LMFDB - Embedded newform 572.2.bh.a.73.3

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			73.3
Character	$\chi$	$=$	572.73
Dual form			572.2.bh.a.525.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.746064 + 2.29615i) q^{3} +(-0.201105 - 0.0318519i) q^{5} +(1.79289 - 3.51875i) q^{7} +(-2.28863 - 1.66279i) q^{9} +O(q^{10})$	\(q+(-0.746064 + 2.29615i) q^{3} +(-0.201105 - 0.0318519i) q^{5} +(1.79289 - 3.51875i) q^{7} +(-2.28863 - 1.66279i) q^{9} +(2.51184 - 2.16579i) q^{11} +(1.36611 - 3.33673i) q^{13} +(0.223174 - 0.438003i) q^{15} +(5.78411 - 4.20240i) q^{17} +(2.28295 + 4.48054i) q^{19} +(6.74196 + 6.74196i) q^{21} +4.39001i q^{23} +(-4.71585 - 1.53227i) q^{25} +(-0.334188 + 0.242802i) q^{27} +(-7.47668 + 2.42932i) q^{29} +(-0.384571 - 2.42809i) q^{31} +(3.09899 + 7.38337i) q^{33} +(-0.472639 + 0.650532i) q^{35} +(0.881606 + 0.449201i) q^{37} +(6.64241 + 5.62620i) q^{39} +(1.16893 + 2.29416i) q^{41} +12.1704 q^{43} +(0.407293 + 0.407293i) q^{45} +(-3.00675 - 5.90108i) q^{47} +(-5.05265 - 6.95438i) q^{49} +(5.33402 + 16.4164i) q^{51} +(4.17746 + 3.03510i) q^{53} +(-0.574128 + 0.355545i) q^{55} +(-11.9912 + 1.89922i) q^{57} +(10.2070 + 5.20074i) q^{59} +(-7.41933 - 10.2118i) q^{61} +(-9.95421 + 5.07193i) q^{63} +(-0.381013 + 0.627520i) q^{65} +(-1.19557 - 1.19557i) q^{67} +(-10.0801 - 3.27522i) q^{69} +(10.4109 + 1.64893i) q^{71} +(1.68813 - 3.31315i) q^{73} +(7.03665 - 9.68512i) q^{75} +(-3.11743 - 12.7216i) q^{77} +(6.95840 - 9.57742i) q^{79} +(-2.93072 - 9.01983i) q^{81} +(-2.63269 + 16.6222i) q^{83} +(-1.29707 + 0.660890i) q^{85} -18.9800i q^{87} +(-7.58555 + 7.58555i) q^{89} +(-9.29183 - 10.7894i) q^{91} +(5.86216 + 0.928475i) q^{93} +(-0.316399 - 0.973775i) q^{95} +(0.438596 + 2.76919i) q^{97} +(-9.34993 + 0.780049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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
$3$	−0.746064	+	2.29615i	−0.430740	+	1.32568i	0.466650	+	0.884442i	$0.345461\pi$
$3$	−0.746064	+	2.29615i	−0.430740	+	1.32568i	−0.897390	+	0.441239i	$0.854539\pi$
$4$		0			0
$5$	−0.201105	−	0.0318519i	−0.0899369	−	0.0142446i	0.111304	−	0.993786i	$-0.464497\pi$
$5$	−0.201105	−	0.0318519i	−0.0899369	−	0.0142446i	−0.201241	+	0.979542i	$0.564497\pi$
$6$		0			0
$7$	1.79289	−	3.51875i	0.677650	−	1.32996i	−0.254211	−	0.967149i	$-0.581816\pi$
$7$	1.79289	−	3.51875i	0.677650	−	1.32996i	0.931861	−	0.362815i	$-0.118184\pi$
$8$		0			0
$9$	−2.28863	−	1.66279i	−0.762877	−	0.554263i
$10$		0			0
$11$	2.51184	−	2.16579i	0.757348	−	0.653012i
$11$	2.51184	−	2.16579i	0.757348	−	0.653012i
$12$		0			0
$13$	1.36611	−	3.33673i	0.378890	−	0.925442i
$13$	1.36611	−	3.33673i	0.378890	−	0.925442i
$14$		0			0
$15$	0.223174	−	0.438003i	0.0576233	−	0.113092i
$16$		0			0
$17$	5.78411	−	4.20240i	1.40285	−	1.01923i	0.408540	−	0.912741i	$-0.366038\pi$
$17$	5.78411	−	4.20240i	1.40285	−	1.01923i	0.994314	−	0.106492i	$-0.0339619\pi$
$18$		0			0
$19$	2.28295	+	4.48054i	0.523744	+	1.02791i	0.989708	+	0.143102i	$0.0457076\pi$
$19$	2.28295	+	4.48054i	0.523744	+	1.02791i	−0.465964	+	0.884804i	$0.654292\pi$
$20$		0			0
$21$	6.74196	+	6.74196i	1.47122	+	1.47122i
$22$		0			0
$23$			4.39001i			0.915380i	0.889112	+	0.457690i	$0.151323\pi$
$23$			4.39001i			0.915380i	−0.889112	+	0.457690i	$0.848677\pi$
$24$		0			0
$25$	−4.71585	−	1.53227i	−0.943171	−	0.306455i
$26$		0			0
$27$	−0.334188	+	0.242802i	−0.0643144	+	0.0467272i
$28$		0			0
$29$	−7.47668	+	2.42932i	−1.38839	+	0.451114i	−0.905417	−	0.424524i	$-0.860441\pi$
$29$	−7.47668	+	2.42932i	−1.38839	+	0.451114i	−0.482968	+	0.875638i	$0.660441\pi$
$30$		0			0
$31$	−0.384571	−	2.42809i	−0.0690710	−	0.436097i	−0.997854	−	0.0654740i	$-0.979144\pi$
$31$	−0.384571	−	2.42809i	−0.0690710	−	0.436097i	0.928783	−	0.370623i	$-0.120856\pi$
$32$		0			0
$33$	3.09899	+	7.38337i	0.539465	+	1.28528i
$34$		0			0
$35$	−0.472639	+	0.650532i	−0.0798906	+	0.109960i
$36$		0			0
$37$	0.881606	+	0.449201i	0.144935	+	0.0738482i	0.524954	−	0.851131i	$-0.324083\pi$
$37$	0.881606	+	0.449201i	0.144935	+	0.0738482i	−0.380019	+	0.924979i	$0.624083\pi$
$38$		0			0
$39$	6.64241	+	5.62620i	1.06364	+	0.900913i
$40$		0			0
$41$	1.16893	+	2.29416i	0.182557	+	0.358288i	0.964090	−	0.265576i	$-0.0855621\pi$
$41$	1.16893	+	2.29416i	0.182557	+	0.358288i	−0.781533	+	0.623864i	$0.785562\pi$
$42$		0			0
$43$	12.1704			1.85597			0.927983	−	0.372623i	$-0.121542\pi$
$43$	12.1704			1.85597			0.927983	+	0.372623i	$0.121542\pi$
$44$		0			0
$45$	0.407293	+	0.407293i	0.0607156	+	0.0607156i
$46$		0			0
$47$	−3.00675	−	5.90108i	−0.438580	−	0.860762i	−0.999460	−	0.0328644i	$-0.989537\pi$
$47$	−3.00675	−	5.90108i	−0.438580	−	0.860762i	0.560880	−	0.827897i	$-0.310463\pi$
$48$		0			0
$49$	−5.05265	−	6.95438i	−0.721808	−	0.993483i
$50$		0			0
$51$	5.33402	+	16.4164i	0.746913	+	2.29876i
$52$		0			0
$53$	4.17746	+	3.03510i	0.573818	+	0.416903i	0.836490	−	0.547982i	$-0.184604\pi$
$53$	4.17746	+	3.03510i	0.573818	+	0.416903i	−0.262672	+	0.964885i	$0.584604\pi$
$54$		0			0
$55$	−0.574128	+	0.355545i	−0.0774155	+	0.0479417i
$56$		0			0
$57$	−11.9912	+	1.89922i	−1.58827	+	0.251558i
$58$		0			0
$59$	10.2070	+	5.20074i	1.32884	+	0.677079i	0.966908	−	0.255124i	$-0.0821164\pi$
$59$	10.2070	+	5.20074i	1.32884	+	0.677079i	0.361934	+	0.932204i	$0.382116\pi$
$60$		0			0
$61$	−7.41933	−	10.2118i	−0.949948	−	1.30749i	−0.951551	−	0.307492i	$-0.900510\pi$
$61$	−7.41933	−	10.2118i	−0.949948	−	1.30749i	0.00160287	−	0.999999i	$-0.499490\pi$
$62$		0			0
$63$	−9.95421	+	5.07193i	−1.25411	+	0.639003i
$64$		0			0
$65$	−0.381013	+	0.627520i	−0.0472588	+	0.0778342i
$66$		0			0
$67$	−1.19557	−	1.19557i	−0.146062	−	0.146062i	0.630294	−	0.776356i	$-0.282934\pi$
$67$	−1.19557	−	1.19557i	−0.146062	−	0.146062i	−0.776356	+	0.630294i	$0.782934\pi$
$68$		0			0
$69$	−10.0801	−	3.27522i	−1.21350	−	0.394291i
$70$		0			0
$71$	10.4109	+	1.64893i	1.23555	+	0.195692i	0.739832	−	0.672792i	$-0.234905\pi$
$71$	10.4109	+	1.64893i	1.23555	+	0.195692i	0.495718	+	0.868484i	$0.334905\pi$
$72$		0			0
$73$	1.68813	−	3.31315i	0.197581	−	0.387774i	−0.770865	−	0.636999i	$-0.780176\pi$
$73$	1.68813	−	3.31315i	0.197581	−	0.387774i	0.968446	+	0.249224i	$0.0801757\pi$
$74$		0			0
$75$	7.03665	−	9.68512i	0.812523	−	1.11834i
$76$		0			0
$77$	−3.11743	−	12.7216i	−0.355264	−	1.44976i
$78$		0			0
$79$	6.95840	−	9.57742i	0.782882	−	1.07754i	−0.212076	−	0.977253i	$-0.568023\pi$
$79$	6.95840	−	9.57742i	0.782882	−	1.07754i	0.994958	−	0.100291i	$-0.0319774\pi$
$80$		0			0
$81$	−2.93072	−	9.01983i	−0.325636	−	1.00220i
$82$		0			0
$83$	−2.63269	+	16.6222i	−0.288976	+	1.82452i	0.234076	+	0.972218i	$0.424794\pi$
$83$	−2.63269	+	16.6222i	−0.288976	+	1.82452i	−0.523051	+	0.852301i	$0.675206\pi$
$84$		0			0
$85$	−1.29707	+	0.660890i	−0.140687	+	0.0716836i
$86$		0			0
$87$		−	18.9800i		−	2.03487i
$88$		0			0
$89$	−7.58555	+	7.58555i	−0.804067	+	0.804067i	−0.983728	−	0.179662i	$-0.942500\pi$
$89$	−7.58555	+	7.58555i	−0.804067	+	0.804067i	0.179662	+	0.983728i	$0.442500\pi$
$90$		0			0
$91$	−9.29183	−	10.7894i	−0.974048	−	1.13104i
$92$		0			0
$93$	5.86216	+	0.928475i	0.607878	+	0.0962784i
$94$		0			0
$95$	−0.316399	−	0.973775i	−0.0324618	−	0.0999072i
$96$		0			0
$97$	0.438596	+	2.76919i	0.0445327	+	0.281168i	0.999898	−	0.0142575i	$-0.00453845\pi$
$97$	0.438596	+	2.76919i	0.0445327	+	0.281168i	−0.955366	+	0.295426i	$0.904538\pi$
$98$		0			0
$99$	−9.34993	+	0.780049i	−0.939703	+	0.0783978i
$100$		0			0
$101$	−6.33822	−	4.60499i	−0.630677	−	0.458213i	0.225958	−	0.974137i	$-0.427449\pi$
$101$	−6.33822	−	4.60499i	−0.630677	−	0.458213i	−0.856635	+	0.515924i	$0.827449\pi$
$102$		0			0
$103$	−16.1537	+	5.24864i	−1.59167	+	0.517164i	−0.965028	−	0.262146i	$-0.915570\pi$
$103$	−16.1537	+	5.24864i	−1.59167	+	0.517164i	−0.626639	+	0.779310i	$0.715570\pi$
$104$		0			0
$105$	−1.14110	−	1.57059i	−0.111360	−	0.153274i
$106$		0			0
$107$	11.8927	+	3.86418i	1.14971	+	0.373565i	0.821036	−	0.570877i	$-0.193397\pi$
$107$	11.8927	+	3.86418i	1.14971	+	0.373565i	0.328679	+	0.944442i	$0.393397\pi$
$108$		0			0
$109$	−1.92723	+	1.92723i	−0.184595	+	0.184595i	−0.793355	−	0.608760i	$-0.791667\pi$
$109$	−1.92723	+	1.92723i	−0.184595	+	0.184595i	0.608760	+	0.793355i	$0.291667\pi$
$110$		0			0
$111$	−1.68917	+	1.68917i	−0.160329	+	0.160329i
$112$		0			0
$113$	−0.974356	+	2.99876i	−0.0916597	+	0.282100i	−0.986369	−	0.164550i	$-0.947383\pi$
$113$	−0.974356	+	2.99876i	−0.0916597	+	0.282100i	0.894709	+	0.446649i	$0.147383\pi$
$114$		0			0
$115$	0.139830	−	0.882853i	0.0130392	−	0.0823265i
$116$		0			0
$117$	−8.67479	+	5.36499i	−0.801985	+	0.495993i
$118$		0			0
$119$	−4.41692	−	27.8873i	−0.404898	−	2.55643i
$120$		0			0
$121$	1.61867	−	10.8803i	0.147152	−	0.989114i
$122$		0			0
$123$	−6.13983	+	0.972454i	−0.553610	+	0.0876832i
$124$		0			0
$125$	1.80667	+	0.920547i	0.161594	+	0.0823362i
$126$		0			0
$127$	−7.00849	+	5.09197i	−0.621903	+	0.451839i	−0.853586	−	0.520952i	$-0.825577\pi$
$127$	−7.00849	+	5.09197i	−0.621903	+	0.451839i	0.231683	+	0.972791i	$0.425577\pi$
$128$		0			0
$129$	−9.07988	+	27.9450i	−0.799439	+	2.46042i
$130$		0			0
$131$		−	1.25641i		−	0.109773i	−0.998493	−	0.0548864i	$-0.982520\pi$
$131$		−	1.25641i		−	0.109773i	0.998493	−	0.0548864i	$-0.0174797\pi$
$132$		0			0
$133$	19.8590			1.72199
$134$		0			0
$135$	0.0749405	−	0.0381841i	0.00644985	−	0.00328637i
$136$		0			0
$137$	−0.537031	+	3.39068i	−0.0458816	+	0.289685i	−0.999951	−	0.00990060i	$-0.996848\pi$
$137$	−0.537031	+	3.39068i	−0.0458816	+	0.289685i	0.954069	+	0.299586i	$0.0968485\pi$
$138$		0			0
$139$	−0.402627	+	0.130821i	−0.0341504	+	0.0110961i	−0.326042	−	0.945355i	$-0.605715\pi$
$139$	−0.402627	+	0.130821i	−0.0341504	+	0.0110961i	0.291892	+	0.956451i	$0.405715\pi$
$140$		0			0
$141$	15.7930	−	2.50136i	1.33001	−	0.210653i
$142$		0			0
$143$	−3.79522	−	11.3400i	−0.317372	−	0.948301i
$144$		0			0
$145$	1.58098	−	0.250402i	0.131293	−	0.0207948i
$146$		0			0
$147$	19.7379	−	6.41323i	1.62795	−	0.528954i
$148$		0			0
$149$	1.92932	−	12.1813i	0.158056	−	0.997929i	−0.773358	−	0.633969i	$-0.781425\pi$
$149$	1.92932	−	12.1813i	0.158056	−	0.997929i	0.931415	−	0.363960i	$-0.118575\pi$
$150$		0			0
$151$	−15.4034	+	7.84843i	−1.25351	+	0.638696i	−0.949439	−	0.313952i	$-0.898347\pi$
$151$	−15.4034	+	7.84843i	−1.25351	+	0.638696i	−0.304073	+	0.952649i	$0.598347\pi$
$152$		0			0
$153$	−20.2254			−1.63513
$154$		0			0
$155$			0.500550i			0.0402052i
$156$		0			0
$157$	−5.98893	+	18.4320i	−0.477968	+	1.47104i	0.363944	+	0.931421i	$0.381430\pi$
$157$	−5.98893	+	18.4320i	−0.477968	+	1.47104i	−0.841912	+	0.539614i	$0.818570\pi$
$158$		0			0
$159$	−10.0857	+	7.32769i	−0.799848	+	0.581123i
$160$		0			0
$161$	15.4473	+	7.87082i	1.21742	+	0.620307i
$162$		0			0
$163$	−3.71090	+	0.587749i	−0.290660	+	0.0460361i	−0.300062	−	0.953920i	$-0.597007\pi$
$163$	−3.71090	+	0.587749i	−0.290660	+	0.0460361i	0.00940155	+	0.999956i	$0.497007\pi$
$164$		0			0
$165$	−0.388048	−	1.58354i	−0.0302095	−	0.123279i
$166$		0			0
$167$	0.971946	+	6.13663i	0.0752115	+	0.474866i	0.996331	+	0.0855861i	$0.0272763\pi$
$167$	0.971946	+	6.13663i	0.0752115	+	0.474866i	−0.921119	+	0.389280i	$0.872724\pi$
$168$		0			0
$169$	−9.26749	−	9.11666i	−0.712884	−	0.701282i
$170$		0			0
$171$	2.22536	−	14.0504i	0.170177	−	1.07446i
$172$		0			0
$173$	−4.10091	+	12.6213i	−0.311787	+	0.959580i	0.665270	+	0.746602i	$0.268316\pi$
$173$	−4.10091	+	12.6213i	−0.311787	+	0.959580i	−0.977057	+	0.212978i	$0.931684\pi$
$174$		0			0
$175$	−13.8467	+	13.8467i	−1.04671	+	1.04671i
$176$		0			0
$177$	−19.5568	+	19.5568i	−1.46998	+	1.46998i
$178$		0			0
$179$	3.69951	+	1.20204i	0.276515	+	0.0898450i	0.443992	−	0.896031i	$-0.353562\pi$
$179$	3.69951	+	1.20204i	0.276515	+	0.0898450i	−0.167477	+	0.985876i	$0.553562\pi$
$180$		0			0
$181$	0.398778	+	0.548871i	0.0296409	+	0.0407972i	0.823580	−	0.567200i	$-0.191973\pi$
$181$	0.398778	+	0.548871i	0.0296409	+	0.0407972i	−0.793939	+	0.607997i	$0.791973\pi$
$182$		0			0
$183$	28.9832	−	9.41720i	2.14250	−	0.696139i
$184$		0			0
$185$	−0.162988	−	0.118417i	−0.0119831	−	0.00870622i
$186$		0			0
$187$	5.42722	−	23.0830i	0.396878	−	1.68799i
$188$		0			0
$189$	0.255195	+	1.61124i	0.0185627	+	0.117201i
$190$		0			0
$191$	−2.13880	−	6.58254i	−0.154758	−	0.476296i	0.843378	−	0.537320i	$-0.180563\pi$
$191$	−2.13880	−	6.58254i	−0.154758	−	0.476296i	−0.998136	+	0.0610244i	$0.980563\pi$
$192$		0			0
$193$	−18.6132	−	2.94804i	−1.33981	−	0.212204i	−0.554950	−	0.831883i	$-0.687263\pi$
$193$	−18.6132	−	2.94804i	−1.33981	−	0.212204i	−0.784855	+	0.619679i	$0.787263\pi$
$194$		0			0
$195$	−1.15662	−	1.34303i	−0.0828271	−	0.0961764i
$196$		0			0
$197$	9.58017	−	9.58017i	0.682559	−	0.682559i	−0.278017	−	0.960576i	$-0.589677\pi$
$197$	9.58017	−	9.58017i	0.682559	−	0.682559i	0.960576	+	0.278017i	$0.0896772\pi$
$198$		0			0
$199$		−	11.6112i		−	0.823098i	−0.911388	−	0.411549i	$-0.864988\pi$
$199$		−	11.6112i		−	0.823098i	0.911388	−	0.411549i	$-0.135012\pi$
$200$		0			0
$201$	3.63718	−	1.85324i	0.256547	−	0.130717i
$202$		0			0
$203$	−4.85672	+	30.6641i	−0.340875	+	2.15220i
$204$		0			0
$205$	−0.162005	−	0.498600i	−0.0113149	−	0.0348238i
$206$		0			0
$207$	7.29965	−	10.0471i	0.507361	−	0.698322i
$208$		0			0
$209$	15.4383	+	6.30999i	1.06789	+	0.436471i
$210$		0			0
$211$	−2.18442	+	3.00659i	−0.150381	+	0.206982i	−0.877561	−	0.479465i	$-0.840831\pi$
$211$	−2.18442	+	3.00659i	−0.150381	+	0.206982i	0.727180	+	0.686447i	$0.240831\pi$
$212$		0			0
$213$	−11.5534	+	22.6748i	−0.791626	+	1.55365i
$214$		0			0
$215$	−2.44753	−	0.387650i	−0.166920	−	0.0264375i
$216$		0			0
$217$	−9.23333	−	3.00009i	−0.626800	−	0.203660i
$218$		0			0
$219$	6.34802	+	6.34802i	0.428959	+	0.428959i
$220$		0			0
$221$	−6.12055	−	25.0409i	−0.411713	−	1.68444i
$222$		0			0
$223$	−21.5412	+	10.9758i	−1.44250	+	0.734992i	−0.987811	−	0.155656i	$-0.950251\pi$
$223$	−21.5412	+	10.9758i	−1.44250	+	0.734992i	−0.454692	+	0.890649i	$0.650251\pi$
$224$		0			0
$225$	8.24501	+	11.3483i	0.549667	+	0.756552i
$226$		0			0
$227$	−5.37511	−	2.73875i	−0.356758	−	0.181777i	0.266420	−	0.963857i	$-0.414159\pi$
$227$	−5.37511	−	2.73875i	−0.356758	−	0.181777i	−0.623179	+	0.782079i	$0.714159\pi$
$228$		0			0
$229$	24.4549	−	3.87328i	1.61603	−	0.255954i	0.718049	−	0.695993i	$-0.245036\pi$
$229$	24.4549	−	3.87328i	1.61603	−	0.255954i	0.897978	+	0.440039i	$0.145036\pi$
$230$		0			0
$231$	31.5364	+	2.33302i	2.07494	+	0.153502i
$232$		0			0
$233$	−3.07212	−	2.23203i	−0.201262	−	0.146225i	0.482590	−	0.875847i	$-0.339696\pi$
$233$	−3.07212	−	2.23203i	−0.201262	−	0.146225i	−0.683851	+	0.729621i	$0.739696\pi$
$234$		0			0
$235$	0.416712	+	1.28251i	0.0271833	+	0.0836617i
$236$		0			0
$237$	16.7998	+	23.1229i	1.09126	+	1.50199i
$238$		0			0
$239$	1.89491	+	3.71896i	0.122571	+	0.240560i	0.944136	−	0.329555i	$-0.106899\pi$
$239$	1.89491	+	3.71896i	0.122571	+	0.240560i	−0.821565	+	0.570115i	$0.806899\pi$
$240$		0			0
$241$	5.88078	+	5.88078i	0.378814	+	0.378814i	0.870674	−	0.491860i	$-0.163683\pi$
$241$	5.88078	+	5.88078i	0.378814	+	0.378814i	−0.491860	+	0.870674i	$0.663683\pi$
$242$		0			0
$243$	21.6581			1.38937
$244$		0			0
$245$	0.794604	+	1.55950i	0.0507654	+	0.0996327i
$246$		0			0
$247$	18.0691	−	1.49667i	1.14971	−	0.0952309i
$248$		0			0
$249$	−36.2028	−	18.4462i	−2.29426	−	1.16898i
$250$		0			0
$251$	−11.9203	+	16.4069i	−0.752403	+	1.03559i	0.245405	+	0.969421i	$0.421079\pi$
$251$	−11.9203	+	16.4069i	−0.752403	+	1.03559i	−0.997808	+	0.0661732i	$0.978921\pi$
$252$		0			0
$253$	9.50785	+	11.0270i	0.597754	+	0.693261i
$254$		0			0
$255$	−0.549804	−	3.47133i	−0.0344301	−	0.217383i
$256$		0			0
$257$	19.6259	−	6.37683i	1.22423	−	0.397776i	0.375607	−	0.926779i	$-0.377434\pi$
$257$	19.6259	−	6.37683i	1.22423	−	0.397776i	0.848620	+	0.529003i	$0.177434\pi$
$258$		0			0
$259$	3.16125	−	2.29678i	0.196431	−	0.142715i
$260$		0			0
$261$	21.1508	+	6.87232i	1.30920	+	0.425386i
$262$		0			0
$263$			7.54626i			0.465323i	0.972558	+	0.232661i	$0.0747434\pi$
$263$			7.54626i			0.465323i	−0.972558	+	0.232661i	$0.925257\pi$
$264$		0			0
$265$	−0.743435	−	0.743435i	−0.0456688	−	0.0456688i
$266$		0			0
$267$	−11.7582	−	23.0768i	−0.719593	−	1.41228i
$268$		0			0
$269$	−1.12422	+	0.816797i	−0.0685452	+	0.0498010i	−0.621530	−	0.783390i	$-0.713489\pi$
$269$	−1.12422	+	0.816797i	−0.0685452	+	0.0498010i	0.552985	+	0.833191i	$0.313489\pi$
$270$		0			0
$271$	10.2277	−	20.0731i	0.621291	−	1.21935i	−0.339114	−	0.940745i	$-0.610127\pi$
$271$	10.2277	−	20.0731i	0.621291	−	1.21935i	0.960405	−	0.278607i	$-0.0898728\pi$
$272$		0			0
$273$	31.7063	−	13.2858i	1.91895	−	0.804095i
$274$		0			0
$275$	−15.1641	+	6.36474i	−0.914427	+	0.383808i
$276$		0			0
$277$	−11.1150	−	8.07552i	−0.667836	−	0.485211i	0.201464	−	0.979496i	$-0.435430\pi$
$277$	−11.1150	−	8.07552i	−0.667836	−	0.485211i	−0.869300	+	0.494285i	$0.835430\pi$
$278$		0			0
$279$	−3.15725	+	6.19646i	−0.189020	+	0.370972i
$280$		0			0
$281$	−12.0425	−	1.90735i	−0.718397	−	0.113783i	−0.213476	−	0.976948i	$-0.568478\pi$
$281$	−12.0425	−	1.90735i	−0.718397	−	0.113783i	−0.504921	+	0.863166i	$0.668478\pi$
$282$		0			0
$283$	−5.09136	+	15.6696i	−0.302650	+	0.931461i	0.677894	+	0.735160i	$0.262893\pi$
$283$	−5.09136	+	15.6696i	−0.302650	+	0.931461i	−0.980544	+	0.196301i	$0.937107\pi$
$284$		0			0
$285$	2.47198			0.146428
$286$		0			0
$287$	10.1684			0.600219
$288$		0			0
$289$	10.5425	−	32.4464i	0.620145	−	1.90861i
$290$		0			0
$291$	−6.68569	−	1.05891i	−0.391922	−	0.0620743i
$292$		0			0
$293$	−7.57697	+	14.8706i	−0.442651	+	0.868752i	0.556627	+	0.830763i	$0.312095\pi$
$293$	−7.57697	+	14.8706i	−0.442651	+	0.868752i	−0.999278	+	0.0379896i	$0.987905\pi$
$294$		0			0
$295$	−1.88703	−	1.37101i	−0.109867	−	0.0798233i
$296$		0			0
$297$	−0.313567	+	1.33366i	−0.0181950	+	0.0773868i
$298$		0			0
$299$	14.6483	+	5.99723i	0.847130	+	0.346829i
$300$		0			0
$301$	21.8202	−	42.8245i	1.25770	−	2.46837i
$302$		0			0
$303$	15.3024	−	11.1179i	0.879103	−	0.638705i
$304$		0			0
$305$	1.16680	+	2.28997i	0.0668107	+	0.131123i
$306$		0			0
$307$	−13.9811	−	13.9811i	−0.797944	−	0.797944i	0.184827	−	0.982771i	$-0.440828\pi$
$307$	−13.9811	−	13.9811i	−0.797944	−	0.797944i	−0.982771	+	0.184827i	$0.940828\pi$
$308$		0			0
$309$		−	41.0070i		−	2.33281i
$310$		0			0
$311$	−5.28089	−	1.71586i	−0.299452	−	0.0972977i	0.155438	−	0.987846i	$-0.450321\pi$
$311$	−5.28089	−	1.71586i	−0.299452	−	0.0972977i	−0.454889	+	0.890548i	$0.650321\pi$
$312$		0			0
$313$	5.29307	−	3.84564i	0.299182	−	0.217368i	−0.428059	−	0.903751i	$-0.640802\pi$
$313$	5.29307	−	3.84564i	0.299182	−	0.217368i	0.727241	+	0.686382i	$0.240802\pi$
$314$		0			0
$315$	2.16339	−	0.702929i	0.121893	−	0.0396056i
$316$		0			0
$317$	0.0940335	+	0.593704i	0.00528145	+	0.0333457i	0.990188	−	0.139739i	$-0.0446265\pi$
$317$	0.0940335	+	0.593704i	0.00528145	+	0.0333457i	−0.984907	+	0.173085i	$0.944626\pi$
$318$		0			0
$319$	−13.5188	+	22.2950i	−0.756908	+	1.24828i
$320$		0			0
$321$	−17.7455	+	24.4245i	−0.990456	+	1.36325i
$322$		0			0
$323$	32.0338	+	16.3221i	1.78241	+	0.908184i
$324$		0			0
$325$	−11.5551	+	13.6423i	−0.640964	+	0.756737i
$326$		0			0
$327$	−2.98737	−	5.86304i	−0.165202	−	0.324227i
$328$		0			0
$329$	−26.1552			−1.44199
$330$		0			0
$331$	−10.4644	−	10.4644i	−0.575176	−	0.575176i	0.358395	−	0.933570i	$-0.383324\pi$
$331$	−10.4644	−	10.4644i	−0.575176	−	0.575176i	−0.933570	+	0.358395i	$0.883324\pi$
$332$		0			0
$333$	−1.27075	−	2.49398i	−0.0696365	−	0.136669i
$334$		0			0
$335$	0.202354	+	0.278517i	0.0110558	+	0.0152170i
$336$		0			0
$337$	4.71659	+	14.5162i	0.256929	+	0.790747i	0.993443	+	0.114325i	$0.0364705\pi$
$337$	4.71659	+	14.5162i	0.256929	+	0.790747i	−0.736514	+	0.676422i	$0.763530\pi$
$338$		0			0
$339$	−6.15866	−	4.47453i	−0.334493	−	0.243023i
$340$		0			0
$341$	−6.22472	−	5.26606i	−0.337087	−	0.285173i
$342$		0			0
$343$	−6.22564	+	0.986045i	−0.336153	+	0.0532414i
$344$		0			0
$345$	1.92284	+	0.979735i	0.103522	+	0.0527472i
$346$		0			0
$347$	4.99689	+	6.87763i	0.268247	+	0.369210i	0.921797	−	0.387673i	$-0.126721\pi$
$347$	4.99689	+	6.87763i	0.268247	+	0.369210i	−0.653550	+	0.756883i	$0.726721\pi$
$348$		0			0
$349$	−7.16254	+	3.64950i	−0.383402	+	0.195353i	−0.635059	−	0.772463i	$-0.719024\pi$
$349$	−7.16254	+	3.64950i	−0.383402	+	0.195353i	0.251657	+	0.967816i	$0.419024\pi$
$350$		0			0
$351$	0.353626	+	1.44679i	0.0188751	+	0.0772237i
$352$		0			0
$353$	3.41433	+	3.41433i	0.181727	+	0.181727i	0.792108	−	0.610381i	$-0.208984\pi$
$353$	3.41433	+	3.41433i	0.181727	+	0.181727i	−0.610381	+	0.792108i	$0.708984\pi$
$354$		0			0
$355$	−2.04117	−	0.663216i	−0.108334	−	0.0351999i
$356$		0			0
$357$	67.3287	+	10.6638i	3.56341	+	0.564389i
$358$		0			0
$359$	4.34721	−	8.53187i	0.229437	−	0.450295i	−0.747373	−	0.664405i	$-0.768685\pi$
$359$	4.34721	−	8.53187i	0.229437	−	0.450295i	0.976810	+	0.214110i	$0.0686851\pi$
$360$		0			0
$361$	−3.69544	+	5.08633i	−0.194497	+	0.267702i
$362$		0			0
$363$	23.7750	+	11.8341i	1.24787	+	0.621128i
$364$		0			0
$365$	−0.445022	+	0.612520i	−0.0232935	+	0.0320608i
$366$		0			0
$367$	7.05642	+	21.7174i	0.368342	+	1.13364i	0.947862	+	0.318682i	$0.103240\pi$
$367$	7.05642	+	21.7174i	0.368342	+	1.13364i	−0.579519	+	0.814959i	$0.696760\pi$
$368$		0			0
$369$	1.13945	−	7.19418i	0.0593172	−	0.374514i
$370$		0			0
$371$	18.1695	−	9.25783i	0.943314	−	0.480643i
$372$		0			0
$373$		−	20.3014i		−	1.05117i	−0.850741	−	0.525585i	$-0.823847\pi$
$373$		−	20.3014i		−	1.05117i	0.850741	−	0.525585i	$-0.176153\pi$
$374$		0			0
$375$	−3.46160	+	3.46160i	−0.178756	+	0.178756i
$376$		0			0
$377$	−2.10798	+	28.2664i	−0.108566	+	1.45579i
$378$		0			0
$379$	−9.05558	−	1.43426i	−0.465154	−	0.0736731i	−0.0805414	−	0.996751i	$-0.525665\pi$
$379$	−9.05558	−	1.43426i	−0.465154	−	0.0736731i	−0.384612	+	0.923078i	$0.625665\pi$
$380$		0			0
$381$	−6.46313	−	19.8915i	−0.331116	−	1.01907i
$382$		0			0
$383$	5.02207	+	31.7081i	0.256616	+	1.62021i	0.693339	+	0.720612i	$0.256139\pi$
$383$	5.02207	+	31.7081i	0.256616	+	1.62021i	−0.436723	+	0.899596i	$0.643861\pi$
$384$		0			0
$385$	0.221725	+	2.65767i	0.0113001	+	0.135447i
$386$		0			0
$387$	−27.8535	−	20.2368i	−1.41587	−	1.02869i
$388$		0			0
$389$	13.7440	−	4.46570i	0.696849	−	0.226420i	0.0608918	−	0.998144i	$-0.480606\pi$
$389$	13.7440	−	4.46570i	0.696849	−	0.226420i	0.635957	+	0.771724i	$0.280606\pi$
$390$		0			0
$391$	18.4486	+	25.3923i	0.932985	+	1.28414i
$392$		0			0
$393$	2.88490	+	0.937359i	0.145524	+	0.0472835i
$394$		0			0
$395$	−1.70443	+	1.70443i	−0.0857592	+	0.0857592i
$396$		0			0
$397$	2.75083	−	2.75083i	0.138060	−	0.138060i	−0.634699	−	0.772759i	$-0.718876\pi$
$397$	2.75083	−	2.75083i	0.138060	−	0.138060i	0.772759	+	0.634699i	$0.218876\pi$
$398$		0			0
$399$	−14.8161	+	45.5991i	−0.741731	+	2.28281i
$400$		0			0
$401$	−2.93911	+	18.5568i	−0.146772	+	0.926684i	0.798877	+	0.601495i	$0.205428\pi$
$401$	−2.93911	+	18.5568i	−0.146772	+	0.926684i	−0.945649	+	0.325189i	$0.894572\pi$
$402$		0			0
$403$	−8.62723	−	2.03382i	−0.429753	−	0.101312i
$404$		0			0
$405$	0.302084	+	1.90728i	0.0150107	+	0.0947737i
$406$		0			0
$407$	3.18733	−	0.781058i	0.157990	−	0.0387156i
$408$		0			0
$409$	10.7614	−	1.70443i	0.532115	−	0.0842788i	0.115406	−	0.993318i	$-0.463183\pi$
$409$	10.7614	−	1.70443i	0.532115	−	0.0842788i	0.416710	+	0.909040i	$0.363183\pi$
$410$		0			0
$411$	−7.38484	−	3.76276i	−0.364267	−	0.185603i
$412$		0			0
$413$	36.6003	−	26.5916i	1.80098	−	1.30849i
$414$		0			0
$415$	1.05890	−	3.25895i	0.0519792	−	0.159975i
$416$		0			0
$417$		−	1.02209i		−	0.0500521i
$418$		0			0
$419$	−30.2247			−1.47657			−0.738286	−	0.674488i	$-0.764365\pi$
$419$	−30.2247			−1.47657			−0.738286	+	0.674488i	$0.764365\pi$
$420$		0			0
$421$	6.94549	−	3.53890i	0.338502	−	0.172476i	−0.276473	−	0.961022i	$-0.589166\pi$
$421$	6.94549	−	3.53890i	0.338502	−	0.172476i	0.614976	+	0.788546i	$0.289166\pi$
$422$		0			0
$423$	−2.93090	+	18.5050i	−0.142505	+	0.899744i
$424$		0			0
$425$	−33.7163	+	10.9551i	−1.63548	+	0.531399i
$426$		0			0
$427$	−49.2350	+	7.79805i	−2.38265	+	0.377374i
$428$		0			0
$429$	28.8699	−	0.253997i	1.39385	−	0.0122631i
$430$		0			0
$431$	3.52597	−	0.558459i	0.169840	−	0.0269000i	−0.0709352	−	0.997481i	$-0.522598\pi$
$431$	3.52597	−	0.558459i	0.169840	−	0.0269000i	0.240775	+	0.970581i	$0.422598\pi$
$432$		0			0
$433$	12.3239	−	4.00427i	0.592248	−	0.192433i	0.00246784	−	0.999997i	$-0.499214\pi$
$433$	12.3239	−	4.00427i	0.592248	−	0.192433i	0.589780	+	0.807564i	$0.299214\pi$
$434$		0			0
$435$	−0.604549	+	3.81697i	−0.0289859	+	0.183010i
$436$		0			0
$437$	−19.6696	+	10.0222i	−0.940924	+	0.479425i
$438$		0			0
$439$	−12.7753			−0.609732			−0.304866	−	0.952395i	$-0.598612\pi$
$439$	−12.7753			−0.609732			−0.304866	+	0.952395i	$0.598612\pi$
$440$		0			0
$441$			24.3175i			1.15798i
$442$		0			0
$443$	3.69303	−	11.3660i	0.175461	−	0.540014i	−0.824193	−	0.566309i	$-0.808371\pi$
$443$	3.69303	−	11.3660i	0.175461	−	0.540014i	0.999654	+	0.0262949i	$0.00837088\pi$
$444$		0			0
$445$	1.76711	−	1.28388i	0.0837689	−	0.0608617i
$446$		0			0
$447$	26.5306	+	13.5180i	1.25485	+	0.639380i
$448$		0			0
$449$	−34.0818	+	5.39803i	−1.60842	+	0.254749i	−0.895027	−	0.446013i	$-0.852844\pi$
$449$	−34.0818	+	5.39803i	−1.60842	+	0.254749i	−0.713395	+	0.700762i	$0.752844\pi$
$450$		0			0
$451$	7.90485	+	3.23089i	0.372225	+	0.152137i
$452$		0			0
$453$	−6.52923	−	41.2239i	−0.306770	−	1.93687i
$454$		0			0
$455$	1.52497	+	2.46577i	0.0714918	+	0.115597i
$456$		0			0
$457$	−2.14210	+	13.5247i	−0.100203	+	0.632658i	0.885561	+	0.464523i	$0.153774\pi$
$457$	−2.14210	+	13.5247i	−0.100203	+	0.632658i	−0.985764	+	0.168135i	$0.946226\pi$
$458$		0			0
$459$	−0.912629	+	2.80878i	−0.0425979	+	0.131103i
$460$		0			0
$461$	−17.1165	+	17.1165i	−0.797196	+	0.797196i	−0.982653	−	0.185456i	$-0.940624\pi$
$461$	−17.1165	+	17.1165i	−0.797196	+	0.797196i	0.185456	+	0.982653i	$0.440624\pi$
$462$		0			0
$463$	2.76598	−	2.76598i	0.128546	−	0.128546i	−0.639907	−	0.768453i	$-0.721027\pi$
$463$	2.76598	−	2.76598i	0.128546	−	0.128546i	0.768453	+	0.639907i	$0.221027\pi$
$464$		0			0
$465$	−1.14934	−	0.373442i	−0.0532992	−	0.0173180i
$466$		0			0
$467$	4.87627	+	6.71161i	0.225647	+	0.310576i	0.906797	−	0.421568i	$-0.138520\pi$
$467$	4.87627	+	6.71161i	0.225647	+	0.310576i	−0.681150	+	0.732144i	$0.738520\pi$
$468$		0			0
$469$	−6.35045	+	2.06339i	−0.293236	+	0.0952783i
$470$		0			0
$471$	−37.8545	−	27.5029i	−1.74424	−	1.26727i
$472$		0			0
$473$	30.5700	−	26.3585i	1.40561	−	1.21197i
$474$		0			0
$475$	−3.90064	−	24.6277i	−0.178974	−	1.12999i
$476$		0			0
$477$	−4.51393	−	13.8925i	−0.206679	−	0.636092i
$478$		0			0
$479$	−1.62709	−	0.257706i	−0.0743437	−	0.0117749i	0.119152	−	0.992876i	$-0.461982\pi$
$479$	−1.62709	−	0.257706i	−0.0743437	−	0.0117749i	−0.193495	+	0.981101i	$0.561982\pi$
$480$		0			0
$481$	2.70323	−	2.32802i	0.123257	−	0.106149i
$482$		0			0
$483$	−29.5973	+	29.5973i	−1.34672	+	1.34672i
$484$		0			0
$485$		−	0.570868i		−	0.0259218i
$486$		0			0
$487$	16.6873	−	8.50258i	0.756172	−	0.385289i	−0.0330046	−	0.999455i	$-0.510508\pi$
$487$	16.6873	−	8.50258i	0.756172	−	0.385289i	0.789177	+	0.614166i	$0.210508\pi$
$488$		0			0
$489$	1.41901	−	8.95928i	0.0641699	−	0.405153i
$490$		0			0
$491$	7.28968	+	22.4353i	0.328979	+	1.01249i	0.969612	+	0.244646i	$0.0786718\pi$
$491$	7.28968	+	22.4353i	0.328979	+	1.01249i	−0.640634	+	0.767847i	$0.721328\pi$
$492$		0			0
$493$	−33.0370	+	45.4715i	−1.48791	+	2.04793i
$494$		0			0
$495$	1.90517	+	0.140942i	0.0856308	+	0.00633485i
$496$		0			0
$497$	24.4679	−	33.6771i	1.09753	−	1.51063i
$498$		0			0
$499$	11.3872	−	22.3486i	0.509759	−	1.00046i	−0.482456	−	0.875920i	$-0.660255\pi$
$499$	11.3872	−	22.3486i	0.509759	−	1.00046i	0.992215	−	0.124538i	$-0.0397450\pi$
$500$		0			0
$501$	−14.8157	−	2.34658i	−0.661918	−	0.104838i
$502$		0			0
$503$	5.61509	+	1.82445i	0.250364	+	0.0813483i	0.431511	−	0.902108i	$-0.357981\pi$
$503$	5.61509	+	1.82445i	0.250364	+	0.0813483i	−0.181146	+	0.983456i	$0.557981\pi$
$504$		0			0
$505$	1.12797	+	1.12797i	0.0501941	+	0.0501941i
$506$		0			0
$507$	27.8473	−	14.4779i	1.23674	−	0.642987i
$508$		0			0
$509$	−12.3608	+	6.29816i	−0.547884	+	0.279161i	−0.705943	−	0.708269i	$-0.749477\pi$
$509$	−12.3608	+	6.29816i	−0.547884	+	0.279161i	0.158059	+	0.987430i	$0.449477\pi$
$510$		0			0
$511$	−8.63150	−	11.8802i	−0.381835	−	0.525551i
$512$		0			0
$513$	−1.85081	−	0.943037i	−0.0817154	−	0.0416361i
$514$		0			0
$515$	3.41576	−	0.541004i	0.150517	−	0.0238395i
$516$		0			0
$517$	−20.3330	−	8.31057i	−0.894245	−	0.365498i
$518$		0			0
$519$	−25.9208	−	18.8326i	−1.13780	−	0.826659i
$520$		0			0
$521$	−2.48911	−	7.66069i	−0.109050	−	0.335621i	0.881610	−	0.471979i	$-0.156460\pi$
$521$	−2.48911	−	7.66069i	−0.109050	−	0.335621i	−0.990660	+	0.136358i	$0.956460\pi$
$522$		0			0
$523$	−18.2343	−	25.0973i	−0.797328	−	1.09743i	−0.993157	−	0.116790i	$-0.962739\pi$
$523$	−18.2343	−	25.0973i	−0.797328	−	1.09743i	0.195828	−	0.980638i	$-0.437261\pi$
$524$		0			0
$525$	−21.4636	−	42.1246i	−0.936747	−	1.83847i
$526$		0			0
$527$	−12.4282	−	12.4282i	−0.541381	−	0.541381i
$528$		0			0
$529$	3.72784			0.162080
$530$		0			0
$531$	−14.7124	−	28.8747i	−0.638464	−	1.25306i
$532$		0			0
$533$	9.25188	−	0.766338i	0.400743	−	0.0331938i
$534$		0			0
$535$	−2.26861	−	1.15591i	−0.0980805	−	0.0499745i
$536$		0			0
$537$	−5.52014	+	7.59783i	−0.238212	+	0.327870i
$538$		0			0
$539$	−27.7532	−	6.52528i	−1.19542	−	0.281064i
$540$		0			0
$541$	6.12697	+	38.6842i	0.263419	+	1.66316i	0.664626	+	0.747176i	$0.268591\pi$
$541$	6.12697	+	38.6842i	0.263419	+	1.66316i	−0.401207	+	0.915987i	$0.631409\pi$
$542$		0			0
$543$	−1.55780	+	0.506161i	−0.0668517	+	0.0217214i
$544$		0			0
$545$	0.448962	−	0.326190i	0.0192314	−	0.0139724i
$546$		0			0
$547$	7.93229	+	2.57736i	0.339160	+	0.110200i	0.473645	−	0.880716i	$-0.342938\pi$
$547$	7.93229	+	2.57736i	0.339160	+	0.110200i	−0.134485	+	0.990916i	$0.542938\pi$
$548$		0			0
$549$			35.7079i			1.52398i
$550$		0			0
$551$	−27.9535	−	27.9535i	−1.19086	−	1.19086i
$552$		0			0
$553$	−21.2249	−	41.6562i	−0.902574	−	1.77140i
$554$		0			0
$555$	0.393503	−	0.285897i	0.0167033	−	0.0121356i
$556$		0			0
$557$	−6.53629	+	12.8282i	−0.276951	+	0.543548i	−0.987022	−	0.160582i	$-0.948663\pi$
$557$	−6.53629	+	12.8282i	−0.276951	+	0.543548i	0.710071	+	0.704130i	$0.248663\pi$
$558$		0			0
$559$	16.6261	−	40.6092i	0.703207	−	1.71759i
$560$		0			0
$561$	48.9528	+	29.6830i	2.06679	+	1.25322i
$562$		0			0
$563$	−3.66880	−	2.66554i	−0.154621	−	0.112339i	0.507785	−	0.861484i	$-0.330465\pi$
$563$	−3.66880	−	2.66554i	−0.154621	−	0.112339i	−0.662406	+	0.749145i	$0.730465\pi$
$564$		0			0
$565$	0.291464	−	0.572031i	0.0122620	−	0.0240655i
$566$		0			0
$567$	−36.9930	−	5.85912i	−1.55356	−	0.246060i
$568$		0			0
$569$	5.38419	−	16.5708i	0.225717	−	0.694686i	−0.772501	−	0.635014i	$-0.780994\pi$
$569$	5.38419	−	16.5708i	0.225717	−	0.694686i	0.998218	−	0.0596723i	$-0.0190056\pi$
$570$		0			0
$571$	−5.97458			−0.250028			−0.125014	−	0.992155i	$-0.539898\pi$
$571$	−5.97458			−0.250028			−0.125014	+	0.992155i	$0.539898\pi$
$572$		0			0
$573$	16.7102			0.698077
$574$		0			0
$575$	6.72669	−	20.7026i	0.280522	−	0.863359i
$576$		0			0
$577$	17.1684	+	2.71921i	0.714730	+	0.113202i	0.503201	−	0.864169i	$-0.332156\pi$
$577$	17.1684	+	2.71921i	0.714730	+	0.113202i	0.211529	+	0.977372i	$0.432156\pi$
$578$		0			0
$579$	20.6557	−	40.5392i	0.858423	−	1.68475i
$580$		0			0
$581$	53.7691	+	39.0656i	2.23072	+	1.62071i
$582$		0			0
$583$	17.0665	−	1.42383i	0.706823	−	0.0589690i
$584$		0			0
$585$	1.91543	−	0.802618i	0.0791933	−	0.0331842i
$586$		0			0
$587$	−16.3469	+	32.0825i	−0.674708	+	1.32419i	0.258904	+	0.965903i	$0.416639\pi$
$587$	−16.3469	+	32.0825i	−0.674708	+	1.32419i	−0.933612	+	0.358285i	$0.883361\pi$
$588$		0			0
$589$	10.0012	−	7.26628i	0.412091	−	0.299402i
$590$		0			0
$591$	14.8501	+	29.1449i	0.610850	+	1.19886i
$592$		0			0
$593$	−20.7661	−	20.7661i	−0.852762	−	0.852762i	0.137711	−	0.990472i	$-0.456026\pi$
$593$	−20.7661	−	20.7661i	−0.852762	−	0.852762i	−0.990472	+	0.137711i	$0.956026\pi$
$594$		0			0
$595$			5.74897i			0.235685i
$596$		0			0
$597$	26.6611	+	8.66271i	1.09117	+	0.354541i
$598$		0			0
$599$	−9.41845	+	6.84290i	−0.384827	+	0.279593i	−0.763333	−	0.646006i	$-0.776438\pi$
$599$	−9.41845	+	6.84290i	−0.384827	+	0.279593i	0.378505	+	0.925599i	$0.376438\pi$
$600$		0			0
$601$	−15.5339	+	5.04726i	−0.633639	+	0.205882i	−0.608187	−	0.793794i	$-0.708103\pi$
$601$	−15.5339	+	5.04726i	−0.633639	+	0.205882i	−0.0254528	+	0.999676i	$0.508103\pi$
$602$		0			0
$603$	0.748240	+	4.72420i	0.0304707	+	0.192384i
$604$		0			0
$605$	−0.672080	+	2.13652i	−0.0273239	+	0.0868618i
$606$		0			0
$607$	−18.8301	+	25.9175i	−0.764292	+	1.05196i	0.232553	+	0.972584i	$0.425292\pi$
$607$	−18.8301	+	25.9175i	−0.764292	+	1.05196i	−0.996845	+	0.0793735i	$0.974708\pi$
$608$		0			0
$609$	−66.7859	−	34.0291i	−2.70630	−	1.37893i
$610$		0			0
$611$	−23.7979	+	1.97119i	−0.962758	+	0.0797458i
$612$		0			0
$613$	3.20557	+	6.29128i	0.129472	+	0.254102i	0.946638	−	0.322300i	$-0.104456\pi$
$613$	3.20557	+	6.29128i	0.129472	+	0.254102i	−0.817166	+	0.576403i	$0.804456\pi$
$614$		0			0
$615$	1.26573			0.0510390
$616$		0			0
$617$	−3.82888	−	3.82888i	−0.154145	−	0.154145i	0.625821	−	0.779966i	$-0.284764\pi$
$617$	−3.82888	−	3.82888i	−0.154145	−	0.154145i	−0.779966	+	0.625821i	$0.784764\pi$
$618$		0			0
$619$	12.7959	+	25.1134i	0.514310	+	1.00939i	0.991441	+	0.130558i	$0.0416770\pi$
$619$	12.7959	+	25.1134i	0.514310	+	1.00939i	−0.477130	+	0.878833i	$0.658323\pi$
$620$		0			0
$621$	−1.06590	−	1.46709i	−0.0427731	−	0.0588721i
$622$		0			0
$623$	13.0916	+	40.2918i	0.524503	+	1.61426i
$624$		0			0
$625$	19.7237	+	14.3301i	0.788949	+	0.573205i
$626$		0			0
$627$	−26.0066	+	30.7410i	−1.03861	+	1.22768i
$628$		0			0
$629$	6.98703	−	1.10664i	0.278591	−	0.0441245i
$630$		0			0
$631$	10.9531	+	5.58090i	0.436038	+	0.222172i	0.658209	−	0.752835i	$-0.271314\pi$
$631$	10.9531	+	5.58090i	0.436038	+	0.222172i	−0.222171	+	0.975008i	$0.571314\pi$
$632$		0			0
$633$	−5.27386	−	7.25885i	−0.209617	−	0.288513i
$634$		0			0
$635$	1.57163	−	0.800787i	0.0623684	−	0.0317783i
$636$		0			0
$637$	−30.1073	+	7.35888i	−1.19290	+	0.291570i
$638$		0			0
$639$	−21.0850	−	21.0850i	−0.834108	−	0.834108i
$640$		0			0
$641$	−36.4837	−	11.8543i	−1.44102	−	0.468215i	−0.518803	−	0.854894i	$-0.673622\pi$
$641$	−36.4837	−	11.8543i	−1.44102	−	0.468215i	−0.922215	+	0.386678i	$0.873622\pi$
$642$		0			0
$643$	−40.0243	−	6.33923i	−1.57841	−	0.249995i	−0.695142	−	0.718872i	$-0.744659\pi$
$643$	−40.0243	−	6.33923i	−1.57841	−	0.249995i	−0.883263	+	0.468877i	$0.844659\pi$
$644$		0			0
$645$	2.71611	−	5.33067i	0.106947	−	0.209895i
$646$		0			0
$647$	−2.53000	+	3.48225i	−0.0994646	+	0.136901i	−0.855848	−	0.517227i	$-0.826964\pi$
$647$	−2.53000	+	3.48225i	−0.0994646	+	0.136901i	0.756384	+	0.654128i	$0.226964\pi$
$648$		0			0
$649$	36.9022	−	9.04290i	1.44854	−	0.354965i
$650$		0			0
$651$	13.7773	−	18.9628i	0.539975	−	0.743212i
$652$		0			0
$653$	0.356644	+	1.09764i	0.0139566	+	0.0429539i	0.957792	−	0.287461i	$-0.0928113\pi$
$653$	0.356644	+	1.09764i	0.0139566	+	0.0429539i	−0.943836	+	0.330415i	$0.892811\pi$
$654$		0			0
$655$	−0.0400190	+	0.252670i	−0.00156367	+	0.00987263i
$656$		0			0
$657$	−9.37257	+	4.77556i	−0.365659	+	0.186312i
$658$		0			0
$659$		−	34.3915i		−	1.33970i	−0.742494	−	0.669852i	$-0.766357\pi$
$659$		−	34.3915i		−	1.33970i	0.742494	−	0.669852i	$-0.233643\pi$
$660$		0			0
$661$	1.87846	−	1.87846i	0.0730635	−	0.0730635i	−0.669631	−	0.742694i	$-0.733548\pi$
$661$	1.87846	−	1.87846i	0.0730635	−	0.0730635i	0.742694	+	0.669631i	$0.233548\pi$
$662$		0			0
$663$	62.0640	+	4.62846i	2.41037	+	0.179754i
$664$		0			0
$665$	−3.99374	−	0.632547i	−0.154871	−	0.0245291i
$666$		0			0
$667$	−10.6647	−	32.8227i	−0.412940	−	1.27090i
$668$		0			0
$669$	−9.13091	−	57.6503i	−0.353022	−	2.22889i
$670$		0			0
$671$	−40.7529	−	9.58174i	−1.57325	−	0.369899i
$672$		0			0
$673$	30.3478	+	22.0490i	1.16982	+	0.849925i	0.990988	−	0.133954i	$-0.0427674\pi$
$673$	30.3478	+	22.0490i	1.16982	+	0.849925i	0.178834	+	0.983879i	$0.442767\pi$
$674$		0			0
$675$	1.94802	−	0.632950i	0.0749793	−	0.0243622i
$676$		0			0
$677$	−0.269277	−	0.370627i	−0.0103491	−	0.0142444i	0.803811	−	0.594885i	$-0.202802\pi$
$677$	−0.269277	−	0.370627i	−0.0103491	−	0.0142444i	−0.814160	+	0.580640i	$0.802802\pi$
$678$		0			0
$679$	10.5304	+	3.42155i	0.404121	+	0.131307i
$680$		0			0
$681$	10.2988	−	10.2988i	0.394649	−	0.394649i
$682$		0			0
$683$	9.72994	−	9.72994i	0.372306	−	0.372306i	−0.496011	−	0.868316i	$-0.665202\pi$
$683$	9.72994	−	9.72994i	0.372306	−	0.372306i	0.868316	+	0.496011i	$0.165202\pi$
$684$		0			0
$685$	0.215999	−	0.664777i	0.00825291	−	0.0253998i
$686$		0			0
$687$	−9.35131	+	59.0418i	−0.356775	+	2.25259i
$688$		0			0
$689$	15.8342	−	9.79276i	0.603234	−	0.373075i
$690$		0			0
$691$	−1.63683	−	10.3345i	−0.0622678	−	0.393144i	−0.999064	−	0.0432668i	$-0.986223\pi$
$691$	−1.63683	−	10.3345i	−0.0622678	−	0.393144i	0.936796	−	0.349877i	$-0.113777\pi$
$692$		0			0
$693$	−14.0186	+	34.2986i	−0.532524	+	1.30290i
$694$		0			0
$695$	0.0851373	−	0.0134844i	0.00322944	−	0.000511493i
$696$		0			0
$697$	16.4022	+	8.35735i	0.621279	+	0.316557i
$698$		0			0
$699$	7.41707	−	5.38882i	0.280539	−	0.203824i
$700$		0			0
$701$	−0.261007	+	0.803295i	−0.00985808	+	0.0303401i	−0.955865	−	0.293808i	$-0.905077\pi$
$701$	−0.261007	+	0.803295i	−0.00985808	+	0.0303401i	0.946006	+	0.324148i	$0.105077\pi$
$702$		0			0
$703$			4.97557i			0.187657i
$704$		0			0
$705$	−3.25572			−0.122618
$706$		0			0
$707$	−27.5676	+	14.0464i	−1.03679	+	0.528268i
$708$		0			0
$709$	−1.56815	+	9.90091i	−0.0588931	+	0.371837i	0.940586	+	0.339556i	$0.110277\pi$
$709$	−1.56815	+	9.90091i	−0.0588931	+	0.371837i	−0.999479	+	0.0322802i	$0.989723\pi$
$710$		0			0
$711$	−31.8504	+	10.3488i	−1.19449	+	0.388112i
$712$		0			0
$713$	10.6593	−	1.68827i	0.399195	−	0.0632262i
$714$		0			0
$715$	0.402036	+	2.40142i	0.0150353	+	0.0898082i
$716$		0			0
$717$	−9.95301	+	1.57640i	−0.371702	+	0.0588718i
$718$		0			0
$719$	8.13267	−	2.64246i	0.303297	−	0.0985473i	−0.153415	−	0.988162i	$-0.549027\pi$
$719$	8.13267	−	2.64246i	0.303297	−	0.0985473i	0.456712	+	0.889615i	$0.349027\pi$
$720$		0			0
$721$	−10.4931	+	66.2510i	−0.390784	+	2.46732i
$722$		0			0
$723$	−17.8906	+	9.11571i	−0.665358	+	0.339017i
$724$		0			0
$725$	38.9813			1.44773
$726$		0			0
$727$		−	16.2330i		−	0.602050i	−0.953616	−	0.301025i	$-0.902671\pi$
$727$		−	16.2330i		−	0.602050i	0.953616	−	0.301025i	$-0.0973288\pi$
$728$		0			0
$729$	−7.36618	+	22.6708i	−0.272822	+	0.839658i
$730$		0			0
$731$	70.3948	−	51.1448i	2.60365	−	1.89166i
$732$		0			0
$733$	37.4849	+	19.0995i	1.38453	+	0.705456i	0.978083	−	0.208217i	$-0.0667659\pi$
$733$	37.4849	+	19.0995i	1.38453	+	0.705456i	0.406452	+	0.913672i	$0.366766\pi$
$734$		0			0
$735$	−4.17366	+	0.661043i	−0.153948	+	0.0243830i
$736$		0			0
$737$	−5.59244	−	0.413721i	−0.206000	−	0.0152396i
$738$		0			0
$739$	7.12890	+	45.0101i	0.262241	+	1.65572i	0.669797	+	0.742544i	$0.266381\pi$
$739$	7.12890	+	45.0101i	0.262241	+	1.65572i	−0.407556	+	0.913180i	$0.633619\pi$
$740$		0			0
$741$	−10.0441	+	42.6059i	−0.368979	+	1.56517i
$742$		0			0
$743$	2.12235	−	13.4000i	0.0778614	−	0.491597i	−0.917684	−	0.397312i	$-0.869943\pi$
$743$	2.12235	−	13.4000i	0.0778614	−	0.491597i	0.995545	−	0.0942858i	$-0.0300568\pi$
$744$		0			0
$745$	−0.775994	+	2.38826i	−0.0284302	+	0.0874992i
$746$		0			0
$747$	33.6644	−	33.6644i	1.23172	−	1.23172i
$748$		0			0
$749$	34.9195	−	34.9195i	1.27593	−	1.27593i
$750$		0			0
$751$	36.9779	+	12.0148i	1.34934	+	0.438428i	0.892471	−	0.451106i	$-0.148970\pi$
$751$	36.9779	+	12.0148i	1.34934	+	0.438428i	0.456871	+	0.889533i	$0.348970\pi$
$752$		0			0
$753$	−28.7793	−	39.6114i	−1.04878	−	1.44352i
$754$		0			0
$755$	3.34769	−	1.08773i	0.121835	−	0.0395866i
$756$		0			0
$757$	−12.3770	−	8.99241i	−0.449849	−	0.326835i	0.339687	−	0.940539i	$-0.389679\pi$
$757$	−12.3770	−	8.99241i	−0.449849	−	0.326835i	−0.789536	+	0.613704i	$0.789679\pi$
$758$		0			0
$759$	−32.4131	+	13.6046i	−1.17652	+	0.493815i
$760$		0			0
$761$	5.69052	+	35.9285i	0.206281	+	1.30241i	0.845745	+	0.533587i	$0.179156\pi$
$761$	5.69052	+	35.9285i	0.206281	+	1.30241i	−0.639464	+	0.768821i	$0.720844\pi$
$762$		0			0
$763$	3.32613	+	10.2368i	0.120414	+	0.370596i
$764$		0			0
$765$	4.06743	+	0.644218i	0.147058	+	0.0232918i
$766$		0			0
$767$	31.2974	−	26.9533i	1.13008	−	0.973227i
$768$		0			0
$769$	−5.55383	+	5.55383i	−0.200276	+	0.200276i	−0.800118	−	0.599842i	$-0.795230\pi$
$769$	−5.55383	+	5.55383i	−0.200276	+	0.200276i	0.599842	+	0.800118i	$0.295230\pi$
$770$		0			0
$771$			49.8214i			1.79427i
$772$		0			0
$773$	10.7618	−	5.48340i	0.387074	−	0.197224i	−0.249614	−	0.968345i	$-0.580304\pi$
$773$	10.7618	−	5.48340i	0.387074	−	0.197224i	0.636688	+	0.771121i	$0.280304\pi$
$774$		0			0
$775$	−1.90691	+	12.0398i	−0.0684983	+	0.432481i
$776$		0			0
$777$	2.91526	+	8.97225i	0.104584	+	0.321878i
$778$		0			0
$779$	−7.61046	+	10.4749i	−0.272673	+	0.375302i
$780$		0			0
$781$	29.7218	−	18.4061i	1.06353	−	0.658621i
$782$		0			0
$783$	1.90877	−	2.62720i	0.0682139	−	0.0938884i
$784$		0			0
$785$	1.79150	−	3.51601i	0.0639413	−	0.125492i
$786$		0			0
$787$	28.1900	+	4.46486i	1.00487	+	0.159155i	0.637114	−	0.770769i	$-0.280128\pi$
$787$	28.1900	+	4.46486i	1.00487	+	0.159155i	0.367751	+	0.929924i	$0.380128\pi$
$788$		0			0
$789$	−17.3273	−	5.62999i	−0.616869	−	0.200433i
$790$		0			0
$791$	8.80498	+	8.80498i	0.313069	+	0.313069i
$792$		0			0
$793$	−44.2097	+	10.8058i	−1.56993	+	0.383725i
$794$		0			0
$795$	2.26169	−	1.15239i	0.0802137	−	0.0408709i
$796$		0			0
$797$	−11.7675	−	16.1966i	−0.416827	−	0.573713i	0.548040	−	0.836452i	$-0.315374\pi$
$797$	−11.7675	−	16.1966i	−0.416827	−	0.573713i	−0.964867	+	0.262739i	$0.915374\pi$
$798$		0			0
$799$	−42.1901	−	21.4969i	−1.49258	−	0.760507i
$800$		0			0
$801$	29.9737	−	4.74737i	1.05907	−	0.167740i
$802$		0			0
$803$	−2.93528	−	11.9782i	−0.103584	−	0.422703i
$804$		0			0
$805$	−2.85584	−	2.07489i	−0.100655	−	0.0731302i
$806$		0			0
$807$	−1.03674	−	3.19077i	−0.0364951	−	0.112320i
$808$		0			0
$809$	13.0883	+	18.0146i	0.460162	+	0.633358i	0.974542	−	0.224204i	$-0.0719781\pi$
$809$	13.0883	+	18.0146i	0.460162	+	0.633358i	−0.514381	+	0.857562i	$0.671978\pi$
$810$		0			0
$811$	13.6888	+	26.8657i	0.480678	+	0.943383i	0.996249	+	0.0865362i	$0.0275798\pi$
$811$	13.6888	+	26.8657i	0.480678	+	0.943383i	−0.515571	+	0.856847i	$0.672420\pi$
$812$		0			0
$813$	38.4602	+	38.4602i	1.34886	+	1.34886i
$814$		0			0
$815$	0.765003			0.0267969
$816$		0			0
$817$	27.7843	+	54.5298i	0.972051	+	1.90776i
$818$		0			0
$819$	3.32509	+	40.1433i	0.116188	+	1.40272i
$820$		0			0
$821$	20.2090	+	10.2970i	0.705298	+	0.359367i	0.769568	−	0.638565i	$-0.220472\pi$
$821$	20.2090	+	10.2970i	0.705298	+	0.359367i	−0.0642698	+	0.997933i	$0.520472\pi$
$822$		0			0
$823$	22.0648	−	30.3695i	0.769129	−	1.05862i	−0.227270	−	0.973832i	$-0.572980\pi$
$823$	22.0648	−	30.3695i	0.769129	−	1.05862i	0.996399	−	0.0847836i	$-0.0270199\pi$
$824$		0			0
$825$	−3.30104	−	39.5674i	−0.114927	−	1.37756i
$826$		0			0
$827$	8.12087	+	51.2732i	0.282390	+	1.78294i	0.566410	+	0.824124i	$0.308332\pi$
$827$	8.12087	+	51.2732i	0.282390	+	1.78294i	−0.284019	+	0.958819i	$0.591668\pi$
$828$		0			0
$829$	−23.9729	+	7.78926i	−0.832613	+	0.270532i	−0.694145	−	0.719835i	$-0.744218\pi$
$829$	−23.9729	+	7.78926i	−0.832613	+	0.270532i	−0.138467	+	0.990367i	$0.544218\pi$
$830$		0			0
$831$	26.8351	−	19.4968i	0.930899	−	0.676338i
$832$		0			0
$833$	−58.4502	−	18.9916i	−2.02518	−	0.658021i
$834$		0			0
$835$		−	1.26507i		−	0.0437794i
$836$		0			0
$837$	0.718062	+	0.718062i	0.0248199	+	0.0248199i
$838$		0			0
$839$	−11.5377	−	22.6440i	−0.398326	−	0.781759i	0.601528	−	0.798852i	$-0.294559\pi$
$839$	−11.5377	−	22.6440i	−0.398326	−	0.781759i	−0.999854	+	0.0170927i	$0.994559\pi$
$840$		0			0
$841$	26.5377	−	19.2808i	0.915092	−	0.664854i
$842$		0			0
$843$	13.3640	−	26.2284i	0.460282	−	0.903354i
$844$		0			0
$845$	1.57336	+	2.12860i	0.0541251	+	0.0732259i
$846$		0			0
$847$	−35.3828	−	25.2028i	−1.21577	−	0.865980i
$848$		0			0
$849$	−32.1812	−	23.3810i	−1.10446	−	0.802435i
$850$		0			0
$851$	−1.97200	+	3.87026i	−0.0675991	+	0.132671i
$852$		0			0
$853$	24.2195	+	3.83599i	0.829260	+	0.131342i	0.556612	−	0.830772i	$-0.312101\pi$
$853$	24.2195	+	3.83599i	0.829260	+	0.131342i	0.272647	+	0.962114i	$0.412101\pi$
$854$		0			0
$855$	−0.895062	+	2.75472i	−0.0306105	+	0.0942093i
$856$		0			0
$857$	−1.63370			−0.0558061			−0.0279031	−	0.999611i	$-0.508883\pi$
$857$	−1.63370			−0.0558061			−0.0279031	+	0.999611i	$0.508883\pi$
$858$		0			0
$859$	−19.6530			−0.670550			−0.335275	−	0.942120i	$-0.608829\pi$
$859$	−19.6530			−0.670550			−0.335275	+	0.942120i	$0.608829\pi$
$860$		0			0
$861$	−7.58624	+	23.3480i	−0.258538	+	0.795699i
$862$		0			0
$863$	−10.1813	−	1.61256i	−0.346575	−	0.0548920i	−0.0192793	−	0.999814i	$-0.506137\pi$
$863$	−10.1813	−	1.61256i	−0.346575	−	0.0548920i	−0.327295	+	0.944922i	$0.606137\pi$
$864$		0			0
$865$	1.22673	−	2.40759i	0.0417100	−	0.0818605i
$866$		0			0
$867$	66.6363	+	48.4141i	2.26309	+	1.64423i
$868$		0			0
$869$	−3.26433	−	39.1274i	−0.110735	−	1.32731i
$870$		0			0
$871$	−5.62257	+	2.35601i	−0.190514	+	0.0798305i
$872$		0			0
$873$	3.60079	−	7.06694i	0.121868	−	0.239180i
$874$		0			0
$875$	6.47835	−	4.70680i	0.219008	−	0.159119i
$876$		0			0
$877$	−1.40068	−	2.74899i	−0.0472975	−	0.0928267i	0.866148	−	0.499787i	$-0.166589\pi$
$877$	−1.40068	−	2.74899i	−0.0472975	−	0.0928267i	−0.913446	+	0.406961i	$0.866589\pi$
$878$		0			0
$879$	−28.4923	−	28.4923i	−0.961021	−	0.961021i
$880$		0			0
$881$			8.13496i			0.274074i	0.990566	+	0.137037i	$0.0437579\pi$
$881$			8.13496i			0.274074i	−0.990566	+	0.137037i	$0.956242\pi$
$882$		0			0
$883$	−24.8132	−	8.06231i	−0.835032	−	0.271318i	−0.139869	−	0.990170i	$-0.544668\pi$
$883$	−24.8132	−	8.06231i	−0.835032	−	0.271318i	−0.695164	+	0.718852i	$0.744668\pi$
$884$		0			0
$885$	4.55589	−	3.31005i	0.153144	−	0.111266i
$886$		0			0
$887$	15.2417	−	4.95234i	0.511767	−	0.166283i	−0.0417388	−	0.999129i	$-0.513290\pi$
$887$	15.2417	−	4.95234i	0.511767	−	0.166283i	0.553506	+	0.832845i	$0.313290\pi$
$888$		0			0
$889$	5.35189	+	33.7905i	0.179497	+	1.13330i
$890$		0			0
$891$	−26.8966	−	16.3090i	−0.901070	−	0.546373i
$892$		0			0
$893$	19.5758	−	26.9437i	0.655078	−	0.901637i
$894$		0			0
$895$	−0.705704	−	0.359574i	−0.0235891	−	0.0120192i
$896$		0			0
$897$	−24.6990	+	29.1602i	−0.824677	+	0.973632i
$898$		0			0
$899$	8.77392	+	17.2198i	0.292627	+	0.574312i
$900$		0			0
$901$	36.9176			1.22990
$902$		0			0
$903$	82.0522	+	82.0522i	2.73053	+	2.73053i
$904$		0			0
$905$	−0.0627137	−	0.123083i	−0.00208467	−	0.00409140i
$906$		0			0
$907$	−31.5232	−	43.3880i	−1.04671	−	1.44067i	−0.891626	−	0.452772i	$-0.850435\pi$
$907$	−31.5232	−	43.3880i	−1.04671	−	1.44067i	−0.155084	−	0.987901i	$-0.549565\pi$
$908$		0			0
$909$	6.84874	+	21.0782i	0.227158	+	0.699121i
$910$		0			0
$911$	−4.95288	−	3.59848i	−0.164096	−	0.119223i	0.502707	−	0.864457i	$-0.332338\pi$
$911$	−4.95288	−	3.59848i	−0.164096	−	0.119223i	−0.666803	+	0.745234i	$0.732338\pi$
$912$		0			0
$913$	29.3873	+	47.4541i	0.972577	+	1.57050i
$914$		0			0
$915$	−6.12862	+	0.970678i	−0.202606	+	0.0320896i
$916$		0			0
$917$	−4.42098	−	2.25260i	−0.145994	−	0.0743875i
$918$		0			0
$919$	−7.45745	−	10.2643i	−0.245999	−	0.338588i	0.668106	−	0.744066i	$-0.267105\pi$
$919$	−7.45745	−	10.2643i	−0.245999	−	0.338588i	−0.914105	+	0.405478i	$0.867105\pi$
$920$		0			0
$921$	42.5335	−	21.6719i	1.40153	−	0.714113i
$922$		0			0
$923$	19.7245	−	32.4858i	0.649239	−	1.06928i
$924$		0			0
$925$	−3.46923	−	3.46923i	−0.114068	−	0.114068i
$926$		0			0
$927$	45.6972	+	14.8479i	1.50089	+	0.487669i
$928$		0			0
$929$	−50.7390	−	8.03627i	−1.66469	−	0.263662i	−0.748131	−	0.663552i	$-0.769048\pi$
$929$	−50.7390	−	8.03627i	−1.66469	−	0.263662i	−0.916563	+	0.399890i	$0.869048\pi$
$930$		0			0
$931$	19.6244	−	38.5151i	0.643164	−	1.26228i
$932$		0			0
$933$	7.87976	−	10.8456i	0.257972	−	0.355067i
$934$		0			0
$935$	−1.82668	+	4.46923i	−0.0597388	+	0.146160i
$936$		0			0
$937$	−18.9584	+	26.0941i	−0.619345	+	0.852456i	−0.997305	−	0.0733663i	$-0.976626\pi$
$937$	−18.9584	+	26.0941i	−0.619345	+	0.852456i	0.377960	+	0.925822i	$0.376626\pi$
$938$		0			0
$939$	4.88119	+	15.0228i	0.159292	+	0.490249i
$940$		0			0
$941$	8.40959	−	53.0961i	0.274145	−	1.73088i	−0.338889	−	0.940826i	$-0.610051\pi$
$941$	8.40959	−	53.0961i	0.274145	−	1.73088i	0.613034	−	0.790057i	$-0.289949\pi$
$942$		0			0
$943$	−10.0714	+	5.13163i	−0.327969	+	0.167109i
$944$		0			0
$945$		−	0.332157i		−	0.0108051i
$946$		0			0
$947$	22.2629	−	22.2629i	0.723448	−	0.723448i	−0.245858	−	0.969306i	$-0.579070\pi$
$947$	22.2629	−	22.2629i	0.723448	−	0.723448i	0.969306	+	0.245858i	$0.0790696\pi$
$948$		0			0
$949$	−8.74889	−	10.1590i	−0.284001	−	0.329774i
$950$		0			0
$951$	−1.43339	−	0.227026i	−0.0464808	−	0.00736183i
$952$		0			0
$953$	−7.49889	−	23.0792i	−0.242913	−	0.747609i	−0.995973	−	0.0896571i	$-0.971423\pi$
$953$	−7.49889	−	23.0792i	−0.242913	−	0.747609i	0.753060	−	0.657952i	$-0.228577\pi$
$954$		0			0
$955$	0.220456	+	1.39191i	0.00713380	+	0.0450410i
$956$		0			0
$957$	−41.1068	−	47.6747i	−1.32879	−	1.54110i
$958$		0			0
$959$	10.9681	+	7.96880i	0.354179	+	0.257326i
$960$		0			0
$961$	23.7350	−	7.71198i	0.765646	−	0.248774i
$962$		0			0
$963$	−20.7928	−	28.6188i	−0.670038	−	0.922228i
$964$		0			0
$965$	3.64931	+	1.18573i	0.117475	+	0.0381700i
$966$		0			0
$967$	20.0548	−	20.0548i	0.644919	−	0.644919i	−0.306841	−	0.951761i	$-0.599272\pi$
$967$	20.0548	−	20.0548i	0.644919	−	0.644919i	0.951761	+	0.306841i	$0.0992721\pi$
$968$		0			0
$969$	−61.3771	+	61.3771i	−1.97172	+	1.97172i
$970$		0			0
$971$	−12.4274	+	38.2476i	−0.398814	+	1.22742i	0.527137	+	0.849780i	$0.323265\pi$
$971$	−12.4274	+	38.2476i	−0.398814	+	1.22742i	−0.925951	+	0.377643i	$0.876735\pi$
$972$		0			0
$973$	−0.261539	+	1.65129i	−0.00838456	+	0.0529381i
$974$		0			0
$975$	−22.7038	−	36.7103i	−0.727103	−	1.17567i
$976$		0			0
$977$	−6.32356	−	39.9254i	−0.202309	−	1.27733i	−0.854572	−	0.519334i	$-0.826180\pi$
$977$	−6.32356	−	39.9254i	−0.202309	−	1.27733i	0.652263	−	0.757993i	$-0.273820\pi$
$978$		0			0
$979$	−2.62494	+	35.4824i	−0.0838935	+	1.13402i
$980$		0			0
$981$	7.61529	−	1.20614i	0.243138	−	0.0385092i
$982$		0			0
$983$	25.0632	+	12.7703i	0.799392	+	0.407311i	0.805445	−	0.592671i	$-0.201927\pi$
$983$	25.0632	+	12.7703i	0.799392	+	0.407311i	−0.00605236	+	0.999982i	$0.501927\pi$
$984$		0			0
$985$	−2.23177	+	1.62148i	−0.0711101	+	0.0516645i
$986$		0			0
$987$	19.5135	−	60.0563i	0.621121	−	1.91161i
$988$		0			0
$989$			53.4281i			1.69891i
$990$		0			0
$991$	4.00082			0.127090			0.0635452	−	0.997979i	$-0.479759\pi$
$991$	4.00082			0.127090			0.0635452	+	0.997979i	$0.479759\pi$
$992$		0			0
$993$	31.8349	−	16.2207i	1.01025	−	0.514749i
$994$		0			0
$995$	−0.369840	+	2.33508i	−0.0117247	+	0.0740269i
$996$		0			0
$997$	1.43263	−	0.465491i	0.0453720	−	0.0147422i	−0.286243	−	0.958157i	$-0.592406\pi$
$997$	1.43263	−	0.465491i	0.0453720	−	0.0147422i	0.331615	+	0.943415i	$0.392406\pi$
$998$		0			0
$999$	−0.403689	+	0.0639380i	−0.0127721	+	0.00202291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.73.3	✓	112
11.8	odd	10	inner	572.2.bh.a.437.3	yes	112
13.5	odd	4	inner	572.2.bh.a.161.3	yes	112
143.96	even	20	inner	572.2.bh.a.525.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.73.3	✓	112	1.1	even	1	trivial
572.2.bh.a.161.3	yes	112	13.5	odd	4	inner
572.2.bh.a.437.3	yes	112	11.8	odd	10	inner
572.2.bh.a.525.3	yes	112	143.96	even	20	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)

\(f(q)\)	\(=\)	\(q+(-0.746064 + 2.29615i) q^{3} +(-0.201105 - 0.0318519i) q^{5} +(1.79289 - 3.51875i) q^{7} +(-2.28863 - 1.66279i) q^{9} +O(q^{10})\)	\(q+(-0.746064 + 2.29615i) q^{3} +(-0.201105 - 0.0318519i) q^{5} +(1.79289 - 3.51875i) q^{7} +(-2.28863 - 1.66279i) q^{9} +(2.51184 - 2.16579i) q^{11} +(1.36611 - 3.33673i) q^{13} +(0.223174 - 0.438003i) q^{15} +(5.78411 - 4.20240i) q^{17} +(2.28295 + 4.48054i) q^{19} +(6.74196 + 6.74196i) q^{21} +4.39001i q^{23} +(-4.71585 - 1.53227i) q^{25} +(-0.334188 + 0.242802i) q^{27} +(-7.47668 + 2.42932i) q^{29} +(-0.384571 - 2.42809i) q^{31} +(3.09899 + 7.38337i) q^{33} +(-0.472639 + 0.650532i) q^{35} +(0.881606 + 0.449201i) q^{37} +(6.64241 + 5.62620i) q^{39} +(1.16893 + 2.29416i) q^{41} +12.1704 q^{43} +(0.407293 + 0.407293i) q^{45} +(-3.00675 - 5.90108i) q^{47} +(-5.05265 - 6.95438i) q^{49} +(5.33402 + 16.4164i) q^{51} +(4.17746 + 3.03510i) q^{53} +(-0.574128 + 0.355545i) q^{55} +(-11.9912 + 1.89922i) q^{57} +(10.2070 + 5.20074i) q^{59} +(-7.41933 - 10.2118i) q^{61} +(-9.95421 + 5.07193i) q^{63} +(-0.381013 + 0.627520i) q^{65} +(-1.19557 - 1.19557i) q^{67} +(-10.0801 - 3.27522i) q^{69} +(10.4109 + 1.64893i) q^{71} +(1.68813 - 3.31315i) q^{73} +(7.03665 - 9.68512i) q^{75} +(-3.11743 - 12.7216i) q^{77} +(6.95840 - 9.57742i) q^{79} +(-2.93072 - 9.01983i) q^{81} +(-2.63269 + 16.6222i) q^{83} +(-1.29707 + 0.660890i) q^{85} -18.9800i q^{87} +(-7.58555 + 7.58555i) q^{89} +(-9.29183 - 10.7894i) q^{91} +(5.86216 + 0.928475i) q^{93} +(-0.316399 - 0.973775i) q^{95} +(0.438596 + 2.76919i) q^{97} +(-9.34993 + 0.780049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 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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