LMFDB - Embedded newform 546.2.p.c.281.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.9
Root			$-1.25702 + 1.19160i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.c.239.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.0462556 - 1.73143i) q^{3} -1.00000i q^{4} +(1.43062 - 1.43062i) q^{5} +(-1.19160 - 1.25702i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99572 - 0.160177i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.0462556 - 1.73143i) q^{3} -1.00000i q^{4} +(1.43062 - 1.43062i) q^{5} +(-1.19160 - 1.25702i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99572 - 0.160177i) q^{9} -2.02321i q^{10} +(-3.59738 - 3.59738i) q^{11} +(-1.73143 - 0.0462556i) q^{12} +(2.66989 + 2.42316i) q^{13} +1.00000i q^{14} +(-2.41086 - 2.54321i) q^{15} -1.00000 q^{16} +4.10312 q^{17} +(-2.23156 + 2.00503i) q^{18} +(-4.90374 - 4.90374i) q^{19} +(-1.43062 - 1.43062i) q^{20} +(1.19160 + 1.25702i) q^{21} -5.08746 q^{22} +4.97697 q^{23} +(-1.25702 + 1.19160i) q^{24} +0.906626i q^{25} +(3.60133 - 0.174466i) q^{26} +(-0.415904 + 5.17948i) q^{27} +(0.707107 + 0.707107i) q^{28} +2.59352i q^{29} +(-3.50305 - 0.0935847i) q^{30} +(-1.00229 - 1.00229i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.39501 + 6.06222i) q^{33} +(2.90134 - 2.90134i) q^{34} +2.02321i q^{35} +(-0.160177 + 2.99572i) q^{36} +(8.01932 - 8.01932i) q^{37} -6.93493 q^{38} +(4.31903 - 4.51065i) q^{39} -2.02321 q^{40} +(-0.185417 + 0.185417i) q^{41} +(1.73143 + 0.0462556i) q^{42} +8.21380i q^{43} +(-3.59738 + 3.59738i) q^{44} +(-4.51491 + 4.05660i) q^{45} +(3.51925 - 3.51925i) q^{46} +(2.56188 + 2.56188i) q^{47} +(-0.0462556 + 1.73143i) q^{48} -1.00000i q^{49} +(0.641081 + 0.641081i) q^{50} +(0.189792 - 7.10428i) q^{51} +(2.42316 - 2.66989i) q^{52} -7.36477i q^{53} +(3.36836 + 3.95653i) q^{54} -10.2930 q^{55} +1.00000 q^{56} +(-8.71732 + 8.26367i) q^{57} +(1.83390 + 1.83390i) q^{58} +(-1.33972 - 1.33972i) q^{59} +(-2.54321 + 2.41086i) q^{60} -10.1389 q^{61} -1.41746 q^{62} +(2.23156 - 2.00503i) q^{63} +1.00000i q^{64} +(7.28624 - 0.352981i) q^{65} +(-0.235323 + 8.80859i) q^{66} +(3.13832 + 3.13832i) q^{67} -4.10312i q^{68} +(0.230213 - 8.61729i) q^{69} +(1.43062 + 1.43062i) q^{70} +(9.44085 - 9.44085i) q^{71} +(2.00503 + 2.23156i) q^{72} +(-0.868139 + 0.868139i) q^{73} -11.3410i q^{74} +(1.56976 + 0.0419365i) q^{75} +(-4.90374 + 4.90374i) q^{76} +5.08746 q^{77} +(-0.135495 - 6.24353i) q^{78} +12.6610 q^{79} +(-1.43062 + 1.43062i) q^{80} +(8.94869 + 0.959690i) q^{81} +0.262219i q^{82} +(-0.232559 + 0.232559i) q^{83} +(1.25702 - 1.19160i) q^{84} +(5.87003 - 5.87003i) q^{85} +(5.80804 + 5.80804i) q^{86} +(4.49051 + 0.119965i) q^{87} +5.08746i q^{88} +(3.93141 + 3.93141i) q^{89} +(-0.324071 + 6.06097i) q^{90} +(-3.60133 + 0.174466i) q^{91} -4.97697i q^{92} +(-1.78176 + 1.68904i) q^{93} +3.62305 q^{94} -14.0308 q^{95} +(1.19160 + 1.25702i) q^{96} +(7.65788 + 7.65788i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(10.2005 + 11.3530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.0462556	−	1.73143i	0.0267057	−	0.999643i
$3$	0.0462556	−	1.73143i	0.0267057	−	0.999643i
$4$		−	1.00000i		−	0.500000i
$5$	1.43062	−	1.43062i	0.639795	−	0.639795i	−0.310710	−	0.950505i	$-0.600567\pi$
$5$	1.43062	−	1.43062i	0.639795	−	0.639795i	0.950505	+	0.310710i	$0.100567\pi$
$6$	−1.19160	−	1.25702i	−0.486469	−	0.513175i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.99572	−	0.160177i	−0.998574	−	0.0533923i
$10$		−	2.02321i		−	0.639795i
$11$	−3.59738	−	3.59738i	−1.08465	−	1.08465i	−0.996069	−	0.0885807i	$-0.971767\pi$
$11$	−3.59738	−	3.59738i	−1.08465	−	1.08465i	−0.0885807	−	0.996069i	$-0.528233\pi$
$12$	−1.73143	−	0.0462556i	−0.499822	−	0.0133528i
$13$	2.66989	+	2.42316i	0.740494	+	0.672063i
$13$	2.66989	+	2.42316i	0.740494	+	0.672063i
$14$			1.00000i			0.267261i
$15$	−2.41086	−	2.54321i	−0.622480	−	0.656653i
$16$	−1.00000			−0.250000
$17$	4.10312			0.995153			0.497577	−	0.867420i	$-0.334223\pi$
$17$	4.10312			0.995153			0.497577	+	0.867420i	$0.334223\pi$
$18$	−2.23156	+	2.00503i	−0.525983	+	0.472591i
$19$	−4.90374	−	4.90374i	−1.12499	−	1.12499i	−0.990979	−	0.134015i	$-0.957213\pi$
$19$	−4.90374	−	4.90374i	−1.12499	−	1.12499i	−0.134015	−	0.990979i	$-0.542787\pi$
$20$	−1.43062	−	1.43062i	−0.319897	−	0.319897i
$21$	1.19160	+	1.25702i	0.260029	+	0.274303i
$22$	−5.08746			−1.08465
$23$	4.97697			1.03777			0.518885	−	0.854844i	$-0.326347\pi$
$23$	4.97697			1.03777			0.518885	+	0.854844i	$0.326347\pi$
$24$	−1.25702	+	1.19160i	−0.256587	+	0.243234i
$25$			0.906626i			0.181325i
$26$	3.60133	−	0.174466i	0.706278	−	0.0342156i
$27$	−0.415904	+	5.17948i	−0.0800408	+	0.996792i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$			2.59352i			0.481605i	0.970574	+	0.240803i	$0.0774107\pi$
$29$			2.59352i			0.481605i	−0.970574	+	0.240803i	$0.922589\pi$
$30$	−3.50305	−	0.0935847i	−0.639567	−	0.0170862i
$31$	−1.00229	−	1.00229i	−0.180017	−	0.180017i	0.611346	−	0.791363i	$-0.290628\pi$
$31$	−1.00229	−	1.00229i	−0.180017	−	0.180017i	−0.791363	+	0.611346i	$0.790628\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−6.39501	+	6.06222i	−1.11323	+	1.05530i
$34$	2.90134	−	2.90134i	0.497577	−	0.497577i
$35$			2.02321i			0.341985i
$36$	−0.160177	+	2.99572i	−0.0266961	+	0.499287i
$37$	8.01932	−	8.01932i	1.31837	−	1.31837i	0.403301	−	0.915067i	$-0.367863\pi$
$37$	8.01932	−	8.01932i	1.31837	−	1.31837i	0.915067	−	0.403301i	$-0.132137\pi$
$38$	−6.93493			−1.12499
$39$	4.31903	−	4.51065i	0.691599	−	0.722282i
$40$	−2.02321			−0.319897
$41$	−0.185417	+	0.185417i	−0.0289573	+	0.0289573i	−0.721437	−	0.692480i	$-0.756518\pi$
$41$	−0.185417	+	0.185417i	−0.0289573	+	0.0289573i	0.692480	+	0.721437i	$0.256518\pi$
$42$	1.73143	+	0.0462556i	0.267166	+	0.00713739i
$43$			8.21380i			1.25259i	0.779585	+	0.626297i	$0.215430\pi$
$43$			8.21380i			1.25259i	−0.779585	+	0.626297i	$0.784570\pi$
$44$	−3.59738	+	3.59738i	−0.542325	+	0.542325i
$45$	−4.51491	+	4.05660i	−0.673042	+	0.604722i
$46$	3.51925	−	3.51925i	0.518885	−	0.518885i
$47$	2.56188	+	2.56188i	0.373689	+	0.373689i	0.868819	−	0.495130i	$-0.164880\pi$
$47$	2.56188	+	2.56188i	0.373689	+	0.373689i	−0.495130	+	0.868819i	$0.664880\pi$
$48$	−0.0462556	+	1.73143i	−0.00667642	+	0.249911i
$49$		−	1.00000i		−	0.142857i
$50$	0.641081	+	0.641081i	0.0906626	+	0.0906626i
$51$	0.189792	−	7.10428i	0.0265762	−	0.994798i
$52$	2.42316	−	2.66989i	0.336031	−	0.370247i
$53$		−	7.36477i		−	1.01163i	−0.862642	−	0.505814i	$-0.831192\pi$
$53$		−	7.36477i		−	1.01163i	0.862642	−	0.505814i	$-0.168808\pi$
$54$	3.36836	+	3.95653i	0.458375	+	0.538416i
$55$	−10.2930			−1.38791
$56$	1.00000			0.133631
$57$	−8.71732	+	8.26367i	−1.15464	+	1.09455i
$58$	1.83390	+	1.83390i	0.240803	+	0.240803i
$59$	−1.33972	−	1.33972i	−0.174417	−	0.174417i	0.614500	−	0.788917i	$-0.289358\pi$
$59$	−1.33972	−	1.33972i	−0.174417	−	0.174417i	−0.788917	+	0.614500i	$0.789358\pi$
$60$	−2.54321	+	2.41086i	−0.328326	+	0.311240i
$61$	−10.1389			−1.29815			−0.649075	−	0.760725i	$-0.724844\pi$
$61$	−10.1389			−1.29815			−0.649075	+	0.760725i	$0.724844\pi$
$62$	−1.41746			−0.180017
$63$	2.23156	−	2.00503i	0.281150	−	0.252610i
$64$			1.00000i			0.125000i
$65$	7.28624	−	0.352981i	0.903747	−	0.0437820i
$66$	−0.235323	+	8.80859i	−0.0289663	+	1.08426i
$67$	3.13832	+	3.13832i	0.383407	+	0.383407i	0.872328	−	0.488921i	$-0.162609\pi$
$67$	3.13832	+	3.13832i	0.383407	+	0.383407i	−0.488921	+	0.872328i	$0.662609\pi$
$68$		−	4.10312i		−	0.497577i
$69$	0.230213	−	8.61729i	0.0277143	−	1.03740i
$70$	1.43062	+	1.43062i	0.170992	+	0.170992i
$71$	9.44085	−	9.44085i	1.12042	−	1.12042i	0.128745	−	0.991678i	$-0.458905\pi$
$71$	9.44085	−	9.44085i	1.12042	−	1.12042i	0.991678	−	0.128745i	$-0.0410947\pi$
$72$	2.00503	+	2.23156i	0.236295	+	0.262991i
$73$	−0.868139	+	0.868139i	−0.101608	+	0.101608i	−0.756083	−	0.654475i	$-0.772890\pi$
$73$	−0.868139	+	0.868139i	−0.101608	+	0.101608i	0.654475	+	0.756083i	$0.272890\pi$
$74$		−	11.3410i		−	1.31837i
$75$	1.56976	+	0.0419365i	0.181261	+	0.00484241i
$76$	−4.90374	+	4.90374i	−0.562497	+	0.562497i
$77$	5.08746			0.579770
$78$	−0.135495	−	6.24353i	−0.0153418	−	0.706940i
$79$	12.6610			1.42448			0.712239	−	0.701937i	$-0.247681\pi$
$79$	12.6610			1.42448			0.712239	+	0.701937i	$0.247681\pi$
$80$	−1.43062	+	1.43062i	−0.159949	+	0.159949i
$81$	8.94869	+	0.959690i	0.994299	+	0.106632i
$82$			0.262219i			0.0289573i
$83$	−0.232559	+	0.232559i	−0.0255266	+	0.0255266i	−0.719755	−	0.694228i	$-0.755746\pi$
$83$	−0.232559	+	0.232559i	−0.0255266	+	0.0255266i	0.694228	+	0.719755i	$0.255746\pi$
$84$	1.25702	−	1.19160i	0.137152	−	0.130014i
$85$	5.87003	−	5.87003i	0.636694	−	0.636694i
$86$	5.80804	+	5.80804i	0.626297	+	0.626297i
$87$	4.49051	+	0.119965i	0.481434	+	0.0128616i
$88$			5.08746i			0.542325i
$89$	3.93141	+	3.93141i	0.416728	+	0.416728i	0.884074	−	0.467346i	$-0.154790\pi$
$89$	3.93141	+	3.93141i	0.416728	+	0.416728i	−0.467346	+	0.884074i	$0.654790\pi$
$90$	−0.324071	+	6.06097i	−0.0341601	+	0.638882i
$91$	−3.60133	+	0.174466i	−0.377522	+	0.0182890i
$92$		−	4.97697i		−	0.518885i
$93$	−1.78176	+	1.68904i	−0.184760	+	0.175145i
$94$	3.62305			0.373689
$95$	−14.0308			−1.43953
$96$	1.19160	+	1.25702i	0.121617	+	0.128294i
$97$	7.65788	+	7.65788i	0.777540	+	0.777540i	0.979412	−	0.201872i	$-0.0647025\pi$
$97$	7.65788	+	7.65788i	0.777540	+	0.777540i	−0.201872	+	0.979412i	$0.564702\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	10.2005	+	11.3530i	1.02519	+	1.14101i
$100$	0.906626			0.0906626
$101$	3.05876			0.304358			0.152179	−	0.988353i	$-0.451371\pi$
$101$	3.05876			0.304358			0.152179	+	0.988353i	$0.451371\pi$
$102$	−4.88928	−	5.15769i	−0.484111	−	0.510687i
$103$			8.89812i			0.876758i	0.898790	+	0.438379i	$0.144447\pi$
$103$			8.89812i			0.876758i	−0.898790	+	0.438379i	$0.855553\pi$
$104$	−0.174466	−	3.60133i	−0.0171078	−	0.353139i
$105$	3.50305	+	0.0935847i	0.341863	+	0.00913293i
$106$	−5.20768	−	5.20768i	−0.505814	−	0.505814i
$107$		−	16.1853i		−	1.56469i	−0.622844	−	0.782346i	$-0.714023\pi$
$107$		−	16.1853i		−	1.56469i	0.622844	−	0.782346i	$-0.285977\pi$
$108$	5.17948	+	0.415904i	0.498396	+	0.0400204i
$109$	1.55437	+	1.55437i	0.148882	+	0.148882i	0.777618	−	0.628736i	$-0.216428\pi$
$109$	1.55437	+	1.55437i	0.148882	+	0.148882i	−0.628736	+	0.777618i	$0.716428\pi$
$110$	−7.27824	+	7.27824i	−0.693953	+	0.693953i
$111$	−13.5140	−	14.2559i	−1.28269	−	1.35311i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$		−	1.67224i		−	0.157311i	−0.996902	−	0.0786557i	$-0.974937\pi$
$113$		−	1.67224i		−	0.157311i	0.996902	−	0.0786557i	$-0.0250628\pi$
$114$	−0.320779	+	12.0074i	−0.0300437	+	1.12459i
$115$	7.12018	−	7.12018i	0.663960	−	0.663960i
$116$	2.59352			0.240803
$117$	−7.61011	−	7.68676i	−0.703555	−	0.710641i
$118$	−1.89465			−0.174417
$119$	−2.90134	+	2.90134i	−0.265966	+	0.265966i
$120$	−0.0935847	+	3.50305i	−0.00854308	+	0.319783i
$121$			14.8822i			1.35293i
$122$	−7.16926	+	7.16926i	−0.649075	+	0.649075i
$123$	0.312461	+	0.329614i	0.0281736	+	0.0297203i
$124$	−1.00229	+	1.00229i	−0.0900085	+	0.0900085i
$125$	8.45017	+	8.45017i	0.755806	+	0.755806i
$126$	0.160177	−	2.99572i	0.0142697	−	0.266880i
$127$			19.5094i			1.73118i	0.500754	+	0.865590i	$0.333056\pi$
$127$			19.5094i			1.73118i	−0.500754	+	0.865590i	$0.666944\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	14.2216	+	0.379934i	1.25215	+	0.0334513i
$130$	4.90255	−	5.40174i	0.429982	−	0.473764i
$131$		−	12.4313i		−	1.08613i	−0.839691	−	0.543064i	$-0.817264\pi$
$131$		−	12.4313i		−	1.08613i	0.839691	−	0.543064i	$-0.182736\pi$
$132$	6.06222	+	6.39501i	0.527648	+	0.556615i
$133$	6.93493			0.601335
$134$	4.43825			0.383407
$135$	6.81489	+	8.00490i	0.586532	+	0.688952i
$136$	−2.90134	−	2.90134i	−0.248788	−	0.248788i
$137$	9.19378	+	9.19378i	0.785477	+	0.785477i	0.980749	−	0.195272i	$-0.0625589\pi$
$137$	9.19378	+	9.19378i	0.785477	+	0.785477i	−0.195272	+	0.980749i	$0.562559\pi$
$138$	−5.93056	−	6.25613i	−0.504843	−	0.532557i
$139$	−19.0489			−1.61570			−0.807852	−	0.589385i	$-0.799370\pi$
$139$	−19.0489			−1.61570			−0.807852	+	0.589385i	$0.799370\pi$
$140$	2.02321			0.170992
$141$	4.55423	−	4.31722i	0.383535	−	0.363576i
$142$		−	13.3514i		−	1.12042i
$143$	−0.887589	−	18.3216i	−0.0742239	−	1.53213i
$144$	2.99572	+	0.160177i	0.249643	+	0.0133481i
$145$	3.71036	+	3.71036i	0.308129	+	0.308129i
$146$			1.22773i			0.101608i
$147$	−1.73143	−	0.0462556i	−0.142806	−	0.00381510i
$148$	−8.01932	−	8.01932i	−0.659184	−	0.659184i
$149$	−4.55291	+	4.55291i	−0.372989	+	0.372989i	−0.868565	−	0.495576i	$-0.834957\pi$
$149$	−4.55291	+	4.55291i	−0.372989	+	0.372989i	0.495576	+	0.868565i	$0.334957\pi$
$150$	1.13964	−	1.08034i	0.0930515	−	0.0882091i
$151$	12.4782	−	12.4782i	1.01546	−	1.01546i	0.0155842	−	0.999879i	$-0.495039\pi$
$151$	12.4782	−	12.4782i	1.01546	−	1.01546i	0.999879	−	0.0155842i	$-0.00496082\pi$
$152$			6.93493i			0.562497i
$153$	−12.2918	−	0.657225i	−0.993734	−	0.0531335i
$154$	3.59738	−	3.59738i	0.289885	−	0.289885i
$155$	−2.86781			−0.230348
$156$	−4.51065	−	4.31903i	−0.361141	−	0.345799i
$157$	13.8447			1.10493			0.552466	−	0.833536i	$-0.313687\pi$
$157$	13.8447			1.10493			0.552466	+	0.833536i	$0.313687\pi$
$158$	8.95271	−	8.95271i	0.712239	−	0.712239i
$159$	−12.7516	−	0.340662i	−1.01127	−	0.0270162i
$160$			2.02321i			0.159949i
$161$	−3.51925	+	3.51925i	−0.277356	+	0.277356i
$162$	7.00628	−	5.64907i	0.550465	−	0.443833i
$163$	−2.76536	+	2.76536i	−0.216600	+	0.216600i	−0.807064	−	0.590464i	$-0.798945\pi$
$163$	−2.76536	+	2.76536i	−0.216600	+	0.216600i	0.590464	+	0.807064i	$0.298945\pi$
$164$	0.185417	+	0.185417i	0.0144786	+	0.0144786i
$165$	−0.476108	+	17.8216i	−0.0370650	+	1.38741i
$166$			0.328888i			0.0255266i
$167$	−13.6345	−	13.6345i	−1.05507	−	1.05507i	−0.998392	−	0.0566794i	$-0.981949\pi$
$167$	−13.6345	−	13.6345i	−1.05507	−	1.05507i	−0.0566794	−	0.998392i	$-0.518051\pi$
$168$	0.0462556	−	1.73143i	0.00356870	−	0.133583i
$169$	1.25662	+	12.9391i	0.0966630	+	0.995317i
$170$		−	8.30147i		−	0.636694i
$171$	13.9048	+	15.4757i	1.06332	+	1.18346i
$172$	8.21380			0.626297
$173$	−21.9642			−1.66991			−0.834955	−	0.550318i	$-0.814506\pi$
$173$	−21.9642			−1.66991			−0.834955	+	0.550318i	$0.814506\pi$
$174$	3.26010	−	3.09044i	0.247148	−	0.234286i
$175$	−0.641081	−	0.641081i	−0.0484612	−	0.0484612i
$176$	3.59738	+	3.59738i	0.271162	+	0.271162i
$177$	−2.38161	+	2.25767i	−0.179012	+	0.169697i
$178$	5.55985			0.416728
$179$	−8.56403			−0.640105			−0.320053	−	0.947400i	$-0.603701\pi$
$179$	−8.56403			−0.640105			−0.320053	+	0.947400i	$0.603701\pi$
$180$	4.05660	+	4.51491i	0.302361	+	0.336521i
$181$		−	0.973124i		−	0.0723318i	−0.999346	−	0.0361659i	$-0.988486\pi$
$181$		−	0.973124i		−	0.0723318i	0.999346	−	0.0361659i	$-0.0115145\pi$
$182$	−2.42316	+	2.66989i	−0.179616	+	0.197905i
$183$	−0.468979	+	17.5548i	−0.0346679	+	1.29769i
$184$	−3.51925	−	3.51925i	−0.259442	−	0.259442i
$185$		−	22.9453i		−	1.68697i
$186$	−0.0655652	+	2.45423i	−0.00480747	+	0.179953i
$187$	−14.7605	−	14.7605i	−1.07939	−	1.07939i
$188$	2.56188	−	2.56188i	0.186844	−	0.186844i
$189$	−3.36836	−	3.95653i	−0.245012	−	0.287796i
$190$	−9.92128	+	9.92128i	−0.719765	+	0.719765i
$191$			12.7937i			0.925721i	0.886431	+	0.462860i	$0.153177\pi$
$191$			12.7937i			0.925721i	−0.886431	+	0.462860i	$0.846823\pi$
$192$	1.73143	+	0.0462556i	0.124955	+	0.00333821i
$193$	8.73551	−	8.73551i	0.628796	−	0.628796i	−0.318969	−	0.947765i	$-0.603337\pi$
$193$	8.73551	−	8.73551i	0.628796	−	0.628796i	0.947765	+	0.318969i	$0.103337\pi$
$194$	10.8299			0.777540
$195$	−0.274134	−	12.6320i	−0.0196312	−	0.904593i
$196$	−1.00000			−0.0714286
$197$	−6.29467	+	6.29467i	−0.448477	+	0.448477i	−0.894848	−	0.446371i	$-0.852716\pi$
$197$	−6.29467	+	6.29467i	−0.448477	+	0.448477i	0.446371	+	0.894848i	$0.352716\pi$
$198$	15.2406	+	0.814893i	1.08310	+	0.0579119i
$199$			12.0446i			0.853823i	0.904294	+	0.426911i	$0.140398\pi$
$199$			12.0446i			0.853823i	−0.904294	+	0.426911i	$0.859602\pi$
$200$	0.641081	−	0.641081i	0.0453313	−	0.0453313i
$201$	5.57895	−	5.28862i	0.393509	−	0.373031i
$202$	2.16287	−	2.16287i	0.152179	−	0.152179i
$203$	−1.83390	−	1.83390i	−0.128714	−	0.128714i
$204$	−7.10428	−	0.189792i	−0.497399	−	0.0132881i
$205$			0.530525i			0.0370534i
$206$	6.29192	+	6.29192i	0.438379	+	0.438379i
$207$	−14.9096	−	0.797195i	−1.03629	−	0.0554089i
$208$	−2.66989	−	2.42316i	−0.185124	−	0.168016i
$209$			35.2812i			2.44045i
$210$	2.54321	−	2.41086i	0.175498	−	0.166365i
$211$	−23.3032			−1.60426			−0.802129	−	0.597151i	$-0.796299\pi$
$211$	−23.3032			−1.60426			−0.802129	+	0.597151i	$0.796299\pi$
$212$	−7.36477			−0.505814
$213$	−15.9095	−	16.7829i	−1.09010	−	1.14994i
$214$	−11.4447	−	11.4447i	−0.782346	−	0.782346i
$215$	11.7509	+	11.7509i	0.801403	+	0.801403i
$216$	3.95653	−	3.36836i	0.269208	−	0.229188i
$217$	1.41746			0.0962231
$218$	2.19822			0.148882
$219$	1.46297	+	1.54328i	0.0988582	+	0.104285i
$220$			10.2930i			0.693953i
$221$	10.9549	+	9.94251i	0.736905	+	0.668805i
$222$	−19.6362	−	0.524586i	−1.31790	−	0.0352079i
$223$	11.2055	+	11.2055i	0.750374	+	0.750374i	0.974549	−	0.224175i	$-0.0719686\pi$
$223$	11.2055	+	11.2055i	0.750374	+	0.750374i	−0.224175	+	0.974549i	$0.571969\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	0.145221	−	2.71600i	0.00968137	−	0.181067i
$226$	−1.18245	−	1.18245i	−0.0786557	−	0.0786557i
$227$	2.20653	−	2.20653i	0.146452	−	0.146452i	−0.630079	−	0.776531i	$-0.716977\pi$
$227$	2.20653	−	2.20653i	0.146452	−	0.146452i	0.776531	+	0.630079i	$0.216977\pi$
$228$	8.26367	+	8.71732i	0.547275	+	0.577318i
$229$	−17.4293	+	17.4293i	−1.15176	+	1.15176i	−0.165559	+	0.986200i	$0.552943\pi$
$229$	−17.4293	+	17.4293i	−1.15176	+	1.15176i	−0.986200	+	0.165559i	$0.947057\pi$
$230$		−	10.0694i		−	0.663960i
$231$	0.235323	−	8.80859i	0.0154831	−	0.579563i
$232$	1.83390	−	1.83390i	0.120401	−	0.120401i
$233$	7.03391			0.460806			0.230403	−	0.973095i	$-0.425995\pi$
$233$	7.03391			0.460806			0.230403	+	0.973095i	$0.425995\pi$
$234$	−10.8165	−	0.0541977i	−0.707098	−	0.00354301i
$235$	7.33018			0.478168
$236$	−1.33972	+	1.33972i	−0.0872084	+	0.0872084i
$237$	0.585644	−	21.9217i	0.0380417	−	1.42397i
$238$			4.10312i			0.265966i
$239$	2.66524	−	2.66524i	0.172400	−	0.172400i	−0.615633	−	0.788033i	$-0.711100\pi$
$239$	2.66524	−	2.66524i	0.172400	−	0.172400i	0.788033	+	0.615633i	$0.211100\pi$
$240$	2.41086	+	2.54321i	0.155620	+	0.164163i
$241$	−1.43539	+	1.43539i	−0.0924614	+	0.0924614i	−0.751825	−	0.659363i	$-0.770826\pi$
$241$	−1.43539	+	1.43539i	−0.0924614	+	0.0924614i	0.659363	+	0.751825i	$0.270826\pi$
$242$	10.5233	+	10.5233i	0.676465	+	0.676465i
$243$	2.07557	−	15.4497i	0.133148	−	0.991096i
$244$			10.1389i			0.649075i
$245$	−1.43062	−	1.43062i	−0.0913993	−	0.0913993i
$246$	0.454015	+	0.0121291i	0.0289470	+	0.000773324i
$247$	−1.20991	−	24.9750i	−0.0769847	−	1.58912i
$248$			1.41746i			0.0900085i
$249$	0.391903	+	0.413417i	0.0248358	+	0.0261992i
$250$	11.9503			0.755806
$251$	9.15010			0.577549			0.288775	−	0.957397i	$-0.406752\pi$
$251$	9.15010			0.577549			0.288775	+	0.957397i	$0.406752\pi$
$252$	−2.00503	−	2.23156i	−0.126305	−	0.140575i
$253$	−17.9040	−	17.9040i	−1.12562	−	1.12562i
$254$	13.7952	+	13.7952i	0.865590	+	0.865590i
$255$	−9.89204	−	10.4351i	−0.619463	−	0.653470i
$256$	1.00000			0.0625000
$257$	−3.54392			−0.221064			−0.110532	−	0.993873i	$-0.535255\pi$
$257$	−3.54392			−0.221064			−0.110532	+	0.993873i	$0.535255\pi$
$258$	10.3249	−	9.78757i	0.642799	−	0.609348i
$259$			11.3410i			0.704698i
$260$	−0.352981	−	7.28624i	−0.0218910	−	0.451873i
$261$	0.415423	−	7.76947i	0.0257140	−	0.480918i
$262$	−8.79026	−	8.79026i	−0.543064	−	0.543064i
$263$			27.6411i			1.70442i	0.523199	+	0.852211i	$0.324739\pi$
$263$			27.6411i			1.70442i	−0.523199	+	0.852211i	$0.675261\pi$
$264$	8.80859	+	0.235323i	0.542131	+	0.0144831i
$265$	−10.5362	−	10.5362i	−0.647235	−	0.647235i
$266$	4.90374	−	4.90374i	0.300667	−	0.300667i
$267$	6.98882	−	6.62512i	0.427709	−	0.405451i
$268$	3.13832	−	3.13832i	0.191703	−	0.191703i
$269$			20.0051i			1.21973i	0.792504	+	0.609867i	$0.208777\pi$
$269$			20.0051i			1.21973i	−0.792504	+	0.609867i	$0.791223\pi$
$270$	10.4792	+	0.841461i	0.637742	+	0.0512097i
$271$	−5.17783	+	5.17783i	−0.314531	+	0.314531i	−0.846662	−	0.532131i	$-0.821391\pi$
$271$	−5.17783	+	5.17783i	−0.314531	+	0.314531i	0.532131	+	0.846662i	$0.321391\pi$
$272$	−4.10312			−0.248788
$273$	0.135495	+	6.24353i	0.00820052	+	0.377876i
$274$	13.0020			0.785477
$275$	3.26148	−	3.26148i	0.196674	−	0.196674i
$276$	−8.61729	−	0.230213i	−0.518700	−	0.0138572i
$277$		−	11.9350i		−	0.717107i	−0.933509	−	0.358554i	$-0.883270\pi$
$277$		−	11.9350i		−	0.717107i	0.933509	−	0.358554i	$-0.116730\pi$
$278$	−13.4696	+	13.4696i	−0.807852	+	0.807852i
$279$	2.84204	+	3.16313i	0.170149	+	0.189372i
$280$	1.43062	−	1.43062i	0.0854962	−	0.0854962i
$281$	−19.4431	−	19.4431i	−1.15988	−	1.15988i	−0.984502	−	0.175374i	$-0.943887\pi$
$281$	−19.4431	−	19.4431i	−1.15988	−	1.15988i	−0.175374	−	0.984502i	$-0.556113\pi$
$282$	0.167586	−	6.27306i	0.00997961	−	0.373555i
$283$			10.9224i			0.649272i	0.945839	+	0.324636i	$0.105242\pi$
$283$			10.9224i			0.649272i	−0.945839	+	0.324636i	$0.894758\pi$
$284$	−9.44085	−	9.44085i	−0.560211	−	0.560211i
$285$	−0.649003	+	24.2934i	−0.0384436	+	1.43902i
$286$	−13.5830	−	12.3277i	−0.803177	−	0.728953i
$287$		−	0.262219i		−	0.0154783i
$288$	2.23156	−	2.00503i	0.131496	−	0.118148i
$289$	−0.164395			−0.00967032
$290$	5.24724			0.308129
$291$	13.6133	−	12.9049i	0.798027	−	0.756498i
$292$	0.868139	+	0.868139i	0.0508040	+	0.0508040i
$293$	−1.81919	−	1.81919i	−0.106278	−	0.106278i	0.651968	−	0.758246i	$-0.273944\pi$
$293$	−1.81919	−	1.81919i	−0.106278	−	0.106278i	−0.758246	+	0.651968i	$0.773944\pi$
$294$	−1.25702	+	1.19160i	−0.0733106	+	0.0694955i
$295$	−3.83327			−0.223182
$296$	−11.3410			−0.659184
$297$	20.1287	−	17.1364i	1.16799	−	0.994353i
$298$			6.43879i			0.372989i
$299$	13.2880	+	12.0600i	0.768462	+	0.697447i
$300$	0.0419365	−	1.56976i	0.00242121	−	0.0906303i
$301$	−5.80804	−	5.80804i	−0.334770	−	0.334770i
$302$		−	17.6469i		−	1.01546i
$303$	0.141485	−	5.29604i	0.00812809	−	0.304250i
$304$	4.90374	+	4.90374i	0.281249	+	0.281249i
$305$	−14.5049	+	14.5049i	−0.830549	+	0.830549i
$306$	−9.15635	+	8.22689i	−0.523434	+	0.470300i
$307$	−9.17766	+	9.17766i	−0.523797	+	0.523797i	−0.918716	−	0.394919i	$-0.870773\pi$
$307$	−9.17766	+	9.17766i	−0.523797	+	0.523797i	0.394919	+	0.918716i	$0.370773\pi$
$308$		−	5.08746i		−	0.289885i
$309$	15.4065	+	0.411588i	0.876445	+	0.0234144i
$310$	−2.02785	+	2.02785i	−0.115174	+	0.115174i
$311$	−2.34596			−0.133027			−0.0665135	−	0.997786i	$-0.521188\pi$
$311$	−2.34596			−0.133027			−0.0665135	+	0.997786i	$0.521188\pi$
$312$	−6.24353	+	0.135495i	−0.353470	+	0.00767089i
$313$	−13.3871			−0.756683			−0.378341	−	0.925666i	$-0.623505\pi$
$313$	−13.3871			−0.756683			−0.378341	+	0.925666i	$0.623505\pi$
$314$	9.78972	−	9.78972i	0.552466	−	0.552466i
$315$	0.324071	−	6.06097i	0.0182593	−	0.341497i
$316$		−	12.6610i		−	0.712239i
$317$	−12.9987	+	12.9987i	−0.730081	+	0.730081i	−0.970636	−	0.240555i	$-0.922671\pi$
$317$	−12.9987	+	12.9987i	−0.730081	+	0.730081i	0.240555	+	0.970636i	$0.422671\pi$
$318$	−9.25763	+	8.77586i	−0.519142	+	0.492126i
$319$	9.32988	−	9.32988i	0.522373	−	0.522373i
$320$	1.43062	+	1.43062i	0.0799743	+	0.0799743i
$321$	−28.0238	−	0.748661i	−1.56413	−	0.0417862i
$322$			4.97697i			0.277356i
$323$	−20.1206	−	20.1206i	−1.11954	−	1.11954i
$324$	0.959690	−	8.94869i	0.0533161	−	0.497149i
$325$	−2.19690	+	2.42059i	−0.121862	+	0.134270i
$326$			3.91081i			0.216600i
$327$	2.76319	−	2.61939i	0.152805	−	0.144853i
$328$	0.262219			0.0144786
$329$	−3.62305			−0.199745
$330$	12.2651	+	12.9384i	0.675173	+	0.712238i
$331$	0.549427	+	0.549427i	0.0301992	+	0.0301992i	0.722045	−	0.691846i	$-0.243202\pi$
$331$	0.549427	+	0.549427i	0.0301992	+	0.0301992i	−0.691846	+	0.722045i	$0.743202\pi$
$332$	0.232559	+	0.232559i	0.0127633	+	0.0127633i
$333$	−25.3082	+	22.7391i	−1.38688	+	1.24610i
$334$	−19.2821			−1.05507
$335$	8.97951			0.490603
$336$	−1.19160	−	1.25702i	−0.0650071	−	0.0685758i
$337$		−	20.1204i		−	1.09603i	−0.836470	−	0.548013i	$-0.815384\pi$
$337$		−	20.1204i		−	1.09603i	0.836470	−	0.548013i	$-0.184616\pi$
$338$	10.0379	+	8.26078i	0.545990	+	0.449327i
$339$	−2.89538	−	0.0773505i	−0.157255	−	0.00420110i
$340$	−5.87003	−	5.87003i	−0.318347	−	0.318347i
$341$			7.21124i			0.390511i
$342$	20.7751	+	1.11082i	1.12339	+	0.0600660i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	5.80804	−	5.80804i	0.313148	−	0.313148i
$345$	−11.9988	−	12.6575i	−0.645991	−	0.681454i
$346$	−15.5311	+	15.5311i	−0.834955	+	0.834955i
$347$		−	16.4340i		−	0.882225i	−0.897452	−	0.441113i	$-0.854584\pi$
$347$		−	16.4340i		−	0.882225i	0.897452	−	0.441113i	$-0.145416\pi$
$348$	0.119965	−	4.49051i	0.00643080	−	0.240717i
$349$	9.67441	−	9.67441i	0.517859	−	0.517859i	−0.399064	−	0.916923i	$-0.630665\pi$
$349$	9.67441	−	9.67441i	0.517859	−	0.517859i	0.916923	+	0.399064i	$0.130665\pi$
$350$	−0.906626			−0.0484612
$351$	−13.6611	+	12.8208i	−0.729176	+	0.684326i
$352$	5.08746			0.271162
$353$	−2.54751	+	2.54751i	−0.135590	+	0.135590i	−0.771645	−	0.636054i	$-0.780566\pi$
$353$	−2.54751	+	2.54751i	−0.135590	+	0.135590i	0.636054	+	0.771645i	$0.280566\pi$
$354$	−0.0876382	+	3.28046i	−0.00465792	+	0.174354i
$355$		−	27.0126i		−	1.43368i
$356$	3.93141	−	3.93141i	0.208364	−	0.208364i
$357$	4.88928	+	5.15769i	0.258768	+	0.272974i
$358$	−6.05568	+	6.05568i	−0.320053	+	0.320053i
$359$	−21.4323	−	21.4323i	−1.13115	−	1.13115i	−0.989986	−	0.141166i	$-0.954915\pi$
$359$	−21.4323	−	21.4323i	−1.13115	−	1.13115i	−0.141166	−	0.989986i	$-0.545085\pi$
$360$	6.06097	+	0.324071i	0.319441	+	0.0170801i
$361$			29.0933i			1.53122i
$362$	−0.688103	−	0.688103i	−0.0361659	−	0.0361659i
$363$	25.7676	+	0.688386i	1.35245	+	0.0361309i
$364$	0.174466	+	3.60133i	0.00914451	+	0.188761i
$365$			2.48396i			0.130017i
$366$	12.0815	+	12.7447i	0.631509	+	0.666177i
$367$	−12.2166			−0.637703			−0.318852	−	0.947805i	$-0.603297\pi$
$367$	−12.2166			−0.637703			−0.318852	+	0.947805i	$0.603297\pi$
$368$	−4.97697			−0.259442
$369$	0.585157	−	0.525758i	0.0304621	−	0.0273699i
$370$	−16.2248	−	16.2248i	−0.843485	−	0.843485i
$371$	5.20768	+	5.20768i	0.270369	+	0.270369i
$372$	1.68904	+	1.78176i	0.0875727	+	0.0923801i
$373$	5.78239			0.299401			0.149700	−	0.988731i	$-0.452169\pi$
$373$	5.78239			0.299401			0.149700	+	0.988731i	$0.452169\pi$
$374$	−20.8745			−1.07939
$375$	15.0218	−	14.2400i	0.775720	−	0.735352i
$376$		−	3.62305i		−	0.186844i
$377$	−6.28452	+	6.92442i	−0.323669	+	0.356626i
$378$	−5.17948	−	0.415904i	−0.266404	−	0.0213918i
$379$	18.4746	+	18.4746i	0.948977	+	0.948977i	0.998760	−	0.0497833i	$-0.0158531\pi$
$379$	18.4746	+	18.4746i	0.948977	+	0.948977i	−0.0497833	+	0.998760i	$0.515853\pi$
$380$			14.0308i			0.719765i
$381$	33.7792	+	0.902419i	1.73056	+	0.0462323i
$382$	9.04652	+	9.04652i	0.462860	+	0.462860i
$383$	−22.5886	+	22.5886i	−1.15422	+	1.15422i	−0.168528	+	0.985697i	$0.553901\pi$
$383$	−22.5886	+	22.5886i	−1.15422	+	1.15422i	−0.985697	+	0.168528i	$0.946099\pi$
$384$	1.25702	−	1.19160i	0.0641468	−	0.0608086i
$385$	7.27824	−	7.27824i	0.370934	−	0.370934i
$386$		−	12.3539i		−	0.628796i
$387$	1.31566	−	24.6063i	0.0668788	−	1.25081i
$388$	7.65788	−	7.65788i	0.388770	−	0.388770i
$389$	5.36671			0.272103			0.136051	−	0.990702i	$-0.456559\pi$
$389$	5.36671			0.272103			0.136051	+	0.990702i	$0.456559\pi$
$390$	−9.12599	−	8.73830i	−0.462112	−	0.442481i
$391$	20.4211			1.03274
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	−21.5240	−	0.575017i	−1.08574	−	0.0290058i
$394$			8.90201i			0.448477i
$395$	18.1132	−	18.1132i	0.911374	−	0.911374i
$396$	11.3530	−	10.2005i	0.570507	−	0.512595i
$397$	14.5043	−	14.5043i	0.727949	−	0.727949i	−0.242262	−	0.970211i	$-0.577889\pi$
$397$	14.5043	−	14.5043i	0.727949	−	0.727949i	0.970211	+	0.242262i	$0.0778893\pi$
$398$	8.51685	+	8.51685i	0.426911	+	0.426911i
$399$	0.320779	−	12.0074i	0.0160590	−	0.601120i
$400$		−	0.906626i		−	0.0453313i
$401$	24.1397	+	24.1397i	1.20548	+	1.20548i	0.972476	+	0.233004i	$0.0748554\pi$
$401$	24.1397	+	24.1397i	1.20548	+	1.20548i	0.233004	+	0.972476i	$0.425145\pi$
$402$	0.205294	−	7.68454i	0.0102391	−	0.383270i
$403$	−0.247298	−	5.10472i	−0.0123188	−	0.254284i
$404$		−	3.05876i		−	0.152179i
$405$	14.1752	−	11.4293i	0.704370	−	0.567924i
$406$	−2.59352			−0.128714
$407$	−57.6970			−2.85994
$408$	−5.15769	+	4.88928i	−0.255344	+	0.242055i
$409$	−11.7934	−	11.7934i	−0.583147	−	0.583147i	0.352620	−	0.935767i	$-0.385291\pi$
$409$	−11.7934	−	11.7934i	−0.583147	−	0.583147i	−0.935767	+	0.352620i	$0.885291\pi$
$410$	0.375138	+	0.375138i	0.0185267	+	0.0185267i
$411$	16.3437	−	15.4931i	0.806174	−	0.764220i
$412$	8.89812			0.438379
$413$	1.89465			0.0932297
$414$	−11.1064	+	9.97898i	−0.545849	+	0.490440i
$415$			0.665409i			0.0326636i
$416$	−3.60133	+	0.174466i	−0.176570	+	0.00855391i
$417$	−0.881117	+	32.9818i	−0.0431485	+	1.61513i
$418$	24.9476	+	24.9476i	1.22022	+	1.22022i
$419$			37.7287i			1.84317i	0.388177	+	0.921585i	$0.373105\pi$
$419$			37.7287i			1.84317i	−0.388177	+	0.921585i	$0.626895\pi$
$420$	0.0935847	−	3.50305i	0.00456647	−	0.170931i
$421$	−2.50345	−	2.50345i	−0.122011	−	0.122011i	0.643465	−	0.765476i	$-0.277496\pi$
$421$	−2.50345	−	2.50345i	−0.122011	−	0.122011i	−0.765476	+	0.643465i	$0.777496\pi$
$422$	−16.4778	+	16.4778i	−0.802129	+	0.802129i
$423$	−7.26432	−	8.08503i	−0.353204	−	0.393108i
$424$	−5.20768	+	5.20768i	−0.252907	+	0.252907i
$425$			3.72000i			0.180446i
$426$	−23.1170	−	0.617576i	−1.12002	−	0.0299216i
$427$	7.16926	−	7.16926i	0.346945	−	0.346945i
$428$	−16.1853			−0.782346
$429$	−31.7637	+	0.689325i	−1.53357	+	0.0332809i
$430$	16.6182			0.801403
$431$	−3.13738	+	3.13738i	−0.151122	+	0.151122i	−0.778619	−	0.627497i	$-0.784080\pi$
$431$	−3.13738	+	3.13738i	−0.151122	+	0.151122i	0.627497	+	0.778619i	$0.284080\pi$
$432$	0.415904	−	5.17948i	0.0200102	−	0.249198i
$433$			32.9365i			1.58283i	0.611280	+	0.791415i	$0.290655\pi$
$433$			32.9365i			1.58283i	−0.611280	+	0.791415i	$0.709345\pi$
$434$	1.00229	−	1.00229i	0.0481116	−	0.0481116i
$435$	6.59586	−	6.25261i	0.316247	−	0.299790i
$436$	1.55437	−	1.55437i	0.0744410	−	0.0744410i
$437$	−24.4057	−	24.4057i	−1.16749	−	1.16749i
$438$	2.12574	+	0.0567895i	0.101572	+	0.00271351i
$439$			15.3322i			0.731768i	0.930660	+	0.365884i	$0.119233\pi$
$439$			15.3322i			0.731768i	−0.930660	+	0.365884i	$0.880767\pi$
$440$	7.27824	+	7.27824i	0.346977	+	0.346977i
$441$	−0.160177	+	2.99572i	−0.00762747	+	0.142653i
$442$	14.7767	−	0.715856i	0.702855	−	0.0340498i
$443$		−	26.4837i		−	1.25828i	−0.777292	−	0.629140i	$-0.783407\pi$
$443$		−	26.4837i		−	1.25828i	0.777292	−	0.629140i	$-0.216593\pi$
$444$	−14.2559	+	13.5140i	−0.676553	+	0.641345i
$445$	11.2487			0.533241
$446$	15.8469			0.750374
$447$	7.67247	+	8.09366i	0.362895	+	0.382817i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	3.73104	+	3.73104i	0.176079	+	0.176079i	0.789644	−	0.613565i	$-0.210265\pi$
$449$	3.73104	+	3.73104i	0.176079	+	0.176079i	−0.613565	+	0.789644i	$0.710265\pi$
$450$	−1.81781	−	2.02319i	−0.0856926	−	0.0953740i
$451$	1.33403			0.0628170
$452$	−1.67224			−0.0786557
$453$	−21.0280	−	22.1824i	−0.987982	−	1.04222i
$454$		−	3.12050i		−	0.146452i
$455$	−4.90255	+	5.40174i	−0.229835	+	0.253238i
$456$	12.0074	+	0.320779i	0.562296	+	0.0150219i
$457$	21.6075	+	21.6075i	1.01075	+	1.01075i	0.999942	+	0.0108124i	$0.00344174\pi$
$457$	21.6075	+	21.6075i	1.01075	+	1.01075i	0.0108124	+	0.999942i	$0.496558\pi$
$458$			24.6487i			1.15176i
$459$	−1.70651	+	21.2520i	−0.0796529	+	0.991960i
$460$	−7.12018	−	7.12018i	−0.331980	−	0.331980i
$461$	−7.48400	+	7.48400i	−0.348565	+	0.348565i	−0.859575	−	0.511010i	$-0.829271\pi$
$461$	−7.48400	+	7.48400i	−0.348565	+	0.348565i	0.511010	+	0.859575i	$0.329271\pi$
$462$	−6.06222	−	6.39501i	−0.282040	−	0.297523i
$463$	−0.469041	+	0.469041i	−0.0217982	+	0.0217982i	−0.717922	−	0.696124i	$-0.754907\pi$
$463$	−0.469041	+	0.469041i	−0.0217982	+	0.0217982i	0.696124	+	0.717922i	$0.254907\pi$
$464$		−	2.59352i		−	0.120401i
$465$	−0.132652	+	4.96542i	−0.00615159	+	0.230266i
$466$	4.97372	−	4.97372i	0.230403	−	0.230403i
$467$	32.9039			1.52261			0.761306	−	0.648393i	$-0.224559\pi$
$467$	32.9039			1.52261			0.761306	+	0.648393i	$0.224559\pi$
$468$	−7.68676	+	7.61011i	−0.355320	+	0.351777i
$469$	−4.43825			−0.204940
$470$	5.18322	−	5.18322i	0.239084	−	0.239084i
$471$	0.640397	−	23.9713i	0.0295079	−	1.10454i
$472$			1.89465i			0.0872084i
$473$	29.5481	−	29.5481i	1.35862	−	1.35862i
$474$	−15.0869	−	15.9151i	−0.692964	−	0.731006i
$475$	4.44586	−	4.44586i	0.203990	−	0.203990i
$476$	2.90134	+	2.90134i	0.132983	+	0.132983i
$477$	−1.17967	+	22.0628i	−0.0540132	+	1.01019i
$478$		−	3.76921i		−	0.172400i
$479$	−8.56901	−	8.56901i	−0.391528	−	0.391528i	0.483704	−	0.875232i	$-0.339291\pi$
$479$	−8.56901	−	8.56901i	−0.391528	−	0.391528i	−0.875232	+	0.483704i	$0.839291\pi$
$480$	3.50305	+	0.0935847i	0.159892	+	0.00427154i
$481$	40.8428	−	1.97863i	1.86227	−	0.0902176i
$482$			2.02994i			0.0924614i
$483$	5.93056	+	6.25613i	0.269850	+	0.284664i
$484$	14.8822			0.676465
$485$	21.9111			0.994932
$486$	−9.45691	−	12.3922i	−0.428974	−	0.562122i
$487$	−25.4916	−	25.4916i	−1.15513	−	1.15513i	−0.985509	−	0.169624i	$-0.945745\pi$
$487$	−25.4916	−	25.4916i	−1.15513	−	1.15513i	−0.169624	−	0.985509i	$-0.554255\pi$
$488$	7.16926	+	7.16926i	0.324537	+	0.324537i
$489$	4.66012	+	4.91595i	0.210738	+	0.222307i
$490$	−2.02321			−0.0913993
$491$	42.6747			1.92588			0.962941	−	0.269712i	$-0.0869287\pi$
$491$	42.6747			1.92588			0.962941	+	0.269712i	$0.0869287\pi$
$492$	0.329614	−	0.312461i	0.0148601	−	0.0140868i
$493$			10.6415i			0.479271i
$494$	−18.5155	−	16.8044i	−0.833052	−	0.756067i
$495$	30.8349	+	1.64870i	1.38593	+	0.0741035i
$496$	1.00229	+	1.00229i	0.0450042	+	0.0450042i
$497$			13.3514i			0.598891i
$498$	0.569447	+	0.0152129i	0.0255175	+	0.000681706i
$499$	21.6317	+	21.6317i	0.968368	+	0.968368i	0.999515	−	0.0311468i	$-0.00991594\pi$
$499$	21.6317	+	21.6317i	0.968368	+	0.968368i	−0.0311468	+	0.999515i	$0.509916\pi$
$500$	8.45017	−	8.45017i	0.377903	−	0.377903i
$501$	−24.2380	+	22.9766i	−1.08287	+	1.02652i
$502$	6.47010	−	6.47010i	0.288775	−	0.288775i
$503$			9.32655i			0.415850i	0.978145	+	0.207925i	$0.0666710\pi$
$503$			9.32655i			0.415850i	−0.978145	+	0.207925i	$0.933329\pi$
$504$	−2.99572	−	0.160177i	−0.133440	−	0.00713485i
$505$	4.37594	−	4.37594i	0.194727	−	0.194727i
$506$	−25.3201			−1.12562
$507$	22.4614	−	1.57725i	0.997544	−	0.0700479i
$508$	19.5094			0.865590
$509$	1.25938	−	1.25938i	0.0558209	−	0.0558209i	−0.678645	−	0.734466i	$-0.737433\pi$
$509$	1.25938	−	1.25938i	0.0558209	−	0.0558209i	0.734466	+	0.678645i	$0.237433\pi$
$510$	−14.3734	−	0.383989i	−0.636467	−	0.0170033i
$511$		−	1.22773i		−	0.0543117i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	27.4383	−	23.3593i	1.21143	−	1.03134i
$514$	−2.50593	+	2.50593i	−0.110532	+	0.110532i
$515$	12.7299	+	12.7299i	0.560945	+	0.560945i
$516$	0.379934	−	14.2216i	0.0167257	−	0.626073i
$517$		−	18.4321i		−	0.810643i
$518$	8.01932	+	8.01932i	0.352349	+	0.352349i
$519$	−1.01597	+	38.0296i	−0.0445961	+	1.66931i
$520$	−5.40174	−	4.90255i	−0.236882	−	0.214991i
$521$		−	38.5430i		−	1.68860i	−0.535872	−	0.844299i	$-0.680017\pi$
$521$		−	38.5430i		−	1.68860i	0.535872	−	0.844299i	$-0.319983\pi$
$522$	−5.20010	−	5.78760i	−0.227602	−	0.253316i
$523$	7.07627			0.309424			0.154712	−	0.987960i	$-0.450555\pi$
$523$	7.07627			0.309424			0.154712	+	0.987960i	$0.450555\pi$
$524$	−12.4313			−0.543064
$525$	−1.13964	+	1.08034i	−0.0497381	+	0.0471497i
$526$	19.5452	+	19.5452i	0.852211	+	0.852211i
$527$	−4.11253	−	4.11253i	−0.179144	−	0.179144i
$528$	6.39501	−	6.06222i	0.278307	−	0.263824i
$529$	1.77022			0.0769662
$530$	−14.9005			−0.647235
$531$	3.79884	+	4.22802i	0.164855	+	0.183480i
$532$		−	6.93493i		−	0.300667i
$533$	−0.944338	+	0.0457484i	−0.0409038	+	0.00198158i
$534$	0.257174	−	9.62650i	0.0111290	−	0.416580i
$535$	−23.1551	−	23.1551i	−1.00108	−	1.00108i
$536$		−	4.43825i		−	0.191703i
$537$	−0.396134	+	14.8280i	−0.0170944	+	0.639877i
$538$	14.1458	+	14.1458i	0.609867	+	0.609867i
$539$	−3.59738	+	3.59738i	−0.154950	+	0.154950i
$540$	8.00490	−	6.81489i	0.344476	−	0.293266i
$541$	6.35434	−	6.35434i	0.273194	−	0.273194i	−0.557190	−	0.830385i	$-0.688121\pi$
$541$	6.35434	−	6.35434i	0.273194	−	0.273194i	0.830385	+	0.557190i	$0.188121\pi$
$542$			7.32256i			0.314531i
$543$	−1.68490	−	0.0450124i	−0.0723060	−	0.00193167i
$544$	−2.90134	+	2.90134i	−0.124394	+	0.124394i
$545$	4.44745			0.190508
$546$	4.51065	+	4.31903i	0.193038	+	0.184837i
$547$	10.2100			0.436548			0.218274	−	0.975888i	$-0.429957\pi$
$547$	10.2100			0.436548			0.218274	+	0.975888i	$0.429957\pi$
$548$	9.19378	−	9.19378i	0.392739	−	0.392739i
$549$	30.3732	+	1.62401i	1.29630	+	0.0693112i
$550$		−	4.61242i		−	0.196674i
$551$	12.7180	−	12.7180i	0.541803	−	0.541803i
$552$	−6.25613	+	5.93056i	−0.266279	+	0.252421i
$553$	−8.95271	+	8.95271i	−0.380708	+	0.380708i
$554$	−8.43935	−	8.43935i	−0.358554	−	0.358554i
$555$	−39.7282	−	1.06135i	−1.68637	−	0.0450517i
$556$			19.0489i			0.807852i
$557$	1.56817	+	1.56817i	0.0664457	+	0.0664457i	0.739549	−	0.673103i	$-0.235039\pi$
$557$	1.56817	+	1.56817i	0.0664457	+	0.0664457i	−0.673103	+	0.739549i	$0.735039\pi$
$558$	4.24630	+	0.227044i	0.179760	+	0.00961152i
$559$	−19.9033	+	21.9299i	−0.841821	+	0.927538i
$560$		−	2.02321i		−	0.0854962i
$561$	−26.2395	+	24.8740i	−1.10783	+	1.05018i
$562$	−27.4966			−1.15988
$563$	20.2496			0.853418			0.426709	−	0.904389i	$-0.359673\pi$
$563$	20.2496			0.853418			0.426709	+	0.904389i	$0.359673\pi$
$564$	−4.31722	−	4.55423i	−0.181788	−	0.191767i
$565$	−2.39235	−	2.39235i	−0.100647	−	0.100647i
$566$	7.72333	+	7.72333i	0.324636	+	0.324636i
$567$	−7.00628	+	5.64907i	−0.294236	+	0.237239i
$568$	−13.3514			−0.560211
$569$	−16.8511			−0.706437			−0.353218	−	0.935541i	$-0.614913\pi$
$569$	−16.8511			−0.706437			−0.353218	+	0.935541i	$0.614913\pi$
$570$	16.7191	+	17.6370i	0.700287	+	0.738731i
$571$		−	8.55891i		−	0.358179i	−0.983833	−	0.179090i	$-0.942685\pi$
$571$		−	8.55891i		−	0.358179i	0.983833	−	0.179090i	$-0.0573152\pi$
$572$	−18.3216	+	0.887589i	−0.766065	+	0.0371120i
$573$	22.1515	+	0.591781i	0.925391	+	0.0247220i
$574$	−0.185417	−	0.185417i	−0.00773916	−	0.00773916i
$575$			4.51225i			0.188174i
$576$	0.160177	−	2.99572i	0.00667404	−	0.124822i
$577$	−11.4457	−	11.4457i	−0.476492	−	0.476492i	0.427516	−	0.904008i	$-0.359389\pi$
$577$	−11.4457	−	11.4457i	−0.476492	−	0.476492i	−0.904008	+	0.427516i	$0.859389\pi$
$578$	−0.116245	+	0.116245i	−0.00483516	+	0.00483516i
$579$	−14.7209	−	15.5290i	−0.611779	−	0.645364i
$580$	3.71036	−	3.71036i	0.154064	−	0.154064i
$581$		−	0.328888i		−	0.0136446i
$582$	0.500942	−	18.7512i	0.0207647	−	0.777263i
$583$	−26.4938	+	26.4938i	−1.09726	+	1.09726i
$584$	1.22773			0.0508040
$585$	−21.8841	−	0.109653i	−0.904795	−	0.00453360i
$586$	−2.57273			−0.106278
$587$	−19.6840	+	19.6840i	−0.812445	+	0.812445i	−0.985000	−	0.172555i	$-0.944798\pi$
$587$	−19.6840	+	19.6840i	−0.812445	+	0.812445i	0.172555	+	0.985000i	$0.444798\pi$
$588$	−0.0462556	+	1.73143i	−0.00190755	+	0.0714031i
$589$			9.82995i			0.405036i
$590$	−2.71053	+	2.71053i	−0.111591	+	0.111591i
$591$	10.6076	+	11.1900i	0.436340	+	0.460294i
$592$	−8.01932	+	8.01932i	−0.329592	+	0.329592i
$593$	−18.7038	−	18.7038i	−0.768073	−	0.768073i	0.209694	−	0.977767i	$-0.432753\pi$
$593$	−18.7038	−	18.7038i	−0.768073	−	0.768073i	−0.977767	+	0.209694i	$0.932753\pi$
$594$	2.11590	−	26.3504i	0.0868163	−	1.08117i
$595$			8.30147i			0.340327i
$596$	4.55291	+	4.55291i	0.186495	+	0.186495i
$597$	20.8545	+	0.557132i	0.853518	+	0.0228019i
$598$	17.9237	−	0.868312i	0.732955	−	0.0355079i
$599$		−	6.41962i		−	0.262299i	−0.991363	−	0.131149i	$-0.958133\pi$
$599$		−	6.41962i		−	0.262299i	0.991363	−	0.131149i	$-0.0418667\pi$
$600$	−1.08034	−	1.13964i	−0.0441045	−	0.0465257i
$601$	35.9129			1.46492			0.732459	−	0.680812i	$-0.238373\pi$
$601$	35.9129			1.46492			0.732459	+	0.680812i	$0.238373\pi$
$602$	−8.21380			−0.334770
$603$	−8.89884	−	9.90421i	−0.362389	−	0.403331i
$604$	−12.4782	−	12.4782i	−0.507731	−	0.507731i
$605$	21.2909	+	21.2909i	0.865597	+	0.865597i
$606$	−3.64482	−	3.84491i	−0.148061	−	0.156189i
$607$	−3.97978			−0.161534			−0.0807672	−	0.996733i	$-0.525737\pi$
$607$	−3.97978			−0.161534			−0.0807672	+	0.996733i	$0.525737\pi$
$608$	6.93493			0.281249
$609$	−3.26010	+	3.09044i	−0.132106	+	0.125231i
$610$			20.5130i			0.830549i
$611$	0.632099	+	13.0478i	0.0255720	+	0.527857i
$612$	−0.657225	+	12.2918i	−0.0265668	+	0.496867i
$613$	−10.2278	−	10.2278i	−0.413096	−	0.413096i	0.469720	−	0.882816i	$-0.344355\pi$
$613$	−10.2278	−	10.2278i	−0.413096	−	0.413096i	−0.882816	+	0.469720i	$0.844355\pi$
$614$			12.9792i			0.523797i
$615$	0.918568	+	0.0245397i	0.0370402	+	0.000989537i
$616$	−3.59738	−	3.59738i	−0.144942	−	0.144942i
$617$	28.6473	−	28.6473i	1.15330	−	1.15330i	0.167410	−	0.985887i	$-0.446460\pi$
$617$	28.6473	−	28.6473i	1.15330	−	1.15330i	0.985887	−	0.167410i	$-0.0535403\pi$
$618$	11.1851	−	10.6030i	0.449930	−	0.426515i
$619$	−7.15856	+	7.15856i	−0.287727	+	0.287727i	−0.836181	−	0.548454i	$-0.815217\pi$
$619$	−7.15856	+	7.15856i	−0.287727	+	0.287727i	0.548454	+	0.836181i	$0.315217\pi$
$620$			2.86781i			0.115174i
$621$	−2.06994	+	25.7781i	−0.0830640	+	1.03444i
$622$	−1.65884	+	1.65884i	−0.0665135	+	0.0665135i
$623$	−5.55985			−0.222751
$624$	−4.31903	+	4.51065i	−0.172900	+	0.180571i
$625$	19.6449			0.785796
$626$	−9.46610	+	9.46610i	−0.378341	+	0.378341i
$627$	61.0870	+	1.63195i	2.43958	+	0.0651738i
$628$		−	13.8447i		−	0.552466i
$629$	32.9043	−	32.9043i	1.31198	−	1.31198i
$630$	−4.05660	−	4.51491i	−0.161619	−	0.179878i
$631$	30.9238	−	30.9238i	1.23106	−	1.23106i	0.267498	−	0.963558i	$-0.413803\pi$
$631$	30.9238	−	30.9238i	1.23106	−	1.23106i	0.963558	−	0.267498i	$-0.0861970\pi$
$632$	−8.95271	−	8.95271i	−0.356120	−	0.356120i
$633$	−1.07790	+	40.3479i	−0.0428428	+	1.60369i
$634$			18.3830i			0.730081i
$635$	27.9106	+	27.9106i	1.10760	+	1.10760i
$636$	−0.340662	+	12.7516i	−0.0135081	+	0.505634i
$637$	2.42316	−	2.66989i	0.0960090	−	0.105785i
$638$		−	13.1944i		−	0.522373i
$639$	−29.7943	+	26.7699i	−1.17865	+	1.05900i
$640$	2.02321			0.0799743
$641$	−19.3831			−0.765585			−0.382792	−	0.923834i	$-0.625038\pi$
$641$	−19.3831			−0.765585			−0.382792	+	0.923834i	$0.625038\pi$
$642$	−20.3452	+	19.2864i	−0.802960	+	0.761174i
$643$	14.9960	+	14.9960i	0.591384	+	0.591384i	0.938005	−	0.346621i	$-0.112671\pi$
$643$	14.9960	+	14.9960i	0.591384	+	0.591384i	−0.346621	+	0.938005i	$0.612671\pi$
$644$	3.51925	+	3.51925i	0.138678	+	0.138678i
$645$	20.8894	−	19.8023i	0.822519	−	0.779715i
$646$	−28.4549			−1.11954
$647$	17.5674			0.690648			0.345324	−	0.938484i	$-0.387769\pi$
$647$	17.5674			0.690648			0.345324	+	0.938484i	$0.387769\pi$
$648$	−5.64907	−	7.00628i	−0.221917	−	0.275233i
$649$			9.63895i			0.378362i
$650$	0.158176	+	3.26506i	0.00620416	+	0.128066i
$651$	0.0655652	−	2.45423i	0.00256970	−	0.0961888i
$652$	2.76536	+	2.76536i	0.108300	+	0.108300i
$653$			13.2124i			0.517040i	0.966006	+	0.258520i	$0.0832347\pi$
$653$			13.2124i			0.517040i	−0.966006	+	0.258520i	$0.916765\pi$
$654$	0.101680	−	3.80606i	0.00397599	−	0.148829i
$655$	−17.7845	−	17.7845i	−0.694899	−	0.694899i
$656$	0.185417	−	0.185417i	0.00723932	−	0.00723932i
$657$	2.73976	−	2.46165i	0.106888	−	0.0960380i
$658$	−2.56188	+	2.56188i	−0.0998725	+	0.0998725i
$659$			25.7020i			1.00121i	0.865677	+	0.500603i	$0.166888\pi$
$659$			25.7020i			1.00121i	−0.865677	+	0.500603i	$0.833112\pi$
$660$	17.8216	+	0.476108i	0.693706	+	0.0185325i
$661$	24.0774	−	24.0774i	0.936502	−	0.936502i	−0.0615994	−	0.998101i	$-0.519620\pi$
$661$	24.0774	−	24.0774i	0.936502	−	0.936502i	0.998101	+	0.0615994i	$0.0196201\pi$
$662$	0.777007			0.0301992
$663$	17.7215	−	18.5077i	0.688246	−	0.718781i
$664$	0.328888			0.0127633
$665$	9.92128	−	9.92128i	0.384731	−	0.384731i
$666$	−1.81657	+	33.9746i	−0.0703907	+	1.31649i
$667$			12.9079i			0.499795i
$668$	−13.6345	+	13.6345i	−0.527536	+	0.527536i
$669$	19.9199	−	18.8832i	0.770146	−	0.730068i
$670$	6.34947	−	6.34947i	0.245302	−	0.245302i
$671$	36.4733	+	36.4733i	1.40804	+	1.40804i
$672$	−1.73143	−	0.0462556i	−0.0667915	−	0.00178435i
$673$			18.7017i			0.720898i	0.932779	+	0.360449i	$0.117377\pi$
$673$			18.7017i			0.720898i	−0.932779	+	0.360449i	$0.882623\pi$
$674$	−14.2273	−	14.2273i	−0.548013	−	0.548013i
$675$	−4.69585	−	0.377070i	−0.180743	−	0.0145134i
$676$	12.9391	−	1.25662i	0.497659	−	0.0483315i
$677$		−	23.9791i		−	0.921593i	−0.887506	−	0.460797i	$-0.847564\pi$
$677$		−	23.9791i		−	0.921593i	0.887506	−	0.460797i	$-0.152436\pi$
$678$	−2.10203	+	1.99264i	−0.0807282	+	0.0765271i
$679$	−10.8299			−0.415613
$680$	−8.30147			−0.318347
$681$	−3.71839	−	3.92252i	−0.142489	−	0.150311i
$682$	5.09912	+	5.09912i	0.195255	+	0.195255i
$683$	−23.6663	−	23.6663i	−0.905564	−	0.905564i	0.0903464	−	0.995910i	$-0.471203\pi$
$683$	−23.6663	−	23.6663i	−0.905564	−	0.905564i	−0.995910	+	0.0903464i	$0.971203\pi$
$684$	15.4757	−	13.9048i	0.591728	−	0.531662i
$685$	26.3057			1.00509
$686$	1.00000			0.0381802
$687$	29.3714	+	30.9838i	1.12059	+	1.18211i
$688$		−	8.21380i		−	0.313148i
$689$	17.8460	−	19.6631i	0.679878	−	0.749105i
$690$	−17.4346	−	0.465768i	−0.663723	−	0.0177315i
$691$	3.19271	+	3.19271i	0.121456	+	0.121456i	0.765222	−	0.643766i	$-0.222629\pi$
$691$	3.19271	+	3.19271i	0.121456	+	0.121456i	−0.643766	+	0.765222i	$0.722629\pi$
$692$			21.9642i			0.834955i
$693$	−15.2406	−	0.814893i	−0.578943	−	0.0309552i
$694$	−11.6206	−	11.6206i	−0.441113	−	0.441113i
$695$	−27.2518	+	27.2518i	−1.03372	+	1.03372i
$696$	−3.09044	−	3.26010i	−0.117143	−	0.123574i
$697$	−0.760789	+	0.760789i	−0.0288169	+	0.0288169i
$698$		−	13.6817i		−	0.517859i
$699$	0.325357	−	12.1787i	0.0123061	−	0.460642i
$700$	−0.641081	+	0.641081i	−0.0242306	+	0.0242306i
$701$	−24.7374			−0.934318			−0.467159	−	0.884173i	$-0.654722\pi$
$701$	−24.7374			−0.934318			−0.467159	+	0.884173i	$0.654722\pi$
$702$	−0.594164	+	18.7256i	−0.0224253	+	0.706751i
$703$	−78.6493			−2.96631
$704$	3.59738	−	3.59738i	0.135581	−	0.135581i
$705$	0.339062	−	12.6917i	0.0127698	−	0.477998i
$706$			3.60273i			0.135590i
$707$	−2.16287	+	2.16287i	−0.0813431	+	0.0813431i
$708$	2.25767	+	2.38161i	0.0848483	+	0.0895062i
$709$	12.7061	−	12.7061i	0.477187	−	0.477187i	−0.427044	−	0.904231i	$-0.640445\pi$
$709$	12.7061	−	12.7061i	0.477187	−	0.477187i	0.904231	+	0.427044i	$0.140445\pi$
$710$	−19.1008	−	19.1008i	−0.716840	−	0.716840i
$711$	−37.9289	−	2.02801i	−1.42245	−	0.0760562i
$712$		−	5.55985i		−	0.208364i
$713$	−4.98838	−	4.98838i	−0.186816	−	0.186816i
$714$	7.10428	+	0.189792i	0.265871	+	0.00710280i
$715$	−27.4811	−	24.9415i	−1.02774	−	0.932760i
$716$			8.56403i			0.320053i
$717$	−4.49140	−	4.73796i	−0.167734	−	0.176942i
$718$	−30.3098			−1.13115
$719$	19.2223			0.716870			0.358435	−	0.933555i	$-0.383310\pi$
$719$	19.2223			0.716870			0.358435	+	0.933555i	$0.383310\pi$
$720$	4.51491	−	4.05660i	0.168261	−	0.151181i
$721$	−6.29192	−	6.29192i	−0.234323	−	0.234323i
$722$	20.5720	+	20.5720i	0.765612	+	0.765612i
$723$	2.41888	+	2.55167i	0.0899592	+	0.0948977i
$724$	−0.973124			−0.0361659
$725$	−2.35136			−0.0873272
$726$	18.7072	−	17.7337i	0.694289	−	0.658158i
$727$		−	49.4631i		−	1.83448i	−0.398330	−	0.917242i	$-0.630410\pi$
$727$		−	49.4631i		−	1.83448i	0.398330	−	0.917242i	$-0.369590\pi$
$728$	2.66989	+	2.42316i	0.0989527	+	0.0898082i
$729$	−26.6540	−	4.30834i	−0.987187	−	0.159568i
$730$	1.75643	+	1.75643i	0.0650083	+	0.0650083i
$731$			33.7022i			1.24652i
$732$	17.5548	+	0.468979i	0.648843	+	0.0173340i
$733$	−7.14061	−	7.14061i	−0.263744	−	0.263744i	0.562829	−	0.826573i	$-0.309713\pi$
$733$	−7.14061	−	7.14061i	−0.263744	−	0.263744i	−0.826573	+	0.562829i	$0.809713\pi$
$734$	−8.63847	+	8.63847i	−0.318852	+	0.318852i
$735$	−2.54321	+	2.41086i	−0.0938075	+	0.0889258i
$736$	−3.51925	+	3.51925i	−0.129721	+	0.129721i
$737$		−	22.5794i		−	0.831724i
$738$	0.0420015	−	0.785536i	0.00154610	−	0.0289160i
$739$	−23.2049	+	23.2049i	−0.853607	+	0.853607i	−0.990575	−	0.136968i	$-0.956264\pi$
$739$	−23.2049	+	23.2049i	−0.853607	+	0.853607i	0.136968	+	0.990575i	$0.456264\pi$
$740$	−22.9453			−0.843485
$741$	−43.2984	+	0.939648i	−1.59061	+	0.0345188i
$742$	7.36477			0.270369
$743$	15.5087	−	15.5087i	0.568959	−	0.568959i	−0.362878	−	0.931837i	$-0.618206\pi$
$743$	15.5087	−	15.5087i	0.568959	−	0.568959i	0.931837	+	0.362878i	$0.118206\pi$
$744$	2.45423	+	0.0655652i	0.0899764	+	0.00240374i
$745$			13.0270i			0.477273i
$746$	4.08877	−	4.08877i	0.149700	−	0.149700i
$747$	0.733932	−	0.659431i	0.0268532	−	0.0241273i
$748$	−14.7605	+	14.7605i	−0.539696	+	0.539696i
$749$	11.4447	+	11.4447i	0.418182	+	0.418182i
$750$	0.552770	−	20.6912i	0.0201843	−	0.755536i
$751$			15.4920i			0.565311i	0.959221	+	0.282656i	$0.0912154\pi$
$751$			15.4920i			0.565311i	−0.959221	+	0.282656i	$0.908785\pi$
$752$	−2.56188	−	2.56188i	−0.0934222	−	0.0934222i
$753$	0.423243	−	15.8428i	0.0154238	−	0.577343i
$754$	0.452482	+	9.34013i	0.0164784	+	0.340147i
$755$		−	35.7033i		−	1.29938i
$756$	−3.95653	+	3.36836i	−0.143898	+	0.122506i
$757$	3.34900			0.121721			0.0608607	−	0.998146i	$-0.480615\pi$
$757$	3.34900			0.121721			0.0608607	+	0.998146i	$0.480615\pi$
$758$	26.1270			0.948977
$759$	−31.8278	+	30.1715i	−1.15528	+	1.09515i
$760$	9.92128	+	9.92128i	0.359883	+	0.359883i
$761$	−34.2779	−	34.2779i	−1.24257	−	1.24257i	−0.958930	−	0.283642i	$-0.908457\pi$
$761$	−34.2779	−	34.2779i	−1.24257	−	1.24257i	−0.283642	−	0.958930i	$-0.591543\pi$
$762$	24.5236	−	23.2474i	0.888397	−	0.842165i
$763$	−2.19822			−0.0795807
$764$	12.7937			0.462860
$765$	−18.5252	+	16.6447i	−0.669780	+	0.601791i
$766$			31.9451i			1.15422i
$767$	−0.330552	−	6.82326i	−0.0119356	−	0.246374i
$768$	0.0462556	−	1.73143i	0.00166910	−	0.0624777i
$769$	−26.5941	−	26.5941i	−0.959007	−	0.959007i	0.0401857	−	0.999192i	$-0.487205\pi$
$769$	−26.5941	−	26.5941i	−0.959007	−	0.959007i	−0.999192	+	0.0401857i	$0.987205\pi$
$770$		−	10.2930i		−	0.370934i
$771$	−0.163926	+	6.13606i	−0.00590365	+	0.220985i
$772$	−8.73551	−	8.73551i	−0.314398	−	0.314398i
$773$	−33.0906	+	33.0906i	−1.19018	+	1.19018i	−0.213170	+	0.977015i	$0.568379\pi$
$773$	−33.0906	+	33.0906i	−1.19018	+	1.19018i	−0.977015	+	0.213170i	$0.931621\pi$
$774$	−16.4689	−	18.3296i	−0.591964	−	0.658843i
$775$	0.908704	−	0.908704i	0.0326416	−	0.0326416i
$776$		−	10.8299i		−	0.388770i
$777$	19.6362	+	0.524586i	0.704446	+	0.0188194i
$778$	3.79484	−	3.79484i	0.136051	−	0.136051i
$779$	1.81847			0.0651536
$780$	−12.6320	+	0.274134i	−0.452297	+	0.00981559i
$781$	−67.9245			−2.43053
$782$	14.4399	−	14.4399i	0.516370	−	0.516370i
$783$	−13.4331	−	1.07866i	−0.480060	−	0.0385481i
$784$			1.00000i			0.0357143i
$785$	19.8066	−	19.8066i	0.706929	−	0.706929i
$786$	−15.6263	+	14.8131i	−0.557373	+	0.528367i
$787$	−6.98321	+	6.98321i	−0.248925	+	0.248925i	−0.820529	−	0.571605i	$-0.806321\pi$
$787$	−6.98321	+	6.98321i	−0.248925	+	0.248925i	0.571605	+	0.820529i	$0.306321\pi$
$788$	6.29467	+	6.29467i	0.224238	+	0.224238i
$789$	47.8587	+	1.27855i	1.70381	+	0.0455177i
$790$		−	25.6159i		−	0.911374i
$791$	1.18245	+	1.18245i	0.0420432	+	0.0420432i
$792$	0.814893	−	15.2406i	0.0289560	−	0.541551i
$793$	−27.0697	−	24.5681i	−0.961272	−	0.872438i
$794$		−	20.5121i		−	0.727949i
$795$	−18.7301	+	17.7554i	−0.664289	+	0.629719i
$796$	12.0446			0.426911
$797$	−41.4764			−1.46917			−0.734585	−	0.678516i	$-0.762623\pi$
$797$	−41.4764			−1.46917			−0.734585	+	0.678516i	$0.762623\pi$
$798$	−8.26367	−	8.71732i	−0.292531	−	0.308590i
$799$	10.5117	+	10.5117i	0.371877	+	0.371877i
$800$	−0.641081	−	0.641081i	−0.0226657	−	0.0226657i
$801$	−11.1477	−	12.4071i	−0.393884	−	0.438384i
$802$	34.1387			1.20548
$803$	6.24604			0.220418
$804$	−5.28862	−	5.57895i	−0.186515	−	0.196755i
$805$			10.0694i			0.354901i
$806$	−3.78445	−	3.43472i	−0.133302	−	0.120983i
$807$	34.6375	+	0.925348i	1.21930	+	0.0325738i
$808$	−2.16287	−	2.16287i	−0.0760895	−	0.0760895i
$809$		−	15.0063i		−	0.527595i	−0.964578	−	0.263797i	$-0.915025\pi$
$809$		−	15.0063i		−	0.527595i	0.964578	−	0.263797i	$-0.0849751\pi$
$810$	1.94165	−	18.1051i	0.0682228	−	0.636147i
$811$	−2.46485	−	2.46485i	−0.0865525	−	0.0865525i	0.662505	−	0.749057i	$-0.269493\pi$
$811$	−2.46485	−	2.46485i	−0.0865525	−	0.0865525i	−0.749057	+	0.662505i	$0.769493\pi$
$812$	−1.83390	+	1.83390i	−0.0643572	+	0.0643572i
$813$	8.72556	+	9.20457i	0.306019	+	0.322818i
$814$	−40.7980	+	40.7980i	−1.42997	+	1.42997i
$815$			7.91238i			0.277159i
$816$	−0.189792	+	7.10428i	−0.00664406	+	0.248700i
$817$	40.2783	−	40.2783i	1.40916	−	1.40916i
$818$	−16.6784			−0.583147
$819$	10.8165	+	0.0541977i	0.377960	+	0.00189382i
$820$	0.530525			0.0185267
$821$	13.9453	−	13.9453i	0.486694	−	0.486694i	−0.420567	−	0.907261i	$-0.638169\pi$
$821$	13.9453	−	13.9453i	0.486694	−	0.486694i	0.907261	+	0.420567i	$0.138169\pi$
$822$	0.601413	−	22.5120i	0.0209767	−	0.785197i
$823$			3.91631i			0.136514i	0.997668	+	0.0682570i	$0.0217438\pi$
$823$			3.91631i			0.136514i	−0.997668	+	0.0682570i	$0.978256\pi$
$824$	6.29192	−	6.29192i	0.219189	−	0.219189i
$825$	−5.49616	−	5.79789i	−0.191352	−	0.201857i
$826$	1.33972	−	1.33972i	0.0466148	−	0.0466148i
$827$	8.29105	+	8.29105i	0.288308	+	0.288308i	0.836411	−	0.548103i	$-0.184650\pi$
$827$	8.29105	+	8.29105i	0.288308	+	0.288308i	−0.548103	+	0.836411i	$0.684650\pi$
$828$	−0.797195	+	14.9096i	−0.0277045	+	0.518145i
$829$		−	21.6511i		−	0.751975i	−0.926625	−	0.375988i	$-0.877304\pi$
$829$		−	21.6511i		−	0.751975i	0.926625	−	0.375988i	$-0.122696\pi$
$830$	0.470515	+	0.470515i	0.0163318	+	0.0163318i
$831$	−20.6647	−	0.552062i	−0.716851	−	0.0191508i
$832$	−2.42316	+	2.66989i	−0.0840079	+	0.0925618i
$833$		−	4.10312i		−	0.142165i
$834$	22.6986	+	23.9447i	0.785990	+	0.829138i
$835$	−39.0118			−1.35006
$836$	35.2812			1.22022
$837$	5.60821	−	4.77450i	0.193848	−	0.165031i
$838$	26.6783	+	26.6783i	0.921585	+	0.921585i
$839$	−27.5249	−	27.5249i	−0.950266	−	0.950266i	0.0485547	−	0.998821i	$-0.484538\pi$
$839$	−27.5249	−	27.5249i	−0.950266	−	0.950266i	−0.998821	+	0.0485547i	$0.984538\pi$
$840$	−2.41086	−	2.54321i	−0.0831825	−	0.0877489i
$841$	22.2736			0.768056
$842$	−3.54041			−0.122011
$843$	−34.5637	+	32.7650i	−1.19044	+	1.12849i
$844$			23.3032i			0.802129i
$845$	20.3088	+	16.7133i	0.698643	+	0.574954i
$846$	−10.8536	−	0.580328i	−0.373156	−	0.0199521i
$847$	−10.5233	−	10.5233i	−0.361586	−	0.361586i
$848$			7.36477i			0.252907i
$849$	18.9115	+	0.505224i	0.649040	+	0.0173392i
$850$	2.63044	+	2.63044i	0.0902232	+	0.0902232i
$851$	39.9119	−	39.9119i	1.36816	−	1.36816i
$852$	−16.7829	+	15.9095i	−0.574972	+	0.545051i
$853$	−14.9776	+	14.9776i	−0.512822	+	0.512822i	−0.915390	−	0.402568i	$-0.868118\pi$
$853$	−14.9776	+	14.9776i	−0.512822	+	0.512822i	0.402568	+	0.915390i	$0.368118\pi$
$854$		−	10.1389i		−	0.346945i
$855$	42.0324	+	2.24741i	1.43748	+	0.0768599i
$856$	−11.4447	+	11.4447i	−0.391173	+	0.391173i
$857$	−4.13872			−0.141376			−0.0706880	−	0.997498i	$-0.522519\pi$
$857$	−4.13872			−0.141376			−0.0706880	+	0.997498i	$0.522519\pi$
$858$	−21.9729	+	22.9477i	−0.750142	+	0.783423i
$859$	3.48885			0.119038			0.0595191	−	0.998227i	$-0.481043\pi$
$859$	3.48885			0.119038			0.0595191	+	0.998227i	$0.481043\pi$
$860$	11.7509	−	11.7509i	0.400701	−	0.400701i
$861$	−0.454015	−	0.0121291i	−0.0154728	−	0.000413359i
$862$			4.43693i			0.151122i
$863$	13.8885	−	13.8885i	0.472770	−	0.472770i	−0.430040	−	0.902810i	$-0.641500\pi$
$863$	13.8885	−	13.8885i	0.472770	−	0.472770i	0.902810	+	0.430040i	$0.141500\pi$
$864$	−3.36836	−	3.95653i	−0.114594	−	0.134604i
$865$	−31.4226	+	31.4226i	−1.06840	+	1.06840i
$866$	23.2897	+	23.2897i	0.791415	+	0.791415i
$867$	−0.00760420	+	0.284640i	−0.000258252	+	0.00966687i
$868$		−	1.41746i		−	0.0481116i
$869$	−45.5465	−	45.5465i	−1.54506	−	1.54506i
$870$	0.242714	−	9.08525i	0.00822878	−	0.308019i
$871$	0.774325	+	15.9836i	0.0262370	+	0.541584i
$872$		−	2.19822i		−	0.0744410i
$873$	−21.7143	−	24.1675i	−0.734916	−	0.817946i
$874$	−34.5149			−1.16749
$875$	−11.9503			−0.403995
$876$	1.54328	−	1.46297i	0.0521426	−	0.0494291i
$877$	−18.9431	−	18.9431i	−0.639663	−	0.639663i	0.310809	−	0.950472i	$-0.399400\pi$
$877$	−18.9431	−	18.9431i	−0.639663	−	0.639663i	−0.950472	+	0.310809i	$0.899400\pi$
$878$	10.8415	+	10.8415i	0.365884	+	0.365884i
$879$	−3.23396	+	3.06566i	−0.109079	+	0.103402i
$880$	10.2930			0.346977
$881$	−23.3396			−0.786333			−0.393166	−	0.919467i	$-0.628620\pi$
$881$	−23.3396			−0.786333			−0.393166	+	0.919467i	$0.628620\pi$
$882$	2.00503	+	2.23156i	0.0675130	+	0.0751404i
$883$		−	48.4835i		−	1.63160i	−0.578334	−	0.815800i	$-0.696297\pi$
$883$		−	48.4835i		−	1.63160i	0.578334	−	0.815800i	$-0.303703\pi$
$884$	9.94251	−	10.9549i	0.334403	−	0.368452i
$885$	−0.177310	+	6.63706i	−0.00596022	+	0.223102i
$886$	−18.7268	−	18.7268i	−0.629140	−	0.629140i
$887$		−	20.5435i		−	0.689782i	−0.938643	−	0.344891i	$-0.887916\pi$
$887$		−	20.5435i		−	0.689782i	0.938643	−	0.344891i	$-0.112084\pi$
$888$	−0.524586	+	19.6362i	−0.0176040	+	0.658949i
$889$	−13.7952	−	13.7952i	−0.462677	−	0.462677i
$890$	7.95406	−	7.95406i	0.266621	−	0.266621i
$891$	−28.7394	−	35.6442i	−0.962807	−	1.19412i
$892$	11.2055	−	11.2055i	0.375187	−	0.375187i
$893$		−	25.1256i		−	0.840795i
$894$	11.1483	+	0.297830i	0.372856	+	0.00996093i
$895$	−12.2519	+	12.2519i	−0.409536	+	0.409536i
$896$	−1.00000			−0.0334077
$897$	21.4957	−	22.4494i	0.717720	−	0.749563i
$898$	5.27649			0.176079
$899$	2.59947	−	2.59947i	0.0866971	−	0.0866971i
$900$	−2.71600	−	0.145221i	−0.0905333	−	0.00484069i
$901$		−	30.2185i		−	1.00673i
$902$	0.943302	−	0.943302i	0.0314085	−	0.0314085i
$903$	−10.3249	+	9.78757i	−0.343590	+	0.325710i
$904$	−1.18245	+	1.18245i	−0.0393278	+	0.0393278i
$905$	−1.39218	−	1.39218i	−0.0462775	−	0.0462775i
$906$	−30.5544	−	0.816266i	−1.01510	−	0.0271186i
$907$		−	20.3036i		−	0.674169i	−0.941474	−	0.337085i	$-0.890559\pi$
$907$		−	20.3036i		−	0.674169i	0.941474	−	0.337085i	$-0.109441\pi$
$908$	−2.20653	−	2.20653i	−0.0732261	−	0.0732261i
$909$	−9.16320	−	0.489943i	−0.303924	−	0.0162504i
$910$	0.352981	+	7.28624i	0.0117012	+	0.241536i
$911$			4.80500i			0.159197i	0.996827	+	0.0795984i	$0.0253638\pi$
$911$			4.80500i			0.159197i	−0.996827	+	0.0795984i	$0.974636\pi$
$912$	8.71732	−	8.26367i	0.288659	−	0.273637i
$913$	1.67320			0.0553749
$914$	30.5575			1.01075
$915$	24.4434	+	25.7852i	0.808072	+	0.852433i
$916$	17.4293	+	17.4293i	0.575879	+	0.575879i
$917$	8.79026	+	8.79026i	0.290280	+	0.290280i
$918$	13.8208	+	16.2341i	0.456154	+	0.535807i
$919$	8.07961			0.266522			0.133261	−	0.991081i	$-0.457455\pi$
$919$	8.07961			0.266522			0.133261	+	0.991081i	$0.457455\pi$
$920$	−10.0694			−0.331980
$921$	15.4660	+	16.3150i	0.509622	+	0.537598i
$922$			10.5840i			0.348565i
$923$	48.0827	−	2.32936i	1.58266	−	0.0766719i
$924$	−8.80859	−	0.235323i	−0.289781	−	0.00774157i
$925$	7.27053	+	7.27053i	0.239053	+	0.239053i
$926$			0.663324i			0.0217982i
$927$	1.42527	−	26.6563i	0.0468121	−	0.875507i
$928$	−1.83390	−	1.83390i	−0.0602007	−	0.0602007i
$929$	−15.7251	+	15.7251i	−0.515924	+	0.515924i	−0.916335	−	0.400412i	$-0.868867\pi$
$929$	−15.7251	+	15.7251i	−0.515924	+	0.515924i	0.400412	+	0.916335i	$0.368867\pi$
$930$	3.41728	+	3.60488i	0.112057	+	0.118209i
$931$	−4.90374	+	4.90374i	−0.160713	+	0.160713i
$932$		−	7.03391i		−	0.230403i
$933$	−0.108514	+	4.06187i	−0.00355257	+	0.132980i
$934$	23.2666	−	23.2666i	0.761306	−	0.761306i
$935$	−42.2334			−1.38118
$936$	−0.0541977	+	10.8165i	−0.00177151	+	0.353549i
$937$	22.7249			0.742389			0.371195	−	0.928555i	$-0.378948\pi$
$937$	22.7249			0.742389			0.371195	+	0.928555i	$0.378948\pi$
$938$	−3.13832	+	3.13832i	−0.102470	+	0.102470i
$939$	−0.619227	+	23.1788i	−0.0202077	+	0.756413i
$940$		−	7.33018i		−	0.239084i
$941$	26.5724	−	26.5724i	0.866234	−	0.866234i	−0.125819	−	0.992053i	$-0.540156\pi$
$941$	26.5724	−	26.5724i	0.866234	−	0.866234i	0.992053	+	0.125819i	$0.0401559\pi$
$942$	−16.4974	−	17.4031i	−0.537515	−	0.567023i
$943$	−0.922815	+	0.922815i	−0.0300510	+	0.0300510i
$944$	1.33972	+	1.33972i	0.0436042	+	0.0436042i
$945$	−10.4792	−	0.841461i	−0.340887	−	0.0273727i
$946$		−	41.7874i		−	1.35862i
$947$	14.4108	+	14.4108i	0.468288	+	0.468288i	0.901360	−	0.433071i	$-0.142570\pi$
$947$	14.4108	+	14.4108i	0.468288	+	0.468288i	−0.433071	+	0.901360i	$0.642570\pi$
$948$	−21.9217	−	0.585644i	−0.711985	−	0.0190208i
$949$	−4.42147	+	0.214198i	−0.143527	+	0.00695316i
$950$		−	6.28739i		−	0.203990i
$951$	21.9051	+	23.1077i	0.710323	+	0.749318i
$952$	4.10312			0.132983
$953$	11.5458			0.374004			0.187002	−	0.982360i	$-0.440123\pi$
$953$	11.5458			0.374004			0.187002	+	0.982360i	$0.440123\pi$
$954$	14.7666	+	16.4349i	0.478086	+	0.532100i
$955$	18.3030	+	18.3030i	0.592271	+	0.592271i
$956$	−2.66524	−	2.66524i	−0.0861999	−	0.0861999i
$957$	−15.7225	−	16.5856i	−0.508236	−	0.536137i
$958$	−12.1184			−0.391528
$959$	−13.0020			−0.419855
$960$	2.54321	−	2.41086i	0.0820816	−	0.0778101i
$961$		−	28.9908i		−	0.935188i
$962$	27.4811	−	30.2793i	0.886026	−	0.976244i
$963$	−2.59251	+	48.4867i	−0.0835425	+	1.56246i
$964$	1.43539	+	1.43539i	0.0462307	+	0.0462307i
$965$		−	24.9945i		−	0.804601i
$966$	8.61729	+	0.230213i	0.277257	+	0.00740697i
$967$	13.0289	+	13.0289i	0.418982	+	0.418982i	0.884853	−	0.465871i	$-0.154259\pi$
$967$	13.0289	+	13.0289i	0.418982	+	0.418982i	−0.465871	+	0.884853i	$0.654259\pi$
$968$	10.5233	−	10.5233i	0.338232	−	0.338232i
$969$	−35.7682	+	33.9068i	−1.14904	+	1.08924i
$970$	15.4935	−	15.4935i	0.497466	−	0.497466i
$971$			34.4228i			1.10468i	0.833619	+	0.552340i	$0.186265\pi$
$971$			34.4228i			1.10468i	−0.833619	+	0.552340i	$0.813735\pi$
$972$	−15.4497	−	2.07557i	−0.495548	−	0.0665738i
$973$	13.4696	−	13.4696i	0.431815	−	0.431815i
$974$	−36.0505			−1.15513
$975$	4.08947	+	3.91575i	0.130968	+	0.125404i
$976$	10.1389			0.324537
$977$	−13.4816	+	13.4816i	−0.431314	+	0.431314i	−0.889075	−	0.457761i	$-0.848651\pi$
$977$	−13.4816	+	13.4816i	−0.431314	+	0.431314i	0.457761	+	0.889075i	$0.348651\pi$
$978$	6.77130	+	0.180897i	0.216522	+	0.00578444i
$979$		−	28.2855i		−	0.904008i
$980$	−1.43062	+	1.43062i	−0.0456996	+	0.0456996i
$981$	−4.40749	−	4.90544i	−0.140720	−	0.156619i
$982$	30.1756	−	30.1756i	0.962941	−	0.962941i
$983$	−5.99104	−	5.99104i	−0.191085	−	0.191085i	0.605080	−	0.796165i	$-0.293141\pi$
$983$	−5.99104	−	5.99104i	−0.191085	−	0.191085i	−0.796165	+	0.605080i	$0.793141\pi$
$984$	0.0121291	−	0.454015i	0.000386662	−	0.0144735i
$985$			18.0106i			0.573866i
$986$	7.52471	+	7.52471i	0.239635	+	0.239635i
$987$	−0.167586	+	6.27306i	−0.00533432	+	0.199674i
$988$	−24.9750	+	1.20991i	−0.794559	+	0.0384924i
$989$			40.8798i			1.29990i
$990$	22.9694	−	20.6378i	0.730015	−	0.655912i
$991$	−18.7348			−0.595131			−0.297566	−	0.954701i	$-0.596175\pi$
$991$	−18.7348			−0.595131			−0.297566	+	0.954701i	$0.596175\pi$
$992$	1.41746			0.0450042
$993$	0.976710	−	0.925881i	0.0309949	−	0.0293820i
$994$	9.44085	+	9.44085i	0.299445	+	0.299445i
$995$	17.2314	+	17.2314i	0.546271	+	0.546271i
$996$	0.413417	−	0.391903i	0.0130996	−	0.0124179i
$997$	−17.7862			−0.563294			−0.281647	−	0.959518i	$-0.590881\pi$
$997$	−17.7862			−0.563294			−0.281647	+	0.959518i	$0.590881\pi$
$998$	30.5918			0.968368
$999$	38.2007	+	44.8712i	1.20862	+	1.41966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.c.281.9	yes	20
3.2	odd	2		546.2.p.d.281.4	yes	20
13.5	odd	4		546.2.p.d.239.4	yes	20
39.5	even	4	inner	546.2.p.c.239.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.9	✓	20	39.5	even	4	inner
546.2.p.c.281.9	yes	20	1.1	even	1	trivial
546.2.p.d.239.4	yes	20	13.5	odd	4
546.2.p.d.281.4	yes	20	3.2	odd	2

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.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.0462556 - 1.73143i) q^{3} -1.00000i q^{4} +(1.43062 - 1.43062i) q^{5} +(-1.19160 - 1.25702i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99572 - 0.160177i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.0462556 - 1.73143i) q^{3} -1.00000i q^{4} +(1.43062 - 1.43062i) q^{5} +(-1.19160 - 1.25702i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99572 - 0.160177i) q^{9} -2.02321i q^{10} +(-3.59738 - 3.59738i) q^{11} +(-1.73143 - 0.0462556i) q^{12} +(2.66989 + 2.42316i) q^{13} +1.00000i q^{14} +(-2.41086 - 2.54321i) q^{15} -1.00000 q^{16} +4.10312 q^{17} +(-2.23156 + 2.00503i) q^{18} +(-4.90374 - 4.90374i) q^{19} +(-1.43062 - 1.43062i) q^{20} +(1.19160 + 1.25702i) q^{21} -5.08746 q^{22} +4.97697 q^{23} +(-1.25702 + 1.19160i) q^{24} +0.906626i q^{25} +(3.60133 - 0.174466i) q^{26} +(-0.415904 + 5.17948i) q^{27} +(0.707107 + 0.707107i) q^{28} +2.59352i q^{29} +(-3.50305 - 0.0935847i) q^{30} +(-1.00229 - 1.00229i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.39501 + 6.06222i) q^{33} +(2.90134 - 2.90134i) q^{34} +2.02321i q^{35} +(-0.160177 + 2.99572i) q^{36} +(8.01932 - 8.01932i) q^{37} -6.93493 q^{38} +(4.31903 - 4.51065i) q^{39} -2.02321 q^{40} +(-0.185417 + 0.185417i) q^{41} +(1.73143 + 0.0462556i) q^{42} +8.21380i q^{43} +(-3.59738 + 3.59738i) q^{44} +(-4.51491 + 4.05660i) q^{45} +(3.51925 - 3.51925i) q^{46} +(2.56188 + 2.56188i) q^{47} +(-0.0462556 + 1.73143i) q^{48} -1.00000i q^{49} +(0.641081 + 0.641081i) q^{50} +(0.189792 - 7.10428i) q^{51} +(2.42316 - 2.66989i) q^{52} -7.36477i q^{53} +(3.36836 + 3.95653i) q^{54} -10.2930 q^{55} +1.00000 q^{56} +(-8.71732 + 8.26367i) q^{57} +(1.83390 + 1.83390i) q^{58} +(-1.33972 - 1.33972i) q^{59} +(-2.54321 + 2.41086i) q^{60} -10.1389 q^{61} -1.41746 q^{62} +(2.23156 - 2.00503i) q^{63} +1.00000i q^{64} +(7.28624 - 0.352981i) q^{65} +(-0.235323 + 8.80859i) q^{66} +(3.13832 + 3.13832i) q^{67} -4.10312i q^{68} +(0.230213 - 8.61729i) q^{69} +(1.43062 + 1.43062i) q^{70} +(9.44085 - 9.44085i) q^{71} +(2.00503 + 2.23156i) q^{72} +(-0.868139 + 0.868139i) q^{73} -11.3410i q^{74} +(1.56976 + 0.0419365i) q^{75} +(-4.90374 + 4.90374i) q^{76} +5.08746 q^{77} +(-0.135495 - 6.24353i) q^{78} +12.6610 q^{79} +(-1.43062 + 1.43062i) q^{80} +(8.94869 + 0.959690i) q^{81} +0.262219i q^{82} +(-0.232559 + 0.232559i) q^{83} +(1.25702 - 1.19160i) q^{84} +(5.87003 - 5.87003i) q^{85} +(5.80804 + 5.80804i) q^{86} +(4.49051 + 0.119965i) q^{87} +5.08746i q^{88} +(3.93141 + 3.93141i) q^{89} +(-0.324071 + 6.06097i) q^{90} +(-3.60133 + 0.174466i) q^{91} -4.97697i q^{92} +(-1.78176 + 1.68904i) q^{93} +3.62305 q^{94} -14.0308 q^{95} +(1.19160 + 1.25702i) q^{96} +(7.65788 + 7.65788i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(10.2005 + 11.3530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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