LMFDB - Embedded newform 288.2.r.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(49,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("288.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.820200 - 1.15207i$ of defining polynomial
Character	$\chi$	$=$	288.49
Dual form			288.2.r.b.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69028 + 0.378078i) q^{3} +(-1.97542 - 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +(2.71411 - 1.27812i) q^{9} +O(q^{10})$	\(q+(-1.69028 + 0.378078i) q^{3} +(-1.97542 - 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +(2.71411 - 1.27812i) q^{9} +(4.24153 - 2.44885i) q^{11} +(4.00895 + 2.31457i) q^{13} +(3.77023 + 1.18092i) q^{15} +1.92788 q^{17} +2.12907i q^{19} +(-2.12897 - 2.31457i) q^{21} +(1.15765 - 2.00511i) q^{23} +(0.101535 + 0.175863i) q^{25} +(-4.10439 + 3.18653i) q^{27} +(3.16440 - 1.82697i) q^{29} +(2.65800 - 4.60379i) q^{31} +(-6.24353 + 5.74287i) q^{33} -4.14154i q^{35} +7.98438i q^{37} +(-7.65135 - 2.39658i) q^{39} +(-2.36240 + 4.09180i) q^{41} +(2.20800 - 1.27479i) q^{43} +(-6.81924 - 0.570655i) q^{45} +(2.02005 + 3.49884i) q^{47} +(1.85171 - 3.20726i) q^{49} +(-3.25866 + 0.728888i) q^{51} -8.95958i q^{53} -11.1718 q^{55} +(-0.804954 - 3.59873i) q^{57} +(-3.05255 - 1.76239i) q^{59} +(1.71675 - 0.991165i) q^{61} +(4.47365 + 3.10736i) q^{63} +(-5.27959 - 9.14451i) q^{65} +(7.72723 + 4.46132i) q^{67} +(-1.19867 + 3.82688i) q^{69} -13.3561 q^{71} -11.5592 q^{73} +(-0.238112 - 0.258870i) q^{75} +(7.70112 + 4.44625i) q^{77} +(4.97330 + 8.61401i) q^{79} +(5.73283 - 6.93791i) q^{81} +(-3.12153 + 1.80221i) q^{83} +(-3.80838 - 2.19877i) q^{85} +(-4.65800 + 4.28448i) q^{87} +2.49965 q^{89} +8.40489i q^{91} +(-2.75218 + 8.78664i) q^{93} +(2.42823 - 4.20582i) q^{95} +(6.99370 + 12.1134i) q^{97} +(8.38208 - 12.0676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 6 * q^7 + 2 * q^9	$ 16 q - 6 q^{7} + 2 q^{9} + 10 q^{15} - 28 q^{17} + 10 q^{23} + 2 q^{25} + 10 q^{31} - 2 q^{39} - 8 q^{41} - 6 q^{47} + 18 q^{49} + 4 q^{55} + 10 q^{57} - 2 q^{63} - 14 q^{65} - 72 q^{71} - 44 q^{73} + 30 q^{79} + 10 q^{81} - 42 q^{87} + 64 q^{89} - 44 q^{95}+O(q^{100}) $ 16 * q - 6 * q^7 + 2 * q^9 + 10 * q^15 - 28 * q^17 + 10 * q^23 + 2 * q^25 + 10 * q^31 - 2 * q^39 - 8 * q^41 - 6 * q^47 + 18 * q^49 + 4 * q^55 + 10 * q^57 - 2 * q^63 - 14 * q^65 - 72 * q^71 - 44 * q^73 + 30 * q^79 + 10 * q^81 - 42 * q^87 + 64 * q^89 - 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.69028	+	0.378078i	−0.975885	+	0.218283i
$3$	−1.69028	+	0.378078i	−0.975885	+	0.218283i
$4$		0			0
$5$	−1.97542	−	1.14051i	−0.883437	−	0.510052i	−0.0116467	−	0.999932i	$-0.503707\pi$
$5$	−1.97542	−	1.14051i	−0.883437	−	0.510052i	−0.871790	+	0.489880i	$0.837041\pi$
$6$		0			0
$7$	0.907824	+	1.57240i	0.343125	+	0.594311i	0.985011	−	0.172490i	$-0.0551811\pi$
$7$	0.907824	+	1.57240i	0.343125	+	0.594311i	−0.641886	+	0.766800i	$0.721848\pi$
$8$		0			0
$9$	2.71411	−	1.27812i	0.904705	−	0.426039i
$10$		0			0
$11$	4.24153	−	2.44885i	1.27887	−	0.738355i	0.302228	−	0.953236i	$-0.402270\pi$
$11$	4.24153	−	2.44885i	1.27887	−	0.738355i	0.976640	+	0.214880i	$0.0689362\pi$
$12$		0			0
$13$	4.00895	+	2.31457i	1.11188	+	0.641946i	0.939317	−	0.343052i	$-0.111461\pi$
$13$	4.00895	+	2.31457i	1.11188	+	0.641946i	0.172567	+	0.984998i	$0.444794\pi$
$14$		0			0
$15$	3.77023	+	1.18092i	0.973469	+	0.304913i
$16$		0			0
$17$	1.92788			0.467579			0.233790	−	0.972287i	$-0.424887\pi$
$17$	1.92788			0.467579			0.233790	+	0.972287i	$0.424887\pi$
$18$		0			0
$19$			2.12907i			0.488442i	0.969720	+	0.244221i	$0.0785322\pi$
$19$			2.12907i			0.488442i	−0.969720	+	0.244221i	$0.921468\pi$
$20$		0			0
$21$	−2.12897	−	2.31457i	−0.464579	−	0.505080i
$22$		0			0
$23$	1.15765	−	2.00511i	0.241387	−	0.418094i	−0.719723	−	0.694261i	$-0.755731\pi$
$23$	1.15765	−	2.00511i	0.241387	−	0.418094i	0.961109	+	0.276168i	$0.0890645\pi$
$24$		0			0
$25$	0.101535	+	0.175863i	0.0203069	+	0.0351726i
$26$		0			0
$27$	−4.10439	+	3.18653i	−0.789891	+	0.613247i
$28$		0			0
$29$	3.16440	−	1.82697i	0.587615	−	0.339260i	−0.176539	−	0.984294i	$-0.556490\pi$
$29$	3.16440	−	1.82697i	0.587615	−	0.339260i	0.764154	+	0.645034i	$0.223157\pi$
$30$		0			0
$31$	2.65800	−	4.60379i	0.477391	−	0.826865i	−0.522273	−	0.852778i	$-0.674916\pi$
$31$	2.65800	−	4.60379i	0.477391	−	0.826865i	0.999664	+	0.0259130i	$0.00824928\pi$
$32$		0			0
$33$	−6.24353	+	5.74287i	−1.08686	+	0.999706i
$34$		0			0
$35$		−	4.14154i		−	0.700048i
$36$		0			0
$37$			7.98438i			1.31262i	0.754489	+	0.656312i	$0.227885\pi$
$37$			7.98438i			1.31262i	−0.754489	+	0.656312i	$0.772115\pi$
$38$		0			0
$39$	−7.65135	−	2.39658i	−1.22520	−	0.383760i
$40$		0			0
$41$	−2.36240	+	4.09180i	−0.368946	+	0.639033i	−0.989401	−	0.145209i	$-0.953614\pi$
$41$	−2.36240	+	4.09180i	−0.368946	+	0.639033i	0.620455	+	0.784242i	$0.286948\pi$
$42$		0			0
$43$	2.20800	−	1.27479i	0.336717	−	0.194404i	−0.322102	−	0.946705i	$-0.604390\pi$
$43$	2.20800	−	1.27479i	0.336717	−	0.194404i	0.658819	+	0.752301i	$0.271056\pi$
$44$		0			0
$45$	−6.81924	−	0.570655i	−1.01655	−	0.0850683i
$46$		0			0
$47$	2.02005	+	3.49884i	0.294655	+	0.510358i	0.974905	−	0.222623i	$-0.0714619\pi$
$47$	2.02005	+	3.49884i	0.294655	+	0.510358i	−0.680249	+	0.732981i	$0.738129\pi$
$48$		0			0
$49$	1.85171	−	3.20726i	0.264530	−	0.458179i
$50$		0			0
$51$	−3.25866	+	0.728888i	−0.456304	+	0.102065i
$52$		0			0
$53$		−	8.95958i		−	1.23069i	−0.788257	−	0.615347i	$-0.789016\pi$
$53$		−	8.95958i		−	1.23069i	0.788257	−	0.615347i	$-0.210984\pi$
$54$		0			0
$55$	−11.1718			−1.50640
$56$		0			0
$57$	−0.804954	−	3.59873i	−0.106619	−	0.476663i
$58$		0			0
$59$	−3.05255	−	1.76239i	−0.397408	−	0.229444i	0.287957	−	0.957643i	$-0.407024\pi$
$59$	−3.05255	−	1.76239i	−0.397408	−	0.229444i	−0.685365	+	0.728200i	$0.740357\pi$
$60$		0			0
$61$	1.71675	−	0.991165i	0.219807	−	0.126906i	−0.386054	−	0.922476i	$-0.626162\pi$
$61$	1.71675	−	0.991165i	0.219807	−	0.126906i	0.605861	+	0.795571i	$0.292829\pi$
$62$		0			0
$63$	4.47365	+	3.10736i	0.563627	+	0.391491i
$64$		0			0
$65$	−5.27959	−	9.14451i	−0.654852	−	1.13424i
$66$		0			0
$67$	7.72723	+	4.46132i	0.944031	+	0.545036i	0.891222	−	0.453568i	$-0.149849\pi$
$67$	7.72723	+	4.46132i	0.944031	+	0.545036i	0.0528093	+	0.998605i	$0.483182\pi$
$68$		0			0
$69$	−1.19867	+	3.82688i	−0.144303	+	0.460702i
$70$		0			0
$71$	−13.3561			−1.58508			−0.792539	−	0.609821i	$-0.791241\pi$
$71$	−13.3561			−1.58508			−0.792539	+	0.609821i	$0.791241\pi$
$72$		0			0
$73$	−11.5592			−1.35290			−0.676450	−	0.736489i	$-0.736482\pi$
$73$	−11.5592			−1.35290			−0.676450	+	0.736489i	$0.736482\pi$
$74$		0			0
$75$	−0.238112	−	0.258870i	−0.0274948	−	0.0298918i
$76$		0			0
$77$	7.70112	+	4.44625i	0.877625	+	0.506697i
$78$		0			0
$79$	4.97330	+	8.61401i	0.559540	+	0.969151i	0.997535	+	0.0701739i	$0.0223554\pi$
$79$	4.97330	+	8.61401i	0.559540	+	0.969151i	−0.437995	+	0.898977i	$0.644311\pi$
$80$		0			0
$81$	5.73283	−	6.93791i	0.636981	−	0.770879i
$82$		0			0
$83$	−3.12153	+	1.80221i	−0.342632	+	0.197819i	−0.661435	−	0.750002i	$-0.730052\pi$
$83$	−3.12153	+	1.80221i	−0.342632	+	0.197819i	0.318803	+	0.947821i	$0.396719\pi$
$84$		0			0
$85$	−3.80838	−	2.19877i	−0.413077	−	0.238490i
$86$		0			0
$87$	−4.65800	+	4.28448i	−0.499390	+	0.459345i
$88$		0			0
$89$	2.49965			0.264962			0.132481	−	0.991186i	$-0.457706\pi$
$89$	2.49965			0.264962			0.132481	+	0.991186i	$0.457706\pi$
$90$		0			0
$91$			8.40489i			0.881072i
$92$		0			0
$93$	−2.75218	+	8.78664i	−0.285388	+	0.911132i
$94$		0			0
$95$	2.42823	−	4.20582i	0.249131	−	0.431508i
$96$		0			0
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	0.964818	+	0.262918i	$0.0846849\pi$
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	−0.254715	+	0.967016i	$0.581982\pi$
$98$		0			0
$99$	8.38208	−	12.0676i	0.842430	−	1.21284i
$100$		0			0
$101$	−1.13087	+	0.652911i	−0.112526	+	0.0649671i	−0.555207	−	0.831712i	$-0.687361\pi$
$101$	−1.13087	+	0.652911i	−0.112526	+	0.0649671i	0.442681	+	0.896679i	$0.354028\pi$
$102$		0			0
$103$	3.22312	−	5.58261i	0.317584	−	0.550071i	−0.662400	−	0.749151i	$-0.730462\pi$
$103$	3.22312	−	5.58261i	0.317584	−	0.550071i	0.979983	+	0.199080i	$0.0637952\pi$
$104$		0			0
$105$	1.56582	+	7.00037i	0.152809	+	0.683166i
$106$		0			0
$107$			3.10427i			0.300101i	0.988678	+	0.150051i	$0.0479437\pi$
$107$			3.10427i			0.300101i	−0.988678	+	0.150051i	$0.952056\pi$
$108$		0			0
$109$		−	18.0837i		−	1.73210i	−0.499955	−	0.866051i	$-0.666650\pi$
$109$		−	18.0837i		−	1.73210i	0.499955	−	0.866051i	$-0.333350\pi$
$110$		0			0
$111$	−3.01872	−	13.4959i	−0.286524	−	1.28097i
$112$		0			0
$113$	−1.41718	+	2.45463i	−0.133317	+	0.230913i	−0.924953	−	0.380080i	$-0.875896\pi$
$113$	−1.41718	+	2.45463i	−0.133317	+	0.230913i	0.791636	+	0.610993i	$0.209230\pi$
$114$		0			0
$115$	−4.57370	+	2.64063i	−0.426500	+	0.246240i
$116$		0			0
$117$	13.8390	+	1.15810i	1.27942	+	0.107066i
$118$		0			0
$119$	1.75018	+	3.03139i	0.160438	+	0.277887i
$120$		0			0
$121$	6.49370	−	11.2474i	0.590337	−	1.02249i
$122$		0			0
$123$	2.44611	−	7.80948i	0.220558	−	0.704157i
$124$		0			0
$125$			10.9419i			0.978674i
$126$		0			0
$127$	7.44962			0.661047			0.330523	−	0.943798i	$-0.392775\pi$
$127$	7.44962			0.661047			0.330523	+	0.943798i	$0.392775\pi$
$128$		0			0
$129$	−3.25018	+	2.98955i	−0.286162	+	0.263215i
$130$		0			0
$131$	3.12153	+	1.80221i	0.272729	+	0.157460i	0.630127	−	0.776492i	$-0.283003\pi$
$131$	3.12153	+	1.80221i	0.272729	+	0.157460i	−0.357398	+	0.933952i	$0.616336\pi$
$132$		0			0
$133$	−3.34774	+	1.93282i	−0.290286	+	0.167597i
$134$		0			0
$135$	11.7422	−	1.61363i	1.01061	−	0.138879i
$136$		0			0
$137$	5.88147	+	10.1870i	0.502488	+	0.870335i	0.999996	+	0.00287543i	$0.000915278\pi$
$137$	5.88147	+	10.1870i	0.502488	+	0.870335i	−0.497508	+	0.867460i	$0.665751\pi$
$138$		0			0
$139$	−11.0400	−	6.37395i	−0.936400	−	0.540631i	−0.0475703	−	0.998868i	$-0.515148\pi$
$139$	−11.0400	−	6.37395i	−0.936400	−	0.540631i	−0.888830	+	0.458237i	$0.848481\pi$
$140$		0			0
$141$	−4.73730	−	5.15029i	−0.398952	−	0.433732i
$142$		0			0
$143$	22.6721			1.89594
$144$		0			0
$145$	−8.33472			−0.692161
$146$		0			0
$147$	−1.91732	+	6.12126i	−0.158138	+	0.504873i
$148$		0			0
$149$	−6.59790	−	3.80930i	−0.540521	−	0.312070i	0.204769	−	0.978810i	$-0.434356\pi$
$149$	−6.59790	−	3.80930i	−0.540521	−	0.312070i	−0.745290	+	0.666740i	$0.767689\pi$
$150$		0			0
$151$	−2.26988	−	3.93155i	−0.184720	−	0.319945i	0.758762	−	0.651368i	$-0.225805\pi$
$151$	−2.26988	−	3.93155i	−0.184720	−	0.319945i	−0.943482	+	0.331423i	$0.892471\pi$
$152$		0			0
$153$	5.23248	−	2.46405i	0.423021	−	0.199207i
$154$		0			0
$155$	−10.5014	+	6.06296i	−0.843489	+	0.486989i
$156$		0			0
$157$	−11.4105	−	6.58787i	−0.910659	−	0.525769i	−0.0300161	−	0.999549i	$-0.509556\pi$
$157$	−11.4105	−	6.58787i	−0.910659	−	0.525769i	−0.880643	+	0.473780i	$0.842889\pi$
$158$		0			0
$159$	3.38742	+	15.1442i	0.268640	+	1.20102i
$160$		0			0
$161$	4.20377			0.331303
$162$		0			0
$163$		−	20.5911i		−	1.61282i	−0.591358	−	0.806409i	$-0.701408\pi$
$163$		−	20.5911i		−	1.61282i	0.591358	−	0.806409i	$-0.298592\pi$
$164$		0			0
$165$	18.8834	−	4.22379i	1.47007	−	0.328822i
$166$		0			0
$167$	−2.53912	+	4.39789i	−0.196483	+	0.340319i	−0.947386	−	0.320094i	$-0.896285\pi$
$167$	−2.53912	+	4.39789i	−0.196483	+	0.340319i	0.750903	+	0.660413i	$0.229619\pi$
$168$		0			0
$169$	4.21446	+	7.29967i	0.324190	+	0.561513i
$170$		0			0
$171$	2.72120	+	5.77854i	0.208095	+	0.441896i
$172$		0			0
$173$	−11.0398	+	6.37385i	−0.839343	+	0.484595i	−0.857041	−	0.515248i	$-0.827700\pi$
$173$	−11.0398	+	6.37385i	−0.839343	+	0.484595i	0.0176977	+	0.999843i	$0.494366\pi$
$174$		0			0
$175$	−0.184351	+	0.319306i	−0.0139356	+	0.0241372i
$176$		0			0
$177$	5.82599	+	1.82484i	0.437908	+	0.137163i
$178$		0			0
$179$			8.82019i			0.659252i	0.944112	+	0.329626i	$0.106923\pi$
$179$			8.82019i			0.659252i	−0.944112	+	0.329626i	$0.893077\pi$
$180$		0			0
$181$			15.4369i			1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$181$			15.4369i			1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$182$		0			0
$183$	−2.52705	+	2.32441i	−0.186805	+	0.171826i
$184$		0			0
$185$	9.10628	−	15.7725i	0.669507	−	1.15962i
$186$		0			0
$187$	8.17715	−	4.72108i	0.597972	−	0.345239i
$188$		0			0
$189$	−8.73656	−	3.56093i	−0.635491	−	0.259020i
$190$		0			0
$191$	−4.81698	−	8.34326i	−0.348545	−	0.603697i	0.637446	−	0.770495i	$-0.279991\pi$
$191$	−4.81698	−	8.34326i	−0.348545	−	0.603697i	−0.985991	+	0.166797i	$0.946657\pi$
$192$		0			0
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	−0.712470	−	0.701702i	$-0.752424\pi$
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	0.963927	+	0.266166i	$0.0857570\pi$
$194$		0			0
$195$	12.3813	+	13.4607i	0.886646	+	0.963942i
$196$		0			0
$197$			4.31842i			0.307675i	0.988096	+	0.153837i	$0.0491632\pi$
$197$			4.31842i			0.307675i	−0.988096	+	0.153837i	$0.950837\pi$
$198$		0			0
$199$	−5.90649			−0.418700			−0.209350	−	0.977841i	$-0.567135\pi$
$199$	−5.90649			−0.418700			−0.209350	+	0.977841i	$0.567135\pi$
$200$		0			0
$201$	−14.7479	−	4.61939i	−1.04024	−	0.325827i
$202$		0			0
$203$	5.74544	+	3.31713i	0.403251	+	0.232817i
$204$		0			0
$205$	9.33350	−	5.38870i	0.651880	−	0.376363i
$206$		0			0
$207$	0.579230	−	6.92170i	0.0402593	−	0.481092i
$208$		0			0
$209$	5.21376	+	9.03050i	0.360644	+	0.624653i
$210$		0			0
$211$	−15.8781	−	9.16723i	−1.09309	−	0.631098i	−0.158696	−	0.987328i	$-0.550729\pi$
$211$	−15.8781	−	9.16723i	−1.09309	−	0.631098i	−0.934399	+	0.356229i	$0.884062\pi$
$212$		0			0
$213$	22.5756	−	5.04965i	1.54685	−	0.345996i
$214$		0			0
$215$	−5.81565			−0.396624
$216$		0			0
$217$	9.65199			0.655220
$218$		0			0
$219$	19.5383	−	4.37027i	1.32027	−	0.295315i
$220$		0			0
$221$	7.72877	+	4.46221i	0.519893	+	0.300161i
$222$		0			0
$223$	2.63263	+	4.55986i	0.176294	+	0.305350i	0.940608	−	0.339494i	$-0.110256\pi$
$223$	2.63263	+	4.55986i	0.176294	+	0.305350i	−0.764314	+	0.644844i	$0.776922\pi$
$224$		0			0
$225$	0.500350	+	0.347539i	0.0333567	+	0.0231693i
$226$		0			0
$227$	1.53638	−	0.887027i	0.101973	−	0.0588741i	−0.448146	−	0.893960i	$-0.647916\pi$
$227$	1.53638	−	0.887027i	0.101973	−	0.0588741i	0.550119	+	0.835086i	$0.314582\pi$
$228$		0			0
$229$	3.30687	+	1.90922i	0.218524	+	0.126165i	0.605267	−	0.796023i	$-0.293066\pi$
$229$	3.30687	+	1.90922i	0.218524	+	0.126165i	−0.386742	+	0.922188i	$0.626400\pi$
$230$		0			0
$231$	−14.6981	−	4.60379i	−0.967064	−	0.302907i
$232$		0			0
$233$	−20.3207			−1.33125			−0.665627	−	0.746284i	$-0.731836\pi$
$233$	−20.3207			−1.33125			−0.665627	+	0.746284i	$0.731836\pi$
$234$		0			0
$235$		−	9.21558i		−	0.601158i
$236$		0			0
$237$	−11.6630	−	12.6798i	−0.757596	−	0.823642i
$238$		0			0
$239$	−8.69811	+	15.0656i	−0.562634	+	0.974510i	0.434632	+	0.900608i	$0.356879\pi$
$239$	−8.69811	+	15.0656i	−0.562634	+	0.974510i	−0.997266	+	0.0739020i	$0.976455\pi$
$240$		0			0
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	0.556171	−	0.831068i	$-0.312270\pi$
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	−0.997811	+	0.0661240i	$0.978937\pi$
$242$		0			0
$243$	−7.06704	+	13.8945i	−0.453351	+	0.891332i
$244$		0			0
$245$	−7.31583	+	4.22379i	−0.467391	+	0.269848i
$246$		0			0
$247$	−4.92788	+	8.53534i	−0.313553	+	0.543090i
$248$		0			0
$249$	4.59489	−	4.22643i	0.291189	−	0.267839i
$250$		0			0
$251$			4.50751i			0.284512i	0.989830	+	0.142256i	$0.0454356\pi$
$251$			4.50751i			0.284512i	−0.989830	+	0.142256i	$0.954564\pi$
$252$		0			0
$253$		−	11.3396i		−	0.712916i
$254$		0			0
$255$	7.26854	+	2.27668i	0.455174	+	0.142571i
$256$		0			0
$257$	−4.11258	+	7.12320i	−0.256536	+	0.444333i	−0.965311	−	0.261101i	$-0.915914\pi$
$257$	−4.11258	+	7.12320i	−0.256536	+	0.444333i	0.708776	+	0.705434i	$0.249248\pi$
$258$		0			0
$259$	−12.5546	+	7.24842i	−0.780106	+	0.450395i
$260$		0			0
$261$	6.25347	−	9.00308i	0.387080	−	0.557277i
$262$		0			0
$263$	−2.51376	−	4.35395i	−0.155005	−	0.268476i	0.778056	−	0.628195i	$-0.216206\pi$
$263$	−2.51376	−	4.35395i	−0.155005	−	0.268476i	−0.933061	+	0.359719i	$0.882873\pi$
$264$		0			0
$265$	−10.2185	+	17.6990i	−0.627718	+	1.08724i
$266$		0			0
$267$	−4.22512	+	0.945062i	−0.258573	+	0.0578369i
$268$		0			0
$269$			23.1577i			1.41195i	0.708236	+	0.705976i	$0.249491\pi$
$269$			23.1577i			1.41195i	−0.708236	+	0.705976i	$0.750509\pi$
$270$		0			0
$271$	−20.9367			−1.27181			−0.635906	−	0.771766i	$-0.719373\pi$
$271$	−20.9367			−1.27181			−0.635906	+	0.771766i	$0.719373\pi$
$272$		0			0
$273$	−3.17770	−	14.2066i	−0.192323	−	0.859825i
$274$		0			0
$275$	0.861323	+	0.497285i	0.0519398	+	0.0299874i
$276$		0			0
$277$	−19.2687	+	11.1248i	−1.15775	+	0.668425i	−0.950763	−	0.309920i	$-0.899698\pi$
$277$	−19.2687	+	11.1248i	−1.15775	+	0.668425i	−0.206983	+	0.978345i	$0.566364\pi$
$278$		0			0
$279$	1.32993	−	15.8924i	0.0796208	−	0.951456i
$280$		0			0
$281$	−9.28029	−	16.0739i	−0.553616	−	0.958890i	−0.998010	−	0.0630590i	$-0.979914\pi$
$281$	−9.28029	−	16.0739i	−0.553616	−	0.958890i	0.444394	−	0.895831i	$-0.353419\pi$
$282$		0			0
$283$	1.75962	+	1.01592i	0.104599	+	0.0603901i	0.551387	−	0.834250i	$-0.314099\pi$
$283$	1.75962	+	1.01592i	0.104599	+	0.0603901i	−0.446788	+	0.894640i	$0.647432\pi$
$284$		0			0
$285$	−2.51427	+	8.02708i	−0.148932	+	0.475483i
$286$		0			0
$287$	−8.57859			−0.506378
$288$		0			0
$289$	−13.2833			−0.781370
$290$		0			0
$291$	−16.4012	−	17.8310i	−0.961453	−	1.04527i
$292$		0			0
$293$	−29.5484	−	17.0598i	−1.72623	−	0.996642i	−0.904057	−	0.427411i	$-0.859426\pi$
$293$	−29.5484	−	17.0598i	−1.72623	−	0.996642i	−0.822178	−	0.569231i	$-0.807241\pi$
$294$		0			0
$295$	4.02005	+	6.96294i	0.234057	+	0.405398i
$296$		0			0
$297$	−9.60558	+	23.5668i	−0.557372	+	1.36748i
$298$		0			0
$299$	9.28192	−	5.35892i	0.536787	−	0.309914i
$300$		0			0
$301$	4.00895	+	2.31457i	0.231072	+	0.133410i
$302$		0			0
$303$	1.66465	−	1.53116i	0.0956315	−	0.0879630i
$304$		0			0
$305$	−4.52174			−0.258914
$306$		0			0
$307$			4.77588i			0.272574i	0.990669	+	0.136287i	$0.0435169\pi$
$307$			4.77588i			0.272574i	−0.990669	+	0.136287i	$0.956483\pi$
$308$		0			0
$309$	−3.33733	+	10.6548i	−0.189854	+	0.606130i
$310$		0			0
$311$	11.1771	−	19.3592i	0.633793	−	1.09776i	−0.352976	−	0.935632i	$-0.614830\pi$
$311$	11.1771	−	19.3592i	0.633793	−	1.09776i	0.986769	−	0.162130i	$-0.0518364\pi$
$312$		0			0
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	0.898545	−	0.438881i	$-0.144625\pi$
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	−0.829355	+	0.558723i	$0.811292\pi$
$314$		0			0
$315$	−5.29337	−	11.2406i	−0.298248	−	0.633336i
$316$		0			0
$317$	14.2886	−	8.24953i	0.802528	−	0.463340i	−0.0418263	−	0.999125i	$-0.513318\pi$
$317$	14.2886	−	8.24953i	0.802528	−	0.463340i	0.844354	+	0.535785i	$0.179984\pi$
$318$		0			0
$319$	8.94793	−	15.4983i	0.500988	−	0.867737i
$320$		0			0
$321$	−1.17366	−	5.24710i	−0.0655071	−	0.292864i
$322$		0			0
$323$			4.10459i			0.228385i
$324$		0			0
$325$			0.940035i			0.0521438i
$326$		0			0
$327$	6.83704	+	30.5665i	0.378089	+	1.69033i
$328$		0			0
$329$	−3.66771	+	6.35266i	−0.202207	+	0.350233i
$330$		0			0
$331$	−0.329200	+	0.190064i	−0.0180945	+	0.0104469i	−0.509020	−	0.860755i	$-0.669992\pi$
$331$	−0.329200	+	0.190064i	−0.0180945	+	0.0104469i	0.490925	+	0.871202i	$0.336659\pi$
$332$		0			0
$333$	10.2050	+	21.6705i	0.559229	+	1.18754i
$334$		0			0
$335$	−10.1764	−	17.6260i	−0.555994	−	0.963010i
$336$		0			0
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	−0.926437	−	0.376450i	$-0.877145\pi$
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	0.789234	+	0.614093i	$0.210478\pi$
$338$		0			0
$339$	1.46740	−	4.68483i	0.0796982	−	0.254445i
$340$		0			0
$341$		−	26.0361i		−	1.40994i
$342$		0			0
$343$	19.4337			1.04932
$344$		0			0
$345$	6.73248	−	6.19262i	0.362465	−	0.333399i
$346$		0			0
$347$	−8.40337	−	4.85169i	−0.451116	−	0.260452i	0.257185	−	0.966362i	$-0.417205\pi$
$347$	−8.40337	−	4.85169i	−0.451116	−	0.260452i	−0.708302	+	0.705910i	$0.750538\pi$
$348$		0			0
$349$	26.1239	−	15.0827i	1.39838	−	0.807356i	0.404158	−	0.914689i	$-0.367564\pi$
$349$	26.1239	−	15.0827i	1.39838	−	0.807356i	0.994223	+	0.107333i	$0.0342312\pi$
$350$		0			0
$351$	−23.8298	+	3.27473i	−1.27194	+	0.174792i
$352$		0			0
$353$	13.2376	+	22.9282i	0.704565	+	1.22034i	0.966848	+	0.255352i	$0.0821913\pi$
$353$	13.2376	+	22.9282i	0.704565	+	1.22034i	−0.262283	+	0.964991i	$0.584475\pi$
$354$		0			0
$355$	26.3840	+	15.2328i	1.40032	+	0.808473i
$356$		0			0
$357$	−4.10439	−	4.46221i	−0.217228	−	0.236165i
$358$		0			0
$359$	23.4619			1.23827			0.619135	−	0.785285i	$-0.287483\pi$
$359$	23.4619			1.23827			0.619135	+	0.785285i	$0.287483\pi$
$360$		0			0
$361$	14.4671			0.761424
$362$		0			0
$363$	−6.72379	+	21.4665i	−0.352908	+	1.12670i
$364$		0			0
$365$	22.8343	+	13.1834i	1.19520	+	0.690050i
$366$		0			0
$367$	−9.62599	−	16.6727i	−0.502472	−	0.870308i	−0.999996	−	0.00285720i	$-0.999091\pi$
$367$	−9.62599	−	16.6727i	−0.502472	−	0.870308i	0.497524	−	0.867450i	$-0.334243\pi$
$368$		0			0
$369$	−1.18203	+	14.1251i	−0.0615340	+	0.735321i
$370$		0			0
$371$	14.0880	−	8.13373i	0.731414	−	0.422282i
$372$		0			0
$373$	9.09206	+	5.24930i	0.470769	+	0.271799i	0.716562	−	0.697524i	$-0.245715\pi$
$373$	9.09206	+	5.24930i	0.470769	+	0.271799i	−0.245793	+	0.969322i	$0.579048\pi$
$374$		0			0
$375$	−4.13690	−	18.4949i	−0.213628	−	0.955074i
$376$		0			0
$377$	16.9146			0.871145
$378$		0			0
$379$			35.5203i			1.82455i	0.409574	+	0.912277i	$0.365677\pi$
$379$			35.5203i			1.82455i	−0.409574	+	0.912277i	$0.634323\pi$
$380$		0			0
$381$	−12.5920	+	2.81654i	−0.645106	+	0.144296i
$382$		0			0
$383$	−18.0395	+	31.2453i	−0.921774	+	1.59656i	−0.125105	+	0.992144i	$0.539927\pi$
$383$	−18.0395	+	31.2453i	−0.921774	+	1.59656i	−0.796669	+	0.604416i	$0.793407\pi$
$384$		0			0
$385$	−10.1420	−	17.5664i	−0.516884	−	0.895269i
$386$		0			0
$387$	4.36343	−	6.28201i	0.221806	−	0.319332i
$388$		0			0
$389$	17.5243	−	10.1177i	0.888519	−	0.512987i	0.0150612	−	0.999887i	$-0.495206\pi$
$389$	17.5243	−	10.1177i	0.888519	−	0.512987i	0.873458	+	0.486900i	$0.161872\pi$
$390$		0			0
$391$	2.23181	−	3.86560i	0.112867	−	0.195492i
$392$		0			0
$393$	−5.95764	−	1.86607i	−0.300523	−	0.0941309i
$394$		0			0
$395$		−	22.6884i		−	1.14158i
$396$		0			0
$397$		−	3.99499i		−	0.200503i	−0.994962	−	0.100251i	$-0.968035\pi$
$397$		−	3.99499i		−	0.200503i	0.994962	−	0.100251i	$-0.0319647\pi$
$398$		0			0
$399$	4.92788	−	4.53272i	0.246702	−	0.226920i
$400$		0			0
$401$	14.0124	−	24.2702i	0.699747	−	1.21200i	−0.268807	−	0.963194i	$-0.586629\pi$
$401$	14.0124	−	24.2702i	0.699747	−	1.21200i	0.968554	−	0.248803i	$-0.0800372\pi$
$402$		0			0
$403$	21.3116	−	12.3042i	1.06161	−	0.612918i
$404$		0			0
$405$	−19.2375	+	7.16696i	−0.955921	+	0.356129i
$406$		0			0
$407$	19.5525	+	33.8660i	0.969183	+	1.67867i
$408$		0			0
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	−0.587826	−	0.808987i	$-0.700016\pi$
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	0.994517	+	0.104579i	$0.0333494\pi$
$410$		0			0
$411$	−13.7928	−	14.9953i	−0.680350	−	0.739662i
$412$		0			0
$413$		−	6.39976i		−	0.314912i
$414$		0			0
$415$	8.22179			0.403592
$416$		0			0
$417$	21.0706	+	6.59979i	1.03183	+	0.323193i
$418$		0			0
$419$	−20.5573	−	11.8688i	−1.00429	−	0.579827i	−0.0947752	−	0.995499i	$-0.530213\pi$
$419$	−20.5573	−	11.8688i	−1.00429	−	0.579827i	−0.909515	+	0.415672i	$0.863547\pi$
$420$		0			0
$421$	−25.9420	+	14.9776i	−1.26433	+	0.729963i	−0.973910	−	0.226935i	$-0.927130\pi$
$421$	−25.9420	+	14.9776i	−1.26433	+	0.729963i	−0.290424	+	0.956898i	$0.593796\pi$
$422$		0			0
$423$	9.95458	+	6.91437i	0.484008	+	0.336188i
$424$		0			0
$425$	0.195746	+	0.339043i	0.00949509	+	0.0164460i
$426$		0			0
$427$	3.11701	+	1.79961i	0.150843	+	0.0870891i
$428$		0			0
$429$	−38.3223	+	8.57182i	−1.85022	+	0.413851i
$430$		0			0
$431$	11.0367			0.531621			0.265810	−	0.964025i	$-0.414360\pi$
$431$	11.0367			0.531621			0.265810	+	0.964025i	$0.414360\pi$
$432$		0			0
$433$	34.9394			1.67908			0.839541	−	0.543297i	$-0.182824\pi$
$433$	34.9394			1.67908			0.839541	+	0.543297i	$0.182824\pi$
$434$		0			0
$435$	14.0880	−	3.15117i	0.675469	−	0.151087i
$436$		0			0
$437$	4.26901	+	2.46472i	0.204215	+	0.117903i
$438$		0			0
$439$	6.58518	+	11.4059i	0.314293	+	0.544372i	0.979287	−	0.202477i	$-0.0648991\pi$
$439$	6.58518	+	11.4059i	0.314293	+	0.544372i	−0.664994	+	0.746849i	$0.731566\pi$
$440$		0			0
$441$	0.926503	−	11.0716i	0.0441192	−	0.527217i
$442$		0			0
$443$	−23.6849	+	13.6745i	−1.12530	+	0.649694i	−0.942749	−	0.333502i	$-0.891770\pi$
$443$	−23.6849	+	13.6745i	−1.12530	+	0.649694i	−0.182554	+	0.983196i	$0.558436\pi$
$444$		0			0
$445$	−4.93787	−	2.85088i	−0.234077	−	0.135145i
$446$		0			0
$447$	12.5925	+	3.94427i	0.595606	+	0.186558i
$448$		0			0
$449$	−13.8225			−0.652323			−0.326161	−	0.945314i	$-0.605755\pi$
$449$	−13.8225			−0.652323			−0.326161	+	0.945314i	$0.605755\pi$
$450$		0			0
$451$			23.1407i			1.08965i
$452$		0			0
$453$	5.32317	+	5.78723i	0.250104	+	0.271908i
$454$		0			0
$455$	9.58588	−	16.6032i	0.449393	−	0.778371i
$456$		0			0
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	0.791288	−	0.611443i	$-0.209411\pi$
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	−0.925170	+	0.379554i	$0.876077\pi$
$458$		0			0
$459$	−7.91277	+	6.14324i	−0.369337	+	0.286742i
$460$		0			0
$461$	19.3717	−	11.1843i	0.902231	−	0.520903i	0.0243074	−	0.999705i	$-0.492262\pi$
$461$	19.3717	−	11.1843i	0.902231	−	0.520903i	0.877923	+	0.478801i	$0.158929\pi$
$462$		0			0
$463$	−18.5733	+	32.1699i	−0.863174	+	1.49506i	0.00567564	+	0.999984i	$0.498193\pi$
$463$	−18.5733	+	32.1699i	−0.863174	+	1.49506i	−0.868849	+	0.495077i	$0.835140\pi$
$464$		0			0
$465$	15.4580	−	14.2184i	0.716847	−	0.659365i
$466$		0			0
$467$		−	22.6850i		−	1.04974i	−0.851184	−	0.524868i	$-0.824115\pi$
$467$		−	22.6850i		−	1.04974i	0.851184	−	0.524868i	$-0.175885\pi$
$468$		0			0
$469$			16.2004i			0.748063i
$470$		0			0
$471$	21.7778	+	6.82130i	1.00347	+	0.314309i
$472$		0			0
$473$	6.24353	−	10.8141i	0.287078	−	0.497233i
$474$		0			0
$475$	−0.374425	+	0.216174i	−0.0171798	+	0.00991875i
$476$		0			0
$477$	−11.4514	−	24.3173i	−0.524324	−	1.11341i
$478$		0			0
$479$	−13.1576	−	22.7897i	−0.601188	−	1.04129i	−0.992641	−	0.121091i	$-0.961361\pi$
$479$	−13.1576	−	22.7897i	−0.601188	−	1.04129i	0.391453	−	0.920198i	$-0.371973\pi$
$480$		0			0
$481$	−18.4804	+	32.0090i	−0.842634	+	1.45948i
$482$		0			0
$483$	−7.10556	+	1.58935i	−0.323314	+	0.0723180i
$484$		0			0
$485$		−	31.9056i		−	1.44876i
$486$		0			0
$487$	24.0388			1.08930			0.544652	−	0.838662i	$-0.316662\pi$
$487$	24.0388			1.08930			0.544652	+	0.838662i	$0.316662\pi$
$488$		0			0
$489$	7.78504	+	34.8048i	0.352051	+	1.57393i
$490$		0			0
$491$	27.2256	+	15.7187i	1.22867	+	0.709374i	0.966752	−	0.255715i	$-0.0823109\pi$
$491$	27.2256	+	15.7187i	1.22867	+	0.709374i	0.261920	+	0.965090i	$0.415644\pi$
$492$		0			0
$493$	6.10058	−	3.52217i	0.274756	−	0.158631i
$494$		0			0
$495$	−30.3214	+	14.2788i	−1.36285	+	0.641785i
$496$		0			0
$497$	−12.1250	−	21.0011i	−0.543881	−	0.942029i
$498$		0			0
$499$	5.08156	+	2.93384i	0.227482	+	0.131337i	0.609410	−	0.792855i	$-0.291406\pi$
$499$	5.08156	+	2.93384i	0.227482	+	0.131337i	−0.381928	+	0.924192i	$0.624740\pi$
$500$		0			0
$501$	2.62909	−	8.39366i	0.117459	−	0.375001i
$502$		0			0
$503$	−32.4317			−1.44606			−0.723029	−	0.690818i	$-0.757251\pi$
$503$	−32.4317			−1.44606			−0.723029	+	0.690818i	$0.757251\pi$
$504$		0			0
$505$	2.97861			0.132546
$506$		0			0
$507$	−9.88348	−	10.7451i	−0.438941	−	0.477207i
$508$		0			0
$509$	13.6855	+	7.90133i	0.606599	+	0.350220i	0.771633	−	0.636068i	$-0.219440\pi$
$509$	13.6855	+	7.90133i	0.606599	+	0.350220i	−0.165034	+	0.986288i	$0.552773\pi$
$510$		0			0
$511$	−10.4937	−	18.1756i	−0.464214	−	0.804042i
$512$		0			0
$513$	−6.78434	−	8.73854i	−0.299536	−	0.385816i
$514$		0			0
$515$	−12.7341	+	7.35202i	−0.561130	+	0.323969i
$516$		0			0
$517$	17.1362	+	9.89361i	0.753650	+	0.435120i
$518$		0			0
$519$	16.2506	−	14.9475i	0.713324	−	0.656124i
$520$		0			0
$521$	5.50310			0.241095			0.120548	−	0.992708i	$-0.461535\pi$
$521$	5.50310			0.241095			0.120548	+	0.992708i	$0.461535\pi$
$522$		0			0
$523$		−	38.5894i		−	1.68740i	−0.536818	−	0.843698i	$-0.680374\pi$
$523$		−	38.5894i		−	1.68740i	0.536818	−	0.843698i	$-0.319626\pi$
$524$		0			0
$525$	0.190883	−	0.609416i	0.00833083	−	0.0265971i
$526$		0			0
$527$	5.12430	−	8.87555i	0.223218	−	0.386625i
$528$		0			0
$529$	8.81970	+	15.2762i	0.383465	+	0.664181i
$530$		0			0
$531$	−10.5375	−	0.881812i	−0.457289	−	0.0382674i
$532$		0			0
$533$	−18.9415	+	10.9359i	−0.820449	+	0.473686i
$534$		0			0
$535$	3.54046	−	6.13225i	0.153067	−	0.265120i
$536$		0			0
$537$	−3.33472	−	14.9086i	−0.143904	−	0.643354i
$538$		0			0
$539$		−	18.1382i		−	0.781268i
$540$		0			0
$541$			22.5666i			0.970214i	0.874455	+	0.485107i	$0.161219\pi$
$541$			22.5666i			0.970214i	−0.874455	+	0.485107i	$0.838781\pi$
$542$		0			0
$543$	−5.83634	−	26.0927i	−0.250461	−	1.11974i
$544$		0			0
$545$	−20.6246	+	35.7229i	−0.883463	+	1.53020i
$546$		0			0
$547$	−11.2679	+	6.50552i	−0.481780	+	0.278156i	−0.721158	−	0.692770i	$-0.756390\pi$
$547$	−11.2679	+	6.50552i	−0.481780	+	0.278156i	0.239378	+	0.970927i	$0.423057\pi$
$548$		0			0
$549$	3.39262	−	4.88434i	0.144794	−	0.208458i
$550$		0			0
$551$	3.88974	+	6.73723i	0.165709	+	0.287016i
$552$		0			0
$553$	−9.02976	+	15.6400i	−0.383985	+	0.665081i
$554$		0			0
$555$	−9.42895	+	30.1029i	−0.400236	+	1.27780i
$556$		0			0
$557$		−	5.73693i		−	0.243081i	−0.992586	−	0.121541i	$-0.961217\pi$
$557$		−	5.73693i		−	0.243081i	0.992586	−	0.121541i	$-0.0387835\pi$
$558$		0			0
$559$	11.8024			0.499186
$560$		0			0
$561$	−12.0368	+	11.0716i	−0.508192	+	0.467442i
$562$		0			0
$563$	13.2510	+	7.65045i	0.558462	+	0.322428i	0.752528	−	0.658560i	$-0.228834\pi$
$563$	13.2510	+	7.65045i	0.558462	+	0.322428i	−0.194066	+	0.980988i	$0.562168\pi$
$564$		0			0
$565$	5.59908	−	3.23263i	0.235555	−	0.135998i
$566$		0			0
$567$	16.1136	+	2.71589i	0.676706	+	0.114057i
$568$		0			0
$569$	6.63095	+	11.4851i	0.277984	+	0.481482i	0.970884	−	0.239552i	$-0.0770005\pi$
$569$	6.63095	+	11.4851i	0.277984	+	0.481482i	−0.692900	+	0.721034i	$0.743667\pi$
$570$		0			0
$571$	23.4262	+	13.5251i	0.980357	+	0.566009i	0.902378	−	0.430946i	$-0.141820\pi$
$571$	23.4262	+	13.5251i	0.980357	+	0.566009i	0.0779788	+	0.996955i	$0.475153\pi$
$572$		0			0
$573$	11.2965	+	12.2813i	0.471917	+	0.513058i
$574$		0			0
$575$	0.470166			0.0196073
$576$		0			0
$577$	−4.78434			−0.199174			−0.0995872	−	0.995029i	$-0.531752\pi$
$577$	−4.78434			−0.199174			−0.0995872	+	0.995029i	$0.531752\pi$
$578$		0			0
$579$	−3.61713	+	11.5481i	−0.150323	+	0.479922i
$580$		0			0
$581$	−5.66760	−	3.27219i	−0.235132	−	0.135753i
$582$		0			0
$583$	−21.9406	−	38.0023i	−0.908689	−	1.57390i
$584$		0			0
$585$	−26.0172	−	18.0713i	−1.07568	−	0.747157i
$586$		0			0
$587$	37.0796	−	21.4079i	1.53044	−	0.883598i	0.531095	−	0.847312i	$-0.321781\pi$
$587$	37.0796	−	21.4079i	1.53044	−	0.883598i	0.999341	−	0.0362861i	$-0.0115528\pi$
$588$		0			0
$589$	9.80179	+	5.65906i	0.403876	+	0.233178i
$590$		0			0
$591$	−1.63270	−	7.29935i	−0.0671602	−	0.300255i
$592$		0			0
$593$	−0.825572			−0.0339022			−0.0169511	−	0.999856i	$-0.505396\pi$
$593$	−0.825572			−0.0339022			−0.0169511	+	0.999856i	$0.505396\pi$
$594$		0			0
$595$		−	7.98438i		−	0.327328i
$596$		0			0
$597$	9.98364	−	2.23311i	0.408603	−	0.0913952i
$598$		0			0
$599$	0.961228	−	1.66490i	0.0392747	−	0.0680258i	−0.845720	−	0.533627i	$-0.820829\pi$
$599$	0.961228	−	1.66490i	0.0392747	−	0.0680258i	0.884995	+	0.465601i	$0.154162\pi$
$600$		0			0
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.850425	−	0.526096i	$-0.823655\pi$
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.0303994	−	0.999538i	$-0.509678\pi$
$602$		0			0
$603$	26.6747	+	2.23222i	1.08628	+	0.0909030i
$604$		0			0
$605$	−25.6556	+	14.8123i	−1.04305	+	0.602205i
$606$		0			0
$607$	−20.5078	+	35.5206i	−0.832386	+	1.44174i	0.0637546	+	0.997966i	$0.479693\pi$
$607$	−20.5078	+	35.5206i	−0.832386	+	1.44174i	−0.896141	+	0.443770i	$0.853641\pi$
$608$		0			0
$609$	−10.9656	−	3.43467i	−0.444347	−	0.139180i
$610$		0			0
$611$			18.7022i			0.756611i
$612$		0			0
$613$		−	5.05878i		−	0.204322i	−0.994768	−	0.102161i	$-0.967424\pi$
$613$		−	5.05878i		−	0.204322i	0.994768	−	0.102161i	$-0.0325757\pi$
$614$		0			0
$615$	−13.7389	+	12.6372i	−0.554007	+	0.509582i
$616$		0			0
$617$	−16.0739	+	27.8408i	−0.647112	+	1.12083i	0.336698	+	0.941613i	$0.390690\pi$
$617$	−16.0739	+	27.8408i	−0.647112	+	1.12083i	−0.983809	+	0.179217i	$0.942643\pi$
$618$		0			0
$619$	−27.3562	+	15.7941i	−1.09954	+	0.634820i	−0.936100	−	0.351734i	$-0.885592\pi$
$619$	−27.3562	+	15.7941i	−1.09954	+	0.634820i	−0.163440	+	0.986553i	$0.552259\pi$
$620$		0			0
$621$	1.63788	+	11.9186i	0.0657259	+	0.478278i
$622$		0			0
$623$	2.26924	+	3.93044i	0.0909153	+	0.157470i
$624$		0			0
$625$	12.9871	−	22.4942i	0.519482	−	0.899770i
$626$		0			0
$627$	−12.2270	−	13.2929i	−0.488298	−	0.530867i
$628$		0			0
$629$			15.3929i			0.613756i
$630$		0			0
$631$	15.4885			0.616586			0.308293	−	0.951292i	$-0.400242\pi$
$631$	15.4885			0.616586			0.308293	+	0.951292i	$0.400242\pi$
$632$		0			0
$633$	30.3044	+	9.49205i	1.20449	+	0.377275i
$634$		0			0
$635$	−14.7162	−	8.49638i	−0.583993	−	0.337168i
$636$		0			0
$637$	14.8468	−	8.57182i	0.588253	−	0.339628i
$638$		0			0
$639$	−36.2500	+	17.0707i	−1.43403	+	0.675305i
$640$		0			0
$641$	−15.2248	−	26.3701i	−0.601344	−	1.04156i	−0.992618	−	0.121284i	$-0.961299\pi$
$641$	−15.2248	−	26.3701i	−0.601344	−	1.04156i	0.391274	−	0.920274i	$-0.372034\pi$
$642$		0			0
$643$	−14.5911	−	8.42419i	−0.575418	−	0.332218i	0.183893	−	0.982946i	$-0.441130\pi$
$643$	−14.5911	−	8.42419i	−0.575418	−	0.332218i	−0.759310	+	0.650729i	$0.774463\pi$
$644$		0			0
$645$	9.83009	−	2.19877i	0.387060	−	0.0865764i
$646$		0			0
$647$	−18.6734			−0.734126			−0.367063	−	0.930196i	$-0.619637\pi$
$647$	−18.6734			−0.734126			−0.367063	+	0.930196i	$0.619637\pi$
$648$		0			0
$649$	−17.2633			−0.677644
$650$		0			0
$651$	−16.3146	+	3.64920i	−0.639419	+	0.143024i
$652$		0			0
$653$	−31.4276	−	18.1448i	−1.22986	−	0.710059i	−0.262858	−	0.964834i	$-0.584665\pi$
$653$	−31.4276	−	18.1448i	−1.22986	−	0.710059i	−0.967000	+	0.254775i	$0.917999\pi$
$654$		0			0
$655$	−4.11089	−	7.12028i	−0.160626	−	0.278212i
$656$		0			0
$657$	−31.3729	+	14.7740i	−1.22397	+	0.576388i
$658$		0			0
$659$	19.3088	−	11.1480i	0.752166	−	0.434263i	−0.0743103	−	0.997235i	$-0.523676\pi$
$659$	19.3088	−	11.1480i	0.752166	−	0.434263i	0.826476	+	0.562972i	$0.190342\pi$
$660$		0			0
$661$	−5.19793	−	3.00103i	−0.202176	−	0.116726i	0.395494	−	0.918469i	$-0.370573\pi$
$661$	−5.19793	−	3.00103i	−0.202176	−	0.116726i	−0.597670	+	0.801742i	$0.703907\pi$
$662$		0			0
$663$	−14.7509	−	4.62032i	−0.572877	−	0.179438i
$664$		0			0
$665$	8.81762			0.341933
$666$		0			0
$667$		−	8.45996i		−	0.327571i
$668$		0			0
$669$	−6.17388	−	6.71211i	−0.238696	−	0.259505i
$670$		0			0
$671$	4.85442	−	8.40810i	0.187403	−	0.324591i
$672$		0			0
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	0.785753	−	0.618541i	$-0.212276\pi$
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	−0.928548	+	0.371211i	$0.878943\pi$
$674$		0			0
$675$	−0.977130	−	0.398269i	−0.0376098	−	0.0153294i
$676$		0			0
$677$	−8.57613	+	4.95143i	−0.329607	+	0.190299i	−0.655667	−	0.755050i	$-0.727612\pi$
$677$	−8.57613	+	4.95143i	−0.329607	+	0.190299i	0.326059	+	0.945349i	$0.394279\pi$
$678$		0			0
$679$	−12.6981	+	21.9938i	−0.487309	+	0.844043i
$680$		0			0
$681$	−2.26154	+	2.08020i	−0.0866626	+	0.0797133i
$682$		0			0
$683$			39.0736i			1.49511i	0.664200	+	0.747555i	$0.268772\pi$
$683$			39.0736i			1.49511i	−0.664200	+	0.747555i	$0.731228\pi$
$684$		0			0
$685$		−	26.8316i		−	1.02518i
$686$		0			0
$687$	−6.31139	−	1.97687i	−0.240794	−	0.0754224i
$688$		0			0
$689$	20.7376	−	35.9185i	0.790039	−	1.36839i
$690$		0			0
$691$	2.07502	−	1.19801i	0.0789375	−	0.0455746i	−0.460012	−	0.887913i	$-0.652155\pi$
$691$	2.07502	−	1.19801i	0.0789375	−	0.0455746i	0.538949	+	0.842338i	$0.318821\pi$
$692$		0			0
$693$	26.5846	+	2.22468i	1.00986	+	0.0845086i
$694$		0			0
$695$	14.5391	+	25.1825i	0.551500	+	0.955227i
$696$		0			0
$697$	−4.55443	+	7.88850i	−0.172511	+	0.298798i
$698$		0			0
$699$	34.3478	−	7.68281i	1.29915	−	0.290591i
$700$		0			0
$701$			30.9184i			1.16777i	0.811836	+	0.583885i	$0.198468\pi$
$701$			30.9184i			1.16777i	−0.811836	+	0.583885i	$0.801532\pi$
$702$		0			0
$703$	−16.9993			−0.641141
$704$		0			0
$705$	3.48421	+	15.5769i	0.131223	+	0.586662i
$706$		0			0
$707$	−2.05327	−	1.18546i	−0.0772212	−	0.0445837i
$708$		0			0
$709$	4.46959	−	2.58052i	0.167859	−	0.0969133i	−0.413717	−	0.910406i	$-0.635770\pi$
$709$	4.46959	−	2.58052i	0.167859	−	0.0969133i	0.581576	+	0.813492i	$0.302436\pi$
$710$		0			0
$711$	24.5078	+	17.0229i	0.919115	+	0.638410i
$712$		0			0
$713$	−6.15406	−	10.6591i	−0.230471	−	0.399188i
$714$		0			0
$715$	−44.7870	−	25.8578i	−1.67494	−	0.967027i
$716$		0			0
$717$	9.00631	−	28.7536i	0.336347	−	1.07382i
$718$		0			0
$719$	−14.7871			−0.551465			−0.275733	−	0.961234i	$-0.588920\pi$
$719$	−14.7871			−0.551465			−0.275733	+	0.961234i	$0.588920\pi$
$720$		0			0
$721$	11.7041			0.435884
$722$		0			0
$723$	16.0785	+	17.4802i	0.597965	+	0.650095i
$724$		0			0
$725$	0.642593	+	0.371001i	0.0238653	+	0.0137786i
$726$		0			0
$727$	1.06681	+	1.84777i	0.0395658	+	0.0685299i	0.885130	−	0.465344i	$-0.154069\pi$
$727$	1.06681	+	1.84777i	0.0395658	+	0.0685299i	−0.845564	+	0.533873i	$0.820736\pi$
$728$		0			0
$729$	6.69210	−	26.1575i	0.247855	−	0.968797i
$730$		0			0
$731$	4.25675	−	2.45764i	0.157442	−	0.0908990i
$732$		0			0
$733$	−22.2298	−	12.8344i	−0.821076	−	0.474048i	0.0297113	−	0.999559i	$-0.490541\pi$
$733$	−22.2298	−	12.8344i	−0.821076	−	0.474048i	−0.850787	+	0.525510i	$0.823875\pi$
$734$		0			0
$735$	10.7689	−	9.90536i	0.397217	−	0.365365i
$736$		0			0
$737$	43.7003			1.60972
$738$		0			0
$739$			5.46282i			0.200953i	0.994939	+	0.100476i	$0.0320367\pi$
$739$			5.46282i			0.200953i	−0.994939	+	0.100476i	$0.967963\pi$
$740$		0			0
$741$	5.10249	−	16.2903i	0.187445	−	0.598438i
$742$		0			0
$743$	16.8170	−	29.1279i	0.616955	−	1.06860i	−0.373083	−	0.927798i	$-0.621699\pi$
$743$	16.8170	−	29.1279i	0.616955	−	1.06860i	0.990038	−	0.140800i	$-0.0449674\pi$
$744$		0			0
$745$	8.68910	+	15.0500i	0.318344	+	0.551388i
$746$		0			0
$747$	−6.16874	+	8.88109i	−0.225702	+	0.324942i
$748$		0			0
$749$	−4.88115	+	2.81813i	−0.178353	+	0.102972i
$750$		0			0
$751$	12.6727	−	21.9498i	0.462435	−	0.800961i	−0.536647	−	0.843807i	$-0.680309\pi$
$751$	12.6727	−	21.9498i	0.462435	−	0.800961i	0.999082	+	0.0428462i	$0.0136426\pi$
$752$		0			0
$753$	−1.70419	−	7.61897i	−0.0621042	−	0.277651i
$754$		0			0
$755$			10.3553i			0.376868i
$756$		0			0
$757$			3.95103i			0.143603i	0.997419	+	0.0718014i	$0.0228748\pi$
$757$			3.95103i			0.143603i	−0.997419	+	0.0718014i	$0.977125\pi$
$758$		0			0
$759$	4.28726	+	19.1672i	0.155618	+	0.695724i
$760$		0			0
$761$	−23.3979	+	40.5264i	−0.848175	+	1.46908i	0.0346607	+	0.999399i	$0.488965\pi$
$761$	−23.3979	+	40.5264i	−0.848175	+	1.46908i	−0.882835	+	0.469682i	$0.844368\pi$
$762$		0			0
$763$	28.4347	−	16.4168i	1.02941	−	0.594328i
$764$		0			0
$765$	−13.1467	−	1.10015i	−0.475318	−	0.0397761i
$766$		0			0
$767$	−8.15835	−	14.1307i	−0.294581	−	0.510229i
$768$		0			0
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	−0.815314	−	0.579019i	$-0.803436\pi$
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	0.909102	+	0.416573i	$0.136769\pi$
$770$		0			0
$771$	4.25830	−	13.5951i	0.153359	−	0.489615i
$772$		0			0
$773$			38.8477i			1.39725i	0.715486	+	0.698627i	$0.246205\pi$
$773$			38.8477i			1.39725i	−0.715486	+	0.698627i	$0.753795\pi$
$774$		0			0
$775$	1.07952			0.0387773
$776$		0			0
$777$	18.4804	−	16.9985i	0.662981	−	0.609818i
$778$		0			0
$779$	−8.71173	−	5.02972i	−0.312130	−	0.180209i
$780$		0			0
$781$	−56.6503	+	32.7071i	−2.02711	+	1.17035i
$782$		0			0
$783$	−7.16627	+	17.5821i	−0.256102	+	0.628331i
$784$		0			0
$785$	15.0271	+	26.0277i	0.536340	+	0.928968i
$786$		0			0
$787$	−40.8579	−	23.5893i	−1.45643	−	0.840869i	−0.457595	−	0.889161i	$-0.651289\pi$
$787$	−40.8579	−	23.5893i	−1.45643	−	0.840869i	−0.998833	+	0.0482918i	$0.984622\pi$
$788$		0			0
$789$	5.89509	+	6.40902i	0.209871	+	0.228167i
$790$		0			0
$791$	−5.14621			−0.182978
$792$		0			0
$793$	9.17648			0.325866
$794$		0			0
$795$	10.5806	−	33.7797i	0.375255	−	1.19804i
$796$		0			0
$797$	−6.35645	−	3.66990i	−0.225157	−	0.129995i	0.383179	−	0.923674i	$-0.374829\pi$
$797$	−6.35645	−	3.66990i	−0.225157	−	0.129995i	−0.608336	+	0.793680i	$0.708163\pi$
$798$		0			0
$799$	3.89442	+	6.74533i	0.137775	+	0.238633i
$800$		0			0
$801$	6.78434	−	3.19485i	0.239713	−	0.112884i
$802$		0			0
$803$	−49.0286	+	28.3067i	−1.73018	+	0.998920i
$804$		0			0
$805$	−8.30423	−	4.79445i	−0.292686	−	0.168982i
$806$		0			0
$807$	−8.75542	−	39.1431i	−0.308205	−	1.37790i
$808$		0			0
$809$	2.25520			0.0792887			0.0396443	−	0.999214i	$-0.487378\pi$
$809$	2.25520			0.0792887			0.0396443	+	0.999214i	$0.487378\pi$
$810$		0			0
$811$		−	15.9986i		−	0.561785i	−0.959739	−	0.280893i	$-0.909369\pi$
$811$		−	15.9986i		−	0.561785i	0.959739	−	0.280893i	$-0.0906305\pi$
$812$		0			0
$813$	35.3889	−	7.91569i	1.24114	−	0.277615i
$814$		0			0
$815$	−23.4844	+	40.6761i	−0.822622	+	1.42482i
$816$		0			0
$817$	2.71411	+	4.70098i	0.0949548	+	0.164467i
$818$		0			0
$819$	10.7424	+	22.8118i	0.375371	+	0.797110i
$820$		0			0
$821$	25.2413	−	14.5731i	0.880928	−	0.508604i	0.00996351	−	0.999950i	$-0.496828\pi$
$821$	25.2413	−	14.5731i	0.880928	−	0.508604i	0.870964	+	0.491347i	$0.163495\pi$
$822$		0			0
$823$	4.15695	−	7.20005i	0.144902	−	0.250978i	−0.784434	−	0.620212i	$-0.787047\pi$
$823$	4.15695	−	7.20005i	0.144902	−	0.250978i	0.929336	+	0.369234i	$0.120380\pi$
$824$		0			0
$825$	−1.64389	−	0.514906i	−0.0572330	−	0.0179267i
$826$		0			0
$827$			43.5035i			1.51277i	0.654129	+	0.756383i	$0.273035\pi$
$827$			43.5035i			1.51277i	−0.654129	+	0.756383i	$0.726965\pi$
$828$		0			0
$829$		−	15.9248i		−	0.553092i	−0.961001	−	0.276546i	$-0.910810\pi$
$829$		−	15.9248i		−	0.553092i	0.961001	−	0.276546i	$-0.0891897\pi$
$830$		0			0
$831$	28.3636	−	26.0892i	0.983921	−	0.905023i
$832$		0			0
$833$	3.56987	−	6.18320i	0.123689	−	0.214235i
$834$		0			0
$835$	10.0317	−	5.79180i	0.347161	−	0.200433i
$836$		0			0
$837$	3.76062	+	27.3656i	0.129986	+	0.945892i
$838$		0			0
$839$	21.0582	+	36.4739i	0.727009	+	1.25922i	0.958142	+	0.286295i	$0.0924237\pi$
$839$	21.0582	+	36.4739i	0.727009	+	1.25922i	−0.231132	+	0.972922i	$0.574243\pi$
$840$		0			0
$841$	−7.82437	+	13.5522i	−0.269806	+	0.467318i
$842$		0			0
$843$	21.7635	+	23.6608i	0.749575	+	0.814922i
$844$		0			0
$845$		−	19.2266i		−	0.661415i
$846$		0			0
$847$	23.5806			0.810238
$848$		0			0
$849$	−3.35836	−	1.05192i	−0.115259	−	0.0361017i
$850$		0			0
$851$	16.0095	+	9.24311i	0.548800	+	0.316850i
$852$		0			0
$853$	34.2013	−	19.7461i	1.17103	−	0.676095i	0.217108	−	0.976148i	$-0.430338\pi$
$853$	34.2013	−	19.7461i	1.17103	−	0.676095i	0.953923	+	0.300053i	$0.0970043\pi$
$854$		0			0
$855$	1.21496	−	14.5186i	0.0415509	−	0.496526i
$856$		0			0
$857$	−12.6170	−	21.8532i	−0.430988	−	0.746493i	0.565971	−	0.824425i	$-0.308501\pi$
$857$	−12.6170	−	21.8532i	−0.430988	−	0.746493i	−0.996959	+	0.0779326i	$0.975168\pi$
$858$		0			0
$859$	47.5539	+	27.4552i	1.62252	+	0.936761i	0.986244	+	0.165297i	$0.0528584\pi$
$859$	47.5539	+	27.4552i	1.62252	+	0.936761i	0.636274	+	0.771463i	$0.280475\pi$
$860$		0			0
$861$	14.5003	−	3.24338i	0.494167	−	0.110534i
$862$		0			0
$863$	54.3877			1.85138			0.925689	−	0.378285i	$-0.123486\pi$
$863$	54.3877			1.85138			0.925689	+	0.378285i	$0.123486\pi$
$864$		0			0
$865$	29.0778			0.988675
$866$		0			0
$867$	22.4525	−	5.02212i	0.762527	−	0.170560i
$868$		0			0
$869$	42.1888	+	24.3577i	1.43116	+	0.826278i
$870$		0			0
$871$	20.6521	+	35.7704i	0.699768	+	1.21203i
$872$		0			0
$873$	34.4641	+	23.9385i	1.16643	+	0.810196i
$874$		0			0
$875$	−17.2050	+	9.93334i	−0.581637	+	0.335808i
$876$		0			0
$877$	−5.90001	−	3.40637i	−0.199229	−	0.115025i	0.397067	−	0.917790i	$-0.370028\pi$
$877$	−5.90001	−	3.40637i	−0.199229	−	0.115025i	−0.596296	+	0.802765i	$0.703361\pi$
$878$		0			0
$879$	56.3951	+	17.6642i	1.90216	+	0.595800i
$880$		0			0
$881$	−43.2881			−1.45841			−0.729207	−	0.684293i	$-0.760111\pi$
$881$	−43.2881			−1.45841			−0.729207	+	0.684293i	$0.760111\pi$
$882$		0			0
$883$		−	31.1510i		−	1.04832i	−0.851621	−	0.524158i	$-0.824380\pi$
$883$		−	31.1510i		−	1.04832i	0.851621	−	0.524158i	$-0.175620\pi$
$884$		0			0
$885$	−9.42756	−	10.2494i	−0.316904	−	0.344531i
$886$		0			0
$887$	24.8886	−	43.1083i	0.835677	−	1.44743i	−0.0578015	−	0.998328i	$-0.518409\pi$
$887$	24.8886	−	43.1083i	0.835677	−	1.44743i	0.893478	−	0.449107i	$-0.148258\pi$
$888$		0			0
$889$	6.76295	+	11.7138i	0.226822	+	0.392867i
$890$		0			0
$891$	7.32608	−	43.4662i	0.245433	−	1.45617i
$892$		0			0
$893$	−7.44926	+	4.30083i	−0.249280	+	0.143922i
$894$		0			0
$895$	10.0595	−	17.4236i	0.336253	−	0.582407i
$896$		0			0
$897$	−13.6630	+	12.5674i	−0.456194	+	0.419613i
$898$		0			0
$899$		−	19.4243i		−	0.647838i
$900$		0			0
$901$		−	17.2730i		−	0.575447i
$902$		0			0
$903$	−7.65135	−	2.39658i	−0.254621	−	0.0797532i
$904$		0			0
$905$	17.6059	−	30.4944i	0.585241	−	1.01367i
$906$		0			0
$907$	−16.6712	+	9.62515i	−0.553559	+	0.319598i	−0.750556	−	0.660806i	$-0.770214\pi$
$907$	−16.6712	+	9.62515i	−0.553559	+	0.319598i	0.196997	+	0.980404i	$0.436881\pi$
$908$		0			0
$909$	−2.23483	+	3.21747i	−0.0741245	+	0.106717i
$910$		0			0
$911$	−11.1396	−	19.2944i	−0.369072	−	0.639252i	0.620348	−	0.784326i	$-0.286991\pi$
$911$	−11.1396	−	19.2944i	−0.369072	−	0.639252i	−0.989421	+	0.145074i	$0.953658\pi$
$912$		0			0
$913$	−8.82669	+	15.2883i	−0.292121	+	0.505968i
$914$		0			0
$915$	7.64302	−	1.70957i	0.252670	−	0.0565166i
$916$		0			0
$917$			6.54438i			0.216114i
$918$		0			0
$919$	−28.0122			−0.924039			−0.462019	−	0.886870i	$-0.652875\pi$
$919$	−28.0122			−0.924039			−0.462019	+	0.886870i	$0.652875\pi$
$920$		0			0
$921$	−1.80565	−	8.07259i	−0.0594983	−	0.266001i
$922$		0			0
$923$	−53.5440	−	30.9136i	−1.76242	−	1.01753i
$924$		0			0
$925$	−1.40416	+	0.810691i	−0.0461684	+	0.0266554i
$926$		0			0
$927$	1.61269	−	19.2714i	0.0529677	−	0.632955i
$928$		0			0
$929$	−3.94220	−	6.82809i	−0.129339	−	0.224022i	0.794081	−	0.607811i	$-0.207952\pi$
$929$	−3.94220	−	6.82809i	−0.129339	−	0.224022i	−0.923421	+	0.383789i	$0.874619\pi$
$930$		0			0
$931$	6.82847	+	3.94242i	0.223794	+	0.129208i
$932$		0			0
$933$	−11.5731	+	36.9484i	−0.378886	+	1.20964i
$934$		0			0
$935$	−21.5378			−0.704361
$936$		0			0
$937$	−8.98600			−0.293560			−0.146780	−	0.989169i	$-0.546891\pi$
$937$	−8.98600			−0.293560			−0.146780	+	0.989169i	$0.546891\pi$
$938$		0			0
$939$	−2.87070	−	3.12096i	−0.0936817	−	0.101849i
$940$		0			0
$941$	21.0227	+	12.1375i	0.685322	+	0.395671i	0.801857	−	0.597516i	$-0.203845\pi$
$941$	21.0227	+	12.1375i	0.685322	+	0.395671i	−0.116535	+	0.993187i	$0.537179\pi$
$942$		0			0
$943$	5.46967	+	9.47375i	0.178117	+	0.308508i
$944$		0			0
$945$	13.1971	+	16.9985i	0.429302	+	0.552961i
$946$		0			0
$947$	−1.71382	+	0.989473i	−0.0556916	+	0.0321536i	−0.527587	−	0.849501i	$-0.676903\pi$
$947$	−1.71382	+	0.989473i	−0.0556916	+	0.0321536i	0.471896	+	0.881654i	$0.343570\pi$
$948$		0			0
$949$	−46.3402	−	26.7545i	−1.50427	−	0.868488i
$950$		0			0
$951$	−21.0328	+	19.3462i	−0.682036	+	0.627345i
$952$		0			0
$953$	28.9674			0.938347			0.469173	−	0.883106i	$-0.344552\pi$
$953$	28.9674			0.938347			0.469173	+	0.883106i	$0.344552\pi$
$954$		0			0
$955$			21.9753i			0.711104i
$956$		0			0
$957$	−9.26498	+	29.5795i	−0.299494	+	0.956169i
$958$		0			0
$959$	−10.6787	+	18.4960i	−0.344833	+	0.597268i
$960$		0			0
$961$	1.37008	+	2.37304i	0.0441961	+	0.0765498i
$962$		0			0
$963$	3.96762	+	8.42535i	0.127855	+	0.271503i
$964$		0			0
$965$	−13.8017	+	7.96842i	−0.444293	+	0.256512i
$966$		0			0
$967$	−0.00531192	+	0.00920052i	−0.000170820	+	0.000295869i	−0.866111	−	0.499852i	$-0.833388\pi$
$967$	−0.00531192	+	0.00920052i	−0.000170820	+	0.000295869i	0.865940	+	0.500148i	$0.166721\pi$
$968$		0			0
$969$	−1.55185	−	6.93791i	−0.0498527	−	0.222878i
$970$		0			0
$971$		−	17.0984i		−	0.548715i	−0.961628	−	0.274357i	$-0.911535\pi$
$971$		−	17.0984i		−	0.548715i	0.961628	−	0.274357i	$-0.0884651\pi$
$972$		0			0
$973$		−	23.1457i		−	0.742017i
$974$		0			0
$975$	−0.355407	−	1.58893i	−0.0113821	−	0.0508864i
$976$		0			0
$977$	−5.50612	+	9.53688i	−0.176156	+	0.305112i	−0.940561	−	0.339625i	$-0.889700\pi$
$977$	−5.50612	+	9.53688i	−0.176156	+	0.305112i	0.764404	+	0.644737i	$0.223033\pi$
$978$		0			0
$979$	10.6023	−	6.12126i	0.338852	−	0.195636i
$980$		0			0
$981$	−23.1131	−	49.0812i	−0.737943	−	1.56704i
$982$		0			0
$983$	−22.7443	−	39.3943i	−0.725432	−	1.25648i	−0.958796	−	0.284095i	$-0.908307\pi$
$983$	−22.7443	−	39.3943i	−0.725432	−	1.25648i	0.233364	−	0.972389i	$-0.425027\pi$
$984$		0			0
$985$	4.92521	−	8.53071i	0.156930	−	0.271811i
$986$		0			0
$987$	3.79767	−	12.1245i	0.120881	−	0.385926i
$988$		0			0
$989$		−	5.90304i		−	0.187706i
$990$		0			0
$991$	−3.93737			−0.125075			−0.0625374	−	0.998043i	$-0.519919\pi$
$991$	−3.93737			−0.125075			−0.0625374	+	0.998043i	$0.519919\pi$
$992$		0			0
$993$	0.484583	−	0.445725i	0.0153778	−	0.0141447i
$994$		0			0
$995$	11.6678	+	6.73642i	0.369895	+	0.213559i
$996$		0			0
$997$	−2.16558	+	1.25030i	−0.0685847	+	0.0395974i	−0.533900	−	0.845547i	$-0.679274\pi$
$997$	−2.16558	+	1.25030i	−0.0685847	+	0.0395974i	0.465316	+	0.885145i	$0.345941\pi$
$998$		0			0
$999$	−25.4424	−	32.7710i	−0.804963	−	1.03683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.r.b.49.1		16
3.2	odd	2		864.2.r.b.145.7		16
4.3	odd	2		72.2.n.b.13.5	✓	16
8.3	odd	2		72.2.n.b.13.6	yes	16
8.5	even	2	inner	288.2.r.b.49.8		16
9.2	odd	6		864.2.r.b.721.2		16
9.4	even	3		2592.2.d.j.1297.7		8
9.5	odd	6		2592.2.d.k.1297.2		8
9.7	even	3	inner	288.2.r.b.241.8		16
12.11	even	2		216.2.n.b.37.4		16
24.5	odd	2		864.2.r.b.145.2		16
24.11	even	2		216.2.n.b.37.3		16
36.7	odd	6		72.2.n.b.61.6	yes	16
36.11	even	6		216.2.n.b.181.3		16
36.23	even	6		648.2.d.k.325.8		8
36.31	odd	6		648.2.d.j.325.1		8
72.5	odd	6		2592.2.d.k.1297.7		8
72.11	even	6		216.2.n.b.181.4		16
72.13	even	6		2592.2.d.j.1297.2		8
72.29	odd	6		864.2.r.b.721.7		16
72.43	odd	6		72.2.n.b.61.5	yes	16
72.59	even	6		648.2.d.k.325.7		8
72.61	even	6	inner	288.2.r.b.241.1		16
72.67	odd	6		648.2.d.j.325.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.5	✓	16	4.3	odd	2
72.2.n.b.13.6	yes	16	8.3	odd	2
72.2.n.b.61.5	yes	16	72.43	odd	6
72.2.n.b.61.6	yes	16	36.7	odd	6
216.2.n.b.37.3		16	24.11	even	2
216.2.n.b.37.4		16	12.11	even	2
216.2.n.b.181.3		16	36.11	even	6
216.2.n.b.181.4		16	72.11	even	6
288.2.r.b.49.1		16	1.1	even	1	trivial
288.2.r.b.49.8		16	8.5	even	2	inner
288.2.r.b.241.1		16	72.61	even	6	inner
288.2.r.b.241.8		16	9.7	even	3	inner
648.2.d.j.325.1		8	36.31	odd	6
648.2.d.j.325.2		8	72.67	odd	6
648.2.d.k.325.7		8	72.59	even	6
648.2.d.k.325.8		8	36.23	even	6
864.2.r.b.145.2		16	24.5	odd	2
864.2.r.b.145.7		16	3.2	odd	2
864.2.r.b.721.2		16	9.2	odd	6
864.2.r.b.721.7		16	72.29	odd	6
2592.2.d.j.1297.2		8	72.13	even	6
2592.2.d.j.1297.7		8	9.4	even	3
2592.2.d.k.1297.2		8	9.5	odd	6
2592.2.d.k.1297.7		8	72.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69028 + 0.378078i) q^{3} +(-1.97542 - 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +(2.71411 - 1.27812i) q^{9} +O(q^{10})\)	\(q+(-1.69028 + 0.378078i) q^{3} +(-1.97542 - 1.14051i) q^{5} +(0.907824 + 1.57240i) q^{7} +(2.71411 - 1.27812i) q^{9} +(4.24153 - 2.44885i) q^{11} +(4.00895 + 2.31457i) q^{13} +(3.77023 + 1.18092i) q^{15} +1.92788 q^{17} +2.12907i q^{19} +(-2.12897 - 2.31457i) q^{21} +(1.15765 - 2.00511i) q^{23} +(0.101535 + 0.175863i) q^{25} +(-4.10439 + 3.18653i) q^{27} +(3.16440 - 1.82697i) q^{29} +(2.65800 - 4.60379i) q^{31} +(-6.24353 + 5.74287i) q^{33} -4.14154i q^{35} +7.98438i q^{37} +(-7.65135 - 2.39658i) q^{39} +(-2.36240 + 4.09180i) q^{41} +(2.20800 - 1.27479i) q^{43} +(-6.81924 - 0.570655i) q^{45} +(2.02005 + 3.49884i) q^{47} +(1.85171 - 3.20726i) q^{49} +(-3.25866 + 0.728888i) q^{51} -8.95958i q^{53} -11.1718 q^{55} +(-0.804954 - 3.59873i) q^{57} +(-3.05255 - 1.76239i) q^{59} +(1.71675 - 0.991165i) q^{61} +(4.47365 + 3.10736i) q^{63} +(-5.27959 - 9.14451i) q^{65} +(7.72723 + 4.46132i) q^{67} +(-1.19867 + 3.82688i) q^{69} -13.3561 q^{71} -11.5592 q^{73} +(-0.238112 - 0.258870i) q^{75} +(7.70112 + 4.44625i) q^{77} +(4.97330 + 8.61401i) q^{79} +(5.73283 - 6.93791i) q^{81} +(-3.12153 + 1.80221i) q^{83} +(-3.80838 - 2.19877i) q^{85} +(-4.65800 + 4.28448i) q^{87} +2.49965 q^{89} +8.40489i q^{91} +(-2.75218 + 8.78664i) q^{93} +(2.42823 - 4.20582i) q^{95} +(6.99370 + 12.1134i) q^{97} +(8.38208 - 12.0676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 6 * q^7 + 2 * q^9	\( 16 q - 6 q^{7} + 2 q^{9} + 10 q^{15} - 28 q^{17} + 10 q^{23} + 2 q^{25} + 10 q^{31} - 2 q^{39} - 8 q^{41} - 6 q^{47} + 18 q^{49} + 4 q^{55} + 10 q^{57} - 2 q^{63} - 14 q^{65} - 72 q^{71} - 44 q^{73} + 30 q^{79} + 10 q^{81} - 42 q^{87} + 64 q^{89} - 44 q^{95}+O(q^{100}) \) 16 * q - 6 * q^7 + 2 * q^9 + 10 * q^15 - 28 * q^17 + 10 * q^23 + 2 * q^25 + 10 * q^31 - 2 * q^39 - 8 * q^41 - 6 * q^47 + 18 * q^49 + 4 * q^55 + 10 * q^57 - 2 * q^63 - 14 * q^65 - 72 * q^71 - 44 * q^73 + 30 * q^79 + 10 * q^81 - 42 * q^87 + 64 * q^89 - 44 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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