LMFDB - Embedded newform 572.2.bh.a.57.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, 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 $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.2
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07031 + 1.50417i) q^{3} +(-3.28934 - 1.67600i) q^{5} +(-2.19381 + 0.347466i) q^{7} +(1.09660 - 3.37499i) q^{9} +O(q^{10})$	\(q+(-2.07031 + 1.50417i) q^{3} +(-3.28934 - 1.67600i) q^{5} +(-2.19381 + 0.347466i) q^{7} +(1.09660 - 3.37499i) q^{9} +(2.90921 - 1.59263i) q^{11} +(-3.18124 - 1.69698i) q^{13} +(9.33093 - 1.47787i) q^{15} +(1.16829 + 3.59562i) q^{17} +(6.12176 + 0.969591i) q^{19} +(4.01922 - 4.01922i) q^{21} +8.37584i q^{23} +(5.07185 + 6.98081i) q^{25} +(0.433888 + 1.33537i) q^{27} +(0.561421 - 0.772730i) q^{29} +(-4.08218 - 8.01174i) q^{31} +(-3.62738 + 7.67317i) q^{33} +(7.79856 + 2.53391i) q^{35} +(-0.188104 - 1.18764i) q^{37} +(9.13867 - 1.27184i) q^{39} +(-3.45353 - 0.546985i) q^{41} +10.9687 q^{43} +(-9.26360 + 9.26360i) q^{45} +(10.9256 + 1.73045i) q^{47} +(-1.96530 + 0.638566i) q^{49} +(-7.82711 - 5.68673i) q^{51} +(0.793973 - 2.44360i) q^{53} +(-12.2387 + 0.362857i) q^{55} +(-14.1323 + 7.20078i) q^{57} +(-0.863506 - 5.45196i) q^{59} +(9.75527 - 3.16968i) q^{61} +(-1.23305 + 7.78515i) q^{63} +(7.62004 + 10.9137i) q^{65} +(8.67305 - 8.67305i) q^{67} +(-12.5987 - 17.3406i) q^{69} +(6.55946 + 3.34221i) q^{71} +(3.48189 - 0.551477i) q^{73} +(-21.0006 - 6.82350i) q^{75} +(-5.82889 + 4.50479i) q^{77} +(-5.58408 - 1.81438i) q^{79} +(5.70593 + 4.14560i) q^{81} +(-7.55299 + 14.8236i) q^{83} +(2.18337 - 13.7853i) q^{85} +2.44426i q^{87} +(-2.68281 - 2.68281i) q^{89} +(7.56869 + 2.61748i) q^{91} +(20.5023 + 10.4465i) q^{93} +(-18.5115 - 13.4494i) q^{95} +(-1.62852 - 3.19615i) q^{97} +(-2.18487 - 11.5651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

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
$3$	−2.07031	+	1.50417i	−1.19529	+	0.868430i	−0.993813	−	0.111063i	$-0.964575\pi$
$3$	−2.07031	+	1.50417i	−1.19529	+	0.868430i	−0.201478	+	0.979493i	$0.564575\pi$
$4$		0			0
$5$	−3.28934	−	1.67600i	−1.47104	−	0.749531i	−0.479281	−	0.877662i	$-0.659102\pi$
$5$	−3.28934	−	1.67600i	−1.47104	−	0.749531i	−0.991757	+	0.128130i	$0.959102\pi$
$6$		0			0
$7$	−2.19381	+	0.347466i	−0.829184	+	0.131330i	−0.556577	−	0.830796i	$-0.687886\pi$
$7$	−2.19381	+	0.347466i	−0.829184	+	0.131330i	−0.272607	+	0.962126i	$0.587886\pi$
$8$		0			0
$9$	1.09660	−	3.37499i	0.365534	−	1.12500i
$10$		0			0
$11$	2.90921	−	1.59263i	0.877161	−	0.480196i
$11$	2.90921	−	1.59263i	0.877161	−	0.480196i
$12$		0			0
$13$	−3.18124	−	1.69698i	−0.882316	−	0.470657i
$13$	−3.18124	−	1.69698i	−0.882316	−	0.470657i
$14$		0			0
$15$	9.33093	−	1.47787i	2.40924	−	0.381585i
$16$		0			0
$17$	1.16829	+	3.59562i	0.283351	+	0.872065i	0.986888	+	0.161406i	$0.0516030\pi$
$17$	1.16829	+	3.59562i	0.283351	+	0.872065i	−0.703537	+	0.710659i	$0.748397\pi$
$18$		0			0
$19$	6.12176	+	0.969591i	1.40443	+	0.222439i	0.812222	−	0.583348i	$-0.198258\pi$
$19$	6.12176	+	0.969591i	1.40443	+	0.222439i	0.592205	+	0.805787i	$0.298258\pi$
$20$		0			0
$21$	4.01922	−	4.01922i	0.877066	−	0.877066i
$22$		0			0
$23$			8.37584i			1.74648i	0.487287	+	0.873242i	$0.337987\pi$
$23$			8.37584i			1.74648i	−0.487287	+	0.873242i	$0.662013\pi$
$24$		0			0
$25$	5.07185	+	6.98081i	1.01437	+	1.39616i
$26$		0			0
$27$	0.433888	+	1.33537i	0.0835019	+	0.256992i
$28$		0			0
$29$	0.561421	−	0.772730i	0.104253	−	0.143492i	−0.753703	−	0.657216i	$-0.771734\pi$
$29$	0.561421	−	0.772730i	0.104253	−	0.143492i	0.857956	+	0.513723i	$0.171734\pi$
$30$		0			0
$31$	−4.08218	−	8.01174i	−0.733182	−	1.43895i	−0.892184	−	0.451672i	$-0.850828\pi$
$31$	−4.08218	−	8.01174i	−0.733182	−	1.43895i	0.159002	−	0.987278i	$-0.449172\pi$
$32$		0			0
$33$	−3.62738	+	7.67317i	−0.631446	+	1.33573i
$34$		0			0
$35$	7.79856	+	2.53391i	1.31820	+	0.428308i
$36$		0			0
$37$	−0.188104	−	1.18764i	−0.0309241	−	0.195247i	0.967390	−	0.253292i	$-0.0815133\pi$
$37$	−0.188104	−	1.18764i	−0.0309241	−	0.195247i	−0.998314	+	0.0580449i	$0.981513\pi$
$38$		0			0
$39$	9.13867	−	1.27184i	1.46336	−	0.203658i
$40$		0			0
$41$	−3.45353	−	0.546985i	−0.539350	−	0.0854247i	−0.119185	−	0.992872i	$-0.538028\pi$
$41$	−3.45353	−	0.546985i	−0.539350	−	0.0854247i	−0.420166	+	0.907447i	$0.638028\pi$
$42$		0			0
$43$	10.9687			1.67271			0.836355	−	0.548188i	$-0.184682\pi$
$43$	10.9687			1.67271			0.836355	+	0.548188i	$0.184682\pi$
$44$		0			0
$45$	−9.26360	+	9.26360i	−1.38094	+	1.38094i
$46$		0			0
$47$	10.9256	+	1.73045i	1.59367	+	0.252412i	0.889266	−	0.457390i	$-0.151216\pi$
$47$	10.9256	+	1.73045i	1.59367	+	0.252412i	0.704401	+	0.709802i	$0.251216\pi$
$48$		0			0
$49$	−1.96530	+	0.638566i	−0.280758	+	0.0912237i
$50$		0			0
$51$	−7.82711	−	5.68673i	−1.09602	−	0.796302i
$52$		0			0
$53$	0.793973	−	2.44360i	0.109061	−	0.335654i	−0.881601	−	0.471995i	$-0.843534\pi$
$53$	0.793973	−	2.44360i	0.109061	−	0.335654i	0.990662	+	0.136341i	$0.0435342\pi$
$54$		0			0
$55$	−12.2387	+	0.362857i	−1.65026	+	0.0489276i
$56$		0			0
$57$	−14.1323	+	7.20078i	−1.87187	+	0.953767i
$58$		0			0
$59$	−0.863506	−	5.45196i	−0.112419	−	0.709785i	−0.977936	−	0.208905i	$-0.933010\pi$
$59$	−0.863506	−	5.45196i	−0.112419	−	0.709785i	0.865517	−	0.500880i	$-0.166990\pi$
$60$		0			0
$61$	9.75527	−	3.16968i	1.24903	−	0.405836i	0.391460	−	0.920195i	$-0.371970\pi$
$61$	9.75527	−	3.16968i	1.24903	−	0.405836i	0.857575	+	0.514359i	$0.171970\pi$
$62$		0			0
$63$	−1.23305	+	7.78515i	−0.155349	+	0.980836i
$64$		0			0
$65$	7.62004	+	10.9137i	0.945149	+	1.35368i
$66$		0			0
$67$	8.67305	−	8.67305i	1.05958	−	1.05958i	0.0614729	−	0.998109i	$-0.480420\pi$
$67$	8.67305	−	8.67305i	1.05958	−	1.05958i	0.998109	−	0.0614729i	$-0.0195798\pi$
$68$		0			0
$69$	−12.5987	−	17.3406i	−1.51670	−	2.08756i
$70$		0			0
$71$	6.55946	+	3.34221i	0.778465	+	0.396648i	0.797613	−	0.603169i	$-0.206096\pi$
$71$	6.55946	+	3.34221i	0.778465	+	0.396648i	−0.0191486	+	0.999817i	$0.506096\pi$
$72$		0			0
$73$	3.48189	−	0.551477i	0.407524	−	0.0645455i	0.0506927	−	0.998714i	$-0.483857\pi$
$73$	3.48189	−	0.551477i	0.407524	−	0.0645455i	0.356831	+	0.934169i	$0.383857\pi$
$74$		0			0
$75$	−21.0006	−	6.82350i	−2.42494	−	0.787910i
$76$		0			0
$77$	−5.82889	+	4.50479i	−0.664264	+	0.513369i
$78$		0			0
$79$	−5.58408	−	1.81438i	−0.628259	−	0.204134i	−0.0224550	−	0.999748i	$-0.507148\pi$
$79$	−5.58408	−	1.81438i	−0.628259	−	0.204134i	−0.605804	+	0.795614i	$0.707148\pi$
$80$		0			0
$81$	5.70593	+	4.14560i	0.633992	+	0.460622i
$82$		0			0
$83$	−7.55299	+	14.8236i	−0.829048	+	1.62710i	−0.0511647	+	0.998690i	$0.516293\pi$
$83$	−7.55299	+	14.8236i	−0.829048	+	1.62710i	−0.777884	+	0.628409i	$0.783707\pi$
$84$		0			0
$85$	2.18337	−	13.7853i	0.236820	−	1.49522i
$86$		0			0
$87$			2.44426i			0.262052i
$88$		0			0
$89$	−2.68281	−	2.68281i	−0.284377	−	0.284377i	0.550475	−	0.834852i	$-0.314447\pi$
$89$	−2.68281	−	2.68281i	−0.284377	−	0.284377i	−0.834852	+	0.550475i	$0.814447\pi$
$90$		0			0
$91$	7.56869	+	2.61748i	0.793414	+	0.274387i
$92$		0			0
$93$	20.5023	+	10.4465i	2.12599	+	1.08325i
$94$		0			0
$95$	−18.5115	−	13.4494i	−1.89924	−	1.37988i
$96$		0			0
$97$	−1.62852	−	3.19615i	−0.165351	−	0.324520i	0.793432	−	0.608659i	$-0.208292\pi$
$97$	−1.62852	−	3.19615i	−0.165351	−	0.324520i	−0.958783	+	0.284139i	$0.908292\pi$
$98$		0			0
$99$	−2.18487	−	11.5651i	−0.219588	−	1.16233i
$100$		0			0
$101$	2.38313	−	7.33451i	0.237130	−	0.729811i	−0.759702	−	0.650272i	$-0.774655\pi$
$101$	2.38313	−	7.33451i	0.237130	−	0.729811i	0.996832	−	0.0795392i	$-0.0253449\pi$
$102$		0			0
$103$	2.82876	−	3.89345i	0.278726	−	0.383633i	−0.646586	−	0.762841i	$-0.723804\pi$
$103$	2.82876	−	3.89345i	0.278726	−	0.383633i	0.925311	+	0.379208i	$0.123804\pi$
$104$		0			0
$105$	−19.9568	+	6.48436i	−1.94759	+	0.632809i
$106$		0			0
$107$	0.547361	+	0.753377i	0.0529154	+	0.0728317i	0.834655	−	0.550774i	$-0.185667\pi$
$107$	0.547361	+	0.753377i	0.0529154	+	0.0728317i	−0.781739	+	0.623605i	$0.785667\pi$
$108$		0			0
$109$	3.18414	+	3.18414i	0.304985	+	0.304985i	0.842961	−	0.537975i	$-0.180811\pi$
$109$	3.18414	+	3.18414i	0.304985	+	0.304985i	−0.537975	+	0.842961i	$0.680811\pi$
$110$		0			0
$111$	2.17584	+	2.17584i	0.206522	+	0.206522i
$112$		0			0
$113$	−5.42024	+	3.93804i	−0.509894	+	0.370459i	−0.812783	−	0.582566i	$-0.802049\pi$
$113$	−5.42024	+	3.93804i	−0.509894	+	0.370459i	0.302890	+	0.953026i	$0.402049\pi$
$114$		0			0
$115$	14.0379	−	27.5510i	1.30904	−	2.56914i
$116$		0			0
$117$	−9.21584	+	8.87575i	−0.852005	+	0.820563i
$118$		0			0
$119$	−3.81236	−	7.48218i	−0.349478	−	0.685890i
$120$		0			0
$121$	5.92705	−	9.26661i	0.538823	−	0.842419i
$122$		0			0
$123$	7.97261	−	4.06225i	0.718866	−	0.366281i
$124$		0			0
$125$	−2.09565	−	13.2314i	−0.187440	−	1.18345i
$126$		0			0
$127$	−2.63651	−	8.11436i	−0.233953	−	0.720033i	−0.997259	−	0.0739953i	$-0.976425\pi$
$127$	−2.63651	−	8.11436i	−0.233953	−	0.720033i	0.763306	−	0.646037i	$-0.223575\pi$
$128$		0			0
$129$	−22.7086	+	16.4987i	−1.99938	+	1.45263i
$130$		0			0
$131$			9.03908i			0.789748i	0.918735	+	0.394874i	$0.129212\pi$
$131$			9.03908i			0.789748i	−0.918735	+	0.394874i	$0.870788\pi$
$132$		0			0
$133$	−13.7669			−1.19374
$134$		0			0
$135$	0.810879	−	5.11969i	0.0697894	−	0.440633i
$136$		0			0
$137$	0.125919	−	0.247129i	0.0107580	−	0.0211137i	−0.885565	−	0.464515i	$-0.846229\pi$
$137$	0.125919	−	0.247129i	0.0107580	−	0.0211137i	0.896323	+	0.443402i	$0.146229\pi$
$138$		0			0
$139$	3.26488	−	4.49372i	0.276924	−	0.381153i	−0.647788	−	0.761820i	$-0.724306\pi$
$139$	3.26488	−	4.49372i	0.276924	−	0.381153i	0.924712	+	0.380668i	$0.124306\pi$
$140$		0			0
$141$	−25.2223	+	12.8514i	−2.12410	+	1.08228i
$142$		0			0
$143$	−11.9576	+	0.129669i	−0.999941	+	0.0108434i
$144$		0			0
$145$	−3.14181	+	1.60083i	−0.260913	+	0.132942i
$146$		0			0
$147$	3.10827	−	4.27817i	0.256366	−	0.352857i
$148$		0			0
$149$	−1.22845	+	2.41096i	−0.100638	+	0.197514i	−0.935836	−	0.352436i	$-0.885353\pi$
$149$	−1.22845	+	2.41096i	−0.100638	+	0.197514i	0.835197	+	0.549950i	$0.185353\pi$
$150$		0			0
$151$	−2.05129	+	12.9514i	−0.166932	+	1.05397i	0.751888	+	0.659290i	$0.229143\pi$
$151$	−2.05129	+	12.9514i	−0.166932	+	1.05397i	−0.918820	+	0.394676i	$0.870857\pi$
$152$		0			0
$153$	13.4163			1.08465
$154$		0			0
$155$			33.1951i			2.66629i
$156$		0			0
$157$	−3.13187	+	2.27544i	−0.249951	+	0.181600i	−0.705705	−	0.708506i	$-0.749370\pi$
$157$	−3.13187	+	2.27544i	−0.249951	+	0.181600i	0.455754	+	0.890106i	$0.349370\pi$
$158$		0			0
$159$	2.03181	+	6.25326i	0.161133	+	0.495916i
$160$		0			0
$161$	−2.91032	−	18.3751i	−0.229366	−	1.44816i
$162$		0			0
$163$	7.55052	−	3.84718i	0.591403	−	0.301335i	−0.132559	−	0.991175i	$-0.542319\pi$
$163$	7.55052	−	3.84718i	0.591403	−	0.301335i	0.723961	+	0.689840i	$0.242319\pi$
$164$		0			0
$165$	24.7920	−	19.1602i	1.93005	−	1.49162i
$166$		0			0
$167$	0.855748	+	1.67950i	0.0662197	+	0.129964i	0.921744	−	0.387800i	$-0.126765\pi$
$167$	0.855748	+	1.67950i	0.0662197	+	0.129964i	−0.855524	+	0.517763i	$0.826765\pi$
$168$		0			0
$169$	7.24054	+	10.7970i	0.556964	+	0.830536i
$170$		0			0
$171$	9.98550	−	19.5976i	0.763610	−	1.49867i
$172$		0			0
$173$	−4.47895	+	3.25415i	−0.340528	+	0.247408i	−0.744885	−	0.667193i	$-0.767496\pi$
$173$	−4.47895	+	3.25415i	−0.340528	+	0.247408i	0.404356	+	0.914601i	$0.367496\pi$
$174$		0			0
$175$	−13.5523	−	13.5523i	−1.02446	−	1.02446i
$176$		0			0
$177$	9.98837	+	9.98837i	0.750772	+	0.750772i
$178$		0			0
$179$	3.13958	+	4.32126i	0.234663	+	0.322986i	0.910066	−	0.414463i	$-0.136030\pi$
$179$	3.13958	+	4.32126i	0.234663	+	0.322986i	−0.675403	+	0.737449i	$0.736030\pi$
$180$		0			0
$181$	−10.7975	+	3.50832i	−0.802572	+	0.260771i	−0.681449	−	0.731866i	$-0.738650\pi$
$181$	−10.7975	+	3.50832i	−0.802572	+	0.260771i	−0.121123	+	0.992637i	$0.538650\pi$
$182$		0			0
$183$	−15.4287	+	21.2357i	−1.14052	+	1.56979i
$184$		0			0
$185$	−1.37175	+	4.22182i	−0.100853	+	0.310395i
$186$		0			0
$187$	9.12529	+	8.59977i	0.667307	+	0.628877i
$188$		0			0
$189$	−1.41587	−	2.77880i	−0.102989	−	0.202128i
$190$		0			0
$191$	18.8313	+	13.6817i	1.36259	+	0.989976i	0.998276	+	0.0586984i	$0.0186950\pi$
$191$	18.8313	+	13.6817i	1.36259	+	0.989976i	0.364310	+	0.931278i	$0.381305\pi$
$192$		0			0
$193$	17.4866	+	8.90985i	1.25871	+	0.641345i	0.950722	−	0.310045i	$-0.100344\pi$
$193$	17.4866	+	8.90985i	1.25871	+	0.641345i	0.307989	+	0.951390i	$0.400344\pi$
$194$		0			0
$195$	−32.1918	−	11.1329i	−2.30530	−	0.797244i
$196$		0			0
$197$	−12.1602	−	12.1602i	−0.866378	−	0.866378i	0.125691	−	0.992069i	$-0.459885\pi$
$197$	−12.1602	−	12.1602i	−0.866378	−	0.866378i	−0.992069	+	0.125691i	$0.959885\pi$
$198$		0			0
$199$			14.5843i			1.03385i	0.856030	+	0.516926i	$0.172924\pi$
$199$			14.5843i			1.03385i	−0.856030	+	0.516926i	$0.827076\pi$
$200$		0			0
$201$	−4.91017	+	31.0016i	−0.346336	+	2.18668i
$202$		0			0
$203$	−0.963157	+	1.89030i	−0.0676004	+	0.132673i
$204$		0			0
$205$	10.4431	+	7.58734i	0.729376	+	0.529923i
$206$		0			0
$207$	28.2684	+	9.18497i	1.96479	+	0.638399i
$208$		0			0
$209$	19.3537	−	6.92896i	1.33872	−	0.479286i
$210$		0			0
$211$	7.80362	+	2.53555i	0.537224	+	0.174555i	0.565048	−	0.825058i	$-0.308858\pi$
$211$	7.80362	+	2.53555i	0.537224	+	0.174555i	−0.0278240	+	0.999613i	$0.508858\pi$
$212$		0			0
$213$	−18.6073	+	2.94711i	−1.27495	+	0.201933i
$214$		0			0
$215$	−36.0798	−	18.3836i	−2.46062	−	1.25375i
$216$		0			0
$217$	11.7394	+	16.1579i	0.796920	+	1.09687i
$218$		0			0
$219$	−6.37906	+	6.37906i	−0.431057	+	0.431057i
$220$		0			0
$221$	2.38508	−	13.4211i	0.160438	−	0.902799i
$222$		0			0
$223$	−0.578472	+	3.65233i	−0.0387374	+	0.244578i	−0.999457	−	0.0329417i	$-0.989512\pi$
$223$	−0.578472	+	3.65233i	−0.0387374	+	0.244578i	0.960720	+	0.277520i	$0.0895124\pi$
$224$		0			0
$225$	29.1220	−	9.46231i	1.94147	−	0.630821i
$226$		0			0
$227$	−1.81603	−	11.4660i	−0.120534	−	0.761024i	−0.971716	−	0.236153i	$-0.924113\pi$
$227$	−1.81603	−	11.4660i	−0.120534	−	0.761024i	0.851182	−	0.524871i	$-0.175887\pi$
$228$		0			0
$229$	−2.86335	+	1.45895i	−0.189216	+	0.0964103i	−0.546032	−	0.837764i	$-0.683862\pi$
$229$	−2.86335	+	1.45895i	−0.189216	+	0.0964103i	0.356816	+	0.934175i	$0.383862\pi$
$230$		0			0
$231$	5.29164	−	18.0939i	0.348164	−	1.19049i
$232$		0			0
$233$	3.40242	−	10.4716i	0.222900	−	0.686016i	−0.775598	−	0.631228i	$-0.782551\pi$
$233$	3.40242	−	10.4716i	0.222900	−	0.686016i	0.998498	−	0.0547889i	$-0.0174486\pi$
$234$		0			0
$235$	−33.0379	−	24.0034i	−2.15515	−	1.56581i
$236$		0			0
$237$	14.2899	−	4.64307i	0.928228	−	0.301600i
$238$		0			0
$239$	27.9983	+	4.43449i	1.81106	+	0.286843i	0.967995	−	0.250971i	$-0.0807497\pi$
$239$	27.9983	+	4.43449i	1.81106	+	0.286843i	0.843064	+	0.537814i	$0.180750\pi$
$240$		0			0
$241$	18.4450	−	18.4450i	1.18814	−	1.18814i	0.210564	−	0.977580i	$-0.432470\pi$
$241$	18.4450	−	18.4450i	1.18814	−	1.18814i	0.977580	−	0.210564i	$-0.0675301\pi$
$242$		0			0
$243$	−22.2610			−1.42804
$244$		0			0
$245$	7.53480	+	1.19339i	0.481380	+	0.0762432i
$246$		0			0
$247$	−17.8294	−	13.4730i	−1.13446	−	0.857265i
$248$		0			0
$249$	−6.66011	−	42.0503i	−0.422067	−	2.66483i
$250$		0			0
$251$	5.90220	+	1.91774i	0.372544	+	0.121047i	0.489304	−	0.872113i	$-0.337251\pi$
$251$	5.90220	+	1.91774i	0.372544	+	0.121047i	−0.116760	+	0.993160i	$0.537251\pi$
$252$		0			0
$253$	13.3396	+	24.3671i	0.838655	+	1.53195i
$254$		0			0
$255$	16.2151	+	31.8239i	1.01543	+	1.99289i
$256$		0			0
$257$	8.20270	−	11.2901i	0.511670	−	0.704254i	−0.472529	−	0.881315i	$-0.656659\pi$
$257$	8.20270	−	11.2901i	0.511670	−	0.704254i	0.984200	+	0.177061i	$0.0566590\pi$
$258$		0			0
$259$	0.825331	+	2.54011i	0.0512835	+	0.157835i
$260$		0			0
$261$	−1.99230	−	2.74217i	−0.123321	−	0.169736i
$262$		0			0
$263$			6.83460i			0.421439i	0.977547	+	0.210720i	$0.0675807\pi$
$263$			6.83460i			0.421439i	−0.977547	+	0.210720i	$0.932419\pi$
$264$		0			0
$265$	−6.70713	+	6.70713i	−0.412015	+	0.412015i
$266$		0			0
$267$	9.58962	+	1.51885i	0.586875	+	0.0929519i
$268$		0			0
$269$	−1.55711	−	4.79230i	−0.0949389	−	0.292192i	0.892299	−	0.451445i	$-0.149091\pi$
$269$	−1.55711	−	4.79230i	−0.0949389	−	0.292192i	−0.987238	+	0.159253i	$0.949091\pi$
$270$		0			0
$271$	16.0402	−	2.54052i	0.974375	−	0.154326i	0.351108	−	0.936335i	$-0.385805\pi$
$271$	16.0402	−	2.54052i	0.974375	−	0.154326i	0.623267	+	0.782009i	$0.285805\pi$
$272$		0			0
$273$	−19.6066	+	5.96557i	−1.18665	+	0.361053i
$274$		0			0
$275$	25.8730	+	12.2311i	1.56020	+	0.737561i
$276$		0			0
$277$	8.45175	−	26.0118i	0.507816	−	1.56290i	−0.288168	−	0.957580i	$-0.593046\pi$
$277$	8.45175	−	26.0118i	0.507816	−	1.56290i	0.795984	−	0.605318i	$-0.206954\pi$
$278$		0			0
$279$	−31.5161	+	4.99166i	−1.88682	+	0.298843i
$280$		0			0
$281$	0.733261	+	0.373615i	0.0437427	+	0.0222880i	0.475725	−	0.879594i	$-0.342186\pi$
$281$	0.733261	+	0.373615i	0.0437427	+	0.0222880i	−0.431982	+	0.901882i	$0.642186\pi$
$282$		0			0
$283$	−5.90504	+	4.29026i	−0.351018	+	0.255030i	−0.749296	−	0.662235i	$-0.769608\pi$
$283$	−5.90504	+	4.29026i	−0.351018	+	0.255030i	0.398278	+	0.917265i	$0.369608\pi$
$284$		0			0
$285$	58.5546			3.46848
$286$		0			0
$287$	7.76646			0.458439
$288$		0			0
$289$	2.18972	−	1.59093i	0.128807	−	0.0935839i
$290$		0			0
$291$	8.17908	+	4.16745i	0.479466	+	0.244300i
$292$		0			0
$293$	−3.97645	+	0.629808i	−0.232307	+	0.0367938i	−0.271502	−	0.962438i	$-0.587520\pi$
$293$	−3.97645	+	0.629808i	−0.232307	+	0.0367938i	0.0391955	+	0.999232i	$0.487520\pi$
$294$		0			0
$295$	−6.29714	+	19.3806i	−0.366634	+	1.12838i
$296$		0			0
$297$	3.38903	+	3.19386i	0.196651	+	0.185326i
$298$		0			0
$299$	14.2136	−	26.6455i	0.821995	−	1.54095i
$300$		0			0
$301$	−24.0633	+	3.81125i	−1.38699	+	0.219677i
$302$		0			0
$303$	6.09851	+	18.7693i	0.350350	+	1.07827i
$304$		0			0
$305$	−37.4008	−	5.92371i	−2.14156	−	0.339190i
$306$		0			0
$307$	−2.27446	+	2.27446i	−0.129810	+	0.129810i	−0.769027	−	0.639217i	$-0.779259\pi$
$307$	−2.27446	+	2.27446i	−0.129810	+	0.129810i	0.639217	+	0.769027i	$0.279259\pi$
$308$		0			0
$309$			12.3155i			0.700607i
$310$		0			0
$311$	9.44555	+	13.0007i	0.535608	+	0.737201i	0.987972	−	0.154632i	$-0.0494192\pi$
$311$	9.44555	+	13.0007i	0.535608	+	0.737201i	−0.452364	+	0.891833i	$0.649419\pi$
$312$		0			0
$313$	3.91306	+	12.0432i	0.221179	+	0.680720i	0.998657	+	0.0518093i	$0.0164988\pi$
$313$	3.91306	+	12.0432i	0.221179	+	0.680720i	−0.777478	+	0.628910i	$0.783501\pi$
$314$		0			0
$315$	17.1038	−	23.5414i	0.963692	−	1.32641i
$316$		0			0
$317$	2.03101	+	3.98608i	0.114073	+	0.223881i	0.940983	−	0.338453i	$-0.109904\pi$
$317$	2.03101	+	3.98608i	0.114073	+	0.223881i	−0.826910	+	0.562334i	$0.809904\pi$
$318$		0			0
$319$	0.402620	−	3.14218i	0.0225424	−	0.175928i
$320$		0			0
$321$	−2.26641	−	0.736401i	−0.126499	−	0.0411019i
$322$		0			0
$323$	3.66569	+	23.1443i	0.203964	+	1.28778i
$324$		0			0
$325$	−4.28850	−	30.8144i	−0.237883	−	1.70928i
$326$		0			0
$327$	−11.3816	−	1.80267i	−0.629405	−	0.0996880i
$328$		0			0
$329$	−24.5701			−1.35459
$330$		0			0
$331$	6.58971	−	6.58971i	0.362203	−	0.362203i	−0.502420	−	0.864623i	$-0.667557\pi$
$331$	6.58971	−	6.58971i	0.362203	−	0.362203i	0.864623	+	0.502420i	$0.167557\pi$
$332$		0			0
$333$	−4.21456	−	0.667521i	−0.230956	−	0.0365799i
$334$		0			0
$335$	−43.0647	+	13.9926i	−2.35287	+	0.764495i
$336$		0			0
$337$	−24.1125	−	17.5187i	−1.31349	−	0.954306i	−0.999989	−	0.00471769i	$-0.998498\pi$
$337$	−24.1125	−	17.5187i	−1.31349	−	0.954306i	−0.313500	−	0.949588i	$-0.601502\pi$
$338$		0			0
$339$	5.29810	−	16.3059i	0.287753	−	0.885614i
$340$		0			0
$341$	−24.6357	−	16.8064i	−1.33410	−	0.910120i
$342$		0			0
$343$	17.9431	−	9.14247i	0.968837	−	0.493647i
$344$		0			0
$345$	12.3784	+	78.1544i	0.666433	+	4.20769i
$346$		0			0
$347$	−1.42417	+	0.462742i	−0.0764536	+	0.0248413i	−0.346994	−	0.937867i	$-0.612798\pi$
$347$	−1.42417	+	0.462742i	−0.0764536	+	0.0248413i	0.270540	+	0.962709i	$0.412798\pi$
$348$		0			0
$349$	4.87098	−	30.7541i	0.260737	−	1.64623i	−0.415534	−	0.909578i	$-0.636405\pi$
$349$	4.87098	−	30.7541i	0.260737	−	1.64623i	0.676271	−	0.736653i	$-0.263595\pi$
$350$		0			0
$351$	0.885793	−	4.98443i	0.0472801	−	0.266049i
$352$		0			0
$353$	10.2225	−	10.2225i	0.544087	−	0.544087i	−0.380638	−	0.924724i	$-0.624295\pi$
$353$	10.2225	−	10.2225i	0.544087	−	0.544087i	0.924724	+	0.380638i	$0.124295\pi$
$354$		0			0
$355$	−15.9747	−	21.9874i	−0.847852	−	1.16697i
$356$		0			0
$357$	19.1472	+	9.75598i	1.01338	+	0.516341i
$358$		0			0
$359$	9.04167	−	1.43206i	0.477201	−	0.0755812i	0.0867992	−	0.996226i	$-0.472336\pi$
$359$	9.04167	−	1.43206i	0.477201	−	0.0755812i	0.390402	+	0.920645i	$0.372336\pi$
$360$		0			0
$361$	18.4657	+	5.99988i	0.971881	+	0.315783i
$362$		0			0
$363$	1.66771	+	28.1000i	0.0875319	+	1.47487i
$364$		0			0
$365$	−12.3774	−	4.02166i	−0.647862	−	0.210503i
$366$		0			0
$367$	−11.4497	−	8.31870i	−0.597670	−	0.434232i	0.247381	−	0.968918i	$-0.420430\pi$
$367$	−11.4497	−	8.31870i	−0.597670	−	0.434232i	−0.845051	+	0.534686i	$0.820430\pi$
$368$		0			0
$369$	−5.63322	+	11.0558i	−0.293254	+	0.575542i
$370$		0			0
$371$	−0.892762	+	5.63668i	−0.0463499	+	0.292642i
$372$		0			0
$373$			0.942519i			0.0488018i	0.999702	+	0.0244009i	$0.00776781\pi$
$373$			0.942519i			0.0488018i	−0.999702	+	0.0244009i	$0.992232\pi$
$374$		0			0
$375$	24.2408	+	24.2408i	1.25179	+	1.25179i
$376$		0			0
$377$	−3.09732	+	1.50552i	−0.159520	+	0.0775382i
$378$		0			0
$379$	−1.88649	−	0.961216i	−0.0969027	−	0.0493744i	0.404867	−	0.914375i	$-0.367318\pi$
$379$	−1.88649	−	0.961216i	−0.0969027	−	0.0493744i	−0.501770	+	0.865001i	$0.667318\pi$
$380$		0			0
$381$	17.6637	+	12.8334i	0.904940	+	0.657477i
$382$		0			0
$383$	10.5801	+	20.7647i	0.540619	+	1.06103i	0.986165	+	0.165766i	$0.0530097\pi$
$383$	10.5801	+	20.7647i	0.540619	+	1.06103i	−0.445546	+	0.895259i	$0.646990\pi$
$384$		0			0
$385$	26.7233	−	5.04856i	1.36194	−	0.257298i
$386$		0			0
$387$	12.0283	−	37.0193i	0.611433	−	1.88180i
$388$		0			0
$389$	−9.69221	+	13.3402i	−0.491415	+	0.676374i	−0.980648	−	0.195779i	$-0.937277\pi$
$389$	−9.69221	+	13.3402i	−0.491415	+	0.676374i	0.489234	+	0.872153i	$0.337277\pi$
$390$		0			0
$391$	−30.1163	+	9.78539i	−1.52305	+	0.494868i
$392$		0			0
$393$	−13.5963	−	18.7137i	−0.685841	−	0.943979i
$394$		0			0
$395$	15.3271	+	15.3271i	0.771188	+	0.771188i
$396$		0			0
$397$	23.3353	+	23.3353i	1.17117	+	1.17117i	0.981932	+	0.189234i	$0.0606006\pi$
$397$	23.3353	+	23.3353i	1.17117	+	1.17117i	0.189234	+	0.981932i	$0.439399\pi$
$398$		0			0
$399$	28.5017	−	20.7077i	1.42687	−	1.03668i
$400$		0			0
$401$	−3.54034	+	6.94830i	−0.176796	+	0.346982i	−0.962351	−	0.271810i	$-0.912378\pi$
$401$	−3.54034	+	6.94830i	−0.176796	+	0.346982i	0.785555	+	0.618792i	$0.212378\pi$
$402$		0			0
$403$	−0.609341	+	32.4146i	−0.0303534	+	1.61469i
$404$		0			0
$405$	−11.8207	−	23.1994i	−0.587375	−	1.15279i
$406$		0			0
$407$	−2.43871	−	3.15552i	−0.120882	−	0.156413i
$408$		0			0
$409$	1.95150	−	0.994339i	0.0964954	−	0.0491669i	−0.405077	−	0.914283i	$-0.632755\pi$
$409$	1.95150	−	0.994339i	0.0964954	−	0.0491669i	0.501572	+	0.865116i	$0.332755\pi$
$410$		0			0
$411$	0.111033	+	0.701036i	0.00547686	+	0.0345796i
$412$		0			0
$413$	3.78874	+	11.6606i	0.186432	+	0.573778i
$414$		0			0
$415$	49.6887	−	36.1010i	2.43912	−	1.77213i
$416$		0			0
$417$			14.2143i			0.696078i
$418$		0			0
$419$	17.0086			0.830922			0.415461	−	0.909611i	$-0.363620\pi$
$419$	17.0086			0.830922			0.415461	+	0.909611i	$0.363620\pi$
$420$		0			0
$421$	0.515557	−	3.25510i	0.0251267	−	0.158644i	−0.971935	−	0.235251i	$-0.924409\pi$
$421$	0.515557	−	3.25510i	0.0251267	−	0.158644i	0.997061	+	0.0766072i	$0.0244087\pi$
$422$		0			0
$423$	17.8213	−	34.9763i	0.866503	−	1.70061i
$424$		0			0
$425$	−19.1749	+	26.3920i	−0.930121	+	1.28020i
$426$		0			0
$427$	−20.2999	+	10.3433i	−0.982381	+	0.500548i
$428$		0			0
$429$	24.5608	−	18.2546i	1.18580	−	0.881340i
$430$		0			0
$431$	−16.9878	+	8.65572i	−0.818274	+	0.416931i	−0.812435	−	0.583052i	$-0.801859\pi$
$431$	−16.9878	+	8.65572i	−0.818274	+	0.416931i	−0.00583870	+	0.999983i	$0.501859\pi$
$432$		0			0
$433$	−8.20704	+	11.2960i	−0.394405	+	0.542852i	−0.959329	−	0.282291i	$-0.908906\pi$
$433$	−8.20704	+	11.2960i	−0.394405	+	0.542852i	0.564924	+	0.825143i	$0.308906\pi$
$434$		0			0
$435$	4.09659	−	8.04000i	0.196416	−	0.385489i
$436$		0			0
$437$	−8.12114	+	51.2749i	−0.388487	+	2.45281i
$438$		0			0
$439$	−14.0879			−0.672379			−0.336189	−	0.941794i	$-0.609138\pi$
$439$	−14.0879			−0.672379			−0.336189	+	0.941794i	$0.609138\pi$
$440$		0			0
$441$			7.33314i			0.349197i
$442$		0			0
$443$	−10.0989	+	7.33728i	−0.479813	+	0.348605i	−0.801253	−	0.598325i	$-0.795833\pi$
$443$	−10.0989	+	7.33728i	−0.479813	+	0.348605i	0.321440	+	0.946930i	$0.395833\pi$
$444$		0			0
$445$	4.32828	+	13.3211i	0.205180	+	0.631479i
$446$		0			0
$447$	−1.08323	−	6.83922i	−0.0512348	−	0.323484i
$448$		0			0
$449$	17.7595	−	9.04892i	0.838123	−	0.427045i	0.0184177	−	0.999830i	$-0.494137\pi$
$449$	17.7595	−	9.04892i	0.838123	−	0.427045i	0.819705	+	0.572785i	$0.194137\pi$
$450$		0			0
$451$	−10.9182	+	3.90890i	−0.514118	+	0.184063i
$452$		0			0
$453$	−15.2342	−	29.8988i	−0.715764	−	1.40477i
$454$		0			0
$455$	−20.5091	−	21.2949i	−0.961481	−	0.998322i
$456$		0			0
$457$	12.5309	−	24.5932i	0.586170	−	1.15042i	−0.387374	−	0.921923i	$-0.626618\pi$
$457$	12.5309	−	24.5932i	0.586170	−	1.15042i	0.973544	−	0.228500i	$-0.0733821\pi$
$458$		0			0
$459$	−4.29458	+	3.12019i	−0.200454	+	0.145638i
$460$		0			0
$461$	−23.7865	−	23.7865i	−1.10785	−	1.10785i	−0.993433	−	0.114417i	$-0.963500\pi$
$461$	−23.7865	−	23.7865i	−1.10785	−	1.10785i	−0.114417	−	0.993433i	$-0.536500\pi$
$462$		0			0
$463$	−1.69684	−	1.69684i	−0.0788586	−	0.0788586i	0.666577	−	0.745436i	$-0.267759\pi$
$463$	−1.69684	−	1.69684i	−0.0788586	−	0.0788586i	−0.745436	+	0.666577i	$0.767759\pi$
$464$		0			0
$465$	−49.9309	−	68.7240i	−2.31549	−	3.18700i
$466$		0			0
$467$	−2.18668	+	0.710496i	−0.101188	+	0.0328778i	−0.359173	−	0.933271i	$-0.616941\pi$
$467$	−2.18668	+	0.710496i	−0.101188	+	0.0328778i	0.257986	+	0.966149i	$0.416941\pi$
$468$		0			0
$469$	−16.0135	+	22.0407i	−0.739434	+	1.01774i
$470$		0			0
$471$	3.06130	−	9.42171i	0.141057	−	0.434130i
$472$		0			0
$473$	31.9103	−	17.4691i	1.46724	−	0.803230i
$474$		0			0
$475$	24.2801	+	47.6524i	1.11405	+	2.18644i
$476$		0			0
$477$	−7.37646	−	5.35931i	−0.337745	−	0.245386i
$478$		0			0
$479$	19.2671	+	9.81709i	0.880338	+	0.448554i	0.834893	−	0.550412i	$-0.185529\pi$
$479$	19.2671	+	9.81709i	0.880338	+	0.448554i	0.0454448	+	0.998967i	$0.485529\pi$
$480$		0			0
$481$	−1.41700	+	4.09738i	−0.0646095	+	0.186824i
$482$		0			0
$483$	33.6644	+	33.6644i	1.53178	+	1.53178i
$484$		0			0
$485$			13.2427i			0.601318i
$486$		0			0
$487$	2.78955	−	17.6125i	0.126407	−	0.798100i	−0.840283	−	0.542148i	$-0.817611\pi$
$487$	2.78955	−	17.6125i	0.126407	−	0.798100i	0.966690	−	0.255952i	$-0.0823889\pi$
$488$		0			0
$489$	−9.84509	+	19.3221i	−0.445210	+	0.873775i
$490$		0			0
$491$	−6.28023	−	4.56286i	−0.283423	−	0.205919i	0.436986	−	0.899468i	$-0.356046\pi$
$491$	−6.28023	−	4.56286i	−0.283423	−	0.205919i	−0.720409	+	0.693549i	$0.756046\pi$
$492$		0			0
$493$	3.43434	+	1.11589i	0.154675	+	0.0502570i
$494$		0			0
$495$	−12.1963	+	41.7033i	−0.548183	+	1.87442i
$496$		0			0
$497$	−15.5515	−	5.05300i	−0.697582	−	0.226658i
$498$		0			0
$499$	−39.5181	+	6.25905i	−1.76907	+	0.280194i	−0.954140	−	0.299361i	$-0.903227\pi$
$499$	−39.5181	+	6.25905i	−1.76907	+	0.280194i	−0.814934	+	0.579554i	$0.803227\pi$
$500$		0			0
$501$	−4.29790	−	2.18989i	−0.192016	−	0.0978371i
$502$		0			0
$503$	−17.4663	−	24.0403i	−0.778783	−	1.07190i	−0.995415	−	0.0956494i	$-0.969507\pi$
$503$	−17.4663	−	24.0403i	−0.778783	−	1.07190i	0.216632	−	0.976253i	$-0.430493\pi$
$504$		0			0
$505$	−20.1316	+	20.1316i	−0.895843	+	0.895843i
$506$		0			0
$507$	−31.2306	−	11.4621i	−1.38700	−	0.509049i
$508$		0			0
$509$	0.0249104	−	0.157278i	0.00110413	−	0.00697122i	−0.987130	−	0.159919i	$-0.948877\pi$
$509$	0.0249104	−	0.157278i	0.00110413	−	0.00697122i	0.988234	+	0.152948i	$0.0488767\pi$
$510$		0			0
$511$	−7.44699	+	2.41968i	−0.329436	+	0.107040i
$512$		0			0
$513$	1.36140	+	8.59551i	0.0601071	+	0.379501i
$514$		0			0
$515$	−15.8302	+	8.06588i	−0.697561	+	0.355425i
$516$		0			0
$517$	34.5410	−	12.3663i	1.51911	−	0.543867i
$518$		0			0
$519$	4.37802	−	13.4742i	0.192174	−	0.591450i
$520$		0			0
$521$	33.3055	+	24.1979i	1.45914	+	1.06013i	0.983586	+	0.180442i	$0.0577530\pi$
$521$	33.3055	+	24.1979i	1.45914	+	1.06013i	0.475556	+	0.879686i	$0.342247\pi$
$522$		0			0
$523$	30.0560	−	9.76579i	1.31426	−	0.427028i	0.433738	−	0.901039i	$-0.357194\pi$
$523$	30.0560	−	9.76579i	1.31426	−	0.427028i	0.880519	+	0.474011i	$0.157194\pi$
$524$		0			0
$525$	48.4423	+	7.67251i	2.11420	+	0.334856i
$526$		0			0
$527$	24.0380	−	24.0380i	1.04711	−	1.04711i
$528$		0			0
$529$	−47.1548			−2.05021
$530$		0			0
$531$	−19.3473	−	3.06431i	−0.839600	−	0.132980i
$532$		0			0
$533$	10.0583	+	7.60064i	0.435672	+	0.329220i
$534$		0			0
$535$	−0.537793	−	3.39549i	−0.0232508	−	0.146800i
$536$		0			0
$537$	−12.9998	−	4.22388i	−0.560982	−	0.182274i
$538$		0			0
$539$	−4.70049	+	4.98773i	−0.202464	+	0.214837i
$540$		0			0
$541$	−7.46994	−	14.6606i	−0.321158	−	0.630308i	0.672830	−	0.739797i	$-0.265078\pi$
$541$	−7.46994	−	14.6606i	−0.321158	−	0.630308i	−0.993988	+	0.109489i	$0.965078\pi$
$542$		0			0
$543$	17.0770	−	23.5045i	0.732846	−	1.00868i
$544$		0			0
$545$	−5.13710	−	15.8104i	−0.220049	−	0.677241i
$546$		0			0
$547$	−15.2202	−	20.9488i	−0.650769	−	0.895707i	0.348363	−	0.937360i	$-0.386738\pi$
$547$	−15.2202	−	20.9488i	−0.650769	−	0.895707i	−0.999132	+	0.0416529i	$0.986738\pi$
$548$		0			0
$549$		−	36.3999i		−	1.55351i
$550$		0			0
$551$	4.18612	−	4.18612i	0.178335	−	0.178335i
$552$		0			0
$553$	12.8809	+	2.04013i	0.547751	+	0.0867552i
$554$		0			0
$555$	−3.51037	−	10.8038i	−0.149007	−	0.458596i
$556$		0			0
$557$	0.869735	−	0.137753i	0.0368519	−	0.00583676i	−0.137981	−	0.990435i	$-0.544061\pi$
$557$	0.869735	−	0.137753i	0.0368519	−	0.00583676i	0.174833	+	0.984598i	$0.444061\pi$
$558$		0			0
$559$	−34.8940	−	18.6136i	−1.47586	−	0.787273i
$560$		0			0
$561$	−31.8276	−	4.07821i	−1.34376	−	0.172182i
$562$		0			0
$563$	−13.4646	+	41.4396i	−0.567463	+	1.74647i	0.0930532	+	0.995661i	$0.470337\pi$
$563$	−13.4646	+	41.4396i	−0.567463	+	1.74647i	−0.660517	+	0.750812i	$0.729663\pi$
$564$		0			0
$565$	24.4292	−	3.86920i	1.02774	−	0.162779i
$566$		0			0
$567$	−13.9582	−	7.11206i	−0.586189	−	0.298678i
$568$		0			0
$569$	10.4217	−	7.57179i	0.436899	−	0.317426i	−0.347502	−	0.937679i	$-0.612970\pi$
$569$	10.4217	−	7.57179i	0.436899	−	0.317426i	0.784402	+	0.620253i	$0.212970\pi$
$570$		0			0
$571$	−30.3552			−1.27033			−0.635163	−	0.772378i	$-0.719067\pi$
$571$	−30.3552			−1.27033			−0.635163	+	0.772378i	$0.719067\pi$
$572$		0			0
$573$	−59.5662			−2.48841
$574$		0			0
$575$	−58.4702	+	42.4811i	−2.43837	+	1.77158i
$576$		0			0
$577$	−27.5331	−	14.0288i	−1.14622	−	0.584027i	−0.225495	−	0.974244i	$-0.572400\pi$
$577$	−27.5331	−	14.0288i	−1.14622	−	0.584027i	−0.920723	+	0.390217i	$0.872400\pi$
$578$		0			0
$579$	−49.6045	+	7.85657i	−2.06149	+	0.326508i
$580$		0			0
$581$	11.4192	−	35.1446i	0.473747	−	1.45804i
$582$		0			0
$583$	−1.58191	−	8.37345i	−0.0655161	−	0.346793i
$584$		0			0
$585$	45.1898	−	13.7496i	1.86837	−	0.568476i
$586$		0			0
$587$	−18.0575	+	2.86002i	−0.745312	+	0.118046i	−0.517528	−	0.855666i	$-0.673148\pi$
$587$	−18.0575	+	2.86002i	−0.745312	+	0.118046i	−0.227784	+	0.973712i	$0.573148\pi$
$588$		0			0
$589$	−17.2220	−	53.0040i	−0.709622	−	2.18399i
$590$		0			0
$591$	43.4663	+	6.88438i	1.78796	+	0.283186i
$592$		0			0
$593$	−15.2734	+	15.2734i	−0.627203	+	0.627203i	−0.947363	−	0.320160i	$-0.896263\pi$
$593$	−15.2734	+	15.2734i	−0.627203	+	0.627203i	0.320160	+	0.947363i	$0.396263\pi$
$594$		0			0
$595$			31.0010i			1.27092i
$596$		0			0
$597$	−21.9372	−	30.1939i	−0.897828	−	1.23575i
$598$		0			0
$599$	−10.1194	−	31.1443i	−0.413467	−	1.27252i	−0.913615	−	0.406580i	$-0.866721\pi$
$599$	−10.1194	−	31.1443i	−0.413467	−	1.27252i	0.500148	−	0.865940i	$-0.333279\pi$
$600$		0			0
$601$	−5.89920	+	8.11955i	−0.240633	+	0.331203i	−0.912203	−	0.409738i	$-0.865620\pi$
$601$	−5.89920	+	8.11955i	−0.240633	+	0.331203i	0.671570	+	0.740941i	$0.265620\pi$
$602$		0			0
$603$	−19.7606	−	38.7824i	−0.804714	−	1.57934i
$604$		0			0
$605$	−35.0270	+	20.5473i	−1.42405	+	0.835366i
$606$		0			0
$607$	−2.27569	−	0.739416i	−0.0923673	−	0.0300120i	0.262469	−	0.964940i	$-0.415463\pi$
$607$	−2.27569	−	0.739416i	−0.0923673	−	0.0300120i	−0.354836	+	0.934929i	$0.615463\pi$
$608$		0			0
$609$	−0.849297	−	5.36225i	−0.0344153	−	0.217289i
$610$		0			0
$611$	−31.8205	−	24.0455i	−1.28732	−	0.972778i
$612$		0			0
$613$	22.6718	+	3.59087i	0.915707	+	0.145034i	0.596465	−	0.802639i	$-0.296572\pi$
$613$	22.6718	+	3.59087i	0.915707	+	0.145034i	0.319243	+	0.947673i	$0.396572\pi$
$614$		0			0
$615$	−33.0330			−1.33202
$616$		0			0
$617$	−22.6342	+	22.6342i	−0.911217	+	0.911217i	−0.996368	−	0.0851509i	$-0.972863\pi$
$617$	−22.6342	+	22.6342i	−0.911217	+	0.911217i	0.0851509	+	0.996368i	$0.472863\pi$
$618$		0			0
$619$	32.9035	+	5.21140i	1.32250	+	0.209464i	0.777454	−	0.628940i	$-0.216511\pi$
$619$	32.9035	+	5.21140i	1.32250	+	0.209464i	0.545050	+	0.838404i	$0.316511\pi$
$620$		0			0
$621$	−11.1849	+	3.63418i	−0.448833	+	0.145835i
$622$		0			0
$623$	6.81777	+	4.95340i	0.273148	+	0.198454i
$624$		0			0
$625$	−1.95040	+	6.00272i	−0.0780161	+	0.240109i
$626$		0			0
$627$	−29.6458	+	43.4562i	−1.18394	+	1.73547i
$628$		0			0
$629$	4.05054	−	2.06386i	0.161506	−	0.0822913i
$630$		0			0
$631$	2.04988	+	12.9425i	0.0816046	+	0.515231i	0.994302	+	0.106596i	$0.0339952\pi$
$631$	2.04988	+	12.9425i	0.0816046	+	0.515231i	−0.912698	+	0.408635i	$0.866005\pi$
$632$		0			0
$633$	−19.9698	+	6.48857i	−0.793727	+	0.257898i
$634$		0			0
$635$	−4.92729	+	31.1097i	−0.195534	+	1.23455i
$636$		0			0
$637$	7.33573	+	1.30365i	0.290652	+	0.0516524i
$638$		0			0
$639$	18.4731	−	18.4731i	0.730783	−	0.730783i
$640$		0			0
$641$	17.8671	+	24.5920i	0.705708	+	0.971324i	0.999879	+	0.0155712i	$0.00495667\pi$
$641$	17.8671	+	24.5920i	0.705708	+	0.971324i	−0.294170	+	0.955753i	$0.595043\pi$
$642$		0			0
$643$	−4.82668	−	2.45932i	−0.190346	−	0.0969860i	0.356220	−	0.934402i	$-0.384065\pi$
$643$	−4.82668	−	2.45932i	−0.190346	−	0.0969860i	−0.546566	+	0.837416i	$0.684065\pi$
$644$		0			0
$645$	102.348	−	16.2104i	4.02995	−	0.638282i
$646$		0			0
$647$	29.2318	+	9.49797i	1.14922	+	0.373404i	0.820849	−	0.571145i	$-0.193501\pi$
$647$	29.2318	+	9.49797i	1.14922	+	0.373404i	0.328370	+	0.944549i	$0.393501\pi$
$648$		0			0
$649$	−11.1951	−	14.4857i	−0.439446	−	0.568613i
$650$		0			0
$651$	−48.6082	−	15.7937i	−1.90510	−	0.619006i
$652$		0			0
$653$	21.5069	+	15.6257i	0.841629	+	0.611479i	0.922825	−	0.385219i	$-0.125874\pi$
$653$	21.5069	+	15.6257i	0.841629	+	0.611479i	−0.0811961	+	0.996698i	$0.525874\pi$
$654$		0			0
$655$	15.1495	−	29.7326i	0.591941	−	1.16175i
$656$		0			0
$657$	1.95701	−	12.3561i	0.0763504	−	0.482057i
$658$		0			0
$659$		−	32.0036i		−	1.24668i	−0.781949	−	0.623342i	$-0.785774\pi$
$659$		−	32.0036i		−	1.24668i	0.781949	−	0.623342i	$-0.214226\pi$
$660$		0			0
$661$	−2.87325	−	2.87325i	−0.111757	−	0.111757i	0.649017	−	0.760774i	$-0.275180\pi$
$661$	−2.87325	−	2.87325i	−0.111757	−	0.111757i	−0.760774	+	0.649017i	$0.775180\pi$
$662$		0			0
$663$	15.2496	+	31.3733i	0.592247	+	1.21844i
$664$		0			0
$665$	45.2840	+	23.0734i	1.75604	+	0.894747i
$666$		0			0
$667$	6.47227	+	4.70238i	0.250607	+	0.182077i
$668$		0			0
$669$	−4.29609	−	8.43156i	−0.166097	−	0.325983i
$670$		0			0
$671$	23.3320	−	24.7578i	0.900723	−	0.955765i
$672$		0			0
$673$	−2.63126	+	8.09818i	−0.101428	+	0.312162i	−0.988875	−	0.148746i	$-0.952476\pi$
$673$	−2.63126	+	8.09818i	−0.101428	+	0.312162i	0.887448	+	0.460908i	$0.152476\pi$
$674$		0			0
$675$	−7.12135	+	9.80170i	−0.274101	+	0.377268i
$676$		0			0
$677$	41.7648	−	13.5702i	1.60515	−	0.521545i	0.636776	−	0.771049i	$-0.280267\pi$
$677$	41.7648	−	13.5702i	1.60515	−	0.521545i	0.968374	+	0.249504i	$0.0802674\pi$
$678$		0			0
$679$	4.68323	+	6.44592i	0.179726	+	0.247372i
$680$		0			0
$681$	21.0065	+	21.0065i	0.804970	+	0.804970i
$682$		0			0
$683$	−23.8827	−	23.8827i	−0.913847	−	0.913847i	0.0827254	−	0.996572i	$-0.473638\pi$
$683$	−23.8827	−	23.8827i	−0.913847	−	0.913847i	−0.996572	+	0.0827254i	$0.973638\pi$
$684$		0			0
$685$	−0.828379	+	0.601853i	−0.0316507	+	0.0229956i
$686$		0			0
$687$	3.73351	−	7.32744i	0.142442	−	0.279559i
$688$		0			0
$689$	−6.67255	+	6.42631i	−0.254204	+	0.244823i
$690$		0			0
$691$	19.2285	+	37.7380i	0.731485	+	1.43562i	0.893607	+	0.448850i	$0.148166\pi$
$691$	19.2285	+	37.7380i	0.731485	+	1.43562i	−0.162121	+	0.986771i	$0.551834\pi$
$692$		0			0
$693$	8.81167	+	24.6124i	0.334728	+	0.934949i
$694$		0			0
$695$	−18.2708	+	9.30944i	−0.693051	+	0.353127i
$696$		0			0
$697$	−2.06796	−	13.0566i	−0.0783296	−	0.494554i
$698$		0			0
$699$	8.70694	+	26.7972i	0.329327	+	1.01356i
$700$		0			0
$701$	25.0124	−	18.1726i	0.944704	−	0.686368i	−0.00484415	−	0.999988i	$-0.501542\pi$
$701$	25.0124	−	18.1726i	0.944704	−	0.686368i	0.949548	+	0.313620i	$0.101542\pi$
$702$		0			0
$703$		−	7.45284i		−	0.281089i
$704$		0			0
$705$	104.504			3.93584
$706$		0			0
$707$	−2.67964	+	16.9186i	−0.100778	+	0.636290i
$708$		0			0
$709$	−11.7043	+	22.9711i	−0.439566	+	0.862697i	0.559852	+	0.828592i	$0.310858\pi$
$709$	−11.7043	+	22.9711i	−0.439566	+	0.862697i	−0.999418	+	0.0341043i	$0.989142\pi$
$710$		0			0
$711$	−12.2470	+	16.8566i	−0.459300	+	0.632172i
$712$		0			0
$713$	67.1051	−	34.1917i	2.51310	−	1.28049i
$714$		0			0
$715$	39.5498	+	19.6144i	1.47908	+	0.733536i
$716$		0			0
$717$	−64.6352	+	32.9333i	−2.41385	+	1.22992i
$718$		0			0
$719$	0.381412	−	0.524968i	0.0142243	−	0.0195780i	−0.801846	−	0.597531i	$-0.796148\pi$
$719$	0.381412	−	0.524968i	0.0142243	−	0.0195780i	0.816070	+	0.577953i	$0.196148\pi$
$720$		0			0
$721$	−4.85293	+	9.52441i	−0.180732	+	0.354707i
$722$		0			0
$723$	−10.4424	+	65.9310i	−0.388359	+	2.45200i
$724$		0			0
$725$	8.24173			0.306090
$726$		0			0
$727$			19.4103i			0.719889i	0.932974	+	0.359945i	$0.117204\pi$
$727$			19.4103i			0.719889i	−0.932974	+	0.359945i	$0.882796\pi$
$728$		0			0
$729$	28.9692	−	21.0474i	1.07293	−	0.779532i
$730$		0			0
$731$	12.8146	+	39.4392i	0.473965	+	1.45871i
$732$		0			0
$733$	−1.77792	−	11.2254i	−0.0656691	−	0.414618i	−0.998521	−	0.0543593i	$-0.982688\pi$
$733$	−1.77792	−	11.2254i	−0.0656691	−	0.414618i	0.932852	−	0.360259i	$-0.117312\pi$
$734$		0			0
$735$	−17.3944	+	8.86289i	−0.641602	+	0.326912i
$736$		0			0
$737$	11.4188	−	39.0447i	0.420616	−	1.43823i
$738$		0			0
$739$	12.1362	+	23.8187i	0.446438	+	0.876185i	0.999085	+	0.0427691i	$0.0136180\pi$
$739$	12.1362	+	23.8187i	0.446438	+	0.876185i	−0.552647	+	0.833416i	$0.686382\pi$
$740$		0			0
$741$	57.1779	+	1.07485i	2.10048	+	0.0394856i
$742$		0			0
$743$	21.2717	−	41.7480i	0.780382	−	1.53159i	−0.0652805	−	0.997867i	$-0.520794\pi$
$743$	21.2717	−	41.7480i	0.780382	−	1.53159i	0.845662	−	0.533718i	$-0.179206\pi$
$744$		0			0
$745$	8.08157	−	5.87160i	0.296086	−	0.215119i
$746$		0			0
$747$	41.7469	+	41.7469i	1.52744	+	1.52744i
$748$		0			0
$749$	−1.46258	−	1.46258i	−0.0534416	−	0.0534416i
$750$		0			0
$751$	−19.4048	−	26.7084i	−0.708090	−	0.974602i	−0.999836	−	0.0181064i	$-0.994236\pi$
$751$	−19.4048	−	26.7084i	−0.708090	−	0.974602i	0.291746	−	0.956496i	$-0.405764\pi$
$752$		0			0
$753$	−15.1040	+	4.90757i	−0.550419	+	0.178842i
$754$		0			0
$755$	28.4539	−	39.1635i	1.03554	−	1.42530i
$756$		0			0
$757$	−6.91077	+	21.2692i	−0.251176	+	0.773041i	0.743383	+	0.668866i	$0.233220\pi$
$757$	−6.91077	+	21.2692i	−0.251176	+	0.773041i	−0.994559	+	0.104174i	$0.966780\pi$
$758$		0			0
$759$	−64.2693	−	30.3824i	−2.33283	−	1.10281i
$760$		0			0
$761$	1.84236	+	3.61583i	0.0667854	+	0.131074i	0.921986	−	0.387224i	$-0.126566\pi$
$761$	1.84236	+	3.61583i	0.0667854	+	0.131074i	−0.855200	+	0.518298i	$0.826566\pi$
$762$		0			0
$763$	−8.09180	−	5.87903i	−0.292943	−	0.212835i
$764$		0			0
$765$	−44.1309	−	22.4858i	−1.59556	−	0.812977i
$766$		0			0
$767$	−6.50484	+	18.8093i	−0.234876	+	0.679166i
$768$		0			0
$769$	−12.8990	−	12.8990i	−0.465151	−	0.465151i	0.435189	−	0.900339i	$-0.356682\pi$
$769$	−12.8990	−	12.8990i	−0.465151	−	0.465151i	−0.900339	+	0.435189i	$0.856682\pi$
$770$		0			0
$771$			35.7121i			1.28614i
$772$		0			0
$773$	−1.49219	+	9.42131i	−0.0536703	+	0.338861i	0.946212	+	0.323546i	$0.104875\pi$
$773$	−1.49219	+	9.42131i	−0.0536703	+	0.338861i	−0.999883	+	0.0153149i	$0.995125\pi$
$774$		0			0
$775$	35.2242	−	69.1313i	1.26529	−	2.48327i
$776$		0			0
$777$	−5.52943	−	4.01736i	−0.198367	−	0.144122i
$778$		0			0
$779$	−20.6113	−	6.69702i	−0.738476	−	0.239946i
$780$		0			0
$781$	24.4058	−	0.723593i	0.873308	−	0.0258922i
$782$		0			0
$783$	1.27548	+	0.414427i	0.0455818	+	0.0148104i
$784$		0			0
$785$	14.1154	−	2.23567i	0.503802	−	0.0797944i
$786$		0			0
$787$	15.9058	+	8.10440i	0.566980	+	0.288891i	0.713888	−	0.700259i	$-0.246932\pi$
$787$	15.9058	+	8.10440i	0.566980	+	0.288891i	−0.146909	+	0.989150i	$0.546932\pi$
$788$		0			0
$789$	−10.2804	−	14.1497i	−0.365991	−	0.503743i
$790$		0			0
$791$	10.5227	−	10.5227i	0.374143	−	0.374143i
$792$		0			0
$793$	−36.4127	−	6.47097i	−1.29305	−	0.229791i
$794$		0			0
$795$	3.79718	−	23.9744i	0.134672	−	0.850285i
$796$		0			0
$797$	−18.9627	+	6.16135i	−0.671692	+	0.218246i	−0.624955	−	0.780661i	$-0.714883\pi$
$797$	−18.9627	+	6.16135i	−0.671692	+	0.218246i	−0.0467378	+	0.998907i	$0.514883\pi$
$798$		0			0
$799$	6.54224	+	41.3060i	0.231448	+	1.46130i
$800$		0			0
$801$	−11.9964	+	6.11249i	−0.423873	+	0.215974i
$802$		0			0
$803$	9.25125	−	7.14972i	0.326470	−	0.252308i
$804$		0			0
$805$	−21.2236	+	65.3195i	−0.748034	+	2.30221i
$806$		0			0
$807$	10.4321	+	7.57937i	0.367228	+	0.266807i
$808$		0			0
$809$	−2.67367	+	0.868728i	−0.0940012	+	0.0305428i	−0.355640	−	0.934623i	$-0.615737\pi$
$809$	−2.67367	+	0.868728i	−0.0940012	+	0.0305428i	0.261639	+	0.965166i	$0.415737\pi$
$810$		0			0
$811$	0.716111	+	0.113421i	0.0251461	+	0.00398274i	0.168995	−	0.985617i	$-0.445948\pi$
$811$	0.716111	+	0.113421i	0.0251461	+	0.00398274i	−0.143849	+	0.989600i	$0.545948\pi$
$812$		0			0
$813$	−29.3868	+	29.3868i	−1.03064	+	1.03064i
$814$		0			0
$815$	−31.2841			−1.09584
$816$		0			0
$817$	67.1477	+	10.6352i	2.34920	+	0.372077i
$818$		0			0
$819$	17.1338	−	22.6739i	0.598704	−	0.792292i
$820$		0			0
$821$	−1.75608	−	11.0874i	−0.0612876	−	0.386954i	−0.999197	−	0.0400735i	$-0.987241\pi$
$821$	−1.75608	−	11.0874i	−0.0612876	−	0.386954i	0.937909	−	0.346881i	$-0.112759\pi$
$822$		0			0
$823$	29.9948	+	9.74589i	1.04555	+	0.339720i	0.780921	−	0.624630i	$-0.214750\pi$
$823$	29.9948	+	9.74589i	1.04555	+	0.339720i	0.264630	+	0.964350i	$0.414750\pi$
$824$		0			0
$825$	−71.9625	+	13.5952i	−2.50541	+	0.473323i
$826$		0			0
$827$	−23.5069	−	46.1348i	−0.817414	−	1.60426i	−0.796620	−	0.604481i	$-0.793381\pi$
$827$	−23.5069	−	46.1348i	−0.817414	−	1.60426i	−0.0207941	−	0.999784i	$-0.506619\pi$
$828$		0			0
$829$	26.8152	−	36.9080i	0.931332	−	1.28187i	−0.0280056	−	0.999608i	$-0.508916\pi$
$829$	26.8152	−	36.9080i	0.931332	−	1.28187i	0.959338	−	0.282261i	$-0.0910844\pi$
$830$		0			0
$831$	21.6283	+	66.5652i	0.750279	+	2.30912i
$832$		0			0
$833$	−4.59208	−	6.32045i	−0.159106	−	0.218991i
$834$		0			0
$835$		−	6.95868i		−	0.240815i
$836$		0			0
$837$	8.92743	−	8.92743i	0.308577	−	0.308577i
$838$		0			0
$839$	37.5794	+	5.95199i	1.29738	+	0.205486i	0.766657	−	0.642057i	$-0.221919\pi$
$839$	37.5794	+	5.95199i	1.29738	+	0.205486i	0.530728	+	0.847543i	$0.321919\pi$
$840$		0			0
$841$	8.67957	+	26.7130i	0.299296	+	0.921137i
$842$		0			0
$843$	−2.08005	+	0.329448i	−0.0716408	+	0.0113468i
$844$		0			0
$845$	−5.72084	−	47.6501i	−0.196803	−	1.63921i
$846$		0			0
$847$	−9.78302	+	22.3887i	−0.336148	+	0.769284i
$848$		0			0
$849$	5.77198	−	17.7643i	0.198094	−	0.609670i
$850$		0			0
$851$	9.94750	−	1.57553i	0.340996	−	0.0540084i
$852$		0			0
$853$	−16.9522	−	8.63757i	−0.580432	−	0.295745i	0.139017	−	0.990290i	$-0.455606\pi$
$853$	−16.9522	−	8.63757i	−0.580432	−	0.295745i	−0.719449	+	0.694545i	$0.755606\pi$
$854$		0			0
$855$	−65.6914	+	47.7276i	−2.24660	+	1.63225i
$856$		0			0
$857$	−4.49141			−0.153424			−0.0767118	−	0.997053i	$-0.524442\pi$
$857$	−4.49141			−0.153424			−0.0767118	+	0.997053i	$0.524442\pi$
$858$		0			0
$859$	50.4568			1.72157			0.860783	−	0.508973i	$-0.169975\pi$
$859$	50.4568			1.72157			0.860783	+	0.508973i	$0.169975\pi$
$860$		0			0
$861$	−16.0789	+	11.6820i	−0.547969	+	0.398123i
$862$		0			0
$863$	27.0614	+	13.7885i	0.921180	+	0.469364i	0.849218	−	0.528043i	$-0.177074\pi$
$863$	27.0614	+	13.7885i	0.921180	+	0.469364i	0.0719619	+	0.997407i	$0.477074\pi$
$864$		0			0
$865$	20.1868	−	3.19727i	0.686370	−	0.108710i
$866$		0			0
$867$	−2.14038	+	6.58741i	−0.0726911	+	0.223720i
$868$		0			0
$869$	−19.1349	+	3.61497i	−0.649108	+	0.122630i
$870$		0			0
$871$	−42.3090	+	12.8731i	−1.43359	+	0.436187i
$872$		0			0
$873$	−12.5728	+	1.99134i	−0.425526	+	0.0673968i
$874$		0			0
$875$	9.19492	+	28.2991i	0.310845	+	0.956683i
$876$		0			0
$877$	−6.18618	−	0.979795i	−0.208893	−	0.0330853i	0.0511111	−	0.998693i	$-0.483724\pi$
$877$	−6.18618	−	0.979795i	−0.208893	−	0.0330853i	−0.260004	+	0.965608i	$0.583724\pi$
$878$		0			0
$879$	7.28514	−	7.28514i	0.245722	−	0.245722i
$880$		0			0
$881$		−	23.5738i		−	0.794222i	−0.917771	−	0.397111i	$-0.870013\pi$
$881$		−	23.5738i		−	0.794222i	0.917771	−	0.397111i	$-0.129987\pi$
$882$		0			0
$883$	−28.8144	−	39.6597i	−0.969683	−	1.33465i	−0.942207	−	0.335031i	$-0.891253\pi$
$883$	−28.8144	−	39.6597i	−0.969683	−	1.33465i	−0.0274757	−	0.999622i	$-0.508747\pi$
$884$		0			0
$885$	−16.1146	−	49.5957i	−0.541687	−	1.66714i
$886$		0			0
$887$	−10.1718	+	14.0003i	−0.341537	+	0.470086i	−0.944890	−	0.327389i	$-0.893831\pi$
$887$	−10.1718	+	14.0003i	−0.341537	+	0.470086i	0.603352	+	0.797475i	$0.293831\pi$
$888$		0			0
$889$	8.60349	+	16.8853i	0.288552	+	0.566315i
$890$		0			0
$891$	23.2022	+	2.97299i	0.777302	+	0.0995990i
$892$		0			0
$893$	65.2062	+	21.1868i	2.18204	+	0.708989i
$894$		0			0
$895$	−3.08470	−	19.4760i	−0.103110	−	0.651012i
$896$		0			0
$897$	10.6528	+	76.5440i	0.355686	+	2.55573i
$898$		0			0
$899$	−8.48274	−	1.34353i	−0.282915	−	0.0448094i
$900$		0			0
$901$	9.71383			0.323615
$902$		0			0
$903$	44.0856	−	44.0856i	1.46708	−	1.46708i
$904$		0			0
$905$	41.3966	+	6.55658i	1.37607	+	0.217948i
$906$		0			0
$907$	−28.9441	+	9.40449i	−0.961071	+	0.312271i	−0.747206	−	0.664592i	$-0.768605\pi$
$907$	−28.9441	+	9.40449i	−0.961071	+	0.312271i	−0.213865	+	0.976863i	$0.568605\pi$
$908$		0			0
$909$	−22.1406	−	16.0861i	−0.734357	−	0.533541i
$910$		0			0
$911$	−14.8119	+	45.5865i	−0.490742	+	1.51035i	0.332748	+	0.943016i	$0.392024\pi$
$911$	−14.8119	+	45.5865i	−0.490742	+	1.51035i	−0.823489	+	0.567332i	$0.807976\pi$
$912$		0			0
$913$	1.63523	+	55.1541i	0.0541183	+	1.82533i
$914$		0			0
$915$	86.3413	−	43.9931i	2.85436	−	1.45437i
$916$		0			0
$917$	−3.14077	−	19.8301i	−0.103717	−	0.654846i
$918$		0			0
$919$	5.44057	−	1.76775i	0.179468	−	0.0583126i	−0.217905	−	0.975970i	$-0.569922\pi$
$919$	5.44057	−	1.76775i	0.179468	−	0.0583126i	0.397372	+	0.917657i	$0.369922\pi$
$920$		0			0
$921$	1.28766	−	8.12998i	0.0424299	−	0.267892i
$922$		0			0
$923$	−15.1955	−	21.7636i	−0.500167	−	0.716358i
$924$		0			0
$925$	7.33666	−	7.33666i	0.241228	−	0.241228i
$926$		0			0
$927$	−10.0384	−	13.8166i	−0.329703	−	0.453797i
$928$		0			0
$929$	21.6206	+	11.0162i	0.709348	+	0.361431i	0.771147	−	0.636658i	$-0.219684\pi$
$929$	21.6206	+	11.0162i	0.709348	+	0.361431i	−0.0617983	+	0.998089i	$0.519684\pi$
$930$		0			0
$931$	−12.6503	+	2.00360i	−0.414596	+	0.0656655i
$932$		0			0
$933$	−39.1104	−	12.7077i	−1.28042	−	0.416032i
$934$		0			0
$935$	−15.6030	−	43.5816i	−0.510271	−	1.42527i
$936$		0			0
$937$	−11.3463	−	3.68665i	−0.370669	−	0.120438i	0.117758	−	0.993042i	$-0.462429\pi$
$937$	−11.3463	−	3.68665i	−0.370669	−	0.120438i	−0.488427	+	0.872605i	$0.662429\pi$
$938$		0			0
$939$	−26.2161	−	19.0471i	−0.855531	−	0.621580i
$940$		0			0
$941$	−23.2391	+	45.6094i	−0.757575	+	1.48682i	0.112366	+	0.993667i	$0.464157\pi$
$941$	−23.2391	+	45.6094i	−0.757575	+	1.48682i	−0.869940	+	0.493157i	$0.835843\pi$
$942$		0			0
$943$	4.58146	−	28.9262i	0.149193	−	0.941967i
$944$		0			0
$945$			11.5134i			0.374531i
$946$		0			0
$947$	−2.60562	−	2.60562i	−0.0846711	−	0.0846711i	0.663503	−	0.748174i	$-0.269069\pi$
$947$	−2.60562	−	2.60562i	−0.0846711	−	0.0846711i	−0.748174	+	0.663503i	$0.769069\pi$
$948$		0			0
$949$	−12.0125	−	4.15430i	−0.389944	−	0.134854i
$950$		0			0
$951$	−10.2005	−	5.19744i	−0.330775	−	0.168538i
$952$		0			0
$953$	−19.8933	−	14.4533i	−0.644406	−	0.468188i	0.216955	−	0.976182i	$-0.430387\pi$
$953$	−19.8933	−	14.4533i	−0.644406	−	0.468188i	−0.861361	+	0.507993i	$0.830387\pi$
$954$		0			0
$955$	−39.0119	−	76.5653i	−1.26240	−	2.47759i
$956$		0			0
$957$	3.89280	+	7.11087i	0.125836	+	0.229862i
$958$		0			0
$959$	−0.190373	+	0.585909i	−0.00614747	+	0.0189200i
$960$		0			0
$961$	−29.3024	+	40.3313i	−0.945238	+	1.30101i
$962$		0			0
$963$	3.14288	−	1.02118i	0.101278	−	0.0329072i
$964$		0			0
$965$	−42.5864	−	58.6151i	−1.37090	−	1.88689i
$966$		0			0
$967$	−24.4627	−	24.4627i	−0.786668	−	0.786668i	0.194279	−	0.980946i	$-0.437763\pi$
$967$	−24.4627	−	24.4627i	−0.786668	−	0.786668i	−0.980946	+	0.194279i	$0.937763\pi$
$968$		0			0
$969$	−42.4019	−	42.4019i	−1.36214	−	1.36214i
$970$		0			0
$971$	39.5770	−	28.7543i	1.27009	−	0.922771i	0.270879	−	0.962613i	$-0.412686\pi$
$971$	39.5770	−	28.7543i	1.27009	−	0.922771i	0.999206	+	0.0398424i	$0.0126856\pi$
$972$		0			0
$973$	−5.60113	+	10.9928i	−0.179564	+	0.352414i
$974$		0			0
$975$	55.2285	+	57.3447i	1.76873	+	1.83650i
$976$		0			0
$977$	26.4035	+	51.8198i	0.844722	+	1.65786i	0.749113	+	0.662442i	$0.230480\pi$
$977$	26.4035	+	51.8198i	0.844722	+	1.65786i	0.0956094	+	0.995419i	$0.469520\pi$
$978$		0			0
$979$	−12.0776	−	3.53214i	−0.386001	−	0.112888i
$980$		0			0
$981$	14.2382	−	7.25472i	0.454591	−	0.231625i
$982$		0			0
$983$	−7.33254	−	46.2959i	−0.233872	−	1.47661i	−0.773011	−	0.634392i	$-0.781250\pi$
$983$	−7.33254	−	46.2959i	−0.233872	−	1.47661i	0.539140	−	0.842216i	$-0.318750\pi$
$984$		0			0
$985$	19.6185	+	60.3796i	0.625098	+	1.92385i
$986$		0			0
$987$	50.8676	−	36.9575i	1.61913	−	1.17637i
$988$		0			0
$989$			91.8721i			2.92136i
$990$		0			0
$991$	32.0298			1.01746			0.508730	−	0.860926i	$-0.330115\pi$
$991$	32.0298			1.01746			0.508730	+	0.860926i	$0.330115\pi$
$992$		0			0
$993$	−3.73070	+	23.5547i	−0.118390	+	0.747486i
$994$		0			0
$995$	24.4433	−	47.9727i	0.774905	−	1.52084i
$996$		0			0
$997$	−22.3500	+	30.7621i	−0.707830	+	0.974245i	0.292011	+	0.956415i	$0.405676\pi$
$997$	−22.3500	+	30.7621i	−0.707830	+	0.974245i	−0.999841	+	0.0178298i	$0.994324\pi$
$998$		0			0
$999$	1.50433	−	0.766493i	0.0475948	−	0.0242508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.2	✓	112
11.6	odd	10	inner	572.2.bh.a.369.2	yes	112
13.8	odd	4	inner	572.2.bh.a.541.2	yes	112
143.138	even	20	inner	572.2.bh.a.281.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.2	✓	112	1.1	even	1	trivial
572.2.bh.a.281.2	yes	112	143.138	even	20	inner
572.2.bh.a.369.2	yes	112	11.6	odd	10	inner
572.2.bh.a.541.2	yes	112	13.8	odd	4	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.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07031 + 1.50417i) q^{3} +(-3.28934 - 1.67600i) q^{5} +(-2.19381 + 0.347466i) q^{7} +(1.09660 - 3.37499i) q^{9} +O(q^{10})\)	\(q+(-2.07031 + 1.50417i) q^{3} +(-3.28934 - 1.67600i) q^{5} +(-2.19381 + 0.347466i) q^{7} +(1.09660 - 3.37499i) q^{9} +(2.90921 - 1.59263i) q^{11} +(-3.18124 - 1.69698i) q^{13} +(9.33093 - 1.47787i) q^{15} +(1.16829 + 3.59562i) q^{17} +(6.12176 + 0.969591i) q^{19} +(4.01922 - 4.01922i) q^{21} +8.37584i q^{23} +(5.07185 + 6.98081i) q^{25} +(0.433888 + 1.33537i) q^{27} +(0.561421 - 0.772730i) q^{29} +(-4.08218 - 8.01174i) q^{31} +(-3.62738 + 7.67317i) q^{33} +(7.79856 + 2.53391i) q^{35} +(-0.188104 - 1.18764i) q^{37} +(9.13867 - 1.27184i) q^{39} +(-3.45353 - 0.546985i) q^{41} +10.9687 q^{43} +(-9.26360 + 9.26360i) q^{45} +(10.9256 + 1.73045i) q^{47} +(-1.96530 + 0.638566i) q^{49} +(-7.82711 - 5.68673i) q^{51} +(0.793973 - 2.44360i) q^{53} +(-12.2387 + 0.362857i) q^{55} +(-14.1323 + 7.20078i) q^{57} +(-0.863506 - 5.45196i) q^{59} +(9.75527 - 3.16968i) q^{61} +(-1.23305 + 7.78515i) q^{63} +(7.62004 + 10.9137i) q^{65} +(8.67305 - 8.67305i) q^{67} +(-12.5987 - 17.3406i) q^{69} +(6.55946 + 3.34221i) q^{71} +(3.48189 - 0.551477i) q^{73} +(-21.0006 - 6.82350i) q^{75} +(-5.82889 + 4.50479i) q^{77} +(-5.58408 - 1.81438i) q^{79} +(5.70593 + 4.14560i) q^{81} +(-7.55299 + 14.8236i) q^{83} +(2.18337 - 13.7853i) q^{85} +2.44426i q^{87} +(-2.68281 - 2.68281i) q^{89} +(7.56869 + 2.61748i) q^{91} +(20.5023 + 10.4465i) q^{93} +(-18.5115 - 13.4494i) q^{95} +(-1.62852 - 3.19615i) q^{97} +(-2.18487 - 11.5651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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