LMFDB - Embedded newform 572.2.bq.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	572.49
Dual form			572.2.bq.a.537.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.319495 + 3.03979i) q^{3} +(-0.103194 - 0.0335297i) q^{5} +(4.65033 - 0.488770i) q^{7} +(-6.20380 - 1.31866i) q^{9} +O(q^{10})$	\(q+(-0.319495 + 3.03979i) q^{3} +(-0.103194 - 0.0335297i) q^{5} +(4.65033 - 0.488770i) q^{7} +(-6.20380 - 1.31866i) q^{9} +(2.84700 + 1.70135i) q^{11} +(2.37321 + 2.71438i) q^{13} +(0.134893 - 0.302975i) q^{15} +(3.88546 + 4.31524i) q^{17} +(-0.749938 - 1.68439i) q^{19} +14.2922i q^{21} +(-2.31370 - 4.00744i) q^{23} +(-4.03556 - 2.93201i) q^{25} +(3.15696 - 9.71612i) q^{27} +(-3.73204 - 1.66161i) q^{29} +(-6.05525 + 1.96747i) q^{31} +(-6.08136 + 8.11070i) q^{33} +(-0.496274 - 0.105486i) q^{35} +(1.60471 - 3.60424i) q^{37} +(-9.00938 + 6.34682i) q^{39} +(-5.20171 - 0.546721i) q^{41} +(5.15808 - 8.93406i) q^{43} +(0.595979 + 0.344089i) q^{45} +(-5.21866 + 7.18287i) q^{47} +(14.5397 - 3.09051i) q^{49} +(-14.3588 + 10.4323i) q^{51} +(2.48490 + 7.64774i) q^{53} +(-0.236747 - 0.271028i) q^{55} +(5.35978 - 1.74150i) q^{57} +(-2.65390 + 0.278937i) q^{59} +(1.01171 + 1.12362i) q^{61} +(-29.4942 - 3.09997i) q^{63} +(-0.153888 - 0.359681i) q^{65} +(6.56569 - 3.79070i) q^{67} +(12.9210 - 5.75280i) q^{69} +(-3.01910 + 2.71841i) q^{71} +(0.708385 + 0.975009i) q^{73} +(10.2020 - 11.3305i) q^{75} +(14.0711 + 6.52034i) q^{77} +(-3.29747 - 10.1486i) q^{79} +(11.1441 + 4.96168i) q^{81} +(11.1145 + 3.61131i) q^{83} +(-0.256267 - 0.575585i) q^{85} +(6.24331 - 10.8137i) q^{87} +(9.83124 - 5.67607i) q^{89} +(12.3629 + 11.4628i) q^{91} +(-4.04607 - 19.0353i) q^{93} +(0.0209119 + 0.198964i) q^{95} +(0.934294 - 4.39551i) q^{97} +(-15.4187 - 14.3091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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			0
$2$		0			0
$3$	−0.319495	+	3.03979i	−0.184460	+	1.75502i	0.375795	+	0.926703i	$0.377370\pi$
$3$	−0.319495	+	3.03979i	−0.184460	+	1.75502i	−0.560255	+	0.828320i	$0.689297\pi$
$4$		0			0
$5$	−0.103194	−	0.0335297i	−0.0461497	−	0.0149949i	0.285851	−	0.958274i	$-0.407724\pi$
$5$	−0.103194	−	0.0335297i	−0.0461497	−	0.0149949i	−0.332001	+	0.943279i	$0.607724\pi$
$6$		0			0
$7$	4.65033	−	0.488770i	1.75766	−	0.184738i	0.829900	−	0.557912i	$-0.188397\pi$
$7$	4.65033	−	0.488770i	1.75766	−	0.184738i	0.927761	+	0.373174i	$0.121731\pi$
$8$		0			0
$9$	−6.20380	−	1.31866i	−2.06793	−	0.439552i
$10$		0			0
$11$	2.84700	+	1.70135i	0.858402	+	0.512978i
$11$	2.84700	+	1.70135i	0.858402	+	0.512978i
$12$		0			0
$13$	2.37321	+	2.71438i	0.658209	+	0.752835i
$13$	2.37321	+	2.71438i	0.658209	+	0.752835i
$14$		0			0
$15$	0.134893	−	0.302975i	0.0348293	−	0.0782278i
$16$		0			0
$17$	3.88546	+	4.31524i	0.942363	+	1.04660i	0.998838	+	0.0481962i	$0.0153473\pi$
$17$	3.88546	+	4.31524i	0.942363	+	1.04660i	−0.0564748	+	0.998404i	$0.517986\pi$
$18$		0			0
$19$	−0.749938	−	1.68439i	−0.172047	−	0.386425i	0.806856	−	0.590748i	$-0.201167\pi$
$19$	−0.749938	−	1.68439i	−0.172047	−	0.386425i	−0.978903	+	0.204323i	$0.934501\pi$
$20$		0			0
$21$			14.2922i			3.11881i
$22$		0			0
$23$	−2.31370	−	4.00744i	−0.482439	−	0.835610i	0.517357	−	0.855769i	$-0.326916\pi$
$23$	−2.31370	−	4.00744i	−0.482439	−	0.835610i	−0.999797	+	0.0201599i	$0.993582\pi$
$24$		0			0
$25$	−4.03556	−	2.93201i	−0.807112	−	0.586401i
$26$		0			0
$27$	3.15696	−	9.71612i	0.607557	−	1.86987i
$28$		0			0
$29$	−3.73204	−	1.66161i	−0.693022	−	0.308553i	0.0298311	−	0.999555i	$-0.490503\pi$
$29$	−3.73204	−	1.66161i	−0.693022	−	0.308553i	−0.722853	+	0.691002i	$0.757170\pi$
$30$		0			0
$31$	−6.05525	+	1.96747i	−1.08755	+	0.353368i	−0.797301	−	0.603582i	$-0.793740\pi$
$31$	−6.05525	+	1.96747i	−1.08755	+	0.353368i	−0.290254	+	0.956950i	$0.593740\pi$
$32$		0			0
$33$	−6.08136	+	8.11070i	−1.05863	+	1.41189i
$34$		0			0
$35$	−0.496274	−	0.105486i	−0.0838857	−	0.0178305i
$36$		0			0
$37$	1.60471	−	3.60424i	0.263813	−	0.592533i	−0.732265	−	0.681020i	$-0.761537\pi$
$37$	1.60471	−	3.60424i	0.263813	−	0.592533i	0.996077	+	0.0884872i	$0.0282032\pi$
$38$		0			0
$39$	−9.00938	+	6.34682i	−1.44266	+	1.01630i
$40$		0			0
$41$	−5.20171	−	0.546721i	−0.812370	−	0.0853835i	−0.310772	−	0.950484i	$-0.600588\pi$
$41$	−5.20171	−	0.546721i	−0.812370	−	0.0853835i	−0.501598	+	0.865101i	$0.667254\pi$
$42$		0			0
$43$	5.15808	−	8.93406i	0.786600	−	1.36243i	−0.141438	−	0.989947i	$-0.545173\pi$
$43$	5.15808	−	8.93406i	0.786600	−	1.36243i	0.928038	−	0.372485i	$-0.121494\pi$
$44$		0			0
$45$	0.595979	+	0.344089i	0.0888434	+	0.0512937i
$46$		0			0
$47$	−5.21866	+	7.18287i	−0.761220	+	1.04773i	0.235891	+	0.971779i	$0.424199\pi$
$47$	−5.21866	+	7.18287i	−0.761220	+	1.04773i	−0.997112	+	0.0759504i	$0.975801\pi$
$48$		0			0
$49$	14.5397	−	3.09051i	2.07710	−	0.441501i
$50$		0			0
$51$	−14.3588	+	10.4323i	−2.01064	+	1.46081i
$52$		0			0
$53$	2.48490	+	7.64774i	0.341327	+	1.05050i	0.963521	+	0.267634i	$0.0862418\pi$
$53$	2.48490	+	7.64774i	0.341327	+	1.05050i	−0.622193	+	0.782864i	$0.713758\pi$
$54$		0			0
$55$	−0.236747	−	0.271028i	−0.0319229	−	0.0365455i
$56$		0			0
$57$	5.35978	−	1.74150i	0.709921	−	0.230667i
$58$		0			0
$59$	−2.65390	+	0.278937i	−0.345509	+	0.0363144i	−0.275694	−	0.961246i	$-0.588908\pi$
$59$	−2.65390	+	0.278937i	−0.345509	+	0.0363144i	−0.0698151	+	0.997560i	$0.522241\pi$
$60$		0			0
$61$	1.01171	+	1.12362i	0.129536	+	0.143864i	0.804423	−	0.594057i	$-0.202474\pi$
$61$	1.01171	+	1.12362i	0.129536	+	0.143864i	−0.674887	+	0.737921i	$0.735808\pi$
$62$		0			0
$63$	−29.4942	−	3.09997i	−3.71593	−	0.390560i
$64$		0			0
$65$	−0.153888	−	0.359681i	−0.0190874	−	0.0446129i
$66$		0			0
$67$	6.56569	−	3.79070i	0.802127	−	0.463108i	−0.0420875	−	0.999114i	$-0.513401\pi$
$67$	6.56569	−	3.79070i	0.802127	−	0.463108i	0.844214	+	0.536006i	$0.180067\pi$
$68$		0			0
$69$	12.9210	−	5.75280i	1.55550	−	0.692555i
$70$		0			0
$71$	−3.01910	+	2.71841i	−0.358302	+	0.322616i	−0.828547	−	0.559919i	$-0.810832\pi$
$71$	−3.01910	+	2.71841i	−0.358302	+	0.322616i	0.470245	+	0.882536i	$0.344165\pi$
$72$		0			0
$73$	0.708385	+	0.975009i	0.0829102	+	0.114116i	0.848458	−	0.529263i	$-0.177532\pi$
$73$	0.708385	+	0.975009i	0.0829102	+	0.114116i	−0.765547	+	0.643380i	$0.777532\pi$
$74$		0			0
$75$	10.2020	−	11.3305i	1.17803	−	1.30833i
$76$		0			0
$77$	14.0711	+	6.52034i	1.60355	+	0.743062i
$78$		0			0
$79$	−3.29747	−	10.1486i	−0.370995	−	1.14180i	−0.946141	−	0.323754i	$-0.895055\pi$
$79$	−3.29747	−	10.1486i	−0.370995	−	1.14180i	0.575147	−	0.818050i	$-0.304945\pi$
$80$		0			0
$81$	11.1441	+	4.96168i	1.23824	+	0.551298i
$82$		0			0
$83$	11.1145	+	3.61131i	1.21997	+	0.396393i	0.847072	−	0.531478i	$-0.178363\pi$
$83$	11.1145	+	3.61131i	1.21997	+	0.396393i	0.372901	+	0.927871i	$0.378363\pi$
$84$		0			0
$85$	−0.256267	−	0.575585i	−0.0277961	−	0.0624310i
$86$		0			0
$87$	6.24331	−	10.8137i	0.669353	−	1.15935i
$88$		0			0
$89$	9.83124	−	5.67607i	1.04211	−	0.601662i	0.121680	−	0.992569i	$-0.461172\pi$
$89$	9.83124	−	5.67607i	1.04211	−	0.601662i	0.920430	+	0.390907i	$0.127839\pi$
$90$		0			0
$91$	12.3629	+	11.4628i	1.29599	+	1.20163i
$92$		0			0
$93$	−4.04607	−	19.0353i	−0.419558	−	1.97387i
$94$		0			0
$95$	0.0209119	+	0.198964i	0.00214552	+	0.0204132i
$96$		0			0
$97$	0.934294	−	4.39551i	0.0948632	−	0.446296i	−0.904922	−	0.425577i	$-0.860071\pi$
$97$	0.934294	−	4.39551i	0.0948632	−	0.446296i	0.999785	−	0.0207190i	$-0.00659553\pi$
$98$		0			0
$99$	−15.4187	−	14.3091i	−1.54964	−	1.43812i
$100$		0			0
$101$	−2.20366	+	2.44741i	−0.219272	+	0.243526i	−0.842738	−	0.538325i	$-0.819057\pi$
$101$	−2.20366	+	2.44741i	−0.219272	+	0.243526i	0.623466	+	0.781851i	$0.285724\pi$
$102$		0			0
$103$	−6.15032	+	4.46847i	−0.606009	+	0.440291i	−0.848007	−	0.529986i	$-0.822197\pi$
$103$	−6.15032	+	4.46847i	−0.606009	+	0.440291i	0.241998	+	0.970277i	$0.422197\pi$
$104$		0			0
$105$	0.479213	−	1.47487i	0.0467664	−	0.143932i
$106$		0			0
$107$	1.74279	−	16.5815i	0.168481	−	1.60299i	−0.504552	−	0.863382i	$-0.668342\pi$
$107$	1.74279	−	16.5815i	0.168481	−	1.60299i	0.673033	−	0.739612i	$-0.264991\pi$
$108$		0			0
$109$			9.49057i			0.909032i	0.890739	+	0.454516i	$0.150188\pi$
$109$			9.49057i			0.909032i	−0.890739	+	0.454516i	$0.849812\pi$
$110$		0			0
$111$	10.4434	+	6.02951i	0.991246	+	0.572296i
$112$		0			0
$113$	−14.8822	+	6.62598i	−1.40000	+	0.623320i	−0.961348	−	0.275338i	$-0.911210\pi$
$113$	−14.8822	+	6.62598i	−1.40000	+	0.623320i	−0.438651	+	0.898657i	$0.644544\pi$
$114$		0			0
$115$	0.104391	+	0.491121i	0.00973451	+	0.0457973i
$116$		0			0
$117$	−11.1436	−	19.9689i	−1.03022	−	1.84613i
$118$		0			0
$119$	20.1779	+	18.1682i	1.84970	+	1.66548i
$120$		0			0
$121$	5.21079	+	9.68750i	0.473708	+	0.880682i
$122$		0			0
$123$	3.32383	−	15.6374i	0.299700	−	1.40998i
$124$		0			0
$125$	0.637022	+	0.876786i	0.0569770	+	0.0784221i
$126$		0			0
$127$	−2.44674	+	0.520071i	−0.217113	+	0.0461488i	−0.315184	−	0.949031i	$-0.602066\pi$
$127$	−2.44674	+	0.520071i	−0.217113	+	0.0461488i	0.0980707	+	0.995179i	$0.468733\pi$
$128$		0			0
$129$	25.5097	+	18.5339i	2.24600	+	1.63182i
$130$		0			0
$131$	−1.58238			−0.138253			−0.0691264	−	0.997608i	$-0.522021\pi$
$131$	−1.58238			−0.138253			−0.0691264	+	0.997608i	$0.522021\pi$
$132$		0			0
$133$	−4.31074	−	7.46642i	−0.373788	−	0.647421i
$134$		0			0
$135$	−0.651557	+	0.896792i	−0.0560771	+	0.0771836i
$136$		0			0
$137$	2.10714	−	1.89728i	0.180025	−	0.162095i	−0.574191	−	0.818721i	$-0.694683\pi$
$137$	2.10714	−	1.89728i	0.180025	−	0.162095i	0.754217	+	0.656626i	$0.228017\pi$
$138$		0			0
$139$	1.02777	+	9.77858i	0.0871743	+	0.829408i	0.947520	+	0.319697i	$0.103581\pi$
$139$	1.02777	+	9.77858i	0.0871743	+	0.829408i	−0.860346	+	0.509711i	$0.829752\pi$
$140$		0			0
$141$	−20.1671	−	18.1585i	−1.69837	−	1.52922i
$142$		0			0
$143$	2.13839	+	11.7655i	0.178821	+	0.983882i
$144$		0			0
$145$	0.329410	+	0.296602i	0.0273560	+	0.0246315i
$146$		0			0
$147$	4.74913	+	45.1850i	0.391702	+	3.72679i
$148$		0			0
$149$	−3.33916	+	3.00659i	−0.273555	+	0.246310i	−0.794477	−	0.607294i	$-0.792255\pi$
$149$	−3.33916	+	3.00659i	−0.273555	+	0.246310i	0.520922	+	0.853604i	$0.325588\pi$
$150$		0			0
$151$	14.3783	−	19.7901i	1.17009	−	1.61049i	0.507028	−	0.861930i	$-0.330744\pi$
$151$	14.3783	−	19.7901i	1.17009	−	1.61049i	0.663064	−	0.748563i	$-0.269256\pi$
$152$		0			0
$153$	−18.4143	−	31.8945i	−1.48871	−	2.57852i
$154$		0			0
$155$	0.690833			0.0554891
$156$		0			0
$157$	7.68865	+	5.58613i	0.613621	+	0.445822i	0.850688	−	0.525672i	$-0.176186\pi$
$157$	7.68865	+	5.58613i	0.613621	+	0.445822i	−0.237067	+	0.971493i	$0.576186\pi$
$158$		0			0
$159$	−24.0414	+	5.11016i	−1.90661	+	0.405262i
$160$		0			0
$161$	−12.7182	−	17.5051i	−1.00233	−	1.37959i
$162$		0			0
$163$	4.99101	−	23.4809i	0.390926	−	1.83916i	−0.137917	−	0.990444i	$-0.544041\pi$
$163$	4.99101	−	23.4809i	0.390926	−	1.83916i	0.528844	−	0.848719i	$-0.322626\pi$
$164$		0			0
$165$	0.899508	−	0.633068i	0.0700266	−	0.0492843i
$166$		0			0
$167$	−13.5607	−	12.2101i	−1.04936	−	0.944847i	−0.0508105	−	0.998708i	$-0.516180\pi$
$167$	−13.5607	−	12.2101i	−1.04936	−	0.944847i	−0.998548	+	0.0538613i	$0.982847\pi$
$168$		0			0
$169$	−1.73577	+	12.8836i	−0.133521	+	0.991046i
$170$		0			0
$171$	2.43133	+	11.4385i	0.185928	+	0.874724i
$172$		0			0
$173$	1.31557	−	0.585731i	0.100021	−	0.0445323i	−0.356116	−	0.934442i	$-0.615899\pi$
$173$	1.31557	−	0.585731i	0.100021	−	0.0445323i	0.456137	+	0.889909i	$0.349233\pi$
$174$		0			0
$175$	−20.1998	−	11.6624i	−1.52696	−	0.881591i
$176$		0			0
$177$		−	8.15643i		−	0.613075i
$178$		0			0
$179$	0.172292	−	1.63925i	0.0128777	−	0.122523i	−0.986194	−	0.165591i	$-0.947047\pi$
$179$	0.172292	−	1.63925i	0.0128777	−	0.122523i	0.999072	+	0.0430685i	$0.0137134\pi$
$180$		0			0
$181$	4.67222	−	14.3796i	0.347283	−	1.06883i	−0.613067	−	0.790031i	$-0.710064\pi$
$181$	4.67222	−	14.3796i	0.347283	−	1.06883i	0.960350	−	0.278797i	$-0.0899356\pi$
$182$		0			0
$183$	−3.73879	+	2.71639i	−0.276379	+	0.200801i
$184$		0			0
$185$	−0.286445	+	0.318130i	−0.0210599	+	0.0233894i
$186$		0			0
$187$	3.72014	+	18.8960i	0.272044	+	1.38181i
$188$		0			0
$189$	9.93197	−	46.7262i	0.722444	−	3.39883i
$190$		0			0
$191$	−1.80896	−	17.2111i	−0.130892	−	1.24535i	−0.840911	−	0.541173i	$-0.817981\pi$
$191$	−1.80896	−	17.2111i	−0.130892	−	1.24535i	0.710019	−	0.704182i	$-0.248686\pi$
$192$		0			0
$193$	0.155609	+	0.732081i	0.0112009	+	0.0526963i	0.983393	−	0.181488i	$-0.0580914\pi$
$193$	0.155609	+	0.732081i	0.0112009	+	0.0526963i	−0.972192	+	0.234184i	$0.924758\pi$
$194$		0			0
$195$	1.14252	−	0.352871i	0.0818176	−	0.0252696i
$196$		0			0
$197$	10.6011	−	6.12057i	0.755300	−	0.436072i	−0.0723060	−	0.997382i	$-0.523036\pi$
$197$	10.6011	−	6.12057i	0.755300	−	0.436072i	0.827606	+	0.561310i	$0.189702\pi$
$198$		0			0
$199$	12.2203	−	21.1662i	0.866274	−	1.50043i	0.000496637	−	1.00000i	$-0.499842\pi$
$199$	12.2203	−	21.1662i	0.866274	−	1.50043i	0.865777	−	0.500430i	$-0.166825\pi$
$200$		0			0
$201$	9.42523	+	21.1694i	0.664805	+	1.49318i
$202$		0			0
$203$	−18.1674	−	5.90294i	−1.27510	−	0.414305i
$204$		0			0
$205$	0.518453	+	0.230830i	0.0362103	+	0.0161219i
$206$		0			0
$207$	9.06927	+	27.9123i	0.630358	+	1.94004i
$208$		0			0
$209$	0.730670	−	6.07136i	0.0505415	−	0.419964i
$210$		0			0
$211$	−2.00323	+	2.22481i	−0.137908	+	0.153162i	−0.808142	−	0.588987i	$-0.799527\pi$
$211$	−2.00323	+	2.22481i	−0.137908	+	0.153162i	0.670234	+	0.742149i	$0.266194\pi$
$212$		0			0
$213$	−7.29881	−	10.0460i	−0.500106	−	0.688337i
$214$		0			0
$215$	−0.831839	+	0.748991i	−0.0567310	+	0.0510808i
$216$		0			0
$217$	−27.1973	+	12.1090i	−1.84627	+	0.822014i
$218$		0			0
$219$	−3.19015	+	1.84183i	−0.215570	+	0.124459i
$220$		0			0
$221$	−2.49222	+	20.7876i	−0.167645	+	1.39833i
$222$		0			0
$223$	−13.7197	−	1.44200i	−0.918741	−	0.0965635i	−0.366661	−	0.930355i	$-0.619499\pi$
$223$	−13.7197	−	1.44200i	−0.918741	−	0.0965635i	−0.552080	+	0.833791i	$0.686166\pi$
$224$		0			0
$225$	21.1695	+	23.5111i	1.41130	+	1.56741i
$226$		0			0
$227$	−16.1323	+	1.69557i	−1.07074	+	0.112539i	−0.623458	−	0.781857i	$-0.714273\pi$
$227$	−16.1323	+	1.69557i	−1.07074	+	0.112539i	−0.447277	+	0.894395i	$0.647606\pi$
$228$		0			0
$229$	−10.5887	+	3.44046i	−0.699718	+	0.227352i	−0.637208	−	0.770692i	$-0.719911\pi$
$229$	−10.5887	+	3.44046i	−0.699718	+	0.227352i	−0.0625103	+	0.998044i	$0.519911\pi$
$230$		0			0
$231$	−24.3161	+	40.6898i	−1.59988	+	2.67719i
$232$		0			0
$233$	3.86905	+	11.9077i	0.253470	+	0.780100i	0.994127	+	0.108217i	$0.0345142\pi$
$233$	3.86905	+	11.9077i	0.253470	+	0.780100i	−0.740657	+	0.671883i	$0.765486\pi$
$234$		0			0
$235$	0.779374	−	0.566248i	0.0508407	−	0.0369380i
$236$		0			0
$237$	31.9031	−	6.78120i	2.07233	−	0.440487i
$238$		0			0
$239$	−4.70757	+	6.47941i	−0.304507	+	0.419118i	−0.933658	−	0.358165i	$-0.883403\pi$
$239$	−4.70757	+	6.47941i	−0.304507	+	0.419118i	0.629151	+	0.777283i	$0.283403\pi$
$240$		0			0
$241$	0.476697	+	0.275221i	0.0307068	+	0.0177286i	0.515275	−	0.857025i	$-0.327690\pi$
$241$	0.476697	+	0.275221i	0.0307068	+	0.0177286i	−0.484568	+	0.874754i	$0.661023\pi$
$242$		0			0
$243$	−3.31876	+	5.74826i	−0.212899	+	0.368751i
$244$		0			0
$245$	−1.60403	−	0.168590i	−0.102478	−	0.0107708i
$246$		0			0
$247$	2.79232	−	6.03302i	0.177671	−	0.383872i
$248$		0			0
$249$	−14.5286	+	32.6319i	−0.920716	+	2.06796i
$250$		0			0
$251$	16.6840	+	3.54630i	1.05309	+	0.223840i	0.701761	−	0.712413i	$-0.252398\pi$
$251$	16.6840	+	3.54630i	1.05309	+	0.223840i	0.351326	+	0.936253i	$0.385731\pi$
$252$		0			0
$253$	0.230988	−	15.3456i	0.0145221	−	0.964770i
$254$		0			0
$255$	1.83153	−	0.595101i	0.114695	−	0.0372667i
$256$		0			0
$257$	13.1483	+	5.85401i	0.820170	+	0.365163i	0.773539	−	0.633749i	$-0.218485\pi$
$257$	13.1483	+	5.85401i	0.820170	+	0.365163i	0.0466311	+	0.998912i	$0.485151\pi$
$258$		0			0
$259$	5.70080	−	17.5452i	0.354230	−	1.09021i
$260$		0			0
$261$	20.9617	+	15.2296i	1.29750	+	0.942687i
$262$		0			0
$263$	6.50797	+	11.2721i	0.401299	+	0.695070i	0.993883	−	0.110439i	$-0.0352256\pi$
$263$	6.50797	+	11.2721i	0.401299	+	0.695070i	−0.592584	+	0.805509i	$0.701892\pi$
$264$		0			0
$265$		−	0.872518i		−	0.0535983i
$266$		0			0
$267$	14.1130	+	31.6984i	0.863703	+	1.93991i
$268$		0			0
$269$	17.2731	+	19.1837i	1.05316	+	1.16965i	0.985102	+	0.171968i	$0.0550127\pi$
$269$	17.2731	+	19.1837i	1.05316	+	1.16965i	0.0680552	+	0.997682i	$0.478321\pi$
$270$		0			0
$271$	2.71877	−	6.10647i	0.165154	−	0.370941i	−0.811943	−	0.583737i	$-0.801590\pi$
$271$	2.71877	−	6.10647i	0.165154	−	0.370941i	0.977097	+	0.212795i	$0.0682567\pi$
$272$		0			0
$273$	−38.7945	+	33.9183i	−2.34795	+	2.05283i
$274$		0			0
$275$	−6.50085	−	15.2133i	−0.392016	−	0.917398i
$276$		0			0
$277$	−5.27653	−	1.12156i	−0.317036	−	0.0673881i	0.0466453	−	0.998912i	$-0.485147\pi$
$277$	−5.27653	−	1.12156i	−0.317036	−	0.0673881i	−0.363681	+	0.931523i	$0.618480\pi$
$278$		0			0
$279$	40.1599	−	4.22098i	2.40431	−	0.252704i
$280$		0			0
$281$	−25.0917	−	8.15279i	−1.49685	−	0.486355i	−0.557750	−	0.830009i	$-0.688335\pi$
$281$	−25.0917	−	8.15279i	−1.49685	−	0.486355i	−0.939096	+	0.343654i	$0.888335\pi$
$282$		0			0
$283$	−1.43929	+	13.6939i	−0.0855569	+	0.814019i	0.864645	+	0.502384i	$0.167543\pi$
$283$	−1.43929	+	13.6939i	−0.0855569	+	0.814019i	−0.950202	+	0.311636i	$0.899123\pi$
$284$		0			0
$285$	−0.611489			−0.0362215
$286$		0			0
$287$	−24.4569			−1.44364
$288$		0			0
$289$	−1.74752	+	16.6266i	−0.102795	+	0.978033i
$290$		0			0
$291$	13.0629	+	4.24440i	0.765761	+	0.248811i
$292$		0			0
$293$	15.8621	−	1.66718i	0.926675	−	0.0973975i	0.370846	−	0.928694i	$-0.379068\pi$
$293$	15.8621	−	1.66718i	0.926675	−	0.0973975i	0.555829	+	0.831297i	$0.312401\pi$
$294$		0			0
$295$	0.283219	+	0.0602001i	0.0164897	+	0.00350499i
$296$		0			0
$297$	25.5184	−	22.2907i	1.48073	−	1.29344i
$298$		0			0
$299$	5.38686	−	15.7908i	0.311530	−	0.913203i
$300$		0			0
$301$	19.6201	−	44.0675i	1.13088	−	2.54001i
$302$		0			0
$303$	−6.73555	−	7.48058i	−0.386947	−	0.429748i
$304$		0			0
$305$	−0.0667276	−	0.149873i	−0.00382081	−	0.00858168i
$306$		0			0
$307$			10.6597i			0.608381i	0.952611	+	0.304190i	$0.0983859\pi$
$307$			10.6597i			0.608381i	−0.952611	+	0.304190i	$0.901614\pi$
$308$		0			0
$309$	−11.6182	−	20.1233i	−0.660936	−	1.14478i
$310$		0			0
$311$	−6.12271	−	4.44841i	−0.347187	−	0.252246i	0.400501	−	0.916296i	$-0.368836\pi$
$311$	−6.12271	−	4.44841i	−0.347187	−	0.252246i	−0.747688	+	0.664050i	$0.768836\pi$
$312$		0			0
$313$	−0.703021	+	2.16368i	−0.0397371	+	0.122298i	−0.968957	−	0.247228i	$-0.920480\pi$
$313$	−0.703021	+	2.16368i	−0.0397371	+	0.122298i	0.929220	+	0.369527i	$0.120480\pi$
$314$		0			0
$315$	2.93968	+	1.30883i	0.165632	+	0.0737443i
$316$		0			0
$317$	2.81375	−	0.914244i	0.158036	−	0.0513491i	−0.228930	−	0.973443i	$-0.573523\pi$
$317$	2.81375	−	0.914244i	0.158036	−	0.0513491i	0.386967	+	0.922094i	$0.373523\pi$
$318$		0			0
$319$	−7.79811	−	11.0801i	−0.436611	−	0.620368i
$320$		0			0
$321$	49.8474	+	10.5954i	2.78221	+	0.591378i
$322$		0			0
$323$	4.35469	−	9.78079i	0.242301	−	0.544218i
$324$		0			0
$325$	−1.61863	−	17.9123i	−0.0897854	−	0.993597i
$326$		0			0
$327$	−28.8493	−	3.03219i	−1.59537	−	0.167680i
$328$		0			0
$329$	−20.7578	+	35.9535i	−1.14441	+	1.98218i
$330$		0			0
$331$	18.4648	+	10.6607i	1.01492	+	0.585963i	0.912628	−	0.408792i	$-0.134050\pi$
$331$	18.4648	+	10.6607i	1.01492	+	0.585963i	0.102290	+	0.994755i	$0.467383\pi$
$332$		0			0
$333$	−14.7080	+	20.2439i	−0.805996	+	1.10936i
$334$		0			0
$335$	−0.804640	+	0.171032i	−0.0439622	+	0.00934445i
$336$		0			0
$337$	6.16541	−	4.47943i	0.335851	−	0.244010i	−0.407058	−	0.913402i	$-0.633445\pi$
$337$	6.16541	−	4.47943i	0.335851	−	0.244010i	0.742909	+	0.669392i	$0.233445\pi$
$338$		0			0
$339$	−15.3868	−	47.3557i	−0.835696	−	2.57201i
$340$		0			0
$341$	−20.5866	−	4.70074i	−1.11483	−	0.254560i
$342$		0			0
$343$	34.9742	−	11.3638i	1.88843	−	0.613588i
$344$		0			0
$345$	−1.52626	+	0.160416i	−0.0821709	+	0.00863651i
$346$		0			0
$347$	11.0134	+	12.2316i	0.591228	+	0.656625i	0.962304	−	0.271977i	$-0.0876776\pi$
$347$	11.0134	+	12.2316i	0.591228	+	0.656625i	−0.371076	+	0.928603i	$0.621011\pi$
$348$		0			0
$349$	0.222039	+	0.0233373i	0.0118855	+	0.00124922i	0.110469	−	0.993880i	$-0.464765\pi$
$349$	0.222039	+	0.0233373i	0.0118855	+	0.00124922i	−0.0985838	+	0.995129i	$0.531431\pi$
$350$		0			0
$351$	33.8654	−	14.4892i	1.80760	−	0.773375i
$352$		0			0
$353$	−22.0083	+	12.7065i	−1.17138	+	0.676299i	−0.954006	−	0.299788i	$-0.903084\pi$
$353$	−22.0083	+	12.7065i	−1.17138	+	0.676299i	−0.217379	+	0.976087i	$0.569751\pi$
$354$		0			0
$355$	0.402701	−	0.179294i	0.0213731	−	0.00951593i
$356$		0			0
$357$	−61.6743	+	55.5318i	−3.26415	+	2.93905i
$358$		0			0
$359$	−6.86298	−	9.44608i	−0.362214	−	0.498545i	0.588550	−	0.808461i	$-0.299699\pi$
$359$	−6.86298	−	9.44608i	−0.362214	−	0.498545i	−0.950764	+	0.309916i	$0.899699\pi$
$360$		0			0
$361$	10.4387	−	11.5934i	0.549407	−	0.610178i
$362$		0			0
$363$	−31.1128	+	12.7446i	−1.63300	+	0.668917i
$364$		0			0
$365$	−0.0404093	−	0.124367i	−0.00211512	−	0.00650966i
$366$		0			0
$367$	14.3028	+	6.36803i	0.746602	+	0.332409i	0.744530	−	0.667589i	$-0.232674\pi$
$367$	14.3028	+	6.36803i	0.746602	+	0.332409i	0.00207204	+	0.999998i	$0.499340\pi$
$368$		0			0
$369$	31.5494	+	10.2510i	1.64240	+	0.533647i
$370$		0			0
$371$	15.2936	+	34.3500i	0.794005	+	1.78336i
$372$		0			0
$373$	−15.0637	+	26.0911i	−0.779968	+	1.35094i	0.151991	+	0.988382i	$0.451432\pi$
$373$	−15.0637	+	26.0911i	−0.779968	+	1.35094i	−0.931959	+	0.362563i	$0.881902\pi$
$374$		0			0
$375$	−2.86877	+	1.65628i	−0.148143	+	0.0855302i
$376$		0			0
$377$	−4.34665	−	14.0735i	−0.223864	−	0.724824i
$378$		0			0
$379$	1.19281	+	5.61174i	0.0612707	+	0.288256i	0.998106	−	0.0615144i	$-0.0195930\pi$
$379$	1.19281	+	5.61174i	0.0612707	+	0.288256i	−0.936836	+	0.349770i	$0.886260\pi$
$380$		0			0
$381$	−0.799185	−	7.60373i	−0.0409435	−	0.389551i
$382$		0			0
$383$	−5.20860	+	24.5045i	−0.266147	+	1.25212i	0.618472	+	0.785807i	$0.287752\pi$
$383$	−5.20860	+	24.5045i	−0.266147	+	1.25212i	−0.884619	+	0.466315i	$0.845581\pi$
$384$		0			0
$385$	−1.23342	−	1.14466i	−0.0628610	−	0.0583372i
$386$		0			0
$387$	−43.7807	+	48.6234i	−2.22550	+	2.47166i
$388$		0			0
$389$	−13.2987	+	9.66209i	−0.674272	+	0.489887i	−0.871453	−	0.490480i	$-0.836822\pi$
$389$	−13.2987	+	9.66209i	−0.674272	+	0.489887i	0.197180	+	0.980367i	$0.436822\pi$
$390$		0			0
$391$	8.30330	−	25.5549i	0.419916	−	1.29237i
$392$		0			0
$393$	0.505561	−	4.81009i	0.0255022	−	0.242637i
$394$		0			0
$395$			1.15783i			0.0582570i
$396$		0			0
$397$	−20.1395	−	11.6275i	−1.01077	−	0.583569i	−0.0993542	−	0.995052i	$-0.531678\pi$
$397$	−20.1395	−	11.6275i	−1.01077	−	0.583569i	−0.911418	+	0.411483i	$0.865011\pi$
$398$		0			0
$399$	24.0736	−	10.7183i	1.20519	−	0.536584i
$400$		0			0
$401$	2.46434	+	11.5938i	0.123064	+	0.578968i	0.995861	+	0.0908863i	$0.0289700\pi$
$401$	2.46434	+	11.5938i	0.123064	+	0.578968i	−0.872798	+	0.488082i	$0.837697\pi$
$402$		0			0
$403$	−19.7108	−	11.7671i	−0.981867	−	0.586159i
$404$		0			0
$405$	−0.983641	−	0.885675i	−0.0488775	−	0.0440095i
$406$		0			0
$407$	10.7007	−	7.53107i	0.530414	−	0.373301i
$408$		0			0
$409$	3.65367	−	17.1892i	0.180662	−	0.849949i	−0.790674	−	0.612238i	$-0.790270\pi$
$409$	3.65367	−	17.1892i	0.180662	−	0.849949i	0.971336	−	0.237711i	$-0.0763971\pi$
$410$		0			0
$411$	5.09410	+	7.01143i	0.251274	+	0.345849i
$412$		0			0
$413$	−12.2052	+	2.59430i	−0.600579	+	0.127657i
$414$		0			0
$415$	−1.02586	−	0.745331i	−0.0503575	−	0.0365869i
$416$		0			0
$417$	−30.0532			−1.47171
$418$		0			0
$419$	−11.5664	−	20.0336i	−0.565055	−	0.978703i	−0.997045	−	0.0768249i	$-0.975522\pi$
$419$	−11.5664	−	20.0336i	−0.565055	−	0.978703i	0.431990	−	0.901878i	$-0.357812\pi$
$420$		0			0
$421$	−15.1530	+	20.8564i	−0.738513	+	1.01648i	0.260189	+	0.965558i	$0.416215\pi$
$421$	−15.1530	+	20.8564i	−0.738513	+	1.01648i	−0.998703	+	0.0509189i	$0.983785\pi$
$422$		0			0
$423$	41.8473	−	37.6795i	2.03468	−	1.83204i
$424$		0			0
$425$	−3.02770	−	28.8066i	−0.146865	−	1.39733i
$426$		0			0
$427$	5.25397	+	4.73070i	0.254258	+	0.228934i
$428$		0			0
$429$	−36.4479	+	2.74122i	−1.75972	+	0.132347i
$430$		0			0
$431$	−2.77616	−	2.49966i	−0.133723	−	0.120405i	0.599555	−	0.800333i	$-0.295344\pi$
$431$	−2.77616	−	2.49966i	−0.133723	−	0.120405i	−0.733278	+	0.679929i	$0.762011\pi$
$432$		0			0
$433$	1.31780	+	12.5380i	0.0633293	+	0.602538i	0.979457	+	0.201652i	$0.0646309\pi$
$433$	1.31780	+	12.5380i	0.0633293	+	0.602538i	−0.916128	+	0.400886i	$0.868702\pi$
$434$		0			0
$435$	−1.00685	+	0.906574i	−0.0482749	+	0.0434669i
$436$		0			0
$437$	−5.01496	+	6.90250i	−0.239898	+	0.330191i
$438$		0			0
$439$	−0.780976	−	1.35269i	−0.0372739	−	0.0645604i	0.846787	−	0.531933i	$-0.178534\pi$
$439$	−0.780976	−	1.35269i	−0.0372739	−	0.0645604i	−0.884061	+	0.467372i	$0.845201\pi$
$440$		0			0
$441$	−94.2766			−4.48936
$442$		0			0
$443$	−11.9058	−	8.65010i	−0.565663	−	0.410979i	0.267864	−	0.963457i	$-0.413682\pi$
$443$	−11.9058	−	8.65010i	−0.565663	−	0.410979i	−0.833527	+	0.552478i	$0.813682\pi$
$444$		0			0
$445$	−1.20484	+	0.256097i	−0.0571150	+	0.0121402i
$446$		0			0
$447$	−8.07256	−	11.1109i	−0.381819	−	0.525529i
$448$		0			0
$449$	−0.969435	+	4.56083i	−0.0457505	+	0.215239i	−0.995084	−	0.0990299i	$-0.968426\pi$
$449$	−0.969435	+	4.56083i	−0.0457505	+	0.215239i	0.949334	+	0.314269i	$0.101759\pi$
$450$		0			0
$451$	−13.8791	−	10.4065i	−0.653540	−	0.490021i
$452$		0			0
$453$	55.5638	+	50.0299i	2.61062	+	2.35061i
$454$		0			0
$455$	−0.891432	−	1.59742i	−0.0417910	−	0.0748882i
$456$		0			0
$457$	−5.69407	−	26.7885i	−0.266357	−	1.25311i	−0.884311	−	0.466899i	$-0.845371\pi$
$457$	−5.69407	−	26.7885i	−0.266357	−	1.25311i	0.617953	−	0.786215i	$-0.287962\pi$
$458$		0			0
$459$	54.1937	−	24.1286i	2.52954	−	1.12623i
$460$		0			0
$461$	0.787071	+	0.454415i	0.0366575	+	0.0211642i	0.518217	−	0.855249i	$-0.326596\pi$
$461$	0.787071	+	0.454415i	0.0366575	+	0.0211642i	−0.481559	+	0.876414i	$0.659929\pi$
$462$		0			0
$463$		−	1.82472i		−	0.0848021i	−0.999101	−	0.0424010i	$-0.986499\pi$
$463$		−	1.82472i		−	0.0848021i	0.999101	−	0.0424010i	$-0.0135007\pi$
$464$		0			0
$465$	−0.220718	+	2.09999i	−0.0102355	+	0.0973846i
$466$		0			0
$467$	12.0359	−	37.0426i	0.556954	−	1.71413i	−0.133771	−	0.991012i	$-0.542709\pi$
$467$	12.0359	−	37.0426i	0.556954	−	1.71413i	0.690726	−	0.723117i	$-0.257291\pi$
$468$		0			0
$469$	28.6799	−	20.8372i	1.32431	−	0.962170i
$470$		0			0
$471$	−19.4371	+	21.5871i	−0.895616	+	0.994682i
$472$		0			0
$473$	29.8851	−	16.6595i	1.37412	−	0.766006i
$474$		0			0
$475$	−1.91222	+	8.99627i	−0.0877385	+	0.412777i
$476$		0			0
$477$	−5.33107	−	50.7217i	−0.244093	−	2.32239i
$478$		0			0
$479$	−0.566005	−	2.66285i	−0.0258614	−	0.121669i	0.963323	−	0.268343i	$-0.0864762\pi$
$479$	−0.566005	−	2.66285i	−0.0258614	−	0.121669i	−0.989185	+	0.146675i	$0.953143\pi$
$480$		0			0
$481$	13.5916	−	4.19780i	0.619724	−	0.191403i
$482$		0			0
$483$	57.2752	−	33.0678i	2.60611	−	1.50464i
$484$		0			0
$485$	−0.243793	+	0.422263i	−0.0110701	+	0.0191740i
$486$		0			0
$487$	1.13854	+	2.55720i	0.0515922	+	0.115878i	0.937502	−	0.347979i	$-0.113132\pi$
$487$	1.13854	+	2.55720i	0.0515922	+	0.115878i	−0.885910	+	0.463857i	$0.846465\pi$
$488$		0			0
$489$	69.7823	+	22.6736i	3.15566	+	1.02534i
$490$		0			0
$491$	−0.914002	−	0.406940i	−0.0412483	−	0.0183649i	0.386009	−	0.922495i	$-0.373853\pi$
$491$	−0.914002	−	0.406940i	−0.0412483	−	0.0183649i	−0.427257	+	0.904130i	$0.640520\pi$
$492$		0			0
$493$	−7.33044	−	22.5608i	−0.330146	−	1.01609i
$494$		0			0
$495$	1.11133	+	1.99359i	0.0499508	+	0.0896053i
$496$		0			0
$497$	−12.7112	+	14.1172i	−0.570174	+	0.633242i
$498$		0			0
$499$	13.0683	+	17.9869i	0.585016	+	0.805206i	0.994234	−	0.107231i	$-0.0341984\pi$
$499$	13.0683	+	17.9869i	0.585016	+	0.805206i	−0.409218	+	0.912437i	$0.634198\pi$
$500$		0			0
$501$	41.4487	−	37.3206i	1.85179	−	1.66736i
$502$		0			0
$503$	−1.16995	+	0.520896i	−0.0521656	+	0.0232256i	−0.432654	−	0.901560i	$-0.642423\pi$
$503$	−1.16995	+	0.520896i	−0.0521656	+	0.0232256i	0.380488	+	0.924786i	$0.375756\pi$
$504$		0			0
$505$	0.309465	−	0.178670i	0.0137710	−	0.00795069i
$506$		0			0
$507$	−38.6088	−	9.39261i	−1.71468	−	0.417141i
$508$		0			0
$509$	−22.9417	−	2.41127i	−1.01687	−	0.106878i	−0.418601	−	0.908170i	$-0.637479\pi$
$509$	−22.9417	−	2.41127i	−1.01687	−	0.106878i	−0.598272	+	0.801293i	$0.704146\pi$
$510$		0			0
$511$	3.77078	+	4.18788i	0.166810	+	0.185261i
$512$		0			0
$513$	−18.7332	+	1.96894i	−0.827092	+	0.0869309i
$514$		0			0
$515$	0.784501	−	0.254900i	0.0345693	−	0.0112322i
$516$		0			0
$517$	−27.0781	+	11.5708i	−1.19090	+	0.508884i
$518$		0			0
$519$	1.36018	+	4.18620i	0.0597053	+	0.183754i
$520$		0			0
$521$	12.8636	−	9.34593i	0.563563	−	0.409453i	−0.269198	−	0.963085i	$-0.586759\pi$
$521$	12.8636	−	9.34593i	0.563563	−	0.409453i	0.832761	+	0.553632i	$0.186759\pi$
$522$		0			0
$523$	−35.2211	+	7.48648i	−1.54011	+	0.327361i	−0.898259	−	0.439466i	$-0.855168\pi$
$523$	−35.2211	+	7.48648i	−1.54011	+	0.327361i	−0.641853	+	0.766827i	$0.721834\pi$
$524$		0			0
$525$	41.9048	−	57.6770i	1.82888	−	2.51723i
$526$		0			0
$527$	−32.0176	−	18.4853i	−1.39471	−	0.805234i
$528$		0			0
$529$	0.793601	−	1.37456i	0.0345044	−	0.0597633i
$530$		0			0
$531$	16.8321	+	1.76912i	0.730451	+	0.0767735i
$532$		0			0
$533$	−10.8607	−	15.4169i	−0.470430	−	0.667781i
$534$		0			0
$535$	−0.735818	+	1.65267i	−0.0318122	+	0.0714513i
$536$		0			0
$537$	4.92791	+	1.04746i	0.212655	+	0.0452013i
$538$		0			0
$539$	46.6525	+	15.9385i	2.00947	+	0.686520i
$540$		0			0
$541$	−7.35553	+	2.38996i	−0.316239	+	0.102752i	−0.462836	−	0.886444i	$-0.653168\pi$
$541$	−7.35553	+	2.38996i	−0.316239	+	0.102752i	0.146597	+	0.989196i	$0.453168\pi$
$542$		0			0
$543$	42.2182	+	18.7968i	1.81176	+	0.806646i
$544$		0			0
$545$	0.318216	−	0.979369i	0.0136309	−	0.0419516i
$546$		0			0
$547$	10.1055	+	7.34204i	0.432078	+	0.313923i	0.782479	−	0.622677i	$-0.213955\pi$
$547$	10.1055	+	7.34204i	0.432078	+	0.313923i	−0.350401	+	0.936600i	$0.613955\pi$
$548$		0			0
$549$	−4.79477	−	8.30478i	−0.204636	−	0.354439i
$550$		0			0
$551$			7.53230i			0.320887i
$552$		0			0
$553$	−20.2947	−	45.5826i	−0.863017	−	1.93837i
$554$		0			0
$555$	−0.875529	−	0.972374i	−0.0371642	−	0.0412750i
$556$		0			0
$557$	−13.5754	+	30.4907i	−0.575206	+	1.29193i	0.358378	+	0.933577i	$0.383330\pi$
$557$	−13.5754	+	30.4907i	−0.575206	+	1.29193i	−0.933584	+	0.358358i	$0.883337\pi$
$558$		0			0
$559$	36.4917	−	7.20136i	1.54343	−	0.304585i
$560$		0			0
$561$	−58.6285	+	5.27127i	−2.47530	+	0.222553i
$562$		0			0
$563$	−42.4585	−	9.02483i	−1.78941	−	0.380351i	−0.810680	−	0.585490i	$-0.800902\pi$
$563$	−42.4585	−	9.02483i	−1.78941	−	0.380351i	−0.978733	+	0.205138i	$0.934236\pi$
$564$		0			0
$565$	1.75792	−	0.184765i	0.0739562	−	0.00777311i
$566$		0			0
$567$	54.2490	+	17.6266i	2.27825	+	0.740247i
$568$		0			0
$569$	−2.44717	+	23.2833i	−0.102591	+	0.976085i	0.815243	+	0.579120i	$0.196604\pi$
$569$	−2.44717	+	23.2833i	−0.102591	+	0.976085i	−0.917833	+	0.396966i	$0.870063\pi$
$570$		0			0
$571$	5.86199			0.245317			0.122658	−	0.992449i	$-0.460858\pi$
$571$	5.86199			0.245317			0.122658	+	0.992449i	$0.460858\pi$
$572$		0			0
$573$	52.8962			2.20977
$574$		0			0
$575$	−2.41278	+	22.9561i	−0.100620	+	0.957334i
$576$		0			0
$577$	−17.2453	−	5.60335i	−0.717933	−	0.233271i	−0.0728063	−	0.997346i	$-0.523195\pi$
$577$	−17.2453	−	5.60335i	−0.717933	−	0.233271i	−0.645127	+	0.764075i	$0.723195\pi$
$578$		0			0
$579$	−2.27509	+	0.239121i	−0.0945494	+	0.00993754i
$580$		0			0
$581$	53.4512	+	11.3614i	2.21753	+	0.471350i
$582$		0			0
$583$	−5.93701	+	26.0008i	−0.245886	+	1.07684i
$584$		0			0
$585$	0.480393	+	2.43431i	0.0198618	+	0.100646i
$586$		0			0
$587$	5.03400	−	11.3066i	0.207776	−	0.466672i	−0.779356	−	0.626581i	$-0.784454\pi$
$587$	5.03400	−	11.3066i	0.207776	−	0.466672i	0.987132	+	0.159910i	$0.0511203\pi$
$588$		0			0
$589$	7.85504	+	8.72391i	0.323661	+	0.359462i
$590$		0			0
$591$	15.2182	+	34.1807i	0.625994	+	1.40601i
$592$		0			0
$593$			3.71514i			0.152562i	0.997086	+	0.0762812i	$0.0243047\pi$
$593$			3.71514i			0.152562i	−0.997086	+	0.0762812i	$0.975695\pi$
$594$		0			0
$595$	−1.47306	−	2.55141i	−0.0603894	−	0.104598i
$596$		0			0
$597$	60.4364	+	43.9096i	2.47350	+	1.79710i
$598$		0			0
$599$	−9.40518	+	28.9462i	−0.384285	+	1.18271i	0.552712	+	0.833372i	$0.313593\pi$
$599$	−9.40518	+	28.9462i	−0.384285	+	1.18271i	−0.936997	+	0.349336i	$0.886407\pi$
$600$		0			0
$601$	−12.5793	−	5.60068i	−0.513122	−	0.228457i	0.133806	−	0.991008i	$-0.457280\pi$
$601$	−12.5793	−	5.60068i	−0.513122	−	0.228457i	−0.646928	+	0.762551i	$0.723947\pi$
$602$		0			0
$603$	−45.7308	+	14.8589i	−1.86230	+	0.605099i
$604$		0			0
$605$	−0.212902	−	1.17441i	−0.00865570	−	0.0477464i
$606$		0			0
$607$	15.4199	+	3.27760i	0.625874	+	0.133034i	0.509921	−	0.860221i	$-0.329674\pi$
$607$	15.4199	+	3.27760i	0.625874	+	0.133034i	0.115953	+	0.993255i	$0.463008\pi$
$608$		0			0
$609$	23.7481	−	53.3390i	0.962320	−	2.16141i
$610$		0			0
$611$	−31.8821	+	2.88099i	−1.28981	+	0.116552i
$612$		0			0
$613$	−33.9914	−	3.57264i	−1.37290	−	0.144297i	−0.610813	−	0.791775i	$-0.709157\pi$
$613$	−33.9914	−	3.57264i	−1.37290	−	0.144297i	−0.762085	+	0.647477i	$0.775824\pi$
$614$		0			0
$615$	−0.867317	+	1.50224i	−0.0349736	+	0.0605761i
$616$		0			0
$617$	−3.10983	−	1.79546i	−0.125197	−	0.0722825i	0.436094	−	0.899901i	$-0.356362\pi$
$617$	−3.10983	−	1.79546i	−0.125197	−	0.0722825i	−0.561291	+	0.827619i	$0.689695\pi$
$618$		0			0
$619$	25.0714	−	34.5078i	1.00771	−	1.38699i	0.0872290	−	0.996188i	$-0.472199\pi$
$619$	25.0714	−	34.5078i	1.00771	−	1.38699i	0.920476	−	0.390799i	$-0.127801\pi$
$620$		0			0
$621$	−46.2410	+	9.82884i	−1.85559	+	0.394418i
$622$		0			0
$623$	42.9443	−	31.2008i	1.72053	−	1.25004i
$624$		0			0
$625$	7.67090	+	23.6086i	0.306836	+	0.944344i
$626$		0			0
$627$	18.2222	+	4.16085i	0.727724	+	0.166168i
$628$		0			0
$629$	21.7882	−	7.07942i	0.868753	−	0.282275i
$630$		0			0
$631$	−19.7215	+	2.07282i	−0.785102	+	0.0825175i	−0.488592	−	0.872512i	$-0.662489\pi$
$631$	−19.7215	+	2.07282i	−0.785102	+	0.0825175i	−0.296510	+	0.955030i	$0.595823\pi$
$632$		0			0
$633$	−6.12293	−	6.80021i	−0.243365	−	0.270284i
$634$		0			0
$635$	0.269926	+	0.0283704i	0.0107117	+	0.00112585i
$636$		0			0
$637$	42.8945	+	32.1319i	1.69954	+	1.27311i
$638$		0			0
$639$	22.3146	−	12.8833i	0.882750	−	0.509656i
$640$		0			0
$641$	11.4989	−	5.11962i	0.454177	−	0.202213i	−0.166881	−	0.985977i	$-0.553370\pi$
$641$	11.4989	−	5.11962i	0.454177	−	0.202213i	0.621059	+	0.783764i	$0.286703\pi$
$642$		0			0
$643$	−31.3455	+	28.2237i	−1.23615	+	1.11303i	−0.246556	+	0.969129i	$0.579299\pi$
$643$	−31.3455	+	28.2237i	−1.23615	+	1.11303i	−0.989592	+	0.143904i	$0.954034\pi$
$644$		0			0
$645$	−2.01101	−	2.76791i	−0.0791833	−	0.108987i
$646$		0			0
$647$	22.7421	−	25.2577i	0.894085	−	0.992982i	−0.105914	−	0.994375i	$-0.533777\pi$
$647$	22.7421	−	25.2577i	0.894085	−	0.992982i	0.999999	+	0.00139341i	$0.000443537\pi$
$648$		0			0
$649$	−8.03023	−	3.72110i	−0.315214	−	0.146066i
$650$		0			0
$651$	−28.1195	−	86.5428i	−1.10209	−	3.39188i
$652$		0			0
$653$	17.2678	+	7.68813i	0.675742	+	0.300860i	0.715767	−	0.698339i	$-0.246077\pi$
$653$	17.2678	+	7.68813i	0.675742	+	0.300860i	−0.0400250	+	0.999199i	$0.512744\pi$
$654$		0			0
$655$	0.163291	+	0.0530566i	0.00638033	+	0.00207309i
$656$		0			0
$657$	−3.10898	−	6.98287i	−0.121293	−	0.272428i
$658$		0			0
$659$	22.0625	−	38.2134i	0.859433	−	1.48858i	−0.0130384	−	0.999915i	$-0.504150\pi$
$659$	22.0625	−	38.2134i	0.859433	−	1.48858i	0.872471	−	0.488666i	$-0.162516\pi$
$660$		0			0
$661$	−33.3015	+	19.2266i	−1.29528	+	0.747828i	−0.979584	−	0.201033i	$-0.935570\pi$
$661$	−33.3015	+	19.2266i	−1.29528	+	0.747828i	−0.315692	+	0.948862i	$0.602237\pi$
$662$		0			0
$663$	−62.3937	−	14.2174i	−2.42317	−	0.552156i
$664$		0			0
$665$	0.194495	+	0.915027i	0.00754219	+	0.0354832i
$666$		0			0
$667$	1.97600	+	18.8004i	0.0765111	+	0.727954i
$668$		0			0
$669$	8.76676	−	41.2443i	0.338942	−	1.59460i
$670$		0			0
$671$	0.968662	+	4.92021i	0.0373948	+	0.189942i
$672$		0			0
$673$	−10.1236	+	11.2434i	−0.390235	+	0.433400i	−0.905966	−	0.423351i	$-0.860854\pi$
$673$	−10.1236	+	11.2434i	−0.390235	+	0.433400i	0.515731	+	0.856751i	$0.327520\pi$
$674$		0			0
$675$	−41.2278	+	29.9538i	−1.58686	+	1.15292i
$676$		0			0
$677$	10.7852	−	33.1933i	0.414507	−	1.27572i	−0.498184	−	0.867071i	$-0.666000\pi$
$677$	10.7852	−	33.1933i	0.414507	−	1.27572i	0.912691	−	0.408650i	$-0.134000\pi$
$678$		0			0
$679$	2.19639	−	20.8972i	0.0842896	−	0.801962i
$680$		0			0
$681$		−	49.5804i		−	1.89992i
$682$		0			0
$683$	−3.06540	−	1.76981i	−0.117294	−	0.0677200i	0.440205	−	0.897897i	$-0.354906\pi$
$683$	−3.06540	−	1.76981i	−0.117294	−	0.0677200i	−0.557499	+	0.830177i	$0.688239\pi$
$684$		0			0
$685$	−0.281059	+	0.125136i	−0.0107387	+	0.00478119i
$686$		0			0
$687$	−7.07526	−	33.2865i	−0.269938	−	1.26996i
$688$		0			0
$689$	−14.8617	+	24.8947i	−0.566186	+	0.948411i
$690$		0			0
$691$	29.3770	+	26.4512i	1.11755	+	1.00625i	0.999913	+	0.0131933i	$0.00419967\pi$
$691$	29.3770	+	26.4512i	1.11755	+	1.00625i	0.117640	+	0.993056i	$0.462467\pi$
$692$		0			0
$693$	−78.6959	−	59.0058i	−2.98941	−	2.24144i
$694$		0			0
$695$	0.221813	−	1.04355i	0.00841386	−	0.0395841i
$696$		0			0
$697$	−17.8518	−	24.5709i	−0.676185	−	0.930689i
$698$		0			0
$699$	−37.4331	+	7.95664i	−1.41585	+	0.300948i
$700$		0			0
$701$	−28.4343	−	20.6587i	−1.07395	−	0.780269i	−0.0973303	−	0.995252i	$-0.531030\pi$
$701$	−28.4343	−	20.6587i	−1.07395	−	0.780269i	−0.976618	+	0.214983i	$0.931030\pi$
$702$		0			0
$703$	−7.27437			−0.274358
$704$		0			0
$705$	1.47227	+	2.55005i	0.0554489	+	0.0960403i
$706$		0			0
$707$	−9.05152	+	12.4583i	−0.340417	+	0.468544i
$708$		0			0
$709$	−31.5089	+	28.3708i	−1.18334	+	1.06549i	−0.186800	+	0.982398i	$0.559812\pi$
$709$	−31.5089	+	28.3708i	−1.18334	+	1.06549i	−0.996542	+	0.0830886i	$0.973522\pi$
$710$		0			0
$711$	7.07435	+	67.3079i	0.265309	+	2.52425i
$712$		0			0
$713$	21.8945	+	19.7139i	0.819957	+	0.738293i
$714$		0			0
$715$	0.173826	−	1.28583i	0.00650073	−	0.0480873i
$716$		0			0
$717$	−18.1920	−	16.3801i	−0.679392	−	0.611728i
$718$		0			0
$719$	4.98218	+	47.4023i	0.185804	+	1.76781i	0.548739	+	0.835994i	$0.315108\pi$
$719$	4.98218	+	47.4023i	0.185804	+	1.76781i	−0.362935	+	0.931815i	$0.618225\pi$
$720$		0			0
$721$	−26.4170	+	23.7860i	−0.983820	+	0.885835i
$722$		0			0
$723$	−0.988916	+	1.36113i	−0.0367782	+	0.0506208i
$724$		0			0
$725$	10.1890	+	17.6479i	0.378410	+	0.655426i
$726$		0			0
$727$	43.1951			1.60202			0.801008	−	0.598654i	$-0.204297\pi$
$727$	43.1951			1.60202			0.801008	+	0.598654i	$0.204297\pi$
$728$		0			0
$729$	13.1938	+	9.58588i	0.488661	+	0.355033i
$730$		0			0
$731$	58.5942	−	12.4546i	2.16718	−	0.460649i
$732$		0			0
$733$	14.5034	+	19.9622i	0.535694	+	0.737320i	0.987985	−	0.154551i	$-0.0493930\pi$
$733$	14.5034	+	19.9622i	0.535694	+	0.737320i	−0.452291	+	0.891871i	$0.649393\pi$
$734$		0			0
$735$	1.02496	−	4.82205i	0.0378062	−	0.177864i
$736$		0			0
$737$	25.1418	+	0.378444i	0.926111	+	0.0139402i
$738$		0			0
$739$	20.4924	+	18.4514i	0.753825	+	0.678747i	0.953594	−	0.301096i	$-0.0973525\pi$
$739$	20.4924	+	18.4514i	0.753825	+	0.678747i	−0.199769	+	0.979843i	$0.564019\pi$
$740$		0			0
$741$	17.4470	+	10.4156i	0.640931	+	0.382626i
$742$		0			0
$743$	−1.97033	−	9.26968i	−0.0722844	−	0.340072i	0.927113	−	0.374782i	$-0.122282\pi$
$743$	−1.97033	−	9.26968i	−0.0722844	−	0.340072i	−0.999397	+	0.0347104i	$0.988949\pi$
$744$		0			0
$745$	0.445391	−	0.198301i	0.0163179	−	0.00726518i
$746$		0			0
$747$	−64.1899	−	37.0601i	−2.34859	−	1.35596i
$748$		0			0
$749$		−	77.9613i		−	2.84865i
$750$		0			0
$751$	−0.585593	+	5.57155i	−0.0213686	+	0.203309i	−0.999997	−	0.00232668i	$-0.999259\pi$
$751$	−0.585593	+	5.57155i	−0.0213686	+	0.203309i	0.978629	+	0.205635i	$0.0659261\pi$
$752$		0			0
$753$	−16.1105	+	49.5829i	−0.587098	+	1.80690i
$754$		0			0
$755$	−2.14731	+	1.56011i	−0.0781486	+	0.0567783i
$756$		0			0
$757$	5.44692	−	6.04941i	0.197972	−	0.219870i	−0.635983	−	0.771703i	$-0.719405\pi$
$757$	5.44692	−	6.04941i	0.197972	−	0.219870i	0.833954	+	0.551834i	$0.186072\pi$
$758$		0			0
$759$	46.5736	+	5.60499i	1.69051	+	0.203448i
$760$		0			0
$761$	1.32156	−	6.21746i	0.0479066	−	0.225383i	−0.947681	−	0.319219i	$-0.896580\pi$
$761$	1.32156	−	6.21746i	0.0479066	−	0.225383i	0.995588	+	0.0938359i	$0.0299129\pi$
$762$		0			0
$763$	4.63871	+	44.1344i	0.167932	+	1.59777i
$764$		0			0
$765$	0.830829	+	3.90874i	0.0300387	+	0.141321i
$766$		0			0
$767$	−7.05541	−	6.54174i	−0.254756	−	0.236209i
$768$		0			0
$769$	22.3444	−	12.9005i	0.805759	−	0.465205i	−0.0397217	−	0.999211i	$-0.512647\pi$
$769$	22.3444	−	12.9005i	0.805759	−	0.465205i	0.845481	+	0.534005i	$0.179314\pi$
$770$		0			0
$771$	−21.9958	+	38.0978i	−0.792158	+	1.37206i
$772$		0			0
$773$	−3.45125	−	7.75164i	−0.124133	−	0.278807i	0.840780	−	0.541377i	$-0.182097\pi$
$773$	−3.45125	−	7.75164i	−0.124133	−	0.278807i	−0.964913	+	0.262570i	$0.915430\pi$
$774$		0			0
$775$	30.2050	+	9.81419i	1.08499	+	0.352536i
$776$		0			0
$777$	51.5125	+	22.9348i	1.84800	+	0.822782i
$778$		0			0
$779$	2.98006	+	9.17170i	0.106772	+	0.328610i
$780$		0			0
$781$	−13.2204	+	2.60275i	−0.473062	+	0.0931337i
$782$		0			0
$783$	−27.9263	+	31.0153i	−0.998004	+	1.10840i
$784$		0			0
$785$	−0.606120	−	0.834253i	−0.0216334	−	0.0297758i
$786$		0			0
$787$	3.85669	−	3.47258i	0.137476	−	0.123784i	−0.597524	−	0.801851i	$-0.703849\pi$
$787$	3.85669	−	3.47258i	0.137476	−	0.123784i	0.735000	+	0.678067i	$0.237182\pi$
$788$		0			0
$789$	−36.3442	+	16.1815i	−1.29389	+	0.576076i
$790$		0			0
$791$	−65.9686	+	38.0870i	−2.34557	+	1.35422i
$792$		0			0
$793$	−0.648932	+	5.41274i	−0.0230442	+	0.192212i
$794$		0			0
$795$	2.65227	+	0.278765i	0.0940663	+	0.00988677i
$796$		0			0
$797$	−13.1132	−	14.5637i	−0.464494	−	0.515873i	0.464698	−	0.885469i	$-0.346163\pi$
$797$	−13.1132	−	14.5637i	−0.464494	−	0.515873i	−0.929193	+	0.369596i	$0.879496\pi$
$798$		0			0
$799$	−51.2728	+	5.38899i	−1.81390	+	0.190649i
$800$		0			0
$801$	−68.4758	+	22.2491i	−2.41947	+	0.786135i
$802$		0			0
$803$	0.357936	+	3.98106i	0.0126313	+	0.140489i
$804$		0			0
$805$	0.725499	+	2.23285i	0.0255705	+	0.0786978i
$806$		0			0
$807$	−63.8330	+	46.3774i	−2.24703	+	1.63256i
$808$		0			0
$809$	−15.3935	+	3.27199i	−0.541207	+	0.115037i	−0.470401	−	0.882453i	$-0.655891\pi$
$809$	−15.3935	+	3.27199i	−0.541207	+	0.115037i	−0.0708066	+	0.997490i	$0.522557\pi$
$810$		0			0
$811$	−15.1804	+	20.8940i	−0.533055	+	0.733688i	−0.987592	−	0.157040i	$-0.949805\pi$
$811$	−15.1804	+	20.8940i	−0.533055	+	0.733688i	0.454537	+	0.890728i	$0.349805\pi$
$812$		0			0
$813$	17.6937	+	10.2155i	0.620546	+	0.358273i
$814$		0			0
$815$	−1.30235	+	2.25573i	−0.0456193	+	0.0790149i
$816$		0			0
$817$	−18.9167	−	1.98822i	−0.661810	−	0.0695591i
$818$		0			0
$819$	−61.5815	−	87.4156i	−2.15183	−	3.05455i
$820$		0			0
$821$	13.4224	−	30.1473i	0.468446	−	1.05215i	−0.512645	−	0.858601i	$-0.671334\pi$
$821$	13.4224	−	30.1473i	0.468446	−	1.05215i	0.981091	−	0.193546i	$-0.0619990\pi$
$822$		0			0
$823$	−7.73062	−	1.64319i	−0.269472	−	0.0572781i	0.0711936	−	0.997463i	$-0.477319\pi$
$823$	−7.73062	−	1.64319i	−0.269472	−	0.0572781i	−0.340666	+	0.940184i	$0.610653\pi$
$824$		0			0
$825$	48.3223	−	14.9006i	1.68237	−	0.518773i
$826$		0			0
$827$	5.72565	−	1.86038i	0.199100	−	0.0646917i	−0.207769	−	0.978178i	$-0.566620\pi$
$827$	5.72565	−	1.86038i	0.199100	−	0.0646917i	0.406870	+	0.913486i	$0.366620\pi$
$828$		0			0
$829$	−25.2680	−	11.2500i	−0.877593	−	0.390729i	−0.0820509	−	0.996628i	$-0.526147\pi$
$829$	−25.2680	−	11.2500i	−0.877593	−	0.390729i	−0.795542	+	0.605899i	$0.792814\pi$
$830$		0			0
$831$	5.09513	−	15.6812i	0.176748	−	0.543975i
$832$		0			0
$833$	69.8297	+	50.7342i	2.41946	+	1.75784i
$834$		0			0
$835$	0.989980	+	1.71470i	0.0342597	+	0.0593395i
$836$		0			0
$837$			65.0447i			2.24828i
$838$		0			0
$839$	−2.17381	−	4.88245i	−0.0750481	−	0.168561i	0.872125	−	0.489282i	$-0.162741\pi$
$839$	−2.17381	−	4.88245i	−0.0750481	−	0.168561i	−0.947174	+	0.320722i	$0.896075\pi$
$840$		0			0
$841$	−8.23763	−	9.14881i	−0.284056	−	0.315476i
$842$		0			0
$843$	32.7994	−	73.6688i	1.12967	−	2.53729i
$844$		0			0
$845$	0.611104	−	1.27131i	0.0210226	−	0.0437343i
$846$		0			0
$847$	28.9669	+	42.5033i	0.995313	+	1.46043i
$848$		0			0
$849$	−41.1668	−	8.75027i	−1.41284	−	0.300308i
$850$		0			0
$851$	−18.1566	+	1.90833i	−0.622400	+	0.0654169i
$852$		0			0
$853$	−21.7291	−	7.06022i	−0.743991	−	0.241737i	−0.0875977	−	0.996156i	$-0.527919\pi$
$853$	−21.7291	−	7.06022i	−0.743991	−	0.241737i	−0.656394	+	0.754418i	$0.727919\pi$
$854$		0			0
$855$	0.132632	−	1.26191i	0.00453591	−	0.0431563i
$856$		0			0
$857$	34.5861			1.18144			0.590720	−	0.806877i	$-0.298844\pi$
$857$	34.5861			1.18144			0.590720	+	0.806877i	$0.298844\pi$
$858$		0			0
$859$	41.7828			1.42561			0.712806	−	0.701362i	$-0.247424\pi$
$859$	41.7828			1.42561			0.712806	+	0.701362i	$0.247424\pi$
$860$		0			0
$861$	7.81385	−	74.3438i	0.266295	−	2.53363i
$862$		0			0
$863$	−12.4786	−	4.05456i	−0.424778	−	0.138019i	0.0888239	−	0.996047i	$-0.471689\pi$
$863$	−12.4786	−	4.05456i	−0.424778	−	0.138019i	−0.513602	+	0.858029i	$0.671689\pi$
$864$		0			0
$865$	−0.155399	+	0.0163330i	−0.00528371	+	0.000555340i
$866$		0			0
$867$	−49.9829	−	10.6242i	−1.69751	−	0.360817i
$868$		0			0
$869$	7.87843	−	34.5031i	0.267257	−	1.17044i
$870$		0			0
$871$	25.8712	+	8.82568i	0.876611	+	0.299047i
$872$		0			0
$873$	−11.5923	+	26.0368i	−0.392341	+	0.881213i
$874$		0			0
$875$	3.39091	+	3.76599i	0.114634	+	0.127314i
$876$		0			0
$877$	7.64547	+	17.1720i	0.258169	+	0.579858i	0.995402	−	0.0957807i	$-0.0305348\pi$
$877$	7.64547	+	17.1720i	0.258169	+	0.579858i	−0.737233	+	0.675638i	$0.763868\pi$
$878$		0			0
$879$			48.7502i			1.64430i
$880$		0			0
$881$	12.6528	+	21.9153i	0.426284	+	0.738346i	0.996539	−	0.0831219i	$-0.0264891\pi$
$881$	12.6528	+	21.9153i	0.426284	+	0.738346i	−0.570255	+	0.821468i	$0.693156\pi$
$882$		0			0
$883$	45.8129	+	33.2850i	1.54173	+	1.12013i	0.949242	+	0.314546i	$0.101852\pi$
$883$	45.8129	+	33.2850i	1.54173	+	1.12013i	0.592483	+	0.805583i	$0.298148\pi$
$884$		0			0
$885$	−0.273483	+	0.841693i	−0.00919302	+	0.0282932i
$886$		0			0
$887$	−45.2226	−	20.1344i	−1.51843	−	0.676047i	−0.532994	−	0.846119i	$-0.678933\pi$
$887$	−45.2226	−	20.1344i	−1.51843	−	0.676047i	−0.985432	+	0.170072i	$0.945600\pi$
$888$		0			0
$889$	−11.1240	+	3.61440i	−0.373086	+	0.121223i
$890$		0			0
$891$	23.2857	+	33.0860i	0.780101	+	1.10842i
$892$		0			0
$893$	16.0124	+	3.40354i	0.535835	+	0.113895i
$894$		0			0
$895$	−0.0727429	+	0.163383i	−0.00243153	+	0.00546130i
$896$		0			0
$897$	46.2795	+	21.4200i	1.54523	+	0.715192i
$898$		0			0
$899$	25.8676	+	2.71879i	0.862732	+	0.0906768i
$900$		0			0
$901$	−23.3469	+	40.4380i	−0.777797	+	1.34718i
$902$		0			0
$903$	127.687	+	73.7203i	4.24917	+	2.45326i
$904$		0			0
$905$	−0.964288	+	1.32723i	−0.0320540	+	0.0441186i
$906$		0			0
$907$	−11.2574	+	2.39284i	−0.373797	+	0.0794530i	−0.390980	−	0.920399i	$-0.627864\pi$
$907$	−11.2574	+	2.39284i	−0.373797	+	0.0794530i	0.0171825	+	0.999852i	$0.494530\pi$
$908$		0			0
$909$	16.8983	−	12.2774i	0.560482	−	0.407214i
$910$		0			0
$911$	−13.0223	−	40.0785i	−0.431448	−	1.32786i	−0.896683	−	0.442672i	$-0.854030\pi$
$911$	−13.0223	−	40.0785i	−0.431448	−	1.32786i	0.465236	−	0.885187i	$-0.345970\pi$
$912$		0			0
$913$	25.4988	+	29.1911i	0.843886	+	0.966084i
$914$		0			0
$915$	0.476900	−	0.154954i	0.0157658	−	0.00512263i
$916$		0			0
$917$	−7.35858	+	0.773418i	−0.243002	+	0.0255405i
$918$		0			0
$919$	−8.62922	−	9.58372i	−0.284652	−	0.316138i	0.583814	−	0.811888i	$-0.301560\pi$
$919$	−8.62922	−	9.58372i	−0.284652	−	0.316138i	−0.868465	+	0.495750i	$0.834893\pi$
$920$		0			0
$921$	−32.4032	−	3.40571i	−1.06772	−	0.112222i
$922$		0			0
$923$	−14.5438	−	1.74365i	−0.478714	−	0.0573929i
$924$		0			0
$925$	−17.0436	+	9.84010i	−0.560388	+	0.323540i
$926$		0			0
$927$	44.0477	−	19.6113i	1.44672	−	0.644119i
$928$		0			0
$929$	33.2184	−	29.9099i	1.08986	−	0.981313i	0.0899660	−	0.995945i	$-0.471324\pi$
$929$	33.2184	−	29.9099i	1.08986	−	0.981313i	0.999893	+	0.0146315i	$0.00465751\pi$
$930$		0			0
$931$	−16.1095	−	22.1728i	−0.527966	−	0.726683i
$932$		0			0
$933$	15.4784	−	17.1905i	0.506740	−	0.562791i
$934$		0			0
$935$	0.249683	−	2.07469i	0.00816550	−	0.0678496i
$936$		0			0
$937$	−7.36588	−	22.6698i	−0.240633	−	0.740591i	−0.996324	−	0.0856636i	$-0.972699\pi$
$937$	−7.36588	−	22.6698i	−0.240633	−	0.740591i	0.755691	−	0.654928i	$-0.227301\pi$
$938$		0			0
$939$	−6.35251	−	2.82832i	−0.207306	−	0.0922987i
$940$		0			0
$941$	−22.5750	−	7.33505i	−0.735922	−	0.239116i	−0.0830096	−	0.996549i	$-0.526453\pi$
$941$	−22.5750	−	7.33505i	−0.735922	−	0.239116i	−0.652913	+	0.757433i	$0.726453\pi$
$942$		0			0
$943$	9.84422	+	22.1105i	0.320572	+	0.720017i
$944$		0			0
$945$	−2.59164	+	4.48884i	−0.0843059	+	0.146022i
$946$		0			0
$947$	12.9029	−	7.44947i	0.419287	−	0.242075i	−0.275485	−	0.961305i	$-0.588839\pi$
$947$	12.9029	−	7.44947i	0.419287	−	0.242075i	0.694772	+	0.719230i	$0.255505\pi$
$948$		0			0
$949$	−0.965404	+	4.23673i	−0.0313383	+	0.137530i
$950$		0			0
$951$	1.88013	+	8.84531i	0.0609674	+	0.286829i
$952$		0			0
$953$	4.02439	+	38.2895i	0.130363	+	1.24032i	0.842662	+	0.538442i	$0.180987\pi$
$953$	4.02439	+	38.2895i	0.130363	+	1.24032i	−0.712300	+	0.701875i	$0.752346\pi$
$954$		0			0
$955$	−0.390411	+	1.83674i	−0.0126334	+	0.0594355i
$956$		0			0
$957$	36.1727	−	20.1646i	1.16930	−	0.651828i
$958$		0			0
$959$	8.87158	−	9.85289i	0.286478	−	0.318166i
$960$		0			0
$961$	7.71558	−	5.60570i	0.248890	−	0.180829i
$962$		0			0
$963$	−32.6772	+	100.570i	−1.05301	+	3.24083i
$964$		0			0
$965$	0.00848861	−	0.0807638i	0.000273258	−	0.00259988i
$966$		0			0
$967$			8.46245i			0.272134i	0.990700	+	0.136067i	$0.0434463\pi$
$967$			8.46245i			0.272134i	−0.990700	+	0.136067i	$0.956554\pi$
$968$		0			0
$969$	28.3402	+	16.3622i	0.910419	+	0.525631i
$970$		0			0
$971$	−43.4366	+	19.3392i	−1.39395	+	0.620626i	−0.959920	−	0.280273i	$-0.909575\pi$
$971$	−43.4366	+	19.3392i	−1.39395	+	0.620626i	−0.434028	+	0.900899i	$0.642908\pi$
$972$		0			0
$973$	9.55895	+	44.9713i	0.306446	+	1.44171i
$974$		0			0
$975$	54.9668	+	0.802599i	1.76035	+	0.0257037i
$976$		0			0
$977$	−16.1311	−	14.5245i	−0.516079	−	0.464680i	0.369458	−	0.929247i	$-0.379543\pi$
$977$	−16.1311	−	14.5245i	−0.516079	−	0.464680i	−0.885538	+	0.464567i	$0.846210\pi$
$978$		0			0
$979$	37.6465	+	0.566670i	1.20319	+	0.0181108i
$980$		0			0
$981$	12.5148	−	58.8776i	0.399567	−	1.87982i
$982$		0			0
$983$	−20.3243	−	27.9740i	−0.648246	−	0.892234i	0.350776	−	0.936459i	$-0.385918\pi$
$983$	−20.3243	−	27.9740i	−0.648246	−	0.892234i	−0.999022	+	0.0442259i	$0.985918\pi$
$984$		0			0
$985$	−1.29919	+	0.276152i	−0.0413957	+	0.00879893i
$986$		0			0
$987$	−102.659	−	74.5862i	−3.26767	−	2.37410i
$988$		0			0
$989$	−47.7370			−1.51795
$990$		0			0
$991$	−12.5253	−	21.6944i	−0.397878	−	0.689144i	0.595586	−	0.803291i	$-0.296920\pi$
$991$	−12.5253	−	21.6944i	−0.397878	−	0.689144i	−0.993464	+	0.114147i	$0.963587\pi$
$992$		0			0
$993$	−38.3056	+	52.7231i	−1.21559	+	1.67312i
$994$		0			0
$995$	−1.97076	+	1.77448i	−0.0624771	+	0.0562547i
$996$		0			0
$997$	−3.26490	−	31.0635i	−0.103401	−	0.983790i	−0.916057	−	0.401048i	$-0.868646\pi$
$997$	−3.26490	−	31.0635i	−0.103401	−	0.983790i	0.812657	−	0.582743i	$-0.198020\pi$
$998$		0			0
$999$	−29.9532	−	26.9700i	−0.947677	−	0.853292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.49.1	✓	112
11.9	even	5	inner	572.2.bq.a.361.14	yes	112
13.4	even	6	inner	572.2.bq.a.225.14	yes	112
143.108	even	30	inner	572.2.bq.a.537.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.49.1	✓	112	1.1	even	1	trivial
572.2.bq.a.225.14	yes	112	13.4	even	6	inner
572.2.bq.a.361.14	yes	112	11.9	even	5	inner
572.2.bq.a.537.1	yes	112	143.108	even	30	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.319495 + 3.03979i) q^{3} +(-0.103194 - 0.0335297i) q^{5} +(4.65033 - 0.488770i) q^{7} +(-6.20380 - 1.31866i) q^{9} +O(q^{10})\)	\(q+(-0.319495 + 3.03979i) q^{3} +(-0.103194 - 0.0335297i) q^{5} +(4.65033 - 0.488770i) q^{7} +(-6.20380 - 1.31866i) q^{9} +(2.84700 + 1.70135i) q^{11} +(2.37321 + 2.71438i) q^{13} +(0.134893 - 0.302975i) q^{15} +(3.88546 + 4.31524i) q^{17} +(-0.749938 - 1.68439i) q^{19} +14.2922i q^{21} +(-2.31370 - 4.00744i) q^{23} +(-4.03556 - 2.93201i) q^{25} +(3.15696 - 9.71612i) q^{27} +(-3.73204 - 1.66161i) q^{29} +(-6.05525 + 1.96747i) q^{31} +(-6.08136 + 8.11070i) q^{33} +(-0.496274 - 0.105486i) q^{35} +(1.60471 - 3.60424i) q^{37} +(-9.00938 + 6.34682i) q^{39} +(-5.20171 - 0.546721i) q^{41} +(5.15808 - 8.93406i) q^{43} +(0.595979 + 0.344089i) q^{45} +(-5.21866 + 7.18287i) q^{47} +(14.5397 - 3.09051i) q^{49} +(-14.3588 + 10.4323i) q^{51} +(2.48490 + 7.64774i) q^{53} +(-0.236747 - 0.271028i) q^{55} +(5.35978 - 1.74150i) q^{57} +(-2.65390 + 0.278937i) q^{59} +(1.01171 + 1.12362i) q^{61} +(-29.4942 - 3.09997i) q^{63} +(-0.153888 - 0.359681i) q^{65} +(6.56569 - 3.79070i) q^{67} +(12.9210 - 5.75280i) q^{69} +(-3.01910 + 2.71841i) q^{71} +(0.708385 + 0.975009i) q^{73} +(10.2020 - 11.3305i) q^{75} +(14.0711 + 6.52034i) q^{77} +(-3.29747 - 10.1486i) q^{79} +(11.1441 + 4.96168i) q^{81} +(11.1145 + 3.61131i) q^{83} +(-0.256267 - 0.575585i) q^{85} +(6.24331 - 10.8137i) q^{87} +(9.83124 - 5.67607i) q^{89} +(12.3629 + 11.4628i) q^{91} +(-4.04607 - 19.0353i) q^{93} +(0.0209119 + 0.198964i) q^{95} +(0.934294 - 4.39551i) q^{97} +(-15.4187 - 14.3091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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