LMFDB - Embedded newform 804.2.y.b.505.2

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:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			505.2
Character	$\chi$	$=$	804.505
Dual form			804.2.y.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-2.07356 - 1.33260i) q^{5} +(4.33337 - 1.73482i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-2.07356 - 1.33260i) q^{5} +(4.33337 - 1.73482i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.101141 + 2.12321i) q^{11} +(-3.24464 - 0.309826i) q^{13} +(-0.350785 - 2.43976i) q^{15} +(1.86970 - 7.70703i) q^{17} +(6.34431 + 2.53988i) q^{19} +(4.14885 + 2.13888i) q^{21} +(1.25405 - 0.241699i) q^{23} +(0.446774 + 0.978298i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-3.89969 - 6.75447i) q^{29} +(6.64520 - 0.634540i) q^{31} +(-1.67085 + 1.31397i) q^{33} +(-11.2974 - 2.17739i) q^{35} +(-1.01966 + 1.76611i) q^{37} +(-1.89064 - 2.65503i) q^{39} +(6.72776 + 6.41491i) q^{41} +(2.12759 - 0.624716i) q^{43} +(1.61413 - 1.86281i) q^{45} +(0.0968303 - 0.279773i) q^{47} +(10.7024 - 10.2047i) q^{49} +(7.04898 - 3.63400i) q^{51} +(-2.36788 - 0.695274i) q^{53} +(3.03911 - 4.26784i) q^{55} +(2.23513 + 6.45798i) q^{57} +(3.15859 - 6.91636i) q^{59} +(-0.399313 - 8.38261i) q^{61} +(1.10046 + 4.53616i) q^{63} +(6.31510 + 4.96625i) q^{65} +(-3.88912 + 7.20241i) q^{67} +(1.00389 + 0.789472i) q^{69} +(2.12361 + 8.75365i) q^{71} +(0.736854 + 15.4685i) q^{73} +(-0.446774 + 0.978298i) q^{75} +(3.24511 + 9.37614i) q^{77} +(6.90329 - 9.69432i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-0.285490 + 0.147180i) q^{83} +(-14.1473 + 13.4895i) q^{85} +(2.55093 - 7.37043i) q^{87} +(-7.78897 + 8.98895i) q^{89} +(-14.5977 + 4.28628i) q^{91} +(4.83124 + 4.60657i) q^{93} +(-9.77070 - 13.7210i) q^{95} +(3.21956 - 5.57645i) q^{97} +(-2.08721 - 0.402276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{7}{33}\right)$	$1$

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
$5$	−2.07356	−	1.33260i	−0.927326	−	0.595956i	−0.0125516	−	0.999921i	$-0.503995\pi$
$5$	−2.07356	−	1.33260i	−0.927326	−	0.595956i	−0.914774	+	0.403965i	$0.867632\pi$
$6$		0			0
$7$	4.33337	−	1.73482i	1.63786	−	0.655701i	0.643868	−	0.765137i	$-0.277329\pi$
$7$	4.33337	−	1.73482i	1.63786	−	0.655701i	0.993994	+	0.109436i	$0.0349044\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−0.101141	+	2.12321i	−0.0304952	+	0.640173i	0.930945	+	0.365159i	$0.118985\pi$
$11$	−0.101141	+	2.12321i	−0.0304952	+	0.640173i	−0.961440	+	0.275014i	$0.911318\pi$
$12$		0			0
$13$	−3.24464	−	0.309826i	−0.899902	−	0.0859302i	−0.365159	−	0.930945i	$-0.618985\pi$
$13$	−3.24464	−	0.309826i	−0.899902	−	0.0859302i	−0.534743	+	0.845015i	$0.679591\pi$
$14$		0			0
$15$	−0.350785	−	2.43976i	−0.0905722	−	0.629944i
$16$		0			0
$17$	1.86970	−	7.70703i	0.453470	−	1.86923i	−0.0395612	−	0.999217i	$-0.512596\pi$
$17$	1.86970	−	7.70703i	0.453470	−	1.86923i	0.493031	−	0.870012i	$-0.335889\pi$
$18$		0			0
$19$	6.34431	+	2.53988i	1.45548	+	0.582688i	0.958505	−	0.285074i	$-0.0920182\pi$
$19$	6.34431	+	2.53988i	1.45548	+	0.582688i	0.496979	+	0.867762i	$0.334442\pi$
$20$		0			0
$21$	4.14885	+	2.13888i	0.905353	+	0.466742i
$22$		0			0
$23$	1.25405	−	0.241699i	0.261488	−	0.0503978i	−0.0568219	−	0.998384i	$-0.518097\pi$
$23$	1.25405	−	0.241699i	0.261488	−	0.0503978i	0.318310	+	0.947987i	$0.396885\pi$
$24$		0			0
$25$	0.446774	+	0.978298i	0.0893548	+	0.195660i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−3.89969	−	6.75447i	−0.724155	−	1.25427i	−0.959321	−	0.282318i	$-0.908897\pi$
$29$	−3.89969	−	6.75447i	−0.724155	−	1.25427i	0.235166	−	0.971955i	$-0.424437\pi$
$30$		0			0
$31$	6.64520	−	0.634540i	1.19351	−	0.113967i	0.520674	−	0.853755i	$-0.325681\pi$
$31$	6.64520	−	0.634540i	1.19351	−	0.113967i	0.672839	+	0.739789i	$0.265074\pi$
$32$		0			0
$33$	−1.67085	+	1.31397i	−0.290858	+	0.228733i
$34$		0			0
$35$	−11.2974	−	2.17739i	−1.90960	−	0.368045i
$36$		0			0
$37$	−1.01966	+	1.76611i	−0.167632	+	0.290346i	−0.937587	−	0.347752i	$-0.886945\pi$
$37$	−1.01966	+	1.76611i	−0.167632	+	0.290346i	0.769955	+	0.638098i	$0.220279\pi$
$38$		0			0
$39$	−1.89064	−	2.65503i	−0.302744	−	0.425145i
$40$		0			0
$41$	6.72776	+	6.41491i	1.05070	+	1.00184i	0.999995	+	0.00312698i	$0.000995352\pi$
$41$	6.72776	+	6.41491i	1.05070	+	1.00184i	0.0507051	+	0.998714i	$0.483853\pi$
$42$		0			0
$43$	2.12759	−	0.624716i	0.324454	−	0.0952683i	−0.115449	−	0.993313i	$-0.536831\pi$
$43$	2.12759	−	0.624716i	0.324454	−	0.0952683i	0.439903	+	0.898045i	$0.355013\pi$
$44$		0			0
$45$	1.61413	−	1.86281i	0.240621	−	0.277691i
$46$		0			0
$47$	0.0968303	−	0.279773i	0.0141241	−	0.0408090i	−0.937718	−	0.347396i	$-0.887066\pi$
$47$	0.0968303	−	0.279773i	0.0141241	−	0.0408090i	0.951843	+	0.306587i	$0.0991871\pi$
$48$		0			0
$49$	10.7024	−	10.2047i	1.52891	−	1.45782i
$50$		0			0
$51$	7.04898	−	3.63400i	0.987055	−	0.508862i
$52$		0			0
$53$	−2.36788	−	0.695274i	−0.325254	−	0.0955032i	0.115029	−	0.993362i	$-0.463304\pi$
$53$	−2.36788	−	0.695274i	−0.325254	−	0.0955032i	−0.440283	+	0.897859i	$0.645122\pi$
$54$		0			0
$55$	3.03911	−	4.26784i	0.409794	−	0.575475i
$56$		0			0
$57$	2.23513	+	6.45798i	0.296050	+	0.855380i
$58$		0			0
$59$	3.15859	−	6.91636i	0.411214	−	0.900433i	−0.584795	−	0.811181i	$-0.698825\pi$
$59$	3.15859	−	6.91636i	0.411214	−	0.900433i	0.996009	−	0.0892519i	$-0.0284476\pi$
$60$		0			0
$61$	−0.399313	−	8.38261i	−0.0511268	−	1.07328i	−0.868031	−	0.496510i	$-0.834615\pi$
$61$	−0.399313	−	8.38261i	−0.0511268	−	1.07328i	0.816904	−	0.576773i	$-0.195688\pi$
$62$		0			0
$63$	1.10046	+	4.53616i	0.138645	+	0.571502i
$64$		0			0
$65$	6.31510	+	4.96625i	0.783292	+	0.615987i
$66$		0			0
$67$	−3.88912	+	7.20241i	−0.475132	+	0.879915i
$67$	−3.88912	+	7.20241i	−0.475132	+	0.879915i
$68$		0			0
$69$	1.00389	+	0.789472i	0.120855	+	0.0950412i
$70$		0			0
$71$	2.12361	+	8.75365i	0.252026	+	1.03887i	0.947358	+	0.320178i	$0.103743\pi$
$71$	2.12361	+	8.75365i	0.252026	+	1.03887i	−0.695331	+	0.718690i	$0.744742\pi$
$72$		0			0
$73$	0.736854	+	15.4685i	0.0862423	+	1.81045i	0.465383	+	0.885109i	$0.345917\pi$
$73$	0.736854	+	15.4685i	0.0862423	+	1.81045i	−0.379141	+	0.925339i	$0.623780\pi$
$74$		0			0
$75$	−0.446774	+	0.978298i	−0.0515890	+	0.112964i
$76$		0			0
$77$	3.24511	+	9.37614i	0.369815	+	1.06851i
$78$		0			0
$79$	6.90329	−	9.69432i	0.776681	−	1.09070i	−0.216746	−	0.976228i	$-0.569544\pi$
$79$	6.90329	−	9.69432i	0.776681	−	1.09070i	0.993427	−	0.114468i	$-0.0365164\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−0.285490	+	0.147180i	−0.0313366	+	0.0161551i	−0.473824	−	0.880620i	$-0.657127\pi$
$83$	−0.285490	+	0.147180i	−0.0313366	+	0.0161551i	0.442487	+	0.896775i	$0.354096\pi$
$84$		0			0
$85$	−14.1473	+	13.4895i	−1.53449	+	1.46314i
$86$		0			0
$87$	2.55093	−	7.37043i	0.273488	−	0.790193i
$88$		0			0
$89$	−7.78897	+	8.98895i	−0.825629	+	0.952826i	−0.999490	−	0.0319438i	$-0.989830\pi$
$89$	−7.78897	+	8.98895i	−0.825629	+	0.952826i	0.173861	+	0.984770i	$0.444376\pi$
$90$		0			0
$91$	−14.5977	+	4.28628i	−1.53026	+	0.449325i
$92$		0			0
$93$	4.83124	+	4.60657i	0.500976	+	0.477680i
$94$		0			0
$95$	−9.77070	−	13.7210i	−1.00245	−	1.40775i
$96$		0			0
$97$	3.21956	−	5.57645i	0.326897	−	0.566202i	−0.654997	−	0.755631i	$-0.727330\pi$
$97$	3.21956	−	5.57645i	0.326897	−	0.566202i	0.981894	+	0.189429i	$0.0606636\pi$
$98$		0			0
$99$	−2.08721	−	0.402276i	−0.209772	−	0.0404303i
$100$		0			0
$101$	−4.81416	+	3.78590i	−0.479027	+	0.376711i	−0.828277	−	0.560319i	$-0.810679\pi$
$101$	−4.81416	+	3.78590i	−0.479027	+	0.376711i	0.349250	+	0.937029i	$0.386436\pi$
$102$		0			0
$103$	−16.3237	+	1.55873i	−1.60843	+	0.153586i	−0.860235	−	0.509897i	$-0.829683\pi$
$103$	−16.3237	+	1.55873i	−1.60843	+	0.153586i	−0.748191	+	0.663483i	$0.769077\pi$
$104$		0			0
$105$	−5.75263	−	9.96385i	−0.561400	−	0.972373i
$106$		0			0
$107$	−4.67973	+	3.00748i	−0.452406	+	0.290744i	−0.746933	−	0.664899i	$-0.768474\pi$
$107$	−4.67973	+	3.00748i	−0.452406	+	0.290744i	0.294527	+	0.955643i	$0.404838\pi$
$108$		0			0
$109$	−1.90863	−	4.17932i	−0.182814	−	0.400306i	0.795931	−	0.605387i	$-0.206982\pi$
$109$	−1.90863	−	4.17932i	−0.182814	−	0.400306i	−0.978745	+	0.205081i	$0.934254\pi$
$110$		0			0
$111$	−2.00247	+	0.385945i	−0.190066	+	0.0366323i
$112$		0			0
$113$	5.39668	+	2.78218i	0.507677	+	0.261725i	0.692981	−	0.720956i	$-0.256297\pi$
$113$	5.39668	+	2.78218i	0.507677	+	0.261725i	−0.185305	+	0.982681i	$0.559327\pi$
$114$		0			0
$115$	−2.92245	−	1.16997i	−0.272520	−	0.109100i
$116$		0			0
$117$	0.768433	−	3.16752i	0.0710416	−	0.292838i
$118$		0			0
$119$	−5.26819	−	36.6410i	−0.482934	−	3.35888i
$120$		0			0
$121$	6.45238	+	0.616128i	0.586580	+	0.0560116i
$122$		0			0
$123$	−0.442317	+	9.28538i	−0.0398824	+	0.837234i
$124$		0			0
$125$	−1.37666	+	9.57487i	−0.123132	+	0.856403i
$126$		0			0
$127$	−8.70362	+	3.48440i	−0.772321	+	0.309191i	−0.724145	−	0.689648i	$-0.757765\pi$
$127$	−8.70362	+	3.48440i	−0.772321	+	0.309191i	−0.0481764	+	0.998839i	$0.515341\pi$
$128$		0			0
$129$	1.86540	+	1.19882i	0.164239	+	0.105550i
$130$		0			0
$131$	2.67073	+	3.08218i	0.233343	+	0.269292i	0.860330	−	0.509738i	$-0.170258\pi$
$131$	2.67073	+	3.08218i	0.233343	+	0.269292i	−0.626987	+	0.779030i	$0.715712\pi$
$132$		0			0
$133$	31.8985			2.76595
$134$		0			0
$135$	2.46485			0.212141
$136$		0			0
$137$	−11.4023	−	13.1590i	−0.974165	−	1.12425i	−0.992231	−	0.124409i	$-0.960296\pi$
$137$	−11.4023	−	13.1590i	−0.974165	−	1.12425i	0.0180663	−	0.999837i	$-0.494249\pi$
$138$		0			0
$139$	−3.04668	−	1.95798i	−0.258416	−	0.166074i	0.405018	−	0.914309i	$-0.367265\pi$
$139$	−3.04668	−	1.95798i	−0.258416	−	0.166074i	−0.663434	+	0.748235i	$0.730902\pi$
$140$		0			0
$141$	0.274848	−	0.110033i	0.0231464	−	0.00926643i
$142$		0			0
$143$	0.985993	−	6.85773i	0.0824529	−	0.573472i
$144$		0			0
$145$	−0.914730	+	19.2025i	−0.0759642	+	1.59468i
$146$		0			0
$147$	14.7208	+	1.40566i	1.21415	+	0.115937i
$148$		0			0
$149$	0.797443	+	5.54634i	0.0653291	+	0.454374i	0.996061	+	0.0886713i	$0.0282621\pi$
$149$	0.797443	+	5.54634i	0.0653291	+	0.454374i	−0.930732	+	0.365702i	$0.880829\pi$
$150$		0			0
$151$	−0.344209	+	1.41885i	−0.0280113	+	0.115464i	−0.984101	−	0.177610i	$-0.943163\pi$
$151$	−0.344209	+	1.41885i	−0.0280113	+	0.115464i	0.956090	+	0.293075i	$0.0946785\pi$
$152$		0			0
$153$	7.36249	+	2.94750i	0.595222	+	0.238291i
$154$		0			0
$155$	−14.6248	−	7.53963i	−1.17470	−	0.605598i
$156$		0			0
$157$	−16.8430	+	3.24622i	−1.34422	+	0.259077i	−0.810079	−	0.586320i	$-0.800576\pi$
$157$	−16.8430	+	3.24622i	−1.34422	+	0.259077i	−0.534138	+	0.845397i	$0.679364\pi$
$158$		0			0
$159$	−1.02518	−	2.24484i	−0.0813022	−	0.178027i
$160$		0			0
$161$	5.01498	−	3.22293i	0.395236	−	0.254003i
$162$		0			0
$163$	0.813592	+	1.40918i	0.0637255	+	0.110376i	0.896128	−	0.443796i	$-0.146368\pi$
$163$	0.813592	+	1.40918i	0.0637255	+	0.110376i	−0.832402	+	0.554172i	$0.813035\pi$
$164$		0			0
$165$	5.21561	−	0.498031i	0.406035	−	0.0387716i
$166$		0			0
$167$	−9.97108	+	7.84134i	−0.771585	+	0.606781i	−0.924378	−	0.381477i	$-0.875416\pi$
$167$	−9.97108	+	7.84134i	−0.771585	+	0.606781i	0.152793	+	0.988258i	$0.451173\pi$
$168$		0			0
$169$	−2.33337	−	0.449720i	−0.179490	−	0.0345938i
$170$		0			0
$171$	−3.41692	+	5.91827i	−0.261298	+	0.452582i
$172$		0			0
$173$	−6.35729	−	8.92757i	−0.483336	−	0.678750i	0.498844	−	0.866692i	$-0.333758\pi$
$173$	−6.35729	−	8.92757i	−0.483336	−	0.678750i	−0.982180	+	0.187941i	$0.939819\pi$
$174$		0			0
$175$	3.63321	+	3.46426i	0.274645	+	0.261873i
$176$		0			0
$177$	7.29547	−	2.14214i	0.548361	−	0.161013i
$178$		0			0
$179$	−15.1818	+	17.5207i	−1.13474	+	1.30956i	−0.189981	+	0.981788i	$0.560843\pi$
$179$	−15.1818	+	17.5207i	−1.13474	+	1.30956i	−0.944758	+	0.327770i	$0.893703\pi$
$180$		0			0
$181$	1.12330	−	3.24556i	0.0834941	−	0.241240i	−0.895524	−	0.445013i	$-0.853199\pi$
$181$	1.12330	−	3.24556i	0.0834941	−	0.241240i	0.979018	+	0.203773i	$0.0653203\pi$
$182$		0			0
$183$	6.07366	−	5.79122i	0.448978	−	0.428099i
$184$		0			0
$185$	4.46785	−	2.30334i	0.328483	−	0.169345i
$186$		0			0
$187$	16.1746	+	4.74928i	1.18280	+	0.347302i
$188$		0			0
$189$	−2.70755	+	3.80222i	−0.196945	+	0.276571i
$190$		0			0
$191$	−4.10854	−	11.8708i	−0.297283	−	0.858944i	−0.990414	−	0.138132i	$-0.955890\pi$
$191$	−4.10854	−	11.8708i	−0.297283	−	0.858944i	0.693130	−	0.720812i	$-0.256231\pi$
$192$		0			0
$193$	6.07807	−	13.3091i	0.437509	−	0.958011i	−0.554540	−	0.832157i	$-0.687106\pi$
$193$	6.07807	−	13.3091i	0.437509	−	0.958011i	0.992049	−	0.125854i	$-0.0401671\pi$
$194$		0			0
$195$	0.382270	+	8.02483i	0.0273749	+	0.574670i
$196$		0			0
$197$	2.18741	+	9.01665i	0.155847	+	0.642409i	0.995118	+	0.0986958i	$0.0314671\pi$
$197$	2.18741	+	9.01665i	0.155847	+	0.642409i	−0.839271	+	0.543714i	$0.817018\pi$
$198$		0			0
$199$	0.646970	+	0.508783i	0.0458625	+	0.0360667i	0.640827	−	0.767685i	$-0.278592\pi$
$199$	0.646970	+	0.508783i	0.0458625	+	0.0360667i	−0.594965	+	0.803752i	$0.702834\pi$
$200$		0			0
$201$	−7.99005	+	1.77737i	−0.563575	+	0.125366i
$202$		0			0
$203$	−28.6166	−	22.5044i	−2.00849	−	1.57950i
$204$		0			0
$205$	−5.40195	−	22.2671i	−0.377289	−	1.55520i
$206$		0			0
$207$	0.0607685	+	1.27569i	0.00422370	+	0.0886664i
$208$		0			0
$209$	−6.03438	+	13.2134i	−0.417407	+	0.913993i
$210$		0			0
$211$	2.53050	+	7.31140i	0.174207	+	0.503338i	0.997976	−	0.0635874i	$-0.0202542\pi$
$211$	2.53050	+	7.31140i	0.174207	+	0.503338i	−0.823769	+	0.566925i	$0.808133\pi$
$212$		0			0
$213$	−5.22490	+	7.33734i	−0.358004	+	0.502746i
$214$		0			0
$215$	−5.24418	−	1.53983i	−0.357650	−	0.105016i
$216$		0			0
$217$	27.6953	−	14.2779i	1.88008	−	0.969250i
$218$		0			0
$219$	−11.2078	+	10.6866i	−0.757350	+	0.722132i
$220$		0			0
$221$	−8.45436	+	24.4273i	−0.568702	+	1.64316i
$222$		0			0
$223$	−12.1065	+	13.9717i	−0.810713	+	0.935613i	−0.998918	−	0.0465169i	$-0.985188\pi$
$223$	−12.1065	+	13.9717i	−0.810713	+	0.935613i	0.188204	+	0.982130i	$0.439733\pi$
$224$		0			0
$225$	−1.03192	+	0.303000i	−0.0687949	+	0.0202000i
$226$		0			0
$227$	12.3618	+	11.7870i	0.820485	+	0.782330i	0.978748	−	0.205066i	$-0.0657411\pi$
$227$	12.3618	+	11.7870i	0.820485	+	0.782330i	−0.158263	+	0.987397i	$0.550590\pi$
$228$		0			0
$229$	15.7836	+	22.1650i	1.04301	+	1.46470i	0.878149	+	0.478387i	$0.158778\pi$
$229$	15.7836	+	22.1650i	1.04301	+	1.46470i	0.164862	+	0.986317i	$0.447282\pi$
$230$		0			0
$231$	−4.96092	+	8.59256i	−0.326404	+	0.565349i
$232$		0			0
$233$	−15.0171	−	2.89431i	−0.983805	−	0.189613i	−0.328111	−	0.944639i	$-0.606412\pi$
$233$	−15.0171	−	2.89431i	−0.983805	−	0.189613i	−0.655694	+	0.755026i	$0.727624\pi$
$234$		0			0
$235$	−0.573609	+	0.451091i	−0.0374181	+	0.0294259i
$236$		0			0
$237$	11.8472	−	1.13127i	0.769557	−	0.0734838i
$238$		0			0
$239$	−3.58145	−	6.20326i	−0.231665	−	0.401256i	0.726633	−	0.687026i	$-0.241084\pi$
$239$	−3.58145	−	6.20326i	−0.231665	−	0.401256i	−0.958298	+	0.285770i	$0.907751\pi$
$240$		0			0
$241$	−15.4573	+	9.93380i	−0.995692	+	0.639892i	−0.933652	−	0.358182i	$-0.883397\pi$
$241$	−15.4573	+	9.93380i	−0.995692	+	0.639892i	−0.0620397	+	0.998074i	$0.519761\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−35.7909	+	6.89813i	−2.28660	+	0.440705i
$246$		0			0
$247$	−19.7981	−	10.2066i	−1.25972	−	0.649432i
$248$		0			0
$249$	−0.298188	−	0.119376i	−0.0188969	−	0.00756517i
$250$		0			0
$251$	2.16104	−	8.90793i	0.136404	−	0.562264i	−0.862058	−	0.506810i	$-0.830824\pi$
$251$	2.16104	−	8.90793i	0.136404	−	0.562264i	0.998461	−	0.0554533i	$-0.0176604\pi$
$252$		0			0
$253$	0.386342	+	2.68707i	0.0242891	+	0.168935i
$254$		0			0
$255$	−19.4592	−	1.85813i	−1.21858	−	0.116360i
$256$		0			0
$257$	−0.606523	+	12.7325i	−0.0378339	+	0.794231i	0.897617	+	0.440775i	$0.145297\pi$
$257$	−0.606523	+	12.7325i	−0.0378339	+	0.794231i	−0.935451	+	0.353456i	$0.885007\pi$
$258$		0			0
$259$	−1.35470	+	9.42214i	−0.0841769	+	0.585463i
$260$		0			0
$261$	7.24070	−	2.89874i	0.448188	−	0.179427i
$262$		0			0
$263$	21.7052	+	13.9491i	1.33840	+	0.860136i	0.996818	−	0.0797163i	$-0.0254014\pi$
$263$	21.7052	+	13.9491i	1.33840	+	0.860136i	0.341580	+	0.939853i	$0.389038\pi$
$264$		0			0
$265$	3.98344	+	4.59713i	0.244701	+	0.282400i
$266$		0			0
$267$	−11.8941			−0.727906
$268$		0			0
$269$	18.9708			1.15667			0.578336	−	0.815799i	$-0.303702\pi$
$269$	18.9708			1.15667			0.578336	+	0.815799i	$0.303702\pi$
$270$		0			0
$271$	−4.17559	−	4.81889i	−0.253649	−	0.292727i	0.614617	−	0.788826i	$-0.289311\pi$
$271$	−4.17559	−	4.81889i	−0.253649	−	0.292727i	−0.868266	+	0.496099i	$0.834765\pi$
$272$		0			0
$273$	−12.7988	−	8.22532i	−0.774621	−	0.497819i
$274$		0			0
$275$	−2.12232	+	0.849650i	−0.127981	+	0.0512358i
$276$		0			0
$277$	2.38541	−	16.5909i	0.143325	−	0.996850i	−0.783509	−	0.621380i	$-0.786572\pi$
$277$	2.38541	−	16.5909i	0.143325	−	0.996850i	0.926835	−	0.375470i	$-0.122519\pi$
$278$		0			0
$279$	−0.317630	+	6.66787i	−0.0190160	+	0.399195i
$280$		0			0
$281$	32.6943	+	3.12193i	1.95038	+	0.186239i	0.994280	−	0.106805i	$-0.0340621\pi$
$281$	32.6943	+	3.12193i	1.95038	+	0.186239i	0.956099	+	0.293044i	$0.0946682\pi$
$282$		0			0
$283$	0.791944	+	5.50809i	0.0470762	+	0.327422i	0.999727	+	0.0233563i	$0.00743523\pi$
$283$	0.791944	+	5.50809i	0.0470762	+	0.327422i	−0.952651	+	0.304066i	$0.901656\pi$
$284$		0			0
$285$	3.97121	−	16.3696i	0.235234	−	0.969649i
$286$		0			0
$287$	40.2826	+	16.1267i	2.37781	+	0.951931i
$288$		0			0
$289$	−40.7923	−	21.0299i	−2.39955	−	1.23705i
$290$		0			0
$291$	6.32276	−	1.21861i	0.370647	−	0.0714363i
$292$		0			0
$293$	−3.38464	−	7.41133i	−0.197733	−	0.432975i	0.784629	−	0.619966i	$-0.212854\pi$
$293$	−3.38464	−	7.41133i	−0.197733	−	0.432975i	−0.982362	+	0.186991i	$0.940126\pi$
$294$		0			0
$295$	−15.7663	+	10.1324i	−0.917948	+	0.589929i
$296$		0			0
$297$	−1.06281	−	1.84084i	−0.0616705	−	0.106816i
$298$		0			0
$299$	−4.14384	+	0.395689i	−0.239644	+	0.0228833i
$300$		0			0
$301$	8.13586	−	6.39811i	0.468943	−	0.368781i
$302$		0			0
$303$	−6.01379	−	1.15906i	−0.345483	−	0.0665865i
$304$		0			0
$305$	−10.3426	+	17.9140i	−0.592218	+	1.02575i
$306$		0			0
$307$	15.9492	+	22.3975i	0.910267	+	1.27829i	0.960135	+	0.279535i	$0.0901803\pi$
$307$	15.9492	+	22.3975i	0.910267	+	1.27829i	−0.0498686	+	0.998756i	$0.515880\pi$
$308$		0			0
$309$	−11.8678	−	11.3159i	−0.675135	−	0.643740i
$310$		0			0
$311$	10.8757	−	3.19340i	0.616705	−	0.181081i	0.0415648	−	0.999136i	$-0.486766\pi$
$311$	10.8757	−	3.19340i	0.616705	−	0.181081i	0.575140	+	0.818055i	$0.304948\pi$
$312$		0			0
$313$	−15.6498	+	18.0608i	−0.884577	+	1.02086i	0.115045	+	0.993360i	$0.463299\pi$
$313$	−15.6498	+	18.0608i	−0.884577	+	1.02086i	−0.999622	+	0.0274959i	$0.991247\pi$
$314$		0			0
$315$	3.76300	−	10.8725i	0.212021	−	0.612595i
$316$		0			0
$317$	11.5956	−	11.0564i	0.651275	−	0.620989i	−0.290644	−	0.956831i	$-0.593869\pi$
$317$	11.5956	−	11.0564i	0.651275	−	0.620989i	0.941918	+	0.335842i	$0.109021\pi$
$318$		0			0
$319$	14.7356	−	7.59673i	0.825035	−	0.425335i
$320$		0			0
$321$	−5.33747	−	1.56722i	−0.297909	−	0.0874738i
$322$		0			0
$323$	31.4369	−	44.1470i	1.74920	−	2.45640i
$324$		0			0
$325$	−1.14652	−	3.31265i	−0.0635974	−	0.183753i
$326$		0			0
$327$	1.90863	−	4.17932i	0.105548	−	0.231117i
$328$		0			0
$329$	−0.0657539	−	1.38034i	−0.00362513	−	0.0761008i
$330$		0			0
$331$	−2.50370	−	10.3204i	−0.137616	−	0.567259i	−0.998309	−	0.0581352i	$-0.981485\pi$
$331$	−2.50370	−	10.3204i	−0.137616	−	0.567259i	0.860693	−	0.509124i	$-0.170031\pi$
$332$		0			0
$333$	−1.60302	−	1.26063i	−0.0878449	−	0.0690820i
$334$		0			0
$335$	17.6623	−	9.75202i	0.964993	−	0.532810i
$336$		0			0
$337$	10.5273	+	8.27878i	0.573460	+	0.450974i	0.862296	−	0.506405i	$-0.169026\pi$
$337$	10.5273	+	8.27878i	0.573460	+	0.450974i	−0.288836	+	0.957379i	$0.593268\pi$
$338$		0			0
$339$	1.43144	+	5.90048i	0.0777451	+	0.320470i
$340$		0			0
$341$	0.675161	+	14.1734i	0.0365620	+	0.767531i
$342$		0			0
$343$	15.1008	−	33.0661i	0.815366	−	1.78540i
$344$		0			0
$345$	−1.02959	−	2.97481i	−0.0554313	−	0.160158i
$346$		0			0
$347$	−17.0162	+	23.8959i	−0.913477	+	1.28280i	0.0453971	+	0.998969i	$0.485545\pi$
$347$	−17.0162	+	23.8959i	−0.913477	+	1.28280i	−0.958874	+	0.283830i	$0.908395\pi$
$348$		0			0
$349$	25.2446	+	7.41247i	1.35131	+	0.396780i	0.875691	−	0.482871i	$-0.160406\pi$
$349$	25.2446	+	7.41247i	1.35131	+	0.396780i	0.475619	+	0.879652i	$0.342224\pi$
$350$		0			0
$351$	2.89707	−	1.49354i	0.154634	−	0.0797195i
$352$		0			0
$353$	−4.48865	+	4.27992i	−0.238907	+	0.227797i	−0.800068	−	0.599910i	$-0.795203\pi$
$353$	−4.48865	+	4.27992i	−0.238907	+	0.227797i	0.561161	+	0.827706i	$0.310355\pi$
$354$		0			0
$355$	7.26166	−	20.9812i	0.385409	−	1.11357i
$356$		0			0
$357$	24.2415	−	27.9762i	1.28300	−	1.48066i
$358$		0			0
$359$	34.3142	−	10.0755i	1.81103	−	0.531767i	0.812354	−	0.583165i	$-0.198186\pi$
$359$	34.3142	−	10.0755i	1.81103	−	0.531767i	0.998678	+	0.0513978i	$0.0163676\pi$
$360$		0			0
$361$	20.0484	+	19.1161i	1.05518	+	1.00611i
$362$		0			0
$363$	3.75977	+	5.27986i	0.197337	+	0.277121i
$364$		0			0
$365$	19.0854	−	33.0568i	0.998973	−	1.73027i
$366$		0			0
$367$	31.2365	+	6.02035i	1.63053	+	0.314260i	0.920748	−	0.390158i	$-0.127580\pi$
$367$	31.2365	+	6.02035i	1.63053	+	0.314260i	0.709785	+	0.704418i	$0.248792\pi$
$368$		0			0
$369$	−7.30708	+	5.74635i	−0.380391	+	0.299143i
$370$		0			0
$371$	−11.4671	+	1.09498i	−0.595343	+	0.0568483i
$372$		0			0
$373$	−9.30706	−	16.1203i	−0.481901	−	0.834678i	0.517883	−	0.855452i	$-0.326720\pi$
$373$	−9.30706	−	16.1203i	−0.481901	−	0.834678i	−0.999784	+	0.0207740i	$0.993387\pi$
$374$		0			0
$375$	−8.13773	+	5.22980i	−0.420230	+	0.270066i
$376$		0			0
$377$	10.5604	+	23.1240i	0.543888	+	1.19095i
$378$		0			0
$379$	−12.7336	+	2.45419i	−0.654079	+	0.126063i	−0.505486	−	0.862835i	$-0.668687\pi$
$379$	−12.7336	+	2.45419i	−0.654079	+	0.126063i	−0.148593	+	0.988898i	$0.547474\pi$
$380$		0			0
$381$	−8.33299	−	4.29596i	−0.426912	−	0.220088i
$382$		0			0
$383$	2.23341	+	0.894124i	0.114122	+	0.0456876i	0.428021	−	0.903769i	$-0.359211\pi$
$383$	2.23341	+	0.894124i	0.114122	+	0.0456876i	−0.313899	+	0.949456i	$0.601635\pi$
$384$		0			0
$385$	5.76568	−	23.7665i	0.293846	−	1.21125i
$386$		0			0
$387$	0.315570	+	2.19484i	0.0160413	+	0.111570i
$388$		0			0
$389$	34.5082	+	3.29514i	1.74964	+	0.167070i	0.920179	−	0.391498i	$-0.128043\pi$
$389$	34.5082	+	3.29514i	1.74964	+	0.167070i	0.829459	+	0.558568i	$0.188649\pi$
$390$		0			0
$391$	0.481929	−	10.1169i	0.0243722	−	0.511635i
$392$		0			0
$393$	−0.580405	+	4.03680i	−0.0292775	+	0.203630i
$394$		0			0
$395$	−27.2331	+	10.9025i	−1.37024	+	0.548563i
$396$		0			0
$397$	−8.01695	−	5.15218i	−0.402359	−	0.258581i	0.323774	−	0.946134i	$-0.395048\pi$
$397$	−8.01695	−	5.15218i	−0.402359	−	0.258581i	−0.726133	+	0.687554i	$0.758685\pi$
$398$		0			0
$399$	20.8891	+	24.1073i	1.04576	+	1.20687i
$400$		0			0
$401$	−21.7179			−1.08454			−0.542270	−	0.840204i	$-0.682435\pi$
$401$	−21.7179			−1.08454			−0.542270	+	0.840204i	$0.682435\pi$
$402$		0			0
$403$	−21.7579			−1.08384
$404$		0			0
$405$	1.61413	+	1.86281i	0.0802070	+	0.0925638i
$406$		0			0
$407$	−3.64670	−	2.34359i	−0.180760	−	0.116167i
$408$		0			0
$409$	−15.9079	+	6.36857i	−0.786596	+	0.314906i	−0.729961	−	0.683489i	$-0.760462\pi$
$409$	−15.9079	+	6.36857i	−0.786596	+	0.314906i	−0.0566358	+	0.998395i	$0.518037\pi$
$410$		0			0
$411$	2.47796	−	17.2346i	0.122229	−	0.850119i
$412$		0			0
$413$	1.68873	−	35.4508i	0.0830969	−	1.74442i
$414$		0			0
$415$	0.788114	+	0.0752558i	0.0386870	+	0.00369416i
$416$		0			0
$417$	−0.515407	−	3.58474i	−0.0252396	−	0.175545i
$418$		0			0
$419$	4.70058	−	19.3760i	0.229638	−	0.946582i	−0.733953	−	0.679201i	$-0.762327\pi$
$419$	4.70058	−	19.3760i	0.229638	−	0.946582i	0.963591	−	0.267381i	$-0.0861583\pi$
$420$		0			0
$421$	−12.8116	−	5.12899i	−0.624400	−	0.249972i	0.0378166	−	0.999285i	$-0.487960\pi$
$421$	−12.8116	−	5.12899i	−0.624400	−	0.249972i	−0.662216	+	0.749313i	$0.730384\pi$
$422$		0			0
$423$	0.263145	+	0.135660i	0.0127945	+	0.00659604i
$424$		0			0
$425$	8.37511	−	1.61417i	0.406252	−	0.0782987i
$426$		0			0
$427$	−16.2727	−	35.6322i	−0.787491	−	1.72436i
$428$		0			0
$429$	5.82841	−	3.74569i	0.281399	−	0.180844i
$430$		0			0
$431$	3.97645	+	6.88741i	0.191539	+	0.331755i	0.945760	−	0.324865i	$-0.105319\pi$
$431$	3.97645	+	6.88741i	0.191539	+	0.331755i	−0.754222	+	0.656620i	$0.771986\pi$
$432$		0			0
$433$	−21.8410	+	2.08556i	−1.04961	+	0.100226i	−0.605578	−	0.795786i	$-0.707058\pi$
$433$	−21.8410	+	2.08556i	−1.04961	+	0.100226i	−0.444031	+	0.896011i	$0.646452\pi$
$434$		0			0
$435$	−15.1113	+	11.8837i	−0.724533	+	0.569779i
$436$		0			0
$437$	8.57000	+	1.65173i	0.409959	+	0.0790130i
$438$		0			0
$439$	4.81358	−	8.33737i	0.229740	−	0.397921i	−0.727991	−	0.685587i	$-0.759546\pi$
$439$	4.81358	−	8.33737i	0.229740	−	0.397921i	0.957731	+	0.287666i	$0.0928791\pi$
$440$		0			0
$441$	8.57773	+	12.0457i	0.408463	+	0.573607i
$442$		0			0
$443$	2.17686	+	2.07564i	0.103426	+	0.0986165i	0.740028	−	0.672576i	$-0.234812\pi$
$443$	2.17686	+	2.07564i	0.103426	+	0.0986165i	−0.636602	+	0.771192i	$0.719661\pi$
$444$		0			0
$445$	28.1296	−	8.25959i	1.33347	−	0.391542i
$446$		0			0
$447$	−3.66943	+	4.23474i	−0.173558	+	0.200297i
$448$		0			0
$449$	−6.94453	+	20.0649i	−0.327733	+	0.946921i	0.653973	+	0.756518i	$0.273101\pi$
$449$	−6.94453	+	20.0649i	−0.327733	+	0.946921i	−0.981706	+	0.190404i	$0.939020\pi$
$450$		0			0
$451$	−14.3007	+	13.6357i	−0.673393	+	0.642079i
$452$		0			0
$453$	−1.29770	+	0.669013i	−0.0609714	+	0.0314330i
$454$		0			0
$455$	35.9812	+	10.5650i	1.68683	+	0.495297i
$456$		0			0
$457$	14.3128	−	20.0995i	0.669525	−	0.940216i	−0.330468	−	0.943817i	$-0.607207\pi$
$457$	14.3128	−	20.0995i	0.669525	−	0.940216i	0.999994	+	0.00360062i	$0.00114612\pi$
$458$		0			0
$459$	2.59384	+	7.49440i	0.121070	+	0.349809i
$460$		0			0
$461$	−4.08804	+	8.95156i	−0.190399	+	0.416916i	−0.980624	−	0.195902i	$-0.937237\pi$
$461$	−4.08804	+	8.95156i	−0.190399	+	0.416916i	0.790225	+	0.612817i	$0.209964\pi$
$462$		0			0
$463$	−1.24041	−	26.0394i	−0.0576468	−	1.21016i	−0.823567	−	0.567219i	$-0.808019\pi$
$463$	−1.24041	−	26.0394i	−0.0576468	−	1.21016i	0.765920	−	0.642936i	$-0.222284\pi$
$464$		0			0
$465$	−3.87916	−	15.9901i	−0.179892	−	0.741524i
$466$		0			0
$467$	−4.71579	−	3.70854i	−0.218221	−	0.171611i	0.503064	−	0.864249i	$-0.332206\pi$
$467$	−4.71579	−	3.70854i	−0.218221	−	0.171611i	−0.721285	+	0.692638i	$0.756448\pi$
$468$		0			0
$469$	−4.35813	+	37.9577i	−0.201240	+	1.75272i
$470$		0			0
$471$	−13.4831	−	10.6033i	−0.621271	−	0.488573i
$472$		0			0
$473$	1.11122	+	4.58051i	0.0510939	+	0.210612i
$474$		0			0
$475$	0.349713	+	7.34138i	0.0160459	+	0.336846i
$476$		0			0
$477$	1.02518	−	2.24484i	0.0469399	−	0.102784i
$478$		0			0
$479$	−0.749908	−	2.16672i	−0.0342642	−	0.0989998i	0.926571	−	0.376119i	$-0.122742\pi$
$479$	−0.749908	−	2.16672i	−0.0342642	−	0.0989998i	−0.960836	+	0.277119i	$0.910620\pi$
$480$		0			0
$481$	3.85563	−	5.41447i	0.175801	−	0.246879i
$482$		0			0
$483$	5.71984	+	1.67950i	0.260262	+	0.0764198i
$484$		0			0
$485$	−14.1071	+	7.27273i	−0.640572	+	0.330238i
$486$		0			0
$487$	−30.1200	+	28.7194i	−1.36487	+	1.30140i	−0.452651	+	0.891688i	$0.649522\pi$
$487$	−30.1200	+	28.7194i	−1.36487	+	1.30140i	−0.912216	+	0.409710i	$0.865630\pi$
$488$		0			0
$489$	−0.532200	+	1.53769i	−0.0240669	+	0.0695368i
$490$		0			0
$491$	2.14196	−	2.47195i	0.0966653	−	0.111558i	−0.705356	−	0.708854i	$-0.749213\pi$
$491$	2.14196	−	2.47195i	0.0966653	−	0.111558i	0.802021	+	0.597296i	$0.203758\pi$
$492$		0			0
$493$	−59.3481	+	17.4262i	−2.67291	+	0.784836i
$494$		0			0
$495$	3.79189	+	3.61556i	0.170433	+	0.162507i
$496$		0			0
$497$	24.3884	+	34.2488i	1.09397	+	1.53627i
$498$		0			0
$499$	4.96471	−	8.59914i	0.222251	−	0.384950i	−0.733240	−	0.679970i	$-0.761993\pi$
$499$	4.96471	−	8.59914i	0.222251	−	0.384950i	0.955491	+	0.295020i	$0.0953262\pi$
$500$		0			0
$501$	−12.4558	−	2.40065i	−0.556482	−	0.107253i
$502$		0			0
$503$	19.6774	−	15.4745i	0.877374	−	0.689974i	−0.0742501	−	0.997240i	$-0.523656\pi$
$503$	19.6774	−	15.4745i	0.877374	−	0.689974i	0.951624	+	0.307265i	$0.0994139\pi$
$504$		0			0
$505$	15.0275	−	1.43496i	0.668717	−	0.0638547i
$506$		0			0
$507$	−1.18816	−	2.05795i	−0.0527679	−	0.0913966i
$508$		0			0
$509$	−9.06152	+	5.82348i	−0.401645	+	0.258121i	−0.725833	−	0.687871i	$-0.758545\pi$
$509$	−9.06152	+	5.82348i	−0.401645	+	0.258121i	0.324188	+	0.945993i	$0.394909\pi$
$510$		0			0
$511$	30.0281	+	65.7524i	1.32837	+	2.90871i
$512$		0			0
$513$	−6.71034	+	1.29331i	−0.296269	+	0.0571011i
$514$		0			0
$515$	35.9255	+	18.5209i	1.58307	+	0.816127i
$516$		0			0
$517$	0.584224	+	0.233888i	0.0256941	+	0.0102864i
$518$		0			0
$519$	2.58386	−	10.6508i	0.113419	−	0.467520i
$520$		0			0
$521$	−0.480912	−	3.34482i	−0.0210691	−	0.146539i	0.976571	−	0.215194i	$-0.0690384\pi$
$521$	−0.480912	−	3.34482i	−0.0210691	−	0.146539i	−0.997640	+	0.0686549i	$0.978129\pi$
$522$		0			0
$523$	0.688467	+	0.0657406i	0.0301046	+	0.00287464i	0.110097	−	0.993921i	$-0.464884\pi$
$523$	0.688467	+	0.0657406i	0.0301046	+	0.00287464i	−0.0799929	+	0.996795i	$0.525490\pi$
$524$		0			0
$525$	−0.238866	+	5.01441i	−0.0104250	+	0.218847i
$526$		0			0
$527$	7.53415	−	52.4012i	0.328193	−	2.28263i
$528$		0			0
$529$	−19.8382	+	7.94203i	−0.862532	+	0.345306i
$530$		0			0
$531$	6.39644	+	4.11074i	0.277582	+	0.178391i
$532$		0			0
$533$	−19.8417	−	22.8985i	−0.859438	−	0.991845i
$534$		0			0
$535$	13.7115			0.592799
$536$		0			0
$537$	−23.1832			−1.00043
$538$		0			0
$539$	20.5843	+	23.7556i	0.886630	+	1.02323i
$540$		0			0
$541$	13.2756	+	8.53173i	0.570764	+	0.366808i	0.793964	−	0.607965i	$-0.208014\pi$
$541$	13.2756	+	8.53173i	0.570764	+	0.366808i	−0.223200	+	0.974773i	$0.571650\pi$
$542$		0			0
$543$	3.18843	−	1.27646i	0.136829	−	0.0547780i
$544$		0			0
$545$	−1.61169	+	11.2095i	−0.0690371	+	0.480164i
$546$		0			0
$547$	0.538464	−	11.3038i	0.0230231	−	0.483314i	−0.957683	−	0.287825i	$-0.907068\pi$
$547$	0.538464	−	11.3038i	0.0230231	−	0.483314i	0.980706	−	0.195488i	$-0.0626292\pi$
$548$		0			0
$549$	8.35411	+	0.797721i	0.356545	+	0.0340459i
$550$		0			0
$551$	−7.58534	−	52.7572i	−0.323146	−	2.24753i
$552$		0			0
$553$	13.0966	−	53.9851i	0.556926	−	2.29568i
$554$		0			0
$555$	4.66657	+	1.86821i	0.198085	+	0.0793012i
$556$		0			0
$557$	7.30490	+	3.76594i	0.309519	+	0.159568i	0.605987	−	0.795475i	$-0.292778\pi$
$557$	7.30490	+	3.76594i	0.309519	+	0.159568i	−0.296468	+	0.955043i	$0.595809\pi$
$558$		0			0
$559$	−7.09681	+	1.36780i	−0.300163	+	0.0578517i
$560$		0			0
$561$	7.00282	+	15.3340i	0.295659	+	0.647404i
$562$		0			0
$563$	0.639741	−	0.411136i	0.0269618	−	0.0173273i	−0.527090	−	0.849809i	$-0.676717\pi$
$563$	0.639741	−	0.411136i	0.0269618	−	0.0173273i	0.554052	+	0.832482i	$0.313081\pi$
$564$		0			0
$565$	−7.48282	−	12.9606i	−0.314805	−	0.545258i
$566$		0			0
$567$	−4.64660	+	0.443696i	−0.195139	+	0.0186335i
$568$		0			0
$569$	30.6437	−	24.0985i	1.28465	−	1.01026i	0.286007	−	0.958228i	$-0.407672\pi$
$569$	30.6437	−	24.0985i	1.28465	−	1.01026i	0.998645	−	0.0520339i	$-0.0165704\pi$
$570$		0			0
$571$	33.4797	+	6.45268i	1.40108	+	0.270036i	0.833153	−	0.553043i	$-0.186533\pi$
$571$	33.4797	+	6.45268i	1.40108	+	0.270036i	0.567927	+	0.823079i	$0.307746\pi$
$572$		0			0
$573$	6.28086	−	10.8788i	0.262387	−	0.454467i
$574$		0			0
$575$	0.796733	+	1.11885i	0.0332260	+	0.0466594i
$576$		0			0
$577$	−22.7097	−	21.6536i	−0.945416	−	0.901452i	0.0498388	−	0.998757i	$-0.484129\pi$
$577$	−22.7097	−	21.6536i	−0.945416	−	0.901452i	−0.995255	+	0.0973052i	$0.968978\pi$
$578$		0			0
$579$	14.0386	−	4.12212i	0.583426	−	0.171309i
$580$		0			0
$581$	−0.981803	+	1.13306i	−0.0407321	+	0.0470073i
$582$		0			0
$583$	1.71571	−	4.95720i	0.0710572	−	0.205306i
$584$		0			0
$585$	−5.81443	+	5.54405i	−0.240397	+	0.229218i
$586$		0			0
$587$	−24.4988	+	12.6300i	−1.01117	+	0.521296i	−0.882461	−	0.470386i	$-0.844115\pi$
$587$	−24.4988	+	12.6300i	−1.01117	+	0.521296i	−0.128713	+	0.991682i	$0.541084\pi$
$588$		0			0
$589$	43.7709	+	12.8523i	1.80355	+	0.529570i
$590$		0			0
$591$	−5.38187	+	7.55778i	−0.221381	+	0.310886i
$592$		0			0
$593$	−1.24223	−	3.58919i	−0.0510124	−	0.147391i	0.916617	−	0.399767i	$-0.130909\pi$
$593$	−1.24223	−	3.58919i	−0.0510124	−	0.147391i	−0.967629	+	0.252377i	$0.918788\pi$
$594$		0			0
$595$	−37.9039	+	82.9979i	−1.55391	+	3.40258i
$596$		0			0
$597$	0.0391629	+	0.822129i	0.00160283	+	0.0336475i
$598$		0			0
$599$	4.69145	+	19.3384i	0.191688	+	0.790147i	0.983726	+	0.179676i	$0.0575048\pi$
$599$	4.69145	+	19.3384i	0.191688	+	0.790147i	−0.792038	+	0.610471i	$0.790980\pi$
$600$		0			0
$601$	−20.5711	−	16.1773i	−0.839114	−	0.659887i	0.103184	−	0.994662i	$-0.467097\pi$
$601$	−20.5711	−	16.1773i	−0.839114	−	0.659887i	−0.942298	+	0.334776i	$0.891339\pi$
$602$		0			0
$603$	−6.57562	−	4.87455i	−0.267780	−	0.198507i
$604$		0			0
$605$	−12.5584	−	9.87602i	−0.510571	−	0.401517i
$606$		0			0
$607$	−3.89247	−	16.0450i	−0.157990	−	0.651246i	−0.994630	−	0.103492i	$-0.966998\pi$
$607$	−3.89247	−	16.0450i	−0.157990	−	0.651246i	0.836640	−	0.547753i	$-0.184517\pi$
$608$		0			0
$609$	−1.73224	−	36.3642i	−0.0701940	−	1.47355i
$610$		0			0
$611$	−0.400860	+	0.877762i	−0.0162171	+	0.0355104i
$612$		0			0
$613$	9.03746	+	26.1120i	0.365020	+	1.05465i	0.966699	+	0.255917i	$0.0823773\pi$
$613$	9.03746	+	26.1120i	0.365020	+	1.05465i	−0.601679	+	0.798738i	$0.705501\pi$
$614$		0			0
$615$	13.2909	−	18.6644i	0.535939	−	0.752621i
$616$		0			0
$617$	37.4452	+	10.9949i	1.50749	+	0.442638i	0.928074	−	0.372397i	$-0.121464\pi$
$617$	37.4452	+	10.9949i	1.50749	+	0.442638i	0.579413	+	0.815034i	$0.303282\pi$
$618$		0			0
$619$	17.3671	−	8.95337i	0.698044	−	0.359867i	−0.0723991	−	0.997376i	$-0.523066\pi$
$619$	17.3671	−	8.95337i	0.698044	−	0.359867i	0.770443	+	0.637509i	$0.220035\pi$
$620$		0			0
$621$	−0.924305	+	0.881323i	−0.0370911	+	0.0353663i
$622$		0			0
$623$	−18.1583	+	52.4649i	−0.727497	+	2.10196i
$624$		0			0
$625$	19.1355	−	22.0836i	0.765421	−	0.883343i
$626$		0			0
$627$	−13.9377	+	4.09249i	−0.556619	+	0.163438i
$628$		0			0
$629$	11.7050	+	11.1607i	0.466708	+	0.445005i
$630$		0			0
$631$	−19.0864	−	26.8032i	−0.759819	−	1.06702i	−0.995460	−	0.0951768i	$-0.969658\pi$
$631$	−19.0864	−	26.8032i	−0.759819	−	1.06702i	0.235641	−	0.971840i	$-0.424281\pi$
$632$		0			0
$633$	−3.86846	+	6.70037i	−0.153758	+	0.266316i
$634$		0			0
$635$	22.6908	+	4.37330i	0.900458	+	0.173549i
$636$		0			0
$637$	−37.8871	+	29.7947i	−1.50114	+	1.18051i
$638$		0			0
$639$	−8.96677	+	0.856223i	−0.354720	+	0.0338717i
$640$		0			0
$641$	7.78774	+	13.4888i	0.307597	+	0.532774i	0.977836	−	0.209371i	$-0.0671417\pi$
$641$	7.78774	+	13.4888i	0.307597	+	0.532774i	−0.670239	+	0.742145i	$0.733808\pi$
$642$		0			0
$643$	−23.2758	+	14.9584i	−0.917907	+	0.589903i	−0.912050	−	0.410080i	$-0.865501\pi$
$643$	−23.2758	+	14.9584i	−0.917907	+	0.589903i	−0.00585732	+	0.999983i	$0.501864\pi$
$644$		0			0
$645$	−2.27048	−	4.97167i	−0.0894002	−	0.195759i
$646$		0			0
$647$	−42.9489	+	8.27773i	−1.68850	+	0.325431i	−0.940890	−	0.338711i	$-0.890009\pi$
$647$	−42.9489	+	8.27773i	−1.68850	+	0.325431i	−0.747606	+	0.664142i	$0.768797\pi$
$648$		0			0
$649$	14.3654	+	7.40590i	0.563893	+	0.290707i
$650$		0			0
$651$	28.9271	+	11.5807i	1.13374	+	0.453883i
$652$		0			0
$653$	−1.39389	+	5.74569i	−0.0545471	+	0.224846i	−0.992560	−	0.121753i	$-0.961148\pi$
$653$	−1.39389	+	5.74569i	−0.0545471	+	0.224846i	0.938013	+	0.346599i	$0.112664\pi$
$654$		0			0
$655$	−1.43061	−	9.95011i	−0.0558986	−	0.388783i
$656$		0			0
$657$	−15.4159	−	1.47204i	−0.601431	−	0.0574297i
$658$		0			0
$659$	−0.453962	+	9.52983i	−0.0176838	+	0.371230i	0.972628	+	0.232368i	$0.0746474\pi$
$659$	−0.453962	+	9.52983i	−0.0176838	+	0.371230i	−0.990312	+	0.138862i	$0.955656\pi$
$660$		0			0
$661$	1.79977	−	12.5177i	0.0700031	−	0.486882i	−0.924416	−	0.381385i	$-0.875447\pi$
$661$	1.79977	−	12.5177i	0.0700031	−	0.486882i	0.994420	−	0.105498i	$-0.0336435\pi$
$662$		0			0
$663$	−23.9973	+	9.60708i	−0.931978	+	0.373108i
$664$		0			0
$665$	−66.1436	−	42.5079i	−2.56494	−	1.64839i
$666$		0			0
$667$	−6.52297	−	7.52791i	−0.252571	−	0.291482i
$668$		0			0
$669$	−18.4872			−0.714756
$670$		0			0
$671$	17.8384			0.688646
$672$		0			0
$673$	−18.7931	−	21.6883i	−0.724419	−	0.836024i	0.267412	−	0.963582i	$-0.413832\pi$
$673$	−18.7931	−	21.6883i	−0.724419	−	0.836024i	−0.991831	+	0.127558i	$0.959286\pi$
$674$		0			0
$675$	−0.904758	−	0.581453i	−0.0348242	−	0.0223801i
$676$		0			0
$677$	−19.3510	+	7.74696i	−0.743718	+	0.297740i	−0.712404	−	0.701770i	$-0.752393\pi$
$677$	−19.3510	+	7.74696i	−0.743718	+	0.297740i	−0.0313141	+	0.999510i	$0.509969\pi$
$678$		0			0
$679$	4.27743	−	29.7502i	0.164153	−	1.14171i
$680$		0			0
$681$	−0.812730	+	17.0613i	−0.0311439	+	0.653790i
$682$		0			0
$683$	−12.7974	−	1.22200i	−0.489679	−	0.0467586i	−0.152703	−	0.988272i	$-0.548798\pi$
$683$	−12.7974	−	1.22200i	−0.489679	−	0.0467586i	−0.336975	+	0.941513i	$0.609404\pi$
$684$		0			0
$685$	6.10780	+	42.4807i	0.233367	+	1.62310i
$686$		0			0
$687$	−6.41511	+	26.4434i	−0.244752	+	1.00888i
$688$		0			0
$689$	7.46752	+	2.98954i	0.284490	+	0.113893i
$690$		0			0
$691$	23.3325	+	12.0287i	0.887611	+	0.457595i	0.840823	−	0.541310i	$-0.182071\pi$
$691$	23.3325	+	12.0287i	0.887611	+	0.457595i	0.0467874	+	0.998905i	$0.485102\pi$
$692$		0			0
$693$	−9.74253	+	1.87772i	−0.370088	+	0.0713287i
$694$		0			0
$695$	3.70828	+	8.12001i	0.140663	+	0.308010i
$696$		0			0
$697$	62.0188	−	39.8571i	2.34913	−	1.50969i
$698$		0			0
$699$	−7.64675	−	13.2446i	−0.289227	−	0.500955i
$700$		0			0
$701$	7.20786	−	0.688267i	0.272237	−	0.0259955i	0.0419554	−	0.999119i	$-0.486641\pi$
$701$	7.20786	−	0.688267i	0.272237	−	0.0259955i	0.230282	+	0.973124i	$0.426035\pi$
$702$		0			0
$703$	−10.9548	+	8.61492i	−0.413167	+	0.324918i
$704$		0			0
$705$	−0.716545	−	0.138103i	−0.0269867	−	0.00520125i
$706$		0			0
$707$	−14.2937	+	24.7574i	−0.537570	+	0.931098i
$708$		0			0
$709$	−22.6780	−	31.8467i	−0.851689	−	1.19603i	−0.978938	−	0.204159i	$-0.934554\pi$
$709$	−22.6780	−	31.8467i	−0.851689	−	1.19603i	0.127249	−	0.991871i	$-0.459385\pi$
$710$		0			0
$711$	8.61321	+	8.21267i	0.323020	+	0.307999i
$712$		0			0
$713$	8.18008	−	2.40189i	0.306346	−	0.0899514i
$714$		0			0
$715$	−11.1831	+	12.9060i	−0.418225	+	0.482657i
$716$		0			0
$717$	2.34276	−	6.76895i	0.0874919	−	0.252791i
$718$		0			0
$719$	1.46309	−	1.39505i	0.0545641	−	0.0520268i	−0.662306	−	0.749233i	$-0.730422\pi$
$719$	1.46309	−	1.39505i	0.0545641	−	0.0520268i	0.716871	+	0.697206i	$0.245574\pi$
$720$		0			0
$721$	−68.0328	+	35.0733i	−2.53367	+	1.30620i
$722$		0			0
$723$	−17.6298	−	5.17659i	−0.655661	−	0.192519i
$724$		0			0
$725$	4.86560	−	6.83278i	0.180704	−	0.253763i
$726$		0			0
$727$	7.06466	+	20.4120i	0.262014	+	0.757039i	0.996888	+	0.0788352i	$0.0251201\pi$
$727$	7.06466	+	20.4120i	0.262014	+	0.757039i	−0.734874	+	0.678204i	$0.762759\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−0.836743	−	17.5654i	−0.0309481	−	0.649680i
$732$		0			0
$733$	−8.87629	−	36.5886i	−0.327853	−	1.35143i	−0.862373	−	0.506274i	$-0.831023\pi$
$733$	−8.87629	−	36.5886i	−0.327853	−	1.35143i	0.534520	−	0.845156i	$-0.320493\pi$
$734$		0			0
$735$	−28.6513	−	22.5316i	−1.05682	−	0.831092i
$736$		0			0
$737$	−14.8989	−	8.98590i	−0.548808	−	0.331000i
$738$		0			0
$739$	2.56542	+	2.01747i	0.0943706	+	0.0742138i	0.664230	−	0.747529i	$-0.268760\pi$
$739$	2.56542	+	2.01747i	0.0943706	+	0.0742138i	−0.569859	+	0.821743i	$0.693002\pi$
$740$		0			0
$741$	−5.25134	−	21.6463i	−0.192913	−	0.795197i
$742$		0			0
$743$	1.69006	+	35.4787i	0.0620023	+	1.30159i	0.788763	+	0.614698i	$0.210722\pi$
$743$	1.69006	+	35.4787i	0.0620023	+	1.30159i	−0.726760	+	0.686891i	$0.758975\pi$
$744$		0			0
$745$	5.73749	−	12.5634i	0.210205	−	0.460286i
$746$		0			0
$747$	−0.105053	−	0.303530i	−0.00384368	−	0.0111056i
$748$		0			0
$749$	−15.0616	+	21.1510i	−0.550338	+	0.772841i
$750$		0			0
$751$	4.19515	+	1.23181i	0.153083	+	0.0449493i	0.357376	−	0.933960i	$-0.383671\pi$
$751$	4.19515	+	1.23181i	0.153083	+	0.0449493i	−0.204293	+	0.978910i	$0.565490\pi$
$752$		0			0
$753$	8.14735	−	4.20025i	0.296906	−	0.153066i
$754$		0			0
$755$	2.60450	−	2.48338i	0.0947873	−	0.0903795i
$756$		0			0
$757$	10.6438	−	30.7532i	0.386855	−	1.11774i	−0.568602	−	0.822613i	$-0.692515\pi$
$757$	10.6438	−	30.7532i	0.386855	−	1.11774i	0.955457	−	0.295131i	$-0.0953634\pi$
$758$		0			0
$759$	−1.77775	+	2.05164i	−0.0645283	+	0.0744696i
$760$		0			0
$761$	24.4200	−	7.17035i	0.885223	−	0.259925i	0.192645	−	0.981268i	$-0.438293\pi$
$761$	24.4200	−	7.17035i	0.885223	−	0.259925i	0.692577	+	0.721344i	$0.256475\pi$
$762$		0			0
$763$	−15.5212	−	14.7994i	−0.561905	−	0.535775i
$764$		0			0
$765$	−11.3388	−	15.9231i	−0.409954	−	0.575700i
$766$		0			0
$767$	−12.3914	+	21.4625i	−0.447426	+	0.774965i
$768$		0			0
$769$	−24.0309	−	4.63158i	−0.866578	−	0.167019i	−0.263459	−	0.964671i	$-0.584863\pi$
$769$	−24.0309	−	4.63158i	−0.866578	−	0.167019i	−0.603119	+	0.797651i	$0.706075\pi$
$770$		0			0
$771$	−10.0198	+	7.87963i	−0.360853	+	0.283778i
$772$		0			0
$773$	−40.3696	+	3.85483i	−1.45199	+	0.138649i	−0.791034	−	0.611772i	$-0.790457\pi$
$773$	−40.3696	+	3.85483i	−1.45199	+	0.138649i	−0.660960	+	0.750421i	$0.729851\pi$
$774$		0			0
$775$	3.58967	+	6.21750i	0.128945	+	0.223339i
$776$		0			0
$777$	−8.00792	+	5.14638i	−0.287283	+	0.184625i
$778$		0			0
$779$	26.3899	+	57.7859i	0.945518	+	2.07039i
$780$		0			0
$781$	−18.8007	+	3.62353i	−0.672740	+	0.129660i
$782$		0			0
$783$	6.93237	+	3.57389i	0.247743	+	0.127720i
$784$		0			0
$785$	39.2509	+	15.7137i	1.40093	+	0.560846i
$786$		0			0
$787$	−4.05549	+	16.7169i	−0.144563	+	0.595895i	0.852730	+	0.522353i	$0.174946\pi$
$787$	−4.05549	+	16.7169i	−0.144563	+	0.595895i	−0.997292	+	0.0735422i	$0.976570\pi$
$788$		0			0
$789$	3.67186	+	25.5384i	0.130722	+	0.909190i
$790$		0			0
$791$	28.2124	+	2.69396i	1.00312	+	0.0957861i
$792$		0			0
$793$	−1.30152	+	27.3223i	−0.0462183	+	0.970242i
$794$		0			0
$795$	−0.865684	+	6.02097i	−0.0307027	+	0.213542i
$796$		0			0
$797$	−16.9869	+	6.80052i	−0.601706	+	0.240887i	−0.652458	−	0.757825i	$-0.726262\pi$
$797$	−16.9869	+	6.80052i	−0.601706	+	0.240887i	0.0507525	+	0.998711i	$0.483838\pi$
$798$		0			0
$799$	−1.97517	−	1.26937i	−0.0698766	−	0.0449069i
$800$		0			0
$801$	−7.78897	−	8.98895i	−0.275210	−	0.317609i
$802$		0			0
$803$	−32.9174			−1.16163
$804$		0			0
$805$	−14.6938			−0.517887
$806$		0			0
$807$	12.4232	+	14.3372i	0.437319	+	0.504693i
$808$		0			0
$809$	−19.6617	−	12.6358i	−0.691268	−	0.444251i	0.147268	−	0.989097i	$-0.452952\pi$
$809$	−19.6617	−	12.6358i	−0.691268	−	0.444251i	−0.838537	+	0.544845i	$0.816588\pi$
$810$		0			0
$811$	10.3277	−	4.13460i	0.362656	−	0.145185i	−0.183176	−	0.983080i	$-0.558638\pi$
$811$	10.3277	−	4.13460i	0.362656	−	0.145185i	0.545832	+	0.837895i	$0.316214\pi$
$812$		0			0
$813$	0.907442	−	6.31140i	0.0318254	−	0.221350i
$814$		0			0
$815$	0.190840	−	4.00622i	0.00668483	−	0.140332i
$816$		0			0
$817$	15.0848	+	1.44042i	0.527750	+	0.0503940i
$818$		0			0
$819$	−2.16518	−	15.0592i	−0.0756575	−	0.526209i
$820$		0			0
$821$	0.0608202	−	0.250704i	0.00212264	−	0.00874963i	−0.970740	−	0.240131i	$-0.922809\pi$
$821$	0.0608202	−	0.250704i	0.00212264	−	0.00874963i	0.972863	+	0.231382i	$0.0743246\pi$
$822$		0			0
$823$	−21.1472	−	8.46605i	−0.737144	−	0.295108i	−0.0274550	−	0.999623i	$-0.508740\pi$
$823$	−21.1472	−	8.46605i	−0.737144	−	0.295108i	−0.709689	+	0.704515i	$0.751165\pi$
$824$		0			0
$825$	−2.03195	−	1.04754i	−0.0707434	−	0.0364708i
$826$		0			0
$827$	44.0975	−	8.49909i	1.53342	−	0.295542i	0.648474	−	0.761237i	$-0.275408\pi$
$827$	44.0975	−	8.49909i	1.53342	−	0.295542i	0.884946	+	0.465694i	$0.154195\pi$
$828$		0			0
$829$	7.81965	+	17.1226i	0.271588	+	0.594694i	0.995454	−	0.0952465i	$-0.0303639\pi$
$829$	7.81965	+	17.1226i	0.271588	+	0.594694i	−0.723866	+	0.689941i	$0.757637\pi$
$830$		0			0
$831$	14.1007	−	9.06195i	0.489147	−	0.314356i
$832$		0			0
$833$	−58.6377	−	101.563i	−2.03167	−	3.51896i
$834$		0			0
$835$	31.1250	−	2.97208i	1.07713	−	0.102853i
$836$		0			0
$837$	−5.24724	+	4.12648i	−0.181371	+	0.142632i
$838$		0			0
$839$	37.7867	+	7.28278i	1.30454	+	0.251430i	0.793733	−	0.608266i	$-0.208135\pi$
$839$	37.7867	+	7.28278i	1.30454	+	0.251430i	0.510807	+	0.859695i	$0.329347\pi$
$840$		0			0
$841$	−15.9152	+	27.5659i	−0.548800	+	0.950550i
$842$		0			0
$843$	19.0508	+	26.7531i	0.656145	+	0.921427i
$844$		0			0
$845$	4.23909	+	4.04197i	0.145829	+	0.139048i
$846$		0			0
$847$	29.0295	−	8.52382i	0.997464	−	0.292882i
$848$		0			0
$849$	−3.64413	+	4.20555i	−0.125066	+	0.144334i
$850$		0			0
$851$	−0.851846	+	2.46125i	−0.0292009	+	0.0843705i
$852$		0			0
$853$	−3.36761	+	3.21100i	−0.115305	+	0.109943i	−0.745538	−	0.666463i	$-0.767808\pi$
$853$	−3.36761	+	3.21100i	−0.115305	+	0.109943i	0.630234	+	0.776405i	$0.282959\pi$
$854$		0			0
$855$	14.9719	−	7.71854i	0.512027	−	0.263969i
$856$		0			0
$857$	35.2974	+	10.3643i	1.20574	+	0.354036i	0.822043	−	0.569425i	$-0.192834\pi$
$857$	35.2974	+	10.3643i	1.20574	+	0.354036i	0.383693	+	0.923461i	$0.374652\pi$
$858$		0			0
$859$	−30.1034	+	42.2744i	−1.02712	+	1.44238i	−0.134854	+	0.990865i	$0.543057\pi$
$859$	−30.1034	+	42.2744i	−1.02712	+	1.44238i	−0.892262	+	0.451518i	$0.850883\pi$
$860$		0			0
$861$	14.1917	+	41.0044i	0.483653	+	1.39742i
$862$		0			0
$863$	5.92774	−	12.9800i	0.201783	−	0.441843i	−0.781505	−	0.623898i	$-0.785548\pi$
$863$	5.92774	−	12.9800i	0.201783	−	0.441843i	0.983288	+	0.182056i	$0.0582752\pi$
$864$		0			0
$865$	1.28539	+	26.9836i	0.0437045	+	0.917470i
$866$		0			0
$867$	−10.8199	−	44.6004i	−0.367464	−	1.51471i
$868$		0			0
$869$	19.8849	+	15.6377i	0.674549	+	0.530471i
$870$		0			0
$871$	14.8503	−	22.1643i	0.503183	−	0.751008i
$872$		0			0
$873$	5.06150	+	3.98040i	0.171306	+	0.134716i
$874$		0			0
$875$	10.6451	+	43.8798i	0.359871	+	1.48341i
$876$		0			0
$877$	−1.08297	−	22.7344i	−0.0365693	−	0.767685i	−0.940457	−	0.339914i	$-0.889602\pi$
$877$	−1.08297	−	22.7344i	−0.0365693	−	0.767685i	0.903887	−	0.427771i	$-0.140701\pi$
$878$		0			0
$879$	3.38464	−	7.41133i	0.114161	−	0.249978i
$880$		0			0
$881$	−4.69426	−	13.5632i	−0.158153	−	0.456954i	0.837888	−	0.545842i	$-0.183790\pi$
$881$	−4.69426	−	13.5632i	−0.158153	−	0.456954i	−0.996042	+	0.0888874i	$0.971669\pi$
$882$		0			0
$883$	−0.866658	+	1.21705i	−0.0291654	+	0.0409570i	−0.828901	−	0.559395i	$-0.811033\pi$
$883$	−0.866658	+	1.21705i	−0.0291654	+	0.0409570i	0.799736	+	0.600352i	$0.204973\pi$
$884$		0			0
$885$	−17.9823	−	5.28007i	−0.604467	−	0.177487i
$886$		0			0
$887$	−38.8514	+	20.0293i	−1.30450	+	0.672517i	−0.963541	−	0.267560i	$-0.913782\pi$
$887$	−38.8514	+	20.0293i	−1.30450	+	0.672517i	−0.340960	+	0.940078i	$0.610752\pi$
$888$		0			0
$889$	−31.6712	+	30.1984i	−1.06222	+	1.01282i
$890$		0			0
$891$	0.695223	−	2.00871i	0.0232908	−	0.0672944i
$892$		0			0
$893$	1.32491	−	1.52903i	0.0443364	−	0.0511670i
$894$		0			0
$895$	54.8284	−	16.0991i	1.83271	−	0.538133i
$896$		0			0
$897$	−3.01268	−	2.87258i	−0.100590	−	0.0959128i
$898$		0			0
$899$	−30.2002	−	42.4103i	−1.00723	−	1.41446i
$900$		0			0
$901$	−9.78574	+	16.9494i	−0.326010	+	0.564666i
$902$		0			0
$903$	10.1632	+	1.95880i	0.338211	+	0.0651848i
$904$		0			0
$905$	−6.65426	+	5.23297i	−0.221195	+	0.173950i
$906$		0			0
$907$	13.0110	−	1.24240i	0.432024	−	0.0412533i	0.123221	−	0.992379i	$-0.460678\pi$
$907$	13.0110	−	1.24240i	0.432024	−	0.0412533i	0.308803	+	0.951126i	$0.400072\pi$
$908$		0			0
$909$	−3.06224	−	5.30395i	−0.101568	−	0.175921i
$910$		0			0
$911$	−45.3411	+	29.1390i	−1.50222	+	0.965417i	−0.507625	+	0.861578i	$0.669476\pi$
$911$	−45.3411	+	29.1390i	−1.50222	+	0.965417i	−0.994594	+	0.103839i	$0.966887\pi$
$912$		0			0
$913$	−0.283620	−	0.621042i	−0.00938647	−	0.0205535i
$914$		0			0
$915$	−20.3115	+	3.91472i	−0.671477	+	0.129417i
$916$		0			0
$917$	16.9203	+	8.72302i	0.558758	+	0.288060i
$918$		0			0
$919$	−41.1368	−	16.4687i	−1.35698	−	0.543252i	−0.424811	−	0.905282i	$-0.639659\pi$
$919$	−41.1368	−	16.4687i	−1.35698	−	0.543252i	−0.932166	+	0.362031i	$0.882084\pi$
$920$		0			0
$921$	−6.48239	+	26.7208i	−0.213602	+	0.880480i
$922$		0			0
$923$	−4.17825	−	29.0604i	−0.137529	−	0.956535i
$924$		0			0
$925$	−2.18334	−	0.208484i	−0.0717878	−	0.00685490i
$926$		0			0
$927$	0.780248	−	16.3794i	0.0256267	−	0.537971i
$928$		0			0
$929$	−7.16385	+	49.8257i	−0.235038	+	1.63473i	0.440749	+	0.897630i	$0.354713\pi$
$929$	−7.16385	+	49.8257i	−0.235038	+	1.63473i	−0.675787	+	0.737097i	$0.736196\pi$
$930$		0			0
$931$	93.8180	−	37.5591i	3.07476	−	1.23095i
$932$		0			0
$933$	9.53548	+	6.12808i	0.312178	+	0.200624i
$934$		0			0
$935$	−27.2101	−	31.4021i	−0.889866	−	1.02696i
$936$		0			0
$937$	−17.6764			−0.577463			−0.288732	−	0.957410i	$-0.593234\pi$
$937$	−17.6764			−0.577463			−0.288732	+	0.957410i	$0.593234\pi$
$938$		0			0
$939$	−23.8979			−0.779877
$940$		0			0
$941$	33.6148	+	38.7935i	1.09581	+	1.26463i	0.961830	+	0.273648i	$0.0882304\pi$
$941$	33.6148	+	38.7935i	1.09581	+	1.26463i	0.133980	+	0.990984i	$0.457224\pi$
$942$		0			0
$943$	9.98746	+	6.41855i	0.325236	+	0.209017i
$944$		0			0
$945$	10.6811	−	4.27608i	0.347457	−	0.139101i
$946$		0			0
$947$	8.29292	−	57.6786i	0.269484	−	1.87430i	−0.183841	−	0.982956i	$-0.558853\pi$
$947$	8.29292	−	57.6786i	0.269484	−	1.87430i	0.453325	−	0.891345i	$-0.350238\pi$
$948$		0			0
$949$	2.40170	−	50.4180i	0.0779626	−	1.63664i
$950$		0			0
$951$	15.9494	+	1.52298i	0.517194	+	0.0493860i
$952$		0			0
$953$	−5.14856	−	35.8091i	−0.166778	−	1.15997i	−0.885489	−	0.464660i	$-0.846177\pi$
$953$	−5.14856	−	35.8091i	−0.166778	−	1.15997i	0.718711	−	0.695309i	$-0.244732\pi$
$954$		0			0
$955$	−7.29975	+	30.0900i	−0.236214	+	0.973689i
$956$		0			0
$957$	15.3910	+	6.16162i	0.497520	+	0.199177i
$958$		0			0
$959$	−72.2389	−	37.2417i	−2.33272	−	1.20260i
$960$		0			0
$961$	13.3163	−	2.56651i	0.429558	−	0.0827905i
$962$		0			0
$963$	−2.31087	−	5.06010i	−0.0744668	−	0.163060i
$964$		0			0
$965$	−30.3390	+	19.4977i	−0.976646	+	0.627652i
$966$		0			0
$967$	20.6301	+	35.7323i	0.663418	+	1.14907i	0.979712	+	0.200412i	$0.0642282\pi$
$967$	20.6301	+	35.7323i	0.663418	+	1.14907i	−0.316294	+	0.948661i	$0.602438\pi$
$968$		0			0
$969$	53.9508	−	5.15168i	1.73315	−	0.165496i
$970$		0			0
$971$	26.4281	−	20.7833i	0.848117	−	0.666967i	−0.0964309	−	0.995340i	$-0.530743\pi$
$971$	26.4281	−	20.7833i	0.848117	−	0.666967i	0.944548	+	0.328373i	$0.106500\pi$
$972$		0			0
$973$	−16.5992	−	3.19923i	−0.532145	−	0.102563i
$974$		0			0
$975$	1.75272	−	3.03581i	0.0561321	−	0.0972236i
$976$		0			0
$977$	9.21521	+	12.9410i	0.294821	+	0.414018i	0.935244	−	0.354005i	$-0.115180\pi$
$977$	9.21521	+	12.9410i	0.294821	+	0.414018i	−0.640423	+	0.768022i	$0.721241\pi$
$978$		0			0
$979$	−18.2977	−	17.4468i	−0.584796	−	0.557602i
$980$		0			0
$981$	4.40841	−	1.29443i	0.140750	−	0.0413278i
$982$		0			0
$983$	23.7201	−	27.3745i	0.756555	−	0.873111i	−0.238632	−	0.971110i	$-0.576699\pi$
$983$	23.7201	−	27.3745i	0.756555	−	0.873111i	0.995186	+	0.0979993i	$0.0312443\pi$
$984$		0			0
$985$	7.47983	−	21.6115i	0.238327	−	0.688601i
$986$		0			0
$987$	1.00013	−	0.953626i	0.0318346	−	0.0303543i
$988$		0			0
$989$	2.51712	−	1.29766i	0.0800396	−	0.0412633i
$990$		0			0
$991$	11.0410	+	3.24192i	0.350728	+	0.102983i	0.452351	−	0.891840i	$-0.350585\pi$
$991$	11.0410	+	3.24192i	0.350728	+	0.102983i	−0.101623	+	0.994823i	$0.532404\pi$
$992$		0			0
$993$	6.16005	−	8.65058i	0.195483	−	0.274518i
$994$		0			0
$995$	−0.663531	−	1.91715i	−0.0210353	−	0.0607776i
$996$		0			0
$997$	−2.59892	+	5.69085i	−0.0823087	+	0.180231i	−0.946312	−	0.323256i	$-0.895223\pi$
$997$	−2.59892	+	5.69085i	−0.0823087	+	0.180231i	0.864003	+	0.503487i	$0.167950\pi$
$998$		0			0
$999$	−0.0970350	−	2.03702i	−0.00307005	−	0.0644483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.505.2	yes	120
67.54	even	33	inner	804.2.y.b.121.2	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.2	✓	120	67.54	even	33	inner
804.2.y.b.505.2	yes	120	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-2.07356 - 1.33260i) q^{5} +(4.33337 - 1.73482i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-2.07356 - 1.33260i) q^{5} +(4.33337 - 1.73482i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.101141 + 2.12321i) q^{11} +(-3.24464 - 0.309826i) q^{13} +(-0.350785 - 2.43976i) q^{15} +(1.86970 - 7.70703i) q^{17} +(6.34431 + 2.53988i) q^{19} +(4.14885 + 2.13888i) q^{21} +(1.25405 - 0.241699i) q^{23} +(0.446774 + 0.978298i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-3.89969 - 6.75447i) q^{29} +(6.64520 - 0.634540i) q^{31} +(-1.67085 + 1.31397i) q^{33} +(-11.2974 - 2.17739i) q^{35} +(-1.01966 + 1.76611i) q^{37} +(-1.89064 - 2.65503i) q^{39} +(6.72776 + 6.41491i) q^{41} +(2.12759 - 0.624716i) q^{43} +(1.61413 - 1.86281i) q^{45} +(0.0968303 - 0.279773i) q^{47} +(10.7024 - 10.2047i) q^{49} +(7.04898 - 3.63400i) q^{51} +(-2.36788 - 0.695274i) q^{53} +(3.03911 - 4.26784i) q^{55} +(2.23513 + 6.45798i) q^{57} +(3.15859 - 6.91636i) q^{59} +(-0.399313 - 8.38261i) q^{61} +(1.10046 + 4.53616i) q^{63} +(6.31510 + 4.96625i) q^{65} +(-3.88912 + 7.20241i) q^{67} +(1.00389 + 0.789472i) q^{69} +(2.12361 + 8.75365i) q^{71} +(0.736854 + 15.4685i) q^{73} +(-0.446774 + 0.978298i) q^{75} +(3.24511 + 9.37614i) q^{77} +(6.90329 - 9.69432i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-0.285490 + 0.147180i) q^{83} +(-14.1473 + 13.4895i) q^{85} +(2.55093 - 7.37043i) q^{87} +(-7.78897 + 8.98895i) q^{89} +(-14.5977 + 4.28628i) q^{91} +(4.83124 + 4.60657i) q^{93} +(-9.77070 - 13.7210i) q^{95} +(3.21956 - 5.57645i) q^{97} +(-2.08721 - 0.402276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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