LMFDB - Embedded newform 252.2.i.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$1.64515 + 0.541745i$ of defining polynomial
Character	$\chi$	$=$	252.121
Dual form			252.2.i.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29174 + 1.15387i) q^{3} +(0.381918 + 0.661502i) q^{5} +(2.62892 + 0.297968i) q^{7} +(0.337180 - 2.98099i) q^{9} +O(q^{10})$	\(q+(-1.29174 + 1.15387i) q^{3} +(0.381918 + 0.661502i) q^{5} +(2.62892 + 0.297968i) q^{7} +(0.337180 - 2.98099i) q^{9} +(-3.01695 + 5.22551i) q^{11} +(-1.26032 + 2.18294i) q^{13} +(-1.25662 - 0.413805i) q^{15} +(1.94444 + 3.36787i) q^{17} +(-2.13503 + 3.69798i) q^{19} +(-3.73969 + 2.64853i) q^{21} +(0.732124 + 1.26808i) q^{23} +(2.20828 - 3.82485i) q^{25} +(3.00412 + 4.23972i) q^{27} +(-3.00732 - 5.20884i) q^{29} +6.56965 q^{31} +(-2.13243 - 10.2311i) q^{33} +(0.806926 + 1.85283i) q^{35} +(4.82492 - 8.35700i) q^{37} +(-0.890819 - 4.27404i) q^{39} +(-2.24844 + 3.89442i) q^{41} +(-2.13503 - 3.69798i) q^{43} +(2.10071 - 0.915450i) q^{45} -6.77848 q^{47} +(6.82243 + 1.56667i) q^{49} +(-6.39778 - 2.10678i) q^{51} +(-0.265581 - 0.460000i) q^{53} -4.60891 q^{55} +(-1.50908 - 7.24036i) q^{57} +11.1985 q^{59} +8.38288 q^{61} +(1.77466 - 7.73632i) q^{63} -1.92536 q^{65} -1.92396 q^{67} +(-2.40890 - 0.793249i) q^{69} +9.90353 q^{71} +(-2.13099 - 3.69098i) q^{73} +(1.56085 + 7.48876i) q^{75} +(-9.48834 + 12.8385i) q^{77} -7.40744 q^{79} +(-8.77262 - 2.01026i) q^{81} +(-8.05178 - 13.9461i) q^{83} +(-1.48523 + 2.57250i) q^{85} +(9.89499 + 3.25841i) q^{87} +(1.76310 - 3.05377i) q^{89} +(-3.96373 + 5.36325i) q^{91} +(-8.48627 + 7.58050i) q^{93} -3.26163 q^{95} +(2.33513 + 4.04456i) q^{97} +(14.5599 + 10.7554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.29174	+	1.15387i	−0.745786	+	0.666186i
$3$	−1.29174	+	1.15387i	−0.745786	+	0.666186i
$4$		0			0
$5$	0.381918	+	0.661502i	0.170799	+	0.295833i	0.938699	−	0.344737i	$-0.112032\pi$
$5$	0.381918	+	0.661502i	0.170799	+	0.295833i	−0.767900	+	0.640569i	$0.778698\pi$
$6$		0			0
$7$	2.62892	+	0.297968i	0.993638	+	0.112621i
$7$	2.62892	+	0.297968i	0.993638	+	0.112621i
$8$		0			0
$9$	0.337180	−	2.98099i	0.112393	−	0.993664i
$10$		0			0
$11$	−3.01695	+	5.22551i	−0.909644	+	1.57555i	−0.0950845	+	0.995469i	$0.530312\pi$
$11$	−3.01695	+	5.22551i	−0.909644	+	1.57555i	−0.814559	+	0.580080i	$0.803021\pi$
$12$		0			0
$13$	−1.26032	+	2.18294i	−0.349551	+	0.605440i	−0.986170	−	0.165739i	$-0.946999\pi$
$13$	−1.26032	+	2.18294i	−0.349551	+	0.605440i	0.636619	+	0.771179i	$0.280332\pi$
$14$		0			0
$15$	−1.25662	−	0.413805i	−0.324459	−	0.106844i
$16$		0			0
$17$	1.94444	+	3.36787i	0.471596	+	0.816828i	0.999472	−	0.0324932i	$-0.0103447\pi$
$17$	1.94444	+	3.36787i	0.471596	+	0.816828i	−0.527876	+	0.849322i	$0.677011\pi$
$18$		0			0
$19$	−2.13503	+	3.69798i	−0.489809	+	0.848375i	−0.999931	−	0.0117275i	$-0.996267\pi$
$19$	−2.13503	+	3.69798i	−0.489809	+	0.848375i	0.510122	+	0.860102i	$0.329600\pi$
$20$		0			0
$21$	−3.73969	+	2.64853i	−0.816068	+	0.577956i
$22$		0			0
$23$	0.732124	+	1.26808i	0.152658	+	0.264412i	0.932204	−	0.361933i	$-0.117883\pi$
$23$	0.732124	+	1.26808i	0.152658	+	0.264412i	−0.779546	+	0.626346i	$0.784550\pi$
$24$		0			0
$25$	2.20828	−	3.82485i	0.441655	−	0.764970i
$26$		0			0
$27$	3.00412	+	4.23972i	0.578143	+	0.815935i
$28$		0			0
$29$	−3.00732	−	5.20884i	−0.558446	−	0.967257i	−0.997626	−	0.0688580i	$-0.978064\pi$
$29$	−3.00732	−	5.20884i	−0.558446	−	0.967257i	0.439180	−	0.898399i	$-0.355269\pi$
$30$		0			0
$31$	6.56965			1.17994			0.589972	−	0.807424i	$-0.299139\pi$
$31$	6.56965			1.17994			0.589972	+	0.807424i	$0.299139\pi$
$32$		0			0
$33$	−2.13243	−	10.2311i	−0.371209	−	1.78101i
$34$		0			0
$35$	0.806926	+	1.85283i	0.136395	+	0.313186i
$36$		0			0
$37$	4.82492	−	8.35700i	0.793211	−	1.37388i	−0.130758	−	0.991414i	$-0.541741\pi$
$37$	4.82492	−	8.35700i	0.793211	−	1.37388i	0.923969	−	0.382468i	$-0.124926\pi$
$38$		0			0
$39$	−0.890819	−	4.27404i	−0.142645	−	0.684394i
$40$		0			0
$41$	−2.24844	+	3.89442i	−0.351148	+	0.608206i	−0.986451	−	0.164057i	$-0.947542\pi$
$41$	−2.24844	+	3.89442i	−0.351148	+	0.608206i	0.635303	+	0.772263i	$0.280875\pi$
$42$		0			0
$43$	−2.13503	−	3.69798i	−0.325589	−	0.563937i	0.656042	−	0.754724i	$-0.272229\pi$
$43$	−2.13503	−	3.69798i	−0.325589	−	0.563937i	−0.981631	+	0.190787i	$0.938896\pi$
$44$		0			0
$45$	2.10071	−	0.915450i	0.313155	−	0.136467i
$46$		0			0
$47$	−6.77848			−0.988744			−0.494372	−	0.869251i	$-0.664602\pi$
$47$	−6.77848			−0.988744			−0.494372	+	0.869251i	$0.664602\pi$
$48$		0			0
$49$	6.82243	+	1.56667i	0.974633	+	0.223809i
$50$		0			0
$51$	−6.39778	−	2.10678i	−0.895869	−	0.295009i
$52$		0			0
$53$	−0.265581	−	0.460000i	−0.0364804	−	0.0631859i	0.847209	−	0.531260i	$-0.178281\pi$
$53$	−0.265581	−	0.460000i	−0.0364804	−	0.0631859i	−0.883689	+	0.468074i	$0.844948\pi$
$54$		0			0
$55$	−4.60891			−0.621465
$56$		0			0
$57$	−1.50908	−	7.24036i	−0.199882	−	0.959010i
$58$		0			0
$59$	11.1985			1.45792			0.728962	−	0.684554i	$-0.240003\pi$
$59$	11.1985			1.45792			0.728962	+	0.684554i	$0.240003\pi$
$60$		0			0
$61$	8.38288			1.07332			0.536659	−	0.843799i	$-0.319686\pi$
$61$	8.38288			1.07332			0.536659	+	0.843799i	$0.319686\pi$
$62$		0			0
$63$	1.77466	−	7.73632i	0.223586	−	0.974684i
$64$		0			0
$65$	−1.92536			−0.238812
$66$		0			0
$67$	−1.92396			−0.235049			−0.117524	−	0.993070i	$-0.537496\pi$
$67$	−1.92396			−0.235049			−0.117524	+	0.993070i	$0.537496\pi$
$68$		0			0
$69$	−2.40890	−	0.793249i	−0.289998	−	0.0954960i
$70$		0			0
$71$	9.90353			1.17533			0.587666	−	0.809103i	$-0.300047\pi$
$71$	9.90353			1.17533			0.587666	+	0.809103i	$0.300047\pi$
$72$		0			0
$73$	−2.13099	−	3.69098i	−0.249413	−	0.431997i	0.713950	−	0.700197i	$-0.246904\pi$
$73$	−2.13099	−	3.69098i	−0.249413	−	0.431997i	−0.963363	+	0.268200i	$0.913571\pi$
$74$		0			0
$75$	1.56085	+	7.48876i	0.180231	+	0.864728i
$76$		0			0
$77$	−9.48834	+	12.8385i	−1.08130	+	1.46308i
$78$		0			0
$79$	−7.40744			−0.833402			−0.416701	−	0.909044i	$-0.636814\pi$
$79$	−7.40744			−0.833402			−0.416701	+	0.909044i	$0.636814\pi$
$80$		0			0
$81$	−8.77262	−	2.01026i	−0.974735	−	0.223362i
$82$		0			0
$83$	−8.05178	−	13.9461i	−0.883798	−	1.53078i	−0.847085	−	0.531457i	$-0.821645\pi$
$83$	−8.05178	−	13.9461i	−0.883798	−	1.53078i	−0.0367125	−	0.999326i	$-0.511689\pi$
$84$		0			0
$85$	−1.48523	+	2.57250i	−0.161096	+	0.279027i
$86$		0			0
$87$	9.89499	+	3.25841i	1.06085	+	0.349338i
$88$		0			0
$89$	1.76310	−	3.05377i	0.186888	−	0.323699i	−0.757323	−	0.653040i	$-0.773493\pi$
$89$	1.76310	−	3.05377i	0.186888	−	0.323699i	0.944211	+	0.329341i	$0.106827\pi$
$90$		0			0
$91$	−3.96373	+	5.36325i	−0.415512	+	0.562221i
$92$		0			0
$93$	−8.48627	+	7.58050i	−0.879985	+	0.786061i
$94$		0			0
$95$	−3.26163			−0.334636
$96$		0			0
$97$	2.33513	+	4.04456i	0.237096	+	0.410662i	0.959880	−	0.280412i	$-0.0904710\pi$
$97$	2.33513	+	4.04456i	0.237096	+	0.410662i	−0.722784	+	0.691074i	$0.757138\pi$
$98$		0			0
$99$	14.5599	+	10.7554i	1.46333	+	1.08096i
$100$		0			0
$101$	2.35982	−	4.08734i	0.234811	−	0.406705i	−0.724407	−	0.689373i	$-0.757886\pi$
$101$	2.35982	−	4.08734i	0.234811	−	0.406705i	0.959218	+	0.282668i	$0.0912194\pi$
$102$		0			0
$103$	−1.58266	−	2.74124i	−0.155944	−	0.270103i	0.777458	−	0.628934i	$-0.216509\pi$
$103$	−1.58266	−	2.74124i	−0.155944	−	0.270103i	−0.933402	+	0.358832i	$0.883175\pi$
$104$		0			0
$105$	−3.18026	−	1.46229i	−0.310362	−	0.142705i
$106$		0			0
$107$	7.65537	−	13.2595i	0.740073	−	1.28184i	−0.212389	−	0.977185i	$-0.568124\pi$
$107$	7.65537	−	13.2595i	0.740073	−	1.28184i	0.952462	−	0.304659i	$-0.0985424\pi$
$108$		0			0
$109$	7.65371	+	13.2566i	0.733092	+	1.26975i	0.955555	+	0.294812i	$0.0952569\pi$
$109$	7.65371	+	13.2566i	0.733092	+	1.26975i	−0.222463	+	0.974941i	$0.571410\pi$
$110$		0			0
$111$	3.41034	+	16.3624i	0.323695	+	1.55305i
$112$		0			0
$113$	−1.56114	+	2.70397i	−0.146860	+	0.254368i	−0.930065	−	0.367395i	$-0.880250\pi$
$113$	−1.56114	+	2.70397i	−0.146860	+	0.254368i	0.783206	+	0.621763i	$0.213583\pi$
$114$		0			0
$115$	−0.559223	+	0.968602i	−0.0521478	+	0.0903226i
$116$		0			0
$117$	6.08238	+	4.49306i	0.562316	+	0.415383i
$118$		0			0
$119$	4.10826	+	9.43324i	0.376604	+	0.864743i
$120$		0			0
$121$	−12.7039	−	22.0039i	−1.15490	−	2.00035i
$122$		0			0
$123$	−1.58924	−	7.62498i	−0.143297	−	0.687521i
$124$		0			0
$125$	7.19271			0.643335
$126$		0			0
$127$	1.27814			0.113416			0.0567082	−	0.998391i	$-0.481940\pi$
$127$	1.27814			0.113416			0.0567082	+	0.998391i	$0.481940\pi$
$128$		0			0
$129$	7.02488	+	2.31328i	0.618506	+	0.203673i
$130$		0			0
$131$	−3.88733	−	6.73305i	−0.339637	−	0.588269i	0.644727	−	0.764413i	$-0.276971\pi$
$131$	−3.88733	−	6.73305i	−0.339637	−	0.588269i	−0.984364	+	0.176144i	$0.943638\pi$
$132$		0			0
$133$	−6.71470	+	9.08552i	−0.582238	+	0.787814i
$134$		0			0
$135$	−1.65726	+	3.60646i	−0.142634	+	0.310395i
$136$		0			0
$137$	−1.41153	+	2.44485i	−0.120596	+	0.208878i	−0.920003	−	0.391912i	$-0.871814\pi$
$137$	−1.41153	+	2.44485i	−0.120596	+	0.208878i	0.799407	+	0.600790i	$0.205147\pi$
$138$		0			0
$139$	−11.2206	+	19.4346i	−0.951718	+	1.64842i	−0.210013	+	0.977699i	$0.567351\pi$
$139$	−11.2206	+	19.4346i	−0.951718	+	1.64842i	−0.741705	+	0.670726i	$0.765983\pi$
$140$		0			0
$141$	8.75603	−	7.82147i	0.737391	−	0.658687i
$142$		0			0
$143$	−7.60466	−	13.1717i	−0.635933	−	1.10147i
$144$		0			0
$145$	2.29710	−	3.97870i	0.190764	−	0.330413i
$146$		0			0
$147$	−10.6205	+	5.84846i	−0.875966	+	0.482373i
$148$		0			0
$149$	10.0851	+	17.4679i	0.826206	+	1.43103i	0.900994	+	0.433831i	$0.142838\pi$
$149$	10.0851	+	17.4679i	0.826206	+	1.43103i	−0.0747887	+	0.997199i	$0.523828\pi$
$150$		0			0
$151$	−4.14725	+	7.18325i	−0.337498	+	0.584564i	−0.983962	−	0.178381i	$-0.942914\pi$
$151$	−4.14725	+	7.18325i	−0.337498	+	0.584564i	0.646463	+	0.762945i	$0.276247\pi$
$152$		0			0
$153$	10.6952	−	4.66078i	0.864657	−	0.376802i
$154$		0			0
$155$	2.50907	+	4.34583i	0.201533	+	0.349066i
$156$		0			0
$157$	−6.66664			−0.532056			−0.266028	−	0.963965i	$-0.585711\pi$
$157$	−6.66664			−0.532056			−0.266028	+	0.963965i	$0.585711\pi$
$158$		0			0
$159$	0.873840	+	0.287755i	0.0693001	+	0.0228204i
$160$		0			0
$161$	1.54685	+	3.55182i	0.121909	+	0.279922i
$162$		0			0
$163$	3.69751	−	6.40428i	0.289611	−	0.501622i	−0.684106	−	0.729383i	$-0.739807\pi$
$163$	3.69751	−	6.40428i	0.289611	−	0.501622i	0.973717	+	0.227761i	$0.0731406\pi$
$164$		0			0
$165$	5.95351	−	5.31807i	0.463480	−	0.414011i
$166$		0			0
$167$	−0.475526	+	0.823635i	−0.0367973	+	0.0637348i	−0.883838	−	0.467794i	$-0.845049\pi$
$167$	−0.475526	+	0.823635i	−0.0367973	+	0.0637348i	0.847040	+	0.531529i	$0.178382\pi$
$168$		0			0
$169$	3.32317	+	5.75590i	0.255629	+	0.442762i
$170$		0			0
$171$	10.3038	+	7.61139i	0.787948	+	0.582057i
$172$		0			0
$173$	4.67108			0.355136			0.177568	−	0.984109i	$-0.443177\pi$
$173$	4.67108			0.355136			0.177568	+	0.984109i	$0.443177\pi$
$174$		0			0
$175$	6.94506	−	9.39722i	0.524997	−	0.710363i
$176$		0			0
$177$	−14.4656	+	12.9216i	−1.08730	+	0.971248i
$178$		0			0
$179$	−7.49486	−	12.9815i	−0.560192	−	0.970281i	−0.997479	−	0.0709591i	$-0.977394\pi$
$179$	−7.49486	−	12.9815i	−0.560192	−	0.970281i	0.437287	−	0.899322i	$-0.355939\pi$
$180$		0			0
$181$	−13.6525			−1.01478			−0.507391	−	0.861716i	$-0.669390\pi$
$181$	−13.6525			−1.01478			−0.507391	+	0.861716i	$0.669390\pi$
$182$		0			0
$183$	−10.8285	+	9.67273i	−0.800466	+	0.715029i
$184$		0			0
$185$	7.37089			0.541919
$186$		0			0
$187$	−23.4651			−1.71594
$188$		0			0
$189$	6.63429	+	12.0410i	0.482573	+	0.875855i
$190$		0			0
$191$	12.2906			0.889313			0.444657	−	0.895701i	$-0.353326\pi$
$191$	12.2906			0.889313			0.444657	+	0.895701i	$0.353326\pi$
$192$		0			0
$193$	7.17156			0.516220			0.258110	−	0.966116i	$-0.416900\pi$
$193$	7.17156			0.516220			0.258110	+	0.966116i	$0.416900\pi$
$194$		0			0
$195$	2.48707	−	2.22161i	0.178102	−	0.159093i
$196$		0			0
$197$	−13.0286			−0.928247			−0.464124	−	0.885770i	$-0.653631\pi$
$197$	−13.0286			−0.928247			−0.464124	+	0.885770i	$0.653631\pi$
$198$		0			0
$199$	−2.48087	−	4.29699i	−0.175864	−	0.304606i	0.764596	−	0.644510i	$-0.222939\pi$
$199$	−2.48087	−	4.29699i	−0.175864	−	0.304606i	−0.940460	+	0.339904i	$0.889605\pi$
$200$		0			0
$201$	2.48525	−	2.21999i	0.175296	−	0.156586i
$202$		0			0
$203$	−6.35395	−	14.5897i	−0.445960	−	1.02400i
$204$		0			0
$205$	−3.43489			−0.239903
$206$		0			0
$207$	4.02698	−	1.75488i	0.279894	−	0.121973i
$208$		0			0
$209$	−12.8825	−	22.3132i	−0.891104	−	1.54344i
$210$		0			0
$211$	2.07384	−	3.59199i	0.142769	−	0.247283i	−0.785769	−	0.618519i	$-0.787733\pi$
$211$	2.07384	−	3.59199i	0.142769	−	0.247283i	0.928538	+	0.371237i	$0.121066\pi$
$212$		0			0
$213$	−12.7928	+	11.4274i	−0.876547	+	0.782990i
$214$		0			0
$215$	1.63081	−	2.82465i	0.111221	−	0.192640i
$216$		0			0
$217$	17.2711	+	1.95754i	1.17244	+	0.132887i
$218$		0			0
$219$	7.01159	+	2.30891i	0.473799	+	0.156021i
$220$		0			0
$221$	−9.80249			−0.659387
$222$		0			0
$223$	−4.63830	−	8.03378i	−0.310604	−	0.537982i	0.667889	−	0.744261i	$-0.267198\pi$
$223$	−4.63830	−	8.03378i	−0.310604	−	0.537982i	−0.978493	+	0.206279i	$0.933865\pi$
$224$		0			0
$225$	−10.6573	−	7.87252i	−0.710483	−	0.524834i
$226$		0			0
$227$	10.6801	−	18.4985i	0.708863	−	1.22779i	−0.256416	−	0.966567i	$-0.582542\pi$
$227$	10.6801	−	18.4985i	0.708863	−	1.22779i	0.965279	−	0.261221i	$-0.0841250\pi$
$228$		0			0
$229$	10.0035	+	17.3266i	0.661052	+	1.14498i	0.980339	+	0.197318i	$0.0632232\pi$
$229$	10.0035	+	17.3266i	0.661052	+	1.14498i	−0.319287	+	0.947658i	$0.603443\pi$
$230$		0			0
$231$	−2.55744	−	27.5323i	−0.168267	−	1.81149i
$232$		0			0
$233$	7.63657	−	13.2269i	0.500288	−	0.866525i	−0.499712	−	0.866192i	$-0.666561\pi$
$233$	7.63657	−	13.2269i	0.500288	−	0.866525i	1.00000		0.000332882i	$-0.000105960\pi$
$234$		0			0
$235$	−2.58883	−	4.48398i	−0.168876	−	0.292503i
$236$		0			0
$237$	9.56848	−	8.54721i	0.621540	−	0.555201i
$238$		0			0
$239$	9.03828	−	15.6548i	0.584638	−	1.01262i	−0.410283	−	0.911958i	$-0.634570\pi$
$239$	9.03828	−	15.6548i	0.584638	−	1.01262i	0.994920	−	0.100664i	$-0.0320967\pi$
$240$		0			0
$241$	−2.15522	+	3.73296i	−0.138830	+	0.240461i	−0.927054	−	0.374928i	$-0.877668\pi$
$241$	−2.15522	+	3.73296i	−0.138830	+	0.240461i	0.788224	+	0.615389i	$0.211001\pi$
$242$		0			0
$243$	13.6515	−	7.52571i	0.875745	−	0.482774i
$244$		0			0
$245$	1.56926	+	5.11139i	0.100256	+	0.326555i
$246$		0			0
$247$	−5.38165	−	9.32130i	−0.342426	−	0.593100i
$248$		0			0
$249$	26.4927	+	8.72403i	1.67891	+	0.552863i
$250$		0			0
$251$	16.3348			1.03104			0.515521	−	0.856877i	$-0.327599\pi$
$251$	16.3348			1.03104			0.515521	+	0.856877i	$0.327599\pi$
$252$		0			0
$253$	−8.83512			−0.555459
$254$		0			0
$255$	−1.04979	−	5.03676i	−0.0657404	−	0.315414i
$256$		0			0
$257$	−0.647698	−	1.12185i	−0.0404023	−	0.0699788i	0.845117	−	0.534581i	$-0.179531\pi$
$257$	−0.647698	−	1.12185i	−0.0404023	−	0.0699788i	−0.885519	+	0.464602i	$0.846197\pi$
$258$		0			0
$259$	15.1744	−	20.5322i	0.942893	−	1.27581i
$260$		0			0
$261$	−16.5415	+	7.20849i	−1.02389	+	0.446194i
$262$		0			0
$263$	−14.1364	+	24.4850i	−0.871687	+	1.50981i	−0.0114371	+	0.999935i	$0.503641\pi$
$263$	−14.1364	+	24.4850i	−0.871687	+	1.50981i	−0.860250	+	0.509872i	$0.829693\pi$
$264$		0			0
$265$	0.202861	−	0.351365i	0.0124616	−	0.0215842i
$266$		0			0
$267$	1.24619	+	5.97906i	0.0762655	+	0.365912i
$268$		0			0
$269$	7.10969	+	12.3143i	0.433485	+	0.750818i	0.997171	−	0.0751711i	$-0.0239503\pi$
$269$	7.10969	+	12.3143i	0.433485	+	0.750818i	−0.563685	+	0.825990i	$0.690617\pi$
$270$		0			0
$271$	−7.18914	+	12.4520i	−0.436709	+	0.756403i	−0.997433	−	0.0716001i	$-0.977189\pi$
$271$	−7.18914	+	12.4520i	−0.436709	+	0.756403i	0.560724	+	0.828003i	$0.310523\pi$
$272$		0			0
$273$	−1.06837	−	11.5015i	−0.0646604	−	0.696105i
$274$		0			0
$275$	13.3245	+	23.0787i	0.803498	+	1.39170i
$276$		0			0
$277$	7.71807	−	13.3681i	0.463734	−	0.803211i	−0.535409	−	0.844593i	$-0.679843\pi$
$277$	7.71807	−	13.3681i	0.463734	−	0.803211i	0.999143	+	0.0413818i	$0.0131760\pi$
$278$		0			0
$279$	2.21515	−	19.5841i	0.132618	−	1.17247i
$280$		0			0
$281$	−9.39609	−	16.2745i	−0.560524	−	0.970856i	−0.997451	−	0.0713587i	$-0.977266\pi$
$281$	−9.39609	−	16.2745i	−0.560524	−	0.970856i	0.436927	−	0.899497i	$-0.356067\pi$
$282$		0			0
$283$	−32.5729			−1.93626			−0.968128	−	0.250455i	$-0.919420\pi$
$283$	−32.5729			−1.93626			−0.968128	+	0.250455i	$0.919420\pi$
$284$		0			0
$285$	4.21317	−	3.76348i	0.249567	−	0.222930i
$286$		0			0
$287$	−7.07139	+	9.56815i	−0.417411	+	0.564790i
$288$		0			0
$289$	0.938304	−	1.62519i	0.0551944	−	0.0955994i
$290$		0			0
$291$	−7.68325	−	2.53009i	−0.450400	−	0.148316i
$292$		0			0
$293$	−1.69821	+	2.94138i	−0.0992103	+	0.171837i	−0.911358	−	0.411615i	$-0.864965\pi$
$293$	−1.69821	+	2.94138i	−0.0992103	+	0.171837i	0.812148	+	0.583452i	$0.198298\pi$
$294$		0			0
$295$	4.27692	+	7.40785i	0.249012	+	0.431302i
$296$		0			0
$297$	−31.2180	+	2.90703i	−1.81145	+	0.168683i
$298$		0			0
$299$	−3.69085			−0.213447
$300$		0			0
$301$	−4.51094	−	10.3579i	−0.260006	−	0.597017i
$302$		0			0
$303$	1.66797	+	8.00270i	0.0958222	+	0.459743i
$304$		0			0
$305$	3.20158	+	5.54529i	0.183322	+	0.317523i
$306$		0			0
$307$	3.69564			0.210921			0.105461	−	0.994423i	$-0.466368\pi$
$307$	3.69564			0.210921			0.105461	+	0.994423i	$0.466368\pi$
$308$		0			0
$309$	5.20741	+	1.71479i	0.296239	+	0.0975512i
$310$		0			0
$311$	−17.1624			−0.973189			−0.486594	−	0.873628i	$-0.661761\pi$
$311$	−17.1624			−0.973189			−0.486594	+	0.873628i	$0.661761\pi$
$312$		0			0
$313$	5.29647			0.299374			0.149687	−	0.988733i	$-0.452173\pi$
$313$	5.29647			0.299374			0.149687	+	0.988733i	$0.452173\pi$
$314$		0			0
$315$	5.79536	−	1.78070i	0.326532	−	0.100331i
$316$		0			0
$317$	28.1779			1.58263			0.791315	−	0.611409i	$-0.209397\pi$
$317$	28.1779			1.58263			0.791315	+	0.611409i	$0.209397\pi$
$318$		0			0
$319$	36.2918			2.03195
$320$		0			0
$321$	5.41096	+	25.9611i	0.302010	+	1.44901i
$322$		0			0
$323$	−16.6057			−0.923968
$324$		0			0
$325$	5.56628	+	9.64109i	0.308762	+	0.534791i
$326$		0			0
$327$	−25.1830	−	8.29272i	−1.39262	−	0.458588i
$328$		0			0
$329$	−17.8201	−	2.01977i	−0.982453	−	0.111354i
$330$		0			0
$331$	29.1720			1.60344			0.801720	−	0.597699i	$-0.203918\pi$
$331$	29.1720			1.60344			0.801720	+	0.597699i	$0.203918\pi$
$332$		0			0
$333$	−23.2853	−	17.2008i	−1.27603	−	0.942600i
$334$		0			0
$335$	−0.734794	−	1.27270i	−0.0401461	−	0.0695351i
$336$		0			0
$337$	−0.447174	+	0.774528i	−0.0243591	+	0.0421912i	−0.877948	−	0.478756i	$-0.841088\pi$
$337$	−0.447174	+	0.774528i	−0.0243591	+	0.0421912i	0.853589	+	0.520947i	$0.174421\pi$
$338$		0			0
$339$	−1.10344	−	5.29417i	−0.0599307	−	0.287540i
$340$		0			0
$341$	−19.8203	+	34.3297i	−1.07333	+	1.85906i
$342$		0			0
$343$	17.4688	+	6.15150i	0.943227	+	0.332150i
$344$		0			0
$345$	−0.395269	−	1.89645i	−0.0212806	−	0.102101i
$346$		0			0
$347$	19.9796			1.07256			0.536282	−	0.844039i	$-0.319828\pi$
$347$	19.9796			1.07256			0.536282	+	0.844039i	$0.319828\pi$
$348$		0			0
$349$	2.58530	+	4.47788i	0.138388	+	0.239695i	0.926887	−	0.375341i	$-0.122475\pi$
$349$	2.58530	+	4.47788i	0.138388	+	0.239695i	−0.788499	+	0.615037i	$0.789141\pi$
$350$		0			0
$351$	−13.0412	+	1.21440i	−0.696090	+	0.0648201i
$352$		0			0
$353$	−16.5611	+	28.6847i	−0.881459	+	1.52673i	−0.0317390	+	0.999496i	$0.510105\pi$
$353$	−16.5611	+	28.6847i	−0.881459	+	1.52673i	−0.849720	+	0.527235i	$0.823229\pi$
$354$		0			0
$355$	3.78234	+	6.55120i	0.200746	+	0.347702i
$356$		0			0
$357$	−16.1915	−	7.44489i	−0.856945	−	0.394026i
$358$		0			0
$359$	−17.2965	+	29.9584i	−0.912874	+	1.58114i	−0.102889	+	0.994693i	$0.532809\pi$
$359$	−17.2965	+	29.9584i	−0.912874	+	1.58114i	−0.809985	+	0.586451i	$0.800525\pi$
$360$		0			0
$361$	0.383301	+	0.663897i	0.0201737	+	0.0349420i
$362$		0			0
$363$	41.7997	+	13.7646i	2.19392	+	0.722454i
$364$		0			0
$365$	1.62773	−	2.81931i	0.0851992	−	0.147569i
$366$		0			0
$367$	1.64805	−	2.85451i	0.0860277	−	0.149004i	−0.819801	−	0.572649i	$-0.805916\pi$
$367$	1.64805	−	2.85451i	0.0860277	−	0.149004i	0.905829	+	0.423644i	$0.139249\pi$
$368$		0			0
$369$	10.8511	+	8.01571i	0.564886	+	0.417281i
$370$		0			0
$371$	−0.561126	−	1.28844i	−0.0291322	−	0.0668923i
$372$		0			0
$373$	11.8377	+	20.5035i	0.612933	+	1.06163i	0.990743	+	0.135748i	$0.0433436\pi$
$373$	11.8377	+	20.5035i	0.612933	+	1.06163i	−0.377811	+	0.925883i	$0.623323\pi$
$374$		0			0
$375$	−9.29110	+	8.29943i	−0.479790	+	0.428581i
$376$		0			0
$377$	15.1608			0.780821
$378$		0			0
$379$	−25.4415			−1.30684			−0.653421	−	0.756995i	$-0.726667\pi$
$379$	−25.4415			−1.30684			−0.653421	+	0.756995i	$0.726667\pi$
$380$		0			0
$381$	−1.65102	+	1.47480i	−0.0845843	+	0.0755564i
$382$		0			0
$383$	−11.8639	−	20.5489i	−0.606218	−	1.05000i	−0.991858	−	0.127351i	$-0.959353\pi$
$383$	−11.8639	−	20.5489i	−0.606218	−	1.05000i	0.385640	−	0.922649i	$-0.373981\pi$
$384$		0			0
$385$	−12.1164	−	1.37331i	−0.617511	−	0.0699902i
$386$		0			0
$387$	−11.7435	+	5.11762i	−0.596957	+	0.260143i
$388$		0			0
$389$	−9.76374	+	16.9113i	−0.495041	+	0.857436i	−0.999984	−	0.00571663i	$-0.998180\pi$
$389$	−9.76374	+	16.9113i	−0.495041	+	0.857436i	0.504943	+	0.863153i	$0.331514\pi$
$390$		0			0
$391$	−2.84714	+	4.93139i	−0.143986	+	0.249391i
$392$		0			0
$393$	12.7905	+	4.21188i	0.645193	+	0.212461i
$394$		0			0
$395$	−2.82904	−	4.90004i	−0.142344	−	0.246548i
$396$		0			0
$397$	14.4468	−	25.0226i	0.725064	−	1.25585i	−0.233884	−	0.972265i	$-0.575144\pi$
$397$	14.4468	−	25.0226i	0.725064	−	1.25585i	0.958948	−	0.283583i	$-0.0915231\pi$
$398$		0			0
$399$	−1.80985	−	19.4840i	−0.0906056	−	0.975419i
$400$		0			0
$401$	−2.75292	−	4.76820i	−0.137474	−	0.238112i	0.789066	−	0.614309i	$-0.210565\pi$
$401$	−2.75292	−	4.76820i	−0.137474	−	0.238112i	−0.926540	+	0.376196i	$0.877232\pi$
$402$		0			0
$403$	−8.27988	+	14.3412i	−0.412450	+	0.714385i
$404$		0			0
$405$	−2.02063	−	6.57086i	−0.100406	−	0.326509i
$406$		0			0
$407$	29.1130	+	50.4253i	1.44308	+	2.49949i
$408$		0			0
$409$	−1.02391			−0.0506290			−0.0253145	−	0.999680i	$-0.508059\pi$
$409$	−1.02391			−0.0506290			−0.0253145	+	0.999680i	$0.508059\pi$
$410$		0			0
$411$	−0.997698	−	4.78683i	−0.0492128	−	0.236117i
$412$		0			0
$413$	29.4400	+	3.33680i	1.44865	+	0.164193i
$414$		0			0
$415$	6.15025	−	10.6525i	0.301904	−	0.522912i
$416$		0			0
$417$	−7.93092	−	38.0516i	−0.388379	−	1.86339i
$418$		0			0
$419$	16.9398	−	29.3405i	0.827562	−	1.43338i	−0.0723837	−	0.997377i	$-0.523061\pi$
$419$	16.9398	−	29.3405i	0.827562	−	1.43338i	0.899946	−	0.436002i	$-0.143606\pi$
$420$		0			0
$421$	0.563823	+	0.976570i	0.0274790	+	0.0475951i	0.879438	−	0.476014i	$-0.157919\pi$
$421$	0.563823	+	0.976570i	0.0274790	+	0.0475951i	−0.851959	+	0.523609i	$0.824585\pi$
$422$		0			0
$423$	−2.28557	+	20.2066i	−0.111128	+	0.982479i
$424$		0			0
$425$	17.1754			0.833132
$426$		0			0
$427$	22.0379	+	2.49783i	1.06649	+	0.120878i
$428$		0			0
$429$	25.0216	+	8.23957i	1.20805	+	0.397810i
$430$		0			0
$431$	−1.44172	−	2.49713i	−0.0694450	−	0.120282i	0.829212	−	0.558934i	$-0.188790\pi$
$431$	−1.44172	−	2.49713i	−0.0694450	−	0.120282i	−0.898657	+	0.438652i	$0.855456\pi$
$432$		0			0
$433$	−14.3808			−0.691097			−0.345548	−	0.938401i	$-0.612307\pi$
$433$	−14.3808			−0.691097			−0.345548	+	0.938401i	$0.612307\pi$
$434$		0			0
$435$	1.62363	+	7.79000i	0.0778473	+	0.373502i
$436$		0			0
$437$	−6.25242			−0.299094
$438$		0			0
$439$	20.9915			1.00187			0.500936	−	0.865484i	$-0.332989\pi$
$439$	20.9915			1.00187			0.500936	+	0.865484i	$0.332989\pi$
$440$		0			0
$441$	6.97060	−	19.8094i	0.331934	−	0.943303i
$442$		0			0
$443$	−20.0586			−0.953014			−0.476507	−	0.879171i	$-0.658097\pi$
$443$	−20.0586			−0.953014			−0.476507	+	0.879171i	$0.658097\pi$
$444$		0			0
$445$	2.69343			0.127681
$446$		0			0
$447$	−33.1830	−	10.9271i	−1.56950	−	0.516836i
$448$		0			0
$449$	−11.4192			−0.538903			−0.269452	−	0.963014i	$-0.586842\pi$
$449$	−11.4192			−0.538903			−0.269452	+	0.963014i	$0.586842\pi$
$450$		0			0
$451$	−13.5669	−	23.4985i	−0.638839	−	1.10650i
$452$		0			0
$453$	−2.93135	−	14.0643i	−0.137727	−	0.660796i
$454$		0			0
$455$	−5.06162	−	0.573696i	−0.237292	−	0.0268953i
$456$		0			0
$457$	−18.2059			−0.851635			−0.425817	−	0.904809i	$-0.640013\pi$
$457$	−18.2059			−0.851635			−0.425817	+	0.904809i	$0.640013\pi$
$458$		0			0
$459$	−8.43750	+	18.3614i	−0.393829	+	0.857036i
$460$		0			0
$461$	−18.6430	−	32.2906i	−0.868289	−	1.50392i	−0.863744	−	0.503931i	$-0.831887\pi$
$461$	−18.6430	−	32.2906i	−0.868289	−	1.50392i	−0.00454533	−	0.999990i	$-0.501447\pi$
$462$		0			0
$463$	−0.530345	+	0.918584i	−0.0246472	+	0.0426902i	−0.878086	−	0.478503i	$-0.841180\pi$
$463$	−0.530345	+	0.918584i	−0.0246472	+	0.0426902i	0.853439	+	0.521193i	$0.174513\pi$
$464$		0			0
$465$	−8.25558	−	2.71855i	−0.382843	−	0.126070i
$466$		0			0
$467$	−14.0374	+	24.3134i	−0.649571	+	1.12509i	0.333654	+	0.942696i	$0.391718\pi$
$467$	−14.0374	+	24.3134i	−0.649571	+	1.12509i	−0.983225	+	0.182395i	$0.941615\pi$
$468$		0			0
$469$	−5.05793	−	0.573277i	−0.233553	−	0.0264715i
$470$		0			0
$471$	8.61156	−	7.69242i	0.396800	−	0.354448i
$472$		0			0
$473$	25.7651			1.18468
$474$		0			0
$475$	9.42947	+	16.3323i	0.432654	+	0.749378i
$476$		0			0
$477$	−1.46080	+	0.636592i	−0.0668856	+	0.0291476i
$478$		0			0
$479$	−3.61705	+	6.26492i	−0.165267	+	0.286251i	−0.936750	−	0.349999i	$-0.886182\pi$
$479$	−3.61705	+	6.26492i	−0.165267	+	0.286251i	0.771483	+	0.636250i	$0.219515\pi$
$480$		0			0
$481$	12.1619	+	21.0650i	0.554535	+	0.960483i
$482$		0			0
$483$	−6.09645	−	2.80316i	−0.277398	−	0.127548i
$484$		0			0
$485$	−1.78365	+	3.08938i	−0.0809916	+	0.140282i
$486$		0			0
$487$	16.9145	+	29.2968i	0.766470	+	1.32756i	0.939466	+	0.342642i	$0.111322\pi$
$487$	16.9145	+	29.2968i	0.766470	+	1.32756i	−0.172996	+	0.984922i	$0.555345\pi$
$488$		0			0
$489$	2.61347	+	12.5391i	0.118185	+	0.567038i
$490$		0			0
$491$	−0.300406	+	0.520319i	−0.0135572	+	0.0234817i	−0.872724	−	0.488213i	$-0.837649\pi$
$491$	−0.300406	+	0.520319i	−0.0135572	+	0.0234817i	0.859167	+	0.511695i	$0.170982\pi$
$492$		0			0
$493$	11.6951	−	20.2565i	0.526722	−	0.912309i
$494$		0			0
$495$	−1.55403	+	13.7391i	−0.0698485	+	0.617528i
$496$		0			0
$497$	26.0356	+	2.95093i	1.16786	+	0.132367i
$498$		0			0
$499$	−2.82067	−	4.88554i	−0.126271	−	0.218707i	0.795958	−	0.605351i	$-0.206967\pi$
$499$	−2.82067	−	4.88554i	−0.126271	−	0.218707i	−0.922229	+	0.386644i	$0.873634\pi$
$500$		0			0
$501$	−0.336110	−	1.61261i	−0.0150163	−	0.0720463i
$502$		0			0
$503$	−31.0034			−1.38237			−0.691186	−	0.722677i	$-0.742911\pi$
$503$	−31.0034			−1.38237			−0.691186	+	0.722677i	$0.742911\pi$
$504$		0			0
$505$	3.60504			0.160422
$506$		0			0
$507$	−10.9342	−	3.60062i	−0.485606	−	0.159909i
$508$		0			0
$509$	−17.3480	−	30.0475i	−0.768935	−	1.33183i	−0.938141	−	0.346253i	$-0.887454\pi$
$509$	−17.3480	−	30.0475i	−0.768935	−	1.33183i	0.169206	−	0.985581i	$-0.445880\pi$
$510$		0			0
$511$	−4.50241	−	10.3383i	−0.199175	−	0.457338i
$512$		0			0
$513$	−22.0923	+	2.05724i	−0.975399	+	0.0908293i
$514$		0			0
$515$	1.20889	−	2.09386i	0.0532701	−	0.0922665i
$516$		0			0
$517$	20.4503	−	35.4210i	0.899405	−	1.55781i
$518$		0			0
$519$	−6.03382	+	5.38981i	−0.264855	+	0.236586i
$520$		0			0
$521$	−12.5083	−	21.6650i	−0.547998	−	0.949161i	−0.998412	−	0.0563408i	$-0.982057\pi$
$521$	−12.5083	−	21.6650i	−0.547998	−	0.949161i	0.450413	−	0.892820i	$-0.351277\pi$
$522$		0			0
$523$	−1.59320	+	2.75950i	−0.0696656	+	0.120664i	−0.898754	−	0.438453i	$-0.855527\pi$
$523$	−1.59320	+	2.75950i	−0.0696656	+	0.120664i	0.829088	+	0.559117i	$0.188860\pi$
$524$		0			0
$525$	1.87194	+	20.1524i	0.0816980	+	0.879524i
$526$		0			0
$527$	12.7743	+	22.1257i	0.556457	+	0.963811i
$528$		0			0
$529$	10.4280	−	18.0618i	0.453391	−	0.785296i
$530$		0			0
$531$	3.77592	−	33.3827i	0.163861	−	1.44869i
$532$		0			0
$533$	−5.66753	−	9.81645i	−0.245488	−	0.425198i
$534$		0			0
$535$	11.6949			0.505615
$536$		0			0
$537$	24.6603	+	8.12061i	1.06417	+	0.350430i
$538$		0			0
$539$	−28.7695	+	30.9241i	−1.23919	+	1.33200i
$540$		0			0
$541$	−6.80693	+	11.7900i	−0.292653	+	0.506890i	−0.974436	−	0.224664i	$-0.927871\pi$
$541$	−6.80693	+	11.7900i	−0.292653	+	0.506890i	0.681783	+	0.731554i	$0.261205\pi$
$542$		0			0
$543$	17.6355	−	15.7532i	0.756810	−	0.676033i
$544$		0			0
$545$	−5.84618	+	10.1259i	−0.250423	+	0.433745i
$546$		0			0
$547$	−5.91254	−	10.2408i	−0.252802	−	0.437866i	0.711494	−	0.702692i	$-0.248019\pi$
$547$	−5.91254	−	10.2408i	−0.252802	−	0.437866i	−0.964296	+	0.264826i	$0.914685\pi$
$548$		0			0
$549$	2.82654	−	24.9893i	0.120634	−	1.06652i
$550$		0			0
$551$	25.6829			1.09413
$552$		0			0
$553$	−19.4736	−	2.20718i	−0.828100	−	0.0938588i
$554$		0			0
$555$	−9.52127	+	8.50503i	−0.404155	+	0.361019i
$556$		0			0
$557$	−9.32911	−	16.1585i	−0.395287	−	0.684657i	0.597851	−	0.801607i	$-0.296021\pi$
$557$	−9.32911	−	16.1585i	−0.395287	−	0.684657i	−0.993138	+	0.116950i	$0.962688\pi$
$558$		0			0
$559$	10.7633			0.455239
$560$		0			0
$561$	30.3108	−	27.0756i	1.27972	−	1.14313i
$562$		0			0
$563$	22.6391			0.954125			0.477062	−	0.878869i	$-0.341702\pi$
$563$	22.6391			0.954125			0.477062	+	0.878869i	$0.341702\pi$
$564$		0			0
$565$	−2.38491			−0.100334
$566$		0			0
$567$	−22.4635	−	7.89877i	−0.943379	−	0.331717i
$568$		0			0
$569$	10.9055			0.457184			0.228592	−	0.973522i	$-0.426588\pi$
$569$	10.9055			0.457184			0.228592	+	0.973522i	$0.426588\pi$
$570$		0			0
$571$	−27.6111			−1.15549			−0.577743	−	0.816218i	$-0.696067\pi$
$571$	−27.6111			−1.15549			−0.577743	+	0.816218i	$0.696067\pi$
$572$		0			0
$573$	−15.8762	+	14.1817i	−0.663237	+	0.592448i
$574$		0			0
$575$	6.46693			0.269690
$576$		0			0
$577$	−10.2592	−	17.7695i	−0.427096	−	0.739753i	0.569517	−	0.821979i	$-0.307130\pi$
$577$	−10.2592	−	17.7695i	−0.427096	−	0.739753i	−0.996614	+	0.0822267i	$0.973797\pi$
$578$		0			0
$579$	−9.26378	+	8.27503i	−0.384990	+	0.343898i
$580$		0			0
$581$	−17.0120	−	39.0623i	−0.705776	−	1.62058i
$582$		0			0
$583$	3.20498			0.132737
$584$		0			0
$585$	−0.649193	+	5.73949i	−0.0268408	+	0.237299i
$586$		0			0
$587$	7.59632	+	13.1572i	0.313534	+	0.543056i	0.979125	−	0.203260i	$-0.0651538\pi$
$587$	7.59632	+	13.1572i	0.313534	+	0.543056i	−0.665591	+	0.746317i	$0.731820\pi$
$588$		0			0
$589$	−14.0264	+	24.2944i	−0.577947	+	1.00103i
$590$		0			0
$591$	16.8295	−	15.0332i	0.692274	−	0.618385i
$592$		0			0
$593$	3.39373	−	5.87812i	0.139364	−	0.241385i	−0.787892	−	0.615813i	$-0.788828\pi$
$593$	3.39373	−	5.87812i	0.139364	−	0.241385i	0.927256	+	0.374428i	$0.122161\pi$
$594$		0			0
$595$	−4.67108	+	6.32035i	−0.191496	+	0.259109i
$596$		0			0
$597$	8.16279	+	2.68800i	0.334081	+	0.110012i
$598$		0			0
$599$	12.6504			0.516880			0.258440	−	0.966027i	$-0.416791\pi$
$599$	12.6504			0.516880			0.258440	+	0.966027i	$0.416791\pi$
$600$		0			0
$601$	−11.3699	−	19.6932i	−0.463787	−	0.803303i	0.535359	−	0.844625i	$-0.320176\pi$
$601$	−11.3699	−	19.6932i	−0.463787	−	0.803303i	−0.999146	+	0.0413219i	$0.986843\pi$
$602$		0			0
$603$	−0.648720	+	5.73530i	−0.0264179	+	0.233559i
$604$		0			0
$605$	9.70374	−	16.8074i	0.394513	−	0.683317i
$606$		0			0
$607$	−20.9613	−	36.3061i	−0.850794	−	1.47362i	−0.880493	−	0.474059i	$-0.842788\pi$
$607$	−20.9613	−	36.3061i	−0.850794	−	1.47362i	0.0296994	−	0.999559i	$-0.490545\pi$
$608$		0			0
$609$	25.0422	+	11.5145i	1.01476	+	0.466590i
$610$		0			0
$611$	8.54308	−	14.7971i	0.345616	−	0.598625i
$612$		0			0
$613$	−13.7038	−	23.7356i	−0.553490	−	0.958673i	−0.998019	−	0.0629086i	$-0.979962\pi$
$613$	−13.7038	−	23.7356i	−0.553490	−	0.958673i	0.444529	−	0.895764i	$-0.353371\pi$
$614$		0			0
$615$	4.43698	−	3.96340i	0.178916	−	0.159820i
$616$		0			0
$617$	5.75420	−	9.96656i	0.231655	−	0.401239i	−0.726640	−	0.687018i	$-0.758919\pi$
$617$	5.75420	−	9.96656i	0.231655	−	0.401239i	0.958295	+	0.285780i	$0.0922526\pi$
$618$		0			0
$619$	−18.8780	+	32.6976i	−0.758770	+	1.31423i	0.184708	+	0.982793i	$0.440866\pi$
$619$	−18.8780	+	32.6976i	−0.758770	+	1.31423i	−0.943478	+	0.331435i	$0.892467\pi$
$620$		0			0
$621$	−3.17690	+	6.91345i	−0.127485	+	0.277427i
$622$		0			0
$623$	5.54496	−	7.50277i	0.222154	−	0.300592i
$624$		0			0
$625$	−8.29436	−	14.3662i	−0.331774	−	0.574650i
$626$		0			0
$627$	42.3874	+	13.9581i	1.69279	+	0.557433i
$628$		0			0
$629$	37.5270			1.49630
$630$		0			0
$631$	45.4466			1.80920			0.904600	−	0.426262i	$-0.140170\pi$
$631$	45.4466			1.80920			0.904600	+	0.426262i	$0.140170\pi$
$632$		0			0
$633$	1.46583	+	7.03285i	0.0582613	+	0.279531i
$634$		0			0
$635$	0.488144	+	0.845490i	0.0193714	+	0.0335523i
$636$		0			0
$637$	−12.0184	+	12.9185i	−0.476187	+	0.511849i
$638$		0			0
$639$	3.33927	−	29.5223i	0.132100	−	1.16789i
$640$		0			0
$641$	0.149803	−	0.259467i	0.00591687	−	0.0102483i	−0.863052	−	0.505115i	$-0.831450\pi$
$641$	0.149803	−	0.259467i	0.00591687	−	0.0102483i	0.868969	+	0.494867i	$0.164783\pi$
$642$		0			0
$643$	−3.61580	+	6.26275i	−0.142593	+	0.246979i	−0.928472	−	0.371401i	$-0.878877\pi$
$643$	−3.61580	+	6.26275i	−0.142593	+	0.246979i	0.785879	+	0.618380i	$0.212211\pi$
$644$		0			0
$645$	1.15269	+	5.53046i	0.0453870	+	0.217761i
$646$		0			0
$647$	−4.78298	−	8.28437i	−0.188039	−	0.325692i	0.756558	−	0.653927i	$-0.226880\pi$
$647$	−4.78298	−	8.28437i	−0.188039	−	0.325692i	−0.944596	+	0.328235i	$0.893546\pi$
$648$		0			0
$649$	−33.7854	+	58.5180i	−1.32619	+	2.29703i
$650$		0			0
$651$	−24.5685	+	17.3999i	−0.962914	+	0.681956i
$652$		0			0
$653$	−19.5035	−	33.7811i	−0.763232	−	1.32196i	−0.941176	−	0.337915i	$-0.890278\pi$
$653$	−19.5035	−	33.7811i	−0.763232	−	1.32196i	0.177945	−	0.984040i	$-0.443055\pi$
$654$		0			0
$655$	2.96928	−	5.14295i	0.116019	−	0.200952i
$656$		0			0
$657$	−11.7213	+	5.10794i	−0.457292	+	0.199280i
$658$		0			0
$659$	−0.251281	−	0.435231i	−0.00978851	−	0.0169542i	0.861090	−	0.508453i	$-0.169782\pi$
$659$	−0.251281	−	0.435231i	−0.00978851	−	0.0169542i	−0.870878	+	0.491499i	$0.836449\pi$
$660$		0			0
$661$	−2.19820			−0.0855002			−0.0427501	−	0.999086i	$-0.513612\pi$
$661$	−2.19820			−0.0855002			−0.0427501	+	0.999086i	$0.513612\pi$
$662$		0			0
$663$	12.6623	−	11.3108i	0.491762	−	0.439274i
$664$		0			0
$665$	−8.57455	−	0.971859i	−0.332507	−	0.0376871i
$666$		0			0
$667$	4.40347	−	7.62703i	0.170503	−	0.295320i
$668$		0			0
$669$	15.2614	+	5.02556i	0.590040	+	0.194299i
$670$		0			0
$671$	−25.2907	+	43.8048i	−0.976337	+	1.69107i
$672$		0			0
$673$	7.50630	+	13.0013i	0.289346	+	0.501163i	0.973654	−	0.228031i	$-0.0732287\pi$
$673$	7.50630	+	13.0013i	0.289346	+	0.501163i	−0.684307	+	0.729194i	$0.739895\pi$
$674$		0			0
$675$	22.8502	−	2.12782i	0.879506	−	0.0818998i
$676$		0			0
$677$	29.6607			1.13995			0.569977	−	0.821661i	$-0.306952\pi$
$677$	29.6607			1.13995			0.569977	+	0.821661i	$0.306952\pi$
$678$		0			0
$679$	4.93371	+	11.3286i	0.189338	+	0.434752i
$680$		0			0
$681$	7.54889	+	36.2186i	0.289274	+	1.38790i
$682$		0			0
$683$	−12.7295	−	22.0482i	−0.487083	−	0.843652i	0.512807	−	0.858504i	$-0.328606\pi$
$683$	−12.7295	−	22.0482i	−0.487083	−	0.843652i	−0.999890	+	0.0148520i	$0.995272\pi$
$684$		0			0
$685$	−2.15636			−0.0823904
$686$		0			0
$687$	−32.9146	−	10.8387i	−1.25577	−	0.413524i
$688$		0			0
$689$	1.33887			0.0510070
$690$		0			0
$691$	−11.9100			−0.453077			−0.226538	−	0.974002i	$-0.572741\pi$
$691$	−11.9100			−0.453077			−0.226538	+	0.974002i	$0.572741\pi$
$692$		0			0
$693$	35.0721	+	32.6135i	1.33228	+	1.23889i
$694$		0			0
$695$	−17.1414			−0.650210
$696$		0			0
$697$	−17.4879			−0.662400
$698$		0			0
$699$	5.39766	+	25.8973i	0.204158	+	0.979527i
$700$		0			0
$701$	−3.84543			−0.145240			−0.0726199	−	0.997360i	$-0.523136\pi$
$701$	−3.84543			−0.145240			−0.0726199	+	0.997360i	$0.523136\pi$
$702$		0			0
$703$	20.6027	+	35.6849i	0.777044	+	1.34588i
$704$		0			0
$705$	8.51801	+	2.80497i	0.320807	+	0.105641i
$706$		0			0
$707$	7.42168	−	10.0421i	0.279121	−	0.377673i
$708$		0			0
$709$	−26.7066			−1.00299			−0.501494	−	0.865161i	$-0.667216\pi$
$709$	−26.7066			−1.00299			−0.501494	+	0.865161i	$0.667216\pi$
$710$		0			0
$711$	−2.49764	+	22.0815i	−0.0936688	+	0.828122i
$712$		0			0
$713$	4.80979	+	8.33081i	0.180128	+	0.311991i
$714$		0			0
$715$	5.80872	−	10.0610i	0.217234	−	0.376260i
$716$		0			0
$717$	6.38842	+	30.6508i	0.238580	+	1.14468i
$718$		0			0
$719$	13.3611	−	23.1420i	0.498284	−	0.863052i	−0.501715	−	0.865033i	$-0.667297\pi$
$719$	13.3611	−	23.1420i	0.498284	−	0.863052i	0.999998	+	0.00198088i	$0.000630534\pi$
$720$		0			0
$721$	−3.34388	−	7.67808i	−0.124532	−	0.285947i
$722$		0			0
$723$	−1.52335	−	7.30885i	−0.0566540	−	0.271819i
$724$		0			0
$725$	−26.5640			−0.986563
$726$		0			0
$727$	−1.13012	−	1.95743i	−0.0419139	−	0.0725970i	0.844307	−	0.535859i	$-0.180012\pi$
$727$	−1.13012	−	1.95743i	−0.0419139	−	0.0725970i	−0.886221	+	0.463262i	$0.846679\pi$
$728$		0			0
$729$	−8.95052	+	25.4733i	−0.331501	+	0.943455i
$730$		0			0
$731$	8.30287	−	14.3810i	0.307093	−	0.531900i
$732$		0			0
$733$	−18.3702	−	31.8181i	−0.678519	−	1.17523i	−0.975427	−	0.220323i	$-0.929289\pi$
$733$	−18.3702	−	31.8181i	−0.678519	−	1.17523i	0.296908	−	0.954906i	$-0.404045\pi$
$734$		0			0
$735$	−7.92494	−	4.79186i	−0.292316	−	0.176751i
$736$		0			0
$737$	5.80448	−	10.0536i	0.213811	−	0.370331i
$738$		0			0
$739$	−17.0909	−	29.6022i	−0.628697	−	1.08894i	−0.987813	−	0.155643i	$-0.950255\pi$
$739$	−17.0909	−	29.6022i	−0.628697	−	1.08894i	0.359116	−	0.933293i	$-0.383078\pi$
$740$		0			0
$741$	17.7072	+	5.83097i	0.650491	+	0.214206i
$742$		0			0
$743$	−4.56487	+	7.90658i	−0.167469	+	0.290064i	−0.937529	−	0.347907i	$-0.886893\pi$
$743$	−4.56487	+	7.90658i	−0.167469	+	0.290064i	0.770061	+	0.637971i	$0.220226\pi$
$744$		0			0
$745$	−7.70339	+	13.3427i	−0.282230	+	0.488837i
$746$		0			0
$747$	−44.2881	+	19.2999i	−1.62042	+	0.706148i
$748$		0			0
$749$	24.0763	−	32.5771i	0.879727	−	1.19034i
$750$		0			0
$751$	19.0648	+	33.0212i	0.695683	+	1.20496i	0.969950	+	0.243305i	$0.0782316\pi$
$751$	19.0648	+	33.0212i	0.695683	+	1.20496i	−0.274266	+	0.961654i	$0.588435\pi$
$752$		0			0
$753$	−21.1003	+	18.8482i	−0.768936	+	0.686865i
$754$		0			0
$755$	−6.33564			−0.230578
$756$		0			0
$757$	18.6952			0.679488			0.339744	−	0.940518i	$-0.389660\pi$
$757$	18.6952			0.679488			0.339744	+	0.940518i	$0.389660\pi$
$758$		0			0
$759$	11.4127	−	10.1946i	0.414253	−	0.370039i
$760$		0			0
$761$	8.07859	+	13.9925i	0.292849	+	0.507229i	0.974482	−	0.224465i	$-0.0720635\pi$
$761$	8.07859	+	13.9925i	0.292849	+	0.507229i	−0.681634	+	0.731694i	$0.738730\pi$
$762$		0			0
$763$	16.1709	+	37.1311i	0.585427	+	1.34424i
$764$		0			0
$765$	7.16781	+	5.29487i	0.259153	+	0.191436i
$766$		0			0
$767$	−14.1138	+	24.4458i	−0.509618	+	0.882685i
$768$		0			0
$769$	−16.9628	+	29.3804i	−0.611694	+	1.05949i	0.379261	+	0.925290i	$0.376178\pi$
$769$	−16.9628	+	29.3804i	−0.611694	+	1.05949i	−0.990955	+	0.134195i	$0.957155\pi$
$770$		0			0
$771$	2.13112	+	0.701774i	0.0767503	+	0.0252738i
$772$		0			0
$773$	19.8452	+	34.3728i	0.713781	+	1.23630i	0.963428	+	0.267968i	$0.0863522\pi$
$773$	19.8452	+	34.3728i	0.713781	+	1.23630i	−0.249647	+	0.968337i	$0.580315\pi$
$774$		0			0
$775$	14.5076	−	25.1279i	0.521128	−	0.902621i
$776$		0			0
$777$	4.09004	+	44.0315i	0.146729	+	1.57962i
$778$		0			0
$779$	−9.60099	−	16.6294i	−0.343991	−	0.595810i
$780$		0			0
$781$	−29.8784	+	51.7509i	−1.06913	+	1.85179i
$782$		0			0
$783$	13.0497	−	28.3982i	0.466357	−	1.01487i
$784$		0			0
$785$	−2.54611	−	4.41000i	−0.0908746	−	0.157400i
$786$		0			0
$787$	−0.317681			−0.0113241			−0.00566204	−	0.999984i	$-0.501802\pi$
$787$	−0.317681			−0.0113241			−0.00566204	+	0.999984i	$0.501802\pi$
$788$		0			0
$789$	−9.99186	−	47.9397i	−0.355719	−	1.70670i
$790$		0			0
$791$	−4.90980	+	6.64335i	−0.174573	+	0.236211i
$792$		0			0
$793$	−10.5651	+	18.2994i	−0.375179	+	0.649829i
$794$		0			0
$795$	0.143385	+	0.687946i	0.00508536	+	0.0243989i
$796$		0			0
$797$	−21.0702	+	36.4946i	−0.746344	+	1.29271i	0.203221	+	0.979133i	$0.434859\pi$
$797$	−21.0702	+	36.4946i	−0.746344	+	1.29271i	−0.949564	+	0.313572i	$0.898474\pi$
$798$		0			0
$799$	−13.1804	−	22.8290i	−0.466288	−	0.807634i
$800$		0			0
$801$	−8.50879	−	6.28544i	−0.300643	−	0.222085i
$802$		0			0
$803$	25.7163			0.907510
$804$		0			0
$805$	−1.75876	+	2.37975i	−0.0619883	+	0.0838751i
$806$		0			0
$807$	−23.3930	−	7.70328i	−0.823472	−	0.271168i
$808$		0			0
$809$	−6.40052	−	11.0860i	−0.225030	−	0.389764i	0.731298	−	0.682058i	$-0.238915\pi$
$809$	−6.40052	−	11.0860i	−0.225030	−	0.389764i	−0.956329	+	0.292294i	$0.905581\pi$
$810$		0			0
$811$	27.1410			0.953051			0.476526	−	0.879161i	$-0.341896\pi$
$811$	27.1410			0.953051			0.476526	+	0.879161i	$0.341896\pi$
$812$		0			0
$813$	−5.08141	−	24.3800i	−0.178213	−	0.855044i
$814$		0			0
$815$	5.64859			0.197861
$816$		0			0
$817$	18.2334			0.637906
$818$		0			0
$819$	14.6513	+	13.6242i	0.511958	+	0.476069i
$820$		0			0
$821$	−11.9185			−0.415958			−0.207979	−	0.978133i	$-0.566689\pi$
$821$	−11.9185			−0.415958			−0.207979	+	0.978133i	$0.566689\pi$
$822$		0			0
$823$	−18.5301			−0.645919			−0.322959	−	0.946413i	$-0.604678\pi$
$823$	−18.5301			−0.645919			−0.322959	+	0.946413i	$0.604678\pi$
$824$		0			0
$825$	−43.8416	−	14.4370i	−1.52637	−	0.502631i
$826$		0			0
$827$	9.64616			0.335430			0.167715	−	0.985836i	$-0.446361\pi$
$827$	9.64616			0.335430			0.167715	+	0.985836i	$0.446361\pi$
$828$		0			0
$829$	10.2155	+	17.6938i	0.354800	+	0.614531i	0.987084	−	0.160206i	$-0.0512158\pi$
$829$	10.2155	+	17.6938i	0.354800	+	0.614531i	−0.632284	+	0.774737i	$0.717882\pi$
$830$		0			0
$831$	5.45527	+	26.1737i	0.189241	+	0.907956i
$832$		0			0
$833$	7.98948	+	26.0233i	0.276819	+	0.901655i
$834$		0			0
$835$	−0.726448			−0.0251398
$836$		0			0
$837$	19.7360	+	27.8535i	0.682176	+	0.962758i
$838$		0			0
$839$	−7.18866	−	12.4511i	−0.248180	−	0.429861i	0.714841	−	0.699287i	$-0.246499\pi$
$839$	−7.18866	−	12.4511i	−0.248180	−	0.429861i	−0.963021	+	0.269427i	$0.913166\pi$
$840$		0			0
$841$	−3.58799	+	6.21459i	−0.123724	+	0.214296i
$842$		0			0
$843$	30.9159	+	10.1806i	1.06480	+	0.350638i
$844$		0			0
$845$	−2.53836	+	4.39657i	−0.0873222	+	0.151247i
$846$		0			0
$847$	−26.8412	−	61.6318i	−0.922274	−	2.11769i
$848$		0			0
$849$	42.0757	−	37.5848i	1.44403	−	1.28991i
$850$		0			0
$851$	14.1297			0.484361
$852$		0			0
$853$	−2.05636	−	3.56173i	−0.0704085	−	0.121951i	0.828672	−	0.559735i	$-0.189097\pi$
$853$	−2.05636	−	3.56173i	−0.0704085	−	0.121951i	−0.899080	+	0.437784i	$0.855764\pi$
$854$		0			0
$855$	−1.09975	+	9.72288i	−0.0376108	+	0.332516i
$856$		0			0
$857$	−25.5542	+	44.2612i	−0.872915	+	1.51193i	−0.0139471	+	0.999903i	$0.504440\pi$
$857$	−25.5542	+	44.2612i	−0.872915	+	1.51193i	−0.858968	+	0.512030i	$0.828894\pi$
$858$		0			0
$859$	−7.65825	−	13.2645i	−0.261296	−	0.452578i	0.705290	−	0.708918i	$-0.250817\pi$
$859$	−7.65825	−	13.2645i	−0.261296	−	0.452578i	−0.966587	+	0.256340i	$0.917483\pi$
$860$		0			0
$861$	−1.90599	−	20.5190i	−0.0649558	−	0.699285i
$862$		0			0
$863$	12.4865	−	21.6272i	0.425045	−	0.736199i	−0.571380	−	0.820686i	$-0.693592\pi$
$863$	12.4865	−	21.6272i	0.425045	−	0.736199i	0.996425	+	0.0844866i	$0.0269250\pi$
$864$		0			0
$865$	1.78397	+	3.08993i	0.0606568	+	0.105061i
$866$		0			0
$867$	0.663210	+	3.18200i	0.0225238	+	0.108066i
$868$		0			0
$869$	22.3479	−	38.7076i	0.758099	−	1.31307i
$870$		0			0
$871$	2.42481	−	4.19989i	0.0821615	−	0.142308i
$872$		0			0
$873$	12.8441	−	5.59725i	0.434708	−	0.189438i
$874$		0			0
$875$	18.9090	+	2.14319i	0.639242	+	0.0724532i
$876$		0			0
$877$	−18.1959	−	31.5162i	−0.614432	−	1.06423i	−0.990484	−	0.137628i	$-0.956052\pi$
$877$	−18.1959	−	31.5162i	−0.614432	−	1.06423i	0.376052	−	0.926598i	$-0.377281\pi$
$878$		0			0
$879$	−1.20032	−	5.75900i	−0.0404859	−	0.194246i
$880$		0			0
$881$	56.1807			1.89277			0.946387	−	0.323035i	$-0.104703\pi$
$881$	56.1807			1.89277			0.946387	+	0.323035i	$0.104703\pi$
$882$		0			0
$883$	−22.7585			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$883$	−22.7585			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$884$		0			0
$885$	−14.0723	−	4.63400i	−0.473037	−	0.155770i
$886$		0			0
$887$	5.01568	+	8.68742i	0.168410	+	0.291695i	0.937861	−	0.347011i	$-0.112803\pi$
$887$	5.01568	+	8.68742i	0.168410	+	0.291695i	−0.769451	+	0.638706i	$0.779470\pi$
$888$		0			0
$889$	3.36012	+	0.380844i	0.112695	+	0.0127731i
$890$		0			0
$891$	36.9712	−	39.7765i	1.23858	−	1.33256i
$892$		0			0
$893$	14.4723	−	25.0667i	0.484296	−	0.838825i
$894$		0			0
$895$	5.72485	−	9.91573i	0.191361	−	0.331446i
$896$		0			0
$897$	4.76762	−	4.25875i	0.159186	−	0.142196i
$898$		0			0
$899$	−19.7571	−	34.2202i	−0.658935	−	1.14131i
$900$		0			0
$901$	1.03281	−	1.78888i	0.0344080	−	0.0595964i
$902$		0			0
$903$	17.7786	+	8.17462i	0.591633	+	0.272034i
$904$		0			0
$905$	−5.21414	−	9.03115i	−0.173324	−	0.300206i
$906$		0			0
$907$	10.2856	−	17.8151i	0.341527	−	0.591542i	−0.643189	−	0.765707i	$-0.722389\pi$
$907$	10.2856	−	17.8151i	0.341527	−	0.591542i	0.984716	+	0.174165i	$0.0557226\pi$
$908$		0			0
$909$	−11.3886	−	8.41278i	−0.377737	−	0.279034i
$910$		0			0
$911$	−1.19047	−	2.06196i	−0.0394421	−	0.0683157i	0.845630	−	0.533769i	$-0.179225\pi$
$911$	−1.19047	−	2.06196i	−0.0394421	−	0.0683157i	−0.885073	+	0.465453i	$0.845891\pi$
$912$		0			0
$913$	97.1672			3.21577
$914$		0			0
$915$	−10.5341	−	3.46888i	−0.348248	−	0.114678i
$916$		0			0
$917$	−8.21323	−	18.8589i	−0.271225	−	0.622777i
$918$		0			0
$919$	−11.8130	+	20.4608i	−0.389676	+	0.674939i	−0.992406	−	0.123007i	$-0.960746\pi$
$919$	−11.8130	+	20.4608i	−0.389676	+	0.674939i	0.602730	+	0.797945i	$0.294080\pi$
$920$		0			0
$921$	−4.77380	+	4.26428i	−0.157302	+	0.140513i
$922$		0			0
$923$	−12.4816	+	21.6188i	−0.410838	+	0.711593i
$924$		0			0
$925$	−21.3095	−	36.9091i	−0.700652	−	1.21356i
$926$		0			0
$927$	−8.70526	+	3.79359i	−0.285918	+	0.124598i
$928$		0			0
$929$	−59.3769			−1.94809			−0.974046	−	0.226349i	$-0.927321\pi$
$929$	−59.3769			−1.94809			−0.974046	+	0.226349i	$0.927321\pi$
$930$		0			0
$931$	−20.3596	+	21.8843i	−0.667258	+	0.717230i
$932$		0			0
$933$	22.1693	−	19.8031i	0.725791	−	0.648325i
$934$		0			0
$935$	−8.96175	−	15.5222i	−0.293081	−	0.507630i
$936$		0			0
$937$	16.1455			0.527451			0.263725	−	0.964598i	$-0.415049\pi$
$937$	16.1455			0.527451			0.263725	+	0.964598i	$0.415049\pi$
$938$		0			0
$939$	−6.84166	+	6.11143i	−0.223269	+	0.199439i
$940$		0			0
$941$	19.7613			0.644198			0.322099	−	0.946706i	$-0.395612\pi$
$941$	19.7613			0.644198			0.322099	+	0.946706i	$0.395612\pi$
$942$		0			0
$943$	−6.58456			−0.214423
$944$		0			0
$945$	−5.43140	+	8.98728i	−0.176684	+	0.292356i
$946$		0			0
$947$	−48.9236			−1.58980			−0.794902	−	0.606738i	$-0.792478\pi$
$947$	−48.9236			−1.58980			−0.794902	+	0.606738i	$0.792478\pi$
$948$		0			0
$949$	10.7429			0.348731
$950$		0			0
$951$	−36.3985	+	32.5136i	−1.18030	+	1.05433i
$952$		0			0
$953$	−48.6464			−1.57581			−0.787905	−	0.615797i	$-0.788834\pi$
$953$	−48.6464			−1.57581			−0.787905	+	0.615797i	$0.788834\pi$
$954$		0			0
$955$	4.69399	+	8.13022i	0.151894	+	0.263088i
$956$		0			0
$957$	−46.8795	+	41.8759i	−1.51540	+	1.35365i
$958$		0			0
$959$	−4.43930	+	6.00672i	−0.143352	+	0.193967i
$960$		0			0
$961$	12.1603			0.392267
$962$		0			0
$963$	−36.9452	−	27.2914i	−1.19054	−	0.879454i
$964$		0			0
$965$	2.73895	+	4.74400i	0.0881699	+	0.152715i
$966$		0			0
$967$	22.1435	−	38.3537i	0.712087	−	1.23337i	−0.251986	−	0.967731i	$-0.581084\pi$
$967$	22.1435	−	38.3537i	0.712087	−	1.23337i	0.964072	−	0.265639i	$-0.0855831\pi$
$968$		0			0
$969$	21.4503	−	19.1608i	0.689083	−	0.615535i
$970$		0			0
$971$	−18.6355	+	32.2776i	−0.598040	+	1.03584i	0.395070	+	0.918651i	$0.370720\pi$
$971$	−18.6355	+	32.2776i	−0.598040	+	1.03584i	−0.993110	+	0.117185i	$0.962613\pi$
$972$		0			0
$973$	−35.2889	+	47.7487i	−1.13131	+	1.53075i
$974$		0			0
$975$	−18.3147	−	6.03102i	−0.586541	−	0.193147i
$976$		0			0
$977$	61.8624			1.97915			0.989577	−	0.144004i	$-0.0459977\pi$
$977$	61.8624			1.97915			0.989577	+	0.144004i	$0.0459977\pi$
$978$		0			0
$979$	10.6383	+	18.4261i	0.340003	+	0.588902i
$980$		0			0
$981$	42.0985	−	18.3458i	1.34410	−	0.585735i
$982$		0			0
$983$	5.48825	−	9.50593i	0.175048	−	0.303192i	−0.765130	−	0.643876i	$-0.777325\pi$
$983$	5.48825	−	9.50593i	0.175048	−	0.303192i	0.940178	+	0.340684i	$0.110659\pi$
$984$		0			0
$985$	−4.97585	−	8.61843i	−0.158544	−	0.274606i
$986$		0			0
$987$	25.3494	−	17.9530i	0.806882	−	0.571450i
$988$		0			0
$989$	3.12621	−	5.41476i	0.0994077	−	0.172179i
$990$		0			0
$991$	−5.43169	−	9.40796i	−0.172543	−	0.298854i	0.766765	−	0.641928i	$-0.221865\pi$
$991$	−5.43169	−	9.40796i	−0.172543	−	0.298854i	−0.939308	+	0.343074i	$0.888532\pi$
$992$		0			0
$993$	−37.6827	+	33.6607i	−1.19582	+	1.06819i
$994$		0			0
$995$	1.89498	−	3.28220i	0.0600749	−	0.104053i
$996$		0			0
$997$	20.4646	−	35.4457i	0.648119	−	1.12258i	−0.335452	−	0.942057i	$-0.608889\pi$
$997$	20.4646	−	35.4457i	0.648119	−	1.12258i	0.983572	−	0.180519i	$-0.0577776\pi$
$998$		0			0
$999$	49.9260	−	4.64912i	1.57959	−	0.147092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.i.b.121.1	yes	14
3.2	odd	2		756.2.i.b.37.4		14
4.3	odd	2		1008.2.q.j.625.7		14
7.2	even	3		1764.2.j.g.589.4		14
7.3	odd	6		1764.2.l.i.949.2		14
7.4	even	3		252.2.l.b.193.6	yes	14
7.5	odd	6		1764.2.j.h.589.4		14
7.6	odd	2		1764.2.i.i.373.7		14
9.2	odd	6		756.2.l.b.289.4		14
9.4	even	3		2268.2.k.e.1297.4		14
9.5	odd	6		2268.2.k.f.1297.4		14
9.7	even	3		252.2.l.b.205.6	yes	14
12.11	even	2		3024.2.q.j.2305.4		14
21.2	odd	6		5292.2.j.h.1765.4		14
21.5	even	6		5292.2.j.g.1765.4		14
21.11	odd	6		756.2.l.b.361.4		14
21.17	even	6		5292.2.l.i.361.4		14
21.20	even	2		5292.2.i.i.1549.4		14
28.11	odd	6		1008.2.t.j.193.2		14
36.7	odd	6		1008.2.t.j.961.2		14
36.11	even	6		3024.2.t.j.289.4		14
63.2	odd	6		5292.2.j.h.3529.4		14
63.4	even	3		2268.2.k.e.1621.4		14
63.11	odd	6		756.2.i.b.613.4		14
63.16	even	3		1764.2.j.g.1177.4		14
63.20	even	6		5292.2.l.i.3313.4		14
63.25	even	3	inner	252.2.i.b.25.1	✓	14
63.32	odd	6		2268.2.k.f.1621.4		14
63.34	odd	6		1764.2.l.i.961.2		14
63.38	even	6		5292.2.i.i.2125.4		14
63.47	even	6		5292.2.j.g.3529.4		14
63.52	odd	6		1764.2.i.i.1537.7		14
63.61	odd	6		1764.2.j.h.1177.4		14
84.11	even	6		3024.2.t.j.1873.4		14
252.11	even	6		3024.2.q.j.2881.4		14
252.151	odd	6		1008.2.q.j.529.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.1	✓	14	63.25	even	3	inner
252.2.i.b.121.1	yes	14	1.1	even	1	trivial
252.2.l.b.193.6	yes	14	7.4	even	3
252.2.l.b.205.6	yes	14	9.7	even	3
756.2.i.b.37.4		14	3.2	odd	2
756.2.i.b.613.4		14	63.11	odd	6
756.2.l.b.289.4		14	9.2	odd	6
756.2.l.b.361.4		14	21.11	odd	6
1008.2.q.j.529.7		14	252.151	odd	6
1008.2.q.j.625.7		14	4.3	odd	2
1008.2.t.j.193.2		14	28.11	odd	6
1008.2.t.j.961.2		14	36.7	odd	6
1764.2.i.i.373.7		14	7.6	odd	2
1764.2.i.i.1537.7		14	63.52	odd	6
1764.2.j.g.589.4		14	7.2	even	3
1764.2.j.g.1177.4		14	63.16	even	3
1764.2.j.h.589.4		14	7.5	odd	6
1764.2.j.h.1177.4		14	63.61	odd	6
1764.2.l.i.949.2		14	7.3	odd	6
1764.2.l.i.961.2		14	63.34	odd	6
2268.2.k.e.1297.4		14	9.4	even	3
2268.2.k.e.1621.4		14	63.4	even	3
2268.2.k.f.1297.4		14	9.5	odd	6
2268.2.k.f.1621.4		14	63.32	odd	6
3024.2.q.j.2305.4		14	12.11	even	2
3024.2.q.j.2881.4		14	252.11	even	6
3024.2.t.j.289.4		14	36.11	even	6
3024.2.t.j.1873.4		14	84.11	even	6
5292.2.i.i.1549.4		14	21.20	even	2
5292.2.i.i.2125.4		14	63.38	even	6
5292.2.j.g.1765.4		14	21.5	even	6
5292.2.j.g.3529.4		14	63.47	even	6
5292.2.j.h.1765.4		14	21.2	odd	6
5292.2.j.h.3529.4		14	63.2	odd	6
5292.2.l.i.361.4		14	21.17	even	6
5292.2.l.i.3313.4		14	63.20	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29174 + 1.15387i) q^{3} +(0.381918 + 0.661502i) q^{5} +(2.62892 + 0.297968i) q^{7} +(0.337180 - 2.98099i) q^{9} +O(q^{10})\)	\(q+(-1.29174 + 1.15387i) q^{3} +(0.381918 + 0.661502i) q^{5} +(2.62892 + 0.297968i) q^{7} +(0.337180 - 2.98099i) q^{9} +(-3.01695 + 5.22551i) q^{11} +(-1.26032 + 2.18294i) q^{13} +(-1.25662 - 0.413805i) q^{15} +(1.94444 + 3.36787i) q^{17} +(-2.13503 + 3.69798i) q^{19} +(-3.73969 + 2.64853i) q^{21} +(0.732124 + 1.26808i) q^{23} +(2.20828 - 3.82485i) q^{25} +(3.00412 + 4.23972i) q^{27} +(-3.00732 - 5.20884i) q^{29} +6.56965 q^{31} +(-2.13243 - 10.2311i) q^{33} +(0.806926 + 1.85283i) q^{35} +(4.82492 - 8.35700i) q^{37} +(-0.890819 - 4.27404i) q^{39} +(-2.24844 + 3.89442i) q^{41} +(-2.13503 - 3.69798i) q^{43} +(2.10071 - 0.915450i) q^{45} -6.77848 q^{47} +(6.82243 + 1.56667i) q^{49} +(-6.39778 - 2.10678i) q^{51} +(-0.265581 - 0.460000i) q^{53} -4.60891 q^{55} +(-1.50908 - 7.24036i) q^{57} +11.1985 q^{59} +8.38288 q^{61} +(1.77466 - 7.73632i) q^{63} -1.92536 q^{65} -1.92396 q^{67} +(-2.40890 - 0.793249i) q^{69} +9.90353 q^{71} +(-2.13099 - 3.69098i) q^{73} +(1.56085 + 7.48876i) q^{75} +(-9.48834 + 12.8385i) q^{77} -7.40744 q^{79} +(-8.77262 - 2.01026i) q^{81} +(-8.05178 - 13.9461i) q^{83} +(-1.48523 + 2.57250i) q^{85} +(9.89499 + 3.25841i) q^{87} +(1.76310 - 3.05377i) q^{89} +(-3.96373 + 5.36325i) q^{91} +(-8.48627 + 7.58050i) q^{93} -3.26163 q^{95} +(2.33513 + 4.04456i) q^{97} +(14.5599 + 10.7554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Introduction

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