LMFDB - Embedded newform 1170.2.bp.h.919.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(289,1170)] 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, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.289"); 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.bp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6,0,0,0,0,0,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			919.4
Root			$1.98293 + 0.531325i$ of defining polynomial
Character	$\chi$	$=$	1170.919
Dual form			1170.2.bp.h.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21432 + 0.311108i) q^{5} +(-3.38028 + 1.95161i) q^{7} +1.00000i q^{8} +(-2.07321 - 0.837733i) q^{10} +(0.533338 - 0.923769i) q^{11} +(2.24483 - 2.82148i) q^{13} -3.90321 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.13545 + 0.655554i) q^{17} +(-3.29605 - 5.70893i) q^{19} +(-1.37659 - 1.76210i) q^{20} +(0.923769 - 0.533338i) q^{22} +(-1.85991 - 1.07382i) q^{23} +(4.80642 - 1.37778i) q^{25} +(3.35482 - 1.32106i) q^{26} +(-3.38028 - 1.95161i) q^{28} +(4.52543 - 7.83827i) q^{29} -6.92396 q^{31} +(-0.866025 + 0.500000i) q^{32} -1.31111 q^{34} +(6.87786 - 5.37311i) q^{35} +(-4.34809 - 2.51037i) q^{37} -6.59210i q^{38} +(-0.311108 - 2.21432i) q^{40} +(-2.97703 + 5.15637i) q^{41} +(-1.73205 + 1.00000i) q^{43} +1.06668 q^{44} +(-1.07382 - 1.85991i) q^{46} +0.0967881i q^{47} +(4.11753 - 7.13177i) q^{49} +(4.85138 + 1.21002i) q^{50} +(3.56589 + 0.533338i) q^{52} -1.49532i q^{53} +(-0.893590 + 2.21145i) q^{55} +(-1.95161 - 3.38028i) q^{56} +(7.83827 - 4.52543i) q^{58} +(-3.59210 - 6.22171i) q^{59} +(-3.94370 - 6.83068i) q^{61} +(-5.99632 - 3.46198i) q^{62} -1.00000 q^{64} +(-4.09298 + 6.94604i) q^{65} +(7.29942 + 4.21432i) q^{67} +(-1.13545 - 0.655554i) q^{68} +(8.64296 - 1.21432i) q^{70} +(-7.73975 - 13.4056i) q^{71} +15.3526i q^{73} +(-2.51037 - 4.34809i) q^{74} +(3.29605 - 5.70893i) q^{76} +4.16346i q^{77} -4.30174 q^{79} +(0.837733 - 2.07321i) q^{80} +(-5.15637 + 2.97703i) q^{82} +9.69381i q^{83} +(2.31031 - 1.80485i) q^{85} -2.00000 q^{86} +(0.923769 + 0.533338i) q^{88} +(-2.26271 + 3.91914i) q^{89} +(-2.08173 + 13.9184i) q^{91} -2.14764i q^{92} +(-0.0483940 + 0.0838209i) q^{94} +(9.07461 + 11.6160i) q^{95} +(-3.68949 + 2.13013i) q^{97} +(7.13177 - 4.11753i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 2 q^{10} + 6 q^{11} - 20 q^{14} - 6 q^{16} - 26 q^{19} + 4 q^{25} + 28 q^{29} + 24 q^{31} - 16 q^{34} + 6 q^{35} - 4 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{49} + 8 q^{50} + 12 q^{55} - 10 q^{56}+ \cdots + 8 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 6 * q^11 - 20 * q^14 - 6 * q^16 - 26 * q^19 + 4 * q^25 + 28 * q^29 + 24 * q^31 - 16 * q^34 + 6 * q^35 - 4 * q^40 + 4 * q^41 + 12 * q^44 - 4 * q^49 + 8 * q^50 + 12 * q^55 - 10 * q^56 - 16 * q^59 - 8 * q^61 - 12 * q^64 + 10 * q^65 + 24 * q^70 - 40 * q^71 + 10 * q^74 + 26 * q^76 + 56 * q^79 - 16 * q^85 - 24 * q^86 - 14 * q^89 - 38 * q^91 - 14 * q^94 + 8 * q^95

Character values

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

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.21432	+	0.311108i	−0.990274	+	0.139132i
$5$	−2.21432	+	0.311108i	−0.990274	+	0.139132i
$6$		0			0
$7$	−3.38028	+	1.95161i	−1.27763	+	0.737638i	−0.976411	−	0.215919i	$-0.930725\pi$
$7$	−3.38028	+	1.95161i	−1.27763	+	0.737638i	−0.301215	+	0.953556i	$0.597392\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.07321	−	0.837733i	−0.655607	−	0.264914i
$11$	0.533338	−	0.923769i	0.160808	−	0.278527i	−0.774351	−	0.632756i	$-0.781923\pi$
$11$	0.533338	−	0.923769i	0.160808	−	0.278527i	0.935159	+	0.354229i	$0.115257\pi$
$12$		0			0
$13$	2.24483	−	2.82148i	0.622603	−	0.782538i
$13$	2.24483	−	2.82148i	0.622603	−	0.782538i
$14$	−3.90321			−1.04318
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.13545	+	0.655554i	−0.275388	+	0.158995i	−0.631334	−	0.775511i	$-0.717492\pi$
$17$	−1.13545	+	0.655554i	−0.275388	+	0.158995i	0.355946	+	0.934507i	$0.384159\pi$
$18$		0			0
$19$	−3.29605	−	5.70893i	−0.756166	−	1.30972i	−0.944792	−	0.327669i	$-0.893737\pi$
$19$	−3.29605	−	5.70893i	−0.756166	−	1.30972i	0.188626	−	0.982049i	$-0.439597\pi$
$20$	−1.37659	−	1.76210i	−0.307814	−	0.394018i
$21$		0			0
$22$	0.923769	−	0.533338i	0.196948	−	0.113708i
$23$	−1.85991	−	1.07382i	−0.387819	−	0.223907i	0.293396	−	0.955991i	$-0.405215\pi$
$23$	−1.85991	−	1.07382i	−0.387819	−	0.223907i	−0.681215	+	0.732084i	$0.738548\pi$
$24$		0			0
$25$	4.80642	−	1.37778i	0.961285	−	0.275557i
$26$	3.35482	−	1.32106i	0.657934	−	0.259081i
$27$		0			0
$28$	−3.38028	−	1.95161i	−0.638813	−	0.368819i
$29$	4.52543	−	7.83827i	0.840351	−	1.45553i	−0.0492475	−	0.998787i	$-0.515682\pi$
$29$	4.52543	−	7.83827i	0.840351	−	1.45553i	0.889598	−	0.456744i	$-0.150984\pi$
$30$		0			0
$31$	−6.92396			−1.24358			−0.621790	−	0.783184i	$-0.713594\pi$
$31$	−6.92396			−1.24358			−0.621790	+	0.783184i	$0.713594\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−1.31111			−0.224853
$35$	6.87786	−	5.37311i	1.16257	−	0.908222i
$36$		0			0
$37$	−4.34809	−	2.51037i	−0.714822	−	0.412703i	0.0980220	−	0.995184i	$-0.468748\pi$
$37$	−4.34809	−	2.51037i	−0.714822	−	0.412703i	−0.812844	+	0.582482i	$0.802082\pi$
$38$		−	6.59210i		−	1.06938i
$39$		0			0
$40$	−0.311108	−	2.21432i	−0.0491905	−	0.350115i
$41$	−2.97703	+	5.15637i	−0.464935	+	0.805290i	−0.999199	−	0.0400274i	$-0.987255\pi$
$41$	−2.97703	+	5.15637i	−0.464935	+	0.805290i	0.534264	+	0.845318i	$0.320589\pi$
$42$		0			0
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	−0.626219	−	0.779647i	$-0.715399\pi$
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	0.362084	+	0.932145i	$0.382065\pi$
$44$	1.06668			0.160808
$45$		0			0
$46$	−1.07382	−	1.85991i	−0.158326	−	0.274229i
$47$			0.0967881i			0.0141180i	0.999975	+	0.00705900i	$0.00224697\pi$
$47$			0.0967881i			0.0141180i	−0.999975	+	0.00705900i	$0.997753\pi$
$48$		0			0
$49$	4.11753	−	7.13177i	0.588219	−	1.01882i
$50$	4.85138	+	1.21002i	0.686088	+	0.171122i
$51$		0			0
$52$	3.56589	+	0.533338i	0.494500	+	0.0739607i
$53$		−	1.49532i		−	0.205397i	−0.994713	−	0.102699i	$-0.967252\pi$
$53$		−	1.49532i		−	0.205397i	0.994713	−	0.102699i	$-0.0327478\pi$
$54$		0			0
$55$	−0.893590	+	2.21145i	−0.120492	+	0.298191i
$56$	−1.95161	−	3.38028i	−0.260794	−	0.451709i
$57$		0			0
$58$	7.83827	−	4.52543i	1.02922	−	0.594218i
$59$	−3.59210	−	6.22171i	−0.467652	−	0.809997i	0.531665	−	0.846955i	$-0.321567\pi$
$59$	−3.59210	−	6.22171i	−0.467652	−	0.809997i	−0.999317	+	0.0369577i	$0.988233\pi$
$60$		0			0
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	−0.999984	−	0.00571183i	$-0.998182\pi$
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	0.495045	−	0.868867i	$-0.335151\pi$
$62$	−5.99632	−	3.46198i	−0.761534	−	0.439672i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.09298	+	6.94604i	−0.507672	+	0.861550i
$66$		0			0
$67$	7.29942	+	4.21432i	0.891766	+	0.514861i	0.874520	−	0.484990i	$-0.161177\pi$
$67$	7.29942	+	4.21432i	0.891766	+	0.514861i	0.0172460	+	0.999851i	$0.494510\pi$
$68$	−1.13545	−	0.655554i	−0.137694	−	0.0794976i
$69$		0			0
$70$	8.64296	−	1.21432i	1.03303	−	0.145139i
$71$	−7.73975	−	13.4056i	−0.918539	−	1.59096i	−0.801636	−	0.597813i	$-0.796037\pi$
$71$	−7.73975	−	13.4056i	−0.918539	−	1.59096i	−0.116903	−	0.993143i	$-0.537297\pi$
$72$		0			0
$73$			15.3526i			1.79689i	0.439091	+	0.898443i	$0.355301\pi$
$73$			15.3526i			1.79689i	−0.439091	+	0.898443i	$0.644699\pi$
$74$	−2.51037	−	4.34809i	−0.291825	−	0.505455i
$75$		0			0
$76$	3.29605	−	5.70893i	0.378083	−	0.654859i
$77$			4.16346i			0.474471i
$78$		0			0
$79$	−4.30174			−0.483984			−0.241992	−	0.970278i	$-0.577801\pi$
$79$	−4.30174			−0.483984			−0.241992	+	0.970278i	$0.577801\pi$
$80$	0.837733	−	2.07321i	0.0936614	−	0.231792i
$81$		0			0
$82$	−5.15637	+	2.97703i	−0.569426	+	0.328758i
$83$			9.69381i			1.06403i	0.846734	+	0.532017i	$0.178566\pi$
$83$			9.69381i			1.06403i	−0.846734	+	0.532017i	$0.821434\pi$
$84$		0			0
$85$	2.31031	−	1.80485i	0.250588	−	0.195764i
$86$	−2.00000			−0.215666
$87$		0			0
$88$	0.923769	+	0.533338i	0.0984741	+	0.0568541i
$89$	−2.26271	+	3.91914i	−0.239847	+	0.415428i	−0.960670	−	0.277692i	$-0.910431\pi$
$89$	−2.26271	+	3.91914i	−0.239847	+	0.415428i	0.720823	+	0.693119i	$0.243764\pi$
$90$		0			0
$91$	−2.08173	+	13.9184i	−0.218225	+	1.45905i
$92$		−	2.14764i		−	0.223907i
$93$		0			0
$94$	−0.0483940	+	0.0838209i	−0.00499146	+	0.00864547i
$95$	9.07461	+	11.6160i	0.931035	+	1.19177i
$96$		0			0
$97$	−3.68949	+	2.13013i	−0.374611	+	0.216282i	−0.675471	−	0.737387i	$-0.736060\pi$
$97$	−3.68949	+	2.13013i	−0.374611	+	0.216282i	0.300860	+	0.953668i	$0.402726\pi$
$98$	7.13177	−	4.11753i	0.720418	−	0.415934i
$99$		0			0
$100$	3.59641	+	3.47359i	0.359641	+	0.347359i
$101$	0.729376	−	1.26332i	0.0725756	−	0.125705i	−0.827454	−	0.561534i	$-0.810211\pi$
$101$	0.729376	−	1.26332i	0.0725756	−	0.125705i	0.900029	+	0.435829i	$0.143545\pi$
$102$		0			0
$103$			10.2444i			1.00941i	0.863291	+	0.504707i	$0.168399\pi$
$103$			10.2444i			1.00941i	−0.863291	+	0.504707i	$0.831601\pi$
$104$	2.82148	+	2.24483i	0.276669	+	0.220123i
$105$		0			0
$106$	0.747658	−	1.29498i	0.0726190	−	0.125780i
$107$	−1.91766	−	1.10716i	−0.185387	−	0.107033i	0.404434	−	0.914567i	$-0.367468\pi$
$107$	−1.91766	−	1.10716i	−0.185387	−	0.107033i	−0.589821	+	0.807534i	$0.700802\pi$
$108$		0			0
$109$	−0.133353			−0.0127729			−0.00638645	−	0.999980i	$-0.502033\pi$
$109$	−0.133353			−0.0127729			−0.00638645	+	0.999980i	$0.502033\pi$
$110$	−1.87959	+	1.46837i	−0.179212	+	0.140004i
$111$		0			0
$112$		−	3.90321i		−	0.368819i
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.946570	−	0.322498i	$-0.895477\pi$
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.193993	+	0.981003i	$0.562144\pi$
$114$		0			0
$115$	4.45252	+	1.79915i	0.415199	+	0.167772i
$116$	9.05086			0.840351
$117$		0			0
$118$		−	7.18421i		−	0.661360i
$119$	2.55877	−	4.43191i	0.234562	−	0.406273i
$120$		0			0
$121$	4.93110	+	8.54092i	0.448282	+	0.776447i
$122$		−	7.88739i		−	0.714091i
$123$		0			0
$124$	−3.46198	−	5.99632i	−0.310895	−	0.538486i
$125$	−10.2143	+	4.54617i	−0.913597	+	0.406622i
$126$		0			0
$127$	−8.65214	−	4.99532i	−0.767753	−	0.443263i	0.0643192	−	0.997929i	$-0.479512\pi$
$127$	−8.65214	−	4.99532i	−0.767753	−	0.443263i	−0.832073	+	0.554667i	$0.812846\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−7.01765	+	3.96896i	−0.615488	+	0.348101i
$131$	−9.25581			−0.808684			−0.404342	−	0.914608i	$-0.632499\pi$
$131$	−9.25581			−0.808684			−0.404342	+	0.914608i	$0.632499\pi$
$132$		0			0
$133$	22.2832	+	12.8652i	1.93220	+	1.11555i
$134$	4.21432	+	7.29942i	0.364062	+	0.630573i
$135$		0			0
$136$	−0.655554	−	1.13545i	−0.0562133	−	0.0973643i
$137$	12.8090	−	7.39530i	1.09435	−	0.631823i	0.159619	−	0.987179i	$-0.448974\pi$
$137$	12.8090	−	7.39530i	1.09435	−	0.631823i	0.934731	+	0.355356i	$0.115640\pi$
$138$		0			0
$139$	−6.34691	−	10.9932i	−0.538338	−	0.932428i	−0.998994	−	0.0448494i	$-0.985719\pi$
$139$	−6.34691	−	10.9932i	−0.538338	−	0.932428i	0.460656	−	0.887579i	$-0.347614\pi$
$140$	8.09218	+	3.26985i	0.683914	+	0.276353i
$141$		0			0
$142$		−	15.4795i		−	1.29901i
$143$	−1.40914	−	3.57851i	−0.117838	−	0.299250i
$144$		0			0
$145$	−7.58220	+	18.7643i	−0.629667	+	1.55829i
$146$	−7.67630	+	13.2957i	−0.635295	+	1.10036i
$147$		0			0
$148$		−	5.02074i		−	0.412703i
$149$	−3.64296	−	6.30979i	−0.298443	−	0.516918i	0.677337	−	0.735673i	$-0.263134\pi$
$149$	−3.64296	−	6.30979i	−0.298443	−	0.516918i	−0.975780	+	0.218755i	$0.929801\pi$
$150$		0			0
$151$	20.1082			1.63638			0.818190	−	0.574949i	$-0.194978\pi$
$151$	20.1082			1.63638			0.818190	+	0.574949i	$0.194978\pi$
$152$	5.70893	−	3.29605i	0.463055	−	0.267345i
$153$		0			0
$154$	−2.08173	+	3.60567i	−0.167751	+	0.290553i
$155$	15.3319	−	2.15410i	1.23148	−	0.173021i
$156$		0			0
$157$		−	1.98418i		−	0.158355i	−0.996861	−	0.0791773i	$-0.974771\pi$
$157$		−	1.98418i		−	0.158355i	0.996861	−	0.0791773i	$-0.0252293\pi$
$158$	−3.72542	−	2.15087i	−0.296378	−	0.171114i
$159$		0			0
$160$	1.76210	−	1.37659i	0.139306	−	0.108829i
$161$	8.38271			0.660650
$162$		0			0
$163$	4.07308	−	2.35159i	0.319028	−	0.184191i	−0.331931	−	0.943304i	$-0.607700\pi$
$163$	4.07308	−	2.35159i	0.319028	−	0.184191i	0.650959	+	0.759113i	$0.274367\pi$
$164$	−5.95407			−0.464935
$165$		0			0
$166$	−4.84691	+	8.39509i	−0.376193	+	0.651585i
$167$	−8.39642	−	4.84767i	−0.649734	−	0.375124i	0.138620	−	0.990346i	$-0.455733\pi$
$167$	−8.39642	−	4.84767i	−0.649734	−	0.375124i	−0.788354	+	0.615221i	$0.789067\pi$
$168$		0			0
$169$	−2.92149	−	12.6675i	−0.224730	−	0.974421i
$170$	2.90321	−	0.407896i	0.222666	−	0.0312842i
$171$		0			0
$172$	−1.73205	−	1.00000i	−0.132068	−	0.0762493i
$173$	20.8466	−	12.0358i	1.58494	−	0.915065i	0.590816	−	0.806806i	$-0.298806\pi$
$173$	20.8466	−	12.0358i	1.58494	−	0.915065i	0.994123	−	0.108259i	$-0.0345275\pi$
$174$		0			0
$175$	−13.5582	+	14.0375i	−1.02490	+	1.06114i
$176$	0.533338	+	0.923769i	0.0402019	+	0.0696317i
$177$		0			0
$178$	−3.91914	+	2.26271i	−0.293752	+	0.169598i
$179$	−1.52543	+	2.64212i	−0.114016	+	0.197481i	−0.917386	−	0.397999i	$-0.869705\pi$
$179$	−1.52543	+	2.64212i	−0.114016	+	0.197481i	0.803370	+	0.595480i	$0.203038\pi$
$180$		0			0
$181$	10.6430			0.791085			0.395542	−	0.918448i	$-0.370557\pi$
$181$	10.6430			0.791085			0.395542	+	0.918448i	$0.370557\pi$
$182$	−8.76204	+	11.0128i	−0.649486	+	0.816325i
$183$		0			0
$184$	1.07382	−	1.85991i	0.0791632	−	0.137115i
$185$	10.4091	+	4.20604i	0.765289	+	0.309234i
$186$		0			0
$187$			1.39853i			0.102270i
$188$	−0.0838209	+	0.0483940i	−0.00611327	+	0.00352950i
$189$		0			0
$190$	2.05086	+	14.5970i	0.148785	+	1.05898i
$191$	7.36519	+	12.7569i	0.532926	+	0.923056i	0.999261	+	0.0384470i	$0.0122411\pi$
$191$	7.36519	+	12.7569i	0.532926	+	0.923056i	−0.466334	+	0.884609i	$0.654426\pi$
$192$		0			0
$193$	−12.1244	−	7.00000i	−0.872730	−	0.503871i	−0.00447566	−	0.999990i	$-0.501425\pi$
$193$	−12.1244	−	7.00000i	−0.872730	−	0.503871i	−0.868255	+	0.496119i	$0.834758\pi$
$194$	−4.26025			−0.305868
$195$		0			0
$196$	8.23506			0.588219
$197$	−9.01776	−	5.20641i	−0.642489	−	0.370941i	0.143084	−	0.989711i	$-0.454298\pi$
$197$	−9.01776	−	5.20641i	−0.642489	−	0.370941i	−0.785573	+	0.618769i	$0.787632\pi$
$198$		0			0
$199$	−2.18421	−	3.78316i	−0.154834	−	0.268181i	0.778164	−	0.628061i	$-0.216151\pi$
$199$	−2.18421	−	3.78316i	−0.154834	−	0.268181i	−0.932999	+	0.359880i	$0.882818\pi$
$200$	1.37778	+	4.80642i	0.0974241	+	0.339865i
$201$		0			0
$202$	1.26332	−	0.729376i	0.0888866	−	0.0513187i
$203$			35.3274i			2.47950i
$204$		0			0
$205$	4.98792	−	12.3440i	0.348371	−	0.862145i
$206$	−5.12222	+	8.87194i	−0.356882	+	0.618137i
$207$		0			0
$208$	1.32106	+	3.35482i	0.0915990	+	0.232615i
$209$	−7.03164			−0.486389
$210$		0			0
$211$	−2.74766	+	4.75908i	−0.189157	+	0.327629i	−0.944969	−	0.327159i	$-0.893909\pi$
$211$	−2.74766	+	4.75908i	−0.189157	+	0.327629i	0.755813	+	0.654788i	$0.227242\pi$
$212$	1.29498	−	0.747658i	0.0889397	−	0.0513494i
$213$		0			0
$214$	−1.10716	−	1.91766i	−0.0756839	−	0.131088i
$215$	3.52421	−	2.75317i	0.240349	−	0.187765i
$216$		0			0
$217$	23.4049	−	13.5128i	1.58883	−	0.917311i
$218$	−0.115487	−	0.0666765i	−0.00782178	−	0.00451591i
$219$		0			0
$220$	−2.36196	+	0.331851i	−0.159244	+	0.0223734i
$221$	−0.699264	+	4.67526i	−0.0470376	+	0.314492i
$222$		0			0
$223$	−17.4043	−	10.0484i	−1.16548	−	0.672890i	−0.212869	−	0.977081i	$-0.568281\pi$
$223$	−17.4043	−	10.0484i	−1.16548	−	0.672890i	−0.952611	+	0.304191i	$0.901614\pi$
$224$	1.95161	−	3.38028i	0.130397	−	0.225855i
$225$		0			0
$226$	−14.0000			−0.931266
$227$	−16.7654	+	9.67952i	−1.11276	+	0.642453i	−0.939543	−	0.342431i	$-0.888750\pi$
$227$	−16.7654	+	9.67952i	−1.11276	+	0.642453i	−0.173218	+	0.984884i	$0.555416\pi$
$228$		0			0
$229$	−15.7255			−1.03917			−0.519584	−	0.854420i	$-0.673913\pi$
$229$	−15.7255			−1.03917			−0.519584	+	0.854420i	$0.673913\pi$
$230$	2.95642	+	3.78437i	0.194940	+	0.249534i
$231$		0			0
$232$	7.83827	+	4.52543i	0.514608	+	0.297109i
$233$		−	14.8825i		−	0.974983i	−0.873128	−	0.487491i	$-0.837912\pi$
$233$		−	14.8825i		−	0.974983i	0.873128	−	0.487491i	$-0.162088\pi$
$234$		0			0
$235$	−0.0301115	−	0.214320i	−0.00196426	−	0.0139807i
$236$	3.59210	−	6.22171i	0.233826	−	0.404999i
$237$		0			0
$238$	4.43191	−	2.55877i	0.287278	−	0.165860i
$239$	4.42219			0.286047			0.143024	−	0.989719i	$-0.454317\pi$
$239$	4.42219			0.286047			0.143024	+	0.989719i	$0.454317\pi$
$240$		0			0
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	0.988508	−	0.151170i	$-0.0483042\pi$
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	−0.625171	+	0.780488i	$0.714971\pi$
$242$			9.86220i			0.633966i
$243$		0			0
$244$	3.94370	−	6.83068i	0.252469	−	0.437290i
$245$	−6.89878	+	17.0730i	−0.440747	+	1.09076i
$246$		0			0
$247$	−23.5067	−	3.51582i	−1.49570	−	0.223706i
$248$		−	6.92396i		−	0.439672i
$249$		0			0
$250$	−11.1189	−	1.17006i	−0.703224	−	0.0740011i
$251$	1.32616	+	2.29698i	0.0837067	+	0.144984i	0.904839	−	0.425753i	$-0.139991\pi$
$251$	1.32616	+	2.29698i	0.0837067	+	0.144984i	−0.821133	+	0.570737i	$0.806657\pi$
$252$		0			0
$253$	−1.98393	+	1.14542i	−0.124728	+	0.0720120i
$254$	−4.99532	−	8.65214i	−0.313434	−	0.542884i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.55219	+	2.05086i	0.221579	+	0.127929i	0.606681	−	0.794945i	$-0.292500\pi$
$257$	3.55219	+	2.05086i	0.221579	+	0.127929i	−0.385102	+	0.922874i	$0.625834\pi$
$258$		0			0
$259$	19.5970			1.21770
$260$	−8.06194	−	0.0716061i	−0.499980	−	0.00444082i
$261$		0			0
$262$	−8.01576	−	4.62790i	−0.495216	−	0.285913i
$263$	9.35479	+	5.40099i	0.576841	+	0.333039i	0.759877	−	0.650067i	$-0.225259\pi$
$263$	9.35479	+	5.40099i	0.576841	+	0.333039i	−0.183036	+	0.983106i	$0.558593\pi$
$264$		0			0
$265$	0.465205	+	3.31111i	0.0285773	+	0.203400i
$266$	12.8652	+	22.2832i	0.788815	+	1.36627i
$267$		0			0
$268$			8.42864i			0.514861i
$269$	9.29137	+	16.0931i	0.566505	+	0.981215i	0.996908	+	0.0785782i	$0.0250380\pi$
$269$	9.29137	+	16.0931i	0.566505	+	0.981215i	−0.430403	+	0.902637i	$0.641629\pi$
$270$		0			0
$271$	−9.88739	+	17.1255i	−0.600616	+	1.04030i	0.392112	+	0.919918i	$0.371745\pi$
$271$	−9.88739	+	17.1255i	−0.600616	+	1.04030i	−0.992728	+	0.120380i	$0.961589\pi$
$272$		−	1.31111i		−	0.0794976i
$273$		0			0
$274$	14.7906			0.893533
$275$	1.29070	−	5.17485i	0.0778319	−	0.312055i
$276$		0			0
$277$	0.177493	−	0.102476i	0.0106645	−	0.00615718i	−0.494658	−	0.869088i	$-0.664707\pi$
$277$	0.177493	−	0.102476i	0.0106645	−	0.00615718i	0.505323	+	0.862930i	$0.331373\pi$
$278$		−	12.6938i		−	0.761324i
$279$		0			0
$280$	5.37311	+	6.87786i	0.321105	+	0.411031i
$281$	20.4558			1.22029			0.610146	−	0.792289i	$-0.291111\pi$
$281$	20.4558			1.22029			0.610146	+	0.792289i	$0.291111\pi$
$282$		0			0
$283$	1.24535	+	0.719004i	0.0740284	+	0.0427403i	0.536557	−	0.843864i	$-0.319725\pi$
$283$	1.24535	+	0.719004i	0.0740284	+	0.0427403i	−0.462529	+	0.886604i	$0.653058\pi$
$284$	7.73975	−	13.4056i	0.459270	−	0.795478i
$285$		0			0
$286$	0.568899	−	3.80365i	0.0336397	−	0.224914i
$287$		−	23.2400i		−	1.37181i
$288$		0			0
$289$	−7.64050	+	13.2337i	−0.449441	+	0.778455i
$290$	−15.9485	+	12.4593i	−0.936531	+	0.731635i
$291$		0			0
$292$	−13.2957	+	7.67630i	−0.778074	+	0.449221i
$293$	−18.1126	+	10.4573i	−1.05815	+	0.610922i	−0.924919	−	0.380164i	$-0.875868\pi$
$293$	−18.1126	+	10.4573i	−1.05815	+	0.610922i	−0.133228	+	0.991085i	$0.542534\pi$
$294$		0			0
$295$	9.88969	+	12.6593i	0.575800	+	0.737054i
$296$	2.51037	−	4.34809i	0.145912	−	0.252728i
$297$		0			0
$298$		−	7.28592i		−	0.422062i
$299$	−7.20495	+	2.83716i	−0.416673	+	0.164077i
$300$		0			0
$301$	3.90321	−	6.76056i	0.224977	−	0.389672i
$302$	17.4142	+	10.0541i	1.00207	+	0.578547i
$303$		0			0
$304$	6.59210			0.378083
$305$	10.8577	+	13.8984i	0.621709	+	0.795820i
$306$		0			0
$307$			12.5303i			0.715145i	0.933885	+	0.357572i	$0.116395\pi$
$307$			12.5303i			0.715145i	−0.933885	+	0.357572i	$0.883605\pi$
$308$	−3.60567	+	2.08173i	−0.205452	+	0.118618i
$309$		0			0
$310$	14.3548	+	5.80042i	0.815299	+	0.329442i
$311$	9.78123			0.554643			0.277321	−	0.960777i	$-0.410553\pi$
$311$	9.78123			0.554643			0.277321	+	0.960777i	$0.410553\pi$
$312$		0			0
$313$		−	17.2128i		−	0.972924i	−0.873702	−	0.486462i	$-0.838287\pi$
$313$		−	17.2128i		−	0.972924i	0.873702	−	0.486462i	$-0.161713\pi$
$314$	0.992089	−	1.71835i	0.0559868	−	0.0969720i
$315$		0			0
$316$	−2.15087	−	3.72542i	−0.120996	−	0.209571i
$317$		−	13.7447i		−	0.771978i	−0.922503	−	0.385989i	$-0.873860\pi$
$317$		−	13.7447i		−	0.771978i	0.922503	−	0.385989i	$-0.126140\pi$
$318$		0			0
$319$	−4.82717	−	8.36090i	−0.270269	−	0.468120i
$320$	2.21432	−	0.311108i	0.123784	−	0.0173915i
$321$		0			0
$322$	7.25964	+	4.19135i	0.404564	+	0.233575i
$323$	7.48502	+	4.32148i	0.416478	+	0.240454i
$324$		0			0
$325$	6.90220	−	16.6541i	0.382865	−	0.923804i
$326$	4.70318			0.260485
$327$		0			0
$328$	−5.15637	−	2.97703i	−0.284713	−	0.164379i
$329$	−0.188892	−	0.327171i	−0.0104140	−	0.0180375i
$330$		0			0
$331$	−9.69381	−	16.7902i	−0.532820	−	0.922872i	−0.999265	−	0.0383216i	$-0.987799\pi$
$331$	−9.69381	−	16.7902i	−0.532820	−	0.922872i	0.466445	−	0.884550i	$-0.345534\pi$
$332$	−8.39509	+	4.84691i	−0.460740	+	0.266009i
$333$		0			0
$334$	−4.84767	−	8.39642i	−0.265253	−	0.459431i
$335$	−17.4743	−	7.06095i	−0.954726	−	0.385781i
$336$		0			0
$337$			0.555539i			0.0302621i	0.999886	+	0.0151311i	$0.00481655\pi$
$337$			0.555539i			0.0302621i	−0.999886	+	0.0151311i	$0.995183\pi$
$338$	3.80365	−	12.4311i	0.206891	−	0.676163i
$339$		0			0
$340$	2.71820	+	1.09836i	0.147415	+	0.0595668i
$341$	−3.69281	+	6.39614i	−0.199977	+	0.346370i
$342$		0			0
$343$			4.82071i			0.260294i
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	24.0716			1.29410
$347$	−5.78890	+	3.34222i	−0.310764	+	0.179420i	−0.647269	−	0.762262i	$-0.724089\pi$
$347$	−5.78890	+	3.34222i	−0.310764	+	0.179420i	0.336504	+	0.941682i	$0.390755\pi$
$348$		0			0
$349$	5.29137	−	9.16492i	0.283240	−	0.490587i	−0.688941	−	0.724818i	$-0.741924\pi$
$349$	5.29137	−	9.16492i	0.283240	−	0.490587i	0.972181	+	0.234231i	$0.0752572\pi$
$350$	−18.7605	+	5.37778i	−1.00279	+	0.287455i
$351$		0			0
$352$			1.06668i			0.0568541i
$353$	7.97557	+	4.60470i	0.424497	+	0.245083i	0.696999	−	0.717072i	$-0.254518\pi$
$353$	7.97557	+	4.60470i	0.424497	+	0.245083i	−0.272503	+	0.962155i	$0.587851\pi$
$354$		0			0
$355$	21.3089	+	27.2765i	1.13096	+	1.44768i
$356$	−4.52543			−0.239847
$357$		0			0
$358$	−2.64212	+	1.52543i	−0.139640	+	0.0806214i
$359$	−4.19358			−0.221328			−0.110664	−	0.993858i	$-0.535298\pi$
$359$	−4.19358			−0.221328			−0.110664	+	0.993858i	$0.535298\pi$
$360$		0			0
$361$	−12.2279	+	21.1794i	−0.643575	+	1.11470i
$362$	9.21707	+	5.32148i	0.484439	+	0.279691i
$363$		0			0
$364$	−13.0946	+	5.15637i	−0.686342	+	0.270267i
$365$	−4.77631	−	33.9956i	−0.250004	−	1.77941i
$366$		0			0
$367$	−12.0970	−	6.98418i	−0.631456	−	0.364571i	0.149860	−	0.988707i	$-0.452118\pi$
$367$	−12.0970	−	6.98418i	−0.631456	−	0.364571i	−0.781316	+	0.624136i	$0.785451\pi$
$368$	1.85991	−	1.07382i	0.0969547	−	0.0559768i
$369$		0			0
$370$	6.91149	+	8.84707i	0.359311	+	0.459937i
$371$	2.91827	+	5.05459i	0.151509	+	0.262421i
$372$		0			0
$373$	−10.2606	+	5.92396i	−0.531273	+	0.306731i	−0.741535	−	0.670914i	$-0.765902\pi$
$373$	−10.2606	+	5.92396i	−0.531273	+	0.306731i	0.210262	+	0.977645i	$0.432568\pi$
$374$	−0.699264	+	1.21116i	−0.0361581	+	0.0626276i
$375$		0			0
$376$	−0.0967881			−0.00499146
$377$	−11.9567	−	30.3640i	−0.615802	−	1.56382i
$378$		0			0
$379$	0.303197	−	0.525153i	0.0155742	−	0.0269753i	−0.858133	−	0.513427i	$-0.828376\pi$
$379$	0.303197	−	0.525153i	0.0155742	−	0.0269753i	0.873707	+	0.486452i	$0.161709\pi$
$380$	−5.52242	+	13.6668i	−0.283294	+	0.701093i
$381$		0			0
$382$			14.7304i			0.753672i
$383$	−30.1201	+	17.3899i	−1.53907	+	0.888580i	−0.540172	+	0.841555i	$0.681641\pi$
$383$	−30.1201	+	17.3899i	−1.53907	+	0.888580i	−0.998894	+	0.0470252i	$0.985026\pi$
$384$		0			0
$385$	−1.29529	−	9.21924i	−0.0660139	−	0.469856i
$386$	−7.00000	−	12.1244i	−0.356291	−	0.617113i
$387$		0			0
$388$	−3.68949	−	2.13013i	−0.187305	−	0.108141i
$389$	−18.6844			−0.947339			−0.473670	−	0.880703i	$-0.657071\pi$
$389$	−18.6844			−0.947339			−0.473670	+	0.880703i	$0.657071\pi$
$390$		0			0
$391$	2.81579			0.142401
$392$	7.13177	+	4.11753i	0.360209	+	0.207967i
$393$		0			0
$394$	−5.20641	−	9.01776i	−0.262295	−	0.454308i
$395$	9.52543	−	1.33830i	0.479276	−	0.0673374i
$396$		0			0
$397$	19.8968	−	11.4874i	0.998590	−	0.576536i	0.0907594	−	0.995873i	$-0.471071\pi$
$397$	19.8968	−	11.4874i	0.998590	−	0.576536i	0.907831	+	0.419337i	$0.137737\pi$
$398$		−	4.36842i		−	0.218969i
$399$		0			0
$400$	−1.21002	+	4.85138i	−0.0605008	+	0.242569i
$401$	−2.18667	+	3.78742i	−0.109197	+	0.189135i	−0.915445	−	0.402443i	$-0.868161\pi$
$401$	−2.18667	+	3.78742i	−0.109197	+	0.189135i	0.806248	+	0.591577i	$0.201495\pi$
$402$		0			0
$403$	−15.5431	+	19.5358i	−0.774256	+	0.973147i
$404$	1.45875			0.0725756
$405$		0			0
$406$	−17.6637	+	30.5944i	−0.876635	+	1.51838i
$407$	−4.63801	+	2.67775i	−0.229897	+	0.132731i
$408$		0			0
$409$	−1.88493	−	3.26479i	−0.0932038	−	0.161434i	0.815654	−	0.578540i	$-0.196377\pi$
$409$	−1.88493	−	3.26479i	−0.0932038	−	0.161434i	−0.908858	+	0.417107i	$0.863044\pi$
$410$	10.4917	−	8.19629i	0.518147	−	0.404786i
$411$		0			0
$412$	−8.87194	+	5.12222i	−0.437089	+	0.252353i
$413$	24.2846	+	14.0207i	1.19497	+	0.689916i
$414$		0			0
$415$	−3.01582	−	21.4652i	−0.148041	−	1.05369i
$416$	−0.533338	+	3.56589i	−0.0261491	+	0.174832i
$417$		0			0
$418$	−6.08958	−	3.51582i	−0.297851	−	0.171964i
$419$	−3.72615	+	6.45388i	−0.182034	+	0.315293i	−0.942573	−	0.334000i	$-0.891602\pi$
$419$	−3.72615	+	6.45388i	−0.182034	+	0.315293i	0.760539	+	0.649292i	$0.224935\pi$
$420$		0			0
$421$	27.6751			1.34880			0.674400	−	0.738366i	$-0.264402\pi$
$421$	27.6751			1.34880			0.674400	+	0.738366i	$0.264402\pi$
$422$	−4.75908	+	2.74766i	−0.231669	+	0.133754i
$423$		0			0
$424$	1.49532			0.0726190
$425$	−4.55425	+	4.71528i	−0.220914	+	0.228725i
$426$		0			0
$427$	26.6616	+	15.3931i	1.29024	+	0.744923i
$428$		−	2.21432i		−	0.107033i
$429$		0			0
$430$	4.42864	−	0.622216i	0.213568	−	0.0300059i
$431$	9.84468	−	17.0515i	0.474202	−	0.821342i	−0.525362	−	0.850879i	$-0.676070\pi$
$431$	9.84468	−	17.0515i	0.474202	−	0.821342i	0.999564	+	0.0295373i	$0.00940339\pi$
$432$		0			0
$433$	11.9046	−	6.87310i	0.572097	−	0.330300i	−0.185890	−	0.982571i	$-0.559517\pi$
$433$	11.9046	−	6.87310i	0.572097	−	0.330300i	0.757986	+	0.652270i	$0.226183\pi$
$434$	27.0257			1.29727
$435$		0			0
$436$	−0.0666765	−	0.115487i	−0.00319323	−	0.00553083i
$437$			14.1575i			0.677244i
$438$		0			0
$439$	20.9114	−	36.2195i	0.998045	−	1.72866i	0.444894	−	0.895583i	$-0.353242\pi$
$439$	20.9114	−	36.2195i	0.998045	−	1.72866i	0.553151	−	0.833081i	$-0.313425\pi$
$440$	−2.21145	−	0.893590i	−0.105427	−	0.0426002i
$441$		0			0
$442$	−2.94321	+	3.69926i	−0.139994	+	0.175956i
$443$		−	23.6829i		−	1.12521i	−0.826726	−	0.562605i	$-0.809799\pi$
$443$		−	23.6829i		−	1.12521i	0.826726	−	0.562605i	$-0.190201\pi$
$444$		0			0
$445$	3.79110	−	9.38217i	0.179715	−	0.444757i
$446$	−10.0484	−	17.4043i	−0.475805	−	0.824119i
$447$		0			0
$448$	3.38028	−	1.95161i	0.159703	−	0.0922047i
$449$	−3.52789	−	6.11048i	−0.166491	−	0.288371i	0.770693	−	0.637207i	$-0.219910\pi$
$449$	−3.52789	−	6.11048i	−0.166491	−	0.288371i	−0.937184	+	0.348836i	$0.886577\pi$
$450$		0			0
$451$	3.17553	+	5.50018i	0.149530	+	0.258993i
$452$	−12.1244	−	7.00000i	−0.570282	−	0.329252i
$453$		0			0
$454$	−19.3590			−0.908565
$455$	0.279494	−	31.4675i	0.0131029	−	1.47522i
$456$		0			0
$457$	30.8994	+	17.8398i	1.44541	+	0.834509i	0.998203	−	0.0599208i	$-0.0190848\pi$
$457$	30.8994	+	17.8398i	1.44541	+	0.834509i	0.447209	+	0.894430i	$0.352418\pi$
$458$	−13.6186	−	7.86273i	−0.636358	−	0.367401i
$459$		0			0
$460$	0.668149	+	4.75557i	0.0311526	+	0.221730i
$461$	−7.30074	−	12.6452i	−0.340029	−	0.588948i	0.644409	−	0.764681i	$-0.277104\pi$
$461$	−7.30074	−	12.6452i	−0.340029	−	0.588948i	−0.984438	+	0.175734i	$0.943770\pi$
$462$		0			0
$463$		−	30.7511i		−	1.42913i	−0.699571	−	0.714563i	$-0.746626\pi$
$463$		−	30.7511i		−	1.42913i	0.699571	−	0.714563i	$-0.253374\pi$
$464$	4.52543	+	7.83827i	0.210088	+	0.363883i
$465$		0			0
$466$	7.44123	−	12.8886i	0.344709	−	0.597053i
$467$			20.5620i			0.951496i	0.879582	+	0.475748i	$0.157822\pi$
$467$			20.5620i			0.951496i	−0.879582	+	0.475748i	$0.842178\pi$
$468$		0			0
$469$	−32.8988			−1.51912
$470$	0.0810825	−	0.200662i	0.00374006	−	0.00925585i
$471$		0			0
$472$	6.22171	−	3.59210i	0.286377	−	0.165340i
$473$			2.13335i			0.0980917i
$474$		0			0
$475$	−23.7079	−	22.8983i	−1.08779	−	1.05065i
$476$	5.11753			0.234562
$477$		0			0
$478$	3.82973	+	2.21109i	0.175168	+	0.101133i
$479$	−5.96666	+	10.3346i	−0.272624	+	0.472198i	−0.969533	−	0.244961i	$-0.921225\pi$
$479$	−5.96666	+	10.3346i	−0.272624	+	0.472198i	0.696909	+	0.717159i	$0.254558\pi$
$480$		0			0
$481$	−16.8437	+	6.63270i	−0.768006	+	0.302425i
$482$			11.2810i			0.513835i
$483$		0			0
$484$	−4.93110	+	8.54092i	−0.224141	+	0.388223i
$485$	7.50701	−	5.86461i	0.340876	−	0.266298i
$486$		0			0
$487$	−24.2244	+	13.9859i	−1.09771	+	0.633764i	−0.935619	−	0.353012i	$-0.885158\pi$
$487$	−24.2244	+	13.9859i	−1.09771	+	0.633764i	−0.162092	+	0.986776i	$0.551824\pi$
$488$	6.83068	−	3.94370i	0.309210	−	0.178523i
$489$		0			0
$490$	−14.5110	+	11.3363i	−0.655542	+	0.512121i
$491$	−10.3906	+	17.9971i	−0.468922	+	0.812197i	−0.999369	−	0.0355214i	$-0.988691\pi$
$491$	−10.3906	+	17.9971i	−0.468922	+	0.812197i	0.530447	+	0.847718i	$0.322024\pi$
$492$		0			0
$493$			11.8666i			0.534447i
$494$	−18.5995	−	14.7981i	−0.836830	−	0.665800i
$495$		0			0
$496$	3.46198	−	5.99632i	0.155447	−	0.269243i
$497$	52.3250	+	30.2099i	2.34710	+	1.35510i
$498$		0			0
$499$	−34.2908			−1.53507			−0.767534	−	0.641008i	$-0.778517\pi$
$499$	−34.2908			−1.53507			−0.767534	+	0.641008i	$0.778517\pi$
$500$	−9.04426	−	6.57277i	−0.404472	−	0.293943i
$501$		0			0
$502$			2.65233i			0.118379i
$503$	−17.5160	+	10.1128i	−0.780998	+	0.450910i	−0.836784	−	0.547533i	$-0.815567\pi$
$503$	−17.5160	+	10.1128i	−0.780998	+	0.450910i	0.0557857	+	0.998443i	$0.482234\pi$
$504$		0			0
$505$	−1.22204	+	3.02430i	−0.0543802	+	0.134580i
$506$	−2.29084			−0.101840
$507$		0			0
$508$		−	9.99063i		−	0.443263i
$509$	13.6889	−	23.7099i	0.606749	−	1.05092i	−0.385023	−	0.922907i	$-0.625806\pi$
$509$	13.6889	−	23.7099i	0.606749	−	1.05092i	0.991772	−	0.128014i	$-0.0408602\pi$
$510$		0			0
$511$	−29.9622	−	51.8961i	−1.32545	−	2.29575i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	2.05086	+	3.55219i	0.0904593	+	0.156680i
$515$	−3.18712	−	22.6844i	−0.140441	−	0.999596i
$516$		0			0
$517$	0.0894098	+	0.0516208i	0.00393224	+	0.00227028i
$518$	16.9715	+	9.79851i	0.745686	+	0.430522i
$519$		0			0
$520$	−6.94604	−	4.09298i	−0.304604	−	0.179489i
$521$	31.2034			1.36705			0.683523	−	0.729929i	$-0.260447\pi$
$521$	31.2034			1.36705			0.683523	+	0.729929i	$0.260447\pi$
$522$		0			0
$523$	−8.52854	−	4.92396i	−0.372927	−	0.215310i	0.301809	−	0.953368i	$-0.402409\pi$
$523$	−8.52854	−	4.92396i	−0.372927	−	0.215310i	−0.674736	+	0.738059i	$0.735743\pi$
$524$	−4.62790	−	8.01576i	−0.202171	−	0.350170i
$525$		0			0
$526$	5.40099	+	9.35479i	0.235494	+	0.407888i
$527$	7.86182	−	4.53903i	0.342466	−	0.197723i
$528$		0			0
$529$	−9.19381	−	15.9242i	−0.399731	−	0.692355i
$530$	−1.25267	+	3.10011i	−0.0544127	+	0.134660i
$531$		0			0
$532$			25.7304i			1.11555i
$533$	7.86567	+	19.9748i	0.340700	+	0.865205i
$534$		0			0
$535$	4.59075	+	1.85501i	0.198476	+	0.0801990i
$536$	−4.21432	+	7.29942i	−0.182031	+	0.315287i
$537$		0			0
$538$			18.5827i			0.801159i
$539$	−4.39207	−	7.60730i	−0.189180	−	0.327669i
$540$		0			0
$541$	41.6149			1.78916			0.894581	−	0.446905i	$-0.147474\pi$
$541$	41.6149			1.78916			0.894581	+	0.446905i	$0.147474\pi$
$542$	−17.1255	+	9.88739i	−0.735602	+	0.424700i
$543$		0			0
$544$	0.655554	−	1.13545i	0.0281066	−	0.0486821i
$545$	0.295286	−	0.0414872i	0.0126487	−	0.00177712i
$546$		0			0
$547$			6.77430i			0.289648i	0.989457	+	0.144824i	$0.0462617\pi$
$547$			6.77430i			0.289648i	−0.989457	+	0.144824i	$0.953738\pi$
$548$	12.8090	+	7.39530i	0.547175	+	0.315912i
$549$		0			0
$550$	3.70520	−	3.83620i	0.157990	−	0.163576i
$551$	−59.6642			−2.54178
$552$		0			0
$553$	14.5411	−	8.39530i	0.618350	−	0.357005i
$554$	0.204952			0.00870757
$555$		0			0
$556$	6.34691	−	10.9932i	0.269169	−	0.466214i
$557$	22.0360	+	12.7225i	0.933694	+	0.539068i	0.887978	−	0.459886i	$-0.152110\pi$
$557$	22.0360	+	12.7225i	0.933694	+	0.539068i	0.0457158	+	0.998954i	$0.485443\pi$
$558$		0			0
$559$	−1.06668	+	7.13177i	−0.0451156	+	0.301642i
$560$	1.21432	+	8.64296i	0.0513144	+	0.365232i
$561$		0			0
$562$	17.7153	+	10.2279i	0.747274	+	0.431439i
$563$	11.4179	−	6.59210i	0.481205	−	0.277824i	−0.239713	−	0.970844i	$-0.577053\pi$
$563$	11.4179	−	6.59210i	0.481205	−	0.277824i	0.720919	+	0.693020i	$0.243720\pi$
$564$		0			0
$565$	24.6694	−	19.2722i	1.03785	−	0.810788i
$566$	0.719004	+	1.24535i	0.0302220	+	0.0523460i
$567$		0			0
$568$	13.4056	−	7.73975i	0.562488	−	0.324753i
$569$	12.2304	−	21.1836i	0.512724	−	0.888064i	−0.487167	−	0.873309i	$-0.661970\pi$
$569$	12.2304	−	21.1836i	0.512724	−	0.888064i	0.999891	−	0.0147555i	$-0.00469698\pi$
$570$		0			0
$571$	24.3526			1.01912			0.509562	−	0.860434i	$-0.329807\pi$
$571$	24.3526			1.01912			0.509562	+	0.860434i	$0.329807\pi$
$572$	2.39451	−	3.00961i	0.100119	−	0.125838i
$573$		0			0
$574$	11.6200	−	20.1264i	0.485009	−	0.840060i
$575$	−10.4190	−	2.59868i	−0.434503	−	0.108373i
$576$		0			0
$577$		−	42.0479i		−	1.75048i	−0.483690	−	0.875239i	$-0.660704\pi$
$577$		−	42.0479i		−	1.75048i	0.483690	−	0.875239i	$-0.339296\pi$
$578$	−13.2337	+	7.64050i	−0.550451	+	0.317803i
$579$		0			0
$580$	−20.0415	+	2.81579i	−0.832177	+	0.116919i
$581$	−18.9185	−	32.7678i	−0.784872	−	1.35944i
$582$		0			0
$583$	−1.38133	−	0.797509i	−0.0572087	−	0.0330295i
$584$	−15.3526			−0.635295
$585$		0			0
$586$	−20.9146			−0.863974
$587$	−6.36195	−	3.67307i	−0.262586	−	0.151604i	0.362928	−	0.931817i	$-0.381777\pi$
$587$	−6.36195	−	3.67307i	−0.262586	−	0.151604i	−0.625513	+	0.780213i	$0.715110\pi$
$588$		0			0
$589$	22.8217	+	39.5284i	0.940353	+	1.62874i
$590$	2.23506	+	15.9081i	0.0920161	+	0.654928i
$591$		0			0
$592$	4.34809	−	2.51037i	0.178705	−	0.103176i
$593$			4.19358i			0.172210i	0.996286	+	0.0861048i	$0.0274420\pi$
$593$			4.19358i			0.172210i	−0.996286	+	0.0861048i	$0.972558\pi$
$594$		0			0
$595$	−4.28712	+	10.6097i	−0.175755	+	0.434956i
$596$	3.64296	−	6.30979i	0.149221	−	0.258459i
$597$		0			0
$598$	−7.65825	−	1.14542i	−0.313169	−	0.0468397i
$599$	9.33630			0.381471			0.190735	−	0.981641i	$-0.438913\pi$
$599$	9.33630			0.381471			0.190735	+	0.981641i	$0.438913\pi$
$600$		0			0
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	−0.834132	−	0.551565i	$-0.814031\pi$
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	0.894735	+	0.446597i	$0.147364\pi$
$602$	6.76056	−	3.90321i	0.275540	−	0.159083i
$603$		0			0
$604$	10.0541	+	17.4142i	0.409095	+	0.708573i
$605$	−13.5762	−	17.3782i	−0.551950	−	0.706525i
$606$		0			0
$607$	−14.8464	+	8.57160i	−0.602599	+	0.347910i	−0.770063	−	0.637968i	$-0.779775\pi$
$607$	−14.8464	+	8.57160i	−0.602599	+	0.347910i	0.167465	+	0.985878i	$0.446442\pi$
$608$	5.70893	+	3.29605i	0.231528	+	0.133673i
$609$		0			0
$610$	2.45383	+	17.4652i	0.0993526	+	0.707145i
$611$	0.273086	+	0.217273i	0.0110479	+	0.00878991i
$612$		0			0
$613$	−25.3610	−	14.6422i	−1.02432	−	0.591393i	−0.108969	−	0.994045i	$-0.534755\pi$
$613$	−25.3610	−	14.6422i	−1.02432	−	0.591393i	−0.915353	+	0.402653i	$0.868088\pi$
$614$	−6.26517	+	10.8516i	−0.252842	+	0.437935i
$615$		0			0
$616$	−4.16346			−0.167751
$617$	11.4453	−	6.60793i	0.460769	−	0.266025i	−0.251599	−	0.967832i	$-0.580956\pi$
$617$	11.4453	−	6.60793i	0.460769	−	0.266025i	0.712368	+	0.701807i	$0.247623\pi$
$618$		0			0
$619$	18.9333			0.760995			0.380497	−	0.924782i	$-0.375753\pi$
$619$	18.9333			0.760995			0.380497	+	0.924782i	$0.375753\pi$
$620$	9.53143	+	12.2007i	0.382791	+	0.489993i
$621$		0			0
$622$	8.47080	+	4.89062i	0.339648	+	0.196096i
$623$		−	17.6637i		−	0.707681i
$624$		0			0
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	8.60639	−	14.9067i	0.343981	−	0.595792i
$627$		0			0
$628$	1.71835	−	0.992089i	0.0685696	−	0.0395887i
$629$	6.58274			0.262471
$630$		0			0
$631$	−1.21432	−	2.10326i	−0.0483413	−	0.0837296i	0.840842	−	0.541280i	$-0.182060\pi$
$631$	−1.21432	−	2.10326i	−0.0483413	−	0.0837296i	−0.889184	+	0.457551i	$0.848727\pi$
$632$		−	4.30174i		−	0.171114i
$633$		0			0
$634$	6.87233	−	11.9032i	0.272935	−	0.472738i
$635$	20.7127	+	8.36948i	0.821958	+	0.332133i
$636$		0			0
$637$	−10.8790	−	27.6271i	−0.431042	−	1.09463i
$638$		−	9.65433i		−	0.382219i
$639$		0			0
$640$	2.07321	+	0.837733i	0.0819509	+	0.0331143i
$641$	7.54371	+	13.0661i	0.297959	+	0.516079i	0.975669	−	0.219250i	$-0.0703609\pi$
$641$	7.54371	+	13.0661i	0.297959	+	0.516079i	−0.677710	+	0.735329i	$0.737028\pi$
$642$		0			0
$643$	5.80513	−	3.35159i	0.228932	−	0.132174i	−0.381147	−	0.924514i	$-0.624471\pi$
$643$	5.80513	−	3.35159i	0.228932	−	0.132174i	0.610079	+	0.792340i	$0.291138\pi$
$644$	4.19135	+	7.25964i	0.165162	+	0.286070i
$645$		0			0
$646$	4.32148	+	7.48502i	0.170026	+	0.294494i
$647$	19.3759	+	11.1867i	0.761744	+	0.439793i	0.829922	−	0.557880i	$-0.188385\pi$
$647$	19.3759	+	11.1867i	0.761744	+	0.439793i	−0.0681773	+	0.997673i	$0.521718\pi$
$648$		0			0
$649$	−7.66323			−0.300808
$650$	14.3045	−	10.9718i	0.561070	−	0.430349i
$651$		0			0
$652$	4.07308	+	2.35159i	0.159514	+	0.0920954i
$653$	−14.2139	−	8.20641i	−0.556234	−	0.321142i	0.195399	−	0.980724i	$-0.437400\pi$
$653$	−14.2139	−	8.20641i	−0.556234	−	0.321142i	−0.751632	+	0.659582i	$0.770733\pi$
$654$		0			0
$655$	20.4953	−	2.87955i	0.800818	−	0.112513i
$656$	−2.97703	−	5.15637i	−0.116234	−	0.201323i
$657$		0			0
$658$		−	0.377784i		−	0.0147276i
$659$	−4.33407	−	7.50684i	−0.168832	−	0.292425i	0.769178	−	0.639035i	$-0.220666\pi$
$659$	−4.33407	−	7.50684i	−0.168832	−	0.292425i	−0.938009	+	0.346610i	$0.887333\pi$
$660$		0			0
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	−0.984241	−	0.176834i	$-0.943414\pi$
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	0.645263	+	0.763960i	$0.276748\pi$
$662$		−	19.3876i		−	0.753522i
$663$		0			0
$664$	−9.69381			−0.376193
$665$	−53.3445	−	21.5552i	−2.06861	−	0.835874i
$666$		0			0
$667$	−16.8338	+	9.71900i	−0.651808	+	0.376321i
$668$		−	9.69535i		−	0.375124i
$669$		0			0
$670$	−11.6028	−	14.8521i	−0.448254	−	0.573788i
$671$	−8.41329			−0.324792
$672$		0			0
$673$	35.0593	+	20.2415i	1.35144	+	0.780253i	0.988451	−	0.151541i	$-0.0484236\pi$
$673$	35.0593	+	20.2415i	1.35144	+	0.780253i	0.362987	+	0.931794i	$0.381757\pi$
$674$	−0.277770	+	0.481111i	−0.0106993	+	0.0185317i
$675$		0			0
$676$	9.50961	−	8.86382i	0.365754	−	0.340916i
$677$		−	40.0228i		−	1.53820i	−0.639129	−	0.769100i	$-0.720705\pi$
$677$		−	40.0228i		−	1.53820i	0.639129	−	0.769100i	$-0.279295\pi$
$678$		0			0
$679$	8.31433	−	14.4008i	0.319075	−	0.552654i
$680$	1.80485	+	2.31031i	0.0692130	+	0.0885962i
$681$		0			0
$682$	−6.39614	+	3.69281i	−0.244921	+	0.141405i
$683$	37.5064	−	21.6543i	1.43514	−	0.828580i	0.437636	−	0.899152i	$-0.355816\pi$
$683$	37.5064	−	21.6543i	1.43514	−	0.828580i	0.997507	+	0.0705721i	$0.0224825\pi$
$684$		0			0
$685$	−26.0626	+	20.3606i	−0.995800	+	0.777937i
$686$	−2.41036	+	4.17486i	−0.0920279	+	0.159397i
$687$		0			0
$688$		−	2.00000i		−	0.0762493i
$689$	−4.21900	−	3.35673i	−0.160731	−	0.127881i
$690$		0			0
$691$	−14.1741	+	24.5502i	−0.539207	+	0.933934i	0.459740	+	0.888054i	$0.347943\pi$
$691$	−14.1741	+	24.5502i	−0.539207	+	0.933934i	−0.998947	+	0.0458806i	$0.985391\pi$
$692$	20.8466	+	12.0358i	0.792469	+	0.457532i
$693$		0			0
$694$	−6.68445			−0.253738
$695$	17.4741	+	22.3678i	0.662832	+	0.848459i
$696$		0			0
$697$		−	7.80642i		−	0.295689i
$698$	9.16492	−	5.29137i	0.346897	−	0.200281i
$699$		0			0
$700$	−18.9360	−	4.72295i	−0.715712	−	0.178511i
$701$	−12.8080			−0.483750			−0.241875	−	0.970307i	$-0.577762\pi$
$701$	−12.8080			−0.483750			−0.241875	+	0.970307i	$0.577762\pi$
$702$		0			0
$703$			33.0973i			1.24829i
$704$	−0.533338	+	0.923769i	−0.0201009	+	0.0348159i
$705$		0			0
$706$	4.60470	+	7.97557i	0.173300	+	0.300165i
$707$			5.69381i			0.214138i
$708$		0			0
$709$	1.26126	+	2.18456i	0.0473675	+	0.0820429i	0.888737	−	0.458417i	$-0.151583\pi$
$709$	1.26126	+	2.18456i	0.0473675	+	0.0820429i	−0.841370	+	0.540460i	$0.818250\pi$
$710$	4.81579	+	34.2766i	0.180733	+	1.28638i
$711$		0			0
$712$	−3.91914	−	2.26271i	−0.146876	−	0.0847988i
$713$	12.8780	+	7.43509i	0.482283	+	0.278446i
$714$		0			0
$715$	4.23359	+	7.48556i	0.158327	+	0.279944i
$716$	−3.05086			−0.114016
$717$		0			0
$718$	−3.63174	−	2.09679i	−0.135535	−	0.0782514i
$719$	−8.51114	−	14.7417i	−0.317412	−	0.549773i	0.662535	−	0.749031i	$-0.269480\pi$
$719$	−8.51114	−	14.7417i	−0.317412	−	0.549773i	−0.979947	+	0.199257i	$0.936147\pi$
$720$		0			0
$721$	−19.9931	−	34.6291i	−0.744582	−	1.28965i
$722$	−21.1794	+	12.2279i	−0.788215	+	0.455076i
$723$		0			0
$724$	5.32148	+	9.21707i	0.197771	+	0.342550i
$725$	10.9517	−	43.9091i	0.406735	−	1.63074i
$726$		0			0
$727$		−	30.5353i		−	1.13249i	−0.824237	−	0.566245i	$-0.808395\pi$
$727$		−	30.5353i		−	1.13249i	0.824237	−	0.566245i	$-0.191605\pi$
$728$	−13.9184	−	2.08173i	−0.515851	−	0.0771541i
$729$		0			0
$730$	12.8614	−	31.8292i	0.476021	−	1.17805i
$731$	1.31111	−	2.27091i	0.0484931	−	0.0839925i
$732$		0			0
$733$		−	24.4499i		−	0.903076i	−0.892252	−	0.451538i	$-0.850876\pi$
$733$		−	24.4499i		−	0.903076i	0.892252	−	0.451538i	$-0.149124\pi$
$734$	−6.98418	−	12.0970i	−0.257791	−	0.446507i
$735$		0			0
$736$	2.14764			0.0791632
$737$	7.78612	−	4.49532i	0.286805	−	0.165587i
$738$		0			0
$739$	−5.39776	+	9.34920i	−0.198560	+	0.343916i	−0.948062	−	0.318086i	$-0.896960\pi$
$739$	−5.39776	+	9.34920i	−0.198560	+	0.343916i	0.749502	+	0.662002i	$0.230293\pi$
$740$	1.56199	+	11.1175i	0.0574200	+	0.408689i
$741$		0			0
$742$			5.83654i			0.214266i
$743$	−25.9248	−	14.9677i	−0.951087	−	0.549110i	−0.0576686	−	0.998336i	$-0.518367\pi$
$743$	−25.9248	−	14.9677i	−0.951087	−	0.549110i	−0.893418	+	0.449225i	$0.851700\pi$
$744$		0			0
$745$	10.0297	+	12.8385i	0.367460	+	0.470368i
$746$	−11.8479			−0.433783
$747$		0			0
$748$	−1.21116	+	0.699264i	−0.0442844	+	0.0255676i
$749$	8.64296			0.315807
$750$		0			0
$751$	−13.4588	+	23.3112i	−0.491117	+	0.850639i	−0.999948	−	0.0102272i	$-0.996745\pi$
$751$	−13.4588	+	23.3112i	−0.491117	+	0.850639i	0.508831	+	0.860866i	$0.330078\pi$
$752$	−0.0838209	−	0.0483940i	−0.00305663	−	0.00176475i
$753$		0			0
$754$	4.82717	−	32.2743i	0.175795	−	1.17536i
$755$	−44.5259	+	6.25581i	−1.62046	+	0.227672i
$756$		0			0
$757$	31.0960	+	17.9533i	1.13020	+	0.652524i	0.943986	−	0.329985i	$-0.107044\pi$
$757$	31.0960	+	17.9533i	1.13020	+	0.652524i	0.186218	+	0.982508i	$0.440377\pi$
$758$	0.525153	−	0.303197i	0.0190744	−	0.0110126i
$759$		0			0
$760$	−11.6160	+	9.07461i	−0.421355	+	0.329171i
$761$	11.2699	+	19.5200i	0.408532	+	0.707598i	0.994725	−	0.102573i	$-0.0327075\pi$
$761$	11.2699	+	19.5200i	0.408532	+	0.707598i	−0.586193	+	0.810171i	$0.699374\pi$
$762$		0			0
$763$	0.450771	−	0.260253i	0.0163190	−	0.00942178i
$764$	−7.36519	+	12.7569i	−0.266463	+	0.461528i
$765$		0			0
$766$	−34.7797			−1.25664
$767$	−25.6181	−	3.83161i	−0.925015	−	0.138352i
$768$		0			0
$769$	1.23729	−	2.14304i	0.0446177	−	0.0772801i	−0.842854	−	0.538142i	$-0.819126\pi$
$769$	1.23729	−	2.14304i	0.0446177	−	0.0772801i	0.887472	+	0.460862i	$0.152460\pi$
$770$	3.48787	−	8.63174i	0.125694	−	0.311066i
$771$		0			0
$772$		−	14.0000i		−	0.503871i
$773$	−38.2788	+	22.1003i	−1.37679	+	0.794891i	−0.991772	−	0.128018i	$-0.959139\pi$
$773$	−38.2788	+	22.1003i	−1.37679	+	0.794891i	−0.385019	+	0.922908i	$0.625805\pi$
$774$		0			0
$775$	−33.2795	+	9.53972i	−1.19543	+	0.342677i
$776$	−2.13013	−	3.68949i	−0.0764671	−	0.132445i
$777$		0			0
$778$	−16.1812	−	9.34222i	−0.580124	−	0.334935i
$779$	39.2498			1.40627
$780$		0			0
$781$	−16.5116			−0.590832
$782$	2.43855	+	1.40790i	0.0872023	+	0.0503463i
$783$		0			0
$784$	4.11753	+	7.13177i	0.147055	+	0.254706i
$785$	0.617293	+	4.39361i	0.0220321	+	0.156815i
$786$		0			0
$787$	29.4714	−	17.0153i	1.05054	−	0.606530i	0.127740	−	0.991808i	$-0.459228\pi$
$787$	29.4714	−	17.0153i	1.05054	−	0.606530i	0.922801	+	0.385278i	$0.125894\pi$
$788$		−	10.4128i		−	0.370941i
$789$		0			0
$790$	8.91841	+	3.60371i	0.317303	+	0.128214i
$791$	27.3225	−	47.3239i	0.971476	−	1.68265i
$792$		0			0
$793$	−28.1255	−	4.20665i	−0.998767	−	0.149382i
$794$	22.9748			0.815346
$795$		0			0
$796$	2.18421	−	3.78316i	0.0774172	−	0.134091i
$797$	−7.04754	+	4.06890i	−0.249637	+	0.144128i	−0.619598	−	0.784919i	$-0.712704\pi$
$797$	−7.04754	+	4.06890i	−0.249637	+	0.144128i	0.369961	+	0.929047i	$0.379371\pi$
$798$		0			0
$799$	−0.0634498	−	0.109898i	−0.00224469	−	0.00388792i
$800$	−3.47359	+	3.59641i	−0.122810	+	0.127152i
$801$		0			0
$802$	−3.78742	+	2.18667i	−0.133739	+	0.0772140i
$803$	14.1823	+	8.18813i	0.500481	+	0.288953i
$804$		0			0
$805$	−18.5620	+	2.60793i	−0.654224	+	0.0919173i
$806$	−23.2286	+	9.14695i	−0.818193	+	0.322188i
$807$		0			0
$808$	1.26332	+	0.729376i	0.0444433	+	0.0256593i
$809$	3.92618	−	6.80034i	0.138037	−	0.239087i	−0.788716	−	0.614757i	$-0.789254\pi$
$809$	3.92618	−	6.80034i	0.138037	−	0.239087i	0.926754	+	0.375670i	$0.122587\pi$
$810$		0			0
$811$	9.33477			0.327788			0.163894	−	0.986478i	$-0.447595\pi$
$811$	9.33477			0.327788			0.163894	+	0.986478i	$0.447595\pi$
$812$	−30.5944	+	17.6637i	−1.07365	+	0.619874i
$813$		0			0
$814$	−5.35551			−0.187711
$815$	−8.28749	+	6.47434i	−0.290298	+	0.226786i
$816$		0			0
$817$	11.4179	+	6.59210i	0.399460	+	0.230629i
$818$		−	3.76986i		−	0.131810i
$819$		0			0
$820$	13.1842	−	1.85236i	0.460413	−	0.0646871i
$821$	−23.7659	+	41.1638i	−0.829437	+	1.43663i	0.0690434	+	0.997614i	$0.478005\pi$
$821$	−23.7659	+	41.1638i	−0.829437	+	1.43663i	−0.898480	+	0.439013i	$0.855328\pi$
$822$		0			0
$823$	1.20131	−	0.693576i	0.0418750	−	0.0241765i	−0.478916	−	0.877861i	$-0.658970\pi$
$823$	1.20131	−	0.693576i	0.0418750	−	0.0241765i	0.520791	+	0.853684i	$0.325637\pi$
$824$	−10.2444			−0.356882
$825$		0			0
$826$	14.0207	+	24.2846i	0.487844	+	0.844971i
$827$			31.5131i			1.09582i	0.836537	+	0.547910i	$0.184576\pi$
$827$			31.5131i			1.09582i	−0.836537	+	0.547910i	$0.815424\pi$
$828$		0			0
$829$	−14.4128	+	24.9637i	−0.500578	+	0.867026i	0.499422	+	0.866359i	$0.333546\pi$
$829$	−14.4128	+	24.9637i	−0.500578	+	0.867026i	−1.00000		0.000667386i	$0.999788\pi$
$830$	8.12082	−	20.0973i	0.281878	−	0.697588i
$831$		0			0
$832$	−2.24483	+	2.82148i	−0.0778254	+	0.0978172i
$833$			10.7971i			0.374096i
$834$		0			0
$835$	20.1005	+	8.12211i	0.695606	+	0.281077i
$836$	−3.51582	−	6.08958i	−0.121597	−	0.210613i
$837$		0			0
$838$	−6.45388	+	3.72615i	−0.222946	+	0.128718i
$839$	−4.21755	−	7.30500i	−0.145606	−	0.252197i	0.783993	−	0.620770i	$-0.213180\pi$
$839$	−4.21755	−	7.30500i	−0.145606	−	0.252197i	−0.929599	+	0.368573i	$0.879846\pi$
$840$		0			0
$841$	−26.4590	−	45.8283i	−0.912379	−	1.58029i
$842$	23.9673	+	13.8375i	0.825968	+	0.476873i
$843$		0			0
$844$	−5.49532			−0.189157
$845$	10.4101	+	27.1409i	0.358117	+	0.933677i
$846$		0			0
$847$	−33.3370	−	19.2471i	−1.14547	−	0.661339i
$848$	1.29498	+	0.747658i	0.0444699	+	0.0256747i
$849$		0			0
$850$	−6.30174	+	1.80642i	−0.216148	+	0.0619598i
$851$	5.39138	+	9.33815i	0.184814	+	0.320108i
$852$		0			0
$853$			40.0656i			1.37182i	0.727686	+	0.685910i	$0.240596\pi$
$853$			40.0656i			1.37182i	−0.727686	+	0.685910i	$0.759404\pi$
$854$	15.3931	+	26.6616i	0.526740	+	0.912341i
$855$		0			0
$856$	1.10716	−	1.91766i	0.0378419	−	0.0655442i
$857$		−	32.0479i		−	1.09474i	−0.836892	−	0.547368i	$-0.815630\pi$
$857$		−	32.0479i		−	1.09474i	0.836892	−	0.547368i	$-0.184370\pi$
$858$		0			0
$859$	26.6894			0.910630			0.455315	−	0.890331i	$-0.349527\pi$
$859$	26.6894			0.910630			0.455315	+	0.890331i	$0.349527\pi$
$860$	4.14642	+	1.67547i	0.141392	+	0.0571329i
$861$		0			0
$862$	17.0515	−	9.84468i	0.580776	−	0.335311i
$863$			30.6593i			1.04365i	0.853052	+	0.521827i	$0.174749\pi$
$863$			30.6593i			1.04365i	−0.853052	+	0.521827i	$0.825251\pi$
$864$		0			0
$865$	−42.4166	+	33.1367i	−1.44221	+	1.12668i
$866$	13.7462			0.467115
$867$		0			0
$868$	23.4049	+	13.5128i	0.794415	+	0.458655i
$869$	−2.29428	+	3.97381i	−0.0778282	+	0.134802i
$870$		0			0
$871$	28.2766	−	11.1347i	0.958114	−	0.377286i
$872$		−	0.133353i		−	0.00451591i
$873$		0			0
$874$	−7.07874	+	12.2607i	−0.239442	+	0.414726i
$875$	25.6549	−	35.3017i	0.867295	−	1.19341i
$876$		0			0
$877$	18.1263	−	10.4652i	0.612081	−	0.353385i	−0.161699	−	0.986840i	$-0.551697\pi$
$877$	18.1263	−	10.4652i	0.612081	−	0.353385i	0.773779	+	0.633455i	$0.218364\pi$
$878$	36.2195	−	20.9114i	1.22235	−	0.705724i
$879$		0			0
$880$	−1.46837	−	1.87959i	−0.0494989	−	0.0633611i
$881$	10.7351	−	18.5937i	0.361673	−	0.626437i	−0.626563	−	0.779371i	$-0.715539\pi$
$881$	10.7351	−	18.5937i	0.361673	−	0.626437i	0.988236	+	0.152934i	$0.0488722\pi$
$882$		0			0
$883$			7.73530i			0.260314i	0.991493	+	0.130157i	$0.0415481\pi$
$883$			7.73530i			0.260314i	−0.991493	+	0.130157i	$0.958452\pi$
$884$	−4.39853	+	1.73205i	−0.147939	+	0.0582552i
$885$		0			0
$886$	11.8415	−	20.5100i	0.397822	−	0.689047i
$887$	−41.9559	−	24.2232i	−1.40874	−	0.813337i	−0.413473	−	0.910516i	$-0.635685\pi$
$887$	−41.9559	−	24.2232i	−1.40874	−	0.813337i	−0.995267	+	0.0971796i	$0.969018\pi$
$888$		0			0
$889$	38.9956			1.30787
$890$	7.97427	−	6.22965i	0.267298	−	0.208818i
$891$		0			0
$892$		−	20.0968i		−	0.672890i
$893$	0.552556	−	0.319019i	0.0184906	−	0.0106755i
$894$		0			0
$895$	2.55580	−	6.32507i	0.0854310	−	0.211424i
$896$	3.90321			0.130397
$897$		0			0
$898$		−	7.05578i		−	0.235454i
$899$	−31.3339	+	54.2718i	−1.04504	+	1.81007i
$900$		0			0
$901$	0.980260	+	1.69786i	0.0326572	+	0.0565639i
$902$			6.35106i			0.211467i
$903$		0			0
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	−23.5669	+	3.31111i	−0.783391	+	0.110065i
$906$		0			0
$907$	−10.4017	−	6.00545i	−0.345384	−	0.199408i	0.317266	−	0.948337i	$-0.397235\pi$
$907$	−10.4017	−	6.00545i	−0.345384	−	0.199408i	−0.662650	+	0.748929i	$0.730568\pi$
$908$	−16.7654	−	9.67952i	−0.556380	−	0.321226i
$909$		0			0
$910$	15.9758	−	27.1119i	0.529592	−	0.898750i
$911$	8.10171			0.268422			0.134211	−	0.990953i	$-0.457150\pi$
$911$	8.10171			0.268422			0.134211	+	0.990953i	$0.457150\pi$
$912$		0			0
$913$	8.95485	+	5.17008i	0.296362	+	0.171105i
$914$	17.8398	+	30.8994i	0.590087	+	1.02206i
$915$		0			0
$916$	−7.86273	−	13.6186i	−0.259792	−	0.449973i
$917$	31.2872	−	18.0637i	1.03320	−	0.596516i
$918$		0			0
$919$	8.29682	+	14.3705i	0.273687	+	0.474039i	0.969803	−	0.243890i	$-0.0784235\pi$
$919$	8.29682	+	14.3705i	0.273687	+	0.474039i	−0.696116	+	0.717929i	$0.745090\pi$
$920$	−1.79915	+	4.45252i	−0.0593162	+	0.146795i
$921$		0			0
$922$		−	14.6015i		−	0.480874i
$923$	−55.1981	−	8.25581i	−1.81687	−	0.271743i
$924$		0			0
$925$	−24.3575	−	6.07518i	−0.800870	−	0.199751i
$926$	15.3756	−	26.6313i	0.505272	−	0.875157i
$927$		0			0
$928$			9.05086i			0.297109i
$929$	−28.5605	−	49.4682i	−0.937038	−	1.62300i	−0.770958	−	0.636886i	$-0.780222\pi$
$929$	−28.5605	−	49.4682i	−0.937038	−	1.62300i	−0.166080	−	0.986112i	$-0.553111\pi$
$930$		0			0
$931$	−54.2864			−1.77916
$932$	12.8886	−	7.44123i	0.422180	−	0.243746i
$933$		0			0
$934$	−10.2810	+	17.8072i	−0.336404	+	0.582670i
$935$	−0.435093	−	3.09679i	−0.0142291	−	0.101276i
$936$		0			0
$937$		−	11.1842i		−	0.365372i	−0.983171	−	0.182686i	$-0.941521\pi$
$937$		−	11.1842i		−	0.365372i	0.983171	−	0.182686i	$-0.0584792\pi$
$938$	−28.4912	−	16.4494i	−0.930270	−	0.537091i
$939$		0			0
$940$	0.170551	−	0.133237i	0.00556275	−	0.00434572i
$941$	7.68598			0.250556			0.125278	−	0.992122i	$-0.460018\pi$
$941$	7.68598			0.250556			0.125278	+	0.992122i	$0.460018\pi$
$942$		0			0
$943$	11.0741	−	6.39361i	0.360621	−	0.208204i
$944$	7.18421			0.233826
$945$		0			0
$946$	−1.06668	+	1.84754i	−0.0346806	+	0.0600686i
$947$	17.9047	+	10.3373i	0.581826	+	0.335917i	0.761859	−	0.647743i	$-0.224287\pi$
$947$	17.9047	+	10.3373i	0.581826	+	0.335917i	−0.180033	+	0.983661i	$0.557620\pi$
$948$		0			0
$949$	43.3170	+	34.4639i	1.40613	+	1.11875i
$950$	−9.08250	−	31.6844i	−0.294675	−	1.02798i
$951$		0			0
$952$	4.43191	+	2.55877i	0.143639	+	0.0829301i
$953$	−26.8254	+	15.4876i	−0.868959	+	0.501694i	−0.867002	−	0.498304i	$-0.833956\pi$
$953$	−26.8254	+	15.4876i	−0.868959	+	0.501694i	−0.00195715	+	0.999998i	$0.500623\pi$
$954$		0			0
$955$	−20.2777	−	25.9564i	−0.656169	−	0.839931i
$956$	2.21109	+	3.82973i	0.0715119	+	0.123862i
$957$		0			0
$958$	−10.3346	+	5.96666i	−0.333895	+	0.192774i
$959$	−28.8654	+	49.9964i	−0.932113	+	1.61447i
$960$		0			0
$961$	16.9412			0.546489
$962$	−17.9034	−	2.67775i	−0.577229	−	0.0863343i
$963$		0			0
$964$	−5.64050	+	9.76963i	−0.181668	+	0.314659i
$965$	29.0250	+	11.7283i	0.934346	+	0.377546i
$966$		0			0
$967$		−	0.529873i		−	0.0170396i	−0.999964	−	0.00851979i	$-0.997288\pi$
$967$		−	0.529873i		−	0.0170396i	0.999964	−	0.00851979i	$-0.00271197\pi$
$968$	−8.54092	+	4.93110i	−0.274515	+	0.158492i
$969$		0			0
$970$	9.43356	−	1.32540i	0.302893	−	0.0425560i
$971$	−17.1620	−	29.7255i	−0.550755	−	0.953936i	−0.998220	−	0.0596344i	$-0.981007\pi$
$971$	−17.1620	−	29.7255i	−0.550755	−	0.953936i	0.447465	−	0.894301i	$-0.352327\pi$
$972$		0			0
$973$	42.9087	+	24.7733i	1.37559	+	0.794196i
$974$	−27.9719			−0.896277
$975$		0			0
$976$	7.88739			0.252469
$977$	17.2931	+	9.98418i	0.553255	+	0.319422i	0.750434	−	0.660945i	$-0.229845\pi$
$977$	17.2931	+	9.98418i	0.553255	+	0.319422i	−0.197179	+	0.980368i	$0.563178\pi$
$978$		0			0
$979$	2.41358	+	4.18045i	0.0771385	+	0.133608i
$980$	−18.2351	+	2.56199i	−0.582498	+	0.0818399i
$981$		0			0
$982$	−17.9971	+	10.3906i	−0.574310	+	0.331578i
$983$		−	20.8524i		−	0.665087i	−0.943088	−	0.332543i	$-0.892093\pi$
$983$		−	20.8524i		−	0.665087i	0.943088	−	0.332543i	$-0.107907\pi$
$984$		0			0
$985$	21.5880	+	8.72316i	0.687850	+	0.277943i
$986$	−5.93332	+	10.2768i	−0.188956	+	0.327281i
$987$		0			0
$988$	−8.70856	−	22.1153i	−0.277056	−	0.703582i
$989$	4.29529			0.136582
$990$		0			0
$991$	1.47949	−	2.56256i	0.0469977	−	0.0814024i	−0.841570	−	0.540149i	$-0.818368\pi$
$991$	1.47949	−	2.56256i	0.0469977	−	0.0814024i	0.888567	+	0.458746i	$0.151701\pi$
$992$	5.99632	−	3.46198i	0.190383	−	0.109918i
$993$		0			0
$994$	30.2099	+	52.3250i	0.958199	+	1.65965i
$995$	6.01351	+	7.69760i	0.190641	+	0.244030i
$996$		0			0
$997$	−18.2281	+	10.5240i	−0.577288	+	0.333297i	−0.760055	−	0.649859i	$-0.774828\pi$
$997$	−18.2281	+	10.5240i	−0.577288	+	0.333297i	0.182767	+	0.983156i	$0.441495\pi$
$998$	−29.6967	−	17.1454i	−0.940034	−	0.542729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bp.h.919.4		12
3.2	odd	2		130.2.n.a.9.3	✓	12
5.4	even	2	inner	1170.2.bp.h.919.1		12
12.11	even	2		1040.2.dh.b.529.1		12
13.3	even	3	inner	1170.2.bp.h.289.1		12
15.2	even	4		650.2.e.k.451.3		6
15.8	even	4		650.2.e.j.451.1		6
15.14	odd	2		130.2.n.a.9.4	yes	12
39.17	odd	6		1690.2.b.b.339.1		6
39.20	even	12		1690.2.c.b.1689.1		6
39.29	odd	6		130.2.n.a.29.4	yes	12
39.32	even	12		1690.2.c.c.1689.1		6
39.35	odd	6		1690.2.b.c.339.4		6
60.59	even	2		1040.2.dh.b.529.6		12
65.29	even	6	inner	1170.2.bp.h.289.4		12
156.107	even	6		1040.2.dh.b.289.6		12
195.17	even	12		8450.2.a.ca.1.1		3
195.29	odd	6		130.2.n.a.29.3	yes	12
195.59	even	12		1690.2.c.c.1689.6		6
195.68	even	12		650.2.e.j.601.1		6
195.74	odd	6		1690.2.b.c.339.3		6
195.107	even	12		650.2.e.k.601.3		6
195.113	even	12		8450.2.a.cb.1.3		3
195.134	odd	6		1690.2.b.b.339.6		6
195.149	even	12		1690.2.c.b.1689.6		6
195.152	even	12		8450.2.a.bu.1.1		3
195.173	even	12		8450.2.a.bt.1.3		3
780.419	even	6		1040.2.dh.b.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.3	✓	12	3.2	odd	2
130.2.n.a.9.4	yes	12	15.14	odd	2
130.2.n.a.29.3	yes	12	195.29	odd	6
130.2.n.a.29.4	yes	12	39.29	odd	6
650.2.e.j.451.1		6	15.8	even	4
650.2.e.j.601.1		6	195.68	even	12
650.2.e.k.451.3		6	15.2	even	4
650.2.e.k.601.3		6	195.107	even	12
1040.2.dh.b.289.1		12	780.419	even	6
1040.2.dh.b.289.6		12	156.107	even	6
1040.2.dh.b.529.1		12	12.11	even	2
1040.2.dh.b.529.6		12	60.59	even	2
1170.2.bp.h.289.1		12	13.3	even	3	inner
1170.2.bp.h.289.4		12	65.29	even	6	inner
1170.2.bp.h.919.1		12	5.4	even	2	inner
1170.2.bp.h.919.4		12	1.1	even	1	trivial
1690.2.b.b.339.1		6	39.17	odd	6
1690.2.b.b.339.6		6	195.134	odd	6
1690.2.b.c.339.3		6	195.74	odd	6
1690.2.b.c.339.4		6	39.35	odd	6
1690.2.c.b.1689.1		6	39.20	even	12
1690.2.c.b.1689.6		6	195.149	even	12
1690.2.c.c.1689.1		6	39.32	even	12
1690.2.c.c.1689.6		6	195.59	even	12
8450.2.a.bt.1.3		3	195.173	even	12
8450.2.a.bu.1.1		3	195.152	even	12
8450.2.a.ca.1.1		3	195.17	even	12
8450.2.a.cb.1.3		3	195.113	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21432 + 0.311108i) q^{5} +(-3.38028 + 1.95161i) q^{7} +1.00000i q^{8} +(-2.07321 - 0.837733i) q^{10} +(0.533338 - 0.923769i) q^{11} +(2.24483 - 2.82148i) q^{13} -3.90321 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.13545 + 0.655554i) q^{17} +(-3.29605 - 5.70893i) q^{19} +(-1.37659 - 1.76210i) q^{20} +(0.923769 - 0.533338i) q^{22} +(-1.85991 - 1.07382i) q^{23} +(4.80642 - 1.37778i) q^{25} +(3.35482 - 1.32106i) q^{26} +(-3.38028 - 1.95161i) q^{28} +(4.52543 - 7.83827i) q^{29} -6.92396 q^{31} +(-0.866025 + 0.500000i) q^{32} -1.31111 q^{34} +(6.87786 - 5.37311i) q^{35} +(-4.34809 - 2.51037i) q^{37} -6.59210i q^{38} +(-0.311108 - 2.21432i) q^{40} +(-2.97703 + 5.15637i) q^{41} +(-1.73205 + 1.00000i) q^{43} +1.06668 q^{44} +(-1.07382 - 1.85991i) q^{46} +0.0967881i q^{47} +(4.11753 - 7.13177i) q^{49} +(4.85138 + 1.21002i) q^{50} +(3.56589 + 0.533338i) q^{52} -1.49532i q^{53} +(-0.893590 + 2.21145i) q^{55} +(-1.95161 - 3.38028i) q^{56} +(7.83827 - 4.52543i) q^{58} +(-3.59210 - 6.22171i) q^{59} +(-3.94370 - 6.83068i) q^{61} +(-5.99632 - 3.46198i) q^{62} -1.00000 q^{64} +(-4.09298 + 6.94604i) q^{65} +(7.29942 + 4.21432i) q^{67} +(-1.13545 - 0.655554i) q^{68} +(8.64296 - 1.21432i) q^{70} +(-7.73975 - 13.4056i) q^{71} +15.3526i q^{73} +(-2.51037 - 4.34809i) q^{74} +(3.29605 - 5.70893i) q^{76} +4.16346i q^{77} -4.30174 q^{79} +(0.837733 - 2.07321i) q^{80} +(-5.15637 + 2.97703i) q^{82} +9.69381i q^{83} +(2.31031 - 1.80485i) q^{85} -2.00000 q^{86} +(0.923769 + 0.533338i) q^{88} +(-2.26271 + 3.91914i) q^{89} +(-2.08173 + 13.9184i) q^{91} -2.14764i q^{92} +(-0.0483940 + 0.0838209i) q^{94} +(9.07461 + 11.6160i) q^{95} +(-3.68949 + 2.13013i) q^{97} +(7.13177 - 4.11753i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 2 q^{10} + 6 q^{11} - 20 q^{14} - 6 q^{16} - 26 q^{19} + 4 q^{25} + 28 q^{29} + 24 q^{31} - 16 q^{34} + 6 q^{35} - 4 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{49} + 8 q^{50} + 12 q^{55} - 10 q^{56}+ \cdots + 8 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 6 * q^11 - 20 * q^14 - 6 * q^16 - 26 * q^19 + 4 * q^25 + 28 * q^29 + 24 * q^31 - 16 * q^34 + 6 * q^35 - 4 * q^40 + 4 * q^41 + 12 * q^44 - 4 * q^49 + 8 * q^50 + 12 * q^55 - 10 * q^56 - 16 * q^59 - 8 * q^61 - 12 * q^64 + 10 * q^65 + 24 * q^70 - 40 * q^71 + 10 * q^74 + 26 * q^76 + 56 * q^79 - 16 * q^85 - 24 * q^86 - 14 * q^89 - 38 * q^91 - 14 * q^94 + 8 * q^95

Introduction

L-functions

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