LMFDB - Embedded newform 1148.2.i.e.821.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			821.10
Character	$\chi$	$=$	1148.821
Dual form			1148.2.i.e.165.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.702089 + 1.21605i) q^{3} +(-1.80784 + 3.13127i) q^{5} +(0.606375 + 2.57533i) q^{7} +(0.514141 - 0.890519i) q^{9} +O(q^{10})$	\(q+(0.702089 + 1.21605i) q^{3} +(-1.80784 + 3.13127i) q^{5} +(0.606375 + 2.57533i) q^{7} +(0.514141 - 0.890519i) q^{9} +(2.82465 + 4.89243i) q^{11} +6.54345 q^{13} -5.07705 q^{15} +(-1.69533 - 2.93640i) q^{17} +(-2.59869 + 4.50106i) q^{19} +(-2.70601 + 2.54549i) q^{21} +(1.40505 - 2.43362i) q^{23} +(-4.03655 - 6.99151i) q^{25} +5.65643 q^{27} +2.17600 q^{29} +(-3.13027 - 5.42179i) q^{31} +(-3.96631 + 6.86985i) q^{33} +(-9.16026 - 2.75705i) q^{35} +(-0.320730 + 0.555521i) q^{37} +(4.59409 + 7.95720i) q^{39} -1.00000 q^{41} -4.44365 q^{43} +(1.85897 + 3.21983i) q^{45} +(-3.34820 + 5.79926i) q^{47} +(-6.26462 + 3.12323i) q^{49} +(2.38055 - 4.12323i) q^{51} +(-2.47639 - 4.28923i) q^{53} -20.4260 q^{55} -7.29805 q^{57} +(5.51446 + 9.55133i) q^{59} +(6.01946 - 10.4260i) q^{61} +(2.60514 + 0.784093i) q^{63} +(-11.8295 + 20.4893i) q^{65} +(-5.29208 - 9.16615i) q^{67} +3.94589 q^{69} -8.70411 q^{71} +(-0.211460 - 0.366259i) q^{73} +(5.66804 - 9.81733i) q^{75} +(-10.8868 + 10.2410i) q^{77} +(7.11326 - 12.3205i) q^{79} +(2.42889 + 4.20697i) q^{81} +5.06521 q^{83} +12.2595 q^{85} +(1.52774 + 2.64613i) q^{87} +(0.782283 - 1.35495i) q^{89} +(3.96779 + 16.8515i) q^{91} +(4.39546 - 7.61317i) q^{93} +(-9.39602 - 16.2744i) q^{95} +16.4451 q^{97} +5.80907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.702089	+	1.21605i	0.405351	+	0.702089i	0.994362	−	0.106036i	$-0.0338158\pi$
$3$	0.702089	+	1.21605i	0.405351	+	0.702089i	−0.589011	+	0.808125i	$0.700482\pi$
$4$		0			0
$5$	−1.80784	+	3.13127i	−0.808489	+	1.40034i	0.105421	+	0.994428i	$0.466381\pi$
$5$	−1.80784	+	3.13127i	−0.808489	+	1.40034i	−0.913910	+	0.405917i	$0.866952\pi$
$6$		0			0
$7$	0.606375	+	2.57533i	0.229188	+	0.973382i
$7$	0.606375	+	2.57533i	0.229188	+	0.973382i
$8$		0			0
$9$	0.514141	−	0.890519i	0.171380	−	0.296840i
$10$		0			0
$11$	2.82465	+	4.89243i	0.851663	+	1.47512i	0.879707	+	0.475517i	$0.157739\pi$
$11$	2.82465	+	4.89243i	0.851663	+	1.47512i	−0.0280437	+	0.999607i	$0.508928\pi$
$12$		0			0
$13$	6.54345			1.81483			0.907414	−	0.420238i	$-0.138053\pi$
$13$	6.54345			1.81483			0.907414	+	0.420238i	$0.138053\pi$
$14$		0			0
$15$	−5.07705			−1.31089
$16$		0			0
$17$	−1.69533	−	2.93640i	−0.411178	−	0.712181i	0.583841	−	0.811868i	$-0.301549\pi$
$17$	−1.69533	−	2.93640i	−0.411178	−	0.712181i	−0.995019	+	0.0996871i	$0.968216\pi$
$18$		0			0
$19$	−2.59869	+	4.50106i	−0.596181	+	1.03262i	0.397199	+	0.917733i	$0.369982\pi$
$19$	−2.59869	+	4.50106i	−0.596181	+	1.03262i	−0.993379	+	0.114882i	$0.963351\pi$
$20$		0			0
$21$	−2.70601	+	2.54549i	−0.590499	+	0.555472i
$22$		0			0
$23$	1.40505	−	2.43362i	0.292974	−	0.507446i	−0.681538	−	0.731783i	$-0.738688\pi$
$23$	1.40505	−	2.43362i	0.292974	−	0.507446i	0.974512	+	0.224337i	$0.0720218\pi$
$24$		0			0
$25$	−4.03655	−	6.99151i	−0.807310	−	1.39830i
$26$		0			0
$27$	5.65643			1.08858
$28$		0			0
$29$	2.17600			0.404072			0.202036	−	0.979378i	$-0.435244\pi$
$29$	2.17600			0.404072			0.202036	+	0.979378i	$0.435244\pi$
$30$		0			0
$31$	−3.13027	−	5.42179i	−0.562214	−	0.973783i	−0.997303	−	0.0733954i	$-0.976616\pi$
$31$	−3.13027	−	5.42179i	−0.562214	−	0.973783i	0.435089	−	0.900387i	$-0.356717\pi$
$32$		0			0
$33$	−3.96631	+	6.86985i	−0.690446	+	1.19589i
$34$		0			0
$35$	−9.16026	−	2.75705i	−1.54837	−	0.466027i
$36$		0			0
$37$	−0.320730	+	0.555521i	−0.0527277	+	0.0913271i	−0.891185	−	0.453641i	$-0.850125\pi$
$37$	−0.320730	+	0.555521i	−0.0527277	+	0.0913271i	0.838457	+	0.544968i	$0.183458\pi$
$38$		0			0
$39$	4.59409	+	7.95720i	0.735643	+	1.27417i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	−4.44365			−0.677650			−0.338825	−	0.940849i	$-0.610029\pi$
$43$	−4.44365			−0.677650			−0.338825	+	0.940849i	$0.610029\pi$
$44$		0			0
$45$	1.85897	+	3.21983i	0.277118	+	0.479983i
$46$		0			0
$47$	−3.34820	+	5.79926i	−0.488386	+	0.845909i	−0.999911	−	0.0133593i	$-0.995747\pi$
$47$	−3.34820	+	5.79926i	−0.488386	+	0.845909i	0.511525	+	0.859268i	$0.329081\pi$
$48$		0			0
$49$	−6.26462	+	3.12323i	−0.894946	+	0.446175i
$50$		0			0
$51$	2.38055	−	4.12323i	0.333343	−	0.577367i
$52$		0			0
$53$	−2.47639	−	4.28923i	−0.340158	−	0.589171i	0.644304	−	0.764770i	$-0.277147\pi$
$53$	−2.47639	−	4.28923i	−0.340158	−	0.589171i	−0.984462	+	0.175599i	$0.943814\pi$
$54$		0			0
$55$	−20.4260			−2.75424
$56$		0			0
$57$	−7.29805			−0.966651
$58$		0			0
$59$	5.51446	+	9.55133i	0.717922	+	1.24348i	0.961822	+	0.273676i	$0.0882397\pi$
$59$	5.51446	+	9.55133i	0.717922	+	1.24348i	−0.243900	+	0.969800i	$0.578427\pi$
$60$		0			0
$61$	6.01946	−	10.4260i	0.770713	−	1.33491i	−0.166460	−	0.986048i	$-0.553234\pi$
$61$	6.01946	−	10.4260i	0.770713	−	1.33491i	0.937173	−	0.348866i	$-0.113433\pi$
$62$		0			0
$63$	2.60514	+	0.784093i	0.328217	+	0.0987865i
$64$		0			0
$65$	−11.8295	+	20.4893i	−1.46727	+	2.54138i
$66$		0			0
$67$	−5.29208	−	9.16615i	−0.646531	−	1.11982i	−0.983946	−	0.178468i	$-0.942886\pi$
$67$	−5.29208	−	9.16615i	−0.646531	−	1.11982i	0.337415	−	0.941356i	$-0.390447\pi$
$68$		0			0
$69$	3.94589			0.475030
$70$		0			0
$71$	−8.70411			−1.03299			−0.516494	−	0.856291i	$-0.672763\pi$
$71$	−8.70411			−1.03299			−0.516494	+	0.856291i	$0.672763\pi$
$72$		0			0
$73$	−0.211460	−	0.366259i	−0.0247495	−	0.0428674i	0.853385	−	0.521281i	$-0.174545\pi$
$73$	−0.211460	−	0.366259i	−0.0247495	−	0.0428674i	−0.878135	+	0.478413i	$0.841212\pi$
$74$		0			0
$75$	5.66804	−	9.81733i	0.654489	−	1.13361i
$76$		0			0
$77$	−10.8868	+	10.2410i	−1.24067	+	1.16707i
$78$		0			0
$79$	7.11326	−	12.3205i	0.800305	−	1.38617i	−0.119111	−	0.992881i	$-0.538004\pi$
$79$	7.11326	−	12.3205i	0.800305	−	1.38617i	0.919416	−	0.393287i	$-0.128662\pi$
$80$		0			0
$81$	2.42889	+	4.20697i	0.269877	+	0.467441i
$82$		0			0
$83$	5.06521			0.555979			0.277989	−	0.960584i	$-0.410332\pi$
$83$	5.06521			0.555979			0.277989	+	0.960584i	$0.410332\pi$
$84$		0			0
$85$	12.2595			1.32973
$86$		0			0
$87$	1.52774	+	2.64613i	0.163791	+	0.283695i
$88$		0			0
$89$	0.782283	−	1.35495i	0.0829218	−	0.143625i	−0.821582	−	0.570090i	$-0.806908\pi$
$89$	0.782283	−	1.35495i	0.0829218	−	0.143625i	0.904504	+	0.426466i	$0.140241\pi$
$90$		0			0
$91$	3.96779	+	16.8515i	0.415937	+	1.76652i
$92$		0			0
$93$	4.39546	−	7.61317i	0.455788	−	0.789448i
$94$		0			0
$95$	−9.39602	−	16.2744i	−0.964011	−	1.66972i
$96$		0			0
$97$	16.4451			1.66975			0.834873	−	0.550442i	$-0.185541\pi$
$97$	16.4451			1.66975			0.834873	+	0.550442i	$0.185541\pi$
$98$		0			0
$99$	5.80907			0.583833
$100$		0			0
$101$	5.57025	+	9.64795i	0.554260	+	0.960007i	0.997961	+	0.0638319i	$0.0203321\pi$
$101$	5.57025	+	9.64795i	0.554260	+	0.960007i	−0.443700	+	0.896175i	$0.646335\pi$
$102$		0			0
$103$	2.50083	−	4.33156i	0.246414	−	0.426801i	−0.716114	−	0.697983i	$-0.754081\pi$
$103$	2.50083	−	4.33156i	0.246414	−	0.426801i	0.962528	+	0.271182i	$0.0874145\pi$
$104$		0			0
$105$	−3.07860	−	13.0751i	−0.300440	−	1.27600i
$106$		0			0
$107$	4.14643	−	7.18184i	0.400851	−	0.694294i	−0.592978	−	0.805219i	$-0.702048\pi$
$107$	4.14643	−	7.18184i	0.400851	−	0.694294i	0.993829	+	0.110925i	$0.0353812\pi$
$108$		0			0
$109$	−5.51397	−	9.55048i	−0.528143	−	0.914770i	−0.999462	−	0.0328071i	$-0.989555\pi$
$109$	−5.51397	−	9.55048i	−0.528143	−	0.914770i	0.471319	−	0.881963i	$-0.343778\pi$
$110$		0			0
$111$	−0.900725			−0.0854930
$112$		0			0
$113$	−8.26658			−0.777654			−0.388827	−	0.921311i	$-0.627120\pi$
$113$	−8.26658			−0.777654			−0.388827	+	0.921311i	$0.627120\pi$
$114$		0			0
$115$	5.08022	+	8.79919i	0.473733	+	0.820529i
$116$		0			0
$117$	3.36426	−	5.82707i	0.311026	−	0.538713i
$118$		0			0
$119$	6.53418	−	6.14659i	0.598987	−	0.563457i
$120$		0			0
$121$	−10.4573	+	18.1125i	−0.950660	+	1.64659i
$122$		0			0
$123$	−0.702089	−	1.21605i	−0.0633053	−	0.109648i
$124$		0			0
$125$	11.1113			0.993828
$126$		0			0
$127$	1.12925			0.100205			0.0501024	−	0.998744i	$-0.484045\pi$
$127$	1.12925			0.100205			0.0501024	+	0.998744i	$0.484045\pi$
$128$		0			0
$129$	−3.11984	−	5.40371i	−0.274686	−	0.475771i
$130$		0			0
$131$	−9.46246	+	16.3895i	−0.826739	+	1.43195i	0.0738447	+	0.997270i	$0.476473\pi$
$131$	−9.46246	+	16.3895i	−0.826739	+	1.43195i	−0.900583	+	0.434684i	$0.856860\pi$
$132$		0			0
$133$	−13.1675	−	3.96315i	−1.14177	−	0.343648i
$134$		0			0
$135$	−10.2259	+	17.7118i	−0.880105	+	1.52439i
$136$		0			0
$137$	−4.18113	−	7.24193i	−0.357218	−	0.618720i	0.630277	−	0.776370i	$-0.282941\pi$
$137$	−4.18113	−	7.24193i	−0.357218	−	0.618720i	−0.987495	+	0.157650i	$0.949608\pi$
$138$		0			0
$139$	18.1952			1.54330			0.771648	−	0.636050i	$-0.219433\pi$
$139$	18.1952			1.54330			0.771648	+	0.636050i	$0.219433\pi$
$140$		0			0
$141$	−9.40296			−0.791872
$142$		0			0
$143$	18.4829	+	32.0134i	1.54562	+	2.67710i
$144$		0			0
$145$	−3.93385	+	6.81362i	−0.326688	+	0.565840i
$146$		0			0
$147$	−8.19634	−	5.42533i	−0.676022	−	0.447474i
$148$		0			0
$149$	6.02318	−	10.4325i	0.493438	−	0.854660i	−0.506533	−	0.862221i	$-0.669073\pi$
$149$	6.02318	−	10.4325i	0.493438	−	0.854660i	0.999971	+	0.00756013i	$0.00240649\pi$
$150$		0			0
$151$	−2.72091	−	4.71275i	−0.221424	−	0.383518i	0.733816	−	0.679348i	$-0.237737\pi$
$151$	−2.72091	−	4.71275i	−0.221424	−	0.383518i	−0.955241	+	0.295830i	$0.904404\pi$
$152$		0			0
$153$	−3.48656			−0.281871
$154$		0			0
$155$	22.6361			1.81818
$156$		0			0
$157$	−10.4620	−	18.1207i	−0.834960	−	1.44619i	−0.894063	−	0.447941i	$-0.852157\pi$
$157$	−10.4620	−	18.1207i	−0.834960	−	1.44619i	0.0591032	−	0.998252i	$-0.481176\pi$
$158$		0			0
$159$	3.47729	−	6.02284i	0.275767	−	0.477642i
$160$		0			0
$161$	7.11937	+	2.14278i	0.561085	+	0.168875i
$162$		0			0
$163$	−8.54290	+	14.7967i	−0.669132	+	1.15897i	0.309015	+	0.951057i	$0.400001\pi$
$163$	−8.54290	+	14.7967i	−0.669132	+	1.15897i	−0.978147	+	0.207913i	$0.933333\pi$
$164$		0			0
$165$	−14.3409	−	24.8391i	−1.11644	−	1.93372i
$166$		0			0
$167$	13.0854			1.01258			0.506289	−	0.862364i	$-0.331017\pi$
$167$	13.0854			1.01258			0.506289	+	0.862364i	$0.331017\pi$
$168$		0			0
$169$	29.8168			2.29360
$170$		0			0
$171$	2.67219	+	4.62837i	0.204347	+	0.353940i
$172$		0			0
$173$	−9.61352	+	16.6511i	−0.730902	+	1.26596i	0.225596	+	0.974221i	$0.427567\pi$
$173$	−9.61352	+	16.6511i	−0.730902	+	1.26596i	−0.956498	+	0.291739i	$0.905766\pi$
$174$		0			0
$175$	15.5578	−	14.6349i	1.17606	−	1.10630i
$176$		0			0
$177$	−7.74329	+	13.4118i	−0.582021	+	1.00809i
$178$		0			0
$179$	4.36507	+	7.56052i	0.326261	+	0.565100i	0.981767	−	0.190090i	$-0.0608780\pi$
$179$	4.36507	+	7.56052i	0.326261	+	0.565100i	−0.655506	+	0.755190i	$0.727545\pi$
$180$		0			0
$181$	−11.2949			−0.839544			−0.419772	−	0.907630i	$-0.637890\pi$
$181$	−11.2949			−0.839544			−0.419772	+	0.907630i	$0.637890\pi$
$182$		0			0
$183$	16.9048			1.24964
$184$		0			0
$185$	−1.15966	−	2.00858i	−0.0852596	−	0.147674i
$186$		0			0
$187$	9.57741	−	16.5886i	0.700370	−	1.21308i
$188$		0			0
$189$	3.42992	+	14.5672i	0.249490	+	1.05960i
$190$		0			0
$191$	8.45419	−	14.6431i	0.611724	−	1.05954i	−0.379226	−	0.925304i	$-0.623810\pi$
$191$	8.45419	−	14.6431i	0.611724	−	1.05954i	0.990950	−	0.134233i	$-0.0428570\pi$
$192$		0			0
$193$	−1.99344	−	3.45274i	−0.143491	−	0.248533i	0.785318	−	0.619093i	$-0.212499\pi$
$193$	−1.99344	−	3.45274i	−0.143491	−	0.248533i	−0.928809	+	0.370559i	$0.879166\pi$
$194$		0			0
$195$	−33.2215			−2.37904
$196$		0			0
$197$	−12.0163			−0.856124			−0.428062	−	0.903749i	$-0.640803\pi$
$197$	−12.0163			−0.856124			−0.428062	+	0.903749i	$0.640803\pi$
$198$		0			0
$199$	5.46266	+	9.46160i	0.387238	+	0.670715i	0.992077	−	0.125632i	$-0.0400960\pi$
$199$	5.46266	+	9.46160i	0.387238	+	0.670715i	−0.604839	+	0.796348i	$0.706763\pi$
$200$		0			0
$201$	7.43103	−	12.8709i	0.524144	−	0.907844i
$202$		0			0
$203$	1.31947	+	5.60390i	0.0926086	+	0.393317i
$204$		0			0
$205$	1.80784	−	3.13127i	0.126265	−	0.218697i
$206$		0			0
$207$	−1.44479	−	2.50245i	−0.100420	−	0.173932i
$208$		0			0
$209$	−29.3615			−2.03098
$210$		0			0
$211$	−7.98904			−0.549988			−0.274994	−	0.961446i	$-0.588676\pi$
$211$	−7.98904			−0.549988			−0.274994	+	0.961446i	$0.588676\pi$
$212$		0			0
$213$	−6.11106	−	10.5847i	−0.418723	−	0.725249i
$214$		0			0
$215$	8.03339	−	13.9142i	0.547873	−	0.948943i
$216$		0			0
$217$	12.0648	−	11.3491i	0.819010	−	0.770428i
$218$		0			0
$219$	0.296927	−	0.514293i	0.0200645	−	0.0347527i
$220$		0			0
$221$	−11.0933	−	19.2142i	−0.746217	−	1.29249i
$222$		0			0
$223$	27.5999			1.84823			0.924115	−	0.382116i	$-0.124804\pi$
$223$	27.5999			1.84823			0.924115	+	0.382116i	$0.124804\pi$
$224$		0			0
$225$	−8.30143			−0.553429
$226$		0			0
$227$	12.1657	+	21.0717i	0.807468	+	1.39858i	0.914612	+	0.404332i	$0.132496\pi$
$227$	12.1657	+	21.0717i	0.807468	+	1.39858i	−0.107144	+	0.994244i	$0.534171\pi$
$228$		0			0
$229$	−0.0548675	+	0.0950332i	−0.00362574	+	0.00627997i	−0.867833	−	0.496857i	$-0.834487\pi$
$229$	−0.0548675	+	0.0950332i	−0.00362574	+	0.00627997i	0.864207	+	0.503137i	$0.167821\pi$
$230$		0			0
$231$	−20.0972	−	6.04884i	−1.32230	−	0.397984i
$232$		0			0
$233$	4.11476	−	7.12698i	0.269567	−	0.466904i	−0.699183	−	0.714943i	$-0.746453\pi$
$233$	4.11476	−	7.12698i	0.269567	−	0.466904i	0.968750	+	0.248039i	$0.0797861\pi$
$234$		0			0
$235$	−12.1060	−	20.9682i	−0.789710	−	1.36782i
$236$		0			0
$237$	19.9766			1.29762
$238$		0			0
$239$	7.13997			0.461846			0.230923	−	0.972972i	$-0.425825\pi$
$239$	7.13997			0.461846			0.230923	+	0.972972i	$0.425825\pi$
$240$		0			0
$241$	−6.15955	−	10.6687i	−0.396771	−	0.687228i	0.596554	−	0.802573i	$-0.296536\pi$
$241$	−6.15955	−	10.6687i	−0.396771	−	0.687228i	−0.993326	+	0.115345i	$0.963203\pi$
$242$		0			0
$243$	5.07404	−	8.78850i	0.325500	−	0.563782i
$244$		0			0
$245$	1.54575	−	25.2625i	0.0987546	−	1.61396i
$246$		0			0
$247$	−17.0044	+	29.4525i	−1.08197	+	1.87402i
$248$		0			0
$249$	3.55623	+	6.15957i	0.225367	+	0.390347i
$250$		0			0
$251$	−6.03854			−0.381149			−0.190575	−	0.981673i	$-0.561035\pi$
$251$	−6.03854			−0.381149			−0.190575	+	0.981673i	$0.561035\pi$
$252$		0			0
$253$	15.8751			0.998060
$254$		0			0
$255$	8.60728	+	14.9082i	0.539009	+	0.933590i
$256$		0			0
$257$	−14.2858	+	24.7437i	−0.891123	+	1.54347i	−0.0525914	+	0.998616i	$0.516748\pi$
$257$	−14.2858	+	24.7437i	−0.891123	+	1.54347i	−0.838531	+	0.544854i	$0.816585\pi$
$258$		0			0
$259$	−1.62513	−	0.489131i	−0.100981	−	0.0303931i
$260$		0			0
$261$	1.11877	−	1.93776i	0.0692501	−	0.119945i
$262$		0			0
$263$	15.3527	+	26.5917i	0.946690	+	1.63971i	0.752333	+	0.658783i	$0.228929\pi$
$263$	15.3527	+	26.5917i	0.946690	+	1.63971i	0.194357	+	0.980931i	$0.437738\pi$
$264$		0			0
$265$	17.9076			1.10006
$266$		0			0
$267$	2.19693			0.134450
$268$		0			0
$269$	−6.08035	−	10.5315i	−0.370726	−	0.642116i	0.618952	−	0.785429i	$-0.287558\pi$
$269$	−6.08035	−	10.5315i	−0.370726	−	0.642116i	−0.989677	+	0.143313i	$0.954224\pi$
$270$		0			0
$271$	−2.92080	+	5.05897i	−0.177426	+	0.307311i	−0.940998	−	0.338412i	$-0.890110\pi$
$271$	−2.92080	+	5.05897i	−0.177426	+	0.307311i	0.763572	+	0.645722i	$0.223444\pi$
$272$		0			0
$273$	−17.7066	+	16.6563i	−1.07165	+	1.00809i
$274$		0			0
$275$	22.8037	−	39.4971i	1.37511	−	2.38176i
$276$		0			0
$277$	11.3917	+	19.7311i	0.684463	+	1.18553i	0.973605	+	0.228239i	$0.0732968\pi$
$277$	11.3917	+	19.7311i	0.684463	+	1.18553i	−0.289142	+	0.957286i	$0.593370\pi$
$278$		0			0
$279$	−6.43761			−0.385410
$280$		0			0
$281$	−2.36022			−0.140799			−0.0703995	−	0.997519i	$-0.522427\pi$
$281$	−2.36022			−0.140799			−0.0703995	+	0.997519i	$0.522427\pi$
$282$		0			0
$283$	−0.0483699	−	0.0837790i	−0.00287529	−	0.00498015i	0.864584	−	0.502488i	$-0.167582\pi$
$283$	−0.0483699	−	0.0837790i	−0.00287529	−	0.00498015i	−0.867459	+	0.497508i	$0.834249\pi$
$284$		0			0
$285$	13.1937	−	22.8521i	0.781527	−	1.35364i
$286$		0			0
$287$	−0.606375	−	2.57533i	−0.0357932	−	0.152017i
$288$		0			0
$289$	2.75171	−	4.76611i	0.161866	−	0.280359i
$290$		0			0
$291$	11.5459	+	19.9981i	0.676834	+	1.17231i
$292$		0			0
$293$	24.8023			1.44897			0.724484	−	0.689292i	$-0.242078\pi$
$293$	24.8023			1.44897			0.724484	+	0.689292i	$0.242078\pi$
$294$		0			0
$295$	−39.8770			−2.32173
$296$		0			0
$297$	15.9774	+	27.6737i	0.927103	+	1.60579i
$298$		0			0
$299$	9.19390	−	15.9243i	0.531697	−	0.920927i
$300$		0			0
$301$	−2.69452	−	11.4438i	−0.155309	−	0.659612i
$302$		0			0
$303$	−7.82162	+	13.5474i	−0.449340	+	0.778281i
$304$		0			0
$305$	21.7644	+	37.6971i	1.24623	+	2.15853i
$306$		0			0
$307$	−3.46391			−0.197696			−0.0988480	−	0.995103i	$-0.531516\pi$
$307$	−3.46391			−0.197696			−0.0988480	+	0.995103i	$0.531516\pi$
$308$		0			0
$309$	7.02321			0.399537
$310$		0			0
$311$	−13.0094	−	22.5330i	−0.737697	−	1.27773i	−0.953530	−	0.301298i	$-0.902580\pi$
$311$	−13.0094	−	22.5330i	−0.737697	−	1.27773i	0.215833	−	0.976430i	$-0.430753\pi$
$312$		0			0
$313$	−2.47911	+	4.29394i	−0.140127	+	0.242708i	−0.927544	−	0.373713i	$-0.878085\pi$
$313$	−2.47911	+	4.29394i	−0.140127	+	0.242708i	0.787417	+	0.616421i	$0.211418\pi$
$314$		0			0
$315$	−7.16487	+	6.73987i	−0.403695	+	0.379749i
$316$		0			0
$317$	−8.50175	+	14.7255i	−0.477506	+	0.827065i	−0.999668	−	0.0257819i	$-0.991792\pi$
$317$	−8.50175	+	14.7255i	−0.477506	+	0.827065i	0.522162	+	0.852847i	$0.325126\pi$
$318$		0			0
$319$	6.14642	+	10.6459i	0.344133	+	0.596056i
$320$		0			0
$321$	11.6447			0.649942
$322$		0			0
$323$	17.6226			0.980545
$324$		0			0
$325$	−26.4130	−	45.7486i	−1.46513	−	2.53768i
$326$		0			0
$327$	7.74260	−	13.4106i	0.428167	−	0.741607i
$328$		0			0
$329$	−16.9653	−	5.10620i	−0.935325	−	0.281514i
$330$		0			0
$331$	−5.63472	+	9.75961i	−0.309712	+	0.536437i	−0.978299	−	0.207197i	$-0.933566\pi$
$331$	−5.63472	+	9.75961i	−0.309712	+	0.536437i	0.668587	+	0.743634i	$0.266899\pi$
$332$		0			0
$333$	0.329801	+	0.571232i	0.0180730	+	0.0313033i
$334$		0			0
$335$	38.2689			2.09085
$336$		0			0
$337$	29.7342			1.61972			0.809862	−	0.586620i	$-0.199542\pi$
$337$	29.7342			1.61972			0.809862	+	0.586620i	$0.199542\pi$
$338$		0			0
$339$	−5.80387	−	10.0526i	−0.315223	−	0.545983i
$340$		0			0
$341$	17.6838	−	30.6293i	0.957633	−	1.65867i
$342$		0			0
$343$	−11.8420	−	14.2396i	−0.639410	−	0.768866i
$344$		0			0
$345$	−7.13353	+	12.3556i	−0.384056	+	0.665205i
$346$		0			0
$347$	−6.83350	−	11.8360i	−0.366841	−	0.635388i	0.622228	−	0.782836i	$-0.286228\pi$
$347$	−6.83350	−	11.8360i	−0.366841	−	0.635388i	−0.989070	+	0.147448i	$0.952894\pi$
$348$		0			0
$349$	−21.4570			−1.14857			−0.574284	−	0.818656i	$-0.694720\pi$
$349$	−21.4570			−1.14857			−0.574284	+	0.818656i	$0.694720\pi$
$350$		0			0
$351$	37.0126			1.97559
$352$		0			0
$353$	−10.0513	−	17.4093i	−0.534974	−	0.926603i	−0.999165	−	0.0408673i	$-0.986988\pi$
$353$	−10.0513	−	17.4093i	−0.534974	−	0.926603i	0.464190	−	0.885736i	$-0.346345\pi$
$354$		0			0
$355$	15.7356	−	27.2549i	0.835159	−	1.44654i
$356$		0			0
$357$	12.0622	+	3.63046i	0.638397	+	0.192144i
$358$		0			0
$359$	6.85540	−	11.8739i	0.361814	−	0.626681i	−0.626445	−	0.779466i	$-0.715491\pi$
$359$	6.85540	−	11.8739i	0.361814	−	0.626681i	0.988260	+	0.152785i	$0.0488241\pi$
$360$		0			0
$361$	−4.00639	−	6.93927i	−0.210863	−	0.365225i
$362$		0			0
$363$	−29.3677			−1.54140
$364$		0			0
$365$	1.52914			0.0800388
$366$		0			0
$367$	−13.5653	−	23.4959i	−0.708105	−	1.22647i	−0.965559	−	0.260184i	$-0.916217\pi$
$367$	−13.5653	−	23.4959i	−0.708105	−	1.22647i	0.257454	−	0.966291i	$-0.417116\pi$
$368$		0			0
$369$	−0.514141	+	0.890519i	−0.0267651	+	0.0463586i
$370$		0			0
$371$	9.54455	−	8.97839i	0.495528	−	0.466135i
$372$		0			0
$373$	5.27865	−	9.14288i	0.273318	−	0.473401i	−0.696391	−	0.717662i	$-0.745212\pi$
$373$	5.27865	−	9.14288i	0.273318	−	0.473401i	0.969709	+	0.244262i	$0.0785455\pi$
$374$		0			0
$375$	7.80115	+	13.5120i	0.402850	+	0.697756i
$376$		0			0
$377$	14.2385			0.733322
$378$		0			0
$379$	24.9019			1.27913			0.639563	−	0.768739i	$-0.279115\pi$
$379$	24.9019			1.27913			0.639563	+	0.768739i	$0.279115\pi$
$380$		0			0
$381$	0.792836	+	1.37323i	0.0406182	+	0.0703528i
$382$		0			0
$383$	−4.37423	+	7.57640i	−0.223513	+	0.387136i	−0.955872	−	0.293783i	$-0.905086\pi$
$383$	−4.37423	+	7.57640i	−0.223513	+	0.387136i	0.732359	+	0.680918i	$0.238419\pi$
$384$		0			0
$385$	−12.3858	−	52.6036i	−0.631240	−	2.68093i
$386$		0			0
$387$	−2.28466	+	3.95715i	−0.116136	+	0.201153i
$388$		0			0
$389$	2.64099	+	4.57433i	0.133903	+	0.231927i	0.925178	−	0.379533i	$-0.123915\pi$
$389$	2.64099	+	4.57433i	0.133903	+	0.231927i	−0.791275	+	0.611461i	$0.790582\pi$
$390$		0			0
$391$	−9.52812			−0.481858
$392$		0			0
$393$	−26.5740			−1.34048
$394$		0			0
$395$	25.7192	+	44.5470i	1.29408	+	2.24140i
$396$		0			0
$397$	4.09690	−	7.09603i	0.205617	−	0.356140i	−0.744712	−	0.667386i	$-0.767413\pi$
$397$	4.09690	−	7.09603i	0.205617	−	0.356140i	0.950329	+	0.311246i	$0.100746\pi$
$398$		0			0
$399$	−4.42536	−	18.7949i	−0.221545	−	0.940920i
$400$		0			0
$401$	−5.87990	+	10.1843i	−0.293628	+	0.508579i	−0.974665	−	0.223670i	$-0.928196\pi$
$401$	−5.87990	+	10.1843i	−0.293628	+	0.508579i	0.681037	+	0.732249i	$0.261529\pi$
$402$		0			0
$403$	−20.4828	−	35.4773i	−1.02032	−	1.76725i
$404$		0			0
$405$	−17.5642			−0.872771
$406$		0			0
$407$	−3.62380			−0.179625
$408$		0			0
$409$	7.07097	+	12.2473i	0.349637	+	0.605589i	0.986185	−	0.165648i	$-0.0529716\pi$
$409$	7.07097	+	12.2473i	0.349637	+	0.605589i	−0.636548	+	0.771237i	$0.719638\pi$
$410$		0			0
$411$	5.87106	−	10.1690i	0.289598	−	0.501598i
$412$		0			0
$413$	−21.2540	+	19.9932i	−1.04584	+	0.983802i
$414$		0			0
$415$	−9.15707	+	15.8605i	−0.449503	+	0.778562i
$416$		0			0
$417$	12.7746	+	22.1263i	0.625577	+	1.08353i
$418$		0			0
$419$	−3.94153			−0.192556			−0.0962781	−	0.995354i	$-0.530694\pi$
$419$	−3.94153			−0.192556			−0.0962781	+	0.995354i	$0.530694\pi$
$420$		0			0
$421$	−28.9273			−1.40983			−0.704914	−	0.709292i	$-0.749015\pi$
$421$	−28.9273			−1.40983			−0.704914	+	0.709292i	$0.749015\pi$
$422$		0			0
$423$	3.44290	+	5.96328i	0.167400	+	0.289944i
$424$		0			0
$425$	−13.6866	+	23.7058i	−0.663896	+	1.14990i
$426$		0			0
$427$	30.5004	+	9.18001i	1.47602	+	0.444252i
$428$		0			0
$429$	−25.9534	+	44.9525i	−1.25304	+	2.17033i
$430$		0			0
$431$	−2.14579	−	3.71662i	−0.103359	−	0.179023i	0.809708	−	0.586834i	$-0.199626\pi$
$431$	−2.14579	−	3.71662i	−0.103359	−	0.179023i	−0.913067	+	0.407810i	$0.866292\pi$
$432$		0			0
$433$	1.69228			0.0813259			0.0406629	−	0.999173i	$-0.487053\pi$
$433$	1.69228			0.0813259			0.0406629	+	0.999173i	$0.487053\pi$
$434$		0			0
$435$	−11.0476			−0.529694
$436$		0			0
$437$	7.30260	+	12.6485i	0.349331	+	0.605059i
$438$		0			0
$439$	2.27633	−	3.94272i	0.108643	−	0.188176i	−0.806578	−	0.591128i	$-0.798683\pi$
$439$	2.27633	−	3.94272i	0.108643	−	0.188176i	0.915221	+	0.402952i	$0.132016\pi$
$440$		0			0
$441$	−0.439606	+	7.18454i	−0.0209336	+	0.342121i
$442$		0			0
$443$	−2.29976	+	3.98329i	−0.109265	+	0.189252i	−0.915473	−	0.402380i	$-0.868183\pi$
$443$	−2.29976	+	3.98329i	−0.109265	+	0.189252i	0.806208	+	0.591632i	$0.201516\pi$
$444$		0			0
$445$	2.82848	+	4.89907i	0.134083	+	0.232238i
$446$		0			0
$447$	16.9153			0.800064
$448$		0			0
$449$	4.72931			0.223190			0.111595	−	0.993754i	$-0.464404\pi$
$449$	4.72931			0.223190			0.111595	+	0.993754i	$0.464404\pi$
$450$		0			0
$451$	−2.82465	−	4.89243i	−0.133007	−	0.230376i
$452$		0			0
$453$	3.82064	−	6.61755i	0.179509	−	0.310919i
$454$		0			0
$455$	−59.9398	−	18.0406i	−2.81002	−	0.845758i
$456$		0			0
$457$	−9.75437	+	16.8951i	−0.456290	+	0.790318i	−0.998761	−	0.0497565i	$-0.984155\pi$
$457$	−9.75437	+	16.8951i	−0.456290	+	0.790318i	0.542471	+	0.840074i	$0.317489\pi$
$458$		0			0
$459$	−9.58951	−	16.6095i	−0.447600	−	0.775266i
$460$		0			0
$461$	1.57849			0.0735178			0.0367589	−	0.999324i	$-0.488297\pi$
$461$	1.57849			0.0735178			0.0367589	+	0.999324i	$0.488297\pi$
$462$		0			0
$463$	4.94122			0.229638			0.114819	−	0.993386i	$-0.463371\pi$
$463$	4.94122			0.229638			0.114819	+	0.993386i	$0.463371\pi$
$464$		0			0
$465$	15.8926	+	27.5267i	0.737000	+	1.27652i
$466$		0			0
$467$	−11.6289	+	20.1418i	−0.538120	+	0.932051i	0.460885	+	0.887460i	$0.347532\pi$
$467$	−11.6289	+	20.1418i	−0.538120	+	0.932051i	−0.999005	+	0.0445914i	$0.985801\pi$
$468$		0			0
$469$	20.3969	−	19.1870i	0.941839	−	0.885972i
$470$		0			0
$471$	14.6905	−	25.4448i	0.676904	−	1.17243i
$472$		0			0
$473$	−12.5517	−	21.7402i	−0.577129	−	0.999617i
$474$		0			0
$475$	41.9590			1.92521
$476$		0			0
$477$	−5.09285			−0.233186
$478$		0			0
$479$	−7.76352	−	13.4468i	−0.354724	−	0.614401i	0.632346	−	0.774686i	$-0.282092\pi$
$479$	−7.76352	−	13.4468i	−0.354724	−	0.614401i	−0.987071	+	0.160285i	$0.948759\pi$
$480$		0			0
$481$	−2.09868	+	3.63503i	−0.0956917	+	0.165743i
$482$		0			0
$483$	2.39269	+	10.1620i	0.108871	+	0.462385i
$484$		0			0
$485$	−29.7301	+	51.4940i	−1.34997	+	2.33822i
$486$		0			0
$487$	−7.98069	−	13.8230i	−0.361640	−	0.626378i	0.626591	−	0.779348i	$-0.284450\pi$
$487$	−7.98069	−	13.8230i	−0.361640	−	0.626378i	−0.988231	+	0.152970i	$0.951116\pi$
$488$		0			0
$489$	−23.9915			−1.08493
$490$		0			0
$491$	−4.11148			−0.185548			−0.0927742	−	0.995687i	$-0.529573\pi$
$491$	−4.11148			−0.185548			−0.0927742	+	0.995687i	$0.529573\pi$
$492$		0			0
$493$	−3.68903	−	6.38959i	−0.166146	−	0.287773i
$494$		0			0
$495$	−10.5018	+	18.1897i	−0.472023	+	0.817568i
$496$		0			0
$497$	−5.27795	−	22.4159i	−0.236749	−	1.00549i
$498$		0			0
$499$	3.57719	−	6.19587i	0.160137	−	0.277365i	−0.774781	−	0.632230i	$-0.782140\pi$
$499$	3.57719	−	6.19587i	0.160137	−	0.277365i	0.934918	+	0.354865i	$0.115473\pi$
$500$		0			0
$501$	9.18712	+	15.9126i	0.410450	+	0.710921i
$502$		0			0
$503$	4.71388			0.210182			0.105091	−	0.994463i	$-0.466487\pi$
$503$	4.71388			0.210182			0.105091	+	0.994463i	$0.466487\pi$
$504$		0			0
$505$	−40.2804			−1.79245
$506$		0			0
$507$	20.9341	+	36.2588i	0.929714	+	1.61031i
$508$		0			0
$509$	9.10920	−	15.7776i	0.403758	−	0.699330i	−0.590418	−	0.807098i	$-0.701037\pi$
$509$	9.10920	−	15.7776i	0.403758	−	0.699330i	0.994176	+	0.107768i	$0.0343704\pi$
$510$		0			0
$511$	0.815013	−	0.766668i	0.0360540	−	0.0339154i
$512$		0			0
$513$	−14.6993	+	25.4599i	−0.648990	+	1.12408i
$514$		0			0
$515$	9.04217	+	15.6615i	0.398446	+	0.690128i
$516$		0			0
$517$	−37.8300			−1.66376
$518$		0			0
$519$	−26.9982			−1.18509
$520$		0			0
$521$	−5.47594	−	9.48461i	−0.239905	−	0.415528i	0.720782	−	0.693162i	$-0.243783\pi$
$521$	−5.47594	−	9.48461i	−0.239905	−	0.415528i	−0.960687	+	0.277634i	$0.910450\pi$
$522$		0			0
$523$	−9.81057	+	16.9924i	−0.428986	+	0.743026i	−0.996783	−	0.0801426i	$-0.974462\pi$
$523$	−9.81057	+	16.9924i	−0.428986	+	0.743026i	0.567797	+	0.823168i	$0.307796\pi$
$524$		0			0
$525$	28.7198	+	8.64407i	1.25343	+	0.377258i
$526$		0			0
$527$	−10.6137	+	18.3835i	−0.462340	+	0.800796i
$528$		0			0
$529$	7.55165	+	13.0798i	0.328333	+	0.568689i
$530$		0			0
$531$	11.3408			0.492151
$532$		0			0
$533$	−6.54345			−0.283428
$534$		0			0
$535$	14.9922	+	25.9672i	0.648167	+	1.12266i
$536$		0			0
$537$	−6.12934	+	10.6163i	−0.264500	+	0.458128i
$538$		0			0
$539$	−32.9755	−	21.8272i	−1.42036	−	0.940164i
$540$		0			0
$541$	−11.2361	+	19.4616i	−0.483080	+	0.836719i	−0.999811	−	0.0194288i	$-0.993815\pi$
$541$	−11.2361	+	19.4616i	−0.483080	+	0.836719i	0.516731	+	0.856148i	$0.327149\pi$
$542$		0			0
$543$	−7.93004	−	13.7352i	−0.340310	−	0.589435i
$544$		0			0
$545$	39.8734			1.70799
$546$		0			0
$547$	−5.78852			−0.247499			−0.123750	−	0.992313i	$-0.539492\pi$
$547$	−5.78852			−0.247499			−0.123750	+	0.992313i	$0.539492\pi$
$548$		0			0
$549$	−6.18971	−	10.7209i	−0.264170	−	0.457556i
$550$		0			0
$551$	−5.65474	+	9.79430i	−0.240900	+	0.417251i
$552$		0			0
$553$	36.0427	+	10.8481i	1.53269	+	0.461309i
$554$		0			0
$555$	1.62836	−	2.82041i	0.0691202	−	0.119720i
$556$		0			0
$557$	−4.11253	−	7.12312i	−0.174254	−	0.301816i	0.765649	−	0.643258i	$-0.222418\pi$
$557$	−4.11253	−	7.12312i	−0.174254	−	0.301816i	−0.939903	+	0.341442i	$0.889085\pi$
$558$		0			0
$559$	−29.0768			−1.22982
$560$		0			0
$561$	26.8968			1.13558
$562$		0			0
$563$	10.2648	+	17.7792i	0.432611	+	0.749305i	0.997097	−	0.0761377i	$-0.0242589\pi$
$563$	10.2648	+	17.7792i	0.432611	+	0.749305i	−0.564486	+	0.825443i	$0.690926\pi$
$564$		0			0
$565$	14.9446	−	25.8848i	0.628725	−	1.08898i
$566$		0			0
$567$	−9.36150	+	8.80620i	−0.393146	+	0.369825i
$568$		0			0
$569$	11.9832	−	20.7556i	0.502364	−	0.870120i	−0.497632	−	0.867388i	$-0.665797\pi$
$569$	11.9832	−	20.7556i	0.502364	−	0.870120i	0.999996	−	0.00273173i	$-0.000869538\pi$
$570$		0			0
$571$	−17.2432	−	29.8661i	−0.721605	−	1.24986i	−0.960356	−	0.278775i	$-0.910072\pi$
$571$	−17.2432	−	29.8661i	−0.721605	−	1.24986i	0.238752	−	0.971081i	$-0.423262\pi$
$572$		0			0
$573$	23.7424			0.991853
$574$		0			0
$575$	−22.6863			−0.946083
$576$		0			0
$577$	20.5178	+	35.5379i	0.854168	+	1.47946i	0.877414	+	0.479733i	$0.159267\pi$
$577$	20.5178	+	35.5379i	0.854168	+	1.47946i	−0.0232459	+	0.999730i	$0.507400\pi$
$578$		0			0
$579$	2.79914	−	4.84826i	0.116328	−	0.201487i
$580$		0			0
$581$	3.07141	+	13.0446i	0.127424	+	0.541180i
$582$		0			0
$583$	13.9898	−	24.2311i	0.579400	−	1.00355i
$584$		0			0
$585$	12.1641	+	21.0688i	0.502922	+	0.871087i
$586$		0			0
$587$	6.21910			0.256690			0.128345	−	0.991730i	$-0.459034\pi$
$587$	6.21910			0.256690			0.128345	+	0.991730i	$0.459034\pi$
$588$		0			0
$589$	32.5385			1.34072
$590$		0			0
$591$	−8.43650	−	14.6124i	−0.347031	−	0.601075i
$592$		0			0
$593$	1.46159	−	2.53155i	0.0600204	−	0.103958i	−0.834454	−	0.551078i	$-0.814217\pi$
$593$	1.46159	−	2.53155i	0.0600204	−	0.103958i	0.894474	+	0.447119i	$0.147550\pi$
$594$		0			0
$595$	7.43387	+	31.5723i	0.304759	+	1.29434i
$596$		0			0
$597$	−7.67055	+	13.2858i	−0.313935	+	0.543751i
$598$		0			0
$599$	6.74150	+	11.6766i	0.275450	+	0.477094i	0.970249	−	0.242111i	$-0.0778397\pi$
$599$	6.74150	+	11.6766i	0.275450	+	0.477094i	−0.694798	+	0.719205i	$0.744506\pi$
$600$		0			0
$601$	−35.1493			−1.43377			−0.716886	−	0.697191i	$-0.754433\pi$
$601$	−35.1493			−1.43377			−0.716886	+	0.697191i	$0.754433\pi$
$602$		0			0
$603$	−10.8835			−0.443211
$604$		0			0
$605$	−37.8100	−	65.4889i	−1.53720	−	2.66250i
$606$		0			0
$607$	−15.8523	+	27.4570i	−0.643425	+	1.11444i	0.341238	+	0.939977i	$0.389154\pi$
$607$	−15.8523	+	27.4570i	−0.643425	+	1.11444i	−0.984663	+	0.174468i	$0.944180\pi$
$608$		0			0
$609$	−5.88826	+	5.53899i	−0.238604	+	0.224451i
$610$		0			0
$611$	−21.9088	+	37.9472i	−0.886336	+	1.53518i
$612$		0			0
$613$	−0.373837	−	0.647504i	−0.0150991	−	0.0261525i	0.858377	−	0.513019i	$-0.171473\pi$
$613$	−0.373837	−	0.647504i	−0.0150991	−	0.0261525i	−0.873476	+	0.486867i	$0.838140\pi$
$614$		0			0
$615$	5.07705			0.204727
$616$		0			0
$617$	16.6618			0.670780			0.335390	−	0.942079i	$-0.391132\pi$
$617$	16.6618			0.670780			0.335390	+	0.942079i	$0.391132\pi$
$618$		0			0
$619$	13.5345	+	23.4425i	0.543999	+	0.942235i	0.998669	+	0.0515745i	$0.0164240\pi$
$619$	13.5345	+	23.4425i	0.543999	+	0.942235i	−0.454670	+	0.890660i	$0.650243\pi$
$620$		0			0
$621$	7.94758	−	13.7656i	0.318926	−	0.552395i
$622$		0			0
$623$	3.96380	+	1.19302i	0.158806	+	0.0477975i
$624$		0			0
$625$	0.0952736	−	0.165019i	0.00381095	−	0.00660075i
$626$		0			0
$627$	−20.6144	−	35.7052i	−0.823261	−	1.42593i
$628$		0			0
$629$	2.17497			0.0867219
$630$		0			0
$631$	−23.1258			−0.920625			−0.460312	−	0.887757i	$-0.652263\pi$
$631$	−23.1258			−0.920625			−0.460312	+	0.887757i	$0.652263\pi$
$632$		0			0
$633$	−5.60902	−	9.71511i	−0.222939	−	0.386141i
$634$		0			0
$635$	−2.04150	+	3.53599i	−0.0810146	+	0.140321i
$636$		0			0
$637$	−40.9922	+	20.4367i	−1.62417	+	0.809732i
$638$		0			0
$639$	−4.47514	+	7.75117i	−0.177034	+	0.306632i
$640$		0			0
$641$	−6.92755	−	11.9989i	−0.273622	−	0.473927i	0.696165	−	0.717882i	$-0.254888\pi$
$641$	−6.92755	−	11.9989i	−0.273622	−	0.473927i	−0.969786	+	0.243955i	$0.921555\pi$
$642$		0			0
$643$	−6.61525			−0.260880			−0.130440	−	0.991456i	$-0.541639\pi$
$643$	−6.61525			−0.260880			−0.130440	+	0.991456i	$0.541639\pi$
$644$		0			0
$645$	22.5606			0.888324
$646$		0			0
$647$	−2.52037	−	4.36540i	−0.0990858	−	0.171622i	0.812221	−	0.583350i	$-0.198258\pi$
$647$	−2.52037	−	4.36540i	−0.0990858	−	0.171622i	−0.911306	+	0.411729i	$0.864925\pi$
$648$		0			0
$649$	−31.1528	+	53.9582i	−1.22285	+	2.11805i
$650$		0			0
$651$	22.2717	+	6.70332i	0.872896	+	0.262724i
$652$		0			0
$653$	−7.98470	+	13.8299i	−0.312465	+	0.541206i	−0.978895	−	0.204362i	$-0.934488\pi$
$653$	−7.98470	+	13.8299i	−0.312465	+	0.541206i	0.666430	+	0.745567i	$0.267821\pi$
$654$		0			0
$655$	−34.2132	−	59.2589i	−1.33682	−	2.31544i
$656$		0			0
$657$	−0.434881			−0.0169663
$658$		0			0
$659$	4.81563			0.187590			0.0937952	−	0.995592i	$-0.470100\pi$
$659$	4.81563			0.187590			0.0937952	+	0.995592i	$0.470100\pi$
$660$		0			0
$661$	11.3200	+	19.6068i	0.440296	+	0.762616i	0.997711	−	0.0676184i	$-0.0215400\pi$
$661$	11.3200	+	19.6068i	0.440296	+	0.762616i	−0.557415	+	0.830234i	$0.688207\pi$
$662$		0			0
$663$	15.5770	−	26.9801i	0.604960	−	1.04782i
$664$		0			0
$665$	36.2143	−	34.0662i	1.40433	−	1.32103i
$666$		0			0
$667$	3.05739	−	5.29556i	0.118383	−	0.205045i
$668$		0			0
$669$	19.3776	+	33.5630i	0.749182	+	1.29762i
$670$		0			0
$671$	68.0114			2.62555
$672$		0			0
$673$	−15.0840			−0.581446			−0.290723	−	0.956807i	$-0.593896\pi$
$673$	−15.0840			−0.581446			−0.290723	+	0.956807i	$0.593896\pi$
$674$		0			0
$675$	−22.8325	−	39.5470i	−0.878822	−	1.52216i
$676$		0			0
$677$	−14.7237	+	25.5021i	−0.565876	+	0.980126i	0.431091	+	0.902308i	$0.358129\pi$
$677$	−14.7237	+	25.5021i	−0.565876	+	0.980126i	−0.996968	+	0.0778181i	$0.975205\pi$
$678$		0			0
$679$	9.97190	+	42.3515i	0.382686	+	1.62530i
$680$		0			0
$681$	−17.0829	+	29.5884i	−0.654617	+	1.13383i
$682$		0			0
$683$	−0.287704	−	0.498319i	−0.0110087	−	0.0190676i	0.860469	−	0.509504i	$-0.170171\pi$
$683$	−0.287704	−	0.498319i	−0.0110087	−	0.0190676i	−0.871477	+	0.490436i	$0.836838\pi$
$684$		0			0
$685$	30.2352			1.15523
$686$		0			0
$687$	−0.154087			−0.00587880
$688$		0			0
$689$	−16.2041	−	28.0664i	−0.617328	−	1.06924i
$690$		0			0
$691$	18.7720	−	32.5140i	0.714120	−	1.23689i	−0.249178	−	0.968458i	$-0.580160\pi$
$691$	18.7720	−	32.5140i	0.714120	−	1.23689i	0.963298	−	0.268434i	$-0.0865063\pi$
$692$		0			0
$693$	3.52247	+	14.9603i	0.133808	+	0.568293i
$694$		0			0
$695$	−32.8939	+	56.9740i	−1.24774	+	2.16115i
$696$		0			0
$697$	1.69533	+	2.93640i	0.0642152	+	0.111224i
$698$		0			0
$699$	11.5557			0.437078
$700$		0			0
$701$	−31.1046			−1.17480			−0.587402	−	0.809295i	$-0.699849\pi$
$701$	−31.1046			−1.17480			−0.587402	+	0.809295i	$0.699849\pi$
$702$		0			0
$703$	−1.66696	−	2.88725i	−0.0628705	−	0.108895i
$704$		0			0
$705$	16.9990	−	29.4432i	0.640220	−	1.10889i
$706$		0			0
$707$	−21.4690	+	20.1955i	−0.807424	+	0.759529i
$708$		0			0
$709$	2.92717	−	5.07001i	0.109932	−	0.190408i	−0.805810	−	0.592174i	$-0.798270\pi$
$709$	2.92717	−	5.07001i	0.109932	−	0.190408i	0.915743	+	0.401765i	$0.131603\pi$
$710$		0			0
$711$	−7.31444	−	12.6690i	−0.274313	−	0.475124i
$712$		0			0
$713$	−17.5928			−0.658856
$714$		0			0
$715$	−133.657			−4.99847
$716$		0			0
$717$	5.01289	+	8.68259i	0.187210	+	0.324257i
$718$		0			0
$719$	−13.8968	+	24.0700i	−0.518264	+	0.897660i	0.481510	+	0.876440i	$0.340088\pi$
$719$	−13.8968	+	24.0700i	−0.518264	+	0.897660i	−0.999775	+	0.0212200i	$0.993245\pi$
$720$		0			0
$721$	12.6716	+	3.81390i	0.471916	+	0.142037i
$722$		0			0
$723$	8.64911	−	14.9807i	0.321664	−	0.557138i
$724$		0			0
$725$	−8.78352	−	15.2135i	−0.326212	−	0.565015i
$726$		0			0
$727$	15.5974			0.578474			0.289237	−	0.957257i	$-0.406598\pi$
$727$	15.5974			0.578474			0.289237	+	0.957257i	$0.406598\pi$
$728$		0			0
$729$	28.8231			1.06752
$730$		0			0
$731$	7.53344	+	13.0483i	0.278635	+	0.482609i
$732$		0			0
$733$	19.8286	−	34.3442i	0.732386	−	1.26853i	−0.223474	−	0.974710i	$-0.571740\pi$
$733$	19.8286	−	34.3442i	0.732386	−	1.26853i	0.955861	−	0.293821i	$-0.0949269\pi$
$734$		0			0
$735$	31.8058	−	15.8568i	1.17317	−	0.584887i
$736$		0			0
$737$	29.8965	−	51.7823i	1.10125	−	1.90742i
$738$		0			0
$739$	6.47389	+	11.2131i	0.238146	+	0.412481i	0.960182	−	0.279374i	$-0.0901270\pi$
$739$	6.47389	+	11.2131i	0.238146	+	0.412481i	−0.722036	+	0.691855i	$0.756794\pi$
$740$		0			0
$741$	−47.7545			−1.75430
$742$		0			0
$743$	−5.12957			−0.188186			−0.0940929	−	0.995563i	$-0.529995\pi$
$743$	−5.12957			−0.188186			−0.0940929	+	0.995563i	$0.529995\pi$
$744$		0			0
$745$	21.7779	+	37.7204i	0.797879	+	1.38197i
$746$		0			0
$747$	2.60423	−	4.51066i	0.0952838	−	0.165036i
$748$		0			0
$749$	21.0099	+	6.32354i	0.767684	+	0.231057i
$750$		0			0
$751$	−9.51888	+	16.4872i	−0.347349	+	0.601626i	−0.985778	−	0.168055i	$-0.946251\pi$
$751$	−9.51888	+	16.4872i	−0.347349	+	0.601626i	0.638429	+	0.769681i	$0.279585\pi$
$752$		0			0
$753$	−4.23959	−	7.34319i	−0.154499	−	0.267601i
$754$		0			0
$755$	19.6758			0.716077
$756$		0			0
$757$	32.8052			1.19233			0.596163	−	0.802864i	$-0.296691\pi$
$757$	32.8052			1.19233			0.596163	+	0.802864i	$0.296691\pi$
$758$		0			0
$759$	11.1458	+	19.3050i	0.404565	+	0.700727i
$760$		0			0
$761$	−20.6336	+	35.7384i	−0.747966	+	1.29552i	0.200830	+	0.979626i	$0.435636\pi$
$761$	−20.6336	+	35.7384i	−0.747966	+	1.29552i	−0.948796	+	0.315889i	$0.897697\pi$
$762$		0			0
$763$	21.2521	−	19.9915i	0.769377	−	0.723739i
$764$		0			0
$765$	6.30312	−	10.9173i	0.227890	−	0.394717i
$766$		0			0
$767$	36.0836	+	62.4987i	1.30290	+	2.25670i
$768$		0			0
$769$	36.2060			1.30562			0.652811	−	0.757520i	$-0.273589\pi$
$769$	36.2060			1.30562			0.652811	+	0.757520i	$0.273589\pi$
$770$		0			0
$771$	−40.1196			−1.44487
$772$		0			0
$773$	11.8148	+	20.4638i	0.424949	+	0.736033i	0.996416	−	0.0845923i	$-0.0269588\pi$
$773$	11.8148	+	20.4638i	0.424949	+	0.736033i	−0.571467	+	0.820625i	$0.693625\pi$
$774$		0			0
$775$	−25.2710	+	43.7707i	−0.907762	+	1.57229i
$776$		0			0
$777$	−0.546177	−	2.31966i	−0.0195940	−	0.0832174i
$778$		0			0
$779$	2.59869	−	4.50106i	0.0931078	−	0.161267i
$780$		0			0
$781$	−24.5860	−	42.5842i	−0.879757	−	1.52378i
$782$		0			0
$783$	12.3084			0.439865
$784$		0			0
$785$	75.6545			2.70022
$786$		0			0
$787$	−4.61785	−	7.99835i	−0.164609	−	0.285110i	0.771908	−	0.635735i	$-0.219303\pi$
$787$	−4.61785	−	7.99835i	−0.164609	−	0.285110i	−0.936516	+	0.350624i	$0.885969\pi$
$788$		0			0
$789$	−21.5580	+	37.3395i	−0.767484	+	1.32932i
$790$		0			0
$791$	−5.01264	−	21.2891i	−0.178229	−	0.756955i
$792$		0			0
$793$	39.3881	−	68.2221i	1.39871	−	2.42264i
$794$		0			0
$795$	12.5727	+	21.7766i	0.445909	+	0.772338i
$796$		0			0
$797$	41.1963			1.45925			0.729624	−	0.683848i	$-0.239695\pi$
$797$	41.1963			1.45925			0.729624	+	0.683848i	$0.239695\pi$
$798$		0			0
$799$	22.7052			0.803254
$800$		0			0
$801$	−0.804407	−	1.39327i	−0.0284223	−	0.0492289i
$802$		0			0
$803$	1.19460	−	2.06910i	0.0421564	−	0.0730171i
$804$		0			0
$805$	−19.5803	+	18.4188i	−0.690114	+	0.649178i
$806$		0			0
$807$	8.53790	−	14.7881i	0.300548	−	0.520565i
$808$		0			0
$809$	−2.00729	−	3.47673i	−0.0705725	−	0.122235i	0.828580	−	0.559871i	$-0.189149\pi$
$809$	−2.00729	−	3.47673i	−0.0705725	−	0.122235i	−0.899152	+	0.437636i	$0.855816\pi$
$810$		0			0
$811$	26.1749			0.919124			0.459562	−	0.888146i	$-0.348006\pi$
$811$	26.1749			0.919124			0.459562	+	0.888146i	$0.348006\pi$
$812$		0			0
$813$	−8.20264			−0.287679
$814$		0			0
$815$	−30.8884	−	53.5002i	−1.08197	−	1.87403i
$816$		0			0
$817$	11.5477	−	20.0011i	0.404002	−	0.699751i
$818$		0			0
$819$	17.0466	+	5.13068i	0.595657	+	0.179280i
$820$		0			0
$821$	20.0242	−	34.6829i	0.698849	−	1.21044i	−0.270017	−	0.962856i	$-0.587029\pi$
$821$	20.0242	−	34.6829i	0.698849	−	1.21044i	0.968866	−	0.247586i	$-0.0796373\pi$
$822$		0			0
$823$	−8.84418	−	15.3186i	−0.308289	−	0.533972i	0.669699	−	0.742632i	$-0.266423\pi$
$823$	−8.84418	−	15.3186i	−0.308289	−	0.533972i	−0.977988	+	0.208661i	$0.933090\pi$
$824$		0			0
$825$	64.0408			2.22961
$826$		0			0
$827$	27.9098			0.970520			0.485260	−	0.874370i	$-0.338725\pi$
$827$	27.9098			0.970520			0.485260	+	0.874370i	$0.338725\pi$
$828$		0			0
$829$	−27.7037	−	47.9843i	−0.962191	−	1.66656i	−0.716981	−	0.697093i	$-0.754476\pi$
$829$	−27.7037	−	47.9843i	−0.962191	−	1.66656i	−0.245210	−	0.969470i	$-0.578857\pi$
$830$		0			0
$831$	−15.9960	+	27.7060i	−0.554897	+	0.961109i
$832$		0			0
$833$	19.7916	+	13.1005i	0.685739	+	0.453906i
$834$		0			0
$835$	−23.6563	+	40.9739i	−0.818659	+	1.41796i
$836$		0			0
$837$	−17.7062	−	30.6680i	−0.612015	−	1.06004i
$838$		0			0
$839$	−46.1671			−1.59386			−0.796932	−	0.604069i	$-0.793545\pi$
$839$	−46.1671			−1.59386			−0.796932	+	0.604069i	$0.793545\pi$
$840$		0			0
$841$	−24.2650			−0.836726
$842$		0			0
$843$	−1.65709	−	2.87016i	−0.0570730	−	0.0988534i
$844$		0			0
$845$	−53.9039	+	93.3643i	−1.85435	+	3.21183i
$846$		0			0
$847$	−52.9866	−	15.9479i	−1.82064	−	0.547976i
$848$		0			0
$849$	0.0679199	−	0.117641i	0.00233101	−	0.00403742i
$850$		0			0
$851$	0.901286	+	1.56107i	0.0308957	+	0.0535129i
$852$		0			0
$853$	−46.7110			−1.59935			−0.799677	−	0.600430i	$-0.794996\pi$
$853$	−46.7110			−1.59935			−0.799677	+	0.600430i	$0.794996\pi$
$854$		0			0
$855$	−19.3235			−0.660851
$856$		0			0
$857$	−14.0046	−	24.2566i	−0.478387	−	0.828590i	0.521306	−	0.853370i	$-0.325445\pi$
$857$	−14.0046	−	24.2566i	−0.478387	−	0.828590i	−0.999693	+	0.0247798i	$0.992112\pi$
$858$		0			0
$859$	−4.86802	+	8.43166i	−0.166095	+	0.287685i	−0.937044	−	0.349213i	$-0.886449\pi$
$859$	−4.86802	+	8.43166i	−0.166095	+	0.287685i	0.770949	+	0.636897i	$0.219782\pi$
$860$		0			0
$861$	2.70601	−	2.54549i	0.0922205	−	0.0867502i
$862$		0			0
$863$	−5.40180	+	9.35620i	−0.183880	+	0.318489i	−0.943198	−	0.332230i	$-0.892199\pi$
$863$	−5.40180	+	9.35620i	−0.183880	+	0.318489i	0.759319	+	0.650719i	$0.225532\pi$
$864$		0			0
$865$	−34.7593	−	60.2050i	−1.18185	−	2.04703i
$866$		0			0
$867$	7.72780			0.262450
$868$		0			0
$869$	80.3698			2.72636
$870$		0			0
$871$	−34.6285	−	59.9783i	−1.17334	−	2.03229i
$872$		0			0
$873$	8.45510	−	14.6447i	0.286162	−	0.495647i
$874$		0			0
$875$	6.73763	+	28.6153i	0.227774	+	0.967374i
$876$		0			0
$877$	−7.06337	+	12.2341i	−0.238513	+	0.413117i	−0.960288	−	0.279011i	$-0.909993\pi$
$877$	−7.06337	+	12.2341i	−0.238513	+	0.413117i	0.721775	+	0.692128i	$0.243327\pi$
$878$		0			0
$879$	17.4134	+	30.1610i	0.587341	+	1.01730i
$880$		0			0
$881$	−37.6737			−1.26926			−0.634630	−	0.772816i	$-0.718847\pi$
$881$	−37.6737			−1.26926			−0.634630	+	0.772816i	$0.718847\pi$
$882$		0			0
$883$	20.1033			0.676531			0.338266	−	0.941051i	$-0.390160\pi$
$883$	20.1033			0.676531			0.338266	+	0.941051i	$0.390160\pi$
$884$		0			0
$885$	−27.9972	−	48.4926i	−0.941116	−	1.63006i
$886$		0			0
$887$	22.0666	−	38.2205i	0.740924	−	1.28332i	−0.211152	−	0.977453i	$-0.567721\pi$
$887$	22.0666	−	38.2205i	0.740924	−	1.28332i	0.952075	−	0.305864i	$-0.0989453\pi$
$888$		0			0
$889$	0.684750	+	2.90819i	0.0229658	+	0.0975377i
$890$		0			0
$891$	−13.7215	+	23.7664i	−0.459689	+	0.796204i
$892$		0			0
$893$	−17.4019	−	30.1410i	−0.582332	−	1.00863i
$894$		0			0
$895$	−31.5653			−1.05511
$896$		0			0
$897$	25.8198			0.862097
$898$		0			0
$899$	−6.81146	−	11.7978i	−0.227175	−	0.393479i
$900$		0			0
$901$	−8.39658	+	14.5433i	−0.279731	+	0.484508i
$902$		0			0
$903$	12.0245	−	11.3113i	0.400152	−	0.376416i
$904$		0			0
$905$	20.4194	−	35.3674i	0.678763	−	1.17565i
$906$		0			0
$907$	−0.928746	−	1.60863i	−0.0308385	−	0.0534138i	0.850194	−	0.526469i	$-0.176484\pi$
$907$	−0.928746	−	1.60863i	−0.0308385	−	0.0534138i	−0.881033	+	0.473055i	$0.843151\pi$
$908$		0			0
$909$	11.4556			0.379957
$910$		0			0
$911$	14.5018			0.480466			0.240233	−	0.970715i	$-0.422776\pi$
$911$	14.5018			0.480466			0.240233	+	0.970715i	$0.422776\pi$
$912$		0			0
$913$	14.3074	+	24.7812i	0.473506	+	0.820137i
$914$		0			0
$915$	−30.5611	+	52.9334i	−1.01032	+	1.74992i
$916$		0			0
$917$	−47.9460	−	14.4308i	−1.58332	−	0.476546i
$918$		0			0
$919$	−10.5812	+	18.3272i	−0.349041	+	0.604557i	−0.986079	−	0.166275i	$-0.946826\pi$
$919$	−10.5812	+	18.3272i	−0.349041	+	0.604557i	0.637038	+	0.770832i	$0.280159\pi$
$920$		0			0
$921$	−2.43198	−	4.21231i	−0.0801364	−	0.138800i
$922$		0			0
$923$	−56.9549			−1.87469
$924$		0			0
$925$	5.17857			0.170270
$926$		0			0
$927$	−2.57156	−	4.45406i	−0.0844610	−	0.146291i
$928$		0			0
$929$	29.8573	−	51.7143i	0.979585	−	1.69669i	0.315696	−	0.948860i	$-0.397762\pi$
$929$	29.8573	−	51.7143i	0.979585	−	1.69669i	0.663889	−	0.747831i	$-0.268905\pi$
$930$		0			0
$931$	2.22196	−	36.3138i	0.0728217	−	1.19014i
$932$		0			0
$933$	18.2676	−	31.6403i	0.598053	−	1.03586i
$934$		0			0
$935$	34.6288	+	59.9789i	1.13248	+	1.96152i
$936$		0			0
$937$	−12.1335			−0.396384			−0.198192	−	0.980163i	$-0.563507\pi$
$937$	−12.1335			−0.396384			−0.198192	+	0.980163i	$0.563507\pi$
$938$		0			0
$939$	−6.96221			−0.227203
$940$		0			0
$941$	−6.40677	−	11.0969i	−0.208855	−	0.361747i	0.742499	−	0.669847i	$-0.233640\pi$
$941$	−6.40677	−	11.0969i	−0.208855	−	0.361747i	−0.951354	+	0.308100i	$0.900307\pi$
$942$		0			0
$943$	−1.40505	+	2.43362i	−0.0457548	+	0.0792497i
$944$		0			0
$945$	−51.8144	−	15.5951i	−1.68552	−	0.507307i
$946$		0			0
$947$	8.61260	−	14.9175i	0.279872	−	0.484752i	−0.691481	−	0.722395i	$-0.743041\pi$
$947$	8.61260	−	14.9175i	0.279872	−	0.484752i	0.971353	+	0.237642i	$0.0763747\pi$
$948$		0			0
$949$	−1.38368	−	2.39660i	−0.0449161	−	0.0777969i
$950$		0			0
$951$	−23.8760			−0.774231
$952$		0			0
$953$	15.2346			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$953$	15.2346			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$954$		0			0
$955$	30.5676	+	52.9447i	0.989145	+	1.71325i
$956$		0			0
$957$	−8.63067	+	14.9488i	−0.278990	+	0.483225i
$958$		0			0
$959$	16.1150	−	15.1591i	0.520381	−	0.489513i
$960$		0			0
$961$	−4.09722	+	7.09660i	−0.132169	+	0.228923i
$962$		0			0
$963$	−4.26371	−	7.38496i	−0.137396	−	0.237977i
$964$		0			0
$965$	14.4152			0.464043
$966$		0			0
$967$	−27.5678			−0.886522			−0.443261	−	0.896393i	$-0.646179\pi$
$967$	−27.5678			−0.886522			−0.443261	+	0.896393i	$0.646179\pi$
$968$		0			0
$969$	12.3726	+	21.4300i	0.397465	+	0.688430i
$970$		0			0
$971$	5.40478	−	9.36136i	0.173448	−	0.300420i	−0.766175	−	0.642632i	$-0.777843\pi$
$971$	5.40478	−	9.36136i	0.173448	−	0.300420i	0.939623	+	0.342211i	$0.111176\pi$
$972$		0			0
$973$	11.0331	+	46.8586i	0.353705	+	1.50222i
$974$		0			0
$975$	37.0885	−	64.2393i	1.18778	−	2.05730i
$976$		0			0
$977$	21.2352	+	36.7804i	0.679373	+	1.17671i	0.975170	+	0.221457i	$0.0710813\pi$
$977$	21.2352	+	36.7804i	0.679373	+	1.17671i	−0.295797	+	0.955251i	$0.595585\pi$
$978$		0			0
$979$	8.83869			0.282486
$980$		0			0
$981$	−11.3398			−0.362053
$982$		0			0
$983$	−30.8082	−	53.3614i	−0.982630	−	1.70196i	−0.652028	−	0.758195i	$-0.726082\pi$
$983$	−30.8082	−	53.3614i	−0.982630	−	1.70196i	−0.330602	−	0.943770i	$-0.607252\pi$
$984$		0			0
$985$	21.7235	−	37.6261i	0.692167	−	1.19887i
$986$		0			0
$987$	−5.70172	−	24.2157i	−0.181488	−	0.770794i
$988$		0			0
$989$	−6.24356	+	10.8142i	−0.198534	+	0.343870i
$990$		0			0
$991$	−21.1466	−	36.6271i	−0.671745	−	1.16350i	−0.977409	−	0.211357i	$-0.932212\pi$
$991$	−21.1466	−	36.6271i	−0.671745	−	1.16350i	0.305664	−	0.952140i	$-0.401122\pi$
$992$		0			0
$993$	−15.8243			−0.502169
$994$		0			0
$995$	−39.5024			−1.25231
$996$		0			0
$997$	−12.6547	−	21.9186i	−0.400778	−	0.694168i	0.593042	−	0.805172i	$-0.297927\pi$
$997$	−12.6547	−	21.9186i	−0.400778	−	0.694168i	−0.993820	+	0.111003i	$0.964594\pi$
$998$		0			0
$999$	−1.81419	+	3.14226i	−0.0573983	+	0.0994168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.e.821.10	yes	30
7.2	even	3		8036.2.a.q.1.6		15
7.4	even	3	inner	1148.2.i.e.165.10	✓	30
7.5	odd	6		8036.2.a.r.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.e.165.10	✓	30	7.4	even	3	inner
1148.2.i.e.821.10	yes	30	1.1	even	1	trivial
8036.2.a.q.1.6		15	7.2	even	3
8036.2.a.r.1.10		15	7.5	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.702089 + 1.21605i) q^{3} +(-1.80784 + 3.13127i) q^{5} +(0.606375 + 2.57533i) q^{7} +(0.514141 - 0.890519i) q^{9} +O(q^{10})\)	\(q+(0.702089 + 1.21605i) q^{3} +(-1.80784 + 3.13127i) q^{5} +(0.606375 + 2.57533i) q^{7} +(0.514141 - 0.890519i) q^{9} +(2.82465 + 4.89243i) q^{11} +6.54345 q^{13} -5.07705 q^{15} +(-1.69533 - 2.93640i) q^{17} +(-2.59869 + 4.50106i) q^{19} +(-2.70601 + 2.54549i) q^{21} +(1.40505 - 2.43362i) q^{23} +(-4.03655 - 6.99151i) q^{25} +5.65643 q^{27} +2.17600 q^{29} +(-3.13027 - 5.42179i) q^{31} +(-3.96631 + 6.86985i) q^{33} +(-9.16026 - 2.75705i) q^{35} +(-0.320730 + 0.555521i) q^{37} +(4.59409 + 7.95720i) q^{39} -1.00000 q^{41} -4.44365 q^{43} +(1.85897 + 3.21983i) q^{45} +(-3.34820 + 5.79926i) q^{47} +(-6.26462 + 3.12323i) q^{49} +(2.38055 - 4.12323i) q^{51} +(-2.47639 - 4.28923i) q^{53} -20.4260 q^{55} -7.29805 q^{57} +(5.51446 + 9.55133i) q^{59} +(6.01946 - 10.4260i) q^{61} +(2.60514 + 0.784093i) q^{63} +(-11.8295 + 20.4893i) q^{65} +(-5.29208 - 9.16615i) q^{67} +3.94589 q^{69} -8.70411 q^{71} +(-0.211460 - 0.366259i) q^{73} +(5.66804 - 9.81733i) q^{75} +(-10.8868 + 10.2410i) q^{77} +(7.11326 - 12.3205i) q^{79} +(2.42889 + 4.20697i) q^{81} +5.06521 q^{83} +12.2595 q^{85} +(1.52774 + 2.64613i) q^{87} +(0.782283 - 1.35495i) q^{89} +(3.96779 + 16.8515i) q^{91} +(4.39546 - 7.61317i) q^{93} +(-9.39602 - 16.2744i) q^{95} +16.4451 q^{97} +5.80907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more