LMFDB - Embedded newform 189.3.k.a.10.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.k (of order $6$, degree $2$, not 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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.14
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67789 - 2.90618i) q^{2} +(-3.63061 - 6.28839i) q^{4} -8.51666i q^{5} +(-2.34142 + 6.59680i) q^{7} -10.9439 q^{8} +O(q^{10})$	\(q+(1.67789 - 2.90618i) q^{2} +(-3.63061 - 6.28839i) q^{4} -8.51666i q^{5} +(-2.34142 + 6.59680i) q^{7} -10.9439 q^{8} +(-24.7510 - 14.2900i) q^{10} -0.0716464 q^{11} +(4.83405 + 2.79094i) q^{13} +(15.2429 + 17.8733i) q^{14} +(-3.84017 + 6.65137i) q^{16} +(-1.11650 - 0.644614i) q^{17} +(14.6079 - 8.43385i) q^{19} +(-53.5561 + 30.9206i) q^{20} +(-0.120215 + 0.208218i) q^{22} -15.2649 q^{23} -47.5335 q^{25} +(16.2220 - 9.36576i) q^{26} +(49.9840 - 9.22663i) q^{28} +(2.50735 + 4.34286i) q^{29} +(52.4315 - 30.2714i) q^{31} +(-9.00103 - 15.5902i) q^{32} +(-3.74673 + 2.16318i) q^{34} +(56.1827 + 19.9410i) q^{35} +(-8.26277 - 14.3115i) q^{37} -56.6042i q^{38} +93.2053i q^{40} +(29.7375 + 17.1690i) q^{41} +(24.9877 + 43.2800i) q^{43} +(0.260120 + 0.450541i) q^{44} +(-25.6128 + 44.3627i) q^{46} +(16.3227 + 9.42391i) q^{47} +(-38.0355 - 30.8917i) q^{49} +(-79.7558 + 138.141i) q^{50} -40.5312i q^{52} +(-8.08916 + 14.0108i) q^{53} +0.610188i q^{55} +(25.6242 - 72.1946i) q^{56} +16.8282 q^{58} +(64.9840 - 37.5186i) q^{59} +(13.5486 + 7.82227i) q^{61} -203.168i q^{62} -91.1322 q^{64} +(23.7695 - 41.1699i) q^{65} +(23.2065 + 40.1948i) q^{67} +9.36135i q^{68} +(152.221 - 129.818i) q^{70} +57.8350 q^{71} +(-31.8573 - 18.3928i) q^{73} -55.4560 q^{74} +(-106.071 - 61.2400i) q^{76} +(0.167754 - 0.472637i) q^{77} +(-37.0237 + 64.1270i) q^{79} +(56.6474 + 32.7054i) q^{80} +(99.7924 - 57.6151i) q^{82} +(-64.6045 + 37.2994i) q^{83} +(-5.48996 + 9.50888i) q^{85} +167.706 q^{86} +0.784090 q^{88} +(-69.0981 + 39.8938i) q^{89} +(-29.7298 + 25.3545i) q^{91} +(55.4209 + 95.9919i) q^{92} +(54.7753 - 31.6245i) q^{94} +(-71.8283 - 124.410i) q^{95} +(65.9955 - 38.1025i) q^{97} +(-153.596 + 58.7055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.67789	−	2.90618i	0.838943	−	1.45309i	−0.0518359	−	0.998656i	$-0.516507\pi$
$2$	1.67789	−	2.90618i	0.838943	−	1.45309i	0.890779	−	0.454437i	$-0.150159\pi$
$3$		0			0
$3$		0			0
$4$	−3.63061	−	6.28839i	−0.907651	−	1.57210i
$5$		−	8.51666i		−	1.70333i	−0.524085	−	0.851666i	$-0.675593\pi$
$5$		−	8.51666i		−	1.70333i	0.524085	−	0.851666i	$-0.324407\pi$
$6$		0			0
$7$	−2.34142	+	6.59680i	−0.334488	+	0.942400i
$7$	−2.34142	+	6.59680i	−0.334488	+	0.942400i
$8$	−10.9439			−1.36799
$9$		0			0
$10$	−24.7510	−	14.2900i	−2.47510	−	1.42900i
$11$	−0.0716464			−0.00651331			−0.00325666	−	0.999995i	$-0.501037\pi$
$11$	−0.0716464			−0.00651331			−0.00325666	+	0.999995i	$0.501037\pi$
$12$		0			0
$13$	4.83405	+	2.79094i	0.371850	+	0.214688i	0.674266	−	0.738488i	$-0.264460\pi$
$13$	4.83405	+	2.79094i	0.371850	+	0.214688i	−0.302416	+	0.953176i	$0.597793\pi$
$14$	15.2429	+	17.8733i	1.08878	+	1.27666i
$15$		0			0
$16$	−3.84017	+	6.65137i	−0.240011	+	0.415710i
$17$	−1.11650	−	0.644614i	−0.0656767	−	0.0379185i	0.466802	−	0.884362i	$-0.345406\pi$
$17$	−1.11650	−	0.644614i	−0.0656767	−	0.0379185i	−0.532479	+	0.846443i	$0.678739\pi$
$18$		0			0
$19$	14.6079	−	8.43385i	0.768835	−	0.443887i	−0.0636240	−	0.997974i	$-0.520266\pi$
$19$	14.6079	−	8.43385i	0.768835	−	0.443887i	0.832459	+	0.554087i	$0.186932\pi$
$20$	−53.5561	+	30.9206i	−2.67781	+	1.54603i
$21$		0			0
$22$	−0.120215	+	0.208218i	−0.00546430	+	0.00946444i
$23$	−15.2649			−0.663693			−0.331846	−	0.943333i	$-0.607672\pi$
$23$	−15.2649			−0.663693			−0.331846	+	0.943333i	$0.607672\pi$
$24$		0			0
$25$	−47.5335			−1.90134
$26$	16.2220	−	9.36576i	0.623922	−	0.360221i
$27$		0			0
$28$	49.9840	−	9.22663i	1.78514	−	0.329523i
$29$	2.50735	+	4.34286i	0.0864604	+	0.149754i	0.906013	−	0.423251i	$-0.139111\pi$
$29$	2.50735	+	4.34286i	0.0864604	+	0.149754i	−0.819552	+	0.573005i	$0.805778\pi$
$30$		0			0
$31$	52.4315	−	30.2714i	1.69134	−	0.976495i	0.737901	−	0.674909i	$-0.235817\pi$
$31$	52.4315	−	30.2714i	1.69134	−	0.976495i	0.953439	−	0.301586i	$-0.0975160\pi$
$32$	−9.00103	−	15.5902i	−0.281282	−	0.487195i
$33$		0			0
$34$	−3.74673	+	2.16318i	−0.110198	+	0.0636229i
$35$	56.1827	+	19.9410i	1.60522	+	0.569744i
$36$		0			0
$37$	−8.26277	−	14.3115i	−0.223318	−	0.386798i	0.732495	−	0.680772i	$-0.238356\pi$
$37$	−8.26277	−	14.3115i	−0.223318	−	0.386798i	−0.955814	+	0.293974i	$0.905022\pi$
$38$		−	56.6042i		−	1.48958i
$39$		0			0
$40$			93.2053i			2.33013i
$41$	29.7375	+	17.1690i	0.725305	+	0.418755i	0.816702	−	0.577059i	$-0.195800\pi$
$41$	29.7375	+	17.1690i	0.725305	+	0.418755i	−0.0913969	+	0.995815i	$0.529133\pi$
$42$		0			0
$43$	24.9877	+	43.2800i	0.581109	+	1.00651i	0.995348	+	0.0963427i	$0.0307145\pi$
$43$	24.9877	+	43.2800i	0.581109	+	1.00651i	−0.414239	+	0.910168i	$0.635952\pi$
$44$	0.260120	+	0.450541i	0.00591181	+	0.0102396i
$45$		0			0
$46$	−25.6128	+	44.3627i	−0.556800	+	0.964407i
$47$	16.3227	+	9.42391i	0.347291	+	0.200509i	0.663492	−	0.748184i	$-0.269074\pi$
$47$	16.3227	+	9.42391i	0.347291	+	0.200509i	−0.316200	+	0.948692i	$0.602407\pi$
$48$		0			0
$49$	−38.0355	−	30.8917i	−0.776236	−	0.630443i
$50$	−79.7558	+	138.141i	−1.59512	+	2.76282i
$51$		0			0
$52$		−	40.5312i		−	0.779446i
$53$	−8.08916	+	14.0108i	−0.152626	+	0.264355i	−0.932192	−	0.361964i	$-0.882106\pi$
$53$	−8.08916	+	14.0108i	−0.152626	+	0.264355i	0.779566	+	0.626320i	$0.215440\pi$
$54$		0			0
$55$			0.610188i			0.0110943i
$56$	25.6242	−	72.1946i	0.457575	−	1.28919i
$57$		0			0
$58$	16.8282			0.290141
$59$	64.9840	−	37.5186i	1.10142	−	0.635908i	0.164830	−	0.986322i	$-0.447293\pi$
$59$	64.9840	−	37.5186i	1.10142	−	0.635908i	0.936595	+	0.350414i	$0.113959\pi$
$60$		0			0
$61$	13.5486	+	7.82227i	0.222108	+	0.128234i	0.606926	−	0.794758i	$-0.292402\pi$
$61$	13.5486	+	7.82227i	0.222108	+	0.128234i	−0.384818	+	0.922992i	$0.625736\pi$
$62$		−	203.168i		−	3.27690i
$63$		0			0
$64$	−91.1322			−1.42394
$65$	23.7695	−	41.1699i	0.365684	−	0.633384i
$66$		0			0
$67$	23.2065	+	40.1948i	0.346365	+	0.599922i	0.985601	−	0.169089i	$-0.0540824\pi$
$67$	23.2065	+	40.1948i	0.346365	+	0.599922i	−0.639236	+	0.769011i	$0.720749\pi$
$68$			9.36135i			0.137667i
$69$		0			0
$70$	152.221	−	129.818i	2.17458	−	1.85455i
$71$	57.8350			0.814578			0.407289	−	0.913299i	$-0.366474\pi$
$71$	57.8350			0.814578			0.407289	+	0.913299i	$0.366474\pi$
$72$		0			0
$73$	−31.8573	−	18.3928i	−0.436401	−	0.251956i	0.265669	−	0.964064i	$-0.414407\pi$
$73$	−31.8573	−	18.3928i	−0.436401	−	0.251956i	−0.702070	+	0.712108i	$0.747741\pi$
$74$	−55.4560			−0.749405
$75$		0			0
$76$	−106.071	−	61.2400i	−1.39567	−	0.805789i
$77$	0.167754	−	0.472637i	0.00217862	−	0.00613814i
$78$		0			0
$79$	−37.0237	+	64.1270i	−0.468655	+	0.811734i	−0.999358	−	0.0358237i	$-0.988595\pi$
$79$	−37.0237	+	64.1270i	−0.468655	+	0.811734i	0.530703	+	0.847558i	$0.321928\pi$
$80$	56.6474	+	32.7054i	0.708093	+	0.408818i
$81$		0			0
$82$	99.7924	−	57.6151i	1.21698	−	0.702624i
$83$	−64.6045	+	37.2994i	−0.778368	+	0.449391i	−0.835852	−	0.548956i	$-0.815026\pi$
$83$	−64.6045	+	37.2994i	−0.778368	+	0.449391i	0.0574836	+	0.998346i	$0.481692\pi$
$84$		0			0
$85$	−5.48996	+	9.50888i	−0.0645877	+	0.111869i
$86$	167.706			1.95007
$87$		0			0
$88$	0.784090			0.00891011
$89$	−69.0981	+	39.8938i	−0.776383	+	0.448245i	−0.835147	−	0.550027i	$-0.814617\pi$
$89$	−69.0981	+	39.8938i	−0.776383	+	0.448245i	0.0587638	+	0.998272i	$0.481284\pi$
$90$		0			0
$91$	−29.7298	+	25.3545i	−0.326701	+	0.278621i
$92$	55.4209	+	95.9919i	0.602402	+	1.04339i
$93$		0			0
$94$	54.7753	−	31.6245i	0.582716	−	0.336431i
$95$	−71.8283	−	124.410i	−0.756087	−	1.30958i
$96$		0			0
$97$	65.9955	−	38.1025i	0.680366	−	0.392809i	−0.119627	−	0.992819i	$-0.538170\pi$
$97$	65.9955	−	38.1025i	0.680366	−	0.392809i	0.799993	+	0.600010i	$0.204837\pi$
$98$	−153.596	+	58.7055i	−1.56731	+	0.599036i
$99$		0			0
$100$	172.575	+	298.909i	1.72575	+	2.98909i
$101$			66.0175i			0.653638i	0.945087	+	0.326819i	$0.105977\pi$
$101$			66.0175i			0.653638i	−0.945087	+	0.326819i	$0.894023\pi$
$102$		0			0
$103$		−	11.1812i		−	0.108555i	−0.998526	−	0.0542776i	$-0.982714\pi$
$103$		−	11.1812i		−	0.108555i	0.998526	−	0.0542776i	$-0.0172856\pi$
$104$	−52.9033	−	30.5437i	−0.508685	−	0.293689i
$105$		0			0
$106$	27.1454	+	47.0172i	0.256088	+	0.443558i
$107$	−13.2112	−	22.8826i	−0.123470	−	0.213856i	0.797664	−	0.603102i	$-0.206069\pi$
$107$	−13.2112	−	22.8826i	−0.123470	−	0.213856i	−0.921134	+	0.389246i	$0.872735\pi$
$108$		0			0
$109$	−90.9918	+	157.602i	−0.834787	+	1.44589i	0.0594165	+	0.998233i	$0.481076\pi$
$109$	−90.9918	+	157.602i	−0.834787	+	1.44589i	−0.894204	+	0.447660i	$0.852257\pi$
$110$	1.77332	+	1.02383i	0.0161211	+	0.00930751i
$111$		0			0
$112$	−34.8863	−	40.9064i	−0.311485	−	0.365236i
$113$	−67.0349	+	116.108i	−0.593229	+	1.02750i	0.400565	+	0.916268i	$0.368814\pi$
$113$	−67.0349	+	116.108i	−0.593229	+	1.02750i	−0.993794	+	0.111234i	$0.964520\pi$
$114$		0			0
$115$			130.006i			1.13049i
$116$	18.2064	−	31.5344i	0.156952	−	0.271848i
$117$		0			0
$118$		−	251.808i		−	2.13396i
$119$	6.86659	−	5.85604i	0.0577024	−	0.0492104i
$120$		0			0
$121$	−120.995			−0.999958
$122$	45.4659	−	26.2498i	0.372672	−	0.215162i
$123$		0			0
$124$	−380.716	−	219.807i	−3.07029	−	1.77263i
$125$			191.910i			1.53528i
$126$		0			0
$127$	43.4456			0.342092			0.171046	−	0.985263i	$-0.445285\pi$
$127$	43.4456			0.342092			0.171046	+	0.985263i	$0.445285\pi$
$128$	−116.905	+	202.486i	−0.913323	+	1.58192i
$129$		0			0
$130$	−79.7650	−	138.157i	−0.613577	−	1.06275i
$131$			163.356i			1.24699i	0.781826	+	0.623497i	$0.214289\pi$
$131$			163.356i			1.24699i	−0.781826	+	0.623497i	$0.785711\pi$
$132$		0			0
$133$	21.4334	+	116.112i	0.161153	+	0.873025i
$134$	155.751			1.16232
$135$		0			0
$136$	12.2189	+	7.05458i	0.0898447	+	0.0518719i
$137$	185.099			1.35109			0.675545	−	0.737319i	$-0.263908\pi$
$137$	185.099			1.35109			0.675545	+	0.737319i	$0.263908\pi$
$138$		0			0
$139$	53.8087	+	31.0665i	0.387113	+	0.223500i	0.680909	−	0.732368i	$-0.261585\pi$
$139$	53.8087	+	31.0665i	0.387113	+	0.223500i	−0.293795	+	0.955868i	$0.594918\pi$
$140$	−78.5801	−	425.697i	−0.561286	−	3.04069i
$141$		0			0
$142$	97.0406	−	168.079i	0.683385	−	1.18366i
$143$	−0.346342	−	0.199961i	−0.00242197	−	0.00139833i
$144$		0			0
$145$	36.9867	−	21.3543i	0.255080	−	0.147271i
$146$	−106.906	+	61.7221i	−0.732231	+	0.422754i
$147$		0			0
$148$	−59.9977	+	103.919i	−0.405390	+	0.702156i
$149$	−12.6390			−0.0848252			−0.0424126	−	0.999100i	$-0.513504\pi$
$149$	−12.6390			−0.0848252			−0.0424126	+	0.999100i	$0.513504\pi$
$150$		0			0
$151$	159.892			1.05889			0.529444	−	0.848345i	$-0.322400\pi$
$151$	159.892			1.05889			0.529444	+	0.848345i	$0.322400\pi$
$152$	−159.867	+	92.2991i	−1.05175	+	0.607231i
$153$		0			0
$154$	−1.09210	−	1.28056i	−0.00709155	−	0.00831530i
$155$	−257.811	−	446.541i	−1.66330	−	2.88091i
$156$		0			0
$157$	−3.79962	+	2.19371i	−0.0242014	+	0.0139727i	−0.512052	−	0.858955i	$-0.671114\pi$
$157$	−3.79962	+	2.19371i	−0.0242014	+	0.0139727i	0.487850	+	0.872927i	$0.337781\pi$
$158$	124.243	+	215.196i	0.786350	+	1.36200i
$159$		0			0
$160$	−132.777	+	76.6587i	−0.829855	+	0.479117i
$161$	35.7416	−	100.700i	0.221997	−	0.625464i
$162$		0			0
$163$	−84.2849	−	145.986i	−0.517085	−	0.895618i	−0.999803	−	0.0198422i	$-0.993684\pi$
$163$	−84.2849	−	145.986i	−0.517085	−	0.895618i	0.482718	−	0.875776i	$-0.339650\pi$
$164$		−	249.335i		−	1.52033i
$165$		0			0
$166$			250.337i			1.50805i
$167$	−167.033	−	96.4367i	−1.00020	−	0.577466i	−0.0918923	−	0.995769i	$-0.529292\pi$
$167$	−167.033	−	96.4367i	−1.00020	−	0.577466i	−0.908307	+	0.418303i	$0.862625\pi$
$168$		0			0
$169$	−68.9213	−	119.375i	−0.407818	−	0.706362i
$170$	18.4230	+	31.9096i	0.108371	+	0.187704i
$171$		0			0
$172$	181.441	−	314.265i	1.05489	−	1.82712i
$173$	244.035	+	140.894i	1.41061	+	0.814414i	0.995445	−	0.0953343i	$-0.0303920\pi$
$173$	244.035	+	140.894i	1.41061	+	0.814414i	0.415161	+	0.909748i	$0.363725\pi$
$174$		0			0
$175$	111.296	−	313.569i	0.635975	−	1.79182i
$176$	0.275134	−	0.476547i	0.00156326	−	0.00270765i
$177$		0			0
$178$			267.749i			1.50421i
$179$	−147.606	+	255.660i	−0.824613	+	1.42827i	0.0776026	+	0.996984i	$0.475273\pi$
$179$	−147.606	+	255.660i	−0.824613	+	1.42827i	−0.902215	+	0.431286i	$0.858060\pi$
$180$		0			0
$181$		−	122.856i		−	0.678763i	−0.940649	−	0.339381i	$-0.889782\pi$
$181$		−	122.856i		−	0.678763i	0.940649	−	0.339381i	$-0.110218\pi$
$182$	23.8017	+	128.942i	0.130778	+	0.708474i
$183$		0			0
$184$	167.058			0.907922
$185$	−121.886	+	70.3712i	−0.658846	+	0.380385i
$186$		0			0
$187$	0.0799935	+	0.0461843i	0.000427773	+	0.000246975i
$188$		−	136.858i		−	0.727968i
$189$		0			0
$190$	−482.079			−2.53726
$191$	145.994	−	252.868i	0.764364	−	1.32392i	−0.176218	−	0.984351i	$-0.556386\pi$
$191$	145.994	−	252.868i	0.764364	−	1.32392i	0.940582	−	0.339566i	$-0.110280\pi$
$192$		0			0
$193$	114.770	+	198.787i	0.594661	+	1.02998i	0.993595	+	0.113004i	$0.0360472\pi$
$193$	114.770	+	198.787i	0.594661	+	1.02998i	−0.398933	+	0.916980i	$0.630619\pi$
$194$		−	255.727i		−	1.31818i
$195$		0			0
$196$	−56.1671	+	351.338i	−0.286567	+	1.79254i
$197$	−189.183			−0.960320			−0.480160	−	0.877181i	$-0.659421\pi$
$197$	−189.183			−0.960320			−0.480160	+	0.877181i	$0.659421\pi$
$198$		0			0
$199$	−195.739	−	113.010i	−0.983611	−	0.567888i	−0.0802524	−	0.996775i	$-0.525573\pi$
$199$	−195.739	−	113.010i	−0.983611	−	0.567888i	−0.903358	+	0.428887i	$0.858906\pi$
$200$	520.201			2.60100
$201$		0			0
$202$	191.859	+	110.770i	0.949797	+	0.548365i
$203$	−34.5197	+	6.37205i	−0.170048	+	0.0313894i
$204$		0			0
$205$	146.222	−	253.264i	0.713279	−	1.23544i
$206$	−32.4946	−	18.7608i	−0.157741	−	0.0910716i
$207$		0			0
$208$	−37.1271	+	21.4354i	−0.178496	+	0.103055i
$209$	−1.04660	+	0.604255i	−0.00500766	+	0.00289117i
$210$		0			0
$211$	−4.03450	+	6.98796i	−0.0191209	+	0.0331183i	−0.875428	−	0.483349i	$-0.839420\pi$
$211$	−4.03450	+	6.98796i	−0.0191209	+	0.0331183i	0.856307	+	0.516468i	$0.172753\pi$
$212$	117.474			0.554123
$213$		0			0
$214$	−88.6679			−0.414336
$215$	368.601	−	212.812i	1.71442	−	0.989822i
$216$		0			0
$217$	76.9301	+	416.758i	0.354516	+	1.92054i
$218$	305.348	+	528.878i	1.40068	+	2.42605i
$219$		0			0
$220$	3.83710	−	2.21535i	0.0174414	−	0.0100698i
$221$	−3.59816	−	6.23219i	−0.0162812	−	0.0281999i
$222$		0			0
$223$	−178.204	+	102.886i	−0.799122	+	0.461373i	−0.843164	−	0.537656i	$-0.819310\pi$
$223$	−178.204	+	102.886i	−0.799122	+	0.461373i	0.0440419	+	0.999030i	$0.485976\pi$
$224$	123.921	−	22.8748i	0.553218	−	0.102119i
$225$		0			0
$226$	224.954	+	389.631i	0.995371	+	1.72403i
$227$			236.642i			1.04247i	0.853412	+	0.521237i	$0.174529\pi$
$227$			236.642i			1.04247i	−0.853412	+	0.521237i	$0.825471\pi$
$228$		0			0
$229$		−	144.780i		−	0.632225i	−0.948722	−	0.316113i	$-0.897622\pi$
$229$		−	144.780i		−	0.632225i	0.948722	−	0.316113i	$-0.102378\pi$
$230$	377.822	+	218.136i	1.64270	+	0.948416i
$231$		0			0
$232$	−27.4402	−	47.5277i	−0.118277	−	0.204861i
$233$	−89.6419	−	155.264i	−0.384729	−	0.666370i	0.607003	−	0.794700i	$-0.292372\pi$
$233$	−89.6419	−	155.264i	−0.384729	−	0.666370i	−0.991732	+	0.128330i	$0.959038\pi$
$234$		0			0
$235$	80.2603	−	139.015i	0.341533	−	0.591553i
$236$	−471.863	−	272.430i	−1.99942	−	1.15437i
$237$		0			0
$238$	−5.49739	−	29.7813i	−0.0230983	−	0.125132i
$239$	200.781	−	347.762i	0.840086	−	1.45507i	−0.0497353	−	0.998762i	$-0.515838\pi$
$239$	200.781	−	347.762i	0.840086	−	1.45507i	0.889821	−	0.456309i	$-0.150829\pi$
$240$		0			0
$241$			19.7561i			0.0819753i	0.999160	+	0.0409877i	$0.0130504\pi$
$241$			19.7561i			0.0819753i	−0.999160	+	0.0409877i	$0.986950\pi$
$242$	−203.016	+	351.633i	−0.838908	+	1.45303i
$243$		0			0
$244$		−	113.598i		−	0.465567i
$245$	−263.094	+	323.936i	−1.07385	+	1.32219i
$246$		0			0
$247$	94.1535			0.381188
$248$	−573.804	+	331.286i	−2.31373	+	1.33583i
$249$		0			0
$250$	557.726	+	322.003i	2.23090	+	1.28801i
$251$		−	141.824i		−	0.565035i	−0.959262	−	0.282517i	$-0.908831\pi$
$251$		−	141.824i		−	0.565035i	0.959262	−	0.282517i	$-0.0911695\pi$
$252$		0			0
$253$	1.09368			0.00432284
$254$	72.8968	−	126.261i	0.286995	−	0.497091i
$255$		0			0
$256$	210.043	+	363.806i	0.820482	+	1.42112i
$257$		−	234.865i		−	0.913873i	−0.889499	−	0.456937i	$-0.848947\pi$
$257$		−	234.865i		−	0.913873i	0.889499	−	0.456937i	$-0.151053\pi$
$258$		0			0
$259$	113.757	−	20.9986i	0.439216	−	0.0810756i
$260$	−345.190			−1.32766
$261$		0			0
$262$	474.743	+	274.093i	1.81200	+	1.04616i
$263$	98.7723			0.375560			0.187780	−	0.982211i	$-0.439871\pi$
$263$	98.7723			0.375560			0.187780	+	0.982211i	$0.439871\pi$
$264$		0			0
$265$	119.325	+	68.8926i	0.450285	+	0.259972i
$266$	373.407	+	132.534i	1.40378	+	0.498248i
$267$		0			0
$268$	168.507	−	291.863i	0.628758	−	1.08904i
$269$	97.3372	+	56.1976i	0.361848	+	0.208913i	0.669891	−	0.742459i	$-0.266341\pi$
$269$	97.3372	+	56.1976i	0.361848	+	0.208913i	−0.308043	+	0.951372i	$0.599674\pi$
$270$		0			0
$271$	349.157	−	201.586i	1.28840	−	0.743859i	0.310033	−	0.950726i	$-0.399660\pi$
$271$	349.157	−	201.586i	1.28840	−	0.743859i	0.978369	+	0.206867i	$0.0663266\pi$
$272$	8.57513	−	4.95085i	0.0315262	−	0.0182017i
$273$		0			0
$274$	310.576	−	537.933i	1.13349	−	1.96326i
$275$	3.40560			0.0123840
$276$		0			0
$277$	−236.285			−0.853014			−0.426507	−	0.904484i	$-0.640256\pi$
$277$	−236.285			−0.853014			−0.426507	+	0.904484i	$0.640256\pi$
$278$	180.570	−	104.252i	0.649532	−	0.375007i
$279$		0			0
$280$	−614.857	−	218.232i	−2.19592	−	0.779401i
$281$	134.034	+	232.154i	0.476990	+	0.826172i	0.999652	−	0.0263685i	$-0.00839433\pi$
$281$	134.034	+	232.154i	0.476990	+	0.826172i	−0.522662	+	0.852540i	$0.675061\pi$
$282$		0			0
$283$	−90.1933	+	52.0731i	−0.318704	+	0.184004i	−0.650815	−	0.759236i	$-0.725573\pi$
$283$	−90.1933	+	52.0731i	−0.318704	+	0.184004i	0.332111	+	0.943240i	$0.392239\pi$
$284$	−209.976	−	363.689i	−0.739353	−	1.28060i
$285$		0			0
$286$	−1.16225	+	0.671023i	−0.00406380	+	0.00234623i
$287$	−182.888	+	155.973i	−0.637241	+	0.543459i
$288$		0			0
$289$	−143.669	−	248.842i	−0.497124	−	0.861045i
$290$		−	143.320i		−	0.494207i
$291$		0			0
$292$			267.108i			0.914753i
$293$	−57.7861	−	33.3628i	−0.197222	−	0.113866i	0.398137	−	0.917326i	$-0.369657\pi$
$293$	−57.7861	−	33.3628i	−0.197222	−	0.113866i	−0.595359	+	0.803460i	$0.702990\pi$
$294$		0			0
$295$	−319.533	−	553.447i	−1.08316	−	1.87609i
$296$	90.4268	+	156.624i	0.305496	+	0.529134i
$297$		0			0
$298$	−21.2067	+	36.7311i	−0.0711636	+	0.123259i
$299$	−73.7914	−	42.6035i	−0.246794	−	0.142487i
$300$		0			0
$301$	−344.016	+	63.5025i	−1.14291	+	0.210972i
$302$	268.281	−	464.676i	0.888348	−	1.53866i
$303$		0			0
$304$			129.550i			0.426150i
$305$	66.6196	−	115.389i	0.218425	−	0.378323i
$306$		0			0
$307$			321.966i			1.04875i	0.851488	+	0.524375i	$0.175701\pi$
$307$			321.966i			1.04875i	−0.851488	+	0.524375i	$0.824299\pi$
$308$	−3.58118	+	0.661055i	−0.0116272	+	0.00214628i
$309$		0			0
$310$	−1730.31			−5.58164
$311$	−199.696	+	115.294i	−0.642108	+	0.370721i	−0.785426	−	0.618956i	$-0.787556\pi$
$311$	−199.696	+	115.294i	−0.642108	+	0.370721i	0.143318	+	0.989677i	$0.454223\pi$
$312$		0			0
$313$	−365.550	−	211.050i	−1.16789	−	0.674282i	−0.214709	−	0.976678i	$-0.568880\pi$
$313$	−365.550	−	211.050i	−1.16789	−	0.674282i	−0.953182	+	0.302396i	$0.902214\pi$
$314$			14.7232i			0.0468892i
$315$		0			0
$316$	537.674			1.70150
$317$	126.024	−	218.279i	0.397551	−	0.688578i	−0.595873	−	0.803079i	$-0.703194\pi$
$317$	126.024	−	218.279i	0.397551	−	0.688578i	0.993423	+	0.114501i	$0.0365270\pi$
$318$		0			0
$319$	−0.179643	−	0.311150i	−0.000563143	−	0.000975393i
$320$			776.142i			2.42544i
$321$		0			0
$322$	−232.682	−	272.834i	−0.722614	−	0.847311i
$323$	−21.7463			−0.0673260
$324$		0			0
$325$	−229.779	−	132.663i	−0.707013	−	0.408194i
$326$	−565.682			−1.73522
$327$		0			0
$328$	−325.444	−	187.895i	−0.992207	−	0.572851i
$329$	−100.386	+	85.6123i	−0.305124	+	0.260220i
$330$		0			0
$331$	66.0877	−	114.467i	0.199661	−	0.345823i	−0.748758	−	0.662844i	$-0.769349\pi$
$331$	66.0877	−	114.467i	0.199661	−	0.345823i	0.948418	+	0.317021i	$0.102683\pi$
$332$	469.107	+	270.839i	1.41297	+	0.815781i
$333$		0			0
$334$	−560.526	+	323.620i	−1.67822	+	0.968922i
$335$	342.325	−	197.642i	1.02187	−	0.589975i
$336$		0			0
$337$	−287.789	+	498.465i	−0.853972	+	1.47912i	0.0236230	+	0.999721i	$0.492480\pi$
$337$	−287.789	+	498.465i	−0.853972	+	1.47912i	−0.877595	+	0.479402i	$0.840853\pi$
$338$	−462.569			−1.36855
$339$		0			0
$340$	79.7274			0.234492
$341$	−3.75653	+	2.16883i	−0.0110162	+	0.00636022i
$342$		0			0
$343$	292.843	−	178.583i	0.853771	−	0.520649i
$344$	−273.462	−	473.651i	−0.794949	−	1.37689i
$345$		0			0
$346$	818.926	−	472.807i	2.36684	−	1.36649i
$347$	106.500	+	184.464i	0.306918	+	0.531597i	0.977686	−	0.210070i	$-0.0673691\pi$
$347$	106.500	+	184.464i	0.306918	+	0.531597i	−0.670769	+	0.741666i	$0.734036\pi$
$348$		0			0
$349$	510.194	−	294.561i	1.46188	−	0.844014i	0.462777	−	0.886475i	$-0.346853\pi$
$349$	510.194	−	294.561i	1.46188	−	0.844014i	0.999098	+	0.0424609i	$0.0135198\pi$
$350$	−724.548	−	849.579i	−2.07014	−	2.42737i
$351$		0			0
$352$	0.644892	+	1.11698i	0.00183208	+	0.00317325i
$353$		−	497.220i		−	1.40855i	−0.709925	−	0.704277i	$-0.751271\pi$
$353$		−	497.220i		−	1.40855i	0.709925	−	0.704277i	$-0.248729\pi$
$354$		0			0
$355$		−	492.561i		−	1.38750i
$356$	501.736	+	289.677i	1.40937	+	0.813700i
$357$		0			0
$358$	495.331	+	857.938i	1.38361	+	2.39648i
$359$	82.4900	+	142.877i	0.229777	+	0.397986i	0.957742	−	0.287629i	$-0.0928669\pi$
$359$	82.4900	+	142.877i	0.229777	+	0.397986i	−0.727965	+	0.685614i	$0.759534\pi$
$360$		0			0
$361$	−38.2402	+	66.2340i	−0.105929	+	0.183474i
$362$	−357.042	−	206.138i	−0.986305	−	0.569443i
$363$		0			0
$364$	267.376	+	94.9004i	0.734550	+	0.260715i
$365$	−156.645	+	271.317i	−0.429165	+	0.743335i
$366$		0			0
$367$			281.159i			0.766100i	0.923728	+	0.383050i	$0.125126\pi$
$367$			281.159i			0.766100i	−0.923728	+	0.383050i	$0.874874\pi$
$368$	58.6199	−	101.533i	0.159293	−	0.275904i
$369$		0			0
$370$			472.300i			1.27649i
$371$	−73.4866	−	86.1677i	−0.198077	−	0.232258i
$372$		0			0
$373$	331.793			0.889526			0.444763	−	0.895648i	$-0.353288\pi$
$373$	331.793			0.889526			0.444763	+	0.895648i	$0.353288\pi$
$374$	0.268440	−	0.154984i	0.000717754	−	0.000414395i
$375$		0			0
$376$	−178.634	−	103.134i	−0.475090	−	0.274293i
$377$			27.9915i			0.0742479i
$378$		0			0
$379$	562.535			1.48426			0.742131	−	0.670255i	$-0.233815\pi$
$379$	562.535			1.48426			0.742131	+	0.670255i	$0.233815\pi$
$380$	−521.560	+	903.369i	−1.37253	+	2.37729i
$381$		0			0
$382$	−489.921	−	848.568i	−1.28252	−	2.22138i
$383$			46.6096i			0.121696i	0.998147	+	0.0608481i	$0.0193805\pi$
$383$			46.6096i			0.121696i	−0.998147	+	0.0608481i	$0.980619\pi$
$384$		0			0
$385$	−4.02529	−	1.42870i	−0.0104553	−	0.00371092i
$386$	770.282			1.99555
$387$		0			0
$388$	−479.207	−	276.670i	−1.23507	−	0.713068i
$389$	−491.009			−1.26223			−0.631117	−	0.775688i	$-0.717403\pi$
$389$	−491.009			−1.26223			−0.631117	+	0.775688i	$0.717403\pi$
$390$		0			0
$391$	17.0434	+	9.83998i	0.0435891	+	0.0251662i
$392$	416.256	+	338.075i	1.06188	+	0.862437i
$393$		0			0
$394$	−317.428	+	549.801i	−0.805654	+	1.39543i
$395$	546.148	+	315.319i	1.38265	+	0.798275i
$396$		0			0
$397$	−323.976	+	187.048i	−0.816061	+	0.471153i	−0.849056	−	0.528302i	$-0.822829\pi$
$397$	−323.976	+	187.048i	−0.816061	+	0.471153i	0.0329951	+	0.999456i	$0.489495\pi$
$398$	−656.854	+	379.235i	−1.65039	+	0.952851i
$399$		0			0
$400$	182.537	−	316.163i	0.456342	−	0.790407i
$401$	409.985			1.02241			0.511203	−	0.859460i	$-0.329200\pi$
$401$	409.985			1.02241			0.511203	+	0.859460i	$0.329200\pi$
$402$		0			0
$403$	337.942			0.838566
$404$	415.144	−	239.683i	1.02758	−	0.593276i
$405$		0			0
$406$	−39.4018	+	111.012i	−0.0970488	+	0.273429i
$407$	0.591998	+	1.02537i	0.00145454	+	0.00251934i
$408$		0			0
$409$	−459.626	+	265.365i	−1.12378	+	0.648815i	−0.942364	−	0.334591i	$-0.891402\pi$
$409$	−459.626	+	265.365i	−1.12378	+	0.648815i	−0.181418	+	0.983406i	$0.558069\pi$
$410$	−490.689	−	849.898i	−1.19680	−	2.07292i
$411$		0			0
$412$	−70.3117	+	40.5945i	−0.170659	+	0.0985303i
$413$	95.3477	+	516.533i	0.230866	+	1.25069i
$414$		0			0
$415$	317.667	+	550.215i	0.765462	+	1.32582i
$416$		−	100.485i		−	0.241551i
$417$		0			0
$418$			4.05549i			0.00970212i
$419$	−490.114	−	282.968i	−1.16972	−	0.675340i	−0.216109	−	0.976369i	$-0.569337\pi$
$419$	−490.114	−	282.968i	−1.16972	−	0.675340i	−0.953615	+	0.301029i	$0.902670\pi$
$420$		0			0
$421$	141.050	+	244.305i	0.335035	+	0.580298i	0.983492	−	0.180954i	$-0.0579185\pi$
$421$	141.050	+	244.305i	0.335035	+	0.580298i	−0.648457	+	0.761252i	$0.724585\pi$
$422$	13.5389	+	23.4500i	0.0320826	+	0.0555688i
$423$		0			0
$424$	88.5268	−	153.333i	0.208790	−	0.361634i
$425$	53.0713	+	30.6407i	0.124874	+	0.0720959i
$426$		0			0
$427$	−83.3248	+	71.0620i	−0.195140	+	0.166422i
$428$	−95.9297	+	166.155i	−0.224135	+	0.388213i
$429$		0			0
$430$		−	1428.30i		−	3.32162i
$431$	226.303	−	391.969i	0.525066	−	0.909440i	−0.474508	−	0.880251i	$-0.657374\pi$
$431$	226.303	−	391.969i	0.525066	−	0.909440i	0.999574	−	0.0291893i	$-0.00929255\pi$
$432$		0			0
$433$		−	46.6278i		−	0.107685i	−0.998549	−	0.0538427i	$-0.982853\pi$
$433$		−	46.6278i		−	0.107685i	0.998549	−	0.0538427i	$-0.0171470\pi$
$434$	1340.26	+	475.700i	3.08815	+	1.09608i
$435$		0			0
$436$	1321.42			3.03078
$437$	−222.988	+	128.742i	−0.510270	+	0.294605i
$438$		0			0
$439$	377.977	+	218.225i	0.860995	+	0.497096i	0.864345	−	0.502899i	$-0.167733\pi$
$439$	377.977	+	218.225i	0.860995	+	0.497096i	−0.00335043	+	0.999994i	$0.501066\pi$
$440$		−	6.67783i		−	0.0151769i
$441$		0			0
$442$	−24.1492			−0.0546362
$443$	−194.198	+	336.361i	−0.438371	+	0.759281i	−0.997564	−	0.0697567i	$-0.977778\pi$
$443$	−194.198	+	336.361i	−0.438371	+	0.759281i	0.559193	+	0.829037i	$0.311111\pi$
$444$		0			0
$445$	339.762	+	588.485i	0.763510	+	1.32244i
$446$			690.526i			1.54826i
$447$		0			0
$448$	213.378	−	601.181i	0.476291	−	1.34192i
$449$	−641.298			−1.42828			−0.714141	−	0.700002i	$-0.753182\pi$
$449$	−641.298			−1.42828			−0.714141	+	0.700002i	$0.753182\pi$
$450$		0			0
$451$	−2.13059	−	1.23009i	−0.00472414	−	0.00272748i
$452$	973.509			2.15378
$453$		0			0
$454$	687.725	+	397.058i	1.51481	+	0.874577i
$455$	215.936	+	253.198i	0.474584	+	0.556480i
$456$		0			0
$457$	−241.068	+	417.542i	−0.527501	+	0.913659i	0.471985	+	0.881607i	$0.343538\pi$
$457$	−241.068	+	417.542i	−0.527501	+	0.913659i	−0.999486	+	0.0320523i	$0.989796\pi$
$458$	−420.756	−	242.924i	−0.918682	−	0.530401i
$459$		0			0
$460$	817.530	−	472.001i	1.77724	−	1.02609i
$461$	307.480	−	177.524i	0.666985	−	0.385084i	−0.127948	−	0.991781i	$-0.540839\pi$
$461$	307.480	−	177.524i	0.666985	−	0.385084i	0.794933	+	0.606697i	$0.207506\pi$
$462$		0			0
$463$	−162.438	+	281.351i	−0.350839	+	0.607670i	−0.986397	−	0.164383i	$-0.947437\pi$
$463$	−162.438	+	281.351i	−0.350839	+	0.607670i	0.635558	+	0.772053i	$0.280770\pi$
$464$	−38.5146			−0.0830056
$465$		0			0
$466$	−601.635			−1.29106
$467$	−614.255	+	354.640i	−1.31532	+	0.759401i	−0.982972	−	0.183755i	$-0.941175\pi$
$467$	−614.255	+	354.640i	−1.31532	+	0.759401i	−0.332349	+	0.943156i	$0.607841\pi$
$468$		0			0
$469$	−319.493	+	58.9758i	−0.681222	+	0.125748i
$470$	−269.335	−	466.502i	−0.573054	−	0.992558i
$471$		0			0
$472$	−711.178	+	410.599i	−1.50673	+	0.869912i
$473$	−1.79028	−	3.10085i	−0.00378495	−	0.00655572i
$474$		0			0
$475$	−694.363	+	400.890i	−1.46182	+	0.843980i
$476$	−61.7550	−	21.9188i	−0.129737	−	0.0460479i
$477$		0			0
$478$	−673.774	−	1167.01i	−1.40957	−	2.44144i
$479$		−	234.479i		−	0.489517i	−0.969584	−	0.244758i	$-0.921291\pi$
$479$		−	234.479i		−	0.489517i	0.969584	−	0.244758i	$-0.0787086\pi$
$480$		0			0
$481$		−	92.2435i		−	0.191775i
$482$	57.4147	+	33.1484i	0.119118	+	0.0687726i
$483$		0			0
$484$	439.285	+	760.863i	0.907613	+	1.57203i
$485$	−324.506	−	562.061i	−0.669085	−	1.15889i
$486$		0			0
$487$	−72.4238	+	125.442i	−0.148714	+	0.257581i	−0.930753	−	0.365650i	$-0.880847\pi$
$487$	−72.4238	+	125.442i	−0.148714	+	0.257581i	0.782038	+	0.623230i	$0.214180\pi$
$488$	−148.274	−	85.6060i	−0.303840	−	0.175422i
$489$		0			0
$490$	499.975	+	1308.13i	1.02036	+	2.66965i
$491$	−7.54425	+	13.0670i	−0.0153651	+	0.0266131i	−0.873606	−	0.486634i	$-0.838224\pi$
$491$	−7.54425	+	13.0670i	−0.0153651	+	0.0266131i	0.858241	+	0.513248i	$0.171558\pi$
$492$		0			0
$493$		−	6.46509i		−	0.0131138i
$494$	157.979	−	273.627i	0.319795	−	0.553902i
$495$		0			0
$496$			464.988i			0.937477i
$497$	−135.416	+	381.526i	−0.272467	+	0.767658i
$498$		0			0
$499$	−64.4622			−0.129183			−0.0645913	−	0.997912i	$-0.520574\pi$
$499$	−64.4622			−0.129183			−0.0645913	+	0.997912i	$0.520574\pi$
$500$	1206.81	−	696.750i	2.41361	−	1.39350i
$501$		0			0
$502$	−412.166	−	237.964i	−0.821047	−	0.474032i
$503$			115.864i			0.230346i	0.993345	+	0.115173i	$0.0367422\pi$
$503$			115.864i			0.230346i	−0.993345	+	0.115173i	$0.963258\pi$
$504$		0			0
$505$	562.248			1.11336
$506$	1.83507	−	3.17843i	0.00362661	−	0.00628148i
$507$		0			0
$508$	−157.734	−	273.203i	−0.310500	−	0.537802i
$509$		−	327.865i		−	0.644136i	−0.946716	−	0.322068i	$-0.895622\pi$
$509$		−	327.865i		−	0.644136i	0.946716	−	0.322068i	$-0.104378\pi$
$510$		0			0
$511$	195.925	−	167.091i	0.383414	−	0.326988i
$512$	474.473			0.926705
$513$		0			0
$514$	−682.562	−	394.078i	−1.32794	−	0.766688i
$515$	−95.2263			−0.184906
$516$		0			0
$517$	−1.16946	−	0.675190i	−0.00226202	−	0.00130598i
$518$	129.845	−	365.832i	0.250667	−	0.706239i
$519$		0			0
$520$	−260.130	+	450.559i	−0.500251	+	0.866460i
$521$	−342.767	−	197.897i	−0.657903	−	0.379840i	0.133575	−	0.991039i	$-0.457354\pi$
$521$	−342.767	−	197.897i	−0.657903	−	0.379840i	−0.791477	+	0.611198i	$0.790688\pi$
$522$		0			0
$523$	86.8586	−	50.1478i	0.166078	−	0.0958850i	−0.414657	−	0.909978i	$-0.636099\pi$
$523$	86.8586	−	50.1478i	0.166078	−	0.0958850i	0.580735	+	0.814093i	$0.302765\pi$
$524$	1027.25	−	593.082i	1.96040	−	1.13184i
$525$		0			0
$526$	165.729	−	287.051i	0.315074	−	0.545723i
$527$	−78.0533			−0.148109
$528$		0			0
$529$	−295.982			−0.559512
$530$	400.429	−	231.188i	0.755527	−	0.436203i
$531$		0			0
$532$	652.344	−	556.339i	1.22621	−	1.04575i
$533$	95.8351	+	165.991i	0.179803	+	0.311428i
$534$		0			0
$535$	−194.883	+	112.516i	−0.364267	+	0.210310i
$536$	−253.969	−	439.887i	−0.473823	−	0.820685i
$537$		0			0
$538$	326.641	−	188.587i	0.607140	−	0.350533i
$539$	2.72511	+	2.21328i	0.00505586	+	0.00410627i
$540$		0			0
$541$	−357.663	−	619.490i	−0.661115	−	1.14508i	−0.980323	−	0.197400i	$-0.936750\pi$
$541$	−357.663	−	619.490i	−0.661115	−	1.14508i	0.319209	−	0.947684i	$-0.396583\pi$
$542$		−	1352.95i		−	2.49622i
$543$		0			0
$544$			23.2088i			0.0426631i
$545$	1342.25	+	774.946i	2.46284	+	1.42192i
$546$		0			0
$547$	−483.976	−	838.270i	−0.884782	−	1.53249i	−0.845964	−	0.533241i	$-0.820974\pi$
$547$	−483.976	−	838.270i	−0.884782	−	1.53249i	−0.0388181	−	0.999246i	$-0.512359\pi$
$548$	−672.023	−	1163.98i	−1.22632	−	2.12405i
$549$		0			0
$550$	5.71422	−	9.89731i	0.0103895	−	0.0179951i
$551$	73.2541	+	42.2933i	0.132948	+	0.0767573i
$552$		0			0
$553$	−336.345	−	394.386i	−0.608219	−	0.713176i
$554$	−396.459	+	686.688i	−0.715631	+	1.23951i
$555$		0			0
$556$		−	451.161i		−	0.811440i
$557$	175.654	−	304.242i	0.315357	−	0.546215i	−0.664156	−	0.747594i	$-0.731209\pi$
$557$	175.654	−	304.242i	0.315357	−	0.546215i	0.979513	+	0.201379i	$0.0645423\pi$
$558$		0			0
$559$			278.957i			0.499028i
$560$	−348.386	+	297.115i	−0.622118	+	0.530562i
$561$		0			0
$562$	899.577			1.60067
$563$	197.271	−	113.895i	0.350393	−	0.202299i	−0.314465	−	0.949269i	$-0.601825\pi$
$563$	197.271	−	113.895i	0.350393	−	0.202299i	0.664858	+	0.746969i	$0.268492\pi$
$564$		0			0
$565$	988.851	+	570.913i	1.75018	+	1.01047i
$566$			349.491i			0.617476i
$567$		0			0
$568$	−632.940			−1.11433
$569$	−357.472	+	619.160i	−0.628247	+	1.08816i	0.359656	+	0.933085i	$0.382894\pi$
$569$	−357.472	+	619.160i	−0.628247	+	1.08816i	−0.987903	+	0.155071i	$0.950439\pi$
$570$		0			0
$571$	−395.507	−	685.038i	−0.692657	−	1.19972i	−0.970964	−	0.239225i	$-0.923107\pi$
$571$	−395.507	−	685.038i	−0.692657	−	1.19972i	0.278307	−	0.960492i	$-0.410227\pi$
$572$			2.90391i			0.00507677i
$573$		0			0
$574$	146.420	+	793.211i	0.255087	+	1.38190i
$575$	725.595			1.26191
$576$		0			0
$577$	572.969	+	330.804i	0.993013	+	0.573316i	0.906174	−	0.422906i	$-0.138990\pi$
$577$	572.969	+	330.804i	0.993013	+	0.573316i	0.0868395	+	0.996222i	$0.472323\pi$
$578$	−964.241			−1.66824
$579$		0			0
$580$	−268.568	−	155.058i	−0.463048	−	0.267341i
$581$	−94.7909	−	513.517i	−0.163151	−	0.883850i
$582$		0			0
$583$	0.579559	−	1.00383i	0.000994098	−	0.00172183i
$584$	348.642	+	201.289i	0.596990	+	0.344672i
$585$		0			0
$586$	−193.917	+	111.958i	−0.330916	+	0.191055i
$587$	−610.107	+	352.246i	−1.03937	+	0.600078i	−0.919653	−	0.392731i	$-0.871530\pi$
$587$	−610.107	+	352.246i	−1.03937	+	0.600078i	−0.119712	+	0.992809i	$0.538197\pi$
$588$		0			0
$589$	510.608	−	884.400i	0.866907	−	1.50153i
$590$	−2144.56			−3.63485
$591$		0			0
$592$	126.922			0.214395
$593$	152.039	−	87.7799i	0.256390	−	0.148027i	−0.366297	−	0.930498i	$-0.619374\pi$
$593$	152.039	−	87.7799i	0.256390	−	0.148027i	0.622687	+	0.782471i	$0.286041\pi$
$594$		0			0
$595$	−49.8739	−	58.4804i	−0.0838217	−	0.0982864i
$596$	45.8871	+	79.4787i	0.0769917	+	0.133354i
$597$		0			0
$598$	−247.627	+	142.968i	−0.414092	+	0.239076i
$599$	182.781	+	316.585i	0.305143	+	0.528523i	0.977293	−	0.211892i	$-0.0679625\pi$
$599$	182.781	+	316.585i	0.305143	+	0.528523i	−0.672150	+	0.740415i	$0.734629\pi$
$600$		0			0
$601$	−817.426	+	471.941i	−1.36011	+	0.785260i	−0.989638	−	0.143583i	$-0.954137\pi$
$601$	−817.426	+	471.941i	−1.36011	+	0.785260i	−0.370472	+	0.928844i	$0.620804\pi$
$602$	−392.670	+	1106.32i	−0.652275	+	1.83775i
$603$		0			0
$604$	−580.506	−	1005.47i	−0.961102	−	1.66468i
$605$			1030.47i			1.70326i
$606$		0			0
$607$			745.782i			1.22864i	0.789059	+	0.614318i	$0.210569\pi$
$607$			745.782i			1.22864i	−0.789059	+	0.614318i	$0.789431\pi$
$608$	−262.972	−	151.827i	−0.432519	−	0.249715i
$609$		0			0
$610$	−223.560	−	387.218i	−0.366492	−	0.634783i
$611$	52.6031	+	91.1113i	0.0860935	+	0.149118i
$612$		0			0
$613$	−513.381	+	889.202i	−0.837490	+	1.45057i	0.0544976	+	0.998514i	$0.482644\pi$
$613$	−513.381	+	889.202i	−0.837490	+	1.45057i	−0.891987	+	0.452061i	$0.850689\pi$
$614$	935.693	+	540.222i	1.52393	+	0.879841i
$615$		0			0
$616$	−1.83588	+	5.17248i	−0.00298033	+	0.00839689i
$617$	390.166	−	675.787i	0.632360	−	1.09528i	−0.354708	−	0.934977i	$-0.615420\pi$
$617$	390.166	−	675.787i	0.632360	−	1.09528i	0.987068	−	0.160302i	$-0.0512469\pi$
$618$		0			0
$619$			511.012i			0.825544i	0.910834	+	0.412772i	$0.135439\pi$
$619$			511.012i			0.825544i	−0.910834	+	0.412772i	$0.864561\pi$
$620$	−1872.02	+	3242.43i	−3.01939	+	5.22973i
$621$		0			0
$622$			773.803i			1.24406i
$623$	−101.384	−	549.234i	−0.162735	−	0.881596i
$624$		0			0
$625$	446.095			0.713753
$626$	−1226.70	+	708.237i	−1.95959	+	1.13137i
$627$		0			0
$628$	27.5899	+	15.9290i	0.0439329	+	0.0253647i
$629$			21.3052i			0.0338715i
$630$		0			0
$631$	−241.238			−0.382311			−0.191156	−	0.981560i	$-0.561224\pi$
$631$	−241.238			−0.382311			−0.191156	+	0.981560i	$0.561224\pi$
$632$	405.183	−	701.798i	0.641113	−	1.11044i
$633$		0			0
$634$	−422.906	−	732.495i	−0.667045	−	1.15536i
$635$		−	370.012i		−	0.582696i
$636$		0			0
$637$	−97.6488	−	255.487i	−0.153295	−	0.401078i
$638$	−1.20568			−0.00188978
$639$		0			0
$640$	1724.50	+	995.643i	2.69454	+	1.55569i
$641$	1245.67			1.94332			0.971660	−	0.236385i	$-0.0759626\pi$
$641$	1245.67			1.94332			0.971660	+	0.236385i	$0.0759626\pi$
$642$		0			0
$643$	−283.285	−	163.554i	−0.440567	−	0.254361i	0.263271	−	0.964722i	$-0.415199\pi$
$643$	−283.285	−	163.554i	−0.440567	−	0.254361i	−0.703838	+	0.710360i	$0.748532\pi$
$644$	−763.003	+	140.844i	−1.18479	+	0.218702i
$645$		0			0
$646$	−36.4878	+	63.1988i	−0.0564827	+	0.0978309i
$647$	802.984	+	463.603i	1.24109	+	0.716542i	0.969316	−	0.245819i	$-0.0790569\pi$
$647$	802.984	+	463.603i	1.24109	+	0.716542i	0.271772	+	0.962362i	$0.412390\pi$
$648$		0			0
$649$	−4.65587	+	2.68807i	−0.00717392	+	0.00414186i
$650$	−771.087	+	445.187i	−1.18629	+	0.684903i
$651$		0			0
$652$	−612.011	+	1060.03i	−0.938666	+	1.62582i
$653$	542.027			0.830056			0.415028	−	0.909809i	$-0.363772\pi$
$653$	542.027			0.830056			0.415028	+	0.909809i	$0.363772\pi$
$654$		0			0
$655$	1391.25			2.12404
$656$	−228.394	+	131.863i	−0.348162	+	0.201011i
$657$		0			0
$658$	80.3689	+	435.388i	0.122141	+	0.661683i
$659$	−289.410	−	501.273i	−0.439166	−	0.760657i	0.558460	−	0.829532i	$-0.311393\pi$
$659$	−289.410	−	501.273i	−0.439166	−	0.760657i	−0.997625	+	0.0688744i	$0.978059\pi$
$660$		0			0
$661$	681.798	−	393.636i	1.03146	−	0.595516i	0.114060	−	0.993474i	$-0.463614\pi$
$661$	681.798	−	393.636i	1.03146	−	0.595516i	0.917404	+	0.397958i	$0.130281\pi$
$662$	−221.775	−	384.126i	−0.335008	−	0.580251i
$663$		0			0
$664$	707.024	−	408.201i	1.06480	−	0.614760i
$665$	988.889	−	182.541i	1.48705	−	0.274497i
$666$		0			0
$667$	−38.2746	−	66.2935i	−0.0573831	−	0.0993905i
$668$			1400.50i			2.09655i
$669$		0			0
$670$		−	1326.48i		−	1.97982i
$671$	−0.970707	−	0.560438i	−0.00144666	−	0.000835228i
$672$		0			0
$673$	−298.863	−	517.646i	−0.444076	−	0.769162i	0.553912	−	0.832575i	$-0.313135\pi$
$673$	−298.863	−	517.646i	−0.444076	−	0.769162i	−0.997987	+	0.0634138i	$0.979801\pi$
$674$	965.753	+	1672.73i	1.43287	+	2.48180i
$675$		0			0
$676$	−500.452	+	866.809i	−0.740314	+	1.28226i
$677$	−283.567	−	163.718i	−0.418859	−	0.241828i	0.275730	−	0.961235i	$-0.411080\pi$
$677$	−283.567	−	163.718i	−0.418859	−	0.241828i	−0.694589	+	0.719407i	$0.744414\pi$
$678$		0			0
$679$	96.8317	+	524.573i	0.142609	+	0.772567i
$680$	60.0814	−	104.064i	0.0883550	−	0.153035i
$681$		0			0
$682$			14.5562i			0.0213434i
$683$	227.200	−	393.522i	0.332650	−	0.576167i	−0.650380	−	0.759609i	$-0.725390\pi$
$683$	227.200	−	393.522i	0.332650	−	0.576167i	0.983031	+	0.183441i	$0.0587237\pi$
$684$		0			0
$685$		−	1576.43i		−	2.30136i
$686$	−27.6358	−	1150.70i	−0.0402854	−	1.67740i
$687$		0			0
$688$	−383.828			−0.557889
$689$	−78.2067	+	45.1527i	−0.113508	+	0.0655336i
$690$		0			0
$691$	−302.776	−	174.808i	−0.438171	−	0.252978i	0.264651	−	0.964344i	$-0.414743\pi$
$691$	−302.776	−	174.808i	−0.438171	−	0.252978i	−0.702821	+	0.711366i	$0.748077\pi$
$692$		−	2046.12i		−	2.95682i
$693$		0			0
$694$	714.782			1.02995
$695$	264.583	−	458.271i	0.380695	−	0.659382i
$696$		0			0
$697$	−22.1347	−	38.3384i	−0.0317571	−	0.0550049i
$698$		−	1976.96i		−	2.83232i
$699$		0			0
$700$	−2375.92	+	438.574i	−3.39416	+	0.626534i
$701$	−449.660			−0.641455			−0.320727	−	0.947172i	$-0.603927\pi$
$701$	−449.660			−0.641455			−0.320727	+	0.947172i	$0.603927\pi$
$702$		0			0
$703$	−241.403	−	139.374i	−0.343389	−	0.198256i
$704$	6.52929			0.00927456
$705$		0			0
$706$	−1445.01	−	834.278i	−2.04676	−	1.18170i
$707$	−435.504	−	154.574i	−0.615989	−	0.218634i
$708$		0			0
$709$	−260.729	+	451.597i	−0.367742	+	0.636949i	−0.989212	−	0.146490i	$-0.953203\pi$
$709$	−260.729	+	451.597i	−0.367742	+	0.636949i	0.621470	+	0.783438i	$0.286536\pi$
$710$	−1431.47	−	826.462i	−2.01616	−	1.16403i
$711$		0			0
$712$	756.201	−	436.593i	1.06208	−	0.613193i
$713$	−800.364	+	462.090i	−1.12253	+	0.648093i
$714$		0			0
$715$	−1.70300	+	2.94968i	−0.00238182	+	0.00412542i
$716$	2143.59			2.99384
$717$		0			0
$718$	553.635			0.771080
$719$	−1009.02	+	582.559i	−1.40337	+	0.810236i	−0.994737	−	0.102463i	$-0.967328\pi$
$719$	−1009.02	+	582.559i	−1.40337	+	0.810236i	−0.408632	+	0.912699i	$0.633994\pi$
$720$		0			0
$721$	73.7600	+	26.1798i	0.102302	+	0.0363104i
$722$	128.326	+	222.266i	0.177736	+	0.307848i
$723$		0			0
$724$	−772.567	+	446.042i	−1.06708	+	0.616080i
$725$	−119.183	−	206.431i	−0.164391	−	0.284733i
$726$		0			0
$727$	988.530	−	570.728i	1.35974	−	0.785046i	0.370151	−	0.928972i	$-0.379306\pi$
$727$	988.530	−	570.728i	1.35974	−	0.785046i	0.989588	+	0.143926i	$0.0459727\pi$
$728$	325.359	−	277.477i	0.446922	−	0.381149i
$729$		0			0
$730$	525.666	+	910.480i	0.720090	+	1.24723i
$731$		−	64.4297i		−	0.0881391i
$732$		0			0
$733$		−	1359.98i		−	1.85536i	−0.373371	−	0.927682i	$-0.621798\pi$
$733$		−	1359.98i		−	1.85536i	0.373371	−	0.927682i	$-0.378202\pi$
$734$	817.099	+	471.752i	1.11321	+	0.642714i
$735$		0			0
$736$	137.400	+	237.984i	0.186685	+	0.323348i
$737$	−1.66266	−	2.87981i	−0.00225598	−	0.00390748i
$738$		0			0
$739$	66.1095	−	114.505i	0.0894580	−	0.154946i	−0.817824	−	0.575468i	$-0.804820\pi$
$739$	66.1095	−	114.505i	0.0894580	−	0.154946i	0.907282	+	0.420522i	$0.138153\pi$
$740$	885.044	+	510.980i	1.19600	+	0.690514i
$741$		0			0
$742$	−373.721	+	68.9858i	−0.503668	+	0.0929728i
$743$	−307.775	+	533.082i	−0.414233	+	0.717473i	−0.995348	−	0.0963491i	$-0.969283\pi$
$743$	−307.775	+	533.082i	−0.414233	+	0.717473i	0.581115	+	0.813822i	$0.302617\pi$
$744$		0			0
$745$			107.642i			0.144486i
$746$	556.711	−	964.252i	0.746262	−	1.29256i
$747$		0			0
$748$		−	0.670707i		−	0.000896668i
$749$	181.885	−	33.5744i	0.242837	−	0.0448256i
$750$		0			0
$751$	21.4559			0.0285698			0.0142849	−	0.999898i	$-0.495453\pi$
$751$	21.4559			0.0285698			0.0142849	+	0.999898i	$0.495453\pi$
$752$	−125.364	+	72.3788i	−0.166707	+	0.0962485i
$753$		0			0
$754$	81.3483	+	46.9665i	0.107889	+	0.0622898i
$755$		−	1361.75i		−	1.80364i
$756$		0			0
$757$	204.896			0.270668			0.135334	−	0.990800i	$-0.456789\pi$
$757$	204.896			0.270668			0.135334	+	0.990800i	$0.456789\pi$
$758$	943.870	−	1634.83i	1.24521	−	2.15677i
$759$		0			0
$760$	786.080	+	1361.53i	1.03432	+	1.79149i
$761$		−	148.922i		−	0.195693i	−0.995202	−	0.0978465i	$-0.968805\pi$
$761$		−	148.922i		−	0.195693i	0.995202	−	0.0978465i	$-0.0311954\pi$
$762$		0			0
$763$	−826.622	−	969.268i	−1.08338	−	1.27034i
$764$	−2120.18			−2.77510
$765$		0			0
$766$	135.456	+	78.2056i	0.176836	+	0.102096i
$767$	418.848			0.546086
$768$		0			0
$769$	515.532	+	297.643i	0.670393	+	0.387052i	0.796226	−	0.605000i	$-0.206827\pi$
$769$	515.532	+	297.643i	0.670393	+	0.387052i	−0.125832	+	0.992052i	$0.540160\pi$
$770$	−10.9061	+	9.30103i	−0.0141637	+	0.0120793i
$771$		0			0
$772$	833.366	−	1443.43i	1.07949	−	1.86973i
$773$	−56.7169	−	32.7455i	−0.0733724	−	0.0423616i	0.462865	−	0.886429i	$-0.346821\pi$
$773$	−56.7169	−	32.7455i	−0.0733724	−	0.0423616i	−0.536237	+	0.844067i	$0.680155\pi$
$774$		0			0
$775$	−2492.25	+	1438.90i	−3.21581	+	1.85665i
$776$	−722.247	+	416.989i	−0.930730	+	0.537357i
$777$		0			0
$778$	−823.857	+	1426.96i	−1.05894	+	1.83414i
$779$	579.202			0.743520
$780$		0			0
$781$	−4.14367			−0.00530560
$782$	57.1936	−	33.0208i	0.0731376	−	0.0422260i
$783$		0			0
$784$	351.535	−	134.359i	0.448386	−	0.171376i
$785$	18.6831	+	32.3601i	0.0238001	+	0.0412230i
$786$		0			0
$787$	−266.038	+	153.597i	−0.338040	+	0.195168i	−0.659405	−	0.751788i	$-0.729192\pi$
$787$	−266.038	+	153.597i	−0.338040	+	0.195168i	0.321365	+	0.946955i	$0.395858\pi$
$788$	686.849	+	1189.66i	0.871636	+	1.50972i
$789$		0			0
$790$	1832.75	−	1058.14i	2.31993	−	1.33941i
$791$	−608.983	−	714.072i	−0.769891	−	0.902746i
$792$		0			0
$793$	43.6630	+	75.6265i	0.0550605	+	0.0953676i
$794$			1255.38i			1.58108i
$795$		0			0
$796$			1641.17i			2.06178i
$797$	−98.3197	−	56.7649i	−0.123362	−	0.0712232i	0.437049	−	0.899438i	$-0.356024\pi$
$797$	−98.3197	−	56.7649i	−0.123362	−	0.0712232i	−0.560411	+	0.828214i	$0.689357\pi$
$798$		0			0
$799$	−12.1496	−	21.0437i	−0.0152060	−	0.0263375i
$800$	427.850	+	741.059i	0.534813	+	0.926323i
$801$		0			0
$802$	687.908	−	1191.49i	0.857741	−	1.48565i
$803$	2.28246	+	1.31778i	0.00284241	+	0.00164107i
$804$		0			0
$805$	−857.625	−	304.399i	−1.06537	−	0.378135i
$806$	567.028	−	982.122i	0.703509	−	1.21851i
$807$		0			0
$808$		−	722.487i		−	0.894168i
$809$	−104.005	+	180.142i	−0.128560	+	0.222672i	−0.923119	−	0.384515i	$-0.874369\pi$
$809$	−104.005	+	180.142i	−0.128560	+	0.222672i	0.794559	+	0.607187i	$0.207702\pi$
$810$		0			0
$811$		−	476.384i		−	0.587403i	−0.955897	−	0.293702i	$-0.905113\pi$
$811$		−	476.384i		−	0.587403i	0.955897	−	0.293702i	$-0.0948872\pi$
$812$	165.398	+	193.939i	0.203692	+	0.238841i
$813$		0			0
$814$	3.97322			0.00488111
$815$	−1243.31	+	717.826i	−1.52554	+	0.880768i
$816$		0			0
$817$	730.034	+	421.485i	0.893554	+	0.515894i
$818$			1781.01i			2.17728i
$819$		0			0
$820$	−2123.50			−2.58964
$821$	−464.705	+	804.892i	−0.566023	+	0.980380i	0.430931	+	0.902385i	$0.358185\pi$
$821$	−464.705	+	804.892i	−0.566023	+	0.980380i	−0.996954	+	0.0779951i	$0.975148\pi$
$822$		0			0
$823$	418.609	+	725.051i	0.508637	+	0.880986i	0.999950	+	0.0100024i	$0.00318391\pi$
$823$	418.609	+	725.051i	0.508637	+	0.880986i	−0.491313	+	0.870983i	$0.663483\pi$
$824$			122.366i			0.148502i
$825$		0			0
$826$	1661.12	+	589.586i	2.01105	+	0.713785i
$827$	1404.16			1.69789			0.848947	−	0.528477i	$-0.177237\pi$
$827$	1404.16			1.69789			0.848947	+	0.528477i	$0.177237\pi$
$828$		0			0
$829$	886.393	+	511.759i	1.06923	+	0.617321i	0.927972	−	0.372651i	$-0.121551\pi$
$829$	886.393	+	511.759i	1.06923	+	0.617321i	0.141260	+	0.989972i	$0.454885\pi$
$830$	2132.03			2.56872
$831$		0			0
$832$	−440.537	−	254.344i	−0.529492	−	0.305702i
$833$	22.5536	+	59.0089i	0.0270752	+	0.0708391i
$834$		0			0
$835$	−821.319	+	1422.57i	−0.983616	+	1.70367i
$836$	7.59959	+	4.38763i	0.00909042	+	0.00524836i
$837$		0			0
$838$	−1644.71	+	949.575i	−1.96266	+	1.13314i
$839$	682.275	−	393.912i	0.813200	−	0.469501i	−0.0348658	−	0.999392i	$-0.511100\pi$
$839$	682.275	−	393.912i	0.813200	−	0.469501i	0.848066	+	0.529891i	$0.177767\pi$
$840$		0			0
$841$	407.926	−	706.549i	0.485049	−	0.840130i
$842$	946.662			1.12430
$843$		0			0
$844$	58.5907			0.0694203
$845$	−1016.68	+	586.979i	−1.20317	+	0.694650i
$846$		0			0
$847$	283.299	−	798.179i	0.334474	−	0.942360i
$848$	−62.1274	−	107.608i	−0.0732635	−	0.126896i
$849$		0			0
$850$	178.095	−	102.823i	0.209524	−	0.120969i
$851$	126.131	+	218.465i	0.148215	+	0.256715i
$852$		0			0
$853$	−965.660	+	557.524i	−1.13208	+	0.653604i	−0.944456	−	0.328638i	$-0.893411\pi$
$853$	−965.660	+	557.524i	−1.13208	+	0.653604i	−0.187619	+	0.982242i	$0.560077\pi$
$854$	66.7098	+	361.391i	0.0781146	+	0.423175i
$855$		0			0
$856$	144.582	+	250.424i	0.168905	+	0.292551i
$857$		−	518.075i		−	0.604521i	−0.953225	−	0.302261i	$-0.902259\pi$
$857$		−	518.075i		−	0.604521i	0.953225	−	0.302261i	$-0.0977413\pi$
$858$		0			0
$859$		−	541.338i		−	0.630195i	−0.949059	−	0.315098i	$-0.897963\pi$
$859$		−	541.338i		−	0.630195i	0.949059	−	0.315098i	$-0.102037\pi$
$860$	−2676.49	−	1545.27i	−3.11219	−	1.79683i
$861$		0			0
$862$	−759.422	−	1315.36i	−0.881000	−	1.52594i
$863$	−574.885	−	995.731i	−0.666148	−	1.15380i	−0.978973	−	0.203991i	$-0.934609\pi$
$863$	−574.885	−	995.731i	−0.666148	−	1.15380i	0.312825	−	0.949811i	$-0.398725\pi$
$864$		0			0
$865$	1199.94	−	2078.36i	1.38722	−	2.40273i
$866$	−135.509	−	78.2362i	−0.156477	−	0.0903420i
$867$		0			0
$868$	2341.44	−	1996.85i	2.69751	−	2.30052i
$869$	2.65262	−	4.59447i	0.00305249	−	0.00528708i
$870$		0			0
$871$			259.071i			0.297441i
$872$	995.803	−	1724.78i	1.14198	−	1.97796i
$873$		0			0
$874$			864.059i			0.988626i
$875$	−1265.99	−	449.341i	−1.44685	−	0.513533i
$876$		0			0
$877$	821.379			0.936578			0.468289	−	0.883575i	$-0.344871\pi$
$877$	821.379			0.936578			0.468289	+	0.883575i	$0.344871\pi$
$878$	1268.40	−	732.313i	1.44465	−	0.834070i
$879$		0			0
$880$	−4.05859	−	2.34323i	−0.00461203	−	0.00266276i
$881$			358.218i			0.406603i	0.979116	+	0.203302i	$0.0651672\pi$
$881$			358.218i			0.406603i	−0.979116	+	0.203302i	$0.934833\pi$
$882$		0			0
$883$	258.969			0.293283			0.146642	−	0.989190i	$-0.453154\pi$
$883$	258.969			0.293283			0.146642	+	0.989190i	$0.453154\pi$
$884$	−26.1270	+	45.2532i	−0.0295554	+	0.0511914i
$885$		0			0
$886$	651.685	+	1128.75i	0.735537	+	1.27399i
$887$			731.208i			0.824361i	0.911102	+	0.412180i	$0.135233\pi$
$887$			731.208i			0.824361i	−0.911102	+	0.412180i	$0.864767\pi$
$888$		0			0
$889$	−101.724	+	286.602i	−0.114426	+	0.322387i
$890$	2280.33			2.56217
$891$		0			0
$892$	1293.98	+	747.079i	1.45065	+	0.837532i
$893$	317.920			0.356013
$894$		0			0
$895$	2177.37	+	1257.11i	2.43282	+	1.40459i
$896$	−1062.04	−	1245.30i	−1.18531	−	1.38985i
$897$		0			0
$898$	−1076.03	+	1863.73i	−1.19825	+	2.07542i
$899$	262.929	+	151.802i	0.292468	+	0.168856i
$900$		0			0
$901$	18.0631	−	10.4288i	0.0200479	−	0.0115747i
$902$	−7.14976	+	4.12792i	−0.00792657	+	0.00457641i
$903$		0			0
$904$	733.622	−	1270.67i	0.811528	−	1.40561i
$905$	−1046.32			−1.15616
$906$		0			0
$907$	442.220			0.487563			0.243782	−	0.969830i	$-0.421612\pi$
$907$	442.220			0.487563			0.243782	+	0.969830i	$0.421612\pi$
$908$	1488.10	−	859.153i	1.63887	−	0.946204i
$909$		0			0
$910$	1098.16	−	202.711i	1.20677	−	0.222759i
$911$	187.670	+	325.054i	0.206004	+	0.356810i	0.950452	−	0.310871i	$-0.100621\pi$
$911$	187.670	+	325.054i	0.206004	+	0.356810i	−0.744448	+	0.667680i	$0.767287\pi$
$912$		0			0
$913$	4.62868	−	2.67237i	0.00506975	−	0.00292702i
$914$	808.970	+	1401.18i	0.885087	+	1.53302i
$915$		0			0
$916$	−910.431	+	525.638i	−0.993920	+	0.573840i
$917$	−1077.63	−	382.485i	−1.17517	−	0.417104i
$918$		0			0
$919$	481.436	+	833.871i	0.523869	+	0.907368i	0.999614	+	0.0277845i	$0.00884522\pi$
$919$	481.436	+	833.871i	0.523869	+	0.907368i	−0.475745	+	0.879583i	$0.657821\pi$
$920$		−	1422.77i		−	1.54649i
$921$		0			0
$922$		−	1191.46i		−	1.29225i
$923$	279.577	+	161.414i	0.302901	+	0.174880i
$924$		0			0
$925$	392.758	+	680.277i	0.424604	+	0.735435i
$926$	545.106	+	944.151i	0.588667	+	1.01960i
$927$		0			0
$928$	45.1375	−	78.1804i	0.0486395	−	0.0842462i
$929$	−1367.86	−	789.732i	−1.47240	−	0.850088i	−0.472878	−	0.881128i	$-0.656785\pi$
$929$	−1367.86	−	789.732i	−1.47240	−	0.850088i	−0.999518	+	0.0310394i	$0.990118\pi$
$930$		0			0
$931$	−816.154	−	130.476i	−0.876642	−	0.140146i
$932$	−650.908	+	1127.41i	−0.698400	+	1.20966i
$933$		0			0
$934$			2380.18i			2.54838i
$935$	0.393336	−	0.681277i	0.000420680	−	0.000728639i
$936$		0			0
$937$			349.950i			0.373480i	0.982409	+	0.186740i	$0.0597921\pi$
$937$			349.950i			0.373480i	−0.982409	+	0.186740i	$0.940208\pi$
$938$	−364.679	+	1027.46i	−0.388783	+	1.09537i
$939$		0			0
$940$	−1165.57			−1.23997
$941$	1407.66	−	812.712i	1.49592	−	0.863669i	0.495929	−	0.868363i	$-0.334827\pi$
$941$	1407.66	−	812.712i	1.49592	−	0.863669i	0.999989	+	0.00469397i	$0.00149414\pi$
$942$		0			0
$943$	−453.941	−	262.083i	−0.481380	−	0.277925i
$944$			576.310i			0.610498i
$945$		0			0
$946$	−12.0155			−0.0127014
$947$	−810.194	+	1403.30i	−0.855537	+	1.48183i	0.0206084	+	0.999788i	$0.493440\pi$
$947$	−810.194	+	1403.30i	−0.855537	+	1.48183i	−0.876146	+	0.482046i	$0.839894\pi$
$948$		0			0
$949$	−102.666	−	177.823i	−0.108184	−	0.187380i
$950$			2690.59i			2.83220i
$951$		0			0
$952$	−75.1471	+	64.0878i	−0.0789361	+	0.0673192i
$953$	−376.872			−0.395459			−0.197730	−	0.980257i	$-0.563357\pi$
$953$	−376.872			−0.395459			−0.197730	+	0.980257i	$0.563357\pi$
$954$		0			0
$955$	−2153.59	−	1243.38i	−2.25507	−	1.30197i
$956$	−2915.82			−3.05002
$957$		0			0
$958$	−681.438	−	393.428i	−0.711313	−	0.410677i
$959$	−433.395	+	1221.06i	−0.451923	+	1.27327i
$960$		0			0
$961$	1352.21	−	2342.10i	1.40709	−	2.43715i
$962$	−268.077	−	154.774i	−0.278666	−	0.160888i
$963$		0			0
$964$	124.234	−	71.7264i	0.128873	−	0.0744050i
$965$	1693.00	−	977.454i	1.75440	−	1.01291i
$966$		0			0
$967$	−684.814	+	1186.13i	−0.708184	+	1.22661i	0.257346	+	0.966319i	$0.417152\pi$
$967$	−684.814	+	1186.13i	−0.708184	+	1.22661i	−0.965530	+	0.260291i	$0.916181\pi$
$968$	1324.15			1.36793
$969$		0			0
$970$	−2177.94			−2.24530
$971$	−279.879	+	161.588i	−0.288238	+	0.166414i	−0.637147	−	0.770742i	$-0.719886\pi$
$971$	−279.879	+	161.588i	−0.288238	+	0.166414i	0.348909	+	0.937157i	$0.386552\pi$
$972$		0			0
$973$	−330.928	+	282.226i	−0.340111	+	0.290057i
$974$	243.038	+	420.954i	0.249526	+	0.432191i
$975$		0			0
$976$	−104.058	+	60.0777i	−0.106616	+	0.0615550i
$977$	−20.6062	−	35.6910i	−0.0210913	−	0.0365312i	0.855287	−	0.518154i	$-0.173381\pi$
$977$	−20.6062	−	35.6910i	−0.0210913	−	0.0365312i	−0.876378	+	0.481623i	$0.840047\pi$
$978$		0			0
$979$	4.95063	−	2.85825i	0.00505682	−	0.00291956i
$980$	2992.23	+	478.356i	3.05329	+	0.488119i
$981$		0			0
$982$	25.3168	+	43.8499i	0.0257808	+	0.0446537i
$983$			190.075i			0.193362i	0.995315	+	0.0966812i	$0.0308227\pi$
$983$			190.075i			0.193362i	−0.995315	+	0.0966812i	$0.969177\pi$
$984$		0			0
$985$			1611.21i			1.63574i
$986$	−18.7888	−	10.8477i	−0.0190555	−	0.0110017i
$987$		0			0
$988$	−341.834	−	592.074i	−0.345986	−	0.599265i
$989$	−381.436	−	660.666i	−0.385678	−	0.668014i
$990$		0			0
$991$	−2.30807	+	3.99769i	−0.00232903	+	0.00403399i	−0.867188	−	0.497982i	$-0.834075\pi$
$991$	−2.30807	+	3.99769i	−0.00232903	+	0.00403399i	0.864859	+	0.502016i	$0.167408\pi$
$992$	−943.875	−	544.947i	−0.951487	−	0.549342i
$993$		0			0
$994$	881.573	+	1033.70i	0.886894	+	1.03994i
$995$	−962.465	+	1667.04i	−0.967302	+	1.67542i
$996$		0			0
$997$		−	384.529i		−	0.385686i	−0.981230	−	0.192843i	$-0.938229\pi$
$997$		−	384.529i		−	0.385686i	0.981230	−	0.192843i	$-0.0617708\pi$
$998$	−108.160	+	187.339i	−0.108377	+	0.187714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.14		28
3.2	odd	2		63.3.k.a.31.1	✓	28
7.5	odd	6		189.3.t.a.145.1		28
9.2	odd	6		63.3.t.a.52.14	yes	28
9.7	even	3		189.3.t.a.73.1		28
21.2	odd	6		441.3.t.a.166.14		28
21.5	even	6		63.3.t.a.40.14	yes	28
21.11	odd	6		441.3.l.a.391.1		28
21.17	even	6		441.3.l.b.391.1		28
21.20	even	2		441.3.k.b.31.1		28
63.2	odd	6		441.3.k.b.313.1		28
63.11	odd	6		441.3.l.b.97.1		28
63.20	even	6		441.3.t.a.178.14		28
63.38	even	6		441.3.l.a.97.1		28
63.47	even	6		63.3.k.a.61.1	yes	28
63.61	odd	6	inner	189.3.k.a.19.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.1	✓	28	3.2	odd	2
63.3.k.a.61.1	yes	28	63.47	even	6
63.3.t.a.40.14	yes	28	21.5	even	6
63.3.t.a.52.14	yes	28	9.2	odd	6
189.3.k.a.10.14		28	1.1	even	1	trivial
189.3.k.a.19.14		28	63.61	odd	6	inner
189.3.t.a.73.1		28	9.7	even	3
189.3.t.a.145.1		28	7.5	odd	6
441.3.k.b.31.1		28	21.20	even	2
441.3.k.b.313.1		28	63.2	odd	6
441.3.l.a.97.1		28	63.38	even	6
441.3.l.a.391.1		28	21.11	odd	6
441.3.l.b.97.1		28	63.11	odd	6
441.3.l.b.391.1		28	21.17	even	6
441.3.t.a.166.14		28	21.2	odd	6
441.3.t.a.178.14		28	63.20	even	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67789 - 2.90618i) q^{2} +(-3.63061 - 6.28839i) q^{4} -8.51666i q^{5} +(-2.34142 + 6.59680i) q^{7} -10.9439 q^{8} +O(q^{10})\)	\(q+(1.67789 - 2.90618i) q^{2} +(-3.63061 - 6.28839i) q^{4} -8.51666i q^{5} +(-2.34142 + 6.59680i) q^{7} -10.9439 q^{8} +(-24.7510 - 14.2900i) q^{10} -0.0716464 q^{11} +(4.83405 + 2.79094i) q^{13} +(15.2429 + 17.8733i) q^{14} +(-3.84017 + 6.65137i) q^{16} +(-1.11650 - 0.644614i) q^{17} +(14.6079 - 8.43385i) q^{19} +(-53.5561 + 30.9206i) q^{20} +(-0.120215 + 0.208218i) q^{22} -15.2649 q^{23} -47.5335 q^{25} +(16.2220 - 9.36576i) q^{26} +(49.9840 - 9.22663i) q^{28} +(2.50735 + 4.34286i) q^{29} +(52.4315 - 30.2714i) q^{31} +(-9.00103 - 15.5902i) q^{32} +(-3.74673 + 2.16318i) q^{34} +(56.1827 + 19.9410i) q^{35} +(-8.26277 - 14.3115i) q^{37} -56.6042i q^{38} +93.2053i q^{40} +(29.7375 + 17.1690i) q^{41} +(24.9877 + 43.2800i) q^{43} +(0.260120 + 0.450541i) q^{44} +(-25.6128 + 44.3627i) q^{46} +(16.3227 + 9.42391i) q^{47} +(-38.0355 - 30.8917i) q^{49} +(-79.7558 + 138.141i) q^{50} -40.5312i q^{52} +(-8.08916 + 14.0108i) q^{53} +0.610188i q^{55} +(25.6242 - 72.1946i) q^{56} +16.8282 q^{58} +(64.9840 - 37.5186i) q^{59} +(13.5486 + 7.82227i) q^{61} -203.168i q^{62} -91.1322 q^{64} +(23.7695 - 41.1699i) q^{65} +(23.2065 + 40.1948i) q^{67} +9.36135i q^{68} +(152.221 - 129.818i) q^{70} +57.8350 q^{71} +(-31.8573 - 18.3928i) q^{73} -55.4560 q^{74} +(-106.071 - 61.2400i) q^{76} +(0.167754 - 0.472637i) q^{77} +(-37.0237 + 64.1270i) q^{79} +(56.6474 + 32.7054i) q^{80} +(99.7924 - 57.6151i) q^{82} +(-64.6045 + 37.2994i) q^{83} +(-5.48996 + 9.50888i) q^{85} +167.706 q^{86} +0.784090 q^{88} +(-69.0981 + 39.8938i) q^{89} +(-29.7298 + 25.3545i) q^{91} +(55.4209 + 95.9919i) q^{92} +(54.7753 - 31.6245i) q^{94} +(-71.8283 - 124.410i) q^{95} +(65.9955 - 38.1025i) q^{97} +(-153.596 + 58.7055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

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