LMFDB - Embedded newform 825.2.n.g.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.2
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.g.526.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456498 + 1.40496i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.147481 + 0.107152i) q^{4} +(-0.456498 + 1.40496i) q^{6} +(-1.85666 + 1.34895i) q^{7} +(2.17239 + 1.57833i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.456498 + 1.40496i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.147481 + 0.107152i) q^{4} +(-0.456498 + 1.40496i) q^{6} +(-1.85666 + 1.34895i) q^{7} +(2.17239 + 1.57833i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-3.12020 + 1.12443i) q^{11} -0.182297 q^{12} +(0.661536 + 2.03600i) q^{13} +(-2.74278 - 1.99274i) q^{14} +(-1.33846 + 4.11937i) q^{16} +(-0.168243 + 0.517799i) q^{17} +(-1.19513 + 0.868312i) q^{18} +(1.76552 + 1.28272i) q^{19} -2.29496 q^{21} +(-3.00415 - 3.87045i) q^{22} -2.03908 q^{23} +(0.829779 + 2.55380i) q^{24} +(-2.55850 + 1.85886i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.129282 - 0.397889i) q^{28} +(8.04603 - 5.84578i) q^{29} +(2.09249 + 6.44002i) q^{31} -1.02811 q^{32} +(-3.18522 - 0.924324i) q^{33} -0.804288 q^{34} +(-0.147481 - 0.107152i) q^{36} +(-7.13520 + 5.18403i) q^{37} +(-0.996215 + 3.06604i) q^{38} +(-0.661536 + 2.03600i) q^{39} +(1.47470 + 1.07143i) q^{41} +(-1.04765 - 3.22433i) q^{42} +0.620713 q^{43} +(0.339687 - 0.500167i) q^{44} +(-0.930836 - 2.86482i) q^{46} +(-0.305816 - 0.222188i) q^{47} +(-3.50415 + 2.54591i) q^{48} +(-0.535571 + 1.64832i) q^{49} +(-0.440466 + 0.320017i) q^{51} +(-0.315724 - 0.229387i) q^{52} +(-3.58246 - 11.0257i) q^{53} -1.47726 q^{54} -6.16248 q^{56} +(0.674367 + 2.07549i) q^{57} +(11.8861 + 8.63574i) q^{58} +(6.53518 - 4.74808i) q^{59} +(2.69647 - 8.29887i) q^{61} +(-8.09273 + 5.87971i) q^{62} +(-1.85666 - 1.34895i) q^{63} +(2.20760 + 6.79429i) q^{64} +(-0.155412 - 4.89705i) q^{66} +9.75802 q^{67} +(-0.0306702 - 0.0943932i) q^{68} +(-1.64965 - 1.19854i) q^{69} +(-4.63426 + 14.2628i) q^{71} +(-0.829779 + 2.55380i) q^{72} +(6.35761 - 4.61907i) q^{73} +(-10.5405 - 7.65815i) q^{74} -0.397826 q^{76} +(4.27637 - 6.29667i) q^{77} -3.16248 q^{78} +(-2.85054 - 8.77306i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.832118 + 2.56099i) q^{82} +(2.92093 - 8.98969i) q^{83} +(0.338464 - 0.245909i) q^{84} +(0.283354 + 0.872075i) q^{86} +9.94544 q^{87} +(-8.55302 - 2.48201i) q^{88} +0.583290 q^{89} +(-3.97470 - 2.88779i) q^{91} +(0.300726 - 0.218490i) q^{92} +(-2.09249 + 6.44002i) q^{93} +(0.172561 - 0.531087i) q^{94} +(-0.831757 - 0.604307i) q^{96} +(1.66190 + 5.11479i) q^{97} -2.56031 q^{98} +(-2.03359 - 2.62002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9	$ 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{16} + q^{18} + 2 q^{19} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 2 q^{26} + 2 q^{27} + 11 q^{28} + 10 q^{29} + 19 q^{31} - 12 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + q^{37} + 20 q^{38} - 4 q^{39} - 9 q^{41} - q^{42} + 17 q^{44} - 22 q^{46} + 19 q^{47} - 13 q^{48} + q^{49} + 10 q^{51} + 2 q^{52} - 25 q^{53} - 6 q^{54} - 16 q^{56} - 7 q^{57} + 12 q^{58} + 13 q^{59} + 13 q^{61} - 35 q^{62} - 3 q^{63} + 39 q^{64} - 11 q^{66} - 2 q^{67} - 19 q^{68} + 9 q^{69} - 11 q^{71} - 4 q^{72} + 7 q^{73} - 43 q^{74} - 38 q^{76} + 7 q^{77} + 8 q^{78} - 22 q^{79} - 2 q^{81} + 35 q^{82} + 21 q^{83} + 4 q^{84} + 20 q^{86} + 30 q^{87} - 59 q^{88} - 20 q^{89} - 11 q^{91} + 28 q^{92} - 19 q^{93} - 35 q^{94} - 8 q^{96} - 31 q^{97} - 22 q^{98} - 7 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9 + 3 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^16 + q^18 + 2 * q^19 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 2 * q^26 + 2 * q^27 + 11 * q^28 + 10 * q^29 + 19 * q^31 - 12 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + q^37 + 20 * q^38 - 4 * q^39 - 9 * q^41 - q^42 + 17 * q^44 - 22 * q^46 + 19 * q^47 - 13 * q^48 + q^49 + 10 * q^51 + 2 * q^52 - 25 * q^53 - 6 * q^54 - 16 * q^56 - 7 * q^57 + 12 * q^58 + 13 * q^59 + 13 * q^61 - 35 * q^62 - 3 * q^63 + 39 * q^64 - 11 * q^66 - 2 * q^67 - 19 * q^68 + 9 * q^69 - 11 * q^71 - 4 * q^72 + 7 * q^73 - 43 * q^74 - 38 * q^76 + 7 * q^77 + 8 * q^78 - 22 * q^79 - 2 * q^81 + 35 * q^82 + 21 * q^83 + 4 * q^84 + 20 * q^86 + 30 * q^87 - 59 * q^88 - 20 * q^89 - 11 * q^91 + 28 * q^92 - 19 * q^93 - 35 * q^94 - 8 * q^96 - 31 * q^97 - 22 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.456498	+	1.40496i	0.322793	+	0.993455i	0.972427	+	0.233208i	$0.0749222\pi$
$2$	0.456498	+	1.40496i	0.322793	+	0.993455i	−0.649634	+	0.760247i	$0.725078\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.147481	+	0.107152i	−0.0737407	+	0.0535758i
$5$		0			0
$5$		0			0
$6$	−0.456498	+	1.40496i	−0.186365	+	0.573572i
$7$	−1.85666	+	1.34895i	−0.701753	+	0.509853i	−0.880503	−	0.474041i	$-0.842795\pi$
$7$	−1.85666	+	1.34895i	−0.701753	+	0.509853i	0.178750	+	0.983895i	$0.442795\pi$
$8$	2.17239	+	1.57833i	0.768055	+	0.558025i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−3.12020	+	1.12443i	−0.940776	+	0.339029i
$11$	−3.12020	+	1.12443i	−0.940776	+	0.339029i
$12$	−0.182297			−0.0526246
$13$	0.661536	+	2.03600i	0.183477	+	0.564684i	0.999919	−	0.0127437i	$-0.00405655\pi$
$13$	0.661536	+	2.03600i	0.183477	+	0.564684i	−0.816442	+	0.577428i	$0.804057\pi$
$14$	−2.74278	−	1.99274i	−0.733038	−	0.532583i
$15$		0			0
$16$	−1.33846	+	4.11937i	−0.334616	+	1.02984i
$17$	−0.168243	+	0.517799i	−0.0408049	+	0.125585i	−0.969384	−	0.245550i	$-0.921031\pi$
$17$	−0.168243	+	0.517799i	−0.0408049	+	0.125585i	0.928579	+	0.371135i	$0.121031\pi$
$18$	−1.19513	+	0.868312i	−0.281694	+	0.204663i
$19$	1.76552	+	1.28272i	0.405037	+	0.294277i	0.771590	−	0.636121i	$-0.219462\pi$
$19$	1.76552	+	1.28272i	0.405037	+	0.294277i	−0.366553	+	0.930397i	$0.619462\pi$
$20$		0			0
$21$	−2.29496			−0.500802
$22$	−3.00415	−	3.87045i	−0.640486	−	0.825183i
$23$	−2.03908			−0.425177			−0.212589	−	0.977142i	$-0.568189\pi$
$23$	−2.03908			−0.425177			−0.212589	+	0.977142i	$0.568189\pi$
$24$	0.829779	+	2.55380i	0.169378	+	0.521291i
$25$		0			0
$26$	−2.55850	+	1.85886i	−0.501763	+	0.364552i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.129282	−	0.397889i	0.0244320	−	0.0751939i
$29$	8.04603	−	5.84578i	1.49411	−	1.08553i	0.521455	−	0.853279i	$-0.325389\pi$
$29$	8.04603	−	5.84578i	1.49411	−	1.08553i	0.972655	−	0.232256i	$-0.0746107\pi$
$30$		0			0
$31$	2.09249	+	6.44002i	0.375822	+	1.15666i	0.942922	+	0.333012i	$0.108065\pi$
$31$	2.09249	+	6.44002i	0.375822	+	1.15666i	−0.567101	+	0.823649i	$0.691935\pi$
$32$	−1.02811			−0.181746
$33$	−3.18522	−	0.924324i	−0.554476	−	0.160904i
$34$	−0.804288			−0.137934
$35$		0			0
$36$	−0.147481	−	0.107152i	−0.0245802	−	0.0178586i
$37$	−7.13520	+	5.18403i	−1.17302	+	0.852249i	−0.991367	−	0.131114i	$-0.958145\pi$
$37$	−7.13520	+	5.18403i	−1.17302	+	0.852249i	−0.181652	+	0.983363i	$0.558145\pi$
$38$	−0.996215	+	3.06604i	−0.161607	+	0.497377i
$39$	−0.661536	+	2.03600i	−0.105930	+	0.326020i
$40$		0			0
$41$	1.47470	+	1.07143i	0.230309	+	0.167329i	0.696955	−	0.717115i	$-0.254538\pi$
$41$	1.47470	+	1.07143i	0.230309	+	0.167329i	−0.466646	+	0.884444i	$0.654538\pi$
$42$	−1.04765	−	3.22433i	−0.161655	−	0.497524i
$43$	0.620713			0.0946578			0.0473289	−	0.998879i	$-0.484929\pi$
$43$	0.620713			0.0946578			0.0473289	+	0.998879i	$0.484929\pi$
$44$	0.339687	−	0.500167i	0.0512098	−	0.0754030i
$45$		0			0
$46$	−0.930836	−	2.86482i	−0.137244	−	0.422394i
$47$	−0.305816	−	0.222188i	−0.0446078	−	0.0324095i	0.565258	−	0.824914i	$-0.308777\pi$
$47$	−0.305816	−	0.222188i	−0.0446078	−	0.0324095i	−0.609866	+	0.792505i	$0.708777\pi$
$48$	−3.50415	+	2.54591i	−0.505780	+	0.367471i
$49$	−0.535571	+	1.64832i	−0.0765102	+	0.235474i
$50$		0			0
$51$	−0.440466	+	0.320017i	−0.0616776	+	0.0448114i
$52$	−0.315724	−	0.229387i	−0.0437831	−	0.0318103i
$53$	−3.58246	−	11.0257i	−0.492089	−	1.51449i	−0.821445	−	0.570288i	$-0.806831\pi$
$53$	−3.58246	−	11.0257i	−0.492089	−	1.51449i	0.329355	−	0.944206i	$-0.393169\pi$
$54$	−1.47726			−0.201030
$55$		0			0
$56$	−6.16248			−0.823496
$57$	0.674367	+	2.07549i	0.0893221	+	0.274905i
$58$	11.8861	+	8.63574i	1.56072	+	1.13393i
$59$	6.53518	−	4.74808i	0.850807	−	0.618148i	−0.0745611	−	0.997216i	$-0.523756\pi$
$59$	6.53518	−	4.74808i	0.850807	−	0.618148i	0.925369	+	0.379069i	$0.123756\pi$
$60$		0			0
$61$	2.69647	−	8.29887i	0.345247	−	1.06256i	−0.616204	−	0.787587i	$-0.711330\pi$
$61$	2.69647	−	8.29887i	0.345247	−	1.06256i	0.961451	−	0.274975i	$-0.0886697\pi$
$62$	−8.09273	+	5.87971i	−1.02778	+	0.746724i
$63$	−1.85666	−	1.34895i	−0.233918	−	0.169951i
$64$	2.20760	+	6.79429i	0.275950	+	0.849286i
$65$		0			0
$66$	−0.155412	−	4.89705i	−0.0191299	−	0.602785i
$67$	9.75802			1.19213			0.596066	−	0.802936i	$-0.296730\pi$
$67$	9.75802			1.19213			0.596066	+	0.802936i	$0.296730\pi$
$68$	−0.0306702	−	0.0943932i	−0.00371931	−	0.0114469i
$69$	−1.64965	−	1.19854i	−0.198594	−	0.144287i
$70$		0			0
$71$	−4.63426	+	14.2628i	−0.549985	+	1.69268i	0.158848	+	0.987303i	$0.449222\pi$
$71$	−4.63426	+	14.2628i	−0.549985	+	1.69268i	−0.708833	+	0.705376i	$0.750778\pi$
$72$	−0.829779	+	2.55380i	−0.0977903	+	0.300968i
$73$	6.35761	−	4.61907i	0.744102	−	0.540622i	−0.149891	−	0.988702i	$-0.547892\pi$
$73$	6.35761	−	4.61907i	0.744102	−	0.540622i	0.893993	+	0.448081i	$0.147892\pi$
$74$	−10.5405	−	7.65815i	−1.22531	−	0.890242i
$75$		0			0
$76$	−0.397826			−0.0456338
$77$	4.27637	−	6.29667i	0.487337	−	0.717572i
$78$	−3.16248			−0.358080
$79$	−2.85054	−	8.77306i	−0.320711	−	0.987046i	−0.973340	−	0.229369i	$-0.926334\pi$
$79$	−2.85054	−	8.77306i	−0.320711	−	0.987046i	0.652629	−	0.757678i	$-0.273666\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−0.832118	+	2.56099i	−0.0918920	+	0.282815i
$83$	2.92093	−	8.98969i	0.320613	−	0.986747i	−0.652769	−	0.757557i	$-0.726393\pi$
$83$	2.92093	−	8.98969i	0.320613	−	0.986747i	0.973382	−	0.229189i	$-0.0736074\pi$
$84$	0.338464	−	0.245909i	0.0369295	−	0.0268309i
$85$		0			0
$86$	0.283354	+	0.872075i	0.0305549	+	0.0940383i
$87$	9.94544			1.06626
$88$	−8.55302	−	2.48201i	−0.911754	−	0.264583i
$89$	0.583290			0.0618287			0.0309143	−	0.999522i	$-0.490158\pi$
$89$	0.583290			0.0618287			0.0309143	+	0.999522i	$0.490158\pi$
$90$		0			0
$91$	−3.97470	−	2.88779i	−0.416662	−	0.302722i
$92$	0.300726	−	0.218490i	0.0313529	−	0.0227792i
$93$	−2.09249	+	6.44002i	−0.216981	+	0.667798i
$94$	0.172561	−	0.531087i	0.0177983	−	0.0547774i
$95$		0			0
$96$	−0.831757	−	0.604307i	−0.0848908	−	0.0616768i
$97$	1.66190	+	5.11479i	0.168740	+	0.519328i	0.999292	−	0.0376122i	$-0.0119751\pi$
$97$	1.66190	+	5.11479i	0.168740	+	0.519328i	−0.830552	+	0.556940i	$0.811975\pi$
$98$	−2.56031			−0.258630
$99$	−2.03359	−	2.62002i	−0.204384	−	0.263322i
$100$		0			0
$101$	−6.03482	−	18.5733i	−0.600487	−	1.84811i	−0.525261	−	0.850941i	$-0.676032\pi$
$101$	−6.03482	−	18.5733i	−0.600487	−	1.84811i	−0.0752256	−	0.997167i	$-0.523968\pi$
$102$	−0.650683	−	0.472749i	−0.0644272	−	0.0468091i
$103$	10.5223	−	7.64487i	1.03679	−	0.753271i	0.0671325	−	0.997744i	$-0.478615\pi$
$103$	10.5223	−	7.64487i	1.03679	−	0.753271i	0.969656	+	0.244473i	$0.0786150\pi$
$104$	−1.77637	+	5.46710i	−0.174187	+	0.536093i
$105$		0			0
$106$	13.8552	−	10.0664i	1.34574	−	0.977737i
$107$	1.59663	+	1.16002i	0.154352	+	0.112144i	0.662281	−	0.749256i	$-0.269589\pi$
$107$	1.59663	+	1.16002i	0.154352	+	0.112144i	−0.507928	+	0.861399i	$0.669589\pi$
$108$	−0.0563329	−	0.173375i	−0.00542064	−	0.0166830i
$109$	10.6212			1.01733			0.508663	−	0.860966i	$-0.330140\pi$
$109$	10.6212			1.01733			0.508663	+	0.860966i	$0.330140\pi$
$110$		0			0
$111$	−8.81959			−0.837119
$112$	−3.07173	−	9.45380i	−0.290251	−	0.893300i
$113$	−13.6688	−	9.93096i	−1.28585	−	0.934226i	−0.286139	−	0.958188i	$-0.592372\pi$
$113$	−13.6688	−	9.93096i	−1.28585	−	0.934226i	−0.999713	+	0.0239621i	$0.992372\pi$
$114$	−2.60813	+	1.89491i	−0.244273	+	0.177475i
$115$		0			0
$116$	−0.560255	+	1.72429i	−0.0520184	+	0.160096i
$117$	−1.73192	+	1.25832i	−0.160116	+	0.116331i
$118$	9.65415	+	7.01415i	0.888737	+	0.645705i
$119$	−0.386111	−	1.18833i	−0.0353948	−	0.108934i
$120$		0			0
$121$	8.47131	−	7.01690i	0.770119	−	0.637900i
$122$	12.8905			1.16705
$123$	0.563285	+	1.73361i	0.0507897	+	0.156314i
$124$	−0.998661	−	0.725569i	−0.0896824	−	0.0651581i
$125$		0			0
$126$	1.04765	−	3.22433i	0.0933318	−	0.287246i
$127$	−1.27701	+	3.93022i	−0.113316	+	0.348751i	−0.991592	−	0.129403i	$-0.958694\pi$
$127$	−1.27701	+	3.93022i	−0.113316	+	0.348751i	0.878276	+	0.478154i	$0.158694\pi$
$128$	−10.2014	+	7.41178i	−0.901689	+	0.655115i
$129$	0.502167	+	0.364846i	0.0442133	+	0.0321229i
$130$		0			0
$131$	−0.436527			−0.0381395			−0.0190698	−	0.999818i	$-0.506070\pi$
$131$	−0.436527			−0.0381395			−0.0190698	+	0.999818i	$0.506070\pi$
$132$	0.568804	−	0.204981i	0.0495080	−	0.0178413i
$133$	−5.00829			−0.434274
$134$	4.45452	+	13.7096i	0.384812	+	1.18433i
$135$		0			0
$136$	−1.18275	+	0.859317i	−0.101420	+	0.0736858i
$137$	2.43131	−	7.48281i	0.207721	−	0.639300i	−0.791870	−	0.610690i	$-0.790892\pi$
$137$	2.43131	−	7.48281i	0.207721	−	0.639300i	0.999591	−	0.0286095i	$-0.00910794\pi$
$138$	0.930836	−	2.86482i	0.0792380	−	0.243869i
$139$	−14.2736	+	10.3704i	−1.21067	+	0.879604i	−0.995292	−	0.0969265i	$-0.969099\pi$
$139$	−14.2736	+	10.3704i	−1.21067	+	0.879604i	−0.215379	+	0.976530i	$0.569099\pi$
$140$		0			0
$141$	−0.116811	−	0.359508i	−0.00983728	−	0.0302760i
$142$	−22.1541			−1.85913
$143$	−4.35346	−	5.60887i	−0.364055	−	0.469037i
$144$	−4.33136			−0.360947
$145$		0			0
$146$	9.39184	+	6.82357i	0.777274	+	0.564723i
$147$	−1.40214	+	1.01872i	−0.115647	+	0.0840224i
$148$	0.496833	−	1.52910i	0.0408394	−	0.125691i
$149$	−3.38687	+	10.4237i	−0.277463	+	0.853943i	0.711094	+	0.703097i	$0.248200\pi$
$149$	−3.38687	+	10.4237i	−0.277463	+	0.853943i	−0.988557	+	0.150846i	$0.951800\pi$
$150$		0			0
$151$	16.2065	+	11.7747i	1.31887	+	0.958214i	0.999946	+	0.0104337i	$0.00332120\pi$
$151$	16.2065	+	11.7747i	1.31887	+	0.958214i	0.318923	+	0.947781i	$0.396679\pi$
$152$	1.81082	+	5.57314i	0.146877	+	0.452041i
$153$	−0.544446			−0.0440158
$154$	10.7987	+	3.13370i	0.870185	+	0.252520i
$155$		0			0
$156$	−0.120596	−	0.371156i	−0.00965541	−	0.0297163i
$157$	7.40629	+	5.38098i	0.591086	+	0.429449i	0.842704	−	0.538377i	$-0.180963\pi$
$157$	7.40629	+	5.38098i	0.591086	+	0.429449i	−0.251618	+	0.967827i	$0.580963\pi$
$158$	11.0245	−	8.00978i	0.877063	−	0.637224i
$159$	3.58246	−	11.0257i	0.284108	−	0.874394i
$160$		0			0
$161$	3.78588	−	2.75060i	0.298369	−	0.216778i
$162$	−1.19513	−	0.868312i	−0.0938982	−	0.0682210i
$163$	3.50181	+	10.7775i	0.274283	+	0.844155i	0.989408	+	0.145159i	$0.0463695\pi$
$163$	3.50181	+	10.7775i	0.274283	+	0.844155i	−0.715126	+	0.698996i	$0.753631\pi$
$164$	−0.332296			−0.0259480
$165$		0			0
$166$	13.9635			1.08378
$167$	−4.66619	−	14.3611i	−0.361081	−	1.11129i	−0.952399	−	0.304854i	$-0.901392\pi$
$167$	−4.66619	−	14.3611i	−0.361081	−	1.11129i	0.591318	−	0.806438i	$-0.298608\pi$
$168$	−4.98555	−	3.62221i	−0.384644	−	0.279460i
$169$	6.80957	−	4.94744i	0.523813	−	0.380572i
$170$		0			0
$171$	−0.674367	+	2.07549i	−0.0515701	+	0.158717i
$172$	−0.0915436	+	0.0665103i	−0.00698013	+	0.00507136i
$173$	14.7760	+	10.7354i	1.12340	+	0.816195i	0.984720	−	0.174143i	$-0.0557153\pi$
$173$	14.7760	+	10.7354i	1.12340	+	0.816195i	0.138676	+	0.990338i	$0.455715\pi$
$174$	4.54008	+	13.9729i	0.344182	+	1.05928i
$175$		0			0
$176$	−0.455671	−	14.3583i	−0.0343475	−	1.08230i
$177$	8.07792			0.607174
$178$	0.266271	+	0.819498i	0.0199579	+	0.0614240i
$179$	0.425073	+	0.308833i	0.0317714	+	0.0230833i	0.603558	−	0.797319i	$-0.293749\pi$
$179$	0.425073	+	0.308833i	0.0317714	+	0.0230833i	−0.571786	+	0.820403i	$0.693749\pi$
$180$		0			0
$181$	−5.47289	+	16.8438i	−0.406797	+	1.25199i	0.512589	+	0.858634i	$0.328687\pi$
$181$	−5.47289	+	16.8438i	−0.406797	+	1.25199i	−0.919386	+	0.393358i	$0.871313\pi$
$182$	2.24278	−	6.90255i	0.166246	−	0.511651i
$183$	7.05944	−	5.12899i	0.521849	−	0.379146i
$184$	−4.42967	−	3.21834i	−0.326560	−	0.237259i
$185$		0			0
$186$	−10.0032			−0.733468
$187$	−0.0572771	−	1.80481i	−0.00418852	−	0.131981i
$188$	0.0689100			0.00502578
$189$	−0.709183	−	2.18264i	−0.0515854	−	0.158764i
$190$		0			0
$191$	13.3908	−	9.72899i	0.968925	−	0.703965i	0.0137185	−	0.999906i	$-0.495633\pi$
$191$	13.3908	−	9.72899i	0.968925	−	0.703965i	0.955206	+	0.295941i	$0.0956331\pi$
$192$	−2.20760	+	6.79429i	−0.159320	+	0.490336i
$193$	7.57191	−	23.3040i	0.545038	−	1.67746i	−0.175860	−	0.984415i	$-0.556271\pi$
$193$	7.57191	−	23.3040i	0.545038	−	1.67746i	0.720899	−	0.693040i	$-0.243729\pi$
$194$	−6.42741	+	4.66979i	−0.461461	+	0.335271i
$195$		0			0
$196$	−0.0976331	−	0.300484i	−0.00697379	−	0.0214631i
$197$	7.50877			0.534978			0.267489	−	0.963561i	$-0.413806\pi$
$197$	7.50877			0.534978			0.267489	+	0.963561i	$0.413806\pi$
$198$	2.75268	−	4.05315i	0.195625	−	0.288045i
$199$	−20.0956			−1.42454			−0.712270	−	0.701906i	$-0.752333\pi$
$199$	−20.0956			−1.42454			−0.712270	+	0.701906i	$0.752333\pi$
$200$		0			0
$201$	7.89440	+	5.73562i	0.556828	+	0.404559i
$202$	23.3398	−	16.9573i	1.64218	−	1.19311i
$203$	−7.05313	+	21.7073i	−0.495033	+	1.52355i
$204$	0.0306702	−	0.0943932i	0.00214734	−	0.00660885i
$205$		0			0
$206$	15.5441	+	11.2935i	1.08301	+	0.786852i
$207$	−0.630110	−	1.93928i	−0.0437956	−	0.134789i
$208$	−9.27247			−0.642930
$209$	−6.95110	−	2.01715i	−0.480817	−	0.139529i
$210$		0			0
$211$	1.67444	+	5.15339i	0.115273	+	0.354774i	0.992004	−	0.126207i	$-0.0402804\pi$
$211$	1.67444	+	5.15339i	0.115273	+	0.354774i	−0.876731	+	0.480981i	$0.840280\pi$
$212$	1.70977	+	1.24222i	0.117427	+	0.0853159i
$213$	−12.1326	+	8.81488i	−0.831315	+	0.603985i
$214$	−0.900921	+	2.77275i	−0.0615857	+	0.189541i
$215$		0			0
$216$	−2.17239	+	1.57833i	−0.147812	+	0.107392i
$217$	−12.5723	−	9.13429i	−0.853462	−	0.620076i
$218$	4.84856	+	14.9223i	0.328386	+	1.01067i
$219$	7.85844			0.531024
$220$		0			0
$221$	−1.16554			−0.0784024
$222$	−4.02613	−	12.3912i	−0.270216	−	0.831640i
$223$	12.7076	+	9.23259i	0.850961	+	0.618260i	0.925411	−	0.378965i	$-0.123720\pi$
$223$	12.7076	+	9.23259i	0.850961	+	0.618260i	−0.0744495	+	0.997225i	$0.523720\pi$
$224$	1.90885	−	1.38686i	0.127541	−	0.0926636i
$225$		0			0
$226$	7.71280	−	23.7375i	0.513048	−	1.57900i
$227$	−1.19040	+	0.864876i	−0.0790096	+	0.0574038i	−0.626589	−	0.779350i	$-0.715549\pi$
$227$	−1.19040	+	0.864876i	−0.0790096	+	0.0574038i	0.547579	+	0.836754i	$0.315549\pi$
$228$	−0.321848	−	0.233837i	−0.0213149	−	0.0154862i
$229$	−4.93656	−	15.1932i	−0.326217	−	1.00399i	−0.970888	−	0.239533i	$-0.923006\pi$
$229$	−4.93656	−	15.1932i	−0.326217	−	1.00399i	0.644671	−	0.764460i	$-0.276994\pi$
$230$		0			0
$231$	7.16075	−	2.58053i	0.471142	−	0.169786i
$232$	26.7057			1.75331
$233$	7.92263	+	24.3833i	0.519029	+	1.59741i	0.775830	+	0.630942i	$0.217331\pi$
$233$	7.92263	+	24.3833i	0.519029	+	1.59741i	−0.256802	+	0.966464i	$0.582669\pi$
$234$	−2.55850	−	1.85886i	−0.167254	−	0.121517i
$235$		0			0
$236$	−0.455053	+	1.40051i	−0.0296214	+	0.0911653i
$237$	2.85054	−	8.77306i	0.185162	−	0.569872i
$238$	1.49329	−	1.08494i	0.0967958	−	0.0703262i
$239$	3.38336	+	2.45816i	0.218851	+	0.159005i	0.691809	−	0.722080i	$-0.256814\pi$
$239$	3.38336	+	2.45816i	0.218851	+	0.159005i	−0.472958	+	0.881085i	$0.656814\pi$
$240$		0			0
$241$	−3.29180			−0.212043			−0.106022	−	0.994364i	$-0.533811\pi$
$241$	−3.29180			−0.212043			−0.106022	+	0.994364i	$0.533811\pi$
$242$	13.7256	+	8.69862i	0.882314	+	0.559169i
$243$	−1.00000			−0.0641500
$244$	0.491558	+	1.51286i	0.0314688	+	0.0968510i
$245$		0			0
$246$	−2.17851	+	1.58278i	−0.138897	+	0.100914i
$247$	−1.44367	+	4.44315i	−0.0918583	+	0.282711i
$248$	−5.61879	+	17.2929i	−0.356794	+	1.09810i
$249$	7.64709	−	5.55593i	0.484614	−	0.352093i
$250$		0			0
$251$	−2.89382	−	8.90626i	−0.182656	−	0.562158i	0.817244	−	0.576292i	$-0.195501\pi$
$251$	−2.89382	−	8.90626i	−0.182656	−	0.562158i	−0.999900	+	0.0141339i	$0.995501\pi$
$252$	0.418365			0.0263545
$253$	6.36233	−	2.29280i	0.399996	−	0.144147i
$254$	−6.10475			−0.383046
$255$		0			0
$256$	−3.51104	−	2.55092i	−0.219440	−	0.159433i
$257$	−10.1705	+	7.38928i	−0.634416	+	0.460930i	−0.857927	−	0.513771i	$-0.828248\pi$
$257$	−10.1705	+	7.38928i	−0.634416	+	0.460930i	0.223511	+	0.974701i	$0.428248\pi$
$258$	−0.283354	+	0.872075i	−0.0176409	+	0.0542930i
$259$	6.25470	−	19.2500i	0.388648	−	1.19614i
$260$		0			0
$261$	8.04603	+	5.84578i	0.498037	+	0.361845i
$262$	−0.199274	−	0.613302i	−0.0123112	−	0.0378899i
$263$	−4.82946			−0.297797			−0.148899	−	0.988852i	$-0.547573\pi$
$263$	−4.82946			−0.297797			−0.148899	+	0.988852i	$0.547573\pi$
$264$	−5.46064	−	7.03533i	−0.336079	−	0.432994i
$265$		0			0
$266$	−2.28628	−	7.03644i	−0.140181	−	0.431432i
$267$	0.471892	+	0.342849i	0.0288793	+	0.0209820i
$268$	−1.43913	+	1.04559i	−0.0879087	+	0.0638694i
$269$	−1.61594	+	4.97335i	−0.0985255	+	0.303230i	−0.988156	−	0.153450i	$-0.950962\pi$
$269$	−1.61594	+	4.97335i	−0.0985255	+	0.303230i	0.889631	+	0.456680i	$0.150962\pi$
$270$		0			0
$271$	−24.5383	+	17.8281i	−1.49060	+	1.08298i	−0.516654	+	0.856194i	$0.672823\pi$
$271$	−24.5383	+	17.8281i	−1.49060	+	1.08298i	−0.973944	+	0.226789i	$0.927177\pi$
$272$	−1.90782	−	1.38611i	−0.115678	−	0.0840453i
$273$	−1.51820	−	4.67254i	−0.0918856	−	0.282795i
$274$	11.6229			0.702167
$275$		0			0
$276$	0.371718			0.0223748
$277$	−4.93483	−	15.1878i	−0.296505	−	0.912549i	−0.982712	−	0.185142i	$-0.940725\pi$
$277$	−4.93483	−	15.1878i	−0.296505	−	0.912549i	0.686206	−	0.727407i	$-0.259275\pi$
$278$	−21.0858	−	15.3197i	−1.26464	−	0.918817i
$279$	−5.47820	+	3.98015i	−0.327972	+	0.238285i
$280$		0			0
$281$	−0.429741	+	1.32261i	−0.0256362	+	0.0789000i	−0.963056	−	0.269301i	$-0.913207\pi$
$281$	−0.429741	+	1.32261i	−0.0256362	+	0.0789000i	0.937420	+	0.348201i	$0.113207\pi$
$282$	0.451769	−	0.328230i	0.0269025	−	0.0195458i
$283$	4.75259	+	3.45296i	0.282512	+	0.205257i	0.720013	−	0.693961i	$-0.244136\pi$
$283$	4.75259	+	3.45296i	0.282512	+	0.205257i	−0.437500	+	0.899218i	$0.644136\pi$
$284$	−0.844811	−	2.60006i	−0.0501303	−	0.154285i
$285$		0			0
$286$	5.89287	−	8.67687i	0.348453	−	0.513074i
$287$	−4.18332			−0.246934
$288$	−0.317703	−	0.977789i	−0.0187208	−	0.0576168i
$289$	13.5135	+	9.81812i	0.794911	+	0.577536i
$290$		0			0
$291$	−1.66190	+	5.11479i	−0.0974221	+	0.299834i
$292$	−0.442688	+	1.36246i	−0.0259064	+	0.0797317i
$293$	16.1597	−	11.7407i	0.944060	−	0.685900i	−0.00533421	−	0.999986i	$-0.501698\pi$
$293$	16.1597	−	11.7407i	0.944060	−	0.685900i	0.949395	+	0.314086i	$0.101698\pi$
$294$	−2.07133	−	1.50491i	−0.120802	−	0.0877681i
$295$		0			0
$296$	−23.6825			−1.37652
$297$	−0.105203	−	3.31496i	−0.00610448	−	0.192353i
$298$	−16.1910			−0.937917
$299$	−1.34892	−	4.15156i	−0.0780102	−	0.240091i
$300$		0			0
$301$	−1.15245	+	0.837307i	−0.0664264	+	0.0482616i
$302$	−9.14475	+	28.1446i	−0.526221	+	1.61954i
$303$	6.03482	−	18.5733i	0.346691	−	1.06701i
$304$	−7.64709	+	5.55593i	−0.438590	+	0.318655i
$305$		0			0
$306$	−0.248539	−	0.764923i	−0.0142080	−	0.0437278i
$307$	−19.4372			−1.10934			−0.554671	−	0.832070i	$-0.687156\pi$
$307$	−19.4372			−1.10934			−0.554671	+	0.832070i	$0.687156\pi$
$308$	0.0440131	+	1.38686i	0.00250788	+	0.0790238i
$309$	13.0062			0.739898
$310$		0			0
$311$	−4.87175	−	3.53954i	−0.276252	−	0.200709i	0.441029	−	0.897493i	$-0.354614\pi$
$311$	−4.87175	−	3.53954i	−0.276252	−	0.200709i	−0.717281	+	0.696784i	$0.754614\pi$
$312$	−4.65059	+	3.37885i	−0.263288	+	0.191290i
$313$	1.57856	−	4.85831i	0.0892256	−	0.274608i	−0.896480	−	0.443084i	$-0.853884\pi$
$313$	1.57856	−	4.85831i	0.0892256	−	0.274608i	0.985706	+	0.168476i	$0.0538845\pi$
$314$	−4.17910	+	12.8619i	−0.235840	+	0.725841i
$315$		0			0
$316$	1.36045	+	0.988424i	0.0765312	+	0.0556032i
$317$	−4.22699	−	13.0093i	−0.237411	−	0.730677i	−0.996792	−	0.0800306i	$-0.974498\pi$
$317$	−4.22699	−	13.0093i	−0.237411	−	0.730677i	0.759381	−	0.650646i	$-0.225502\pi$
$318$	17.1260			0.960379
$319$	−18.5320	+	27.2872i	−1.03760	+	1.52779i
$320$		0			0
$321$	0.609860	+	1.87695i	0.0340390	+	0.104761i
$322$	5.59273	+	4.06336i	0.311671	+	0.226442i
$323$	−0.961227	+	0.698373i	−0.0534841	+	0.0388585i
$324$	0.0563329	−	0.173375i	0.00312961	−	0.00963194i
$325$		0			0
$326$	−13.5433	+	9.83978i	−0.750094	+	0.544975i
$327$	8.59273	+	6.24299i	0.475179	+	0.345238i
$328$	1.51254	+	4.65513i	0.0835162	+	0.257036i
$329$	0.867517			0.0478278
$330$		0			0
$331$	11.4695			0.630418			0.315209	−	0.949022i	$-0.397925\pi$
$331$	11.4695			0.630418			0.315209	+	0.949022i	$0.397925\pi$
$332$	0.532477	+	1.63879i	0.0292234	+	0.0899405i
$333$	−7.13520	−	5.18403i	−0.391007	−	0.284083i
$334$	18.0466	−	13.1116i	0.987465	−	0.717435i
$335$		0			0
$336$	3.07173	−	9.45380i	0.167576	−	0.515747i
$337$	3.04517	−	2.21245i	0.165881	−	0.120520i	−0.501748	−	0.865014i	$-0.667309\pi$
$337$	3.04517	−	2.21245i	0.165881	−	0.120520i	0.667629	+	0.744494i	$0.267309\pi$
$338$	10.0595	+	7.30865i	0.547165	+	0.397538i
$339$	−5.22101	−	16.0686i	−0.283567	−	0.872728i
$340$		0			0
$341$	−13.7703	−	17.7413i	−0.745706	−	0.960744i
$342$	−3.22382			−0.174324
$343$	−6.19339	−	19.0613i	−0.334412	−	1.02921i
$344$	1.34843	+	0.979691i	0.0727024	+	0.0528214i
$345$		0			0
$346$	−8.33754	+	25.6603i	−0.448229	+	1.37951i
$347$	0.122365	−	0.376600i	0.00656888	−	0.0202169i	−0.947718	−	0.319108i	$-0.896617\pi$
$347$	0.122365	−	0.376600i	0.00656888	−	0.0202169i	0.954287	+	0.298891i	$0.0966167\pi$
$348$	−1.46677	+	1.06567i	−0.0786270	+	0.0571259i
$349$	10.6554	+	7.74158i	0.570369	+	0.414398i	0.835239	−	0.549887i	$-0.185329\pi$
$349$	10.6554	+	7.74158i	0.570369	+	0.414398i	−0.264870	+	0.964284i	$0.585329\pi$
$350$		0			0
$351$	−2.14077			−0.114266
$352$	3.20790	−	1.15604i	0.170982	−	0.0616170i
$353$	−11.3853			−0.605977			−0.302989	−	0.952994i	$-0.597984\pi$
$353$	−11.3853			−0.605977			−0.302989	+	0.952994i	$0.597984\pi$
$354$	3.68756	+	11.3491i	0.195992	+	0.603200i
$355$		0			0
$356$	−0.0860245	+	0.0625005i	−0.00455929	+	0.00331252i
$357$	0.386111	−	1.18833i	0.0204352	−	0.0628930i
$358$	−0.239853	+	0.738191i	−0.0126766	+	0.0390146i
$359$	11.6241	−	8.44543i	0.613499	−	0.445733i	−0.237146	−	0.971474i	$-0.576212\pi$
$359$	11.6241	−	8.44543i	0.613499	−	0.445733i	0.850645	+	0.525741i	$0.176212\pi$
$360$		0			0
$361$	−4.39965	−	13.5407i	−0.231561	−	0.712671i
$362$	−26.1632			−1.37511
$363$	10.9779	−	0.697484i	0.576188	−	0.0366084i
$364$	0.895625			0.0469435
$365$		0			0
$366$	10.4286	+	7.57685i	0.545113	+	0.396048i
$367$	−21.2480	+	15.4376i	−1.10914	+	0.805836i	−0.982528	−	0.186117i	$-0.940410\pi$
$367$	−21.2480	+	15.4376i	−1.10914	+	0.805836i	−0.126610	+	0.991953i	$0.540410\pi$
$368$	2.72923	−	8.39972i	0.142271	−	0.437865i
$369$	−0.563285	+	1.73361i	−0.0293234	+	0.0902482i
$370$		0			0
$371$	21.5245	+	15.6384i	1.11750	+	0.811908i
$372$	−0.381454	−	1.17400i	−0.0197775	−	0.0608689i
$373$	−21.8951			−1.13368			−0.566842	−	0.823827i	$-0.691835\pi$
$373$	−21.8951			−1.13368			−0.566842	+	0.823827i	$0.691835\pi$
$374$	2.50954	−	0.904367i	0.129765	−	0.0467637i
$375$		0			0
$376$	−0.313664	−	0.965358i	−0.0161760	−	0.0497845i
$377$	17.2247	+	12.5145i	0.887119	+	0.644529i
$378$	2.74278	−	1.99274i	0.141073	−	0.102496i
$379$	7.89836	−	24.3087i	0.405711	−	1.24865i	−0.514588	−	0.857437i	$-0.672055\pi$
$379$	7.89836	−	24.3087i	0.405711	−	1.24865i	0.920300	−	0.391214i	$-0.127945\pi$
$380$		0			0
$381$	−3.34325	+	2.42901i	−0.171280	+	0.124442i
$382$	19.7817	+	14.3722i	1.01212	+	0.735348i
$383$	−5.88737	−	18.1195i	−0.300831	−	0.925862i	−0.981200	−	0.192992i	$-0.938181\pi$
$383$	−5.88737	−	18.1195i	−0.300831	−	0.925862i	0.680370	−	0.732869i	$-0.261819\pi$
$384$	−12.6097			−0.643485
$385$		0			0
$386$	36.1976			1.84241
$387$	0.191811	+	0.590333i	0.00975029	+	0.0300083i
$388$	−0.793157	−	0.576262i	−0.0402664	−	0.0292553i
$389$	−13.2618	+	9.63528i	−0.672401	+	0.488528i	−0.870828	−	0.491587i	$-0.836417\pi$
$389$	−13.2618	+	9.63528i	−0.672401	+	0.488528i	0.198427	+	0.980116i	$0.436417\pi$
$390$		0			0
$391$	0.343061	−	1.05583i	0.0173493	−	0.0533957i
$392$	−3.76506	+	2.73548i	−0.190164	+	0.138163i
$393$	−0.353158	−	0.256584i	−0.0178145	−	0.0129430i
$394$	3.42774	+	10.5495i	0.172687	+	0.531476i
$395$		0			0
$396$	0.580656	+	0.168502i	0.0291791	+	0.00846752i
$397$	−30.9826			−1.55497			−0.777485	−	0.628901i	$-0.783505\pi$
$397$	−30.9826			−1.55497			−0.777485	+	0.628901i	$0.783505\pi$
$398$	−9.17361	−	28.2335i	−0.459832	−	1.41522i
$399$	−4.05179	−	2.94380i	−0.202843	−	0.147374i
$400$		0			0
$401$	−1.96723	+	6.05453i	−0.0982390	+	0.302349i	−0.988084	−	0.153914i	$-0.950812\pi$
$401$	−1.96723	+	6.05453i	−0.0982390	+	0.302349i	0.889845	+	0.456262i	$0.150812\pi$
$402$	−4.45452	+	13.7096i	−0.222171	+	0.683773i
$403$	−11.7276	+	8.52060i	−0.584193	+	0.424441i
$404$	2.88018	+	2.09257i	0.143294	+	0.104109i
$405$		0			0
$406$	−33.7176			−1.67338
$407$	16.4342	−	24.1982i	0.814612	−	1.19946i
$408$	−1.46196			−0.0723776
$409$	−1.93715	−	5.96193i	−0.0957858	−	0.294798i	0.891672	−	0.452682i	$-0.149533\pi$
$409$	−1.93715	−	5.96193i	−0.0957858	−	0.294798i	−0.987458	+	0.157884i	$0.949533\pi$
$410$		0			0
$411$	6.36526	−	4.62463i	0.313975	−	0.228116i
$412$	−0.732678	+	2.25495i	−0.0360965	+	0.111093i
$413$	−5.72872	+	17.6312i	−0.281892	+	0.867574i
$414$	2.43696	−	1.77055i	0.119770	−	0.0870180i
$415$		0			0
$416$	−0.680130	−	2.09323i	−0.0333461	−	0.102629i
$417$	−17.6431			−0.863988
$418$	−0.339154	−	10.6868i	−0.0165886	−	0.522710i
$419$	3.90332			0.190689			0.0953447	−	0.995444i	$-0.469605\pi$
$419$	3.90332			0.190689			0.0953447	+	0.995444i	$0.469605\pi$
$420$		0			0
$421$	−14.0539	−	10.2107i	−0.684944	−	0.497641i	0.190050	−	0.981774i	$-0.439135\pi$
$421$	−14.0539	−	10.2107i	−0.684944	−	0.497641i	−0.874994	+	0.484134i	$0.839135\pi$
$422$	−6.47592	+	4.70503i	−0.315243	+	0.229037i
$423$	0.116811	−	0.359508i	0.00567956	−	0.0174799i
$424$	9.61970	−	29.6064i	0.467174	−	1.43781i
$425$		0			0
$426$	−17.9231	−	13.0219i	−0.868375	−	0.630911i
$427$	6.18829	+	19.0456i	0.299473	+	0.921682i
$428$	−0.359772			−0.0173902
$429$	−0.225215	−	7.09657i	−0.0108735	−	0.342626i
$430$		0			0
$431$	−2.17440	−	6.69212i	−0.104737	−	0.322348i	0.884931	−	0.465721i	$-0.154205\pi$
$431$	−2.17440	−	6.69212i	−0.104737	−	0.322348i	−0.989669	+	0.143373i	$0.954205\pi$
$432$	−3.50415	−	2.54591i	−0.168593	−	0.122490i
$433$	2.22665	−	1.61776i	0.107006	−	0.0777445i	−0.532995	−	0.846118i	$-0.678934\pi$
$433$	2.22665	−	1.61776i	0.107006	−	0.0777445i	0.640002	+	0.768374i	$0.278934\pi$
$434$	7.09407	−	21.8333i	0.340526	−	1.04803i
$435$		0			0
$436$	−1.56643	+	1.13808i	−0.0750184	+	0.0545041i
$437$	−3.60002	−	2.61557i	−0.172212	−	0.125120i
$438$	3.58736	+	11.0408i	0.171411	+	0.527548i
$439$	−2.73703			−0.130631			−0.0653157	−	0.997865i	$-0.520805\pi$
$439$	−2.73703			−0.130631			−0.0653157	+	0.997865i	$0.520805\pi$
$440$		0			0
$441$	−1.73315			−0.0825307
$442$	−0.532065	−	1.63753i	−0.0253078	−	0.0778893i
$443$	8.98348	+	6.52688i	0.426818	+	0.310102i	0.780375	−	0.625311i	$-0.215028\pi$
$443$	8.98348	+	6.52688i	0.426818	+	0.310102i	−0.353557	+	0.935413i	$0.615028\pi$
$444$	1.30073	−	0.945033i	0.0617297	−	0.0448493i
$445$		0			0
$446$	−7.17041	+	22.0683i	−0.339529	+	1.04496i
$447$	−8.86693	+	6.44220i	−0.419392	+	0.304706i
$448$	−13.2639	−	9.63679i	−0.626660	−	0.455295i
$449$	4.58174	+	14.1012i	0.216226	+	0.665475i	0.999064	+	0.0432498i	$0.0137711\pi$
$449$	4.58174	+	14.1012i	0.216226	+	0.665475i	−0.782838	+	0.622225i	$0.786229\pi$
$450$		0			0
$451$	−5.80610	−	1.68488i	−0.273399	−	0.0793380i
$452$	3.08001			0.144872
$453$	6.19034	+	19.0519i	0.290848	+	0.895137i
$454$	−1.75853	−	1.27765i	−0.0825319	−	0.0599629i
$455$		0			0
$456$	−1.81082	+	5.57314i	−0.0847996	+	0.260986i
$457$	−9.01788	+	27.7542i	−0.421838	+	1.29829i	0.484151	+	0.874985i	$0.339129\pi$
$457$	−9.01788	+	27.7542i	−0.421838	+	1.29829i	−0.905989	+	0.423301i	$0.860871\pi$
$458$	19.0922	−	13.8713i	0.892122	−	0.648165i
$459$	−0.440466	−	0.320017i	−0.0205592	−	0.0149371i
$460$		0			0
$461$	−31.1798			−1.45219			−0.726094	−	0.687595i	$-0.758666\pi$
$461$	−31.1798			−1.45219			−0.726094	+	0.687595i	$0.758666\pi$
$462$	6.89440	+	8.88254i	0.320757	+	0.413253i
$463$	−41.1642			−1.91306			−0.956531	−	0.291631i	$-0.905802\pi$
$463$	−41.1642			−1.91306			−0.956531	+	0.291631i	$0.905802\pi$
$464$	13.3116	+	40.9689i	0.617976	+	1.90194i
$465$		0			0
$466$	−30.6409	+	22.2619i	−1.41941	+	1.03126i
$467$	−11.9826	+	36.8788i	−0.554490	+	1.70655i	0.142795	+	0.989752i	$0.454391\pi$
$467$	−11.9826	+	36.8788i	−0.554490	+	1.70655i	−0.697285	+	0.716794i	$0.745609\pi$
$468$	0.120596	−	0.371156i	0.00557455	−	0.0171567i
$469$	−18.1174	+	13.1630i	−0.836582	+	0.607812i
$470$		0			0
$471$	2.82895	+	8.70662i	0.130351	+	0.401180i
$472$	21.6910			0.998409
$473$	−1.93675	+	0.697949i	−0.0890518	+	0.0320917i
$474$	13.6270			0.625911
$475$		0			0
$476$	0.184276	+	0.133884i	0.00844626	+	0.00613656i
$477$	9.37901	−	6.81425i	0.429435	−	0.312003i
$478$	−1.90911	+	5.87562i	−0.0873205	+	0.268745i
$479$	5.15675	−	15.8708i	0.235618	−	0.725158i	−0.761421	−	0.648258i	$-0.775498\pi$
$479$	5.15675	−	15.8708i	0.235618	−	0.725158i	0.997039	−	0.0768997i	$-0.0245021\pi$
$480$		0			0
$481$	−15.2748	−	11.0978i	−0.696473	−	0.506017i
$482$	−1.50270	−	4.62483i	−0.0684461	−	0.210655i
$483$	4.67961			0.212930
$484$	−0.497489	+	1.94258i	−0.0226131	+	0.0882989i
$485$		0			0
$486$	−0.456498	−	1.40496i	−0.0207072	−	0.0637302i
$487$	2.03220	+	1.47648i	0.0920877	+	0.0669056i	0.632876	−	0.774253i	$-0.281874\pi$
$487$	2.03220	+	1.47648i	0.0920877	+	0.0669056i	−0.540789	+	0.841158i	$0.681874\pi$
$488$	18.9562	−	13.7725i	0.858105	−	0.623450i
$489$	−3.50181	+	10.7775i	−0.158357	+	0.487373i
$490$		0			0
$491$	6.11508	−	4.44286i	0.275970	−	0.200504i	−0.441188	−	0.897415i	$-0.645443\pi$
$491$	6.11508	−	4.44286i	0.275970	−	0.200504i	0.717158	+	0.696911i	$0.245443\pi$
$492$	−0.268833	−	0.195319i	−0.0121199	−	0.00880565i
$493$	1.67325	+	5.14974i	0.0753594	+	0.231932i
$494$	−6.90147			−0.310512
$495$		0			0
$496$	−29.3295			−1.31693
$497$	−10.6354	−	32.7325i	−0.477065	−	1.46825i
$498$	11.2967	+	8.20756i	0.506219	+	0.367789i
$499$	−13.5886	+	9.87269i	−0.608309	+	0.441962i	−0.848818	−	0.528685i	$-0.822685\pi$
$499$	−13.5886	+	9.87269i	−0.608309	+	0.441962i	0.240510	+	0.970647i	$0.422685\pi$
$500$		0			0
$501$	4.66619	−	14.3611i	0.208470	−	0.641605i
$502$	11.1919	−	8.13139i	0.499519	−	0.362922i
$503$	6.17489	+	4.48632i	0.275325	+	0.200035i	0.716876	−	0.697201i	$-0.245572\pi$
$503$	6.17489	+	4.48632i	0.275325	+	0.200035i	−0.441551	+	0.897236i	$0.645572\pi$
$504$	−1.90431	−	5.86087i	−0.0848248	−	0.261064i
$505$		0			0
$506$	6.12569	+	7.89215i	0.272320	+	0.350849i
$507$	8.41709			0.373816
$508$	−0.232795	−	0.716469i	−0.0103286	−	0.0317882i
$509$	−26.6198	−	19.3404i	−1.17990	−	0.857249i	−0.187741	−	0.982219i	$-0.560117\pi$
$509$	−26.6198	−	19.3404i	−1.17990	−	0.857249i	−0.992161	+	0.124970i	$0.960117\pi$
$510$		0			0
$511$	−5.57307	+	17.1521i	−0.246538	+	0.758766i
$512$	−5.81206	+	17.8877i	−0.256859	+	0.790531i
$513$	−1.76552	+	1.28272i	−0.0779494	+	0.0566336i
$514$	−15.0244	−	10.9159i	−0.662699	−	0.481479i
$515$		0			0
$516$	−0.113154			−0.00498133
$517$	1.20404	+	0.349403i	0.0529537	+	0.0153667i
$518$	29.9007			1.31376
$519$	5.64392	+	17.3702i	0.247741	+	0.762467i
$520$		0			0
$521$	−0.645559	+	0.469026i	−0.0282824	+	0.0205484i	−0.601837	−	0.798619i	$-0.705564\pi$
$521$	−0.645559	+	0.469026i	−0.0282824	+	0.0205484i	0.573554	+	0.819168i	$0.305564\pi$
$522$	−4.54008	+	13.9729i	−0.198714	+	0.611578i
$523$	−1.33036	+	4.09443i	−0.0581727	+	0.179037i	−0.975920	−	0.218127i	$-0.930005\pi$
$523$	−1.33036	+	4.09443i	−0.0581727	+	0.179037i	0.917748	+	0.397164i	$0.130005\pi$
$524$	0.0643796	−	0.0467745i	0.00281244	−	0.00204336i
$525$		0			0
$526$	−2.20464	−	6.78519i	−0.0961270	−	0.295848i
$527$	−3.68668			−0.160594
$528$	8.07094	−	11.8839i	0.351242	−	0.517181i
$529$	−18.8422			−0.819224
$530$		0			0
$531$	6.53518	+	4.74808i	0.283602	+	0.206049i
$532$	0.738630	−	0.536646i	0.0320237	−	0.0232666i
$533$	−1.20586	+	3.71127i	−0.0522318	+	0.160753i
$534$	−0.266271	+	0.819498i	−0.0115227	+	0.0354632i
$535$		0			0
$536$	21.1982	+	15.4014i	0.915623	+	0.665239i
$537$	0.162363	+	0.499703i	0.00700649	+	0.0215638i
$538$	−7.72502			−0.333049
$539$	−0.182331	−	5.74530i	−0.00785357	−	0.247468i
$540$		0			0
$541$	−7.01720	−	21.5967i	−0.301693	−	0.928516i	−0.980891	−	0.194560i	$-0.937672\pi$
$541$	−7.01720	−	21.5967i	−0.301693	−	0.928516i	0.679198	−	0.733955i	$-0.262328\pi$
$542$	−36.2495	−	26.3368i	−1.55705	−	1.13126i
$543$	−14.3282	+	10.4101i	−0.614883	+	0.446738i
$544$	0.172972	−	0.532353i	0.00741611	−	0.0228245i
$545$		0			0
$546$	5.87166	−	4.26601i	0.251284	−	0.182568i
$547$	26.0140	+	18.9003i	1.11228	+	0.808117i	0.983021	−	0.183494i	$-0.0587408\pi$
$547$	26.0140	+	18.9003i	1.11228	+	0.808117i	0.129257	+	0.991611i	$0.458741\pi$
$548$	0.443221	+	1.36409i	0.0189335	+	0.0582712i
$549$	8.72595			0.372415
$550$		0			0
$551$	21.7039			0.924617
$552$	−1.69198	−	5.20739i	−0.0720156	−	0.221641i
$553$	17.1269	+	12.4434i	0.728309	+	0.529147i
$554$	19.0855	−	13.8665i	0.810867	−	0.589129i
$555$		0			0
$556$	0.993889	−	3.05888i	0.0421503	−	0.129725i
$557$	30.5122	−	22.1684i	1.29284	−	0.939306i	0.292985	−	0.956117i	$-0.405352\pi$
$557$	30.5122	−	22.1684i	1.29284	−	0.939306i	0.999859	+	0.0168116i	$0.00535155\pi$
$558$	−8.09273	−	5.87971i	−0.342593	−	0.248908i
$559$	0.410623	+	1.26377i	0.0173675	+	0.0534517i
$560$		0			0
$561$	1.01450	−	1.49379i	0.0428324	−	0.0630679i
$562$	−2.05438			−0.0866588
$563$	−6.79438	−	20.9109i	−0.286349	−	0.881291i	−0.985991	−	0.166798i	$-0.946657\pi$
$563$	−6.79438	−	20.9109i	−0.286349	−	0.881291i	0.699642	−	0.714493i	$-0.253343\pi$
$564$	0.0557493	+	0.0405043i	0.00234747	+	0.00170554i
$565$		0			0
$566$	−2.68171	+	8.25347i	−0.112721	+	0.346919i
$567$	0.709183	−	2.18264i	0.0297829	−	0.0916622i
$568$	−32.5788	+	23.6699i	−1.36698	+	0.993166i
$569$	16.5690	+	12.0381i	0.694609	+	0.504663i	0.878172	−	0.478345i	$-0.158763\pi$
$569$	16.5690	+	12.0381i	0.694609	+	0.504663i	−0.183563	+	0.983008i	$0.558763\pi$
$570$		0			0
$571$	17.4373			0.729728			0.364864	−	0.931061i	$-0.381116\pi$
$571$	17.4373			0.729728			0.364864	+	0.931061i	$0.381116\pi$
$572$	1.24305	+	0.360724i	0.0519747	+	0.0150826i
$573$	16.5519			0.691467
$574$	−1.90968	−	5.87739i	−0.0797085	−	0.245317i
$575$		0			0
$576$	−5.77957	+	4.19910i	−0.240815	+	0.174963i
$577$	10.2701	−	31.6082i	0.427551	−	1.31587i	−0.472978	−	0.881074i	$-0.656821\pi$
$577$	10.2701	−	31.6082i	0.427551	−	1.31587i	0.900530	−	0.434794i	$-0.143179\pi$
$578$	−7.62516	+	23.4678i	−0.317165	+	0.976133i
$579$	19.8235	−	14.4026i	0.823838	−	0.598553i
$580$		0			0
$581$	6.70342	+	20.6310i	0.278105	+	0.855918i
$582$	−7.94472			−0.329319
$583$	23.5756	+	30.3741i	0.976403	+	1.25797i
$584$	21.1016			0.873192
$585$		0			0
$586$	23.8721	+	17.3441i	0.986147	+	0.716478i
$587$	−34.6222	+	25.1545i	−1.42901	+	1.03824i	−0.438811	+	0.898580i	$0.644600\pi$
$587$	−34.6222	+	25.1545i	−1.42901	+	1.03824i	−0.990200	+	0.139657i	$0.955400\pi$
$588$	0.0976331	−	0.300484i	0.00402632	−	0.0123917i
$589$	−4.56643	+	14.0540i	−0.188156	+	0.579086i
$590$		0			0
$591$	6.07472	+	4.41354i	0.249881	+	0.181549i
$592$	−11.8047	−	36.3312i	−0.485171	−	1.49320i
$593$	42.6570			1.75171			0.875857	−	0.482570i	$-0.160297\pi$
$593$	42.6570			1.75171			0.875857	+	0.482570i	$0.160297\pi$
$594$	4.60935	−	1.66108i	0.189124	−	0.0681548i
$595$		0			0
$596$	−0.617416	−	1.90021i	−0.0252903	−	0.0778357i
$597$	−16.2577	−	11.8119i	−0.665383	−	0.483429i
$598$	5.21698	−	3.79036i	0.213338	−	0.154999i
$599$	8.75148	−	26.9343i	0.357576	−	1.10051i	−0.596925	−	0.802297i	$-0.703611\pi$
$599$	8.75148	−	26.9343i	0.357576	−	1.10051i	0.954501	−	0.298208i	$-0.0963890\pi$
$600$		0			0
$601$	6.19268	−	4.49925i	0.252605	−	0.183528i	−0.454276	−	0.890861i	$-0.650102\pi$
$601$	6.19268	−	4.49925i	0.252605	−	0.183528i	0.706880	+	0.707333i	$0.250102\pi$
$602$	−1.70248	−	1.23692i	−0.0693877	−	0.0504131i
$603$	3.01539	+	9.28043i	0.122796	+	0.377928i
$604$	−3.65184			−0.148591
$605$		0			0
$606$	28.8495			1.17193
$607$	−3.58415	−	11.0309i	−0.145476	−	0.447730i	0.851596	−	0.524199i	$-0.175635\pi$
$607$	−3.58415	−	11.0309i	−0.145476	−	0.447730i	−0.997072	+	0.0764693i	$0.975635\pi$
$608$	−1.81514	−	1.31878i	−0.0736137	−	0.0534835i
$609$	−18.4653	+	13.4159i	−0.748253	+	0.543638i
$610$		0			0
$611$	0.250066	−	0.769625i	0.0101166	−	0.0311357i
$612$	0.0802957	−	0.0583382i	0.00324576	−	0.00235818i
$613$	−25.9757	−	18.8725i	−1.04915	−	0.762251i	−0.0770985	−	0.997023i	$-0.524566\pi$
$613$	−25.9757	−	18.8725i	−1.04915	−	0.762251i	−0.972050	+	0.234772i	$0.924566\pi$
$614$	−8.87307	−	27.3085i	−0.358088	−	1.10208i
$615$		0			0
$616$	19.2282	−	6.92929i	0.774725	−	0.279189i
$617$	18.7392			0.754414			0.377207	−	0.926129i	$-0.376885\pi$
$617$	18.7392			0.754414			0.377207	+	0.926129i	$0.376885\pi$
$618$	5.93732	+	18.2732i	0.238834	+	0.735056i
$619$	31.6002	+	22.9589i	1.27012	+	0.922796i	0.999207	−	0.0398085i	$-0.0126748\pi$
$619$	31.6002	+	22.9589i	1.27012	+	0.922796i	0.270912	+	0.962604i	$0.412675\pi$
$620$		0			0
$621$	0.630110	−	1.93928i	0.0252854	−	0.0778205i
$622$	2.74895	−	8.46040i	0.110223	−	0.339231i
$623$	−1.08297	+	0.786827i	−0.0433884	+	0.0315236i
$624$	−7.50158	−	5.45022i	−0.300304	−	0.218183i
$625$		0			0
$626$	7.54633			0.301612
$627$	−4.43790	−	5.71766i	−0.177233	−	0.228341i
$628$	−1.66887			−0.0665952
$629$	−1.48383	−	4.56677i	−0.0591644	−	0.182089i
$630$		0			0
$631$	−36.4512	+	26.4833i	−1.45110	+	1.05428i	−0.465524	+	0.885035i	$0.654134\pi$
$631$	−36.4512	+	26.4833i	−1.45110	+	1.05428i	−0.985573	+	0.169249i	$0.945866\pi$
$632$	7.65433	−	23.5576i	0.304473	−	0.937071i
$633$	−1.67444	+	5.15339i	−0.0665530	+	0.204829i
$634$	16.3479	−	11.8775i	0.649260	−	0.471715i
$635$		0			0
$636$	0.653073	+	2.00995i	0.0258960	+	0.0796997i
$637$	−3.71027			−0.147006
$638$	−46.7972	−	13.5802i	−1.85272	−	0.537644i
$639$	−14.9968			−0.593263
$640$		0			0
$641$	−20.9477	−	15.2194i	−0.827384	−	0.601130i	0.0914341	−	0.995811i	$-0.470855\pi$
$641$	−20.9477	−	15.2194i	−0.827384	−	0.601130i	−0.918818	+	0.394682i	$0.870855\pi$
$642$	−2.35864	+	1.71365i	−0.0930882	+	0.0676325i
$643$	−9.46770	+	29.1386i	−0.373370	+	1.14911i	0.571202	+	0.820809i	$0.306477\pi$
$643$	−9.46770	+	29.1386i	−0.373370	+	1.14911i	−0.944572	+	0.328304i	$0.893523\pi$
$644$	−0.263616	+	0.811326i	−0.0103879	+	0.0319707i
$645$		0			0
$646$	−1.41998	−	1.03168i	−0.0558685	−	0.0405908i
$647$	4.66875	+	14.3689i	0.183547	+	0.564901i	0.999920	−	0.0126243i	$-0.00401854\pi$
$647$	4.66875	+	14.3689i	0.183547	+	0.564901i	−0.816373	+	0.577525i	$0.804019\pi$
$648$	−2.68522			−0.105485
$649$	−15.0522	+	22.1633i	−0.590849	+	0.869987i
$650$		0			0
$651$	−4.80218	−	14.7796i	−0.188212	−	0.579258i
$652$	−1.67127	−	1.21425i	−0.0654521	−	0.0475537i
$653$	−4.23543	+	3.07722i	−0.165745	+	0.120421i	−0.667566	−	0.744551i	$-0.732664\pi$
$653$	−4.23543	+	3.07722i	−0.165745	+	0.120421i	0.501821	+	0.864972i	$0.332664\pi$
$654$	−4.84856	+	14.9223i	−0.189594	+	0.583510i
$655$		0			0
$656$	−6.38745	+	4.64075i	−0.249388	+	0.181191i
$657$	6.35761	+	4.61907i	0.248034	+	0.180207i
$658$	0.396020	+	1.21882i	0.0154385	+	0.0475147i
$659$	14.9207			0.581229			0.290615	−	0.956840i	$-0.406140\pi$
$659$	14.9207			0.581229			0.290615	+	0.956840i	$0.406140\pi$
$660$		0			0
$661$	45.7403			1.77909			0.889545	−	0.456847i	$-0.151021\pi$
$661$	45.7403			1.77909			0.889545	+	0.456847i	$0.151021\pi$
$662$	5.23579	+	16.1141i	0.203495	+	0.626292i
$663$	−0.942938	−	0.685085i	−0.0366207	−	0.0266065i
$664$	20.5341	−	14.9189i	0.796878	−	0.578966i
$665$		0			0
$666$	4.02613	−	12.3912i	0.156009	−	0.480147i
$667$	−16.4065	+	11.9200i	−0.635261	+	0.461544i
$668$	2.22699	+	1.61800i	0.0861647	+	0.0626023i
$669$	4.85386	+	14.9386i	0.187661	+	0.577561i
$670$		0			0
$671$	0.917993	+	28.9261i	0.0354387	+	1.11668i
$672$	2.35947			0.0910185
$673$	−6.52294	−	20.0755i	−0.251441	−	0.773855i	−0.994510	−	0.104641i	$-0.966631\pi$
$673$	−6.52294	−	20.0755i	−0.251441	−	0.773855i	0.743069	−	0.669214i	$-0.233369\pi$
$674$	4.49852	+	3.26836i	0.173276	+	0.125893i
$675$		0			0
$676$	−0.474159	+	1.45931i	−0.0182369	+	0.0561273i
$677$	13.6182	−	41.9125i	0.523390	−	1.61083i	−0.244087	−	0.969753i	$-0.578488\pi$
$677$	13.6182	−	41.9125i	0.523390	−	1.61083i	0.767477	−	0.641077i	$-0.221512\pi$
$678$	20.1924	−	14.6706i	0.775483	−	0.563421i
$679$	−9.98516	−	7.25464i	−0.383195	−	0.278408i
$680$		0			0
$681$	−1.47141			−0.0563847
$682$	18.6396	−	27.4456i	0.713748	−	1.05095i
$683$	42.5318			1.62743			0.813717	−	0.581261i	$-0.197440\pi$
$683$	42.5318			1.62743			0.813717	+	0.581261i	$0.197440\pi$
$684$	−0.122935	−	0.378355i	−0.00470054	−	0.0144668i
$685$		0			0
$686$	23.9531	−	17.4029i	0.914532	−	0.664446i
$687$	4.93656	−	15.1932i	0.188342	−	0.579656i
$688$	−0.830802	+	2.55694i	−0.0316740	+	0.0974826i
$689$	20.0783	−	14.5878i	0.764924	−	0.555750i
$690$		0			0
$691$	−1.77552	−	5.46449i	−0.0675439	−	0.207879i	0.911588	−	0.411105i	$-0.134857\pi$
$691$	−1.77552	−	5.46449i	−0.0675439	−	0.207879i	−0.979132	+	0.203227i	$0.934857\pi$
$692$	−3.32949			−0.126568
$693$	7.30996	+	2.12129i	0.277682	+	0.0805811i
$694$	0.584966			0.0222050
$695$		0			0
$696$	21.6054	+	15.6972i	0.818949	+	0.595001i
$697$	−0.802893	+	0.583336i	−0.0304117	+	0.0220954i
$698$	−6.01244	+	18.5044i	−0.227574	+	0.700401i
$699$	−7.92263	+	24.3833i	−0.299661	+	0.922263i
$700$		0			0
$701$	0.983718	+	0.714713i	0.0371545	+	0.0269943i	0.606208	−	0.795307i	$-0.292690\pi$
$701$	0.983718	+	0.714713i	0.0371545	+	0.0269943i	−0.569053	+	0.822301i	$0.692690\pi$
$702$	−0.977260	−	3.00770i	−0.0368843	−	0.113518i
$703$	−19.2470			−0.725913
$704$	−14.5279	−	18.7173i	−0.547540	−	0.705433i
$705$		0			0
$706$	−5.19736	−	15.9958i	−0.195605	−	0.602011i
$707$	36.2589	+	26.3437i	1.36366	+	0.990755i
$708$	−1.19134	+	0.865562i	−0.0447734	+	0.0325298i
$709$	−8.16115	+	25.1174i	−0.306498	+	0.943305i	0.672615	+	0.739992i	$0.265171\pi$
$709$	−8.16115	+	25.1174i	−0.306498	+	0.943305i	−0.979114	+	0.203313i	$0.934829\pi$
$710$		0			0
$711$	7.46281	−	5.42205i	0.279877	−	0.203343i
$712$	1.26713	+	0.920626i	0.0474878	+	0.0345019i
$713$	−4.26675	−	13.1317i	−0.159791	−	0.491786i
$714$	1.84581			0.0690777
$715$		0			0
$716$	−0.0957823			−0.00357955
$717$	1.29233	+	3.97738i	0.0482629	+	0.148538i
$718$	17.1719	+	12.4761i	0.640849	+	0.465604i
$719$	−40.0007	+	29.0622i	−1.49177	+	1.08384i	−0.518255	+	0.855226i	$0.673418\pi$
$719$	−40.0007	+	29.0622i	−1.49177	+	1.08384i	−0.973518	+	0.228611i	$0.926582\pi$
$720$		0			0
$721$	−9.22379	+	28.3879i	−0.343512	+	1.05722i
$722$	17.0157	−	12.3627i	0.633260	−	0.460090i
$723$	−2.66312	−	1.93487i	−0.0990425	−	0.0719586i
$724$	−0.997692	−	3.07058i	−0.0370789	−	0.114117i
$725$		0			0
$726$	5.99131	+	15.1050i	0.222359	+	0.560600i
$727$	39.2447			1.45551			0.727753	−	0.685839i	$-0.240565\pi$
$727$	39.2447			1.45551			0.727753	+	0.685839i	$0.240565\pi$
$728$	−4.07670	−	12.5468i	−0.151093	−	0.465015i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−0.104431	+	0.321404i	−0.00386250	+	0.0118876i
$732$	−0.491558	+	1.51286i	−0.0181685	+	0.0559169i
$733$	4.20624	−	3.05601i	0.155361	−	0.112876i	−0.507389	−	0.861717i	$-0.669389\pi$
$733$	4.20624	−	3.05601i	0.155361	−	0.112876i	0.662750	+	0.748841i	$0.269389\pi$
$734$	−31.3888	−	22.8053i	−1.15858	−	0.841760i
$735$		0			0
$736$	2.09639			0.0772740
$737$	−30.4470	+	10.9722i	−1.12153	+	0.404167i
$738$	−2.69279			−0.0991229
$739$	8.96428	+	27.5892i	0.329757	+	1.01489i	0.969248	+	0.246088i	$0.0791451\pi$
$739$	8.96428	+	27.5892i	0.329757	+	1.01489i	−0.639491	+	0.768799i	$0.720855\pi$
$740$		0			0
$741$	−3.77957	+	2.74602i	−0.138846	+	0.100877i
$742$	−12.1455	+	37.3799i	−0.445874	+	1.37226i
$743$	−2.62874	+	8.09042i	−0.0964390	+	0.296809i	−0.987626	−	0.156827i	$-0.949873\pi$
$743$	−2.62874	+	8.09042i	−0.0964390	+	0.296809i	0.891187	+	0.453636i	$0.149873\pi$
$744$	−14.7102	+	10.6876i	−0.539301	+	0.391825i
$745$		0			0
$746$	−9.99506	−	30.7616i	−0.365945	−	1.12626i
$747$	9.45232			0.345842
$748$	0.201836	+	0.260039i	0.00737985	+	0.00950798i
$749$	−4.52922			−0.165494
$750$		0			0
$751$	28.4006	+	20.6343i	1.03635	+	0.752955i	0.969570	−	0.244813i	$-0.0787264\pi$
$751$	28.4006	+	20.6343i	1.03635	+	0.752955i	0.0667831	+	0.997768i	$0.478726\pi$
$752$	1.32460	−	0.962377i	0.0483032	−	0.0350943i
$753$	2.89382	−	8.90626i	0.105457	−	0.324562i
$754$	−9.71928	+	29.9129i	−0.353955	+	1.08936i
$755$		0			0
$756$	0.338464	+	0.245909i	0.0123098	+	0.00894362i
$757$	2.21972	+	6.83159i	0.0806771	+	0.248298i	0.983257	−	0.182224i	$-0.0583295\pi$
$757$	2.21972	+	6.83159i	0.0806771	+	0.248298i	−0.902580	+	0.430522i	$0.858329\pi$
$758$	37.7582			1.37144
$759$	6.49491	+	1.88477i	0.235750	+	0.0684128i
$760$		0			0
$761$	−13.4072	−	41.2631i	−0.486011	−	1.49579i	−0.830512	−	0.557001i	$-0.811952\pi$
$761$	−13.4072	−	41.2631i	−0.486011	−	1.49579i	0.344501	−	0.938786i	$-0.388048\pi$
$762$	−4.93885	−	3.58828i	−0.178916	−	0.129990i
$763$	−19.7200	+	14.3274i	−0.713912	+	0.518687i
$764$	−0.932419	+	2.86969i	−0.0337337	+	0.103822i
$765$		0			0
$766$	22.7695	−	16.5430i	0.822696	−	0.597724i
$767$	13.9903	+	10.1646i	0.505162	+	0.367021i
$768$	−1.34110	−	4.12748i	−0.0483927	−	0.148937i
$769$	−19.6548			−0.708771			−0.354385	−	0.935099i	$-0.615310\pi$
$769$	−19.6548			−0.708771			−0.354385	+	0.935099i	$0.615310\pi$
$770$		0			0
$771$	−12.5714			−0.452747
$772$	1.38034	+	4.24824i	0.0496795	+	0.152898i
$773$	−19.7691	−	14.3631i	−0.711044	−	0.516604i	0.172466	−	0.985015i	$-0.444826\pi$
$773$	−19.7691	−	14.3631i	−0.711044	−	0.516604i	−0.883510	+	0.468412i	$0.844826\pi$
$774$	−0.741831	+	0.538972i	−0.0266646	+	0.0193729i
$775$		0			0
$776$	−4.46256	+	13.7343i	−0.160196	+	0.493034i
$777$	16.3750	−	11.8971i	0.587450	−	0.426808i
$778$	−19.5912	−	14.2338i	−0.702377	−	0.510307i
$779$	1.22925	+	3.78326i	0.0440426	+	0.135549i
$780$		0			0
$781$	−1.57770	−	49.7136i	−0.0564545	−	1.77889i
$782$	1.64001			0.0586465
$783$	3.07331	+	9.45867i	0.109831	+	0.338025i
$784$	−6.07319	−	4.41243i	−0.216900	−	0.157587i
$785$		0			0
$786$	0.199274	−	0.613302i	0.00710786	−	0.0218758i
$787$	10.5508	−	32.4721i	0.376096	−	1.15750i	−0.566640	−	0.823965i	$-0.691757\pi$
$787$	10.5508	−	32.4721i	0.376096	−	1.15750i	0.942736	−	0.333539i	$-0.108243\pi$
$788$	−1.10740	+	0.804576i	−0.0394496	+	0.0286618i
$789$	−3.90712	−	2.83869i	−0.139097	−	0.101060i
$790$		0			0
$791$	38.7747			1.37867
$792$	−0.282492	−	8.90139i	−0.0100379	−	0.316297i
$793$	18.6803			0.663357
$794$	−14.1435	−	43.5292i	−0.501934	−	1.54479i
$795$		0			0
$796$	2.96373	−	2.15327i	0.105047	−	0.0763208i
$797$	0.940349	−	2.89410i	0.0333089	−	0.102514i	−0.933020	−	0.359825i	$-0.882836\pi$
$797$	0.940349	−	2.89410i	0.0333089	−	0.102514i	0.966329	+	0.257311i	$0.0828364\pi$
$798$	2.28628	−	7.03644i	0.0809333	−	0.249087i
$799$	0.166500	−	0.120969i	0.00589035	−	0.00427959i
$800$		0			0
$801$	0.180247	+	0.554742i	0.00636870	+	0.0196008i
$802$	−9.40439			−0.332081
$803$	−14.6432	+	21.5611i	−0.516747	+	0.760876i
$804$	−1.77886			−0.0627355
$805$		0			0
$806$	−17.3247	−	12.5871i	−0.610237	−	0.443363i
$807$	−4.23058	+	3.07370i	−0.148924	+	0.108199i
$808$	16.2048	−	49.8733i	0.570083	−	1.75454i
$809$	−3.43043	+	10.5578i	−0.120607	+	0.371191i	−0.993075	−	0.117480i	$-0.962518\pi$
$809$	−3.43043	+	10.5578i	−0.120607	+	0.371191i	0.872468	+	0.488672i	$0.162518\pi$
$810$		0			0
$811$	−33.4336	−	24.2909i	−1.17401	−	0.852969i	−0.182528	−	0.983201i	$-0.558428\pi$
$811$	−33.4336	−	24.2909i	−1.17401	−	0.852969i	−0.991484	+	0.130231i	$0.958428\pi$
$812$	−1.28577	−	3.95718i	−0.0451215	−	0.138870i
$813$	−30.3311			−1.06376
$814$	41.4997	+	12.0429i	1.45456	+	0.422102i
$815$		0			0
$816$	−0.728721	−	2.24277i	−0.0255103	−	0.0785128i
$817$	1.09588	+	0.796202i	0.0383399	+	0.0278556i
$818$	7.49195	−	5.44322i	0.261950	−	0.190318i
$819$	1.51820	−	4.67254i	0.0530502	−	0.163272i
$820$		0			0
$821$	−6.61681	+	4.80739i	−0.230928	+	0.167779i	−0.697232	−	0.716845i	$-0.745585\pi$
$821$	−6.61681	+	4.80739i	−0.230928	+	0.167779i	0.466304	+	0.884625i	$0.345585\pi$
$822$	9.40314	+	6.83178i	0.327972	+	0.238286i
$823$	−4.07819	−	12.5514i	−0.142157	−	0.437513i	0.854478	−	0.519488i	$-0.173877\pi$
$823$	−4.07819	−	12.5514i	−0.142157	−	0.437513i	−0.996634	+	0.0819748i	$0.973877\pi$
$824$	34.9246			1.21665
$825$		0			0
$826$	−27.3862			−0.952889
$827$	9.49825	+	29.2326i	0.330287	+	1.01652i	0.968997	+	0.247071i	$0.0794680\pi$
$827$	9.49825	+	29.2326i	0.330287	+	1.01652i	−0.638711	+	0.769447i	$0.720532\pi$
$828$	0.300726	+	0.218490i	0.0104510	+	0.00759306i
$829$	−2.98357	+	2.16769i	−0.103624	+	0.0752871i	−0.638390	−	0.769713i	$-0.720399\pi$
$829$	−2.98357	+	2.16769i	−0.103624	+	0.0752871i	0.534767	+	0.845000i	$0.320399\pi$
$830$		0			0
$831$	4.93483	−	15.1878i	0.171187	−	0.526861i
$832$	−12.3728	+	8.98933i	−0.428948	+	0.311649i
$833$	−0.763391	−	0.554636i	−0.0264499	−	0.0192170i
$834$	−8.05407	−	24.7879i	−0.278889	−	0.858334i
$835$		0			0
$836$	1.24130	−	0.447329i	0.0429312	−	0.0154712i
$837$	−6.77143			−0.234055
$838$	1.78186	+	5.48399i	0.0615533	+	0.189441i
$839$	−35.2341	−	25.5991i	−1.21642	−	0.883778i	−0.220618	−	0.975360i	$-0.570808\pi$
$839$	−35.2341	−	25.5991i	−1.21642	−	0.883778i	−0.995798	+	0.0915823i	$0.970808\pi$
$840$		0			0
$841$	21.6039	−	66.4900i	0.744963	−	2.29276i
$842$	7.93008	−	24.4063i	0.273289	−	0.841096i
$843$	−1.12508	+	0.817415i	−0.0387497	+	0.0281533i
$844$	−0.799143	−	0.580611i	−0.0275076	−	0.0199855i
$845$		0			0
$846$	0.558418			0.0191988
$847$	−6.26295	+	24.4554i	−0.215198	+	0.840296i
$848$	50.2139			1.72435
$849$	1.81533	+	5.58701i	0.0623019	+	0.191746i
$850$		0			0
$851$	14.5492	−	10.5706i	0.498741	−	0.362357i
$852$	0.844811	−	2.60006i	0.0289428	−	0.0890766i
$853$	9.37662	−	28.8583i	0.321049	−	0.988088i	−0.652143	−	0.758096i	$-0.726130\pi$
$853$	9.37662	−	28.8583i	0.321049	−	0.988088i	0.973192	−	0.229992i	$-0.0738701\pi$
$854$	−23.9333	+	17.3886i	−0.818982	+	0.595025i
$855$		0			0
$856$	1.63761	+	5.04004i	0.0559723	+	0.172265i
$857$	−12.5402			−0.428365			−0.214182	−	0.976794i	$-0.568709\pi$
$857$	−12.5402			−0.428365			−0.214182	+	0.976794i	$0.568709\pi$
$858$	9.86757	−	3.55599i	0.336873	−	0.121400i
$859$	−8.67783			−0.296084			−0.148042	−	0.988981i	$-0.547297\pi$
$859$	−8.67783			−0.296084			−0.148042	+	0.988981i	$0.547297\pi$
$860$		0			0
$861$	−3.38438	−	2.45889i	−0.115339	−	0.0837989i
$862$	8.40953	−	6.10988i	0.286430	−	0.208103i
$863$	11.8637	−	36.5128i	0.403846	−	1.24291i	−0.518009	−	0.855375i	$-0.673327\pi$
$863$	11.8637	−	36.5128i	0.403846	−	1.24291i	0.921855	−	0.387535i	$-0.126673\pi$
$864$	0.317703	−	0.977789i	0.0108085	−	0.0332651i
$865$		0			0
$866$	3.28935	+	2.38985i	0.111777	+	0.0812104i
$867$	5.16169	+	15.8860i	0.175300	+	0.539518i
$868$	2.83293			0.0961559
$869$	18.7590	+	24.1685i	0.636354	+	0.819859i
$870$		0			0
$871$	6.45528	+	19.8673i	0.218729	+	0.673178i
$872$	23.0734	+	16.7638i	0.781363	+	0.567693i
$873$	−4.35090	+	3.16111i	−0.147256	+	0.106988i
$874$	2.03136	−	6.25188i	0.0687118	−	0.211473i
$875$		0			0
$876$	−1.15897	+	0.842044i	−0.0391581	+	0.0284500i
$877$	25.3140	+	18.3917i	0.854792	+	0.621043i	0.926463	−	0.376385i	$-0.122833\pi$
$877$	25.3140	+	18.3917i	0.854792	+	0.621043i	−0.0716708	+	0.997428i	$0.522833\pi$
$878$	−1.24945	−	3.84542i	−0.0421669	−	0.129777i
$879$	19.9745			0.673723
$880$		0			0
$881$	49.2703			1.65996			0.829979	−	0.557795i	$-0.188353\pi$
$881$	49.2703			1.65996			0.829979	+	0.557795i	$0.188353\pi$
$882$	−0.791178	−	2.43500i	−0.0266404	−	0.0819906i
$883$	22.8031	+	16.5674i	0.767385	+	0.557537i	0.901166	−	0.433473i	$-0.142712\pi$
$883$	22.8031	+	16.5674i	0.767385	+	0.557537i	−0.133782	+	0.991011i	$0.542712\pi$
$884$	0.171895	−	0.124889i	0.00578145	−	0.00420047i
$885$		0			0
$886$	−5.06905	+	15.6009i	−0.170298	+	0.524123i
$887$	−20.6253	+	14.9852i	−0.692531	+	0.503153i	−0.877491	−	0.479593i	$-0.840784\pi$
$887$	−20.6253	+	14.9852i	−0.692531	+	0.503153i	0.184960	+	0.982746i	$0.440784\pi$
$888$	−19.1596	−	13.9202i	−0.642953	−	0.467133i
$889$	−2.93068	−	9.01972i	−0.0982920	−	0.302512i
$890$		0			0
$891$	1.86337	−	2.74369i	0.0624253	−	0.0919171i
$892$	−2.86342			−0.0958743
$893$	−0.254917	−	0.784553i	−0.00853047	−	0.0262541i
$894$	−13.0988	−	9.51681i	−0.438088	−	0.318290i
$895$		0			0
$896$	8.94256	−	27.5224i	0.298750	−	0.919458i
$897$	1.34892	−	4.15156i	0.0450392	−	0.138616i
$898$	−17.7200	+	12.8743i	−0.591323	+	0.429621i
$899$	54.4831	+	39.5843i	1.81711	+	1.32021i
$900$		0			0
$901$	6.31181			0.210277
$902$	−0.283289	−	8.92648i	−0.00943248	−	0.297219i
$903$	−1.42451			−0.0474048
$904$	−14.0196	−	43.1478i	−0.466284	−	1.43507i
$905$		0			0
$906$	−23.9413	+	17.3943i	−0.795395	+	0.577888i
$907$	−0.766528	+	2.35913i	−0.0254522	+	0.0783337i	−0.962976	−	0.269588i	$-0.913112\pi$
$907$	−0.766528	+	2.35913i	−0.0254522	+	0.0783337i	0.937524	+	0.347922i	$0.113112\pi$
$908$	0.0828891	−	0.255106i	0.00275077	−	0.00846600i
$909$	15.7994	−	11.4789i	0.524031	−	0.380731i
$910$		0			0
$911$	0.839165	+	2.58268i	0.0278028	+	0.0855681i	0.963995	−	0.265920i	$-0.0856757\pi$
$911$	0.839165	+	2.58268i	0.0278028	+	0.0855681i	−0.936192	+	0.351488i	$0.885676\pi$
$912$	−9.45232			−0.312998
$913$	0.994409	+	31.3340i	0.0329101	+	1.03700i
$914$	−43.1101			−1.42595
$915$		0			0
$916$	2.35602	+	1.71175i	0.0778453	+	0.0565579i
$917$	0.810484	−	0.588851i	0.0267645	−	0.0194456i
$918$	0.248539	−	0.764923i	0.00820300	−	0.0252462i
$919$	1.00091	−	3.08047i	0.0330169	−	0.101615i	−0.933190	−	0.359383i	$-0.882987\pi$
$919$	1.00091	−	3.08047i	0.0330169	−	0.101615i	0.966207	+	0.257768i	$0.0829870\pi$
$920$		0			0
$921$	−15.7251	−	11.4249i	−0.518158	−	0.376464i
$922$	−14.2335	−	43.8063i	−0.468757	−	1.44268i
$923$	−32.1047			−1.05674
$924$	−0.779570	+	1.14786i	−0.0256460	+	0.0377620i
$925$		0			0
$926$	−18.7914	−	57.8339i	−0.617523	−	1.90054i
$927$	10.5223	+	7.64487i	0.345596	+	0.251090i
$928$	−8.27219	+	6.01010i	−0.271548	+	0.197291i
$929$	2.21938	−	6.83056i	0.0728156	−	0.224103i	−0.908025	−	0.418916i	$-0.862410\pi$
$929$	2.21938	−	6.83056i	0.0728156	−	0.224103i	0.980840	+	0.194813i	$0.0624100\pi$
$930$		0			0
$931$	−3.05989	+	2.22314i	−0.100284	+	0.0728606i
$932$	−3.78115	−	2.74717i	−0.123856	−	0.0899865i
$933$	−1.86084	−	5.72709i	−0.0609213	−	0.187496i
$934$	−57.2832			−1.87436
$935$		0			0
$936$	−5.74845			−0.187894
$937$	−6.27696	−	19.3185i	−0.205059	−	0.631108i	−0.999711	−	0.0240421i	$-0.992346\pi$
$937$	−6.27696	−	19.3185i	−0.205059	−	0.631108i	0.794652	−	0.607066i	$-0.207654\pi$
$938$	−26.7641	−	19.4452i	−0.873877	−	0.634909i
$939$	4.13273	−	3.00260i	0.134866	−	0.0979862i
$940$		0			0
$941$	−7.85663	+	24.1802i	−0.256119	+	0.788253i	0.737488	+	0.675360i	$0.236012\pi$
$941$	−7.85663	+	24.1802i	−0.256119	+	0.788253i	−0.993607	+	0.112893i	$0.963988\pi$
$942$	−10.9410	+	7.94911i	−0.356478	+	0.258996i
$943$	−3.00702	−	2.18473i	−0.0979222	−	0.0711446i
$944$	10.8120	+	33.2760i	0.351901	+	1.08304i
$945$		0			0
$946$	−1.86471	−	2.40244i	−0.0606270	−	0.0781099i
$947$	4.55536			0.148029			0.0740147	−	0.997257i	$-0.476419\pi$
$947$	4.55536			0.148029			0.0740147	+	0.997257i	$0.476419\pi$
$948$	0.519645	+	1.59930i	0.0168773	+	0.0519430i
$949$	13.6102	+	9.88839i	0.441806	+	0.320991i
$950$		0			0
$951$	4.22699	−	13.0093i	0.137069	−	0.421856i
$952$	1.03679	−	3.19092i	0.0336027	−	0.103418i
$953$	−33.6433	+	24.4433i	−1.08981	+	0.791797i	−0.979368	−	0.202085i	$-0.935228\pi$
$953$	−33.6433	+	24.4433i	−1.08981	+	0.791797i	−0.110447	+	0.993882i	$0.535228\pi$
$954$	13.8552	+	10.0664i	0.448580	+	0.325912i
$955$		0			0
$956$	−0.762378			−0.0246571
$957$	−31.0318	+	11.1830i	−1.00311	+	0.361494i
$958$	24.6519			0.796467
$959$	5.57977	+	17.1728i	0.180180	+	0.554538i
$960$		0			0
$961$	−12.0158	+	8.72996i	−0.387605	+	0.281612i
$962$	8.61903	−	26.5267i	0.277889	−	0.855254i
$963$	−0.609860	+	1.87695i	−0.0196525	+	0.0604840i
$964$	0.485479	−	0.352721i	0.0156362	−	0.0113604i
$965$		0			0
$966$	2.13623	+	6.57465i	0.0687322	+	0.211536i
$967$	16.2161			0.521476			0.260738	−	0.965410i	$-0.416034\pi$
$967$	16.2161			0.521476			0.260738	+	0.965410i	$0.416034\pi$
$968$	29.4780	−	1.87290i	0.947458	−	0.0601972i
$969$	−1.18814			−0.0381686
$970$		0			0
$971$	10.8979	+	7.91778i	0.349730	+	0.254094i	0.748756	−	0.662846i	$-0.230652\pi$
$971$	10.8979	+	7.91778i	0.349730	+	0.254094i	−0.399026	+	0.916940i	$0.630652\pi$
$972$	0.147481	−	0.107152i	0.00473047	−	0.00343689i
$973$	12.5122	−	38.5086i	0.401123	−	1.23453i
$974$	−1.14669	+	3.52916i	−0.0367425	+	0.113082i
$975$		0			0
$976$	30.5770	+	22.2155i	0.978746	+	0.711101i
$977$	4.49311	+	13.8284i	0.143747	+	0.442409i	0.996848	−	0.0793377i	$-0.0252805\pi$
$977$	4.49311	+	13.8284i	0.143747	+	0.442409i	−0.853100	+	0.521747i	$0.825281\pi$
$978$	−16.7404			−0.535300
$979$	−1.81998	+	0.655870i	−0.0581669	+	0.0209617i
$980$		0			0
$981$	3.28213	+	10.1014i	0.104790	+	0.322512i
$982$	9.03356	+	6.56326i	0.288272	+	0.209442i
$983$	−19.8968	+	14.4559i	−0.634611	+	0.461072i	−0.857994	−	0.513659i	$-0.828290\pi$
$983$	−19.8968	+	14.4559i	−0.634611	+	0.461072i	0.223384	+	0.974731i	$0.428290\pi$
$984$	−1.51254	+	4.65513i	−0.0482181	+	0.148400i
$985$		0			0
$986$	−6.47132	+	4.70169i	−0.206089	+	0.149732i
$987$	0.701836	+	0.509914i	0.0223397	+	0.0162307i
$988$	−0.263176	−	0.809973i	−0.00837275	−	0.0257687i
$989$	−1.26568			−0.0402463
$990$		0			0
$991$	4.43775			0.140970			0.0704848	−	0.997513i	$-0.477545\pi$
$991$	4.43775			0.140970			0.0704848	+	0.997513i	$0.477545\pi$
$992$	−2.15130	−	6.62103i	−0.0683040	−	0.210218i
$993$	9.27899	+	6.74158i	0.294460	+	0.213938i
$994$	41.1328	−	29.8847i	1.30465	−	0.947885i
$995$		0			0
$996$	−0.532477	+	1.63879i	−0.0168722	+	0.0519272i
$997$	0.00847083	−	0.00615442i	0.000268274	−	0.000194912i	−0.587651	−	0.809114i	$-0.699947\pi$
$997$	0.00847083	−	0.00615442i	0.000268274	−	0.000194912i	0.587919	+	0.808920i	$0.299947\pi$
$998$	−20.0739	−	14.5845i	−0.635427	−	0.461665i
$999$	−2.72540	−	8.38793i	−0.0862280	−	0.265382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.g.676.2		8
5.2	odd	4		825.2.bx.f.49.1		16
5.3	odd	4		825.2.bx.f.49.4		16
5.4	even	2		165.2.m.d.16.1	✓	8
11.3	even	5		9075.2.a.di.1.3		4
11.8	odd	10		9075.2.a.cm.1.2		4
11.9	even	5	inner	825.2.n.g.526.2		8
15.14	odd	2		495.2.n.a.181.2		8
55.9	even	10		165.2.m.d.31.1	yes	8
55.14	even	10		1815.2.a.p.1.2		4
55.19	odd	10		1815.2.a.w.1.3		4
55.42	odd	20		825.2.bx.f.724.4		16
55.53	odd	20		825.2.bx.f.724.1		16
165.14	odd	10		5445.2.a.bt.1.3		4
165.74	even	10		5445.2.a.bf.1.2		4
165.119	odd	10		495.2.n.a.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.16.1	✓	8	5.4	even	2
165.2.m.d.31.1	yes	8	55.9	even	10
495.2.n.a.181.2		8	15.14	odd	2
495.2.n.a.361.2		8	165.119	odd	10
825.2.n.g.526.2		8	11.9	even	5	inner
825.2.n.g.676.2		8	1.1	even	1	trivial
825.2.bx.f.49.1		16	5.2	odd	4
825.2.bx.f.49.4		16	5.3	odd	4
825.2.bx.f.724.1		16	55.53	odd	20
825.2.bx.f.724.4		16	55.42	odd	20
1815.2.a.p.1.2		4	55.14	even	10
1815.2.a.w.1.3		4	55.19	odd	10
5445.2.a.bf.1.2		4	165.74	even	10
5445.2.a.bt.1.3		4	165.14	odd	10
9075.2.a.cm.1.2		4	11.8	odd	10
9075.2.a.di.1.3		4	11.3	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456498 + 1.40496i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.147481 + 0.107152i) q^{4} +(-0.456498 + 1.40496i) q^{6} +(-1.85666 + 1.34895i) q^{7} +(2.17239 + 1.57833i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.456498 + 1.40496i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.147481 + 0.107152i) q^{4} +(-0.456498 + 1.40496i) q^{6} +(-1.85666 + 1.34895i) q^{7} +(2.17239 + 1.57833i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-3.12020 + 1.12443i) q^{11} -0.182297 q^{12} +(0.661536 + 2.03600i) q^{13} +(-2.74278 - 1.99274i) q^{14} +(-1.33846 + 4.11937i) q^{16} +(-0.168243 + 0.517799i) q^{17} +(-1.19513 + 0.868312i) q^{18} +(1.76552 + 1.28272i) q^{19} -2.29496 q^{21} +(-3.00415 - 3.87045i) q^{22} -2.03908 q^{23} +(0.829779 + 2.55380i) q^{24} +(-2.55850 + 1.85886i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.129282 - 0.397889i) q^{28} +(8.04603 - 5.84578i) q^{29} +(2.09249 + 6.44002i) q^{31} -1.02811 q^{32} +(-3.18522 - 0.924324i) q^{33} -0.804288 q^{34} +(-0.147481 - 0.107152i) q^{36} +(-7.13520 + 5.18403i) q^{37} +(-0.996215 + 3.06604i) q^{38} +(-0.661536 + 2.03600i) q^{39} +(1.47470 + 1.07143i) q^{41} +(-1.04765 - 3.22433i) q^{42} +0.620713 q^{43} +(0.339687 - 0.500167i) q^{44} +(-0.930836 - 2.86482i) q^{46} +(-0.305816 - 0.222188i) q^{47} +(-3.50415 + 2.54591i) q^{48} +(-0.535571 + 1.64832i) q^{49} +(-0.440466 + 0.320017i) q^{51} +(-0.315724 - 0.229387i) q^{52} +(-3.58246 - 11.0257i) q^{53} -1.47726 q^{54} -6.16248 q^{56} +(0.674367 + 2.07549i) q^{57} +(11.8861 + 8.63574i) q^{58} +(6.53518 - 4.74808i) q^{59} +(2.69647 - 8.29887i) q^{61} +(-8.09273 + 5.87971i) q^{62} +(-1.85666 - 1.34895i) q^{63} +(2.20760 + 6.79429i) q^{64} +(-0.155412 - 4.89705i) q^{66} +9.75802 q^{67} +(-0.0306702 - 0.0943932i) q^{68} +(-1.64965 - 1.19854i) q^{69} +(-4.63426 + 14.2628i) q^{71} +(-0.829779 + 2.55380i) q^{72} +(6.35761 - 4.61907i) q^{73} +(-10.5405 - 7.65815i) q^{74} -0.397826 q^{76} +(4.27637 - 6.29667i) q^{77} -3.16248 q^{78} +(-2.85054 - 8.77306i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.832118 + 2.56099i) q^{82} +(2.92093 - 8.98969i) q^{83} +(0.338464 - 0.245909i) q^{84} +(0.283354 + 0.872075i) q^{86} +9.94544 q^{87} +(-8.55302 - 2.48201i) q^{88} +0.583290 q^{89} +(-3.97470 - 2.88779i) q^{91} +(0.300726 - 0.218490i) q^{92} +(-2.09249 + 6.44002i) q^{93} +(0.172561 - 0.531087i) q^{94} +(-0.831757 - 0.604307i) q^{96} +(1.66190 + 5.11479i) q^{97} -2.56031 q^{98} +(-2.03359 - 2.62002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9	\( 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{16} + q^{18} + 2 q^{19} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 2 q^{26} + 2 q^{27} + 11 q^{28} + 10 q^{29} + 19 q^{31} - 12 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + q^{37} + 20 q^{38} - 4 q^{39} - 9 q^{41} - q^{42} + 17 q^{44} - 22 q^{46} + 19 q^{47} - 13 q^{48} + q^{49} + 10 q^{51} + 2 q^{52} - 25 q^{53} - 6 q^{54} - 16 q^{56} - 7 q^{57} + 12 q^{58} + 13 q^{59} + 13 q^{61} - 35 q^{62} - 3 q^{63} + 39 q^{64} - 11 q^{66} - 2 q^{67} - 19 q^{68} + 9 q^{69} - 11 q^{71} - 4 q^{72} + 7 q^{73} - 43 q^{74} - 38 q^{76} + 7 q^{77} + 8 q^{78} - 22 q^{79} - 2 q^{81} + 35 q^{82} + 21 q^{83} + 4 q^{84} + 20 q^{86} + 30 q^{87} - 59 q^{88} - 20 q^{89} - 11 q^{91} + 28 q^{92} - 19 q^{93} - 35 q^{94} - 8 q^{96} - 31 q^{97} - 22 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9 + 3 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^16 + q^18 + 2 * q^19 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 2 * q^26 + 2 * q^27 + 11 * q^28 + 10 * q^29 + 19 * q^31 - 12 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + q^37 + 20 * q^38 - 4 * q^39 - 9 * q^41 - q^42 + 17 * q^44 - 22 * q^46 + 19 * q^47 - 13 * q^48 + q^49 + 10 * q^51 + 2 * q^52 - 25 * q^53 - 6 * q^54 - 16 * q^56 - 7 * q^57 + 12 * q^58 + 13 * q^59 + 13 * q^61 - 35 * q^62 - 3 * q^63 + 39 * q^64 - 11 * q^66 - 2 * q^67 - 19 * q^68 + 9 * q^69 - 11 * q^71 - 4 * q^72 + 7 * q^73 - 43 * q^74 - 38 * q^76 + 7 * q^77 + 8 * q^78 - 22 * q^79 - 2 * q^81 + 35 * q^82 + 21 * q^83 + 4 * q^84 + 20 * q^86 + 30 * q^87 - 59 * q^88 - 20 * q^89 - 11 * q^91 + 28 * q^92 - 19 * q^93 - 35 * q^94 - 8 * q^96 - 31 * q^97 - 22 * q^98 - 7 * q^99

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