LMFDB - Embedded newform 546.2.p.d.239.1

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			239.1
Root			$1.47393 - 0.909692i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.d.281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.68547 + 0.398975i) q^{3} +1.00000i q^{4} +(0.559062 + 0.559062i) q^{5} +(1.47393 + 0.909692i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.68164 - 1.34492i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.68547 + 0.398975i) q^{3} +1.00000i q^{4} +(0.559062 + 0.559062i) q^{5} +(1.47393 + 0.909692i) 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} +(-1.16534 - 0.719233i) q^{15} -1.00000 q^{16} +4.50042 q^{17} +(-2.84721 - 0.945201i) q^{18} +(-3.86509 + 3.86509i) q^{19} +(-0.559062 + 0.559062i) q^{20} +(1.47393 + 0.909692i) q^{21} -0.490813 q^{22} +5.27970 q^{23} +(-0.909692 + 1.47393i) 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} +(-0.446489 + 0.723423i) 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} +(5.40790 - 3.12324i) 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} +(2.25110 + 0.747308i) 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} +(5.17600 + 0.457147i) q^{54} +0.388054 q^{55} -1.00000 q^{56} +(4.97243 - 8.05657i) q^{57} +(7.56362 - 7.56362i) q^{58} +(-3.41247 + 3.41247i) q^{59} +(0.719233 - 1.16534i) q^{60} +6.42464 q^{61} +3.50344 q^{62} +(-2.84721 - 0.945201i) 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} +(0.945201 - 2.84721i) 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} +(-6.03243 - 1.61549i) 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} +(-0.909692 + 1.47393i) 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} +(3.18705 - 5.16382i) q^{93} -3.52590 q^{94} -4.32165 q^{95} +(-1.47393 - 0.909692i) q^{96} +(-0.867358 + 0.867358i) q^{97} +(0.707107 - 0.707107i) q^{98} +(0.463917 - 1.39745i) 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} - 16 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} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 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} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 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} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 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 - 16 * 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 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * 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 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * 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 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * 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	0.820979	−	0.570959i	$-0.193428\pi$
$5$	0.559062	+	0.559062i	0.250020	+	0.250020i	−0.570959	+	0.820979i	$0.693428\pi$
$6$	1.47393	+	0.909692i	0.601728	+	0.371380i
$7$	−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	−0.652848	−	0.757489i	$-0.726426\pi$
$11$	0.347057	−	0.347057i	0.104642	−	0.104642i	0.757489	+	0.652848i	$0.226426\pi$
$12$	−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
$15$	−1.16534	−	0.719233i	−0.300888	−	0.185705i
$16$	−1.00000			−0.250000
$17$	4.50042			1.09151			0.545756	−	0.837944i	$-0.316243\pi$
$17$	4.50042			1.09151			0.545756	+	0.837944i	$0.316243\pi$
$18$	−2.84721	−	0.945201i	−0.671093	−	0.222786i
$19$	−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
$21$	1.47393	+	0.909692i	0.321637	+	0.198511i
$22$	−0.490813			−0.104642
$23$	5.27970			1.10089			0.550447	−	0.834870i	$-0.314457\pi$
$23$	5.27970			1.10089			0.550447	+	0.834870i	$0.314457\pi$
$24$	−0.909692	+	1.47393i	−0.185690	+	0.300864i
$25$		−	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	$0.462726\pi$
$29$			10.6966i			1.98630i	−0.116833	+	0.993152i	$0.537274\pi$
$30$	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
$33$	−0.446489	+	0.723423i	−0.0777237	+	0.125932i
$34$	−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
$39$	5.40790	−	3.12324i	0.865957	−	0.500119i
$40$	0.790633			0.125010
$41$	7.31477	+	7.31477i	1.14237	+	1.14237i	0.988015	+	0.154360i	$0.0493317\pi$
$41$	7.31477	+	7.31477i	1.14237	+	1.14237i	0.154360	+	0.988015i	$0.450668\pi$
$42$	−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
$45$	2.25110	+	0.747308i	0.335574	+	0.111402i
$46$	−3.73331	−	3.73331i	−0.550447	−	0.550447i
$47$	2.49319	−	2.49319i	0.363669	−	0.363669i	−0.501493	−	0.865162i	$-0.667216\pi$
$47$	2.49319	−	2.49319i	0.363669	−	0.363669i	0.865162	+	0.501493i	$0.167216\pi$
$48$	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	$-0.689290\pi$
$53$		−	12.0607i		−	1.65667i	0.560236	−	0.828333i	$-0.310710\pi$
$54$	5.17600	+	0.457147i	0.704365	+	0.0622098i
$55$	0.388054			0.0523251
$56$	−1.00000			−0.133631
$57$	4.97243	−	8.05657i	0.658614	−	1.06712i
$58$	7.56362	−	7.56362i	0.993152	−	0.993152i
$59$	−3.41247	+	3.41247i	−0.444266	+	0.444266i	−0.893443	−	0.449177i	$-0.851717\pi$
$59$	−3.41247	+	3.41247i	−0.444266	+	0.444266i	0.449177	+	0.893443i	$0.351717\pi$
$60$	0.719233	−	1.16534i	0.0928525	−	0.150444i
$61$	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
$63$	−2.84721	−	0.945201i	−0.358715	−	0.119084i
$64$		−	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	$0.00265405\pi$
$71$	8.49611	+	8.49611i	1.00830	+	1.00830i	0.00833786	+	0.999965i	$0.497346\pi$
$72$	0.945201	−	2.84721i	0.111393	−	0.335547i
$73$	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
$78$	−6.03243	−	1.61549i	−0.683038	−	0.182919i
$79$	−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	0.269933	−	0.962879i	$-0.412998\pi$
$83$	−6.31304	−	6.31304i	−0.692946	−	0.692946i	−0.962879	+	0.269933i	$0.912998\pi$
$84$	−0.909692	+	1.47393i	−0.0992555	+	0.160819i
$85$	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	$0.620757\pi$
$89$	−12.2569	+	12.2569i	−1.29923	+	1.29923i	−0.928898	+	0.370335i	$0.879243\pi$
$90$	−1.06334	−	2.12019i	−0.112086	−	0.223488i
$91$	3.17432	+	1.70989i	0.332759	+	0.179245i
$92$			5.27970i			0.550447i
$93$	3.18705	−	5.16382i	0.330482	−	0.535463i
$94$	−3.52590			−0.363669
$95$	−4.32165			−0.443392
$96$	−1.47393	−	0.909692i	−0.150432	−	0.0928450i
$97$	−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
$99$	0.463917	−	1.39745i	0.0466254	−	0.140449i
$100$	4.37490			0.437490
$101$	−3.42487			−0.340787			−0.170393	−	0.985376i	$-0.554504\pi$
$101$	−3.42487			−0.340787			−0.170393	+	0.985376i	$0.554504\pi$
$102$	6.63329	+	4.09399i	0.656794	+	0.405366i
$103$		−	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	$-0.920918\pi$
$107$		−	5.08715i		−	0.491794i	0.969296	−	0.245897i	$-0.0790824\pi$
$108$	−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
$111$	−14.4267	−	8.90400i	−1.36932	−	0.845130i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$		−	2.88604i		−	0.271496i	−0.990743	−	0.135748i	$-0.956656\pi$
$113$		−	2.88604i		−	0.271496i	0.990743	−	0.135748i	$-0.0433438\pi$
$114$	−9.21290	+	2.18082i	−0.862867	+	0.204252i
$115$	2.95168	+	2.95168i	0.275246	+	0.275246i
$116$	−10.6966			−0.993152
$117$	−7.86877	+	7.42176i	−0.727468	+	0.686142i
$118$	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
$123$	−15.2473	−	9.41044i	−1.37480	−	0.848511i
$124$	−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	$0.110206\pi$
$131$			7.76803i			0.678696i	−0.940661	+	0.339348i	$0.889794\pi$
$132$	−0.723423	−	0.446489i	−0.0629659	−	0.0388619i
$133$	5.46606			0.473967
$134$	3.44271			0.297405
$135$	−4.09232	−	0.361436i	−0.352211	−	0.0311074i
$136$	3.18228	−	3.18228i	0.272878	−	0.272878i
$137$	2.35653	−	2.35653i	0.201332	−	0.201332i	−0.599239	−	0.800570i	$-0.704530\pi$
$137$	2.35653	−	2.35653i	0.201332	−	0.201332i	0.800570	+	0.599239i	$0.204530\pi$
$138$	7.78190	+	4.80290i	0.662439	+	0.408850i
$139$	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
$141$	−3.20748	+	5.19692i	−0.270119	+	0.437660i
$142$		−	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	0.370819	−	0.928705i	$-0.379077\pi$
$149$	−6.80987	−	6.80987i	−0.557887	−	0.557887i	−0.928705	+	0.370819i	$0.879077\pi$
$150$	3.97981	−	6.44828i	0.324950	−	0.526500i
$151$	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
$156$	3.12324	+	5.40790i	0.250060	+	0.432978i
$157$	−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
$162$	−8.90640	+	1.29459i	−0.699753	+	0.101712i
$163$	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	−0.796863	−	0.604160i	$-0.793509\pi$
$167$	−2.49027	+	2.49027i	−0.192703	+	0.192703i	0.604160	+	0.796863i	$0.293509\pi$
$168$	1.68547	−	0.398975i	0.130037	−	0.0307816i
$169$	10.8554	−	7.15258i	0.835034	−	0.550199i
$170$		−	3.55818i		−	0.272900i
$171$	−5.16653	+	15.5630i	−0.395094	+	1.19013i
$172$	−7.24514			−0.552437
$173$	13.1775			1.00187			0.500934	−	0.865486i	$-0.332990\pi$
$173$	13.1775			1.00187			0.500934	+	0.865486i	$0.332990\pi$
$174$	−9.73058	+	15.7660i	−0.737673	+	1.19521i
$175$	−3.09352	+	3.09352i	−0.233848	+	0.233848i
$176$	−0.347057	+	0.347057i	−0.0261604	+	0.0261604i
$177$	4.39013	−	7.11311i	0.329983	−	0.534654i
$178$	17.3339			1.29923
$179$	13.9967			1.04616			0.523081	−	0.852283i	$-0.324783\pi$
$179$	13.9967			1.04616			0.523081	+	0.852283i	$0.324783\pi$
$180$	−0.747308	+	2.25110i	−0.0557010	+	0.167787i
$181$		−	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
$189$	5.17600	+	0.457147i	0.376499	+	0.0332525i
$190$	3.05587	+	3.05587i	0.221696	+	0.221696i
$191$		−	26.9246i		−	1.94820i	−0.226120	−	0.974099i	$-0.572604\pi$
$191$		−	26.9246i		−	1.94820i	0.226120	−	0.974099i	$-0.427396\pi$
$192$	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
$195$	4.76944	+	1.27726i	0.341547	+	0.0914668i
$196$	−1.00000			−0.0714286
$197$	15.8927	+	15.8927i	1.13231	+	1.13231i	0.989792	+	0.142517i	$0.0455196\pi$
$197$	15.8927	+	15.8927i	1.13231	+	1.13231i	0.142517	+	0.989792i	$0.454480\pi$
$198$	−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
$201$	3.13181	−	5.07431i	0.220901	−	0.357914i
$202$	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
$210$	0.719233	−	1.16534i	0.0496318	−	0.0804158i
$211$	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
$213$	−17.7097	−	10.9302i	−1.21345	−	0.748927i
$214$	−3.59716	+	3.59716i	−0.245897	+	0.245897i
$215$	−4.05049	+	4.05049i	−0.276241	+	0.276241i
$216$	−0.457147	+	5.17600i	−0.0311049	+	0.352182i
$217$	3.50344			0.237829
$218$	−8.38035			−0.567589
$219$	−12.3657	−	7.63197i	−0.835596	−	0.515721i
$220$			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	$-0.942654\pi$
$227$	−17.5224	−	17.5224i	−1.16300	−	1.16300i	−0.179185	−	0.983815i	$-0.557346\pi$
$228$	8.05657	+	4.97243i	0.533560	+	0.329307i
$229$	−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	$-0.550266\pi$
$233$	−4.80094			−0.314520			−0.157260	+	0.987557i	$0.550266\pi$
$234$	10.8120	+	0.316086i	0.706805	+	0.0206632i
$235$	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	0.932879	−	0.360190i	$-0.117288\pi$
$239$	8.85356	+	8.85356i	0.572689	+	0.572689i	−0.360190	+	0.932879i	$0.617288\pi$
$240$	1.16534	+	0.719233i	0.0752221	+	0.0464263i
$241$	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
$249$	13.1592	+	8.12171i	0.833930	+	0.514693i
$250$	−7.41211			−0.468783
$251$	13.6883			0.863998			0.431999	−	0.901874i	$-0.357808\pi$
$251$	13.6883			0.863998			0.431999	+	0.901874i	$0.357808\pi$
$252$	0.945201	−	2.84721i	0.0595421	−	0.179357i
$253$	1.83236	−	1.83236i	0.115200	−	0.115200i
$254$	−14.9231	+	14.9231i	−0.936356	+	0.936356i
$255$	−5.24450	−	3.23685i	−0.328423	−	0.202699i
$256$	1.00000			0.0625000
$257$	18.2988			1.14145			0.570723	−	0.821142i	$-0.306663\pi$
$257$	18.2988			1.14145			0.570723	+	0.821142i	$0.306663\pi$
$258$	−6.59085	+	10.6788i	−0.410328	+	0.664834i
$259$		−	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	$0.170111\pi$
$263$			16.5203i			1.01868i	−0.860564	+	0.509342i	$0.829889\pi$
$264$	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
$267$	15.7685	−	25.5490i	0.965019	−	1.56357i
$268$	−2.43437	−	2.43437i	−0.148703	−	0.148703i
$269$		−	11.7448i		−	0.716091i	−0.933704	−	0.358046i	$-0.883443\pi$
$269$		−	11.7448i		−	0.716091i	0.933704	−	0.358046i	$-0.116557\pi$
$270$	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
$273$	−6.03243	−	1.61549i	−0.365099	−	0.0977741i
$274$	−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
$279$	−3.31146	+	9.97503i	−0.198252	+	0.597190i
$280$	−0.559062	−	0.559062i	−0.0334104	−	0.0334104i
$281$	2.85196	−	2.85196i	0.170134	−	0.170134i	−0.616904	−	0.787038i	$-0.711613\pi$
$281$	2.85196	−	2.85196i	0.170134	−	0.170134i	0.787038	+	0.616904i	$0.211613\pi$
$282$	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
$288$	2.84721	+	0.945201i	0.167773	+	0.0556965i
$289$	3.25377			0.191398
$290$	8.45707			0.496616
$291$	1.11585	−	1.80796i	0.0654126	−	0.105985i
$292$	−5.93236	+	5.93236i	−0.347165	+	0.347165i
$293$	−13.4365	+	13.4365i	−0.784968	+	0.784968i	−0.980665	−	0.195696i	$-0.937303\pi$
$293$	−13.4365	+	13.4365i	−0.784968	+	0.784968i	0.195696	+	0.980665i	$0.437303\pi$
$294$	−0.909692	+	1.47393i	−0.0530543	+	0.0859612i
$295$	−3.81556			−0.222151
$296$	9.78793			0.568912
$297$	−0.224374	+	2.54045i	−0.0130195	+	0.147412i
$298$			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
$306$	−12.8136	−	4.25380i	−0.732506	−	0.243174i
$307$	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	$-0.107012\pi$
$311$	33.2959			1.88804			0.944019	+	0.329890i	$0.107012\pi$
$312$	1.61549	−	6.03243i	0.0914593	−	0.341519i
$313$	−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	0.642110	−	0.766613i	$-0.278059\pi$
$317$	−2.21672	−	2.21672i	−0.124503	−	0.124503i	−0.766613	+	0.642110i	$0.778059\pi$
$318$	10.9715	−	17.7766i	0.615253	−	0.996862i
$319$	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
$327$	−7.62354	+	12.3520i	−0.421583	+	0.683069i
$328$	10.3446			0.571187
$329$	−3.52590			−0.194389
$330$	0.571963	+	0.353009i	0.0314855	+	0.0194325i
$331$	−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
$333$	27.8683	+	9.25156i	1.52717	+	0.506983i
$334$	3.52177			0.192703
$335$	−2.72192			−0.148715
$336$	−1.47393	−	0.909692i	−0.0804093	−	0.0496277i
$337$			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
$345$	−6.15263	−	3.79734i	−0.331246	−	0.204442i
$346$	−9.31790	−	9.31790i	−0.500934	−	0.500934i
$347$			4.91439i			0.263819i	0.991262	+	0.131909i	$0.0421108\pi$
$347$			4.91439i			0.263819i	−0.991262	+	0.131909i	$0.957889\pi$
$348$	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
$351$	10.3015	−	15.6486i	0.549854	−	0.835261i
$352$	0.490813			0.0261604
$353$	−4.61015	−	4.61015i	−0.245374	−	0.245374i	0.573695	−	0.819069i	$-0.305509\pi$
$353$	−4.61015	−	4.61015i	−0.245374	−	0.245374i	−0.819069	+	0.573695i	$0.805509\pi$
$354$	−8.13402	+	1.92544i	−0.432318	+	0.102336i
$355$			9.49971i			0.504192i
$356$	−12.2569	−	12.2569i	−0.649617	−	0.649617i
$357$	6.63329	+	4.09399i	0.351071	+	0.216677i
$358$	−9.89715	−	9.89715i	−0.523081	−	0.523081i
$359$	−8.91675	+	8.91675i	−0.470608	+	0.470608i	−0.902111	−	0.431503i	$-0.857983\pi$
$359$	−8.91675	+	8.91675i	−0.470608	+	0.470608i	0.431503	+	0.902111i	$0.357983\pi$
$360$	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
$366$	9.46946	+	5.84445i	0.494976	+	0.305494i
$367$	−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
$369$	29.4534	+	9.77777i	1.53328	+	0.509010i
$370$	5.47206	−	5.47206i	0.284479	−	0.284479i
$371$	−8.52821	+	8.52821i	−0.442762	+	0.442762i
$372$	5.16382	+	3.18705i	0.267732	+	0.165241i
$373$	−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
$375$	−6.74273	+	10.9249i	−0.348193	+	0.564160i
$376$		−	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	0.489431	−	0.872042i	$-0.337204\pi$
$383$	−7.48783	−	7.48783i	−0.382610	−	0.382610i	−0.872042	+	0.489431i	$0.837204\pi$
$384$	0.909692	−	1.47393i	0.0464225	−	0.0752160i
$385$	−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	$-0.443159\pi$
$389$	7.00656			0.355247			0.177623	+	0.984099i	$0.443159\pi$
$390$	−2.46934	−	4.27566i	−0.125040	−	0.216507i
$391$	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
$396$	1.39745	+	0.463917i	0.0702244	+	0.0233127i
$397$	−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	$-0.452676\pi$
$401$	22.7703	−	22.7703i	1.13709	−	1.13709i	0.988969	−	0.148126i	$-0.0473240\pi$
$402$	−5.80260	+	1.37356i	−0.289407	+	0.0685067i
$403$	5.99049	−	11.1210i	0.298407	−	0.553978i
$404$		−	3.42487i		−	0.170393i
$405$	7.04170	−	1.02354i	0.349905	−	0.0508603i
$406$	−10.6966			−0.530862
$407$	4.80405			0.238128
$408$	−4.09399	+	6.63329i	−0.202683	+	0.328397i
$409$	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
$411$	−3.03167	+	4.91206i	−0.149541	+	0.242294i
$412$	0.0883069			0.00435057
$413$	4.82596			0.237470
$414$	−15.0324	−	4.99038i	−0.738803	−	0.245264i
$415$		−	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	$-0.929425\pi$
$419$		−	9.00273i		−	0.439812i	0.975521	−	0.219906i	$-0.0705751\pi$
$420$	−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
$423$	3.33269	−	10.0390i	0.162041	−	0.488112i
$424$	−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
$429$	0.792906	−	2.96080i	0.0382819	−	0.142949i
$430$	5.72825			0.276241
$431$	−11.7362	−	11.7362i	−0.565312	−	0.565312i	0.365500	−	0.930811i	$-0.380898\pi$
$431$	−11.7362	−	11.7362i	−0.565312	−	0.565312i	−0.930811	+	0.365500i	$0.880898\pi$
$432$	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
$435$	7.69332	−	12.4651i	0.368867	−	0.597656i
$436$	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	$0.0720713\pi$
$443$			9.44990i			0.448978i	−0.974477	+	0.224489i	$0.927929\pi$
$444$	8.90400	−	14.4267i	0.422565	−	0.684661i
$445$	−13.7048			−0.649669
$446$	10.6028			0.502055
$447$	14.1948	+	8.76089i	0.671392	+	0.414376i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−22.9219	+	22.9219i	−1.08175	+	1.08175i	−0.0854053	+	0.996346i	$0.527219\pi$
$449$	−22.9219	+	22.9219i	−1.08175	+	1.08175i	−0.996346	+	0.0854053i	$0.972781\pi$
$450$	−4.13516	+	12.4562i	−0.194933	+	0.587193i
$451$	5.07729			0.239080
$452$	2.88604			0.135748
$453$	−2.54171	−	1.56872i	−0.119420	−	0.0737047i
$454$			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	0.188007	−	0.982168i	$-0.439797\pi$
$461$	−17.0514	−	17.0514i	−0.794161	−	0.794161i	−0.982168	+	0.188007i	$0.939797\pi$
$462$	−0.723423	−	0.446489i	−0.0336567	−	0.0207725i
$463$	−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	$-0.353709\pi$
$467$	19.1716			0.887156			0.443578	+	0.896236i	$0.353709\pi$
$468$	−7.42176	−	7.86877i	−0.343071	−	0.363734i
$469$	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
$474$	−19.4905	−	12.0293i	−0.895229	−	0.552526i
$475$	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	−0.999745	−	0.0225708i	$-0.992815\pi$
$479$	−21.3865	+	21.3865i	−0.977174	+	0.977174i	0.0225708	+	0.999745i	$0.492815\pi$
$480$	−0.315443	−	1.33259i	−0.0143979	−	0.0608242i
$481$	−31.0700	−	16.7362i	−1.41667	−	0.763107i
$482$		−	12.4375i		−	0.566515i
$483$	7.78190	+	4.80290i	0.354089	+	0.218540i
$484$	−10.7591			−0.489050
$485$	−0.969814			−0.0440370
$486$	14.4950	−	5.73542i	0.657506	−	0.260164i
$487$	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
$489$	−7.25073	−	4.47507i	−0.327889	−	0.202370i
$490$	0.790633			0.0357172
$491$	10.3827			0.468565			0.234283	−	0.972169i	$-0.424726\pi$
$491$	10.3827			0.468565			0.234283	+	0.972169i	$0.424726\pi$
$492$	9.41044	−	15.2473i	0.424255	−	0.687399i
$493$			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
$501$	3.20373	−	5.19084i	0.143132	−	0.231910i
$502$	−9.67910	−	9.67910i	−0.431999	−	0.431999i
$503$		−	0.584892i		−	0.0260790i	−0.999915	−	0.0130395i	$-0.995849\pi$
$503$		−	0.584892i		−	0.0260790i	0.999915	−	0.0130395i	$-0.00415073\pi$
$504$	−2.68164	+	1.34492i	−0.119450	+	0.0599076i
$505$	−1.91471	−	1.91471i	−0.0852037	−	0.0852037i
$506$	−2.59135			−0.115200
$507$	−15.4429	+	16.3865i	−0.685841	+	0.727751i
$508$	21.1044			0.936356
$509$	−14.6995	−	14.6995i	−0.651544	−	0.651544i	0.301821	−	0.953365i	$-0.402406\pi$
$509$	−14.6995	−	14.6995i	−0.651544	−	0.651544i	−0.953365	+	0.301821i	$0.902406\pi$
$510$	1.41962	+	5.99722i	0.0628620	+	0.265561i
$511$		−	8.38963i		−	0.371135i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.49879	−	28.2923i	0.110324	−	1.24914i
$514$	−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	$-0.983218\pi$
$521$		−	2.40567i		−	0.105394i	0.998611	−	0.0526972i	$-0.0167818\pi$
$522$	10.1104	−	30.4554i	0.442521	−	1.33299i
$523$	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
$525$	3.97981	−	6.44828i	0.173693	−	0.281426i
$526$	11.6816	−	11.6816i	0.509342	−	0.509342i
$527$	−11.1489	+	11.1489i	−0.485655	+	0.485655i
$528$	0.446489	−	0.723423i	0.0194309	−	0.0314830i
$529$	4.87527			0.211968
$530$	−9.53560			−0.414200
$531$	−4.56150	+	13.7405i	−0.197952	+	0.596287i
$532$			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
$540$	0.361436	−	4.09232i	0.0155537	−	0.176105i
$541$	−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
$546$	3.12324	+	5.40790i	0.133662	+	0.231437i
$547$	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
$552$	−4.80290	+	7.78190i	−0.204425	+	0.331220i
$553$	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	−0.782610	−	0.622512i	$-0.786112\pi$
$557$	−3.77844	+	3.77844i	−0.160098	+	0.160098i	0.622512	+	0.782610i	$0.286112\pi$
$558$	9.39497	−	4.71186i	0.397721	−	0.199469i
$559$	−7.50241	−	25.0222i	−0.317318	−	1.05833i
$560$			0.790633i			0.0334104i
$561$	−2.00939	+	3.25571i	−0.0848364	+	0.137456i
$562$	−4.03328			−0.170134
$563$	37.3621			1.57462			0.787312	−	0.616555i	$-0.211472\pi$
$563$	37.3621			1.57462			0.787312	+	0.616555i	$0.211472\pi$
$564$	−5.19692	−	3.20748i	−0.218830	−	0.135059i
$565$	1.61348	−	1.61348i	0.0678796	−	0.0678796i
$566$	−10.7904	+	10.7904i	−0.453553	+	0.453553i
$567$	−8.90640	+	1.29459i	−0.374034	+	0.0543675i
$568$	12.0153			0.504152
$569$	−2.27928			−0.0955524			−0.0477762	−	0.998858i	$-0.515213\pi$
$569$	−2.27928			−0.0955524			−0.0477762	+	0.998858i	$0.515213\pi$
$570$	−6.36980	−	3.93137i	−0.266801	−	0.164667i
$571$			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
$579$	31.6262	+	19.5193i	1.31434	+	0.811196i
$580$	−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
$585$	−8.54836	−	0.249908i	−0.353431	−	0.0103324i
$586$	19.0021			0.784968
$587$	−11.1009	−	11.1009i	−0.458182	−	0.458182i	0.439877	−	0.898058i	$-0.355022\pi$
$587$	−11.1009	−	11.1009i	−0.458182	−	0.458182i	−0.898058	+	0.439877i	$0.855022\pi$
$588$	1.68547	−	0.398975i	0.0695077	−	0.0164534i
$589$		−	19.1500i		−	0.789063i
$590$	2.69801	+	2.69801i	0.111075	+	0.111075i
$591$	−33.1275	−	20.4460i	−1.36269	−	0.841034i
$592$	−6.92111	−	6.92111i	−0.284456	−	0.284456i
$593$	7.19619	−	7.19619i	0.295512	−	0.295512i	−0.543741	−	0.839253i	$-0.682993\pi$
$593$	7.19619	−	7.19619i	0.295512	−	0.295512i	0.839253	+	0.543741i	$0.182993\pi$
$594$	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	$-0.979191\pi$
$599$		−	3.19761i		−	0.130651i	0.997864	−	0.0653253i	$-0.0208085\pi$
$600$	6.44828	+	3.97981i	0.263250	+	0.162475i
$601$	−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
$603$	−3.25406	+	9.80212i	−0.132515	+	0.399173i
$604$	−1.21937	+	1.21937i	−0.0496154	+	0.0496154i
$605$	−6.01501	+	6.01501i	−0.244545	+	0.244545i
$606$	−5.04800	−	3.11557i	−0.205061	−	0.126561i
$607$	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
$609$	−9.73058	+	15.7660i	−0.394303	+	0.638869i
$610$		−	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	0.998695	−	0.0510654i	$-0.0162617\pi$
$617$	23.5386	+	23.5386i	0.947630	+	0.947630i	−0.0510654	+	0.998695i	$0.516262\pi$
$618$	0.0803321	−	0.130158i	0.00323143	−	0.00523572i
$619$	−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
$624$	−5.40790	+	3.12324i	−0.216489	+	0.125030i
$625$	−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
$630$	−0.747308	+	2.25110i	−0.0297734	+	0.0896859i
$631$	−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
$639$	34.2101	+	11.3569i	1.35333	+	0.449272i
$640$	−0.790633			−0.0312525
$641$	−22.4925			−0.888400			−0.444200	−	0.895928i	$-0.646512\pi$
$641$	−22.4925			−0.888400			−0.444200	+	0.895928i	$0.646512\pi$
$642$	4.62774	−	7.49809i	0.182642	−	0.295926i
$643$	−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
$645$	5.21094	−	8.44303i	0.205181	−	0.332444i
$646$	24.5996			0.967857
$647$	4.76406			0.187295			0.0936473	−	0.995605i	$-0.470147\pi$
$647$	4.76406			0.187295			0.0936473	+	0.995605i	$0.470147\pi$
$648$	−1.29459	−	8.90640i	−0.0508561	−	0.349877i
$649$			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	$-0.912206\pi$
$653$		−	13.9182i		−	0.544660i	0.962204	−	0.272330i	$-0.0877942\pi$
$654$	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
$657$	23.8870	+	7.92988i	0.931921	+	0.309374i
$658$	2.49319	+	2.49319i	0.0971946	+	0.0971946i
$659$			22.7816i			0.887447i	0.896164	+	0.443724i	$0.146343\pi$
$659$			22.7816i			0.887447i	−0.896164	+	0.443724i	$0.853657\pi$
$660$	−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
$663$	24.3378	−	14.0559i	0.945202	−	0.545886i
$664$	−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
$669$	9.64523	−	15.6277i	0.372906	−	0.604201i
$670$	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	$-0.735520\pi$
$677$		−	38.4320i		−	1.47706i	0.674219	−	0.738531i	$-0.264480\pi$
$678$	2.62541	−	4.25382i	0.100828	−	0.163367i
$679$	1.22663			0.0470737
$680$	3.55818			0.136450
$681$	36.5244	+	22.5425i	1.39962	+	0.863830i
$682$	1.21590	−	1.21590i	0.0465591	−	0.0465591i
$683$	−3.33543	+	3.33543i	−0.127627	+	0.127627i	−0.768035	−	0.640408i	$-0.778765\pi$
$683$	−3.33543	+	3.33543i	−0.127627	+	0.127627i	0.640408	+	0.768035i	$0.278765\pi$
$684$	−15.5630	−	5.16653i	−0.595067	−	0.197547i
$685$	2.63489			0.100674
$686$	−1.00000			−0.0381802
$687$	28.9201	+	17.8492i	1.10337	+	0.680988i
$688$		−	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
$696$	−15.7660	−	9.73058i	−0.597607	−	0.368837i
$697$	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	$-0.430441\pi$
$701$	11.4796			0.433579			0.216790	+	0.976218i	$0.430441\pi$
$702$	−18.3495	+	3.78097i	−0.692557	+	0.142704i
$703$	−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
$708$	7.11311	+	4.39013i	0.267327	+	0.164991i
$709$	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
$717$	−18.4548	−	11.3901i	−0.689207	−	0.425371i
$718$	12.6102			0.470608
$719$	4.45696			0.166217			0.0831084	−	0.996541i	$-0.473515\pi$
$719$	4.45696			0.166217			0.0831084	+	0.996541i	$0.473515\pi$
$720$	−2.25110	−	0.747308i	−0.0838935	−	0.0278505i
$721$	−0.0624424	+	0.0624424i	−0.00232548	+	0.00232548i
$722$	−7.69177	+	7.69177i	−0.286258	+	0.286258i
$723$	−18.3320	−	11.3143i	−0.681776	−	0.420784i
$724$	3.47621			0.129192
$725$	46.7964			1.73797
$726$	−9.78747	+	15.8581i	−0.363247	+	0.588550i
$727$		−	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
$735$	0.719233	−	1.16534i	0.0265293	−	0.0429841i
$736$	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
$741$	−8.83039	+	32.9736i	−0.324392	+	1.21132i
$742$	12.0607			0.442762
$743$	13.1510	+	13.1510i	0.482465	+	0.482465i	0.905918	−	0.423453i	$-0.139182\pi$
$743$	13.1510	+	13.1510i	0.482465	+	0.482465i	−0.423453	+	0.905918i	$0.639182\pi$
$744$	−1.39779	−	5.90496i	−0.0512453	−	0.216486i
$745$		−	7.61429i		−	0.278966i
$746$	19.5183	+	19.5183i	0.714614	+	0.714614i
$747$	−25.4198	−	8.43874i	−0.930063	−	0.308757i
$748$	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
$756$	−0.457147	+	5.17600i	−0.0166263	+	0.188249i
$757$	−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
$759$	−2.35733	+	3.81946i	−0.0855656	+	0.138638i
$760$	−3.05587	+	3.05587i	−0.110848	+	0.110848i
$761$	26.2245	−	26.2245i	0.950637	−	0.950637i	−0.0482010	−	0.998838i	$-0.515349\pi$
$761$	26.2245	−	26.2245i	0.950637	−	0.950637i	0.998838	+	0.0482010i	$0.0153488\pi$
$762$	19.1985	−	31.1063i	0.695488	−	1.12686i
$763$	−8.38035			−0.303389
$764$	26.9246			0.974099
$765$	10.1309	+	3.36320i	0.366283	+	0.121597i
$766$			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	0.997956	−	0.0639117i	$-0.0203576\pi$
$773$	25.9691	+	25.9691i	0.934044	+	0.934044i	−0.0639117	+	0.997956i	$0.520358\pi$
$774$	6.84812	−	20.6284i	0.246151	−	0.741474i
$775$	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
$780$	−1.27726	+	4.76944i	−0.0457334	+	0.170773i
$781$	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
$786$	−7.06651	+	11.4495i	−0.252054	+	0.408390i
$787$	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
$795$	−8.67445	+	14.0548i	−0.307651	+	0.498472i
$796$	−4.30765			−0.152681
$797$	24.6190			0.872049			0.436024	−	0.899935i	$-0.356386\pi$
$797$	24.6190			0.872049			0.436024	+	0.899935i	$0.356386\pi$
$798$	8.05657	+	4.97243i	0.285200	+	0.176022i
$799$	11.2204	−	11.2204i	0.396949	−	0.396949i
$800$	3.09352	−	3.09352i	0.109372	−	0.109372i
$801$	−16.3841	+	49.3533i	−0.578902	+	1.74381i
$802$	−32.2021			−1.13709
$803$	4.11774			0.145312
$804$	5.07431	+	3.13181i	0.178957	+	0.110450i
$805$		−	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	$0.159985\pi$
$809$			27.4026i			0.963423i	−0.876330	+	0.481712i	$0.840015\pi$
$810$	−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
$813$	−20.3401	−	12.5537i	−0.713358	−	0.440277i
$814$	−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
$819$	10.8120	+	0.316086i	0.377803	+	0.0110449i
$820$	−8.17882			−0.285617
$821$	19.3107	+	19.3107i	0.673947	+	0.673947i	0.958624	−	0.284676i	$-0.0918861\pi$
$821$	19.3107	+	19.3107i	0.673947	+	0.673947i	−0.284676	+	0.958624i	$0.591886\pi$
$822$	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
$825$	3.16490	+	1.95334i	0.110188	+	0.0680067i
$826$	−3.41247	−	3.41247i	−0.118735	−	0.118735i
$827$	8.17009	−	8.17009i	0.284102	−	0.284102i	−0.550640	−	0.834743i	$-0.685616\pi$
$827$	8.17009	−	8.17009i	0.284102	−	0.284102i	0.834743	+	0.550640i	$0.185616\pi$
$828$	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
$834$	2.26830	+	1.39997i	0.0785447	+	0.0484769i
$835$	−2.78443			−0.0963593
$836$	−2.68282			−0.0927871
$837$	1.60159	−	18.1338i	0.0553590	−	0.626797i
$838$	−6.36589	+	6.36589i	−0.219906	+	0.219906i
$839$	21.3877	−	21.3877i	0.738387	−	0.738387i	−0.233879	−	0.972266i	$-0.575142\pi$
$839$	21.3877	−	21.3877i	0.738387	−	0.738387i	0.972266	+	0.233879i	$0.0751420\pi$
$840$	1.16534	+	0.719233i	0.0402079	+	0.0248159i
$841$	−85.4166			−2.94540
$842$	2.69953			0.0930321
$843$	−3.66904	+	5.94476i	−0.126369	+	0.204749i
$844$			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
$852$	10.9302	−	17.7097i	0.374464	−	0.606724i
$853$	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	$-0.425253\pi$
$857$	13.6228			0.465345			0.232672	+	0.972555i	$0.425253\pi$
$858$	−2.65427	+	1.53293i	−0.0906152	+	0.0523334i
$859$	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	$0.0366974\pi$
$863$	32.5612	+	32.5612i	1.10839	+	1.10839i	0.115033	+	0.993362i	$0.463303\pi$
$864$	−5.17600	−	0.457147i	−0.176091	−	0.0155525i
$865$	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
$873$	−1.15941	+	3.49247i	−0.0392401	+	0.118202i
$874$	28.8592			0.976176
$875$	−7.41211			−0.250575
$876$	7.63197	−	12.3657i	0.257860	−	0.417798i
$877$	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
$879$	17.2860	−	28.0077i	0.583043	−	0.944675i
$880$	−0.388054			−0.0130813
$881$	−36.4849			−1.22921			−0.614604	−	0.788836i	$-0.710684\pi$
$881$	−36.4849			−1.22921			−0.614604	+	0.788836i	$0.710684\pi$
$882$	0.945201	−	2.84721i	0.0318266	−	0.0958705i
$883$			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	$0.209608\pi$
$887$			36.4498i			1.22387i	−0.790910	+	0.611933i	$0.790392\pi$
$888$	−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
$891$	−0.635400	−	4.37138i	−0.0212867	−	0.146447i
$892$	−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
$897$	28.5521	−	16.4898i	0.953327	−	0.550578i
$898$	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
$903$	−6.59085	+	10.6788i	−0.219330	+	0.355369i
$904$	−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	$-0.926725\pi$
$911$		−	13.7738i		−	0.456347i	0.973620	−	0.228173i	$-0.0732753\pi$
$912$	−4.97243	+	8.05657i	−0.164654	+	0.266780i
$913$	−4.38197			−0.145022
$914$	3.85384			0.127474
$915$	−7.48687	−	4.62081i	−0.247508	−	0.152759i
$916$	13.8742	−	13.8742i	0.458417	−	0.458417i
$917$	5.49282	−	5.49282i	0.181389	−	0.181389i
$918$	23.2942	+	2.05735i	0.768823	+	0.0679027i
$919$	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
$921$	−29.4933	−	18.2030i	−0.971838	−	0.599808i
$922$			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	0.391899	−	0.920008i	$-0.371818\pi$
$929$	−16.0965	−	16.0965i	−0.528110	−	0.528110i	−0.920008	+	0.391899i	$0.871818\pi$
$930$	−4.08269	−	2.51979i	−0.133877	−	0.0826272i
$931$	−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
$936$	−0.316086	+	10.8120i	−0.0103316	+	0.353402i
$937$	−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	0.252911	−	0.967490i	$-0.418612\pi$
$941$	−21.9202	−	21.9202i	−0.714579	−	0.714579i	−0.967490	+	0.252911i	$0.918612\pi$
$942$	−8.30954	−	5.12856i	−0.270739	−	0.167097i
$943$	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	−0.100328	−	0.994954i	$-0.531989\pi$
$947$	27.5307	−	27.5307i	0.894627	−	0.894627i	0.994954	+	0.100328i	$0.0319891\pi$
$948$	5.27585	+	22.2879i	0.171352	+	0.723877i
$949$	−26.6313	−	14.3453i	−0.864490	−	0.465668i
$950$		−	23.9135i		−	0.775855i
$951$	4.62063	+	2.85180i	0.149834	+	0.0924761i
$952$	−4.50042			−0.145859
$953$	1.66813			0.0540361			0.0270181	−	0.999635i	$-0.491399\pi$
$953$	1.66813			0.0540361			0.0270181	+	0.999635i	$0.491399\pi$
$954$	−11.3998	+	34.3393i	−0.369082	+	1.11178i
$955$	15.0526	−	15.0526i	0.487089	−	0.487089i
$956$	−8.85356	+	8.85356i	−0.286345	+	0.286345i
$957$	−7.73815	−	4.77590i	−0.250139	−	0.154383i
$958$	30.2451			0.977174
$959$	−3.33263			−0.107616
$960$	−0.719233	+	1.16534i	−0.0232131	+	0.0376111i
$961$			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
$969$	22.3780	−	36.2580i	0.718885	−	1.16477i
$970$	0.685762	+	0.685762i	0.0220185	+	0.0220185i
$971$		−	1.88008i		−	0.0603345i	−0.999545	−	0.0301672i	$-0.990396\pi$
$971$		−	1.88008i		−	0.0603345i	0.999545	−	0.0301672i	$-0.00960399\pi$
$972$	−14.3051	−	6.19396i	−0.458835	−	0.198671i
$973$	−1.08820	−	1.08820i	−0.0348861	−	0.0348861i
$974$	−34.0479			−1.09096
$975$	−13.6639	−	23.6590i	−0.437594	−	0.757694i
$976$	−6.42464			−0.205648
$977$	3.46359	+	3.46359i	0.110810	+	0.110810i	0.760338	−	0.649528i	$-0.225033\pi$
$977$	3.46359	+	3.46359i	0.110810	+	0.110810i	−0.649528	+	0.760338i	$0.725033\pi$
$978$	1.96269	+	8.29139i	0.0627598	+	0.265129i
$979$			8.50773i			0.271908i
$980$	−0.559062	−	0.559062i	−0.0178586	−	0.0178586i
$981$	7.92112	−	23.8606i	0.252902	−	0.761811i
$982$	−7.34168	−	7.34168i	−0.234283	−	0.234283i
$983$	−8.07529	+	8.07529i	−0.257562	+	0.257562i	−0.824062	−	0.566500i	$-0.808297\pi$
$983$	−8.07529	+	8.07529i	−0.257562	+	0.257562i	0.566500	+	0.824062i	$0.308297\pi$
$984$	−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
$990$	−1.10487	−	0.366789i	−0.0351150	−	0.0116573i
$991$	−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
$993$	28.2130	−	45.7121i	0.895313	−	1.45063i
$994$	−8.49611	+	8.49611i	−0.269480	+	0.269480i
$995$	−2.40824	+	2.40824i	−0.0763464	+	0.0763464i
$996$	−8.12171	+	13.1592i	−0.257346	+	0.416965i
$997$	−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
$999$	−50.6624	−	4.47452i	−1.60289	−	0.141568i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.68547 + 0.398975i) q^{3} +1.00000i q^{4} +(0.559062 + 0.559062i) q^{5} +(1.47393 + 0.909692i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.68164 - 1.34492i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.68547 + 0.398975i) q^{3} +1.00000i q^{4} +(0.559062 + 0.559062i) q^{5} +(1.47393 + 0.909692i) 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} +(-1.16534 - 0.719233i) q^{15} -1.00000 q^{16} +4.50042 q^{17} +(-2.84721 - 0.945201i) q^{18} +(-3.86509 + 3.86509i) q^{19} +(-0.559062 + 0.559062i) q^{20} +(1.47393 + 0.909692i) q^{21} -0.490813 q^{22} +5.27970 q^{23} +(-0.909692 + 1.47393i) 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} +(-0.446489 + 0.723423i) 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} +(5.40790 - 3.12324i) 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} +(2.25110 + 0.747308i) 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} +(5.17600 + 0.457147i) q^{54} +0.388054 q^{55} -1.00000 q^{56} +(4.97243 - 8.05657i) q^{57} +(7.56362 - 7.56362i) q^{58} +(-3.41247 + 3.41247i) q^{59} +(0.719233 - 1.16534i) q^{60} +6.42464 q^{61} +3.50344 q^{62} +(-2.84721 - 0.945201i) 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} +(0.945201 - 2.84721i) 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} +(-6.03243 - 1.61549i) 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} +(-0.909692 + 1.47393i) 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} +(3.18705 - 5.16382i) q^{93} -3.52590 q^{94} -4.32165 q^{95} +(-1.47393 - 0.909692i) q^{96} +(-0.867358 + 0.867358i) q^{97} +(0.707107 - 0.707107i) q^{98} +(0.463917 - 1.39745i) 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	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 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 - 16 * 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 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * 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 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * 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 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

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