LMFDB - Embedded newform 507.2.j.i.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
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:	$\Z[a_1, \ldots, a_{5}]$
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	$\chi$	$=$	507.361
Dual form			507.2.j.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)

$f(q)$	$=$	$q+(-2.04113 + 1.17845i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.77748 - 3.07868i) q^{4} -3.69202i q^{5} +(-2.04113 - 1.17845i) q^{6} +(0.694498 + 0.400969i) q^{7} +3.66487i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.04113 + 1.17845i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.77748 - 3.07868i) q^{4} -3.69202i q^{5} +(-2.04113 - 1.17845i) q^{6} +(0.694498 + 0.400969i) q^{7} +3.66487i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.35086 + 7.53590i) q^{10} +(-2.46891 + 1.42543i) q^{11} +3.55496 q^{12} -1.89008 q^{14} +(3.19738 - 1.84601i) q^{15} +(-0.763906 - 1.32312i) q^{16} +(1.46950 - 2.54525i) q^{17} -2.35690i q^{18} +(-2.11747 - 1.22252i) q^{19} +(-11.3666 - 6.56249i) q^{20} +0.801938i q^{21} +(3.35958 - 5.81897i) q^{22} +(-3.89493 - 6.74621i) q^{23} +(-3.17387 + 1.83244i) q^{24} -8.63102 q^{25} -1.00000 q^{27} +(2.46891 - 1.42543i) q^{28} +(-1.92543 - 3.33494i) q^{29} +(-4.35086 + 7.53590i) q^{30} -2.34481i q^{31} +(-3.22929 - 1.86443i) q^{32} +(-2.46891 - 1.42543i) q^{33} +6.92692i q^{34} +(1.48039 - 2.56410i) q^{35} +(1.77748 + 3.07868i) q^{36} +(6.44760 - 3.72252i) q^{37} +5.76271 q^{38} +13.5308 q^{40} +(0.736862 - 0.425428i) q^{41} +(-0.945042 - 1.63686i) q^{42} +(-0.807979 + 1.39946i) q^{43} +10.1347i q^{44} +(3.19738 + 1.84601i) q^{45} +(15.9001 + 9.17994i) q^{46} +2.44504i q^{47} +(0.763906 - 1.32312i) q^{48} +(-3.17845 - 5.50523i) q^{49} +(17.6171 - 10.1712i) q^{50} +2.93900 q^{51} -9.96077 q^{53} +(2.04113 - 1.17845i) q^{54} +(5.26271 + 9.11528i) q^{55} +(-1.46950 + 2.54525i) q^{56} -2.44504i q^{57} +(7.86010 + 4.53803i) q^{58} +(4.66272 + 2.69202i) q^{59} -13.1250i q^{60} +(6.62833 - 11.4806i) q^{61} +(2.76324 + 4.78607i) q^{62} +(-0.694498 + 0.400969i) q^{63} +11.8442 q^{64} +6.71917 q^{66} +(-12.4653 + 7.19687i) q^{67} +(-5.22401 - 9.04826i) q^{68} +(3.89493 - 6.74621i) q^{69} +6.97823i q^{70} +(7.03644 + 4.06249i) q^{71} +(-3.17387 - 1.83244i) q^{72} -11.8877i q^{73} +(-8.77359 + 15.1963i) q^{74} +(-4.31551 - 7.47468i) q^{75} +(-7.52751 + 4.34601i) q^{76} -2.28621 q^{77} +5.40581 q^{79} +(-4.88500 + 2.82036i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00269 + 1.73671i) q^{82} -7.04892i q^{83} +(2.46891 + 1.42543i) q^{84} +(-9.39712 - 5.42543i) q^{85} -3.80864i q^{86} +(1.92543 - 3.33494i) q^{87} +(-5.22401 - 9.04826i) q^{88} +(0.980069 - 0.565843i) q^{89} -8.70171 q^{90} -27.6926 q^{92} +(2.03067 - 1.17241i) q^{93} +(-2.88135 - 4.99065i) q^{94} +(-4.51357 + 7.81774i) q^{95} -3.72886i q^{96} +(-5.14798 - 2.97219i) q^{97} +(12.9753 + 7.49127i) q^{98} -2.85086i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9	$ 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43} + 22 q^{48} - 30 q^{49} - 4 q^{51} - 68 q^{53} - 6 q^{55} + 2 q^{56} + 26 q^{61} - 4 q^{62} + 36 q^{66} + 26 q^{68} - 30 q^{74} - 22 q^{75} - 60 q^{77} + 12 q^{79} - 6 q^{81} - 6 q^{82} - 4 q^{87} + 26 q^{88} + 4 q^{90} + 28 q^{92} - 42 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9 - 2 * q^10 + 44 * q^12 - 20 * q^14 - 22 * q^16 - 2 * q^17 + 18 * q^22 - 44 * q^25 - 12 * q^27 + 4 * q^29 + 2 * q^30 - 8 * q^35 + 22 * q^36 + 12 * q^40 - 10 * q^42 - 30 * q^43 + 22 * q^48 - 30 * q^49 - 4 * q^51 - 68 * q^53 - 6 * q^55 + 2 * q^56 + 26 * q^61 - 4 * q^62 + 36 * q^66 + 26 * q^68 - 30 * q^74 - 22 * q^75 - 60 * q^77 + 12 * q^79 - 6 * q^81 - 6 * q^82 - 4 * q^87 + 26 * q^88 + 4 * q^90 + 28 * q^92 - 42 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.04113	+	1.17845i	−1.44330	+	0.833289i	−0.998068	−	0.0621278i	$-0.980211\pi$
$2$	−2.04113	+	1.17845i	−1.44330	+	0.833289i	−0.445230	+	0.895416i	$0.646878\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.77748	−	3.07868i	0.888740	−	1.53934i
$5$		−	3.69202i		−	1.65112i	−0.564313	−	0.825561i	$-0.690859\pi$
$5$		−	3.69202i		−	1.65112i	0.564313	−	0.825561i	$-0.309141\pi$
$6$	−2.04113	−	1.17845i	−0.833289	−	0.481099i
$7$	0.694498	+	0.400969i	0.262496	+	0.151552i	0.625473	−	0.780246i	$-0.284906\pi$
$7$	0.694498	+	0.400969i	0.262496	+	0.151552i	−0.362977	+	0.931798i	$0.618240\pi$
$8$			3.66487i			1.29573i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	4.35086	+	7.53590i	1.37586	+	2.38306i
$11$	−2.46891	+	1.42543i	−0.744405	+	0.429783i	−0.823669	−	0.567071i	$-0.808076\pi$
$11$	−2.46891	+	1.42543i	−0.744405	+	0.429783i	0.0792636	+	0.996854i	$0.474743\pi$
$12$	3.55496			1.02623
$13$		0			0
$13$		0			0
$14$	−1.89008			−0.505146
$15$	3.19738	−	1.84601i	0.825561	−	0.476638i
$16$	−0.763906	−	1.32312i	−0.190976	−	0.330781i
$17$	1.46950	−	2.54525i	0.356406	−	0.617314i	−0.630951	−	0.775822i	$-0.717335\pi$
$17$	1.46950	−	2.54525i	0.356406	−	0.617314i	0.987358	+	0.158509i	$0.0506686\pi$
$18$		−	2.35690i		−	0.555526i
$19$	−2.11747	−	1.22252i	−0.485781	−	0.280466i	0.237042	−	0.971499i	$-0.423822\pi$
$19$	−2.11747	−	1.22252i	−0.485781	−	0.280466i	−0.722822	+	0.691034i	$0.757156\pi$
$20$	−11.3666	−	6.56249i	−2.54164	−	1.46742i
$21$			0.801938i			0.174997i
$22$	3.35958	−	5.81897i	0.716266	−	1.24061i
$23$	−3.89493	−	6.74621i	−0.812149	−	1.40668i	−0.911357	−	0.411616i	$-0.864964\pi$
$23$	−3.89493	−	6.74621i	−0.812149	−	1.40668i	0.0992087	−	0.995067i	$-0.468369\pi$
$24$	−3.17387	+	1.83244i	−0.647864	+	0.374045i
$25$	−8.63102			−1.72620
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.46891	−	1.42543i	0.466581	−	0.269380i
$29$	−1.92543	−	3.33494i	−0.357543	−	0.619282i	0.630007	−	0.776590i	$-0.283052\pi$
$29$	−1.92543	−	3.33494i	−0.357543	−	0.619282i	−0.987550	+	0.157307i	$0.949719\pi$
$30$	−4.35086	+	7.53590i	−0.794354	+	1.37586i
$31$		−	2.34481i		−	0.421141i	−0.977579	−	0.210571i	$-0.932468\pi$
$31$		−	2.34481i		−	0.421141i	0.977579	−	0.210571i	$-0.0675322\pi$
$32$	−3.22929	−	1.86443i	−0.570862	−	0.329588i
$33$	−2.46891	−	1.42543i	−0.429783	−	0.248135i
$34$			6.92692i			1.18796i
$35$	1.48039	−	2.56410i	0.250231	−	0.433413i
$36$	1.77748	+	3.07868i	0.296247	+	0.513114i
$37$	6.44760	−	3.72252i	1.05998	−	0.611979i	0.134552	−	0.990907i	$-0.457040\pi$
$37$	6.44760	−	3.72252i	1.05998	−	0.611979i	0.925426	+	0.378928i	$0.123707\pi$
$38$	5.76271			0.934835
$39$		0			0
$40$	13.5308			2.13941
$41$	0.736862	−	0.425428i	0.115079	−	0.0664406i	−0.441356	−	0.897332i	$-0.645502\pi$
$41$	0.736862	−	0.425428i	0.115079	−	0.0664406i	0.556434	+	0.830892i	$0.312169\pi$
$42$	−0.945042	−	1.63686i	−0.145823	−	0.252573i
$43$	−0.807979	+	1.39946i	−0.123216	+	0.213416i	−0.921034	−	0.389482i	$-0.872654\pi$
$43$	−0.807979	+	1.39946i	−0.123216	+	0.213416i	0.797818	+	0.602898i	$0.205987\pi$
$44$			10.1347i			1.52786i
$45$	3.19738	+	1.84601i	0.476638	+	0.275187i
$46$	15.9001	+	9.17994i	2.34435	+	1.35351i
$47$			2.44504i			0.356646i	0.983972	+	0.178323i	$0.0570672\pi$
$47$			2.44504i			0.356646i	−0.983972	+	0.178323i	$0.942933\pi$
$48$	0.763906	−	1.32312i	0.110260	−	0.190976i
$49$	−3.17845	−	5.50523i	−0.454064	−	0.786462i
$50$	17.6171	−	10.1712i	2.49143	−	1.43843i
$51$	2.93900			0.411542
$52$		0			0
$53$	−9.96077			−1.36822			−0.684109	−	0.729380i	$-0.739809\pi$
$53$	−9.96077			−1.36822			−0.684109	+	0.729380i	$0.739809\pi$
$54$	2.04113	−	1.17845i	0.277763	−	0.160366i
$55$	5.26271	+	9.11528i	0.709624	+	1.22910i
$56$	−1.46950	+	2.54525i	−0.196370	+	0.340123i
$57$		−	2.44504i		−	0.323854i
$58$	7.86010	+	4.53803i	1.03208	+	0.595873i
$59$	4.66272	+	2.69202i	0.607034	+	0.350471i	0.771804	−	0.635861i	$-0.219355\pi$
$59$	4.66272	+	2.69202i	0.607034	+	0.350471i	−0.164770	+	0.986332i	$0.552688\pi$
$60$		−	13.1250i		−	1.69443i
$61$	6.62833	−	11.4806i	0.848671	−	1.46994i	−0.0337232	−	0.999431i	$-0.510736\pi$
$61$	6.62833	−	11.4806i	0.848671	−	1.46994i	0.882394	−	0.470510i	$-0.155930\pi$
$62$	2.76324	+	4.78607i	0.350932	+	0.607832i
$63$	−0.694498	+	0.400969i	−0.0874986	+	0.0505173i
$64$	11.8442			1.48052
$65$		0			0
$66$	6.71917			0.827072
$67$	−12.4653	+	7.19687i	−1.52288	+	0.879237i	−0.523249	+	0.852180i	$0.675280\pi$
$67$	−12.4653	+	7.19687i	−1.52288	+	0.879237i	−0.999634	+	0.0270575i	$0.991386\pi$
$68$	−5.22401	−	9.04826i	−0.633505	−	1.09726i
$69$	3.89493	−	6.74621i	0.468894	−	0.812149i
$70$			6.97823i			0.834058i
$71$	7.03644	+	4.06249i	0.835072	+	0.482129i	0.855586	−	0.517661i	$-0.173197\pi$
$71$	7.03644	+	4.06249i	0.835072	+	0.482129i	−0.0205142	+	0.999790i	$0.506530\pi$
$72$	−3.17387	−	1.83244i	−0.374045	−	0.215955i
$73$		−	11.8877i		−	1.39135i	−0.718357	−	0.695674i	$-0.755106\pi$
$73$		−	11.8877i		−	1.39135i	0.718357	−	0.695674i	$-0.244894\pi$
$74$	−8.77359	+	15.1963i	−1.01991	+	1.76654i
$75$	−4.31551	−	7.47468i	−0.498312	−	0.863102i
$76$	−7.52751	+	4.34601i	−0.863465	+	0.498522i
$77$	−2.28621			−0.260538
$78$		0			0
$79$	5.40581			0.608202			0.304101	−	0.952640i	$-0.401644\pi$
$79$	5.40581			0.608202			0.304101	+	0.952640i	$0.401644\pi$
$80$	−4.88500	+	2.82036i	−0.546160	+	0.315325i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.00269	+	1.73671i	−0.110728	+	0.191787i
$83$		−	7.04892i		−	0.773719i	−0.922139	−	0.386860i	$-0.873560\pi$
$83$		−	7.04892i		−	0.773719i	0.922139	−	0.386860i	$-0.126440\pi$
$84$	2.46891	+	1.42543i	0.269380	+	0.155527i
$85$	−9.39712	−	5.42543i	−1.01926	−	0.588470i
$86$		−	3.80864i		−	0.410696i
$87$	1.92543	−	3.33494i	0.206427	−	0.357543i
$88$	−5.22401	−	9.04826i	−0.556882	−	0.964547i
$89$	0.980069	−	0.565843i	0.103887	−	0.0599793i	−0.447156	−	0.894456i	$-0.647563\pi$
$89$	0.980069	−	0.565843i	0.103887	−	0.0599793i	0.551043	+	0.834477i	$0.314230\pi$
$90$	−8.70171			−0.917241
$91$		0			0
$92$	−27.6926			−2.88715
$93$	2.03067	−	1.17241i	0.210571	−	0.121573i
$94$	−2.88135	−	4.99065i	−0.297189	−	0.514746i
$95$	−4.51357	+	7.81774i	−0.463083	+	0.802083i
$96$		−	3.72886i		−	0.380575i
$97$	−5.14798	−	2.97219i	−0.522698	−	0.301780i	0.215340	−	0.976539i	$-0.430914\pi$
$97$	−5.14798	−	2.97219i	−0.522698	−	0.301780i	−0.738038	+	0.674759i	$0.764247\pi$
$98$	12.9753	+	7.49127i	1.31070	+	0.756733i
$99$		−	2.85086i		−	0.286522i
$100$	−15.3415	+	26.5722i	−1.53415	+	2.65722i
$101$	2.31282	+	4.00593i	0.230134	+	0.398605i	0.957848	−	0.287277i	$-0.0927501\pi$
$101$	2.31282	+	4.00593i	0.230134	+	0.398605i	−0.727713	+	0.685882i	$0.759417\pi$
$102$	−5.99889	+	3.46346i	−0.593978	+	0.342934i
$103$	−1.20775			−0.119003			−0.0595016	−	0.998228i	$-0.518951\pi$
$103$	−1.20775			−0.119003			−0.0595016	+	0.998228i	$0.518951\pi$
$104$		0			0
$105$	2.96077			0.288942
$106$	20.3312	−	11.7383i	1.97475	−	1.14012i
$107$	4.76055	+	8.24552i	0.460220	+	0.797124i	0.998972	−	0.0453402i	$-0.0144372\pi$
$107$	4.76055	+	8.24552i	0.460220	+	0.797124i	−0.538752	+	0.842465i	$0.681104\pi$
$108$	−1.77748	+	3.07868i	−0.171038	+	0.296247i
$109$			1.78448i			0.170922i	0.996342	+	0.0854611i	$0.0272363\pi$
$109$			1.78448i			0.170922i	−0.996342	+	0.0854611i	$0.972764\pi$
$110$	−21.4838	−	12.4037i	−2.04840	−	1.18264i
$111$	6.44760	+	3.72252i	0.611979	+	0.353326i
$112$		−	1.22521i		−	0.115771i
$113$	−2.47554	+	4.28776i	−0.232879	+	0.403359i	−0.958654	−	0.284573i	$-0.908148\pi$
$113$	−2.47554	+	4.28776i	−0.232879	+	0.403359i	0.725775	+	0.687932i	$0.241481\pi$
$114$	2.88135	+	4.99065i	0.269864	+	0.467417i
$115$	−24.9072	+	14.3802i	−2.32261	+	1.34096i
$116$	−13.6896			−1.27105
$117$		0			0
$118$	−12.6896			−1.16817
$119$	2.04113	−	1.17845i	0.187110	−	0.108028i
$120$	6.76540	+	11.7180i	0.617593	+	1.06970i
$121$	−1.43631	+	2.48777i	−0.130574	+	0.226161i
$122$			31.2446i			2.82875i
$123$	0.736862	+	0.425428i	0.0664406	+	0.0383595i
$124$	−7.21894	−	4.16786i	−0.648280	−	0.374285i
$125$			13.4058i			1.19905i
$126$	0.945042	−	1.63686i	0.0841910	−	0.145823i
$127$	2.83513	+	4.91058i	0.251577	+	0.435744i	0.963960	−	0.266047i	$-0.0857176\pi$
$127$	2.83513	+	4.91058i	0.251577	+	0.435744i	−0.712383	+	0.701791i	$0.752384\pi$
$128$	−17.7169	+	10.2289i	−1.56597	+	0.904112i
$129$	−1.61596			−0.142277
$130$		0			0
$131$	18.2228			1.59213			0.796067	−	0.605208i	$-0.206910\pi$
$131$	18.2228			1.59213			0.796067	+	0.605208i	$0.206910\pi$
$132$	−8.77688	+	5.06734i	−0.763930	+	0.441055i
$133$	−0.980386	−	1.69808i	−0.0850102	−	0.147242i
$134$	16.9623	−	29.3795i	1.46532	−	2.53800i
$135$			3.69202i			0.317759i
$136$	9.32802	+	5.38553i	0.799871	+	0.461806i
$137$	−8.18430	−	4.72521i	−0.699232	−	0.403702i	0.107829	−	0.994169i	$-0.465610\pi$
$137$	−8.18430	−	4.72521i	−0.699232	−	0.403702i	−0.807061	+	0.590468i	$0.798943\pi$
$138$			18.3599i			1.56290i
$139$	−2.00753	+	3.47715i	−0.170277	+	0.294928i	−0.938517	−	0.345234i	$-0.887799\pi$
$139$	−2.00753	+	3.47715i	−0.170277	+	0.294928i	0.768240	+	0.640162i	$0.221133\pi$
$140$	−5.26271	−	9.11528i	−0.444780	−	0.770382i
$141$	−2.11747	+	1.22252i	−0.178323	+	0.102955i
$142$	−19.1497			−1.60701
$143$		0			0
$144$	1.52781			0.127318
$145$	−12.3127	+	7.10872i	−1.02251	+	0.590347i
$146$	14.0090	+	24.2643i	1.15940	+	2.00813i
$147$	3.17845	−	5.50523i	0.262154	−	0.454064i
$148$		−	26.4668i		−	2.17556i
$149$	16.8059	+	9.70291i	1.37680	+	0.794893i	0.991772	−	0.128014i	$-0.0408602\pi$
$149$	16.8059	+	9.70291i	1.37680	+	0.794893i	0.385023	+	0.922907i	$0.374194\pi$
$150$	17.6171	+	10.1712i	1.43843	+	0.830476i
$151$		−	12.3623i		−	1.00603i	−0.864278	−	0.503014i	$-0.832225\pi$
$151$		−	12.3623i		−	1.00603i	0.864278	−	0.503014i	$-0.167775\pi$
$152$	4.48039	−	7.76026i	0.363407	−	0.629440i
$153$	1.46950	+	2.54525i	0.118802	+	0.205771i
$154$	4.66645	−	2.69418i	0.376033	−	0.217103i
$155$	−8.65710			−0.695355
$156$		0			0
$157$	−18.6775			−1.49063			−0.745315	−	0.666712i	$-0.767701\pi$
$157$	−18.6775			−1.49063			−0.745315	+	0.666712i	$0.767701\pi$
$158$	−11.0340	+	6.37047i	−0.877816	+	0.506807i
$159$	−4.98039	−	8.62628i	−0.394970	−	0.684109i
$160$	−6.88351	+	11.9226i	−0.544189	+	0.942563i
$161$		−	6.24698i		−	0.492331i
$162$	2.04113	+	1.17845i	0.160366	+	0.0925876i
$163$	−10.6863	−	6.16972i	−0.837013	−	0.483250i	0.0192348	−	0.999815i	$-0.493877\pi$
$163$	−10.6863	−	6.16972i	−0.837013	−	0.483250i	−0.856248	+	0.516565i	$0.827210\pi$
$164$		−	3.02475i		−	0.236194i
$165$	−5.26271	+	9.11528i	−0.409701	+	0.709624i
$166$	8.30678	+	14.3878i	0.644731	+	1.11671i
$167$	9.95406	−	5.74698i	0.770268	−	0.444715i	−0.0627020	−	0.998032i	$-0.519972\pi$
$167$	9.95406	−	5.74698i	0.770268	−	0.444715i	0.832970	+	0.553318i	$0.186638\pi$
$168$	−2.93900			−0.226749
$169$		0			0
$170$	25.5743			1.96146
$171$	2.11747	−	1.22252i	0.161927	−	0.0934885i
$172$	2.87233	+	4.97502i	0.219013	+	0.379342i
$173$	6.05711	−	10.4912i	0.460514	−	0.797633i	−0.538473	−	0.842643i	$-0.680998\pi$
$173$	6.05711	−	10.4912i	0.460514	−	0.797633i	0.998987	+	0.0450096i	$0.0143318\pi$
$174$			9.07606i			0.688055i
$175$	−5.99423	−	3.46077i	−0.453121	−	0.261610i
$176$	3.77203	+	2.17778i	0.284328	+	0.164157i
$177$			5.38404i			0.404689i
$178$	−1.33363	+	2.30992i	−0.0999601	+	0.173136i
$179$	−0.269282	−	0.466411i	−0.0201271	−	0.0348612i	0.855786	−	0.517329i	$-0.173074\pi$
$179$	−0.269282	−	0.466411i	−0.0201271	−	0.0348612i	−0.875914	+	0.482468i	$0.839740\pi$
$180$	11.3666	−	6.56249i	0.847214	−	0.489139i
$181$	23.2838			1.73067			0.865336	−	0.501192i	$-0.167105\pi$
$181$	23.2838			1.73067			0.865336	+	0.501192i	$0.167105\pi$
$182$		0			0
$183$	13.2567			0.979961
$184$	24.7240	−	14.2744i	1.82268	−	1.05232i
$185$	−13.7436	−	23.8047i	−1.01045	−	1.75015i
$186$	−2.76324	+	4.78607i	−0.202611	+	0.350932i
$187$			8.37867i			0.612709i
$188$	7.52751	+	4.34601i	0.549000	+	0.316965i
$189$	−0.694498	−	0.400969i	−0.0505173	−	0.0291662i
$190$		−	21.2760i		−	1.54353i
$191$	−8.38285	+	14.5195i	−0.606561	+	1.05060i	0.385241	+	0.922816i	$0.374118\pi$
$191$	−8.38285	+	14.5195i	−0.606561	+	1.05060i	−0.991803	+	0.127779i	$0.959215\pi$
$192$	5.92208	+	10.2573i	0.427389	+	0.740259i
$193$	22.2949	−	12.8720i	1.60482	−	0.926544i	0.614318	−	0.789059i	$-0.289431\pi$
$193$	22.2949	−	12.8720i	1.60482	−	0.926544i	0.990504	−	0.137485i	$-0.0439019\pi$
$194$	14.0103			1.00588
$195$		0			0
$196$	−22.5985			−1.61418
$197$	−18.5510	+	10.7104i	−1.32171	+	0.763087i	−0.984001	−	0.178165i	$-0.942984\pi$
$197$	−18.5510	+	10.7104i	−1.32171	+	0.763087i	−0.337705	+	0.941252i	$0.609651\pi$
$198$	3.35958	+	5.81897i	0.238755	+	0.413536i
$199$	1.76391	−	3.05517i	0.125040	−	0.216576i	−0.796709	−	0.604364i	$-0.793427\pi$
$199$	1.76391	−	3.05517i	0.125040	−	0.216576i	0.921749	+	0.387788i	$0.126761\pi$
$200$		−	31.6316i		−	2.23669i
$201$	−12.4653	−	7.19687i	−0.879237	−	0.507628i
$202$	−9.44155	−	5.45108i	−0.664305	−	0.383537i
$203$		−	3.08815i		−	0.216745i
$204$	5.22401	−	9.04826i	0.365754	−	0.633505i
$205$	−1.57069	−	2.72051i	−0.109702	−	0.190009i
$206$	2.46518	−	1.42327i	0.171757	−	0.0991640i
$207$	7.78986			0.541432
$208$		0			0
$209$	6.97046			0.482157
$210$	−6.04332	+	3.48911i	−0.417029	+	0.240772i
$211$	−0.607760	−	1.05267i	−0.0418399	−	0.0724689i	0.844347	−	0.535797i	$-0.179989\pi$
$211$	−0.607760	−	1.05267i	−0.0418399	−	0.0724689i	−0.886187	+	0.463328i	$0.846655\pi$
$212$	−17.7051	+	30.6661i	−1.21599	+	2.10615i
$213$			8.12498i			0.556715i
$214$	−19.4338	−	11.2201i	−1.32847	−	0.766992i
$215$	5.16684	+	2.98307i	0.352375	+	0.203444i
$216$		−	3.66487i		−	0.249363i
$217$	0.940198	−	1.62847i	0.0638248	−	0.110548i
$218$	−2.10292	−	3.64236i	−0.142427	−	0.246692i
$219$	10.2950	−	5.94385i	0.695674	−	0.401648i
$220$	37.4174			2.52268
$221$		0			0
$222$	−17.5472			−1.17769
$223$	15.0588	−	8.69418i	1.00841	−	0.582205i	0.0976835	−	0.995218i	$-0.468857\pi$
$223$	15.0588	−	8.69418i	1.00841	−	0.582205i	0.910725	+	0.413012i	$0.135523\pi$
$224$	−1.49516	−	2.58969i	−0.0998993	−	0.173031i
$225$	4.31551	−	7.47468i	0.287701	−	0.498312i
$226$		−	11.6692i		−	0.776223i
$227$	15.0823	+	8.70775i	1.00105	+	0.577954i	0.908557	−	0.417760i	$-0.137185\pi$
$227$	15.0823	+	8.70775i	1.00105	+	0.577954i	0.0924878	+	0.995714i	$0.470518\pi$
$228$	−7.52751	−	4.34601i	−0.498522	−	0.287822i
$229$			18.7603i			1.23972i	0.784714	+	0.619858i	$0.212810\pi$
$229$			18.7603i			1.23972i	−0.784714	+	0.619858i	$0.787190\pi$
$230$	33.8925	−	58.7036i	2.23481	−	3.87080i
$231$	−1.14310	−	1.97991i	−0.0752107	−	0.130269i
$232$	12.2221	−	7.05645i	0.802422	−	0.463279i
$233$	−3.95108			−0.258844			−0.129422	−	0.991590i	$-0.541312\pi$
$233$	−3.95108			−0.258844			−0.129422	+	0.991590i	$0.541312\pi$
$234$		0			0
$235$	9.02715			0.588866
$236$	16.5758	−	9.57002i	1.07899	−	0.622955i
$237$	2.70291	+	4.68157i	0.175573	+	0.304101i
$238$	−2.77748	+	4.81073i	−0.180037	+	0.311834i
$239$		−	0.818331i		−	0.0529334i	−0.999650	−	0.0264667i	$-0.991574\pi$
$239$		−	0.818331i		−	0.0529334i	0.999650	−	0.0264667i	$-0.00842560\pi$
$240$	−4.88500	−	2.82036i	−0.315325	−	0.182053i
$241$	−5.22432	−	3.01626i	−0.336528	−	0.194295i	0.322208	−	0.946669i	$-0.395575\pi$
$241$	−5.22432	−	3.01626i	−0.336528	−	0.194295i	−0.658736	+	0.752375i	$0.728908\pi$
$242$		−	6.77048i		−	0.435223i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−23.5635	−	40.8131i	−1.50850	−	2.61279i
$245$	−20.3254	+	11.7349i	−1.29854	+	0.749715i
$246$	−2.00538			−0.127858
$247$		0			0
$248$	8.59345			0.545685
$249$	6.10454	−	3.52446i	0.386860	−	0.223353i
$250$	−15.7981	−	27.3630i	−0.999157	−	1.73059i
$251$	−13.4400	+	23.2787i	−0.848323	+	1.46934i	0.0343812	+	0.999409i	$0.489054\pi$
$251$	−13.4400	+	23.2787i	−0.848323	+	1.46934i	−0.882704	+	0.469929i	$0.844279\pi$
$252$			2.85086i			0.179587i
$253$	19.2325	+	11.1039i	1.20914	+	0.698095i
$254$	−11.5737	−	6.68210i	−0.726200	−	0.419272i
$255$		−	10.8509i		−	0.679507i
$256$	12.2642	−	21.2422i	0.766513	−	1.32764i
$257$	−4.52661	−	7.84033i	−0.282362	−	0.489066i	0.689604	−	0.724187i	$-0.257785\pi$
$257$	−4.52661	−	7.84033i	−0.282362	−	0.489066i	−0.971966	+	0.235121i	$0.924451\pi$
$258$	3.29838	−	1.90432i	0.205348	−	0.118558i
$259$	5.97046			0.370986
$260$		0			0
$261$	3.85086			0.238362
$262$	−37.1952	+	21.4746i	−2.29793	+	1.32671i
$263$	−11.5755	−	20.0494i	−0.713778	−	1.23630i	−0.963429	−	0.267964i	$-0.913649\pi$
$263$	−11.5755	−	20.0494i	−0.713778	−	1.23630i	0.249651	−	0.968336i	$-0.419684\pi$
$264$	5.22401	−	9.04826i	0.321516	−	0.556882i
$265$			36.7754i			2.25909i
$266$	4.00219	+	2.31067i	0.245390	+	0.141676i
$267$	0.980069	+	0.565843i	0.0599793	+	0.0346290i
$268$			51.1691i			3.12565i
$269$	1.21044	−	2.09654i	0.0738018	−	0.127828i	−0.826763	−	0.562551i	$-0.809820\pi$
$269$	1.21044	−	2.09654i	0.0738018	−	0.127828i	0.900565	+	0.434722i	$0.143153\pi$
$270$	−4.35086	−	7.53590i	−0.264785	−	0.458620i
$271$	−18.5720	+	10.7225i	−1.12817	+	0.651347i	−0.943473	−	0.331450i	$-0.892462\pi$
$271$	−18.5720	+	10.7225i	−1.12817	+	0.651347i	−0.184693	+	0.982796i	$0.559129\pi$
$272$	−4.49024			−0.272261
$273$		0			0
$274$	22.2737			1.34560
$275$	21.3092	−	12.3029i	1.28500	−	0.741893i
$276$	−13.8463	−	23.9825i	−0.833450	−	1.44358i
$277$	−7.40366	+	12.8235i	−0.444843	+	0.770490i	−0.998041	−	0.0625593i	$-0.980074\pi$
$277$	−7.40366	+	12.8235i	−0.444843	+	0.770490i	0.553199	+	0.833049i	$0.313407\pi$
$278$		−	9.46309i		−	0.567558i
$279$	2.03067	+	1.17241i	0.121573	+	0.0701902i
$280$	9.39712	+	5.42543i	0.561585	+	0.324231i
$281$			14.5036i			0.865215i	0.901582	+	0.432608i	$0.142406\pi$
$281$			14.5036i			0.865215i	−0.901582	+	0.432608i	$0.857594\pi$
$282$	2.88135	−	4.99065i	0.171582	−	0.297189i
$283$	12.8361	+	22.2328i	0.763026	+	1.32160i	0.941284	+	0.337616i	$0.109621\pi$
$283$	12.8361	+	22.2328i	0.763026	+	1.32160i	−0.178258	+	0.983984i	$0.557046\pi$
$284$	25.0143	−	14.4420i	1.48432	−	0.856974i
$285$	−9.02715			−0.534722
$286$		0			0
$287$	0.682333			0.0402768
$288$	3.22929	−	1.86443i	0.190287	−	0.109863i
$289$	4.18114	+	7.24194i	0.245949	+	0.425997i
$290$	16.7545	−	29.0197i	0.983859	−	1.70409i
$291$		−	5.94438i		−	0.348466i
$292$	−36.5984	−	21.1301i	−2.14176	−	1.23655i
$293$	22.9696	+	13.2615i	1.34190	+	0.774746i	0.987086	−	0.160191i	$-0.0512111\pi$
$293$	22.9696	+	13.2615i	1.34190	+	0.774746i	0.354813	+	0.934937i	$0.384544\pi$
$294$			14.9825i			0.873800i
$295$	9.93900	−	17.2149i	0.578671	−	1.00229i
$296$	13.6426	+	23.6296i	0.792958	+	1.37344i
$297$	2.46891	−	1.42543i	0.143261	−	0.0827117i
$298$	−45.7375			−2.64950
$299$		0			0
$300$	−30.6829			−1.77148
$301$	−1.12228	+	0.647948i	−0.0646871	+	0.0373471i
$302$	14.5683	+	25.2330i	0.838311	+	1.45200i
$303$	−2.31282	+	4.00593i	−0.132868	+	0.230134i
$304$			3.73556i			0.214249i
$305$	−42.3867	−	24.4720i	−2.42705	−	1.40126i
$306$	−5.99889	−	3.46346i	−0.342934	−	0.197993i
$307$		−	8.24698i		−	0.470680i	−0.971913	−	0.235340i	$-0.924380\pi$
$307$		−	8.24698i		−	0.470680i	0.971913	−	0.235340i	$-0.0756204\pi$
$308$	−4.06369	+	7.03851i	−0.231550	+	0.401056i
$309$	−0.603875	−	1.04594i	−0.0343533	−	0.0595016i
$310$	17.6703	−	10.2019i	1.00361	−	0.579432i
$311$	14.4179			0.817564			0.408782	−	0.912632i	$-0.365954\pi$
$311$	14.4179			0.817564			0.408782	+	0.912632i	$0.365954\pi$
$312$		0			0
$313$	14.2338			0.804544			0.402272	−	0.915520i	$-0.368221\pi$
$313$	14.2338			0.804544			0.402272	+	0.915520i	$0.368221\pi$
$314$	38.1233	−	22.0105i	2.15142	−	1.24213i
$315$	1.48039	+	2.56410i	0.0834103	+	0.144471i
$316$	9.60872	−	16.6428i	0.540533	−	0.936230i
$317$			6.84415i			0.384406i	0.981355	+	0.192203i	$0.0615632\pi$
$317$			6.84415i			0.384406i	−0.981355	+	0.192203i	$0.938437\pi$
$318$	20.3312	+	11.7383i	1.14012	+	0.658248i
$319$	9.50743	+	5.48911i	0.532314	+	0.307331i
$320$		−	43.7289i		−	2.44452i
$321$	−4.76055	+	8.24552i	−0.265708	+	0.460220i
$322$	7.36174	+	12.7509i	0.410254	+	0.710580i
$323$	−6.22324	+	3.59299i	−0.346270	+	0.199919i
$324$	−3.55496			−0.197498
$325$		0			0
$326$	29.0828			1.61075
$327$	−1.54540	+	0.892240i	−0.0854611	+	0.0493410i
$328$	1.55914	+	2.70051i	0.0860890	+	0.149111i
$329$	−0.980386	+	1.69808i	−0.0540504	+	0.0936181i
$330$		−	24.8073i		−	1.36560i
$331$	8.17757	+	4.72132i	0.449480	+	0.259507i	0.707611	−	0.706603i	$-0.249773\pi$
$331$	8.17757	+	4.72132i	0.449480	+	0.259507i	−0.258130	+	0.966110i	$0.583106\pi$
$332$	−21.7014	−	12.5293i	−1.19102	−	0.687635i
$333$			7.44504i			0.407986i
$334$	−13.5450	+	23.4607i	−0.741151	+	1.28371i
$335$	26.5710	+	46.0223i	1.45173	+	2.51447i
$336$	1.06106	−	0.612605i	0.0578857	−	0.0334203i
$337$	−2.64310			−0.143979			−0.0719895	−	0.997405i	$-0.522935\pi$
$337$	−2.64310			−0.143979			−0.0719895	+	0.997405i	$0.522935\pi$
$338$		0			0
$339$	−4.95108			−0.268906
$340$	−33.4064	+	19.2872i	−1.81171	+	1.04599i
$341$	3.34236	+	5.78914i	0.180999	+	0.313500i
$342$	−2.88135	+	4.99065i	−0.155806	+	0.269864i
$343$		−	10.7114i		−	0.578361i
$344$	−5.12884	−	2.96114i	−0.276529	−	0.159654i
$345$	−24.9072	−	14.3802i	−1.34096	−	0.774202i
$346$			28.5520i			1.53496i
$347$	5.07942	−	8.79781i	0.272677	−	0.472291i	−0.696869	−	0.717198i	$-0.745424\pi$
$347$	5.07942	−	8.79781i	0.272677	−	0.472291i	0.969547	+	0.244907i	$0.0787575\pi$
$348$	−6.84481	−	11.8556i	−0.366921	−	0.635525i
$349$	9.04102	−	5.21983i	0.483954	−	0.279411i	−0.238109	−	0.971239i	$-0.576527\pi$
$349$	9.04102	−	5.21983i	0.483954	−	0.279411i	0.722063	+	0.691827i	$0.243194\pi$
$350$	16.3134			0.871986
$351$		0			0
$352$	10.6304			0.566604
$353$	−15.8406	+	9.14556i	−0.843108	+	0.486769i	−0.858320	−	0.513115i	$-0.828491\pi$
$353$	−15.8406	+	9.14556i	−0.843108	+	0.486769i	0.0152113	+	0.999884i	$0.495158\pi$
$354$	−6.34481	−	10.9895i	−0.337223	−	0.584087i
$355$	14.9988	−	25.9787i	0.796054	−	1.37881i
$356$		−	4.02310i		−	0.213224i
$357$	2.04113	+	1.17845i	0.108028	+	0.0623701i
$358$	1.09928	+	0.634670i	0.0580988	+	0.0335434i
$359$		−	15.2731i		−	0.806081i	−0.915182	−	0.403041i	$-0.867953\pi$
$359$		−	15.2731i		−	0.806081i	0.915182	−	0.403041i	$-0.132047\pi$
$360$	−6.76540	+	11.7180i	−0.356568	+	0.617593i
$361$	−6.51089	−	11.2772i	−0.342678	−	0.593536i
$362$	−47.5253	+	27.4388i	−2.49788	+	1.44215i
$363$	−2.87263			−0.150774
$364$		0			0
$365$	−43.8896			−2.29729
$366$	−27.0586	+	15.6223i	−1.41438	+	0.816590i
$367$	11.1359	+	19.2879i	0.581288	+	1.00682i	0.995327	+	0.0965606i	$0.0307842\pi$
$367$	11.1359	+	19.2879i	0.581288	+	1.00682i	−0.414040	+	0.910259i	$0.635882\pi$
$368$	−5.95071	+	10.3069i	−0.310202	+	0.537286i
$369$			0.850855i			0.0442937i
$370$	56.1051	+	32.3923i	2.91677	+	1.68400i
$371$	−6.91774	−	3.99396i	−0.359151	−	0.207356i
$372$		−	8.33572i		−	0.432187i
$373$	−2.06315	+	3.57349i	−0.106826	+	0.185028i	−0.914483	−	0.404625i	$-0.867402\pi$
$373$	−2.06315	+	3.57349i	−0.106826	+	0.185028i	0.807657	+	0.589653i	$0.200735\pi$
$374$	−9.87382	−	17.1020i	−0.510563	−	0.884321i
$375$	−11.6098	+	6.70291i	−0.599526	+	0.346137i
$376$	−8.96077			−0.462116
$377$		0			0
$378$	1.89008			0.0972154
$379$	9.27261	−	5.35354i	0.476302	−	0.274993i	−0.242572	−	0.970133i	$-0.577991\pi$
$379$	9.27261	−	5.35354i	0.476302	−	0.274993i	0.718874	+	0.695140i	$0.244658\pi$
$380$	16.0456	+	27.7917i	0.823120	+	1.42569i
$381$	−2.83513	+	4.91058i	−0.145248	+	0.251577i
$382$		−	39.5150i		−	2.02176i
$383$	5.65210	+	3.26324i	0.288809	+	0.166744i	0.637405	−	0.770529i	$-0.280008\pi$
$383$	5.65210	+	3.26324i	0.288809	+	0.166744i	−0.348596	+	0.937273i	$0.613341\pi$
$384$	−17.7169	−	10.2289i	−0.904112	−	0.521989i
$385$			8.44073i			0.430179i
$386$	−30.3379	+	52.5467i	−1.54416	+	2.67456i
$387$	−0.807979	−	1.39946i	−0.0410719	−	0.0711385i
$388$	−18.3009	+	10.5660i	−0.929085	+	0.536408i
$389$	11.7922			0.597891			0.298945	−	0.954270i	$-0.403365\pi$
$389$	11.7922			0.597891			0.298945	+	0.954270i	$0.403365\pi$
$390$		0			0
$391$	−22.8944			−1.15782
$392$	20.1760	−	11.6486i	1.01904	−	0.588344i
$393$	9.11141	+	15.7814i	0.459610	+	0.796067i
$394$	25.2434	−	43.7228i	1.27174	−	2.20272i
$395$		−	19.9584i		−	1.00422i
$396$	−8.77688	−	5.06734i	−0.441055	−	0.254643i
$397$	10.8624	+	6.27144i	0.545171	+	0.314754i	0.747172	−	0.664631i	$-0.231411\pi$
$397$	10.8624	+	6.27144i	0.545171	+	0.314754i	−0.202001	+	0.979385i	$0.564744\pi$
$398$			8.31468i			0.416777i
$399$	0.980386	−	1.69808i	0.0490807	−	0.0850102i
$400$	6.59329	+	11.4199i	0.329664	+	0.570995i
$401$	15.4761	−	8.93512i	0.772838	−	0.446198i	−0.0610479	−	0.998135i	$-0.519444\pi$
$401$	15.4761	−	8.93512i	0.772838	−	0.446198i	0.833886	+	0.551936i	$0.186111\pi$
$402$	33.9245			1.69200
$403$		0			0
$404$	16.4440			0.818118
$405$	−3.19738	+	1.84601i	−0.158879	+	0.0917290i
$406$	3.63922	+	6.30331i	0.180611	+	0.312828i
$407$	−10.6124	+	18.3812i	−0.526036	+	0.911120i
$408$			10.7711i			0.533247i
$409$	−24.1724	−	13.9559i	−1.19525	−	0.690076i	−0.235755	−	0.971812i	$-0.575756\pi$
$409$	−24.1724	−	13.9559i	−1.19525	−	0.690076i	−0.959492	+	0.281736i	$0.909090\pi$
$410$	6.41196	+	3.70195i	0.316664	+	0.182826i
$411$		−	9.45042i		−	0.466155i
$412$	−2.14675	+	3.71828i	−0.105763	+	0.183187i
$413$	2.15883	+	3.73921i	0.106229	+	0.183994i
$414$	−15.9001	+	9.17994i	−0.781448	+	0.451169i
$415$	−26.0248			−1.27750
$416$		0			0
$417$	−4.01507			−0.196619
$418$	−14.2276	+	8.21432i	−0.695896	+	0.401776i
$419$	8.20171	+	14.2058i	0.400680	+	0.693998i	0.993808	−	0.111110i	$-0.0354407\pi$
$419$	8.20171	+	14.2058i	0.400680	+	0.693998i	−0.593128	+	0.805108i	$0.702107\pi$
$420$	5.26271	−	9.11528i	0.256794	−	0.444780i
$421$			3.03684i			0.148006i	0.997258	+	0.0740032i	$0.0235775\pi$
$421$			3.03684i			0.148006i	−0.997258	+	0.0740032i	$0.976423\pi$
$422$	2.48104	+	1.43243i	0.120775	+	0.0697295i
$423$	−2.11747	−	1.22252i	−0.102955	−	0.0594410i
$424$		−	36.5050i		−	1.77284i
$425$	−12.6833	+	21.9681i	−0.615230	+	1.06561i
$426$	−9.57487	−	16.5842i	−0.463904	−	0.803505i
$427$	9.20674	−	5.31551i	0.445545	−	0.257236i
$428$	33.8471			1.63606
$429$		0			0
$430$	−14.0616			−0.678110
$431$	2.89089	−	1.66905i	0.139249	−	0.0803955i	−0.428757	−	0.903420i	$-0.641048\pi$
$431$	2.89089	−	1.66905i	0.139249	−	0.0803955i	0.568006	+	0.823024i	$0.307715\pi$
$432$	0.763906	+	1.32312i	0.0367534	+	0.0636588i
$433$	5.95138	−	10.3081i	0.286005	−	0.495375i	−0.686847	−	0.726802i	$-0.741006\pi$
$433$	5.95138	−	10.3081i	0.286005	−	0.495375i	0.972852	+	0.231426i	$0.0743393\pi$
$434$			4.43190i			0.212738i
$435$	−12.3127	−	7.10872i	−0.590347	−	0.340837i
$436$	5.49385	+	3.17187i	0.263108	+	0.151905i
$437$			19.0465i			0.911119i
$438$	−14.0090	+	24.2643i	−0.669377	+	1.15940i
$439$	1.85905	+	3.21997i	0.0887277	+	0.153681i	0.906974	−	0.421188i	$-0.138387\pi$
$439$	1.85905	+	3.21997i	0.0887277	+	0.153681i	−0.818246	+	0.574868i	$0.805053\pi$
$440$	−33.4064	+	19.2872i	−1.59259	+	0.919480i
$441$	6.35690			0.302709
$442$		0			0
$443$	1.45712			0.0692300			0.0346150	−	0.999401i	$-0.488979\pi$
$443$	1.45712			0.0692300			0.0346150	+	0.999401i	$0.488979\pi$
$444$	22.9209	−	13.2334i	1.08778	−	0.628030i
$445$	−2.08911	−	3.61844i	−0.0990331	−	0.171530i
$446$	−20.4913	+	35.4919i	−0.970290	+	1.68059i
$447$			19.4058i			0.917863i
$448$	8.22574	+	4.74914i	0.388630	+	0.224376i
$449$	10.5026	+	6.06369i	0.495649	+	0.286163i	0.726915	−	0.686727i	$-0.240953\pi$
$449$	10.5026	+	6.06369i	0.495649	+	0.286163i	−0.231266	+	0.972891i	$0.574287\pi$
$450$			20.3424i			0.958951i
$451$	−1.21283	+	2.10069i	−0.0571100	+	0.0989175i
$452$	8.80045	+	15.2428i	0.413938	+	0.716962i
$453$	10.7060	−	6.18114i	0.503014	−	0.290415i
$454$	−41.0465			−1.92641
$455$		0			0
$456$	8.96077			0.419627
$457$	2.98608	−	1.72401i	0.139683	−	0.0806459i	−0.428530	−	0.903528i	$-0.640968\pi$
$457$	2.98608	−	1.72401i	0.139683	−	0.0806459i	0.568213	+	0.822882i	$0.307635\pi$
$458$	−22.1081	−	38.2923i	−1.03304	−	1.78928i
$459$	−1.46950	+	2.54525i	−0.0685904	+	0.118802i
$460$			102.242i			4.76704i
$461$	−5.85087	−	3.37800i	−0.272502	−	0.157329i	0.357522	−	0.933905i	$-0.383622\pi$
$461$	−5.85087	−	3.37800i	−0.272502	−	0.157329i	−0.630024	+	0.776575i	$0.716955\pi$
$462$	4.66645	+	2.69418i	0.217103	+	0.125344i
$463$		−	7.45175i		−	0.346312i	−0.984894	−	0.173156i	$-0.944604\pi$
$463$		−	7.45175i		−	0.346312i	0.984894	−	0.173156i	$-0.0553965\pi$
$464$	−2.94169	+	5.09516i	−0.136565	+	0.236537i
$465$	−4.32855	−	7.49727i	−0.200732	−	0.347678i
$466$	8.06468	−	4.65615i	0.373589	−	0.215692i
$467$	−32.6098			−1.50900			−0.754502	−	0.656298i	$-0.772121\pi$
$467$	−32.6098			−1.50900			−0.754502	+	0.656298i	$0.772121\pi$
$468$		0			0
$469$	−11.5429			−0.533001
$470$	−18.4256	+	10.6380i	−0.849909	+	0.490695i
$471$	−9.33877	−	16.1752i	−0.430308	−	0.745315i
$472$	−9.86592	+	17.0883i	−0.454116	+	0.786552i
$473$		−	4.60686i		−	0.211824i
$474$	−11.0340	−	6.37047i	−0.506807	−	0.292605i
$475$	18.2759	+	10.5516i	0.838557	+	0.484141i
$476$		−	8.37867i		−	0.384036i
$477$	4.98039	−	8.62628i	0.228036	−	0.394970i
$478$	0.964361	+	1.67032i	0.0441088	+	0.0763987i
$479$	2.45006	−	1.41454i	0.111946	−	0.0646321i	−0.442982	−	0.896531i	$-0.646079\pi$
$479$	2.45006	−	1.41454i	0.111946	−	0.0646321i	0.554928	+	0.831899i	$0.312746\pi$
$480$	−13.7670			−0.628376
$481$		0			0
$482$	14.2180			0.647614
$483$	5.41004	−	3.12349i	0.246165	−	0.142124i
$484$	5.10603	+	8.84391i	0.232092	+	0.401996i
$485$	−10.9734	+	19.0065i	−0.498276	+	0.863039i
$486$			2.35690i			0.106911i
$487$	−35.7612	−	20.6468i	−1.62050	−	0.935594i	−0.986787	−	0.162022i	$-0.948199\pi$
$487$	−35.7612	−	20.6468i	−1.62050	−	0.935594i	−0.633709	−	0.773572i	$-0.718468\pi$
$488$	42.0750	+	24.2920i	1.90465	+	1.09965i
$489$		−	12.3394i		−	0.558009i
$490$	27.6579	−	47.9049i	1.24946	−	2.16412i
$491$	−17.3349	−	30.0249i	−0.782313	−	1.35501i	−0.930591	−	0.366060i	$-0.880707\pi$
$491$	−17.3349	−	30.0249i	−0.782313	−	1.35501i	0.148279	−	0.988946i	$-0.452627\pi$
$492$	2.61951	−	1.51238i	0.118097	−	0.0681832i
$493$	−11.3177			−0.509722
$494$		0			0
$495$	−10.5254			−0.473082
$496$	−3.10248	+	1.79122i	−0.139305	+	0.0804280i
$497$	3.25786	+	5.64279i	0.146135	+	0.253114i
$498$	−8.30678	+	14.3878i	−0.372236	+	0.644731i
$499$		−	17.9409i		−	0.803146i	−0.915827	−	0.401573i	$-0.868464\pi$
$499$		−	17.9409i		−	0.803146i	0.915827	−	0.401573i	$-0.131536\pi$
$500$	41.2723	+	23.8286i	1.84575	+	1.06565i
$501$	9.95406	+	5.74698i	0.444715	+	0.256756i
$502$		−	63.3532i		−	2.82759i
$503$	13.0906	−	22.6736i	0.583681	−	1.01096i	−0.411358	−	0.911474i	$-0.634945\pi$
$503$	13.0906	−	22.6736i	0.583681	−	1.01096i	0.995038	−	0.0994909i	$-0.0317214\pi$
$504$	−1.46950	−	2.54525i	−0.0654568	−	0.113374i
$505$	14.7900	−	8.53899i	0.658145	−	0.379980i
$506$	−52.3414			−2.32686
$507$		0			0
$508$	20.1575			0.894345
$509$	4.76837	−	2.75302i	0.211354	−	0.122025i	−0.390586	−	0.920566i	$-0.627728\pi$
$509$	4.76837	−	2.75302i	0.211354	−	0.122025i	0.601941	+	0.798541i	$0.294394\pi$
$510$	12.7872	+	22.1480i	0.566225	+	0.980731i
$511$	4.76659	−	8.25598i	0.210862	−	0.365223i
$512$			16.8955i			0.746681i
$513$	2.11747	+	1.22252i	0.0934885	+	0.0539756i
$514$	18.4788	+	10.6688i	0.815066	+	0.470579i
$515$			4.45904i			0.196489i
$516$	−2.87233	+	4.97502i	−0.126447	+	0.219013i
$517$	−3.48523	−	6.03660i	−0.153280	−	0.265489i
$518$	−12.1865	+	7.03588i	−0.535444	+	0.309139i
$519$	12.1142			0.531756
$520$		0			0
$521$	−26.7211			−1.17067			−0.585336	−	0.810791i	$-0.699037\pi$
$521$	−26.7211			−1.17067			−0.585336	+	0.810791i	$0.699037\pi$
$522$	−7.86010	+	4.53803i	−0.344027	+	0.198624i
$523$	−18.2615	−	31.6299i	−0.798520	−	1.38308i	−0.920580	−	0.390555i	$-0.872283\pi$
$523$	−18.2615	−	31.6299i	−0.798520	−	1.38308i	0.122060	−	0.992523i	$-0.461050\pi$
$524$	32.3907	−	56.1023i	1.41499	−	2.45084i
$525$		−	6.92154i		−	0.302081i
$526$	47.2544	+	27.2823i	2.06039	+	1.18957i
$527$	−5.96814	−	3.44571i	−0.259976	−	0.150097i
$528$			4.35557i			0.189552i
$529$	−18.8409	+	32.6334i	−0.819171	+	1.41885i
$530$	−43.3379	−	75.0634i	−1.88248	−	3.26055i
$531$	−4.66272	+	2.69202i	−0.202345	+	0.116824i
$532$	−6.97046			−0.302208
$533$		0			0
$534$	−2.66727			−0.115424
$535$	30.4426	−	17.5761i	1.31615	−	0.759880i
$536$	−26.3756	−	45.6839i	−1.13925	−	1.97324i
$537$	0.269282	−	0.466411i	0.0116204	−	0.0201271i
$538$			5.70576i			0.245993i
$539$	15.6946	+	9.06129i	0.676015	+	0.390298i
$540$	11.3666	+	6.56249i	0.489139	+	0.282405i
$541$			18.4655i			0.793893i	0.917842	+	0.396947i	$0.129930\pi$
$541$			18.4655i			0.793893i	−0.917842	+	0.396947i	$0.870070\pi$
$542$	25.2719	−	43.7722i	1.08552	−	1.88018i
$543$	11.6419	+	20.1644i	0.499602	+	0.865336i
$544$	−9.49087	+	5.47956i	−0.406918	+	0.234934i
$545$	6.58834			0.282213
$546$		0			0
$547$	39.8471			1.70374			0.851870	−	0.523753i	$-0.175468\pi$
$547$	39.8471			1.70374			0.851870	+	0.523753i	$0.175468\pi$
$548$	−29.0949	+	16.7979i	−1.24287	+	0.717572i
$549$	6.62833	+	11.4806i	0.282890	+	0.489981i
$550$	−28.9966	+	50.2237i	−1.23642	+	2.14154i
$551$			9.41550i			0.401114i
$552$	24.7240	+	14.2744i	1.05232	+	0.607560i
$553$	3.75433	+	2.16756i	0.159650	+	0.0921741i
$554$		−	34.8993i		−	1.48273i
$555$	13.7436	−	23.8047i	0.583384	−	1.01045i
$556$	7.13669	+	12.3611i	0.302663	+	0.524228i
$557$	7.97156	−	4.60238i	0.337766	−	0.195009i	−0.321518	−	0.946904i	$-0.604193\pi$
$557$	7.97156	−	4.60238i	0.337766	−	0.195009i	0.659284	+	0.751894i	$0.270860\pi$
$558$	−5.52648			−0.233955
$559$		0			0
$560$	−4.52350			−0.191153
$561$	−7.25614	+	4.18933i	−0.306354	+	0.176874i
$562$	−17.0918	−	29.6039i	−0.720974	−	1.24876i
$563$	−0.487623	+	0.844588i	−0.0205509	+	0.0355951i	−0.876118	−	0.482097i	$-0.839875\pi$
$563$	−0.487623	+	0.844588i	−0.0205509	+	0.0355951i	0.855567	+	0.517692i	$0.173209\pi$
$564$			8.69202i			0.366000i
$565$	15.8305	+	9.13975i	0.665995	+	0.384512i
$566$	−52.4003	−	30.2533i	−2.20255	−	1.27164i
$567$		−	0.801938i		−	0.0336782i
$568$	−14.8885	+	25.7877i	−0.624708	+	1.08203i
$569$	−8.44720	−	14.6310i	−0.354125	−	0.613362i	0.632843	−	0.774280i	$-0.281888\pi$
$569$	−8.44720	−	14.6310i	−0.354125	−	0.613362i	−0.986968	+	0.160918i	$0.948555\pi$
$570$	18.4256	−	10.6380i	0.771763	−	0.445578i
$571$	44.3226			1.85484			0.927421	−	0.374019i	$-0.122021\pi$
$571$	44.3226			1.85484			0.927421	+	0.374019i	$0.122021\pi$
$572$		0			0
$573$	−16.7657			−0.700397
$574$	−1.39273	+	0.804094i	−0.0581315	+	0.0335622i
$575$	33.6172	+	58.2267i	1.40193	+	2.42822i
$576$	−5.92208	+	10.2573i	−0.246753	+	0.427389i
$577$		−	3.56704i		−	0.148498i	−0.997240	−	0.0742489i	$-0.976344\pi$
$577$		−	3.56704i		−	0.148498i	0.997240	−	0.0742489i	$-0.0236559\pi$
$578$	−17.0685	−	9.85450i	−0.709956	−	0.409893i
$579$	22.2949	+	12.8720i	0.926544	+	0.534940i
$580$			50.5424i			2.09866i
$581$	2.82640	−	4.89546i	0.117259	−	0.203098i
$582$	7.00514	+	12.1333i	0.290372	+	0.502940i
$583$	24.5923	−	14.1984i	1.01851	−	0.588036i
$584$	43.5669			1.80281
$585$		0			0
$586$	−62.5120			−2.58235
$587$	13.9579	−	8.05861i	0.576105	−	0.332614i	−0.183479	−	0.983024i	$-0.558736\pi$
$587$	13.9579	−	8.05861i	0.576105	−	0.332614i	0.759584	+	0.650409i	$0.225403\pi$
$588$	−11.2992	−	19.5709i	−0.465973	−	0.807089i
$589$	−2.86658	+	4.96507i	−0.118116	+	0.204582i
$590$			46.8504i			1.92880i
$591$	−18.5510	−	10.7104i	−0.763087	−	0.440569i
$592$	−9.85071	−	5.68731i	−0.404862	−	0.233747i
$593$		−	42.8611i		−	1.76010i	−0.474885	−	0.880048i	$-0.657510\pi$
$593$		−	42.8611i		−	1.76010i	0.474885	−	0.880048i	$-0.342490\pi$
$594$	−3.35958	+	5.81897i	−0.137845	+	0.238755i
$595$	−4.35086	−	7.53590i	−0.178368	−	0.308942i
$596$	59.7444	−	34.4934i	2.44722	−	1.41291i
$597$	3.52781			0.144384
$598$		0			0
$599$	40.9420			1.67284			0.836422	−	0.548086i	$-0.184643\pi$
$599$	40.9420			1.67284			0.836422	+	0.548086i	$0.184643\pi$
$600$	27.3938	−	15.8158i	1.11835	−	0.645678i
$601$	−0.593523	−	1.02801i	−0.0242103	−	0.0419335i	0.853666	−	0.520820i	$-0.174374\pi$
$601$	−0.593523	−	1.02801i	−0.0242103	−	0.0419335i	−0.877877	+	0.478887i	$0.841040\pi$
$602$	1.52715	−	2.64510i	0.0622419	−	0.107806i
$603$		−	14.3937i		−	0.586158i
$604$	−38.0595	−	21.9737i	−1.54862	−	0.894096i
$605$	9.18489	+	5.30290i	0.373419	+	0.215593i
$606$		−	10.9022i		−	0.442870i
$607$	−9.99612	+	17.3138i	−0.405730	+	0.702745i	−0.994406	−	0.105624i	$-0.966316\pi$
$607$	−9.99612	+	17.3138i	−0.405730	+	0.702745i	0.588676	+	0.808369i	$0.299649\pi$
$608$	4.55861	+	7.89574i	0.184876	+	0.320214i
$609$	2.67441	−	1.54407i	0.108373	−	0.0625690i
$610$	115.356			4.67062
$611$		0			0
$612$	10.4480			0.422336
$613$	28.8922	−	16.6809i	1.16694	−	0.673735i	0.213985	−	0.976837i	$-0.431356\pi$
$613$	28.8922	−	16.6809i	1.16694	−	0.673735i	0.952958	+	0.303102i	$0.0980222\pi$
$614$	9.71864	+	16.8332i	0.392212	+	0.679332i
$615$	1.57069	−	2.72051i	0.0633362	−	0.109702i
$616$		−	8.37867i		−	0.337586i
$617$	10.0660	+	5.81163i	0.405243	+	0.233967i	0.688744	−	0.725005i	$-0.258162\pi$
$617$	10.0660	+	5.81163i	0.405243	+	0.233967i	−0.283501	+	0.958972i	$0.591496\pi$
$618$	2.46518	+	1.42327i	0.0991640	+	0.0572524i
$619$		−	16.5381i		−	0.664722i	−0.943152	−	0.332361i	$-0.892155\pi$
$619$		−	16.5381i		−	0.664722i	0.943152	−	0.332361i	$-0.107845\pi$
$620$	−15.3878	+	26.6525i	−0.617990	+	1.07039i
$621$	3.89493	+	6.74621i	0.156298	+	0.270716i
$622$	−29.4288	+	16.9907i	−1.17999	+	0.681267i
$623$	0.907542			0.0363599
$624$		0			0
$625$	6.33944			0.253577
$626$	−29.0531	+	16.7738i	−1.16120	+	0.670417i
$627$	3.48523	+	6.03660i	0.139187	+	0.241078i
$628$	−33.1989	+	57.5023i	−1.32478	+	2.29459i
$629$		−	21.8810i		−	0.872452i
$630$	−6.04332	−	3.48911i	−0.240772	−	0.139010i
$631$	31.5593	+	18.2208i	1.25636	+	0.725358i	0.972364	−	0.233468i	$-0.0750074\pi$
$631$	31.5593	+	18.2208i	1.25636	+	0.725358i	0.283993	+	0.958826i	$0.408341\pi$
$632$			19.8116i			0.788064i
$633$	0.607760	−	1.05267i	0.0241563	−	0.0418399i
$634$	−8.06547	−	13.9698i	−0.320321	−	0.554812i
$635$	18.1300	−	10.4673i	0.719466	−	0.415384i
$636$	−35.4101			−1.40410
$637$		0			0
$638$	−25.8745			−1.02438
$639$	−7.03644	+	4.06249i	−0.278357	+	0.160710i
$640$	37.7652	+	65.4112i	1.49280	+	2.58560i
$641$	13.6033	−	23.5617i	0.537300	−	0.930630i	−0.461748	−	0.887011i	$-0.652778\pi$
$641$	13.6033	−	23.5617i	0.537300	−	0.930630i	0.999048	−	0.0436195i	$-0.0138889\pi$
$642$		−	22.4403i		−	0.885646i
$643$	−4.39042	−	2.53481i	−0.173141	−	0.0999632i	0.410925	−	0.911669i	$-0.365206\pi$
$643$	−4.39042	−	2.53481i	−0.173141	−	0.0999632i	−0.584066	+	0.811706i	$0.698539\pi$
$644$	−19.2325	−	11.1039i	−0.757866	−	0.437554i
$645$			5.96615i			0.234917i
$646$	8.46830	−	14.6675i	0.333181	−	0.577086i
$647$	9.66033	+	16.7322i	0.379787	+	0.657810i	0.991031	−	0.133632i	$-0.0426641\pi$
$647$	9.66033	+	16.7322i	0.379787	+	0.657810i	−0.611244	+	0.791442i	$0.709331\pi$
$648$	3.17387	−	1.83244i	0.124682	−	0.0719849i
$649$	−15.3491			−0.602506
$650$		0			0
$651$	1.88040			0.0736985
$652$	−37.9892	+	21.9331i	−1.48777	+	0.858966i
$653$	−17.6177	−	30.5148i	−0.689436	−	1.19414i	−0.972021	−	0.234895i	$-0.924525\pi$
$653$	−17.6177	−	30.5148i	−0.689436	−	1.19414i	0.282585	−	0.959242i	$-0.408808\pi$
$654$	2.10292	−	3.64236i	0.0822305	−	0.142427i
$655$		−	67.2790i		−	2.62881i
$656$	−1.12579	−	0.649973i	−0.0439546	−	0.0253772i
$657$	10.2950	+	5.94385i	0.401648	+	0.231891i
$658$		−	4.62133i		−	0.180158i
$659$	2.18084	−	3.77733i	0.0849535	−	0.147144i	−0.820418	−	0.571764i	$-0.806259\pi$
$659$	2.18084	−	3.77733i	0.0849535	−	0.147144i	0.905371	+	0.424621i	$0.139592\pi$
$660$	18.7087	+	32.4044i	0.728236	+	1.26134i
$661$	−13.3982	+	7.73543i	−0.521128	+	0.300873i	−0.737396	−	0.675461i	$-0.763945\pi$
$661$	−13.3982	+	7.73543i	−0.521128	+	0.300873i	0.216268	+	0.976334i	$0.430611\pi$
$662$	−22.2553			−0.864978
$663$		0			0
$664$	25.8334			1.00253
$665$	−6.26934	+	3.61960i	−0.243115	+	0.140362i
$666$	−8.77359	−	15.1963i	−0.339970	−	0.588845i
$667$	−14.9988	+	25.9787i	−0.580756	+	1.00590i
$668$		−	40.8605i		−	1.58094i
$669$	15.0588	+	8.69418i	0.582205	+	0.336136i
$670$	−108.470	−	62.6250i	−4.19055	−	2.41942i
$671$			37.7928i			1.45898i
$672$	1.49516	−	2.58969i	0.0576769	−	0.0998993i
$673$	−5.87047	−	10.1680i	−0.226290	−	0.391946i	0.730416	−	0.683003i	$-0.239326\pi$
$673$	−5.87047	−	10.1680i	−0.226290	−	0.391946i	−0.956706	+	0.291057i	$0.905993\pi$
$674$	5.39492	−	3.11476i	0.207805	−	0.119976i
$675$	8.63102			0.332208
$676$		0			0
$677$	3.44504			0.132404			0.0662019	−	0.997806i	$-0.478912\pi$
$677$	3.44504			0.132404			0.0662019	+	0.997806i	$0.478912\pi$
$678$	10.1058	−	5.83459i	0.388111	−	0.224076i
$679$	−2.38351	−	4.12836i	−0.0914707	−	0.158432i
$680$	19.8835	−	34.4393i	0.762498	−	1.32068i
$681$			17.4155i			0.667363i
$682$	−13.6444	−	7.87760i	−0.522471	−	0.301649i
$683$	−17.6720	−	10.2029i	−0.676198	−	0.390403i	0.122223	−	0.992503i	$-0.460998\pi$
$683$	−17.6720	−	10.2029i	−0.676198	−	0.390403i	−0.798421	+	0.602099i	$0.794331\pi$
$684$		−	8.69202i		−	0.332348i
$685$	−17.4456	+	30.2166i	−0.666561	+	1.15452i
$686$	12.6228	+	21.8634i	0.481942	+	0.834748i
$687$	−16.2469	+	9.38016i	−0.619858	+	0.357875i
$688$	2.46888			0.0941251
$689$		0			0
$690$	67.7851			2.58053
$691$	−24.0788	+	13.9019i	−0.916002	+	0.528854i	−0.882358	−	0.470580i	$-0.844045\pi$
$691$	−24.0788	+	13.9019i	−0.916002	+	0.528854i	−0.0336449	+	0.999434i	$0.510712\pi$
$692$	−21.5328	−	37.2959i	−0.818554	−	1.41778i
$693$	1.14310	−	1.97991i	0.0434229	−	0.0752107i
$694$			23.9433i			0.908876i
$695$	12.8377	+	7.41185i	0.486962	+	0.281148i
$696$	12.2221	+	7.05645i	0.463279	+	0.267474i
$697$		−	2.50066i		−	0.0947194i
$698$	−12.3026	+	21.3087i	−0.465660	+	0.806547i
$699$	−1.97554	−	3.42174i	−0.0747218	−	0.129422i
$700$	−21.3092	+	12.3029i	−0.805414	+	0.465006i
$701$	−11.9715			−0.452158			−0.226079	−	0.974109i	$-0.572591\pi$
$701$	−11.9715			−0.452158			−0.226079	+	0.974109i	$0.572591\pi$
$702$		0			0
$703$	−18.2034			−0.686556
$704$	−29.2422	+	16.8830i	−1.10211	+	0.636301i
$705$	4.51357	+	7.81774i	0.169991	+	0.294433i
$706$	21.5551	−	37.3346i	0.811238	−	1.40510i
$707$			3.70948i			0.139509i
$708$	16.5758	+	9.57002i	0.622955	+	0.359664i
$709$	−27.9435	−	16.1332i	−1.04944	−	0.605894i	−0.126947	−	0.991909i	$-0.540518\pi$
$709$	−27.9435	−	16.1332i	−1.04944	−	0.605894i	−0.922492	+	0.386015i	$0.873851\pi$
$710$			70.7012i			2.65337i
$711$	−2.70291	+	4.68157i	−0.101367	+	0.175573i
$712$	2.07374	+	3.59183i	0.0777169	+	0.134610i
$713$	−15.8186	+	9.13288i	−0.592412	+	0.342029i
$714$	−5.55496			−0.207889
$715$		0			0
$716$	−1.91457			−0.0715510
$717$	0.708696	−	0.409166i	0.0264667	−	0.0152806i
$718$	17.9985	+	31.1743i	0.671698	+	1.16342i
$719$	6.05429	−	10.4863i	0.225787	−	0.391075i	−0.730768	−	0.682626i	$-0.760838\pi$
$719$	6.05429	−	10.4863i	0.225787	−	0.391075i	0.956555	+	0.291551i	$0.0941713\pi$
$720$		−	5.64071i		−	0.210217i
$721$	−0.838781	−	0.484271i	−0.0312378	−	0.0180352i
$722$	26.5791	+	15.3455i	0.989173	+	0.571100i
$723$		−	6.03252i		−	0.224352i
$724$	41.3865	−	71.6835i	1.53812	−	2.66410i
$725$	16.6184	+	28.7839i	0.617192	+	1.06901i
$726$	5.86341	−	3.38524i	0.217611	−	0.125638i
$727$	16.6200			0.616402			0.308201	−	0.951321i	$-0.400273\pi$
$727$	16.6200			0.616402			0.308201	+	0.951321i	$0.400273\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	89.5845	−	51.7216i	3.31567	−	1.91430i
$731$	2.37465	+	4.11301i	0.0878296	+	0.152125i
$732$	23.5635	−	40.8131i	0.870930	−	1.50850i
$733$		−	17.7912i		−	0.657132i	−0.944481	−	0.328566i	$-0.893435\pi$
$733$		−	17.7912i		−	0.657132i	0.944481	−	0.328566i	$-0.106565\pi$
$734$	−45.4595	−	26.2461i	−1.67794	−	0.968760i
$735$	−20.3254	−	11.7349i	−0.749715	−	0.432848i
$736$			29.0473i			1.07070i
$737$	20.5172	−	35.5369i	0.755762	−	1.30902i
$738$	−1.00269	−	1.73671i	−0.0369095	−	0.0639291i
$739$	−23.6960	+	13.6809i	−0.871672	+	0.503260i	−0.867903	−	0.496733i	$-0.834533\pi$
$739$	−23.6960	+	13.6809i	−0.871672	+	0.503260i	−0.00376844	+	0.999993i	$0.501200\pi$
$740$	−97.7160			−3.59211
$741$		0			0
$742$	18.8267			0.691150
$743$	−7.26246	+	4.19298i	−0.266434	+	0.153826i	−0.627266	−	0.778805i	$-0.715826\pi$
$743$	−7.26246	+	4.19298i	−0.266434	+	0.153826i	0.360832	+	0.932631i	$0.382493\pi$
$744$	4.29672	+	7.44215i	0.157526	+	0.272842i
$745$	35.8233	−	62.0478i	1.31247	−	2.27326i
$746$		−	9.72528i		−	0.356068i
$747$	6.10454	+	3.52446i	0.223353	+	0.128953i
$748$	25.7953	+	14.8929i	0.943168	+	0.544538i
$749$			7.63533i			0.278989i
$750$	15.7981	−	27.3630i	0.576863	−	0.999157i
$751$	−19.3889	−	33.5825i	−0.707511	−	1.22544i	−0.965778	−	0.259371i	$-0.916485\pi$
$751$	−19.3889	−	33.5825i	−0.707511	−	1.22544i	0.258267	−	0.966073i	$-0.416848\pi$
$752$	3.23509	−	1.86778i	0.117972	−	0.0681110i
$753$	−26.8799			−0.979559
$754$		0			0
$755$	−45.6418			−1.66107
$756$	−2.46891	+	1.42543i	−0.0897935	+	0.0518423i
$757$	−6.48643	−	11.2348i	−0.235753	−	0.408336i	0.723738	−	0.690075i	$-0.242422\pi$
$757$	−6.48643	−	11.2348i	−0.235753	−	0.408336i	−0.959491	+	0.281738i	$0.909089\pi$
$758$	−12.6177	+	21.8546i	−0.458297	+	0.793794i
$759$			22.2078i			0.806090i
$760$	−28.6510	−	16.5417i	−1.03928	−	0.600030i
$761$	4.46510	+	2.57792i	0.161860	+	0.0934497i	0.578742	−	0.815511i	$-0.303544\pi$
$761$	4.46510	+	2.57792i	0.161860	+	0.0934497i	−0.416882	+	0.908961i	$0.636877\pi$
$762$		−	13.3642i		−	0.484134i
$763$	−0.715521	+	1.23932i	−0.0259036	+	0.0448663i
$764$	29.8007	+	51.6163i	1.07815	+	1.86741i
$765$	9.39712	−	5.42543i	0.339753	−	0.196157i
$766$	−15.3822			−0.555783
$767$		0			0
$768$	24.5284			0.885092
$769$	30.7450	−	17.7506i	1.10869	−	0.640104i	0.170202	−	0.985409i	$-0.445558\pi$
$769$	30.7450	−	17.7506i	1.10869	−	0.640104i	0.938490	+	0.345305i	$0.112225\pi$
$770$	−9.94696	−	17.2286i	−0.358464	−	0.620877i
$771$	4.52661	−	7.84033i	0.163022	−	0.282362i
$772$		−	91.5186i		−	3.29383i
$773$	−5.33112	−	3.07792i	−0.191747	−	0.110705i	0.401053	−	0.916055i	$-0.368644\pi$
$773$	−5.33112	−	3.07792i	−0.191747	−	0.110705i	−0.592800	+	0.805350i	$0.701978\pi$
$774$	3.29838	+	1.90432i	0.118558	+	0.0684494i
$775$			20.2381i			0.726976i
$776$	10.8927	−	18.8667i	0.391025	−	0.677275i
$777$	2.98523	+	5.17057i	0.107095	+	0.185493i
$778$	−24.0695	+	13.8966i	−0.862935	+	0.498216i
$779$	−2.08038			−0.0745372
$780$		0			0
$781$	−23.1631			−0.828843
$782$	46.7305	−	26.9799i	1.67108	−	0.964798i
$783$	1.92543	+	3.33494i	0.0688092	+	0.119181i
$784$	−4.85607	+	8.41096i	−0.173431	+	0.300391i
$785$			68.9579i			2.46121i
$786$	−37.1952	−	21.4746i	−1.32671	−	0.765975i
$787$	−12.3069	−	7.10537i	−0.438692	−	0.253279i	0.264351	−	0.964427i	$-0.414842\pi$
$787$	−12.3069	−	7.10537i	−0.438692	−	0.253279i	−0.703043	+	0.711148i	$0.748176\pi$
$788$			76.1503i			2.71274i
$789$	11.5755	−	20.0494i	0.412100	−	0.713778i
$790$	23.5199	+	40.7377i	0.836801	+	1.44938i
$791$	−3.43852	+	1.98523i	−0.122260	+	0.0705867i
$792$	10.4480			0.371254
$793$		0			0
$794$	−29.5623			−1.04913
$795$	−31.8484	+	18.3877i	−1.12955	+	0.652144i
$796$	−6.27061	−	10.8610i	−0.222256	−	0.384958i
$797$	5.95108	−	10.3076i	0.210798	−	0.365113i	−0.741166	−	0.671321i	$-0.765727\pi$
$797$	5.95108	−	10.3076i	0.210798	−	0.365113i	0.951965	+	0.306208i	$0.0990604\pi$
$798$			4.62133i			0.163593i
$799$	6.22324	+	3.59299i	0.220162	+	0.127111i
$800$	27.8720	+	16.0919i	0.985425	+	0.568935i
$801$			1.13169i			0.0399862i
$802$	−21.0591	+	36.4755i	−0.743624	+	1.28799i
$803$	16.9450	+	29.3497i	0.597978	+	1.03573i
$804$	−44.3138	+	25.5846i	−1.56283	+	0.902298i
$805$	−23.0640			−0.812899
$806$		0			0
$807$	2.42088			0.0852190
$808$	−14.6812	+	8.47621i	−0.516483	+	0.298192i
$809$	−0.807979	−	1.39946i	−0.0284070	−	0.0492024i	0.851472	−	0.524399i	$-0.175710\pi$
$809$	−0.807979	−	1.39946i	−0.0284070	−	0.0492024i	−0.879879	+	0.475197i	$0.842377\pi$
$810$	4.35086	−	7.53590i	0.152873	−	0.264785i
$811$			51.9657i			1.82476i	0.409342	+	0.912381i	$0.365758\pi$
$811$			51.9657i			1.82476i	−0.409342	+	0.912381i	$0.634242\pi$
$812$	−9.50743	−	5.48911i	−0.333645	−	0.192630i
$813$	−18.5720	−	10.7225i	−0.651347	−	0.376055i
$814$		−	50.0245i		−	1.75336i
$815$	−22.7787	+	39.4539i	−0.797904	+	1.38201i
$816$	−2.24512	−	3.88866i	−0.0785949	−	0.136130i
$817$	3.42174	−	1.97554i	0.119711	−	0.0691154i
$818$	65.7853			2.30013
$819$		0			0
$820$	−11.1675			−0.389985
$821$	−47.4865	+	27.4163i	−1.65729	+	0.956837i	−0.683331	+	0.730108i	$0.739470\pi$
$821$	−47.4865	+	27.4163i	−1.65729	+	0.956837i	−0.973958	+	0.226728i	$0.927197\pi$
$822$	11.1368	+	19.2895i	0.388441	+	0.672800i
$823$	−23.4257	+	40.5745i	−0.816569	+	1.41434i	0.0916262	+	0.995793i	$0.470794\pi$
$823$	−23.4257	+	40.5745i	−0.816569	+	1.41434i	−0.908196	+	0.418546i	$0.862540\pi$
$824$		−	4.42626i		−	0.154196i
$825$	21.3092	+	12.3029i	0.741893	+	0.428332i
$826$	−8.81293	−	5.08815i	−0.306641	−	0.177039i
$827$			21.2021i			0.737270i	0.929574	+	0.368635i	$0.120175\pi$
$827$			21.2021i			0.737270i	−0.929574	+	0.368635i	$0.879825\pi$
$828$	13.8463	−	23.9825i	0.481192	−	0.833450i
$829$	9.14861	+	15.8459i	0.317744	+	0.550350i	0.980017	−	0.198913i	$-0.0637413\pi$
$829$	9.14861	+	15.8459i	0.317744	+	0.550350i	−0.662273	+	0.749263i	$0.730408\pi$
$830$	53.1200	−	30.6688i	1.84382	−	1.06453i
$831$	−14.8073			−0.513660
$832$		0			0
$833$	−18.6829			−0.647325
$834$	8.19528	−	4.73155i	0.283779	−	0.163840i
$835$	−21.2180	−	36.7506i	−0.734278	−	1.27181i
$836$	12.3898	−	21.4598i	0.428512	−	0.742204i
$837$			2.34481i			0.0810486i
$838$	−33.4815	−	19.3306i	−1.15660	−	0.667764i
$839$	−18.3090	−	10.5707i	−0.632096	−	0.364941i	0.149468	−	0.988767i	$-0.452244\pi$
$839$	−18.3090	−	10.5707i	−0.632096	−	0.364941i	−0.781563	+	0.623826i	$0.785577\pi$
$840$			10.8509i			0.374390i
$841$	7.08546	−	12.2724i	0.244326	−	0.423185i
$842$	−3.57875	−	6.19858i	−0.123332	−	0.213617i
$843$	−12.5605	+	7.25182i	−0.432608	+	0.249766i
$844$	−4.32113			−0.148739
$845$		0			0
$846$	5.76271			0.198126
$847$	−1.99503	+	1.15183i	−0.0685502	+	0.0395775i
$848$	7.60909	+	13.1793i	0.261297	+	0.452580i
$849$	−12.8361	+	22.2328i	−0.440533	+	0.763026i
$850$		−	59.7864i		−	2.05066i
$851$	−50.2258	−	28.9979i	−1.72172	−	0.994035i
$852$	25.0143	+	14.4420i	0.856974	+	0.494774i
$853$		−	7.13036i		−	0.244139i	−0.992522	−	0.122069i	$-0.961047\pi$
$853$		−	7.13036i		−	0.244139i	0.992522	−	0.122069i	$-0.0389531\pi$
$854$	−12.5281	+	21.6993i	−0.428703	+	0.742535i
$855$	−4.51357	−	7.81774i	−0.154361	−	0.267361i
$856$	−30.2188	+	17.4468i	−1.03286	+	0.596320i
$857$	44.7741			1.52945			0.764726	−	0.644355i	$-0.222874\pi$
$857$	44.7741			1.52945			0.764726	+	0.644355i	$0.222874\pi$
$858$		0			0
$859$	57.3782			1.95772			0.978859	−	0.204535i	$-0.0655681\pi$
$859$	57.3782			1.95772			0.978859	+	0.204535i	$0.0655681\pi$
$860$	18.3679	−	10.6047i	0.626340	−	0.361617i
$861$	0.341166	+	0.590918i	0.0116269	+	0.0201384i
$862$	−3.93379	+	6.81352i	−0.133985	+	0.232069i
$863$			6.67563i			0.227241i	0.993524	+	0.113621i	$0.0362448\pi$
$863$			6.67563i			0.227241i	−0.993524	+	0.113621i	$0.963755\pi$
$864$	3.22929	+	1.86443i	0.109863	+	0.0634291i
$865$	−38.7338	−	22.3630i	−1.31699	−	0.760365i
$866$			28.0536i			0.953299i
$867$	−4.18114	+	7.24194i	−0.141999	+	0.245949i
$868$	−3.34236	−	5.78914i	−0.113447	−	0.196496i
$869$	−13.3465	+	7.70560i	−0.452748	+	0.261394i
$870$	33.5090			1.13606
$871$		0			0
$872$	−6.53989			−0.221469
$873$	5.14798	−	2.97219i	0.174233	−	0.100593i
$874$	−22.4453	−	38.8765i	−0.759225	−	1.31502i
$875$	−5.37531	+	9.31032i	−0.181719	+	0.314746i
$876$		−	42.2602i		−	1.42784i
$877$	21.9090	+	12.6491i	0.739813	+	0.427131i	0.822001	−	0.569486i	$-0.192858\pi$
$877$	21.9090	+	12.6491i	0.739813	+	0.427131i	−0.0821883	+	0.996617i	$0.526191\pi$
$878$	−7.58914	−	4.38159i	−0.256121	−	0.147872i
$879$			26.5230i			0.894599i
$880$	8.04043	−	13.9264i	0.271043	−	0.469460i
$881$	−17.6893	−	30.6388i	−0.595969	−	1.03225i	−0.993409	−	0.114620i	$-0.963435\pi$
$881$	−17.6893	−	30.6388i	−0.595969	−	1.03225i	0.397441	−	0.917628i	$-0.369898\pi$
$882$	−12.9753	+	7.49127i	−0.436900	+	0.252244i
$883$	11.5851			0.389869			0.194935	−	0.980816i	$-0.437551\pi$
$883$	11.5851			0.389869			0.194935	+	0.980816i	$0.437551\pi$
$884$		0			0
$885$	19.8780			0.668192
$886$	−2.97418	+	1.71714i	−0.0999196	+	0.0576886i
$887$	13.6446	+	23.6331i	0.458141	+	0.793523i	0.998863	−	0.0476784i	$-0.0151822\pi$
$887$	13.6446	+	23.6331i	0.458141	+	0.793523i	−0.540722	+	0.841201i	$0.681849\pi$
$888$	−13.6426	+	23.6296i	−0.457815	+	0.792958i
$889$			4.54719i			0.152508i
$890$	8.52828	+	4.92380i	0.285869	+	0.165046i
$891$	2.46891	+	1.42543i	0.0827117	+	0.0477536i
$892$		−	61.8149i		−	2.06972i
$893$	2.98911	−	5.17730i	0.100027	−	0.173252i
$894$	−22.8687	−	39.6098i	−0.764845	−	1.32475i
$895$	−1.72200	+	0.994196i	−0.0575601	+	0.0332323i
$896$	−16.4058			−0.548080
$897$		0			0
$898$	−28.5830			−0.953826
$899$	−7.81981	+	4.51477i	−0.260805	+	0.150576i
$900$	−15.3415	−	26.5722i	−0.511382	−	0.885740i
$901$	−14.6374	+	25.3526i	−0.487641	+	0.844619i
$902$		−	5.71704i		−	0.190357i
$903$	−1.12228	−	0.647948i	−0.0373471	−	0.0215624i
$904$	−15.7141	−	9.07255i	−0.522644	−	0.301748i
$905$		−	85.9643i		−	2.85755i
$906$	−14.5683	+	25.2330i	−0.483999	+	0.838311i
$907$	−15.2110	−	26.3462i	−0.505072	−	0.874810i	−0.999983	−	0.00586661i	$-0.998133\pi$
$907$	−15.2110	−	26.3462i	−0.505072	−	0.874810i	0.494911	−	0.868944i	$-0.335201\pi$
$908$	53.6168	−	30.9557i	1.77934	−	1.02730i
$909$	−4.62565			−0.153423
$910$		0			0
$911$	53.5719			1.77492			0.887459	−	0.460887i	$-0.152469\pi$
$911$	53.5719			1.77492			0.887459	+	0.460887i	$0.152469\pi$
$912$	−3.23509	+	1.86778i	−0.107125	+	0.0618484i
$913$	10.0477	+	17.4032i	0.332531	+	0.575961i
$914$	−4.06332	+	7.03787i	−0.134403	+	0.232792i
$915$		−	48.9439i		−	1.61804i
$916$	57.7571	+	33.3461i	1.90835	+	1.10179i
$917$	12.6557	+	7.30678i	0.417929	+	0.241291i
$918$		−	6.92692i		−	0.228622i
$919$	18.0836	−	31.3217i	0.596523	−	1.03321i	−0.396807	−	0.917902i	$-0.629882\pi$
$919$	18.0836	−	31.3217i	0.596523	−	1.03321i	0.993330	−	0.115306i	$-0.0367848\pi$
$920$	−52.7015	−	91.2816i	−1.73752	−	3.00947i
$921$	7.14209	−	4.12349i	0.235340	−	0.135874i
$922$	15.9232			0.524403
$923$		0			0
$924$	−8.12737			−0.267371
$925$	−55.6493	+	32.1292i	−1.82974	+	1.05640i
$926$	8.78150	+	15.2100i	0.288578	+	0.499831i
$927$	0.603875	−	1.04594i	0.0198339	−	0.0343533i
$928$			14.3593i			0.471367i
$929$	−11.5595	−	6.67390i	−0.379256	−	0.218964i	0.298239	−	0.954491i	$-0.403601\pi$
$929$	−11.5595	−	6.67390i	−0.379256	−	0.218964i	−0.677494	+	0.735528i	$0.736934\pi$
$930$	17.6703	+	10.2019i	0.579432	+	0.334535i
$931$			15.5429i			0.509397i
$932$	−7.02297	+	12.1641i	−0.230045	+	0.398449i
$933$	7.20895	+	12.4863i	0.236010	+	0.408782i
$934$	66.5610	−	38.4290i	2.17794	−	1.25744i
$935$	30.9342			1.01166
$936$		0			0
$937$	38.6872			1.26386			0.631928	−	0.775027i	$-0.282264\pi$
$937$	38.6872			1.26386			0.631928	+	0.775027i	$0.282264\pi$
$938$	23.5605	−	13.6027i	0.769279	−	0.444143i
$939$	7.11692	+	12.3269i	0.232252	+	0.402272i
$940$	16.0456	−	27.7917i	0.523349	−	0.906466i
$941$		−	35.7275i		−	1.16468i	−0.812944	−	0.582342i	$-0.802136\pi$
$941$		−	35.7275i		−	1.16468i	0.812944	−	0.582342i	$-0.197864\pi$
$942$	38.1233	+	22.0105i	1.24213	+	0.717141i
$943$	−5.74005	−	3.31402i	−0.186922	−	0.107919i
$944$		−	8.22580i		−	0.267727i
$945$	−1.48039	+	2.56410i	−0.0481569	+	0.0834103i
$946$	5.42894	+	9.40321i	0.176510	+	0.305725i
$947$	−15.4530	+	8.92178i	−0.502154	+	0.289919i	−0.729603	−	0.683871i	$-0.760295\pi$
$947$	−15.4530	+	8.92178i	−0.502154	+	0.289919i	0.227448	+	0.973790i	$0.426962\pi$
$948$	19.2174			0.624153
$949$		0			0
$950$	−49.7381			−1.61372
$951$	−5.92721	+	3.42208i	−0.192203	+	0.110968i
$952$	4.31886	+	7.48049i	0.139975	+	0.242444i
$953$	10.0846	−	17.4670i	0.326671	−	0.565810i	−0.655178	−	0.755474i	$-0.727406\pi$
$953$	10.0846	−	17.4670i	0.326671	−	0.565810i	0.981849	+	0.189664i	$0.0607398\pi$
$954$			23.4765i			0.760080i
$955$	53.6064	+	30.9496i	1.73466	+	1.00151i
$956$	−2.51938	−	1.45457i	−0.0814827	−	0.0470440i
$957$			10.9782i			0.354876i
$958$	−3.33393	+	5.77453i	−0.107714	+	0.186567i
$959$	−3.78932	−	6.56330i	−0.122364	−	0.211940i
$960$	37.8703	−	21.8644i	1.22226	−	0.705671i
$961$	25.5018			0.822640
$962$		0			0
$963$	−9.52111			−0.306813
$964$	−18.5722	+	10.7227i	−0.598171	+	0.345354i
$965$	−47.5236	−	82.3132i	−1.52984	−	2.64976i
$966$	−7.36174	+	12.7509i	−0.236860	+	0.410254i
$967$			32.7894i			1.05444i	0.849730	+	0.527218i	$0.176765\pi$
$967$			32.7894i			1.05444i	−0.849730	+	0.527218i	$0.823235\pi$
$968$	−9.11735	−	5.26391i	−0.293043	−	0.169188i
$969$	−6.22324	−	3.59299i	−0.199919	−	0.115423i
$970$		−	51.7263i		−	1.66083i
$971$	13.4922	−	23.3692i	0.432986	−	0.749954i	−0.564143	−	0.825677i	$-0.690793\pi$
$971$	13.4922	−	23.3692i	0.432986	−	0.749954i	0.997129	+	0.0757231i	$0.0241265\pi$
$972$	−1.77748	−	3.07868i	−0.0570127	−	0.0987488i
$973$	−2.78846	+	1.60992i	−0.0893938	+	0.0516115i
$974$	97.3245			3.11848
$975$		0			0
$976$	−20.2537			−0.648305
$977$	14.6852	−	8.47853i	0.469822	−	0.271252i	−0.246343	−	0.969183i	$-0.579229\pi$
$977$	14.6852	−	8.47853i	0.469822	−	0.271252i	0.716165	+	0.697931i	$0.245896\pi$
$978$	14.5414	+	25.1864i	0.464982	+	0.805373i
$979$	−1.61314	+	2.79404i	−0.0515561	+	0.0892978i
$980$			83.4341i			2.66521i
$981$	−1.54540	−	0.892240i	−0.0493410	−	0.0284870i
$982$	70.7656	+	40.8565i	2.25822	+	1.30378i
$983$		−	32.6631i		−	1.04179i	−0.853621	−	0.520895i	$-0.825598\pi$
$983$		−	32.6631i		−	1.04179i	0.853621	−	0.520895i	$-0.174402\pi$
$984$	−1.55914	+	2.70051i	−0.0497035	+	0.0860890i
$985$	39.5432	+	68.4908i	1.25995	+	2.18230i
$986$	23.1008	−	13.3373i	0.735681	−	0.424746i
$987$	−1.96077			−0.0624120
$988$		0			0
$989$	12.5881			0.400277
$990$	21.4838	−	12.4037i	0.682799	−	0.394214i
$991$	−3.82155	−	6.61912i	−0.121396	−	0.210263i	0.798923	−	0.601434i	$-0.205404\pi$
$991$	−3.82155	−	6.61912i	−0.121396	−	0.210263i	−0.920318	+	0.391170i	$0.872070\pi$
$992$	−4.37174	+	7.57207i	−0.138803	+	0.240414i
$993$			9.44265i			0.299653i
$994$	−13.2995	−	7.67845i	−0.421833	−	0.243546i
$995$	−11.2798	−	6.51238i	−0.357593	−	0.206456i
$996$		−	25.0586i		−	0.794012i
$997$	−18.0628	+	31.2857i	−0.572054	+	0.990827i	0.424301	+	0.905521i	$0.360520\pi$
$997$	−18.0628	+	31.2857i	−0.572054	+	0.990827i	−0.996355	+	0.0853055i	$0.972813\pi$
$998$	21.1424	+	36.6198i	0.669252	+	1.15918i
$999$	−6.44760	+	3.72252i	−0.203993	+	0.117775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.i.361.2		12
13.2	odd	12		507.2.a.i.1.2	✓	3
13.3	even	3		507.2.b.f.337.2		6
13.4	even	6	inner	507.2.j.i.316.2		12
13.5	odd	4		507.2.e.l.484.2		6
13.6	odd	12		507.2.e.l.22.2		6
13.7	odd	12		507.2.e.i.22.2		6
13.8	odd	4		507.2.e.i.484.2		6
13.9	even	3	inner	507.2.j.i.316.5		12
13.10	even	6		507.2.b.f.337.5		6
13.11	odd	12		507.2.a.l.1.2	yes	3
13.12	even	2	inner	507.2.j.i.361.5		12
39.2	even	12		1521.2.a.s.1.2		3
39.11	even	12		1521.2.a.n.1.2		3
39.23	odd	6		1521.2.b.k.1351.2		6
39.29	odd	6		1521.2.b.k.1351.5		6
52.11	even	12		8112.2.a.cp.1.3		3
52.15	even	12		8112.2.a.cg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.2	✓	3	13.2	odd	12
507.2.a.l.1.2	yes	3	13.11	odd	12
507.2.b.f.337.2		6	13.3	even	3
507.2.b.f.337.5		6	13.10	even	6
507.2.e.i.22.2		6	13.7	odd	12
507.2.e.i.484.2		6	13.8	odd	4
507.2.e.l.22.2		6	13.6	odd	12
507.2.e.l.484.2		6	13.5	odd	4
507.2.j.i.316.2		12	13.4	even	6	inner
507.2.j.i.316.5		12	13.9	even	3	inner
507.2.j.i.361.2		12	1.1	even	1	trivial
507.2.j.i.361.5		12	13.12	even	2	inner
1521.2.a.n.1.2		3	39.11	even	12
1521.2.a.s.1.2		3	39.2	even	12
1521.2.b.k.1351.2		6	39.23	odd	6
1521.2.b.k.1351.5		6	39.29	odd	6
8112.2.a.cg.1.1		3	52.15	even	12
8112.2.a.cp.1.3		3	52.11	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.04113 + 1.17845i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.77748 - 3.07868i) q^{4} -3.69202i q^{5} +(-2.04113 - 1.17845i) q^{6} +(0.694498 + 0.400969i) q^{7} +3.66487i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.04113 + 1.17845i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.77748 - 3.07868i) q^{4} -3.69202i q^{5} +(-2.04113 - 1.17845i) q^{6} +(0.694498 + 0.400969i) q^{7} +3.66487i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.35086 + 7.53590i) q^{10} +(-2.46891 + 1.42543i) q^{11} +3.55496 q^{12} -1.89008 q^{14} +(3.19738 - 1.84601i) q^{15} +(-0.763906 - 1.32312i) q^{16} +(1.46950 - 2.54525i) q^{17} -2.35690i q^{18} +(-2.11747 - 1.22252i) q^{19} +(-11.3666 - 6.56249i) q^{20} +0.801938i q^{21} +(3.35958 - 5.81897i) q^{22} +(-3.89493 - 6.74621i) q^{23} +(-3.17387 + 1.83244i) q^{24} -8.63102 q^{25} -1.00000 q^{27} +(2.46891 - 1.42543i) q^{28} +(-1.92543 - 3.33494i) q^{29} +(-4.35086 + 7.53590i) q^{30} -2.34481i q^{31} +(-3.22929 - 1.86443i) q^{32} +(-2.46891 - 1.42543i) q^{33} +6.92692i q^{34} +(1.48039 - 2.56410i) q^{35} +(1.77748 + 3.07868i) q^{36} +(6.44760 - 3.72252i) q^{37} +5.76271 q^{38} +13.5308 q^{40} +(0.736862 - 0.425428i) q^{41} +(-0.945042 - 1.63686i) q^{42} +(-0.807979 + 1.39946i) q^{43} +10.1347i q^{44} +(3.19738 + 1.84601i) q^{45} +(15.9001 + 9.17994i) q^{46} +2.44504i q^{47} +(0.763906 - 1.32312i) q^{48} +(-3.17845 - 5.50523i) q^{49} +(17.6171 - 10.1712i) q^{50} +2.93900 q^{51} -9.96077 q^{53} +(2.04113 - 1.17845i) q^{54} +(5.26271 + 9.11528i) q^{55} +(-1.46950 + 2.54525i) q^{56} -2.44504i q^{57} +(7.86010 + 4.53803i) q^{58} +(4.66272 + 2.69202i) q^{59} -13.1250i q^{60} +(6.62833 - 11.4806i) q^{61} +(2.76324 + 4.78607i) q^{62} +(-0.694498 + 0.400969i) q^{63} +11.8442 q^{64} +6.71917 q^{66} +(-12.4653 + 7.19687i) q^{67} +(-5.22401 - 9.04826i) q^{68} +(3.89493 - 6.74621i) q^{69} +6.97823i q^{70} +(7.03644 + 4.06249i) q^{71} +(-3.17387 - 1.83244i) q^{72} -11.8877i q^{73} +(-8.77359 + 15.1963i) q^{74} +(-4.31551 - 7.47468i) q^{75} +(-7.52751 + 4.34601i) q^{76} -2.28621 q^{77} +5.40581 q^{79} +(-4.88500 + 2.82036i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00269 + 1.73671i) q^{82} -7.04892i q^{83} +(2.46891 + 1.42543i) q^{84} +(-9.39712 - 5.42543i) q^{85} -3.80864i q^{86} +(1.92543 - 3.33494i) q^{87} +(-5.22401 - 9.04826i) q^{88} +(0.980069 - 0.565843i) q^{89} -8.70171 q^{90} -27.6926 q^{92} +(2.03067 - 1.17241i) q^{93} +(-2.88135 - 4.99065i) q^{94} +(-4.51357 + 7.81774i) q^{95} -3.72886i q^{96} +(-5.14798 - 2.97219i) q^{97} +(12.9753 + 7.49127i) q^{98} -2.85086i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9	\( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43} + 22 q^{48} - 30 q^{49} - 4 q^{51} - 68 q^{53} - 6 q^{55} + 2 q^{56} + 26 q^{61} - 4 q^{62} + 36 q^{66} + 26 q^{68} - 30 q^{74} - 22 q^{75} - 60 q^{77} + 12 q^{79} - 6 q^{81} - 6 q^{82} - 4 q^{87} + 26 q^{88} + 4 q^{90} + 28 q^{92} - 42 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9 - 2 * q^10 + 44 * q^12 - 20 * q^14 - 22 * q^16 - 2 * q^17 + 18 * q^22 - 44 * q^25 - 12 * q^27 + 4 * q^29 + 2 * q^30 - 8 * q^35 + 22 * q^36 + 12 * q^40 - 10 * q^42 - 30 * q^43 + 22 * q^48 - 30 * q^49 - 4 * q^51 - 68 * q^53 - 6 * q^55 + 2 * q^56 + 26 * q^61 - 4 * q^62 + 36 * q^66 + 26 * q^68 - 30 * q^74 - 22 * q^75 - 60 * q^77 + 12 * q^79 - 6 * q^81 - 6 * q^82 - 4 * q^87 + 26 * q^88 + 4 * q^90 + 28 * q^92 - 42 * q^95

Introduction

L-functions

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