LMFDB - Embedded newform 912.2.bn.n.65.7

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			65.7
Root			$1.70042 - 0.329508i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.n.449.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13557 + 1.30785i) q^{3} +(1.87360 + 1.08173i) q^{5} -3.41109 q^{7} +(-0.420952 + 2.97032i) q^{9} +O(q^{10})$	\(q+(1.13557 + 1.30785i) q^{3} +(1.87360 + 1.08173i) q^{5} -3.41109 q^{7} +(-0.420952 + 2.97032i) q^{9} -2.39878i q^{11} +(-4.61325 + 2.66346i) q^{13} +(0.712876 + 3.67877i) q^{15} +(5.15639 + 2.97704i) q^{17} +(-1.09489 + 4.21915i) q^{19} +(-3.87354 - 4.46120i) q^{21} +(-3.01506 + 1.74074i) q^{23} +(-0.159737 - 0.276673i) q^{25} +(-4.36276 + 2.82247i) q^{27} +(4.68230 + 8.10997i) q^{29} +4.72348i q^{31} +(3.13725 - 2.72399i) q^{33} +(-6.39103 - 3.68986i) q^{35} +1.54267i q^{37} +(-8.72209 - 3.00889i) q^{39} +(4.63304 - 8.02466i) q^{41} +(-0.248758 + 0.430862i) q^{43} +(-4.00177 + 5.10985i) q^{45} +(7.18941 - 4.15081i) q^{47} +4.63553 q^{49} +(1.96192 + 10.1244i) q^{51} +(-4.46423 - 7.73227i) q^{53} +(2.59482 - 4.49437i) q^{55} +(-6.76135 + 3.35919i) q^{57} +(-0.192159 + 0.332829i) q^{59} +(-1.38846 - 2.40489i) q^{61} +(1.43591 - 10.1320i) q^{63} -11.5245 q^{65} +(4.99235 - 2.88233i) q^{67} +(-5.70045 - 1.96651i) q^{69} +(-0.344463 + 0.596628i) q^{71} +(4.06570 - 7.04199i) q^{73} +(0.180454 - 0.523095i) q^{75} +8.18246i q^{77} +(6.09876 + 3.52112i) q^{79} +(-8.64560 - 2.50073i) q^{81} -1.73935i q^{83} +(6.44069 + 11.1556i) q^{85} +(-5.28956 + 15.3332i) q^{87} +(8.86507 + 15.3547i) q^{89} +(15.7362 - 9.08530i) q^{91} +(-6.17761 + 5.36385i) q^{93} +(-6.61535 + 6.72064i) q^{95} +(-12.3326 - 7.12025i) q^{97} +(7.12515 + 1.00977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * 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
$3$	1.13557	+	1.30785i	0.655623	+	0.755089i
$3$	1.13557	+	1.30785i	0.655623	+	0.755089i
$4$		0			0
$5$	1.87360	+	1.08173i	0.837901	+	0.483763i	0.856550	−	0.516063i	$-0.172603\pi$
$5$	1.87360	+	1.08173i	0.837901	+	0.483763i	−0.0186489	+	0.999826i	$0.505936\pi$
$6$		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
$9$	−0.420952	+	2.97032i	−0.140317	+	0.990107i
$10$		0			0
$11$		−	2.39878i		−	0.723260i	−0.932322	−	0.361630i	$-0.882220\pi$
$11$		−	2.39878i		−	0.723260i	0.932322	−	0.361630i	$-0.117780\pi$
$12$		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
$15$	0.712876	+	3.67877i	0.184064	+	0.949856i
$16$		0			0
$17$	5.15639	+	2.97704i	1.25061	+	0.722039i	0.971230	−	0.238142i	$-0.0765384\pi$
$17$	5.15639	+	2.97704i	1.25061	+	0.722039i	0.279378	+	0.960181i	$0.409872\pi$
$18$		0			0
$19$	−1.09489	+	4.21915i	−0.251185	+	0.967939i
$19$	−1.09489	+	4.21915i	−0.251185	+	0.967939i
$20$		0			0
$21$	−3.87354	−	4.46120i	−0.845275	−	0.973514i
$22$		0			0
$23$	−3.01506	+	1.74074i	−0.628682	+	0.362970i	−0.780242	−	0.625478i	$-0.784904\pi$
$23$	−3.01506	+	1.74074i	−0.628682	+	0.362970i	0.151559	+	0.988448i	$0.451571\pi$
$24$		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	$0.168880\pi$
$29$	4.68230	+	8.10997i	0.869481	+	1.50598i	0.00695209	+	0.999976i	$0.497787\pi$
$30$		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
$33$	3.13725	−	2.72399i	0.546125	−	0.474186i
$34$		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	$-0.575838\pi$
$41$	4.63304	−	8.02466i	0.723559	−	1.25324i	0.959564	−	0.281490i	$-0.0908285\pi$
$42$		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	0.126403	−	0.991979i	$-0.459657\pi$
$47$	7.18941	−	4.15081i	1.04868	−	0.605458i	0.922280	+	0.386521i	$0.126323\pi$
$48$		0			0
$49$	4.63553			0.662219
$50$		0			0
$51$	1.96192	+	10.1244i	0.274724	+	1.41771i
$52$		0			0
$53$	−4.46423	−	7.73227i	−0.613209	−	1.06211i	−0.990696	−	0.136094i	$-0.956545\pi$
$53$	−4.46423	−	7.73227i	−0.613209	−	1.06211i	0.377487	−	0.926015i	$-0.376788\pi$
$54$		0			0
$55$	2.59482	−	4.49437i	0.349886	−	0.606020i
$56$		0			0
$57$	−6.76135	+	3.35919i	−0.895562	+	0.444936i
$58$		0			0
$59$	−0.192159	+	0.332829i	−0.0250169	+	0.0433306i	−0.878263	−	0.478178i	$-0.841297\pi$
$59$	−0.192159	+	0.332829i	−0.0250169	+	0.0433306i	0.853246	+	0.521509i	$0.174631\pi$
$60$		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
$63$	1.43591	−	10.1320i	0.180907	−	1.27652i
$64$		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	−0.885742	−	0.464179i	$-0.846350\pi$
$71$	−0.344463	+	0.596628i	−0.0408803	+	0.0708067i	0.844861	+	0.534985i	$0.179683\pi$
$72$		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
$81$	−8.64560	−	2.50073i	−0.960622	−	0.277858i
$82$		0			0
$83$		−	1.73935i		−	0.190919i	−0.995433	−	0.0954593i	$-0.969568\pi$
$83$		−	1.73935i		−	0.190919i	0.995433	−	0.0954593i	$-0.0304320\pi$
$84$		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	$0.222225\pi$
$89$	8.86507	+	15.3547i	0.939695	+	1.62760i	0.173655	+	0.984806i	$0.444442\pi$
$90$		0			0
$91$	15.7362	−	9.08530i	1.64960	−	0.952398i
$92$		0			0
$93$	−6.17761	+	5.36385i	−0.640589	+	0.556206i
$94$		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
$99$	7.12515	+	1.00977i	0.716104	+	0.101486i
$100$		0			0
$101$	−9.31911	+	5.38039i	−0.927286	+	0.535369i	−0.885952	−	0.463776i	$-0.846494\pi$
$101$	−9.31911	+	5.38039i	−0.927286	+	0.535369i	−0.0413340	+	0.999145i	$0.513161\pi$
$102$		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
$105$	−2.43168	−	12.5486i	−0.237308	−	1.22462i
$106$		0			0
$107$	17.9400			1.73433			0.867165	−	0.498021i	$-0.165940\pi$
$107$	17.9400			1.73433			0.867165	+	0.498021i	$0.165940\pi$
$108$		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
$111$	−2.01758	+	1.75181i	−0.191500	+	0.166275i
$112$		0			0
$113$	−6.20466			−0.583686			−0.291843	−	0.956466i	$-0.594268\pi$
$113$	−6.20466			−0.583686			−0.291843	+	0.956466i	$0.594268\pi$
$114$		0			0
$115$	−7.53203			−0.702365
$116$		0			0
$117$	−5.96937	−	14.8240i	−0.551869	−	1.37048i
$118$		0			0
$119$	−17.5889	−	10.1550i	−1.61237	−	0.930904i
$120$		0			0
$121$	5.24585			0.476895
$122$		0			0
$123$	15.7562	−	3.05325i	1.42069	−	0.275302i
$124$		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
$129$	−0.845986	+	0.163936i	−0.0744849	+	0.0144337i
$130$		0			0
$131$	1.78152	+	1.02856i	0.155652	+	0.0898656i	0.575803	−	0.817589i	$-0.304690\pi$
$131$	1.78152	+	1.02856i	0.155652	+	0.0898656i	−0.420151	+	0.907454i	$0.638023\pi$
$132$		0			0
$133$	3.73477	−	14.3919i	0.323846	−	1.24794i
$134$		0			0
$135$	−11.2272	+	0.568880i	−0.966286	+	0.0489614i
$136$		0			0
$137$	1.98284	−	1.14479i	0.169405	−	0.0978062i	−0.412900	−	0.910776i	$-0.635484\pi$
$137$	1.98284	−	1.14479i	0.169405	−	0.0978062i	0.582305	+	0.812970i	$0.302151\pi$
$138$		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
$147$	5.26398	+	6.06259i	0.434166	+	0.500034i
$148$		0			0
$149$	−2.52225	−	1.45622i	−0.206631	−	0.119298i	0.393114	−	0.919490i	$-0.371398\pi$
$149$	−2.52225	−	1.45622i	−0.206631	−	0.119298i	−0.599745	+	0.800192i	$0.704731\pi$
$150$		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
$165$	8.82458	−	1.71003i	0.686992	−	0.133126i
$166$		0			0
$167$	3.09989	+	5.36917i	0.239877	+	0.415479i	0.960679	−	0.277662i	$-0.0895596\pi$
$167$	3.09989	+	5.36917i	0.239877	+	0.415479i	−0.720802	+	0.693141i	$0.756226\pi$
$168$		0			0
$169$	7.68804	−	13.3161i	0.591388	−	1.02431i
$170$		0			0
$171$	−12.0713	−	5.02823i	−0.923117	−	0.384519i
$172$		0			0
$173$	2.99652	−	5.19012i	0.227821	−	0.394597i	−0.729341	−	0.684150i	$-0.760173\pi$
$173$	2.99652	−	5.19012i	0.227821	−	0.394597i	0.957162	+	0.289553i	$0.0935066\pi$
$174$		0			0
$175$	0.544878	+	0.943756i	0.0411889	+	0.0713413i
$176$		0			0
$177$	−0.653501	+	0.126636i	−0.0491201	+	0.00951853i
$178$		0			0
$179$	8.68090			0.648841			0.324420	−	0.945913i	$-0.394831\pi$
$179$	8.68090			0.648841			0.324420	+	0.945913i	$0.394831\pi$
$180$		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	$-0.983684\pi$
$191$		−	1.41621i		−	0.102473i	0.998687	−	0.0512367i	$-0.0163163\pi$
$192$		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
$195$	−13.0869	−	15.0724i	−0.937176	−	1.07936i
$196$		0			0
$197$		−	8.04107i		−	0.572903i	−0.958095	−	0.286451i	$-0.907524\pi$
$197$		−	8.04107i		−	0.572903i	0.958095	−	0.286451i	$-0.0924757\pi$
$198$		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
$207$	−3.90137	−	9.68845i	−0.271164	−	0.673394i
$208$		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
$213$	−1.17146	+	0.227007i	−0.0802674	+	0.0155543i
$214$		0			0
$215$	−0.932149	+	0.538176i	−0.0635720	+	0.0367033i
$216$		0			0
$217$		−	16.1122i		−	1.09377i
$218$		0			0
$219$	13.8268	−	2.67936i	0.934327	−	0.181055i
$220$		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
$225$	0.889049	−	0.358005i	0.0592699	−	0.0238670i
$226$		0			0
$227$	0.460625			0.0305727			0.0152864	−	0.999883i	$-0.495134\pi$
$227$	0.460625			0.0305727			0.0152864	+	0.999883i	$0.495134\pi$
$228$		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
$231$	−10.7014	+	9.29177i	−0.704103	+	0.611354i
$232$		0			0
$233$	2.41962	+	1.39697i	0.158515	+	0.0915185i	0.577159	−	0.816632i	$-0.304161\pi$
$233$	2.41962	+	1.39697i	0.158515	+	0.0915185i	−0.418644	+	0.908150i	$0.637495\pi$
$234$		0			0
$235$	17.9601			1.17159
$236$		0			0
$237$	2.32048	+	11.9748i	0.150731	+	0.777844i
$238$		0			0
$239$		−	12.5259i		−	0.810233i	−0.914265	−	0.405117i	$-0.867231\pi$
$239$		−	12.5259i		−	0.810233i	0.914265	−	0.405117i	$-0.132769\pi$
$240$		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
$243$	−6.54712	−	14.1469i	−0.419998	−	0.907525i
$244$		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
$249$	2.27481	−	1.97516i	0.144160	−	0.125171i
$250$		0			0
$251$	−8.63458	+	4.98518i	−0.545010	+	0.314661i	−0.747107	−	0.664704i	$-0.768558\pi$
$251$	−8.63458	+	4.98518i	−0.545010	+	0.314661i	0.202097	+	0.979365i	$0.435224\pi$
$252$		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	0.512981	−	0.858400i	$-0.328541\pi$
$257$	−7.80570	−	13.5199i	−0.486906	−	0.843346i	−0.999887	+	0.0150543i	$0.995208\pi$
$258$		0			0
$259$		−	5.26218i		−	0.326976i
$260$		0			0
$261$	−26.0602	+	10.4940i	−1.61309	+	0.649563i
$262$		0			0
$263$	20.3095	+	11.7257i	1.25234	+	0.723037i	0.971573	−	0.236740i	$-0.0760788\pi$
$263$	20.3095	+	11.7257i	1.25234	+	0.723037i	0.280764	+	0.959777i	$0.409412\pi$
$264$		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	$-0.555924\pi$
$269$	12.5518	−	21.7404i	0.765299	−	1.32554i	0.940088	−	0.340931i	$-0.110742\pi$
$270$		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
$279$	−14.0302	−	1.98836i	−0.839969	−	0.119040i
$280$		0			0
$281$	5.36734	+	9.29650i	0.320188	+	0.554583i	0.980527	−	0.196386i	$-0.0629204\pi$
$281$	5.36734	+	9.29650i	0.320188	+	0.554583i	−0.660338	+	0.750968i	$0.729587\pi$
$282$		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
$285$	−16.3018	−	1.02013i	−0.965636	−	0.0604271i
$286$		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
$291$	−4.69236	−	24.2148i	−0.275071	−	1.41950i
$292$		0			0
$293$	13.8101			0.806795			0.403397	−	0.915025i	$-0.367829\pi$
$293$	13.8101			0.806795			0.403397	+	0.915025i	$0.367829\pi$
$294$		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
$309$	15.6652	−	13.6017i	0.891163	−	0.773773i
$310$		0			0
$311$		−	19.5486i		−	1.10850i	−0.832351	−	0.554248i	$-0.813006\pi$
$311$		−	19.5486i		−	1.10850i	0.832351	−	0.554248i	$-0.186994\pi$
$312$		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	0.998000	−	0.0632155i	$-0.0201355\pi$
$317$	7.90971	+	13.7000i	0.444254	+	0.769470i	−0.553746	+	0.832686i	$0.686802\pi$
$318$		0			0
$319$	19.4541	−	11.2318i	1.08922	−	0.628860i
$320$		0			0
$321$	20.3722	+	23.4629i	1.13707	+	1.30957i
$322$		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
$327$	5.28529	+	27.2746i	0.292277	+	1.50829i
$328$		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
$333$	−4.58222	−	0.649390i	−0.251104	−	0.0355864i
$334$		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
$339$	−7.04584	−	8.11478i	−0.382678	−	0.440734i
$340$		0			0
$341$	11.3306			0.613586
$342$		0			0
$343$	8.06541			0.435491
$344$		0			0
$345$	−8.55316	−	9.85078i	−0.460487	−	0.530348i
$346$		0			0
$347$	7.14444	+	4.12484i	0.383534	+	0.221433i	0.679355	−	0.733810i	$-0.262260\pi$
$347$	7.14444	+	4.12484i	0.383534	+	0.221433i	−0.295821	+	0.955243i	$0.595593\pi$
$348$		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
$351$	12.6090	−	24.6408i	0.673016	−	1.31523i
$352$		0			0
$353$		−	28.6305i		−	1.52385i	−0.647668	−	0.761923i	$-0.724255\pi$
$353$		−	28.6305i		−	1.52385i	0.647668	−	0.761923i	$-0.275745\pi$
$354$		0			0
$355$	−1.29078	+	0.745230i	−0.0685073	+	0.0395527i
$356$		0			0
$357$	−6.69229	−	34.5354i	−0.354194	−	1.82781i
$358$		0			0
$359$	−7.22382	−	4.17068i	−0.381259	−	0.220120i	0.297107	−	0.954844i	$-0.403978\pi$
$359$	−7.22382	−	4.17068i	−0.381259	−	0.220120i	−0.678366	+	0.734724i	$0.737312\pi$
$360$		0			0
$361$	−16.6024	−	9.23901i	−0.873812	−	0.486264i
$362$		0			0
$363$	5.95704	+	6.86079i	0.312664	+	0.360098i
$364$		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
$375$	15.0513	−	13.0687i	0.777247	−	0.674862i
$376$		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	−0.732870	−	0.680368i	$-0.761820\pi$
$383$	4.35991	−	7.55159i	0.222781	−	0.385868i	0.955651	+	0.294500i	$0.0951531\pi$
$384$		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	$0.682171\pi$
$389$	−30.3812	+	17.5406i	−1.54039	+	0.889343i	−0.998814	+	0.0486899i	$0.984495\pi$
$390$		0			0
$391$	−20.7291			−1.04831
$392$		0			0
$393$	0.677838	+	3.49796i	0.0341924	+	0.176449i
$394$		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
$399$	23.0636	−	11.4585i	1.15462	−	0.573643i
$400$		0			0
$401$	−14.7129	+	25.4834i	−0.734726	+	1.27258i	0.220118	+	0.975473i	$0.429356\pi$
$401$	−14.7129	+	25.4834i	−0.734726	+	1.27258i	−0.954843	+	0.297109i	$0.903977\pi$
$402$		0			0
$403$	−12.5808	−	21.7906i	−0.626695	−	1.08547i
$404$		0			0
$405$	−13.4933	−	14.0375i	−0.670489	−	0.697531i
$406$		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	$-0.988012\pi$
$419$		−	1.54149i		−	0.0753069i	0.999291	−	0.0376534i	$-0.0119883\pi$
$420$		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
$423$	9.30283	+	23.1021i	0.452319	+	1.12326i
$424$		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	0.996417	−	0.0845782i	$-0.0269543\pi$
$431$	8.82243	+	15.2809i	0.424962	+	0.736055i	−0.571455	+	0.820633i	$0.693621\pi$
$432$		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
$435$	−26.4969	+	23.0065i	−1.27043	+	1.10308i
$436$		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
$441$	−1.95134	+	13.7690i	−0.0929208	+	0.655667i
$442$		0			0
$443$	24.5333	−	14.1643i	1.16561	−	0.672966i	0.212969	−	0.977059i	$-0.431687\pi$
$443$	24.5333	−	14.1643i	1.16561	−	0.672966i	0.952642	+	0.304093i	$0.0983533\pi$
$444$		0			0
$445$			38.3583i			1.81836i
$446$		0			0
$447$	−0.959674	−	4.95237i	−0.0453910	−	0.234239i
$448$		0			0
$449$	25.6491			1.21046			0.605228	−	0.796052i	$-0.293082\pi$
$449$	25.6491			1.21046			0.605228	+	0.796052i	$0.293082\pi$
$450$		0			0
$451$	−19.2494	−	11.1136i	−0.906419	−	0.523321i
$452$		0			0
$453$	8.89569	−	7.72389i	0.417956	−	0.362900i
$454$		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
$459$	−30.8987	+	1.56563i	−1.44223	+	0.0730773i
$460$		0			0
$461$	6.23418	+	3.59931i	0.290355	+	0.167636i	0.638102	−	0.769952i	$-0.279720\pi$
$461$	6.23418	+	3.59931i	0.290355	+	0.167636i	−0.347747	+	0.937588i	$0.613053\pi$
$462$		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
$465$	−17.3766	+	3.36725i	−0.805822	+	0.156153i
$466$		0			0
$467$			29.3832i			1.35969i	0.733354	+	0.679847i	$0.237954\pi$
$467$			29.3832i			1.35969i	−0.733354	+	0.679847i	$0.762046\pi$
$468$		0			0
$469$	−17.0293	+	9.83189i	−0.786342	+	0.453995i
$470$		0			0
$471$	0.526020	−	0.101933i	0.0242377	−	0.00469680i
$472$		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
$477$	24.8465	−	10.0053i	1.13764	−	0.458110i
$478$		0			0
$479$	33.0915	−	19.1054i	1.51199	−	0.872949i	0.512090	−	0.858932i	$-0.328872\pi$
$479$	33.0915	−	19.1054i	1.51199	−	0.872949i	0.999902	−	0.0140167i	$-0.00446181\pi$
$480$		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
$489$	21.6554	+	24.9408i	0.979292	+	1.12786i
$490$		0			0
$491$	−8.95372	−	5.16943i	−0.404076	−	0.233293i	0.284165	−	0.958775i	$-0.408284\pi$
$491$	−8.95372	−	5.16943i	−0.404076	−	0.233293i	−0.688241	+	0.725482i	$0.741617\pi$
$492$		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	$0.677192\pi$
$503$	−34.2652	+	19.7830i	−1.52781	+	0.882082i	−0.999453	+	0.0330599i	$0.989475\pi$
$504$		0			0
$505$	−23.2804			−1.03597
$506$		0			0
$507$	26.1458	−	5.06655i	1.16117	−	0.225013i
$508$		0			0
$509$	4.22536	+	7.31853i	0.187286	+	0.324388i	0.944344	−	0.328959i	$-0.106698\pi$
$509$	4.22536	+	7.31853i	0.187286	+	0.324388i	−0.757059	+	0.653347i	$0.773364\pi$
$510$		0			0
$511$	−13.8685	+	24.0209i	−0.613504	+	1.06262i
$512$		0			0
$513$	−7.13167	−	21.4974i	−0.314871	−	0.949134i
$514$		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
$519$	10.1907	−	1.97475i	0.447321	−	0.0866821i
$520$		0			0
$521$	25.7517			1.12820			0.564101	−	0.825706i	$-0.309223\pi$
$521$	25.7517			1.12820			0.564101	+	0.825706i	$0.309223\pi$
$522$		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
$537$	9.85778	+	11.3533i	0.425395	+	0.489932i
$538$		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
$549$	7.72777	−	3.11184i	0.329813	−	0.132810i
$550$		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
$555$	−5.67513	+	1.09973i	−0.240896	+	0.0466810i
$556$		0			0
$557$	9.79812	−	5.65695i	0.415160	−	0.239693i	−0.277845	−	0.960626i	$-0.589620\pi$
$557$	9.79812	−	5.65695i	0.415160	−	0.239693i	0.693004	+	0.720934i	$0.256287\pi$
$558$		0			0
$559$		−	2.65023i		−	0.112093i
$560$		0			0
$561$	24.2863	−	4.70622i	1.02537	−	0.198697i
$562$		0			0
$563$	−3.55642			−0.149885			−0.0749426	−	0.997188i	$-0.523877\pi$
$563$	−3.55642			−0.149885			−0.0749426	+	0.997188i	$0.523877\pi$
$564$		0			0
$565$	−11.6251	−	6.71175i	−0.489071	−	0.282365i
$566$		0			0
$567$	29.4909	+	8.53020i	1.23850	+	0.358235i
$568$		0			0
$569$	−26.7017			−1.11939			−0.559697	−	0.828697i	$-0.689082\pi$
$569$	−26.7017			−1.11939			−0.559697	+	0.828697i	$0.689082\pi$
$570$		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
$573$	1.85219	−	1.60821i	0.0773765	−	0.0671839i
$574$		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
$579$	0.167735	+	0.865590i	0.00697081	+	0.0359727i
$580$		0			0
$581$			5.93308i			0.246146i
$582$		0			0
$583$	−18.5480	+	10.7087i	−0.768181	+	0.443509i
$584$		0			0
$585$	4.85128	−	34.2316i	0.200576	−	1.41530i
$586$		0			0
$587$	−26.7557	−	15.4474i	−1.10433	−	0.637582i	−0.166972	−	0.985962i	$-0.553399\pi$
$587$	−26.7557	−	15.4474i	−1.10433	−	0.637582i	−0.937354	+	0.348379i	$0.886732\pi$
$588$		0			0
$589$	−19.9291	−	5.17169i	−0.821163	−	0.213096i
$590$		0			0
$591$	10.5165	−	9.13122i	0.432592	−	0.375608i
$592$		0			0
$593$	−29.5805	+	17.0783i	−1.21473	+	0.701323i	−0.963785	−	0.266679i	$-0.914074\pi$
$593$	−29.5805	+	17.0783i	−1.21473	+	0.701323i	−0.250942	+	0.968002i	$0.580740\pi$
$594$		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	0.770432	−	0.637522i	$-0.220040\pi$
$599$	−4.08464	−	7.07481i	−0.166894	−	0.289069i	−0.937326	+	0.348453i	$0.886707\pi$
$600$		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
$603$	6.45991	+	16.0422i	0.263068	+	0.653288i
$604$		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	−0.360783	−	0.932650i	$-0.617491\pi$
$617$	6.62030	−	3.82223i	0.266523	−	0.153877i	0.627307	+	0.778772i	$0.284157\pi$
$618$		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
$621$	8.24077	−	16.1043i	0.330691	−	0.646245i
$622$		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
$627$	8.05797	+	16.2190i	0.321804	+	0.647724i
$628$		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
$633$	1.41208	+	7.28702i	0.0561253	+	0.289633i
$634$		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	−0.639506	−	0.768786i	$-0.720861\pi$
$641$	8.76090	−	15.1743i	0.346035	−	0.599350i	0.985541	+	0.169436i	$0.0541946\pi$
$642$		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	$-0.738122\pi$
$647$		−	37.2892i		−	1.46599i	0.680234	−	0.732995i	$-0.261878\pi$
$648$		0			0
$649$	0.798383	+	0.460947i	0.0313393	+	0.0180937i
$650$		0			0
$651$	21.0724	−	18.2966i	0.825892	−	0.717100i
$652$		0			0
$653$			15.4674i			0.605285i	0.953104	+	0.302643i	$0.0978689\pi$
$653$			15.4674i			0.605285i	−0.953104	+	0.302643i	$0.902131\pi$
$654$		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	$-0.822682\pi$
$659$	−22.6487	−	39.2287i	−0.882268	−	1.52813i	−0.0334547	−	0.999440i	$-0.510651\pi$
$660$		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
$663$	−36.0169	−	41.4811i	−1.39878	−	1.61099i
$664$		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
$669$	−0.0517583	−	0.267097i	−0.00200109	−	0.0103266i
$670$		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
$675$	1.47780	+	0.756204i	0.0568804	+	0.0291063i
$676$		0			0
$677$	42.3867			1.62905			0.814527	−	0.580126i	$-0.196997\pi$
$677$	42.3867			1.62905			0.814527	+	0.580126i	$0.196997\pi$
$678$		0			0
$679$	42.0677	+	24.2878i	1.61441	+	0.932080i
$680$		0			0
$681$	0.523072	+	0.602429i	0.0200442	+	0.0230851i
$682$		0			0
$683$	34.4320			1.31750			0.658752	−	0.752360i	$-0.271085\pi$
$683$	34.4320			1.31750			0.658752	+	0.752360i	$0.271085\pi$
$684$		0			0
$685$	4.95341			0.189260
$686$		0			0
$687$	11.4459	+	13.1824i	0.436689	+	0.502940i
$688$		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
$693$	−24.3045	−	3.44442i	−0.923252	−	0.130843i
$694$		0			0
$695$			34.9412i			1.32539i
$696$		0			0
$697$	47.7795	−	27.5855i	1.80978	−	1.04488i
$698$		0			0
$699$	0.920626	+	4.75086i	0.0348213	+	0.179694i
$700$		0			0
$701$	23.8208	+	13.7529i	0.899699	+	0.519441i	0.877102	−	0.480303i	$-0.159473\pi$
$701$	23.8208	+	13.7529i	0.899699	+	0.519441i	0.0225963	+	0.999745i	$0.492807\pi$
$702$		0			0
$703$	−6.50875	−	1.68905i	−0.245482	−	0.0637039i
$704$		0			0
$705$	20.3950	+	23.4892i	0.768122	+	0.884655i
$706$		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
$717$	16.3820	−	14.2241i	0.611798	−	0.531208i
$718$		0			0
$719$	−27.0486	−	15.6165i	−1.00874	−	0.582398i	−0.0979190	−	0.995194i	$-0.531219\pi$
$719$	−27.0486	−	15.6165i	−1.00874	−	0.582398i	−0.910823	+	0.412797i	$0.864552\pi$
$720$		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
$735$	3.30456	+	17.0531i	0.121890	+	0.629012i
$736$		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
$741$	22.2447	−	33.5054i	0.817180	−	1.23085i
$742$		0			0
$743$	9.64272	−	16.7017i	0.353757	−	0.612725i	−0.633147	−	0.774031i	$-0.718237\pi$
$743$	9.64272	−	16.7017i	0.353757	−	0.612725i	0.986904	+	0.161306i	$0.0515707\pi$
$744$		0			0
$745$	−3.15046	−	5.45676i	−0.115424	−	0.199920i
$746$		0			0
$747$	5.16643	+	0.732183i	0.189030	+	0.0267892i
$748$		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	$-0.880710\pi$
$761$		−	20.1959i		−	0.732101i	0.930595	−	0.366051i	$-0.119290\pi$
$762$		0			0
$763$	−47.3834	−	27.3568i	−1.71539	−	0.990383i
$764$		0			0
$765$	−35.8469	+	14.4349i	−1.29605	+	0.521896i
$766$		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	0.923991	−	0.382415i	$-0.124908\pi$
$773$	3.63700	+	6.29947i	0.130814	+	0.226576i	−0.793177	+	0.608992i	$0.791574\pi$
$774$		0			0
$775$	1.30686	−	0.754516i	0.0469438	−	0.0271030i
$776$		0			0
$777$	6.88216	−	5.97559i	0.246896	−	0.214373i
$778$		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
$783$	−43.3179	−	22.1662i	−1.54805	−	0.792156i
$784$		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
$789$	7.72743	+	39.8772i	0.275104	+	1.41967i
$790$		0			0
$791$	21.1647			0.752529
$792$		0			0
$793$	12.8107	+	7.39624i	0.454920	+	0.262648i
$794$		0			0
$795$	25.2628	−	21.9350i	0.895981	−	0.777956i
$796$		0			0
$797$	3.28414			0.116330			0.0581651	−	0.998307i	$-0.481475\pi$
$797$	3.28414			0.116330			0.0581651	+	0.998307i	$0.481475\pi$
$798$		0			0
$799$	49.4285			1.74866
$800$		0			0
$801$	−49.3403	+	19.8685i	−1.74335	+	0.702018i
$802$		0			0
$803$	−16.8922	−	9.75272i	−0.596113	−	0.344166i
$804$		0			0
$805$	25.6924			0.905539
$806$		0			0
$807$	42.6868	−	8.27187i	1.50265	−	0.291184i
$808$		0			0
$809$		−	10.0754i		−	0.354232i	−0.984190	−	0.177116i	$-0.943323\pi$
$809$		−	10.0754i		−	0.354232i	0.984190	−	0.177116i	$-0.0566768\pi$
$810$		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
$813$	−28.0152	+	5.42881i	−0.982538	+	0.190397i
$814$		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
$819$	20.3621	+	50.5660i	0.711508	+	1.76692i
$820$		0			0
$821$	−3.26277	+	1.88376i	−0.113872	+	0.0657438i	−0.555854	−	0.831280i	$-0.687609\pi$
$821$	−3.26277	+	1.88376i	−0.113872	+	0.0657438i	0.441983	+	0.897024i	$0.354275\pi$
$822$		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	0.652107	−	0.758127i	$-0.273885\pi$
$827$	−9.50448	−	16.4622i	−0.330503	−	0.572448i	−0.982611	+	0.185678i	$0.940552\pi$
$828$		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
$831$	−19.1873	−	22.0983i	−0.665602	−	0.766581i
$832$		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	−0.701591	−	0.712580i	$-0.747527\pi$
$839$	7.71399	−	13.3610i	0.266317	−	0.461274i	0.967908	+	0.251306i	$0.0808600\pi$
$840$		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
$849$	−34.6157	+	6.70785i	−1.18801	+	0.230213i
$850$		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
$855$	−17.1777	−	22.4788i	−0.587465	−	0.768758i
$856$		0			0
$857$	−22.3851	+	38.7721i	−0.764659	+	1.32443i	0.175767	+	0.984432i	$0.443759\pi$
$857$	−22.3851	+	38.7721i	−0.764659	+	1.32443i	−0.940427	+	0.339997i	$0.889574\pi$
$858$		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
$861$	−53.7459	+	10.4149i	−1.83165	+	0.354939i
$862$		0			0
$863$	−18.5718			−0.632190			−0.316095	−	0.948728i	$-0.602372\pi$
$863$	−18.5718			−0.632190			−0.316095	+	0.948728i	$0.602372\pi$
$864$		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
$879$	15.6824	+	18.0616i	0.528953	+	0.609202i
$880$		0			0
$881$		−	17.8174i		−	0.600282i	−0.953895	−	0.300141i	$-0.902966\pi$
$881$		−	17.8174i		−	0.600282i	0.953895	−	0.300141i	$-0.0970338\pi$
$882$		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	$-0.944400\pi$
$887$	−19.1470	−	33.1636i	−0.642894	−	1.11353i	0.341890	−	0.939740i	$-0.388933\pi$
$888$		0			0
$889$	58.5324	−	33.7937i	1.96311	−	1.13340i
$890$		0			0
$891$	−5.99869	+	20.7389i	−0.200964	+	0.694779i
$892$		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
$897$	31.5353	−	6.11093i	1.05293	−	0.204038i
$898$		0			0
$899$	−38.3073	+	22.1167i	−1.27762	+	0.737634i
$900$		0			0
$901$		−	53.1608i		−	1.77104i
$902$		0			0
$903$	2.88573	−	0.559200i	0.0960312	−	0.0186090i
$904$		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
$909$	−12.0586	−	29.9456i	−0.399958	−	0.993234i
$910$		0			0
$911$	−30.4928			−1.01027			−0.505136	−	0.863039i	$-0.668558\pi$
$911$	−30.4928			−1.01027			−0.505136	+	0.863039i	$0.668558\pi$
$912$		0			0
$913$	−4.17232			−0.138084
$914$		0			0
$915$	7.85725	−	6.82224i	0.259753	−	0.225536i
$916$		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
$921$	−0.0146250	−	0.0754719i	−0.000481910	−	0.00248688i
$922$		0			0
$923$		−	3.66986i		−	0.120795i
$924$		0			0
$925$	0.426815	−	0.246422i	0.0140336	−	0.00810230i
$926$		0			0
$927$	35.5780	+	5.04209i	1.16853	+	0.165604i
$928$		0			0
$929$	0.520570	+	0.300551i	0.0170793	+	0.00986077i	0.508515	−	0.861053i	$-0.330195\pi$
$929$	0.520570	+	0.300551i	0.0170793	+	0.00986077i	−0.491436	+	0.870914i	$0.663528\pi$
$930$		0			0
$931$	−5.07540	+	19.5580i	−0.166340	+	0.640988i
$932$		0			0
$933$	25.5666	−	22.1988i	0.837013	−	0.726756i
$934$		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	$-0.888153\pi$
$941$	−23.5445	−	40.7802i	−0.767528	−	1.32940i	0.171372	−	0.985206i	$-0.445180\pi$
$942$		0			0
$943$			32.2597i			1.05052i
$944$		0			0
$945$	38.2971	−	1.94050i	1.24580	−	0.0631245i
$946$		0			0
$947$	20.7806	+	11.9977i	0.675280	+	0.389873i	0.798074	−	0.602559i	$-0.205852\pi$
$947$	20.7806	+	11.9977i	0.675280	+	0.389873i	−0.122794	+	0.992432i	$0.539185\pi$
$948$		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	$0.369982\pi$
$953$	−18.4045	+	31.8775i	−0.596180	+	1.03261i	−0.993379	+	0.114881i	$0.963351\pi$
$954$		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
$963$	−7.55190	+	53.2877i	−0.243357	+	1.71717i
$964$		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
$969$	−44.8646	−	2.80752i	−1.44126	−	0.0901904i
$970$		0			0
$971$	2.19360	−	3.79943i	0.0703961	−	0.121930i	−0.828679	−	0.559724i	$-0.810907\pi$
$971$	2.19360	−	3.79943i	0.0703961	−	0.121930i	0.899075	+	0.437795i	$0.144240\pi$
$972$		0			0
$973$	−27.5457	−	47.7105i	−0.883073	−	1.52953i
$974$		0			0
$975$	0.560762	+	2.89380i	0.0179588	+	0.0926757i
$976$		0			0
$977$	−5.88126			−0.188158			−0.0940791	−	0.995565i	$-0.529991\pi$
$977$	−5.88126			−0.188158			−0.0940791	+	0.995565i	$0.529991\pi$
$978$		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	−0.557840	−	0.829948i	$-0.688370\pi$
$983$	13.7901	−	23.8852i	0.439836	−	0.761819i	0.997676	+	0.0681296i	$0.0217031\pi$
$984$		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
$993$	−11.1640	+	9.69340i	−0.354279	+	0.307611i
$994$		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.n.65.7		16
3.2	odd	2		912.2.bn.o.65.8		16
4.3	odd	2		456.2.bf.d.65.2	yes	16
12.11	even	2		456.2.bf.c.65.1	✓	16
19.12	odd	6		912.2.bn.o.449.8		16
57.50	even	6	inner	912.2.bn.n.449.7		16
76.31	even	6		456.2.bf.c.449.1	yes	16
228.107	odd	6		456.2.bf.d.449.2	yes	16

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

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)

\(f(q)\)	\(=\)	\(q+(1.13557 + 1.30785i) q^{3} +(1.87360 + 1.08173i) q^{5} -3.41109 q^{7} +(-0.420952 + 2.97032i) q^{9} +O(q^{10})\)	\(q+(1.13557 + 1.30785i) q^{3} +(1.87360 + 1.08173i) q^{5} -3.41109 q^{7} +(-0.420952 + 2.97032i) q^{9} -2.39878i q^{11} +(-4.61325 + 2.66346i) q^{13} +(0.712876 + 3.67877i) q^{15} +(5.15639 + 2.97704i) q^{17} +(-1.09489 + 4.21915i) q^{19} +(-3.87354 - 4.46120i) q^{21} +(-3.01506 + 1.74074i) q^{23} +(-0.159737 - 0.276673i) q^{25} +(-4.36276 + 2.82247i) q^{27} +(4.68230 + 8.10997i) q^{29} +4.72348i q^{31} +(3.13725 - 2.72399i) q^{33} +(-6.39103 - 3.68986i) q^{35} +1.54267i q^{37} +(-8.72209 - 3.00889i) q^{39} +(4.63304 - 8.02466i) q^{41} +(-0.248758 + 0.430862i) q^{43} +(-4.00177 + 5.10985i) q^{45} +(7.18941 - 4.15081i) q^{47} +4.63553 q^{49} +(1.96192 + 10.1244i) q^{51} +(-4.46423 - 7.73227i) q^{53} +(2.59482 - 4.49437i) q^{55} +(-6.76135 + 3.35919i) q^{57} +(-0.192159 + 0.332829i) q^{59} +(-1.38846 - 2.40489i) q^{61} +(1.43591 - 10.1320i) q^{63} -11.5245 q^{65} +(4.99235 - 2.88233i) q^{67} +(-5.70045 - 1.96651i) q^{69} +(-0.344463 + 0.596628i) q^{71} +(4.06570 - 7.04199i) q^{73} +(0.180454 - 0.523095i) q^{75} +8.18246i q^{77} +(6.09876 + 3.52112i) q^{79} +(-8.64560 - 2.50073i) q^{81} -1.73935i q^{83} +(6.44069 + 11.1556i) q^{85} +(-5.28956 + 15.3332i) q^{87} +(8.86507 + 15.3547i) q^{89} +(15.7362 - 9.08530i) q^{91} +(-6.17761 + 5.36385i) q^{93} +(-6.61535 + 6.72064i) q^{95} +(-12.3326 - 7.12025i) q^{97} +(7.12515 + 1.00977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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