LMFDB - Embedded newform 585.2.w.g.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(73,585)]

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, 3, 1]))

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

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

chi := DirichletCharacter("585.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.w (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			73.6
Character	$\chi$	$=$	585.73
Dual form			585.2.w.g.577.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.709689 q^{2} -1.49634 q^{4} +(-0.408252 - 2.19848i) q^{5} +3.37036i q^{7} +2.48132 q^{8} +O(q^{10})$	\(q-0.709689 q^{2} -1.49634 q^{4} +(-0.408252 - 2.19848i) q^{5} +3.37036i q^{7} +2.48132 q^{8} +(0.289732 + 1.56024i) q^{10} +(-2.01861 + 2.01861i) q^{11} +(1.71659 - 3.17069i) q^{13} -2.39191i q^{14} +1.23172 q^{16} +(-0.258136 - 0.258136i) q^{17} +(4.89795 - 4.89795i) q^{19} +(0.610884 + 3.28968i) q^{20} +(1.43259 - 1.43259i) q^{22} +(2.48275 - 2.48275i) q^{23} +(-4.66666 + 1.79507i) q^{25} +(-1.21825 + 2.25021i) q^{26} -5.04321i q^{28} -3.27189i q^{29} +(-4.71763 - 4.71763i) q^{31} -5.83677 q^{32} +(0.183196 + 0.183196i) q^{34} +(7.40968 - 1.37596i) q^{35} -2.60346i q^{37} +(-3.47602 + 3.47602i) q^{38} +(-1.01300 - 5.45513i) q^{40} +(-0.826745 - 0.826745i) q^{41} +(8.17249 - 8.17249i) q^{43} +(3.02053 - 3.02053i) q^{44} +(-1.76198 + 1.76198i) q^{46} -10.3158i q^{47} -4.35931 q^{49} +(3.31188 - 1.27394i) q^{50} +(-2.56861 + 4.74444i) q^{52} +(-2.08807 - 2.08807i) q^{53} +(5.26198 + 3.61378i) q^{55} +8.36292i q^{56} +2.32202i q^{58} +(10.0428 + 10.0428i) q^{59} +3.76391 q^{61} +(3.34805 + 3.34805i) q^{62} +1.67885 q^{64} +(-7.67152 - 2.47946i) q^{65} +5.66937 q^{67} +(0.386259 + 0.386259i) q^{68} +(-5.25857 + 0.976500i) q^{70} +(9.70973 + 9.70973i) q^{71} -3.03447 q^{73} +1.84765i q^{74} +(-7.32900 + 7.32900i) q^{76} +(-6.80344 - 6.80344i) q^{77} -0.584062i q^{79} +(-0.502853 - 2.70792i) q^{80} +(0.586732 + 0.586732i) q^{82} -8.97380i q^{83} +(-0.462123 + 0.672892i) q^{85} +(-5.79993 + 5.79993i) q^{86} +(-5.00881 + 5.00881i) q^{88} +(3.15550 + 3.15550i) q^{89} +(10.6864 + 5.78554i) q^{91} +(-3.71504 + 3.71504i) q^{92} +7.32100i q^{94} +(-12.7677 - 8.76846i) q^{95} +1.30416 q^{97} +3.09376 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8	$ 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 28 q^{16} - 28 q^{17} - 12 q^{20} - 32 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{31} + 68 q^{32} - 28 q^{34} - 48 q^{40} - 4 q^{41} + 40 q^{44} - 16 q^{46} + 28 q^{49} - 4 q^{50} + 48 q^{52} - 20 q^{53} - 8 q^{55} + 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} - 64 q^{65} + 32 q^{67} - 60 q^{68} - 16 q^{70} - 40 q^{71} + 56 q^{73} - 40 q^{76} - 48 q^{77} + 12 q^{80} - 4 q^{82} + 44 q^{85} - 16 q^{86} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 56 q^{95} + 48 q^{97} + 12 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8 + 8 * q^11 + 28 * q^16 - 28 * q^17 - 12 * q^20 - 32 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^31 + 68 * q^32 - 28 * q^34 - 48 * q^40 - 4 * q^41 + 40 * q^44 - 16 * q^46 + 28 * q^49 - 4 * q^50 + 48 * q^52 - 20 * q^53 - 8 * q^55 + 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 - 64 * q^65 + 32 * q^67 - 60 * q^68 - 16 * q^70 - 40 * q^71 + 56 * q^73 - 40 * q^76 - 48 * q^77 + 12 * q^80 - 4 * q^82 + 44 * q^85 - 16 * q^86 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 56 * q^95 + 48 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.709689			−0.501826			−0.250913	−	0.968010i	$-0.580731\pi$
$2$	−0.709689			−0.501826			−0.250913	+	0.968010i	$0.580731\pi$
$3$		0			0
$3$		0			0
$4$	−1.49634			−0.748171
$5$	−0.408252	−	2.19848i	−0.182576	−	0.983192i
$5$	−0.408252	−	2.19848i	−0.182576	−	0.983192i
$6$		0			0
$7$			3.37036i			1.27388i	0.770915	+	0.636938i	$0.219799\pi$
$7$			3.37036i			1.27388i	−0.770915	+	0.636938i	$0.780201\pi$
$8$	2.48132			0.877277
$9$		0			0
$10$	0.289732	+	1.56024i	0.0916213	+	0.493391i
$11$	−2.01861	+	2.01861i	−0.608634	+	0.608634i	−0.942589	−	0.333955i	$-0.891617\pi$
$11$	−2.01861	+	2.01861i	−0.608634	+	0.608634i	0.333955	+	0.942589i	$0.391617\pi$
$12$		0			0
$13$	1.71659	−	3.17069i	0.476098	−	0.879392i
$13$	1.71659	−	3.17069i	0.476098	−	0.879392i
$14$		−	2.39191i		−	0.639264i
$15$		0			0
$16$	1.23172			0.307930
$17$	−0.258136	−	0.258136i	−0.0626071	−	0.0626071i	0.675110	−	0.737717i	$-0.264096\pi$
$17$	−0.258136	−	0.258136i	−0.0626071	−	0.0626071i	−0.737717	+	0.675110i	$0.764096\pi$
$18$		0			0
$19$	4.89795	−	4.89795i	1.12367	−	1.12367i	0.132481	−	0.991186i	$-0.457706\pi$
$19$	4.89795	−	4.89795i	1.12367	−	1.12367i	0.991186	−	0.132481i	$-0.0422942\pi$
$20$	0.610884	+	3.28968i	0.136598	+	0.735595i
$21$		0			0
$22$	1.43259	−	1.43259i	0.305428	−	0.305428i
$23$	2.48275	−	2.48275i	0.517688	−	0.517688i	−0.399183	−	0.916871i	$-0.630706\pi$
$23$	2.48275	−	2.48275i	0.517688	−	0.517688i	0.916871	+	0.399183i	$0.130706\pi$
$24$		0			0
$25$	−4.66666	+	1.79507i	−0.933332	+	0.359014i
$26$	−1.21825	+	2.25021i	−0.238918	+	0.441302i
$27$		0			0
$28$		−	5.04321i		−	0.953076i
$29$		−	3.27189i		−	0.607574i	−0.952740	−	0.303787i	$-0.901749\pi$
$29$		−	3.27189i		−	0.607574i	0.952740	−	0.303787i	$-0.0982512\pi$
$30$		0			0
$31$	−4.71763	−	4.71763i	−0.847312	−	0.847312i	0.142485	−	0.989797i	$-0.454491\pi$
$31$	−4.71763	−	4.71763i	−0.847312	−	0.847312i	−0.989797	+	0.142485i	$0.954491\pi$
$32$	−5.83677			−1.03180
$33$		0			0
$34$	0.183196	+	0.183196i	0.0314179	+	0.0314179i
$35$	7.40968	−	1.37596i	1.25246	−	0.232579i
$36$		0			0
$37$		−	2.60346i		−	0.428007i	−0.976833	−	0.214003i	$-0.931350\pi$
$37$		−	2.60346i		−	0.428007i	0.976833	−	0.214003i	$-0.0686504\pi$
$38$	−3.47602	+	3.47602i	−0.563885	+	0.563885i
$39$		0			0
$40$	−1.01300	−	5.45513i	−0.160170	−	0.862532i
$41$	−0.826745	−	0.826745i	−0.129116	−	0.129116i	0.639596	−	0.768712i	$-0.279102\pi$
$41$	−0.826745	−	0.826745i	−0.129116	−	0.129116i	−0.768712	+	0.639596i	$0.779102\pi$
$42$		0			0
$43$	8.17249	−	8.17249i	1.24629	−	1.24629i	0.288948	−	0.957345i	$-0.406694\pi$
$43$	8.17249	−	8.17249i	1.24629	−	1.24629i	0.957345	−	0.288948i	$-0.0933055\pi$
$44$	3.02053	−	3.02053i	0.455362	−	0.455362i
$45$		0			0
$46$	−1.76198	+	1.76198i	−0.259789	+	0.259789i
$47$		−	10.3158i		−	1.50471i	−0.658757	−	0.752356i	$-0.728917\pi$
$47$		−	10.3158i		−	1.50471i	0.658757	−	0.752356i	$-0.271083\pi$
$48$		0			0
$49$	−4.35931			−0.622759
$50$	3.31188	−	1.27394i	0.468370	−	0.180163i
$51$		0			0
$52$	−2.56861	+	4.74444i	−0.356202	+	0.657936i
$53$	−2.08807	−	2.08807i	−0.286818	−	0.286818i	0.549003	−	0.835821i	$-0.315008\pi$
$53$	−2.08807	−	2.08807i	−0.286818	−	0.286818i	−0.835821	+	0.549003i	$0.815008\pi$
$54$		0			0
$55$	5.26198	+	3.61378i	0.709526	+	0.487282i
$56$			8.36292i			1.11754i
$57$		0			0
$58$			2.32202i			0.304897i
$59$	10.0428	+	10.0428i	1.30746	+	1.30746i	0.923240	+	0.384223i	$0.125531\pi$
$59$	10.0428	+	10.0428i	1.30746	+	1.30746i	0.384223	+	0.923240i	$0.374469\pi$
$60$		0			0
$61$	3.76391			0.481919			0.240960	−	0.970535i	$-0.422538\pi$
$61$	3.76391			0.481919			0.240960	+	0.970535i	$0.422538\pi$
$62$	3.34805	+	3.34805i	0.425203	+	0.425203i
$63$		0			0
$64$	1.67885			0.209856
$65$	−7.67152	−	2.47946i	−0.951535	−	0.307539i
$66$		0			0
$67$	5.66937			0.692624			0.346312	−	0.938119i	$-0.387434\pi$
$67$	5.66937			0.692624			0.346312	+	0.938119i	$0.387434\pi$
$68$	0.386259	+	0.386259i	0.0468408	+	0.0468408i
$69$		0			0
$70$	−5.25857	+	0.976500i	−0.628519	+	0.116714i
$71$	9.70973	+	9.70973i	1.15233	+	1.15233i	0.986084	+	0.166250i	$0.0531658\pi$
$71$	9.70973	+	9.70973i	1.15233	+	1.15233i	0.166250	+	0.986084i	$0.446834\pi$
$72$		0			0
$73$	−3.03447			−0.355158			−0.177579	−	0.984107i	$-0.556827\pi$
$73$	−3.03447			−0.355158			−0.177579	+	0.984107i	$0.556827\pi$
$74$			1.84765i			0.214785i
$75$		0			0
$76$	−7.32900	+	7.32900i	−0.840694	+	0.840694i
$77$	−6.80344	−	6.80344i	−0.775324	−	0.775324i
$78$		0			0
$79$		−	0.584062i		−	0.0657121i	−0.999460	−	0.0328560i	$-0.989540\pi$
$79$		−	0.584062i		−	0.0657121i	0.999460	−	0.0328560i	$-0.0104603\pi$
$80$	−0.502853	−	2.70792i	−0.0562206	−	0.302755i
$81$		0			0
$82$	0.586732	+	0.586732i	0.0647937	+	0.0647937i
$83$		−	8.97380i		−	0.985003i	−0.870312	−	0.492501i	$-0.836083\pi$
$83$		−	8.97380i		−	0.985003i	0.870312	−	0.492501i	$-0.163917\pi$
$84$		0			0
$85$	−0.462123	+	0.672892i	−0.0501243	+	0.0729854i
$86$	−5.79993	+	5.79993i	−0.625422	+	0.625422i
$87$		0			0
$88$	−5.00881	+	5.00881i	−0.533941	+	0.533941i
$89$	3.15550	+	3.15550i	0.334482	+	0.334482i	0.854286	−	0.519804i	$-0.173995\pi$
$89$	3.15550	+	3.15550i	0.334482	+	0.334482i	−0.519804	+	0.854286i	$0.673995\pi$
$90$		0			0
$91$	10.6864	+	5.78554i	1.12024	+	0.606489i
$92$	−3.71504	+	3.71504i	−0.387319	+	0.387319i
$93$		0			0
$94$			7.32100i			0.755104i
$95$	−12.7677	−	8.76846i	−1.30993	−	0.899625i
$96$		0			0
$97$	1.30416			0.132417			0.0662084	−	0.997806i	$-0.478910\pi$
$97$	1.30416			0.132417			0.0662084	+	0.997806i	$0.478910\pi$
$98$	3.09376			0.312517
$99$		0			0
$100$	6.98292	−	2.68604i	0.698292	−	0.268604i
$101$		−	7.70150i		−	0.766328i	−0.923680	−	0.383164i	$-0.874834\pi$
$101$		−	7.70150i		−	0.766328i	0.923680	−	0.383164i	$-0.125166\pi$
$102$		0			0
$103$	−0.763019	+	0.763019i	−0.0751825	+	0.0751825i	−0.743698	−	0.668516i	$-0.766930\pi$
$103$	−0.763019	+	0.763019i	−0.0751825	+	0.0751825i	0.668516	+	0.743698i	$0.266930\pi$
$104$	4.25941	−	7.86749i	0.417670	−	0.771471i
$105$		0			0
$106$	1.48188	+	1.48188i	0.143933	+	0.143933i
$107$	−5.39611	+	5.39611i	−0.521661	+	0.521661i	−0.918073	−	0.396412i	$-0.870255\pi$
$107$	−5.39611	+	5.39611i	−0.521661	+	0.521661i	0.396412	+	0.918073i	$0.370255\pi$
$108$		0			0
$109$	−14.2093	+	14.2093i	−1.36101	+	1.36101i	−0.488374	+	0.872634i	$0.662410\pi$
$109$	−14.2093	+	14.2093i	−1.36101	+	1.36101i	−0.872634	+	0.488374i	$0.837590\pi$
$110$	−3.73437	−	2.56466i	−0.356058	−	0.244531i
$111$		0			0
$112$			4.15134i			0.392265i
$113$	−9.14444	−	9.14444i	−0.860237	−	0.860237i	0.131128	−	0.991365i	$-0.458140\pi$
$113$	−9.14444	−	9.14444i	−0.860237	−	0.860237i	−0.991365	+	0.131128i	$0.958140\pi$
$114$		0			0
$115$	−6.47186	−	4.44469i	−0.603504	−	0.414469i
$116$			4.89586i			0.454569i
$117$		0			0
$118$	−7.12728	−	7.12728i	−0.656119	−	0.656119i
$119$	0.870010	−	0.870010i	0.0797537	−	0.0797537i
$120$		0			0
$121$			2.85042i			0.259129i
$122$	−2.67121			−0.241840
$123$		0			0
$124$	7.05919	+	7.05919i	0.633934	+	0.633934i
$125$	5.85161	+	9.52674i	0.523384	+	0.852097i
$126$		0			0
$127$	−14.1692	−	14.1692i	−1.25731	−	1.25731i	−0.952371	−	0.304942i	$-0.901363\pi$
$127$	−14.1692	−	14.1692i	−1.25731	−	1.25731i	−0.304942	−	0.952371i	$-0.598637\pi$
$128$	10.4821			0.926494
$129$		0			0
$130$	5.44440	+	1.75965i	0.477505	+	0.154331i
$131$	3.79799			0.331832			0.165916	−	0.986140i	$-0.446942\pi$
$131$	3.79799			0.331832			0.165916	+	0.986140i	$0.446942\pi$
$132$		0			0
$133$	16.5078	+	16.5078i	1.43141	+	1.43141i
$134$	−4.02349			−0.347576
$135$		0			0
$136$	−0.640516	−	0.640516i	−0.0549238	−	0.0549238i
$137$		−	2.37615i		−	0.203008i	−0.994835	−	0.101504i	$-0.967635\pi$
$137$		−	2.37615i		−	0.203008i	0.994835	−	0.101504i	$-0.0323655\pi$
$138$		0			0
$139$		−	4.16122i		−	0.352950i	−0.984305	−	0.176475i	$-0.943530\pi$
$139$		−	4.16122i		−	0.352950i	0.984305	−	0.176475i	$-0.0564695\pi$
$140$	−11.0874	+	2.05890i	−0.937057	+	0.174009i
$141$		0			0
$142$	−6.89089	−	6.89089i	−0.578271	−	0.578271i
$143$	2.93526	+	9.86553i	0.245459	+	0.824997i
$144$		0			0
$145$	−7.19319	+	1.33576i	−0.597362	+	0.110928i
$146$	2.15353			0.178227
$147$		0			0
$148$			3.89567i			0.320222i
$149$	−11.9153	+	11.9153i	−0.976137	+	0.976137i	−0.999722	−	0.0235847i	$-0.992492\pi$
$149$	−11.9153	+	11.9153i	−0.976137	+	0.976137i	0.0235847	+	0.999722i	$0.492492\pi$
$150$		0			0
$151$	5.87597	−	5.87597i	0.478179	−	0.478179i	−0.426370	−	0.904549i	$-0.640208\pi$
$151$	5.87597	−	5.87597i	0.478179	−	0.478179i	0.904549	+	0.426370i	$0.140208\pi$
$152$	12.1534	−	12.1534i	0.985767	−	0.985767i
$153$		0			0
$154$	4.82833	+	4.82833i	0.389078	+	0.389078i
$155$	−8.44566	+	12.2976i	−0.678372	+	0.987769i
$156$		0			0
$157$	−1.11230	+	1.11230i	−0.0887711	+	0.0887711i	−0.750098	−	0.661327i	$-0.769994\pi$
$157$	−1.11230	+	1.11230i	−0.0887711	+	0.0887711i	0.661327	+	0.750098i	$0.269994\pi$
$158$			0.414502i			0.0329760i
$159$		0			0
$160$	2.38287	+	12.8320i	0.188383	+	1.01446i
$161$	8.36774	+	8.36774i	0.659470	+	0.659470i
$162$		0			0
$163$	−11.0857			−0.868303			−0.434151	−	0.900840i	$-0.642952\pi$
$163$	−11.0857			−0.868303			−0.434151	+	0.900840i	$0.642952\pi$
$164$	1.23709	+	1.23709i	0.0966008	+	0.0966008i
$165$		0			0
$166$			6.36861i			0.494300i
$167$			19.8530i			1.53627i	0.640285	+	0.768137i	$0.278816\pi$
$167$			19.8530i			1.53627i	−0.640285	+	0.768137i	$0.721184\pi$
$168$		0			0
$169$	−7.10661	−	10.8856i	−0.546662	−	0.837353i
$170$	0.327964	−	0.477544i	0.0251537	−	0.0366259i
$171$		0			0
$172$	−12.2288	+	12.2288i	−0.932440	+	0.932440i
$173$	9.88084	−	9.88084i	0.751226	−	0.751226i	−0.223482	−	0.974708i	$-0.571742\pi$
$173$	9.88084	−	9.88084i	0.751226	−	0.751226i	0.974708	+	0.223482i	$0.0717423\pi$
$174$		0			0
$175$	−6.05003	−	15.7283i	−0.457339	−	1.18895i
$176$	−2.48637	+	2.48637i	−0.187417	+	0.187417i
$177$		0			0
$178$	−2.23942	−	2.23942i	−0.167852	−	0.167852i
$179$	4.78409			0.357580			0.178790	−	0.983887i	$-0.442782\pi$
$179$	4.78409			0.357580			0.178790	+	0.983887i	$0.442782\pi$
$180$		0			0
$181$			3.60052i			0.267625i	0.991007	+	0.133812i	$0.0427220\pi$
$181$			3.60052i			0.267625i	−0.991007	+	0.133812i	$0.957278\pi$
$182$	−7.58400	−	4.10593i	−0.562164	−	0.304352i
$183$		0			0
$184$	6.16047	−	6.16047i	0.454156	−	0.454156i
$185$	−5.72367	+	1.06287i	−0.420813	+	0.0781437i
$186$		0			0
$187$	1.04215			0.0762096
$188$			15.4359i			1.12578i
$189$		0			0
$190$	9.06106	+	6.22288i	0.657359	+	0.451455i
$191$	4.12937			0.298791			0.149395	−	0.988778i	$-0.452267\pi$
$191$	4.12937			0.298791			0.149395	+	0.988778i	$0.452267\pi$
$192$		0			0
$193$	9.34123			0.672396			0.336198	−	0.941791i	$-0.390859\pi$
$193$	9.34123			0.672396			0.336198	+	0.941791i	$0.390859\pi$
$194$	−0.925544			−0.0664502
$195$		0			0
$196$	6.52302			0.465930
$197$	14.0808			1.00322			0.501609	−	0.865094i	$-0.332742\pi$
$197$	14.0808			1.00322			0.501609	+	0.865094i	$0.332742\pi$
$198$		0			0
$199$	20.0664			1.42247			0.711234	−	0.702956i	$-0.248137\pi$
$199$	20.0664			1.42247			0.711234	+	0.702956i	$0.248137\pi$
$200$	−11.5795	+	4.45414i	−0.818791	+	0.314955i
$201$		0			0
$202$			5.46567i			0.384563i
$203$	11.0274			0.773974
$204$		0			0
$205$	−1.48007	+	2.15511i	−0.103372	+	0.150519i
$206$	0.541506	−	0.541506i	0.0377285	−	0.0377285i
$207$		0			0
$208$	2.11437	−	3.90541i	0.146605	−	0.270792i
$209$			19.7741i			1.36780i
$210$		0			0
$211$	−17.3456			−1.19412			−0.597059	−	0.802198i	$-0.703664\pi$
$211$	−17.3456			−1.19412			−0.597059	+	0.802198i	$0.703664\pi$
$212$	3.12446	+	3.12446i	0.214589	+	0.214589i
$213$		0			0
$214$	3.82956	−	3.82956i	0.261783	−	0.261783i
$215$	−21.3035	−	14.6306i	−1.45289	−	0.997802i
$216$		0			0
$217$	15.9001	−	15.9001i	1.07937	−	1.07937i
$218$	10.0842	−	10.0842i	0.682989	−	0.682989i
$219$		0			0
$220$	−7.87373	−	5.40745i	−0.530846	−	0.364570i
$221$	−1.26158	+	0.375355i	−0.0848633	+	0.0252491i
$222$		0			0
$223$		−	8.93688i		−	0.598458i	−0.954181	−	0.299229i	$-0.903271\pi$
$223$		−	8.93688i		−	0.598458i	0.954181	−	0.299229i	$-0.0967294\pi$
$224$		−	19.6720i		−	1.31439i
$225$		0			0
$226$	6.48971	+	6.48971i	0.431689	+	0.431689i
$227$	21.4655			1.42471			0.712357	−	0.701817i	$-0.247628\pi$
$227$	21.4655			1.42471			0.712357	+	0.701817i	$0.247628\pi$
$228$		0			0
$229$	−2.10572	−	2.10572i	−0.139150	−	0.139150i	0.634100	−	0.773251i	$-0.281371\pi$
$229$	−2.10572	−	2.10572i	−0.139150	−	0.139150i	−0.773251	+	0.634100i	$0.781371\pi$
$230$	4.59301	+	3.15435i	0.302854	+	0.207991i
$231$		0			0
$232$		−	8.11859i		−	0.533011i
$233$	12.8697	−	12.8697i	0.843124	−	0.843124i	−0.146140	−	0.989264i	$-0.546685\pi$
$233$	12.8697	−	12.8697i	0.843124	−	0.843124i	0.989264	+	0.146140i	$0.0466849\pi$
$234$		0			0
$235$	−22.6791	+	4.21144i	−1.47942	+	0.274724i
$236$	−15.0275	−	15.0275i	−0.978206	−	0.978206i
$237$		0			0
$238$	−0.617437	+	0.617437i	−0.0400225	+	0.0400225i
$239$	−8.51706	+	8.51706i	−0.550923	+	0.550923i	−0.926707	−	0.375784i	$-0.877373\pi$
$239$	−8.51706	+	8.51706i	−0.550923	+	0.550923i	0.375784	+	0.926707i	$0.377373\pi$
$240$		0			0
$241$	−1.96701	+	1.96701i	−0.126706	+	0.126706i	−0.767616	−	0.640910i	$-0.778557\pi$
$241$	−1.96701	+	1.96701i	−0.126706	+	0.126706i	0.640910	+	0.767616i	$0.278557\pi$
$242$		−	2.02291i		−	0.130038i
$243$		0			0
$244$	−5.63210			−0.360558
$245$	1.77970	+	9.58388i	0.113701	+	0.612291i
$246$		0			0
$247$	−7.12211	−	23.9377i	−0.453169	−	1.52312i
$248$	−11.7059	−	11.7059i	−0.743328	−	0.743328i
$249$		0			0
$250$	−4.15282	−	6.76102i	−0.262647	−	0.427604i
$251$			20.4999i			1.29394i	0.762515	+	0.646971i	$0.223964\pi$
$251$			20.4999i			1.29394i	−0.762515	+	0.646971i	$0.776036\pi$
$252$		0			0
$253$			10.0234i			0.630165i
$254$	10.0557	+	10.0557i	0.630952	+	0.630952i
$255$		0			0
$256$	−10.7967			−0.674794
$257$	−11.3944	−	11.3944i	−0.710762	−	0.710762i	0.255932	−	0.966695i	$-0.417618\pi$
$257$	−11.3944	−	11.3944i	−0.710762	−	0.710762i	−0.966695	+	0.255932i	$0.917618\pi$
$258$		0			0
$259$	8.77460			0.545227
$260$	11.4792	+	3.71012i	0.711911	+	0.230092i
$261$		0			0
$262$	−2.69539			−0.166522
$263$	−13.0709	−	13.0709i	−0.805985	−	0.805985i	0.178039	−	0.984023i	$-0.443025\pi$
$263$	−13.0709	−	13.0709i	−0.805985	−	0.805985i	−0.984023	+	0.178039i	$0.943025\pi$
$264$		0			0
$265$	−3.73813	+	5.44304i	−0.229631	+	0.334363i
$266$	−11.7154	−	11.7154i	−0.718319	−	0.718319i
$267$		0			0
$268$	−8.48331			−0.518201
$269$		−	23.0050i		−	1.40264i	−0.712845	−	0.701321i	$-0.752594\pi$
$269$		−	23.0050i		−	1.40264i	0.712845	−	0.701321i	$-0.247406\pi$
$270$		0			0
$271$	−9.77588	+	9.77588i	−0.593843	+	0.593843i	−0.938667	−	0.344825i	$-0.887938\pi$
$271$	−9.77588	+	9.77588i	−0.593843	+	0.593843i	0.344825	+	0.938667i	$0.387938\pi$
$272$	−0.317951	−	0.317951i	−0.0192786	−	0.0192786i
$273$		0			0
$274$			1.68633i			0.101875i
$275$	5.79662	−	13.0437i	0.349549	−	0.786566i
$276$		0			0
$277$	14.2931	+	14.2931i	0.858788	+	0.858788i	0.991195	−	0.132407i	$-0.0422707\pi$
$277$	14.2931	+	14.2931i	0.858788	+	0.858788i	−0.132407	+	0.991195i	$0.542271\pi$
$278$			2.95317i			0.177120i
$279$		0			0
$280$	18.3857	−	3.41418i	1.09876	−	0.204036i
$281$	−10.3177	+	10.3177i	−0.615504	+	0.615504i	−0.944375	−	0.328871i	$-0.893332\pi$
$281$	−10.3177	+	10.3177i	−0.615504	+	0.615504i	0.328871	+	0.944375i	$0.393332\pi$
$282$		0			0
$283$	4.64455	−	4.64455i	0.276090	−	0.276090i	−0.555456	−	0.831546i	$-0.687456\pi$
$283$	4.64455	−	4.64455i	0.276090	−	0.276090i	0.831546	+	0.555456i	$0.187456\pi$
$284$	−14.5291	−	14.5291i	−0.862142	−	0.862142i
$285$		0			0
$286$	−2.08312	−	7.00146i	−0.123178	−	0.414005i
$287$	2.78643	−	2.78643i	0.164478	−	0.164478i
$288$		0			0
$289$		−	16.8667i		−	0.992161i
$290$	5.10493	−	0.947971i	0.299772	−	0.0556668i
$291$		0			0
$292$	4.54060			0.265719
$293$	−8.28255			−0.483872			−0.241936	−	0.970292i	$-0.577782\pi$
$293$	−8.28255			−0.483872			−0.241936	+	0.970292i	$0.577782\pi$
$294$		0			0
$295$	17.9790	−	26.1790i	1.04678	−	1.52420i
$296$		−	6.46001i		−	0.375481i
$297$		0			0
$298$	8.45614	−	8.45614i	0.489851	−	0.489851i
$299$	−3.61016	−	12.1339i	−0.208781	−	0.701721i
$300$		0			0
$301$	27.5442	+	27.5442i	1.58762	+	1.58762i
$302$	−4.17011	+	4.17011i	−0.239963	+	0.239963i
$303$		0			0
$304$	6.03291	−	6.03291i	0.346011	−	0.346011i
$305$	−1.53662	−	8.27490i	−0.0879869	−	0.473819i
$306$		0			0
$307$			9.69106i			0.553098i	0.961000	+	0.276549i	$0.0891908\pi$
$307$			9.69106i			0.553098i	−0.961000	+	0.276549i	$0.910809\pi$
$308$	10.1803	+	10.1803i	0.580075	+	0.580075i
$309$		0			0
$310$	5.99379	−	8.72749i	0.340424	−	0.495688i
$311$		−	34.3557i		−	1.94813i	−0.226262	−	0.974066i	$-0.572651\pi$
$311$		−	34.3557i		−	1.94813i	0.226262	−	0.974066i	$-0.427349\pi$
$312$		0			0
$313$	6.96851	+	6.96851i	0.393883	+	0.393883i	0.876069	−	0.482186i	$-0.160157\pi$
$313$	6.96851	+	6.96851i	0.393883	+	0.393883i	−0.482186	+	0.876069i	$0.660157\pi$
$314$	0.789386	−	0.789386i	0.0445476	−	0.0445476i
$315$		0			0
$316$			0.873956i			0.0491639i
$317$	5.40286			0.303455			0.151727	−	0.988422i	$-0.451516\pi$
$317$	5.40286			0.303455			0.151727	+	0.988422i	$0.451516\pi$
$318$		0			0
$319$	6.60467	+	6.60467i	0.369790	+	0.369790i
$320$	−0.685393	−	3.69092i	−0.0383146	−	0.206329i
$321$		0			0
$322$	−5.93849	−	5.93849i	−0.330939	−	0.330939i
$323$	−2.52867			−0.140699
$324$		0			0
$325$	−2.31914	+	17.8780i	−0.128643	+	0.991691i
$326$	7.86743			0.435737
$327$		0			0
$328$	−2.05142	−	2.05142i	−0.113270	−	0.113270i
$329$	34.7679			1.91682
$330$		0			0
$331$	−1.12915	−	1.12915i	−0.0620636	−	0.0620636i	0.675394	−	0.737457i	$-0.263974\pi$
$331$	−1.12915	−	1.12915i	−0.0620636	−	0.0620636i	−0.737457	+	0.675394i	$0.763974\pi$
$332$			13.4279i			0.736950i
$333$		0			0
$334$		−	14.0895i		−	0.770943i
$335$	−2.31453	−	12.4640i	−0.126456	−	0.680982i
$336$		0			0
$337$	5.02125	+	5.02125i	0.273525	+	0.273525i	0.830517	−	0.556993i	$-0.188045\pi$
$337$	5.02125	+	5.02125i	0.273525	+	0.273525i	−0.556993	+	0.830517i	$0.688045\pi$
$338$	5.04348	+	7.72539i	0.274329	+	0.420206i
$339$		0			0
$340$	0.691494	−	1.00688i	0.0375015	−	0.0546055i
$341$	19.0461			1.03141
$342$		0			0
$343$			8.90006i			0.480558i
$344$	20.2785	−	20.2785i	1.09334	−	1.09334i
$345$		0			0
$346$	−7.01232	+	7.01232i	−0.376985	+	0.376985i
$347$	−11.0474	+	11.0474i	−0.593056	+	0.593056i	−0.938456	−	0.345400i	$-0.887743\pi$
$347$	−11.0474	+	11.0474i	−0.593056	+	0.593056i	0.345400	+	0.938456i	$0.387743\pi$
$348$		0			0
$349$	12.3419	+	12.3419i	0.660647	+	0.660647i	0.955532	−	0.294886i	$-0.0952816\pi$
$349$	12.3419	+	12.3419i	0.660647	+	0.660647i	−0.294886	+	0.955532i	$0.595282\pi$
$350$	4.29364	+	11.1622i	0.229505	+	0.596645i
$351$		0			0
$352$	11.7822	−	11.7822i	0.627991	−	0.627991i
$353$			29.3287i			1.56101i	0.625150	+	0.780505i	$0.285038\pi$
$353$			29.3287i			1.56101i	−0.625150	+	0.780505i	$0.714962\pi$
$354$		0			0
$355$	17.3827	−	25.3107i	0.922576	−	1.34335i
$356$	−4.72170	−	4.72170i	−0.250250	−	0.250250i
$357$		0			0
$358$	−3.39521			−0.179443
$359$	12.3136	+	12.3136i	0.649885	+	0.649885i	0.952965	−	0.303080i	$-0.0980150\pi$
$359$	12.3136	+	12.3136i	0.649885	+	0.649885i	−0.303080	+	0.952965i	$0.598015\pi$
$360$		0			0
$361$		−	28.9798i		−	1.52525i
$362$		−	2.55525i		−	0.134301i
$363$		0			0
$364$	−15.9905	−	8.65714i	−0.838128	−	0.453757i
$365$	1.23883	+	6.67123i	0.0648432	+	0.349188i
$366$		0			0
$367$	−3.94866	+	3.94866i	−0.206118	+	0.206118i	−0.802615	−	0.596497i	$-0.796559\pi$
$367$	−3.94866	+	3.94866i	−0.206118	+	0.206118i	0.596497	+	0.802615i	$0.296559\pi$
$368$	3.05805	−	3.05805i	0.159412	−	0.159412i
$369$		0			0
$370$	4.06203	−	0.754307i	0.211175	−	0.0392145i
$371$	7.03754	−	7.03754i	0.365371	−	0.365371i
$372$		0			0
$373$	−14.0272	−	14.0272i	−0.726303	−	0.726303i	0.243578	−	0.969881i	$-0.421679\pi$
$373$	−14.0272	−	14.0272i	−0.726303	−	0.726303i	−0.969881	+	0.243578i	$0.921679\pi$
$374$	−0.739603			−0.0382440
$375$		0			0
$376$		−	25.5967i		−	1.32005i
$377$	−10.3742	−	5.61651i	−0.534296	−	0.289265i
$378$		0			0
$379$	14.9883	−	14.9883i	0.769895	−	0.769895i	−0.208193	−	0.978088i	$-0.566758\pi$
$379$	14.9883	−	14.9883i	0.769895	−	0.769895i	0.978088	+	0.208193i	$0.0667581\pi$
$380$	19.1048	+	13.1206i	0.980054	+	0.673073i
$381$		0			0
$382$	−2.93057			−0.149941
$383$		−	7.99003i		−	0.408271i	−0.978943	−	0.204136i	$-0.934562\pi$
$383$		−	7.99003i		−	0.408271i	0.978943	−	0.204136i	$-0.0654384\pi$
$384$		0			0
$385$	−12.1797	+	17.7348i	−0.620737	+	0.903847i
$386$	−6.62936			−0.337426
$387$		0			0
$388$	−1.95146			−0.0990704
$389$	−32.8048			−1.66327			−0.831636	−	0.555321i	$-0.812595\pi$
$389$	−32.8048			−1.66327			−0.831636	+	0.555321i	$0.812595\pi$
$390$		0			0
$391$	−1.28177			−0.0648219
$392$	−10.8168			−0.546332
$393$		0			0
$394$	−9.99301			−0.503441
$395$	−1.28405	+	0.238444i	−0.0646076	+	0.0119974i
$396$		0			0
$397$			29.5213i			1.48163i	0.671707	+	0.740817i	$0.265561\pi$
$397$			29.5213i			1.48163i	−0.671707	+	0.740817i	$0.734439\pi$
$398$	−14.2409			−0.713831
$399$		0			0
$400$	−5.74802	+	2.21103i	−0.287401	+	0.110551i
$401$	−9.84804	+	9.84804i	−0.491788	+	0.491788i	−0.908869	−	0.417081i	$-0.863053\pi$
$401$	−9.84804	+	9.84804i	−0.491788	+	0.491788i	0.417081	+	0.908869i	$0.363053\pi$
$402$		0			0
$403$	−23.0564	+	6.85991i	−1.14852	+	0.341717i
$404$			11.5241i			0.573344i
$405$		0			0
$406$	−7.82605			−0.388400
$407$	5.25538	+	5.25538i	0.260499	+	0.260499i
$408$		0			0
$409$	−15.2040	+	15.2040i	−0.751789	+	0.751789i	−0.974813	−	0.223024i	$-0.928407\pi$
$409$	−15.2040	+	15.2040i	−0.751789	+	0.751789i	0.223024	+	0.974813i	$0.428407\pi$
$410$	1.05039	−	1.52946i	0.0518749	−	0.0755344i
$411$		0			0
$412$	1.14174	−	1.14174i	0.0562493	−	0.0562493i
$413$	−33.8479	+	33.8479i	−1.66555	+	1.66555i
$414$		0			0
$415$	−19.7288	+	3.66357i	−0.968446	+	0.179838i
$416$	−10.0194	+	18.5066i	−0.491240	+	0.907361i
$417$		0			0
$418$		−	14.0335i		−	0.686399i
$419$			3.79858i			0.185573i	0.995686	+	0.0927864i	$0.0295774\pi$
$419$			3.79858i			0.185573i	−0.995686	+	0.0927864i	$0.970423\pi$
$420$		0			0
$421$	−26.0026	−	26.0026i	−1.26729	−	1.26729i	−0.947483	−	0.319807i	$-0.896382\pi$
$421$	−26.0026	−	26.0026i	−1.26729	−	1.26729i	−0.319807	−	0.947483i	$-0.603618\pi$
$422$	12.3099			0.599239
$423$		0			0
$424$	−5.18115	−	5.18115i	−0.251619	−	0.251619i
$425$	1.66800	+	0.741260i	0.0809101	+	0.0359564i
$426$		0			0
$427$			12.6857i			0.613905i
$428$	8.07442	−	8.07442i	0.390292	−	0.390292i
$429$		0			0
$430$	15.1189	+	10.3832i	0.729097	+	0.500723i
$431$	14.6349	+	14.6349i	0.704940	+	0.704940i	0.965467	−	0.260527i	$-0.0838962\pi$
$431$	14.6349	+	14.6349i	0.704940	+	0.704940i	−0.260527	+	0.965467i	$0.583896\pi$
$432$		0			0
$433$	−13.6870	+	13.6870i	−0.657756	+	0.657756i	−0.954849	−	0.297092i	$-0.903983\pi$
$433$	−13.6870	+	13.6870i	−0.657756	+	0.657756i	0.297092	+	0.954849i	$0.403983\pi$
$434$	−11.2841	+	11.2841i	−0.541656	+	0.541656i
$435$		0			0
$436$	21.2620	−	21.2620i	1.01827	−	1.01827i
$437$		−	24.3207i		−	1.16342i
$438$		0			0
$439$	16.6920			0.796668			0.398334	−	0.917241i	$-0.369589\pi$
$439$	16.6920			0.796668			0.398334	+	0.917241i	$0.369589\pi$
$440$	13.0566	+	8.96693i	0.622451	+	0.427481i
$441$		0			0
$442$	0.895332	−	0.266385i	0.0425866	−	0.0126707i
$443$	−12.8562	−	12.8562i	−0.610818	−	0.610818i	0.332341	−	0.943159i	$-0.392161\pi$
$443$	−12.8562	−	12.8562i	−0.610818	−	0.610818i	−0.943159	+	0.332341i	$0.892161\pi$
$444$		0			0
$445$	5.64907	−	8.22555i	0.267792	−	0.389928i
$446$			6.34240i			0.300322i
$447$		0			0
$448$			5.65832i			0.267330i
$449$	4.94187	+	4.94187i	0.233221	+	0.233221i	0.814036	−	0.580815i	$-0.197266\pi$
$449$	4.94187	+	4.94187i	0.233221	+	0.233221i	−0.580815	+	0.814036i	$0.697266\pi$
$450$		0			0
$451$	3.33775			0.157169
$452$	13.6832	+	13.6832i	0.643604	+	0.643604i
$453$		0			0
$454$	−15.2338			−0.714959
$455$	8.35668	−	25.8558i	0.391767	−	1.21214i
$456$		0			0
$457$	−28.0433			−1.31181			−0.655905	−	0.754843i	$-0.727713\pi$
$457$	−28.0433			−1.31181			−0.655905	+	0.754843i	$0.727713\pi$
$458$	1.49441	+	1.49441i	0.0698292	+	0.0698292i
$459$		0			0
$460$	9.68411	+	6.65077i	0.451524	+	0.310094i
$461$	−11.5623	−	11.5623i	−0.538510	−	0.538510i	0.384581	−	0.923091i	$-0.374346\pi$
$461$	−11.5623	−	11.5623i	−0.538510	−	0.538510i	−0.923091	+	0.384581i	$0.874346\pi$
$462$		0			0
$463$	19.6555			0.913469			0.456735	−	0.889603i	$-0.349019\pi$
$463$	19.6555			0.913469			0.456735	+	0.889603i	$0.349019\pi$
$464$		−	4.03005i		−	0.187091i
$465$		0			0
$466$	−9.13351	+	9.13351i	−0.423102	+	0.423102i
$467$	3.57594	+	3.57594i	0.165475	+	0.165475i	0.784987	−	0.619512i	$-0.212670\pi$
$467$	3.57594	+	3.57594i	0.165475	+	0.165475i	−0.619512	+	0.784987i	$0.712670\pi$
$468$		0			0
$469$			19.1078i			0.882316i
$470$	16.0951	−	2.98881i	0.742412	−	0.137864i
$471$		0			0
$472$	24.9194	+	24.9194i	1.14701	+	1.14701i
$473$			32.9941i			1.51707i
$474$		0			0
$475$	−14.0649	+	31.6492i	−0.645342	+	1.45217i
$476$	−1.30183	+	1.30183i	−0.0596694	+	0.0596694i
$477$		0			0
$478$	6.04446	−	6.04446i	0.276467	−	0.276467i
$479$	−17.9026	−	17.9026i	−0.817993	−	0.817993i	0.167824	−	0.985817i	$-0.446326\pi$
$479$	−17.9026	−	17.9026i	−0.817993	−	0.817993i	−0.985817	+	0.167824i	$0.946326\pi$
$480$		0			0
$481$	−8.25479	−	4.46909i	−0.376386	−	0.203773i
$482$	1.39596	−	1.39596i	0.0635844	−	0.0635844i
$483$		0			0
$484$		−	4.26521i		−	0.193873i
$485$	−0.532424	−	2.86716i	−0.0241761	−	0.130191i
$486$		0			0
$487$	26.8513			1.21675			0.608374	−	0.793650i	$-0.291822\pi$
$487$	26.8513			1.21675			0.608374	+	0.793650i	$0.291822\pi$
$488$	9.33945			0.422777
$489$		0			0
$490$	−1.26303	−	6.80157i	−0.0570580	−	0.307264i
$491$		−	3.68146i		−	0.166142i	−0.996544	−	0.0830709i	$-0.973527\pi$
$491$		−	3.68146i		−	0.166142i	0.996544	−	0.0830709i	$-0.0264728\pi$
$492$		0			0
$493$	−0.844592	+	0.844592i	−0.0380385	+	0.0380385i
$494$	5.05448	+	16.9883i	0.227412	+	0.764340i
$495$		0			0
$496$	−5.81081	−	5.81081i	−0.260913	−	0.260913i
$497$	−32.7253	+	32.7253i	−1.46793	+	1.46793i
$498$		0			0
$499$	−27.4864	+	27.4864i	−1.23046	+	1.23046i	−0.266675	+	0.963787i	$0.585925\pi$
$499$	−27.4864	+	27.4864i	−1.23046	+	1.23046i	−0.963787	+	0.266675i	$0.914075\pi$
$500$	−8.75600	−	14.2553i	−0.391580	−	0.637514i
$501$		0			0
$502$		−	14.5485i		−	0.649333i
$503$	−19.0138	−	19.0138i	−0.847782	−	0.847782i	0.142074	−	0.989856i	$-0.454623\pi$
$503$	−19.0138	−	19.0138i	−0.847782	−	0.847782i	−0.989856	+	0.142074i	$0.954623\pi$
$504$		0			0
$505$	−16.9316	+	3.14415i	−0.753448	+	0.139913i
$506$		−	7.11349i		−	0.316233i
$507$		0			0
$508$	21.2020	+	21.2020i	0.940685	+	0.940685i
$509$	−16.1675	+	16.1675i	−0.716612	+	0.716612i	−0.967910	−	0.251298i	$-0.919143\pi$
$509$	−16.1675	+	16.1675i	−0.716612	+	0.716612i	0.251298	+	0.967910i	$0.419143\pi$
$510$		0			0
$511$		−	10.2273i		−	0.452427i
$512$	−13.3018			−0.587864
$513$		0			0
$514$	8.08647	+	8.08647i	0.356679	+	0.356679i
$515$	1.98899	+	1.36598i	0.0876453	+	0.0601923i
$516$		0			0
$517$	20.8236	+	20.8236i	0.915819	+	0.915819i
$518$	−6.22724			−0.273609
$519$		0			0
$520$	−19.0355	−	6.15233i	−0.834760	−	0.269797i
$521$	18.2034			0.797507			0.398753	−	0.917058i	$-0.369443\pi$
$521$	18.2034			0.797507			0.398753	+	0.917058i	$0.369443\pi$
$522$		0			0
$523$	0.0785003	+	0.0785003i	0.00343258	+	0.00343258i	0.708821	−	0.705388i	$-0.249227\pi$
$523$	0.0785003	+	0.0785003i	0.00343258	+	0.00343258i	−0.705388	+	0.708821i	$0.749227\pi$
$524$	−5.68309			−0.248267
$525$		0			0
$526$	9.27626	+	9.27626i	0.404464	+	0.404464i
$527$			2.43558i			0.106096i
$528$		0			0
$529$			10.6720i			0.463998i
$530$	2.65291	−	3.86287i	0.115235	−	0.167792i
$531$		0			0
$532$	−24.7014	−	24.7014i	−1.07094	−	1.07094i
$533$	−4.04054	+	1.20217i	−0.175015	+	0.0520718i
$534$		0			0
$535$	14.0662	+	9.66028i	0.608136	+	0.417650i
$536$	14.0675			0.607623
$537$		0			0
$538$			16.3264i			0.703882i
$539$	8.79975	−	8.79975i	0.379032	−	0.379032i
$540$		0			0
$541$	27.4232	−	27.4232i	1.17902	−	1.17902i	0.199022	−	0.979995i	$-0.436224\pi$
$541$	27.4232	−	27.4232i	1.17902	−	1.17902i	0.979995	−	0.199022i	$-0.0637765\pi$
$542$	6.93784	−	6.93784i	0.298006	−	0.298006i
$543$		0			0
$544$	1.50668	+	1.50668i	0.0645983	+	0.0645983i
$545$	37.0400	+	25.4380i	1.58662	+	1.08964i
$546$		0			0
$547$	10.4237	−	10.4237i	0.445685	−	0.445685i	−0.448232	−	0.893917i	$-0.647946\pi$
$547$	10.4237	−	10.4237i	0.445685	−	0.445685i	0.893917	+	0.448232i	$0.147946\pi$
$548$			3.55553i			0.151885i
$549$		0			0
$550$	−4.11380	+	9.25698i	−0.175413	+	0.394719i
$551$	−16.0255	−	16.0255i	−0.682711	−	0.682711i
$552$		0			0
$553$	1.96850			0.0837090
$554$	−10.1436	−	10.1436i	−0.430962	−	0.430962i
$555$		0			0
$556$			6.22661i			0.264067i
$557$		−	21.2426i		−	0.900078i	−0.893009	−	0.450039i	$-0.851410\pi$
$557$		−	21.2426i		−	0.900078i	0.893009	−	0.450039i	$-0.148590\pi$
$558$		0			0
$559$	−11.8836	−	39.9413i	−0.502623	−	1.68934i
$560$	9.12666	−	1.69479i	0.385672	−	0.0716181i
$561$		0			0
$562$	7.32237	−	7.32237i	0.308876	−	0.308876i
$563$	18.3122	−	18.3122i	0.771766	−	0.771766i	−0.206649	−	0.978415i	$-0.566256\pi$
$563$	18.3122	−	18.3122i	0.771766	−	0.771766i	0.978415	+	0.206649i	$0.0662558\pi$
$564$		0			0
$565$	−16.3707	+	23.8371i	−0.688719	+	1.00284i
$566$	−3.29618	+	3.29618i	−0.138549	+	0.138549i
$567$		0			0
$568$	24.0929	+	24.0929i	1.01092	+	1.01092i
$569$	6.44231			0.270076			0.135038	−	0.990840i	$-0.456884\pi$
$569$	6.44231			0.270076			0.135038	+	0.990840i	$0.456884\pi$
$570$		0			0
$571$			47.2795i			1.97859i	0.145943	+	0.989293i	$0.453379\pi$
$571$			47.2795i			1.97859i	−0.145943	+	0.989293i	$0.546621\pi$
$572$	−4.39215	−	14.7622i	−0.183645	−	0.617239i
$573$		0			0
$574$	−1.97750	+	1.97750i	−0.0825391	+	0.0825391i
$575$	−7.12943	+	16.0428i	−0.297318	+	0.669032i
$576$		0			0
$577$	−10.9755			−0.456916			−0.228458	−	0.973554i	$-0.573368\pi$
$577$	−10.9755			−0.456916			−0.228458	+	0.973554i	$0.573368\pi$
$578$			11.9701i			0.497892i
$579$		0			0
$580$	10.7635	−	1.99875i	0.446929	−	0.0829934i
$581$	30.2449			1.25477
$582$		0			0
$583$	8.42999			0.349135
$584$	−7.52948			−0.311572
$585$		0			0
$586$	5.87803			0.242819
$587$	5.69542			0.235075			0.117538	−	0.993068i	$-0.462500\pi$
$587$	5.69542			0.235075			0.117538	+	0.993068i	$0.462500\pi$
$588$		0			0
$589$	−46.2134			−1.90419
$590$	−12.7595	+	18.5789i	−0.525299	+	0.764882i
$591$		0			0
$592$		−	3.20674i		−	0.131796i
$593$	21.5593			0.885334			0.442667	−	0.896686i	$-0.354032\pi$
$593$	21.5593			0.885334			0.442667	+	0.896686i	$0.354032\pi$
$594$		0			0
$595$	−2.26789	−	1.55752i	−0.0929743	−	0.0638521i
$596$	17.8293	−	17.8293i	0.730317	−	0.730317i
$597$		0			0
$598$	2.56209	+	8.61129i	0.104772	+	0.352142i
$599$		−	4.86091i		−	0.198611i	−0.995057	−	0.0993057i	$-0.968338\pi$
$599$		−	4.86091i		−	0.198611i	0.995057	−	0.0993057i	$-0.0316622\pi$
$600$		0			0
$601$	−9.29477			−0.379142			−0.189571	−	0.981867i	$-0.560710\pi$
$601$	−9.29477			−0.379142			−0.189571	+	0.981867i	$0.560710\pi$
$602$	−19.5478	−	19.5478i	−0.796710	−	0.796710i
$603$		0			0
$604$	−8.79245	+	8.79245i	−0.357760	+	0.357760i
$605$	6.26661	−	1.16369i	0.254774	−	0.0473108i
$606$		0			0
$607$	−5.88199	+	5.88199i	−0.238743	+	0.238743i	−0.816329	−	0.577587i	$-0.803995\pi$
$607$	−5.88199	+	5.88199i	−0.238743	+	0.238743i	0.577587	+	0.816329i	$0.303995\pi$
$608$	−28.5882	+	28.5882i	−1.15940	+	1.15940i
$609$		0			0
$610$	1.09053	+	5.87260i	0.0441541	+	0.237775i
$611$	−32.7082	−	17.7080i	−1.32323	−	0.716390i
$612$		0			0
$613$		−	12.1423i		−	0.490423i	−0.969470	−	0.245211i	$-0.921143\pi$
$613$		−	12.1423i		−	0.490423i	0.969470	−	0.245211i	$-0.0788574\pi$
$614$		−	6.87764i		−	0.277559i
$615$		0			0
$616$	−16.8815	−	16.8815i	−0.680174	−	0.680174i
$617$	10.4358			0.420129			0.210064	−	0.977688i	$-0.432633\pi$
$617$	10.4358			0.420129			0.210064	+	0.977688i	$0.432633\pi$
$618$		0			0
$619$	20.9799	+	20.9799i	0.843253	+	0.843253i	0.989281	−	0.146027i	$-0.0466487\pi$
$619$	20.9799	+	20.9799i	0.843253	+	0.843253i	−0.146027	+	0.989281i	$0.546649\pi$
$620$	12.6376	−	18.4014i	0.507538	−	0.739020i
$621$		0			0
$622$			24.3819i			0.977624i
$623$	−10.6352	+	10.6352i	−0.426089	+	0.426089i
$624$		0			0
$625$	18.5554	−	16.7540i	0.742218	−	0.670159i
$626$	−4.94547	−	4.94547i	−0.197661	−	0.197661i
$627$		0			0
$628$	1.66438	−	1.66438i	0.0664159	−	0.0664159i
$629$	−0.672047	+	0.672047i	−0.0267963	+	0.0267963i
$630$		0			0
$631$	9.35181	−	9.35181i	0.372290	−	0.372290i	−0.496021	−	0.868311i	$-0.665206\pi$
$631$	9.35181	−	9.35181i	0.372290	−	0.372290i	0.868311	+	0.496021i	$0.165206\pi$
$632$		−	1.44924i		−	0.0576477i
$633$		0			0
$634$	−3.83435			−0.152282
$635$	−25.3661	+	36.9354i	−1.00662	+	1.46573i
$636$		0			0
$637$	−7.48317	+	13.8220i	−0.296494	+	0.547649i
$638$	−4.68726	−	4.68726i	−0.185570	−	0.185570i
$639$		0			0
$640$	−4.27933	−	23.0447i	−0.169155	−	0.910921i
$641$			3.29186i			0.130021i	0.997885	+	0.0650103i	$0.0207080\pi$
$641$			3.29186i			0.130021i	−0.997885	+	0.0650103i	$0.979292\pi$
$642$		0			0
$643$		−	0.630386i		−	0.0248600i	−0.999923	−	0.0124300i	$-0.996043\pi$
$643$		−	0.630386i		−	0.0248600i	0.999923	−	0.0124300i	$-0.00395669\pi$
$644$	−12.5210	−	12.5210i	−0.493396	−	0.493396i
$645$		0			0
$646$	1.79457			0.0706064
$647$	3.05833	+	3.05833i	0.120235	+	0.120235i	0.764664	−	0.644429i	$-0.222905\pi$
$647$	3.05833	+	3.05833i	0.120235	+	0.120235i	−0.644429	+	0.764664i	$0.722905\pi$
$648$		0			0
$649$	−40.5451			−1.59153
$650$	1.64587	−	12.6878i	0.0645563	−	0.497656i
$651$		0			0
$652$	16.5881			0.649639
$653$	31.1590	+	31.1590i	1.21935	+	1.21935i	0.967861	+	0.251486i	$0.0809192\pi$
$653$	31.1590	+	31.1590i	1.21935	+	1.21935i	0.251486	+	0.967861i	$0.419081\pi$
$654$		0			0
$655$	−1.55054	−	8.34981i	−0.0605845	−	0.326254i
$656$	−1.01832	−	1.01832i	−0.0397587	−	0.0397587i
$657$		0			0
$658$	−24.6744			−0.961908
$659$			47.0995i			1.83474i	0.398039	+	0.917368i	$0.369691\pi$
$659$			47.0995i			1.83474i	−0.398039	+	0.917368i	$0.630309\pi$
$660$		0			0
$661$	23.2004	−	23.2004i	0.902390	−	0.902390i	−0.0932527	−	0.995642i	$-0.529726\pi$
$661$	23.2004	−	23.2004i	0.902390	−	0.902390i	0.995642	+	0.0932527i	$0.0297264\pi$
$662$	0.801344	+	0.801344i	0.0311451	+	0.0311451i
$663$		0			0
$664$		−	22.2668i		−	0.864120i
$665$	29.5528	−	43.0316i	1.14601	−	1.66869i
$666$		0			0
$667$	−8.12327	−	8.12327i	−0.314534	−	0.314534i
$668$		−	29.7069i		−	1.14940i
$669$		0			0
$670$	1.64260	+	8.84557i	0.0634591	+	0.341734i
$671$	−7.59787	+	7.59787i	−0.293313	+	0.293313i
$672$		0			0
$673$	−12.2612	+	12.2612i	−0.472634	+	0.472634i	−0.902766	−	0.430132i	$-0.858467\pi$
$673$	−12.2612	+	12.2612i	−0.472634	+	0.472634i	0.430132	+	0.902766i	$0.358467\pi$
$674$	−3.56352	−	3.56352i	−0.137262	−	0.137262i
$675$		0			0
$676$	10.6339	+	16.2886i	0.408997	+	0.626483i
$677$	21.8438	−	21.8438i	0.839525	−	0.839525i	−0.149271	−	0.988796i	$-0.547693\pi$
$677$	21.8438	−	21.8438i	0.839525	−	0.839525i	0.988796	+	0.149271i	$0.0476928\pi$
$678$		0			0
$679$			4.39547i			0.168683i
$680$	−1.14667	+	1.66966i	−0.0439729	+	0.0640284i
$681$		0			0
$682$	−13.5168			−0.517586
$683$	−6.96020			−0.266325			−0.133162	−	0.991094i	$-0.542513\pi$
$683$	−6.96020			−0.266325			−0.133162	+	0.991094i	$0.542513\pi$
$684$		0			0
$685$	−5.22392	+	0.970067i	−0.199596	+	0.0370644i
$686$		−	6.31628i		−	0.241157i
$687$		0			0
$688$	10.0662	−	10.0662i	0.383771	−	0.383771i
$689$	−10.2050	+	3.03626i	−0.388779	+	0.115672i
$690$		0			0
$691$	27.7459	+	27.7459i	1.05550	+	1.05550i	0.998366	+	0.0571369i	$0.0181971\pi$
$691$	27.7459	+	27.7459i	1.05550	+	1.05550i	0.0571369	+	0.998366i	$0.481803\pi$
$692$	−14.7851	+	14.7851i	−0.562046	+	0.562046i
$693$		0			0
$694$	7.84022	−	7.84022i	0.297611	−	0.297611i
$695$	−9.14838	+	1.69883i	−0.347018	+	0.0644402i
$696$		0			0
$697$			0.426825i			0.0161672i
$698$	−8.75891	−	8.75891i	−0.331530	−	0.331530i
$699$		0			0
$700$	9.05291	+	23.5349i	0.342168	+	0.889537i
$701$		−	18.4254i		−	0.695919i	−0.937510	−	0.347959i	$-0.886875\pi$
$701$		−	18.4254i		−	0.695919i	0.937510	−	0.347959i	$-0.113125\pi$
$702$		0			0
$703$	−12.7516	−	12.7516i	−0.480937	−	0.480937i
$704$	−3.38894	+	3.38894i	−0.127725	+	0.127725i
$705$		0			0
$706$		−	20.8143i		−	0.783355i
$707$	25.9568			0.976207
$708$		0			0
$709$	10.5925	+	10.5925i	0.397808	+	0.397808i	0.877459	−	0.479651i	$-0.159237\pi$
$709$	10.5925	+	10.5925i	0.397808	+	0.397808i	−0.479651	+	0.877459i	$0.659237\pi$
$710$	−12.3363	+	17.9627i	−0.462973	+	0.674129i
$711$		0			0
$712$	7.82978	+	7.82978i	0.293434	+	0.293434i
$713$	−23.4254			−0.877287
$714$		0			0
$715$	20.4909	−	10.4807i	0.766316	−	0.391958i
$716$	−7.15863			−0.267531
$717$		0			0
$718$	−8.73880	−	8.73880i	−0.326129	−	0.326129i
$719$	−5.00557			−0.186676			−0.0933382	−	0.995634i	$-0.529754\pi$
$719$	−5.00557			−0.186676			−0.0933382	+	0.995634i	$0.529754\pi$
$720$		0			0
$721$	−2.57165	−	2.57165i	−0.0957731	−	0.0957731i
$722$			20.5666i			0.765411i
$723$		0			0
$724$		−	5.38761i		−	0.200229i
$725$	5.87327	+	15.2688i	0.218128	+	0.567069i
$726$		0			0
$727$	−0.146074	−	0.146074i	−0.00541757	−	0.00541757i	0.704393	−	0.709810i	$-0.251219\pi$
$727$	−0.146074	−	0.146074i	−0.00541757	−	0.00541757i	−0.709810	+	0.704393i	$0.751219\pi$
$728$	26.5163	+	14.3557i	0.982758	+	0.532059i
$729$		0			0
$730$	−0.879183	−	4.73450i	−0.0325400	−	0.175232i
$731$	−4.21922			−0.156054
$732$		0			0
$733$		−	32.5476i		−	1.20217i	−0.799183	−	0.601087i	$-0.794734\pi$
$733$		−	32.5476i		−	1.20217i	0.799183	−	0.601087i	$-0.205266\pi$
$734$	2.80232	−	2.80232i	0.103436	−	0.103436i
$735$		0			0
$736$	−14.4912	+	14.4912i	−0.534153	+	0.534153i
$737$	−11.4442	+	11.4442i	−0.421554	+	0.421554i
$738$		0			0
$739$	19.9901	+	19.9901i	0.735346	+	0.735346i	0.971673	−	0.236327i	$-0.0759438\pi$
$739$	19.9901	+	19.9901i	0.735346	+	0.735346i	−0.236327	+	0.971673i	$0.575944\pi$
$740$	8.56457	−	1.59042i	0.314840	−	0.0584648i
$741$		0			0
$742$	−4.99446	+	4.99446i	−0.183352	+	0.183352i
$743$		−	12.0051i		−	0.440424i	−0.975452	−	0.220212i	$-0.929325\pi$
$743$		−	12.0051i		−	0.440424i	0.975452	−	0.220212i	$-0.0706749\pi$
$744$		0			0
$745$	31.0600	+	21.3311i	1.13795	+	0.781511i
$746$	9.95498	+	9.95498i	0.364478	+	0.364478i
$747$		0			0
$748$	−1.55941			−0.0570178
$749$	−18.1868	−	18.1868i	−0.664531	−	0.664531i
$750$		0			0
$751$			0.0685957i			0.00250309i	0.999999	+	0.00125155i	$0.000398380\pi$
$751$			0.0685957i			0.00250309i	−0.999999	+	0.00125155i	$0.999602\pi$
$752$		−	12.7062i		−	0.463347i
$753$		0			0
$754$	7.36243	+	3.98597i	0.268124	+	0.145161i
$755$	−15.3171	−	10.5193i	−0.557446	−	0.382838i
$756$		0			0
$757$	0.222451	−	0.222451i	0.00808511	−	0.00808511i	−0.703053	−	0.711138i	$-0.748180\pi$
$757$	0.222451	−	0.222451i	0.00808511	−	0.00808511i	0.711138	+	0.703053i	$0.248180\pi$
$758$	−10.6370	+	10.6370i	−0.386353	+	0.386353i
$759$		0			0
$760$	−31.6806	−	21.7573i	−1.14918	−	0.789221i
$761$	−13.4488	+	13.4488i	−0.487520	+	0.487520i	−0.907523	−	0.420003i	$-0.862029\pi$
$761$	−13.4488	+	13.4488i	−0.487520	+	0.487520i	0.420003	+	0.907523i	$0.362029\pi$
$762$		0			0
$763$	−47.8906	−	47.8906i	−1.73376	−	1.73376i
$764$	−6.17895			−0.223547
$765$		0			0
$766$			5.67044i			0.204881i
$767$	49.0821	−	14.6033i	1.77225	−	0.527293i
$768$		0			0
$769$	−0.244139	+	0.244139i	−0.00880389	+	0.00880389i	−0.711495	−	0.702691i	$-0.751982\pi$
$769$	−0.244139	+	0.244139i	−0.00880389	+	0.00880389i	0.702691	+	0.711495i	$0.251982\pi$
$770$	8.64382	−	12.5862i	0.311502	−	0.453574i
$771$		0			0
$772$	−13.9777			−0.503067
$773$			30.4846i			1.09646i	0.836329	+	0.548228i	$0.184697\pi$
$773$			30.4846i			1.09646i	−0.836329	+	0.548228i	$0.815303\pi$
$774$		0			0
$775$	30.4841	+	13.5471i	1.09502	+	0.486627i
$776$	3.23602			0.116166
$777$		0			0
$778$	23.2812			0.834673
$779$	−8.09871			−0.290166
$780$		0			0
$781$	−39.2003			−1.40270
$782$	0.909659			0.0325293
$783$		0			0
$784$	−5.36946			−0.191766
$785$	2.89947	+	1.99127i	0.103486	+	0.0710715i
$786$		0			0
$787$			7.63189i			0.272047i	0.990706	+	0.136024i	$0.0434323\pi$
$787$			7.63189i			0.272047i	−0.990706	+	0.136024i	$0.956568\pi$
$788$	−21.0697			−0.750578
$789$		0			0
$790$	0.911276	−	0.169221i	0.0324218	−	0.00602063i
$791$	30.8201	−	30.8201i	1.09583	−	1.09583i
$792$		0			0
$793$	6.46111	−	11.9342i	0.229441	−	0.423796i
$794$		−	20.9510i		−	0.743522i
$795$		0			0
$796$	−30.0261			−1.06425
$797$	22.9940	+	22.9940i	0.814490	+	0.814490i	0.985303	−	0.170813i	$-0.0546394\pi$
$797$	22.9940	+	22.9940i	0.814490	+	0.814490i	−0.170813	+	0.985303i	$0.554639\pi$
$798$		0			0
$799$	−2.66287	+	2.66287i	−0.0942057	+	0.0942057i
$800$	27.2382	−	10.4774i	0.963017	−	0.370432i
$801$		0			0
$802$	6.98904	−	6.98904i	0.246792	−	0.246792i
$803$	6.12541	−	6.12541i	0.216161	−	0.216161i
$804$		0			0
$805$	14.9802	−	21.8125i	0.527982	−	0.768789i
$806$	16.3629	−	4.86840i	0.576359	−	0.171482i
$807$		0			0
$808$		−	19.1099i		−	0.672283i
$809$			41.9671i			1.47549i	0.675082	+	0.737743i	$0.264108\pi$
$809$			41.9671i			1.47549i	−0.675082	+	0.737743i	$0.735892\pi$
$810$		0			0
$811$	0.246736	+	0.246736i	0.00866406	+	0.00866406i	0.711426	−	0.702761i	$-0.248050\pi$
$811$	0.246736	+	0.246736i	0.00866406	+	0.00866406i	−0.702761	+	0.711426i	$0.748050\pi$
$812$	−16.5008			−0.579065
$813$		0			0
$814$	−3.72968	−	3.72968i	−0.130725	−	0.130725i
$815$	4.52578	+	24.3718i	0.158531	+	0.853708i
$816$		0			0
$817$		−	80.0568i		−	2.80083i
$818$	10.7901	−	10.7901i	0.377267	−	0.377267i
$819$		0			0
$820$	2.21468	−	3.22478i	0.0773401	−	0.112614i
$821$	−11.2528	−	11.2528i	−0.392726	−	0.392726i	0.482932	−	0.875658i	$-0.339572\pi$
$821$	−11.2528	−	11.2528i	−0.392726	−	0.392726i	−0.875658	+	0.482932i	$0.839572\pi$
$822$		0			0
$823$	−24.5480	+	24.5480i	−0.855689	+	0.855689i	−0.990827	−	0.135138i	$-0.956852\pi$
$823$	−24.5480	+	24.5480i	−0.855689	+	0.855689i	0.135138	+	0.990827i	$0.456852\pi$
$824$	−1.89329	+	1.89329i	−0.0659559	+	0.0659559i
$825$		0			0
$826$	24.0215	−	24.0215i	0.835814	−	0.835814i
$827$			6.83411i			0.237645i	0.992915	+	0.118823i	$0.0379120\pi$
$827$			6.83411i			0.237645i	−0.992915	+	0.118823i	$0.962088\pi$
$828$		0			0
$829$	21.4950			0.746551			0.373276	−	0.927720i	$-0.378235\pi$
$829$	21.4950			0.746551			0.373276	+	0.927720i	$0.378235\pi$
$830$	14.0013	−	2.60000i	0.485991	−	0.0902472i
$831$		0			0
$832$	2.88190	−	5.32311i	0.0999120	−	0.184546i
$833$	1.12529	+	1.12529i	0.0389891	+	0.0389891i
$834$		0			0
$835$	43.6466	−	8.10505i	1.51045	−	0.280487i
$836$		−	29.5888i		−	1.02335i
$837$		0			0
$838$		−	2.69581i		−	0.0931252i
$839$	21.2069	+	21.2069i	0.732144	+	0.732144i	0.971044	−	0.238900i	$-0.0767868\pi$
$839$	21.2069	+	21.2069i	0.732144	+	0.732144i	−0.238900	+	0.971044i	$0.576787\pi$
$840$		0			0
$841$	18.2947			0.630853
$842$	18.4538	+	18.4538i	0.635959	+	0.635959i
$843$		0			0
$844$	25.9549			0.893404
$845$	−21.0305	+	20.0678i	−0.723472	+	0.690354i
$846$		0			0
$847$	−9.60695			−0.330099
$848$	−2.57192	−	2.57192i	−0.0883200	−	0.0883200i
$849$		0			0
$850$	−1.18376	−	0.526064i	−0.0406028	−	0.0180439i
$851$	−6.46374	−	6.46374i	−0.221574	−	0.221574i
$852$		0			0
$853$	−22.7972			−0.780562			−0.390281	−	0.920696i	$-0.627622\pi$
$853$	−22.7972			−0.780562			−0.390281	+	0.920696i	$0.627622\pi$
$854$		−	9.00292i		−	0.308074i
$855$		0			0
$856$	−13.3894	+	13.3894i	−0.457642	+	0.457642i
$857$	−2.25877	−	2.25877i	−0.0771581	−	0.0771581i	0.667475	−	0.744633i	$-0.267375\pi$
$857$	−2.25877	−	2.25877i	−0.0771581	−	0.0771581i	−0.744633	+	0.667475i	$0.767375\pi$
$858$		0			0
$859$			2.55625i			0.0872180i	0.999049	+	0.0436090i	$0.0138856\pi$
$859$			2.55625i			0.0872180i	−0.999049	+	0.0436090i	$0.986114\pi$
$860$	31.8773	+	21.8924i	1.08701	+	0.746526i
$861$		0			0
$862$	−10.3863	−	10.3863i	−0.353757	−	0.353757i
$863$		−	21.1105i		−	0.718611i	−0.933220	−	0.359305i	$-0.883014\pi$
$863$		−	21.1105i		−	0.718611i	0.933220	−	0.359305i	$-0.116986\pi$
$864$		0			0
$865$	−25.7567	−	17.6890i	−0.875755	−	0.601444i
$866$	9.71353	−	9.71353i	0.330079	−	0.330079i
$867$		0			0
$868$	−23.7920	+	23.7920i	−0.807553	+	0.807553i
$869$	1.17899	+	1.17899i	0.0399946	+	0.0399946i
$870$		0			0
$871$	9.73201	−	17.9758i	0.329756	−	0.609088i
$872$	−35.2579	+	35.2579i	−1.19398	+	1.19398i
$873$		0			0
$874$			17.2601i			0.583833i
$875$	−32.1085	+	19.7220i	−1.08547	+	0.666726i
$876$		0			0
$877$	9.92888			0.335274			0.167637	−	0.985849i	$-0.446386\pi$
$877$	9.92888			0.335274			0.167637	+	0.985849i	$0.446386\pi$
$878$	−11.8462			−0.399788
$879$		0			0
$880$	6.48130	+	4.45117i	0.218484	+	0.150049i
$881$		−	38.3675i		−	1.29263i	−0.763069	−	0.646317i	$-0.776308\pi$
$881$		−	38.3675i		−	1.29263i	0.763069	−	0.646317i	$-0.223692\pi$
$882$		0			0
$883$	19.6819	−	19.6819i	0.662347	−	0.662347i	−0.293586	−	0.955933i	$-0.594849\pi$
$883$	19.6819	−	19.6819i	0.662347	−	0.662347i	0.955933	+	0.293586i	$0.0948486\pi$
$884$	1.88776	−	0.561660i	0.0634923	−	0.0188907i
$885$		0			0
$886$	9.12392	+	9.12392i	0.306524	+	0.306524i
$887$	22.3933	−	22.3933i	0.751894	−	0.751894i	−0.222938	−	0.974833i	$-0.571565\pi$
$887$	22.3933	−	22.3933i	0.751894	−	0.751894i	0.974833	+	0.222938i	$0.0715648\pi$
$888$		0			0
$889$	47.7553	−	47.7553i	1.60166	−	1.60166i
$890$	−4.00908	+	5.83758i	−0.134385	+	0.195676i
$891$		0			0
$892$			13.3726i			0.447749i
$893$	−50.5262	−	50.5262i	−1.69079	−	1.69079i
$894$		0			0
$895$	−1.95311	−	10.5177i	−0.0652854	−	0.351569i
$896$			35.3284i			1.18024i
$897$		0			0
$898$	−3.50719	−	3.50719i	−0.117037	−	0.117037i
$899$	−15.4356	+	15.4356i	−0.514805	+	0.514805i
$900$		0			0
$901$			1.07801i			0.0359137i
$902$	−2.36877			−0.0788713
$903$		0			0
$904$	−22.6902	−	22.6902i	−0.754666	−	0.754666i
$905$	7.91569	−	1.46992i	0.263127	−	0.0488618i
$906$		0			0
$907$	−8.61904	−	8.61904i	−0.286191	−	0.286191i	0.549381	−	0.835572i	$-0.314863\pi$
$907$	−8.61904	−	8.61904i	−0.286191	−	0.286191i	−0.835572	+	0.549381i	$0.814863\pi$
$908$	−32.1197			−1.06593
$909$		0			0
$910$	−5.93064	+	18.3496i	−0.196599	+	0.608282i
$911$	17.0310			0.564263			0.282131	−	0.959376i	$-0.408959\pi$
$911$	17.0310			0.564263			0.282131	+	0.959376i	$0.408959\pi$
$912$		0			0
$913$	18.1146	+	18.1146i	0.599506	+	0.599506i
$914$	19.9020			0.658300
$915$		0			0
$916$	3.15088	+	3.15088i	0.104108	+	0.104108i
$917$			12.8006i			0.422712i
$918$		0			0
$919$			6.49512i			0.214254i	0.994245	+	0.107127i	$0.0341652\pi$
$919$			6.49512i			0.214254i	−0.994245	+	0.107127i	$0.965835\pi$
$920$	−16.0587	−	11.0287i	−0.529441	−	0.363605i
$921$		0			0
$922$	8.20563	+	8.20563i	0.270238	+	0.270238i
$923$	47.4543	−	14.1189i	1.56198	−	0.464730i
$924$		0			0
$925$	4.67340	+	12.1495i	0.153660	+	0.399472i
$926$	−13.9493			−0.458403
$927$		0			0
$928$			19.0973i			0.626898i
$929$	−14.5250	+	14.5250i	−0.476550	+	0.476550i	−0.904027	−	0.427476i	$-0.859403\pi$
$929$	−14.5250	+	14.5250i	−0.476550	+	0.476550i	0.427476	+	0.904027i	$0.359403\pi$
$930$		0			0
$931$	−21.3517	+	21.3517i	−0.699773	+	0.699773i
$932$	−19.2575	+	19.2575i	−0.630801	+	0.630801i
$933$		0			0
$934$	−2.53780	−	2.53780i	−0.0830394	−	0.0830394i
$935$	−0.425460	−	2.29115i	−0.0139140	−	0.0749287i
$936$		0			0
$937$	−25.7347	+	25.7347i	−0.840717	+	0.840717i	−0.988952	−	0.148235i	$-0.952641\pi$
$937$	−25.7347	+	25.7347i	−0.840717	+	0.840717i	0.148235	+	0.988952i	$0.452641\pi$
$938$		−	13.5606i		−	0.442769i
$939$		0			0
$940$	33.9357	−	6.30175i	1.10686	−	0.205541i
$941$	−15.0385	−	15.0385i	−0.490240	−	0.490240i	0.418142	−	0.908382i	$-0.362682\pi$
$941$	−15.0385	−	15.0385i	−0.490240	−	0.490240i	−0.908382	+	0.418142i	$0.862682\pi$
$942$		0			0
$943$	−4.10520			−0.133684
$944$	12.3700	+	12.3700i	0.402608	+	0.402608i
$945$		0			0
$946$		−	23.4156i		−	0.761306i
$947$		−	13.6176i		−	0.442513i	−0.975216	−	0.221257i	$-0.928984\pi$
$947$		−	13.6176i		−	0.442513i	0.975216	−	0.221257i	$-0.0710158\pi$
$948$		0			0
$949$	−5.20895	+	9.62138i	−0.169090	+	0.312323i
$950$	9.98170	−	22.4611i	0.323849	−	0.728734i
$951$		0			0
$952$	2.15877	−	2.15877i	0.0699661	−	0.0699661i
$953$	−14.0740	+	14.0740i	−0.455903	+	0.455903i	−0.897308	−	0.441405i	$-0.854480\pi$
$953$	−14.0740	+	14.0740i	−0.455903	+	0.455903i	0.441405	+	0.897308i	$0.354480\pi$
$954$		0			0
$955$	−1.68582	−	9.07836i	−0.0545520	−	0.293769i
$956$	12.7444	−	12.7444i	0.412184	−	0.412184i
$957$		0			0
$958$	12.7053	+	12.7053i	0.410490	+	0.410490i
$959$	8.00847			0.258607
$960$		0			0
$961$			13.5121i			0.435876i
$962$	5.85833	+	3.17166i	0.188880	+	0.102259i
$963$		0			0
$964$	2.94332	−	2.94332i	0.0947978	−	0.0947978i
$965$	−3.81357	−	20.5365i	−0.122763	−	0.661094i
$966$		0			0
$967$	0.391119			0.0125775			0.00628877	−	0.999980i	$-0.497998\pi$
$967$	0.391119			0.0125775			0.00628877	+	0.999980i	$0.497998\pi$
$968$			7.07280i			0.227328i
$969$		0			0
$970$	0.377855	+	2.03479i	0.0121322	+	0.0653333i
$971$	−6.47482			−0.207787			−0.103893	−	0.994588i	$-0.533130\pi$
$971$	−6.47482			−0.207787			−0.103893	+	0.994588i	$0.533130\pi$
$972$		0			0
$973$	14.0248			0.449615
$974$	−19.0561			−0.610596
$975$		0			0
$976$	4.63609			0.148398
$977$	8.42709			0.269606			0.134803	−	0.990872i	$-0.456960\pi$
$977$	8.42709			0.269606			0.134803	+	0.990872i	$0.456960\pi$
$978$		0			0
$979$	−12.7394			−0.407154
$980$	−2.66304	−	14.3408i	−0.0850676	−	0.458099i
$981$		0			0
$982$			2.61269i			0.0833743i
$983$	53.4163			1.70372			0.851858	−	0.523773i	$-0.175476\pi$
$983$	53.4163			1.70372			0.851858	+	0.523773i	$0.175476\pi$
$984$		0			0
$985$	−5.74853	−	30.9565i	−0.183163	−	0.986356i
$986$	0.599397	−	0.599397i	0.0190887	−	0.0190887i
$987$		0			0
$988$	10.6571	+	35.8190i	0.339048	+	1.13955i
$989$		−	40.5804i		−	1.29038i
$990$		0			0
$991$	14.5093			0.460903			0.230451	−	0.973084i	$-0.425980\pi$
$991$	14.5093			0.460903			0.230451	+	0.973084i	$0.425980\pi$
$992$	27.5357	+	27.5357i	0.874261	+	0.874261i
$993$		0			0
$994$	23.2248	−	23.2248i	0.736645	−	0.736645i
$995$	−8.19214	−	44.1156i	−0.259708	−	1.39856i
$996$		0			0
$997$	−4.06604	+	4.06604i	−0.128773	+	0.128773i	−0.768556	−	0.639783i	$-0.779024\pi$
$997$	−4.06604	+	4.06604i	−0.128773	+	0.128773i	0.639783	+	0.768556i	$0.279024\pi$
$998$	19.5068	−	19.5068i	0.617477	−	0.617477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.w.g.73.6		28
3.2	odd	2		195.2.t.a.73.9	yes	28
5.2	odd	4		585.2.n.g.307.6		28
13.5	odd	4		585.2.n.g.343.9		28
15.2	even	4		195.2.k.a.112.9	✓	28
15.8	even	4		975.2.k.d.307.6		28
15.14	odd	2		975.2.t.d.268.6		28
39.5	even	4		195.2.k.a.148.6	yes	28
65.57	even	4	inner	585.2.w.g.577.6		28
195.44	even	4		975.2.k.d.343.9		28
195.83	odd	4		975.2.t.d.382.6		28
195.122	odd	4		195.2.t.a.187.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.9	✓	28	15.2	even	4
195.2.k.a.148.6	yes	28	39.5	even	4
195.2.t.a.73.9	yes	28	3.2	odd	2
195.2.t.a.187.9	yes	28	195.122	odd	4
585.2.n.g.307.6		28	5.2	odd	4
585.2.n.g.343.9		28	13.5	odd	4
585.2.w.g.73.6		28	1.1	even	1	trivial
585.2.w.g.577.6		28	65.57	even	4	inner
975.2.k.d.307.6		28	15.8	even	4
975.2.k.d.343.9		28	195.44	even	4
975.2.t.d.268.6		28	15.14	odd	2
975.2.t.d.382.6		28	195.83	odd	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.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.709689 q^{2} -1.49634 q^{4} +(-0.408252 - 2.19848i) q^{5} +3.37036i q^{7} +2.48132 q^{8} +O(q^{10})\)	\(q-0.709689 q^{2} -1.49634 q^{4} +(-0.408252 - 2.19848i) q^{5} +3.37036i q^{7} +2.48132 q^{8} +(0.289732 + 1.56024i) q^{10} +(-2.01861 + 2.01861i) q^{11} +(1.71659 - 3.17069i) q^{13} -2.39191i q^{14} +1.23172 q^{16} +(-0.258136 - 0.258136i) q^{17} +(4.89795 - 4.89795i) q^{19} +(0.610884 + 3.28968i) q^{20} +(1.43259 - 1.43259i) q^{22} +(2.48275 - 2.48275i) q^{23} +(-4.66666 + 1.79507i) q^{25} +(-1.21825 + 2.25021i) q^{26} -5.04321i q^{28} -3.27189i q^{29} +(-4.71763 - 4.71763i) q^{31} -5.83677 q^{32} +(0.183196 + 0.183196i) q^{34} +(7.40968 - 1.37596i) q^{35} -2.60346i q^{37} +(-3.47602 + 3.47602i) q^{38} +(-1.01300 - 5.45513i) q^{40} +(-0.826745 - 0.826745i) q^{41} +(8.17249 - 8.17249i) q^{43} +(3.02053 - 3.02053i) q^{44} +(-1.76198 + 1.76198i) q^{46} -10.3158i q^{47} -4.35931 q^{49} +(3.31188 - 1.27394i) q^{50} +(-2.56861 + 4.74444i) q^{52} +(-2.08807 - 2.08807i) q^{53} +(5.26198 + 3.61378i) q^{55} +8.36292i q^{56} +2.32202i q^{58} +(10.0428 + 10.0428i) q^{59} +3.76391 q^{61} +(3.34805 + 3.34805i) q^{62} +1.67885 q^{64} +(-7.67152 - 2.47946i) q^{65} +5.66937 q^{67} +(0.386259 + 0.386259i) q^{68} +(-5.25857 + 0.976500i) q^{70} +(9.70973 + 9.70973i) q^{71} -3.03447 q^{73} +1.84765i q^{74} +(-7.32900 + 7.32900i) q^{76} +(-6.80344 - 6.80344i) q^{77} -0.584062i q^{79} +(-0.502853 - 2.70792i) q^{80} +(0.586732 + 0.586732i) q^{82} -8.97380i q^{83} +(-0.462123 + 0.672892i) q^{85} +(-5.79993 + 5.79993i) q^{86} +(-5.00881 + 5.00881i) q^{88} +(3.15550 + 3.15550i) q^{89} +(10.6864 + 5.78554i) q^{91} +(-3.71504 + 3.71504i) q^{92} +7.32100i q^{94} +(-12.7677 - 8.76846i) q^{95} +1.30416 q^{97} +3.09376 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8	\( 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 28 q^{16} - 28 q^{17} - 12 q^{20} - 32 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{31} + 68 q^{32} - 28 q^{34} - 48 q^{40} - 4 q^{41} + 40 q^{44} - 16 q^{46} + 28 q^{49} - 4 q^{50} + 48 q^{52} - 20 q^{53} - 8 q^{55} + 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} - 64 q^{65} + 32 q^{67} - 60 q^{68} - 16 q^{70} - 40 q^{71} + 56 q^{73} - 40 q^{76} - 48 q^{77} + 12 q^{80} - 4 q^{82} + 44 q^{85} - 16 q^{86} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 56 q^{95} + 48 q^{97} + 12 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8 + 8 * q^11 + 28 * q^16 - 28 * q^17 - 12 * q^20 - 32 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^31 + 68 * q^32 - 28 * q^34 - 48 * q^40 - 4 * q^41 + 40 * q^44 - 16 * q^46 + 28 * q^49 - 4 * q^50 + 48 * q^52 - 20 * q^53 - 8 * q^55 + 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 - 64 * q^65 + 32 * q^67 - 60 * q^68 - 16 * q^70 - 40 * q^71 + 56 * q^73 - 40 * q^76 - 48 * q^77 + 12 * q^80 - 4 * q^82 + 44 * q^85 - 16 * q^86 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 56 * q^95 + 48 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more