LMFDB - Embedded newform 504.2.bu.a.41.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(41,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))

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

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

chi := DirichletCharacter("504.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bu (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.15
Character	$\chi$	$=$	504.41
Dual form			504.2.bu.a.209.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.610344 - 1.62095i) q^{3} +(1.91834 - 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +(-2.25496 - 1.97867i) q^{9} +O(q^{10})$	\(q+(0.610344 - 1.62095i) q^{3} +(1.91834 - 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +(-2.25496 - 1.97867i) q^{9} +(0.585698 - 0.338153i) q^{11} +(4.22006 + 2.43645i) q^{13} +(-4.21502 - 5.13749i) q^{15} -5.79523 q^{17} +4.22456i q^{19} +(3.21114 - 3.26934i) q^{21} +(4.76574 + 2.75150i) q^{23} +(-4.86003 - 8.41782i) q^{25} +(-4.58363 + 2.44751i) q^{27} +(-6.85239 + 3.95623i) q^{29} +(-1.78257 - 1.02917i) q^{31} +(-0.190652 - 1.15578i) q^{33} +(8.19684 - 5.98768i) q^{35} -8.71513 q^{37} +(6.52506 - 5.35344i) q^{39} +(4.84009 - 8.38328i) q^{41} +(3.57545 + 6.19287i) q^{43} +(-10.9002 + 3.69670i) q^{45} +(-0.666092 - 1.15370i) q^{47} +(4.71066 + 5.17781i) q^{49} +(-3.53708 + 9.39379i) q^{51} -5.18304i q^{53} -2.59476i q^{55} +(6.84780 + 2.57843i) q^{57} +(2.09619 - 3.63071i) q^{59} +(2.38178 - 1.37512i) q^{61} +(-3.33953 - 7.20052i) q^{63} +(16.1910 - 9.34787i) q^{65} +(-3.27636 + 5.67483i) q^{67} +(7.36878 - 6.04566i) q^{69} +11.1515i q^{71} +3.65100i q^{73} +(-16.6112 + 2.74010i) q^{75} +(1.77905 - 0.191621i) q^{77} +(-5.61720 - 9.72928i) q^{79} +(1.16970 + 8.92367i) q^{81} +(4.61279 + 7.98959i) q^{83} +(-11.1172 + 19.2556i) q^{85} +(2.23054 + 13.5220i) q^{87} +1.79702 q^{89} +(7.60487 + 10.4107i) q^{91} +(-2.75621 + 2.26131i) q^{93} +(14.0368 + 8.10413i) q^{95} +(-2.60513 + 1.50407i) q^{97} +(-1.98982 - 0.396384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91} + 16 q^{93} - 108 q^{95} + 44 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.610344	−	1.62095i	0.352382	−	0.935856i
$3$	0.610344	−	1.62095i	0.352382	−	0.935856i
$4$		0			0
$5$	1.91834	−	3.32266i	0.857906	−	1.48594i	−0.0160164	−	0.999872i	$-0.505098\pi$
$5$	1.91834	−	3.32266i	0.857906	−	1.48594i	0.873923	−	0.486065i	$-0.161568\pi$
$6$		0			0
$7$	2.41978	+	1.06989i	0.914590	+	0.404382i
$7$	2.41978	+	1.06989i	0.914590	+	0.404382i
$8$		0			0
$9$	−2.25496	−	1.97867i	−0.751654	−	0.659558i
$10$		0			0
$11$	0.585698	−	0.338153i	0.176595	−	0.101957i	−0.409097	−	0.912491i	$-0.634156\pi$
$11$	0.585698	−	0.338153i	0.176595	−	0.101957i	0.585692	+	0.810534i	$0.300823\pi$
$12$		0			0
$13$	4.22006	+	2.43645i	1.17043	+	0.675751i	0.953782	−	0.300498i	$-0.0971530\pi$
$13$	4.22006	+	2.43645i	1.17043	+	0.675751i	0.216652	+	0.976249i	$0.430486\pi$
$14$		0			0
$15$	−4.21502	−	5.13749i	−1.08831	−	1.32649i
$16$		0			0
$17$	−5.79523			−1.40555			−0.702775	−	0.711412i	$-0.748056\pi$
$17$	−5.79523			−1.40555			−0.702775	+	0.711412i	$0.748056\pi$
$18$		0			0
$19$			4.22456i			0.969181i	0.874741	+	0.484590i	$0.161031\pi$
$19$			4.22456i			0.969181i	−0.874741	+	0.484590i	$0.838969\pi$
$20$		0			0
$21$	3.21114	−	3.26934i	0.700728	−	0.713428i
$22$		0			0
$23$	4.76574	+	2.75150i	0.993725	+	0.573727i	0.906386	−	0.422451i	$-0.138830\pi$
$23$	4.76574	+	2.75150i	0.993725	+	0.573727i	0.0873394	+	0.996179i	$0.472164\pi$
$24$		0			0
$25$	−4.86003	−	8.41782i	−0.972006	−	1.68356i
$26$		0			0
$27$	−4.58363	+	2.44751i	−0.882121	+	0.471023i
$28$		0			0
$29$	−6.85239	+	3.95623i	−1.27246	+	0.734653i	−0.975450	−	0.220222i	$-0.929322\pi$
$29$	−6.85239	+	3.95623i	−1.27246	+	0.734653i	−0.297007	+	0.954875i	$0.595988\pi$
$30$		0			0
$31$	−1.78257	−	1.02917i	−0.320159	−	0.184844i	0.331305	−	0.943524i	$-0.392511\pi$
$31$	−1.78257	−	1.02917i	−0.320159	−	0.184844i	−0.651463	+	0.758680i	$0.725845\pi$
$32$		0			0
$33$	−0.190652	−	1.15578i	−0.0331882	−	0.201195i
$34$		0			0
$35$	8.19684	−	5.98768i	1.38552	−	1.01210i
$36$		0			0
$37$	−8.71513			−1.43276			−0.716380	−	0.697711i	$-0.754202\pi$
$37$	−8.71513			−1.43276			−0.716380	+	0.697711i	$0.754202\pi$
$38$		0			0
$39$	6.52506	−	5.35344i	1.04485	−	0.857236i
$40$		0			0
$41$	4.84009	−	8.38328i	0.755895	−	1.30925i	−0.189033	−	0.981971i	$-0.560535\pi$
$41$	4.84009	−	8.38328i	0.755895	−	1.30925i	0.944928	−	0.327278i	$-0.106131\pi$
$42$		0			0
$43$	3.57545	+	6.19287i	0.545251	+	0.944403i	0.998591	+	0.0530654i	$0.0168992\pi$
$43$	3.57545	+	6.19287i	0.545251	+	0.944403i	−0.453340	+	0.891338i	$0.649767\pi$
$44$		0			0
$45$	−10.9002	+	3.69670i	−1.62491	+	0.551071i
$46$		0			0
$47$	−0.666092	−	1.15370i	−0.0971594	−	0.168285i	0.813348	−	0.581777i	$-0.197642\pi$
$47$	−0.666092	−	1.15370i	−0.0971594	−	0.168285i	−0.910508	+	0.413492i	$0.864309\pi$
$48$		0			0
$49$	4.71066	+	5.17781i	0.672951	+	0.739687i
$50$		0			0
$51$	−3.53708	+	9.39379i	−0.495291	+	1.31539i
$52$		0			0
$53$		−	5.18304i		−	0.711945i	−0.934496	−	0.355972i	$-0.884150\pi$
$53$		−	5.18304i		−	0.711945i	0.934496	−	0.355972i	$-0.115850\pi$
$54$		0			0
$55$		−	2.59476i		−	0.349878i
$56$		0			0
$57$	6.84780	+	2.57843i	0.907014	+	0.341522i
$58$		0			0
$59$	2.09619	−	3.63071i	0.272901	−	0.472678i	−0.696703	−	0.717360i	$-0.745350\pi$
$59$	2.09619	−	3.63071i	0.272901	−	0.472678i	0.969603	+	0.244682i	$0.0786837\pi$
$60$		0			0
$61$	2.38178	−	1.37512i	0.304956	−	0.176066i	−0.339711	−	0.940530i	$-0.610329\pi$
$61$	2.38178	−	1.37512i	0.304956	−	0.176066i	0.644667	+	0.764463i	$0.276996\pi$
$62$		0			0
$63$	−3.33953	−	7.20052i	−0.420742	−	0.907180i
$64$		0			0
$65$	16.1910	−	9.34787i	2.00825	−	1.15946i
$66$		0			0
$67$	−3.27636	+	5.67483i	−0.400271	+	0.693290i	−0.993758	−	0.111553i	$-0.964417\pi$
$67$	−3.27636	+	5.67483i	−0.400271	+	0.693290i	0.593487	+	0.804844i	$0.297751\pi$
$68$		0			0
$69$	7.36878	−	6.04566i	0.887097	−	0.727812i
$70$		0			0
$71$			11.1515i			1.32344i	0.749751	+	0.661721i	$0.230173\pi$
$71$			11.1515i			1.32344i	−0.749751	+	0.661721i	$0.769827\pi$
$72$		0			0
$73$			3.65100i			0.427318i	0.976908	+	0.213659i	$0.0685381\pi$
$73$			3.65100i			0.427318i	−0.976908	+	0.213659i	$0.931462\pi$
$74$		0			0
$75$	−16.6112	+	2.74010i	−1.91809	+	0.316400i
$76$		0			0
$77$	1.77905	−	0.191621i	0.202741	−	0.0218372i
$78$		0			0
$79$	−5.61720	−	9.72928i	−0.631985	−	1.09463i	−0.987145	−	0.159825i	$-0.948907\pi$
$79$	−5.61720	−	9.72928i	−0.631985	−	1.09463i	0.355161	−	0.934805i	$-0.384426\pi$
$80$		0			0
$81$	1.16970	+	8.92367i	0.129966	+	0.991518i
$82$		0			0
$83$	4.61279	+	7.98959i	0.506320	+	0.876971i	0.999973	+	0.00731261i	$0.00232770\pi$
$83$	4.61279	+	7.98959i	0.506320	+	0.876971i	−0.493654	+	0.869659i	$0.664339\pi$
$84$		0			0
$85$	−11.1172	+	19.2556i	−1.20583	+	2.08856i
$86$		0			0
$87$	2.23054	+	13.5220i	0.239139	+	1.44972i
$88$		0			0
$89$	1.79702			0.190484			0.0952419	−	0.995454i	$-0.469638\pi$
$89$	1.79702			0.190484			0.0952419	+	0.995454i	$0.469638\pi$
$90$		0			0
$91$	7.60487	+	10.4107i	0.797207	+	1.09134i
$92$		0			0
$93$	−2.75621	+	2.26131i	−0.285805	+	0.234487i
$94$		0			0
$95$	14.0368	+	8.10413i	1.44014	+	0.831466i
$96$		0			0
$97$	−2.60513	+	1.50407i	−0.264511	+	0.152715i	−0.626390	−	0.779509i	$-0.715468\pi$
$97$	−2.60513	+	1.50407i	−0.264511	+	0.152715i	0.361880	+	0.932225i	$0.382135\pi$
$98$		0			0
$99$	−1.98982	−	0.396384i	−0.199984	−	0.0398381i
$100$		0			0
$101$	−4.15494	−	7.19657i	−0.413432	−	0.716085i	0.581830	−	0.813310i	$-0.302337\pi$
$101$	−4.15494	−	7.19657i	−0.413432	−	0.716085i	−0.995262	+	0.0972249i	$0.969003\pi$
$102$		0			0
$103$	−6.74606	−	3.89484i	−0.664709	−	0.383770i	0.129360	−	0.991598i	$-0.458708\pi$
$103$	−6.74606	−	3.89484i	−0.664709	−	0.383770i	−0.794069	+	0.607828i	$0.792041\pi$
$104$		0			0
$105$	−4.70284	−	16.9412i	−0.458950	−	1.65329i
$106$		0			0
$107$			5.50520i			0.532207i	0.963944	+	0.266104i	$0.0857364\pi$
$107$			5.50520i			0.532207i	−0.963944	+	0.266104i	$0.914264\pi$
$108$		0			0
$109$	14.2890			1.36864			0.684320	−	0.729182i	$-0.260099\pi$
$109$	14.2890			1.36864			0.684320	+	0.729182i	$0.260099\pi$
$110$		0			0
$111$	−5.31923	+	14.1268i	−0.504879	+	1.34086i
$112$		0			0
$113$	−4.58249	−	2.64570i	−0.431085	−	0.248887i	0.268724	−	0.963217i	$-0.413398\pi$
$113$	−4.58249	−	2.64570i	−0.431085	−	0.248887i	−0.699809	+	0.714330i	$0.746731\pi$
$114$		0			0
$115$	18.2846	−	10.5566i	1.70505	−	0.984409i
$116$		0			0
$117$	−4.69512	−	13.8442i	−0.434064	−	1.27990i
$118$		0			0
$119$	−14.0232	−	6.20028i	−1.28550	−	0.568379i
$120$		0			0
$121$	−5.27131	+	9.13017i	−0.479210	+	0.830015i
$122$		0			0
$123$	−10.6348	−	12.9622i	−0.958905	−	1.16877i
$124$		0			0
$125$	−18.1093			−1.61975
$126$		0			0
$127$	−2.23048			−0.197923			−0.0989615	−	0.995091i	$-0.531552\pi$
$127$	−2.23048			−0.197923			−0.0989615	+	0.995091i	$0.531552\pi$
$128$		0			0
$129$	12.2206	−	2.01585i	1.07596	−	0.177486i
$130$		0			0
$131$	−0.474634	+	0.822091i	−0.0414690	+	0.0718264i	−0.886015	−	0.463657i	$-0.846537\pi$
$131$	−0.474634	+	0.822091i	−0.0414690	+	0.0718264i	0.844546	+	0.535483i	$0.179870\pi$
$132$		0			0
$133$	−4.51983	+	10.2225i	−0.391919	+	0.886403i
$134$		0			0
$135$	−0.660725	+	19.9250i	−0.0568662	+	1.71487i
$136$		0			0
$137$	10.4037	−	6.00658i	0.888848	−	0.513177i	0.0152823	−	0.999883i	$-0.495135\pi$
$137$	10.4037	−	6.00658i	0.888848	−	0.513177i	0.873565	+	0.486707i	$0.161802\pi$
$138$		0			0
$139$	1.92937	+	1.11392i	0.163647	+	0.0944816i	0.579587	−	0.814911i	$-0.303214\pi$
$139$	1.92937	+	1.11392i	0.163647	+	0.0944816i	−0.415940	+	0.909392i	$0.636547\pi$
$140$		0			0
$141$	−2.27664	+	0.375545i	−0.191728	+	0.0316266i
$142$		0			0
$143$	3.29557			0.275590
$144$		0			0
$145$			30.3575i			2.52105i
$146$		0			0
$147$	11.2681	−	4.47549i	0.929377	−	0.369133i
$148$		0			0
$149$	5.64079	+	3.25671i	0.462111	+	0.266800i	0.712932	−	0.701234i	$-0.247367\pi$
$149$	5.64079	+	3.25671i	0.462111	+	0.266800i	−0.250820	+	0.968034i	$0.580700\pi$
$150$		0			0
$151$	−1.17106	−	2.02834i	−0.0952997	−	0.165064i	0.814434	−	0.580256i	$-0.197048\pi$
$151$	−1.17106	−	2.02834i	−0.0952997	−	0.165064i	−0.909734	+	0.415192i	$0.863714\pi$
$152$		0			0
$153$	13.0680	+	11.4669i	1.05649	+	0.927042i
$154$		0			0
$155$	−6.83913	+	3.94857i	−0.549332	+	0.317157i
$156$		0			0
$157$	−2.03731	−	1.17624i	−0.162595	−	0.0938742i	0.416495	−	0.909138i	$-0.363258\pi$
$157$	−2.03731	−	1.17624i	−0.162595	−	0.0938742i	−0.579089	+	0.815264i	$0.696592\pi$
$158$		0			0
$159$	−8.40145	−	3.16343i	−0.666278	−	0.250877i
$160$		0			0
$161$	8.58822	+	11.7569i	0.676846	+	0.926570i
$162$		0			0
$163$	17.0419			1.33482			0.667412	−	0.744689i	$-0.267402\pi$
$163$	17.0419			1.33482			0.667412	+	0.744689i	$0.267402\pi$
$164$		0			0
$165$	−4.20598	−	1.58370i	−0.327435	−	0.123291i
$166$		0			0
$167$	2.89906	−	5.02133i	0.224336	−	0.388562i	−0.731784	−	0.681537i	$-0.761312\pi$
$167$	2.89906	−	5.02133i	0.224336	−	0.388562i	0.956120	+	0.292975i	$0.0946452\pi$
$168$		0			0
$169$	5.37261	+	9.30563i	0.413278	+	0.715818i
$170$		0			0
$171$	8.35903	−	9.52622i	0.639231	−	0.728488i
$172$		0			0
$173$	−1.97021	−	3.41251i	−0.149792	−	0.259448i	0.781358	−	0.624083i	$-0.214527\pi$
$173$	−1.97021	−	3.41251i	−0.149792	−	0.259448i	−0.931151	+	0.364635i	$0.881194\pi$
$174$		0			0
$175$	−2.75403	−	25.5690i	−0.208185	−	1.93283i
$176$		0			0
$177$	−4.60580	−	5.61380i	−0.346193	−	0.421959i
$178$		0			0
$179$		−	6.52749i		−	0.487888i	−0.969789	−	0.243944i	$-0.921559\pi$
$179$		−	6.52749i		−	0.487888i	0.969789	−	0.243944i	$-0.0784412\pi$
$180$		0			0
$181$			6.39901i			0.475635i	0.971310	+	0.237817i	$0.0764320\pi$
$181$			6.39901i			0.475635i	−0.971310	+	0.237817i	$0.923568\pi$
$182$		0			0
$183$	−0.775300	−	4.70005i	−0.0573118	−	0.347438i
$184$		0			0
$185$	−16.7186	+	28.9574i	−1.22917	+	2.12899i
$186$		0			0
$187$	−3.39426	+	1.95967i	−0.248213	+	0.143306i
$188$		0			0
$189$	−13.7100	+	1.01843i	−0.997252	+	0.0740796i
$190$		0			0
$191$	−15.5755	+	8.99253i	−1.12701	+	0.650677i	−0.943180	−	0.332282i	$-0.892181\pi$
$191$	−15.5755	+	8.99253i	−1.12701	+	0.650677i	−0.183825	+	0.982959i	$0.558848\pi$
$192$		0			0
$193$	7.67270	−	13.2895i	0.552293	−	0.956599i	−0.445816	−	0.895125i	$-0.647086\pi$
$193$	7.67270	−	13.2895i	0.552293	−	0.956599i	0.998109	−	0.0614746i	$-0.0195803\pi$
$194$		0			0
$195$	−5.27037	−	31.9502i	−0.377419	−	2.28800i
$196$		0			0
$197$			11.3420i			0.808086i	0.914740	+	0.404043i	$0.132395\pi$
$197$			11.3420i			0.808086i	−0.914740	+	0.404043i	$0.867605\pi$
$198$		0			0
$199$		−	11.2568i		−	0.797971i	−0.916957	−	0.398986i	$-0.869362\pi$
$199$		−	11.2568i		−	0.797971i	0.916957	−	0.398986i	$-0.130638\pi$
$200$		0			0
$201$	7.19890	+	8.77442i	0.507772	+	0.618900i
$202$		0			0
$203$	−20.8140	+	2.24187i	−1.46086	+	0.157348i
$204$		0			0
$205$	−18.5698	−	32.1639i	−1.29697	−	2.24643i
$206$		0			0
$207$	−5.30223	−	15.6344i	−0.368530	−	1.08666i
$208$		0			0
$209$	1.42855	+	2.47432i	0.0988147	+	0.171152i
$210$		0			0
$211$	−3.79773	+	6.57785i	−0.261446	+	0.452838i	−0.966626	−	0.256190i	$-0.917533\pi$
$211$	−3.79773	+	6.57785i	−0.261446	+	0.452838i	0.705180	+	0.709028i	$0.250866\pi$
$212$		0			0
$213$	18.0761	+	6.80626i	1.23855	+	0.466357i
$214$		0			0
$215$	27.4357			1.87110
$216$		0			0
$217$	−3.21232	−	4.39751i	−0.218067	−	0.298522i
$218$		0			0
$219$	5.91810	+	2.22837i	0.399908	+	0.150579i
$220$		0			0
$221$	−24.4562	−	14.1198i	−1.64510	−	0.949801i
$222$		0			0
$223$	20.2215	−	11.6749i	1.35413	−	0.781807i	0.365304	−	0.930888i	$-0.380965\pi$
$223$	20.2215	−	11.6749i	1.35413	−	0.781807i	0.988825	+	0.149081i	$0.0476316\pi$
$224$		0			0
$225$	−5.69694	+	28.5983i	−0.379796	+	1.90655i
$226$		0			0
$227$	−7.81056	−	13.5283i	−0.518405	−	0.897904i	−0.999771	−	0.0213844i	$-0.993193\pi$
$227$	−7.81056	−	13.5283i	−0.518405	−	0.897904i	0.481366	−	0.876520i	$-0.340141\pi$
$228$		0			0
$229$	−9.15650	−	5.28651i	−0.605078	−	0.349342i	0.165959	−	0.986133i	$-0.446928\pi$
$229$	−9.15650	−	5.28651i	−0.605078	−	0.349342i	−0.771037	+	0.636791i	$0.780262\pi$
$230$		0			0
$231$	0.775223	−	3.00070i	0.0510059	−	0.197432i
$232$		0			0
$233$		−	5.08862i		−	0.333367i	−0.986010	−	0.166683i	$-0.946694\pi$
$233$		−	5.08862i		−	0.333367i	0.986010	−	0.166683i	$-0.0533057\pi$
$234$		0			0
$235$	−5.11115			−0.333415
$236$		0			0
$237$	−19.1991	+	3.16700i	−1.24712	+	0.205719i
$238$		0			0
$239$	−6.73315	−	3.88739i	−0.435531	−	0.251454i	0.266169	−	0.963926i	$-0.414242\pi$
$239$	−6.73315	−	3.88739i	−0.435531	−	0.251454i	−0.701700	+	0.712472i	$0.747575\pi$
$240$		0			0
$241$	21.5690	−	12.4529i	1.38938	−	0.802161i	0.396137	−	0.918191i	$-0.370350\pi$
$241$	21.5690	−	12.4529i	1.38938	−	0.802161i	0.993246	+	0.116030i	$0.0370170\pi$
$242$		0			0
$243$	15.1787	+	3.55048i	0.973716	+	0.227764i
$244$		0			0
$245$	26.2407	−	5.71911i	1.67646	−	0.365380i
$246$		0			0
$247$	−10.2929	+	17.8279i	−0.654924	+	1.13436i
$248$		0			0
$249$	15.7661	−	2.60071i	0.999137	−	0.164813i
$250$		0			0
$251$	−9.76999			−0.616676			−0.308338	−	0.951277i	$-0.599773\pi$
$251$	−9.76999			−0.616676			−0.308338	+	0.951277i	$0.599773\pi$
$252$		0			0
$253$	3.72171			0.233982
$254$		0			0
$255$	24.4270	+	29.7730i	1.52968	+	1.86445i
$256$		0			0
$257$	7.49085	−	12.9745i	0.467267	−	0.809329i	−0.532034	−	0.846723i	$-0.678572\pi$
$257$	7.49085	−	12.9745i	0.467267	−	0.809329i	0.999301	+	0.0373936i	$0.0119055\pi$
$258$		0			0
$259$	−21.0887	−	9.32427i	−1.31039	−	0.579382i
$260$		0			0
$261$	23.2800	+	4.63751i	1.44099	+	0.287054i
$262$		0			0
$263$	14.3343	−	8.27590i	0.883889	−	0.510314i	0.0119504	−	0.999929i	$-0.496196\pi$
$263$	14.3343	−	8.27590i	0.883889	−	0.510314i	0.871939	+	0.489615i	$0.162863\pi$
$264$		0			0
$265$	−17.2214	−	9.94281i	−1.05791	−	0.610782i
$266$		0			0
$267$	1.09680	−	2.91288i	0.0671231	−	0.178265i
$268$		0			0
$269$	0.269785			0.0164491			0.00822455	−	0.999966i	$-0.497382\pi$
$269$	0.269785			0.0164491			0.00822455	+	0.999966i	$0.497382\pi$
$270$		0			0
$271$		−	13.3371i		−	0.810172i	−0.914279	−	0.405086i	$-0.867242\pi$
$271$		−	13.3371i		−	0.810172i	0.914279	−	0.405086i	$-0.132758\pi$
$272$		0			0
$273$	21.5168	−	5.97301i	1.30226	−	0.361503i
$274$		0			0
$275$	−5.69302	−	3.28687i	−0.343302	−	0.198205i
$276$		0			0
$277$	−1.03411	−	1.79113i	−0.0621336	−	0.107619i	0.833285	−	0.552843i	$-0.186457\pi$
$277$	−1.03411	−	1.79113i	−0.0621336	−	0.107619i	−0.895419	+	0.445225i	$0.853124\pi$
$278$		0			0
$279$	1.98324	+	5.84785i	0.118733	+	0.350102i
$280$		0			0
$281$	−5.06406	+	2.92374i	−0.302096	+	0.174415i	−0.643384	−	0.765543i	$-0.722470\pi$
$281$	−5.06406	+	2.92374i	−0.302096	+	0.174415i	0.341288	+	0.939959i	$0.389137\pi$
$282$		0			0
$283$	−20.5862	−	11.8854i	−1.22372	−	0.706515i	−0.258011	−	0.966142i	$-0.583067\pi$
$283$	−20.5862	−	11.8854i	−1.22372	−	0.706515i	−0.965709	+	0.259626i	$0.916401\pi$
$284$		0			0
$285$	21.7036	−	17.8066i	1.28561	−	1.05477i
$286$		0			0
$287$	20.6812	−	15.1073i	1.22077	−	0.891756i
$288$		0			0
$289$	16.5847			0.975572
$290$		0			0
$291$	0.848001	+	5.14079i	0.0497107	+	0.301358i
$292$		0			0
$293$	1.47112	−	2.54805i	0.0859437	−	0.148859i	−0.819849	−	0.572579i	$-0.805943\pi$
$293$	1.47112	−	2.54805i	0.0859437	−	0.148859i	0.905793	+	0.423721i	$0.139276\pi$
$294$		0			0
$295$	−8.04239	−	13.9298i	−0.468246	−	0.811026i
$296$		0			0
$297$	−1.85699	+	2.98347i	−0.107754	+	0.173118i
$298$		0			0
$299$	13.4078	+	23.2230i	0.775393	+	1.34302i
$300$		0			0
$301$	2.02610	+	18.8107i	0.116782	+	1.08423i
$302$		0			0
$303$	−14.2012	+	2.34257i	−0.815839	+	0.134577i
$304$		0			0
$305$		−	10.5518i		−	0.604194i
$306$		0			0
$307$		−	22.8040i		−	1.30149i	−0.759296	−	0.650745i	$-0.774457\pi$
$307$		−	22.8040i		−	1.30149i	0.759296	−	0.650745i	$-0.225543\pi$
$308$		0			0
$309$	−10.4308	+	8.55784i	−0.593385	+	0.486839i
$310$		0			0
$311$	−15.2514	+	26.4163i	−0.864830	+	1.49793i	0.00238601	+	0.999997i	$0.499241\pi$
$311$	−15.2514	+	26.4163i	−0.864830	+	1.49793i	−0.867216	+	0.497932i	$0.834093\pi$
$312$		0			0
$313$	7.08223	−	4.08892i	0.400311	−	0.231120i	−0.286307	−	0.958138i	$-0.592428\pi$
$313$	7.08223	−	4.08892i	0.400311	−	0.231120i	0.686618	+	0.727018i	$0.259094\pi$
$314$		0			0
$315$	−30.3312	−	2.71690i	−1.70897	−	0.153080i
$316$		0			0
$317$	−12.3445	+	7.12707i	−0.693334	+	0.400296i	−0.804860	−	0.593465i	$-0.797759\pi$
$317$	−12.3445	+	7.12707i	−0.693334	+	0.400296i	0.111526	+	0.993762i	$0.464426\pi$
$318$		0			0
$319$	−2.67562	+	4.63431i	−0.149806	+	0.259472i
$320$		0			0
$321$	8.92365	+	3.36006i	0.498070	+	0.187540i
$322$		0			0
$323$		−	24.4823i		−	1.36223i
$324$		0			0
$325$		−	47.3649i		−	2.62733i
$326$		0			0
$327$	8.72122	−	23.1618i	0.482284	−	1.28085i
$328$		0			0
$329$	−0.377453	−	3.50436i	−0.0208097	−	0.193201i
$330$		0			0
$331$	10.0254	+	17.3646i	0.551048	+	0.954444i	0.998199	+	0.0599851i	$0.0191053\pi$
$331$	10.0254	+	17.3646i	0.551048	+	0.954444i	−0.447151	+	0.894458i	$0.647561\pi$
$332$		0			0
$333$	19.6523	+	17.2444i	1.07694	+	0.944988i
$334$		0			0
$335$	12.5703	+	21.7725i	0.686791	+	1.18956i
$336$		0			0
$337$	14.6930	−	25.4490i	0.800378	−	1.38629i	−0.118990	−	0.992895i	$-0.537966\pi$
$337$	14.6930	−	25.4490i	0.800378	−	1.38629i	0.919368	−	0.393399i	$-0.128701\pi$
$338$		0			0
$339$	−7.08545	+	5.81321i	−0.384829	+	0.315730i
$340$		0			0
$341$	−1.39206			−0.0753844
$342$		0			0
$343$	5.85904	+	17.5691i	0.316358	+	0.948640i
$344$		0			0
$345$	−5.95186	−	36.0816i	−0.320437	−	1.94257i
$346$		0			0
$347$	1.57973	+	0.912059i	0.0848045	+	0.0489619i	0.541803	−	0.840506i	$-0.317742\pi$
$347$	1.57973	+	0.912059i	0.0848045	+	0.0489619i	−0.456998	+	0.889468i	$0.651075\pi$
$348$		0			0
$349$	−21.9455	+	12.6703i	−1.17472	+	0.678224i	−0.954787	−	0.297292i	$-0.903917\pi$
$349$	−21.9455	+	12.6703i	−1.17472	+	0.678224i	−0.219931	+	0.975515i	$0.570583\pi$
$350$		0			0
$351$	−25.3065	−	0.839178i	−1.35076	−	0.0447920i
$352$		0			0
$353$	−6.86705	−	11.8941i	−0.365496	−	0.633058i	0.623360	−	0.781935i	$-0.285767\pi$
$353$	−6.86705	−	11.8941i	−0.365496	−	0.633058i	−0.988856	+	0.148878i	$0.952434\pi$
$354$		0			0
$355$	37.0526	+	21.3924i	1.96655	+	1.13539i
$356$		0			0
$357$	−18.6093	+	18.9466i	−0.984909	+	1.00276i
$358$		0			0
$359$		−	5.77932i		−	0.305021i	−0.988302	−	0.152510i	$-0.951264\pi$
$359$		−	5.77932i		−	0.305021i	0.988302	−	0.152510i	$-0.0487357\pi$
$360$		0			0
$361$	1.15309			0.0606891
$362$		0			0
$363$	11.5822	+	14.1171i	0.607910	+	0.740954i
$364$		0			0
$365$	12.1310	+	7.00385i	0.634967	+	0.366598i
$366$		0			0
$367$	−29.9207	+	17.2747i	−1.56185	+	0.901734i	−0.564780	+	0.825242i	$0.691039\pi$
$367$	−29.9207	+	17.2747i	−1.56185	+	0.901734i	−0.997070	+	0.0764926i	$0.975628\pi$
$368$		0			0
$369$	−27.5020	+	9.32701i	−1.43170	+	0.485545i
$370$		0			0
$371$	5.54530	−	12.5418i	0.287897	−	0.651138i
$372$		0			0
$373$	0.720369	−	1.24772i	0.0372993	−	0.0646043i	−0.846773	−	0.531954i	$-0.821458\pi$
$373$	0.720369	−	1.24772i	0.0372993	−	0.0646043i	0.884072	+	0.467350i	$0.154791\pi$
$374$		0			0
$375$	−11.0529	+	29.3543i	−0.570770	+	1.51585i
$376$		0			0
$377$	−38.5567			−1.98577
$378$		0			0
$379$	−4.53029			−0.232705			−0.116353	−	0.993208i	$-0.537120\pi$
$379$	−4.53029			−0.232705			−0.116353	+	0.993208i	$0.537120\pi$
$380$		0			0
$381$	−1.36136	+	3.61550i	−0.0697446	+	0.185227i
$382$		0			0
$383$	7.49154	−	12.9757i	0.382800	−	0.663029i	−0.608662	−	0.793430i	$-0.708293\pi$
$383$	7.49154	−	12.9757i	0.382800	−	0.663029i	0.991461	+	0.130401i	$0.0416266\pi$
$384$		0			0
$385$	2.77612	−	6.27875i	0.141484	−	0.319995i
$386$		0			0
$387$	4.19116	−	21.0393i	0.213049	−	1.06949i
$388$		0			0
$389$	−32.3559	+	18.6807i	−1.64051	+	0.947148i	−0.659855	+	0.751393i	$0.729383\pi$
$389$	−32.3559	+	18.6807i	−1.64051	+	0.947148i	−0.980653	+	0.195755i	$0.937284\pi$
$390$		0			0
$391$	−27.6186	−	15.9456i	−1.39673	−	0.806403i
$392$		0			0
$393$	1.04288	+	1.27112i	0.0526062	+	0.0641193i
$394$		0			0
$395$	−43.1027			−2.16873
$396$		0			0
$397$			18.4269i			0.924820i	0.886666	+	0.462410i	$0.153015\pi$
$397$			18.4269i			0.924820i	−0.886666	+	0.462410i	$0.846985\pi$
$398$		0			0
$399$	13.8115	+	13.5657i	0.691441	+	0.679132i
$400$		0			0
$401$	−27.6794	−	15.9807i	−1.38224	−	0.798038i	−0.389818	−	0.920892i	$-0.627462\pi$
$401$	−27.6794	−	15.9807i	−1.38224	−	0.798038i	−0.992425	+	0.122854i	$0.960795\pi$
$402$		0			0
$403$	−5.01503	−	8.68628i	−0.249816	−	0.432695i
$404$		0			0
$405$	31.8941	+	13.2321i	1.58483	+	0.657508i
$406$		0			0
$407$	−5.10444	+	2.94705i	−0.253018	+	0.146080i
$408$		0			0
$409$	−1.67567	−	0.967449i	−0.0828566	−	0.0478373i	0.457999	−	0.888953i	$-0.348566\pi$
$409$	−1.67567	−	0.967449i	−0.0828566	−	0.0478373i	−0.540856	+	0.841115i	$0.681900\pi$
$410$		0			0
$411$	−3.38653	−	20.5300i	−0.167045	−	1.01267i
$412$		0			0
$413$	8.95678	−	6.54281i	0.440734	−	0.321950i
$414$		0			0
$415$	35.3955			1.73750
$416$		0			0
$417$	2.98319	−	2.44754i	0.146088	−	0.119856i
$418$		0			0
$419$	−15.0386	+	26.0476i	−0.734684	+	1.27251i	0.220178	+	0.975460i	$0.429336\pi$
$419$	−15.0386	+	26.0476i	−0.734684	+	1.27251i	−0.954862	+	0.297050i	$0.903997\pi$
$420$		0			0
$421$	1.17975	+	2.04338i	0.0574974	+	0.0995885i	0.893341	−	0.449379i	$-0.148355\pi$
$421$	1.17975	+	2.04338i	0.0574974	+	0.0995885i	−0.835844	+	0.548967i	$0.815021\pi$
$422$		0			0
$423$	−0.780795	+	3.91954i	−0.0379635	+	0.190574i
$424$		0			0
$425$	28.1650	+	48.7832i	1.36620	+	2.36633i
$426$		0			0
$427$	7.23462	−	0.779239i	0.350108	−	0.0377100i
$428$		0			0
$429$	2.01143	−	5.34196i	0.0971129	−	0.257912i
$430$		0			0
$431$			33.3518i			1.60650i	0.595643	+	0.803249i	$0.296897\pi$
$431$			33.3518i			1.60650i	−0.595643	+	0.803249i	$0.703103\pi$
$432$		0			0
$433$			11.9121i			0.572459i	0.958161	+	0.286229i	$0.0924019\pi$
$433$			11.9121i			0.572459i	−0.958161	+	0.286229i	$0.907598\pi$
$434$		0			0
$435$	49.2080	+	18.5285i	2.35934	+	0.888374i
$436$		0			0
$437$	−11.6239	+	20.1331i	−0.556045	+	0.963099i
$438$		0			0
$439$	−34.1958	+	19.7429i	−1.63207	+	0.942279i	−0.648622	+	0.761110i	$0.724655\pi$
$439$	−34.1958	+	19.7429i	−1.63207	+	0.942279i	−0.983452	+	0.181168i	$0.942012\pi$
$440$		0			0
$441$	−0.377143	−	20.9966i	−0.0179592	−	0.999839i
$442$		0			0
$443$	−25.7023	+	14.8392i	−1.22115	+	0.705034i	−0.965164	−	0.261645i	$-0.915735\pi$
$443$	−25.7023	+	14.8392i	−1.22115	+	0.705034i	−0.255990	+	0.966679i	$0.582402\pi$
$444$		0			0
$445$	3.44729	−	5.97088i	0.163417	−	0.283047i
$446$		0			0
$447$	8.72179	−	7.15573i	0.412526	−	0.338454i
$448$		0			0
$449$			27.9245i			1.31784i	0.752213	+	0.658920i	$0.228986\pi$
$449$			27.9245i			1.31784i	−0.752213	+	0.658920i	$0.771014\pi$
$450$		0			0
$451$		−	6.54676i		−	0.308275i
$452$		0			0
$453$	−4.00259	+	0.660249i	−0.188058	+	0.0310212i
$454$		0			0
$455$	49.1798	−	5.29715i	2.30559	−	0.248334i
$456$		0			0
$457$	18.0390	+	31.2444i	0.843828	+	1.46155i	0.886635	+	0.462469i	$0.153036\pi$
$457$	18.0390	+	31.2444i	0.843828	+	1.46155i	−0.0428078	+	0.999083i	$0.513630\pi$
$458$		0			0
$459$	26.5632	−	14.1839i	1.23987	−	0.662047i
$460$		0			0
$461$	−1.34942	−	2.33727i	−0.0628488	−	0.108857i	0.832889	−	0.553440i	$-0.186685\pi$
$461$	−1.34942	−	2.33727i	−0.0628488	−	0.108857i	−0.895738	+	0.444583i	$0.853352\pi$
$462$		0			0
$463$	14.9993	−	25.9796i	0.697077	−	1.20737i	−0.272399	−	0.962184i	$-0.587817\pi$
$463$	14.9993	−	25.9796i	0.697077	−	1.20737i	0.969476	−	0.245188i	$-0.0788497\pi$
$464$		0			0
$465$	2.22622	+	13.4959i	0.103238	+	0.625856i
$466$		0			0
$467$	−14.1160			−0.653211			−0.326605	−	0.945161i	$-0.605905\pi$
$467$	−14.1160			−0.653211			−0.326605	+	0.945161i	$0.605905\pi$
$468$		0			0
$469$	−13.9995	+	10.2265i	−0.646438	+	0.472214i
$470$		0			0
$471$	−3.15009	+	2.58446i	−0.145148	+	0.119086i
$472$		0			0
$473$	4.18827	+	2.41810i	0.192577	+	0.111184i
$474$		0			0
$475$	35.5616	−	20.5315i	1.63168	−	0.942049i
$476$		0			0
$477$	−10.2555	+	11.6875i	−0.469569	+	0.535136i
$478$		0			0
$479$	−17.3516	−	30.0538i	−0.792815	−	1.37320i	−0.924218	−	0.381866i	$-0.875281\pi$
$479$	−17.3516	−	30.0538i	−0.792815	−	1.37320i	0.131403	−	0.991329i	$-0.458052\pi$
$480$		0			0
$481$	−36.7784	−	21.2340i	−1.67695	−	0.968188i
$482$		0			0
$483$	24.2990	−	6.74535i	1.10564	−	0.306924i
$484$		0			0
$485$			11.5413i			0.524062i
$486$		0			0
$487$	36.2125			1.64094			0.820472	−	0.571686i	$-0.193711\pi$
$487$	36.2125			1.64094			0.820472	+	0.571686i	$0.193711\pi$
$488$		0			0
$489$	10.4014	−	27.6240i	0.470368	−	1.24920i
$490$		0			0
$491$	29.3233	+	16.9298i	1.32334	+	0.764032i	0.984260	−	0.176724i	$-0.0565501\pi$
$491$	29.3233	+	16.9298i	1.32334	+	0.764032i	0.339082	+	0.940757i	$0.389883\pi$
$492$		0			0
$493$	39.7112	−	22.9273i	1.78850	−	1.03259i
$494$		0			0
$495$	−5.13419	+	5.85109i	−0.230765	+	0.262987i
$496$		0			0
$497$	−11.9309	+	26.9842i	−0.535175	+	1.21041i
$498$		0			0
$499$	−13.8586	+	24.0038i	−0.620395	+	1.07456i	0.369017	+	0.929423i	$0.379694\pi$
$499$	−13.8586	+	24.0038i	−0.620395	+	1.07456i	−0.989412	+	0.145133i	$0.953639\pi$
$500$		0			0
$501$	−6.36990	−	7.76398i	−0.284586	−	0.346869i
$502$		0			0
$503$	−9.08643			−0.405144			−0.202572	−	0.979267i	$-0.564930\pi$
$503$	−9.08643			−0.405144			−0.202572	+	0.979267i	$0.564930\pi$
$504$		0			0
$505$	−31.8823			−1.41874
$506$		0			0
$507$	18.3631	−	3.02910i	0.815534	−	0.134527i
$508$		0			0
$509$	13.7675	−	23.8461i	0.610236	−	1.05696i	−0.380965	−	0.924590i	$-0.624408\pi$
$509$	13.7675	−	23.8461i	0.610236	−	1.05696i	0.991200	−	0.132370i	$-0.0422586\pi$
$510$		0			0
$511$	−3.90619	+	8.83462i	−0.172799	+	0.390821i
$512$		0			0
$513$	−10.3396	−	19.3638i	−0.456506	−	0.854934i
$514$		0			0
$515$	−25.8824	+	14.9432i	−1.14052	+	0.658478i
$516$		0			0
$517$	−0.780257	−	0.450482i	−0.0343157	−	0.0198122i
$518$		0			0
$519$	−6.73401	+	1.11081i	−0.295590	+	0.0487593i
$520$		0			0
$521$	−3.47559			−0.152268			−0.0761341	−	0.997098i	$-0.524258\pi$
$521$	−3.47559			−0.152268			−0.0761341	+	0.997098i	$0.524258\pi$
$522$		0			0
$523$			0.315295i			0.0137869i	0.999976	+	0.00689344i	$0.00219427\pi$
$523$			0.315295i			0.0137869i	−0.999976	+	0.00689344i	$0.997806\pi$
$524$		0			0
$525$	−43.1269	−	11.1417i	−1.88221	−	0.486265i
$526$		0			0
$527$	10.3304	+	5.96425i	0.449999	+	0.259807i
$528$		0			0
$529$	3.64150	+	6.30727i	0.158326	+	0.274229i
$530$		0			0
$531$	−11.9108	+	4.03942i	−0.516885	+	0.175296i
$532$		0			0
$533$	40.8509	−	23.5853i	1.76945	−	1.02159i
$534$		0			0
$535$	18.2919	+	10.5608i	0.790827	+	0.456584i
$536$		0			0
$537$	−10.5807	−	3.98401i	−0.456593	−	0.171923i
$538$		0			0
$539$	4.50991	+	1.43971i	0.194256	+	0.0620128i
$540$		0			0
$541$	39.0741			1.67993			0.839964	−	0.542643i	$-0.182576\pi$
$541$	39.0741			1.67993			0.839964	+	0.542643i	$0.182576\pi$
$542$		0			0
$543$	10.3725	+	3.90560i	0.445126	+	0.167605i
$544$		0			0
$545$	27.4111	−	47.4775i	1.17416	−	2.03371i
$546$		0			0
$547$	−0.609894	−	1.05637i	−0.0260772	−	0.0451670i	0.852692	−	0.522413i	$-0.174968\pi$
$547$	−0.609894	−	1.05637i	−0.0260772	−	0.0451670i	−0.878769	+	0.477246i	$0.841635\pi$
$548$		0			0
$549$	−8.09175	−	1.61192i	−0.345347	−	0.0687952i
$550$		0			0
$551$	−16.7133	−	28.9483i	−0.712012	−	1.23324i
$552$		0			0
$553$	−3.18309	−	29.5525i	−0.135359	−	1.25670i
$554$		0			0
$555$	36.7344	+	44.7739i	1.55929	+	1.90055i
$556$		0			0
$557$			0.456650i			0.0193489i	0.999953	+	0.00967444i	$0.00307952\pi$
$557$			0.456650i			0.0193489i	−0.999953	+	0.00967444i	$0.996920\pi$
$558$		0			0
$559$			34.8457i			1.47382i
$560$		0			0
$561$	1.10487	+	6.69800i	0.0466477	+	0.282790i
$562$		0			0
$563$	−15.7680	+	27.3110i	−0.664541	+	1.15102i	0.314868	+	0.949135i	$0.398040\pi$
$563$	−15.7680	+	27.3110i	−0.664541	+	1.15102i	−0.979409	+	0.201884i	$0.935294\pi$
$564$		0			0
$565$	−17.5815	+	10.1507i	−0.739660	+	0.427043i
$566$		0			0
$567$	−6.71697	+	22.8447i	−0.282086	+	0.959389i
$568$		0			0
$569$	24.1376	−	13.9359i	1.01190	−	0.584221i	0.100153	−	0.994972i	$-0.468067\pi$
$569$	24.1376	−	13.9359i	1.01190	−	0.584221i	0.911748	+	0.410751i	$0.134733\pi$
$570$		0			0
$571$	−13.2588	+	22.9649i	−0.554864	+	0.961052i	0.443050	+	0.896497i	$0.353896\pi$
$571$	−13.2588	+	22.9649i	−0.554864	+	0.961052i	−0.997914	+	0.0645555i	$0.979437\pi$
$572$		0			0
$573$	5.07002	+	30.7357i	0.211803	+	1.28400i
$574$		0			0
$575$		−	53.4895i		−	2.23067i
$576$		0			0
$577$		−	6.69146i		−	0.278569i	−0.990252	−	0.139285i	$-0.955520\pi$
$577$		−	6.69146i		−	0.278569i	0.990252	−	0.139285i	$-0.0444803\pi$
$578$		0			0
$579$	−16.8586	−	20.5482i	−0.700621	−	0.853955i
$580$		0			0
$581$	2.61392	+	24.2682i	0.108444	+	1.00682i
$582$		0			0
$583$	−1.75266	−	3.03569i	−0.0725877	−	0.125726i
$584$		0			0
$585$	−55.0064	−	10.9576i	−2.27424	−	0.453041i
$586$		0			0
$587$	3.49388	+	6.05157i	0.144208	+	0.249775i	0.929077	−	0.369886i	$-0.120603\pi$
$587$	3.49388	+	6.05157i	0.144208	+	0.249775i	−0.784869	+	0.619661i	$0.787270\pi$
$588$		0			0
$589$	4.34777	−	7.53056i	0.179147	−	0.310291i
$590$		0			0
$591$	18.3849	+	6.92254i	0.756253	+	0.284755i
$592$		0			0
$593$	−8.96766			−0.368258			−0.184129	−	0.982902i	$-0.558946\pi$
$593$	−8.96766			−0.368258			−0.184129	+	0.982902i	$0.558946\pi$
$594$		0			0
$595$	−47.5026	+	34.7000i	−1.94742	+	1.42256i
$596$		0			0
$597$	−18.2467	−	6.87050i	−0.746786	−	0.281191i
$598$		0			0
$599$	−24.5323	−	14.1637i	−1.00236	−	0.578714i	−0.0934151	−	0.995627i	$-0.529778\pi$
$599$	−24.5323	−	14.1637i	−1.00236	−	0.578714i	−0.908946	+	0.416914i	$0.863112\pi$
$600$		0			0
$601$	8.23991	−	4.75731i	0.336113	−	0.194055i	−0.322439	−	0.946590i	$-0.604503\pi$
$601$	8.23991	−	4.75731i	0.336113	−	0.194055i	0.658552	+	0.752535i	$0.271169\pi$
$602$		0			0
$603$	18.6167	−	6.31366i	0.758131	−	0.257112i
$604$		0			0
$605$	20.2243	+	35.0295i	0.822234	+	1.42415i
$606$		0			0
$607$	12.7545	+	7.36381i	0.517689	+	0.298888i	0.735988	−	0.676994i	$-0.236718\pi$
$607$	12.7545	+	7.36381i	0.517689	+	0.298888i	−0.218300	+	0.975882i	$0.570051\pi$
$608$		0			0
$609$	−9.06974	+	35.1068i	−0.367524	+	1.42260i
$610$		0			0
$611$		−	6.49160i		−	0.262622i
$612$		0			0
$613$	−8.63782			−0.348878			−0.174439	−	0.984668i	$-0.555811\pi$
$613$	−8.63782			−0.348878			−0.174439	+	0.984668i	$0.555811\pi$
$614$		0			0
$615$	−63.4701	+	10.4698i	−2.55936	+	0.422181i
$616$		0			0
$617$	−14.8009	−	8.54533i	−0.595864	−	0.344022i	0.171549	−	0.985176i	$-0.445123\pi$
$617$	−14.8009	−	8.54533i	−0.595864	−	0.344022i	−0.767413	+	0.641154i	$0.778456\pi$
$618$		0			0
$619$	9.66939	−	5.58263i	0.388646	−	0.224385i	−0.292928	−	0.956135i	$-0.594629\pi$
$619$	9.66939	−	5.58263i	0.388646	−	0.224385i	0.681573	+	0.731750i	$0.261296\pi$
$620$		0			0
$621$	−28.5787	−	0.947689i	−1.14682	−	0.0380294i
$622$		0			0
$623$	4.34839	+	1.92262i	0.174215	+	0.0770282i
$624$		0			0
$625$	−10.4396	+	18.0820i	−0.417585	+	0.723278i
$626$		0			0
$627$	4.88265	−	0.805420i	0.194994	−	0.0321654i
$628$		0			0
$629$	50.5062			2.01382
$630$		0			0
$631$	−37.1187			−1.47767			−0.738835	−	0.673886i	$-0.764624\pi$
$631$	−37.1187			−1.47767			−0.738835	+	0.673886i	$0.764624\pi$
$632$		0			0
$633$	8.34446	+	10.1707i	0.331662	+	0.404248i
$634$		0			0
$635$	−4.27881	+	7.41112i	−0.169799	+	0.294101i
$636$		0			0
$637$	7.26376	+	33.3280i	0.287801	+	1.32050i
$638$		0			0
$639$	22.0652	−	25.1462i	0.872886	−	0.994769i
$640$		0			0
$641$	16.1548	−	9.32700i	0.638078	−	0.368395i	−0.145796	−	0.989315i	$-0.546574\pi$
$641$	16.1548	−	9.32700i	0.638078	−	0.368395i	0.783874	+	0.620920i	$0.213241\pi$
$642$		0			0
$643$	33.1356	+	19.1309i	1.30674	+	0.754448i	0.981551	−	0.191201i	$-0.0612381\pi$
$643$	33.1356	+	19.1309i	1.30674	+	0.754448i	0.325191	+	0.945648i	$0.394571\pi$
$644$		0			0
$645$	16.7452	−	44.4719i	0.659342	−	1.75108i
$646$		0			0
$647$	2.28252			0.0897350			0.0448675	−	0.998993i	$-0.485713\pi$
$647$	2.28252			0.0897350			0.0448675	+	0.998993i	$0.485713\pi$
$648$		0			0
$649$		−	2.83533i		−	0.111296i
$650$		0			0
$651$	−9.08877	+	2.52302i	−0.356217	+	0.0988849i
$652$		0			0
$653$	−34.7684	−	20.0735i	−1.36059	−	0.785538i	−0.370889	−	0.928677i	$-0.620947\pi$
$653$	−34.7684	−	20.0735i	−1.36059	−	0.785538i	−0.989703	+	0.143139i	$0.954280\pi$
$654$		0			0
$655$	1.82102	+	3.15409i	0.0711530	+	0.123241i
$656$		0			0
$657$	7.22415	−	8.23287i	0.281841	−	0.321195i
$658$		0			0
$659$	33.7362	−	19.4776i	1.31418	−	0.758740i	0.331391	−	0.943493i	$-0.392482\pi$
$659$	33.7362	−	19.4776i	1.31418	−	0.758740i	0.982785	+	0.184753i	$0.0591486\pi$
$660$		0			0
$661$	−7.33192	−	4.23309i	−0.285179	−	0.164648i	0.350587	−	0.936530i	$-0.385982\pi$
$661$	−7.33192	−	4.23309i	−0.285179	−	0.164648i	−0.635766	+	0.771882i	$0.719315\pi$
$662$		0			0
$663$	−37.8142	+	31.0244i	−1.46858	+	1.20489i
$664$		0			0
$665$	25.2953	+	34.6280i	0.980910	+	1.34282i
$666$		0			0
$667$	−43.5423			−1.68596
$668$		0			0
$669$	−6.58234	−	39.9037i	−0.254488	−	1.54277i
$670$		0			0
$671$	0.930003	−	1.61081i	0.0359024	−	0.0621848i
$672$		0			0
$673$	−8.72960	−	15.1201i	−0.336501	−	0.582837i	0.647271	−	0.762260i	$-0.275910\pi$
$673$	−8.72960	−	15.1201i	−0.336501	−	0.582837i	−0.983772	+	0.179423i	$0.942577\pi$
$674$		0			0
$675$	42.8793	+	26.6892i	1.65042	+	1.02727i
$676$		0			0
$677$	−24.5011	−	42.4372i	−0.941654	−	1.63099i	−0.762315	−	0.647206i	$-0.775937\pi$
$677$	−24.5011	−	42.4372i	−0.941654	−	1.63099i	−0.179339	−	0.983787i	$-0.557396\pi$
$678$		0			0
$679$	−7.91303	+	0.852310i	−0.303674	+	0.0327087i
$680$		0			0
$681$	−26.6958	+	4.40362i	−1.02299	+	0.168747i
$682$		0			0
$683$		−	22.1852i		−	0.848893i	−0.905453	−	0.424446i	$-0.860469\pi$
$683$		−	22.1852i		−	0.848893i	0.905453	−	0.424446i	$-0.139531\pi$
$684$		0			0
$685$		−	46.0905i		−	1.76103i
$686$		0			0
$687$	−14.1578	+	11.6156i	−0.540153	+	0.443164i
$688$		0			0
$689$	12.6282	−	21.8727i	0.481097	−	0.833285i
$690$		0			0
$691$	−26.7708	+	15.4561i	−1.01841	+	0.587978i	−0.913642	−	0.406519i	$-0.866742\pi$
$691$	−26.7708	+	15.4561i	−1.01841	+	0.587978i	−0.104765	+	0.994497i	$0.533409\pi$
$692$		0			0
$693$	−4.39084	−	3.08806i	−0.166794	−	0.117306i
$694$		0			0
$695$	7.40236	−	4.27375i	0.280788	−	0.162113i
$696$		0			0
$697$	−28.0495	+	48.5831i	−1.06245	+	1.84022i
$698$		0			0
$699$	−8.24840	−	3.10581i	−0.311983	−	0.117472i
$700$		0			0
$701$		−	32.4719i		−	1.22645i	−0.789910	−	0.613223i	$-0.789873\pi$
$701$		−	32.4719i		−	1.22645i	0.789910	−	0.613223i	$-0.210127\pi$
$702$		0			0
$703$		−	36.8176i		−	1.38860i
$704$		0			0
$705$	−3.11956	+	8.28492i	−0.117489	+	0.312028i
$706$		0			0
$707$	−2.35447	−	21.8594i	−0.0885491	−	0.822109i
$708$		0			0
$709$	−25.6834	−	44.4849i	−0.964560	−	1.67067i	−0.710792	−	0.703402i	$-0.751663\pi$
$709$	−25.6834	−	44.4849i	−0.964560	−	1.67067i	−0.253768	−	0.967265i	$-0.581670\pi$
$710$		0			0
$711$	−6.58451	+	33.0538i	−0.246938	+	1.23961i
$712$		0			0
$713$	−5.66350	−	9.80947i	−0.212100	−	0.367367i
$714$		0			0
$715$	6.32202	−	10.9501i	0.236430	−	0.409509i
$716$		0			0
$717$	−10.4108	+	8.54146i	−0.388798	+	0.318987i
$718$		0			0
$719$	37.9805			1.41643			0.708216	−	0.705996i	$-0.249500\pi$
$719$	37.9805			1.41643			0.708216	+	0.705996i	$0.249500\pi$
$720$		0			0
$721$	−12.1569	−	16.6422i	−0.452747	−	0.619789i
$722$		0			0
$723$	−7.02098	−	42.5629i	−0.261113	−	1.58293i
$724$		0			0
$725$	66.6056	+	38.4548i	2.47367	+	1.42817i
$726$		0			0
$727$	14.6498	−	8.45808i	0.543332	−	0.313693i	−0.203096	−	0.979159i	$-0.565101\pi$
$727$	14.6498	−	8.45808i	0.543332	−	0.313693i	0.746428	+	0.665466i	$0.231767\pi$
$728$		0			0
$729$	15.0194	−	22.4370i	0.556274	−	0.830999i
$730$		0			0
$731$	−20.7206	−	35.8891i	−0.766378	−	1.32741i
$732$		0			0
$733$	26.4599	+	15.2766i	0.977320	+	0.564256i	0.901460	−	0.432863i	$-0.142496\pi$
$733$	26.4599	+	15.2766i	0.977320	+	0.564256i	0.0758600	+	0.997118i	$0.475830\pi$
$734$		0			0
$735$	6.74547	−	46.0255i	0.248810	−	1.69768i
$736$		0			0
$737$			4.43165i			0.163242i
$738$		0			0
$739$	−23.0562			−0.848138			−0.424069	−	0.905630i	$-0.639399\pi$
$739$	−23.0562			−0.848138			−0.424069	+	0.905630i	$0.639399\pi$
$740$		0			0
$741$	22.6159	+	27.5655i	0.830816	+	1.01264i
$742$		0			0
$743$	−1.88934	−	1.09081i	−0.0693130	−	0.0400179i	0.464943	−	0.885341i	$-0.346075\pi$
$743$	−1.88934	−	1.09081i	−0.0693130	−	0.0400179i	−0.534256	+	0.845323i	$0.679408\pi$
$744$		0			0
$745$	21.6419	−	12.4949i	0.792897	−	0.457779i
$746$		0			0
$747$	5.40713	−	27.1434i	0.197837	−	0.993126i
$748$		0			0
$749$	−5.88997	+	13.3214i	−0.215215	+	0.486752i
$750$		0			0
$751$	9.46865	−	16.4002i	0.345516	−	0.598451i	−0.639931	−	0.768432i	$-0.721037\pi$
$751$	9.46865	−	16.4002i	0.345516	−	0.598451i	0.985447	+	0.169981i	$0.0543706\pi$
$752$		0			0
$753$	−5.96305	+	15.8367i	−0.217306	+	0.577120i
$754$		0			0
$755$	−8.98597			−0.327033
$756$		0			0
$757$	11.6383			0.423002			0.211501	−	0.977378i	$-0.432165\pi$
$757$	11.6383			0.423002			0.211501	+	0.977378i	$0.432165\pi$
$758$		0			0
$759$	2.27152	−	6.03271i	0.0824511	−	0.218973i
$760$		0			0
$761$	4.13819	−	7.16755i	0.150009	−	0.259824i	−0.781221	−	0.624254i	$-0.785403\pi$
$761$	4.13819	−	7.16755i	0.150009	−	0.259824i	0.931231	+	0.364430i	$0.118736\pi$
$762$		0			0
$763$	34.5763	+	15.2877i	1.25174	+	0.553453i
$764$		0			0
$765$	63.1694	−	21.4232i	2.28389	−	0.774558i
$766$		0			0
$767$	17.6921	−	10.2145i	0.638824	−	0.368825i
$768$		0			0
$769$	45.8329	+	26.4616i	1.65277	+	0.954230i	0.975924	+	0.218110i	$0.0699890\pi$
$769$	45.8329	+	26.4616i	1.65277	+	0.954230i	0.676851	+	0.736120i	$0.263344\pi$
$770$		0			0
$771$	−16.4591	−	20.0612i	−0.592759	−	0.722488i
$772$		0			0
$773$	−11.1905			−0.402494			−0.201247	−	0.979540i	$-0.564499\pi$
$773$	−11.1905			−0.402494			−0.201247	+	0.979540i	$0.564499\pi$
$774$		0			0
$775$			20.0071i			0.718676i
$776$		0			0
$777$	−27.9855	+	28.4927i	−1.00398	+	1.02217i
$778$		0			0
$779$	35.4157	+	20.4473i	1.26890	+	0.732599i
$780$		0			0
$781$	3.77092	+	6.53142i	0.134934	+	0.233713i
$782$		0			0
$783$	21.7259	−	34.9052i	0.776422	−	1.24741i
$784$		0			0
$785$	−7.81648	+	4.51285i	−0.278982	+	0.161070i
$786$		0			0
$787$	24.5820	+	14.1924i	0.876254	+	0.505905i	0.869421	−	0.494071i	$-0.164492\pi$
$787$	24.5820	+	14.1924i	0.876254	+	0.505905i	0.00683237	+	0.999977i	$0.497825\pi$
$788$		0			0
$789$	−4.66598	−	28.2863i	−0.166113	−	1.00702i
$790$		0			0
$791$	−8.25800	−	11.3048i	−0.293621	−	0.401952i
$792$		0			0
$793$	13.4017			0.475908
$794$		0			0
$795$	−26.6278	+	21.8466i	−0.944391	+	0.774818i
$796$		0			0
$797$	0.351421	−	0.608679i	0.0124480	−	0.0215605i	−0.859734	−	0.510742i	$-0.829371\pi$
$797$	0.351421	−	0.608679i	0.0124480	−	0.0215605i	0.872182	+	0.489181i	$0.162704\pi$
$798$		0			0
$799$	3.86016	+	6.68599i	0.136562	+	0.236533i
$800$		0			0
$801$	−4.05221	−	3.55572i	−0.143178	−	0.125635i
$802$		0			0
$803$	1.23460	+	2.13839i	0.0435680	+	0.0754620i
$804$		0			0
$805$	55.5391	−	5.98210i	1.95749	−	0.210841i
$806$		0			0
$807$	0.164662	−	0.437309i	0.00579637	−	0.0153940i
$808$		0			0
$809$			40.0190i			1.40699i	0.710699	+	0.703496i	$0.248379\pi$
$809$			40.0190i			1.40699i	−0.710699	+	0.703496i	$0.751621\pi$
$810$		0			0
$811$			16.5473i			0.581055i	0.956867	+	0.290528i	$0.0938309\pi$
$811$			16.5473i			0.581055i	−0.956867	+	0.290528i	$0.906169\pi$
$812$		0			0
$813$	−21.6188	−	8.14023i	−0.758205	−	0.285490i
$814$		0			0
$815$	32.6921	−	56.6243i	1.14515	−	1.98346i
$816$		0			0
$817$	−26.1621	+	15.1047i	−0.915297	+	0.528447i
$818$		0			0
$819$	3.45069	−	38.5233i	0.120577	−	1.34611i
$820$		0			0
$821$	−17.7148	+	10.2277i	−0.618251	+	0.356948i	−0.776188	−	0.630502i	$-0.782849\pi$
$821$	−17.7148	+	10.2277i	−0.618251	+	0.356948i	0.157937	+	0.987449i	$0.449516\pi$
$822$		0			0
$823$	1.49600	−	2.59115i	0.0521474	−	0.0903220i	−0.838773	−	0.544481i	$-0.816727\pi$
$823$	1.49600	−	2.59115i	0.0521474	−	0.0903220i	0.890921	+	0.454159i	$0.150060\pi$
$824$		0			0
$825$	−8.80255	+	7.22198i	−0.306465	+	0.251437i
$826$		0			0
$827$			37.3399i			1.29843i	0.760603	+	0.649217i	$0.224903\pi$
$827$			37.3399i			1.29843i	−0.760603	+	0.649217i	$0.775097\pi$
$828$		0			0
$829$		−	12.7334i		−	0.442250i	−0.975246	−	0.221125i	$-0.929027\pi$
$829$		−	12.7334i		−	0.442250i	0.975246	−	0.221125i	$-0.0709728\pi$
$830$		0			0
$831$	−3.53450	+	0.583035i	−0.122610	+	0.0202253i
$832$		0			0
$833$	−27.2993	−	30.0066i	−0.945866	−	1.03967i
$834$		0			0
$835$	−11.1228	−	19.2652i	−0.384919	−	0.666699i
$836$		0			0
$837$	10.6895	+	0.354472i	0.369484	+	0.0122523i
$838$		0			0
$839$	−1.35897	−	2.35381i	−0.0469169	−	0.0812625i	0.841613	−	0.540081i	$-0.181606\pi$
$839$	−1.35897	−	2.35381i	−0.0469169	−	0.0812625i	−0.888530	+	0.458818i	$0.848273\pi$
$840$		0			0
$841$	16.8035	−	29.1045i	0.579431	−	1.00360i
$842$		0			0
$843$	1.64841	+	9.99307i	0.0567744	+	0.344180i
$844$		0			0
$845$	41.2259			1.41821
$846$		0			0
$847$	−22.5237	+	16.4532i	−0.773923	+	0.565340i
$848$		0			0
$849$	−31.8303	+	26.1150i	−1.09241	+	0.896263i
$850$		0			0
$851$	−41.5340	−	23.9797i	−1.42377	−	0.822013i
$852$		0			0
$853$	−43.6414	+	25.1964i	−1.49425	+	0.862707i	−0.999978	−	0.00659961i	$-0.997899\pi$
$853$	−43.6414	+	25.1964i	−1.49425	+	0.862707i	−0.494274	+	0.869306i	$0.664566\pi$
$854$		0			0
$855$	−15.6169	−	46.0487i	−0.534087	−	1.57483i
$856$		0			0
$857$	8.97633	+	15.5475i	0.306626	+	0.531091i	0.977622	−	0.210370i	$-0.0674667\pi$
$857$	8.97633	+	15.5475i	0.306626	+	0.531091i	−0.670996	+	0.741461i	$0.734133\pi$
$858$		0			0
$859$	11.0055	+	6.35400i	0.375501	+	0.216796i	0.675859	−	0.737031i	$-0.263773\pi$
$859$	11.0055	+	6.35400i	0.375501	+	0.216796i	−0.300358	+	0.953827i	$0.597106\pi$
$860$		0			0
$861$	−11.8656	−	42.7438i	−0.404378	−	1.45670i
$862$		0			0
$863$			2.05813i			0.0700595i	0.999386	+	0.0350298i	$0.0111526\pi$
$863$			2.05813i			0.0700595i	−0.999386	+	0.0350298i	$0.988847\pi$
$864$		0			0
$865$	−15.1181			−0.514031
$866$		0			0
$867$	10.1224	−	26.8830i	0.343774	−	0.912995i
$868$		0			0
$869$	−6.57997	−	3.79895i	−0.223210	−	0.128870i
$870$		0			0
$871$	−27.6529	+	15.9654i	−0.936983	+	0.540967i
$872$		0			0
$873$	8.85053	+	1.76308i	0.299545	+	0.0596712i
$874$		0			0
$875$	−43.8205	−	19.3750i	−1.48140	−	0.654996i
$876$		0			0
$877$	13.8077	−	23.9156i	0.466253	−	0.807574i	−0.533004	−	0.846113i	$-0.678937\pi$
$877$	13.8077	−	23.9156i	0.466253	−	0.807574i	0.999257	+	0.0385389i	$0.0122704\pi$
$878$		0			0
$879$	−3.23238	−	3.93980i	−0.109025	−	0.132886i
$880$		0			0
$881$	−10.2629			−0.345765			−0.172882	−	0.984942i	$-0.555308\pi$
$881$	−10.2629			−0.345765			−0.172882	+	0.984942i	$0.555308\pi$
$882$		0			0
$883$	49.8978			1.67919			0.839597	−	0.543210i	$-0.182791\pi$
$883$	49.8978			1.67919			0.839597	+	0.543210i	$0.182791\pi$
$884$		0			0
$885$	−27.4882	+	4.53433i	−0.924006	+	0.152420i
$886$		0			0
$887$	−12.5367	+	21.7141i	−0.420940	+	0.729089i	−0.996032	−	0.0889997i	$-0.971633\pi$
$887$	−12.5367	+	21.7141i	−0.420940	+	0.729089i	0.575092	+	0.818089i	$0.304966\pi$
$888$		0			0
$889$	−5.39727	−	2.38638i	−0.181018	−	0.0800365i
$890$		0			0
$891$	3.70265	+	4.83104i	0.124044	+	0.161846i
$892$		0			0
$893$	4.87389	−	2.81394i	0.163099	−	0.0941650i
$894$		0			0
$895$	−21.6886	−	12.5219i	−0.724970	−	0.418562i
$896$		0			0
$897$	45.8267	−	7.55937i	1.53011	−	0.252400i
$898$		0			0
$899$	16.2865			0.543184
$900$		0			0
$901$			30.0369i			1.00067i
$902$		0			0
$903$	31.7279	+	8.19680i	1.05584	+	0.272773i
$904$		0			0
$905$	21.2617	+	12.2755i	0.706763	+	0.408050i
$906$		0			0
$907$	9.84739	+	17.0562i	0.326977	+	0.566341i	0.981911	−	0.189346i	$-0.0606366\pi$
$907$	9.84739	+	17.0562i	0.326977	+	0.566341i	−0.654933	+	0.755687i	$0.727303\pi$
$908$		0			0
$909$	−4.87044	+	24.4493i	−0.161542	+	0.810930i
$910$		0			0
$911$	10.9666	−	6.33157i	0.363340	−	0.209774i	−0.307205	−	0.951643i	$-0.599394\pi$
$911$	10.9666	−	6.33157i	0.363340	−	0.209774i	0.670545	+	0.741869i	$0.266060\pi$
$912$		0			0
$913$	5.40340	+	3.11966i	0.178827	+	0.103246i
$914$		0			0
$915$	−17.1039	−	6.44022i	−0.565439	−	0.212907i
$916$		0			0
$917$	−2.02806	+	1.48147i	−0.0669724	+	0.0489224i
$918$		0			0
$919$	−34.9422			−1.15264			−0.576318	−	0.817226i	$-0.695511\pi$
$919$	−34.9422			−1.15264			−0.576318	+	0.817226i	$0.695511\pi$
$920$		0			0
$921$	−36.9641	−	13.9183i	−1.21801	−	0.458622i
$922$		0			0
$923$	−27.1701	+	47.0601i	−0.894316	+	1.54900i
$924$		0			0
$925$	42.3558	+	73.3624i	1.39265	+	2.41214i
$926$		0			0
$927$	7.50549	+	22.1310i	0.246513	+	0.726877i
$928$		0			0
$929$	−11.9097	−	20.6283i	−0.390746	−	0.676792i	0.601802	−	0.798645i	$-0.294450\pi$
$929$	−11.9097	−	20.6283i	−0.390746	−	0.676792i	−0.992548	+	0.121853i	$0.961116\pi$
$930$		0			0
$931$	−21.8740	+	19.9004i	−0.716890	+	0.652211i
$932$		0			0
$933$	33.5108	+	40.8448i	1.09710	+	1.33720i
$934$		0			0
$935$			15.0373i			0.491771i
$936$		0			0
$937$		−	30.0910i		−	0.983029i	−0.870869	−	0.491514i	$-0.836444\pi$
$937$		−	30.0910i		−	0.983029i	0.870869	−	0.491514i	$-0.163556\pi$
$938$		0			0
$939$	−2.30535	−	13.9756i	−0.0752323	−	0.456076i
$940$		0			0
$941$	−11.1672	+	19.3422i	−0.364042	+	0.630539i	−0.988622	−	0.150422i	$-0.951937\pi$
$941$	−11.1672	+	19.3422i	−0.364042	+	0.630539i	0.624580	+	0.780961i	$0.285270\pi$
$942$		0			0
$943$	46.1332	−	26.6350i	1.50230	−	0.867355i
$944$		0			0
$945$	−22.9164	+	47.5071i	−0.745471	+	1.54541i
$946$		0			0
$947$	31.7683	−	18.3414i	1.03233	−	0.596016i	0.114679	−	0.993403i	$-0.463416\pi$
$947$	31.7683	−	18.3414i	1.03233	−	0.596016i	0.917651	+	0.397386i	$0.130083\pi$
$948$		0			0
$949$	−8.89550	+	15.4075i	−0.288760	+	0.500147i
$950$		0			0
$951$	4.01827	+	24.3597i	0.130301	+	0.789918i
$952$		0			0
$953$			23.4461i			0.759495i	0.925090	+	0.379747i	$0.123989\pi$
$953$			23.4461i			0.759495i	−0.925090	+	0.379747i	$0.876011\pi$
$954$		0			0
$955$			69.0028i			2.23288i
$956$		0			0
$957$	5.87894	+	7.16557i	0.190039	+	0.231630i
$958$		0			0
$959$	31.6010	−	3.40374i	1.02045	−	0.109912i
$960$		0			0
$961$	−13.3816	−	23.1777i	−0.431666	−	0.747667i
$962$		0			0
$963$	10.8930	−	12.4140i	0.351022	−	0.400036i
$964$		0			0
$965$	−29.4376	−	50.9875i	−0.947631	−	1.64134i
$966$		0			0
$967$	21.2372	−	36.7839i	0.682941	−	1.18289i	−0.291138	−	0.956681i	$-0.594034\pi$
$967$	21.2372	−	36.7839i	0.682941	−	1.18289i	0.974079	−	0.226208i	$-0.0726329\pi$
$968$		0			0
$969$	−39.6846	−	14.9426i	−1.27485	−	0.480026i
$970$		0			0
$971$	12.9007			0.414002			0.207001	−	0.978341i	$-0.433630\pi$
$971$	12.9007			0.414002			0.207001	+	0.978341i	$0.433630\pi$
$972$		0			0
$973$	3.47687	+	4.75966i	0.111463	+	0.152588i
$974$		0			0
$975$	−76.7762	−	28.9089i	−2.45881	−	0.925826i
$976$		0			0
$977$	4.22775	+	2.44089i	0.135258	+	0.0780911i	0.566102	−	0.824335i	$-0.308451\pi$
$977$	4.22775	+	2.44089i	0.135258	+	0.0780911i	−0.430844	+	0.902426i	$0.641784\pi$
$978$		0			0
$979$	1.05251	−	0.607668i	0.0336384	−	0.0194211i
$980$		0			0
$981$	−32.2212	−	28.2733i	−1.02874	−	0.902698i
$982$		0			0
$983$	−9.48312	−	16.4252i	−0.302464	−	0.523884i	0.674229	−	0.738522i	$-0.264476\pi$
$983$	−9.48312	−	16.4252i	−0.302464	−	0.523884i	−0.976694	+	0.214638i	$0.931143\pi$
$984$		0			0
$985$	37.6857	+	21.7578i	1.20077	+	0.693262i
$986$		0			0
$987$	−5.91076	−	1.52703i	−0.188142	−	0.0486059i
$988$		0			0
$989$			39.3514i			1.25130i
$990$		0			0
$991$	−34.1369			−1.08439			−0.542197	−	0.840251i	$-0.682407\pi$
$991$	−34.1369			−1.08439			−0.542197	+	0.840251i	$0.682407\pi$
$992$		0			0
$993$	34.2661	−	5.65238i	1.08740	−	0.179373i
$994$		0			0
$995$	−37.4024	−	21.5943i	−1.18573	−	0.684584i
$996$		0			0
$997$	9.92534	−	5.73040i	0.314339	−	0.181484i	−0.334528	−	0.942386i	$-0.608577\pi$
$997$	9.92534	−	5.73040i	0.314339	−	0.181484i	0.648866	+	0.760902i	$0.275243\pi$
$998$		0			0
$999$	39.9470	−	21.3304i	1.26387	−	0.674863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bu.a.41.15	yes	48
3.2	odd	2		1512.2.bu.a.881.1		48
4.3	odd	2		1008.2.cc.d.545.10		48
7.6	odd	2	inner	504.2.bu.a.41.10	✓	48
9.2	odd	6	inner	504.2.bu.a.209.10	yes	48
9.4	even	3		4536.2.k.a.3401.1		48
9.5	odd	6		4536.2.k.a.3401.48		48
9.7	even	3		1512.2.bu.a.1385.24		48
12.11	even	2		3024.2.cc.d.881.1		48
21.20	even	2		1512.2.bu.a.881.24		48
28.27	even	2		1008.2.cc.d.545.15		48
36.7	odd	6		3024.2.cc.d.2897.24		48
36.11	even	6		1008.2.cc.d.209.15		48
63.13	odd	6		4536.2.k.a.3401.47		48
63.20	even	6	inner	504.2.bu.a.209.15	yes	48
63.34	odd	6		1512.2.bu.a.1385.1		48
63.41	even	6		4536.2.k.a.3401.2		48
84.83	odd	2		3024.2.cc.d.881.24		48
252.83	odd	6		1008.2.cc.d.209.10		48
252.223	even	6		3024.2.cc.d.2897.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.10	✓	48	7.6	odd	2	inner
504.2.bu.a.41.15	yes	48	1.1	even	1	trivial
504.2.bu.a.209.10	yes	48	9.2	odd	6	inner
504.2.bu.a.209.15	yes	48	63.20	even	6	inner
1008.2.cc.d.209.10		48	252.83	odd	6
1008.2.cc.d.209.15		48	36.11	even	6
1008.2.cc.d.545.10		48	4.3	odd	2
1008.2.cc.d.545.15		48	28.27	even	2
1512.2.bu.a.881.1		48	3.2	odd	2
1512.2.bu.a.881.24		48	21.20	even	2
1512.2.bu.a.1385.1		48	63.34	odd	6
1512.2.bu.a.1385.24		48	9.7	even	3
3024.2.cc.d.881.1		48	12.11	even	2
3024.2.cc.d.881.24		48	84.83	odd	2
3024.2.cc.d.2897.1		48	252.223	even	6
3024.2.cc.d.2897.24		48	36.7	odd	6
4536.2.k.a.3401.1		48	9.4	even	3
4536.2.k.a.3401.2		48	63.41	even	6
4536.2.k.a.3401.47		48	63.13	odd	6
4536.2.k.a.3401.48		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.610344 - 1.62095i) q^{3} +(1.91834 - 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +(-2.25496 - 1.97867i) q^{9} +O(q^{10})\)	\(q+(0.610344 - 1.62095i) q^{3} +(1.91834 - 3.32266i) q^{5} +(2.41978 + 1.06989i) q^{7} +(-2.25496 - 1.97867i) q^{9} +(0.585698 - 0.338153i) q^{11} +(4.22006 + 2.43645i) q^{13} +(-4.21502 - 5.13749i) q^{15} -5.79523 q^{17} +4.22456i q^{19} +(3.21114 - 3.26934i) q^{21} +(4.76574 + 2.75150i) q^{23} +(-4.86003 - 8.41782i) q^{25} +(-4.58363 + 2.44751i) q^{27} +(-6.85239 + 3.95623i) q^{29} +(-1.78257 - 1.02917i) q^{31} +(-0.190652 - 1.15578i) q^{33} +(8.19684 - 5.98768i) q^{35} -8.71513 q^{37} +(6.52506 - 5.35344i) q^{39} +(4.84009 - 8.38328i) q^{41} +(3.57545 + 6.19287i) q^{43} +(-10.9002 + 3.69670i) q^{45} +(-0.666092 - 1.15370i) q^{47} +(4.71066 + 5.17781i) q^{49} +(-3.53708 + 9.39379i) q^{51} -5.18304i q^{53} -2.59476i q^{55} +(6.84780 + 2.57843i) q^{57} +(2.09619 - 3.63071i) q^{59} +(2.38178 - 1.37512i) q^{61} +(-3.33953 - 7.20052i) q^{63} +(16.1910 - 9.34787i) q^{65} +(-3.27636 + 5.67483i) q^{67} +(7.36878 - 6.04566i) q^{69} +11.1515i q^{71} +3.65100i q^{73} +(-16.6112 + 2.74010i) q^{75} +(1.77905 - 0.191621i) q^{77} +(-5.61720 - 9.72928i) q^{79} +(1.16970 + 8.92367i) q^{81} +(4.61279 + 7.98959i) q^{83} +(-11.1172 + 19.2556i) q^{85} +(2.23054 + 13.5220i) q^{87} +1.79702 q^{89} +(7.60487 + 10.4107i) q^{91} +(-2.75621 + 2.26131i) q^{93} +(14.0368 + 8.10413i) q^{95} +(-2.60513 + 1.50407i) q^{97} +(-1.98982 - 0.396384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91} + 16 q^{93} - 108 q^{95} + 44 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Introduction

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