LMFDB - Embedded newform 585.2.bs.b.334.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.1
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.01317 - 1.16230i) q^{2} +(1.70191 + 2.94779i) q^{4} +(0.174568 - 2.22924i) q^{5} +(0.473110 - 0.273150i) q^{7} -3.26331i q^{8} +O(q^{10})$	\(q+(-2.01317 - 1.16230i) q^{2} +(1.70191 + 2.94779i) q^{4} +(0.174568 - 2.22924i) q^{5} +(0.473110 - 0.273150i) q^{7} -3.26331i q^{8} +(-2.94250 + 4.28495i) q^{10} +(-1.98674 + 3.44114i) q^{11} +(-3.05988 + 1.90712i) q^{13} -1.26993 q^{14} +(-0.389155 + 0.674036i) q^{16} +(-0.724112 + 0.418066i) q^{17} +(-2.56141 - 4.43649i) q^{19} +(6.86843 - 3.27937i) q^{20} +(7.99930 - 4.61840i) q^{22} +(-2.12324 - 1.22585i) q^{23} +(-4.93905 - 0.778310i) q^{25} +(8.37673 - 0.282845i) q^{26} +(1.61038 + 0.929751i) q^{28} +(-2.89828 + 5.01997i) q^{29} +2.43711 q^{31} +(-4.08536 + 2.35868i) q^{32} +1.94368 q^{34} +(-0.526328 - 1.10236i) q^{35} +(-5.13992 - 2.96753i) q^{37} +11.9086i q^{38} +(-7.27472 - 0.569671i) q^{40} +(3.45841 - 5.99014i) q^{41} +(-10.2200 + 5.90050i) q^{43} -13.5250 q^{44} +(2.84963 + 4.93571i) q^{46} -0.222038i q^{47} +(-3.35078 + 5.80372i) q^{49} +(9.03852 + 7.30756i) q^{50} +(-10.8294 - 5.77414i) q^{52} +11.6660i q^{53} +(7.32431 + 5.02964i) q^{55} +(-0.891375 - 1.54391i) q^{56} +(11.6695 - 6.73737i) q^{58} +(-3.31514 - 5.74200i) q^{59} +(5.38277 + 9.32323i) q^{61} +(-4.90631 - 2.83266i) q^{62} +12.5226 q^{64} +(3.71728 + 7.15415i) q^{65} +(12.1831 + 7.03390i) q^{67} +(-2.46474 - 1.42302i) q^{68} +(-0.221690 + 2.83099i) q^{70} +(-3.18868 - 5.52296i) q^{71} +1.41487i q^{73} +(6.89836 + 11.9483i) q^{74} +(8.71855 - 15.1010i) q^{76} +2.17071i q^{77} -8.13239 q^{79} +(1.43466 + 0.985186i) q^{80} +(-13.9247 + 8.03945i) q^{82} +1.14843i q^{83} +(0.805564 + 1.68720i) q^{85} +27.4327 q^{86} +(11.2295 + 6.48336i) q^{88} +(3.83234 - 6.63781i) q^{89} +(-0.926730 + 1.73809i) q^{91} -8.34515i q^{92} +(-0.258076 + 0.447000i) q^{94} +(-10.3372 + 4.93553i) q^{95} +(-12.8791 + 7.43574i) q^{97} +(13.4914 - 7.78925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) $ 24 * q + 8 * q^4 - 4 * q^5	$ 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) $ 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.01317	−	1.16230i	−1.42353	−	0.821874i	−0.426929	−	0.904285i	$-0.640404\pi$
$2$	−2.01317	−	1.16230i	−1.42353	−	0.821874i	−0.996598	+	0.0824116i	$0.973738\pi$
$3$		0			0
$3$		0			0
$4$	1.70191	+	2.94779i	0.850953	+	1.47389i
$5$	0.174568	−	2.22924i	0.0780693	−	0.996948i
$5$	0.174568	−	2.22924i	0.0780693	−	0.996948i
$6$		0			0
$7$	0.473110	−	0.273150i	0.178819	−	0.103241i	−0.407919	−	0.913018i	$-0.633745\pi$
$7$	0.473110	−	0.273150i	0.178819	−	0.103241i	0.586738	+	0.809777i	$0.300412\pi$
$8$		−	3.26331i		−	1.15376i
$9$		0			0
$10$	−2.94250	+	4.28495i	−0.930499	+	1.35502i
$11$	−1.98674	+	3.44114i	−0.599025	+	1.03754i	0.393940	+	0.919136i	$0.371112\pi$
$11$	−1.98674	+	3.44114i	−0.599025	+	1.03754i	−0.992965	+	0.118406i	$0.962222\pi$
$12$		0			0
$13$	−3.05988	+	1.90712i	−0.848659	+	0.528940i
$13$	−3.05988	+	1.90712i	−0.848659	+	0.528940i
$14$	−1.26993			−0.339404
$15$		0			0
$16$	−0.389155	+	0.674036i	−0.0972887	+	0.168509i
$17$	−0.724112	+	0.418066i	−0.175623	+	0.101396i	−0.585235	−	0.810864i	$-0.698998\pi$
$17$	−0.724112	+	0.418066i	−0.175623	+	0.101396i	0.409612	+	0.912260i	$0.365664\pi$
$18$		0			0
$19$	−2.56141	−	4.43649i	−0.587627	−	1.01780i	−0.994542	−	0.104334i	$-0.966729\pi$
$19$	−2.56141	−	4.43649i	−0.587627	−	1.01780i	0.406915	−	0.913466i	$-0.366605\pi$
$20$	6.86843	−	3.27937i	1.53583	−	0.733290i
$21$		0			0
$22$	7.99930	−	4.61840i	1.70546	−	0.984646i
$23$	−2.12324	−	1.22585i	−0.442727	−	0.255608i	0.262027	−	0.965061i	$-0.415609\pi$
$23$	−2.12324	−	1.22585i	−0.442727	−	0.255608i	−0.704753	+	0.709452i	$0.748942\pi$
$24$		0			0
$25$	−4.93905	−	0.778310i	−0.987810	−	0.155662i
$26$	8.37673	−	0.282845i	1.64281	−	0.0554705i
$27$		0			0
$28$	1.61038	+	0.929751i	0.304333	+	0.175706i
$29$	−2.89828	+	5.01997i	−0.538197	+	0.932185i	0.460804	+	0.887502i	$0.347561\pi$
$29$	−2.89828	+	5.01997i	−0.538197	+	0.932185i	−0.999001	+	0.0446832i	$0.985772\pi$
$30$		0			0
$31$	2.43711			0.437717			0.218859	−	0.975757i	$-0.429767\pi$
$31$	2.43711			0.437717			0.218859	+	0.975757i	$0.429767\pi$
$32$	−4.08536	+	2.35868i	−0.722196	+	0.416960i
$33$		0			0
$34$	1.94368			0.333339
$35$	−0.526328	−	1.10236i	−0.0889657	−	0.186333i
$36$		0			0
$37$	−5.13992	−	2.96753i	−0.844998	−	0.487860i	0.0139622	−	0.999903i	$-0.495556\pi$
$37$	−5.13992	−	2.96753i	−0.844998	−	0.487860i	−0.858960	+	0.512043i	$0.828889\pi$
$38$			11.9086i			1.93182i
$39$		0			0
$40$	−7.27472	−	0.569671i	−1.15023	−	0.0900729i
$41$	3.45841	−	5.99014i	0.540113	−	0.935502i	−0.458784	−	0.888548i	$-0.651715\pi$
$41$	3.45841	−	5.99014i	0.540113	−	0.935502i	0.998897	−	0.0469548i	$-0.0149517\pi$
$42$		0			0
$43$	−10.2200	+	5.90050i	−1.55853	+	0.899818i	−0.561133	+	0.827726i	$0.689634\pi$
$43$	−10.2200	+	5.90050i	−1.55853	+	0.899818i	−0.997398	+	0.0720920i	$0.977032\pi$
$44$	−13.5250			−2.03897
$45$		0			0
$46$	2.84963	+	4.93571i	0.420155	+	0.727731i
$47$		−	0.222038i		−	0.0323875i	−0.999869	−	0.0161938i	$-0.994845\pi$
$47$		−	0.222038i		−	0.0323875i	0.999869	−	0.0161938i	$-0.00515486\pi$
$48$		0			0
$49$	−3.35078	+	5.80372i	−0.478683	+	0.829103i
$50$	9.03852	+	7.30756i	1.27824	+	1.03344i
$51$		0			0
$52$	−10.8294	−	5.77414i	−1.50177	−	0.800730i
$53$			11.6660i			1.60244i	0.598367	+	0.801222i	$0.295816\pi$
$53$			11.6660i			1.60244i	−0.598367	+	0.801222i	$0.704184\pi$
$54$		0			0
$55$	7.32431	+	5.02964i	0.987610	+	0.678197i
$56$	−0.891375	−	1.54391i	−0.119115	−	0.206313i
$57$		0			0
$58$	11.6695	−	6.73737i	1.53228	−	0.884661i
$59$	−3.31514	−	5.74200i	−0.431595	−	0.747545i	0.565416	−	0.824806i	$-0.308716\pi$
$59$	−3.31514	−	5.74200i	−0.431595	−	0.747545i	−0.997011	+	0.0772615i	$0.975382\pi$
$60$		0			0
$61$	5.38277	+	9.32323i	0.689193	+	1.19372i	0.972099	+	0.234570i	$0.0753681\pi$
$61$	5.38277	+	9.32323i	0.689193	+	1.19372i	−0.282906	+	0.959148i	$0.591299\pi$
$62$	−4.90631	−	2.83266i	−0.623103	−	0.359748i
$63$		0			0
$64$	12.5226			1.56533
$65$	3.71728	+	7.15415i	0.461072	+	0.887363i
$66$		0			0
$67$	12.1831	+	7.03390i	1.48840	+	0.859327i	0.999912	−	0.0132448i	$-0.00421606\pi$
$67$	12.1831	+	7.03390i	1.48840	+	0.859327i	0.488486	+	0.872572i	$0.337549\pi$
$68$	−2.46474	−	1.42302i	−0.298894	−	0.172566i
$69$		0			0
$70$	−0.221690	+	2.83099i	−0.0264970	+	0.338368i
$71$	−3.18868	−	5.52296i	−0.378427	−	0.655454i	0.612407	−	0.790543i	$-0.290201\pi$
$71$	−3.18868	−	5.52296i	−0.378427	−	0.655454i	−0.990834	+	0.135088i	$0.956868\pi$
$72$		0			0
$73$			1.41487i			0.165598i	0.996566	+	0.0827991i	$0.0263860\pi$
$73$			1.41487i			0.165598i	−0.996566	+	0.0827991i	$0.973614\pi$
$74$	6.89836	+	11.9483i	0.801918	+	1.38896i
$75$		0			0
$76$	8.71855	−	15.1010i	1.00009	−	1.73220i
$77$			2.17071i			0.247376i
$78$		0			0
$79$	−8.13239			−0.914965			−0.457483	−	0.889219i	$-0.651249\pi$
$79$	−8.13239			−0.914965			−0.457483	+	0.889219i	$0.651249\pi$
$80$	1.43466	+	0.985186i	0.160399	+	0.110147i
$81$		0			0
$82$	−13.9247	+	8.03945i	−1.53773	+	0.887809i
$83$			1.14843i			0.126057i	0.998012	+	0.0630284i	$0.0200759\pi$
$83$			1.14843i			0.126057i	−0.998012	+	0.0630284i	$0.979924\pi$
$84$		0			0
$85$	0.805564	+	1.68720i	0.0873757	+	0.183003i
$86$	27.4327			2.95815
$87$		0			0
$88$	11.2295	+	6.48336i	1.19707	+	0.691129i
$89$	3.83234	−	6.63781i	0.406227	−	0.703606i	−0.588236	−	0.808689i	$-0.700178\pi$
$89$	3.83234	−	6.63781i	0.406227	−	0.703606i	0.994463	+	0.105083i	$0.0335108\pi$
$90$		0			0
$91$	−0.926730	+	1.73809i	−0.0971477	+	0.182201i
$92$		−	8.34515i		−	0.870042i
$93$		0			0
$94$	−0.258076	+	0.447000i	−0.0266185	+	0.0461045i
$95$	−10.3372	+	4.93553i	−1.06057	+	0.506375i
$96$		0			0
$97$	−12.8791	+	7.43574i	−1.30767	+	0.754985i	−0.981707	−	0.190397i	$-0.939023\pi$
$97$	−12.8791	+	7.43574i	−1.30767	+	0.754985i	−0.325965	+	0.945382i	$0.605689\pi$
$98$	13.4914	−	7.78925i	1.36284	−	0.786833i
$99$		0			0
$100$	−6.11151	−	15.8839i	−0.611151	−	1.58839i
$101$	−5.89449	+	10.2096i	−0.586524	+	1.01589i	0.408160	+	0.912910i	$0.366171\pi$
$101$	−5.89449	+	10.2096i	−0.586524	+	1.01589i	−0.994684	+	0.102978i	$0.967163\pi$
$102$		0			0
$103$		−	15.8508i		−	1.56182i	−0.624643	−	0.780910i	$-0.714756\pi$
$103$		−	15.8508i		−	1.56182i	0.624643	−	0.780910i	$-0.285244\pi$
$104$	6.22354	+	9.98536i	0.610268	+	0.979145i
$105$		0			0
$106$	13.5594	−	23.4856i	1.31701	−	2.28112i
$107$	0.620197	+	0.358071i	0.0599567	+	0.0346160i	0.529679	−	0.848198i	$-0.322313\pi$
$107$	0.620197	+	0.358071i	0.0599567	+	0.0346160i	−0.469722	+	0.882814i	$0.655646\pi$
$108$		0			0
$109$	−8.47658			−0.811909			−0.405955	−	0.913893i	$-0.633061\pi$
$109$	−8.47658			−0.811909			−0.405955	+	0.913893i	$0.633061\pi$
$110$	−8.89911	−	18.6386i	−0.848497	−	1.77712i
$111$		0			0
$112$			0.425191i			0.0401768i
$113$	8.71582	−	5.03208i	0.819915	−	0.473378i	−0.0304721	−	0.999536i	$-0.509701\pi$
$113$	8.71582	−	5.03208i	0.819915	−	0.473378i	0.850387	+	0.526157i	$0.176368\pi$
$114$		0			0
$115$	−3.10338	+	4.51923i	−0.289391	+	0.421420i
$116$	−19.7304			−1.83192
$117$		0			0
$118$			15.4128i			1.41887i
$119$	−0.228390	+	0.395582i	−0.0209364	+	0.0362630i
$120$		0			0
$121$	−2.39428	−	4.14702i	−0.217662	−	0.377001i
$122$		−	25.0257i		−	2.26572i
$123$		0			0
$124$	4.14773	+	7.18407i	0.372477	+	0.645149i
$125$	−2.59724	+	10.8745i	−0.232304	+	0.972643i
$126$		0			0
$127$	2.14091	+	1.23606i	0.189975	+	0.109682i	0.591971	−	0.805959i	$-0.298350\pi$
$127$	2.14091	+	1.23606i	0.189975	+	0.109682i	−0.401996	+	0.915642i	$0.631683\pi$
$128$	−17.0395	−	9.83777i	−1.50610	−	0.869544i
$129$		0			0
$130$	0.831779	−	18.7231i	0.0729519	−	1.64213i
$131$	7.29790			0.637621			0.318810	−	0.947819i	$-0.396717\pi$
$131$	7.29790			0.637621			0.318810	+	0.947819i	$0.396717\pi$
$132$		0			0
$133$	−2.42365	−	1.39930i	−0.210158	−	0.121335i
$134$	−16.3511	−	28.3209i	−1.41252	−	2.44655i
$135$		0			0
$136$	1.36428	+	2.36300i	0.116986	+	0.202626i
$137$	−10.3267	+	5.96210i	−0.882266	+	0.509377i	−0.871405	−	0.490564i	$-0.836791\pi$
$137$	−10.3267	+	5.96210i	−0.882266	+	0.509377i	−0.0108612	+	0.999941i	$0.503457\pi$
$138$		0			0
$139$	−10.0035	−	17.3265i	−0.848484	−	1.46962i	−0.882561	−	0.470199i	$-0.844182\pi$
$139$	−10.0035	−	17.3265i	−0.848484	−	1.46962i	0.0340763	−	0.999419i	$-0.489151\pi$
$140$	2.35376	−	3.42762i	0.198929	−	0.289686i
$141$		0			0
$142$			14.8249i			1.24408i
$143$	−0.483470	−	14.3184i	−0.0404298	−	1.19737i
$144$		0			0
$145$	10.6848	+	7.33730i	0.887323	+	0.609330i
$146$	1.64451	−	2.84838i	0.136101	−	0.235733i
$147$		0			0
$148$		−	20.2019i		−	1.66058i
$149$	−4.67003	−	8.08873i	−0.382584	−	0.662655i	0.608847	−	0.793288i	$-0.291632\pi$
$149$	−4.67003	−	8.08873i	−0.382584	−	0.662655i	−0.991431	+	0.130633i	$0.958299\pi$
$150$		0			0
$151$	−0.540637			−0.0439964			−0.0219982	−	0.999758i	$-0.507003\pi$
$151$	−0.540637			−0.0439964			−0.0219982	+	0.999758i	$0.507003\pi$
$152$	−14.4777	+	8.35868i	−1.17429	+	0.677979i
$153$		0			0
$154$	2.52303	−	4.37002i	0.203312	−	0.352146i
$155$	0.425441	−	5.43291i	0.0341723	−	0.436381i
$156$		0			0
$157$		−	12.0187i		−	0.959200i	−0.877487	−	0.479600i	$-0.840782\pi$
$157$		−	12.0187i		−	0.959200i	0.877487	−	0.479600i	$-0.159218\pi$
$158$	16.3719	+	9.45232i	1.30248	+	0.751986i
$159$		0			0
$160$	4.54490	+	9.51900i	0.359306	+	0.752543i
$161$	−1.33937			−0.105557
$162$		0			0
$163$	17.5927	−	10.1572i	1.37797	−	0.795571i	0.386055	−	0.922476i	$-0.373837\pi$
$163$	17.5927	−	10.1572i	1.37797	−	0.795571i	0.991915	+	0.126904i	$0.0405041\pi$
$164$	23.5435			1.83844
$165$		0			0
$166$	1.33483	−	2.31199i	0.103603	−	0.179445i
$167$	−5.84480	−	3.37450i	−0.452284	−	0.261127i	0.256510	−	0.966542i	$-0.417427\pi$
$167$	−5.84480	−	3.37450i	−0.452284	−	0.261127i	−0.708794	+	0.705415i	$0.750761\pi$
$168$		0			0
$169$	5.72577	−	11.6711i	0.440444	−	0.897780i
$170$	0.339305	−	4.33294i	0.0260235	−	0.332321i
$171$		0			0
$172$	−34.7868	−	20.0842i	−2.65247	−	1.53141i
$173$	14.4562	−	8.34629i	1.09908	−	0.634557i	0.163104	−	0.986609i	$-0.447849\pi$
$173$	14.4562	−	8.34629i	1.09908	−	0.634557i	0.935980	+	0.352052i	$0.114516\pi$
$174$		0			0
$175$	−2.54931	+	0.980876i	−0.192710	+	0.0741473i
$176$	−1.54630	−	2.67827i	−0.116557	−	0.201882i
$177$		0			0
$178$	−15.4303	+	8.90869i	−1.15655	+	0.667735i
$179$	−10.8810	+	18.8465i	−0.813287	+	1.40865i	0.0972642	+	0.995259i	$0.468991\pi$
$179$	−10.8810	+	18.8465i	−0.813287	+	1.40865i	−0.910551	+	0.413396i	$0.864343\pi$
$180$		0			0
$181$	11.5303			0.857041			0.428521	−	0.903532i	$-0.359035\pi$
$181$	11.5303			0.857041			0.428521	+	0.903532i	$0.359035\pi$
$182$	3.88585	−	2.42192i	0.288039	−	0.179525i
$183$		0			0
$184$	−4.00035	+	6.92881i	−0.294910	+	0.510798i
$185$	−7.51262	+	10.9401i	−0.552339	+	0.804332i
$186$		0			0
$187$		−	3.32236i		−	0.242955i
$188$	0.654520	−	0.377887i	0.0477358	−	0.0275603i
$189$		0			0
$190$	26.5471	+	2.07885i	1.92593	+	0.150816i
$191$	−11.2214	−	19.4360i	−0.811951	−	1.40634i	−0.911497	−	0.411308i	$-0.865072\pi$
$191$	−11.2214	−	19.4360i	−0.811951	−	1.40634i	0.0995455	−	0.995033i	$-0.468261\pi$
$192$		0			0
$193$	−2.96058	−	1.70929i	−0.213107	−	0.123038i	0.389647	−	0.920964i	$-0.372597\pi$
$193$	−2.96058	−	1.70929i	−0.213107	−	0.123038i	−0.602755	+	0.797927i	$0.705930\pi$
$194$	34.5704			2.48201
$195$		0			0
$196$	−22.8108			−1.62935
$197$	−3.00983	−	1.73772i	−0.214441	−	0.123808i	0.388932	−	0.921266i	$-0.372844\pi$
$197$	−3.00983	−	1.73772i	−0.214441	−	0.123808i	−0.603374	+	0.797459i	$0.706177\pi$
$198$		0			0
$199$	−4.76331	−	8.25030i	−0.337662	−	0.584848i	0.646330	−	0.763058i	$-0.276303\pi$
$199$	−4.76331	−	8.25030i	−0.337662	−	0.584848i	−0.983993	+	0.178209i	$0.942970\pi$
$200$	−2.53987	+	16.1177i	−0.179596	+	1.13969i
$201$		0			0
$202$	23.7332	−	13.7024i	1.66986	−	0.964097i
$203$			3.16666i			0.222256i
$204$		0			0
$205$	−12.7497	−	8.75532i	−0.890481	−	0.611498i
$206$	−18.4234	+	31.9103i	−1.28362	+	2.22329i
$207$		0			0
$208$	−0.0947002	−	2.80464i	−0.00656628	−	0.194467i
$209$	20.3554			1.40801
$210$		0			0
$211$	−11.7711	+	20.3881i	−0.810355	+	1.40358i	0.102261	+	0.994758i	$0.467392\pi$
$211$	−11.7711	+	20.3881i	−0.810355	+	1.40358i	−0.912616	+	0.408818i	$0.865941\pi$
$212$	−34.3888	+	19.8544i	−2.36183	+	1.36360i
$213$		0			0
$214$	−0.832376	−	1.44172i	−0.0569000	−	0.0985537i
$215$	11.3696	+	23.8128i	0.775398	+	1.62402i
$216$		0			0
$217$	1.15302	−	0.665696i	0.0782721	−	0.0451904i
$218$	17.0648	+	9.85237i	1.15577	+	0.667287i
$219$		0			0
$220$	−2.36103	+	30.1505i	−0.159181	+	2.03275i
$221$	1.41839	−	2.66020i	0.0954115	−	0.178945i
$222$		0			0
$223$	−4.22036	−	2.43662i	−0.282616	−	0.163168i	0.351991	−	0.936003i	$-0.385505\pi$
$223$	−4.22036	−	2.43662i	−0.282616	−	0.163168i	−0.634607	+	0.772835i	$0.718838\pi$
$224$	−1.28855	+	2.23183i	−0.0860947	+	0.149120i
$225$		0			0
$226$	−23.3952			−1.55623
$227$	−1.49187	+	0.861329i	−0.0990186	+	0.0571684i	−0.548692	−	0.836025i	$-0.684874\pi$
$227$	−1.49187	+	0.861329i	−0.0990186	+	0.0571684i	0.449673	+	0.893193i	$0.351541\pi$
$228$		0			0
$229$	4.01974			0.265632			0.132816	−	0.991141i	$-0.457598\pi$
$229$	4.01974			0.265632			0.132816	+	0.991141i	$0.457598\pi$
$230$	11.5004	−	5.49091i	0.758311	−	0.362060i
$231$		0			0
$232$	16.3817	+	9.45800i	1.07551	+	0.620948i
$233$		−	20.8357i		−	1.36499i	−0.730888	−	0.682497i	$-0.760894\pi$
$233$		−	20.8357i		−	1.36499i	0.730888	−	0.682497i	$-0.239106\pi$
$234$		0			0
$235$	−0.494976	−	0.0387607i	−0.0322887	−	0.00252847i
$236$	11.2841	−	19.5447i	0.734534	−	1.27225i
$237$		0			0
$238$	0.919575	−	0.530917i	0.0596072	−	0.0344142i
$239$	−19.9784			−1.29229			−0.646147	−	0.763213i	$-0.723621\pi$
$239$	−19.9784			−1.29229			−0.646147	+	0.763213i	$0.723621\pi$
$240$		0			0
$241$	8.77272	+	15.1948i	0.565101	+	0.978783i	0.997040	+	0.0768804i	$0.0244960\pi$
$241$	8.77272	+	15.1948i	0.565101	+	0.978783i	−0.431940	+	0.901902i	$0.642171\pi$
$242$			11.1315i			0.715562i
$243$		0			0
$244$	−18.3219	+	31.7345i	−1.17294	+	2.03159i
$245$	12.3530	+	8.48284i	0.789202	+	0.541949i
$246$		0			0
$247$	16.2985	+	8.69022i	1.03705	+	0.552946i
$248$		−	7.95305i		−	0.505019i
$249$		0			0
$250$	17.8682	−	18.8734i	1.13008	−	1.19366i
$251$	2.07934	+	3.60153i	0.131247	+	0.227326i	0.924157	−	0.382012i	$-0.124769\pi$
$251$	2.07934	+	3.60153i	0.131247	+	0.227326i	−0.792911	+	0.609338i	$0.791435\pi$
$252$		0			0
$253$	8.43666	−	4.87091i	0.530409	−	0.306231i
$254$	−2.87335	−	4.97678i	−0.180290	−	0.312271i
$255$		0			0
$256$	10.3463	+	17.9204i	0.646646	+	1.12002i
$257$	17.2354	+	9.95085i	1.07511	+	0.620717i	0.929574	−	0.368636i	$-0.120175\pi$
$257$	17.2354	+	9.95085i	1.07511	+	0.620717i	0.145539	+	0.989352i	$0.453508\pi$
$258$		0			0
$259$	−3.24233			−0.201469
$260$	−14.7624	+	23.1334i	−0.915528	+	1.43467i
$261$		0			0
$262$	−14.6919	−	8.48239i	−0.907670	−	0.524044i
$263$	−5.23715	−	3.02367i	−0.322937	−	0.186448i	0.329764	−	0.944063i	$-0.393031\pi$
$263$	−5.23715	−	3.02367i	−0.322937	−	0.186448i	−0.652701	+	0.757616i	$0.726364\pi$
$264$		0			0
$265$	26.0063	+	2.03651i	1.59755	+	0.125102i
$266$	3.25282	+	5.63405i	0.199443	+	0.345446i
$267$		0			0
$268$			47.8841i			2.92499i
$269$	−4.67105	−	8.09049i	−0.284799	−	0.493286i	0.687762	−	0.725937i	$-0.258593\pi$
$269$	−4.67105	−	8.09049i	−0.284799	−	0.493286i	−0.972560	+	0.232651i	$0.925260\pi$
$270$		0			0
$271$	5.09339	−	8.82201i	0.309401	−	0.535899i	−0.668830	−	0.743415i	$-0.733205\pi$
$271$	5.09339	−	8.82201i	0.309401	−	0.535899i	0.978232	+	0.207516i	$0.0665380\pi$
$272$		−	0.650770i		−	0.0394587i
$273$		0			0
$274$	27.7191			1.67457
$275$	12.4909	−	15.4497i	0.753229	−	0.931649i
$276$		0			0
$277$	11.3297	−	6.54119i	0.680734	−	0.393022i	−0.119398	−	0.992847i	$-0.538096\pi$
$277$	11.3297	−	6.54119i	0.680734	−	0.393022i	0.800132	+	0.599825i	$0.204763\pi$
$278$			46.5084i			2.78939i
$279$		0			0
$280$	−3.59735	+	1.71757i	−0.214983	+	0.102645i
$281$	1.49859			0.0893983			0.0446992	−	0.999000i	$-0.485767\pi$
$281$	1.49859			0.0893983			0.0446992	+	0.999000i	$0.485767\pi$
$282$		0			0
$283$	7.77287	+	4.48767i	0.462049	+	0.266764i	0.712906	−	0.701260i	$-0.247379\pi$
$283$	7.77287	+	4.48767i	0.462049	+	0.266764i	−0.250856	+	0.968024i	$0.580712\pi$
$284$	10.8537	−	18.7991i	0.644047	−	1.11552i
$285$		0			0
$286$	−15.6691	+	29.3874i	−0.926532	+	1.73771i
$287$		−	3.77866i		−	0.223047i
$288$		0			0
$289$	−8.15044	+	14.1170i	−0.479438	+	0.830411i
$290$	−12.9821	−	27.1902i	−0.762337	−	1.59667i
$291$		0			0
$292$	−4.17074	+	2.40798i	−0.244074	+	0.140916i
$293$	−1.21135	+	0.699370i	−0.0707675	+	0.0408577i	−0.534966	−	0.844873i	$-0.679676\pi$
$293$	−1.21135	+	0.699370i	−0.0707675	+	0.0408577i	0.464199	+	0.885731i	$0.346342\pi$
$294$		0			0
$295$	−13.3790	+	6.38789i	−0.778957	+	0.371918i
$296$	−9.68400	+	16.7732i	−0.562871	+	0.974921i
$297$		0			0
$298$			21.7120i			1.25774i
$299$	8.83473	−	0.298310i	0.510925	−	0.0172517i
$300$		0			0
$301$	−3.22344	+	5.58317i	−0.185796	+	0.321809i
$302$	1.08840	+	0.628385i	0.0626301	+	0.0361595i
$303$		0			0
$304$	3.98714			0.228678
$305$	21.7234	−	10.3720i	1.24388	−	0.593897i
$306$		0			0
$307$		−	2.77371i		−	0.158304i	−0.996863	−	0.0791521i	$-0.974779\pi$
$307$		−	2.77371i		−	0.158304i	0.996863	−	0.0791521i	$-0.0252213\pi$
$308$	−6.39880	+	3.69435i	−0.364606	+	0.210505i
$309$		0			0
$310$	−7.17118	+	10.4429i	−0.407296	+	0.593116i
$311$	−15.9062			−0.901957			−0.450979	−	0.892535i	$-0.648925\pi$
$311$	−15.9062			−0.901957			−0.450979	+	0.892535i	$0.648925\pi$
$312$		0			0
$313$		−	2.44092i		−	0.137969i	−0.997618	−	0.0689845i	$-0.978024\pi$
$313$		−	2.44092i		−	0.137969i	0.997618	−	0.0689845i	$-0.0219759\pi$
$314$	−13.9694	+	24.1958i	−0.788341	+	1.36545i
$315$		0			0
$316$	−13.8406	−	23.9726i	−0.778592	−	1.34856i
$317$			7.76757i			0.436270i	0.975919	+	0.218135i	$0.0699973\pi$
$317$			7.76757i			0.436270i	−0.975919	+	0.218135i	$0.930003\pi$
$318$		0			0
$319$	−11.5163	−	19.9468i	−0.644787	−	1.11680i
$320$	2.18606	−	27.9160i	0.122204	−	1.56055i
$321$		0			0
$322$	2.69638	+	1.55675i	0.150263	+	0.0867546i
$323$	3.70949	+	2.14168i	0.206402	+	0.119166i
$324$		0			0
$325$	16.5973	−	7.03784i	0.920650	−	0.390389i
$326$	−47.2229			−2.61544
$327$		0			0
$328$	−19.5477	−	11.2859i	−1.07934	−	0.623158i
$329$	−0.0606496	−	0.105048i	−0.00334372	−	0.00579150i
$330$		0			0
$331$	−14.2289	−	24.6451i	−0.782089	−	1.35462i	−0.930722	−	0.365726i	$-0.880821\pi$
$331$	−14.2289	−	24.6451i	−0.782089	−	1.35462i	0.148633	−	0.988892i	$-0.452513\pi$
$332$	−3.38533	+	1.95452i	−0.185794	+	0.107268i
$333$		0			0
$334$	7.84439	+	13.5869i	0.429226	+	0.743441i
$335$	17.8070	−	25.9311i	0.972902	−	1.41677i
$336$		0			0
$337$			13.8935i			0.756828i	0.925637	+	0.378414i	$0.123530\pi$
$337$			13.8935i			0.756828i	−0.925637	+	0.378414i	$0.876470\pi$
$338$	−25.0924	+	16.8409i	−1.36485	+	0.916025i
$339$		0			0
$340$	−3.60252	+	5.24609i	−0.195374	+	0.284509i
$341$	−4.84190	+	8.38642i	−0.262204	+	0.454150i
$342$		0			0
$343$			7.48516i			0.404161i
$344$	19.2552	+	33.3510i	1.03817	+	1.79816i
$345$		0			0
$346$	−38.8037			−2.08610
$347$	18.2655	−	10.5456i	0.980543	−	0.566117i	0.0781091	−	0.996945i	$-0.475112\pi$
$347$	18.2655	−	10.5456i	0.980543	−	0.566117i	0.902434	+	0.430828i	$0.141778\pi$
$348$		0			0
$349$	−7.79330	+	13.4984i	−0.417166	+	0.722553i	−0.995653	−	0.0931388i	$-0.970310\pi$
$349$	−7.79330	+	13.4984i	−0.417166	+	0.722553i	0.578487	+	0.815691i	$0.303643\pi$
$350$	6.27227	+	0.988403i	0.335267	+	0.0528323i
$351$		0			0
$352$		−	18.7444i		−	0.999077i
$353$	−25.3715	−	14.6483i	−1.35039	−	0.779649i	−0.362087	−	0.932144i	$-0.617936\pi$
$353$	−25.3715	−	14.6483i	−1.35039	−	0.779649i	−0.988304	+	0.152496i	$0.951269\pi$
$354$		0			0
$355$	−12.8687	+	6.14421i	−0.682997	+	0.326101i
$356$	26.0891			1.38272
$357$		0			0
$358$	43.8108	−	25.2942i	2.31547	−	1.33684i
$359$	−8.27786			−0.436889			−0.218444	−	0.975849i	$-0.570098\pi$
$359$	−8.27786			−0.436889			−0.218444	+	0.975849i	$0.570098\pi$
$360$		0			0
$361$	−3.62163	+	6.27284i	−0.190612	+	0.330150i
$362$	−23.2125	−	13.4017i	−1.22002	−	0.704380i
$363$		0			0
$364$	−6.70071	+	0.226254i	−0.351213	+	0.0118589i
$365$	3.15409	+	0.246991i	0.165093	+	0.0129281i
$366$		0			0
$367$	−20.2834	−	11.7106i	−1.05878	−	0.611289i	−0.133687	−	0.991024i	$-0.542682\pi$
$367$	−20.2834	−	11.7106i	−1.05878	−	0.611289i	−0.925095	+	0.379735i	$0.876015\pi$
$368$	1.65254	−	0.954094i	0.0861446	−	0.0497356i
$369$		0			0
$370$	27.8399	−	13.2923i	1.44733	−	0.691035i
$371$	3.18656	+	5.51928i	0.165438	+	0.286547i
$372$		0			0
$373$	−13.1394	+	7.58603i	−0.680332	+	0.392790i	−0.799980	−	0.600027i	$-0.795157\pi$
$373$	−13.1394	+	7.58603i	−0.680332	+	0.392790i	0.119648	+	0.992816i	$0.461823\pi$
$374$	−3.86159	+	6.68847i	−0.199678	+	0.345853i
$375$		0			0
$376$	−0.724579			−0.0373673
$377$	−0.705292	−	20.8879i	−0.0363244	−	1.07578i
$378$		0			0
$379$	3.89146	−	6.74020i	0.199891	−	0.346221i	−0.748602	−	0.663020i	$-0.769275\pi$
$379$	3.89146	−	6.74020i	0.199891	−	0.346221i	0.948493	+	0.316799i	$0.102608\pi$
$380$	−32.1418	−	22.0719i	−1.64884	−	1.13227i
$381$		0			0
$382$			52.1707i			2.66929i
$383$	−15.7893	+	9.11593i	−0.806794	+	0.465802i	−0.845841	−	0.533435i	$-0.820901\pi$
$383$	−15.7893	+	9.11593i	−0.806794	+	0.465802i	0.0390476	+	0.999237i	$0.487568\pi$
$384$		0			0
$385$	4.83905	+	0.378938i	0.246621	+	0.0193124i
$386$	3.97344	+	6.88219i	0.202243	+	0.350294i
$387$		0			0
$388$	−43.8380	−	25.3099i	−2.22554	−	1.28491i
$389$	35.3347			1.79154			0.895771	−	0.444516i	$-0.146624\pi$
$389$	35.3347			1.79154			0.895771	+	0.444516i	$0.146624\pi$
$390$		0			0
$391$	2.04995			0.103671
$392$	18.9394	+	10.9346i	0.956582	+	0.552283i
$393$		0			0
$394$	4.03953	+	6.99667i	0.203509	+	0.352487i
$395$	−1.41966	+	18.1291i	−0.0714307	+	0.912173i
$396$		0			0
$397$	−12.3906	+	7.15371i	−0.621866	+	0.359034i	−0.777595	−	0.628765i	$-0.783561\pi$
$397$	−12.3906	+	7.15371i	−0.621866	+	0.359034i	0.155729	+	0.987800i	$0.450227\pi$
$398$			22.1457i			1.11006i
$399$		0			0
$400$	2.44667	−	3.02622i	0.122333	−	0.151311i
$401$	−8.99627	+	15.5820i	−0.449252	+	0.778128i	−0.998338	−	0.0576387i	$-0.981643\pi$
$401$	−8.99627	+	15.5820i	−0.449252	+	0.778128i	0.549085	+	0.835766i	$0.314976\pi$
$402$		0			0
$403$	−7.45726	+	4.64786i	−0.371473	+	0.231526i
$404$	−40.1275			−1.99642
$405$		0			0
$406$	3.68063	−	6.37504i	0.182667	−	0.316388i
$407$	20.4234	−	11.7914i	1.01235	−	0.584480i
$408$		0			0
$409$	13.0981	+	22.6866i	0.647661	+	1.12178i	0.983680	+	0.179927i	$0.0575861\pi$
$409$	13.0981	+	22.6866i	0.647661	+	1.12178i	−0.336019	+	0.941855i	$0.609081\pi$
$410$	15.4911	+	32.4451i	0.765050	+	1.60235i
$411$		0			0
$412$	46.7246	−	26.9765i	2.30196	−	1.32904i
$413$	−3.13685	−	1.81106i	−0.154355	−	0.0891166i
$414$		0			0
$415$	2.56013	+	0.200480i	0.125672	+	0.00984115i
$416$	8.00242	−	15.0086i	0.392351	−	0.735855i
$417$		0			0
$418$	−40.9790	−	23.6592i	−2.00435	−	1.15721i
$419$	1.28855	−	2.23183i	0.0629497	−	0.109032i	−0.832833	−	0.553524i	$-0.813283\pi$
$419$	1.28855	−	2.23183i	0.0629497	−	0.109032i	0.895783	+	0.444492i	$0.146616\pi$
$420$		0			0
$421$	15.7580			0.767998			0.383999	−	0.923333i	$-0.374547\pi$
$421$	15.7580			0.767998			0.383999	+	0.923333i	$0.374547\pi$
$422$	47.3944	−	27.3632i	2.30712	−	1.33202i
$423$		0			0
$424$	38.0697			1.84883
$425$	3.90181	−	1.50127i	0.189266	−	0.0728221i
$426$		0			0
$427$	5.09328	+	2.94061i	0.246481	+	0.142306i
$428$			2.43761i			0.117826i
$429$		0			0
$430$	4.78888	−	61.1542i	0.230940	−	2.94912i
$431$	12.1455	−	21.0366i	0.585028	−	1.01330i	−0.409844	−	0.912156i	$-0.634417\pi$
$431$	12.1455	−	21.0366i	0.585028	−	1.01330i	0.994872	−	0.101142i	$-0.0322497\pi$
$432$		0			0
$433$	23.1798	−	13.3828i	1.11395	−	0.643139i	0.174100	−	0.984728i	$-0.444299\pi$
$433$	23.1798	−	13.3828i	1.11395	−	0.643139i	0.939849	+	0.341589i	$0.110965\pi$
$434$	−3.09497			−0.148563
$435$		0			0
$436$	−14.4263	−	24.9872i	−0.690897	−	1.19667i
$437$			12.5597i			0.600810i
$438$		0			0
$439$	13.4640	−	23.3204i	0.642603	−	1.11302i	−0.342247	−	0.939610i	$-0.611188\pi$
$439$	13.4640	−	23.3204i	0.642603	−	1.11302i	0.984850	−	0.173411i	$-0.0554788\pi$
$440$	16.4133	−	23.9015i	0.782474	−	1.13946i
$441$		0			0
$442$	−5.94744	+	3.70684i	−0.282891	+	0.176316i
$443$		−	8.03269i		−	0.381644i	−0.981625	−	0.190822i	$-0.938885\pi$
$443$		−	8.03269i		−	0.381644i	0.981625	−	0.190822i	$-0.0611154\pi$
$444$		0			0
$445$	−14.1283	−	9.70197i	−0.669745	−	0.459917i
$446$	5.66420	+	9.81069i	0.268208	+	0.464549i
$447$		0			0
$448$	5.92459	−	3.42056i	0.279910	−	0.161606i
$449$	−17.3131	−	29.9872i	−0.817055	−	1.41518i	−0.907843	−	0.419311i	$-0.862272\pi$
$449$	−17.3131	−	29.9872i	−0.817055	−	1.41518i	0.0907874	−	0.995870i	$-0.471062\pi$
$450$		0			0
$451$	13.7419	+	23.8017i	0.647082	+	1.12078i
$452$	29.6670	+	17.1283i	1.39542	+	0.805645i
$453$		0			0
$454$	4.00451			0.187941
$455$	3.71284	+	2.36932i	0.174061	+	0.111076i
$456$		0			0
$457$	−5.92616	−	3.42147i	−0.277214	−	0.160050i	0.354947	−	0.934886i	$-0.384499\pi$
$457$	−5.92616	−	3.42147i	−0.277214	−	0.160050i	−0.632162	+	0.774837i	$0.717832\pi$
$458$	−8.09242	−	4.67216i	−0.378134	−	0.218316i
$459$		0			0
$460$	−18.6034	−	1.45680i	−0.867387	−	0.0679236i
$461$	−1.68674	−	2.92151i	−0.0785591	−	0.136068i	0.824069	−	0.566489i	$-0.191699\pi$
$461$	−1.68674	−	2.92151i	−0.0785591	−	0.136068i	−0.902628	+	0.430421i	$0.858365\pi$
$462$		0			0
$463$			7.66504i			0.356225i	0.984010	+	0.178112i	$0.0569991\pi$
$463$			7.66504i			0.356225i	−0.984010	+	0.178112i	$0.943001\pi$
$464$	−2.25576	−	3.90709i	−0.104721	−	0.181382i
$465$		0			0
$466$	−24.2175	+	41.9459i	−1.12185	+	1.94311i
$467$			25.9819i			1.20230i	0.799136	+	0.601150i	$0.205291\pi$
$467$			25.9819i			1.20230i	−0.799136	+	0.601150i	$0.794709\pi$
$468$		0			0
$469$	7.68524			0.354871
$470$	0.951420	+	0.653345i	0.0438857	+	0.0301366i
$471$		0			0
$472$	−18.7379	+	10.8184i	−0.862484	+	0.497955i
$473$		−	46.8911i		−	2.15605i
$474$		0			0
$475$	9.19797	+	23.9056i	0.422032	+	1.09687i
$476$	−1.55479			−0.0712637
$477$		0			0
$478$	40.2199	+	23.2210i	1.83962	+	1.06210i
$479$	−4.79868	+	8.31156i	−0.219257	+	0.379765i	−0.954581	−	0.297951i	$-0.903697\pi$
$479$	−4.79868	+	8.31156i	−0.219257	+	0.379765i	0.735324	+	0.677716i	$0.237030\pi$
$480$		0			0
$481$	21.3870	−	0.722145i	0.975164	−	0.0329270i
$482$		−	40.7863i		−	1.85777i
$483$		0			0
$484$	8.14968	−	14.1157i	0.370440	−	0.641621i
$485$	14.3278	+	30.0087i	0.650592	+	1.36262i
$486$		0			0
$487$	−3.89281	+	2.24752i	−0.176400	+	0.101845i	−0.585600	−	0.810600i	$-0.699141\pi$
$487$	−3.89281	+	2.24752i	−0.176400	+	0.101845i	0.409200	+	0.912445i	$0.365808\pi$
$488$	30.4246	−	17.5657i	1.37726	−	0.795160i
$489$		0			0
$490$	−15.0090	−	31.4353i	−0.678036	−	1.42010i
$491$	−4.49848	+	7.79160i	−0.203014	+	0.351630i	−0.949498	−	0.313773i	$-0.898407\pi$
$491$	−4.49848	+	7.79160i	−0.203014	+	0.351630i	0.746484	+	0.665403i	$0.231740\pi$
$492$		0			0
$493$		−	4.84669i		−	0.218284i
$494$	−22.7111	−	36.4388i	−1.02182	−	1.63946i
$495$		0			0
$496$	−0.948412	+	1.64270i	−0.0425850	+	0.0737593i
$497$	−3.01719	−	1.74198i	−0.135340	−	0.0781383i
$498$		0			0
$499$	5.16537			0.231234			0.115617	−	0.993294i	$-0.463116\pi$
$499$	5.16537			0.231234			0.115617	+	0.993294i	$0.463116\pi$
$500$	−36.4759	+	10.8512i	−1.63125	+	0.485281i
$501$		0			0
$502$		−	9.66732i		−	0.431473i
$503$	−34.4121	+	19.8678i	−1.53436	+	0.885864i	−0.535207	+	0.844721i	$0.679767\pi$
$503$	−34.4121	+	19.8678i	−1.53436	+	0.885864i	−0.999153	+	0.0411429i	$0.986900\pi$
$504$		0			0
$505$	21.7306	+	14.9225i	0.966999	+	0.664043i
$506$	−22.6459			−1.00673
$507$		0			0
$508$			8.41460i			0.373338i
$509$	3.27529	−	5.67297i	0.145175	−	0.251450i	−0.784263	−	0.620428i	$-0.786959\pi$
$509$	3.27529	−	5.67297i	0.145175	−	0.251450i	0.929438	+	0.368978i	$0.120292\pi$
$510$		0			0
$511$	0.386472	+	0.669389i	0.0170965	+	0.0296120i
$512$		−	8.75131i		−	0.386757i
$513$		0			0
$514$	−23.1318	−	40.0655i	−1.02030	−	1.76721i
$515$	−35.3352	−	2.76704i	−1.55705	−	0.121930i
$516$		0			0
$517$	0.764062	+	0.441132i	0.0336034	+	0.0194009i
$518$	6.52736	+	3.76858i	0.286796	+	0.165582i
$519$		0			0
$520$	23.3462	−	12.1307i	1.02380	−	0.531964i
$521$	24.7520			1.08441			0.542203	−	0.840248i	$-0.317591\pi$
$521$	24.7520			1.08441			0.542203	+	0.840248i	$0.317591\pi$
$522$		0			0
$523$	−1.13562	−	0.655651i	−0.0496572	−	0.0286696i	0.474966	−	0.880004i	$-0.342460\pi$
$523$	−1.13562	−	0.655651i	−0.0496572	−	0.0286696i	−0.524623	+	0.851335i	$0.675794\pi$
$524$	12.4203	+	21.5127i	0.542585	+	0.939785i
$525$		0			0
$526$	7.02885	+	12.1743i	0.306473	+	0.530826i
$527$	−1.76474	+	1.01887i	−0.0768732	+	0.0443828i
$528$		0			0
$529$	−8.49456	−	14.7130i	−0.369329	−	0.639696i
$530$	−49.9881	−	34.3271i	−2.17134	−	1.49107i
$531$		0			0
$532$		−	9.52589i		−	0.413000i
$533$	0.841598	+	24.9247i	0.0364537	+	1.07961i
$534$		0			0
$535$	0.906494	−	1.32006i	0.0391912	−	0.0570713i
$536$	22.9538	−	39.7572i	0.991454	−	1.71725i
$537$		0			0
$538$			21.7167i			0.936275i
$539$	−13.3143	−	23.0610i	−0.573486	−	0.993306i
$540$		0			0
$541$	−22.9805			−0.988007			−0.494004	−	0.869460i	$-0.664467\pi$
$541$	−22.9805			−0.988007			−0.494004	+	0.869460i	$0.664467\pi$
$542$	−20.5077	+	11.8401i	−0.880882	+	0.508578i
$543$		0			0
$544$	1.97217	−	3.41590i	0.0845560	−	0.146455i
$545$	−1.47974	+	18.8964i	−0.0633852	+	0.809431i
$546$		0			0
$547$			0.733809i			0.0313754i	0.999877	+	0.0156877i	$0.00499376\pi$
$547$			0.733809i			0.0313754i	−0.999877	+	0.0156877i	$0.995006\pi$
$548$	−35.1500	−	20.2939i	−1.50153	−	0.866911i
$549$		0			0
$550$	−43.1035	+	16.5846i	−1.83794	+	0.707169i
$551$	29.6947			1.26504
$552$		0			0
$553$	−3.84751	+	2.22136i	−0.163613	+	0.0944620i
$554$	−30.4114			−1.29206
$555$		0			0
$556$	34.0500	−	58.9763i	1.44404	−	2.50115i
$557$	9.56639	+	5.52316i	0.405341	+	0.234024i	0.688786	−	0.724965i	$-0.258144\pi$
$557$	9.56639	+	5.52316i	0.405341	+	0.234024i	−0.283445	+	0.958989i	$0.591477\pi$
$558$		0			0
$559$	20.0189	−	37.5456i	0.846711	−	1.58801i
$560$	0.947854	+	0.0742248i	0.0400541	+	0.00313657i
$561$		0			0
$562$	−3.01692	−	1.74182i	−0.127261	−	0.0734741i
$563$	−4.22962	+	2.44197i	−0.178257	+	0.102917i	−0.586474	−	0.809968i	$-0.699484\pi$
$563$	−4.22962	+	2.44197i	−0.178257	+	0.102917i	0.408216	+	0.912885i	$0.366151\pi$
$564$		0			0
$565$	−9.69623	−	20.3081i	−0.407923	−	0.854369i
$566$	−10.4321	−	18.0689i	−0.438493	−	0.759492i
$567$		0			0
$568$	−18.0231	+	10.4057i	−0.756234	+	0.436612i
$569$	−22.7862	+	39.4669i	−0.955249	+	1.65454i	−0.221451	+	0.975171i	$0.571079\pi$
$569$	−22.7862	+	39.4669i	−0.955249	+	1.65454i	−0.733798	+	0.679368i	$0.762254\pi$
$570$		0			0
$571$	−14.7941			−0.619114			−0.309557	−	0.950881i	$-0.600181\pi$
$571$	−14.7941			−0.619114			−0.309557	+	0.950881i	$0.600181\pi$
$572$	41.3849	−	25.7938i	1.73039	−	1.07849i
$573$		0			0
$574$	−4.39195	+	7.60708i	−0.183317	+	0.317514i
$575$	9.53271	+	7.70710i	0.397541	+	0.321408i
$576$		0			0
$577$			28.3896i			1.18187i	0.806718	+	0.590936i	$0.201242\pi$
$577$			28.3896i			1.18187i	−0.806718	+	0.590936i	$0.798758\pi$
$578$	32.8165	−	18.9466i	1.36499	−	0.788075i
$579$		0			0
$580$	−3.44430	+	43.9839i	−0.143017	+	1.82633i
$581$	0.313694	+	0.543334i	0.0130142	+	0.0225413i
$582$		0			0
$583$	−40.1442	−	23.1773i	−1.66260	−	0.959904i
$584$	4.61717			0.191060
$585$		0			0
$586$	3.25153			0.134319
$587$	9.94780	+	5.74337i	0.410590	+	0.237054i	0.691043	−	0.722814i	$-0.257151\pi$
$587$	9.94780	+	5.74337i	0.410590	+	0.237054i	−0.280453	+	0.959868i	$0.590485\pi$
$588$		0			0
$589$	−6.24243	−	10.8122i	−0.257215	−	0.445509i
$590$	34.3590	+	2.69059i	1.41454	+	0.110770i
$591$		0			0
$592$	4.00045	−	2.30966i	0.164418	−	0.0949265i
$593$			9.16504i			0.376363i	0.982134	+	0.188182i	$0.0602593\pi$
$593$			9.16504i			0.376363i	−0.982134	+	0.188182i	$0.939741\pi$
$594$		0			0
$595$	0.841980	+	0.578192i	0.0345178	+	0.0237036i
$596$	15.8959	−	27.5325i	0.651122	−	1.12778i
$597$		0			0
$598$	−18.1325	−	9.66810i	−0.741495	−	0.395358i
$599$	40.7038			1.66311			0.831556	−	0.555441i	$-0.187450\pi$
$599$	40.7038			1.66311			0.831556	+	0.555441i	$0.187450\pi$
$600$		0			0
$601$	4.49121	−	7.77900i	0.183200	−	0.317312i	−0.759768	−	0.650194i	$-0.774688\pi$
$601$	4.49121	−	7.77900i	0.183200	−	0.317312i	0.942969	+	0.332882i	$0.108021\pi$
$602$	12.9787	−	7.49325i	0.528972	−	0.305402i
$603$		0			0
$604$	−0.920114	−	1.59368i	−0.0374389	−	0.0648461i
$605$	−9.66267	+	4.61350i	−0.392844	+	0.187565i
$606$		0			0
$607$	−24.5187	+	14.1559i	−0.995183	+	0.574569i	−0.906820	−	0.421519i	$-0.861497\pi$
$607$	−24.5187	+	14.1559i	−0.995183	+	0.574569i	−0.0883637	+	0.996088i	$0.528164\pi$
$608$	20.9285	+	12.0831i	0.848764	+	0.490034i
$609$		0			0
$610$	−55.7883	−	4.36869i	−2.25880	−	0.176883i
$611$	0.423453	+	0.679410i	0.0171311	+	0.0274860i
$612$		0			0
$613$	30.7566	+	17.7573i	1.24225	+	0.717212i	0.969551	−	0.244888i	$-0.0787513\pi$
$613$	30.7566	+	17.7573i	1.24225	+	0.717212i	0.272696	+	0.962100i	$0.412085\pi$
$614$	−3.22390	+	5.58396i	−0.130106	+	0.225350i
$615$		0			0
$616$	7.08372			0.285411
$617$	−31.7005	+	18.3023i	−1.27621	+	0.736822i	−0.976150	−	0.217097i	$-0.930341\pi$
$617$	−31.7005	+	18.3023i	−1.27621	+	0.736822i	−0.300064	+	0.953919i	$0.597008\pi$
$618$		0			0
$619$	−4.45845			−0.179200			−0.0896000	−	0.995978i	$-0.528559\pi$
$619$	−4.45845			−0.179200			−0.0896000	+	0.995978i	$0.528559\pi$
$620$	16.7391	−	7.99218i	0.672259	−	0.320974i
$621$		0			0
$622$	32.0219	+	18.4878i	1.28396	+	0.741295i
$623$		−	4.18721i		−	0.167757i
$624$		0			0
$625$	23.7885	+	7.68823i	0.951539	+	0.307529i
$626$	−2.83709	+	4.91399i	−0.113393	+	0.196402i
$627$		0			0
$628$	35.4287	−	20.4548i	1.41376	−	0.816234i
$629$	4.96250			0.197868
$630$		0			0
$631$	−9.25408	−	16.0285i	−0.368399	−	0.638086i	0.620916	−	0.783877i	$-0.286761\pi$
$631$	−9.25408	−	16.0285i	−0.368399	−	0.638086i	−0.989315	+	0.145791i	$0.953427\pi$
$632$			26.5385i			1.05565i
$633$		0			0
$634$	9.02828	−	15.6374i	0.358559	−	0.621042i
$635$	3.12920	−	4.55684i	0.124179	−	0.180833i
$636$		0			0
$637$	−0.815406	−	24.1490i	−0.0323076	−	0.956820i
$638$			53.5417i			2.11974i
$639$		0			0
$640$	−24.9053	+	36.2679i	−0.984470	+	1.43361i
$641$	18.7470	+	32.4708i	0.740463	+	1.28252i	0.952285	+	0.305211i	$0.0987269\pi$
$641$	18.7470	+	32.4708i	0.740463	+	1.28252i	−0.211822	+	0.977308i	$0.567940\pi$
$642$		0			0
$643$	−1.56920	+	0.905981i	−0.0618834	+	0.0357284i	−0.530622	−	0.847608i	$-0.678042\pi$
$643$	−1.56920	+	0.905981i	−0.0618834	+	0.0357284i	0.468739	+	0.883337i	$0.344708\pi$
$644$	−2.27948	−	3.94817i	−0.0898241	−	0.155580i
$645$		0			0
$646$	−4.97856	−	8.62312i	−0.195879	−	0.339272i
$647$	−18.3657	−	10.6034i	−0.722030	−	0.416864i	0.0934696	−	0.995622i	$-0.470204\pi$
$647$	−18.3657	−	10.6034i	−0.722030	−	0.416864i	−0.815499	+	0.578758i	$0.803538\pi$
$648$		0			0
$649$	26.3453			1.03414
$650$	−41.5932	−	5.12270i	−1.63142	−	0.200929i
$651$		0			0
$652$	59.8824	+	34.5731i	2.34518	+	1.35399i
$653$	−33.9342	−	19.5919i	−1.32795	−	0.766691i	−0.342966	−	0.939348i	$-0.611432\pi$
$653$	−33.9342	−	19.5919i	−1.32795	−	0.766691i	−0.984982	+	0.172657i	$0.944765\pi$
$654$		0			0
$655$	1.27398	−	16.2688i	0.0497786	−	0.635675i
$656$	2.69171	+	4.66218i	0.105094	+	0.182028i
$657$		0			0
$658$			0.281974i			0.0109925i
$659$	12.4427	+	21.5513i	0.484697	+	0.839520i	0.999845	−	0.0175810i	$-0.00559650\pi$
$659$	12.4427	+	21.5513i	0.484697	+	0.839520i	−0.515148	+	0.857101i	$0.672263\pi$
$660$		0			0
$661$	14.1266	−	24.4680i	0.549462	−	0.951696i	−0.448850	−	0.893607i	$-0.648166\pi$
$661$	14.1266	−	24.4680i	0.549462	−	0.951696i	0.998311	−	0.0580885i	$-0.0185005\pi$
$662$			66.1532i			2.57112i
$663$		0			0
$664$	3.74769			0.145439
$665$	−3.54247	+	5.15864i	−0.137371	+	0.200044i
$666$		0			0
$667$	12.3075	−	7.10574i	0.476549	−	0.275135i
$668$		−	22.9723i		−	0.888825i
$669$		0			0
$670$	−65.9885	+	31.5066i	−2.54936	+	1.21721i
$671$	−42.7767			−1.65138
$672$		0			0
$673$	26.1101	+	15.0747i	1.00647	+	0.581086i	0.910156	−	0.414265i	$-0.135961\pi$
$673$	26.1101	+	15.0747i	1.00647	+	0.581086i	0.0963139	+	0.995351i	$0.469295\pi$
$674$	16.1485	−	27.9700i	0.622017	−	1.07736i
$675$		0			0
$676$	44.1488	−	2.98482i	1.69803	−	0.114801i
$677$			18.8880i			0.725925i	0.931804	+	0.362963i	$0.118235\pi$
$677$			18.8880i			0.725925i	−0.931804	+	0.362963i	$0.881765\pi$
$678$		0			0
$679$	−4.06215	+	7.03584i	−0.155891	+	0.270011i
$680$	5.50587	−	2.62881i	0.211141	−	0.100810i
$681$		0			0
$682$	19.4952	−	11.2555i	0.746508	−	0.430997i
$683$	42.0421	−	24.2730i	1.60869	−	0.928780i	0.619032	−	0.785366i	$-0.287525\pi$
$683$	42.0421	−	24.2730i	1.60869	−	0.928780i	0.989663	−	0.143415i	$-0.0458083\pi$
$684$		0			0
$685$	11.4883	+	24.0614i	0.438944	+	0.919340i
$686$	8.70004	−	15.0689i	0.332169	−	0.575334i
$687$		0			0
$688$		−	9.18484i		−	0.350169i
$689$	−22.2484	−	35.6965i	−0.847598	−	1.35993i
$690$		0			0
$691$	4.12393	−	7.14285i	0.156882	−	0.271727i	−0.776861	−	0.629672i	$-0.783189\pi$
$691$	4.12393	−	7.14285i	0.156882	−	0.271727i	0.933743	+	0.357945i	$0.116523\pi$
$692$	49.2062	+	28.4092i	1.87054	+	1.07996i
$693$		0			0
$694$	−49.0288			−1.86111
$695$	−40.3714	+	19.2755i	−1.53137	+	0.731163i
$696$		0			0
$697$			5.78337i			0.219061i
$698$	31.3785	−	18.1164i	1.18769	−	0.685716i
$699$		0			0
$700$	−7.23010	−	5.84546i	−0.273272	−	0.220938i
$701$	32.7065			1.23531			0.617655	−	0.786449i	$-0.288083\pi$
$701$	32.7065			1.23531			0.617655	+	0.786449i	$0.288083\pi$
$702$		0			0
$703$			30.4043i			1.14672i
$704$	−24.8793	+	43.0921i	−0.937672	+	1.62410i
$705$		0			0
$706$	34.0515	+	58.9789i	1.28155	+	2.21970i
$707$			6.44032i			0.242213i
$708$		0			0
$709$	23.6447	+	40.9538i	0.887994	+	1.53805i	0.842243	+	0.539098i	$0.181235\pi$
$709$	23.6447	+	40.9538i	0.887994	+	1.53805i	0.0457508	+	0.998953i	$0.485432\pi$
$710$	33.0483	+	2.58795i	1.24028	+	0.0971241i
$711$		0			0
$712$	−21.6612	−	12.5061i	−0.811790	−	0.468687i
$713$	−5.17457	−	2.98754i	−0.193789	−	0.111884i
$714$		0			0
$715$	−32.0037	−	1.42177i	−1.19687	−	0.0531712i
$716$	−74.0740			−2.76828
$717$		0			0
$718$	16.6648	+	9.62140i	0.621923	+	0.359068i
$719$	0.599321	+	1.03805i	0.0223509	+	0.0387129i	0.876985	−	0.480519i	$-0.159552\pi$
$719$	0.599321	+	1.03805i	0.0223509	+	0.0387129i	−0.854634	+	0.519232i	$0.826218\pi$
$720$		0			0
$721$	−4.32963	−	7.49915i	−0.161244	−	0.279283i
$722$	14.5819	−	8.41887i	0.542683	−	0.313318i
$723$		0			0
$724$	19.6235	+	33.9889i	0.729302	+	1.26319i
$725$	18.2219	−	22.5381i	0.676743	−	0.837045i
$726$		0			0
$727$		−	40.0433i		−	1.48512i	−0.669778	−	0.742562i	$-0.733611\pi$
$727$		−	40.0433i		−	1.48512i	0.669778	−	0.742562i	$-0.266389\pi$
$728$	5.67192	+	3.02421i	0.210215	+	0.112085i
$729$		0			0
$730$	−6.06265	−	4.16325i	−0.224389	−	0.154089i
$731$	4.93360	−	8.54524i	0.182476	−	0.316057i
$732$		0			0
$733$		−	41.6374i		−	1.53791i	−0.639301	−	0.768957i	$-0.720776\pi$
$733$		−	41.6374i		−	1.53791i	0.639301	−	0.768957i	$-0.279224\pi$
$734$	27.2226	+	47.1509i	1.00480	+	1.74037i
$735$		0			0
$736$	11.5656			0.426314
$737$	−48.4092	+	27.9491i	−1.78318	+	1.02952i
$738$		0			0
$739$	−12.7223	+	22.0356i	−0.467996	+	0.810592i	−0.999331	−	0.0365694i	$-0.988357\pi$
$739$	−12.7223	+	22.0356i	−0.467996	+	0.810592i	0.531336	+	0.847161i	$0.321690\pi$
$740$	−45.0349	−	3.52660i	−1.65551	−	0.129640i
$741$		0			0
$742$		−	14.8150i		−	0.543877i
$743$	21.7552	+	12.5604i	0.798120	+	0.460795i	0.842813	−	0.538206i	$-0.180898\pi$
$743$	21.7552	+	12.5604i	0.798120	+	0.460795i	−0.0446932	+	0.999001i	$0.514231\pi$
$744$		0			0
$745$	−18.8470	+	8.99860i	−0.690500	+	0.329683i
$746$	35.2691			1.29129
$747$		0			0
$748$	9.79360	−	5.65434i	0.358089	−	0.206743i
$749$	0.391229			0.0142952
$750$		0			0
$751$	9.34229	−	16.1813i	0.340905	−	0.590465i	−0.643696	−	0.765281i	$-0.722600\pi$
$751$	9.34229	−	16.1813i	0.340905	−	0.590465i	0.984601	+	0.174816i	$0.0559332\pi$
$752$	0.149661	+	0.0864071i	0.00545759	+	0.00315094i
$753$		0			0
$754$	−22.8582	+	42.8707i	−0.832448	+	1.56126i
$755$	−0.0943781	+	1.20521i	−0.00343477	+	0.0438622i
$756$		0			0
$757$	−2.22585	−	1.28509i	−0.0808997	−	0.0467075i	0.459004	−	0.888434i	$-0.348206\pi$
$757$	−2.22585	−	1.28509i	−0.0808997	−	0.0467075i	−0.539904	+	0.841726i	$0.681540\pi$
$758$	−15.6683	+	9.04612i	−0.569100	+	0.328570i
$759$		0			0
$760$	16.1062	+	33.7334i	0.584233	+	1.22364i
$761$	3.00229	+	5.20012i	0.108833	+	0.188504i	0.915298	−	0.402778i	$-0.131955\pi$
$761$	3.00229	+	5.20012i	0.108833	+	0.188504i	−0.806465	+	0.591282i	$0.798622\pi$
$762$		0			0
$763$	−4.01035	+	2.31538i	−0.145185	+	0.0838224i
$764$	38.1955	−	66.1565i	1.38186	−	2.39346i
$765$		0			0
$766$	42.3820			1.53132
$767$	21.0946	+	11.2475i	0.761683	+	0.406122i
$768$		0			0
$769$	−20.6697	+	35.8010i	−0.745368	+	1.29102i	0.204655	+	0.978834i	$0.434393\pi$
$769$	−20.6697	+	35.8010i	−0.745368	+	1.29102i	−0.950023	+	0.312181i	$0.898940\pi$
$770$	−9.30139	−	6.38732i	−0.335199	−	0.230183i
$771$		0			0
$772$		−	11.6362i		−	0.418796i
$773$	11.1282	−	6.42488i	0.400254	−	0.231087i	−0.286339	−	0.958128i	$-0.592438\pi$
$773$	11.1282	−	6.42488i	0.400254	−	0.231087i	0.686594	+	0.727041i	$0.259105\pi$
$774$		0			0
$775$	−12.0370	−	1.89682i	−0.432382	−	0.0681360i
$776$	24.2652	+	42.0285i	0.871069	+	1.50873i
$777$		0			0
$778$	−71.1349	−	41.0697i	−2.55031	−	1.47242i
$779$	−35.4336			−1.26954
$780$		0			0
$781$	25.3403			0.906748
$782$	−4.12690	−	2.38267i	−0.147578	−	0.0852041i
$783$		0			0
$784$	−2.60794	−	4.51709i	−0.0931408	−	0.161325i
$785$	−26.7927	−	2.09809i	−0.956272	−	0.0748840i
$786$		0			0
$787$	6.34292	−	3.66209i	0.226101	−	0.130539i	−0.382671	−	0.923885i	$-0.624996\pi$
$787$	6.34292	−	3.66209i	0.226101	−	0.130539i	0.608772	+	0.793345i	$0.291662\pi$
$788$		−	11.8298i		−	0.421418i
$789$		0			0
$790$	23.9295	−	34.8469i	0.851374	−	1.23980i
$791$	2.74903	−	4.76145i	0.0977441	−	0.169298i
$792$		0			0
$793$	−34.2512	−	18.2624i	−1.21630	−	0.648517i
$794$	33.2592			1.18032
$795$		0			0
$796$	16.2134	−	28.0825i	0.574670	−	0.995357i
$797$	−1.18318	+	0.683108i	−0.0419103	+	0.0241969i	−0.520809	−	0.853673i	$-0.674370\pi$
$797$	−1.18318	+	0.683108i	−0.0419103	+	0.0241969i	0.478898	+	0.877870i	$0.341036\pi$
$798$		0			0
$799$	0.0928265	+	0.160780i	0.00328396	+	0.00568799i
$800$	22.0136	−	8.46998i	0.778297	−	0.299459i
$801$		0			0
$802$	36.2221	−	20.9128i	1.27905	−	0.738457i
$803$	−4.86877	−	2.81098i	−0.171815	−	0.0991974i
$804$		0			0
$805$	−0.233811	+	2.98578i	−0.00824076	+	0.105235i
$806$	20.4150	−	0.689324i	0.719087	−	0.0242804i
$807$		0			0
$808$	33.3170	+	19.2356i	1.17209	+	0.676705i
$809$	−9.58061	+	16.5941i	−0.336836	+	0.583418i	−0.983836	−	0.179073i	$-0.942690\pi$
$809$	−9.58061	+	16.5941i	−0.336836	+	0.583418i	0.647000	+	0.762490i	$0.276024\pi$
$810$		0			0
$811$	19.2819			0.677078			0.338539	−	0.940952i	$-0.390067\pi$
$811$	19.2819			0.677078			0.338539	+	0.940952i	$0.390067\pi$
$812$	−9.33465	+	5.38936i	−0.327582	+	0.189130i
$813$		0			0
$814$	−54.8210			−1.92148
$815$	−19.5717	−	40.9916i	−0.685566	−	1.43587i
$816$		0			0
$817$	52.3550	+	30.2272i	1.83167	+	1.05752i
$818$		−	60.8961i		−	2.12918i
$819$		0			0
$820$	4.10995	−	52.4843i	0.143526	−	1.83283i
$821$	−3.83806	+	6.64771i	−0.133949	+	0.232007i	−0.925196	−	0.379491i	$-0.876099\pi$
$821$	−3.83806	+	6.64771i	−0.133949	+	0.232007i	0.791246	+	0.611497i	$0.209433\pi$
$822$		0			0
$823$	17.2949	−	9.98521i	0.602862	−	0.348063i	−0.167305	−	0.985905i	$-0.553506\pi$
$823$	17.2949	−	9.98521i	0.602862	−	0.348063i	0.770167	+	0.637843i	$0.220173\pi$
$824$	−51.7260			−1.80196
$825$		0			0
$826$	4.21002	+	7.29196i	0.146485	+	0.253720i
$827$		−	5.69676i		−	0.198096i	−0.995083	−	0.0990478i	$-0.968420\pi$
$827$		−	5.69676i		−	0.198096i	0.995083	−	0.0990478i	$-0.0315797\pi$
$828$		0			0
$829$	−10.0643	+	17.4318i	−0.349547	+	0.605432i	−0.986169	−	0.165743i	$-0.946998\pi$
$829$	−10.0643	+	17.4318i	−0.349547	+	0.605432i	0.636622	+	0.771176i	$0.280331\pi$
$830$	−4.92097	−	3.37925i	−0.170809	−	0.117296i
$831$		0			0
$832$	−38.3178	+	23.8822i	−1.32843	+	0.827967i
$833$		−	5.60339i		−	0.194146i
$834$		0			0
$835$	−8.54289	+	12.4404i	−0.295639	+	0.430518i
$836$	34.6430	+	60.0035i	1.19815	+	2.07526i
$837$		0			0
$838$	−5.18813	+	2.99537i	−0.179221	+	0.103473i
$839$	18.7825	+	32.5323i	0.648445	+	1.12314i	0.983494	+	0.180939i	$0.0579137\pi$
$839$	18.7825	+	32.5323i	0.648445	+	1.12314i	−0.335049	+	0.942201i	$0.608753\pi$
$840$		0			0
$841$	−2.30007	−	3.98384i	−0.0793129	−	0.137374i
$842$	−31.7236	−	18.3156i	−1.09327	−	0.631198i
$843$		0			0
$844$	−80.1331			−2.75830
$845$	−25.0183	−	14.8016i	−0.860655	−	0.509189i
$846$		0			0
$847$	−2.26552	−	1.30800i	−0.0778440	−	0.0449433i
$848$	−7.86328	−	4.53987i	−0.270026	−	0.155900i
$849$		0			0
$850$	−9.59994	−	1.51279i	−0.329275	−	0.0518881i
$851$	7.27553	+	12.6016i	0.249402	+	0.431977i
$852$		0			0
$853$		−	25.2418i		−	0.864264i	−0.901810	−	0.432132i	$-0.857761\pi$
$853$		−	25.2418i		−	0.864264i	0.901810	−	0.432132i	$-0.142239\pi$
$854$	−6.83577	−	11.8399i	−0.233915	−	0.405153i
$855$		0			0
$856$	1.16850	−	2.02390i	0.0399385	−	0.0691754i
$857$		−	36.2644i		−	1.23877i	−0.785088	−	0.619384i	$-0.787382\pi$
$857$		−	36.2644i		−	1.23877i	0.785088	−	0.619384i	$-0.212618\pi$
$858$		0			0
$859$	−19.7872			−0.675130			−0.337565	−	0.941302i	$-0.609603\pi$
$859$	−19.7872			−0.675130			−0.337565	+	0.941302i	$0.609603\pi$
$860$	−50.8452	+	74.0423i	−1.73381	+	2.52482i
$861$		0			0
$862$	−48.9019	+	28.2335i	−1.66561	+	0.961638i
$863$		−	21.7459i		−	0.740238i	−0.928984	−	0.370119i	$-0.879317\pi$
$863$		−	21.7459i		−	0.740238i	0.928984	−	0.370119i	$-0.120683\pi$
$864$		0			0
$865$	−16.0823	−	33.6834i	−0.546815	−	1.14527i
$866$	−62.2198			−2.11432
$867$		0			0
$868$	3.92466	+	2.26590i	0.133212	+	0.0769098i
$869$	16.1570	−	27.9847i	0.548087	−	0.949315i
$870$		0			0
$871$	−50.6932	+	1.71169i	−1.71768	+	0.0579983i
$872$			27.6618i			0.936745i
$873$		0			0
$874$	14.5981	−	25.2847i	0.493790	−	0.855269i
$875$	1.74158	+	5.85426i	0.0588763	+	0.197910i
$876$		0			0
$877$	11.1644	−	6.44578i	0.376996	−	0.217659i	−0.299515	−	0.954092i	$-0.596825\pi$
$877$	11.1644	−	6.44578i	0.376996	−	0.217659i	0.676510	+	0.736433i	$0.263491\pi$
$878$	−54.2108	+	31.2986i	−1.82953	+	1.05628i
$879$		0			0
$880$	−6.24045	+	2.97954i	−0.210366	+	0.100440i
$881$	27.5539	−	47.7247i	0.928313	−	1.60789i	0.142170	−	0.989842i	$-0.454592\pi$
$881$	27.5539	−	47.7247i	0.928313	−	1.60789i	0.786144	−	0.618044i	$-0.212074\pi$
$882$		0			0
$883$		−	28.3338i		−	0.953509i	−0.879036	−	0.476755i	$-0.841813\pi$
$883$		−	28.3338i		−	0.953509i	0.879036	−	0.476755i	$-0.158187\pi$
$884$	10.2557	−	0.346289i	0.344936	−	0.0116470i
$885$		0			0
$886$	−9.33643	+	16.1712i	−0.313664	+	0.543281i
$887$	17.4774	+	10.0906i	0.586834	+	0.338809i	0.763845	−	0.645400i	$-0.223309\pi$
$887$	17.4774	+	10.0906i	0.586834	+	0.338809i	−0.177011	+	0.984209i	$0.556643\pi$
$888$		0			0
$889$	1.35051			0.0452948
$890$	17.1660	+	35.9531i	0.575406	+	1.20515i
$891$		0			0
$892$		−	16.5876i		−	0.555395i
$893$	−0.985068	+	0.568730i	−0.0329641	+	0.0190318i
$894$		0			0
$895$	40.1140	+	27.5465i	1.34086	+	0.920778i
$896$	−10.7488			−0.359091
$897$		0			0
$898$			80.4924i			2.68607i
$899$	−7.06342	+	12.2342i	−0.235578	+	0.408034i
$900$		0			0
$901$	−4.87715	−	8.44746i	−0.162481	−	0.281426i
$902$		−	63.8892i		−	2.12728i
$903$		0			0
$904$	−16.4213	−	28.4425i	−0.546163	−	0.945982i
$905$	2.01282	−	25.7039i	0.0669086	−	0.854425i
$906$		0			0
$907$	−26.0441	−	15.0365i	−0.864779	−	0.499280i	0.000830700	−	1.00000i	$-0.499736\pi$
$907$	−26.0441	−	15.0365i	−0.864779	−	0.499280i	−0.865610	+	0.500719i	$0.833069\pi$
$908$	−5.07803	−	2.93180i	−0.168520	−	0.0972952i
$909$		0			0
$910$	−4.72070	−	9.08530i	−0.156490	−	0.301175i
$911$	19.7591			0.654648			0.327324	−	0.944912i	$-0.393853\pi$
$911$	19.7591			0.654648			0.327324	+	0.944912i	$0.393853\pi$
$912$		0			0
$913$	−3.95191	−	2.28164i	−0.130789	−	0.0755111i
$914$	7.95359	+	13.7760i	0.263081	+	0.455670i
$915$		0			0
$916$	6.84121	+	11.8493i	0.226040	+	0.391513i
$917$	3.45271	−	1.99342i	0.114019	−	0.0658286i
$918$		0			0
$919$	1.79782	+	3.11392i	0.0593047	+	0.102719i	0.894153	−	0.447761i	$-0.147778\pi$
$919$	1.79782	+	3.11392i	0.0593047	+	0.102719i	−0.834849	+	0.550479i	$0.814445\pi$
$920$	14.7477	+	10.1273i	0.486216	+	0.333887i
$921$		0			0
$922$			7.84201i			0.258263i
$923$	20.2899	+	10.8184i	0.667852	+	0.356092i
$924$		0			0
$925$	23.0767	+	18.6573i	0.758756	+	0.613447i
$926$	8.90912	−	15.4310i	0.292772	−	0.507096i
$927$		0			0
$928$		−	27.3445i		−	0.897627i
$929$	−6.45032	−	11.1723i	−0.211628	−	0.366550i	0.740596	−	0.671950i	$-0.234543\pi$
$929$	−6.45032	−	11.1723i	−0.211628	−	0.366550i	−0.952224	+	0.305400i	$0.901210\pi$
$930$		0			0
$931$	34.3308			1.12515
$932$	61.4193	−	35.4605i	2.01186	−	1.16155i
$933$		0			0
$934$	30.1989	−	52.3061i	0.988139	−	1.71151i
$935$	−7.40634	−	0.579978i	−0.242213	−	0.0189673i
$936$		0			0
$937$			20.3783i			0.665731i	0.942974	+	0.332866i	$0.108016\pi$
$937$			20.3783i			0.665731i	−0.942974	+	0.332866i	$0.891984\pi$
$938$	−15.4717	−	8.93259i	−0.505169	−	0.291659i
$939$		0			0
$940$	−0.728145	−	1.52505i	−0.0237495	−	0.0497417i
$941$	−25.5053			−0.831448			−0.415724	−	0.909491i	$-0.636472\pi$
$941$	−25.5053			−0.831448			−0.415724	+	0.909491i	$0.636472\pi$
$942$		0			0
$943$	−14.6861	+	8.47901i	−0.478244	+	0.276114i
$944$	5.16042			0.167957
$945$		0			0
$946$	−54.5017	+	94.3998i	−1.77200	+	3.06920i
$947$	1.50003	+	0.866042i	0.0487444	+	0.0281426i	0.524174	−	0.851611i	$-0.324374\pi$
$947$	1.50003	+	0.866042i	0.0487444	+	0.0281426i	−0.475430	+	0.879754i	$0.657707\pi$
$948$		0			0
$949$	−2.69833	−	4.32934i	−0.0875916	−	0.140536i
$950$	9.26854	−	58.8170i	0.300711	−	1.90827i
$951$		0			0
$952$	1.29091	+	0.745307i	0.0418386	+	0.0241555i
$953$	−8.37301	+	4.83416i	−0.271228	+	0.156594i	−0.629446	−	0.777044i	$-0.716718\pi$
$953$	−8.37301	+	4.83416i	−0.271228	+	0.156594i	0.358217	+	0.933638i	$0.383385\pi$
$954$		0			0
$955$	−45.2865	+	21.6223i	−1.46544	+	0.699681i
$956$	−34.0013	−	58.8920i	−1.09968	−	1.90470i
$957$		0			0
$958$	19.3211	−	11.1551i	0.624238	−	0.360404i
$959$	−3.25710	+	5.64146i	−0.105177	+	0.182172i
$960$		0			0
$961$	−25.0605			−0.808403
$962$	−43.8951	−	23.4044i	−1.41523	−	0.754589i
$963$		0			0
$964$	−29.8607	+	51.7202i	−0.961748	+	1.66580i
$965$	−4.32725	+	6.30147i	−0.139299	+	0.202851i
$966$		0			0
$967$			11.6844i			0.375747i	0.982193	+	0.187873i	$0.0601594\pi$
$967$			11.6844i			0.375747i	−0.982193	+	0.187873i	$0.939841\pi$
$968$	−13.5330	+	7.81329i	−0.434968	+	0.251129i
$969$		0			0
$970$	6.03489	−	77.0658i	0.193769	−	2.47443i
$971$	2.17815	+	3.77267i	0.0699002	+	0.121071i	0.898857	−	0.438242i	$-0.144399\pi$
$971$	2.17815	+	3.77267i	0.0699002	+	0.121071i	−0.828957	+	0.559312i	$0.811065\pi$
$972$		0			0
$973$	−9.46549	−	5.46490i	−0.303450	−	0.175197i
$974$	10.4492			0.334814
$975$		0			0
$976$	−8.37892			−0.268203
$977$	15.5093	+	8.95430i	0.496186	+	0.286473i	0.727137	−	0.686492i	$-0.240850\pi$
$977$	15.5093	+	8.95430i	0.496186	+	0.286473i	−0.230951	+	0.972965i	$0.574184\pi$
$978$		0			0
$979$	15.2277	+	26.3752i	0.486680	+	0.842955i
$980$	−3.98205	+	50.8509i	−0.127202	+	1.62437i
$981$		0			0
$982$	18.1124	−	10.4572i	0.577991	−	0.333703i
$983$		−	23.6966i		−	0.755803i	−0.925846	−	0.377901i	$-0.876646\pi$
$983$		−	23.6966i		−	0.755803i	0.925846	−	0.377901i	$-0.123354\pi$
$984$		0			0
$985$	−4.39923	+	6.40628i	−0.140171	+	0.204121i
$986$	−5.63334	+	9.75722i	−0.179402	+	0.310733i
$987$		0			0
$988$	2.12165	+	62.8346i	0.0674985	+	1.99903i
$989$	28.9326			0.920004
$990$		0			0
$991$	5.82701	−	10.0927i	0.185101	−	0.320604i	−0.758510	−	0.651662i	$-0.774072\pi$
$991$	5.82701	−	10.0927i	0.185101	−	0.320604i	0.943611	+	0.331058i	$0.107405\pi$
$992$	−9.95645	+	5.74836i	−0.316118	+	0.182511i
$993$		0			0
$994$	4.04942	+	7.01380i	0.128440	+	0.222464i
$995$	−19.2235	+	9.17835i	−0.609424	+	0.290973i
$996$		0			0
$997$	−2.76226	+	1.59479i	−0.0874817	+	0.0505076i	−0.543103	−	0.839666i	$-0.682751\pi$
$997$	−2.76226	+	1.59479i	−0.0874817	+	0.0505076i	0.455621	+	0.890174i	$0.349417\pi$
$998$	−10.3988	−	6.00374i	−0.329168	−	0.190045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.b.334.1		24
3.2	odd	2		195.2.ba.a.139.12	yes	24
5.4	even	2	inner	585.2.bs.b.334.12		24
13.3	even	3	inner	585.2.bs.b.289.12		24
15.2	even	4		975.2.i.o.451.1		12
15.8	even	4		975.2.i.q.451.6		12
15.14	odd	2		195.2.ba.a.139.1	yes	24
39.29	odd	6		195.2.ba.a.94.1	✓	24
65.29	even	6	inner	585.2.bs.b.289.1		24
195.29	odd	6		195.2.ba.a.94.12	yes	24
195.68	even	12		975.2.i.q.601.6		12
195.107	even	12		975.2.i.o.601.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.1	✓	24	39.29	odd	6
195.2.ba.a.94.12	yes	24	195.29	odd	6
195.2.ba.a.139.1	yes	24	15.14	odd	2
195.2.ba.a.139.12	yes	24	3.2	odd	2
585.2.bs.b.289.1		24	65.29	even	6	inner
585.2.bs.b.289.12		24	13.3	even	3	inner
585.2.bs.b.334.1		24	1.1	even	1	trivial
585.2.bs.b.334.12		24	5.4	even	2	inner
975.2.i.o.451.1		12	15.2	even	4
975.2.i.o.601.1		12	195.107	even	12
975.2.i.q.451.6		12	15.8	even	4
975.2.i.q.601.6		12	195.68	even	12

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.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.01317 - 1.16230i) q^{2} +(1.70191 + 2.94779i) q^{4} +(0.174568 - 2.22924i) q^{5} +(0.473110 - 0.273150i) q^{7} -3.26331i q^{8} +O(q^{10})\)	\(q+(-2.01317 - 1.16230i) q^{2} +(1.70191 + 2.94779i) q^{4} +(0.174568 - 2.22924i) q^{5} +(0.473110 - 0.273150i) q^{7} -3.26331i q^{8} +(-2.94250 + 4.28495i) q^{10} +(-1.98674 + 3.44114i) q^{11} +(-3.05988 + 1.90712i) q^{13} -1.26993 q^{14} +(-0.389155 + 0.674036i) q^{16} +(-0.724112 + 0.418066i) q^{17} +(-2.56141 - 4.43649i) q^{19} +(6.86843 - 3.27937i) q^{20} +(7.99930 - 4.61840i) q^{22} +(-2.12324 - 1.22585i) q^{23} +(-4.93905 - 0.778310i) q^{25} +(8.37673 - 0.282845i) q^{26} +(1.61038 + 0.929751i) q^{28} +(-2.89828 + 5.01997i) q^{29} +2.43711 q^{31} +(-4.08536 + 2.35868i) q^{32} +1.94368 q^{34} +(-0.526328 - 1.10236i) q^{35} +(-5.13992 - 2.96753i) q^{37} +11.9086i q^{38} +(-7.27472 - 0.569671i) q^{40} +(3.45841 - 5.99014i) q^{41} +(-10.2200 + 5.90050i) q^{43} -13.5250 q^{44} +(2.84963 + 4.93571i) q^{46} -0.222038i q^{47} +(-3.35078 + 5.80372i) q^{49} +(9.03852 + 7.30756i) q^{50} +(-10.8294 - 5.77414i) q^{52} +11.6660i q^{53} +(7.32431 + 5.02964i) q^{55} +(-0.891375 - 1.54391i) q^{56} +(11.6695 - 6.73737i) q^{58} +(-3.31514 - 5.74200i) q^{59} +(5.38277 + 9.32323i) q^{61} +(-4.90631 - 2.83266i) q^{62} +12.5226 q^{64} +(3.71728 + 7.15415i) q^{65} +(12.1831 + 7.03390i) q^{67} +(-2.46474 - 1.42302i) q^{68} +(-0.221690 + 2.83099i) q^{70} +(-3.18868 - 5.52296i) q^{71} +1.41487i q^{73} +(6.89836 + 11.9483i) q^{74} +(8.71855 - 15.1010i) q^{76} +2.17071i q^{77} -8.13239 q^{79} +(1.43466 + 0.985186i) q^{80} +(-13.9247 + 8.03945i) q^{82} +1.14843i q^{83} +(0.805564 + 1.68720i) q^{85} +27.4327 q^{86} +(11.2295 + 6.48336i) q^{88} +(3.83234 - 6.63781i) q^{89} +(-0.926730 + 1.73809i) q^{91} -8.34515i q^{92} +(-0.258076 + 0.447000i) q^{94} +(-10.3372 + 4.93553i) q^{95} +(-12.8791 + 7.43574i) q^{97} +(13.4914 - 7.78925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 24 * q + 8 * q^4 - 4 * q^5	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) \) 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

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