LMFDB - Embedded newform 360.2.b.d.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(251,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("360.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.b (of order $2$, degree $1$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.2580992.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + x^{4} + 2x^{2} - 8x + 8 $ x^6 - 2x^5 + x^4 + 2x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.3
Root			$0.681664 + 1.23909i$ of defining polynomial
Character	$\chi$	$=$	360.251
Dual form			360.2.b.d.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.681664 - 1.23909i) q^{2} +(-1.07067 - 1.68928i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(-2.82300 + 0.175128i) q^{8} +O(q^{10})$	\(q+(0.681664 - 1.23909i) q^{2} +(-1.07067 - 1.68928i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(-2.82300 + 0.175128i) q^{8} +(0.681664 - 1.23909i) q^{10} -6.37056i q^{11} +3.54213i q^{13} +(-1.75233 - 0.964019i) q^{14} +(-1.70734 + 3.61732i) q^{16} -3.92870i q^{17} +1.27334 q^{19} +(-1.07067 - 1.68928i) q^{20} +(-7.89367 - 4.34258i) q^{22} +6.28267 q^{23} +1.00000 q^{25} +(4.38900 + 2.41454i) q^{26} +(-2.38900 + 1.51415i) q^{28} -9.00933 q^{29} +3.92870i q^{31} +(3.31834 + 4.58134i) q^{32} +(-4.86799 - 2.67805i) q^{34} -1.41421i q^{35} +2.51448i q^{37} +(0.867993 - 1.57778i) q^{38} +(-2.82300 + 0.175128i) q^{40} +5.27029i q^{41} +1.55602 q^{43} +(-10.7617 + 6.82075i) q^{44} +(4.28267 - 7.78477i) q^{46} +9.73599 q^{47} +5.00000 q^{49} +(0.681664 - 1.23909i) q^{50} +(5.98365 - 3.79245i) q^{52} +5.55602 q^{53} -6.37056i q^{55} +(0.247668 + 3.99233i) q^{56} +(-6.14134 + 11.1633i) q^{58} -0.313944i q^{59} +12.7411i q^{61} +(4.86799 + 2.67805i) q^{62} +(7.93866 - 0.988770i) q^{64} +3.54213i q^{65} -7.00933 q^{67} +(-6.63667 + 4.20633i) q^{68} +(-1.75233 - 0.964019i) q^{70} -0.990671 q^{71} +12.0187 q^{73} +(3.11566 + 1.71403i) q^{74} +(-1.36333 - 2.15103i) q^{76} -9.00933 q^{77} -8.18453i q^{79} +(-1.70734 + 3.61732i) q^{80} +(6.53034 + 3.59257i) q^{82} +5.02897i q^{83} -3.92870i q^{85} +(1.06068 - 1.92804i) q^{86} +(1.11566 + 17.9841i) q^{88} -0.386566i q^{89} +5.00933 q^{91} +(-6.72666 - 10.6132i) q^{92} +(6.63667 - 12.0637i) q^{94} +1.27334 q^{95} +10.4626 q^{97} +(3.40832 - 6.19543i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8} + 2 q^{10} - 6 q^{16} + 16 q^{19} + 2 q^{20} - 20 q^{22} + 4 q^{23} + 6 q^{25} + 20 q^{26} - 8 q^{28} - 12 q^{29} + 22 q^{32} - 4 q^{34} - 20 q^{38} + 2 q^{40} - 16 q^{43} - 12 q^{44} - 8 q^{46} + 8 q^{47} + 30 q^{49} + 2 q^{50} - 4 q^{52} + 8 q^{53} + 12 q^{56} - 20 q^{58} + 4 q^{62} + 14 q^{64} - 44 q^{68} - 48 q^{71} - 12 q^{73} + 4 q^{74} - 4 q^{76} - 12 q^{77} - 6 q^{80} + 16 q^{82} - 40 q^{86} - 8 q^{88} - 12 q^{91} - 32 q^{92} + 44 q^{94} + 16 q^{95} + 4 q^{97} + 10 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8 + 2 * q^10 - 6 * q^16 + 16 * q^19 + 2 * q^20 - 20 * q^22 + 4 * q^23 + 6 * q^25 + 20 * q^26 - 8 * q^28 - 12 * q^29 + 22 * q^32 - 4 * q^34 - 20 * q^38 + 2 * q^40 - 16 * q^43 - 12 * q^44 - 8 * q^46 + 8 * q^47 + 30 * q^49 + 2 * q^50 - 4 * q^52 + 8 * q^53 + 12 * q^56 - 20 * q^58 + 4 * q^62 + 14 * q^64 - 44 * q^68 - 48 * q^71 - 12 * q^73 + 4 * q^74 - 4 * q^76 - 12 * q^77 - 6 * q^80 + 16 * q^82 - 40 * q^86 - 8 * q^88 - 12 * q^91 - 32 * q^92 + 44 * q^94 + 16 * q^95 + 4 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	0.681664	−	1.23909i	0.482009	−	0.876166i
$2$	0.681664	−	1.23909i	0.482009	−	0.876166i
$3$		0			0
$3$		0			0
$4$	−1.07067	−	1.68928i	−0.535334	−	0.844640i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$		−	1.41421i		−	0.534522i	−0.963624	−	0.267261i	$-0.913881\pi$
$7$		−	1.41421i		−	0.534522i	0.963624	−	0.267261i	$-0.0861187\pi$
$8$	−2.82300	+	0.175128i	−0.998081	+	0.0619170i
$9$		0			0
$10$	0.681664	−	1.23909i	0.215561	−	0.391833i
$11$		−	6.37056i		−	1.92080i	−0.278633	−	0.960398i	$-0.589881\pi$
$11$		−	6.37056i		−	1.92080i	0.278633	−	0.960398i	$-0.410119\pi$
$12$		0			0
$13$			3.54213i			0.982410i	0.871044	+	0.491205i	$0.163443\pi$
$13$			3.54213i			0.982410i	−0.871044	+	0.491205i	$0.836557\pi$
$14$	−1.75233	−	0.964019i	−0.468330	−	0.257645i
$15$		0			0
$16$	−1.70734	+	3.61732i	−0.426835	+	0.904330i
$17$		−	3.92870i		−	0.952849i	−0.879215	−	0.476424i	$-0.841933\pi$
$17$		−	3.92870i		−	0.952849i	0.879215	−	0.476424i	$-0.158067\pi$
$18$		0			0
$19$	1.27334			0.292125			0.146063	−	0.989275i	$-0.453340\pi$
$19$	1.27334			0.292125			0.146063	+	0.989275i	$0.453340\pi$
$20$	−1.07067	−	1.68928i	−0.239409	−	0.377735i
$21$		0			0
$22$	−7.89367	−	4.34258i	−1.68294	−	0.925841i
$23$	6.28267			1.31003			0.655014	−	0.755617i	$-0.272663\pi$
$23$	6.28267			1.31003			0.655014	+	0.755617i	$0.272663\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	4.38900	+	2.41454i	0.860754	+	0.473531i
$27$		0			0
$28$	−2.38900	+	1.51415i	−0.451479	+	0.286148i
$29$	−9.00933			−1.67299			−0.836495	−	0.547974i	$-0.815399\pi$
$29$	−9.00933			−1.67299			−0.836495	+	0.547974i	$0.815399\pi$
$30$		0			0
$31$			3.92870i			0.705615i	0.935696	+	0.352807i	$0.114773\pi$
$31$			3.92870i			0.705615i	−0.935696	+	0.352807i	$0.885227\pi$
$32$	3.31834	+	4.58134i	0.586604	+	0.809874i
$33$		0			0
$34$	−4.86799	−	2.67805i	−0.834854	−	0.459282i
$35$		−	1.41421i		−	0.239046i
$36$		0			0
$37$			2.51448i			0.413378i	0.978407	+	0.206689i	$0.0662689\pi$
$37$			2.51448i			0.413378i	−0.978407	+	0.206689i	$0.933731\pi$
$38$	0.867993	−	1.57778i	0.140807	−	0.255950i
$39$		0			0
$40$	−2.82300	+	0.175128i	−0.446356	+	0.0276901i
$41$			5.27029i			0.823081i	0.911392	+	0.411540i	$0.135009\pi$
$41$			5.27029i			0.823081i	−0.911392	+	0.411540i	$0.864991\pi$
$42$		0			0
$43$	1.55602			0.237290			0.118645	−	0.992937i	$-0.462145\pi$
$43$	1.55602			0.237290			0.118645	+	0.992937i	$0.462145\pi$
$44$	−10.7617	+	6.82075i	−1.62238	+	1.02827i
$45$		0			0
$46$	4.28267	−	7.78477i	0.631446	−	1.14780i
$47$	9.73599			1.42014			0.710070	−	0.704131i	$-0.248663\pi$
$47$	9.73599			1.42014			0.710070	+	0.704131i	$0.248663\pi$
$48$		0			0
$49$	5.00000			0.714286
$50$	0.681664	−	1.23909i	0.0964019	−	0.175233i
$51$		0			0
$52$	5.98365	−	3.79245i	0.829783	−	0.525918i
$53$	5.55602			0.763177			0.381589	−	0.924332i	$-0.375377\pi$
$53$	5.55602			0.763177			0.381589	+	0.924332i	$0.375377\pi$
$54$		0			0
$55$		−	6.37056i		−	0.859006i
$56$	0.247668	+	3.99233i	0.0330960	+	0.533497i
$57$		0			0
$58$	−6.14134	+	11.1633i	−0.806397	+	1.46582i
$59$		−	0.313944i		−	0.0408721i	−0.999791	−	0.0204360i	$-0.993495\pi$
$59$		−	0.313944i		−	0.0408721i	0.999791	−	0.0204360i	$-0.00650544\pi$
$60$		0			0
$61$			12.7411i			1.63133i	0.578523	+	0.815666i	$0.303629\pi$
$61$			12.7411i			1.63133i	−0.578523	+	0.815666i	$0.696371\pi$
$62$	4.86799	+	2.67805i	0.618236	+	0.340113i
$63$		0			0
$64$	7.93866	−	0.988770i	0.992333	−	0.123596i
$65$			3.54213i			0.439347i
$66$		0			0
$67$	−7.00933			−0.856326			−0.428163	−	0.903702i	$-0.640839\pi$
$67$	−7.00933			−0.856326			−0.428163	+	0.903702i	$0.640839\pi$
$68$	−6.63667	+	4.20633i	−0.804815	+	0.510092i
$69$		0			0
$70$	−1.75233	−	0.964019i	−0.209444	−	0.115222i
$71$	−0.990671			−0.117571			−0.0587855	−	0.998271i	$-0.518723\pi$
$71$	−0.990671			−0.117571			−0.0587855	+	0.998271i	$0.518723\pi$
$72$		0			0
$73$	12.0187			1.40668			0.703339	−	0.710855i	$-0.251692\pi$
$73$	12.0187			1.40668			0.703339	+	0.710855i	$0.251692\pi$
$74$	3.11566	+	1.71403i	0.362188	+	0.199252i
$75$		0			0
$76$	−1.36333	−	2.15103i	−0.156384	−	0.246741i
$77$	−9.00933			−1.02671
$78$		0			0
$79$		−	8.18453i		−	0.920832i	−0.887703	−	0.460416i	$-0.847700\pi$
$79$		−	8.18453i		−	0.920832i	0.887703	−	0.460416i	$-0.152300\pi$
$80$	−1.70734	+	3.61732i	−0.190886	+	0.404428i
$81$		0			0
$82$	6.53034	+	3.59257i	0.721155	+	0.396733i
$83$			5.02897i			0.552001i	0.961158	+	0.276000i	$0.0890091\pi$
$83$			5.02897i			0.552001i	−0.961158	+	0.276000i	$0.910991\pi$
$84$		0			0
$85$		−	3.92870i		−	0.426127i
$86$	1.06068	−	1.92804i	0.114376	−	0.207906i
$87$		0			0
$88$	1.11566	+	17.9841i	0.118930	+	1.91711i
$89$		−	0.386566i		−	0.0409759i	−0.999790	−	0.0204880i	$-0.993478\pi$
$89$		−	0.386566i		−	0.0409759i	0.999790	−	0.0204880i	$-0.00652198\pi$
$90$		0			0
$91$	5.00933			0.525120
$92$	−6.72666	−	10.6132i	−0.701302	−	1.10650i
$93$		0			0
$94$	6.63667	−	12.0637i	0.684520	−	1.24428i
$95$	1.27334			0.130642
$96$		0			0
$97$	10.4626			1.06232			0.531160	−	0.847271i	$-0.321756\pi$
$97$	10.4626			1.06232			0.531160	+	0.847271i	$0.321756\pi$
$98$	3.40832	−	6.19543i	0.344292	−	0.625833i
$99$		0			0
$100$	−1.07067	−	1.68928i	−0.107067	−	0.168928i
$101$	−13.1120			−1.30470			−0.652348	−	0.757920i	$-0.726216\pi$
$101$	−13.1120			−1.30470			−0.652348	+	0.757920i	$0.726216\pi$
$102$		0			0
$103$		−	6.04342i		−	0.595476i	−0.954648	−	0.297738i	$-0.903768\pi$
$103$		−	6.04342i		−	0.595476i	0.954648	−	0.297738i	$-0.0962322\pi$
$104$	−0.620325	−	9.99943i	−0.0608278	−	0.980525i
$105$		0			0
$106$	3.78734	−	6.88438i	0.367859	−	0.668670i
$107$		−	2.82843i		−	0.273434i	−0.990610	−	0.136717i	$-0.956345\pi$
$107$		−	2.82843i		−	0.273434i	0.990610	−	0.136717i	$-0.0436552\pi$
$108$		0			0
$109$		−	7.08426i		−	0.678549i	−0.940687	−	0.339275i	$-0.889818\pi$
$109$		−	7.08426i		−	0.678549i	0.940687	−	0.339275i	$-0.110182\pi$
$110$	−7.89367	−	4.34258i	−0.752632	−	0.414049i
$111$		0			0
$112$	5.11566	+	2.41454i	0.483384	+	0.228153i
$113$			16.6698i			1.56816i	0.620657	+	0.784082i	$0.286866\pi$
$113$			16.6698i			1.56816i	−0.620657	+	0.784082i	$0.713134\pi$
$114$		0			0
$115$	6.28267			0.585862
$116$	9.64600	+	15.2193i	0.895609	+	1.41308i
$117$		0			0
$118$	−0.389004	−	0.214005i	−0.0358107	−	0.0197007i
$119$	−5.55602			−0.509319
$120$		0			0
$121$	−29.5840			−2.68945
$122$	15.7873	+	8.68516i	1.42932	+	0.786318i
$123$		0			0
$124$	6.63667	−	4.20633i	0.595991	−	0.377740i
$125$	1.00000			0.0894427
$126$		0			0
$127$			16.5840i			1.47159i	0.677203	+	0.735796i	$0.263192\pi$
$127$			16.5840i			1.47159i	−0.677203	+	0.735796i	$0.736808\pi$
$128$	4.18633	−	10.5107i	0.370023	−	0.929023i
$129$		0			0
$130$	4.38900	+	2.41454i	0.384941	+	0.211769i
$131$		−	4.96954i		−	0.434190i	−0.976150	−	0.217095i	$-0.930342\pi$
$131$		−	4.96954i		−	0.434190i	0.976150	−	0.217095i	$-0.0696582\pi$
$132$		0			0
$133$		−	1.80078i		−	0.156147i
$134$	−4.77801	+	8.68516i	−0.412757	+	0.750284i
$135$		0			0
$136$	0.688023	+	11.0907i	0.0589975	+	0.951021i
$137$			2.50129i			0.213700i	0.994275	+	0.106850i	$0.0340764\pi$
$137$			2.50129i			0.213700i	−0.994275	+	0.106850i	$0.965924\pi$
$138$		0			0
$139$	−18.8480			−1.59867			−0.799334	−	0.600887i	$-0.794814\pi$
$139$	−18.8480			−1.59867			−0.799334	+	0.600887i	$0.794814\pi$
$140$	−2.38900	+	1.51415i	−0.201908	+	0.127969i
$141$		0			0
$142$	−0.675305	+	1.22753i	−0.0566703	+	0.103012i
$143$	22.5653			1.88701
$144$		0			0
$145$	−9.00933			−0.748184
$146$	8.19269	−	14.8921i	0.678032	−	1.23248i
$147$		0			0
$148$	4.24767	−	2.69218i	0.349156	−	0.221296i
$149$	−1.00933			−0.0826874			−0.0413437	−	0.999145i	$-0.513164\pi$
$149$	−1.00933			−0.0826874			−0.0413437	+	0.999145i	$0.513164\pi$
$150$		0			0
$151$		−	16.5246i		−	1.34475i	−0.740211	−	0.672375i	$-0.765274\pi$
$151$		−	16.5246i		−	1.34475i	0.740211	−	0.672375i	$-0.234726\pi$
$152$	−3.59465	+	0.222998i	−0.291565	+	0.0180875i
$153$		0			0
$154$	−6.14134	+	11.1633i	−0.494883	+	0.899567i
$155$			3.92870i			0.315560i
$156$		0			0
$157$		−	10.2266i		−	0.816174i	−0.912943	−	0.408087i	$-0.866196\pi$
$157$		−	10.2266i		−	0.816174i	0.912943	−	0.408087i	$-0.133804\pi$
$158$	−10.1413	−	5.57910i	−0.806801	−	0.443849i
$159$		0			0
$160$	3.31834	+	4.58134i	0.262337	+	0.362186i
$161$		−	8.88504i		−	0.700239i
$162$		0			0
$163$	−6.54669			−0.512776			−0.256388	−	0.966574i	$-0.582532\pi$
$163$	−6.54669			−0.512776			−0.256388	+	0.966574i	$0.582532\pi$
$164$	8.90300	−	5.64273i	0.695207	−	0.440623i
$165$		0			0
$166$	6.23132	+	3.42807i	0.483644	+	0.266069i
$167$	−22.8480			−1.76803			−0.884016	−	0.467456i	$-0.845171\pi$
$167$	−22.8480			−1.76803			−0.884016	+	0.467456i	$0.845171\pi$
$168$		0			0
$169$	0.453313			0.0348702
$170$	−4.86799	−	2.67805i	−0.373358	−	0.205397i
$171$		0			0
$172$	−1.66598	−	2.62855i	−0.127030	−	0.200425i
$173$	17.5560			1.33476			0.667380	−	0.744718i	$-0.267416\pi$
$173$	17.5560			1.33476			0.667380	+	0.744718i	$0.267416\pi$
$174$		0			0
$175$		−	1.41421i		−	0.106904i
$176$	23.0443	+	10.8767i	1.73703	+	0.819863i
$177$		0			0
$178$	−0.478989	−	0.263508i	−0.0359017	−	0.0197508i
$179$		−	1.48684i		−	0.111131i	−0.998455	−	0.0555656i	$-0.982304\pi$
$179$		−	1.48684i		−	0.111131i	0.998455	−	0.0555656i	$-0.0176962\pi$
$180$		0			0
$181$			16.1974i			1.20395i	0.798517	+	0.601973i	$0.205618\pi$
$181$			16.1974i			1.20395i	−0.798517	+	0.601973i	$0.794382\pi$
$182$	3.41468	−	6.20699i	0.253113	−	0.460093i
$183$		0			0
$184$	−17.7360	+	1.10027i	−1.30751	+	0.0811129i
$185$			2.51448i			0.184868i
$186$		0			0
$187$	−25.0280			−1.83023
$188$	−10.4240	−	16.4468i	−0.760249	−	1.19951i
$189$		0			0
$190$	0.867993	−	1.57778i	0.0629708	−	0.114464i
$191$	−24.0373			−1.73928			−0.869640	−	0.493687i	$-0.835649\pi$
$191$	−24.0373			−1.73928			−0.869640	+	0.493687i	$0.835649\pi$
$192$		0			0
$193$	−18.4626			−1.32897			−0.664485	−	0.747302i	$-0.731349\pi$
$193$	−18.4626			−1.32897			−0.664485	+	0.747302i	$0.731349\pi$
$194$	7.13201	−	12.9641i	0.512048	−	0.930769i
$195$		0			0
$196$	−5.35334	−	8.44640i	−0.382381	−	0.603315i
$197$	−11.4533			−0.816015			−0.408007	−	0.912979i	$-0.633776\pi$
$197$	−11.4533			−0.816015			−0.408007	+	0.912979i	$0.633776\pi$
$198$		0			0
$199$		−	2.50129i		−	0.177312i	−0.996062	−	0.0886559i	$-0.971743\pi$
$199$		−	2.50129i		−	0.177312i	0.996062	−	0.0886559i	$-0.0282571\pi$
$200$	−2.82300	+	0.175128i	−0.199616	+	0.0123834i
$201$		0			0
$202$	−8.93800	+	16.2469i	−0.628876	+	1.14313i
$203$			12.7411i			0.894251i
$204$		0			0
$205$			5.27029i			0.368093i
$206$	−7.48832	−	4.11958i	−0.521736	−	0.287025i
$207$		0			0
$208$	−12.8130	−	6.04762i	−0.888423	−	0.419327i
$209$		−	8.11191i		−	0.561112i
$210$		0			0
$211$	17.1893			1.18336			0.591680	−	0.806173i	$-0.298465\pi$
$211$	17.1893			1.18336			0.591680	+	0.806173i	$0.298465\pi$
$212$	−5.94865	−	9.38567i	−0.408555	−	0.644611i
$213$		0			0
$214$	−3.50466	−	1.92804i	−0.239574	−	0.131798i
$215$	1.55602			0.106119
$216$		0			0
$217$	5.55602			0.377167
$218$	−8.77801	−	4.82909i	−0.594522	−	0.327067i
$219$		0			0
$220$	−10.7617	+	6.82075i	−0.725551	+	0.459855i
$221$	13.9160			0.936088
$222$		0			0
$223$			2.04210i			0.136749i	0.997660	+	0.0683746i	$0.0217813\pi$
$223$			2.04210i			0.136749i	−0.997660	+	0.0683746i	$0.978219\pi$
$224$	6.47899	−	4.69284i	0.432896	−	0.313553i
$225$		0			0
$226$	20.6553	+	11.3632i	1.37397	+	0.755870i
$227$			21.2264i			1.40885i	0.709781	+	0.704423i	$0.248794\pi$
$227$			21.2264i			1.40885i	−0.709781	+	0.704423i	$0.751206\pi$
$228$		0			0
$229$		−	13.3690i		−	0.883449i	−0.897151	−	0.441724i	$-0.854367\pi$
$229$		−	13.3690i		−	0.883449i	0.897151	−	0.441724i	$-0.145633\pi$
$230$	4.28267	−	7.78477i	0.282391	−	0.513313i
$231$		0			0
$232$	25.4333	−	1.57778i	1.66978	−	0.103586i
$233$		−	17.2977i		−	1.13321i	−0.823990	−	0.566605i	$-0.808257\pi$
$233$		−	17.2977i		−	1.13321i	0.823990	−	0.566605i	$-0.191743\pi$
$234$		0			0
$235$	9.73599			0.635106
$236$	−0.530340	+	0.336130i	−0.0345222	+	0.0218802i
$237$		0			0
$238$	−3.78734	+	6.88438i	−0.245497	+	0.446248i
$239$	13.4533			0.870222			0.435111	−	0.900377i	$-0.356709\pi$
$239$	13.4533			0.870222			0.435111	+	0.900377i	$0.356709\pi$
$240$		0			0
$241$	−4.56534			−0.294080			−0.147040	−	0.989131i	$-0.546975\pi$
$241$	−4.56534			−0.294080			−0.147040	+	0.989131i	$0.546975\pi$
$242$	−20.1664	+	36.6571i	−1.29634	+	2.35641i
$243$		0			0
$244$	21.5233	−	13.6415i	1.37789	−	0.873308i
$245$	5.00000			0.319438
$246$		0			0
$247$			4.51035i			0.286987i
$248$	−0.688023	−	11.0907i	−0.0436895	−	0.704261i
$249$		0			0
$250$	0.681664	−	1.23909i	0.0431122	−	0.0783667i
$251$		−	25.9414i		−	1.63741i	−0.574216	−	0.818704i	$-0.694693\pi$
$251$		−	25.9414i		−	1.63741i	0.574216	−	0.818704i	$-0.305307\pi$
$252$		0			0
$253$		−	40.0241i		−	2.51630i
$254$	20.5490	+	11.3047i	1.28936	+	0.709321i
$255$		0			0
$256$	−10.1700	−	12.3520i	−0.635624	−	0.771999i
$257$		−	24.3820i		−	1.52090i	−0.649394	−	0.760452i	$-0.724977\pi$
$257$		−	24.3820i		−	1.52090i	0.649394	−	0.760452i	$-0.275023\pi$
$258$		0			0
$259$	3.55602			0.220960
$260$	5.98365	−	3.79245i	0.371090	−	0.235198i
$261$		0			0
$262$	−6.15768	−	3.38755i	−0.380423	−	0.209284i
$263$	−11.7360			−0.723672			−0.361836	−	0.932242i	$-0.617850\pi$
$263$	−11.7360			−0.723672			−0.361836	+	0.932242i	$0.617850\pi$
$264$		0			0
$265$	5.55602			0.341303
$266$	−2.23132	−	1.22753i	−0.136811	−	0.0752645i
$267$		0			0
$268$	7.50466	+	11.8407i	0.458420	+	0.723287i
$269$	11.0280			0.672388			0.336194	−	0.941793i	$-0.390860\pi$
$269$	11.0280			0.672388			0.336194	+	0.941793i	$0.390860\pi$
$270$		0			0
$271$			20.2714i			1.23140i	0.787981	+	0.615699i	$0.211126\pi$
$271$			20.2714i			1.23140i	−0.787981	+	0.615699i	$0.788874\pi$
$272$	14.2113	+	6.70762i	0.861689	+	0.406709i
$273$		0			0
$274$	3.09931	+	1.70504i	0.187236	+	0.103005i
$275$		−	6.37056i		−	0.384159i
$276$		0			0
$277$			3.28762i			0.197534i	0.995111	+	0.0987668i	$0.0314898\pi$
$277$			3.28762i			0.197534i	−0.995111	+	0.0987668i	$0.968510\pi$
$278$	−12.8480	+	23.3543i	−0.770573	+	1.40070i
$279$		0			0
$280$	0.247668	+	3.99233i	0.0148010	+	0.238587i
$281$			23.4401i			1.39832i	0.714965	+	0.699160i	$0.246443\pi$
$281$			23.4401i			1.39832i	−0.714965	+	0.699160i	$0.753557\pi$
$282$		0			0
$283$	27.0093			1.60554			0.802769	−	0.596290i	$-0.203359\pi$
$283$	27.0093			1.60554			0.802769	+	0.596290i	$0.203359\pi$
$284$	1.06068	+	1.67352i	0.0629398	+	0.0993053i
$285$		0			0
$286$	15.3820	−	27.9604i	0.909556	−	1.65333i
$287$	7.45331			0.439955
$288$		0			0
$289$	1.56534			0.0920791
$290$	−6.14134	+	11.1633i	−0.360632	+	0.655533i
$291$		0			0
$292$	−12.8680	−	20.3029i	−0.753042	−	1.18814i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$		−	0.313944i		−	0.0182785i
$296$	−0.440355	−	7.09839i	−0.0255951	−	0.412585i
$297$		0			0
$298$	−0.688023	+	1.25065i	−0.0398561	+	0.0724479i
$299$			22.2540i			1.28698i
$300$		0			0
$301$		−	2.20054i		−	0.126837i
$302$	−20.4754	−	11.2642i	−1.17822	−	0.648182i
$303$		0			0
$304$	−2.17403	+	4.60609i	−0.124689	+	0.264177i
$305$			12.7411i			0.729554i
$306$		0			0
$307$	−0.565344			−0.0322659			−0.0161330	−	0.999870i	$-0.505136\pi$
$307$	−0.565344			−0.0322659			−0.0161330	+	0.999870i	$0.505136\pi$
$308$	9.64600	+	15.2193i	0.549632	+	0.867199i
$309$		0			0
$310$	4.86799	+	2.67805i	0.276483	+	0.152103i
$311$	−25.4533			−1.44332			−0.721662	−	0.692245i	$-0.756622\pi$
$311$	−25.4533			−1.44332			−0.721662	+	0.692245i	$0.756622\pi$
$312$		0			0
$313$	29.5747			1.67166			0.835830	−	0.548989i	$-0.184987\pi$
$313$	29.5747			1.67166			0.835830	+	0.548989i	$0.184987\pi$
$314$	−12.6717	−	6.97113i	−0.715104	−	0.393404i
$315$		0			0
$316$	−13.8260	+	8.76291i	−0.777772	+	0.492952i
$317$	6.56534			0.368746			0.184373	−	0.982856i	$-0.440974\pi$
$317$	6.56534			0.368746			0.184373	+	0.982856i	$0.440974\pi$
$318$		0			0
$319$			57.3944i			3.21347i
$320$	7.93866	−	0.988770i	0.443785	−	0.0552740i
$321$		0			0
$322$	−11.0093	−	6.05661i	−0.613526	−	0.337522i
$323$		−	5.00258i		−	0.278351i
$324$		0			0
$325$			3.54213i			0.196482i
$326$	−4.46264	+	8.11191i	−0.247163	+	0.449277i
$327$		0			0
$328$	−0.922973	−	14.8780i	−0.0509627	−	0.821501i
$329$		−	13.7688i		−	0.759096i
$330$		0			0
$331$	7.29200			0.400805			0.200402	−	0.979714i	$-0.435775\pi$
$331$	7.29200			0.400805			0.200402	+	0.979714i	$0.435775\pi$
$332$	8.49534	−	5.38435i	0.466242	−	0.295505i
$333$		0			0
$334$	−15.5747	+	28.3107i	−0.852208	+	1.54909i
$335$	−7.00933			−0.382961
$336$		0			0
$337$	19.1307			1.04212			0.521058	−	0.853522i	$-0.325538\pi$
$337$	19.1307			1.04212			0.521058	+	0.853522i	$0.325538\pi$
$338$	0.309007	−	0.561694i	0.0168078	−	0.0305521i
$339$		0			0
$340$	−6.63667	+	4.20633i	−0.359924	+	0.228120i
$341$	25.0280			1.35534
$342$		0			0
$343$		−	16.9706i		−	0.916324i
$344$	−4.39263	+	0.272501i	−0.236835	+	0.0146923i
$345$		0			0
$346$	11.9673	−	21.7534i	0.643366	−	1.16947i
$347$			21.8807i			1.17462i	0.809364	+	0.587308i	$0.199812\pi$
$347$			21.8807i			1.17462i	−0.809364	+	0.587308i	$0.800188\pi$
$348$		0			0
$349$			24.8543i			1.33042i	0.746655	+	0.665211i	$0.231658\pi$
$349$			24.8543i			1.33042i	−0.746655	+	0.665211i	$0.768342\pi$
$350$	−1.75233	−	0.964019i	−0.0936661	−	0.0515290i
$351$		0			0
$352$	29.1857	−	21.1396i	1.55560	−	1.12675i
$353$			8.18453i			0.435619i	0.975991	+	0.217809i	$0.0698911\pi$
$353$			8.18453i			0.435619i	−0.975991	+	0.217809i	$0.930109\pi$
$354$		0			0
$355$	−0.990671			−0.0525794
$356$	−0.653019	+	0.413884i	−0.0346099	+	0.0219358i
$357$		0			0
$358$	−1.84232	−	1.01352i	−0.0973695	−	0.0535663i
$359$	−11.8973			−0.627915			−0.313958	−	0.949437i	$-0.601655\pi$
$359$	−11.8973			−0.627915			−0.313958	+	0.949437i	$0.601655\pi$
$360$		0			0
$361$	−17.3786			−0.914663
$362$	20.0700	+	11.0412i	1.05486	+	0.580313i
$363$		0			0
$364$	−5.36333	−	8.46216i	−0.281115	−	0.443538i
$365$	12.0187			0.629085
$366$		0			0
$367$			6.67131i			0.348239i	0.984724	+	0.174120i	$0.0557080\pi$
$367$			6.67131i			0.348239i	−0.984724	+	0.174120i	$0.944292\pi$
$368$	−10.7267	+	22.7264i	−0.559166	+	1.18470i
$369$		0			0
$370$	3.11566	+	1.71403i	0.161975	+	0.0891083i
$371$		−	7.85739i		−	0.407936i
$372$		0			0
$373$		−	0.340330i		−	0.0176216i	−0.999961	−	0.00881081i	$-0.997195\pi$
$373$		−	0.340330i		−	0.0176216i	0.999961	−	0.00881081i	$-0.00280460\pi$
$374$	−17.0607	+	31.0118i	−0.882187	+	1.60358i
$375$		0			0
$376$	−27.4847	+	1.70504i	−1.41741	+	0.0879307i
$377$		−	31.9122i		−	1.64356i
$378$		0			0
$379$	20.3013			1.04281			0.521405	−	0.853310i	$-0.325408\pi$
$379$	20.3013			1.04281			0.521405	+	0.853310i	$0.325408\pi$
$380$	−1.36333	−	2.15103i	−0.0699373	−	0.110346i
$381$		0			0
$382$	−16.3854	+	29.7843i	−0.838349	+	1.52390i
$383$	−10.3013			−0.526373			−0.263187	−	0.964745i	$-0.584774\pi$
$383$	−10.3013			−0.526373			−0.263187	+	0.964745i	$0.584774\pi$
$384$		0			0
$385$	−9.00933			−0.459158
$386$	−12.5853	+	22.8768i	−0.640576	+	1.16440i
$387$		0			0
$388$	−11.2020	−	17.6743i	−0.568696	−	0.897279i
$389$	19.1307			0.969964			0.484982	−	0.874524i	$-0.338826\pi$
$389$	19.1307			0.969964			0.484982	+	0.874524i	$0.338826\pi$
$390$		0			0
$391$		−	24.6827i		−	1.24826i
$392$	−14.1150	+	0.875638i	−0.712915	+	0.0442264i
$393$		0			0
$394$	−7.80731	+	14.1916i	−0.393327	+	0.714964i
$395$		−	8.18453i		−	0.411808i
$396$		0			0
$397$		−	3.39689i		−	0.170485i	−0.996360	−	0.0852424i	$-0.972834\pi$
$397$		−	3.39689i		−	0.170485i	0.996360	−	0.0852424i	$-0.0271665\pi$
$398$	−3.09931	−	1.70504i	−0.155355	−	0.0854659i
$399$		0			0
$400$	−1.70734	+	3.61732i	−0.0853670	+	0.180866i
$401$			10.2993i			0.514320i	0.966369	+	0.257160i	$0.0827868\pi$
$401$			10.2993i			0.514320i	−0.966369	+	0.257160i	$0.917213\pi$
$402$		0			0
$403$	−13.9160			−0.693203
$404$	14.0386	+	22.1499i	0.698448	+	1.10200i
$405$		0			0
$406$	15.7873	+	8.68516i	0.783512	+	0.431037i
$407$	16.0187			0.794015
$408$		0			0
$409$	9.11203			0.450561			0.225280	−	0.974294i	$-0.427670\pi$
$409$	9.11203			0.450561			0.225280	+	0.974294i	$0.427670\pi$
$410$	6.53034	+	3.59257i	0.322511	+	0.177424i
$411$		0			0
$412$	−10.2090	+	6.47050i	−0.502963	+	0.318779i
$413$	−0.443984			−0.0218470
$414$		0			0
$415$			5.02897i			0.246862i
$416$	−16.2277	+	11.7540i	−0.795628	+	0.576286i
$417$		0			0
$418$	−10.0514	−	5.52960i	−0.491628	−	0.270461i
$419$			8.17134i			0.399196i	0.979878	+	0.199598i	$0.0639636\pi$
$419$			8.17134i			0.399196i	−0.979878	+	0.199598i	$0.936036\pi$
$420$		0			0
$421$		−	3.60156i		−	0.175529i	−0.996141	−	0.0877646i	$-0.972028\pi$
$421$		−	3.60156i		−	0.175529i	0.996141	−	0.0877646i	$-0.0279723\pi$
$422$	11.7173	−	21.2990i	0.570391	−	1.03682i
$423$		0			0
$424$	−15.6846	+	0.973012i	−0.761713	+	0.0472536i
$425$		−	3.92870i		−	0.190570i
$426$		0			0
$427$	18.0187			0.871984
$428$	−4.77801	+	3.02831i	−0.230954	+	0.146379i
$429$		0			0
$430$	1.06068	−	1.92804i	0.0511505	−	0.0929782i
$431$	8.10270			0.390293			0.195147	−	0.980774i	$-0.437482\pi$
$431$	8.10270			0.390293			0.195147	+	0.980774i	$0.437482\pi$
$432$		0			0
$433$	−8.01866			−0.385352			−0.192676	−	0.981262i	$-0.561717\pi$
$433$	−8.01866			−0.385352			−0.192676	+	0.981262i	$0.561717\pi$
$434$	3.78734	−	6.88438i	0.181798	−	0.330461i
$435$		0			0
$436$	−11.9673	+	7.58489i	−0.573130	+	0.363250i
$437$	8.00000			0.382692
$438$		0			0
$439$		−	13.8150i		−	0.659354i	−0.944094	−	0.329677i	$-0.893060\pi$
$439$		−	13.8150i		−	0.659354i	0.944094	−	0.329677i	$-0.106940\pi$
$440$	1.11566	+	17.9841i	0.0531870	+	0.857358i
$441$		0			0
$442$	9.48601	−	17.2431i	0.451203	−	0.820169i
$443$			12.7147i			0.604095i	0.953293	+	0.302048i	$0.0976701\pi$
$443$			12.7147i			0.604095i	−0.953293	+	0.302048i	$0.902330\pi$
$444$		0			0
$445$		−	0.386566i		−	0.0183250i
$446$	2.53034	+	1.39203i	0.119815	+	0.0659144i
$447$		0			0
$448$	−1.39833	−	11.2270i	−0.0660650	−	0.530424i
$449$		−	4.24264i		−	0.200223i	−0.994976	−	0.100111i	$-0.968080\pi$
$449$		−	4.24264i		−	0.200223i	0.994976	−	0.100111i	$-0.0319199\pi$
$450$		0			0
$451$	33.5747			1.58097
$452$	28.1600	−	17.8478i	1.32453	−	0.839492i
$453$		0			0
$454$	26.3013	+	14.4693i	1.23438	+	0.679077i
$455$	5.00933			0.234841
$456$		0			0
$457$	3.35061			0.156735			0.0783675	−	0.996925i	$-0.475029\pi$
$457$	3.35061			0.156735			0.0783675	+	0.996925i	$0.475029\pi$
$458$	−16.5653	−	9.11317i	−0.774048	−	0.425830i
$459$		0			0
$460$	−6.72666	−	10.6132i	−0.313632	−	0.494843i
$461$	−18.1400			−0.844865			−0.422432	−	0.906394i	$-0.638824\pi$
$461$	−18.1400			−0.844865			−0.422432	+	0.906394i	$0.638824\pi$
$462$		0			0
$463$			32.9267i			1.53023i	0.643892	+	0.765116i	$0.277318\pi$
$463$			32.9267i			1.53023i	−0.643892	+	0.765116i	$0.722682\pi$
$464$	15.3820	−	32.5896i	0.714091	−	1.51293i
$465$		0			0
$466$	−21.4333	−	11.7912i	−0.992880	−	0.546218i
$467$		−	6.42999i		−	0.297544i	−0.988872	−	0.148772i	$-0.952468\pi$
$467$		−	6.42999i		−	0.297544i	0.988872	−	0.148772i	$-0.0475321\pi$
$468$		0			0
$469$			9.91269i			0.457725i
$470$	6.63667	−	12.0637i	0.306127	−	0.556458i
$471$		0			0
$472$	0.0549803	+	0.886265i	0.00253067	+	0.0407936i
$473$		−	9.91269i		−	0.455786i
$474$		0			0
$475$	1.27334			0.0584250
$476$	5.94865	+	9.38567i	0.272656	+	0.430192i
$477$		0			0
$478$	9.17064	−	16.6698i	0.419455	−	0.762459i
$479$	29.0280			1.32632			0.663161	−	0.748477i	$-0.269214\pi$
$479$	29.0280			1.32632			0.663161	+	0.748477i	$0.269214\pi$
$480$		0			0
$481$	−8.90663			−0.406107
$482$	−3.11203	+	5.65685i	−0.141749	+	0.257663i
$483$		0			0
$484$	31.6746	+	49.9757i	1.43976	+	2.27162i
$485$	10.4626			0.475084
$486$		0			0
$487$			11.7267i			0.531386i	0.964058	+	0.265693i	$0.0856007\pi$
$487$			11.7267i			0.531386i	−0.964058	+	0.265693i	$0.914399\pi$
$488$	−2.23132	−	35.9682i	−0.101007	−	1.62820i
$489$		0			0
$490$	3.40832	−	6.19543i	0.153972	−	0.279881i
$491$		−	8.02609i		−	0.362213i	−0.983464	−	0.181106i	$-0.942032\pi$
$491$		−	8.02609i		−	0.362213i	0.983464	−	0.181106i	$-0.0579678\pi$
$492$		0			0
$493$			35.3949i			1.59411i
$494$	5.58871	+	3.07454i	0.251448	+	0.138330i
$495$		0			0
$496$	−14.2113	−	6.70762i	−0.638108	−	0.301181i
$497$			1.40102i			0.0628444i
$498$		0			0
$499$	−26.4040			−1.18201			−0.591003	−	0.806669i	$-0.701268\pi$
$499$	−26.4040			−1.18201			−0.591003	+	0.806669i	$0.701268\pi$
$500$	−1.07067	−	1.68928i	−0.0478817	−	0.0755469i
$501$		0			0
$502$	−32.1436	−	17.6833i	−1.43464	−	0.789246i
$503$	−31.3947			−1.39982			−0.699910	−	0.714231i	$-0.746777\pi$
$503$	−31.3947			−1.39982			−0.699910	+	0.714231i	$0.746777\pi$
$504$		0			0
$505$	−13.1120			−0.583478
$506$	−49.5933	−	27.2830i	−2.20469	−	1.21288i
$507$		0			0
$508$	28.0150	−	17.7560i	1.24297	−	0.787793i
$509$	−26.9253			−1.19344			−0.596721	−	0.802449i	$-0.703530\pi$
$509$	−26.9253			−1.19344			−0.596721	+	0.802449i	$0.703530\pi$
$510$		0			0
$511$		−	16.9969i		−	0.751901i
$512$	−22.2377	+	4.18158i	−0.982776	+	0.184801i
$513$		0			0
$514$	−30.2113	−	16.6203i	−1.33257	−	0.733090i
$515$		−	6.04342i		−	0.266305i
$516$		0			0
$517$		−	62.0237i		−	2.72780i
$518$	2.42401	−	4.40621i	0.106505	−	0.193598i
$519$		0			0
$520$	−0.620325	−	9.99943i	−0.0272030	−	0.438504i
$521$			0.641081i			0.0280863i	0.999901	+	0.0140431i	$0.00447022\pi$
$521$			0.641081i			0.0280863i	−0.999901	+	0.0140431i	$0.995530\pi$
$522$		0			0
$523$	−13.1307			−0.574165			−0.287082	−	0.957906i	$-0.592685\pi$
$523$	−13.1307			−0.574165			−0.287082	+	0.957906i	$0.592685\pi$
$524$	−8.39494	+	5.32072i	−0.366735	+	0.232437i
$525$		0			0
$526$	−8.00000	+	14.5419i	−0.348817	+	0.634057i
$527$	15.4347			0.672344
$528$		0			0
$529$	16.4720			0.716173
$530$	3.78734	−	6.88438i	0.164511	−	0.299038i
$531$		0			0
$532$	−3.04202	+	1.92804i	−0.131888	+	0.0835910i
$533$	−18.6680			−0.808603
$534$		0			0
$535$		−	2.82843i		−	0.122284i
$536$	19.7873	−	1.22753i	0.854683	−	0.0530211i
$537$		0			0
$538$	7.51738	−	13.6646i	0.324097	−	0.589124i
$539$		−	31.8528i		−	1.37200i
$540$		0			0
$541$		−	12.8864i		−	0.554028i	−0.960866	−	0.277014i	$-0.910655\pi$
$541$		−	12.8864i		−	0.554028i	0.960866	−	0.277014i	$-0.0893448\pi$
$542$	25.1180	+	13.8183i	1.07891	+	0.593545i
$543$		0			0
$544$	17.9987	−	13.0367i	0.771687	−	0.558945i
$545$		−	7.08426i		−	0.303456i
$546$		0			0
$547$	−30.4813			−1.30329			−0.651643	−	0.758526i	$-0.725920\pi$
$547$	−30.4813			−1.30329			−0.651643	+	0.758526i	$0.725920\pi$
$548$	4.22538	−	2.67805i	0.180499	−	0.114401i
$549$		0			0
$550$	−7.89367	−	4.34258i	−0.336587	−	0.185168i
$551$	−11.4720			−0.488722
$552$		0			0
$553$	−11.5747			−0.492205
$554$	4.07364	+	2.24105i	0.173072	+	0.0952131i
$555$		0			0
$556$	20.1800	+	31.8396i	0.855821	+	1.35030i
$557$	−0.462642			−0.0196028			−0.00980138	−	0.999952i	$-0.503120\pi$
$557$	−0.462642			−0.0196028			−0.00980138	+	0.999952i	$0.503120\pi$
$558$		0			0
$559$			5.51161i			0.233116i
$560$	5.11566	+	2.41454i	0.216176	+	0.102033i
$561$		0			0
$562$	29.0443	+	15.9783i	1.22516	+	0.674004i
$563$		−	36.7959i		−	1.55076i	−0.631493	−	0.775382i	$-0.717557\pi$
$563$		−	36.7959i		−	1.55076i	0.631493	−	0.775382i	$-0.282443\pi$
$564$		0			0
$565$			16.6698i			0.701304i
$566$	18.4113	−	33.4669i	0.773884	−	1.40672i
$567$		0			0
$568$	2.79667	−	0.173494i	0.117345	−	0.00727964i
$569$			7.44444i			0.312087i	0.987750	+	0.156044i	$0.0498740\pi$
$569$			7.44444i			0.312087i	−0.987750	+	0.156044i	$0.950126\pi$
$570$		0			0
$571$	10.1986			0.426799			0.213400	−	0.976965i	$-0.431546\pi$
$571$	10.1986			0.426799			0.213400	+	0.976965i	$0.431546\pi$
$572$	−24.1600	−	38.1192i	−1.01018	−	1.59384i
$573$		0			0
$574$	5.08066	−	9.23530i	0.212062	−	0.385474i
$575$	6.28267			0.262006
$576$		0			0
$577$	0.443984			0.0184833			0.00924165	−	0.999957i	$-0.497058\pi$
$577$	0.443984			0.0184833			0.00924165	+	0.999957i	$0.497058\pi$
$578$	1.06704	−	1.93960i	0.0443830	−	0.0806766i
$579$		0			0
$580$	9.64600	+	15.2193i	0.400528	+	0.631946i
$581$	7.11203			0.295057
$582$		0			0
$583$		−	35.3949i		−	1.46591i
$584$	−33.9287	+	2.10480i	−1.40398	+	0.0870972i
$585$		0			0
$586$	−4.08998	+	7.43452i	−0.168956	+	0.307117i
$587$		−	30.3660i		−	1.25334i	−0.779286	−	0.626668i	$-0.784418\pi$
$587$		−	30.3660i		−	1.25334i	0.779286	−	0.626668i	$-0.215582\pi$
$588$		0			0
$589$			5.00258i			0.206128i
$590$	−0.389004	−	0.214005i	−0.0160150	−	0.00881043i
$591$		0			0
$592$	−9.09568	−	4.29308i	−0.373830	−	0.176444i
$593$		−	23.1262i		−	0.949679i	−0.880073	−	0.474839i	$-0.842506\pi$
$593$		−	23.1262i		−	0.949679i	0.880073	−	0.474839i	$-0.157494\pi$
$594$		0			0
$595$	−5.55602			−0.227774
$596$	1.08066	+	1.70504i	0.0442654	+	0.0698411i
$597$		0			0
$598$	27.5747	+	15.1698i	1.12761	+	0.620339i
$599$	−16.1027			−0.657939			−0.328969	−	0.944341i	$-0.606701\pi$
$599$	−16.1027			−0.657939			−0.328969	+	0.944341i	$0.606701\pi$
$600$		0			0
$601$	−8.20541			−0.334705			−0.167353	−	0.985897i	$-0.553522\pi$
$601$	−8.20541			−0.334705			−0.167353	+	0.985897i	$0.553522\pi$
$602$	−2.72666	−	1.50003i	−0.111130	−	0.0611366i
$603$		0			0
$604$	−27.9146	+	17.6923i	−1.13583	+	0.719891i
$605$	−29.5840			−1.20276
$606$		0			0
$607$		−	5.81529i		−	0.236035i	−0.993011	−	0.118018i	$-0.962346\pi$
$607$		−	5.81529i		−	0.236035i	0.993011	−	0.118018i	$-0.0376540\pi$
$608$	4.22538	+	5.83362i	0.171362	+	0.236584i
$609$		0			0
$610$	15.7873	+	8.68516i	0.639211	+	0.351652i
$611$			34.4861i			1.39516i
$612$		0			0
$613$			0.0858146i			0.00346602i	0.999998	+	0.00173301i	$0.000551635\pi$
$613$			0.0858146i			0.00346602i	−0.999998	+	0.00173301i	$0.999448\pi$
$614$	−0.385375	+	0.700510i	−0.0155525	+	0.0282703i
$615$		0			0
$616$	25.4333	−	1.57778i	1.02474	−	0.0635707i
$617$			39.3236i			1.58311i	0.611099	+	0.791555i	$0.290728\pi$
$617$			39.3236i			1.58311i	−0.611099	+	0.791555i	$0.709272\pi$
$618$		0			0
$619$	−28.0959			−1.12927			−0.564635	−	0.825341i	$-0.690983\pi$
$619$	−28.0959			−1.12927			−0.564635	+	0.825341i	$0.690983\pi$
$620$	6.63667	−	4.20633i	0.266535	−	0.168930i
$621$		0			0
$622$	−17.3506	+	31.5388i	−0.695696	+	1.26459i
$623$	−0.546687			−0.0219026
$624$		0			0
$625$	1.00000			0.0400000
$626$	20.1600	−	36.6456i	0.805755	−	1.46465i
$627$		0			0
$628$	−17.2757	+	10.9493i	−0.689374	+	0.436926i
$629$	9.87864			0.393887
$630$		0			0
$631$		−	18.8440i		−	0.750166i	−0.926991	−	0.375083i	$-0.877614\pi$
$631$		−	18.8440i		−	0.750166i	0.926991	−	0.375083i	$-0.122386\pi$
$632$	1.43334	+	23.1049i	0.0570151	+	0.919065i
$633$		0			0
$634$	4.47536	−	8.13503i	0.177739	−	0.323083i
$635$			16.5840i			0.658116i
$636$		0			0
$637$			17.7107i			0.701722i
$638$	71.1167	+	39.1237i	2.81554	+	1.54892i
$639$		0			0
$640$	4.18633	−	10.5107i	0.165479	−	0.415472i
$641$			14.1817i			0.560144i	0.959979	+	0.280072i	$0.0903583\pi$
$641$			14.1817i			0.560144i	−0.959979	+	0.280072i	$0.909642\pi$
$642$		0			0
$643$	−18.5467			−0.731410			−0.365705	−	0.930731i	$-0.619172\pi$
$643$	−18.5467			−0.731410			−0.365705	+	0.930731i	$0.619172\pi$
$644$	−15.0093	+	9.51293i	−0.591450	+	0.374862i
$645$		0			0
$646$	−6.19863	−	3.41008i	−0.243882	−	0.134168i
$647$	7.75464			0.304866			0.152433	−	0.988314i	$-0.451289\pi$
$647$	7.75464			0.304866			0.152433	+	0.988314i	$0.451289\pi$
$648$		0			0
$649$	−2.00000			−0.0785069
$650$	4.38900	+	2.41454i	0.172151	+	0.0947062i
$651$		0			0
$652$	7.00933	+	11.0592i	0.274506	+	0.433111i
$653$	−27.6960			−1.08383			−0.541915	−	0.840433i	$-0.682300\pi$
$653$	−27.6960			−1.08383			−0.541915	+	0.840433i	$0.682300\pi$
$654$		0			0
$655$		−	4.96954i		−	0.194176i
$656$	−19.0643	−	8.99817i	−0.744336	−	0.351320i
$657$		0			0
$658$	−17.0607	−	9.38567i	−0.665095	−	0.365892i
$659$			28.1420i			1.09625i	0.836395	+	0.548127i	$0.184659\pi$
$659$			28.1420i			1.09625i	−0.836395	+	0.548127i	$0.815341\pi$
$660$		0			0
$661$			19.7990i			0.770091i	0.922897	+	0.385046i	$0.125814\pi$
$661$			19.7990i			0.770091i	−0.922897	+	0.385046i	$0.874186\pi$
$662$	4.97070	−	9.03542i	0.193192	−	0.351171i
$663$		0			0
$664$	−0.880711	−	14.1968i	−0.0341782	−	0.550942i
$665$		−	1.80078i		−	0.0698312i
$666$		0			0
$667$	−56.6027			−2.19166
$668$	24.4626	+	38.5967i	0.946488	+	1.49335i
$669$		0			0
$670$	−4.77801	+	8.68516i	−0.184591	+	0.335537i
$671$	81.1680			3.13346
$672$		0			0
$673$	11.8133			0.455367			0.227684	−	0.973735i	$-0.426885\pi$
$673$	11.8133			0.455367			0.227684	+	0.973735i	$0.426885\pi$
$674$	13.0407	−	23.7046i	0.502309	−	0.913066i
$675$		0			0
$676$	−0.485348	−	0.765773i	−0.0186672	−	0.0294528i
$677$	−11.4533			−0.440187			−0.220093	−	0.975479i	$-0.570636\pi$
$677$	−11.4533			−0.440187			−0.220093	+	0.975479i	$0.570636\pi$
$678$		0			0
$679$		−	14.7964i		−	0.567834i
$680$	0.688023	+	11.0907i	0.0263845	+	0.425309i
$681$		0			0
$682$	17.0607	−	31.0118i	0.653287	−	1.18750i
$683$			41.0254i			1.56979i	0.619627	+	0.784896i	$0.287284\pi$
$683$			41.0254i			1.56979i	−0.619627	+	0.784896i	$0.712716\pi$
$684$		0			0
$685$			2.50129i			0.0955694i
$686$	−21.0280	−	11.5682i	−0.802852	−	0.441677i
$687$		0			0
$688$	−2.65665	+	5.62860i	−0.101284	+	0.214589i
$689$			19.6801i			0.749753i
$690$		0			0
$691$	4.38538			0.166828			0.0834138	−	0.996515i	$-0.473418\pi$
$691$	4.38538			0.166828			0.0834138	+	0.996515i	$0.473418\pi$
$692$	−18.7967	−	29.6570i	−0.714542	−	1.12739i
$693$		0			0
$694$	27.1120	+	14.9153i	1.02916	+	0.566176i
$695$	−18.8480			−0.714946
$696$		0			0
$697$	20.7054			0.784272
$698$	30.7967	+	16.9423i	1.16567	+	0.641276i
$699$		0			0
$700$	−2.38900	+	1.51415i	−0.0902959	+	0.0572296i
$701$	5.11203			0.193079			0.0965394	−	0.995329i	$-0.469223\pi$
$701$	5.11203			0.193079			0.0965394	+	0.995329i	$0.469223\pi$
$702$		0			0
$703$			3.20180i			0.120758i
$704$	−6.29902	−	50.5737i	−0.237403	−	1.90607i
$705$		0			0
$706$	10.1413	+	5.57910i	0.381674	+	0.209972i
$707$			18.5432i			0.697389i
$708$		0			0
$709$		−	32.6853i		−	1.22752i	−0.789491	−	0.613762i	$-0.789655\pi$
$709$		−	32.6853i		−	1.22752i	0.789491	−	0.613762i	$-0.210345\pi$
$710$	−0.675305	+	1.22753i	−0.0253437	+	0.0460683i
$711$		0			0
$712$	0.0676984	+	1.09128i	0.00253710	+	0.0408973i
$713$			24.6827i			0.924375i
$714$		0			0
$715$	22.5653			0.843896
$716$	−2.51168	+	1.59191i	−0.0938660	+	0.0594924i
$717$		0			0
$718$	−8.10996	+	14.7418i	−0.302661	+	0.550158i
$719$	−10.4813			−0.390886			−0.195443	−	0.980715i	$-0.562615\pi$
$719$	−10.4813			−0.390886			−0.195443	+	0.980715i	$0.562615\pi$
$720$		0			0
$721$	−8.54669			−0.318295
$722$	−11.8464	+	21.5336i	−0.440876	+	0.801397i
$723$		0			0
$724$	27.3620	−	17.3421i	1.01690	−	0.644513i
$725$	−9.00933			−0.334598
$726$		0			0
$727$		−	48.5226i		−	1.79960i	−0.436299	−	0.899802i	$-0.643711\pi$
$727$		−	48.5226i		−	1.79960i	0.436299	−	0.899802i	$-0.356289\pi$
$728$	−14.1413	+	0.877272i	−0.524113	+	0.0325139i
$729$		0			0
$730$	8.19269	−	14.8921i	0.303225	−	0.551183i
$731$		−	6.11311i		−	0.226102i
$732$		0			0
$733$			8.94447i			0.330372i	0.986262	+	0.165186i	$0.0528224\pi$
$733$			8.94447i			0.330372i	−0.986262	+	0.165186i	$0.947178\pi$
$734$	8.26633	+	4.54759i	0.305116	+	0.167855i
$735$		0			0
$736$	20.8480	+	28.7830i	0.768468	+	1.06096i
$737$			44.6533i			1.64483i
$738$		0			0
$739$	4.17997			0.153763			0.0768813	−	0.997040i	$-0.475504\pi$
$739$	4.17997			0.153763			0.0768813	+	0.997040i	$0.475504\pi$
$740$	4.24767	−	2.69218i	0.156147	−	0.0989664i
$741$		0			0
$742$	−9.73599	−	5.35610i	−0.357419	−	0.196629i
$743$	−0.245357			−0.00900129			−0.00450065	−	0.999990i	$-0.501433\pi$
$743$	−0.245357			−0.00900129			−0.00450065	+	0.999990i	$0.501433\pi$
$744$		0			0
$745$	−1.00933			−0.0369789
$746$	−0.421698	−	0.231991i	−0.0154395	−	0.00849378i
$747$		0			0
$748$	26.7967	+	42.2793i	0.979783	+	1.54588i
$749$	−4.00000			−0.146157
$750$		0			0
$751$			8.78603i			0.320607i	0.987068	+	0.160303i	$0.0512473\pi$
$751$			8.78603i			0.320607i	−0.987068	+	0.160303i	$0.948753\pi$
$752$	−16.6226	+	35.2182i	−0.606165	+	1.28427i
$753$		0			0
$754$	−39.5420	−	21.7534i	−1.44003	−	0.792213i
$755$		−	16.5246i		−	0.601391i
$756$		0			0
$757$			41.3393i			1.50250i	0.660016	+	0.751252i	$0.270550\pi$
$757$			41.3393i			1.50250i	−0.660016	+	0.751252i	$0.729450\pi$
$758$	13.8387	−	25.1551i	0.502644	−	0.913674i
$759$		0			0
$760$	−3.59465	+	0.222998i	−0.130392	+	0.00808897i
$761$			10.6726i			0.386882i	0.981112	+	0.193441i	$0.0619649\pi$
$761$			10.6726i			0.386882i	−0.981112	+	0.193441i	$0.938035\pi$
$762$		0			0
$763$	−10.0187			−0.362700
$764$	25.7360	+	40.6058i	0.931095	+	1.46907i
$765$		0			0
$766$	−7.02205	+	12.7642i	−0.253717	+	0.461190i
$767$	1.11203			0.0401531
$768$		0			0
$769$	−28.2427			−1.01846			−0.509229	−	0.860631i	$-0.670069\pi$
$769$	−28.2427			−1.01846			−0.509229	+	0.860631i	$0.670069\pi$
$770$	−6.14134	+	11.1633i	−0.221318	+	0.402299i
$771$		0			0
$772$	19.7674	+	31.1886i	0.711443	+	1.12250i
$773$	−41.4720			−1.49164			−0.745822	−	0.666146i	$-0.767943\pi$
$773$	−41.4720			−1.49164			−0.745822	+	0.666146i	$0.767943\pi$
$774$		0			0
$775$			3.92870i			0.141123i
$776$	−29.5360	+	1.83230i	−1.06028	+	0.0657756i
$777$		0			0
$778$	13.0407	−	23.7046i	0.467532	−	0.849850i
$779$			6.71089i			0.240442i
$780$		0			0
$781$			6.31113i			0.225830i
$782$	−30.5840	−	16.8253i	−1.09368	−	0.601672i
$783$		0			0
$784$	−8.53670	+	18.0866i	−0.304882	+	0.645950i
$785$		−	10.2266i		−	0.365004i
$786$		0			0
$787$	45.1680			1.61007			0.805033	−	0.593230i	$-0.202148\pi$
$787$	45.1680			1.61007			0.805033	+	0.593230i	$0.202148\pi$
$788$	12.2627	+	19.3479i	0.436840	+	0.689239i
$789$		0			0
$790$	−10.1413	−	5.57910i	−0.360813	−	0.198495i
$791$	23.5747			0.838219
$792$		0			0
$793$	−45.1307			−1.60264
$794$	−4.20903	−	2.31554i	−0.149373	−	0.0821753i
$795$		0			0
$796$	−4.22538	+	2.67805i	−0.149765	+	0.0949210i
$797$	−12.4626			−0.441449			−0.220725	−	0.975336i	$-0.570842\pi$
$797$	−12.4626			−0.441449			−0.220725	+	0.975336i	$0.570842\pi$
$798$		0			0
$799$		−	38.2497i		−	1.35318i
$800$	3.31834	+	4.58134i	0.117321	+	0.161975i
$801$		0			0
$802$	12.7617	+	7.02063i	0.450630	+	0.247907i
$803$		−	76.5655i		−	2.70194i
$804$		0			0
$805$		−	8.88504i		−	0.313157i
$806$	−9.48601	+	17.2431i	−0.334130	+	0.607361i
$807$		0			0
$808$	37.0153	−	2.29628i	1.30219	−	0.0807828i
$809$			34.7802i			1.22281i	0.791319	+	0.611404i	$0.209395\pi$
$809$			34.7802i			1.22281i	−0.791319	+	0.611404i	$0.790605\pi$
$810$		0			0
$811$	−31.7360			−1.11440			−0.557201	−	0.830378i	$-0.688125\pi$
$811$	−31.7360			−1.11440			−0.557201	+	0.830378i	$0.688125\pi$
$812$	21.5233	−	13.6415i	0.755321	−	0.478723i
$813$		0			0
$814$	10.9193	−	19.8485i	0.382723	−	0.695689i
$815$	−6.54669			−0.229320
$816$		0			0
$817$	1.98134			0.0693184
$818$	6.21134	−	11.2906i	0.217175	−	0.394766i
$819$		0			0
$820$	8.90300	−	5.64273i	0.310906	−	0.197053i
$821$	4.97201			0.173524			0.0867622	−	0.996229i	$-0.472348\pi$
$821$	4.97201			0.173524			0.0867622	+	0.996229i	$0.472348\pi$
$822$		0			0
$823$			44.0386i			1.53509i	0.640995	+	0.767545i	$0.278522\pi$
$823$			44.0386i			1.53509i	−0.640995	+	0.767545i	$0.721478\pi$
$824$	1.05837	+	17.0606i	0.0368701	+	0.594333i
$825$		0			0
$826$	−0.302648	+	0.550135i	−0.0105305	+	0.0191416i
$827$			32.0838i			1.11566i	0.829954	+	0.557832i	$0.188367\pi$
$827$			32.0838i			1.11566i	−0.829954	+	0.557832i	$0.811633\pi$
$828$		0			0
$829$		−	41.1706i		−	1.42992i	−0.699168	−	0.714958i	$-0.746446\pi$
$829$		−	41.1706i		−	1.42992i	0.699168	−	0.714958i	$-0.253554\pi$
$830$	6.23132	+	3.42807i	0.216292	+	0.118990i
$831$		0			0
$832$	3.50235	+	28.1198i	0.121422	+	0.974878i
$833$		−	19.6435i		−	0.680606i
$834$		0			0
$835$	−22.8480			−0.790688
$836$	−13.7033	+	8.68516i	−0.473938	+	0.300383i
$837$		0			0
$838$	10.1250	+	5.57011i	0.349762	+	0.192416i
$839$	39.9346			1.37870			0.689348	−	0.724430i	$-0.257897\pi$
$839$	39.9346			1.37870			0.689348	+	0.724430i	$0.257897\pi$
$840$		0			0
$841$	52.1680			1.79890
$842$	−4.46264	−	2.45505i	−0.153793	−	0.0846067i
$843$		0			0
$844$	−18.4040	−	29.0376i	−0.633493	−	0.999514i
$845$	0.453313			0.0155944
$846$		0			0
$847$			41.8381i			1.43757i
$848$	−9.48601	+	20.0979i	−0.325751	+	0.690164i
$849$		0			0
$850$	−4.86799	−	2.67805i	−0.166971	−	0.0918564i
$851$			15.7977i			0.541537i
$852$		0			0
$853$			36.0822i			1.23543i	0.786401	+	0.617716i	$0.211942\pi$
$853$			36.0822i			1.23543i	−0.786401	+	0.617716i	$0.788058\pi$
$854$	12.2827	−	22.3267i	0.420304	−	0.764003i
$855$		0			0
$856$	0.495336	+	7.98465i	0.0169302	+	0.272910i
$857$		−	23.0998i		−	0.789074i	−0.918880	−	0.394537i	$-0.870905\pi$
$857$		−	23.0998i		−	0.789074i	0.918880	−	0.394537i	$-0.129095\pi$
$858$		0			0
$859$	44.3013			1.51154			0.755771	−	0.654836i	$-0.227262\pi$
$859$	44.3013			1.51154			0.755771	+	0.654836i	$0.227262\pi$
$860$	−1.66598	−	2.62855i	−0.0568093	−	0.0896327i
$861$		0			0
$862$	5.52332	−	10.0399i	0.188125	−	0.341962i
$863$	25.5492			0.869706			0.434853	−	0.900501i	$-0.356800\pi$
$863$	25.5492			0.869706			0.434853	+	0.900501i	$0.356800\pi$
$864$		0			0
$865$	17.5560			0.596922
$866$	−5.46603	+	9.93581i	−0.185743	+	0.337632i
$867$		0			0
$868$	−5.94865	−	9.38567i	−0.201910	−	0.318570i
$869$	−52.1400			−1.76873
$870$		0			0
$871$		−	24.8280i		−	0.841263i
$872$	1.24065	+	19.9989i	0.0420137	+	0.677247i
$873$		0			0
$874$	5.45331	−	9.91269i	0.184461	−	0.335302i
$875$		−	1.41421i		−	0.0478091i
$876$		0			0
$877$			0.168701i			0.00569661i	0.999996	+	0.00284831i	$0.000906645\pi$
$877$			0.168701i			0.00569661i	−0.999996	+	0.00284831i	$0.999093\pi$
$878$	−17.1180	−	9.41719i	−0.577704	−	0.317815i
$879$		0			0
$880$	23.0443	+	10.8767i	0.776824	+	0.366654i
$881$			29.4704i			0.992881i	0.868071	+	0.496441i	$0.165360\pi$
$881$			29.4704i			0.992881i	−0.868071	+	0.496441i	$0.834640\pi$
$882$		0			0
$883$	−3.43466			−0.115585			−0.0577927	−	0.998329i	$-0.518406\pi$
$883$	−3.43466			−0.115585			−0.0577927	+	0.998329i	$0.518406\pi$
$884$	−14.8994	−	23.5080i	−0.501120	−	0.790658i
$885$		0			0
$886$	15.7546	+	8.66717i	0.529288	+	0.291179i
$887$	−16.6240			−0.558178			−0.279089	−	0.960265i	$-0.590032\pi$
$887$	−16.6240			−0.558178			−0.279089	+	0.960265i	$0.590032\pi$
$888$		0			0
$889$	23.4533			0.786599
$890$	−0.478989	−	0.263508i	−0.0160557	−	0.00883282i
$891$		0			0
$892$	3.44968	−	2.18641i	0.115504	−	0.0732065i
$893$	12.3973			0.414858
$894$		0			0
$895$		−	1.48684i		−	0.0496994i
$896$	−14.8644	−	5.92036i	−0.496584	−	0.197785i
$897$		0			0
$898$	−5.25700	−	2.89206i	−0.175428	−	0.0965092i
$899$		−	35.3949i		−	1.18049i
$900$		0			0
$901$		−	21.8279i		−	0.727193i
$902$	22.8867	−	41.6019i	0.762042	−	1.38519i
$903$		0			0
$904$	−2.91934	−	47.0589i	−0.0970959	−	1.56516i
$905$			16.1974i			0.538421i
$906$		0			0
$907$	50.1587			1.66549			0.832746	−	0.553656i	$-0.186768\pi$
$907$	50.1587			1.66549			0.832746	+	0.553656i	$0.186768\pi$
$908$	35.8573	−	22.7264i	1.18997	−	0.754203i
$909$		0			0
$910$	3.41468	−	6.20699i	0.113196	−	0.205760i
$911$	−26.5467			−0.879531			−0.439765	−	0.898113i	$-0.644938\pi$
$911$	−26.5467			−0.879531			−0.439765	+	0.898113i	$0.644938\pi$
$912$		0			0
$913$	32.0373			1.06028
$914$	2.28399	−	4.15169i	0.0755477	−	0.137326i
$915$		0			0
$916$	−22.5840	+	14.3138i	−0.746196	+	0.472940i
$917$	−7.02799			−0.232085
$918$		0			0
$919$		−	39.3236i		−	1.29717i	−0.761144	−	0.648583i	$-0.775362\pi$
$919$		−	39.3236i		−	1.29717i	0.761144	−	0.648583i	$-0.224638\pi$
$920$	−17.7360	+	1.10027i	−0.584738	+	0.0362748i
$921$		0			0
$922$	−12.3654	+	22.4770i	−0.407233	+	0.740242i
$923$		−	3.50909i		−	0.115503i
$924$		0			0
$925$			2.51448i			0.0826757i
$926$	40.7990	+	22.4449i	1.34074	+	0.737586i
$927$		0			0
$928$	−29.8960	−	41.2748i	−0.981384	−	1.35491i
$929$		−	38.9833i		−	1.27900i	−0.768791	−	0.639500i	$-0.779141\pi$
$929$		−	38.9833i		−	1.27900i	0.768791	−	0.639500i	$-0.220859\pi$
$930$		0			0
$931$	6.36672			0.208661
$932$	−29.2207	+	18.5201i	−0.957155	+	0.606646i
$933$		0			0
$934$	−7.96731	−	4.38309i	−0.260698	−	0.143419i
$935$	−25.0280			−0.818503
$936$		0			0
$937$	−11.1307			−0.363624			−0.181812	−	0.983333i	$-0.558196\pi$
$937$	−11.1307			−0.363624			−0.181812	+	0.983333i	$0.558196\pi$
$938$	12.2827	+	6.75712i	0.401043	+	0.220628i
$939$		0			0
$940$	−10.4240	−	16.4468i	−0.339994	−	0.536436i
$941$	46.2427			1.50747			0.753735	−	0.657179i	$-0.228250\pi$
$941$	46.2427			1.50747			0.753735	+	0.657179i	$0.228250\pi$
$942$		0			0
$943$			33.1115i			1.07826i
$944$	1.13564	+	0.536010i	0.0369618	+	0.0174456i
$945$		0			0
$946$	−12.2827	−	6.75712i	−0.399344	−	0.219693i
$947$			16.3163i			0.530208i	0.964220	+	0.265104i	$0.0854063\pi$
$947$			16.3163i			0.530208i	−0.964220	+	0.265104i	$0.914594\pi$
$948$		0			0
$949$			42.5717i			1.38193i
$950$	0.867993	−	1.57778i	0.0281614	−	0.0511900i
$951$		0			0
$952$	15.6846	−	0.973012i	0.508342	−	0.0315355i
$953$			8.01290i			0.259563i	0.991543	+	0.129782i	$0.0414276\pi$
$953$			8.01290i			0.259563i	−0.991543	+	0.129782i	$0.958572\pi$
$954$		0			0
$955$	−24.0373			−0.777829
$956$	−14.4040	−	22.7264i	−0.465860	−	0.735025i
$957$		0			0
$958$	19.7873	−	35.9682i	0.639300	−	1.16208i
$959$	3.53736			0.114227
$960$		0			0
$961$	15.5653			0.502108
$962$	−6.07133	+	11.0361i	−0.195747	+	0.355817i
$963$		0			0
$964$	4.88797	+	7.71215i	0.157431	+	0.248392i
$965$	−18.4626			−0.594333
$966$		0			0
$967$		−	61.0092i		−	1.96192i	−0.194201	−	0.980962i	$-0.562211\pi$
$967$		−	61.0092i		−	1.96192i	0.194201	−	0.980962i	$-0.437789\pi$
$968$	83.5156	−	5.18098i	2.68429	−	0.166523i
$969$		0			0
$970$	7.13201	−	12.9641i	0.228995	−	0.416253i
$971$		−	16.0023i		−	0.513540i	−0.966473	−	0.256770i	$-0.917342\pi$
$971$		−	16.0023i		−	0.513540i	0.966473	−	0.256770i	$-0.0826582\pi$
$972$		0			0
$973$			26.6551i			0.854524i
$974$	14.5303	+	7.99364i	0.465582	+	0.256133i
$975$		0			0
$976$	−46.0887	−	21.7534i	−1.47526	−	0.696310i
$977$		−	34.2683i		−	1.09634i	−0.836367	−	0.548169i	$-0.815325\pi$
$977$		−	34.2683i		−	1.09634i	0.836367	−	0.548169i	$-0.184675\pi$
$978$		0			0
$979$	−2.46264			−0.0787064
$980$	−5.35334	−	8.44640i	−0.171006	−	0.269810i
$981$		0			0
$982$	−9.94502	−	5.47110i	−0.317358	−	0.174590i
$983$	15.3947			0.491015			0.245507	−	0.969395i	$-0.421045\pi$
$983$	15.3947			0.491015			0.245507	+	0.969395i	$0.421045\pi$
$984$		0			0
$985$	−11.4533			−0.364933
$986$	43.8573	+	24.1274i	1.39670	+	0.768374i
$987$		0			0
$988$	7.61925	−	4.82909i	0.242401	−	0.153634i
$989$	9.77594			0.310857
$990$		0			0
$991$		−	14.6145i		−	0.464245i	−0.972687	−	0.232123i	$-0.925433\pi$
$991$		−	14.6145i		−	0.464245i	0.972687	−	0.232123i	$-0.0745671\pi$
$992$	−17.9987	+	13.0367i	−0.571459	+	0.413917i
$993$		0			0
$994$	1.73599	+	0.955026i	0.0550621	+	0.0302916i
$995$		−	2.50129i		−	0.0792962i
$996$		0			0
$997$			44.7655i			1.41774i	0.705340	+	0.708869i	$0.250794\pi$
$997$			44.7655i			1.41774i	−0.705340	+	0.708869i	$0.749206\pi$
$998$	−17.9987	+	32.7169i	−0.569738	+	1.03563i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.b.d.251.3	yes	6
3.2	odd	2		360.2.b.c.251.4	yes	6
4.3	odd	2		1440.2.b.d.431.6		6
5.2	odd	4		1800.2.m.e.899.12		12
5.3	odd	4		1800.2.m.e.899.1		12
5.4	even	2		1800.2.b.d.251.4		6
8.3	odd	2		360.2.b.c.251.3	✓	6
8.5	even	2		1440.2.b.c.431.3		6
12.11	even	2		1440.2.b.c.431.4		6
15.2	even	4		1800.2.m.d.899.1		12
15.8	even	4		1800.2.m.d.899.12		12
15.14	odd	2		1800.2.b.e.251.3		6
20.3	even	4		7200.2.m.e.3599.12		12
20.7	even	4		7200.2.m.e.3599.6		12
20.19	odd	2		7200.2.b.e.4751.3		6
24.5	odd	2		1440.2.b.d.431.1		6
24.11	even	2	inner	360.2.b.d.251.4	yes	6
40.3	even	4		1800.2.m.d.899.2		12
40.13	odd	4		7200.2.m.d.3599.6		12
40.19	odd	2		1800.2.b.e.251.4		6
40.27	even	4		1800.2.m.d.899.11		12
40.29	even	2		7200.2.b.d.4751.6		6
40.37	odd	4		7200.2.m.d.3599.12		12
60.23	odd	4		7200.2.m.d.3599.7		12
60.47	odd	4		7200.2.m.d.3599.1		12
60.59	even	2		7200.2.b.d.4751.1		6
120.29	odd	2		7200.2.b.e.4751.4		6
120.53	even	4		7200.2.m.e.3599.1		12
120.59	even	2		1800.2.b.d.251.3		6
120.77	even	4		7200.2.m.e.3599.7		12
120.83	odd	4		1800.2.m.e.899.11		12
120.107	odd	4		1800.2.m.e.899.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.b.c.251.3	✓	6	8.3	odd	2
360.2.b.c.251.4	yes	6	3.2	odd	2
360.2.b.d.251.3	yes	6	1.1	even	1	trivial
360.2.b.d.251.4	yes	6	24.11	even	2	inner
1440.2.b.c.431.3		6	8.5	even	2
1440.2.b.c.431.4		6	12.11	even	2
1440.2.b.d.431.1		6	24.5	odd	2
1440.2.b.d.431.6		6	4.3	odd	2
1800.2.b.d.251.3		6	120.59	even	2
1800.2.b.d.251.4		6	5.4	even	2
1800.2.b.e.251.3		6	15.14	odd	2
1800.2.b.e.251.4		6	40.19	odd	2
1800.2.m.d.899.1		12	15.2	even	4
1800.2.m.d.899.2		12	40.3	even	4
1800.2.m.d.899.11		12	40.27	even	4
1800.2.m.d.899.12		12	15.8	even	4
1800.2.m.e.899.1		12	5.3	odd	4
1800.2.m.e.899.2		12	120.107	odd	4
1800.2.m.e.899.11		12	120.83	odd	4
1800.2.m.e.899.12		12	5.2	odd	4
7200.2.b.d.4751.1		6	60.59	even	2
7200.2.b.d.4751.6		6	40.29	even	2
7200.2.b.e.4751.3		6	20.19	odd	2
7200.2.b.e.4751.4		6	120.29	odd	2
7200.2.m.d.3599.1		12	60.47	odd	4
7200.2.m.d.3599.6		12	40.13	odd	4
7200.2.m.d.3599.7		12	60.23	odd	4
7200.2.m.d.3599.12		12	40.37	odd	4
7200.2.m.e.3599.1		12	120.53	even	4
7200.2.m.e.3599.6		12	20.7	even	4
7200.2.m.e.3599.7		12	120.77	even	4
7200.2.m.e.3599.12		12	20.3	even	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.681664 - 1.23909i) q^{2} +(-1.07067 - 1.68928i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(-2.82300 + 0.175128i) q^{8} +O(q^{10})\)	\(q+(0.681664 - 1.23909i) q^{2} +(-1.07067 - 1.68928i) q^{4} +1.00000 q^{5} -1.41421i q^{7} +(-2.82300 + 0.175128i) q^{8} +(0.681664 - 1.23909i) q^{10} -6.37056i q^{11} +3.54213i q^{13} +(-1.75233 - 0.964019i) q^{14} +(-1.70734 + 3.61732i) q^{16} -3.92870i q^{17} +1.27334 q^{19} +(-1.07067 - 1.68928i) q^{20} +(-7.89367 - 4.34258i) q^{22} +6.28267 q^{23} +1.00000 q^{25} +(4.38900 + 2.41454i) q^{26} +(-2.38900 + 1.51415i) q^{28} -9.00933 q^{29} +3.92870i q^{31} +(3.31834 + 4.58134i) q^{32} +(-4.86799 - 2.67805i) q^{34} -1.41421i q^{35} +2.51448i q^{37} +(0.867993 - 1.57778i) q^{38} +(-2.82300 + 0.175128i) q^{40} +5.27029i q^{41} +1.55602 q^{43} +(-10.7617 + 6.82075i) q^{44} +(4.28267 - 7.78477i) q^{46} +9.73599 q^{47} +5.00000 q^{49} +(0.681664 - 1.23909i) q^{50} +(5.98365 - 3.79245i) q^{52} +5.55602 q^{53} -6.37056i q^{55} +(0.247668 + 3.99233i) q^{56} +(-6.14134 + 11.1633i) q^{58} -0.313944i q^{59} +12.7411i q^{61} +(4.86799 + 2.67805i) q^{62} +(7.93866 - 0.988770i) q^{64} +3.54213i q^{65} -7.00933 q^{67} +(-6.63667 + 4.20633i) q^{68} +(-1.75233 - 0.964019i) q^{70} -0.990671 q^{71} +12.0187 q^{73} +(3.11566 + 1.71403i) q^{74} +(-1.36333 - 2.15103i) q^{76} -9.00933 q^{77} -8.18453i q^{79} +(-1.70734 + 3.61732i) q^{80} +(6.53034 + 3.59257i) q^{82} +5.02897i q^{83} -3.92870i q^{85} +(1.06068 - 1.92804i) q^{86} +(1.11566 + 17.9841i) q^{88} -0.386566i q^{89} +5.00933 q^{91} +(-6.72666 - 10.6132i) q^{92} +(6.63667 - 12.0637i) q^{94} +1.27334 q^{95} +10.4626 q^{97} +(3.40832 - 6.19543i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{5} + 2 q^{8} + 2 q^{10} - 6 q^{16} + 16 q^{19} + 2 q^{20} - 20 q^{22} + 4 q^{23} + 6 q^{25} + 20 q^{26} - 8 q^{28} - 12 q^{29} + 22 q^{32} - 4 q^{34} - 20 q^{38} + 2 q^{40} - 16 q^{43} - 12 q^{44} - 8 q^{46} + 8 q^{47} + 30 q^{49} + 2 q^{50} - 4 q^{52} + 8 q^{53} + 12 q^{56} - 20 q^{58} + 4 q^{62} + 14 q^{64} - 44 q^{68} - 48 q^{71} - 12 q^{73} + 4 q^{74} - 4 q^{76} - 12 q^{77} - 6 q^{80} + 16 q^{82} - 40 q^{86} - 8 q^{88} - 12 q^{91} - 32 q^{92} + 44 q^{94} + 16 q^{95} + 4 q^{97} + 10 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^5 + 2 * q^8 + 2 * q^10 - 6 * q^16 + 16 * q^19 + 2 * q^20 - 20 * q^22 + 4 * q^23 + 6 * q^25 + 20 * q^26 - 8 * q^28 - 12 * q^29 + 22 * q^32 - 4 * q^34 - 20 * q^38 + 2 * q^40 - 16 * q^43 - 12 * q^44 - 8 * q^46 + 8 * q^47 + 30 * q^49 + 2 * q^50 - 4 * q^52 + 8 * q^53 + 12 * q^56 - 20 * q^58 + 4 * q^62 + 14 * q^64 - 44 * q^68 - 48 * q^71 - 12 * q^73 + 4 * q^74 - 4 * q^76 - 12 * q^77 - 6 * q^80 + 16 * q^82 - 40 * q^86 - 8 * q^88 - 12 * q^91 - 32 * q^92 + 44 * q^94 + 16 * q^95 + 4 * q^97 + 10 * q^98

Introduction

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