LMFDB - Embedded newform 546.2.bz.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.a.229.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.535417 + 1.99820i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.54628 + 0.718636i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.535417 + 1.99820i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.54628 + 0.718636i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.03435 + 1.79154i) q^{10} +(-1.83193 + 0.490864i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.43996 + 2.65454i) q^{13} +(-2.64552 + 0.0351224i) q^{14} +(-1.46279 + 1.46279i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.24802 + 2.16164i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.191351 - 0.714132i) q^{19} +(-1.46279 + 1.46279i) q^{20} +(-2.56446 - 0.650785i) q^{21} -1.89655 q^{22} +(7.35489 - 4.24635i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.623983 + 0.360257i) q^{25} +(1.66978 + 3.19560i) q^{26} +1.00000i q^{27} +(-2.56446 - 0.650785i) q^{28} -8.10492 q^{29} +(-1.79154 + 1.03435i) q^{30} +(7.23277 - 1.93801i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.83193 - 0.490864i) q^{33} +(-1.76497 + 1.76497i) q^{34} +(-0.0726574 - 5.47276i) q^{35} +1.00000i q^{36} +(-0.793796 + 2.96249i) q^{37} +(0.369662 - 0.640273i) q^{38} +(0.785800 + 3.51888i) q^{39} +(-1.79154 + 1.03435i) q^{40} +(-0.895842 - 0.895842i) q^{41} +(-2.30865 - 1.29234i) q^{42} -10.4587i q^{43} +(-1.83193 - 0.490864i) q^{44} +(-1.99820 + 0.535417i) q^{45} +(8.20332 - 2.19807i) q^{46} +(1.80147 + 0.482703i) q^{47} +1.00000i q^{48} +(5.96712 - 3.65970i) q^{49} +(0.509480 + 0.509480i) q^{50} +(-2.16164 + 1.24802i) q^{51} +(0.785800 + 3.51888i) q^{52} +(2.70278 - 4.68135i) q^{53} +(-0.258819 + 0.965926i) q^{54} -3.92339i q^{55} +(-2.30865 - 1.29234i) q^{56} +(0.522781 - 0.522781i) q^{57} +(-7.82875 - 2.09771i) q^{58} +(3.48328 + 12.9998i) q^{59} +(-1.99820 + 0.535417i) q^{60} +(8.23336 - 4.75353i) q^{61} +7.48791 q^{62} +(-1.89550 - 1.84583i) q^{63} +1.00000i q^{64} +(-6.61071 + 3.45426i) q^{65} +(-1.64246 - 0.948277i) q^{66} +(-2.30701 - 8.60990i) q^{67} +(-2.16164 + 1.24802i) q^{68} +8.49270 q^{69} +(1.34627 - 5.30509i) q^{70} +(-4.51316 + 4.51316i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.185948 + 0.693968i) q^{73} +(-1.53350 + 2.65609i) q^{74} +(0.360257 + 0.623983i) q^{75} +(0.522781 - 0.522781i) q^{76} +(4.31186 - 2.56637i) q^{77} +(-0.151729 + 3.60236i) q^{78} +(4.82081 + 8.34988i) q^{79} +(-1.99820 + 0.535417i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.633456 - 1.09718i) q^{82} +(-1.63597 - 1.63597i) q^{83} +(-1.89550 - 1.84583i) q^{84} +(-3.65119 - 3.65119i) q^{85} +(2.70692 - 10.1024i) q^{86} +(-7.01907 - 4.05246i) q^{87} +(-1.64246 - 0.948277i) q^{88} +(-3.24008 - 0.868177i) q^{89} -2.06869 q^{90} +(-8.12049 - 5.00577i) q^{91} +8.49270 q^{92} +(7.23277 + 1.93801i) q^{93} +(1.61516 + 0.932511i) q^{94} +(1.32453 + 0.764717i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(1.08804 + 1.08804i) q^{97} +(6.71100 - 1.99060i) q^{98} +(-1.34107 - 1.34107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 + 20 * q^9	$ 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.535417	+	1.99820i	−0.239446	+	0.893624i	0.736649	+	0.676276i	$0.236407\pi$
$5$	−0.535417	+	1.99820i	−0.239446	+	0.893624i	−0.976094	+	0.217348i	$0.930259\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−2.54628	+	0.718636i	−0.962405	+	0.271619i
$7$	−2.54628	+	0.718636i	−0.962405	+	0.271619i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.03435	+	1.79154i	−0.327089	+	0.566535i
$11$	−1.83193	+	0.490864i	−0.552348	+	0.148001i	−0.524188	−	0.851602i	$-0.675631\pi$
$11$	−1.83193	+	0.490864i	−0.552348	+	0.148001i	−0.0281594	+	0.999603i	$0.508965\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.43996	+	2.65454i	0.676724	+	0.736237i
$13$	2.43996	+	2.65454i	0.676724	+	0.736237i
$14$	−2.64552	+	0.0351224i	−0.707044	+	0.00938685i
$15$	−1.46279	+	1.46279i	−0.377690	+	0.377690i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.24802	+	2.16164i	−0.302690	+	0.524275i	−0.976744	−	0.214407i	$-0.931218\pi$
$17$	−1.24802	+	2.16164i	−0.302690	+	0.524275i	0.674054	+	0.738682i	$0.264551\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	0.191351	−	0.714132i	0.0438989	−	0.163833i	−0.940497	−	0.339803i	$-0.889640\pi$
$19$	0.191351	−	0.714132i	0.0438989	−	0.163833i	0.984396	+	0.175970i	$0.0563062\pi$
$20$	−1.46279	+	1.46279i	−0.327089	+	0.327089i
$21$	−2.56446	−	0.650785i	−0.559612	−	0.142013i
$22$	−1.89655			−0.404347
$23$	7.35489	−	4.24635i	1.53360	−	0.885425i	0.534410	−	0.845225i	$-0.320534\pi$
$23$	7.35489	−	4.24635i	1.53360	−	0.885425i	0.999192	−	0.0401997i	$-0.0127994\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	0.623983	+	0.360257i	0.124797	+	0.0720513i
$26$	1.66978	+	3.19560i	0.327470	+	0.626708i
$27$			1.00000i			0.192450i
$28$	−2.56446	−	0.650785i	−0.484638	−	0.122987i
$29$	−8.10492			−1.50505			−0.752523	−	0.658566i	$-0.771163\pi$
$29$	−8.10492			−1.50505			−0.752523	+	0.658566i	$0.771163\pi$
$30$	−1.79154	+	1.03435i	−0.327089	+	0.188845i
$31$	7.23277	−	1.93801i	1.29904	−	0.348078i	0.457955	−	0.888975i	$-0.348582\pi$
$31$	7.23277	−	1.93801i	1.29904	−	0.348078i	0.841089	+	0.540898i	$0.181915\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−1.83193	−	0.490864i	−0.318898	−	0.0854485i
$34$	−1.76497	+	1.76497i	−0.302690	+	0.302690i
$35$	−0.0726574	−	5.47276i	−0.0122813	−	0.925066i
$36$			1.00000i			0.166667i
$37$	−0.793796	+	2.96249i	−0.130499	+	0.487030i	−0.999976	−	0.00694419i	$-0.997790\pi$
$37$	−0.793796	+	2.96249i	−0.130499	+	0.487030i	0.869477	+	0.493974i	$0.164456\pi$
$38$	0.369662	−	0.640273i	0.0599671	−	0.103866i
$39$	0.785800	+	3.51888i	0.125829	+	0.563472i
$40$	−1.79154	+	1.03435i	−0.283267	+	0.163544i
$41$	−0.895842	−	0.895842i	−0.139907	−	0.139907i	0.633685	−	0.773592i	$-0.281542\pi$
$41$	−0.895842	−	0.895842i	−0.139907	−	0.139907i	−0.773592	+	0.633685i	$0.781542\pi$
$42$	−2.30865	−	1.29234i	−0.356232	−	0.199413i
$43$		−	10.4587i		−	1.59494i	−0.603357	−	0.797471i	$-0.706171\pi$
$43$		−	10.4587i		−	1.59494i	0.603357	−	0.797471i	$-0.293829\pi$
$44$	−1.83193	−	0.490864i	−0.276174	−	0.0740006i
$45$	−1.99820	+	0.535417i	−0.297875	+	0.0798152i
$46$	8.20332	−	2.19807i	1.20951	−	0.324088i
$47$	1.80147	+	0.482703i	0.262772	+	0.0704095i	0.387799	−	0.921744i	$-0.373235\pi$
$47$	1.80147	+	0.482703i	0.262772	+	0.0704095i	−0.125028	+	0.992153i	$0.539902\pi$
$48$			1.00000i			0.144338i
$49$	5.96712	−	3.65970i	0.852446	−	0.522815i
$50$	0.509480	+	0.509480i	0.0720513	+	0.0720513i
$51$	−2.16164	+	1.24802i	−0.302690	+	0.174758i
$52$	0.785800	+	3.51888i	0.108971	+	0.487981i
$53$	2.70278	−	4.68135i	0.371255	−	0.643032i	−0.618504	−	0.785782i	$-0.712261\pi$
$53$	2.70278	−	4.68135i	0.371255	−	0.643032i	0.989759	+	0.142749i	$0.0455942\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$		−	3.92339i		−	0.529029i
$56$	−2.30865	−	1.29234i	−0.308506	−	0.172696i
$57$	0.522781	−	0.522781i	0.0692440	−	0.0692440i
$58$	−7.82875	−	2.09771i	−1.02797	−	0.275443i
$59$	3.48328	+	12.9998i	0.453485	+	1.69243i	0.692505	+	0.721413i	$0.256507\pi$
$59$	3.48328	+	12.9998i	0.453485	+	1.69243i	−0.239021	+	0.971015i	$0.576826\pi$
$60$	−1.99820	+	0.535417i	−0.257967	+	0.0691220i
$61$	8.23336	−	4.75353i	1.05417	−	0.608628i	0.130359	−	0.991467i	$-0.458387\pi$
$61$	8.23336	−	4.75353i	1.05417	−	0.608628i	0.923815	+	0.382839i	$0.125054\pi$
$62$	7.48791			0.950966
$63$	−1.89550	−	1.84583i	−0.238810	−	0.232553i
$64$			1.00000i			0.125000i
$65$	−6.61071	+	3.45426i	−0.819957	+	0.428448i
$66$	−1.64246	−	0.948277i	−0.202173	−	0.116725i
$67$	−2.30701	−	8.60990i	−0.281847	−	1.05187i	−0.951113	−	0.308843i	$-0.900058\pi$
$67$	−2.30701	−	8.60990i	−0.281847	−	1.05187i	0.669266	−	0.743023i	$-0.266609\pi$
$68$	−2.16164	+	1.24802i	−0.262138	+	0.151345i
$69$	8.49270			1.02240
$70$	1.34627	−	5.30509i	0.160910	−	0.634079i
$71$	−4.51316	+	4.51316i	−0.535614	+	0.535614i	−0.922238	−	0.386624i	$-0.873641\pi$
$71$	−4.51316	+	4.51316i	−0.535614	+	0.535614i	0.386624	+	0.922238i	$0.373641\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	0.185948	+	0.693968i	0.0217636	+	0.0812228i	0.975954	−	0.217979i	$-0.0699464\pi$
$73$	0.185948	+	0.693968i	0.0217636	+	0.0812228i	−0.954190	+	0.299202i	$0.903280\pi$
$74$	−1.53350	+	2.65609i	−0.178265	+	0.308765i
$75$	0.360257	+	0.623983i	0.0415989	+	0.0720513i
$76$	0.522781	−	0.522781i	0.0599671	−	0.0599671i
$77$	4.31186	−	2.56637i	0.491382	−	0.292465i
$78$	−0.151729	+	3.60236i	−0.0171799	+	0.407887i
$79$	4.82081	+	8.34988i	0.542383	+	0.939435i	0.998767	+	0.0496517i	$0.0158111\pi$
$79$	4.82081	+	8.34988i	0.542383	+	0.939435i	−0.456384	+	0.889783i	$0.650856\pi$
$80$	−1.99820	+	0.535417i	−0.223406	+	0.0598614i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.633456	−	1.09718i	−0.0699535	−	0.121163i
$83$	−1.63597	−	1.63597i	−0.179571	−	0.179571i	0.611598	−	0.791169i	$-0.290527\pi$
$83$	−1.63597	−	1.63597i	−0.179571	−	0.179571i	−0.791169	+	0.611598i	$0.790527\pi$
$84$	−1.89550	−	1.84583i	−0.206816	−	0.201396i
$85$	−3.65119	−	3.65119i	−0.396027	−	0.396027i
$86$	2.70692	−	10.1024i	0.291895	−	1.08937i
$87$	−7.01907	−	4.05246i	−0.752523	−	0.434469i
$88$	−1.64246	−	0.948277i	−0.175087	−	0.101087i
$89$	−3.24008	−	0.868177i	−0.343448	−	0.0920266i	0.0829721	−	0.996552i	$-0.473559\pi$
$89$	−3.24008	−	0.868177i	−0.343448	−	0.0920266i	−0.426420	+	0.904525i	$0.640225\pi$
$90$	−2.06869			−0.218059
$91$	−8.12049	−	5.00577i	−0.851258	−	0.524747i
$92$	8.49270			0.885425
$93$	7.23277	+	1.93801i	0.750003	+	0.200963i
$94$	1.61516	+	0.932511i	0.166591	+	0.0961812i
$95$	1.32453	+	0.764717i	0.135894	+	0.0784583i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	1.08804	+	1.08804i	0.110474	+	0.110474i	0.760183	−	0.649709i	$-0.225109\pi$
$97$	1.08804	+	1.08804i	0.110474	+	0.110474i	−0.649709	+	0.760183i	$0.725109\pi$
$98$	6.71100	−	1.99060i	0.677913	−	0.201081i
$99$	−1.34107	−	1.34107i	−0.134782	−	0.134782i
$100$	0.360257	+	0.623983i	0.0360257	+	0.0623983i
$101$	2.09697	−	3.63206i	0.208656	−	0.361403i	−0.742635	−	0.669696i	$-0.766424\pi$
$101$	2.09697	−	3.63206i	0.208656	−	0.361403i	0.951292	+	0.308293i	$0.0997576\pi$
$102$	−2.41100	+	0.646025i	−0.238724	+	0.0639660i
$103$	2.81044	+	4.86783i	0.276921	+	0.479641i	0.970618	−	0.240626i	$-0.0773527\pi$
$103$	2.81044	+	4.86783i	0.276921	+	0.479641i	−0.693697	+	0.720267i	$0.744019\pi$
$104$	−0.151729	+	3.60236i	−0.0148782	+	0.353240i
$105$	2.67346	−	4.77588i	0.260903	−	0.466078i
$106$	3.82230	−	3.82230i	0.371255	−	0.371255i
$107$	−0.379487	−	0.657292i	−0.0366864	−	0.0635428i	0.847099	−	0.531435i	$-0.178347\pi$
$107$	−0.379487	−	0.657292i	−0.0366864	−	0.0635428i	−0.883786	+	0.467892i	$0.845014\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.87584	−	14.4648i	−0.371238	−	1.38548i	−0.858764	−	0.512371i	$-0.828767\pi$
$109$	−3.87584	−	14.4648i	−0.371238	−	1.38548i	0.487526	−	0.873108i	$-0.337899\pi$
$110$	1.01545	−	3.78970i	0.0968191	−	0.361334i
$111$	−2.16869	+	2.16869i	−0.205843	+	0.205843i
$112$	−1.89550	−	1.84583i	−0.179108	−	0.174414i
$113$	−11.3984			−1.07228			−0.536138	−	0.844131i	$-0.680117\pi$
$113$	−11.3984			−1.07228			−0.536138	+	0.844131i	$0.680117\pi$
$114$	0.640273	−	0.369662i	0.0599671	−	0.0346220i
$115$	4.54714	+	16.9701i	0.424023	+	1.58247i
$116$	−7.01907	−	4.05246i	−0.651704	−	0.376262i
$117$	−1.07892	+	3.44034i	−0.0997459	+	0.318060i
$118$			13.4584i			1.23894i
$119$	1.62439	−	6.40103i	0.148908	−	0.586781i
$120$	−2.06869			−0.188845
$121$	−6.41126	+	3.70154i	−0.582842	+	0.336504i
$122$	9.18312	−	2.46061i	0.831401	−	0.222773i
$123$	−0.327901	−	1.22374i	−0.0295658	−	0.110341i
$124$	7.23277	+	1.93801i	0.649522	+	0.174039i
$125$	−8.36789	+	8.36789i	−0.748447	+	0.748447i
$126$	−1.35318	−	2.27352i	−0.120550	−	0.202542i
$127$		−	10.4391i		−	0.926322i	−0.886274	−	0.463161i	$-0.846715\pi$
$127$		−	10.4391i		−	0.926322i	0.886274	−	0.463161i	$-0.153285\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	5.22937	−	9.05753i	0.460420	−	0.797471i
$130$	−7.27948	+	1.62558i	−0.638453	+	0.142573i
$131$	16.3242	−	9.42477i	1.42625	−	0.823446i	0.429428	−	0.903101i	$-0.358715\pi$
$131$	16.3242	−	9.42477i	1.42625	−	0.823446i	0.996823	+	0.0796546i	$0.0253817\pi$
$132$	−1.34107	−	1.34107i	−0.116725	−	0.116725i
$133$	0.0259668	+	1.95589i	0.00225161	+	0.169598i
$134$		−	8.91362i		−	0.770020i
$135$	−1.99820	−	0.535417i	−0.171978	−	0.0460813i
$136$	−2.41100	+	0.646025i	−0.206741	+	0.0553962i
$137$	−16.1564	+	4.32908i	−1.38033	+	0.369858i	−0.871241	−	0.490855i	$-0.836684\pi$
$137$	−16.1564	+	4.32908i	−1.38033	+	0.369858i	−0.509089	+	0.860714i	$0.670018\pi$
$138$	8.20332	+	2.19807i	0.698313	+	0.187112i
$139$		−	16.3078i		−	1.38321i	−0.722276	−	0.691604i	$-0.756904\pi$
$139$		−	16.3078i		−	1.38321i	0.722276	−	0.691604i	$-0.243096\pi$
$140$	2.67346	−	4.77588i	0.225948	−	0.403636i
$141$	1.31877	+	1.31877i	0.111060	+	0.111060i
$142$	−5.52747	+	3.19129i	−0.463855	+	0.267807i
$143$	−5.77286	−	3.66524i	−0.482751	−	0.306503i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.33951	−	16.1953i	0.360377	−	1.34494i
$146$			0.718449i			0.0594592i
$147$	6.99753	−	0.185834i	0.577147	−	0.0153273i
$148$	−2.16869	+	2.16869i	−0.178265	+	0.178265i
$149$	10.6332	+	2.84914i	0.871102	+	0.233411i	0.666564	−	0.745448i	$-0.267764\pi$
$149$	10.6332	+	2.84914i	0.871102	+	0.233411i	0.204538	+	0.978859i	$0.434431\pi$
$150$	0.186483	+	0.695963i	0.0152262	+	0.0568251i
$151$	20.2695	−	5.43118i	1.64950	−	0.441983i	0.690031	−	0.723780i	$-0.257597\pi$
$151$	20.2695	−	5.43118i	1.64950	−	0.441983i	0.959474	+	0.281797i	$0.0909304\pi$
$152$	0.640273	−	0.369662i	0.0519330	−	0.0299835i
$153$	−2.49605			−0.201794
$154$	4.82917	−	1.36293i	0.389145	−	0.109828i
$155$			15.4902i			1.24420i
$156$	−1.07892	+	3.44034i	−0.0863825	+	0.275448i
$157$	12.5512	+	7.24646i	1.00170	+	0.578331i	0.908750	−	0.417340i	$-0.137038\pi$
$157$	12.5512	+	7.24646i	1.00170	+	0.578331i	0.0929479	+	0.995671i	$0.470371\pi$
$158$	2.49543	+	9.31308i	0.198526	+	0.740909i
$159$	4.68135	−	2.70278i	0.371255	−	0.214344i
$160$	−2.06869			−0.163544
$161$	−15.6761	+	16.0979i	−1.23545	+	1.26869i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	4.33588	−	16.1817i	0.339612	−	1.26745i	−0.559170	−	0.829053i	$-0.688880\pi$
$163$	4.33588	−	16.1817i	0.339612	−	1.26745i	0.898782	−	0.438396i	$-0.144453\pi$
$164$	−0.327901	−	1.22374i	−0.0256048	−	0.0955583i
$165$	1.96169	−	3.39775i	0.152718	−	0.264515i
$166$	−1.15681	−	2.00365i	−0.0897857	−	0.155513i
$167$	−12.6275	+	12.6275i	−0.977145	+	0.977145i	−0.999745	−	0.0225997i	$-0.992806\pi$
$167$	−12.6275	+	12.6275i	−0.977145	+	0.977145i	0.0225997	+	0.999745i	$0.492806\pi$
$168$	−1.35318	−	2.27352i	−0.104400	−	0.175406i
$169$	−1.09316	+	12.9540i	−0.0840893	+	0.996458i
$170$	−2.58178	−	4.47177i	−0.198013	−	0.342969i
$171$	0.714132	−	0.191351i	0.0546110	−	0.0146330i
$172$	5.22937	−	9.05753i	0.398736	−	0.690630i
$173$	−2.45036	−	4.24415i	−0.186297	−	0.322677i	0.757716	−	0.652585i	$-0.226315\pi$
$173$	−2.45036	−	4.24415i	−0.186297	−	0.322677i	−0.944013	+	0.329908i	$0.892982\pi$
$174$	−5.73105	−	5.73105i	−0.434469	−	0.434469i
$175$	−1.84773	−	0.468899i	−0.139675	−	0.0354455i
$176$	−1.34107	−	1.34107i	−0.101087	−	0.101087i
$177$	−3.48328	+	12.9998i	−0.261819	+	0.977123i
$178$	−2.90498	−	1.67719i	−0.217737	−	0.125711i
$179$	−7.09276	−	4.09501i	−0.530138	−	0.306075i	0.210935	−	0.977500i	$-0.432349\pi$
$179$	−7.09276	−	4.09501i	−0.530138	−	0.306075i	−0.741073	+	0.671425i	$0.765683\pi$
$180$	−1.99820	−	0.535417i	−0.148937	−	0.0399076i
$181$	4.96102			0.368750			0.184375	−	0.982856i	$-0.440974\pi$
$181$	4.96102			0.368750			0.184375	+	0.982856i	$0.440974\pi$
$182$	−6.54820	−	6.93694i	−0.485385	−	0.514200i
$183$	9.50707			0.702783
$184$	8.20332	+	2.19807i	0.604757	+	0.162044i
$185$	−5.49464	−	3.17233i	−0.403974	−	0.233234i
$186$	6.48472	+	3.74396i	0.475483	+	0.274520i
$187$	1.22522	−	4.57259i	0.0895971	−	0.334381i
$188$	1.31877	+	1.31877i	0.0961812	+	0.0961812i
$189$	−0.718636	−	2.54628i	−0.0522731	−	0.185215i
$190$	1.08147	+	1.08147i	0.0784583	+	0.0784583i
$191$	5.98826	+	10.3720i	0.433295	+	0.750489i	0.997155	−	0.0753815i	$-0.0240175\pi$
$191$	5.98826	+	10.3720i	0.433295	+	0.750489i	−0.563860	+	0.825871i	$0.690684\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−12.8306	+	3.43795i	−0.923568	+	0.247469i	−0.689110	−	0.724657i	$-0.741998\pi$
$193$	−12.8306	+	3.43795i	−0.923568	+	0.247469i	−0.234458	+	0.972126i	$0.575332\pi$
$194$	0.769362	+	1.33257i	0.0552369	+	0.0956732i
$195$	−7.45217	−	0.313880i	−0.533661	−	0.0224774i
$196$	6.99753	−	0.185834i	0.499824	−	0.0132738i
$197$	−7.34311	+	7.34311i	−0.523175	+	0.523175i	−0.918529	−	0.395354i	$-0.870622\pi$
$197$	−7.34311	+	7.34311i	−0.523175	+	0.523175i	0.395354	+	0.918529i	$0.370622\pi$
$198$	−0.948277	−	1.64246i	−0.0673911	−	0.116725i
$199$	0.781653	−	1.35386i	0.0554099	−	0.0959727i	−0.836990	−	0.547218i	$-0.815687\pi$
$199$	0.781653	−	1.35386i	0.0554099	−	0.0959727i	0.892400	+	0.451245i	$0.149020\pi$
$200$	0.186483	+	0.695963i	0.0131863	+	0.0492120i
$201$	2.30701	−	8.60990i	0.162724	−	0.607295i
$202$	2.96556	−	2.96556i	0.208656	−	0.208656i
$203$	20.6374	−	5.82449i	1.44846	−	0.408799i
$204$	−2.49605			−0.174758
$205$	2.26972	−	1.31043i	0.158524	−	0.0915241i
$206$	1.45479	+	5.42935i	0.101360	+	0.378281i
$207$	7.35489	+	4.24635i	0.511200	+	0.295142i
$208$	−1.07892	+	3.44034i	−0.0748094	+	0.238545i
$209$			1.40217i			0.0969900i
$210$	3.81845	−	3.92120i	0.263498	−	0.270589i
$211$	−27.0456			−1.86190			−0.930948	−	0.365153i	$-0.881017\pi$
$211$	−27.0456			−1.86190			−0.930948	+	0.365153i	$0.881017\pi$
$212$	4.68135	−	2.70278i	0.321516	−	0.185627i
$213$	−6.16510	+	1.65193i	−0.422426	+	0.113189i
$214$	−0.196437	−	0.733114i	−0.0134282	−	0.0501146i
$215$	20.8987	+	5.59979i	1.42528	+	0.381902i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−17.0240	+	10.1325i	−1.15566	+	0.687837i
$218$		−	14.9751i		−	1.01424i
$219$	−0.185948	+	0.693968i	−0.0125652	+	0.0468940i
$220$	1.96169	−	3.39775i	0.132257	−	0.229076i
$221$	−8.78330	+	1.96140i	−0.590828	+	0.131938i
$222$	−2.65609	+	1.53350i	−0.178265	+	0.102922i
$223$	12.4943	+	12.4943i	0.836678	+	0.836678i	0.988420	−	0.151742i	$-0.0484883\pi$
$223$	12.4943	+	12.4943i	0.836678	+	0.836678i	−0.151742	+	0.988420i	$0.548488\pi$
$224$	−1.35318	−	2.27352i	−0.0904129	−	0.151906i
$225$			0.720513i			0.0480342i
$226$	−11.0101	−	2.95013i	−0.732378	−	0.196240i
$227$	−18.3072	+	4.90540i	−1.21509	+	0.325583i	−0.808758	−	0.588142i	$-0.799860\pi$
$227$	−18.3072	+	4.90540i	−1.21509	+	0.325583i	−0.406334	+	0.913725i	$0.633193\pi$
$228$	0.714132	−	0.191351i	0.0472945	−	0.0126725i
$229$	−8.24865	−	2.21022i	−0.545086	−	0.146055i	−0.0242405	−	0.999706i	$-0.507717\pi$
$229$	−8.24865	−	2.21022i	−0.545086	−	0.146055i	−0.520846	+	0.853651i	$0.674383\pi$
$230$			17.5688i			1.15845i
$231$	5.01737	−	0.0666115i	0.330119	−	0.00438271i
$232$	−5.73105	−	5.73105i	−0.376262	−	0.376262i
$233$	11.1360	−	6.42938i	0.729544	−	0.421202i	−0.0887114	−	0.996057i	$-0.528275\pi$
$233$	11.1360	−	6.42938i	0.729544	−	0.421202i	0.818255	+	0.574855i	$0.194942\pi$
$234$	−1.93258	+	3.04387i	−0.126337	+	0.198984i
$235$	−1.92908	+	3.34126i	−0.125839	+	0.217960i
$236$	−3.48328	+	12.9998i	−0.226742	+	0.846214i
$237$			9.64161i			0.626290i
$238$	3.22575	−	5.76250i	0.209094	−	0.373527i
$239$	11.1656	−	11.1656i	0.722246	−	0.722246i	−0.246817	−	0.969062i	$-0.579385\pi$
$239$	11.1656	−	11.1656i	0.722246	−	0.722246i	0.969062	+	0.246817i	$0.0793846\pi$
$240$	−1.99820	−	0.535417i	−0.128983	−	0.0345610i
$241$	0.827886	+	3.08971i	0.0533289	+	0.199026i	0.987450	−	0.157929i	$-0.0504817\pi$
$241$	0.827886	+	3.08971i	0.0533289	+	0.199026i	−0.934122	+	0.356955i	$0.883815\pi$
$242$	−7.15083	+	1.91606i	−0.459673	+	0.123169i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	9.50707			0.608628
$245$	4.11793	+	13.8830i	0.263085	+	0.886952i
$246$		−	1.26691i		−	0.0807754i
$247$	2.36258	−	1.23451i	0.150327	−	0.0785498i
$248$	6.48472	+	3.74396i	0.411780	+	0.237742i
$249$	−0.598808	−	2.23478i	−0.0379479	−	0.141624i
$250$	−10.2485	+	5.91699i	−0.648174	+	0.374223i
$251$	−11.0842			−0.699628			−0.349814	−	0.936819i	$-0.613755\pi$
$251$	−11.0842			−0.699628			−0.349814	+	0.936819i	$0.613755\pi$
$252$	−0.718636	−	2.54628i	−0.0452698	−	0.160401i
$253$	−11.3893	+	11.3893i	−0.716038	+	0.716038i
$254$	2.70184	−	10.0834i	0.169529	−	0.632690i
$255$	−1.33643	−	4.98761i	−0.0836903	−	0.312336i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.23585	+	5.60466i	0.201847	+	0.349609i	0.949124	−	0.314904i	$-0.101972\pi$
$257$	3.23585	+	5.60466i	0.201847	+	0.349609i	−0.747277	+	0.664513i	$0.768639\pi$
$258$	7.39544	−	7.39544i	0.460420	−	0.460420i
$259$	−0.107720	−	8.11378i	−0.00669340	−	0.504166i
$260$	−7.45217	−	0.313880i	−0.462164	−	0.0194660i
$261$	−4.05246	−	7.01907i	−0.250841	−	0.434469i
$262$	18.2073	−	4.87862i	1.12485	−	0.301402i
$263$	−1.88597	+	3.26660i	−0.116294	+	0.201427i	−0.918296	−	0.395894i	$-0.870435\pi$
$263$	−1.88597	+	3.26660i	−0.116294	+	0.201427i	0.802002	+	0.597321i	$0.203768\pi$
$264$	−0.948277	−	1.64246i	−0.0583624	−	0.101087i
$265$	7.90717	+	7.90717i	0.485734	+	0.485734i
$266$	−0.481141	+	1.89597i	−0.0295006	+	0.116249i
$267$	−2.37190	−	2.37190i	−0.145158	−	0.145158i
$268$	2.30701	−	8.60990i	0.140923	−	0.525933i
$269$	−17.0994	−	9.87236i	−1.04257	−	0.601929i	−0.122011	−	0.992529i	$-0.538934\pi$
$269$	−17.0994	−	9.87236i	−1.04257	−	0.601929i	−0.920560	+	0.390600i	$0.872268\pi$
$270$	−1.79154	−	1.03435i	−0.109030	−	0.0629483i
$271$	19.7652	+	5.29606i	1.20065	+	0.321713i	0.803086	−	0.595863i	$-0.203190\pi$
$271$	19.7652	+	5.29606i	1.20065	+	0.321713i	0.397562	+	0.917575i	$0.369856\pi$
$272$	−2.49605			−0.151345
$273$	−4.52966	−	8.39536i	−0.274148	−	0.508111i
$274$	−16.7263			−1.01047
$275$	−1.31993	−	0.353674i	−0.0795948	−	0.0213274i
$276$	7.35489	+	4.24635i	0.442713	+	0.255600i
$277$	9.03468	+	5.21618i	0.542841	+	0.313410i	0.746230	−	0.665689i	$-0.231862\pi$
$277$	9.03468	+	5.21618i	0.542841	+	0.313410i	−0.203388	+	0.979098i	$0.565195\pi$
$278$	4.22077	−	15.7521i	0.253145	−	0.944749i
$279$	5.29475	+	5.29475i	0.316989	+	0.316989i
$280$	3.81845	−	3.92120i	0.228196	−	0.234337i
$281$	−11.6966	−	11.6966i	−0.697760	−	0.697760i	0.266167	−	0.963927i	$-0.414243\pi$
$281$	−11.6966	−	11.6966i	−0.697760	−	0.697760i	−0.963927	+	0.266167i	$0.914243\pi$
$282$	0.932511	+	1.61516i	0.0555302	+	0.0961812i
$283$	−9.94003	+	17.2166i	−0.590874	+	1.02342i	0.403242	+	0.915094i	$0.367883\pi$
$283$	−9.94003	+	17.2166i	−0.590874	+	1.02342i	−0.994115	+	0.108329i	$0.965450\pi$
$284$	−6.16510	+	1.65193i	−0.365831	+	0.0980242i
$285$	0.764717	+	1.32453i	0.0452979	+	0.0784583i
$286$	−4.62752	−	5.03448i	−0.273631	−	0.297695i
$287$	2.92485	+	1.63728i	0.172649	+	0.0966458i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	5.38487	+	9.32687i	0.316757	+	0.548639i
$290$	8.38329	−	14.5203i	0.492284	−	0.852661i
$291$	0.398251	+	1.48629i	0.0233459	+	0.0871280i
$292$	−0.185948	+	0.693968i	−0.0108818	+	0.0406114i
$293$	−9.58678	+	9.58678i	−0.560065	+	0.560065i	−0.929326	−	0.369261i	$-0.879611\pi$
$293$	−9.58678	+	9.58678i	−0.560065	+	0.560065i	0.369261	+	0.929326i	$0.379611\pi$
$294$	6.80719	+	1.63159i	0.397004	+	0.0951564i
$295$	−27.8412			−1.62098
$296$	−2.65609	+	1.53350i	−0.154382	+	0.0891327i
$297$	−0.490864	−	1.83193i	−0.0284828	−	0.106299i
$298$	9.53342	+	5.50412i	0.552256	+	0.318845i
$299$	29.2178	+	9.16292i	1.68971	+	0.529905i
$300$			0.720513i			0.0415989i
$301$	7.51603	+	26.6309i	0.433217	+	1.53498i
$302$	20.9845			1.20752
$303$	3.63206	−	2.09697i	0.208656	−	0.120468i
$304$	0.714132	−	0.191351i	0.0409583	−	0.0109747i
$305$	5.09024	+	18.9971i	0.291467	+	1.08777i
$306$	−2.41100	−	0.646025i	−0.137828	−	0.0369308i
$307$	−21.4796	+	21.4796i	−1.22590	+	1.22590i	−0.260405	+	0.965500i	$0.583856\pi$
$307$	−21.4796	+	21.4796i	−1.22590	+	1.22590i	−0.965500	+	0.260405i	$0.916144\pi$
$308$	5.01737	−	0.0666115i	0.285891	−	0.00379554i
$309$			5.62088i			0.319761i
$310$	−4.00916	+	14.9624i	−0.227705	+	0.849806i
$311$	0.270874	−	0.469167i	0.0153599	−	0.0266040i	−0.858243	−	0.513243i	$-0.828444\pi$
$311$	0.270874	−	0.469167i	0.0153599	−	0.0266040i	0.873603	+	0.486639i	$0.161777\pi$
$312$	−1.93258	+	3.04387i	−0.109411	+	0.172325i
$313$	−13.5790	+	7.83985i	−0.767531	+	0.443135i	−0.831993	−	0.554786i	$-0.812800\pi$
$313$	−13.5790	+	7.83985i	−0.767531	+	0.443135i	0.0644618	+	0.997920i	$0.479467\pi$
$314$	10.2480	+	10.2480i	0.578331	+	0.578331i
$315$	4.70322	−	2.79930i	0.264997	−	0.157723i
$316$			9.64161i			0.542383i
$317$	1.10595	+	0.296338i	0.0621163	+	0.0166440i	0.289743	−	0.957104i	$-0.406430\pi$
$317$	1.10595	+	0.296338i	0.0621163	+	0.0166440i	−0.227627	+	0.973748i	$0.573097\pi$
$318$	5.22136	−	1.39906i	0.292800	−	0.0784554i
$319$	14.8477	−	3.97842i	0.831309	−	0.222749i
$320$	−1.99820	−	0.535417i	−0.111703	−	0.0299307i
$321$		−	0.758975i		−	0.0423619i
$322$	−19.3084	+	11.4921i	−1.07601	+	0.640431i
$323$	1.30489	+	1.30489i	0.0726058	+	0.0726058i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	0.566180	+	2.53540i	0.0314060	+	0.140639i
$326$	8.37627	−	14.5081i	0.463919	−	0.803531i
$327$	3.87584	−	14.4648i	0.214334	−	0.799907i
$328$		−	1.26691i		−	0.0699535i
$329$	−4.93395	+	0.0655040i	−0.272017	+	0.00361135i
$330$	2.77425	−	2.77425i	0.152718	−	0.152718i
$331$	−15.4855	−	4.14933i	−0.851161	−	0.228068i	−0.193237	−	0.981152i	$-0.561899\pi$
$331$	−15.4855	−	4.14933i	−0.851161	−	0.228068i	−0.657924	+	0.753084i	$0.728565\pi$
$332$	−0.598808	−	2.23478i	−0.0328639	−	0.122650i
$333$	−2.96249	+	0.793796i	−0.162343	+	0.0434998i
$334$	−15.4655	+	8.92899i	−0.846232	+	0.488572i
$335$	18.4395			1.00746
$336$	−0.718636	−	2.54628i	−0.0392048	−	0.138911i
$337$			10.4788i			0.570818i	0.958406	+	0.285409i	$0.0921295\pi$
$337$			10.4788i			0.570818i	−0.958406	+	0.285409i	$0.907871\pi$
$338$	−4.40864	+	12.2296i	−0.239799	+	0.665204i
$339$	−9.87134	−	5.69922i	−0.536138	−	0.309539i
$340$	−1.33643	−	4.98761i	−0.0724779	−	0.270491i
$341$	−12.2986	+	7.10062i	−0.666008	+	0.384520i
$342$	0.739324			0.0399780
$343$	−12.5640	+	13.6068i	−0.678392	+	0.734700i
$344$	7.39544	−	7.39544i	0.398736	−	0.398736i
$345$	−4.54714	+	16.9701i	−0.244810	+	0.913642i
$346$	−1.26840	−	4.73373i	−0.0681896	−	0.254487i
$347$	11.9993	−	20.7834i	0.644158	−	1.11571i	−0.340338	−	0.940303i	$-0.610541\pi$
$347$	11.9993	−	20.7834i	0.644158	−	1.11571i	0.984495	−	0.175411i	$-0.0561253\pi$
$348$	−4.05246	−	7.01907i	−0.217235	−	0.376262i
$349$	6.10083	−	6.10083i	0.326570	−	0.326570i	−0.524711	−	0.851281i	$-0.675826\pi$
$349$	6.10083	−	6.10083i	0.326570	−	0.326570i	0.851281	+	0.524711i	$0.175826\pi$
$350$	−1.66341	−	0.931150i	−0.0889131	−	0.0497721i
$351$	−2.65454	+	2.43996i	−0.141689	+	0.130236i
$352$	−0.948277	−	1.64246i	−0.0505433	−	0.0875436i
$353$	32.6885	−	8.75886i	1.73983	−	0.466187i	0.757424	−	0.652924i	$-0.226458\pi$
$353$	32.6885	−	8.75886i	1.73983	−	0.466187i	0.982410	+	0.186737i	$0.0597911\pi$
$354$	−6.72918	+	11.6553i	−0.357652	+	0.619471i
$355$	−6.60179	−	11.4346i	−0.350387	−	0.606888i
$356$	−2.37190	−	2.37190i	−0.125711	−	0.125711i
$357$	4.60728	−	4.73126i	0.243843	−	0.250405i
$358$	−5.79122	−	5.79122i	−0.306075	−	0.306075i
$359$	8.31664	−	31.0381i	0.438935	−	1.63813i	−0.292534	−	0.956255i	$-0.594499\pi$
$359$	8.31664	−	31.0381i	0.438935	−	1.63813i	0.731470	−	0.681874i	$-0.238835\pi$
$360$	−1.79154	−	1.03435i	−0.0944224	−	0.0545148i
$361$	15.9811	+	9.22670i	0.841111	+	0.485616i
$362$	4.79198	+	1.28401i	0.251861	+	0.0674859i
$363$	−7.40308			−0.388561
$364$	−4.52966	−	8.39536i	−0.237419	−	0.440037i
$365$	−1.48625			−0.0777938
$366$	9.18312	+	2.46061i	0.480010	+	0.128618i
$367$	11.7708	+	6.79586i	0.614429	+	0.354741i	0.774697	−	0.632333i	$-0.217902\pi$
$367$	11.7708	+	6.79586i	0.614429	+	0.354741i	−0.160268	+	0.987074i	$0.551236\pi$
$368$	7.35489	+	4.24635i	0.383400	+	0.221356i
$369$	0.327901	−	1.22374i	0.0170698	−	0.0637055i
$370$	−4.48635	−	4.48635i	−0.233234	−	0.233234i
$371$	−3.51785	+	13.8624i	−0.182638	+	0.719697i
$372$	5.29475	+	5.29475i	0.274520	+	0.274520i
$373$	−14.0828	−	24.3922i	−0.729181	−	1.26298i	−0.957230	−	0.289329i	$-0.906568\pi$
$373$	−14.0828	−	24.3922i	−0.729181	−	1.26298i	0.228048	−	0.973650i	$-0.426766\pi$
$374$	2.36695	−	4.09967i	0.122392	−	0.211989i
$375$	−11.4307	+	3.06286i	−0.590281	+	0.158165i
$376$	0.932511	+	1.61516i	0.0480906	+	0.0832953i
$377$	−19.7757	−	21.5148i	−1.01850	−	1.10807i
$378$	−0.0351224	−	2.64552i	−0.00180650	−	0.136071i
$379$	6.88941	−	6.88941i	0.353885	−	0.353885i	−0.507668	−	0.861553i	$-0.669492\pi$
$379$	6.88941	−	6.88941i	0.353885	−	0.353885i	0.861553	+	0.507668i	$0.169492\pi$
$380$	0.764717	+	1.32453i	0.0392291	+	0.0679468i
$381$	5.21956	−	9.04054i	0.267406	−	0.463161i
$382$	3.09975	+	11.5684i	0.158597	+	0.591892i
$383$	4.51837	−	16.8628i	0.230878	−	0.861649i	−0.749086	−	0.662473i	$-0.769507\pi$
$383$	4.51837	−	16.8628i	0.230878	−	0.861649i	0.979964	−	0.199176i	$-0.0638265\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	2.81949	+	9.99006i	0.143694	+	0.509140i
$386$	−13.2832			−0.676099
$387$	9.05753	−	5.22937i	0.460420	−	0.265824i
$388$	0.398251	+	1.48629i	0.0202181	+	0.0754551i
$389$	12.2815	+	7.09075i	0.622699	+	0.359515i	0.777919	−	0.628365i	$-0.216275\pi$
$389$	12.2815	+	7.09075i	0.622699	+	0.359515i	−0.155220	+	0.987880i	$0.549609\pi$
$390$	−7.11700	−	2.23195i	−0.360383	−	0.113019i
$391$			21.1982i			1.07204i
$392$	6.80719	+	1.63159i	0.343815	+	0.0824079i
$393$	18.8495			0.950834
$394$	−8.99344	+	5.19236i	−0.453083	+	0.261587i
$395$	−19.2659	+	5.16228i	−0.969372	+	0.259743i
$396$	−0.490864	−	1.83193i	−0.0246669	−	0.0920580i
$397$	−13.6046	−	3.64533i	−0.682793	−	0.182954i	−0.0992823	−	0.995059i	$-0.531655\pi$
$397$	−13.6046	−	3.64533i	−0.682793	−	0.182954i	−0.583511	+	0.812105i	$0.698321\pi$
$398$	1.10542	−	1.10542i	0.0554099	−	0.0554099i
$399$	−0.955459	+	1.70684i	−0.0478328	+	0.0854488i
$400$			0.720513i			0.0360257i
$401$	−6.98254	+	26.0592i	−0.348692	+	1.30133i	0.539548	+	0.841955i	$0.318595\pi$
$401$	−6.98254	+	26.0592i	−0.348692	+	1.30133i	−0.888240	+	0.459380i	$0.848072\pi$
$402$	4.45681	−	7.71942i	0.222285	−	0.385010i
$403$	22.7922	+	14.4710i	1.13536	+	0.720851i
$404$	3.63206	−	2.09697i	0.180702	−	0.104328i
$405$	−1.46279	−	1.46279i	−0.0726864	−	0.0726864i
$406$	21.4417	−	0.284664i	1.06413	−	0.0141276i
$407$		−	5.81672i		−	0.288324i
$408$	−2.41100	−	0.646025i	−0.119362	−	0.0319830i
$409$	−24.1329	+	6.46638i	−1.19329	+	0.319742i	−0.800187	−	0.599751i	$-0.795266\pi$
$409$	−24.1329	+	6.46638i	−1.19329	+	0.319742i	−0.393106	+	0.919493i	$0.628600\pi$
$410$	2.53155	−	0.678326i	0.125024	−	0.0335001i
$411$	−16.1564	−	4.32908i	−0.796934	−	0.213538i
$412$			5.62088i			0.276921i
$413$	−18.2115	−	30.5979i	−0.896131	−	1.50563i
$414$	6.00525	+	6.00525i	0.295142	+	0.295142i
$415$	4.14494	−	2.39308i	0.203467	−	0.117472i
$416$	−1.93258	+	3.04387i	−0.0947525	+	0.149238i
$417$	8.15390	−	14.1230i	0.399298	−	0.691604i
$418$	−0.362908	+	1.35439i	−0.0177504	+	0.0662454i
$419$		−	4.75756i		−	0.232422i	−0.993225	−	0.116211i	$-0.962925\pi$
$419$		−	4.75756i		−	0.232422i	0.993225	−	0.116211i	$-0.0370749\pi$
$420$	4.70322	−	2.79930i	0.229494	−	0.136592i
$421$	8.93076	−	8.93076i	0.435258	−	0.435258i	−0.455154	−	0.890413i	$-0.650416\pi$
$421$	8.93076	−	8.93076i	0.435258	−	0.435258i	0.890413	+	0.455154i	$0.150416\pi$
$422$	−26.1240	−	6.99991i	−1.27170	−	0.340751i
$423$	0.482703	+	1.80147i	0.0234698	+	0.0875906i
$424$	5.22136	−	1.39906i	0.253572	−	0.0679444i
$425$	−1.55749	+	0.899218i	−0.0755495	+	0.0436185i
$426$	−6.38258			−0.309237
$427$	−17.5484	+	18.0206i	−0.849227	+	0.872080i
$428$		−	0.758975i		−	0.0366864i
$429$	−3.16682	−	6.06062i	−0.152896	−	0.292610i
$430$	18.7372	+	10.8180i	0.903590	+	0.521688i
$431$	−1.55805	−	5.81472i	−0.0750485	−	0.280085i	0.918196	−	0.396127i	$-0.129646\pi$
$431$	−1.55805	−	5.81472i	−0.0750485	−	0.280085i	−0.993244	+	0.116042i	$0.962979\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−28.5687			−1.37292			−0.686462	−	0.727166i	$-0.740837\pi$
$433$	−28.5687			−1.37292			−0.686462	+	0.727166i	$0.740837\pi$
$434$	−19.0664	+	5.38109i	−0.915214	+	0.258300i
$435$	11.8558	−	11.8558i	0.568441	−	0.568441i
$436$	3.87584	−	14.4648i	0.185619	−	0.692740i
$437$	−1.62509	−	6.06491i	−0.0777385	−	0.290124i
$438$	−0.359224	+	0.622195i	−0.0171644	+	0.0297296i
$439$	−1.21420	−	2.10306i	−0.0579508	−	0.100374i	0.835595	−	0.549347i	$-0.185123\pi$
$439$	−1.21420	−	2.10306i	−0.0579508	−	0.100374i	−0.893545	+	0.448973i	$0.851790\pi$
$440$	2.77425	−	2.77425i	0.132257	−	0.132257i
$441$	6.15296	+	3.33783i	0.292998	+	0.158944i
$442$	−8.99166	−	0.378722i	−0.427690	−	0.0180140i
$443$	10.2364	+	17.7300i	0.486347	+	0.842377i	0.999877	−	0.0156943i	$-0.00499587\pi$
$443$	10.2364	+	17.7300i	0.486347	+	0.842377i	−0.513530	+	0.858072i	$0.671663\pi$
$444$	−2.96249	+	0.793796i	−0.140593	+	0.0376719i
$445$	3.46959	−	6.00950i	0.164474	−	0.284878i
$446$	8.83478	+	15.3023i	0.418339	+	0.724585i
$447$	7.78401	+	7.78401i	0.368171	+	0.368171i
$448$	−0.718636	−	2.54628i	−0.0339524	−	0.120301i
$449$	23.9396	+	23.9396i	1.12978	+	1.12978i	0.990213	+	0.139567i	$0.0445712\pi$
$449$	23.9396	+	23.9396i	1.12978	+	1.12978i	0.139567	+	0.990213i	$0.455429\pi$
$450$	−0.186483	+	0.695963i	−0.00879087	+	0.0328080i
$451$	2.08086	+	1.20138i	0.0979838	+	0.0565710i
$452$	−9.87134	−	5.69922i	−0.464309	−	0.268069i
$453$	20.2695	+	5.43118i	0.952342	+	0.255179i
$454$	−18.9530			−0.889509
$455$	14.3504	−	13.5462i	0.672756	−	0.635056i
$456$	0.739324			0.0346220
$457$	18.3636	+	4.92051i	0.859013	+	0.230172i	0.661331	−	0.750094i	$-0.269992\pi$
$457$	18.3636	+	4.92051i	0.859013	+	0.230172i	0.197682	+	0.980266i	$0.436659\pi$
$458$	−7.39554	−	4.26982i	−0.345571	−	0.199515i
$459$	−2.16164	−	1.24802i	−0.100897	−	0.0582528i
$460$	−4.54714	+	16.9701i	−0.212011	+	0.791237i
$461$	2.30429	+	2.30429i	0.107321	+	0.107321i	0.758728	−	0.651407i	$-0.225821\pi$
$461$	2.30429	+	2.30429i	0.107321	+	0.107321i	−0.651407	+	0.758728i	$0.725821\pi$
$462$	4.86365	+	1.23425i	0.226277	+	0.0574225i
$463$	−10.7497	−	10.7497i	−0.499583	−	0.499583i	0.411725	−	0.911308i	$-0.364926\pi$
$463$	−10.7497	−	10.7497i	−0.499583	−	0.499583i	−0.911308	+	0.411725i	$0.864926\pi$
$464$	−4.05246	−	7.01907i	−0.188131	−	0.325852i
$465$	−7.74509	+	13.4149i	−0.359170	+	0.622101i
$466$	12.4206	−	3.32809i	0.575373	−	0.154171i
$467$	−3.84255	−	6.65549i	−0.177812	−	0.307979i	0.763319	−	0.646022i	$-0.223569\pi$
$467$	−3.84255	−	6.65549i	−0.177812	−	0.307979i	−0.941131	+	0.338043i	$0.890235\pi$
$468$	−2.65454	+	2.43996i	−0.122706	+	0.112787i
$469$	12.0617	+	20.2653i	0.556957	+	0.935766i
$470$	−2.72813	+	2.72813i	−0.125839	+	0.125839i
$471$	7.24646	+	12.5512i	0.333899	+	0.578331i
$472$	−6.72918	+	11.6553i	−0.309736	+	0.536478i
$473$	5.13382	+	19.1597i	0.236053	+	0.880963i
$474$	−2.49543	+	9.31308i	−0.114619	+	0.427764i
$475$	0.376671	−	0.376671i	0.0172828	−	0.0172828i
$476$	4.60728	−	4.73126i	0.211174	−	0.216857i
$477$	5.40555			0.247503
$478$	13.6751	−	7.89530i	0.625483	−	0.361123i
$479$	−5.11748	−	19.0987i	−0.233824	−	0.872642i	−0.978676	−	0.205412i	$-0.934147\pi$
$479$	−5.11748	−	19.0987i	−0.233824	−	0.872642i	0.744852	−	0.667230i	$-0.232520\pi$
$480$	−1.79154	−	1.03435i	−0.0817722	−	0.0472112i
$481$	−9.80087	+	5.12120i	−0.446881	+	0.233506i
$482$			3.19871i			0.145697i
$483$	−21.6248	+	6.10316i	−0.983964	+	0.277703i
$484$	−7.40308			−0.336504
$485$	−2.75668	+	1.59157i	−0.125175	+	0.0722696i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	−6.67597	−	24.9150i	−0.302517	−	1.12901i	−0.935062	−	0.354485i	$-0.884656\pi$
$487$	−6.67597	−	24.9150i	−0.302517	−	1.12901i	0.632545	−	0.774524i	$-0.282010\pi$
$488$	9.18312	+	2.46061i	0.415700	+	0.111387i
$489$	11.8458	−	11.8458i	0.535687	−	0.535687i
$490$	0.384433	+	14.4757i	0.0173669	+	0.653947i
$491$		−	31.8912i		−	1.43923i	−0.694372	−	0.719616i	$-0.744318\pi$
$491$		−	31.8912i		−	1.43923i	0.694372	−	0.719616i	$-0.255682\pi$
$492$	0.327901	−	1.22374i	0.0147829	−	0.0551706i
$493$	10.1151	−	17.5199i	0.455563	−	0.789058i
$494$	2.60159	−	0.580961i	0.117051	−	0.0261387i
$495$	3.39775	−	1.96169i	0.152718	−	0.0881716i
$496$	5.29475	+	5.29475i	0.237742	+	0.237742i
$497$	8.24848	−	14.7351i	0.369995	−	0.660961i
$498$		−	2.31362i		−	0.103676i
$499$	13.1317	+	3.51862i	0.587854	+	0.157515i	0.540472	−	0.841362i	$-0.318246\pi$
$499$	13.1317	+	3.51862i	0.587854	+	0.157515i	0.0473819	+	0.998877i	$0.484912\pi$
$500$	−11.4307	+	3.06286i	−0.511199	+	0.136975i
$501$	−17.2495	+	4.62198i	−0.770650	+	0.206495i
$502$	−10.7065	−	2.86880i	−0.477855	−	0.128041i
$503$		−	43.5652i		−	1.94248i	−0.238106	−	0.971239i	$-0.576527\pi$
$503$		−	43.5652i		−	1.94248i	0.238106	−	0.971239i	$-0.423473\pi$
$504$	−0.0351224	−	2.64552i	−0.00156447	−	0.117841i
$505$	6.13484	+	6.13484i	0.272997	+	0.272997i
$506$	−13.9490	+	8.05343i	−0.620107	+	0.358019i
$507$	−7.42368	+	10.6719i	−0.329697	+	0.473955i
$508$	5.21956	−	9.04054i	0.231580	−	0.401109i
$509$	9.25062	−	34.5238i	0.410026	−	1.53024i	−0.384567	−	0.923097i	$-0.625649\pi$
$509$	9.25062	−	34.5238i	0.410026	−	1.53024i	0.794593	−	0.607142i	$-0.207684\pi$
$510$		−	5.16356i		−	0.228646i
$511$	−0.972188	−	1.63341i	−0.0430070	−	0.0722579i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.714132	+	0.191351i	0.0315297	+	0.00844836i
$514$	1.67500	+	6.25118i	0.0738811	+	0.275728i
$515$	−11.2317	+	3.00951i	−0.494926	+	0.132615i
$516$	9.05753	−	5.22937i	0.398736	−	0.230210i
$517$	−3.53712			−0.155562
$518$	1.99595	−	7.86519i	0.0876971	−	0.345577i
$519$		−	4.90072i		−	0.215118i
$520$	−7.11700	−	2.23195i	−0.312101	−	0.0978774i
$521$	−23.9727	−	13.8407i	−1.05026	−	0.606371i	−0.127541	−	0.991833i	$-0.540709\pi$
$521$	−23.9727	−	13.8407i	−1.05026	−	0.606371i	−0.922723	+	0.385463i	$0.874042\pi$
$522$	−2.09771	−	7.82875i	−0.0918142	−	0.342655i
$523$	−3.26644	+	1.88588i	−0.142831	+	0.0824638i	−0.569713	−	0.821844i	$-0.692946\pi$
$523$	−3.26644	+	1.88588i	−0.142831	+	0.0824638i	0.426881	+	0.904308i	$0.359612\pi$
$524$	18.8495			0.823446
$525$	−1.36573	−	1.32994i	−0.0596055	−	0.0580435i
$526$	−2.66717	+	2.66717i	−0.116294	+	0.116294i
$527$	−4.83738	+	18.0533i	−0.210720	+	0.786416i
$528$	−0.490864	−	1.83193i	−0.0213621	−	0.0797246i
$529$	24.5630	−	42.5443i	1.06796	−	1.84975i
$530$	5.59121	+	9.68427i	0.242867	+	0.420658i
$531$	−9.51650	+	9.51650i	−0.412981	+	0.412981i
$532$	−0.955459	+	1.70684i	−0.0414244	+	0.0740008i
$533$	0.192227	−	4.56387i	0.00832626	−	0.197683i
$534$	−1.67719	−	2.90498i	−0.0725791	−	0.125711i
$535$	1.51659	−	0.406368i	0.0655677	−	0.0175688i
$536$	4.45681	−	7.71942i	0.192505	−	0.333428i
$537$	−4.09501	−	7.09276i	−0.176713	−	0.306075i
$538$	−13.9616	−	13.9616i	−0.601929	−	0.601929i
$539$	−9.13494	+	9.63337i	−0.393470	+	0.414939i
$540$	−1.46279	−	1.46279i	−0.0629483	−	0.0629483i
$541$	−1.83777	+	6.85865i	−0.0790119	+	0.294876i	−0.994113	−	0.108348i	$-0.965444\pi$
$541$	−1.83777	+	6.85865i	−0.0790119	+	0.294876i	0.915101	+	0.403224i	$0.132111\pi$
$542$	17.7210	+	10.2312i	0.761180	+	0.439468i
$543$	4.29637	+	2.48051i	0.184375	+	0.106449i
$544$	−2.41100	−	0.646025i	−0.103371	−	0.0276981i
$545$	30.9789			1.32699
$546$	−2.20244	−	9.28166i	−0.0942557	−	0.397218i
$547$	25.4103			1.08646			0.543232	−	0.839582i	$-0.317200\pi$
$547$	25.4103			1.08646			0.543232	+	0.839582i	$0.317200\pi$
$548$	−16.1564	−	4.32908i	−0.690165	−	0.184929i
$549$	8.23336	+	4.75353i	0.351391	+	0.202876i
$550$	−1.18342	−	0.683246i	−0.0504611	−	0.0291337i
$551$	−1.55089	+	5.78798i	−0.0660699	+	0.246576i
$552$	6.00525	+	6.00525i	0.255600	+	0.255600i
$553$	−18.2757	−	17.7968i	−0.777160	−	0.756795i
$554$	7.37679	+	7.37679i	0.313410	+	0.313410i
$555$	−3.17233	−	5.49464i	−0.134658	−	0.233234i
$556$	8.15390	−	14.1230i	0.345802	−	0.598947i
$557$	−6.39319	+	1.71305i	−0.270888	+	0.0725843i	−0.391706	−	0.920090i	$-0.628115\pi$
$557$	−6.39319	+	1.71305i	−0.270888	+	0.0725843i	0.120818	+	0.992675i	$0.461448\pi$
$558$	3.74396	+	6.48472i	0.158494	+	0.274520i
$559$	27.7631	−	25.5189i	1.17426	−	1.07934i
$560$	4.70322	−	2.79930i	0.198747	−	0.118292i
$561$	3.34737	−	3.34737i	0.141326	−	0.141326i
$562$	−8.27074	−	14.3253i	−0.348880	−	0.604278i
$563$	17.5835	−	30.4555i	0.741057	−	1.28355i	−0.210958	−	0.977495i	$-0.567658\pi$
$563$	17.5835	−	30.4555i	0.741057	−	1.28355i	0.952015	−	0.306053i	$-0.0990084\pi$
$564$	0.482703	+	1.80147i	0.0203255	+	0.0758557i
$565$	6.10292	−	22.7764i	0.256752	−	0.958211i
$566$	−14.0573	+	14.0573i	−0.590874	+	0.590874i
$567$	0.650785	−	2.56446i	0.0273304	−	0.107697i
$568$	−6.38258			−0.267807
$569$	26.3141	−	15.1925i	1.10315	−	0.636902i	0.166101	−	0.986109i	$-0.446882\pi$
$569$	26.3141	−	15.1925i	1.10315	−	0.636902i	0.937046	+	0.349207i	$0.113549\pi$
$570$	0.395846	+	1.47732i	0.0165802	+	0.0618781i
$571$	−5.27769	−	3.04708i	−0.220864	−	0.127516i	0.385486	−	0.922714i	$-0.374034\pi$
$571$	−5.27769	−	3.04708i	−0.220864	−	0.127516i	−0.606350	+	0.795198i	$0.707367\pi$
$572$	−3.16682	−	6.06062i	−0.132412	−	0.253407i
$573$			11.9765i			0.500326i
$574$	2.40143	+	2.33850i	0.100234	+	0.0976072i
$575$	6.11911			0.255184
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	10.7161	−	2.87138i	0.446118	−	0.119537i	−0.0287645	−	0.999586i	$-0.509157\pi$
$577$	10.7161	−	2.87138i	0.446118	−	0.119537i	0.474882	+	0.880049i	$0.342491\pi$
$578$	2.78741	+	10.4028i	0.115941	+	0.432698i
$579$	−12.8306	−	3.43795i	−0.533222	−	0.142876i
$580$	11.8558	−	11.8558i	0.492284	−	0.492284i
$581$	5.34132	+	2.98998i	0.221595	+	0.124045i
$582$			1.53872i			0.0637821i
$583$	−2.65339	+	9.90260i	−0.109892	+	0.410124i
$584$	−0.359224	+	0.622195i	−0.0148648	+	0.0257466i
$585$	−6.29683	−	3.99791i	−0.260342	−	0.165293i
$586$	−11.7414	+	6.77887i	−0.485031	+	0.280033i
$587$	−21.2423	−	21.2423i	−0.876762	−	0.876762i	0.116436	−	0.993198i	$-0.462853\pi$
$587$	−21.2423	−	21.2423i	−0.876762	−	0.876762i	−0.993198	+	0.116436i	$0.962853\pi$
$588$	6.15296	+	3.33783i	0.253744	+	0.137650i
$589$		−	5.53599i		−	0.228107i
$590$	−26.8925	−	7.20584i	−1.10715	−	0.296660i
$591$	−10.0309	+	2.68776i	−0.412615	+	0.110560i
$592$	−2.96249	+	0.793796i	−0.121757	+	0.0326248i
$593$	−7.88502	−	2.11279i	−0.323799	−	0.0867617i	0.0932580	−	0.995642i	$-0.470272\pi$
$593$	−7.88502	−	2.11279i	−0.323799	−	0.0867617i	−0.417057	+	0.908880i	$0.636939\pi$
$594$		−	1.89655i		−	0.0778166i
$595$	11.9208	+	6.67308i	0.488706	+	0.273570i
$596$	7.78401	+	7.78401i	0.318845	+	0.318845i
$597$	1.35386	−	0.781653i	0.0554099	−	0.0319909i
$598$	25.8507	+	16.4128i	1.05711	+	0.671170i
$599$	−3.39696	+	5.88370i	−0.138796	+	0.240401i	−0.927041	−	0.374960i	$-0.877657\pi$
$599$	−3.39696	+	5.88370i	−0.138796	+	0.240401i	0.788245	+	0.615361i	$0.210990\pi$
$600$	−0.186483	+	0.695963i	−0.00761312	+	0.0284126i
$601$		−	27.2049i		−	1.10971i	−0.831947	−	0.554856i	$-0.812773\pi$
$601$		−	27.2049i		−	1.10971i	0.831947	−	0.554856i	$-0.187227\pi$
$602$	0.367336	+	27.6688i	0.0149715	+	1.12770i
$603$	6.30288	−	6.30288i	0.256673	−	0.256673i
$604$	20.2695	+	5.43118i	0.824752	+	0.220992i
$605$	−3.96374	−	14.7929i	−0.161149	−	0.601415i
$606$	4.05104	−	1.08547i	0.164562	−	0.0440943i
$607$	−18.9113	+	10.9185i	−0.767588	+	0.443167i	−0.832013	−	0.554755i	$-0.812812\pi$
$607$	−18.9113	+	10.9185i	−0.767588	+	0.443167i	0.0644256	+	0.997923i	$0.479478\pi$
$608$	0.739324			0.0299835
$609$	20.7848	+	5.27456i	0.842242	+	0.213736i
$610$			19.6672i			0.796302i
$611$	3.11417	+	5.95986i	0.125986	+	0.241110i
$612$	−2.16164	−	1.24802i	−0.0873792	−	0.0504484i
$613$	−6.58005	−	24.5571i	−0.265766	−	0.991851i	−0.961780	−	0.273823i	$-0.911712\pi$
$613$	−6.58005	−	24.5571i	−0.265766	−	0.991851i	0.696014	−	0.718028i	$-0.254955\pi$
$614$	−26.3070	+	15.1884i	−1.06166	+	0.612952i
$615$	2.62085			0.105683
$616$	4.86365	+	1.23425i	0.195962	+	0.0497293i
$617$	15.2184	−	15.2184i	0.612670	−	0.612670i	−0.330971	−	0.943641i	$-0.607376\pi$
$617$	15.2184	−	15.2184i	0.612670	−	0.612670i	0.943641	+	0.330971i	$0.107376\pi$
$618$	−1.45479	+	5.42935i	−0.0585203	+	0.218401i
$619$	−9.86290	−	36.8088i	−0.396423	−	1.47947i	−0.819342	−	0.573305i	$-0.805661\pi$
$619$	−9.86290	−	36.8088i	−0.396423	−	1.47947i	0.422919	−	0.906168i	$-0.361006\pi$
$620$	−7.74509	+	13.4149i	−0.311050	+	0.538755i
$621$	4.24635	+	7.35489i	0.170400	+	0.295142i
$622$	0.383074	−	0.383074i	0.0153599	−	0.0153599i
$623$	8.87407	−	0.117814i	0.355532	−	0.00472011i
$624$	−2.65454	+	2.43996i	−0.106267	+	0.0976767i
$625$	−10.4391	−	18.0811i	−0.417566	−	0.723245i
$626$	−15.1454	+	4.05820i	−0.605333	+	0.162198i
$627$	−0.701084	+	1.21431i	−0.0279986	+	0.0484950i
$628$	7.24646	+	12.5512i	0.289165	+	0.500849i
$629$	−5.41316	−	5.41316i	−0.215837	−	0.215837i
$630$	5.26748	−	1.48664i	0.209861	−	0.0592290i
$631$	−15.3622	−	15.3622i	−0.611561	−	0.611561i	0.331792	−	0.943353i	$-0.392347\pi$
$631$	−15.3622	−	15.3622i	−0.611561	−	0.611561i	−0.943353	+	0.331792i	$0.892347\pi$
$632$	−2.49543	+	9.31308i	−0.0992630	+	0.370454i
$633$	−23.4222	−	13.5228i	−0.930948	−	0.537483i
$634$	0.991566	+	0.572481i	0.0393801	+	0.0227361i
$635$	20.8595	+	5.58928i	0.827783	+	0.221804i
$636$	5.40555			0.214344
$637$	24.2744	+	6.91043i	0.961786	+	0.273801i
$638$	15.3714			0.608561
$639$	−6.16510	−	1.65193i	−0.243887	−	0.0653495i
$640$	−1.79154	−	1.03435i	−0.0708168	−	0.0408861i
$641$	−14.5601	−	8.40626i	−0.575088	−	0.332027i	0.184091	−	0.982909i	$-0.441066\pi$
$641$	−14.5601	−	8.40626i	−0.575088	−	0.332027i	−0.759179	+	0.650882i	$0.774399\pi$
$642$	0.196437	−	0.733114i	0.00775276	−	0.0289337i
$643$	−19.0614	−	19.0614i	−0.751709	−	0.751709i	0.223089	−	0.974798i	$-0.428386\pi$
$643$	−19.0614	−	19.0614i	−0.751709	−	0.751709i	−0.974798	+	0.223089i	$0.928386\pi$
$644$	−21.6248	+	6.10316i	−0.852138	+	0.240498i
$645$	15.2989	+	15.2989i	0.602393	+	0.602393i
$646$	0.922694	+	1.59815i	0.0363029	+	0.0628785i
$647$	5.26682	−	9.12241i	0.207060	−	0.358639i	−0.743727	−	0.668483i	$-0.766944\pi$
$647$	5.26682	−	9.12241i	0.207060	−	0.358639i	0.950787	+	0.309845i	$0.100277\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−12.7623	−	22.1049i	−0.500962	−	0.867692i
$650$	−0.109322	+	2.59555i	−0.00428798	+	0.101806i
$651$	−19.8094	+	0.262993i	−0.776392	+	0.0103075i
$652$	11.8458	−	11.8458i	0.463919	−	0.463919i
$653$	20.6492	+	35.7655i	0.808066	+	1.39961i	0.914202	+	0.405259i	$0.132819\pi$
$653$	20.6492	+	35.7655i	0.808066	+	1.39961i	−0.106136	+	0.994352i	$0.533848\pi$
$654$	7.48755	−	12.9688i	0.292786	−	0.507121i
$655$	10.0924	+	37.6652i	0.394341	+	1.47170i
$656$	0.327901	−	1.22374i	0.0128024	−	0.0477791i
$657$	−0.508020	+	0.508020i	−0.0198197	+	0.0198197i
$658$	−4.78278	−	1.21373i	−0.186452	−	0.0473160i
$659$	4.37942			0.170598			0.0852990	−	0.996355i	$-0.472815\pi$
$659$	4.37942			0.170598			0.0852990	+	0.996355i	$0.472815\pi$
$660$	3.39775	−	1.96169i	0.132257	−	0.0763588i
$661$	7.04959	+	26.3094i	0.274197	+	1.02332i	0.956377	+	0.292134i	$0.0943654\pi$
$661$	7.04959	+	26.3094i	0.274197	+	1.02332i	−0.682180	+	0.731184i	$0.738968\pi$
$662$	−13.8839	−	8.01590i	−0.539615	−	0.311547i
$663$	−8.58726	−	2.69303i	−0.333501	−	0.104589i
$664$		−	2.31362i		−	0.0897857i
$665$	−3.92218	−	0.995332i	−0.152096	−	0.0385973i
$666$	−3.06699			−0.118844
$667$	−59.6108	+	34.4163i	−2.30814	+	1.33261i
$668$	−17.2495	+	4.62198i	−0.667402	+	0.178830i
$669$	4.57322	+	17.0675i	0.176811	+	0.659867i
$670$	17.8112	+	4.77250i	0.688108	+	0.184378i
$671$	−12.7496	+	12.7496i	−0.492193	+	0.492193i
$672$	−0.0351224	−	2.64552i	−0.00135487	−	0.102053i
$673$			16.9296i			0.652587i	0.945268	+	0.326294i	$0.105800\pi$
$673$			16.9296i			0.652587i	−0.945268	+	0.326294i	$0.894200\pi$
$674$	−2.71212	+	10.1218i	−0.104467	+	0.389876i
$675$	−0.360257	+	0.623983i	−0.0138663	+	0.0240171i
$676$	−7.42368	+	10.6719i	−0.285526	+	0.410457i
$677$	−38.3011	+	22.1132i	−1.47203	+	0.849878i	−0.999506	−	0.0314383i	$-0.989991\pi$
$677$	−38.3011	+	22.1132i	−1.47203	+	0.849878i	−0.472527	+	0.881316i	$0.656658\pi$
$678$	−8.05992	−	8.05992i	−0.309539	−	0.309539i
$679$	−3.55237	−	1.98856i	−0.136327	−	0.0763138i
$680$		−	5.16356i		−	0.198013i
$681$	−18.3072	−	4.90540i	−0.701534	−	0.187975i
$682$	−13.7173	+	3.67555i	−0.525264	+	0.140744i
$683$	−1.37310	+	0.367922i	−0.0525403	+	0.0140781i	−0.284993	−	0.958529i	$-0.591991\pi$
$683$	−1.37310	+	0.367922i	−0.0525403	+	0.0140781i	0.232453	+	0.972608i	$0.425325\pi$
$684$	0.714132	+	0.191351i	0.0273055	+	0.00731649i
$685$		−	34.6015i		−	1.32206i
$686$	−15.6576	+	9.89139i	−0.597810	+	0.377655i
$687$	−6.03843	−	6.03843i	−0.230381	−	0.230381i
$688$	9.05753	−	5.22937i	0.345315	−	0.199368i
$689$	19.0215	−	4.24769i	0.724661	−	0.161824i
$690$	−8.78439	+	15.2150i	−0.334416	+	0.579226i
$691$	−9.44939	+	35.2656i	−0.359472	+	1.34157i	0.515291	+	0.857015i	$0.327684\pi$
$691$	−9.44939	+	35.2656i	−0.359472	+	1.34157i	−0.874763	+	0.484551i	$0.838983\pi$
$692$		−	4.90072i		−	0.186297i
$693$	4.37847	+	2.45100i	0.166324	+	0.0931057i
$694$	16.9696	−	16.9696i	0.644158	−	0.644158i
$695$	32.5863	+	8.73147i	1.23607	+	0.331203i
$696$	−2.09771	−	7.82875i	−0.0795134	−	0.296748i
$697$	3.05452	−	0.818457i	0.115698	−	0.0310013i
$698$	7.47196	−	4.31394i	0.282818	−	0.163285i
$699$	12.8588			0.486363
$700$	−1.36573	−	1.32994i	−0.0516198	−	0.0502672i
$701$			32.9830i			1.24575i	0.782321	+	0.622876i	$0.214036\pi$
$701$			32.9830i			1.24575i	−0.782321	+	0.622876i	$0.785964\pi$
$702$	−3.19560	+	1.66978i	−0.120610	+	0.0630217i
$703$	1.96371	+	1.13375i	0.0740628	+	0.0427602i
$704$	−0.490864	−	1.83193i	−0.0185001	−	0.0690435i
$705$	−3.34126	+	1.92908i	−0.125839	+	0.0726533i
$706$	33.8416			1.27365
$707$	−2.72935	+	10.7552i	−0.102648	+	0.404491i
$708$	−9.51650	+	9.51650i	−0.357652	+	0.357652i
$709$	8.04771	−	30.0344i	0.302238	−	1.12797i	−0.633059	−	0.774104i	$-0.718201\pi$
$709$	8.04771	−	30.0344i	0.302238	−	1.12797i	0.935297	−	0.353864i	$-0.115132\pi$
$710$	−3.41734	−	12.7537i	−0.128250	−	0.478637i
$711$	−4.82081	+	8.34988i	−0.180794	+	0.313145i
$712$	−1.67719	−	2.90498i	−0.0628553	−	0.108869i
$713$	44.9668	−	44.9668i	1.68402	−	1.68402i
$714$	5.67483	−	3.37759i	0.212375	−	0.126403i
$715$	10.4148	−	9.57292i	0.389491	−	0.358007i
$716$	−4.09501	−	7.09276i	−0.153038	−	0.265069i
$717$	15.2526	−	4.08691i	0.569617	−	0.152628i
$718$	16.0665	−	27.8280i	0.599597	−	1.03853i
$719$	8.59059	+	14.8793i	0.320375	+	0.554906i	0.980565	−	0.196192i	$-0.0628577\pi$
$719$	8.59059	+	14.8793i	0.320375	+	0.554906i	−0.660190	+	0.751098i	$0.729524\pi$
$720$	−1.46279	−	1.46279i	−0.0545148	−	0.0545148i
$721$	−10.6544	−	10.3752i	−0.396790	−	0.386392i
$722$	13.0485	+	13.0485i	0.485616	+	0.485616i
$723$	−0.827886	+	3.08971i	−0.0307894	+	0.114908i
$724$	4.29637	+	2.48051i	0.159673	+	0.0921875i
$725$	−5.05733	−	2.91985i	−0.187825	−	0.108441i
$726$	−7.15083	−	1.91606i	−0.265392	−	0.0711116i
$727$	−43.0733			−1.59750			−0.798751	−	0.601662i	$-0.794505\pi$
$727$	−43.0733			−1.59750			−0.798751	+	0.601662i	$0.794505\pi$
$728$	−2.20244	−	9.28166i	−0.0816279	−	0.344001i
$729$	−1.00000			−0.0370370
$730$	−1.43561	−	0.384670i	−0.0531342	−	0.0142373i
$731$	22.6080	+	13.0528i	0.836189	+	0.482774i
$732$	8.23336	+	4.75353i	0.304314	+	0.175696i
$733$	−1.86110	+	6.94573i	−0.0687414	+	0.256547i	−0.991741	−	0.128253i	$-0.959063\pi$
$733$	−1.86110	+	6.94573i	−0.0687414	+	0.256547i	0.923000	+	0.384800i	$0.125730\pi$
$734$	9.61079	+	9.61079i	0.354741	+	0.354741i
$735$	−3.37526	+	14.0820i	−0.124498	+	0.519422i
$736$	6.00525	+	6.00525i	0.221356	+	0.221356i
$737$	8.45258	+	14.6403i	0.311355	+	0.539282i
$738$	0.633456	−	1.09718i	0.0233178	−	0.0403877i
$739$	−36.8403	+	9.87132i	−1.35519	+	0.363122i	−0.862048	−	0.506826i	$-0.830819\pi$
$739$	−36.8403	+	9.87132i	−1.35519	+	0.363122i	−0.493143	+	0.869948i	$0.664152\pi$
$740$	−3.17233	−	5.49464i	−0.116617	−	0.201987i
$741$	2.66331	+	0.112177i	0.0978391	+	0.00412091i
$742$	−6.98583	+	12.4795i	−0.256458	+	0.458137i
$743$	−17.3632	+	17.3632i	−0.636994	+	0.636994i	−0.949813	−	0.312819i	$-0.898727\pi$
$743$	−17.3632	+	17.3632i	−0.636994	+	0.636994i	0.312819	+	0.949813i	$0.398727\pi$
$744$	3.74396	+	6.48472i	0.137260	+	0.237742i
$745$	−11.3863	+	19.7217i	−0.417163	+	0.722548i
$746$	−7.28981	−	27.2059i	−0.266899	−	0.996080i
$747$	0.598808	−	2.23478i	0.0219092	−	0.0817664i
$748$	3.34737	−	3.34737i	0.122392	−	0.122392i
$749$	1.43864	+	1.40094i	0.0525666	+	0.0511891i
$750$	−11.8340			−0.432116
$751$	23.5978	−	13.6242i	0.861097	−	0.497155i	−0.00328238	−	0.999995i	$-0.501045\pi$
$751$	23.5978	−	13.6242i	0.861097	−	0.497155i	0.864380	+	0.502840i	$0.167711\pi$
$752$	0.482703	+	1.80147i	0.0176024	+	0.0656930i
$753$	−9.59919	−	5.54210i	−0.349814	−	0.201965i
$754$	−13.5334	−	25.9001i	−0.492858	−	0.943225i
$755$			43.4104i			1.57987i
$756$	0.650785	−	2.56446i	0.0236688	−	0.0932687i
$757$	11.8716			0.431482			0.215741	−	0.976451i	$-0.430783\pi$
$757$	11.8716			0.431482			0.215741	+	0.976451i	$0.430783\pi$
$758$	8.43777	−	4.87155i	0.306474	−	0.176943i
$759$	−15.5580	+	4.16876i	−0.564721	+	0.151317i
$760$	0.395846	+	1.47732i	0.0143589	+	0.0535880i
$761$	−15.5216	−	4.15900i	−0.562657	−	0.150764i	−0.0337304	−	0.999431i	$-0.510739\pi$
$761$	−15.5216	−	4.15900i	−0.562657	−	0.150764i	−0.528927	+	0.848667i	$0.677405\pi$
$762$	7.38157	−	7.38157i	0.267406	−	0.267406i
$763$	20.2639	+	34.0463i	0.733604	+	1.23256i
$764$			11.9765i			0.433295i
$765$	1.33643	−	4.98761i	0.0483186	−	0.180327i
$766$	8.72883	−	15.1188i	0.315385	−	0.546263i
$767$	−26.0094	+	40.9655i	−0.939144	+	1.47918i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	23.9532	+	23.9532i	0.863776	+	0.863776i	0.991774	−	0.127999i	$-0.0408553\pi$
$769$	23.9532	+	23.9532i	0.863776	+	0.863776i	−0.127999	+	0.991774i	$0.540855\pi$
$770$	0.137799	+	10.3794i	0.00496592	+	0.374047i
$771$			6.47170i			0.233073i
$772$	−12.8306	−	3.43795i	−0.461784	−	0.123735i
$773$	−28.9254	+	7.75055i	−1.04038	+	0.278768i	−0.738269	−	0.674506i	$-0.764357\pi$
$773$	−28.9254	+	7.75055i	−1.04038	+	0.278768i	−0.302107	+	0.953274i	$0.597690\pi$
$774$	10.1024	−	2.70692i	0.363122	−	0.0972983i
$775$	5.21131	+	1.39637i	0.187196	+	0.0501589i
$776$			1.53872i			0.0552369i
$777$	3.96360	−	7.08060i	0.142193	−	0.254015i
$778$	10.0278	+	10.0278i	0.359515	+	0.359515i
$779$	−0.811170	+	0.468329i	−0.0290632	+	0.0167796i
$780$	−6.29683	−	3.99791i	−0.225463	−	0.143148i
$781$	6.05245	−	10.4832i	0.216574	−	0.375117i
$782$	−5.48650	+	20.4759i	−0.196197	+	0.732216i
$783$		−	8.10492i		−	0.289646i
$784$	6.15296	+	3.33783i	0.219749	+	0.119208i
$785$	−21.2001	+	21.2001i	−0.756662	+	0.756662i
$786$	18.2073	+	4.87862i	0.649432	+	0.174015i
$787$	10.4680	+	39.0670i	0.373143	+	1.39259i	0.856039	+	0.516912i	$0.172918\pi$
$787$	10.4680	+	39.0670i	0.373143	+	1.39259i	−0.482895	+	0.875678i	$0.660415\pi$
$788$	−10.0309	+	2.68776i	−0.357335	+	0.0957477i
$789$	−3.26660	+	1.88597i	−0.116294	+	0.0671425i
$790$	−19.9455			−0.709630
$791$	29.0237	−	8.19133i	1.03196	−	0.291250i
$792$		−	1.89655i		−	0.0673911i
$793$	32.7075	+	10.2573i	1.16148	+	0.364249i
$794$	−12.1975	−	7.04223i	−0.432873	−	0.249920i
$795$	2.89422	+	10.8014i	0.102648	+	0.383086i
$796$	1.35386	−	0.781653i	0.0479864	−	0.0277049i
$797$	34.8869			1.23576			0.617878	−	0.786274i	$-0.287993\pi$
$797$	34.8869			1.23576			0.617878	+	0.786274i	$0.287993\pi$
$798$	−1.36466	+	1.40139i	−0.0483086	+	0.0496086i
$799$	−3.29171	+	3.29171i	−0.116452	+	0.116452i
$800$	−0.186483	+	0.695963i	−0.00659316	+	0.0246060i
$801$	−0.868177	−	3.24008i	−0.0306755	−	0.114483i
$802$	−13.4892	+	23.3640i	−0.476322	+	0.825013i
$803$	−0.681289	−	1.18003i	−0.0240422	−	0.0416422i
$804$	6.30288	−	6.30288i	0.222285	−	0.222285i
$805$	−23.7737	−	39.9431i	−0.837911	−	1.40781i
$806$	18.2702	+	19.8770i	0.643542	+	0.700136i
$807$	−9.87236	−	17.0994i	−0.347524	−	0.601929i
$808$	4.05104	−	1.08547i	0.142515	−	0.0381868i
$809$	−4.40858	+	7.63588i	−0.154997	+	0.268463i	−0.933058	−	0.359726i	$-0.882870\pi$
$809$	−4.40858	+	7.63588i	−0.154997	+	0.268463i	0.778061	+	0.628189i	$0.216204\pi$
$810$	−1.03435	−	1.79154i	−0.0363432	−	0.0629483i
$811$	19.6274	+	19.6274i	0.689212	+	0.689212i	0.962058	−	0.272846i	$-0.0879648\pi$
$811$	19.6274	+	19.6274i	0.689212	+	0.689212i	−0.272846	+	0.962058i	$0.587965\pi$
$812$	20.7848	+	5.27456i	0.729403	+	0.185101i
$813$	14.4691	+	14.4691i	0.507454	+	0.507454i
$814$	1.50548	−	5.61852i	0.0527670	−	0.196929i
$815$	30.0128	+	17.3279i	1.05130	+	0.606970i
$816$	−2.16164	−	1.24802i	−0.0756726	−	0.0436896i
$817$	−7.46892	−	2.00129i	−0.261304	−	0.0700163i
$818$	−24.9842			−0.873551
$819$	0.274877	−	9.53543i	0.00960499	−	0.333195i
$820$	2.62085			0.0915241
$821$	−35.4754	−	9.50562i	−1.23810	−	0.331748i	−0.420373	−	0.907352i	$-0.638101\pi$
$821$	−35.4754	−	9.50562i	−1.23810	−	0.331748i	−0.817729	+	0.575603i	$0.804767\pi$
$822$	−14.4854	−	8.36314i	−0.505236	−	0.291698i
$823$	−5.73445	−	3.31079i	−0.199890	−	0.115407i	0.396714	−	0.917942i	$-0.370150\pi$
$823$	−5.73445	−	3.31079i	−0.199890	−	0.115407i	−0.596604	+	0.802536i	$0.703484\pi$
$824$	−1.45479	+	5.42935i	−0.0506800	+	0.189141i
$825$	−0.966256	−	0.966256i	−0.0336407	−	0.0336407i
$826$	−9.67167	−	34.2688i	−0.336520	−	1.19236i
$827$	5.24742	+	5.24742i	0.182471	+	0.182471i	0.792432	−	0.609961i	$-0.208815\pi$
$827$	5.24742	+	5.24742i	0.182471	+	0.182471i	−0.609961	+	0.792432i	$0.708815\pi$
$828$	4.24635	+	7.35489i	0.147571	+	0.255600i
$829$	−6.94513	+	12.0293i	−0.241214	+	0.417795i	−0.961060	−	0.276338i	$-0.910879\pi$
$829$	−6.94513	+	12.0293i	−0.241214	+	0.417795i	0.719846	+	0.694134i	$0.244212\pi$
$830$	4.62308	−	1.23875i	0.160469	−	0.0429976i
$831$	5.21618	+	9.03468i	0.180947	+	0.313410i
$832$	−2.65454	+	2.43996i	−0.0920296	+	0.0845905i
$833$	0.463850	+	17.4662i	0.0160714	+	0.605167i
$834$	11.5313	−	11.5313i	0.399298	−	0.399298i
$835$	−18.4713	−	31.9933i	−0.639227	−	1.10717i
$836$	−0.701084	+	1.21431i	−0.0242475	+	0.0419979i
$837$	1.93801	+	7.23277i	0.0669876	+	0.250001i
$838$	1.23135	−	4.59545i	0.0425362	−	0.158747i
$839$	−0.975055	+	0.975055i	−0.0336626	+	0.0336626i	−0.723738	−	0.690075i	$-0.757577\pi$
$839$	−0.975055	+	0.975055i	−0.0336626	+	0.0336626i	0.690075	+	0.723738i	$0.257577\pi$
$840$	5.26748	−	1.48664i	0.181745	−	0.0512938i
$841$	36.6898			1.26516
$842$	10.9379	−	6.31500i	0.376945	−	0.217629i
$843$	−4.28125	−	15.9778i	−0.147454	−	0.550306i
$844$	−23.4222	−	13.5228i	−0.806224	−	0.465474i
$845$	−25.2993	−	9.12012i	−0.870324	−	0.313742i
$846$			1.86502i			0.0641208i
$847$	13.6648	−	14.0325i	0.469529	−	0.482164i
$848$	5.40555			0.185627
$849$	−17.2166	+	9.94003i	−0.590874	+	0.341141i
$850$	−1.73716	+	0.465470i	−0.0595840	+	0.0159655i
$851$	6.74147	+	25.1595i	0.231095	+	0.862457i
$852$	−6.16510	−	1.65193i	−0.211213	−	0.0565943i
$853$	2.36861	−	2.36861i	0.0810996	−	0.0810996i	−0.665393	−	0.746493i	$-0.731736\pi$
$853$	2.36861	−	2.36861i	0.0810996	−	0.0810996i	0.746493	+	0.665393i	$0.231736\pi$
$854$	−21.6146	+	12.8647i	−0.739635	+	0.440222i
$855$			1.52943i			0.0523055i
$856$	0.196437	−	0.733114i	0.00671408	−	0.0250573i
$857$	11.3833	−	19.7165i	0.388847	−	0.673503i	−0.603448	−	0.797403i	$-0.706207\pi$
$857$	11.3833	−	19.7165i	0.388847	−	0.673503i	0.992295	+	0.123900i	$0.0395401\pi$
$858$	−1.49031	−	6.67375i	−0.0508784	−	0.227838i
$859$	30.8712	−	17.8235i	1.05331	−	0.608130i	0.129737	−	0.991548i	$-0.458587\pi$
$859$	30.8712	−	17.8235i	1.05331	−	0.608130i	0.923575	+	0.383419i	$0.125253\pi$
$860$	15.2989	+	15.2989i	0.521688	+	0.521688i
$861$	1.71436	+	2.88036i	0.0584251	+	0.0981623i
$862$		−	6.01984i		−	0.205036i
$863$	20.7394	+	5.55709i	0.705976	+	0.189166i	0.593906	−	0.804535i	$-0.297585\pi$
$863$	20.7394	+	5.55709i	0.705976	+	0.189166i	0.112070	+	0.993700i	$0.464252\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	9.79263	−	2.62393i	0.332959	−	0.0892162i
$866$	−27.5952	−	7.39412i	−0.937724	−	0.251263i
$867$			10.7697i			0.365760i
$868$	−19.8094	+	0.262993i	−0.672375	+	0.00892657i
$869$	−12.9300	−	12.9300i	−0.438622	−	0.438622i
$870$	14.5203	−	8.38329i	0.492284	−	0.284220i
$871$	17.2263	−	27.1319i	0.583690	−	0.919329i
$872$	7.48755	−	12.9688i	0.253560	−	0.439179i
$873$	−0.398251	+	1.48629i	−0.0134787	+	0.0503034i
$874$		−	6.27886i		−	0.212385i
$875$	15.2936	−	27.3205i	0.517016	−	0.923601i
$876$	−0.508020	+	0.508020i	−0.0171644	+	0.0171644i
$877$	18.6936	+	5.00894i	0.631239	+	0.169140i	0.560232	−	0.828336i	$-0.310712\pi$
$877$	18.6936	+	5.00894i	0.631239	+	0.169140i	0.0710071	+	0.997476i	$0.477379\pi$
$878$	−0.628518	−	2.34566i	−0.0212114	−	0.0791622i
$879$	−13.0958	+	3.50900i	−0.441710	+	0.118356i
$880$	3.39775	−	1.96169i	0.114538	−	0.0661287i
$881$	0.495142			0.0166817			0.00834087	−	0.999965i	$-0.497345\pi$
$881$	0.495142			0.0166817			0.00834087	+	0.999965i	$0.497345\pi$
$882$	5.07941	+	4.81660i	0.171033	+	0.162183i
$883$			37.7485i			1.27034i	0.772374	+	0.635168i	$0.219069\pi$
$883$			37.7485i			1.27034i	−0.772374	+	0.635168i	$0.780931\pi$
$884$	−8.58726	−	2.69303i	−0.288821	−	0.0905764i
$885$	−24.1112	−	13.9206i	−0.810489	−	0.467936i
$886$	5.29876	+	19.7752i	0.178015	+	0.664362i
$887$	−42.2775	+	24.4089i	−1.41954	+	0.819572i	−0.996258	−	0.0864267i	$-0.972455\pi$
$887$	−42.2775	+	24.4089i	−1.41954	+	0.819572i	−0.423281	+	0.905998i	$0.639122\pi$
$888$	−3.06699			−0.102922
$889$	7.50193	+	26.5810i	0.251607	+	0.891497i
$890$	4.90674	−	4.90674i	0.164474	−	0.164474i
$891$	0.490864	−	1.83193i	0.0164446	−	0.0613720i
$892$	4.57322	+	17.0675i	0.153123	+	0.571462i
$893$	0.689428	−	1.19412i	0.0230708	−	0.0399598i
$894$	5.50412	+	9.53342i	0.184085	+	0.318845i
$895$	11.9802	−	11.9802i	0.400455	−	0.400455i
$896$	−0.0351224	−	2.64552i	−0.00117336	−	0.0883806i
$897$	20.7219	+	22.5442i	0.691883	+	0.752729i
$898$	16.9279	+	29.3199i	0.564890	+	0.978418i
$899$	−58.6210	+	15.7075i	−1.95512	+	0.523873i
$900$	−0.360257	+	0.623983i	−0.0120086	+	0.0207994i
$901$	6.74626	+	11.6849i	0.224751	+	0.389279i
$902$	1.69901	+	1.69901i	0.0565710	+	0.0565710i
$903$	−6.80639	+	26.8211i	−0.226502	+	0.892549i
$904$	−8.05992	−	8.05992i	−0.268069	−	0.268069i
$905$	−2.65621	+	9.91313i	−0.0882956	+	0.329524i
$906$	18.1731	+	10.4922i	0.603761	+	0.348581i
$907$	−2.78754	−	1.60939i	−0.0925589	−	0.0534389i	0.453006	−	0.891507i	$-0.350352\pi$
$907$	−2.78754	−	1.60939i	−0.0925589	−	0.0534389i	−0.545565	+	0.838069i	$0.683685\pi$
$908$	−18.3072	−	4.90540i	−0.607546	−	0.162791i
$909$	4.19394			0.139104
$910$	17.3674	−	9.37048i	0.575724	−	0.310628i
$911$	20.5603			0.681193			0.340597	−	0.940209i	$-0.389371\pi$
$911$	20.5603			0.681193			0.340597	+	0.940209i	$0.389371\pi$
$912$	0.714132	+	0.191351i	0.0236473	+	0.00633627i
$913$	3.80003	+	2.19395i	0.125763	+	0.0726091i
$914$	16.4644	+	9.50570i	0.544593	+	0.314421i
$915$	−5.09024	+	18.9971i	−0.168278	+	0.628023i
$916$	−6.03843	−	6.03843i	−0.199515	−	0.199515i
$917$	−34.7930	+	35.7293i	−1.14897	+	1.17989i
$918$	−1.76497	−	1.76497i	−0.0582528	−	0.0582528i
$919$	16.4951	+	28.5703i	0.544123	+	0.942448i	0.998662	+	0.0517211i	$0.0164707\pi$
$919$	16.4951	+	28.5703i	0.544123	+	0.942448i	−0.454539	+	0.890727i	$0.650196\pi$
$920$	−8.78439	+	15.2150i	−0.289613	+	0.501624i
$921$	−29.3417	+	7.86207i	−0.966840	+	0.259064i
$922$	1.62938	+	2.82216i	0.0536607	+	0.0929430i
$923$	−22.9923	−	0.968419i	−0.756802	−	0.0318759i
$924$	4.37847	+	2.45100i	0.144041	+	0.0806319i
$925$	−1.56257	+	1.56257i	−0.0513770	+	0.0513770i
$926$	−7.60122	−	13.1657i	−0.249792	−	0.432652i
$927$	−2.81044	+	4.86783i	−0.0923070	+	0.159880i
$928$	−2.09771	−	7.82875i	−0.0688606	−	0.256991i
$929$	−5.38769	+	20.1071i	−0.176764	+	0.659693i	0.819480	+	0.573108i	$0.194262\pi$
$929$	−5.38769	+	20.1071i	−0.176764	+	0.659693i	−0.996244	+	0.0865856i	$0.972404\pi$
$930$	−10.9532	+	10.9532i	−0.359170	+	0.359170i
$931$	−1.47170	−	4.96160i	−0.0482329	−	0.162610i
$932$	12.8588			0.421202
$933$	0.469167	−	0.270874i	0.0153599	−	0.00886801i
$934$	−1.98905	−	7.42323i	−0.0650837	−	0.242896i
$935$	8.48096	+	4.89648i	0.277357	+	0.160132i
$936$	−3.19560	+	1.66978i	−0.104451	+	0.0545784i
$937$		−	9.29800i		−	0.303753i	−0.988400	−	0.151876i	$-0.951468\pi$
$937$		−	9.29800i		−	0.303753i	0.988400	−	0.151876i	$-0.0485315\pi$
$938$	6.40565	+	22.6966i	0.209152	+	0.741071i
$939$	−15.6797			−0.511688
$940$	−3.34126	+	1.92908i	−0.108980	+	0.0629196i
$941$	−3.16829	+	0.848942i	−0.103283	+	0.0276747i	−0.310091	−	0.950707i	$-0.600359\pi$
$941$	−3.16829	+	0.848942i	−0.103283	+	0.0276747i	0.206807	+	0.978382i	$0.433693\pi$
$942$	3.75105	+	13.9991i	0.122216	+	0.456115i
$943$	−10.3929	−	2.78477i	−0.338439	−	0.0906844i
$944$	−9.51650	+	9.51650i	−0.309736	+	0.309736i
$945$	5.47276	−	0.0726574i	0.178029	−	0.00236354i
$946$			19.8356i			0.644910i
$947$	−7.27725	+	27.1591i	−0.236479	+	0.882551i	0.740998	+	0.671507i	$0.234353\pi$
$947$	−7.27725	+	27.1591i	−0.236479	+	0.882551i	−0.977477	+	0.211043i	$0.932314\pi$
$948$	−4.82081	+	8.34988i	−0.156572	+	0.271191i
$949$	−1.38846	+	2.18686i	−0.0450713	+	0.0709886i
$950$	0.461325	−	0.266346i	0.0149674	−	0.00864142i
$951$	0.809610	+	0.809610i	0.0262534	+	0.0262534i
$952$	5.67483	−	3.37759i	0.183922	−	0.109468i
$953$			0.810435i			0.0262526i	0.999914	+	0.0131263i	$0.00417835\pi$
$953$			0.810435i			0.0262526i	−0.999914	+	0.0131263i	$0.995822\pi$
$954$	5.22136	+	1.39906i	0.169048	+	0.0452963i
$955$	−23.9315	+	6.41243i	−0.774405	+	0.207501i
$956$	15.2526	−	4.08691i	0.493303	−	0.132180i
$957$	14.8477	+	3.97842i	0.479957	+	0.128604i
$958$		−	19.7724i		−	0.638818i
$959$	38.0276	−	22.6336i	1.22798	−	0.730877i
$960$	−1.46279	−	1.46279i	−0.0472112	−	0.0472112i
$961$	21.7103	−	12.5344i	0.700331	−	0.404336i
$962$	−10.7924	+	2.41004i	−0.347960	+	0.0777029i
$963$	0.379487	−	0.657292i	0.0122288	−	0.0211809i
$964$	−0.827886	+	3.08971i	−0.0266644	+	0.0995130i
$965$		−	27.4789i		−	0.884578i
$966$	−22.4676	+	0.298284i	−0.722883	+	0.00959712i
$967$	−0.150065	+	0.150065i	−0.00482576	+	0.00482576i	−0.709516	−	0.704690i	$-0.751086\pi$
$967$	−0.150065	+	0.150065i	−0.00482576	+	0.00482576i	0.704690	+	0.709516i	$0.251086\pi$
$968$	−7.15083	−	1.91606i	−0.229836	−	0.0615845i
$969$	0.477622	+	1.78251i	0.0153434	+	0.0572624i
$970$	−3.07468	+	0.823858i	−0.0987221	+	0.0264525i
$971$	−10.7495	+	6.20622i	−0.344968	+	0.199167i	−0.662467	−	0.749091i	$-0.730490\pi$
$971$	−10.7495	+	6.20622i	−0.344968	+	0.199167i	0.317499	+	0.948259i	$0.397157\pi$
$972$	−1.00000			−0.0320750
$973$	11.7194	+	41.5243i	0.375706	+	1.33121i
$974$		−	25.7940i		−	0.826492i
$975$	−0.777374	+	2.47881i	−0.0248959	+	0.0793855i
$976$	8.23336	+	4.75353i	0.263544	+	0.152157i
$977$	10.8285	+	40.4126i	0.346435	+	1.29291i	0.890927	+	0.454147i	$0.150056\pi$
$977$	10.8285	+	40.4126i	0.346435	+	1.29291i	−0.544491	+	0.838767i	$0.683277\pi$
$978$	14.5081	−	8.37627i	0.463919	−	0.267844i
$979$	6.36176			0.203323
$980$	−3.37526	+	14.0820i	−0.107819	+	0.449833i
$981$	10.5890	−	10.5890i	0.338081	−	0.338081i
$982$	8.25406	−	30.8046i	0.263398	−	0.983014i
$983$	4.27890	+	15.9691i	0.136476	+	0.509335i	0.999987	+	0.00500575i	$0.00159339\pi$
$983$	4.27890	+	15.9691i	0.136476	+	0.509335i	−0.863512	+	0.504329i	$0.831740\pi$
$984$	0.633456	−	1.09718i	0.0201938	−	0.0349768i
$985$	−10.7414	−	18.6046i	−0.342249	−	0.592793i
$986$	14.3050	−	14.3050i	0.455563	−	0.455563i
$987$	−4.30568	−	2.41025i	−0.137051	−	0.0767190i
$988$	2.66331	+	0.112177i	0.0847311	+	0.00356881i
$989$	−44.4115	−	76.9229i	−1.41220	−	2.44601i
$990$	3.78970	−	1.01545i	0.120445	−	0.0322730i
$991$	21.8253	−	37.8026i	0.693305	−	1.20084i	−0.277444	−	0.960742i	$-0.589487\pi$
$991$	21.8253	−	37.8026i	0.693305	−	1.20084i	0.970749	−	0.240097i	$-0.0771793\pi$
$992$	3.74396	+	6.48472i	0.118871	+	0.205890i
$993$	−11.3362	−	11.3362i	−0.359743	−	0.359743i
$994$	11.7811	−	12.0982i	0.373675	−	0.383731i
$995$	2.28678	+	2.28678i	0.0724958	+	0.0724958i
$996$	0.598808	−	2.23478i	0.0189740	−	0.0708118i
$997$	−14.0983	−	8.13966i	−0.446498	−	0.257786i	0.259852	−	0.965648i	$-0.416326\pi$
$997$	−14.0983	−	8.13966i	−0.446498	−	0.257786i	−0.706350	+	0.707863i	$0.749660\pi$
$998$	11.7735	+	6.79745i	0.372685	+	0.215170i
$999$	−2.96249	−	0.793796i	−0.0937289	−	0.0251146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.a.31.7	✓	40
7.5	odd	6		546.2.bz.b.187.2	yes	40
13.8	odd	4		546.2.bz.b.73.2	yes	40
91.47	even	12	inner	546.2.bz.a.229.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.7	✓	40	1.1	even	1	trivial
546.2.bz.a.229.7	yes	40	91.47	even	12	inner
546.2.bz.b.73.2	yes	40	13.8	odd	4
546.2.bz.b.187.2	yes	40	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.535417 + 1.99820i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.54628 + 0.718636i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.535417 + 1.99820i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.54628 + 0.718636i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.03435 + 1.79154i) q^{10} +(-1.83193 + 0.490864i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.43996 + 2.65454i) q^{13} +(-2.64552 + 0.0351224i) q^{14} +(-1.46279 + 1.46279i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.24802 + 2.16164i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.191351 - 0.714132i) q^{19} +(-1.46279 + 1.46279i) q^{20} +(-2.56446 - 0.650785i) q^{21} -1.89655 q^{22} +(7.35489 - 4.24635i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.623983 + 0.360257i) q^{25} +(1.66978 + 3.19560i) q^{26} +1.00000i q^{27} +(-2.56446 - 0.650785i) q^{28} -8.10492 q^{29} +(-1.79154 + 1.03435i) q^{30} +(7.23277 - 1.93801i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.83193 - 0.490864i) q^{33} +(-1.76497 + 1.76497i) q^{34} +(-0.0726574 - 5.47276i) q^{35} +1.00000i q^{36} +(-0.793796 + 2.96249i) q^{37} +(0.369662 - 0.640273i) q^{38} +(0.785800 + 3.51888i) q^{39} +(-1.79154 + 1.03435i) q^{40} +(-0.895842 - 0.895842i) q^{41} +(-2.30865 - 1.29234i) q^{42} -10.4587i q^{43} +(-1.83193 - 0.490864i) q^{44} +(-1.99820 + 0.535417i) q^{45} +(8.20332 - 2.19807i) q^{46} +(1.80147 + 0.482703i) q^{47} +1.00000i q^{48} +(5.96712 - 3.65970i) q^{49} +(0.509480 + 0.509480i) q^{50} +(-2.16164 + 1.24802i) q^{51} +(0.785800 + 3.51888i) q^{52} +(2.70278 - 4.68135i) q^{53} +(-0.258819 + 0.965926i) q^{54} -3.92339i q^{55} +(-2.30865 - 1.29234i) q^{56} +(0.522781 - 0.522781i) q^{57} +(-7.82875 - 2.09771i) q^{58} +(3.48328 + 12.9998i) q^{59} +(-1.99820 + 0.535417i) q^{60} +(8.23336 - 4.75353i) q^{61} +7.48791 q^{62} +(-1.89550 - 1.84583i) q^{63} +1.00000i q^{64} +(-6.61071 + 3.45426i) q^{65} +(-1.64246 - 0.948277i) q^{66} +(-2.30701 - 8.60990i) q^{67} +(-2.16164 + 1.24802i) q^{68} +8.49270 q^{69} +(1.34627 - 5.30509i) q^{70} +(-4.51316 + 4.51316i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.185948 + 0.693968i) q^{73} +(-1.53350 + 2.65609i) q^{74} +(0.360257 + 0.623983i) q^{75} +(0.522781 - 0.522781i) q^{76} +(4.31186 - 2.56637i) q^{77} +(-0.151729 + 3.60236i) q^{78} +(4.82081 + 8.34988i) q^{79} +(-1.99820 + 0.535417i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.633456 - 1.09718i) q^{82} +(-1.63597 - 1.63597i) q^{83} +(-1.89550 - 1.84583i) q^{84} +(-3.65119 - 3.65119i) q^{85} +(2.70692 - 10.1024i) q^{86} +(-7.01907 - 4.05246i) q^{87} +(-1.64246 - 0.948277i) q^{88} +(-3.24008 - 0.868177i) q^{89} -2.06869 q^{90} +(-8.12049 - 5.00577i) q^{91} +8.49270 q^{92} +(7.23277 + 1.93801i) q^{93} +(1.61516 + 0.932511i) q^{94} +(1.32453 + 0.764717i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(1.08804 + 1.08804i) q^{97} +(6.71100 - 1.99060i) q^{98} +(-1.34107 - 1.34107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 + 20 * q^9	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Introduction

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