LMFDB - Embedded newform 804.2.y.a.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.4
Character	$\chi$	$=$	804.121
Dual form			804.2.y.a.505.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{3} +(2.57269 - 1.65337i) q^{5} +(-1.89045 - 0.756823i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{3} +(2.57269 - 1.65337i) q^{5} +(-1.89045 - 0.756823i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.169367 + 3.55545i) q^{11} +(2.55353 - 0.243832i) q^{13} +(-0.435222 + 3.02704i) q^{15} +(-0.606162 - 2.49863i) q^{17} +(6.42715 - 2.57304i) q^{19} +(1.80995 - 0.933095i) q^{21} +(1.00549 + 0.193792i) q^{23} +(1.80804 - 3.95905i) q^{25} +(0.841254 + 0.540641i) q^{27} +(3.05230 - 5.28675i) q^{29} +(-3.48094 - 0.332389i) q^{31} +(-2.79794 - 2.20033i) q^{33} +(-6.11486 + 1.17854i) q^{35} +(-0.624781 - 1.08215i) q^{37} +(-1.48793 + 2.08950i) q^{39} +(2.62871 - 2.50647i) q^{41} +(9.19524 + 2.69996i) q^{43} +(-2.00267 - 2.31121i) q^{45} +(0.669649 + 1.93482i) q^{47} +(-2.06511 - 1.96908i) q^{49} +(2.28529 + 1.17815i) q^{51} +(9.76769 - 2.86805i) q^{53} +(6.31420 + 8.86705i) q^{55} +(-2.26431 + 6.54230i) q^{57} +(-1.86731 - 4.08883i) q^{59} +(-0.101230 + 2.12509i) q^{61} +(-0.480080 + 1.97892i) q^{63} +(6.16629 - 4.84922i) q^{65} +(-2.38416 + 7.83044i) q^{67} +(-0.804912 + 0.632989i) q^{69} +(2.09784 - 8.64742i) q^{71} +(-0.610726 + 12.8207i) q^{73} +(1.80804 + 3.95905i) q^{75} +(2.37067 - 6.84959i) q^{77} +(-2.04169 - 2.86715i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(14.5606 + 7.50653i) q^{83} +(-5.69063 - 5.42600i) q^{85} +(1.99662 + 5.76886i) q^{87} +(-3.38923 - 3.91138i) q^{89} +(-5.01186 - 1.47161i) q^{91} +(2.53073 - 2.41305i) q^{93} +(12.2809 - 17.2461i) q^{95} +(6.88168 + 11.9194i) q^{97} +(3.49516 - 0.673636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{26}{33}\right)$	$1$

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
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$		0			0
$5$	2.57269	−	1.65337i	1.15054	−	0.739409i	0.180795	−	0.983521i	$-0.442133\pi$
$5$	2.57269	−	1.65337i	1.15054	−	0.739409i	0.969747	+	0.244112i	$0.0784965\pi$
$6$		0			0
$7$	−1.89045	−	0.756823i	−0.714524	−	0.286052i	−0.0142219	−	0.999899i	$-0.504527\pi$
$7$	−1.89045	−	0.756823i	−0.714524	−	0.286052i	−0.700302	+	0.713847i	$0.746951\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	0.169367	+	3.55545i	0.0510661	+	1.07201i	0.868406	+	0.495853i	$0.165145\pi$
$11$	0.169367	+	3.55545i	0.0510661	+	1.07201i	−0.817340	+	0.576155i	$0.804552\pi$
$12$		0			0
$13$	2.55353	−	0.243832i	0.708221	−	0.0676269i	0.265272	−	0.964174i	$-0.414538\pi$
$13$	2.55353	−	0.243832i	0.708221	−	0.0676269i	0.442949	+	0.896547i	$0.353932\pi$
$14$		0			0
$15$	−0.435222	+	3.02704i	−0.112374	+	0.781577i
$16$		0			0
$17$	−0.606162	−	2.49863i	−0.147016	−	0.606008i	−0.996875	−	0.0789974i	$-0.974828\pi$
$17$	−0.606162	−	2.49863i	−0.147016	−	0.606008i	0.849859	−	0.527010i	$-0.176687\pi$
$18$		0			0
$19$	6.42715	−	2.57304i	1.47449	−	0.590296i	0.511367	−	0.859362i	$-0.329139\pi$
$19$	6.42715	−	2.57304i	1.47449	−	0.590296i	0.963122	+	0.269066i	$0.0867151\pi$
$20$		0			0
$21$	1.80995	−	0.933095i	0.394964	−	0.203618i
$22$		0			0
$23$	1.00549	+	0.193792i	0.209658	+	0.0404084i	0.292999	−	0.956113i	$-0.405347\pi$
$23$	1.00549	+	0.193792i	0.209658	+	0.0404084i	−0.0833405	+	0.996521i	$0.526559\pi$
$24$		0			0
$25$	1.80804	−	3.95905i	0.361607	−	0.791810i
$26$		0			0
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$		0			0
$29$	3.05230	−	5.28675i	0.566799	−	0.981724i	−0.430081	−	0.902790i	$-0.641515\pi$
$29$	3.05230	−	5.28675i	0.566799	−	0.981724i	0.996880	−	0.0789338i	$-0.0251516\pi$
$30$		0			0
$31$	−3.48094	−	0.332389i	−0.625195	−	0.0596989i	−0.222350	−	0.974967i	$-0.571373\pi$
$31$	−3.48094	−	0.332389i	−0.625195	−	0.0596989i	−0.402845	+	0.915268i	$0.631979\pi$
$32$		0			0
$33$	−2.79794	−	2.20033i	−0.487059	−	0.383027i
$34$		0			0
$35$	−6.11486	+	1.17854i	−1.03360	+	0.199210i
$36$		0			0
$37$	−0.624781	−	1.08215i	−0.102713	−	0.177905i	0.810088	−	0.586308i	$-0.199419\pi$
$37$	−0.624781	−	1.08215i	−0.102713	−	0.177905i	−0.912802	+	0.408403i	$0.866086\pi$
$38$		0			0
$39$	−1.48793	+	2.08950i	−0.238259	+	0.334588i
$40$		0			0
$41$	2.62871	−	2.50647i	0.410535	−	0.391445i	−0.456474	−	0.889737i	$-0.650888\pi$
$41$	2.62871	−	2.50647i	0.410535	−	0.391445i	0.867009	+	0.498292i	$0.166039\pi$
$42$		0			0
$43$	9.19524	+	2.69996i	1.40226	+	0.411741i	0.893460	−	0.449144i	$-0.148271\pi$
$43$	9.19524	+	2.69996i	1.40226	+	0.411741i	0.508801	+	0.860884i	$0.330089\pi$
$44$		0			0
$45$	−2.00267	−	2.31121i	−0.298541	−	0.344534i
$46$		0			0
$47$	0.669649	+	1.93482i	0.0976784	+	0.282223i	0.983245	−	0.182289i	$-0.0583508\pi$
$47$	0.669649	+	1.93482i	0.0976784	+	0.282223i	−0.885567	+	0.464513i	$0.846230\pi$
$48$		0			0
$49$	−2.06511	−	1.96908i	−0.295015	−	0.281297i
$50$		0			0
$51$	2.28529	+	1.17815i	0.320005	+	0.164974i
$52$		0			0
$53$	9.76769	−	2.86805i	1.34170	−	0.393957i	0.469421	−	0.882974i	$-0.344463\pi$
$53$	9.76769	−	2.86805i	1.34170	−	0.393957i	0.872274	+	0.489017i	$0.162644\pi$
$54$		0			0
$55$	6.31420	+	8.86705i	0.851406	+	1.19563i
$56$		0			0
$57$	−2.26431	+	6.54230i	−0.299915	+	0.866548i
$58$		0			0
$59$	−1.86731	−	4.08883i	−0.243102	−	0.532320i	0.748270	−	0.663394i	$-0.230885\pi$
$59$	−1.86731	−	4.08883i	−0.243102	−	0.532320i	−0.991373	+	0.131074i	$0.958157\pi$
$60$		0			0
$61$	−0.101230	+	2.12509i	−0.0129612	+	0.272089i	0.983079	+	0.183183i	$0.0586402\pi$
$61$	−0.101230	+	2.12509i	−0.0129612	+	0.272089i	−0.996040	+	0.0889062i	$0.971663\pi$
$62$		0			0
$63$	−0.480080	+	1.97892i	−0.0604844	+	0.249320i
$64$		0			0
$65$	6.16629	−	4.84922i	0.764834	−	0.601472i
$66$		0			0
$67$	−2.38416	+	7.83044i	−0.291272	+	0.956640i
$67$	−2.38416	+	7.83044i	−0.291272	+	0.956640i
$68$		0			0
$69$	−0.804912	+	0.632989i	−0.0969000	+	0.0762030i
$70$		0			0
$71$	2.09784	−	8.64742i	0.248968	−	1.02626i	−0.700813	−	0.713345i	$-0.747179\pi$
$71$	2.09784	−	8.64742i	0.248968	−	1.02626i	0.949781	−	0.312915i	$-0.101305\pi$
$72$		0			0
$73$	−0.610726	+	12.8207i	−0.0714800	+	1.50055i	0.623671	+	0.781687i	$0.285640\pi$
$73$	−0.610726	+	12.8207i	−0.0714800	+	1.50055i	−0.695151	+	0.718864i	$0.744663\pi$
$74$		0			0
$75$	1.80804	+	3.95905i	0.208774	+	0.457152i
$76$		0			0
$77$	2.37067	−	6.84959i	0.270162	−	0.780583i
$78$		0			0
$79$	−2.04169	−	2.86715i	−0.229708	−	0.322579i	0.683594	−	0.729862i	$-0.260416\pi$
$79$	−2.04169	−	2.86715i	−0.229708	−	0.322579i	−0.913302	+	0.407283i	$0.866476\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	14.5606	+	7.50653i	1.59824	+	0.823949i	0.999739	+	0.0228254i	$0.00726617\pi$
$83$	14.5606	+	7.50653i	1.59824	+	0.823949i	0.598499	+	0.801124i	$0.295764\pi$
$84$		0			0
$85$	−5.69063	−	5.42600i	−0.617235	−	0.588533i
$86$		0			0
$87$	1.99662	+	5.76886i	0.214060	+	0.618487i
$88$		0			0
$89$	−3.38923	−	3.91138i	−0.359258	−	0.414606i	0.547133	−	0.837046i	$-0.315719\pi$
$89$	−3.38923	−	3.91138i	−0.359258	−	0.414606i	−0.906391	+	0.422440i	$0.861174\pi$
$90$		0			0
$91$	−5.01186	−	1.47161i	−0.525385	−	0.154267i
$92$		0			0
$93$	2.53073	−	2.41305i	0.262425	−	0.250221i
$94$		0			0
$95$	12.2809	−	17.2461i	1.25999	−	1.76941i
$96$		0			0
$97$	6.88168	+	11.9194i	0.698729	+	1.21023i	0.968907	+	0.247423i	$0.0795839\pi$
$97$	6.88168	+	11.9194i	0.698729	+	1.21023i	−0.270179	+	0.962810i	$0.587083\pi$
$98$		0			0
$99$	3.49516	−	0.673636i	0.351276	−	0.0677030i
$100$		0			0
$101$	0.224928	+	0.176885i	0.0223811	+	0.0176007i	0.629287	−	0.777173i	$-0.283347\pi$
$101$	0.224928	+	0.176885i	0.0223811	+	0.0176007i	−0.606906	+	0.794774i	$0.707589\pi$
$102$		0			0
$103$	−15.4398	−	1.47432i	−1.52133	−	0.145270i	−0.699348	−	0.714781i	$-0.746526\pi$
$103$	−15.4398	−	1.47432i	−1.52133	−	0.145270i	−0.821983	+	0.569512i	$0.807132\pi$
$104$		0			0
$105$	3.11370	−	5.39308i	0.303866	−	0.526311i
$106$		0			0
$107$	−16.2432	−	10.4389i	−1.57029	−	1.00917i	−0.979282	−	0.202501i	$-0.935093\pi$
$107$	−16.2432	−	10.4389i	−1.57029	−	1.00917i	−0.591010	−	0.806664i	$-0.701271\pi$
$108$		0			0
$109$	−1.47108	+	3.22121i	−0.140904	+	0.308536i	−0.966907	−	0.255129i	$-0.917882\pi$
$109$	−1.47108	+	3.22121i	−0.140904	+	0.308536i	0.826003	+	0.563665i	$0.190609\pi$
$110$		0			0
$111$	1.22698	+	0.236481i	0.116460	+	0.0224458i
$112$		0			0
$113$	−0.983328	+	0.506941i	−0.0925037	+	0.0476890i	−0.503858	−	0.863787i	$-0.668086\pi$
$113$	−0.983328	+	0.506941i	−0.0925037	+	0.0476890i	0.411354	+	0.911476i	$0.365056\pi$
$114$		0			0
$115$	2.90721	−	1.16387i	0.271099	−	0.108532i
$116$		0			0
$117$	−0.604755	−	2.49283i	−0.0559096	−	0.230463i
$118$		0			0
$119$	−0.745103	+	5.18231i	−0.0683035	+	0.475061i
$120$		0			0
$121$	−1.66235	+	0.158735i	−0.151122	+	0.0144304i
$122$		0			0
$123$	0.172825	+	3.62803i	0.0155831	+	0.327129i
$124$		0			0
$125$	0.281866	+	1.96042i	0.0252109	+	0.175345i
$126$		0			0
$127$	−8.55357	−	3.42433i	−0.759007	−	0.303860i	−0.0403128	−	0.999187i	$-0.512835\pi$
$127$	−8.55357	−	3.42433i	−0.759007	−	0.303860i	−0.718694	+	0.695327i	$0.755260\pi$
$128$		0			0
$129$	−8.06210	+	5.18119i	−0.709828	+	0.456179i
$130$		0			0
$131$	−4.18362	+	4.82816i	−0.365525	+	0.421838i	−0.908483	−	0.417922i	$-0.862759\pi$
$131$	−4.18362	+	4.82816i	−0.365525	+	0.421838i	0.542958	+	0.839760i	$0.317304\pi$
$132$		0			0
$133$	−14.0976			−1.22241
$134$		0			0
$135$	3.05816			0.263205
$136$		0			0
$137$	−3.57339	+	4.12391i	−0.305295	+	0.352330i	−0.887579	−	0.460656i	$-0.847614\pi$
$137$	−3.57339	+	4.12391i	−0.305295	+	0.352330i	0.582283	+	0.812986i	$0.302159\pi$
$138$		0			0
$139$	−11.7633	+	7.55982i	−0.997751	+	0.641216i	−0.934195	−	0.356763i	$-0.883880\pi$
$139$	−11.7633	+	7.55982i	−0.997751	+	0.641216i	−0.0635559	+	0.997978i	$0.520244\pi$
$140$		0			0
$141$	−1.90077	−	0.760953i	−0.160074	−	0.0640838i
$142$		0			0
$143$	1.29942	+	9.03764i	0.108663	+	0.755765i
$144$		0			0
$145$	−0.888301	−	18.6477i	−0.0737694	−	1.54861i
$146$		0			0
$147$	2.84049	−	0.271234i	0.234279	−	0.0223710i
$148$		0			0
$149$	1.75081	−	12.1771i	0.143432	−	0.997588i	−0.783241	−	0.621718i	$-0.786435\pi$
$149$	1.75081	−	12.1771i	0.143432	−	0.997588i	0.926672	−	0.375870i	$-0.122656\pi$
$150$		0			0
$151$	1.72840	+	7.12454i	0.140655	+	0.579787i	0.997894	+	0.0648683i	$0.0206627\pi$
$151$	1.72840	+	7.12454i	0.140655	+	0.579787i	−0.857239	+	0.514919i	$0.827822\pi$
$152$		0			0
$153$	−2.38693	+	0.955585i	−0.192972	+	0.0772544i
$154$		0			0
$155$	−9.50494	+	4.90014i	−0.763455	+	0.393588i
$156$		0			0
$157$	−17.7816	−	3.42712i	−1.41913	−	0.273514i	−0.578744	−	0.815509i	$-0.696457\pi$
$157$	−17.7816	−	3.42712i	−1.41913	−	0.273514i	−0.840382	+	0.541995i	$0.817669\pi$
$158$		0			0
$159$	−4.22895	+	9.26010i	−0.335377	+	0.734374i
$160$		0			0
$161$	−1.75416	−	1.12733i	−0.138247	−	0.0888460i
$162$		0			0
$163$	−5.58141	+	9.66729i	−0.437170	+	0.757200i	−0.997470	−	0.0710893i	$-0.977352\pi$
$163$	−5.58141	+	9.66729i	−0.437170	+	0.757200i	0.560300	+	0.828290i	$0.310686\pi$
$164$		0			0
$165$	−10.8362	−	1.03473i	−0.843596	−	0.0805536i
$166$		0			0
$167$	−15.2352	−	11.9811i	−1.17894	−	0.927126i	−0.180531	−	0.983569i	$-0.557782\pi$
$167$	−15.2352	−	11.9811i	−1.17894	−	0.927126i	−0.998406	+	0.0564429i	$0.982024\pi$
$168$		0			0
$169$	−6.30403	+	1.21500i	−0.484926	+	0.0934617i
$170$		0			0
$171$	−3.46153	−	5.99555i	−0.264710	−	0.458491i
$172$		0			0
$173$	−6.17094	+	8.66588i	−0.469168	+	0.658855i	−0.979575	−	0.201078i	$-0.935555\pi$
$173$	−6.17094	+	8.66588i	−0.469168	+	0.658855i	0.510407	+	0.859933i	$0.329495\pi$
$174$		0			0
$175$	−6.41431	+	6.11603i	−0.484876	+	0.462328i
$176$		0			0
$177$	4.31296	+	1.26640i	0.324182	+	0.0951883i
$178$		0			0
$179$	−2.89504	−	3.34105i	−0.216385	−	0.249722i	0.637171	−	0.770722i	$-0.280104\pi$
$179$	−2.89504	−	3.34105i	−0.216385	−	0.249722i	−0.853556	+	0.521000i	$0.825559\pi$
$180$		0			0
$181$	3.38741	+	9.78729i	0.251785	+	0.727484i	0.998084	+	0.0618733i	$0.0197075\pi$
$181$	3.38741	+	9.78729i	0.251785	+	0.727484i	−0.746299	+	0.665610i	$0.768171\pi$
$182$		0			0
$183$	−1.53974	−	1.46814i	−0.113821	−	0.108528i
$184$		0			0
$185$	−3.39656	−	1.75105i	−0.249720	−	0.128740i
$186$		0			0
$187$	8.78110	−	2.57836i	0.642138	−	0.188549i
$188$		0			0
$189$	−1.18118	−	1.65874i	−0.0859182	−	0.120655i
$190$		0			0
$191$	1.78567	−	5.15934i	0.129206	−	0.373317i	−0.861780	−	0.507283i	$-0.830650\pi$
$191$	1.78567	−	5.15934i	0.129206	−	0.373317i	0.990986	+	0.133966i	$0.0427712\pi$
$192$		0			0
$193$	3.17107	+	6.94368i	0.228259	+	0.499817i	0.988759	−	0.149521i	$-0.0477732\pi$
$193$	3.17107	+	6.94368i	0.228259	+	0.499817i	−0.760500	+	0.649338i	$0.775046\pi$
$194$		0			0
$195$	−0.373262	+	7.83574i	−0.0267299	+	0.561129i
$196$		0			0
$197$	1.92033	−	7.91572i	0.136818	−	0.563972i	−0.861592	−	0.507602i	$-0.830532\pi$
$197$	1.92033	−	7.91572i	0.136818	−	0.563972i	0.998410	−	0.0563701i	$-0.0179527\pi$
$198$		0			0
$199$	15.8017	−	12.4266i	1.12015	−	0.880896i	0.126341	−	0.991987i	$-0.459677\pi$
$199$	15.8017	−	12.4266i	1.12015	−	0.880896i	0.993810	+	0.111091i	$0.0354344\pi$
$200$		0			0
$201$	−4.35656	−	6.92968i	−0.307288	−	0.488782i
$202$		0			0
$203$	−9.77137	+	7.68429i	−0.685815	+	0.539331i
$204$		0			0
$205$	2.61874	−	10.7946i	0.182901	−	0.753927i
$206$		0			0
$207$	0.0487235	−	1.02283i	0.00338652	−	0.0710917i
$208$		0			0
$209$	10.2369	+	22.4156i	0.708099	+	1.55052i
$210$		0			0
$211$	−1.60603	+	4.64033i	−0.110564	+	0.319453i	−0.986686	−	0.162635i	$-0.948001\pi$
$211$	−1.60603	+	4.64033i	−0.110564	+	0.319453i	0.876122	+	0.482089i	$0.160122\pi$
$212$		0			0
$213$	5.16149	+	7.24829i	0.353659	+	0.496645i
$214$		0			0
$215$	28.1205	−	8.25693i	1.91780	−	0.563118i
$216$		0			0
$217$	6.32899	+	3.26282i	0.429640	+	0.221495i
$218$		0			0
$219$	−9.28931	−	8.85733i	−0.627713	−	0.598523i
$220$		0			0
$221$	−2.15710	−	6.23252i	−0.145102	−	0.419245i
$222$		0			0
$223$	10.3612	+	11.9574i	0.693836	+	0.800730i	0.987906	−	0.155054i	$-0.0495553\pi$
$223$	10.3612	+	11.9574i	0.693836	+	0.800730i	−0.294070	+	0.955784i	$0.595010\pi$
$224$		0			0
$225$	−4.17606	−	1.22620i	−0.278404	−	0.0817468i
$226$		0			0
$227$	2.89773	−	2.76298i	0.192329	−	0.183385i	−0.587796	−	0.809009i	$-0.700004\pi$
$227$	2.89773	−	2.76298i	0.192329	−	0.183385i	0.780125	+	0.625624i	$0.215156\pi$
$228$		0			0
$229$	5.30175	−	7.44526i	0.350349	−	0.491997i	−0.601368	−	0.798972i	$-0.705377\pi$
$229$	5.30175	−	7.44526i	0.350349	−	0.491997i	0.951718	+	0.306975i	$0.0993169\pi$
$230$		0			0
$231$	3.62412	+	6.27716i	0.238450	+	0.413007i
$232$		0			0
$233$	−22.6302	+	4.36161i	−1.48255	+	0.285739i	−0.865391	−	0.501098i	$-0.832930\pi$
$233$	−22.6302	+	4.36161i	−1.48255	+	0.285739i	−0.617162	+	0.786836i	$0.711718\pi$
$234$		0			0
$235$	4.92178	+	3.87053i	0.321061	+	0.252485i
$236$		0			0
$237$	3.50387	+	0.334579i	0.227601	+	0.0217332i
$238$		0			0
$239$	−14.7538	+	25.5543i	−0.954345	+	1.65297i	−0.218483	+	0.975841i	$0.570111\pi$
$239$	−14.7538	+	25.5543i	−0.954345	+	1.65297i	−0.735861	+	0.677133i	$0.763222\pi$
$240$		0			0
$241$	−0.126028	−	0.0809932i	−0.00811817	−	0.00521723i	0.536575	−	0.843852i	$-0.319718\pi$
$241$	−0.126028	−	0.0809932i	−0.00811817	−	0.00521723i	−0.544694	+	0.838635i	$0.683354\pi$
$242$		0			0
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$		0			0
$245$	−8.56849	−	1.65144i	−0.547421	−	0.105507i
$246$		0			0
$247$	15.7845	−	8.13747i	1.00434	−	0.517775i
$248$		0			0
$249$	−15.2083	+	6.08847i	−0.963784	+	0.385841i
$250$		0			0
$251$	−2.18285	−	8.99782i	−0.137780	−	0.567938i	−0.998287	−	0.0584994i	$-0.981368\pi$
$251$	−2.18285	−	8.99782i	−0.137780	−	0.567938i	0.860507	−	0.509438i	$-0.170147\pi$
$252$		0			0
$253$	−0.518720	+	3.60778i	−0.0326117	+	0.226819i
$254$		0			0
$255$	7.82727	−	0.747413i	0.490162	−	0.0468048i
$256$		0			0
$257$	0.238442	+	5.00552i	0.0148736	+	0.312236i	0.994028	+	0.109121i	$0.0348035\pi$
$257$	0.238442	+	5.00552i	0.0148736	+	0.312236i	−0.979155	+	0.203115i	$0.934893\pi$
$258$		0			0
$259$	0.362121	+	2.51861i	0.0225011	+	0.156499i
$260$		0			0
$261$	−5.66732	−	2.26885i	−0.350798	−	0.140438i
$262$		0			0
$263$	8.42362	−	5.41353i	0.519423	−	0.333813i	−0.254521	−	0.967067i	$-0.581918\pi$
$263$	8.42362	−	5.41353i	0.519423	−	0.333813i	0.773943	+	0.633255i	$0.218281\pi$
$264$		0			0
$265$	20.3873	−	23.5282i	1.25238	−	1.44533i
$266$		0			0
$267$	5.17550			0.316736
$268$		0			0
$269$	−6.28627			−0.383281			−0.191640	−	0.981465i	$-0.561381\pi$
$269$	−6.28627			−0.383281			−0.191640	+	0.981465i	$0.561381\pi$
$270$		0			0
$271$	7.77854	−	8.97692i	0.472513	−	0.545309i	−0.468596	−	0.883413i	$-0.655240\pi$
$271$	7.77854	−	8.97692i	0.472513	−	0.545309i	0.941109	+	0.338104i	$0.109785\pi$
$272$		0			0
$273$	4.39424	−	2.82401i	0.265952	−	0.170917i
$274$		0			0
$275$	14.3824	+	5.75785i	0.867293	+	0.347212i
$276$		0			0
$277$	1.46439	+	10.1851i	0.0879868	+	0.611962i	0.985334	+	0.170637i	$0.0545824\pi$
$277$	1.46439	+	10.1851i	0.0879868	+	0.611962i	−0.897347	+	0.441325i	$0.854509\pi$
$278$		0			0
$279$	0.166383	+	3.49281i	0.00996109	+	0.209109i
$280$		0			0
$281$	25.8039	−	2.46397i	1.53933	−	0.146988i	0.709381	−	0.704825i	$-0.248975\pi$
$281$	25.8039	−	2.46397i	1.53933	−	0.146988i	0.829950	+	0.557837i	$0.188369\pi$
$282$		0			0
$283$	−3.01000	+	20.9350i	−0.178926	+	1.24446i	0.680328	+	0.732908i	$0.261837\pi$
$283$	−3.01000	+	20.9350i	−0.178926	+	1.24446i	−0.859254	+	0.511549i	$0.829072\pi$
$284$		0			0
$285$	4.99145	+	20.5750i	0.295668	+	1.21876i
$286$		0			0
$287$	−6.86640	+	2.74889i	−0.405311	+	0.162262i
$288$		0			0
$289$	9.23447	−	4.76070i	0.543204	−	0.280041i
$290$		0			0
$291$	−13.5146	−	2.60473i	−0.792242	−	0.152692i
$292$		0			0
$293$	0.457977	−	1.00283i	0.0267553	−	0.0585859i	−0.895783	−	0.444492i	$-0.853384\pi$
$293$	0.457977	−	1.00283i	0.0267553	−	0.0585859i	0.922538	+	0.385907i	$0.126111\pi$
$294$		0			0
$295$	−11.5643	−	7.43195i	−0.673302	−	0.432705i
$296$		0			0
$297$	−1.77974	+	3.08260i	−0.103271	+	0.178871i
$298$		0			0
$299$	2.61479	+	0.249682i	0.151217	+	0.0144395i
$300$		0			0
$301$	−15.3398	−	12.0633i	−0.884169	−	0.695318i
$302$		0			0
$303$	−0.280977	+	0.0541539i	−0.0161417	+	0.00311106i
$304$		0			0
$305$	3.25312	+	5.63456i	0.186273	+	0.322634i
$306$		0			0
$307$	−8.39346	+	11.7870i	−0.479040	+	0.672718i	−0.981407	−	0.191937i	$-0.938523\pi$
$307$	−8.39346	+	11.7870i	−0.479040	+	0.672718i	0.502367	+	0.864654i	$0.332463\pi$
$308$		0			0
$309$	11.2252	−	10.7032i	0.638577	−	0.608882i
$310$		0			0
$311$	7.38303	+	2.16785i	0.418653	+	0.122928i	0.484273	−	0.874917i	$-0.339084\pi$
$311$	7.38303	+	2.16785i	0.418653	+	0.122928i	−0.0656197	+	0.997845i	$0.520902\pi$
$312$		0			0
$313$	−16.3664	−	18.8878i	−0.925083	−	1.06760i	−0.997531	−	0.0702303i	$-0.977627\pi$
$313$	−16.3664	−	18.8878i	−0.925083	−	1.06760i	0.0724480	−	0.997372i	$-0.476919\pi$
$314$		0			0
$315$	2.03678	+	5.88489i	0.114760	+	0.331576i
$316$		0			0
$317$	3.99229	+	3.80664i	0.224229	+	0.213802i	0.793863	−	0.608096i	$-0.208067\pi$
$317$	3.99229	+	3.80664i	0.224229	+	0.213802i	−0.569634	+	0.821898i	$0.692915\pi$
$318$		0			0
$319$	19.3137	+	9.95691i	1.08136	+	0.557480i
$320$		0			0
$321$	18.5262	−	5.43979i	1.03403	−	0.303620i
$322$		0			0
$323$	−10.3250	−	14.4994i	−0.574497	−	0.806768i
$324$		0			0
$325$	3.65153	−	10.5504i	0.202550	−	0.585230i
$326$		0			0
$327$	−1.47108	−	3.22121i	−0.0813507	−	0.178133i
$328$		0			0
$329$	0.198380	−	4.16450i	0.0109370	−	0.229596i
$330$		0			0
$331$	1.45559	−	6.00001i	0.0800063	−	0.329790i	−0.917717	−	0.397235i	$-0.869970\pi$
$331$	1.45559	−	6.00001i	0.0800063	−	0.329790i	0.997723	+	0.0674451i	$0.0214848\pi$
$332$		0			0
$333$	−0.982222	+	0.772428i	−0.0538254	+	0.0423288i
$334$		0			0
$335$	6.81288	+	24.0872i	0.372228	+	1.31602i
$336$		0			0
$337$	−11.5998	+	9.12215i	−0.631879	+	0.496915i	−0.881969	−	0.471308i	$-0.843782\pi$
$337$	−11.5998	+	9.12215i	−0.631879	+	0.496915i	0.250090	+	0.968223i	$0.419540\pi$
$338$		0			0
$339$	0.260823	−	1.07513i	0.0141659	−	0.0583928i
$340$		0			0
$341$	0.592237	−	12.4326i	0.0320715	−	0.673263i
$342$		0			0
$343$	8.33517	+	18.2515i	0.450057	+	0.985487i
$344$		0			0
$345$	−1.02422	+	2.95930i	−0.0551424	+	0.159323i
$346$		0			0
$347$	−4.08520	−	5.73687i	−0.219305	−	0.307971i	0.690236	−	0.723584i	$-0.257507\pi$
$347$	−4.08520	−	5.73687i	−0.219305	−	0.307971i	−0.909542	+	0.415613i	$0.863567\pi$
$348$		0			0
$349$	−23.8895	+	7.01460i	−1.27878	+	0.375483i	−0.849451	−	0.527667i	$-0.823067\pi$
$349$	−23.8895	+	7.01460i	−1.27878	+	0.375483i	−0.429325	+	0.903150i	$0.641249\pi$
$350$		0			0
$351$	2.27999	+	1.17542i	0.121697	+	0.0627391i
$352$		0			0
$353$	−17.1329	−	16.3362i	−0.911893	−	0.869488i	0.0799705	−	0.996797i	$-0.474517\pi$
$353$	−17.1329	−	16.3362i	−0.911893	−	0.869488i	−0.991863	+	0.127309i	$0.959366\pi$
$354$		0			0
$355$	−8.90027	−	25.7156i	−0.472377	−	1.36484i
$356$		0			0
$357$	−3.42859	−	3.95680i	−0.181460	−	0.209416i
$358$		0			0
$359$	−26.8531	−	7.88479i	−1.41725	−	0.416143i	−0.518681	−	0.854968i	$-0.673577\pi$
$359$	−26.8531	−	7.88479i	−1.41725	−	0.416143i	−0.898573	+	0.438824i	$0.855395\pi$
$360$		0			0
$361$	20.9367	−	19.9631i	1.10193	−	1.05069i
$362$		0			0
$363$	0.968642	−	1.36027i	0.0508405	−	0.0713955i
$364$		0			0
$365$	19.6261	+	33.9935i	1.02728	+	1.77930i
$366$		0			0
$367$	−10.2880	+	1.98285i	−0.537029	+	0.103504i	−0.450552	−	0.892750i	$-0.648773\pi$
$367$	−10.2880	+	1.98285i	−0.537029	+	0.103504i	−0.0864767	+	0.996254i	$0.527561\pi$
$368$		0			0
$369$	−2.85506	−	2.24524i	−0.148629	−	0.116883i
$370$		0			0
$371$	−20.6360	−	1.97050i	−1.07137	−	0.102303i
$372$		0			0
$373$	−3.77214	+	6.53353i	−0.195314	+	0.338294i	−0.947003	−	0.321224i	$-0.895906\pi$
$373$	−3.77214	+	6.53353i	−0.195314	+	0.338294i	0.751689	+	0.659517i	$0.229239\pi$
$374$		0			0
$375$	−1.66617	−	1.07078i	−0.0860407	−	0.0552950i
$376$		0			0
$377$	6.50506	−	14.2441i	0.335028	−	0.733608i
$378$		0			0
$379$	−13.9186	−	2.68260i	−0.714953	−	0.137796i	−0.181212	−	0.983444i	$-0.558002\pi$
$379$	−13.9186	−	2.68260i	−0.714953	−	0.137796i	−0.533741	+	0.845648i	$0.679214\pi$
$380$		0			0
$381$	8.18933	−	4.22190i	0.419552	−	0.216294i
$382$		0			0
$383$	−11.0428	+	4.42086i	−0.564259	+	0.225895i	−0.636214	−	0.771513i	$-0.719500\pi$
$383$	−11.0428	+	4.42086i	−0.564259	+	0.225895i	0.0719551	+	0.997408i	$0.477076\pi$
$384$		0			0
$385$	−5.22590	−	21.5415i	−0.266337	−	1.09785i
$386$		0			0
$387$	1.36386	−	9.48589i	0.0693291	−	0.482195i
$388$		0			0
$389$	30.2543	−	2.88893i	1.53395	−	0.146475i	0.706380	−	0.707833i	$-0.250327\pi$
$389$	30.2543	−	2.88893i	1.53395	−	0.146475i	0.827573	+	0.561359i	$0.189721\pi$
$390$		0			0
$391$	−0.125273	−	2.62981i	−0.00633535	−	0.132995i
$392$		0			0
$393$	−0.909188	−	6.32354i	−0.0458624	−	0.318980i
$394$		0			0
$395$	−9.99308	−	4.00063i	−0.502806	−	0.201293i
$396$		0			0
$397$	−21.4877	+	13.8093i	−1.07844	+	0.693068i	−0.954195	−	0.299184i	$-0.903286\pi$
$397$	−21.4877	+	13.8093i	−1.07844	+	0.693068i	−0.124240	+	0.992252i	$0.539649\pi$
$398$		0			0
$399$	9.23193	−	10.6542i	0.462175	−	0.533378i
$400$		0			0
$401$	14.1158			0.704908			0.352454	−	0.935829i	$-0.385347\pi$
$401$	14.1158			0.704908			0.352454	+	0.935829i	$0.385347\pi$
$402$		0			0
$403$	−8.96971			−0.446813
$404$		0			0
$405$	−2.00267	+	2.31121i	−0.0995135	+	0.114845i
$406$		0			0
$407$	3.74172	−	2.40466i	0.185470	−	0.119194i
$408$		0			0
$409$	6.43371	+	2.57567i	0.318127	+	0.127359i	0.525230	−	0.850960i	$-0.323979\pi$
$409$	6.43371	+	2.57567i	0.318127	+	0.127359i	−0.207103	+	0.978319i	$0.566404\pi$
$410$		0			0
$411$	−0.776572	−	5.40118i	−0.0383055	−	0.266420i
$412$		0			0
$413$	0.435533	+	9.14296i	0.0214312	+	0.449895i
$414$		0			0
$415$	49.8711	−	4.76211i	2.44808	−	0.233763i
$416$		0			0
$417$	1.99000	−	13.8407i	0.0974507	−	0.677784i
$418$		0			0
$419$	4.56254	+	18.8071i	0.222895	+	0.918785i	0.967821	+	0.251638i	$0.0809693\pi$
$419$	4.56254	+	18.8071i	0.222895	+	0.918785i	−0.744927	+	0.667146i	$0.767516\pi$
$420$		0			0
$421$	36.0092	−	14.4159i	1.75498	−	0.702588i	0.756141	−	0.654408i	$-0.227082\pi$
$421$	36.0092	−	14.4159i	1.75498	−	0.702588i	0.998839	−	0.0481796i	$-0.0153420\pi$
$422$		0			0
$423$	1.81983	−	0.938187i	0.0884831	−	0.0456162i
$424$		0			0
$425$	−10.9882	−	2.11780i	−0.533005	−	0.102728i
$426$		0			0
$427$	1.79969	−	3.94076i	0.0870929	−	0.190707i
$428$		0			0
$429$	−7.68113	−	4.93636i	−0.370848	−	0.238330i
$430$		0			0
$431$	11.8973	−	20.6067i	0.573072	−	0.992589i	−0.423176	−	0.906047i	$-0.639085\pi$
$431$	11.8973	−	20.6067i	0.573072	−	0.992589i	0.996248	−	0.0865421i	$-0.0275817\pi$
$432$		0			0
$433$	20.5012	+	1.95763i	0.985226	+	0.0940777i	0.575214	−	0.818003i	$-0.304919\pi$
$433$	20.5012	+	1.95763i	0.985226	+	0.0940777i	0.410011	+	0.912080i	$0.365525\pi$
$434$		0			0
$435$	14.6747	+	11.5403i	0.703600	+	0.553317i
$436$		0			0
$437$	6.96104	−	1.34163i	0.332992	−	0.0641789i
$438$		0			0
$439$	7.55590	+	13.0872i	0.360623	+	0.624618i	0.988064	−	0.154047i	$-0.0492307\pi$
$439$	7.55590	+	13.0872i	0.360623	+	0.624618i	−0.627440	+	0.778665i	$0.715897\pi$
$440$		0			0
$441$	−1.65514	+	2.32432i	−0.0788161	+	0.110682i
$442$		0			0
$443$	16.8401	−	16.0570i	0.800099	−	0.762893i	−0.175022	−	0.984564i	$-0.556000\pi$
$443$	16.8401	−	16.0570i	0.800099	−	0.762893i	0.975121	+	0.221672i	$0.0711513\pi$
$444$		0			0
$445$	−15.1864	−	4.45913i	−0.719905	−	0.211383i
$446$		0			0
$447$	8.05632	+	9.29749i	0.381051	+	0.439756i
$448$		0			0
$449$	12.2095	+	35.2769i	0.576200	+	1.66482i	0.735447	+	0.677582i	$0.236972\pi$
$449$	12.2095	+	35.2769i	0.576200	+	1.66482i	−0.159247	+	0.987239i	$0.550907\pi$
$450$		0			0
$451$	9.35684	+	8.92173i	0.440596	+	0.420108i
$452$		0			0
$453$	−6.51623	−	3.35935i	−0.306159	−	0.157836i
$454$		0			0
$455$	−15.3271	+	4.50044i	−0.718545	+	0.210984i
$456$		0			0
$457$	21.1271	+	29.6689i	0.988285	+	1.38785i	0.920758	+	0.390134i	$0.127571\pi$
$457$	21.1271	+	29.6689i	0.988285	+	1.38785i	0.0675268	+	0.997717i	$0.478489\pi$
$458$		0			0
$459$	0.840927	−	2.42970i	0.0392511	−	0.113409i
$460$		0			0
$461$	4.49276	+	9.83776i	0.209249	+	0.458190i	0.984934	−	0.172929i	$-0.0553231\pi$
$461$	4.49276	+	9.83776i	0.209249	+	0.458190i	−0.775686	+	0.631119i	$0.782596\pi$
$462$		0			0
$463$	−0.821022	+	17.2354i	−0.0381561	+	0.800996i	0.895983	+	0.444088i	$0.146472\pi$
$463$	−0.821022	+	17.2354i	−0.0381561	+	0.800996i	−0.934139	+	0.356908i	$0.883831\pi$
$464$		0			0
$465$	2.52113	−	10.3923i	0.116915	−	0.481929i
$466$		0			0
$467$	−6.35828	+	5.00021i	−0.294226	+	0.231382i	−0.754349	−	0.656473i	$-0.772048\pi$
$467$	−6.35828	+	5.00021i	−0.294226	+	0.231382i	0.460123	+	0.887855i	$0.347805\pi$
$468$		0			0
$469$	10.4334	−	12.9987i	0.481770	−	0.600224i
$470$		0			0
$471$	14.2345	−	11.1941i	0.655892	−	0.515799i
$472$		0			0
$473$	−8.04222	+	33.1505i	−0.369782	+	1.52426i
$474$		0			0
$475$	1.43372	−	30.0975i	0.0657837	−	1.38097i
$476$		0			0
$477$	−4.22895	−	9.26010i	−0.193630	−	0.423991i
$478$		0			0
$479$	10.3181	−	29.8122i	0.471447	−	1.36216i	−0.419379	−	0.907811i	$-0.637752\pi$
$479$	10.3181	−	29.8122i	0.471447	−	1.36216i	0.890826	−	0.454345i	$-0.150126\pi$
$480$		0			0
$481$	−1.85926	−	2.61096i	−0.0847749	−	0.119050i
$482$		0			0
$483$	2.00071	−	0.587461i	0.0910354	−	0.0267304i
$484$		0			0
$485$	37.4116	+	19.2870i	1.69877	+	0.875779i
$486$		0			0
$487$	31.0961	+	29.6500i	1.40910	+	1.34357i	0.862387	+	0.506249i	$0.168969\pi$
$487$	31.0961	+	29.6500i	1.40910	+	1.34357i	0.546710	+	0.837322i	$0.315880\pi$
$488$		0			0
$489$	−3.65100	−	10.5489i	−0.165104	−	0.477037i
$490$		0			0
$491$	−19.7565	−	22.8002i	−0.891598	−	1.02896i	−0.999395	−	0.0347859i	$-0.988925\pi$
$491$	−19.7565	−	22.8002i	−0.891598	−	1.02896i	0.107797	−	0.994173i	$-0.465620\pi$
$492$		0			0
$493$	−15.0598	−	4.42196i	−0.678261	−	0.199155i
$494$		0			0
$495$	7.87819	−	7.51184i	0.354098	−	0.337632i
$496$		0			0
$497$	−10.5104	+	14.7598i	−0.471457	+	0.662069i
$498$		0			0
$499$	−11.2582	−	19.4998i	−0.503987	−	0.872930i	−0.999989	−	0.00460936i	$-0.998533\pi$
$499$	−11.2582	−	19.4998i	−0.503987	−	0.872930i	0.496003	−	0.868321i	$-0.334801\pi$
$500$		0			0
$501$	19.0317	−	3.66805i	0.850272	−	0.163877i
$502$		0			0
$503$	23.6918	+	18.6315i	1.05637	+	0.830736i	0.985993	−	0.166784i	$-0.0533383\pi$
$503$	23.6918	+	18.6315i	1.05637	+	0.830736i	0.0703739	+	0.997521i	$0.477581\pi$
$504$		0			0
$505$	0.871125	+	0.0831824i	0.0387646	+	0.00370157i
$506$		0			0
$507$	3.21003	−	5.55993i	0.142562	−	0.246925i
$508$		0			0
$509$	34.3255	+	22.0597i	1.52145	+	0.977778i	0.991551	+	0.129719i	$0.0414075\pi$
$509$	34.3255	+	22.0597i	1.52145	+	0.977778i	0.529901	+	0.848059i	$0.322229\pi$
$510$		0			0
$511$	10.8576	−	23.7747i	0.480310	−	1.05173i
$512$		0			0
$513$	6.79795	+	1.31020i	0.300137	+	0.0578466i
$514$		0			0
$515$	−42.1595	+	21.7347i	−1.85777	+	0.957747i
$516$		0			0
$517$	−6.76575	+	2.70860i	−0.297558	+	0.119124i
$518$		0			0
$519$	−2.50813	−	10.3386i	−0.110094	−	0.453816i
$520$		0			0
$521$	−3.35277	+	23.3191i	−0.146888	+	1.02163i	0.774387	+	0.632713i	$0.218059\pi$
$521$	−3.35277	+	23.3191i	−0.146888	+	1.02163i	−0.921274	+	0.388914i	$0.872850\pi$
$522$		0			0
$523$	2.44896	−	0.233847i	0.107085	−	0.0102254i	−0.0413758	−	0.999144i	$-0.513174\pi$
$523$	2.44896	−	0.233847i	0.107085	−	0.0102254i	0.148461	+	0.988918i	$0.452568\pi$
$524$		0			0
$525$	−0.421709	−	8.85276i	−0.0184049	−	0.386366i
$526$		0			0
$527$	1.27949	+	8.89907i	0.0557356	+	0.387649i
$528$		0			0
$529$	−20.3790	−	8.15853i	−0.886044	−	0.354719i
$530$		0			0
$531$	−3.78146	+	2.43020i	−0.164102	+	0.105462i
$532$		0			0
$533$	6.10132	−	7.04130i	0.264277	−	0.304992i
$534$		0			0
$535$	−59.0481			−2.55287
$536$		0			0
$537$	4.42085			0.190774
$538$		0			0
$539$	6.65119	−	7.67588i	0.286487	−	0.330624i
$540$		0			0
$541$	−19.9671	+	12.8321i	−0.858453	+	0.551694i	−0.894200	−	0.447667i	$-0.852255\pi$
$541$	−19.9671	+	12.8321i	−0.858453	+	0.551694i	0.0357476	+	0.999361i	$0.488619\pi$
$542$		0			0
$543$	−9.61503	−	3.84928i	−0.412620	−	0.165188i
$544$		0			0
$545$	1.54122	+	10.7194i	0.0660185	+	0.459169i
$546$		0			0
$547$	−1.71049	−	35.9077i	−0.0731354	−	1.53530i	−0.675668	−	0.737206i	$-0.736145\pi$
$547$	−1.71049	−	35.9077i	−0.0731354	−	1.53530i	0.602532	−	0.798094i	$-0.294158\pi$
$548$		0			0
$549$	2.11786	−	0.202231i	0.0903882	−	0.00863103i
$550$		0			0
$551$	6.01459	−	41.8324i	0.256230	−	1.78212i
$552$		0			0
$553$	1.68979	+	6.96540i	0.0718571	+	0.296199i
$554$		0			0
$555$	3.54763	−	1.42026i	0.150589	−	0.0602866i
$556$		0			0
$557$	−23.9081	+	12.3255i	−1.01302	+	0.522249i	−0.883055	−	0.469270i	$-0.844517\pi$
$557$	−23.9081	+	12.3255i	−1.01302	+	0.522249i	−0.129966	+	0.991518i	$0.541487\pi$
$558$		0			0
$559$	24.1386	+	4.65234i	1.02095	+	0.196773i
$560$		0			0
$561$	−3.80180	+	8.32478i	−0.160512	+	0.351473i
$562$		0			0
$563$	−26.0791	−	16.7600i	−1.09910	−	0.706350i	−0.140210	−	0.990122i	$-0.544778\pi$
$563$	−26.0791	−	16.7600i	−1.09910	−	0.706350i	−0.958892	+	0.283772i	$0.908414\pi$
$564$		0			0
$565$	−1.69164	+	2.93001i	−0.0711678	+	0.123266i
$566$		0			0
$567$	2.02710	+	0.193564i	0.0851301	+	0.00812894i
$568$		0			0
$569$	8.06476	+	6.34220i	0.338092	+	0.265879i	0.772741	−	0.634721i	$-0.218885\pi$
$569$	8.06476	+	6.34220i	0.338092	+	0.265879i	−0.434649	+	0.900600i	$0.643127\pi$
$570$		0			0
$571$	20.3040	−	3.91328i	0.849697	−	0.163766i	0.254228	−	0.967144i	$-0.418179\pi$
$571$	20.3040	−	3.91328i	0.849697	−	0.163766i	0.595469	+	0.803379i	$0.296966\pi$
$572$		0			0
$573$	2.72981	+	4.72817i	0.114039	+	0.197522i
$574$		0			0
$575$	2.58519	−	3.63039i	0.107810	−	0.151398i
$576$		0			0
$577$	32.8573	−	31.3294i	1.36787	−	1.30426i	0.458245	−	0.888826i	$-0.348478\pi$
$577$	32.8573	−	31.3294i	1.36787	−	1.30426i	0.909623	−	0.415434i	$-0.136370\pi$
$578$		0			0
$579$	−7.32430	−	2.15061i	−0.304387	−	0.0893762i
$580$		0			0
$581$	−21.8451	−	25.2106i	−0.906287	−	1.04591i
$582$		0			0
$583$	11.8515	+	34.2428i	0.490841	+	1.41819i
$584$		0			0
$585$	−5.67742	−	5.41341i	−0.234732	−	0.223817i
$586$		0			0
$587$	−10.1504	−	5.23291i	−0.418953	−	0.215985i	0.235843	−	0.971791i	$-0.424215\pi$
$587$	−10.1504	−	5.23291i	−0.418953	−	0.215985i	−0.654796	+	0.755806i	$0.727245\pi$
$588$		0			0
$589$	−23.2277	+	6.82028i	−0.957083	+	0.281025i
$590$		0			0
$591$	4.72475	+	6.63499i	0.194350	+	0.272927i
$592$		0			0
$593$	−10.3097	+	29.7880i	−0.423370	+	1.22325i	0.508693	+	0.860948i	$0.330129\pi$
$593$	−10.3097	+	29.7880i	−0.423370	+	1.22325i	−0.932062	+	0.362298i	$0.881992\pi$
$594$		0			0
$595$	6.65134	+	14.5644i	0.272678	+	0.597082i
$596$		0			0
$597$	−0.956518	+	20.0798i	−0.0391477	+	0.821811i
$598$		0			0
$599$	−5.17644	+	21.3376i	−0.211504	+	0.871830i	0.762808	+	0.646625i	$0.223820\pi$
$599$	−5.17644	+	21.3376i	−0.211504	+	0.871830i	−0.974312	+	0.225205i	$0.927695\pi$
$600$		0			0
$601$	−24.3789	+	19.1718i	−0.994435	+	0.782032i	−0.975994	−	0.217798i	$-0.930113\pi$
$601$	−24.3789	+	19.1718i	−0.994435	+	0.782032i	−0.0184408	+	0.999830i	$0.505870\pi$
$602$		0			0
$603$	8.09004	+	1.24551i	0.329452	+	0.0507210i
$604$		0			0
$605$	−4.01426	+	3.15685i	−0.163203	+	0.128344i
$606$		0			0
$607$	8.24911	−	34.0033i	0.334821	−	1.38015i	−0.516851	−	0.856075i	$-0.672896\pi$
$607$	8.24911	−	34.0033i	0.334821	−	1.38015i	0.851672	−	0.524075i	$-0.175589\pi$
$608$		0			0
$609$	0.591487	−	12.4168i	0.0239683	−	0.503156i
$610$		0			0
$611$	2.18174	+	4.77734i	0.0882637	+	0.193271i
$612$		0			0
$613$	0.163751	−	0.473128i	0.00661385	−	0.0191095i	−0.941646	−	0.336606i	$-0.890721\pi$
$613$	0.163751	−	0.473128i	0.00661385	−	0.0191095i	0.948259	+	0.317497i	$0.102842\pi$
$614$		0			0
$615$	6.44310	+	9.04807i	0.259811	+	0.364853i
$616$		0			0
$617$	13.5998	−	3.99327i	0.547508	−	0.160763i	0.00373185	−	0.999993i	$-0.498812\pi$
$617$	13.5998	−	3.99327i	0.547508	−	0.160763i	0.543776	+	0.839230i	$0.316994\pi$
$618$		0			0
$619$	−14.7400	−	7.59901i	−0.592452	−	0.305430i	0.135804	−	0.990736i	$-0.456638\pi$
$619$	−14.7400	−	7.59901i	−0.592452	−	0.305430i	−0.728255	+	0.685306i	$0.759669\pi$
$620$		0			0
$621$	0.741097	+	0.706635i	0.0297392	+	0.0283563i
$622$		0			0
$623$	3.44696	+	9.95934i	0.138100	+	0.399012i
$624$		0			0
$625$	18.2174	+	21.0240i	0.728696	+	0.840960i
$626$		0			0
$627$	−23.6443	−	6.94260i	−0.944263	−	0.277261i
$628$		0			0
$629$	−2.32518	+	2.21706i	−0.0927111	+	0.0883999i
$630$		0			0
$631$	3.03230	−	4.25826i	0.120714	−	0.169519i	−0.749797	−	0.661668i	$-0.769849\pi$
$631$	3.03230	−	4.25826i	0.120714	−	0.169519i	0.870511	+	0.492149i	$0.163788\pi$
$632$		0			0
$633$	−2.45520	−	4.25253i	−0.0975854	−	0.169023i
$634$		0			0
$635$	−27.6674	+	5.33245i	−1.09795	+	0.211612i
$636$		0			0
$637$	−5.75343	−	4.52455i	−0.227959	−	0.179269i
$638$		0			0
$639$	−8.85795	−	0.845832i	−0.350415	−	0.0334606i
$640$		0			0
$641$	−7.72181	+	13.3746i	−0.304993	+	0.528264i	−0.977260	−	0.212045i	$-0.931988\pi$
$641$	−7.72181	+	13.3746i	−0.304993	+	0.528264i	0.672267	+	0.740309i	$0.265321\pi$
$642$		0			0
$643$	−17.1281	−	11.0076i	−0.675466	−	0.434096i	0.157426	−	0.987531i	$-0.449680\pi$
$643$	−17.1281	−	11.0076i	−0.675466	−	0.434096i	−0.832892	+	0.553435i	$0.813317\pi$
$644$		0			0
$645$	−12.1749	+	26.6592i	−0.479385	+	1.04971i
$646$		0			0
$647$	19.0684	+	3.67513i	0.749655	+	0.144484i	0.549748	−	0.835331i	$-0.314724\pi$
$647$	19.0684	+	3.67513i	0.749655	+	0.144484i	0.199907	+	0.979815i	$0.435936\pi$
$648$		0			0
$649$	14.2214	−	7.33162i	0.558237	−	0.287791i
$650$		0			0
$651$	−6.61048	+	2.64644i	−0.259085	+	0.103722i
$652$		0			0
$653$	−1.19650	−	4.93205i	−0.0468227	−	0.193006i	0.943597	−	0.331097i	$-0.107419\pi$
$653$	−1.19650	−	4.93205i	−0.0468227	−	0.193006i	−0.990420	+	0.138091i	$0.955903\pi$
$654$		0			0
$655$	−2.78044	+	19.3384i	−0.108641	+	0.755614i
$656$		0			0
$657$	12.7771	−	1.22007i	0.498483	−	0.0475994i
$658$		0			0
$659$	1.06761	+	22.4119i	0.0415883	+	0.873045i	0.919228	+	0.393725i	$0.128814\pi$
$659$	1.06761	+	22.4119i	0.0415883	+	0.873045i	−0.877640	+	0.479320i	$0.840883\pi$
$660$		0			0
$661$	−7.01398	−	48.7833i	−0.272812	−	1.89745i	−0.418659	−	0.908144i	$-0.637500\pi$
$661$	−7.01398	−	48.7833i	−0.272812	−	1.89745i	0.145846	−	0.989307i	$-0.453409\pi$
$662$		0			0
$663$	6.12283	+	2.45121i	0.237791	+	0.0951971i
$664$		0			0
$665$	−36.2686	+	23.3084i	−1.40644	+	0.903863i
$666$		0			0
$667$	4.09358	−	4.72424i	0.158504	−	0.182923i
$668$		0			0
$669$	−15.8220			−0.611712
$670$		0			0
$671$	−7.57278			−0.292344
$672$		0			0
$673$	−0.951277	+	1.09783i	−0.0366690	+	0.0423183i	−0.773788	−	0.633445i	$-0.781640\pi$
$673$	−0.951277	+	1.09783i	−0.0366690	+	0.0423183i	0.737119	+	0.675763i	$0.236186\pi$
$674$		0			0
$675$	3.66144	−	2.35306i	0.140929	−	0.0905695i
$676$		0			0
$677$	−21.7619	−	8.71213i	−0.836376	−	0.334834i	−0.0863681	−	0.996263i	$-0.527526\pi$
$677$	−21.7619	−	8.71213i	−0.836376	−	0.334834i	−0.750008	+	0.661429i	$0.769950\pi$
$678$		0			0
$679$	−3.98860	−	27.7413i	−0.153068	−	1.06461i
$680$		0			0
$681$	0.190511	+	3.99932i	0.00730041	+	0.153254i
$682$		0			0
$683$	10.2799	−	0.981608i	0.393348	−	0.0375602i	0.103492	−	0.994630i	$-0.466999\pi$
$683$	10.2799	−	0.981608i	0.393348	−	0.0375602i	0.289856	+	0.957070i	$0.406392\pi$
$684$		0			0
$685$	−2.37488	+	16.5177i	−0.0907396	+	0.631108i
$686$		0			0
$687$	2.15485	+	8.88240i	0.0822126	+	0.338885i
$688$		0			0
$689$	24.2427	−	9.70532i	0.923574	−	0.369743i
$690$		0			0
$691$	−38.5575	+	19.8778i	−1.46680	+	0.756186i	−0.992275	−	0.124059i	$-0.960409\pi$
$691$	−38.5575	+	19.8778i	−1.46680	+	0.756186i	−0.474521	+	0.880244i	$0.657379\pi$
$692$		0			0
$693$	−7.11725	−	1.37174i	−0.270362	−	0.0521080i
$694$		0			0
$695$	−17.7642	+	38.8982i	−0.673834	+	1.47549i
$696$		0			0
$697$	−7.85617	−	5.04885i	−0.297574	−	0.191239i
$698$		0			0
$699$	11.5233	−	19.9590i	0.435852	−	0.754919i
$700$		0			0
$701$	32.3642	+	3.09041i	1.22238	+	0.116723i	0.686220	−	0.727394i	$-0.259269\pi$
$701$	32.3642	+	3.09041i	1.22238	+	0.116723i	0.536159	+	0.844117i	$0.319875\pi$
$702$		0			0
$703$	−6.79998	−	5.34757i	−0.256466	−	0.201687i
$704$		0			0
$705$	−6.14823	+	1.18497i	−0.231556	+	0.0446287i
$706$		0			0
$707$	−0.291344	−	0.504623i	−0.0109571	−	0.0189783i
$708$		0			0
$709$	−14.5157	+	20.3845i	−0.545149	+	0.765554i	−0.991612	−	0.129248i	$-0.958744\pi$
$709$	−14.5157	+	20.3845i	−0.545149	+	0.765554i	0.446464	+	0.894802i	$0.352683\pi$
$710$		0			0
$711$	−2.54740	+	2.42894i	−0.0955351	+	0.0910925i
$712$		0			0
$713$	−3.43562	−	1.00879i	−0.128665	−	0.0377795i
$714$		0			0
$715$	18.2855	+	21.1026i	0.683840	+	0.789194i
$716$		0			0
$717$	−9.65100	−	27.8847i	−0.360423	−	1.04137i
$718$		0			0
$719$	−24.9704	−	23.8093i	−0.931241	−	0.887936i	0.0626802	−	0.998034i	$-0.480035\pi$
$719$	−24.9704	−	23.8093i	−0.931241	−	0.887936i	−0.993921	+	0.110098i	$0.964884\pi$
$720$		0			0
$721$	28.0725	+	14.4724i	1.04547	+	0.538979i
$722$		0			0
$723$	0.143741	−	0.0422062i	0.00534579	−	0.00156967i
$724$		0			0
$725$	−15.4118	−	21.6428i	−0.572380	−	0.803795i
$726$		0			0
$727$	3.21096	−	9.27747i	0.119088	−	0.344082i	−0.869664	−	0.493643i	$-0.835665\pi$
$727$	3.21096	−	9.27747i	0.119088	−	0.344082i	0.988752	+	0.149561i	$0.0477861\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	1.17242	−	24.6121i	0.0433635	−	0.910313i
$732$		0			0
$733$	−1.74075	+	7.17548i	−0.0642962	+	0.265032i	−0.994882	−	0.101041i	$-0.967783\pi$
$733$	−1.74075	+	7.17548i	−0.0642962	+	0.265032i	0.930586	+	0.366073i	$0.119298\pi$
$734$		0			0
$735$	6.85925	−	5.39417i	0.253007	−	0.198967i
$736$		0			0
$737$	−28.2445	−	7.15055i	−1.04040	−	0.263394i
$738$		0			0
$739$	−7.00601	+	5.50959i	−0.257720	+	0.202673i	−0.738656	−	0.674082i	$-0.764539\pi$
$739$	−7.00601	+	5.50959i	−0.257720	+	0.202673i	0.480936	+	0.876756i	$0.340297\pi$
$740$		0			0
$741$	−4.18676	+	17.2580i	−0.153804	+	0.633990i
$742$		0			0
$743$	0.634117	−	13.3118i	0.0232635	−	0.488361i	−0.956930	−	0.290319i	$-0.906239\pi$
$743$	0.634117	−	13.3118i	0.0232635	−	0.488361i	0.980194	−	0.198042i	$-0.0634583\pi$
$744$		0			0
$745$	−15.6290	−	34.2227i	−0.572601	−	1.25382i
$746$		0			0
$747$	5.35793	−	15.4807i	0.196036	−	0.566410i
$748$		0			0
$749$	22.8067	+	32.0275i	0.833337	+	1.17026i
$750$		0			0
$751$	45.6480	−	13.4034i	1.66572	−	0.489099i	0.692970	−	0.720966i	$-0.256302\pi$
$751$	45.6480	−	13.4034i	1.66572	−	0.489099i	0.972747	+	0.231867i	$0.0744836\pi$
$752$		0			0
$753$	8.22956	+	4.24263i	0.299902	+	0.154610i
$754$		0			0
$755$	16.2261	+	15.4716i	0.590529	+	0.563068i
$756$		0			0
$757$	−3.66335	−	10.5846i	−0.133147	−	0.384702i	0.858644	−	0.512572i	$-0.171307\pi$
$757$	−3.66335	−	10.5846i	−0.133147	−	0.384702i	−0.991791	+	0.127870i	$0.959186\pi$
$758$		0			0
$759$	−2.38689	−	2.75462i	−0.0866385	−	0.0999862i
$760$		0			0
$761$	−46.3102	−	13.5979i	−1.67874	−	0.492923i	−0.702880	−	0.711308i	$-0.748103\pi$
$761$	−46.3102	−	13.5979i	−1.67874	−	0.492923i	−0.975863	+	0.218385i	$0.929921\pi$
$762$		0			0
$763$	5.21888	−	4.97620i	0.188936	−	0.180150i
$764$		0			0
$765$	−4.56091	+	6.40491i	−0.164900	+	0.231570i
$766$		0			0
$767$	−5.76520	−	9.98562i	−0.208169	−	0.360560i
$768$		0			0
$769$	−48.4225	+	9.33267i	−1.74616	+	0.336545i	−0.959685	−	0.281079i	$-0.909308\pi$
$769$	−48.4225	+	9.33267i	−1.74616	+	0.336545i	−0.786474	+	0.617623i	$0.788096\pi$
$770$		0			0
$771$	−3.93907	−	3.09772i	−0.141862	−	0.111562i
$772$		0			0
$773$	18.2504	+	1.74270i	0.656420	+	0.0626805i	0.417951	−	0.908470i	$-0.362748\pi$
$773$	18.2504	+	1.74270i	0.656420	+	0.0626805i	0.238469	+	0.971150i	$0.423355\pi$
$774$		0			0
$775$	−7.60961	+	13.1802i	−0.273345	+	0.473448i
$776$		0			0
$777$	−2.14057	−	1.37566i	−0.0767927	−	0.0493517i
$778$		0			0
$779$	10.4459	−	22.8732i	0.374261	−	0.819518i
$780$		0			0
$781$	31.1008	+	5.99418i	1.11287	+	0.214489i
$782$		0			0
$783$	5.42599	−	2.79729i	0.193909	−	0.0999671i
$784$		0			0
$785$	−51.4128	+	20.5826i	−1.83500	+	0.734624i
$786$		0			0
$787$	−10.8493	−	44.7214i	−0.386736	−	1.59415i	−0.749329	−	0.662198i	$-0.769624\pi$
$787$	−10.8493	−	44.7214i	−0.386736	−	1.59415i	0.362593	−	0.931948i	$-0.381892\pi$
$788$		0			0
$789$	−1.42502	+	9.91125i	−0.0507322	+	0.352850i
$790$		0			0
$791$	2.24260	−	0.214142i	0.0797377	−	0.00761402i
$792$		0			0
$793$	0.259670	+	5.45115i	0.00922116	+	0.193576i
$794$		0			0
$795$	4.43058	+	30.8154i	0.157137	+	1.09291i
$796$		0			0
$797$	33.7305	+	13.5037i	1.19480	+	0.478324i	0.881888	−	0.471460i	$-0.156273\pi$
$797$	33.7305	+	13.5037i	1.19480	+	0.478324i	0.312908	+	0.949784i	$0.398697\pi$
$798$		0			0
$799$	4.42850	−	2.84602i	0.156669	−	0.100685i
$800$		0			0
$801$	−3.38923	+	3.91138i	−0.119753	+	0.138202i
$802$		0			0
$803$	−45.6868			−1.61225
$804$		0			0
$805$	−6.37680			−0.224753
$806$		0			0
$807$	4.11663	−	4.75085i	0.144912	−	0.167238i
$808$		0			0
$809$	−29.9848	+	19.2701i	−1.05421	+	0.677500i	−0.948461	−	0.316893i	$-0.897360\pi$
$809$	−29.9848	+	19.2701i	−1.05421	+	0.677500i	−0.105749	+	0.994393i	$0.533724\pi$
$810$		0			0
$811$	13.3011	+	5.32497i	0.467066	+	0.186985i	0.593244	−	0.805023i	$-0.297847\pi$
$811$	13.3011	+	5.32497i	0.467066	+	0.186985i	−0.126178	+	0.992008i	$0.540271\pi$
$812$		0			0
$813$	1.69044	+	11.7573i	0.0592863	+	0.412345i
$814$		0			0
$815$	1.62434	+	34.0991i	0.0568981	+	1.19444i
$816$		0			0
$817$	66.0463	−	6.30665i	2.31067	−	0.220642i
$818$		0			0
$819$	−0.743374	+	5.17028i	−0.0259756	+	0.180664i
$820$		0			0
$821$	−12.6096	−	51.9776i	−0.440079	−	1.81403i	−0.568955	−	0.822369i	$-0.692652\pi$
$821$	−12.6096	−	51.9776i	−0.440079	−	1.81403i	0.128876	−	0.991661i	$-0.458863\pi$
$822$		0			0
$823$	23.8017	−	9.52878i	0.829677	−	0.332152i	0.0823451	−	0.996604i	$-0.473759\pi$
$823$	23.8017	−	9.52878i	0.829677	−	0.332152i	0.747331	+	0.664451i	$0.231335\pi$
$824$		0			0
$825$	−13.7700	+	7.09892i	−0.479409	+	0.247153i
$826$		0			0
$827$	−12.9273	−	2.49154i	−0.449527	−	0.0866392i	−0.0405369	−	0.999178i	$-0.512907\pi$
$827$	−12.9273	−	2.49154i	−0.449527	−	0.0866392i	−0.408990	+	0.912539i	$0.634119\pi$
$828$		0			0
$829$	−1.03521	+	2.26679i	−0.0359542	+	0.0787287i	−0.926757	−	0.375661i	$-0.877416\pi$
$829$	−1.03521	+	2.26679i	−0.0359542	+	0.0787287i	0.890803	+	0.454390i	$0.150143\pi$
$830$		0			0
$831$	−8.65634	−	5.56309i	−0.300285	−	0.192981i
$832$		0			0
$833$	−3.66821	+	6.35353i	−0.127096	+	0.220137i
$834$		0			0
$835$	−59.0047	−	5.63427i	−2.04194	−	0.194982i
$836$		0			0
$837$	−2.74865	−	2.16156i	−0.0950072	−	0.0747145i
$838$		0			0
$839$	−7.01909	+	1.35282i	−0.242326	+	0.0467045i	−0.308968	−	0.951072i	$-0.599984\pi$
$839$	−7.01909	+	1.35282i	−0.242326	+	0.0467045i	0.0666421	+	0.997777i	$0.478771\pi$
$840$		0			0
$841$	−4.13312	−	7.15877i	−0.142521	−	0.246854i
$842$		0			0
$843$	−15.0358	+	21.1148i	−0.517861	+	0.727234i
$844$		0			0
$845$	−14.2095	+	13.5487i	−0.488821	+	0.466090i
$846$		0			0
$847$	3.26272	+	0.958022i	0.112108	+	0.0329180i
$848$		0			0
$849$	−13.8505	−	15.9843i	−0.475348	−	0.548581i
$850$		0			0
$851$	−0.418497	−	1.20917i	−0.0143459	−	0.0414497i
$852$		0			0
$853$	28.6758	+	27.3423i	0.981841	+	0.936184i	0.997970	−	0.0636861i	$-0.0202856\pi$
$853$	28.6758	+	27.3423i	0.981841	+	0.936184i	−0.0161286	+	0.999870i	$0.505134\pi$
$854$		0			0
$855$	−18.8183	−	9.70150i	−0.643572	−	0.331784i
$856$		0			0
$857$	23.0035	−	6.75444i	0.785785	−	0.230727i	0.135862	−	0.990728i	$-0.456619\pi$
$857$	23.0035	−	6.75444i	0.785785	−	0.230727i	0.649923	+	0.760000i	$0.274801\pi$
$858$		0			0
$859$	−4.19657	−	5.89326i	−0.143185	−	0.201076i	0.736755	−	0.676160i	$-0.236357\pi$
$859$	−4.19657	−	5.89326i	−0.143185	−	0.201076i	−0.879940	+	0.475084i	$0.842418\pi$
$860$		0			0
$861$	2.41906	−	6.98942i	0.0824414	−	0.238199i
$862$		0			0
$863$	12.3293	+	26.9974i	0.419694	+	0.919003i	0.994888	+	0.100985i	$0.0321995\pi$
$863$	12.3293	+	26.9974i	0.419694	+	0.919003i	−0.575194	+	0.818017i	$0.695073\pi$
$864$		0			0
$865$	−1.54805	+	32.4975i	−0.0526351	+	1.10495i
$866$		0			0
$867$	−2.44939	+	10.0965i	−0.0831858	+	0.342896i
$868$		0			0
$869$	9.84821	−	7.74472i	0.334078	−	0.262722i
$870$		0			0
$871$	−4.17871	+	20.5766i	−0.141590	+	0.697210i
$872$		0			0
$873$	10.8187	−	8.50794i	0.366159	−	0.287950i
$874$		0			0
$875$	0.950838	−	3.91941i	0.0321442	−	0.132500i
$876$		0			0
$877$	−2.19923	+	46.1676i	−0.0742629	+	1.55897i	0.587480	+	0.809239i	$0.300120\pi$
$877$	−2.19923	+	46.1676i	−0.0742629	+	1.55897i	−0.661743	+	0.749731i	$0.730183\pi$
$878$		0			0
$879$	0.457977	+	1.00283i	0.0154472	+	0.0338246i
$880$		0			0
$881$	−1.18463	+	3.42276i	−0.0399112	+	0.115316i	−0.963196	−	0.268801i	$-0.913373\pi$
$881$	−1.18463	+	3.42276i	−0.0399112	+	0.115316i	0.923285	+	0.384117i	$0.125494\pi$
$882$		0			0
$883$	−4.43885	−	6.23349i	−0.149379	−	0.209774i	0.733105	−	0.680115i	$-0.238070\pi$
$883$	−4.43885	−	6.23349i	−0.149379	−	0.209774i	−0.882485	+	0.470341i	$0.844131\pi$
$884$		0			0
$885$	13.1897	−	3.87285i	0.443368	−	0.130184i
$886$		0			0
$887$	2.64860	+	1.36545i	0.0889312	+	0.0458472i	0.502118	−	0.864799i	$-0.332554\pi$
$887$	2.64860	+	1.36545i	0.0889312	+	0.0458472i	−0.413187	+	0.910646i	$0.635584\pi$
$888$		0			0
$889$	13.5785	+	12.9471i	0.455408	+	0.434231i
$890$		0			0
$891$	−1.16419	−	3.36371i	−0.0390019	−	0.112689i
$892$		0			0
$893$	9.28232	+	10.7124i	0.310621	+	0.358476i
$894$		0			0
$895$	−12.9720	−	3.80893i	−0.433607	−	0.127319i
$896$		0			0
$897$	−1.90102	+	1.81262i	−0.0634732	+	0.0605216i
$898$		0			0
$899$	−12.3821	+	17.3883i	−0.412967	+	0.579931i
$900$		0			0
$901$	−13.0870	−	22.6674i	−0.435992	−	0.755160i
$902$		0			0
$903$	19.1623	−	3.69322i	0.637680	−	0.122903i
$904$		0			0
$905$	24.8968	+	19.5790i	0.827596	+	0.650829i
$906$		0			0
$907$	−27.4681	−	2.62288i	−0.912062	−	0.0870914i	−0.371536	−	0.928419i	$-0.621169\pi$
$907$	−27.4681	−	2.62288i	−0.912062	−	0.0870914i	−0.540526	+	0.841327i	$0.681775\pi$
$908$		0			0
$909$	0.143074	−	0.247812i	0.00474547	−	0.00821939i
$910$		0			0
$911$	−0.686271	−	0.441040i	−0.0227372	−	0.0146123i	0.529223	−	0.848483i	$-0.322484\pi$
$911$	−0.686271	−	0.441040i	−0.0227372	−	0.0146123i	−0.551960	+	0.833871i	$0.686120\pi$
$912$		0			0
$913$	−24.2230	+	53.0410i	−0.801665	+	1.75540i
$914$		0			0
$915$	−6.38866	−	1.23131i	−0.211202	−	0.0407059i
$916$		0			0
$917$	11.5630	−	5.96114i	0.381844	−	0.196854i
$918$		0			0
$919$	15.3192	−	6.13289i	0.505334	−	0.202305i	−0.104966	−	0.994476i	$-0.533473\pi$
$919$	15.3192	−	6.13289i	0.505334	−	0.202305i	0.610300	+	0.792171i	$0.291049\pi$
$920$		0			0
$921$	−3.41145	−	14.0622i	−0.112411	−	0.463364i
$922$		0			0
$923$	3.24837	−	22.5929i	0.106921	−	0.743655i
$924$		0			0
$925$	−5.41392	+	0.516967i	−0.178009	+	0.0169978i
$926$		0			0
$927$	0.737998	+	15.4925i	0.0242390	+	0.508840i
$928$		0			0
$929$	−7.96913	−	55.4265i	−0.261459	−	1.81848i	−0.521914	−	0.852998i	$-0.674782\pi$
$929$	−7.96913	−	55.4265i	−0.261459	−	1.81848i	0.260456	−	0.965486i	$-0.416127\pi$
$930$		0			0
$931$	−18.3393	−	7.34194i	−0.601045	−	0.240622i
$932$		0			0
$933$	−6.47321	+	4.16008i	−0.211923	+	0.136195i
$934$		0			0
$935$	18.3281	−	21.1517i	0.599392	−	0.691735i
$936$		0			0
$937$	−47.7488			−1.55988			−0.779942	−	0.625851i	$-0.784752\pi$
$937$	−47.7488			−1.55988			−0.779942	+	0.625851i	$0.784752\pi$
$938$		0			0
$939$	24.9922			0.815588
$940$		0			0
$941$	27.6675	−	31.9300i	0.901934	−	1.04089i	−0.0970251	−	0.995282i	$-0.530933\pi$
$941$	27.6675	−	31.9300i	0.901934	−	1.04089i	0.998960	−	0.0456058i	$-0.0145218\pi$
$942$		0			0
$943$	3.12886	−	2.01080i	0.101890	−	0.0654806i
$944$		0			0
$945$	−5.78131	−	2.31449i	−0.188066	−	0.0752903i
$946$		0			0
$947$	−1.26348	−	8.78772i	−0.0410577	−	0.285562i	−0.999998	−	0.00195482i	$-0.999378\pi$
$947$	−1.26348	−	8.78772i	−0.0410577	−	0.285562i	0.958940	−	0.283608i	$-0.0915313\pi$
$948$		0			0
$949$	1.56660	+	32.8869i	0.0508539	+	1.06755i
$950$		0			0
$951$	−5.49126	+	0.524351i	−0.178066	+	0.0170033i
$952$		0			0
$953$	2.15454	−	14.9852i	0.0697924	−	0.485417i	−0.924707	−	0.380679i	$-0.875690\pi$
$953$	2.15454	−	14.9852i	0.0697924	−	0.485417i	0.994500	−	0.104738i	$-0.0334004\pi$
$954$		0			0
$955$	−3.93632	−	16.2257i	−0.127376	−	0.525053i
$956$		0			0
$957$	−20.1727	+	8.07594i	−0.652092	+	0.261058i
$958$		0			0
$959$	9.87640	−	5.09164i	0.318925	−	0.164417i
$960$		0			0
$961$	−18.4333	−	3.55274i	−0.594624	−	0.114604i
$962$		0			0
$963$	−8.02098	+	17.5635i	−0.258473	+	0.565976i
$964$		0			0
$965$	19.6387	+	12.6210i	0.632191	+	0.406284i
$966$		0			0
$967$	−9.05206	+	15.6786i	−0.291095	+	0.504191i	−0.974069	−	0.226252i	$-0.927353\pi$
$967$	−9.05206	+	15.6786i	−0.291095	+	0.504191i	0.682974	+	0.730442i	$0.260686\pi$
$968$		0			0
$969$	17.7193	+	1.69199i	0.569227	+	0.0543546i
$970$		0			0
$971$	−8.50673	−	6.68976i	−0.272994	−	0.214685i	0.472271	−	0.881454i	$-0.343434\pi$
$971$	−8.50673	−	6.68976i	−0.272994	−	0.214685i	−0.745265	+	0.666769i	$0.767677\pi$
$972$		0			0
$973$	27.9594	−	5.38874i	0.896338	−	0.172755i
$974$		0			0
$975$	5.58221	+	9.66868i	0.178774	+	0.309645i
$976$		0			0
$977$	−4.42428	+	6.21304i	−0.141545	+	0.198773i	−0.879263	−	0.476337i	$-0.841964\pi$
$977$	−4.42428	+	6.21304i	−0.141545	+	0.198773i	0.737717	+	0.675110i	$0.235904\pi$
$978$		0			0
$979$	13.3327	−	12.7127i	0.426115	−	0.406300i
$980$		0			0
$981$	3.39778	+	0.997677i	0.108483	+	0.0318534i
$982$		0			0
$983$	−33.8673	−	39.0850i	−1.08020	−	1.24662i	−0.967468	−	0.252993i	$-0.918585\pi$
$983$	−33.8673	−	39.0850i	−1.08020	−	1.24662i	−0.112732	−	0.993625i	$-0.535960\pi$
$984$		0			0
$985$	−8.14718	−	23.5397i	−0.259591	−	0.750038i
$986$		0			0
$987$	3.01741	+	2.87709i	0.0960452	+	0.0915789i
$988$		0			0
$989$	8.72246	+	4.49674i	0.277358	+	0.142988i
$990$		0			0
$991$	−32.5640	+	9.56164i	−1.03443	+	0.303736i	−0.754510	−	0.656288i	$-0.772125\pi$
$991$	−32.5640	+	9.56164i	−1.03443	+	0.303736i	−0.279918	+	0.960024i	$0.590307\pi$
$992$		0			0
$993$	3.58130	+	5.02923i	0.113649	+	0.159598i
$994$		0			0
$995$	20.1071	−	58.0957i	0.637439	−	1.84176i
$996$		0			0
$997$	−5.59779	−	12.2574i	−0.177284	−	0.388197i	0.800040	−	0.599946i	$-0.204811\pi$
$997$	−5.59779	−	12.2574i	−0.177284	−	0.388197i	−0.977324	+	0.211749i	$0.932084\pi$
$998$		0			0
$999$	0.0594566	−	1.24815i	0.00188112	−	0.0394896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.121.4	✓	100
67.36	even	33	inner	804.2.y.a.505.4	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.121.4	✓	100	1.1	even	1	trivial
804.2.y.a.505.4	yes	100	67.36	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{3} +(2.57269 - 1.65337i) q^{5} +(-1.89045 - 0.756823i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{3} +(2.57269 - 1.65337i) q^{5} +(-1.89045 - 0.756823i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.169367 + 3.55545i) q^{11} +(2.55353 - 0.243832i) q^{13} +(-0.435222 + 3.02704i) q^{15} +(-0.606162 - 2.49863i) q^{17} +(6.42715 - 2.57304i) q^{19} +(1.80995 - 0.933095i) q^{21} +(1.00549 + 0.193792i) q^{23} +(1.80804 - 3.95905i) q^{25} +(0.841254 + 0.540641i) q^{27} +(3.05230 - 5.28675i) q^{29} +(-3.48094 - 0.332389i) q^{31} +(-2.79794 - 2.20033i) q^{33} +(-6.11486 + 1.17854i) q^{35} +(-0.624781 - 1.08215i) q^{37} +(-1.48793 + 2.08950i) q^{39} +(2.62871 - 2.50647i) q^{41} +(9.19524 + 2.69996i) q^{43} +(-2.00267 - 2.31121i) q^{45} +(0.669649 + 1.93482i) q^{47} +(-2.06511 - 1.96908i) q^{49} +(2.28529 + 1.17815i) q^{51} +(9.76769 - 2.86805i) q^{53} +(6.31420 + 8.86705i) q^{55} +(-2.26431 + 6.54230i) q^{57} +(-1.86731 - 4.08883i) q^{59} +(-0.101230 + 2.12509i) q^{61} +(-0.480080 + 1.97892i) q^{63} +(6.16629 - 4.84922i) q^{65} +(-2.38416 + 7.83044i) q^{67} +(-0.804912 + 0.632989i) q^{69} +(2.09784 - 8.64742i) q^{71} +(-0.610726 + 12.8207i) q^{73} +(1.80804 + 3.95905i) q^{75} +(2.37067 - 6.84959i) q^{77} +(-2.04169 - 2.86715i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(14.5606 + 7.50653i) q^{83} +(-5.69063 - 5.42600i) q^{85} +(1.99662 + 5.76886i) q^{87} +(-3.38923 - 3.91138i) q^{89} +(-5.01186 - 1.47161i) q^{91} +(2.53073 - 2.41305i) q^{93} +(12.2809 - 17.2461i) q^{95} +(6.88168 + 11.9194i) q^{97} +(3.49516 - 0.673636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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