LMFDB - Embedded newform 845.2.m.i.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-1.07992 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.i.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07992 + 0.623490i) q^{2} +(0.0990311 + 0.171527i) q^{3} +(-0.222521 + 0.385418i) q^{4} -1.00000i q^{5} +(-0.213891 - 0.123490i) q^{6} +(0.171527 + 0.0990311i) q^{7} -3.04892i q^{8} +(1.48039 - 2.56410i) q^{9} +O(q^{10})$	\(q+(-1.07992 + 0.623490i) q^{2} +(0.0990311 + 0.171527i) q^{3} +(-0.222521 + 0.385418i) q^{4} -1.00000i q^{5} +(-0.213891 - 0.123490i) q^{6} +(0.171527 + 0.0990311i) q^{7} -3.04892i q^{8} +(1.48039 - 2.56410i) q^{9} +(0.623490 + 1.07992i) q^{10} +(-3.50647 + 2.02446i) q^{11} -0.0881460 q^{12} -0.246980 q^{14} +(0.171527 - 0.0990311i) q^{15} +(1.45593 + 2.52174i) q^{16} +(-2.70291 + 4.68157i) q^{17} +3.69202i q^{18} +(-1.89311 - 1.09299i) q^{19} +(0.385418 + 0.222521i) q^{20} +0.0392287i q^{21} +(2.52446 - 4.37249i) q^{22} +(3.61745 + 6.26561i) q^{23} +(0.522971 - 0.301938i) q^{24} -1.00000 q^{25} +1.18060 q^{27} +(-0.0763367 + 0.0440730i) q^{28} +(3.53803 + 6.12805i) q^{29} +(-0.123490 + 0.213891i) q^{30} +0.0217703i q^{31} +(2.13632 + 1.23341i) q^{32} +(-0.694498 - 0.400969i) q^{33} -6.74094i q^{34} +(0.0990311 - 0.171527i) q^{35} +(0.658834 + 1.14113i) q^{36} +(-1.29381 + 0.746980i) q^{37} +2.72587 q^{38} -3.04892 q^{40} +(-9.49231 + 5.48039i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.77748 + 6.54279i) q^{43} -1.80194i q^{44} +(-2.56410 - 1.48039i) q^{45} +(-7.81308 - 4.51089i) q^{46} -1.03923i q^{47} +(-0.288364 + 0.499461i) q^{48} +(-3.48039 - 6.02820i) q^{49} +(1.07992 - 0.623490i) q^{50} -1.07069 q^{51} -0.554958 q^{53} +(-1.27495 + 0.736094i) q^{54} +(2.02446 + 3.50647i) q^{55} +(0.301938 - 0.522971i) q^{56} -0.432960i q^{57} +(-7.64156 - 4.41185i) q^{58} +(3.36891 + 1.94504i) q^{59} +0.0881460i q^{60} +(2.77748 - 4.81073i) q^{61} +(-0.0135735 - 0.0235101i) q^{62} +(0.507852 - 0.293209i) q^{63} -8.89977 q^{64} +1.00000 q^{66} +(-4.91058 + 2.83513i) q^{67} +(-1.20291 - 2.08350i) q^{68} +(-0.716480 + 1.24098i) q^{69} +0.246980i q^{70} +(8.24552 + 4.76055i) q^{71} +(-7.81774 - 4.51357i) q^{72} +11.5797i q^{73} +(0.931468 - 1.61335i) q^{74} +(-0.0990311 - 0.171527i) q^{75} +(0.842515 - 0.486426i) q^{76} -0.801938 q^{77} -15.8291 q^{79} +(2.52174 - 1.45593i) q^{80} +(-4.32424 - 7.48980i) q^{81} +(6.83393 - 11.8367i) q^{82} +17.3448i q^{83} +(-0.0151194 - 0.00872920i) q^{84} +(4.68157 + 2.70291i) q^{85} -9.42088i q^{86} +(-0.700751 + 1.21374i) q^{87} +(6.17241 + 10.6909i) q^{88} +(2.64510 - 1.52715i) q^{89} +3.69202 q^{90} -3.21983 q^{92} +(-0.00373419 + 0.00215593i) q^{93} +(0.647948 + 1.12228i) q^{94} +(-1.09299 + 1.89311i) q^{95} +0.488582i q^{96} +(-4.34898 - 2.51089i) q^{97} +(7.51705 + 4.33997i) q^{98} +11.9879i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{3} - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 12 * q + 10 * q^3 - 2 * q^4 - 8 * q^9	$ 12 q + 10 q^{3} - 2 q^{4} - 8 q^{9} - 2 q^{10} - 16 q^{12} + 16 q^{14} + 10 q^{16} - 6 q^{17} + 12 q^{22} - 4 q^{23} - 12 q^{25} - 32 q^{27} + 12 q^{29} + 8 q^{30} + 10 q^{35} - 26 q^{36} + 76 q^{38} + 18 q^{42} - 46 q^{43} + 2 q^{48} - 16 q^{49} + 36 q^{51} - 8 q^{53} + 6 q^{55} - 14 q^{56} + 34 q^{61} + 12 q^{62} - 16 q^{64} + 12 q^{66} + 12 q^{68} + 30 q^{69} + 22 q^{74} - 10 q^{75} + 8 q^{77} - 148 q^{79} - 54 q^{81} - 4 q^{82} - 20 q^{87} + 28 q^{88} + 24 q^{90} - 44 q^{92} - 20 q^{94} + 16 q^{95}+O(q^{100}) $ 12 * q + 10 * q^3 - 2 * q^4 - 8 * q^9 - 2 * q^10 - 16 * q^12 + 16 * q^14 + 10 * q^16 - 6 * q^17 + 12 * q^22 - 4 * q^23 - 12 * q^25 - 32 * q^27 + 12 * q^29 + 8 * q^30 + 10 * q^35 - 26 * q^36 + 76 * q^38 + 18 * q^42 - 46 * q^43 + 2 * q^48 - 16 * q^49 + 36 * q^51 - 8 * q^53 + 6 * q^55 - 14 * q^56 + 34 * q^61 + 12 * q^62 - 16 * q^64 + 12 * q^66 + 12 * q^68 + 30 * q^69 + 22 * q^74 - 10 * q^75 + 8 * q^77 - 148 * q^79 - 54 * q^81 - 4 * q^82 - 20 * q^87 + 28 * q^88 + 24 * q^90 - 44 * q^92 - 20 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.07992	+	0.623490i	−0.763616	+	0.440874i	−0.830593	−	0.556881i	$-0.811998\pi$
$2$	−1.07992	+	0.623490i	−0.763616	+	0.440874i	0.0669766	+	0.997755i	$0.478665\pi$
$3$	0.0990311	+	0.171527i	0.0571757	+	0.0990311i	0.893197	−	0.449667i	$-0.148457\pi$
$3$	0.0990311	+	0.171527i	0.0571757	+	0.0990311i	−0.836021	+	0.548698i	$0.815124\pi$
$4$	−0.222521	+	0.385418i	−0.111260	+	0.192709i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.213891	−	0.123490i	−0.0873205	−	0.0504145i
$7$	0.171527	+	0.0990311i	0.0648311	+	0.0374302i	0.532065	−	0.846703i	$-0.321416\pi$
$7$	0.171527	+	0.0990311i	0.0648311	+	0.0374302i	−0.467234	+	0.884134i	$0.654749\pi$
$8$		−	3.04892i		−	1.07796i
$9$	1.48039	−	2.56410i	0.493462	−	0.854701i
$10$	0.623490	+	1.07992i	0.197165	+	0.341499i
$11$	−3.50647	+	2.02446i	−1.05724	+	0.610397i	−0.924667	−	0.380776i	$-0.875657\pi$
$11$	−3.50647	+	2.02446i	−1.05724	+	0.610397i	−0.132572	+	0.991173i	$0.542324\pi$
$12$	−0.0881460			−0.0254456
$13$		0			0
$13$		0			0
$14$	−0.246980			−0.0660081
$15$	0.171527	−	0.0990311i	0.0442881	−	0.0255697i
$16$	1.45593	+	2.52174i	0.363982	+	0.630435i
$17$	−2.70291	+	4.68157i	−0.655551	+	1.13545i	0.326204	+	0.945299i	$0.394230\pi$
$17$	−2.70291	+	4.68157i	−0.655551	+	1.13545i	−0.981755	+	0.190149i	$0.939103\pi$
$18$			3.69202i			0.870218i
$19$	−1.89311	−	1.09299i	−0.434310	−	0.250749i	0.266871	−	0.963732i	$-0.414010\pi$
$19$	−1.89311	−	1.09299i	−0.434310	−	0.250749i	−0.701181	+	0.712983i	$0.747344\pi$
$20$	0.385418	+	0.222521i	0.0861820	+	0.0497572i
$21$			0.0392287i			0.00856040i
$22$	2.52446	−	4.37249i	0.538216	−	0.932218i
$23$	3.61745	+	6.26561i	0.754290	+	1.30647i	0.945726	+	0.324964i	$0.105352\pi$
$23$	3.61745	+	6.26561i	0.754290	+	1.30647i	−0.191436	+	0.981505i	$0.561314\pi$
$24$	0.522971	−	0.301938i	0.106751	−	0.0616328i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.18060			0.227207
$28$	−0.0763367	+	0.0440730i	−0.0144263	+	0.00832901i
$29$	3.53803	+	6.12805i	0.656996	+	1.13795i	0.981389	+	0.192028i	$0.0615065\pi$
$29$	3.53803	+	6.12805i	0.656996	+	1.13795i	−0.324393	+	0.945922i	$0.605160\pi$
$30$	−0.123490	+	0.213891i	−0.0225461	+	0.0390509i
$31$			0.0217703i			0.00391005i	0.999998	+	0.00195503i	$0.000622305\pi$
$31$			0.0217703i			0.00391005i	−0.999998	+	0.00195503i	$0.999378\pi$
$32$	2.13632	+	1.23341i	0.377652	+	0.218037i
$33$	−0.694498	−	0.400969i	−0.120897	−	0.0697997i
$34$		−	6.74094i		−	1.15606i
$35$	0.0990311	−	0.171527i	0.0167393	−	0.0289933i
$36$	0.658834	+	1.14113i	0.109806	+	0.190189i
$37$	−1.29381	+	0.746980i	−0.212700	+	0.122803i	−0.602566	−	0.798069i	$-0.705855\pi$
$37$	−1.29381	+	0.746980i	−0.212700	+	0.122803i	0.389865	+	0.920872i	$0.372522\pi$
$38$	2.72587			0.442195
$39$		0			0
$40$	−3.04892			−0.482076
$41$	−9.49231	+	5.48039i	−1.48245	+	0.855892i	−0.999802	−	0.0199222i	$-0.993658\pi$
$41$	−9.49231	+	5.48039i	−1.48245	+	0.855892i	−0.482648	+	0.875815i	$0.660325\pi$
$42$	−0.0244587	−	0.0423637i	−0.00377405	−	0.00653685i
$43$	−3.77748	+	6.54279i	−0.576060	+	0.997765i	0.419865	+	0.907586i	$0.362077\pi$
$43$	−3.77748	+	6.54279i	−0.576060	+	0.997765i	−0.995926	+	0.0901791i	$0.971256\pi$
$44$		−	1.80194i		−	0.271652i
$45$	−2.56410	−	1.48039i	−0.382234	−	0.220683i
$46$	−7.81308	−	4.51089i	−1.15198	−	0.665094i
$47$		−	1.03923i		−	0.151587i	−0.997124	−	0.0757935i	$-0.975851\pi$
$47$		−	1.03923i		−	0.151587i	0.997124	−	0.0757935i	$-0.0241490\pi$
$48$	−0.288364	+	0.499461i	−0.0416218	+	0.0720910i
$49$	−3.48039	−	6.02820i	−0.497198	−	0.861172i
$50$	1.07992	−	0.623490i	0.152723	−	0.0881748i
$51$	−1.07069			−0.149926
$52$		0			0
$53$	−0.554958			−0.0762294			−0.0381147	−	0.999273i	$-0.512135\pi$
$53$	−0.554958			−0.0762294			−0.0381147	+	0.999273i	$0.512135\pi$
$54$	−1.27495	+	0.736094i	−0.173499	+	0.100170i
$55$	2.02446	+	3.50647i	0.272978	+	0.472812i
$56$	0.301938	−	0.522971i	0.0403481	−	0.0698850i
$57$		−	0.432960i		−	0.0573470i
$58$	−7.64156	−	4.41185i	−1.00339	−	0.579305i
$59$	3.36891	+	1.94504i	0.438595	+	0.253223i	0.703001	−	0.711188i	$-0.251843\pi$
$59$	3.36891	+	1.94504i	0.438595	+	0.253223i	−0.264407	+	0.964411i	$0.585176\pi$
$60$			0.0881460i			0.0113796i
$61$	2.77748	−	4.81073i	0.355620	−	0.615951i	−0.631604	−	0.775291i	$-0.717603\pi$
$61$	2.77748	−	4.81073i	0.355620	−	0.615951i	0.987224	+	0.159340i	$0.0509365\pi$
$62$	−0.0135735	−	0.0235101i	−0.00172384	−	0.00298578i
$63$	0.507852	−	0.293209i	0.0639833	−	0.0369408i
$64$	−8.89977			−1.11247
$65$		0			0
$66$	1.00000			0.123091
$67$	−4.91058	+	2.83513i	−0.599923	+	0.346366i	−0.769011	−	0.639235i	$-0.779251\pi$
$67$	−4.91058	+	2.83513i	−0.599923	+	0.346366i	0.169088	+	0.985601i	$0.445918\pi$
$68$	−1.20291	−	2.08350i	−0.145874	−	0.252661i
$69$	−0.716480	+	1.24098i	−0.0862541	+	0.149396i
$70$			0.246980i			0.0295197i
$71$	8.24552	+	4.76055i	0.978563	+	0.564974i	0.901836	−	0.432078i	$-0.142220\pi$
$71$	8.24552	+	4.76055i	0.978563	+	0.564974i	0.0767271	+	0.997052i	$0.475553\pi$
$72$	−7.81774	−	4.51357i	−0.921329	−	0.531930i
$73$			11.5797i			1.35530i	0.735383	+	0.677651i	$0.237002\pi$
$73$			11.5797i			1.35530i	−0.735383	+	0.677651i	$0.762998\pi$
$74$	0.931468	−	1.61335i	0.108281	−	0.187548i
$75$	−0.0990311	−	0.171527i	−0.0114351	−	0.0198062i
$76$	0.842515	−	0.486426i	0.0966431	−	0.0557969i
$77$	−0.801938			−0.0913893
$78$		0			0
$79$	−15.8291			−1.78091			−0.890456	−	0.455070i	$-0.849614\pi$
$79$	−15.8291			−1.78091			−0.890456	+	0.455070i	$0.849614\pi$
$80$	2.52174	−	1.45593i	0.281939	−	0.162778i
$81$	−4.32424	−	7.48980i	−0.480471	−	0.832200i
$82$	6.83393	−	11.8367i	0.754681	−	1.30715i
$83$			17.3448i			1.90384i	0.306346	+	0.951920i	$0.400894\pi$
$83$			17.3448i			1.90384i	−0.306346	+	0.951920i	$0.599106\pi$
$84$	−0.0151194	−	0.00872920i	−0.00164966	−	0.000952434i
$85$	4.68157	+	2.70291i	0.507788	+	0.293171i
$86$		−	9.42088i		−	1.01588i
$87$	−0.700751	+	1.21374i	−0.0751284	+	0.130126i
$88$	6.17241	+	10.6909i	0.657981	+	1.13966i
$89$	2.64510	−	1.52715i	0.280380	−	0.161877i	−0.353216	−	0.935542i	$-0.614912\pi$
$89$	2.64510	−	1.52715i	0.280380	−	0.161877i	0.633595	+	0.773665i	$0.281578\pi$
$90$	3.69202			0.389173
$91$		0			0
$92$	−3.21983			−0.335691
$93$	−0.00373419	+	0.00215593i	−0.000387217	+	0.000223560i
$94$	0.647948	+	1.12228i	0.0668308	+	0.115754i
$95$	−1.09299	+	1.89311i	−0.112138	+	0.194229i
$96$			0.488582i			0.0498657i
$97$	−4.34898	−	2.51089i	−0.441572	−	0.254942i	0.262692	−	0.964880i	$-0.415390\pi$
$97$	−4.34898	−	2.51089i	−0.441572	−	0.254942i	−0.704264	+	0.709938i	$0.748723\pi$
$98$	7.51705	+	4.33997i	0.759337	+	0.438403i
$99$			11.9879i			1.20483i
$100$	0.222521	−	0.385418i	0.0222521	−	0.0385418i
$101$	−6.47434	−	11.2139i	−0.644221	−	1.11582i	−0.984481	−	0.175493i	$-0.943848\pi$
$101$	−6.47434	−	11.2139i	−0.644221	−	1.11582i	0.340259	−	0.940332i	$-0.389485\pi$
$102$	1.15625	−	0.667563i	0.114486	−	0.0660986i
$103$	13.4058			1.32091			0.660457	−	0.750864i	$-0.270363\pi$
$103$	13.4058			1.32091			0.660457	+	0.750864i	$0.270363\pi$
$104$		0			0
$105$	0.0392287			0.00382833
$106$	0.599308	−	0.346011i	0.0582100	−	0.0336075i
$107$	−0.497312	−	0.861369i	−0.0480769	−	0.0832717i	0.840985	−	0.541058i	$-0.181976\pi$
$107$	−0.497312	−	0.861369i	−0.0480769	−	0.0832717i	−0.889062	+	0.457786i	$0.848643\pi$
$108$	−0.262709	+	0.455025i	−0.0252792	+	0.0437848i
$109$		−	19.3056i		−	1.84914i	−0.381013	−	0.924570i	$-0.624425\pi$
$109$		−	19.3056i		−	1.84914i	0.381013	−	0.924570i	$-0.375575\pi$
$110$	−4.37249	−	2.52446i	−0.416901	−	0.240698i
$111$	−0.256254	−	0.147948i	−0.0243226	−	0.0140426i
$112$			0.576728i			0.0544957i
$113$	−9.80678	+	16.9858i	−0.922544	+	1.59789i	−0.127081	+	0.991892i	$0.540561\pi$
$113$	−9.80678	+	16.9858i	−0.922544	+	1.59789i	−0.795463	+	0.606002i	$0.792773\pi$
$114$	0.269946	+	0.467561i	0.0252828	+	0.0437911i
$115$	6.26561	−	3.61745i	0.584271	−	0.337329i
$116$	−3.14914			−0.292391
$117$		0			0
$118$	−4.85086			−0.446557
$119$	−0.927243	+	0.535344i	−0.0850002	+	0.0490749i
$120$	−0.301938	−	0.522971i	−0.0275630	−	0.0477405i
$121$	2.69687	−	4.67111i	0.245170	−	0.424646i
$122$			6.92692i			0.627134i
$123$	−1.88007	−	1.08546i	−0.169520	−	0.0978724i
$124$	−0.00839064	−	0.00484434i	−0.000753502	−	0.000435035i
$125$			1.00000i			0.0894427i
$126$	−0.365625	+	0.633281i	−0.0325725	+	0.0564172i
$127$	−4.88135	−	8.45475i	−0.433150	−	0.750238i	0.563992	−	0.825780i	$-0.309265\pi$
$127$	−4.88135	−	8.45475i	−0.433150	−	0.750238i	−0.997143	+	0.0755418i	$0.975931\pi$
$128$	5.33836	−	3.08211i	0.471849	−	0.272422i
$129$	−1.49635			−0.131746
$130$		0			0
$131$	14.6189			1.27726			0.638631	−	0.769513i	$-0.279501\pi$
$131$	14.6189			1.27726			0.638631	+	0.769513i	$0.279501\pi$
$132$	0.309081	−	0.178448i	0.0269020	−	0.0155319i
$133$	−0.216480	−	0.374955i	−0.0187712	−	0.0325127i
$134$	3.53534	−	6.12340i	0.305407	−	0.528981i
$135$		−	1.18060i		−	0.101610i
$136$	14.2737	+	8.24094i	1.22396	+	0.706655i
$137$	−4.80027	−	2.77144i	−0.410115	−	0.236780i	0.280724	−	0.959788i	$-0.409425\pi$
$137$	−4.80027	−	2.77144i	−0.410115	−	0.236780i	−0.690839	+	0.723009i	$0.742759\pi$
$138$		−	1.78687i		−	0.152109i
$139$	0.272635	−	0.472217i	0.0231246	−	0.0400529i	−0.854232	−	0.519893i	$-0.825972\pi$
$139$	0.272635	−	0.472217i	0.0231246	−	0.0400529i	0.877356	+	0.479840i	$0.159305\pi$
$140$	0.0440730	+	0.0763367i	0.00372485	+	0.00645163i
$141$	0.178256	−	0.102916i	0.0150118	−	0.00866709i
$142$	−11.8726			−0.996329
$143$		0			0
$144$	8.62133			0.718444
$145$	6.12805	−	3.53803i	0.508907	−	0.293818i
$146$	−7.21983	−	12.5051i	−0.597518	−	1.03493i
$147$	0.689333	−	1.19396i	0.0568552	−	0.0984762i
$148$		−	0.664874i		−	0.0546523i
$149$	−0.665182	−	0.384043i	−0.0544938	−	0.0314620i	0.472506	−	0.881328i	$-0.343350\pi$
$149$	−0.665182	−	0.384043i	−0.0544938	−	0.0314620i	−0.526999	+	0.849866i	$0.676683\pi$
$150$	0.213891	+	0.123490i	0.0174641	+	0.0100829i
$151$			14.0097i			1.14009i	0.821613	+	0.570046i	$0.193075\pi$
$151$			14.0097i			1.14009i	−0.821613	+	0.570046i	$0.806925\pi$
$152$	−3.33244	+	5.77195i	−0.270296	+	0.468167i
$153$	8.00269	+	13.8611i	0.646979	+	1.12060i
$154$	0.866025	−	0.500000i	0.0697863	−	0.0402911i
$155$	0.0217703			0.00174863
$156$		0			0
$157$	16.2620			1.29785			0.648926	−	0.760851i	$-0.275218\pi$
$157$	16.2620			1.29785			0.648926	+	0.760851i	$0.275218\pi$
$158$	17.0941	−	9.86927i	1.35993	−	0.785157i
$159$	−0.0549581	−	0.0951903i	−0.00435846	−	0.00754908i
$160$	1.23341	−	2.13632i	0.0975093	−	0.168891i
$161$			1.43296i			0.112933i
$162$	9.33963	+	5.39224i	0.733791	+	0.423654i
$163$	10.7098	+	6.18329i	0.838854	+	0.484313i	0.856875	−	0.515525i	$-0.172403\pi$
$163$	10.7098	+	6.18329i	0.838854	+	0.484313i	−0.0180202	+	0.999838i	$0.505736\pi$
$164$		−	4.87800i		−	0.380908i
$165$	−0.400969	+	0.694498i	−0.0312154	+	0.0540666i
$166$	−10.8143	−	18.7309i	−0.839354	−	1.45380i
$167$	−18.5783	+	10.7262i	−1.43763	+	0.830016i	−0.997685	−	0.0680089i	$-0.978335\pi$
$167$	−18.5783	+	10.7262i	−1.43763	+	0.830016i	−0.439945	+	0.898025i	$0.645002\pi$
$168$	0.119605			0.00922772
$169$		0			0
$170$	−6.74094			−0.517006
$171$	−5.60508	+	3.23609i	−0.428631	+	0.247470i
$172$	−1.68114	−	2.91181i	−0.128185	−	0.222024i
$173$	−1.28501	+	2.22571i	−0.0976976	+	0.169217i	−0.910731	−	0.412999i	$-0.864481\pi$
$173$	−1.28501	+	2.22571i	−0.0976976	+	0.169217i	0.813034	+	0.582217i	$0.197814\pi$
$174$		−	1.74764i		−	0.132489i
$175$	−0.171527	−	0.0990311i	−0.0129662	−	0.00748605i
$176$	−10.2103	−	5.89493i	−0.769631	−	0.444347i
$177$			0.770479i			0.0579127i
$178$	−1.90432	+	3.29838i	−0.142735	+	0.247224i
$179$	−7.59903	−	13.1619i	−0.567978	−	0.983767i	−0.996766	−	0.0803618i	$-0.974392\pi$
$179$	−7.59903	−	13.1619i	−0.567978	−	0.983767i	0.428788	−	0.903405i	$-0.358941\pi$
$180$	1.14113	−	0.658834i	0.0850551	−	0.0491066i
$181$	−0.686645			−0.0510379			−0.0255189	−	0.999674i	$-0.508124\pi$
$181$	−0.686645			−0.0510379			−0.0255189	+	0.999674i	$0.508124\pi$
$182$		0			0
$183$	1.10023			0.0813312
$184$	19.1033	−	11.0293i	1.40831	−	0.813091i
$185$	0.746980	+	1.29381i	0.0549190	+	0.0951226i
$186$	0.00268841	−	0.00465646i	0.000197123	−	0.000341428i
$187$		−	21.8877i		−	1.60059i
$188$	0.400537	+	0.231250i	0.0292122	+	0.0168656i
$189$	0.202505	+	0.116917i	0.0147301	+	0.00850443i
$190$		−	2.72587i		−	0.197756i
$191$	−1.73609	+	3.00700i	−0.125619	+	0.217579i	−0.921975	−	0.387250i	$-0.873425\pi$
$191$	−1.73609	+	3.00700i	−0.125619	+	0.217579i	0.796355	+	0.604829i	$0.206758\pi$
$192$	−0.881355	−	1.52655i	−0.0636063	−	0.110169i
$193$	7.62644	−	4.40312i	0.548963	−	0.316944i	−0.199741	−	0.979849i	$-0.564010\pi$
$193$	7.62644	−	4.40312i	0.548963	−	0.316944i	0.748704	+	0.662905i	$0.230677\pi$
$194$	6.26205			0.449589
$195$		0			0
$196$	3.09783			0.221274
$197$	10.6767	−	6.16421i	0.760685	−	0.439182i	−0.0688565	−	0.997627i	$-0.521935\pi$
$197$	10.6767	−	6.16421i	0.760685	−	0.439182i	0.829542	+	0.558445i	$0.188602\pi$
$198$	−7.47434	−	12.9459i	−0.531179	−	0.920028i
$199$	3.24094	−	5.61347i	0.229744	−	0.397928i	−0.727988	−	0.685590i	$-0.759544\pi$
$199$	3.24094	−	5.61347i	0.229744	−	0.397928i	0.957732	+	0.287661i	$0.0928778\pi$
$200$			3.04892i			0.215591i
$201$	−0.972601	−	0.561531i	−0.0686020	−	0.0396074i
$202$	13.9835	+	8.07338i	0.983875	+	0.568041i
$203$			1.40150i			0.0983661i
$204$	0.238250	−	0.412662i	0.0166809	−	0.0288921i
$205$	5.48039	+	9.49231i	0.382767	+	0.662971i
$206$	−14.4772	+	8.35839i	−1.00867	+	0.582356i
$207$	21.4209			1.48885
$208$		0			0
$209$	8.85086			0.612226
$210$	−0.0423637	+	0.0244587i	−0.00292337	+	0.00168781i
$211$	7.30798	+	12.6578i	0.503102	+	0.871398i	0.999994	+	0.00358558i	$0.00114133\pi$
$211$	7.30798	+	12.6578i	0.503102	+	0.871398i	−0.496892	+	0.867813i	$0.665525\pi$
$212$	0.123490	−	0.213891i	0.00848131	−	0.0146901i
$213$			1.88577i			0.129211i
$214$	1.07411	+	0.620137i	0.0734246	+	0.0423917i
$215$	6.54279	+	3.77748i	0.446214	+	0.257622i
$216$		−	3.59956i		−	0.244919i
$217$	−0.00215593	+	0.00373419i	−0.000146354	+	0.000253493i
$218$	12.0368	+	20.8484i	0.815237	+	1.41203i
$219$	−1.98623	+	1.14675i	−0.134217	+	0.0774903i
$220$	−1.80194			−0.121487
$221$		0			0
$222$	0.368977			0.0247641
$223$	22.0528	−	12.7322i	1.47677	−	0.852612i	0.477111	−	0.878843i	$-0.341684\pi$
$223$	22.0528	−	12.7322i	1.47677	−	0.852612i	0.999656	+	0.0262312i	$0.00835060\pi$
$224$	0.244291	+	0.423125i	0.0163224	+	0.0282712i
$225$	−1.48039	+	2.56410i	−0.0986924	+	0.170940i
$226$		−	24.4577i		−	1.62690i
$227$	17.9555	+	10.3666i	1.19175	+	0.688054i	0.958702	−	0.284412i	$-0.0917984\pi$
$227$	17.9555	+	10.3666i	1.19175	+	0.688054i	0.233043	+	0.972466i	$0.425132\pi$
$228$	0.166870	+	0.0963427i	0.0110513	+	0.00638045i
$229$		−	7.28621i		−	0.481486i	−0.970589	−	0.240743i	$-0.922609\pi$
$229$		−	7.28621i		−	0.481486i	0.970589	−	0.240743i	$-0.0773911\pi$
$230$	−4.51089	+	7.81308i	−0.297439	+	0.515179i
$231$	−0.0794168	−	0.137554i	−0.00522524	−	0.00905038i
$232$	18.6839	−	10.7872i	1.22666	−	0.708212i
$233$	6.06638			0.397421			0.198711	−	0.980058i	$-0.436325\pi$
$233$	6.06638			0.397421			0.198711	+	0.980058i	$0.436325\pi$
$234$		0			0
$235$	−1.03923			−0.0677918
$236$	−1.49931	+	0.865625i	−0.0975965	+	0.0563474i
$237$	−1.56757	−	2.71511i	−0.101825	−	0.176366i
$238$	0.667563	−	1.15625i	0.0432717	−	0.0749487i
$239$			12.8213i			0.829342i	0.909971	+	0.414671i	$0.136103\pi$
$239$			12.8213i			0.829342i	−0.909971	+	0.414671i	$0.863897\pi$
$240$	0.499461	+	0.288364i	0.0322401	+	0.0186138i
$241$	4.90966	+	2.83459i	0.316259	+	0.182592i	0.649724	−	0.760170i	$-0.274885\pi$
$241$	4.90966	+	2.83459i	0.316259	+	0.182592i	−0.333465	+	0.942763i	$0.608218\pi$
$242$			6.72587i			0.432356i
$243$	2.62737	−	4.55075i	0.168546	−	0.291931i
$244$	1.23609	+	2.14098i	0.0791328	+	0.137062i
$245$	−6.02820	+	3.48039i	−0.385128	+	0.222354i
$246$	2.70709			0.172598
$247$		0			0
$248$	0.0663757			0.00421486
$249$	−2.97510	+	1.71768i	−0.188540	+	0.108853i
$250$	−0.623490	−	1.07992i	−0.0394330	−	0.0682999i
$251$	7.68210	−	13.3058i	0.484890	−	0.839853i	−0.514960	−	0.857214i	$-0.672193\pi$
$251$	7.68210	−	13.3058i	0.484890	−	0.839853i	0.999849	+	0.0173610i	$0.00552645\pi$
$252$			0.260980i			0.0164402i
$253$	−25.3689	−	14.6468i	−1.59493	−	0.920833i
$254$	10.5429	+	6.08695i	0.661521	+	0.381929i
$255$			1.07069i			0.0670491i
$256$	5.05645	−	8.75803i	0.316028	−	0.547377i
$257$	−8.43296	−	14.6063i	−0.526034	−	0.911117i	−0.999540	−	0.0303266i	$-0.990345\pi$
$257$	−8.43296	−	14.6063i	−0.526034	−	0.911117i	0.473506	−	0.880790i	$-0.342988\pi$
$258$	1.61593	−	0.932960i	0.100604	−	0.0580836i
$259$	−0.295897			−0.0183861
$260$		0			0
$261$	20.9506			1.29681
$262$	−15.7872	+	9.11476i	−0.975338	+	0.563112i
$263$	3.01961	+	5.23013i	0.186197	+	0.322503i	0.943979	−	0.330005i	$-0.107050\pi$
$263$	3.01961	+	5.23013i	0.186197	+	0.322503i	−0.757782	+	0.652508i	$0.773717\pi$
$264$	−1.22252	+	2.11747i	−0.0752410	+	0.130321i
$265$			0.554958i			0.0340908i
$266$	0.467561	+	0.269946i	0.0286680	+	0.0165515i
$267$	0.523894	+	0.302470i	0.0320618	+	0.0185109i
$268$		−	2.52350i		−	0.154147i
$269$	−7.84817	+	13.5934i	−0.478511	+	0.828806i	−0.999696	−	0.0246379i	$-0.992157\pi$
$269$	−7.84817	+	13.5934i	−0.478511	+	0.828806i	0.521185	+	0.853444i	$0.325490\pi$
$270$	0.736094	+	1.27495i	0.0447973	+	0.0775912i
$271$	−13.5369	+	7.81551i	−0.822306	+	0.474758i	−0.851211	−	0.524824i	$-0.824131\pi$
$271$	−13.5369	+	7.81551i	−0.822306	+	0.474758i	0.0289051	+	0.999582i	$0.490798\pi$
$272$	−15.7409			−0.954435
$273$		0			0
$274$	6.91185			0.417560
$275$	3.50647	−	2.02446i	0.211448	−	0.122079i
$276$	−0.318864	−	0.552288i	−0.0191933	−	0.0332438i
$277$	−8.80947	+	15.2585i	−0.529310	+	0.916791i	0.470106	+	0.882610i	$0.344216\pi$
$277$	−8.80947	+	15.2585i	−0.529310	+	0.916791i	−0.999416	+	0.0341814i	$0.989118\pi$
$278$			0.679940i			0.0407801i
$279$	0.0558212	+	0.0322284i	0.00334193	+	0.00192946i
$280$	−0.522971	−	0.301938i	−0.0312535	−	0.0180442i
$281$		−	4.04461i		−	0.241281i	−0.992696	−	0.120640i	$-0.961505\pi$
$281$		−	4.04461i		−	0.241281i	0.992696	−	0.120640i	$-0.0384948\pi$
$282$	−0.128334	+	0.222281i	−0.00764219	+	0.0132367i
$283$	−8.37047	−	14.4981i	−0.497573	−	0.861821i	0.502423	−	0.864622i	$-0.332442\pi$
$283$	−8.37047	−	14.4981i	−0.497573	−	0.861821i	−0.999996	+	0.00280047i	$0.999109\pi$
$284$	−3.66960	+	2.11865i	−0.217751	+	0.125718i
$285$	−0.432960			−0.0256464
$286$		0			0
$287$	−2.17092			−0.128145
$288$	6.32516	−	3.65183i	0.372714	−	0.215186i
$289$	−6.11141	−	10.5853i	−0.359495	−	0.622663i
$290$	−4.41185	+	7.64156i	−0.259073	+	0.448728i
$291$		−	0.994623i		−	0.0583058i
$292$	−4.46302	−	2.57673i	−0.261179	−	0.150792i
$293$	7.51239	+	4.33728i	0.438879	+	0.253387i	0.703122	−	0.711069i	$-0.251789\pi$
$293$	7.51239	+	4.33728i	0.438879	+	0.253387i	−0.264243	+	0.964456i	$0.585122\pi$
$294$			1.71917i			0.100264i
$295$	1.94504	−	3.36891i	0.113245	−	0.196146i
$296$	2.27748	+	3.94471i	0.132376	+	0.229282i
$297$	−4.13975	+	2.39008i	−0.240212	+	0.138687i
$298$	0.957787			0.0554831
$299$		0			0
$300$	0.0881460			0.00508911
$301$	−1.29588	+	0.748176i	−0.0746932	+	0.0431242i
$302$	−8.73490	−	15.1293i	−0.502637	−	0.870593i
$303$	1.28232	−	2.22105i	0.0736676	−	0.127596i
$304$		−	6.36526i		−	0.365073i
$305$	−4.81073	−	2.77748i	−0.275462	−	0.159038i
$306$	−17.2845	−	9.97919i	−0.988087	−	0.570472i
$307$		−	15.6069i		−	0.890731i	−0.895349	−	0.445365i	$-0.853074\pi$
$307$		−	15.6069i		−	0.890731i	0.895349	−	0.445365i	$-0.146926\pi$
$308$	0.178448	−	0.309081i	0.0101680	−	0.0176115i
$309$	1.32759	+	2.29946i	0.0755241	+	0.130812i
$310$	−0.0235101	+	0.0135735i	−0.00133528	+	0.000770925i
$311$	−22.0965			−1.25298			−0.626489	−	0.779430i	$-0.715509\pi$
$311$	−22.0965			−1.25298			−0.626489	+	0.779430i	$0.715509\pi$
$312$		0			0
$313$	−19.6015			−1.10794			−0.553971	−	0.832536i	$-0.686888\pi$
$313$	−19.6015			−1.10794			−0.553971	+	0.832536i	$0.686888\pi$
$314$	−17.5616	+	10.1392i	−0.991061	+	0.572189i
$315$	−0.293209	−	0.507852i	−0.0165204	−	0.0286142i
$316$	3.52230	−	6.10081i	0.198145	−	0.343197i
$317$			13.2470i			0.744024i	0.928228	+	0.372012i	$0.121332\pi$
$317$			13.2470i			0.744024i	−0.928228	+	0.372012i	$0.878668\pi$
$318$	0.118700	+	0.0685317i	0.00665638	+	0.00384307i
$319$	−24.8120	−	14.3252i	−1.38920	−	0.802057i
$320$			8.89977i			0.497512i
$321$	0.0984987	−	0.170605i	0.00549766	−	0.00952222i
$322$	−0.893436	−	1.54748i	−0.0497892	−	0.0862375i
$323$	10.2338	−	5.90850i	0.569425	−	0.328758i
$324$	3.84894			0.213830
$325$		0			0
$326$	−15.4209			−0.854083
$327$	3.31143	−	1.91185i	0.183122	−	0.105726i
$328$	16.7092	+	28.9413i	0.922614	+	1.59801i
$329$	0.102916	−	0.178256i	0.00567394	−	0.00982756i
$330$		−	1.00000i		−	0.0550482i
$331$	10.5760	+	6.10603i	0.581307	+	0.335618i	0.761653	−	0.647985i	$-0.224388\pi$
$331$	10.5760	+	6.10603i	0.581307	+	0.335618i	−0.180346	+	0.983603i	$0.557722\pi$
$332$	−6.68500	−	3.85958i	−0.366887	−	0.211822i
$333$			4.42327i			0.242394i
$334$	13.3753	−	23.1667i	0.731865	−	1.26763i
$335$	2.83513	+	4.91058i	0.154899	+	0.268294i
$336$	−0.0989245	+	0.0571141i	−0.00539677	+	0.00311583i
$337$	−5.59611			−0.304839			−0.152420	−	0.988316i	$-0.548707\pi$
$337$	−5.59611			−0.304839			−0.152420	+	0.988316i	$0.548707\pi$
$338$		0			0
$339$	−3.88471			−0.210988
$340$	−2.08350	+	1.20291i	−0.112993	+	0.0652368i
$341$	−0.0440730	−	0.0763367i	−0.00238669	−	0.00413386i
$342$	4.03534	−	6.98942i	0.218206	−	0.377945i
$343$		−	2.76510i		−	0.149301i
$344$	19.9484	+	11.5172i	1.07555	+	0.620967i
$345$	1.24098	+	0.716480i	0.0668121	+	0.0385740i
$346$		−	3.20477i		−	0.172289i
$347$	10.4324	−	18.0695i	0.560042	−	0.970021i	−0.437450	−	0.899243i	$-0.644118\pi$
$347$	10.4324	−	18.0695i	0.560042	−	0.970021i	0.997492	−	0.0707786i	$-0.0225484\pi$
$348$	−0.311863	−	0.540163i	−0.0167176	−	0.0289558i
$349$	15.2491	−	8.80409i	0.816268	−	0.471272i	−0.0328601	−	0.999460i	$-0.510462\pi$
$349$	15.2491	−	8.80409i	0.816268	−	0.471272i	0.849128	+	0.528188i	$0.177128\pi$
$350$	0.246980			0.0132016
$351$		0			0
$352$	−9.98792			−0.532358
$353$	−22.7802	+	13.1521i	−1.21247	+	0.700017i	−0.963296	−	0.268443i	$-0.913491\pi$
$353$	−22.7802	+	13.1521i	−1.21247	+	0.700017i	−0.249170	+	0.968460i	$0.580158\pi$
$354$	−0.480386	−	0.832052i	−0.0255322	−	0.0442231i
$355$	4.76055	−	8.24552i	0.252664	−	0.437627i
$356$			1.35929i			0.0720422i
$357$	−0.183652	−	0.106031i	−0.00971988	−	0.00561178i
$358$	16.4126	+	9.47584i	0.867434	+	0.500814i
$359$			10.9685i			0.578897i	0.957194	+	0.289449i	$0.0934720\pi$
$359$			10.9685i			0.578897i	−0.957194	+	0.289449i	$0.906528\pi$
$360$	−4.51357	+	7.81774i	−0.237886	+	0.412031i
$361$	−7.11074	−	12.3162i	−0.374250	−	0.648219i
$362$	0.741519	−	0.428116i	0.0389734	−	0.0225013i
$363$	1.06829			0.0560709
$364$		0			0
$365$	11.5797			0.606110
$366$	−1.18815	+	0.685981i	−0.0621058	+	0.0358568i
$367$	16.1347	+	27.9461i	0.842223	+	1.45877i	0.888011	+	0.459822i	$0.152087\pi$
$367$	16.1347	+	27.9461i	0.842223	+	1.45877i	−0.0457883	+	0.998951i	$0.514580\pi$
$368$	−10.5335	+	18.2445i	−0.549096	+	0.951062i
$369$			32.4523i			1.68940i
$370$	−1.61335	−	0.931468i	−0.0838741	−	0.0484247i
$371$	−0.0951903	−	0.0549581i	−0.00494203	−	0.00285328i
$372$		−	0.00191896i		−	9.94935e-5i
$373$	−3.44169	+	5.96118i	−0.178204	+	0.308658i	−0.941265	−	0.337668i	$-0.890362\pi$
$373$	−3.44169	+	5.96118i	−0.178204	+	0.308658i	0.763061	+	0.646326i	$0.223695\pi$
$374$	13.6468	+	23.6369i	0.705657	+	1.22223i
$375$	−0.171527	+	0.0990311i	−0.00885761	+	0.00511395i
$376$	−3.16852			−0.163404
$377$		0			0
$378$	−0.291585			−0.0149975
$379$	−10.6334	+	6.13922i	−0.546203	+	0.315351i	−0.747589	−	0.664161i	$-0.768789\pi$
$379$	−10.6334	+	6.13922i	−0.546203	+	0.315351i	0.201386	+	0.979512i	$0.435455\pi$
$380$	−0.486426	−	0.842515i	−0.0249532	−	0.0432201i
$381$	0.966812	−	1.67457i	0.0495313	−	0.0857907i
$382$		−	4.32975i		−	0.221529i
$383$	−7.30316	−	4.21648i	−0.373174	−	0.215452i	0.301670	−	0.953412i	$-0.402456\pi$
$383$	−7.30316	−	4.21648i	−0.373174	−	0.215452i	−0.674844	+	0.737960i	$0.735789\pi$
$384$	1.05733	+	0.610449i	0.0539566	+	0.0311518i
$385$			0.801938i			0.0408705i
$386$	−5.49061	+	9.51001i	−0.279465	+	0.484047i
$387$	11.1843	+	19.3717i	0.568527	+	0.984718i
$388$	1.93548	−	1.11745i	0.0982590	−	0.0567299i
$389$	20.4198			1.03533			0.517663	−	0.855585i	$-0.326802\pi$
$389$	20.4198			1.03533			0.517663	+	0.855585i	$0.326802\pi$
$390$		0			0
$391$	−39.1105			−1.97790
$392$	−18.3795	+	10.6114i	−0.928305	+	0.535957i
$393$	1.44773	+	2.50754i	0.0730283	+	0.126489i
$394$	−7.68664	+	13.3137i	−0.387248	+	0.670732i
$395$			15.8291i			0.796448i
$396$	−4.62035	−	2.66756i	−0.232182	−	0.134050i
$397$	−16.1454	−	9.32155i	−0.810314	−	0.467835i	0.0367506	−	0.999324i	$-0.488299\pi$
$397$	−16.1454	−	9.32155i	−0.810314	−	0.467835i	−0.847065	+	0.531489i	$0.821633\pi$
$398$			8.08277i			0.405153i
$399$	0.0428765	−	0.0742644i	0.00214651	−	0.00371787i
$400$	−1.45593	−	2.52174i	−0.0727963	−	0.126087i
$401$	26.8322	−	15.4916i	1.33994	−	0.773612i	0.353138	−	0.935571i	$-0.385115\pi$
$401$	26.8322	−	15.4916i	1.33994	−	0.773612i	0.986797	+	0.161959i	$0.0517814\pi$
$402$	1.40044			0.0698474
$403$		0			0
$404$	5.76271			0.286705
$405$	−7.48980	+	4.32424i	−0.372171	+	0.214873i
$406$	−0.873822	−	1.51350i	−0.0433670	−	0.0751139i
$407$	3.02446	−	5.23852i	0.149917	−	0.259664i
$408$			3.26444i			0.161614i
$409$	−20.6177	−	11.9037i	−1.01948	−	0.588598i	−0.105528	−	0.994416i	$-0.533653\pi$
$409$	−20.6177	−	11.9037i	−1.01948	−	0.588598i	−0.913954	+	0.405818i	$0.866987\pi$
$410$	−11.8367	−	6.83393i	−0.584574	−	0.337504i
$411$		−	1.09783i		−	0.0541522i
$412$	−2.98307	+	5.16684i	−0.146966	+	0.254552i
$413$	0.385239	+	0.667254i	0.0189564	+	0.0328334i
$414$	−23.1327	+	13.3557i	−1.13691	+	0.656397i
$415$	17.3448			0.851423
$416$		0			0
$417$	0.107997			0.00528865
$418$	−9.55818	+	5.51842i	−0.467506	+	0.269915i
$419$	−6.05765	−	10.4922i	−0.295935	−	0.512575i	0.679267	−	0.733892i	$-0.262298\pi$
$419$	−6.05765	−	10.4922i	−0.295935	−	0.512575i	−0.975202	+	0.221316i	$0.928965\pi$
$420$	−0.00872920	+	0.0151194i	−0.000425941	+	0.000737752i
$421$			11.2537i			0.548471i	0.961663	+	0.274236i	$0.0884248\pi$
$421$			11.2537i			0.548471i	−0.961663	+	0.274236i	$0.911575\pi$
$422$	−15.7840	−	9.11290i	−0.768353	−	0.443609i
$423$	−2.66469	−	1.53846i	−0.129562	−	0.0748024i
$424$			1.69202i			0.0821718i
$425$	2.70291	−	4.68157i	0.131110	−	0.227090i
$426$	−1.17576	−	2.03648i	−0.0569657	−	0.0986675i
$427$	0.952825	−	0.550114i	0.0461104	−	0.0266219i
$428$	0.442649			0.0213962
$429$		0			0
$430$	−9.42088			−0.454315
$431$	−15.0320	+	8.67874i	−0.724067	+	0.418040i	−0.816248	−	0.577702i	$-0.803950\pi$
$431$	−15.0320	+	8.67874i	−0.724067	+	0.418040i	0.0921807	+	0.995742i	$0.470616\pi$
$432$	1.71887	+	2.97718i	0.0826993	+	0.143239i
$433$	−3.58695	+	6.21278i	−0.172378	+	0.298567i	−0.939251	−	0.343232i	$-0.888478\pi$
$433$	−3.58695	+	6.21278i	−0.172378	+	0.298567i	0.766873	+	0.641799i	$0.221812\pi$
$434$		−	0.00537681i		−	0.000258095i
$435$	1.21374	+	0.700751i	0.0581942	+	0.0335984i
$436$	7.44071	+	4.29590i	0.356345	+	0.205736i
$437$		−	15.8153i		−	0.756551i
$438$	1.42998	−	2.47679i	0.0683269	−	0.118346i
$439$	5.16033	+	8.93795i	0.246289	+	0.426585i	0.962493	−	0.271306i	$-0.0874555\pi$
$439$	5.16033	+	8.93795i	0.246289	+	0.426585i	−0.716204	+	0.697891i	$0.754122\pi$
$440$	10.6909	−	6.17241i	0.509670	−	0.294258i
$441$	−20.6093			−0.981393
$442$		0			0
$443$	−30.2271			−1.43613			−0.718067	−	0.695974i	$-0.754973\pi$
$443$	−30.2271			−1.43613			−0.718067	+	0.695974i	$0.754973\pi$
$444$	0.114044	−	0.0658433i	0.00541228	−	0.00312478i
$445$	−1.52715	−	2.64510i	−0.0723937	−	0.125390i
$446$	−15.8768	+	27.4994i	−0.751789	+	1.30214i
$447$		−	0.152129i		−	0.00719545i
$448$	−1.52655	−	0.881355i	−0.0721227	−	0.0416401i
$449$	−21.3914	−	12.3503i	−1.00952	−	0.582848i	−0.0984703	−	0.995140i	$-0.531395\pi$
$449$	−21.3914	−	12.3503i	−1.00952	−	0.582848i	−0.911052	+	0.412292i	$0.864728\pi$
$450$		−	3.69202i		−	0.174044i
$451$	22.1896	−	38.4336i	1.04487	−	1.80977i
$452$	−4.36443	−	7.55941i	−0.205285	−	0.355565i
$453$	−2.40304	+	1.38740i	−0.112905	+	0.0651855i
$454$	−25.8538			−1.21338
$455$		0			0
$456$	−1.32006			−0.0618175
$457$	13.1808	−	7.60992i	0.616570	−	0.355977i	−0.158962	−	0.987285i	$-0.550815\pi$
$457$	13.1808	−	7.60992i	0.616570	−	0.355977i	0.775532	+	0.631308i	$0.217482\pi$
$458$	4.54288	+	7.86849i	0.212275	+	0.367671i
$459$	−3.19106	+	5.52708i	−0.148946	+	0.257982i
$460$			3.21983i			0.150125i
$461$	−10.2187	−	5.89977i	−0.475933	−	0.274780i	0.242787	−	0.970080i	$-0.421938\pi$
$461$	−10.2187	−	5.89977i	−0.475933	−	0.274780i	−0.718720	+	0.695300i	$0.755272\pi$
$462$	0.171527	+	0.0990311i	0.00798016	+	0.00460735i
$463$		−	13.2325i		−	0.614967i	−0.951553	−	0.307483i	$-0.900513\pi$
$463$		−	13.2325i		−	0.614967i	0.951553	−	0.307483i	$-0.0994868\pi$
$464$	−10.3022	+	17.8440i	−0.478269	+	0.828387i
$465$	0.00215593	+	0.00373419i	9.99790e−5	+	0.000173169i
$466$	−6.55118	+	3.78232i	−0.303477	+	0.175213i
$467$	8.01507			0.370893			0.185446	−	0.982654i	$-0.440627\pi$
$467$	8.01507			0.370893			0.185446	+	0.982654i	$0.440627\pi$
$468$		0			0
$469$	−1.12306			−0.0518582
$470$	1.12228	−	0.647948i	0.0517669	−	0.0298876i
$471$	1.61045	+	2.78938i	0.0742056	+	0.128528i
$472$	5.93027	−	10.2715i	0.272963	−	0.472786i
$473$		−	30.5894i		−	1.40650i
$474$	3.38569	+	1.95473i	0.155510	+	0.0897837i
$475$	1.89311	+	1.09299i	0.0868621	+	0.0501498i
$476$		−	0.476501i		−	0.0218404i
$477$	−0.821552	+	1.42297i	−0.0376163	+	0.0651533i
$478$	−7.99396	−	13.8459i	−0.365635	−	0.633299i
$479$	−5.82736	+	3.36443i	−0.266259	+	0.153725i	−0.627186	−	0.778869i	$-0.715794\pi$
$479$	−5.82736	+	3.36443i	−0.266259	+	0.153725i	0.360927	+	0.932594i	$0.382460\pi$
$480$	0.488582			0.0223006
$481$		0			0
$482$	−7.06936			−0.322001
$483$	−0.245791	+	0.141908i	−0.0111839	+	0.00645702i
$484$	1.20022	+	2.07884i	0.0545554	+	0.0944927i
$485$	−2.51089	+	4.34898i	−0.114013	+	0.197477i
$486$			6.55257i			0.297230i
$487$	−8.03278	−	4.63773i	−0.364000	−	0.210155i	0.306834	−	0.951763i	$-0.400730\pi$
$487$	−8.03278	−	4.63773i	−0.364000	−	0.210155i	−0.670834	+	0.741608i	$0.734064\pi$
$488$	−14.6675	−	8.46830i	−0.663968	−	0.383342i
$489$			2.44935i			0.110764i
$490$	4.33997	−	7.51705i	0.196060	−	0.339586i
$491$	3.97315	+	6.88169i	0.179306	+	0.310567i	0.941643	−	0.336613i	$-0.109282\pi$
$491$	3.97315	+	6.88169i	0.179306	+	0.310567i	−0.762337	+	0.647180i	$0.775948\pi$
$492$	0.836709	−	0.483074i	0.0377217	−	0.0217787i
$493$	−38.2519			−1.72278
$494$		0			0
$495$	11.9879			0.538817
$496$	−0.0548989	+	0.0316959i	−0.00246503	+	0.00142319i
$497$	0.942886	+	1.63313i	0.0422942	+	0.0732557i
$498$	2.14191	−	3.70989i	0.0959812	−	0.166244i
$499$			22.0291i			0.986156i	0.869985	+	0.493078i	$0.164128\pi$
$499$			22.0291i			0.986156i	−0.869985	+	0.493078i	$0.835872\pi$
$500$	−0.385418	−	0.222521i	−0.0172364	−	0.00995144i
$501$	−3.67965	−	2.12445i	−0.164395	−	0.0949134i
$502$			19.1588i			0.855101i
$503$	13.1347	−	22.7499i	0.585646	−	1.01437i	−0.409149	−	0.912468i	$-0.634174\pi$
$503$	13.1347	−	22.7499i	0.585646	−	1.01437i	0.994795	−	0.101901i	$-0.0324924\pi$
$504$	−0.893969	−	1.54840i	−0.0398205	−	0.0689712i
$505$	−11.2139	+	6.47434i	−0.499012	+	0.288105i
$506$	36.5284			1.62389
$507$		0			0
$508$	4.34481			0.192770
$509$	−30.7252	+	17.7392i	−1.36187	+	0.786277i	−0.989873	−	0.141957i	$-0.954661\pi$
$509$	−30.7252	+	17.7392i	−1.36187	+	0.786277i	−0.371998	+	0.928233i	$0.621327\pi$
$510$	−0.667563	−	1.15625i	−0.0295602	−	0.0511997i
$511$	−1.14675	+	1.98623i	−0.0507293	+	0.0878658i
$512$			24.9390i			1.10216i
$513$	−2.23502	−	1.29039i	−0.0986785	−	0.0569720i
$514$	18.2138	+	10.5157i	0.803375	+	0.463829i
$515$		−	13.4058i		−	0.590731i
$516$	0.332970	−	0.576720i	0.0146582	−	0.0253887i
$517$	2.10388	+	3.64402i	0.0925283	+	0.160264i
$518$	0.319544	−	0.184489i	0.0140400	−	0.00810597i
$519$	−0.509025			−0.0223437
$520$		0			0
$521$	30.2295			1.32438			0.662190	−	0.749336i	$-0.269627\pi$
$521$	30.2295			1.32438			0.662190	+	0.749336i	$0.269627\pi$
$522$	−22.6249	+	13.0625i	−0.990265	+	0.571730i
$523$	−1.11596	−	1.93289i	−0.0487974	−	0.0845196i	0.840595	−	0.541664i	$-0.182206\pi$
$523$	−1.11596	−	1.93289i	−0.0487974	−	0.0845196i	−0.889392	+	0.457145i	$0.848872\pi$
$524$	−3.25302	+	5.63440i	−0.142109	+	0.246140i
$525$		−	0.0392287i		−	0.00171208i
$526$	−6.52186	−	3.76540i	−0.284367	−	0.164179i
$527$	−0.101919	−	0.0588430i	−0.00443966	−	0.00256324i
$528$		−	2.33513i		−	0.101623i
$529$	−14.6719	+	25.4124i	−0.637908	+	1.10489i
$530$	−0.346011	−	0.599308i	−0.0150297	−	0.0260323i
$531$	9.97458	−	5.75882i	0.432860	−	0.249912i
$532$	0.192685			0.00835397
$533$		0			0
$534$	−0.754348			−0.0326438
$535$	−0.861369	+	0.497312i	−0.0372402	+	0.0215007i
$536$	8.64406	+	14.9720i	0.373367	+	0.646690i
$537$	1.50508	−	2.60688i	0.0649491	−	0.112495i
$538$		−	19.5730i		−	0.843852i
$539$	24.4077	+	14.0918i	1.05131	+	0.606977i
$540$	0.455025	+	0.262709i	0.0195812	+	0.0113052i
$541$		−	17.4306i		−	0.749399i	−0.927146	−	0.374699i	$-0.877746\pi$
$541$		−	17.4306i		−	0.749399i	0.927146	−	0.374699i	$-0.122254\pi$
$542$	9.74578	−	16.8802i	0.418617	−	0.725066i
$543$	−0.0679992	−	0.117778i	−0.00291812	−	0.00505434i
$544$	−11.5486	+	6.66756i	−0.495140	+	0.285869i
$545$	−19.3056			−0.826960
$546$		0			0
$547$	2.65578			0.113553			0.0567764	−	0.998387i	$-0.481918\pi$
$547$	2.65578			0.113553			0.0567764	+	0.998387i	$0.481918\pi$
$548$	2.13632	−	1.23341i	0.0912592	−	0.0526885i
$549$	−8.22348	−	14.2435i	−0.350970	−	0.607897i
$550$	−2.52446	+	4.37249i	−0.107643	+	0.186444i
$551$		−	15.4681i		−	0.658965i
$552$	3.78365	+	2.18449i	0.161043	+	0.0929780i
$553$	−2.71511	−	1.56757i	−0.115458	−	0.0666600i
$554$		−	21.9705i		−	0.933435i
$555$	−0.147948	+	0.256254i	−0.00628006	+	0.0108774i
$556$	0.121334	+	0.210156i	0.00514570	+	0.00891262i
$557$	−26.3746	+	15.2274i	−1.11753	+	0.645204i	−0.940768	−	0.339050i	$-0.889894\pi$
$557$	−26.3746	+	15.2274i	−1.11753	+	0.645204i	−0.176758	+	0.984254i	$0.556561\pi$
$558$	−0.0803763			−0.00340260
$559$		0			0
$560$	0.576728			0.0243712
$561$	3.75433	−	2.16756i	0.158508	−	0.0915146i
$562$	2.52177	+	4.36783i	0.106374	+	0.184246i
$563$	18.9085	−	32.7505i	0.796898	−	1.38027i	−0.124728	−	0.992191i	$-0.539806\pi$
$563$	18.9085	−	32.7505i	0.796898	−	1.38027i	0.921627	−	0.388077i	$-0.126861\pi$
$564$			0.0916038i			0.00385722i
$565$	16.9858	+	9.80678i	0.714600	+	0.412574i
$566$	18.0788	+	10.4378i	0.759909	+	0.438734i
$567$		−	1.71294i		−	0.0719366i
$568$	14.5145	−	25.1399i	0.609016	−	1.05485i
$569$	10.6860	+	18.5087i	0.447980	+	0.775923i	0.998254	−	0.0590602i	$-0.0188104\pi$
$569$	10.6860	+	18.5087i	0.447980	+	0.775923i	−0.550275	+	0.834984i	$0.685477\pi$
$570$	0.467561	−	0.269946i	0.0195840	−	0.0113068i
$571$	18.8412			0.788478			0.394239	−	0.919008i	$-0.371008\pi$
$571$	18.8412			0.788478			0.394239	+	0.919008i	$0.371008\pi$
$572$		0			0
$573$	−0.687710			−0.0287295
$574$	2.34441	−	1.35354i	0.0978536	−	0.0564958i
$575$	−3.61745	−	6.26561i	−0.150858	−	0.261294i
$576$	−13.1751	+	22.8199i	−0.548962	+	0.950831i
$577$		−	37.6407i		−	1.56700i	−0.621390	−	0.783502i	$-0.713432\pi$
$577$		−	37.6407i		−	1.56700i	0.621390	−	0.783502i	$-0.286568\pi$
$578$	13.1996	+	7.62080i	0.549032	+	0.316984i
$579$	1.51051	+	0.872093i	0.0627746	+	0.0362429i
$580$			3.14914i			0.130761i
$581$	−1.71768	+	2.97510i	−0.0712612	+	0.123428i
$582$	0.620137	+	1.07411i	0.0257055	+	0.0445233i
$583$	1.94594	−	1.12349i	0.0805927	−	0.0465302i
$584$	35.3056			1.46096
$585$		0			0
$586$	−10.8170			−0.446846
$587$	34.6087	−	19.9813i	1.42845	−	0.824718i	0.431455	−	0.902134i	$-0.358000\pi$
$587$	34.6087	−	19.9813i	1.42845	−	0.824718i	0.996999	+	0.0774160i	$0.0246669\pi$
$588$	0.306782	+	0.531362i	0.0126515	+	0.0219130i
$589$	0.0237947	−	0.0412136i	0.000980443	−	0.00169818i
$590$			4.85086i			0.199707i
$591$	2.11466	+	1.22090i	0.0869853	+	0.0502210i
$592$	−3.76738	−	2.17510i	−0.154838	−	0.0893959i
$593$		−	28.0116i		−	1.15030i	−0.818048	−	0.575149i	$-0.804944\pi$
$593$		−	28.0116i		−	1.15030i	0.818048	−	0.575149i	$-0.195056\pi$
$594$	2.98039	−	5.16218i	0.122287	−	0.211807i
$595$	0.535344	+	0.927243i	0.0219470	+	0.0380132i
$596$	0.296034	−	0.170915i	0.0121260	−	0.00700096i
$597$	1.28382			0.0525431
$598$		0			0
$599$	−5.40880			−0.220997			−0.110499	−	0.993876i	$-0.535245\pi$
$599$	−5.40880			−0.220997			−0.110499	+	0.993876i	$0.535245\pi$
$600$	−0.522971	+	0.301938i	−0.0213502	+	0.0123266i
$601$	13.6631	+	23.6653i	0.557331	+	0.965326i	0.997718	+	0.0675180i	$0.0215080\pi$
$601$	13.6631	+	23.6653i	0.557331	+	0.965326i	−0.440387	+	0.897808i	$0.645159\pi$
$602$	0.932960	−	1.61593i	0.0380246	−	0.0658606i
$603$			16.7883i			0.683673i
$604$	−5.39958	−	3.11745i	−0.219706	−	0.126847i
$605$	−4.67111	−	2.69687i	−0.189908	−	0.109643i
$606$			3.19806i			0.129912i
$607$	−13.9046	+	24.0835i	−0.564371	+	0.977519i	0.432737	+	0.901520i	$0.357548\pi$
$607$	−13.9046	+	24.0835i	−0.564371	+	0.977519i	−0.997108	+	0.0759990i	$0.975785\pi$
$608$	−2.69620	−	4.66996i	−0.109345	−	0.189392i
$609$	−0.240395	+	0.138792i	−0.00974131	+	0.00562415i
$610$	6.92692			0.280463
$611$		0			0
$612$	−7.12306			−0.287933
$613$	10.0263	−	5.78866i	0.404957	−	0.233802i	−0.283664	−	0.958924i	$-0.591550\pi$
$613$	10.0263	−	5.78866i	0.404957	−	0.233802i	0.688620	+	0.725122i	$0.258217\pi$
$614$	9.73072	+	16.8541i	0.392700	+	0.680176i
$615$	−1.08546	+	1.88007i	−0.0437699	+	0.0758116i
$616$			2.44504i			0.0985135i
$617$	−21.4074	−	12.3596i	−0.861831	−	0.497578i	0.00279428	−	0.999996i	$-0.499111\pi$
$617$	−21.4074	−	12.3596i	−0.861831	−	0.497578i	−0.864625	+	0.502418i	$0.832444\pi$
$618$	−2.86738	−	1.65548i	−0.115343	−	0.0665932i
$619$			10.4983i			0.421961i	0.977490	+	0.210981i	$0.0676657\pi$
$619$			10.4983i			0.421961i	−0.977490	+	0.210981i	$0.932334\pi$
$620$	−0.00484434	+	0.00839064i	−0.000194553	+	0.000336976i
$621$	4.27077	+	7.39720i	0.171380	+	0.296839i
$622$	23.8624	−	13.7769i	0.956794	−	0.552405i
$623$	0.604940			0.0242364
$624$		0			0
$625$	1.00000			0.0400000
$626$	21.1680	−	12.2213i	0.846042	−	0.488462i
$627$	0.876510	+	1.51816i	0.0350044	+	0.0606295i
$628$	−3.61865	+	6.26768i	−0.144400	+	0.250108i
$629$		−	8.07606i		−	0.322014i
$630$	0.633281	+	0.365625i	0.0252305	+	0.0145669i
$631$	29.3690	+	16.9562i	1.16916	+	0.675017i	0.953483	−	0.301447i	$-0.0974698\pi$
$631$	29.3690	+	16.9562i	1.16916	+	0.675017i	0.215680	+	0.976464i	$0.430803\pi$
$632$			48.2616i			1.91974i
$633$	−1.44743	+	2.50703i	−0.0575304	+	0.0996455i
$634$	−8.25936	−	14.3056i	−0.328021	−	0.568149i
$635$	−8.45475	+	4.88135i	−0.335517	+	0.193711i
$636$	0.0489173			0.00193970
$637$		0			0
$638$	35.7265			1.41442
$639$	24.4131	−	14.0949i	0.965767	−	0.557586i
$640$	−3.08211	−	5.33836i	−0.121831	−	0.211017i
$641$	5.90850	−	10.2338i	0.233372	−	0.404212i	−0.725426	−	0.688300i	$-0.758357\pi$
$641$	5.90850	−	10.2338i	0.233372	−	0.404212i	0.958798	+	0.284088i	$0.0916908\pi$
$642$			0.245652i			0.00969510i
$643$	23.1008	+	13.3373i	0.911009	+	0.525971i	0.880756	−	0.473571i	$-0.157035\pi$
$643$	23.1008	+	13.3373i	0.911009	+	0.525971i	0.0302530	+	0.999542i	$0.490369\pi$
$644$	−0.552288	−	0.318864i	−0.0217632	−	0.0125650i
$645$			1.49635i			0.0589188i
$646$	−7.36778	+	12.7614i	−0.289881	+	0.502089i
$647$	16.3242	+	28.2744i	0.641772	+	1.11158i	0.985037	+	0.172343i	$0.0551338\pi$
$647$	16.3242	+	28.2744i	0.641772	+	1.11158i	−0.343265	+	0.939239i	$0.611533\pi$
$648$	−22.8358	+	13.1843i	−0.897075	+	0.517926i
$649$	−15.7506			−0.618266
$650$		0			0
$651$	−0.000854018	0		−3.34716e−5	0
$652$	−4.76630	+	2.75182i	−0.186663	+	0.107770i
$653$	−2.03468	−	3.52417i	−0.0796232	−	0.137911i	0.823464	−	0.567368i	$-0.192038\pi$
$653$	−2.03468	−	3.52417i	−0.0796232	−	0.137911i	−0.903087	+	0.429457i	$0.858705\pi$
$654$	−2.38404	+	4.12928i	−0.0932235	+	0.161468i
$655$		−	14.6189i		−	0.571209i
$656$	−27.6402	−	15.9581i	−1.07917	−	0.623058i
$657$	29.6916	+	17.1424i	1.15838	+	0.668790i
$658$			0.256668i			0.0100060i
$659$	10.9955	−	19.0447i	0.428322	−	0.741875i	−0.568402	−	0.822751i	$-0.692438\pi$
$659$	10.9955	−	19.0447i	0.428322	−	0.741875i	0.996724	+	0.0808754i	$0.0257716\pi$
$660$	−0.178448	−	0.309081i	−0.00694608	−	0.0120310i
$661$	10.2678	−	5.92812i	0.399371	−	0.230577i	−0.286842	−	0.957978i	$-0.592605\pi$
$661$	10.2678	−	5.92812i	0.399371	−	0.230577i	0.686213	+	0.727401i	$0.259272\pi$
$662$	−15.2282			−0.591861
$663$		0			0
$664$	52.8829			2.05225
$665$	−0.374955	+	0.216480i	−0.0145401	+	0.00839474i
$666$	−2.75786	−	4.77676i	−0.106865	−	0.185096i
$667$	−25.5973	+	44.3358i	−0.991131	+	1.71669i
$668$		−	9.54719i		−	0.369392i
$669$	4.36783	+	2.52177i	0.168870	+	0.0974973i
$670$	−6.12340	−	3.53534i	−0.236567	−	0.136582i
$671$			22.4916i			0.868277i
$672$	−0.0483849	+	0.0838050i	−0.00186649	+	0.00323285i
$673$	−12.0972	−	20.9529i	−0.466312	−	0.807675i	0.532948	−	0.846148i	$-0.321084\pi$
$673$	−12.0972	−	20.9529i	−0.466312	−	0.807675i	−0.999260	+	0.0384725i	$0.987751\pi$
$674$	6.04332	−	3.48911i	0.232780	−	0.134396i
$675$	−1.18060			−0.0454415
$676$		0			0
$677$	25.3806			0.975455			0.487728	−	0.872996i	$-0.337826\pi$
$677$	25.3806			0.975455			0.487728	+	0.872996i	$0.337826\pi$
$678$	4.19516	−	2.42208i	0.161114	−	0.0930192i
$679$	−0.497312	−	0.861369i	−0.0190851	−	0.0330563i
$680$	8.24094	−	14.2737i	0.316026	−	0.547372i
$681$			4.10646i			0.157360i
$682$	0.0951903	+	0.0549581i	0.00364502	+	0.00210446i
$683$	−16.6919	−	9.63706i	−0.638697	−	0.368752i	0.145415	−	0.989371i	$-0.453548\pi$
$683$	−16.6919	−	9.63706i	−0.638697	−	0.368752i	−0.784112	+	0.620619i	$0.786881\pi$
$684$		−	2.88040i		−	0.110135i
$685$	−2.77144	+	4.80027i	−0.105891	+	0.183409i
$686$	1.72401	+	2.98608i	0.0658231	+	0.114009i
$687$	1.24978	−	0.721561i	0.0476821	−	0.0275293i
$688$	−21.9989			−0.838702
$689$		0			0
$690$	−1.78687			−0.0680251
$691$	29.2759	−	16.9025i	1.11371	−	0.643000i	0.173921	−	0.984760i	$-0.444356\pi$
$691$	29.2759	−	16.9025i	1.11371	−	0.643000i	0.939787	+	0.341760i	$0.111023\pi$
$692$	−0.571884	−	0.990532i	−0.0217398	−	0.0376544i
$693$	−1.18718	+	2.05625i	−0.0450971	+	0.0781105i
$694$			26.0180i			0.987632i
$695$	−0.472217	−	0.272635i	−0.0179122	−	0.0103416i
$696$	3.70058	+	2.13653i	0.140270	+	0.0809850i
$697$		−	59.2519i		−	2.24433i
$698$	−10.9785	+	19.0154i	−0.415543	+	0.719742i
$699$	0.600760	+	1.04055i	0.0227228	+	0.0393571i
$700$	0.0763367	−	0.0440730i	0.00288526	−	0.00166580i
$701$	−15.5907			−0.588854			−0.294427	−	0.955674i	$-0.595129\pi$
$701$	−15.5907			−0.588854			−0.294427	+	0.955674i	$0.595129\pi$
$702$		0			0
$703$	3.26577			0.123171
$704$	31.2067	−	18.0172i	1.17615	−	0.679050i
$705$	−0.102916	−	0.178256i	−0.00387604	−	0.00671350i
$706$	16.4004	−	28.4064i	0.617239	−	1.06909i
$707$		−	2.56465i		−	0.0964535i
$708$	−0.296956	−	0.171448i	−0.0111603	−	0.00644340i
$709$	5.27830	+	3.04743i	0.198231	+	0.114448i	0.595830	−	0.803111i	$-0.296823\pi$
$709$	5.27830	+	3.04743i	0.198231	+	0.114448i	−0.397599	+	0.917559i	$0.630157\pi$
$710$			11.8726i			0.445572i
$711$	−23.4332	+	40.5874i	−0.878812	+	1.52215i
$712$	−4.65615	−	8.06468i	−0.174496	−	0.302237i
$713$	−0.136404	+	0.0787528i	−0.00510837	+	0.00294932i
$714$	0.264438			0.00989634
$715$		0			0
$716$	6.76377			0.252774
$717$	−2.19920	+	1.26971i	−0.0821307	+	0.0474182i
$718$	−6.83877	−	11.8451i	−0.255221	−	0.442055i
$719$	13.2981	−	23.0329i	0.495934	−	0.858982i	−0.504055	−	0.863671i	$-0.668159\pi$
$719$	13.2981	−	23.0329i	0.495934	−	0.858982i	0.999989	+	0.00468903i	$0.00149257\pi$
$720$		−	8.62133i		−	0.321298i
$721$	2.29946	+	1.32759i	0.0856363	+	0.0494421i
$722$	15.3580	+	8.86695i	0.571566	+	0.329994i
$723$			1.12285i			0.0417593i
$724$	0.152793	−	0.264645i	0.00567850	−	0.00983545i
$725$	−3.53803	−	6.12805i	−0.131399	−	0.227590i
$726$	−1.15367	+	0.666071i	−0.0428167	+	0.0247202i
$727$	9.91915			0.367881			0.183940	−	0.982937i	$-0.441115\pi$
$727$	9.91915			0.367881			0.183940	+	0.982937i	$0.441115\pi$
$728$		0			0
$729$	−24.9047			−0.922395
$730$	−12.5051	+	7.21983i	−0.462835	+	0.267218i
$731$	−20.4203	−	35.3691i	−0.755274	−	1.30817i
$732$	−0.244824	+	0.424047i	−0.00904894	+	0.0156732i
$733$		−	26.2194i		−	0.968434i	−0.874948	−	0.484217i	$-0.839105\pi$
$733$		−	26.2194i		−	0.968434i	0.874948	−	0.484217i	$-0.160895\pi$
$734$	−34.8482	−	20.1196i	−1.28627	−	0.742628i
$735$	−1.19396	−	0.689333i	−0.0440399	−	0.0254264i
$736$			17.8471i			0.657854i
$737$	11.4792	−	19.8825i	0.422841	−	0.732383i
$738$	−20.2337	−	35.0458i	−0.744813	−	1.29005i
$739$	3.03517	−	1.75236i	0.111651	−	0.0644615i	−0.443135	−	0.896455i	$-0.646134\pi$
$739$	3.03517	−	1.75236i	0.111651	−	0.0644615i	0.554785	+	0.831994i	$0.312800\pi$
$740$	−0.664874			−0.0244413
$741$		0			0
$742$	0.137063			0.00503175
$743$	−15.3406	+	8.85690i	−0.562792	+	0.324928i	−0.754265	−	0.656570i	$-0.772007\pi$
$743$	−15.3406	+	8.85690i	−0.562792	+	0.324928i	0.191473	+	0.981498i	$0.438673\pi$
$744$	0.00657326	+	0.0113852i	0.000240988	+	0.000417403i
$745$	−0.384043	+	0.665182i	−0.0140702	+	0.0243704i
$746$		−	8.58343i		−	0.314262i
$747$	44.4739	+	25.6770i	1.62721	+	0.939473i
$748$	8.43590	+	4.87047i	0.308447	+	0.178082i
$749$		−	0.196997i		−	0.00719813i
$750$	0.123490	−	0.213891i	0.00450921	−	0.00781018i
$751$	25.0939	+	43.4640i	0.915691	+	1.58602i	0.805886	+	0.592071i	$0.201689\pi$
$751$	25.0939	+	43.4640i	0.915691	+	1.58602i	0.109805	+	0.993953i	$0.464977\pi$
$752$	2.62066	−	1.51304i	0.0955658	−	0.0551749i
$753$	3.04307			0.110896
$754$		0			0
$755$	14.0097			0.509865
$756$	−0.0901234	+	0.0520328i	−0.00327776	+	0.00189241i
$757$	−18.9128	−	32.7580i	−0.687398	−	1.19061i	−0.972677	−	0.232164i	$-0.925420\pi$
$757$	−18.9128	−	32.7580i	−0.687398	−	1.19061i	0.285279	−	0.958445i	$-0.407914\pi$
$758$	7.65548	−	13.2597i	0.278060	−	0.481613i
$759$		−	5.80194i		−	0.210597i
$760$	5.77195	+	3.33244i	0.209371	+	0.120880i
$761$	−11.5250	−	6.65399i	−0.417783	−	0.241207i	0.276346	−	0.961058i	$-0.410877\pi$
$761$	−11.5250	−	6.65399i	−0.417783	−	0.241207i	−0.694128	+	0.719851i	$0.744210\pi$
$762$			2.41119i			0.0873482i
$763$	1.91185	−	3.31143i	0.0692138	−	0.119882i
$764$	−0.772635	−	1.33824i	−0.0279529	−	0.0484159i
$765$	13.8611	−	8.00269i	0.501148	−	0.289338i
$766$	10.5157			0.379949
$767$		0			0
$768$	2.00298			0.0722765
$769$	8.19177	−	4.72952i	0.295403	−	0.170551i	−0.344973	−	0.938613i	$-0.612112\pi$
$769$	8.19177	−	4.72952i	0.295403	−	0.170551i	0.640376	+	0.768062i	$0.278779\pi$
$770$	−0.500000	−	0.866025i	−0.0180187	−	0.0312094i
$771$	1.67025	−	2.89296i	0.0601526	−	0.104187i
$772$			3.91915i			0.141053i
$773$	43.4864	+	25.1069i	1.56410	+	0.903031i	0.996835	+	0.0794922i	$0.0253299\pi$
$773$	43.4864	+	25.1069i	1.56410	+	0.903031i	0.567260	+	0.823539i	$0.308003\pi$
$774$	−24.1561	−	13.9465i	−0.868273	−	0.501298i
$775$		−	0.0217703i		−	0.000782011i
$776$	−7.65548	+	13.2597i	−0.274816	+	0.475995i
$777$	−0.0293030	−	0.0507543i	−0.00105124	−	0.00182080i
$778$	−22.0517	+	12.7315i	−0.790591	+	0.456448i
$779$	23.9600			0.858457
$780$		0			0
$781$	−38.5502			−1.37943
$782$	42.2361	−	24.3850i	1.51036	−	0.872006i
$783$	4.17701	+	7.23480i	0.149274	+	0.258551i
$784$	10.1344	−	17.5533i	0.361942	−	0.626902i
$785$		−	16.2620i		−	0.580417i
$786$	−3.12685	−	1.80529i	−0.111531	−	0.0643926i
$787$	4.39227	+	2.53588i	0.156567	+	0.0903942i	0.576237	−	0.817283i	$-0.304521\pi$
$787$	4.39227	+	2.53588i	0.156567	+	0.0903942i	−0.419669	+	0.907677i	$0.637854\pi$
$788$			5.48666i			0.195454i
$789$	−0.598072	+	1.03589i	−0.0212919	+	0.0368787i
$790$	−9.86927	−	17.0941i	−0.351133	−	0.608180i
$791$	−3.36425	+	1.94235i	−0.119619	+	0.0690621i
$792$	36.5502			1.29875
$793$		0			0
$794$	23.2476			0.825025
$795$	−0.0951903	+	0.0549581i	−0.00337605	+	0.00194916i
$796$	1.44235	+	2.49823i	0.0511229	+	0.0885474i
$797$	−4.53899	+	7.86176i	−0.160779	+	0.278478i	−0.935148	−	0.354256i	$-0.884734\pi$
$797$	−4.53899	+	7.86176i	−0.160779	+	0.278478i	0.774369	+	0.632734i	$0.218067\pi$
$798$			0.106932i			0.00378536i
$799$	4.86522	+	2.80894i	0.172119	+	0.0993731i
$800$	−2.13632	−	1.23341i	−0.0755304	−	0.0436075i
$801$		−	9.04307i		−	0.319521i
$802$	−19.3177	+	33.4592i	−0.682131	+	1.18148i
$803$	−23.4426	−	40.6039i	−0.827273	−	1.43288i
$804$	0.432848	−	0.249905i	0.0152654	−	0.00881347i
$805$	1.43296			0.0505052
$806$		0			0
$807$	−3.10885			−0.109437
$808$	−34.1902	+	19.7397i	−1.20281	+	0.694442i
$809$	−16.6277	−	28.8000i	−0.584598	−	1.01255i	−0.994925	−	0.100615i	$-0.967919\pi$
$809$	−16.6277	−	28.8000i	−0.584598	−	1.01255i	0.410328	−	0.911938i	$-0.365414\pi$
$810$	5.39224	−	9.33963i	0.189464	−	0.328161i
$811$			21.0258i			0.738316i	0.929367	+	0.369158i	$0.120354\pi$
$811$			21.0258i			0.738316i	−0.929367	+	0.369158i	$0.879646\pi$
$812$	−0.540163	−	0.311863i	−0.0189560	−	0.0109443i
$813$	−2.68114	−	1.54796i	−0.0940317	−	0.0542893i
$814$			7.54288i			0.264378i
$815$	6.18329	−	10.7098i	0.216591	−	0.375147i
$816$	−1.55884	−	2.70000i	−0.0545704	−	0.0945187i
$817$	14.3024	−	8.25750i	0.500378	−	0.288893i
$818$	29.6872			1.03799
$819$		0			0
$820$	−4.87800			−0.170347
$821$	11.9047	−	6.87316i	0.415475	−	0.239875i	−0.277664	−	0.960678i	$-0.589560\pi$
$821$	11.9047	−	6.87316i	0.415475	−	0.239875i	0.693140	+	0.720803i	$0.256227\pi$
$822$	0.684489	+	1.18557i	0.0238743	+	0.0413515i
$823$	18.6579	−	32.3165i	0.650375	−	1.12648i	−0.332657	−	0.943048i	$-0.607945\pi$
$823$	18.6579	−	32.3165i	0.650375	−	1.12648i	0.983032	−	0.183434i	$-0.0587214\pi$
$824$		−	40.8732i		−	1.42389i
$825$	0.694498	+	0.400969i	0.0241793	+	0.0139599i
$826$	−0.832052	−	0.480386i	−0.0289508	−	0.0167148i
$827$			36.5478i			1.27089i	0.772146	+	0.635445i	$0.219183\pi$
$827$			36.5478i			1.27089i	−0.772146	+	0.635445i	$0.780817\pi$
$828$	−4.76659	+	8.25598i	−0.165651	+	0.286915i
$829$	−16.2283	−	28.1083i	−0.563633	−	0.976241i	−0.997175	−	0.0751079i	$-0.976070\pi$
$829$	−16.2283	−	28.1083i	−0.563633	−	0.976241i	0.433542	−	0.901133i	$-0.357263\pi$
$830$	−18.7309	+	10.8143i	−0.650161	+	0.375370i
$831$	−3.48965			−0.121055
$832$		0			0
$833$	37.6286			1.30375
$834$	−0.116628	+	0.0673352i	−0.00403850	+	0.00233163i
$835$	10.7262	+	18.5783i	0.371194	+	0.642928i
$836$	−1.96950	+	3.41127i	−0.0681166	+	0.117981i
$837$			0.0257021i			0.000888393i
$838$	13.0835	+	7.55376i	0.451962	+	0.260940i
$839$	10.8834	+	6.28352i	0.375736	+	0.216931i	0.675961	−	0.736937i	$-0.263729\pi$
$839$	10.8834	+	6.28352i	0.375736	+	0.216931i	−0.300226	+	0.953868i	$0.597062\pi$
$840$		−	0.119605i		−	0.00412676i
$841$	−10.5353	+	18.2478i	−0.363288	+	0.629233i
$842$	−7.01656	−	12.1530i	−0.241807	−	0.418821i
$843$	0.693759	−	0.400542i	0.0238943	−	0.0137954i
$844$	−6.50471			−0.223901
$845$		0			0
$846$	3.83685			0.131914
$847$	0.925170	−	0.534147i	0.0317892	−	0.0183535i
$848$	−0.807979	−	1.39946i	−0.0277461	−	0.0480576i
$849$	1.65787	−	2.87152i	0.0568981	−	0.0985504i
$850$			6.74094i			0.231212i
$851$	−9.36056	−	5.40432i	−0.320876	−	0.185258i
$852$	−0.726810	−	0.419624i	−0.0249001	−	0.0143761i
$853$			38.3220i			1.31212i	0.754709	+	0.656060i	$0.227778\pi$
$853$			38.3220i			1.31212i	−0.754709	+	0.656060i	$0.772222\pi$
$854$	−0.685981	+	1.18815i	−0.0234738	+	0.0406578i
$855$	3.23609	+	5.60508i	0.110672	+	0.191690i
$856$	−2.62624	+	1.51626i	−0.0897631	+	0.0518248i
$857$	−35.9081			−1.22660			−0.613299	−	0.789851i	$-0.710158\pi$
$857$	−35.9081			−1.22660			−0.613299	+	0.789851i	$0.710158\pi$
$858$		0			0
$859$	−46.2881			−1.57933			−0.789665	−	0.613538i	$-0.789746\pi$
$859$	−46.2881			−1.57933			−0.789665	+	0.613538i	$0.789746\pi$
$860$	−2.91181	+	1.68114i	−0.0992920	+	0.0573263i
$861$	−0.214988	−	0.372370i	−0.00732678	−	0.0126904i
$862$	10.8222	−	18.7446i	0.368606	−	0.638445i
$863$			7.86725i			0.267804i	0.990995	+	0.133902i	$0.0427508\pi$
$863$			7.86725i			0.267804i	−0.990995	+	0.133902i	$0.957249\pi$
$864$	2.52215	+	1.45616i	0.0858053	+	0.0495397i
$865$	2.22571	+	1.28501i	0.0756763	+	0.0436917i
$866$		−	8.94571i		−	0.303987i
$867$	1.21044	−	2.09654i	0.0411087	−	0.0712023i
$868$	−0.000959481	−	0.00166187i	−3.25669e−5	−	5.64075e-5i
$869$	55.5041	−	32.0453i	1.88285	−	1.08706i
$870$	−1.74764			−0.0592507
$871$		0			0
$872$	−58.8611			−1.99329
$873$	−12.8763	+	7.43416i	−0.435798	+	0.251608i
$874$	9.86071	+	17.0792i	0.333543	+	0.577714i
$875$	−0.0990311	+	0.171527i	−0.00334786	+	0.00579867i
$876$		−	1.02071i		−	0.0344864i
$877$	−35.8460	−	20.6957i	−1.21043	−	0.698843i	−0.247578	−	0.968868i	$-0.579635\pi$
$877$	−35.8460	−	20.6957i	−1.21043	−	0.698843i	−0.962853	+	0.270025i	$0.912968\pi$
$878$	−11.1454	−	6.43482i	−0.376140	−	0.217165i
$879$			1.71810i			0.0579502i
$880$	−5.89493	+	10.2103i	−0.198718	+	0.344190i
$881$	19.4279	+	33.6501i	0.654542	+	1.13370i	0.982008	+	0.188837i	$0.0604718\pi$
$881$	19.4279	+	33.6501i	0.654542	+	1.13370i	−0.327467	+	0.944863i	$0.606195\pi$
$882$	22.2563	−	12.8497i	0.749407	−	0.432671i
$883$	6.22713			0.209560			0.104780	−	0.994495i	$-0.466586\pi$
$883$	6.22713			0.209560			0.104780	+	0.994495i	$0.466586\pi$
$884$		0			0
$885$	0.770479			0.0258994
$886$	32.6428	−	18.8463i	1.09665	−	0.633154i
$887$	−18.1637	−	31.4604i	−0.609877	−	1.05634i	−0.991260	−	0.131920i	$-0.957886\pi$
$887$	−18.1637	−	31.4604i	−0.609877	−	1.05634i	0.381384	−	0.924417i	$-0.375448\pi$
$888$	−0.451083	+	0.781298i	−0.0151373	+	0.0262186i
$889$		−	1.93362i		−	0.0648517i
$890$	3.29838	+	1.90432i	0.110562	+	0.0638330i
$891$	30.3256	+	17.5085i	1.01595	+	0.586557i
$892$			11.3327i			0.379448i
$893$	−1.13587	+	1.96738i	−0.0380103	+	0.0658358i
$894$	0.0948508	+	0.164286i	0.00317228	+	0.00549456i
$895$	−13.1619	+	7.59903i	−0.439954	+	0.254008i
$896$	1.22090			0.0407873
$897$		0			0
$898$	30.8012			1.02785
$899$	−0.133409	+	0.0770239i	−0.00444945	+	0.00256889i
$900$	−0.658834	−	1.14113i	−0.0219611	−	0.0380378i
$901$	1.50000	−	2.59808i	0.0499722	−	0.0865545i
$902$			55.3400i			1.84262i
$903$	−0.256665	−	0.148185i	−0.00854127	−	0.00493130i
$904$	51.7884	+	29.9001i	1.72246	+	0.994461i
$905$			0.686645i			0.0228248i
$906$	1.73005	−	2.99654i	0.0574772	−	0.0995534i
$907$	−2.17360	−	3.76479i	−0.0721733	−	0.125008i	0.827680	−	0.561200i	$-0.189660\pi$
$907$	−2.17360	−	3.76479i	−0.0721733	−	0.125008i	−0.899854	+	0.436192i	$0.856327\pi$
$908$	−7.99093	+	4.61356i	−0.265188	+	0.153107i
$909$	−38.3381			−1.27159
$910$		0			0
$911$	−21.8866			−0.725136			−0.362568	−	0.931957i	$-0.618100\pi$
$911$	−21.8866			−0.725136			−0.362568	+	0.931957i	$0.618100\pi$
$912$	1.09181	−	0.630359i	0.0361535	−	0.0208733i
$913$	−35.1139	−	60.8190i	−1.16210	−	2.01281i
$914$	−9.48941	+	16.4361i	−0.313882	+	0.543659i
$915$		−	1.10023i		−	0.0363724i
$916$	2.80823	+	1.62133i	0.0927866	+	0.0535704i
$917$	2.50754	+	1.44773i	0.0828063	+	0.0478083i
$918$		−	7.95838i		−	0.262666i
$919$	−12.8146	+	22.1956i	−0.422715	+	0.732164i	−0.996204	−	0.0870494i	$-0.972256\pi$
$919$	−12.8146	+	22.1956i	−0.422715	+	0.732164i	0.573489	+	0.819213i	$0.305590\pi$
$920$	−11.0293	−	19.1033i	−0.363625	−	0.629818i
$921$	2.67700	−	1.54556i	0.0882101	−	0.0509281i
$922$	14.7138			0.484573
$923$		0			0
$924$	0.0706876			0.00232545
$925$	1.29381	−	0.746980i	0.0425401	−	0.0245605i
$926$	8.25033	+	14.2900i	0.271123	+	0.469598i
$927$	19.8458	−	34.3739i	0.651821	−	1.12899i
$928$			17.4553i			0.572999i
$929$	11.8330	+	6.83177i	0.388227	+	0.224143i	0.681392	−	0.731919i	$-0.261375\pi$
$929$	11.8330	+	6.83177i	0.388227	+	0.224143i	−0.293164	+	0.956062i	$0.594708\pi$
$930$	−0.00465646	−	0.00268841i	−0.000152691	−	8.81563e-5i
$931$			15.2161i			0.498688i
$932$	−1.34990	+	2.33809i	−0.0442173	+	0.0765866i
$933$	−2.18824	−	3.79015i	−0.0716398	−	0.124084i
$934$	−8.65560	+	4.99731i	−0.283220	+	0.163517i
$935$	−21.8877			−0.715804
$936$		0			0
$937$	17.1381			0.559878			0.279939	−	0.960018i	$-0.409686\pi$
$937$	17.1381			0.559878			0.279939	+	0.960018i	$0.409686\pi$
$938$	1.21281	−	0.700218i	0.0395998	−	0.0228629i
$939$	−1.94116	−	3.36218i	−0.0633473	−	0.109721i
$940$	0.231250	−	0.400537i	0.00754255	−	0.0130641i
$941$			2.58775i			0.0843581i	0.999110	+	0.0421790i	$0.0134300\pi$
$941$			2.58775i			0.0843581i	−0.999110	+	0.0421790i	$0.986570\pi$
$942$	−3.47830	−	2.00820i	−0.113329	−	0.0654306i
$943$	−68.6759	−	39.6500i	−2.23639	−	1.29118i
$944$			11.3274i			0.368674i
$945$	0.116917	−	0.202505i	0.00380330	−	0.00658750i
$946$	19.0722	+	33.0340i	0.620090	+	1.07403i
$947$	−9.70620	+	5.60388i	−0.315409	+	0.182101i	−0.649344	−	0.760494i	$-0.724957\pi$
$947$	−9.70620	+	5.60388i	−0.315409	+	0.182101i	0.333935	+	0.942596i	$0.391623\pi$
$948$	1.39527			0.0453163
$949$		0			0
$950$	−2.72587			−0.0884390
$951$	−2.27221	+	1.31186i	−0.0736816	+	0.0425401i
$952$	1.63222	+	2.82709i	0.0529005	+	0.0916264i
$953$	−19.1295	+	33.1333i	−0.619666	+	1.07329i	0.369880	+	0.929079i	$0.379399\pi$
$953$	−19.1295	+	33.1333i	−0.619666	+	1.07329i	−0.989547	+	0.144214i	$0.953935\pi$
$954$		−	2.04892i		−	0.0663361i
$955$	3.00700	+	1.73609i	0.0973044	+	0.0561787i
$956$	−4.94156	−	2.85301i	−0.159821	−	0.0922730i
$957$		−	5.67456i		−	0.183433i
$958$	4.19537	−	7.26660i	0.135546	−	0.234773i
$959$	−0.548917	−	0.950753i	−0.0177255	−	0.0307014i
$960$	−1.52655	+	0.881355i	−0.0492692	+	0.0284456i
$961$	30.9995			0.999985
$962$		0			0
$963$	−2.94485			−0.0948965
$964$	−2.18500	+	1.26151i	−0.0703742	+	0.0406306i
$965$	−4.40312	−	7.62644i	−0.141742	−	0.245504i
$966$	0.176956	−	0.306497i	0.00569347	−	0.00986137i
$967$		−	5.26875i		−	0.169432i	−0.996405	−	0.0847158i	$-0.973002\pi$
$967$		−	5.26875i		−	0.169432i	0.996405	−	0.0847158i	$-0.0269982\pi$
$968$	−14.2418	−	8.22252i	−0.457750	−	0.264282i
$969$	2.02693	+	1.17025i	0.0651145	+	0.0375939i
$970$		−	6.26205i		−	0.201062i
$971$	3.65601	−	6.33240i	0.117327	−	0.203216i	−0.801381	−	0.598155i	$-0.795901\pi$
$971$	3.65601	−	6.33240i	0.117327	−	0.203216i	0.918708	+	0.394938i	$0.129234\pi$
$972$	1.16929	+	2.02527i	0.0375050	+	0.0649607i
$973$	0.0935284	−	0.0539987i	0.00299838	−	0.00173112i
$974$	11.5663			0.370608
$975$		0			0
$976$	16.1752			0.517756
$977$	27.1638	−	15.6831i	0.869049	−	0.501745i	0.00201658	−	0.999998i	$-0.499358\pi$
$977$	27.1638	−	15.6831i	0.869049	−	0.501745i	0.867032	+	0.498253i	$0.166025\pi$
$978$	−1.52715	−	2.64510i	−0.0488328	−	0.0845809i
$979$	−6.18329	+	10.7098i	−0.197619	+	0.342286i
$980$		−	3.09783i		−	0.0989567i
$981$	−49.5015	−	28.5797i	−1.58046	−	0.912480i
$982$	−8.58133	−	4.95444i	−0.273841	−	0.158102i
$983$			35.9724i			1.14734i	0.819086	+	0.573670i	$0.194481\pi$
$983$			35.9724i			1.14734i	−0.819086	+	0.573670i	$0.805519\pi$
$984$	−3.30947	+	5.73217i	−0.105502	+	0.182735i
$985$	−6.16421	−	10.6767i	−0.196408	−	0.340189i
$986$	41.3088	−	23.8497i	1.31554	−	0.759528i
$987$	0.0407675			0.00129765
$988$		0			0
$989$	−54.6594			−1.73807
$990$	−12.9459	+	7.47434i	−0.411449	+	0.237550i
$991$	−10.6238	−	18.4009i	−0.337476	−	0.584525i	0.646482	−	0.762930i	$-0.276240\pi$
$991$	−10.6238	−	18.4009i	−0.337476	−	0.584525i	−0.983957	+	0.178405i	$0.942906\pi$
$992$	−0.0268516	+	0.0465083i	−0.000852538	+	0.00147664i
$993$			2.41875i			0.0767567i
$994$	−2.03648	−	1.17576i	−0.0645931	−	0.0372928i
$995$	−5.61347	−	3.24094i	−0.177959	−	0.102745i
$996$		−	1.52888i		−	0.0484443i
$997$	−19.2020	+	33.2588i	−0.608134	+	1.05332i	0.383414	+	0.923577i	$0.374748\pi$
$997$	−19.2020	+	33.2588i	−0.608134	+	1.05332i	−0.991548	+	0.129742i	$0.958585\pi$
$998$	−13.7349	−	23.7895i	−0.434771	−	0.753045i
$999$	−1.52747	+	0.881887i	−0.0483271	+	0.0279017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.i.361.2		12
13.2	odd	12		845.2.a.j.1.1	yes	3
13.3	even	3		845.2.c.f.506.2		6
13.4	even	6	inner	845.2.m.i.316.2		12
13.5	odd	4		845.2.e.j.146.3		6
13.6	odd	12		845.2.e.j.191.3		6
13.7	odd	12		845.2.e.l.191.1		6
13.8	odd	4		845.2.e.l.146.1		6
13.9	even	3	inner	845.2.m.i.316.5		12
13.10	even	6		845.2.c.f.506.5		6
13.11	odd	12		845.2.a.h.1.3	✓	3
13.12	even	2	inner	845.2.m.i.361.5		12
39.2	even	12		7605.2.a.br.1.3		3
39.11	even	12		7605.2.a.by.1.1		3
65.24	odd	12		4225.2.a.bf.1.1		3
65.54	odd	12		4225.2.a.bd.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.h.1.3	✓	3	13.11	odd	12
845.2.a.j.1.1	yes	3	13.2	odd	12
845.2.c.f.506.2		6	13.3	even	3
845.2.c.f.506.5		6	13.10	even	6
845.2.e.j.146.3		6	13.5	odd	4
845.2.e.j.191.3		6	13.6	odd	12
845.2.e.l.146.1		6	13.8	odd	4
845.2.e.l.191.1		6	13.7	odd	12
845.2.m.i.316.2		12	13.4	even	6	inner
845.2.m.i.316.5		12	13.9	even	3	inner
845.2.m.i.361.2		12	1.1	even	1	trivial
845.2.m.i.361.5		12	13.12	even	2	inner
4225.2.a.bd.1.3		3	65.54	odd	12
4225.2.a.bf.1.1		3	65.24	odd	12
7605.2.a.br.1.3		3	39.2	even	12
7605.2.a.by.1.1		3	39.11	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07992 + 0.623490i) q^{2} +(0.0990311 + 0.171527i) q^{3} +(-0.222521 + 0.385418i) q^{4} -1.00000i q^{5} +(-0.213891 - 0.123490i) q^{6} +(0.171527 + 0.0990311i) q^{7} -3.04892i q^{8} +(1.48039 - 2.56410i) q^{9} +O(q^{10})\)	\(q+(-1.07992 + 0.623490i) q^{2} +(0.0990311 + 0.171527i) q^{3} +(-0.222521 + 0.385418i) q^{4} -1.00000i q^{5} +(-0.213891 - 0.123490i) q^{6} +(0.171527 + 0.0990311i) q^{7} -3.04892i q^{8} +(1.48039 - 2.56410i) q^{9} +(0.623490 + 1.07992i) q^{10} +(-3.50647 + 2.02446i) q^{11} -0.0881460 q^{12} -0.246980 q^{14} +(0.171527 - 0.0990311i) q^{15} +(1.45593 + 2.52174i) q^{16} +(-2.70291 + 4.68157i) q^{17} +3.69202i q^{18} +(-1.89311 - 1.09299i) q^{19} +(0.385418 + 0.222521i) q^{20} +0.0392287i q^{21} +(2.52446 - 4.37249i) q^{22} +(3.61745 + 6.26561i) q^{23} +(0.522971 - 0.301938i) q^{24} -1.00000 q^{25} +1.18060 q^{27} +(-0.0763367 + 0.0440730i) q^{28} +(3.53803 + 6.12805i) q^{29} +(-0.123490 + 0.213891i) q^{30} +0.0217703i q^{31} +(2.13632 + 1.23341i) q^{32} +(-0.694498 - 0.400969i) q^{33} -6.74094i q^{34} +(0.0990311 - 0.171527i) q^{35} +(0.658834 + 1.14113i) q^{36} +(-1.29381 + 0.746980i) q^{37} +2.72587 q^{38} -3.04892 q^{40} +(-9.49231 + 5.48039i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.77748 + 6.54279i) q^{43} -1.80194i q^{44} +(-2.56410 - 1.48039i) q^{45} +(-7.81308 - 4.51089i) q^{46} -1.03923i q^{47} +(-0.288364 + 0.499461i) q^{48} +(-3.48039 - 6.02820i) q^{49} +(1.07992 - 0.623490i) q^{50} -1.07069 q^{51} -0.554958 q^{53} +(-1.27495 + 0.736094i) q^{54} +(2.02446 + 3.50647i) q^{55} +(0.301938 - 0.522971i) q^{56} -0.432960i q^{57} +(-7.64156 - 4.41185i) q^{58} +(3.36891 + 1.94504i) q^{59} +0.0881460i q^{60} +(2.77748 - 4.81073i) q^{61} +(-0.0135735 - 0.0235101i) q^{62} +(0.507852 - 0.293209i) q^{63} -8.89977 q^{64} +1.00000 q^{66} +(-4.91058 + 2.83513i) q^{67} +(-1.20291 - 2.08350i) q^{68} +(-0.716480 + 1.24098i) q^{69} +0.246980i q^{70} +(8.24552 + 4.76055i) q^{71} +(-7.81774 - 4.51357i) q^{72} +11.5797i q^{73} +(0.931468 - 1.61335i) q^{74} +(-0.0990311 - 0.171527i) q^{75} +(0.842515 - 0.486426i) q^{76} -0.801938 q^{77} -15.8291 q^{79} +(2.52174 - 1.45593i) q^{80} +(-4.32424 - 7.48980i) q^{81} +(6.83393 - 11.8367i) q^{82} +17.3448i q^{83} +(-0.0151194 - 0.00872920i) q^{84} +(4.68157 + 2.70291i) q^{85} -9.42088i q^{86} +(-0.700751 + 1.21374i) q^{87} +(6.17241 + 10.6909i) q^{88} +(2.64510 - 1.52715i) q^{89} +3.69202 q^{90} -3.21983 q^{92} +(-0.00373419 + 0.00215593i) q^{93} +(0.647948 + 1.12228i) q^{94} +(-1.09299 + 1.89311i) q^{95} +0.488582i q^{96} +(-4.34898 - 2.51089i) q^{97} +(7.51705 + 4.33997i) q^{98} +11.9879i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{3} - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 12 * q + 10 * q^3 - 2 * q^4 - 8 * q^9	\( 12 q + 10 q^{3} - 2 q^{4} - 8 q^{9} - 2 q^{10} - 16 q^{12} + 16 q^{14} + 10 q^{16} - 6 q^{17} + 12 q^{22} - 4 q^{23} - 12 q^{25} - 32 q^{27} + 12 q^{29} + 8 q^{30} + 10 q^{35} - 26 q^{36} + 76 q^{38} + 18 q^{42} - 46 q^{43} + 2 q^{48} - 16 q^{49} + 36 q^{51} - 8 q^{53} + 6 q^{55} - 14 q^{56} + 34 q^{61} + 12 q^{62} - 16 q^{64} + 12 q^{66} + 12 q^{68} + 30 q^{69} + 22 q^{74} - 10 q^{75} + 8 q^{77} - 148 q^{79} - 54 q^{81} - 4 q^{82} - 20 q^{87} + 28 q^{88} + 24 q^{90} - 44 q^{92} - 20 q^{94} + 16 q^{95}+O(q^{100}) \) 12 * q + 10 * q^3 - 2 * q^4 - 8 * q^9 - 2 * q^10 - 16 * q^12 + 16 * q^14 + 10 * q^16 - 6 * q^17 + 12 * q^22 - 4 * q^23 - 12 * q^25 - 32 * q^27 + 12 * q^29 + 8 * q^30 + 10 * q^35 - 26 * q^36 + 76 * q^38 + 18 * q^42 - 46 * q^43 + 2 * q^48 - 16 * q^49 + 36 * q^51 - 8 * q^53 + 6 * q^55 - 14 * q^56 + 34 * q^61 + 12 * q^62 - 16 * q^64 + 12 * q^66 + 12 * q^68 + 30 * q^69 + 22 * q^74 - 10 * q^75 + 8 * q^77 - 148 * q^79 - 54 * q^81 - 4 * q^82 - 20 * q^87 + 28 * q^88 + 24 * q^90 - 44 * q^92 - 20 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more