LMFDB - Embedded newform 304.2.i.f.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("304.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.2
Root			$1.17146 + 2.02903i$ of defining polynomial
Character	$\chi$	$=$	304.49
Dual form			304.2.i.f.273.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0731827 + 0.126756i) q^{3} +(-1.17146 + 2.02903i) q^{5} -3.83221 q^{7} +(1.48929 + 2.57952i) q^{9} +O(q^{10})$	\(q+(-0.0731827 + 0.126756i) q^{3} +(-1.17146 + 2.02903i) q^{5} -3.83221 q^{7} +(1.48929 + 2.57952i) q^{9} -3.34292 q^{11} +(-3.08757 - 5.34782i) q^{13} +(-0.171462 - 0.296980i) q^{15} +(-2.59828 + 4.50035i) q^{17} +(3.01438 + 3.14857i) q^{19} +(0.280452 - 0.485757i) q^{21} +(1.17146 + 2.02903i) q^{23} +(-0.244644 - 0.423736i) q^{25} -0.875057 q^{27} +(-0.0250961 - 0.0434676i) q^{29} +3.43910 q^{31} +(0.244644 - 0.423736i) q^{33} +(4.48929 - 7.77568i) q^{35} -5.43910 q^{37} +0.903827 q^{39} +(3.64637 - 6.31569i) q^{41} +(-4.43049 + 7.67383i) q^{43} -6.97858 q^{45} +(5.36802 + 9.29768i) q^{47} +7.68585 q^{49} +(-0.380298 - 0.658696i) q^{51} +(1.59828 + 2.76830i) q^{53} +(3.91611 - 6.78289i) q^{55} +(-0.619702 + 0.151671i) q^{57} +(1.92682 - 3.33735i) q^{59} +(-1.46419 - 2.53606i) q^{61} +(-5.70727 - 9.88528i) q^{63} +14.4679 q^{65} +(-5.75903 - 9.97493i) q^{67} -0.342923 q^{69} +(0.744644 - 1.28976i) q^{71} +(3.84292 - 6.65614i) q^{73} +0.0716150 q^{75} +12.8108 q^{77} +(0.0875674 - 0.151671i) q^{79} +(-4.40383 + 7.62765i) q^{81} +7.00735 q^{83} +(-6.08757 - 10.5440i) q^{85} +0.00734639 q^{87} +(6.77341 + 11.7319i) q^{89} +(11.8322 + 20.4940i) q^{91} +(-0.251683 + 0.435927i) q^{93} +(-9.91978 + 2.42785i) q^{95} +(1.84292 - 3.19204i) q^{97} +(-4.97858 - 8.62315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} - q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 6 * q + q^3 - q^5 + 4 * q^7 - 6 * q^9	$ 6 q + q^{3} - q^{5} + 4 q^{7} - 6 q^{9} - 8 q^{11} + q^{13} + 5 q^{15} - 11 q^{17} + 6 q^{21} + q^{23} + 6 q^{25} - 38 q^{27} + 3 q^{29} + 12 q^{31} - 6 q^{33} + 12 q^{35} - 24 q^{37} + 2 q^{39} + 19 q^{41} + 5 q^{43} - 12 q^{45} + 17 q^{47} + 22 q^{49} + 23 q^{51} + 5 q^{53} + 10 q^{55} - 29 q^{57} + 13 q^{59} + 3 q^{61} - 40 q^{63} + 42 q^{65} - 9 q^{67} + 10 q^{69} - 3 q^{71} + 11 q^{73} + 24 q^{75} + 20 q^{77} - 19 q^{79} - 23 q^{81} - 24 q^{83} - 17 q^{85} - 66 q^{87} - 3 q^{89} + 44 q^{91} - 42 q^{93} - 13 q^{95} - q^{97}+O(q^{100}) $ 6 * q + q^3 - q^5 + 4 * q^7 - 6 * q^9 - 8 * q^11 + q^13 + 5 * q^15 - 11 * q^17 + 6 * q^21 + q^23 + 6 * q^25 - 38 * q^27 + 3 * q^29 + 12 * q^31 - 6 * q^33 + 12 * q^35 - 24 * q^37 + 2 * q^39 + 19 * q^41 + 5 * q^43 - 12 * q^45 + 17 * q^47 + 22 * q^49 + 23 * q^51 + 5 * q^53 + 10 * q^55 - 29 * q^57 + 13 * q^59 + 3 * q^61 - 40 * q^63 + 42 * q^65 - 9 * q^67 + 10 * q^69 - 3 * q^71 + 11 * q^73 + 24 * q^75 + 20 * q^77 - 19 * q^79 - 23 * q^81 - 24 * q^83 - 17 * q^85 - 66 * q^87 - 3 * q^89 + 44 * q^91 - 42 * q^93 - 13 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.0731827	+	0.126756i	−0.0422521	+	0.0731827i	−0.886378	−	0.462962i	$-0.846787\pi$
$3$	−0.0731827	+	0.126756i	−0.0422521	+	0.0731827i	0.844126	+	0.536145i	$0.180120\pi$
$4$		0			0
$5$	−1.17146	+	2.02903i	−0.523894	+	0.907410i	0.475720	+	0.879597i	$0.342188\pi$
$5$	−1.17146	+	2.02903i	−0.523894	+	0.907410i	−0.999613	+	0.0278132i	$0.991146\pi$
$6$		0			0
$7$	−3.83221			−1.44844			−0.724220	−	0.689569i	$-0.757800\pi$
$7$	−3.83221			−1.44844			−0.724220	+	0.689569i	$0.757800\pi$
$8$		0			0
$9$	1.48929	+	2.57952i	0.496430	+	0.859841i
$10$		0			0
$11$	−3.34292			−1.00793			−0.503965	−	0.863724i	$-0.668126\pi$
$11$	−3.34292			−1.00793			−0.503965	+	0.863724i	$0.668126\pi$
$12$		0			0
$13$	−3.08757	−	5.34782i	−0.856337	−	1.48322i	−0.875399	−	0.483401i	$-0.839401\pi$
$13$	−3.08757	−	5.34782i	−0.856337	−	1.48322i	0.0190619	−	0.999818i	$-0.493932\pi$
$14$		0			0
$15$	−0.171462	−	0.296980i	−0.0442712	−	0.0766799i
$16$		0			0
$17$	−2.59828	+	4.50035i	−0.630175	+	1.09150i	0.357340	+	0.933974i	$0.383684\pi$
$17$	−2.59828	+	4.50035i	−0.630175	+	1.09150i	−0.987516	+	0.157521i	$0.949650\pi$
$18$		0			0
$19$	3.01438	+	3.14857i	0.691547	+	0.722331i
$19$	3.01438	+	3.14857i	0.691547	+	0.722331i
$20$		0			0
$21$	0.280452	−	0.485757i	0.0611996	−	0.106001i
$22$		0			0
$23$	1.17146	+	2.02903i	0.244267	+	0.423082i	0.961925	−	0.273313i	$-0.0881195\pi$
$23$	1.17146	+	2.02903i	0.244267	+	0.423082i	−0.717659	+	0.696395i	$0.754786\pi$
$24$		0			0
$25$	−0.244644	−	0.423736i	−0.0489289	−	0.0847473i
$26$		0			0
$27$	−0.875057			−0.168405
$28$		0			0
$29$	−0.0250961	−	0.0434676i	−0.00466022	−	0.00807174i	0.863686	−	0.504030i	$-0.168150\pi$
$29$	−0.0250961	−	0.0434676i	−0.00466022	−	0.00807174i	−0.868346	+	0.495959i	$0.834817\pi$
$30$		0			0
$31$	3.43910			0.617680			0.308840	−	0.951114i	$-0.400059\pi$
$31$	3.43910			0.617680			0.308840	+	0.951114i	$0.400059\pi$
$32$		0			0
$33$	0.244644	−	0.423736i	0.0425871	−	0.0737630i
$34$		0			0
$35$	4.48929	−	7.77568i	0.758828	−	1.31433i
$36$		0			0
$37$	−5.43910			−0.894182			−0.447091	−	0.894488i	$-0.647540\pi$
$37$	−5.43910			−0.894182			−0.447091	+	0.894488i	$0.647540\pi$
$38$		0			0
$39$	0.903827			0.144728
$40$		0			0
$41$	3.64637	−	6.31569i	0.569467	−	0.986345i	−0.427152	−	0.904180i	$-0.640483\pi$
$41$	3.64637	−	6.31569i	0.569467	−	0.986345i	0.996619	−	0.0821653i	$-0.0261836\pi$
$42$		0			0
$43$	−4.43049	+	7.67383i	−0.675643	+	1.17025i	0.300637	+	0.953739i	$0.402801\pi$
$43$	−4.43049	+	7.67383i	−0.675643	+	1.17025i	−0.976280	+	0.216510i	$0.930533\pi$
$44$		0			0
$45$	−6.97858			−1.04030
$46$		0			0
$47$	5.36802	+	9.29768i	0.783006	+	1.35621i	0.930183	+	0.367096i	$0.119648\pi$
$47$	5.36802	+	9.29768i	0.783006	+	1.35621i	−0.147177	+	0.989110i	$0.547019\pi$
$48$		0			0
$49$	7.68585			1.09798
$50$		0			0
$51$	−0.380298	−	0.658696i	−0.0532524	−	0.0922359i
$52$		0			0
$53$	1.59828	+	2.76830i	0.219540	+	0.380255i	0.954668	−	0.297674i	$-0.0962109\pi$
$53$	1.59828	+	2.76830i	0.219540	+	0.380255i	−0.735127	+	0.677929i	$0.762878\pi$
$54$		0			0
$55$	3.91611	−	6.78289i	0.528048	−	0.914605i
$56$		0			0
$57$	−0.619702	+	0.151671i	−0.0820815	+	0.0200893i
$58$		0			0
$59$	1.92682	−	3.33735i	0.250850	−	0.434485i	−0.712910	−	0.701256i	$-0.752623\pi$
$59$	1.92682	−	3.33735i	0.250850	−	0.434485i	0.963760	+	0.266770i	$0.0859565\pi$
$60$		0			0
$61$	−1.46419	−	2.53606i	−0.187471	−	0.324709i	0.756936	−	0.653489i	$-0.226696\pi$
$61$	−1.46419	−	2.53606i	−0.187471	−	0.324709i	−0.944406	+	0.328781i	$0.893362\pi$
$62$		0			0
$63$	−5.70727	−	9.88528i	−0.719048	−	1.24543i
$64$		0			0
$65$	14.4679			1.79452
$66$		0			0
$67$	−5.75903	−	9.97493i	−0.703577	−	1.21863i	−0.967203	−	0.254007i	$-0.918252\pi$
$67$	−5.75903	−	9.97493i	−0.703577	−	1.21863i	0.263625	−	0.964625i	$-0.415082\pi$
$68$		0			0
$69$	−0.342923			−0.0412831
$70$		0			0
$71$	0.744644	−	1.28976i	0.0883730	−	0.153067i	−0.818451	−	0.574577i	$-0.805167\pi$
$71$	0.744644	−	1.28976i	0.0883730	−	0.153067i	0.906824	+	0.421510i	$0.138500\pi$
$72$		0			0
$73$	3.84292	−	6.65614i	0.449780	−	0.779042i	−0.548591	−	0.836091i	$-0.684836\pi$
$73$	3.84292	−	6.65614i	0.449780	−	0.779042i	0.998371	+	0.0570486i	$0.0181690\pi$
$74$		0			0
$75$	0.0716150			0.00826938
$76$		0			0
$77$	12.8108			1.45992
$78$		0			0
$79$	0.0875674	−	0.151671i	0.00985210	−	0.0170643i	−0.861057	−	0.508508i	$-0.830197\pi$
$79$	0.0875674	−	0.151671i	0.00985210	−	0.0170643i	0.870909	+	0.491444i	$0.163531\pi$
$80$		0			0
$81$	−4.40383	+	7.62765i	−0.489314	+	0.847517i
$82$		0			0
$83$	7.00735			0.769156			0.384578	−	0.923092i	$-0.374347\pi$
$83$	7.00735			0.769156			0.384578	+	0.923092i	$0.374347\pi$
$84$		0			0
$85$	−6.08757	−	10.5440i	−0.660289	−	1.14365i
$86$		0			0
$87$	0.00734639			0.000787616
$88$		0			0
$89$	6.77341	+	11.7319i	0.717980	+	1.24358i	0.961799	+	0.273758i	$0.0882666\pi$
$89$	6.77341	+	11.7319i	0.717980	+	1.24358i	−0.243818	+	0.969821i	$0.578400\pi$
$90$		0			0
$91$	11.8322	+	20.4940i	1.24035	+	2.14835i
$92$		0			0
$93$	−0.251683	+	0.435927i	−0.0260983	+	0.0452035i
$94$		0			0
$95$	−9.91978	+	2.42785i	−1.01775	+	0.249092i
$96$		0			0
$97$	1.84292	−	3.19204i	0.187120	−	0.324102i	−0.757169	−	0.653220i	$-0.773418\pi$
$97$	1.84292	−	3.19204i	0.187120	−	0.324102i	0.944289	+	0.329117i	$0.106751\pi$
$98$		0			0
$99$	−4.97858	−	8.62315i	−0.500366	−	0.866659i
$100$		0			0
$101$	3.80712	+	6.59412i	0.378822	+	0.656139i	0.990891	−	0.134665i	$-0.0429959\pi$
$101$	3.80712	+	6.59412i	0.378822	+	0.656139i	−0.612069	+	0.790804i	$0.709663\pi$
$102$		0			0
$103$	−16.6430			−1.63988			−0.819942	−	0.572447i	$-0.805994\pi$
$103$	−16.6430			−1.63988			−0.819942	+	0.572447i	$0.805994\pi$
$104$		0			0
$105$	0.657077	+	1.13809i	0.0641241	+	0.111066i
$106$		0			0
$107$	6.29273			0.608341			0.304171	−	0.952618i	$-0.401621\pi$
$107$	6.29273			0.608341			0.304171	+	0.952618i	$0.401621\pi$
$108$		0			0
$109$	−5.57686	+	9.65940i	−0.534166	+	0.925203i	0.465037	+	0.885291i	$0.346041\pi$
$109$	−5.57686	+	9.65940i	−0.534166	+	0.925203i	−0.999203	+	0.0399114i	$0.987292\pi$
$110$		0			0
$111$	0.398048	−	0.689439i	0.0377810	−	0.0654387i
$112$		0			0
$113$	−17.7606			−1.67078			−0.835388	−	0.549660i	$-0.814757\pi$
$113$	−17.7606			−1.67078			−0.835388	+	0.549660i	$0.814757\pi$
$114$		0			0
$115$	−5.48929			−0.511879
$116$		0			0
$117$	9.19656	−	15.9289i	0.850222	−	1.47263i
$118$		0			0
$119$	9.95715	−	17.2463i	0.912771	−	1.58097i
$120$		0			0
$121$	0.175135			0.0159213
$122$		0			0
$123$	0.533702	+	0.924399i	0.0481223	+	0.0833503i
$124$		0			0
$125$	−10.5682			−0.945253
$126$		0			0
$127$	9.21251	+	15.9565i	0.817478	+	1.41591i	0.907535	+	0.419977i	$0.137962\pi$
$127$	9.21251	+	15.9565i	0.817478	+	1.41591i	−0.0900567	+	0.995937i	$0.528705\pi$
$128$		0			0
$129$	−0.648471	−	1.12318i	−0.0570947	−	0.0988909i
$130$		0			0
$131$	−1.61266	+	2.79321i	−0.140899	+	0.244044i	−0.927835	−	0.372990i	$-0.878333\pi$
$131$	−1.61266	+	2.79321i	−0.140899	+	0.244044i	0.786936	+	0.617034i	$0.211666\pi$
$132$		0			0
$133$	−11.5518	−	12.0660i	−1.00166	−	1.04625i
$134$		0			0
$135$	1.02510	−	1.77552i	0.0882262	−	0.152812i
$136$		0			0
$137$	2.98929	+	5.17760i	0.255392	+	0.442352i	0.965002	−	0.262243i	$-0.0844621\pi$
$137$	2.98929	+	5.17760i	0.255392	+	0.442352i	−0.709610	+	0.704595i	$0.751129\pi$
$138$		0			0
$139$	−4.58389	−	7.93954i	−0.388801	−	0.673423i	0.603488	−	0.797372i	$-0.293777\pi$
$139$	−4.58389	−	7.93954i	−0.388801	−	0.673423i	−0.992289	+	0.123950i	$0.960444\pi$
$140$		0			0
$141$	−1.57139			−0.132335
$142$		0			0
$143$	10.3215	+	17.8774i	0.863127	+	1.49498i
$144$		0			0
$145$	0.117596			0.00976584
$146$		0			0
$147$	−0.562471	+	0.974229i	−0.0463919	+	0.0803530i
$148$		0			0
$149$	−3.07529	+	5.32656i	−0.251937	+	0.436368i	−0.964059	−	0.265688i	$-0.914401\pi$
$149$	−3.07529	+	5.32656i	−0.251937	+	0.436368i	0.712122	+	0.702056i	$0.247734\pi$
$150$		0			0
$151$	−5.14637			−0.418805			−0.209403	−	0.977830i	$-0.567152\pi$
$151$	−5.14637			−0.418805			−0.209403	+	0.977830i	$0.567152\pi$
$152$		0			0
$153$	−15.4783			−1.25135
$154$		0			0
$155$	−4.02877	+	6.97803i	−0.323599	+	0.560489i
$156$		0			0
$157$	−2.20516	+	3.81946i	−0.175991	+	0.304826i	−0.940504	−	0.339783i	$-0.889646\pi$
$157$	−2.20516	+	3.81946i	−0.175991	+	0.304826i	0.764513	+	0.644609i	$0.222980\pi$
$158$		0			0
$159$	−0.467866			−0.0371042
$160$		0			0
$161$	−4.48929	−	7.77568i	−0.353806	−	0.612809i
$162$		0			0
$163$	−12.3215			−0.965094			−0.482547	−	0.875870i	$-0.660288\pi$
$163$	−12.3215			−0.965094			−0.482547	+	0.875870i	$0.660288\pi$
$164$		0			0
$165$	0.573183	+	0.992782i	0.0446222	+	0.0772879i
$166$		0			0
$167$	2.89101	+	5.00738i	0.223713	+	0.387482i	0.955933	−	0.293586i	$-0.0948488\pi$
$167$	2.89101	+	5.00738i	0.223713	+	0.387482i	−0.732220	+	0.681069i	$0.761515\pi$
$168$		0			0
$169$	−12.5661	+	21.7652i	−0.966627	+	1.67425i
$170$		0			0
$171$	−3.63252	+	12.4648i	−0.277786	+	0.953207i
$172$		0			0
$173$	0.912433	−	1.58038i	0.0693710	−	0.120154i	−0.829254	−	0.558872i	$-0.811234\pi$
$173$	0.912433	−	1.58038i	0.0693710	−	0.120154i	0.898625	+	0.438718i	$0.144567\pi$
$174$		0			0
$175$	0.937529	+	1.62385i	0.0708705	+	0.122751i
$176$		0			0
$177$	0.282020	+	0.488472i	0.0211979	+	0.0367158i
$178$		0			0
$179$	−8.26396			−0.617678			−0.308839	−	0.951114i	$-0.599940\pi$
$179$	−8.26396			−0.617678			−0.308839	+	0.951114i	$0.599940\pi$
$180$		0			0
$181$	10.8573	+	18.8054i	0.807017	+	1.39780i	0.914921	+	0.403634i	$0.132253\pi$
$181$	10.8573	+	18.8054i	0.807017	+	1.39780i	−0.107903	+	0.994161i	$0.534414\pi$
$182$		0			0
$183$	0.428615			0.0316841
$184$		0			0
$185$	6.37169	−	11.0361i	0.468456	−	0.811390i
$186$		0			0
$187$	8.68585	−	15.0443i	0.635172	−	1.10015i
$188$		0			0
$189$	3.35341			0.243924
$190$		0			0
$191$	4.58546			0.331792			0.165896	−	0.986143i	$-0.446948\pi$
$191$	4.58546			0.331792			0.165896	+	0.986143i	$0.446948\pi$
$192$		0			0
$193$	6.08757	−	10.5440i	0.438193	−	0.758972i	−0.559357	−	0.828927i	$-0.688952\pi$
$193$	6.08757	−	10.5440i	0.438193	−	0.758972i	0.997550	+	0.0699545i	$0.0222854\pi$
$194$		0			0
$195$	−1.05880	+	1.83389i	−0.0758221	+	0.131328i
$196$		0			0
$197$	−4.26817			−0.304095			−0.152047	−	0.988373i	$-0.548587\pi$
$197$	−4.26817			−0.304095			−0.152047	+	0.988373i	$0.548587\pi$
$198$		0			0
$199$	−1.43049	−	2.47768i	−0.101405	−	0.175638i	0.810859	−	0.585242i	$-0.199000\pi$
$199$	−1.43049	−	2.47768i	−0.101405	−	0.175638i	−0.912264	+	0.409604i	$0.865667\pi$
$200$		0			0
$201$	1.68585			0.118910
$202$		0			0
$203$	0.0961734	+	0.166577i	0.00675005	+	0.0116914i
$204$		0			0
$205$	8.54315	+	14.7972i	0.596680	+	1.03348i
$206$		0			0
$207$	−3.48929	+	6.04363i	−0.242522	+	0.420061i
$208$		0			0
$209$	−10.0769	−	10.5254i	−0.697031	−	0.728059i
$210$		0			0
$211$	9.13776	−	15.8271i	0.629069	−	1.08958i	−0.358670	−	0.933465i	$-0.616769\pi$
$211$	9.13776	−	15.8271i	0.629069	−	1.08958i	0.987739	−	0.156115i	$-0.0498972\pi$
$212$		0			0
$213$	0.108990	+	0.188777i	0.00746789	+	0.0129348i
$214$		0			0
$215$	−10.3803	−	17.9792i	−0.707930	−	1.22617i
$216$		0			0
$217$	−13.1793			−0.894672
$218$		0			0
$219$	0.562471	+	0.974229i	0.0380083	+	0.0658323i
$220$		0			0
$221$	32.0894			2.15857
$222$		0			0
$223$	−6.02510	+	10.4358i	−0.403470	+	0.698831i	−0.994142	−	0.108081i	$-0.965529\pi$
$223$	−6.02510	+	10.4358i	−0.403470	+	0.698831i	0.590672	+	0.806912i	$0.298863\pi$
$224$		0			0
$225$	0.728692	−	1.26213i	0.0485795	−	0.0841421i
$226$		0			0
$227$	8.71462			0.578409			0.289205	−	0.957267i	$-0.406609\pi$
$227$	8.71462			0.578409			0.289205	+	0.957267i	$0.406609\pi$
$228$		0			0
$229$	15.5640			1.02850			0.514250	−	0.857640i	$-0.328070\pi$
$229$	15.5640			1.02850			0.514250	+	0.857640i	$0.328070\pi$
$230$		0			0
$231$	−0.937529	+	1.62385i	−0.0616849	+	0.106841i
$232$		0			0
$233$	11.2146	−	19.4243i	0.734694	−	1.27253i	−0.220164	−	0.975463i	$-0.570659\pi$
$233$	11.2146	−	19.4243i	0.734694	−	1.27253i	0.954858	−	0.297064i	$-0.0960075\pi$
$234$		0			0
$235$	−25.1537			−1.64085
$236$		0			0
$237$	0.0128168	+	0.0221994i	0.000832543	+	0.00144201i
$238$		0			0
$239$	−30.7434			−1.98862			−0.994312	−	0.106505i	$-0.966034\pi$
$239$	−30.7434			−1.98862			−0.994312	+	0.106505i	$0.966034\pi$
$240$		0			0
$241$	−2.47858	−	4.29302i	−0.159659	−	0.276538i	0.775087	−	0.631855i	$-0.217706\pi$
$241$	−2.47858	−	4.29302i	−0.159659	−	0.276538i	−0.934746	+	0.355317i	$0.884373\pi$
$242$		0			0
$243$	−1.95715	−	3.38989i	−0.125552	−	0.217462i
$244$		0			0
$245$	−9.00367	+	15.5948i	−0.575224	+	0.996316i
$246$		0			0
$247$	7.53087	−	25.8418i	0.479178	−	1.64428i
$248$		0			0
$249$	−0.512817	+	0.888225i	−0.0324984	+	0.0562890i
$250$		0			0
$251$	13.7664	+	23.8441i	0.868926	+	1.50502i	0.863095	+	0.505041i	$0.168523\pi$
$251$	13.7664	+	23.8441i	0.868926	+	1.50502i	0.00583044	+	0.999983i	$0.498144\pi$
$252$		0			0
$253$	−3.91611	−	6.78289i	−0.246203	−	0.426437i
$254$		0			0
$255$	1.78202			0.111594
$256$		0			0
$257$	5.94331	+	10.2941i	0.370733	+	0.642129i	0.989679	−	0.143305i	$-0.0457731\pi$
$257$	5.94331	+	10.2941i	0.370733	+	0.642129i	−0.618945	+	0.785434i	$0.712440\pi$
$258$		0			0
$259$	20.8438			1.29517
$260$		0			0
$261$	0.0747505	−	0.129472i	0.00462694	−	0.00801410i
$262$		0			0
$263$	9.71094	−	16.8198i	0.598802	−	1.03716i	−0.394196	−	0.919026i	$-0.628977\pi$
$263$	9.71094	−	16.8198i	0.598802	−	1.03716i	0.992998	−	0.118130i	$-0.0376898\pi$
$264$		0			0
$265$	−7.48929			−0.460063
$266$		0			0
$267$	−1.98279			−0.121345
$268$		0			0
$269$	−9.24128	+	16.0064i	−0.563451	+	0.975925i	0.433741	+	0.901037i	$0.357193\pi$
$269$	−9.24128	+	16.0064i	−0.563451	+	0.975925i	−0.997192	+	0.0748878i	$0.976140\pi$
$270$		0			0
$271$	8.17146	−	14.1534i	0.496381	−	0.859757i	−0.503610	−	0.863931i	$-0.667995\pi$
$271$	8.17146	−	14.1534i	0.496381	−	0.859757i	0.999991	+	0.00417390i	$0.00132860\pi$
$272$		0			0
$273$	−3.46365			−0.209630
$274$		0			0
$275$	0.817827	+	1.41652i	0.0493168	+	0.0854192i
$276$		0			0
$277$	15.7894			0.948691			0.474346	−	0.880339i	$-0.342685\pi$
$277$	15.7894			0.948691			0.474346	+	0.880339i	$0.342685\pi$
$278$		0			0
$279$	5.12181	+	8.87123i	0.306635	+	0.531107i
$280$		0			0
$281$	−4.21462	−	7.29993i	−0.251423	−	0.435477i	0.712495	−	0.701677i	$-0.247565\pi$
$281$	−4.21462	−	7.29993i	−0.251423	−	0.435477i	−0.963918	+	0.266200i	$0.914232\pi$
$282$		0			0
$283$	0.905394	−	1.56819i	0.0538201	−	0.0932192i	−0.837860	−	0.545885i	$-0.816194\pi$
$283$	0.905394	−	1.56819i	0.0538201	−	0.0932192i	0.891680	+	0.452666i	$0.149527\pi$
$284$		0			0
$285$	0.418211	−	1.43507i	0.0247727	−	0.0850063i
$286$		0			0
$287$	−13.9736	+	24.2031i	−0.824838	+	1.42866i
$288$		0			0
$289$	−5.00211	−	8.66390i	−0.294241	−	0.509641i
$290$		0			0
$291$	0.269740	+	0.467204i	0.0158125	+	0.0273880i
$292$		0			0
$293$	24.2400			1.41612			0.708059	−	0.706154i	$-0.249571\pi$
$293$	24.2400			1.41612			0.708059	+	0.706154i	$0.249571\pi$
$294$		0			0
$295$	4.51438	+	7.81914i	0.262838	+	0.455248i
$296$		0			0
$297$	2.92525			0.169740
$298$		0			0
$299$	7.23393	−	12.5295i	0.418349	−	0.724602i
$300$		0			0
$301$	16.9786	−	29.4078i	0.978629	−	1.69504i
$302$		0			0
$303$	−1.11446			−0.0640241
$304$		0			0
$305$	6.86098			0.392859
$306$		0			0
$307$	11.0016	−	19.0553i	0.627893	−	1.08754i	−0.360081	−	0.932921i	$-0.617251\pi$
$307$	11.0016	−	19.0553i	0.627893	−	1.08754i	0.987974	−	0.154621i	$-0.0494156\pi$
$308$		0			0
$309$	1.21798	−	2.10960i	0.0692885	−	0.120011i
$310$		0			0
$311$	32.4752			1.84150			0.920750	−	0.390153i	$-0.127578\pi$
$311$	32.4752			1.84150			0.920750	+	0.390153i	$0.127578\pi$
$312$		0			0
$313$	4.62494	+	8.01064i	0.261417	+	0.452788i	0.966619	−	0.256219i	$-0.0824768\pi$
$313$	4.62494	+	8.01064i	0.261417	+	0.452788i	−0.705202	+	0.709007i	$0.749143\pi$
$314$		0			0
$315$	26.7434			1.50682
$316$		0			0
$317$	−3.08757	−	5.34782i	−0.173415	−	0.300364i	0.766197	−	0.642606i	$-0.222147\pi$
$317$	−3.08757	−	5.34782i	−0.173415	−	0.300364i	−0.939612	+	0.342243i	$0.888814\pi$
$318$		0			0
$319$	0.0838942	+	0.145309i	0.00469717	+	0.00813574i
$320$		0			0
$321$	−0.460519	+	0.797643i	−0.0257037	+	0.0445201i
$322$		0			0
$323$	−22.0019	+	5.38493i	−1.22422	+	0.299625i
$324$		0			0
$325$	−1.51071	+	2.61663i	−0.0837992	+	0.145144i
$326$		0			0
$327$	−0.816259	−	1.41380i	−0.0451392	−	0.0781835i
$328$		0			0
$329$	−20.5714	−	35.6307i	−1.13414	−	1.96438i
$330$		0			0
$331$	10.3643			0.569676			0.284838	−	0.958576i	$-0.408060\pi$
$331$	10.3643			0.569676			0.284838	+	0.958576i	$0.408060\pi$
$332$		0			0
$333$	−8.10038	−	14.0303i	−0.443898	−	0.768854i
$334$		0			0
$335$	26.9859			1.47440
$336$		0			0
$337$	−10.3108	+	17.8588i	−0.561664	+	0.972831i	0.435687	+	0.900098i	$0.356505\pi$
$337$	−10.3108	+	17.8588i	−0.561664	+	0.972831i	−0.997351	+	0.0727331i	$0.976828\pi$
$338$		0			0
$339$	1.29977	−	2.25127i	0.0705938	−	0.122272i
$340$		0			0
$341$	−11.4966			−0.622578
$342$		0			0
$343$	−2.62831			−0.141915
$344$		0			0
$345$	0.401721	−	0.695802i	0.0216279	−	0.0374607i
$346$		0			0
$347$	−13.9054	+	24.0848i	−0.746481	+	1.29294i	0.203019	+	0.979175i	$0.434925\pi$
$347$	−13.9054	+	24.0848i	−0.746481	+	1.29294i	−0.949500	+	0.313768i	$0.898409\pi$
$348$		0			0
$349$	5.60688			0.300130			0.150065	−	0.988676i	$-0.452052\pi$
$349$	5.60688			0.300130			0.150065	+	0.988676i	$0.452052\pi$
$350$		0			0
$351$	2.70180	+	4.67965i	0.144211	+	0.249781i
$352$		0			0
$353$	−30.0105			−1.59730			−0.798648	−	0.601798i	$-0.794451\pi$
$353$	−30.0105			−1.59730			−0.798648	+	0.601798i	$0.794451\pi$
$354$		0			0
$355$	1.74464	+	3.02181i	0.0925961	+	0.160381i
$356$		0			0
$357$	1.45738	+	2.52426i	0.0771329	+	0.133598i
$358$		0			0
$359$	−4.48562	+	7.76931i	−0.236742	+	0.410049i	−0.959777	−	0.280762i	$-0.909413\pi$
$359$	−4.48562	+	7.76931i	−0.236742	+	0.410049i	0.723036	+	0.690811i	$0.242746\pi$
$360$		0			0
$361$	−0.826971	+	18.9820i	−0.0435248	+	0.999052i
$362$		0			0
$363$	−0.0128168	+	0.0221994i	−0.000672710	+	0.00116517i
$364$		0			0
$365$	9.00367	+	15.5948i	0.471274	+	0.816270i
$366$		0			0
$367$	−5.24621	−	9.08671i	−0.273850	−	0.474322i	0.695994	−	0.718047i	$-0.254964\pi$
$367$	−5.24621	−	9.08671i	−0.273850	−	0.474322i	−0.969844	+	0.243725i	$0.921631\pi$
$368$		0			0
$369$	21.7220			1.13080
$370$		0			0
$371$	−6.12494	−	10.6087i	−0.317991	−	0.550777i
$372$		0			0
$373$	−18.3074			−0.947922			−0.473961	−	0.880546i	$-0.657176\pi$
$373$	−18.3074			−0.947922			−0.473961	+	0.880546i	$0.657176\pi$
$374$		0			0
$375$	0.773414	−	1.33959i	0.0399389	−	0.0691762i
$376$		0			0
$377$	−0.154972	+	0.268419i	−0.00798144	+	0.0138243i
$378$		0			0
$379$	−24.8438			−1.27614			−0.638069	−	0.769979i	$-0.720267\pi$
$379$	−24.8438			−1.27614			−0.638069	+	0.769979i	$0.720267\pi$
$380$		0			0
$381$	−2.69679			−0.138161
$382$		0			0
$383$	1.58600	−	2.74703i	0.0810408	−	0.140367i	−0.822656	−	0.568539i	$-0.807509\pi$
$383$	1.58600	−	2.74703i	0.0810408	−	0.140367i	0.903697	+	0.428172i	$0.140842\pi$
$384$		0			0
$385$	−15.0073	+	25.9935i	−0.764845	+	1.32475i
$386$		0			0
$387$	−26.3931			−1.34164
$388$		0			0
$389$	5.69445	+	9.86308i	0.288720	+	0.500078i	0.973505	−	0.228668i	$-0.0734369\pi$
$389$	5.69445	+	9.86308i	0.288720	+	0.500078i	−0.684784	+	0.728746i	$0.740104\pi$
$390$		0			0
$391$	−12.1751			−0.615723
$392$		0			0
$393$	−0.236038	−	0.408830i	−0.0119066	−	0.0206228i
$394$		0			0
$395$	0.205164	+	0.355354i	0.0103229	+	0.0178798i
$396$		0			0
$397$	9.44277	−	16.3554i	0.473919	−	0.820852i	−0.525635	−	0.850710i	$-0.676172\pi$
$397$	9.44277	−	16.3554i	0.473919	−	0.820852i	0.999554	+	0.0298583i	$0.00950560\pi$
$398$		0			0
$399$	2.37483	−	0.581236i	0.118890	−	0.0290982i
$400$		0			0
$401$	10.0107	−	17.3391i	0.499911	−	0.865871i	−0.500089	−	0.865974i	$-0.666699\pi$
$401$	10.0107	−	17.3391i	0.499911	−	0.865871i	1.00000		0.000102681i	$3.26845e-5\pi$
$402$		0			0
$403$	−10.6184	−	18.3917i	−0.528942	−	0.916155i
$404$		0			0
$405$	−10.3178	−	17.8710i	−0.512697	−	0.888017i
$406$		0			0
$407$	18.1825			0.901272
$408$		0			0
$409$	−5.45715	−	9.45207i	−0.269839	−	0.467375i	0.698981	−	0.715140i	$-0.253637\pi$
$409$	−5.45715	−	9.45207i	−0.269839	−	0.467375i	−0.968820	+	0.247765i	$0.920304\pi$
$410$		0			0
$411$	−0.875057			−0.0431634
$412$		0			0
$413$	−7.38397	+	12.7894i	−0.363341	+	0.629326i
$414$		0			0
$415$	−8.20884	+	14.2181i	−0.402956	+	0.697940i
$416$		0			0
$417$	1.34185			0.0657106
$418$		0			0
$419$	15.4145			0.753049			0.376525	−	0.926407i	$-0.377119\pi$
$419$	15.4145			0.753049			0.376525	+	0.926407i	$0.377119\pi$
$420$		0			0
$421$	2.98225	−	5.16541i	0.145346	−	0.251747i	−0.784156	−	0.620564i	$-0.786904\pi$
$421$	2.98225	−	5.16541i	0.145346	−	0.251747i	0.929502	+	0.368817i	$0.120237\pi$
$422$		0			0
$423$	−15.9891	+	27.6939i	−0.777415	+	1.34652i
$424$		0			0
$425$	2.54262			0.123335
$426$		0			0
$427$	5.61110	+	9.71870i	0.271540	+	0.470321i
$428$		0			0
$429$	−3.02142			−0.145876
$430$		0			0
$431$	−14.5095	−	25.1311i	−0.698896	−	1.21052i	−0.968850	−	0.247650i	$-0.920342\pi$
$431$	−14.5095	−	25.1311i	−0.698896	−	1.21052i	0.269954	−	0.962873i	$-0.412992\pi$
$432$		0			0
$433$	9.19109	+	15.9194i	0.441695	+	0.765039i	0.997815	−	0.0660630i	$-0.0210438\pi$
$433$	9.19109	+	15.9194i	0.441695	+	0.765039i	−0.556120	+	0.831102i	$0.687711\pi$
$434$		0			0
$435$	−0.00860602	+	0.0149061i	−0.000412627	+	0.000714691i
$436$		0			0
$437$	−2.85731	+	9.80471i	−0.136684	+	0.469023i
$438$		0			0
$439$	3.80712	−	6.59412i	0.181704	−	0.314720i	−0.760757	−	0.649037i	$-0.775172\pi$
$439$	3.80712	−	6.59412i	0.181704	−	0.314720i	0.942461	+	0.334317i	$0.108505\pi$
$440$		0			0
$441$	11.4464	+	19.8258i	0.545069	+	0.944087i
$442$		0			0
$443$	3.75168	+	6.49810i	0.178248	+	0.308734i	0.941280	−	0.337626i	$-0.109624\pi$
$443$	3.75168	+	6.49810i	0.178248	+	0.308734i	−0.763033	+	0.646360i	$0.776290\pi$
$444$		0			0
$445$	−31.7392			−1.50458
$446$		0			0
$447$	−0.450116	−	0.779624i	−0.0212898	−	0.0368749i
$448$		0			0
$449$	9.31836			0.439761			0.219880	−	0.975527i	$-0.429433\pi$
$449$	9.31836			0.439761			0.219880	+	0.975527i	$0.429433\pi$
$450$		0			0
$451$	−12.1895	+	21.1129i	−0.573982	+	0.994166i
$452$		0			0
$453$	0.376625	−	0.652334i	0.0176954	−	0.0306493i
$454$		0			0
$455$	−55.4439			−2.59925
$456$		0			0
$457$	22.4893			1.05200			0.526002	−	0.850483i	$-0.323690\pi$
$457$	22.4893			1.05200			0.526002	+	0.850483i	$0.323690\pi$
$458$		0			0
$459$	2.27364	−	3.93807i	0.106125	−	0.183813i
$460$		0			0
$461$	−1.67303	+	2.89777i	−0.0779207	+	0.134963i	−0.902353	−	0.430998i	$-0.858161\pi$
$461$	−1.67303	+	2.89777i	−0.0779207	+	0.134963i	0.824432	+	0.565961i	$0.191495\pi$
$462$		0			0
$463$	26.0147			1.20901			0.604503	−	0.796603i	$-0.293372\pi$
$463$	26.0147			1.20901			0.604503	+	0.796603i	$0.293372\pi$
$464$		0			0
$465$	−0.589673	−	1.02134i	−0.0273454	−	0.0473637i
$466$		0			0
$467$	11.3429			0.524888			0.262444	−	0.964947i	$-0.415472\pi$
$467$	11.3429			0.524888			0.262444	+	0.964947i	$0.415472\pi$
$468$		0			0
$469$	22.0698	+	38.2260i	1.01909	+	1.76511i
$470$		0			0
$471$	−0.322760	−	0.559036i	−0.0148720	−	0.0257590i
$472$		0			0
$473$	14.8108	−	25.6530i	0.681001	−	1.17953i
$474$		0			0
$475$	0.596711	−	2.04758i	0.0273790	−	0.0939496i
$476$		0			0
$477$	−4.76060	+	8.24560i	−0.217973	+	0.377540i
$478$		0			0
$479$	−5.75199	−	9.96274i	−0.262815	−	0.455209i	0.704174	−	0.710028i	$-0.251318\pi$
$479$	−5.75199	−	9.96274i	−0.262815	−	0.455209i	−0.966989	+	0.254818i	$0.917984\pi$
$480$		0			0
$481$	16.7936	+	29.0873i	0.765721	+	1.32627i
$482$		0			0
$483$	1.31415			0.0597961
$484$		0			0
$485$	4.31783	+	7.47870i	0.196062	+	0.339590i
$486$		0			0
$487$	−22.3832			−1.01428			−0.507141	−	0.861863i	$-0.669298\pi$
$487$	−22.3832			−1.01428			−0.507141	+	0.861863i	$0.669298\pi$
$488$		0			0
$489$	0.901721	−	1.56183i	0.0407772	−	0.0706283i
$490$		0			0
$491$	−11.0160	+	19.0802i	−0.497143	+	0.861077i	−0.999995	−	0.00329588i	$-0.998951\pi$
$491$	−11.0160	+	19.0802i	−0.497143	+	0.861077i	0.502852	+	0.864373i	$0.332284\pi$
$492$		0			0
$493$	0.260826			0.0117470
$494$		0			0
$495$	23.3288			1.04855
$496$		0			0
$497$	−2.85363	+	4.94264i	−0.128003	+	0.221708i
$498$		0			0
$499$	−0.605317	+	1.04844i	−0.0270977	+	0.0469346i	−0.879256	−	0.476349i	$-0.841960\pi$
$499$	−0.605317	+	1.04844i	−0.0270977	+	0.0469346i	0.852159	+	0.523284i	$0.175293\pi$
$500$		0			0
$501$	−0.846288			−0.0378094
$502$		0			0
$503$	−15.2462	−	26.4072i	−0.679795	−	1.17744i	−0.975042	−	0.222019i	$-0.928735\pi$
$503$	−15.2462	−	26.4072i	−0.679795	−	1.17744i	0.295247	−	0.955421i	$-0.404598\pi$
$504$		0			0
$505$	−17.8396			−0.793850
$506$		0			0
$507$	−1.83925	−	3.18567i	−0.0816840	−	0.141481i
$508$		0			0
$509$	0.423144	+	0.732907i	0.0187555	+	0.0324855i	0.875251	−	0.483669i	$-0.160696\pi$
$509$	0.423144	+	0.732907i	0.0187555	+	0.0324855i	−0.856495	+	0.516155i	$0.827363\pi$
$510$		0			0
$511$	−14.7269	+	25.5077i	−0.651479	+	1.12840i
$512$		0			0
$513$	−2.63776	−	2.75518i	−0.116460	−	0.121644i
$514$		0			0
$515$	19.4966	−	33.7692i	0.859124	−	1.48805i
$516$		0			0
$517$	−17.9449	−	31.0814i	−0.789215	−	1.36696i
$518$		0			0
$519$	0.133549	+	0.231313i	0.00586214	+	0.0101535i
$520$		0			0
$521$	−42.6044			−1.86653			−0.933266	−	0.359187i	$-0.883054\pi$
$521$	−42.6044			−1.86653			−0.933266	+	0.359187i	$0.883054\pi$
$522$		0			0
$523$	−5.86224	−	10.1537i	−0.256338	−	0.443990i	0.708920	−	0.705289i	$-0.249183\pi$
$523$	−5.86224	−	10.1537i	−0.256338	−	0.443990i	−0.965258	+	0.261299i	$0.915849\pi$
$524$		0			0
$525$	−0.274444			−0.0119777
$526$		0			0
$527$	−8.93573	+	15.4771i	−0.389247	+	0.674195i
$528$		0			0
$529$	8.75536	−	15.1647i	0.380668	−	0.659336i
$530$		0			0
$531$	11.4783			0.498118
$532$		0			0
$533$	−45.0336			−1.95062
$534$		0			0
$535$	−7.37169	+	12.7681i	−0.318706	+	0.552015i
$536$		0			0
$537$	0.604779	−	1.04751i	0.0260982	−	0.0452033i
$538$		0			0
$539$	−25.6932			−1.10668
$540$		0			0
$541$	9.06614	+	15.7030i	0.389784	+	0.675126i	0.992420	−	0.122890i	$-0.0392163\pi$
$541$	9.06614	+	15.7030i	0.389784	+	0.675126i	−0.602636	+	0.798016i	$0.705883\pi$
$542$		0			0
$543$	−3.17827			−0.136393
$544$		0			0
$545$	−13.0661	−	22.6312i	−0.559692	−	0.969415i
$546$		0			0
$547$	21.7018	+	37.5886i	0.927902	+	1.60717i	0.786826	+	0.617174i	$0.211723\pi$
$547$	21.7018	+	37.5886i	0.927902	+	1.60717i	0.141076	+	0.989999i	$0.454944\pi$
$548$		0			0
$549$	4.36121	−	7.55384i	0.186132	−	0.322390i
$550$		0			0
$551$	0.0612117	−	0.210045i	0.00260771	−	0.00894821i
$552$		0			0
$553$	−0.335577	+	0.581236i	−0.0142702	+	0.0247167i
$554$		0			0
$555$	0.932596	+	1.61530i	0.0395865	+	0.0685658i
$556$		0			0
$557$	−4.59828	−	7.96445i	−0.194835	−	0.337465i	0.752011	−	0.659150i	$-0.229084\pi$
$557$	−4.59828	−	7.96445i	−0.194835	−	0.337465i	−0.946847	+	0.321686i	$0.895751\pi$
$558$		0			0
$559$	54.7178			2.31431
$560$		0			0
$561$	1.27131	+	2.20197i	0.0536747	+	0.0929673i
$562$		0			0
$563$	−41.3576			−1.74302			−0.871508	−	0.490382i	$-0.836857\pi$
$563$	−41.3576			−1.74302			−0.871508	+	0.490382i	$0.836857\pi$
$564$		0			0
$565$	20.8059	−	36.0368i	0.875309	−	1.51608i
$566$		0			0
$567$	16.8764	−	29.2308i	0.708742	−	1.22758i
$568$		0			0
$569$	1.22219			0.0512369			0.0256185	−	0.999672i	$-0.491844\pi$
$569$	1.22219			0.0512369			0.0256185	+	0.999672i	$0.491844\pi$
$570$		0			0
$571$	4.32150			0.180849			0.0904246	−	0.995903i	$-0.471178\pi$
$571$	4.32150			0.180849			0.0904246	+	0.995903i	$0.471178\pi$
$572$		0			0
$573$	−0.335577	+	0.581236i	−0.0140189	+	0.0242815i
$574$		0			0
$575$	0.573183	−	0.992782i	0.0239034	−	0.0414019i
$576$		0			0
$577$	2.03863			0.0848695			0.0424347	−	0.999099i	$-0.486489\pi$
$577$	2.03863			0.0848695			0.0424347	+	0.999099i	$0.486489\pi$
$578$		0			0
$579$	0.891010	+	1.54327i	0.0370291	+	0.0641363i
$580$		0			0
$581$	−26.8536			−1.11408
$582$		0			0
$583$	−5.34292	−	9.25421i	−0.221281	−	0.383270i
$584$		0			0
$585$	21.5468	+	37.3202i	0.890852	+	1.54300i
$586$		0			0
$587$	−4.33011	+	7.49996i	−0.178723	+	0.309557i	−0.941443	−	0.337171i	$-0.890530\pi$
$587$	−4.33011	+	7.49996i	−0.178723	+	0.309557i	0.762721	+	0.646728i	$0.223863\pi$
$588$		0			0
$589$	10.3668	+	10.8282i	0.427155	+	0.446170i
$590$		0			0
$591$	0.312357	−	0.541017i	0.0128486	−	0.0222545i
$592$		0			0
$593$	−5.48592	−	9.50190i	−0.225280	−	0.390196i	0.731123	−	0.682245i	$-0.238996\pi$
$593$	−5.48592	−	9.50190i	−0.225280	−	0.390196i	−0.956403	+	0.292049i	$0.905663\pi$
$594$		0			0
$595$	23.3288	+	40.4067i	0.956389	+	1.65652i
$596$		0			0
$597$	0.418749			0.0171383
$598$		0			0
$599$	22.7109	+	39.3365i	0.927944	+	1.60725i	0.786757	+	0.617263i	$0.211759\pi$
$599$	22.7109	+	39.3365i	0.927944	+	1.60725i	0.141187	+	0.989983i	$0.454908\pi$
$600$		0			0
$601$	29.8757			1.21865			0.609327	−	0.792919i	$-0.291440\pi$
$601$	29.8757			1.21865			0.609327	+	0.792919i	$0.291440\pi$
$602$		0			0
$603$	17.1537	−	29.7111i	0.698553	−	1.20993i
$604$		0			0
$605$	−0.205164	+	0.355354i	−0.00834109	+	0.0144472i
$606$		0			0
$607$	34.7764			1.41153			0.705765	−	0.708446i	$-0.250604\pi$
$607$	34.7764			1.41153			0.705765	+	0.708446i	$0.250604\pi$
$608$		0			0
$609$	−0.0281529			−0.00114081
$610$		0			0
$611$	33.1482	−	57.4144i	1.34103	−	2.32274i
$612$		0			0
$613$	−7.38030	+	12.7831i	−0.298087	+	0.516303i	−0.975698	−	0.219118i	$-0.929682\pi$
$613$	−7.38030	+	12.7831i	−0.298087	+	0.516303i	0.677611	+	0.735421i	$0.263015\pi$
$614$		0			0
$615$	−2.50085			−0.100844
$616$		0			0
$617$	13.0181	+	22.5479i	0.524087	+	0.907746i	0.999607	+	0.0280406i	$0.00892677\pi$
$617$	13.0181	+	22.5479i	0.524087	+	0.907746i	−0.475520	+	0.879705i	$0.657740\pi$
$618$		0			0
$619$	40.7497			1.63787			0.818933	−	0.573888i	$-0.194566\pi$
$619$	40.7497			1.63787			0.818933	+	0.573888i	$0.194566\pi$
$620$		0			0
$621$	−1.02510	−	1.77552i	−0.0411357	−	0.0712491i
$622$		0			0
$623$	−25.9572	−	44.9591i	−1.03995	−	1.80125i
$624$		0			0
$625$	13.6035	−	23.5620i	0.544141	−	0.942479i
$626$		0			0
$627$	2.07161	−	0.507025i	0.0827323	−	0.0202486i
$628$		0			0
$629$	14.1323	−	24.4778i	0.563491	−	0.975996i
$630$		0			0
$631$	15.9106	+	27.5580i	0.633392	+	1.09707i	0.986853	+	0.161619i	$0.0516714\pi$
$631$	15.9106	+	27.5580i	0.633392	+	1.09707i	−0.353461	+	0.935449i	$0.614995\pi$
$632$		0			0
$633$	1.33745	+	2.31654i	0.0531590	+	0.0920740i
$634$		0			0
$635$	−43.1684			−1.71309
$636$		0			0
$637$	−23.7306	−	41.1025i	−0.940239	−	1.62854i
$638$		0			0
$639$	4.43596			0.175484
$640$		0			0
$641$	4.08233	−	7.07080i	0.161242	−	0.279280i	−0.774072	−	0.633097i	$-0.781783\pi$
$641$	4.08233	−	7.07080i	0.161242	−	0.279280i	0.935314	+	0.353818i	$0.115117\pi$
$642$		0			0
$643$	3.29851	−	5.71319i	0.130081	−	0.225306i	−0.793627	−	0.608405i	$-0.791810\pi$
$643$	3.29851	−	5.71319i	0.130081	−	0.225306i	0.923707	+	0.383099i	$0.125143\pi$
$644$		0			0
$645$	3.03863			0.119646
$646$		0			0
$647$	−2.60015			−0.102223			−0.0511113	−	0.998693i	$-0.516276\pi$
$647$	−2.60015			−0.102223			−0.0511113	+	0.998693i	$0.516276\pi$
$648$		0			0
$649$	−6.44120	+	11.1565i	−0.252839	+	0.437930i
$650$		0			0
$651$	0.964501	−	1.67056i	0.0378018	−	0.0654746i
$652$		0			0
$653$	−2.39312			−0.0936498			−0.0468249	−	0.998903i	$-0.514910\pi$
$653$	−2.39312			−0.0936498			−0.0468249	+	0.998903i	$0.514910\pi$
$654$		0			0
$655$	−3.77835	−	6.54429i	−0.147632	−	0.255706i
$656$		0			0
$657$	22.8929			0.893137
$658$		0			0
$659$	11.3417	+	19.6443i	0.441808	+	0.765235i	0.997824	−	0.0659373i	$-0.0210037\pi$
$659$	11.3417	+	19.6443i	0.441808	+	0.765235i	−0.556015	+	0.831172i	$0.687670\pi$
$660$		0			0
$661$	−20.2750	−	35.1173i	−0.788605	−	1.36590i	−0.926821	−	0.375502i	$-0.877470\pi$
$661$	−20.2750	−	35.1173i	−0.788605	−	1.36590i	0.138216	−	0.990402i	$-0.455863\pi$
$662$		0			0
$663$	−2.34839	+	4.06754i	−0.0912040	+	0.157970i
$664$		0			0
$665$	38.0147	−	9.30404i	1.47415	−	0.360795i
$666$		0			0
$667$	0.0587981	−	0.101841i	0.00227667	−	0.00394331i
$668$		0			0
$669$	−0.881866	−	1.52744i	−0.0340949	−	0.0590541i
$670$		0			0
$671$	4.89468	+	8.47784i	0.188957	+	0.327283i
$672$		0			0
$673$	−20.1004			−0.774813			−0.387406	−	0.921909i	$-0.626629\pi$
$673$	−20.1004			−0.774813			−0.387406	+	0.921909i	$0.626629\pi$
$674$		0			0
$675$	0.214078	+	0.370794i	0.00823986	+	0.0142719i
$676$		0			0
$677$	−19.3717			−0.744515			−0.372257	−	0.928130i	$-0.621416\pi$
$677$	−19.3717			−0.744515			−0.372257	+	0.928130i	$0.621416\pi$
$678$		0			0
$679$	−7.06247	+	12.2326i	−0.271033	+	0.469443i
$680$		0			0
$681$	−0.637759	+	1.10463i	−0.0244390	+	0.0423296i
$682$		0			0
$683$	16.1151			0.616626			0.308313	−	0.951285i	$-0.400236\pi$
$683$	16.1151			0.616626			0.308313	+	0.951285i	$0.400236\pi$
$684$		0			0
$685$	−14.0073			−0.535193
$686$		0			0
$687$	−1.13902	+	1.97284i	−0.0434563	+	0.0752685i
$688$		0			0
$689$	9.86959	−	17.0946i	0.376001	−	0.651253i
$690$		0			0
$691$	−15.4145			−0.586397			−0.293198	−	0.956052i	$-0.594720\pi$
$691$	−15.4145			−0.586397			−0.293198	+	0.956052i	$0.594720\pi$
$692$		0			0
$693$	19.0790	+	33.0457i	0.724750	+	1.25530i
$694$		0			0
$695$	21.4794			0.814761
$696$		0			0
$697$	18.9485	+	32.8198i	0.717727	+	1.24314i
$698$		0			0
$699$	1.64143	+	2.84304i	0.0620847	+	0.107534i
$700$		0			0
$701$	−17.9148	+	31.0294i	−0.676634	+	1.17197i	0.299354	+	0.954142i	$0.403229\pi$
$701$	−17.9148	+	31.0294i	−0.676634	+	1.17197i	−0.975988	+	0.217823i	$0.930104\pi$
$702$		0			0
$703$	−16.3955	−	17.1254i	−0.618369	−	0.645896i
$704$		0			0
$705$	1.84082	−	3.18839i	0.0693292	−	0.120082i
$706$		0			0
$707$	−14.5897	−	25.2701i	−0.548701	−	0.950378i
$708$		0			0
$709$	−4.41400	−	7.64527i	−0.165771	−	0.287124i	0.771158	−	0.636644i	$-0.219678\pi$
$709$	−4.41400	−	7.64527i	−0.165771	−	0.287124i	−0.936929	+	0.349520i	$0.886345\pi$
$710$		0			0
$711$	0.521652			0.0195635
$712$		0			0
$713$	4.02877	+	6.97803i	0.150879	+	0.261329i
$714$		0			0
$715$	−48.3650			−1.80875
$716$		0			0
$717$	2.24989	−	3.89692i	0.0840235	−	0.145533i
$718$		0			0
$719$	−8.13355	+	14.0877i	−0.303330	+	0.525383i	−0.976888	−	0.213751i	$-0.931432\pi$
$719$	−8.13355	+	14.0877i	−0.303330	+	0.525383i	0.673558	+	0.739134i	$0.264765\pi$
$720$		0			0
$721$	63.7795			2.37527
$722$		0			0
$723$	0.725556			0.0269837
$724$		0			0
$725$	−0.0122792	+	0.0212682i	−0.000456038	+	0.000789882i
$726$		0			0
$727$	20.3803	−	35.2997i	0.755863	−	1.30919i	−0.189081	−	0.981962i	$-0.560551\pi$
$727$	20.3803	−	35.2997i	0.755863	−	1.30919i	0.944944	−	0.327232i	$-0.106116\pi$
$728$		0			0
$729$	−25.8500			−0.957409
$730$		0			0
$731$	−23.0233	−	39.8775i	−0.851547	−	1.47492i
$732$		0			0
$733$	19.6827			0.726998			0.363499	−	0.931595i	$-0.381582\pi$
$733$	19.6827			0.726998			0.363499	+	0.931595i	$0.381582\pi$
$734$		0			0
$735$	−1.31783	−	2.28254i	−0.0486088	−	0.0841929i
$736$		0			0
$737$	19.2520	+	33.3454i	0.709156	+	1.22829i
$738$		0			0
$739$	−21.3775	+	37.0269i	−0.786383	+	1.36206i	0.141786	+	0.989897i	$0.454715\pi$
$739$	−21.3775	+	37.0269i	−0.786383	+	1.36206i	−0.928169	+	0.372158i	$0.878618\pi$
$740$		0			0
$741$	2.72448	+	2.84576i	0.100086	+	0.104542i
$742$		0			0
$743$	−8.34239	+	14.4494i	−0.306052	+	0.530098i	−0.977495	−	0.210958i	$-0.932342\pi$
$743$	−8.34239	+	14.4494i	−0.306052	+	0.530098i	0.671443	+	0.741057i	$0.265675\pi$
$744$		0			0
$745$	−7.20516	−	12.4797i	−0.263977	−	0.457221i
$746$		0			0
$747$	10.4360	+	18.0756i	0.381832	+	0.661352i
$748$		0			0
$749$	−24.1151			−0.881146
$750$		0			0
$751$	−15.4305	−	26.7264i	−0.563067	−	0.975260i	−0.997227	−	0.0744242i	$-0.976288\pi$
$751$	−15.4305	−	26.7264i	−0.563067	−	0.975260i	0.434160	−	0.900836i	$-0.357045\pi$
$752$		0			0
$753$	−4.02984			−0.146856
$754$		0			0
$755$	6.02877	−	10.4421i	0.219409	−	0.380028i
$756$		0			0
$757$	7.99139	−	13.8415i	0.290452	−	0.503078i	−0.683465	−	0.729984i	$-0.739528\pi$
$757$	7.99139	−	13.8415i	0.290452	−	0.503078i	0.973917	+	0.226906i	$0.0728610\pi$
$758$		0			0
$759$	1.14637			0.0416104
$760$		0			0
$761$	22.9975			0.833658			0.416829	−	0.908985i	$-0.363141\pi$
$761$	22.9975			0.833658			0.416829	+	0.908985i	$0.363141\pi$
$762$		0			0
$763$	21.3717	−	37.0169i	0.773707	−	1.34010i
$764$		0			0
$765$	18.1323	−	31.4060i	0.655574	−	1.13549i
$766$		0			0
$767$	−23.7967			−0.859249
$768$		0			0
$769$	−14.9731	−	25.9342i	−0.539944	−	0.935211i	−0.998906	−	0.0467548i	$-0.985112\pi$
$769$	−14.9731	−	25.9342i	−0.539944	−	0.935211i	0.458962	−	0.888456i	$-0.348221\pi$
$770$		0			0
$771$	−1.73979			−0.0626570
$772$		0			0
$773$	−2.75379	−	4.76970i	−0.0990469	−	0.171554i	0.812244	−	0.583318i	$-0.198246\pi$
$773$	−2.75379	−	4.76970i	−0.0990469	−	0.171554i	−0.911290	+	0.411764i	$0.864913\pi$
$774$		0			0
$775$	−0.841355	−	1.45727i	−0.0302224	−	0.0523467i
$776$		0			0
$777$	−1.52540	+	2.64208i	−0.0547236	+	0.0947840i
$778$		0			0
$779$	30.8769	−	7.55709i	1.10628	−	0.270761i
$780$		0			0
$781$	−2.48929	+	4.31157i	−0.0890737	+	0.154280i
$782$		0			0
$783$	0.0219605	+	0.0380367i	0.000784804	+	0.00135932i
$784$		0			0
$785$	−5.16653	−	8.94869i	−0.184401	−	0.319392i
$786$		0			0
$787$	8.40719			0.299684			0.149842	−	0.988710i	$-0.452123\pi$
$787$	8.40719			0.299684			0.149842	+	0.988710i	$0.452123\pi$
$788$		0			0
$789$	1.42135	+	2.46184i	0.0506013	+	0.0876440i
$790$		0			0
$791$	68.0624			2.42002
$792$		0			0
$793$	−9.04159	+	15.6605i	−0.321076	+	0.556120i
$794$		0			0
$795$	0.548087	−	0.949314i	0.0194386	−	0.0336687i
$796$		0			0
$797$	33.2186			1.17666			0.588332	−	0.808620i	$-0.299785\pi$
$797$	33.2186			1.17666			0.588332	+	0.808620i	$0.299785\pi$
$798$		0			0
$799$	−55.7904			−1.97372
$800$		0			0
$801$	−20.1751	+	34.9444i	−0.712853	+	1.23470i
$802$		0			0
$803$	−12.8466	+	22.2510i	−0.453347	+	0.785219i
$804$		0			0
$805$	21.0361			0.741426
$806$		0			0
$807$	−1.35260	−	2.34278i	−0.0476139	−	0.0824697i
$808$		0			0
$809$	12.8971			0.453438			0.226719	−	0.973960i	$-0.427200\pi$
$809$	12.8971			0.453438			0.226719	+	0.973960i	$0.427200\pi$
$810$		0			0
$811$	−1.33432	−	2.31110i	−0.0468542	−	0.0811539i	0.841647	−	0.540028i	$-0.181586\pi$
$811$	−1.33432	−	2.31110i	−0.0468542	−	0.0811539i	−0.888501	+	0.458874i	$0.848253\pi$
$812$		0			0
$813$	1.19602	+	2.07157i	0.0419463	+	0.0726530i
$814$		0			0
$815$	14.4342	−	25.0007i	0.505607	−	0.875736i
$816$		0			0
$817$	−37.5168	+	9.18219i	−1.31255	+	0.321244i
$818$		0			0
$819$	−35.2432	+	61.0429i	−1.23150	+	2.13301i
$820$		0			0
$821$	16.8267	+	29.1448i	0.587257	+	1.01716i	0.994590	+	0.103880i	$0.0331257\pi$
$821$	16.8267	+	29.1448i	0.587257	+	1.01716i	−0.407333	+	0.913280i	$0.633541\pi$
$822$		0			0
$823$	8.91978	+	15.4495i	0.310924	+	0.538536i	0.978563	−	0.205949i	$-0.0660282\pi$
$823$	8.91978	+	15.4495i	0.310924	+	0.538536i	−0.667639	+	0.744485i	$0.732695\pi$
$824$		0			0
$825$	−0.239403			−0.00833495
$826$		0			0
$827$	1.87663	+	3.25041i	0.0652567	+	0.113028i	0.896808	−	0.442420i	$-0.145880\pi$
$827$	1.87663	+	3.25041i	0.0652567	+	0.113028i	−0.831551	+	0.555448i	$0.812547\pi$
$828$		0			0
$829$	2.77781			0.0964773			0.0482386	−	0.998836i	$-0.484639\pi$
$829$	2.77781			0.0964773			0.0482386	+	0.998836i	$0.484639\pi$
$830$		0			0
$831$	−1.15551	+	2.00140i	−0.0400842	+	0.0694278i
$832$		0			0
$833$	−19.9700	+	34.5890i	−0.691918	+	1.19844i
$834$		0			0
$835$	−13.5468			−0.468807
$836$		0			0
$837$	−3.00941			−0.104020
$838$		0			0
$839$	−28.1114	+	48.6904i	−0.970513	+	1.68098i	−0.276504	+	0.961013i	$0.589176\pi$
$839$	−28.1114	+	48.6904i	−0.970513	+	1.68098i	−0.694010	+	0.719966i	$0.744157\pi$
$840$		0			0
$841$	14.4987	−	25.1126i	0.499957	−	0.865950i
$842$		0			0
$843$	1.23375			0.0424926
$844$		0			0
$845$	−29.4415	−	50.9942i	−1.01282	−	1.75425i
$846$		0			0
$847$	−0.671153			−0.0230611
$848$		0			0
$849$	0.132518	+	0.229529i	0.00454802	+	0.00787741i
$850$		0			0
$851$	−6.37169	−	11.0361i	−0.218419	−	0.378312i
$852$		0			0
$853$	5.16232	−	8.94140i	0.176754	−	0.306148i	−0.764013	−	0.645201i	$-0.776774\pi$
$853$	5.16232	−	8.94140i	0.176754	−	0.306148i	0.940767	+	0.339054i	$0.110107\pi$
$854$		0			0
$855$	−21.0361	−	21.9725i	−0.719420	−	0.751445i
$856$		0			0
$857$	−26.5894	+	46.0543i	−0.908278	+	1.57318i	−0.0918226	+	0.995775i	$0.529269\pi$
$857$	−26.5894	+	46.0543i	−0.908278	+	1.57318i	−0.816455	+	0.577408i	$0.804064\pi$
$858$		0			0
$859$	−5.12651	−	8.87938i	−0.174914	−	0.302960i	0.765217	−	0.643772i	$-0.222631\pi$
$859$	−5.12651	−	8.87938i	−0.174914	−	0.302960i	−0.940132	+	0.340812i	$0.889298\pi$
$860$		0			0
$861$	−2.04526	−	3.54249i	−0.0697022	−	0.120728i
$862$		0			0
$863$	10.7679			0.366545			0.183273	−	0.983062i	$-0.441331\pi$
$863$	10.7679			0.366545			0.183273	+	0.983062i	$0.441331\pi$
$864$		0			0
$865$	2.13776	+	3.70271i	0.0726860	+	0.125896i
$866$		0			0
$867$	1.46427			0.0497293
$868$		0			0
$869$	−0.292731	+	0.507025i	−0.00993022	+	0.0171996i
$870$		0			0
$871$	−35.5628	+	61.5965i	−1.20500	+	2.08712i
$872$		0			0
$873$	10.9786			0.371569
$874$		0			0
$875$	40.4998			1.36914
$876$		0			0
$877$	−11.3638	+	19.6827i	−0.383729	+	0.664637i	−0.991592	−	0.129404i	$-0.958693\pi$
$877$	−11.3638	+	19.6827i	−0.383729	+	0.664637i	0.607863	+	0.794042i	$0.292027\pi$
$878$		0			0
$879$	−1.77395	+	3.07257i	−0.0598339	+	0.103635i
$880$		0			0
$881$	−8.44644			−0.284568			−0.142284	−	0.989826i	$-0.545445\pi$
$881$	−8.44644			−0.284568			−0.142284	+	0.989826i	$0.545445\pi$
$882$		0			0
$883$	22.5196	+	39.0051i	0.757846	+	1.31263i	0.943947	+	0.330097i	$0.107081\pi$
$883$	22.5196	+	39.0051i	0.757846	+	1.31263i	−0.186101	+	0.982531i	$0.559585\pi$
$884$		0			0
$885$	−1.32150			−0.0444217
$886$		0			0
$887$	−10.4231	−	18.0534i	−0.349975	−	0.606174i	0.636270	−	0.771467i	$-0.280477\pi$
$887$	−10.4231	−	18.0534i	−0.349975	−	0.606174i	−0.986245	+	0.165292i	$0.947143\pi$
$888$		0			0
$889$	−35.3043	−	61.1488i	−1.18407	−	2.05087i
$890$		0			0
$891$	14.7217	−	25.4987i	0.493194	−	0.854237i
$892$		0			0
$893$	−13.0931	+	44.9284i	−0.438144	+	1.50347i
$894$		0			0
$895$	9.68091	−	16.7678i	0.323597	−	0.560487i
$896$		0			0
$897$	1.05880	+	1.83389i	0.0353522	+	0.0612319i
$898$		0			0
$899$	−0.0863077	−	0.149489i	−0.00287852	−	0.00498575i
$900$		0			0
$901$	−16.6111			−0.553396
$902$		0			0
$903$	2.48508	+	4.30428i	0.0826982	+	0.143238i
$904$		0			0
$905$	−50.8757			−1.69116
$906$		0			0
$907$	12.2055	−	21.1405i	0.405276	−	0.701959i	−0.589078	−	0.808077i	$-0.700509\pi$
$907$	12.2055	−	21.1405i	0.405276	−	0.701959i	0.994354	+	0.106118i	$0.0338421\pi$
$908$		0			0
$909$	−11.3398	+	19.6411i	−0.376117	+	0.651454i
$910$		0			0
$911$	−24.2744			−0.804248			−0.402124	−	0.915585i	$-0.631728\pi$
$911$	−24.2744			−0.804248			−0.402124	+	0.915585i	$0.631728\pi$
$912$		0			0
$913$	−23.4250			−0.775255
$914$		0			0
$915$	−0.502105	+	0.869672i	−0.0165991	+	0.0287505i
$916$		0			0
$917$	6.18007	−	10.7042i	0.204084	−	0.353484i
$918$		0			0
$919$	31.8568			1.05086			0.525429	−	0.850837i	$-0.323905\pi$
$919$	31.8568			1.05086			0.525429	+	0.850837i	$0.323905\pi$
$920$		0			0
$921$	1.61025	+	2.78903i	0.0530595	+	0.0919018i
$922$		0			0
$923$	−9.19656			−0.302708
$924$		0			0
$925$	1.33064	+	2.30474i	0.0437513	+	0.0757795i
$926$		0			0
$927$	−24.7862	−	42.9310i	−0.814087	−	1.41004i
$928$		0			0
$929$	25.1044	−	43.4820i	0.823648	−	1.42660i	−0.0793010	−	0.996851i	$-0.525269\pi$
$929$	25.1044	−	43.4820i	0.823648	−	1.42660i	0.902949	−	0.429749i	$-0.141398\pi$
$930$		0			0
$931$	23.1681	+	24.1994i	0.759304	+	0.793104i
$932$		0			0
$933$	−2.37663	+	4.11644i	−0.0778072	+	0.134766i
$934$		0			0
$935$	20.3503	+	35.2477i	0.665525	+	1.15272i
$936$		0			0
$937$	2.32800	+	4.03222i	0.0760525	+	0.131727i	0.901543	−	0.432689i	$-0.142435\pi$
$937$	2.32800	+	4.03222i	0.0760525	+	0.131727i	−0.825491	+	0.564415i	$0.809102\pi$
$938$		0			0
$939$	−1.35386			−0.0441817
$940$		0			0
$941$	11.6987	+	20.2627i	0.381366	+	0.660544i	0.991258	−	0.131940i	$-0.0421206\pi$
$941$	11.6987	+	20.2627i	0.381366	+	0.660544i	−0.609892	+	0.792484i	$0.708787\pi$
$942$		0			0
$943$	17.0863			0.556407
$944$		0			0
$945$	−3.92839	+	6.80416i	−0.127790	+	0.221339i
$946$		0			0
$947$	−28.7134	+	49.7330i	−0.933059	+	1.61611i	−0.154999	+	0.987915i	$0.549537\pi$
$947$	−28.7134	+	49.7330i	−0.933059	+	1.61611i	−0.778060	+	0.628190i	$0.783796\pi$
$948$		0			0
$949$	−47.4611			−1.54065
$950$		0			0
$951$	0.903827			0.0293086
$952$		0			0
$953$	19.9966	−	34.6352i	0.647755	−	1.12194i	−0.335903	−	0.941896i	$-0.609042\pi$
$953$	19.9966	−	34.6352i	0.647755	−	1.12194i	0.983658	−	0.180047i	$-0.0576251\pi$
$954$		0			0
$955$	−5.37169	+	9.30404i	−0.173824	+	0.301072i
$956$		0			0
$957$	−0.0245584			−0.000793861
$958$		0			0
$959$	−11.4556	−	19.8417i	−0.369920	−	0.640721i
$960$		0			0
$961$	−19.1726			−0.618471
$962$		0			0
$963$	9.37169	+	16.2322i	0.301999	+	0.523077i
$964$		0			0
$965$	14.2627	+	24.7037i	0.459133	+	0.795241i
$966$		0			0
$967$	−1.94120	+	3.36226i	−0.0624248	+	0.108123i	−0.895549	−	0.444963i	$-0.853217\pi$
$967$	−1.94120	+	3.36226i	−0.0624248	+	0.108123i	0.833124	+	0.553086i	$0.186550\pi$
$968$		0			0
$969$	0.927584	−	3.18296i	0.0297983	−	0.102251i
$970$		0			0
$971$	−0.687414	+	1.19064i	−0.0220602	+	0.0382093i	−0.876845	−	0.480774i	$-0.840356\pi$
$971$	−0.687414	+	1.19064i	−0.0220602	+	0.0382093i	0.854785	+	0.518983i	$0.173689\pi$
$972$		0			0
$973$	17.5665	+	30.4260i	0.563155	+	0.975412i
$974$		0			0
$975$	−0.221116	−	0.382984i	−0.00708138	−	0.0122653i
$976$		0			0
$977$	20.2541			0.647986			0.323993	−	0.946059i	$-0.394975\pi$
$977$	20.2541			0.647986			0.323993	+	0.946059i	$0.394975\pi$
$978$		0			0
$979$	−22.6430	−	39.2188i	−0.723673	−	1.25344i
$980$		0			0
$981$	−33.2222			−1.06070
$982$		0			0
$983$	6.38030	−	11.0510i	0.203500	−	0.352472i	−0.746154	−	0.665774i	$-0.768102\pi$
$983$	6.38030	−	11.0510i	0.203500	−	0.352472i	0.949654	+	0.313301i	$0.101435\pi$
$984$		0			0
$985$	5.00000	−	8.66025i	0.159313	−	0.275939i
$986$		0			0
$987$	6.02188			0.191679
$988$		0			0
$989$	−20.7606			−0.660149
$990$		0			0
$991$	−9.47647	+	16.4137i	−0.301030	+	0.521399i	−0.976370	−	0.216108i	$-0.930664\pi$
$991$	−9.47647	+	16.4137i	−0.301030	+	0.521399i	0.675339	+	0.737507i	$0.263997\pi$
$992$		0			0
$993$	−0.758491	+	1.31375i	−0.0240700	+	0.0416905i
$994$		0			0
$995$	6.70306			0.212501
$996$		0			0
$997$	6.03244	+	10.4485i	0.191049	+	0.330907i	0.945598	−	0.325337i	$-0.105478\pi$
$997$	6.03244	+	10.4485i	0.191049	+	0.330907i	−0.754549	+	0.656244i	$0.772144\pi$
$998$		0			0
$999$	4.75952			0.150585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.i.f.49.2		6
3.2	odd	2		2736.2.s.y.1873.3		6
4.3	odd	2		152.2.i.c.49.2	✓	6
8.3	odd	2		1216.2.i.n.961.2		6
8.5	even	2		1216.2.i.m.961.2		6
12.11	even	2		1368.2.s.k.505.3		6
19.7	even	3	inner	304.2.i.f.273.2		6
19.8	odd	6		5776.2.a.bq.1.2		3
19.11	even	3		5776.2.a.bk.1.2		3
57.26	odd	6		2736.2.s.y.577.3		6
76.7	odd	6		152.2.i.c.121.2	yes	6
76.11	odd	6		2888.2.a.r.1.2		3
76.27	even	6		2888.2.a.n.1.2		3
152.45	even	6		1216.2.i.m.577.2		6
152.83	odd	6		1216.2.i.n.577.2		6
228.83	even	6		1368.2.s.k.577.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.i.c.49.2	✓	6	4.3	odd	2
152.2.i.c.121.2	yes	6	76.7	odd	6
304.2.i.f.49.2		6	1.1	even	1	trivial
304.2.i.f.273.2		6	19.7	even	3	inner
1216.2.i.m.577.2		6	152.45	even	6
1216.2.i.m.961.2		6	8.5	even	2
1216.2.i.n.577.2		6	152.83	odd	6
1216.2.i.n.961.2		6	8.3	odd	2
1368.2.s.k.505.3		6	12.11	even	2
1368.2.s.k.577.3		6	228.83	even	6
2736.2.s.y.577.3		6	57.26	odd	6
2736.2.s.y.1873.3		6	3.2	odd	2
2888.2.a.n.1.2		3	76.27	even	6
2888.2.a.r.1.2		3	76.11	odd	6
5776.2.a.bk.1.2		3	19.11	even	3
5776.2.a.bq.1.2		3	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0731827 + 0.126756i) q^{3} +(-1.17146 + 2.02903i) q^{5} -3.83221 q^{7} +(1.48929 + 2.57952i) q^{9} +O(q^{10})\)	\(q+(-0.0731827 + 0.126756i) q^{3} +(-1.17146 + 2.02903i) q^{5} -3.83221 q^{7} +(1.48929 + 2.57952i) q^{9} -3.34292 q^{11} +(-3.08757 - 5.34782i) q^{13} +(-0.171462 - 0.296980i) q^{15} +(-2.59828 + 4.50035i) q^{17} +(3.01438 + 3.14857i) q^{19} +(0.280452 - 0.485757i) q^{21} +(1.17146 + 2.02903i) q^{23} +(-0.244644 - 0.423736i) q^{25} -0.875057 q^{27} +(-0.0250961 - 0.0434676i) q^{29} +3.43910 q^{31} +(0.244644 - 0.423736i) q^{33} +(4.48929 - 7.77568i) q^{35} -5.43910 q^{37} +0.903827 q^{39} +(3.64637 - 6.31569i) q^{41} +(-4.43049 + 7.67383i) q^{43} -6.97858 q^{45} +(5.36802 + 9.29768i) q^{47} +7.68585 q^{49} +(-0.380298 - 0.658696i) q^{51} +(1.59828 + 2.76830i) q^{53} +(3.91611 - 6.78289i) q^{55} +(-0.619702 + 0.151671i) q^{57} +(1.92682 - 3.33735i) q^{59} +(-1.46419 - 2.53606i) q^{61} +(-5.70727 - 9.88528i) q^{63} +14.4679 q^{65} +(-5.75903 - 9.97493i) q^{67} -0.342923 q^{69} +(0.744644 - 1.28976i) q^{71} +(3.84292 - 6.65614i) q^{73} +0.0716150 q^{75} +12.8108 q^{77} +(0.0875674 - 0.151671i) q^{79} +(-4.40383 + 7.62765i) q^{81} +7.00735 q^{83} +(-6.08757 - 10.5440i) q^{85} +0.00734639 q^{87} +(6.77341 + 11.7319i) q^{89} +(11.8322 + 20.4940i) q^{91} +(-0.251683 + 0.435927i) q^{93} +(-9.91978 + 2.42785i) q^{95} +(1.84292 - 3.19204i) q^{97} +(-4.97858 - 8.62315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} - q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 6 * q + q^3 - q^5 + 4 * q^7 - 6 * q^9	\( 6 q + q^{3} - q^{5} + 4 q^{7} - 6 q^{9} - 8 q^{11} + q^{13} + 5 q^{15} - 11 q^{17} + 6 q^{21} + q^{23} + 6 q^{25} - 38 q^{27} + 3 q^{29} + 12 q^{31} - 6 q^{33} + 12 q^{35} - 24 q^{37} + 2 q^{39} + 19 q^{41} + 5 q^{43} - 12 q^{45} + 17 q^{47} + 22 q^{49} + 23 q^{51} + 5 q^{53} + 10 q^{55} - 29 q^{57} + 13 q^{59} + 3 q^{61} - 40 q^{63} + 42 q^{65} - 9 q^{67} + 10 q^{69} - 3 q^{71} + 11 q^{73} + 24 q^{75} + 20 q^{77} - 19 q^{79} - 23 q^{81} - 24 q^{83} - 17 q^{85} - 66 q^{87} - 3 q^{89} + 44 q^{91} - 42 q^{93} - 13 q^{95} - q^{97}+O(q^{100}) \) 6 * q + q^3 - q^5 + 4 * q^7 - 6 * q^9 - 8 * q^11 + q^13 + 5 * q^15 - 11 * q^17 + 6 * q^21 + q^23 + 6 * q^25 - 38 * q^27 + 3 * q^29 + 12 * q^31 - 6 * q^33 + 12 * q^35 - 24 * q^37 + 2 * q^39 + 19 * q^41 + 5 * q^43 - 12 * q^45 + 17 * q^47 + 22 * q^49 + 23 * q^51 + 5 * q^53 + 10 * q^55 - 29 * q^57 + 13 * q^59 + 3 * q^61 - 40 * q^63 + 42 * q^65 - 9 * q^67 + 10 * q^69 - 3 * q^71 + 11 * q^73 + 24 * q^75 + 20 * q^77 - 19 * q^79 - 23 * q^81 - 24 * q^83 - 17 * q^85 - 66 * q^87 - 3 * q^89 + 44 * q^91 - 42 * q^93 - 13 * q^95 - q^97

Introduction

L-functions

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