LMFDB - Embedded newform 585.2.n.g.343.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(307,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("585.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.13
Character	$\chi$	$=$	585.343
Dual form			585.2.n.g.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.21780i q^{2} -2.91862 q^{4} +(-1.59963 - 1.56243i) q^{5} +4.11325 q^{7} -2.03732i q^{8} +O(q^{10})$	\(q+2.21780i q^{2} -2.91862 q^{4} +(-1.59963 - 1.56243i) q^{5} +4.11325 q^{7} -2.03732i q^{8} +(3.46515 - 3.54765i) q^{10} +(2.59303 + 2.59303i) q^{11} +(-3.29198 + 1.47066i) q^{13} +9.12235i q^{14} -1.31889 q^{16} +(1.98080 + 1.98080i) q^{17} +(2.76089 + 2.76089i) q^{19} +(4.66871 + 4.56015i) q^{20} +(-5.75081 + 5.75081i) q^{22} +(1.53954 - 1.53954i) q^{23} +(0.117620 + 4.99862i) q^{25} +(-3.26162 - 7.30095i) q^{26} -12.0050 q^{28} +8.40712i q^{29} +(2.11332 - 2.11332i) q^{31} -6.99966i q^{32} +(-4.39301 + 4.39301i) q^{34} +(-6.57967 - 6.42667i) q^{35} -7.83564 q^{37} +(-6.12310 + 6.12310i) q^{38} +(-3.18317 + 3.25895i) q^{40} +(-1.65250 + 1.65250i) q^{41} +(-1.27192 + 1.27192i) q^{43} +(-7.56807 - 7.56807i) q^{44} +(3.41439 + 3.41439i) q^{46} +6.35092 q^{47} +9.91882 q^{49} +(-11.0859 + 0.260858i) q^{50} +(9.60806 - 4.29230i) q^{52} +(-5.31987 - 5.31987i) q^{53} +(-0.0964538 - 8.19931i) q^{55} -8.38000i q^{56} -18.6453 q^{58} +(6.51015 - 6.51015i) q^{59} +7.84876 q^{61} +(4.68691 + 4.68691i) q^{62} +12.8861 q^{64} +(7.56375 + 2.79099i) q^{65} +12.3496i q^{67} +(-5.78120 - 5.78120i) q^{68} +(14.2530 - 14.5924i) q^{70} +(7.75627 - 7.75627i) q^{71} +5.27944i q^{73} -17.3779i q^{74} +(-8.05801 - 8.05801i) q^{76} +(10.6658 + 10.6658i) q^{77} -8.45538i q^{79} +(2.10973 + 2.06067i) q^{80} +(-3.66491 - 3.66491i) q^{82} -4.49388 q^{83} +(-0.0736805 - 6.26340i) q^{85} +(-2.82085 - 2.82085i) q^{86} +(5.28283 - 5.28283i) q^{88} +(-8.91884 + 8.91884i) q^{89} +(-13.5408 + 6.04919i) q^{91} +(-4.49334 + 4.49334i) q^{92} +14.0850i q^{94} +(-0.102698 - 8.73011i) q^{95} -17.6029i q^{97} +21.9979i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} - 8 q^{5}+O(q^{10}) $ 28 * q - 28 * q^4 - 8 * q^5	$ 28 q - 28 q^{4} - 8 q^{5} + 8 q^{11} - 12 q^{13} + 28 q^{16} + 28 q^{17} - 32 q^{22} - 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} - 48 q^{40} - 4 q^{41} - 40 q^{44} - 16 q^{46} + 24 q^{47} - 28 q^{49} + 32 q^{50} + 52 q^{52} - 20 q^{53} - 8 q^{55} - 8 q^{58} - 32 q^{59} + 8 q^{61} - 72 q^{62} - 28 q^{64} + 8 q^{65} - 60 q^{68} + 64 q^{70} - 40 q^{71} - 40 q^{76} + 48 q^{77} + 32 q^{80} + 4 q^{82} + 104 q^{83} - 4 q^{85} - 16 q^{86} + 72 q^{88} + 36 q^{89} - 56 q^{91} + 32 q^{92} - 56 q^{95}+O(q^{100}) $ 28 * q - 28 * q^4 - 8 * q^5 + 8 * q^11 - 12 * q^13 + 28 * q^16 + 28 * q^17 - 32 * q^22 - 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 - 48 * q^40 - 4 * q^41 - 40 * q^44 - 16 * q^46 + 24 * q^47 - 28 * q^49 + 32 * q^50 + 52 * q^52 - 20 * q^53 - 8 * q^55 - 8 * q^58 - 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 8 * q^65 - 60 * q^68 + 64 * q^70 - 40 * q^71 - 40 * q^76 + 48 * q^77 + 32 * q^80 + 4 * q^82 + 104 * q^83 - 4 * q^85 - 16 * q^86 + 72 * q^88 + 36 * q^89 - 56 * q^91 + 32 * q^92 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			2.21780i			1.56822i	0.620622	+	0.784110i	$0.286880\pi$
$2$			2.21780i			1.56822i	−0.620622	+	0.784110i	$0.713120\pi$
$3$		0			0
$3$		0			0
$4$	−2.91862			−1.45931
$5$	−1.59963	−	1.56243i	−0.715375	−	0.698740i
$5$	−1.59963	−	1.56243i	−0.715375	−	0.698740i
$6$		0			0
$7$	4.11325			1.55466			0.777331	−	0.629092i	$-0.216573\pi$
$7$	4.11325			1.55466			0.777331	+	0.629092i	$0.216573\pi$
$8$		−	2.03732i		−	0.720301i
$9$		0			0
$10$	3.46515	−	3.54765i	1.09578	−	1.12187i
$11$	2.59303	+	2.59303i	0.781827	+	0.781827i	0.980139	−	0.198312i	$-0.0635458\pi$
$11$	2.59303	+	2.59303i	0.781827	+	0.781827i	−0.198312	+	0.980139i	$0.563546\pi$
$12$		0			0
$13$	−3.29198	+	1.47066i	−0.913032	+	0.407887i
$13$	−3.29198	+	1.47066i	−0.913032	+	0.407887i
$14$			9.12235i			2.43805i
$15$		0			0
$16$	−1.31889			−0.329721
$17$	1.98080	+	1.98080i	0.480414	+	0.480414i	0.905264	−	0.424850i	$-0.139673\pi$
$17$	1.98080	+	1.98080i	0.480414	+	0.480414i	−0.424850	+	0.905264i	$0.639673\pi$
$18$		0			0
$19$	2.76089	+	2.76089i	0.633393	+	0.633393i	0.948917	−	0.315525i	$-0.102181\pi$
$19$	2.76089	+	2.76089i	0.633393	+	0.633393i	−0.315525	+	0.948917i	$0.602181\pi$
$20$	4.66871	+	4.56015i	1.04396	+	1.01968i
$21$		0			0
$22$	−5.75081	+	5.75081i	−1.22608	+	1.22608i
$23$	1.53954	−	1.53954i	0.321017	−	0.321017i	−0.528140	−	0.849157i	$-0.677110\pi$
$23$	1.53954	−	1.53954i	0.321017	−	0.321017i	0.849157	+	0.528140i	$0.177110\pi$
$24$		0			0
$25$	0.117620	+	4.99862i	0.0235241	+	0.999723i
$26$	−3.26162	−	7.30095i	−0.639657	−	1.43183i
$27$		0			0
$28$	−12.0050			−2.26874
$29$			8.40712i			1.56116i	0.625054	+	0.780582i	$0.285077\pi$
$29$			8.40712i			1.56116i	−0.625054	+	0.780582i	$0.714923\pi$
$30$		0			0
$31$	2.11332	−	2.11332i	0.379563	−	0.379563i	−0.491381	−	0.870944i	$-0.663508\pi$
$31$	2.11332	−	2.11332i	0.379563	−	0.379563i	0.870944	+	0.491381i	$0.163508\pi$
$32$		−	6.99966i		−	1.23738i
$33$		0			0
$34$	−4.39301	+	4.39301i	−0.753395	+	0.753395i
$35$	−6.57967	−	6.42667i	−1.11217	−	1.08631i
$36$		0			0
$37$	−7.83564			−1.28817			−0.644086	−	0.764953i	$-0.722762\pi$
$37$	−7.83564			−1.28817			−0.644086	+	0.764953i	$0.722762\pi$
$38$	−6.12310	+	6.12310i	−0.993299	+	0.993299i
$39$		0			0
$40$	−3.18317	+	3.25895i	−0.503304	+	0.515286i
$41$	−1.65250	+	1.65250i	−0.258077	+	0.258077i	−0.824272	−	0.566195i	$-0.808415\pi$
$41$	−1.65250	+	1.65250i	−0.258077	+	0.258077i	0.566195	+	0.824272i	$0.308415\pi$
$42$		0			0
$43$	−1.27192	+	1.27192i	−0.193965	+	0.193965i	−0.797407	−	0.603442i	$-0.793796\pi$
$43$	−1.27192	+	1.27192i	−0.193965	+	0.193965i	0.603442	+	0.797407i	$0.293796\pi$
$44$	−7.56807	−	7.56807i	−1.14093	−	1.14093i
$45$		0			0
$46$	3.41439	+	3.41439i	0.503425	+	0.503425i
$47$	6.35092			0.926376			0.463188	−	0.886260i	$-0.346705\pi$
$47$	6.35092			0.926376			0.463188	+	0.886260i	$0.346705\pi$
$48$		0			0
$49$	9.91882			1.41697
$50$	−11.0859	+	0.260858i	−1.56779	+	0.0368909i
$51$		0			0
$52$	9.60806	−	4.29230i	1.33240	−	0.595235i
$53$	−5.31987	−	5.31987i	−0.730740	−	0.730740i	0.240027	−	0.970766i	$-0.422844\pi$
$53$	−5.31987	−	5.31987i	−0.730740	−	0.730740i	−0.970766	+	0.240027i	$0.922844\pi$
$54$		0			0
$55$	−0.0964538	−	8.19931i	−0.0130058	−	1.10559i
$56$		−	8.38000i		−	1.11983i
$57$		0			0
$58$	−18.6453			−2.44825
$59$	6.51015	−	6.51015i	0.847550	−	0.847550i	−0.142277	−	0.989827i	$-0.545442\pi$
$59$	6.51015	−	6.51015i	0.847550	−	0.847550i	0.989827	+	0.142277i	$0.0454423\pi$
$60$		0			0
$61$	7.84876			1.00493			0.502465	−	0.864597i	$-0.332426\pi$
$61$	7.84876			1.00493			0.502465	+	0.864597i	$0.332426\pi$
$62$	4.68691	+	4.68691i	0.595238	+	0.595238i
$63$		0			0
$64$	12.8861			1.61076
$65$	7.56375	+	2.79099i	0.938168	+	0.346180i
$66$		0			0
$67$			12.3496i			1.50874i	0.656447	+	0.754372i	$0.272058\pi$
$67$			12.3496i			1.50874i	−0.656447	+	0.754372i	$0.727942\pi$
$68$	−5.78120	−	5.78120i	−0.701074	−	0.701074i
$69$		0			0
$70$	14.2530	−	14.5924i	1.70356	−	1.74412i
$71$	7.75627	−	7.75627i	0.920500	−	0.920500i	−0.0765650	−	0.997065i	$-0.524395\pi$
$71$	7.75627	−	7.75627i	0.920500	−	0.920500i	0.997065	+	0.0765650i	$0.0243953\pi$
$72$		0			0
$73$			5.27944i			0.617912i	0.951076	+	0.308956i	$0.0999796\pi$
$73$			5.27944i			0.617912i	−0.951076	+	0.308956i	$0.900020\pi$
$74$		−	17.3779i		−	2.02014i
$75$		0			0
$76$	−8.05801	−	8.05801i	−0.924317	−	0.924317i
$77$	10.6658	+	10.6658i	1.21548	+	1.21548i
$78$		0			0
$79$		−	8.45538i		−	0.951305i	−0.879633	−	0.475653i	$-0.842212\pi$
$79$		−	8.45538i		−	0.951305i	0.879633	−	0.475653i	$-0.157788\pi$
$80$	2.10973	+	2.06067i	0.235874	+	0.230390i
$81$		0			0
$82$	−3.66491	−	3.66491i	−0.404722	−	0.404722i
$83$	−4.49388			−0.493267			−0.246634	−	0.969109i	$-0.579324\pi$
$83$	−4.49388			−0.493267			−0.246634	+	0.969109i	$0.579324\pi$
$84$		0			0
$85$	−0.0736805	−	6.26340i	−0.00799177	−	0.679361i
$86$	−2.82085	−	2.82085i	−0.304180	−	0.304180i
$87$		0			0
$88$	5.28283	−	5.28283i	0.563151	−	0.563151i
$89$	−8.91884	+	8.91884i	−0.945395	+	0.945395i	−0.998584	−	0.0531890i	$-0.983061\pi$
$89$	−8.91884	+	8.91884i	−0.945395	+	0.945395i	0.0531890	+	0.998584i	$0.483061\pi$
$90$		0			0
$91$	−13.5408	+	6.04919i	−1.41946	+	0.634127i
$92$	−4.49334	+	4.49334i	−0.468464	+	0.468464i
$93$		0			0
$94$			14.0850i			1.45276i
$95$	−0.102698	−	8.73011i	−0.0105366	−	0.895691i
$96$		0			0
$97$		−	17.6029i		−	1.78730i	−0.448765	−	0.893650i	$-0.648136\pi$
$97$		−	17.6029i		−	1.78730i	0.448765	−	0.893650i	$-0.351864\pi$
$98$			21.9979i			2.22213i
$99$		0			0
$100$	−0.343289	−	14.5891i	−0.0343289	−	1.45891i
$101$			4.66632i			0.464316i	0.972678	+	0.232158i	$0.0745787\pi$
$101$			4.66632i			0.464316i	−0.972678	+	0.232158i	$0.925421\pi$
$102$		0			0
$103$	2.08089	−	2.08089i	0.205036	−	0.205036i	−0.597118	−	0.802154i	$-0.703687\pi$
$103$	2.08089	−	2.08089i	0.205036	−	0.205036i	0.802154	+	0.597118i	$0.203687\pi$
$104$	2.99620	+	6.70683i	0.293802	+	0.657658i
$105$		0			0
$106$	11.7984	−	11.7984i	1.14596	−	1.14596i
$107$	−1.71214	+	1.71214i	−0.165519	+	0.165519i	−0.785006	−	0.619488i	$-0.787340\pi$
$107$	−1.71214	+	1.71214i	−0.165519	+	0.165519i	0.619488	+	0.785006i	$0.287340\pi$
$108$		0			0
$109$	−4.77725	−	4.77725i	−0.457578	−	0.457578i	0.440282	−	0.897860i	$-0.354879\pi$
$109$	−4.77725	−	4.77725i	−0.457578	−	0.457578i	−0.897860	+	0.440282i	$0.854879\pi$
$110$	18.1844	−	0.213915i	1.73381	−	0.0203960i
$111$		0			0
$112$	−5.42490			−0.512605
$113$	1.95021	+	1.95021i	0.183460	+	0.183460i	0.792862	−	0.609402i	$-0.208590\pi$
$113$	1.95021	+	1.95021i	0.183460	+	0.183460i	−0.609402	+	0.792862i	$0.708590\pi$
$114$		0			0
$115$	−4.86812	+	0.0572669i	−0.453955	+	0.00534017i
$116$		−	24.5372i		−	2.27822i
$117$		0			0
$118$	14.4382	+	14.4382i	1.32914	+	1.32914i
$119$	8.14752	+	8.14752i	0.746882	+	0.746882i
$120$		0			0
$121$			2.44759i			0.222508i
$122$			17.4070i			1.57595i
$123$		0			0
$124$	−6.16798	+	6.16798i	−0.553901	+	0.553901i
$125$	7.62184	−	8.17970i	0.681718	−	0.731615i
$126$		0			0
$127$	4.33250	+	4.33250i	0.384447	+	0.384447i	0.872701	−	0.488254i	$-0.162366\pi$
$127$	4.33250	+	4.33250i	0.384447	+	0.384447i	−0.488254	+	0.872701i	$0.662366\pi$
$128$			14.5793i			1.28864i
$129$		0			0
$130$	−6.18985	+	16.7749i	−0.542886	+	1.47125i
$131$	11.7646			1.02788			0.513939	−	0.857827i	$-0.328186\pi$
$131$	11.7646			1.02788			0.513939	+	0.857827i	$0.328186\pi$
$132$		0			0
$133$	11.3562	+	11.3562i	0.984712	+	0.984712i
$134$	−27.3889			−2.36604
$135$		0			0
$136$	4.03552	−	4.03552i	0.346043	−	0.346043i
$137$	−12.3668			−1.05657			−0.528286	−	0.849067i	$-0.677165\pi$
$137$	−12.3668			−1.05657			−0.528286	+	0.849067i	$0.677165\pi$
$138$		0			0
$139$		−	15.1730i		−	1.28695i	−0.765466	−	0.643477i	$-0.777491\pi$
$139$		−	15.1730i		−	1.28695i	0.765466	−	0.643477i	$-0.222509\pi$
$140$	19.2036	+	18.7570i	1.62300	+	1.58526i
$141$		0			0
$142$	17.2018	+	17.2018i	1.44355	+	1.44355i
$143$	−12.3497	−	4.72275i	−1.03273	−	0.394936i
$144$		0			0
$145$	13.1355	−	13.4483i	1.09085	−	1.11682i
$146$	−11.7087			−0.969022
$147$		0			0
$148$	22.8693			1.87984
$149$	−6.53739	−	6.53739i	−0.535564	−	0.535564i	0.386659	−	0.922223i	$-0.373629\pi$
$149$	−6.53739	−	6.53739i	−0.535564	−	0.535564i	−0.922223	+	0.386659i	$0.873629\pi$
$150$		0			0
$151$	2.56165	+	2.56165i	0.208464	+	0.208464i	0.803614	−	0.595150i	$-0.202907\pi$
$151$	2.56165	+	2.56165i	0.208464	+	0.208464i	−0.595150	+	0.803614i	$0.702907\pi$
$152$	5.62483	−	5.62483i	0.456234	−	0.456234i
$153$		0			0
$154$	−23.6545	+	23.6545i	−1.90613	+	1.90613i
$155$	−6.68243	+	0.0786099i	−0.536746	+	0.00631410i
$156$		0			0
$157$	−2.92797	+	2.92797i	−0.233678	+	0.233678i	−0.814226	−	0.580548i	$-0.802838\pi$
$157$	−2.92797	+	2.92797i	−0.233678	+	0.233678i	0.580548	+	0.814226i	$0.302838\pi$
$158$	18.7523			1.49185
$159$		0			0
$160$	−10.9365	+	11.1969i	−0.864605	+	0.885189i
$161$	6.33252	−	6.33252i	0.499073	−	0.499073i
$162$		0			0
$163$			8.49438i			0.665331i	0.943045	+	0.332666i	$0.107948\pi$
$163$			8.49438i			0.665331i	−0.943045	+	0.332666i	$0.892052\pi$
$164$	4.82302	−	4.82302i	0.376615	−	0.376615i
$165$		0			0
$166$		−	9.96651i		−	0.773551i
$167$	−13.2559			−1.02577			−0.512886	−	0.858457i	$-0.671424\pi$
$167$	−13.2559			−1.02577			−0.512886	+	0.858457i	$0.671424\pi$
$168$		0			0
$169$	8.67432	−	9.68277i	0.667256	−	0.744829i
$170$	13.8910	−	0.163408i	1.06539	−	0.0125329i
$171$		0			0
$172$	3.71224	−	3.71224i	0.283056	−	0.283056i
$173$	7.94523	−	7.94523i	0.604065	−	0.604065i	−0.337324	−	0.941389i	$-0.609522\pi$
$173$	7.94523	−	7.94523i	0.604065	−	0.604065i	0.941389	+	0.337324i	$0.109522\pi$
$174$		0			0
$175$	0.483802	+	20.5606i	0.0365720	+	1.55423i
$176$	−3.41991	−	3.41991i	−0.257785	−	0.257785i
$177$		0			0
$178$	−19.7802	−	19.7802i	−1.48259	−	1.48259i
$179$	−1.37631			−0.102870			−0.0514350	−	0.998676i	$-0.516379\pi$
$179$	−1.37631			−0.102870			−0.0514350	+	0.998676i	$0.516379\pi$
$180$		0			0
$181$		−	23.4687i		−	1.74442i	−0.489136	−	0.872208i	$-0.662688\pi$
$181$		−	23.4687i		−	1.74442i	0.489136	−	0.872208i	$-0.337312\pi$
$182$	−13.4159	−	30.0306i	−0.994450	−	2.22602i
$183$		0			0
$184$	−3.13654	−	3.13654i	−0.231229	−	0.231229i
$185$	12.5341	+	12.2427i	0.921527	+	0.900098i
$186$		0			0
$187$			10.2725i			0.751202i
$188$	−18.5359			−1.35187
$189$		0			0
$190$	19.3616	−	0.227763i	1.40464	−	0.0165237i
$191$	2.92479			0.211630			0.105815	−	0.994386i	$-0.466255\pi$
$191$	2.92479			0.211630			0.105815	+	0.994386i	$0.466255\pi$
$192$		0			0
$193$		−	20.6977i		−	1.48985i	−0.667146	−	0.744927i	$-0.732484\pi$
$193$		−	20.6977i		−	1.48985i	0.667146	−	0.744927i	$-0.267516\pi$
$194$	39.0396			2.80288
$195$		0			0
$196$	−28.9493			−2.06781
$197$		−	6.16201i		−	0.439025i	−0.975610	−	0.219513i	$-0.929553\pi$
$197$		−	6.16201i		−	0.439025i	0.975610	−	0.219513i	$-0.0704467\pi$
$198$		0			0
$199$	23.2876			1.65081			0.825407	−	0.564538i	$-0.190946\pi$
$199$	23.2876			1.65081			0.825407	+	0.564538i	$0.190946\pi$
$200$	10.1838	−	0.239630i	0.720102	−	0.0169444i
$201$		0			0
$202$	−10.3489			−0.728150
$203$			34.5806i			2.42708i
$204$		0			0
$205$	5.22530	−	0.0614687i	0.364951	−	0.00429316i
$206$	4.61499	+	4.61499i	0.321542	+	0.321542i
$207$		0			0
$208$	4.34175	−	1.93963i	0.301046	−	0.134489i
$209$			14.3182i			0.990407i
$210$		0			0
$211$	11.6786			0.803990			0.401995	−	0.915642i	$-0.368317\pi$
$211$	11.6786			0.803990			0.401995	+	0.915642i	$0.368317\pi$
$212$	15.5267	+	15.5267i	1.06638	+	1.06638i
$213$		0			0
$214$	−3.79718	−	3.79718i	−0.259570	−	0.259570i
$215$	4.02187	−	0.0473119i	0.274289	−	0.00322665i
$216$		0			0
$217$	8.69260	−	8.69260i	0.590092	−	0.590092i
$218$	10.5950	−	10.5950i	0.717583	−	0.717583i
$219$		0			0
$220$	0.281512	+	23.9307i	0.0189796	+	1.61341i
$221$	−9.43384	−	3.60768i	−0.634588	−	0.242679i
$222$		0			0
$223$	−16.7954			−1.12470			−0.562351	−	0.826898i	$-0.690103\pi$
$223$	−16.7954			−1.12470			−0.562351	+	0.826898i	$0.690103\pi$
$224$		−	28.7913i		−	1.92370i
$225$		0			0
$226$	−4.32517	+	4.32517i	−0.287706	+	0.287706i
$227$		−	22.2305i		−	1.47549i	−0.675078	−	0.737746i	$-0.735890\pi$
$227$		−	22.2305i		−	1.47549i	0.675078	−	0.737746i	$-0.264110\pi$
$228$		0			0
$229$	1.99942	−	1.99942i	0.132125	−	0.132125i	−0.637951	−	0.770077i	$-0.720218\pi$
$229$	1.99942	−	1.99942i	0.132125	−	0.132125i	0.770077	+	0.637951i	$0.220218\pi$
$230$	−0.127006	−	10.7965i	−0.00837456	−	0.711901i
$231$		0			0
$232$	17.1280			1.12451
$233$	7.60402	−	7.60402i	0.498156	−	0.498156i	−0.412708	−	0.910863i	$-0.635417\pi$
$233$	7.60402	−	7.60402i	0.498156	−	0.498156i	0.910863	+	0.412708i	$0.135417\pi$
$234$		0			0
$235$	−10.1591	−	9.92287i	−0.662707	−	0.647296i
$236$	−19.0007	+	19.0007i	−1.23684	+	1.23684i
$237$		0			0
$238$	−18.0695	+	18.0695i	−1.17127	+	1.17127i
$239$	−17.2164	−	17.2164i	−1.11363	−	1.11363i	−0.992655	−	0.120979i	$-0.961397\pi$
$239$	−17.2164	−	17.2164i	−1.11363	−	1.11363i	−0.120979	−	0.992655i	$-0.538603\pi$
$240$		0			0
$241$	10.2155	+	10.2155i	0.658040	+	0.658040i	0.954916	−	0.296876i	$-0.0959447\pi$
$241$	10.2155	+	10.2155i	0.658040	+	0.658040i	−0.296876	+	0.954916i	$0.595945\pi$
$242$	−5.42825			−0.348941
$243$		0			0
$244$	−22.9076			−1.46651
$245$	−15.8664	−	15.4975i	−1.01367	−	0.990097i
$246$		0			0
$247$	−13.1492	−	5.02849i	−0.836661	−	0.319955i
$248$	−4.30550	−	4.30550i	−0.273400	−	0.273400i
$249$		0			0
$250$	18.1409	+	16.9037i	1.14733	+	1.06908i
$251$			18.7574i			1.18396i	0.805954	+	0.591978i	$0.201653\pi$
$251$			18.7574i			1.18396i	−0.805954	+	0.591978i	$0.798347\pi$
$252$		0			0
$253$	7.98415			0.501959
$254$	−9.60860	+	9.60860i	−0.602897	+	0.602897i
$255$		0			0
$256$	−6.56189			−0.410118
$257$	−1.40078	−	1.40078i	−0.0873784	−	0.0873784i	0.662067	−	0.749445i	$-0.269680\pi$
$257$	−1.40078	−	1.40078i	−0.0873784	−	0.0873784i	−0.749445	+	0.662067i	$0.769680\pi$
$258$		0			0
$259$	−32.2300			−2.00267
$260$	−22.0757	−	8.14585i	−1.36908	−	0.505184i
$261$		0			0
$262$			26.0915i			1.61194i
$263$	−15.8782	−	15.8782i	−0.979092	−	0.979092i	0.0206938	−	0.999786i	$-0.493413\pi$
$263$	−15.8782	−	15.8782i	−0.979092	−	0.979092i	−0.999786	+	0.0206938i	$0.993413\pi$
$264$		0			0
$265$	0.197885	+	16.8217i	0.0121560	+	1.03335i
$266$	−25.1859	+	25.1859i	−1.54424	+	1.54424i
$267$		0			0
$268$		−	36.0438i		−	2.20173i
$269$		−	0.349269i		−	0.0212953i	−0.999943	−	0.0106477i	$-0.996611\pi$
$269$		−	0.349269i		−	0.0212953i	0.999943	−	0.0106477i	$-0.00338932\pi$
$270$		0			0
$271$	8.52139	+	8.52139i	0.517637	+	0.517637i	0.916856	−	0.399218i	$-0.130719\pi$
$271$	8.52139	+	8.52139i	0.517637	+	0.517637i	−0.399218	+	0.916856i	$0.630719\pi$
$272$	−2.61245	−	2.61245i	−0.158403	−	0.158403i
$273$		0			0
$274$		−	27.4272i		−	1.65694i
$275$	−12.6566	+	13.2665i	−0.763219	+	0.800003i
$276$		0			0
$277$	−5.27671	−	5.27671i	−0.317047	−	0.317047i	0.530585	−	0.847632i	$-0.321972\pi$
$277$	−5.27671	−	5.27671i	−0.317047	−	0.317047i	−0.847632	+	0.530585i	$0.821972\pi$
$278$	33.6505			2.01823
$279$		0			0
$280$	−13.0932	+	13.4049i	−0.782467	+	0.801095i
$281$	5.98480	+	5.98480i	0.357023	+	0.357023i	0.862714	−	0.505691i	$-0.168763\pi$
$281$	5.98480	+	5.98480i	0.357023	+	0.357023i	−0.505691	+	0.862714i	$0.668763\pi$
$282$		0			0
$283$	−2.56174	+	2.56174i	−0.152280	+	0.152280i	−0.779135	−	0.626856i	$-0.784342\pi$
$283$	−2.56174	+	2.56174i	−0.152280	+	0.152280i	0.626856	+	0.779135i	$0.284342\pi$
$284$	−22.6376	+	22.6376i	−1.34330	+	1.34330i
$285$		0			0
$286$	10.4741	−	27.3891i	0.619346	−	1.61955i
$287$	−6.79714	+	6.79714i	−0.401223	+	0.401223i
$288$		0			0
$289$		−	9.15288i		−	0.538404i
$290$	29.8255	+	29.1320i	1.75142	+	1.71069i
$291$		0			0
$292$		−	15.4087i		−	0.901727i
$293$		−	5.91537i		−	0.345579i	−0.984959	−	0.172790i	$-0.944722\pi$
$293$		−	5.91537i		−	0.345579i	0.984959	−	0.172790i	$-0.0552781\pi$
$294$		0			0
$295$	−20.5855	+	0.242161i	−1.19853	+	0.0140991i
$296$			15.9637i			0.927872i
$297$		0			0
$298$	14.4986	−	14.4986i	0.839882	−	0.839882i
$299$	−2.80401	+	7.33229i	−0.162160	+	0.424037i
$300$		0			0
$301$	−5.23170	+	5.23170i	−0.301550	+	0.301550i
$302$	−5.68122	+	5.68122i	−0.326918	+	0.326918i
$303$		0			0
$304$	−3.64130	−	3.64130i	−0.208843	−	0.208843i
$305$	−12.5551	−	12.2631i	−0.718903	−	0.702186i
$306$		0			0
$307$	−2.81730			−0.160792			−0.0803960	−	0.996763i	$-0.525618\pi$
$307$	−2.81730			−0.160792			−0.0803960	+	0.996763i	$0.525618\pi$
$308$	−31.1294	−	31.1294i	−1.77376	−	1.77376i
$309$		0			0
$310$	−0.174341	−	14.8203i	−0.00990189	−	0.841735i
$311$		−	9.18067i		−	0.520588i	−0.965529	−	0.260294i	$-0.916180\pi$
$311$		−	9.18067i		−	0.520588i	0.965529	−	0.260294i	$-0.0838195\pi$
$312$		0			0
$313$	16.4881	+	16.4881i	0.931960	+	0.931960i	0.997828	−	0.0658683i	$-0.0209817\pi$
$313$	16.4881	+	16.4881i	0.931960	+	0.931960i	−0.0658683	+	0.997828i	$0.520982\pi$
$314$	−6.49365	−	6.49365i	−0.366458	−	0.366458i
$315$		0			0
$316$			24.6781i			1.38825i
$317$			13.3835i			0.751695i	0.926682	+	0.375847i	$0.122648\pi$
$317$			13.3835i			0.751695i	−0.926682	+	0.375847i	$0.877352\pi$
$318$		0			0
$319$	−21.7999	+	21.7999i	−1.22056	+	1.22056i
$320$	−20.6129	−	20.1336i	−1.15230	−	1.12550i
$321$		0			0
$322$	14.0442	+	14.0442i	0.782655	+	0.782655i
$323$			10.9376i			0.608582i
$324$		0			0
$325$	−7.73846	−	16.2824i	−0.429253	−	0.903184i
$326$	−18.8388			−1.04339
$327$		0			0
$328$	3.36667	+	3.36667i	0.185893	+	0.185893i
$329$	26.1229			1.44020
$330$		0			0
$331$	−13.7828	+	13.7828i	−0.757572	+	0.757572i	−0.975880	−	0.218308i	$-0.929946\pi$
$331$	−13.7828	+	13.7828i	−0.757572	+	0.757572i	0.218308	+	0.975880i	$0.429946\pi$
$332$	13.1159			0.719831
$333$		0			0
$334$		−	29.3989i		−	1.60863i
$335$	19.2954	−	19.7548i	1.05422	−	1.07932i
$336$		0			0
$337$	−24.8025	−	24.8025i	−1.35108	−	1.35108i	−0.884459	−	0.466618i	$-0.845472\pi$
$337$	−24.8025	−	24.8025i	−1.35108	−	1.35108i	−0.466618	−	0.884459i	$-0.654528\pi$
$338$	21.4744	+	19.2379i	1.16805	+	1.04640i
$339$		0			0
$340$	0.215046	+	18.2805i	0.0116625	+	0.991400i
$341$	10.9598			0.593506
$342$		0			0
$343$	12.0058			0.648254
$344$	2.59130	+	2.59130i	0.139713	+	0.139713i
$345$		0			0
$346$	17.6209	+	17.6209i	0.947306	+	0.947306i
$347$	−2.24725	+	2.24725i	−0.120639	+	0.120639i	−0.764849	−	0.644210i	$-0.777186\pi$
$347$	−2.24725	+	2.24725i	−0.120639	+	0.120639i	0.644210	+	0.764849i	$0.277186\pi$
$348$		0			0
$349$	−19.2780	+	19.2780i	−1.03193	+	1.03193i	−0.0324525	+	0.999473i	$0.510332\pi$
$349$	−19.2780	+	19.2780i	−1.03193	+	1.03193i	−0.999473	+	0.0324525i	$0.989668\pi$
$350$	−45.5991	+	1.07297i	−2.43738	+	0.0573529i
$351$		0			0
$352$	18.1503	−	18.1503i	0.967415	−	0.967415i
$353$	−20.5850			−1.09563			−0.547814	−	0.836600i	$-0.684540\pi$
$353$	−20.5850			−1.09563			−0.547814	+	0.836600i	$0.684540\pi$
$354$		0			0
$355$	−24.5258	+	0.288513i	−1.30169	+	0.0153127i
$356$	26.0307	−	26.0307i	1.37963	−	1.37963i
$357$		0			0
$358$		−	3.05237i		−	0.161323i
$359$	10.6029	−	10.6029i	0.559602	−	0.559602i	−0.369592	−	0.929194i	$-0.620503\pi$
$359$	10.6029	−	10.6029i	0.559602	−	0.559602i	0.929194	+	0.369592i	$0.120503\pi$
$360$		0			0
$361$		−	3.75492i		−	0.197627i
$362$	52.0488			2.73563
$363$		0			0
$364$	39.5204	−	17.6553i	2.07143	−	0.925389i
$365$	8.24877	−	8.44515i	0.431760	−	0.442039i
$366$		0			0
$367$	−1.02534	+	1.02534i	−0.0535221	+	0.0535221i	−0.733361	−	0.679839i	$-0.762050\pi$
$367$	−1.02534	+	1.02534i	−0.0535221	+	0.0535221i	0.679839	+	0.733361i	$0.262050\pi$
$368$	−2.03048	+	2.03048i	−0.105846	+	0.105846i
$369$		0			0
$370$	−27.1517	+	27.7981i	−1.41155	+	1.44516i
$371$	−21.8819	−	21.8819i	−1.13605	−	1.13605i
$372$		0			0
$373$	8.41567	+	8.41567i	0.435747	+	0.435747i	0.890578	−	0.454831i	$-0.150300\pi$
$373$	8.41567	+	8.41567i	0.435747	+	0.435747i	−0.454831	+	0.890578i	$0.650300\pi$
$374$	−22.7824			−1.17805
$375$		0			0
$376$		−	12.9388i		−	0.667270i
$377$	−12.3640	−	27.6761i	−0.636779	−	1.42539i
$378$		0			0
$379$	5.03557	+	5.03557i	0.258660	+	0.258660i	0.824509	−	0.565849i	$-0.191452\pi$
$379$	5.03557	+	5.03557i	0.258660	+	0.258660i	−0.565849	+	0.824509i	$0.691452\pi$
$380$	0.299737	+	25.4799i	0.0153762	+	1.30709i
$381$		0			0
$382$			6.48659i			0.331883i
$383$	0.483559			0.0247087			0.0123543	−	0.999924i	$-0.496067\pi$
$383$	0.483559			0.0247087			0.0123543	+	0.999924i	$0.496067\pi$
$384$		0			0
$385$	−0.396739	−	33.7258i	−0.0202197	−	1.71883i
$386$	45.9033			2.33642
$387$		0			0
$388$			51.3761i			2.60823i
$389$	17.5944			0.892070			0.446035	−	0.895015i	$-0.352836\pi$
$389$	17.5944			0.892070			0.446035	+	0.895015i	$0.352836\pi$
$390$		0			0
$391$	6.09905			0.308442
$392$		−	20.2078i		−	1.02065i
$393$		0			0
$394$	13.6661			0.688488
$395$	−13.2110	+	13.5255i	−0.664715	+	0.680540i
$396$		0			0
$397$	−9.63810			−0.483722			−0.241861	−	0.970311i	$-0.577758\pi$
$397$	−9.63810			−0.483722			−0.241861	+	0.970311i	$0.577758\pi$
$398$			51.6472i			2.58884i
$399$		0			0
$400$	−0.155128	−	6.59260i	−0.00775638	−	0.329630i
$401$	16.8784	+	16.8784i	0.842865	+	0.842865i	0.989231	−	0.146365i	$-0.0467575\pi$
$401$	16.8784	+	16.8784i	0.842865	+	0.842865i	−0.146365	+	0.989231i	$0.546757\pi$
$402$		0			0
$403$	−3.84904	+	10.0650i	−0.191734	+	0.501372i
$404$		−	13.6192i		−	0.677582i
$405$		0			0
$406$	−76.6927			−3.80620
$407$	−20.3180	−	20.3180i	−1.00713	−	1.00713i
$408$		0			0
$409$	3.65546	+	3.65546i	0.180751	+	0.180751i	0.791683	−	0.610932i	$-0.209205\pi$
$409$	3.65546	+	3.65546i	0.180751	+	0.180751i	−0.610932	+	0.791683i	$0.709205\pi$
$410$	0.136325	+	11.5887i	0.00673261	+	0.572323i
$411$		0			0
$412$	−6.07334	+	6.07334i	−0.299212	+	0.299212i
$413$	26.7779	−	26.7779i	1.31765	−	1.31765i
$414$		0			0
$415$	7.18853	+	7.02137i	0.352871	+	0.344666i
$416$	10.2941	+	23.0428i	0.504710	+	1.12976i
$417$		0			0
$418$	−31.7548			−1.55318
$419$			33.9420i			1.65818i	0.559117	+	0.829089i	$0.311140\pi$
$419$			33.9420i			1.65818i	−0.559117	+	0.829089i	$0.688860\pi$
$420$		0			0
$421$	−19.7073	+	19.7073i	−0.960474	+	0.960474i	−0.999248	−	0.0387742i	$-0.987655\pi$
$421$	−19.7073	+	19.7073i	−0.960474	+	0.960474i	0.0387742	+	0.999248i	$0.487655\pi$
$422$			25.9008i			1.26083i
$423$		0			0
$424$	−10.8383	+	10.8383i	−0.526353	+	0.526353i
$425$	−9.66827	+	10.1342i	−0.468980	+	0.491583i
$426$		0			0
$427$	32.2839			1.56233
$428$	4.99709	−	4.99709i	0.241543	−	0.241543i
$429$		0			0
$430$	0.104928	+	8.91969i	0.00506009	+	0.430146i
$431$	−10.7665	+	10.7665i	−0.518606	+	0.518606i	−0.917150	−	0.398543i	$-0.869516\pi$
$431$	−10.7665	+	10.7665i	−0.518606	+	0.518606i	0.398543	+	0.917150i	$0.369516\pi$
$432$		0			0
$433$	11.8525	−	11.8525i	0.569594	−	0.569594i	−0.362421	−	0.932015i	$-0.618050\pi$
$433$	11.8525	−	11.8525i	0.569594	−	0.569594i	0.932015	+	0.362421i	$0.118050\pi$
$434$	19.2784	+	19.2784i	0.925394	+	0.925394i
$435$		0			0
$436$	13.9430	+	13.9430i	0.667749	+	0.667749i
$437$	8.50103			0.406659
$438$		0			0
$439$	2.02222			0.0965152			0.0482576	−	0.998835i	$-0.484633\pi$
$439$	2.02222			0.0965152			0.0482576	+	0.998835i	$0.484633\pi$
$440$	−16.7046	+	0.196507i	−0.796361	+	0.00936812i
$441$		0			0
$442$	8.00110	−	20.9223i	0.380573	−	0.995174i
$443$	−0.127396	−	0.127396i	−0.00605277	−	0.00605277i	0.704074	−	0.710127i	$-0.251362\pi$
$443$	−0.127396	−	0.127396i	−0.00605277	−	0.00605277i	−0.710127	+	0.704074i	$0.751362\pi$
$444$		0			0
$445$	28.2019	−	0.331758i	1.33690	−	0.0157268i
$446$		−	37.2488i		−	1.76378i
$447$		0			0
$448$	53.0035			2.50418
$449$	−24.8640	+	24.8640i	−1.17341	+	1.17341i	−0.192014	+	0.981392i	$0.561502\pi$
$449$	−24.8640	+	24.8640i	−1.17341	+	1.17341i	−0.981392	+	0.192014i	$0.938498\pi$
$450$		0			0
$451$	−8.56996			−0.403544
$452$	−5.69192	−	5.69192i	−0.267726	−	0.267726i
$453$		0			0
$454$	49.3028			2.31390
$455$	31.1116	+	11.4800i	1.45853	+	0.538193i
$456$		0			0
$457$		−	32.3018i		−	1.51101i	−0.655140	−	0.755507i	$-0.727390\pi$
$457$		−	32.3018i		−	1.51101i	0.655140	−	0.755507i	$-0.272610\pi$
$458$	4.43430	+	4.43430i	0.207201	+	0.207201i
$459$		0			0
$460$	14.2082	−	0.167141i	0.662462	−	0.00779297i
$461$	14.5631	−	14.5631i	0.678272	−	0.678272i	−0.281337	−	0.959609i	$-0.590778\pi$
$461$	14.5631	−	14.5631i	0.678272	−	0.678272i	0.959609	+	0.281337i	$0.0907779\pi$
$462$		0			0
$463$			13.2720i			0.616800i	0.951257	+	0.308400i	$0.0997935\pi$
$463$			13.2720i			0.616800i	−0.951257	+	0.308400i	$0.900206\pi$
$464$		−	11.0880i		−	0.514749i
$465$		0			0
$466$	16.8642	+	16.8642i	0.781217	+	0.781217i
$467$	21.6107	+	21.6107i	1.00002	+	1.00002i	1.00000		2.29542e-5i	$7.30656e-6\pi$
$467$	21.6107	+	21.6107i	1.00002	+	1.00002i	2.29542e−5		1.00000i	$0.499993\pi$
$468$		0			0
$469$			50.7970i			2.34559i
$470$	22.0069	−	22.5308i	1.01510	−	1.03927i
$471$		0			0
$472$	−13.2633	−	13.2633i	−0.610491	−	0.610491i
$473$	−6.59622			−0.303295
$474$		0			0
$475$	−13.4759	+	14.1254i	−0.618317	+	0.648117i
$476$	−23.7795	−	23.7795i	−1.08993	−	1.08993i
$477$		0			0
$478$	38.1824	−	38.1824i	1.74642	−	1.74642i
$479$	13.5992	−	13.5992i	0.621361	−	0.621361i	−0.324518	−	0.945879i	$-0.605202\pi$
$479$	13.5992	−	13.5992i	0.621361	−	0.621361i	0.945879	+	0.324518i	$0.105202\pi$
$480$		0			0
$481$	25.7948	−	11.5236i	1.17614	−	0.525429i
$482$	−22.6560	+	22.6560i	−1.03195	+	1.03195i
$483$		0			0
$484$		−	7.14359i		−	0.324708i
$485$	−27.5032	+	28.1580i	−1.24886	+	1.27859i
$486$		0			0
$487$		−	16.1028i		−	0.729687i	−0.931069	−	0.364844i	$-0.881122\pi$
$487$		−	16.1028i		−	0.729687i	0.931069	−	0.364844i	$-0.118878\pi$
$488$		−	15.9904i		−	0.723853i
$489$		0			0
$490$	34.3702	−	35.1885i	1.55269	−	1.58965i
$491$		−	20.7163i		−	0.934915i	−0.884016	−	0.467457i	$-0.845170\pi$
$491$		−	20.7163i		−	0.934915i	0.884016	−	0.467457i	$-0.154830\pi$
$492$		0			0
$493$	−16.6528	+	16.6528i	−0.750005	+	0.750005i
$494$	11.1522	−	29.1622i	0.501760	−	1.31207i
$495$		0			0
$496$	−2.78722	+	2.78722i	−0.125150	+	0.125150i
$497$	31.9035	−	31.9035i	1.43107	−	1.43107i
$498$		0			0
$499$	4.09738	+	4.09738i	0.183424	+	0.183424i	0.792846	−	0.609422i	$-0.208599\pi$
$499$	4.09738	+	4.09738i	0.183424	+	0.183424i	−0.609422	+	0.792846i	$0.708599\pi$
$500$	−22.2453	+	23.8735i	−0.994840	+	1.06765i
$501$		0			0
$502$	−41.6001			−1.85670
$503$	23.4993	+	23.4993i	1.04778	+	1.04778i	0.998800	+	0.0489821i	$0.0155977\pi$
$503$	23.4993	+	23.4993i	1.04778	+	1.04778i	0.0489821	+	0.998800i	$0.484402\pi$
$504$		0			0
$505$	7.29080	−	7.46438i	0.324436	−	0.332160i
$506$			17.7072i			0.787182i
$507$		0			0
$508$	−12.6449	−	12.6449i	−0.561028	−	0.561028i
$509$	−13.7959	−	13.7959i	−0.611492	−	0.611492i	0.331843	−	0.943335i	$-0.392330\pi$
$509$	−13.7959	−	13.7959i	−0.611492	−	0.611492i	−0.943335	+	0.331843i	$0.892330\pi$
$510$		0			0
$511$			21.7157i			0.960645i
$512$			14.6057i			0.645488i
$513$		0			0
$514$	3.10665	−	3.10665i	0.137029	−	0.137029i
$515$	−6.57990	+	0.0774037i	−0.289945	+	0.00341081i
$516$		0			0
$517$	16.4681	+	16.4681i	0.724266	+	0.724266i
$518$		−	71.4795i		−	3.14063i
$519$		0			0
$520$	5.68614	−	15.4098i	0.249354	−	0.675764i
$521$	20.4402			0.895503			0.447752	−	0.894158i	$-0.352225\pi$
$521$	20.4402			0.895503			0.447752	+	0.894158i	$0.352225\pi$
$522$		0			0
$523$	1.95338	+	1.95338i	0.0854154	+	0.0854154i	0.748524	−	0.663108i	$-0.230763\pi$
$523$	1.95338	+	1.95338i	0.0854154	+	0.0854154i	−0.663108	+	0.748524i	$0.730763\pi$
$524$	−34.3364			−1.49999
$525$		0			0
$526$	35.2146	−	35.2146i	1.53543	−	1.53543i
$527$	8.37211			0.364695
$528$		0			0
$529$			18.2596i			0.793896i
$530$	−37.3072	+	0.438869i	−1.62052	+	0.0190632i
$531$		0			0
$532$	−33.1446	−	33.1446i	−1.43700	−	1.43700i
$533$	3.00974	−	7.87027i	0.130366	−	0.340899i
$534$		0			0
$535$	5.41388	−	0.0636871i	0.234063	−	0.00275343i
$536$	25.1601			1.08675
$537$		0			0
$538$	0.774608			0.0333957
$539$	25.7198	+	25.7198i	1.10783	+	1.10783i
$540$		0			0
$541$	28.9135	+	28.9135i	1.24309	+	1.24309i	0.958714	+	0.284374i	$0.0917856\pi$
$541$	28.9135	+	28.9135i	1.24309	+	1.24309i	0.284374	+	0.958714i	$0.408214\pi$
$542$	−18.8987	+	18.8987i	−0.811769	+	0.811769i
$543$		0			0
$544$	13.8649	−	13.8649i	0.594453	−	0.594453i
$545$	0.177701	+	15.1060i	0.00761189	+	0.647068i
$546$		0			0
$547$	−21.7628	+	21.7628i	−0.930509	+	0.930509i	−0.997738	−	0.0672284i	$-0.978584\pi$
$547$	−21.7628	+	21.7628i	−0.930509	+	0.930509i	0.0672284	+	0.997738i	$0.478584\pi$
$548$	36.0942			1.54187
$549$		0			0
$550$	−29.4225	−	28.0697i	−1.25458	−	1.19690i
$551$	−23.2112	+	23.2112i	−0.988830	+	0.988830i
$552$		0			0
$553$		−	34.7791i		−	1.47896i
$554$	11.7027	−	11.7027i	0.497199	−	0.497199i
$555$		0			0
$556$			44.2842i			1.87807i
$557$	−37.6115			−1.59365			−0.796825	−	0.604210i	$-0.793489\pi$
$557$	−37.6115			−1.59365			−0.796825	+	0.604210i	$0.793489\pi$
$558$		0			0
$559$	2.31657	−	6.05768i	0.0979805	−	0.256212i
$560$	8.67783	+	8.47604i	0.366705	+	0.358178i
$561$		0			0
$562$	−13.2731	+	13.2731i	−0.559890	+	0.559890i
$563$	−27.8463	+	27.8463i	−1.17358	+	1.17358i	−0.192234	+	0.981349i	$0.561573\pi$
$563$	−27.8463	+	27.8463i	−1.17358	+	1.17358i	−0.981349	+	0.192234i	$0.938427\pi$
$564$		0			0
$565$	−0.0725426	−	6.16667i	−0.00305189	−	0.259434i
$566$	−5.68142	−	5.68142i	−0.238808	−	0.238808i
$567$		0			0
$568$	−15.8020	−	15.8020i	−0.663037	−	0.663037i
$569$	−1.85521			−0.0777743			−0.0388872	−	0.999244i	$-0.512381\pi$
$569$	−1.85521			−0.0777743			−0.0388872	+	0.999244i	$0.512381\pi$
$570$		0			0
$571$		−	33.3973i		−	1.39763i	−0.715302	−	0.698816i	$-0.753711\pi$
$571$		−	33.3973i		−	1.39763i	0.715302	−	0.698816i	$-0.246289\pi$
$572$	36.0440	+	13.7839i	1.50708	+	0.576335i
$573$		0			0
$574$	−15.0747	−	15.0747i	−0.629205	−	0.629205i
$575$	7.87666	+	7.51450i	0.328480	+	0.313376i
$576$		0			0
$577$			17.7281i			0.738030i	0.929423	+	0.369015i	$0.120305\pi$
$577$			17.7281i			0.738030i	−0.929423	+	0.369015i	$0.879695\pi$
$578$	20.2992			0.844336
$579$		0			0
$580$	−38.3377	+	39.2504i	−1.59189	+	1.62979i
$581$	−18.4844			−0.766864
$582$		0			0
$583$		−	27.5891i		−	1.14262i
$584$	10.7559			0.445083
$585$		0			0
$586$	13.1191			0.541944
$587$		−	33.3826i		−	1.37785i	−0.724834	−	0.688924i	$-0.758083\pi$
$587$		−	33.3826i		−	1.37785i	0.724834	−	0.688924i	$-0.241917\pi$
$588$		0			0
$589$	11.6693			0.480825
$590$	−0.537063	−	45.6544i	−0.0221105	−	1.87956i
$591$		0			0
$592$	10.3343			0.424738
$593$		−	26.1087i		−	1.07216i	−0.844169	−	0.536078i	$-0.819905\pi$
$593$		−	26.1087i		−	1.07216i	0.844169	−	0.536078i	$-0.180095\pi$
$594$		0			0
$595$	−0.303066	−	25.7629i	−0.0124245	−	1.05618i
$596$	19.0802	+	19.0802i	0.781555	+	0.781555i
$597$		0			0
$598$	−16.2615	−	6.21872i	−0.664984	−	0.254302i
$599$		−	1.98183i		−	0.0809755i	−0.999180	−	0.0404877i	$-0.987109\pi$
$599$		−	1.98183i		−	0.0809755i	0.999180	−	0.0404877i	$-0.0128912\pi$
$600$		0			0
$601$	−7.83403			−0.319557			−0.159778	−	0.987153i	$-0.551078\pi$
$601$	−7.83403			−0.319557			−0.159778	+	0.987153i	$0.551078\pi$
$602$	−11.6029	−	11.6029i	−0.472897	−	0.472897i
$603$		0			0
$604$	−7.47650	−	7.47650i	−0.304214	−	0.304214i
$605$	3.82419	−	3.91523i	0.155475	−	0.159177i
$606$		0			0
$607$	15.2335	−	15.2335i	0.618309	−	0.618309i	−0.326788	−	0.945098i	$-0.605966\pi$
$607$	15.2335	−	15.2335i	0.618309	−	0.618309i	0.945098	+	0.326788i	$0.105966\pi$
$608$	19.3253	−	19.3253i	0.783745	−	0.783745i
$609$		0			0
$610$	27.1972	−	27.8447i	1.10118	−	1.12740i
$611$	−20.9071	+	9.34003i	−0.845811	+	0.377857i
$612$		0			0
$613$	−34.9526			−1.41172			−0.705862	−	0.708349i	$-0.749440\pi$
$613$	−34.9526			−1.41172			−0.705862	+	0.708349i	$0.749440\pi$
$614$		−	6.24821i		−	0.252157i
$615$		0			0
$616$	21.7296	−	21.7296i	0.875510	−	0.875510i
$617$			12.6145i			0.507842i	0.967225	+	0.253921i	$0.0817204\pi$
$617$			12.6145i			0.507842i	−0.967225	+	0.253921i	$0.918280\pi$
$618$		0			0
$619$	−21.5568	+	21.5568i	−0.866442	+	0.866442i	−0.992077	−	0.125635i	$-0.959903\pi$
$619$	−21.5568	+	21.5568i	−0.866442	+	0.866442i	0.125635	+	0.992077i	$0.459903\pi$
$620$	19.5035	−	0.229433i	0.783280	−	0.00921423i
$621$		0			0
$622$	20.3609			0.816396
$623$	−36.6854	+	36.6854i	−1.46977	+	1.46977i
$624$		0			0
$625$	−24.9723	+	1.17588i	−0.998893	+	0.0470351i
$626$	−36.5672	+	36.5672i	−1.46152	+	1.46152i
$627$		0			0
$628$	8.54565	−	8.54565i	0.341009	−	0.341009i
$629$	−15.5208	−	15.5208i	−0.618856	−	0.618856i
$630$		0			0
$631$	−25.2174	−	25.2174i	−1.00389	−	1.00389i	−0.999992	−	0.00389463i	$-0.998760\pi$
$631$	−25.2174	−	25.2174i	−1.00389	−	1.00389i	−0.00389463	−	0.999992i	$-0.501240\pi$
$632$	−17.2263			−0.685226
$633$		0			0
$634$	−29.6820			−1.17882
$635$	−0.161158	−	13.6996i	−0.00639534	−	0.543653i
$636$		0			0
$637$	−32.6526	+	14.5872i	−1.29374	+	0.577966i
$638$	−48.3478	−	48.3478i	−1.91411	−	1.91411i
$639$		0			0
$640$	22.7792	−	23.3215i	0.900427	−	0.921863i
$641$			15.3670i			0.606961i	0.952838	+	0.303481i	$0.0981487\pi$
$641$			15.3670i			0.606961i	−0.952838	+	0.303481i	$0.901851\pi$
$642$		0			0
$643$	5.80970			0.229112			0.114556	−	0.993417i	$-0.463455\pi$
$643$	5.80970			0.229112			0.114556	+	0.993417i	$0.463455\pi$
$644$	−18.4822	+	18.4822i	−0.728302	+	0.728302i
$645$		0			0
$646$	−24.2573			−0.954389
$647$	21.0666	+	21.0666i	0.828212	+	0.828212i	0.987269	−	0.159057i	$-0.0508454\pi$
$647$	21.0666	+	21.0666i	0.828212	+	0.828212i	−0.159057	+	0.987269i	$0.550845\pi$
$648$		0			0
$649$	33.7620			1.32528
$650$	36.1110	−	17.1623i	1.41639	−	0.673162i
$651$		0			0
$652$		−	24.7919i		−	0.970926i
$653$	9.40721	+	9.40721i	0.368132	+	0.368132i	0.866796	−	0.498663i	$-0.166176\pi$
$653$	9.40721	+	9.40721i	0.368132	+	0.368132i	−0.498663	+	0.866796i	$0.666176\pi$
$654$		0			0
$655$	−18.8190	−	18.3814i	−0.735319	−	0.718220i
$656$	2.17946	−	2.17946i	0.0850935	−	0.0850935i
$657$		0			0
$658$			57.9353i			2.25855i
$659$		−	2.27833i		−	0.0887510i	−0.999015	−	0.0443755i	$-0.985870\pi$
$659$		−	2.27833i		−	0.0887510i	0.999015	−	0.0443755i	$-0.0141298\pi$
$660$		0			0
$661$	22.0600	+	22.0600i	0.858036	+	0.858036i	0.991107	−	0.133071i	$-0.0424837\pi$
$661$	22.0600	+	22.0600i	0.858036	+	0.858036i	−0.133071	+	0.991107i	$0.542484\pi$
$662$	−30.5675	−	30.5675i	−1.18804	−	1.18804i
$663$		0			0
$664$			9.15547i			0.355301i
$665$	−0.422423	−	35.9091i	−0.0163808	−	1.39250i
$666$		0			0
$667$	12.9431	+	12.9431i	0.501160	+	0.501160i
$668$	38.6889			1.49692
$669$		0			0
$670$	43.8121	+	42.7933i	1.69261	+	1.65325i
$671$	20.3521	+	20.3521i	0.785682	+	0.785682i
$672$		0			0
$673$	−24.7463	+	24.7463i	−0.953900	+	0.953900i	−0.998983	−	0.0450834i	$-0.985645\pi$
$673$	−24.7463	+	24.7463i	−0.953900	+	0.953900i	0.0450834	+	0.998983i	$0.485645\pi$
$674$	55.0069	−	55.0069i	2.11879	−	2.11879i
$675$		0			0
$676$	−25.3171	+	28.2604i	−0.973734	+	1.08694i
$677$	11.5334	−	11.5334i	0.443265	−	0.443265i	−0.449843	−	0.893108i	$-0.648520\pi$
$677$	11.5334	−	11.5334i	0.443265	−	0.443265i	0.893108	+	0.449843i	$0.148520\pi$
$678$		0			0
$679$		−	72.4049i		−	2.77865i
$680$	−12.7605	+	0.150111i	−0.489345	+	0.00575648i
$681$		0			0
$682$			24.3066i			0.930747i
$683$		−	33.8458i		−	1.29507i	−0.762035	−	0.647536i	$-0.775800\pi$
$683$		−	33.8458i		−	1.29507i	0.762035	−	0.647536i	$-0.224200\pi$
$684$		0			0
$685$	19.7824	+	19.3223i	0.755845	+	0.738269i
$686$			26.6265i			1.01660i
$687$		0			0
$688$	1.67751	−	1.67751i	0.0639545	−	0.0639545i
$689$	25.3366	+	9.68921i	0.965248	+	0.369129i
$690$		0			0
$691$	13.6461	−	13.6461i	0.519121	−	0.519121i	−0.398185	−	0.917305i	$-0.630360\pi$
$691$	13.6461	−	13.6461i	0.519121	−	0.519121i	0.917305	+	0.398185i	$0.130360\pi$
$692$	−23.1891	+	23.1891i	−0.881518	+	0.881518i
$693$		0			0
$694$	−4.98395	−	4.98395i	−0.189188	−	0.189188i
$695$	−23.7067	+	24.2711i	−0.899246	+	0.920655i
$696$		0			0
$697$	−6.54654			−0.247968
$698$	−42.7546	−	42.7546i	−1.61829	−	1.61829i
$699$		0			0
$700$	−1.41203	−	60.0085i	−0.0533699	−	2.26811i
$701$		−	36.0430i		−	1.36133i	−0.732597	−	0.680663i	$-0.761692\pi$
$701$		−	36.0430i		−	1.36133i	0.732597	−	0.680663i	$-0.238308\pi$
$702$		0			0
$703$	−21.6334	−	21.6334i	−0.815919	−	0.815919i
$704$	33.4139	+	33.4139i	1.25933	+	1.25933i
$705$		0			0
$706$		−	45.6533i		−	1.71819i
$707$			19.1937i			0.721855i
$708$		0			0
$709$	11.7237	−	11.7237i	0.440292	−	0.440292i	−0.451818	−	0.892110i	$-0.649224\pi$
$709$	11.7237	−	11.7237i	0.440292	−	0.440292i	0.892110	+	0.451818i	$0.149224\pi$
$710$	−0.639863	−	54.3932i	−0.0240136	−	2.04134i
$711$		0			0
$712$	18.1705	+	18.1705i	0.680970	+	0.680970i
$713$		−	6.50708i		−	0.243692i
$714$		0			0
$715$	12.3759	+	26.8501i	0.462833	+	1.00414i
$716$	4.01692			0.150119
$717$		0			0
$718$	23.5152	+	23.5152i	0.877578	+	0.877578i
$719$	−15.7258			−0.586474			−0.293237	−	0.956040i	$-0.594733\pi$
$719$	−15.7258			−0.586474			−0.293237	+	0.956040i	$0.594733\pi$
$720$		0			0
$721$	8.55922	−	8.55922i	0.318762	−	0.318762i
$722$	8.32765			0.309923
$723$		0			0
$724$			68.4963i			2.54565i
$725$	−42.0240	+	0.988848i	−1.56073	+	0.0367249i
$726$		0			0
$727$	29.7923	+	29.7923i	1.10494	+	1.10494i	0.993806	+	0.111131i	$0.0354474\pi$
$727$	29.7923	+	29.7923i	1.10494	+	1.10494i	0.111131	+	0.993806i	$0.464553\pi$
$728$	12.3241	+	27.5868i	0.456763	+	1.02244i
$729$		0			0
$730$	18.7296	+	18.2941i	0.693214	+	0.677095i
$731$	−5.03881			−0.186367
$732$		0			0
$733$	21.4923			0.793836			0.396918	−	0.917854i	$-0.370080\pi$
$733$	21.4923			0.793836			0.396918	+	0.917854i	$0.370080\pi$
$734$	−2.27399	−	2.27399i	−0.0839344	−	0.0839344i
$735$		0			0
$736$	−10.7763	−	10.7763i	−0.397219	−	0.397219i
$737$	−32.0229	+	32.0229i	−1.17958	+	1.17958i
$738$		0			0
$739$	0.314385	−	0.314385i	0.0115649	−	0.0115649i	−0.701301	−	0.712866i	$-0.747397\pi$
$739$	0.314385	−	0.314385i	0.0115649	−	0.0115649i	0.712866	+	0.701301i	$0.247397\pi$
$740$	−36.5824	−	35.7317i	−1.34479	−	1.31352i
$741$		0			0
$742$	48.5297	−	48.5297i	1.78158	−	1.78158i
$743$	22.1368			0.812122			0.406061	−	0.913846i	$-0.366902\pi$
$743$	22.1368			0.812122			0.406061	+	0.913846i	$0.366902\pi$
$744$		0			0
$745$	0.243174	+	20.6716i	0.00890920	+	0.757350i
$746$	−18.6642	+	18.6642i	−0.683347	+	0.683347i
$747$		0			0
$748$		−	29.9816i		−	1.09624i
$749$	−7.04245	+	7.04245i	−0.257326	+	0.257326i
$750$		0			0
$751$		−	0.516848i		−	0.0188600i	−0.999956	−	0.00943002i	$-0.996998\pi$
$751$		−	0.516848i		−	0.0188600i	0.999956	−	0.00943002i	$-0.00300171\pi$
$752$	−8.37613			−0.305446
$753$		0			0
$754$	61.3800	−	27.4209i	2.23533	−	0.998609i
$755$	−0.0952867	−	8.10010i	−0.00346784	−	0.294793i
$756$		0			0
$757$	−24.0375	+	24.0375i	−0.873657	+	0.873657i	−0.992869	−	0.119212i	$-0.961963\pi$
$757$	−24.0375	+	24.0375i	−0.873657	+	0.873657i	0.119212	+	0.992869i	$0.461963\pi$
$758$	−11.1679	+	11.1679i	−0.405635	+	0.405635i
$759$		0			0
$760$	−17.7860	+	0.209229i	−0.645167	+	0.00758952i
$761$	36.2711	+	36.2711i	1.31483	+	1.31483i	0.917812	+	0.397015i	$0.129954\pi$
$761$	36.2711	+	36.2711i	1.31483	+	1.31483i	0.397015	+	0.917812i	$0.370046\pi$
$762$		0			0
$763$	−19.6500	−	19.6500i	−0.711379	−	0.711379i
$764$	−8.53636			−0.308835
$765$		0			0
$766$			1.07243i			0.0387486i
$767$	−11.8571	+	31.0055i	−0.428136	+	1.11955i
$768$		0			0
$769$	−5.51342	−	5.51342i	−0.198819	−	0.198819i	0.600675	−	0.799494i	$-0.294899\pi$
$769$	−5.51342	−	5.51342i	−0.198819	−	0.198819i	−0.799494	+	0.600675i	$0.794899\pi$
$770$	74.7970	−	0.879886i	2.69550	−	0.0317089i
$771$		0			0
$772$			60.4088i			2.17416i
$773$	37.1946			1.33780			0.668899	−	0.743353i	$-0.266766\pi$
$773$	37.1946			1.33780			0.668899	+	0.743353i	$0.266766\pi$
$774$		0			0
$775$	10.8122	+	10.3151i	0.388387	+	0.370529i
$776$	−35.8627			−1.28739
$777$		0			0
$778$			39.0208i			1.39896i
$779$	−9.12476			−0.326928
$780$		0			0
$781$	40.2244			1.43934
$782$			13.5264i			0.483705i
$783$		0			0
$784$	−13.0818			−0.467207
$785$	9.25843	−	0.108913i	0.330447	−	0.00388727i
$786$		0			0
$787$	−16.6120			−0.592154			−0.296077	−	0.955164i	$-0.595679\pi$
$787$	−16.6120			−0.592154			−0.296077	+	0.955164i	$0.595679\pi$
$788$			17.9846i			0.640674i
$789$		0			0
$790$	−29.9967	−	29.2992i	−1.06724	−	1.04242i
$791$	8.02169	+	8.02169i	0.285219	+	0.285219i
$792$		0			0
$793$	−25.8380	+	11.5428i	−0.917534	+	0.409899i
$794$		−	21.3753i		−	0.758582i
$795$		0			0
$796$	−67.9677			−2.40905
$797$	23.0821	+	23.0821i	0.817611	+	0.817611i	0.985761	−	0.168150i	$-0.0537793\pi$
$797$	23.0821	+	23.0821i	0.817611	+	0.817611i	−0.168150	+	0.985761i	$0.553779\pi$
$798$		0			0
$799$	12.5799	+	12.5799i	0.445044	+	0.445044i
$800$	34.9886	−	0.823302i	1.23703	−	0.0291081i
$801$		0			0
$802$	−37.4328	+	37.4328i	−1.32180	+	1.32180i
$803$	−13.6897	+	13.6897i	−0.483101	+	0.483101i
$804$		0			0
$805$	−20.0238	+	0.235553i	−0.705746	+	0.00830216i
$806$	−22.3221	−	8.53639i	−0.786262	−	0.300681i
$807$		0			0
$808$	9.50678			0.334448
$809$		−	10.9372i		−	0.384533i	−0.981343	−	0.192267i	$-0.938416\pi$
$809$		−	10.9372i		−	0.384533i	0.981343	−	0.192267i	$-0.0615838\pi$
$810$		0			0
$811$	17.0726	−	17.0726i	0.599501	−	0.599501i	−0.340679	−	0.940180i	$-0.610657\pi$
$811$	17.0726	−	17.0726i	0.599501	−	0.599501i	0.940180	+	0.340679i	$0.110657\pi$
$812$		−	100.928i		−	3.54187i
$813$		0			0
$814$	45.0613	−	45.0613i	1.57940	−	1.57940i
$815$	13.2719	−	13.5879i	0.464894	−	0.475962i
$816$		0			0
$817$	−7.02325			−0.245712
$818$	−8.10707	+	8.10707i	−0.283457	+	0.283457i
$819$		0			0
$820$	−15.2507	+	0.179404i	−0.532577	+	0.00626506i
$821$	7.58466	−	7.58466i	0.264706	−	0.264706i	−0.562256	−	0.826963i	$-0.690067\pi$
$821$	7.58466	−	7.58466i	0.264706	−	0.264706i	0.826963	+	0.562256i	$0.190067\pi$
$822$		0			0
$823$	−20.2348	+	20.2348i	−0.705341	+	0.705341i	−0.965552	−	0.260211i	$-0.916208\pi$
$823$	−20.2348	+	20.2348i	−0.705341	+	0.705341i	0.260211	+	0.965552i	$0.416208\pi$
$824$	−4.23944	−	4.23944i	−0.147688	−	0.147688i
$825$		0			0
$826$	59.3879	+	59.3879i	2.06637	+	2.06637i
$827$	0.322011			0.0111974			0.00559871	−	0.999984i	$-0.498218\pi$
$827$	0.322011			0.0111974			0.00559871	+	0.999984i	$0.498218\pi$
$828$		0			0
$829$	−2.29166			−0.0795925			−0.0397963	−	0.999208i	$-0.512671\pi$
$829$	−2.29166			−0.0795925			−0.0397963	+	0.999208i	$0.512671\pi$
$830$	−15.5720	+	15.9427i	−0.540511	+	0.553380i
$831$		0			0
$832$	−42.4207	+	18.9510i	−1.47067	+	0.657007i
$833$	19.6472	+	19.6472i	0.680735	+	0.680735i
$834$		0			0
$835$	21.2045	+	20.7114i	0.733812	+	0.716748i
$836$		−	41.7893i		−	1.44531i
$837$		0			0
$838$	−75.2766			−2.60039
$839$	0.488256	−	0.488256i	0.0168565	−	0.0168565i	−0.698628	−	0.715485i	$-0.746206\pi$
$839$	0.488256	−	0.488256i	0.0168565	−	0.0168565i	0.715485	+	0.698628i	$0.246206\pi$
$840$		0			0
$841$	−41.6797			−1.43723
$842$	−43.7067	−	43.7067i	−1.50623	−	1.50623i
$843$		0			0
$844$	−34.0855			−1.17327
$845$	−29.0044	+	1.93580i	−0.997780	+	0.0665937i
$846$		0			0
$847$			10.0675i			0.345925i
$848$	7.01629	+	7.01629i	0.240940	+	0.240940i
$849$		0			0
$850$	−22.4757	−	21.4423i	−0.770909	−	0.735463i
$851$	−12.0633	+	12.0633i	−0.413525	+	0.413525i
$852$		0			0
$853$		−	2.53904i		−	0.0869352i	−0.999055	−	0.0434676i	$-0.986159\pi$
$853$		−	2.53904i		−	0.0869352i	0.999055	−	0.0434676i	$-0.0138405\pi$
$854$			71.5992i			2.45007i
$855$		0			0
$856$	3.48817	+	3.48817i	0.119223	+	0.119223i
$857$	−3.15552	−	3.15552i	−0.107791	−	0.107791i	0.651155	−	0.758945i	$-0.274285\pi$
$857$	−3.15552	−	3.15552i	−0.107791	−	0.107791i	−0.758945	+	0.651155i	$0.774285\pi$
$858$		0			0
$859$			36.8208i			1.25631i	0.778088	+	0.628155i	$0.216190\pi$
$859$			36.8208i			1.25631i	−0.778088	+	0.628155i	$0.783810\pi$
$860$	−11.7383	+	0.138086i	−0.400274	+	0.00470868i
$861$		0			0
$862$	−23.8780	−	23.8780i	−0.813288	−	0.813288i
$863$	11.3029			0.384754			0.192377	−	0.981321i	$-0.438380\pi$
$863$	11.3029			0.384754			0.192377	+	0.981321i	$0.438380\pi$
$864$		0			0
$865$	−25.1233	+	0.295542i	−0.854217	+	0.0100487i
$866$	26.2864	+	26.2864i	0.893248	+	0.893248i
$867$		0			0
$868$	−25.3704	+	25.3704i	−0.861129	+	0.861129i
$869$	21.9250	−	21.9250i	0.743756	−	0.743756i
$870$		0			0
$871$	−18.1620	−	40.6547i	−0.615397	−	1.37753i
$872$	−9.73279	+	9.73279i	−0.329594	+	0.329594i
$873$		0			0
$874$			18.8536i			0.637731i
$875$	31.3505	−	33.6451i	1.05984	−	1.13741i
$876$		0			0
$877$		−	11.1316i		−	0.375889i	−0.982180	−	0.187944i	$-0.939818\pi$
$877$		−	11.1316i		−	0.375889i	0.982180	−	0.187944i	$-0.0601824\pi$
$878$			4.48487i			0.151357i
$879$		0			0
$880$	0.127212	+	10.8139i	0.00428830	+	0.364538i
$881$		−	25.7462i		−	0.867410i	−0.901055	−	0.433705i	$-0.857206\pi$
$881$		−	25.7462i		−	0.867410i	0.901055	−	0.433705i	$-0.142794\pi$
$882$		0			0
$883$	−3.65379	+	3.65379i	−0.122960	+	0.122960i	−0.765909	−	0.642949i	$-0.777711\pi$
$883$	−3.65379	+	3.65379i	−0.122960	+	0.122960i	0.642949	+	0.765909i	$0.277711\pi$
$884$	27.5338	+	10.5295i	0.926062	+	0.354144i
$885$		0			0
$886$	0.282539	−	0.282539i	0.00949208	−	0.00949208i
$887$	9.40170	−	9.40170i	0.315678	−	0.315678i	−0.531426	−	0.847105i	$-0.678344\pi$
$887$	9.40170	−	9.40170i	0.315678	−	0.315678i	0.847105	+	0.531426i	$0.178344\pi$
$888$		0			0
$889$	17.8206	+	17.8206i	0.597685	+	0.597685i
$890$	0.735771	+	62.5461i	0.0246631	+	2.09655i
$891$		0			0
$892$	49.0194			1.64129
$893$	17.5342	+	17.5342i	0.586760	+	0.586760i
$894$		0			0
$895$	2.20158	+	2.15038i	0.0735907	+	0.0718794i
$896$			59.9684i			2.00340i
$897$		0			0
$898$	−55.1434	−	55.1434i	−1.84016	−	1.84016i
$899$	17.7669	+	17.7669i	0.592560	+	0.592560i
$900$		0			0
$901$		−	21.0752i		−	0.702115i
$902$		−	19.0064i		−	0.632845i
$903$		0			0
$904$	3.97320	−	3.97320i	0.132147	−	0.132147i
$905$	−36.6682	+	37.5412i	−1.21889	+	1.24791i
$906$		0			0
$907$	0.772139	+	0.772139i	0.0256384	+	0.0256384i	0.719810	−	0.694171i	$-0.244229\pi$
$907$	0.772139	+	0.772139i	0.0256384	+	0.0256384i	−0.694171	+	0.719810i	$0.744229\pi$
$908$			64.8825i			2.15320i
$909$		0			0
$910$	−25.4604	+	68.9992i	−0.844004	+	2.28730i
$911$	6.21262			0.205833			0.102917	−	0.994690i	$-0.467182\pi$
$911$	6.21262			0.205833			0.102917	+	0.994690i	$0.467182\pi$
$912$		0			0
$913$	−11.6528	−	11.6528i	−0.385650	−	0.385650i
$914$	71.6388			2.36960
$915$		0			0
$916$	−5.83555	+	5.83555i	−0.192812	+	0.192812i
$917$	48.3907			1.59800
$918$		0			0
$919$			29.9003i			0.986320i	0.869939	+	0.493160i	$0.164158\pi$
$919$			29.9003i			0.986320i	−0.869939	+	0.493160i	$0.835842\pi$
$920$	0.116671	+	9.91792i	0.00384653	+	0.326984i
$921$		0			0
$922$	32.2980	+	32.2980i	1.06368	+	1.06368i
$923$	−14.1267	+	36.9403i	−0.464986	+	1.21591i
$924$		0			0
$925$	−0.921631	−	39.1674i	−0.0303030	−	1.28782i
$926$	−29.4345			−0.967278
$927$		0			0
$928$	58.8470			1.93175
$929$	16.4364	+	16.4364i	0.539260	+	0.539260i	0.923312	−	0.384052i	$-0.125472\pi$
$929$	16.4364	+	16.4364i	0.539260	+	0.539260i	−0.384052	+	0.923312i	$0.625472\pi$
$930$		0			0
$931$	27.3848	+	27.3848i	0.897501	+	0.897501i
$932$	−22.1933	+	22.1933i	−0.726964	+	0.726964i
$933$		0			0
$934$	−47.9281	+	47.9281i	−1.56826	+	1.56826i
$935$	16.0501	−	16.4322i	0.524895	−	0.537391i
$936$		0			0
$937$	15.7357	−	15.7357i	0.514064	−	0.514064i	−0.401705	−	0.915769i	$-0.631582\pi$
$937$	15.7357	−	15.7357i	0.514064	−	0.514064i	0.915769	+	0.401705i	$0.131582\pi$
$938$	−112.657			−3.67839
$939$		0			0
$940$	29.6506	+	28.9611i	0.967096	+	0.944607i
$941$	6.42421	−	6.42421i	0.209423	−	0.209423i	−0.594599	−	0.804022i	$-0.702689\pi$
$941$	6.42421	−	6.42421i	0.209423	−	0.209423i	0.804022	+	0.594599i	$0.202689\pi$
$942$		0			0
$943$			5.08819i			0.165694i
$944$	−8.58615	+	8.58615i	−0.279455	+	0.279455i
$945$		0			0
$946$		−	14.6291i		−	0.475633i
$947$	12.4887			0.405827			0.202914	−	0.979197i	$-0.434959\pi$
$947$	12.4887			0.405827			0.202914	+	0.979197i	$0.434959\pi$
$948$		0			0
$949$	−7.76426	−	17.3799i	−0.252039	−	0.564174i
$950$	−31.3272	−	29.8868i	−1.01639	−	0.969657i
$951$		0			0
$952$	16.5991	−	16.5991i	0.537980	−	0.537980i
$953$	−30.2555	+	30.2555i	−0.980072	+	0.980072i	−0.999805	−	0.0197332i	$-0.993718\pi$
$953$	−30.2555	+	30.2555i	−0.980072	+	0.980072i	0.0197332	+	0.999805i	$0.493718\pi$
$954$		0			0
$955$	−4.67858	−	4.56978i	−0.151395	−	0.147875i
$956$	50.2481	+	50.2481i	1.62514	+	1.62514i
$957$		0			0
$958$	30.1602	+	30.1602i	0.974431	+	0.974431i
$959$	−50.8679			−1.64261
$960$		0			0
$961$			22.0678i			0.711864i
$962$	25.5569	+	57.2077i	0.823988	+	1.84445i
$963$		0			0
$964$	−29.8153	−	29.8153i	−0.960286	−	0.960286i
$965$	−32.3387	+	33.1086i	−1.04102	+	1.06580i
$966$		0			0
$967$		−	35.6086i		−	1.14510i	−0.819871	−	0.572548i	$-0.805955\pi$
$967$		−	35.6086i		−	1.14510i	0.819871	−	0.572548i	$-0.194045\pi$
$968$	4.98652			0.160273
$969$		0			0
$970$	−62.4488	−	60.9966i	−2.00511	−	1.95848i
$971$	28.4165			0.911929			0.455964	−	0.889998i	$-0.349294\pi$
$971$	28.4165			0.911929			0.455964	+	0.889998i	$0.349294\pi$
$972$		0			0
$973$		−	62.4102i		−	2.00078i
$974$	35.7127			1.14431
$975$		0			0
$976$	−10.3516			−0.331347
$977$		−	42.8927i		−	1.37226i	−0.727479	−	0.686130i	$-0.759308\pi$
$977$		−	42.8927i		−	1.37226i	0.727479	−	0.686130i	$-0.240692\pi$
$978$		0			0
$979$	−46.2536			−1.47827
$980$	46.3081	+	45.2313i	1.47926	+	1.44486i
$981$		0			0
$982$	45.9446			1.46615
$983$		−	39.1642i		−	1.24914i	−0.780967	−	0.624572i	$-0.785273\pi$
$983$		−	39.1642i		−	1.24914i	0.780967	−	0.624572i	$-0.214727\pi$
$984$		0			0
$985$	−9.62772	+	9.85693i	−0.306765	+	0.314068i
$986$	−36.9326	−	36.9326i	−1.17617	−	1.17617i
$987$		0			0
$988$	38.3774	+	14.6763i	1.22095	+	0.466914i
$989$			3.91633i			0.124532i
$990$		0			0
$991$	7.60282			0.241512			0.120756	−	0.992682i	$-0.461468\pi$
$991$	7.60282			0.241512			0.120756	+	0.992682i	$0.461468\pi$
$992$	−14.7925	−	14.7925i	−0.469662	−	0.469662i
$993$		0			0
$994$	70.7554	+	70.7554i	2.24422	+	2.24422i
$995$	−37.2515	−	36.3853i	−1.18095	−	1.15349i
$996$		0			0
$997$	−1.06259	+	1.06259i	−0.0336527	+	0.0336527i	−0.723733	−	0.690080i	$-0.757575\pi$
$997$	−1.06259	+	1.06259i	−0.0336527	+	0.0336527i	0.690080	+	0.723733i	$0.257575\pi$
$998$	−9.08715	+	9.08715i	−0.287649	+	0.287649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.n.g.343.13		28
3.2	odd	2		195.2.k.a.148.2	yes	28
5.2	odd	4		585.2.w.g.577.2		28
13.8	odd	4		585.2.w.g.73.2		28
15.2	even	4		195.2.t.a.187.13	yes	28
15.8	even	4		975.2.t.d.382.2		28
15.14	odd	2		975.2.k.d.343.13		28
39.8	even	4		195.2.t.a.73.13	yes	28
65.47	even	4	inner	585.2.n.g.307.2		28
195.8	odd	4		975.2.k.d.307.2		28
195.47	odd	4		195.2.k.a.112.13	✓	28
195.164	even	4		975.2.t.d.268.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.13	✓	28	195.47	odd	4
195.2.k.a.148.2	yes	28	3.2	odd	2
195.2.t.a.73.13	yes	28	39.8	even	4
195.2.t.a.187.13	yes	28	15.2	even	4
585.2.n.g.307.2		28	65.47	even	4	inner
585.2.n.g.343.13		28	1.1	even	1	trivial
585.2.w.g.73.2		28	13.8	odd	4
585.2.w.g.577.2		28	5.2	odd	4
975.2.k.d.307.2		28	195.8	odd	4
975.2.k.d.343.13		28	15.14	odd	2
975.2.t.d.268.2		28	195.164	even	4
975.2.t.d.382.2		28	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.21780i q^{2} -2.91862 q^{4} +(-1.59963 - 1.56243i) q^{5} +4.11325 q^{7} -2.03732i q^{8} +O(q^{10})\)	\(q+2.21780i q^{2} -2.91862 q^{4} +(-1.59963 - 1.56243i) q^{5} +4.11325 q^{7} -2.03732i q^{8} +(3.46515 - 3.54765i) q^{10} +(2.59303 + 2.59303i) q^{11} +(-3.29198 + 1.47066i) q^{13} +9.12235i q^{14} -1.31889 q^{16} +(1.98080 + 1.98080i) q^{17} +(2.76089 + 2.76089i) q^{19} +(4.66871 + 4.56015i) q^{20} +(-5.75081 + 5.75081i) q^{22} +(1.53954 - 1.53954i) q^{23} +(0.117620 + 4.99862i) q^{25} +(-3.26162 - 7.30095i) q^{26} -12.0050 q^{28} +8.40712i q^{29} +(2.11332 - 2.11332i) q^{31} -6.99966i q^{32} +(-4.39301 + 4.39301i) q^{34} +(-6.57967 - 6.42667i) q^{35} -7.83564 q^{37} +(-6.12310 + 6.12310i) q^{38} +(-3.18317 + 3.25895i) q^{40} +(-1.65250 + 1.65250i) q^{41} +(-1.27192 + 1.27192i) q^{43} +(-7.56807 - 7.56807i) q^{44} +(3.41439 + 3.41439i) q^{46} +6.35092 q^{47} +9.91882 q^{49} +(-11.0859 + 0.260858i) q^{50} +(9.60806 - 4.29230i) q^{52} +(-5.31987 - 5.31987i) q^{53} +(-0.0964538 - 8.19931i) q^{55} -8.38000i q^{56} -18.6453 q^{58} +(6.51015 - 6.51015i) q^{59} +7.84876 q^{61} +(4.68691 + 4.68691i) q^{62} +12.8861 q^{64} +(7.56375 + 2.79099i) q^{65} +12.3496i q^{67} +(-5.78120 - 5.78120i) q^{68} +(14.2530 - 14.5924i) q^{70} +(7.75627 - 7.75627i) q^{71} +5.27944i q^{73} -17.3779i q^{74} +(-8.05801 - 8.05801i) q^{76} +(10.6658 + 10.6658i) q^{77} -8.45538i q^{79} +(2.10973 + 2.06067i) q^{80} +(-3.66491 - 3.66491i) q^{82} -4.49388 q^{83} +(-0.0736805 - 6.26340i) q^{85} +(-2.82085 - 2.82085i) q^{86} +(5.28283 - 5.28283i) q^{88} +(-8.91884 + 8.91884i) q^{89} +(-13.5408 + 6.04919i) q^{91} +(-4.49334 + 4.49334i) q^{92} +14.0850i q^{94} +(-0.102698 - 8.73011i) q^{95} -17.6029i q^{97} +21.9979i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} - 8 q^{5}+O(q^{10}) \) 28 * q - 28 * q^4 - 8 * q^5	\( 28 q - 28 q^{4} - 8 q^{5} + 8 q^{11} - 12 q^{13} + 28 q^{16} + 28 q^{17} - 32 q^{22} - 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} - 48 q^{40} - 4 q^{41} - 40 q^{44} - 16 q^{46} + 24 q^{47} - 28 q^{49} + 32 q^{50} + 52 q^{52} - 20 q^{53} - 8 q^{55} - 8 q^{58} - 32 q^{59} + 8 q^{61} - 72 q^{62} - 28 q^{64} + 8 q^{65} - 60 q^{68} + 64 q^{70} - 40 q^{71} - 40 q^{76} + 48 q^{77} + 32 q^{80} + 4 q^{82} + 104 q^{83} - 4 q^{85} - 16 q^{86} + 72 q^{88} + 36 q^{89} - 56 q^{91} + 32 q^{92} - 56 q^{95}+O(q^{100}) \) 28 * q - 28 * q^4 - 8 * q^5 + 8 * q^11 - 12 * q^13 + 28 * q^16 + 28 * q^17 - 32 * q^22 - 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 - 48 * q^40 - 4 * q^41 - 40 * q^44 - 16 * q^46 + 24 * q^47 - 28 * q^49 + 32 * q^50 + 52 * q^52 - 20 * q^53 - 8 * q^55 - 8 * q^58 - 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 8 * q^65 - 60 * q^68 + 64 * q^70 - 40 * q^71 - 40 * q^76 + 48 * q^77 + 32 * q^80 + 4 * q^82 + 104 * q^83 - 4 * q^85 - 16 * q^86 + 72 * q^88 + 36 * q^89 - 56 * q^91 + 32 * q^92 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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