LMFDB - Embedded newform 546.2.bv.a.515.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.17
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.69438 + 0.359266i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.75102 - 1.00508i) q^{5} +(-1.54366 - 0.785563i) q^{6} +(1.18204 + 2.36702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.74186 + 1.21747i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.69438 + 0.359266i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.75102 - 1.00508i) q^{5} +(-1.54366 - 0.785563i) q^{6} +(1.18204 + 2.36702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.74186 + 1.21747i) q^{9} +(3.36308 + 1.94167i) q^{10} +(1.60373 - 0.429718i) q^{11} +(1.28774 + 1.15832i) q^{12} +(-2.02005 + 2.98654i) q^{13} +(-0.529138 - 2.59230i) q^{14} +(-5.99457 - 3.05061i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.0575760 + 0.0997246i) q^{17} +(-2.33333 - 1.88563i) q^{18} +(-0.398277 + 1.48639i) q^{19} +(-2.74594 - 2.74594i) q^{20} +(1.15244 + 4.43530i) q^{21} -1.66030 q^{22} +(3.63473 + 6.29553i) q^{23} +(-0.944069 - 1.45215i) q^{24} +(8.72986 + 5.04019i) q^{25} +(2.72419 - 2.36195i) q^{26} +(4.20835 + 3.04791i) q^{27} +(-0.159828 + 2.64092i) q^{28} +4.96875i q^{29} +(5.00075 + 4.49817i) q^{30} +(-0.532053 + 0.142563i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.87171 - 0.151940i) q^{33} +(0.0814248 - 0.0814248i) q^{34} +(-2.05483 - 10.0668i) q^{35} +(1.76578 + 2.42529i) q^{36} +(3.30353 + 0.885179i) q^{37} +(0.769411 - 1.33266i) q^{38} +(-4.49569 + 4.33460i) q^{39} +(1.94167 + 3.36308i) q^{40} +(-7.86460 + 7.86460i) q^{41} +(0.0347642 - 4.58244i) q^{42} -11.3975i q^{43} +(1.60373 + 0.429718i) q^{44} +(-9.06111 - 7.32255i) q^{45} +(-1.88147 - 7.02175i) q^{46} +(0.604808 - 2.25717i) q^{47} +(0.536057 + 1.64701i) q^{48} +(-4.20554 + 5.59584i) q^{49} +(-7.12790 - 7.12790i) q^{50} +(-0.133383 + 0.148286i) q^{51} +(-3.24268 + 1.57639i) q^{52} +(3.26558 + 1.88538i) q^{53} +(-3.27610 - 4.03326i) q^{54} -6.44753 q^{55} +(0.837902 - 2.50957i) q^{56} +(-1.20884 + 2.37542i) q^{57} +(1.28601 - 4.79945i) q^{58} +(5.02522 - 1.34650i) q^{59} +(-3.66615 - 5.63919i) q^{60} +(2.22068 + 3.84633i) q^{61} +0.550821 q^{62} +(0.359226 + 7.92912i) q^{63} +1.00000i q^{64} +(10.5790 - 9.17226i) q^{65} +(-2.81319 - 0.596491i) q^{66} +(9.47855 - 2.53977i) q^{67} +(-0.0997246 + 0.0575760i) q^{68} +(3.89684 + 11.9729i) q^{69} +(-0.620668 + 10.2556i) q^{70} +(-7.46475 + 7.46475i) q^{71} +(-1.07790 - 2.79966i) q^{72} +(-1.57016 - 5.85991i) q^{73} +(-2.96187 - 1.71003i) q^{74} +(12.9809 + 11.6763i) q^{75} +(-1.08811 + 1.08811i) q^{76} +(2.91283 + 3.28811i) q^{77} +(5.46438 - 3.02333i) q^{78} +(-7.63053 - 13.2165i) q^{79} +(-1.00508 - 3.75102i) q^{80} +(6.03554 + 6.67624i) q^{81} +(9.63213 - 5.56111i) q^{82} +(3.41557 - 3.41557i) q^{83} +(-1.21960 + 4.41730i) q^{84} +(0.316201 - 0.316201i) q^{85} +(-2.94990 + 11.0092i) q^{86} +(-1.78511 + 8.41896i) q^{87} +(-1.43787 - 0.830152i) q^{88} +(0.0126633 - 0.0472602i) q^{89} +(6.85714 + 9.41822i) q^{90} +(-9.45697 - 1.25127i) q^{91} +7.26945i q^{92} +(-0.952718 + 0.0504076i) q^{93} +(-1.16840 + 2.02373i) q^{94} +(2.98789 - 5.17518i) q^{95} +(-0.0915135 - 1.72963i) q^{96} +(-4.27601 - 4.27601i) q^{97} +(5.51055 - 4.31669i) q^{98} +(4.92037 + 0.774265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	1.69438	+	0.359266i	0.978251	+	0.207422i
$3$	1.69438	+	0.359266i	0.978251	+	0.207422i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−3.75102	−	1.00508i	−1.67751	−	0.449487i	−0.710389	−	0.703809i	$-0.751481\pi$
$5$	−3.75102	−	1.00508i	−1.67751	−	0.449487i	−0.967120	+	0.254322i	$0.918148\pi$
$6$	−1.54366	−	0.785563i	−0.630197	−	0.320705i
$7$	1.18204	+	2.36702i	0.446771	+	0.894648i
$7$	1.18204	+	2.36702i	0.446771	+	0.894648i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.74186	+	1.21747i	0.913952	+	0.405823i
$10$	3.36308	+	1.94167i	1.06350	+	0.614011i
$11$	1.60373	−	0.429718i	0.483543	−	0.129565i	−0.00880890	−	0.999961i	$-0.502804\pi$
$11$	1.60373	−	0.429718i	0.483543	−	0.129565i	0.492352	+	0.870396i	$0.336137\pi$
$12$	1.28774	+	1.15832i	0.371740	+	0.334379i
$13$	−2.02005	+	2.98654i	−0.560260	+	0.828317i
$13$	−2.02005	+	2.98654i	−0.560260	+	0.828317i
$14$	−0.529138	−	2.59230i	−0.141418	−	0.692821i
$15$	−5.99457	−	3.05061i	−1.54779	−	0.787664i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.0575760	+	0.0997246i	−0.0139642	+	0.0241868i	−0.872923	−	0.487858i	$-0.837778\pi$
$17$	−0.0575760	+	0.0997246i	−0.0139642	+	0.0241868i	0.858959	+	0.512045i	$0.171112\pi$
$18$	−2.33333	−	1.88563i	−0.549970	−	0.444447i
$19$	−0.398277	+	1.48639i	−0.0913709	+	0.341001i	−0.996444	−	0.0842546i	$-0.973149\pi$
$19$	−0.398277	+	1.48639i	−0.0913709	+	0.341001i	0.905073	+	0.425255i	$0.139816\pi$
$20$	−2.74594	−	2.74594i	−0.614011	−	0.614011i
$21$	1.15244	+	4.43530i	0.251484	+	0.967861i
$22$	−1.66030			−0.353978
$23$	3.63473	+	6.29553i	0.757893	+	1.31271i	0.943923	+	0.330165i	$0.107104\pi$
$23$	3.63473	+	6.29553i	0.757893	+	1.31271i	−0.186030	+	0.982544i	$0.559562\pi$
$24$	−0.944069	−	1.45215i	−0.192707	−	0.296418i
$25$	8.72986	+	5.04019i	1.74597	+	1.00804i
$26$	2.72419	−	2.36195i	0.534257	−	0.463216i
$27$	4.20835	+	3.04791i	0.809898	+	0.586571i
$28$	−0.159828	+	2.64092i	−0.0302047	+	0.499087i
$29$			4.96875i			0.922674i	0.887225	+	0.461337i	$0.152630\pi$
$29$			4.96875i			0.922674i	−0.887225	+	0.461337i	$0.847370\pi$
$30$	5.00075	+	4.49817i	0.913009	+	0.821250i
$31$	−0.532053	+	0.142563i	−0.0955595	+	0.0256051i	−0.306282	−	0.951941i	$-0.599085\pi$
$31$	−0.532053	+	0.142563i	−0.0955595	+	0.0256051i	0.210722	+	0.977546i	$0.432418\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	2.87171	−	0.151940i	0.499901	−	0.0264494i
$34$	0.0814248	−	0.0814248i	0.0139642	−	0.0139642i
$35$	−2.05483	−	10.0668i	−0.347329	−	1.70160i
$36$	1.76578	+	2.42529i	0.294297	+	0.404214i
$37$	3.30353	+	0.885179i	0.543097	+	0.145522i	0.519930	−	0.854209i	$-0.325958\pi$
$37$	3.30353	+	0.885179i	0.543097	+	0.145522i	0.0231677	+	0.999732i	$0.492625\pi$
$38$	0.769411	−	1.33266i	0.124815	−	0.216186i
$39$	−4.49569	+	4.33460i	−0.719887	+	0.694091i
$40$	1.94167	+	3.36308i	0.307005	+	0.531749i
$41$	−7.86460	+	7.86460i	−1.22824	+	1.22824i	−0.263617	+	0.964627i	$0.584916\pi$
$41$	−7.86460	+	7.86460i	−1.22824	+	1.22824i	−0.964627	+	0.263617i	$0.915084\pi$
$42$	0.0347642	−	4.58244i	0.00536423	−	0.707086i
$43$		−	11.3975i		−	1.73811i	−0.494716	−	0.869054i	$-0.664728\pi$
$43$		−	11.3975i		−	1.73811i	0.494716	−	0.869054i	$-0.335272\pi$
$44$	1.60373	+	0.429718i	0.241771	+	0.0647825i
$45$	−9.06111	−	7.32255i	−1.35075	−	1.09158i
$46$	−1.88147	−	7.02175i	−0.277408	−	1.03530i
$47$	0.604808	−	2.25717i	0.0882203	−	0.329243i	−0.907684	−	0.419654i	$-0.862151\pi$
$47$	0.604808	−	2.25717i	0.0882203	−	0.329243i	0.995905	+	0.0904113i	$0.0288181\pi$
$48$	0.536057	+	1.64701i	0.0773731	+	0.237725i
$49$	−4.20554	+	5.59584i	−0.600792	+	0.799406i
$50$	−7.12790	−	7.12790i	−1.00804	−	1.00804i
$51$	−0.133383	+	0.148286i	−0.0186774	+	0.0207642i
$52$	−3.24268	+	1.57639i	−0.449679	+	0.218606i
$53$	3.26558	+	1.88538i	0.448562	+	0.258977i	0.707223	−	0.706991i	$-0.249948\pi$
$53$	3.26558	+	1.88538i	0.448562	+	0.258977i	−0.258661	+	0.965968i	$0.583281\pi$
$54$	−3.27610	−	4.03326i	−0.445821	−	0.548857i
$55$	−6.44753			−0.869385
$56$	0.837902	−	2.50957i	0.111969	−	0.335355i
$57$	−1.20884	+	2.37542i	−0.160115	+	0.314632i
$58$	1.28601	−	4.79945i	0.168861	−	0.630198i
$59$	5.02522	−	1.34650i	0.654228	−	0.175300i	0.0835881	−	0.996500i	$-0.473362\pi$
$59$	5.02522	−	1.34650i	0.654228	−	0.175300i	0.570640	+	0.821201i	$0.306695\pi$
$60$	−3.66615	−	5.63919i	−0.473297	−	0.728017i
$61$	2.22068	+	3.84633i	0.284329	+	0.492472i	0.972446	−	0.233128i	$-0.0748960\pi$
$61$	2.22068	+	3.84633i	0.284329	+	0.492472i	−0.688118	+	0.725599i	$0.741563\pi$
$62$	0.550821			0.0699544
$63$	0.359226	+	7.92912i	0.0452583	+	0.998975i
$64$			1.00000i			0.125000i
$65$	10.5790	−	9.17226i	1.31216	−	1.13768i
$66$	−2.81319	−	0.596491i	−0.346280	−	0.0734230i
$67$	9.47855	−	2.53977i	1.15799	−	0.310282i	0.371827	−	0.928302i	$-0.378732\pi$
$67$	9.47855	−	2.53977i	1.15799	−	0.310282i	0.786162	+	0.618020i	$0.212065\pi$
$68$	−0.0997246	+	0.0575760i	−0.0120934	+	0.00698212i
$69$	3.89684	+	11.9729i	0.469124	+	1.44136i
$70$	−0.620668	+	10.2556i	−0.0741841	+	1.22578i
$71$	−7.46475	+	7.46475i	−0.885903	+	0.885903i	−0.994127	−	0.108223i	$-0.965484\pi$
$71$	−7.46475	+	7.46475i	−0.885903	+	0.885903i	0.108223	+	0.994127i	$0.465484\pi$
$72$	−1.07790	−	2.79966i	−0.127032	−	0.329944i
$73$	−1.57016	−	5.85991i	−0.183773	−	0.685851i	−0.994890	−	0.100967i	$-0.967806\pi$
$73$	−1.57016	−	5.85991i	−0.183773	−	0.685851i	0.811117	−	0.584885i	$-0.198860\pi$
$74$	−2.96187	−	1.71003i	−0.344310	−	0.198787i
$75$	12.9809	+	11.6763i	1.49891	+	1.34827i
$76$	−1.08811	+	1.08811i	−0.124815	+	0.124815i
$77$	2.91283	+	3.28811i	0.331948	+	0.374715i
$78$	5.46438	−	3.02333i	0.618719	−	0.342325i
$79$	−7.63053	−	13.2165i	−0.858501	−	1.48697i	−0.873358	−	0.487078i	$-0.838063\pi$
$79$	−7.63053	−	13.2165i	−0.858501	−	1.48697i	0.0148570	−	0.999890i	$-0.495271\pi$
$80$	−1.00508	−	3.75102i	−0.112372	−	0.419377i
$81$	6.03554	+	6.67624i	0.670616	+	0.741805i
$82$	9.63213	−	5.56111i	1.06369	−	0.614122i
$83$	3.41557	−	3.41557i	0.374908	−	0.374908i	−0.494353	−	0.869261i	$-0.664595\pi$
$83$	3.41557	−	3.41557i	0.374908	−	0.374908i	0.869261	+	0.494353i	$0.164595\pi$
$84$	−1.21960	+	4.41730i	−0.133070	+	0.481967i
$85$	0.316201	−	0.316201i	0.0342968	−	0.0342968i
$86$	−2.94990	+	11.0092i	−0.318096	+	1.18715i
$87$	−1.78511	+	8.41896i	−0.191383	+	0.902608i
$88$	−1.43787	−	0.830152i	−0.153277	−	0.0884945i
$89$	0.0126633	−	0.0472602i	0.00134231	−	0.00500957i	−0.965251	−	0.261323i	$-0.915841\pi$
$89$	0.0126633	−	0.0472602i	0.00134231	−	0.00500957i	0.966594	+	0.256313i	$0.0825079\pi$
$90$	6.85714	+	9.41822i	0.722806	+	0.992768i
$91$	−9.45697	−	1.25127i	−0.991360	−	0.131168i
$92$			7.26945i			0.757893i
$93$	−0.952718	+	0.0504076i	−0.0987923	+	0.00522703i
$94$	−1.16840	+	2.02373i	−0.120511	+	0.208731i
$95$	2.98789	−	5.17518i	0.306551	−	0.530962i
$96$	−0.0915135	−	1.72963i	−0.00934006	−	0.176530i
$97$	−4.27601	−	4.27601i	−0.434163	−	0.434163i	0.455879	−	0.890042i	$-0.349325\pi$
$97$	−4.27601	−	4.27601i	−0.434163	−	0.434163i	−0.890042	+	0.455879i	$0.849325\pi$
$98$	5.51055	−	4.31669i	0.556650	−	0.436052i
$99$	4.92037	+	0.774265i	0.494515	+	0.0778166i
$100$	5.04019	+	8.72986i	0.504019	+	0.872986i
$101$	4.86905	−	8.43344i	0.484489	−	0.839159i	−0.515353	−	0.856978i	$-0.672339\pi$
$101$	4.86905	−	8.43344i	0.484489	−	0.839159i	0.999841	+	0.0178194i	$0.00567239\pi$
$102$	0.167218	−	0.108711i	0.0165570	−	0.0107640i
$103$	−14.7567	+	8.51979i	−1.45402	+	0.839480i	−0.998706	−	0.0508501i	$-0.983807\pi$
$103$	−14.7567	+	8.51979i	−1.45402	+	0.839480i	−0.455316	+	0.890330i	$0.650474\pi$
$104$	3.54019	−	0.683412i	0.347144	−	0.0670140i
$105$	0.135001	−	17.7952i	0.0131748	−	1.73663i
$106$	−2.66633	−	2.66633i	−0.258977	−	0.258977i
$107$	−2.59138	+	1.49613i	−0.250518	+	0.144637i	−0.620001	−	0.784601i	$-0.712868\pi$
$107$	−2.59138	+	1.49613i	−0.250518	+	0.144637i	0.369483	+	0.929237i	$0.379535\pi$
$108$	2.12058	+	4.74375i	0.204053	+	0.456467i
$109$	8.33469	−	2.23327i	0.798319	−	0.213909i	0.163473	−	0.986548i	$-0.447730\pi$
$109$	8.33469	−	2.23327i	0.798319	−	0.213909i	0.634846	+	0.772639i	$0.281064\pi$
$110$	6.22784	+	1.66874i	0.593801	+	0.159109i
$111$	5.27943	+	2.68668i	0.501101	+	0.255008i
$112$	−1.45888	+	2.20719i	−0.137851	+	0.208560i
$113$		−	7.28013i		−	0.684857i	−0.939544	−	0.342429i	$-0.888750\pi$
$113$		−	7.28013i		−	0.684857i	0.939544	−	0.342429i	$-0.111250\pi$
$114$	1.78246	−	1.98161i	0.166942	−	0.185595i
$115$	−7.30641	−	27.2679i	−0.681326	−	2.54274i
$116$	−2.48438	+	4.30307i	−0.230669	+	0.399530i
$117$	−9.17469	+	5.72931i	−0.848201	+	0.529675i
$118$	−5.20249			−0.478928
$119$	−0.304107	−	0.0184045i	−0.0278775	−	0.00168714i
$120$	2.08169	+	6.39591i	0.190032	+	0.583864i
$121$	−7.13899	+	4.12170i	−0.648999	+	0.374700i
$122$	−1.14951	−	4.29002i	−0.104071	−	0.388400i
$123$	−16.1511	+	10.5001i	−1.45630	+	0.946767i
$124$	−0.532053	−	0.142563i	−0.0477797	−	0.0128025i
$125$	−13.9504	−	13.9504i	−1.24776	−	1.24776i
$126$	1.70522	−	7.75192i	0.151913	−	0.690596i
$127$		−	1.68233i		−	0.149283i	−0.997210	−	0.0746414i	$-0.976219\pi$
$127$		−	1.68233i		−	0.149283i	0.997210	−	0.0746414i	$-0.0237812\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	4.09475	−	19.3118i	0.360523	−	1.70031i
$130$	−12.5925	+	6.12168i	−1.10443	+	0.536907i
$131$	14.6267	−	8.44474i	1.27794	−	0.737820i	0.301473	−	0.953475i	$-0.402522\pi$
$131$	14.6267	−	8.44474i	1.27794	−	0.737820i	0.976470	+	0.215654i	$0.0691885\pi$
$132$	2.56295	+	1.30427i	0.223076	+	0.113522i
$133$	−3.98909	+	0.814249i	−0.345898	+	0.0706044i
$134$	−9.81292			−0.847707
$135$	−12.7222	−	15.6625i	−1.09495	−	1.34802i
$136$	0.111228	−	0.0298035i	0.00953775	−	0.00255563i
$137$	6.54788	−	1.75450i	0.559423	−	0.149897i	0.0319820	−	0.999488i	$-0.489818\pi$
$137$	6.54788	−	1.75450i	0.559423	−	0.149897i	0.527441	+	0.849591i	$0.323151\pi$
$138$	−0.665253	−	12.5735i	−0.0566301	−	1.07033i
$139$	16.4394			1.39437			0.697185	−	0.716891i	$-0.254435\pi$
$139$	16.4394			1.39437			0.697185	+	0.716891i	$0.254435\pi$
$140$	3.25386	−	9.74551i	0.275002	−	0.823646i
$141$	1.83570	−	3.60723i	0.154594	−	0.303783i
$142$	9.14242	−	5.27838i	0.767215	−	0.442952i
$143$	−1.95624	+	5.65765i	−0.163589	+	0.473117i
$144$	0.316569	+	2.98325i	0.0263808	+	0.248604i
$145$	4.99401	−	18.6379i	0.414730	−	1.54779i
$146$			6.06663i			0.502078i
$147$	−9.13619	+	7.97057i	−0.753540	+	0.657402i
$148$	2.41835	+	2.41835i	0.198787	+	0.198787i
$149$	−21.4408	−	5.74506i	−1.75650	−	0.470653i	−0.770507	−	0.637431i	$-0.779997\pi$
$149$	−21.4408	−	5.74506i	−1.75650	−	0.470653i	−0.985995	+	0.166778i	$0.946664\pi$
$150$	−9.51656	−	14.6382i	−0.777024	−	1.19520i
$151$	5.02891	+	18.7681i	0.409247	+	1.52733i	0.796087	+	0.605183i	$0.206900\pi$
$151$	5.02891	+	18.7681i	0.409247	+	1.52733i	−0.386840	+	0.922147i	$0.626433\pi$
$152$	1.33266	−	0.769411i	0.108093	−	0.0624075i
$153$	−0.279277	+	0.203333i	−0.0225782	+	0.0164385i
$154$	−1.96255	−	3.92997i	−0.158147	−	0.316686i
$155$	2.13903			0.171811
$156$	−6.06068	+	1.50603i	−0.485243	+	0.120579i
$157$	2.55645	−	4.42790i	0.204027	−	0.353385i	−0.745795	−	0.666175i	$-0.767930\pi$
$157$	2.55645	−	4.42790i	0.204027	−	0.353385i	0.949822	+	0.312790i	$0.101264\pi$
$158$	3.94985	+	14.7410i	0.314233	+	1.17273i
$159$	4.85578	+	4.36777i	0.385089	+	0.346387i
$160$			3.88335i			0.307005i
$161$	−10.6052	+	16.0451i	−0.835809	+	1.26453i
$162$	−4.10195	−	8.01087i	−0.322279	−	0.629393i
$163$	−1.46907	−	0.393636i	−0.115066	−	0.0308319i	0.200826	−	0.979627i	$-0.435637\pi$
$163$	−1.46907	−	0.393636i	−0.115066	−	0.0308319i	−0.315893	+	0.948795i	$0.602304\pi$
$164$	−10.7432	+	2.87864i	−0.838907	+	0.224784i
$165$	−10.9246	−	2.31638i	−0.850477	−	0.180330i
$166$	−4.18320	+	2.41517i	−0.324680	+	0.187454i
$167$	−9.95271	−	9.95271i	−0.770164	−	0.770164i	0.207971	−	0.978135i	$-0.433314\pi$
$167$	−9.95271	−	9.95271i	−0.770164	−	0.770164i	−0.978135	+	0.207971i	$0.933314\pi$
$168$	2.32133	−	3.95113i	0.179094	−	0.304836i
$169$	−4.83882	−	12.0659i	−0.372217	−	0.928146i
$170$	−0.387265	+	0.223588i	−0.0297019	+	0.0171484i
$171$	−2.90165	+	3.59057i	−0.221894	+	0.274578i
$172$	5.69877	−	9.87056i	0.434527	−	0.752623i
$173$	−9.91681	−	17.1764i	−0.753961	−	1.30590i	−0.945889	−	0.324490i	$-0.894807\pi$
$173$	−9.91681	−	17.1764i	−0.753961	−	1.30590i	0.191928	−	0.981409i	$-0.438526\pi$
$174$	3.90327	−	7.67007i	0.295906	−	0.581467i
$175$	−1.61113	+	26.6214i	−0.121790	+	2.01239i
$176$	1.17401	+	1.17401i	0.0884945	+	0.0884945i
$177$	8.99839	−	0.476098i	0.676360	−	0.0357857i
$178$	−0.0244637	+	0.0423724i	−0.00183363	+	0.00317594i
$179$	0.337604	−	0.584747i	0.0252337	−	0.0437060i	−0.853133	−	0.521694i	$-0.825300\pi$
$179$	0.337604	−	0.584747i	0.0252337	−	0.0437060i	0.878366	+	0.477988i	$0.158634\pi$
$180$	−4.18588	−	10.8721i	−0.311997	−	0.810356i
$181$			0.00682105i			0.000507004i	1.00000		0.000253502i	$8.06922e-5\pi$
$181$			0.00682105i			0.000507004i	−1.00000		0.000253502i	$0.999919\pi$
$182$	8.81088	+	3.65628i	0.653106	+	0.271021i
$183$	2.38082	+	7.31496i	0.175995	+	0.540737i
$184$	1.88147	−	7.02175i	0.138704	−	0.517650i
$185$	−11.5019	−	6.64065i	−0.845640	−	0.488231i
$186$	0.933301	+	0.197892i	0.0684330	+	0.0145101i
$187$	−0.0494829	+	0.184673i	−0.00361855	+	0.0135046i
$188$	1.65237	−	1.65237i	0.120511	−	0.120511i
$189$	−2.24000	+	13.5640i	−0.162936	+	0.986637i
$190$	−4.22551	+	4.22551i	−0.306551	+	0.306551i
$191$	2.69000	−	1.55307i	0.194642	−	0.112376i	−0.399512	−	0.916728i	$-0.630820\pi$
$191$	2.69000	−	1.55307i	0.194642	−	0.112376i	0.594154	+	0.804352i	$0.297487\pi$
$192$	−0.359266	+	1.69438i	−0.0259278	+	0.122281i
$193$	−4.51043	−	16.8332i	−0.324668	−	1.21168i	−0.914645	−	0.404257i	$-0.867530\pi$
$193$	−4.51043	−	16.8332i	−0.324668	−	1.21168i	0.589977	−	0.807420i	$-0.299137\pi$
$194$	3.02359	+	5.23702i	0.217081	+	0.375996i
$195$	21.2201	−	11.7406i	1.51960	−	0.840764i
$196$	−6.44003	+	2.74337i	−0.460002	+	0.195955i
$197$	13.2890	−	13.2890i	0.946804	−	0.946804i	−0.0518509	−	0.998655i	$-0.516512\pi$
$197$	13.2890	−	13.2890i	0.946804	−	0.946804i	0.998655	+	0.0518509i	$0.0165121\pi$
$198$	−4.55231	−	2.02137i	−0.323519	−	0.143652i
$199$	0.842978	+	0.486694i	0.0597571	+	0.0345008i	0.529581	−	0.848259i	$-0.322349\pi$
$199$	0.842978	+	0.486694i	0.0597571	+	0.0345008i	−0.469824	+	0.882760i	$0.655683\pi$
$200$	−2.60899	−	9.73689i	−0.184484	−	0.688502i
$201$	16.9727	−	0.898015i	1.19716	−	0.0633411i
$202$	−6.88588	+	6.88588i	−0.484489	+	0.484489i
$203$	−11.7611	+	5.87329i	−0.825469	+	0.412224i
$204$	−0.189657	+	0.0617280i	−0.0132786	+	0.00432183i
$205$	37.4049	−	21.5957i	2.61247	−	1.50831i
$206$	16.4590	−	4.41017i	1.14675	−	0.307271i
$207$	2.30129	+	21.6866i	0.159950	+	1.50732i
$208$	−3.59644	−	0.256144i	−0.249368	−	0.0177604i
$209$			2.55491i			0.176727i
$210$	−4.73614	+	17.1539i	−0.326825	+	1.18373i
$211$	−10.4146			−0.716968			−0.358484	−	0.933536i	$-0.616706\pi$
$211$	−10.4146			−0.716968			−0.358484	+	0.933536i	$0.616706\pi$
$212$	1.88538	+	3.26558i	0.129489	+	0.224281i
$213$	−15.3300	+	9.96631i	−1.05039	+	0.682880i
$214$	2.89031	−	0.774455i	0.197577	−	0.0529407i
$215$	−11.4555	+	42.7525i	−0.781258	+	2.91569i
$216$	−0.820556	−	5.13095i	−0.0558318	−	0.349117i
$217$	−0.966359	−	1.09086i	−0.0656007	−	0.0740525i
$218$	−8.62871			−0.584410
$219$	−0.555179	−	10.4930i	−0.0375155	−	0.709054i
$220$	−5.58373	−	3.22377i	−0.376455	−	0.217346i
$221$	−0.181525	−	0.373401i	−0.0122107	−	0.0251177i
$222$	−4.40417	−	3.96155i	−0.295589	−	0.265882i
$223$	17.8540	+	17.8540i	1.19559	+	1.19559i	0.975473	+	0.220119i	$0.0706446\pi$
$223$	17.8540	+	17.8540i	1.19559	+	1.19559i	0.220119	+	0.975473i	$0.429355\pi$
$224$	1.98043	−	1.75440i	0.132323	−	0.117221i
$225$	17.7997	+	24.4478i	1.18665	+	1.62985i
$226$	−1.88424	+	7.03207i	−0.125338	+	0.467766i
$227$	1.11378	+	4.15669i	0.0739244	+	0.275890i	0.992987	−	0.118221i	$-0.0377192\pi$
$227$	1.11378	+	4.15669i	0.0739244	+	0.275890i	−0.919063	+	0.394111i	$0.871053\pi$
$228$	−2.23460	+	1.45275i	−0.147990	+	0.0962110i
$229$	6.48375	+	1.73732i	0.428458	+	0.114805i	0.466602	−	0.884467i	$-0.345478\pi$
$229$	6.48375	+	1.73732i	0.428458	+	0.114805i	−0.0381441	+	0.999272i	$0.512145\pi$
$230$			28.2298i			1.86142i
$231$	3.75414	+	6.61780i	0.247004	+	0.435419i
$232$	3.51344	−	3.51344i	0.230669	−	0.230669i
$233$	12.6485	+	21.9079i	0.828632	+	1.43523i	0.899112	+	0.437719i	$0.144213\pi$
$233$	12.6485	+	21.9079i	0.828632	+	1.43523i	−0.0704803	+	0.997513i	$0.522453\pi$
$234$	10.3449	−	3.15950i	0.676269	−	0.206543i
$235$	−4.53730	+	7.85883i	−0.295981	+	0.512653i
$236$	5.02522	+	1.34650i	0.327114	+	0.0876499i
$237$	−8.18079	−	25.1351i	−0.531400	−	1.63270i
$238$	0.288982	+	0.0964862i	0.0187319	+	0.00625427i
$239$	18.6250	−	18.6250i	1.20475	−	1.20475i	0.232043	−	0.972706i	$-0.425459\pi$
$239$	18.6250	−	18.6250i	1.20475	−	1.20475i	0.972706	−	0.232043i	$-0.0745410\pi$
$240$	−0.355379	−	6.71676i	−0.0229396	−	0.433565i
$241$	3.37308	+	12.5885i	0.217279	+	0.810897i	0.985352	+	0.170534i	$0.0545494\pi$
$241$	3.37308	+	12.5885i	0.217279	+	0.810897i	−0.768072	+	0.640363i	$0.778784\pi$
$242$	7.96250	−	2.13355i	0.511849	−	0.137150i
$243$	7.82796	+	13.4805i	0.502164	+	0.864772i
$244$			4.44135i			0.284329i
$245$	21.3994	−	16.7632i	1.36716	−	1.07096i
$246$	18.3184	−	5.96215i	1.16794	−	0.380133i
$247$	−3.63462	−	4.19204i	−0.231265	−	0.266733i
$248$	0.477025	+	0.275411i	0.0302911	+	0.0174886i
$249$	7.01438	−	4.56018i	0.444518	−	0.288990i
$250$	9.86442	+	17.0857i	0.623881	+	1.08059i
$251$	−0.347306			−0.0219218			−0.0109609	−	0.999940i	$-0.503489\pi$
$251$	−0.347306			−0.0219218			−0.0109609	+	0.999940i	$0.503489\pi$
$252$	−3.65346	+	7.04643i	−0.230146	+	0.443884i
$253$	8.53443	+	8.53443i	0.536555	+	0.536555i
$254$	−0.435419	+	1.62501i	−0.0273206	+	0.101962i
$255$	0.649364	−	0.422164i	0.0406648	−	0.0264369i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.48837	+	4.30998i	0.155220	+	0.268849i	0.933139	−	0.359515i	$-0.117058\pi$
$257$	2.48837	+	4.30998i	0.155220	+	0.268849i	−0.777919	+	0.628365i	$0.783725\pi$
$258$	−8.95348	+	17.5939i	−0.557420	+	1.09535i
$259$	1.80969	+	8.86584i	0.112449	+	0.550896i
$260$	13.7478	−	2.65392i	0.852601	−	0.164589i
$261$	−6.04930	+	13.6236i	−0.374442	+	0.843280i
$262$	−16.3140	+	4.37132i	−1.00788	+	0.270061i
$263$	20.7522	+	11.9813i	1.27964	+	0.738798i	0.976781	−	0.214239i	$-0.0687272\pi$
$263$	20.7522	+	11.9813i	1.27964	+	0.738798i	0.302854	+	0.953037i	$0.402061\pi$
$264$	−2.13805	−	1.92317i	−0.131588	−	0.118363i
$265$	−10.3543	−	10.3543i	−0.636059	−	0.636059i
$266$	4.06391	+	0.245947i	0.249174	+	0.0150800i
$267$	0.0384355	−	0.0755273i	0.00235222	−	0.00462220i
$268$	9.47855	+	2.53977i	0.578995	+	0.155141i
$269$	−13.6301	−	7.86934i	−0.831042	−	0.479802i	0.0231673	−	0.999732i	$-0.492625\pi$
$269$	−13.6301	−	7.86934i	−0.831042	−	0.479802i	−0.854209	+	0.519929i	$0.825958\pi$
$270$	8.23496	+	18.4216i	0.501164	+	1.12110i
$271$	−9.18902	−	2.46219i	−0.558193	−	0.149567i	−0.0313170	−	0.999510i	$-0.509970\pi$
$271$	−9.18902	−	2.46219i	−0.558193	−	0.149567i	−0.526876	+	0.849942i	$0.676637\pi$
$272$	−0.115152			−0.00698212
$273$	−15.5742	−	5.51770i	−0.942592	−	0.333946i
$274$	−6.77887			−0.409526
$275$	16.1662	+	4.33172i	0.974859	+	0.261213i
$276$	−2.61167	+	12.3172i	−0.157204	+	0.741410i
$277$	−18.5644	−	10.7181i	−1.11542	−	0.643991i	−0.175196	−	0.984534i	$-0.556056\pi$
$277$	−18.5644	−	10.7181i	−1.11542	−	0.643991i	−0.940229	+	0.340543i	$0.889389\pi$
$278$	−15.8792	−	4.25483i	−0.952373	−	0.255188i
$279$	−1.63238	−	0.256870i	−0.0977279	−	0.0153784i
$280$	−5.66532	+	8.57128i	−0.338567	+	0.512232i
$281$	13.9815	+	13.9815i	0.834065	+	0.834065i	0.988070	−	0.154005i	$-0.0492172\pi$
$281$	13.9815	+	13.9815i	0.834065	+	0.834065i	−0.154005	+	0.988070i	$0.549217\pi$
$282$	−2.70677	+	3.00920i	−0.161186	+	0.179195i
$283$	1.56318	+	0.902500i	0.0929212	+	0.0536481i	0.545741	−	0.837954i	$-0.316248\pi$
$283$	1.56318	+	0.902500i	0.0929212	+	0.0536481i	−0.452819	+	0.891602i	$0.649582\pi$
$284$	−10.1970	+	2.73229i	−0.605083	+	0.162132i
$285$	6.92189	−	7.69527i	0.410017	−	0.455829i
$286$	3.35389	−	4.95856i	0.198320	−	0.293206i
$287$	−27.9120	−	9.31934i	−1.64759	−	0.550103i
$288$	0.466340	−	2.96353i	0.0274793	−	0.174628i
$289$	8.49337	+	14.7109i	0.499610	+	0.865350i
$290$	−9.64769	+	16.7103i	−0.566532	+	0.981262i
$291$	−5.70896	−	8.78141i	−0.334665	−	0.514775i
$292$	1.57016	−	5.85991i	0.0918866	−	0.342926i
$293$	17.9914	+	17.9914i	1.05107	+	1.05107i	0.998624	+	0.0524444i	$0.0167012\pi$
$293$	17.9914	+	17.9914i	1.05107	+	1.05107i	0.0524444	+	0.998624i	$0.483299\pi$
$294$	10.8878	−	5.33436i	0.634990	−	0.311106i
$295$	−20.2031			−1.17627
$296$	−1.71003	−	2.96187i	−0.0993937	−	0.172155i
$297$	8.05881	+	3.07962i	0.467619	+	0.178698i
$298$	19.2233	+	11.0986i	1.11358	+	0.642924i
$299$	−26.1442	−	1.86202i	−1.51196	−	0.107684i
$300$	5.40365	+	16.6025i	0.311980	+	0.958544i
$301$	26.9782	−	13.4724i	1.55500	−	0.776536i
$302$		−	19.4302i		−	1.11808i
$303$	11.2799	−	12.5402i	0.648012	−	0.720414i
$304$	−1.48639	+	0.398277i	−0.0852502	+	0.0228427i
$305$	−4.46393	−	16.6596i	−0.255604	−	0.953927i
$306$	0.322387	−	0.124123i	0.0184296	−	0.00709563i
$307$	−4.04476	+	4.04476i	−0.230847	+	0.230847i	−0.813046	−	0.582199i	$-0.802192\pi$
$307$	−4.04476	+	4.04476i	−0.230847	+	0.230847i	0.582199	+	0.813046i	$0.302192\pi$
$308$	0.878530	+	4.30400i	0.0500589	+	0.245243i
$309$	−28.0644	+	9.13419i	−1.59653	+	0.519626i
$310$	−2.06614	−	0.553622i	−0.117349	−	0.0314436i
$311$	−12.2673	+	21.2476i	−0.695617	+	1.20484i	0.274356	+	0.961628i	$0.411535\pi$
$311$	−12.2673	+	21.2476i	−0.695617	+	1.20484i	−0.969972	+	0.243215i	$0.921798\pi$
$312$	6.24396	+	0.113911i	0.353495	+	0.00644894i
$313$	−6.33079	−	10.9653i	−0.357837	−	0.619793i	0.629762	−	0.776788i	$-0.283152\pi$
$313$	−6.33079	−	10.9653i	−0.357837	−	0.619793i	−0.987599	+	0.156996i	$0.949819\pi$
$314$	−3.61536	+	3.61536i	−0.204027	+	0.204027i
$315$	6.62196	−	30.1034i	0.373105	−	1.69613i
$316$		−	15.2611i		−	0.858501i
$317$	23.7864	+	6.37354i	1.33598	+	0.357974i	0.854940	−	0.518727i	$-0.173594\pi$
$317$	23.7864	+	6.37354i	1.33598	+	0.357974i	0.481037	+	0.876701i	$0.340260\pi$
$318$	−3.55986	−	5.47571i	−0.199627	−	0.307063i
$319$	2.13516	+	7.96854i	0.119546	+	0.446153i
$320$	1.00508	−	3.75102i	0.0561859	−	0.209689i
$321$	−4.92829	+	1.60402i	−0.275070	+	0.0895279i
$322$	14.3966	−	12.7535i	0.802293	−	0.710725i
$323$	−0.125298	−	0.125298i	−0.00697178	−	0.00697178i
$324$	1.88881	+	8.79957i	0.104934	+	0.488865i
$325$	−32.6874	+	15.8906i	−1.81317	+	0.881454i
$326$	1.31713	+	0.760446i	0.0729491	+	0.0421172i
$327$	14.9245	−	0.789644i	0.825326	−	0.0436674i
$328$	11.1222			0.614122
$329$	6.05768	−	1.23649i	0.333971	−	0.0681698i
$330$	9.95281	+	5.06494i	0.547884	+	0.278816i
$331$	−3.59268	+	13.4081i	−0.197472	+	0.736975i	0.794141	+	0.607733i	$0.207921\pi$
$331$	−3.59268	+	13.4081i	−0.197472	+	0.736975i	−0.991613	+	0.129242i	$0.958746\pi$
$332$	4.66576	−	1.25019i	0.256067	−	0.0686129i
$333$	7.98013	+	6.44898i	0.437308	+	0.353402i
$334$	7.03763	+	12.1895i	0.385082	+	0.666981i
$335$	−38.1069			−2.08200
$336$	−3.26486	+	3.21570i	−0.178113	+	0.175431i
$337$		−	31.7316i		−	1.72853i	−0.503037	−	0.864265i	$-0.667784\pi$
$337$		−	31.7316i		−	1.72853i	0.503037	−	0.864265i	$-0.332216\pi$
$338$	1.55105	+	12.9071i	0.0843662	+	0.702056i
$339$	2.61551	−	12.3353i	0.142055	−	0.669963i
$340$	0.431938	−	0.115737i	0.0234251	−	0.00627674i
$341$	−0.792007	+	0.457265i	−0.0428896	+	0.0247623i
$342$	3.73208	−	2.71723i	0.201808	−	0.146931i
$343$	−18.2166	−	3.34006i	−0.983603	−	0.180346i
$344$	−8.05928	+	8.05928i	−0.434527	+	0.434527i
$345$	−2.58341	−	48.8271i	−0.139086	−	2.62877i
$346$	5.13332	+	19.1578i	0.275969	+	1.02993i
$347$	−17.3715	−	10.0295i	−0.932553	−	0.538410i	−0.0449347	−	0.998990i	$-0.514308\pi$
$347$	−17.3715	−	10.0295i	−0.932553	−	0.538410i	−0.887618	+	0.460580i	$0.847641\pi$
$348$	−5.75543	+	6.39848i	−0.308523	+	0.342995i
$349$	7.87668	−	7.87668i	0.421629	−	0.421629i	−0.464135	−	0.885764i	$-0.653635\pi$
$349$	7.87668	−	7.87668i	0.421629	−	0.421629i	0.885764	+	0.464135i	$0.153635\pi$
$350$	8.44637	−	25.2974i	0.451477	−	1.35220i
$351$	−17.6038	+	6.41148i	−0.939620	+	0.342219i
$352$	−0.830152	−	1.43787i	−0.0442473	−	0.0766385i
$353$	−1.74028	−	6.49482i	−0.0926258	−	0.345684i	0.904023	−	0.427484i	$-0.140600\pi$
$353$	−1.74028	−	6.49482i	−0.0926258	−	0.345684i	−0.996649	+	0.0817996i	$0.973933\pi$
$354$	−8.81500	−	1.86908i	−0.468512	−	0.0993404i
$355$	35.5032	−	20.4978i	1.88431	−	1.08791i
$356$	0.0345969	−	0.0345969i	0.00183363	−	0.00183363i
$357$	−0.508661	−	0.140440i	−0.0269212	−	0.00743286i
$358$	−0.477444	+	0.477444i	−0.0252337	+	0.0252337i
$359$	−3.05190	+	11.3898i	−0.161073	+	0.601133i	0.837435	+	0.546536i	$0.184054\pi$
$359$	−3.05190	+	11.3898i	−0.161073	+	0.601133i	−0.998508	+	0.0545965i	$0.982613\pi$
$360$	1.22935	+	11.5850i	0.0647923	+	0.610583i
$361$	14.4038	+	8.31601i	0.758092	+	0.437685i
$362$	0.00176542	−	0.00658862i	9.27882e−5	−	0.000346290i
$363$	−13.5769	+	4.41893i	−0.712605	+	0.231933i
$364$	−7.56434	−	5.81212i	−0.396479	−	0.304638i
$365$			23.5588i			1.23312i
$366$	−0.406444	−	7.68191i	−0.0212452	−	0.401540i
$367$	9.53041	−	16.5072i	0.497483	−	0.861666i	−0.502512	−	0.864570i	$-0.667591\pi$
$367$	9.53041	−	16.5072i	0.497483	−	0.861666i	0.999996	+	0.00290350i	$0.000924215\pi$
$368$	−3.63473	+	6.29553i	−0.189473	+	0.328177i
$369$	−31.1385	+	11.9887i	−1.62101	+	0.624107i
$370$	9.39130	+	9.39130i	0.488231	+	0.488231i
$371$	−0.602675	+	9.95829i	−0.0312893	+	0.517009i
$372$	−0.850282	−	0.432705i	−0.0440851	−	0.0224347i
$373$	6.65563	+	11.5279i	0.344615	+	0.596891i	0.985284	−	0.170926i	$-0.0546760\pi$
$373$	6.65563	+	11.5279i	0.344615	+	0.596891i	−0.640668	+	0.767818i	$0.721343\pi$
$374$	0.0955937	−	0.165573i	0.00494303	−	0.00856158i
$375$	−18.6254	−	28.6492i	−0.961811	−	1.47944i
$376$	−2.02373	+	1.16840i	−0.104366	+	0.0602556i
$377$	−14.8394	−	10.0371i	−0.764266	−	0.516938i
$378$	5.67430	−	12.5221i	0.291854	−	0.644066i
$379$	23.5222	+	23.5222i	1.20825	+	1.20825i	0.971592	+	0.236660i	$0.0760528\pi$
$379$	23.5222	+	23.5222i	1.20825	+	1.20825i	0.236660	+	0.971592i	$0.423947\pi$
$380$	5.17518	−	2.98789i	0.265481	−	0.153275i
$381$	0.604405	−	2.85051i	0.0309646	−	0.146036i
$382$	−3.00031	+	0.803930i	−0.153509	+	0.0411326i
$383$	7.92419	+	2.12328i	0.404907	+	0.108495i	0.455524	−	0.890224i	$-0.349452\pi$
$383$	7.92419	+	2.12328i	0.404907	+	0.108495i	−0.0506167	+	0.998718i	$0.516119\pi$
$384$	0.785563	−	1.54366i	0.0400881	−	0.0787747i
$385$	−7.62127	−	15.2614i	−0.388416	−	0.777794i
$386$			17.4270i			0.887009i
$387$	13.8761	−	31.2504i	0.705364	−	1.58855i
$388$	−1.56513	−	5.84113i	−0.0794573	−	0.296539i
$389$	14.1756	−	24.5528i	0.718729	−	1.24488i	−0.242775	−	0.970083i	$-0.578058\pi$
$389$	14.1756	−	24.5528i	0.718729	−	1.24488i	0.961504	−	0.274792i	$-0.0886091\pi$
$390$	−23.5357	+	5.84842i	−1.19178	+	0.296146i
$391$	−0.837092			−0.0423336
$392$	6.93062	−	0.983088i	0.350049	−	0.0496534i
$393$	27.8172	−	9.05372i	1.40319	−	0.456700i
$394$	−16.2757	+	9.39676i	−0.819956	+	0.473402i
$395$	15.3386	+	57.2446i	0.771771	+	2.88029i
$396$	3.87403	+	3.13072i	0.194677	+	0.157324i
$397$	−28.5371	−	7.64650i	−1.43224	−	0.383767i	−0.542429	−	0.840101i	$-0.682495\pi$
$397$	−28.5371	−	7.64650i	−1.43224	−	0.383767i	−0.889808	+	0.456334i	$0.849162\pi$
$398$	−0.688289	−	0.688289i	−0.0345008	−	0.0345008i
$399$	−7.05157	−	0.0534959i	−0.353020	−	0.00267815i
$400$			10.0804i			0.504019i
$401$	−3.39116	+	12.6560i	−0.169346	+	0.632009i	0.828100	+	0.560581i	$0.189422\pi$
$401$	−3.39116	+	12.6560i	−0.169346	+	0.632009i	−0.997446	+	0.0714277i	$0.977244\pi$
$402$	−16.6268	−	3.52545i	−0.829270	−	0.175833i
$403$	0.649002	−	1.87698i	0.0323291	−	0.0934990i
$404$	8.43344	−	4.86905i	0.419579	−	0.242244i
$405$	−15.9293	−	31.1090i	−0.791532	−	1.54582i
$406$	12.8805	−	2.62916i	0.639248	−	0.130483i
$407$	5.67835			0.281466
$408$	0.199171	−	0.0105380i	0.00986041	−	0.000521707i
$409$	11.1414	−	2.98534i	0.550909	−	0.147616i	0.0273824	−	0.999625i	$-0.491283\pi$
$409$	11.1414	−	2.98534i	0.550909	−	0.147616i	0.523526	+	0.852009i	$0.324616\pi$
$410$	−41.7197	+	11.1788i	−2.06039	+	0.552080i
$411$	11.7249	−	0.620358i	0.578349	−	0.0306000i
$412$	−17.0396			−0.839480
$413$	9.12723	+	10.3032i	0.449122	+	0.506985i
$414$	3.39003	−	21.5433i	0.166611	−	1.05879i
$415$	−16.2448	+	9.37895i	−0.797427	+	0.460395i
$416$	3.40760	+	1.17824i	0.167071	+	0.0577681i
$417$	27.8546	+	5.90612i	1.36405	+	0.289224i
$418$	0.661260	−	2.46786i	0.0323433	−	0.120707i
$419$		−	5.02683i		−	0.245577i	−0.992433	−	0.122788i	$-0.960816\pi$
$419$		−	5.02683i		−	0.245577i	0.992433	−	0.122788i	$-0.0391836\pi$
$420$	9.01452	−	15.3436i	0.439864	−	0.748691i
$421$	16.5897	+	16.5897i	0.808531	+	0.808531i	0.984412	−	0.175880i	$-0.0562771\pi$
$421$	16.5897	+	16.5897i	0.808531	+	0.808531i	−0.175880	+	0.984412i	$0.556277\pi$
$422$	10.0597	+	2.69549i	0.489699	+	0.131214i
$423$	4.40633	−	5.45251i	0.214243	−	0.265110i
$424$	−0.975946	−	3.64228i	−0.0473961	−	0.176885i
$425$	−1.00526	+	0.580388i	−0.0487623	+	0.0281529i
$426$	17.3871	−	5.65902i	0.842407	−	0.274181i
$427$	−6.47938	+	9.80291i	−0.313559	+	0.474396i
$428$	−2.99227			−0.144637
$429$	−5.34722	+	8.88341i	−0.258166	+	0.428895i
$430$	22.1303	−	38.3308i	1.06722	−	1.84848i
$431$	−4.15728	−	15.5152i	−0.200249	−	0.747339i	−0.990845	−	0.135002i	$-0.956896\pi$
$431$	−4.15728	−	15.5152i	−0.200249	−	0.747339i	0.790596	−	0.612338i	$-0.209771\pi$
$432$	−0.535392	+	5.16850i	−0.0257591	+	0.248669i
$433$			26.7031i			1.28327i	0.767010	+	0.641635i	$0.221744\pi$
$433$			26.7031i			1.28327i	−0.767010	+	0.641635i	$0.778256\pi$
$434$	0.651095	+	1.30380i	0.0312536	+	0.0625846i
$435$	15.1577	−	29.7855i	0.726758	−	1.42811i
$436$	8.33469	+	2.23327i	0.399159	+	0.106954i
$437$	−10.8052	+	2.89525i	−0.516884	+	0.138499i
$438$	−2.17954	+	10.2792i	−0.104142	+	0.491158i
$439$	−0.927098	+	0.535260i	−0.0442480	+	0.0255466i	−0.521961	−	0.852969i	$-0.674799\pi$
$439$	−0.927098	+	0.535260i	−0.0442480	+	0.0255466i	0.477713	+	0.878516i	$0.341466\pi$
$440$	4.55910	+	4.55910i	0.217346	+	0.217346i
$441$	−18.3437	+	10.2229i	−0.873512	+	0.486803i
$442$	0.0786962	+	0.407660i	0.00374320	+	0.0193904i
$443$	17.3480	−	10.0159i	0.824227	−	0.475868i	−0.0276451	−	0.999618i	$-0.508801\pi$
$443$	17.3480	−	10.0159i	0.824227	−	0.475868i	0.851872	+	0.523750i	$0.175467\pi$
$444$	3.22878	+	4.96645i	0.153231	+	0.235697i
$445$	−0.0950010	+	0.164546i	−0.00450348	+	0.00780025i
$446$	−12.6247	−	21.8666i	−0.597796	−	1.03541i
$447$	−34.2649	−	17.4373i	−1.62068	−	0.824755i
$448$	−2.36702	+	1.18204i	−0.111831	+	0.0558463i
$449$	4.25837	+	4.25837i	0.200965	+	0.200965i	0.800413	−	0.599448i	$-0.204613\pi$
$449$	4.25837	+	4.25837i	0.200965	+	0.200965i	−0.599448	+	0.800413i	$0.704613\pi$
$450$	−10.8657	−	28.2217i	−0.512213	−	1.33038i
$451$	−9.23314	+	15.9923i	−0.434772	+	0.753047i
$452$	3.64007	−	6.30478i	0.171214	−	0.296552i
$453$	1.77813	+	33.6071i	0.0835437	+	1.57900i
$454$		−	4.30333i		−	0.201965i
$455$	34.2157	+	14.1986i	1.60406	+	0.665640i
$456$	2.53446	−	0.824896i	0.118687	−	0.0386293i
$457$	5.88954	−	21.9801i	0.275501	−	1.02818i	−0.680004	−	0.733209i	$-0.738022\pi$
$457$	5.88954	−	21.9801i	0.275501	−	1.02818i	0.955505	−	0.294976i	$-0.0953116\pi$
$458$	−5.81317	−	3.35624i	−0.271632	−	0.156827i
$459$	−0.546252	+	0.244190i	−0.0254969	+	0.0113978i
$460$	7.30641	−	27.2679i	0.340663	−	1.27137i
$461$	−10.4546	+	10.4546i	−0.486917	+	0.486917i	−0.907332	−	0.420415i	$-0.861885\pi$
$461$	−10.4546	+	10.4546i	−0.486917	+	0.486917i	0.420415	+	0.907332i	$0.361885\pi$
$462$	−1.91341	−	7.36394i	−0.0890198	−	0.342602i
$463$	7.65222	−	7.65222i	0.355629	−	0.355629i	−0.506570	−	0.862199i	$-0.669087\pi$
$463$	7.65222	−	7.65222i	0.355629	−	0.355629i	0.862199	+	0.506570i	$0.169087\pi$
$464$	−4.30307	+	2.48438i	−0.199765	+	0.115334i
$465$	3.62433	+	0.768481i	0.168074	+	0.0356375i
$466$	−6.54735	−	24.4350i	−0.303300	−	1.13193i
$467$	−8.43515	−	14.6101i	−0.390332	−	0.676075i	0.602161	−	0.798375i	$-0.294307\pi$
$467$	−8.43515	−	14.6101i	−0.390332	−	0.676075i	−0.992493	+	0.122299i	$0.960973\pi$
$468$	−10.8102	+	0.374383i	−0.499700	+	0.0173058i
$469$	17.2157	+	19.4338i	0.794949	+	0.897368i
$470$	6.41671	−	6.41671i	0.295981	−	0.295981i
$471$	5.92239	−	6.58410i	0.272889	−	0.303379i
$472$	−4.50549	−	2.60124i	−0.207382	−	0.119732i
$473$	−4.89773	−	18.2786i	−0.225198	−	0.840450i
$474$	1.39659	+	26.3960i	0.0641476	+	1.21241i
$475$	−10.9686	+	10.9686i	−0.503273	+	0.503273i
$476$	−0.254162	−	0.167992i	−0.0116495	−	0.00769992i
$477$	6.65835	+	9.14519i	0.304865	+	0.418729i
$478$	−22.8108	+	13.1698i	−1.04334	+	0.602374i
$479$	26.1862	−	7.01658i	1.19648	−	0.320596i	0.395035	−	0.918666i	$-0.370732\pi$
$479$	26.1862	−	7.01658i	1.19648	−	0.320596i	0.801444	+	0.598070i	$0.204066\pi$
$480$	−1.39516	+	6.57987i	−0.0636798	+	0.300328i
$481$	−9.31691	+	8.07802i	−0.424815	+	0.368326i
$482$		−	13.0326i		−	0.593618i
$483$	−23.7337	+	23.3763i	−1.07992	+	1.06366i
$484$	−8.24339			−0.374700
$485$	11.7417	+	20.3371i	0.533161	+	0.923462i
$486$	−4.07223	−	15.0472i	−0.184720	−	0.682553i
$487$	11.7633	−	3.15197i	0.533047	−	0.142829i	0.0177518	−	0.999842i	$-0.494349\pi$
$487$	11.7633	−	3.15197i	0.533047	−	0.142829i	0.515295	+	0.857013i	$0.327682\pi$
$488$	1.14951	−	4.29002i	0.0520357	−	0.194200i
$489$	−2.34774	−	1.19476i	−0.106169	−	0.0540287i
$490$	−25.0088	+	10.6534i	−1.12978	+	0.481274i
$491$	−15.4732			−0.698297			−0.349149	−	0.937067i	$-0.613529\pi$
$491$	−15.4732			−0.698297			−0.349149	+	0.937067i	$0.613529\pi$
$492$	−19.2374	+	1.01783i	−0.867287	+	0.0458875i
$493$	−0.495507	−	0.286081i	−0.0223165	−	0.0128844i
$494$	2.42579	+	4.98991i	0.109141	+	0.224507i
$495$	−17.6782	−	7.84967i	−0.794576	−	0.352816i
$496$	−0.389490	−	0.389490i	−0.0174886	−	0.0174886i
$497$	−26.4929	−	8.84553i	−1.18837	−	0.396776i
$498$	−7.95563	+	2.58934i	−0.356500	+	0.116031i
$499$	−4.56088	+	17.0214i	−0.204173	+	0.761984i	0.785527	+	0.618827i	$0.212392\pi$
$499$	−4.56088	+	17.0214i	−0.204173	+	0.761984i	−0.989700	+	0.143157i	$0.954275\pi$
$500$	−5.10620	−	19.0566i	−0.228356	−	0.852237i
$501$	−13.2880	−	20.4394i	−0.593665	−	0.913163i
$502$	0.335472	+	0.0898895i	0.0149729	+	0.00401196i
$503$			6.14841i			0.274144i	0.990561	+	0.137072i	$0.0437692\pi$
$503$			6.14841i			0.274144i	−0.990561	+	0.137072i	$0.956231\pi$
$504$	5.35272	−	5.86075i	0.238429	−	0.261058i
$505$	−26.7402	+	26.7402i	−1.18992	+	1.18992i
$506$	−6.03475	−	10.4525i	−0.268277	−	0.464670i
$507$	−3.86393	−	22.1827i	−0.171603	−	0.985166i
$508$	0.841165	−	1.45694i	0.0373207	−	0.0646413i
$509$	−11.4544	−	3.06919i	−0.507706	−	0.136039i	−0.00413183	−	0.999991i	$-0.501315\pi$
$509$	−11.4544	−	3.06919i	−0.507706	−	0.136039i	−0.503574	+	0.863952i	$0.667982\pi$
$510$	−0.736502	+	0.239711i	−0.0326129	+	0.0106146i
$511$	12.0145	−	10.6433i	0.531491	−	0.470831i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.20647	+	5.04133i	−0.274022	+	0.222580i
$514$	−1.28807	−	4.80716i	−0.0568145	−	0.212035i
$515$	63.9159	−	17.1262i	2.81647	−	0.754671i
$516$	13.2021	−	14.6771i	0.581188	−	0.646124i
$517$		−	3.87979i		−	0.170633i
$518$	0.546624	−	9.03212i	0.0240173	−	0.396849i
$519$	−10.6319	−	32.6662i	−0.466691	−	1.43389i
$520$	−13.9662	−	0.994694i	−0.612459	−	0.0436202i
$521$	6.51520	+	3.76155i	0.285436	+	0.164797i	0.635882	−	0.771786i	$-0.280637\pi$
$521$	6.51520	+	3.76155i	0.285436	+	0.164797i	−0.350446	+	0.936583i	$0.613970\pi$
$522$	9.36922	−	11.5937i	0.410080	−	0.507443i
$523$	−16.9961	−	29.4381i	−0.743188	−	1.28724i	−0.951036	−	0.309079i	$-0.899979\pi$
$523$	−16.9961	−	29.4381i	−0.743188	−	1.28724i	0.207848	−	0.978161i	$-0.433354\pi$
$524$	16.8895			0.737820
$525$	−12.2941	+	44.5281i	−0.536557	+	1.94336i
$526$	−16.9441	−	16.9441i	−0.738798	−	0.738798i
$527$	0.0164164	−	0.0612669i	0.000715111	−	0.00266883i
$528$	1.56744	+	2.41101i	0.0682141	+	0.104926i
$529$	−14.9225	+	25.8465i	−0.648803	+	1.12376i
$530$	7.32159	+	12.6814i	0.318030	+	0.550844i
$531$	15.4177	+	2.42613i	0.669073	+	0.105285i
$532$	−3.86178	−	1.28938i	−0.167429	−	0.0559018i
$533$	−7.60106	−	39.3748i	−0.329239	−	1.70551i
$534$	−0.0566738	+	0.0630059i	−0.00245251	+	0.00272653i
$535$	11.2241	−	3.00748i	0.485258	−	0.130025i
$536$	−8.49823	−	4.90646i	−0.367068	−	0.211927i
$537$	0.782109	−	0.869494i	0.0337505	−	0.0375214i
$538$	11.1289	+	11.1289i	0.479802	+	0.479802i
$539$	−4.33992	+	10.7814i	−0.186934	+	0.464388i
$540$	−3.18650	−	19.9253i	−0.137125	−	0.857447i
$541$	−1.09015	−	0.292104i	−0.0468691	−	0.0125585i	0.235308	−	0.971921i	$-0.424390\pi$
$541$	−1.09015	−	0.292104i	−0.0468691	−	0.0125585i	−0.282177	+	0.959362i	$0.591057\pi$
$542$	8.23865	+	4.75659i	0.353880	+	0.204313i
$543$	−0.00245057	+	0.0115575i	−0.000105164	+	0.000495978i
$544$	0.111228	+	0.0298035i	0.00476887	+	0.00127782i
$545$	−33.5083			−1.43534
$546$	13.6154	+	9.36058i	0.582686	+	0.400596i
$547$	−38.4866			−1.64557			−0.822785	−	0.568353i	$-0.807581\pi$
$547$	−38.4866			−1.64557			−0.822785	+	0.568353i	$0.807581\pi$
$548$	6.54788	+	1.75450i	0.279712	+	0.0749485i
$549$	1.40600	+	13.2497i	0.0600065	+	0.565482i
$550$	−14.4942	−	8.36824i	−0.618036	−	0.356823i
$551$	−7.38550	−	1.97894i	−0.314633	−	0.0843056i
$552$	5.71061	−	11.2216i	0.243060	−	0.477622i
$553$	22.2640	−	33.6840i	0.946760	−	1.43239i
$554$	15.1577	+	15.1577i	0.643991	+	0.643991i
$555$	−17.1029	−	15.3841i	−0.725979	−	0.653017i
$556$	14.2369	+	8.21970i	0.603780	+	0.348593i
$557$	15.3629	−	4.11647i	0.650946	−	0.174420i	0.0817892	−	0.996650i	$-0.473937\pi$
$557$	15.3629	−	4.11647i	0.650946	−	0.174420i	0.569156	+	0.822229i	$0.307270\pi$
$558$	1.51027	+	0.670607i	0.0639349	+	0.0283891i
$559$	34.0392	+	23.0236i	1.43970	+	0.973794i
$560$	7.69068	−	6.81293i	0.324991	−	0.287899i
$561$	−0.150190	+	0.295129i	−0.00634101	+	0.0124603i
$562$	−9.88640	−	17.1237i	−0.417033	−	0.722322i
$563$	−15.1190	+	26.1868i	−0.637188	+	1.10364i	0.348859	+	0.937175i	$0.386569\pi$
$563$	−15.1190	+	26.1868i	−0.637188	+	1.10364i	−0.986047	+	0.166467i	$0.946764\pi$
$564$	3.39338	−	2.20610i	0.142887	−	0.0928935i
$565$	−7.31714	+	27.3080i	−0.307835	+	1.14885i
$566$	−1.27633	−	1.27633i	−0.0536481	−	0.0536481i
$567$	−8.66851	+	22.1778i	−0.364043	+	0.931382i
$568$	10.5568			0.442952
$569$	7.47917	+	12.9543i	0.313543	+	0.543072i	0.979127	−	0.203251i	$-0.0651507\pi$
$569$	7.47917	+	12.9543i	0.313543	+	0.543072i	−0.665584	+	0.746323i	$0.731817\pi$
$570$	−8.67772	+	5.64155i	−0.363469	+	0.236298i
$571$	9.20784	+	5.31615i	0.385336	+	0.222474i	0.680137	−	0.733085i	$-0.261920\pi$
$571$	9.20784	+	5.31615i	0.385336	+	0.222474i	−0.294801	+	0.955559i	$0.595253\pi$
$572$	−4.52298	+	3.92155i	−0.189115	+	0.163968i
$573$	5.11585	−	1.66507i	0.213718	−	0.0695593i
$574$	24.5489	+	16.2259i	1.02465	+	0.677258i
$575$			73.2788i			3.05594i
$576$	−1.21747	+	2.74186i	−0.0507278	+	0.114244i
$577$	6.74416	−	1.80709i	0.280763	−	0.0752303i	−0.115689	−	0.993285i	$-0.536908\pi$
$577$	6.74416	−	1.80709i	0.280763	−	0.0752303i	0.396453	+	0.918055i	$0.370241\pi$
$578$	−4.39649	−	16.4079i	−0.182870	−	0.682480i
$579$	−1.59480	−	30.1422i	−0.0662778	−	1.25267i
$580$	13.6439	−	13.6439i	0.566532	−	0.566532i
$581$	12.1221	+	4.04736i	0.502908	+	0.167913i
$582$	3.24164	+	9.95978i	0.134370	+	0.412846i
$583$	6.04729	+	1.62037i	0.250453	+	0.0671088i
$584$	−3.03331	+	5.25386i	−0.125519	+	0.217406i
$585$	40.1729	−	12.2694i	1.66095	−	0.507279i
$586$	−12.7218	−	22.0349i	−0.525534	−	0.910252i
$587$	15.0653	−	15.0653i	0.621813	−	0.621813i	−0.324182	−	0.945995i	$-0.605089\pi$
$587$	15.0653	−	15.0653i	0.621813	−	0.621813i	0.945995	+	0.324182i	$0.105089\pi$
$588$	−11.8975	+	2.33463i	−0.490643	+	0.0962783i
$589$		−	0.847616i		−	0.0349254i
$590$	19.5147	+	5.22894i	0.803406	+	0.215272i
$591$	27.2910	−	17.7424i	1.12260	−	0.729824i
$592$	0.885179	+	3.30353i	0.0363806	+	0.135774i
$593$	0.0643968	−	0.240332i	0.00264446	−	0.00986926i	−0.964591	−	0.263750i	$-0.915041\pi$
$593$	0.0643968	−	0.240332i	0.00264446	−	0.00986926i	0.967235	+	0.253881i	$0.0817072\pi$
$594$	−6.98715	−	5.06046i	−0.286686	−	0.207633i
$595$	1.12222	+	0.374689i	0.0460063	+	0.0153608i
$596$	−15.6958	−	15.6958i	−0.642924	−	0.642924i
$597$	1.25347	+	1.12750i	0.0513013	+	0.0461454i
$598$	24.7714	+	8.56518i	1.01298	+	0.350256i
$599$	−18.4405	−	10.6466i	−0.753458	−	0.435009i	0.0734837	−	0.997296i	$-0.476588\pi$
$599$	−18.4405	−	10.6466i	−0.753458	−	0.435009i	−0.826942	+	0.562287i	$0.809922\pi$
$600$	−0.922490	−	17.4353i	−0.0376605	−	0.711794i
$601$	12.6355			0.515412			0.257706	−	0.966223i	$-0.417033\pi$
$601$	12.6355			0.515412			0.257706	+	0.966223i	$0.417033\pi$
$602$	−29.5458	+	6.03087i	−1.20420	+	0.245800i
$603$	29.0809	+	4.57615i	1.18427	+	0.186355i
$604$	−5.02891	+	18.7681i	−0.204623	+	0.763665i
$605$	30.9212	−	8.28530i	1.25712	−	0.336845i
$606$	−14.1412	+	9.19344i	−0.574445	+	0.373458i
$607$	0.452617	+	0.783955i	0.0183711	+	0.0318198i	0.875065	−	0.484006i	$-0.160819\pi$
$607$	0.452617	+	0.783955i	0.0183711	+	0.0318198i	−0.856694	+	0.515825i	$0.827485\pi$
$608$	1.53882			0.0624075
$609$	−22.0379	+	5.72621i	−0.893021	+	0.232038i
$610$			17.2473i			0.698323i
$611$	5.51939	+	6.36588i	0.223291	+	0.257536i
$612$	−0.343527	+	0.0364536i	−0.0138863	+	0.00147355i
$613$	−12.6274	+	3.38351i	−0.510017	+	0.136659i	−0.504645	−	0.863327i	$-0.668377\pi$
$613$	−12.6274	+	3.38351i	−0.510017	+	0.136659i	−0.00537192	+	0.999986i	$0.501710\pi$
$614$	4.95380	−	2.86008i	0.199919	−	0.115423i
$615$	71.1368	−	23.1531i	2.86851	−	0.933622i
$616$	0.265364	−	4.38473i	0.0106918	−	0.176666i
$617$	6.56476	−	6.56476i	0.264287	−	0.264287i	−0.562506	−	0.826793i	$-0.690163\pi$
$617$	6.56476	−	6.56476i	0.264287	−	0.264287i	0.826793	+	0.562506i	$0.190163\pi$
$618$	29.4722	−	1.55935i	1.18555	−	0.0627263i
$619$	−0.885089	−	3.30320i	−0.0355747	−	0.132767i	0.945855	−	0.324590i	$-0.105226\pi$
$619$	−0.885089	−	3.30320i	−0.0355747	−	0.132767i	−0.981429	+	0.191824i	$0.938560\pi$
$620$	1.85245	+	1.06951i	0.0743963	+	0.0429527i
$621$	−3.89201	+	37.5721i	−0.156181	+	1.50772i
$622$	17.3486	−	17.3486i	0.695617	−	0.695617i
$623$	0.126834	−	0.0258893i	0.00508151	−	0.00103723i
$624$	−6.00172	−	1.72609i	−0.240261	−	0.0690987i
$625$	13.1060	+	22.7003i	0.524241	+	0.908012i
$626$	3.27706	+	12.2301i	0.130978	+	0.488815i
$627$	−0.917894	+	4.32900i	−0.0366572	+	0.172883i
$628$	4.42790	−	2.55645i	0.176692	−	0.102013i
$629$	−0.278478	+	0.278478i	−0.0111037	+	0.0111037i
$630$	−14.1877	+	27.3637i	−0.565250	+	1.09020i
$631$	19.4368	−	19.4368i	0.773766	−	0.773766i	−0.204996	−	0.978763i	$-0.565718\pi$
$631$	19.4368	−	19.4368i	0.773766	−	0.773766i	0.978763	+	0.204996i	$0.0657183\pi$
$632$	−3.94985	+	14.7410i	−0.157117	+	0.586367i
$633$	−17.6462	−	3.74160i	−0.701375	−	0.148715i
$634$	−21.3263	−	12.3127i	−0.846975	−	0.489001i
$635$	−1.69088	+	6.31046i	−0.0671007	+	0.250423i
$636$	2.02135	+	6.21049i	0.0801516	+	0.246262i
$637$	−8.21679	−	23.8639i	−0.325561	−	0.945521i
$638$		−	8.24964i		−	0.326606i
$639$	−29.5554	+	11.3792i	−1.16919	+	0.450153i
$640$	−1.94167	+	3.36308i	−0.0767514	+	0.132937i
$641$	−5.56004	+	9.63027i	−0.219608	+	0.380373i	−0.954688	−	0.297608i	$-0.903811\pi$
$641$	−5.56004	+	9.63027i	−0.219608	+	0.380373i	0.735080	+	0.677981i	$0.237145\pi$
$642$	5.17552	−	0.273833i	0.204261	−	0.0108073i
$643$	−18.7436	−	18.7436i	−0.739176	−	0.739176i	0.233242	−	0.972419i	$-0.425066\pi$
$643$	−18.7436	−	18.7436i	−0.739176	−	0.739176i	−0.972419	+	0.233242i	$0.925066\pi$
$644$	−17.2069	+	8.59282i	−0.678048	+	0.338604i
$645$	−34.7695	+	68.3234i	−1.36905	+	2.69023i
$646$	0.0885992	+	0.153458i	0.00348589	+	0.00603774i
$647$	14.7726	−	25.5869i	0.580771	−	1.00593i	−0.414617	−	0.909996i	$-0.636084\pi$
$647$	14.7726	−	25.5869i	0.580771	−	1.00593i	0.995388	−	0.0959291i	$-0.0305822\pi$
$648$	0.453044	−	8.98859i	0.0177972	−	0.353105i
$649$	7.48048	−	4.31886i	0.293635	−	0.169530i
$650$	35.6864	−	6.88905i	1.39974	−	0.270211i
$651$	−1.24547	−	2.19552i	−0.0488138	−	0.0860491i
$652$	−1.07543	−	1.07543i	−0.0421172	−	0.0421172i
$653$	−17.8677	+	10.3159i	−0.699217	+	0.403693i	−0.807056	−	0.590475i	$-0.798940\pi$
$653$	−17.8677	+	10.3159i	−0.699217	+	0.403693i	0.107839	+	0.994168i	$0.465607\pi$
$654$	−14.6203	−	3.10001i	−0.571700	−	0.121220i
$655$	−63.3528	+	16.9753i	−2.47540	+	0.663282i
$656$	−10.7432	−	2.87864i	−0.419453	−	0.112392i
$657$	2.82911	−	17.9787i	0.110374	−	0.701414i
$658$	−6.17129	−	0.373486i	−0.240582	−	0.0145600i
$659$		−	39.7576i		−	1.54874i	−0.632734	−	0.774369i	$-0.718067\pi$
$659$		−	39.7576i		−	1.54874i	0.632734	−	0.774369i	$-0.281933\pi$
$660$	−8.30277	−	7.46834i	−0.323185	−	0.290705i
$661$	−2.27602	−	8.49424i	−0.0885271	−	0.330388i	0.907432	−	0.420200i	$-0.138040\pi$
$661$	−2.27602	−	8.49424i	−0.0885271	−	0.330388i	−0.995959	+	0.0898122i	$0.971373\pi$
$662$	6.94053	−	12.0214i	0.269752	−	0.467223i
$663$	−0.173422	−	0.697900i	−0.00673515	−	0.0271042i
$664$	−4.83035			−0.187454
$665$	15.7815	+	0.955098i	0.611982	+	0.0370371i
$666$	−6.03910	−	8.29464i	−0.234010	−	0.321411i
$667$	−31.2809	+	18.0601i	−1.21120	+	0.699288i
$668$	−3.64294	−	13.5957i	−0.140950	−	0.526032i
$669$	23.8371	+	36.6658i	0.921597	+	1.41758i
$670$	36.8085	+	9.86280i	1.42204	+	0.381033i
$671$	5.21420	+	5.21420i	0.201292	+	0.201292i
$672$	3.98589	−	2.26112i	0.153759	−	0.0872244i
$673$		−	50.3529i		−	1.94096i	−0.241179	−	0.970481i	$-0.577534\pi$
$673$		−	50.3529i		−	1.94096i	0.241179	−	0.970481i	$-0.422466\pi$
$674$	−8.21274	+	30.6504i	−0.316343	+	1.18061i
$675$	21.3763	+	47.8187i	0.822774	+	1.84054i
$676$	1.84241	−	12.8688i	0.0708620	−	0.494953i
$677$	44.2683	−	25.5583i	1.70137	−	0.982287i	0.756994	−	0.653422i	$-0.226667\pi$
$677$	44.2683	−	25.5583i	1.70137	−	0.982287i	0.944377	−	0.328865i	$-0.106666\pi$
$678$	−5.71900	+	11.2381i	−0.219637	+	0.431595i
$679$	5.06695	−	15.1758i	0.194452	−	0.582394i
$680$	−0.447175			−0.0171484
$681$	0.393813	+	7.44317i	0.0150909	+	0.285223i
$682$	0.883369	−	0.236698i	0.0338260	−	0.00906364i
$683$	5.20735	−	1.39531i	0.199254	−	0.0533899i	−0.157812	−	0.987469i	$-0.550444\pi$
$683$	5.20735	−	1.39531i	0.199254	−	0.0533899i	0.357066	+	0.934079i	$0.383777\pi$
$684$	−4.30819	+	1.65870i	−0.164728	+	0.0634221i
$685$	−26.3247			−1.00581
$686$	16.7314	+	7.94105i	0.638808	+	0.303191i
$687$	10.3618	+	5.27307i	0.395327	+	0.201180i
$688$	9.87056	−	5.69877i	0.376312	−	0.217264i
$689$	−12.2274	+	5.94421i	−0.465827	+	0.226456i
$690$	−10.1420	+	47.8320i	−0.386100	+	1.82093i
$691$	−6.91208	+	25.7962i	−0.262948	+	0.981335i	0.700547	+	0.713607i	$0.252940\pi$
$691$	−6.91208	+	25.7962i	−0.262948	+	0.981335i	−0.963495	+	0.267728i	$0.913727\pi$
$692$		−	19.8336i		−	0.753961i
$693$	3.98339	+	12.5618i	0.151317	+	0.477184i
$694$	14.1838	+	14.1838i	0.538410	+	0.538410i
$695$	−61.6645	−	16.5230i	−2.33907	−	0.626752i
$696$	7.21537	−	4.69085i	0.273498	−	0.177806i
$697$	−0.331482	−	1.23711i	−0.0125558	−	0.0468588i
$698$	−9.64693	+	5.56965i	−0.365142	+	0.210815i
$699$	13.5606	+	41.6645i	0.512911	+	1.57589i
$700$	−14.7060	+	22.2493i	−0.555835	+	0.840944i
$701$	−50.8532			−1.92070			−0.960350	−	0.278798i	$-0.910064\pi$
$701$	−50.8532			−1.92070			−0.960350	+	0.278798i	$0.910064\pi$
$702$	18.6634	−	1.63682i	0.704403	−	0.0617778i
$703$	−2.63144	+	4.55779i	−0.0992466	+	0.171900i
$704$	0.429718	+	1.60373i	0.0161956	+	0.0604429i
$705$	−10.5113	+	11.6858i	−0.395879	+	0.440111i
$706$			6.72393i			0.253058i
$707$	25.7175	+	1.55642i	0.967207	+	0.0585353i
$708$	8.03088	+	4.08688i	0.301819	+	0.153594i
$709$	−41.6608	−	11.1630i	−1.56460	−	0.419234i	−0.630486	−	0.776201i	$-0.717144\pi$
$709$	−41.6608	−	11.1630i	−1.56460	−	0.419234i	−0.934117	+	0.356967i	$0.883811\pi$
$710$	−39.5986	+	10.6104i	−1.48611	+	0.398202i
$711$	−4.83118	−	45.5275i	−0.181183	−	1.70742i
$712$	−0.0423724	+	0.0244637i	−0.00158797	+	0.000916816i
$713$	−2.83138	−	2.83138i	−0.106036	−	0.106036i
$714$	0.454981	+	0.267306i	0.0170272	+	0.0100037i
$715$	13.0243	−	19.2558i	0.487082	−	0.720126i
$716$	0.584747	−	0.337604i	0.0218530	−	0.0126168i
$717$	38.2491	−	24.8665i	1.42844	−	0.928655i
$718$	5.89581	−	10.2118i	0.220030	−	0.381103i
$719$	−15.9927	−	27.7001i	−0.596426	−	1.03304i	−0.993344	−	0.115186i	$-0.963254\pi$
$719$	−15.9927	−	27.7001i	−0.596426	−	1.03304i	0.396918	−	0.917854i	$-0.370080\pi$
$720$	1.81096	−	11.5084i	0.0674904	−	0.428894i
$721$	−37.6096	−	24.8586i	−1.40065	−	0.925783i
$722$	−11.7606	−	11.7606i	−0.437685	−	0.437685i
$723$	1.19266	+	22.5416i	0.0443554	+	0.838330i
$724$	−0.00341052	+	0.00590720i	−0.000126751	+	0.000219539i
$725$	−25.0434	+	43.3765i	−0.930090	+	1.61096i
$726$	14.2580	−	0.754382i	0.529165	−	0.0279977i
$727$		−	3.98635i		−	0.147846i	−0.997264	−	0.0739228i	$-0.976448\pi$
$727$		−	3.98635i		−	0.147846i	0.997264	−	0.0739228i	$-0.0235518\pi$
$728$	5.80231	+	7.57187i	0.215048	+	0.280632i
$729$	8.42047	+	25.6534i	0.311869	+	0.950125i
$730$	6.09747	−	22.7561i	0.225678	−	0.842240i
$731$	1.13662	+	0.656225i	0.0420392	+	0.0242714i
$732$	−1.59563	+	7.52535i	−0.0589761	+	0.278145i
$733$	2.57883	−	9.62431i	0.0952511	−	0.355482i	−0.901806	−	0.432140i	$-0.857758\pi$
$733$	2.57883	−	9.62431i	0.0952511	−	0.355482i	0.997057	+	0.0766585i	$0.0244251\pi$
$734$	−13.4780	+	13.4780i	−0.497483	+	0.497483i
$735$	42.2812	−	20.7152i	1.55956	−	0.764091i
$736$	5.14028	−	5.14028i	0.189473	−	0.189473i
$737$	14.1097	−	8.14621i	0.519736	−	0.300070i
$738$	33.1804	−	3.52096i	1.22139	−	0.129608i
$739$	−5.09752	−	19.0242i	−0.187515	−	0.699817i	−0.994078	−	0.108668i	$-0.965341\pi$
$739$	−5.09752	−	19.0242i	−0.187515	−	0.699817i	0.806563	−	0.591149i	$-0.201325\pi$
$740$	−6.64065	−	11.5019i	−0.244115	−	0.422820i
$741$	−4.65237	−	8.40871i	−0.170909	−	0.308902i
$742$	3.15953	−	9.46299i	0.115990	−	0.347397i
$743$	−18.6277	+	18.6277i	−0.683384	+	0.683384i	−0.960761	−	0.277377i	$-0.910535\pi$
$743$	−18.6277	+	18.6277i	−0.683384	+	0.683384i	0.277377	+	0.960761i	$0.410535\pi$
$744$	0.709317	+	0.638030i	0.0260048	+	0.0233913i
$745$	74.6508	+	43.0997i	2.73499	+	1.57905i
$746$	−3.44521	−	12.8577i	−0.126138	−	0.470753i
$747$	13.5234	−	5.20665i	0.494794	−	0.190502i
$748$	−0.135190	+	0.135190i	−0.00494303	+	0.00494303i
$749$	−6.60449	−	4.36534i	−0.241323	−	0.159506i
$750$	10.5758	+	32.4936i	0.386173	+	1.18650i
$751$	−5.48150	+	3.16474i	−0.200023	+	0.115483i	−0.596666	−	0.802490i	$-0.703508\pi$
$751$	−5.48150	+	3.16474i	−0.200023	+	0.115483i	0.396643	+	0.917973i	$0.370175\pi$
$752$	2.25717	−	0.604808i	0.0823106	−	0.0220551i
$753$	−0.588469	−	0.124775i	−0.0214450	−	0.00454707i
$754$	11.7359	+	13.5358i	0.427397	+	0.492946i
$755$		−	75.4542i		−	2.74606i
$756$	−8.72190	+	10.6268i	−0.317213	+	0.386492i
$757$	18.4902			0.672036			0.336018	−	0.941855i	$-0.390920\pi$
$757$	18.4902			0.672036			0.336018	+	0.941855i	$0.390920\pi$
$758$	−16.6327	−	28.8087i	−0.604126	−	1.04638i
$759$	11.3944	+	17.5267i	0.413592	+	0.636179i
$760$	−5.77216	+	1.54665i	−0.209378	+	0.0561027i
$761$	3.15296	−	11.7670i	0.114295	−	0.426554i	−0.884938	−	0.465708i	$-0.845800\pi$
$761$	3.15296	−	11.7670i	0.114295	−	0.426554i	0.999233	+	0.0391543i	$0.0124664\pi$
$762$	−1.32158	+	2.59695i	−0.0478757	+	0.0940775i
$763$	15.1382	+	17.0885i	0.548039	+	0.618647i
$764$	3.10615			0.112376
$765$	1.25194	−	0.482012i	0.0452640	−	0.0174272i
$766$	−7.10463	−	4.10186i	−0.256701	−	0.148206i
$767$	−6.12980	+	17.7280i	−0.221334	+	0.640121i
$768$	−1.15832	+	1.28774i	−0.0417974	+	0.0464675i
$769$	−24.4015	−	24.4015i	−0.879941	−	0.879941i	0.113587	−	0.993528i	$-0.463766\pi$
$769$	−24.4015	−	24.4015i	−0.879941	−	0.879941i	−0.993528	+	0.113587i	$0.963766\pi$
$770$	3.41164	+	16.7139i	0.122947	+	0.602328i
$771$	2.66781	+	8.19673i	0.0960789	+	0.295198i
$772$	4.51043	−	16.8332i	0.162334	−	0.605839i
$773$	−11.9614	−	44.6405i	−0.430221	−	1.60561i	−0.752250	−	0.658878i	$-0.771032\pi$
$773$	−11.9614	−	44.6405i	−0.430221	−	1.60561i	0.322029	−	0.946730i	$-0.395635\pi$
$774$	−21.4915	+	26.5942i	−0.772497	+	0.955908i
$775$	−5.36329	−	1.43709i	−0.192655	−	0.0516217i
$776$			6.04719i			0.217081i
$777$	−0.118896	+	15.6723i	−0.00426537	+	0.562240i
$778$	−20.0473	+	20.0473i	−0.718729	+	0.718729i
$779$	−8.55757	−	14.8221i	−0.306607	−	0.531058i
$780$	24.2474	+	0.442356i	0.868198	+	0.0158389i
$781$	−8.76371	+	15.1792i	−0.313590	+	0.543154i
$782$	0.808569	+	0.216655i	0.0289144	+	0.00774758i
$783$	−15.1443	+	20.9103i	−0.541214	+	0.747272i
$784$	−6.94891	−	0.844187i	−0.248175	−	0.0301495i
$785$	−14.0397	+	14.0397i	−0.501099	+	0.501099i
$786$	−29.2126	+	1.54562i	−1.04198	+	0.0551303i
$787$	10.3261	+	38.5375i	0.368085	+	1.37371i	0.863190	+	0.504880i	$0.168463\pi$
$787$	10.3261	+	38.5375i	0.368085	+	1.37371i	−0.495104	+	0.868834i	$0.664870\pi$
$788$	18.1531	−	4.86412i	0.646679	−	0.173277i
$789$	30.8577	+	27.7564i	1.09856	+	0.988155i
$790$		−	59.2639i		−	2.10852i
$791$	17.2322	−	8.60544i	0.612707	−	0.305974i
$792$	−2.93174	−	4.02671i	−0.104175	−	0.143083i
$793$	−15.9731	−	1.13762i	−0.567220	−	0.0403982i
$794$	25.5857	+	14.7719i	0.908002	+	0.524235i
$795$	−13.8242	−	21.2641i	−0.490293	−	0.754159i
$796$	0.486694	+	0.842978i	0.0172504	+	0.0298786i
$797$	−15.2312			−0.539517			−0.269758	−	0.962928i	$-0.586944\pi$
$797$	−15.2312			−0.539517			−0.269758	+	0.962928i	$0.586944\pi$
$798$	6.79744	+	1.87675i	0.240627	+	0.0664363i
$799$	0.190273	+	0.190273i	0.00673138	+	0.00673138i
$800$	2.60899	−	9.73689i	0.0922418	−	0.344251i
$801$	0.0922589	−	0.114163i	0.00325981	−	0.00403377i
$802$	6.55121	−	11.3470i	0.231331	−	0.400678i
$803$	−5.03623	−	8.72300i	−0.177725	−	0.307828i
$804$	15.1478	+	7.70866i	0.534222	+	0.271864i
$805$	55.9071	−	49.5263i	1.97047	−	1.74557i
$806$	−1.11269	+	1.64505i	−0.0391927	+	0.0579444i
$807$	−20.2674	−	18.2305i	−0.713446	−	0.641744i
$808$	−9.40628	+	2.52041i	−0.330912	+	0.0886676i
$809$	−16.5983	−	9.58305i	−0.583566	−	0.336922i	0.178983	−	0.983852i	$-0.442719\pi$
$809$	−16.5983	−	9.58305i	−0.583566	−	0.336922i	−0.762549	+	0.646930i	$0.776053\pi$
$810$	7.33491	+	34.1718i	0.257722	+	1.20067i
$811$	1.68984	+	1.68984i	0.0593384	+	0.0593384i	0.736153	−	0.676815i	$-0.236640\pi$
$811$	1.68984	+	1.68984i	0.0593384	+	0.0593384i	−0.676815	+	0.736153i	$0.736640\pi$
$812$	−13.1221	−	0.794147i	−0.460495	−	0.0278691i
$813$	−14.6851	−	7.47319i	−0.515030	−	0.262096i
$814$	−5.48487	−	1.46967i	−0.192245	−	0.0515118i
$815$	5.11487	+	2.95307i	0.179166	+	0.103442i
$816$	−0.195111	−	0.0413702i	−0.00683027	−	0.00144825i
$817$	16.9412	+	4.53937i	0.592697	+	0.158813i
$818$	−11.5345			−0.403293
$819$	−24.4063	−	14.9444i	−0.852824	−	0.522198i
$820$	43.1915			1.50831
$821$	17.9934	+	4.82131i	0.627973	+	0.168265i	0.558750	−	0.829336i	$-0.311281\pi$
$821$	17.9934	+	4.82131i	0.627973	+	0.168265i	0.0692231	+	0.997601i	$0.477948\pi$
$822$	−11.4860	−	2.43542i	−0.400620	−	0.0849450i
$823$	22.9357	+	13.2419i	0.799487	+	0.461584i	0.843292	−	0.537456i	$-0.180615\pi$
$823$	22.9357	+	13.2419i	0.799487	+	0.461584i	−0.0438048	+	0.999040i	$0.513948\pi$
$824$	16.4590	+	4.41017i	0.573375	+	0.153635i
$825$	25.8355	+	13.1476i	0.899475	+	0.457739i
$826$	−6.14957	−	12.3144i	−0.213971	−	0.428472i
$827$	−11.5256	−	11.5256i	−0.400784	−	0.400784i	0.477725	−	0.878509i	$-0.341462\pi$
$827$	−11.5256	−	11.5256i	−0.400784	−	0.400784i	−0.878509	+	0.477725i	$0.841462\pi$
$828$	−8.85033	+	19.9318i	−0.307570	+	0.692678i
$829$	−16.5962	−	9.58183i	−0.576410	−	0.332791i	0.183295	−	0.983058i	$-0.441324\pi$
$829$	−16.5962	−	9.58183i	−0.576410	−	0.332791i	−0.759706	+	0.650267i	$0.774657\pi$
$830$	18.1187	−	4.85490i	0.628911	−	0.168516i
$831$	−27.6044	−	24.8302i	−0.957588	−	0.861349i
$832$	−2.98654	−	2.02005i	−0.103540	−	0.0700325i
$833$	−0.315904	−	0.741582i	−0.0109454	−	0.0256943i
$834$	−25.3769	−	12.9142i	−0.878729	−	0.447181i
$835$	27.3295	+	47.3362i	0.945778	+	1.63814i
$836$	−1.27746	+	2.21262i	−0.0441818	+	0.0765250i
$837$	−2.67358	−	1.02169i	−0.0924126	−	0.0353149i
$838$	−1.30104	+	4.85554i	−0.0449436	+	0.167732i
$839$	−4.96262	−	4.96262i	−0.171329	−	0.171329i	0.616234	−	0.787563i	$-0.288657\pi$
$839$	−4.96262	−	4.96262i	−0.171329	−	0.171329i	−0.787563	+	0.616234i	$0.788657\pi$
$840$	−12.6786	+	12.4877i	−0.437452	+	0.430865i
$841$	4.31149			0.148672
$842$	−11.7307	−	20.3181i	−0.404266	−	0.700209i
$843$	18.6669	+	28.7130i	0.642922	+	0.988929i
$844$	−9.01928	−	5.20728i	−0.310456	−	0.179242i
$845$	6.02328	+	50.1229i	0.207207	+	1.72428i
$846$	−5.66740	+	4.12628i	−0.194849	+	0.141864i
$847$	−18.1947	−	12.0261i	−0.625178	−	0.413221i
$848$			3.77077i			0.129489i
$849$	2.32438	+	2.09078i	0.0797725	+	0.0717553i
$850$	1.12122	−	0.300431i	0.0384576	−	0.0103047i
$851$	6.43477	+	24.0149i	0.220581	+	0.823219i
$852$	−18.2593	+	0.966086i	−0.625553	+	0.0330976i
$853$	10.4379	−	10.4379i	0.357386	−	0.357386i	−0.505463	−	0.862849i	$-0.668678\pi$
$853$	10.4379	−	10.4379i	0.357386	−	0.357386i	0.862849	+	0.505463i	$0.168678\pi$
$854$	8.79578	−	7.79190i	0.300985	−	0.266633i
$855$	14.4930	−	10.5519i	0.495649	−	0.360868i
$856$	2.89031	+	0.774455i	0.0987886	+	0.0264703i
$857$	2.34286	−	4.05795i	0.0800305	−	0.138617i	−0.823232	−	0.567705i	$-0.807832\pi$
$857$	2.34286	−	4.05795i	0.0800305	−	0.138617i	0.903263	+	0.429088i	$0.141165\pi$
$858$	7.46422	−	7.19675i	0.254824	−	0.245693i
$859$	13.2187	+	22.8954i	0.451016	+	0.781182i	0.998449	−	0.0556669i	$-0.0177285\pi$
$859$	13.2187	+	22.8954i	0.451016	+	0.781182i	−0.547434	+	0.836849i	$0.684395\pi$
$860$	−31.2970	+	31.2970i	−1.06722	+	1.06722i
$861$	−43.9454	−	25.8183i	−1.49765	−	0.879887i
$862$			16.0625i			0.547090i
$863$	−18.2741	−	4.89654i	−0.622059	−	0.166680i	−0.0659954	−	0.997820i	$-0.521022\pi$
$863$	−18.2741	−	4.89654i	−0.622059	−	0.166680i	−0.556064	+	0.831140i	$0.687689\pi$
$864$	1.85485	−	4.85381i	0.0631034	−	0.165130i
$865$	19.9344	+	74.3964i	0.677792	+	2.52955i
$866$	6.91128	−	25.7932i	0.234855	−	0.876490i
$867$	9.10586	+	27.9773i	0.309251	+	0.950160i
$868$	−0.291460	−	1.42789i	−0.00989281	−	0.0484659i
$869$	−17.9167	−	17.9167i	−0.607781	−	0.607781i
$870$	−22.3503	+	24.8475i	−0.757747	+	0.842410i
$871$	−11.5620	+	33.4385i	−0.391763	+	1.13302i
$872$	−7.47268	−	4.31436i	−0.253057	−	0.146103i
$873$	−6.51829	−	16.9301i	−0.220611	−	0.572997i
$874$	11.1864			0.378385
$875$	16.5308	−	49.5108i	0.558844	−	1.67377i
$876$	4.76572	−	9.36482i	0.161019	−	0.316408i
$877$	10.0478	−	37.4990i	0.339291	−	1.26625i	−0.559850	−	0.828594i	$-0.689141\pi$
$877$	10.0478	−	37.4990i	0.339291	−	1.26625i	0.899141	−	0.437658i	$-0.144192\pi$
$878$	1.03404	−	0.277071i	0.0348973	−	0.00935070i
$879$	24.0206	+	36.9480i	0.810194	+	1.24622i
$880$	−3.22377	−	5.58373i	−0.108673	−	0.188227i
$881$	19.3219			0.650971			0.325485	−	0.945547i	$-0.394472\pi$
$881$	19.3219			0.650971			0.325485	+	0.945547i	$0.394472\pi$
$882$	20.3646	−	5.12682i	0.685711	−	0.172629i
$883$			33.7328i			1.13520i	0.823304	+	0.567600i	$0.192128\pi$
$883$			33.7328i			1.13520i	−0.823304	+	0.567600i	$0.807872\pi$
$884$	0.0294955	−	0.414137i	0.000992039	−	0.0139290i
$885$	−34.2317	−	7.25828i	−1.15069	−	0.243984i
$886$	−19.3491	+	5.18459i	−0.650047	+	0.174180i
$887$	−19.7788	+	11.4193i	−0.664107	+	0.383422i	−0.793840	−	0.608127i	$-0.791921\pi$
$887$	−19.7788	+	11.4193i	−0.664107	+	0.383422i	0.129733	+	0.991549i	$0.458588\pi$
$888$	−1.83335	−	5.63289i	−0.0615232	−	0.189027i
$889$	3.98211	−	1.98859i	0.133556	−	0.0666951i
$890$	0.134352	−	0.134352i	0.00450348	−	0.00450348i
$891$	12.5483	+	8.11331i	0.420383	+	0.271806i
$892$	6.53502	+	24.3890i	0.218809	+	0.816605i
$893$	3.11416	+	1.79796i	0.104211	+	0.0601664i
$894$	28.5843	+	25.7115i	0.956002	+	0.859923i
$895$	−1.85408	+	1.85408i	−0.0619750	+	0.0619750i
$896$	2.59230	−	0.529138i	0.0866026	−	0.0176773i
$897$	−43.6292	−	12.5477i	−1.45674	−	0.418955i
$898$	−3.01112	−	5.21542i	−0.100482	−	0.174041i
$899$	−0.708361	−	2.64364i	−0.0236252	−	0.0881703i
$900$	3.19114	+	30.0723i	0.106371	+	1.00241i
$901$	−0.376038	+	0.217106i	−0.0125276	+	0.00723284i
$902$	13.0576	−	13.0576i	0.434772	−	0.434772i
$903$	50.5515	−	13.1350i	1.68225	−	0.437106i
$904$	−5.14783	+	5.14783i	−0.171214	+	0.171214i
$905$	0.00685572	−	0.0255859i	0.000227892	−	0.000850504i
$906$	6.98062	−	32.9222i	0.231916	−	1.09377i
$907$	27.5416	+	15.9011i	0.914504	+	0.527989i	0.881877	−	0.471479i	$-0.156280\pi$
$907$	27.5416	+	15.9011i	0.914504	+	0.527989i	0.0326262	+	0.999468i	$0.489613\pi$
$908$	−1.11378	+	4.15669i	−0.0369622	+	0.137945i
$909$	23.6177	−	17.1954i	0.783349	−	0.570334i
$910$	−29.3750	−	22.5705i	−0.973771	−	0.748203i
$911$			3.03745i			0.100635i	0.998733	+	0.0503176i	$0.0160233\pi$
$911$			3.03745i			0.100635i	−0.998733	+	0.0503176i	$0.983977\pi$
$912$	−2.66160	+	0.140823i	−0.0881342	+	0.00466312i
$913$	4.00992	−	6.94539i	0.132709	−	0.229859i
$914$	−11.3777	+	19.7068i	−0.376342	+	0.651843i
$915$	−1.57836	−	29.8315i	−0.0521791	−	0.986199i
$916$	4.74643	+	4.74643i	0.156827	+	0.156827i
$917$	37.2783	+	24.6396i	1.23104	+	0.813673i
$918$	0.590840	−	0.0944887i	0.0195006	−	0.00311859i
$919$	2.26435	+	3.92197i	0.0746940	+	0.129374i	0.900953	−	0.433916i	$-0.142869\pi$
$919$	2.26435	+	3.92197i	0.0746940	+	0.129374i	−0.826259	+	0.563290i	$0.809535\pi$
$920$	−14.1149	+	24.4477i	−0.465354	+	0.806017i
$921$	−8.30651	+	5.40022i	−0.273709	+	0.177943i
$922$	12.8042	−	7.39249i	0.421683	−	0.243459i
$923$	−7.21461	−	37.3729i	−0.237472	−	1.23014i
$924$	−0.0577191	+	7.60825i	−0.00189882	+	0.250293i
$925$	24.3779	+	24.3779i	0.801540	+	0.801540i
$926$	−9.37202	+	5.41094i	−0.307984	+	0.177814i
$927$	−50.8333	+	5.39421i	−1.66959	+	0.177169i
$928$	4.79945	−	1.28601i	0.157550	−	0.0422153i
$929$	40.7401	+	10.9163i	1.33664	+	0.358152i	0.855187	−	0.518320i	$-0.173442\pi$
$929$	40.7401	+	10.9163i	1.33664	+	0.358152i	0.481454	+	0.876471i	$0.340109\pi$
$930$	−3.30194	−	1.68034i	−0.108275	−	0.0551006i
$931$	−6.64262	−	8.47976i	−0.217703	−	0.277913i
$932$			25.2970i			0.828632i
$933$	−28.4191	+	31.5944i	−0.930400	+	1.03435i
$934$	4.36636	+	16.2955i	0.142872	+	0.533204i
$935$	0.371223	−	0.642978i	0.0121403	−	0.0210276i
$936$	10.5387	+	2.43625i	0.344469	+	0.0796314i
$937$	2.95014			0.0963768			0.0481884	−	0.998838i	$-0.484655\pi$
$937$	2.95014			0.0963768			0.0481884	+	0.998838i	$0.484655\pi$
$938$	−11.5993	−	23.2273i	−0.378731	−	0.758400i
$939$	−6.78733	−	20.8538i	−0.221496	−	0.680537i
$940$	−7.85883	+	4.53730i	−0.256327	+	0.147990i
$941$	−3.15063	−	11.7583i	−0.102707	−	0.383310i	0.895368	−	0.445328i	$-0.146913\pi$
$941$	−3.15063	−	11.7583i	−0.102707	−	0.383310i	−0.998075	+	0.0620184i	$0.980246\pi$
$942$	−7.42468	+	4.82693i	−0.241909	+	0.157270i
$943$	−78.0975	−	20.9262i	−2.54321	−	0.681450i
$944$	3.67872	+	3.67872i	0.119732	+	0.119732i
$945$	22.0353	−	48.6275i	0.716807	−	1.58185i
$946$			18.9234i			0.615252i
$947$	−1.58817	+	5.92713i	−0.0516086	+	0.192606i	−0.986917	−	0.161227i	$-0.948455\pi$
$947$	−1.58817	+	5.92713i	−0.0516086	+	0.192606i	0.935309	+	0.353832i	$0.115122\pi$
$948$	5.48278	−	25.8580i	0.178072	−	0.839830i
$949$	20.6727	+	7.14797i	0.671063	+	0.232033i
$950$	13.4337	−	7.75595i	0.435847	−	0.251636i
$951$	38.0134	+	19.3449i	1.23267	+	0.627300i
$952$	0.202022	+	0.228050i	0.00654758	+	0.00739115i
$953$	5.71882			0.185251			0.0926254	−	0.995701i	$-0.470474\pi$
$953$	5.71882			0.185251			0.0926254	+	0.995701i	$0.470474\pi$
$954$	−4.06453	−	10.5569i	−0.131594	−	0.341792i
$955$	−11.6512	+	3.12194i	−0.377025	+	0.101024i
$956$	25.4422	−	6.81721i	0.822858	−	0.220484i
$957$	0.754954	+	14.2688i	0.0244042	+	0.461246i
$958$	−27.1100			−0.875883
$959$	11.8928	+	13.4251i	0.384039	+	0.433518i
$960$	3.05061	−	5.99457i	0.0984581	−	0.193474i
$961$	−26.5840	+	15.3483i	−0.857549	+	0.495106i
$962$	11.0902	−	5.39137i	0.357562	−	0.173825i
$963$	−8.92668	+	0.947259i	−0.287658	+	0.0305250i
$964$	−3.37308	+	12.5885i	−0.108640	+	0.405449i
$965$			67.6749i			2.17853i
$966$	28.9753	−	16.4371i	0.932264	−	0.528854i
$967$	−10.7665	−	10.7665i	−0.346227	−	0.346227i	0.512475	−	0.858702i	$-0.328729\pi$
$967$	−10.7665	−	10.7665i	−0.346227	−	0.346227i	−0.858702	+	0.512475i	$0.828729\pi$
$968$	7.96250	+	2.13355i	0.255925	+	0.0685748i
$969$	−0.167288	−	0.257318i	−0.00537405	−	0.00826626i
$970$	−6.07793	−	22.6831i	−0.195150	−	0.728312i
$971$	15.6521	−	9.03674i	0.502300	−	0.290003i	−0.227363	−	0.973810i	$-0.573010\pi$
$971$	15.6521	−	9.03674i	0.502300	−	0.290003i	0.729663	+	0.683807i	$0.239677\pi$
$972$	0.0389785	+	15.5884i	0.00125024	+	0.499998i
$973$	19.4321	+	38.9123i	0.622964	+	1.24747i
$974$	−12.1783			−0.390217
$975$	−61.0939	+	15.1813i	−1.95657	+	0.486191i
$976$	−2.22068	+	3.84633i	−0.0710821	+	0.123118i
$977$	3.67117	+	13.7010i	0.117451	+	0.438334i	0.999459	−	0.0329019i	$-0.0104749\pi$
$977$	3.67117	+	13.7010i	0.117451	+	0.438334i	−0.882007	+	0.471235i	$0.843808\pi$
$978$	1.95852	+	1.76169i	0.0626265	+	0.0563325i
$979$		−	0.0812343i		−	0.00259626i
$980$	26.9140	−	3.81767i	0.859736	−	0.121951i
$981$	25.5715	+	4.02391i	0.816434	+	0.128474i
$982$	14.9460	+	4.00477i	0.476946	+	0.127797i
$983$	25.8374	−	6.92310i	0.824084	−	0.220813i	0.177953	−	0.984039i	$-0.443053\pi$
$983$	25.8374	−	6.92310i	0.824084	−	0.220813i	0.646131	+	0.763227i	$0.276386\pi$
$984$	18.8453	+	3.99584i	0.600766	+	0.127383i
$985$	−63.2040	+	36.4909i	−2.01385	+	1.16270i
$986$	0.404580	+	0.404580i	0.0128844	+	0.0128844i
$987$	10.7082	+	0.0812369i	0.340847	+	0.00258580i
$988$	−1.05165	−	5.44772i	−0.0334574	−	0.173315i
$989$	71.7536	−	41.4269i	2.28163	−	1.31730i
$990$	15.0442	+	12.1577i	0.478136	+	0.386396i
$991$	15.0508	−	26.0687i	0.478104	−	0.828101i	−0.521581	−	0.853202i	$-0.674657\pi$
$991$	15.0508	−	26.0687i	0.478104	−	0.828101i	0.999685	+	0.0251009i	$0.00799072\pi$
$992$	0.275411	+	0.477025i	0.00874430	+	0.0151456i
$993$	−10.9045	+	21.4277i	−0.346042	+	0.679987i
$994$	23.3008	+	15.4010i	0.739055	+	0.488490i
$995$	−2.67286	−	2.67286i	−0.0847354	−	0.0847354i
$996$	8.35472	−	0.442042i	0.264729	−	0.0140066i
$997$	17.5485	−	30.3949i	0.555766	−	0.962615i	−0.442078	−	0.896977i	$-0.645758\pi$
$997$	17.5485	−	30.3949i	0.555766	−	0.962615i	0.997843	−	0.0656381i	$-0.0209083\pi$
$998$	8.81094	−	15.2610i	0.278906	−	0.483079i
$999$	11.2045	+	13.7940i	0.354494	+	0.436423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.17	yes	144
3.2	odd	2	inner	546.2.bv.a.515.23	yes	144
7.2	even	3	inner	546.2.bv.a.359.23	yes	144
13.5	odd	4	inner	546.2.bv.a.473.17	yes	144
21.2	odd	6	inner	546.2.bv.a.359.17	yes	144
39.5	even	4	inner	546.2.bv.a.473.23	yes	144
91.44	odd	12	inner	546.2.bv.a.317.23	yes	144
273.44	even	12	inner	546.2.bv.a.317.17	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.17	✓	144	273.44	even	12	inner
546.2.bv.a.317.23	yes	144	91.44	odd	12	inner
546.2.bv.a.359.17	yes	144	21.2	odd	6	inner
546.2.bv.a.359.23	yes	144	7.2	even	3	inner
546.2.bv.a.473.17	yes	144	13.5	odd	4	inner
546.2.bv.a.473.23	yes	144	39.5	even	4	inner
546.2.bv.a.515.17	yes	144	1.1	even	1	trivial
546.2.bv.a.515.23	yes	144	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.69438 + 0.359266i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.75102 - 1.00508i) q^{5} +(-1.54366 - 0.785563i) q^{6} +(1.18204 + 2.36702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.74186 + 1.21747i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.69438 + 0.359266i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-3.75102 - 1.00508i) q^{5} +(-1.54366 - 0.785563i) q^{6} +(1.18204 + 2.36702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.74186 + 1.21747i) q^{9} +(3.36308 + 1.94167i) q^{10} +(1.60373 - 0.429718i) q^{11} +(1.28774 + 1.15832i) q^{12} +(-2.02005 + 2.98654i) q^{13} +(-0.529138 - 2.59230i) q^{14} +(-5.99457 - 3.05061i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.0575760 + 0.0997246i) q^{17} +(-2.33333 - 1.88563i) q^{18} +(-0.398277 + 1.48639i) q^{19} +(-2.74594 - 2.74594i) q^{20} +(1.15244 + 4.43530i) q^{21} -1.66030 q^{22} +(3.63473 + 6.29553i) q^{23} +(-0.944069 - 1.45215i) q^{24} +(8.72986 + 5.04019i) q^{25} +(2.72419 - 2.36195i) q^{26} +(4.20835 + 3.04791i) q^{27} +(-0.159828 + 2.64092i) q^{28} +4.96875i q^{29} +(5.00075 + 4.49817i) q^{30} +(-0.532053 + 0.142563i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.87171 - 0.151940i) q^{33} +(0.0814248 - 0.0814248i) q^{34} +(-2.05483 - 10.0668i) q^{35} +(1.76578 + 2.42529i) q^{36} +(3.30353 + 0.885179i) q^{37} +(0.769411 - 1.33266i) q^{38} +(-4.49569 + 4.33460i) q^{39} +(1.94167 + 3.36308i) q^{40} +(-7.86460 + 7.86460i) q^{41} +(0.0347642 - 4.58244i) q^{42} -11.3975i q^{43} +(1.60373 + 0.429718i) q^{44} +(-9.06111 - 7.32255i) q^{45} +(-1.88147 - 7.02175i) q^{46} +(0.604808 - 2.25717i) q^{47} +(0.536057 + 1.64701i) q^{48} +(-4.20554 + 5.59584i) q^{49} +(-7.12790 - 7.12790i) q^{50} +(-0.133383 + 0.148286i) q^{51} +(-3.24268 + 1.57639i) q^{52} +(3.26558 + 1.88538i) q^{53} +(-3.27610 - 4.03326i) q^{54} -6.44753 q^{55} +(0.837902 - 2.50957i) q^{56} +(-1.20884 + 2.37542i) q^{57} +(1.28601 - 4.79945i) q^{58} +(5.02522 - 1.34650i) q^{59} +(-3.66615 - 5.63919i) q^{60} +(2.22068 + 3.84633i) q^{61} +0.550821 q^{62} +(0.359226 + 7.92912i) q^{63} +1.00000i q^{64} +(10.5790 - 9.17226i) q^{65} +(-2.81319 - 0.596491i) q^{66} +(9.47855 - 2.53977i) q^{67} +(-0.0997246 + 0.0575760i) q^{68} +(3.89684 + 11.9729i) q^{69} +(-0.620668 + 10.2556i) q^{70} +(-7.46475 + 7.46475i) q^{71} +(-1.07790 - 2.79966i) q^{72} +(-1.57016 - 5.85991i) q^{73} +(-2.96187 - 1.71003i) q^{74} +(12.9809 + 11.6763i) q^{75} +(-1.08811 + 1.08811i) q^{76} +(2.91283 + 3.28811i) q^{77} +(5.46438 - 3.02333i) q^{78} +(-7.63053 - 13.2165i) q^{79} +(-1.00508 - 3.75102i) q^{80} +(6.03554 + 6.67624i) q^{81} +(9.63213 - 5.56111i) q^{82} +(3.41557 - 3.41557i) q^{83} +(-1.21960 + 4.41730i) q^{84} +(0.316201 - 0.316201i) q^{85} +(-2.94990 + 11.0092i) q^{86} +(-1.78511 + 8.41896i) q^{87} +(-1.43787 - 0.830152i) q^{88} +(0.0126633 - 0.0472602i) q^{89} +(6.85714 + 9.41822i) q^{90} +(-9.45697 - 1.25127i) q^{91} +7.26945i q^{92} +(-0.952718 + 0.0504076i) q^{93} +(-1.16840 + 2.02373i) q^{94} +(2.98789 - 5.17518i) q^{95} +(-0.0915135 - 1.72963i) q^{96} +(-4.27601 - 4.27601i) q^{97} +(5.51055 - 4.31669i) q^{98} +(4.92037 + 0.774265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more