LMFDB - Embedded newform 572.2.n.a.521.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			521.5
Root			$1.86439 + 1.35456i$ of defining polynomial
Character	$\chi$	$=$	572.521
Dual form			572.2.n.a.157.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.712135 - 2.19173i) q^{3} +(0.270974 - 0.196874i) q^{5} +(0.132310 + 0.407207i) q^{7} +(-1.86947 - 1.35825i) q^{9} +O(q^{10})$	\(q+(0.712135 - 2.19173i) q^{3} +(0.270974 - 0.196874i) q^{5} +(0.132310 + 0.407207i) q^{7} +(-1.86947 - 1.35825i) q^{9} +(-0.852017 - 3.20532i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.238524 - 0.734102i) q^{15} +(4.82213 - 3.50348i) q^{17} +(1.78080 - 5.48073i) q^{19} +0.986709 q^{21} -8.85292 q^{23} +(-1.51042 + 4.64859i) q^{25} +(1.28495 - 0.933569i) q^{27} +(-0.385914 - 1.18772i) q^{29} +(5.49829 + 3.99474i) q^{31} +(-7.63193 - 0.415231i) q^{33} +(0.116021 + 0.0842943i) q^{35} +(-0.727524 - 2.23909i) q^{37} +(-1.86439 + 1.35456i) q^{39} +(-2.01426 + 6.19926i) q^{41} -8.32438 q^{43} -0.773984 q^{45} +(0.558924 - 1.72019i) q^{47} +(5.51481 - 4.00674i) q^{49} +(-4.24467 - 13.0637i) q^{51} +(9.39104 + 6.82299i) q^{53} +(-0.861920 - 0.700819i) q^{55} +(-10.7441 - 7.80603i) q^{57} +(-0.904131 - 2.78263i) q^{59} +(-11.3657 + 8.25765i) q^{61} +(0.305741 - 0.940973i) q^{63} -0.334943 q^{65} +13.6646 q^{67} +(-6.30447 + 19.4032i) q^{69} +(5.83330 - 4.23814i) q^{71} +(3.33642 + 10.2684i) q^{73} +(9.11280 + 6.62084i) q^{75} +(1.19250 - 0.771042i) q^{77} +(-0.262479 - 0.190702i) q^{79} +(-3.27330 - 10.0742i) q^{81} +(9.48779 - 6.89328i) q^{83} +(0.616928 - 1.89871i) q^{85} -2.87798 q^{87} +11.6449 q^{89} +(0.132310 - 0.407207i) q^{91} +(12.6709 - 9.20595i) q^{93} +(-0.596465 - 1.83573i) q^{95} +(6.84423 + 4.97262i) q^{97} +(-2.76081 + 7.14951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.712135	−	2.19173i	0.411151	−	1.26539i	−0.504497	−	0.863413i	$-0.668322\pi$
$3$	0.712135	−	2.19173i	0.411151	−	1.26539i	0.915648	−	0.401980i	$-0.131678\pi$
$4$		0			0
$5$	0.270974	−	0.196874i	0.121183	−	0.0880449i	−0.525543	−	0.850767i	$-0.676138\pi$
$5$	0.270974	−	0.196874i	0.121183	−	0.0880449i	0.646726	+	0.762722i	$0.276138\pi$
$6$		0			0
$7$	0.132310	+	0.407207i	0.0500083	+	0.153910i	0.972942	−	0.231049i	$-0.0742157\pi$
$7$	0.132310	+	0.407207i	0.0500083	+	0.153910i	−0.922934	+	0.384959i	$0.874216\pi$
$8$		0			0
$9$	−1.86947	−	1.35825i	−0.623158	−	0.452751i
$10$		0			0
$11$	−0.852017	−	3.20532i	−0.256893	−	0.966440i
$11$	−0.852017	−	3.20532i	−0.256893	−	0.966440i
$12$		0			0
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$		0			0
$15$	−0.238524	−	0.734102i	−0.0615867	−	0.189544i
$16$		0			0
$17$	4.82213	−	3.50348i	1.16954	−	0.849720i	0.178585	−	0.983924i	$-0.442848\pi$
$17$	4.82213	−	3.50348i	1.16954	−	0.849720i	0.990954	+	0.134205i	$0.0428480\pi$
$18$		0			0
$19$	1.78080	−	5.48073i	0.408543	−	1.25737i	−0.509358	−	0.860555i	$-0.670117\pi$
$19$	1.78080	−	5.48073i	0.408543	−	1.25737i	0.917901	−	0.396810i	$-0.129883\pi$
$20$		0			0
$21$	0.986709			0.215317
$22$		0			0
$23$	−8.85292			−1.84596			−0.922980	−	0.384847i	$-0.874254\pi$
$23$	−8.85292			−1.84596			−0.922980	+	0.384847i	$0.874254\pi$
$24$		0			0
$25$	−1.51042	+	4.64859i	−0.302083	+	0.929717i
$26$		0			0
$27$	1.28495	−	0.933569i	0.247288	−	0.179665i
$28$		0			0
$29$	−0.385914	−	1.18772i	−0.0716625	−	0.220554i	0.908810	−	0.417210i	$-0.136992\pi$
$29$	−0.385914	−	1.18772i	−0.0716625	−	0.220554i	−0.980473	+	0.196655i	$0.936992\pi$
$30$		0			0
$31$	5.49829	+	3.99474i	0.987522	+	0.717477i	0.959377	−	0.282127i	$-0.0910399\pi$
$31$	5.49829	+	3.99474i	0.987522	+	0.717477i	0.0281453	+	0.999604i	$0.491040\pi$
$32$		0			0
$33$	−7.63193	−	0.415231i	−1.32855	−	0.0722824i
$34$		0			0
$35$	0.116021	+	0.0842943i	0.0196112	+	0.0142483i
$36$		0			0
$37$	−0.727524	−	2.23909i	−0.119604	−	0.368104i	0.873275	−	0.487227i	$-0.161992\pi$
$37$	−0.727524	−	2.23909i	−0.119604	−	0.368104i	−0.992879	+	0.119123i	$0.961992\pi$
$38$		0			0
$39$	−1.86439	+	1.35456i	−0.298542	+	0.216903i
$40$		0			0
$41$	−2.01426	+	6.19926i	−0.314575	+	0.968162i	0.661354	+	0.750074i	$0.269982\pi$
$41$	−2.01426	+	6.19926i	−0.314575	+	0.968162i	−0.975929	+	0.218088i	$0.930018\pi$
$42$		0			0
$43$	−8.32438			−1.26946			−0.634728	−	0.772735i	$-0.718888\pi$
$43$	−8.32438			−1.26946			−0.634728	+	0.772735i	$0.718888\pi$
$44$		0			0
$45$	−0.773984			−0.115379
$46$		0			0
$47$	0.558924	−	1.72019i	0.0815275	−	0.250916i	−0.901982	−	0.431774i	$-0.857888\pi$
$47$	0.558924	−	1.72019i	0.0815275	−	0.250916i	0.983509	+	0.180859i	$0.0578876\pi$
$48$		0			0
$49$	5.51481	−	4.00674i	0.787830	−	0.572392i
$50$		0			0
$51$	−4.24467	−	13.0637i	−0.594372	−	1.82929i
$52$		0			0
$53$	9.39104	+	6.82299i	1.28996	+	0.937210i	0.999805	−	0.0197700i	$-0.00629340\pi$
$53$	9.39104	+	6.82299i	1.28996	+	0.937210i	0.290154	+	0.956980i	$0.406293\pi$
$54$		0			0
$55$	−0.861920	−	0.700819i	−0.116221	−	0.0944984i
$56$		0			0
$57$	−10.7441	−	7.80603i	−1.42309	−	1.03393i
$58$		0			0
$59$	−0.904131	−	2.78263i	−0.117708	−	0.362267i	0.874794	−	0.484494i	$-0.160996\pi$
$59$	−0.904131	−	2.78263i	−0.117708	−	0.362267i	−0.992502	+	0.122227i	$0.960996\pi$
$60$		0			0
$61$	−11.3657	+	8.25765i	−1.45523	+	1.05728i	−0.470652	+	0.882319i	$0.655981\pi$
$61$	−11.3657	+	8.25765i	−1.45523	+	1.05728i	−0.984575	+	0.174965i	$0.944019\pi$
$62$		0			0
$63$	0.305741	−	0.940973i	0.0385197	−	0.118551i
$64$		0			0
$65$	−0.334943			−0.0415445
$66$		0			0
$67$	13.6646			1.66940			0.834698	−	0.550708i	$-0.185642\pi$
$67$	13.6646			1.66940			0.834698	+	0.550708i	$0.185642\pi$
$68$		0			0
$69$	−6.30447	+	19.4032i	−0.758969	+	2.33587i
$70$		0			0
$71$	5.83330	−	4.23814i	0.692286	−	0.502975i	−0.185125	−	0.982715i	$-0.559269\pi$
$71$	5.83330	−	4.23814i	0.692286	−	0.502975i	0.877411	+	0.479740i	$0.159269\pi$
$72$		0			0
$73$	3.33642	+	10.2684i	0.390498	+	1.20183i	0.932412	+	0.361396i	$0.117700\pi$
$73$	3.33642	+	10.2684i	0.390498	+	1.20183i	−0.541914	+	0.840434i	$0.682300\pi$
$74$		0			0
$75$	9.11280	+	6.62084i	1.05226	+	0.764509i
$76$		0			0
$77$	1.19250	−	0.771042i	0.135898	−	0.0878684i
$78$		0			0
$79$	−0.262479	−	0.190702i	−0.0295312	−	0.0214557i	0.572922	−	0.819610i	$-0.305810\pi$
$79$	−0.262479	−	0.190702i	−0.0295312	−	0.0214557i	−0.602453	+	0.798154i	$0.705810\pi$
$80$		0			0
$81$	−3.27330	−	10.0742i	−0.363700	−	1.11935i
$82$		0			0
$83$	9.48779	−	6.89328i	1.04142	−	0.756636i	0.0708578	−	0.997486i	$-0.477426\pi$
$83$	9.48779	−	6.89328i	1.04142	−	0.756636i	0.970562	+	0.240851i	$0.0774264\pi$
$84$		0			0
$85$	0.616928	−	1.89871i	0.0669152	−	0.205944i
$86$		0			0
$87$	−2.87798			−0.308552
$88$		0			0
$89$	11.6449			1.23435			0.617177	−	0.786824i	$-0.288276\pi$
$89$	11.6449			1.23435			0.617177	+	0.786824i	$0.288276\pi$
$90$		0			0
$91$	0.132310	−	0.407207i	0.0138698	−	0.0426869i
$92$		0			0
$93$	12.6709	−	9.20595i	1.31391	−	0.954613i
$94$		0			0
$95$	−0.596465	−	1.83573i	−0.0611960	−	0.188342i
$96$		0			0
$97$	6.84423	+	4.97262i	0.694926	+	0.504893i	0.878276	−	0.478154i	$-0.158694\pi$
$97$	6.84423	+	4.97262i	0.694926	+	0.504893i	−0.183350	+	0.983048i	$0.558694\pi$
$98$		0			0
$99$	−2.76081	+	7.14951i	−0.277471	+	0.718553i
$100$		0			0
$101$	−10.7294	−	7.79534i	−1.06761	−	0.775665i	−0.0921299	−	0.995747i	$-0.529367\pi$
$101$	−10.7294	−	7.79534i	−1.06761	−	0.775665i	−0.975481	+	0.220082i	$0.929367\pi$
$102$		0			0
$103$	4.95813	+	15.2595i	0.488539	+	1.50357i	0.826789	+	0.562512i	$0.190165\pi$
$103$	4.95813	+	15.2595i	0.488539	+	1.50357i	−0.338250	+	0.941056i	$0.609835\pi$
$104$		0			0
$105$	0.267373	−	0.194258i	0.0260929	−	0.0189576i
$106$		0			0
$107$	−0.196156	+	0.603705i	−0.0189631	+	0.0583624i	−0.960090	−	0.279690i	$-0.909768\pi$
$107$	−0.196156	+	0.603705i	−0.0189631	+	0.0583624i	0.941127	+	0.338053i	$0.109768\pi$
$108$		0			0
$109$	2.90640			0.278382			0.139191	−	0.990266i	$-0.455550\pi$
$109$	2.90640			0.278382			0.139191	+	0.990266i	$0.455550\pi$
$110$		0			0
$111$	−5.42556			−0.514972
$112$		0			0
$113$	1.08963	−	3.35355i	0.102504	−	0.315475i	−0.886632	−	0.462475i	$-0.846962\pi$
$113$	1.08963	−	3.35355i	0.102504	−	0.315475i	0.989137	+	0.147000i	$0.0469616\pi$
$114$		0			0
$115$	−2.39891	+	1.74291i	−0.223700	+	0.162527i
$116$		0			0
$117$	0.714075	+	2.19770i	0.0660163	+	0.203177i
$118$		0			0
$119$	2.06466	+	1.50006i	0.189267	+	0.137510i
$120$		0			0
$121$	−9.54813	+	5.46197i	−0.868012	+	0.496543i
$122$		0			0
$123$	12.1527	+	8.82942i	1.09577	+	0.796122i
$124$		0			0
$125$	1.02342	+	3.14976i	0.0915373	+	0.281723i
$126$		0			0
$127$	−3.86193	+	2.80586i	−0.342691	+	0.248980i	−0.745796	−	0.666174i	$-0.767931\pi$
$127$	−3.86193	+	2.80586i	−0.342691	+	0.248980i	0.403105	+	0.915154i	$0.367931\pi$
$128$		0			0
$129$	−5.92808	+	18.2448i	−0.521939	+	1.60636i
$130$		0			0
$131$	17.7374			1.54972			0.774862	−	0.632131i	$-0.217819\pi$
$131$	17.7374			1.54972			0.774862	+	0.632131i	$0.217819\pi$
$132$		0			0
$133$	2.46741			0.213951
$134$		0			0
$135$	0.164392	−	0.505946i	0.0141486	−	0.0435449i
$136$		0			0
$137$	−14.0568	+	10.2129i	−1.20095	+	0.872545i	−0.994378	−	0.105886i	$-0.966232\pi$
$137$	−14.0568	+	10.2129i	−1.20095	+	0.872545i	−0.206576	+	0.978430i	$0.566232\pi$
$138$		0			0
$139$	−1.13915	−	3.50594i	−0.0966212	−	0.297370i	0.891052	−	0.453902i	$-0.149968\pi$
$139$	−1.13915	−	3.50594i	−0.0966212	−	0.297370i	−0.987673	+	0.156532i	$0.949968\pi$
$140$		0			0
$141$	−3.37216	−	2.45002i	−0.283987	−	0.206329i
$142$		0			0
$143$	−1.19474	+	3.09396i	−0.0999094	+	0.258730i
$144$		0			0
$145$	−0.338405	−	0.245866i	−0.0281030	−	0.0204180i
$146$		0			0
$147$	−4.85439	−	14.9403i	−0.400384	−	1.23225i
$148$		0			0
$149$	13.2942	−	9.65877i	1.08910	−	0.791278i	0.109853	−	0.993948i	$-0.464962\pi$
$149$	13.2942	−	9.65877i	1.08910	−	0.791278i	0.979247	+	0.202670i	$0.0649620\pi$
$150$		0			0
$151$	−1.74244	+	5.36267i	−0.141797	+	0.436408i	−0.996585	−	0.0825699i	$-0.973687\pi$
$151$	−1.74244	+	5.36267i	−0.141797	+	0.436408i	0.854788	+	0.518978i	$0.173687\pi$
$152$		0			0
$153$	−13.7735			−1.11352
$154$		0			0
$155$	2.27636			0.182842
$156$		0			0
$157$	−2.09153	+	6.43707i	−0.166922	+	0.513734i	−0.999173	−	0.0406657i	$-0.987052\pi$
$157$	−2.09153	+	6.43707i	−0.166922	+	0.513734i	0.832250	+	0.554400i	$0.187052\pi$
$158$		0			0
$159$	21.6418	−	15.7237i	1.71631	−	1.24697i
$160$		0			0
$161$	−1.17133	−	3.60497i	−0.0923134	−	0.284112i
$162$		0			0
$163$	4.51559	+	3.28077i	0.353689	+	0.256970i	0.750415	−	0.660967i	$-0.229854\pi$
$163$	4.51559	+	3.28077i	0.353689	+	0.256970i	−0.396726	+	0.917937i	$0.629854\pi$
$164$		0			0
$165$	−2.14980	+	1.39001i	−0.167362	+	0.108212i
$166$		0			0
$167$	5.71772	+	4.15416i	0.442450	+	0.321459i	0.786608	−	0.617453i	$-0.211835\pi$
$167$	5.71772	+	4.15416i	0.442450	+	0.321459i	−0.344158	+	0.938912i	$0.611835\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$		0			0
$171$	−10.7734	+	7.82730i	−0.823859	+	0.598569i
$172$		0			0
$173$	−3.60679	+	11.1006i	−0.274220	+	0.843961i	0.715205	+	0.698914i	$0.246333\pi$
$173$	−3.60679	+	11.1006i	−0.274220	+	0.843961i	−0.989425	+	0.145047i	$0.953667\pi$
$174$		0			0
$175$	−2.09278			−0.158199
$176$		0			0
$177$	−6.74262			−0.506806
$178$		0			0
$179$	−4.42075	+	13.6057i	−0.330423	+	1.01694i	0.638511	+	0.769613i	$0.279551\pi$
$179$	−4.42075	+	13.6057i	−0.330423	+	1.01694i	−0.968933	+	0.247323i	$0.920449\pi$
$180$		0			0
$181$	−4.28538	+	3.11351i	−0.318529	+	0.231425i	−0.735548	−	0.677473i	$-0.763075\pi$
$181$	−4.28538	+	3.11351i	−0.318529	+	0.231425i	0.417018	+	0.908898i	$0.363075\pi$
$182$		0			0
$183$	10.0046	+	30.7910i	0.739562	+	2.27614i
$184$		0			0
$185$	−0.637960	−	0.463505i	−0.0469037	−	0.0340776i
$186$		0			0
$187$	−15.3383	−	12.4714i	−1.12165	−	0.912002i
$188$		0			0
$189$	0.550167	+	0.399720i	0.0400188	+	0.0290753i
$190$		0			0
$191$	1.02259	+	3.14720i	0.0739919	+	0.227724i	0.981212	−	0.192933i	$-0.0617999\pi$
$191$	1.02259	+	3.14720i	0.0739919	+	0.227724i	−0.907220	+	0.420656i	$0.861800\pi$
$192$		0			0
$193$	−13.4367	+	9.76236i	−0.967198	+	0.702710i	−0.954811	−	0.297213i	$-0.903943\pi$
$193$	−13.4367	+	9.76236i	−0.967198	+	0.702710i	−0.0123864	+	0.999923i	$0.503943\pi$
$194$		0			0
$195$	−0.238524	+	0.734102i	−0.0170811	+	0.0525702i
$196$		0			0
$197$	−3.92735			−0.279812			−0.139906	−	0.990165i	$-0.544680\pi$
$197$	−3.92735			−0.279812			−0.139906	+	0.990165i	$0.544680\pi$
$198$		0			0
$199$	0.0912952			0.00647174			0.00323587	−	0.999995i	$-0.498970\pi$
$199$	0.0912952			0.00647174			0.00323587	+	0.999995i	$0.498970\pi$
$200$		0			0
$201$	9.73103	−	29.9490i	0.686374	−	2.11244i
$202$		0			0
$203$	0.432589	−	0.314294i	0.0303618	−	0.0220591i
$204$		0			0
$205$	0.674662	+	2.07640i	0.0471205	+	0.145022i
$206$		0			0
$207$	16.5503	+	12.0245i	1.15032	+	0.835760i
$208$		0			0
$209$	−19.0847	−	1.03835i	−1.32012	−	0.0718238i
$210$		0			0
$211$	−13.6430	−	9.91224i	−0.939224	−	0.682386i	0.00900949	−	0.999959i	$-0.497132\pi$
$211$	−13.6430	−	9.91224i	−0.939224	−	0.682386i	−0.948234	+	0.317573i	$0.897132\pi$
$212$		0			0
$213$	−5.13475	−	15.8031i	−0.351827	−	1.08281i
$214$		0			0
$215$	−2.25569	+	1.63886i	−0.153837	+	0.111769i
$216$		0			0
$217$	−0.899211	+	2.76749i	−0.0610424	+	0.187869i
$218$		0			0
$219$	24.8816			1.68134
$220$		0			0
$221$	−5.96048			−0.400945
$222$		0			0
$223$	−4.06288	+	12.5043i	−0.272071	+	0.837348i	0.717909	+	0.696137i	$0.245099\pi$
$223$	−4.06288	+	12.5043i	−0.272071	+	0.837348i	−0.989980	+	0.141211i	$0.954901\pi$
$224$		0			0
$225$	9.13764	−	6.63888i	0.609176	−	0.442592i
$226$		0			0
$227$	−7.32883	−	22.5558i	−0.486432	−	1.49708i	−0.829896	−	0.557918i	$-0.811600\pi$
$227$	−7.32883	−	22.5558i	−0.486432	−	1.49708i	0.343464	−	0.939166i	$-0.388400\pi$
$228$		0			0
$229$	19.8550	+	14.4255i	1.31205	+	0.953264i	0.999995	+	0.00320129i	$0.00101900\pi$
$229$	19.8550	+	14.4255i	1.31205	+	0.953264i	0.312060	+	0.950062i	$0.398981\pi$
$230$		0			0
$231$	−0.840693	−	3.16272i	−0.0553135	−	0.208091i
$232$		0			0
$233$	−19.3104	−	14.0298i	−1.26507	−	0.919126i	−0.266073	−	0.963953i	$-0.585726\pi$
$233$	−19.3104	−	14.0298i	−1.26507	−	0.919126i	−0.998995	+	0.0448270i	$0.985726\pi$
$234$		0			0
$235$	−0.187208	−	0.576166i	−0.0122121	−	0.0375849i
$236$		0			0
$237$	−0.604888	+	0.439477i	−0.0392917	+	0.0285471i
$238$		0			0
$239$	5.58637	−	17.1931i	0.361352	−	1.11213i	−0.590881	−	0.806758i	$-0.701220\pi$
$239$	5.58637	−	17.1931i	0.361352	−	1.11213i	0.952234	−	0.305370i	$-0.0987801\pi$
$240$		0			0
$241$	13.4012			0.863248			0.431624	−	0.902054i	$-0.357941\pi$
$241$	13.4012			0.863248			0.431624	+	0.902054i	$0.357941\pi$
$242$		0			0
$243$	−19.6460			−1.26029
$244$		0			0
$245$	0.705546	−	2.17145i	0.0450757	−	0.138729i
$246$		0			0
$247$	−4.66218	+	3.38728i	−0.296648	+	0.215527i
$248$		0			0
$249$	−8.35160	−	25.7036i	−0.529261	−	1.62890i
$250$		0			0
$251$	5.80758	+	4.21945i	0.366571	+	0.266329i	0.755788	−	0.654817i	$-0.227254\pi$
$251$	5.80758	+	4.21945i	0.366571	+	0.266329i	−0.389217	+	0.921146i	$0.627254\pi$
$252$		0			0
$253$	7.54284	+	28.3764i	0.474214	+	1.78401i
$254$		0			0
$255$	−3.72211	−	2.70427i	−0.233088	−	0.169348i
$256$		0			0
$257$	−3.91769	−	12.0574i	−0.244379	−	0.752121i	−0.995738	−	0.0922275i	$-0.970601\pi$
$257$	−3.91769	−	12.0574i	−0.244379	−	0.752121i	0.751359	−	0.659894i	$-0.229399\pi$
$258$		0			0
$259$	0.815515	−	0.592506i	0.0506736	−	0.0368165i
$260$		0			0
$261$	−0.891769	+	2.74458i	−0.0551991	+	0.169885i
$262$		0			0
$263$	2.83479			0.174801			0.0874003	−	0.996173i	$-0.472144\pi$
$263$	2.83479			0.174801			0.0874003	+	0.996173i	$0.472144\pi$
$264$		0			0
$265$	3.88800			0.238838
$266$		0			0
$267$	8.29272	−	25.5224i	0.507506	−	1.56194i
$268$		0			0
$269$	12.7382	−	9.25483i	0.776660	−	0.564277i	−0.127314	−	0.991862i	$-0.540636\pi$
$269$	12.7382	−	9.25483i	0.776660	−	0.564277i	0.903975	+	0.427586i	$0.140636\pi$
$270$		0			0
$271$	−8.94627	−	27.5338i	−0.543447	−	1.67256i	−0.724653	−	0.689113i	$-0.758000\pi$
$271$	−8.94627	−	27.5338i	−0.543447	−	1.67256i	0.181206	−	0.983445i	$-0.442000\pi$
$272$		0			0
$273$	−0.798264	−	0.579973i	−0.0483131	−	0.0351016i
$274$		0			0
$275$	16.1871	+	0.880693i	0.976119	+	0.0531078i
$276$		0			0
$277$	15.6731	+	11.3872i	0.941707	+	0.684190i	0.948831	−	0.315785i	$-0.102268\pi$
$277$	15.6731	+	11.3872i	0.941707	+	0.684190i	−0.00712418	+	0.999975i	$0.502268\pi$
$278$		0			0
$279$	−4.85304	−	14.9361i	−0.290544	−	0.894203i
$280$		0			0
$281$	−8.24663	+	5.99153i	−0.491953	+	0.357425i	−0.805935	−	0.592004i	$-0.798337\pi$
$281$	−8.24663	+	5.99153i	−0.491953	+	0.357425i	0.313982	+	0.949429i	$0.398337\pi$
$282$		0			0
$283$	−3.34988	+	10.3099i	−0.199130	+	0.612858i	0.800774	+	0.598967i	$0.204422\pi$
$283$	−3.34988	+	10.3099i	−0.199130	+	0.612858i	−0.999904	+	0.0138915i	$0.995578\pi$
$284$		0			0
$285$	−4.44818			−0.263487
$286$		0			0
$287$	−2.79089			−0.164741
$288$		0			0
$289$	5.72527	−	17.6206i	0.336780	−	1.03650i
$290$		0			0
$291$	15.7726	−	11.4595i	0.924608	−	0.671767i
$292$		0			0
$293$	−6.49843	−	20.0001i	−0.379642	−	1.16842i	−0.940293	−	0.340366i	$-0.889449\pi$
$293$	−6.49843	−	20.0001i	−0.379642	−	1.16842i	0.560651	−	0.828052i	$-0.310551\pi$
$294$		0			0
$295$	−0.792825	−	0.576021i	−0.0461600	−	0.0335372i
$296$		0			0
$297$	−4.08718	−	3.32325i	−0.237162	−	0.192834i
$298$		0			0
$299$	7.16216	+	5.20361i	0.414198	+	0.300933i
$300$		0			0
$301$	−1.10140	−	3.38975i	−0.0634834	−	0.195382i
$302$		0			0
$303$	−24.7260	+	17.9645i	−1.42047	+	1.03203i
$304$		0			0
$305$	−1.45409	+	4.47522i	−0.0832609	+	0.256251i
$306$		0			0
$307$	−9.55072			−0.545088			−0.272544	−	0.962143i	$-0.587865\pi$
$307$	−9.55072			−0.545088			−0.272544	+	0.962143i	$0.587865\pi$
$308$		0			0
$309$	36.9756			2.10347
$310$		0			0
$311$	3.12470	−	9.61685i	0.177186	−	0.545322i	−0.822541	−	0.568706i	$-0.807444\pi$
$311$	3.12470	−	9.61685i	0.177186	−	0.545322i	0.999727	+	0.0233845i	$0.00744419\pi$
$312$		0			0
$313$	−7.11934	+	5.17250i	−0.402409	+	0.292367i	−0.770522	−	0.637414i	$-0.780004\pi$
$313$	−7.11934	+	5.17250i	−0.402409	+	0.292367i	0.368112	+	0.929781i	$0.380004\pi$
$314$		0			0
$315$	−0.102406	−	0.315172i	−0.00576990	−	0.0177579i
$316$		0			0
$317$	13.2426	+	9.62130i	0.743778	+	0.540386i	0.893892	−	0.448282i	$-0.147964\pi$
$317$	13.2426	+	9.62130i	0.743778	+	0.540386i	−0.150114	+	0.988669i	$0.547964\pi$
$318$		0			0
$319$	−3.47822	+	2.24894i	−0.194743	+	0.125916i
$320$		0			0
$321$	1.18347	+	0.859839i	0.0660547	+	0.0479915i
$322$		0			0
$323$	−10.6144	−	32.6678i	−0.590601	−	1.81768i
$324$		0			0
$325$	3.95432	−	2.87298i	0.219346	−	0.159365i
$326$		0			0
$327$	2.06975	−	6.37002i	0.114457	−	0.352263i
$328$		0			0
$329$	0.774426			0.0426955
$330$		0			0
$331$	−15.7514			−0.865777			−0.432888	−	0.901448i	$-0.642506\pi$
$331$	−15.7514			−0.865777			−0.432888	+	0.901448i	$0.642506\pi$
$332$		0			0
$333$	−1.68116	+	5.17408i	−0.0921270	+	0.283538i
$334$		0			0
$335$	3.70275	−	2.69021i	0.202303	−	0.146982i
$336$		0			0
$337$	−0.834225	−	2.56748i	−0.0454431	−	0.139860i	0.925761	−	0.378110i	$-0.123426\pi$
$337$	−0.834225	−	2.56748i	−0.0454431	−	0.139860i	−0.971204	+	0.238251i	$0.923426\pi$
$338$		0			0
$339$	−6.57409	−	4.77635i	−0.357055	−	0.259416i
$340$		0			0
$341$	8.11978	−	21.0274i	0.439711	−	1.13870i
$342$		0			0
$343$	4.78597	+	3.47721i	0.258418	+	0.187752i
$344$		0			0
$345$	2.11164	+	6.49895i	0.113687	+	0.349892i
$346$		0			0
$347$	−15.4660	+	11.2367i	−0.830260	+	0.603219i	−0.919633	−	0.392779i	$-0.871514\pi$
$347$	−15.4660	+	11.2367i	−0.830260	+	0.603219i	0.0893727	+	0.995998i	$0.471514\pi$
$348$		0			0
$349$	−3.03528	+	9.34163i	−0.162475	+	0.500046i	−0.998841	−	0.0481247i	$-0.984676\pi$
$349$	−3.03528	+	9.34163i	−0.162475	+	0.500046i	0.836367	+	0.548171i	$0.184676\pi$
$350$		0			0
$351$	−1.58828			−0.0847763
$352$		0			0
$353$	−1.86287			−0.0991508			−0.0495754	−	0.998770i	$-0.515787\pi$
$353$	−1.86287			−0.0991508			−0.0495754	+	0.998770i	$0.515787\pi$
$354$		0			0
$355$	0.746294	−	2.29686i	0.0396092	−	0.121904i
$356$		0			0
$357$	4.75804	−	3.45692i	0.251822	−	0.182960i
$358$		0			0
$359$	−6.66614	−	20.5163i	−0.351825	−	1.08281i	−0.957827	−	0.287344i	$-0.907228\pi$
$359$	−6.66614	−	20.5163i	−0.351825	−	1.08281i	0.606002	−	0.795463i	$-0.292772\pi$
$360$		0			0
$361$	−11.4958	−	8.35220i	−0.605043	−	0.439589i
$362$		0			0
$363$	5.17159	+	24.8165i	0.271438	+	1.30253i
$364$		0			0
$365$	2.92568	+	2.12563i	0.153137	+	0.111260i
$366$		0			0
$367$	−1.86096	−	5.72746i	−0.0971415	−	0.298971i	0.890664	−	0.454661i	$-0.150240\pi$
$367$	−1.86096	−	5.72746i	−0.0971415	−	0.298971i	−0.987806	+	0.155691i	$0.950240\pi$
$368$		0			0
$369$	12.1858	−	8.85348i	0.634366	−	0.460894i
$370$		0			0
$371$	−1.53585	+	4.72685i	−0.0797371	+	0.245406i
$372$		0			0
$373$	19.8623			1.02843			0.514215	−	0.857661i	$-0.328083\pi$
$373$	19.8623			1.02843			0.514215	+	0.857661i	$0.328083\pi$
$374$		0			0
$375$	7.63221			0.394126
$376$		0			0
$377$	−0.385914	+	1.18772i	−0.0198756	+	0.0611708i
$378$		0			0
$379$	−31.2831	+	22.7285i	−1.60691	+	1.16749i	−0.734638	+	0.678459i	$0.762648\pi$
$379$	−31.2831	+	22.7285i	−1.60691	+	1.16749i	−0.872268	+	0.489027i	$0.837352\pi$
$380$		0			0
$381$	3.39946	+	10.4624i	0.174159	+	0.536007i
$382$		0			0
$383$	−22.2523	−	16.1673i	−1.13704	−	0.826108i	−0.150336	−	0.988635i	$-0.548036\pi$
$383$	−22.2523	−	16.1673i	−1.13704	−	0.826108i	−0.986704	+	0.162527i	$0.948036\pi$
$384$		0			0
$385$	0.171338	−	0.443705i	0.00873220	−	0.0226133i
$386$		0			0
$387$	15.5622	+	11.3066i	0.791072	+	0.574747i
$388$		0			0
$389$	2.53277	+	7.79507i	0.128417	+	0.395226i	0.994508	−	0.104660i	$-0.0333754\pi$
$389$	2.53277	+	7.79507i	0.128417	+	0.395226i	−0.866091	+	0.499886i	$0.833375\pi$
$390$		0			0
$391$	−42.6899	+	31.0161i	−2.15892	+	1.56855i
$392$		0			0
$393$	12.6314	−	38.8755i	0.637171	−	1.96101i
$394$		0			0
$395$	−0.108670			−0.00546776
$396$		0			0
$397$	−17.6124			−0.883940			−0.441970	−	0.897030i	$-0.645720\pi$
$397$	−17.6124			−0.883940			−0.441970	+	0.897030i	$0.645720\pi$
$398$		0			0
$399$	1.75713	−	5.40788i	0.0879664	−	0.270733i
$400$		0			0
$401$	4.12441	−	2.99656i	0.205963	−	0.149641i	−0.480022	−	0.877256i	$-0.659371\pi$
$401$	4.12441	−	2.99656i	0.205963	−	0.149641i	0.685985	+	0.727615i	$0.259371\pi$
$402$		0			0
$403$	−2.10016	−	6.46363i	−0.104616	−	0.321976i
$404$		0			0
$405$	−2.87033	−	2.08541i	−0.142628	−	0.103625i
$406$		0			0
$407$	−6.55713	+	4.23969i	−0.325025	+	0.210154i
$408$		0			0
$409$	−20.0625	−	14.5762i	−0.992025	−	0.720748i	−0.0316613	−	0.999499i	$-0.510080\pi$
$409$	−20.0625	−	14.5762i	−0.992025	−	0.720748i	−0.960364	+	0.278750i	$0.910080\pi$
$410$		0			0
$411$	12.3735	+	38.0816i	0.610338	+	1.87843i
$412$		0			0
$413$	1.01348	−	0.736337i	0.0498702	−	0.0362328i
$414$		0			0
$415$	1.21384	−	3.73580i	0.0595849	−	0.183383i
$416$		0			0
$417$	−8.49528			−0.416015
$418$		0			0
$419$	−25.4491			−1.24327			−0.621636	−	0.783307i	$-0.713532\pi$
$419$	−25.4491			−1.24327			−0.621636	+	0.783307i	$0.713532\pi$
$420$		0			0
$421$	4.61457	−	14.2022i	0.224901	−	0.692173i	−0.773401	−	0.633917i	$-0.781446\pi$
$421$	4.61457	−	14.2022i	0.224901	−	0.692173i	0.998302	−	0.0582558i	$-0.0185539\pi$
$422$		0			0
$423$	−3.38135	+	2.45669i	−0.164407	+	0.119449i
$424$		0			0
$425$	9.00282	+	27.7078i	0.436701	+	1.34403i
$426$		0			0
$427$	−4.86637	−	3.53562i	−0.235500	−	0.171101i
$428$		0			0
$429$	5.93029	+	4.82186i	0.286317	+	0.232802i
$430$		0			0
$431$	24.1263	+	17.5288i	1.16212	+	0.844331i	0.990045	−	0.140752i	$-0.0449520\pi$
$431$	24.1263	+	17.5288i	1.16212	+	0.844331i	0.172078	+	0.985083i	$0.444952\pi$
$432$		0			0
$433$	6.42441	+	19.7723i	0.308737	+	0.950196i	0.978256	+	0.207401i	$0.0665005\pi$
$433$	6.42441	+	19.7723i	0.308737	+	0.950196i	−0.669519	+	0.742795i	$0.733500\pi$
$434$		0			0
$435$	−0.779860	+	0.566601i	−0.0373914	+	0.0271664i
$436$		0			0
$437$	−15.7652	+	48.5204i	−0.754154	+	2.32105i
$438$		0			0
$439$	18.2726			0.872103			0.436052	−	0.899922i	$-0.356377\pi$
$439$	18.2726			0.872103			0.436052	+	0.899922i	$0.356377\pi$
$440$		0			0
$441$	−15.7519			−0.750093
$442$		0			0
$443$	−2.13128	+	6.55940i	−0.101260	+	0.311647i	−0.988835	−	0.149018i	$-0.952389\pi$
$443$	−2.13128	+	6.55940i	−0.101260	+	0.311647i	0.887574	+	0.460664i	$0.152389\pi$
$444$		0			0
$445$	3.15546	−	2.29258i	0.149583	−	0.108679i
$446$		0			0
$447$	−11.7021	−	36.0155i	−0.553492	−	1.70347i
$448$		0			0
$449$	15.4403	+	11.2180i	0.728673	+	0.529412i	0.889143	−	0.457629i	$-0.151301\pi$
$449$	15.4403	+	11.2180i	0.728673	+	0.529412i	−0.160471	+	0.987041i	$0.551301\pi$
$450$		0			0
$451$	21.5868	+	1.17447i	1.01648	+	0.0553038i
$452$		0			0
$453$	10.5126	+	7.63789i	0.493927	+	0.358859i
$454$		0			0
$455$	−0.0443161	−	0.136391i	−0.00207757	−	0.00639411i
$456$		0			0
$457$	3.97616	−	2.88885i	0.185997	−	0.135135i	−0.490890	−	0.871221i	$-0.663328\pi$
$457$	3.97616	−	2.88885i	0.185997	−	0.135135i	0.676887	+	0.736087i	$0.263328\pi$
$458$		0			0
$459$	2.92544	−	9.00359i	0.136548	−	0.420251i
$460$		0			0
$461$	10.7089			0.498764			0.249382	−	0.968405i	$-0.419773\pi$
$461$	10.7089			0.498764			0.249382	+	0.968405i	$0.419773\pi$
$462$		0			0
$463$	−40.1003			−1.86362			−0.931810	−	0.362947i	$-0.881771\pi$
$463$	−40.1003			−1.86362			−0.931810	+	0.362947i	$0.881771\pi$
$464$		0			0
$465$	1.62107	−	4.98915i	0.0751755	−	0.231366i
$466$		0			0
$467$	−7.81087	+	5.67493i	−0.361444	+	0.262604i	−0.753654	−	0.657271i	$-0.771711\pi$
$467$	−7.81087	+	5.67493i	−0.361444	+	0.262604i	0.392210	+	0.919876i	$0.371711\pi$
$468$		0			0
$469$	1.80796	+	5.56432i	0.0834837	+	0.256936i
$470$		0			0
$471$	12.6188	+	9.16812i	0.581445	+	0.422445i
$472$		0			0
$473$	7.09252	+	26.6823i	0.326114	+	1.22685i
$474$		0			0
$475$	22.7879	+	16.5564i	1.04558	+	0.759658i
$476$		0			0
$477$	−8.28896	−	25.5108i	−0.379525	−	1.16806i
$478$		0			0
$479$	−31.8351	+	23.1295i	−1.45458	+	1.05681i	−0.469847	+	0.882748i	$0.655691\pi$
$479$	−31.8351	+	23.1295i	−1.45458	+	1.05681i	−0.984734	+	0.174067i	$0.944309\pi$
$480$		0			0
$481$	−0.727524	+	2.23909i	−0.0331722	+	0.102094i
$482$		0			0
$483$	−8.73525			−0.397468
$484$		0			0
$485$	2.83359			0.128667
$486$		0			0
$487$	0.882123	−	2.71490i	0.0399728	−	0.123024i	−0.929079	−	0.369882i	$-0.879398\pi$
$487$	0.882123	−	2.71490i	0.0399728	−	0.123024i	0.969052	+	0.246858i	$0.0793982\pi$
$488$		0			0
$489$	10.4063	−	7.56059i	0.470587	−	0.341902i
$490$		0			0
$491$	−7.11214	−	21.8889i	−0.320967	−	0.987834i	−0.973228	−	0.229840i	$-0.926180\pi$
$491$	−7.11214	−	21.8889i	−0.320967	−	0.987834i	0.652262	−	0.757994i	$-0.273820\pi$
$492$		0			0
$493$	−6.02209	−	4.37531i	−0.271222	−	0.197054i
$494$		0			0
$495$	0.659448	+	2.48087i	0.0296400	+	0.111507i
$496$		0			0
$497$	2.49760	+	1.81462i	0.112033	+	0.0813967i
$498$		0			0
$499$	9.85916	+	30.3434i	0.441357	+	1.35836i	0.886430	+	0.462862i	$0.153178\pi$
$499$	9.85916	+	30.3434i	0.441357	+	1.35836i	−0.445073	+	0.895494i	$0.646822\pi$
$500$		0			0
$501$	13.1766	−	9.57334i	0.588686	−	0.427705i
$502$		0			0
$503$	−3.27616	+	10.0830i	−0.146077	+	0.449578i	−0.997148	−	0.0754724i	$-0.975954\pi$
$503$	−3.27616	+	10.0830i	−0.146077	+	0.449578i	0.851071	+	0.525050i	$0.175954\pi$
$504$		0			0
$505$	−4.44208			−0.197670
$506$		0			0
$507$	2.30452			0.102347
$508$		0			0
$509$	2.92009	−	8.98711i	0.129431	−	0.398347i	−0.865252	−	0.501338i	$-0.832841\pi$
$509$	2.92009	−	8.98711i	0.129431	−	0.398347i	0.994682	+	0.102991i	$0.0328414\pi$
$510$		0			0
$511$	−3.73994	+	2.71723i	−0.165445	+	0.120203i
$512$		0			0
$513$	−2.82841	−	8.70494i	−0.124877	−	0.384333i
$514$		0			0
$515$	4.34774	+	3.15882i	0.191584	+	0.139194i
$516$		0			0
$517$	−5.98998	−	0.325897i	−0.263439	−	0.0143329i
$518$		0			0
$519$	21.7609	+	15.8102i	0.955197	+	0.693991i
$520$		0			0
$521$	−7.41954	−	22.8350i	−0.325056	−	1.00042i	−0.971415	−	0.237386i	$-0.923709\pi$
$521$	−7.41954	−	22.8350i	−0.325056	−	1.00042i	0.646359	−	0.763033i	$-0.276291\pi$
$522$		0			0
$523$	7.14013	−	5.18761i	0.312216	−	0.226838i	−0.420631	−	0.907232i	$-0.638191\pi$
$523$	7.14013	−	5.18761i	0.312216	−	0.226838i	0.732847	+	0.680394i	$0.238191\pi$
$524$		0			0
$525$	−1.49034	+	4.58680i	−0.0650439	+	0.200184i
$526$		0			0
$527$	40.5090			1.76460
$528$		0			0
$529$	55.3741			2.40757
$530$		0			0
$531$	−2.08926	+	6.43009i	−0.0906662	+	0.279042i
$532$		0			0
$533$	5.27341	−	3.83135i	0.228417	−	0.165954i
$534$		0			0
$535$	0.0657009	+	0.202207i	0.00284050	+	0.00874216i
$536$		0			0
$537$	26.6717	+	19.3782i	1.15097	+	0.836229i
$538$		0			0
$539$	−17.5416	−	14.2629i	−0.755570	−	0.614347i
$540$		0			0
$541$	−20.2134	−	14.6859i	−0.869043	−	0.631397i	0.0612872	−	0.998120i	$-0.480479\pi$
$541$	−20.2134	−	14.6859i	−0.869043	−	0.631397i	−0.930330	+	0.366724i	$0.880479\pi$
$542$		0			0
$543$	3.77219	+	11.6096i	0.161880	+	0.498216i
$544$		0			0
$545$	0.787559	−	0.572195i	0.0337353	−	0.0245101i
$546$		0			0
$547$	−9.71090	+	29.8871i	−0.415208	+	1.27788i	0.496856	+	0.867833i	$0.334488\pi$
$547$	−9.71090	+	29.8871i	−0.415208	+	1.27788i	−0.912065	+	0.410047i	$0.865512\pi$
$548$		0			0
$549$	32.4638			1.38552
$550$		0			0
$551$	−7.19681			−0.306595
$552$		0			0
$553$	0.0429268	−	0.132115i	0.00182543	−	0.00561811i
$554$		0			0
$555$	−1.47019	+	1.06815i	−0.0624060	+	0.0453406i
$556$		0			0
$557$	10.3731	+	31.9251i	0.439522	+	1.35271i	0.888381	+	0.459108i	$0.151831\pi$
$557$	10.3731	+	31.9251i	0.439522	+	1.35271i	−0.448858	+	0.893603i	$0.648169\pi$
$558$		0			0
$559$	6.73457	+	4.89295i	0.284842	+	0.206950i
$560$		0			0
$561$	−38.2569	+	24.7360i	−1.61521	+	1.04436i
$562$		0			0
$563$	−11.8353	−	8.59883i	−0.498798	−	0.362398i	0.309760	−	0.950815i	$-0.399751\pi$
$563$	−11.8353	−	8.59883i	−0.498798	−	0.362398i	−0.808557	+	0.588417i	$0.799751\pi$
$564$		0			0
$565$	−0.364965	−	1.12325i	−0.0153542	−	0.0472553i
$566$		0			0
$567$	3.66919	−	2.66582i	0.154091	−	0.111954i
$568$		0			0
$569$	2.48068	−	7.63474i	0.103995	−	0.320065i	−0.885498	−	0.464643i	$-0.846183\pi$
$569$	2.48068	−	7.63474i	0.103995	−	0.320065i	0.989493	+	0.144578i	$0.0461826\pi$
$570$		0			0
$571$	1.88136			0.0787326			0.0393663	−	0.999225i	$-0.487466\pi$
$571$	1.88136			0.0787326			0.0393663	+	0.999225i	$0.487466\pi$
$572$		0			0
$573$	7.62603			0.318582
$574$		0			0
$575$	13.3716	−	41.1536i	0.557634	−	1.71622i
$576$		0			0
$577$	21.7645	−	15.8129i	0.906070	−	0.658298i	−0.0339482	−	0.999424i	$-0.510808\pi$
$577$	21.7645	−	15.8129i	0.906070	−	0.658298i	0.940018	+	0.341125i	$0.110808\pi$
$578$		0			0
$579$	11.8276	+	36.4018i	0.491540	+	1.51281i
$580$		0			0
$581$	4.06232	+	2.95145i	0.168533	+	0.122447i
$582$		0			0
$583$	13.8685	−	35.9146i	0.574376	−	1.48743i
$584$		0			0
$585$	0.626166	+	0.454936i	0.0258888	+	0.0188093i
$586$		0			0
$587$	−3.76483	−	11.5869i	−0.155391	−	0.478244i	0.842809	−	0.538212i	$-0.180900\pi$
$587$	−3.76483	−	11.5869i	−0.155391	−	0.478244i	−0.998200	+	0.0599680i	$0.980900\pi$
$588$		0			0
$589$	31.6854	−	23.0208i	1.30558	−	0.948556i
$590$		0			0
$591$	−2.79680	+	8.60767i	−0.115045	+	0.354072i
$592$		0			0
$593$	−8.05137			−0.330630			−0.165315	−	0.986241i	$-0.552864\pi$
$593$	−8.05137			−0.330630			−0.165315	+	0.986241i	$0.552864\pi$
$594$		0			0
$595$	0.854793			0.0350431
$596$		0			0
$597$	0.0650145	−	0.200094i	0.00266087	−	0.00818930i
$598$		0			0
$599$	−20.1979	+	14.6746i	−0.825264	+	0.599589i	−0.918215	−	0.396081i	$-0.870370\pi$
$599$	−20.1979	+	14.6746i	−0.825264	+	0.599589i	0.0929516	+	0.995671i	$0.470370\pi$
$600$		0			0
$601$	−0.802303	−	2.46923i	−0.0327266	−	0.100722i	0.933359	−	0.358945i	$-0.116863\pi$
$601$	−0.802303	−	2.46923i	−0.0327266	−	0.100722i	−0.966086	+	0.258222i	$0.916863\pi$
$602$		0			0
$603$	−25.5456	−	18.5600i	−1.04030	−	0.755820i
$604$		0			0
$605$	−1.51198	+	3.35984i	−0.0614706	+	0.136597i
$606$		0			0
$607$	10.7932	+	7.84171i	0.438082	+	0.318285i	0.784872	−	0.619658i	$-0.212728\pi$
$607$	10.7932	+	7.84171i	0.438082	+	0.318285i	−0.346790	+	0.937943i	$0.612728\pi$
$608$		0			0
$609$	−0.380785	−	1.17194i	−0.0154302	−	0.0474892i
$610$		0			0
$611$	−1.46328	+	1.06314i	−0.0591981	+	0.0430099i
$612$		0			0
$613$	−4.86434	+	14.9709i	−0.196469	+	0.604669i	0.803487	+	0.595322i	$0.202975\pi$
$613$	−4.86434	+	14.9709i	−0.196469	+	0.604669i	−0.999956	+	0.00934746i	$0.997025\pi$
$614$		0			0
$615$	5.03134			0.202883
$616$		0			0
$617$	8.98782			0.361836			0.180918	−	0.983498i	$-0.442093\pi$
$617$	8.98782			0.361836			0.180918	+	0.983498i	$0.442093\pi$
$618$		0			0
$619$	10.2573	−	31.5686i	0.412275	−	1.26885i	−0.502392	−	0.864640i	$-0.667546\pi$
$619$	10.2573	−	31.5686i	0.412275	−	1.26885i	0.914666	−	0.404210i	$-0.132454\pi$
$620$		0			0
$621$	−11.3755	+	8.26481i	−0.456484	+	0.331655i
$622$		0			0
$623$	1.54073	+	4.74188i	0.0617280	+	0.189979i
$624$		0			0
$625$	−18.8742	−	13.7129i	−0.754968	−	0.548516i
$626$		0			0
$627$	−15.8667	+	41.0891i	−0.633654	+	1.64094i
$628$		0			0
$629$	−11.3528	−	8.24831i	−0.452667	−	0.328882i
$630$		0			0
$631$	−8.71313	−	26.8163i	−0.346864	−	1.06754i	−0.960578	−	0.278010i	$-0.910325\pi$
$631$	−8.71313	−	26.8163i	−0.346864	−	1.06754i	0.613714	−	0.789529i	$-0.289675\pi$
$632$		0			0
$633$	−31.4406	+	22.8429i	−1.24965	+	0.907924i
$634$		0			0
$635$	−0.494083	+	1.52063i	−0.0196071	+	0.0603444i
$636$		0			0
$637$	−6.81668			−0.270087
$638$		0			0
$639$	−16.6617			−0.659125
$640$		0			0
$641$	4.06223	−	12.5023i	0.160449	−	0.493810i	−0.838223	−	0.545327i	$-0.816406\pi$
$641$	4.06223	−	12.5023i	0.160449	−	0.493810i	0.998672	+	0.0515167i	$0.0164055\pi$
$642$		0			0
$643$	−22.0678	+	16.0332i	−0.870269	+	0.632287i	−0.930659	−	0.365888i	$-0.880765\pi$
$643$	−22.0678	+	16.0332i	−0.870269	+	0.632287i	0.0603905	+	0.998175i	$0.480765\pi$
$644$		0			0
$645$	1.98557	+	6.11095i	0.0781816	+	0.240618i
$646$		0			0
$647$	12.3798	+	8.99443i	0.486699	+	0.353608i	0.803914	−	0.594746i	$-0.202747\pi$
$647$	12.3798	+	8.99443i	0.486699	+	0.353608i	−0.317214	+	0.948354i	$0.602747\pi$
$648$		0			0
$649$	−8.14888	+	5.26888i	−0.319871	+	0.206821i
$650$		0			0
$651$	5.42521	+	3.94165i	0.212631	+	0.154485i
$652$		0			0
$653$	0.615099	+	1.89308i	0.0240707	+	0.0740819i	0.962370	−	0.271742i	$-0.0875996\pi$
$653$	0.615099	+	1.89308i	0.0240707	+	0.0740819i	−0.938300	+	0.345823i	$0.887600\pi$
$654$		0			0
$655$	4.80638	−	3.49204i	0.187801	−	0.136445i
$656$		0			0
$657$	7.70978	−	23.7283i	0.300787	−	0.925728i
$658$		0			0
$659$	31.2153			1.21598			0.607988	−	0.793947i	$-0.291977\pi$
$659$	31.2153			1.21598			0.607988	+	0.793947i	$0.291977\pi$
$660$		0			0
$661$	35.7323			1.38983			0.694913	−	0.719094i	$-0.255443\pi$
$661$	35.7323			1.38983			0.694913	+	0.719094i	$0.255443\pi$
$662$		0			0
$663$	−4.24467	+	13.0637i	−0.164849	+	0.507354i
$664$		0			0
$665$	0.668604	−	0.485769i	0.0259274	−	0.0188373i
$666$		0			0
$667$	3.41647	+	10.5148i	0.132286	+	0.407135i
$668$		0			0
$669$	24.5126	+	17.8094i	0.947712	+	0.688553i
$670$		0			0
$671$	36.1522	+	29.3950i	1.39564	+	1.13478i
$672$		0			0
$673$	16.9504	+	12.3152i	0.653390	+	0.474715i	0.864424	−	0.502763i	$-0.167683\pi$
$673$	16.9504	+	12.3152i	0.653390	+	0.474715i	−0.211034	+	0.977479i	$0.567683\pi$
$674$		0			0
$675$	2.39897	+	7.38327i	0.0923364	+	0.284182i
$676$		0			0
$677$	−19.8253	+	14.4039i	−0.761949	+	0.553589i	−0.899508	−	0.436905i	$-0.856075\pi$
$677$	−19.8253	+	14.4039i	−0.761949	+	0.553589i	0.137558	+	0.990494i	$0.456075\pi$
$678$		0			0
$679$	−1.11933	+	3.44494i	−0.0429560	+	0.132205i
$680$		0			0
$681$	−54.6553			−2.09440
$682$		0			0
$683$	36.0260			1.37850			0.689249	−	0.724525i	$-0.257941\pi$
$683$	36.0260			1.37850			0.689249	+	0.724525i	$0.257941\pi$
$684$		0			0
$685$	−1.79838	+	5.53485i	−0.0687127	+	0.211476i
$686$		0			0
$687$	45.7562	−	33.2438i	1.74571	−	1.26833i
$688$		0			0
$689$	−3.58706	−	11.0398i	−0.136656	−	0.420584i
$690$		0			0
$691$	5.83319	+	4.23806i	0.221905	+	0.161223i	0.693184	−	0.720761i	$-0.256207\pi$
$691$	5.83319	+	4.23806i	0.221905	+	0.161223i	−0.471279	+	0.881984i	$0.656207\pi$
$692$		0			0
$693$	−3.27661	−	0.178271i	−0.124468	−	0.00677195i
$694$		0			0
$695$	−0.998909	−	0.725750i	−0.0378908	−	0.0275293i
$696$		0			0
$697$	12.0060	+	36.9506i	0.454759	+	1.39960i
$698$		0			0
$699$	−44.5012	+	32.3320i	−1.68319	+	1.22291i
$700$		0			0
$701$	2.92071	−	8.98903i	0.110314	−	0.339511i	−0.880627	−	0.473810i	$-0.842878\pi$
$701$	2.92071	−	8.98903i	0.110314	−	0.339511i	0.990941	+	0.134299i	$0.0428783\pi$
$702$		0			0
$703$	−13.5674			−0.511705
$704$		0			0
$705$	−1.39611			−0.0525807
$706$		0			0
$707$	1.75472	−	5.40047i	0.0659930	−	0.203106i
$708$		0			0
$709$	9.24771	−	6.71885i	0.347305	−	0.252332i	−0.400433	−	0.916326i	$-0.631140\pi$
$709$	9.24771	−	6.71885i	0.347305	−	0.252332i	0.747738	+	0.663994i	$0.231140\pi$
$710$		0			0
$711$	0.231676	+	0.713026i	0.00868853	+	0.0267406i
$712$		0			0
$713$	−48.6759	−	35.3651i	−1.82293	−	1.32443i
$714$		0			0
$715$	0.285377	+	1.07360i	0.0106725	+	0.0401503i
$716$		0			0
$717$	−33.7043	−	24.4876i	−1.25871	−	0.914506i
$718$		0			0
$719$	1.32077	+	4.06491i	0.0492564	+	0.151596i	0.972659	−	0.232236i	$-0.0746042\pi$
$719$	1.32077	+	4.06491i	0.0492564	+	0.151596i	−0.923403	+	0.383832i	$0.874604\pi$
$720$		0			0
$721$	−5.55779	+	4.03797i	−0.206983	+	0.150382i
$722$		0			0
$723$	9.54347	−	29.3718i	0.354925	−	1.09235i
$724$		0			0
$725$	6.10412			0.226701
$726$		0			0
$727$	−50.5033			−1.87306			−0.936532	−	0.350581i	$-0.885984\pi$
$727$	−50.5033			−1.87306			−0.936532	+	0.350581i	$0.885984\pi$
$728$		0			0
$729$	−4.17071	+	12.8361i	−0.154471	+	0.475412i
$730$		0			0
$731$	−40.1413	+	29.1643i	−1.48468	+	1.07868i
$732$		0			0
$733$	−16.2575	−	50.0354i	−0.600484	−	1.84810i	−0.525277	−	0.850932i	$-0.676038\pi$
$733$	−16.2575	−	50.0354i	−0.600484	−	1.84810i	−0.0752074	−	0.997168i	$-0.523962\pi$
$734$		0			0
$735$	−4.25677	−	3.09273i	−0.157013	−	0.114077i
$736$		0			0
$737$	−11.6425	−	43.7994i	−0.428856	−	1.61337i
$738$		0			0
$739$	−4.22147	−	3.06707i	−0.155289	−	0.112824i	0.507427	−	0.861695i	$-0.330597\pi$
$739$	−4.22147	−	3.06707i	−0.155289	−	0.112824i	−0.662717	+	0.748870i	$0.730597\pi$
$740$		0			0
$741$	4.10387	+	12.6304i	0.150760	+	0.463990i
$742$		0			0
$743$	18.3650	−	13.3430i	0.673748	−	0.489506i	−0.197530	−	0.980297i	$-0.563292\pi$
$743$	18.3650	−	13.3430i	0.673748	−	0.489506i	0.871278	+	0.490790i	$0.163292\pi$
$744$		0			0
$745$	1.70081	−	5.23456i	0.0623129	−	0.191779i
$746$		0			0
$747$	−27.1000			−0.991536
$748$		0			0
$749$	−0.271787			−0.00993086
$750$		0			0
$751$	0.617941	−	1.90183i	0.0225490	−	0.0693987i	−0.939149	−	0.343511i	$-0.888384\pi$
$751$	0.617941	−	1.90183i	0.0225490	−	0.0693987i	0.961698	+	0.274112i	$0.0883839\pi$
$752$		0			0
$753$	13.3837	−	9.72379i	0.487727	−	0.354355i
$754$		0			0
$755$	0.583616	+	1.79619i	0.0212400	+	0.0653699i
$756$		0			0
$757$	7.37492	+	5.35819i	0.268046	+	0.194747i	0.713687	−	0.700465i	$-0.247024\pi$
$757$	7.37492	+	5.35819i	0.268046	+	0.194747i	−0.445641	+	0.895212i	$0.647024\pi$
$758$		0			0
$759$	67.5648	+	3.67600i	2.45245	+	0.133431i
$760$		0			0
$761$	−18.8730	−	13.7120i	−0.684145	−	0.497061i	0.190585	−	0.981671i	$-0.438962\pi$
$761$	−18.8730	−	13.7120i	−0.684145	−	0.497061i	−0.874730	+	0.484610i	$0.838962\pi$
$762$		0			0
$763$	0.384544	+	1.18351i	0.0139214	+	0.0428458i
$764$		0			0
$765$	−3.73225	+	2.71164i	−0.134940	+	0.0980396i
$766$		0			0
$767$	−0.904131	+	2.78263i	−0.0326463	+	0.100475i
$768$		0			0
$769$	6.61703			0.238616			0.119308	−	0.992857i	$-0.461932\pi$
$769$	6.61703			0.238616			0.119308	+	0.992857i	$0.461932\pi$
$770$		0			0
$771$	−29.2165			−1.05221
$772$		0			0
$773$	−12.7416	+	39.2147i	−0.458284	+	1.41045i	0.408951	+	0.912556i	$0.365895\pi$
$773$	−12.7416	+	39.2147i	−0.458284	+	1.41045i	−0.867236	+	0.497898i	$0.834105\pi$
$774$		0			0
$775$	−26.8746	+	19.5256i	−0.965365	+	0.701379i
$776$		0			0
$777$	−0.717854	−	2.20933i	−0.0257529	−	0.0792592i
$778$		0			0
$779$	30.3895	+	22.0792i	1.08882	+	0.791071i
$780$		0			0
$781$	−18.5547	−	15.0866i	−0.663938	−	0.539842i
$782$		0			0
$783$	−1.60470	−	1.16588i	−0.0573473	−	0.0416653i
$784$		0			0
$785$	0.700543	+	2.15605i	0.0250035	+	0.0769527i
$786$		0			0
$787$	24.7491	−	17.9813i	0.882210	−	0.640963i	−0.0516251	−	0.998667i	$-0.516440\pi$
$787$	24.7491	−	17.9813i	0.882210	−	0.640963i	0.933835	+	0.357703i	$0.116440\pi$
$788$		0			0
$789$	2.01875	−	6.21308i	0.0718695	−	0.221191i
$790$		0			0
$791$	1.50976			0.0536808
$792$		0			0
$793$	14.0488			0.498886
$794$		0			0
$795$	2.76878	−	8.52143i	0.0981986	−	0.302224i
$796$		0			0
$797$	−39.5732	+	28.7516i	−1.40175	+	1.01843i	−0.407295	+	0.913297i	$0.633528\pi$
$797$	−39.5732	+	28.7516i	−1.40175	+	1.01843i	−0.994458	+	0.105137i	$0.966472\pi$
$798$		0			0
$799$	−3.33146	−	10.2532i	−0.117859	−	0.362731i
$800$		0			0
$801$	−21.7698	−	15.8167i	−0.769197	−	0.558854i
$802$		0			0
$803$	30.0709	−	19.4432i	1.06118	−	0.686135i
$804$		0			0
$805$	−1.02713	−	0.746251i	−0.0362014	−	0.0263019i
$806$		0			0
$807$	−11.2127	−	34.5093i	−0.394707	−	1.21478i
$808$		0			0
$809$	22.6757	−	16.4749i	0.797236	−	0.579226i	−0.112866	−	0.993610i	$-0.536003\pi$
$809$	22.6757	−	16.4749i	0.797236	−	0.579226i	0.910102	+	0.414385i	$0.136003\pi$
$810$		0			0
$811$	−12.5841	+	38.7298i	−0.441887	+	1.35999i	0.443976	+	0.896039i	$0.353568\pi$
$811$	−12.5841	+	38.7298i	−0.441887	+	1.35999i	−0.885862	+	0.463948i	$0.846432\pi$
$812$		0			0
$813$	−66.7175			−2.33988
$814$		0			0
$815$	1.86951			0.0654861
$816$		0			0
$817$	−14.8240	+	45.6237i	−0.518627	+	1.59617i
$818$		0			0
$819$	−0.800439	+	0.581553i	−0.0279696	+	0.0203211i
$820$		0			0
$821$	5.88620	+	18.1159i	0.205430	+	0.632248i	0.999695	+	0.0246772i	$0.00785579\pi$
$821$	5.88620	+	18.1159i	0.205430	+	0.632248i	−0.794266	+	0.607571i	$0.792144\pi$
$822$		0			0
$823$	−40.6628	−	29.5432i	−1.41741	−	1.02981i	−0.992192	−	0.124724i	$-0.960196\pi$
$823$	−40.6628	−	29.5432i	−1.41741	−	1.02981i	−0.425223	−	0.905088i	$-0.639804\pi$
$824$		0			0
$825$	13.4576	−	34.8505i	0.468535	−	1.21334i
$826$		0			0
$827$	−12.3927	−	9.00383i	−0.430937	−	0.313094i	0.351087	−	0.936343i	$-0.385812\pi$
$827$	−12.3927	−	9.00383i	−0.430937	−	0.313094i	−0.782023	+	0.623249i	$0.785812\pi$
$828$		0			0
$829$	−11.5045	−	35.4072i	−0.399568	−	1.22974i	−0.925347	−	0.379122i	$-0.876226\pi$
$829$	−11.5045	−	35.4072i	−0.399568	−	1.22974i	0.525779	−	0.850621i	$-0.323774\pi$
$830$		0			0
$831$	36.1190	−	26.2420i	1.25295	−	0.910324i
$832$		0			0
$833$	12.5556	−	38.6421i	0.435025	−	1.33887i
$834$		0			0
$835$	2.36720			0.0819204
$836$		0			0
$837$	10.7944			0.373109
$838$		0			0
$839$	−10.7270	+	33.0143i	−0.370337	+	1.13978i	0.576234	+	0.817285i	$0.304522\pi$
$839$	−10.7270	+	33.0143i	−0.370337	+	1.13978i	−0.946571	+	0.322495i	$0.895478\pi$
$840$		0			0
$841$	22.1997	−	16.1291i	0.765508	−	0.556174i
$842$		0			0
$843$	7.25907	+	22.3411i	0.250016	+	0.769469i
$844$		0			0
$845$	0.270974	+	0.196874i	0.00932180	+	0.00677268i
$846$		0			0
$847$	−3.48747	−	3.16540i	−0.119831	−	0.108764i
$848$		0			0
$849$	20.2108	+	14.6840i	0.693634	+	0.503955i
$850$		0			0
$851$	6.44071	+	19.8225i	0.220785	+	0.679506i
$852$		0			0
$853$	28.3529	−	20.5996i	0.970783	−	0.705315i	0.0151532	−	0.999885i	$-0.495176\pi$
$853$	28.3529	−	20.5996i	0.970783	−	0.705315i	0.955630	+	0.294570i	$0.0951764\pi$
$854$		0			0
$855$	−1.37831	+	4.24200i	−0.0471371	+	0.145073i
$856$		0			0
$857$	−34.2434			−1.16973			−0.584867	−	0.811129i	$-0.698853\pi$
$857$	−34.2434			−1.16973			−0.584867	+	0.811129i	$0.698853\pi$
$858$		0			0
$859$	47.5673			1.62298			0.811488	−	0.584369i	$-0.198658\pi$
$859$	47.5673			1.62298			0.811488	+	0.584369i	$0.198658\pi$
$860$		0			0
$861$	−1.98749	+	6.11687i	−0.0677335	+	0.208462i
$862$		0			0
$863$	−6.69014	+	4.86067i	−0.227735	+	0.165459i	−0.695802	−	0.718234i	$-0.744951\pi$
$863$	−6.69014	+	4.86067i	−0.227735	+	0.165459i	0.468067	+	0.883693i	$0.344951\pi$
$864$		0			0
$865$	1.20807	+	3.71806i	0.0410756	+	0.126418i
$866$		0			0
$867$	−34.5423	−	25.0964i	−1.17312	−	0.852319i
$868$		0			0
$869$	−0.387625	+	1.00381i	−0.0131493	+	0.0340520i
$870$		0			0
$871$	−11.0549	−	8.03185i	−0.374581	−	0.272149i
$872$		0			0
$873$	−6.04103	−	18.5924i	−0.204458	−	0.629256i
$874$		0			0
$875$	−1.14720	+	0.833487i	−0.0387823	+	0.0281770i
$876$		0			0
$877$	11.5988	−	35.6975i	0.391664	−	1.20542i	−0.539865	−	0.841751i	$-0.681525\pi$
$877$	11.5988	−	35.6975i	0.391664	−	1.20542i	0.931529	−	0.363666i	$-0.118475\pi$
$878$		0			0
$879$	−48.4625			−1.63460
$880$		0			0
$881$	16.7456			0.564175			0.282087	−	0.959389i	$-0.408973\pi$
$881$	16.7456			0.564175			0.282087	+	0.959389i	$0.408973\pi$
$882$		0			0
$883$	11.4837	−	35.3431i	0.386456	−	1.18939i	−0.548963	−	0.835847i	$-0.684977\pi$
$883$	11.4837	−	35.3431i	0.386456	−	1.18939i	0.935419	−	0.353542i	$-0.115023\pi$
$884$		0			0
$885$	−1.82708	+	1.32745i	−0.0614165	+	0.0446217i
$886$		0			0
$887$	0.592588	+	1.82380i	0.0198972	+	0.0612372i	0.960512	−	0.278238i	$-0.0897505\pi$
$887$	0.592588	+	1.82380i	0.0198972	+	0.0612372i	−0.940615	+	0.339475i	$0.889750\pi$
$888$		0			0
$889$	−1.65354	−	1.20137i	−0.0554579	−	0.0402925i
$890$		0			0
$891$	−29.5020	+	19.0753i	−0.988355	+	0.639047i
$892$		0			0
$893$	−8.43258	−	6.12663i	−0.282185	−	0.205020i
$894$		0			0
$895$	1.48070	+	4.55712i	0.0494943	+	0.152328i
$896$		0			0
$897$	16.5053	−	11.9918i	0.551096	−	0.400395i
$898$		0			0
$899$	2.62277	−	8.07207i	0.0874744	−	0.269219i
$900$		0			0
$901$	69.1891			2.30502
$902$		0			0
$903$	−8.21374			−0.273336
$904$		0			0
$905$	−0.548257	+	1.68736i	−0.0182247	+	0.0560898i
$906$		0			0
$907$	41.5720	−	30.2038i	1.38037	−	1.00290i	0.383529	−	0.923529i	$-0.374708\pi$
$907$	41.5720	−	30.2038i	1.38037	−	1.00290i	0.996845	−	0.0793721i	$-0.0252915\pi$
$908$		0			0
$909$	9.47022	+	29.1463i	0.314107	+	0.966723i
$910$		0			0
$911$	−1.43973	−	1.04602i	−0.0477003	−	0.0346563i	0.563680	−	0.825994i	$-0.309385\pi$
$911$	−1.43973	−	1.04602i	−0.0477003	−	0.0346563i	−0.611380	+	0.791337i	$0.709385\pi$
$912$		0			0
$913$	−30.1789	−	24.5382i	−0.998776	−	0.812095i
$914$		0			0
$915$	8.77295	+	6.37392i	0.290025	+	0.210715i
$916$		0			0
$917$	2.34683	+	7.22280i	0.0774991	+	0.238518i
$918$		0			0
$919$	10.3105	−	7.49103i	0.340113	−	0.247106i	−0.404597	−	0.914495i	$-0.632588\pi$
$919$	10.3105	−	7.49103i	0.340113	−	0.247106i	0.744709	+	0.667389i	$0.232588\pi$
$920$		0			0
$921$	−6.80140	+	20.9326i	−0.224114	+	0.689751i
$922$		0			0
$923$	−7.21036			−0.237332
$924$		0			0
$925$	11.5075			0.378363
$926$		0			0
$927$	11.4572	−	35.2617i	0.376305	−	1.15815i
$928$		0			0
$929$	13.5359	−	9.83438i	0.444097	−	0.322656i	−0.343163	−	0.939276i	$-0.611498\pi$
$929$	13.5359	−	9.83438i	0.444097	−	0.322656i	0.787261	+	0.616620i	$0.211498\pi$
$930$		0			0
$931$	−12.1391	−	37.3603i	−0.397843	−	1.22444i
$932$		0			0
$933$	−18.8523	−	13.6970i	−0.617196	−	0.448419i
$934$		0			0
$935$	−6.61160	−	0.359718i	−0.216222	−	0.0117640i
$936$		0			0
$937$	15.2967	+	11.1137i	0.499723	+	0.363070i	0.808911	−	0.587931i	$-0.200057\pi$
$937$	15.2967	+	11.1137i	0.499723	+	0.363070i	−0.309188	+	0.951001i	$0.600057\pi$
$938$		0			0
$939$	6.26678	+	19.2872i	0.204509	+	0.629413i
$940$		0			0
$941$	7.50275	−	5.45107i	0.244583	−	0.177700i	−0.458740	−	0.888571i	$-0.651699\pi$
$941$	7.50275	−	5.45107i	0.244583	−	0.177700i	0.703322	+	0.710871i	$0.251699\pi$
$942$		0			0
$943$	17.8321	−	54.8815i	0.580693	−	1.78719i
$944$		0			0
$945$	0.227776			0.00740954
$946$		0			0
$947$	42.3123			1.37497			0.687483	−	0.726200i	$-0.258716\pi$
$947$	42.3123			1.37497			0.687483	+	0.726200i	$0.258716\pi$
$948$		0			0
$949$	3.33642	−	10.2684i	0.108305	−	0.333328i
$950$		0			0
$951$	30.5178	−	22.1724i	0.989606	−	0.718991i
$952$		0			0
$953$	5.95626	+	18.3315i	0.192942	+	0.593815i	0.999994	+	0.00333475i	$0.00106149\pi$
$953$	5.95626	+	18.3315i	0.192942	+	0.593815i	−0.807052	+	0.590480i	$0.798939\pi$
$954$		0			0
$955$	0.896699	+	0.651490i	0.0290165	+	0.0210817i
$956$		0			0
$957$	2.45209	+	9.22485i	0.0792649	+	0.298197i
$958$		0			0
$959$	−6.01861	−	4.37277i	−0.194351	−	0.141204i
$960$		0			0
$961$	4.69372	+	14.4458i	0.151410	+	0.465993i
$962$		0			0
$963$	1.18669	−	0.862182i	0.0382406	−	0.0277834i
$964$		0			0
$965$	−1.71905	+	5.29070i	−0.0553382	+	0.170314i
$966$		0			0
$967$	18.8872			0.607370			0.303685	−	0.952772i	$-0.401783\pi$
$967$	18.8872			0.607370			0.303685	+	0.952772i	$0.401783\pi$
$968$		0			0
$969$	−79.1577			−2.54291
$970$		0			0
$971$	−13.8241	+	42.5464i	−0.443638	+	1.36538i	0.440333	+	0.897835i	$0.354861\pi$
$971$	−13.8241	+	42.5464i	−0.443638	+	1.36538i	−0.883971	+	0.467543i	$0.845139\pi$
$972$		0			0
$973$	1.27692	−	0.927738i	0.0409362	−	0.0297419i
$974$		0			0
$975$	−3.48078	−	10.7127i	−0.111474	−	0.343082i
$976$		0			0
$977$	8.89344	+	6.46146i	0.284526	+	0.206721i	0.720889	−	0.693050i	$-0.243734\pi$
$977$	8.89344	+	6.46146i	0.284526	+	0.206721i	−0.436363	+	0.899771i	$0.643734\pi$
$978$		0			0
$979$	−9.92163	−	37.3255i	−0.317097	−	1.19293i
$980$		0			0
$981$	−5.43343	−	3.94762i	−0.173476	−	0.126038i
$982$		0			0
$983$	−2.96149	−	9.11454i	−0.0944570	−	0.290709i	0.892655	−	0.450741i	$-0.148840\pi$
$983$	−2.96149	−	9.11454i	−0.0944570	−	0.290709i	−0.987112	+	0.160032i	$0.948840\pi$
$984$		0			0
$985$	−1.06421	+	0.773194i	−0.0339086	+	0.0246360i
$986$		0			0
$987$	0.551496	−	1.69733i	0.0175543	−	0.0540266i
$988$		0			0
$989$	73.6951			2.34337
$990$		0			0
$991$	6.48835			0.206109			0.103055	−	0.994676i	$-0.467138\pi$
$991$	6.48835			0.206109			0.103055	+	0.994676i	$0.467138\pi$
$992$		0			0
$993$	−11.2171	+	34.5228i	−0.355965	+	1.09555i
$994$		0			0
$995$	0.0247387	−	0.0179737i	0.000784268	−	0.000569804i
$996$		0			0
$997$	2.34954	+	7.23115i	0.0744108	+	0.229013i	0.981344	−	0.192263i	$-0.0615825\pi$
$997$	2.34954	+	7.23115i	0.0744108	+	0.229013i	−0.906933	+	0.421276i	$0.861583\pi$
$998$		0			0
$999$	−3.02517	−	2.19792i	−0.0957123	−	0.0695391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.521.5	yes	20
11.3	even	5	inner	572.2.n.a.157.5	✓	20
11.5	even	5		6292.2.a.w.1.9		10
11.6	odd	10		6292.2.a.x.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.157.5	✓	20	11.3	even	5	inner
572.2.n.a.521.5	yes	20	1.1	even	1	trivial
6292.2.a.w.1.9		10	11.5	even	5
6292.2.a.x.1.9		10	11.6	odd	10

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.712135 - 2.19173i) q^{3} +(0.270974 - 0.196874i) q^{5} +(0.132310 + 0.407207i) q^{7} +(-1.86947 - 1.35825i) q^{9} +O(q^{10})\)	\(q+(0.712135 - 2.19173i) q^{3} +(0.270974 - 0.196874i) q^{5} +(0.132310 + 0.407207i) q^{7} +(-1.86947 - 1.35825i) q^{9} +(-0.852017 - 3.20532i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.238524 - 0.734102i) q^{15} +(4.82213 - 3.50348i) q^{17} +(1.78080 - 5.48073i) q^{19} +0.986709 q^{21} -8.85292 q^{23} +(-1.51042 + 4.64859i) q^{25} +(1.28495 - 0.933569i) q^{27} +(-0.385914 - 1.18772i) q^{29} +(5.49829 + 3.99474i) q^{31} +(-7.63193 - 0.415231i) q^{33} +(0.116021 + 0.0842943i) q^{35} +(-0.727524 - 2.23909i) q^{37} +(-1.86439 + 1.35456i) q^{39} +(-2.01426 + 6.19926i) q^{41} -8.32438 q^{43} -0.773984 q^{45} +(0.558924 - 1.72019i) q^{47} +(5.51481 - 4.00674i) q^{49} +(-4.24467 - 13.0637i) q^{51} +(9.39104 + 6.82299i) q^{53} +(-0.861920 - 0.700819i) q^{55} +(-10.7441 - 7.80603i) q^{57} +(-0.904131 - 2.78263i) q^{59} +(-11.3657 + 8.25765i) q^{61} +(0.305741 - 0.940973i) q^{63} -0.334943 q^{65} +13.6646 q^{67} +(-6.30447 + 19.4032i) q^{69} +(5.83330 - 4.23814i) q^{71} +(3.33642 + 10.2684i) q^{73} +(9.11280 + 6.62084i) q^{75} +(1.19250 - 0.771042i) q^{77} +(-0.262479 - 0.190702i) q^{79} +(-3.27330 - 10.0742i) q^{81} +(9.48779 - 6.89328i) q^{83} +(0.616928 - 1.89871i) q^{85} -2.87798 q^{87} +11.6449 q^{89} +(0.132310 - 0.407207i) q^{91} +(12.6709 - 9.20595i) q^{93} +(-0.596465 - 1.83573i) q^{95} +(6.84423 + 4.97262i) q^{97} +(-2.76081 + 7.14951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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