LMFDB - Embedded newform 912.2.bn.o.65.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.8
Root			$1.70042 - 0.329508i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.o.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70042 + 0.329508i) q^{3} +(-1.87360 - 1.08173i) q^{5} -3.41109 q^{7} +(2.78285 + 1.12060i) q^{9} +O(q^{10})$	\(q+(1.70042 + 0.329508i) q^{3} +(-1.87360 - 1.08173i) q^{5} -3.41109 q^{7} +(2.78285 + 1.12060i) q^{9} +2.39878i q^{11} +(-4.61325 + 2.66346i) q^{13} +(-2.82947 - 2.45676i) q^{15} +(-5.15639 - 2.97704i) q^{17} +(-1.09489 + 4.21915i) q^{19} +(-5.80028 - 1.12398i) q^{21} +(3.01506 - 1.74074i) q^{23} +(-0.159737 - 0.276673i) q^{25} +(4.36276 + 2.82247i) q^{27} +(-4.68230 - 8.10997i) q^{29} +4.72348i q^{31} +(-0.790418 + 4.07893i) q^{33} +(6.39103 + 3.68986i) q^{35} +1.54267i q^{37} +(-8.72209 + 3.00889i) q^{39} +(-4.63304 + 8.02466i) q^{41} +(-0.248758 + 0.430862i) q^{43} +(-4.00177 - 5.10985i) q^{45} +(-7.18941 + 4.15081i) q^{47} +4.63553 q^{49} +(-7.78706 - 6.76129i) q^{51} +(4.46423 + 7.73227i) q^{53} +(2.59482 - 4.49437i) q^{55} +(-3.25202 + 6.81354i) q^{57} +(0.192159 - 0.332829i) q^{59} +(-1.38846 - 2.40489i) q^{61} +(-9.49255 - 3.82248i) q^{63} +11.5245 q^{65} +(4.99235 - 2.88233i) q^{67} +(5.70045 - 1.96651i) q^{69} +(0.344463 - 0.596628i) q^{71} +(4.06570 - 7.04199i) q^{73} +(-0.180454 - 0.523095i) q^{75} -8.18246i q^{77} +(6.09876 + 3.52112i) q^{79} +(6.48849 + 6.23695i) q^{81} +1.73935i q^{83} +(6.44069 + 11.1556i) q^{85} +(-5.28956 - 15.3332i) q^{87} +(-8.86507 - 15.3547i) q^{89} +(15.7362 - 9.08530i) q^{91} +(-1.55643 + 8.03190i) q^{93} +(6.61535 - 6.72064i) q^{95} +(-12.3326 - 7.12025i) q^{97} +(-2.68808 + 6.67544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70042	+	0.329508i	0.981737	+	0.190242i
$3$	1.70042	+	0.329508i	0.981737	+	0.190242i
$4$		0			0
$5$	−1.87360	−	1.08173i	−0.837901	−	0.483763i	0.0186489	−	0.999826i	$-0.494064\pi$
$5$	−1.87360	−	1.08173i	−0.837901	−	0.483763i	−0.856550	+	0.516063i	$0.827397\pi$
$6$		0			0
$7$	−3.41109			−1.28927			−0.644635	−	0.764490i	$-0.722991\pi$
$7$	−3.41109			−1.28927			−0.644635	+	0.764490i	$0.722991\pi$
$8$		0			0
$9$	2.78285	+	1.12060i	0.927616	+	0.373535i
$10$		0			0
$11$			2.39878i			0.723260i	0.932322	+	0.361630i	$0.117780\pi$
$11$			2.39878i			0.723260i	−0.932322	+	0.361630i	$0.882220\pi$
$12$		0			0
$13$	−4.61325	+	2.66346i	−1.27948	+	0.738711i	−0.976754	−	0.214365i	$-0.931232\pi$
$13$	−4.61325	+	2.66346i	−1.27948	+	0.738711i	−0.302731	+	0.953076i	$0.597898\pi$
$14$		0			0
$15$	−2.82947	−	2.45676i	−0.730567	−	0.634332i
$16$		0			0
$17$	−5.15639	−	2.97704i	−1.25061	−	0.722039i	−0.279378	−	0.960181i	$-0.590128\pi$
$17$	−5.15639	−	2.97704i	−1.25061	−	0.722039i	−0.971230	+	0.238142i	$0.923462\pi$
$18$		0			0
$19$	−1.09489	+	4.21915i	−0.251185	+	0.967939i
$19$	−1.09489	+	4.21915i	−0.251185	+	0.967939i
$20$		0			0
$21$	−5.80028	−	1.12398i	−1.26573	−	0.245273i
$22$		0			0
$23$	3.01506	−	1.74074i	0.628682	−	0.362970i	−0.151559	−	0.988448i	$-0.548429\pi$
$23$	3.01506	−	1.74074i	0.628682	−	0.362970i	0.780242	+	0.625478i	$0.215096\pi$
$24$		0			0
$25$	−0.159737	−	0.276673i	−0.0319474	−	0.0553346i
$26$		0			0
$27$	4.36276	+	2.82247i	0.839613	+	0.543184i
$28$		0			0
$29$	−4.68230	−	8.10997i	−0.869481	−	1.50598i	−0.862528	−	0.506009i	$-0.831120\pi$
$29$	−4.68230	−	8.10997i	−0.869481	−	1.50598i	−0.00695209	−	0.999976i	$-0.502213\pi$
$30$		0			0
$31$			4.72348i			0.848362i	0.905577	+	0.424181i	$0.139438\pi$
$31$			4.72348i			0.848362i	−0.905577	+	0.424181i	$0.860562\pi$
$32$		0			0
$33$	−0.790418	+	4.07893i	−0.137594	+	0.710051i
$34$		0			0
$35$	6.39103	+	3.68986i	1.08028	+	0.623701i
$36$		0			0
$37$			1.54267i			0.253613i	0.991927	+	0.126807i	$0.0404728\pi$
$37$			1.54267i			0.253613i	−0.991927	+	0.126807i	$0.959527\pi$
$38$		0			0
$39$	−8.72209	+	3.00889i	−1.39665	+	0.481809i
$40$		0			0
$41$	−4.63304	+	8.02466i	−0.723559	+	1.25324i	0.236005	+	0.971752i	$0.424162\pi$
$41$	−4.63304	+	8.02466i	−0.723559	+	1.25324i	−0.959564	+	0.281490i	$0.909171\pi$
$42$		0			0
$43$	−0.248758	+	0.430862i	−0.0379353	+	0.0657058i	−0.884370	−	0.466787i	$-0.845411\pi$
$43$	−0.248758	+	0.430862i	−0.0379353	+	0.0657058i	0.846434	+	0.532493i	$0.178745\pi$
$44$		0			0
$45$	−4.00177	−	5.10985i	−0.596549	−	0.761731i
$46$		0			0
$47$	−7.18941	+	4.15081i	−1.04868	+	0.605458i	−0.922280	−	0.386521i	$-0.873677\pi$
$47$	−7.18941	+	4.15081i	−1.04868	+	0.605458i	−0.126403	+	0.991979i	$0.540343\pi$
$48$		0			0
$49$	4.63553			0.662219
$50$		0			0
$51$	−7.78706	−	6.76129i	−1.09041	−	0.946771i
$52$		0			0
$53$	4.46423	+	7.73227i	0.613209	+	1.06211i	0.990696	+	0.136094i	$0.0434549\pi$
$53$	4.46423	+	7.73227i	0.613209	+	1.06211i	−0.377487	+	0.926015i	$0.623212\pi$
$54$		0			0
$55$	2.59482	−	4.49437i	0.349886	−	0.606020i
$56$		0			0
$57$	−3.25202	+	6.81354i	−0.430740	+	0.902476i
$58$		0			0
$59$	0.192159	−	0.332829i	0.0250169	−	0.0433306i	−0.853246	−	0.521509i	$-0.825369\pi$
$59$	0.192159	−	0.332829i	0.0250169	−	0.0433306i	0.878263	+	0.478178i	$0.158703\pi$
$60$		0			0
$61$	−1.38846	−	2.40489i	−0.177775	−	0.307915i	0.763343	−	0.645993i	$-0.223556\pi$
$61$	−1.38846	−	2.40489i	−0.177775	−	0.307915i	−0.941118	+	0.338078i	$0.890223\pi$
$62$		0			0
$63$	−9.49255	−	3.82248i	−1.19595	−	0.481588i
$64$		0			0
$65$	11.5245			1.42944
$66$		0			0
$67$	4.99235	−	2.88233i	0.609912	−	0.352133i	−0.163019	−	0.986623i	$-0.552123\pi$
$67$	4.99235	−	2.88233i	0.609912	−	0.352133i	0.772931	+	0.634490i	$0.218790\pi$
$68$		0			0
$69$	5.70045	−	1.96651i	0.686253	−	0.236740i
$70$		0			0
$71$	0.344463	−	0.596628i	0.0408803	−	0.0708067i	−0.844861	−	0.534985i	$-0.820317\pi$
$71$	0.344463	−	0.596628i	0.0408803	−	0.0708067i	0.885742	+	0.464179i	$0.153650\pi$
$72$		0			0
$73$	4.06570	−	7.04199i	0.475854	−	0.824203i	−0.523764	−	0.851864i	$-0.675472\pi$
$73$	4.06570	−	7.04199i	0.475854	−	0.824203i	0.999617	+	0.0276607i	$0.00880579\pi$
$74$		0			0
$75$	−0.180454	−	0.523095i	−0.0208370	−	0.0604018i
$76$		0			0
$77$		−	8.18246i		−	0.932478i
$78$		0			0
$79$	6.09876	+	3.52112i	0.686164	+	0.396157i	0.802173	−	0.597091i	$-0.203677\pi$
$79$	6.09876	+	3.52112i	0.686164	+	0.396157i	−0.116010	+	0.993248i	$0.537010\pi$
$80$		0			0
$81$	6.48849	+	6.23695i	0.720943	+	0.692994i
$82$		0			0
$83$			1.73935i			0.190919i	0.995433	+	0.0954593i	$0.0304320\pi$
$83$			1.73935i			0.190919i	−0.995433	+	0.0954593i	$0.969568\pi$
$84$		0			0
$85$	6.44069	+	11.1556i	0.698591	+	1.21000i
$86$		0			0
$87$	−5.28956	−	15.3332i	−0.567100	−	1.64389i
$88$		0			0
$89$	−8.86507	−	15.3547i	−0.939695	−	1.62760i	−0.766040	−	0.642793i	$-0.777775\pi$
$89$	−8.86507	−	15.3547i	−0.939695	−	1.62760i	−0.173655	−	0.984806i	$-0.555558\pi$
$90$		0			0
$91$	15.7362	−	9.08530i	1.64960	−	0.952398i
$92$		0			0
$93$	−1.55643	+	8.03190i	−0.161394	+	0.832869i
$94$		0			0
$95$	6.61535	−	6.72064i	0.678721	−	0.689524i
$96$		0			0
$97$	−12.3326	−	7.12025i	−1.25219	−	0.722952i	−0.280645	−	0.959812i	$-0.590548\pi$
$97$	−12.3326	−	7.12025i	−1.25219	−	0.722952i	−0.971544	+	0.236860i	$0.923882\pi$
$98$		0			0
$99$	−2.68808	+	6.67544i	−0.270163	+	0.670907i
$100$		0			0
$101$	9.31911	−	5.38039i	0.927286	−	0.535369i	0.0413340	−	0.999145i	$-0.486839\pi$
$101$	9.31911	−	5.38039i	0.927286	−	0.535369i	0.885952	+	0.463776i	$0.153506\pi$
$102$		0			0
$103$		−	11.9778i		−	1.18021i	−0.807326	−	0.590105i	$-0.799086\pi$
$103$		−	11.9778i		−	1.18021i	0.807326	−	0.590105i	$-0.200914\pi$
$104$		0			0
$105$	9.65159	+	8.38021i	0.941899	+	0.817825i
$106$		0			0
$107$	−17.9400			−1.73433			−0.867165	−	0.498021i	$-0.834060\pi$
$107$	−17.9400			−1.73433			−0.867165	+	0.498021i	$0.834060\pi$
$108$		0			0
$109$	13.8910	+	8.01996i	1.33051	+	0.768173i	0.985378	−	0.170380i	$-0.0544994\pi$
$109$	13.8910	+	8.01996i	1.33051	+	0.768173i	0.345136	+	0.938553i	$0.387833\pi$
$110$		0			0
$111$	−0.508323	+	2.62318i	−0.0482478	+	0.248982i
$112$		0			0
$113$	6.20466			0.583686			0.291843	−	0.956466i	$-0.405732\pi$
$113$	6.20466			0.583686			0.291843	+	0.956466i	$0.405732\pi$
$114$		0			0
$115$	−7.53203			−0.702365
$116$		0			0
$117$	−15.8227	+	2.24238i	−1.46281	+	0.207308i
$118$		0			0
$119$	17.5889	+	10.1550i	1.61237	+	0.930904i
$120$		0			0
$121$	5.24585			0.476895
$122$		0			0
$123$	−10.5223	+	12.1187i	−0.948764	+	1.09270i
$124$		0			0
$125$			11.5084i			1.02935i
$126$		0			0
$127$	−17.1594	+	9.90701i	−1.52265	+	0.879105i	−0.523013	+	0.852325i	$0.675192\pi$
$127$	−17.1594	+	9.90701i	−1.52265	+	0.879105i	−0.999641	+	0.0267797i	$0.991475\pi$
$128$		0			0
$129$	−0.564966	+	0.650678i	−0.0497424	+	0.0572890i
$130$		0			0
$131$	−1.78152	−	1.02856i	−0.155652	−	0.0898656i	0.420151	−	0.907454i	$-0.361977\pi$
$131$	−1.78152	−	1.02856i	−0.155652	−	0.0898656i	−0.575803	+	0.817589i	$0.695310\pi$
$132$		0			0
$133$	3.73477	−	14.3919i	0.323846	−	1.24794i
$134$		0			0
$135$	−5.12095	−	10.0075i	−0.440741	−	0.861309i
$136$		0			0
$137$	−1.98284	+	1.14479i	−0.169405	+	0.0978062i	−0.582305	−	0.812970i	$-0.697849\pi$
$137$	−1.98284	+	1.14479i	−0.169405	+	0.0978062i	0.412900	+	0.910776i	$0.364516\pi$
$138$		0			0
$139$	8.07533	+	13.9869i	0.684940	+	1.18635i	0.973456	+	0.228876i	$0.0735050\pi$
$139$	8.07533	+	13.9869i	0.684940	+	1.18635i	−0.288515	+	0.957475i	$0.593162\pi$
$140$		0			0
$141$	−13.5927	+	4.68914i	−1.14471	+	0.394897i
$142$		0			0
$143$	−6.38906	−	11.0662i	−0.534280	−	0.925400i
$144$		0			0
$145$			20.2598i			1.68249i
$146$		0			0
$147$	7.88235	+	1.52745i	0.650125	+	0.125982i
$148$		0			0
$149$	2.52225	+	1.45622i	0.206631	+	0.119298i	0.599745	−	0.800192i	$-0.295269\pi$
$149$	2.52225	+	1.45622i	0.206631	+	0.119298i	−0.393114	+	0.919490i	$0.628602\pi$
$150$		0			0
$151$		−	6.80176i		−	0.553519i	−0.960939	−	0.276760i	$-0.910739\pi$
$151$		−	6.80176i		−	0.553519i	0.960939	−	0.276760i	$-0.0892606\pi$
$152$		0			0
$153$	−11.0134	−	14.0629i	−0.890378	−	1.13692i
$154$		0			0
$155$	5.10951	−	8.84994i	0.410406	−	0.710844i
$156$		0			0
$157$	0.154674	−	0.267903i	0.0123443	−	0.0213810i	−0.859787	−	0.510652i	$-0.829404\pi$
$157$	0.154674	−	0.267903i	0.0123443	−	0.0213810i	0.872132	+	0.489271i	$0.162737\pi$
$158$		0			0
$159$	5.04321	+	14.6191i	0.399953	+	1.15937i
$160$		0			0
$161$	−10.2846	+	5.93783i	−0.810542	+	0.467967i
$162$		0			0
$163$	19.0701			1.49368			0.746841	−	0.665002i	$-0.231570\pi$
$163$	19.0701			1.49368			0.746841	+	0.665002i	$0.231570\pi$
$164$		0			0
$165$	5.89322	−	6.78729i	0.458786	−	0.528390i
$166$		0			0
$167$	−3.09989	−	5.36917i	−0.239877	−	0.415479i	0.720802	−	0.693141i	$-0.243774\pi$
$167$	−3.09989	−	5.36917i	−0.239877	−	0.415479i	−0.960679	+	0.277662i	$0.910440\pi$
$168$		0			0
$169$	7.68804	−	13.3161i	0.591388	−	1.02431i
$170$		0			0
$171$	−7.77491	+	10.5143i	−0.594562	+	0.804050i
$172$		0			0
$173$	−2.99652	+	5.19012i	−0.227821	+	0.394597i	−0.957162	−	0.289553i	$-0.906493\pi$
$173$	−2.99652	+	5.19012i	−0.227821	+	0.394597i	0.729341	+	0.684150i	$0.239827\pi$
$174$		0			0
$175$	0.544878	+	0.943756i	0.0411889	+	0.0713413i
$176$		0			0
$177$	0.436420	−	0.502630i	0.0328034	−	0.0377800i
$178$		0			0
$179$	−8.68090			−0.648841			−0.324420	−	0.945913i	$-0.605169\pi$
$179$	−8.68090			−0.648841			−0.324420	+	0.945913i	$0.605169\pi$
$180$		0			0
$181$	0.974461	−	0.562605i	0.0724311	−	0.0418181i	−0.463347	−	0.886177i	$-0.653352\pi$
$181$	0.974461	−	0.562605i	0.0724311	−	0.0418181i	0.535778	+	0.844359i	$0.320018\pi$
$182$		0			0
$183$	−1.56854	−	4.54683i	−0.115950	−	0.336112i
$184$		0			0
$185$	1.66875	−	2.89035i	0.122689	−	0.212503i
$186$		0			0
$187$	7.14128	−	12.3691i	0.522222	−	0.904515i
$188$		0			0
$189$	−14.8818	−	9.62769i	−1.08249	−	0.700312i
$190$		0			0
$191$			1.41621i			0.102473i	0.998687	+	0.0512367i	$0.0163163\pi$
$191$			1.41621i			0.102473i	−0.998687	+	0.0512367i	$0.983684\pi$
$192$		0			0
$193$	0.440846	+	0.254523i	0.0317328	+	0.0183209i	0.515782	−	0.856720i	$-0.327501\pi$
$193$	0.440846	+	0.254523i	0.0317328	+	0.0183209i	−0.484050	+	0.875041i	$0.660835\pi$
$194$		0			0
$195$	19.5965	+	3.79743i	1.40334	+	0.271940i
$196$		0			0
$197$			8.04107i			0.572903i	0.958095	+	0.286451i	$0.0924757\pi$
$197$			8.04107i			0.572903i	−0.958095	+	0.286451i	$0.907524\pi$
$198$		0			0
$199$	−1.24876	−	2.16291i	−0.0885221	−	0.153325i	0.818365	−	0.574700i	$-0.194881\pi$
$199$	−1.24876	−	2.16291i	−0.0885221	−	0.153325i	−0.906887	+	0.421375i	$0.861548\pi$
$200$		0			0
$201$	9.43883	−	3.25615i	0.665764	−	0.229671i
$202$		0			0
$203$	15.9717	+	27.6638i	1.12100	+	1.94162i
$204$		0			0
$205$	17.3610	−	10.0234i	1.21254	−	0.700062i
$206$		0			0
$207$	10.3411	−	1.46554i	0.718758	−	0.101862i
$208$		0			0
$209$	−10.1208	−	2.62640i	−0.700071	−	0.181672i
$210$		0			0
$211$	3.71129	+	2.14271i	0.255495	+	0.147510i	0.622278	−	0.782796i	$-0.286207\pi$
$211$	3.71129	+	2.14271i	0.255495	+	0.147510i	−0.366783	+	0.930307i	$0.619541\pi$
$212$		0			0
$213$	0.782326	−	0.901014i	0.0536041	−	0.0617364i
$214$		0			0
$215$	0.932149	−	0.538176i	0.0635720	−	0.0367033i
$216$		0			0
$217$		−	16.1122i		−	1.09377i
$218$		0			0
$219$	9.23378	−	10.6347i	0.623961	−	0.718624i
$220$		0			0
$221$	31.7169			2.13351
$222$		0			0
$223$	−0.136033	−	0.0785386i	−0.00910943	−	0.00525933i	0.495438	−	0.868643i	$-0.335007\pi$
$223$	−0.136033	−	0.0785386i	−0.00910943	−	0.00525933i	−0.504548	+	0.863384i	$0.668341\pi$
$224$		0			0
$225$	−0.134483	−	0.948941i	−0.00896557	−	0.0632628i
$226$		0			0
$227$	−0.460625			−0.0305727			−0.0152864	−	0.999883i	$-0.504866\pi$
$227$	−0.460625			−0.0305727			−0.0152864	+	0.999883i	$0.504866\pi$
$228$		0			0
$229$	10.0794			0.666067			0.333033	−	0.942915i	$-0.391928\pi$
$229$	10.0794			0.666067			0.333033	+	0.942915i	$0.391928\pi$
$230$		0			0
$231$	2.69619	−	13.9136i	0.177396	−	0.915448i
$232$		0			0
$233$	−2.41962	−	1.39697i	−0.158515	−	0.0915185i	0.418644	−	0.908150i	$-0.362505\pi$
$233$	−2.41962	−	1.39697i	−0.158515	−	0.0915185i	−0.577159	+	0.816632i	$0.695839\pi$
$234$		0			0
$235$	17.9601			1.17159
$236$		0			0
$237$	9.21020	+	7.99697i	0.598267	+	0.519459i
$238$		0			0
$239$			12.5259i			0.810233i	0.914265	+	0.405117i	$0.132769\pi$
$239$			12.5259i			0.810233i	−0.914265	+	0.405117i	$0.867231\pi$
$240$		0			0
$241$	−15.1777	+	8.76287i	−0.977683	+	0.564466i	−0.901570	−	0.432633i	$-0.857584\pi$
$241$	−15.1777	+	8.76287i	−0.977683	+	0.564466i	−0.0761135	+	0.997099i	$0.524251\pi$
$242$		0			0
$243$	8.97803	+	12.7434i	0.575941	+	0.817492i
$244$		0			0
$245$	−8.68516	−	5.01438i	−0.554874	−	0.320357i
$246$		0			0
$247$	−6.18653	−	22.3802i	−0.393640	−	1.42402i
$248$		0			0
$249$	−0.573131	+	2.95762i	−0.0363207	+	0.187432i
$250$		0			0
$251$	8.63458	−	4.98518i	0.545010	−	0.314661i	−0.202097	−	0.979365i	$-0.564776\pi$
$251$	8.63458	−	4.98518i	0.545010	−	0.314661i	0.747107	+	0.664704i	$0.231442\pi$
$252$		0			0
$253$	4.17566	+	7.23246i	0.262522	+	0.454701i
$254$		0			0
$255$	7.27601	+	21.0915i	0.455641	+	1.32080i
$256$		0			0
$257$	7.80570	+	13.5199i	0.486906	+	0.843346i	0.999887	−	0.0150543i	$-0.00479212\pi$
$257$	7.80570	+	13.5199i	0.486906	+	0.843346i	−0.512981	+	0.858400i	$0.671459\pi$
$258$		0			0
$259$		−	5.26218i		−	0.326976i
$260$		0			0
$261$	−3.94205	−	27.8158i	−0.244006	−	1.72176i
$262$		0			0
$263$	−20.3095	−	11.7257i	−1.25234	−	0.723037i	−0.280764	−	0.959777i	$-0.590588\pi$
$263$	−20.3095	−	11.7257i	−1.25234	−	0.723037i	−0.971573	+	0.236740i	$0.923921\pi$
$264$		0			0
$265$		−	19.3163i		−	1.18659i
$266$		0			0
$267$	−10.0148	−	29.0306i	−0.612896	−	1.77664i
$268$		0			0
$269$	−12.5518	+	21.7404i	−0.765299	+	1.32554i	0.174789	+	0.984606i	$0.444076\pi$
$269$	−12.5518	+	21.7404i	−0.765299	+	1.32554i	−0.940088	+	0.340931i	$0.889258\pi$
$270$		0			0
$271$	−8.23775	+	14.2682i	−0.500408	+	0.866731i	0.499592	+	0.866261i	$0.333483\pi$
$271$	−8.23775	+	14.2682i	−0.500408	+	0.866731i	−1.00000		0.000470727i	$0.999850\pi$
$272$		0			0
$273$	29.7518	−	10.2636i	1.80066	−	0.621182i
$274$		0			0
$275$	0.663678	−	0.383175i	0.0400213	−	0.0231063i
$276$		0			0
$277$	−16.8966			−1.01522			−0.507610	−	0.861587i	$-0.669471\pi$
$277$	−16.8966			−1.01522			−0.507610	+	0.861587i	$0.669471\pi$
$278$		0			0
$279$	−5.29315	+	13.1447i	−0.316893	+	0.786955i
$280$		0			0
$281$	−5.36734	−	9.29650i	−0.320188	−	0.554583i	0.660338	−	0.750968i	$-0.270413\pi$
$281$	−5.36734	−	9.29650i	−0.320188	−	0.554583i	−0.980527	+	0.196386i	$0.937080\pi$
$282$		0			0
$283$	−10.1786	+	17.6298i	−0.605053	+	1.04798i	0.386990	+	0.922084i	$0.373515\pi$
$283$	−10.1786	+	17.6298i	−0.605053	+	1.04798i	−0.992043	+	0.125899i	$0.959818\pi$
$284$		0			0
$285$	13.4634	−	9.24810i	0.797502	−	0.547810i
$286$		0			0
$287$	15.8037	−	27.3728i	0.932864	−	1.61577i
$288$		0			0
$289$	9.22558	+	15.9792i	0.542681	+	0.939951i
$290$		0			0
$291$	−18.6245	−	16.1711i	−1.09179	−	0.947967i
$292$		0			0
$293$	−13.8101			−0.806795			−0.403397	−	0.915025i	$-0.632171\pi$
$293$	−13.8101			−0.806795			−0.403397	+	0.915025i	$0.632171\pi$
$294$		0			0
$295$	−0.720059	+	0.415726i	−0.0419235	+	0.0242045i
$296$		0			0
$297$	−6.77048	+	10.4653i	−0.392863	+	0.607259i
$298$		0			0
$299$	−9.27280	+	16.0610i	−0.536260	+	0.928829i
$300$		0			0
$301$	0.848536	−	1.46971i	0.0489088	−	0.0847126i
$302$		0			0
$303$	17.6193	−	6.07819i	1.01220	−	0.349183i
$304$		0			0
$305$			6.00775i			0.344003i
$306$		0			0
$307$	−0.0384379	−	0.0221921i	−0.00219377	−	0.00126657i	0.498903	−	0.866658i	$-0.333736\pi$
$307$	−0.0384379	−	0.0221921i	−0.00219377	−	0.00126657i	−0.501096	+	0.865391i	$0.667070\pi$
$308$		0			0
$309$	3.94680	−	20.3673i	0.224525	−	1.15866i
$310$		0			0
$311$			19.5486i			1.10850i	0.832351	+	0.554248i	$0.186994\pi$
$311$			19.5486i			1.10850i	−0.832351	+	0.554248i	$0.813006\pi$
$312$		0			0
$313$	−12.1315	−	21.0124i	−0.685714	−	1.18769i	−0.973212	−	0.229911i	$-0.926157\pi$
$313$	−12.1315	−	21.0124i	−0.685714	−	1.18769i	0.287497	−	0.957781i	$-0.407177\pi$
$314$		0			0
$315$	13.6504	+	17.4302i	0.769113	+	0.982078i
$316$		0			0
$317$	−7.90971	−	13.7000i	−0.444254	−	0.769470i	0.553746	−	0.832686i	$-0.313198\pi$
$317$	−7.90971	−	13.7000i	−0.444254	−	0.769470i	−0.998000	+	0.0632155i	$0.979864\pi$
$318$		0			0
$319$	19.4541	−	11.2318i	1.08922	−	0.628860i
$320$		0			0
$321$	−30.5056	−	5.91140i	−1.70266	−	0.329942i
$322$		0			0
$323$	18.2063	−	18.4960i	1.01302	−	1.02915i
$324$		0			0
$325$	1.47382	+	0.850908i	0.0817526	+	0.0471999i
$326$		0			0
$327$	20.9778	+	18.2145i	1.16008	+	1.00726i
$328$		0			0
$329$	24.5237	−	14.1588i	1.35204	−	0.780599i
$330$		0			0
$331$			8.53614i			0.469189i	0.972093	+	0.234594i	$0.0753762\pi$
$331$			8.53614i			0.469189i	−0.972093	+	0.234594i	$0.924624\pi$
$332$		0			0
$333$	−1.72872	+	4.29302i	−0.0947334	+	0.235256i
$334$		0			0
$335$	−12.4716			−0.681395
$336$		0			0
$337$	−3.61617	−	2.08780i	−0.196985	−	0.113729i	0.398263	−	0.917271i	$-0.369613\pi$
$337$	−3.61617	−	2.08780i	−0.196985	−	0.113729i	−0.595249	+	0.803542i	$0.702946\pi$
$338$		0			0
$339$	10.5505	+	2.04449i	0.573026	+	0.111041i
$340$		0			0
$341$	−11.3306			−0.613586
$342$		0			0
$343$	8.06541			0.435491
$344$		0			0
$345$	−12.8076	−	2.48187i	−0.689538	−	0.133619i
$346$		0			0
$347$	−7.14444	−	4.12484i	−0.383534	−	0.221433i	0.295821	−	0.955243i	$-0.404407\pi$
$347$	−7.14444	−	4.12484i	−0.383534	−	0.221433i	−0.679355	+	0.733810i	$0.737740\pi$
$348$		0			0
$349$	24.0142			1.28545			0.642727	−	0.766096i	$-0.277803\pi$
$349$	24.0142			1.28545			0.642727	+	0.766096i	$0.277803\pi$
$350$		0			0
$351$	−27.6440	−	1.40071i	−1.47553	−	0.0747646i
$352$		0			0
$353$			28.6305i			1.52385i	0.647668	+	0.761923i	$0.275745\pi$
$353$			28.6305i			1.52385i	−0.647668	+	0.761923i	$0.724255\pi$
$354$		0			0
$355$	−1.29078	+	0.745230i	−0.0685073	+	0.0395527i
$356$		0			0
$357$	26.5624	+	23.0634i	1.40583	+	1.22064i
$358$		0			0
$359$	7.22382	+	4.17068i	0.381259	+	0.220120i	0.678366	−	0.734724i	$-0.262688\pi$
$359$	7.22382	+	4.17068i	0.381259	+	0.220120i	−0.297107	+	0.954844i	$0.596022\pi$
$360$		0			0
$361$	−16.6024	−	9.23901i	−0.873812	−	0.486264i
$362$		0			0
$363$	8.92014	+	1.72855i	0.468186	+	0.0907254i
$364$		0			0
$365$	−15.2350	+	8.79594i	−0.797437	+	0.460401i
$366$		0			0
$367$	−12.7339	−	22.0558i	−0.664706	−	1.15130i	−0.979365	−	0.202099i	$-0.935224\pi$
$367$	−12.7339	−	22.0558i	−0.664706	−	1.15130i	0.314659	−	0.949205i	$-0.398110\pi$
$368$		0			0
$369$	−21.8855	+	17.1396i	−1.13931	+	0.892252i
$370$		0			0
$371$	−15.2279	−	26.3755i	−0.790592	−	1.36935i
$372$		0			0
$373$			20.8865i			1.08146i	0.841196	+	0.540731i	$0.181852\pi$
$373$			20.8865i			1.08146i	−0.841196	+	0.540731i	$0.818148\pi$
$374$		0			0
$375$	−3.79212	+	19.5691i	−0.195824	+	1.01055i
$376$		0			0
$377$	43.2012	+	24.9422i	2.22497	+	1.28459i
$378$		0			0
$379$			38.4960i			1.97740i	0.149893	+	0.988702i	$0.452107\pi$
$379$			38.4960i			1.97740i	−0.149893	+	0.988702i	$0.547893\pi$
$380$		0			0
$381$	−32.4427	+	11.1919i	−1.66209	+	0.573377i
$382$		0			0
$383$	−4.35991	+	7.55159i	−0.222781	+	0.385868i	−0.955651	−	0.294500i	$-0.904847\pi$
$383$	−4.35991	+	7.55159i	−0.222781	+	0.385868i	0.732870	+	0.680368i	$0.238180\pi$
$384$		0			0
$385$	−8.85118	+	15.3307i	−0.451098	+	0.781324i
$386$		0			0
$387$	−1.17508	+	0.920263i	−0.0597328	+	0.0467796i
$388$		0			0
$389$	30.3812	−	17.5406i	1.54039	−	0.889343i	0.541574	−	0.840653i	$-0.317829\pi$
$389$	30.3812	−	17.5406i	1.54039	−	0.889343i	0.998814	−	0.0486899i	$-0.0155046\pi$
$390$		0			0
$391$	−20.7291			−1.04831
$392$		0			0
$393$	−2.69041	−	2.33601i	−0.135713	−	0.117836i
$394$		0			0
$395$	−7.61777	−	13.1944i	−0.383292	−	0.663881i
$396$		0			0
$397$	−2.21576	+	3.83781i	−0.111206	+	0.192614i	−0.916257	−	0.400592i	$-0.868805\pi$
$397$	−2.21576	+	3.83781i	−0.111206	+	0.192614i	0.805051	+	0.593206i	$0.202138\pi$
$398$		0			0
$399$	11.0929	−	23.2416i	0.555341	−	1.16354i
$400$		0			0
$401$	14.7129	−	25.4834i	0.734726	−	1.27258i	−0.220118	−	0.975473i	$-0.570644\pi$
$401$	14.7129	−	25.4834i	0.734726	−	1.27258i	0.954843	−	0.297109i	$-0.0960226\pi$
$402$		0			0
$403$	−12.5808	−	21.7906i	−0.626695	−	1.08547i
$404$		0			0
$405$	−5.41020	−	18.7043i	−0.268835	−	0.929426i
$406$		0			0
$407$	−3.70053			−0.183428
$408$		0			0
$409$	−3.64277	+	2.10316i	−0.180124	+	0.103994i	−0.587351	−	0.809333i	$-0.699829\pi$
$409$	−3.64277	+	2.10316i	−0.180124	+	0.103994i	0.407227	+	0.913327i	$0.366496\pi$
$410$		0			0
$411$	−3.74887	+	1.29326i	−0.184918	+	0.0637920i
$412$		0			0
$413$	−0.655471	+	1.13531i	−0.0322536	+	0.0558649i
$414$		0			0
$415$	1.88150	−	3.25885i	0.0923592	−	0.159971i
$416$		0			0
$417$	9.12264	+	26.4444i	0.446738	+	1.29499i
$418$		0			0
$419$			1.54149i			0.0753069i	0.999291	+	0.0376534i	$0.0119883\pi$
$419$			1.54149i			0.0753069i	−0.999291	+	0.0376534i	$0.988012\pi$
$420$		0			0
$421$	2.20580	+	1.27352i	0.107504	+	0.0620676i	0.552788	−	0.833322i	$-0.313564\pi$
$421$	2.20580	+	1.27352i	0.107504	+	0.0620676i	−0.445284	+	0.895389i	$0.646897\pi$
$422$		0			0
$423$	−24.6585	+	3.49458i	−1.19894	+	0.169912i
$424$		0			0
$425$			1.90218i			0.0922692i
$426$		0			0
$427$	4.73618	+	8.20330i	0.229200	+	0.396985i
$428$		0			0
$429$	−7.21768	−	20.9224i	−0.348473	−	1.01014i
$430$		0			0
$431$	−8.82243	−	15.2809i	−0.424962	−	0.736055i	0.571455	−	0.820633i	$-0.306379\pi$
$431$	−8.82243	−	15.2809i	−0.424962	−	0.736055i	−0.996417	+	0.0845782i	$0.973046\pi$
$432$		0			0
$433$	14.8385	−	8.56702i	0.713094	−	0.411705i	−0.0991119	−	0.995076i	$-0.531600\pi$
$433$	14.8385	−	8.56702i	0.713094	−	0.411705i	0.812205	+	0.583372i	$0.198267\pi$
$434$		0			0
$435$	−6.67579	+	34.4502i	−0.320080	+	1.65176i
$436$		0			0
$437$	4.04330	+	14.6269i	0.193417	+	0.699699i
$438$		0			0
$439$	−24.5109	−	14.1514i	−1.16984	−	0.675409i	−0.216200	−	0.976349i	$-0.569366\pi$
$439$	−24.5109	−	14.1514i	−1.16984	−	0.675409i	−0.953643	+	0.300940i	$0.902700\pi$
$440$		0			0
$441$	12.9000	+	5.19460i	0.614285	+	0.247362i
$442$		0			0
$443$	−24.5333	+	14.1643i	−1.16561	+	0.672966i	−0.952642	−	0.304093i	$-0.901647\pi$
$443$	−24.5333	+	14.1643i	−1.16561	+	0.672966i	−0.212969	+	0.977059i	$0.568313\pi$
$444$		0			0
$445$			38.3583i			1.81836i
$446$		0			0
$447$	3.80904	+	3.30729i	0.180161	+	0.156429i
$448$		0			0
$449$	−25.6491			−1.21046			−0.605228	−	0.796052i	$-0.706918\pi$
$449$	−25.6491			−1.21046			−0.605228	+	0.796052i	$0.706918\pi$
$450$		0			0
$451$	−19.2494	−	11.1136i	−0.906419	−	0.523321i
$452$		0			0
$453$	2.24124	−	11.5658i	0.105303	−	0.543411i
$454$		0			0
$455$	−39.3112			−1.84294
$456$		0			0
$457$	−27.7707			−1.29906			−0.649530	−	0.760336i	$-0.725034\pi$
$457$	−27.7707			−1.29906			−0.649530	+	0.760336i	$0.725034\pi$
$458$		0			0
$459$	−14.0935	−	27.5419i	−0.657827	−	1.28554i
$460$		0			0
$461$	−6.23418	−	3.59931i	−0.290355	−	0.167636i	0.347747	−	0.937588i	$-0.386947\pi$
$461$	−6.23418	−	3.59931i	−0.290355	−	0.167636i	−0.638102	+	0.769952i	$0.720280\pi$
$462$		0			0
$463$	−6.54276			−0.304068			−0.152034	−	0.988375i	$-0.548582\pi$
$463$	−6.54276			−0.304068			−0.152034	+	0.988375i	$0.548582\pi$
$464$		0			0
$465$	11.6044	−	13.3650i	0.538143	−	0.619786i
$466$		0			0
$467$		−	29.3832i		−	1.35969i	−0.733354	−	0.679847i	$-0.762046\pi$
$467$		−	29.3832i		−	1.35969i	0.733354	−	0.679847i	$-0.237954\pi$
$468$		0			0
$469$	−17.0293	+	9.83189i	−0.786342	+	0.453995i
$470$		0			0
$471$	0.351286	−	0.404581i	0.0161864	−	0.0186421i
$472$		0			0
$473$	−1.03354	−	0.596716i	−0.0475224	−	0.0274370i
$474$		0			0
$475$	1.34222	−	0.371029i	0.0615852	−	0.0170240i
$476$		0			0
$477$	3.75845	+	26.5204i	0.172088	+	1.21428i
$478$		0			0
$479$	−33.0915	+	19.1054i	−1.51199	+	0.872949i	−0.512090	+	0.858932i	$0.671128\pi$
$479$	−33.0915	+	19.1054i	−1.51199	+	0.872949i	−0.999902	+	0.0140167i	$0.995538\pi$
$480$		0			0
$481$	−4.10884	−	7.11672i	−0.187347	−	0.324494i
$482$		0			0
$483$	−19.4447	+	6.70793i	−0.884766	+	0.305221i
$484$		0			0
$485$	15.4043	+	26.6811i	0.699474	+	1.21152i
$486$		0			0
$487$			31.9397i			1.44733i	0.690153	+	0.723663i	$0.257543\pi$
$487$			31.9397i			1.44733i	−0.690153	+	0.723663i	$0.742457\pi$
$488$		0			0
$489$	32.4271	+	6.28374i	1.46640	+	0.284161i
$490$		0			0
$491$	8.95372	+	5.16943i	0.404076	+	0.233293i	0.688241	−	0.725482i	$-0.258383\pi$
$491$	8.95372	+	5.16943i	0.404076	+	0.233293i	−0.284165	+	0.958775i	$0.591716\pi$
$492$		0			0
$493$			55.7576i			2.51120i
$494$		0			0
$495$	12.2574	−	9.59937i	0.550930	−	0.431460i
$496$		0			0
$497$	−1.17499	+	2.03515i	−0.0527057	+	0.0912890i
$498$		0			0
$499$	−14.8210	+	25.6707i	−0.663479	+	1.14918i	0.316217	+	0.948687i	$0.397587\pi$
$499$	−14.8210	+	25.6707i	−0.663479	+	1.14918i	−0.979695	+	0.200492i	$0.935746\pi$
$500$		0			0
$501$	−3.50193	−	10.1513i	−0.156455	−	0.453526i
$502$		0			0
$503$	34.2652	−	19.7830i	1.52781	−	0.882082i	0.528357	−	0.849022i	$-0.322808\pi$
$503$	34.2652	−	19.7830i	1.52781	−	0.882082i	0.999453	−	0.0330599i	$-0.0105252\pi$
$504$		0			0
$505$	−23.2804			−1.03597
$506$		0			0
$507$	17.4607	−	20.1096i	0.775455	−	0.893100i
$508$		0			0
$509$	−4.22536	−	7.31853i	−0.187286	−	0.324388i	0.757059	−	0.653347i	$-0.226636\pi$
$509$	−4.22536	−	7.31853i	−0.187286	−	0.324388i	−0.944344	+	0.328959i	$0.893302\pi$
$510$		0			0
$511$	−13.8685	+	24.0209i	−0.613504	+	1.06262i
$512$		0			0
$513$	−16.6852	+	15.3168i	−0.736668	+	0.676255i
$514$		0			0
$515$	−12.9567	+	22.4417i	−0.570942	+	0.988900i
$516$		0			0
$517$	−9.95688	−	17.2458i	−0.437903	−	0.758470i
$518$		0			0
$519$	−6.80552	+	7.83800i	−0.298729	+	0.344050i
$520$		0			0
$521$	−25.7517			−1.12820			−0.564101	−	0.825706i	$-0.690777\pi$
$521$	−25.7517			−1.12820			−0.564101	+	0.825706i	$0.690777\pi$
$522$		0			0
$523$	−13.7046	+	7.91236i	−0.599261	+	0.345983i	−0.768751	−	0.639549i	$-0.779121\pi$
$523$	−13.7046	+	7.91236i	−0.599261	+	0.345983i	0.169490	+	0.985532i	$0.445788\pi$
$524$		0			0
$525$	0.615545	+	1.78432i	0.0268646	+	0.0778742i
$526$		0			0
$527$	14.0620	−	24.3561i	0.612551	−	1.06097i
$528$		0			0
$529$	−5.43963	+	9.42171i	−0.236506	+	0.409640i
$530$		0			0
$531$	0.907718	−	0.710878i	0.0393916	−	0.0308495i
$532$		0			0
$533$		−	49.3597i		−	2.13800i
$534$		0			0
$535$	33.6126	+	19.4062i	1.45320	+	0.839004i
$536$		0			0
$537$	−14.7612	−	2.86043i	−0.636991	−	0.123437i
$538$		0			0
$539$			11.1196i			0.478956i
$540$		0			0
$541$	3.99608	+	6.92142i	0.171805	+	0.297575i	0.939051	−	0.343778i	$-0.111707\pi$
$541$	3.99608	+	6.92142i	0.171805	+	0.297575i	−0.767246	+	0.641353i	$0.778373\pi$
$542$		0			0
$543$	1.84237	−	0.635572i	0.0790639	−	0.0272750i
$544$		0			0
$545$	−17.3508	−	30.0525i	−0.743227	−	1.28731i
$546$		0			0
$547$	32.8767	−	18.9813i	1.40570	−	0.811584i	0.410734	−	0.911755i	$-0.365272\pi$
$547$	32.8767	−	18.9813i	1.40570	−	0.811584i	0.994970	+	0.100171i	$0.0319391\pi$
$548$		0			0
$549$	−1.16895	−	8.24837i	−0.0498898	−	0.352032i
$550$		0			0
$551$	39.3438	−	10.8758i	1.67610	−	0.463323i
$552$		0			0
$553$	−20.8034	−	12.0109i	−0.884651	−	0.510753i
$554$		0			0
$555$	3.78996	−	4.36494i	0.160875	−	0.185282i
$556$		0			0
$557$	−9.79812	+	5.65695i	−0.415160	+	0.239693i	−0.693004	−	0.720934i	$-0.743713\pi$
$557$	−9.79812	+	5.65695i	−0.415160	+	0.239693i	0.277845	+	0.960626i	$0.410380\pi$
$558$		0			0
$559$		−	2.65023i		−	0.112093i
$560$		0			0
$561$	16.2189	−	18.6795i	0.684761	−	0.788647i
$562$		0			0
$563$	3.55642			0.149885			0.0749426	−	0.997188i	$-0.476123\pi$
$563$	3.55642			0.149885			0.0749426	+	0.997188i	$0.476123\pi$
$564$		0			0
$565$	−11.6251	−	6.71175i	−0.489071	−	0.282365i
$566$		0			0
$567$	−22.1328	−	21.2748i	−0.929491	−	0.893457i
$568$		0			0
$569$	26.7017			1.11939			0.559697	−	0.828697i	$-0.310918\pi$
$569$	26.7017			1.11939			0.559697	+	0.828697i	$0.310918\pi$
$570$		0			0
$571$	−28.8237			−1.20624			−0.603118	−	0.797652i	$-0.706075\pi$
$571$	−28.8237			−1.20624			−0.603118	+	0.797652i	$0.706075\pi$
$572$		0			0
$573$	−0.466653	+	2.40815i	−0.0194947	+	0.100602i
$574$		0			0
$575$	−0.963233	−	0.556123i	−0.0401696	−	0.0231919i
$576$		0			0
$577$	−19.6944			−0.819890			−0.409945	−	0.912110i	$-0.634452\pi$
$577$	−19.6944			−0.819890			−0.409945	+	0.912110i	$0.634452\pi$
$578$		0			0
$579$	0.665755	+	0.578057i	0.0276679	+	0.0240232i
$580$		0			0
$581$		−	5.93308i		−	0.246146i
$582$		0			0
$583$	−18.5480	+	10.7087i	−0.768181	+	0.443509i
$584$		0			0
$585$	32.0710	+	12.9145i	1.32597	+	0.533947i
$586$		0			0
$587$	26.7557	+	15.4474i	1.10433	+	0.637582i	0.937354	−	0.348379i	$-0.113268\pi$
$587$	26.7557	+	15.4474i	1.10433	+	0.637582i	0.166972	+	0.985962i	$0.446601\pi$
$588$		0			0
$589$	−19.9291	−	5.17169i	−0.821163	−	0.213096i
$590$		0			0
$591$	−2.64960	+	13.6732i	−0.108990	+	0.562440i
$592$		0			0
$593$	29.5805	−	17.0783i	1.21473	−	0.701323i	0.250942	−	0.968002i	$-0.419260\pi$
$593$	29.5805	−	17.0783i	1.21473	−	0.701323i	0.963785	+	0.266679i	$0.0859263\pi$
$594$		0			0
$595$	−21.9698	−	38.0528i	−0.900673	−	1.56001i
$596$		0			0
$597$	−1.41071	−	4.08933i	−0.0577367	−	0.167365i
$598$		0			0
$599$	4.08464	+	7.07481i	0.166894	+	0.289069i	0.937326	−	0.348453i	$-0.113293\pi$
$599$	4.08464	+	7.07481i	0.166894	+	0.289069i	−0.770432	+	0.637522i	$0.779960\pi$
$600$		0			0
$601$		−	10.6875i		−	0.435951i	−0.975954	−	0.217975i	$-0.930055\pi$
$601$		−	10.6875i		−	0.435951i	0.975954	−	0.217975i	$-0.0699453\pi$
$602$		0			0
$603$	17.1229	−	2.42665i	0.697298	−	0.0988208i
$604$		0			0
$605$	−9.82865	−	5.67457i	−0.399591	−	0.230704i
$606$		0			0
$607$			18.3048i			0.742971i	0.928439	+	0.371485i	$0.121151\pi$
$607$			18.3048i			0.742971i	−0.928439	+	0.371485i	$0.878849\pi$
$608$		0			0
$609$	18.0432	+	52.3030i	0.731146	+	2.11942i
$610$		0			0
$611$	22.1110	−	38.2974i	0.894516	−	1.54935i
$612$		0			0
$613$	13.9095	−	24.0920i	0.561800	−	0.973067i	−0.435539	−	0.900170i	$-0.643442\pi$
$613$	13.9095	−	24.0920i	0.561800	−	0.973067i	0.997339	−	0.0728971i	$-0.0232245\pi$
$614$		0			0
$615$	32.8237	−	11.3233i	1.32358	−	0.456601i
$616$		0			0
$617$	−6.62030	+	3.82223i	−0.266523	+	0.153877i	−0.627307	−	0.778772i	$-0.715843\pi$
$617$	−6.62030	+	3.82223i	−0.266523	+	0.153877i	0.360783	+	0.932650i	$0.382509\pi$
$618$		0			0
$619$	−40.8851			−1.64331			−0.821656	−	0.569983i	$-0.806950\pi$
$619$	−40.8851			−1.64331			−0.821656	+	0.569983i	$0.806950\pi$
$620$		0			0
$621$	18.0672	+	0.915457i	0.725010	+	0.0367360i
$622$		0			0
$623$	30.2395	+	52.3764i	1.21152	+	2.09842i
$624$		0			0
$625$	11.6503	−	20.1789i	0.466011	−	0.807155i
$626$		0			0
$627$	−16.3442	−	7.80088i	−0.652724	−	0.311537i
$628$		0			0
$629$	4.59259	−	7.95461i	0.183119	−	0.317171i
$630$		0			0
$631$	2.88883	+	5.00360i	0.115003	+	0.199190i	0.917781	−	0.397087i	$-0.129979\pi$
$631$	2.88883	+	5.00360i	0.115003	+	0.199190i	−0.802778	+	0.596278i	$0.796646\pi$
$632$		0			0
$633$	5.60470	+	4.86641i	0.222767	+	0.193422i
$634$		0			0
$635$	42.8667			1.70111
$636$		0			0
$637$	−21.3849	+	12.3466i	−0.847299	+	0.489188i
$638$		0			0
$639$	1.62717	−	1.27432i	0.0643700	−	0.0504112i
$640$		0			0
$641$	−8.76090	+	15.1743i	−0.346035	+	0.599350i	−0.985541	−	0.169436i	$-0.945805\pi$
$641$	−8.76090	+	15.1743i	−0.346035	+	0.599350i	0.639506	+	0.768786i	$0.279139\pi$
$642$		0			0
$643$	16.7361	−	28.9878i	0.660009	−	1.14317i	−0.320604	−	0.947213i	$-0.603886\pi$
$643$	16.7361	−	28.9878i	0.660009	−	1.14317i	0.980613	−	0.195955i	$-0.0627807\pi$
$644$		0			0
$645$	1.76238	−	0.607974i	0.0693935	−	0.0239390i
$646$		0			0
$647$			37.2892i			1.46599i	0.680234	+	0.732995i	$0.261878\pi$
$647$			37.2892i			1.46599i	−0.680234	+	0.732995i	$0.738122\pi$
$648$		0			0
$649$	0.798383	+	0.460947i	0.0313393	+	0.0180937i
$650$		0			0
$651$	5.30911	−	27.3975i	0.208080	−	1.07379i
$652$		0			0
$653$		−	15.4674i		−	0.605285i	−0.953104	−	0.302643i	$-0.902131\pi$
$653$		−	15.4674i		−	0.605285i	0.953104	−	0.302643i	$-0.0978689\pi$
$654$		0			0
$655$	2.22524	+	3.85423i	0.0869473	+	0.150597i
$656$		0			0
$657$	19.2055	−	15.0408i	0.749278	−	0.586796i
$658$		0			0
$659$	22.6487	+	39.2287i	0.882268	+	1.52813i	0.848813	+	0.528693i	$0.177318\pi$
$659$	22.6487	+	39.2287i	0.882268	+	1.52813i	0.0334547	+	0.999440i	$0.489349\pi$
$660$		0			0
$661$	7.05122	−	4.07102i	0.274261	−	0.158344i	−0.356562	−	0.934272i	$-0.616051\pi$
$661$	7.05122	−	4.07102i	0.274261	−	0.158344i	0.630822	+	0.775927i	$0.282718\pi$
$662$		0			0
$663$	53.9321	+	10.4510i	2.09455	+	0.405883i
$664$		0			0
$665$	−22.5656	+	22.9247i	−0.875055	+	0.888983i
$666$		0			0
$667$	−28.2348	−	16.3013i	−1.09325	−	0.631191i
$668$		0			0
$669$	−0.205434	−	0.178372i	−0.00794253	−	0.00689628i
$670$		0			0
$671$	5.76881	−	3.33062i	0.222702	−	0.128577i
$672$		0			0
$673$		−	29.1954i		−	1.12540i	−0.826662	−	0.562699i	$-0.809763\pi$
$673$		−	29.1954i		−	1.12540i	0.826662	−	0.562699i	$-0.190237\pi$
$674$		0			0
$675$	0.0840059	−	1.65791i	0.00323339	−	0.0638130i
$676$		0			0
$677$	−42.3867			−1.62905			−0.814527	−	0.580126i	$-0.803003\pi$
$677$	−42.3867			−1.62905			−0.814527	+	0.580126i	$0.803003\pi$
$678$		0			0
$679$	42.0677	+	24.2878i	1.61441	+	0.932080i
$680$		0			0
$681$	−0.783255	−	0.151780i	−0.0300144	−	0.00581621i
$682$		0			0
$683$	−34.4320			−1.31750			−0.658752	−	0.752360i	$-0.728915\pi$
$683$	−34.4320			−1.31750			−0.658752	+	0.752360i	$0.728915\pi$
$684$		0			0
$685$	4.95341			0.189260
$686$		0			0
$687$	17.1392	+	3.32125i	0.653903	+	0.126714i
$688$		0			0
$689$	−41.1892	−	23.7806i	−1.56918	−	0.905968i
$690$		0			0
$691$	−16.0168			−0.609308			−0.304654	−	0.952463i	$-0.598541\pi$
$691$	−16.0168			−0.609308			−0.304654	+	0.952463i	$0.598541\pi$
$692$		0			0
$693$	9.16930	−	22.7705i	0.348313	−	0.864981i
$694$		0			0
$695$		−	34.9412i		−	1.32539i
$696$		0			0
$697$	47.7795	−	27.5855i	1.80978	−	1.04488i
$698$		0			0
$699$	−3.65406	−	3.17272i	−0.138209	−	0.120003i
$700$		0			0
$701$	−23.8208	−	13.7529i	−0.899699	−	0.519441i	−0.0225963	−	0.999745i	$-0.507193\pi$
$701$	−23.8208	−	13.7529i	−0.899699	−	0.519441i	−0.877102	+	0.480303i	$0.840527\pi$
$702$		0			0
$703$	−6.50875	−	1.68905i	−0.245482	−	0.0637039i
$704$		0			0
$705$	30.5398	+	5.91802i	1.15019	+	0.222886i
$706$		0			0
$707$	−31.7883	+	18.3530i	−1.19552	+	0.690236i
$708$		0			0
$709$	−16.3647	−	28.3445i	−0.614588	−	1.06450i	−0.990457	−	0.137825i	$-0.955989\pi$
$709$	−16.3647	−	28.3445i	−0.614588	−	1.06450i	0.375868	−	0.926673i	$-0.377345\pi$
$710$		0			0
$711$	13.0261	+	16.6330i	0.488518	+	0.623787i
$712$		0			0
$713$	8.22237	+	14.2416i	0.307930	+	0.533350i
$714$		0			0
$715$			27.6448i			1.03386i
$716$		0			0
$717$	−4.12739	+	21.2993i	−0.154140	+	0.795436i
$718$		0			0
$719$	27.0486	+	15.6165i	1.00874	+	0.582398i	0.910823	−	0.412797i	$-0.135448\pi$
$719$	27.0486	+	15.6165i	1.00874	+	0.582398i	0.0979190	+	0.995194i	$0.468781\pi$
$720$		0			0
$721$			40.8574i			1.52161i
$722$		0			0
$723$	−28.6959	+	9.89935i	−1.06721	+	0.368161i
$724$		0			0
$725$	−1.49587	+	2.59093i	−0.0555554	+	0.0962247i
$726$		0			0
$727$	15.6620	−	27.1273i	0.580870	−	1.00610i	−0.414507	−	0.910046i	$-0.636046\pi$
$727$	15.6620	−	27.1273i	0.580870	−	1.00610i	0.995377	−	0.0960497i	$-0.0306208\pi$
$728$		0			0
$729$	11.0673	+	24.6275i	0.409901	+	0.912130i
$730$		0			0
$731$	2.56539	−	1.48113i	0.0948843	−	0.0547815i
$732$		0			0
$733$	−26.2383			−0.969132			−0.484566	−	0.874755i	$-0.661023\pi$
$733$	−26.2383			−0.969132			−0.484566	+	0.874755i	$0.661023\pi$
$734$		0			0
$735$	−13.1161	−	11.3884i	−0.483795	−	0.420066i
$736$		0			0
$737$	6.91408	+	11.9755i	0.254684	+	0.441125i
$738$		0			0
$739$	14.4088	−	24.9567i	0.530035	−	0.918047i	−0.469351	−	0.883011i	$-0.655512\pi$
$739$	14.4088	−	24.9567i	0.530035	−	0.918047i	0.999386	−	0.0350355i	$-0.0111544\pi$
$740$		0			0
$741$	−3.14524	−	40.0942i	−0.115543	−	1.47290i
$742$		0			0
$743$	−9.64272	+	16.7017i	−0.353757	+	0.612725i	−0.986904	−	0.161306i	$-0.948429\pi$
$743$	−9.64272	+	16.7017i	−0.353757	+	0.612725i	0.633147	+	0.774031i	$0.281763\pi$
$744$		0			0
$745$	−3.15046	−	5.45676i	−0.115424	−	0.199920i
$746$		0			0
$747$	−1.94912	+	4.84035i	−0.0713147	+	0.177099i
$748$		0			0
$749$	61.1951			2.23602
$750$		0			0
$751$	27.7735	−	16.0350i	1.01347	−	0.585127i	0.101263	−	0.994860i	$-0.467711\pi$
$751$	27.7735	−	16.0350i	1.01347	−	0.585127i	0.912205	+	0.409733i	$0.134378\pi$
$752$		0			0
$753$	16.3251	−	5.63172i	0.594918	−	0.205231i
$754$		0			0
$755$	−7.35764	+	12.7438i	−0.267772	+	0.463795i
$756$		0			0
$757$	5.01914	−	8.69341i	0.182424	−	0.315967i	−0.760282	−	0.649594i	$-0.774939\pi$
$757$	5.01914	−	8.69341i	0.182424	−	0.315967i	0.942705	+	0.333626i	$0.108272\pi$
$758$		0			0
$759$	4.71722	+	13.6741i	0.171224	+	0.496339i
$760$		0			0
$761$			20.1959i			0.732101i	0.930595	+	0.366051i	$0.119290\pi$
$761$			20.1959i			0.732101i	−0.930595	+	0.366051i	$0.880710\pi$
$762$		0			0
$763$	−47.3834	−	27.3568i	−1.71539	−	0.990383i
$764$		0			0
$765$	5.42245	+	38.2618i	0.196049	+	1.38336i
$766$		0			0
$767$			2.04723i			0.0739212i
$768$		0			0
$769$	21.6397	+	37.4810i	0.780347	+	1.35160i	0.931740	+	0.363127i	$0.118291\pi$
$769$	21.6397	+	37.4810i	0.780347	+	1.35160i	−0.151392	+	0.988474i	$0.548376\pi$
$770$		0			0
$771$	8.81804	+	25.5615i	0.317574	+	0.920574i
$772$		0			0
$773$	−3.63700	−	6.29947i	−0.130814	−	0.226576i	0.793177	−	0.608992i	$-0.208426\pi$
$773$	−3.63700	−	6.29947i	−0.130814	−	0.226576i	−0.923991	+	0.382415i	$0.875092\pi$
$774$		0			0
$775$	1.30686	−	0.754516i	0.0469438	−	0.0271030i
$776$		0			0
$777$	1.73393	−	8.94792i	0.0622045	−	0.321005i
$778$		0			0
$779$	−28.7846	−	28.3336i	−1.03131	−	1.01516i
$780$		0			0
$781$	1.43118	+	0.826292i	0.0512116	+	0.0295670i
$782$		0			0
$783$	2.46242	−	48.5975i	0.0879998	−	1.73673i
$784$		0			0
$785$	−0.579595	+	0.334629i	−0.0206866	+	0.0119434i
$786$		0			0
$787$			43.6380i			1.55553i	0.628558	+	0.777763i	$0.283645\pi$
$787$			43.6380i			1.55553i	−0.628558	+	0.777763i	$0.716355\pi$
$788$		0			0
$789$	−30.6709	−	26.6307i	−1.09191	−	0.948079i
$790$		0			0
$791$	−21.1647			−0.752529
$792$		0			0
$793$	12.8107	+	7.39624i	0.454920	+	0.262648i
$794$		0			0
$795$	6.36488	−	32.8458i	0.225739	−	1.16492i
$796$		0			0
$797$	−3.28414			−0.116330			−0.0581651	−	0.998307i	$-0.518525\pi$
$797$	−3.28414			−0.116330			−0.0581651	+	0.998307i	$0.518525\pi$
$798$		0			0
$799$	49.4285			1.74866
$800$		0			0
$801$	−7.46354	−	52.6642i	−0.263711	−	1.86080i
$802$		0			0
$803$	16.8922	+	9.75272i	0.596113	+	0.344166i
$804$		0			0
$805$	25.6924			0.905539
$806$		0			0
$807$	−28.5070	+	32.8319i	−1.00350	+	1.15574i
$808$		0			0
$809$			10.0754i			0.354232i	0.984190	+	0.177116i	$0.0566768\pi$
$809$			10.0754i			0.354232i	−0.984190	+	0.177116i	$0.943323\pi$
$810$		0			0
$811$	22.6877	−	13.0988i	0.796674	−	0.459960i	−0.0456327	−	0.998958i	$-0.514530\pi$
$811$	22.6877	−	13.0988i	0.796674	−	0.459960i	0.842307	+	0.538998i	$0.181197\pi$
$812$		0			0
$813$	−18.7091	+	21.5475i	−0.656157	+	0.755704i
$814$		0			0
$815$	−35.7297	−	20.6286i	−1.25156	−	0.722588i
$816$		0			0
$817$	−1.54551	−	1.52129i	−0.0540704	−	0.0532233i
$818$		0			0
$819$	53.9725	−	7.64896i	1.88595	−	0.267276i
$820$		0			0
$821$	3.26277	−	1.88376i	0.113872	−	0.0657438i	−0.441983	−	0.897024i	$-0.645725\pi$
$821$	3.26277	−	1.88376i	0.113872	−	0.0657438i	0.555854	+	0.831280i	$0.312391\pi$
$822$		0			0
$823$	−7.17620	−	12.4295i	−0.250146	−	0.433266i	0.713419	−	0.700737i	$-0.247145\pi$
$823$	−7.17620	−	12.4295i	−0.250146	−	0.433266i	−0.963566	+	0.267471i	$0.913812\pi$
$824$		0			0
$825$	1.25479	−	0.432870i	0.0436862	−	0.0150706i
$826$		0			0
$827$	9.50448	+	16.4622i	0.330503	+	0.572448i	0.982611	−	0.185678i	$-0.0594482\pi$
$827$	9.50448	+	16.4622i	0.330503	+	0.572448i	−0.652107	+	0.758127i	$0.726115\pi$
$828$		0			0
$829$			13.1294i			0.456004i	0.973661	+	0.228002i	$0.0732193\pi$
$829$			13.1294i			0.456004i	−0.973661	+	0.228002i	$0.926781\pi$
$830$		0			0
$831$	−28.7314	−	5.56758i	−0.996680	−	0.193137i
$832$		0			0
$833$	−23.9026	−	13.8002i	−0.828177	−	0.478148i
$834$		0			0
$835$			13.4129i			0.464174i
$836$		0			0
$837$	−13.3319	+	20.6074i	−0.460817	+	0.712296i
$838$		0			0
$839$	−7.71399	+	13.3610i	−0.266317	+	0.461274i	−0.967908	−	0.251306i	$-0.919140\pi$
$839$	−7.71399	+	13.3610i	−0.266317	+	0.461274i	0.701591	+	0.712580i	$0.252473\pi$
$840$		0			0
$841$	−29.3478	+	50.8319i	−1.01199	+	1.75282i
$842$		0			0
$843$	−6.06345	−	17.5765i	−0.208836	−	0.605368i
$844$		0			0
$845$	−28.8087	+	16.6327i	−0.991049	+	0.572183i
$846$		0			0
$847$	−17.8941			−0.614847
$848$		0			0
$849$	−23.1170	+	26.6241i	−0.793374	+	0.913738i
$850$		0			0
$851$	2.68539	+	4.65123i	0.0920540	+	0.159442i
$852$		0			0
$853$	5.65239	−	9.79022i	0.193534	−	0.335211i	−0.752885	−	0.658152i	$-0.771338\pi$
$853$	5.65239	−	9.79022i	0.193534	−	0.335211i	0.946419	+	0.322941i	$0.104672\pi$
$854$		0			0
$855$	25.9407	−	11.2893i	0.887154	−	0.386087i
$856$		0			0
$857$	22.3851	−	38.7721i	0.764659	−	1.32443i	−0.175767	−	0.984432i	$-0.556241\pi$
$857$	22.3851	−	38.7721i	0.764659	−	1.32443i	0.940427	−	0.339997i	$-0.110426\pi$
$858$		0			0
$859$	−12.4297	−	21.5289i	−0.424097	−	0.734558i	0.572238	−	0.820087i	$-0.306075\pi$
$859$	−12.4297	−	21.5289i	−0.424097	−	0.734558i	−0.996336	+	0.0855293i	$0.972742\pi$
$860$		0			0
$861$	35.8925	−	41.3378i	1.22321	−	1.40879i
$862$		0			0
$863$	18.5718			0.632190			0.316095	−	0.948728i	$-0.397628\pi$
$863$	18.5718			0.632190			0.316095	+	0.948728i	$0.397628\pi$
$864$		0			0
$865$	11.2286	−	6.48282i	0.381783	−	0.220423i
$866$		0			0
$867$	10.4221	+	30.2112i	0.353952	+	1.02603i
$868$		0			0
$869$	−8.44639	+	14.6296i	−0.286524	+	0.496274i
$870$		0			0
$871$	−15.3540	+	26.5938i	−0.520249	+	0.901098i
$872$		0			0
$873$	−26.3409	−	33.6346i	−0.891503	−	1.13836i
$874$		0			0
$875$		−	39.2563i		−	1.32710i
$876$		0			0
$877$	43.9858	+	25.3952i	1.48530	+	0.857536i	0.999860	−	0.0167363i	$-0.00532759\pi$
$877$	43.9858	+	25.3952i	1.48530	+	0.857536i	0.485436	+	0.874272i	$0.338661\pi$
$878$		0			0
$879$	−23.4830	−	4.55055i	−0.792061	−	0.153486i
$880$		0			0
$881$			17.8174i			0.600282i	0.953895	+	0.300141i	$0.0970338\pi$
$881$			17.8174i			0.600282i	−0.953895	+	0.300141i	$0.902966\pi$
$882$		0			0
$883$	−4.55094	−	7.88246i	−0.153151	−	0.265266i	0.779233	−	0.626734i	$-0.215609\pi$
$883$	−4.55094	−	7.88246i	−0.153151	−	0.265266i	−0.932384	+	0.361469i	$0.882276\pi$
$884$		0			0
$885$	−1.36139	+	0.469643i	−0.0457625	+	0.0157869i
$886$		0			0
$887$	19.1470	+	33.1636i	0.642894	+	1.11353i	0.984784	+	0.173785i	$0.0555998\pi$
$887$	19.1470	+	33.1636i	0.642894	+	1.11353i	−0.341890	+	0.939740i	$0.611067\pi$
$888$		0			0
$889$	58.5324	−	33.7937i	1.96311	−	1.13340i
$890$		0			0
$891$	−14.9611	+	15.5645i	−0.501215	+	0.521429i
$892$		0			0
$893$	−9.64126	−	34.8779i	−0.322632	−	1.16714i
$894$		0			0
$895$	16.2646	+	9.39035i	0.543665	+	0.313885i
$896$		0			0
$897$	−21.0599	+	24.2549i	−0.703168	+	0.809847i
$898$		0			0
$899$	38.3073	−	22.1167i	1.27762	−	0.737634i
$900$		0			0
$901$		−	53.1608i		−	1.77104i
$902$		0			0
$903$	1.92715	−	2.21952i	0.0641315	−	0.0738610i
$904$		0			0
$905$	−2.43434			−0.0809202
$906$		0			0
$907$	−0.418757	−	0.241769i	−0.0139046	−	0.00802782i	0.493032	−	0.870011i	$-0.335889\pi$
$907$	−0.418757	−	0.241769i	−0.0139046	−	0.00802782i	−0.506936	+	0.861984i	$0.669222\pi$
$908$		0			0
$909$	31.9630	−	4.52978i	1.06014	−	0.150243i
$910$		0			0
$911$	30.4928			1.01027			0.505136	−	0.863039i	$-0.331442\pi$
$911$	30.4928			1.01027			0.505136	+	0.863039i	$0.331442\pi$
$912$		0			0
$913$	−4.17232			−0.138084
$914$		0			0
$915$	−1.97961	+	10.2157i	−0.0654437	+	0.337721i
$916$		0			0
$917$	6.07691	+	3.50851i	0.200677	+	0.115861i
$918$		0			0
$919$	51.6834			1.70488			0.852439	−	0.522827i	$-0.175123\pi$
$919$	51.6834			1.70488			0.852439	+	0.522827i	$0.175123\pi$
$920$		0			0
$921$	−0.0580481	−	0.0504016i	−0.00191275	−	0.00166079i
$922$		0			0
$923$			3.66986i			0.120795i
$924$		0			0
$925$	0.426815	−	0.246422i	0.0140336	−	0.00810230i
$926$		0			0
$927$	13.4224	−	33.3325i	0.440850	−	1.09478i
$928$		0			0
$929$	−0.520570	−	0.300551i	−0.0170793	−	0.00986077i	0.491436	−	0.870914i	$-0.336472\pi$
$929$	−0.520570	−	0.300551i	−0.0170793	−	0.00986077i	−0.508515	+	0.861053i	$0.669805\pi$
$930$		0			0
$931$	−5.07540	+	19.5580i	−0.166340	+	0.640988i
$932$		0			0
$933$	−6.44141	+	33.2407i	−0.210882	+	1.08825i
$934$		0			0
$935$	−26.7599	+	15.4498i	−0.875141	+	0.505263i
$936$		0			0
$937$	−27.5574	−	47.7309i	−0.900262	−	1.55930i	−0.827154	−	0.561976i	$-0.810041\pi$
$937$	−27.5574	−	47.7309i	−0.900262	−	1.55930i	−0.0731087	−	0.997324i	$-0.523292\pi$
$938$		0			0
$939$	−13.7049	−	39.7274i	−0.447243	−	1.29645i
$940$		0			0
$941$	23.5445	+	40.7802i	0.767528	+	1.32940i	0.938900	+	0.344190i	$0.111847\pi$
$941$	23.5445	+	40.7802i	0.767528	+	1.32940i	−0.171372	+	0.985206i	$0.554820\pi$
$942$		0			0
$943$			32.2597i			1.05052i
$944$		0			0
$945$	17.4680	+	34.1365i	0.568234	+	1.11046i
$946$		0			0
$947$	−20.7806	−	11.9977i	−0.675280	−	0.389873i	0.122794	−	0.992432i	$-0.460815\pi$
$947$	−20.7806	−	11.9977i	−0.675280	−	0.389873i	−0.798074	+	0.602559i	$0.794148\pi$
$948$		0			0
$949$			43.3153i			1.40607i
$950$		0			0
$951$	−8.93555	−	25.9021i	−0.289755	−	0.839933i
$952$		0			0
$953$	18.4045	−	31.8775i	0.596180	−	1.03261i	−0.397199	−	0.917732i	$-0.630018\pi$
$953$	18.4045	−	31.8775i	0.596180	−	1.03261i	0.993379	−	0.114881i	$-0.0366488\pi$
$954$		0			0
$955$	1.53195	−	2.65342i	0.0495728	−	0.0858626i
$956$		0			0
$957$	36.7810	−	12.6885i	1.18896	−	0.410161i
$958$		0			0
$959$	6.76364	−	3.90499i	0.218409	−	0.126099i
$960$		0			0
$961$	8.68873			0.280281
$962$		0			0
$963$	−49.9244	−	20.1037i	−1.60879	−	0.647833i
$964$		0			0
$965$	−0.550647	−	0.953749i	−0.0177260	−	0.0307023i
$966$		0			0
$967$	26.4881	−	45.8787i	0.851799	−	1.47536i	−0.0277835	−	0.999614i	$-0.508845\pi$
$967$	26.4881	−	45.8787i	0.851799	−	1.47536i	0.879583	−	0.475746i	$-0.157822\pi$
$968$		0			0
$969$	37.0529	−	25.4519i	1.19031	−	0.817633i
$970$		0			0
$971$	−2.19360	+	3.79943i	−0.0703961	+	0.121930i	−0.899075	−	0.437795i	$-0.855760\pi$
$971$	−2.19360	+	3.79943i	−0.0703961	+	0.121930i	0.828679	+	0.559724i	$0.189093\pi$
$972$		0			0
$973$	−27.5457	−	47.7105i	−0.883073	−	1.52953i
$974$		0			0
$975$	2.22572	+	1.93253i	0.0712801	+	0.0618906i
$976$		0			0
$977$	5.88126			0.188158			0.0940791	−	0.995565i	$-0.470009\pi$
$977$	5.88126			0.188158			0.0940791	+	0.995565i	$0.470009\pi$
$978$		0			0
$979$	36.8327	−	21.2654i	1.17718	−	0.679644i
$980$		0			0
$981$	29.6693	+	37.8846i	0.947267	+	1.20956i
$982$		0			0
$983$	−13.7901	+	23.8852i	−0.439836	+	0.761819i	−0.997676	−	0.0681296i	$-0.978297\pi$
$983$	−13.7901	+	23.8852i	−0.439836	+	0.761819i	0.557840	+	0.829948i	$0.311630\pi$
$984$		0			0
$985$	8.69824	−	15.0658i	0.277149	−	0.480036i
$986$		0			0
$987$	46.3660	−	15.9951i	1.47585	−	0.509129i
$988$		0			0
$989$			1.73210i			0.0550774i
$990$		0			0
$991$	31.3962	+	18.1266i	0.997332	+	0.575810i	0.907458	−	0.420143i	$-0.138020\pi$
$991$	31.3962	+	18.1266i	0.997332	+	0.575810i	0.0898745	+	0.995953i	$0.471353\pi$
$992$		0			0
$993$	−2.81273	+	14.5150i	−0.0892593	+	0.460620i
$994$		0			0
$995$			5.40326i			0.171295i
$996$		0			0
$997$	18.1181	+	31.3815i	0.573806	+	0.993862i	0.996170	+	0.0874354i	$0.0278672\pi$
$997$	18.1181	+	31.3815i	0.573806	+	0.993862i	−0.422364	+	0.906426i	$0.638800\pi$
$998$		0			0
$999$	−4.35414	+	6.73030i	−0.137759	+	0.212937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.o.65.8		16
3.2	odd	2		912.2.bn.n.65.7		16
4.3	odd	2		456.2.bf.c.65.1	✓	16
12.11	even	2		456.2.bf.d.65.2	yes	16
19.12	odd	6		912.2.bn.n.449.7		16
57.50	even	6	inner	912.2.bn.o.449.8		16
76.31	even	6		456.2.bf.d.449.2	yes	16
228.107	odd	6		456.2.bf.c.449.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.1	✓	16	4.3	odd	2
456.2.bf.c.449.1	yes	16	228.107	odd	6
456.2.bf.d.65.2	yes	16	12.11	even	2
456.2.bf.d.449.2	yes	16	76.31	even	6
912.2.bn.n.65.7		16	3.2	odd	2
912.2.bn.n.449.7		16	19.12	odd	6
912.2.bn.o.65.8		16	1.1	even	1	trivial
912.2.bn.o.449.8		16	57.50	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70042 + 0.329508i) q^{3} +(-1.87360 - 1.08173i) q^{5} -3.41109 q^{7} +(2.78285 + 1.12060i) q^{9} +O(q^{10})\)	\(q+(1.70042 + 0.329508i) q^{3} +(-1.87360 - 1.08173i) q^{5} -3.41109 q^{7} +(2.78285 + 1.12060i) q^{9} +2.39878i q^{11} +(-4.61325 + 2.66346i) q^{13} +(-2.82947 - 2.45676i) q^{15} +(-5.15639 - 2.97704i) q^{17} +(-1.09489 + 4.21915i) q^{19} +(-5.80028 - 1.12398i) q^{21} +(3.01506 - 1.74074i) q^{23} +(-0.159737 - 0.276673i) q^{25} +(4.36276 + 2.82247i) q^{27} +(-4.68230 - 8.10997i) q^{29} +4.72348i q^{31} +(-0.790418 + 4.07893i) q^{33} +(6.39103 + 3.68986i) q^{35} +1.54267i q^{37} +(-8.72209 + 3.00889i) q^{39} +(-4.63304 + 8.02466i) q^{41} +(-0.248758 + 0.430862i) q^{43} +(-4.00177 - 5.10985i) q^{45} +(-7.18941 + 4.15081i) q^{47} +4.63553 q^{49} +(-7.78706 - 6.76129i) q^{51} +(4.46423 + 7.73227i) q^{53} +(2.59482 - 4.49437i) q^{55} +(-3.25202 + 6.81354i) q^{57} +(0.192159 - 0.332829i) q^{59} +(-1.38846 - 2.40489i) q^{61} +(-9.49255 - 3.82248i) q^{63} +11.5245 q^{65} +(4.99235 - 2.88233i) q^{67} +(5.70045 - 1.96651i) q^{69} +(0.344463 - 0.596628i) q^{71} +(4.06570 - 7.04199i) q^{73} +(-0.180454 - 0.523095i) q^{75} -8.18246i q^{77} +(6.09876 + 3.52112i) q^{79} +(6.48849 + 6.23695i) q^{81} +1.73935i q^{83} +(6.44069 + 11.1556i) q^{85} +(-5.28956 - 15.3332i) q^{87} +(-8.86507 - 15.3547i) q^{89} +(15.7362 - 9.08530i) q^{91} +(-1.55643 + 8.03190i) q^{93} +(6.61535 - 6.72064i) q^{95} +(-12.3326 - 7.12025i) q^{97} +(-2.68808 + 6.67544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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