LMFDB - Embedded newform 1512.2.c.g.757.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.11
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.g.757.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.417332 - 1.35123i) q^{2} +(-1.65167 + 1.12783i) q^{4} -3.04340i q^{5} +1.00000 q^{7} +(2.21325 + 1.76111i) q^{8} +O(q^{10})$	\(q+(-0.417332 - 1.35123i) q^{2} +(-1.65167 + 1.12783i) q^{4} -3.04340i q^{5} +1.00000 q^{7} +(2.21325 + 1.76111i) q^{8} +(-4.11235 + 1.27011i) q^{10} -0.128573i q^{11} +6.30135i q^{13} +(-0.417332 - 1.35123i) q^{14} +(1.45602 - 3.72559i) q^{16} +5.32168 q^{17} -6.68215i q^{19} +(3.43243 + 5.02669i) q^{20} +(-0.173732 + 0.0536575i) q^{22} +5.18212 q^{23} -4.26229 q^{25} +(8.51460 - 2.62975i) q^{26} +(-1.65167 + 1.12783i) q^{28} -9.96821i q^{29} +3.27122 q^{31} +(-5.64179 - 0.412618i) q^{32} +(-2.22090 - 7.19083i) q^{34} -3.04340i q^{35} -0.796970i q^{37} +(-9.02915 + 2.78867i) q^{38} +(5.35978 - 6.73581i) q^{40} -2.96782 q^{41} +6.99100i q^{43} +(0.145008 + 0.212360i) q^{44} +(-2.16266 - 7.00226i) q^{46} +4.76595 q^{47} +1.00000 q^{49} +(1.77879 + 5.75936i) q^{50} +(-7.10682 - 10.4077i) q^{52} +1.14264i q^{53} -0.391299 q^{55} +(2.21325 + 1.76111i) q^{56} +(-13.4694 + 4.16005i) q^{58} +11.0999i q^{59} -14.6662i q^{61} +(-1.36518 - 4.42018i) q^{62} +(1.79695 + 7.79557i) q^{64} +19.1775 q^{65} -1.05725i q^{67} +(-8.78965 + 6.00192i) q^{68} +(-4.11235 + 1.27011i) q^{70} +1.10582 q^{71} -12.1019 q^{73} +(-1.07689 + 0.332601i) q^{74} +(7.53630 + 11.0367i) q^{76} -0.128573i q^{77} +2.62426 q^{79} +(-11.3385 - 4.43125i) q^{80} +(1.23856 + 4.01022i) q^{82} -6.46403i q^{83} -16.1960i q^{85} +(9.44648 - 2.91757i) q^{86} +(0.226432 - 0.284564i) q^{88} -2.23283 q^{89} +6.30135i q^{91} +(-8.55915 + 5.84453i) q^{92} +(-1.98898 - 6.43992i) q^{94} -20.3365 q^{95} -7.88097 q^{97} +(-0.417332 - 1.35123i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) $ 24 * q + 6 * q^4 + 24 * q^7	$ 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) $ 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−0.417332	−	1.35123i	−0.295098	−	0.955467i
$2$	−0.417332	−	1.35123i	−0.295098	−	0.955467i
$3$		0			0
$3$		0			0
$4$	−1.65167	+	1.12783i	−0.825834	+	0.563913i
$5$		−	3.04340i		−	1.36105i	−0.732725	−	0.680525i	$-0.761752\pi$
$5$		−	3.04340i		−	1.36105i	0.732725	−	0.680525i	$-0.238248\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.21325	+	1.76111i	0.782502	+	0.622648i
$9$		0			0
$10$	−4.11235	+	1.27011i	−1.30044	+	0.401643i
$11$		−	0.128573i		−	0.0387662i	−0.999812	−	0.0193831i	$-0.993830\pi$
$11$		−	0.128573i		−	0.0387662i	0.999812	−	0.0193831i	$-0.00617022\pi$
$12$		0			0
$13$			6.30135i			1.74768i	0.486214	+	0.873840i	$0.338378\pi$
$13$			6.30135i			1.74768i	−0.486214	+	0.873840i	$0.661622\pi$
$14$	−0.417332	−	1.35123i	−0.111537	−	0.361133i
$15$		0			0
$16$	1.45602	−	3.72559i	0.364005	−	0.931397i
$17$	5.32168			1.29070			0.645348	−	0.763889i	$-0.276712\pi$
$17$	5.32168			1.29070			0.645348	+	0.763889i	$0.276712\pi$
$18$		0			0
$19$		−	6.68215i		−	1.53299i	−0.642250	−	0.766495i	$-0.721999\pi$
$19$		−	6.68215i		−	1.53299i	0.642250	−	0.766495i	$-0.278001\pi$
$20$	3.43243	+	5.02669i	0.767514	+	1.12400i
$21$		0			0
$22$	−0.173732	+	0.0536575i	−0.0370398	+	0.0114398i
$23$	5.18212			1.08055			0.540273	−	0.841490i	$-0.318321\pi$
$23$	5.18212			1.08055			0.540273	+	0.841490i	$0.318321\pi$
$24$		0			0
$25$	−4.26229			−0.852459
$26$	8.51460	−	2.62975i	1.66985	−	0.515737i
$27$		0			0
$28$	−1.65167	+	1.12783i	−0.312136	+	0.213139i
$29$		−	9.96821i		−	1.85105i	−0.378686	−	0.925525i	$-0.623624\pi$
$29$		−	9.96821i		−	1.85105i	0.378686	−	0.925525i	$-0.376376\pi$
$30$		0			0
$31$	3.27122			0.587528			0.293764	−	0.955878i	$-0.405092\pi$
$31$	3.27122			0.587528			0.293764	+	0.955878i	$0.405092\pi$
$32$	−5.64179	−	0.412618i	−0.997336	−	0.0729412i
$33$		0			0
$34$	−2.22090	−	7.19083i	−0.380882	−	1.23322i
$35$		−	3.04340i		−	0.514429i
$36$		0			0
$37$		−	0.796970i		−	0.131021i	−0.997852	−	0.0655106i	$-0.979132\pi$
$37$		−	0.796970i		−	0.131021i	0.997852	−	0.0655106i	$-0.0208676\pi$
$38$	−9.02915	+	2.78867i	−1.46472	+	0.452382i
$39$		0			0
$40$	5.35978	−	6.73581i	0.847455	−	1.06502i
$41$	−2.96782			−0.463496			−0.231748	−	0.972776i	$-0.574444\pi$
$41$	−2.96782			−0.463496			−0.231748	+	0.972776i	$0.574444\pi$
$42$		0			0
$43$			6.99100i			1.06612i	0.846078	+	0.533059i	$0.178958\pi$
$43$			6.99100i			1.06612i	−0.846078	+	0.533059i	$0.821042\pi$
$44$	0.145008	+	0.212360i	0.0218607	+	0.0320145i
$45$		0			0
$46$	−2.16266	−	7.00226i	−0.318867	−	1.03243i
$47$	4.76595			0.695186			0.347593	−	0.937646i	$-0.386999\pi$
$47$	4.76595			0.695186			0.347593	+	0.937646i	$0.386999\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	1.77879	+	5.75936i	0.251559	+	0.814496i
$51$		0			0
$52$	−7.10682	−	10.4077i	−0.985539	−	1.44329i
$53$			1.14264i			0.156954i	0.996916	+	0.0784772i	$0.0250058\pi$
$53$			1.14264i			0.156954i	−0.996916	+	0.0784772i	$0.974994\pi$
$54$		0			0
$55$	−0.391299			−0.0527627
$56$	2.21325	+	1.76111i	0.295758	+	0.235339i
$57$		0			0
$58$	−13.4694	+	4.16005i	−1.76862	+	0.546241i
$59$			11.0999i			1.44508i	0.691329	+	0.722540i	$0.257025\pi$
$59$			11.0999i			1.44508i	−0.691329	+	0.722540i	$0.742975\pi$
$60$		0			0
$61$		−	14.6662i		−	1.87782i	−0.344165	−	0.938909i	$-0.611838\pi$
$61$		−	14.6662i		−	1.87782i	0.344165	−	0.938909i	$-0.388162\pi$
$62$	−1.36518	−	4.42018i	−0.173378	−	0.561364i
$63$		0			0
$64$	1.79695	+	7.79557i	0.224619	+	0.974447i
$65$	19.1775			2.37868
$66$		0			0
$67$		−	1.05725i		−	0.129163i	−0.997912	−	0.0645816i	$-0.979429\pi$
$67$		−	1.05725i		−	0.129163i	0.997912	−	0.0645816i	$-0.0205713\pi$
$68$	−8.78965	+	6.00192i	−1.06590	+	0.727840i
$69$		0			0
$70$	−4.11235	+	1.27011i	−0.491520	+	0.151807i
$71$	1.10582			0.131237			0.0656185	−	0.997845i	$-0.479098\pi$
$71$	1.10582			0.131237			0.0656185	+	0.997845i	$0.479098\pi$
$72$		0			0
$73$	−12.1019			−1.41642			−0.708212	−	0.706000i	$-0.750498\pi$
$73$	−12.1019			−1.41642			−0.708212	+	0.706000i	$0.750498\pi$
$74$	−1.07689	+	0.332601i	−0.125186	+	0.0386641i
$75$		0			0
$76$	7.53630	+	11.0367i	0.864473	+	1.26600i
$77$		−	0.128573i		−	0.0146522i
$78$		0			0
$79$	2.62426			0.295253			0.147626	−	0.989043i	$-0.452837\pi$
$79$	2.62426			0.295253			0.147626	+	0.989043i	$0.452837\pi$
$80$	−11.3385	−	4.43125i	−1.26768	−	0.495429i
$81$		0			0
$82$	1.23856	+	4.01022i	0.136777	+	0.442855i
$83$		−	6.46403i		−	0.709520i	−0.934957	−	0.354760i	$-0.884563\pi$
$83$		−	6.46403i		−	0.709520i	0.934957	−	0.354760i	$-0.115437\pi$
$84$		0			0
$85$		−	16.1960i		−	1.75670i
$86$	9.44648	−	2.91757i	1.01864	−	0.314609i
$87$		0			0
$88$	0.226432	−	0.284564i	0.0241377	−	0.0303346i
$89$	−2.23283			−0.236680			−0.118340	−	0.992973i	$-0.537757\pi$
$89$	−2.23283			−0.236680			−0.118340	+	0.992973i	$0.537757\pi$
$90$		0			0
$91$			6.30135i			0.660561i
$92$	−8.55915	+	5.84453i	−0.892353	+	0.609334i
$93$		0			0
$94$	−1.98898	−	6.43992i	−0.205148	−	0.664227i
$95$	−20.3365			−2.08648
$96$		0			0
$97$	−7.88097			−0.800192			−0.400096	−	0.916473i	$-0.631023\pi$
$97$	−7.88097			−0.800192			−0.400096	+	0.916473i	$0.631023\pi$
$98$	−0.417332	−	1.35123i	−0.0421569	−	0.136495i
$99$		0			0
$100$	7.03990	−	4.80712i	0.703990	−	0.480712i
$101$		−	16.9693i		−	1.68851i	−0.535945	−	0.844253i	$-0.680045\pi$
$101$		−	16.9693i		−	1.68851i	0.535945	−	0.844253i	$-0.319955\pi$
$102$		0			0
$103$	−10.7049			−1.05479			−0.527393	−	0.849621i	$-0.676830\pi$
$103$	−10.7049			−1.05479			−0.527393	+	0.849621i	$0.676830\pi$
$104$	−11.0974	+	13.9465i	−1.08819	+	1.36756i
$105$		0			0
$106$	1.54398	−	0.476862i	0.149965	−	0.0463169i
$107$		−	1.31462i		−	0.127089i	−0.997979	−	0.0635445i	$-0.979760\pi$
$107$		−	1.31462i		−	0.127089i	0.997979	−	0.0635445i	$-0.0202405\pi$
$108$		0			0
$109$		−	10.2677i		−	0.983465i	−0.870746	−	0.491732i	$-0.836364\pi$
$109$		−	10.2677i		−	0.983465i	0.870746	−	0.491732i	$-0.163636\pi$
$110$	0.163301	+	0.528737i	0.0155702	+	0.0504131i
$111$		0			0
$112$	1.45602	−	3.72559i	0.137581	−	0.352035i
$113$	−13.1796			−1.23983			−0.619916	−	0.784668i	$-0.712834\pi$
$113$	−13.1796			−1.23983			−0.619916	+	0.784668i	$0.712834\pi$
$114$		0			0
$115$		−	15.7713i		−	1.47068i
$116$	11.2424	+	16.4642i	1.04383	+	1.52866i
$117$		0			0
$118$	14.9985	−	4.63232i	1.38073	−	0.426440i
$119$	5.32168			0.487837
$120$		0			0
$121$	10.9835			0.998497
$122$	−19.8175	+	6.12068i	−1.79419	+	0.554140i
$123$		0			0
$124$	−5.40297	+	3.68936i	−0.485201	+	0.331315i
$125$		−	2.24514i		−	0.200811i
$126$		0			0
$127$	−0.840201			−0.0745558			−0.0372779	−	0.999305i	$-0.511869\pi$
$127$	−0.840201			−0.0745558			−0.0372779	+	0.999305i	$0.511869\pi$
$128$	9.78372	−	5.68144i	0.864767	−	0.502173i
$129$		0			0
$130$	−8.00339	−	25.9133i	−0.701944	−	2.27275i
$131$		−	7.39979i		−	0.646523i	−0.946310	−	0.323261i	$-0.895221\pi$
$131$		−	7.39979i		−	0.646523i	0.946310	−	0.323261i	$-0.104779\pi$
$132$		0			0
$133$		−	6.68215i		−	0.579416i
$134$	−1.42859	+	0.441222i	−0.123411	+	0.0381158i
$135$		0			0
$136$	11.7782	+	9.37208i	1.00997	+	0.803649i
$137$	5.61682			0.479877			0.239939	−	0.970788i	$-0.422873\pi$
$137$	5.61682			0.479877			0.239939	+	0.970788i	$0.422873\pi$
$138$		0			0
$139$		−	5.19553i		−	0.440679i	−0.975423	−	0.220339i	$-0.929284\pi$
$139$		−	5.19553i		−	0.440679i	0.975423	−	0.220339i	$-0.0707165\pi$
$140$	3.43243	+	5.02669i	0.290093	+	0.424833i
$141$		0			0
$142$	−0.461495	−	1.49423i	−0.0387278	−	0.125393i
$143$	0.810183			0.0677509
$144$		0			0
$145$	−30.3373			−2.51937
$146$	5.05052	+	16.3525i	0.417984	+	1.35335i
$147$		0			0
$148$	0.898844	+	1.31633i	0.0738845	+	0.108202i
$149$		−	11.6207i		−	0.952009i	−0.879443	−	0.476004i	$-0.842085\pi$
$149$		−	11.6207i		−	0.952009i	0.879443	−	0.476004i	$-0.157915\pi$
$150$		0			0
$151$	21.5154			1.75090			0.875448	−	0.483313i	$-0.160567\pi$
$151$	21.5154			1.75090			0.875448	+	0.483313i	$0.160567\pi$
$152$	11.7680	−	14.7893i	0.954514	−	1.19957i
$153$		0			0
$154$	−0.173732	+	0.0536575i	−0.0139997	+	0.00432385i
$155$		−	9.95563i		−	0.799655i
$156$		0			0
$157$			18.3001i			1.46050i	0.683178	+	0.730252i	$0.260597\pi$
$157$			18.3001i			1.46050i	−0.683178	+	0.730252i	$0.739403\pi$
$158$	−1.09519	−	3.54599i	−0.0871284	−	0.282104i
$159$		0			0
$160$	−1.25576	+	17.1702i	−0.0992767	+	1.35743i
$161$	5.18212			0.408408
$162$		0			0
$163$			18.8550i			1.47684i	0.674344	+	0.738418i	$0.264427\pi$
$163$			18.8550i			1.47684i	−0.674344	+	0.738418i	$0.735573\pi$
$164$	4.90185	−	3.34718i	0.382771	−	0.261371i
$165$		0			0
$166$	−8.73442	+	2.69764i	−0.677922	+	0.209378i
$167$	20.8283			1.61174			0.805872	−	0.592089i	$-0.201697\pi$
$167$	20.8283			1.61174			0.805872	+	0.592089i	$0.201697\pi$
$168$		0			0
$169$	−26.7070			−2.05438
$170$	−21.8846	+	6.75910i	−1.67847	+	0.518399i
$171$		0			0
$172$	−7.88463	−	11.5468i	−0.601198	−	0.880437i
$173$		−	5.49174i		−	0.417529i	−0.977966	−	0.208765i	$-0.933056\pi$
$173$		−	5.49174i		−	0.417529i	0.977966	−	0.208765i	$-0.0669443\pi$
$174$		0			0
$175$	−4.26229			−0.322199
$176$	−0.479010	−	0.187205i	−0.0361067	−	0.0141111i
$177$		0			0
$178$	0.931830	+	3.01708i	0.0698436	+	0.226139i
$179$		−	7.62941i		−	0.570249i	−0.958491	−	0.285124i	$-0.907965\pi$
$179$		−	7.62941i		−	0.570249i	0.958491	−	0.285124i	$-0.0920349\pi$
$180$		0			0
$181$			10.0176i			0.744600i	0.928113	+	0.372300i	$0.121431\pi$
$181$			10.0176i			0.744600i	−0.928113	+	0.372300i	$0.878569\pi$
$182$	8.51460	−	2.62975i	0.631144	−	0.194930i
$183$		0			0
$184$	11.4693	+	9.12631i	0.845530	+	0.672800i
$185$	−2.42550			−0.178326
$186$		0			0
$187$		−	0.684223i		−	0.0500354i
$188$	−7.87178	+	5.37516i	−0.574108	+	0.392024i
$189$		0			0
$190$	8.48705	+	27.4793i	0.615715	+	1.99356i
$191$	−6.25601			−0.452669			−0.226335	−	0.974050i	$-0.572674\pi$
$191$	−6.25601			−0.452669			−0.226335	+	0.974050i	$0.572674\pi$
$192$		0			0
$193$	2.46446			0.177396			0.0886980	−	0.996059i	$-0.471729\pi$
$193$	2.46446			0.177396			0.0886980	+	0.996059i	$0.471729\pi$
$194$	3.28898	+	10.6490i	0.236135	+	0.764557i
$195$		0			0
$196$	−1.65167	+	1.12783i	−0.117976	+	0.0805590i
$197$			23.8105i			1.69643i	0.529654	+	0.848214i	$0.322322\pi$
$197$			23.8105i			1.69643i	−0.529654	+	0.848214i	$0.677678\pi$
$198$		0			0
$199$	24.1296			1.71050			0.855252	−	0.518212i	$-0.173402\pi$
$199$	24.1296			1.71050			0.855252	+	0.518212i	$0.173402\pi$
$200$	−9.43352	−	7.50639i	−0.667051	−	0.530782i
$201$		0			0
$202$	−22.9295	+	7.08181i	−1.61331	+	0.498274i
$203$		−	9.96821i		−	0.699631i
$204$		0			0
$205$			9.03227i			0.630841i
$206$	4.46750	+	14.4648i	0.311265	+	1.00781i
$207$		0			0
$208$	23.4762	+	9.17488i	1.62778	+	0.636164i
$209$	−0.859144			−0.0594282
$210$		0			0
$211$			14.9668i			1.03036i	0.857083	+	0.515179i	$0.172274\pi$
$211$			14.9668i			1.03036i	−0.857083	+	0.515179i	$0.827726\pi$
$212$	−1.28870	−	1.88727i	−0.0885085	−	0.129618i
$213$		0			0
$214$	−1.77636	+	0.548632i	−0.121429	+	0.0375037i
$215$	21.2764			1.45104
$216$		0			0
$217$	3.27122			0.222065
$218$	−13.8740	+	4.28502i	−0.939668	+	0.290218i
$219$		0			0
$220$	0.646296	−	0.441317i	0.0435733	−	0.0297536i
$221$			33.5337i			2.25572i
$222$		0			0
$223$	11.6108			0.777518			0.388759	−	0.921340i	$-0.372904\pi$
$223$	11.6108			0.777518			0.388759	+	0.921340i	$0.372904\pi$
$224$	−5.64179	−	0.412618i	−0.376958	−	0.0275692i
$225$		0			0
$226$	5.50026	+	17.8087i	0.365872	+	1.18462i
$227$		−	0.939445i		−	0.0623531i	−0.999514	−	0.0311766i	$-0.990075\pi$
$227$		−	0.939445i		−	0.0623531i	0.999514	−	0.0311766i	$-0.00992542\pi$
$228$		0			0
$229$			0.0137124i			0.000906143i	1.00000		0.000453071i	$0.000144217\pi$
$229$			0.0137124i			0.000906143i	−1.00000		0.000453071i	$0.999856\pi$
$230$	−21.3107	+	6.58185i	−1.40519	+	0.433994i
$231$		0			0
$232$	17.5552	−	22.0621i	1.15255	−	1.44845i
$233$	−18.2195			−1.19360			−0.596800	−	0.802390i	$-0.703561\pi$
$233$	−18.2195			−1.19360			−0.596800	+	0.802390i	$0.703561\pi$
$234$		0			0
$235$		−	14.5047i		−	0.946183i
$236$	−12.5187	−	18.3333i	−0.814899	−	1.19340i
$237$		0			0
$238$	−2.22090	−	7.19083i	−0.143960	−	0.466112i
$239$	1.37153			0.0887169			0.0443585	−	0.999016i	$-0.485876\pi$
$239$	1.37153			0.0887169			0.0443585	+	0.999016i	$0.485876\pi$
$240$		0			0
$241$	−10.5054			−0.676711			−0.338355	−	0.941018i	$-0.609871\pi$
$241$	−10.5054			−0.676711			−0.338355	+	0.941018i	$0.609871\pi$
$242$	−4.58375	−	14.8412i	−0.294654	−	0.954031i
$243$		0			0
$244$	16.5409	+	24.2238i	1.05893	+	1.55077i
$245$		−	3.04340i		−	0.194436i
$246$		0			0
$247$	42.1066			2.67918
$248$	7.24002	+	5.76099i	0.459742	+	0.365823i
$249$		0			0
$250$	−3.03371	+	0.936967i	−0.191869	+	0.0592590i
$251$		−	20.0556i		−	1.26590i	−0.774192	−	0.632950i	$-0.781844\pi$
$251$		−	20.0556i		−	1.26590i	0.774192	−	0.632950i	$-0.218156\pi$
$252$		0			0
$253$		−	0.666280i		−	0.0418887i
$254$	0.350643	+	1.13531i	0.0220013	+	0.0712356i
$255$		0			0
$256$	−11.7600	−	10.8491i	−0.735001	−	0.678066i
$257$	24.6631			1.53844			0.769220	−	0.638984i	$-0.220645\pi$
$257$	24.6631			1.53844			0.769220	+	0.638984i	$0.220645\pi$
$258$		0			0
$259$		−	0.796970i		−	0.0495213i
$260$	−31.6749	+	21.6289i	−1.96440	+	1.34137i
$261$		0			0
$262$	−9.99885	+	3.08817i	−0.617731	+	0.190788i
$263$	14.0542			0.866616			0.433308	−	0.901246i	$-0.357346\pi$
$263$	14.0542			0.866616			0.433308	+	0.901246i	$0.357346\pi$
$264$		0			0
$265$	3.47753			0.213623
$266$	−9.02915	+	2.78867i	−0.553613	+	0.170984i
$267$		0			0
$268$	1.19239	+	1.74622i	0.0728368	+	0.106667i
$269$		−	13.1276i		−	0.800404i	−0.916427	−	0.400202i	$-0.868940\pi$
$269$		−	13.1276i		−	0.800404i	0.916427	−	0.400202i	$-0.131060\pi$
$270$		0			0
$271$	−15.4626			−0.939285			−0.469642	−	0.882857i	$-0.655617\pi$
$271$	−15.4626			−0.939285			−0.469642	+	0.882857i	$0.655617\pi$
$272$	7.74846	−	19.8264i	0.469820	−	1.20215i
$273$		0			0
$274$	−2.34407	−	7.58964i	−0.141611	−	0.458507i
$275$			0.548015i			0.0330466i
$276$		0			0
$277$			11.1880i			0.672223i	0.941822	+	0.336112i	$0.109112\pi$
$277$			11.1880i			0.672223i	−0.941822	+	0.336112i	$0.890888\pi$
$278$	−7.02037	+	2.16826i	−0.421054	+	0.130043i
$279$		0			0
$280$	5.35978	−	6.73581i	0.320308	−	0.402542i
$281$	−0.179766			−0.0107240			−0.00536198	−	0.999986i	$-0.501707\pi$
$281$	−0.179766			−0.0107240			−0.00536198	+	0.999986i	$0.501707\pi$
$282$		0			0
$283$			29.0480i			1.72673i	0.504583	+	0.863363i	$0.331646\pi$
$283$			29.0480i			1.72673i	−0.504583	+	0.863363i	$0.668354\pi$
$284$	−1.82645	+	1.24717i	−0.108380	+	0.0740062i
$285$		0			0
$286$	−0.338115	−	1.09475i	−0.0199931	−	0.0647337i
$287$	−2.96782			−0.175185
$288$		0			0
$289$	11.3202			0.665897
$290$	12.6607	+	40.9928i	0.743462	+	2.40718i
$291$		0			0
$292$	19.9884	−	13.6489i	1.16973	−	0.798739i
$293$		−	4.42498i		−	0.258510i	−0.991611	−	0.129255i	$-0.958741\pi$
$293$		−	4.42498i		−	0.258510i	0.991611	−	0.129255i	$-0.0412586\pi$
$294$		0			0
$295$	33.7813			1.96683
$296$	1.40356	−	1.76389i	0.0815800	−	0.102524i
$297$		0			0
$298$	−15.7024	+	4.84970i	−0.909613	+	0.280936i
$299$			32.6543i			1.88845i
$300$		0			0
$301$			6.99100i			0.402955i
$302$	−8.97904	−	29.0723i	−0.516686	−	1.67292i
$303$		0			0
$304$	−24.8949	−	9.72934i	−1.42782	−	0.558016i
$305$	−44.6352			−2.55581
$306$		0			0
$307$		−	8.36831i		−	0.477605i	−0.971068	−	0.238802i	$-0.923245\pi$
$307$		−	8.36831i		−	0.477605i	0.971068	−	0.238802i	$-0.0767548\pi$
$308$	0.145008	+	0.212360i	0.00826259	+	0.0121003i
$309$		0			0
$310$	−13.4524	+	4.15480i	−0.764044	+	0.235977i
$311$	−28.1701			−1.59738			−0.798690	−	0.601743i	$-0.794473\pi$
$311$	−28.1701			−1.59738			−0.798690	+	0.601743i	$0.794473\pi$
$312$		0			0
$313$	14.0081			0.791784			0.395892	−	0.918297i	$-0.370435\pi$
$313$	14.0081			0.791784			0.395892	+	0.918297i	$0.370435\pi$
$314$	24.7277	−	7.63719i	1.39546	−	0.430992i
$315$		0			0
$316$	−4.33441	+	2.95971i	−0.243830	+	0.166497i
$317$		−	14.4390i		−	0.810974i	−0.914101	−	0.405487i	$-0.867102\pi$
$317$		−	14.4390i		−	0.810974i	0.914101	−	0.405487i	$-0.132898\pi$
$318$		0			0
$319$	−1.28164			−0.0717582
$320$	23.7251	−	5.46885i	1.32627	−	0.305718i
$321$		0			0
$322$	−2.16266	−	7.00226i	−0.120520	−	0.390221i
$323$		−	35.5603i		−	1.97863i
$324$		0			0
$325$		−	26.8582i		−	1.48982i
$326$	25.4775	−	7.86877i	1.41107	−	0.435811i
$327$		0			0
$328$	−6.56853	−	5.22667i	−0.362686	−	0.288595i
$329$	4.76595			0.262756
$330$		0			0
$331$			32.5738i			1.79042i	0.445648	+	0.895208i	$0.352973\pi$
$331$			32.5738i			1.79042i	−0.445648	+	0.895208i	$0.647027\pi$
$332$	7.29030	+	10.6764i	0.400107	+	0.585946i
$333$		0			0
$334$	−8.69232	−	28.1440i	−0.475623	−	1.53997i
$335$	−3.21762			−0.175798
$336$		0			0
$337$	−2.17181			−0.118306			−0.0591529	−	0.998249i	$-0.518840\pi$
$337$	−2.17181			−0.118306			−0.0591529	+	0.998249i	$0.518840\pi$
$338$	11.1457	+	36.0874i	0.606244	+	1.96290i
$339$		0			0
$340$	18.2663	+	26.7504i	0.990627	+	1.45075i
$341$		−	0.420590i		−	0.0227762i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−12.3120	+	15.4728i	−0.663816	+	0.834240i
$345$		0			0
$346$	−7.42063	+	2.29188i	−0.398935	+	0.123212i
$347$			2.79477i			0.150031i	0.997182	+	0.0750157i	$0.0239007\pi$
$347$			2.79477i			0.150031i	−0.997182	+	0.0750157i	$0.976099\pi$
$348$		0			0
$349$			3.19085i			0.170802i	0.996347	+	0.0854011i	$0.0272172\pi$
$349$			3.19085i			0.170802i	−0.996347	+	0.0854011i	$0.972783\pi$
$350$	1.77879	+	5.75936i	0.0950803	+	0.307851i
$351$		0			0
$352$	−0.0530515	+	0.725381i	−0.00282765	+	0.0386629i
$353$	8.10245			0.431250			0.215625	−	0.976476i	$-0.430821\pi$
$353$	8.10245			0.431250			0.215625	+	0.976476i	$0.430821\pi$
$354$		0			0
$355$		−	3.36546i		−	0.178620i
$356$	3.68790	−	2.51824i	0.195458	−	0.133467i
$357$		0			0
$358$	−10.3091	+	3.18399i	−0.544854	+	0.168279i
$359$	−17.2635			−0.911134			−0.455567	−	0.890202i	$-0.650563\pi$
$359$	−17.2635			−0.911134			−0.455567	+	0.890202i	$0.650563\pi$
$360$		0			0
$361$	−25.6511			−1.35006
$362$	13.5361	−	4.18064i	0.711440	−	0.219730i
$363$		0			0
$364$	−7.10682	−	10.4077i	−0.372499	−	0.545514i
$365$			36.8310i			1.92782i
$366$		0			0
$367$	−13.5508			−0.707348			−0.353674	−	0.935369i	$-0.615068\pi$
$367$	−13.5508			−0.707348			−0.353674	+	0.935369i	$0.615068\pi$
$368$	7.54527	−	19.3064i	0.393324	−	1.00642i
$369$		0			0
$370$	1.01224	+	3.27742i	0.0526238	+	0.170385i
$371$			1.14264i			0.0593232i
$372$		0			0
$373$			16.3399i			0.846048i	0.906118	+	0.423024i	$0.139031\pi$
$373$			16.3399i			0.846048i	−0.906118	+	0.423024i	$0.860969\pi$
$374$	−0.924546	+	0.285548i	−0.0478072	+	0.0147653i
$375$		0			0
$376$	10.5482	+	8.39339i	0.543984	+	0.432856i
$377$	62.8132			3.23504
$378$		0			0
$379$		−	2.37754i		−	0.122126i	−0.998134	−	0.0610630i	$-0.980551\pi$
$379$		−	2.37754i		−	0.122126i	0.998134	−	0.0610630i	$-0.0194491\pi$
$380$	33.5891	−	22.9360i	1.72309	−	1.17659i
$381$		0			0
$382$	2.61083	+	8.45334i	0.133582	+	0.432511i
$383$	−17.6210			−0.900389			−0.450194	−	0.892931i	$-0.648645\pi$
$383$	−17.6210			−0.900389			−0.450194	+	0.892931i	$0.648645\pi$
$384$		0			0
$385$	−0.391299			−0.0199424
$386$	−1.02850	−	3.33007i	−0.0523492	−	0.169496i
$387$		0			0
$388$	13.0168	−	8.88836i	0.660826	−	0.451238i
$389$			12.6831i			0.643058i	0.946900	+	0.321529i	$0.104197\pi$
$389$			12.6831i			0.643058i	−0.946900	+	0.321529i	$0.895803\pi$
$390$		0			0
$391$	27.5776			1.39466
$392$	2.21325	+	1.76111i	0.111786	+	0.0889497i
$393$		0			0
$394$	32.1736	−	9.93687i	1.62088	−	0.500612i
$395$		−	7.98668i		−	0.401854i
$396$		0			0
$397$		−	34.3856i		−	1.72576i	−0.505405	−	0.862882i	$-0.668657\pi$
$397$		−	34.3856i		−	1.72576i	0.505405	−	0.862882i	$-0.331343\pi$
$398$	−10.0701	−	32.6048i	−0.504767	−	1.63433i
$399$		0			0
$400$	−6.20598	+	15.8795i	−0.310299	+	0.793977i
$401$	−3.75947			−0.187739			−0.0938696	−	0.995585i	$-0.529924\pi$
$401$	−3.75947			−0.187739			−0.0938696	+	0.995585i	$0.529924\pi$
$402$		0			0
$403$			20.6131i			1.02681i
$404$	19.1384	+	28.0276i	0.952170	+	1.39443i
$405$		0			0
$406$	−13.4694	+	4.16005i	−0.668475	+	0.206460i
$407$	−0.102469			−0.00507919
$408$		0			0
$409$	13.0996			0.647731			0.323866	−	0.946103i	$-0.395017\pi$
$409$	13.0996			0.647731			0.323866	+	0.946103i	$0.395017\pi$
$410$	12.2047	−	3.76945i	0.602748	−	0.186160i
$411$		0			0
$412$	17.6810	−	12.0733i	0.871079	−	0.594807i
$413$			11.0999i			0.546189i
$414$		0			0
$415$	−19.6726			−0.965692
$416$	2.60005	−	35.5509i	0.127478	−	1.74302i
$417$		0			0
$418$	0.358548	+	1.16090i	0.0175371	+	0.0567817i
$419$		−	24.4344i		−	1.19370i	−0.802353	−	0.596849i	$-0.796419\pi$
$419$		−	24.4344i		−	1.19370i	0.802353	−	0.596849i	$-0.203581\pi$
$420$		0			0
$421$			26.3907i			1.28620i	0.765781	+	0.643101i	$0.222353\pi$
$421$			26.3907i			1.28620i	−0.765781	+	0.643101i	$0.777647\pi$
$422$	20.2237	−	6.24612i	0.984472	−	0.304056i
$423$		0			0
$424$	−2.01233	+	2.52896i	−0.0977273	+	0.122817i
$425$	−22.6825			−1.10027
$426$		0			0
$427$		−	14.6662i		−	0.709749i
$428$	1.48266	+	2.17132i	0.0716671	+	0.104954i
$429$		0			0
$430$	−8.87933	−	28.7494i	−0.428199	−	1.38642i
$431$	32.7161			1.57588			0.787940	−	0.615751i	$-0.211147\pi$
$431$	32.7161			1.57588			0.787940	+	0.615751i	$0.211147\pi$
$432$		0			0
$433$	12.3235			0.592228			0.296114	−	0.955153i	$-0.404309\pi$
$433$	12.3235			0.592228			0.296114	+	0.955153i	$0.404309\pi$
$434$	−1.36518	−	4.42018i	−0.0655308	−	0.212176i
$435$		0			0
$436$	11.5801	+	16.9588i	0.554588	+	0.812179i
$437$		−	34.6277i		−	1.65647i
$438$		0			0
$439$	4.67878			0.223306			0.111653	−	0.993747i	$-0.464385\pi$
$439$	4.67878			0.223306			0.111653	+	0.993747i	$0.464385\pi$
$440$	−0.866043	−	0.689122i	−0.0412870	−	0.0328526i
$441$		0			0
$442$	45.3119	−	13.9947i	2.15527	−	0.665659i
$443$			35.6471i			1.69364i	0.531877	+	0.846821i	$0.321487\pi$
$443$			35.6471i			1.69364i	−0.531877	+	0.846821i	$0.678513\pi$
$444$		0			0
$445$			6.79540i			0.322133i
$446$	−4.84556	−	15.6889i	−0.229444	−	0.742892i
$447$		0			0
$448$	1.79695	+	7.79557i	0.0848980	+	0.368306i
$449$	6.02786			0.284472			0.142236	−	0.989833i	$-0.454571\pi$
$449$	6.02786			0.284472			0.142236	+	0.989833i	$0.454571\pi$
$450$		0			0
$451$			0.381581i			0.0179680i
$452$	21.7683	−	14.8643i	1.02390	−	0.699158i
$453$		0			0
$454$	−1.26941	+	0.392060i	−0.0595764	+	0.0184003i
$455$	19.1775			0.899057
$456$		0			0
$457$	4.88761			0.228633			0.114316	−	0.993444i	$-0.463532\pi$
$457$	4.88761			0.228633			0.114316	+	0.993444i	$0.463532\pi$
$458$	0.0185287	−	0.00572263i	0.000865789	−	0.000267401i
$459$		0			0
$460$	17.7872	+	26.0489i	0.829335	+	1.21454i
$461$		−	9.16306i		−	0.426766i	−0.976969	−	0.213383i	$-0.931552\pi$
$461$		−	9.16306i		−	0.426766i	0.976969	−	0.213383i	$-0.0684483\pi$
$462$		0			0
$463$	32.8412			1.52626			0.763130	−	0.646245i	$-0.223662\pi$
$463$	32.8412			1.52626			0.763130	+	0.646245i	$0.223662\pi$
$464$	−37.1374	−	14.5139i	−1.72406	−	0.673791i
$465$		0			0
$466$	7.60358	+	24.6188i	0.352229	+	1.14045i
$467$			6.40559i			0.296415i	0.988956	+	0.148208i	$0.0473504\pi$
$467$			6.40559i			0.296415i	−0.988956	+	0.148208i	$0.952650\pi$
$468$		0			0
$469$		−	1.05725i		−	0.0488191i
$470$	−19.5993	+	6.05327i	−0.904047	+	0.279217i
$471$		0			0
$472$	−19.5481	+	24.5668i	−0.899776	+	1.13078i
$473$	0.898854			0.0413293
$474$		0			0
$475$			28.4813i			1.30681i
$476$	−8.78965	+	6.00192i	−0.402873	+	0.275098i
$477$		0			0
$478$	−0.572383	−	1.85326i	−0.0261802	−	0.0847661i
$479$	27.3218			1.24837			0.624184	−	0.781278i	$-0.285432\pi$
$479$	27.3218			1.24837			0.624184	+	0.781278i	$0.285432\pi$
$480$		0			0
$481$	5.02199			0.228983
$482$	4.38423	+	14.1952i	0.199696	+	0.646575i
$483$		0			0
$484$	−18.1411	+	12.3874i	−0.824593	+	0.563065i
$485$			23.9850i			1.08910i
$486$		0			0
$487$	9.05264			0.410214			0.205107	−	0.978740i	$-0.434246\pi$
$487$	9.05264			0.410214			0.205107	+	0.978740i	$0.434246\pi$
$488$	25.8289	−	32.4600i	1.16922	−	1.46940i
$489$		0			0
$490$	−4.11235	+	1.27011i	−0.185777	+	0.0573776i
$491$			10.1183i			0.456632i	0.973587	+	0.228316i	$0.0733219\pi$
$491$			10.1183i			0.456632i	−0.973587	+	0.228316i	$0.926678\pi$
$492$		0			0
$493$		−	53.0476i		−	2.38914i
$494$	−17.5724	−	56.8958i	−0.790619	−	2.55986i
$495$		0			0
$496$	4.76296	−	12.1872i	0.213863	−	0.547222i
$497$	1.10582			0.0496029
$498$		0			0
$499$			19.9396i			0.892621i	0.894878	+	0.446310i	$0.147262\pi$
$499$			19.9396i			0.892621i	−0.894878	+	0.446310i	$0.852738\pi$
$500$	2.53212	+	3.70823i	0.113240	+	0.165837i
$501$		0			0
$502$	−27.0999	+	8.36985i	−1.20953	+	0.373565i
$503$	24.3936			1.08766			0.543828	−	0.839197i	$-0.316974\pi$
$503$	24.3936			1.08766			0.543828	+	0.839197i	$0.316974\pi$
$504$		0			0
$505$	−51.6443			−2.29814
$506$	−0.900301	+	0.278060i	−0.0400233	+	0.0123613i
$507$		0			0
$508$	1.38773	−	0.947601i	0.0615708	−	0.0420430i
$509$			7.20394i			0.319309i	0.987173	+	0.159655i	$0.0510381\pi$
$509$			7.20394i			0.319309i	−0.987173	+	0.159655i	$0.948962\pi$
$510$		0			0
$511$	−12.1019			−0.535358
$512$	−9.75179	+	20.4182i	−0.430972	+	0.902365i
$513$		0			0
$514$	−10.2927	−	33.3256i	−0.453991	−	1.46993i
$515$			32.5793i			1.43562i
$516$		0			0
$517$		−	0.612773i		−	0.0269497i
$518$	−1.07689	+	0.332601i	−0.0473160	+	0.0146136i
$519$		0			0
$520$	42.4447	+	33.7738i	1.86132	+	1.48108i
$521$	14.8648			0.651240			0.325620	−	0.945501i	$-0.394427\pi$
$521$	14.8648			0.651240			0.325620	+	0.945501i	$0.394427\pi$
$522$		0			0
$523$		−	32.1286i		−	1.40489i	−0.711740	−	0.702443i	$-0.752093\pi$
$523$		−	32.1286i		−	1.40489i	0.711740	−	0.702443i	$-0.247907\pi$
$524$	8.34567	+	12.2220i	0.364582	+	0.533921i
$525$		0			0
$526$	−5.86524	−	18.9905i	−0.255737	−	0.828023i
$527$	17.4084			0.758320
$528$		0			0
$529$	3.85438			0.167582
$530$	−1.45128	−	4.69895i	−0.0630396	−	0.204109i
$531$		0			0
$532$	7.53630	+	11.0367i	0.326740	+	0.478502i
$533$		−	18.7013i		−	0.810042i
$534$		0			0
$535$	−4.00091			−0.172975
$536$	1.86193	−	2.33995i	0.0804232	−	0.101070i
$537$		0			0
$538$	−17.7385	+	5.47856i	−0.764760	+	0.236198i
$539$		−	0.128573i		−	0.00553803i
$540$		0			0
$541$			30.6123i			1.31612i	0.752964	+	0.658062i	$0.228624\pi$
$541$			30.6123i			1.31612i	−0.752964	+	0.658062i	$0.771376\pi$
$542$	6.45302	+	20.8936i	0.277181	+	0.897456i
$543$		0			0
$544$	−30.0238	−	2.19582i	−1.28726	−	0.0941449i
$545$	−31.2487			−1.33855
$546$		0			0
$547$		−	7.64518i		−	0.326884i	−0.986553	−	0.163442i	$-0.947740\pi$
$547$		−	7.64518i		−	0.326884i	0.986553	−	0.163442i	$-0.0522597\pi$
$548$	−9.27712	+	6.33479i	−0.396299	+	0.270609i
$549$		0			0
$550$	0.740497	−	0.228704i	0.0315749	−	0.00975198i
$551$	−66.6091			−2.83764
$552$		0			0
$553$	2.62426			0.111595
$554$	15.1176	−	4.66911i	0.642287	−	0.198372i
$555$		0			0
$556$	5.85965	+	8.58129i	0.248504	+	0.363928i
$557$			24.9682i			1.05794i	0.848641	+	0.528969i	$0.177421\pi$
$557$			24.9682i			1.05794i	−0.848641	+	0.528969i	$0.822579\pi$
$558$		0			0
$559$	−44.0527			−1.86323
$560$	−11.3385	−	4.43125i	−0.479137	−	0.187255i
$561$		0			0
$562$	0.0750222	+	0.242907i	0.00316462	+	0.0102464i
$563$			33.1836i			1.39852i	0.714865	+	0.699262i	$0.246488\pi$
$563$			33.1836i			1.39852i	−0.714865	+	0.699262i	$0.753512\pi$
$564$		0			0
$565$			40.1108i			1.68748i
$566$	39.2507	−	12.1227i	1.64983	−	0.509553i
$567$		0			0
$568$	2.44746	+	1.94748i	0.102693	+	0.0817144i
$569$	−17.0679			−0.715523			−0.357761	−	0.933813i	$-0.616460\pi$
$569$	−17.0679			−0.715523			−0.357761	+	0.933813i	$0.616460\pi$
$570$		0			0
$571$		−	5.13058i		−	0.214708i	−0.994221	−	0.107354i	$-0.965762\pi$
$571$		−	5.13058i		−	0.214708i	0.994221	−	0.107354i	$-0.0342378\pi$
$572$	−1.33815	+	0.913745i	−0.0559510	+	0.0382056i
$573$		0			0
$574$	1.23856	+	4.01022i	0.0516967	+	0.167383i
$575$	−22.0877			−0.921121
$576$		0			0
$577$	−47.5819			−1.98086			−0.990429	−	0.138021i	$-0.955926\pi$
$577$	−47.5819			−1.98086			−0.990429	+	0.138021i	$0.955926\pi$
$578$	−4.72430	−	15.2963i	−0.196505	−	0.636242i
$579$		0			0
$580$	50.1071	−	34.2151i	2.08058	−	1.42071i
$581$		−	6.46403i		−	0.268173i
$582$		0			0
$583$	0.146913			0.00608452
$584$	−26.7846	−	21.3129i	−1.10835	−	0.881933i
$585$		0			0
$586$	−5.97919	+	1.84668i	−0.246998	+	0.0762858i
$587$			23.6803i			0.977390i	0.872455	+	0.488695i	$0.162527\pi$
$587$			23.6803i			0.977390i	−0.872455	+	0.488695i	$0.837473\pi$
$588$		0			0
$589$		−	21.8588i		−	0.900675i
$590$	−14.0980	−	45.6465i	−0.580406	−	1.87924i
$591$		0			0
$592$	−2.96918	−	1.16040i	−0.122033	−	0.0476923i
$593$	−17.8919			−0.734734			−0.367367	−	0.930076i	$-0.619741\pi$
$593$	−17.8919			−0.734734			−0.367367	+	0.930076i	$0.619741\pi$
$594$		0			0
$595$		−	16.1960i		−	0.663971i
$596$	13.1062	+	19.1936i	0.536850	+	0.786201i
$597$		0			0
$598$	44.1237	−	13.6277i	1.80435	−	0.557278i
$599$	−32.0167			−1.30817			−0.654083	−	0.756423i	$-0.726945\pi$
$599$	−32.0167			−1.30817			−0.654083	+	0.756423i	$0.726945\pi$
$600$		0			0
$601$	23.7187			0.967507			0.483754	−	0.875204i	$-0.339273\pi$
$601$	23.7187			0.967507			0.483754	+	0.875204i	$0.339273\pi$
$602$	9.44648	−	2.91757i	0.385010	−	0.118911i
$603$		0			0
$604$	−35.5362	+	24.2656i	−1.44595	+	0.987352i
$605$		−	33.4271i		−	1.35901i
$606$		0			0
$607$	−14.4444			−0.586281			−0.293141	−	0.956069i	$-0.594700\pi$
$607$	−14.4444			−0.586281			−0.293141	+	0.956069i	$0.594700\pi$
$608$	−2.75717	+	37.6993i	−0.111818	+	1.52891i
$609$		0			0
$610$	18.6277	+	60.3127i	0.754213	+	2.44199i
$611$			30.0319i			1.21496i
$612$		0			0
$613$		−	16.2817i		−	0.657610i	−0.944398	−	0.328805i	$-0.893354\pi$
$613$		−	16.2817i		−	0.657610i	0.944398	−	0.328805i	$-0.106646\pi$
$614$	−11.3076	+	3.49236i	−0.456336	+	0.140940i
$615$		0			0
$616$	0.226432	−	0.284564i	0.00912319	−	0.0114654i
$617$	−28.7753			−1.15845			−0.579225	−	0.815167i	$-0.696645\pi$
$617$	−28.7753			−1.15845			−0.579225	+	0.815167i	$0.696645\pi$
$618$		0			0
$619$		−	36.0871i		−	1.45046i	−0.688506	−	0.725231i	$-0.741733\pi$
$619$		−	36.0871i		−	1.45046i	0.688506	−	0.725231i	$-0.258267\pi$
$620$	11.2282	+	16.4434i	0.450936	+	0.660383i
$621$		0			0
$622$	11.7563	+	38.0644i	0.471383	+	1.52624i
$623$	−2.23283			−0.0894564
$624$		0			0
$625$	−28.1443			−1.12577
$626$	−5.84602	−	18.9282i	−0.233654	−	0.756524i
$627$		0			0
$628$	−20.6393	−	30.2256i	−0.823596	−	1.20613i
$629$		−	4.24122i		−	0.169108i
$630$		0			0
$631$	18.0509			0.718595			0.359297	−	0.933223i	$-0.383016\pi$
$631$	18.0509			0.718595			0.359297	+	0.933223i	$0.383016\pi$
$632$	5.80815	+	4.62163i	0.231036	+	0.183838i
$633$		0			0
$634$	−19.5104	+	6.02584i	−0.774859	+	0.239317i
$635$			2.55707i			0.101474i
$636$		0			0
$637$			6.30135i			0.249668i
$638$	0.534870	+	1.73180i	0.0211757	+	0.0685626i
$639$		0			0
$640$	−17.2909	−	29.7758i	−0.683483	−	1.17699i
$641$	−12.0253			−0.474971			−0.237486	−	0.971391i	$-0.576323\pi$
$641$	−12.0253			−0.474971			−0.237486	+	0.971391i	$0.576323\pi$
$642$		0			0
$643$			9.54316i			0.376345i	0.982136	+	0.188173i	$0.0602565\pi$
$643$			9.54316i			0.376345i	−0.982136	+	0.188173i	$0.939744\pi$
$644$	−8.55915	+	5.84453i	−0.337278	+	0.230307i
$645$		0			0
$646$	−48.0502	+	14.8404i	−1.89051	+	0.583888i
$647$	−32.2201			−1.26670			−0.633351	−	0.773865i	$-0.718321\pi$
$647$	−32.2201			−1.26670			−0.633351	+	0.773865i	$0.718321\pi$
$648$		0			0
$649$	1.42714			0.0560202
$650$	−36.2917	+	11.2088i	−1.42348	+	0.439644i
$651$		0			0
$652$	−21.2651	−	31.1422i	−0.832806	−	1.21962i
$653$		−	14.5245i		−	0.568388i	−0.958767	−	0.284194i	$-0.908274\pi$
$653$		−	14.5245i		−	0.568388i	0.958767	−	0.284194i	$-0.0917259\pi$
$654$		0			0
$655$	−22.5205			−0.879950
$656$	−4.32120	+	11.0569i	−0.168715	+	0.431698i
$657$		0			0
$658$	−1.98898	−	6.43992i	−0.0775386	−	0.251054i
$659$			10.5726i			0.411849i	0.978568	+	0.205924i	$0.0660201\pi$
$659$			10.5726i			0.411849i	−0.978568	+	0.205924i	$0.933980\pi$
$660$		0			0
$661$		−	27.0965i		−	1.05393i	−0.849887	−	0.526965i	$-0.823330\pi$
$661$		−	27.0965i		−	1.05393i	0.849887	−	0.526965i	$-0.176670\pi$
$662$	44.0148	−	13.5941i	1.71068	−	0.528348i
$663$		0			0
$664$	11.3839	−	14.3065i	0.441781	−	0.555200i
$665$	−20.3365			−0.788614
$666$		0			0
$667$		−	51.6565i		−	2.00015i
$668$	−34.4015	+	23.4907i	−1.33103	+	0.908883i
$669$		0			0
$670$	1.34282	+	4.34777i	0.0518775	+	0.167969i
$671$	−1.88568			−0.0727959
$672$		0			0
$673$	38.2417			1.47411			0.737055	−	0.675833i	$-0.236216\pi$
$673$	38.2417			1.47411			0.737055	+	0.675833i	$0.236216\pi$
$674$	0.906363	+	2.93462i	0.0349118	+	0.113037i
$675$		0			0
$676$	44.1111	−	30.1208i	1.69658	−	1.15849i
$677$			14.2289i			0.546860i	0.961892	+	0.273430i	$0.0881582\pi$
$677$			14.2289i			0.546860i	−0.961892	+	0.273430i	$0.911842\pi$
$678$		0			0
$679$	−7.88097			−0.302444
$680$	28.5230	−	35.8458i	1.09381	−	1.37462i
$681$		0			0
$682$	−0.568316	+	0.175525i	−0.0217619	+	0.00672122i
$683$			39.0552i			1.49441i	0.664596	+	0.747203i	$0.268603\pi$
$683$			39.0552i			1.49441i	−0.664596	+	0.747203i	$0.731397\pi$
$684$		0			0
$685$		−	17.0942i		−	0.653137i
$686$	−0.417332	−	1.35123i	−0.0159338	−	0.0515904i
$687$		0			0
$688$	26.0456	+	10.1790i	0.992979	+	0.388072i
$689$	−7.20020			−0.274306
$690$		0			0
$691$			20.1602i			0.766929i	0.923556	+	0.383464i	$0.125269\pi$
$691$			20.1602i			0.766929i	−0.923556	+	0.383464i	$0.874731\pi$
$692$	6.19373	+	9.07054i	0.235450	+	0.344810i
$693$		0			0
$694$	3.77639	−	1.16635i	0.143350	−	0.0442739i
$695$	−15.8121			−0.599786
$696$		0			0
$697$	−15.7938			−0.598232
$698$	4.31159	−	1.33164i	0.163196	−	0.0504034i
$699$		0			0
$700$	7.03990	−	4.80712i	0.266083	−	0.181692i
$701$		−	22.4760i		−	0.848908i	−0.905449	−	0.424454i	$-0.860466\pi$
$701$		−	22.4760i		−	0.848908i	0.905449	−	0.424454i	$-0.139534\pi$
$702$		0			0
$703$	−5.32548			−0.200854
$704$	1.00230	−	0.231039i	0.0377756	−	0.00870762i
$705$		0			0
$706$	−3.38141	−	10.9483i	−0.127261	−	0.412045i
$707$		−	16.9693i		−	0.638195i
$708$		0			0
$709$		−	20.2609i		−	0.760915i	−0.924798	−	0.380458i	$-0.875767\pi$
$709$		−	20.2609i		−	0.760915i	0.924798	−	0.380458i	$-0.124233\pi$
$710$	−4.54753	+	1.40451i	−0.170666	+	0.0527104i
$711$		0			0
$712$	−4.94181	−	3.93227i	−0.185202	−	0.147368i
$713$	16.9518			0.634852
$714$		0			0
$715$		−	2.46571i		−	0.0922124i
$716$	8.60464	+	12.6013i	0.321571	+	0.470931i
$717$		0			0
$718$	7.20461	+	23.3271i	0.268874	+	0.870558i
$719$	−21.2440			−0.792269			−0.396134	−	0.918193i	$-0.629649\pi$
$719$	−21.2440			−0.792269			−0.396134	+	0.918193i	$0.629649\pi$
$720$		0			0
$721$	−10.7049			−0.398672
$722$	10.7050	+	34.6607i	0.398400	+	1.28994i
$723$		0			0
$724$	−11.2981	−	16.5457i	−0.419889	−	0.614916i
$725$			42.4874i			1.57794i
$726$		0			0
$727$	−32.9048			−1.22037			−0.610185	−	0.792259i	$-0.708905\pi$
$727$	−32.9048			−1.22037			−0.610185	+	0.792259i	$0.708905\pi$
$728$	−11.0974	+	13.9465i	−0.411297	+	0.516890i
$729$		0			0
$730$	49.7674	−	15.3708i	1.84197	−	0.568897i
$731$			37.2039i			1.37603i
$732$		0			0
$733$			32.0598i			1.18415i	0.805881	+	0.592077i	$0.201692\pi$
$733$			32.0598i			1.18415i	−0.805881	+	0.592077i	$0.798308\pi$
$734$	5.65519	+	18.3104i	0.208737	+	0.675847i
$735$		0			0
$736$	−29.2364	−	2.13823i	−1.07767	−	0.0788164i
$737$	−0.135933			−0.00500716
$738$		0			0
$739$			46.3826i			1.70621i	0.521738	+	0.853106i	$0.325284\pi$
$739$			46.3826i			1.70621i	−0.521738	+	0.853106i	$0.674716\pi$
$740$	4.00612	−	2.73554i	0.147268	−	0.100561i
$741$		0			0
$742$	1.54398	−	0.476862i	0.0566813	−	0.0175061i
$743$	12.1782			0.446777			0.223388	−	0.974730i	$-0.428288\pi$
$743$	12.1782			0.446777			0.223388	+	0.974730i	$0.428288\pi$
$744$		0			0
$745$	−35.3666			−1.29573
$746$	22.0790	−	6.81916i	0.808371	−	0.249667i
$747$		0			0
$748$	0.771685	+	1.13011i	0.0282156	+	0.0413209i
$749$		−	1.31462i		−	0.0480351i
$750$		0			0
$751$	24.4371			0.891723			0.445862	−	0.895102i	$-0.352897\pi$
$751$	24.4371			0.891723			0.445862	+	0.895102i	$0.352897\pi$
$752$	6.93932	−	17.7560i	0.253051	−	0.647494i
$753$		0			0
$754$	−26.2139	−	84.8753i	−0.954655	−	3.09098i
$755$		−	65.4799i		−	2.38306i
$756$		0			0
$757$			7.15224i			0.259953i	0.991517	+	0.129976i	$0.0414902\pi$
$757$			7.15224i			0.259953i	−0.991517	+	0.129976i	$0.958510\pi$
$758$	−3.21261	+	0.992223i	−0.116687	+	0.0360391i
$759$		0			0
$760$	−45.0097	−	35.8148i	−1.63267	−	1.29914i
$761$	14.7809			0.535806			0.267903	−	0.963446i	$-0.413669\pi$
$761$	14.7809			0.535806			0.267903	+	0.963446i	$0.413669\pi$
$762$		0			0
$763$		−	10.2677i		−	0.371715i
$764$	10.3329	−	7.05569i	0.373830	−	0.255266i
$765$		0			0
$766$	7.35378	+	23.8100i	0.265703	+	0.860292i
$767$	−69.9441			−2.52554
$768$		0			0
$769$	−1.90576			−0.0687235			−0.0343618	−	0.999409i	$-0.510940\pi$
$769$	−1.90576			−0.0687235			−0.0343618	+	0.999409i	$0.510940\pi$
$770$	0.163301	+	0.528737i	0.00588497	+	0.0190543i
$771$		0			0
$772$	−4.07048	+	2.77948i	−0.146500	+	0.100036i
$773$			6.63435i			0.238621i	0.992857	+	0.119310i	$0.0380684\pi$
$773$			6.63435i			0.238621i	−0.992857	+	0.119310i	$0.961932\pi$
$774$		0			0
$775$	−13.9429			−0.500843
$776$	−17.4426	−	13.8793i	−0.626152	−	0.498238i
$777$		0			0
$778$	17.1378	−	5.29305i	0.614421	−	0.189765i
$779$			19.8314i			0.710534i
$780$		0			0
$781$		−	0.142179i		−	0.00508756i
$782$	−11.5090	−	37.2638i	−0.411561	−	1.33255i
$783$		0			0
$784$	1.45602	−	3.72559i	0.0520007	−	0.133057i
$785$	55.6944			1.98782
$786$		0			0
$787$		−	2.91096i		−	0.103765i	−0.998653	−	0.0518823i	$-0.983478\pi$
$787$		−	2.91096i		−	0.103765i	0.998653	−	0.0518823i	$-0.0165221\pi$
$788$	−26.8541	−	39.3271i	−0.956637	−	1.40097i
$789$		0			0
$790$	−10.7919	+	3.33309i	−0.383958	+	0.118586i
$791$	−13.1796			−0.468613
$792$		0			0
$793$	92.4170			3.28182
$794$	−46.4630	+	14.3502i	−1.64891	+	0.509270i
$795$		0			0
$796$	−39.8542	+	27.2140i	−1.41259	+	0.964576i
$797$			6.96910i			0.246858i	0.992353	+	0.123429i	$0.0393891\pi$
$797$			6.96910i			0.246858i	−0.992353	+	0.123429i	$0.960611\pi$
$798$		0			0
$799$	25.3629			0.897274
$800$	24.0469	+	1.75870i	0.850188	+	0.0621793i
$801$		0			0
$802$	1.56895	+	5.07993i	0.0554014	+	0.179379i
$803$			1.55598i			0.0549094i
$804$		0			0
$805$		−	15.7713i		−	0.555864i
$806$	27.8531	−	8.60249i	0.981084	−	0.303010i
$807$		0			0
$808$	29.8848	−	37.5572i	1.05134	−	1.32126i
$809$	−21.3012			−0.748909			−0.374454	−	0.927245i	$-0.622170\pi$
$809$	−21.3012			−0.748909			−0.374454	+	0.927245i	$0.622170\pi$
$810$		0			0
$811$			18.1357i			0.636832i	0.947951	+	0.318416i	$0.103151\pi$
$811$			18.1357i			0.636832i	−0.947951	+	0.318416i	$0.896849\pi$
$812$	11.2424	+	16.4642i	0.394531	+	0.577780i
$813$		0			0
$814$	0.0427635	+	0.138459i	0.00149886	+	0.00485300i
$815$	57.3832			2.01005
$816$		0			0
$817$	46.7149			1.63435
$818$	−5.46686	−	17.7006i	−0.191144	−	0.618886i
$819$		0			0
$820$	−10.1868	−	14.9183i	−0.355739	−	0.520970i
$821$			24.3030i			0.848180i	0.905620	+	0.424090i	$0.139406\pi$
$821$			24.3030i			0.848180i	−0.905620	+	0.424090i	$0.860594\pi$
$822$		0			0
$823$	1.29306			0.0450734			0.0225367	−	0.999746i	$-0.492826\pi$
$823$	1.29306			0.0450734			0.0225367	+	0.999746i	$0.492826\pi$
$824$	−23.6926	−	18.8526i	−0.825372	−	0.656760i
$825$		0			0
$826$	14.9985	−	4.63232i	0.521865	−	0.161179i
$827$			23.6268i			0.821585i	0.911729	+	0.410792i	$0.134748\pi$
$827$			23.6268i			0.821585i	−0.911729	+	0.410792i	$0.865252\pi$
$828$		0			0
$829$			5.66492i			0.196751i	0.995149	+	0.0983754i	$0.0313646\pi$
$829$			5.66492i			0.196751i	−0.995149	+	0.0983754i	$0.968635\pi$
$830$	8.21001	+	26.5823i	0.284974	+	0.922687i
$831$		0			0
$832$	−49.1226	+	11.3232i	−1.70302	+	0.392562i
$833$	5.32168			0.184385
$834$		0			0
$835$		−	63.3890i		−	2.19367i
$836$	1.41902	−	0.968964i	0.0490779	−	0.0335123i
$837$		0			0
$838$	−33.0166	+	10.1972i	−1.14054	+	0.352258i
$839$	−21.1554			−0.730366			−0.365183	−	0.930936i	$-0.618994\pi$
$839$	−21.1554			−0.730366			−0.365183	+	0.930936i	$0.618994\pi$
$840$		0			0
$841$	−70.3652			−2.42639
$842$	35.6600	−	11.0137i	1.22892	−	0.379556i
$843$		0			0
$844$	−16.8799	−	24.7202i	−0.581032	−	0.850904i
$845$			81.2801i			2.79612i
$846$		0			0
$847$	10.9835			0.377396
$848$	4.25702	+	1.66371i	0.146187	+	0.0571321i
$849$		0			0
$850$	9.46614	+	30.6494i	0.324686	+	1.05127i
$851$		−	4.13000i		−	0.141574i
$852$		0			0
$853$			4.41255i			0.151083i	0.997143	+	0.0755413i	$0.0240685\pi$
$853$			4.41255i			0.151083i	−0.997143	+	0.0755413i	$0.975932\pi$
$854$	−19.8175	+	6.12068i	−0.678141	+	0.209445i
$855$		0			0
$856$	2.31519	−	2.90958i	0.0791317	−	0.0994474i
$857$	20.9783			0.716606			0.358303	−	0.933605i	$-0.383356\pi$
$857$	20.9783			0.716606			0.358303	+	0.933605i	$0.383356\pi$
$858$		0			0
$859$		−	15.6318i		−	0.533351i	−0.963786	−	0.266676i	$-0.914075\pi$
$859$		−	15.6318i		−	0.533351i	0.963786	−	0.266676i	$-0.0859253\pi$
$860$	−35.1416	+	23.9961i	−1.19832	+	0.818260i
$861$		0			0
$862$	−13.6535	−	44.2072i	−0.465039	−	1.50570i
$863$	16.1880			0.551047			0.275523	−	0.961294i	$-0.411149\pi$
$863$	16.1880			0.551047			0.275523	+	0.961294i	$0.411149\pi$
$864$		0			0
$865$	−16.7136			−0.568278
$866$	−5.14297	−	16.6519i	−0.174765	−	0.565855i
$867$		0			0
$868$	−5.40297	+	3.68936i	−0.183389	+	0.125225i
$869$		−	0.337409i		−	0.0114458i
$870$		0			0
$871$	6.66208			0.225736
$872$	18.0826	−	22.7249i	0.612352	−	0.769563i
$873$		0			0
$874$	−46.7902	+	14.4512i	−1.58270	+	0.488820i
$875$		−	2.24514i		−	0.0758995i
$876$		0			0
$877$			38.1001i			1.28655i	0.765636	+	0.643274i	$0.222424\pi$
$877$			38.1001i			1.28655i	−0.765636	+	0.643274i	$0.777576\pi$
$878$	−1.95260	−	6.32213i	−0.0658972	−	0.213362i
$879$		0			0
$880$	−0.569739	+	1.45782i	−0.0192059	+	0.0491431i
$881$	−46.4289			−1.56423			−0.782114	−	0.623135i	$-0.785859\pi$
$881$	−46.4289			−1.56423			−0.782114	+	0.623135i	$0.785859\pi$
$882$		0			0
$883$		−	17.8873i		−	0.601956i	−0.953631	−	0.300978i	$-0.902687\pi$
$883$		−	17.8873i		−	0.601956i	0.953631	−	0.300978i	$-0.0973131\pi$
$884$	−37.8202	−	55.3866i	−1.27203	−	1.86285i
$885$		0			0
$886$	48.1675	−	14.8766i	1.61822	−	0.499791i
$887$	35.5228			1.19274			0.596369	−	0.802711i	$-0.296610\pi$
$887$	35.5228			1.19274			0.596369	+	0.802711i	$0.296610\pi$
$888$		0			0
$889$	−0.840201			−0.0281795
$890$	9.18218	−	2.83593i	0.307787	−	0.0950607i
$891$		0			0
$892$	−19.1772	+	13.0950i	−0.642101	+	0.438452i
$893$		−	31.8468i		−	1.06571i
$894$		0			0
$895$	−23.2194			−0.776137
$896$	9.78372	−	5.68144i	0.326851	−	0.189804i
$897$		0			0
$898$	−2.51562	−	8.14505i	−0.0839472	−	0.271804i
$899$		−	32.6082i		−	1.08754i
$900$		0			0
$901$			6.08079i			0.202580i
$902$	0.515606	−	0.159246i	0.0171678	−	0.00530231i
$903$		0			0
$904$	−29.1698	−	23.2108i	−0.970172	−	0.771979i
$905$	30.4875			1.01344
$906$		0			0
$907$		−	41.8996i		−	1.39125i	−0.718404	−	0.695627i	$-0.755127\pi$
$907$		−	41.8996i		−	1.39125i	0.718404	−	0.695627i	$-0.244873\pi$
$908$	1.05953	+	1.55165i	0.0351617	+	0.0514934i
$909$		0			0
$910$	−8.00339	−	25.9133i	−0.265310	−	0.859019i
$911$	5.35427			0.177395			0.0886974	−	0.996059i	$-0.471730\pi$
$911$	5.35427			0.177395			0.0886974	+	0.996059i	$0.471730\pi$
$912$		0			0
$913$	−0.831099			−0.0275054
$914$	−2.03975	−	6.60431i	−0.0674691	−	0.218451i
$915$		0			0
$916$	−0.0154652	−	0.0226484i	−0.000510985	−	0.000748324i
$917$		−	7.39979i		−	0.244363i
$918$		0			0
$919$	−54.8843			−1.81047			−0.905234	−	0.424914i	$-0.860304\pi$
$919$	−54.8843			−1.81047			−0.905234	+	0.424914i	$0.860304\pi$
$920$	27.7750	−	34.9058i	0.915715	−	1.15081i
$921$		0			0
$922$	−12.3814	+	3.82403i	−0.407761	+	0.125938i
$923$			6.96817i			0.229360i
$924$		0			0
$925$			3.39692i			0.111690i
$926$	−13.7057	−	44.3761i	−0.450396	−	1.45829i
$927$		0			0
$928$	−4.11306	+	56.2385i	−0.135018	+	1.84612i
$929$	−10.4091			−0.341512			−0.170756	−	0.985313i	$-0.554621\pi$
$929$	−10.4091			−0.341512			−0.170756	+	0.985313i	$0.554621\pi$
$930$		0			0
$931$		−	6.68215i		−	0.218999i
$932$	30.0926	−	20.5484i	0.985716	−	0.673086i
$933$		0			0
$934$	8.65545	−	2.67325i	0.283215	−	0.0874715i
$935$	−2.08237			−0.0681007
$936$		0			0
$937$	49.8177			1.62747			0.813737	−	0.581233i	$-0.197430\pi$
$937$	49.8177			1.62747			0.813737	+	0.581233i	$0.197430\pi$
$938$	−1.42859	+	0.441222i	−0.0466450	+	0.0144064i
$939$		0			0
$940$	16.3588	+	23.9570i	0.533565	+	0.781390i
$941$			5.61503i			0.183045i	0.995803	+	0.0915224i	$0.0291733\pi$
$941$			5.61503i			0.183045i	−0.995803	+	0.0915224i	$0.970827\pi$
$942$		0			0
$943$	−15.3796			−0.500829
$944$	41.3535	+	16.1616i	1.34594	+	0.526016i
$945$		0			0
$946$	−0.375120	−	1.21456i	−0.0121962	−	0.0394888i
$947$		−	22.3495i		−	0.726262i	−0.931738	−	0.363131i	$-0.881708\pi$
$947$		−	22.3495i		−	0.726262i	0.931738	−	0.363131i	$-0.118292\pi$
$948$		0			0
$949$		−	76.2585i		−	2.47545i
$950$	38.4849	−	11.8861i	1.24861	−	0.385637i
$951$		0			0
$952$	11.7782	+	9.37208i	0.381734	+	0.303751i
$953$	−19.9449			−0.646080			−0.323040	−	0.946385i	$-0.604705\pi$
$953$	−19.9449			−0.646080			−0.323040	+	0.946385i	$0.604705\pi$
$954$		0			0
$955$			19.0396i			0.616106i
$956$	−2.26531	+	1.54685i	−0.0732655	+	0.0500286i
$957$		0			0
$958$	−11.4023	−	36.9182i	−0.368391	−	1.19277i
$959$	5.61682			0.181376
$960$		0			0
$961$	−20.2991			−0.654811
$962$	−2.09583	−	6.78588i	−0.0675724	−	0.218786i
$963$		0			0
$964$	17.3514	−	11.8482i	0.558851	−	0.381606i
$965$		−	7.50035i		−	0.241445i
$966$		0			0
$967$	32.6951			1.05140			0.525702	−	0.850669i	$-0.323803\pi$
$967$	32.6951			1.05140			0.525702	+	0.850669i	$0.323803\pi$
$968$	24.3092	+	19.3431i	0.781326	+	0.621712i
$969$		0			0
$970$	32.4093	−	10.0097i	1.04060	−	0.321392i
$971$			33.7391i			1.08274i	0.840785	+	0.541369i	$0.182094\pi$
$971$			33.7391i			1.08274i	−0.840785	+	0.541369i	$0.817906\pi$
$972$		0			0
$973$		−	5.19553i		−	0.166561i
$974$	−3.77795	−	12.2322i	−0.121053	−	0.391946i
$975$		0			0
$976$	−54.6403	−	21.3543i	−1.74899	−	0.683535i
$977$	−45.8374			−1.46647			−0.733235	−	0.679976i	$-0.761990\pi$
$977$	−45.8374			−1.46647			−0.733235	+	0.679976i	$0.761990\pi$
$978$		0			0
$979$			0.287081i			0.00917516i
$980$	3.43243	+	5.02669i	0.109645	+	0.160572i
$981$		0			0
$982$	13.6722	−	4.22268i	0.436296	−	0.134751i
$983$	14.0557			0.448307			0.224154	−	0.974554i	$-0.428038\pi$
$983$	14.0557			0.448307			0.224154	+	0.974554i	$0.428038\pi$
$984$		0			0
$985$	72.4649			2.30892
$986$	−71.6797	+	22.1384i	−2.28275	+	0.705031i
$987$		0			0
$988$	−69.5461	+	47.4889i	−2.21256	+	1.51082i
$989$			36.2282i			1.15199i
$990$		0			0
$991$	18.3875			0.584099			0.292050	−	0.956403i	$-0.405663\pi$
$991$	18.3875			0.584099			0.292050	+	0.956403i	$0.405663\pi$
$992$	−18.4555	−	1.34976i	−0.585963	−	0.0428550i
$993$		0			0
$994$	−0.461495	−	1.49423i	−0.0146377	−	0.0473939i
$995$		−	73.4362i		−	2.32808i
$996$		0			0
$997$			20.8011i			0.658776i	0.944195	+	0.329388i	$0.106842\pi$
$997$			20.8011i			0.658776i	−0.944195	+	0.329388i	$0.893158\pi$
$998$	26.9431	−	8.32144i	0.852870	−	0.263411i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.g.757.11	✓	24
3.2	odd	2	inner	1512.2.c.g.757.14	yes	24
4.3	odd	2		6048.2.c.f.3025.4		24
8.3	odd	2		6048.2.c.f.3025.21		24
8.5	even	2	inner	1512.2.c.g.757.12	yes	24
12.11	even	2		6048.2.c.f.3025.22		24
24.5	odd	2	inner	1512.2.c.g.757.13	yes	24
24.11	even	2		6048.2.c.f.3025.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.g.757.11	✓	24	1.1	even	1	trivial
1512.2.c.g.757.12	yes	24	8.5	even	2	inner
1512.2.c.g.757.13	yes	24	24.5	odd	2	inner
1512.2.c.g.757.14	yes	24	3.2	odd	2	inner
6048.2.c.f.3025.3		24	24.11	even	2
6048.2.c.f.3025.4		24	4.3	odd	2
6048.2.c.f.3025.21		24	8.3	odd	2
6048.2.c.f.3025.22		24	12.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.417332 - 1.35123i) q^{2} +(-1.65167 + 1.12783i) q^{4} -3.04340i q^{5} +1.00000 q^{7} +(2.21325 + 1.76111i) q^{8} +O(q^{10})\)	\(q+(-0.417332 - 1.35123i) q^{2} +(-1.65167 + 1.12783i) q^{4} -3.04340i q^{5} +1.00000 q^{7} +(2.21325 + 1.76111i) q^{8} +(-4.11235 + 1.27011i) q^{10} -0.128573i q^{11} +6.30135i q^{13} +(-0.417332 - 1.35123i) q^{14} +(1.45602 - 3.72559i) q^{16} +5.32168 q^{17} -6.68215i q^{19} +(3.43243 + 5.02669i) q^{20} +(-0.173732 + 0.0536575i) q^{22} +5.18212 q^{23} -4.26229 q^{25} +(8.51460 - 2.62975i) q^{26} +(-1.65167 + 1.12783i) q^{28} -9.96821i q^{29} +3.27122 q^{31} +(-5.64179 - 0.412618i) q^{32} +(-2.22090 - 7.19083i) q^{34} -3.04340i q^{35} -0.796970i q^{37} +(-9.02915 + 2.78867i) q^{38} +(5.35978 - 6.73581i) q^{40} -2.96782 q^{41} +6.99100i q^{43} +(0.145008 + 0.212360i) q^{44} +(-2.16266 - 7.00226i) q^{46} +4.76595 q^{47} +1.00000 q^{49} +(1.77879 + 5.75936i) q^{50} +(-7.10682 - 10.4077i) q^{52} +1.14264i q^{53} -0.391299 q^{55} +(2.21325 + 1.76111i) q^{56} +(-13.4694 + 4.16005i) q^{58} +11.0999i q^{59} -14.6662i q^{61} +(-1.36518 - 4.42018i) q^{62} +(1.79695 + 7.79557i) q^{64} +19.1775 q^{65} -1.05725i q^{67} +(-8.78965 + 6.00192i) q^{68} +(-4.11235 + 1.27011i) q^{70} +1.10582 q^{71} -12.1019 q^{73} +(-1.07689 + 0.332601i) q^{74} +(7.53630 + 11.0367i) q^{76} -0.128573i q^{77} +2.62426 q^{79} +(-11.3385 - 4.43125i) q^{80} +(1.23856 + 4.01022i) q^{82} -6.46403i q^{83} -16.1960i q^{85} +(9.44648 - 2.91757i) q^{86} +(0.226432 - 0.284564i) q^{88} -2.23283 q^{89} +6.30135i q^{91} +(-8.55915 + 5.84453i) q^{92} +(-1.98898 - 6.43992i) q^{94} -20.3365 q^{95} -7.88097 q^{97} +(-0.417332 - 1.35123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q + 6 * q^4 + 24 * q^7	\( 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) \) 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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