LMFDB - Embedded newform 588.2.o.b.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(19,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("588.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$0.856419 + 1.12541i$ of defining polynomial
Character	$\chi$	$=$	588.31
Dual form			588.2.o.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40284 + 0.178976i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.93594 + 0.502151i) q^{4} +(3.33878 - 1.92764i) q^{5} +(-0.856419 + 1.12541i) q^{6} +(2.62594 + 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.40284 + 0.178976i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.93594 + 0.502151i) q^{4} +(3.33878 - 1.92764i) q^{5} +(-0.856419 + 1.12541i) q^{6} +(2.62594 + 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(5.02878 - 2.10662i) q^{10} +(-1.17975 - 0.681127i) q^{11} +(-1.40284 + 1.42549i) q^{12} -0.369798i q^{13} +3.85529i q^{15} +(3.49569 + 1.94426i) q^{16} +(-3.89853 - 2.25082i) q^{17} +(-0.546424 - 1.30439i) q^{18} +(0.0330925 + 0.0573178i) q^{19} +(7.43162 - 2.05523i) q^{20} +(-1.53309 - 1.16666i) q^{22} +(-2.77902 + 1.60447i) q^{23} +(-2.22310 + 1.74867i) q^{24} +(4.93162 - 8.54182i) q^{25} +(0.0661849 - 0.518768i) q^{26} +1.00000 q^{27} -3.11951 q^{29} +(-0.690004 + 5.40836i) q^{30} +(-3.01852 + 5.22824i) q^{31} +(4.55593 + 3.35314i) q^{32} +(1.17975 - 0.681127i) q^{33} +(-5.06618 - 3.85529i) q^{34} +(-0.533092 - 1.92764i) q^{36} +(2.74593 + 4.75609i) q^{37} +(0.0361650 + 0.0863307i) q^{38} +(0.320254 + 0.184899i) q^{39} +(10.7932 - 1.55307i) q^{40} +8.45017i q^{41} +6.30324i q^{43} +(-1.94188 - 1.91103i) q^{44} +(-3.33878 - 1.92764i) q^{45} +(-4.18569 + 1.75344i) q^{46} +(-0.712838 - 1.23467i) q^{47} +(-3.43162 + 2.05523i) q^{48} +(8.44708 - 11.1002i) q^{50} +(3.89853 - 2.25082i) q^{51} +(0.185694 - 0.715904i) q^{52} +(1.27259 - 2.20420i) q^{53} +(1.40284 + 0.178976i) q^{54} -5.25188 q^{55} -0.0661849 q^{57} +(-4.37618 - 0.558317i) q^{58} +(1.71879 - 2.97703i) q^{59} +(-1.93594 + 7.46359i) q^{60} +(-1.23998 + 0.715904i) q^{61} +(-5.17024 + 6.79415i) q^{62} +(5.79112 + 5.51933i) q^{64} +(-0.712838 - 1.23467i) q^{65} +(1.77690 - 0.744367i) q^{66} +(-8.45877 - 4.88367i) q^{67} +(-6.41706 - 6.31509i) q^{68} -3.20894i q^{69} -12.9518i q^{71} +(-0.402843 - 2.79959i) q^{72} +(1.56024 + 0.900803i) q^{73} +(3.00088 + 7.16350i) q^{74} +(4.93162 + 8.54182i) q^{75} +(0.0352827 + 0.127581i) q^{76} +(0.416174 + 0.316702i) q^{78} +(-10.8156 + 6.24438i) q^{79} +(15.4192 - 0.246989i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.51238 + 11.8543i) q^{82} +12.2889 q^{83} -17.3551 q^{85} +(-1.12813 + 8.84246i) q^{86} +(1.55975 - 2.70157i) q^{87} +(-2.38213 - 3.02842i) q^{88} +(-1.11951 + 0.646349i) q^{89} +(-4.33878 - 3.30174i) q^{90} +(-6.18569 + 1.71066i) q^{92} +(-3.01852 - 5.22824i) q^{93} +(-0.779023 - 1.85963i) q^{94} +(0.220977 + 0.127581i) q^{95} +(-5.18187 + 2.26898i) q^{96} -2.88422i q^{97} +1.36225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9} + 13 q^{10} - 6 q^{11} - q^{12} + 7 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 6 q^{22} - 11 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} - 16 q^{29} - 5 q^{30} + 6 q^{31} + 21 q^{32} + 6 q^{33} - 28 q^{34} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 6 q^{39} + 13 q^{40} + 19 q^{44} - 12 q^{46} + 4 q^{47} + 10 q^{48} + 2 q^{50} - 20 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 12 q^{57} - 23 q^{58} - 14 q^{59} + q^{60} - 12 q^{61} - 48 q^{62} + 2 q^{64} + 4 q^{65} + 21 q^{66} - 42 q^{67} + 10 q^{68} + 7 q^{72} + 18 q^{73} - 28 q^{74} + 2 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{79} + 33 q^{80} - 4 q^{81} + 14 q^{82} + 4 q^{83} - 32 q^{85} - 42 q^{86} + 8 q^{87} + 11 q^{88} - 8 q^{90} - 28 q^{92} + 6 q^{93} + 16 q^{94} + 24 q^{95} - 9 q^{96}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9 + 13 * q^10 - 6 * q^11 - q^12 + 7 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 6 * q^22 - 11 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 - 16 * q^29 - 5 * q^30 + 6 * q^31 + 21 * q^32 + 6 * q^33 - 28 * q^34 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 6 * q^39 + 13 * q^40 + 19 * q^44 - 12 * q^46 + 4 * q^47 + 10 * q^48 + 2 * q^50 - 20 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 12 * q^57 - 23 * q^58 - 14 * q^59 + q^60 - 12 * q^61 - 48 * q^62 + 2 * q^64 + 4 * q^65 + 21 * q^66 - 42 * q^67 + 10 * q^68 + 7 * q^72 + 18 * q^73 - 28 * q^74 + 2 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^79 + 33 * q^80 - 4 * q^81 + 14 * q^82 + 4 * q^83 - 32 * q^85 - 42 * q^86 + 8 * q^87 + 11 * q^88 - 8 * q^90 - 28 * q^92 + 6 * q^93 + 16 * q^94 + 24 * q^95 - 9 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.40284	+	0.178976i	0.991960	+	0.126555i
$2$	1.40284	+	0.178976i	0.991960	+	0.126555i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.93594	+	0.502151i	0.967968	+	0.251075i
$5$	3.33878	−	1.92764i	1.49315	−	0.862069i	0.493178	−	0.869929i	$-0.335835\pi$
$5$	3.33878	−	1.92764i	1.49315	−	0.862069i	0.999969	+	0.00785986i	$0.00250190\pi$
$6$	−0.856419	+	1.12541i	−0.349632	+	0.459446i
$7$		0			0
$7$		0			0
$8$	2.62594	+	1.05092i	0.928410	+	0.371558i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	5.02878	−	2.10662i	1.59024	−	0.666172i
$11$	−1.17975	−	0.681127i	−0.355707	−	0.205367i	0.311489	−	0.950250i	$-0.399172\pi$
$11$	−1.17975	−	0.681127i	−0.355707	−	0.205367i	−0.667196	+	0.744882i	$0.732506\pi$
$12$	−1.40284	+	1.42549i	−0.404966	+	0.411505i
$13$		−	0.369798i		−	0.102563i	−0.998684	−	0.0512817i	$-0.983669\pi$
$13$		−	0.369798i		−	0.102563i	0.998684	−	0.0512817i	$-0.0163306\pi$
$14$		0			0
$15$			3.85529i			0.995431i
$16$	3.49569	+	1.94426i	0.873922	+	0.486065i
$17$	−3.89853	−	2.25082i	−0.945533	−	0.545904i	−0.0538425	−	0.998549i	$-0.517147\pi$
$17$	−3.89853	−	2.25082i	−0.945533	−	0.545904i	−0.891690	+	0.452646i	$0.850480\pi$
$18$	−0.546424	−	1.30439i	−0.128793	−	0.307447i
$19$	0.0330925	+	0.0573178i	0.00759193	+	0.0131496i	0.869796	−	0.493411i	$-0.164250\pi$
$19$	0.0330925	+	0.0573178i	0.00759193	+	0.0131496i	−0.862204	+	0.506560i	$0.830917\pi$
$20$	7.43162	−	2.05523i	1.66176	−	0.459562i
$21$		0			0
$22$	−1.53309	−	1.16666i	−0.326856	−	0.248733i
$23$	−2.77902	+	1.60447i	−0.579466	+	0.334555i	−0.760921	−	0.648844i	$-0.775253\pi$
$23$	−2.77902	+	1.60447i	−0.579466	+	0.334555i	0.181455	+	0.983399i	$0.441919\pi$
$24$	−2.22310	+	1.74867i	−0.453788	+	0.356945i
$25$	4.93162	−	8.54182i	0.986325	−	1.70836i
$26$	0.0661849	−	0.518768i	0.0129799	−	0.101739i
$27$	1.00000			0.192450
$28$		0			0
$29$	−3.11951			−0.579278			−0.289639	−	0.957136i	$-0.593535\pi$
$29$	−3.11951			−0.579278			−0.289639	+	0.957136i	$0.593535\pi$
$30$	−0.690004	+	5.40836i	−0.125977	+	0.987428i
$31$	−3.01852	+	5.22824i	−0.542143	+	0.939019i	0.456638	+	0.889653i	$0.349054\pi$
$31$	−3.01852	+	5.22824i	−0.542143	+	0.939019i	−0.998781	+	0.0493663i	$0.984280\pi$
$32$	4.55593	+	3.35314i	0.805382	+	0.592757i
$33$	1.17975	−	0.681127i	0.205367	−	0.118569i
$34$	−5.06618	−	3.85529i	−0.868844	−	0.661177i
$35$		0			0
$36$	−0.533092	−	1.92764i	−0.0888487	−	0.321274i
$37$	2.74593	+	4.75609i	0.451428	+	0.781897i	0.998475	−	0.0552054i	$-0.0175814\pi$
$37$	2.74593	+	4.75609i	0.451428	+	0.781897i	−0.547047	+	0.837102i	$0.684248\pi$
$38$	0.0361650	+	0.0863307i	0.00586674	+	0.0140047i
$39$	0.320254	+	0.184899i	0.0512817	+	0.0296075i
$40$	10.7932	−	1.55307i	1.70656	−	0.245563i
$41$			8.45017i			1.31970i	0.751399	+	0.659848i	$0.229379\pi$
$41$			8.45017i			1.31970i	−0.751399	+	0.659848i	$0.770621\pi$
$42$		0			0
$43$			6.30324i			0.961236i	0.876930	+	0.480618i	$0.159588\pi$
$43$			6.30324i			0.961236i	−0.876930	+	0.480618i	$0.840412\pi$
$44$	−1.94188	−	1.91103i	−0.292750	−	0.288098i
$45$	−3.33878	−	1.92764i	−0.497716	−	0.287356i
$46$	−4.18569	+	1.75344i	−0.617147	+	0.258531i
$47$	−0.712838	−	1.23467i	−0.103978	−	0.180095i	0.809342	−	0.587338i	$-0.199824\pi$
$47$	−0.712838	−	1.23467i	−0.103978	−	0.180095i	−0.913320	+	0.407242i	$0.866491\pi$
$48$	−3.43162	+	2.05523i	−0.495312	+	0.296646i
$49$		0			0
$50$	8.44708	−	11.1002i	1.19460	−	1.56980i
$51$	3.89853	−	2.25082i	0.545904	−	0.315178i
$52$	0.185694	−	0.715904i	0.0257511	−	0.0992781i
$53$	1.27259	−	2.20420i	0.174804	−	0.302770i	−0.765289	−	0.643686i	$-0.777404\pi$
$53$	1.27259	−	2.20420i	0.174804	−	0.302770i	0.940093	+	0.340917i	$0.110737\pi$
$54$	1.40284	+	0.178976i	0.190903	+	0.0243556i
$55$	−5.25188			−0.708163
$56$		0			0
$57$	−0.0661849			−0.00876641
$58$	−4.37618	−	0.558317i	−0.574621	−	0.0733107i
$59$	1.71879	−	2.97703i	0.223767	−	0.387576i	−0.732182	−	0.681109i	$-0.761498\pi$
$59$	1.71879	−	2.97703i	0.223767	−	0.387576i	0.955949	+	0.293533i	$0.0948312\pi$
$60$	−1.93594	+	7.46359i	−0.249928	+	0.963545i
$61$	−1.23998	+	0.715904i	−0.158763	+	0.0916621i	−0.577277	−	0.816549i	$-0.695885\pi$
$61$	−1.23998	+	0.715904i	−0.158763	+	0.0916621i	0.418513	+	0.908211i	$0.362551\pi$
$62$	−5.17024	+	6.79415i	−0.656622	+	0.862858i
$63$		0			0
$64$	5.79112	+	5.51933i	0.723890	+	0.689916i
$65$	−0.712838	−	1.23467i	−0.0884167	−	0.153142i
$66$	1.77690	−	0.744367i	0.218722	−	0.0916253i
$67$	−8.45877	−	4.88367i	−1.03340	−	0.596636i	−0.115445	−	0.993314i	$-0.536830\pi$
$67$	−8.45877	−	4.88367i	−1.03340	−	0.596636i	−0.917958	+	0.396678i	$0.870163\pi$
$68$	−6.41706	−	6.31509i	−0.778182	−	0.765817i
$69$		−	3.20894i		−	0.386311i
$70$		0			0
$71$		−	12.9518i		−	1.53710i	−0.639792	−	0.768549i	$-0.720979\pi$
$71$		−	12.9518i		−	1.53710i	0.639792	−	0.768549i	$-0.279021\pi$
$72$	−0.402843	−	2.79959i	−0.0474755	−	0.329935i
$73$	1.56024	+	0.900803i	0.182612	+	0.105431i	0.588519	−	0.808483i	$-0.299711\pi$
$73$	1.56024	+	0.900803i	0.182612	+	0.105431i	−0.405907	+	0.913914i	$0.633044\pi$
$74$	3.00088	+	7.16350i	0.348845	+	0.832740i
$75$	4.93162	+	8.54182i	0.569455	+	0.986325i
$76$	0.0352827	+	0.127581i	0.00404720	+	0.0146345i
$77$		0			0
$78$	0.416174	+	0.316702i	0.0471224	+	0.0358594i
$79$	−10.8156	+	6.24438i	−1.21685	+	0.702548i	−0.964243	−	0.265021i	$-0.914621\pi$
$79$	−10.8156	+	6.24438i	−1.21685	+	0.702548i	−0.252606	+	0.967569i	$0.581288\pi$
$80$	15.4192	−	0.246989i	1.72392	−	0.0276142i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.51238	+	11.8543i	−0.167014	+	1.30908i
$83$	12.2889			1.34888			0.674442	−	0.738327i	$-0.264384\pi$
$83$	12.2889			1.34888			0.674442	+	0.738327i	$0.264384\pi$
$84$		0			0
$85$	−17.3551			−1.88243
$86$	−1.12813	+	8.84246i	−0.121649	+	0.953507i
$87$	1.55975	−	2.70157i	0.167223	−	0.289639i
$88$	−2.38213	−	3.02842i	−0.253936	−	0.322831i
$89$	−1.11951	+	0.646349i	−0.118668	+	0.0685128i	−0.558159	−	0.829734i	$-0.688492\pi$
$89$	−1.11951	+	0.646349i	−0.118668	+	0.0685128i	0.439491	+	0.898247i	$0.355159\pi$
$90$	−4.33878	−	3.30174i	−0.457347	−	0.348034i
$91$		0			0
$92$	−6.18569	+	1.71066i	−0.644903	+	0.178349i
$93$	−3.01852	−	5.22824i	−0.313006	−	0.542143i
$94$	−0.779023	−	1.85963i	−0.0803501	−	0.191806i
$95$	0.220977	+	0.127581i	0.0226717	+	0.0130895i
$96$	−5.18187	+	2.26898i	−0.528872	+	0.231577i
$97$		−	2.88422i		−	0.292848i	−0.989222	−	0.146424i	$-0.953224\pi$
$97$		−	2.88422i		−	0.292848i	0.989222	−	0.146424i	$-0.0467764\pi$
$98$		0			0
$99$			1.36225i			0.136912i
$100$	13.8366	−	14.0600i	1.38366	−	1.40600i
$101$	−5.35949	−	3.09430i	−0.533289	−	0.307895i	0.209066	−	0.977902i	$-0.432958\pi$
$101$	−5.35949	−	3.09430i	−0.533289	−	0.307895i	−0.742355	+	0.670007i	$0.766291\pi$
$102$	5.87187	−	2.45980i	0.581402	−	0.243557i
$103$	−8.89634	−	15.4089i	−0.876583	−	1.51829i	−0.855067	−	0.518517i	$-0.826484\pi$
$103$	−8.89634	−	15.4089i	−0.876583	−	1.51829i	−0.0215154	−	0.999769i	$-0.506849\pi$
$104$	0.388629	−	0.971066i	0.0381082	−	0.0952209i
$105$		0			0
$106$	2.17975	−	2.86438i	0.211716	−	0.278213i
$107$	5.27683	−	3.04658i	0.510131	−	0.294524i	−0.222757	−	0.974874i	$-0.571506\pi$
$107$	5.27683	−	3.04658i	0.510131	−	0.294524i	0.732887	+	0.680350i	$0.238172\pi$
$108$	1.93594	+	0.502151i	0.186285	+	0.0483195i
$109$	−3.93162	+	6.80977i	−0.376581	+	0.652258i	−0.990562	−	0.137063i	$-0.956234\pi$
$109$	−3.93162	+	6.80977i	−0.376581	+	0.652258i	0.613981	+	0.789321i	$0.289567\pi$
$110$	−7.36756	−	0.939961i	−0.702469	−	0.0896217i
$111$	−5.49186			−0.521264
$112$		0			0
$113$	4.70669			0.442768			0.221384	−	0.975187i	$-0.428943\pi$
$113$	4.70669			0.442768			0.221384	+	0.975187i	$0.428943\pi$
$114$	−0.0928470	−	0.0118455i	−0.00869592	−	0.00110943i
$115$	−6.18569	+	10.7139i	−0.576819	+	0.999080i
$116$	−6.03917	−	1.56646i	−0.560723	−	0.145442i
$117$	−0.320254	+	0.184899i	−0.0296075	+	0.0170939i
$118$	2.94400	−	3.86868i	0.271017	−	0.356141i
$119$		0			0
$120$	−4.05162	+	10.1238i	−0.369860	+	0.924168i
$121$	−4.57213	−	7.91917i	−0.415648	−	0.719924i
$122$	−1.86763	+	0.782374i	−0.169087	+	0.0708328i
$123$	−7.31806	−	4.22509i	−0.659848	−	0.380963i
$124$	−8.46903	+	8.60577i	−0.760541	+	0.772821i
$125$		−	18.7492i		−	1.67698i
$126$		0			0
$127$		−	2.70312i		−	0.239863i	−0.992782	−	0.119931i	$-0.961733\pi$
$127$		−	2.70312i		−	0.239863i	0.992782	−	0.119931i	$-0.0382675\pi$
$128$	7.13620	+	8.77922i	0.630757	+	0.775981i
$129$	−5.45877	−	3.15162i	−0.480618	−	0.277485i
$130$	−0.779023	−	1.85963i	−0.0683249	−	0.163100i
$131$	−3.88644	−	6.73151i	−0.339560	−	0.588135i	0.644790	−	0.764360i	$-0.276945\pi$
$131$	−3.88644	−	6.73151i	−0.339560	−	0.588135i	−0.984350	+	0.176225i	$0.943611\pi$
$132$	2.62594	−	0.726207i	0.228559	−	0.0632082i
$133$		0			0
$134$	−10.9923	−	8.36494i	−0.949587	−	0.722621i
$135$	3.33878	−	1.92764i	0.287356	−	0.165905i
$136$	−7.87187	−	10.0076i	−0.675007	−	0.858143i
$137$	−1.42568	+	2.46934i	−0.121804	+	0.210970i	−0.920479	−	0.390792i	$-0.872201\pi$
$137$	−1.42568	+	2.46934i	−0.121804	+	0.210970i	0.798675	+	0.601762i	$0.205535\pi$
$138$	0.574323	−	4.50164i	0.0488897	−	0.383205i
$139$	−7.15656			−0.607011			−0.303506	−	0.952830i	$-0.598157\pi$
$139$	−7.15656			−0.607011			−0.303506	+	0.952830i	$0.598157\pi$
$140$		0			0
$141$	1.42568			0.120064
$142$	2.31806	−	18.1694i	0.194528	−	1.52474i
$143$	−0.251879	+	0.436267i	−0.0210632	+	0.0364825i
$144$	−0.0640649	−	3.99949i	−0.00533874	−	0.333291i
$145$	−10.4153	+	6.01330i	−0.864948	+	0.499378i
$146$	2.02754	+	1.54293i	0.167801	+	0.127694i
$147$		0			0
$148$	2.92767	+	10.5864i	0.240653	+	0.870193i
$149$	−10.6776	−	18.4941i	−0.874739	−	1.51509i	−0.857040	−	0.515250i	$-0.827699\pi$
$149$	−10.6776	−	18.4941i	−0.874739	−	1.51509i	−0.0176994	−	0.999843i	$-0.505634\pi$
$150$	5.38951	+	12.8655i	0.440052	+	1.05046i
$151$	19.2373	+	11.1067i	1.56551	+	0.903848i	0.996682	+	0.0813911i	$0.0259363\pi$
$151$	19.2373	+	11.1067i	1.56551	+	0.903848i	0.568828	+	0.822457i	$0.307397\pi$
$152$	0.0266621	+	0.185291i	0.00216258	+	0.0150291i
$153$			4.50164i			0.363936i
$154$		0			0
$155$			23.2746i			1.86946i
$156$	0.527144	+	0.518768i	0.0422053	+	0.0415347i
$157$	4.71898	+	2.72451i	0.376616	+	0.217439i	0.676345	−	0.736585i	$-0.263563\pi$
$157$	4.71898	+	2.72451i	0.376616	+	0.217439i	−0.299729	+	0.954024i	$0.596896\pi$
$158$	−16.2902	+	6.82416i	−1.29598	+	0.542901i
$159$	1.27259	+	2.20420i	0.100923	+	0.174804i
$160$	21.6749	+	2.41318i	1.71355	+	0.190778i
$161$		0			0
$162$	−0.856419	+	1.12541i	−0.0672866	+	0.0884205i
$163$	−4.11951	+	2.37840i	−0.322665	+	0.186291i	−0.652580	−	0.757720i	$-0.726313\pi$
$163$	−4.11951	+	2.37840i	−0.322665	+	0.186291i	0.329915	+	0.944011i	$0.392980\pi$
$164$	−4.24326	+	16.3590i	−0.331343	+	1.27742i
$165$	2.62594	−	4.54826i	0.204429	−	0.354082i
$166$	17.2394	+	2.19942i	1.33804	+	0.170708i
$167$	14.0618			1.08814			0.544068	−	0.839041i	$-0.316884\pi$
$167$	14.0618			1.08814			0.544068	+	0.839041i	$0.316884\pi$
$168$		0			0
$169$	12.8632			0.989481
$170$	−24.3465	−	3.10615i	−1.86729	−	0.238231i
$171$	0.0330925	−	0.0573178i	0.00253064	−	0.00438320i
$172$	−3.16518	+	12.2027i	−0.241342	+	0.930445i
$173$	−1.53904	+	0.888566i	−0.117011	+	0.0675564i	−0.557363	−	0.830269i	$-0.688187\pi$
$173$	−1.53904	+	0.888566i	−0.117011	+	0.0675564i	0.440352	+	0.897825i	$0.354854\pi$
$174$	2.67161	−	3.51072i	0.202534	−	0.266147i
$175$		0			0
$176$	−2.79974	−	4.67474i	−0.211038	−	0.352372i
$177$	1.71879	+	2.97703i	0.129192	+	0.223767i
$178$	−1.68618	+	0.706360i	−0.126384	+	0.0529440i
$179$	2.81607	+	1.62586i	0.210483	+	0.121522i	0.601536	−	0.798846i	$-0.294556\pi$
$179$	2.81607	+	1.62586i	0.210483	+	0.121522i	−0.391053	+	0.920368i	$0.627889\pi$
$180$	−5.49569	−	5.40836i	−0.409625	−	0.403116i
$181$			23.5015i			1.74685i	0.486954	+	0.873427i	$0.338108\pi$
$181$			23.5015i			1.74685i	−0.486954	+	0.873427i	$0.661892\pi$
$182$		0			0
$183$		−	1.43181i		−	0.105842i
$184$	−8.98372	+	1.29270i	−0.662289	+	0.0952989i
$185$	18.3361	+	10.5864i	1.34810	+	0.778324i
$186$	−3.29878	−	7.87464i	−0.241879	−	0.577396i
$187$	3.06618	+	5.31079i	0.224222	+	0.388363i
$188$	−0.760017	−	2.74820i	−0.0554300	−	0.200433i
$189$		0			0
$190$	0.287162	+	0.218526i	0.0208329	+	0.0158535i
$191$	20.6956	−	11.9486i	1.49748	−	0.864571i	0.497485	−	0.867473i	$-0.334257\pi$
$191$	20.6956	−	11.9486i	1.49748	−	0.864571i	0.999996	+	0.00290157i	$0.000923599\pi$
$192$	−7.67544	+	2.25559i	−0.553927	+	0.162783i
$193$	−9.93757	+	17.2124i	−0.715322	+	1.23897i	0.247513	+	0.968885i	$0.420387\pi$
$193$	−9.93757	+	17.2124i	−0.715322	+	1.23897i	−0.962835	+	0.270090i	$0.912947\pi$
$194$	0.516207	−	4.04611i	0.0370615	−	0.290494i
$195$	1.42568			0.102095
$196$		0			0
$197$	19.0198			1.35511			0.677553	−	0.735474i	$-0.263041\pi$
$197$	19.0198			1.35511			0.677553	+	0.735474i	$0.263041\pi$
$198$	−0.243811	+	1.91103i	−0.0173269	+	0.135811i
$199$	7.42568	−	12.8616i	0.526392	−	0.911738i	−0.473135	−	0.880990i	$-0.656878\pi$
$199$	7.42568	−	12.8616i	0.526392	−	0.911738i	0.999527	−	0.0307481i	$-0.00978898\pi$
$200$	21.9270	−	17.2476i	1.55047	−	1.21959i
$201$	8.45877	−	4.88367i	0.596636	−	0.344468i
$202$	−6.96472	−	5.30004i	−0.490036	−	0.372910i
$203$		0			0
$204$	8.67756	−	2.39979i	0.607550	−	0.168019i
$205$	16.2889	+	28.2132i	1.13767	+	1.97050i
$206$	−9.72234	−	23.2085i	−0.677388	−	1.61701i
$207$	2.77902	+	1.60447i	0.193155	+	0.111518i
$208$	0.718983	−	1.29270i	0.0498525	−	0.0896325i
$209$		−	0.0901606i		−	0.00623654i
$210$		0			0
$211$		−	19.6676i		−	1.35398i	−0.735994	−	0.676988i	$-0.763285\pi$
$211$		−	19.6676i		−	1.35398i	0.735994	−	0.676988i	$-0.236715\pi$
$212$	3.57050	−	3.62815i	0.245223	−	0.249182i
$213$	11.2166	+	6.47590i	0.768549	+	0.443722i
$214$	7.94783	−	3.32945i	0.543303	−	0.227596i
$215$	12.1504	+	21.0451i	0.828651	+	1.43527i
$216$	2.62594	+	1.05092i	0.178673	+	0.0715063i
$217$		0			0
$218$	−6.73424	+	8.84937i	−0.456100	+	0.599355i
$219$	−1.56024	+	0.900803i	−0.105431	+	0.0608706i
$220$	−10.1673	−	2.63723i	−0.685479	−	0.177802i
$221$	−0.832347	+	1.44167i	−0.0559897	+	0.0969771i
$222$	−7.70422	−	0.982912i	−0.517073	−	0.0659687i
$223$	−8.10323			−0.542633			−0.271316	−	0.962490i	$-0.587459\pi$
$223$	−8.10323			−0.542633			−0.271316	+	0.962490i	$0.587459\pi$
$224$		0			0
$225$	−9.86325			−0.657550
$226$	6.60275	+	0.842385i	0.439208	+	0.0560346i
$227$	6.04300	−	10.4668i	0.401088	−	0.694704i	−0.592770	−	0.805372i	$-0.701966\pi$
$227$	6.04300	−	10.4668i	0.401088	−	0.694704i	0.993857	+	0.110668i	$0.0352989\pi$
$228$	−0.128130	−	0.0332348i	−0.00848560	−	0.00220103i
$229$	−20.5963	+	11.8913i	−1.36104	+	0.785799i	−0.989763	−	0.142722i	$-0.954414\pi$
$229$	−20.5963	+	11.8913i	−1.36104	+	0.785799i	−0.371280	+	0.928521i	$0.621081\pi$
$230$	−10.5951	+	13.9229i	−0.698620	+	0.918047i
$231$		0			0
$232$	−8.19164	−	3.27837i	−0.537808	−	0.215235i
$233$	9.96472	+	17.2594i	0.652810	+	1.13070i	0.982438	+	0.186590i	$0.0597435\pi$
$233$	9.96472	+	17.2594i	0.652810	+	1.13070i	−0.329628	+	0.944111i	$0.606923\pi$
$234$	−0.482359	+	0.202066i	−0.0315328	+	0.0132095i
$235$	−4.76002	−	2.74820i	−0.310509	−	0.179273i
$236$	4.82237	−	4.90024i	0.313910	−	0.318978i
$237$		−	12.4888i		−	0.811233i
$238$		0			0
$239$		−	9.60993i		−	0.621615i	−0.950473	−	0.310807i	$-0.899401\pi$
$239$		−	9.60993i		−	0.621615i	0.950473	−	0.310807i	$-0.100599\pi$
$240$	−7.49569	+	13.4769i	−0.483845	+	0.869930i
$241$	9.01386	+	5.20415i	0.580634	+	0.335229i	0.761385	−	0.648300i	$-0.224520\pi$
$241$	9.01386	+	5.20415i	0.580634	+	0.335229i	−0.180752	+	0.983529i	$0.557853\pi$
$242$	−4.99664	−	11.9276i	−0.321196	−	0.766738i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.76002	+	0.763286i	−0.176692	+	0.0488644i
$245$		0			0
$246$	−9.50990	−	7.23689i	−0.606329	−	0.461407i
$247$	0.0211960	−	0.0122375i	0.00134867	−	0.000778654i
$248$	−13.4209	+	10.5568i	−0.852231	+	0.670357i
$249$	−6.14446	+	10.6425i	−0.389390	+	0.674442i
$250$	3.35566	−	26.3022i	0.212231	−	1.66350i
$251$	−20.6860			−1.30569			−0.652846	−	0.757491i	$-0.726425\pi$
$251$	−20.6860			−1.30569			−0.652846	+	0.757491i	$0.726425\pi$
$252$		0			0
$253$	4.37139			0.274827
$254$	0.483793	−	3.79205i	0.0303559	−	0.237934i
$255$	8.67756	−	15.0300i	0.543410	−	0.941213i
$256$	8.43969	+	13.5931i	0.527481	+	0.849567i
$257$	15.3732	−	8.87569i	0.958951	−	0.553651i	0.0631009	−	0.998007i	$-0.479901\pi$
$257$	15.3732	−	8.87569i	0.958951	−	0.553651i	0.895850	+	0.444357i	$0.146568\pi$
$258$	−7.09373	−	5.39822i	−0.441636	−	0.336078i
$259$		0			0
$260$	−0.760017	−	2.74820i	−0.0471343	−	0.170436i
$261$	1.55975	+	2.70157i	0.0965464	+	0.167223i
$262$	−4.24728	−	10.1388i	−0.262398	−	0.626379i
$263$	1.80241	+	1.04062i	0.111141	+	0.0641675i	0.554540	−	0.832157i	$-0.312894\pi$
$263$	1.80241	+	1.04062i	0.111141	+	0.0641675i	−0.443399	+	0.896324i	$0.646227\pi$
$264$	3.81375	−	0.548774i	0.234720	−	0.0337747i
$265$		−	9.81243i		−	0.602773i
$266$		0			0
$267$		−	1.29270i		−	0.0791118i
$268$	−13.9233	−	13.7020i	−0.850500	−	0.836986i
$269$	−3.08075	−	1.77867i	−0.187837	−	0.108448i	0.403133	−	0.915142i	$-0.367921\pi$
$269$	−3.08075	−	1.77867i	−0.187837	−	0.108448i	−0.590970	+	0.806694i	$0.701255\pi$
$270$	5.02878	−	2.10662i	0.306042	−	0.128205i
$271$	6.18399	+	10.7110i	0.375650	+	0.650646i	0.990424	−	0.138058i	$-0.0440860\pi$
$271$	6.18399	+	10.7110i	0.375650	+	0.650646i	−0.614774	+	0.788704i	$0.710753\pi$
$272$	−9.25188	−	15.4479i	−0.560978	−	0.936668i
$273$		0			0
$274$	−2.44195	+	3.20894i	−0.147524	+	0.193859i
$275$	−11.6361	+	6.71812i	−0.701685	+	0.405118i
$276$	1.61137	−	6.21230i	0.0969931	−	0.373936i
$277$	5.93162	−	10.2739i	0.356397	−	0.617297i	−0.630959	−	0.775816i	$-0.717338\pi$
$277$	5.93162	−	10.2739i	0.356397	−	0.617297i	0.987356	+	0.158519i	$0.0506718\pi$
$278$	−10.0395	−	1.28085i	−0.602131	−	0.0768204i
$279$	6.03705			0.361429
$280$		0			0
$281$	−19.3428			−1.15390			−0.576948	−	0.816781i	$-0.695756\pi$
$281$	−19.3428			−1.15390			−0.576948	+	0.816781i	$0.695756\pi$
$282$	2.00000	+	0.255162i	0.119098	+	0.0151947i
$283$	−12.4707	+	21.5998i	−0.741304	+	1.28398i	0.210598	+	0.977573i	$0.432459\pi$
$283$	−12.4707	+	21.5998i	−0.741304	+	1.28398i	−0.951902	+	0.306404i	$0.900874\pi$
$284$	6.50376	−	25.0739i	0.385927	−	1.48786i
$285$	−0.220977	+	0.127581i	−0.0130895	+	0.00755725i
$286$	−0.431428	+	0.566934i	−0.0255109	+	0.0335235i
$287$		0			0
$288$	0.625940	−	5.62212i	0.0368838	−	0.331286i
$289$	1.63237	+	2.82735i	0.0960218	+	0.166315i
$290$	−15.6873	+	6.57162i	−0.921192	+	0.385899i
$291$	2.49781	+	1.44211i	0.146424	+	0.0845381i
$292$	2.56818	+	2.52737i	0.150291	+	0.147903i
$293$			6.88234i			0.402071i	0.979584	+	0.201035i	$0.0644306\pi$
$293$			6.88234i			0.402071i	−0.979584	+	0.201035i	$0.935569\pi$
$294$		0			0
$295$		−	13.2528i		−	0.771610i
$296$	2.21236	+	15.3750i	0.128591	+	0.893652i
$297$	−1.17975	−	0.681127i	−0.0684558	−	0.0395230i
$298$	−11.6689	−	27.8553i	−0.675963	−	1.61361i
$299$	0.593329	+	1.02768i	0.0343131	+	0.0594321i
$300$	5.25802	+	19.0128i	0.303572	+	1.09771i
$301$		0			0
$302$	24.9991	+	19.0239i	1.43854	+	1.09470i
$303$	5.35949	−	3.09430i	0.307895	−	0.177763i
$304$	0.00424013	+	0.264706i	0.000243188	+	0.0151819i
$305$	−2.76002	+	4.78049i	−0.158038	+	0.273730i
$306$	−0.805685	+	6.31509i	−0.0460580	+	0.361010i
$307$	17.4213			0.994286			0.497143	−	0.867669i	$-0.334382\pi$
$307$	17.4213			0.994286			0.497143	+	0.867669i	$0.334382\pi$
$308$		0			0
$309$	17.7927			1.01219
$310$	−4.16559	+	32.6505i	−0.236590	+	1.85443i
$311$	12.5580	−	21.7512i	0.712101	−	1.23340i	−0.251965	−	0.967736i	$-0.581077\pi$
$311$	12.5580	−	21.7512i	0.712101	−	1.23340i	0.964067	−	0.265660i	$-0.0855898\pi$
$312$	0.646653	+	0.822096i	0.0366095	+	0.0465420i
$313$	19.1361	−	11.0482i	1.08164	−	0.624484i	0.150300	−	0.988640i	$-0.451976\pi$
$313$	19.1361	−	11.0482i	1.08164	−	0.624484i	0.931338	+	0.364156i	$0.118643\pi$
$314$	6.13237	+	4.66664i	0.346070	+	0.263354i
$315$		0			0
$316$	−24.0739	+	6.65767i	−1.35426	+	0.374523i
$317$	0.811634	+	1.40579i	0.0455859	+	0.0789571i	0.887918	−	0.460002i	$-0.152151\pi$
$317$	0.811634	+	1.40579i	0.0455859	+	0.0789571i	−0.842332	+	0.538959i	$0.818818\pi$
$318$	1.39075	+	3.31990i	0.0779894	+	0.186171i
$319$	3.68023	+	2.12478i	0.206053	+	0.118965i
$320$	29.9746	+	7.26459i	1.67563	+	0.406103i
$321$			6.09316i			0.340087i
$322$		0			0
$323$		−	0.297941i		−	0.0165779i
$324$	−1.40284	+	1.42549i	−0.0779357	+	0.0791941i
$325$	−3.15875	−	1.82370i	−0.175216	−	0.101161i
$326$	−6.20470	+	2.59923i	−0.343647	+	0.143958i
$327$	−3.93162	−	6.80977i	−0.217419	−	0.376581i
$328$	−8.88049	+	22.1896i	−0.490343	+	1.22522i
$329$		0			0
$330$	4.49781	−	5.91051i	0.247596	−	0.325363i
$331$	−23.0949	+	13.3338i	−1.26941	+	0.732894i	−0.974876	−	0.222747i	$-0.928498\pi$
$331$	−23.0949	+	13.3338i	−1.26941	+	0.732894i	−0.294534	+	0.955641i	$0.595164\pi$
$332$	23.7906	+	6.17089i	1.30568	+	0.338672i
$333$	2.74593	−	4.75609i	0.150476	−	0.260632i
$334$	19.7265	+	2.51673i	1.07939	+	0.137709i
$335$	−37.6559			−2.05736
$336$		0			0
$337$	29.8426			1.62563			0.812815	−	0.582522i	$-0.197934\pi$
$337$	29.8426			1.62563			0.812815	+	0.582522i	$0.197934\pi$
$338$	18.0451	+	2.30221i	0.981525	+	0.125224i
$339$	−2.35335	+	4.07612i	−0.127816	+	0.221384i
$340$	−33.5984	−	8.71488i	−1.82213	−	0.472631i
$341$	7.12218	−	4.11199i	0.385688	−	0.222677i
$342$	0.0566820	−	0.0744851i	0.00306501	−	0.00402769i
$343$		0			0
$344$	−6.62423	+	16.5519i	−0.357155	+	0.892421i
$345$	−6.18569	−	10.7139i	−0.333027	−	0.576819i
$346$	−2.31806	+	0.971066i	−0.124620	+	0.0522048i
$347$	−0.820451	−	0.473688i	−0.0440441	−	0.0254289i	0.477816	−	0.878460i	$-0.341428\pi$
$347$	−0.820451	−	0.473688i	−0.0440441	−	0.0254289i	−0.521860	+	0.853031i	$0.674762\pi$
$348$	4.37618	−	4.44684i	0.234588	−	0.238376i
$349$			6.41788i			0.343541i	0.985137	+	0.171771i	$0.0549488\pi$
$349$			6.41788i			0.343541i	−0.985137	+	0.171771i	$0.945051\pi$
$350$		0			0
$351$		−	0.369798i		−	0.0197383i
$352$	−3.09092	−	7.05901i	−0.164747	−	0.376247i
$353$	−12.0146	−	6.93665i	−0.639474	−	0.369200i	0.144938	−	0.989441i	$-0.453702\pi$
$353$	−12.0146	−	6.93665i	−0.639474	−	0.369200i	−0.784412	+	0.620240i	$0.787035\pi$
$354$	1.87837	+	4.48392i	0.0998343	+	0.238318i
$355$	−24.9665	−	43.2432i	−1.32508	−	2.29511i
$356$	−2.49186	+	0.689127i	−0.132068	+	0.0365237i
$357$		0			0
$358$	3.65951	+	2.78483i	0.193411	+	0.147183i
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$	−6.74162	−	8.57068i	−0.355315	−	0.451714i
$361$	9.49781	−	16.4507i	0.499885	−	0.865826i
$362$	−4.20621	+	32.9689i	−0.221074	+	1.73281i
$363$	9.14427			0.479950
$364$		0			0
$365$	6.94571			0.363555
$366$	0.256259	−	2.00860i	0.0133949	−	0.104991i
$367$	9.65903	−	16.7299i	0.504197	−	0.873295i	−0.495791	−	0.868442i	$-0.665122\pi$
$367$	9.65903	−	16.7299i	0.504197	−	0.873295i	0.999988	−	0.00485350i	$-0.00154492\pi$
$368$	−12.8341	+	0.205580i	−0.669024	+	0.0107166i
$369$	7.31806	−	4.22509i	0.380963	−	0.219949i
$370$	23.8280	+	18.1327i	1.23876	+	0.942675i
$371$		0			0
$372$	−3.21830	−	11.6373i	−0.166861	−	0.603365i
$373$	−5.63832	−	9.76585i	−0.291941	−	0.505657i	0.682328	−	0.731047i	$-0.260968\pi$
$373$	−5.63832	−	9.76585i	−0.291941	−	0.505657i	−0.974269	+	0.225390i	$0.927634\pi$
$374$	3.35087	+	7.99897i	0.173269	+	0.413617i
$375$	16.2373	+	9.37462i	0.838491	+	0.484103i
$376$	−0.574323	−	3.99131i	−0.0296185	−	0.205836i
$377$			1.15359i			0.0594128i
$378$		0			0
$379$			25.1457i			1.29165i	0.763486	+	0.645824i	$0.223486\pi$
$379$			25.1457i			1.29165i	−0.763486	+	0.645824i	$0.776514\pi$
$380$	0.363732	+	0.357952i	0.0186590	+	0.0183626i
$381$	2.34097	+	1.35156i	0.119931	+	0.0692424i
$382$	31.1712	−	13.0580i	1.59486	−	0.668105i
$383$	8.88226	+	15.3845i	0.453862	+	0.786112i	0.998622	−	0.0524799i	$-0.0167126\pi$
$383$	8.88226	+	15.3845i	0.453862	+	0.786112i	−0.544760	+	0.838592i	$0.683379\pi$
$384$	−11.1711	+	1.79052i	−0.570074	+	0.0913721i
$385$		0			0
$386$	−17.0215	+	22.3677i	−0.866369	+	1.13848i
$387$	5.45877	−	3.15162i	0.277485	−	0.160206i
$388$	1.44831	−	5.58367i	0.0735270	−	0.283468i
$389$	−7.07233	+	12.2496i	−0.358581	+	0.621081i	−0.987724	−	0.156209i	$-0.950073\pi$
$389$	−7.07233	+	12.2496i	−0.358581	+	0.621081i	0.629143	+	0.777290i	$0.283406\pi$
$390$	2.00000	+	0.255162i	0.101274	+	0.0129206i
$391$	14.4455			0.730539
$392$		0			0
$393$	7.77288			0.392090
$394$	26.6818	+	3.40409i	1.34421	+	0.171496i
$395$	−24.0739	+	41.6972i	−1.21129	+	2.09801i
$396$	−0.684056	+	2.63723i	−0.0343751	+	0.132526i
$397$	10.9558	−	6.32534i	0.549856	−	0.317460i	−0.199208	−	0.979957i	$-0.563837\pi$
$397$	10.9558	−	6.32534i	0.549856	−	0.317460i	0.749064	+	0.662498i	$0.230503\pi$
$398$	12.7190	−	16.7139i	0.637545	−	0.837790i
$399$		0			0
$400$	33.8470	−	20.2712i	1.69235	−	1.01356i
$401$	12.3904	+	21.4608i	0.618747	+	1.07170i	0.989715	+	0.143055i	$0.0456926\pi$
$401$	12.3904	+	21.4608i	0.618747	+	1.07170i	−0.370968	+	0.928646i	$0.620974\pi$
$402$	12.7404	−	5.33711i	0.635433	−	0.266191i
$403$	1.93339	+	1.11624i	0.0963090	+	0.0556040i
$404$	−8.82182	−	8.68164i	−0.438902	−	0.431928i
$405$			3.85529i			0.191571i
$406$		0			0
$407$		−	7.48131i		−	0.370835i
$408$	12.6028	−	1.81345i	0.623929	−	0.0897792i
$409$	5.02003	+	2.89832i	0.248225	+	0.143313i	0.618951	−	0.785430i	$-0.287558\pi$
$409$	5.02003	+	2.89832i	0.248225	+	0.143313i	−0.370726	+	0.928742i	$0.620891\pi$
$410$	17.8013	+	42.4941i	0.879144	+	2.09863i
$411$	−1.42568	−	2.46934i	−0.0703234	−	0.121804i
$412$	−9.48515	−	34.2980i	−0.467300	−	1.68974i
$413$		0			0
$414$	3.61137	+	2.74820i	0.177489	+	0.135067i
$415$	41.0300	−	23.6887i	2.01408	−	1.16283i
$416$	1.23998	−	1.68477i	0.0607951	−	0.0826027i
$417$	3.57828	−	6.19776i	0.175229	−	0.303506i
$418$	0.0161366	−	0.126481i	0.000789267	−	0.00618640i
$419$	2.42966			0.118697			0.0593484	−	0.998237i	$-0.481098\pi$
$419$	2.42966			0.118697			0.0593484	+	0.998237i	$0.481098\pi$
$420$		0			0
$421$	−25.9373			−1.26411			−0.632054	−	0.774924i	$-0.717788\pi$
$421$	−25.9373			−1.26411			−0.632054	+	0.774924i	$0.717788\pi$
$422$	3.52003	−	27.5906i	0.171353	−	1.34309i
$423$	−0.712838	+	1.23467i	−0.0346594	+	0.0600318i
$424$	5.65819	−	4.45069i	0.274786	−	0.216144i
$425$	−38.4522	+	22.2004i	−1.86521	+	1.07688i
$426$	14.5761	+	11.0922i	0.706214	+	0.537418i
$427$		0			0
$428$	11.7454	−	3.24822i	0.567738	−	0.157009i
$429$	−0.251879	−	0.436267i	−0.0121608	−	0.0210632i
$430$	13.2785	+	31.6976i	0.640348	+	1.52860i
$431$	12.7781	+	7.37742i	0.615497	+	0.355358i	0.775114	−	0.631821i	$-0.217692\pi$
$431$	12.7781	+	7.37742i	0.615497	+	0.355358i	−0.159616	+	0.987179i	$0.551026\pi$
$432$	3.49569	+	1.94426i	0.168186	+	0.0935433i
$433$		−	35.7396i		−	1.71754i	−0.512364	−	0.858769i	$-0.671230\pi$
$433$		−	35.7396i		−	1.71754i	0.512364	−	0.858769i	$-0.328770\pi$
$434$		0			0
$435$		−	12.0266i		−	0.576632i
$436$	−11.0309	+	11.2090i	−0.528284	+	0.536814i
$437$	−0.183929	−	0.106192i	−0.00879854	−	0.00507984i
$438$	−2.34999	+	0.984440i	−0.112287	+	0.0470384i
$439$	9.91925	+	17.1806i	0.473420	+	0.819987i	0.999537	−	0.0304249i	$-0.00968604\pi$
$439$	9.91925	+	17.1806i	0.473420	+	0.819987i	−0.526117	+	0.850412i	$0.676353\pi$
$440$	−13.7911	−	5.51933i	−0.657466	−	0.263124i
$441$		0			0
$442$	−1.42568	+	1.87346i	−0.0678125	+	0.0891116i
$443$	−16.4378	+	9.49035i	−0.780982	+	0.450900i	−0.836778	−	0.547542i	$-0.815564\pi$
$443$	−16.4378	+	9.49035i	−0.780982	+	0.450900i	0.0557962	+	0.998442i	$0.482230\pi$
$444$	−10.6319	−	2.75774i	−0.504567	−	0.130877i
$445$	−2.49186	+	4.31603i	−0.118126	+	0.204599i
$446$	−11.3676	−	1.45028i	−0.538270	−	0.0686730i
$447$	21.3551			1.01006
$448$		0			0
$449$	−25.2845			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$449$	−25.2845			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$450$	−13.8366	−	1.76529i	−0.652263	−	0.0832164i
$451$	5.75564	−	9.96906i	0.271022	−	0.469425i
$452$	9.11185	+	2.36347i	0.428586	+	0.111168i
$453$	−19.2373	+	11.1067i	−0.903848	+	0.521837i
$454$	10.3507	−	13.6017i	0.485781	−	0.638359i
$455$		0			0
$456$	−0.173798	−	0.0695553i	−0.00813882	−	0.00325723i
$457$	−11.4837	−	19.8904i	−0.537186	−	0.930433i	−0.999054	−	0.0434847i	$-0.986154\pi$
$457$	−11.4837	−	19.8904i	−0.537186	−	0.930433i	0.461868	−	0.886949i	$-0.347179\pi$
$458$	−31.0217	+	12.9954i	−1.44955	+	0.607233i
$459$	−3.89853	−	2.25082i	−0.181968	−	0.105059i
$460$	−17.3551	+	17.6353i	−0.809186	+	0.822252i
$461$		−	2.95838i		−	0.137786i	−0.997624	−	0.0688928i	$-0.978053\pi$
$461$		−	2.95838i		−	0.137786i	0.997624	−	0.0688928i	$-0.0219466\pi$
$462$		0			0
$463$		−	3.30669i		−	0.153675i	−0.997044	−	0.0768374i	$-0.975518\pi$
$463$		−	3.30669i		−	0.153675i	0.997044	−	0.0768374i	$-0.0244822\pi$
$464$	−10.9048	−	6.06514i	−0.506244	−	0.281567i
$465$	−20.1564	−	11.6373i	−0.934729	−	0.539666i
$466$	10.8899	+	25.9957i	0.504465	+	1.20423i
$467$	−5.95282	−	10.3106i	−0.275464	−	0.477117i	0.694788	−	0.719214i	$-0.255498\pi$
$467$	−5.95282	−	10.3106i	−0.275464	−	0.477117i	−0.970252	+	0.242097i	$0.922165\pi$
$468$	−0.712838	+	0.197136i	−0.0329510	+	0.00911263i
$469$		0			0
$470$	−6.18569	−	4.70722i	−0.285325	−	0.217128i
$471$	−4.71898	+	2.72451i	−0.217439	+	0.125539i
$472$	7.64206	−	6.01117i	0.351754	−	0.276687i
$473$	4.29331	−	7.43623i	0.197406	−	0.341918i
$474$	2.23519	−	17.5198i	0.102666	−	0.804710i
$475$	0.652798			0.0299524
$476$		0			0
$477$	−2.54519			−0.116536
$478$	1.71995	−	13.4812i	0.0786686	−	0.616617i
$479$	5.95186	−	10.3089i	0.271947	−	0.471026i	−0.697413	−	0.716669i	$-0.745666\pi$
$479$	5.95186	−	10.3089i	0.271947	−	0.471026i	0.969360	+	0.245643i	$0.0789990\pi$
$480$	−12.9273	+	17.5644i	−0.590048	+	0.801702i
$481$	1.75879	−	1.01544i	0.0801940	−	0.0463000i
$482$	11.7136	+	8.91387i	0.533540	+	0.406016i
$483$		0			0
$484$	−4.87474	−	17.6269i	−0.221579	−	0.801222i
$485$	−5.55975	−	9.62978i	−0.252455	−	0.437266i
$486$	−0.546424	−	1.30439i	−0.0247863	−	0.0591681i
$487$	6.50151	+	3.75365i	0.294612	+	0.170094i	0.640020	−	0.768358i	$-0.278926\pi$
$487$	6.50151	+	3.75365i	0.294612	+	0.170094i	−0.345408	+	0.938453i	$0.612260\pi$
$488$	−4.00848	+	0.576794i	−0.181455	+	0.0261102i
$489$		−	4.75680i		−	0.215110i
$490$		0			0
$491$			22.0031i			0.992988i	0.868040	+	0.496494i	$0.165380\pi$
$491$			22.0031i			0.992988i	−0.868040	+	0.496494i	$0.834620\pi$
$492$	−12.0457	−	11.8543i	−0.543061	−	0.534431i
$493$	12.1615	+	7.02145i	0.547727	+	0.316230i
$494$	0.0319249	−	0.0133737i	0.00143637	−	0.000601713i
$495$	2.62594	+	4.54826i	0.118027	+	0.204429i
$496$	−20.7169	+	12.4075i	−0.930215	+	0.557113i
$497$		0			0
$498$	−10.5245	+	13.8301i	−0.471613	+	0.619740i
$499$	1.22277	−	0.705968i	0.0547389	−	0.0316035i	−0.472381	−	0.881395i	$-0.656605\pi$
$499$	1.22277	−	0.705968i	0.0547389	−	0.0316035i	0.527120	+	0.849791i	$0.323272\pi$
$500$	9.41494	−	36.2973i	0.421049	−	1.62326i
$501$	−7.03090	+	12.1779i	−0.314118	+	0.544068i
$502$	−29.0193	−	3.70231i	−1.29519	−	0.165242i
$503$	26.2303			1.16955			0.584775	−	0.811196i	$-0.301183\pi$
$503$	26.2303			1.16955			0.584775	+	0.811196i	$0.301183\pi$
$504$		0			0
$505$	−23.8589			−1.06171
$506$	6.13237	+	0.782374i	0.272617	+	0.0347808i
$507$	−6.43162	+	11.1399i	−0.285638	+	0.494740i
$508$	1.35737	−	5.23306i	0.0602236	−	0.232179i
$509$	4.38419	−	2.53121i	0.194326	−	0.112194i	−0.399680	−	0.916655i	$-0.630879\pi$
$509$	4.38419	−	2.53121i	0.194326	−	0.112194i	0.594006	+	0.804461i	$0.297545\pi$
$510$	14.8632	−	19.5316i	0.658156	−	0.864874i
$511$		0			0
$512$	9.40673	+	20.5794i	0.415723	+	0.909491i
$513$	0.0330925	+	0.0573178i	0.00146107	+	0.00253064i
$514$	23.1547	−	9.69978i	1.02131	−	0.427839i
$515$	−59.4058	−	34.2980i	−2.61773	−	1.51135i
$516$	−8.98523	−	8.84246i	−0.395553	−	0.389268i
$517$			1.94213i			0.0854149i
$518$		0			0
$519$		−	1.77713i		−	0.0780074i
$520$	−0.574323	−	3.99131i	−0.0251857	−	0.175031i
$521$	8.60044	+	4.96547i	0.376792	+	0.217541i	0.676422	−	0.736515i	$-0.263530\pi$
$521$	8.60044	+	4.96547i	0.376792	+	0.217541i	−0.299630	+	0.954056i	$0.596863\pi$
$522$	1.70457	+	4.06904i	0.0746071	+	0.178097i
$523$	15.6686	+	27.1389i	0.685142	+	1.18670i	0.973392	+	0.229146i	$0.0735933\pi$
$523$	15.6686	+	27.1389i	0.685142	+	1.18670i	−0.288250	+	0.957555i	$0.593073\pi$
$524$	−4.14366	−	14.9833i	−0.181017	−	0.654550i
$525$		0			0
$526$	2.34225	+	1.78242i	0.102127	+	0.0777171i
$527$	23.5356	−	13.5883i	1.02523	−	0.591916i
$528$	5.44831	−	0.0872726i	0.237107	−	0.00379805i
$529$	−6.35135	+	11.0009i	−0.276146	+	0.478299i
$530$	1.75619	−	13.7653i	0.0762840	−	0.597926i
$531$	−3.43757			−0.149178
$532$		0			0
$533$	3.12485			0.135352
$534$	0.231362	−	1.81345i	0.0100120	−	0.0784757i
$535$	11.7454	−	20.3437i	0.507800	−	0.879535i
$536$	−17.0798	−	21.7138i	−0.737737	−	0.937891i
$537$	−2.81607	+	1.62586i	−0.121522	+	0.0701610i
$538$	−4.00347	−	3.04658i	−0.172602	−	0.131347i
$539$		0			0
$540$	7.43162	−	2.05523i	0.319806	−	0.0884428i
$541$	2.09313	+	3.62541i	0.0899908	+	0.155869i	0.907507	−	0.420037i	$-0.137983\pi$
$541$	2.09313	+	3.62541i	0.0899908	+	0.155869i	−0.817516	+	0.575906i	$0.804650\pi$
$542$	6.75815	+	16.1326i	0.290287	+	0.692955i
$543$	−20.3529	−	11.7508i	−0.873427	−	0.504274i
$544$	−10.2141	−	23.3269i	−0.437927	−	1.00013i
$545$			30.3151i			1.29856i
$546$		0			0
$547$			12.4674i			0.533067i	0.963826	+	0.266533i	$0.0858782\pi$
$547$			12.4674i			0.533067i	−0.963826	+	0.266533i	$0.914122\pi$
$548$	−4.00000	+	4.06459i	−0.170872	+	0.173631i
$549$	1.23998	+	0.715904i	0.0529212	+	0.0305540i
$550$	−17.5260	+	7.34188i	−0.747313	+	0.313059i
$551$	−0.103232	−	0.178803i	−0.00439784	−	0.00761728i
$552$	3.37235	−	8.42648i	0.143537	−	0.358655i
$553$		0			0
$554$	10.1599	−	13.3510i	0.431653	−	0.567230i
$555$	−18.3361	+	10.5864i	−0.778324	+	0.449366i
$556$	−13.8546	−	3.59367i	−0.587567	−	0.152405i
$557$	18.2744	−	31.6521i	0.774309	−	1.34114i	−0.160872	−	0.986975i	$-0.551431\pi$
$557$	18.2744	−	31.6521i	0.774309	−	1.34114i	0.935182	−	0.354168i	$-0.115236\pi$
$558$	8.46903	+	1.08049i	0.358523	+	0.0457407i
$559$	2.33092			0.0985876
$560$		0			0
$561$	−6.13237			−0.258909
$562$	−27.1349	−	3.46190i	−1.14462	−	0.146032i
$563$	−21.3672	+	37.0091i	−0.900520	+	1.55975i	−0.0737002	+	0.997280i	$0.523481\pi$
$563$	−21.3672	+	37.0091i	−0.900520	+	1.55975i	−0.826820	+	0.562466i	$0.809853\pi$
$564$	2.76002	+	0.715904i	0.116218	+	0.0301450i
$565$	15.7146	−	9.07283i	0.661118	−	0.381697i
$566$	−21.3602	+	28.0692i	−0.897838	+	1.17984i
$567$		0			0
$568$	13.6114	−	34.0107i	0.571120	−	1.42706i
$569$	−10.7265	−	18.5788i	−0.449678	−	0.778866i	0.548687	−	0.836028i	$-0.315128\pi$
$569$	−10.7265	−	18.5788i	−0.449678	−	0.778866i	−0.998365	+	0.0571625i	$0.981795\pi$
$570$	−0.332830	+	0.139427i	−0.0139407	+	0.00583993i
$571$	−18.3349	−	10.5856i	−0.767291	−	0.442996i	0.0646165	−	0.997910i	$-0.479418\pi$
$571$	−18.3349	−	10.5856i	−0.767291	−	0.442996i	−0.831907	+	0.554915i	$0.812751\pi$
$572$	−0.706693	+	0.718104i	−0.0295483	+	0.0300254i
$573$			23.8972i			0.998321i
$574$		0			0
$575$			31.6506i			1.31992i
$576$	1.88432	−	7.77492i	0.0785133	−	0.323955i
$577$	−4.10289	−	2.36880i	−0.170806	−	0.0986146i	0.412160	−	0.911111i	$-0.364774\pi$
$577$	−4.10289	−	2.36880i	−0.170806	−	0.0986146i	−0.582966	+	0.812497i	$0.698108\pi$
$578$	1.78393	+	4.25848i	0.0742017	+	0.177129i
$579$	−9.93757	−	17.2124i	−0.412991	−	0.715322i
$580$	−23.1830	+	6.41129i	−0.962623	+	0.266214i
$581$		0			0
$582$	3.24593	+	2.47010i	0.134548	+	0.102389i
$583$	−3.00267	+	1.73359i	−0.124358	+	0.0717981i
$584$	3.15041	+	4.00514i	0.130365	+	0.165734i
$585$	−0.712838	+	1.23467i	−0.0294722	+	0.0510474i
$586$	−1.23177	+	9.65484i	−0.0508841	+	0.398838i
$587$	−29.8450			−1.23184			−0.615918	−	0.787810i	$-0.711215\pi$
$587$	−29.8450			−1.23184			−0.615918	+	0.787810i	$0.711215\pi$
$588$		0			0
$589$	−0.399562			−0.0164636
$590$	2.37194	−	18.5916i	0.0976512	−	0.765406i
$591$	−9.50990	+	16.4716i	−0.391185	+	0.677553i
$592$	0.351835	+	21.9646i	0.0144603	+	0.902741i
$593$	−22.9586	+	13.2551i	−0.942796	+	0.544323i	−0.890836	−	0.454326i	$-0.849880\pi$
$593$	−22.9586	+	13.2551i	−0.942796	+	0.544323i	−0.0519600	+	0.998649i	$0.516547\pi$
$594$	−1.53309	−	1.16666i	−0.0629035	−	0.0478686i
$595$		0			0
$596$	−11.3842	−	41.1651i	−0.466317	−	1.68619i
$597$	7.42568	+	12.8616i	0.303913	+	0.526392i
$598$	0.648418	+	1.54786i	0.0265158	+	0.0632967i
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	0.820416	−	0.571767i	$-0.193742\pi$
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	−0.0849563	+	0.996385i	$0.527075\pi$
$600$	3.97334	+	27.6131i	0.162211	+	1.12730i
$601$			10.8255i			0.441581i	0.975321	+	0.220790i	$0.0708637\pi$
$601$			10.8255i			0.441581i	−0.975321	+	0.220790i	$0.929136\pi$
$602$		0			0
$603$			9.76735i			0.397757i
$604$	31.6650	+	31.1618i	1.28843	+	1.26796i
$605$	−30.5307	−	17.6269i	−1.24125	−	0.716635i
$606$	8.07233	−	3.38160i	0.327916	−	0.137368i
$607$	−6.95330	−	12.0435i	−0.282226	−	0.488830i	0.689707	−	0.724089i	$-0.257739\pi$
$607$	−6.95330	−	12.0435i	−0.282226	−	0.488830i	−0.971933	+	0.235259i	$0.924406\pi$
$608$	−0.0414278	+	0.372099i	−0.00168012	+	0.0150906i
$609$		0			0
$610$	−4.72746	+	6.21230i	−0.191409	+	0.251529i
$611$	−0.456579	+	0.263606i	−0.0184712	+	0.0106644i
$612$	−2.26050	+	8.71488i	−0.0913753	+	0.352278i
$613$	−0.322444	+	0.558490i	−0.0130234	+	0.0225572i	−0.872464	−	0.488679i	$-0.837479\pi$
$613$	−0.322444	+	0.558490i	−0.0130234	+	0.0225572i	0.859440	+	0.511236i	$0.170812\pi$
$614$	24.4393	+	3.11800i	0.986291	+	0.125832i
$615$	−32.5779			−1.31367
$616$		0			0
$617$	12.3626			0.497701			0.248850	−	0.968542i	$-0.419947\pi$
$617$	12.3626			0.497701			0.248850	+	0.968542i	$0.419947\pi$
$618$	24.9603	+	3.18446i	1.00405	+	0.128098i
$619$	−5.69875	+	9.87053i	−0.229052	+	0.396730i	−0.957527	−	0.288342i	$-0.906896\pi$
$619$	−5.69875	+	9.87053i	−0.229052	+	0.396730i	0.728475	+	0.685072i	$0.240229\pi$
$620$	−11.6873	+	45.0580i	−0.469375	+	1.80957i
$621$	−2.77902	+	1.60447i	−0.111518	+	0.0643852i
$622$	21.5099	−	28.2659i	0.862469	−	1.13336i
$623$		0			0
$624$	0.760017	+	1.26901i	0.0304250	+	0.0508009i
$625$	−11.4837	−	19.8904i	−0.459349	−	0.795616i
$626$	28.8223	−	12.0740i	1.15197	−	0.482576i
$627$	0.0780814	+	0.0450803i	0.00311827	+	0.00180033i
$628$	7.76753	+	7.64411i	0.309958	+	0.305033i
$629$		−	24.7224i		−	0.985745i
$630$		0			0
$631$		−	10.8050i		−	0.430140i	−0.976599	−	0.215070i	$-0.931002\pi$
$631$		−	10.8050i		−	0.430140i	0.976599	−	0.215070i	$-0.0689979\pi$
$632$	−34.9635	+	5.03101i	−1.39077	+	0.200123i
$633$	17.0327	+	9.83381i	0.676988	+	0.390859i
$634$	0.886991	+	2.11737i	0.0352269	+	0.0840913i
$635$	−5.21065	−	9.02511i	−0.206778	−	0.358150i
$636$	1.35682	+	4.90621i	0.0538014	+	0.194544i
$637$		0			0
$638$	4.78250	+	3.63941i	0.189341	+	0.144085i
$639$	−11.2166	+	6.47590i	−0.443722	+	0.256183i
$640$	40.7494	+	15.5558i	1.61076	+	0.614897i
$641$	−1.12662	+	1.95136i	−0.0444988	+	0.0770741i	−0.887417	−	0.460968i	$-0.847502\pi$
$641$	−1.12662	+	1.95136i	−0.0444988	+	0.0770741i	0.842918	+	0.538042i	$0.180836\pi$
$642$	−1.09053	+	8.54775i	−0.0430398	+	0.337353i
$643$	−22.0574			−0.869860			−0.434930	−	0.900464i	$-0.643227\pi$
$643$	−22.0574			−0.869860			−0.434930	+	0.900464i	$0.643227\pi$
$644$		0			0
$645$	−24.3008			−0.956844
$646$	0.0533242	−	0.417964i	0.00209801	−	0.0164446i
$647$	−2.26417	+	3.92166i	−0.0890137	+	0.154176i	−0.907094	−	0.420927i	$-0.861705\pi$
$647$	−2.26417	+	3.92166i	−0.0890137	+	0.154176i	0.818081	+	0.575103i	$0.195038\pi$
$648$	−2.22310	+	1.74867i	−0.0873315	+	0.0686942i
$649$	−4.05546	+	2.34142i	−0.159191	+	0.0919089i
$650$	−4.10483	−	3.12371i	−0.161004	−	0.122522i
$651$		0			0
$652$	−9.16942	+	2.53581i	−0.359102	+	0.0993101i
$653$	−20.6749	−	35.8099i	−0.809071	−	1.40135i	−0.913508	−	0.406820i	$-0.866638\pi$
$653$	−20.6749	−	35.8099i	−0.809071	−	1.40135i	0.104438	−	0.994531i	$-0.466696\pi$
$654$	−4.29666	−	10.2567i	−0.168013	−	0.401069i
$655$	−25.9519	−	14.9833i	−1.01403	−	0.585448i
$656$	−16.4293	+	29.5392i	−0.641458	+	1.15331i
$657$		−	1.80161i		−	0.0702874i
$658$		0			0
$659$		−	10.6413i		−	0.414526i	−0.978285	−	0.207263i	$-0.933544\pi$
$659$		−	10.6413i		−	0.414526i	0.978285	−	0.207263i	$-0.0664556\pi$
$660$	7.36756	−	7.48652i	0.286782	−	0.291412i
$661$	−41.7871	−	24.1258i	−1.62533	−	0.938384i	−0.985462	−	0.169899i	$-0.945656\pi$
$661$	−41.7871	−	24.1258i	−1.62533	−	0.938384i	−0.639867	−	0.768485i	$-0.721011\pi$
$662$	−34.7849	+	14.5719i	−1.35196	+	0.566351i
$663$	−0.832347	−	1.44167i	−0.0323257	−	0.0559897i
$664$	32.2700	+	12.9147i	1.25232	+	0.501189i
$665$		0			0
$666$	4.70334	−	6.18059i	0.182251	−	0.239493i
$667$	8.66919	−	5.00516i	0.335672	−	0.193801i
$668$	27.2227	+	7.06114i	1.05328	+	0.273204i
$669$	4.05162	−	7.01760i	0.156645	−	0.271316i
$670$	−52.8254	−	6.73951i	−2.04082	−	0.260370i
$671$	1.95049			0.0752977
$672$		0			0
$673$	−0.148647			−0.00572991			−0.00286496	−	0.999996i	$-0.500912\pi$
$673$	−0.148647			−0.00572991			−0.00286496	+	0.999996i	$0.500912\pi$
$674$	41.8645	+	5.34111i	1.61256	+	0.205732i
$675$	4.93162	−	8.54182i	0.189818	−	0.328775i
$676$	24.9024	+	6.45929i	0.957785	+	0.248434i
$677$	34.3935	−	19.8571i	1.32185	−	0.763170i	0.337825	−	0.941209i	$-0.390309\pi$
$677$	34.3935	−	19.8571i	1.32185	−	0.763170i	0.984023	+	0.178039i	$0.0569754\pi$
$678$	−4.03090	+	5.29696i	−0.154806	+	0.203428i
$679$		0			0
$680$	−45.5735	−	18.2389i	−1.74766	−	0.699430i
$681$	6.04300	+	10.4668i	0.231568	+	0.401088i
$682$	10.7272	−	4.49378i	0.410768	−	0.172076i
$683$	36.9070	+	21.3083i	1.41221	+	0.815339i	0.995596	−	0.0937450i	$-0.0298838\pi$
$683$	36.9070	+	21.3083i	1.41221	+	0.815339i	0.416613	+	0.909084i	$0.363217\pi$
$684$	0.0928470	−	0.0943462i	0.00355010	−	0.00360742i
$685$			10.9928i			0.420013i
$686$		0			0
$687$		−	23.7826i		−	0.907362i
$688$	−12.2552	+	22.0342i	−0.467223	+	0.840045i
$689$	−0.815106	−	0.470602i	−0.0310531	−	0.0179285i
$690$	−6.76002	−	16.1371i	−0.257349	−	0.614327i
$691$	−2.22317	−	3.85064i	−0.0845733	−	0.146485i	0.820636	−	0.571451i	$-0.193619\pi$
$691$	−2.22317	−	3.85064i	−0.0845733	−	0.146485i	−0.905209	+	0.424966i	$0.860286\pi$
$692$	−3.42568	+	0.947375i	−0.130225	+	0.0360138i
$693$		0			0
$694$	−1.06618	−	0.811350i	−0.0404718	−	0.0307984i
$695$	−23.8942	+	13.7953i	−0.906357	+	0.523285i
$696$	6.93497	−	5.45499i	0.262869	−	0.206771i
$697$	19.0198	−	32.9433i	0.720427	−	1.24782i
$698$	−1.14865	+	9.00327i	−0.0434769	+	0.340779i
$699$	−19.9294			−0.753800
$700$		0			0
$701$	−24.9907			−0.943885			−0.471942	−	0.881629i	$-0.656447\pi$
$701$	−24.9907			−0.943885			−0.471942	+	0.881629i	$0.656447\pi$
$702$	0.0661849	−	0.518768i	0.00249799	−	0.0195796i
$703$	−0.181739	+	0.314782i	−0.00685442	+	0.0118722i
$704$	−3.07269	−	10.4559i	−0.115806	−	0.394071i
$705$	4.76002	−	2.74820i	0.179273	−	0.103503i
$706$	−15.6131	−	11.8814i	−0.587608	−	0.447161i
$707$		0			0
$708$	1.83254	+	6.62642i	0.0688712	+	0.249036i
$709$	−9.07409	−	15.7168i	−0.340785	−	0.590257i	0.643794	−	0.765199i	$-0.277359\pi$
$709$	−9.07409	−	15.7168i	−0.340785	−	0.590257i	−0.984579	+	0.174942i	$0.944026\pi$
$710$	−27.2845	−	65.1318i	−1.02397	−	2.44435i
$711$	10.8156	+	6.24438i	0.405616	+	0.234183i
$712$	−3.61903	+	0.520754i	−0.135629	+	0.0195161i
$713$		−	19.3725i		−	0.725507i
$714$		0			0
$715$			1.94213i			0.0726316i
$716$	4.63530	+	4.56165i	0.173229	+	0.170477i
$717$	8.32244	+	4.80497i	0.310807	+	0.179445i
$718$	−9.03705	+	3.78573i	−0.337260	+	0.141282i
$719$	−20.5818	−	35.6488i	−0.767573	−	1.32948i	−0.938875	−	0.344257i	$-0.888131\pi$
$719$	−20.5818	−	35.6488i	−0.767573	−	1.32948i	0.171302	−	0.985219i	$-0.445203\pi$
$720$	−7.92349	−	13.2299i	−0.295291	−	0.493049i
$721$		0			0
$722$	16.2682	−	21.3778i	0.605440	−	0.795601i
$723$	−9.01386	+	5.20415i	−0.335229	+	0.193545i
$724$	−11.8013	+	45.4974i	−0.438592	+	1.69090i
$725$	−15.3842	+	26.6463i	−0.571357	+	0.989619i
$726$	12.8280	+	1.63660i	0.476091	+	0.0607401i
$727$	−5.77231			−0.214083			−0.107042	−	0.994255i	$-0.534138\pi$
$727$	−5.77231			−0.214083			−0.107042	+	0.994255i	$0.534138\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	9.74374	+	1.24312i	0.360632	+	0.0460098i
$731$	14.1875	−	24.5734i	0.524742	−	0.908880i
$732$	0.718983	−	2.77189i	0.0265744	−	0.102452i
$733$	6.63928	−	3.83319i	0.245227	−	0.141582i	−0.372350	−	0.928093i	$-0.621448\pi$
$733$	6.63928	−	3.83319i	0.245227	−	0.141582i	0.617577	+	0.786510i	$0.288114\pi$
$734$	16.5444	−	21.7407i	0.610663	−	0.802465i
$735$		0			0
$736$	−18.0410	−	2.00860i	−0.665001	−	0.0740381i
$737$	6.65280	+	11.5230i	0.245059	+	0.424455i
$738$	11.0223	−	4.61737i	0.405736	−	0.169968i
$739$	−17.3753	−	10.0317i	−0.639162	−	0.369021i	0.145129	−	0.989413i	$-0.453640\pi$
$739$	−17.3753	−	10.0317i	−0.639162	−	0.369021i	−0.784292	+	0.620392i	$0.786973\pi$
$740$	30.1816	+	29.7020i	1.10950	+	1.09187i
$741$			0.0244750i			0.000899113i
$742$		0			0
$743$		−	8.26368i		−	0.303165i	−0.988445	−	0.151583i	$-0.951563\pi$
$743$		−	8.26368i		−	0.303165i	0.988445	−	0.151583i	$-0.0484369\pi$
$744$	−2.43198	−	16.9013i	−0.0891607	−	0.619631i
$745$	−71.3000	−	41.1651i	−2.61223	−	1.50817i
$746$	−6.16182	−	14.7091i	−0.225600	−	0.538538i
$747$	−6.14446	−	10.6425i	−0.224814	−	0.389390i
$748$	3.26912	+	11.8210i	0.119531	+	0.432220i
$749$		0			0
$750$	21.1006	+	16.0572i	0.770484	+	0.586326i
$751$	−23.4113	+	13.5165i	−0.854289	+	0.493224i	−0.862096	−	0.506746i	$-0.830848\pi$
$751$	−23.4113	+	13.5165i	−0.854289	+	0.493224i	0.00780684	+	0.999970i	$0.497515\pi$
$752$	−0.0913358	−	5.70197i	−0.00333067	−	0.207930i
$753$	10.3430	−	17.9146i	0.376921	−	0.652846i
$754$	−0.206464	+	1.61830i	−0.00751899	+	0.0589351i
$755$	85.6388			3.11672
$756$		0			0
$757$	21.9417			0.797486			0.398743	−	0.917063i	$-0.369447\pi$
$757$	21.9417			0.797486			0.398743	+	0.917063i	$0.369447\pi$
$758$	−4.50048	+	35.2755i	−0.163465	+	1.28126i
$759$	−2.18569	+	3.78573i	−0.0793357	+	0.137413i
$760$	0.446194	+	0.567250i	0.0161851	+	0.0205763i
$761$	−1.02680	+	0.592825i	−0.0372216	+	0.0214899i	−0.518495	−	0.855080i	$-0.673508\pi$
$761$	−1.02680	+	0.592825i	−0.0372216	+	0.0214899i	0.481274	+	0.876570i	$0.340174\pi$
$762$	3.04211	+	2.31500i	0.110204	+	0.0838636i
$763$		0			0
$764$	46.0653	−	12.7394i	1.66659	−	0.460896i
$765$	8.67756	+	15.0300i	0.313738	+	0.543410i
$766$	9.70695	+	23.1718i	0.350726	+	0.837230i
$767$	−1.10090	−	0.635603i	−0.0397511	−	0.0229503i
$768$	−15.9918	+	0.512453i	−0.577054	+	0.0184916i
$769$			19.0892i			0.688373i	0.938901	+	0.344186i	$0.111845\pi$
$769$			19.0892i			0.688373i	−0.938901	+	0.344186i	$0.888155\pi$
$770$		0			0
$771$			17.7514i			0.639301i
$772$	−27.8817	+	28.3319i	−1.00348	+	1.01969i
$773$	30.7887	+	17.7759i	1.10739	+	0.639353i	0.938153	−	0.346222i	$-0.112535\pi$
$773$	30.7887	+	17.7759i	1.10739	+	0.639353i	0.169240	+	0.985575i	$0.445869\pi$
$774$	8.22186	−	3.44424i	0.295529	−	0.123801i
$775$	29.7725	+	51.5674i	1.06946	+	1.85236i
$776$	3.03110	−	7.57379i	0.108810	−	0.271883i
$777$		0			0
$778$	−12.1138	+	15.9185i	−0.434299	+	0.570707i
$779$	−0.484346	+	0.279637i	−0.0173535	+	0.0100190i
$780$	2.76002	+	0.715904i	0.0988245	+	0.0256335i
$781$	−8.82182	+	15.2798i	−0.315670	+	0.546756i
$782$	20.2647	+	2.58540i	0.724666	+	0.0924536i
$783$	−3.11951			−0.111482
$784$		0			0
$785$	21.0075			0.749790
$786$	10.9041	+	1.39116i	0.388937	+	0.0496210i
$787$	−21.3018	+	36.8958i	−0.759327	+	1.31519i	0.183868	+	0.982951i	$0.441138\pi$
$787$	−21.3018	+	36.8958i	−0.759327	+	1.31519i	−0.943194	+	0.332241i	$0.892195\pi$
$788$	36.8211	+	9.55081i	1.31170	+	0.340233i
$789$	−1.80241	+	1.04062i	−0.0641675	+	0.0370471i
$790$	−41.2347	+	54.1860i	−1.46706	+	1.92785i
$791$		0			0
$792$	−1.43162	+	3.57719i	−0.0508706	+	0.127110i
$793$	0.264740	+	0.458543i	0.00940118	+	0.0162833i
$794$	16.5014	−	6.91263i	0.585612	−	0.245320i
$795$	8.49781	+	4.90621i	0.301386	+	0.174005i
$796$	20.8341	−	21.1705i	0.738446	−	0.750369i
$797$		−	23.1179i		−	0.818879i	−0.912337	−	0.409440i	$-0.865724\pi$
$797$		−	23.1179i		−	0.818879i	0.912337	−	0.409440i	$-0.134276\pi$
$798$		0			0
$799$			6.41788i			0.227048i
$800$	51.1100	−	22.3795i	1.80701	−	0.791235i
$801$	1.11951	+	0.646349i	0.0395559	+	0.0228376i
$802$	13.5408	+	32.3237i	0.478142	+	1.14139i
$803$	−1.22712	−	2.12544i	−0.0433042	−	0.0750051i
$804$	18.8280	−	5.20690i	0.664011	−	0.183633i
$805$		0			0
$806$	2.51246	+	1.91194i	0.0884976	+	0.0673453i
$807$	3.08075	−	1.77867i	0.108448	−	0.0626123i
$808$	−10.8218	−	13.7579i	−0.380710	−	0.484000i
$809$	16.0852	−	27.8604i	0.565525	−	0.979518i	−0.431475	−	0.902125i	$-0.642007\pi$
$809$	16.0852	−	27.8604i	0.565525	−	0.979518i	0.997001	−	0.0773937i	$-0.0246598\pi$
$810$	−0.690004	+	5.40836i	−0.0242443	+	0.190031i
$811$	41.0797			1.44250			0.721251	−	0.692673i	$-0.243567\pi$
$811$	41.0797			1.44250			0.721251	+	0.692673i	$0.243567\pi$
$812$		0			0
$813$	−12.3680			−0.433764
$814$	1.33897	−	10.4951i	0.0469310	−	0.367853i
$815$	−9.16942	+	15.8819i	−0.321191	+	0.556319i
$816$	18.0042	−	0.288397i	0.630274	−	0.0100959i
$817$	−0.361288	+	0.208590i	−0.0126399	+	0.00729764i
$818$	6.52359	+	4.96435i	0.228092	+	0.173574i
$819$		0			0
$820$	17.3670	+	62.7985i	0.606482	+	2.19302i
$821$	14.6233	+	25.3283i	0.510358	+	0.883965i	0.999928	+	0.0120014i	$0.00382026\pi$
$821$	14.6233	+	25.3283i	0.510358	+	0.883965i	−0.489570	+	0.871964i	$0.662846\pi$
$822$	−1.55805	−	3.71926i	−0.0543431	−	0.129724i
$823$	17.0790	+	9.86059i	0.595338	+	0.343719i	0.767205	−	0.641401i	$-0.221647\pi$
$823$	17.0790	+	9.86059i	0.595338	+	0.343719i	−0.171867	+	0.985120i	$0.554980\pi$
$824$	−7.16765	−	49.8123i	−0.249697	−	1.73529i
$825$		−	13.4362i		−	0.467790i
$826$		0			0
$827$		−	16.1125i		−	0.560286i	−0.959958	−	0.280143i	$-0.909618\pi$
$827$		−	16.1125i		−	0.560286i	0.959958	−	0.280143i	$-0.0903819\pi$
$828$	4.57432	+	4.50164i	0.158969	+	0.156443i
$829$	40.9056	+	23.6169i	1.42071	+	0.820248i	0.996360	−	0.0852497i	$-0.0271688\pi$
$829$	40.9056	+	23.6169i	1.42071	+	0.820248i	0.424351	+	0.905498i	$0.360502\pi$
$830$	61.7983	−	25.8881i	2.14505	−	0.898589i
$831$	5.93162	+	10.2739i	0.205766	+	0.356397i
$832$	2.04103	−	2.14154i	0.0707601	−	0.0742446i
$833$		0			0
$834$	6.12901	−	8.05406i	0.212230	−	0.278889i
$835$	46.9492	−	27.1062i	1.62475	−	0.938047i
$836$	0.0452742	−	0.174545i	0.00156584	−	0.00603677i
$837$	−3.01852	+	5.22824i	−0.104335	+	0.180714i
$838$	3.40844	+	0.434852i	0.117742	+	0.0150217i
$839$	−25.3551			−0.875356			−0.437678	−	0.899132i	$-0.644199\pi$
$839$	−25.3551			−0.875356			−0.437678	+	0.899132i	$0.644199\pi$
$840$		0			0
$841$	−19.2687			−0.664437
$842$	−36.3860	−	4.64216i	−1.25394	−	0.159980i
$843$	9.67141	−	16.7514i	0.333101	−	0.576948i
$844$	9.87611	−	38.0753i	0.339950	−	1.31060i
$845$	42.9475	−	24.7958i	1.47744	−	0.853000i
$846$	−1.22098	+	1.60447i	−0.0419780	+	0.0551628i
$847$		0			0
$848$	8.73412	−	5.23093i	0.299931	−	0.179631i
$849$	−12.4707	−	21.5998i	−0.427992	−	0.741304i
$850$	−57.9157	+	24.2616i	−1.98649	+	0.832167i
$851$	−15.2620	−	8.81153i	−0.523175	−	0.302055i
$852$	18.4627	+	18.1694i	0.632522	+	0.622472i
$853$		−	24.3802i		−	0.834763i	−0.908731	−	0.417382i	$-0.862948\pi$
$853$		−	24.3802i		−	0.834763i	0.908731	−	0.417382i	$-0.137052\pi$
$854$		0			0
$855$		−	0.255162i		−	0.00872636i
$856$	17.0584	−	2.45459i	0.583043	−	0.0838960i
$857$	22.4742	+	12.9755i	0.767705	+	0.443235i	0.832055	−	0.554693i	$-0.187164\pi$
$857$	22.4742	+	12.9755i	0.767705	+	0.443235i	−0.0643503	+	0.997927i	$0.520498\pi$
$858$	−0.275265	−	0.657095i	−0.00939740	−	0.0224328i
$859$	28.4213	+	49.2271i	0.969722	+	1.67961i	0.696354	+	0.717698i	$0.254804\pi$
$859$	28.4213	+	49.2271i	0.969722	+	1.67961i	0.273368	+	0.961909i	$0.411862\pi$
$860$	12.9546	+	46.8433i	0.441748	+	1.59734i
$861$		0			0
$862$	16.6052	+	12.6363i	0.565576	+	0.430395i
$863$	−15.3044	+	8.83597i	−0.520966	+	0.300780i	−0.737330	−	0.675533i	$-0.763914\pi$
$863$	−15.3044	+	8.83597i	−0.520966	+	0.300780i	0.216364	+	0.976313i	$0.430580\pi$
$864$	4.55593	+	3.35314i	0.154996	+	0.114076i
$865$	−3.42568	+	5.93345i	−0.116476	+	0.201743i
$866$	6.39654	−	50.1371i	0.217363	−	1.70373i
$867$	−3.26474			−0.110876
$868$		0			0
$869$	17.0129			0.577122
$870$	2.15247	−	16.8714i	0.0729757	−	0.571995i
$871$	−1.80597	+	3.12803i	−0.0611930	+	0.105989i
$872$	−17.4808	+	13.7502i	−0.591973	+	0.465641i
$873$	−2.49781	+	1.44211i	−0.0845381	+	0.0488081i
$874$	−0.239018	−	0.181889i	−0.00808491	−	0.00615250i
$875$		0			0
$876$	−3.47286	+	0.960423i	−0.117337	+	0.0324497i
$877$	6.17283	+	10.6917i	0.208442	+	0.361032i	0.951224	−	0.308502i	$-0.0998275\pi$
$877$	6.17283	+	10.6917i	0.208442	+	0.361032i	−0.742782	+	0.669533i	$0.766494\pi$
$878$	10.8402	+	25.8770i	0.365840	+	0.873308i
$879$	−5.96028	−	3.44117i	−0.201035	−	0.116068i
$880$	−18.3589	−	10.2110i	−0.618880	−	0.344214i
$881$			33.0442i			1.11329i	0.830751	+	0.556644i	$0.187911\pi$
$881$			33.0442i			1.11329i	−0.830751	+	0.556644i	$0.812089\pi$
$882$		0			0
$883$			39.2680i			1.32147i	0.750618	+	0.660737i	$0.229756\pi$
$883$			39.2680i			1.32147i	−0.750618	+	0.660737i	$0.770244\pi$
$884$	−2.33531	+	2.37301i	−0.0785448	+	0.0798130i
$885$	11.4773	+	6.62642i	0.385805	+	0.222745i
$886$	−24.7582	+	10.3715i	−0.831766	+	0.348437i
$887$	−19.7517	−	34.2109i	−0.663196	−	1.14869i	−0.979771	−	0.200121i	$-0.935866\pi$
$887$	−19.7517	−	34.2109i	−0.663196	−	1.14869i	0.316576	−	0.948567i	$-0.397467\pi$
$888$	−14.4213	−	5.77153i	−0.483947	−	0.193680i
$889$		0			0
$890$	−4.26816	+	5.60873i	−0.143069	+	0.188005i
$891$	1.17975	−	0.681127i	0.0395230	−	0.0228186i
$892$	−15.6873	−	4.06904i	−0.525251	−	0.136242i
$893$	0.0471792	−	0.0817167i	0.00157879	−	0.00273454i
$894$	29.9579	+	3.82205i	1.00194	+	0.127829i
$895$	12.5363			0.419043
$896$		0			0
$897$	−1.18666			−0.0396214
$898$	−35.4702	−	4.52533i	−1.18366	−	0.151012i
$899$	9.41631	−	16.3095i	0.314052	−	0.543953i
$900$	−19.0946	−	4.95284i	−0.636487	−	0.165095i
$901$	−9.92249	+	5.72875i	−0.330566	+	0.190852i
$902$	9.85848	−	12.9549i	0.328251	−	0.431351i
$903$		0			0
$904$	12.3595	+	4.94638i	0.411071	+	0.164514i
$905$	45.3026	+	78.4664i	1.50591	+	2.60831i
$906$	−28.9747	+	12.1379i	−0.962621	+	0.403254i
$907$	4.46372	+	2.57713i	0.148215	+	0.0855722i	0.572274	−	0.820063i	$-0.306062\pi$
$907$	4.46372	+	2.57713i	0.148215	+	0.0855722i	−0.424058	+	0.905635i	$0.639395\pi$
$908$	16.9547	−	17.2285i	0.562663	−	0.571748i
$909$			6.18861i			0.205263i
$910$		0			0
$911$		−	25.8365i		−	0.856002i	−0.903778	−	0.428001i	$-0.859218\pi$
$911$		−	25.8365i		−	0.856002i	0.903778	−	0.428001i	$-0.140782\pi$
$912$	−0.231362	−	0.128681i	−0.00766116	−	0.00426105i
$913$	−14.4978	−	8.37031i	−0.479807	−	0.277017i
$914$	−12.5500	−	29.9584i	−0.415116	−	0.990936i
$915$	−2.76002	−	4.78049i	−0.0912434	−	0.158038i
$916$	−45.8444	+	12.6783i	−1.51474	+	0.418903i
$917$		0			0
$918$	−5.06618	−	3.85529i	−0.167209	−	0.127243i
$919$	30.6881	−	17.7178i	1.01231	−	0.584455i	0.100440	−	0.994943i	$-0.467975\pi$
$919$	30.6881	−	17.7178i	1.01231	−	0.584455i	0.911866	+	0.410488i	$0.134642\pi$
$920$	−27.5028	+	21.6335i	−0.906740	+	0.713234i
$921$	−8.71065	+	15.0873i	−0.287026	+	0.497143i
$922$	0.529479	−	4.15014i	0.0174375	−	0.136678i
$923$	−4.78955			−0.157650
$924$		0			0
$925$	54.1676			1.78102
$926$	0.591818	−	4.63876i	0.0194483	−	0.152439i
$927$	−8.89634	+	15.4089i	−0.292194	+	0.506095i
$928$	−14.2123	−	10.4601i	−0.466540	−	0.343371i
$929$	−47.6452	+	27.5080i	−1.56319	+	0.902508i	−0.566258	+	0.824228i	$0.691609\pi$
$929$	−47.6452	+	27.5080i	−1.56319	+	0.902508i	−0.996931	+	0.0782797i	$0.975057\pi$
$930$	−26.1934	−	19.9328i	−0.858916	−	0.653622i
$931$		0			0
$932$	10.6242	+	38.4169i	0.348008	+	1.25839i
$933$	12.5580	+	21.7512i	0.411132	+	0.712101i
$934$	−6.50552	−	15.5295i	−0.212867	−	0.508142i
$935$	20.4746	+	11.8210i	0.669592	+	0.386589i
$936$	−1.03528	+	0.148970i	−0.0338393	+	0.00486925i
$937$			6.90001i			0.225414i	0.993628	+	0.112707i	$0.0359521\pi$
$937$			6.90001i			0.225414i	−0.993628	+	0.112707i	$0.964048\pi$
$938$		0			0
$939$			22.0965i			0.721092i
$940$	−7.83508	−	7.71058i	−0.255552	−	0.251491i
$941$	−16.2597	−	9.38756i	−0.530052	−	0.306026i	0.210986	−	0.977489i	$-0.432333\pi$
$941$	−16.2597	−	9.38756i	−0.530052	−	0.306026i	−0.741038	+	0.671463i	$0.765666\pi$
$942$	−7.10761	+	2.97747i	−0.231579	+	0.0970112i
$943$	−13.5580	−	23.4832i	−0.441511	−	0.764719i
$944$	11.7965	−	7.06499i	0.383942	−	0.229946i
$945$		0			0
$946$	7.35374	−	9.66346i	0.239091	−	0.314186i
$947$	25.7931	−	14.8916i	0.838162	−	0.483913i	−0.0184768	−	0.999829i	$-0.505882\pi$
$947$	25.7931	−	14.8916i	0.838162	−	0.483913i	0.856639	+	0.515916i	$0.172548\pi$
$948$	6.27124	−	24.1774i	0.203680	−	0.785247i
$949$	0.333115	−	0.576972i	0.0108134	−	0.0187293i
$950$	0.915774	+	0.116835i	0.0297116	+	0.00379064i
$951$	−1.62327			−0.0526380
$952$		0			0
$953$	−23.2676			−0.753711			−0.376856	−	0.926272i	$-0.622995\pi$
$953$	−23.2676			−0.753711			−0.376856	+	0.926272i	$0.622995\pi$
$954$	−3.57050	−	0.455527i	−0.115599	−	0.0147482i
$955$	46.0653	−	79.7875i	1.49064	−	2.58186i
$956$	4.82563	−	18.6042i	0.156072	−	0.601703i
$957$	−3.68023	+	2.12478i	−0.118965	+	0.0686844i
$958$	10.1946	−	13.3966i	0.329372	−	0.432823i
$959$		0			0
$960$	−21.2786	+	22.3264i	−0.686764	+	0.720582i
$961$	−2.72297	−	4.71632i	−0.0878377	−	0.152139i
$962$	2.64905	−	1.10972i	0.0854087	−	0.0357788i
$963$	−5.27683	−	3.04658i	−0.170044	−	0.0981747i
$964$	14.8370	+	14.6012i	0.477867	+	0.470274i
$965$			76.6244i			2.46663i
$966$		0			0
$967$			16.9691i			0.545690i	0.962058	+	0.272845i	$0.0879646\pi$
$967$			16.9691i			0.545690i	−0.962058	+	0.272845i	$0.912035\pi$
$968$	−3.68370	−	25.6002i	−0.118399	−	0.822822i
$969$	0.258024	+	0.148970i	0.00828893	+	0.00478561i
$970$	−6.07596	−	14.5041i	−0.195087	−	0.465699i
$971$	22.8349	+	39.5512i	0.732806	+	1.26926i	0.955679	+	0.294410i	$0.0951231\pi$
$971$	22.8349	+	39.5512i	0.732806	+	1.26926i	−0.222873	+	0.974847i	$0.571544\pi$
$972$	−0.533092	−	1.92764i	−0.0170989	−	0.0618292i
$973$		0			0
$974$	8.44878	+	6.42939i	0.270717	+	0.206011i
$975$	3.15875	−	1.82370i	0.101161	−	0.0584052i
$976$	−5.72650	+	0.0917286i	−0.183301	+	0.00293616i
$977$	23.7102	−	41.0673i	0.758557	−	1.31386i	−0.185029	−	0.982733i	$-0.559238\pi$
$977$	23.7102	−	41.0673i	0.758557	−	1.31386i	0.943586	−	0.331127i	$-0.107429\pi$
$978$	0.851353	−	6.67304i	0.0272233	−	0.213380i
$979$	1.76098			0.0562812
$980$		0			0
$981$	7.86325			0.251054
$982$	−3.93804	+	30.8670i	−0.125668	+	0.985004i
$983$	17.6956	−	30.6497i	0.564402	−	0.977573i	−0.432703	−	0.901536i	$-0.642440\pi$
$983$	17.6956	−	30.6497i	0.564402	−	0.977573i	0.997105	−	0.0760363i	$-0.0242265\pi$
$984$	−14.7765	−	18.7856i	−0.471059	−	0.598862i
$985$	63.5029	−	36.6634i	2.02337	−	1.16819i
$986$	15.8040	+	12.0266i	0.503302	+	0.383005i
$987$		0			0
$988$	0.0471792	−	0.0130475i	0.00150097	−	0.000415095i
$989$	−10.1134	−	17.5169i	−0.321586	−	0.557004i
$990$	2.86975	+	6.85047i	0.0912066	+	0.217722i
$991$	10.0136	+	5.78134i	0.318092	+	0.183650i	0.650542	−	0.759471i	$-0.274542\pi$
$991$	10.0136	+	5.78134i	0.318092	+	0.183650i	−0.332450	+	0.943121i	$0.607875\pi$
$992$	−31.2832	+	13.6979i	−0.993242	+	0.434910i
$993$		−	26.6677i		−	0.846274i
$994$		0			0
$995$		−	57.2563i		−	1.81515i
$996$	−17.2394	+	17.5178i	−0.546252	+	0.555072i
$997$	10.6832	+	6.16793i	0.338339	+	0.195340i	0.659537	−	0.751672i	$-0.270752\pi$
$997$	10.6832	+	6.16793i	0.338339	+	0.195340i	−0.321198	+	0.947012i	$0.604086\pi$
$998$	1.84171	−	0.771516i	0.0582983	−	0.0244219i
$999$	2.74593	+	4.75609i	0.0868774	+	0.150476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.b.31.4		8
4.3	odd	2		588.2.o.d.31.2		8
7.2	even	3		84.2.o.a.19.2	✓	8
7.3	odd	6		588.2.b.a.391.4		8
7.4	even	3		588.2.b.b.391.4		8
7.5	odd	6		588.2.o.d.19.2		8
7.6	odd	2		84.2.o.b.31.4	yes	8
21.2	odd	6		252.2.bf.g.19.3		8
21.11	odd	6		1764.2.b.i.1567.5		8
21.17	even	6		1764.2.b.j.1567.5		8
21.20	even	2		252.2.bf.f.199.1		8
28.3	even	6		588.2.b.b.391.3		8
28.11	odd	6		588.2.b.a.391.3		8
28.19	even	6	inner	588.2.o.b.19.4		8
28.23	odd	6		84.2.o.b.19.4	yes	8
28.27	even	2		84.2.o.a.31.2	yes	8
56.13	odd	2		1344.2.bl.i.703.4		8
56.27	even	2		1344.2.bl.j.703.4		8
56.37	even	6		1344.2.bl.j.1279.4		8
56.51	odd	6		1344.2.bl.i.1279.4		8
84.11	even	6		1764.2.b.j.1567.6		8
84.23	even	6		252.2.bf.f.19.1		8
84.59	odd	6		1764.2.b.i.1567.6		8
84.83	odd	2		252.2.bf.g.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.2	✓	8	7.2	even	3
84.2.o.a.31.2	yes	8	28.27	even	2
84.2.o.b.19.4	yes	8	28.23	odd	6
84.2.o.b.31.4	yes	8	7.6	odd	2
252.2.bf.f.19.1		8	84.23	even	6
252.2.bf.f.199.1		8	21.20	even	2
252.2.bf.g.19.3		8	21.2	odd	6
252.2.bf.g.199.3		8	84.83	odd	2
588.2.b.a.391.3		8	28.11	odd	6
588.2.b.a.391.4		8	7.3	odd	6
588.2.b.b.391.3		8	28.3	even	6
588.2.b.b.391.4		8	7.4	even	3
588.2.o.b.19.4		8	28.19	even	6	inner
588.2.o.b.31.4		8	1.1	even	1	trivial
588.2.o.d.19.2		8	7.5	odd	6
588.2.o.d.31.2		8	4.3	odd	2
1344.2.bl.i.703.4		8	56.13	odd	2
1344.2.bl.i.1279.4		8	56.51	odd	6
1344.2.bl.j.703.4		8	56.27	even	2
1344.2.bl.j.1279.4		8	56.37	even	6
1764.2.b.i.1567.5		8	21.11	odd	6
1764.2.b.i.1567.6		8	84.59	odd	6
1764.2.b.j.1567.5		8	21.17	even	6
1764.2.b.j.1567.6		8	84.11	even	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40284 + 0.178976i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.93594 + 0.502151i) q^{4} +(3.33878 - 1.92764i) q^{5} +(-0.856419 + 1.12541i) q^{6} +(2.62594 + 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.40284 + 0.178976i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.93594 + 0.502151i) q^{4} +(3.33878 - 1.92764i) q^{5} +(-0.856419 + 1.12541i) q^{6} +(2.62594 + 1.05092i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(5.02878 - 2.10662i) q^{10} +(-1.17975 - 0.681127i) q^{11} +(-1.40284 + 1.42549i) q^{12} -0.369798i q^{13} +3.85529i q^{15} +(3.49569 + 1.94426i) q^{16} +(-3.89853 - 2.25082i) q^{17} +(-0.546424 - 1.30439i) q^{18} +(0.0330925 + 0.0573178i) q^{19} +(7.43162 - 2.05523i) q^{20} +(-1.53309 - 1.16666i) q^{22} +(-2.77902 + 1.60447i) q^{23} +(-2.22310 + 1.74867i) q^{24} +(4.93162 - 8.54182i) q^{25} +(0.0661849 - 0.518768i) q^{26} +1.00000 q^{27} -3.11951 q^{29} +(-0.690004 + 5.40836i) q^{30} +(-3.01852 + 5.22824i) q^{31} +(4.55593 + 3.35314i) q^{32} +(1.17975 - 0.681127i) q^{33} +(-5.06618 - 3.85529i) q^{34} +(-0.533092 - 1.92764i) q^{36} +(2.74593 + 4.75609i) q^{37} +(0.0361650 + 0.0863307i) q^{38} +(0.320254 + 0.184899i) q^{39} +(10.7932 - 1.55307i) q^{40} +8.45017i q^{41} +6.30324i q^{43} +(-1.94188 - 1.91103i) q^{44} +(-3.33878 - 1.92764i) q^{45} +(-4.18569 + 1.75344i) q^{46} +(-0.712838 - 1.23467i) q^{47} +(-3.43162 + 2.05523i) q^{48} +(8.44708 - 11.1002i) q^{50} +(3.89853 - 2.25082i) q^{51} +(0.185694 - 0.715904i) q^{52} +(1.27259 - 2.20420i) q^{53} +(1.40284 + 0.178976i) q^{54} -5.25188 q^{55} -0.0661849 q^{57} +(-4.37618 - 0.558317i) q^{58} +(1.71879 - 2.97703i) q^{59} +(-1.93594 + 7.46359i) q^{60} +(-1.23998 + 0.715904i) q^{61} +(-5.17024 + 6.79415i) q^{62} +(5.79112 + 5.51933i) q^{64} +(-0.712838 - 1.23467i) q^{65} +(1.77690 - 0.744367i) q^{66} +(-8.45877 - 4.88367i) q^{67} +(-6.41706 - 6.31509i) q^{68} -3.20894i q^{69} -12.9518i q^{71} +(-0.402843 - 2.79959i) q^{72} +(1.56024 + 0.900803i) q^{73} +(3.00088 + 7.16350i) q^{74} +(4.93162 + 8.54182i) q^{75} +(0.0352827 + 0.127581i) q^{76} +(0.416174 + 0.316702i) q^{78} +(-10.8156 + 6.24438i) q^{79} +(15.4192 - 0.246989i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.51238 + 11.8543i) q^{82} +12.2889 q^{83} -17.3551 q^{85} +(-1.12813 + 8.84246i) q^{86} +(1.55975 - 2.70157i) q^{87} +(-2.38213 - 3.02842i) q^{88} +(-1.11951 + 0.646349i) q^{89} +(-4.33878 - 3.30174i) q^{90} +(-6.18569 + 1.71066i) q^{92} +(-3.01852 - 5.22824i) q^{93} +(-0.779023 - 1.85963i) q^{94} +(0.220977 + 0.127581i) q^{95} +(-5.18187 + 2.26898i) q^{96} -2.88422i q^{97} +1.36225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 4 q^{8} - 4 q^{9} + 13 q^{10} - 6 q^{11} - q^{12} + 7 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 6 q^{22} - 11 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} - 16 q^{29} - 5 q^{30} + 6 q^{31} + 21 q^{32} + 6 q^{33} - 28 q^{34} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 6 q^{39} + 13 q^{40} + 19 q^{44} - 12 q^{46} + 4 q^{47} + 10 q^{48} + 2 q^{50} - 20 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 12 q^{57} - 23 q^{58} - 14 q^{59} + q^{60} - 12 q^{61} - 48 q^{62} + 2 q^{64} + 4 q^{65} + 21 q^{66} - 42 q^{67} + 10 q^{68} + 7 q^{72} + 18 q^{73} - 28 q^{74} + 2 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{79} + 33 q^{80} - 4 q^{81} + 14 q^{82} + 4 q^{83} - 32 q^{85} - 42 q^{86} + 8 q^{87} + 11 q^{88} - 8 q^{90} - 28 q^{92} + 6 q^{93} + 16 q^{94} + 24 q^{95} - 9 q^{96}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 4 * q^8 - 4 * q^9 + 13 * q^10 - 6 * q^11 - q^12 + 7 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 6 * q^22 - 11 * q^24 + 2 * q^25 - 12 * q^26 + 8 * q^27 - 16 * q^29 - 5 * q^30 + 6 * q^31 + 21 * q^32 + 6 * q^33 - 28 * q^34 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 6 * q^39 + 13 * q^40 + 19 * q^44 - 12 * q^46 + 4 * q^47 + 10 * q^48 + 2 * q^50 - 20 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 12 * q^57 - 23 * q^58 - 14 * q^59 + q^60 - 12 * q^61 - 48 * q^62 + 2 * q^64 + 4 * q^65 + 21 * q^66 - 42 * q^67 + 10 * q^68 + 7 * q^72 + 18 * q^73 - 28 * q^74 + 2 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^79 + 33 * q^80 - 4 * q^81 + 14 * q^82 + 4 * q^83 - 32 * q^85 - 42 * q^86 + 8 * q^87 + 11 * q^88 - 8 * q^90 - 28 * q^92 + 6 * q^93 + 16 * q^94 + 24 * q^95 - 9 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more