LMFDB - Embedded newform 546.2.p.c.239.6

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			239.6
Root			$1.47393 - 0.909692i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.c.281.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.68547 - 0.398975i) q^{3} +1.00000i q^{4} +(-0.559062 - 0.559062i) q^{5} +(-0.909692 - 1.47393i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.68164 + 1.34492i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.68547 - 0.398975i) q^{3} +1.00000i q^{4} +(-0.559062 - 0.559062i) q^{5} +(-0.909692 - 1.47393i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.68164 + 1.34492i) q^{9} -0.790633i q^{10} +(-0.347057 + 0.347057i) q^{11} +(0.398975 - 1.68547i) q^{12} +(-3.45365 + 1.03551i) q^{13} -1.00000i q^{14} +(0.719233 + 1.16534i) q^{15} -1.00000 q^{16} -4.50042 q^{17} +(0.945201 + 2.84721i) q^{18} +(-3.86509 + 3.86509i) q^{19} +(0.559062 - 0.559062i) q^{20} +(0.909692 + 1.47393i) q^{21} -0.490813 q^{22} -5.27970 q^{23} +(1.47393 - 0.909692i) q^{24} -4.37490i q^{25} +(-3.17432 - 1.70989i) q^{26} +(-3.98324 - 3.33674i) q^{27} +(0.707107 - 0.707107i) q^{28} -10.6966i q^{29} +(-0.315443 + 1.33259i) q^{30} +(-2.47731 + 2.47731i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.723423 - 0.446489i) q^{33} +(-3.18228 - 3.18228i) q^{34} +0.790633i q^{35} +(-1.34492 + 2.68164i) q^{36} +(6.92111 + 6.92111i) q^{37} -5.46606 q^{38} +(6.23418 - 0.367403i) q^{39} +0.790633 q^{40} +(-7.31477 - 7.31477i) q^{41} +(-0.398975 + 1.68547i) q^{42} +7.24514i q^{43} +(-0.347057 - 0.347057i) q^{44} +(-0.747308 - 2.25110i) q^{45} +(-3.73331 - 3.73331i) q^{46} +(-2.49319 + 2.49319i) q^{47} +(1.68547 + 0.398975i) q^{48} +1.00000i q^{49} +(3.09352 - 3.09352i) q^{50} +(7.58533 + 1.79555i) q^{51} +(-1.03551 - 3.45365i) q^{52} +12.0607i q^{53} +(-0.457147 - 5.17600i) q^{54} +0.388054 q^{55} +1.00000 q^{56} +(8.05657 - 4.97243i) q^{57} +(7.56362 - 7.56362i) q^{58} +(3.41247 - 3.41247i) q^{59} +(-1.16534 + 0.719233i) q^{60} +6.42464 q^{61} -3.50344 q^{62} +(-0.945201 - 2.84721i) q^{63} -1.00000i q^{64} +(2.50972 + 1.35189i) q^{65} +(0.827253 + 0.195822i) q^{66} +(-2.43437 + 2.43437i) q^{67} -4.50042i q^{68} +(8.89880 + 2.10647i) q^{69} +(-0.559062 + 0.559062i) q^{70} +(-8.49611 - 8.49611i) q^{71} +(-2.84721 + 0.945201i) q^{72} +(5.93236 + 5.93236i) q^{73} +9.78793i q^{74} +(-1.74547 + 7.37377i) q^{75} +(-3.86509 - 3.86509i) q^{76} +0.490813 q^{77} +(4.66802 + 4.14844i) q^{78} -13.2235 q^{79} +(0.559062 + 0.559062i) q^{80} +(5.38237 + 7.21319i) q^{81} -10.3446i q^{82} +(6.31304 + 6.31304i) q^{83} +(-1.47393 + 0.909692i) q^{84} +(2.51601 + 2.51601i) q^{85} +(-5.12309 + 5.12309i) q^{86} +(-4.26766 + 18.0288i) q^{87} -0.490813i q^{88} +(12.2569 - 12.2569i) q^{89} +(1.06334 - 2.12019i) q^{90} +(3.17432 + 1.70989i) q^{91} -5.27970i q^{92} +(5.16382 - 3.18705i) q^{93} -3.52590 q^{94} +4.32165 q^{95} +(0.909692 + 1.47393i) q^{96} +(-0.867358 + 0.867358i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-1.39745 + 0.463917i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.68547	−	0.398975i	−0.973108	−	0.230348i
$3$	−1.68547	−	0.398975i	−0.973108	−	0.230348i
$4$			1.00000i			0.500000i
$5$	−0.559062	−	0.559062i	−0.250020	−	0.250020i	0.570959	−	0.820979i	$-0.306572\pi$
$5$	−0.559062	−	0.559062i	−0.250020	−	0.250020i	−0.820979	+	0.570959i	$0.806572\pi$
$6$	−0.909692	−	1.47393i	−0.371380	−	0.601728i
$7$	−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
$9$	2.68164	+	1.34492i	0.893879	+	0.448307i
$10$		−	0.790633i		−	0.250020i
$11$	−0.347057	+	0.347057i	−0.104642	+	0.104642i	−0.757489	−	0.652848i	$-0.773574\pi$
$11$	−0.347057	+	0.347057i	−0.104642	+	0.104642i	0.652848	+	0.757489i	$0.273574\pi$
$12$	0.398975	−	1.68547i	0.115174	−	0.486554i
$13$	−3.45365	+	1.03551i	−0.957871	+	0.287199i
$13$	−3.45365	+	1.03551i	−0.957871	+	0.287199i
$14$		−	1.00000i		−	0.267261i
$15$	0.719233	+	1.16534i	0.185705	+	0.300888i
$16$	−1.00000			−0.250000
$17$	−4.50042			−1.09151			−0.545756	−	0.837944i	$-0.683757\pi$
$17$	−4.50042			−1.09151			−0.545756	+	0.837944i	$0.683757\pi$
$18$	0.945201	+	2.84721i	0.222786	+	0.671093i
$19$	−3.86509	+	3.86509i	−0.886712	+	0.886712i	−0.994206	−	0.107494i	$-0.965717\pi$
$19$	−3.86509	+	3.86509i	−0.886712	+	0.886712i	0.107494	+	0.994206i	$0.465717\pi$
$20$	0.559062	−	0.559062i	0.125010	−	0.125010i
$21$	0.909692	+	1.47393i	0.198511	+	0.321637i
$22$	−0.490813			−0.104642
$23$	−5.27970			−1.10089			−0.550447	−	0.834870i	$-0.685543\pi$
$23$	−5.27970			−1.10089			−0.550447	+	0.834870i	$0.685543\pi$
$24$	1.47393	−	0.909692i	0.300864	−	0.185690i
$25$		−	4.37490i		−	0.874980i
$26$	−3.17432	−	1.70989i	−0.622535	−	0.335336i
$27$	−3.98324	−	3.33674i	−0.766575	−	0.642155i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$		−	10.6966i		−	1.98630i	−0.116833	−	0.993152i	$-0.537274\pi$
$29$		−	10.6966i		−	1.98630i	0.116833	−	0.993152i	$-0.462726\pi$
$30$	−0.315443	+	1.33259i	−0.0575917	+	0.243297i
$31$	−2.47731	+	2.47731i	−0.444938	+	0.444938i	−0.893667	−	0.448730i	$-0.851877\pi$
$31$	−2.47731	+	2.47731i	−0.444938	+	0.444938i	0.448730	+	0.893667i	$0.351877\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.723423	−	0.446489i	0.125932	−	0.0777237i
$34$	−3.18228	−	3.18228i	−0.545756	−	0.545756i
$35$			0.790633i			0.133641i
$36$	−1.34492	+	2.68164i	−0.224154	+	0.446940i
$37$	6.92111	+	6.92111i	1.13782	+	1.13782i	0.988840	+	0.148984i	$0.0476004\pi$
$37$	6.92111	+	6.92111i	1.13782	+	1.13782i	0.148984	+	0.988840i	$0.452400\pi$
$38$	−5.46606			−0.886712
$39$	6.23418	−	0.367403i	0.998268	−	0.0588315i
$40$	0.790633			0.125010
$41$	−7.31477	−	7.31477i	−1.14237	−	1.14237i	−0.988015	−	0.154360i	$-0.950668\pi$
$41$	−7.31477	−	7.31477i	−1.14237	−	1.14237i	−0.154360	−	0.988015i	$-0.549332\pi$
$42$	−0.398975	+	1.68547i	−0.0615631	+	0.260074i
$43$			7.24514i			1.10487i	0.833555	+	0.552437i	$0.186302\pi$
$43$			7.24514i			1.10487i	−0.833555	+	0.552437i	$0.813698\pi$
$44$	−0.347057	−	0.347057i	−0.0523209	−	0.0523209i
$45$	−0.747308	−	2.25110i	−0.111402	−	0.335574i
$46$	−3.73331	−	3.73331i	−0.550447	−	0.550447i
$47$	−2.49319	+	2.49319i	−0.363669	+	0.363669i	−0.865162	−	0.501493i	$-0.832784\pi$
$47$	−2.49319	+	2.49319i	−0.363669	+	0.363669i	0.501493	+	0.865162i	$0.332784\pi$
$48$	1.68547	+	0.398975i	0.243277	+	0.0575870i
$49$			1.00000i			0.142857i
$50$	3.09352	−	3.09352i	0.437490	−	0.437490i
$51$	7.58533	+	1.79555i	1.06216	+	0.251428i
$52$	−1.03551	−	3.45365i	−0.143599	−	0.478936i
$53$			12.0607i			1.65667i	0.560236	+	0.828333i	$0.310710\pi$
$53$			12.0607i			1.65667i	−0.560236	+	0.828333i	$0.689290\pi$
$54$	−0.457147	−	5.17600i	−0.0622098	−	0.704365i
$55$	0.388054			0.0523251
$56$	1.00000			0.133631
$57$	8.05657	−	4.97243i	1.06712	−	0.658614i
$58$	7.56362	−	7.56362i	0.993152	−	0.993152i
$59$	3.41247	−	3.41247i	0.444266	−	0.444266i	−0.449177	−	0.893443i	$-0.648283\pi$
$59$	3.41247	−	3.41247i	0.444266	−	0.444266i	0.893443	+	0.449177i	$0.148283\pi$
$60$	−1.16534	+	0.719233i	−0.150444	+	0.0928525i
$61$	6.42464			0.822591			0.411296	−	0.911502i	$-0.365076\pi$
$61$	6.42464			0.822591			0.411296	+	0.911502i	$0.365076\pi$
$62$	−3.50344			−0.444938
$63$	−0.945201	−	2.84721i	−0.119084	−	0.358715i
$64$		−	1.00000i		−	0.125000i
$65$	2.50972	+	1.35189i	0.311293	+	0.167682i
$66$	0.827253	+	0.195822i	0.101828	+	0.0241040i
$67$	−2.43437	+	2.43437i	−0.297405	+	0.297405i	−0.839997	−	0.542592i	$-0.817443\pi$
$67$	−2.43437	+	2.43437i	−0.297405	+	0.297405i	0.542592	+	0.839997i	$0.317443\pi$
$68$		−	4.50042i		−	0.545756i
$69$	8.89880	+	2.10647i	1.07129	+	0.253589i
$70$	−0.559062	+	0.559062i	−0.0668207	+	0.0668207i
$71$	−8.49611	−	8.49611i	−1.00830	−	1.00830i	−0.999965	−	0.00833786i	$-0.997346\pi$
$71$	−8.49611	−	8.49611i	−1.00830	−	1.00830i	−0.00833786	−	0.999965i	$-0.502654\pi$
$72$	−2.84721	+	0.945201i	−0.335547	+	0.111393i
$73$	5.93236	+	5.93236i	0.694330	+	0.694330i	0.963182	−	0.268851i	$-0.0866440\pi$
$73$	5.93236	+	5.93236i	0.694330	+	0.694330i	−0.268851	+	0.963182i	$0.586644\pi$
$74$			9.78793i			1.13782i
$75$	−1.74547	+	7.37377i	−0.201550	+	0.851450i
$76$	−3.86509	−	3.86509i	−0.443356	−	0.443356i
$77$	0.490813			0.0559334
$78$	4.66802	+	4.14844i	0.528550	+	0.469718i
$79$	−13.2235			−1.48776			−0.743882	−	0.668311i	$-0.767017\pi$
$79$	−13.2235			−1.48776			−0.743882	+	0.668311i	$0.767017\pi$
$80$	0.559062	+	0.559062i	0.0625051	+	0.0625051i
$81$	5.38237	+	7.21319i	0.598041	+	0.801466i
$82$		−	10.3446i		−	1.14237i
$83$	6.31304	+	6.31304i	0.692946	+	0.692946i	0.962879	−	0.269933i	$-0.0870016\pi$
$83$	6.31304	+	6.31304i	0.692946	+	0.692946i	−0.269933	+	0.962879i	$0.587002\pi$
$84$	−1.47393	+	0.909692i	−0.160819	+	0.0992555i
$85$	2.51601	+	2.51601i	0.272900	+	0.272900i
$86$	−5.12309	+	5.12309i	−0.552437	+	0.552437i
$87$	−4.26766	+	18.0288i	−0.457541	+	1.93289i
$88$		−	0.490813i		−	0.0523209i
$89$	12.2569	−	12.2569i	1.29923	−	1.29923i	0.370335	−	0.928898i	$-0.379243\pi$
$89$	12.2569	−	12.2569i	1.29923	−	1.29923i	0.928898	−	0.370335i	$-0.120757\pi$
$90$	1.06334	−	2.12019i	0.112086	−	0.223488i
$91$	3.17432	+	1.70989i	0.332759	+	0.179245i
$92$		−	5.27970i		−	0.550447i
$93$	5.16382	−	3.18705i	0.535463	−	0.330482i
$94$	−3.52590			−0.363669
$95$	4.32165			0.443392
$96$	0.909692	+	1.47393i	0.0928450	+	0.150432i
$97$	−0.867358	+	0.867358i	−0.0880669	+	0.0880669i	−0.749768	−	0.661701i	$-0.769835\pi$
$97$	−0.867358	+	0.867358i	−0.0880669	+	0.0880669i	0.661701	+	0.749768i	$0.269835\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−1.39745	+	0.463917i	−0.140449	+	0.0466254i
$100$	4.37490			0.437490
$101$	3.42487			0.340787			0.170393	−	0.985376i	$-0.445496\pi$
$101$	3.42487			0.340787			0.170393	+	0.985376i	$0.445496\pi$
$102$	4.09399	+	6.63329i	0.405366	+	0.656794i
$103$		−	0.0883069i		−	0.00870114i	−0.999991	−	0.00435057i	$-0.998615\pi$
$103$		−	0.0883069i		−	0.00870114i	0.999991	−	0.00435057i	$-0.00138483\pi$
$104$	1.70989	−	3.17432i	0.167668	−	0.311267i
$105$	0.315443	−	1.33259i	0.0307841	−	0.130048i
$106$	−8.52821	+	8.52821i	−0.828333	+	0.828333i
$107$			5.08715i			0.491794i	0.969296	+	0.245897i	$0.0790824\pi$
$107$			5.08715i			0.491794i	−0.969296	+	0.245897i	$0.920918\pi$
$108$	3.33674	−	3.98324i	0.321078	−	0.383287i
$109$	5.92580	−	5.92580i	0.567589	−	0.567589i	−0.363863	−	0.931452i	$-0.618542\pi$
$109$	5.92580	−	5.92580i	0.567589	−	0.567589i	0.931452	+	0.363863i	$0.118542\pi$
$110$	0.274395	+	0.274395i	0.0261626	+	0.0261626i
$111$	−8.90400	−	14.4267i	−0.845130	−	1.36932i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$			2.88604i			0.271496i	0.990743	+	0.135748i	$0.0433438\pi$
$113$			2.88604i			0.271496i	−0.990743	+	0.135748i	$0.956656\pi$
$114$	9.21290	+	2.18082i	0.862867	+	0.204252i
$115$	2.95168	+	2.95168i	0.275246	+	0.275246i
$116$	10.6966			0.993152
$117$	−10.6541	−	1.86803i	−0.984975	−	0.172700i
$118$	4.82596			0.444266
$119$	3.18228	+	3.18228i	0.291719	+	0.291719i
$120$	−1.33259	−	0.315443i	−0.121648	−	0.0287959i
$121$			10.7591i			0.978100i
$122$	4.54291	+	4.54291i	0.411296	+	0.411296i
$123$	9.41044	+	15.2473i	0.848511	+	1.37480i
$124$	−2.47731	−	2.47731i	−0.222469	−	0.222469i
$125$	−5.24115	+	5.24115i	−0.468783	+	0.468783i
$126$	1.34492	−	2.68164i	0.119815	−	0.238899i
$127$		−	21.1044i		−	1.87271i	−0.351053	−	0.936356i	$-0.614176\pi$
$127$		−	21.1044i		−	1.87271i	0.351053	−	0.936356i	$-0.385824\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	2.89063	−	12.2115i	0.254506	−	1.07516i
$130$	0.818708	+	2.73057i	0.0718055	+	0.239487i
$131$		−	7.76803i		−	0.678696i	−0.940661	−	0.339348i	$-0.889794\pi$
$131$		−	7.76803i		−	0.678696i	0.940661	−	0.339348i	$-0.110206\pi$
$132$	0.446489	+	0.723423i	0.0388619	+	0.0629659i
$133$	5.46606			0.473967
$134$	−3.44271			−0.297405
$135$	0.361436	+	4.09232i	0.0311074	+	0.352211i
$136$	3.18228	−	3.18228i	0.272878	−	0.272878i
$137$	−2.35653	+	2.35653i	−0.201332	+	0.201332i	−0.800570	−	0.599239i	$-0.795470\pi$
$137$	−2.35653	+	2.35653i	−0.201332	+	0.201332i	0.599239	+	0.800570i	$0.295470\pi$
$138$	4.80290	+	7.78190i	0.408850	+	0.662439i
$139$	1.53895			0.130532			0.0652659	−	0.997868i	$-0.479210\pi$
$139$	1.53895			0.130532			0.0652659	+	0.997868i	$0.479210\pi$
$140$	−0.790633			−0.0668207
$141$	5.19692	−	3.20748i	0.437660	−	0.270119i
$142$		−	12.0153i		−	1.00830i
$143$	0.839235	−	1.55800i	0.0701803	−	0.130286i
$144$	−2.68164	−	1.34492i	−0.223470	−	0.112077i
$145$	−5.98005	+	5.98005i	−0.496616	+	0.496616i
$146$			8.38963i			0.694330i
$147$	0.398975	−	1.68547i	0.0329069	−	0.139015i
$148$	−6.92111	+	6.92111i	−0.568912	+	0.568912i
$149$	6.80987	+	6.80987i	0.557887	+	0.557887i	0.928705	−	0.370819i	$-0.120923\pi$
$149$	6.80987	+	6.80987i	0.557887	+	0.557887i	−0.370819	+	0.928705i	$0.620923\pi$
$150$	−6.44828	+	3.97981i	−0.526500	+	0.324950i
$151$	1.21937	+	1.21937i	0.0992308	+	0.0992308i	0.754979	−	0.655749i	$-0.227647\pi$
$151$	1.21937	+	1.21937i	0.0992308	+	0.0992308i	−0.655749	+	0.754979i	$0.727647\pi$
$152$		−	5.46606i		−	0.443356i
$153$	−12.0685	−	6.05271i	−0.975680	−	0.489333i
$154$	0.347057	+	0.347057i	0.0279667	+	0.0279667i
$155$	2.76994			0.222487
$156$	0.367403	+	6.23418i	0.0294158	+	0.499134i
$157$	−5.63769			−0.449936			−0.224968	−	0.974366i	$-0.572228\pi$
$157$	−5.63769			−0.449936			−0.224968	+	0.974366i	$0.572228\pi$
$158$	−9.35045	−	9.35045i	−0.743882	−	0.743882i
$159$	4.81192	−	20.3280i	0.381610	−	1.61211i
$160$			0.790633i			0.0625051i
$161$	3.73331	+	3.73331i	0.294226	+	0.294226i
$162$	−1.29459	+	8.90640i	−0.101712	+	0.699753i
$163$	3.47849	+	3.47849i	0.272456	+	0.272456i	0.830088	−	0.557632i	$-0.188290\pi$
$163$	3.47849	+	3.47849i	0.272456	+	0.272456i	−0.557632	+	0.830088i	$0.688290\pi$
$164$	7.31477	−	7.31477i	0.571187	−	0.571187i
$165$	−0.654054	−	0.154824i	−0.0509180	−	0.0120530i
$166$			8.92798i			0.692946i
$167$	2.49027	−	2.49027i	0.192703	−	0.192703i	−0.604160	−	0.796863i	$-0.706491\pi$
$167$	2.49027	−	2.49027i	0.192703	−	0.192703i	0.796863	+	0.604160i	$0.206491\pi$
$168$	−1.68547	−	0.398975i	−0.130037	−	0.0307816i
$169$	10.8554	−	7.15258i	0.835034	−	0.550199i
$170$			3.55818i			0.272900i
$171$	−15.5630	+	5.16653i	−1.19013	+	0.395094i
$172$	−7.24514			−0.552437
$173$	−13.1775			−1.00187			−0.500934	−	0.865486i	$-0.667010\pi$
$173$	−13.1775			−1.00187			−0.500934	+	0.865486i	$0.667010\pi$
$174$	−15.7660	+	9.73058i	−1.19521	+	0.737673i
$175$	−3.09352	+	3.09352i	−0.233848	+	0.233848i
$176$	0.347057	−	0.347057i	0.0261604	−	0.0261604i
$177$	−7.11311	+	4.39013i	−0.534654	+	0.329983i
$178$	17.3339			1.29923
$179$	−13.9967			−1.04616			−0.523081	−	0.852283i	$-0.675217\pi$
$179$	−13.9967			−1.04616			−0.523081	+	0.852283i	$0.675217\pi$
$180$	2.25110	−	0.747308i	0.167787	−	0.0557010i
$181$		−	3.47621i		−	0.258385i	−0.991620	−	0.129192i	$-0.958762\pi$
$181$		−	3.47621i		−	0.258385i	0.991620	−	0.129192i	$-0.0412384\pi$
$182$	1.03551	+	3.45365i	0.0767571	+	0.256002i
$183$	−10.8286	−	2.56327i	−0.800471	−	0.189482i
$184$	3.73331	−	3.73331i	0.275224	−	0.275224i
$185$		−	7.73867i		−	0.568958i
$186$	5.90496	+	1.39779i	0.432973	+	0.102491i
$187$	1.56190	−	1.56190i	0.114218	−	0.114218i
$188$	−2.49319	−	2.49319i	−0.181834	−	0.181834i
$189$	0.457147	+	5.17600i	0.0332525	+	0.376499i
$190$	3.05587	+	3.05587i	0.221696	+	0.221696i
$191$			26.9246i			1.94820i	0.226120	+	0.974099i	$0.427396\pi$
$191$			26.9246i			1.94820i	−0.226120	+	0.974099i	$0.572604\pi$
$192$	−0.398975	+	1.68547i	−0.0287935	+	0.121639i
$193$	−15.1725	−	15.1725i	−1.09214	−	1.09214i	−0.995300	−	0.0968371i	$-0.969127\pi$
$193$	−15.1725	−	15.1725i	−1.09214	−	1.09214i	−0.0968371	−	0.995300i	$-0.530873\pi$
$194$	−1.22663			−0.0880669
$195$	−3.69070	−	3.27989i	−0.264296	−	0.234878i
$196$	−1.00000			−0.0714286
$197$	−15.8927	−	15.8927i	−1.13231	−	1.13231i	−0.989792	−	0.142517i	$-0.954480\pi$
$197$	−15.8927	−	15.8927i	−1.13231	−	1.13231i	−0.142517	−	0.989792i	$-0.545520\pi$
$198$	−1.31618	−	0.660106i	−0.0935371	−	0.0469117i
$199$			4.30765i			0.305361i	0.988276	+	0.152681i	$0.0487905\pi$
$199$			4.30765i			0.305361i	−0.988276	+	0.152681i	$0.951209\pi$
$200$	3.09352	+	3.09352i	0.218745	+	0.218745i
$201$	5.07431	−	3.13181i	0.357914	−	0.220901i
$202$	2.42175	+	2.42175i	0.170393	+	0.170393i
$203$	−7.56362	+	7.56362i	−0.530862	+	0.530862i
$204$	−1.79555	+	7.58533i	−0.125714	+	0.531080i
$205$			8.17882i			0.571234i
$206$	0.0624424	−	0.0624424i	0.00435057	−	0.00435057i
$207$	−14.1583	−	7.10079i	−0.984067	−	0.493539i
$208$	3.45365	−	1.03551i	0.239468	−	0.0717997i
$209$		−	2.68282i		−	0.185574i
$210$	1.16534	−	0.719233i	0.0804158	−	0.0496318i
$211$	9.69453			0.667399			0.333700	−	0.942679i	$-0.391703\pi$
$211$	9.69453			0.667399			0.333700	+	0.942679i	$0.391703\pi$
$212$	−12.0607			−0.828333
$213$	10.9302	+	17.7097i	0.748927	+	1.21345i
$214$	−3.59716	+	3.59716i	−0.245897	+	0.245897i
$215$	4.05049	−	4.05049i	0.276241	−	0.276241i
$216$	5.17600	−	0.457147i	0.352182	−	0.0311049i
$217$	3.50344			0.237829
$218$	8.38035			0.567589
$219$	−7.63197	−	12.3657i	−0.515721	−	0.835596i
$220$			0.388054i			0.0261626i
$221$	15.5429	−	4.66023i	1.04553	−	0.313481i
$222$	3.90514	−	16.4973i	0.262096	−	1.10723i
$223$	−7.49728	+	7.49728i	−0.502055	+	0.502055i	−0.912076	−	0.410021i	$-0.865521\pi$
$223$	−7.49728	+	7.49728i	−0.502055	+	0.502055i	0.410021	+	0.912076i	$0.365521\pi$
$224$			1.00000i			0.0668153i
$225$	5.88390	−	11.7319i	0.392260	−	0.782126i
$226$	−2.04074	+	2.04074i	−0.135748	+	0.135748i
$227$	17.5224	+	17.5224i	1.16300	+	1.16300i	0.983815	+	0.179185i	$0.0573459\pi$
$227$	17.5224	+	17.5224i	1.16300	+	1.16300i	0.179185	+	0.983815i	$0.442654\pi$
$228$	4.97243	+	8.05657i	0.329307	+	0.533560i
$229$	−13.8742	−	13.8742i	−0.916834	−	0.916834i	0.0799635	−	0.996798i	$-0.474520\pi$
$229$	−13.8742	−	13.8742i	−0.916834	−	0.916834i	−0.996798	+	0.0799635i	$0.974520\pi$
$230$			4.17431i			0.275246i
$231$	−0.827253	−	0.195822i	−0.0544292	−	0.0128842i
$232$	7.56362	+	7.56362i	0.496576	+	0.496576i
$233$	4.80094			0.314520			0.157260	−	0.987557i	$-0.449734\pi$
$233$	4.80094			0.314520			0.157260	+	0.987557i	$0.449734\pi$
$234$	−6.21271	−	8.85451i	−0.406137	−	0.578837i
$235$	2.78770			0.181849
$236$	3.41247	+	3.41247i	0.222133	+	0.222133i
$237$	22.2879	+	5.27585i	1.44775	+	0.342703i
$238$			4.50042i			0.291719i
$239$	−8.85356	−	8.85356i	−0.572689	−	0.572689i	0.360190	−	0.932879i	$-0.382712\pi$
$239$	−8.85356	−	8.85356i	−0.572689	−	0.572689i	−0.932879	+	0.360190i	$0.882712\pi$
$240$	−0.719233	−	1.16534i	−0.0464263	−	0.0752221i
$241$	8.79467	+	8.79467i	0.566515	+	0.566515i	0.931150	−	0.364636i	$-0.118806\pi$
$241$	8.79467	+	8.79467i	0.566515	+	0.566515i	−0.364636	+	0.931150i	$0.618806\pi$
$242$	−7.60783	+	7.60783i	−0.489050	+	0.489050i
$243$	−6.19396	−	14.3051i	−0.397343	−	0.917670i
$244$			6.42464i			0.411296i
$245$	0.559062	−	0.559062i	0.0357172	−	0.0357172i
$246$	−4.12725	+	17.4356i	−0.263144	+	1.11165i
$247$	9.34634	−	17.3510i	0.594693	−	1.10402i
$248$		−	3.50344i		−	0.222469i
$249$	−8.12171	−	13.1592i	−0.514693	−	0.833930i
$250$	−7.41211			−0.468783
$251$	−13.6883			−0.863998			−0.431999	−	0.901874i	$-0.642192\pi$
$251$	−13.6883			−0.863998			−0.431999	+	0.901874i	$0.642192\pi$
$252$	2.84721	−	0.945201i	0.179357	−	0.0595421i
$253$	1.83236	−	1.83236i	0.115200	−	0.115200i
$254$	14.9231	−	14.9231i	0.936356	−	0.936356i
$255$	−3.23685	−	5.24450i	−0.202699	−	0.328423i
$256$	1.00000			0.0625000
$257$	−18.2988			−1.14145			−0.570723	−	0.821142i	$-0.693337\pi$
$257$	−18.2988			−1.14145			−0.570723	+	0.821142i	$0.693337\pi$
$258$	10.6788	−	6.59085i	0.664834	−	0.410328i
$259$		−	9.78793i		−	0.608192i
$260$	−1.35189	+	2.50972i	−0.0838408	+	0.155646i
$261$	14.3861	−	28.6843i	0.890474	−	1.77552i
$262$	5.49282	−	5.49282i	0.339348	−	0.339348i
$263$		−	16.5203i		−	1.01868i	−0.860564	−	0.509342i	$-0.829889\pi$
$263$		−	16.5203i		−	1.01868i	0.860564	−	0.509342i	$-0.170111\pi$
$264$	−0.195822	+	0.827253i	−0.0120520	+	0.0509139i
$265$	6.74269	−	6.74269i	0.414200	−	0.414200i
$266$	3.86509	+	3.86509i	0.236984	+	0.236984i
$267$	−25.5490	+	15.7685i	−1.56357	+	0.965019i
$268$	−2.43437	−	2.43437i	−0.148703	−	0.148703i
$269$			11.7448i			0.716091i	0.933704	+	0.358046i	$0.116557\pi$
$269$			11.7448i			0.716091i	−0.933704	+	0.358046i	$0.883443\pi$
$270$	−2.63814	+	3.14928i	−0.160552	+	0.191659i
$271$	9.75803	+	9.75803i	0.592758	+	0.592758i	0.938375	−	0.345618i	$-0.112331\pi$
$271$	9.75803	+	9.75803i	0.592758	+	0.592758i	−0.345618	+	0.938375i	$0.612331\pi$
$272$	4.50042			0.272878
$273$	−4.66802	−	4.14844i	−0.282522	−	0.251075i
$274$	−3.33263			−0.201332
$275$	1.51834	+	1.51834i	0.0915594	+	0.0915594i
$276$	−2.10647	+	8.89880i	−0.126794	+	0.535645i
$277$		−	1.88463i		−	0.113236i	−0.998396	−	0.0566181i	$-0.981968\pi$
$277$		−	1.88463i		−	0.113236i	0.998396	−	0.0566181i	$-0.0180318\pi$
$278$	1.08820	+	1.08820i	0.0652659	+	0.0652659i
$279$	−9.97503	+	3.31146i	−0.597190	+	0.198252i
$280$	−0.559062	−	0.559062i	−0.0334104	−	0.0334104i
$281$	−2.85196	+	2.85196i	−0.170134	+	0.170134i	−0.787038	−	0.616904i	$-0.788387\pi$
$281$	−2.85196	+	2.85196i	−0.170134	+	0.170134i	0.616904	+	0.787038i	$0.288387\pi$
$282$	5.94281	+	1.40675i	0.353889	+	0.0837705i
$283$		−	15.2599i		−	0.907107i	−0.891229	−	0.453553i	$-0.850156\pi$
$283$		−	15.2599i		−	0.907107i	0.891229	−	0.453553i	$-0.149844\pi$
$284$	8.49611	−	8.49611i	0.504152	−	0.504152i
$285$	−7.28402	−	1.72423i	−0.431468	−	0.102134i
$286$	1.69510	−	0.508242i	0.100233	−	0.0300530i
$287$			10.3446i			0.610625i
$288$	−0.945201	−	2.84721i	−0.0556965	−	0.167773i
$289$	3.25377			0.191398
$290$	−8.45707			−0.496616
$291$	1.80796	−	1.11585i	0.105985	−	0.0654126i
$292$	−5.93236	+	5.93236i	−0.347165	+	0.347165i
$293$	13.4365	−	13.4365i	0.784968	−	0.784968i	−0.195696	−	0.980665i	$-0.562697\pi$
$293$	13.4365	−	13.4365i	0.784968	−	0.784968i	0.980665	+	0.195696i	$0.0626967\pi$
$294$	1.47393	−	0.909692i	0.0859612	−	0.0530543i
$295$	−3.81556			−0.222151
$296$	−9.78793			−0.568912
$297$	2.54045	−	0.224374i	0.147412	−	0.0130195i
$298$			9.63062i			0.557887i
$299$	18.2343	−	5.46718i	1.05451	−	0.316175i
$300$	−7.37377	−	1.74547i	−0.425725	−	0.100775i
$301$	5.12309	−	5.12309i	0.295290	−	0.295290i
$302$			1.72445i			0.0992308i
$303$	−5.77252	−	1.36644i	−0.331623	−	0.0784997i
$304$	3.86509	−	3.86509i	0.221678	−	0.221678i
$305$	−3.59178	−	3.59178i	−0.205665	−	0.205665i
$306$	−4.25380	−	12.8136i	−0.243174	−	0.732506i
$307$	14.1492	+	14.1492i	0.807539	+	0.807539i	0.984261	−	0.176722i	$-0.0565493\pi$
$307$	14.1492	+	14.1492i	0.807539	+	0.807539i	−0.176722	+	0.984261i	$0.556549\pi$
$308$			0.490813i			0.0279667i
$309$	−0.0352322	+	0.148839i	−0.00200429	+	0.00846715i
$310$	1.95864	+	1.95864i	0.111243	+	0.111243i
$311$	−33.2959			−1.88804			−0.944019	−	0.329890i	$-0.892988\pi$
$311$	−33.2959			−1.88804			−0.944019	+	0.329890i	$0.892988\pi$
$312$	−4.14844	+	4.66802i	−0.234859	+	0.264275i
$313$	−23.5153			−1.32917			−0.664583	−	0.747214i	$-0.731391\pi$
$313$	−23.5153			−1.32917			−0.664583	+	0.747214i	$0.731391\pi$
$314$	−3.98645	−	3.98645i	−0.224968	−	0.224968i
$315$	−1.06334	+	2.12019i	−0.0599124	+	0.119459i
$316$		−	13.2235i		−	0.743882i
$317$	2.21672	+	2.21672i	0.124503	+	0.124503i	0.766613	−	0.642110i	$-0.221941\pi$
$317$	2.21672	+	2.21672i	0.124503	+	0.124503i	−0.642110	+	0.766613i	$0.721941\pi$
$318$	17.7766	−	10.9715i	0.996862	−	0.615253i
$319$	3.71232	+	3.71232i	0.207850	+	0.207850i
$320$	−0.559062	+	0.559062i	−0.0312525	+	0.0312525i
$321$	2.02965	−	8.57426i	0.113284	−	0.478568i
$322$			5.27970i			0.294226i
$323$	17.3945	−	17.3945i	0.967857	−	0.967857i
$324$	−7.21319	+	5.38237i	−0.400733	+	0.299020i
$325$	4.53025	+	15.1094i	0.251293	+	0.838118i
$326$			4.91933i			0.272456i
$327$	−12.3520	+	7.62354i	−0.683069	+	0.421583i
$328$	10.3446			0.571187
$329$	3.52590			0.194389
$330$	−0.353009	−	0.571963i	−0.0194325	−	0.0314855i
$331$	−21.9301	+	21.9301i	−1.20539	+	1.20539i	−0.232882	+	0.972505i	$0.574816\pi$
$331$	−21.9301	+	21.9301i	−1.20539	+	1.20539i	−0.972505	+	0.232882i	$0.925184\pi$
$332$	−6.31304	+	6.31304i	−0.346473	+	0.346473i
$333$	9.25156	+	27.8683i	0.506983	+	1.52717i
$334$	3.52177			0.192703
$335$	2.72192			0.148715
$336$	−0.909692	−	1.47393i	−0.0496277	−	0.0804093i
$337$			12.0386i			0.655785i	0.944715	+	0.327892i	$0.106338\pi$
$337$			12.0386i			0.655785i	−0.944715	+	0.327892i	$0.893662\pi$
$338$	12.7336	+	2.61832i	0.692616	+	0.142418i
$339$	1.15146	−	4.86435i	0.0625387	−	0.264195i
$340$	−2.51601	+	2.51601i	−0.136450	+	0.136450i
$341$		−	1.71954i		−	0.0931181i
$342$	−14.6580	−	7.35142i	−0.792614	−	0.397519i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−5.12309	−	5.12309i	−0.276219	−	0.276219i
$345$	−3.79734	−	6.15263i	−0.204442	−	0.331246i
$346$	−9.31790	−	9.31790i	−0.500934	−	0.500934i
$347$		−	4.91439i		−	0.263819i	−0.991262	−	0.131909i	$-0.957889\pi$
$347$		−	4.91439i		−	0.263819i	0.991262	−	0.131909i	$-0.0421108\pi$
$348$	−18.0288	−	4.26766i	−0.966444	−	0.228771i
$349$	−3.33670	−	3.33670i	−0.178609	−	0.178609i	0.612140	−	0.790749i	$-0.290309\pi$
$349$	−3.33670	−	3.33670i	−0.178609	−	0.178609i	−0.790749	+	0.612140i	$0.790309\pi$
$350$	−4.37490			−0.233848
$351$	17.2119	+	7.39925i	0.918706	+	0.394943i
$352$	0.490813			0.0261604
$353$	4.61015	+	4.61015i	0.245374	+	0.245374i	0.819069	−	0.573695i	$-0.194491\pi$
$353$	4.61015	+	4.61015i	0.245374	+	0.245374i	−0.573695	+	0.819069i	$0.694491\pi$
$354$	−8.13402	−	1.92544i	−0.432318	−	0.102336i
$355$			9.49971i			0.504192i
$356$	12.2569	+	12.2569i	0.649617	+	0.649617i
$357$	−4.09399	−	6.63329i	−0.216677	−	0.351071i
$358$	−9.89715	−	9.89715i	−0.523081	−	0.523081i
$359$	8.91675	−	8.91675i	0.470608	−	0.470608i	−0.431503	−	0.902111i	$-0.642017\pi$
$359$	8.91675	−	8.91675i	0.470608	−	0.470608i	0.902111	+	0.431503i	$0.142017\pi$
$360$	2.12019	+	1.06334i	0.111744	+	0.0560430i
$361$		−	10.8778i		−	0.572516i
$362$	2.45805	−	2.45805i	0.129192	−	0.129192i
$363$	4.29261	−	18.1342i	0.225304	−	0.951797i
$364$	−1.70989	+	3.17432i	−0.0896224	+	0.166379i
$365$		−	6.63312i		−	0.347193i
$366$	−5.84445	−	9.46946i	−0.305494	−	0.494976i
$367$	−25.6357			−1.33817			−0.669087	−	0.743184i	$-0.733315\pi$
$367$	−25.6357			−1.33817			−0.669087	+	0.743184i	$0.733315\pi$
$368$	5.27970			0.275224
$369$	−9.77777	−	29.4534i	−0.509010	−	1.53328i
$370$	5.47206	−	5.47206i	0.284479	−	0.284479i
$371$	8.52821	−	8.52821i	0.442762	−	0.442762i
$372$	3.18705	+	5.16382i	0.165241	+	0.267732i
$373$	−27.6030			−1.42923			−0.714614	−	0.699519i	$-0.753398\pi$
$373$	−27.6030			−1.42923			−0.714614	+	0.699519i	$0.753398\pi$
$374$	2.20887			0.114218
$375$	10.9249	−	6.74273i	0.564160	−	0.348193i
$376$		−	3.52590i		−	0.181834i
$377$	11.0764	+	36.9422i	0.570464	+	1.90262i
$378$	−3.33674	+	3.98324i	−0.171623	+	0.204876i
$379$	−15.2188	+	15.2188i	−0.781739	+	0.781739i	−0.980124	−	0.198385i	$-0.936430\pi$
$379$	−15.2188	+	15.2188i	−0.781739	+	0.781739i	0.198385	+	0.980124i	$0.436430\pi$
$380$			4.32165i			0.221696i
$381$	−8.42012	+	35.5709i	−0.431376	+	1.82235i
$382$	−19.0386	+	19.0386i	−0.974099	+	0.974099i
$383$	7.48783	+	7.48783i	0.382610	+	0.382610i	0.872042	−	0.489431i	$-0.162796\pi$
$383$	7.48783	+	7.48783i	0.382610	+	0.382610i	−0.489431	+	0.872042i	$0.662796\pi$
$384$	−1.47393	+	0.909692i	−0.0752160	+	0.0464225i
$385$	−0.274395	−	0.274395i	−0.0139845	−	0.0139845i
$386$		−	21.4571i		−	1.09214i
$387$	−9.74415	+	19.4289i	−0.495323	+	0.987624i
$388$	−0.867358	−	0.867358i	−0.0440334	−	0.0440334i
$389$	−7.00656			−0.355247			−0.177623	−	0.984099i	$-0.556841\pi$
$389$	−7.00656			−0.355247			−0.177623	+	0.984099i	$0.556841\pi$
$390$	−0.290481	−	4.92895i	−0.0147091	−	0.249587i
$391$	23.7609			1.20164
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	−3.09925	+	13.0928i	−0.156336	+	0.660444i
$394$		−	22.4757i		−	1.13231i
$395$	7.39278	+	7.39278i	0.371971	+	0.371971i
$396$	−0.463917	−	1.39745i	−0.0233127	−	0.0702244i
$397$	−5.42804	−	5.42804i	−0.272425	−	0.272425i	0.557650	−	0.830076i	$-0.311703\pi$
$397$	−5.42804	−	5.42804i	−0.272425	−	0.272425i	−0.830076	+	0.557650i	$0.811703\pi$
$398$	−3.04597	+	3.04597i	−0.152681	+	0.152681i
$399$	−9.21290	−	2.18082i	−0.461222	−	0.109178i
$400$			4.37490i			0.218745i
$401$	−22.7703	+	22.7703i	−1.13709	+	1.13709i	−0.148126	+	0.988969i	$0.547324\pi$
$401$	−22.7703	+	22.7703i	−1.13709	+	1.13709i	−0.988969	+	0.148126i	$0.952676\pi$
$402$	5.80260	+	1.37356i	0.289407	+	0.0685067i
$403$	5.99049	−	11.1210i	0.298407	−	0.553978i
$404$			3.42487i			0.170393i
$405$	1.02354	−	7.04170i	0.0508603	−	0.349905i
$406$	−10.6966			−0.530862
$407$	−4.80405			−0.238128
$408$	−6.63329	+	4.09399i	−0.328397	+	0.202683i
$409$	5.64482	−	5.64482i	0.279118	−	0.279118i	−0.553639	−	0.832757i	$-0.686761\pi$
$409$	5.64482	−	5.64482i	0.279118	−	0.279118i	0.832757	+	0.553639i	$0.186761\pi$
$410$	−5.78330	+	5.78330i	−0.285617	+	0.285617i
$411$	4.91206	−	3.03167i	0.242294	−	0.149541i
$412$	0.0883069			0.00435057
$413$	−4.82596			−0.237470
$414$	−4.99038	−	15.0324i	−0.245264	−	0.738803i
$415$		−	7.05876i		−	0.346501i
$416$	3.17432	+	1.70989i	0.155634	+	0.0838341i
$417$	−2.59385	−	0.614001i	−0.127022	−	0.0300678i
$418$	1.89704	−	1.89704i	0.0927871	−	0.0927871i
$419$			9.00273i			0.439812i	0.975521	+	0.219906i	$0.0705751\pi$
$419$			9.00273i			0.439812i	−0.975521	+	0.219906i	$0.929425\pi$
$420$	1.33259	+	0.315443i	0.0650238	+	0.0153920i
$421$	−1.90886	+	1.90886i	−0.0930321	+	0.0930321i	−0.752091	−	0.659059i	$-0.770955\pi$
$421$	−1.90886	+	1.90886i	−0.0930321	+	0.0930321i	0.659059	+	0.752091i	$0.270955\pi$
$422$	6.85507	+	6.85507i	0.333700	+	0.333700i
$423$	−10.0390	+	3.33269i	−0.488112	+	0.162041i
$424$	−8.52821	−	8.52821i	−0.414166	−	0.414166i
$425$			19.6889i			0.955051i
$426$	−4.79381	+	20.2515i	−0.232261	+	0.981188i
$427$	−4.54291	−	4.54291i	−0.219847	−	0.219847i
$428$	−5.08715			−0.245897
$429$	−2.03611	+	2.29113i	−0.0983043	+	0.110617i
$430$	5.72825			0.276241
$431$	11.7362	+	11.7362i	0.565312	+	0.565312i	0.930811	−	0.365500i	$-0.119102\pi$
$431$	11.7362	+	11.7362i	0.565312	+	0.565312i	−0.365500	+	0.930811i	$0.619102\pi$
$432$	3.98324	+	3.33674i	0.191644	+	0.160539i
$433$			13.9122i			0.668577i	0.942471	+	0.334289i	$0.108496\pi$
$433$			13.9122i			0.668577i	−0.942471	+	0.334289i	$0.891504\pi$
$434$	2.47731	+	2.47731i	0.118915	+	0.118915i
$435$	12.4651	−	7.69332i	0.597656	−	0.368867i
$436$	5.92580	+	5.92580i	0.283795	+	0.283795i
$437$	20.4065	−	20.4065i	0.976176	−	0.976176i
$438$	3.34725	−	14.1405i	0.159938	−	0.675659i
$439$		−	8.24651i		−	0.393584i	−0.980445	−	0.196792i	$-0.936948\pi$
$439$		−	8.24651i		−	0.393584i	0.980445	−	0.196792i	$-0.0630524\pi$
$440$	−0.274395	+	0.274395i	−0.0130813	+	0.0130813i
$441$	−1.34492	+	2.68164i	−0.0640439	+	0.127697i
$442$	14.2858	+	7.69520i	0.679504	+	0.366023i
$443$		−	9.44990i		−	0.448978i	−0.974477	−	0.224489i	$-0.927929\pi$
$443$		−	9.44990i		−	0.448978i	0.974477	−	0.224489i	$-0.0720713\pi$
$444$	14.4267	−	8.90400i	0.684661	−	0.422565i
$445$	−13.7048			−0.649669
$446$	−10.6028			−0.502055
$447$	−8.76089	−	14.1948i	−0.414376	−	0.671392i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	22.9219	−	22.9219i	1.08175	−	1.08175i	0.0854053	−	0.996346i	$-0.472781\pi$
$449$	22.9219	−	22.9219i	1.08175	−	1.08175i	0.996346	−	0.0854053i	$-0.0272185\pi$
$450$	12.4562	−	4.13516i	0.587193	−	0.194933i
$451$	5.07729			0.239080
$452$	−2.88604			−0.135748
$453$	−1.56872	−	2.54171i	−0.0737047	−	0.119420i
$454$			24.7804i			1.16300i
$455$	−0.818708	−	2.73057i	−0.0383816	−	0.128011i
$456$	−2.18082	+	9.21290i	−0.102126	+	0.431433i
$457$	−2.72508	+	2.72508i	−0.127474	+	0.127474i	−0.767965	−	0.640492i	$-0.778731\pi$
$457$	−2.72508	+	2.72508i	−0.127474	+	0.127474i	0.640492	+	0.767965i	$0.278731\pi$
$458$		−	19.6211i		−	0.916834i
$459$	17.9262	+	15.0167i	0.836725	+	0.700920i
$460$	−2.95168	+	2.95168i	−0.137623	+	0.137623i
$461$	17.0514	+	17.0514i	0.794161	+	0.794161i	0.982168	−	0.188007i	$-0.0602026\pi$
$461$	17.0514	+	17.0514i	0.794161	+	0.794161i	−0.188007	+	0.982168i	$0.560203\pi$
$462$	−0.446489	−	0.723423i	−0.0207725	−	0.0336567i
$463$	−7.20273	−	7.20273i	−0.334739	−	0.334739i	0.519644	−	0.854383i	$-0.326065\pi$
$463$	−7.20273	−	7.20273i	−0.334739	−	0.334739i	−0.854383	+	0.519644i	$0.826065\pi$
$464$			10.6966i			0.496576i
$465$	−4.66866	−	1.10514i	−0.216504	−	0.0512494i
$466$	3.39478	+	3.39478i	0.157260	+	0.157260i
$467$	−19.1716			−0.887156			−0.443578	−	0.896236i	$-0.646291\pi$
$467$	−19.1716			−0.887156			−0.443578	+	0.896236i	$0.646291\pi$
$468$	1.86803	−	10.6541i	0.0863499	−	0.492487i
$469$	3.44271			0.158970
$470$	1.97120	+	1.97120i	0.0909246	+	0.0909246i
$471$	9.50217	+	2.24929i	0.437837	+	0.103642i
$472$			4.82596i			0.222133i
$473$	−2.51448	−	2.51448i	−0.115616	−	0.115616i
$474$	12.0293	+	19.4905i	0.552526	+	0.895229i
$475$	16.9094	+	16.9094i	0.775855	+	0.775855i
$476$	−3.18228	+	3.18228i	−0.145859	+	0.145859i
$477$	−16.2207	+	32.3425i	−0.742695	+	1.48086i
$478$		−	12.5208i		−	0.572689i
$479$	21.3865	−	21.3865i	0.977174	−	0.977174i	−0.0225708	−	0.999745i	$-0.507185\pi$
$479$	21.3865	−	21.3865i	0.977174	−	0.977174i	0.999745	+	0.0225708i	$0.00718511\pi$
$480$	0.315443	−	1.33259i	0.0143979	−	0.0608242i
$481$	−31.0700	−	16.7362i	−1.41667	−	0.763107i
$482$			12.4375i			0.566515i
$483$	−4.80290	−	7.78190i	−0.218540	−	0.354089i
$484$	−10.7591			−0.489050
$485$	0.969814			0.0440370
$486$	5.73542	−	14.4950i	0.260164	−	0.657506i
$487$	24.0755	−	24.0755i	1.09096	−	1.09096i	0.0955392	−	0.995426i	$-0.469542\pi$
$487$	24.0755	−	24.0755i	1.09096	−	1.09096i	0.995426	−	0.0955392i	$-0.0304575\pi$
$488$	−4.54291	+	4.54291i	−0.205648	+	0.205648i
$489$	−4.47507	−	7.25073i	−0.202370	−	0.327889i
$490$	0.790633			0.0357172
$491$	−10.3827			−0.468565			−0.234283	−	0.972169i	$-0.575274\pi$
$491$	−10.3827			−0.468565			−0.234283	+	0.972169i	$0.575274\pi$
$492$	−15.2473	+	9.41044i	−0.687399	+	0.424255i
$493$			48.1390i			2.16807i
$494$	18.8779	−	5.66016i	0.849356	−	0.254662i
$495$	1.04062	+	0.521902i	0.0467724	+	0.0234577i
$496$	2.47731	−	2.47731i	0.111234	−	0.111234i
$497$			12.0153i			0.538961i
$498$	3.56204	−	15.0479i	0.159619	−	0.674311i
$499$	3.48978	−	3.48978i	0.156224	−	0.156224i	−0.624667	−	0.780891i	$-0.714765\pi$
$499$	3.48978	−	3.48978i	0.156224	−	0.156224i	0.780891	+	0.624667i	$0.214765\pi$
$500$	−5.24115	−	5.24115i	−0.234391	−	0.234391i
$501$	−5.19084	+	3.20373i	−0.231910	+	0.143132i
$502$	−9.67910	−	9.67910i	−0.431999	−	0.431999i
$503$			0.584892i			0.0260790i	0.999915	+	0.0130395i	$0.00415073\pi$
$503$			0.584892i			0.0260790i	−0.999915	+	0.0130395i	$0.995849\pi$
$504$	2.68164	+	1.34492i	0.119450	+	0.0599076i
$505$	−1.91471	−	1.91471i	−0.0852037	−	0.0852037i
$506$	2.59135			0.115200
$507$	−21.1503	+	7.72444i	−0.939316	+	0.343054i
$508$	21.1044			0.936356
$509$	14.6995	+	14.6995i	0.651544	+	0.651544i	0.953365	−	0.301821i	$-0.0975944\pi$
$509$	14.6995	+	14.6995i	0.651544	+	0.651544i	−0.301821	+	0.953365i	$0.597594\pi$
$510$	1.41962	−	5.99722i	0.0628620	−	0.265561i
$511$		−	8.38963i		−	0.371135i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	28.2923	−	2.49879i	1.24914	−	0.110324i
$514$	−12.9392	−	12.9392i	−0.570723	−	0.570723i
$515$	−0.0493691	+	0.0493691i	−0.00217546	+	0.00217546i
$516$	12.2115	+	2.89063i	0.537581	+	0.127253i
$517$		−	1.73056i		−	0.0761099i
$518$	6.92111	−	6.92111i	0.304096	−	0.304096i
$519$	22.2103	+	5.25749i	0.974925	+	0.230778i
$520$	−2.73057	+	0.818708i	−0.119744	+	0.0359027i
$521$			2.40567i			0.105394i	0.998611	+	0.0526972i	$0.0167818\pi$
$521$			2.40567i			0.105394i	−0.998611	+	0.0526972i	$0.983218\pi$
$522$	30.4554	−	10.1104i	1.33299	−	0.442521i
$523$	30.2590			1.32313			0.661567	−	0.749886i	$-0.269892\pi$
$523$	30.2590			1.32313			0.661567	+	0.749886i	$0.269892\pi$
$524$	7.76803			0.339348
$525$	6.44828	−	3.97981i	0.281426	−	0.173693i
$526$	11.6816	−	11.6816i	0.509342	−	0.509342i
$527$	11.1489	−	11.1489i	0.485655	−	0.485655i
$528$	−0.723423	+	0.446489i	−0.0314830	+	0.0194309i
$529$	4.87527			0.211968
$530$	9.53560			0.414200
$531$	13.7405	−	4.56150i	0.596287	−	0.197952i
$532$			5.46606i			0.236984i
$533$	32.8372	+	17.6882i	1.42234	+	0.766159i
$534$	−29.2159	−	6.91580i	−1.26429	−	0.299276i
$535$	2.84404	−	2.84404i	0.122958	−	0.122958i
$536$		−	3.44271i		−	0.148703i
$537$	23.5910	+	5.58432i	1.01803	+	0.240981i
$538$	−8.30481	+	8.30481i	−0.358046	+	0.358046i
$539$	−0.347057	−	0.347057i	−0.0149488	−	0.0149488i
$540$	−4.09232	+	0.361436i	−0.176105	+	0.0155537i
$541$	−11.6253	−	11.6253i	−0.499812	−	0.499812i	0.411567	−	0.911379i	$-0.364981\pi$
$541$	−11.6253	−	11.6253i	−0.499812	−	0.499812i	−0.911379	+	0.411567i	$0.864981\pi$
$542$			13.7999i			0.592758i
$543$	−1.38692	+	5.85906i	−0.0595184	+	0.251436i
$544$	3.18228	+	3.18228i	0.136439	+	0.136439i
$545$	−6.62579			−0.283818
$546$	−0.367403	−	6.23418i	−0.0157234	−	0.266798i
$547$	16.5437			0.707359			0.353680	−	0.935367i	$-0.384930\pi$
$547$	16.5437			0.707359			0.353680	+	0.935367i	$0.384930\pi$
$548$	−2.35653	−	2.35653i	−0.100666	−	0.100666i
$549$	17.2286	+	8.64065i	0.735298	+	0.368774i
$550$			2.14726i			0.0915594i
$551$	41.3432	+	41.3432i	1.76128	+	1.76128i
$552$	−7.78190	+	4.80290i	−0.331220	+	0.204425i
$553$	9.35045	+	9.35045i	0.397621	+	0.397621i
$554$	1.33263	−	1.33263i	0.0566181	−	0.0566181i
$555$	−3.08753	+	13.0433i	−0.131058	+	0.553658i
$556$			1.53895i			0.0652659i
$557$	3.77844	−	3.77844i	0.160098	−	0.160098i	−0.622512	−	0.782610i	$-0.713888\pi$
$557$	3.77844	−	3.77844i	0.160098	−	0.160098i	0.782610	+	0.622512i	$0.213888\pi$
$558$	−9.39497	−	4.71186i	−0.397721	−	0.199469i
$559$	−7.50241	−	25.0222i	−0.317318	−	1.05833i
$560$		−	0.790633i		−	0.0334104i
$561$	−3.25571	+	2.00939i	−0.137456	+	0.0848364i
$562$	−4.03328			−0.170134
$563$	−37.3621			−1.57462			−0.787312	−	0.616555i	$-0.788528\pi$
$563$	−37.3621			−1.57462			−0.787312	+	0.616555i	$0.788528\pi$
$564$	3.20748	+	5.19692i	0.135059	+	0.218830i
$565$	1.61348	−	1.61348i	0.0678796	−	0.0678796i
$566$	10.7904	−	10.7904i	0.453553	−	0.453553i
$567$	1.29459	−	8.90640i	0.0543675	−	0.374034i
$568$	12.0153			0.504152
$569$	2.27928			0.0955524			0.0477762	−	0.998858i	$-0.484787\pi$
$569$	2.27928			0.0955524			0.0477762	+	0.998858i	$0.484787\pi$
$570$	−3.93137	−	6.36980i	−0.164667	−	0.266801i
$571$			8.84959i			0.370344i	0.982706	+	0.185172i	$0.0592842\pi$
$571$			8.84959i			0.370344i	−0.982706	+	0.185172i	$0.940716\pi$
$572$	1.55800	+	0.839235i	0.0651431	+	0.0350902i
$573$	10.7423	−	45.3808i	0.448764	−	1.89581i
$574$	−7.31477	+	7.31477i	−0.305313	+	0.305313i
$575$			23.0982i			0.963260i
$576$	1.34492	−	2.68164i	0.0560384	−	0.111735i
$577$	19.6466	−	19.6466i	0.817899	−	0.817899i	−0.167904	−	0.985803i	$-0.553700\pi$
$577$	19.6466	−	19.6466i	0.817899	−	0.817899i	0.985803	+	0.167904i	$0.0536999\pi$
$578$	2.30076	+	2.30076i	0.0956991	+	0.0956991i
$579$	19.5193	+	31.6262i	0.811196	+	1.31434i
$580$	−5.98005	−	5.98005i	−0.248308	−	0.248308i
$581$		−	8.92798i		−	0.370395i
$582$	2.06745	+	0.489394i	0.0856986	+	0.0202860i
$583$	−4.18576	−	4.18576i	−0.173356	−	0.173356i
$584$	−8.38963			−0.347165
$585$	4.91197	+	7.00067i	0.203085	+	0.289442i
$586$	19.0021			0.784968
$587$	11.1009	+	11.1009i	0.458182	+	0.458182i	0.898058	−	0.439877i	$-0.144978\pi$
$587$	11.1009	+	11.1009i	0.458182	+	0.458182i	−0.439877	+	0.898058i	$0.644978\pi$
$588$	1.68547	+	0.398975i	0.0695077	+	0.0164534i
$589$		−	19.1500i		−	0.789063i
$590$	−2.69801	−	2.69801i	−0.111075	−	0.111075i
$591$	20.4460	+	33.1275i	0.841034	+	1.36269i
$592$	−6.92111	−	6.92111i	−0.284456	−	0.284456i
$593$	−7.19619	+	7.19619i	−0.295512	+	0.295512i	−0.839253	−	0.543741i	$-0.817007\pi$
$593$	−7.19619	+	7.19619i	−0.295512	+	0.295512i	0.543741	+	0.839253i	$0.317007\pi$
$594$	1.95503	+	1.63771i	0.0802157	+	0.0671962i
$595$		−	3.55818i		−	0.145871i
$596$	−6.80987	+	6.80987i	−0.278943	+	0.278943i
$597$	1.71864	−	7.26042i	0.0703394	−	0.297149i
$598$	16.7595	+	9.02769i	0.685345	+	0.369170i
$599$			3.19761i			0.130651i	0.997864	+	0.0653253i	$0.0208085\pi$
$599$			3.19761i			0.130651i	−0.997864	+	0.0653253i	$0.979191\pi$
$600$	−3.97981	−	6.44828i	−0.162475	−	0.263250i
$601$	−2.82987			−0.115433			−0.0577165	−	0.998333i	$-0.518382\pi$
$601$	−2.82987			−0.115433			−0.0577165	+	0.998333i	$0.518382\pi$
$602$	7.24514			0.295290
$603$	−9.80212	+	3.25406i	−0.399173	+	0.132515i
$604$	−1.21937	+	1.21937i	−0.0496154	+	0.0496154i
$605$	6.01501	−	6.01501i	0.244545	−	0.244545i
$606$	−3.11557	−	5.04800i	−0.126561	−	0.205061i
$607$	31.5745			1.28157			0.640784	−	0.767721i	$-0.278609\pi$
$607$	31.5745			1.28157			0.640784	+	0.767721i	$0.278609\pi$
$608$	5.46606			0.221678
$609$	15.7660	−	9.73058i	0.638869	−	0.394303i
$610$		−	5.07954i		−	0.205665i
$611$	6.02889	−	11.1923i	0.243903	−	0.452793i
$612$	6.05271	−	12.0685i	0.244666	−	0.487840i
$613$	−9.86043	+	9.86043i	−0.398259	+	0.398259i	−0.877619	−	0.479360i	$-0.840869\pi$
$613$	−9.86043	+	9.86043i	−0.398259	+	0.398259i	0.479360	+	0.877619i	$0.340869\pi$
$614$			20.0100i			0.807539i
$615$	3.26314	−	13.7852i	0.131583	−	0.555872i
$616$	−0.347057	+	0.347057i	−0.0139833	+	0.0139833i
$617$	−23.5386	−	23.5386i	−0.947630	−	0.947630i	0.0510654	−	0.998695i	$-0.483738\pi$
$617$	−23.5386	−	23.5386i	−0.947630	−	0.947630i	−0.998695	+	0.0510654i	$0.983738\pi$
$618$	−0.130158	+	0.0803321i	−0.00523572	+	0.00323143i
$619$	−6.25762	−	6.25762i	−0.251515	−	0.251515i	0.570077	−	0.821592i	$-0.306914\pi$
$619$	−6.25762	−	6.25762i	−0.251515	−	0.251515i	−0.821592	+	0.570077i	$0.806914\pi$
$620$			2.76994i			0.111243i
$621$	21.0303	+	17.6170i	0.843918	+	0.706945i
$622$	−23.5438	−	23.5438i	−0.944019	−	0.944019i
$623$	−17.3339			−0.694469
$624$	−6.23418	+	0.367403i	−0.249567	+	0.0147079i
$625$	−16.0142			−0.640569
$626$	−16.6279	−	16.6279i	−0.664583	−	0.664583i
$627$	−1.07038	+	4.52181i	−0.0427467	+	0.180584i
$628$		−	5.63769i		−	0.224968i
$629$	−31.1479	−	31.1479i	−1.24195	−	1.24195i
$630$	−2.25110	+	0.747308i	−0.0896859	+	0.0297734i
$631$	−1.59821	−	1.59821i	−0.0636237	−	0.0636237i	0.674579	−	0.738203i	$-0.264325\pi$
$631$	−1.59821	−	1.59821i	−0.0636237	−	0.0636237i	−0.738203	+	0.674579i	$0.764325\pi$
$632$	9.35045	−	9.35045i	0.371941	−	0.371941i
$633$	−16.3399	−	3.86787i	−0.649452	−	0.153734i
$634$			3.13491i			0.124503i
$635$	−11.7987	+	11.7987i	−0.468216	+	0.468216i
$636$	20.3280	+	4.81192i	0.806057	+	0.190805i
$637$	−1.03551	−	3.45365i	−0.0410284	−	0.136839i
$638$			5.25002i			0.207850i
$639$	−11.3569	−	34.2101i	−0.449272	−	1.35333i
$640$	−0.790633			−0.0312525
$641$	22.4925			0.888400			0.444200	−	0.895928i	$-0.353488\pi$
$641$	22.4925			0.888400			0.444200	+	0.895928i	$0.353488\pi$
$642$	7.49809	−	4.62774i	0.295926	−	0.182642i
$643$	−12.9119	+	12.9119i	−0.509196	+	0.509196i	−0.914280	−	0.405083i	$-0.867242\pi$
$643$	−12.9119	+	12.9119i	−0.509196	+	0.509196i	0.405083	+	0.914280i	$0.367242\pi$
$644$	−3.73331	+	3.73331i	−0.147113	+	0.147113i
$645$	−8.44303	+	5.21094i	−0.332444	+	0.205181i
$646$	24.5996			0.967857
$647$	−4.76406			−0.187295			−0.0936473	−	0.995605i	$-0.529853\pi$
$647$	−4.76406			−0.187295			−0.0936473	+	0.995605i	$0.529853\pi$
$648$	−8.90640	−	1.29459i	−0.349877	−	0.0508561i
$649$			2.36865i			0.0929775i
$650$	−7.48058	+	13.8873i	−0.293412	+	0.544705i
$651$	−5.90496	−	1.39779i	−0.231434	−	0.0547835i
$652$	−3.47849	+	3.47849i	−0.136228	+	0.136228i
$653$			13.9182i			0.544660i	0.962204	+	0.272330i	$0.0877942\pi$
$653$			13.9182i			0.544660i	−0.962204	+	0.272330i	$0.912206\pi$
$654$	−14.1249	−	3.34355i	−0.552326	−	0.130743i
$655$	−4.34281	+	4.34281i	−0.169688	+	0.169688i
$656$	7.31477	+	7.31477i	0.285594	+	0.285594i
$657$	7.92988	+	23.8870i	0.309374	+	0.931921i
$658$	2.49319	+	2.49319i	0.0971946	+	0.0971946i
$659$		−	22.7816i		−	0.887447i	−0.896164	−	0.443724i	$-0.853657\pi$
$659$		−	22.7816i		−	0.887447i	0.896164	−	0.443724i	$-0.146343\pi$
$660$	0.154824	−	0.654054i	0.00602650	−	0.0254590i
$661$	−3.75702	−	3.75702i	−0.146131	−	0.146131i	0.630256	−	0.776387i	$-0.282950\pi$
$661$	−3.75702	−	3.75702i	−0.146131	−	0.146131i	−0.776387	+	0.630256i	$0.782950\pi$
$662$	−31.0138			−1.20539
$663$	−28.0564	+	1.65347i	−1.08962	+	0.0642153i
$664$	−8.92798			−0.346473
$665$	−3.05587	−	3.05587i	−0.118501	−	0.118501i
$666$	−13.1640	+	26.2477i	−0.510095	+	1.01708i
$667$			56.4747i			2.18671i
$668$	2.49027	+	2.49027i	0.0963515	+	0.0963515i
$669$	15.6277	−	9.64523i	0.604201	−	0.372906i
$670$	1.92469	+	1.92469i	0.0743573	+	0.0743573i
$671$	−2.22972	+	2.22972i	−0.0860774	+	0.0860774i
$672$	0.398975	−	1.68547i	0.0153908	−	0.0650185i
$673$			17.2981i			0.666792i	0.942787	+	0.333396i	$0.108195\pi$
$673$			17.2981i			0.666792i	−0.942787	+	0.333396i	$0.891805\pi$
$674$	−8.51258	+	8.51258i	−0.327892	+	0.327892i
$675$	−14.5979	+	17.4263i	−0.561873	+	0.670737i
$676$	7.15258	+	10.8554i	0.275099	+	0.417517i
$677$			38.4320i			1.47706i	0.674219	+	0.738531i	$0.264480\pi$
$677$			38.4320i			1.47706i	−0.674219	+	0.738531i	$0.735520\pi$
$678$	4.25382	−	2.62541i	0.163367	−	0.100828i
$679$	1.22663			0.0470737
$680$	−3.55818			−0.136450
$681$	−22.5425	−	36.5244i	−0.863830	−	1.39962i
$682$	1.21590	−	1.21590i	0.0465591	−	0.0465591i
$683$	3.33543	−	3.33543i	0.127627	−	0.127627i	−0.640408	−	0.768035i	$-0.721235\pi$
$683$	3.33543	−	3.33543i	0.127627	−	0.127627i	0.768035	+	0.640408i	$0.221235\pi$
$684$	−5.16653	−	15.5630i	−0.197547	−	0.595067i
$685$	2.63489			0.100674
$686$	1.00000			0.0381802
$687$	17.8492	+	28.9201i	0.680988	+	1.10337i
$688$		−	7.24514i		−	0.276219i
$689$	−12.4890	−	41.6535i	−0.475792	−	1.58687i
$690$	1.66544	−	7.03569i	0.0634024	−	0.267844i
$691$	11.0166	−	11.0166i	0.419092	−	0.419092i	−0.465799	−	0.884891i	$-0.654233\pi$
$691$	11.0166	−	11.0166i	0.419092	−	0.419092i	0.884891	+	0.465799i	$0.154233\pi$
$692$		−	13.1775i		−	0.500934i
$693$	1.31618	+	0.660106i	0.0499977	+	0.0250753i
$694$	3.47500	−	3.47500i	0.131909	−	0.131909i
$695$	−0.860367	−	0.860367i	−0.0326356	−	0.0326356i
$696$	−9.73058	−	15.7660i	−0.368837	−	0.597607i
$697$	32.9195	+	32.9195i	1.24692	+	1.24692i
$698$		−	4.71881i		−	0.178609i
$699$	−8.09186	−	1.91545i	−0.306062	−	0.0724491i
$700$	−3.09352	−	3.09352i	−0.116924	−	0.116924i
$701$	−11.4796			−0.433579			−0.216790	−	0.976218i	$-0.569559\pi$
$701$	−11.4796			−0.433579			−0.216790	+	0.976218i	$0.569559\pi$
$702$	6.93863	+	17.4027i	0.261882	+	0.656824i
$703$	−53.5014			−2.01784
$704$	0.347057	+	0.347057i	0.0130802	+	0.0130802i
$705$	−4.69859	−	1.11222i	−0.176959	−	0.0418886i
$706$			6.51974i			0.245374i
$707$	−2.42175	−	2.42175i	−0.0910792	−	0.0910792i
$708$	−4.39013	−	7.11311i	−0.164991	−	0.267327i
$709$	18.4081	+	18.4081i	0.691331	+	0.691331i	0.962525	−	0.271193i	$-0.0874183\pi$
$709$	18.4081	+	18.4081i	0.691331	+	0.691331i	−0.271193	+	0.962525i	$0.587418\pi$
$710$	−6.71731	+	6.71731i	−0.252096	+	0.252096i
$711$	−35.4607	−	17.7846i	−1.32988	−	0.666975i
$712$			17.3339i			0.649617i
$713$	13.0795	−	13.0795i	0.489829	−	0.489829i
$714$	1.79555	−	7.58533i	0.0671969	−	0.283874i
$715$	−1.34020	+	0.401833i	−0.0501207	+	0.0150277i
$716$		−	13.9967i		−	0.523081i
$717$	11.3901	+	18.4548i	0.425371	+	0.689207i
$718$	12.6102			0.470608
$719$	−4.45696			−0.166217			−0.0831084	−	0.996541i	$-0.526485\pi$
$719$	−4.45696			−0.166217			−0.0831084	+	0.996541i	$0.526485\pi$
$720$	0.747308	+	2.25110i	0.0278505	+	0.0838935i
$721$	−0.0624424	+	0.0624424i	−0.00232548	+	0.00232548i
$722$	7.69177	−	7.69177i	0.286258	−	0.286258i
$723$	−11.3143	−	18.3320i	−0.420784	−	0.681776i
$724$	3.47621			0.129192
$725$	−46.7964			−1.73797
$726$	15.8581	−	9.78747i	0.588550	−	0.363247i
$727$		−	48.0910i		−	1.78360i	−0.452432	−	0.891799i	$-0.649443\pi$
$727$		−	48.0910i		−	1.78360i	0.452432	−	0.891799i	$-0.350557\pi$
$728$	−3.45365	+	1.03551i	−0.128001	+	0.0383785i
$729$	4.73239	+	26.5820i	0.175274	+	0.984520i
$730$	4.69032	−	4.69032i	0.173597	−	0.173597i
$731$		−	32.6062i		−	1.20598i
$732$	2.56327	−	10.8286i	0.0947412	−	0.400235i
$733$	12.2239	−	12.2239i	0.451499	−	0.451499i	−0.444353	−	0.895852i	$-0.646566\pi$
$733$	12.2239	−	12.2239i	0.451499	−	0.451499i	0.895852	+	0.444353i	$0.146566\pi$
$734$	−18.1272	−	18.1272i	−0.669087	−	0.669087i
$735$	−1.16534	+	0.719233i	−0.0429841	+	0.0265293i
$736$	3.73331	+	3.73331i	0.137612	+	0.137612i
$737$		−	1.68973i		−	0.0622420i
$738$	13.9127	−	27.7406i	0.512135	−	1.02115i
$739$	−0.378213	−	0.378213i	−0.0139128	−	0.0139128i	0.700116	−	0.714029i	$-0.253132\pi$
$739$	−0.378213	−	0.378213i	−0.0139128	−	0.0139128i	−0.714029	+	0.700116i	$0.753132\pi$
$740$	7.73867			0.284479
$741$	−22.6756	+	25.5157i	−0.833009	+	0.937343i
$742$	12.0607			0.442762
$743$	−13.1510	−	13.1510i	−0.482465	−	0.482465i	0.423453	−	0.905918i	$-0.360818\pi$
$743$	−13.1510	−	13.1510i	−0.482465	−	0.482465i	−0.905918	+	0.423453i	$0.860818\pi$
$744$	−1.39779	+	5.90496i	−0.0512453	+	0.216486i
$745$		−	7.61429i		−	0.278966i
$746$	−19.5183	−	19.5183i	−0.714614	−	0.714614i
$747$	8.43874	+	25.4198i	0.308757	+	0.930063i
$748$	1.56190	+	1.56190i	0.0571089	+	0.0571089i
$749$	3.59716	−	3.59716i	0.131437	−	0.131437i
$750$	12.4929	+	2.95724i	0.456177	+	0.107983i
$751$		−	21.7792i		−	0.794735i	−0.917660	−	0.397367i	$-0.869924\pi$
$751$		−	21.7792i		−	0.794735i	0.917660	−	0.397367i	$-0.130076\pi$
$752$	2.49319	−	2.49319i	0.0909172	−	0.0909172i
$753$	23.0713	+	5.46129i	0.840764	+	0.199020i
$754$	−18.2899	+	33.9543i	−0.666079	+	1.23654i
$755$		−	1.36341i		−	0.0496194i
$756$	−5.17600	+	0.457147i	−0.188249	+	0.0166263i
$757$	−7.96654			−0.289549			−0.144774	−	0.989465i	$-0.546246\pi$
$757$	−7.96654			−0.289549			−0.144774	+	0.989465i	$0.546246\pi$
$758$	−21.5227			−0.781739
$759$	−3.81946	+	2.35733i	−0.138638	+	0.0855656i
$760$	−3.05587	+	3.05587i	−0.110848	+	0.110848i
$761$	−26.2245	+	26.2245i	−0.950637	+	0.950637i	−0.998838	−	0.0482010i	$-0.984651\pi$
$761$	−26.2245	+	26.2245i	−0.950637	+	0.950637i	0.0482010	+	0.998838i	$0.484651\pi$
$762$	−31.1063	+	19.1985i	−1.12686	+	0.695488i
$763$	−8.38035			−0.303389
$764$	−26.9246			−0.974099
$765$	3.36320	+	10.1309i	0.121597	+	0.366283i
$766$			10.5894i			0.382610i
$767$	−8.25184	+	15.3191i	−0.297957	+	0.553142i
$768$	−1.68547	−	0.398975i	−0.0608193	−	0.0143968i
$769$	4.82224	−	4.82224i	0.173894	−	0.173894i	−0.614794	−	0.788688i	$-0.710761\pi$
$769$	4.82224	−	4.82224i	0.173894	−	0.173894i	0.788688	+	0.614794i	$0.210761\pi$
$770$		−	0.388054i		−	0.0139845i
$771$	30.8421	+	7.30075i	1.11075	+	0.262930i
$772$	15.1725	−	15.1725i	0.546069	−	0.546069i
$773$	−25.9691	−	25.9691i	−0.934044	−	0.934044i	0.0639117	−	0.997956i	$-0.479642\pi$
$773$	−25.9691	−	25.9691i	−0.934044	−	0.934044i	−0.997956	+	0.0639117i	$0.979642\pi$
$774$	−20.6284	+	6.84812i	−0.741474	+	0.246151i
$775$	10.8380	+	10.8380i	0.389311	+	0.389311i
$776$		−	1.22663i		−	0.0440334i
$777$	−3.90514	+	16.4973i	−0.140096	+	0.591837i
$778$	−4.95439	−	4.95439i	−0.177623	−	0.177623i
$779$	56.5444			2.02592
$780$	3.27989	−	3.69070i	0.117439	−	0.132148i
$781$	5.89728			0.211021
$782$	16.8015	+	16.8015i	0.600820	+	0.600820i
$783$	−35.6916	+	42.6070i	−1.27551	+	1.52265i
$784$		−	1.00000i		−	0.0357143i
$785$	3.15182	+	3.15182i	0.112493	+	0.112493i
$786$	−11.4495	+	7.06651i	−0.408390	+	0.252054i
$787$	11.4728	+	11.4728i	0.408961	+	0.408961i	0.881376	−	0.472415i	$-0.156618\pi$
$787$	11.4728	+	11.4728i	0.408961	+	0.408961i	−0.472415	+	0.881376i	$0.656618\pi$
$788$	15.8927	−	15.8927i	0.566155	−	0.566155i
$789$	−6.59117	+	27.8445i	−0.234652	+	0.991289i
$790$			10.4550i			0.371971i
$791$	2.04074	−	2.04074i	0.0725604	−	0.0725604i
$792$	0.660106	−	1.31618i	0.0234558	−	0.0467686i
$793$	−22.1885	+	6.65278i	−0.787936	+	0.236247i
$794$		−	7.67641i		−	0.272425i
$795$	−14.0548	+	8.67445i	−0.498472	+	0.307651i
$796$	−4.30765			−0.152681
$797$	−24.6190			−0.872049			−0.436024	−	0.899935i	$-0.643614\pi$
$797$	−24.6190			−0.872049			−0.436024	+	0.899935i	$0.643614\pi$
$798$	−4.97243	−	8.05657i	−0.176022	−	0.285200i
$799$	11.2204	−	11.2204i	0.396949	−	0.396949i
$800$	−3.09352	+	3.09352i	−0.109372	+	0.109372i
$801$	49.3533	−	16.3841i	1.74381	−	0.578902i
$802$	−32.2021			−1.13709
$803$	−4.11774			−0.145312
$804$	3.13181	+	5.07431i	0.110450	+	0.178957i
$805$		−	4.17431i		−	0.147125i
$806$	12.0997	−	3.62785i	0.426193	−	0.127786i
$807$	4.68587	−	19.7955i	0.164950	−	0.696834i
$808$	−2.42175	+	2.42175i	−0.0851967	+	0.0851967i
$809$		−	27.4026i		−	0.963423i	−0.876330	−	0.481712i	$-0.840015\pi$
$809$		−	27.4026i		−	0.963423i	0.876330	−	0.481712i	$-0.159985\pi$
$810$	5.70299	−	4.25548i	0.200383	−	0.149522i
$811$	−18.7220	+	18.7220i	−0.657418	+	0.657418i	−0.954768	−	0.297351i	$-0.903897\pi$
$811$	−18.7220	+	18.7220i	−0.657418	+	0.657418i	0.297351	+	0.954768i	$0.403897\pi$
$812$	−7.56362	−	7.56362i	−0.265431	−	0.265431i
$813$	−12.5537	−	20.3401i	−0.440277	−	0.713358i
$814$	−3.39697	−	3.39697i	−0.119064	−	0.119064i
$815$		−	3.88938i		−	0.136239i
$816$	−7.58533	−	1.79555i	−0.265540	−	0.0628569i
$817$	−28.0031	−	28.0031i	−0.979705	−	0.979705i
$818$	7.98298			0.279118
$819$	6.21271	+	8.85451i	0.217090	+	0.309401i
$820$	−8.17882			−0.285617
$821$	−19.3107	−	19.3107i	−0.673947	−	0.673947i	0.284676	−	0.958624i	$-0.408114\pi$
$821$	−19.3107	−	19.3107i	−0.673947	−	0.673947i	−0.958624	+	0.284676i	$0.908114\pi$
$822$	5.61707	+	1.32964i	0.195918	+	0.0463764i
$823$		−	44.6167i		−	1.55524i	−0.628735	−	0.777620i	$-0.716427\pi$
$823$		−	44.6167i		−	1.55524i	0.628735	−	0.777620i	$-0.283573\pi$
$824$	0.0624424	+	0.0624424i	0.00217528	+	0.00217528i
$825$	−1.95334	−	3.16490i	−0.0680067	−	0.110188i
$826$	−3.41247	−	3.41247i	−0.118735	−	0.118735i
$827$	−8.17009	+	8.17009i	−0.284102	+	0.284102i	−0.834743	−	0.550640i	$-0.814384\pi$
$827$	−8.17009	+	8.17009i	−0.284102	+	0.284102i	0.550640	+	0.834743i	$0.314384\pi$
$828$	7.10079	−	14.1583i	0.246770	−	0.492033i
$829$		−	14.0314i		−	0.487331i	−0.969859	−	0.243665i	$-0.921650\pi$
$829$		−	14.0314i		−	0.487331i	0.969859	−	0.243665i	$-0.0783499\pi$
$830$	4.99130	−	4.99130i	0.173251	−	0.173251i
$831$	−0.751918	+	3.17649i	−0.0260838	+	0.110191i
$832$	1.03551	+	3.45365i	0.0358998	+	0.119734i
$833$		−	4.50042i		−	0.155930i
$834$	−1.39997	−	2.26830i	−0.0484769	−	0.0785447i
$835$	−2.78443			−0.0963593
$836$	2.68282			0.0927871
$837$	18.1338	−	1.60159i	0.626797	−	0.0553590i
$838$	−6.36589	+	6.36589i	−0.219906	+	0.219906i
$839$	−21.3877	+	21.3877i	−0.738387	+	0.738387i	−0.972266	−	0.233879i	$-0.924858\pi$
$839$	−21.3877	+	21.3877i	−0.738387	+	0.738387i	0.233879	+	0.972266i	$0.424858\pi$
$840$	0.719233	+	1.16534i	0.0248159	+	0.0402079i
$841$	−85.4166			−2.94540
$842$	−2.69953			−0.0930321
$843$	5.94476	−	3.66904i	0.204749	−	0.126369i
$844$			9.69453i			0.333700i
$845$	−10.0676	−	2.07013i	−0.346336	−	0.0712146i
$846$	−9.45519	−	4.74206i	−0.325076	−	0.163035i
$847$	7.60783	−	7.60783i	0.261408	−	0.261408i
$848$		−	12.0607i		−	0.414166i
$849$	−6.08831	+	25.7201i	−0.208950	+	0.882713i
$850$	−13.9221	+	13.9221i	−0.477525	+	0.477525i
$851$	−36.5414	−	36.5414i	−1.25262	−	1.25262i
$852$	−17.7097	+	10.9302i	−0.606724	+	0.374464i
$853$	1.29289	+	1.29289i	0.0442677	+	0.0442677i	0.728894	−	0.684626i	$-0.240035\pi$
$853$	1.29289	+	1.29289i	0.0442677	+	0.0442677i	−0.684626	+	0.728894i	$0.740035\pi$
$854$		−	6.42464i		−	0.219847i
$855$	11.5891	+	5.81228i	0.396339	+	0.198776i
$856$	−3.59716	−	3.59716i	−0.122948	−	0.122948i
$857$	−13.6228			−0.465345			−0.232672	−	0.972555i	$-0.574747\pi$
$857$	−13.6228			−0.465345			−0.232672	+	0.972555i	$0.574747\pi$
$858$	−3.05982	+	0.180326i	−0.104461	+	0.00615624i
$859$	51.0261			1.74099			0.870494	−	0.492180i	$-0.163800\pi$
$859$	51.0261			1.74099			0.870494	+	0.492180i	$0.163800\pi$
$860$	4.05049	+	4.05049i	0.138120	+	0.138120i
$861$	4.12725	−	17.4356i	0.140656	−	0.594204i
$862$			16.5975i			0.565312i
$863$	−32.5612	−	32.5612i	−1.10839	−	1.10839i	−0.993362	−	0.115033i	$-0.963303\pi$
$863$	−32.5612	−	32.5612i	−1.10839	−	1.10839i	−0.115033	−	0.993362i	$-0.536697\pi$
$864$	0.457147	+	5.17600i	0.0155525	+	0.176091i
$865$	7.36705	+	7.36705i	0.250487	+	0.250487i
$866$	−9.83740	+	9.83740i	−0.334289	+	0.334289i
$867$	−5.48414	−	1.29817i	−0.186251	−	0.0440882i
$868$			3.50344i			0.118915i
$869$	4.58932	−	4.58932i	0.155682	−	0.155682i
$870$	14.2542	+	3.37416i	0.483261	+	0.114395i
$871$	5.88665	−	10.9283i	0.199461	−	0.370290i
$872$			8.38035i			0.283795i
$873$	−3.49247	+	1.15941i	−0.118202	+	0.0392401i
$874$	28.8592			0.976176
$875$	7.41211			0.250575
$876$	12.3657	−	7.63197i	0.417798	−	0.257860i
$877$	4.82932	−	4.82932i	0.163075	−	0.163075i	−0.620853	−	0.783927i	$-0.713213\pi$
$877$	4.82932	−	4.82932i	0.163075	−	0.163075i	0.783927	+	0.620853i	$0.213213\pi$
$878$	5.83116	−	5.83116i	0.196792	−	0.196792i
$879$	−28.0077	+	17.2860i	−0.944675	+	0.583043i
$880$	−0.388054			−0.0130813
$881$	36.4849			1.22921			0.614604	−	0.788836i	$-0.289316\pi$
$881$	36.4849			1.22921			0.614604	+	0.788836i	$0.289316\pi$
$882$	−2.84721	+	0.945201i	−0.0958705	+	0.0318266i
$883$			51.3777i			1.72900i	0.502636	+	0.864498i	$0.332364\pi$
$883$			51.3777i			1.72900i	−0.502636	+	0.864498i	$0.667636\pi$
$884$	4.66023	+	15.5429i	0.156740	+	0.522764i
$885$	6.43103	+	1.52231i	0.216177	+	0.0511720i
$886$	6.68209	−	6.68209i	0.224489	−	0.224489i
$887$		−	36.4498i		−	1.22387i	−0.790910	−	0.611933i	$-0.790392\pi$
$887$		−	36.4498i		−	1.22387i	0.790910	−	0.611933i	$-0.209608\pi$
$888$	16.4973	+	3.90514i	0.553613	+	0.131048i
$889$	−14.9231	+	14.9231i	−0.500503	+	0.500503i
$890$	−9.69075	−	9.69075i	−0.324835	−	0.324835i
$891$	−4.37138	−	0.635400i	−0.146447	−	0.0212867i
$892$	−7.49728	−	7.49728i	−0.251027	−	0.251027i
$893$		−	19.2728i		−	0.644939i
$894$	3.84237	−	16.2321i	0.128508	−	0.542884i
$895$	7.82502	+	7.82502i	0.261561	+	0.261561i
$896$	−1.00000			−0.0334077
$897$	−32.9146	+	1.93978i	−1.09899	+	0.0647673i
$898$	32.4165			1.08175
$899$	26.4987	+	26.4987i	0.883781	+	0.883781i
$900$	11.7319	+	5.88390i	0.391063	+	0.196130i
$901$		−	54.2782i		−	1.80827i
$902$	3.59019	+	3.59019i	0.119540	+	0.119540i
$903$	−10.6788	+	6.59085i	−0.355369	+	0.219330i
$904$	−2.04074	−	2.04074i	−0.0678741	−	0.0678741i
$905$	−1.94342	+	1.94342i	−0.0646014	+	0.0646014i
$906$	0.688011	−	2.90651i	0.0228576	−	0.0965623i
$907$		−	9.19731i		−	0.305392i	−0.988273	−	0.152696i	$-0.951204\pi$
$907$		−	9.19731i		−	0.305392i	0.988273	−	0.152696i	$-0.0487955\pi$
$908$	−17.5224	+	17.5224i	−0.581500	+	0.581500i
$909$	9.18425	+	4.60618i	0.304622	+	0.152777i
$910$	1.35189	−	2.50972i	0.0448148	−	0.0831965i
$911$			13.7738i			0.456347i	0.973620	+	0.228173i	$0.0732753\pi$
$911$			13.7738i			0.456347i	−0.973620	+	0.228173i	$0.926725\pi$
$912$	−8.05657	+	4.97243i	−0.266780	+	0.164654i
$913$	−4.38197			−0.145022
$914$	−3.85384			−0.127474
$915$	4.62081	+	7.48687i	0.152759	+	0.247508i
$916$	13.8742	−	13.8742i	0.458417	−	0.458417i
$917$	−5.49282	+	5.49282i	−0.181389	+	0.181389i
$918$	2.05735	+	23.2942i	0.0679027	+	0.768823i
$919$	43.2369			1.42625			0.713127	−	0.701035i	$-0.247278\pi$
$919$	43.2369			1.42625			0.713127	+	0.701035i	$0.247278\pi$
$920$	−4.17431			−0.137623
$921$	−18.2030	−	29.4933i	−0.599808	−	0.971838i
$922$			24.1143i			0.794161i
$923$	38.1404	+	20.5448i	1.25541	+	0.676241i
$924$	0.195822	−	0.827253i	0.00644208	−	0.0272146i
$925$	30.2792	−	30.2792i	0.995573	−	0.995573i
$926$		−	10.1862i		−	0.334739i
$927$	0.118766	−	0.236807i	0.00390079	−	0.00777777i
$928$	−7.56362	+	7.56362i	−0.248288	+	0.248288i
$929$	16.0965	+	16.0965i	0.528110	+	0.528110i	0.920008	−	0.391899i	$-0.128182\pi$
$929$	16.0965	+	16.0965i	0.528110	+	0.528110i	−0.391899	+	0.920008i	$0.628182\pi$
$930$	−2.51979	−	4.08269i	−0.0826272	−	0.133877i
$931$	−3.86509	−	3.86509i	−0.126673	−	0.126673i
$932$			4.80094i			0.157260i
$933$	56.1194	+	13.2842i	1.83727	+	0.434906i
$934$	−13.5564	−	13.5564i	−0.443578	−	0.443578i
$935$	−1.74640			−0.0571135
$936$	8.85451	−	6.21271i	0.289419	−	0.203069i
$937$	−19.1143			−0.624438			−0.312219	−	0.950010i	$-0.601072\pi$
$937$	−19.1143			−0.624438			−0.312219	+	0.950010i	$0.601072\pi$
$938$	2.43437	+	2.43437i	0.0794849	+	0.0794849i
$939$	39.6345	+	9.38203i	1.29342	+	0.306171i
$940$			2.78770i			0.0909246i
$941$	21.9202	+	21.9202i	0.714579	+	0.714579i	0.967490	−	0.252911i	$-0.0813880\pi$
$941$	21.9202	+	21.9202i	0.714579	+	0.714579i	−0.252911	+	0.967490i	$0.581388\pi$
$942$	5.12856	+	8.30954i	0.167097	+	0.270739i
$943$	38.6198	+	38.6198i	1.25763	+	1.25763i
$944$	−3.41247	+	3.41247i	−0.111066	+	0.111066i
$945$	2.63814	−	3.14928i	0.0858185	−	0.102446i
$946$		−	3.55601i		−	0.115616i
$947$	−27.5307	+	27.5307i	−0.894627	+	0.894627i	−0.994954	−	0.100328i	$-0.968011\pi$
$947$	−27.5307	+	27.5307i	−0.894627	+	0.894627i	0.100328	+	0.994954i	$0.468011\pi$
$948$	−5.27585	+	22.2879i	−0.171352	+	0.723877i
$949$	−26.6313	−	14.3453i	−0.864490	−	0.465668i
$950$			23.9135i			0.775855i
$951$	−2.85180	−	4.62063i	−0.0924761	−	0.149834i
$952$	−4.50042			−0.145859
$953$	−1.66813			−0.0540361			−0.0270181	−	0.999635i	$-0.508601\pi$
$953$	−1.66813			−0.0540361			−0.0270181	+	0.999635i	$0.508601\pi$
$954$	−34.3393	+	11.3998i	−1.11178	+	0.369082i
$955$	15.0526	−	15.0526i	0.487089	−	0.487089i
$956$	8.85356	−	8.85356i	0.286345	−	0.286345i
$957$	−4.77590	−	7.73815i	−0.154383	−	0.250139i
$958$	30.2451			0.977174
$959$	3.33263			0.107616
$960$	1.16534	−	0.719233i	0.0376111	−	0.0232131i
$961$			18.7259i			0.604061i
$962$	−10.1355	−	33.8041i	−0.326781	−	1.08989i
$963$	−6.84183	+	13.6419i	−0.220475	+	0.439604i
$964$	−8.79467	+	8.79467i	−0.283257	+	0.283257i
$965$			16.9647i			0.546113i
$966$	2.10647	−	8.89880i	0.0677745	−	0.286314i
$967$	31.0792	−	31.0792i	0.999438	−	0.999438i	−0.000561611	−	1.00000i	$-0.500179\pi$
$967$	31.0792	−	31.0792i	0.999438	−	0.999438i	1.00000		0.000561611i	$0.000178766\pi$
$968$	−7.60783	−	7.60783i	−0.244525	−	0.244525i
$969$	−36.2580	+	22.3780i	−1.16477	+	0.718885i
$970$	0.685762	+	0.685762i	0.0220185	+	0.0220185i
$971$			1.88008i			0.0603345i	0.999545	+	0.0301672i	$0.00960399\pi$
$971$			1.88008i			0.0603345i	−0.999545	+	0.0301672i	$0.990396\pi$
$972$	14.3051	−	6.19396i	0.458835	−	0.198671i
$973$	−1.08820	−	1.08820i	−0.0348861	−	0.0348861i
$974$	34.0479			1.09096
$975$	−1.60735	−	27.2739i	−0.0514764	−	0.873464i
$976$	−6.42464			−0.205648
$977$	−3.46359	−	3.46359i	−0.110810	−	0.110810i	0.649528	−	0.760338i	$-0.274967\pi$
$977$	−3.46359	−	3.46359i	−0.110810	−	0.110810i	−0.760338	+	0.649528i	$0.774967\pi$
$978$	1.96269	−	8.29139i	0.0627598	−	0.265129i
$979$			8.50773i			0.271908i
$980$	0.559062	+	0.559062i	0.0178586	+	0.0178586i
$981$	23.8606	−	7.92112i	0.761811	−	0.252902i
$982$	−7.34168	−	7.34168i	−0.234283	−	0.234283i
$983$	8.07529	−	8.07529i	0.257562	−	0.257562i	−0.566500	−	0.824062i	$-0.691703\pi$
$983$	8.07529	−	8.07529i	0.257562	−	0.257562i	0.824062	+	0.566500i	$0.191703\pi$
$984$	−17.4356	−	4.12725i	−0.555827	−	0.131572i
$985$			17.7700i			0.566201i
$986$	−34.0394	+	34.0394i	−1.08404	+	1.08404i
$987$	−5.94281	−	1.40675i	−0.189162	−	0.0447772i
$988$	17.3510	+	9.34634i	0.552009	+	0.297347i
$989$		−	38.2522i		−	1.21635i
$990$	0.366789	+	1.10487i	0.0116573	+	0.0351150i
$991$	−22.5280			−0.715624			−0.357812	−	0.933794i	$-0.616477\pi$
$991$	−22.5280			−0.715624			−0.357812	+	0.933794i	$0.616477\pi$
$992$	3.50344			0.111234
$993$	45.7121	−	28.2130i	1.45063	−	0.895313i
$994$	−8.49611	+	8.49611i	−0.269480	+	0.269480i
$995$	2.40824	−	2.40824i	0.0763464	−	0.0763464i
$996$	13.1592	−	8.12171i	0.416965	−	0.257346i
$997$	−53.8521			−1.70551			−0.852757	−	0.522309i	$-0.825071\pi$
$997$	−53.8521			−1.70551			−0.852757	+	0.522309i	$0.825071\pi$
$998$	4.93530			0.156224
$999$	−4.47452	−	50.6624i	−0.141568	−	1.60289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.c.239.6	✓	20
3.2	odd	2		546.2.p.d.239.1	yes	20
13.8	odd	4		546.2.p.d.281.1	yes	20
39.8	even	4	inner	546.2.p.c.281.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.6	✓	20	1.1	even	1	trivial
546.2.p.c.281.6	yes	20	39.8	even	4	inner
546.2.p.d.239.1	yes	20	3.2	odd	2
546.2.p.d.281.1	yes	20	13.8	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.68547 - 0.398975i) q^{3} +1.00000i q^{4} +(-0.559062 - 0.559062i) q^{5} +(-0.909692 - 1.47393i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.68164 + 1.34492i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.68547 - 0.398975i) q^{3} +1.00000i q^{4} +(-0.559062 - 0.559062i) q^{5} +(-0.909692 - 1.47393i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.68164 + 1.34492i) q^{9} -0.790633i q^{10} +(-0.347057 + 0.347057i) q^{11} +(0.398975 - 1.68547i) q^{12} +(-3.45365 + 1.03551i) q^{13} -1.00000i q^{14} +(0.719233 + 1.16534i) q^{15} -1.00000 q^{16} -4.50042 q^{17} +(0.945201 + 2.84721i) q^{18} +(-3.86509 + 3.86509i) q^{19} +(0.559062 - 0.559062i) q^{20} +(0.909692 + 1.47393i) q^{21} -0.490813 q^{22} -5.27970 q^{23} +(1.47393 - 0.909692i) q^{24} -4.37490i q^{25} +(-3.17432 - 1.70989i) q^{26} +(-3.98324 - 3.33674i) q^{27} +(0.707107 - 0.707107i) q^{28} -10.6966i q^{29} +(-0.315443 + 1.33259i) q^{30} +(-2.47731 + 2.47731i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.723423 - 0.446489i) q^{33} +(-3.18228 - 3.18228i) q^{34} +0.790633i q^{35} +(-1.34492 + 2.68164i) q^{36} +(6.92111 + 6.92111i) q^{37} -5.46606 q^{38} +(6.23418 - 0.367403i) q^{39} +0.790633 q^{40} +(-7.31477 - 7.31477i) q^{41} +(-0.398975 + 1.68547i) q^{42} +7.24514i q^{43} +(-0.347057 - 0.347057i) q^{44} +(-0.747308 - 2.25110i) q^{45} +(-3.73331 - 3.73331i) q^{46} +(-2.49319 + 2.49319i) q^{47} +(1.68547 + 0.398975i) q^{48} +1.00000i q^{49} +(3.09352 - 3.09352i) q^{50} +(7.58533 + 1.79555i) q^{51} +(-1.03551 - 3.45365i) q^{52} +12.0607i q^{53} +(-0.457147 - 5.17600i) q^{54} +0.388054 q^{55} +1.00000 q^{56} +(8.05657 - 4.97243i) q^{57} +(7.56362 - 7.56362i) q^{58} +(3.41247 - 3.41247i) q^{59} +(-1.16534 + 0.719233i) q^{60} +6.42464 q^{61} -3.50344 q^{62} +(-0.945201 - 2.84721i) q^{63} -1.00000i q^{64} +(2.50972 + 1.35189i) q^{65} +(0.827253 + 0.195822i) q^{66} +(-2.43437 + 2.43437i) q^{67} -4.50042i q^{68} +(8.89880 + 2.10647i) q^{69} +(-0.559062 + 0.559062i) q^{70} +(-8.49611 - 8.49611i) q^{71} +(-2.84721 + 0.945201i) q^{72} +(5.93236 + 5.93236i) q^{73} +9.78793i q^{74} +(-1.74547 + 7.37377i) q^{75} +(-3.86509 - 3.86509i) q^{76} +0.490813 q^{77} +(4.66802 + 4.14844i) q^{78} -13.2235 q^{79} +(0.559062 + 0.559062i) q^{80} +(5.38237 + 7.21319i) q^{81} -10.3446i q^{82} +(6.31304 + 6.31304i) q^{83} +(-1.47393 + 0.909692i) q^{84} +(2.51601 + 2.51601i) q^{85} +(-5.12309 + 5.12309i) q^{86} +(-4.26766 + 18.0288i) q^{87} -0.490813i q^{88} +(12.2569 - 12.2569i) q^{89} +(1.06334 - 2.12019i) q^{90} +(3.17432 + 1.70989i) q^{91} -5.27970i q^{92} +(5.16382 - 3.18705i) q^{93} -3.52590 q^{94} +4.32165 q^{95} +(0.909692 + 1.47393i) q^{96} +(-0.867358 + 0.867358i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-1.39745 + 0.463917i) 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

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