LMFDB - Embedded newform 675.2.l.c.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			601.1
Root			$0.500000 + 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	675.601
Dual form			675.2.l.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.753189 + 0.274138i) q^{2} +(1.68842 - 0.386327i) q^{3} +(-1.03995 + 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(-1.82076 - 1.52780i) q^{7} +(1.34559 - 2.33062i) q^{8} +(2.70150 - 1.30456i) q^{9} +O(q^{10})$	\(q+(-0.753189 + 0.274138i) q^{2} +(1.68842 - 0.386327i) q^{3} +(-1.03995 + 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(-1.82076 - 1.52780i) q^{7} +(1.34559 - 2.33062i) q^{8} +(2.70150 - 1.30456i) q^{9} +(-0.0434396 + 0.246358i) q^{11} +(-1.41875 + 1.87510i) q^{12} +(2.45446 + 0.893351i) q^{13} +(1.79020 + 0.651581i) q^{14} +(0.0969067 - 0.549585i) q^{16} +(-0.146688 - 0.254072i) q^{17} +(-1.67711 + 1.72317i) q^{18} +(1.39237 - 2.41166i) q^{19} +(-3.66443 - 1.87615i) q^{21} +(-0.0348180 - 0.197463i) q^{22} +(5.12472 - 4.30015i) q^{23} +(1.37153 - 4.45490i) q^{24} -2.09357 q^{26} +(4.05728 - 3.24631i) q^{27} +3.22668 q^{28} +(0.333645 - 0.121437i) q^{29} +(2.11847 - 1.77761i) q^{31} +(1.01231 + 5.74108i) q^{32} +(0.0218307 + 0.432738i) q^{33} +(0.180135 + 0.151151i) q^{34} +(-1.67103 + 3.71406i) q^{36} +(-3.49619 - 6.05558i) q^{37} +(-0.387591 + 2.19814i) q^{38} +(4.48928 + 0.560124i) q^{39} +(9.13156 + 3.32362i) q^{41} +(3.27434 + 0.408537i) q^{42} +(-0.0452712 + 0.256746i) q^{43} +(-0.169802 - 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(8.75249 + 7.34421i) q^{47} +(-0.0487006 - 0.965367i) q^{48} +(-0.234540 - 1.33014i) q^{49} +(-0.345826 - 0.372309i) q^{51} +(-3.33207 + 1.21277i) q^{52} -5.43137 q^{53} +(-2.16596 + 3.55734i) q^{54} +(-6.01071 + 2.18772i) q^{56} +(1.41922 - 4.60980i) q^{57} +(-0.218007 + 0.182930i) q^{58} +(1.03788 + 5.88612i) q^{59} +(-9.07515 - 7.61495i) q^{61} +(-1.10830 + 1.91963i) q^{62} +(-6.91190 - 1.75206i) q^{63} +(-1.77824 - 3.08001i) q^{64} +(-0.135073 - 0.319949i) q^{66} +(1.70113 + 0.619160i) q^{67} +(0.374256 + 0.136218i) q^{68} +(6.99139 - 9.24026i) q^{69} +(0.185255 + 0.320871i) q^{71} +(0.594663 - 8.05158i) q^{72} +(2.51339 - 4.35333i) q^{73} +(4.29336 + 3.60255i) q^{74} +(0.656467 + 3.72301i) q^{76} +(0.455479 - 0.382193i) q^{77} +(-3.53483 + 0.808804i) q^{78} +(-0.754406 + 0.274581i) q^{79} +(5.59624 - 7.04855i) q^{81} -7.78892 q^{82} +(-2.58947 + 0.942488i) q^{83} +(5.44798 - 1.24655i) q^{84} +(-0.0362861 - 0.205789i) q^{86} +(0.516417 - 0.333932i) q^{87} +(0.515717 + 0.432738i) q^{88} +(-5.22533 + 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-1.57704 + 8.94385i) q^{92} +(2.89012 - 3.81976i) q^{93} +(-8.60560 - 3.13218i) q^{94} +(3.92713 + 9.30225i) q^{96} +(2.57600 - 14.6092i) q^{97} +(0.541296 + 0.937552i) q^{98} +(0.204037 + 0.722208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	−0.753189	+	0.274138i	−0.532585	+	0.193845i	−0.594292	−	0.804249i	$-0.702568\pi$
$2$	−0.753189	+	0.274138i	−0.532585	+	0.193845i	0.0617072	+	0.998094i	$0.480346\pi$
$3$	1.68842	−	0.386327i	0.974808	−	0.223046i
$3$	1.68842	−	0.386327i	0.974808	−	0.223046i
$4$	−1.03995	+	0.872619i	−0.519974	+	0.436310i
$5$		0			0
$5$		0			0
$6$	−1.16579	+	0.753837i	−0.475932	+	0.307753i
$7$	−1.82076	−	1.52780i	−0.688183	−	0.577454i	0.230202	−	0.973143i	$-0.426061\pi$
$7$	−1.82076	−	1.52780i	−0.688183	−	0.577454i	−0.918385	+	0.395689i	$0.870506\pi$
$8$	1.34559	−	2.33062i	0.475736	−	0.823999i
$9$	2.70150	−	1.30456i	0.900501	−	0.434854i
$10$		0			0
$11$	−0.0434396	+	0.246358i	−0.0130975	+	0.0742798i	−0.990656	−	0.136385i	$-0.956452\pi$
$11$	−0.0434396	+	0.246358i	−0.0130975	+	0.0742798i	0.977558	+	0.210665i	$0.0675628\pi$
$12$	−1.41875	+	1.87510i	−0.409557	+	0.541296i
$13$	2.45446	+	0.893351i	0.680745	+	0.247771i	0.659167	−	0.751996i	$-0.270909\pi$
$13$	2.45446	+	0.893351i	0.680745	+	0.247771i	0.0215777	+	0.999767i	$0.493131\pi$
$14$	1.79020	+	0.651581i	0.478452	+	0.174142i
$15$		0			0
$16$	0.0969067	−	0.549585i	0.0242267	−	0.137396i
$17$	−0.146688	−	0.254072i	−0.0355772	−	0.0616215i	0.847689	−	0.530494i	$-0.177994\pi$
$17$	−0.146688	−	0.254072i	−0.0355772	−	0.0616215i	−0.883266	+	0.468873i	$0.844660\pi$
$18$	−1.67711	+	1.72317i	−0.395299	+	0.406154i
$19$	1.39237	−	2.41166i	0.319432	−	0.553273i	−0.660937	−	0.750441i	$-0.729841\pi$
$19$	1.39237	−	2.41166i	0.319432	−	0.553273i	0.980370	+	0.197168i	$0.0631745\pi$
$20$		0			0
$21$	−3.66443	−	1.87615i	−0.799645	−	0.409410i
$22$	−0.0348180	−	0.197463i	−0.00742323	−	0.0420992i
$23$	5.12472	−	4.30015i	1.06858	−	0.896643i	0.0736543	−	0.997284i	$-0.476534\pi$
$23$	5.12472	−	4.30015i	1.06858	−	0.896643i	0.994923	+	0.100641i	$0.0320894\pi$
$24$	1.37153	−	4.45490i	0.279962	−	0.909352i
$25$		0			0
$26$	−2.09357			−0.410584
$27$	4.05728	−	3.24631i	0.780823	−	0.624752i
$28$	3.22668			0.609786
$29$	0.333645	−	0.121437i	0.0619562	−	0.0225502i	−0.310856	−	0.950457i	$-0.600616\pi$
$29$	0.333645	−	0.121437i	0.0619562	−	0.0225502i	0.372812	+	0.927907i	$0.378394\pi$
$30$		0			0
$31$	2.11847	−	1.77761i	0.380488	−	0.319268i	−0.432406	−	0.901679i	$-0.642335\pi$
$31$	2.11847	−	1.77761i	0.380488	−	0.319268i	0.812894	+	0.582411i	$0.197891\pi$
$32$	1.01231	+	5.74108i	0.178952	+	1.01489i
$33$	0.0218307	+	0.432738i	0.00380023	+	0.0753299i
$34$	0.180135	+	0.151151i	0.0308929	+	0.0259222i
$35$		0			0
$36$	−1.67103	+	3.71406i	−0.278506	+	0.619010i
$37$	−3.49619	−	6.05558i	−0.574770	−	0.995531i	−0.996067	−	0.0886080i	$-0.971758\pi$
$37$	−3.49619	−	6.05558i	−0.574770	−	0.995531i	0.421297	−	0.906923i	$-0.361575\pi$
$38$	−0.387591	+	2.19814i	−0.0628756	+	0.356585i
$39$	4.48928	+	0.560124i	0.718860	+	0.0896917i
$40$		0			0
$41$	9.13156	+	3.32362i	1.42611	+	0.519062i	0.935814	−	0.352494i	$-0.114666\pi$
$41$	9.13156	+	3.32362i	1.42611	+	0.519062i	0.490296	+	0.871556i	$0.336888\pi$
$42$	3.27434	+	0.408537i	0.505241	+	0.0630386i
$43$	−0.0452712	+	0.256746i	−0.00690379	+	0.0391534i	−0.988065	−	0.154037i	$-0.950772\pi$
$43$	−0.0452712	+	0.256746i	−0.00690379	+	0.0391534i	0.981161	+	0.193191i	$0.0618836\pi$
$44$	−0.169802	−	0.294106i	−0.0255986	−	0.0443381i
$45$		0			0
$46$	−2.68104	+	4.64370i	−0.395298	+	0.684677i
$47$	8.75249	+	7.34421i	1.27668	+	1.07126i	0.993692	+	0.112140i	$0.0357704\pi$
$47$	8.75249	+	7.34421i	1.27668	+	1.07126i	0.282989	+	0.959123i	$0.408674\pi$
$48$	−0.0487006	−	0.965367i	−0.00702933	−	0.139339i
$49$	−0.234540	−	1.33014i	−0.0335057	−	0.190020i
$50$		0			0
$51$	−0.345826	−	0.372309i	−0.0484253	−	0.0521337i
$52$	−3.33207	+	1.21277i	−0.462074	+	0.168181i
$53$	−5.43137			−0.746056			−0.373028	−	0.927820i	$-0.621680\pi$
$53$	−5.43137			−0.746056			−0.373028	+	0.927820i	$0.621680\pi$
$54$	−2.16596	+	3.55734i	−0.294750	+	0.484092i
$55$		0			0
$56$	−6.01071	+	2.18772i	−0.803215	+	0.292346i
$57$	1.41922	−	4.60980i	0.187980	−	0.610583i
$58$	−0.218007	+	0.182930i	−0.0286257	+	0.0240198i
$59$	1.03788	+	5.88612i	0.135121	+	0.766308i	0.974776	+	0.223188i	$0.0716462\pi$
$59$	1.03788	+	5.88612i	0.135121	+	0.766308i	−0.839655	+	0.543121i	$0.817243\pi$
$60$		0			0
$61$	−9.07515	−	7.61495i	−1.16195	−	0.974995i	−0.162023	−	0.986787i	$-0.551802\pi$
$61$	−9.07515	−	7.61495i	−1.16195	−	0.974995i	−0.999930	+	0.0117924i	$0.996246\pi$
$62$	−1.10830	+	1.91963i	−0.140754	+	0.243793i
$63$	−6.91190	−	1.75206i	−0.870817	−	0.220739i
$64$	−1.77824	−	3.08001i	−0.222281	−	0.385001i
$65$		0			0
$66$	−0.135073	−	0.319949i	−0.0166263	−	0.0393829i
$67$	1.70113	+	0.619160i	0.207826	+	0.0756424i	0.443835	−	0.896108i	$-0.353617\pi$
$67$	1.70113	+	0.619160i	0.207826	+	0.0756424i	−0.236010	+	0.971751i	$0.575840\pi$
$68$	0.374256	+	0.136218i	0.0453852	+	0.0165189i
$69$	6.99139	−	9.24026i	0.841665	−	1.11240i
$70$		0			0
$71$	0.185255	+	0.320871i	0.0219857	+	0.0380804i	0.876809	−	0.480839i	$-0.159668\pi$
$71$	0.185255	+	0.320871i	0.0219857	+	0.0380804i	−0.854823	+	0.518919i	$0.826334\pi$
$72$	0.594663	−	8.05158i	0.0700817	−	0.948888i
$73$	2.51339	−	4.35333i	0.294171	−	0.509518i	−0.680621	−	0.732636i	$-0.738290\pi$
$73$	2.51339	−	4.35333i	0.294171	−	0.509518i	0.974792	+	0.223117i	$0.0716233\pi$
$74$	4.29336	+	3.60255i	0.499093	+	0.418789i
$75$		0			0
$76$	0.656467	+	3.72301i	0.0753019	+	0.427059i
$77$	0.455479	−	0.382193i	0.0519067	−	0.0435549i
$78$	−3.53483	+	0.808804i	−0.400240	+	0.0915790i
$79$	−0.754406	+	0.274581i	−0.0848773	+	0.0308928i	−0.384110	−	0.923287i	$-0.625492\pi$
$79$	−0.754406	+	0.274581i	−0.0848773	+	0.0308928i	0.299233	+	0.954180i	$0.403269\pi$
$80$		0			0
$81$	5.59624	−	7.04855i	0.621804	−	0.783173i
$82$	−7.78892			−0.860143
$83$	−2.58947	+	0.942488i	−0.284231	+	0.103452i	−0.480201	−	0.877158i	$-0.659436\pi$
$83$	−2.58947	+	0.942488i	−0.284231	+	0.103452i	0.195971	+	0.980610i	$0.437214\pi$
$84$	5.44798	−	1.24655i	0.594424	−	0.136010i
$85$		0			0
$86$	−0.0362861	−	0.205789i	−0.00391283	−	0.0221908i
$87$	0.516417	−	0.333932i	0.0553657	−	0.0358012i
$88$	0.515717	+	0.432738i	0.0549756	+	0.0461300i
$89$	−5.22533	+	9.05054i	−0.553884	+	0.959356i	0.444105	+	0.895975i	$0.353522\pi$
$89$	−5.22533	+	9.05054i	−0.553884	+	0.959356i	−0.997989	+	0.0633809i	$0.979812\pi$
$90$		0			0
$91$	−3.10412	−	5.37650i	−0.325401	−	0.563611i
$92$	−1.57704	+	8.94385i	−0.164418	+	0.932461i
$93$	2.89012	−	3.81976i	0.299692	−	0.396091i
$94$	−8.60560	−	3.13218i	−0.887600	−	0.323060i
$95$		0			0
$96$	3.92713	+	9.30225i	0.400811	+	0.949407i
$97$	2.57600	−	14.6092i	0.261553	−	1.48334i	−0.517120	−	0.855913i	$-0.672996\pi$
$97$	2.57600	−	14.6092i	0.261553	−	1.48334i	0.778673	−	0.627430i	$-0.215893\pi$
$98$	0.541296	+	0.937552i	0.0546791	+	0.0947070i
$99$	0.204037	+	0.722208i	0.0205065	+	0.0725846i
$100$		0			0
$101$	3.06826	+	2.57457i	0.305303	+	0.256180i	0.782548	−	0.622591i	$-0.213920\pi$
$101$	3.06826	+	2.57457i	0.305303	+	0.256180i	−0.477244	+	0.878771i	$0.658364\pi$
$102$	0.362537	+	0.185615i	0.0358965	+	0.0183786i
$103$	1.02789	+	5.82943i	0.101281	+	0.574391i	0.992641	+	0.121095i	$0.0386407\pi$
$103$	1.02789	+	5.82943i	0.101281	+	0.574391i	−0.891360	+	0.453296i	$0.850248\pi$
$104$	5.38475	−	4.51834i	0.528018	−	0.443060i
$105$		0			0
$106$	4.09085	−	1.48895i	0.397338	−	0.144619i
$107$	0.258978			0.0250364			0.0125182	−	0.999922i	$-0.496015\pi$
$107$	0.258978			0.0250364			0.0125182	+	0.999922i	$0.496015\pi$
$108$	−1.38656	+	6.91645i	−0.133422	+	0.665535i
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$		0			0
$111$	−8.24246	−	8.87367i	−0.782340	−	0.842251i
$112$	−1.01610	+	0.852609i	−0.0960124	+	0.0805640i
$113$	0.541640	+	3.07179i	0.0509532	+	0.288970i	0.999628	−	0.0272843i	$-0.00868592\pi$
$113$	0.541640	+	3.07179i	0.0509532	+	0.288970i	−0.948675	+	0.316254i	$0.897575\pi$
$114$	0.194784	+	3.86111i	0.0182432	+	0.361626i
$115$		0			0
$116$	−0.241005	+	0.417432i	−0.0223767	+	0.0387576i
$117$	7.79617	−	0.788606i	0.720756	−	0.0729066i
$118$	−2.39533	−	4.14884i	−0.220508	−	0.381932i
$119$	−0.121086	+	0.686714i	−0.0111000	+	0.0629510i
$120$		0			0
$121$	10.2778	+	3.74082i	0.934347	+	0.340074i
$122$	8.92285	+	3.24765i	0.807837	+	0.294029i
$123$	16.7019	+	2.08388i	1.50596	+	0.187897i
$124$	−0.651922	+	3.69724i	−0.0585444	+	0.332022i
$125$		0			0
$126$	5.68627	−	0.575183i	0.506573	−	0.0512414i
$127$	−9.22726	+	15.9821i	−0.818787	+	1.41818i	0.0877893	+	0.996139i	$0.472020\pi$
$127$	−9.22726	+	15.9821i	−0.818787	+	1.41818i	−0.906576	+	0.422042i	$0.861314\pi$
$128$	−6.74783	−	5.66210i	−0.596430	−	0.500464i
$129$	0.0227511	+	0.450983i	0.00200312	+	0.0397069i
$130$		0			0
$131$	10.8973	−	9.14396i	0.952105	−	0.798911i	−0.0275454	−	0.999621i	$-0.508769\pi$
$131$	10.8973	−	9.14396i	0.952105	−	0.798911i	0.979651	+	0.200709i	$0.0643246\pi$
$132$	−0.400318	−	0.430974i	−0.0348432	−	0.0375115i
$133$	−6.21971	+	2.26379i	−0.539317	+	0.196295i
$134$	−1.45101			−0.125348
$135$		0			0
$136$	−0.789527			−0.0677014
$137$	−18.4984	+	6.73287i	−1.58042	+	0.575228i	−0.975296	−	0.220900i	$-0.929100\pi$
$137$	−18.4984	+	6.73287i	−1.58042	+	0.575228i	−0.605128	+	0.796128i	$0.706878\pi$
$138$	−2.73273	+	8.87627i	−0.232626	+	0.755598i
$139$	−13.7206	+	11.5129i	−1.16377	+	0.976515i	−0.999950	−	0.00997617i	$-0.996824\pi$
$139$	−13.7206	+	11.5129i	−1.16377	+	0.976515i	−0.163815	+	0.986491i	$0.552380\pi$
$140$		0			0
$141$	17.6151	+	9.01876i	1.48346	+	0.759517i
$142$	−0.227495	−	0.190891i	−0.0190910	−	0.0160192i
$143$	−0.326705	+	0.565870i	−0.0273205	+	0.0473205i
$144$	−0.455174	−	1.61113i	−0.0379312	−	0.134261i
$145$		0			0
$146$	−0.699647	+	3.96789i	−0.0579032	+	0.328385i
$147$	−0.909870	−	2.15522i	−0.0750449	−	0.177760i
$148$	8.92007	+	3.24664i	0.733225	+	0.266872i
$149$	−15.3071	−	5.57132i	−1.25401	−	0.456421i	−0.372252	−	0.928132i	$-0.621414\pi$
$149$	−15.3071	−	5.57132i	−1.25401	−	0.456421i	−0.881753	+	0.471711i	$0.843637\pi$
$150$		0			0
$151$	2.47880	−	14.0580i	0.201722	−	1.14402i	−0.700793	−	0.713365i	$-0.747170\pi$
$151$	2.47880	−	14.0580i	0.201722	−	1.14402i	0.902515	−	0.430659i	$-0.141719\pi$
$152$	−3.74711	−	6.49019i	−0.303931	−	0.526424i
$153$	−0.727731	−	0.495012i	−0.0588336	−	0.0400193i
$154$	−0.238288	+	0.412728i	−0.0192018	+	0.0332585i
$155$		0			0
$156$	−5.15739	+	3.33493i	−0.412922	+	0.267008i
$157$	−0.132555	−	0.751757i	−0.0105790	−	0.0599968i	0.979061	−	0.203566i	$-0.0652531\pi$
$157$	−0.132555	−	0.751757i	−0.0105790	−	0.0599968i	−0.989640	+	0.143569i	$0.954142\pi$
$158$	0.492937	−	0.413623i	0.0392159	−	0.0329061i
$159$	−9.17041	+	2.09828i	−0.727261	+	0.166405i
$160$		0			0
$161$	−15.9006			−1.25315
$162$	−2.28275	+	6.84304i	−0.179349	+	0.537640i
$163$	−5.12834			−0.401682			−0.200841	−	0.979624i	$-0.564368\pi$
$163$	−5.12834			−0.401682			−0.200841	+	0.979624i	$0.564368\pi$
$164$	−12.3966	+	4.51199i	−0.968011	+	0.352327i
$165$		0			0
$166$	1.69198	−	1.41974i	0.131323	−	0.110193i
$167$	−1.54566	−	8.76590i	−0.119607	−	0.678325i	−0.984366	−	0.176137i	$-0.943640\pi$
$167$	−1.54566	−	8.76590i	−0.119607	−	0.678325i	0.864759	−	0.502188i	$-0.167471\pi$
$168$	−9.30341	+	6.01588i	−0.717774	+	0.464135i
$169$	−4.73227	−	3.97085i	−0.364021	−	0.305450i
$170$		0			0
$171$	0.615340	−	8.33154i	0.0470562	−	0.637129i
$172$	−0.176962	−	0.306507i	−0.0134932	−	0.0233709i
$173$	1.18276	−	6.70776i	0.0899235	−	0.509982i	−0.906262	−	0.422717i	$-0.861076\pi$
$173$	1.18276	−	6.70776i	0.0899235	−	0.509982i	0.996185	−	0.0872644i	$-0.0278125\pi$
$174$	−0.297416	+	0.393083i	−0.0225470	+	0.0297996i
$175$		0			0
$176$	0.131185	+	0.0477476i	0.00988847	+	0.00359911i
$177$	4.02635	+	9.53727i	0.302639	+	0.716865i
$178$	1.45456	−	8.24923i	0.109024	−	0.618306i
$179$	9.17382	+	15.8895i	0.685684	+	1.18764i	0.973221	+	0.229870i	$0.0738301\pi$
$179$	9.17382	+	15.8895i	0.685684	+	1.18764i	−0.287538	+	0.957769i	$0.592837\pi$
$180$		0			0
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	−0.996029	−	0.0890276i	$-0.971624\pi$
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	0.575115	+	0.818073i	$0.304957\pi$
$182$	3.81190	+	3.19856i	0.282557	+	0.237093i
$183$	−18.2645	−	9.35124i	−1.35015	−	0.691264i
$184$	−3.12628	−	17.7300i	−0.230472	−	1.30707i
$185$		0			0
$186$	−1.12966	+	3.66930i	−0.0828310	+	0.269046i
$187$	0.0689648	−	0.0251011i	0.00504321	−	0.00183558i
$188$	−15.5108			−1.13124
$189$	−12.3470	−	0.287957i	−0.898115	−	0.0209458i
$190$		0			0
$191$	−6.44480	+	2.34571i	−0.466329	+	0.169730i	−0.564489	−	0.825441i	$-0.690927\pi$
$191$	−6.44480	+	2.34571i	−0.466329	+	0.169730i	0.0981596	+	0.995171i	$0.468704\pi$
$192$	−4.19231	−	4.51336i	−0.302554	−	0.325724i
$193$	−15.6371	+	13.1211i	−1.12558	+	0.944477i	−0.998873	−	0.0474627i	$-0.984886\pi$
$193$	−15.6371	+	13.1211i	−1.12558	+	0.944477i	−0.126711	+	0.991940i	$0.540442\pi$
$194$	2.06474	+	11.7097i	0.148239	+	0.840707i
$195$		0			0
$196$	1.40462	+	1.17861i	0.100330	+	0.0841866i
$197$	1.51786	−	2.62902i	0.108143	−	0.187310i	−0.806875	−	0.590723i	$-0.798843\pi$
$197$	1.51786	−	2.62902i	0.108143	−	0.187310i	0.915018	+	0.403413i	$0.132176\pi$
$198$	−0.351663	−	0.488024i	−0.0249916	−	0.0346824i
$199$	1.13124	+	1.95936i	0.0801912	+	0.138895i	0.903332	−	0.428942i	$-0.141114\pi$
$199$	1.13124	+	1.95936i	0.0801912	+	0.138895i	−0.823141	+	0.567837i	$0.807780\pi$
$200$		0			0
$201$	3.11141	+	0.388209i	0.219462	+	0.0273821i
$202$	−3.01677	−	1.09801i	−0.212259	−	0.0772560i
$203$	−0.793018	−	0.288635i	−0.0556589	−	0.0202582i
$204$	0.684525	+	0.0854077i	0.0479263	+	0.00597974i
$205$		0			0
$206$	−2.37226	−	4.10888i	−0.165283	−	0.286279i
$207$	8.23463	−	18.3024i	0.572346	−	1.27210i
$208$	0.728826	−	1.26236i	0.0505350	−	0.0875292i
$209$	0.533649	+	0.447784i	0.0369132	+	0.0309739i
$210$		0			0
$211$	4.41601	+	25.0445i	0.304011	+	1.72413i	0.628124	+	0.778113i	$0.283823\pi$
$211$	4.41601	+	25.0445i	0.304011	+	1.72413i	−0.324113	+	0.946018i	$0.605066\pi$
$212$	5.64834	−	4.73952i	0.387929	−	0.325511i
$213$	0.436749	+	0.470195i	0.0299255	+	0.0322172i
$214$	−0.195060	+	0.0709959i	−0.0133340	+	0.00485318i
$215$		0			0
$216$	−2.10650	−	13.8242i	−0.143329	−	0.940615i
$217$	−6.57305			−0.446208
$218$	6.44569	−	2.34604i	0.436557	−	0.158894i
$219$	2.56185	−	8.32122i	0.173114	−	0.562296i
$220$		0			0
$221$	−0.133066	−	0.754654i	−0.00895097	−	0.0507635i
$222$	8.64074	+	4.42398i	0.579929	+	0.296918i
$223$	2.93497	+	2.46274i	0.196540	+	0.164917i	0.735747	−	0.677257i	$-0.236831\pi$
$223$	2.93497	+	2.46274i	0.196540	+	0.164917i	−0.539206	+	0.842174i	$0.681276\pi$
$224$	6.92805	−	11.9997i	0.462900	−	0.801766i
$225$		0			0
$226$	−1.25005	−	2.16515i	−0.0831523	−	0.144024i
$227$	−0.436897	+	2.47777i	−0.0289979	+	0.164455i	−0.995868	−	0.0908142i	$-0.971053\pi$
$227$	−0.436897	+	2.47777i	−0.0289979	+	0.164455i	0.966870	+	0.255269i	$0.0821642\pi$
$228$	2.54669	+	6.03238i	0.168659	+	0.399504i
$229$	14.9783	+	5.45167i	0.989797	+	0.360257i	0.785642	−	0.618682i	$-0.212333\pi$
$229$	14.9783	+	5.45167i	0.989797	+	0.360257i	0.204155	+	0.978939i	$0.434555\pi$
$230$		0			0
$231$	0.621388	−	0.821264i	0.0408843	−	0.0540352i
$232$	0.165924	−	0.941003i	0.0108935	−	0.0617799i
$233$	14.0641	+	24.3598i	0.921372	+	1.59586i	0.797295	+	0.603590i	$0.206264\pi$
$233$	14.0641	+	24.3598i	0.921372	+	1.59586i	0.124077	+	0.992273i	$0.460403\pi$
$234$	−5.65580	+	2.73120i	−0.369731	+	0.178544i
$235$		0			0
$236$	−6.21569	−	5.21558i	−0.404607	−	0.339505i
$237$	−1.16767	+	0.755055i	−0.0758485	+	0.0490461i
$238$	−0.0970539	−	0.550420i	−0.00629107	−	0.0356784i
$239$	−11.2653	+	9.45270i	−0.728691	+	0.611444i	−0.929774	−	0.368130i	$-0.879998\pi$
$239$	−11.2653	+	9.45270i	−0.728691	+	0.611444i	0.201083	+	0.979574i	$0.435554\pi$
$240$		0			0
$241$	−7.93378	+	2.88766i	−0.511059	+	0.186010i	−0.584662	−	0.811277i	$-0.698773\pi$
$241$	−7.93378	+	2.88766i	−0.511059	+	0.186010i	0.0736022	+	0.997288i	$0.476550\pi$
$242$	−8.76664			−0.563541
$243$	6.72574	−	14.0629i	0.431456	−	0.902134i
$244$	16.0826			1.02958
$245$		0			0
$246$	−13.1509	+	3.00907i	−0.838474	+	0.191851i
$247$	5.57198	−	4.67545i	0.354537	−	0.297492i
$248$	−1.29235	−	7.32927i	−0.0820642	−	0.465409i
$249$	−4.00799	+	2.59169i	−0.253996	+	0.164242i
$250$		0			0
$251$	11.6102	−	20.1095i	0.732832	−	1.26930i	−0.222835	−	0.974856i	$-0.571531\pi$
$251$	11.6102	−	20.1095i	0.732832	−	1.26930i	0.955668	−	0.294447i	$-0.0951354\pi$
$252$	8.71689	−	4.20940i	0.549112	−	0.265168i
$253$	0.836762	+	1.44931i	0.0526067	+	0.0911176i
$254$	2.56857	−	14.5671i	0.161166	−	0.914020i
$255$		0			0
$256$	13.3186	+	4.84758i	0.832413	+	0.302973i
$257$	6.45118	+	2.34804i	0.402413	+	0.146466i	0.535294	−	0.844666i	$-0.320201\pi$
$257$	6.45118	+	2.34804i	0.402413	+	0.146466i	−0.132881	+	0.991132i	$0.542423\pi$
$258$	−0.140768	−	0.333439i	−0.00876382	−	0.0207590i
$259$	−2.88598	+	16.3672i	−0.179326	+	1.01701i
$260$		0			0
$261$	0.742920	−	0.763321i	0.0459856	−	0.0472484i
$262$	−5.70105	+	9.87451i	−0.352212	+	0.610049i
$263$	−2.56850	−	2.15523i	−0.158381	−	0.132897i	0.560154	−	0.828389i	$-0.310742\pi$
$263$	−2.56850	−	2.15523i	−0.158381	−	0.132897i	−0.718534	+	0.695492i	$0.755187\pi$
$264$	1.03792	+	0.531406i	0.0638797	+	0.0327058i
$265$		0			0
$266$	4.06402	−	3.41012i	0.249181	−	0.209088i
$267$	−5.32607	+	17.2998i	−0.325950	+	1.05873i
$268$	−2.30937	+	0.840543i	−0.141067	+	0.0513444i
$269$	12.7416			0.776869			0.388434	−	0.921476i	$-0.373016\pi$
$269$	12.7416			0.776869			0.388434	+	0.921476i	$0.373016\pi$
$270$		0			0
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	−0.153849	+	0.0559965i	−0.00932848	+	0.00339529i
$273$	−7.31814	−	7.87857i	−0.442914	−	0.476833i
$274$	12.0871	−	10.1422i	0.730206	−	0.612715i
$275$		0			0
$276$	0.792545	+	15.7102i	0.0477056	+	0.945643i
$277$	−3.20300	−	2.68763i	−0.192450	−	0.161484i	0.541472	−	0.840719i	$-0.317867\pi$
$277$	−3.20300	−	2.68763i	−0.192450	−	0.161484i	−0.733921	+	0.679235i	$0.762312\pi$
$278$	7.17806	−	12.4328i	0.430511	−	0.745667i
$279$	3.40406	−	7.56589i	0.203795	−	0.452958i
$280$		0			0
$281$	−3.75705	+	21.3073i	−0.224127	+	1.27109i	0.640220	+	0.768192i	$0.278843\pi$
$281$	−3.75705	+	21.3073i	−0.224127	+	1.27109i	−0.864347	+	0.502896i	$0.832268\pi$
$282$	−15.7399	−	1.96386i	−0.937297	−	0.116946i
$283$	4.91209	+	1.78785i	0.291993	+	0.106277i	0.483864	−	0.875143i	$-0.339233\pi$
$283$	4.91209	+	1.78785i	0.291993	+	0.106277i	−0.191870	+	0.981420i	$0.561455\pi$
$284$	−0.472654	−	0.172032i	−0.0280468	−	0.0102082i
$285$		0			0
$286$	0.0909441	−	0.515770i	0.00537764	−	0.0304981i
$287$	−11.5486	−	20.0027i	−0.681690	−	1.18072i
$288$	10.2243	+	14.1889i	0.602475	+	0.836090i
$289$	8.45697	−	14.6479i	0.497469	−	0.861641i
$290$		0			0
$291$	−1.29457	−	25.6617i	−0.0758893	−	1.50431i
$292$	1.18500	+	6.72047i	0.0693468	+	0.393285i
$293$	4.70517	−	3.94811i	0.274879	−	0.230651i	−0.494918	−	0.868940i	$-0.664802\pi$
$293$	4.70517	−	3.94811i	0.274879	−	0.230651i	0.769797	+	0.638289i	$0.220357\pi$
$294$	1.27613	+	1.37386i	0.0744257	+	0.0801252i
$295$		0			0
$296$	−18.8177			−1.09376
$297$	0.623508	+	1.14056i	0.0361796	+	0.0661821i
$298$	13.0564			0.756339
$299$	16.4200	−	5.97638i	0.949591	−	0.345623i
$300$		0			0
$301$	0.474684	−	0.398307i	0.0273603	−	0.0229580i
$302$	1.98683	+	11.2679i	0.114329	+	0.648393i
$303$	6.17513	+	3.16160i	0.354752	+	0.181629i
$304$	−1.19048	−	0.998934i	−0.0682789	−	0.0572928i
$305$		0			0
$306$	0.683821	+	0.173338i	0.0390914	+	0.00990909i
$307$	9.50194	+	16.4578i	0.542304	+	0.939298i	0.998771	+	0.0495580i	$0.0157813\pi$
$307$	9.50194	+	16.4578i	0.542304	+	0.939298i	−0.456467	+	0.889740i	$0.650885\pi$
$308$	−0.140166	+	0.794920i	−0.00798669	+	0.0452948i
$309$	3.98757	+	9.44541i	0.226845	+	0.537331i
$310$		0			0
$311$	20.2475	+	7.36948i	1.14813	+	0.417885i	0.844843	−	0.535015i	$-0.179694\pi$
$311$	20.2475	+	7.36948i	1.14813	+	0.417885i	0.303286	+	0.952900i	$0.401916\pi$
$312$	7.34615	−	9.70912i	0.415894	−	0.549671i
$313$	0.662228	−	3.75568i	0.0374313	−	0.212284i	−0.960355	−	0.278778i	$-0.910070\pi$
$313$	0.662228	−	3.75568i	0.0374313	−	0.212284i	0.997787	+	0.0664949i	$0.0211816\pi$
$314$	0.305925	+	0.529877i	0.0172643	+	0.0299027i
$315$		0			0
$316$	0.544937	−	0.943859i	0.0306551	−	0.0530962i
$317$	−3.25913	−	2.73473i	−0.183051	−	0.153598i	0.546658	−	0.837356i	$-0.315900\pi$
$317$	−3.25913	−	2.73473i	−0.183051	−	0.153598i	−0.729709	+	0.683758i	$0.760344\pi$
$318$	6.33183	−	4.09437i	0.355072	−	0.229601i
$319$	0.0154235	+	0.0874713i	0.000863553	+	0.00489745i
$320$		0			0
$321$	0.437264	−	0.100050i	0.0244057	−	0.00558426i
$322$	11.9762	−	4.35898i	0.667407	−	0.242916i
$323$	−0.816980			−0.0454580
$324$	0.330912	+	12.2135i	0.0183840	+	0.678528i
$325$		0			0
$326$	3.86261	−	1.40587i	0.213930	−	0.0778642i
$327$	−14.4493	+	3.30614i	−0.799046	+	0.182830i
$328$	20.0334	−	16.8100i	1.10616	−	0.928178i
$329$	−4.71570	−	26.7441i	−0.259985	−	1.47445i
$330$		0			0
$331$	−10.9497	−	9.18787i	−0.601849	−	0.505011i	0.290191	−	0.956969i	$-0.406281\pi$
$331$	−10.9497	−	9.18787i	−0.601849	−	0.505011i	−0.892039	+	0.451958i	$0.850726\pi$
$332$	1.87047	−	3.23976i	0.102656	−	0.177805i
$333$	−17.3448	−	11.7982i	−0.950491	−	0.646536i
$334$	3.56725	+	6.17865i	0.195191	+	0.338081i
$335$		0			0
$336$	−1.38621	+	1.83211i	−0.0756242	+	0.0999496i
$337$	33.5644	+	12.2164i	1.82837	+	0.665472i	0.993333	+	0.115278i	$0.0367759\pi$
$337$	33.5644	+	12.2164i	1.82837	+	0.665472i	0.835037	+	0.550194i	$0.185446\pi$
$338$	4.65286	+	1.69350i	0.253082	+	0.0921143i
$339$	2.10123	+	4.97721i	0.114123	+	0.270325i
$340$		0			0
$341$	0.345903	+	0.599121i	0.0187317	+	0.0324442i
$342$	1.82053	+	6.44391i	0.0984429	+	0.348447i
$343$	−9.92407	+	17.1890i	−0.535849	+	0.928118i
$344$	0.537461	+	0.450983i	0.0289780	+	0.0243154i
$345$		0			0
$346$	0.948013	+	5.37645i	0.0509655	+	0.289040i
$347$	14.8931	−	12.4968i	0.799502	−	0.670862i	−0.148575	−	0.988901i	$-0.547469\pi$
$347$	14.8931	−	12.4968i	0.799502	−	0.670862i	0.948078	+	0.318039i	$0.103024\pi$
$348$	−0.245651	+	0.797906i	−0.0131683	+	0.0427723i
$349$	7.53700	−	2.74324i	0.403446	−	0.146842i	−0.132323	−	0.991207i	$-0.542244\pi$
$349$	7.53700	−	2.74324i	0.403446	−	0.146842i	0.535770	+	0.844364i	$0.320022\pi$
$350$		0			0
$351$	12.8585	−	4.34336i	0.686337	−	0.231832i
$352$	−1.45834			−0.0777296
$353$	8.22589	−	2.99398i	0.437820	−	0.159354i	−0.113700	−	0.993515i	$-0.536270\pi$
$353$	8.22589	−	2.99398i	0.437820	−	0.159354i	0.551520	+	0.834162i	$0.314048\pi$
$354$	−5.64713	−	6.07959i	−0.300142	−	0.323127i
$355$		0			0
$356$	−2.46361	−	13.9718i	−0.130571	−	0.740505i
$357$	0.0608521	+	1.20624i	0.00322063	+	0.0638409i
$358$	−11.2656	−	9.45292i	−0.595403	−	0.499602i
$359$	4.13896	−	7.16888i	0.218446	−	0.378359i	−0.735887	−	0.677104i	$-0.763235\pi$
$359$	4.13896	−	7.16888i	0.218446	−	0.378359i	0.954333	+	0.298745i	$0.0965680\pi$
$360$		0			0
$361$	5.62260	+	9.73862i	0.295926	+	0.512559i
$362$	1.57635	−	8.93990i	0.0828509	−	0.469871i
$363$	18.7984	+	2.34547i	0.986661	+	0.123105i
$364$	7.91977	+	2.88256i	0.415108	+	0.151087i
$365$		0			0
$366$	16.3201	+	2.03625i	0.853068	+	0.106437i
$367$	2.56997	−	14.5750i	0.134151	−	0.760809i	−0.841296	−	0.540575i	$-0.818207\pi$
$367$	2.56997	−	14.5750i	0.134151	−	0.760809i	0.975447	−	0.220234i	$-0.0706822\pi$
$368$	−1.86668	−	3.23318i	−0.0973074	−	0.168541i
$369$	29.0048	−	2.93392i	1.50993	−	0.152734i
$370$		0			0
$371$	9.88922	+	8.29804i	0.513423	+	0.430813i
$372$	0.327625	+	6.49433i	0.0169865	+	0.336715i
$373$	−4.43383	−	25.1455i	−0.229575	−	1.30198i	−0.853743	−	0.520694i	$-0.825673\pi$
$373$	−4.43383	−	25.1455i	−0.229575	−	1.30198i	0.624168	−	0.781290i	$-0.285438\pi$
$374$	−0.0450623	+	0.0378118i	−0.00233012	+	0.00195520i
$375$		0			0
$376$	28.8938	−	10.5165i	1.49008	−	0.542346i
$377$	0.927403			0.0477637
$378$	9.37859	−	3.16791i	0.482383	−	0.162940i
$379$	20.1244			1.03372			0.516861	−	0.856070i	$-0.327101\pi$
$379$	20.1244			1.03372			0.516861	+	0.856070i	$0.327101\pi$
$380$		0			0
$381$	−9.40516	+	30.5492i	−0.481841	+	1.56508i
$382$	4.21110	−	3.53353i	0.215459	−	0.180791i
$383$	4.14346	+	23.4987i	0.211721	+	1.20073i	0.886507	+	0.462716i	$0.153125\pi$
$383$	4.14346	+	23.4987i	0.211721	+	1.20073i	−0.674785	+	0.738014i	$0.735764\pi$
$384$	−13.5806	−	6.95312i	−0.693031	−	0.354825i
$385$		0			0
$386$	8.18070	−	14.1694i	0.416387	−	0.721203i
$387$	0.212640	+	0.752659i	0.0108091	+	0.0382598i
$388$	10.0694	+	17.4407i	0.511196	+	0.885418i
$389$	6.59400	−	37.3964i	0.334329	−	1.89607i	−0.0994307	−	0.995044i	$-0.531702\pi$
$389$	6.59400	−	37.3964i	0.334329	−	1.89607i	0.433760	−	0.901029i	$-0.357187\pi$
$390$		0			0
$391$	−1.84428	−	0.671264i	−0.0932694	−	0.0339473i
$392$	−3.41565	−	1.24320i	−0.172516	−	0.0627908i
$393$	14.8667	−	19.6487i	0.749926	−	0.991148i
$394$	−0.422524	+	2.39625i	−0.0212864	+	0.120721i
$395$		0			0
$396$	−0.842400	−	0.573011i	−0.0423322	−	0.0287949i
$397$	10.1747	−	17.6230i	0.510651	−	0.884474i	−0.489272	−	0.872131i	$-0.662738\pi$
$397$	10.1747	−	17.6230i	0.510651	−	0.884474i	0.999924	−	0.0123433i	$-0.00392909\pi$
$398$	−1.38917	−	1.16565i	−0.0696328	−	0.0584289i
$399$	−9.62690	+	6.22506i	−0.481948	+	0.311643i
$400$		0			0
$401$	5.32015	−	4.46414i	0.265676	−	0.222928i	−0.500212	−	0.865903i	$-0.666744\pi$
$401$	5.32015	−	4.46414i	0.265676	−	0.222928i	0.765887	+	0.642975i	$0.222300\pi$
$402$	−2.44990	+	0.560563i	−0.122190	+	0.0279583i
$403$	6.78773	−	2.47053i	0.338121	−	0.123066i
$404$	−5.43745			−0.270523
$405$		0			0
$406$	0.676418			0.0335701
$407$	1.64372	−	0.598264i	0.0814760	−	0.0296548i
$408$	−1.33305	+	0.305015i	−0.0659958	+	0.0151005i
$409$	−8.35444	+	7.01021i	−0.413101	+	0.346633i	−0.825531	−	0.564356i	$-0.809124\pi$
$409$	−8.35444	+	7.01021i	−0.413101	+	0.346633i	0.412431	+	0.910989i	$0.364680\pi$
$410$		0			0
$411$	−28.6319	+	18.5143i	−1.41231	+	0.913244i
$412$	−6.15582	−	5.16535i	−0.303276	−	0.254478i
$413$	7.10308	−	12.3029i	0.349520	−	0.605386i
$414$	−1.18485	+	16.0426i	−0.0582322	+	0.788449i
$415$		0			0
$416$	−2.64413	+	14.9956i	−0.129639	+	0.735220i
$417$	−18.7183	+	24.7393i	−0.916640	+	1.21149i
$418$	−0.524693	−	0.190973i	−0.0256636	−	0.00934078i
$419$	9.46194	+	3.44386i	0.462246	+	0.168244i	0.562637	−	0.826704i	$-0.309787\pi$
$419$	9.46194	+	3.44386i	0.462246	+	0.168244i	−0.100391	+	0.994948i	$0.532009\pi$
$420$		0			0
$421$	−0.539623	+	3.06035i	−0.0262996	+	0.149152i	−0.995130	−	0.0985733i	$-0.968572\pi$
$421$	−0.539623	+	3.06035i	−0.0262996	+	0.149152i	0.968830	+	0.247726i	$0.0796832\pi$
$422$	−10.1917	−	17.6526i	−0.496126	−	0.859315i
$423$	33.2258	+	8.42224i	1.61550	+	0.409504i
$424$	−7.30837	+	12.6585i	−0.354926	+	0.614750i
$425$		0			0
$426$	−0.457853	−	0.234416i	−0.0221830	−	0.0113575i
$427$	4.88955	+	27.7300i	0.236622	+	1.34195i
$428$	−0.269324	+	0.225990i	−0.0130183	+	0.0109236i
$429$	−0.333004	+	1.08164i	−0.0160776	+	0.0522221i
$430$		0			0
$431$	−28.0701			−1.35209			−0.676044	−	0.736862i	$-0.736307\pi$
$431$	−28.0701			−1.35209			−0.676044	+	0.736862i	$0.736307\pi$
$432$	−1.39095	−	2.54441i	−0.0669219	−	0.122418i
$433$	−19.5251			−0.938317			−0.469158	−	0.883114i	$-0.655443\pi$
$433$	−19.5251			−0.938317			−0.469158	+	0.883114i	$0.655443\pi$
$434$	4.95075	−	1.80193i	0.237644	−	0.0864952i
$435$		0			0
$436$	8.89973	−	7.46776i	0.426220	−	0.357641i
$437$	−3.23498	−	18.3465i	−0.154750	−	0.877631i
$438$	0.351609	+	6.96975i	0.0168005	+	0.333028i
$439$	11.2069	+	9.40371i	0.534876	+	0.448815i	0.869781	−	0.493437i	$-0.164260\pi$
$439$	11.2069	+	9.40371i	0.534876	+	0.448815i	−0.334905	+	0.942252i	$0.608704\pi$
$440$		0			0
$441$	−2.36886	−	3.28741i	−0.112803	−	0.156543i
$442$	0.307103	+	0.531918i	0.0146074	+	0.0253008i
$443$	−3.18748	+	18.0771i	−0.151442	+	0.858868i	0.810526	+	0.585703i	$0.199182\pi$
$443$	−3.18748	+	18.0771i	−0.151442	+	0.858868i	−0.961967	+	0.273165i	$0.911930\pi$
$444$	16.3151	+	2.03562i	0.774278	+	0.0966062i
$445$		0			0
$446$	−2.88572	−	1.05032i	−0.136643	−	0.0497339i
$447$	−27.9971	−	3.49318i	−1.32422	−	0.165222i
$448$	−1.46788	+	8.32476i	−0.0693508	+	0.393308i
$449$	−6.92969	−	12.0026i	−0.327032	−	0.566437i	0.654889	−	0.755725i	$-0.272715\pi$
$449$	−6.92969	−	12.0026i	−0.327032	−	0.566437i	−0.981922	+	0.189288i	$0.939382\pi$
$450$		0			0
$451$	−1.21547	+	2.10526i	−0.0572344	+	0.0991328i
$452$	−3.24378	−	2.72185i	−0.152575	−	0.128025i
$453$	−1.24573	−	24.6934i	−0.0585294	−	1.16020i
$454$	−0.350185	−	1.98600i	−0.0164350	−	0.0932075i
$455$		0			0
$456$	−8.83402	−	9.51053i	−0.413691	−	0.445372i
$457$	16.5838	−	6.03602i	0.775758	−	0.282353i	0.0763555	−	0.997081i	$-0.475672\pi$
$457$	16.5838	−	6.03602i	0.775758	−	0.282353i	0.699403	+	0.714728i	$0.253449\pi$
$458$	−12.7760			−0.596985
$459$	−1.41995	−	0.554644i	−0.0662776	−	0.0258886i
$460$		0			0
$461$	−24.0919	+	8.76872i	−1.12207	+	0.408400i	−0.835407	−	0.549631i	$-0.814768\pi$
$461$	−24.0919	+	8.76872i	−1.12207	+	0.408400i	−0.286663	+	0.958032i	$0.592546\pi$
$462$	−0.242882	+	0.788913i	−0.0112999	+	0.0367036i
$463$	−14.0549	+	11.7935i	−0.653189	+	0.548090i	−0.908037	−	0.418891i	$-0.862419\pi$
$463$	−14.0549	+	11.7935i	−0.653189	+	0.548090i	0.254848	+	0.966981i	$0.417975\pi$
$464$	−0.0344074	−	0.195134i	−0.00159732	−	0.00905888i
$465$		0			0
$466$	−17.2709	−	14.4920i	−0.800059	−	0.671329i
$467$	−8.13092	+	14.0832i	−0.376254	+	0.651692i	−0.990514	−	0.137412i	$-0.956121\pi$
$467$	−8.13092	+	14.0832i	−0.376254	+	0.651692i	0.614260	+	0.789104i	$0.289455\pi$
$468$	−7.41945	+	7.62319i	−0.342964	+	0.352382i
$469$	−2.15139	−	3.72632i	−0.0993421	−	0.172066i
$470$		0			0
$471$	−0.514232	−	1.21807i	−0.0236946	−	0.0561257i
$472$	15.1149	+	5.50137i	0.695719	+	0.253221i
$473$	−0.0612849	−	0.0223059i	−0.00281788	−	0.00102563i
$474$	0.672489	−	0.888803i	0.0308884	−	0.0408241i
$475$		0			0
$476$	−0.473317	−	0.819809i	−0.0216944	−	0.0375759i
$477$	−14.6729	+	7.08555i	−0.671824	+	0.324425i
$478$	5.89354	−	10.2079i	0.269564	−	0.466899i
$479$	−7.25575	−	6.08830i	−0.331524	−	0.278181i	0.461797	−	0.886986i	$-0.347205\pi$
$479$	−7.25575	−	6.08830i	−0.331524	−	0.278181i	−0.793320	+	0.608804i	$0.791649\pi$
$480$		0			0
$481$	−3.17151	−	17.9865i	−0.144608	−	0.820114i
$482$	5.18401	−	4.34990i	0.236125	−	0.198133i
$483$	−26.8469	+	6.14284i	−1.22158	+	0.279509i
$484$	−13.9527	+	5.07836i	−0.634213	+	0.230835i
$485$		0			0
$486$	−1.21058	+	12.4358i	−0.0549129	+	0.564099i
$487$	0.467564			0.0211874			0.0105937	−	0.999944i	$-0.496628\pi$
$487$	0.467564			0.0211874			0.0105937	+	0.999944i	$0.496628\pi$
$488$	−29.9590	+	10.9042i	−1.35618	+	0.493608i
$489$	−8.65877	+	1.98121i	−0.391563	+	0.0895936i
$490$		0			0
$491$	4.34936	+	24.6665i	0.196284	+	1.11318i	0.910578	+	0.413337i	$0.135637\pi$
$491$	4.34936	+	24.6665i	0.196284	+	1.11318i	−0.714294	+	0.699846i	$0.753252\pi$
$492$	−19.1875	+	12.4073i	−0.865040	+	0.559363i
$493$	−0.0797954	−	0.0669563i	−0.00359380	−	0.00301556i
$494$	−2.91504	+	5.04899i	−0.131154	+	0.227165i
$495$		0			0
$496$	−0.771653	−	1.33654i	−0.0346482	−	0.0600125i
$497$	0.152922	−	0.867261i	0.00685947	−	0.0389020i
$498$	2.30829	−	3.05078i	0.103437	−	0.136709i
$499$	13.1878	+	4.79996i	0.590367	+	0.214876i	0.619891	−	0.784688i	$-0.287177\pi$
$499$	13.1878	+	4.79996i	0.590367	+	0.214876i	−0.0295240	+	0.999564i	$0.509399\pi$
$500$		0			0
$501$	−5.99623	−	14.2034i	−0.267892	−	0.634559i
$502$	−3.23191	+	18.3291i	−0.144247	+	0.818068i
$503$	14.1558	+	24.5186i	0.631176	+	1.09323i	0.987312	+	0.158794i	$0.0507607\pi$
$503$	14.1558	+	24.5186i	0.631176	+	1.09323i	−0.356136	+	0.934434i	$0.615906\pi$
$504$	−13.3839	+	13.7515i	−0.596168	+	0.612539i
$505$		0			0
$506$	−1.02755	−	0.862218i	−0.0456803	−	0.0383303i
$507$	−9.52410	−	4.87624i	−0.422980	−	0.216562i
$508$	−4.35041	−	24.6724i	−0.193018	−	1.09466i
$509$	−21.9759	+	18.4399i	−0.974063	+	0.817336i	−0.983183	−	0.182622i	$-0.941541\pi$
$509$	−21.9759	+	18.4399i	−0.974063	+	0.817336i	0.00912008	+	0.999958i	$0.497097\pi$
$510$		0			0
$511$	−11.2273	+	4.08640i	−0.496666	+	0.180772i
$512$	6.25700			0.276523
$513$	−2.17975	−	14.3048i	−0.0962382	−	0.631574i
$514$	−5.50264			−0.242711
$515$		0			0
$516$	−0.417197	−	0.449146i	−0.0183661	−	0.0197725i
$517$	−2.18951	+	1.83722i	−0.0962946	+	0.0808008i
$518$	−2.31319	−	13.1188i	−0.101636	−	0.576406i
$519$	−0.594397	−	11.7824i	−0.0260911	−	0.517191i
$520$		0			0
$521$	12.4548	−	21.5724i	0.545655	−	0.945102i	−0.452910	−	0.891556i	$-0.649614\pi$
$521$	12.4548	−	21.5724i	0.545655	−	0.945102i	0.998565	−	0.0535462i	$-0.0170525\pi$
$522$	−0.350304	+	0.778588i	−0.0153324	+	0.0340779i
$523$	−12.9324	−	22.3995i	−0.565494	−	0.979464i	−0.997004	−	0.0773554i	$-0.975352\pi$
$523$	−12.9324	−	22.3995i	−0.565494	−	0.979464i	0.431510	−	0.902108i	$-0.357981\pi$
$524$	−3.35347	+	19.0185i	−0.146497	+	0.830826i
$525$		0			0
$526$	2.52540	+	0.919169i	0.110113	+	0.0400777i
$527$	−0.762395	−	0.277489i	−0.0332104	−	0.0120876i
$528$	0.239942	+	0.0299374i	0.0104421	+	0.00130286i
$529$	3.77754	−	21.4235i	0.164241	−	0.931456i
$530$		0			0
$531$	10.4827	+	14.5474i	0.454908	+	0.631303i
$532$	4.49274	−	7.78166i	0.194785	−	0.337378i
$533$	19.4439	+	16.3154i	0.842209	+	0.706698i
$534$	−0.730992	−	14.4901i	−0.0316331	−	0.627047i
$535$		0			0
$536$	3.73204	−	3.13155i	0.161200	−	0.135262i
$537$	21.6278	+	23.2841i	0.933308	+	1.00478i
$538$	−9.59683	+	3.49296i	−0.413749	+	0.150592i
$539$	0.337880			0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	17.7426	−	6.45777i	0.762109	−	0.277385i
$543$	−5.77200	+	18.7482i	−0.247700	+	0.804562i
$544$	1.31015	−	1.09935i	0.0561723	−	0.0471342i
$545$		0			0
$546$	7.67176	+	3.92787i	0.328321	+	0.168097i
$547$	7.64210	+	6.41248i	0.326752	+	0.274178i	0.791375	−	0.611331i	$-0.209366\pi$
$547$	7.64210	+	6.41248i	0.326752	+	0.274178i	−0.464623	+	0.885509i	$0.653810\pi$
$548$	13.3621	−	23.1439i	0.570802	−	0.988658i
$549$	−34.4507	−	8.73273i	−1.47032	−	0.372704i
$550$		0			0
$551$	0.171694	−	0.973722i	0.00731439	−	0.0414820i
$552$	−12.1280	−	28.7278i	−0.516203	−	1.22274i
$553$	1.79310	+	0.652634i	0.0762502	+	0.0277528i
$554$	3.14925	+	1.14623i	0.133799	+	0.0486987i
$555$		0			0
$556$	4.22227	−	23.9457i	0.179064	−	1.01552i
$557$	−9.26650	−	16.0500i	−0.392634	−	0.680062i	0.600162	−	0.799879i	$-0.295103\pi$
$557$	−9.26650	−	16.0500i	−0.392634	−	0.680062i	−0.992796	+	0.119816i	$0.961769\pi$
$558$	−0.489797	+	6.63172i	−0.0207348	+	0.280743i
$559$	−0.340480	+	0.589729i	−0.0144008	+	0.0249429i
$560$		0			0
$561$	0.106744	−	0.0690241i	0.00450674	−	0.00291420i
$562$	−3.01138	−	17.0784i	−0.127027	−	0.720408i
$563$	−33.4632	+	28.0789i	−1.41031	+	1.18339i	−0.454005	+	0.890999i	$0.650005\pi$
$563$	−33.4632	+	28.0789i	−1.41031	+	1.18339i	−0.956300	+	0.292388i	$0.905550\pi$
$564$	−26.1887	+	5.99225i	−1.10274	+	0.252319i
$565$		0			0
$566$	−4.18985			−0.176113
$567$	−20.9582	+	4.28380i	−0.880161	+	0.179903i
$568$	0.997105			0.0418376
$569$	−12.7485	+	4.64008i	−0.534446	+	0.194522i	−0.595122	−	0.803635i	$-0.702896\pi$
$569$	−12.7485	+	4.64008i	−0.534446	+	0.194522i	0.0606766	+	0.998157i	$0.480674\pi$
$570$		0			0
$571$	18.1926	−	15.2654i	0.761335	−	0.638836i	−0.177139	−	0.984186i	$-0.556684\pi$
$571$	18.1926	−	15.2654i	0.761335	−	0.638836i	0.938474	+	0.345350i	$0.112240\pi$
$572$	−0.154033	−	0.873565i	−0.00644044	−	0.0365256i
$573$	−9.97529	+	6.45034i	−0.416724	+	0.269467i
$574$	14.1818	+	11.8999i	0.591935	+	0.496693i
$575$		0			0
$576$	−8.82200	−	6.00083i	−0.367583	−	0.250034i
$577$	−4.05951	−	7.03128i	−0.169000	−	0.292716i	0.769069	−	0.639166i	$-0.220720\pi$
$577$	−4.05951	−	7.03128i	−0.169000	−	0.292716i	−0.938068	+	0.346450i	$0.887387\pi$
$578$	−2.35414	+	13.3510i	−0.0979194	+	0.555329i
$579$	−21.3329	+	28.1949i	−0.886566	+	1.17174i
$580$		0			0
$581$	6.15473	+	2.24014i	0.255341	+	0.0929366i
$582$	8.00990	+	18.9732i	0.332021	+	0.786464i
$583$	0.235937	−	1.33806i	0.00977150	−	0.0554169i
$584$	−6.76397	−	11.7155i	−0.279895	−	0.484793i
$585$		0			0
$586$	−2.46156	+	4.26354i	−0.101686	+	0.176125i
$587$	2.82823	+	2.37317i	0.116734	+	0.0979511i	0.699286	−	0.714842i	$-0.253501\pi$
$587$	2.82823	+	2.37317i	0.116734	+	0.0979511i	−0.582552	+	0.812793i	$0.697946\pi$
$588$	2.82691	+	1.44735i	0.116580	+	0.0596877i
$589$	−1.33729	−	7.58412i	−0.0551019	−	0.312498i
$590$		0			0
$591$	1.54713	−	5.02527i	0.0636403	−	0.206712i
$592$	−3.66686	+	1.33463i	−0.150707	+	0.0548529i
$593$	−29.4590			−1.20974			−0.604869	−	0.796325i	$-0.706774\pi$
$593$	−29.4590			−1.20974			−0.604869	+	0.796325i	$0.706774\pi$
$594$	−0.782291	−	0.688131i	−0.0320978	−	0.0282344i
$595$		0			0
$596$	20.7802	−	7.56338i	0.851190	−	0.309808i
$597$	2.66695	+	2.87119i	0.109151	+	0.117510i
$598$	−10.7290	+	9.00268i	−0.438740	+	0.368147i
$599$	−3.79862	−	21.5431i	−0.155207	−	0.880225i	−0.958596	−	0.284770i	$-0.908083\pi$
$599$	−3.79862	−	21.5431i	−0.155207	−	0.880225i	0.803388	−	0.595455i	$-0.203028\pi$
$600$		0			0
$601$	27.9764	+	23.4750i	1.14118	+	0.957566i	0.999477	−	0.0323424i	$-0.0102967\pi$
$601$	27.9764	+	23.4750i	1.14118	+	0.957566i	0.141706	+	0.989909i	$0.454741\pi$
$602$	−0.248335	+	0.430130i	−0.0101214	+	0.0175308i
$603$	5.40333	−	0.546563i	0.220041	−	0.0222578i
$604$	9.68946	+	16.7826i	0.394258	+	0.682876i
$605$		0			0
$606$	−5.51775	−	0.688447i	−0.224143	−	0.0279662i
$607$	−6.18395	−	2.25077i	−0.250999	−	0.0913561i	0.213457	−	0.976953i	$-0.431528\pi$
$607$	−6.18395	−	2.25077i	−0.250999	−	0.0913561i	−0.464456	+	0.885596i	$0.653750\pi$
$608$	15.2550	+	5.55238i	0.618674	+	0.225179i
$609$	−1.45045	−	0.180972i	−0.0587753	−	0.00733335i
$610$		0			0
$611$	14.9217	+	25.8451i	0.603667	+	1.04558i
$612$	1.18876	−	0.120247i	0.0480527	−	0.00486068i
$613$	−3.57434	+	6.19093i	−0.144366	+	0.250049i	−0.929136	−	0.369737i	$-0.879448\pi$
$613$	−3.57434	+	6.19093i	−0.144366	+	0.250049i	0.784770	+	0.619787i	$0.212781\pi$
$614$	−11.6685	−	9.79101i	−0.470901	−	0.395133i
$615$		0			0
$616$	−0.277860	−	1.57582i	−0.0111953	−	0.0634917i
$617$	−12.6684	+	10.6301i	−0.510012	+	0.427951i	−0.861133	−	0.508379i	$-0.830245\pi$
$617$	−12.6684	+	10.6301i	−0.510012	+	0.427951i	0.351121	+	0.936330i	$0.385800\pi$
$618$	−5.59274	−	6.02103i	−0.224973	−	0.242202i
$619$	1.40893	−	0.512808i	0.0566296	−	0.0206115i	−0.313550	−	0.949572i	$-0.601518\pi$
$619$	1.40893	−	0.512808i	0.0566296	−	0.0206115i	0.370180	+	0.928960i	$0.379296\pi$
$620$		0			0
$621$	6.83279	−	34.0833i	0.274190	−	1.36772i
$622$	−17.2704			−0.692481
$623$	23.3415	−	8.49561i	0.935157	−	0.340369i
$624$	0.742878	−	2.41296i	0.0297389	−	0.0965958i
$625$		0			0
$626$	0.530793	+	3.01028i	0.0212148	+	0.120315i
$627$	1.07401	+	0.549884i	0.0428919	+	0.0219602i
$628$	0.793848	+	0.666118i	0.0316780	+	0.0265810i
$629$	−1.02570	+	1.77657i	−0.0408974	+	0.0708363i
$630$		0			0
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	0.963189	+	0.268826i	$0.0866356\pi$
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	−0.248785	+	0.968559i	$0.580031\pi$
$632$	−0.375172	+	2.12771i	−0.0149235	+	0.0846356i
$633$	17.1314	+	40.5795i	0.680913	+	1.61289i
$634$	3.20443	+	1.16632i	0.127264	+	0.0463204i
$635$		0			0
$636$	7.70574	−	10.1844i	0.305553	−	0.403837i
$637$	0.612614	−	3.47431i	0.0242727	−	0.137657i
$638$	−0.0355961	−	0.0616542i	−0.00140926	−	0.00244091i
$639$	0.919063	+	0.625157i	0.0363576	+	0.0247308i
$640$		0			0
$641$	30.0504	+	25.2152i	1.18692	+	0.995942i	0.999908	+	0.0135840i	$0.00432406\pi$
$641$	30.0504	+	25.2152i	1.18692	+	0.995942i	0.187010	+	0.982358i	$0.440120\pi$
$642$	−0.301914	+	0.195227i	−0.0119156	+	0.00770501i
$643$	1.80915	+	10.2602i	0.0713461	+	0.404624i	0.999476	+	0.0323674i	$0.0103047\pi$
$643$	1.80915	+	10.2602i	0.0713461	+	0.404624i	−0.928130	+	0.372256i	$0.878584\pi$
$644$	16.5358	−	13.8752i	0.651603	−	0.546760i
$645$		0			0
$646$	0.615340	−	0.223965i	0.0242102	−	0.00881180i
$647$	39.1517			1.53921			0.769606	−	0.638519i	$-0.220453\pi$
$647$	39.1517			1.53921			0.769606	+	0.638519i	$0.220453\pi$
$648$	−8.89730	−	22.5271i	−0.349519	−	0.884950i
$649$	−1.49518			−0.0586910
$650$		0			0
$651$	−11.0981	+	2.53935i	−0.434967	+	0.0995248i
$652$	5.33320	−	4.47509i	0.208864	−	0.175258i
$653$	−5.71474	−	32.4099i	−0.223635	−	1.26830i	−0.865277	−	0.501294i	$-0.832858\pi$
$653$	−5.71474	−	32.4099i	−0.223635	−	1.26830i	0.641642	−	0.767004i	$-0.278253\pi$
$654$	9.97668	−	6.45124i	0.390119	−	0.252263i
$655$		0			0
$656$	2.71152	−	4.69649i	0.105867	−	0.183367i
$657$	1.11076	−	15.0394i	0.0433349	−	0.586743i
$658$	10.8834	+	18.8506i	0.424279	+	0.734873i
$659$	−3.74532	+	21.2407i	−0.145897	+	0.827422i	0.820746	+	0.571293i	$0.193558\pi$
$659$	−3.74532	+	21.2407i	−0.145897	+	0.827422i	−0.966643	+	0.256128i	$0.917553\pi$
$660$		0			0
$661$	−24.7105	−	8.99389i	−0.961127	−	0.349822i	−0.186652	−	0.982426i	$-0.559764\pi$
$661$	−24.7105	−	8.99389i	−0.961127	−	0.349822i	−0.774475	+	0.632604i	$0.781986\pi$
$662$	10.7659	+	3.91848i	0.418430	+	0.152296i
$663$	−0.516213	−	1.22276i	−0.0200481	−	0.0474882i
$664$	−1.28776	+	7.30326i	−0.0499749	+	0.283422i
$665$		0			0
$666$	16.2983	+	4.13136i	0.631545	+	0.160087i
$667$	1.18764	−	2.05705i	0.0459855	−	0.0796493i
$668$	9.25670	+	7.76729i	0.358152	+	0.300526i
$669$	5.90688	+	3.02427i	0.228373	+	0.116925i
$670$		0			0
$671$	2.27023	−	1.90495i	0.0876412	−	0.0735397i
$672$	7.06161	−	22.9370i	0.272408	−	0.884815i
$673$	10.8272	−	3.94080i	0.417360	−	0.151907i	−0.124800	−	0.992182i	$-0.539829\pi$
$673$	10.8272	−	3.94080i	0.417360	−	0.151907i	0.542160	+	0.840275i	$0.317607\pi$
$674$	−28.6293			−1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	−31.8791	+	11.6030i	−1.22521	+	0.445941i	−0.871955	−	0.489585i	$-0.837148\pi$
$677$	−31.8791	+	11.6030i	−1.22521	+	0.445941i	−0.353257	+	0.935526i	$0.614926\pi$
$678$	−2.94707	−	3.17275i	−0.113181	−	0.121849i
$679$	−27.0103	+	22.6643i	−1.03656	+	0.869776i
$680$		0			0
$681$	0.219563	+	4.35229i	0.00841369	+	0.166780i
$682$	−0.424772	−	0.356426i	−0.0162654	−	0.0136483i
$683$	18.3777	−	31.8310i	0.703201	−	1.21798i	−0.264135	−	0.964486i	$-0.585087\pi$
$683$	18.3777	−	31.8310i	0.703201	−	1.21798i	0.967337	−	0.253495i	$-0.0815801\pi$
$684$	6.63034	+	9.20132i	0.253518	+	0.351821i
$685$		0			0
$686$	2.76254	−	15.6671i	0.105474	−	0.598174i
$687$	27.3958	+	3.41816i	1.04522	+	0.130411i
$688$	0.136717	+	0.0497608i	0.00521227	+	0.00189711i
$689$	−13.3311	−	4.85212i	−0.507874	−	0.184851i
$690$		0			0
$691$	2.32309	−	13.1749i	0.0883744	−	0.501196i	−0.908203	−	0.418530i	$-0.862545\pi$
$691$	2.32309	−	13.1749i	0.0883744	−	0.501196i	0.996577	−	0.0826660i	$-0.0263435\pi$
$692$	4.62331	+	8.00781i	0.175752	+	0.304411i
$693$	0.731885	−	1.62670i	0.0278020	−	0.0617930i
$694$	−7.79146	+	13.4952i	−0.295760	+	0.512271i
$695$		0			0
$696$	−0.0833854	−	1.65291i	−0.00316072	−	0.0626532i
$697$	−0.495057	−	2.80761i	−0.0187516	−	0.106346i
$698$	−4.92475	+	4.13236i	−0.186405	+	0.156412i
$699$	33.1570	+	35.6961i	1.25411	+	1.35015i
$700$		0			0
$701$	5.00452			0.189018			0.0945091	−	0.995524i	$-0.469872\pi$
$701$	5.00452			0.189018			0.0945091	+	0.995524i	$0.469872\pi$
$702$	−8.49421	+	6.79639i	−0.320593	+	0.256513i
$703$	−19.4720			−0.734400
$704$	0.836033	−	0.304291i	0.0315092	−	0.0114684i
$705$		0			0
$706$	−5.37489	+	4.51007i	−0.202287	+	0.169739i
$707$	−1.65313	−	9.37537i	−0.0621724	−	0.352597i
$708$	−12.5096	−	6.40479i	−0.470139	−	0.240707i
$709$	13.1330	+	11.0199i	0.493218	+	0.413859i	0.855178	−	0.518334i	$-0.173448\pi$
$709$	13.1330	+	11.0199i	0.493218	+	0.413859i	−0.361960	+	0.932194i	$0.617892\pi$
$710$		0			0
$711$	−1.67982	+	1.72595i	−0.0629982	+	0.0647282i
$712$	14.0623	+	24.3566i	0.527006	+	0.912800i
$713$	3.21258	−	18.2195i	0.120312	−	0.682324i
$714$	−0.376509	−	0.891844i	−0.0140905	−	0.0333764i
$715$		0			0
$716$	−23.4058	−	8.51902i	−0.874716	−	0.318371i
$717$	−15.3687	+	20.3122i	−0.573954	+	0.758572i
$718$	−1.15215	+	6.53417i	−0.0429979	+	0.243853i
$719$	21.6760	+	37.5439i	0.808377	+	1.40015i	0.913987	+	0.405742i	$0.132987\pi$
$719$	21.6760	+	37.5439i	0.808377	+	1.40015i	−0.105610	+	0.994408i	$0.533680\pi$
$720$		0			0
$721$	7.03467	−	12.1844i	0.261985	−	0.453771i
$722$	−6.90461	−	5.79365i	−0.256963	−	0.215617i
$723$	−12.2799	+	7.94060i	−0.456696	+	0.295314i
$724$	−2.66987	−	15.1416i	−0.0992251	−	0.562733i
$725$		0			0
$726$	−14.8017	+	3.38679i	−0.549344	+	0.125695i
$727$	−34.1521	+	12.4303i	−1.26663	+	0.461016i	−0.885989	−	0.463706i	$-0.846519\pi$
$727$	−34.1521	+	12.4303i	−1.26663	+	0.461016i	−0.380642	+	0.924722i	$0.624297\pi$
$728$	−16.7075			−0.619220
$729$	5.92298	−	26.3423i	0.219370	−	0.975642i
$730$		0			0
$731$	0.0718726	−	0.0261595i	0.00265830	−	0.000967544i
$732$	27.1542	−	6.21315i	1.00365	−	0.229645i
$733$	−2.96889	+	2.49119i	−0.109658	+	0.0920143i	−0.695968	−	0.718073i	$-0.745025\pi$
$733$	−2.96889	+	2.49119i	−0.109658	+	0.0920143i	0.586310	+	0.810087i	$0.300580\pi$
$734$	2.05990	+	11.6823i	0.0760322	+	0.431200i
$735$		0			0
$736$	29.8753	+	25.0683i	1.10122	+	0.924031i
$737$	−0.226432	+	0.392191i	−0.00834071	+	0.0144465i
$738$	−21.0418	+	10.1611i	−0.774559	+	0.374036i
$739$	−13.2241	−	22.9048i	−0.486456	−	0.842567i	0.513422	−	0.858136i	$-0.328377\pi$
$739$	−13.2241	−	22.9048i	−0.486456	−	0.842567i	−0.999879	+	0.0155689i	$0.995044\pi$
$740$		0			0
$741$	7.60158	−	10.0467i	0.279251	−	0.369075i
$742$	−9.72326	−	3.53898i	−0.356952	−	0.129920i
$743$	−12.6514	−	4.60474i	−0.464136	−	0.168932i	0.0993584	−	0.995052i	$-0.468321\pi$
$743$	−12.6514	−	4.60474i	−0.464136	−	0.168932i	−0.563494	+	0.826120i	$0.690543\pi$
$744$	−5.01352	−	11.8756i	−0.183805	−	0.435381i
$745$		0			0
$746$	10.2329	+	17.7238i	0.374651	+	0.648915i
$747$	−5.76591	+	5.92425i	−0.210964	+	0.216757i
$748$	−0.0498160	+	0.0862839i	−0.00182145	+	0.00315485i
$749$	−0.471538	−	0.395667i	−0.0172296	−	0.0144574i
$750$		0			0
$751$	0.654359	+	3.71106i	0.0238779	+	0.135418i	0.994416	−	0.105528i	$-0.0336533\pi$
$751$	0.654359	+	3.71106i	0.0238779	+	0.135418i	−0.970538	+	0.240946i	$0.922542\pi$
$752$	4.88444	−	4.09854i	0.178117	−	0.149458i
$753$	11.8341	−	38.4386i	0.431258	−	1.40078i
$754$	−0.698510	+	0.254237i	−0.0254382	+	0.00925876i
$755$		0			0
$756$	13.0915	−	10.4748i	0.476135	−	0.380965i
$757$	33.7073			1.22511			0.612556	−	0.790427i	$-0.290141\pi$
$757$	33.7073			1.22511			0.612556	+	0.790427i	$0.290141\pi$
$758$	−15.1575	+	5.51687i	−0.550544	+	0.200382i
$759$	1.97271	+	2.12378i	0.0716049	+	0.0770884i
$760$		0			0
$761$	−1.67665	−	9.50874i	−0.0607784	−	0.344692i	−0.999999	−	0.00137744i	$-0.999562\pi$
$761$	−1.67665	−	9.50874i	−0.0607784	−	0.344692i	0.939221	−	0.343314i	$-0.111550\pi$
$762$	−1.29084	−	25.5876i	−0.0467621	−	0.926941i
$763$	15.5818	+	13.0747i	0.564100	+	0.473336i
$764$	4.65533	−	8.06327i	0.168424	−	0.291719i
$765$		0			0
$766$	−9.56272	−	16.5631i	−0.345515	−	0.598450i
$767$	−2.71093	+	15.3745i	−0.0978861	+	0.555139i
$768$	24.3601	+	3.03939i	0.879019	+	0.109675i
$769$	−36.3764	−	13.2399i	−1.31177	−	0.477445i	−0.410957	−	0.911655i	$-0.634805\pi$
$769$	−36.3764	−	13.2399i	−1.31177	−	0.477445i	−0.900812	+	0.434210i	$0.857027\pi$
$770$		0			0
$771$	11.7994	+	1.47220i	0.424944	+	0.0530200i
$772$	4.81205	−	27.2905i	0.173189	−	0.982206i
$773$	12.1519	+	21.0478i	0.437075	+	0.757036i	0.997462	−	0.0711944i	$-0.0226811\pi$
$773$	12.1519	+	21.0478i	0.437075	+	0.757036i	−0.560387	+	0.828231i	$0.689348\pi$
$774$	−0.366491	−	0.508601i	−0.0131732	−	0.0182813i
$775$		0			0
$776$	−30.5824	−	25.6617i	−1.09784	−	0.921200i
$777$	1.45036	+	28.7496i	0.0520312	+	1.03139i
$778$	5.28527	+	29.9742i	0.189486	+	1.07463i
$779$	20.7300	−	17.3945i	0.742728	−	0.623223i
$780$		0			0
$781$	−0.0870967	+	0.0317006i	−0.00311656	+	0.00113434i
$782$	1.57311			0.0562544
$783$	0.959467	−	1.57581i	0.0342886	−	0.0563150i
$784$	−0.753755			−0.0269198
$785$		0			0
$786$	−5.81096	+	18.8748i	−0.207270	+	0.673240i
$787$	−16.0414	+	13.4604i	−0.571816	+	0.479810i	−0.882248	−	0.470785i	$-0.843971\pi$
$787$	−16.0414	+	13.4604i	−0.571816	+	0.479810i	0.310432	+	0.950596i	$0.399526\pi$
$788$	0.715633	+	4.05856i	0.0254934	+	0.144580i
$789$	−5.16932	−	2.64664i	−0.184033	−	0.0942229i
$790$		0			0
$791$	3.70688	−	6.42051i	0.131802	−	0.228287i
$792$	1.95774	+	0.496258i	0.0695654	+	0.0176338i
$793$	−15.4718	−	26.7979i	−0.549419	−	0.951621i
$794$	−2.83229	+	16.0627i	−0.100514	+	0.570045i
$795$		0			0
$796$	−2.88620	−	1.05049i	−0.102299	−	0.0372337i
$797$	11.2169	+	4.08261i	0.397322	+	0.144614i	0.532951	−	0.846146i	$-0.321083\pi$
$797$	11.2169	+	4.08261i	0.397322	+	0.144614i	−0.135628	+	0.990760i	$0.543305\pi$
$798$	5.54435	−	7.32775i	0.196268	−	0.259400i
$799$	0.582068	−	3.30107i	0.0205921	−	0.116783i
$800$		0			0
$801$	−2.30926	+	31.2668i	−0.0815939	+	1.10476i
$802$	−2.78329	+	4.82080i	−0.0982814	+	0.170228i
$803$	0.963297	+	0.808303i	0.0339940	+	0.0285244i
$804$	−3.57446	+	2.31136i	−0.126062	+	0.0815154i
$805$		0			0
$806$	−4.43518	+	3.72155i	−0.156222	+	0.131086i
$807$	21.5131	−	4.92242i	0.757298	−	0.173277i
$808$	10.1290	−	3.68664i	0.356336	−	0.129696i
$809$	8.60808			0.302644			0.151322	−	0.988485i	$-0.451647\pi$
$809$	8.60808			0.302644			0.151322	+	0.988485i	$0.451647\pi$
$810$		0			0
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	1.07656	−	0.391837i	0.0377800	−	0.0137508i
$813$	−39.7734	+	9.10055i	−1.39491	+	0.319170i
$814$	−1.07402	+	0.901211i	−0.0376444	+	0.0315874i
$815$		0			0
$816$	−0.238129	+	0.153982i	−0.00833617	+	0.00539043i
$817$	0.556149	+	0.466665i	0.0194572	+	0.0163265i
$818$	4.37071	−	7.57029i	0.152818	−	0.264689i
$819$	−15.3998	−	10.4751i	−0.538112	−	0.366030i
$820$		0			0
$821$	5.03168	−	28.5361i	0.175607	−	0.995915i	−0.761835	−	0.647772i	$-0.775701\pi$
$821$	5.03168	−	28.5361i	0.175607	−	0.995915i	0.937441	−	0.348144i	$-0.113188\pi$
$822$	16.4898	−	21.7939i	0.575147	−	0.760149i
$823$	−10.5779	−	3.85004i	−0.368722	−	0.134204i	0.151012	−	0.988532i	$-0.451747\pi$
$823$	−10.5779	−	3.85004i	−0.368722	−	0.134204i	−0.519734	+	0.854328i	$0.673969\pi$
$824$	14.9693	+	5.44838i	0.521481	+	0.189803i
$825$		0			0
$826$	−1.97727	+	11.2136i	−0.0687979	+	0.390172i
$827$	15.4640	+	26.7844i	0.537734	+	0.931383i	0.999026	+	0.0441346i	$0.0140530\pi$
$827$	15.4640	+	26.7844i	0.537734	+	0.931383i	−0.461291	+	0.887249i	$0.652614\pi$
$828$	7.40742	+	26.2192i	0.257426	+	0.911180i
$829$	4.91762	−	8.51757i	0.170796	−	0.295827i	−0.767902	−	0.640567i	$-0.778699\pi$
$829$	4.91762	−	8.51757i	0.170796	−	0.295827i	0.938698	+	0.344739i	$0.112033\pi$
$830$		0			0
$831$	−6.44630	−	3.30044i	−0.223620	−	0.114491i
$832$	−1.61310	−	9.14836i	−0.0559243	−	0.317162i
$833$	−0.303547	+	0.254706i	−0.0105173	+	0.00882505i
$834$	7.31644	−	23.7648i	0.253348	−	0.822906i
$835$		0			0
$836$	−0.945711			−0.0327081
$837$	2.82456	−	14.0894i	0.0976310	−	0.487003i
$838$	−8.07072			−0.278798
$839$	12.3506	−	4.49524i	0.426389	−	0.155193i	−0.119907	−	0.992785i	$-0.538260\pi$
$839$	12.3506	−	4.49524i	0.426389	−	0.155193i	0.546296	+	0.837592i	$0.316037\pi$
$840$		0			0
$841$	−22.1187	+	18.5598i	−0.762714	+	0.639993i
$842$	−0.432522	−	2.45296i	−0.0149057	−	0.0845344i
$843$	1.88811	+	37.4271i	0.0650301	+	1.28906i
$844$	−26.4467	−	22.1914i	−0.910333	−	0.763860i
$845$		0			0
$846$	−27.3342	+	2.76494i	−0.939769	+	0.0950604i
$847$	−12.9982	−	22.5136i	−0.446624	−	0.773575i
$848$	−0.526336	+	2.98500i	−0.0180745	+	0.102505i
$849$	8.98435	+	1.12097i	0.308342	+	0.0384717i
$850$		0			0
$851$	−43.9569	−	15.9990i	−1.50682	−	0.548438i
$852$	−0.864497	−	0.107863i	−0.0296172	−	0.00369531i
$853$	−2.68153	+	15.2077i	−0.0918139	+	0.520703i	0.903863	+	0.427821i	$0.140719\pi$
$853$	−2.68153	+	15.2077i	−0.0918139	+	0.520703i	−0.995677	+	0.0928812i	$0.970392\pi$
$854$	−11.2846	−	19.5455i	−0.386151	−	0.668834i
$855$		0			0
$856$	0.348478	−	0.603581i	0.0119107	−	0.0206300i
$857$	−16.8398	−	14.1302i	−0.575235	−	0.482680i	0.308143	−	0.951340i	$-0.400292\pi$
$857$	−16.8398	−	14.1302i	−0.575235	−	0.482680i	−0.883378	+	0.468660i	$0.844737\pi$
$858$	−0.0457041	−	0.905968i	−0.00156031	−	0.0309293i
$859$	3.39772	+	19.2694i	0.115929	+	0.657464i	0.986286	+	0.165044i	$0.0527765\pi$
$859$	3.39772	+	19.2694i	0.115929	+	0.657464i	−0.870358	+	0.492420i	$0.836112\pi$
$860$		0			0
$861$	−27.2264	−	29.3114i	−0.927873	−	0.998929i
$862$	21.1421	−	7.69508i	0.720101	−	0.262095i
$863$	−21.8676			−0.744383			−0.372191	−	0.928156i	$-0.621393\pi$
$863$	−21.8676			−0.744383			−0.372191	+	0.928156i	$0.621393\pi$
$864$	22.7445	+	20.0069i	0.773784	+	0.680648i
$865$		0			0
$866$	14.7061	−	5.35258i	0.499733	−	0.181888i
$867$	8.62001	−	27.9989i	0.292751	−	0.950893i
$868$	6.83563	−	5.73577i	0.232016	−	0.194685i
$869$	−0.0348743	−	0.197782i	−0.00118303	−	0.00670929i
$870$		0			0
$871$	3.62223	+	3.03941i	0.122734	+	0.102986i
$872$	−11.5153	+	19.9452i	−0.389959	+	0.675428i
$873$	−12.0996	−	42.8275i	−0.409508	−	1.44949i
$874$	7.46602	+	12.9315i	0.252542	+	0.437416i
$875$		0			0
$876$	4.59707	+	10.8891i	0.155321	+	0.367910i
$877$	−36.7419	−	13.3729i	−1.24068	−	0.451572i	−0.363441	−	0.931617i	$-0.618398\pi$
$877$	−36.7419	−	13.3729i	−1.24068	−	0.451572i	−0.877244	+	0.480045i	$0.840620\pi$
$878$	−11.0188	−	4.01053i	−0.371868	−	0.135349i
$879$	6.41903	−	8.48379i	0.216509	−	0.286151i
$880$		0			0
$881$	3.65254	+	6.32639i	0.123057	+	0.213141i	0.920972	−	0.389629i	$-0.127397\pi$
$881$	3.65254	+	6.32639i	0.123057	+	0.213141i	−0.797915	+	0.602771i	$0.794063\pi$
$882$	2.68541	+	1.82665i	0.0904223	+	0.0615063i
$883$	−1.74646	+	3.02496i	−0.0587732	+	0.101798i	−0.893915	−	0.448237i	$-0.852052\pi$
$883$	−1.74646	+	3.02496i	−0.0587732	+	0.101798i	0.835142	+	0.550035i	$0.185386\pi$
$884$	0.796907	+	0.668684i	0.0268029	+	0.0224903i
$885$		0			0
$886$	−2.55485	−	14.4893i	−0.0858318	−	0.486776i
$887$	−21.7720	+	18.2688i	−0.731031	+	0.613408i	−0.930413	−	0.366514i	$-0.880551\pi$
$887$	−21.7720	+	18.2688i	−0.731031	+	0.613408i	0.199381	+	0.979922i	$0.436107\pi$
$888$	−31.7721	+	7.26978i	−1.06620	+	0.243958i
$889$	41.2181	−	15.0021i	1.38241	−	0.503156i
$890$		0			0
$891$	1.49337	+	1.68487i	0.0500298	+	0.0564452i
$892$	−5.20125			−0.174151
$893$	29.8985	−	10.8821i	1.00051	−	0.364157i
$894$	22.0447	−	5.04405i	0.737286	−	0.168698i
$895$		0			0
$896$	3.63563	+	20.6187i	0.121458	+	0.688821i
$897$	25.4149	−	16.4341i	0.848579	−	0.548718i
$898$	8.50974	+	7.14052i	0.283974	+	0.238282i
$899$	0.490949	−	0.850349i	0.0163741	−	0.0283607i
$900$		0			0
$901$	0.796719	+	1.37996i	0.0265426	+	0.0459731i
$902$	0.338348	−	1.91887i	0.0112658	−	0.0638913i
$903$	0.647588	−	0.855892i	0.0215504	−	0.0284823i
$904$	7.88800	+	2.87100i	0.262351	+	0.0954880i
$905$		0			0
$906$	7.70767	+	18.2573i	0.256070	+	0.606558i
$907$	−9.22362	+	52.3097i	−0.306265	+	1.73692i	0.311224	+	0.950337i	$0.399261\pi$
$907$	−9.22362	+	52.3097i	−0.306265	+	1.73692i	−0.617489	+	0.786579i	$0.711850\pi$
$908$	−1.70780	−	2.95799i	−0.0566753	−	0.0981644i
$909$	11.6476	+	2.95249i	0.386327	+	0.0979279i
$910$		0			0
$911$	−6.18649	−	5.19108i	−0.204968	−	0.171988i	0.534526	−	0.845152i	$-0.320490\pi$
$911$	−6.18649	−	5.19108i	−0.204968	−	0.171988i	−0.739493	+	0.673164i	$0.764935\pi$
$912$	−2.39595	−	1.22670i	−0.0793377	−	0.0406201i
$913$	−0.119704	−	0.678878i	−0.00396164	−	0.0224676i
$914$	−10.8360	+	9.09252i	−0.358424	+	0.300754i
$915$		0			0
$916$	−20.3339	+	7.40094i	−0.671852	+	0.244534i
$917$	−33.8116			−1.11656
$918$	1.22154	+	0.0284888i	0.0403168	+	0.000940269i
$919$	−47.9961			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$919$	−47.9961			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$920$		0			0
$921$	22.4013	+	24.1168i	0.738149	+	0.794677i
$922$	15.7419	−	13.2090i	0.518431	−	0.435016i
$923$	0.168051	+	0.953063i	0.00553146	+	0.0313705i
$924$	0.0704406	+	1.39631i	0.00231732	+	0.0459351i
$925$		0			0
$926$	7.35298	−	12.7357i	0.241634	−	0.418522i
$927$	10.3817	+	14.4073i	0.340979	+	0.473197i
$928$	1.03493	+	1.79255i	0.0339732	+	0.0588433i
$929$	−5.03474	+	28.5534i	−0.165185	+	0.936808i	0.783689	+	0.621153i	$0.213335\pi$
$929$	−5.03474	+	28.5534i	−0.165185	+	0.936808i	−0.948874	+	0.315655i	$0.897776\pi$
$930$		0			0
$931$	−3.53442	−	1.28642i	−0.115836	−	0.0421608i
$932$	−35.8828	−	13.0603i	−1.17538	−	0.427803i
$933$	37.0332	+	4.62061i	1.21241	+	0.151272i
$934$	2.26338	−	12.8363i	0.0740602	−	0.420016i
$935$		0			0
$936$	8.65246	−	19.2311i	0.282815	−	0.628587i
$937$	2.51425	−	4.35481i	0.0821369	−	0.142265i	−0.822031	−	0.569443i	$-0.807159\pi$
$937$	2.51425	−	4.35481i	0.0821369	−	0.142265i	0.904168	+	0.427178i	$0.140492\pi$
$938$	2.64193	+	2.21685i	0.0862622	+	0.0723826i
$939$	−0.332803	−	6.59699i	−0.0108606	−	0.215285i
$940$		0			0
$941$	−42.7767	+	35.8939i	−1.39448	+	1.17011i	−0.430995	+	0.902354i	$0.641837\pi$
$941$	−42.7767	+	35.8939i	−1.39448	+	1.17011i	−0.963487	+	0.267755i	$0.913718\pi$
$942$	0.721234	+	0.776466i	0.0234991	+	0.0252986i
$943$	61.0887	−	22.2345i	1.98932	−	0.724054i
$944$	3.33551			0.108561
$945$		0			0
$946$	0.0522740			0.00169957
$947$	39.9645	−	14.5459i	1.29867	−	0.472678i	0.402109	−	0.915592i	$-0.368277\pi$
$947$	39.9645	−	14.5459i	1.29867	−	0.472678i	0.896564	+	0.442914i	$0.146055\pi$
$948$	0.555443	−	1.80415i	0.0180400	−	0.0585961i
$949$	10.0581	−	8.43973i	0.326499	−	0.273965i
$950$		0			0
$951$	−6.55926	−	3.35828i	−0.212699	−	0.108900i
$952$	1.43754	+	1.20624i	0.0465909	+	0.0390944i
$953$	10.9074	−	18.8922i	0.353325	−	0.611977i	−0.633505	−	0.773739i	$-0.718384\pi$
$953$	10.9074	−	18.8922i	0.353325	−	0.611977i	0.986830	+	0.161762i	$0.0517175\pi$
$954$	9.10901	−	9.35916i	0.294915	−	0.303014i
$955$		0			0
$956$	3.46670	−	19.6606i	0.112121	−	0.635870i
$957$	0.0598339	+	0.141729i	0.00193415	+	0.00458146i
$958$	7.13399	+	2.59656i	0.230489	+	0.0838910i
$959$	43.9676	+	16.0029i	1.41979	+	0.516761i
$960$		0			0
$961$	−4.05507	+	22.9974i	−0.130809	+	0.741852i
$962$	7.31954	+	12.6778i	0.235991	+	0.408749i
$963$	0.699631	−	0.337853i	0.0225453	−	0.0108872i
$964$	5.73088	−	9.92618i	0.184579	−	0.319701i
$965$		0			0
$966$	18.5368	−	11.9865i	0.596412	−	0.385659i
$967$	−0.803746	−	4.55827i	−0.0258467	−	0.146584i	0.969153	−	0.246459i	$-0.0792669\pi$
$967$	−0.803746	−	4.55827i	−0.0258467	−	0.146584i	−0.995000	+	0.0998746i	$0.968156\pi$
$968$	22.5481	−	18.9201i	0.724724	−	0.608115i
$969$	−1.37940	+	0.315621i	−0.0443128	+	0.0101392i
$970$		0			0
$971$	−21.6509			−0.694809			−0.347405	−	0.937715i	$-0.612937\pi$
$971$	−21.6509			−0.694809			−0.347405	+	0.937715i	$0.612937\pi$
$972$	5.27712	+	20.4937i	0.169264	+	0.657334i
$973$	42.5714			1.36478
$974$	−0.352164	+	0.128177i	−0.0112841	+	0.00410707i
$975$		0			0
$976$	−5.06451	+	4.24963i	−0.162111	+	0.136027i
$977$	3.83499	+	21.7493i	0.122692	+	0.695822i	0.982652	+	0.185460i	$0.0593774\pi$
$977$	3.83499	+	21.7493i	0.122692	+	0.695822i	−0.859960	+	0.510362i	$0.829511\pi$
$978$	5.97856	−	3.86593i	0.191173	−	0.123619i
$979$	−2.00269	−	1.68046i	−0.0640063	−	0.0537076i
$980$		0			0
$981$	−23.1191	+	11.1643i	−0.738137	+	0.356448i
$982$	−10.0379	−	17.3862i	−0.320323	−	0.554815i
$983$	2.40729	−	13.6524i	0.0767807	−	0.435445i	−0.922049	−	0.387074i	$-0.873486\pi$
$983$	2.40729	−	13.6524i	0.0767807	−	0.435445i	0.998829	−	0.0483713i	$-0.0154031\pi$
$984$	27.3306	−	36.1217i	0.871266	−	1.15152i
$985$		0			0
$986$	0.0784563	+	0.0285558i	0.00249856	+	0.000909401i
$987$	−18.2940	−	43.3334i	−0.582305	−	1.37932i
$988$	−1.71468	+	9.72444i	−0.0545513	+	0.309376i
$989$	0.872042	+	1.51042i	0.0277293	+	0.0480286i
$990$		0			0
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	0.444966	+	0.895548i	$0.353216\pi$
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	−0.998050	+	0.0624224i	$0.980117\pi$
$992$	12.3499	+	10.3628i	0.392111	+	0.329020i
$993$	−22.0371	−	11.2828i	−0.699328	−	0.358049i
$994$	0.122571	+	0.695133i	0.00388771	+	0.0220483i
$995$		0			0
$996$	1.90653	−	6.19267i	0.0604109	−	0.196222i
$997$	−23.2572	+	8.46492i	−0.736562	+	0.268087i	−0.682940	−	0.730475i	$-0.739299\pi$
$997$	−23.2572	+	8.46492i	−0.736562	+	0.268087i	−0.0536221	+	0.998561i	$0.517077\pi$
$998$	−11.2488			−0.356073
$999$	−33.8433	−	13.2195i	−1.07075	−	0.418245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.c.601.1		12
5.2	odd	4		675.2.u.b.574.2		24
5.3	odd	4		675.2.u.b.574.3		24
5.4	even	2		27.2.e.a.7.2	yes	12
15.14	odd	2		81.2.e.a.19.1		12
20.19	odd	2		432.2.u.c.385.2		12
27.4	even	9	inner	675.2.l.c.301.1		12
45.4	even	6		243.2.e.c.217.1		12
45.14	odd	6		243.2.e.b.217.2		12
45.29	odd	6		243.2.e.a.136.2		12
45.34	even	6		243.2.e.d.136.1		12
135.4	even	18		27.2.e.a.4.2	✓	12
135.14	odd	18		243.2.e.a.109.2		12
135.29	odd	18		729.2.a.d.1.4		6
135.34	even	18		729.2.c.e.487.4		12
135.49	even	18		243.2.e.c.28.1		12
135.58	odd	36		675.2.u.b.274.2		24
135.59	odd	18		243.2.e.b.28.2		12
135.74	odd	18		729.2.c.b.487.3		12
135.79	even	18		729.2.a.a.1.3		6
135.94	even	18		243.2.e.d.109.1		12
135.104	odd	18		81.2.e.a.64.1		12
135.112	odd	36		675.2.u.b.274.3		24
135.119	odd	18		729.2.c.b.244.3		12
135.124	even	18		729.2.c.e.244.4		12
540.139	odd	18		432.2.u.c.193.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	135.4	even	18
27.2.e.a.7.2	yes	12	5.4	even	2
81.2.e.a.19.1		12	15.14	odd	2
81.2.e.a.64.1		12	135.104	odd	18
243.2.e.a.109.2		12	135.14	odd	18
243.2.e.a.136.2		12	45.29	odd	6
243.2.e.b.28.2		12	135.59	odd	18
243.2.e.b.217.2		12	45.14	odd	6
243.2.e.c.28.1		12	135.49	even	18
243.2.e.c.217.1		12	45.4	even	6
243.2.e.d.109.1		12	135.94	even	18
243.2.e.d.136.1		12	45.34	even	6
432.2.u.c.193.2		12	540.139	odd	18
432.2.u.c.385.2		12	20.19	odd	2
675.2.l.c.301.1		12	27.4	even	9	inner
675.2.l.c.601.1		12	1.1	even	1	trivial
675.2.u.b.274.2		24	135.58	odd	36
675.2.u.b.274.3		24	135.112	odd	36
675.2.u.b.574.2		24	5.2	odd	4
675.2.u.b.574.3		24	5.3	odd	4
729.2.a.a.1.3		6	135.79	even	18
729.2.a.d.1.4		6	135.29	odd	18
729.2.c.b.244.3		12	135.119	odd	18
729.2.c.b.487.3		12	135.74	odd	18
729.2.c.e.244.4		12	135.124	even	18
729.2.c.e.487.4		12	135.34	even	18

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.753189 + 0.274138i) q^{2} +(1.68842 - 0.386327i) q^{3} +(-1.03995 + 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(-1.82076 - 1.52780i) q^{7} +(1.34559 - 2.33062i) q^{8} +(2.70150 - 1.30456i) q^{9} +O(q^{10})\)	\(q+(-0.753189 + 0.274138i) q^{2} +(1.68842 - 0.386327i) q^{3} +(-1.03995 + 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(-1.82076 - 1.52780i) q^{7} +(1.34559 - 2.33062i) q^{8} +(2.70150 - 1.30456i) q^{9} +(-0.0434396 + 0.246358i) q^{11} +(-1.41875 + 1.87510i) q^{12} +(2.45446 + 0.893351i) q^{13} +(1.79020 + 0.651581i) q^{14} +(0.0969067 - 0.549585i) q^{16} +(-0.146688 - 0.254072i) q^{17} +(-1.67711 + 1.72317i) q^{18} +(1.39237 - 2.41166i) q^{19} +(-3.66443 - 1.87615i) q^{21} +(-0.0348180 - 0.197463i) q^{22} +(5.12472 - 4.30015i) q^{23} +(1.37153 - 4.45490i) q^{24} -2.09357 q^{26} +(4.05728 - 3.24631i) q^{27} +3.22668 q^{28} +(0.333645 - 0.121437i) q^{29} +(2.11847 - 1.77761i) q^{31} +(1.01231 + 5.74108i) q^{32} +(0.0218307 + 0.432738i) q^{33} +(0.180135 + 0.151151i) q^{34} +(-1.67103 + 3.71406i) q^{36} +(-3.49619 - 6.05558i) q^{37} +(-0.387591 + 2.19814i) q^{38} +(4.48928 + 0.560124i) q^{39} +(9.13156 + 3.32362i) q^{41} +(3.27434 + 0.408537i) q^{42} +(-0.0452712 + 0.256746i) q^{43} +(-0.169802 - 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(8.75249 + 7.34421i) q^{47} +(-0.0487006 - 0.965367i) q^{48} +(-0.234540 - 1.33014i) q^{49} +(-0.345826 - 0.372309i) q^{51} +(-3.33207 + 1.21277i) q^{52} -5.43137 q^{53} +(-2.16596 + 3.55734i) q^{54} +(-6.01071 + 2.18772i) q^{56} +(1.41922 - 4.60980i) q^{57} +(-0.218007 + 0.182930i) q^{58} +(1.03788 + 5.88612i) q^{59} +(-9.07515 - 7.61495i) q^{61} +(-1.10830 + 1.91963i) q^{62} +(-6.91190 - 1.75206i) q^{63} +(-1.77824 - 3.08001i) q^{64} +(-0.135073 - 0.319949i) q^{66} +(1.70113 + 0.619160i) q^{67} +(0.374256 + 0.136218i) q^{68} +(6.99139 - 9.24026i) q^{69} +(0.185255 + 0.320871i) q^{71} +(0.594663 - 8.05158i) q^{72} +(2.51339 - 4.35333i) q^{73} +(4.29336 + 3.60255i) q^{74} +(0.656467 + 3.72301i) q^{76} +(0.455479 - 0.382193i) q^{77} +(-3.53483 + 0.808804i) q^{78} +(-0.754406 + 0.274581i) q^{79} +(5.59624 - 7.04855i) q^{81} -7.78892 q^{82} +(-2.58947 + 0.942488i) q^{83} +(5.44798 - 1.24655i) q^{84} +(-0.0362861 - 0.205789i) q^{86} +(0.516417 - 0.333932i) q^{87} +(0.515717 + 0.432738i) q^{88} +(-5.22533 + 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-1.57704 + 8.94385i) q^{92} +(2.89012 - 3.81976i) q^{93} +(-8.60560 - 3.13218i) q^{94} +(3.92713 + 9.30225i) q^{96} +(2.57600 - 14.6092i) q^{97} +(0.541296 + 0.937552i) q^{98} +(0.204037 + 0.722208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

Introduction

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