LMFDB - Embedded newform 546.2.by.a.115.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.5
Character	$\chi$	$=$	546.115
Dual form			546.2.by.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.85793 - 0.765779i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.565013 - 2.58472i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.85793 - 0.765779i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.565013 - 2.58472i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -2.95874 q^{10} +(-3.08784 + 3.08784i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.11321 - 3.42940i) q^{13} +(-0.123214 - 2.64288i) q^{14} +(-0.765779 + 2.85793i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.464402 - 0.804367i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(0.118112 - 0.118112i) q^{19} +(-2.85793 + 0.765779i) q^{20} +(-2.58472 - 0.565013i) q^{21} +(-2.18344 + 3.78182i) q^{22} +(-1.39712 - 0.806627i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(3.25120 + 1.87708i) q^{25} +(-1.96287 - 3.02443i) q^{26} +1.00000i q^{27} +(-0.803043 - 2.52094i) q^{28} +(1.94582 + 3.37026i) q^{29} +2.95874i q^{30} +(-2.23248 - 8.33172i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.08784 + 3.08784i) q^{33} +(-0.656763 - 0.656763i) q^{34} +(-3.59409 + 6.95426i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.80326 - 6.72985i) q^{37} +(0.0835178 - 0.144657i) q^{38} +(-3.42940 + 1.11321i) q^{39} +(-2.56235 + 1.47937i) q^{40} +(9.71078 + 2.60200i) q^{41} +(-2.64288 + 0.123214i) q^{42} +(4.51157 + 2.60476i) q^{43} +(-1.13023 + 4.21807i) q^{44} +(2.85793 + 0.765779i) q^{45} +(-1.55828 - 0.417541i) q^{46} +(2.34364 - 8.74657i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-6.36152 - 2.92080i) q^{49} +(3.62625 + 0.971650i) q^{50} +(-0.804367 + 0.464402i) q^{51} +(-2.67876 - 2.41334i) q^{52} +(1.13857 - 1.97205i) q^{53} +(0.258819 + 0.965926i) q^{54} +(11.1894 - 6.46023i) q^{55} +(-1.42815 - 2.22720i) q^{56} +(-0.118112 - 0.118112i) q^{57} +(2.75181 + 2.75181i) q^{58} +(0.903133 - 3.37054i) q^{59} +(0.765779 + 2.85793i) q^{60} +9.81168i q^{61} +(-4.31282 - 7.47002i) q^{62} +(-0.565013 + 2.58472i) q^{63} -1.00000i q^{64} +(0.555299 + 10.6534i) q^{65} +(3.78182 + 2.18344i) q^{66} +(3.86455 + 3.86455i) q^{67} +(-0.804367 - 0.464402i) q^{68} +(-0.806627 + 1.39712i) q^{69} +(-1.67173 + 7.64751i) q^{70} +(7.17756 - 1.92322i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(6.21826 - 1.66618i) q^{73} +(-3.48363 - 6.03382i) q^{74} +(1.87708 - 3.25120i) q^{75} +(0.0432320 - 0.161344i) q^{76} +(6.23653 + 9.72588i) q^{77} +(-3.02443 + 1.96287i) q^{78} +(4.30390 + 7.45458i) q^{79} +(-2.09215 + 2.09215i) q^{80} +1.00000 q^{81} +10.0533 q^{82} +(1.81174 - 1.81174i) q^{83} +(-2.52094 + 0.803043i) q^{84} +(0.711258 + 2.65445i) q^{85} +(5.03200 + 1.34832i) q^{86} +(3.37026 - 1.94582i) q^{87} +4.36687i q^{88} +(-11.7436 + 3.14668i) q^{89} +2.95874 q^{90} +(-9.49300 + 0.939668i) q^{91} -1.61325 q^{92} +(-8.33172 + 2.23248i) q^{93} -9.05511i q^{94} +(-0.428003 + 0.247108i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(-2.87536 - 10.7310i) q^{97} +(-6.90072 - 1.17479i) q^{98} +(3.08784 - 3.08784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.85793	−	0.765779i	−1.27810	−	0.342467i	−0.444974	−	0.895544i	$-0.646787\pi$
$5$	−2.85793	−	0.765779i	−1.27810	−	0.342467i	−0.833130	+	0.553077i	$0.813454\pi$
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	0.565013	−	2.58472i	0.213555	−	0.976931i
$7$	0.565013	−	2.58472i	0.213555	−	0.976931i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−2.95874			−0.935637
$11$	−3.08784	+	3.08784i	−0.931020	+	0.931020i	−0.997770	−	0.0667496i	$-0.978737\pi$
$11$	−3.08784	+	3.08784i	−0.931020	+	0.931020i	0.0667496	+	0.997770i	$0.478737\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.11321	−	3.42940i	−0.308748	−	0.951144i
$13$	−1.11321	−	3.42940i	−0.308748	−	0.951144i
$14$	−0.123214	−	2.64288i	−0.0329302	−	0.706340i
$15$	−0.765779	+	2.85793i	−0.197723	+	0.737914i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.464402	−	0.804367i	−0.112634	−	0.195088i	0.804198	−	0.594362i	$-0.202595\pi$
$17$	−0.464402	−	0.804367i	−0.112634	−	0.195088i	−0.916831	+	0.399274i	$0.869262\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	0.118112	−	0.118112i	0.0270967	−	0.0270967i	−0.693429	−	0.720525i	$-0.743901\pi$
$19$	0.118112	−	0.118112i	0.0270967	−	0.0270967i	0.720525	+	0.693429i	$0.243901\pi$
$20$	−2.85793	+	0.765779i	−0.639052	+	0.171233i
$21$	−2.58472	−	0.565013i	−0.564031	−	0.123296i
$22$	−2.18344	+	3.78182i	−0.465510	+	0.806287i
$23$	−1.39712	−	0.806627i	−0.291320	−	0.168193i	0.347217	−	0.937785i	$-0.387127\pi$
$23$	−1.39712	−	0.806627i	−0.291320	−	0.168193i	−0.638537	+	0.769591i	$0.720460\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	3.25120	+	1.87708i	0.650241	+	0.375417i
$26$	−1.96287	−	3.02443i	−0.384950	−	0.593139i
$27$			1.00000i			0.192450i
$28$	−0.803043	−	2.52094i	−0.151761	−	0.476412i
$29$	1.94582	+	3.37026i	0.361330	+	0.625842i	0.988180	−	0.153298i	$-0.0489894\pi$
$29$	1.94582	+	3.37026i	0.361330	+	0.625842i	−0.626850	+	0.779140i	$0.715656\pi$
$30$			2.95874i			0.540190i
$31$	−2.23248	−	8.33172i	−0.400965	−	1.49642i	−0.811378	−	0.584521i	$-0.801282\pi$
$31$	−2.23248	−	8.33172i	−0.400965	−	1.49642i	0.410413	−	0.911900i	$-0.365384\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	3.08784	+	3.08784i	0.537525	+	0.537525i
$34$	−0.656763	−	0.656763i	−0.112634	−	0.112634i
$35$	−3.59409	+	6.95426i	−0.607512	+	1.17548i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−1.80326	−	6.72985i	−0.296454	−	1.10638i	−0.940056	−	0.341020i	$-0.889228\pi$
$37$	−1.80326	−	6.72985i	−0.296454	−	1.10638i	0.643602	−	0.765360i	$-0.277439\pi$
$38$	0.0835178	−	0.144657i	0.0135484	−	0.0234665i
$39$	−3.42940	+	1.11321i	−0.549143	+	0.178256i
$40$	−2.56235	+	1.47937i	−0.405143	+	0.233909i
$41$	9.71078	+	2.60200i	1.51657	+	0.406363i	0.918611	−	0.395164i	$-0.129312\pi$
$41$	9.71078	+	2.60200i	1.51657	+	0.406363i	0.597958	+	0.801527i	$0.295979\pi$
$42$	−2.64288	+	0.123214i	−0.407805	+	0.0190123i
$43$	4.51157	+	2.60476i	0.688008	+	0.397222i	0.802865	−	0.596160i	$-0.203308\pi$
$43$	4.51157	+	2.60476i	0.688008	+	0.397222i	−0.114857	+	0.993382i	$0.536641\pi$
$44$	−1.13023	+	4.21807i	−0.170389	+	0.635899i
$45$	2.85793	+	0.765779i	0.426035	+	0.114156i
$46$	−1.55828	−	0.417541i	−0.229756	−	0.0615631i
$47$	2.34364	−	8.74657i	0.341854	−	1.27582i	−0.554390	−	0.832257i	$-0.687048\pi$
$47$	2.34364	−	8.74657i	0.341854	−	1.27582i	0.896244	−	0.443561i	$-0.146285\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−6.36152	−	2.92080i	−0.908789	−	0.417257i
$50$	3.62625	+	0.971650i	0.512829	+	0.137412i
$51$	−0.804367	+	0.464402i	−0.112634	+	0.0650292i
$52$	−2.67876	−	2.41334i	−0.371478	−	0.334670i
$53$	1.13857	−	1.97205i	0.156394	−	0.270882i	−0.777172	−	0.629289i	$-0.783346\pi$
$53$	1.13857	−	1.97205i	0.156394	−	0.270882i	0.933566	+	0.358406i	$0.116680\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	11.1894	−	6.46023i	1.50878	−	0.871097i
$56$	−1.42815	−	2.22720i	−0.190844	−	0.297621i
$57$	−0.118112	−	0.118112i	−0.0156443	−	0.0156443i
$58$	2.75181	+	2.75181i	0.361330	+	0.361330i
$59$	0.903133	−	3.37054i	0.117578	−	0.438807i	−0.881889	−	0.471457i	$-0.843728\pi$
$59$	0.903133	−	3.37054i	0.117578	−	0.438807i	0.999467	+	0.0326504i	$0.0103948\pi$
$60$	0.765779	+	2.85793i	0.0988617	+	0.368957i
$61$			9.81168i			1.25626i	0.778110	+	0.628129i	$0.216179\pi$
$61$			9.81168i			1.25626i	−0.778110	+	0.628129i	$0.783821\pi$
$62$	−4.31282	−	7.47002i	−0.547728	−	0.948693i
$63$	−0.565013	+	2.58472i	−0.0711849	+	0.325644i
$64$		−	1.00000i		−	0.125000i
$65$	0.555299	+	10.6534i	0.0688763	+	1.32140i
$66$	3.78182	+	2.18344i	0.465510	+	0.268762i
$67$	3.86455	+	3.86455i	0.472130	+	0.472130i	0.902603	−	0.430473i	$-0.141653\pi$
$67$	3.86455	+	3.86455i	0.472130	+	0.472130i	−0.430473	+	0.902603i	$0.641653\pi$
$68$	−0.804367	−	0.464402i	−0.0975439	−	0.0563170i
$69$	−0.806627	+	1.39712i	−0.0971065	+	0.168193i
$70$	−1.67173	+	7.64751i	−0.199810	+	0.914053i
$71$	7.17756	−	1.92322i	0.851820	−	0.228244i	0.193610	−	0.981079i	$-0.437980\pi$
$71$	7.17756	−	1.92322i	0.851820	−	0.228244i	0.658210	+	0.752834i	$0.271314\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	6.21826	−	1.66618i	0.727792	−	0.195011i	0.124146	−	0.992264i	$-0.460381\pi$
$73$	6.21826	−	1.66618i	0.727792	−	0.195011i	0.603646	+	0.797253i	$0.293714\pi$
$74$	−3.48363	−	6.03382i	−0.404963	−	0.701417i
$75$	1.87708	−	3.25120i	0.216747	−	0.375417i
$76$	0.0432320	−	0.161344i	0.00495905	−	0.0185074i
$77$	6.23653	+	9.72588i	0.710719	+	1.10837i
$78$	−3.02443	+	1.96287i	−0.342449	+	0.222251i
$79$	4.30390	+	7.45458i	0.484227	+	0.838705i	0.999836	−	0.0181185i	$-0.00576761\pi$
$79$	4.30390	+	7.45458i	0.484227	+	0.838705i	−0.515609	+	0.856824i	$0.672434\pi$
$80$	−2.09215	+	2.09215i	−0.233909	+	0.233909i
$81$	1.00000			0.111111
$82$	10.0533			1.11021
$83$	1.81174	−	1.81174i	0.198864	−	0.198864i	−0.600649	−	0.799513i	$-0.705091\pi$
$83$	1.81174	−	1.81174i	0.198864	−	0.198864i	0.799513	+	0.600649i	$0.205091\pi$
$84$	−2.52094	+	0.803043i	−0.275057	+	0.0876192i
$85$	0.711258	+	2.65445i	0.0771468	+	0.287916i
$86$	5.03200	+	1.34832i	0.542615	+	0.145393i
$87$	3.37026	−	1.94582i	0.361330	−	0.208614i
$88$			4.36687i			0.465510i
$89$	−11.7436	+	3.14668i	−1.24481	+	0.333547i	−0.820331	−	0.571889i	$-0.806211\pi$
$89$	−11.7436	+	3.14668i	−1.24481	+	0.333547i	−0.424483	+	0.905436i	$0.639544\pi$
$90$	2.95874			0.311879
$91$	−9.49300	+	0.939668i	−0.995137	+	0.0985039i
$92$	−1.61325			−0.168193
$93$	−8.33172	+	2.23248i	−0.863959	+	0.231497i
$94$		−	9.05511i		−	0.933964i
$95$	−0.428003	+	0.247108i	−0.0439122	+	0.0253527i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	−2.87536	−	10.7310i	−0.291948	−	1.08957i	−0.943611	−	0.331056i	$-0.892595\pi$
$97$	−2.87536	−	10.7310i	−0.291948	−	1.08957i	0.651663	−	0.758509i	$-0.274072\pi$
$98$	−6.90072	−	1.17479i	−0.697078	−	0.118672i
$99$	3.08784	−	3.08784i	0.310340	−	0.310340i
$100$	3.75417			0.375417
$101$	7.77274			0.773417			0.386708	−	0.922202i	$-0.373612\pi$
$101$	7.77274			0.773417			0.386708	+	0.922202i	$0.373612\pi$
$102$	−0.656763	+	0.656763i	−0.0650292	+	0.0650292i
$103$	−4.87420	−	8.44236i	−0.480269	−	0.831850i	0.519475	−	0.854486i	$-0.326128\pi$
$103$	−4.87420	−	8.44236i	−0.480269	−	0.831850i	−0.999744	+	0.0226355i	$0.992794\pi$
$104$	−3.21211	−	1.63780i	−0.314973	−	0.160599i
$105$	6.95426	+	3.59409i	0.678666	+	0.350747i
$106$	0.589365	−	2.19954i	0.0572442	−	0.213638i
$107$	4.16560	−	7.21503i	0.402703	−	0.697503i	−0.591348	−	0.806417i	$-0.701404\pi$
$107$	4.16560	−	7.21503i	0.402703	−	0.697503i	0.994051	+	0.108914i	$0.0347373\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−6.59020	+	1.76584i	−0.631227	+	0.169137i	−0.560226	−	0.828339i	$-0.689286\pi$
$109$	−6.59020	+	1.76584i	−0.631227	+	0.169137i	−0.0710006	+	0.997476i	$0.522619\pi$
$110$	9.13614	−	9.13614i	0.871097	−	0.871097i
$111$	−6.72985	+	1.80326i	−0.638769	+	0.171158i
$112$	−1.95592	−	1.78167i	−0.184817	−	0.168352i
$113$	0.175357	−	0.303727i	0.0164962	−	0.0285722i	−0.857659	−	0.514218i	$-0.828082\pi$
$113$	0.175357	−	0.303727i	0.0164962	−	0.0285722i	0.874156	+	0.485646i	$0.161416\pi$
$114$	−0.144657	−	0.0835178i	−0.0135484	−	0.00782215i
$115$	3.37517	+	3.37517i	0.314736	+	0.314736i
$116$	3.37026	+	1.94582i	0.312921	+	0.180665i
$117$	1.11321	+	3.42940i	0.102916	+	0.317048i
$118$		−	3.48944i		−	0.321229i
$119$	−2.34145	+	0.745869i	−0.214641	+	0.0683737i
$120$	1.47937	+	2.56235i	0.135048	+	0.233909i
$121$		−	8.06957i		−	0.733597i
$122$	2.53945	+	9.47736i	0.229911	+	0.858040i
$123$	2.60200	−	9.71078i	0.234614	−	0.875592i
$124$	−6.09924	−	6.09924i	−0.547728	−	0.547728i
$125$	2.60647	+	2.60647i	0.233130	+	0.233130i
$126$	0.123214	+	2.64288i	0.0109767	+	0.235447i
$127$	18.1902	−	10.5021i	1.61412	−	0.931914i	0.625722	−	0.780046i	$-0.284804\pi$
$127$	18.1902	−	10.5021i	1.61412	−	0.931914i	0.988401	−	0.151868i	$-0.0485289\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	2.60476	−	4.51157i	0.229336	−	0.397222i
$130$	3.29369	+	10.1467i	0.288876	+	0.889925i
$131$	−17.8105	+	10.2829i	−1.55611	+	0.898420i	−0.558485	+	0.829514i	$0.688617\pi$
$131$	−17.8105	+	10.2829i	−1.55611	+	0.898420i	−0.997623	+	0.0689054i	$0.978049\pi$
$132$	4.21807	+	1.13023i	0.367136	+	0.0983739i
$133$	−0.238551	−	0.372021i	−0.0206850	−	0.0322583i
$134$	4.73309	+	2.73265i	0.408877	+	0.236065i
$135$	0.765779	−	2.85793i	0.0659078	−	0.245971i
$136$	−0.897155	−	0.240392i	−0.0769304	−	0.0206134i
$137$	−12.4042	−	3.32369i	−1.05976	−	0.283962i	−0.313481	−	0.949595i	$-0.601495\pi$
$137$	−12.4042	−	3.32369i	−1.05976	−	0.283962i	−0.746280	+	0.665633i	$0.768162\pi$
$138$	−0.417541	+	1.55828i	−0.0355435	+	0.132650i
$139$	17.3133	+	9.99586i	1.46850	+	0.847838i	0.999377	−	0.0352960i	$-0.0112374\pi$
$139$	17.3133	+	9.99586i	1.46850	+	0.847838i	0.469121	+	0.883134i	$0.344571\pi$
$140$	0.364557	+	7.81961i	0.0308107	+	0.660877i
$141$	−8.74657	−	2.34364i	−0.736594	−	0.197370i
$142$	6.43523	−	3.71538i	0.540032	−	0.311788i
$143$	14.0269	+	7.15204i	1.17298	+	0.598084i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.98014	−	11.1220i	−0.247487	−	0.923635i
$146$	5.57514	−	3.21881i	0.461402	−	0.266390i
$147$	−2.92080	+	6.36152i	−0.240903	+	0.524689i
$148$	−4.92659	−	4.92659i	−0.404963	−	0.404963i
$149$	−6.73159	−	6.73159i	−0.551473	−	0.551473i	0.375393	−	0.926866i	$-0.377508\pi$
$149$	−6.73159	−	6.73159i	−0.551473	−	0.551473i	−0.926866	+	0.375393i	$0.877508\pi$
$150$	0.971650	−	3.62625i	0.0793348	−	0.296082i
$151$	3.93110	+	14.6710i	0.319908	+	1.19391i	0.919332	+	0.393482i	$0.128730\pi$
$151$	3.93110	+	14.6710i	0.319908	+	1.19391i	−0.599424	+	0.800431i	$0.704604\pi$
$152$		−	0.167036i		−	0.0135484i
$153$	0.464402	+	0.804367i	0.0375446	+	0.0650292i
$154$	8.54127	+	7.78034i	0.688275	+	0.626958i
$155$			25.5210i			2.04990i
$156$	−2.41334	+	2.67876i	−0.193222	+	0.214473i
$157$	13.1171	+	7.57314i	1.04686	+	0.604403i	0.921768	−	0.387743i	$-0.126745\pi$
$157$	13.1171	+	7.57314i	1.04686	+	0.604403i	0.125089	+	0.992146i	$0.460079\pi$
$158$	6.08664	+	6.08664i	0.484227	+	0.484227i
$159$	−1.97205	−	1.13857i	−0.156394	−	0.0902942i
$160$	−1.47937	+	2.56235i	−0.116955	+	0.202571i
$161$	−2.87429	+	3.15540i	−0.226526	+	0.248681i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	5.53190	−	5.53190i	0.433292	−	0.433292i	−0.456455	−	0.889747i	$-0.650881\pi$
$163$	5.53190	−	5.53190i	0.433292	−	0.433292i	0.889747	+	0.456455i	$0.150881\pi$
$164$	9.71078	−	2.60200i	0.758285	−	0.203182i
$165$	−6.46023	−	11.1894i	−0.502928	−	0.871097i
$166$	1.28109	−	2.21892i	0.0994321	−	0.172221i
$167$	−1.05970	+	3.95484i	−0.0820018	+	0.306035i	−0.994730	−	0.102533i	$-0.967305\pi$
$167$	−1.05970	+	3.95484i	−0.0820018	+	0.306035i	0.912728	+	0.408568i	$0.133972\pi$
$168$	−2.22720	+	1.42815i	−0.171832	+	0.110184i
$169$	−10.5215	+	7.63525i	−0.809350	+	0.587327i
$170$	1.37405	+	2.37992i	0.105384	+	0.182531i
$171$	−0.118112	+	0.118112i	−0.00903225	+	0.00903225i
$172$	5.20951			0.397222
$173$	−24.3026			−1.84769			−0.923846	−	0.382764i	$-0.874972\pi$
$173$	−24.3026			−1.84769			−0.923846	+	0.382764i	$0.874972\pi$
$174$	2.75181	−	2.75181i	0.208614	−	0.208614i
$175$	6.68870	−	7.34286i	0.505618	−	0.555068i
$176$	1.13023	+	4.21807i	0.0851943	+	0.317949i
$177$	−3.37054	−	0.903133i	−0.253345	−	0.0678837i
$178$	−10.5290	+	6.07891i	−0.789181	+	0.455634i
$179$		−	8.40690i		−	0.628361i	−0.949363	−	0.314180i	$-0.898270\pi$
$179$		−	8.40690i		−	0.628361i	0.949363	−	0.314180i	$-0.101730\pi$
$180$	2.85793	−	0.765779i	0.213017	−	0.0570778i
$181$	−16.6914			−1.24066			−0.620330	−	0.784341i	$-0.713001\pi$
$181$	−16.6914			−1.24066			−0.620330	+	0.784341i	$0.713001\pi$
$182$	−8.92633	+	3.36462i	−0.661664	+	0.249402i
$183$	9.81168			0.725300
$184$	−1.55828	+	0.417541i	−0.114878	+	0.0307815i
$185$			20.6143i			1.51559i
$186$	−7.47002	+	4.31282i	−0.547728	+	0.316231i
$187$	3.91776	+	1.04976i	0.286495	+	0.0767661i
$188$	−2.34364	−	8.74657i	−0.170927	−	0.637909i
$189$	2.58472	+	0.565013i	0.188010	+	0.0410986i
$190$	−0.349463	+	0.349463i	−0.0253527	+	0.0253527i
$191$	14.7976			1.07072			0.535358	−	0.844626i	$-0.320177\pi$
$191$	14.7976			1.07072			0.535358	+	0.844626i	$0.320177\pi$
$192$	−1.00000			−0.0721688
$193$	17.5073	−	17.5073i	1.26021	−	1.26021i	0.309213	−	0.950993i	$-0.399934\pi$
$193$	17.5073	−	17.5073i	1.26021	−	1.26021i	0.950993	−	0.309213i	$-0.100066\pi$
$194$	−5.55476	−	9.62113i	−0.398809	−	0.690757i
$195$	10.6534	−	0.555299i	0.762909	−	0.0397658i
$196$	−6.96964	+	0.651277i	−0.497831	+	0.0465198i
$197$	−4.85782	+	18.1296i	−0.346105	+	1.29168i	0.545211	+	0.838299i	$0.316450\pi$
$197$	−4.85782	+	18.1296i	−0.346105	+	1.29168i	−0.891316	+	0.453383i	$0.850217\pi$
$198$	2.18344	−	3.78182i	0.155170	−	0.268762i
$199$	−5.49616	−	9.51962i	−0.389612	−	0.674828i	0.602785	−	0.797904i	$-0.294058\pi$
$199$	−5.49616	−	9.51962i	−0.389612	−	0.674828i	−0.992397	+	0.123075i	$0.960724\pi$
$200$	3.62625	−	0.971650i	0.256414	−	0.0687060i
$201$	3.86455	−	3.86455i	0.272585	−	0.272585i
$202$	7.50789	−	2.01173i	0.528253	−	0.141545i
$203$	9.81059	−	3.12516i	0.688569	−	0.219343i
$204$	−0.464402	+	0.804367i	−0.0325146	+	0.0563170i
$205$	−25.7601	−	14.8726i	−1.79917	−	1.03875i
$206$	−6.89316	−	6.89316i	−0.480269	−	0.480269i
$207$	1.39712	+	0.806627i	0.0971065	+	0.0560645i
$208$	−3.52655	−	0.750635i	−0.244522	−	0.0520472i
$209$			0.729423i			0.0504552i
$210$	7.64751	+	1.67173i	0.527729	+	0.115360i
$211$	4.81334	+	8.33694i	0.331364	+	0.573939i	0.982780	−	0.184782i	$-0.0591579\pi$
$211$	4.81334	+	8.33694i	0.331364	+	0.573939i	−0.651416	+	0.758721i	$0.725825\pi$
$212$		−	2.27713i		−	0.156394i
$213$	−1.92322	−	7.17756i	−0.131777	−	0.491799i
$214$	2.15627	−	8.04732i	0.147400	−	0.550103i
$215$	−10.8991	−	10.8991i	−0.743311	−	0.743311i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−22.7965	+	1.06279i	−1.54753	+	0.0721472i
$218$	−5.90862	+	3.41134i	−0.400182	+	0.231045i
$219$	−1.66618	−	6.21826i	−0.112590	−	0.420191i
$220$	6.46023	−	11.1894i	0.435548	−	0.754392i
$221$	−2.24152	+	2.48804i	−0.150781	+	0.167364i
$222$	−6.03382	+	3.48363i	−0.404963	+	0.233806i
$223$	4.61883	+	1.23761i	0.309300	+	0.0828767i	0.410130	−	0.912027i	$-0.365483\pi$
$223$	4.61883	+	1.23761i	0.309300	+	0.0828767i	−0.100830	+	0.994904i	$0.532150\pi$
$224$	−2.35041	−	1.21473i	−0.157043	−	0.0811628i
$225$	−3.25120	−	1.87708i	−0.216747	−	0.125139i
$226$	0.0907714	−	0.338763i	0.00603802	−	0.0225342i
$227$	−24.1898	−	6.48163i	−1.60553	−	0.430201i	−0.658825	−	0.752297i	$-0.728946\pi$
$227$	−24.1898	−	6.48163i	−1.60553	−	0.430201i	−0.946707	+	0.322096i	$0.895613\pi$
$228$	−0.161344	−	0.0432320i	−0.0106853	−	0.00286311i
$229$	3.96732	−	14.8062i	0.262168	−	0.978424i	−0.701793	−	0.712381i	$-0.747617\pi$
$229$	3.96732	−	14.8062i	0.262168	−	0.978424i	0.963961	−	0.266043i	$-0.0857163\pi$
$230$	4.13372	+	2.38660i	0.272569	+	0.157368i
$231$	9.72588	−	6.23653i	0.639916	−	0.410334i
$232$	3.75904	+	1.00723i	0.246793	+	0.0661280i
$233$	−10.5926	+	6.11566i	−0.693947	+	0.400650i	−0.805089	−	0.593154i	$-0.797883\pi$
$233$	−10.5926	+	6.11566i	−0.693947	+	0.400650i	0.111142	+	0.993805i	$0.464549\pi$
$234$	1.96287	+	3.02443i	0.128317	+	0.197713i
$235$	−13.3959	+	23.2023i	−0.873851	+	1.51355i
$236$	−0.903133	−	3.37054i	−0.0587890	−	0.219403i
$237$	7.45458	−	4.30390i	0.484227	−	0.279568i
$238$	−2.06863	+	1.32647i	−0.134089	+	0.0859821i
$239$	−17.9887	−	17.9887i	−1.16359	−	1.16359i	−0.983683	−	0.179909i	$-0.942420\pi$
$239$	−17.9887	−	17.9887i	−1.16359	−	1.16359i	−0.179909	−	0.983683i	$-0.557580\pi$
$240$	2.09215	+	2.09215i	0.135048	+	0.135048i
$241$	−5.96249	+	22.2523i	−0.384078	+	1.43340i	0.455538	+	0.890216i	$0.349447\pi$
$241$	−5.96249	+	22.2523i	−0.384078	+	1.43340i	−0.839616	+	0.543181i	$0.817220\pi$
$242$	−2.08856	−	7.79460i	−0.134258	−	0.501056i
$243$		−	1.00000i		−	0.0641500i
$244$	4.90584	+	8.49717i	0.314064	+	0.543975i
$245$	15.9441	+	13.2189i	1.01863	+	0.844527i
$246$		−	10.0533i		−	0.640978i
$247$	−0.536536	−	0.273570i	−0.0341390	−	0.0174068i
$248$	−7.47002	−	4.31282i	−0.474346	−	0.273864i
$249$	−1.81174	−	1.81174i	−0.114814	−	0.114814i
$250$	3.19226	+	1.84305i	0.201896	+	0.116565i
$251$	10.6293	−	18.4105i	0.670915	−	1.16206i	−0.306730	−	0.951797i	$-0.599235\pi$
$251$	10.6293	−	18.4105i	0.670915	−	1.16206i	0.977645	−	0.210263i	$-0.0674319\pi$
$252$	0.803043	+	2.52094i	0.0505870	+	0.158804i
$253$	6.80483	−	1.82335i	0.427816	−	0.114633i
$254$	14.8523	−	14.8523i	0.931914	−	0.931914i
$255$	2.65445	−	0.711258i	0.166228	−	0.0445407i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.59693	+	14.8903i	−0.536262	+	0.928833i	0.462839	+	0.886442i	$0.346831\pi$
$257$	−8.59693	+	14.8903i	−0.536262	+	0.928833i	−0.999101	+	0.0423908i	$0.986503\pi$
$258$	1.34832	−	5.03200i	0.0839428	−	0.313279i
$259$	−18.4136	+	0.858460i	−1.14417	+	0.0533421i
$260$	5.80762	+	8.94850i	0.360173	+	0.554962i
$261$	−1.94582	−	3.37026i	−0.120443	−	0.208614i
$262$	−14.5422	+	14.5422i	−0.898420	+	0.898420i
$263$	8.61235			0.531060			0.265530	−	0.964103i	$-0.414453\pi$
$263$	8.61235			0.531060			0.265530	+	0.964103i	$0.414453\pi$
$264$	4.36687			0.268762
$265$	−4.76410	+	4.76410i	−0.292656	+	0.292656i
$266$	−0.326709	−	0.297603i	−0.0200318	−	0.0182472i
$267$	3.14668	+	11.7436i	0.192574	+	0.718694i
$268$	5.27908	+	1.41452i	0.322471	+	0.0864059i
$269$	6.61549	−	3.81946i	0.403354	−	0.232876i	−0.284576	−	0.958653i	$-0.591853\pi$
$269$	6.61549	−	3.81946i	0.403354	−	0.232876i	0.687930	+	0.725777i	$0.258520\pi$
$270$		−	2.95874i		−	0.180063i
$271$	15.9764	−	4.28087i	0.970499	−	0.260044i	0.261460	−	0.965214i	$-0.415796\pi$
$271$	15.9764	−	4.28087i	0.970499	−	0.260044i	0.709038	+	0.705170i	$0.249129\pi$
$272$	−0.928803			−0.0563170
$273$	0.939668	+	9.49300i	0.0568713	+	0.574542i
$274$	−12.8418			−0.775799
$275$	−15.8353	+	4.24307i	−0.954907	+	0.255867i
$276$			1.61325i			0.0971065i
$277$	−20.5926	+	11.8892i	−1.23729	+	0.714350i	−0.968540	−	0.248859i	$-0.919944\pi$
$277$	−20.5926	+	11.8892i	−1.23729	+	0.714350i	−0.268752	+	0.963210i	$0.586611\pi$
$278$	19.3105	+	5.17424i	1.15817	+	0.310330i
$279$	2.23248	+	8.33172i	0.133655	+	0.498807i
$280$	2.37600	+	7.45881i	0.141993	+	0.445749i
$281$	−2.54618	+	2.54618i	−0.151893	+	0.151893i	−0.778963	−	0.627070i	$-0.784254\pi$
$281$	−2.54618	+	2.54618i	−0.151893	+	0.151893i	0.627070	+	0.778963i	$0.284254\pi$
$282$	−9.05511			−0.539224
$283$	−1.78984			−0.106395			−0.0531976	−	0.998584i	$-0.516941\pi$
$283$	−1.78984			−0.106395			−0.0531976	+	0.998584i	$0.516941\pi$
$284$	5.25434	−	5.25434i	0.311788	−	0.311788i
$285$	0.247108	+	0.428003i	0.0146374	+	0.0253527i
$286$	15.4000	+	3.27793i	0.910620	+	0.193828i
$287$	12.2121	−	23.6295i	0.720860	−	1.39480i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	8.06866	−	13.9753i	0.474627	−	0.822078i
$290$	−5.75719	−	9.97175i	−0.338074	−	0.585561i
$291$	−10.7310	+	2.87536i	−0.629061	+	0.168556i
$292$	4.55208	−	4.55208i	0.266390	−	0.266390i
$293$	−4.02574	+	1.07869i	−0.235186	+	0.0630179i	−0.374487	−	0.927232i	$-0.622181\pi$
$293$	−4.02574	+	1.07869i	−0.235186	+	0.0630179i	0.139301	+	0.990250i	$0.455514\pi$
$294$	−1.17479	+	6.90072i	−0.0685151	+	0.402458i
$295$	−5.16218	+	8.94116i	−0.300554	+	0.520574i
$296$	−6.03382	−	3.48363i	−0.350709	−	0.202482i
$297$	−3.08784	−	3.08784i	−0.179175	−	0.179175i
$298$	−8.24448	−	4.75995i	−0.477590	−	0.275737i
$299$	−1.21097	+	5.68922i	−0.0700319	+	0.329016i
$300$		−	3.75417i		−	0.216747i
$301$	9.28166	−	10.1894i	0.534986	−	0.587308i
$302$	7.59429	+	13.1537i	0.437002	+	0.756910i
$303$		−	7.77274i		−	0.446532i
$304$	−0.0432320	−	0.161344i	−0.00247952	−	0.00925371i
$305$	7.51358	−	28.0411i	0.430226	−	1.60563i
$306$	0.656763	+	0.656763i	0.0375446	+	0.0375446i
$307$	−4.14745	−	4.14745i	−0.236708	−	0.236708i	0.578778	−	0.815485i	$-0.303530\pi$
$307$	−4.14745	−	4.14745i	−0.236708	−	0.236708i	−0.815485	+	0.578778i	$0.803530\pi$
$308$	10.2639	+	5.30459i	0.584842	+	0.302257i
$309$	−8.44236	+	4.87420i	−0.480269	+	0.277283i
$310$	6.60533	+	24.6514i	0.375157	+	1.40011i
$311$	16.7488	−	29.0098i	0.949737	−	1.64499i	0.203759	−	0.979021i	$-0.434684\pi$
$311$	16.7488	−	29.0098i	0.949737	−	1.64499i	0.745977	−	0.665971i	$-0.231983\pi$
$312$	−1.63780	+	3.21211i	−0.0927219	+	0.181850i
$313$	−13.8517	+	7.99730i	−0.782946	+	0.452034i	−0.837473	−	0.546478i	$-0.815968\pi$
$313$	−13.8517	+	7.99730i	−0.782946	+	0.452034i	0.0545271	+	0.998512i	$0.482635\pi$
$314$	14.6302	+	3.92015i	0.825629	+	0.221227i
$315$	3.59409	−	6.95426i	0.202504	−	0.391828i
$316$	7.45458	+	4.30390i	0.419353	+	0.242113i
$317$	3.21447	−	11.9966i	0.180543	−	0.673794i	−0.814998	−	0.579463i	$-0.803262\pi$
$317$	3.21447	−	11.9966i	0.180543	−	0.673794i	0.995541	−	0.0943308i	$-0.0300711\pi$
$318$	−2.19954	−	0.589365i	−0.123344	−	0.0330500i
$319$	−16.4153	−	4.39845i	−0.919078	−	0.246266i
$320$	−0.765779	+	2.85793i	−0.0428084	+	0.159763i
$321$	−7.21503	−	4.16560i	−0.402703	−	0.232501i
$322$	−1.95968	+	3.79181i	−0.109208	+	0.211309i
$323$	−0.149857	−	0.0401540i	−0.00833825	−	0.00223423i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	2.81801	−	13.2392i	0.156315	−	0.734381i
$326$	3.91165	−	6.77517i	0.216646	−	0.375242i
$327$	1.76584	+	6.59020i	0.0976512	+	0.364439i
$328$	8.70645	−	5.02667i	0.480733	−	0.277551i
$329$	−21.2832	−	10.9996i	−1.17338	−	0.606425i
$330$	−9.13614	−	9.13614i	−0.502928	−	0.502928i
$331$	0.444469	+	0.444469i	0.0244302	+	0.0244302i	0.719216	−	0.694786i	$-0.244501\pi$
$331$	0.444469	+	0.444469i	0.0244302	+	0.0244302i	−0.694786	+	0.719216i	$0.744501\pi$
$332$	0.663142	−	2.47488i	0.0363947	−	0.135827i
$333$	1.80326	+	6.72985i	0.0988179	+	0.368793i
$334$			4.09436i			0.224033i
$335$	−8.08522	−	14.0040i	−0.441743	−	0.765121i
$336$	−1.78167	+	1.95592i	−0.0971983	+	0.106704i
$337$		−	0.617536i		−	0.0336393i	−0.999859	−	0.0168197i	$-0.994646\pi$
$337$		−	0.617536i		−	0.0336393i	0.999859	−	0.0168197i	$-0.00535412\pi$
$338$	−8.18688	+	10.0983i	−0.445308	+	0.549273i
$339$	−0.303727	−	0.175357i	−0.0164962	−	0.00952408i
$340$	1.94319	+	1.94319i	0.105384	+	0.105384i
$341$	32.6206	+	18.8335i	1.76650	+	1.01989i
$342$	−0.0835178	+	0.144657i	−0.00451612	+	0.00782215i
$343$	−11.1438	+	14.7924i	−0.601707	+	0.798717i
$344$	5.03200	−	1.34832i	0.271308	−	0.0726966i
$345$	3.37517	−	3.37517i	0.181713	−	0.181713i
$346$	−23.4745	+	6.28998i	−1.26200	+	0.338151i
$347$	9.77923	+	16.9381i	0.524976	+	0.909286i	0.999577	+	0.0290845i	$0.00925918\pi$
$347$	9.77923	+	16.9381i	0.524976	+	0.909286i	−0.474601	+	0.880201i	$0.657407\pi$
$348$	1.94582	−	3.37026i	0.104307	−	0.180665i
$349$	−3.35788	+	12.5318i	−0.179743	+	0.670810i	0.815952	+	0.578120i	$0.196213\pi$
$349$	−3.35788	+	12.5318i	−0.179743	+	0.670810i	−0.995695	+	0.0926905i	$0.970453\pi$
$350$	4.56031	−	8.82382i	0.243759	−	0.471653i
$351$	3.42940	−	1.11321i	0.183048	−	0.0594185i
$352$	2.18344	+	3.78182i	0.116378	+	0.201572i
$353$	8.18804	−	8.18804i	0.435805	−	0.435805i	−0.454792	−	0.890598i	$-0.650287\pi$
$353$	8.18804	−	8.18804i	0.435805	−	0.435805i	0.890598	+	0.454792i	$0.150287\pi$
$354$	−3.48944			−0.185462
$355$	−21.9857			−1.16688
$356$	−8.59688	+	8.59688i	−0.455634	+	0.455634i
$357$	0.745869	+	2.34145i	0.0394756	+	0.123923i
$358$	−2.17586	−	8.12044i	−0.114998	−	0.429179i
$359$	−12.5996	−	3.37607i	−0.664984	−	0.178182i	−0.0894898	−	0.995988i	$-0.528524\pi$
$359$	−12.5996	−	3.37607i	−0.664984	−	0.178182i	−0.575494	+	0.817806i	$0.695190\pi$
$360$	2.56235	−	1.47937i	0.135048	−	0.0779697i
$361$			18.9721i			0.998532i
$362$	−16.1226	+	4.32005i	−0.847387	+	0.227057i
$363$	−8.06957			−0.423543
$364$	−7.75134	+	5.56028i	−0.406281	+	0.291438i
$365$	−19.0473			−0.996979
$366$	9.47736	−	2.53945i	0.495389	−	0.132739i
$367$			25.1026i			1.31035i	0.755478	+	0.655174i	$0.227405\pi$
$367$			25.1026i			1.31035i	−0.755478	+	0.655174i	$0.772595\pi$
$368$	−1.39712	+	0.806627i	−0.0728299	+	0.0420484i
$369$	−9.71078	−	2.60200i	−0.505523	−	0.135454i
$370$	5.33538	+	19.9119i	0.277373	+	1.03517i
$371$	−4.45390	−	4.05711i	−0.231235	−	0.210634i
$372$	−6.09924	+	6.09924i	−0.316231	+	0.316231i
$373$	16.5288			0.855829			0.427915	−	0.903819i	$-0.359248\pi$
$373$	16.5288			0.855829			0.427915	+	0.903819i	$0.359248\pi$
$374$	4.05597			0.209729
$375$	2.60647	−	2.60647i	0.134598	−	0.134598i
$376$	−4.52756	−	7.84196i	−0.233491	−	0.404418i
$377$	9.39188	−	10.4248i	0.483706	−	0.536905i
$378$	2.64288	−	0.123214i	0.135935	−	0.00633742i
$379$	5.26805	−	19.6606i	0.270602	−	1.00990i	−0.688130	−	0.725587i	$-0.741568\pi$
$379$	5.26805	−	19.6606i	0.270602	−	1.00990i	0.958732	−	0.284312i	$-0.0917651\pi$
$380$	−0.247108	+	0.428003i	−0.0126764	+	0.0219561i
$381$	−10.5021	−	18.1902i	−0.538041	−	0.931914i
$382$	14.2934	−	3.82989i	0.731312	−	0.195954i
$383$	1.93943	−	1.93943i	0.0991001	−	0.0991001i	−0.655819	−	0.754919i	$-0.727676\pi$
$383$	1.93943	−	1.93943i	0.0991001	−	0.0991001i	0.754919	+	0.655819i	$0.227676\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	−10.3757	−	32.5716i	−0.528794	−	1.66000i
$386$	12.3796	−	21.4420i	0.630103	−	1.09137i
$387$	−4.51157	−	2.60476i	−0.229336	−	0.132407i
$388$	−7.85562	−	7.85562i	−0.398809	−	0.398809i
$389$	−2.29812	−	1.32682i	−0.116519	−	0.0672724i	0.440608	−	0.897700i	$-0.354763\pi$
$389$	−2.29812	−	1.32682i	−0.116519	−	0.0672724i	−0.557127	+	0.830427i	$0.688096\pi$
$390$	10.1467	−	3.29369i	0.513799	−	0.166782i
$391$			1.49840i			0.0757772i
$392$	−6.56359	+	2.43296i	−0.331511	+	0.122883i
$393$	10.2829	+	17.8105i	0.518703	+	0.898420i
$394$			18.7692i			0.945577i
$395$	−6.59168	−	24.6005i	−0.331663	−	1.23778i
$396$	1.13023	−	4.21807i	0.0567962	−	0.211966i
$397$	8.93860	+	8.93860i	0.448615	+	0.448615i	0.894894	−	0.446279i	$-0.147251\pi$
$397$	8.93860	+	8.93860i	0.448615	+	0.448615i	−0.446279	+	0.894894i	$0.647251\pi$
$398$	−7.77274	−	7.77274i	−0.389612	−	0.389612i
$399$	−0.372021	+	0.238551i	−0.0186243	+	0.0119425i
$400$	3.25120	−	1.87708i	0.162560	−	0.0938541i
$401$	6.26409	+	23.3779i	0.312814	+	1.16744i	0.926008	+	0.377505i	$0.123218\pi$
$401$	6.26409	+	23.3779i	0.312814	+	1.16744i	−0.613194	+	0.789932i	$0.710116\pi$
$402$	2.73265	−	4.73309i	0.136292	−	0.236065i
$403$	−26.0876	+	16.9310i	−1.29951	+	0.843392i
$404$	6.73139	−	3.88637i	0.334899	−	0.193354i
$405$	−2.85793	−	0.765779i	−0.142012	−	0.0380519i
$406$	8.66746	−	5.55784i	0.430159	−	0.275831i
$407$	26.3489	+	15.2125i	1.30607	+	0.754058i
$408$	−0.240392	+	0.897155i	−0.0119012	+	0.0444158i
$409$	−28.0905	−	7.52684i	−1.38899	−	0.372178i	−0.514610	−	0.857424i	$-0.672063\pi$
$409$	−28.0905	−	7.52684i	−1.38899	−	0.372178i	−0.874378	+	0.485246i	$0.838730\pi$
$410$	−28.7317	−	7.69864i	−1.41896	−	0.380209i
$411$	−3.32369	+	12.4042i	−0.163946	+	0.611853i
$412$	−8.44236	−	4.87420i	−0.415925	−	0.240134i
$413$	−8.20161	−	4.23874i	−0.403575	−	0.208575i
$414$	1.55828	+	0.417541i	0.0765855	+	0.0205210i
$415$	−6.56521	+	3.79042i	−0.322273	+	0.186065i
$416$	−3.60066	+	0.187680i	−0.176537	+	0.00920179i
$417$	9.99586	−	17.3133i	0.489499	−	0.847838i
$418$	0.188788	+	0.704568i	0.00923395	+	0.0344616i
$419$	−1.80135	+	1.04001i	−0.0880017	+	0.0508078i	−0.543355	−	0.839503i	$-0.682846\pi$
$419$	−1.80135	+	1.04001i	−0.0880017	+	0.0508078i	0.455353	+	0.890311i	$0.349513\pi$
$420$	7.81961	−	0.364557i	0.381558	−	0.0177886i
$421$	23.4430	+	23.4430i	1.14254	+	1.14254i	0.987984	+	0.154559i	$0.0493958\pi$
$421$	23.4430	+	23.4430i	1.14254	+	1.14254i	0.154559	+	0.987984i	$0.450604\pi$
$422$	6.80709	+	6.80709i	0.331364	+	0.331364i
$423$	−2.34364	+	8.74657i	−0.113951	+	0.425273i
$424$	−0.589365	−	2.19954i	−0.0286221	−	0.106819i
$425$		−	3.48688i		−	0.169139i
$426$	−3.71538	−	6.43523i	−0.180011	−	0.311788i
$427$	25.3604	+	5.54372i	1.22728	+	0.268280i
$428$		−	8.33119i		−	0.402703i
$429$	7.15204	−	14.0269i	0.345304	−	0.677223i
$430$	−13.3486	−	7.70681i	−0.643726	−	0.371655i
$431$	−13.9336	−	13.9336i	−0.671156	−	0.671156i	0.286827	−	0.957983i	$-0.407400\pi$
$431$	−13.9336	−	13.9336i	−0.671156	−	0.671156i	−0.957983	+	0.286827i	$0.907400\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−10.1105	+	17.5119i	−0.485879	+	0.841566i	−0.999868	−	0.0162300i	$-0.994834\pi$
$433$	−10.1105	+	17.5119i	−0.485879	+	0.841566i	0.513990	+	0.857796i	$0.328167\pi$
$434$	−21.7447	+	6.92675i	−1.04378	+	0.332495i
$435$	−11.1220	+	2.98014i	−0.533261	+	0.142887i
$436$	−4.82436	+	4.82436i	−0.231045	+	0.231045i
$437$	−0.260289	+	0.0697442i	−0.0124513	+	0.00333632i
$438$	−3.21881	−	5.57514i	−0.153801	−	0.266390i
$439$	16.7154	−	28.9520i	0.797784	−	1.38180i	−0.123272	−	0.992373i	$-0.539339\pi$
$439$	16.7154	−	28.9520i	0.797784	−	1.38180i	0.921056	−	0.389430i	$-0.127328\pi$
$440$	3.34406	−	12.4802i	0.159422	−	0.594970i
$441$	6.36152	+	2.92080i	0.302930	+	0.139086i
$442$	−1.52119	+	2.98341i	−0.0723556	+	0.141907i
$443$	−0.726887	−	1.25900i	−0.0345354	−	0.0598171i	0.848241	−	0.529610i	$-0.177662\pi$
$443$	−0.726887	−	1.25900i	−0.0345354	−	0.0598171i	−0.882777	+	0.469793i	$0.844328\pi$
$444$	−4.92659	+	4.92659i	−0.233806	+	0.233806i
$445$	35.9719			1.70523
$446$	4.78177			0.226423
$447$	−6.73159	+	6.73159i	−0.318393	+	0.318393i
$448$	−2.58472	−	0.565013i	−0.122116	−	0.0266943i
$449$	−6.78725	−	25.3304i	−0.320310	−	1.19541i	−0.918943	−	0.394390i	$-0.870956\pi$
$449$	−6.78725	−	25.3304i	−0.320310	−	1.19541i	0.598633	−	0.801023i	$-0.295711\pi$
$450$	−3.62625	−	0.971650i	−0.170943	−	0.0458040i
$451$	−38.0199	+	21.9508i	−1.79029	+	1.03362i
$452$		−	0.350714i		−	0.0164962i
$453$	14.6710	−	3.93110i	0.689306	−	0.184699i
$454$	−25.0431			−1.17533
$455$	27.8499	+	4.58404i	1.30562	+	0.214903i
$456$	−0.167036			−0.00782215
$457$	24.7442	−	6.63018i	1.15748	−	0.310147i	0.371523	−	0.928424i	$-0.378836\pi$
$457$	24.7442	−	6.63018i	1.15748	−	0.310147i	0.785960	+	0.618277i	$0.212169\pi$
$458$		−	15.3285i		−	0.716256i
$459$	0.804367	−	0.464402i	0.0375446	−	0.0216764i
$460$	4.61056	+	1.23540i	0.214969	+	0.0576007i
$461$	3.62598	+	13.5323i	0.168879	+	0.630264i	0.997514	+	0.0704742i	$0.0224513\pi$
$461$	3.62598	+	13.5323i	0.168879	+	0.630264i	−0.828635	+	0.559789i	$0.810882\pi$
$462$	7.78034	−	8.54127i	0.361974	−	0.397376i
$463$	18.1441	−	18.1441i	0.843229	−	0.843229i	−0.146048	−	0.989277i	$-0.546655\pi$
$463$	18.1441	−	18.1441i	0.843229	−	0.843229i	0.989277	+	0.146048i	$0.0466554\pi$
$464$	3.89165			0.180665
$465$	25.5210			1.18351
$466$	−8.64886	+	8.64886i	−0.400650	+	0.400650i
$467$	4.26229	+	7.38250i	0.197235	+	0.341621i	0.947631	−	0.319367i	$-0.103470\pi$
$467$	4.26229	+	7.38250i	0.197235	+	0.341621i	−0.750396	+	0.660989i	$0.770137\pi$
$468$	2.67876	+	2.41334i	0.123826	+	0.111557i
$469$	12.1723	−	7.80525i	0.562065	−	0.360413i
$470$	−6.93422	+	25.8789i	−0.319852	+	1.19370i
$471$	7.57314	−	13.1171i	0.348952	−	0.604403i
$472$	−1.74472	−	3.02194i	−0.0803072	−	0.139096i
$473$	−21.9741	+	5.88795i	−1.01037	+	0.270728i
$474$	6.08664	−	6.08664i	0.279568	−	0.279568i
$475$	0.605712	−	0.162300i	0.0277920	−	0.00744683i
$476$	−1.65482	+	1.81667i	−0.0758488	+	0.0832669i
$477$	−1.13857	+	1.97205i	−0.0521314	+	0.0902942i
$478$	−22.0316	−	12.7199i	−1.00770	−	0.581796i
$479$	17.0579	+	17.0579i	0.779397	+	0.779397i	0.979728	−	0.200331i	$-0.0642018\pi$
$479$	17.0579	+	17.0579i	0.779397	+	0.779397i	−0.200331	+	0.979728i	$0.564202\pi$
$480$	2.56235	+	1.47937i	0.116955	+	0.0675238i
$481$	−21.0719	+	13.6758i	−0.960798	+	0.623563i
$482$			23.0373i			1.04932i
$483$	3.15540	+	2.87429i	0.143576	+	0.130785i
$484$	−4.03478	−	6.98845i	−0.183399	−	0.317657i
$485$			32.8702i			1.49256i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	−6.47359	+	24.1598i	−0.293347	+	1.09478i	0.649175	+	0.760639i	$0.275114\pi$
$487$	−6.47359	+	24.1598i	−0.293347	+	1.09478i	−0.942522	+	0.334145i	$0.891552\pi$
$488$	6.93791	+	6.93791i	0.314064	+	0.314064i
$489$	−5.53190	−	5.53190i	−0.250161	−	0.250161i
$490$	18.8221	+	8.64189i	0.850296	+	0.390401i
$491$	24.9338	−	14.3955i	1.12525	−	0.649661i	0.182511	−	0.983204i	$-0.441578\pi$
$491$	24.9338	−	14.3955i	1.12525	−	0.649661i	0.942735	+	0.333543i	$0.108244\pi$
$492$	−2.60200	−	9.71078i	−0.117307	−	0.437796i
$493$	1.80729	−	3.13031i	0.0813961	−	0.140982i
$494$	−0.589059	−	0.125383i	−0.0265030	−	0.00564123i
$495$	−11.1894	+	6.46023i	−0.502928	+	0.290366i
$496$	−8.33172	−	2.23248i	−0.374105	−	0.100241i
$497$	−0.915570	−	19.6386i	−0.0410689	−	0.880912i
$498$	−2.21892	−	1.28109i	−0.0994321	−	0.0574071i
$499$	−2.95669	+	11.0345i	−0.132360	+	0.493972i	−0.999995	−	0.00322879i	$-0.998972\pi$
$499$	−2.95669	+	11.0345i	−0.132360	+	0.493972i	0.867635	+	0.497201i	$0.165639\pi$
$500$	3.56050	+	0.954034i	0.159231	+	0.0426657i
$501$	3.95484	+	1.05970i	0.176689	+	0.0473438i
$502$	5.50213	−	20.5342i	0.245572	−	0.916487i
$503$	20.5073	+	11.8399i	0.914374	+	0.527914i	0.881836	−	0.471556i	$-0.156308\pi$
$503$	20.5073	+	11.8399i	0.914374	+	0.527914i	0.0325383	+	0.999470i	$0.489641\pi$
$504$	1.42815	+	2.22720i	0.0636147	+	0.0992072i
$505$	−22.2139	−	5.95220i	−0.988507	−	0.264870i
$506$	6.10104	−	3.52244i	0.271224	−	0.156591i
$507$	7.63525	+	10.5215i	0.339093	+	0.467278i
$508$	10.5021	−	18.1902i	0.465957	−	0.807061i
$509$	5.00677	+	18.6855i	0.221921	+	0.828221i	0.983615	+	0.180283i	$0.0577015\pi$
$509$	5.00677	+	18.6855i	0.221921	+	0.828221i	−0.761694	+	0.647937i	$0.775632\pi$
$510$	2.37992	−	1.37405i	0.105384	−	0.0608438i
$511$	−0.793201	−	17.0138i	−0.0350892	−	0.752648i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.118112	+	0.118112i	0.00521477	+	0.00521477i
$514$	−4.45010	+	16.6080i	−0.196286	+	0.732548i
$515$	7.46512	+	27.8602i	0.328952	+	1.22767i
$516$		−	5.20951i		−	0.229336i
$517$	19.7713	+	34.2448i	0.869539	+	1.50609i
$518$	−17.5640	+	5.59500i	−0.771718	+	0.245830i
$519$			24.3026i			1.06677i
$520$	7.92578	+	7.14046i	0.347568	+	0.313130i
$521$	31.7915	+	18.3549i	1.39281	+	0.804141i	0.993626	−	0.112729i	$-0.0359592\pi$
$521$	31.7915	+	18.3549i	1.39281	+	0.804141i	0.399187	+	0.916870i	$0.369293\pi$
$522$	−2.75181	−	2.75181i	−0.120443	−	0.120443i
$523$	3.40826	+	1.96776i	0.149033	+	0.0860441i	0.572662	−	0.819792i	$-0.305911\pi$
$523$	3.40826	+	1.96776i	0.149033	+	0.0860441i	−0.423629	+	0.905836i	$0.639244\pi$
$524$	−10.2829	+	17.8105i	−0.449210	+	0.778054i
$525$	−7.34286	−	6.68870i	−0.320469	−	0.291919i
$526$	8.31889	−	2.22904i	0.362721	−	0.0971908i
$527$	−5.66500	+	5.66500i	−0.246771	+	0.246771i
$528$	4.21807	−	1.13023i	0.183568	−	0.0491869i
$529$	−10.1987	−	17.6647i	−0.443422	−	0.768029i
$530$	−3.36873	+	5.83480i	−0.146328	+	0.253448i
$531$	−0.903133	+	3.37054i	−0.0391927	+	0.146269i
$532$	−0.392602	−	0.202904i	−0.0170214	−	0.00879699i
$533$	−1.88682	−	36.1987i	−0.0817271	−	1.56794i
$534$	6.07891	+	10.5290i	0.263060	+	0.455634i
$535$	−17.4301	+	17.4301i	−0.753569	+	0.753569i
$536$	5.46530			0.236065
$537$	−8.40690			−0.362784
$538$	5.40153	−	5.40153i	0.232876	−	0.232876i
$539$	28.6624	−	10.6244i	1.23457	−	0.457626i
$540$	−0.765779	−	2.85793i	−0.0329539	−	0.122986i
$541$	28.6868	+	7.68661i	1.23334	+	0.330473i	0.815880	−	0.578221i	$-0.196253\pi$
$541$	28.6868	+	7.68661i	1.23334	+	0.330473i	0.417462	+	0.908694i	$0.362920\pi$
$542$	14.3241	−	8.27001i	0.615271	−	0.355227i
$543$			16.6914i			0.716295i
$544$	−0.897155	+	0.240392i	−0.0384652	+	0.0103067i
$545$	20.1866			0.864698
$546$	3.36462	+	8.92633i	0.143992	+	0.382012i
$547$	19.7265			0.843446			0.421723	−	0.906725i	$-0.361426\pi$
$547$	19.7265			0.843446			0.421723	+	0.906725i	$0.361426\pi$
$548$	−12.4042	+	3.32369i	−0.529880	+	0.141981i
$549$		−	9.81168i		−	0.418752i
$550$	−14.1976	+	8.19698i	−0.605387	+	0.349520i
$551$	0.627893	+	0.168244i	0.0267492	+	0.00716742i
$552$	0.417541	+	1.55828i	0.0177717	+	0.0663250i
$553$	21.6997	−	6.91244i	0.922766	−	0.293947i
$554$	−16.8138	+	16.8138i	−0.714350	+	0.714350i
$555$	20.6143			0.875029
$556$	19.9917			0.847838
$557$	30.0096	−	30.0096i	1.27155	−	1.27155i	0.326272	−	0.945276i	$-0.394207\pi$
$557$	30.0096	−	30.0096i	1.27155	−	1.27155i	0.945276	−	0.326272i	$-0.105793\pi$
$558$	4.31282	+	7.47002i	0.182576	+	0.316231i
$559$	3.91044	−	18.3716i	0.165394	−	0.777036i
$560$	4.22552	+	6.58970i	0.178561	+	0.278466i
$561$	1.04976	−	3.91776i	0.0443209	−	0.165408i
$562$	−1.80042	+	3.11843i	−0.0759463	+	0.131543i
$563$	−1.24795	−	2.16152i	−0.0525949	−	0.0910970i	0.838529	−	0.544856i	$-0.183416\pi$
$563$	−1.24795	−	2.16152i	−0.0525949	−	0.0910970i	−0.891124	+	0.453759i	$0.850083\pi$
$564$	−8.74657	+	2.34364i	−0.368297	+	0.0986849i
$565$	−0.733745	+	0.733745i	−0.0308689	+	0.0308689i
$566$	−1.72886	+	0.463246i	−0.0726693	+	0.0194717i
$567$	0.565013	−	2.58472i	0.0237283	−	0.108548i
$568$	3.71538	−	6.43523i	0.155894	−	0.270016i
$569$	19.3886	+	11.1940i	0.812814	+	0.469278i	0.847932	−	0.530105i	$-0.177847\pi$
$569$	19.3886	+	11.1940i	0.812814	+	0.469278i	−0.0351183	+	0.999383i	$0.511181\pi$
$570$	0.349463	+	0.349463i	0.0146374	+	0.0146374i
$571$	29.1379	+	16.8228i	1.21938	+	0.704011i	0.964786	−	0.263036i	$-0.0847238\pi$
$571$	29.1379	+	16.8228i	1.21938	+	0.704011i	0.254597	+	0.967047i	$0.418057\pi$
$572$	15.7236	−	0.819577i	0.657438	−	0.0342682i
$573$		−	14.7976i		−	0.618178i
$574$	5.68026	−	25.9850i	0.237090	−	1.08459i
$575$	−3.02821	−	5.24502i	−0.126285	−	0.218732i
$576$			1.00000i			0.0416667i
$577$	6.71327	+	25.0543i	0.279477	+	1.04302i	0.952781	+	0.303657i	$0.0982078\pi$
$577$	6.71327	+	25.0543i	0.279477	+	1.04302i	−0.673304	+	0.739366i	$0.735126\pi$
$578$	4.17665	−	15.5875i	0.173726	−	0.648353i
$579$	−17.5073	−	17.5073i	−0.727580	−	0.727580i
$580$	−8.14190	−	8.14190i	−0.338074	−	0.338074i
$581$	−3.65918	−	5.70649i	−0.151808	−	0.236745i
$582$	−9.62113	+	5.55476i	−0.398809	+	0.230252i
$583$	2.57368	+	9.60511i	0.106591	+	0.397803i
$584$	3.21881	−	5.57514i	0.133195	−	0.230701i
$585$	−0.555299	−	10.6534i	−0.0229588	−	0.440466i
$586$	−3.60938	+	2.08388i	−0.149102	+	0.0860841i
$587$	34.8159	+	9.32890i	1.43701	+	0.385045i	0.891484	−	0.453052i	$-0.149665\pi$
$587$	34.8159	+	9.32890i	1.43701	+	0.385045i	0.545522	+	0.838096i	$0.316331\pi$
$588$	0.651277	+	6.96964i	0.0268582	+	0.287423i
$589$	−1.24776	−	0.720393i	−0.0514130	−	0.0296833i
$590$	−2.67214	+	9.97256i	−0.110010	+	0.410564i
$591$	18.1296	+	4.85782i	0.745753	+	0.199824i
$592$	−6.72985	−	1.80326i	−0.276595	−	0.0741134i
$593$	6.56716	−	24.5090i	0.269681	−	1.00646i	−0.689642	−	0.724151i	$-0.742232\pi$
$593$	6.56716	−	24.5090i	0.269681	−	1.00646i	0.959323	−	0.282312i	$-0.0911014\pi$
$594$	−3.78182	−	2.18344i	−0.155170	−	0.0895875i
$595$	7.26288	−	0.338602i	0.297749	−	0.0138813i
$596$	−9.19552	−	2.46393i	−0.376663	−	0.100927i
$597$	−9.51962	+	5.49616i	−0.389612	+	0.224943i
$598$	0.302776	+	5.80879i	0.0123814	+	0.237539i
$599$	24.4230	−	42.3019i	0.997897	−	1.72841i	0.442808	−	0.896617i	$-0.353982\pi$
$599$	24.4230	−	42.3019i	0.997897	−	1.72841i	0.555089	−	0.831791i	$-0.312684\pi$
$600$	−0.971650	−	3.62625i	−0.0396674	−	0.148041i
$601$	−20.2207	+	11.6744i	−0.824820	+	0.476210i	−0.852076	−	0.523418i	$-0.824657\pi$
$601$	−20.2207	+	11.6744i	−0.824820	+	0.476210i	0.0272557	+	0.999628i	$0.491323\pi$
$602$	6.32818	−	12.2445i	0.257917	−	0.499048i
$603$	−3.86455	−	3.86455i	−0.157377	−	0.157377i
$604$	10.7400	+	10.7400i	0.437002	+	0.437002i
$605$	−6.17951	+	23.0622i	−0.251233	+	0.937613i
$606$	−2.01173	−	7.50789i	−0.0817211	−	0.304987i
$607$			39.0229i			1.58389i	0.610591	+	0.791946i	$0.290932\pi$
$607$			39.0229i			1.58389i	−0.610591	+	0.791946i	$0.709068\pi$
$608$	−0.0835178	−	0.144657i	−0.00338709	−	0.00586662i
$609$	−3.12516	−	9.81059i	−0.126638	−	0.397545i
$610$		−	29.0303i		−	1.17540i
$611$	−32.6044	+	1.69947i	−1.31903	+	0.0687531i
$612$	0.804367	+	0.464402i	0.0325146	+	0.0187723i
$613$	5.12073	+	5.12073i	0.206824	+	0.206824i	0.802916	−	0.596092i	$-0.203281\pi$
$613$	5.12073	+	5.12073i	0.206824	+	0.206824i	−0.596092	+	0.802916i	$0.703281\pi$
$614$	−5.07957	−	2.93269i	−0.204995	−	0.118354i
$615$	−14.8726	+	25.7601i	−0.599722	+	1.03875i
$616$	11.2871	+	2.46734i	0.454771	+	0.0994119i
$617$	−8.86874	+	2.37637i	−0.357042	+	0.0956691i	−0.432881	−	0.901451i	$-0.642503\pi$
$617$	−8.86874	+	2.37637i	−0.357042	+	0.0956691i	0.0758393	+	0.997120i	$0.475836\pi$
$618$	−6.89316	+	6.89316i	−0.277283	+	0.277283i
$619$	−5.08319	+	1.36204i	−0.204311	+	0.0547449i	−0.359523	−	0.933136i	$-0.617061\pi$
$619$	−5.08319	+	1.36204i	−0.204311	+	0.0547449i	0.155212	+	0.987881i	$0.450394\pi$
$620$	12.7605	+	22.1019i	0.512475	+	0.887632i
$621$	0.806627	−	1.39712i	0.0323688	−	0.0560645i
$622$	8.66981	−	32.3562i	0.347628	−	1.29736i
$623$	1.49801	+	32.1317i	0.0600165	+	1.28733i
$624$	−0.750635	+	3.52655i	−0.0300494	+	0.141175i
$625$	−14.8385	−	25.7011i	−0.593541	−	1.02804i
$626$	−11.3099	+	11.3099i	−0.452034	+	0.452034i
$627$	0.729423			0.0291303
$628$	15.1463			0.604403
$629$	−4.57583	+	4.57583i	−0.182450	+	0.182450i
$630$	1.67173	−	7.64751i	0.0666032	−	0.304684i
$631$	−6.94295	−	25.9114i	−0.276394	−	1.03152i	−0.954901	−	0.296924i	$-0.904039\pi$
$631$	−6.94295	−	25.9114i	−0.276394	−	1.03152i	0.678507	−	0.734594i	$-0.262627\pi$
$632$	8.31450	+	2.22786i	0.330733	+	0.0886197i
$633$	8.33694	−	4.81334i	0.331364	−	0.191313i
$634$		−	12.4198i		−	0.493252i
$635$	−60.0287	+	16.0846i	−2.38217	+	0.638300i
$636$	−2.27713			−0.0902942
$637$	−2.93489	+	25.0676i	−0.116285	+	0.993216i
$638$	−16.9943			−0.672812
$639$	−7.17756	+	1.92322i	−0.283940	+	0.0760815i
$640$			2.95874i			0.116955i
$641$	8.22804	−	4.75046i	0.324988	−	0.187632i	−0.328626	−	0.944460i	$-0.606585\pi$
$641$	8.22804	−	4.75046i	0.324988	−	0.187632i	0.653614	+	0.756828i	$0.273252\pi$
$642$	−8.04732	−	2.15627i	−0.317602	−	0.0851013i
$643$	−1.89475	−	7.07129i	−0.0747215	−	0.278865i	0.918448	−	0.395541i	$-0.129443\pi$
$643$	−1.89475	−	7.07129i	−0.0747215	−	0.278865i	−0.993170	+	0.116676i	$0.962776\pi$
$644$	−0.911509	+	4.16981i	−0.0359185	+	0.164313i
$645$	−10.8991	+	10.8991i	−0.429151	+	0.429151i
$646$	−0.155143			−0.00610402
$647$	−4.33884			−0.170577			−0.0852887	−	0.996356i	$-0.527181\pi$
$647$	−4.33884			−0.170577			−0.0852887	+	0.996356i	$0.527181\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	7.61897	+	13.1964i	0.299071	+	0.518006i
$650$	−0.704584	−	13.5175i	−0.0276360	−	0.530199i
$651$	1.06279	+	22.7965i	0.0416542	+	0.893466i
$652$	2.02482	−	7.55672i	0.0792980	−	0.295944i
$653$	−16.3540	+	28.3260i	−0.639983	+	1.10848i	0.345453	+	0.938436i	$0.387725\pi$
$653$	−16.3540	+	28.3260i	−0.639983	+	1.10848i	−0.985436	+	0.170047i	$0.945608\pi$
$654$	3.41134	+	5.90862i	0.133394	+	0.231045i
$655$	58.7755	−	15.7488i	2.29655	−	0.615358i
$656$	7.10878	−	7.10878i	0.277551	−	0.277551i
$657$	−6.21826	+	1.66618i	−0.242597	+	0.0650038i
$658$	−23.4049	−	5.11625i	−0.912418	−	0.199452i
$659$	−16.4529	+	28.4972i	−0.640913	+	1.11009i	0.344316	+	0.938854i	$0.388111\pi$
$659$	−16.4529	+	28.4972i	−0.640913	+	1.11009i	−0.985229	+	0.171241i	$0.945222\pi$
$660$	−11.1894	−	6.46023i	−0.435548	−	0.251464i
$661$	−24.2282	−	24.2282i	−0.942369	−	0.942369i	0.0560590	−	0.998427i	$-0.482147\pi$
$661$	−24.2282	−	24.2282i	−0.942369	−	0.942369i	−0.998427	+	0.0560590i	$0.982147\pi$
$662$	0.544361	+	0.314287i	0.0211572	+	0.0122151i
$663$	2.48804	+	2.24152i	0.0966276	+	0.0870535i
$664$		−	2.56219i		−	0.0994321i
$665$	0.396876	+	1.24589i	0.0153902	+	0.0483134i
$666$	3.48363	+	6.03382i	0.134988	+	0.233806i
$667$		−	6.27822i		−	0.243093i
$668$	1.05970	+	3.95484i	0.0410009	+	0.153018i
$669$	1.23761	−	4.61883i	0.0478489	−	0.178574i
$670$	−11.4342	−	11.4342i	−0.441743	−	0.441743i
$671$	−30.2969	−	30.2969i	−1.16960	−	1.16960i
$672$	−1.21473	+	2.35041i	−0.0468594	+	0.0906690i
$673$	26.3740	−	15.2270i	1.01664	−	0.586959i	0.103513	−	0.994628i	$-0.466992\pi$
$673$	26.3740	−	15.2270i	1.01664	−	0.586959i	0.913130	+	0.407669i	$0.133658\pi$
$674$	−0.159830	−	0.596494i	−0.00615642	−	0.0229761i
$675$	−1.87708	+	3.25120i	−0.0722489	+	0.125139i
$676$	−5.29430	+	11.8731i	−0.203627	+	0.456657i
$677$	24.6190	−	14.2138i	0.946185	−	0.546280i	0.0542912	−	0.998525i	$-0.482710\pi$
$677$	24.6190	−	14.2138i	0.946185	−	0.546280i	0.891894	+	0.452245i	$0.149377\pi$
$678$	−0.338763	−	0.0907714i	−0.0130101	−	0.00348605i
$679$	−29.3611	+	1.36884i	−1.12678	+	0.0525314i
$680$	2.37992	+	1.37405i	0.0912656	+	0.0526922i
$681$	−6.48163	+	24.1898i	−0.248377	+	0.926954i
$682$	36.3836	+	9.74894i	1.39320	+	0.373306i
$683$	−42.6877	−	11.4381i	−1.63340	−	0.437668i	−0.678501	−	0.734599i	$-0.737370\pi$
$683$	−42.6877	−	11.4381i	−1.63340	−	0.437668i	−0.954899	+	0.296931i	$0.904037\pi$
$684$	−0.0432320	+	0.161344i	−0.00165302	+	0.00616914i
$685$	32.9050	+	18.9977i	1.25724	+	0.725866i
$686$	−6.93549	+	17.1726i	−0.264798	+	0.655654i
$687$	−14.8062	−	3.96732i	−0.564893	−	0.151363i
$688$	4.51157	−	2.60476i	0.172002	−	0.0993054i
$689$	−8.03042	−	1.70929i	−0.305935	−	0.0651189i
$690$	2.38660	−	4.13372i	0.0908564	−	0.157368i
$691$	2.10920	+	7.87165i	0.0802378	+	0.299452i	0.994370	−	0.105965i	$-0.0337931\pi$
$691$	2.10920	+	7.87165i	0.0802378	+	0.299452i	−0.914132	+	0.405417i	$0.867126\pi$
$692$	−21.0467	+	12.1513i	−0.800074	+	0.461923i
$693$	−6.23653	−	9.72588i	−0.236906	−	0.369455i
$694$	13.8299	+	13.8299i	0.524976	+	0.524976i
$695$	−41.8256	−	41.8256i	−1.58654	−	1.58654i
$696$	1.00723	−	3.75904i	0.0381790	−	0.142486i
$697$	−2.41674	−	9.01941i	−0.0915406	−	0.341634i
$698$			12.9738i			0.491067i
$699$	6.11566	+	10.5926i	0.231316	+	0.400650i
$700$	2.12115	−	9.70345i	0.0801720	−	0.366756i
$701$		−	15.6543i		−	0.591254i	−0.955303	−	0.295627i	$-0.904471\pi$
$701$		−	15.6543i		−	0.591254i	0.955303	−	0.295627i	$-0.0955286\pi$
$702$	3.02443	−	1.96287i	0.114150	−	0.0740837i
$703$	−1.00786	−	0.581889i	−0.0380122	−	0.0219464i
$704$	3.08784	+	3.08784i	0.116378	+	0.116378i
$705$	23.2023	+	13.3959i	0.873851	+	0.504518i
$706$	5.78982	−	10.0283i	0.217903	−	0.377418i
$707$	4.39170	−	20.0903i	0.165167	−	0.755575i
$708$	−3.37054	+	0.903133i	−0.126673	+	0.0339418i
$709$	−2.05144	+	2.05144i	−0.0770436	+	0.0770436i	−0.744579	−	0.667535i	$-0.767349\pi$
$709$	−2.05144	+	2.05144i	−0.0770436	+	0.0770436i	0.667535	+	0.744579i	$0.267349\pi$
$710$	−21.2366	+	5.69032i	−0.796994	+	0.213554i
$711$	−4.30390	−	7.45458i	−0.161409	−	0.279568i
$712$	−6.07891	+	10.5290i	−0.227817	+	0.394590i
$713$	−3.60155	+	13.4412i	−0.134879	+	0.503376i
$714$	1.32647	+	2.06863i	0.0496418	+	0.0774164i
$715$	−34.6108	−	31.1815i	−1.29437	−	1.16612i
$716$	−4.20345	−	7.28059i	−0.157090	−	0.272088i
$717$	−17.9887	+	17.9887i	−0.671800	+	0.671800i
$718$	−13.0441			−0.486802
$719$	8.87640			0.331034			0.165517	−	0.986207i	$-0.447071\pi$
$719$	8.87640			0.331034			0.165517	+	0.986207i	$0.447071\pi$
$720$	2.09215	−	2.09215i	0.0779697	−	0.0779697i
$721$	−24.5751	+	7.82838i	−0.915224	+	0.291544i
$722$	4.91034	+	18.3256i	0.182744	+	0.682010i
$723$	22.2523	+	5.96249i	0.827572	+	0.221747i
$724$	−14.4552	+	8.34569i	−0.537222	+	0.310165i
$725$			14.6099i			0.542597i
$726$	−7.79460	+	2.08856i	−0.289285	+	0.0775137i
$727$	−7.55567			−0.280224			−0.140112	−	0.990136i	$-0.544746\pi$
$727$	−7.55567			−0.280224			−0.140112	+	0.990136i	$0.544746\pi$
$728$	−6.04812	+	7.37701i	−0.224158	+	0.273410i
$729$	−1.00000			−0.0370370
$730$	−18.3982	+	4.92979i	−0.680949	+	0.182460i
$731$		−	4.83861i		−	0.178963i
$732$	8.49717	−	4.90584i	0.314064	−	0.181325i
$733$	8.11440	+	2.17425i	0.299712	+	0.0803076i	0.405541	−	0.914077i	$-0.367083\pi$
$733$	8.11440	+	2.17425i	0.299712	+	0.0803076i	−0.105829	+	0.994384i	$0.533750\pi$
$734$	6.49704	+	24.2473i	0.239810	+	0.894984i
$735$	13.2189	−	15.9441i	0.487588	−	0.588106i
$736$	−1.14074	+	1.14074i	−0.0420484	+	0.0420484i
$737$	−23.8663			−0.879126
$738$	−10.0533			−0.370069
$739$	22.7413	−	22.7413i	0.836551	−	0.836551i	−0.151852	−	0.988403i	$-0.548524\pi$
$739$	22.7413	−	22.7413i	0.836551	−	0.836551i	0.988403	+	0.151852i	$0.0485237\pi$
$740$	10.3072	+	17.8525i	0.378899	+	0.656272i
$741$	−0.273570	+	0.536536i	−0.0100498	+	0.0197101i
$742$	−5.35219	−	2.76611i	−0.196485	−	0.101547i
$743$	9.74900	−	36.3837i	0.357656	−	1.33479i	−0.519453	−	0.854499i	$-0.673864\pi$
$743$	9.74900	−	36.3837i	0.357656	−	1.33479i	0.877109	−	0.480291i	$-0.159469\pi$
$744$	−4.31282	+	7.47002i	−0.158115	+	0.273864i
$745$	14.0835	+	24.3933i	0.515979	+	0.893701i
$746$	15.9656	−	4.27797i	0.584542	−	0.156628i
$747$	−1.81174	+	1.81174i	−0.0662880	+	0.0662880i
$748$	3.91776	−	1.04976i	0.143248	−	0.0383831i
$749$	−16.2952	−	14.8435i	−0.595413	−	0.542369i
$750$	1.84305	−	3.19226i	0.0672988	−	0.116565i
$751$	−4.89476	−	2.82599i	−0.178612	−	0.103122i	0.408028	−	0.912969i	$-0.366216\pi$
$751$	−4.89476	−	2.82599i	−0.178612	−	0.103122i	−0.586640	+	0.809847i	$0.699550\pi$
$752$	−6.40293	−	6.40293i	−0.233491	−	0.233491i
$753$	−18.4105	−	10.6293i	−0.670915	−	0.387353i
$754$	6.37372	−	12.5004i	0.232117	−	0.455237i
$755$		−	44.9391i		−	1.63550i
$756$	2.52094	−	0.803043i	0.0916856	−	0.0292064i
$757$	−14.4076	−	24.9546i	−0.523652	−	0.906991i	−0.999621	−	0.0275293i	$-0.991236\pi$
$757$	−14.4076	−	24.9546i	−0.523652	−	0.906991i	0.475969	−	0.879462i	$-0.342097\pi$
$758$		−	20.3542i		−	0.739297i
$759$	−1.82335	−	6.80483i	−0.0661833	−	0.247000i
$760$	−0.127912	+	0.477375i	−0.00463987	+	0.0173162i
$761$	25.4424	+	25.4424i	0.922287	+	0.922287i	0.997191	−	0.0749034i	$-0.0238648\pi$
$761$	25.4424	+	25.4424i	0.922287	+	0.922287i	−0.0749034	+	0.997191i	$0.523865\pi$
$762$	−14.8523	−	14.8523i	−0.538041	−	0.538041i
$763$	0.840647	+	18.0315i	0.0304335	+	0.652785i
$764$	12.8151	−	7.39879i	0.463633	−	0.267679i
$765$	−0.711258	−	2.65445i	−0.0257156	−	0.0959719i
$766$	1.37138	−	2.37530i	0.0495500	−	0.0858232i
$767$	−12.5643	+	0.654900i	−0.453671	+	0.0236471i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	4.05486	+	1.08650i	0.146222	+	0.0391801i	0.331188	−	0.943565i	$-0.392551\pi$
$769$	4.05486	+	1.08650i	0.146222	+	0.0391801i	−0.184966	+	0.982745i	$0.559217\pi$
$770$	−18.4523	−	28.7764i	−0.664975	−	1.03703i
$771$	14.8903	+	8.59693i	0.536262	+	0.309611i
$772$	6.40813	−	23.9155i	0.230634	−	0.860737i
$773$	27.7001	+	7.42223i	0.996304	+	0.266959i	0.719896	−	0.694082i	$-0.244189\pi$
$773$	27.7001	+	7.42223i	0.996304	+	0.266959i	0.276408	+	0.961040i	$0.410856\pi$
$774$	−5.03200	−	1.34832i	−0.180872	−	0.0484644i
$775$	8.38109	−	31.2787i	0.301058	−	1.12356i
$776$	−9.62113	−	5.55476i	−0.345378	−	0.199404i
$777$	0.858460	+	18.4136i	0.0307971	+	0.660585i
$778$	−2.56322	−	0.686812i	−0.0918959	−	0.0246234i
$779$	1.45429	−	0.839632i	0.0521052	−	0.0300830i
$780$	8.94850	−	5.80762i	0.320408	−	0.207946i
$781$	−16.2246	+	28.1018i	−0.580561	+	1.00556i
$782$	0.387813	+	1.44734i	0.0138682	+	0.0517568i
$783$	−3.37026	+	1.94582i	−0.120443	+	0.0695380i
$784$	−5.71024	+	4.04884i	−0.203937	+	0.144601i
$785$	−31.6883	−	31.6883i	−1.13100	−	1.13100i
$786$	14.5422	+	14.5422i	0.518703	+	0.518703i
$787$	7.04651	−	26.2979i	0.251181	−	0.937420i	−0.718994	−	0.695016i	$-0.755397\pi$
$787$	7.04651	−	26.2979i	0.251181	−	0.937420i	0.970175	−	0.242404i	$-0.0779360\pi$
$788$	4.85782	+	18.1296i	0.173053	+	0.645841i
$789$		−	8.61235i		−	0.306608i
$790$	−12.7341	−	22.0562i	−0.453061	−	0.784724i
$791$	−0.685969	−	0.624857i	−0.0243903	−	0.0222174i
$792$		−	4.36687i		−	0.155170i
$793$	33.6482	−	10.9224i	1.19488	−	0.387866i
$794$	10.9475	+	6.32054i	0.388512	+	0.224308i
$795$	4.76410	+	4.76410i	0.168965	+	0.168965i
$796$	−9.51962	−	5.49616i	−0.337414	−	0.194806i
$797$	−7.28549	+	12.6188i	−0.258065	+	0.446982i	−0.965724	−	0.259572i	$-0.916418\pi$
$797$	−7.28549	+	12.6188i	−0.258065	+	0.446982i	0.707658	+	0.706555i	$0.249752\pi$
$798$	−0.297603	+	0.326709i	−0.0105350	+	0.0115654i
$799$	−8.12384	+	2.17678i	−0.287401	+	0.0770088i
$800$	2.65460	−	2.65460i	0.0938541	−	0.0938541i
$801$	11.7436	−	3.14668i	0.414938	−	0.111182i
$802$	12.1013	+	20.9601i	0.427312	+	0.740125i
$803$	−14.0561	+	24.3459i	−0.496030	+	0.859149i
$804$	1.41452	−	5.27908i	0.0498864	−	0.186179i
$805$	10.6309	−	6.81684i	0.374689	−	0.240262i
$806$	−20.8166	+	23.1060i	−0.733234	+	0.813875i
$807$	−3.81946	−	6.61549i	−0.134451	−	0.232876i
$808$	5.49616	−	5.49616i	0.193354	−	0.193354i
$809$	−15.1798			−0.533693			−0.266847	−	0.963739i	$-0.585982\pi$
$809$	−15.1798			−0.533693			−0.266847	+	0.963739i	$0.585982\pi$
$810$	−2.95874			−0.103960
$811$	−3.93386	+	3.93386i	−0.138136	+	0.138136i	−0.772794	−	0.634657i	$-0.781141\pi$
$811$	−3.93386	+	3.93386i	−0.138136	+	0.138136i	0.634657	+	0.772794i	$0.281141\pi$
$812$	6.93364	−	7.61176i	0.243323	−	0.267121i
$813$	−4.28087	−	15.9764i	−0.150137	−	0.560318i
$814$	29.3884	+	7.87459i	1.03006	+	0.276004i
$815$	−20.0460	+	11.5736i	−0.702181	+	0.405404i
$816$			0.928803i			0.0325146i
$817$	0.840523	−	0.225218i	0.0294062	−	0.00787937i
$818$	−29.0815			−1.01681
$819$	9.49300	−	0.939668i	0.331712	−	0.0328346i
$820$	−29.7453			−1.03875
$821$	5.13969	−	1.37718i	0.179376	−	0.0480638i	−0.168013	−	0.985785i	$-0.553735\pi$
$821$	5.13969	−	1.37718i	0.179376	−	0.0480638i	0.347389	+	0.937721i	$0.387068\pi$
$822$			12.8418i			0.447908i
$823$	8.64548	−	4.99147i	0.301363	−	0.173992i	−0.341692	−	0.939812i	$-0.611000\pi$
$823$	8.64548	−	4.99147i	0.301363	−	0.173992i	0.643055	+	0.765820i	$0.277667\pi$
$824$	−9.41623	−	2.52307i	−0.328030	−	0.0878953i
$825$	4.24307	+	15.8353i	0.147725	+	0.551316i
$826$	−9.01921	−	1.97158i	−0.313819	−	0.0686000i
$827$	−26.7429	+	26.7429i	−0.929943	+	0.929943i	−0.997702	−	0.0677589i	$-0.978415\pi$
$827$	−26.7429	+	26.7429i	−0.929943	+	0.929943i	0.0677589	+	0.997702i	$0.478415\pi$
$828$	1.61325			0.0560645
$829$	−5.71525			−0.198499			−0.0992494	−	0.995063i	$-0.531644\pi$
$829$	−5.71525			−0.198499			−0.0992494	+	0.995063i	$0.531644\pi$
$830$	−5.36047	+	5.36047i	−0.186065	+	0.186065i
$831$	11.8892	+	20.5926i	0.412430	+	0.714350i
$832$	−3.42940	+	1.11321i	−0.118893	+	0.0385935i
$833$	0.604909	+	6.47342i	0.0209588	+	0.224291i
$834$	5.17424	−	19.3105i	0.179169	−	0.668669i
$835$	6.05707	−	10.4912i	0.209614	−	0.363062i
$836$	0.364711	+	0.631699i	0.0126138	+	0.0218478i
$837$	8.33172	−	2.23248i	0.287986	−	0.0771657i
$838$	−1.47080	+	1.47080i	−0.0508078	+	0.0508078i
$839$	−24.9742	+	6.69183i	−0.862206	+	0.231027i	−0.662715	−	0.748872i	$-0.730596\pi$
$839$	−24.9742	+	6.69183i	−0.862206	+	0.231027i	−0.199492	+	0.979900i	$0.563929\pi$
$840$	7.45881	−	2.37600i	0.257353	−	0.0819797i
$841$	6.92755	−	11.9989i	0.238881	−	0.413754i
$842$	28.7117	+	16.5767i	0.989471	+	0.571271i
$843$	2.54618	+	2.54618i	0.0876952	+	0.0876952i
$844$	8.33694	+	4.81334i	0.286969	+	0.165682i
$845$	35.9167	−	13.7638i	1.23557	−	0.473489i
$846$			9.05511i			0.311321i
$847$	−20.8575	−	4.55941i	−0.716674	−	0.156663i
$848$	−1.13857	−	1.97205i	−0.0390985	−	0.0677206i
$849$			1.78984i			0.0614273i
$850$	−0.902471	−	3.36807i	−0.0309545	−	0.115524i
$851$	−2.90911	+	10.8570i	−0.0997231	+	0.372172i
$852$	−5.25434	−	5.25434i	−0.180011	−	0.180011i
$853$	−30.2068	−	30.2068i	−1.03426	−	1.03426i	−0.999392	−	0.0348675i	$-0.988899\pi$
$853$	−30.2068	−	30.2068i	−1.03426	−	1.03426i	−0.0348675	−	0.999392i	$-0.511101\pi$
$854$	25.9311	−	1.20893i	0.887344	−	0.0413688i
$855$	0.428003	−	0.247108i	0.0146374	−	0.00845090i
$856$	−2.15627	−	8.04732i	−0.0736999	−	0.275052i
$857$	−6.20537	+	10.7480i	−0.211971	+	0.367145i	−0.952331	−	0.305065i	$-0.901322\pi$
$857$	−6.20537	+	10.7480i	−0.211971	+	0.367145i	0.740360	+	0.672211i	$0.234655\pi$
$858$	3.27793	−	15.4000i	0.111907	−	0.525747i
$859$	−39.8604	+	23.0134i	−1.36002	+	0.785207i	−0.989626	−	0.143668i	$-0.954110\pi$
$859$	−39.8604	+	23.0134i	−1.36002	+	0.785207i	−0.370393	+	0.928875i	$0.620777\pi$
$860$	−14.8884	−	3.98934i	−0.507691	−	0.136035i
$861$	−23.6295	−	12.2121i	−0.805290	−	0.416188i
$862$	−17.0651	−	9.85251i	−0.581238	−	0.335578i
$863$	4.65804	−	17.3840i	0.158562	−	0.591760i	−0.840212	−	0.542257i	$-0.817570\pi$
$863$	4.65804	−	17.3840i	0.158562	−	0.591760i	0.998774	−	0.0495024i	$-0.0157635\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	69.4551	+	18.6104i	2.36154	+	0.632773i
$866$	−5.23357	+	19.5319i	−0.177844	+	0.663722i
$867$	−13.9753	−	8.06866i	−0.474627	−	0.274026i
$868$	−19.2110	+	12.3187i	−0.652063	+	0.418123i
$869$	−36.3084	−	9.72880i	−1.23168	−	0.330027i
$870$	−9.97175	+	5.75719i	−0.338074	+	0.195187i
$871$	8.95105	−	17.5551i	0.303295	−	0.594833i
$872$	−3.41134	+	5.90862i	−0.115523	+	0.200091i
$873$	2.87536	+	10.7310i	0.0973160	+	0.363188i
$874$	−0.233369	+	0.134735i	−0.00789381	+	0.00455749i
$875$	8.20968	−	5.26430i	0.277538	−	0.177966i
$876$	−4.55208	−	4.55208i	−0.153801	−	0.153801i
$877$	−26.6549	−	26.6549i	−0.900073	−	0.900073i	0.0953692	−	0.995442i	$-0.469597\pi$
$877$	−26.6549	−	26.6549i	−0.900073	−	0.900073i	−0.995442	+	0.0953692i	$0.969597\pi$
$878$	8.65254	−	32.2917i	0.292009	−	1.08979i
$879$	1.07869	+	4.02574i	0.0363834	+	0.135785i
$880$		−	12.9205i		−	0.435548i
$881$	−6.87680	−	11.9110i	−0.231685	−	0.401291i	0.726619	−	0.687041i	$-0.241091\pi$
$881$	−6.87680	−	11.9110i	−0.231685	−	0.401291i	−0.958304	+	0.285750i	$0.907757\pi$
$882$	6.90072	+	1.17479i	0.232359	+	0.0395572i
$883$		−	15.0786i		−	0.507437i	−0.967278	−	0.253718i	$-0.918346\pi$
$883$		−	15.0786i		−	0.507437i	0.967278	−	0.253718i	$-0.0816537\pi$
$884$	−0.697192	+	3.27547i	−0.0234491	+	0.110166i
$885$	8.94116	+	5.16218i	0.300554	+	0.173525i
$886$	−1.02797	−	1.02797i	−0.0345354	−	0.0345354i
$887$	37.0661	+	21.4001i	1.24456	+	0.718545i	0.970019	−	0.243031i	$-0.0781416\pi$
$887$	37.0661	+	21.4001i	1.24456	+	0.718545i	0.274539	+	0.961576i	$0.411475\pi$
$888$	−3.48363	+	6.03382i	−0.116903	+	0.202482i
$889$	−16.8673	−	52.9505i	−0.565712	−	1.77590i
$890$	34.7462	−	9.31021i	1.16469	−	0.312079i
$891$	−3.08784	+	3.08784i	−0.103447	+	0.103447i
$892$	4.61883	−	1.23761i	0.154650	−	0.0414383i
$893$	−0.756263	−	1.30989i	−0.0253074	−	0.0438336i
$894$	−4.75995	+	8.24448i	−0.159197	+	0.275737i
$895$	−6.43783	+	24.0263i	−0.215193	+	0.803111i
$896$	−2.64288	+	0.123214i	−0.0882924	+	0.00411628i
$897$	5.68922	+	1.21097i	0.189958	+	0.0404329i
$898$	−13.1120	−	22.7106i	−0.437552	−	0.757862i
$899$	23.7361	−	23.7361i	0.791643	−	0.791643i
$900$	−3.75417			−0.125139
$901$	−2.11501			−0.0704611
$902$	−31.0432	+	31.0432i	−1.03362	+	1.03362i
$903$	−10.1894	−	9.28166i	−0.339082	−	0.308874i
$904$	−0.0907714	−	0.338763i	−0.00301901	−	0.0112671i
$905$	47.7027	+	12.7819i	1.58569	+	0.424885i
$906$	13.1537	−	7.59429i	0.437002	−	0.252303i
$907$		−	7.22339i		−	0.239849i	−0.992783	−	0.119924i	$-0.961735\pi$
$907$		−	7.22339i		−	0.239849i	0.992783	−	0.119924i	$-0.0382652\pi$
$908$	−24.1898	+	6.48163i	−0.802766	+	0.215100i
$909$	−7.77274			−0.257806
$910$	28.0874	−	2.78024i	0.931087	−	0.0921639i
$911$	19.7139			0.653149			0.326575	−	0.945171i	$-0.394106\pi$
$911$	19.7139			0.653149			0.326575	+	0.945171i	$0.394106\pi$
$912$	−0.161344	+	0.0432320i	−0.00534263	+	0.00143155i
$913$			11.1887i			0.370293i
$914$	22.1850	−	12.8085i	0.733815	−	0.423668i
$915$	−28.0411	−	7.51358i	−0.927009	−	0.248391i
$916$	−3.96732	−	14.8062i	−0.131084	−	0.489212i
$917$	16.5152	+	51.8450i	0.545380	+	1.71207i
$918$	0.656763	−	0.656763i	0.0216764	−	0.0216764i
$919$	−26.9549			−0.889159			−0.444580	−	0.895739i	$-0.646647\pi$
$919$	−26.9549			−0.889159			−0.444580	+	0.895739i	$0.646647\pi$
$920$	4.77321			0.157368
$921$	−4.14745	+	4.14745i	−0.136663	+	0.136663i
$922$	7.00485	+	12.1328i	0.230692	+	0.399571i
$923$	−14.5856	−	22.4738i	−0.480091	−	0.739734i
$924$	5.30459	−	10.2639i	0.174508	−	0.337659i
$925$	6.76973	−	25.2650i	0.222587	−	0.830707i
$926$	12.8298	−	22.2219i	0.421615	−	0.730258i
$927$	4.87420	+	8.44236i	0.160090	+	0.277283i
$928$	3.75904	−	1.00723i	0.123397	−	0.0330640i
$929$	0.420075	−	0.420075i	0.0137822	−	0.0137822i	−0.700182	−	0.713964i	$-0.746898\pi$
$929$	0.420075	−	0.420075i	0.0137822	−	0.0137822i	0.713964	+	0.700182i	$0.246898\pi$
$930$	24.6514	−	6.60533i	0.808352	−	0.216597i
$931$	−1.09635	+	0.406391i	−0.0359315	+	0.0133189i
$932$	−6.11566	+	10.5926i	−0.200325	+	0.346974i
$933$	−29.0098	−	16.7488i	−0.949737	−	0.548331i
$934$	6.02779	+	6.02779i	0.197235	+	0.197235i
$935$	−10.3928	−	6.00028i	−0.339881	−	0.196230i
$936$	3.21211	+	1.63780i	0.104991	+	0.0535330i
$937$			6.82244i			0.222879i	0.993771	+	0.111440i	$0.0355462\pi$
$937$			6.82244i			0.222879i	−0.993771	+	0.111440i	$0.964454\pi$
$938$	9.73739	−	10.6897i	0.317937	−	0.349032i
$939$	7.99730	+	13.8517i	0.260982	+	0.452034i
$940$			26.7918i			0.873851i
$941$	5.51963	+	20.5995i	0.179935	+	0.671526i	0.995658	+	0.0930839i	$0.0296725\pi$
$941$	5.51963	+	20.5995i	0.179935	+	0.671526i	−0.815723	+	0.578442i	$0.803661\pi$
$942$	3.92015	−	14.6302i	0.127725	−	0.476677i
$943$	−11.4683	−	11.4683i	−0.373459	−	0.373459i
$944$	−2.46741	−	2.46741i	−0.0803072	−	0.0803072i
$945$	−6.95426	−	3.59409i	−0.226222	−	0.116916i
$946$	−19.7015	+	11.3746i	−0.640550	+	0.369821i
$947$	−4.86017	−	18.1384i	−0.157934	−	0.589418i	−0.998836	−	0.0482310i	$-0.984642\pi$
$947$	−4.86017	−	18.1384i	−0.157934	−	0.589418i	0.840902	−	0.541187i	$-0.182025\pi$
$948$	4.30390	−	7.45458i	0.139784	−	0.242113i
$949$	−12.6362	−	19.4701i	−0.410188	−	0.632026i
$950$	0.543066	−	0.313539i	0.0176194	−	0.0101726i
$951$	−11.9966	−	3.21447i	−0.389015	−	0.104236i
$952$	−1.12825	+	2.18307i	−0.0365668	+	0.0707536i
$953$	14.2393	+	8.22104i	0.461255	+	0.266306i	0.712572	−	0.701599i	$-0.247530\pi$
$953$	14.2393	+	8.22104i	0.461255	+	0.266306i	−0.251317	+	0.967905i	$0.580864\pi$
$954$	−0.589365	+	2.19954i	−0.0190814	+	0.0712128i
$955$	−42.2904	−	11.3317i	−1.36848	−	0.366684i
$956$	−24.5730	−	6.58432i	−0.794749	−	0.212952i
$957$	−4.39845	+	16.4153i	−0.142182	+	0.530630i
$958$	20.8916	+	12.0618i	0.674978	+	0.389698i
$959$	−15.5993	+	30.1834i	−0.503728	+	0.974672i
$960$	2.85793	+	0.765779i	0.0922392	+	0.0247154i
$961$	−37.5868	+	21.7008i	−1.21248	+	0.700024i
$962$	−16.8144	+	18.6636i	−0.542117	+	0.601739i
$963$	−4.16560	+	7.21503i	−0.134234	+	0.232501i
$964$	5.96249	+	22.2523i	0.192039	+	0.716699i
$965$	−63.4415	+	36.6279i	−2.04225	+	1.17910i
$966$	3.79181	+	1.95968i	0.121999	+	0.0630515i
$967$	30.3414	+	30.3414i	0.975713	+	0.975713i	0.999712	−	0.0239988i	$-0.00763980\pi$
$967$	30.3414	+	30.3414i	0.975713	+	0.975713i	−0.0239988	+	0.999712i	$0.507640\pi$
$968$	−5.70605	−	5.70605i	−0.183399	−	0.183399i
$969$	−0.0401540	+	0.149857i	−0.00128993	+	0.00481409i
$970$	8.50744	+	31.7502i	0.273157	+	1.01944i
$971$		−	53.1779i		−	1.70656i	−0.521453	−	0.853280i	$-0.674610\pi$
$971$		−	53.1779i		−	1.70656i	0.521453	−	0.853280i	$-0.325390\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	35.6187	−	39.1023i	1.14188	−	1.25356i
$974$			25.0120i			0.801438i
$975$	−13.2392	−	2.81801i	−0.423995	−	0.0902485i
$976$	8.49717	+	4.90584i	0.271988	+	0.157032i
$977$	14.7201	+	14.7201i	0.470939	+	0.470939i	0.902218	−	0.431280i	$-0.141938\pi$
$977$	14.7201	+	14.7201i	0.470939	+	0.470939i	−0.431280	+	0.902218i	$0.641938\pi$
$978$	−6.77517	−	3.91165i	−0.216646	−	0.125081i
$979$	26.5458	−	45.9787i	0.848409	−	1.46949i
$980$	20.4174	+	3.47590i	0.652211	+	0.111034i
$981$	6.59020	−	1.76584i	0.210409	−	0.0563789i
$982$	20.3583	−	20.3583i	0.649661	−	0.649661i
$983$	−39.1482	+	10.4897i	−1.24863	+	0.334571i	−0.821809	−	0.569763i	$-0.807035\pi$
$983$	−39.1482	+	10.4897i	−1.24863	+	0.334571i	−0.426826	+	0.904334i	$0.640368\pi$
$984$	−5.02667	−	8.70645i	−0.160244	−	0.277551i
$985$	27.7666	−	48.0931i	0.884717	−	1.53237i
$986$	0.935521	−	3.49141i	0.0297930	−	0.111189i
$987$	−10.9996	+	21.2832i	−0.350120	+	0.677452i
$988$	−0.601439	+	0.0313493i	−0.0191343	+	0.000997354i
$989$	−4.20214	−	7.27831i	−0.133620	−	0.231437i
$990$	−9.13614	+	9.13614i	−0.290366	+	0.290366i
$991$	−23.2188			−0.737571			−0.368785	−	0.929515i	$-0.620226\pi$
$991$	−23.2188			−0.737571			−0.368785	+	0.929515i	$0.620226\pi$
$992$	−8.62563			−0.273864
$993$	0.444469	−	0.444469i	0.0141048	−	0.0141048i
$994$	−5.96722	−	18.7325i	−0.189269	−	0.594158i
$995$	8.41768	+	31.4152i	0.266859	+	0.995930i
$996$	−2.47488	−	0.663142i	−0.0784196	−	0.0210125i
$997$	−4.07018	+	2.34992i	−0.128904	+	0.0744227i	−0.563065	−	0.826412i	$-0.690378\pi$
$997$	−4.07018	+	2.34992i	−0.128904	+	0.0744227i	0.434161	+	0.900835i	$0.357045\pi$
$998$			11.4238i			0.361613i
$999$	6.72985	−	1.80326i	0.212923	−	0.0570525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.115.5	yes	32
7.5	odd	6		546.2.cg.a.271.1	yes	32
13.6	odd	12		546.2.cg.a.409.1	yes	32
91.19	even	12	inner	546.2.by.a.19.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.5	✓	32	91.19	even	12	inner
546.2.by.a.115.5	yes	32	1.1	even	1	trivial
546.2.cg.a.271.1	yes	32	7.5	odd	6
546.2.cg.a.409.1	yes	32	13.6	odd	12

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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.85793 - 0.765779i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.565013 - 2.58472i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.85793 - 0.765779i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.565013 - 2.58472i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -2.95874 q^{10} +(-3.08784 + 3.08784i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.11321 - 3.42940i) q^{13} +(-0.123214 - 2.64288i) q^{14} +(-0.765779 + 2.85793i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.464402 - 0.804367i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(0.118112 - 0.118112i) q^{19} +(-2.85793 + 0.765779i) q^{20} +(-2.58472 - 0.565013i) q^{21} +(-2.18344 + 3.78182i) q^{22} +(-1.39712 - 0.806627i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(3.25120 + 1.87708i) q^{25} +(-1.96287 - 3.02443i) q^{26} +1.00000i q^{27} +(-0.803043 - 2.52094i) q^{28} +(1.94582 + 3.37026i) q^{29} +2.95874i q^{30} +(-2.23248 - 8.33172i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.08784 + 3.08784i) q^{33} +(-0.656763 - 0.656763i) q^{34} +(-3.59409 + 6.95426i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.80326 - 6.72985i) q^{37} +(0.0835178 - 0.144657i) q^{38} +(-3.42940 + 1.11321i) q^{39} +(-2.56235 + 1.47937i) q^{40} +(9.71078 + 2.60200i) q^{41} +(-2.64288 + 0.123214i) q^{42} +(4.51157 + 2.60476i) q^{43} +(-1.13023 + 4.21807i) q^{44} +(2.85793 + 0.765779i) q^{45} +(-1.55828 - 0.417541i) q^{46} +(2.34364 - 8.74657i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-6.36152 - 2.92080i) q^{49} +(3.62625 + 0.971650i) q^{50} +(-0.804367 + 0.464402i) q^{51} +(-2.67876 - 2.41334i) q^{52} +(1.13857 - 1.97205i) q^{53} +(0.258819 + 0.965926i) q^{54} +(11.1894 - 6.46023i) q^{55} +(-1.42815 - 2.22720i) q^{56} +(-0.118112 - 0.118112i) q^{57} +(2.75181 + 2.75181i) q^{58} +(0.903133 - 3.37054i) q^{59} +(0.765779 + 2.85793i) q^{60} +9.81168i q^{61} +(-4.31282 - 7.47002i) q^{62} +(-0.565013 + 2.58472i) q^{63} -1.00000i q^{64} +(0.555299 + 10.6534i) q^{65} +(3.78182 + 2.18344i) q^{66} +(3.86455 + 3.86455i) q^{67} +(-0.804367 - 0.464402i) q^{68} +(-0.806627 + 1.39712i) q^{69} +(-1.67173 + 7.64751i) q^{70} +(7.17756 - 1.92322i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(6.21826 - 1.66618i) q^{73} +(-3.48363 - 6.03382i) q^{74} +(1.87708 - 3.25120i) q^{75} +(0.0432320 - 0.161344i) q^{76} +(6.23653 + 9.72588i) q^{77} +(-3.02443 + 1.96287i) q^{78} +(4.30390 + 7.45458i) q^{79} +(-2.09215 + 2.09215i) q^{80} +1.00000 q^{81} +10.0533 q^{82} +(1.81174 - 1.81174i) q^{83} +(-2.52094 + 0.803043i) q^{84} +(0.711258 + 2.65445i) q^{85} +(5.03200 + 1.34832i) q^{86} +(3.37026 - 1.94582i) q^{87} +4.36687i q^{88} +(-11.7436 + 3.14668i) q^{89} +2.95874 q^{90} +(-9.49300 + 0.939668i) q^{91} -1.61325 q^{92} +(-8.33172 + 2.23248i) q^{93} -9.05511i q^{94} +(-0.428003 + 0.247108i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(-2.87536 - 10.7310i) q^{97} +(-6.90072 - 1.17479i) q^{98} +(3.08784 - 3.08784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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