LMFDB - Embedded newform 756.2.ck.a.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.277790 + 1.70963i) q^{3} +(0.630118 - 3.57358i) q^{5} +(-2.41159 + 1.08823i) q^{7} +(-2.84567 + 0.949836i) q^{9} +O(q^{10})$	\(q+(0.277790 + 1.70963i) q^{3} +(0.630118 - 3.57358i) q^{5} +(-2.41159 + 1.08823i) q^{7} +(-2.84567 + 0.949836i) q^{9} +(-5.37077 + 0.947012i) q^{11} +(3.07790 - 3.66809i) q^{13} +(6.28454 + 0.0845642i) q^{15} -3.33090 q^{17} -5.54597i q^{19} +(-2.53039 - 3.82062i) q^{21} +(-4.97574 + 5.92986i) q^{23} +(-7.67496 - 2.79346i) q^{25} +(-2.41437 - 4.60118i) q^{27} +(-4.08440 - 4.86760i) q^{29} +(1.15746 + 3.18009i) q^{31} +(-3.11099 - 8.91896i) q^{33} +(2.36929 + 9.30371i) q^{35} +(0.690046 + 1.19519i) q^{37} +(7.12609 + 4.24310i) q^{39} +(4.74638 + 3.98269i) q^{41} +(-1.78595 - 0.650033i) q^{43} +(1.60121 + 10.7677i) q^{45} +(-5.57250 - 2.02822i) q^{47} +(4.63151 - 5.24873i) q^{49} +(-0.925291 - 5.69461i) q^{51} +(6.01547 - 3.47303i) q^{53} +19.7896i q^{55} +(9.48155 - 1.54061i) q^{57} +(-8.58135 - 7.20060i) q^{59} +(-0.712093 + 1.95646i) q^{61} +(5.82893 - 5.38735i) q^{63} +(-11.1688 - 13.3104i) q^{65} +(1.69045 - 9.58704i) q^{67} +(-11.5201 - 6.85942i) q^{69} +(-1.02203 - 0.590072i) q^{71} +(3.38838 + 1.95628i) q^{73} +(2.64375 - 13.8973i) q^{75} +(11.9215 - 8.12844i) q^{77} +(1.24492 + 7.06031i) q^{79} +(7.19562 - 5.40583i) q^{81} +(7.60660 - 6.38269i) q^{83} +(-2.09886 + 11.9032i) q^{85} +(7.18718 - 8.33498i) q^{87} -6.67102 q^{89} +(-3.43088 + 12.1954i) q^{91} +(-5.11525 + 2.86222i) q^{93} +(-19.8189 - 3.49462i) q^{95} +(-3.89819 + 10.7102i) q^{97} +(14.3839 - 7.79623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.277790	+	1.70963i	0.160382	+	0.987055i
$3$	0.277790	+	1.70963i	0.160382	+	0.987055i
$4$		0			0
$5$	0.630118	−	3.57358i	0.281798	−	1.59815i	−0.434708	−	0.900572i	$-0.643148\pi$
$5$	0.630118	−	3.57358i	0.281798	−	1.59815i	0.716505	−	0.697582i	$-0.245741\pi$
$6$		0			0
$7$	−2.41159	+	1.08823i	−0.911494	+	0.411313i
$7$	−2.41159	+	1.08823i	−0.911494	+	0.411313i
$8$		0			0
$9$	−2.84567	+	0.949836i	−0.948555	+	0.316612i
$10$		0			0
$11$	−5.37077	+	0.947012i	−1.61935	+	0.285535i	−0.908524	−	0.417833i	$-0.862790\pi$
$11$	−5.37077	+	0.947012i	−1.61935	+	0.285535i	−0.710825	+	0.703368i	$0.751678\pi$
$12$		0			0
$13$	3.07790	−	3.66809i	0.853655	−	1.01735i	−0.145952	−	0.989292i	$-0.546624\pi$
$13$	3.07790	−	3.66809i	0.853655	−	1.01735i	0.999606	−	0.0280542i	$-0.00893109\pi$
$14$		0			0
$15$	6.28454	+	0.0845642i	1.62266	+	0.0218344i
$16$		0			0
$17$	−3.33090			−0.807862			−0.403931	−	0.914789i	$-0.632356\pi$
$17$	−3.33090			−0.807862			−0.403931	+	0.914789i	$0.632356\pi$
$18$		0			0
$19$		−	5.54597i		−	1.27233i	−0.771552	−	0.636166i	$-0.780519\pi$
$19$		−	5.54597i		−	1.27233i	0.771552	−	0.636166i	$-0.219481\pi$
$20$		0			0
$21$	−2.53039	−	3.82062i	−0.552176	−	0.833728i
$22$		0			0
$23$	−4.97574	+	5.92986i	−1.03751	+	1.23646i	−0.0664127	+	0.997792i	$0.521155\pi$
$23$	−4.97574	+	5.92986i	−1.03751	+	1.23646i	−0.971101	+	0.238669i	$0.923289\pi$
$24$		0			0
$25$	−7.67496	−	2.79346i	−1.53499	−	0.558691i
$26$		0			0
$27$	−2.41437	−	4.60118i	−0.464645	−	0.885497i
$28$		0			0
$29$	−4.08440	−	4.86760i	−0.758454	−	0.903890i	0.239295	−	0.970947i	$-0.423084\pi$
$29$	−4.08440	−	4.86760i	−0.758454	−	0.903890i	−0.997749	+	0.0670565i	$0.978639\pi$
$30$		0			0
$31$	1.15746	+	3.18009i	0.207886	+	0.571161i	0.999189	−	0.0402624i	$-0.0128194\pi$
$31$	1.15746	+	3.18009i	0.207886	+	0.571161i	−0.791303	+	0.611424i	$0.790597\pi$
$32$		0			0
$33$	−3.11099	−	8.91896i	−0.541553	−	1.55259i
$34$		0			0
$35$	2.36929	+	9.30371i	0.400484	+	1.57261i
$36$		0			0
$37$	0.690046	+	1.19519i	0.113443	+	0.196489i	0.917156	−	0.398528i	$-0.130479\pi$
$37$	0.690046	+	1.19519i	0.113443	+	0.196489i	−0.803713	+	0.595017i	$0.797145\pi$
$38$		0			0
$39$	7.12609	+	4.24310i	1.14109	+	0.679440i
$40$		0			0
$41$	4.74638	+	3.98269i	0.741260	+	0.621991i	0.933176	−	0.359420i	$-0.117026\pi$
$41$	4.74638	+	3.98269i	0.741260	+	0.621991i	−0.191916	+	0.981411i	$0.561470\pi$
$42$		0			0
$43$	−1.78595	−	0.650033i	−0.272355	−	0.0991291i	0.202232	−	0.979338i	$-0.435180\pi$
$43$	−1.78595	−	0.650033i	−0.272355	−	0.0991291i	−0.474587	+	0.880209i	$0.657403\pi$
$44$		0			0
$45$	1.60121	+	10.7677i	0.238694	+	1.60516i
$46$		0			0
$47$	−5.57250	−	2.02822i	−0.812832	−	0.295847i	−0.0980389	−	0.995183i	$-0.531257\pi$
$47$	−5.57250	−	2.02822i	−0.812832	−	0.295847i	−0.714793	+	0.699336i	$0.753479\pi$
$48$		0			0
$49$	4.63151	−	5.24873i	0.661644	−	0.749818i
$50$		0			0
$51$	−0.925291	−	5.69461i	−0.129567	−	0.797404i
$52$		0			0
$53$	6.01547	−	3.47303i	0.826288	−	0.477057i	−0.0262922	−	0.999654i	$-0.508370\pi$
$53$	6.01547	−	3.47303i	0.826288	−	0.477057i	0.852580	+	0.522597i	$0.175037\pi$
$54$		0			0
$55$			19.7896i			2.66843i
$56$		0			0
$57$	9.48155	−	1.54061i	1.25586	−	0.204059i
$58$		0			0
$59$	−8.58135	−	7.20060i	−1.11720	−	0.937439i	−0.118737	−	0.992926i	$-0.537884\pi$
$59$	−8.58135	−	7.20060i	−1.11720	−	0.937439i	−0.998459	+	0.0554869i	$0.982329\pi$
$60$		0			0
$61$	−0.712093	+	1.95646i	−0.0911741	+	0.250499i	−0.976895	−	0.213719i	$-0.931442\pi$
$61$	−0.712093	+	1.95646i	−0.0911741	+	0.250499i	0.885721	+	0.464218i	$0.153665\pi$
$62$		0			0
$63$	5.82893	−	5.38735i	0.734376	−	0.678743i
$64$		0			0
$65$	−11.1688	−	13.3104i	−1.38532	−	1.65096i
$66$		0			0
$67$	1.69045	−	9.58704i	0.206522	−	1.17124i	−0.688505	−	0.725231i	$-0.741733\pi$
$67$	1.69045	−	9.58704i	0.206522	−	1.17124i	0.895027	−	0.446012i	$-0.147156\pi$
$68$		0			0
$69$	−11.5201	−	6.85942i	−1.38685	−	0.825777i
$70$		0			0
$71$	−1.02203	−	0.590072i	−0.121293	−	0.0700286i	0.438126	−	0.898914i	$-0.355642\pi$
$71$	−1.02203	−	0.590072i	−0.121293	−	0.0700286i	−0.559419	+	0.828885i	$0.688976\pi$
$72$		0			0
$73$	3.38838	+	1.95628i	0.396580	+	0.228965i	0.685007	−	0.728536i	$-0.259799\pi$
$73$	3.38838	+	1.95628i	0.396580	+	0.228965i	−0.288428	+	0.957502i	$0.593132\pi$
$74$		0			0
$75$	2.64375	−	13.8973i	0.305274	−	1.60472i
$76$		0			0
$77$	11.9215	−	8.12844i	1.35858	−	0.926322i
$78$		0			0
$79$	1.24492	+	7.06031i	0.140065	+	0.794347i	0.971198	+	0.238274i	$0.0765815\pi$
$79$	1.24492	+	7.06031i	0.140065	+	0.794347i	−0.831133	+	0.556073i	$0.812307\pi$
$80$		0			0
$81$	7.19562	−	5.40583i	0.799514	−	0.600648i
$82$		0			0
$83$	7.60660	−	6.38269i	0.834932	−	0.700592i	−0.121485	−	0.992593i	$-0.538766\pi$
$83$	7.60660	−	6.38269i	0.834932	−	0.700592i	0.956418	+	0.292002i	$0.0943213\pi$
$84$		0			0
$85$	−2.09886	+	11.9032i	−0.227654	+	1.29109i
$86$		0			0
$87$	7.18718	−	8.33498i	0.770547	−	0.893604i
$88$		0			0
$89$	−6.67102			−0.707126			−0.353563	−	0.935411i	$-0.615030\pi$
$89$	−6.67102			−0.707126			−0.353563	+	0.935411i	$0.615030\pi$
$90$		0			0
$91$	−3.43088	+	12.1954i	−0.359654	+	1.27842i
$92$		0			0
$93$	−5.11525	+	2.86222i	−0.530426	+	0.296799i
$94$		0			0
$95$	−19.8189	−	3.49462i	−2.03338	−	0.358540i
$96$		0			0
$97$	−3.89819	+	10.7102i	−0.395802	+	1.08746i	0.568508	+	0.822678i	$0.307521\pi$
$97$	−3.89819	+	10.7102i	−0.395802	+	1.08746i	−0.964309	+	0.264778i	$0.914701\pi$
$98$		0			0
$99$	14.3839	−	7.79623i	1.44564	−	0.783551i
$100$		0			0
$101$	−0.268163	+	0.225015i	−0.0266832	+	0.0223899i	−0.656032	−	0.754733i	$-0.727766\pi$
$101$	−0.268163	+	0.225015i	−0.0266832	+	0.0223899i	0.629349	+	0.777123i	$0.283322\pi$
$102$		0			0
$103$	15.9438	+	2.81132i	1.57099	+	0.277007i	0.890233	−	0.455506i	$-0.150542\pi$
$103$	15.9438	+	2.81132i	1.57099	+	0.277007i	0.680753	+	0.732513i	$0.261653\pi$
$104$		0			0
$105$	−15.2477	+	6.63509i	−1.48803	+	0.647519i
$106$		0			0
$107$	2.20395	+	1.27245i	0.213064	+	0.123012i	0.602734	−	0.797942i	$-0.294078\pi$
$107$	2.20395	+	1.27245i	0.213064	+	0.123012i	−0.389671	+	0.920954i	$0.627411\pi$
$108$		0			0
$109$	−2.93214	−	5.07862i	−0.280848	−	0.486444i	0.690746	−	0.723098i	$-0.257282\pi$
$109$	−2.93214	−	5.07862i	−0.280848	−	0.486444i	−0.971594	+	0.236654i	$0.923949\pi$
$110$		0			0
$111$	−1.85165	+	1.51174i	−0.175751	+	0.143488i
$112$		0			0
$113$	3.59529	+	9.87798i	0.338217	+	0.929242i	0.985900	+	0.167333i	$0.0535156\pi$
$113$	3.59529	+	9.87798i	0.338217	+	0.929242i	−0.647684	+	0.761909i	$0.724262\pi$
$114$		0			0
$115$	18.0555	+	21.5177i	1.68368	+	2.00654i
$116$		0			0
$117$	−5.27457	+	13.3617i	−0.487634	+	1.23529i
$118$		0			0
$119$	8.03276	−	3.62479i	0.736362	−	0.332284i
$120$		0			0
$121$	17.6118	−	6.41015i	1.60107	−	0.582741i
$122$		0			0
$123$	−5.49042	+	9.22090i	−0.495055	+	0.831421i
$124$		0			0
$125$	−5.74700	+	9.95409i	−0.514027	+	0.890321i
$126$		0			0
$127$	−5.79930	−	10.0447i	−0.514605	−	0.891322i	−0.999856	−	0.0169471i	$-0.994605\pi$
$127$	−5.79930	−	10.0447i	−0.514605	−	0.891322i	0.485252	−	0.874375i	$-0.338728\pi$
$128$		0			0
$129$	0.615196	−	3.23389i	0.0541650	−	0.284728i
$130$		0			0
$131$	1.18226	+	0.992033i	0.103294	+	0.0866743i	0.692972	−	0.720964i	$-0.256301\pi$
$131$	1.18226	+	0.992033i	0.103294	+	0.0866743i	−0.589678	+	0.807639i	$0.700745\pi$
$132$		0			0
$133$	6.03529	+	13.3746i	0.523326	+	1.15972i
$134$		0			0
$135$	−17.9640	+	5.72864i	−1.54610	+	0.493043i
$136$		0			0
$137$	−0.508156	+	1.39615i	−0.0434147	+	0.119281i	−0.959505	−	0.281690i	$-0.909105\pi$
$137$	−0.508156	+	1.39615i	−0.0434147	+	0.119281i	0.916091	+	0.400971i	$0.131327\pi$
$138$		0			0
$139$	−17.2879	−	3.04832i	−1.46634	−	0.258555i	−0.617234	−	0.786780i	$-0.711747\pi$
$139$	−17.2879	−	3.04832i	−1.46634	−	0.258555i	−0.849105	+	0.528224i	$0.822858\pi$
$140$		0			0
$141$	1.91953	−	10.0903i	0.161653	−	0.849758i
$142$		0			0
$143$	−13.0569	+	22.6153i	−1.09188	+	1.89119i
$144$		0			0
$145$	−19.9684	+	11.5288i	−1.65829	+	0.957412i
$146$		0			0
$147$	10.2600	+	6.46012i	0.846228	+	0.532822i
$148$		0			0
$149$	1.32136	+	3.63041i	0.108250	+	0.297415i	0.981977	−	0.189003i	$-0.0605256\pi$
$149$	1.32136	+	3.63041i	0.108250	+	0.297415i	−0.873726	+	0.486418i	$0.838303\pi$
$150$		0			0
$151$	0.227371	+	1.28949i	0.0185032	+	0.104937i	0.992661	−	0.120933i	$-0.0385887\pi$
$151$	0.227371	+	1.28949i	0.0185032	+	0.104937i	−0.974157	+	0.225870i	$0.927478\pi$
$152$		0			0
$153$	9.47863	−	3.16381i	0.766302	−	0.255779i
$154$		0			0
$155$	12.0936	−	2.13244i	0.971385	−	0.171281i
$156$		0			0
$157$	−14.5617	+	17.3540i	−1.16215	+	1.38500i	−0.253555	+	0.967321i	$0.581600\pi$
$157$	−14.5617	+	17.3540i	−1.16215	+	1.38500i	−0.908596	+	0.417676i	$0.862845\pi$
$158$		0			0
$159$	7.60863	+	9.31944i	0.603404	+	0.739080i
$160$		0			0
$161$	5.54638	−	19.7151i	0.437116	−	1.55377i
$162$		0			0
$163$	8.18989	−	14.1853i	0.641481	−	1.11108i	−0.343621	−	0.939109i	$-0.611653\pi$
$163$	8.18989	−	14.1853i	0.641481	−	1.11108i	0.985102	−	0.171970i	$-0.0550132\pi$
$164$		0			0
$165$	−33.8329	+	5.49736i	−2.63389	+	0.427969i
$166$		0			0
$167$	10.1535	−	3.69558i	0.785704	−	0.285973i	0.0821551	−	0.996620i	$-0.473820\pi$
$167$	10.1535	−	3.69558i	0.785704	−	0.285973i	0.703549	+	0.710647i	$0.251597\pi$
$168$		0			0
$169$	−1.72404	−	9.77751i	−0.132618	−	0.752116i
$170$		0			0
$171$	5.26776	+	15.7820i	0.402836	+	1.20688i
$172$		0			0
$173$	−6.04200	+	5.06984i	−0.459365	+	0.385453i	−0.842897	−	0.538075i	$-0.819152\pi$
$173$	−6.04200	+	5.06984i	−0.459365	+	0.385453i	0.383533	+	0.923527i	$0.374707\pi$
$174$		0			0
$175$	21.5487	−	1.61546i	1.62893	−	0.122117i
$176$		0			0
$177$	9.92655	−	16.6712i	0.746125	−	1.25308i
$178$		0			0
$179$			18.3182i			1.36916i	0.728936	+	0.684582i	$0.240015\pi$
$179$			18.3182i			1.36916i	−0.728936	+	0.684582i	$0.759985\pi$
$180$		0			0
$181$	−12.1885	+	7.03703i	−0.905963	+	0.523058i	−0.879130	−	0.476582i	$-0.841876\pi$
$181$	−12.1885	+	7.03703i	−0.905963	+	0.523058i	−0.0268333	+	0.999640i	$0.508542\pi$
$182$		0			0
$183$	−3.54263	−	0.673930i	−0.261879	−	0.0498183i
$184$		0			0
$185$	4.70593	−	1.71282i	0.345987	−	0.125929i
$186$		0			0
$187$	17.8895	−	3.15440i	1.30821	−	0.230673i
$188$		0			0
$189$	10.8296	+	8.46876i	0.787737	+	0.616011i
$190$		0			0
$191$	−12.8418	+	2.26435i	−0.929197	+	0.163843i	−0.617708	−	0.786407i	$-0.711939\pi$
$191$	−12.8418	+	2.26435i	−0.929197	+	0.163843i	−0.311489	+	0.950250i	$0.600828\pi$
$192$		0			0
$193$	−9.60938	+	3.49753i	−0.691698	+	0.251758i	−0.663862	−	0.747855i	$-0.731084\pi$
$193$	−9.60938	+	3.49753i	−0.691698	+	0.251758i	−0.0278360	+	0.999613i	$0.508862\pi$
$194$		0			0
$195$	19.6533	−	22.7920i	1.40740	−	1.63217i
$196$		0			0
$197$	−3.72816	+	2.15245i	−0.265620	+	0.153356i	−0.626896	−	0.779103i	$-0.715675\pi$
$197$	−3.72816	+	2.15245i	−0.265620	+	0.153356i	0.361275	+	0.932459i	$0.382341\pi$
$198$		0			0
$199$		−	19.8295i		−	1.40568i	−0.711350	−	0.702838i	$-0.751916\pi$
$199$		−	19.8295i		−	1.40568i	0.711350	−	0.702838i	$-0.248084\pi$
$200$		0			0
$201$	16.8599	+	0.226865i	1.18920	+	0.0160018i
$202$		0			0
$203$	15.1470	+	7.29387i	1.06311	+	0.511929i
$204$		0			0
$205$	17.2232	−	14.4520i	1.20292	−	1.00937i
$206$		0			0
$207$	8.52690	−	21.6005i	0.592661	−	1.50134i
$208$		0			0
$209$	5.25210	+	29.7861i	0.363295	+	2.06035i
$210$		0			0
$211$	10.3867	−	3.78043i	0.715047	−	0.260256i	0.0412251	−	0.999150i	$-0.486874\pi$
$211$	10.3867	−	3.78043i	0.715047	−	0.260256i	0.673821	+	0.738894i	$0.264652\pi$
$212$		0			0
$213$	0.724893	−	1.91122i	0.0496689	−	0.130954i
$214$		0			0
$215$	−3.44830	+	5.97264i	−0.235172	+	0.407330i
$216$		0			0
$217$	−6.25198	−	6.40949i	−0.424412	−	0.435104i
$218$		0			0
$219$	−2.40326	+	6.33630i	−0.162397	+	0.428168i
$220$		0			0
$221$	−10.2522	+	12.2181i	−0.689635	+	0.821875i
$222$		0			0
$223$	10.1929	−	1.79728i	0.682567	−	0.120355i	0.178396	−	0.983959i	$-0.442909\pi$
$223$	10.1929	−	1.79728i	0.682567	−	0.120355i	0.504171	+	0.863604i	$0.331798\pi$
$224$		0			0
$225$	24.4937	+	0.659289i	1.63291	+	0.0439526i
$226$		0			0
$227$	−3.56670	−	20.2278i	−0.236730	−	1.34257i	−0.838939	−	0.544226i	$-0.816823\pi$
$227$	−3.56670	−	20.2278i	−0.236730	−	1.34257i	0.602208	−	0.798339i	$-0.294288\pi$
$228$		0			0
$229$	0.382724	+	1.05153i	0.0252911	+	0.0694867i	0.951696	−	0.307043i	$-0.0993395\pi$
$229$	0.382724	+	1.05153i	0.0252911	+	0.0694867i	−0.926405	+	0.376530i	$0.877117\pi$
$230$		0			0
$231$	17.2083	+	18.1234i	1.13222	+	1.19243i
$232$		0			0
$233$	2.76526	−	1.59653i	0.181159	−	0.104592i	−0.406678	−	0.913571i	$-0.633313\pi$
$233$	2.76526	−	1.59653i	0.181159	−	0.104592i	0.587837	+	0.808979i	$0.299980\pi$
$234$		0			0
$235$	−10.7593	+	18.6357i	−0.701862	+	1.21566i
$236$		0			0
$237$	−11.7247	+	4.08964i	−0.761600	+	0.265651i
$238$		0			0
$239$	−7.88449	−	1.39025i	−0.510006	−	0.0899277i	−0.0872770	−	0.996184i	$-0.527817\pi$
$239$	−7.88449	−	1.39025i	−0.510006	−	0.0899277i	−0.422729	+	0.906256i	$0.638928\pi$
$240$		0			0
$241$	−5.02001	+	13.7924i	−0.323367	+	0.888444i	0.666380	+	0.745612i	$0.267843\pi$
$241$	−5.02001	+	13.7924i	−0.323367	+	0.888444i	−0.989747	+	0.142831i	$0.954379\pi$
$242$		0			0
$243$	11.2408	+	10.8002i	0.721100	+	0.692831i
$244$		0			0
$245$	−15.8383	−	19.8584i	−1.01187	−	1.26871i
$246$		0			0
$247$	−20.3431	−	17.0699i	−1.29440	−	1.08613i
$248$		0			0
$249$	13.0251	+	11.2314i	0.825431	+	0.711762i
$250$		0			0
$251$	−12.8272	−	22.2173i	−0.809645	−	1.40235i	−0.913110	−	0.407713i	$-0.866326\pi$
$251$	−12.8272	−	22.2173i	−0.809645	−	1.40235i	0.103466	−	0.994633i	$-0.467007\pi$
$252$		0			0
$253$	21.1079	−	36.5600i	1.32704	−	2.29851i
$254$		0			0
$255$	−20.9332	−	0.281675i	−1.31089	−	0.0176392i
$256$		0			0
$257$	−0.877450	+	0.319366i	−0.0547338	+	0.0199215i	−0.369242	−	0.929333i	$-0.620383\pi$
$257$	−0.877450	+	0.319366i	−0.0547338	+	0.0199215i	0.314508	+	0.949255i	$0.398160\pi$
$258$		0			0
$259$	−2.96475	−	2.13139i	−0.184221	−	0.132438i
$260$		0			0
$261$	16.2463	+	9.97205i	1.00562	+	0.617254i
$262$		0			0
$263$	−10.6594	−	12.7034i	−0.657287	−	0.783324i	0.329707	−	0.944083i	$-0.393050\pi$
$263$	−10.6594	−	12.7034i	−0.657287	−	0.783324i	−0.986994	+	0.160759i	$0.948606\pi$
$264$		0			0
$265$	−8.62069	−	23.6852i	−0.529565	−	1.45497i
$266$		0			0
$267$	−1.85314	−	11.4050i	−0.113410	−	0.697973i
$268$		0			0
$269$	−1.93665	−	3.35438i	−0.118080	−	0.204520i	0.800927	−	0.598762i	$-0.204341\pi$
$269$	−1.93665	−	3.35438i	−0.118080	−	0.204520i	−0.919007	+	0.394242i	$0.871007\pi$
$270$		0			0
$271$	24.5867	+	14.1952i	1.49354	+	0.862295i	0.999973	−	0.00741404i	$-0.00235998\pi$
$271$	24.5867	+	14.1952i	1.49354	+	0.862295i	0.493566	+	0.869709i	$0.335693\pi$
$272$		0			0
$273$	−21.8027	−	2.47778i	−1.31956	−	0.149962i
$274$		0			0
$275$	43.8659	+	7.73474i	2.64521	+	0.466422i
$276$		0			0
$277$	6.59930	−	5.53747i	0.396513	−	0.332714i	−0.422631	−	0.906302i	$-0.638893\pi$
$277$	6.59930	−	5.53747i	0.396513	−	0.332714i	0.819144	+	0.573588i	$0.194449\pi$
$278$		0			0
$279$	−6.31430	−	7.95008i	−0.378028	−	0.475959i
$280$		0			0
$281$	3.95484	−	10.8658i	0.235926	−	0.648201i	−0.764070	−	0.645134i	$-0.776802\pi$
$281$	3.95484	−	10.8658i	0.235926	−	0.648201i	0.999995	−	0.00306676i	$-0.000976183\pi$
$282$		0			0
$283$	−6.43295	−	1.13430i	−0.382399	−	0.0674273i	−0.0208556	−	0.999782i	$-0.506639\pi$
$283$	−6.43295	−	1.13430i	−0.382399	−	0.0674273i	−0.361544	+	0.932355i	$0.617750\pi$
$284$		0			0
$285$	0.468990	−	34.8538i	0.0277806	−	2.06456i
$286$		0			0
$287$	−15.7804	−	4.43944i	−0.931487	−	0.262052i
$288$		0			0
$289$	−5.90510			−0.347359
$290$		0			0
$291$	−19.3934	−	3.68928i	−1.13686	−	0.216269i
$292$		0			0
$293$	2.53946	−	14.4020i	0.148357	−	0.841372i	−0.816254	−	0.577693i	$-0.803953\pi$
$293$	2.53946	−	14.4020i	0.148357	−	0.841372i	0.964611	−	0.263679i	$-0.0849359\pi$
$294$		0			0
$295$	−31.1392	+	26.1289i	−1.81299	+	1.52128i
$296$		0			0
$297$	17.3244	+	22.4255i	1.00526	+	1.30126i
$298$		0			0
$299$	6.43646	+	36.5030i	0.372230	+	2.11102i
$300$		0			0
$301$	5.01436	−	0.375915i	0.289023	−	0.0216674i
$302$		0			0
$303$	−0.459186	−	0.395952i	−0.0263795	−	0.0227469i
$304$		0			0
$305$	6.54286	+	3.77752i	0.374643	+	0.216300i
$306$		0			0
$307$	7.18349	+	4.14739i	0.409984	+	0.236704i	0.690783	−	0.723062i	$-0.257266\pi$
$307$	7.18349	+	4.14739i	0.409984	+	0.236704i	−0.280799	+	0.959767i	$0.590599\pi$
$308$		0			0
$309$	−0.377289	+	28.0389i	−0.0214632	+	1.59508i
$310$		0			0
$311$	3.30946	−	18.7689i	0.187662	−	1.06429i	−0.734825	−	0.678257i	$-0.762736\pi$
$311$	3.30946	−	18.7689i	0.187662	−	1.06429i	0.922487	−	0.386028i	$-0.126153\pi$
$312$		0			0
$313$	−7.42127	−	8.84433i	−0.419475	−	0.499911i	0.514380	−	0.857562i	$-0.328022\pi$
$313$	−7.42127	−	8.84433i	−0.419475	−	0.499911i	−0.933855	+	0.357651i	$0.883578\pi$
$314$		0			0
$315$	−15.5792	−	24.2248i	−0.877789	−	1.36491i
$316$		0			0
$317$	−6.33640	+	17.4091i	−0.355888	+	0.977793i	0.624554	+	0.780982i	$0.285281\pi$
$317$	−6.33640	+	17.4091i	−0.355888	+	0.977793i	−0.980441	+	0.196811i	$0.936941\pi$
$318$		0			0
$319$	26.5461	+	22.2748i	1.48629	+	1.24715i
$320$		0			0
$321$	−1.56318	+	4.12141i	−0.0872483	+	0.230034i
$322$		0			0
$323$			18.4731i			1.02787i
$324$		0			0
$325$	−33.8694	+	19.5545i	−1.87873	+	1.08469i
$326$		0			0
$327$	7.86804	−	6.42367i	0.435104	−	0.355230i
$328$		0			0
$329$	15.6457	−	1.17293i	0.862577	−	0.0646655i
$330$		0			0
$331$	21.9733	+	7.99762i	1.20776	+	0.439589i	0.865926	−	0.500172i	$-0.166730\pi$
$331$	21.9733	+	7.99762i	1.20776	+	0.439589i	0.341834	+	0.939760i	$0.388952\pi$
$332$		0			0
$333$	−3.09888	−	2.74569i	−0.169817	−	0.150463i
$334$		0			0
$335$	−33.1948	−	12.0819i	−1.81363	−	0.660107i
$336$		0			0
$337$	−19.4319	−	16.3053i	−1.05852	−	0.888207i	−0.0645595	−	0.997914i	$-0.520564\pi$
$337$	−19.4319	−	16.3053i	−1.05852	−	0.888207i	−0.993964	+	0.109707i	$0.965009\pi$
$338$		0			0
$339$	−15.8890	+	8.89062i	−0.862969	+	0.482872i
$340$		0			0
$341$	−9.22803	−	15.9834i	−0.499726	−	0.865551i
$342$		0			0
$343$	−5.45746	+	17.6979i	−0.294675	+	0.955597i
$344$		0			0
$345$	−31.7717	+	36.8456i	−1.71053	+	1.98370i
$346$		0			0
$347$	−9.46873	−	26.0151i	−0.508308	−	1.39657i	−0.882981	−	0.469408i	$-0.844467\pi$
$347$	−9.46873	−	26.0151i	−0.508308	−	1.39657i	0.374673	−	0.927157i	$-0.377755\pi$
$348$		0			0
$349$	14.4724	+	17.2475i	0.774690	+	0.923240i	0.998681	−	0.0513514i	$-0.0163529\pi$
$349$	14.4724	+	17.2475i	0.774690	+	0.923240i	−0.223990	+	0.974591i	$0.571908\pi$
$350$		0			0
$351$	−24.3087	−	5.30583i	−1.29750	−	0.283204i
$352$		0			0
$353$	21.0176	+	7.64979i	1.11866	+	0.407157i	0.834161	−	0.551520i	$-0.185952\pi$
$353$	21.0176	+	7.64979i	1.11866	+	0.407157i	0.284494	+	0.958678i	$0.408174\pi$
$354$		0			0
$355$	−2.75267	+	3.28051i	−0.146097	+	0.174111i
$356$		0			0
$357$	8.42847	+	12.7261i	0.446082	+	0.673537i
$358$		0			0
$359$			12.2285i			0.645394i	0.946502	+	0.322697i	$0.104590\pi$
$359$			12.2285i			0.645394i	−0.946502	+	0.322697i	$0.895410\pi$
$360$		0			0
$361$	−11.7577			−0.618828
$362$		0			0
$363$	15.8514	+	28.3289i	0.831981	+	1.48688i
$364$		0			0
$365$	9.12600	−	10.8759i	0.477677	−	0.569273i
$366$		0			0
$367$	−11.3381	+	1.99921i	−0.591843	+	0.104358i	−0.461545	−	0.887117i	$-0.652705\pi$
$367$	−11.3381	+	1.99921i	−0.591843	+	0.104358i	−0.130298	+	0.991475i	$0.541594\pi$
$368$		0			0
$369$	−17.2895	−	6.82511i	−0.900056	−	0.355301i
$370$		0			0
$371$	−10.7274	+	14.9217i	−0.556937	+	0.774698i
$372$		0			0
$373$	3.57680	−	20.2850i	0.185199	−	1.05032i	−0.740499	−	0.672057i	$-0.765411\pi$
$373$	3.57680	−	20.2850i	0.185199	−	1.05032i	0.925699	−	0.378261i	$-0.123478\pi$
$374$		0			0
$375$	−18.6143	−	7.06009i	−0.961236	−	0.364581i
$376$		0			0
$377$	−30.4262			−1.56703
$378$		0			0
$379$	−23.0701			−1.18503			−0.592516	−	0.805559i	$-0.701865\pi$
$379$	−23.0701			−1.18503			−0.592516	+	0.805559i	$0.701865\pi$
$380$		0			0
$381$	15.5617	−	12.7050i	0.797250	−	0.650895i
$382$		0			0
$383$	1.26488	−	7.17350i	0.0646324	−	0.366549i	−0.935287	−	0.353889i	$-0.884859\pi$
$383$	1.26488	−	7.17350i	0.0646324	−	0.366549i	0.999920	−	0.0126597i	$-0.00402981\pi$
$384$		0			0
$385$	−21.5357	−	47.7244i	−1.09756	−	2.43226i
$386$		0			0
$387$	5.69964	+	0.153416i	0.289729	+	0.00779855i
$388$		0			0
$389$	−16.3643	+	2.88546i	−0.829701	+	0.146299i	−0.572340	−	0.820017i	$-0.693964\pi$
$389$	−16.3643	+	2.88546i	−0.829701	+	0.146299i	−0.257361	+	0.966315i	$0.582853\pi$
$390$		0			0
$391$	16.5737	−	19.7518i	0.838168	−	0.998890i
$392$		0			0
$393$	−1.36759	+	2.29680i	−0.0689857	+	0.115858i
$394$		0			0
$395$	26.0150			1.30896
$396$		0			0
$397$		−	33.8573i		−	1.69925i	−0.527387	−	0.849625i	$-0.676828\pi$
$397$		−	33.8573i		−	1.69925i	0.527387	−	0.849625i	$-0.323172\pi$
$398$		0			0
$399$	−21.1890	+	14.0334i	−1.06078	+	0.702551i
$400$		0			0
$401$	18.6906	−	22.2746i	0.933364	−	1.11234i	−0.0600993	−	0.998192i	$-0.519142\pi$
$401$	18.6906	−	22.2746i	0.933364	−	1.11234i	0.993464	−	0.114148i	$-0.0364138\pi$
$402$		0			0
$403$	15.2274	+	5.54232i	0.758531	+	0.276083i
$404$		0			0
$405$	−14.7841	−	29.1204i	−0.734626	−	1.44701i
$406$		0			0
$407$	−4.83794	−	5.76564i	−0.239808	−	0.285792i
$408$		0			0
$409$	1.79133	+	4.92163i	0.0885754	+	0.243359i	0.976069	−	0.217461i	$-0.0697776\pi$
$409$	1.79133	+	4.92163i	0.0885754	+	0.243359i	−0.887494	+	0.460820i	$0.847555\pi$
$410$		0			0
$411$	−2.52806	−	0.480923i	−0.124700	−	0.0237222i
$412$		0			0
$413$	28.5306	+	8.02640i	1.40390	+	0.394953i
$414$		0			0
$415$	−18.0160	−	31.2046i	−0.884371	−	1.53177i
$416$		0			0
$417$	0.409096	−	30.4027i	0.0200335	−	1.48882i
$418$		0			0
$419$	10.1018	+	8.47646i	0.493507	+	0.414102i	0.855281	−	0.518164i	$-0.173384\pi$
$419$	10.1018	+	8.47646i	0.493507	+	0.414102i	−0.361774	+	0.932266i	$0.617829\pi$
$420$		0			0
$421$	15.3884	+	5.60092i	0.749985	+	0.272972i	0.688599	−	0.725142i	$-0.258226\pi$
$421$	15.3884	+	5.60092i	0.749985	+	0.272972i	0.0613855	+	0.998114i	$0.480448\pi$
$422$		0			0
$423$	17.7839	+	0.478685i	0.864685	+	0.0232745i
$424$		0			0
$425$	25.5645	+	9.30472i	1.24006	+	0.451345i
$426$		0			0
$427$	−0.411805	−	5.49309i	−0.0199286	−	0.265829i
$428$		0			0
$429$	−42.2909	−	16.0402i	−2.04182	−	0.774430i
$430$		0			0
$431$	8.99505	−	5.19329i	0.433276	−	0.250152i	−0.267465	−	0.963568i	$-0.586186\pi$
$431$	8.99505	−	5.19329i	0.433276	−	0.250152i	0.700741	+	0.713415i	$0.252853\pi$
$432$		0			0
$433$		−	31.5263i		−	1.51506i	−0.652802	−	0.757528i	$-0.726407\pi$
$433$		−	31.5263i		−	1.51506i	0.652802	−	0.757528i	$-0.273593\pi$
$434$		0			0
$435$	−25.2569	−	30.9360i	−1.21098	−	1.48327i
$436$		0			0
$437$	32.8868	+	27.5953i	1.57319	+	1.32006i
$438$		0			0
$439$	−10.9952	+	30.2091i	−0.524773	+	1.44180i	0.340376	+	0.940289i	$0.389446\pi$
$439$	−10.9952	+	30.2091i	−0.524773	+	1.44180i	−0.865150	+	0.501514i	$0.832777\pi$
$440$		0			0
$441$	−8.19429	+	19.3353i	−0.390204	+	0.920728i
$442$		0			0
$443$	−10.5359	−	12.5562i	−0.500574	−	0.596561i	0.455300	−	0.890338i	$-0.349532\pi$
$443$	−10.5359	−	12.5562i	−0.500574	−	0.596561i	−0.955874	+	0.293777i	$0.905088\pi$
$444$		0			0
$445$	−4.20353	+	23.8394i	−0.199266	+	1.13010i
$446$		0			0
$447$	−5.83959	+	3.26753i	−0.276203	+	0.154549i
$448$		0			0
$449$	−27.4796	−	15.8654i	−1.29684	−	0.748733i	−0.316986	−	0.948430i	$-0.602671\pi$
$449$	−27.4796	−	15.8654i	−1.29684	−	0.748733i	−0.979858	+	0.199697i	$0.936004\pi$
$450$		0			0
$451$	−29.2634	−	16.8952i	−1.37796	−	0.795565i
$452$		0			0
$453$	−2.14138	+	0.746926i	−0.100611	+	0.0350937i
$454$		0			0
$455$	41.4193	+	19.9451i	1.94177	+	0.935039i
$456$		0			0
$457$	−6.52474	−	37.0037i	−0.305215	−	1.73096i	−0.622493	−	0.782626i	$-0.713880\pi$
$457$	−6.52474	−	37.0037i	−0.305215	−	1.73096i	0.317278	−	0.948333i	$-0.397231\pi$
$458$		0			0
$459$	8.04201	+	15.3261i	0.375369	+	0.715360i
$460$		0			0
$461$	18.5831	−	15.5931i	0.865504	−	0.726244i	−0.0976428	−	0.995222i	$-0.531130\pi$
$461$	18.5831	−	15.5931i	0.865504	−	0.726244i	0.963146	+	0.268978i	$0.0866858\pi$
$462$		0			0
$463$	3.22506	−	18.2902i	0.149881	−	0.850019i	−0.813436	−	0.581654i	$-0.802406\pi$
$463$	3.22506	−	18.2902i	0.149881	−	0.850019i	0.963317	−	0.268364i	$-0.0864831\pi$
$464$		0			0
$465$	7.00517	+	20.0833i	0.324857	+	0.931340i
$466$		0			0
$467$	−0.199729			−0.00924236			−0.00462118	−	0.999989i	$-0.501471\pi$
$467$	−0.199729			−0.00924236			−0.00462118	+	0.999989i	$0.501471\pi$
$468$		0			0
$469$	6.35623	+	24.9596i	0.293503	+	1.15253i
$470$		0			0
$471$	−33.7139	−	20.0744i	−1.55346	−	0.924978i
$472$		0			0
$473$	10.2075	+	1.79986i	0.469342	+	0.0827577i
$474$		0			0
$475$	−15.4924	+	42.5650i	−0.710840	+	1.95302i
$476$		0			0
$477$	−13.8192	+	15.5968i	−0.632737	+	0.714128i
$478$		0			0
$479$	10.0571	−	8.43895i	0.459523	−	0.385585i	−0.383433	−	0.923569i	$-0.625258\pi$
$479$	10.0571	−	8.43895i	0.459523	−	0.385585i	0.842955	+	0.537983i	$0.180814\pi$
$480$		0			0
$481$	6.50797	+	1.14753i	0.296738	+	0.0523229i
$482$		0			0
$483$	35.2463	+	4.00559i	1.60376	+	0.182261i
$484$		0			0
$485$	35.8174	+	20.6792i	1.62639	+	0.938994i
$486$		0			0
$487$	−15.3472	−	26.5821i	−0.695448	−	1.20455i	−0.970030	−	0.242987i	$-0.921873\pi$
$487$	−15.3472	−	26.5821i	−0.695448	−	1.20455i	0.274582	−	0.961564i	$-0.411461\pi$
$488$		0			0
$489$	26.5267	+	10.0611i	1.19958	+	0.454980i
$490$		0			0
$491$	−6.76951	−	18.5991i	−0.305504	−	0.839365i	−0.993519	−	0.113668i	$-0.963740\pi$
$491$	−6.76951	−	18.5991i	−0.305504	−	0.839365i	0.688015	−	0.725696i	$-0.258482\pi$
$492$		0			0
$493$	13.6047	+	16.2135i	0.612726	+	0.730219i
$494$		0			0
$495$	−18.7969	−	56.3146i	−0.844857	−	2.53115i
$496$		0			0
$497$	3.10686	+	0.310801i	0.139362	+	0.0139413i
$498$		0			0
$499$	−17.8458	+	6.49533i	−0.798887	+	0.290771i	−0.709025	−	0.705183i	$-0.750865\pi$
$499$	−17.8458	+	6.49533i	−0.798887	+	0.290771i	−0.0898617	+	0.995954i	$0.528643\pi$
$500$		0			0
$501$	9.13863	+	16.3322i	0.408284	+	0.729668i
$502$		0			0
$503$	5.81026	−	10.0637i	0.259067	−	0.448717i	−0.706925	−	0.707288i	$-0.749918\pi$
$503$	5.81026	−	10.0637i	0.259067	−	0.448717i	0.965992	+	0.258571i	$0.0832517\pi$
$504$		0			0
$505$	0.635136	+	1.10009i	0.0282632	+	0.0489533i
$506$		0			0
$507$	16.2370	−	5.66356i	0.721110	−	0.251528i
$508$		0			0
$509$	−0.957091	−	0.803094i	−0.0424223	−	0.0355965i	0.621330	−	0.783549i	$-0.286593\pi$
$509$	−0.957091	−	0.803094i	−0.0424223	−	0.0355965i	−0.663752	+	0.747952i	$0.731037\pi$
$510$		0			0
$511$	−10.3003	−	1.03041i	−0.455656	−	0.0455824i
$512$		0			0
$513$	−25.5180	+	13.3900i	−1.12665	+	0.591182i
$514$		0			0
$515$	20.0929	−	55.2049i	0.885400	−	2.43262i
$516$		0			0
$517$	31.8494	+	5.61590i	1.40073	+	0.246987i
$518$		0			0
$519$	−10.3460	−	8.92123i	−0.454137	−	0.391598i
$520$		0			0
$521$	−15.1411	+	26.2251i	−0.663342	+	1.14894i	0.316390	+	0.948629i	$0.397529\pi$
$521$	−15.1411	+	26.2251i	−0.663342	+	1.14894i	−0.979732	+	0.200313i	$0.935804\pi$
$522$		0			0
$523$	33.3913	−	19.2785i	1.46010	−	0.842989i	0.461085	−	0.887356i	$-0.347460\pi$
$523$	33.3913	−	19.2785i	1.46010	−	0.842989i	0.999015	+	0.0443672i	$0.0141271\pi$
$524$		0			0
$525$	8.74787	+	36.3916i	0.381788	+	1.58826i
$526$		0			0
$527$	−3.85538	−	10.5926i	−0.167943	−	0.461420i
$528$		0			0
$529$	−6.41130	−	36.3603i	−0.278752	−	1.58088i
$530$		0			0
$531$	31.2590	+	12.3396i	1.35653	+	0.535495i
$532$		0			0
$533$	29.2177	−	5.15187i	1.26556	−	0.223152i
$534$		0			0
$535$	5.93595	−	7.07419i	0.256633	−	0.305844i
$536$		0			0
$537$	−31.3173	+	5.08860i	−1.35144	+	0.219589i
$538$		0			0
$539$	−19.9042	+	32.5758i	−0.857333	+	1.40314i
$540$		0			0
$541$	−16.4143	+	28.4305i	−0.705707	+	1.22232i	0.260728	+	0.965412i	$0.416037\pi$
$541$	−16.4143	+	28.4305i	−0.705707	+	1.22232i	−0.966436	+	0.256909i	$0.917296\pi$
$542$		0			0
$543$	−15.4166	−	18.8830i	−0.661588	−	0.810347i
$544$		0			0
$545$	−19.9965	+	7.27811i	−0.856554	+	0.311760i
$546$		0			0
$547$	2.00894	+	11.3933i	0.0858961	+	0.487141i	0.997160	+	0.0753172i	$0.0239969\pi$
$547$	2.00894	+	11.3933i	0.0858961	+	0.487141i	−0.911264	+	0.411824i	$0.864892\pi$
$548$		0			0
$549$	0.168062	−	6.24380i	0.00717273	−	0.266479i
$550$		0			0
$551$	−26.9955	+	22.6519i	−1.15005	+	0.965005i
$552$		0			0
$553$	−10.6855	−	15.6718i	−0.454393	−	0.666432i
$554$		0			0
$555$	4.23555	+	7.56959i	0.179789	+	0.321311i
$556$		0			0
$557$			32.9309i			1.39533i	0.716426	+	0.697663i	$0.245777\pi$
$557$			32.9309i			1.39533i	−0.716426	+	0.697663i	$0.754223\pi$
$558$		0			0
$559$	−7.88135	+	4.55030i	−0.333345	+	0.192457i
$560$		0			0
$561$	10.3624	+	29.7082i	0.437501	+	1.25428i
$562$		0			0
$563$	−32.2541	+	11.7395i	−1.35935	+	0.494763i	−0.915853	−	0.401513i	$-0.868484\pi$
$563$	−32.2541	+	11.7395i	−1.35935	+	0.494763i	−0.443497	+	0.896276i	$0.646262\pi$
$564$		0			0
$565$	37.5652	−	6.62376i	1.58038	−	0.278664i
$566$		0			0
$567$	−11.4701	+	20.8671i	−0.481698	+	0.876337i
$568$		0			0
$569$	30.0162	−	5.29267i	1.25835	−	0.221880i	0.495584	−	0.868560i	$-0.334954\pi$
$569$	30.0162	−	5.29267i	1.25835	−	0.221880i	0.762762	+	0.646679i	$0.223843\pi$
$570$		0			0
$571$	2.68710	−	0.978023i	0.112452	−	0.0409290i	−0.285182	−	0.958474i	$-0.592054\pi$
$571$	2.68710	−	0.978023i	0.112452	−	0.0409290i	0.397633	+	0.917545i	$0.369832\pi$
$572$		0			0
$573$	−7.43851	−	21.3256i	−0.310748	−	0.890891i
$574$		0			0
$575$	54.7534	−	31.6119i	2.28337	−	1.31831i
$576$		0			0
$577$		−	14.5845i		−	0.607162i	−0.952806	−	0.303581i	$-0.901818\pi$
$577$		−	14.5845i		−	0.607162i	0.952806	−	0.303581i	$-0.0981823\pi$
$578$		0			0
$579$	−8.64887	−	15.4569i	−0.359435	−	0.642367i
$580$		0			0
$581$	−11.3981	+	23.6702i	−0.472874	+	0.982003i
$582$		0			0
$583$	−29.0187	+	24.3496i	−1.20183	+	1.00846i
$584$		0			0
$585$	44.4253	+	27.2685i	1.83676	+	1.12742i
$586$		0			0
$587$	−1.69475	−	9.61138i	−0.0699497	−	0.396704i	−0.999601	−	0.0282626i	$-0.991003\pi$
$587$	−1.69475	−	9.61138i	−0.0699497	−	0.396704i	0.929651	−	0.368442i	$-0.120109\pi$
$588$		0			0
$589$	17.6367	−	6.41922i	0.726707	−	0.264500i
$590$		0			0
$591$	−4.71554	−	5.77584i	−0.193972	−	0.237586i
$592$		0			0
$593$	−8.66155	+	15.0022i	−0.355687	+	0.616068i	−0.987235	−	0.159269i	$-0.949086\pi$
$593$	−8.66155	+	15.0022i	−0.355687	+	0.616068i	0.631548	+	0.775337i	$0.282420\pi$
$594$		0			0
$595$	−7.89188	−	30.9897i	−0.323536	−	1.27046i
$596$		0			0
$597$	33.9011	−	5.50844i	1.38748	−	0.225445i
$598$		0			0
$599$	−15.1161	+	18.0147i	−0.617628	+	0.736060i	−0.980661	−	0.195716i	$-0.937297\pi$
$599$	−15.1161	+	18.0147i	−0.617628	+	0.736060i	0.363033	+	0.931776i	$0.381741\pi$
$600$		0			0
$601$	0.356342	−	0.0628327i	0.0145355	−	0.00256300i	−0.166376	−	0.986062i	$-0.553206\pi$
$601$	0.356342	−	0.0628327i	0.0145355	−	0.00256300i	0.180911	+	0.983499i	$0.442095\pi$
$602$		0			0
$603$	4.29565	+	28.8871i	0.174932	+	1.17638i
$604$		0			0
$605$	−11.8097	−	66.9762i	−0.480133	−	2.72297i
$606$		0			0
$607$	2.83802	+	7.79739i	0.115192	+	0.316486i	0.983869	−	0.178893i	$-0.0572515\pi$
$607$	2.83802	+	7.79739i	0.115192	+	0.316486i	−0.868677	+	0.495379i	$0.835029\pi$
$608$		0			0
$609$	−8.26214	+	27.9218i	−0.334799	+	1.13145i
$610$		0			0
$611$	−24.5913	+	14.1978i	−0.994856	+	0.574380i
$612$		0			0
$613$	−13.1528	+	22.7813i	−0.531236	+	0.920127i	0.468100	+	0.883676i	$0.344939\pi$
$613$	−13.1528	+	22.7813i	−0.531236	+	0.920127i	−0.999335	+	0.0364515i	$0.988395\pi$
$614$		0			0
$615$	29.4920	+	25.4307i	1.18923	+	1.02547i
$616$		0			0
$617$	5.77193	+	1.01775i	0.232369	+	0.0409730i	0.288620	−	0.957444i	$-0.406804\pi$
$617$	5.77193	+	1.01775i	0.232369	+	0.0409730i	−0.0562509	+	0.998417i	$0.517915\pi$
$618$		0			0
$619$	6.60976	−	18.1602i	0.265669	−	0.729919i	−0.733091	−	0.680131i	$-0.761923\pi$
$619$	6.60976	−	18.1602i	0.265669	−	0.729919i	0.998760	−	0.0497885i	$-0.0158547\pi$
$620$		0			0
$621$	39.2976	+	8.57743i	1.57696	+	0.344200i
$622$		0			0
$623$	16.0877	−	7.25961i	0.644542	−	0.290850i
$624$		0			0
$625$	0.667031	+	0.559705i	0.0266812	+	0.0223882i
$626$		0			0
$627$	−49.4643	+	17.2534i	−1.97541	+	0.689036i
$628$		0			0
$629$	−2.29847	−	3.98107i	−0.0916462	−	0.158736i
$630$		0			0
$631$	−5.39911	+	9.35153i	−0.214935	+	0.372279i	−0.953252	−	0.302175i	$-0.902287\pi$
$631$	−5.39911	+	9.35153i	−0.214935	+	0.372279i	0.738317	+	0.674453i	$0.235621\pi$
$632$		0			0
$633$	9.34845	+	16.7072i	0.371567	+	0.664050i
$634$		0			0
$635$	−39.5497	+	14.3949i	−1.56948	+	0.571245i
$636$		0			0
$637$	−4.99752	−	33.1438i	−0.198009	−	1.31321i
$638$		0			0
$639$	3.46884	+	0.708382i	0.137225	+	0.0280231i
$640$		0			0
$641$	4.57485	+	5.45210i	0.180696	+	0.215345i	0.848788	−	0.528734i	$-0.177333\pi$
$641$	4.57485	+	5.45210i	0.180696	+	0.215345i	−0.668092	+	0.744079i	$0.732889\pi$
$642$		0			0
$643$	−13.7176	−	37.6889i	−0.540971	−	1.48630i	−0.845591	−	0.533831i	$-0.820752\pi$
$643$	−13.7176	−	37.6889i	−0.540971	−	1.48630i	0.304621	−	0.952474i	$-0.401470\pi$
$644$		0			0
$645$	−11.1689	−	4.23618i	−0.439775	−	0.166799i
$646$		0			0
$647$	9.02415	+	15.6303i	0.354776	+	0.614490i	0.987080	−	0.160231i	$-0.0512239\pi$
$647$	9.02415	+	15.6303i	0.354776	+	0.614490i	−0.632304	+	0.774721i	$0.717891\pi$
$648$		0			0
$649$	52.9075	+	30.5462i	2.07680	+	1.19904i
$650$		0			0
$651$	9.22111	−	12.4691i	0.361404	−	0.488701i
$652$		0			0
$653$	−1.86090	−	0.328127i	−0.0728226	−	0.0128406i	0.137118	−	0.990555i	$-0.456216\pi$
$653$	−1.86090	−	0.328127i	−0.0728226	−	0.0128406i	−0.209941	+	0.977714i	$0.567327\pi$
$654$		0			0
$655$	4.29007	−	3.59980i	0.167627	−	0.140656i
$656$		0			0
$657$	−11.5003	−	2.34852i	−0.448671	−	0.0916244i
$658$		0			0
$659$	−7.91790	+	21.7542i	−0.308438	+	0.847425i	0.684524	+	0.728990i	$0.260010\pi$
$659$	−7.91790	+	21.7542i	−0.308438	+	0.847425i	−0.992962	+	0.118435i	$0.962212\pi$
$660$		0			0
$661$	−15.6928	−	2.76706i	−0.610378	−	0.107626i	−0.140089	−	0.990139i	$-0.544739\pi$
$661$	−15.6928	−	2.76706i	−0.610378	−	0.107626i	−0.470288	+	0.882513i	$0.655850\pi$
$662$		0			0
$663$	−23.7363	−	14.1333i	−0.921841	−	0.548894i
$664$		0			0
$665$	51.5981	−	13.1400i	2.00089	−	0.509548i
$666$		0			0
$667$	49.1871			1.90453
$668$		0			0
$669$	5.90418	+	16.9268i	0.228269	+	0.654429i
$670$		0			0
$671$	1.97170	−	11.1821i	0.0761166	−	0.431679i
$672$		0			0
$673$	−24.9316	+	20.9201i	−0.961043	+	0.806411i	−0.981122	−	0.193387i	$-0.938053\pi$
$673$	−24.9316	+	20.9201i	−0.961043	+	0.806411i	0.0200793	+	0.999798i	$0.493608\pi$
$674$		0			0
$675$	5.67696	+	42.0583i	0.218506	+	1.61882i
$676$		0			0
$677$	−6.21630	−	35.2544i	−0.238912	−	1.35494i	−0.834217	−	0.551436i	$-0.814080\pi$
$677$	−6.21630	−	35.2544i	−0.238912	−	1.35494i	0.595306	−	0.803499i	$-0.297031\pi$
$678$		0			0
$679$	−2.25433	−	30.0707i	−0.0865134	−	1.15401i
$680$		0			0
$681$	33.5912	−	11.7168i	1.28722	−	0.448989i
$682$		0			0
$683$	21.7726	+	12.5704i	0.833105	+	0.480993i	0.854915	−	0.518769i	$-0.173609\pi$
$683$	21.7726	+	12.5704i	0.833105	+	0.480993i	−0.0218096	+	0.999762i	$0.506943\pi$
$684$		0			0
$685$	4.66904	+	2.69567i	0.178395	+	0.102996i
$686$		0			0
$687$	−1.69140	+	0.946419i	−0.0645310	+	0.0361081i
$688$		0			0
$689$	5.77557	−	32.7549i	0.220032	−	1.24786i
$690$		0			0
$691$	17.8024	+	21.2160i	0.677234	+	0.807096i	0.989749	−	0.142817i	$-0.0456161\pi$
$691$	17.8024	+	21.2160i	0.677234	+	0.807096i	−0.312515	+	0.949913i	$0.601172\pi$
$692$		0			0
$693$	−26.2040	+	34.4543i	−0.995407	+	1.30881i
$694$		0			0
$695$	−21.7868	+	59.8588i	−0.826421	+	2.27057i
$696$		0			0
$697$	−15.8097	−	13.2659i	−0.598836	−	0.502483i
$698$		0			0
$699$	3.49763	+	4.28408i	0.132293	+	0.162039i
$700$		0			0
$701$		−	36.4801i		−	1.37783i	−0.724840	−	0.688917i	$-0.758087\pi$
$701$		−	36.4801i		−	1.37783i	0.724840	−	0.688917i	$-0.241913\pi$
$702$		0			0
$703$	6.62851	−	3.82697i	0.249999	−	0.144337i
$704$		0			0
$705$	−34.8490	−	13.2177i	−1.31249	−	0.497806i
$706$		0			0
$707$	0.401830	−	0.834468i	0.0151124	−	0.0313834i
$708$		0			0
$709$	−45.4492	−	16.5422i	−1.70688	−	0.621254i	−0.710301	−	0.703898i	$-0.751441\pi$
$709$	−45.4492	−	16.5422i	−1.70688	−	0.621254i	−0.996579	+	0.0826445i	$0.973663\pi$
$710$		0			0
$711$	−10.2488	−	18.9088i	−0.384359	−	0.709135i
$712$		0			0
$713$	−24.6167	−	8.95975i	−0.921903	−	0.335545i
$714$		0			0
$715$	72.5901	+	60.9104i	2.71472	+	2.27792i
$716$		0			0
$717$	0.186576	−	13.8658i	0.00696783	−	0.517826i
$718$		0			0
$719$	12.5049	+	21.6590i	0.466352	+	0.807746i	0.999261	−	0.0384266i	$-0.0122346\pi$
$719$	12.5049	+	21.6590i	0.466352	+	0.807746i	−0.532909	+	0.846173i	$0.678901\pi$
$720$		0			0
$721$	−41.5092	+	10.5708i	−1.54588	+	0.393676i
$722$		0			0
$723$	−24.9743	−	4.75097i	−0.928805	−	0.176691i
$724$		0			0
$725$	17.7502	+	48.7682i	0.659225	+	1.81121i
$726$		0			0
$727$	−24.6457	−	29.3716i	−0.914058	−	1.08933i	−0.995697	−	0.0926696i	$-0.970460\pi$
$727$	−24.6457	−	29.3716i	−0.914058	−	1.08933i	0.0816392	−	0.996662i	$-0.473984\pi$
$728$		0			0
$729$	−15.3417	+	22.2179i	−0.568210	+	0.822883i
$730$		0			0
$731$	5.94882	+	2.16519i	0.220025	+	0.0800826i
$732$		0			0
$733$	6.65784	−	7.93450i	0.245913	−	0.293067i	−0.628942	−	0.777452i	$-0.716512\pi$
$733$	6.65784	−	7.93450i	0.245913	−	0.293067i	0.874855	+	0.484384i	$0.160956\pi$
$734$		0			0
$735$	29.5507	−	32.5942i	1.09000	−	1.20225i
$736$		0			0
$737$			53.0907i			1.95562i
$738$		0			0
$739$	26.9803			0.992486			0.496243	−	0.868184i	$-0.334713\pi$
$739$	26.9803			0.992486			0.496243	+	0.868184i	$0.334713\pi$
$740$		0			0
$741$	23.5321	−	39.5210i	0.864473	−	1.45184i
$742$		0			0
$743$	−3.94022	+	4.69577i	−0.144553	+	0.172271i	−0.833463	−	0.552576i	$-0.813645\pi$
$743$	−3.94022	+	4.69577i	−0.144553	+	0.172271i	0.688910	+	0.724847i	$0.258089\pi$
$744$		0			0
$745$	13.8062	−	2.43440i	0.505819	−	0.0891895i
$746$		0			0
$747$	−15.5833	+	25.3880i	−0.570164	+	0.928899i
$748$		0			0
$749$	−6.69973	−	0.670220i	−0.244803	−	0.0244893i
$750$		0			0
$751$	0.534990	−	3.03408i	0.0195221	−	0.110715i	−0.973490	−	0.228731i	$-0.926542\pi$
$751$	0.534990	−	3.03408i	0.0195221	−	0.110715i	0.993012	+	0.118016i	$0.0376534\pi$
$752$		0			0
$753$	34.4201	−	28.1015i	1.25434	−	1.02408i
$754$		0			0
$755$	4.75135			0.172919
$756$		0			0
$757$	5.55567			0.201924			0.100962	−	0.994890i	$-0.467808\pi$
$757$	5.55567			0.201924			0.100962	+	0.994890i	$0.467808\pi$
$758$		0			0
$759$	68.3676	+	25.9307i	2.48159	+	0.941226i
$760$		0			0
$761$	−3.33014	+	18.8862i	−0.120718	+	0.684624i	0.863042	+	0.505132i	$0.168556\pi$
$761$	−3.33014	+	18.8862i	−0.120718	+	0.684624i	−0.983760	+	0.179491i	$0.942555\pi$
$762$		0			0
$763$	12.5978	+	9.05669i	0.456072	+	0.327874i
$764$		0			0
$765$	−5.33347	−	35.8662i	−0.192832	−	1.29675i
$766$		0			0
$767$	−52.8250	+	9.31447i	−1.90740	+	0.336326i
$768$		0			0
$769$	−2.74887	+	3.27598i	−0.0991269	+	0.118135i	−0.813327	−	0.581807i	$-0.802346\pi$
$769$	−2.74887	+	3.27598i	−0.0991269	+	0.118135i	0.714200	+	0.699941i	$0.246791\pi$
$770$		0			0
$771$	−0.789744	−	1.41140i	−0.0284419	−	0.0508302i
$772$		0			0
$773$	−34.2221			−1.23088			−0.615442	−	0.788182i	$-0.711023\pi$
$773$	−34.2221			−1.23088			−0.615442	+	0.788182i	$0.711023\pi$
$774$		0			0
$775$		−	27.6404i		−	0.992871i
$776$		0			0
$777$	2.82030	−	5.66071i	0.101178	−	0.203077i
$778$		0			0
$779$	22.0878	−	26.3233i	0.791379	−	0.943129i
$780$		0			0
$781$	6.04792	+	2.20126i	0.216412	+	0.0787674i
$782$		0			0
$783$	−12.5355	+	30.5452i	−0.447981	+	1.09160i
$784$		0			0
$785$	52.8402	+	62.9725i	1.88595	+	2.24758i
$786$		0			0
$787$	−1.14022	−	3.13272i	−0.0406444	−	0.111669i	0.917710	−	0.397251i	$-0.130036\pi$
$787$	−1.14022	−	3.13272i	−0.0406444	−	0.111669i	−0.958355	+	0.285581i	$0.907813\pi$
$788$		0			0
$789$	18.7570	−	21.7525i	0.667767	−	0.774409i
$790$		0			0
$791$	−19.4199	−	19.9091i	−0.690492	−	0.707886i
$792$		0			0
$793$	4.98473	+	8.63380i	0.177013	+	0.306595i
$794$		0			0
$795$	38.0981	−	21.3177i	1.35120	−	0.756061i
$796$		0			0
$797$	0.222252	+	0.186492i	0.00787258	+	0.00660588i	0.646715	−	0.762731i	$-0.276142\pi$
$797$	0.222252	+	0.186492i	0.00787258	+	0.00660588i	−0.638843	+	0.769337i	$0.720587\pi$
$798$		0			0
$799$	18.5614	+	6.75581i	0.656656	+	0.239003i
$800$		0			0
$801$	18.9835	−	6.33637i	0.670748	−	0.223885i
$802$		0			0
$803$	−20.0508	−	7.29790i	−0.707578	−	0.257537i
$804$		0			0
$805$	−66.9587	−	32.2433i	−2.35998	−	1.13643i
$806$		0			0
$807$	5.19676	−	4.24277i	0.182935	−	0.149353i
$808$		0			0
$809$	43.1506	−	24.9130i	1.51709	−	0.875894i	0.517295	−	0.855807i	$-0.326939\pi$
$809$	43.1506	−	24.9130i	1.51709	−	0.875894i	0.999798	−	0.0200865i	$-0.00639417\pi$
$810$		0			0
$811$			43.3138i			1.52095i	0.649365	+	0.760477i	$0.275035\pi$
$811$			43.3138i			1.52095i	−0.649365	+	0.760477i	$0.724965\pi$
$812$		0			0
$813$	−17.4385	+	45.9775i	−0.611595	+	1.61250i
$814$		0			0
$815$	−45.5317	−	38.2056i	−1.59491	−	1.33828i
$816$		0			0
$817$	−3.60506	+	9.90482i	−0.126125	+	0.346526i
$818$		0			0
$819$	−1.82048	−	37.9628i	−0.0636126	−	1.32653i
$820$		0			0
$821$	11.1814	+	13.3255i	0.390234	+	0.465063i	0.925017	−	0.379927i	$-0.124051\pi$
$821$	11.1814	+	13.3255i	0.390234	+	0.465063i	−0.534782	+	0.844990i	$0.679606\pi$
$822$		0			0
$823$	−5.98276	+	33.9299i	−0.208546	+	1.18272i	0.683216	+	0.730216i	$0.260581\pi$
$823$	−5.98276	+	33.9299i	−0.208546	+	1.18272i	−0.891762	+	0.452505i	$0.850530\pi$
$824$		0			0
$825$	−1.03803	+	77.1430i	−0.0361396	+	2.68578i
$826$		0			0
$827$	−3.85173	−	2.22380i	−0.133938	−	0.0773290i	0.431534	−	0.902097i	$-0.357973\pi$
$827$	−3.85173	−	2.22380i	−0.133938	−	0.0773290i	−0.565472	+	0.824768i	$0.691306\pi$
$828$		0			0
$829$	21.6114	+	12.4773i	0.750595	+	0.433356i	0.825909	−	0.563804i	$-0.190663\pi$
$829$	21.6114	+	12.4773i	0.750595	+	0.433356i	−0.0753141	+	0.997160i	$0.523996\pi$
$830$		0			0
$831$	11.3002	+	9.74410i	0.392001	+	0.338019i
$832$		0			0
$833$	−15.4271	+	17.4830i	−0.534517	+	0.605750i
$834$		0			0
$835$	−6.80854	−	38.6131i	−0.235619	−	1.33626i
$836$		0			0
$837$	11.8376	−	13.0036i	0.409169	−	0.449469i
$838$		0			0
$839$	−19.5137	+	16.3739i	−0.673686	+	0.565290i	−0.914154	−	0.405367i	$-0.867144\pi$
$839$	−19.5137	+	16.3739i	−0.673686	+	0.565290i	0.240468	+	0.970657i	$0.422699\pi$
$840$		0			0
$841$	−1.97539	+	11.2030i	−0.0681170	+	0.386311i
$842$		0			0
$843$	19.6751	+	3.74289i	0.677648	+	0.128912i
$844$		0			0
$845$	−36.0270			−1.23937
$846$		0			0
$847$	−35.4966	+	34.6243i	−1.21968	+	1.18971i
$848$		0			0
$849$	0.152228	−	11.3131i	0.00522443	−	0.388263i
$850$		0			0
$851$	−10.5208	−	1.85510i	−0.360649	−	0.0635922i
$852$		0			0
$853$	−13.8711	+	38.1106i	−0.474938	+	1.30488i	0.438802	+	0.898584i	$0.355403\pi$
$853$	−13.8711	+	38.1106i	−0.474938	+	1.30488i	−0.913740	+	0.406299i	$0.866819\pi$
$854$		0			0
$855$	59.7174	−	8.88025i	2.04229	−	0.303698i
$856$		0			0
$857$	24.2881	−	20.3801i	0.829665	−	0.696171i	−0.125549	−	0.992087i	$-0.540069\pi$
$857$	24.2881	−	20.3801i	0.829665	−	0.696171i	0.955214	+	0.295916i	$0.0956249\pi$
$858$		0			0
$859$	−25.9755	−	4.58018i	−0.886271	−	0.156274i	−0.288060	−	0.957612i	$-0.593010\pi$
$859$	−25.9755	−	4.58018i	−0.886271	−	0.156274i	−0.598211	+	0.801339i	$0.704122\pi$
$860$		0			0
$861$	3.20616	−	28.2119i	0.109266	−	0.961458i
$862$		0			0
$863$	30.6470	+	17.6941i	1.04324	+	0.602313i	0.920749	−	0.390156i	$-0.127579\pi$
$863$	30.6470	+	17.6941i	1.04324	+	0.602313i	0.122489	+	0.992470i	$0.460912\pi$
$864$		0			0
$865$	14.3103	+	24.7862i	0.486565	+	0.842755i
$866$		0			0
$867$	−1.64038	−	10.0955i	−0.0557101	−	0.342862i
$868$		0			0
$869$	−13.3724	−	36.7404i	−0.453627	−	1.24633i
$870$		0			0
$871$	−29.9631	−	35.7086i	−1.01526	−	1.20994i
$872$		0			0
$873$	0.920021	−	34.1803i	0.0311380	−	1.15683i
$874$		0			0
$875$	3.02704	−	30.2592i	0.102333	−	1.02295i
$876$		0			0
$877$	34.6333	−	12.6055i	1.16948	−	0.425657i	0.317006	−	0.948423i	$-0.397322\pi$
$877$	34.6333	−	12.6055i	1.16948	−	0.425657i	0.852476	+	0.522767i	$0.175100\pi$
$878$		0			0
$879$	25.3275	+	0.340804i	0.854274	+	0.0114950i
$880$		0			0
$881$	5.59859	−	9.69704i	0.188621	−	0.326702i	−0.756170	−	0.654376i	$-0.772931\pi$
$881$	5.59859	−	9.69704i	0.188621	−	0.326702i	0.944791	+	0.327674i	$0.106265\pi$
$882$		0			0
$883$	−10.1486	−	17.5779i	−0.341528	−	0.591544i	0.643189	−	0.765708i	$-0.277611\pi$
$883$	−10.1486	−	17.5779i	−0.341528	−	0.591544i	−0.984717	+	0.174164i	$0.944278\pi$
$884$		0			0
$885$	−53.3209	−	45.9781i	−1.79236	−	1.54554i
$886$		0			0
$887$	19.5058	+	16.3673i	0.654942	+	0.549562i	0.908566	−	0.417741i	$-0.137178\pi$
$887$	19.5058	+	16.3673i	0.654942	+	0.549562i	−0.253624	+	0.967303i	$0.581623\pi$
$888$		0			0
$889$	24.9165	+	17.9127i	0.835671	+	0.600771i
$890$		0			0
$891$	−33.5267	+	35.8478i	−1.12319	+	1.20095i
$892$		0			0
$893$	−11.2485	+	30.9049i	−0.376415	+	1.03419i
$894$		0			0
$895$	65.4614	+	11.5426i	2.18813	+	0.385827i
$896$		0			0
$897$	−60.6186	+	21.1441i	−2.02399	+	0.705981i
$898$		0			0
$899$	10.7519	−	18.6228i	0.358595	−	0.621105i
$900$		0			0
$901$	−20.0369	+	11.5683i	−0.667527	+	0.385397i
$902$		0			0
$903$	2.03562	+	8.46827i	0.0677410	+	0.281806i
$904$		0			0
$905$	17.4672	+	47.9907i	0.580629	+	1.59526i
$906$		0			0
$907$	−3.28687	−	18.6408i	−0.109139	−	0.618957i	−0.989486	−	0.144627i	$-0.953802\pi$
$907$	−3.28687	−	18.6408i	−0.109139	−	0.618957i	0.880347	−	0.474329i	$-0.157309\pi$
$908$		0			0
$909$	0.549374	−	0.895030i	0.0182216	−	0.0296863i
$910$		0			0
$911$	−34.3270	+	6.05277i	−1.13730	+	0.200537i	−0.710426	−	0.703772i	$-0.751498\pi$
$911$	−34.3270	+	6.05277i	−1.13730	+	0.200537i	−0.426878	+	0.904309i	$0.640387\pi$
$912$		0			0
$913$	−34.8088	+	41.4835i	−1.15200	+	1.37290i
$914$		0			0
$915$	−4.64062	+	12.2352i	−0.153414	+	0.404484i
$916$		0			0
$917$	−3.93068	−	1.10580i	−0.129803	−	0.0365169i
$918$		0			0
$919$	−21.6469	+	37.4935i	−0.714065	+	1.23680i	0.249255	+	0.968438i	$0.419814\pi$
$919$	−21.6469	+	37.4935i	−0.714065	+	1.23680i	−0.963319	+	0.268358i	$0.913519\pi$
$920$		0			0
$921$	−5.09500	+	13.4332i	−0.167886	+	0.442639i
$922$		0			0
$923$	−5.31015	+	1.93274i	−0.174786	+	0.0636168i
$924$		0			0
$925$	−1.95735	−	11.1007i	−0.0643572	−	0.364988i
$926$		0			0
$927$	−48.0409	+	7.14390i	−1.57787	+	0.234636i
$928$		0			0
$929$	26.0089	−	21.8240i	0.853323	−	0.716023i	−0.107196	−	0.994238i	$-0.534187\pi$
$929$	26.0089	−	21.8240i	0.853323	−	0.716023i	0.960519	+	0.278215i	$0.0897427\pi$
$930$		0			0
$931$	−29.1093	−	25.6862i	−0.954018	−	0.841831i
$932$		0			0
$933$	33.0072	+	0.444142i	1.08061	+	0.0145405i
$934$		0			0
$935$		−	65.9172i		−	2.15572i
$936$		0			0
$937$	−2.54086	+	1.46697i	−0.0830064	+	0.0479238i	−0.540929	−	0.841068i	$-0.681927\pi$
$937$	−2.54086	+	1.46697i	−0.0830064	+	0.0479238i	0.457922	+	0.888992i	$0.348594\pi$
$938$		0			0
$939$	13.0590	−	15.1445i	0.426163	−	0.494222i
$940$		0			0
$941$	19.1233	−	6.96032i	0.623402	−	0.226900i	−0.0109548	−	0.999940i	$-0.503487\pi$
$941$	19.1233	−	6.96032i	0.623402	−	0.226900i	0.634357	+	0.773040i	$0.281265\pi$
$942$		0			0
$943$	−47.2335	+	8.32855i	−1.53814	+	0.271215i
$944$		0			0
$945$	37.0877	−	33.3641i	1.20646	−	1.08533i
$946$		0			0
$947$	48.4753	−	8.54751i	1.57524	−	0.277757i	0.683376	−	0.730067i	$-0.260511\pi$
$947$	48.4753	−	8.54751i	1.57524	−	0.277757i	0.891861	+	0.452310i	$0.149400\pi$
$948$		0			0
$949$	17.6049	−	6.40766i	0.571479	−	0.208001i
$950$		0			0
$951$	−31.5233	−	5.99681i	−1.02221	−	0.194460i
$952$		0			0
$953$	20.0983	−	11.6038i	0.651049	−	0.375883i	−0.137809	−	0.990459i	$-0.544006\pi$
$953$	20.0983	−	11.6038i	0.651049	−	0.375883i	0.788858	+	0.614576i	$0.210673\pi$
$954$		0			0
$955$			47.3179i			1.53117i
$956$		0			0
$957$	−30.7074	+	51.5716i	−0.992629	+	1.66707i
$958$		0			0
$959$	−0.293868	−	3.91992i	−0.00948948	−	0.126581i
$960$		0			0
$961$	14.9741	−	12.5648i	0.483036	−	0.405315i
$962$		0			0
$963$	−7.48031	−	1.52758i	−0.241050	−	0.0492255i
$964$		0			0
$965$	6.44365	+	36.5437i	0.207428	+	1.17638i
$966$		0			0
$967$	−1.90482	+	0.693298i	−0.0612549	+	0.0222949i	−0.372466	−	0.928046i	$-0.621488\pi$
$967$	−1.90482	+	0.693298i	−0.0612549	+	0.0222949i	0.311211	+	0.950341i	$0.399265\pi$
$968$		0			0
$969$	−31.5821	+	5.13163i	−1.01456	+	0.164852i
$970$		0			0
$971$	−24.9930	+	43.2891i	−0.802062	+	1.38921i	0.116194	+	0.993227i	$0.462931\pi$
$971$	−24.9930	+	43.2891i	−0.802062	+	1.38921i	−0.918256	+	0.395986i	$0.870403\pi$
$972$		0			0
$973$	45.0085	−	11.4619i	1.44291	−	0.367452i
$974$		0			0
$975$	−42.8395	−	52.4720i	−1.37196	−	1.68045i
$976$		0			0
$977$	29.9950	−	35.7467i	0.959626	−	1.14364i	−0.0299387	−	0.999552i	$-0.509531\pi$
$977$	29.9950	−	35.7467i	0.959626	−	1.14364i	0.989565	−	0.144086i	$-0.0460243\pi$
$978$		0			0
$979$	35.8285	−	6.31753i	1.14508	−	0.201909i
$980$		0			0
$981$	13.1678	+	11.6670i	0.420414	+	0.372499i
$982$		0			0
$983$	5.86604	+	33.2680i	0.187098	+	1.06108i	0.923231	+	0.384246i	$0.125539\pi$
$983$	5.86604	+	33.2680i	0.187098	+	1.06108i	−0.736133	+	0.676837i	$0.763350\pi$
$984$		0			0
$985$	5.34278	+	14.6792i	0.170235	+	0.467717i
$986$		0			0
$987$	6.35150	+	26.4226i	0.202170	+	0.841040i
$988$		0			0
$989$	12.7410	−	7.35604i	0.405141	−	0.233908i
$990$		0			0
$991$	0.746159	−	1.29239i	0.0237025	−	0.0410540i	−0.853931	−	0.520387i	$-0.825788\pi$
$991$	0.746159	−	1.29239i	0.0237025	−	0.0410540i	0.877633	+	0.479333i	$0.159121\pi$
$992$		0			0
$993$	−7.56900	+	39.7878i	−0.240195	+	1.26263i
$994$		0			0
$995$	−70.8623	−	12.4949i	−2.24649	−	0.396116i
$996$		0			0
$997$	−8.99117	+	24.7030i	−0.284753	+	0.782353i	0.712026	+	0.702153i	$0.247778\pi$
$997$	−8.99117	+	24.7030i	−0.284753	+	0.782353i	−0.996779	+	0.0801995i	$0.974444\pi$
$998$		0			0
$999$	3.83328	−	6.06066i	0.121280	−	0.191751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.14	yes	144
7.3	odd	6		756.2.ca.a.437.4	yes	144
27.11	odd	18		756.2.ca.a.173.4	✓	144
189.38	even	18	inner	756.2.ck.a.605.14	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.4	✓	144	27.11	odd	18
756.2.ca.a.437.4	yes	144	7.3	odd	6
756.2.ck.a.5.14	yes	144	1.1	even	1	trivial
756.2.ck.a.605.14	yes	144	189.38	even	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.277790 + 1.70963i) q^{3} +(0.630118 - 3.57358i) q^{5} +(-2.41159 + 1.08823i) q^{7} +(-2.84567 + 0.949836i) q^{9} +O(q^{10})\)	\(q+(0.277790 + 1.70963i) q^{3} +(0.630118 - 3.57358i) q^{5} +(-2.41159 + 1.08823i) q^{7} +(-2.84567 + 0.949836i) q^{9} +(-5.37077 + 0.947012i) q^{11} +(3.07790 - 3.66809i) q^{13} +(6.28454 + 0.0845642i) q^{15} -3.33090 q^{17} -5.54597i q^{19} +(-2.53039 - 3.82062i) q^{21} +(-4.97574 + 5.92986i) q^{23} +(-7.67496 - 2.79346i) q^{25} +(-2.41437 - 4.60118i) q^{27} +(-4.08440 - 4.86760i) q^{29} +(1.15746 + 3.18009i) q^{31} +(-3.11099 - 8.91896i) q^{33} +(2.36929 + 9.30371i) q^{35} +(0.690046 + 1.19519i) q^{37} +(7.12609 + 4.24310i) q^{39} +(4.74638 + 3.98269i) q^{41} +(-1.78595 - 0.650033i) q^{43} +(1.60121 + 10.7677i) q^{45} +(-5.57250 - 2.02822i) q^{47} +(4.63151 - 5.24873i) q^{49} +(-0.925291 - 5.69461i) q^{51} +(6.01547 - 3.47303i) q^{53} +19.7896i q^{55} +(9.48155 - 1.54061i) q^{57} +(-8.58135 - 7.20060i) q^{59} +(-0.712093 + 1.95646i) q^{61} +(5.82893 - 5.38735i) q^{63} +(-11.1688 - 13.3104i) q^{65} +(1.69045 - 9.58704i) q^{67} +(-11.5201 - 6.85942i) q^{69} +(-1.02203 - 0.590072i) q^{71} +(3.38838 + 1.95628i) q^{73} +(2.64375 - 13.8973i) q^{75} +(11.9215 - 8.12844i) q^{77} +(1.24492 + 7.06031i) q^{79} +(7.19562 - 5.40583i) q^{81} +(7.60660 - 6.38269i) q^{83} +(-2.09886 + 11.9032i) q^{85} +(7.18718 - 8.33498i) q^{87} -6.67102 q^{89} +(-3.43088 + 12.1954i) q^{91} +(-5.11525 + 2.86222i) q^{93} +(-19.8189 - 3.49462i) q^{95} +(-3.89819 + 10.7102i) q^{97} +(14.3839 - 7.79623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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