LMFDB - Embedded newform 1170.2.bj.b.199.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(199,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.199"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$1.83766i$ of defining polynomial
Character	$\chi$	$=$	1170.199
Dual form			1170.2.bj.b.829.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.21022 - 0.339024i) q^{5} +(2.39871 + 4.15469i) q^{7} -1.00000 q^{8} +(0.811505 - 2.08362i) q^{10} +(-1.43026 - 0.825763i) q^{11} +(-1.09146 - 3.43638i) q^{13} +4.79742 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0697360 - 0.0402621i) q^{17} +(3.67867 - 2.12388i) q^{19} +(-1.39871 - 1.74459i) q^{20} +(-1.43026 + 0.825763i) q^{22} +(5.10893 + 2.94964i) q^{23} +(4.77013 - 1.49863i) q^{25} +(-3.52172 - 0.772959i) q^{26} +(2.39871 - 4.15469i) q^{28} +(-2.21022 + 3.82821i) q^{29} +4.06163i q^{31} +(0.500000 + 0.866025i) q^{32} -0.0805241i q^{34} +(6.71022 + 8.36955i) q^{35} +(0.908541 - 1.57364i) q^{37} -4.24776i q^{38} +(-2.21022 + 0.339024i) q^{40} +(5.87906 + 3.39427i) q^{41} +(7.35733 - 4.24776i) q^{43} +1.65153i q^{44} +(5.10893 - 2.94964i) q^{46} -0.448597 q^{47} +(-8.00764 + 13.8696i) q^{49} +(1.08721 - 4.88037i) q^{50} +(-2.43026 + 2.66342i) q^{52} -11.5770i q^{53} +(-3.44115 - 1.34022i) q^{55} +(-2.39871 - 4.15469i) q^{56} +(2.21022 + 3.82821i) q^{58} +(-1.82559 + 1.05400i) q^{59} +(1.56416 + 2.70920i) q^{61} +(3.51747 + 2.03081i) q^{62} +1.00000 q^{64} +(-3.57738 - 7.22512i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-0.0697360 - 0.0402621i) q^{68} +(10.6034 - 1.62644i) q^{70} +(6.36584 - 3.67532i) q^{71} -10.5752 q^{73} +(-0.908541 - 1.57364i) q^{74} +(-3.67867 - 2.12388i) q^{76} -7.92308i q^{77} -14.6468 q^{79} +(-0.811505 + 2.08362i) q^{80} +(5.87906 - 3.39427i) q^{82} +12.4289 q^{83} +(0.140482 - 0.112630i) q^{85} -8.49552i q^{86} +(1.43026 + 0.825763i) q^{88} +(-7.23958 - 4.17978i) q^{89} +(11.6590 - 12.7776i) q^{91} -5.89928i q^{92} +(-0.224298 + 0.388496i) q^{94} +(7.41061 - 5.94139i) q^{95} +(-2.90296 - 5.02808i) q^{97} +(8.00764 + 13.8696i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} + 5 q^{7} - 8 q^{8} + 3 q^{11} + 4 q^{13} + 10 q^{14} - 4 q^{16} + 15 q^{17} + 9 q^{19} + 3 q^{20} + 3 q^{22} + 6 q^{23} + 5 q^{25} - q^{26} + 5 q^{28} + 3 q^{29} + 4 q^{32}+ \cdots + 15 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 + 5 * q^7 - 8 * q^8 + 3 * q^11 + 4 * q^13 + 10 * q^14 - 4 * q^16 + 15 * q^17 + 9 * q^19 + 3 * q^20 + 3 * q^22 + 6 * q^23 + 5 * q^25 - q^26 + 5 * q^28 + 3 * q^29 + 4 * q^32 + 33 * q^35 + 20 * q^37 + 3 * q^40 - 21 * q^41 + 18 * q^43 + 6 * q^46 - 6 * q^47 - 15 * q^49 + q^50 - 5 * q^52 - 23 * q^55 - 5 * q^56 - 3 * q^58 - 30 * q^59 - 5 * q^61 + 6 * q^62 + 8 * q^64 + 6 * q^65 - 16 * q^67 - 15 * q^68 + 18 * q^70 + 26 * q^73 - 20 * q^74 - 9 * q^76 + 4 * q^79 - 21 * q^82 + 48 * q^83 - 34 * q^85 - 3 * q^88 + 39 * q^89 + 19 * q^91 - 3 * q^94 - 9 * q^95 - 4 * q^97 + 15 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.21022	−	0.339024i	0.988439	−	0.151616i
$5$	2.21022	−	0.339024i	0.988439	−	0.151616i
$6$		0			0
$7$	2.39871	+	4.15469i	0.906628	+	1.57033i	0.818717	+	0.574198i	$0.194686\pi$
$7$	2.39871	+	4.15469i	0.906628	+	1.57033i	0.0879113	+	0.996128i	$0.471981\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.811505	−	2.08362i	0.256621	−	0.658897i
$11$	−1.43026	−	0.825763i	−0.431241	−	0.248977i	0.268634	−	0.963242i	$-0.413428\pi$
$11$	−1.43026	−	0.825763i	−0.431241	−	0.248977i	−0.699875	+	0.714265i	$0.746761\pi$
$12$		0			0
$13$	−1.09146	−	3.43638i	−0.302716	−	0.953081i
$13$	−1.09146	−	3.43638i	−0.302716	−	0.953081i
$14$	4.79742			1.28217
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0697360	−	0.0402621i	0.0169135	−	0.00976499i	−0.491519	−	0.870867i	$-0.663558\pi$
$17$	0.0697360	−	0.0402621i	0.0169135	−	0.00976499i	0.508433	+	0.861102i	$0.330225\pi$
$18$		0			0
$19$	3.67867	−	2.12388i	0.843944	−	0.487251i	−0.0146590	−	0.999893i	$-0.504666\pi$
$19$	3.67867	−	2.12388i	0.843944	−	0.487251i	0.858603	+	0.512641i	$0.171333\pi$
$20$	−1.39871	−	1.74459i	−0.312762	−	0.390103i
$21$		0			0
$22$	−1.43026	+	0.825763i	−0.304933	+	0.176053i
$23$	5.10893	+	2.94964i	1.06529	+	0.615043i	0.926890	−	0.375334i	$-0.122472\pi$
$23$	5.10893	+	2.94964i	1.06529	+	0.615043i	0.138396	+	0.990377i	$0.455805\pi$
$24$		0			0
$25$	4.77013	−	1.49863i	0.954025	−	0.299727i
$26$	−3.52172	−	0.772959i	−0.690667	−	0.151590i
$27$		0			0
$28$	2.39871	−	4.15469i	0.453314	−	0.785163i
$29$	−2.21022	+	3.82821i	−0.410427	+	0.710881i	−0.994936	−	0.100506i	$-0.967954\pi$
$29$	−2.21022	+	3.82821i	−0.410427	+	0.710881i	0.584509	+	0.811387i	$0.301287\pi$
$30$		0			0
$31$			4.06163i			0.729490i	0.931108	+	0.364745i	$0.118844\pi$
$31$			4.06163i			0.729490i	−0.931108	+	0.364745i	$0.881156\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	0.0805241i		−	0.0138098i
$35$	6.71022	+	8.36955i	1.13423	+	1.41471i
$36$		0			0
$37$	0.908541	−	1.57364i	0.149363	−	0.258705i	−0.781629	−	0.623744i	$-0.785611\pi$
$37$	0.908541	−	1.57364i	0.149363	−	0.258705i	0.930992	+	0.365039i	$0.118944\pi$
$38$		−	4.24776i		−	0.689077i
$39$		0			0
$40$	−2.21022	+	0.339024i	−0.349466	+	0.0536044i
$41$	5.87906	+	3.39427i	0.918154	+	0.530097i	0.883046	−	0.469287i	$-0.155489\pi$
$41$	5.87906	+	3.39427i	0.918154	+	0.530097i	0.0351085	+	0.999384i	$0.488822\pi$
$42$		0			0
$43$	7.35733	−	4.24776i	1.12198	−	0.647777i	0.180076	−	0.983653i	$-0.442366\pi$
$43$	7.35733	−	4.24776i	1.12198	−	0.647777i	0.941906	+	0.335876i	$0.109032\pi$
$44$			1.65153i			0.248977i
$45$		0			0
$46$	5.10893	−	2.94964i	0.753271	−	0.434901i
$47$	−0.448597			−0.0654345			−0.0327173	−	0.999465i	$-0.510416\pi$
$47$	−0.448597			−0.0654345			−0.0327173	+	0.999465i	$0.510416\pi$
$48$		0			0
$49$	−8.00764	+	13.8696i	−1.14395	+	1.98138i
$50$	1.08721	−	4.88037i	0.153754	−	0.690188i
$51$		0			0
$52$	−2.43026	+	2.66342i	−0.337017	+	0.369350i
$53$		−	11.5770i		−	1.59022i	−0.606463	−	0.795112i	$-0.707412\pi$
$53$		−	11.5770i		−	1.59022i	0.606463	−	0.795112i	$-0.292588\pi$
$54$		0			0
$55$	−3.44115	−	1.34022i	−0.464004	−	0.180716i
$56$	−2.39871	−	4.15469i	−0.320541	−	0.555194i
$57$		0			0
$58$	2.21022	+	3.82821i	0.290216	+	0.502669i
$59$	−1.82559	+	1.05400i	−0.237671	+	0.137219i	−0.614106	−	0.789224i	$-0.710483\pi$
$59$	−1.82559	+	1.05400i	−0.237671	+	0.137219i	0.376435	+	0.926443i	$0.377150\pi$
$60$		0			0
$61$	1.56416	+	2.70920i	0.200270	+	0.346878i	0.948615	−	0.316431i	$-0.102485\pi$
$61$	1.56416	+	2.70920i	0.200270	+	0.346878i	−0.748345	+	0.663309i	$0.769151\pi$
$62$	3.51747	+	2.03081i	0.446719	+	0.257913i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.57738	−	7.22512i	−0.443719	−	0.896166i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	−0.0697360	−	0.0402621i	−0.00845673	−	0.00488249i
$69$		0			0
$70$	10.6034	−	1.62644i	1.26734	−	0.194397i
$71$	6.36584	−	3.67532i	0.755486	−	0.436180i	−0.0721869	−	0.997391i	$-0.522998\pi$
$71$	6.36584	−	3.67532i	0.755486	−	0.436180i	0.827673	+	0.561211i	$0.189664\pi$
$72$		0			0
$73$	−10.5752			−1.23773			−0.618866	−	0.785496i	$-0.712408\pi$
$73$	−10.5752			−1.23773			−0.618866	+	0.785496i	$0.712408\pi$
$74$	−0.908541	−	1.57364i	−0.105616	−	0.182932i
$75$		0			0
$76$	−3.67867	−	2.12388i	−0.421972	−	0.243626i
$77$		−	7.92308i		−	0.902918i
$78$		0			0
$79$	−14.6468			−1.64789			−0.823947	−	0.566667i	$-0.808233\pi$
$79$	−14.6468			−1.64789			−0.823947	+	0.566667i	$0.808233\pi$
$80$	−0.811505	+	2.08362i	−0.0907291	+	0.232955i
$81$		0			0
$82$	5.87906	−	3.39427i	0.649233	−	0.374835i
$83$	12.4289			1.36425			0.682127	−	0.731234i	$-0.261055\pi$
$83$	12.4289			1.36425			0.682127	+	0.731234i	$0.261055\pi$
$84$		0			0
$85$	0.140482	−	0.112630i	0.0152374	−	0.0122165i
$86$		−	8.49552i		−	0.916095i
$87$		0			0
$88$	1.43026	+	0.825763i	0.152467	+	0.0880267i
$89$	−7.23958	−	4.17978i	−0.767394	−	0.443055i	0.0645500	−	0.997914i	$-0.479439\pi$
$89$	−7.23958	−	4.17978i	−0.767394	−	0.443055i	−0.831944	+	0.554859i	$0.812772\pi$
$90$		0			0
$91$	11.6590	−	12.7776i	1.22220	−	1.33945i
$92$		−	5.89928i		−	0.615043i
$93$		0			0
$94$	−0.224298	+	0.388496i	−0.0231346	+	0.0400703i
$95$	7.41061	−	5.94139i	0.760312	−	0.609574i
$96$		0			0
$97$	−2.90296	−	5.02808i	−0.294751	−	0.510524i	0.680176	−	0.733049i	$-0.261903\pi$
$97$	−2.90296	−	5.02808i	−0.294751	−	0.510524i	−0.974927	+	0.222525i	$0.928570\pi$
$98$	8.00764	+	13.8696i	0.808894	+	1.40105i
$99$		0			0
$100$	−3.68292	−	3.38173i	−0.368292	−	0.338173i
$101$	0.618759	−	1.07172i	0.0615688	−	0.106640i	−0.833598	−	0.552372i	$-0.813723\pi$
$101$	0.618759	−	1.07172i	0.0615688	−	0.106640i	0.895167	+	0.445731i	$0.147056\pi$
$102$		0			0
$103$		−	9.38847i		−	0.925073i	−0.886600	−	0.462537i	$-0.846939\pi$
$103$		−	9.38847i		−	0.925073i	0.886600	−	0.462537i	$-0.153061\pi$
$104$	1.09146	+	3.43638i	0.107026	+	0.336965i
$105$		0			0
$106$	−10.0260	−	5.78850i	−0.973809	−	0.562229i
$107$	−16.0272	−	9.25330i	−1.54941	−	0.894550i	−0.998187	−	0.0601893i	$-0.980830\pi$
$107$	−16.0272	−	9.25330i	−1.54941	−	0.894550i	−0.551219	−	0.834361i	$-0.685837\pi$
$108$		0			0
$109$			9.08638i			0.870317i	0.900354	+	0.435158i	$0.143308\pi$
$109$			9.08638i			0.870317i	−0.900354	+	0.435158i	$0.856692\pi$
$110$	−2.88124	+	2.31001i	−0.274716	+	0.220251i
$111$		0			0
$112$	−4.79742			−0.453314
$113$	−13.8051	+	7.97036i	−1.29867	+	0.749788i	−0.980175	−	0.198136i	$-0.936511\pi$
$113$	−13.8051	+	7.97036i	−1.29867	+	0.749788i	−0.318497	+	0.947924i	$0.603178\pi$
$114$		0			0
$115$	12.2918	+	4.78730i	1.14622	+	0.446418i
$116$	4.42044			0.410427
$117$		0			0
$118$			2.10800i			0.194058i
$119$	0.334553	+	0.193154i	0.0306684	+	0.0177064i
$120$		0			0
$121$	−4.13623	−	7.16416i	−0.376021	−	0.651287i
$122$	3.12832			0.283225
$123$		0			0
$124$	3.51747	−	2.03081i	0.315878	−	0.182372i
$125$	10.0349	−	4.92950i	0.897553	−	0.440908i
$126$		0			0
$127$	0.773321	+	0.446477i	0.0686211	+	0.0396184i	0.533918	−	0.845536i	$-0.320719\pi$
$127$	0.773321	+	0.446477i	0.0686211	+	0.0396184i	−0.465297	+	0.885155i	$0.654052\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.04583	−	0.514459i	−0.705666	−	0.0451211i
$131$	1.11770			0.0976541			0.0488271	−	0.998807i	$-0.484452\pi$
$131$	1.11770			0.0976541			0.0488271	+	0.998807i	$0.484452\pi$
$132$		0			0
$133$	17.6481	+	10.1891i	1.53029	+	0.883511i
$134$	2.00000	+	3.46410i	0.172774	+	0.299253i
$135$		0			0
$136$	−0.0697360	+	0.0402621i	−0.00597981	+	0.00345244i
$137$	4.10468	+	7.10951i	0.350686	+	0.607407i	0.986370	−	0.164543i	$-0.0526150\pi$
$137$	4.10468	+	7.10951i	0.350686	+	0.607407i	−0.635684	+	0.771950i	$0.719282\pi$
$138$		0			0
$139$	2.55885	+	4.43206i	0.217039	+	0.375922i	0.953901	−	0.300120i	$-0.0970268\pi$
$139$	2.55885	+	4.43206i	0.217039	+	0.375922i	−0.736862	+	0.676043i	$0.763693\pi$
$140$	3.89314	−	9.99600i	0.329030	−	0.844816i
$141$		0			0
$142$		−	7.35063i		−	0.616852i
$143$	−1.27656	+	5.81622i	−0.106752	+	0.486377i
$144$		0			0
$145$	−3.58721	+	9.21049i	−0.297901	+	0.764890i
$146$	−5.28760	+	9.15839i	−0.437605	+	0.757953i
$147$		0			0
$148$	−1.81708			−0.149363
$149$	−3.58721	+	2.07107i	−0.293875	+	0.169669i	−0.639688	−	0.768634i	$-0.720937\pi$
$149$	−3.58721	+	2.07107i	−0.293875	+	0.169669i	0.345813	+	0.938304i	$0.387603\pi$
$150$		0			0
$151$			4.43389i			0.360825i	0.983591	+	0.180412i	$0.0577432\pi$
$151$			4.43389i			0.360825i	−0.983591	+	0.180412i	$0.942257\pi$
$152$	−3.67867	+	2.12388i	−0.298379	+	0.172269i
$153$		0			0
$154$	−6.86158	−	3.96154i	−0.552922	−	0.319230i
$155$	1.37699	+	8.97708i	0.110602	+	0.721056i
$156$		0			0
$157$		−	8.32411i		−	0.664337i	−0.943220	−	0.332168i	$-0.892220\pi$
$157$		−	8.32411i		−	0.664337i	0.943220	−	0.332168i	$-0.107780\pi$
$158$	−7.32340	+	12.6845i	−0.582618	+	1.00912i
$159$		0			0
$160$	1.39871	+	1.74459i	0.110578	+	0.137922i
$161$			28.3014i			2.23046i
$162$		0			0
$163$	−0.471644	−	0.816912i	−0.0369420	−	0.0639855i	0.846963	−	0.531651i	$-0.178428\pi$
$163$	−0.471644	−	0.816912i	−0.0369420	−	0.0639855i	−0.883905	+	0.467666i	$0.845095\pi$
$164$		−	6.78855i		−	0.530097i
$165$		0			0
$166$	6.21447	−	10.7638i	0.482336	−	0.835431i
$167$	−2.15031	+	3.72445i	−0.166396	+	0.288206i	−0.937150	−	0.348926i	$-0.886546\pi$
$167$	−2.15031	+	3.72445i	−0.166396	+	0.288206i	0.770754	+	0.637133i	$0.219880\pi$
$168$		0			0
$169$	−10.6174	+	7.50134i	−0.816726	+	0.577026i
$170$	−0.0272996	−	0.177976i	−0.00209379	−	0.0136501i
$171$		0			0
$172$	−7.35733	−	4.24776i	−0.560991	−	0.323888i
$173$	0.861584	−	0.497436i	0.0655050	−	0.0378194i	−0.466890	−	0.884316i	$-0.654626\pi$
$173$	0.861584	−	0.497436i	0.0655050	−	0.0378194i	0.532395	+	0.846496i	$0.321292\pi$
$174$		0			0
$175$	17.6685	+	16.2236i	1.33561	+	1.22639i
$176$	1.43026	−	0.825763i	0.107810	−	0.0622443i
$177$		0			0
$178$	−7.23958	+	4.17978i	−0.542630	+	0.313287i
$179$	−10.2179	+	17.6979i	−0.763719	+	1.32280i	0.177203	+	0.984174i	$0.443295\pi$
$179$	−10.2179	+	17.6979i	−0.763719	+	1.32280i	−0.940921	+	0.338625i	$0.890038\pi$
$180$		0			0
$181$	−19.9522			−1.48303			−0.741517	−	0.670934i	$-0.765893\pi$
$181$	−19.9522			−1.48303			−0.741517	+	0.670934i	$0.765893\pi$
$182$	−5.23619	−	16.4858i	−0.388132	−	1.22201i
$183$		0			0
$184$	−5.10893	−	2.94964i	−0.376635	−	0.217451i
$185$	1.47457	−	3.78610i	0.108413	−	0.278360i
$186$		0			0
$187$	−0.132988			−0.00972503
$188$	0.224298	+	0.388496i	0.0163586	+	0.0283340i
$189$		0			0
$190$	−1.44009	−	9.38847i	−0.104475	−	0.681111i
$191$	−3.83986	−	6.65083i	−0.277843	−	0.481238i	0.693006	−	0.720932i	$-0.256286\pi$
$191$	−3.83986	−	6.65083i	−0.277843	−	0.481238i	−0.970848	+	0.239695i	$0.922953\pi$
$192$		0			0
$193$	−7.59571	+	13.1562i	−0.546751	+	0.947001i	0.451743	+	0.892148i	$0.350802\pi$
$193$	−7.59571	+	13.1562i	−0.546751	+	0.947001i	−0.998494	+	0.0548529i	$0.982531\pi$
$194$	−5.80593			−0.416841
$195$		0			0
$196$	16.0153			1.14395
$197$	−1.50663	+	2.60956i	−0.107343	+	0.185924i	−0.914693	−	0.404149i	$-0.867568\pi$
$197$	−1.50663	+	2.60956i	−0.107343	+	0.185924i	0.807350	+	0.590073i	$0.200901\pi$
$198$		0			0
$199$	4.86053	+	8.41868i	0.344554	+	0.596785i	0.985273	−	0.170991i	$-0.0546969\pi$
$199$	4.86053	+	8.41868i	0.344554	+	0.596785i	−0.640719	+	0.767776i	$0.721364\pi$
$200$	−4.77013	+	1.49863i	−0.337299	+	0.105969i
$201$		0			0
$202$	−0.618759	−	1.07172i	−0.0435357	−	0.0754061i
$203$	−21.2067			−1.48842
$204$		0			0
$205$	14.1447	+	5.50894i	0.987911	+	0.384761i
$206$	−8.13065	−	4.69423i	−0.566489	−	0.327063i
$207$		0			0
$208$	3.52172	+	0.772959i	0.244188	+	0.0535951i
$209$	−7.01529			−0.485257
$210$		0			0
$211$	2.39532	−	4.14882i	0.164901	−	0.285616i	−0.771719	−	0.635963i	$-0.780603\pi$
$211$	2.39532	−	4.14882i	0.164901	−	0.285616i	0.936620	+	0.350347i	$0.113936\pi$
$212$	−10.0260	+	5.78850i	−0.688587	+	0.397556i
$213$		0			0
$214$	−16.0272	+	9.25330i	−1.09560	+	0.632542i
$215$	14.8212	−	11.8828i	1.01080	−	0.810399i
$216$		0			0
$217$	−16.8748	+	9.74267i	−1.14554	+	0.661376i
$218$	7.86903	+	4.54319i	0.532958	+	0.307704i
$219$		0			0
$220$	0.559907	+	3.65023i	0.0377490	+	0.246099i
$221$	−0.214470	−	0.195695i	−0.0144268	−	0.0131639i
$222$		0			0
$223$	7.02172	−	12.1620i	0.470209	−	0.814426i	−0.529210	−	0.848491i	$-0.677512\pi$
$223$	7.02172	−	12.1620i	0.470209	−	0.814426i	0.999420	+	0.0340642i	$0.0108451\pi$
$224$	−2.39871	+	4.15469i	−0.160271	+	0.277597i
$225$		0			0
$226$			15.9407i			1.06036i
$227$	−1.44009	−	2.49431i	−0.0955823	−	0.165553i	0.814269	−	0.580487i	$-0.197138\pi$
$227$	−1.44009	−	2.49431i	−0.0955823	−	0.165553i	−0.909851	+	0.414934i	$0.863805\pi$
$228$		0			0
$229$		−	6.70802i		−	0.443279i	−0.975129	−	0.221639i	$-0.928859\pi$
$229$		−	6.70802i		−	0.443279i	0.975129	−	0.221639i	$-0.0711408\pi$
$230$	10.2918	−	8.25140i	0.678624	−	0.544081i
$231$		0			0
$232$	2.21022	−	3.82821i	0.145108	−	0.251334i
$233$		−	17.5959i		−	1.15275i	−0.817186	−	0.576374i	$-0.804467\pi$
$233$		−	17.5959i		−	1.15275i	0.817186	−	0.576374i	$-0.195533\pi$
$234$		0			0
$235$	−0.991496	+	0.152085i	−0.0646781	+	0.00992094i
$236$	1.82559	+	1.05400i	0.118836	+	0.0686097i
$237$		0			0
$238$	0.334553	−	0.193154i	0.0216858	−	0.0125203i
$239$		−	11.3119i		−	0.731708i	−0.930672	−	0.365854i	$-0.880777\pi$
$239$		−	11.3119i		−	0.731708i	0.930672	−	0.365854i	$-0.119223\pi$
$240$		0			0
$241$	−4.39957	+	2.54010i	−0.283401	+	0.163622i	−0.634962	−	0.772543i	$-0.718984\pi$
$241$	−4.39957	+	2.54010i	−0.283401	+	0.163622i	0.351561	+	0.936165i	$0.385651\pi$
$242$	−8.27246			−0.531774
$243$		0			0
$244$	1.56416	−	2.70920i	0.100135	−	0.173439i
$245$	−12.9965	+	33.3697i	−0.830315	+	2.13191i
$246$		0			0
$247$	−11.3136	−	10.3232i	−0.719865	−	0.656848i
$248$		−	4.06163i		−	0.257913i
$249$		0			0
$250$	0.748402	−	11.1553i	0.0473331	−	0.705521i
$251$	−9.78522	−	16.9485i	−0.617637	−	1.06978i	−0.989916	−	0.141658i	$-0.954757\pi$
$251$	−9.78522	−	16.9485i	−0.617637	−	1.06978i	0.372278	−	0.928121i	$-0.378577\pi$
$252$		0			0
$253$	−4.87141	−	8.43753i	−0.306263	−	0.530463i
$254$	0.773321	−	0.446477i	0.0485225	−	0.0280145i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.71818	−	0.991989i	−0.107177	−	0.0618786i	0.445453	−	0.895305i	$-0.353042\pi$
$257$	−1.71818	−	0.991989i	−0.107177	−	0.0618786i	−0.552630	+	0.833427i	$0.686376\pi$
$258$		0			0
$259$	8.71731			0.541668
$260$	−4.46845	+	6.71066i	−0.277121	+	0.416178i
$261$		0			0
$262$	0.558851	−	0.967959i	0.0345259	−	0.0598007i
$263$	0.527031	+	0.304282i	0.0324981	+	0.0187628i	0.516161	−	0.856492i	$-0.327361\pi$
$263$	0.527031	+	0.304282i	0.0324981	+	0.0187628i	−0.483663	+	0.875254i	$0.660694\pi$
$264$		0			0
$265$	−3.92488	−	25.5877i	−0.241104	−	1.57184i
$266$	17.6481	−	10.1891i	1.08208	−	0.624737i
$267$		0			0
$268$	4.00000			0.244339
$269$	8.87242	+	15.3675i	0.540961	+	0.936972i	0.998849	+	0.0479623i	$0.0152727\pi$
$269$	8.87242	+	15.3675i	0.540961	+	0.936972i	−0.457888	+	0.889010i	$0.651394\pi$
$270$		0			0
$271$	−13.8806	−	8.01395i	−0.843185	−	0.486813i	0.0151607	−	0.999885i	$-0.495174\pi$
$271$	−13.8806	−	8.01395i	−0.843185	−	0.486813i	−0.858346	+	0.513072i	$0.828507\pi$
$272$			0.0805241i			0.00488249i
$273$		0			0
$274$	8.20936			0.495945
$275$	−8.06006	−	1.79555i	−0.486040	−	0.108276i
$276$		0			0
$277$	10.3093	−	5.95209i	0.619427	−	0.357626i	−0.157219	−	0.987564i	$-0.550253\pi$
$277$	10.3093	−	5.95209i	0.619427	−	0.357626i	0.776646	+	0.629937i	$0.216919\pi$
$278$	5.11770			0.306939
$279$		0			0
$280$	−6.71022	−	8.36955i	−0.401012	−	0.500176i
$281$			11.3975i			0.679920i	0.940440	+	0.339960i	$0.110413\pi$
$281$			11.3975i			0.679920i	−0.940440	+	0.339960i	$0.889587\pi$
$282$		0			0
$283$	−17.6776	−	10.2062i	−1.05082	−	0.606694i	−0.127945	−	0.991781i	$-0.540838\pi$
$283$	−17.6776	−	10.2062i	−1.05082	−	0.606694i	−0.922880	+	0.385087i	$0.874171\pi$
$284$	−6.36584	−	3.67532i	−0.377743	−	0.218090i
$285$		0			0
$286$	4.39871	+	4.01365i	0.260101	+	0.237332i
$287$			32.5676i			1.92240i
$288$		0			0
$289$	−8.49676	+	14.7168i	−0.499809	+	0.865695i
$290$	6.18292	+	7.71186i	0.363073	+	0.452856i
$291$		0			0
$292$	5.28760	+	9.15839i	0.309433	+	0.535954i
$293$	2.09384	+	3.62664i	0.122323	+	0.211870i	0.920684	−	0.390310i	$-0.127632\pi$
$293$	2.09384	+	3.62664i	0.122323	+	0.211870i	−0.798360	+	0.602180i	$0.794299\pi$
$294$		0			0
$295$	−3.67761	+	2.94849i	−0.214119	+	0.171668i
$296$	−0.908541	+	1.57364i	−0.0528079	+	0.0914659i
$297$		0			0
$298$			4.14215i			0.239948i
$299$	4.55991	−	20.7756i	0.263706	−	1.20149i
$300$		0			0
$301$	35.2962	+	20.3783i	2.03444	+	1.17459i
$302$	3.83986	+	2.21694i	0.220959	+	0.127571i
$303$		0			0
$304$			4.24776i			0.243626i
$305$	4.37562	+	5.45764i	0.250547	+	0.312504i
$306$		0			0
$307$	−18.0170			−1.02828			−0.514142	−	0.857705i	$-0.671890\pi$
$307$	−18.0170			−1.02828			−0.514142	+	0.857705i	$0.671890\pi$
$308$	−6.86158	+	3.96154i	−0.390975	+	0.225730i
$309$		0			0
$310$	8.46287	+	3.29603i	0.480659	+	0.187202i
$311$	5.17816			0.293626			0.146813	−	0.989164i	$-0.453098\pi$
$311$	5.17816			0.293626			0.146813	+	0.989164i	$0.453098\pi$
$312$		0			0
$313$			32.6333i			1.84455i	0.386539	+	0.922273i	$0.373670\pi$
$313$			32.6333i			1.84455i	−0.386539	+	0.922273i	$0.626330\pi$
$314$	−7.20889	−	4.16206i	−0.406821	−	0.234878i
$315$		0			0
$316$	7.32340	+	12.6845i	0.411973	+	0.713559i
$317$	−23.7385			−1.33328			−0.666642	−	0.745378i	$-0.732269\pi$
$317$	−23.7385			−1.33328			−0.666642	+	0.745378i	$0.732269\pi$
$318$		0			0
$319$	6.32239	−	3.65023i	0.353986	−	0.204374i
$320$	2.21022	−	0.339024i	0.123555	−	0.0189520i
$321$		0			0
$322$	24.5097	+	14.1507i	1.36587	+	0.788587i
$323$	0.171024	−	0.296221i	0.00951600	−	0.0164822i
$324$		0			0
$325$	−10.3563	−	14.7563i	−0.574463	−	0.818531i
$326$	−0.943288			−0.0522439
$327$		0			0
$328$	−5.87906	−	3.39427i	−0.324617	−	0.187417i
$329$	−1.07605	−	1.86378i	−0.0593248	−	0.102754i
$330$		0			0
$331$	26.3923	−	15.2376i	1.45065	−	0.837534i	0.452132	−	0.891951i	$-0.350663\pi$
$331$	26.3923	−	15.2376i	1.45065	−	0.837534i	0.998518	+	0.0544174i	$0.0173301\pi$
$332$	−6.21447	−	10.7638i	−0.341063	−	0.590739i
$333$		0			0
$334$	2.15031	+	3.72445i	0.117660	+	0.203793i
$335$	−3.24602	+	8.33447i	−0.177349	+	0.455361i
$336$		0			0
$337$			19.2799i			1.05024i	0.851027	+	0.525121i	$0.175980\pi$
$337$			19.2799i			1.05024i	−0.851027	+	0.525121i	$0.824020\pi$
$338$	1.18763	+	12.9456i	0.0645987	+	0.704150i
$339$		0			0
$340$	−0.167781	−	0.0653458i	−0.00909923	−	0.00354387i
$341$	3.35394	−	5.80920i	0.181626	−	0.314586i
$342$		0			0
$343$	−43.2502			−2.33529
$344$	−7.35733	+	4.24776i	−0.396681	+	0.229024i
$345$		0			0
$346$		−	0.994872i		−	0.0534846i
$347$	13.3125	−	7.68598i	0.714653	−	0.412605i	−0.0981283	−	0.995174i	$-0.531286\pi$
$347$	13.3125	−	7.68598i	0.714653	−	0.412605i	0.812782	+	0.582569i	$0.197952\pi$
$348$		0			0
$349$	−13.1667	−	7.60177i	−0.704795	−	0.406913i	0.104336	−	0.994542i	$-0.466728\pi$
$349$	−13.1667	−	7.60177i	−0.704795	−	0.406913i	−0.809131	+	0.587629i	$0.800062\pi$
$350$	22.8843	−	7.18959i	1.22322	−	0.384300i
$351$		0			0
$352$		−	1.65153i		−	0.0880267i
$353$	13.4509	−	23.2976i	0.715917	−	1.24000i	−0.246688	−	0.969095i	$-0.579342\pi$
$353$	13.4509	−	23.2976i	0.715917	−	1.24000i	0.962605	−	0.270909i	$-0.0873244\pi$
$354$		0			0
$355$	12.8239	−	10.2814i	0.680620	−	0.545681i
$356$			8.35955i			0.443055i
$357$		0			0
$358$	10.2179	+	17.6979i	0.540031	+	0.935361i
$359$			20.8348i			1.09962i	0.835291	+	0.549809i	$0.185299\pi$
$359$			20.8348i			1.09962i	−0.835291	+	0.549809i	$0.814701\pi$
$360$		0			0
$361$	−0.478277	+	0.828400i	−0.0251725	+	0.0436000i
$362$	−9.97609	+	17.2791i	−0.524332	+	0.908169i
$363$		0			0
$364$	−16.8952	−	3.70821i	−0.885549	−	0.194363i
$365$	−23.3735	+	3.58525i	−1.22342	+	0.187660i
$366$		0			0
$367$	29.9410	+	17.2865i	1.56291	+	0.902346i	0.996961	+	0.0779051i	$0.0248231\pi$
$367$	29.9410	+	17.2865i	1.56291	+	0.902346i	0.565948	+	0.824441i	$0.308510\pi$
$368$	−5.10893	+	2.94964i	−0.266321	+	0.153761i
$369$		0			0
$370$	−2.54157	−	3.17007i	−0.132130	−	0.164804i
$371$	48.0989	−	27.7699i	2.49717	−	1.44174i
$372$		0			0
$373$	21.6562	−	12.5032i	1.12131	−	0.647391i	0.179578	−	0.983744i	$-0.442527\pi$
$373$	21.6562	−	12.5032i	1.12131	−	0.647391i	0.941736	+	0.336353i	$0.109194\pi$
$374$	−0.0664939	+	0.115171i	−0.00343832	+	0.00595534i
$375$		0			0
$376$	0.448597			0.0231346
$377$	15.5676	+	3.41682i	0.801770	+	0.175975i
$378$		0			0
$379$	−3.25585	−	1.87977i	−0.167242	−	0.0965571i	0.414043	−	0.910257i	$-0.364116\pi$
$379$	−3.25585	−	1.87977i	−0.167242	−	0.0965571i	−0.581285	+	0.813700i	$0.697450\pi$
$380$	−8.85070	−	3.44708i	−0.454031	−	0.176831i
$381$		0			0
$382$	−7.67972			−0.392929
$383$	−1.96946	−	3.41120i	−0.100635	−	0.174304i	0.811312	−	0.584614i	$-0.198754\pi$
$383$	−1.96946	−	3.41120i	−0.100635	−	0.174304i	−0.911946	+	0.410310i	$0.865421\pi$
$384$		0			0
$385$	−2.68611	−	17.5117i	−0.136897	−	0.892480i
$386$	7.59571	+	13.1562i	0.386612	+	0.669631i
$387$		0			0
$388$	−2.90296	+	5.02808i	−0.147376	+	0.255262i
$389$	19.1589			0.971394			0.485697	−	0.874127i	$-0.338566\pi$
$389$	19.1589			0.971394			0.485697	+	0.874127i	$0.338566\pi$
$390$		0			0
$391$	0.475035			0.0240235
$392$	8.00764	−	13.8696i	0.404447	−	0.700523i
$393$		0			0
$394$	1.50663	+	2.60956i	0.0759031	+	0.131468i
$395$	−32.3726	+	4.96562i	−1.62884	+	0.249847i
$396$		0			0
$397$	−3.22769	−	5.59052i	−0.161993	−	0.280580i	0.773590	−	0.633686i	$-0.218459\pi$
$397$	−3.22769	−	5.59052i	−0.161993	−	0.280580i	−0.935583	+	0.353106i	$0.885126\pi$
$398$	9.72106			0.487273
$399$		0			0
$400$	−1.08721	+	4.88037i	−0.0543604	+	0.244018i
$401$	−30.0012	−	17.3212i	−1.49819	−	0.864980i	−0.498191	−	0.867067i	$-0.666002\pi$
$401$	−30.0012	−	17.3212i	−1.49819	−	0.864980i	−0.999998	+	0.00208777i	$0.999335\pi$
$402$		0			0
$403$	13.9573	−	4.43310i	0.695262	−	0.220828i
$404$	−1.23752			−0.0615688
$405$		0			0
$406$	−10.6034	+	18.3655i	−0.526236	+	0.911467i
$407$	−2.59891	+	1.50048i	−0.128823	+	0.0743760i
$408$		0			0
$409$	−16.1142	+	9.30356i	−0.796798	+	0.460031i	−0.842350	−	0.538931i	$-0.818829\pi$
$409$	−16.1142	+	9.30356i	−0.796798	+	0.460031i	0.0455524	+	0.998962i	$0.485495\pi$
$410$	11.8433	−	9.49523i	0.584897	−	0.468936i
$411$		0			0
$412$	−8.13065	+	4.69423i	−0.400569	+	0.231268i
$413$	−8.75811	−	5.05650i	−0.430958	−	0.248814i
$414$		0			0
$415$	27.4707	−	4.21371i	1.34848	−	0.206843i
$416$	2.43026	−	2.66342i	0.119153	−	0.130585i
$417$		0			0
$418$	−3.50764	+	6.07542i	−0.171564	+	0.297158i
$419$	−11.4748	+	19.8749i	−0.560579	+	0.970951i	0.436867	+	0.899526i	$0.356088\pi$
$419$	−11.4748	+	19.8749i	−0.560579	+	0.970951i	−0.997446	+	0.0714252i	$0.977245\pi$
$420$		0			0
$421$			34.8196i			1.69700i	0.529194	+	0.848501i	$0.322495\pi$
$421$			34.8196i			1.69700i	−0.529194	+	0.848501i	$0.677505\pi$
$422$	−2.39532	−	4.14882i	−0.116602	−	0.201961i
$423$		0			0
$424$			11.5770i			0.562229i
$425$	0.272311	−	0.296564i	0.0132090	−	0.0143855i
$426$		0			0
$427$	−7.50394	+	12.9972i	−0.363141	+	0.628979i
$428$			18.5066i			0.894550i
$429$		0			0
$430$	−2.88019	−	18.7769i	−0.138895	−	0.905504i
$431$	−17.7523	−	10.2493i	−0.855100	−	0.493692i	0.00726828	−	0.999974i	$-0.497686\pi$
$431$	−17.7523	−	10.2493i	−0.855100	−	0.493692i	−0.862368	+	0.506281i	$0.831020\pi$
$432$		0			0
$433$	−1.85765	+	1.07251i	−0.0892728	+	0.0515417i	−0.543972	−	0.839103i	$-0.683080\pi$
$433$	−1.85765	+	1.07251i	−0.0892728	+	0.0515417i	0.454699	+	0.890645i	$0.349747\pi$
$434$			19.4853i			0.935326i
$435$		0			0
$436$	7.86903	−	4.54319i	0.376858	−	0.217579i
$437$	25.0587			1.19872
$438$		0			0
$439$	−0.525975	+	0.911016i	−0.0251034	+	0.0434804i	−0.878304	−	0.478102i	$-0.841325\pi$
$439$	−0.525975	+	0.911016i	−0.0251034	+	0.0434804i	0.853201	+	0.521583i	$0.174658\pi$
$440$	3.44115	+	1.34022i	0.164050	+	0.0638926i
$441$		0			0
$442$	−0.276712	+	0.0878888i	−0.0131618	+	0.00418044i
$443$		−	18.3043i		−	0.869665i	−0.900511	−	0.434833i	$-0.856807\pi$
$443$		−	18.3043i		−	0.869665i	0.900511	−	0.434833i	$-0.143193\pi$
$444$		0			0
$445$	−17.4181	−	6.78382i	−0.825697	−	0.321584i
$446$	−7.02172	−	12.1620i	−0.332488	−	0.575887i
$447$		0			0
$448$	2.39871	+	4.15469i	0.113329	+	0.196291i
$449$	12.0831	−	6.97618i	0.570237	−	0.329226i	−0.187007	−	0.982359i	$-0.559879\pi$
$449$	12.0831	−	6.97618i	0.570237	−	0.329226i	0.757244	+	0.653132i	$0.226545\pi$
$450$		0			0
$451$	−5.60573	−	9.70942i	−0.263964	−	0.457199i
$452$	13.8051	+	7.97036i	0.649336	+	0.374894i
$453$		0			0
$454$	−2.88019			−0.135174
$455$	21.4370	−	32.1939i	1.00498	−	1.50927i
$456$		0			0
$457$	14.7165	−	25.4898i	0.688411	−	1.19236i	−0.283941	−	0.958842i	$-0.591642\pi$
$457$	14.7165	−	25.4898i	0.688411	−	1.19236i	0.972352	−	0.233520i	$-0.0750245\pi$
$458$	−5.80932	−	3.35401i	−0.271452	−	0.156723i
$459$		0			0
$460$	−2.00000	−	13.0387i	−0.0932505	−	0.607933i
$461$	−7.87540	+	4.54686i	−0.366794	+	0.211768i	−0.672057	−	0.740500i	$-0.734589\pi$
$461$	−7.87540	+	4.54686i	−0.366794	+	0.211768i	0.305263	+	0.952268i	$0.401256\pi$
$462$		0			0
$463$	41.6642			1.93630			0.968150	−	0.250372i	$-0.0805529\pi$
$463$	41.6642			1.93630			0.968150	+	0.250372i	$0.0805529\pi$
$464$	−2.21022	−	3.82821i	−0.102607	−	0.177720i
$465$		0			0
$466$	−15.2385	−	8.79797i	−0.705911	−	0.407558i
$467$			38.1079i			1.76342i	0.471789	+	0.881712i	$0.343609\pi$
$467$			38.1079i			1.76342i	−0.471789	+	0.881712i	$0.656391\pi$
$468$		0			0
$469$	−19.1897			−0.886098
$470$	−0.364038	+	0.934703i	−0.0167918	+	0.0431146i
$471$		0			0
$472$	1.82559	−	1.05400i	0.0840294	−	0.0485144i
$473$	−14.0306			−0.645126
$474$		0			0
$475$	14.3648	−	15.6441i	0.659101	−	0.717803i
$476$		−	0.386309i		−	0.0177064i
$477$		0			0
$478$	−9.79641	−	5.65596i	−0.448078	−	0.258698i
$479$	13.0228	+	7.51871i	0.595026	+	0.343538i	0.767082	−	0.641549i	$-0.221708\pi$
$479$	13.0228	+	7.51871i	0.595026	+	0.343538i	−0.172056	+	0.985087i	$0.555041\pi$
$480$		0			0
$481$	−6.39926	−	1.40453i	−0.291781	−	0.0640411i
$482$			5.08019i			0.231396i
$483$		0			0
$484$	−4.13623	+	7.16416i	−0.188010	+	0.325644i
$485$	−8.12082	−	10.1290i	−0.368748	−	0.459933i
$486$		0			0
$487$	−2.28128	−	3.95129i	−0.103375	−	0.179050i	0.809698	−	0.586846i	$-0.199631\pi$
$487$	−2.28128	−	3.95129i	−0.103375	−	0.179050i	−0.913073	+	0.407796i	$0.866297\pi$
$488$	−1.56416	−	2.70920i	−0.0708062	−	0.122640i
$489$		0			0
$490$	22.4008	+	27.9401i	1.01196	+	1.26221i
$491$	−4.20803	+	7.28853i	−0.189906	+	0.328927i	−0.945219	−	0.326438i	$-0.894152\pi$
$491$	−4.20803	+	7.28853i	−0.189906	+	0.328927i	0.755313	+	0.655364i	$0.227485\pi$
$492$		0			0
$493$			0.355952i			0.0160313i
$494$	−14.5969	+	4.63625i	−0.656746	+	0.208595i
$495$		0			0
$496$	−3.51747	−	2.03081i	−0.157939	−	0.0911862i
$497$	30.5396	+	17.6321i	1.36989	+	0.790906i
$498$		0			0
$499$		−	12.5587i		−	0.562206i	−0.959678	−	0.281103i	$-0.909300\pi$
$499$		−	12.5587i		−	0.562206i	0.959678	−	0.281103i	$-0.0907002\pi$
$500$	−9.28654	−	6.22577i	−0.415307	−	0.278425i
$501$		0			0
$502$	−19.5704			−0.873471
$503$	6.79244	−	3.92162i	0.302860	−	0.174856i	−0.340867	−	0.940112i	$-0.610721\pi$
$503$	6.79244	−	3.92162i	0.302860	−	0.174856i	0.643727	+	0.765255i	$0.277387\pi$
$504$		0			0
$505$	1.00425	−	2.57851i	0.0446886	−	0.114742i
$506$	−9.74283			−0.433121
$507$		0			0
$508$		−	0.892954i		−	0.0396184i
$509$	−31.4237	−	18.1425i	−1.39283	−	0.804152i	−0.399203	−	0.916862i	$-0.630713\pi$
$509$	−31.4237	−	18.1425i	−1.39283	−	0.804152i	−0.993628	+	0.112711i	$0.964047\pi$
$510$		0			0
$511$	−25.3668	−	43.9367i	−1.12216	−	1.94364i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−1.71818	+	0.991989i	−0.0757855	+	0.0437548i
$515$	−3.18292	−	20.7506i	−0.140256	−	0.914379i
$516$		0			0
$517$	0.641611	+	0.370435i	0.0282180	+	0.0162917i
$518$	4.35866	−	7.54942i	0.191508	−	0.331702i
$519$		0			0
$520$	3.57738	+	7.22512i	0.156878	+	0.316842i
$521$	−1.95007			−0.0854341			−0.0427171	−	0.999087i	$-0.513601\pi$
$521$	−1.95007			−0.0854341			−0.0427171	+	0.999087i	$0.513601\pi$
$522$		0			0
$523$	7.86903	+	4.54319i	0.344089	+	0.198660i	0.662079	−	0.749434i	$-0.269674\pi$
$523$	7.86903	+	4.54319i	0.344089	+	0.198660i	−0.317990	+	0.948094i	$0.603008\pi$
$524$	−0.558851	−	0.967959i	−0.0244135	−	0.0422855i
$525$		0			0
$526$	0.527031	−	0.304282i	0.0229797	−	0.0132673i
$527$	0.163529	+	0.283241i	0.00712346	+	0.0123382i
$528$		0			0
$529$	5.90078	+	10.2204i	0.256556	+	0.444367i
$530$	−24.1220	−	9.39480i	−1.04779	−	0.408084i
$531$		0			0
$532$		−	20.3783i		−	0.883511i
$533$	5.24727	−	23.9074i	0.227285	−	1.03554i
$534$		0			0
$535$	−38.5606	−	15.0182i	−1.66712	−	0.649293i
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$		0			0
$538$	17.7448			0.765035
$539$	22.9061	−	13.2248i	0.986635	−	0.569634i
$540$		0			0
$541$		−	35.7827i		−	1.53842i	−0.638997	−	0.769209i	$-0.720650\pi$
$541$		−	35.7827i		−	1.53842i	0.638997	−	0.769209i	$-0.279350\pi$
$542$	−13.8806	+	8.01395i	−0.596222	+	0.344229i
$543$		0			0
$544$	0.0697360	+	0.0402621i	0.00298990	+	0.00172622i
$545$	3.08050	+	20.0829i	0.131954	+	0.860256i
$546$		0			0
$547$			29.0584i			1.24245i	0.783634	+	0.621223i	$0.213364\pi$
$547$			29.0584i			1.24245i	−0.783634	+	0.621223i	$0.786636\pi$
$548$	4.10468	−	7.10951i	0.175343	−	0.303703i
$549$		0			0
$550$	−5.58502	+	6.08244i	−0.238146	+	0.259356i
$551$			18.7769i			0.799925i
$552$		0			0
$553$	−35.1335	−	60.8529i	−1.49403	−	2.58773i
$554$		−	11.9042i		−	0.505760i
$555$		0			0
$556$	2.55885	−	4.43206i	0.108519	−	0.187961i
$557$	16.5492	−	28.6641i	0.701213	−	1.21454i	−0.266828	−	0.963744i	$-0.585976\pi$
$557$	16.5492	−	28.6641i	0.701213	−	1.21454i	0.968041	−	0.250792i	$-0.0806911\pi$
$558$		0			0
$559$	−22.6271	−	20.6463i	−0.957026	−	0.873247i
$560$	−10.6034	+	1.62644i	−0.448073	+	0.0687298i
$561$		0			0
$562$	9.87055	+	5.69877i	0.416364	+	0.240388i
$563$	9.06138	−	5.23159i	0.381892	−	0.220485i	−0.296749	−	0.954955i	$-0.595903\pi$
$563$	9.06138	−	5.23159i	0.381892	−	0.220485i	0.678641	+	0.734470i	$0.262569\pi$
$564$		0			0
$565$	−27.8101	+	22.2965i	−1.16998	+	0.938020i
$566$	−17.6776	+	10.2062i	−0.743045	+	0.428997i
$567$		0			0
$568$	−6.36584	+	3.67532i	−0.267105	+	0.154213i
$569$	4.31622	−	7.47591i	0.180945	−	0.313407i	−0.761257	−	0.648450i	$-0.775418\pi$
$569$	4.31622	−	7.47591i	0.180945	−	0.313407i	0.942203	+	0.335043i	$0.108751\pi$
$570$		0			0
$571$	14.3069			0.598724			0.299362	−	0.954140i	$-0.403226\pi$
$571$	14.3069			0.598724			0.299362	+	0.954140i	$0.403226\pi$
$572$	5.67528	−	1.80257i	0.237295	−	0.0753694i
$573$		0			0
$574$	28.2043	+	16.2838i	1.17723	+	0.679672i
$575$	28.7907	+	6.41374i	1.20065	+	0.267472i
$576$		0			0
$577$	11.9697			0.498306			0.249153	−	0.968464i	$-0.419848\pi$
$577$	11.9697			0.498306			0.249153	+	0.968464i	$0.419848\pi$
$578$	8.49676	+	14.7168i	0.353419	+	0.612139i
$579$		0			0
$580$	9.77013	−	1.49863i	0.405682	−	0.0622274i
$581$	29.8135	+	51.6384i	1.23687	+	2.14232i
$582$		0			0
$583$	−9.55986	+	16.5582i	−0.395929	+	0.685769i
$584$	10.5752			0.437605
$585$		0			0
$586$	4.18768			0.172991
$587$	2.75398	−	4.77003i	0.113669	−	0.196880i	−0.803578	−	0.595199i	$-0.797073\pi$
$587$	2.75398	−	4.77003i	0.113669	−	0.196880i	0.917247	+	0.398319i	$0.130406\pi$
$588$		0			0
$589$	8.62640	+	14.9414i	0.355445	+	0.615648i
$590$	0.714665	+	4.65915i	0.0294223	+	0.191814i
$591$		0			0
$592$	0.908541	+	1.57364i	0.0373408	+	0.0646762i
$593$	24.6037			1.01035			0.505177	−	0.863016i	$-0.331427\pi$
$593$	24.6037			1.01035			0.505177	+	0.863016i	$0.331427\pi$
$594$		0			0
$595$	0.804919	+	0.313491i	0.0329985	+	0.0128519i
$596$	3.58721	+	2.07107i	0.146938	+	0.0848345i
$597$		0			0
$598$	−15.7123	−	14.3368i	−0.642523	−	0.586276i
$599$	−35.3159			−1.44297			−0.721484	−	0.692431i	$-0.756540\pi$
$599$	−35.3159			−1.44297			−0.721484	+	0.692431i	$0.756540\pi$
$600$		0			0
$601$	−17.4607	+	30.2428i	−0.712236	+	1.23363i	0.251780	+	0.967785i	$0.418984\pi$
$601$	−17.4607	+	30.2428i	−0.712236	+	1.23363i	−0.964016	+	0.265845i	$0.914349\pi$
$602$	35.2962	−	20.3783i	1.43857	−	0.830557i
$603$		0			0
$604$	3.83986	−	2.21694i	0.156242	−	0.0902062i
$605$	−11.5708	−	14.4321i	−0.470420	−	0.586747i
$606$		0			0
$607$	21.6183	−	12.4813i	0.877461	−	0.506602i	0.00764039	−	0.999971i	$-0.497568\pi$
$607$	21.6183	−	12.4813i	0.877461	−	0.506602i	0.869820	+	0.493369i	$0.164235\pi$
$608$	3.67867	+	2.12388i	0.149190	+	0.0861347i
$609$		0			0
$610$	6.91427	−	1.06058i	0.279950	−	0.0429415i
$611$	0.489625	+	1.54155i	0.0198081	+	0.0623644i
$612$		0			0
$613$	8.06330	−	13.9660i	0.325674	−	0.564083i	−0.655975	−	0.754783i	$-0.727742\pi$
$613$	8.06330	−	13.9660i	0.325674	−	0.564083i	0.981648	+	0.190700i	$0.0610756\pi$
$614$	−9.00850	+	15.6032i	−0.363554	+	0.629693i
$615$		0			0
$616$			7.92308i			0.319230i
$617$	−14.2537	−	24.6881i	−0.573831	−	0.993904i	−0.996168	−	0.0874652i	$-0.972123\pi$
$617$	−14.2537	−	24.6881i	−0.573831	−	0.993904i	0.422337	−	0.906439i	$-0.361210\pi$
$618$		0			0
$619$			0.338217i			0.0135941i	0.999977	+	0.00679705i	$0.00216358\pi$
$619$			0.338217i			0.0135941i	−0.999977	+	0.00679705i	$0.997836\pi$
$620$	7.08588	−	5.68105i	0.284576	−	0.228156i
$621$		0			0
$622$	2.58908	−	4.48442i	0.103813	−	0.179809i
$623$		−	40.1043i		−	1.60675i
$624$		0			0
$625$	20.5082	−	14.2973i	0.820328	−	0.571894i
$626$	28.2613	+	16.3167i	1.12955	+	0.652145i
$627$		0			0
$628$	−7.20889	+	4.16206i	−0.287666	+	0.166084i
$629$		−	0.146319i		−	0.00583412i
$630$		0			0
$631$	27.8799	−	16.0965i	1.10988	−	0.640791i	0.171084	−	0.985256i	$-0.445273\pi$
$631$	27.8799	−	16.0965i	1.10988	−	0.640791i	0.938799	+	0.344465i	$0.111940\pi$
$632$	14.6468			0.582618
$633$		0			0
$634$	−11.8692	+	20.5581i	−0.471387	+	0.816467i
$635$	1.86057	+	0.724637i	0.0738346	+	0.0287563i
$636$		0			0
$637$	56.4014	+	12.3792i	2.23470	+	0.490480i
$638$		−	7.30047i		−	0.289028i
$639$		0			0
$640$	0.811505	−	2.08362i	0.0320776	−	0.0823622i
$641$	−6.29981	−	10.9116i	−0.248827	−	0.430982i	0.714373	−	0.699765i	$-0.246712\pi$
$641$	−6.29981	−	10.9116i	−0.248827	−	0.430982i	−0.963201	+	0.268783i	$0.913379\pi$
$642$		0			0
$643$	9.70277	+	16.8057i	0.382640	+	0.662752i	0.991439	−	0.130573i	$-0.0416817\pi$
$643$	9.70277	+	16.8057i	0.382640	+	0.662752i	−0.608799	+	0.793325i	$0.708348\pi$
$644$	24.5097	−	14.1507i	0.965818	−	0.557615i
$645$		0			0
$646$	−0.171024	−	0.296221i	−0.00672883	−	0.0116547i
$647$	−16.1897	−	9.34715i	−0.636485	−	0.367475i	0.146774	−	0.989170i	$-0.453111\pi$
$647$	−16.1897	−	9.34715i	−0.636485	−	0.367475i	−0.783259	+	0.621695i	$0.786444\pi$
$648$		0			0
$649$	3.48143			0.136658
$650$	−17.9574	+	1.59066i	−0.704349	+	0.0623909i
$651$		0			0
$652$	−0.471644	+	0.816912i	−0.0184710	+	0.0319927i
$653$	−15.4758	−	8.93497i	−0.605616	−	0.349652i	0.165632	−	0.986188i	$-0.447034\pi$
$653$	−15.4758	−	8.93497i	−0.605616	−	0.349652i	−0.771248	+	0.636535i	$0.780367\pi$
$654$		0			0
$655$	2.47037	−	0.378928i	0.0965252	−	0.0148059i
$656$	−5.87906	+	3.39427i	−0.229539	+	0.132524i
$657$		0			0
$658$	−2.15211			−0.0838979
$659$	19.5447	+	33.8523i	0.761352	+	1.31870i	0.942154	+	0.335180i	$0.108797\pi$
$659$	19.5447	+	33.8523i	0.761352	+	1.31870i	−0.180803	+	0.983519i	$0.557870\pi$
$660$		0			0
$661$	−34.9611	−	20.1848i	−1.35983	−	0.785098i	−0.370229	−	0.928941i	$-0.620721\pi$
$661$	−34.9611	−	20.1848i	−1.35983	−	0.785098i	−0.989601	+	0.143843i	$0.954054\pi$
$662$		−	30.4752i		−	1.18445i
$663$		0			0
$664$	−12.4289			−0.482336
$665$	42.4606	+	16.5371i	1.64655	+	0.641281i
$666$		0			0
$667$	−22.5837	+	13.0387i	−0.874444	+	0.504861i
$668$	4.30062			0.166396
$669$		0			0
$670$	5.59485	+	6.97837i	0.216148	+	0.269598i
$671$		−	5.16650i		−	0.199451i
$672$		0			0
$673$	18.3453	+	10.5917i	0.707160	+	0.408279i	0.810009	−	0.586418i	$-0.199462\pi$
$673$	18.3453	+	10.5917i	0.707160	+	0.408279i	−0.102849	+	0.994697i	$0.532796\pi$
$674$	16.6969	+	9.63995i	0.643140	+	0.371317i
$675$		0			0
$676$	11.8051	+	5.44430i	0.454041	+	0.209396i
$677$			2.48027i			0.0953245i	0.998864	+	0.0476622i	$0.0151771\pi$
$677$			2.48027i			0.0953245i	−0.998864	+	0.0476622i	$0.984823\pi$
$678$		0			0
$679$	13.9268	−	24.1218i	0.534460	−	0.925711i
$680$	−0.140482	+	0.112630i	−0.00538723	+	0.00431917i
$681$		0			0
$682$	−3.35394	−	5.80920i	−0.128429	−	0.222446i
$683$	−6.42894	−	11.1352i	−0.245997	−	0.426078i	0.716415	−	0.697675i	$-0.245782\pi$
$683$	−6.42894	−	11.1352i	−0.245997	−	0.426078i	−0.962411	+	0.271596i	$0.912449\pi$
$684$		0			0
$685$	11.4825	+	14.3220i	0.438725	+	0.547215i
$686$	−21.6251	+	37.4557i	−0.825649	+	1.43007i
$687$		0			0
$688$			8.49552i			0.323888i
$689$	−39.7830	+	12.6358i	−1.51561	+	0.481386i
$690$		0			0
$691$	0.975544	+	0.563231i	0.0371115	+	0.0214263i	0.518441	−	0.855113i	$-0.326513\pi$
$691$	0.975544	+	0.563231i	0.0371115	+	0.0214263i	−0.481329	+	0.876540i	$0.659846\pi$
$692$	−0.861584	−	0.497436i	−0.0327525	−	0.0189097i
$693$		0			0
$694$		−	15.3720i		−	0.583512i
$695$	7.15819	+	8.92831i	0.271526	+	0.338670i
$696$		0			0
$697$	0.546642			0.0207055
$698$	−13.1667	+	7.60177i	−0.498365	+	0.287731i
$699$		0			0
$700$	5.21579	−	23.4132i	0.197138	−	0.884936i
$701$	−9.39602			−0.354883			−0.177441	−	0.984131i	$-0.556782\pi$
$701$	−9.39602			−0.354883			−0.177441	+	0.984131i	$0.556782\pi$
$702$		0			0
$703$		−	7.71852i		−	0.291110i
$704$	−1.43026	−	0.825763i	−0.0539051	−	0.0311221i
$705$		0			0
$706$	−13.4509	−	23.2976i	−0.506230	−	0.876816i
$707$	5.93690			0.223280
$708$		0			0
$709$	15.4770	−	8.93567i	0.581252	−	0.335586i	−0.180379	−	0.983597i	$-0.557732\pi$
$709$	15.4770	−	8.93567i	0.581252	−	0.335586i	0.761631	+	0.648011i	$0.224399\pi$
$710$	−2.49204	−	16.2465i	−0.0935247	−	0.609720i
$711$		0			0
$712$	7.23958	+	4.17978i	0.271315	+	0.156644i
$713$	−11.9803	+	20.7506i	−0.448667	+	0.777115i
$714$		0			0
$715$	−0.849643	+	13.2879i	−0.0317749	+	0.496939i
$716$	20.4357			0.763719
$717$		0			0
$718$	18.0434	+	10.4174i	0.673375	+	0.388773i
$719$	−1.15648	−	2.00308i	−0.0431294	−	0.0747023i	0.843655	−	0.536886i	$-0.180399\pi$
$719$	−1.15648	−	2.00308i	−0.0431294	−	0.0747023i	−0.886784	+	0.462184i	$0.847066\pi$
$720$		0			0
$721$	39.0062	−	22.5202i	1.45267	−	0.838698i
$722$	0.478277	+	0.828400i	0.0177996	+	0.0308299i
$723$		0			0
$724$	9.97609	+	17.2791i	0.370759	+	0.642173i
$725$	−4.80593	+	21.5733i	−0.178488	+	0.801214i
$726$		0			0
$727$		−	17.9866i		−	0.667087i	−0.942735	−	0.333543i	$-0.891756\pi$
$727$		−	17.9866i		−	0.667087i	0.942735	−	0.333543i	$-0.108244\pi$
$728$	−11.6590	+	12.7776i	−0.432112	+	0.473568i
$729$		0			0
$730$	−8.58183	+	22.0346i	−0.317628	+	0.815539i
$731$	0.342047	−	0.592443i	0.0126511	−	0.0219123i
$732$		0			0
$733$	−45.2898			−1.67282			−0.836408	−	0.548108i	$-0.815348\pi$
$733$	−45.2898			−1.67282			−0.836408	+	0.548108i	$0.815348\pi$
$734$	29.9410	−	17.2865i	1.10514	−	0.638055i
$735$		0			0
$736$			5.89928i			0.217451i
$737$	5.72106	−	3.30305i	0.210738	−	0.121670i
$738$		0			0
$739$	38.9749	+	22.5022i	1.43372	+	0.827756i	0.997402	−	0.0720387i	$-0.0229505\pi$
$739$	38.9749	+	22.5022i	1.43372	+	0.827756i	0.436314	+	0.899795i	$0.356284\pi$
$740$	−4.01615	+	0.616035i	−0.147636	+	0.0226459i
$741$		0			0
$742$		−	55.5398i		−	2.03893i
$743$	−3.28334	+	5.68692i	−0.120454	+	0.208633i	−0.919947	−	0.392043i	$-0.871768\pi$
$743$	−3.28334	+	5.68692i	−0.120454	+	0.208633i	0.799493	+	0.600676i	$0.205102\pi$
$744$		0			0
$745$	−7.22636	+	5.79368i	−0.264754	+	0.212264i
$746$		−	25.0064i		−	0.915549i
$747$		0			0
$748$	0.0664939	+	0.115171i	0.00243126	+	0.00421106i
$749$		−	88.7840i		−	3.24410i
$750$		0			0
$751$	−13.6750	+	23.6857i	−0.499006	+	0.864304i	−0.999999	−	0.00114692i	$-0.999635\pi$
$751$	−13.6750	+	23.6857i	−0.499006	+	0.864304i	0.500993	+	0.865451i	$0.332968\pi$
$752$	0.224298	−	0.388496i	0.00817932	−	0.0141670i
$753$		0			0
$754$	10.7428	−	11.7735i	0.391231	−	0.428765i
$755$	1.50320	+	9.79986i	0.0547069	+	0.356653i
$756$		0			0
$757$	−33.8205	−	19.5263i	−1.22923	−	0.709696i	−0.262360	−	0.964970i	$-0.584501\pi$
$757$	−33.8205	−	19.5263i	−1.22923	−	0.709696i	−0.966869	+	0.255275i	$0.917834\pi$
$758$	−3.25585	+	1.87977i	−0.118258	+	0.0682762i
$759$		0			0
$760$	−7.41061	+	5.94139i	−0.268811	+	0.215517i
$761$	24.6247	−	14.2171i	0.892645	−	0.515369i	0.0178384	−	0.999841i	$-0.494322\pi$
$761$	24.6247	−	14.2171i	0.892645	−	0.515369i	0.874807	+	0.484472i	$0.160988\pi$
$762$		0			0
$763$	−37.7511	+	21.7956i	−1.36668	+	0.789054i
$764$	−3.83986	+	6.65083i	−0.138921	+	0.240619i
$765$		0			0
$766$	−3.93892			−0.142319
$767$	5.61451	+	5.12301i	0.202728	+	0.184981i
$768$		0			0
$769$	−25.3247	−	14.6212i	−0.913231	−	0.527254i	−0.0317619	−	0.999495i	$-0.510112\pi$
$769$	−25.3247	−	14.6212i	−0.913231	−	0.527254i	−0.881469	+	0.472241i	$0.843445\pi$
$770$	−16.5087	−	6.42962i	−0.594931	−	0.231707i
$771$		0			0
$772$	15.1914			0.546751
$773$	10.4106	+	18.0317i	0.374444	+	0.648555i	0.990244	−	0.139347i	$-0.0445004\pi$
$773$	10.4106	+	18.0317i	0.374444	+	0.648555i	−0.615800	+	0.787902i	$0.711167\pi$
$774$		0			0
$775$	6.08689	+	19.3745i	0.218648	+	0.695951i
$776$	2.90296	+	5.02808i	0.104210	+	0.180498i
$777$		0			0
$778$	9.57944	−	16.5921i	0.343440	−	0.594855i
$779$	28.8361			1.03316
$780$		0			0
$781$	−12.1398			−0.434395
$782$	0.237517	−	0.411392i	0.00849361	−	0.0147114i
$783$		0			0
$784$	−8.00764	−	13.8696i	−0.285987	−	0.495344i
$785$	−2.82208	−	18.3981i	−0.100724	−	0.656656i
$786$		0			0
$787$	10.4784	+	18.1492i	0.373516	+	0.646948i	0.990104	−	0.140338i	$-0.0448189\pi$
$787$	10.4784	+	18.1492i	0.373516	+	0.646948i	−0.616588	+	0.787286i	$0.711486\pi$
$788$	3.01327			0.107343
$789$		0			0
$790$	−11.8860	+	30.5183i	−0.422883	+	1.08579i
$791$	−66.2288	−	38.2372i	−2.35482	−	1.35956i
$792$		0			0
$793$	7.60264	−	8.33203i	0.269978	−	0.295879i
$794$	−6.45538			−0.229093
$795$		0			0
$796$	4.86053	−	8.41868i	0.172277	−	0.298392i
$797$	−16.0855	+	9.28699i	−0.569779	+	0.328962i	−0.757061	−	0.653344i	$-0.773365\pi$
$797$	−16.0855	+	9.28699i	−0.569779	+	0.328962i	0.187282	+	0.982306i	$0.440032\pi$
$798$		0			0
$799$	−0.0312833	+	0.0180614i	−0.00110672	+	0.000638967i
$800$	3.68292	+	3.38173i	0.130211	+	0.119562i
$801$		0			0
$802$	−30.0012	+	17.3212i	−1.05938	+	0.611633i
$803$	15.1253	+	8.73261i	0.533761	+	0.308167i
$804$		0			0
$805$	9.59485	+	62.5522i	0.338174	+	2.20468i
$806$	3.13947	−	14.3039i	0.110583	−	0.503834i
$807$		0			0
$808$	−0.618759	+	1.07172i	−0.0217679	+	0.0377030i
$809$	−14.0705	+	24.3708i	−0.494692	+	0.856831i	−0.999981	−	0.00611875i	$-0.998052\pi$
$809$	−14.0705	+	24.3708i	−0.494692	+	0.856831i	0.505290	+	0.862950i	$0.331386\pi$
$810$		0			0
$811$			17.1410i			0.601903i	0.953639	+	0.300952i	$0.0973043\pi$
$811$			17.1410i			0.601903i	−0.953639	+	0.300952i	$0.902696\pi$
$812$	10.6034	+	18.3655i	0.372105	+	0.644504i
$813$		0			0
$814$			3.00096i			0.105184i
$815$	−1.31939	−	1.64565i	−0.0462162	−	0.0576447i
$816$		0			0
$817$	18.0434	−	31.2522i	0.631260	−	1.09337i
$818$			18.6071i			0.650583i
$819$		0			0
$820$	−2.30148	−	15.0042i	−0.0803712	−	0.523968i
$821$	−11.5893	−	6.69111i	−0.404471	−	0.233521i	0.283940	−	0.958842i	$-0.408358\pi$
$821$	−11.5893	−	6.69111i	−0.404471	−	0.233521i	−0.688411	+	0.725321i	$0.741692\pi$
$822$		0			0
$823$	18.7144	−	10.8047i	0.652341	−	0.376629i	−0.137011	−	0.990569i	$-0.543750\pi$
$823$	18.7144	−	10.8047i	0.652341	−	0.376629i	0.789353	+	0.613940i	$0.210416\pi$
$824$			9.38847i			0.327063i
$825$		0			0
$826$	−8.75811	+	5.05650i	−0.304734	+	0.175938i
$827$	5.85827			0.203712			0.101856	−	0.994799i	$-0.467522\pi$
$827$	5.85827			0.203712			0.101856	+	0.994799i	$0.467522\pi$
$828$		0			0
$829$	10.6392	−	18.4276i	0.369513	−	0.640016i	−0.619976	−	0.784621i	$-0.712858\pi$
$829$	10.6392	−	18.4276i	0.369513	−	0.640016i	0.989489	+	0.144605i	$0.0461911\pi$
$830$	10.0862	−	25.8971i	0.350095	−	0.898903i
$831$		0			0
$832$	−1.09146	−	3.43638i	−0.0378395	−	0.119135i
$833$			1.28962i			0.0446826i
$834$		0			0
$835$	−3.48998	+	8.96085i	−0.120776	+	0.310103i
$836$	3.50764	+	6.07542i	0.121314	+	0.210123i
$837$		0			0
$838$	11.4748	+	19.8749i	0.396389	+	0.686566i
$839$	16.9067	−	9.76109i	0.583684	−	0.336990i	−0.178912	−	0.983865i	$-0.557258\pi$
$839$	16.9067	−	9.76109i	0.583684	−	0.336990i	0.762596	+	0.646875i	$0.223924\pi$
$840$		0			0
$841$	4.72987	+	8.19238i	0.163099	+	0.282496i
$842$	30.1546	+	17.4098i	1.03920	+	0.599981i
$843$		0			0
$844$	−4.79064			−0.164901
$845$	−20.9237	+	20.1792i	−0.719797	+	0.694184i
$846$		0			0
$847$	19.8433	−	34.3695i	0.681822	−	1.18095i
$848$	10.0260	+	5.78850i	0.344293	+	0.198778i
$849$		0			0
$850$	−0.120676	−	0.384110i	−0.00413916	−	0.0131749i
$851$	9.28334	−	5.35974i	0.318229	−	0.183730i
$852$		0			0
$853$	33.3923			1.14333			0.571665	−	0.820487i	$-0.306298\pi$
$853$	33.3923			1.14333			0.571665	+	0.820487i	$0.306298\pi$
$854$	7.50394	+	12.9972i	0.256779	+	0.444755i
$855$		0			0
$856$	16.0272	+	9.25330i	0.547798	+	0.316271i
$857$		−	22.7514i		−	0.777172i	−0.921412	−	0.388586i	$-0.872964\pi$
$857$		−	22.7514i		−	0.777172i	0.921412	−	0.388586i	$-0.127036\pi$
$858$		0			0
$859$	−7.99391			−0.272749			−0.136374	−	0.990657i	$-0.543545\pi$
$859$	−7.99391			−0.272749			−0.136374	+	0.990657i	$0.543545\pi$
$860$	−17.7014	−	6.89416i	−0.603613	−	0.235089i
$861$		0			0
$862$	−17.7523	+	10.2493i	−0.604647	+	0.349093i
$863$	11.7205			0.398971			0.199486	−	0.979901i	$-0.436073\pi$
$863$	11.7205			0.398971			0.199486	+	0.979901i	$0.436073\pi$
$864$		0			0
$865$	1.73565	−	1.39154i	0.0590137	−	0.0473138i
$866$			2.14503i			0.0728909i
$867$		0			0
$868$	16.8748	+	9.74267i	0.572768	+	0.330688i
$869$	20.9488	+	12.0948i	0.710639	+	0.410288i
$870$		0			0
$871$	14.0869	+	3.09184i	0.477316	+	0.104763i
$872$		−	9.08638i		−	0.307704i
$873$		0			0
$874$	12.5294	−	21.7015i	0.423812	−	0.734064i
$875$	44.5515	+	29.8676i	1.50611	+	1.00971i
$876$		0			0
$877$	−0.864038	−	1.49656i	−0.0291765	−	0.0505352i	0.851068	−	0.525055i	$-0.175955\pi$
$877$	−0.864038	−	1.49656i	−0.0291765	−	0.0505352i	−0.880245	+	0.474520i	$0.842622\pi$
$878$	0.525975	+	0.911016i	0.0177508	+	0.0307453i
$879$		0			0
$880$	2.88124	−	2.31001i	0.0971266	−	0.0778705i
$881$	16.7831	−	29.0691i	0.565436	−	0.979364i	−0.431573	−	0.902078i	$-0.642041\pi$
$881$	16.7831	−	29.0691i	0.565436	−	0.979364i	0.997009	−	0.0772861i	$-0.0246255\pi$
$882$		0			0
$883$		−	18.2526i		−	0.614249i	−0.951669	−	0.307124i	$-0.900633\pi$
$883$		−	18.2526i		−	0.614249i	0.951669	−	0.307124i	$-0.0993667\pi$
$884$	−0.0622419	+	0.283584i	−0.00209342	+	0.00953795i
$885$		0			0
$886$	−15.8520	−	9.15217i	−0.532559	−	0.307473i
$887$	20.3335	+	11.7395i	0.682732	+	0.394176i	0.800884	−	0.598820i	$-0.204364\pi$
$887$	20.3335	+	11.7395i	0.682732	+	0.394176i	−0.118152	+	0.992996i	$0.537697\pi$
$888$		0			0
$889$			4.28388i			0.143677i
$890$	−14.5840	+	11.6926i	−0.488857	+	0.391937i
$891$		0			0
$892$	−14.0434			−0.470209
$893$	−1.65024	+	0.952765i	−0.0552231	+	0.0318831i
$894$		0			0
$895$	−16.5837	+	42.5802i	−0.554332	+	1.42330i
$896$	4.79742			0.160271
$897$		0			0
$898$		−	13.9524i		−	0.465596i
$899$	−15.5488	−	8.97708i	−0.518580	−	0.299402i
$900$		0			0
$901$	−0.466114	−	0.807333i	−0.0155285	−	0.0268962i
$902$	−11.2115			−0.373301
$903$		0			0
$904$	13.8051	−	7.97036i	0.459150	−	0.265090i
$905$	−44.0987	+	6.76427i	−1.46589	+	0.224852i
$906$		0			0
$907$	−23.1056	−	13.3400i	−0.767208	−	0.442948i	0.0646698	−	0.997907i	$-0.479401\pi$
$907$	−23.1056	−	13.3400i	−0.767208	−	0.442948i	−0.831878	+	0.554959i	$0.812734\pi$
$908$	−1.44009	+	2.49431i	−0.0477911	+	0.0827767i
$909$		0			0
$910$	−17.1622	−	34.6620i	−0.568922	−	1.14903i
$911$	33.1591			1.09861			0.549305	−	0.835622i	$-0.314892\pi$
$911$	33.1591			1.09861			0.549305	+	0.835622i	$0.314892\pi$
$912$		0			0
$913$	−17.7767	−	10.2634i	−0.588322	−	0.339668i
$914$	−14.7165	−	25.4898i	−0.486780	−	0.843127i
$915$		0			0
$916$	−5.80932	+	3.35401i	−0.191945	+	0.110820i
$917$	2.68105	+	4.64371i	0.0885360	+	0.153349i
$918$		0			0
$919$	−19.2895	−	33.4103i	−0.636301	−	1.10211i	−0.986238	−	0.165332i	$-0.947130\pi$
$919$	−19.2895	−	33.4103i	−0.636301	−	1.10211i	0.349937	−	0.936773i	$-0.386203\pi$
$920$	−12.2918	−	4.78730i	−0.405250	−	0.157833i
$921$		0			0
$922$			9.09372i			0.299486i
$923$	−19.5778	−	17.8640i	−0.644413	−	0.588000i
$924$		0			0
$925$	1.97554	−	8.86803i	0.0649555	−	0.291579i
$926$	20.8321	−	36.0823i	0.684585	−	1.18574i
$927$		0			0
$928$	−4.42044			−0.145108
$929$	−21.3019	+	12.2986i	−0.698892	+	0.403505i	−0.806935	−	0.590641i	$-0.798875\pi$
$929$	−21.3019	+	12.2986i	−0.698892	+	0.403505i	0.108043	+	0.994146i	$0.465542\pi$
$930$		0			0
$931$			68.0291i			2.22956i
$932$	−15.2385	+	8.79797i	−0.499155	+	0.288187i
$933$		0			0
$934$	33.0024	+	19.0540i	1.07987	+	0.623464i
$935$	−0.293932	+	0.0450861i	−0.00961260	+	0.00147447i
$936$		0			0
$937$			25.6787i			0.838886i	0.907782	+	0.419443i	$0.137775\pi$
$937$			25.6787i			0.838886i	−0.907782	+	0.419443i	$0.862225\pi$
$938$	−9.59485	+	16.6188i	−0.313283	+	0.542622i
$939$		0			0
$940$	0.627458	+	0.782618i	0.0204654	+	0.0255262i
$941$			27.7630i			0.905047i	0.891752	+	0.452524i	$0.149476\pi$
$941$			27.7630i			0.905047i	−0.891752	+	0.452524i	$0.850524\pi$
$942$		0			0
$943$	20.0238	+	34.6822i	0.652064	+	1.12941i
$944$		−	2.10800i		−	0.0686097i
$945$		0			0
$946$	−7.01529	+	12.1508i	−0.228087	+	0.395058i
$947$	5.01454	−	8.68544i	0.162951	−	0.282239i	−0.772975	−	0.634437i	$-0.781232\pi$
$947$	5.01454	−	8.68544i	0.162951	−	0.282239i	0.935926	+	0.352198i	$0.114565\pi$
$948$		0			0
$949$	11.5424	+	36.3404i	0.374682	+	1.17966i
$950$	−6.36584	−	20.2623i	−0.206535	−	0.657397i
$951$		0			0
$952$	−0.334553	−	0.193154i	−0.0108429	−	0.00626017i
$953$	−30.2756	+	17.4796i	−0.980722	+	0.566220i	−0.902488	−	0.430715i	$-0.858262\pi$
$953$	−30.2756	+	17.4796i	−0.980722	+	0.566220i	−0.0782342	+	0.996935i	$0.524928\pi$
$954$		0			0
$955$	−10.7417	−	13.3980i	−0.347594	−	0.433549i
$956$	−9.79641	+	5.65596i	−0.316839	+	0.182927i
$957$		0			0
$958$	13.0228	−	7.51871i	0.420747	−	0.242918i
$959$	−19.6919	+	34.1073i	−0.635884	+	1.10138i
$960$		0			0
$961$	14.5032			0.467845
$962$	−4.41599	+	4.83966i	−0.142377	+	0.156037i
$963$		0			0
$964$	4.39957	+	2.54010i	0.141701	+	0.0818110i
$965$	−12.3279	+	31.6531i	−0.396850	+	1.01895i
$966$		0			0
$967$	−8.61013			−0.276883			−0.138442	−	0.990371i	$-0.544209\pi$
$967$	−8.61013			−0.276883			−0.138442	+	0.990371i	$0.544209\pi$
$968$	4.13623	+	7.16416i	0.132943	+	0.230265i
$969$		0			0
$970$	−12.8324	+	1.96835i	−0.412022	+	0.0631999i
$971$	−14.2447	−	24.6725i	−0.457134	−	0.791779i	0.541674	−	0.840589i	$-0.317791\pi$
$971$	−14.2447	−	24.6725i	−0.457134	−	0.791779i	−0.998808	+	0.0488092i	$0.984457\pi$
$972$		0			0
$973$	−12.2759	+	21.2625i	−0.393547	+	0.681644i
$974$	−4.56256			−0.146194
$975$		0			0
$976$	−3.12832			−0.100135
$977$	−11.5564	+	20.0163i	−0.369722	+	0.640377i	−0.989522	−	0.144383i	$-0.953880\pi$
$977$	−11.5564	+	20.0163i	−0.369722	+	0.640377i	0.619800	+	0.784760i	$0.287214\pi$
$978$		0			0
$979$	6.90301	+	11.9564i	0.220621	+	0.382127i
$980$	35.3973	−	5.42957i	1.13072	−	0.173441i
$981$		0			0
$982$	4.20803	+	7.28853i	0.134284	+	0.232586i
$983$	−28.0211			−0.893736			−0.446868	−	0.894600i	$-0.647461\pi$
$983$	−28.0211			−0.893736			−0.446868	+	0.894600i	$0.647461\pi$
$984$		0			0
$985$	−2.44528	+	6.27849i	−0.0779131	+	0.200049i
$986$	0.308263	+	0.177976i	0.00981710	+	0.00566791i
$987$		0			0
$988$	−3.28334	+	14.9594i	−0.104457	+	0.475923i
$989$	50.1175			1.59364
$990$		0			0
$991$	−12.4357	+	21.5393i	−0.395034	+	0.684218i	−0.993105	−	0.117224i	$-0.962600\pi$
$991$	−12.4357	+	21.5393i	−0.395034	+	0.684218i	0.598072	+	0.801443i	$0.295934\pi$
$992$	−3.51747	+	2.03081i	−0.111680	+	0.0644784i
$993$		0			0
$994$	30.5396	−	17.6321i	0.968658	−	0.559255i
$995$	13.5970	+	16.9593i	0.431053	+	0.537645i
$996$		0			0
$997$	−23.1135	+	13.3446i	−0.732012	+	0.422627i	−0.819158	−	0.573568i	$-0.805559\pi$
$997$	−23.1135	+	13.3446i	−0.732012	+	0.422627i	0.0871459	+	0.996196i	$0.472225\pi$
$998$	−10.8762	−	6.27936i	−0.344279	−	0.198770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.b.199.4		8
3.2	odd	2		130.2.m.a.69.3	yes	8
5.4	even	2		1170.2.bj.a.199.1		8
12.11	even	2		1040.2.df.c.849.2		8
13.10	even	6		1170.2.bj.a.829.1		8
15.2	even	4		650.2.m.e.251.3		16
15.8	even	4		650.2.m.e.251.6		16
15.14	odd	2		130.2.m.b.69.2	yes	8
39.17	odd	6		1690.2.c.e.1689.3		8
39.20	even	12		1690.2.b.e.339.11		16
39.23	odd	6		130.2.m.b.49.2	yes	8
39.32	even	12		1690.2.b.e.339.3		16
39.35	odd	6		1690.2.c.f.1689.3		8
60.59	even	2		1040.2.df.a.849.3		8
65.49	even	6	inner	1170.2.bj.b.829.4		8
156.23	even	6		1040.2.df.a.49.3		8
195.23	even	12		650.2.m.e.101.6		16
195.32	odd	12		8450.2.a.cs.1.3		8
195.59	even	12		1690.2.b.e.339.6		16
195.62	even	12		650.2.m.e.101.3		16
195.74	odd	6		1690.2.c.e.1689.6		8
195.98	odd	12		8450.2.a.cs.1.6		8
195.134	odd	6		1690.2.c.f.1689.6		8
195.137	odd	12		8450.2.a.cr.1.3		8
195.149	even	12		1690.2.b.e.339.14		16
195.179	odd	6		130.2.m.a.49.3	✓	8
195.188	odd	12		8450.2.a.cr.1.6		8
780.179	even	6		1040.2.df.c.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.3	✓	8	195.179	odd	6
130.2.m.a.69.3	yes	8	3.2	odd	2
130.2.m.b.49.2	yes	8	39.23	odd	6
130.2.m.b.69.2	yes	8	15.14	odd	2
650.2.m.e.101.3		16	195.62	even	12
650.2.m.e.101.6		16	195.23	even	12
650.2.m.e.251.3		16	15.2	even	4
650.2.m.e.251.6		16	15.8	even	4
1040.2.df.a.49.3		8	156.23	even	6
1040.2.df.a.849.3		8	60.59	even	2
1040.2.df.c.49.2		8	780.179	even	6
1040.2.df.c.849.2		8	12.11	even	2
1170.2.bj.a.199.1		8	5.4	even	2
1170.2.bj.a.829.1		8	13.10	even	6
1170.2.bj.b.199.4		8	1.1	even	1	trivial
1170.2.bj.b.829.4		8	65.49	even	6	inner
1690.2.b.e.339.3		16	39.32	even	12
1690.2.b.e.339.6		16	195.59	even	12
1690.2.b.e.339.11		16	39.20	even	12
1690.2.b.e.339.14		16	195.149	even	12
1690.2.c.e.1689.3		8	39.17	odd	6
1690.2.c.e.1689.6		8	195.74	odd	6
1690.2.c.f.1689.3		8	39.35	odd	6
1690.2.c.f.1689.6		8	195.134	odd	6
8450.2.a.cr.1.3		8	195.137	odd	12
8450.2.a.cr.1.6		8	195.188	odd	12
8450.2.a.cs.1.3		8	195.32	odd	12
8450.2.a.cs.1.6		8	195.98	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.21022 - 0.339024i) q^{5} +(2.39871 + 4.15469i) q^{7} -1.00000 q^{8} +(0.811505 - 2.08362i) q^{10} +(-1.43026 - 0.825763i) q^{11} +(-1.09146 - 3.43638i) q^{13} +4.79742 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0697360 - 0.0402621i) q^{17} +(3.67867 - 2.12388i) q^{19} +(-1.39871 - 1.74459i) q^{20} +(-1.43026 + 0.825763i) q^{22} +(5.10893 + 2.94964i) q^{23} +(4.77013 - 1.49863i) q^{25} +(-3.52172 - 0.772959i) q^{26} +(2.39871 - 4.15469i) q^{28} +(-2.21022 + 3.82821i) q^{29} +4.06163i q^{31} +(0.500000 + 0.866025i) q^{32} -0.0805241i q^{34} +(6.71022 + 8.36955i) q^{35} +(0.908541 - 1.57364i) q^{37} -4.24776i q^{38} +(-2.21022 + 0.339024i) q^{40} +(5.87906 + 3.39427i) q^{41} +(7.35733 - 4.24776i) q^{43} +1.65153i q^{44} +(5.10893 - 2.94964i) q^{46} -0.448597 q^{47} +(-8.00764 + 13.8696i) q^{49} +(1.08721 - 4.88037i) q^{50} +(-2.43026 + 2.66342i) q^{52} -11.5770i q^{53} +(-3.44115 - 1.34022i) q^{55} +(-2.39871 - 4.15469i) q^{56} +(2.21022 + 3.82821i) q^{58} +(-1.82559 + 1.05400i) q^{59} +(1.56416 + 2.70920i) q^{61} +(3.51747 + 2.03081i) q^{62} +1.00000 q^{64} +(-3.57738 - 7.22512i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-0.0697360 - 0.0402621i) q^{68} +(10.6034 - 1.62644i) q^{70} +(6.36584 - 3.67532i) q^{71} -10.5752 q^{73} +(-0.908541 - 1.57364i) q^{74} +(-3.67867 - 2.12388i) q^{76} -7.92308i q^{77} -14.6468 q^{79} +(-0.811505 + 2.08362i) q^{80} +(5.87906 - 3.39427i) q^{82} +12.4289 q^{83} +(0.140482 - 0.112630i) q^{85} -8.49552i q^{86} +(1.43026 + 0.825763i) q^{88} +(-7.23958 - 4.17978i) q^{89} +(11.6590 - 12.7776i) q^{91} -5.89928i q^{92} +(-0.224298 + 0.388496i) q^{94} +(7.41061 - 5.94139i) q^{95} +(-2.90296 - 5.02808i) q^{97} +(8.00764 + 13.8696i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} + 5 q^{7} - 8 q^{8} + 3 q^{11} + 4 q^{13} + 10 q^{14} - 4 q^{16} + 15 q^{17} + 9 q^{19} + 3 q^{20} + 3 q^{22} + 6 q^{23} + 5 q^{25} - q^{26} + 5 q^{28} + 3 q^{29} + 4 q^{32}+ \cdots + 15 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 + 5 * q^7 - 8 * q^8 + 3 * q^11 + 4 * q^13 + 10 * q^14 - 4 * q^16 + 15 * q^17 + 9 * q^19 + 3 * q^20 + 3 * q^22 + 6 * q^23 + 5 * q^25 - q^26 + 5 * q^28 + 3 * q^29 + 4 * q^32 + 33 * q^35 + 20 * q^37 + 3 * q^40 - 21 * q^41 + 18 * q^43 + 6 * q^46 - 6 * q^47 - 15 * q^49 + q^50 - 5 * q^52 - 23 * q^55 - 5 * q^56 - 3 * q^58 - 30 * q^59 - 5 * q^61 + 6 * q^62 + 8 * q^64 + 6 * q^65 - 16 * q^67 - 15 * q^68 + 18 * q^70 + 26 * q^73 - 20 * q^74 - 9 * q^76 + 4 * q^79 - 21 * q^82 + 48 * q^83 - 34 * q^85 - 3 * q^88 + 39 * q^89 + 19 * q^91 - 3 * q^94 - 9 * q^95 - 4 * q^97 + 15 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more