LMFDB - Embedded newform 546.2.p.d.281.1

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			281.1
Root			$1.47393 + 0.909692i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.d.239.1

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−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	$-0.693428\pi$
$5$	0.559062	−	0.559062i	0.250020	−	0.250020i	0.820979	+	0.570959i	$0.193428\pi$
$6$	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	0.757489	−	0.652848i	$-0.226426\pi$
$11$	0.347057	+	0.347057i	0.104642	+	0.104642i	−0.652848	+	0.757489i	$0.726426\pi$
$12$	−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	0.107494	−	0.994206i	$-0.465717\pi$
$19$	−3.86509	−	3.86509i	−0.886712	−	0.886712i	−0.994206	+	0.107494i	$0.965717\pi$
$20$	−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	$-0.537274\pi$
$29$		−	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	0.448730	−	0.893667i	$-0.351877\pi$
$31$	−2.47731	−	2.47731i	−0.444938	−	0.444938i	−0.893667	+	0.448730i	$0.851877\pi$
$32$	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	0.148984	−	0.988840i	$-0.452400\pi$
$37$	6.92111	−	6.92111i	1.13782	−	1.13782i	0.988840	−	0.148984i	$-0.0476004\pi$
$38$	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	0.154360	−	0.988015i	$-0.450668\pi$
$41$	7.31477	−	7.31477i	1.14237	−	1.14237i	0.988015	−	0.154360i	$-0.0493317\pi$
$42$	−0.398975	+	1.68547i	−0.0615631	+	0.260074i
$43$		−	7.24514i		−	1.10487i	−0.833555	−	0.552437i	$-0.813698\pi$
$43$		−	7.24514i		−	1.10487i	0.833555	−	0.552437i	$-0.186302\pi$
$44$	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	0.865162	−	0.501493i	$-0.167216\pi$
$47$	2.49319	+	2.49319i	0.363669	+	0.363669i	−0.501493	+	0.865162i	$0.667216\pi$
$48$	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	$0.689290\pi$
$54$	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	0.449177	−	0.893443i	$-0.351717\pi$
$59$	−3.41247	−	3.41247i	−0.444266	−	0.444266i	−0.893443	+	0.449177i	$0.851717\pi$
$60$	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	0.542592	−	0.839997i	$-0.317443\pi$
$67$	−2.43437	−	2.43437i	−0.297405	−	0.297405i	−0.839997	+	0.542592i	$0.817443\pi$
$68$		−	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	0.00833786	−	0.999965i	$-0.497346\pi$
$71$	8.49611	−	8.49611i	1.00830	−	1.00830i	0.999965	−	0.00833786i	$-0.00265405\pi$
$72$	0.945201	+	2.84721i	0.111393	+	0.335547i
$73$	5.93236	−	5.93236i	0.694330	−	0.694330i	−0.268851	−	0.963182i	$-0.586644\pi$
$73$	5.93236	−	5.93236i	0.694330	−	0.694330i	0.963182	+	0.268851i	$0.0866440\pi$
$74$			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	−0.962879	−	0.269933i	$-0.912998\pi$
$83$	−6.31304	+	6.31304i	−0.692946	+	0.692946i	0.269933	+	0.962879i	$0.412998\pi$
$84$	−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	−0.928898	−	0.370335i	$-0.879243\pi$
$89$	−12.2569	−	12.2569i	−1.29923	−	1.29923i	−0.370335	−	0.928898i	$-0.620757\pi$
$90$	−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	0.661701	−	0.749768i	$-0.269835\pi$
$97$	−0.867358	−	0.867358i	−0.0880669	−	0.0880669i	−0.749768	+	0.661701i	$0.769835\pi$
$98$	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	$0.00138483\pi$
$103$			0.0883069i			0.00870114i	−0.999991	+	0.00435057i	$0.998615\pi$
$104$	−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	0.931452	−	0.363863i	$-0.118542\pi$
$109$	5.92580	+	5.92580i	0.567589	+	0.567589i	−0.363863	+	0.931452i	$0.618542\pi$
$110$	−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	$0.0433438\pi$
$113$			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
$117$	−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	$0.385824\pi$
$127$			21.1044i			1.87271i	−0.351053	+	0.936356i	$0.614176\pi$
$128$	−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	$-0.110206\pi$
$132$	−0.723423	+	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	0.800570	−	0.599239i	$-0.204530\pi$
$137$	2.35653	+	2.35653i	0.201332	+	0.201332i	−0.599239	+	0.800570i	$0.704530\pi$
$138$	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	−0.928705	−	0.370819i	$-0.879077\pi$
$149$	−6.80987	+	6.80987i	−0.557887	+	0.557887i	0.370819	+	0.928705i	$0.379077\pi$
$150$	3.97981	+	6.44828i	0.324950	+	0.526500i
$151$	1.21937	−	1.21937i	0.0992308	−	0.0992308i	−0.655749	−	0.754979i	$-0.727647\pi$
$151$	1.21937	−	1.21937i	0.0992308	−	0.0992308i	0.754979	+	0.655749i	$0.227647\pi$
$152$		−	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	−0.557632	−	0.830088i	$-0.688290\pi$
$163$	3.47849	−	3.47849i	0.272456	−	0.272456i	0.830088	+	0.557632i	$0.188290\pi$
$164$	−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	$-0.293509\pi$
$167$	−2.49027	−	2.49027i	−0.192703	−	0.192703i	−0.796863	+	0.604160i	$0.793509\pi$
$168$	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	$0.0412384\pi$
$181$			3.47621i			0.258385i	−0.991620	+	0.129192i	$0.958762\pi$
$182$	−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	$0.427396\pi$
$191$			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	−0.0968371	+	0.995300i	$0.530873\pi$
$193$	−15.1725	+	15.1725i	−1.09214	+	1.09214i	−0.995300	+	0.0968371i	$0.969127\pi$
$194$	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	0.142517	−	0.989792i	$-0.454480\pi$
$197$	15.8927	−	15.8927i	1.13231	−	1.13231i	0.989792	−	0.142517i	$-0.0455196\pi$
$198$	−1.31618	−	0.660106i	−0.0935371	−	0.0469117i
$199$		−	4.30765i		−	0.305361i	−0.988276	−	0.152681i	$-0.951209\pi$
$199$		−	4.30765i		−	0.305361i	0.988276	−	0.152681i	$-0.0487905\pi$
$200$	−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	0.410021	−	0.912076i	$-0.365521\pi$
$223$	−7.49728	−	7.49728i	−0.502055	−	0.502055i	−0.912076	+	0.410021i	$0.865521\pi$
$224$			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	−0.179185	+	0.983815i	$0.557346\pi$
$227$	−17.5224	+	17.5224i	−1.16300	+	1.16300i	−0.983815	+	0.179185i	$0.942654\pi$
$228$	8.05657	−	4.97243i	0.533560	−	0.329307i
$229$	−13.8742	+	13.8742i	−0.916834	+	0.916834i	−0.996798	−	0.0799635i	$-0.974520\pi$
$229$	−13.8742	+	13.8742i	−0.916834	+	0.916834i	0.0799635	+	0.996798i	$0.474520\pi$
$230$			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	−0.360190	−	0.932879i	$-0.617288\pi$
$239$	8.85356	−	8.85356i	0.572689	−	0.572689i	0.932879	+	0.360190i	$0.117288\pi$
$240$	1.16534	−	0.719233i	0.0752221	−	0.0464263i
$241$	8.79467	−	8.79467i	0.566515	−	0.566515i	−0.364636	−	0.931150i	$-0.618806\pi$
$241$	8.79467	−	8.79467i	0.566515	−	0.566515i	0.931150	+	0.364636i	$0.118806\pi$
$242$	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	$-0.829889\pi$
$263$		−	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
$267$	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	$0.116557\pi$
$269$			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	−0.345618	−	0.938375i	$-0.612331\pi$
$271$	9.75803	−	9.75803i	0.592758	−	0.592758i	0.938375	+	0.345618i	$0.112331\pi$
$272$	−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	$0.0180318\pi$
$277$			1.88463i			0.113236i	−0.998396	+	0.0566181i	$0.981968\pi$
$278$	−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	0.787038	−	0.616904i	$-0.211613\pi$
$281$	2.85196	+	2.85196i	0.170134	+	0.170134i	−0.616904	+	0.787038i	$0.711613\pi$
$282$	5.94281	+	1.40675i	0.353889	+	0.0837705i
$283$			15.2599i			0.907107i	0.891229	+	0.453553i	$0.149844\pi$
$283$			15.2599i			0.907107i	−0.891229	+	0.453553i	$0.850156\pi$
$284$	−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	0.195696	−	0.980665i	$-0.437303\pi$
$293$	−13.4365	−	13.4365i	−0.784968	−	0.784968i	−0.980665	+	0.195696i	$0.937303\pi$
$294$	−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	−0.176722	−	0.984261i	$-0.556549\pi$
$307$	14.1492	−	14.1492i	0.807539	−	0.807539i	0.984261	+	0.176722i	$0.0565493\pi$
$308$			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	−0.766613	−	0.642110i	$-0.778059\pi$
$317$	−2.21672	+	2.21672i	−0.124503	+	0.124503i	0.642110	+	0.766613i	$0.278059\pi$
$318$	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	−0.972505	−	0.232882i	$-0.925184\pi$
$331$	−21.9301	−	21.9301i	−1.20539	−	1.20539i	−0.232882	−	0.972505i	$-0.574816\pi$
$332$	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	$-0.893662\pi$
$337$		−	12.0386i		−	0.655785i	0.944715	−	0.327892i	$-0.106338\pi$
$338$	−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	$-0.957889\pi$
$347$		−	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	−0.790749	−	0.612140i	$-0.790309\pi$
$349$	−3.33670	+	3.33670i	−0.178609	+	0.178609i	0.612140	+	0.790749i	$0.290309\pi$
$350$	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	−0.819069	−	0.573695i	$-0.805509\pi$
$353$	−4.61015	+	4.61015i	−0.245374	+	0.245374i	0.573695	+	0.819069i	$0.305509\pi$
$354$	−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	0.431503	−	0.902111i	$-0.357983\pi$
$359$	−8.91675	−	8.91675i	−0.470608	−	0.470608i	−0.902111	+	0.431503i	$0.857983\pi$
$360$	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	0.198385	−	0.980124i	$-0.436430\pi$
$379$	−15.2188	−	15.2188i	−0.781739	−	0.781739i	−0.980124	+	0.198385i	$0.936430\pi$
$380$			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	$-0.837204\pi$
$383$	−7.48783	+	7.48783i	−0.382610	+	0.382610i	0.489431	+	0.872042i	$0.337204\pi$
$384$	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	−0.830076	−	0.557650i	$-0.811703\pi$
$397$	−5.42804	+	5.42804i	−0.272425	+	0.272425i	0.557650	+	0.830076i	$0.311703\pi$
$398$	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	0.988969	+	0.148126i	$0.0473240\pi$
$401$	22.7703	+	22.7703i	1.13709	+	1.13709i	0.148126	+	0.988969i	$0.452676\pi$
$402$	−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	0.832757	−	0.553639i	$-0.186761\pi$
$409$	5.64482	+	5.64482i	0.279118	+	0.279118i	−0.553639	+	0.832757i	$0.686761\pi$
$410$	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	$0.0705751\pi$
$419$			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	0.659059	−	0.752091i	$-0.270955\pi$
$421$	−1.90886	−	1.90886i	−0.0930321	−	0.0930321i	−0.752091	+	0.659059i	$0.770955\pi$
$422$	−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	−0.930811	−	0.365500i	$-0.880898\pi$
$431$	−11.7362	+	11.7362i	−0.565312	+	0.565312i	0.365500	+	0.930811i	$0.380898\pi$
$432$	3.98324	+	3.33674i	0.191644	+	0.160539i
$433$		−	13.9122i		−	0.668577i	−0.942471	−	0.334289i	$-0.891504\pi$
$433$		−	13.9122i		−	0.668577i	0.942471	−	0.334289i	$-0.108496\pi$
$434$	−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	$0.0630524\pi$
$439$			8.24651i			0.393584i	−0.980445	+	0.196792i	$0.936948\pi$
$440$	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	$-0.0720713\pi$
$444$	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	−0.996346	−	0.0854053i	$-0.972781\pi$
$449$	−22.9219	−	22.9219i	−1.08175	−	1.08175i	−0.0854053	−	0.996346i	$-0.527219\pi$
$450$	−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	0.640492	−	0.767965i	$-0.278731\pi$
$457$	−2.72508	−	2.72508i	−0.127474	−	0.127474i	−0.767965	+	0.640492i	$0.778731\pi$
$458$		−	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	$-0.939797\pi$
$461$	−17.0514	+	17.0514i	−0.794161	+	0.794161i	0.188007	+	0.982168i	$0.439797\pi$
$462$	−0.723423	+	0.446489i	−0.0336567	+	0.0207725i
$463$	−7.20273	+	7.20273i	−0.334739	+	0.334739i	−0.854383	−	0.519644i	$-0.826065\pi$
$463$	−7.20273	+	7.20273i	−0.334739	+	0.334739i	0.519644	+	0.854383i	$0.326065\pi$
$464$			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	0.0225708	−	0.999745i	$-0.492815\pi$
$479$	−21.3865	−	21.3865i	−0.977174	−	0.977174i	−0.999745	+	0.0225708i	$0.992815\pi$
$480$	−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	0.995426	+	0.0955392i	$0.0304575\pi$
$487$	24.0755	+	24.0755i	1.09096	+	1.09096i	0.0955392	+	0.995426i	$0.469542\pi$
$488$	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	0.780891	−	0.624667i	$-0.214765\pi$
$499$	3.48978	+	3.48978i	0.156224	+	0.156224i	−0.624667	+	0.780891i	$0.714765\pi$
$500$	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	$0.00415073\pi$
$503$			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
$507$	−15.4429	−	16.3865i	−0.685841	−	0.727751i
$508$	21.1044			0.936356
$509$	−14.6995	+	14.6995i	−0.651544	+	0.651544i	−0.953365	−	0.301821i	$-0.902406\pi$
$509$	−14.6995	+	14.6995i	−0.651544	+	0.651544i	0.301821	+	0.953365i	$0.402406\pi$
$510$	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	$0.0167818\pi$
$521$			2.40567i			0.105394i	−0.998611	+	0.0526972i	$0.983218\pi$
$522$	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	−0.911379	−	0.411567i	$-0.864981\pi$
$541$	−11.6253	+	11.6253i	−0.499812	+	0.499812i	0.411567	+	0.911379i	$0.364981\pi$
$542$			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	0.622512	−	0.782610i	$-0.286112\pi$
$557$	−3.77844	−	3.77844i	−0.160098	−	0.160098i	−0.782610	+	0.622512i	$0.786112\pi$
$558$	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	$-0.940716\pi$
$571$		−	8.84959i		−	0.370344i	0.982706	−	0.185172i	$-0.0592842\pi$
$572$	−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	0.985803	−	0.167904i	$-0.0536999\pi$
$577$	19.6466	+	19.6466i	0.817899	+	0.817899i	−0.167904	+	0.985803i	$0.553700\pi$
$578$	−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	−0.898058	−	0.439877i	$-0.855022\pi$
$587$	−11.1009	+	11.1009i	−0.458182	+	0.458182i	0.439877	+	0.898058i	$0.355022\pi$
$588$	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	0.839253	−	0.543741i	$-0.182993\pi$
$593$	7.19619	+	7.19619i	0.295512	+	0.295512i	−0.543741	+	0.839253i	$0.682993\pi$
$594$	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	$0.979191\pi$
$600$	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	0.479360	−	0.877619i	$-0.340869\pi$
$613$	−9.86043	−	9.86043i	−0.398259	−	0.398259i	−0.877619	+	0.479360i	$0.840869\pi$
$614$			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	$-0.516262\pi$
$617$	23.5386	−	23.5386i	0.947630	−	0.947630i	0.998695	+	0.0510654i	$0.0162617\pi$
$618$	0.0803321	+	0.130158i	0.00323143	+	0.00523572i
$619$	−6.25762	+	6.25762i	−0.251515	+	0.251515i	−0.821592	−	0.570077i	$-0.806914\pi$
$619$	−6.25762	+	6.25762i	−0.251515	+	0.251515i	0.570077	+	0.821592i	$0.306914\pi$
$620$			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	−0.738203	−	0.674579i	$-0.764325\pi$
$631$	−1.59821	+	1.59821i	−0.0636237	+	0.0636237i	0.674579	+	0.738203i	$0.264325\pi$
$632$	−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	0.405083	−	0.914280i	$-0.367242\pi$
$643$	−12.9119	−	12.9119i	−0.509196	−	0.509196i	−0.914280	+	0.405083i	$0.867242\pi$
$644$	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	$0.0877942\pi$
$653$			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
$657$	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	$-0.853657\pi$
$659$		−	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	−0.776387	−	0.630256i	$-0.782950\pi$
$661$	−3.75702	+	3.75702i	−0.146131	+	0.146131i	0.630256	+	0.776387i	$0.282950\pi$
$662$	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	$-0.891805\pi$
$673$		−	17.2981i		−	0.666792i	0.942787	−	0.333396i	$-0.108195\pi$
$674$	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	$0.735520\pi$
$678$	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	0.640408	−	0.768035i	$-0.278765\pi$
$683$	−3.33543	−	3.33543i	−0.127627	−	0.127627i	−0.768035	+	0.640408i	$0.778765\pi$
$684$	−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	0.884891	−	0.465799i	$-0.154233\pi$
$691$	11.0166	+	11.0166i	0.419092	+	0.419092i	−0.465799	+	0.884891i	$0.654233\pi$
$692$		−	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	−0.271193	−	0.962525i	$-0.587418\pi$
$709$	18.4081	−	18.4081i	0.691331	−	0.691331i	0.962525	+	0.271193i	$0.0874183\pi$
$710$	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	$0.350557\pi$
$727$			48.0910i			1.78360i	−0.452432	+	0.891799i	$0.649443\pi$
$728$	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	0.895852	−	0.444353i	$-0.146566\pi$
$733$	12.2239	+	12.2239i	0.451499	+	0.451499i	−0.444353	+	0.895852i	$0.646566\pi$
$734$	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	−0.714029	−	0.700116i	$-0.753132\pi$
$739$	−0.378213	+	0.378213i	−0.0139128	+	0.0139128i	0.700116	+	0.714029i	$0.253132\pi$
$740$	−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	−0.423453	−	0.905918i	$-0.639182\pi$
$743$	13.1510	−	13.1510i	0.482465	−	0.482465i	0.905918	+	0.423453i	$0.139182\pi$
$744$	−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	$0.130076\pi$
$751$			21.7792i			0.794735i	−0.917660	+	0.397367i	$0.869924\pi$
$752$	−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	0.998838	−	0.0482010i	$-0.0153488\pi$
$761$	26.2245	+	26.2245i	0.950637	+	0.950637i	−0.0482010	+	0.998838i	$0.515349\pi$
$762$	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	0.788688	−	0.614794i	$-0.210761\pi$
$769$	4.82224	+	4.82224i	0.173894	+	0.173894i	−0.614794	+	0.788688i	$0.710761\pi$
$770$		−	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	$-0.520358\pi$
$773$	25.9691	−	25.9691i	0.934044	−	0.934044i	0.997956	+	0.0639117i	$0.0203576\pi$
$774$	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	−0.472415	−	0.881376i	$-0.656618\pi$
$787$	11.4728	−	11.4728i	0.408961	−	0.408961i	0.881376	+	0.472415i	$0.156618\pi$
$788$	−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	$-0.840015\pi$
$809$		−	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	0.297351	−	0.954768i	$-0.403897\pi$
$811$	−18.7220	−	18.7220i	−0.657418	−	0.657418i	−0.954768	+	0.297351i	$0.903897\pi$
$812$	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	−0.284676	−	0.958624i	$-0.591886\pi$
$821$	19.3107	−	19.3107i	0.673947	−	0.673947i	0.958624	+	0.284676i	$0.0918861\pi$
$822$	5.61707	+	1.32964i	0.195918	+	0.0463764i
$823$			44.6167i			1.55524i	0.628735	+	0.777620i	$0.283573\pi$
$823$			44.6167i			1.55524i	−0.628735	+	0.777620i	$0.716427\pi$
$824$	−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	0.834743	−	0.550640i	$-0.185616\pi$
$827$	8.17009	+	8.17009i	0.284102	+	0.284102i	−0.550640	+	0.834743i	$0.685616\pi$
$828$	7.10079	−	14.1583i	0.246770	−	0.492033i
$829$			14.0314i			0.487331i	0.969859	+	0.243665i	$0.0783499\pi$
$829$			14.0314i			0.487331i	−0.969859	+	0.243665i	$0.921650\pi$
$830$	−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	0.972266	−	0.233879i	$-0.0751420\pi$
$839$	21.3877	+	21.3877i	0.738387	+	0.738387i	−0.233879	+	0.972266i	$0.575142\pi$
$840$	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	−0.684626	−	0.728894i	$-0.740035\pi$
$853$	1.29289	−	1.29289i	0.0442677	−	0.0442677i	0.728894	+	0.684626i	$0.240035\pi$
$854$		−	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	0.115033	−	0.993362i	$-0.463303\pi$
$863$	32.5612	−	32.5612i	1.10839	−	1.10839i	0.993362	−	0.115033i	$-0.0366974\pi$
$864$	−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	0.783927	−	0.620853i	$-0.213213\pi$
$877$	4.82932	+	4.82932i	0.163075	+	0.163075i	−0.620853	+	0.783927i	$0.713213\pi$
$878$	−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	$-0.667636\pi$
$883$		−	51.3777i		−	1.72900i	0.502636	−	0.864498i	$-0.332364\pi$
$884$	−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
$891$	−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	$0.0487955\pi$
$907$			9.19731i			0.305392i	−0.988273	+	0.152696i	$0.951204\pi$
$908$	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	$0.926725\pi$
$912$	−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	−0.920008	−	0.391899i	$-0.871818\pi$
$929$	−16.0965	+	16.0965i	−0.528110	+	0.528110i	0.391899	+	0.920008i	$0.371818\pi$
$930$	−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	−0.967490	−	0.252911i	$-0.918612\pi$
$941$	−21.9202	+	21.9202i	−0.714579	+	0.714579i	0.252911	+	0.967490i	$0.418612\pi$
$942$	−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	0.994954	−	0.100328i	$-0.0319891\pi$
$947$	27.5307	+	27.5307i	0.894627	+	0.894627i	−0.100328	+	0.994954i	$0.531989\pi$
$948$	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	1.00000		0.000561611i	$-0.000178766\pi$
$967$	31.0792	+	31.0792i	0.999438	+	0.999438i	−0.000561611		1.00000i	$0.500179\pi$
$968$	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	$0.00960399\pi$
$971$			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
$975$	−13.6639	+	23.6590i	−0.437594	+	0.757694i
$976$	−6.42464			−0.205648
$977$	3.46359	−	3.46359i	0.110810	−	0.110810i	−0.649528	−	0.760338i	$-0.725033\pi$
$977$	3.46359	−	3.46359i	0.110810	−	0.110810i	0.760338	+	0.649528i	$0.225033\pi$
$978$	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	0.566500	−	0.824062i	$-0.308297\pi$
$983$	−8.07529	−	8.07529i	−0.257562	−	0.257562i	−0.824062	+	0.566500i	$0.808297\pi$
$984$	−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.281.1	yes	20
3.2	odd	2		546.2.p.c.281.6	yes	20
13.5	odd	4		546.2.p.c.239.6	✓	20
39.5	even	4	inner	546.2.p.d.239.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.6	✓	20	13.5	odd	4
546.2.p.c.281.6	yes	20	3.2	odd	2
546.2.p.d.239.1	yes	20	39.5	even	4	inner
546.2.p.d.281.1	yes	20	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

Varieties

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