LMFDB - Embedded newform 572.2.bg.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	572.9
Dual form			572.2.bg.a.445.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.351299 - 3.34239i) q^{3} +(-0.419191 - 1.29014i) q^{5} +(-0.149591 + 1.42326i) q^{7} +(-8.11369 + 1.72462i) q^{9} +O(q^{10})$	\(q+(-0.351299 - 3.34239i) q^{3} +(-0.419191 - 1.29014i) q^{5} +(-0.149591 + 1.42326i) q^{7} +(-8.11369 + 1.72462i) q^{9} +(-2.28148 + 2.40725i) q^{11} +(-3.35779 + 1.31349i) q^{13} +(-4.16488 + 1.85432i) q^{15} +(4.18885 - 4.65218i) q^{17} +(-4.90405 - 2.18342i) q^{19} +4.80965 q^{21} +(-2.44211 + 4.22986i) q^{23} +(2.55635 - 1.85730i) q^{25} +(5.49903 + 16.9243i) q^{27} +(1.15520 - 0.514327i) q^{29} +(2.62985 - 8.09386i) q^{31} +(8.84743 + 6.77992i) q^{33} +(1.89892 - 0.403627i) q^{35} +(-6.08999 + 2.71144i) q^{37} +(5.56978 + 10.7616i) q^{39} +(-0.208648 - 1.98515i) q^{41} +(-6.24522 - 10.8170i) q^{43} +(5.62618 + 9.74483i) q^{45} +(-7.82041 + 5.68186i) q^{47} +(4.84373 + 1.02957i) q^{49} +(-17.0209 - 12.3664i) q^{51} +(-0.367680 + 1.13160i) q^{53} +(4.06206 + 1.93433i) q^{55} +(-5.57505 + 17.1583i) q^{57} +(0.0435320 - 0.414180i) q^{59} +(5.63957 - 6.26337i) q^{61} +(-1.24085 - 11.8059i) q^{63} +(3.10214 + 3.78141i) q^{65} +(-0.751821 + 1.30219i) q^{67} +(14.9957 + 6.67652i) q^{69} +(-6.83820 + 7.59459i) q^{71} +(-5.57192 - 4.04824i) q^{73} +(-7.10584 - 7.89184i) q^{75} +(-3.08486 - 3.60725i) q^{77} +(0.677064 - 2.08379i) q^{79} +(31.9022 - 14.2038i) q^{81} +(-4.26977 - 13.1410i) q^{83} +(-7.75789 - 3.45404i) q^{85} +(-2.12490 - 3.68043i) q^{87} +(-2.10815 + 3.65142i) q^{89} +(-1.36715 - 4.97551i) q^{91} +(-27.9767 - 5.94662i) q^{93} +(-0.761183 + 7.24217i) q^{95} +(8.89672 - 1.89106i) q^{97} +(14.3596 - 23.4663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.351299	−	3.34239i	−0.202822	−	1.92973i	−0.342476	−	0.939527i	$-0.611266\pi$
$3$	−0.351299	−	3.34239i	−0.202822	−	1.92973i	0.139654	−	0.990200i	$-0.455401\pi$
$4$		0			0
$5$	−0.419191	−	1.29014i	−0.187468	−	0.576968i	0.812514	−	0.582942i	$-0.198098\pi$
$5$	−0.419191	−	1.29014i	−0.187468	−	0.576968i	−0.999982	+	0.00597408i	$0.998098\pi$
$6$		0			0
$7$	−0.149591	+	1.42326i	−0.0565401	+	0.537944i	0.929189	+	0.369605i	$0.120507\pi$
$7$	−0.149591	+	1.42326i	−0.0565401	+	0.537944i	−0.985729	+	0.168339i	$0.946160\pi$
$8$		0			0
$9$	−8.11369	+	1.72462i	−2.70456	+	0.574872i
$10$		0			0
$11$	−2.28148	+	2.40725i	−0.687892	+	0.725813i
$11$	−2.28148	+	2.40725i	−0.687892	+	0.725813i
$12$		0			0
$13$	−3.35779	+	1.31349i	−0.931283	+	0.364297i
$13$	−3.35779	+	1.31349i	−0.931283	+	0.364297i
$14$		0			0
$15$	−4.16488	+	1.85432i	−1.07537	+	0.478784i
$16$		0			0
$17$	4.18885	−	4.65218i	1.01594	−	1.12832i	0.0242496	−	0.999706i	$-0.492280\pi$
$17$	4.18885	−	4.65218i	1.01594	−	1.12832i	0.991695	−	0.128614i	$-0.0410530\pi$
$18$		0			0
$19$	−4.90405	−	2.18342i	−1.12507	−	0.500912i	−0.242054	−	0.970263i	$-0.577821\pi$
$19$	−4.90405	−	2.18342i	−1.12507	−	0.500912i	−0.883012	+	0.469351i	$0.844488\pi$
$20$		0			0
$21$	4.80965			1.04955
$22$		0			0
$23$	−2.44211	+	4.22986i	−0.509215	+	0.881986i	0.490728	+	0.871313i	$0.336731\pi$
$23$	−2.44211	+	4.22986i	−0.509215	+	0.881986i	−0.999943	+	0.0106732i	$0.996603\pi$
$24$		0			0
$25$	2.55635	−	1.85730i	0.511270	−	0.371459i
$26$		0			0
$27$	5.49903	+	16.9243i	1.05829	+	3.25708i
$28$		0			0
$29$	1.15520	−	0.514327i	0.214515	−	0.0955080i	−0.296666	−	0.954981i	$-0.595875\pi$
$29$	1.15520	−	0.514327i	0.214515	−	0.0955080i	0.511181	+	0.859473i	$0.329208\pi$
$30$		0			0
$31$	2.62985	−	8.09386i	0.472336	−	1.45370i	−0.377182	−	0.926139i	$-0.623107\pi$
$31$	2.62985	−	8.09386i	0.472336	−	1.45370i	0.849517	−	0.527560i	$-0.176893\pi$
$32$		0			0
$33$	8.84743	+	6.77992i	1.54014	+	1.18023i
$34$		0			0
$35$	1.89892	−	0.403627i	0.320975	−	0.0682254i
$36$		0			0
$37$	−6.08999	+	2.71144i	−1.00119	+	0.445758i	−0.840829	−	0.541301i	$-0.817932\pi$
$37$	−6.08999	+	2.71144i	−1.00119	+	0.445758i	−0.160359	+	0.987059i	$0.551265\pi$
$38$		0			0
$39$	5.56978	+	10.7616i	0.891879	+	1.72323i
$40$		0			0
$41$	−0.208648	−	1.98515i	−0.0325853	−	0.310029i	−0.998659	−	0.0517634i	$-0.983516\pi$
$41$	−0.208648	−	1.98515i	−0.0325853	−	0.310029i	0.966074	−	0.258265i	$-0.0831508\pi$
$42$		0			0
$43$	−6.24522	−	10.8170i	−0.952387	−	1.64958i	−0.740236	−	0.672347i	$-0.765286\pi$
$43$	−6.24522	−	10.8170i	−0.952387	−	1.64958i	−0.212151	−	0.977237i	$-0.568047\pi$
$44$		0			0
$45$	5.62618	+	9.74483i	0.838702	+	1.45267i
$46$		0			0
$47$	−7.82041	+	5.68186i	−1.14072	+	0.828785i	−0.987220	−	0.159363i	$-0.949056\pi$
$47$	−7.82041	+	5.68186i	−1.14072	+	0.828785i	−0.153504	+	0.988148i	$0.549056\pi$
$48$		0			0
$49$	4.84373	+	1.02957i	0.691961	+	0.147081i
$50$		0			0
$51$	−17.0209	−	12.3664i	−2.38341	−	1.73165i
$52$		0			0
$53$	−0.367680	+	1.13160i	−0.0505047	+	0.155437i	−0.973128	−	0.230265i	$-0.926041\pi$
$53$	−0.367680	+	1.13160i	−0.0505047	+	0.155437i	0.922623	+	0.385702i	$0.126041\pi$
$54$		0			0
$55$	4.06206	+	1.93433i	0.547728	+	0.260825i
$56$		0			0
$57$	−5.57505	+	17.1583i	−0.738434	+	2.27267i
$58$		0			0
$59$	0.0435320	−	0.414180i	0.00566739	−	0.0539216i	−0.991323	−	0.131451i	$-0.958036\pi$
$59$	0.0435320	−	0.414180i	0.00566739	−	0.0539216i	0.996990	+	0.0775292i	$0.0247031\pi$
$60$		0			0
$61$	5.63957	−	6.26337i	0.722072	−	0.801943i	−0.264652	−	0.964344i	$-0.585257\pi$
$61$	5.63957	−	6.26337i	0.722072	−	0.801943i	0.986725	+	0.162401i	$0.0519239\pi$
$62$		0			0
$63$	−1.24085	−	11.8059i	−0.156333	−	1.48740i
$64$		0			0
$65$	3.10214	+	3.78141i	0.384773	+	0.469026i
$66$		0			0
$67$	−0.751821	+	1.30219i	−0.0918495	+	0.159088i	−0.908289	−	0.418342i	$-0.862611\pi$
$67$	−0.751821	+	1.30219i	−0.0918495	+	0.159088i	0.816440	+	0.577430i	$0.195945\pi$
$68$		0			0
$69$	14.9957	+	6.67652i	1.80527	+	0.803759i
$70$		0			0
$71$	−6.83820	+	7.59459i	−0.811545	+	0.901312i	−0.996681	−	0.0814010i	$-0.974061\pi$
$71$	−6.83820	+	7.59459i	−0.811545	+	0.901312i	0.185137	+	0.982713i	$0.440727\pi$
$72$		0			0
$73$	−5.57192	−	4.04824i	−0.652144	−	0.473810i	0.211857	−	0.977301i	$-0.432049\pi$
$73$	−5.57192	−	4.04824i	−0.652144	−	0.473810i	−0.864001	+	0.503491i	$0.832049\pi$
$74$		0			0
$75$	−7.10584	−	7.89184i	−0.820512	−	0.911271i
$76$		0			0
$77$	−3.08486	−	3.60725i	−0.351553	−	0.411085i
$78$		0			0
$79$	0.677064	−	2.08379i	0.0761757	−	0.234445i	−0.905717	−	0.423883i	$-0.860667\pi$
$79$	0.677064	−	2.08379i	0.0761757	−	0.234445i	0.981893	+	0.189438i	$0.0606667\pi$
$80$		0			0
$81$	31.9022	−	14.2038i	3.54469	−	1.57820i
$82$		0			0
$83$	−4.26977	−	13.1410i	−0.468668	−	1.44241i	−0.854310	−	0.519764i	$-0.826020\pi$
$83$	−4.26977	−	13.1410i	−0.468668	−	1.44241i	0.385641	−	0.922649i	$-0.373980\pi$
$84$		0			0
$85$	−7.75789	−	3.45404i	−0.841461	−	0.374643i
$86$		0			0
$87$	−2.12490	−	3.68043i	−0.227813	−	0.394583i
$88$		0			0
$89$	−2.10815	+	3.65142i	−0.223463	+	0.387050i	−0.955857	−	0.293831i	$-0.905070\pi$
$89$	−2.10815	+	3.65142i	−0.223463	+	0.387050i	0.732394	+	0.680881i	$0.238403\pi$
$90$		0			0
$91$	−1.36715	−	4.97551i	−0.143316	−	0.521575i
$92$		0			0
$93$	−27.9767	−	5.94662i	−2.90104	−	0.616636i
$94$		0			0
$95$	−0.761183	+	7.24217i	−0.0780957	+	0.743031i
$96$		0			0
$97$	8.89672	−	1.89106i	0.903325	−	0.192008i	0.267243	−	0.963629i	$-0.413887\pi$
$97$	8.89672	−	1.89106i	0.903325	−	0.192008i	0.636082	+	0.771621i	$0.280554\pi$
$98$		0			0
$99$	14.3596	−	23.4663i	1.44320	−	2.35846i
$100$		0			0
$101$	−3.20633	−	3.56099i	−0.319042	−	0.354332i	0.562197	−	0.827003i	$-0.309956\pi$
$101$	−3.20633	−	3.56099i	−0.319042	−	0.354332i	−0.881239	+	0.472672i	$0.843290\pi$
$102$		0			0
$103$	5.78111	+	4.20022i	0.569629	+	0.413860i	0.834971	−	0.550295i	$-0.185485\pi$
$103$	5.78111	+	4.20022i	0.569629	+	0.413860i	−0.265341	+	0.964155i	$0.585485\pi$
$104$		0			0
$105$	−2.01616	−	6.20512i	−0.196758	−	0.605557i
$106$		0			0
$107$	−0.0164188	−	0.156214i	−0.00158726	−	0.0151018i	0.993700	−	0.112076i	$-0.0357501\pi$
$107$	−0.0164188	−	0.156214i	−0.00158726	−	0.0151018i	−0.995287	+	0.0969746i	$0.969083\pi$
$108$		0			0
$109$	−1.52625			−0.146188			−0.0730941	−	0.997325i	$-0.523287\pi$
$109$	−1.52625			−0.146188			−0.0730941	+	0.997325i	$0.523287\pi$
$110$		0			0
$111$	11.2021	+	19.4026i	1.06325	+	1.84161i
$112$		0			0
$113$	−2.97952	−	1.32657i	−0.280289	−	0.124793i	0.261777	−	0.965128i	$-0.415691\pi$
$113$	−2.97952	−	1.32657i	−0.280289	−	0.124793i	−0.542067	+	0.840335i	$0.682358\pi$
$114$		0			0
$115$	6.48081	+	1.37754i	0.604339	+	0.128456i
$116$		0			0
$117$	24.9788	−	16.4482i	2.30929	−	1.52063i
$118$		0			0
$119$	5.99468	+	6.65776i	0.549531	+	0.610316i
$120$		0			0
$121$	−0.589693	−	10.9842i	−0.0536084	−	0.998562i
$122$		0			0
$123$	−6.56184	+	1.39476i	−0.591661	+	0.125762i
$124$		0			0
$125$	−8.95506	−	6.50623i	−0.800965	−	0.581935i
$126$		0			0
$127$	−11.1627	−	2.37270i	−0.990528	−	0.210543i	−0.315973	−	0.948768i	$-0.602331\pi$
$127$	−11.1627	−	2.37270i	−0.990528	−	0.210543i	−0.674555	+	0.738225i	$0.735664\pi$
$128$		0			0
$129$	−33.9608	+	24.6740i	−2.99008	+	2.17242i
$130$		0			0
$131$	0.585522			0.0511573			0.0255786	−	0.999673i	$-0.491857\pi$
$131$	0.585522			0.0511573			0.0255786	+	0.999673i	$0.491857\pi$
$132$		0			0
$133$	3.84119	−	6.65314i	0.333074	−	0.576900i
$134$		0			0
$135$	19.5295	−	14.1890i	1.68083	−	1.22120i
$136$		0			0
$137$	−2.65786	+	2.95185i	−0.227076	+	0.252193i	−0.845907	−	0.533331i	$-0.820940\pi$
$137$	−2.65786	+	2.95185i	−0.227076	+	0.252193i	0.618831	+	0.785524i	$0.287607\pi$
$138$		0			0
$139$	−0.266231	+	2.53302i	−0.0225815	+	0.214848i	0.977412	+	0.211341i	$0.0677830\pi$
$139$	−0.266231	+	2.53302i	−0.0225815	+	0.214848i	−0.999994	+	0.00350720i	$0.998884\pi$
$140$		0			0
$141$	21.7383	+	24.1428i	1.83069	+	2.03319i
$142$		0			0
$143$	4.49883	−	11.0797i	0.376211	−	0.926534i
$144$		0			0
$145$	−1.14780	−	1.27476i	−0.0953197	−	0.105863i
$146$		0			0
$147$	1.73961	−	16.5513i	0.143481	−	1.36513i
$148$		0			0
$149$	2.99510	−	3.32639i	0.245368	−	0.272509i	−0.607863	−	0.794042i	$-0.707973\pi$
$149$	2.99510	−	3.32639i	0.245368	−	0.272509i	0.853231	+	0.521533i	$0.174640\pi$
$150$		0			0
$151$	10.5550	−	7.66865i	0.858953	−	0.624066i	−0.0686466	−	0.997641i	$-0.521868\pi$
$151$	10.5550	−	7.66865i	0.858953	−	0.624066i	0.927600	+	0.373575i	$0.121868\pi$
$152$		0			0
$153$	−25.9637	+	44.9705i	−2.09904	+	3.63565i
$154$		0			0
$155$	−11.5446			−0.927285
$156$		0			0
$157$	9.91794	−	7.20581i	0.791538	−	0.575086i	−0.116882	−	0.993146i	$-0.537290\pi$
$157$	9.91794	−	7.20581i	0.791538	−	0.575086i	0.908419	+	0.418060i	$0.137290\pi$
$158$		0			0
$159$	3.91141	+	0.831397i	0.310195	+	0.0659340i
$160$		0			0
$161$	−5.65489	−	4.10852i	−0.445668	−	0.323796i
$162$		0			0
$163$	−17.5654	+	3.73363i	−1.37583	+	0.292441i	−0.835720	−	0.549156i	$-0.814949\pi$
$163$	−17.5654	+	3.73363i	−1.37583	+	0.292441i	−0.540106	+	0.841597i	$0.681616\pi$
$164$		0			0
$165$	5.03827	−	14.2565i	0.392229	−	1.10987i
$166$		0			0
$167$	7.75135	+	8.60875i	0.599817	+	0.666165i	0.964228	−	0.265074i	$-0.0853963\pi$
$167$	7.75135	+	8.60875i	0.599817	+	0.666165i	−0.364411	+	0.931238i	$0.618730\pi$
$168$		0			0
$169$	9.54948	−	8.82085i	0.734576	−	0.678527i
$170$		0			0
$171$	43.5555	+	9.25800i	3.33077	+	0.707977i
$172$		0			0
$173$	16.1618	+	7.19570i	1.22876	+	0.547079i	0.915396	−	0.402555i	$-0.131878\pi$
$173$	16.1618	+	7.19570i	1.22876	+	0.547079i	0.313363	+	0.949633i	$0.398544\pi$
$174$		0			0
$175$	2.26102	+	3.91620i	0.170917	+	0.296037i
$176$		0			0
$177$	−1.39964			−0.105203
$178$		0			0
$179$	−0.893061	−	8.49691i	−0.0667505	−	0.635089i	−0.975840	−	0.218487i	$-0.929888\pi$
$179$	−0.893061	−	8.49691i	−0.0667505	−	0.635089i	0.909089	−	0.416601i	$-0.136779\pi$
$180$		0			0
$181$	−0.731251	−	2.25056i	−0.0543535	−	0.167283i	0.920195	−	0.391461i	$-0.128030\pi$
$181$	−0.731251	−	2.25056i	−0.0543535	−	0.167283i	−0.974548	+	0.224178i	$0.928030\pi$
$182$		0			0
$183$	−22.9158	−	16.6493i	−1.69398	−	1.23075i
$184$		0			0
$185$	6.05100	+	6.72032i	0.444879	+	0.494088i
$186$		0			0
$187$	1.64219	+	20.6975i	0.120089	+	1.51355i
$188$		0			0
$189$	−24.9103	+	5.29486i	−1.81196	+	0.385144i
$190$		0			0
$191$	0.678987	−	6.46013i	0.0491297	−	0.467438i	−0.942104	−	0.335320i	$-0.891156\pi$
$191$	0.678987	−	6.46013i	0.0491297	−	0.467438i	0.991234	−	0.132118i	$-0.0421778\pi$
$192$		0			0
$193$	1.14073	+	0.242471i	0.0821119	+	0.0174534i	0.248784	−	0.968559i	$-0.419969\pi$
$193$	1.14073	+	0.242471i	0.0821119	+	0.0174534i	−0.166673	+	0.986012i	$0.553302\pi$
$194$		0			0
$195$	11.5491	−	11.6970i	0.827051	−	0.837636i
$196$		0			0
$197$	5.04903	−	8.74517i	0.359728	−	0.623068i	−0.628187	−	0.778062i	$-0.716203\pi$
$197$	5.04903	−	8.74517i	0.359728	−	0.623068i	0.987915	+	0.154995i	$0.0495360\pi$
$198$		0			0
$199$	3.00984	+	5.21319i	0.213362	+	0.369553i	0.952764	−	0.303710i	$-0.0982254\pi$
$199$	3.00984	+	5.21319i	0.213362	+	0.369553i	−0.739403	+	0.673263i	$0.764892\pi$
$200$		0			0
$201$	4.61654	+	2.05542i	0.325626	+	0.144978i
$202$		0			0
$203$	0.559216	+	1.72109i	0.0392492	+	0.120797i
$204$		0			0
$205$	−2.47366	+	1.10134i	−0.172768	+	0.0769211i
$206$		0			0
$207$	12.5196	−	38.5314i	0.870174	−	2.67812i
$208$		0			0
$209$	16.4445	−	6.82383i	1.13749	−	0.472014i
$210$		0			0
$211$	1.79678	+	1.99552i	0.123695	+	0.137378i	0.801811	−	0.597577i	$-0.203870\pi$
$211$	1.79678	+	1.99552i	0.123695	+	0.137378i	−0.678116	+	0.734955i	$0.737203\pi$
$212$		0			0
$213$	27.7863	+	20.1879i	1.90389	+	1.38325i
$214$		0			0
$215$	−11.3375	+	12.5916i	−0.773214	+	0.858741i
$216$		0			0
$217$	11.1263	+	4.95375i	0.755302	+	0.336282i
$218$		0			0
$219$	−11.5734	+	20.0456i	−0.782055	+	1.35456i
$220$		0			0
$221$	−7.95465	+	21.1231i	−0.535088	+	1.42089i
$222$		0			0
$223$	−0.440788	−	4.19382i	−0.0295174	−	0.280839i	−0.999318	−	0.0369381i	$-0.988240\pi$
$223$	−0.440788	−	4.19382i	−0.0295174	−	0.280839i	0.969800	−	0.243901i	$-0.0784271\pi$
$224$		0			0
$225$	−17.5383	+	19.4782i	−1.16922	+	1.29855i
$226$		0			0
$227$	−0.202812	+	1.92962i	−0.0134611	+	0.128074i	−0.999189	−	0.0402748i	$-0.987177\pi$
$227$	−0.202812	+	1.92962i	−0.0134611	+	0.128074i	0.985728	+	0.168348i	$0.0538433\pi$
$228$		0			0
$229$	−3.05973	+	9.41687i	−0.202192	+	0.622284i	0.797625	+	0.603154i	$0.206090\pi$
$229$	−3.05973	+	9.41687i	−0.202192	+	0.622284i	−0.999817	+	0.0191299i	$0.993910\pi$
$230$		0			0
$231$	−10.9731	+	11.5780i	−0.721979	+	0.761778i
$232$		0			0
$233$	−1.51560	+	4.66454i	−0.0992902	+	0.305584i	−0.988348	−	0.152211i	$-0.951361\pi$
$233$	−1.51560	+	4.66454i	−0.0992902	+	0.305584i	0.889058	+	0.457795i	$0.151361\pi$
$234$		0			0
$235$	10.6086	+	7.70763i	0.692031	+	0.502790i
$236$		0			0
$237$	−7.20268	−	1.53098i	−0.467864	−	0.0994476i
$238$		0			0
$239$	−4.85175	+	3.52500i	−0.313833	+	0.228013i	−0.733540	−	0.679647i	$-0.762133\pi$
$239$	−4.85175	+	3.52500i	−0.313833	+	0.228013i	0.419706	+	0.907660i	$0.362133\pi$
$240$		0			0
$241$	−7.56539	−	13.1036i	−0.487330	−	0.844080i	0.512564	−	0.858649i	$-0.328696\pi$
$241$	−7.56539	−	13.1036i	−0.487330	−	0.844080i	−0.999894	+	0.0145691i	$0.995362\pi$
$242$		0			0
$243$	−31.9889	−	55.4064i	−2.05209	−	3.55432i
$244$		0			0
$245$	−0.702166	−	6.68067i	−0.0448598	−	0.426812i
$246$		0			0
$247$	19.3347	+	0.890048i	1.23023	+	0.0566324i
$248$		0			0
$249$	−42.4224	+	18.8876i	−2.68841	+	1.19696i
$250$		0			0
$251$	−28.7621	+	6.11358i	−1.81545	+	0.385886i	−0.985187	−	0.171486i	$-0.945143\pi$
$251$	−28.7621	+	6.11358i	−1.81545	+	0.385886i	−0.830263	+	0.557371i	$0.811810\pi$
$252$		0			0
$253$	−4.61069	−	15.5291i	−0.289872	−	0.976306i
$254$		0			0
$255$	−8.81938	+	27.1433i	−0.552291	+	1.69978i
$256$		0			0
$257$	−12.3433	+	5.49561i	−0.769957	+	0.342807i	−0.753836	−	0.657063i	$-0.771798\pi$
$257$	−12.3433	+	5.49561i	−0.769957	+	0.342807i	−0.0161214	+	0.999870i	$0.505132\pi$
$258$		0			0
$259$	−2.94809	−	9.07328i	−0.183185	−	0.563786i
$260$		0			0
$261$	−8.48588	+	6.16535i	−0.525263	+	0.381626i
$262$		0			0
$263$	8.95008	−	15.5020i	0.551885	−	0.955894i	−0.446253	−	0.894907i	$-0.647242\pi$
$263$	8.95008	−	15.5020i	0.551885	−	0.955894i	0.998139	−	0.0609868i	$-0.0194247\pi$
$264$		0			0
$265$	1.61405			0.0991504
$266$		0			0
$267$	12.9450	+	5.76350i	0.792223	+	0.352721i
$268$		0			0
$269$	−3.72488	+	4.13690i	−0.227110	+	0.252231i	−0.845920	−	0.533309i	$-0.820948\pi$
$269$	−3.72488	+	4.13690i	−0.227110	+	0.252231i	0.618810	+	0.785540i	$0.287615\pi$
$270$		0			0
$271$	23.3558	−	10.3987i	1.41876	−	0.631673i	0.453096	−	0.891462i	$-0.350320\pi$
$271$	23.3558	−	10.3987i	1.41876	−	0.631673i	0.965665	+	0.259789i	$0.0836530\pi$
$272$		0			0
$273$	−16.1498	+	6.31743i	−0.977430	+	0.382348i
$274$		0			0
$275$	−1.36129	+	10.3912i	−0.0820887	+	0.626610i
$276$		0			0
$277$	6.28236	−	1.33536i	0.377470	−	0.0802338i	−0.0152695	−	0.999883i	$-0.504861\pi$
$277$	6.28236	−	1.33536i	0.377470	−	0.0802338i	0.392740	+	0.919650i	$0.371527\pi$
$278$		0			0
$279$	−7.37900	+	70.2065i	−0.441769	+	4.20315i
$280$		0			0
$281$	5.79822	+	17.8451i	0.345893	+	1.06455i	0.961104	+	0.276186i	$0.0890705\pi$
$281$	5.79822	+	17.8451i	0.345893	+	1.06455i	−0.615212	+	0.788362i	$0.710929\pi$
$282$		0			0
$283$	−2.37310	−	22.5785i	−0.141066	−	1.34215i	−0.804515	−	0.593932i	$-0.797575\pi$
$283$	−2.37310	−	22.5785i	−0.141066	−	1.34215i	0.663449	−	0.748222i	$-0.269092\pi$
$284$		0			0
$285$	24.4735			1.44969
$286$		0			0
$287$	2.85661			0.168620
$288$		0			0
$289$	−2.31941	−	22.0677i	−0.136436	−	1.29810i
$290$		0			0
$291$	−9.44605	−	29.0719i	−0.553737	−	1.70423i
$292$		0			0
$293$	0.894537	−	8.51095i	0.0522594	−	0.497215i	−0.936818	−	0.349817i	$-0.886244\pi$
$293$	0.894537	−	8.51095i	0.0522594	−	0.497215i	0.989077	−	0.147398i	$-0.0470897\pi$
$294$		0			0
$295$	−0.552598	+	0.117458i	−0.0321735	+	0.00683868i
$296$		0			0
$297$	−53.2869	−	25.3749i	−3.09202	−	1.47240i
$298$		0			0
$299$	2.64420	−	17.4106i	0.152918	−	1.00688i
$300$		0			0
$301$	16.3297	−	7.27047i	0.941231	−	0.419063i
$302$		0			0
$303$	−10.7758	+	11.9678i	−0.619055	+	0.687530i
$304$		0			0
$305$	−10.4447	−	4.65027i	−0.598060	−	0.266274i
$306$		0			0
$307$	29.6098			1.68992			0.844961	−	0.534829i	$-0.179624\pi$
$307$	29.6098			1.68992			0.844961	+	0.534829i	$0.179624\pi$
$308$		0			0
$309$	12.0079	−	20.7982i	0.683103	−	1.18317i
$310$		0			0
$311$	−7.45969	+	5.41978i	−0.423000	+	0.307328i	−0.778844	−	0.627218i	$-0.784194\pi$
$311$	−7.45969	+	5.41978i	−0.423000	+	0.307328i	0.355844	+	0.934545i	$0.384194\pi$
$312$		0			0
$313$	−2.46701	−	7.59266i	−0.139443	−	0.429163i	0.856811	−	0.515630i	$-0.172442\pi$
$313$	−2.46701	−	7.59266i	−0.139443	−	0.429163i	−0.996255	+	0.0864675i	$0.972442\pi$
$314$		0			0
$315$	−14.7111	+	6.54981i	−0.828877	+	0.369040i
$316$		0			0
$317$	3.48960	−	10.7399i	0.195995	−	0.603212i	−0.803968	−	0.594672i	$-0.797282\pi$
$317$	3.48960	−	10.7399i	0.195995	−	0.603212i	0.999964	−	0.00853950i	$-0.00271824\pi$
$318$		0			0
$319$	−1.39745	+	3.95427i	−0.0782420	+	0.221397i
$320$		0			0
$321$	−0.516360	+	0.109756i	−0.0288204	+	0.00612597i
$322$		0			0
$323$	−30.7000	+	13.6685i	−1.70819	+	0.760536i
$324$		0			0
$325$	−6.14414	+	9.59415i	−0.340815	+	0.532188i
$326$		0			0
$327$	0.536170	+	5.10132i	0.0296503	+	0.282103i
$328$		0			0
$329$	−6.91693	−	11.9805i	−0.381343	−	0.660505i
$330$		0			0
$331$	−3.77553	−	6.53941i	−0.207522	−	0.359438i	0.743411	−	0.668834i	$-0.233206\pi$
$331$	−3.77553	−	6.53941i	−0.207522	−	0.359438i	−0.950933	+	0.309396i	$0.899873\pi$
$332$		0			0
$333$	44.7361	−	32.5027i	2.45152	−	1.78113i
$334$		0			0
$335$	1.99516	+	0.424085i	0.109007	+	0.0231703i
$336$		0			0
$337$	−4.33169	−	3.14716i	−0.235962	−	0.171437i	0.463520	−	0.886086i	$-0.346586\pi$
$337$	−4.33169	−	3.14716i	−0.235962	−	0.171437i	−0.699483	+	0.714650i	$0.746586\pi$
$338$		0			0
$339$	−3.38720	+	10.4247i	−0.183967	+	0.566193i
$340$		0			0
$341$	13.4840	+	24.7967i	0.730198	+	1.34282i
$342$		0			0
$343$	−5.28557	+	16.2673i	−0.285394	+	0.878353i
$344$		0			0
$345$	2.32756	−	22.1453i	0.125312	−	1.19226i
$346$		0			0
$347$	−18.9116	+	21.0035i	−1.01523	+	1.12753i	−0.0234297	+	0.999725i	$0.507459\pi$
$347$	−18.9116	+	21.0035i	−1.01523	+	1.12753i	−0.991800	+	0.127801i	$0.959208\pi$
$348$		0			0
$349$	0.149268	+	1.42019i	0.00799011	+	0.0760208i	0.997790	−	0.0664417i	$-0.0211646\pi$
$349$	0.149268	+	1.42019i	0.00799011	+	0.0760208i	−0.989800	+	0.142462i	$0.954498\pi$
$350$		0			0
$351$	−40.6945	−	49.6052i	−2.17211	−	2.64773i
$352$		0			0
$353$	−3.09444	+	5.35973i	−0.164701	+	0.285270i	−0.936549	−	0.350537i	$-0.885999\pi$
$353$	−3.09444	+	5.35973i	−0.164701	+	0.285270i	0.771848	+	0.635807i	$0.219332\pi$
$354$		0			0
$355$	12.6646	+	5.63864i	0.672166	+	0.299268i
$356$		0			0
$357$	20.1469	−	22.3754i	1.06629	−	1.18423i
$358$		0			0
$359$	18.6780	+	13.5704i	0.985787	+	0.716216i	0.958995	−	0.283425i	$-0.0914706\pi$
$359$	18.6780	+	13.5704i	0.985787	+	0.716216i	0.0267928	+	0.999641i	$0.491471\pi$
$360$		0			0
$361$	6.56887	+	7.29547i	0.345730	+	0.383972i
$362$		0			0
$363$	−36.5062	+	5.82971i	−1.91608	+	0.305980i
$364$		0			0
$365$	−2.88708	+	8.88553i	−0.151117	+	0.465090i
$366$		0			0
$367$	−26.8371	+	11.9486i	−1.40088	+	0.623713i	−0.961555	−	0.274613i	$-0.911450\pi$
$367$	−26.8371	+	11.9486i	−1.40088	+	0.623713i	−0.439328	+	0.898327i	$0.644783\pi$
$368$		0			0
$369$	5.11653	+	15.7471i	0.266356	+	0.819759i
$370$		0			0
$371$	−1.55557	−	0.692583i	−0.0807610	−	0.0359571i
$372$		0			0
$373$	−3.64937	−	6.32089i	−0.188957	−	0.327283i	0.755946	−	0.654634i	$-0.227177\pi$
$373$	−3.64937	−	6.32089i	−0.188957	−	0.327283i	−0.944903	+	0.327351i	$0.893844\pi$
$374$		0			0
$375$	−18.6004	+	32.2169i	−0.960522	+	1.66367i
$376$		0			0
$377$	−3.20334	+	3.24434i	−0.164980	+	0.167092i
$378$		0			0
$379$	2.19705	+	0.466998i	0.112855	+	0.0239881i	0.263993	−	0.964525i	$-0.414960\pi$
$379$	2.19705	+	0.466998i	0.112855	+	0.0239881i	−0.151138	+	0.988513i	$0.548294\pi$
$380$		0			0
$381$	−4.00904	+	38.1435i	−0.205390	+	1.95415i
$382$		0			0
$383$	25.3890	−	5.39659i	1.29731	−	0.275753i	0.493038	−	0.870008i	$-0.335886\pi$
$383$	25.3890	−	5.39659i	1.29731	−	0.275753i	0.804277	+	0.594255i	$0.202553\pi$
$384$		0			0
$385$	−3.36071	+	5.49203i	−0.171278	+	0.279900i
$386$		0			0
$387$	69.3270	+	76.9955i	3.52409	+	3.91390i
$388$		0			0
$389$	25.1945	+	18.3049i	1.27741	+	0.928096i	0.999472	−	0.0325018i	$-0.0103475\pi$
$389$	25.1945	+	18.3049i	1.27741	+	0.928096i	0.277943	+	0.960598i	$0.410347\pi$
$390$		0			0
$391$	9.44845	+	29.0793i	0.477829	+	1.47061i
$392$		0			0
$393$	−0.205693	−	1.95704i	−0.0103759	−	0.0987196i
$394$		0			0
$395$	−2.97220			−0.149547
$396$		0			0
$397$	−10.1256	−	17.5381i	−0.508191	−	0.880212i	−0.999955	−	0.00948392i	$-0.996981\pi$
$397$	−10.1256	−	17.5381i	−0.508191	−	0.880212i	0.491764	−	0.870728i	$-0.336352\pi$
$398$		0			0
$399$	−23.5868	−	10.5015i	−1.18081	−	0.525733i
$400$		0			0
$401$	13.4116	+	2.85072i	0.669744	+	0.142358i	0.530220	−	0.847860i	$-0.322109\pi$
$401$	13.4116	+	2.85072i	0.669744	+	0.142358i	0.139524	+	0.990219i	$0.455443\pi$
$402$		0			0
$403$	1.80072	+	30.6317i	0.0897002	+	1.52588i
$404$		0			0
$405$	−31.6980	−	35.2042i	−1.57509	−	1.74931i
$406$		0			0
$407$	7.36709	−	20.8462i	0.365173	−	1.03331i
$408$		0			0
$409$	30.1831	−	6.41561i	1.49246	−	0.317231i	0.611809	−	0.791005i	$-0.290442\pi$
$409$	30.1831	−	6.41561i	1.49246	−	0.317231i	0.880647	+	0.473774i	$0.157109\pi$
$410$		0			0
$411$	10.7999	+	7.84659i	0.532720	+	0.387044i
$412$		0			0
$413$	0.582975	+	0.123915i	0.0286863	+	0.00609747i
$414$		0			0
$415$	−15.1639	+	11.0172i	−0.744365	+	0.540813i
$416$		0			0
$417$	8.55986			0.419178
$418$		0			0
$419$	−1.53696	+	2.66209i	−0.0750854	+	0.130052i	−0.901123	−	0.433563i	$-0.857256\pi$
$419$	−1.53696	+	2.66209i	−0.0750854	+	0.130052i	0.826038	+	0.563614i	$0.190590\pi$
$420$		0			0
$421$	−11.2000	+	8.13731i	−0.545857	+	0.396588i	−0.826256	−	0.563295i	$-0.809533\pi$
$421$	−11.2000	+	8.13731i	−0.545857	+	0.396588i	0.280399	+	0.959884i	$0.409533\pi$
$422$		0			0
$423$	53.6533	−	59.5881i	2.60871	−	2.89727i
$424$		0			0
$425$	2.06767	−	19.6725i	0.100297	−	0.954258i
$426$		0			0
$427$	8.07081	+	8.96354i	0.390574	+	0.433776i
$428$		0			0
$429$	−38.6132	−	11.1445i	−1.86426	−	0.538063i
$430$		0			0
$431$	23.9966	+	26.6509i	1.15588	+	1.28373i	0.952469	+	0.304635i	$0.0985346\pi$
$431$	23.9966	+	26.6509i	1.15588	+	1.28373i	0.203407	+	0.979094i	$0.434799\pi$
$432$		0			0
$433$	−0.169926	+	1.61674i	−0.00816613	+	0.0776955i	−0.997846	−	0.0656009i	$-0.979104\pi$
$433$	−0.169926	+	1.61674i	−0.00816613	+	0.0776955i	0.989680	+	0.143296i	$0.0457702\pi$
$434$		0			0
$435$	−3.85752	+	4.28422i	−0.184954	+	0.205412i
$436$		0			0
$437$	21.2118	−	15.4113i	1.01470	−	0.737221i
$438$		0			0
$439$	15.8235	−	27.4071i	0.755214	−	1.30807i	−0.190054	−	0.981774i	$-0.560866\pi$
$439$	15.8235	−	27.4071i	0.755214	−	1.30807i	0.945268	−	0.326295i	$-0.105800\pi$
$440$		0			0
$441$	−41.0761			−1.95600
$442$		0			0
$443$	17.4608	−	12.6860i	0.829586	−	0.602730i	−0.0898560	−	0.995955i	$-0.528641\pi$
$443$	17.4608	−	12.6860i	0.829586	−	0.602730i	0.919442	+	0.393225i	$0.128641\pi$
$444$		0			0
$445$	5.59455	+	1.18916i	0.265207	+	0.0563716i
$446$		0			0
$447$	−12.1703	−	8.84221i	−0.575633	−	0.418222i
$448$		0			0
$449$	31.5011	−	6.69577i	1.48663	−	0.315993i	0.608169	−	0.793808i	$-0.291904\pi$
$449$	31.5011	−	6.69577i	1.48663	−	0.315993i	0.878461	+	0.477815i	$0.158571\pi$
$450$		0			0
$451$	5.25478	+	4.02682i	0.247438	+	0.189615i
$452$		0			0
$453$	−29.3396	−	32.5849i	−1.37849	−	1.53097i
$454$		0			0
$455$	−5.84600	+	3.84950i	−0.274065	+	0.180468i
$456$		0			0
$457$	−18.5132	−	3.93510i	−0.866010	−	0.184076i	−0.246575	−	0.969124i	$-0.579305\pi$
$457$	−18.5132	−	3.93510i	−0.866010	−	0.184076i	−0.619435	+	0.785048i	$0.712638\pi$
$458$		0			0
$459$	101.769	+	45.3107i	4.75019	+	2.11492i
$460$		0			0
$461$	18.6097	+	32.2330i	0.866741	+	1.50124i	0.865309	+	0.501240i	$0.167122\pi$
$461$	18.6097	+	32.2330i	0.866741	+	1.50124i	0.00143202	+	0.999999i	$0.499544\pi$
$462$		0			0
$463$	3.07639			0.142972			0.0714861	−	0.997442i	$-0.477226\pi$
$463$	3.07639			0.142972			0.0714861	+	0.997442i	$0.477226\pi$
$464$		0			0
$465$	4.05561	+	38.5865i	0.188074	+	1.78941i
$466$		0			0
$467$	8.53556	+	26.2698i	0.394979	+	1.21562i	0.928978	+	0.370134i	$0.120688\pi$
$467$	8.53556	+	26.2698i	0.394979	+	1.21562i	−0.534000	+	0.845485i	$0.679312\pi$
$468$		0			0
$469$	−1.74090	−	1.26484i	−0.0803872	−	0.0584047i
$470$		0			0
$471$	−27.5687	−	30.6182i	−1.27030	−	1.41081i
$472$		0			0
$473$	40.2877	+	9.64507i	1.85243	+	0.443481i
$474$		0			0
$475$	−16.5917	+	3.52668i	−0.761280	+	0.161815i
$476$		0			0
$477$	1.03166	−	9.81556i	0.0472363	−	0.449424i
$478$		0			0
$479$	−29.4629	−	6.26253i	−1.34619	−	0.286142i	−0.522240	−	0.852799i	$-0.674903\pi$
$479$	−29.4629	−	6.26253i	−1.34619	−	0.286142i	−0.823954	+	0.566656i	$0.808237\pi$
$480$		0			0
$481$	16.8874	−	17.1036i	0.770001	−	0.779856i
$482$		0			0
$483$	−11.7457	+	20.3441i	−0.534447	+	0.925690i
$484$		0			0
$485$	−6.16915	−	10.6853i	−0.280127	−	0.485194i
$486$		0			0
$487$	−37.6755	−	16.7742i	−1.70724	−	0.760112i	−0.998506	−	0.0546344i	$-0.982601\pi$
$487$	−37.6755	−	16.7742i	−1.70724	−	0.760112i	−0.708732	−	0.705477i	$-0.750733\pi$
$488$		0			0
$489$	18.6499	+	57.3986i	0.843379	+	2.59565i
$490$		0			0
$491$	1.82736	−	0.813595i	0.0824678	−	0.0367170i	−0.365088	−	0.930973i	$-0.618961\pi$
$491$	1.82736	−	0.813595i	0.0824678	−	0.0367170i	0.447556	+	0.894256i	$0.352295\pi$
$492$		0			0
$493$	2.44620	−	7.52862i	0.110171	−	0.339072i
$494$		0			0
$495$	−36.2943	−	8.68903i	−1.63131	−	0.390543i
$496$		0			0
$497$	−9.78618	−	10.8686i	−0.438970	−	0.487526i
$498$		0			0
$499$	8.67304	+	6.30133i	0.388259	+	0.282086i	0.764741	−	0.644337i	$-0.222867\pi$
$499$	8.67304	+	6.30133i	0.388259	+	0.282086i	−0.376483	+	0.926424i	$0.622867\pi$
$500$		0			0
$501$	26.0507	−	28.9322i	1.16386	−	1.29260i
$502$		0			0
$503$	17.8515	+	7.94800i	0.795959	+	0.354384i	0.764091	−	0.645108i	$-0.223188\pi$
$503$	17.8515	+	7.94800i	0.795959	+	0.354384i	0.0318681	+	0.999492i	$0.489854\pi$
$504$		0			0
$505$	−3.25011	+	5.62935i	−0.144628	+	0.250503i
$506$		0			0
$507$	−32.8374	−	28.8193i	−1.45836	−	1.27991i
$508$		0			0
$509$	−1.29058	−	12.2790i	−0.0572039	−	0.544259i	−0.985168	−	0.171590i	$-0.945110\pi$
$509$	−1.29058	−	12.2790i	−0.0572039	−	0.544259i	0.927965	−	0.372668i	$-0.121557\pi$
$510$		0			0
$511$	6.59522	−	7.32474i	0.291755	−	0.324027i
$512$		0			0
$513$	9.98535	−	95.0042i	0.440864	−	4.19454i
$514$		0			0
$515$	2.99548	−	9.21913i	0.131996	−	0.406243i
$516$		0			0
$517$	4.16446	−	31.7887i	0.183153	−	1.39807i
$518$		0			0
$519$	18.3732	−	56.5468i	0.806493	−	2.48213i
$520$		0			0
$521$	15.1118	+	10.9794i	0.662060	+	0.481015i	0.867358	−	0.497685i	$-0.165816\pi$
$521$	15.1118	+	10.9794i	0.662060	+	0.481015i	−0.205298	+	0.978700i	$0.565816\pi$
$522$		0			0
$523$	−4.47665	−	0.951540i	−0.195750	−	0.0416080i	0.108993	−	0.994042i	$-0.465237\pi$
$523$	−4.47665	−	0.951540i	−0.195750	−	0.0416080i	−0.304743	+	0.952435i	$0.598571\pi$
$524$		0			0
$525$	12.2951	−	8.93294i	0.536604	−	0.389866i
$526$		0			0
$527$	−26.6381	−	46.1385i	−1.16037	−	2.00982i
$528$		0			0
$529$	−0.427786	−	0.740947i	−0.0185994	−	0.0322151i
$530$		0			0
$531$	0.361096	+	3.43560i	0.0156702	+	0.149092i
$532$		0			0
$533$	3.30807	+	6.39166i	0.143289	+	0.276854i
$534$		0			0
$535$	−0.194655	+	0.0866661i	−0.00841568	+	0.00374690i
$536$		0			0
$537$	−28.0862	+	5.96991i	−1.21201	+	0.257621i
$538$		0			0
$539$	−13.5293	+	9.31112i	−0.582748	+	0.401058i
$540$		0			0
$541$	9.54493	−	29.3763i	0.410369	−	1.26298i	−0.505960	−	0.862557i	$-0.668862\pi$
$541$	9.54493	−	29.3763i	0.410369	−	1.26298i	0.916328	−	0.400427i	$-0.131138\pi$
$542$		0			0
$543$	−7.26535	+	3.23474i	−0.311786	+	0.138816i
$544$		0			0
$545$	0.639791	+	1.96907i	0.0274056	+	0.0843459i
$546$		0			0
$547$	−16.9245	+	12.2964i	−0.723640	+	0.525755i	−0.887545	−	0.460721i	$-0.847591\pi$
$547$	−16.9245	+	12.2964i	−0.723640	+	0.525755i	0.163905	+	0.986476i	$0.447591\pi$
$548$		0			0
$549$	−34.9557	+	60.5451i	−1.49187	+	2.58400i
$550$		0			0
$551$	−6.78813			−0.289184
$552$		0			0
$553$	2.86450	+	1.27536i	0.121811	+	0.0542338i
$554$		0			0
$555$	20.3362	−	22.5856i	0.863223	−	0.958706i
$556$		0			0
$557$	−27.0753	+	12.0547i	−1.14722	+	0.510774i	−0.890172	−	0.455626i	$-0.849416\pi$
$557$	−27.0753	+	12.0547i	−1.14722	+	0.510774i	−0.257045	+	0.966399i	$0.582749\pi$
$558$		0			0
$559$	35.1782	+	28.1183i	1.48788	+	1.18928i
$560$		0			0
$561$	68.6020	−	12.7598i	2.89638	−	0.538721i
$562$		0			0
$563$	−23.7137	+	5.04050i	−0.999413	+	0.212432i	−0.678439	−	0.734656i	$-0.737343\pi$
$563$	−23.7137	+	5.04050i	−0.999413	+	0.212432i	−0.320974	+	0.947088i	$0.604010\pi$
$564$		0			0
$565$	−0.462467	+	4.40008i	−0.0194561	+	0.185113i
$566$		0			0
$567$	15.4435	+	47.5301i	0.648564	+	1.99608i
$568$		0			0
$569$	−2.81981	−	26.8287i	−0.118212	−	1.12472i	−0.879366	−	0.476146i	$-0.842034\pi$
$569$	−2.81981	−	26.8287i	−0.118212	−	1.12472i	0.761154	−	0.648571i	$-0.224633\pi$
$570$		0			0
$571$	25.0290			1.04743			0.523716	−	0.851893i	$-0.324545\pi$
$571$	25.0290			1.04743			0.523716	+	0.851893i	$0.324545\pi$
$572$		0			0
$573$	−21.8308			−0.911993
$574$		0			0
$575$	1.61321	+	15.3487i	0.0672757	+	0.640085i
$576$		0			0
$577$	−10.2323	−	31.4917i	−0.425975	−	1.31102i	−0.902057	−	0.431616i	$-0.857944\pi$
$577$	−10.2323	−	31.4917i	−0.425975	−	1.31102i	0.476082	−	0.879401i	$-0.342056\pi$
$578$		0			0
$579$	0.409691	−	3.89795i	0.0170262	−	0.161993i
$580$		0			0
$581$	19.3419	−	4.11124i	0.802435	−	0.170563i
$582$		0			0
$583$	−1.88519	−	3.46682i	−0.0780767	−	0.143581i
$584$		0			0
$585$	−31.6913	−	25.3311i	−1.31027	−	1.04731i
$586$		0			0
$587$	1.44187	−	0.641963i	0.0595125	−	0.0264967i	−0.376765	−	0.926309i	$-0.622963\pi$
$587$	1.44187	−	0.641963i	0.0595125	−	0.0264967i	0.436277	+	0.899812i	$0.356297\pi$
$588$		0			0
$589$	−30.5692	+	33.9506i	−1.25958	+	1.39891i
$590$		0			0
$591$	−31.0035	−	13.8036i	−1.27531	−	0.567805i
$592$		0			0
$593$	−38.1089			−1.56494			−0.782471	−	0.622686i	$-0.786041\pi$
$593$	−38.1089			−1.56494			−0.782471	+	0.622686i	$0.786041\pi$
$594$		0			0
$595$	6.07652	−	10.5248i	0.249113	−	0.431476i
$596$		0			0
$597$	16.3671	−	11.8914i	0.669862	−	0.486683i
$598$		0			0
$599$	−8.22083	−	25.3011i	−0.335894	−	1.03378i	−0.966280	−	0.257494i	$-0.917103\pi$
$599$	−8.22083	−	25.3011i	−0.335894	−	1.03378i	0.630386	−	0.776282i	$-0.282897\pi$
$600$		0			0
$601$	−20.0488	+	8.92632i	−0.817810	+	0.364112i	−0.772622	−	0.634866i	$-0.781055\pi$
$601$	−20.0488	+	8.92632i	−0.817810	+	0.364112i	−0.0451875	+	0.998979i	$0.514389\pi$
$602$		0			0
$603$	3.85425	−	11.8622i	0.156957	−	0.483065i
$604$		0			0
$605$	−13.9239	+	5.36526i	−0.566088	+	0.218129i
$606$		0			0
$607$	−6.46960	+	1.37516i	−0.262593	+	0.0558159i	−0.337327	−	0.941388i	$-0.609523\pi$
$607$	−6.46960	+	1.37516i	−0.262593	+	0.0558159i	0.0747336	+	0.997204i	$0.476189\pi$
$608$		0			0
$609$	5.55609	−	2.47373i	0.225144	−	0.100241i
$610$		0			0
$611$	18.7962	−	29.3505i	0.760413	−	1.18740i
$612$		0			0
$613$	3.04252	+	28.9477i	0.122886	+	1.16919i	0.866008	+	0.500030i	$0.166678\pi$
$613$	3.04252	+	28.9477i	0.122886	+	1.16919i	−0.743122	+	0.669156i	$0.766656\pi$
$614$		0			0
$615$	4.55011	+	7.88101i	0.183478	+	0.317793i
$616$		0			0
$617$	5.15624	+	8.93087i	0.207582	+	0.359543i	0.950952	−	0.309337i	$-0.100107\pi$
$617$	5.15624	+	8.93087i	0.207582	+	0.359543i	−0.743370	+	0.668880i	$0.766774\pi$
$618$		0			0
$619$	27.0999	−	19.6892i	1.08924	−	0.791377i	0.109967	−	0.993935i	$-0.464926\pi$
$619$	27.0999	−	19.6892i	1.08924	−	0.791377i	0.979270	+	0.202558i	$0.0649255\pi$
$620$		0			0
$621$	−85.0165	−	18.0708i	−3.41160	−	0.725157i
$622$		0			0
$623$	−4.88158	−	3.54667i	−0.195576	−	0.142094i
$624$		0			0
$625$	0.242137	−	0.745220i	0.00968547	−	0.0298088i
$626$		0			0
$627$	−28.5848	−	52.5668i	−1.14157	−	2.09931i
$628$		0			0
$629$	−12.8959	+	39.6896i	−0.514194	+	1.58253i
$630$		0			0
$631$	0.920292	−	8.75599i	0.0366362	−	0.348570i	−0.960813	−	0.277196i	$-0.910595\pi$
$631$	0.920292	−	8.75599i	0.0366362	−	0.348570i	0.997450	−	0.0713744i	$-0.0227385\pi$
$632$		0			0
$633$	6.03860	−	6.70655i	0.240013	−	0.266561i
$634$		0			0
$635$	1.61819	+	15.3960i	0.0642158	+	0.610972i
$636$		0			0
$637$	−17.6165	+	2.90513i	−0.697993	+	0.115105i
$638$		0			0
$639$	42.3852	−	73.4134i	1.67673	−	2.90419i
$640$		0			0
$641$	−24.2818	−	10.8110i	−0.959074	−	0.427007i	−0.133342	−	0.991070i	$-0.542571\pi$
$641$	−24.2818	−	10.8110i	−0.959074	−	0.427007i	−0.825732	+	0.564063i	$0.809238\pi$
$642$		0			0
$643$	11.9960	−	13.3229i	0.473075	−	0.525403i	−0.458626	−	0.888629i	$-0.651658\pi$
$643$	11.9960	−	13.3229i	0.473075	−	0.525403i	0.931701	+	0.363227i	$0.118325\pi$
$644$		0			0
$645$	46.0689	+	33.4710i	1.81396	+	1.31792i
$646$		0			0
$647$	29.6277	+	32.9049i	1.16479	+	1.29363i	0.948312	+	0.317338i	$0.102789\pi$
$647$	29.6277	+	32.9049i	1.16479	+	1.29363i	0.216474	+	0.976288i	$0.430544\pi$
$648$		0			0
$649$	0.897716	+	1.04974i	0.0352384	+	0.0412057i
$650$		0			0
$651$	12.6487	−	38.9286i	0.495741	−	1.52573i
$652$		0			0
$653$	43.7162	−	19.4637i	1.71075	−	0.761673i	0.712551	−	0.701620i	$-0.247540\pi$
$653$	43.7162	−	19.4637i	1.71075	−	0.761673i	0.998195	−	0.0600531i	$-0.0191270\pi$
$654$		0			0
$655$	−0.245446	−	0.755405i	−0.00959036	−	0.0295161i
$656$		0			0
$657$	52.1904	+	23.2367i	2.03614	+	0.906549i
$658$		0			0
$659$	1.81039	+	3.13569i	0.0705227	+	0.122149i	0.899131	−	0.437681i	$-0.144200\pi$
$659$	1.81039	+	3.13569i	0.0705227	+	0.122149i	−0.828608	+	0.559830i	$0.810867\pi$
$660$		0			0
$661$	−19.9845	+	34.6142i	−0.777308	+	1.34634i	0.156181	+	0.987728i	$0.450082\pi$
$661$	−19.9845	+	34.6142i	−0.777308	+	1.34634i	−0.933488	+	0.358608i	$0.883252\pi$
$662$		0			0
$663$	73.3959	+	19.1670i	2.85046	+	0.744385i
$664$		0			0
$665$	−10.1937	−	2.16673i	−0.395293	−	0.0840222i
$666$		0			0
$667$	−0.645587	+	6.14235i	−0.0249972	+	0.237833i
$668$		0			0
$669$	−13.8625	+	2.94657i	−0.535956	+	0.113921i
$670$		0			0
$671$	2.21093	+	27.8656i	0.0853522	+	1.07574i
$672$		0			0
$673$	−5.26576	−	5.84822i	−0.202980	−	0.225432i	0.633057	−	0.774105i	$-0.281800\pi$
$673$	−5.26576	−	5.84822i	−0.202980	−	0.225432i	−0.836037	+	0.548673i	$0.815133\pi$
$674$		0			0
$675$	45.4909	+	33.0510i	1.75094	+	1.27214i
$676$		0			0
$677$	−14.1789	−	43.6382i	−0.544940	−	1.67715i	−0.721133	−	0.692797i	$-0.756378\pi$
$677$	−14.1789	−	43.6382i	−0.544940	−	1.67715i	0.176193	−	0.984356i	$-0.443622\pi$
$678$		0			0
$679$	1.36060	+	12.9453i	0.0522152	+	0.496794i
$680$		0			0
$681$	6.52079			0.249877
$682$		0			0
$683$	1.21301	+	2.10099i	0.0464145	+	0.0803922i	0.888299	−	0.459265i	$-0.151887\pi$
$683$	1.21301	+	2.10099i	0.0464145	+	0.0803922i	−0.841885	+	0.539657i	$0.818554\pi$
$684$		0			0
$685$	4.92244	+	2.19161i	0.188077	+	0.0837372i
$686$		0			0
$687$	32.5497	+	6.91865i	1.24185	+	0.263963i
$688$		0			0
$689$	−0.251758	−	4.28262i	−0.00959123	−	0.163155i
$690$		0			0
$691$	8.57028	+	9.51826i	0.326029	+	0.362092i	0.883769	−	0.467924i	$-0.154998\pi$
$691$	8.57028	+	9.51826i	0.326029	+	0.362092i	−0.557740	+	0.830016i	$0.688331\pi$
$692$		0			0
$693$	31.2507	+	23.9479i	1.18712	+	0.909706i
$694$		0			0
$695$	3.37955	−	0.718346i	0.128194	−	0.0272484i
$696$		0			0
$697$	−10.1093	−	7.34482i	−0.382916	−	0.278205i
$698$		0			0
$699$	16.1231	+	3.42707i	0.609832	+	0.129624i
$700$		0			0
$701$	−20.5920	+	14.9610i	−0.777750	+	0.565068i	−0.904303	−	0.426891i	$-0.859609\pi$
$701$	−20.5920	+	14.9610i	−0.777750	+	0.565068i	0.126553	+	0.991960i	$0.459609\pi$
$702$		0			0
$703$	35.7858			1.34969
$704$		0			0
$705$	22.0351	−	38.1658i	0.829888	−	1.43741i
$706$		0			0
$707$	5.54787	−	4.03076i	0.208649	−	0.151592i
$708$		0			0
$709$	−0.0690171	+	0.0766513i	−0.00259199	+	0.00287870i	−0.744439	−	0.667690i	$-0.767283\pi$
$709$	−0.0690171	+	0.0766513i	−0.00259199	+	0.00287870i	0.741847	+	0.670569i	$0.233950\pi$
$710$		0			0
$711$	−1.89975	+	18.0749i	−0.0712461	+	0.677861i
$712$		0			0
$713$	27.8135	+	30.8900i	1.04162	+	1.15684i
$714$		0			0
$715$	−16.1803	−	1.15958i	−0.605108	−	0.0433659i
$716$		0			0
$717$	13.4863	+	14.9781i	0.503656	+	0.559367i
$718$		0			0
$719$	1.17899	−	11.2173i	0.0439687	−	0.418335i	−0.950293	−	0.311358i	$-0.899216\pi$
$719$	1.17899	−	11.2173i	0.0439687	−	0.418335i	0.994262	−	0.106977i	$-0.0341171\pi$
$720$		0			0
$721$	−6.84283	+	7.59973i	−0.254840	+	0.283029i
$722$		0			0
$723$	−41.1397	+	29.8897i	−1.53000	+	1.11161i
$724$		0			0
$725$	1.99783	−	3.46034i	0.0741975	−	0.128514i
$726$		0			0
$727$	−34.1274			−1.26572			−0.632858	−	0.774268i	$-0.718118\pi$
$727$	−34.1274			−1.26572			−0.632858	+	0.774268i	$0.718118\pi$
$728$		0			0
$729$	−89.1959	+	64.8046i	−3.30355	+	2.40017i
$730$		0			0
$731$	−76.4831	−	16.2570i	−2.82883	−	0.601287i
$732$		0			0
$733$	−21.9888	−	15.9758i	−0.812175	−	0.590080i	0.102285	−	0.994755i	$-0.467385\pi$
$733$	−21.9888	−	15.9758i	−0.812175	−	0.590080i	−0.914461	+	0.404675i	$0.867385\pi$
$734$		0			0
$735$	−22.0827	+	4.69382i	−0.814532	+	0.173134i
$736$		0			0
$737$	−1.41943	−	4.78074i	−0.0522855	−	0.176101i
$738$		0			0
$739$	−1.60732	−	1.78511i	−0.0591261	−	0.0656662i	0.712856	−	0.701310i	$-0.247401\pi$
$739$	−1.60732	−	1.78511i	−0.0591261	−	0.0656662i	−0.771982	+	0.635644i	$0.780735\pi$
$740$		0			0
$741$	−3.81736	−	64.9366i	−0.140234	−	2.38550i
$742$		0			0
$743$	−23.8396	−	5.06726i	−0.874589	−	0.185900i	−0.251317	−	0.967905i	$-0.580864\pi$
$743$	−23.8396	−	5.06726i	−0.874589	−	0.185900i	−0.623272	+	0.782005i	$0.714197\pi$
$744$		0			0
$745$	−5.54702	−	2.46969i	−0.203227	−	0.0904826i
$746$		0			0
$747$	57.3068	+	99.2583i	2.09675	+	3.63167i
$748$		0			0
$749$	0.224790			0.00821365
$750$		0			0
$751$	−0.972408	−	9.25184i	−0.0354837	−	0.337604i	−0.997833	−	0.0657904i	$-0.979043\pi$
$751$	−0.972408	−	9.25184i	−0.0354837	−	0.337604i	0.962350	−	0.271814i	$-0.0876236\pi$
$752$		0			0
$753$	30.5380	+	93.9864i	1.11287	+	3.42506i
$754$		0			0
$755$	−14.3182	−	10.4028i	−0.521092	−	0.378596i
$756$		0			0
$757$	33.6635	+	37.3871i	1.22352	+	1.35886i	0.912826	+	0.408349i	$0.133895\pi$
$757$	33.6635	+	37.3871i	1.22352	+	1.35886i	0.310696	+	0.950509i	$0.399438\pi$
$758$		0			0
$759$	−50.2845	+	20.8661i	−1.82521	+	0.757390i
$760$		0			0
$761$	−16.2184	+	3.44732i	−0.587915	+	0.124965i	−0.492258	−	0.870449i	$-0.663828\pi$
$761$	−16.2184	+	3.44732i	−0.587915	+	0.124965i	−0.0956566	+	0.995414i	$0.530495\pi$
$762$		0			0
$763$	0.228314	−	2.17226i	0.00826551	−	0.0786410i
$764$		0			0
$765$	68.9020	+	14.6456i	2.49116	+	0.529512i
$766$		0			0
$767$	0.397850	+	1.44791i	0.0143655	+	0.0522809i
$768$		0			0
$769$	−2.12113	+	3.67391i	−0.0764900	+	0.132485i	−0.901733	−	0.432293i	$-0.857705\pi$
$769$	−2.12113	+	3.67391i	−0.0764900	+	0.132485i	0.825243	+	0.564777i	$0.191038\pi$
$770$		0			0
$771$	22.7047	+	39.3256i	0.817688	+	1.41628i
$772$		0			0
$773$	−36.9279	−	16.4414i	−1.32820	−	0.591355i	−0.384800	−	0.923000i	$-0.625730\pi$
$773$	−36.9279	−	16.4414i	−1.32820	−	0.591355i	−0.943404	+	0.331645i	$0.892396\pi$
$774$		0			0
$775$	−8.30987	−	25.5751i	−0.298499	−	0.918686i
$776$		0			0
$777$	−29.2907	+	13.0411i	−1.05080	+	0.467846i
$778$		0			0
$779$	−3.31121	+	10.1908i	−0.118636	+	0.365125i
$780$		0			0
$781$	−2.68085	−	33.7881i	−0.0959282	−	1.20904i
$782$		0			0
$783$	15.0571	+	16.7226i	0.538096	+	0.597616i
$784$		0			0
$785$	−13.4540	−	9.77491i	−0.480194	−	0.348881i
$786$		0			0
$787$	−18.1933	+	20.2057i	−0.648521	+	0.720255i	−0.974316	−	0.225185i	$-0.927701\pi$
$787$	−18.1933	+	20.2057i	−0.648521	+	0.720255i	0.325795	+	0.945440i	$0.394368\pi$
$788$		0			0
$789$	−54.9578	−	24.4688i	−1.95655	−	0.871111i
$790$		0			0
$791$	2.33377	−	4.04220i	0.0829792	−	0.143724i
$792$		0			0
$793$	−10.7096	+	28.4386i	−0.380308	+	1.00988i
$794$		0			0
$795$	−0.567014	−	5.39478i	−0.0201099	−	0.191333i
$796$		0			0
$797$	−3.10607	+	3.44964i	−0.110023	+	0.122193i	−0.795640	−	0.605769i	$-0.792865\pi$
$797$	−3.10607	+	3.44964i	−0.110023	+	0.122193i	0.685618	+	0.727962i	$0.259532\pi$
$798$		0			0
$799$	−6.32543	+	60.1824i	−0.223778	+	2.12910i
$800$		0			0
$801$	10.8075	−	33.2622i	0.381866	−	1.17526i
$802$		0			0
$803$	22.4573	−	4.17702i	0.792502	−	0.147404i
$804$		0			0
$805$	−2.93007	+	9.01784i	−0.103272	+	0.317837i
$806$		0			0
$807$	15.1356	+	10.9967i	0.532800	+	0.387102i
$808$		0			0
$809$	−25.0420	−	5.32284i	−0.880429	−	0.187141i	−0.254549	−	0.967060i	$-0.581927\pi$
$809$	−25.0420	−	5.32284i	−0.880429	−	0.187141i	−0.625881	+	0.779919i	$0.715260\pi$
$810$		0			0
$811$	33.8152	−	24.5682i	1.18741	−	0.862706i	0.194425	−	0.980917i	$-0.437716\pi$
$811$	33.8152	−	24.5682i	1.18741	−	0.862706i	0.992988	+	0.118211i	$0.0377160\pi$
$812$		0			0
$813$	−42.9611	−	74.4109i	−1.50671	−	2.60970i
$814$		0			0
$815$	12.1802	+	21.0966i	0.426652	+	0.738983i
$816$		0			0
$817$	7.00869	+	66.6833i	0.245203	+	2.33295i
$818$		0			0
$819$	19.6735	+	38.0119i	0.687447	+	1.32824i
$820$		0			0
$821$	−1.56816	+	0.698189i	−0.0547291	+	0.0243670i	−0.433919	−	0.900952i	$-0.642869\pi$
$821$	−1.56816	+	0.698189i	−0.0547291	+	0.0243670i	0.379190	+	0.925319i	$0.376203\pi$
$822$		0			0
$823$	−9.34935	+	1.98727i	−0.325898	+	0.0692717i	−0.367955	−	0.929843i	$-0.619942\pi$
$823$	−9.34935	+	1.98727i	−0.325898	+	0.0692717i	0.0420574	+	0.999115i	$0.486609\pi$
$824$		0			0
$825$	35.2095	+	0.899544i	1.22584	+	0.0313181i
$826$		0			0
$827$	13.7277	−	42.2497i	0.477360	−	1.46916i	−0.365387	−	0.930856i	$-0.619063\pi$
$827$	13.7277	−	42.2497i	0.477360	−	1.46916i	0.842748	−	0.538309i	$-0.180937\pi$
$828$		0			0
$829$	−22.0943	+	9.83702i	−0.767367	+	0.341654i	−0.752808	−	0.658240i	$-0.771301\pi$
$829$	−22.0943	+	9.83702i	−0.767367	+	0.341654i	−0.0145592	+	0.999894i	$0.504634\pi$
$830$		0			0
$831$	−6.67026	−	20.5290i	−0.231389	−	0.712142i
$832$		0			0
$833$	25.0794	−	18.2212i	0.868948	−	0.631328i
$834$		0			0
$835$	7.85718	−	13.6090i	0.271909	−	0.470960i
$836$		0			0
$837$	151.444			5.23468
$838$		0			0
$839$	3.51478	+	1.56488i	0.121344	+	0.0540256i	0.466510	−	0.884516i	$-0.345511\pi$
$839$	3.51478	+	1.56488i	0.121344	+	0.0540256i	−0.345167	+	0.938541i	$0.612178\pi$
$840$		0			0
$841$	−18.3348	+	20.3629i	−0.632236	+	0.702169i
$842$		0			0
$843$	57.6082	−	25.6488i	1.98413	−	0.883392i
$844$		0			0
$845$	−15.3832	−	8.62253i	−0.529198	−	0.296624i
$846$		0			0
$847$	15.7216	+	0.803848i	0.540201	+	0.0276205i
$848$		0			0
$849$	−74.6325	+	15.8636i	−2.56138	+	0.544438i
$850$		0			0
$851$	3.40342	−	32.3814i	0.116668	−	1.11002i
$852$		0			0
$853$	−5.98756	−	18.4278i	−0.205010	−	0.630956i	−0.999713	−	0.0239577i	$-0.992373\pi$
$853$	−5.98756	−	18.4278i	−0.205010	−	0.630956i	0.794703	−	0.606999i	$-0.207627\pi$
$854$		0			0
$855$	−6.31398	−	60.0735i	−0.215933	−	2.05447i
$856$		0			0
$857$	−24.4992			−0.836878			−0.418439	−	0.908245i	$-0.637423\pi$
$857$	−24.4992			−0.836878			−0.418439	+	0.908245i	$0.637423\pi$
$858$		0			0
$859$	−9.20783			−0.314167			−0.157084	−	0.987585i	$-0.550209\pi$
$859$	−9.20783			−0.314167			−0.157084	+	0.987585i	$0.550209\pi$
$860$		0			0
$861$	−1.00352	−	9.54788i	−0.0342000	−	0.325391i
$862$		0			0
$863$	14.3908	+	44.2904i	0.489869	+	1.50766i	0.824803	+	0.565421i	$0.191286\pi$
$863$	14.3908	+	44.2904i	0.489869	+	1.50766i	−0.334933	+	0.942242i	$0.608714\pi$
$864$		0			0
$865$	2.50856	−	23.8673i	0.0852935	−	0.811514i
$866$		0			0
$867$	−72.9439	+	15.5047i	−2.47731	+	0.526567i
$868$		0			0
$869$	3.47149	+	6.38399i	0.117762	+	0.216562i
$870$		0			0
$871$	0.814037	−	5.35999i	0.0275826	−	0.181616i
$872$		0			0
$873$	−68.9238	+	30.6869i	−2.33272	+	1.03859i
$874$		0			0
$875$	10.5997	−	11.7721i	0.358335	−	0.397971i
$876$		0			0
$877$	−29.7216	−	13.2329i	−1.00363	−	0.446843i	−0.161935	−	0.986801i	$-0.551773\pi$
$877$	−29.7216	−	13.2329i	−1.00363	−	0.446843i	−0.841692	+	0.539958i	$0.818440\pi$
$878$		0			0
$879$	−28.7611			−0.970089
$880$		0			0
$881$	2.91824	−	5.05454i	0.0983181	−	0.170292i	−0.812671	−	0.582723i	$-0.801987\pi$
$881$	2.91824	−	5.05454i	0.0983181	−	0.170292i	0.910989	+	0.412432i	$0.135320\pi$
$882$		0			0
$883$	−7.35838	+	5.34618i	−0.247629	+	0.179913i	−0.704675	−	0.709530i	$-0.748907\pi$
$883$	−7.35838	+	5.34618i	−0.247629	+	0.179913i	0.457046	+	0.889443i	$0.348907\pi$
$884$		0			0
$885$	0.586718	+	1.80573i	0.0197223	+	0.0606990i
$886$		0			0
$887$	−0.737068	+	0.328164i	−0.0247483	+	0.0110187i	−0.419073	−	0.907952i	$-0.637645\pi$
$887$	−0.737068	+	0.328164i	−0.0247483	+	0.0110187i	0.394325	+	0.918971i	$0.370978\pi$
$888$		0			0
$889$	5.04682	−	15.5325i	0.169265	−	0.520944i
$890$		0			0
$891$	−38.5923	+	109.202i	−1.29289	+	3.65841i
$892$		0			0
$893$	50.7576	−	10.7889i	1.69854	−	0.361035i
$894$		0			0
$895$	−10.5878	+	4.71401i	−0.353912	+	0.157572i
$896$		0			0
$897$	−59.1220	−	2.72161i	−1.97403	−	0.0908719i
$898$		0			0
$899$	−1.12489	−	10.7026i	−0.0375171	−	0.356952i
$900$		0			0
$901$	3.72427	+	6.45062i	0.124073	+	0.214901i
$902$		0			0
$903$	−30.0373	−	52.0262i	−0.999580	−	1.73132i
$904$		0			0
$905$	−2.59700	+	1.88683i	−0.0863272	+	0.0627204i
$906$		0			0
$907$	−18.7140	−	3.97778i	−0.621387	−	0.132080i	−0.113549	−	0.993532i	$-0.536222\pi$
$907$	−18.7140	−	3.97778i	−0.621387	−	0.132080i	−0.507838	+	0.861452i	$0.669555\pi$
$908$		0			0
$909$	32.1565	+	23.3631i	1.06656	+	0.774904i
$910$		0			0
$911$	14.5025	−	44.6342i	0.480490	−	1.47880i	−0.357917	−	0.933753i	$-0.616513\pi$
$911$	14.5025	−	44.6342i	0.480490	−	1.47880i	0.838407	−	0.545044i	$-0.183487\pi$
$912$		0			0
$913$	41.3751	+	19.7026i	1.36932	+	0.652059i
$914$		0			0
$915$	−11.8738	+	36.5438i	−0.392535	+	1.20810i
$916$		0			0
$917$	−0.0875889	+	0.833353i	−0.00289244	+	0.0275197i
$918$		0			0
$919$	28.0979	−	31.2059i	0.926864	−	1.02939i	−0.0726227	−	0.997359i	$-0.523137\pi$
$919$	28.0979	−	31.2059i	0.926864	−	1.02939i	0.999487	−	0.0320276i	$-0.0101964\pi$
$920$		0			0
$921$	−10.4019	−	98.9674i	−0.342754	−	3.26109i
$922$		0			0
$923$	12.9858	−	34.4829i	0.427433	−	1.13502i
$924$		0			0
$925$	−10.5322	+	18.2423i	−0.346296	+	0.599803i
$926$		0			0
$927$	−54.1499	−	24.1091i	−1.77851	−	0.791846i
$928$		0			0
$929$	−17.7598	+	19.7242i	−0.582679	+	0.647130i	−0.960346	−	0.278811i	$-0.910060\pi$
$929$	−17.7598	+	19.7242i	−0.582679	+	0.647130i	0.377667	+	0.925941i	$0.376726\pi$
$930$		0			0
$931$	−21.5059	−	15.6249i	−0.704827	−	0.512087i
$932$		0			0
$933$	20.7356	+	23.0292i	0.678852	+	0.753942i
$934$		0			0
$935$	26.0142	−	10.7949i	0.850755	−	0.353030i
$936$		0			0
$937$	0.887109	−	2.73024i	0.0289806	−	0.0891931i	−0.935520	−	0.353274i	$-0.885068\pi$
$937$	0.887109	−	2.73024i	0.0289806	−	0.0891931i	0.964501	+	0.264081i	$0.0850685\pi$
$938$		0			0
$939$	−24.5109	+	10.9130i	−0.799884	+	0.356131i
$940$		0			0
$941$	4.91154	+	15.1162i	0.160112	+	0.492773i	0.998643	−	0.0520803i	$-0.0165852\pi$
$941$	4.91154	+	15.1162i	0.160112	+	0.492773i	−0.838531	+	0.544854i	$0.816585\pi$
$942$		0			0
$943$	8.90644	+	3.96540i	0.290034	+	0.129131i
$944$		0			0
$945$	17.2733	+	29.9182i	0.561901	+	0.973240i
$946$		0			0
$947$	1.42496	−	2.46811i	0.0463051	−	0.0802028i	−0.841944	−	0.539565i	$-0.818589\pi$
$947$	1.42496	−	2.46811i	0.0463051	−	0.0802028i	0.888249	+	0.459362i	$0.151922\pi$
$948$		0			0
$949$	24.0266	+	6.27445i	0.779938	+	0.203677i
$950$		0			0
$951$	−37.1227	−	7.89068i	−1.20379	−	0.255873i
$952$		0			0
$953$	3.44190	−	32.7475i	0.111494	−	1.06079i	−0.785533	−	0.618819i	$-0.787611\pi$
$953$	3.44190	−	32.7475i	0.111494	−	1.06079i	0.897027	−	0.441975i	$-0.145722\pi$
$954$		0			0
$955$	−8.61908	+	1.83204i	−0.278907	+	0.0592835i
$956$		0			0
$957$	13.7076	+	3.28167i	0.443104	+	0.106081i
$958$		0			0
$959$	−3.80367	−	4.22440i	−0.122827	−	0.136413i
$960$		0			0
$961$	−33.5149	−	24.3500i	−1.08112	−	0.785483i
$962$		0			0
$963$	0.402626	+	1.23916i	0.0129745	+	0.0399313i
$964$		0			0
$965$	−0.165365	−	1.57335i	−0.00532330	−	0.0506478i
$966$		0			0
$967$	−52.4181			−1.68565			−0.842826	−	0.538187i	$-0.819110\pi$
$967$	−52.4181			−1.68565			−0.842826	+	0.538187i	$0.819110\pi$
$968$		0			0
$969$	56.4703	+	97.8094i	1.81409	+	3.14209i
$970$		0			0
$971$	−33.1244	−	14.7479i	−1.06301	−	0.473284i	−0.200697	−	0.979653i	$-0.564321\pi$
$971$	−33.1244	−	14.7479i	−1.06301	−	0.473284i	−0.862317	+	0.506370i	$0.830987\pi$
$972$		0			0
$973$	−3.56534	−	0.757836i	−0.114299	−	0.0242951i
$974$		0			0
$975$	34.2258	+	17.1657i	1.09610	+	0.549741i
$976$		0			0
$977$	−7.43344	−	8.25567i	−0.237817	−	0.264122i	0.612408	−	0.790542i	$-0.290201\pi$
$977$	−7.43344	−	8.25567i	−0.237817	−	0.264122i	−0.850225	+	0.526419i	$0.823534\pi$
$978$		0			0
$979$	−3.98018	−	13.4055i	−0.127207	−	0.428441i
$980$		0			0
$981$	12.3835	−	2.63220i	0.395375	−	0.0840396i
$982$		0			0
$983$	−14.1468	−	10.2782i	−0.451212	−	0.327825i	0.338862	−	0.940836i	$-0.389958\pi$
$983$	−14.1468	−	10.2782i	−0.451212	−	0.327825i	−0.790074	+	0.613011i	$0.789958\pi$
$984$		0			0
$985$	−13.3990	−	2.84804i	−0.426927	−	0.0907462i
$986$		0			0
$987$	−37.6135	+	27.3278i	−1.19725	+	0.869853i
$988$		0			0
$989$	61.0060			1.93988
$990$		0			0
$991$	−17.1936	+	29.7802i	−0.546173	+	0.945999i	0.452359	+	0.891836i	$0.350582\pi$
$991$	−17.1936	+	29.7802i	−0.546173	+	0.945999i	−0.998532	+	0.0541632i	$0.982751\pi$
$992$		0			0
$993$	−20.5309	+	14.9166i	−0.651528	+	0.473363i
$994$		0			0
$995$	5.46404	−	6.06843i	0.173222	−	0.192382i
$996$		0			0
$997$	−1.71817	+	16.3473i	−0.0544150	+	0.517724i	0.933034	+	0.359787i	$0.117151\pi$
$997$	−1.71817	+	16.3473i	−0.0544150	+	0.517724i	−0.987449	+	0.157936i	$0.949516\pi$
$998$		0			0
$999$	−79.3782	−	88.1584i	−2.51142	−	2.78921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.9.1	✓	112
11.5	even	5	inner	572.2.bg.a.269.14	yes	112
13.3	even	3	inner	572.2.bg.a.185.14	yes	112
143.16	even	15	inner	572.2.bg.a.445.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.1	✓	112	1.1	even	1	trivial
572.2.bg.a.185.14	yes	112	13.3	even	3	inner
572.2.bg.a.269.14	yes	112	11.5	even	5	inner
572.2.bg.a.445.1	yes	112	143.16	even	15	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.351299 - 3.34239i) q^{3} +(-0.419191 - 1.29014i) q^{5} +(-0.149591 + 1.42326i) q^{7} +(-8.11369 + 1.72462i) q^{9} +O(q^{10})\)	\(q+(-0.351299 - 3.34239i) q^{3} +(-0.419191 - 1.29014i) q^{5} +(-0.149591 + 1.42326i) q^{7} +(-8.11369 + 1.72462i) q^{9} +(-2.28148 + 2.40725i) q^{11} +(-3.35779 + 1.31349i) q^{13} +(-4.16488 + 1.85432i) q^{15} +(4.18885 - 4.65218i) q^{17} +(-4.90405 - 2.18342i) q^{19} +4.80965 q^{21} +(-2.44211 + 4.22986i) q^{23} +(2.55635 - 1.85730i) q^{25} +(5.49903 + 16.9243i) q^{27} +(1.15520 - 0.514327i) q^{29} +(2.62985 - 8.09386i) q^{31} +(8.84743 + 6.77992i) q^{33} +(1.89892 - 0.403627i) q^{35} +(-6.08999 + 2.71144i) q^{37} +(5.56978 + 10.7616i) q^{39} +(-0.208648 - 1.98515i) q^{41} +(-6.24522 - 10.8170i) q^{43} +(5.62618 + 9.74483i) q^{45} +(-7.82041 + 5.68186i) q^{47} +(4.84373 + 1.02957i) q^{49} +(-17.0209 - 12.3664i) q^{51} +(-0.367680 + 1.13160i) q^{53} +(4.06206 + 1.93433i) q^{55} +(-5.57505 + 17.1583i) q^{57} +(0.0435320 - 0.414180i) q^{59} +(5.63957 - 6.26337i) q^{61} +(-1.24085 - 11.8059i) q^{63} +(3.10214 + 3.78141i) q^{65} +(-0.751821 + 1.30219i) q^{67} +(14.9957 + 6.67652i) q^{69} +(-6.83820 + 7.59459i) q^{71} +(-5.57192 - 4.04824i) q^{73} +(-7.10584 - 7.89184i) q^{75} +(-3.08486 - 3.60725i) q^{77} +(0.677064 - 2.08379i) q^{79} +(31.9022 - 14.2038i) q^{81} +(-4.26977 - 13.1410i) q^{83} +(-7.75789 - 3.45404i) q^{85} +(-2.12490 - 3.68043i) q^{87} +(-2.10815 + 3.65142i) q^{89} +(-1.36715 - 4.97551i) q^{91} +(-27.9767 - 5.94662i) q^{93} +(-0.761183 + 7.24217i) q^{95} +(8.89672 - 1.89106i) q^{97} +(14.3596 - 23.4663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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