			0
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	−0.978419	−	0.206632i	$-0.933750\pi$
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	0.668158	+	0.744019i	$0.267083\pi$
$398$		0			0
$399$	19.4717	+	10.0154i	0.974804	+	0.501396i
$400$		0			0
$401$	−30.5136			−1.52378			−0.761889	−	0.647708i	$-0.775728\pi$
$401$	−30.5136			−1.52378			−0.761889	+	0.647708i	$0.775728\pi$
$402$		0			0
$403$	41.1355			2.04910
$404$		0			0
$405$	0.0340656	−	4.21338i	0.00169273	−	0.209365i
$406$		0			0
$407$	−7.06948	+	12.2447i	−0.350421	+	0.606947i
$408$		0			0
$409$	2.62723	−	4.55050i	0.129908	−	0.225008i	−0.793733	−	0.608267i	$-0.791865\pi$
$409$	2.62723	−	4.55050i	0.129908	−	0.225008i	0.923641	+	0.383259i	$0.125198\pi$
$410$		0			0
$411$	−10.0598	+	24.1484i	−0.496215	+	1.19115i
$412$		0			0
$413$	−0.823443	+	10.2267i	−0.0405190	+	0.503224i
$414$		0			0
$415$	−2.29530	+	3.97558i	−0.112672	+	0.195154i
$416$		0			0
$417$	−7.51747	+	0.974240i	−0.368132	+	0.0477088i
$418$		0			0
$419$	15.2824	+	26.4699i	0.746594	+	1.29314i	0.949446	+	0.313930i	$0.101646\pi$
$419$	15.2824	+	26.4699i	0.746594	+	1.29314i	−0.202852	+	0.979209i	$0.565021\pi$
$420$		0			0
$421$	3.11608	−	5.39721i	0.151869	−	0.263044i	−0.780046	−	0.625722i	$-0.784804\pi$
$421$	3.11608	−	5.39721i	0.151869	−	0.263044i	0.931914	+	0.362678i	$0.118138\pi$
$422$		0			0
$423$	8.66063	−	31.8070i	0.421094	−	1.54651i
$424$		0			0
$425$	11.8143	+	20.4630i	0.573080	+	0.992604i
$426$		0			0
$427$	8.15475	+	5.62631i	0.394636	+	0.272276i
$428$		0			0
$429$	14.6625	−	1.90021i	0.707911	−	0.0917430i
$430$		0			0
$431$	14.8142	+	25.6590i	0.713576	+	1.23595i	0.963506	+	0.267686i	$0.0862590\pi$
$431$	14.8142	+	25.6590i	0.713576	+	1.23595i	−0.249930	+	0.968264i	$0.580408\pi$
$432$		0			0
$433$	7.36815			0.354091			0.177045	−	0.984203i	$-0.443346\pi$
$433$	7.36815			0.354091			0.177045	+	0.984203i	$0.443346\pi$
$434$		0			0
$435$	−1.77798	−	2.32683i	−0.0852476	−	0.111563i
$436$		0			0
$437$	18.2240	−	31.5649i	0.871773	−	1.50996i
$438$		0			0
$439$	−5.22135	−	9.04364i	−0.249201	−	0.431629i	0.714103	−	0.700041i	$-0.246835\pi$
$439$	−5.22135	−	9.04364i	−0.249201	−	0.431629i	−0.963304	+	0.268411i	$0.913501\pi$
$440$		0			0
$441$	−20.9011	+	2.03519i	−0.995293	+	0.0969137i
$442$		0			0
$443$	−2.83332	−	4.90745i	−0.134615	−	0.233160i	0.790835	−	0.612029i	$-0.209646\pi$
$443$	−2.83332	−	4.90745i	−0.134615	−	0.233160i	−0.925450	+	0.378869i	$0.876313\pi$
$444$		0			0
$445$	−2.48461	+	4.30348i	−0.117782	+	0.204004i
$446$		0			0
$447$	−7.83046	+	18.7969i	−0.370368	+	0.889061i
$448$		0			0
$449$	11.4794			0.541748			0.270874	−	0.962615i	$-0.412687\pi$
$449$	11.4794			0.541748			0.270874	+	0.962615i	$0.412687\pi$
$450$		0			0
$451$	0.0339345	+	0.0587763i	0.00159791	+	0.00276767i
$452$		0			0
$453$	−3.42558	+	8.22304i	−0.160948	+	0.386352i
$454$		0			0
$455$	−6.45343	−	4.45250i	−0.302541	−	0.208736i
$456$		0			0
$457$	−9.79361	−	16.9630i	−0.458126	−	0.793497i	0.540736	−	0.841192i	$-0.318146\pi$
$457$	−9.79361	−	16.9630i	−0.458126	−	0.793497i	−0.998862	+	0.0476953i	$0.984812\pi$
$458$		0			0
$459$	20.2793	+	15.7571i	0.946556	+	0.735480i
$460$		0			0
$461$	17.3028	−	29.9693i	0.805871	−	1.39581i	−0.109830	−	0.993950i	$-0.535031\pi$
$461$	17.3028	−	29.9693i	0.805871	−	1.39581i	0.915701	−	0.401859i	$-0.131636\pi$
$462$		0			0
$463$	6.91882	+	11.9837i	0.321545	+	0.556932i	0.980807	−	0.194981i	$-0.0624646\pi$
$463$	6.91882	+	11.9837i	0.321545	+	0.556932i	−0.659262	+	0.751913i	$0.729131\pi$
$464$		0			0
$465$	−3.19960	−	4.18730i	−0.148378	−	0.194181i
$466$		0			0
$467$	3.71088	−	6.42743i	0.171719	−	0.297426i	−0.767302	−	0.641286i	$-0.778401\pi$
$467$	3.71088	−	6.42743i	0.171719	−	0.297426i	0.939021	+	0.343860i	$0.111735\pi$
$468$		0			0
$469$	−0.562442	+	6.98523i	−0.0259712	+	0.322548i
$470$		0			0
$471$	−12.7130	−	16.6375i	−0.585786	−	0.766615i
$472$		0			0
$473$	0.582412	−	1.00877i	0.0267793	−	0.0463832i
$474$		0			0
$475$	−11.4218	+	19.7832i	−0.524070	+	0.907716i
$476$		0			0
$477$	9.22114	−	33.8656i	0.422207	−	1.55060i
$478$		0			0
$479$	−7.79154			−0.356005			−0.178002	−	0.984030i	$-0.556963\pi$
$479$	−7.79154			−0.356005			−0.178002	+	0.984030i	$0.556963\pi$
$480$		0			0
$481$	−66.3627			−3.02588
$482$		0			0
$483$	1.69585	+	34.9147i	0.0771636	+	1.58867i
$484$		0			0
$485$	−3.26684	+	5.65834i	−0.148340	+	0.256932i
$486$		0			0
$487$	−1.04434	−	1.80886i	−0.0473238	−	0.0819672i	0.841393	−	0.540423i	$-0.181736\pi$
$487$	−1.04434	−	1.80886i	−0.0473238	−	0.0819672i	−0.888717	+	0.458456i	$0.848403\pi$
$488$		0			0
$489$	5.77686	+	7.56014i	0.261239	+	0.341881i
$490$		0			0
$491$	−16.8767	−	29.2312i	−0.761633	−	1.31919i	−0.942008	−	0.335590i	$-0.891064\pi$
$491$	−16.8767	−	29.2312i	−0.761633	−	1.31919i	0.180375	−	0.983598i	$-0.442269\pi$
$492$		0			0
$493$	17.8484			0.803853
$494$		0			0
$495$	−1.33390	−	1.34473i	−0.0599545	−	0.0604412i
$496$		0			0
$497$	16.8395	−	7.99475i	0.755356	−	0.358613i
$498$		0			0
$499$	41.8196			1.87210			0.936052	−	0.351862i	$-0.114451\pi$
$499$	41.8196			1.87210			0.936052	+	0.351862i	$0.114451\pi$
$500$		0			0
$501$	−12.3460	+	1.60000i	−0.551577	+	0.0714826i
$502$		0			0
$503$	6.54978			0.292040			0.146020	−	0.989282i	$-0.453354\pi$
$503$	6.54978			0.292040			0.146020	+	0.989282i	$0.453354\pi$
$504$		0			0
$505$	−1.98946			−0.0885299
$506$		0			0
$507$	28.4627	+	37.2490i	1.26407	+	1.65429i
$508$		0			0
$509$	−12.6131			−0.559064			−0.279532	−	0.960136i	$-0.590179\pi$
$509$	−12.6131			−0.559064			−0.279532	+	0.960136i	$0.590179\pi$
$510$		0			0
$511$	14.3781	+	9.92004i	0.636048	+	0.438837i
$512$		0			0
$513$	−3.38994	+	24.5957i	−0.149669	+	1.08593i
$514$		0			0
$515$	4.19311			0.184771
$516$		0			0
$517$	−7.40936	−	12.8334i	−0.325863	−	0.564412i
$518$		0			0
$519$	13.6711	−	1.77173i	0.600095	−	0.0777703i
$520$		0			0
$521$	10.2688	+	17.7861i	0.449883	+	0.779221i	0.998378	−	0.0569331i	$-0.0181322\pi$
$521$	10.2688	+	17.7861i	0.449883	+	0.779221i	−0.548495	+	0.836154i	$0.684799\pi$
$522$		0			0
$523$	14.4579	−	25.0419i	0.632202	−	1.09501i	−0.354899	−	0.934905i	$-0.615485\pi$
$523$	14.4579	−	25.0419i	0.632202	−	1.09501i	0.987101	−	0.160101i	$-0.0511820\pi$
$524$		0			0
$525$	−1.06287	−	21.8827i	−0.0463873	−	0.955038i
$526$		0			0
$527$	32.1195			1.39915
$528$		0			0
$529$	35.1862			1.52983
$530$		0			0
$531$	−11.2492	+	2.96553i	−0.488174	+	0.128693i
$532$		0			0
$533$	−0.159275	+	0.275873i	−0.00689897	+	0.0119494i
$534$		0			0
$535$	0.379559	−	0.657416i	0.0164098	−	0.0284226i
$536$		0			0
$537$	0.579961	−	0.0751611i	0.0250272	−	0.00324344i
$538$		0			0
$539$	−5.96730	+	7.31483i	−0.257030	+	0.315072i
$540$		0			0
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	−0.786524	−	0.617560i	$-0.788121\pi$
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	0.928085	+	0.372369i	$0.121455\pi$
$542$		0			0
$543$	4.70106	−	11.2848i	0.201742	−	0.484277i
$544$		0			0
$545$	−1.39348	−	2.41357i	−0.0596900	−	0.103386i
$546$		0			0
$547$	4.46777	−	7.73840i	0.191028	−	0.330870i	−0.754563	−	0.656227i	$-0.772151\pi$
$547$	4.46777	−	7.73840i	0.191028	−	0.330870i	0.945591	+	0.325357i	$0.105485\pi$
$548$		0			0
$549$	−2.95138	+	10.8392i	−0.125962	+	0.462608i
$550$		0			0
$551$	8.62774	+	14.9437i	0.367554	+	0.636622i
$552$		0			0
$553$	6.92302	+	4.77649i	0.294397	+	0.203117i
$554$		0			0
$555$	5.16182	+	6.75525i	0.219107	+	0.286744i
$556$		0			0
$557$	−2.93523	−	5.08396i	−0.124370	−	0.215414i	0.797117	−	0.603825i	$-0.206358\pi$
$557$	−2.93523	−	5.08396i	−0.124370	−	0.215414i	−0.921486	+	0.388411i	$0.873024\pi$
$558$		0			0
$559$	5.46723			0.231239
$560$		0			0
$561$	11.4488	−	1.48373i	0.483368	−	0.0626430i
$562$		0			0
$563$	−13.7986	+	23.8998i	−0.581541	+	1.00726i	0.413756	+	0.910388i	$0.364217\pi$
$563$	−13.7986	+	23.8998i	−0.581541	+	1.00726i	−0.995297	+	0.0968707i	$0.969117\pi$
$564$		0			0
$565$	−1.93984	−	3.35991i	−0.0816098	−	0.141352i
$566$		0			0
$567$	−10.0382	−	21.5925i	−0.421563	−	0.906799i
$568$		0			0
$569$	13.9601	+	24.1796i	0.585238	+	1.01366i	0.994846	+	0.101400i	$0.0323321\pi$
$569$	13.9601	+	24.1796i	0.585238	+	1.01366i	−0.409608	+	0.912262i	$0.634335\pi$
$570$		0			0
$571$	15.8987	−	27.5373i	0.665339	−	1.15240i	−0.313854	−	0.949471i	$-0.601620\pi$
$571$	15.8987	−	27.5373i	0.665339	−	1.15240i	0.979193	−	0.202930i	$-0.0650463\pi$
$572$		0			0
$573$	−30.4351	+	3.94430i	−1.27145	+	0.164775i
$574$		0			0
$575$	−36.4680			−1.52082
$576$		0			0
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	0.996327	+	0.0856281i	$0.0272897\pi$
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	−0.424007	+	0.905659i	$0.639377\pi$
$578$		0			0
$579$	−17.6699	−	23.1244i	−0.734334	−	0.961019i
$580$		0			0
$581$	−2.08214	+	25.8591i	−0.0863817	+	1.07281i
$582$		0			0
$583$	−7.88889	−	13.6640i	−0.326725	−	0.565904i
$584$		0			0
$585$	2.33563	−	8.57785i	0.0965666	−	0.354651i
$586$		0			0
$587$	−7.12422	+	12.3395i	−0.294048	+	0.509306i	−0.974763	−	0.223242i	$-0.928336\pi$
$587$	−7.12422	+	12.3395i	−0.294048	+	0.509306i	0.680715	+	0.732548i	$0.261669\pi$
$588$		0			0
$589$	15.5262	+	26.8922i	0.639747	+	1.10807i
$590$		0			0
$591$	3.98001	−	9.55393i	0.163716	−	0.392996i
$592$		0			0
$593$	15.4636	−	26.7838i	0.635015	−	1.09988i	−0.351498	−	0.936189i	$-0.614327\pi$
$593$	15.4636	−	26.7838i	0.635015	−	1.09988i	0.986512	−	0.163689i	$-0.0523392\pi$
$594$		0			0
$595$	−5.03898	−	3.47661i	−0.206578	−	0.142527i
$596$		0			0
$597$	21.5086	−	2.78745i	0.880290	−	0.114083i
$598$		0			0
$599$	−18.2657	+	31.6372i	−0.746318	+	1.29266i	0.203258	+	0.979125i	$0.434847\pi$
$599$	−18.2657	+	31.6372i	−0.746318	+	1.29266i	−0.949576	+	0.313536i	$0.898486\pi$
$600$		0			0
$601$	7.11575	−	12.3248i	0.290257	−	0.502741i	−0.683613	−	0.729845i	$-0.739592\pi$
$601$	7.11575	−	12.3248i	0.290257	−	0.502741i	0.973871	+	0.227104i	$0.0729257\pi$
$602$		0			0
$603$	−7.68363	+	2.02557i	−0.312902	+	0.0824875i
$604$		0			0
$605$	4.29841			0.174755
$606$		0			0
$607$	−29.3457			−1.19111			−0.595553	−	0.803316i	$-0.703067\pi$
$607$	−29.3457			−1.19111			−0.595553	+	0.803316i	$0.703067\pi$
$608$		0			0
$609$	−14.7164	−	7.56947i	−0.596340	−	0.306730i
$610$		0			0
$611$	34.7766	−	60.2349i	1.40691	−	2.43684i
$612$		0			0
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	0.779213	−	0.626760i	$-0.215619\pi$
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	−0.932396	+	0.361438i	$0.882286\pi$
$614$		0			0
$615$	0.0404706	−	0.00524486i	0.00163193	−	0.000211493i
$616$		0			0
$617$	−10.4367	−	18.0769i	−0.420165	−	0.727748i	0.575790	−	0.817598i	$-0.304695\pi$
$617$	−10.4367	−	18.0769i	−0.420165	−	0.727748i	−0.995955	+	0.0898500i	$0.971361\pi$
$618$		0			0
$619$	−25.2600			−1.01528			−0.507642	−	0.861568i	$-0.669483\pi$
$619$	−25.2600			−1.01528			−0.507642	+	0.861568i	$0.669483\pi$
$620$		0			0
$621$	−36.7104	+	14.9458i	−1.47314	+	0.599754i
$622$		0			0
$623$	−2.25387	+	27.9919i	−0.0902995	+	1.12147i
$624$		0			0
$625$	21.7603			0.870412
$626$		0			0
$627$	6.77648	+	8.86833i	0.270626	+	0.354167i
$628$		0			0
$629$	−51.8175			−2.06610
$630$		0			0
$631$	−34.0114			−1.35397			−0.676986	−	0.735996i	$-0.736714\pi$
$631$	−34.0114			−1.35397			−0.676986	+	0.735996i	$0.736714\pi$
$632$		0			0
$633$	4.04303	−	0.523963i	0.160696	−	0.0208257i
$634$		0			0
$635$	−3.80326			−0.150928
$636$		0			0
$637$	−43.7373	−	7.08931i	−1.73293	−	0.280889i
$638$		0			0
$639$	14.8855	+	15.0063i	0.588860	+	0.593641i
$640$		0			0
$641$	5.29894			0.209296			0.104648	−	0.994509i	$-0.466628\pi$
$641$	5.29894			0.209296			0.104648	+	0.994509i	$0.466628\pi$
$642$		0			0
$643$	19.4304	+	33.6544i	0.766260	+	1.32720i	0.939578	+	0.342335i	$0.111218\pi$
$643$	19.4304	+	33.6544i	0.766260	+	1.32720i	−0.173318	+	0.984866i	$0.555449\pi$
$644$		0			0
$645$	−0.425252	−	0.556525i	−0.0167443	−	0.0219131i
$646$		0			0
$647$	4.11420	+	7.12601i	0.161746	+	0.280152i	0.935495	−	0.353340i	$-0.114954\pi$
$647$	4.11420	+	7.12601i	0.161746	+	0.280152i	−0.773749	+	0.633492i	$0.781621\pi$
$648$		0			0
$649$	−2.61480	+	4.52897i	−0.102640	+	0.177778i
$650$		0			0
$651$	−26.4832	−	13.6218i	−1.03796	−	0.533880i
$652$		0			0
$653$	42.0328			1.64487			0.822436	−	0.568858i	$-0.192615\pi$
$653$	42.0328			1.64487			0.822436	+	0.568858i	$0.192615\pi$
$654$		0			0
$655$	−9.12764			−0.356647
$656$		0			0
$657$	−5.20373	+	19.1112i	−0.203017	+	0.745600i
$658$		0			0
$659$	7.33484	−	12.7043i	0.285725	−	0.494890i	−0.687060	−	0.726601i	$-0.741099\pi$
$659$	7.33484	−	12.7043i	0.285725	−	0.494890i	0.972785	+	0.231711i	$0.0744323\pi$
$660$		0			0
$661$	−2.93303	+	5.08015i	−0.114081	+	0.197595i	−0.917412	−	0.397938i	$-0.869726\pi$
$661$	−2.93303	+	5.08015i	−0.114081	+	0.197595i	0.803331	+	0.595533i	$0.203059\pi$
$662$		0			0
$663$	32.8991	+	43.0548i	1.27769	+	1.67211i
$664$		0			0
$665$	0.475018	−	5.89947i	0.0184204	−	0.228771i
$666$		0			0
$667$	−13.7734	+	23.8563i	−0.533310	+	0.923720i
$668$		0			0
$669$	−11.1622	−	14.6078i	−0.431554	−	0.564772i
$670$		0			0
$671$	2.52497	+	4.37338i	0.0974754	+	0.168832i
$672$		0			0
$673$	9.42591	−	16.3261i	0.363342	−	0.629327i	−0.625167	−	0.780491i	$-0.714969\pi$
$673$	9.42591	−	16.3261i	0.363342	−	0.629327i	0.988509	+	0.151165i	$0.0483023\pi$
$674$		0			0
$675$	23.0081	−	9.36723i	0.885582	−	0.360545i
$676$		0			0
$677$	−14.9572	−	25.9067i	−0.574852	−	0.995674i	−0.996058	−	0.0887082i	$-0.971726\pi$
$677$	−14.9572	−	25.9067i	−0.574852	−	0.995674i	0.421205	−	0.906965i	$-0.361607\pi$
$678$		0			0
$679$	−2.96346	+	36.8045i	−0.113727	+	1.41243i
$680$		0			0
$681$	0.849558	−	2.03935i	0.0325551	−	0.0781479i
$682$		0			0
$683$	12.8525	+	22.2612i	0.491788	+	0.851802i	0.999955	−	0.00945677i	$-0.00301023\pi$
$683$	12.8525	+	22.2612i	0.491788	+	0.851802i	−0.508167	+	0.861258i	$0.669677\pi$
$684$		0			0
$685$	7.07099			0.270169
$686$		0			0
$687$	−8.96934	+	21.5307i	−0.342202	+	0.821448i
$688$		0			0
$689$	37.0274	−	64.1333i	1.41063	−	2.44328i
$690$		0			0
$691$	−19.2010	−	33.2571i	−0.730440	−	1.26516i	−0.956695	−	0.291092i	$-0.905982\pi$
$691$	−19.2010	−	33.2571i	−0.730440	−	1.26516i	0.226255	−	0.974068i	$-0.427352\pi$
$692$		0			0
$693$	−10.0690	−	3.63204i	−0.382491	−	0.137970i
$694$		0			0
$695$	1.02447	+	1.77444i	0.0388605	+	0.0673084i
$696$		0			0
$697$	−0.124366	+	0.215408i	−0.00471069	+	0.00815915i
$698$		0			0
$699$	−21.0012	−	27.4841i	−0.794337	−	1.03954i
$700$		0			0
$701$	11.5694			0.436972			0.218486	−	0.975840i	$-0.429888\pi$
$701$	11.5694			0.436972			0.218486	+	0.975840i	$0.429888\pi$
$702$		0			0
$703$	−25.0480	−	43.3844i	−0.944703	−	1.63627i
$704$		0			0
$705$	−8.83648	+	1.14518i	−0.332801	+	0.0431299i
$706$		0			0
$707$	−10.1565	+	4.82190i	−0.381974	+	0.181346i
$708$		0			0
$709$	−26.0275	−	45.0810i	−0.977483	−	1.69305i	−0.671484	−	0.741019i	$-0.734343\pi$
$709$	−26.0275	−	45.0810i	−0.977483	−	1.69305i	−0.305999	−	0.952032i	$-0.598990\pi$
$710$		0			0
$711$	−2.50559	+	9.20203i	−0.0939669	+	0.345103i
$712$		0			0
$713$	−24.7863	+	42.9311i	−0.928254	+	1.60778i
$714$		0			0
$715$	−1.99819	−	3.46096i	−0.0747280	−	0.129433i
$716$		0			0
$717$	−48.4705	+	6.28162i	−1.81016	+	0.234591i
$718$		0			0
$719$	0.416175	−	0.720836i	0.0155207	−	0.0268827i	−0.858161	−	0.513381i	$-0.828393\pi$
$719$	0.416175	−	0.720836i	0.0155207	−	0.0268827i	0.873681	+	0.486498i	$0.161726\pi$
$720$		0			0
$721$	21.4064	−	10.1629i	0.797217	−	0.378488i
$722$		0			0
$723$	−11.5578	+	27.7442i	−0.429838	+	1.03182i
$724$		0			0
$725$	8.63247	−	14.9519i	0.320602	−	0.555299i
$726$		0			0
$727$	10.7029	−	18.5379i	0.396948	−	0.687534i	−0.596400	−	0.802687i	$-0.703403\pi$
$727$	10.7029	−	18.5379i	0.396948	−	0.687534i	0.993348	+	0.115154i	$0.0367361\pi$
$728$		0			0
$729$	19.3220	−	18.8590i	0.715630	−	0.698480i
$730$		0			0
$731$	4.26894			0.157892
$732$		0			0
$733$	−7.45240			−0.275261			−0.137630	−	0.990484i	$-0.543949\pi$
$733$	−7.45240			−0.275261			−0.137630	+	0.990484i	$0.543949\pi$
$734$		0			0
$735$	2.68033	+	5.00356i	0.0988655	+	0.184559i
$736$		0			0
$737$	−1.78601	+	3.09346i	−0.0657885	+	0.113949i
$738$		0			0
$739$	−17.9473	−	31.0857i	−0.660203	−	1.14351i	−0.980562	−	0.196210i	$-0.937137\pi$
$739$	−17.9473	−	31.0857i	−0.660203	−	1.14351i	0.320358	−	0.947296i	$-0.396197\pi$
$740$		0			0
$741$	−20.1448	+	48.3571i	−0.740037	+	1.77644i
$742$		0			0
$743$	16.8379	+	29.1641i	0.617723	+	1.06993i	0.989900	+	0.141766i	$0.0452781\pi$
$743$	16.8379	+	29.1641i	0.617723	+	1.06993i	−0.372177	+	0.928162i	$0.621389\pi$
$744$		0			0
$745$	5.50398			0.201650
$746$		0			0
$747$	−28.4445	+	7.49858i	−1.04073	+	0.274359i
$748$		0			0
$749$	0.344310	−	4.27615i	0.0125808	−	0.156247i
$750$		0			0
$751$	15.0338			0.548590			0.274295	−	0.961646i	$-0.411555\pi$
$751$	15.0338			0.548590			0.274295	+	0.961646i	$0.411555\pi$
$752$		0			0
$753$	4.18986	−	10.0577i	0.152687	−	0.366522i
$754$		0			0
$755$	2.40782			0.0876295
$756$		0			0
$757$	−34.2548			−1.24501			−0.622507	−	0.782615i	$-0.713886\pi$
$757$	−34.2548			−1.24501			−0.622507	+	0.782615i	$0.713886\pi$
$758$		0			0
$759$	−6.85176	+	16.4475i	−0.248703	+	0.597006i
$760$		0			0
$761$	42.2086			1.53006			0.765031	−	0.643993i	$-0.222724\pi$
$761$	42.2086			1.53006			0.765031	+	0.643993i	$0.222724\pi$
$762$		0			0
$763$	−12.9637	−	8.94423i	−0.469318	−	0.323803i
$764$		0			0
$765$	1.82372	−	6.69778i	0.0659366	−	0.242159i
$766$		0			0
$767$	−24.5457			−0.886294
$768$		0			0
$769$	22.2741	+	38.5799i	0.803226	+	1.39123i	0.917482	+	0.397777i	$0.130218\pi$
$769$	22.2741	+	38.5799i	0.803226	+	1.39123i	−0.114256	+	0.993451i	$0.536448\pi$
$770$		0			0
$771$	−4.08719	+	9.81122i	−0.147197	+	0.353343i
$772$		0			0
$773$	−9.61003	−	16.6451i	−0.345649	−	0.598681i	0.639823	−	0.768523i	$-0.279008\pi$
$773$	−9.61003	−	16.6451i	−0.345649	−	0.598681i	−0.985471	+	0.169841i	$0.945674\pi$
$774$		0			0
$775$	15.5347	−	26.9069i	0.558024	−	0.966526i
$776$		0			0
$777$	42.7247	+	21.9757i	1.53274	+	0.788372i
$778$		0			0
$779$	−0.240468			−0.00861566
$780$		0			0
$781$	9.50162			0.339995
$782$		0			0
$783$	2.56207	−	18.5891i	0.0915608	−	0.664320i
$784$		0			0
$785$	−2.82984	+	4.90142i	−0.101001	+	0.174939i
$786$		0			0
$787$	20.1751	−	34.9443i	0.719165	−	1.24563i	−0.242166	−	0.970235i	$-0.577858\pi$
$787$	20.1751	−	34.9443i	0.719165	−	1.24563i	0.961331	−	0.275396i	$-0.0888089\pi$
$788$		0			0
$789$	3.91586	−	9.39994i	0.139408	−	0.334647i
$790$		0			0
$791$	−18.0466	−	12.4512i	−0.641665	−	0.442712i
$792$		0			0
$793$	−11.8512	+	20.5269i	−0.420849	+	0.728932i
$794$		0			0
$795$	−9.40837	+	1.21929i	−0.333680	+	0.0432439i
$796$		0			0
$797$	22.4965	+	38.9651i	0.796867	+	1.38021i	0.921647	+	0.388029i	$0.126844\pi$
$797$	22.4965	+	38.9651i	0.796867	+	1.38021i	−0.124780	+	0.992184i	$0.539823\pi$
$798$		0			0
$799$	27.1544	−	47.0328i	0.960653	−	1.66390i
$800$		0			0
$801$	−30.7906	+	8.11705i	−1.08793	+	0.286802i
$802$		0			0
$803$	4.45191	+	7.71093i	0.157104	+	0.272113i
$804$		0			0
$805$	8.53539	−	4.05227i	0.300833	−	0.142824i
$806$		0			0
$807$	−53.1221	+	6.88445i	−1.86999	+	0.242344i
$808$		0			0
$809$	16.8858	+	29.2470i	0.593672	+	1.02827i	0.993733	+	0.111782i	$0.0356558\pi$
$809$	16.8858	+	29.2470i	0.593672	+	1.02827i	−0.400061	+	0.916489i	$0.631011\pi$
$810$		0			0
$811$	−31.7254			−1.11403			−0.557014	−	0.830503i	$-0.688053\pi$
$811$	−31.7254			−1.11403			−0.557014	+	0.830503i	$0.688053\pi$
$812$		0			0
$813$	−11.4528	−	14.9882i	−0.401667	−	0.525659i
$814$		0			0
$815$	1.28589	−	2.22722i	0.0450427	−	0.0780162i
$816$		0			0
$817$	2.06356	+	3.57418i	0.0721947	+	0.125045i
$818$		0			0
$819$	−8.86659	−	49.4521i	−0.309824	−	1.72800i
$820$		0			0
$821$	5.87521	+	10.1762i	0.205046	+	0.355151i	0.950147	−	0.311801i	$-0.100932\pi$
$821$	5.87521	+	10.1762i	0.205046	+	0.355151i	−0.745101	+	0.666951i	$0.767599\pi$
$822$		0			0
$823$	4.25371	−	7.36764i	0.148275	−	0.256820i	−0.782315	−	0.622883i	$-0.785961\pi$
$823$	4.25371	−	7.36764i	0.148275	−	0.256820i	0.930590	+	0.366063i	$0.119295\pi$
$824$		0			0
$825$	4.29432	−	10.3084i	0.149509	−	0.358893i
$826$		0			0
$827$	−13.9662			−0.485651			−0.242825	−	0.970070i	$-0.578074\pi$
$827$	−13.9662			−0.485651			−0.242825	+	0.970070i	$0.578074\pi$
$828$		0			0
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	−0.984483	−	0.175480i	$-0.943852\pi$
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	0.340271	−	0.940327i	$-0.389481\pi$
$830$		0			0
$831$	13.0481	−	31.3217i	0.452633	−	1.08654i
$832$		0			0
$833$	−34.1511	−	5.53549i	−1.18326	−	0.191793i
$834$		0			0
$835$	1.68250	+	2.91417i	0.0582252	+	0.100849i
$836$		0			0
$837$	4.61062	−	33.4524i	0.159366	−	1.15628i
$838$		0			0
$839$	−1.32105	+	2.28813i	−0.0456077	+	0.0789949i	−0.887928	−	0.459982i	$-0.847856\pi$
$839$	−1.32105	+	2.28813i	−0.0456077	+	0.0789949i	0.842320	+	0.538977i	$0.181189\pi$
$840$		0			0
$841$	7.97928	+	13.8205i	0.275148	+	0.476570i
$842$		0			0
$843$	0.299664	+	0.392169i	0.0103210	+	0.0135070i
$844$		0			0
$845$	6.33561	−	10.9736i	0.217952	−	0.377503i
$846$		0			0
$847$	21.9440	−	10.4181i	0.754004	−	0.357972i
$848$		0			0
$849$	2.98945	+	3.91228i	0.102598	+	0.134269i
$850$		0			0
$851$	39.9870	−	69.2595i	1.37074	−	2.37419i
$852$		0			0
$853$	17.3405	−	30.0346i	0.593726	−	1.02836i	−0.399999	−	0.916516i	$-0.630990\pi$
$853$	17.3405	−	30.0346i	0.593726	−	1.02836i	0.993725	−	0.111848i	$-0.0356771\pi$
$854$		0			0
$855$	6.48931	−	1.71072i	0.221930	−	0.0585054i
$856$		0			0
$857$	23.7223			0.810338			0.405169	−	0.914242i	$-0.367213\pi$
$857$	23.7223			0.810338			0.405169	+	0.914242i	$0.367213\pi$
$858$		0			0
$859$	−21.8150			−0.744317			−0.372158	−	0.928169i	$-0.621382\pi$
$859$	−21.8150			−0.744317			−0.372158	+	0.928169i	$0.621382\pi$
$860$		0			0
$861$	0.193896	−	0.124865i	0.00660796	−	0.00425540i
$862$		0			0
$863$	−14.6899	+	25.4436i	−0.500049	+	0.866111i	0.499951	+	0.866054i	$0.333351\pi$
$863$	−14.6899	+	25.4436i	−0.500049	+	0.866111i	−1.00000		5.68129e-5i	$0.999982\pi$
$864$		0			0
$865$	−1.86308	−	3.22696i	−0.0633467	−	0.109720i
$866$		0			0
$867$	7.81071	+	10.2218i	0.265266	+	0.347152i
$868$		0			0
$869$	2.14359	+	3.71280i	0.0727162	+	0.125948i
$870$		0			0
$871$	−16.7656			−0.568082
$872$		0			0
$873$	−40.4844	+	10.6725i	−1.37019	+	0.361211i
$874$		0			0
$875$	−10.9443	+	5.19593i	−0.369985	+	0.175655i
$876$		0			0
$877$	−5.62129			−0.189817			−0.0949087	−	0.995486i	$-0.530256\pi$
$877$	−5.62129			−0.189817			−0.0949087	+	0.995486i	$0.530256\pi$
$878$		0			0
$879$	−5.01491	+	0.649916i	−0.169149	+	0.0219211i
$880$		0			0
$881$	2.75442			0.0927987			0.0463994	−	0.998923i	$-0.485225\pi$
$881$	2.75442			0.0927987			0.0463994	+	0.998923i	$0.485225\pi$
$882$		0			0
$883$	33.8917			1.14055			0.570274	−	0.821455i	$-0.306837\pi$
$883$	33.8917			1.14055			0.570274	+	0.821455i	$0.306837\pi$
$884$		0			0
$885$	1.90921	+	2.49858i	0.0641775	+	0.0839887i
$886$		0			0
$887$	−55.6893			−1.86986			−0.934932	−	0.354827i	$-0.884540\pi$
$887$	−55.6893			−1.86986			−0.934932	+	0.354827i	$0.884540\pi$
$888$		0			0
$889$	−19.4162	+	9.21803i	−0.651197	+	0.309163i
$890$		0			0
$891$	0.0981276	−	12.1369i	0.00328740	−	0.406600i
$892$		0			0
$893$	52.5045			1.75700
$894$		0			0
$895$	−0.0790366	−	0.136895i	−0.00264190	−	0.00457591i
$896$		0			0
$897$	−82.9352	+	10.7481i	−2.76913	+	0.358870i
$898$		0			0
$899$	−11.7345	−	20.3247i	−0.391367	−	0.677868i
$900$		0			0
$901$	28.9118	−	50.0767i	0.963192	−	1.66830i
$902$		0			0
$903$	−3.51983	−	1.81044i	−0.117133	−	0.0602478i
$904$		0			0
$905$	−3.30434			−0.109840
$906$		0			0
$907$	53.4626			1.77519			0.887597	−	0.460620i	$-0.152373\pi$
$907$	53.4626			1.77519			0.887597	+	0.460620i	$0.152373\pi$
$908$		0			0
$909$	−8.97793	−	9.05081i	−0.297779	−	0.300196i
$910$		0			0
$911$	9.77060	−	16.9232i	0.323714	−	0.560690i	−0.657537	−	0.753422i	$-0.728402\pi$
$911$	9.77060	−	16.9232i	0.323714	−	0.560690i	0.981251	+	0.192732i	$0.0617350\pi$
$912$		0			0
$913$	−6.61174	+	11.4519i	−0.218817	+	0.379001i
$914$		0			0
$915$	3.01130	−	0.390255i	0.0995507	−	0.0129014i
$916$		0			0
$917$	−46.5979	+	22.1229i	−1.53880	+	0.730561i
$918$		0			0
$919$	0.0878895	−	0.152229i	0.00289921	−	0.00502157i	−0.864572	−	0.502509i	$-0.832410\pi$
$919$	0.0878895	−	0.152229i	0.00289921	−	0.00502157i	0.867471	+	0.497487i	$0.165744\pi$
$920$		0			0
$921$	−2.74785	+	6.59616i	−0.0905448	+	0.217351i
$922$		0			0
$923$	22.2984	+	38.6220i	0.733962	+	1.27126i
$924$		0			0
$925$	−25.0617	+	43.4082i	−0.824025	+	1.42725i
$926$		0			0
$927$	18.9224	+	19.0761i	0.621495	+	0.626540i
$928$		0			0
$929$	12.3008	+	21.3056i	0.403576	+	0.699014i	0.994155	−	0.107966i	$-0.0344338\pi$
$929$	12.3008	+	21.3056i	0.403576	+	0.699014i	−0.590579	+	0.806980i	$0.701100\pi$
$930$		0			0
$931$	−11.8736	−	31.2689i	−0.389142	−	1.02480i
$932$		0			0
$933$	16.1863	+	21.1829i	0.529915	+	0.693496i
$934$		0			0
$935$	−1.56023	−	2.70240i	−0.0510250	−	0.0883779i
$936$		0			0
$937$	−28.5655			−0.933195			−0.466598	−	0.884470i	$-0.654520\pi$
$937$	−28.5655			−0.933195			−0.466598	+	0.884470i	$0.654520\pi$
$938$		0			0
$939$	35.5973	−	4.61329i	1.16167	−	0.150549i
$940$		0			0
$941$	−18.7802	+	32.5283i	−0.612217	+	1.06039i	0.378648	+	0.925541i	$0.376389\pi$
$941$	−18.7802	+	32.5283i	−0.612217	+	1.06039i	−0.990866	+	0.134851i	$0.956944\pi$
$942$		0			0
$943$	−0.191943	−	0.332456i	−0.00625053	−	0.0108262i
$944$		0			0
$945$	−4.34421	+	4.74904i	−0.141317	+	0.154486i
$946$		0			0
$947$	−4.83381	−	8.37241i	−0.157078	−	0.272067i	0.776736	−	0.629827i	$-0.216874\pi$
$947$	−4.83381	−	8.37241i	−0.157078	−	0.272067i	−0.933814	+	0.357760i	$0.883541\pi$
$948$		0			0
$949$	−20.8955	+	36.1921i	−0.678297	+	1.17484i
$950$		0			0
$951$	0.838732	−	0.108697i	0.0271977	−	0.00352474i
$952$		0			0
$953$	58.1964			1.88517			0.942583	−	0.333971i	$-0.108389\pi$
$953$	58.1964			1.88517			0.942583	+	0.333971i	$0.108389\pi$
$954$		0			0
$955$	4.14767	+	7.18397i	0.134215	+	0.232468i
$956$		0			0
$957$	−5.12156	−	6.70256i	−0.165557	−	0.216663i
$958$		0			0
$959$	36.0984	−	17.1381i	1.16568	−	0.553418i
$960$		0			0
$961$	−5.61704	−	9.72900i	−0.181195	−	0.313839i
$962$		0			0
$963$	4.70369	−	1.23999i	0.151574	−	0.0399582i
$964$		0			0
$965$	−3.93319	+	6.81248i	−0.126614	+	0.219301i
$966$		0			0
$967$	7.97991	+	13.8216i	0.256617	+	0.444473i	0.965333	−	0.261020i	$-0.0840589\pi$
$967$	7.97991	+	13.8216i	0.256617	+	0.444473i	−0.708717	+	0.705493i	$0.750726\pi$
$968$		0			0
$969$	−15.7295	+	37.7583i	−0.505305	+	1.21297i
$970$		0			0
$971$	−1.67394	+	2.89935i	−0.0537193	+	0.0930445i	−0.891635	−	0.452756i	$-0.850441\pi$
$971$	−1.67394	+	2.89935i	−0.0537193	+	0.0930445i	0.837915	+	0.545800i	$0.183774\pi$
$972$		0			0
$973$	9.53083	+	6.57573i	0.305544	+	0.210808i
$974$		0			0
$975$	51.9794	−	6.73636i	1.66467	−	0.215736i
$976$		0			0
$977$	−11.9402	+	20.6810i	−0.382000	+	0.661643i	−0.991348	−	0.131260i	$-0.958098\pi$
$977$	−11.9402	+	20.6810i	−0.382000	+	0.661643i	0.609348	+	0.792903i	$0.291431\pi$
$978$		0			0
$979$	−7.15706	+	12.3964i	−0.228741	+	0.396190i
$980$		0			0
$981$	4.69185	−	17.2313i	0.149799	−	0.550153i
$982$		0			0
$983$	37.7573			1.20427			0.602135	−	0.798394i	$-0.294317\pi$
$983$	37.7573			1.20427			0.602135	+	0.798394i	$0.294317\pi$
$984$		0			0
$985$	−2.79752			−0.0891364
$986$		0			0
$987$	−42.3359	+	27.2635i	−1.34756	+	0.867805i
$988$		0			0
$989$	−3.29429	+	5.70588i	−0.104752	+	0.181436i
$990$		0			0
$991$	−1.08487	−	1.87904i	−0.0344619	−	0.0596898i	0.848280	−	0.529548i	$-0.177638\pi$
$991$	−1.08487	−	1.87904i	−0.0344619	−	0.0596898i	−0.882742	+	0.469858i	$0.844305\pi$
$992$		0			0
$993$	32.5627	−	4.22002i	1.03335	−	0.133918i
$994$		0			0
$995$	−2.93117	−	5.07694i	−0.0929245	−	0.160950i
$996$		0			0
$997$	−8.69454			−0.275359			−0.137679	−	0.990477i	$-0.543964\pi$
$997$	−8.69454			−0.275359			−0.137679	+	0.990477i	$0.543964\pi$
$998$		0			0
$999$	−7.43818	+	53.9678i	−0.235334	+	1.70746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.457.7	yes	22
3.2	odd	2		1512.2.t.c.289.7		22
4.3	odd	2		1008.2.t.l.961.5		22
7.4	even	3		504.2.q.c.25.1	✓	22
9.4	even	3		504.2.q.c.121.1	yes	22
9.5	odd	6		1512.2.q.d.793.5		22
12.11	even	2		3024.2.t.k.289.7		22
21.11	odd	6		1512.2.q.d.1369.5		22
28.11	odd	6		1008.2.q.l.529.11		22
36.23	even	6		3024.2.q.l.2305.5		22
36.31	odd	6		1008.2.q.l.625.11		22
63.4	even	3	inner	504.2.t.c.193.7	yes	22
63.32	odd	6		1512.2.t.c.361.7		22
84.11	even	6		3024.2.q.l.2881.5		22
252.67	odd	6		1008.2.t.l.193.5		22
252.95	even	6		3024.2.t.k.1873.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.1	✓	22	7.4	even	3
504.2.q.c.121.1	yes	22	9.4	even	3
504.2.t.c.193.7	yes	22	63.4	even	3	inner
504.2.t.c.457.7	yes	22	1.1	even	1	trivial
1008.2.q.l.529.11		22	28.11	odd	6
1008.2.q.l.625.11		22	36.31	odd	6
1008.2.t.l.193.5		22	252.67	odd	6
1008.2.t.l.961.5		22	4.3	odd	2
1512.2.q.d.793.5		22	9.5	odd	6
1512.2.q.d.1369.5		22	21.11	odd	6
1512.2.t.c.289.7		22	3.2	odd	2
1512.2.t.c.361.7		22	63.32	odd	6
3024.2.q.l.2305.5		22	36.23	even	6
3024.2.q.l.2881.5		22	84.11	even	6
3024.2.t.k.289.7		22	12.11	even	2
3024.2.t.k.1873.7		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)

\(f(q)\)	\(=\)	\(q+(0.666060 - 1.59886i) q^{3} -0.468169 q^{5} +(-2.39007 + 1.13471i) q^{7} +(-2.11273 - 2.12988i) q^{9} +O(q^{10})\)	\(q+(0.666060 - 1.59886i) q^{3} -0.468169 q^{5} +(-2.39007 + 1.13471i) q^{7} +(-2.11273 - 2.12988i) q^{9} -1.34859 q^{11} +(-3.16486 - 5.48171i) q^{13} +(-0.311829 + 0.748538i) q^{15} +(-2.47120 - 4.28024i) q^{17} +(2.38910 - 4.13804i) q^{19} +(0.222319 + 4.57718i) q^{21} +7.62799 q^{23} -4.78082 q^{25} +(-4.81259 + 1.95934i) q^{27} +(-1.80565 + 3.12747i) q^{29} +(-3.24939 + 5.62810i) q^{31} +(-0.898239 + 2.15620i) q^{33} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(-10.8725 + 1.40904i) q^{39} +(-0.0251630 - 0.0435837i) q^{41} +(-0.431869 + 0.748019i) q^{43} +(0.989114 + 0.997143i) q^{45} +(5.49417 + 9.51619i) q^{47} +(4.42486 - 5.42408i) q^{49} +(-8.48948 + 1.10021i) q^{51} +(5.84976 + 10.1321i) q^{53} +0.631366 q^{55} +(-5.02488 - 6.57603i) q^{57} +(1.93892 - 3.35831i) q^{59} +(-1.87231 - 3.24294i) q^{61} +(7.46636 + 2.69322i) q^{63} +(1.48169 + 2.56637i) q^{65} +(1.32436 - 2.29385i) q^{67} +(5.08070 - 12.1961i) q^{69} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(-3.18431 + 7.64387i) q^{75} +(3.22321 - 1.53026i) q^{77} +(-1.58951 - 2.75311i) q^{79} +(-0.0727634 + 8.99971i) q^{81} +(4.90272 - 8.49176i) q^{83} +(1.15694 + 2.00388i) q^{85} +(3.79773 + 4.97007i) q^{87} +(5.30709 - 9.19214i) q^{89} +(13.7844 + 9.51045i) q^{91} +(6.83428 + 8.94398i) q^{93} +(-1.11850 + 1.93730i) q^{95} +(6.97792 - 12.0861i) q^{97} +(2.84919 + 2.87232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 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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