LMFDB - Embedded newform 504.2.bk.b.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599802 - 1.28072i) q^{2} +(-1.28048 - 1.53635i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(-2.39181 + 1.13104i) q^{7} +(-2.73567 + 0.718419i) q^{8} +O(q^{10})$	\(q+(0.599802 - 1.28072i) q^{2} +(-1.28048 - 1.53635i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(-2.39181 + 1.13104i) q^{7} +(-2.73567 + 0.718419i) q^{8} +(1.66993 + 2.39337i) q^{10} +(0.982155 + 1.70114i) q^{11} -4.20219 q^{13} +(0.0139241 + 3.74163i) q^{14} +(-0.720766 + 3.93453i) q^{16} +(-3.09983 + 1.78969i) q^{17} +(-4.36777 - 2.52173i) q^{19} +(4.06686 - 0.703166i) q^{20} +(2.76778 - 0.237515i) q^{22} +(5.31120 + 3.06642i) q^{23} +(0.370777 + 0.642204i) q^{25} +(-2.52048 + 5.38182i) q^{26} +(4.80033 + 2.22640i) q^{28} +6.34977i q^{29} +(-3.42356 - 5.92978i) q^{31} +(4.60670 + 3.28303i) q^{32} +(0.432800 + 5.04346i) q^{34} +(0.446563 - 5.44148i) q^{35} +(-3.56564 - 2.05862i) q^{37} +(-5.84942 + 4.08133i) q^{38} +(1.53875 - 5.63026i) q^{40} -2.45849i q^{41} +4.33560 q^{43} +(1.35593 - 3.68721i) q^{44} +(7.11289 - 4.96290i) q^{46} +(4.88612 - 8.46301i) q^{47} +(4.44152 - 5.41045i) q^{49} +(1.04487 - 0.0896650i) q^{50} +(5.38080 + 6.45605i) q^{52} +(-11.2291 + 6.48313i) q^{53} -4.05355 q^{55} +(5.73064 - 4.81246i) q^{56} +(8.13226 + 3.80860i) q^{58} +(-6.17173 + 3.56325i) q^{59} +(1.03175 - 1.78704i) q^{61} +(-9.64783 + 0.827920i) q^{62} +(6.96775 - 3.93071i) q^{64} +(4.33582 - 7.50986i) q^{65} +(2.77372 + 4.80422i) q^{67} +(6.71884 + 2.47078i) q^{68} +(-6.70115 - 3.83573i) q^{70} -9.44037i q^{71} +(-10.7122 + 6.18471i) q^{73} +(-4.77520 + 3.33181i) q^{74} +(1.71855 + 9.93945i) q^{76} +(-4.27318 - 2.95796i) q^{77} +(-0.778628 - 0.449541i) q^{79} +(-6.28782 - 5.34775i) q^{80} +(-3.14863 - 1.47461i) q^{82} +9.58499i q^{83} -7.38639i q^{85} +(2.60050 - 5.55268i) q^{86} +(-3.90898 - 3.94816i) q^{88} +(12.6502 + 7.30359i) q^{89} +(10.0508 - 4.75282i) q^{91} +(-2.08975 - 12.0864i) q^{92} +(-7.90802 - 11.3339i) q^{94} +(9.01332 - 5.20384i) q^{95} -0.550439i q^{97} +(-4.26522 - 8.93353i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4}+O(q^{10}) $ 32 * q + 2 * q^4	$ 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) $ 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.599802	−	1.28072i	0.424124	−	0.905604i
$2$	0.599802	−	1.28072i	0.424124	−	0.905604i
$3$		0			0
$3$		0			0
$4$	−1.28048	−	1.53635i	−0.640238	−	0.768177i
$5$	−1.03180	+	1.78713i	−0.461435	+	0.799229i	−0.999033	−	0.0439725i	$-0.985999\pi$
$5$	−1.03180	+	1.78713i	−0.461435	+	0.799229i	0.537598	+	0.843201i	$0.319332\pi$
$6$		0			0
$7$	−2.39181	+	1.13104i	−0.904020	+	0.427491i
$7$	−2.39181	+	1.13104i	−0.904020	+	0.427491i
$8$	−2.73567	+	0.718419i	−0.967204	+	0.254000i
$9$		0			0
$10$	1.66993	+	2.39337i	0.528079	+	0.756850i
$11$	0.982155	+	1.70114i	0.296131	+	0.512914i	0.975247	−	0.221117i	$-0.0709702\pi$
$11$	0.982155	+	1.70114i	0.296131	+	0.512914i	−0.679116	+	0.734031i	$0.737637\pi$
$12$		0			0
$13$	−4.20219			−1.16548			−0.582738	−	0.812660i	$-0.698019\pi$
$13$	−4.20219			−1.16548			−0.582738	+	0.812660i	$0.698019\pi$
$14$	0.0139241	+	3.74163i	0.00372138	+	0.999993i
$15$		0			0
$16$	−0.720766	+	3.93453i	−0.180192	+	0.983632i
$17$	−3.09983	+	1.78969i	−0.751819	+	0.434063i	−0.826351	−	0.563156i	$-0.809587\pi$
$17$	−3.09983	+	1.78969i	−0.751819	+	0.434063i	0.0745321	+	0.997219i	$0.476254\pi$
$18$		0			0
$19$	−4.36777	−	2.52173i	−1.00203	−	0.578525i	−0.0931845	−	0.995649i	$-0.529705\pi$
$19$	−4.36777	−	2.52173i	−1.00203	−	0.578525i	−0.908849	+	0.417124i	$0.863038\pi$
$20$	4.06686	−	0.703166i	0.909377	−	0.157233i
$21$		0			0
$22$	2.76778	−	0.237515i	0.590093	−	0.0506383i
$23$	5.31120	+	3.06642i	1.10746	+	0.639393i	0.938171	−	0.346173i	$-0.112519\pi$
$23$	5.31120	+	3.06642i	1.10746	+	0.639393i	0.169291	+	0.985566i	$0.445852\pi$
$24$		0			0
$25$	0.370777	+	0.642204i	0.0741553	+	0.128441i
$26$	−2.52048	+	5.38182i	−0.494307	+	1.05546i
$27$		0			0
$28$	4.80033	+	2.22640i	0.907176	+	0.420751i
$29$			6.34977i			1.17912i	0.807724	+	0.589561i	$0.200699\pi$
$29$			6.34977i			1.17912i	−0.807724	+	0.589561i	$0.799301\pi$
$30$		0			0
$31$	−3.42356	−	5.92978i	−0.614889	−	1.06502i	−0.990404	−	0.138203i	$-0.955867\pi$
$31$	−3.42356	−	5.92978i	−0.614889	−	1.06502i	0.375514	−	0.926817i	$-0.377466\pi$
$32$	4.60670	+	3.28303i	0.814357	+	0.580364i
$33$		0			0
$34$	0.432800	+	5.04346i	0.0742246	+	0.864946i
$35$	0.446563	−	5.44148i	0.0754830	−	0.919778i
$36$		0			0
$37$	−3.56564	−	2.05862i	−0.586188	−	0.338436i	0.177401	−	0.984139i	$-0.443231\pi$
$37$	−3.56564	−	2.05862i	−0.586188	−	0.338436i	−0.763589	+	0.645703i	$0.776564\pi$
$38$	−5.84942	+	4.08133i	−0.948901	+	0.662080i
$39$		0			0
$40$	1.53875	−	5.63026i	0.243298	−	0.890222i
$41$		−	2.45849i		−	0.383952i	−0.981400	−	0.191976i	$-0.938510\pi$
$41$		−	2.45849i		−	0.383952i	0.981400	−	0.191976i	$-0.0614896\pi$
$42$		0			0
$43$	4.33560			0.661173			0.330586	−	0.943776i	$-0.392753\pi$
$43$	4.33560			0.661173			0.330586	+	0.943776i	$0.392753\pi$
$44$	1.35593	−	3.68721i	0.204414	−	0.555868i
$45$		0			0
$46$	7.11289	−	4.96290i	1.04874	−	0.731740i
$47$	4.88612	−	8.46301i	0.712714	−	1.23446i	−0.251121	−	0.967956i	$-0.580799\pi$
$47$	4.88612	−	8.46301i	0.712714	−	1.23446i	0.963835	−	0.266501i	$-0.0858676\pi$
$48$		0			0
$49$	4.44152	−	5.41045i	0.634503	−	0.772921i
$50$	1.04487	−	0.0896650i	0.147768	−	0.0126805i
$51$		0			0
$52$	5.38080	+	6.45605i	0.746182	+	0.895293i
$53$	−11.2291	+	6.48313i	−1.54244	+	0.890527i	−0.543754	+	0.839245i	$0.682998\pi$
$53$	−11.2291	+	6.48313i	−1.54244	+	0.890527i	−0.998684	+	0.0512824i	$0.983669\pi$
$54$		0			0
$55$	−4.05355			−0.546581
$56$	5.73064	−	4.81246i	0.765789	−	0.643092i
$57$		0			0
$58$	8.13226	+	3.80860i	1.06782	+	0.500094i
$59$	−6.17173	+	3.56325i	−0.803491	+	0.463896i	−0.844690	−	0.535255i	$-0.820215\pi$
$59$	−6.17173	+	3.56325i	−0.803491	+	0.463896i	0.0411994	+	0.999151i	$0.486882\pi$
$60$		0			0
$61$	1.03175	−	1.78704i	0.132102	−	0.228807i	−0.792385	−	0.610022i	$-0.791161\pi$
$61$	1.03175	−	1.78704i	0.132102	−	0.228807i	0.924487	+	0.381214i	$0.124494\pi$
$62$	−9.64783	+	0.827920i	−1.22528	+	0.105146i
$63$		0			0
$64$	6.96775	−	3.93071i	0.870968	−	0.491339i
$65$	4.33582	−	7.50986i	0.537792	−	0.931483i
$66$		0			0
$67$	2.77372	+	4.80422i	0.338864	+	0.586929i	0.984219	−	0.176953i	$-0.0566242\pi$
$67$	2.77372	+	4.80422i	0.338864	+	0.586929i	−0.645356	+	0.763882i	$0.723291\pi$
$68$	6.71884	+	2.47078i	0.814779	+	0.299626i
$69$		0			0
$70$	−6.70115	−	3.83573i	−0.800941	−	0.458458i
$71$		−	9.44037i		−	1.12037i	−0.828369	−	0.560183i	$-0.810731\pi$
$71$		−	9.44037i		−	1.12037i	0.828369	−	0.560183i	$-0.189269\pi$
$72$		0			0
$73$	−10.7122	+	6.18471i	−1.25377	+	0.723865i	−0.971856	−	0.235574i	$-0.924303\pi$
$73$	−10.7122	+	6.18471i	−1.25377	+	0.723865i	−0.281915	+	0.959439i	$0.590970\pi$
$74$	−4.77520	+	3.33181i	−0.555105	+	0.387316i
$75$		0			0
$76$	1.71855	+	9.93945i	0.197131	+	1.14013i
$77$	−4.27318	−	2.95796i	−0.486974	−	0.337091i
$78$		0			0
$79$	−0.778628	−	0.449541i	−0.0876025	−	0.0505773i	0.455559	−	0.890206i	$-0.349439\pi$
$79$	−0.778628	−	0.449541i	−0.0876025	−	0.0505773i	−0.543161	+	0.839628i	$0.682773\pi$
$80$	−6.28782	−	5.34775i	−0.703000	−	0.597896i
$81$		0			0
$82$	−3.14863	−	1.47461i	−0.347709	−	0.162843i
$83$			9.58499i			1.05209i	0.850457	+	0.526045i	$0.176326\pi$
$83$			9.58499i			1.05209i	−0.850457	+	0.526045i	$0.823674\pi$
$84$		0			0
$85$		−	7.38639i		−	0.801167i
$86$	2.60050	−	5.55268i	0.280419	−	0.598761i
$87$		0			0
$88$	−3.90898	−	3.94816i	−0.416699	−	0.420875i
$89$	12.6502	+	7.30359i	1.34092	+	0.774179i	0.986942	−	0.161076i	$-0.0514964\pi$
$89$	12.6502	+	7.30359i	1.34092	+	0.774179i	0.353975	+	0.935255i	$0.384830\pi$
$90$		0			0
$91$	10.0508	−	4.75282i	1.05361	−	0.498231i
$92$	−2.08975	−	12.0864i	−0.217871	−	1.26009i
$93$		0			0
$94$	−7.90802	−	11.3339i	−0.815650	−	1.16900i
$95$	9.01332	−	5.20384i	0.924747	−	0.533903i
$96$		0			0
$97$		−	0.550439i		−	0.0558886i	−0.999609	−	0.0279443i	$-0.991104\pi$
$97$		−	0.550439i		−	0.0558886i	0.999609	−	0.0279443i	$-0.00889611\pi$
$98$	−4.26522	−	8.93353i	−0.430852	−	0.902422i
$99$		0			0
$100$	0.511882	−	1.39197i	0.0511882	−	0.139197i
$101$	−0.425077	−	0.736255i	−0.0422967	−	0.0732601i	0.844102	−	0.536183i	$-0.180134\pi$
$101$	−0.425077	−	0.736255i	−0.0422967	−	0.0732601i	−0.886399	+	0.462922i	$0.846801\pi$
$102$		0			0
$103$	−0.216400	+	0.374816i	−0.0213225	+	0.0369317i	−0.876490	−	0.481420i	$-0.840121\pi$
$103$	−0.216400	+	0.374816i	−0.0213225	+	0.0369317i	0.855167	+	0.518352i	$0.173454\pi$
$104$	11.4958	−	3.01893i	1.12725	−	0.296031i
$105$		0			0
$106$	1.56782	+	18.2699i	0.152280	+	1.77453i
$107$	4.77094	−	8.26350i	0.461224	−	0.798863i	−0.537798	−	0.843073i	$-0.680744\pi$
$107$	4.77094	−	8.26350i	0.461224	−	0.798863i	0.999022	+	0.0442104i	$0.0140772\pi$
$108$		0			0
$109$	−15.0609	+	8.69539i	−1.44257	+	0.832867i	−0.998021	−	0.0628884i	$-0.979969\pi$
$109$	−15.0609	+	8.69539i	−1.44257	+	0.832867i	−0.444547	+	0.895755i	$0.646635\pi$
$110$	−2.43133	+	5.19146i	−0.231818	+	0.494986i
$111$		0			0
$112$	−2.72615	−	10.2259i	−0.257597	−	0.966252i
$113$	−17.4719			−1.64362			−0.821811	−	0.569761i	$-0.807036\pi$
$113$	−17.4719			−1.64362			−0.821811	+	0.569761i	$0.807036\pi$
$114$		0			0
$115$	−10.9602	+	6.32787i	−1.02204	+	0.590077i
$116$	9.75549	−	8.13072i	0.905774	−	0.754918i
$117$		0			0
$118$	0.861702	+	10.0415i	0.0793261	+	0.924394i
$119$	5.39000	−	7.78660i	0.494101	−	0.713797i
$120$		0			0
$121$	3.57074	−	6.18471i	0.324613	−	0.562246i
$122$	−1.66985	−	2.39325i	−0.151181	−	0.216675i
$123$		0			0
$124$	−4.72646	+	12.8527i	−0.424448	+	1.15421i
$125$	−11.8483			−1.05974
$126$		0			0
$127$			13.6577i			1.21193i	0.795493	+	0.605963i	$0.207212\pi$
$127$			13.6577i			1.21193i	−0.795493	+	0.605963i	$0.792788\pi$
$128$	−0.854864	−	11.2814i	−0.0755600	−	0.997141i
$129$		0			0
$130$	−7.01737	−	10.0574i	−0.615464	−	0.882091i
$131$	7.01700	+	4.05127i	0.613078	+	0.353961i	0.774169	−	0.632979i	$-0.218168\pi$
$131$	7.01700	+	4.05127i	0.613078	+	0.353961i	−0.161091	+	0.986940i	$0.551501\pi$
$132$		0			0
$133$	13.2990	+	1.09141i	1.15317	+	0.0946368i
$134$	7.81653	−	0.670769i	0.675245	−	0.0579456i
$135$		0			0
$136$	7.19435	−	7.12296i	0.616910	−	0.610789i
$137$	3.50702	+	6.07434i	0.299625	+	0.518966i	0.976050	−	0.217545i	$-0.0698050\pi$
$137$	3.50702	+	6.07434i	0.299625	+	0.518966i	−0.676425	+	0.736512i	$0.736472\pi$
$138$		0			0
$139$		−	5.14626i		−	0.436500i	−0.975893	−	0.218250i	$-0.929965\pi$
$139$		−	5.14626i		−	0.436500i	0.975893	−	0.218250i	$-0.0700348\pi$
$140$	−8.93185	+	6.28160i	−0.754879	+	0.530892i
$141$		0			0
$142$	−12.0904	−	5.66235i	−1.01461	−	0.475174i
$143$	−4.12720	−	7.14852i	−0.345134	−	0.597789i
$144$		0			0
$145$	−11.3479	−	6.55169i	−0.942388	−	0.544088i
$146$	1.49565	+	17.4289i	0.123781	+	1.44243i
$147$		0			0
$148$	1.40294	+	8.11411i	0.115321	+	0.666975i
$149$	2.48868	+	1.43684i	0.203880	+	0.117710i	0.598464	−	0.801150i	$-0.295778\pi$
$149$	2.48868	+	1.43684i	0.203880	+	0.117710i	−0.394584	+	0.918860i	$0.629111\pi$
$150$		0			0
$151$	11.2968	−	6.52218i	0.919317	−	0.530768i	0.0358996	−	0.999355i	$-0.488570\pi$
$151$	11.2968	−	6.52218i	0.919317	−	0.530768i	0.883417	+	0.468588i	$0.155237\pi$
$152$	13.7604	+	3.76073i	1.11612	+	0.305035i
$153$		0			0
$154$	−6.35137	+	3.69855i	−0.511808	+	0.298038i
$155$	14.1297			1.13493
$156$		0			0
$157$	5.06779	+	8.77767i	0.404453	+	0.700534i	0.994258	−	0.107012i	$-0.0341284\pi$
$157$	5.06779	+	8.77767i	0.404453	+	0.700534i	−0.589804	+	0.807546i	$0.700795\pi$
$158$	−1.04276	+	0.727567i	−0.0829573	+	0.0578821i
$159$		0			0
$160$	−10.6204	+	4.84534i	−0.839617	+	0.383058i
$161$	−16.1716	−	1.32715i	−1.27450	−	0.104594i
$162$		0			0
$163$	0.741553	−	1.28441i	0.0580829	−	0.100603i	−0.835522	−	0.549457i	$-0.814835\pi$
$163$	0.741553	−	1.28441i	0.0580829	−	0.100603i	0.893605	+	0.448855i	$0.148168\pi$
$164$	−3.77711	+	3.14804i	−0.294943	+	0.245821i
$165$		0			0
$166$	12.2757	+	5.74910i	0.952777	+	0.446217i
$167$	8.09679			0.626549			0.313274	−	0.949663i	$-0.398574\pi$
$167$	8.09679			0.626549			0.313274	+	0.949663i	$0.398574\pi$
$168$		0			0
$169$	4.65838			0.358337
$170$	−9.45989	−	4.43037i	−0.725540	−	0.339794i
$171$		0			0
$172$	−5.55163	−	6.66102i	−0.423308	−	0.507898i
$173$	−7.79366	+	13.4990i	−0.592541	+	1.02631i	0.401348	+	0.915926i	$0.368542\pi$
$173$	−7.79366	+	13.4990i	−0.592541	+	1.02631i	−0.993889	+	0.110385i	$0.964791\pi$
$174$		0			0
$175$	−1.61318	−	1.11667i	−0.121945	−	0.0844122i
$176$	−7.40110	+	2.63819i	−0.557879	+	0.198861i
$177$		0			0
$178$	16.9414	−	11.8206i	1.26981	−	0.885992i
$179$	−5.91790	−	10.2501i	−0.442324	−	0.766128i	0.555537	−	0.831492i	$-0.312513\pi$
$179$	−5.91790	−	10.2501i	−0.442324	−	0.766128i	−0.997862	+	0.0653634i	$0.979179\pi$
$180$		0			0
$181$	15.2646			1.13461			0.567304	−	0.823508i	$-0.307986\pi$
$181$	15.2646			1.13461			0.567304	+	0.823508i	$0.307986\pi$
$182$	−0.0585118	−	15.7230i	−0.00433718	−	1.16547i
$183$		0			0
$184$	−16.7326	−	4.57304i	−1.23355	−	0.337129i
$185$	7.35806	−	4.24818i	0.540975	−	0.312332i
$186$		0			0
$187$	−6.08902	−	3.51550i	−0.445274	−	0.257079i
$188$	−19.2587	+	3.32986i	−1.40459	+	0.242855i
$189$		0			0
$190$	−1.25845	−	14.6648i	−0.0912973	−	1.06390i
$191$	−0.333843	−	0.192744i	−0.0241560	−	0.0139465i	0.487873	−	0.872914i	$-0.337773\pi$
$191$	−0.333843	−	0.192744i	−0.0241560	−	0.0139465i	−0.512029	+	0.858968i	$0.671106\pi$
$192$		0			0
$193$	12.9186	+	22.3757i	0.929901	+	1.61064i	0.783483	+	0.621414i	$0.213441\pi$
$193$	12.9186	+	22.3757i	0.929901	+	1.61064i	0.146419	+	0.989223i	$0.453225\pi$
$194$	−0.704957	−	0.330154i	−0.0506130	−	0.0237037i
$195$		0			0
$196$	−13.9996	+	0.104198i	−0.999972	+	0.00744271i
$197$		−	7.58382i		−	0.540325i	−0.962815	−	0.270163i	$-0.912923\pi$
$197$		−	7.58382i		−	0.540325i	0.962815	−	0.270163i	$-0.0870774\pi$
$198$		0			0
$199$	−1.32902	−	2.30193i	−0.0942115	−	0.163179i	0.815068	−	0.579366i	$-0.196700\pi$
$199$	−1.32902	−	2.30193i	−0.0942115	−	0.163179i	−0.909279	+	0.416187i	$0.863366\pi$
$200$	−1.47569	−	1.49048i	−0.104347	−	0.105393i
$201$		0			0
$202$	−1.19790	+	0.102796i	−0.0842837	+	0.00723273i
$203$	−7.18181	−	15.1874i	−0.504064	−	1.06595i
$204$		0			0
$205$	4.39365	+	2.53667i	0.306866	+	0.177169i
$206$	0.350236	+	0.501963i	0.0244021	+	0.0349734i
$207$		0			0
$208$	3.02879	−	16.5336i	0.210009	−	1.14640i
$209$		−	9.90692i		−	0.685276i
$210$		0			0
$211$	−13.8830			−0.955748			−0.477874	−	0.878428i	$-0.658592\pi$
$211$	−13.8830			−0.955748			−0.477874	+	0.878428i	$0.658592\pi$
$212$	24.3390	+	8.95041i	1.67161	+	0.614716i
$213$		0			0
$214$	−7.72160	−	11.0667i	−0.527838	−	0.756503i
$215$	−4.47347	+	7.74828i	−0.305088	+	0.528429i
$216$		0			0
$217$	14.8953	+	10.3107i	1.01116	+	0.699939i
$218$	2.10281	+	24.5042i	0.142420	+	1.65963i
$219$		0			0
$220$	5.19047	+	6.22769i	0.349942	+	0.419871i
$221$	13.0261	−	7.52060i	0.876227	−	0.505890i
$222$		0			0
$223$	26.4494			1.77119			0.885593	−	0.464463i	$-0.153753\pi$
$223$	26.4494			1.77119			0.885593	+	0.464463i	$0.153753\pi$
$224$	−14.7316	−	2.64206i	−0.984295	−	0.176530i
$225$		0			0
$226$	−10.4797	+	22.3766i	−0.697099	+	1.48847i
$227$	−15.5967	+	9.00473i	−1.03519	+	0.597665i	−0.918466	−	0.395500i	$-0.870571\pi$
$227$	−15.5967	+	9.00473i	−1.03519	+	0.597665i	−0.116720	+	0.993165i	$0.537238\pi$
$228$		0			0
$229$	6.00160	−	10.3951i	0.396597	−	0.686926i	−0.596707	−	0.802459i	$-0.703524\pi$
$229$	6.00160	−	10.3951i	0.396597	−	0.686926i	0.993304	+	0.115533i	$0.0368577\pi$
$230$	1.53027	+	17.8324i	0.100903	+	1.17583i
$231$		0			0
$232$	−4.56179	−	17.3708i	−0.299496	−	1.14045i
$233$	4.80735	−	8.32657i	0.314940	−	0.545492i	−0.664485	−	0.747302i	$-0.731349\pi$
$233$	4.80735	−	8.32657i	0.314940	−	0.545492i	0.979425	+	0.201810i	$0.0646824\pi$
$234$		0			0
$235$	10.0830	+	17.4643i	0.657742	+	1.13924i
$236$	13.3772	+	4.91931i	0.870779	+	0.320220i
$237$		0			0
$238$	−6.73951	−	11.5735i	−0.436857	−	0.750198i
$239$			21.7827i			1.40901i	0.709701	+	0.704503i	$0.248830\pi$
$239$			21.7827i			1.40901i	−0.709701	+	0.704503i	$0.751170\pi$
$240$		0			0
$241$	−6.56572	+	3.79072i	−0.422935	+	0.244182i	−0.696332	−	0.717720i	$-0.745186\pi$
$241$	−6.56572	+	3.79072i	−0.422935	+	0.244182i	0.273397	+	0.961901i	$0.411853\pi$
$242$	−5.77912	−	8.28271i	−0.371496	−	0.532433i
$243$		0			0
$244$	−4.06666	+	0.703131i	−0.260341	+	0.0450133i
$245$	5.08641	+	13.5201i	0.324959	+	0.863766i
$246$		0			0
$247$	18.3542	+	10.5968i	1.16785	+	0.674257i
$248$	13.6258	+	13.7623i	0.865238	+	0.873910i
$249$		0			0
$250$	−7.10662	+	15.1743i	−0.449462	+	0.959706i
$251$			31.3509i			1.97885i	0.145038	+	0.989426i	$0.453670\pi$
$251$			31.3509i			1.97885i	−0.145038	+	0.989426i	$0.546330\pi$
$252$		0			0
$253$			12.0468i			0.757376i
$254$	17.4917	+	8.19193i	1.09753	+	0.514007i
$255$		0			0
$256$	−14.9610	−	5.67175i	−0.935062	−	0.354484i
$257$	23.4653	+	13.5477i	1.46373	+	0.845084i	0.999181	−	0.0404650i	$-0.0128839\pi$
$257$	23.4653	+	13.5477i	1.46373	+	0.845084i	0.464547	+	0.885549i	$0.346217\pi$
$258$		0			0
$259$	10.8567	+	0.890973i	0.674604	+	0.0553624i
$260$	−17.0897	+	2.95484i	−1.05986	+	0.183251i
$261$		0			0
$262$	9.39734	−	6.55684i	0.580570	−	0.405083i
$263$	−11.5439	+	6.66486i	−0.711826	+	0.410973i	−0.811737	−	0.584023i	$-0.801478\pi$
$263$	−11.5439	+	6.66486i	−0.711826	+	0.410973i	0.0999108	+	0.994996i	$0.468144\pi$
$264$		0			0
$265$		−	26.7572i		−	1.64368i
$266$	9.37457	−	16.3777i	0.574792	−	1.00418i
$267$		0			0
$268$	3.82930	−	10.4131i	0.233912	−	0.636081i
$269$	4.69826	+	8.13762i	0.286458	+	0.496160i	0.972962	−	0.230967i	$-0.0741888\pi$
$269$	4.69826	+	8.13762i	0.286458	+	0.496160i	−0.686504	+	0.727126i	$0.740855\pi$
$270$		0			0
$271$	−0.995028	+	1.72344i	−0.0604436	+	0.104691i	−0.894664	−	0.446740i	$-0.852585\pi$
$271$	−0.995028	+	1.72344i	−0.0604436	+	0.104691i	0.834220	+	0.551432i	$0.185918\pi$
$272$	−4.80732	−	13.4863i	−0.291486	−	0.817727i
$273$		0			0
$274$	9.88304	−	0.848104i	0.597056	−	0.0512358i
$275$	−0.728321	+	1.26149i	−0.0439194	+	0.0760706i
$276$		0			0
$277$	22.2114	−	12.8238i	1.33455	−	0.770505i	0.348560	−	0.937287i	$-0.386671\pi$
$277$	22.2114	−	12.8238i	1.33455	−	0.770505i	0.985994	+	0.166782i	$0.0533375\pi$
$278$	−6.59090	−	3.08673i	−0.395296	−	0.185130i
$279$		0			0
$280$	2.68762	+	15.2069i	0.160616	+	0.908786i
$281$	−16.3449			−0.975055			−0.487528	−	0.873108i	$-0.662101\pi$
$281$	−16.3449			−0.975055			−0.487528	+	0.873108i	$0.662101\pi$
$282$		0			0
$283$	−19.1923	+	11.0807i	−1.14086	+	0.658679i	−0.946645	−	0.322279i	$-0.895551\pi$
$283$	−19.1923	+	11.0807i	−1.14086	+	0.658679i	−0.194220	+	0.980958i	$0.562218\pi$
$284$	−14.5037	+	12.0882i	−0.860639	+	0.717300i
$285$		0			0
$286$	−11.6307	+	0.998082i	−0.687740	+	0.0590178i
$287$	2.78064	+	5.88025i	0.164136	+	0.347100i
$288$		0			0
$289$	−2.09405	+	3.62700i	−0.123179	+	0.213353i
$290$	−15.1973	+	10.6037i	−0.892418	+	0.622670i
$291$		0			0
$292$	23.2186	+	8.53840i	1.35877	+	0.499672i
$293$	11.0720			0.646831			0.323416	−	0.946257i	$-0.395169\pi$
$293$	11.0720			0.646831			0.323416	+	0.946257i	$0.395169\pi$
$294$		0			0
$295$		−	14.7063i		−	0.856231i
$296$	11.2334	+	3.07008i	0.652926	+	0.178445i
$297$		0			0
$298$	3.33290	−	2.32547i	0.193070	−	0.134711i
$299$	−22.3186	−	12.8857i	−1.29072	−	0.745198i
$300$		0			0
$301$	−10.3699	+	4.90372i	−0.597713	+	0.282646i
$302$	−1.57726	−	18.3800i	−0.0907612	−	1.05765i
$303$		0			0
$304$	13.0700	−	15.3675i	0.749613	−	0.881387i
$305$	2.12912	+	3.68774i	0.121913	+	0.211159i
$306$		0			0
$307$		−	29.0896i		−	1.66023i	−0.557592	−	0.830115i	$-0.688275\pi$
$307$		−	29.0896i		−	1.66023i	0.557592	−	0.830115i	$-0.311725\pi$
$308$	0.927232	+	10.3527i	0.0528339	+	0.589901i
$309$		0			0
$310$	8.47503	−	18.0962i	0.481349	−	1.02779i
$311$	6.99160	+	12.1098i	0.396457	+	0.686684i	0.993286	−	0.115685i	$-0.0369062\pi$
$311$	6.99160	+	12.1098i	0.396457	+	0.686684i	−0.596829	+	0.802369i	$0.703573\pi$
$312$		0			0
$313$	−1.58902	−	0.917424i	−0.0898170	−	0.0518558i	0.454419	−	0.890788i	$-0.349847\pi$
$313$	−1.58902	−	0.917424i	−0.0898170	−	0.0518558i	−0.544236	+	0.838932i	$0.683180\pi$
$314$	14.2814	−	1.22554i	0.805945	−	0.0691615i
$315$		0			0
$316$	0.306360	+	1.77187i	0.0172341	+	0.0996757i
$317$	0.691742	+	0.399378i	0.0388521	+	0.0224313i	0.519300	−	0.854592i	$-0.326193\pi$
$317$	0.691742	+	0.399378i	0.0388521	+	0.0224313i	−0.480448	+	0.877023i	$0.659526\pi$
$318$		0			0
$319$	−10.8019	+	6.23646i	−0.604788	+	0.349175i
$320$	−0.164629	+	16.5080i	−0.00920302	+	0.922824i
$321$		0			0
$322$	−11.3995	+	19.9152i	−0.635267	+	1.10983i
$323$	18.0524			1.00446
$324$		0			0
$325$	−1.55807	−	2.69866i	−0.0864263	−	0.149695i
$326$	−1.20018	−	1.72011i	−0.0664718	−	0.0952681i
$327$		0			0
$328$	1.76623	+	6.72562i	0.0975236	+	0.371360i
$329$	−2.11471	+	25.7683i	−0.116588	+	1.42065i
$330$		0			0
$331$	6.56773	−	11.3756i	0.360995	−	0.625262i	−0.627130	−	0.778915i	$-0.715770\pi$
$331$	6.56773	−	11.3756i	0.360995	−	0.625262i	0.988125	+	0.153653i	$0.0491038\pi$
$332$	14.7259	−	12.2733i	0.808191	−	0.673588i
$333$		0			0
$334$	4.85647	−	10.3697i	0.265734	−	0.567405i
$335$	−11.4477			−0.625454
$336$		0			0
$337$	−28.3541			−1.54455			−0.772273	−	0.635291i	$-0.780880\pi$
$337$	−28.3541			−1.54455			−0.772273	+	0.635291i	$0.780880\pi$
$338$	2.79410	−	5.96606i	0.151979	−	0.324511i
$339$		0			0
$340$	−11.3481	+	9.45810i	−0.615438	+	0.512937i
$341$	6.72493	−	11.6479i	0.364176	−	0.630771i
$342$		0			0
$343$	−4.50387	+	17.9643i	−0.243186	+	0.969980i
$344$	−11.8608	+	3.11478i	−0.639489	+	0.167938i
$345$		0			0
$346$	12.6138	+	18.0782i	0.678121	+	0.971891i
$347$	2.55279	+	4.42156i	0.137041	+	0.237362i	0.926375	−	0.376602i	$-0.122907\pi$
$347$	2.55279	+	4.42156i	0.137041	+	0.237362i	−0.789334	+	0.613964i	$0.789574\pi$
$348$		0			0
$349$	−15.3398			−0.821120			−0.410560	−	0.911834i	$-0.634667\pi$
$349$	−15.3398			−0.821120			−0.410560	+	0.911834i	$0.634667\pi$
$350$	−2.39773	+	1.39625i	−0.128164	+	0.0746328i
$351$		0			0
$352$	−1.06042	+	11.0611i	−0.0565203	+	0.589559i
$353$	−6.55692	+	3.78564i	−0.348990	+	0.201489i	−0.664240	−	0.747519i	$-0.731245\pi$
$353$	−6.55692	+	3.78564i	−0.348990	+	0.201489i	0.315251	+	0.949008i	$0.397911\pi$
$354$		0			0
$355$	16.8712	+	9.74057i	0.895429	+	0.516976i
$356$	−4.97735	−	28.7872i	−0.263799	−	1.52572i
$357$		0			0
$358$	−16.6770	+	1.43113i	−0.881409	+	0.0756374i
$359$	−25.7846	−	14.8868i	−1.36086	−	0.785694i	−0.371123	−	0.928584i	$-0.621027\pi$
$359$	−25.7846	−	14.8868i	−1.36086	−	0.785694i	−0.989739	+	0.142890i	$0.954360\pi$
$360$		0			0
$361$	3.21825	+	5.57417i	0.169381	+	0.293377i
$362$	9.15573	−	19.5496i	0.481215	−	1.02751i
$363$		0			0
$364$	−20.1719	−	9.35577i	−1.05729	−	0.490376i
$365$		−	25.5255i		−	1.33607i
$366$		0			0
$367$	−2.10765	−	3.65055i	−0.110018	−	0.190557i	0.805759	−	0.592243i	$-0.201758\pi$
$367$	−2.10765	−	3.65055i	−0.110018	−	0.190557i	−0.915777	+	0.401686i	$0.868424\pi$
$368$	−15.8930	+	18.6869i	−0.828482	+	0.974121i
$369$		0			0
$370$	−1.02734	−	11.9717i	−0.0534088	−	0.622377i
$371$	19.5253	−	28.2070i	1.01370	−	1.46443i
$372$		0			0
$373$	10.1033	+	5.83313i	0.523128	+	0.302028i	0.738214	−	0.674567i	$-0.235670\pi$
$373$	10.1033	+	5.83313i	0.523128	+	0.302028i	−0.215085	+	0.976595i	$0.569003\pi$
$374$	−8.15457	+	5.68972i	−0.421663	+	0.294208i
$375$		0			0
$376$	−7.28681	+	26.6623i	−0.375789	+	1.37500i
$377$		−	26.6829i		−	1.37424i
$378$		0			0
$379$	−5.40673			−0.277725			−0.138863	−	0.990312i	$-0.544345\pi$
$379$	−5.40673			−0.277725			−0.138863	+	0.990312i	$0.544345\pi$
$380$	−19.5363	−	7.18426i	−1.00219	−	0.368545i
$381$		0			0
$382$	−0.447091	+	0.311950i	−0.0228752	+	0.0159608i
$383$	−18.3729	+	31.8228i	−0.938812	+	1.62607i	−0.171121	+	0.985250i	$0.554739\pi$
$383$	−18.3729	+	31.8228i	−0.938812	+	1.62607i	−0.767691	+	0.640820i	$0.778594\pi$
$384$		0			0
$385$	9.69533	−	4.58471i	0.494120	−	0.233659i
$386$	36.4055	−	3.12411i	1.85299	−	0.159013i
$387$		0			0
$388$	−0.845669	+	0.704824i	−0.0429324	+	0.0357820i
$389$	17.1039	−	9.87494i	0.867202	−	0.500679i	0.000784673	−	1.00000i	$-0.499750\pi$
$389$	17.1039	−	9.87494i	0.867202	−	0.500679i	0.866417	+	0.499320i	$0.166417\pi$
$390$		0			0
$391$	−21.9517			−1.11015
$392$	−8.26355	+	17.9920i	−0.417372	+	0.908736i
$393$		0			0
$394$	−9.71274	−	4.54879i	−0.489321	−	0.229165i
$395$	1.60678	−	0.927673i	0.0808457	−	0.0466763i
$396$		0			0
$397$	−16.3033	+	28.2382i	−0.818240	+	1.41723i	0.0887372	+	0.996055i	$0.471717\pi$
$397$	−16.3033	+	28.2382i	−0.818240	+	1.41723i	−0.906978	+	0.421179i	$0.861616\pi$
$398$	−3.74526	+	0.321397i	−0.187733	+	0.0161102i
$399$		0			0
$400$	−2.79401	+	0.995952i	−0.139701	+	0.0497976i
$401$	5.79246	−	10.0328i	0.289262	−	0.501016i	−0.684372	−	0.729133i	$-0.739924\pi$
$401$	5.79246	−	10.0328i	0.289262	−	0.501016i	0.973634	+	0.228117i	$0.0732569\pi$
$402$		0			0
$403$	14.3864	+	24.9180i	0.716639	+	1.24126i
$404$	−0.586848	+	1.59583i	−0.0291968	+	0.0793953i
$405$		0			0
$406$	−23.7585	+	0.0884150i	−1.17911	+	0.00438796i
$407$		−	8.08756i		−	0.400885i
$408$		0			0
$409$	−18.1957	+	10.5053i	−0.899720	+	0.519454i	−0.877109	−	0.480290i	$-0.840531\pi$
$409$	−18.1957	+	10.5053i	−0.899720	+	0.519454i	−0.0226110	+	0.999744i	$0.507198\pi$
$410$	5.88408	−	4.10552i	0.290594	−	0.202757i
$411$		0			0
$412$	0.852945	−	0.147475i	0.0420216	−	0.00726559i
$413$	10.7315	−	15.5031i	0.528060	−	0.762856i
$414$		0			0
$415$	−17.1296	−	9.88980i	−0.840861	−	0.485471i
$416$	−19.3582	−	13.7959i	−0.949115	−	0.676401i
$417$		0			0
$418$	−12.6880	−	5.94219i	−0.620589	−	0.290642i
$419$			13.0738i			0.638695i	0.947638	+	0.319348i	$0.103464\pi$
$419$			13.0738i			0.638695i	−0.947638	+	0.319348i	$0.896536\pi$
$420$		0			0
$421$		−	30.7209i		−	1.49724i	−0.662998	−	0.748622i	$-0.730716\pi$
$421$		−	30.7209i		−	1.49724i	0.662998	−	0.748622i	$-0.269284\pi$
$422$	−8.32707	+	17.7802i	−0.405356	+	0.865529i
$423$		0			0
$424$	26.0615	−	25.8029i	1.26566	−	1.25310i
$425$	−2.29869	−	1.32715i	−0.111503	−	0.0643761i
$426$		0			0
$427$	−0.446541	+	5.44121i	−0.0216096	+	0.263319i
$428$	−18.8047	+	3.25137i	−0.908961	+	0.157161i
$429$		0			0
$430$	7.24017	+	10.3767i	0.349152	+	0.500409i
$431$	−1.43904	+	0.830828i	−0.0693159	+	0.0400196i	−0.534257	−	0.845322i	$-0.679409\pi$
$431$	−1.43904	+	0.830828i	−0.0693159	+	0.0400196i	0.464941	+	0.885341i	$0.346075\pi$
$432$		0			0
$433$		−	27.3884i		−	1.31620i	−0.752930	−	0.658101i	$-0.771360\pi$
$433$		−	27.3884i		−	1.31620i	0.752930	−	0.658101i	$-0.228640\pi$
$434$	22.1394	−	12.8923i	1.06272	−	0.618849i
$435$		0			0
$436$	32.6442	+	12.0046i	1.56338	+	0.574915i
$437$	−15.4654	−	26.7868i	−0.739809	−	1.28139i
$438$		0			0
$439$	4.22139	−	7.31167i	0.201476	−	0.348967i	−0.747528	−	0.664230i	$-0.768759\pi$
$439$	4.22139	−	7.31167i	0.201476	−	0.348967i	0.949004	+	0.315263i	$0.102093\pi$
$440$	11.0892	−	2.91215i	0.528655	−	0.138831i
$441$		0			0
$442$	−1.81871	−	21.1936i	−0.0865071	−	1.00808i
$443$	−2.07830	+	3.59973i	−0.0987432	+	0.171028i	−0.911165	−	0.412042i	$-0.864816\pi$
$443$	−2.07830	+	3.59973i	−0.0987432	+	0.171028i	0.812421	+	0.583071i	$0.198149\pi$
$444$		0			0
$445$	−26.1049	+	15.0717i	−1.23749	+	0.714467i
$446$	15.8644	−	33.8743i	0.751202	−	1.60399i
$447$		0			0
$448$	−12.2198	+	17.2823i	−0.577329	+	0.816511i
$449$	−18.8169			−0.888024			−0.444012	−	0.896021i	$-0.646445\pi$
$449$	−18.8169			−0.888024			−0.444012	+	0.896021i	$0.646445\pi$
$450$		0			0
$451$	4.18225	−	2.41462i	0.196934	−	0.113700i
$452$	22.3724	+	26.8431i	1.05231	+	1.26259i
$453$		0			0
$454$	2.17762	+	25.3760i	0.102201	+	1.19095i
$455$	−1.87654	+	22.8661i	−0.0879737	+	1.07198i
$456$		0			0
$457$	2.83560	−	4.91140i	0.132644	−	0.229746i	−0.792051	−	0.610455i	$-0.790987\pi$
$457$	2.83560	−	4.91140i	0.132644	−	0.229746i	0.924695	+	0.380709i	$0.124320\pi$
$458$	−9.71339	−	13.9213i	−0.453877	−	0.650502i
$459$		0			0
$460$	23.7561	+	8.73605i	1.10763	+	0.407320i
$461$	30.3245			1.41235			0.706176	−	0.708036i	$-0.250419\pi$
$461$	30.3245			1.41235			0.706176	+	0.708036i	$0.250419\pi$
$462$		0			0
$463$		−	8.41268i		−	0.390970i	−0.980707	−	0.195485i	$-0.937372\pi$
$463$		−	8.41268i		−	0.390970i	0.980707	−	0.195485i	$-0.0626282\pi$
$464$	−24.9833	−	4.57670i	−1.15982	−	0.212468i
$465$		0			0
$466$	−7.78053	−	11.1511i	−0.360426	−	0.516567i
$467$	−28.1557	−	16.2557i	−1.30289	−	0.752225i	−0.321993	−	0.946742i	$-0.604353\pi$
$467$	−28.1557	−	16.2557i	−1.30289	−	0.752225i	−0.980899	+	0.194517i	$0.937686\pi$
$468$		0			0
$469$	−12.0680	−	8.35361i	−0.557246	−	0.385734i
$470$	28.4146	−	2.43837i	1.31067	−	0.112474i
$471$		0			0
$472$	14.3239	−	14.1818i	0.659311	−	0.652768i
$473$	4.25823	+	7.37548i	0.195794	+	0.339125i
$474$		0			0
$475$		−	3.74000i		−	0.171603i
$476$	−18.8647	+	1.68960i	−0.864664	+	0.0774429i
$477$		0			0
$478$	27.8975	+	13.0653i	1.27600	+	0.597593i
$479$	−14.4033	−	24.9473i	−0.658105	−	1.13987i	−0.981106	−	0.193472i	$-0.938025\pi$
$479$	−14.4033	−	24.9473i	−0.658105	−	1.13987i	0.323001	−	0.946399i	$-0.395308\pi$
$480$		0			0
$481$	14.9835	+	8.65073i	0.683189	+	0.394439i
$482$	0.916710	+	10.6825i	0.0417550	+	0.486575i
$483$		0			0
$484$	−14.0741	+	2.43344i	−0.639734	+	0.110611i
$485$	0.983707	+	0.567943i	0.0446678	+	0.0257890i
$486$		0			0
$487$	−21.8839	+	12.6347i	−0.991654	+	0.572532i	−0.905768	−	0.423773i	$-0.860705\pi$
$487$	−21.8839	+	12.6347i	−0.991654	+	0.572532i	−0.0858860	+	0.996305i	$0.527372\pi$
$488$	−1.53868	+	5.62998i	−0.0696526	+	0.254857i
$489$		0			0
$490$	20.3662	+	1.59511i	0.920053	+	0.0720596i
$491$	25.8080			1.16470			0.582350	−	0.812938i	$-0.302133\pi$
$491$	25.8080			1.16470			0.582350	+	0.812938i	$0.302133\pi$
$492$		0			0
$493$	−11.3641	−	19.6832i	−0.511813	−	0.886486i
$494$	24.5804	−	17.1505i	1.10592	−	0.771639i
$495$		0			0
$496$	25.7985	−	9.19610i	1.15838	−	0.412917i
$497$	10.6774	+	22.5796i	0.478946	+	1.01283i
$498$		0			0
$499$	11.3093	−	19.5883i	0.506273	−	0.876891i	−0.493701	−	0.869632i	$-0.664356\pi$
$499$	11.3093	−	19.5883i	0.506273	−	0.876891i	0.999974	−	0.00725870i	$-0.00231054\pi$
$500$	15.1714	+	18.2031i	0.678486	+	0.814069i
$501$		0			0
$502$	40.1517	+	18.8043i	1.79206	+	0.839279i
$503$	−30.3245			−1.35210			−0.676051	−	0.736855i	$-0.736310\pi$
$503$	−30.3245			−1.35210			−0.676051	+	0.736855i	$0.736310\pi$
$504$		0			0
$505$	1.75438			0.0780688
$506$	15.4286	+	7.22570i	0.685883	+	0.321222i
$507$		0			0
$508$	20.9831	−	17.4884i	0.930974	−	0.775921i
$509$	16.5822	−	28.7212i	0.734993	−	1.27305i	−0.219734	−	0.975560i	$-0.570519\pi$
$509$	16.5822	−	28.7212i	0.734993	−	1.27305i	0.954726	−	0.297485i	$-0.0961479\pi$
$510$		0			0
$511$	18.6265	−	26.9086i	0.823988	−	1.19036i
$512$	−16.2375	+	15.7589i	−0.717605	+	0.696451i
$513$		0			0
$514$	31.4254	−	21.9265i	1.38611	−	0.967138i
$515$	−0.446563	−	0.773470i	−0.0196779	−	0.0340832i
$516$		0			0
$517$	19.1957			0.844227
$518$	7.65297	−	13.3700i	0.336252	−	0.587443i
$519$		0			0
$520$	−6.46613	+	23.6594i	−0.283558	+	1.03753i
$521$	20.1778	−	11.6497i	0.884006	−	0.510381i	0.0120290	−	0.999928i	$-0.496171\pi$
$521$	20.1778	−	11.6497i	0.884006	−	0.510381i	0.871977	+	0.489546i	$0.162838\pi$
$522$		0			0
$523$	−29.9745	−	17.3058i	−1.31069	−	0.756728i	−0.328481	−	0.944511i	$-0.606537\pi$
$523$	−29.9745	−	17.3058i	−1.31069	−	0.756728i	−0.982211	+	0.187782i	$0.939870\pi$
$524$	−2.76092	−	15.9682i	−0.120611	−	0.697572i
$525$		0			0
$526$	1.61176	+	18.7820i	0.0702763	+	0.818936i
$527$	21.2249	+	12.2542i	0.924571	+	0.533801i
$528$		0			0
$529$	7.30588	+	12.6542i	0.317647	+	0.550181i
$530$	−34.2684	−	16.0490i	−1.48852	−	0.697125i
$531$		0			0
$532$	−15.3523	−	21.8295i	−0.665607	−	0.946431i
$533$			10.3310i			0.447487i
$534$		0			0
$535$	9.84531	+	17.0526i	0.425650	+	0.737247i
$536$	−11.0394	−	11.1501i	−0.476830	−	0.481609i
$537$		0			0
$538$	13.2400	−	1.13618i	0.570818	−	0.0489842i
$539$	13.5662	+	2.24176i	0.584338	+	0.0965594i
$540$		0			0
$541$	−27.1035	−	15.6482i	−1.16527	−	0.672769i	−0.212709	−	0.977116i	$-0.568229\pi$
$541$	−27.1035	−	15.6482i	−1.16527	−	0.672769i	−0.952561	+	0.304347i	$0.901562\pi$
$542$	1.61042	+	2.30807i	0.0691734	+	0.0991402i
$543$		0			0
$544$	−20.1556	−	1.93229i	−0.864163	−	0.0828463i
$545$		−	35.8876i		−	1.53726i
$546$		0			0
$547$	−6.11696			−0.261542			−0.130771	−	0.991413i	$-0.541745\pi$
$547$	−6.11696			−0.261542			−0.130771	+	0.991413i	$0.541745\pi$
$548$	4.84168	−	13.1661i	0.206826	−	0.562427i
$549$		0			0
$550$	1.17876	+	1.68942i	0.0502626	+	0.0720370i
$551$	16.0124	−	27.7343i	0.682151	−	1.18152i
$552$		0			0
$553$	2.37078	+	0.194561i	0.100816	+	0.00827359i
$554$	−3.10117	−	36.1382i	−0.131756	−	1.53537i
$555$		0			0
$556$	−7.90647	+	6.58966i	−0.335309	+	0.279464i
$557$	−5.79102	+	3.34345i	−0.245374	+	0.141666i	−0.617644	−	0.786458i	$-0.711913\pi$
$557$	−5.79102	+	3.34345i	−0.245374	+	0.141666i	0.372270	+	0.928124i	$0.378579\pi$
$558$		0			0
$559$	−18.2190			−0.770582
$560$	21.0878	+	5.67905i	0.891121	+	0.239984i
$561$		0			0
$562$	−9.80371	+	20.9332i	−0.413544	+	0.883014i
$563$	−6.41527	+	3.70386i	−0.270372	+	0.156099i	−0.629056	−	0.777360i	$-0.716559\pi$
$563$	−6.41527	+	3.70386i	−0.270372	+	0.156099i	0.358685	+	0.933459i	$0.383225\pi$
$564$		0			0
$565$	18.0275	−	31.2246i	0.758425	−	1.31363i
$566$	2.67965	+	31.2262i	0.112634	+	1.31253i
$567$		0			0
$568$	6.78214	+	25.8257i	0.284572	+	1.08362i
$569$	−12.2574	+	21.2304i	−0.513857	+	0.890026i	0.486014	+	0.873951i	$0.338450\pi$
$569$	−12.2574	+	21.2304i	−0.513857	+	0.890026i	−0.999871	+	0.0160749i	$0.994883\pi$
$570$		0			0
$571$	−4.88466	−	8.46048i	−0.204417	−	0.354060i	0.745530	−	0.666472i	$-0.232196\pi$
$571$	−4.88466	−	8.46048i	−0.204417	−	0.354060i	−0.949947	+	0.312412i	$0.898863\pi$
$572$	−5.69788	+	15.4943i	−0.238240	+	0.647851i
$573$		0			0
$574$	9.19877	−	0.0342324i	0.383949	−	0.00142883i
$575$			4.54783i			0.189658i
$576$		0			0
$577$	8.36436	−	4.82917i	0.348213	−	0.201041i	−0.315685	−	0.948864i	$-0.602234\pi$
$577$	8.36436	−	4.82917i	0.348213	−	0.201041i	0.663898	+	0.747823i	$0.268901\pi$
$578$	3.38914	+	4.85736i	0.140970	+	0.202040i
$579$		0			0
$580$	4.46494	+	25.8236i	0.185397	+	1.07227i
$581$	−10.8410	−	22.9255i	−0.449759	−	0.951110i
$582$		0			0
$583$	−22.0575	−	12.7349i	−0.913527	−	0.527425i
$584$	24.8619	−	24.6152i	1.02879	−	1.01858i
$585$		0			0
$586$	6.64099	−	14.1801i	0.274337	−	0.585773i
$587$			2.08560i			0.0860820i	0.999073	+	0.0430410i	$0.0137046\pi$
$587$			2.08560i			0.0860820i	−0.999073	+	0.0430410i	$0.986295\pi$
$588$		0			0
$589$			34.5332i			1.42291i
$590$	−18.8346	−	8.82084i	−0.775406	−	0.363148i
$591$		0			0
$592$	10.6697	−	12.5453i	0.438522	−	0.515610i
$593$	27.3663	+	15.7999i	1.12380	+	0.648826i	0.942368	−	0.334578i	$-0.108594\pi$
$593$	27.3663	+	15.7999i	1.12380	+	0.648826i	0.181431	+	0.983404i	$0.441927\pi$
$594$		0			0
$595$	8.35427	+	17.6669i	0.342492	+	0.724271i
$596$	−0.979198	−	5.66333i	−0.0401095	−	0.231979i
$597$		0			0
$598$	−29.8897	+	20.8550i	−1.22228	+	0.852826i
$599$	−26.7061	+	15.4188i	−1.09118	+	0.629995i	−0.933891	−	0.357558i	$-0.883610\pi$
$599$	−26.7061	+	15.4188i	−1.09118	+	0.629995i	−0.157292	+	0.987552i	$0.550276\pi$
$600$		0			0
$601$			16.8538i			0.687481i	0.939065	+	0.343741i	$0.111694\pi$
$601$			16.8538i			0.687481i	−0.939065	+	0.343741i	$0.888306\pi$
$602$	0.0603695	+	16.2222i	0.00246048	+	0.661168i
$603$		0			0
$604$	−24.4856	−	9.00431i	−0.996305	−	0.366380i
$605$	7.36858	+	12.7628i	0.299576	+	0.518880i
$606$		0			0
$607$	−2.84212	+	4.92270i	−0.115358	+	0.199806i	−0.917923	−	0.396759i	$-0.870135\pi$
$607$	−2.84212	+	4.92270i	−0.115358	+	0.199806i	0.802565	+	0.596565i	$0.203468\pi$
$608$	−11.8421	−	25.9564i	−0.480259	−	1.05267i
$609$		0			0
$610$	6.00000	−	0.514885i	0.242933	−	0.0208471i
$611$	−20.5324	+	35.5631i	−0.830652	+	1.43873i
$612$		0			0
$613$	14.7968	−	8.54292i	0.597636	−	0.345045i	−0.170475	−	0.985362i	$-0.554530\pi$
$613$	14.7968	−	8.54292i	0.597636	−	0.345045i	0.768111	+	0.640317i	$0.221197\pi$
$614$	−37.2555	−	17.4480i	−1.50351	−	0.704144i
$615$		0			0
$616$	13.8151	+	5.02206i	0.556625	+	0.202344i
$617$	−34.1007			−1.37284			−0.686421	−	0.727205i	$-0.740819\pi$
$617$	−34.1007			−1.37284			−0.686421	+	0.727205i	$0.740819\pi$
$618$		0			0
$619$	−14.3212	+	8.26832i	−0.575616	+	0.332332i	−0.759389	−	0.650637i	$-0.774502\pi$
$619$	−14.3212	+	8.26832i	−0.575616	+	0.332332i	0.183773	+	0.982969i	$0.441169\pi$
$620$	−18.0928	−	21.7082i	−0.726622	−	0.871824i
$621$		0			0
$622$	19.7028	−	1.69078i	0.790011	−	0.0677941i
$623$	−38.5175	−	3.16099i	−1.54317	−	0.126643i
$624$		0			0
$625$	10.3712	−	17.9634i	0.414847	−	0.718535i
$626$	−2.12806	+	1.48482i	−0.0850544	+	0.0593453i
$627$		0			0
$628$	6.99642	−	19.0255i	0.279188	−	0.759200i
$629$	14.7372			0.587609
$630$		0			0
$631$		−	26.8671i		−	1.06956i	−0.844991	−	0.534781i	$-0.820394\pi$
$631$		−	26.8671i		−	1.06956i	0.844991	−	0.534781i	$-0.179606\pi$
$632$	2.45302	+	0.670413i	0.0975761	+	0.0266676i
$633$		0			0
$634$	0.926398	−	0.646379i	0.0367920	−	0.0256710i
$635$	−24.4081	−	14.0920i	−0.968607	−	0.559226i
$636$		0			0
$637$	−18.6641	+	22.7357i	−0.739498	+	0.900821i
$638$	1.50816	+	17.5748i	0.0597088	+	0.695792i
$639$		0			0
$640$	21.0433	+	10.1124i	0.831810	+	0.399726i
$641$	14.0425	+	24.3223i	0.554645	+	0.960674i	0.997931	+	0.0642934i	$0.0204793\pi$
$641$	14.0425	+	24.3223i	0.554645	+	0.960674i	−0.443286	+	0.896380i	$0.646187\pi$
$642$		0			0
$643$		−	23.4648i		−	0.925363i	−0.886525	−	0.462682i	$-0.846887\pi$
$643$		−	23.4648i		−	0.925363i	0.886525	−	0.462682i	$-0.153113\pi$
$644$	18.6684	+	26.5447i	0.735637	+	1.04601i
$645$		0			0
$646$	10.8279	−	23.1201i	0.426017	−	0.909646i
$647$	23.4291	+	40.5803i	0.921092	+	1.59538i	0.797729	+	0.603017i	$0.206035\pi$
$647$	23.4291	+	40.5803i	0.921092	+	1.59538i	0.123363	+	0.992362i	$0.460632\pi$
$648$		0			0
$649$	−12.1232	−	6.99933i	−0.475877	−	0.274748i
$650$	−4.39076	+	0.376789i	−0.172220	+	0.0147789i
$651$		0			0
$652$	−2.92285	+	0.505365i	−0.114467	+	0.0197916i
$653$	−12.2356	−	7.06424i	−0.478817	−	0.276445i	0.241106	−	0.970499i	$-0.422490\pi$
$653$	−12.2356	−	7.06424i	−0.478817	−	0.276445i	−0.719923	+	0.694054i	$0.755823\pi$
$654$		0			0
$655$	−14.4803	+	8.36020i	−0.565792	+	0.326660i
$656$	9.67300	+	1.77200i	0.377667	+	0.0691849i
$657$		0			0
$658$	31.7335	+	18.1642i	1.23710	+	0.708115i
$659$	37.6955			1.46841			0.734205	−	0.678928i	$-0.237555\pi$
$659$	37.6955			1.46841			0.734205	+	0.678928i	$0.237555\pi$
$660$		0			0
$661$	−20.9383	−	36.2662i	−0.814406	−	1.41059i	−0.909754	−	0.415148i	$-0.863730\pi$
$661$	−20.9383	−	36.2662i	−0.814406	−	1.41059i	0.0953478	−	0.995444i	$-0.469604\pi$
$662$	−10.6296	−	15.2345i	−0.413133	−	0.592107i
$663$		0			0
$664$	−6.88605	−	26.2214i	−0.267230	−	1.01759i
$665$	−15.6724	+	22.6410i	−0.607751	+	0.877980i
$666$		0			0
$667$	−19.4711	+	33.7249i	−0.753922	+	1.30583i
$668$	−10.3677	−	12.4395i	−0.401140	−	0.481300i
$669$		0			0
$670$	−6.86635	+	14.6613i	−0.265270	+	0.566414i
$671$	4.05335			0.156478
$672$		0			0
$673$	15.2830			0.589115			0.294558	−	0.955634i	$-0.404828\pi$
$673$	15.2830			0.589115			0.294558	+	0.955634i	$0.404828\pi$
$674$	−17.0068	+	36.3136i	−0.655079	+	1.39875i
$675$		0			0
$676$	−5.96494	−	7.15691i	−0.229421	−	0.275266i
$677$	−7.97531	+	13.8136i	−0.306516	+	0.530901i	−0.977598	−	0.210482i	$-0.932497\pi$
$677$	−7.97531	+	13.8136i	−0.306516	+	0.530901i	0.671082	+	0.741383i	$0.265830\pi$
$678$		0			0
$679$	0.622566	+	1.31655i	0.0238919	+	0.0505244i
$680$	5.30653	+	20.2067i	0.203496	+	0.774892i
$681$		0			0
$682$	−10.8841	−	15.5992i	−0.416773	−	0.597324i
$683$	−20.4434	−	35.4089i	−0.782244	−	1.35489i	−0.930632	−	0.365957i	$-0.880742\pi$
$683$	−20.4434	−	35.4089i	−0.782244	−	1.35489i	0.148388	−	0.988929i	$-0.452591\pi$
$684$		0			0
$685$	−14.4742			−0.553030
$686$	20.3057	+	16.5432i	0.775277	+	0.631622i
$687$		0			0
$688$	−3.12495	+	17.0585i	−0.119138	+	0.650351i
$689$	47.1869	−	27.2433i	1.79768	−	1.03789i
$690$		0			0
$691$	−3.32796	−	1.92140i	−0.126601	−	0.0730933i	0.435362	−	0.900256i	$-0.356620\pi$
$691$	−3.32796	−	1.92140i	−0.126601	−	0.0730933i	−0.561963	+	0.827162i	$0.689954\pi$
$692$	30.7189	−	5.31134i	1.16776	−	0.201907i
$693$		0			0
$694$	7.19394	−	0.617342i	0.273078	−	0.0234340i
$695$	9.19703	+	5.30991i	0.348863	+	0.201416i
$696$		0			0
$697$	4.39993	+	7.62090i	0.166659	+	0.288662i
$698$	−9.20083	+	19.6459i	−0.348257	+	0.743610i
$699$		0			0
$700$	0.350042	+	3.90829i	0.0132304	+	0.147719i
$701$			20.0865i			0.758657i	0.925262	+	0.379328i	$0.123845\pi$
$701$			20.0865i			0.758657i	−0.925262	+	0.379328i	$0.876155\pi$
$702$		0			0
$703$	10.3826	+	17.9832i	0.391587	+	0.678248i
$704$	13.5301	+	7.99257i	0.509935	+	0.301231i
$705$		0			0
$706$	0.915482	+	10.6682i	0.0344546	+	0.401503i
$707$	1.84943	+	1.28021i	0.0695551	+	0.0481471i
$708$		0			0
$709$	26.4625	+	15.2782i	0.993821	+	0.573783i	0.906414	−	0.422390i	$-0.138809\pi$
$709$	26.4625	+	15.2782i	0.993821	+	0.573783i	0.0874070	+	0.996173i	$0.472142\pi$
$710$	22.5943	−	15.7648i	0.847948	−	0.591642i
$711$		0			0
$712$	−39.8537	−	10.8920i	−1.49358	−	0.408197i
$713$		−	41.9923i		−	1.57262i
$714$		0			0
$715$	17.0338			0.637027
$716$	−8.17006	+	22.2170i	−0.305329	+	0.830288i
$717$		0			0
$718$	−34.5314	+	24.0937i	−1.28870	+	0.899170i
$719$	8.17064	−	14.1520i	0.304714	−	0.527779i	−0.672484	−	0.740112i	$-0.734773\pi$
$719$	8.17064	−	14.1520i	0.304714	−	0.527779i	0.977198	+	0.212332i	$0.0681059\pi$
$720$		0			0
$721$	0.0936580	−	1.14124i	0.00348801	−	0.0425022i
$722$	9.06925	−	0.778270i	0.337522	−	0.0289642i
$723$		0			0
$724$	−19.5459	−	23.4518i	−0.726419	−	0.871580i
$725$	−4.07785	+	2.35435i	−0.151447	+	0.0874382i
$726$		0			0
$727$	22.7202			0.842646			0.421323	−	0.906911i	$-0.361566\pi$
$727$	22.7202			0.842646			0.421323	+	0.906911i	$0.361566\pi$
$728$	−24.0812	+	20.2229i	−0.892509	+	0.749509i
$729$		0			0
$730$	−32.6910	−	15.3103i	−1.20995	−	0.566658i
$731$	−13.4396	+	7.75936i	−0.497082	+	0.286990i
$732$		0			0
$733$	−23.1635	+	40.1204i	−0.855565	+	1.48188i	0.0205547	+	0.999789i	$0.493457\pi$
$733$	−23.1635	+	40.1204i	−0.855565	+	1.48188i	−0.876120	+	0.482093i	$0.839877\pi$
$734$	−5.93949	+	0.509692i	−0.219231	+	0.0188131i
$735$		0			0
$736$	14.3999	+	31.5629i	0.530788	+	1.16343i
$737$	−5.44844	+	9.43698i	−0.200696	+	0.347616i
$738$		0			0
$739$	−7.30928	−	12.6600i	−0.268876	−	0.465707i	0.699696	−	0.714441i	$-0.253319\pi$
$739$	−7.30928	−	12.6600i	−0.268876	−	0.465707i	−0.968572	+	0.248734i	$0.919986\pi$
$740$	−15.9485	−	5.86490i	−0.586279	−	0.215598i
$741$		0			0
$742$	−24.4139	−	41.9250i	−0.896261	−	1.53911i
$743$			21.9948i			0.806912i	0.914999	+	0.403456i	$0.132191\pi$
$743$			21.9948i			0.806912i	−0.914999	+	0.403456i	$0.867809\pi$
$744$		0			0
$745$	−5.13564	+	2.96506i	−0.188155	+	0.108631i
$746$	13.5306	−	9.44073i	0.495389	−	0.345650i
$747$		0			0
$748$	2.39579	+	13.8564i	0.0875989	+	0.506640i
$749$	−2.06486	+	25.1608i	−0.0754484	+	0.919357i
$750$		0			0
$751$	−6.81783	−	3.93627i	−0.248786	−	0.143637i	0.370422	−	0.928863i	$-0.379213\pi$
$751$	−6.81783	−	3.93627i	−0.248786	−	0.143637i	−0.619208	+	0.785227i	$0.712546\pi$
$752$	29.7762	+	25.3244i	1.08583	+	0.923487i
$753$		0			0
$754$	−34.1733	−	16.0045i	−1.24452	−	0.582848i
$755$			26.9184i			0.979659i
$756$		0			0
$757$			31.6014i			1.14857i	0.818655	+	0.574285i	$0.194720\pi$
$757$			31.6014i			1.14857i	−0.818655	+	0.574285i	$0.805280\pi$
$758$	−3.24297	+	6.92450i	−0.117790	+	0.251509i
$759$		0			0
$760$	−20.9189	+	20.7113i	−0.758808	+	0.751279i
$761$	−21.1485	−	12.2101i	−0.766634	−	0.442616i	0.0650388	−	0.997883i	$-0.479283\pi$
$761$	−21.1485	−	12.2101i	−0.766634	−	0.442616i	−0.831672	+	0.555267i	$0.812616\pi$
$762$		0			0
$763$	26.1879	−	37.8321i	0.948066	−	1.36961i
$764$	0.131354	+	0.759705i	0.00475223	+	0.0274852i
$765$		0			0
$766$	29.7359	+	42.6179i	1.07440	+	1.53985i
$767$	25.9348	−	14.9734i	0.936450	−	0.540660i
$768$		0			0
$769$			15.1803i			0.547415i	0.961813	+	0.273707i	$0.0882500\pi$
$769$			15.1803i			0.547415i	−0.961813	+	0.273707i	$0.911750\pi$
$770$	−0.0564422	−	15.1669i	−0.00203404	−	0.546577i
$771$		0			0
$772$	17.8350	−	48.4990i	0.641896	−	1.74552i
$773$	24.1092	+	41.7583i	0.867147	+	1.50194i	0.864899	+	0.501946i	$0.167382\pi$
$773$	24.1092	+	41.7583i	0.867147	+	1.50194i	0.00224824	+	0.999997i	$0.499284\pi$
$774$		0			0
$775$	2.53875	−	4.39725i	0.0911947	−	0.157954i
$776$	0.395446	+	1.50582i	0.0141957	+	0.0540557i
$777$		0			0
$778$	−2.38806	−	27.8283i	−0.0856161	−	0.997692i
$779$	−6.19965	+	10.7381i	−0.222126	+	0.384733i
$780$		0			0
$781$	16.0594	−	9.27191i	0.574651	−	0.331775i
$782$	−13.1667	+	28.1140i	−0.470840	+	1.00535i
$783$		0			0
$784$	18.0862	+	21.3749i	0.645937	+	0.763391i
$785$	−20.9158			−0.746516
$786$		0			0
$787$	17.0492	−	9.84337i	0.607739	−	0.350878i	−0.164341	−	0.986404i	$-0.552550\pi$
$787$	17.0492	−	9.84337i	0.607739	−	0.350878i	0.772080	+	0.635525i	$0.219216\pi$
$788$	−11.6514	+	9.71090i	−0.415065	+	0.345936i
$789$		0			0
$790$	−0.224339	−	2.61425i	−0.00798163	−	0.0930107i
$791$	41.7896	−	19.7614i	1.48587	−	0.702634i
$792$		0			0
$793$	−4.33560	+	7.50948i	−0.153962	+	0.266669i
$794$	26.3864	+	37.8173i	0.936417	+	1.34208i
$795$		0			0
$796$	−1.83480	+	4.98940i	−0.0650327	+	0.176845i
$797$	−25.6614			−0.908975			−0.454487	−	0.890753i	$-0.650178\pi$
$797$	−25.6614			−0.908975			−0.454487	+	0.890753i	$0.650178\pi$
$798$		0			0
$799$			34.9785i			1.23745i
$800$	−0.400321	+	4.17571i	−0.0141535	+	0.147634i
$801$		0			0
$802$	−9.37490	−	13.4362i	−0.331039	−	0.474449i
$803$	−21.0421	−	12.1487i	−0.742561	−	0.428718i
$804$		0			0
$805$	19.0577	−	27.5314i	0.671694	−	0.970355i
$806$	40.5420	−	3.47908i	1.42803	−	0.122545i
$807$		0			0
$808$	1.69181	+	1.70876i	0.0595176	+	0.0601141i
$809$	−16.1716	−	28.0101i	−0.568564	−	0.984781i	−0.996708	−	0.0810709i	$-0.974166\pi$
$809$	−16.1716	−	28.0101i	−0.568564	−	0.984781i	0.428145	−	0.903710i	$-0.359167\pi$
$810$		0			0
$811$			45.9933i			1.61504i	0.589838	+	0.807521i	$0.299191\pi$
$811$			45.9933i			1.61504i	−0.589838	+	0.807521i	$0.700809\pi$
$812$	−14.1372	+	30.4809i	−0.496117	+	1.06967i
$813$		0			0
$814$	−10.3579	−	4.85093i	−0.363043	−	0.170025i
$815$	1.53027	+	2.65051i	0.0536030	+	0.0928431i
$816$		0			0
$817$	−18.9369	−	10.9332i	−0.662518	−	0.382505i
$818$	2.54050	+	29.6047i	0.0888265	+	1.03510i
$819$		0			0
$820$	−1.72873	−	9.99834i	−0.0603698	−	0.349157i
$821$	12.8183	+	7.40064i	0.447361	+	0.258284i	0.706715	−	0.707498i	$-0.250176\pi$
$821$	12.8183	+	7.40064i	0.447361	+	0.258284i	−0.259354	+	0.965782i	$0.583510\pi$
$822$		0			0
$823$	11.2556	−	6.49843i	0.392346	−	0.226521i	−0.290830	−	0.956775i	$-0.593931\pi$
$823$	11.2556	−	6.49843i	0.392346	−	0.226521i	0.683176	+	0.730254i	$0.260598\pi$
$824$	0.322724	−	1.18084i	0.0112426	−	0.0411364i
$825$		0			0
$826$	−13.4183	−	23.0427i	−0.466883	−	0.801759i
$827$	37.8013			1.31448			0.657240	−	0.753681i	$-0.271724\pi$
$827$	37.8013			1.31448			0.657240	+	0.753681i	$0.271724\pi$
$828$		0			0
$829$	8.63343	+	14.9535i	0.299851	+	0.519358i	0.976102	−	0.217314i	$-0.0697296\pi$
$829$	8.63343	+	14.9535i	0.299851	+	0.519358i	−0.676250	+	0.736672i	$0.736396\pi$
$830$	−22.9404	+	16.0063i	−0.796274	+	0.555587i
$831$		0			0
$832$	−29.2798	+	16.5176i	−1.01509	+	0.572644i
$833$	−4.08494	+	24.7204i	−0.141535	+	0.856510i
$834$		0			0
$835$	−8.35427	+	14.4700i	−0.289112	+	0.500756i
$836$	−15.2205	+	12.6856i	−0.526413	+	0.438740i
$837$		0			0
$838$	16.7438	+	7.84167i	0.578405	+	0.270886i
$839$	2.55046			0.0880517			0.0440259	−	0.999030i	$-0.485982\pi$
$839$	2.55046			0.0880517			0.0440259	+	0.999030i	$0.485982\pi$
$840$		0			0
$841$	−11.3195			−0.390329
$842$	−39.3447	−	18.4264i	−1.35591	−	0.635017i
$843$		0			0
$844$	17.7769	+	21.3293i	0.611906	+	0.734183i
$845$	−4.80651	+	8.32513i	−0.165349	+	0.286393i
$846$		0			0
$847$	−1.54542	+	18.8313i	−0.0531012	+	0.647050i
$848$	−17.4145	−	48.8541i	−0.598016	−	1.67766i
$849$		0			0
$850$	−3.07846	+	2.14794i	−0.105590	+	0.0736739i
$851$	−12.6252	−	21.8675i	−0.432787	−	0.749609i
$852$		0			0
$853$	14.8204			0.507442			0.253721	−	0.967277i	$-0.418345\pi$
$853$	14.8204			0.507442			0.253721	+	0.967277i	$0.418345\pi$
$854$	6.70081	+	3.83554i	0.229297	+	0.131249i
$855$		0			0
$856$	−7.11503	+	26.0337i	−0.243187	+	0.889814i
$857$	7.96620	−	4.59929i	0.272120	−	0.157109i	−0.357730	−	0.933825i	$-0.616449\pi$
$857$	7.96620	−	4.59929i	0.272120	−	0.157109i	0.629851	+	0.776716i	$0.283116\pi$
$858$		0			0
$859$	23.1202	+	13.3484i	0.788850	+	0.455443i	0.839558	−	0.543271i	$-0.182814\pi$
$859$	23.1202	+	13.3484i	0.788850	+	0.455443i	−0.0507075	+	0.998714i	$0.516148\pi$
$860$	17.6323	−	3.04865i	0.601256	−	0.103958i
$861$		0			0
$862$	0.200919	+	2.34133i	0.00684334	+	0.0797460i
$863$	−0.837724	−	0.483660i	−0.0285165	−	0.0164640i	0.485674	−	0.874140i	$-0.338574\pi$
$863$	−0.837724	−	0.483660i	−0.0285165	−	0.0164640i	−0.514190	+	0.857676i	$0.671908\pi$
$864$		0			0
$865$	−16.0830	−	27.8566i	−0.546838	−	0.947152i
$866$	−35.0768	−	16.4276i	−1.19196	−	0.558233i
$867$		0			0
$868$	−3.23211	−	36.0871i	−0.109705	−	1.22488i
$869$		−	1.76608i		−	0.0599100i
$870$		0			0
$871$	−11.6557	−	20.1882i	−0.394938	−	0.684052i
$872$	34.9545	−	34.6077i	1.18371	−	1.17196i
$873$		0			0
$874$	−43.5825	+	3.74000i	−1.47420	+	0.126507i
$875$	28.3388	−	13.4008i	0.958027	−	0.453030i
$876$		0			0
$877$	3.70815	+	2.14090i	0.125215	+	0.0722932i	0.561299	−	0.827613i	$-0.310302\pi$
$877$	3.70815	+	2.14090i	0.125215	+	0.0722932i	−0.436084	+	0.899906i	$0.643635\pi$
$878$	−6.83218	−	9.79197i	−0.230575	−	0.330463i
$879$		0			0
$880$	2.92166	−	15.9488i	0.0984892	−	0.537634i
$881$			20.1386i			0.678487i	0.940699	+	0.339244i	$0.110171\pi$
$881$			20.1386i			0.678487i	−0.940699	+	0.339244i	$0.889829\pi$
$882$		0			0
$883$	3.01850			0.101580			0.0507902	−	0.998709i	$-0.483826\pi$
$883$	3.01850			0.101580			0.0507902	+	0.998709i	$0.483826\pi$
$884$	−28.2338	−	10.3827i	−0.949607	−	0.349208i
$885$		0			0
$886$	3.36367	+	4.82085i	0.113005	+	0.161959i
$887$	6.56652	−	11.3736i	0.220482	−	0.381886i	−0.734472	−	0.678639i	$-0.762570\pi$
$887$	6.56652	−	11.3736i	0.220482	−	0.381886i	0.954955	+	0.296752i	$0.0959036\pi$
$888$		0			0
$889$	−15.4474	−	32.6667i	−0.518088	−	1.09561i
$890$	3.64479	+	42.4731i	0.122174	+	1.42370i
$891$		0			0
$892$	−33.8678	−	40.6357i	−1.13398	−	1.36058i
$893$	−42.6829	+	24.6430i	−1.42833	+	0.824645i
$894$		0			0
$895$	24.4244			0.816416
$896$	14.8043	+	26.0160i	0.494577	+	0.869134i
$897$		0			0
$898$	−11.2864	+	24.0991i	−0.376632	+	0.804198i
$899$	37.6527	−	21.7388i	1.25579	−	0.725030i
$900$		0			0
$901$	23.2056	−	40.1932i	0.773089	−	1.33903i
$902$	−0.583928	−	6.80457i	−0.0194427	−	0.226567i
$903$		0			0
$904$	47.7974	−	12.5522i	1.58972	−	0.417479i
$905$	−15.7500	+	27.2798i	−0.523548	+	0.906812i
$906$		0			0
$907$	−10.8627	−	18.8148i	−0.360691	−	0.624736i	0.627383	−	0.778711i	$-0.284126\pi$
$907$	−10.8627	−	18.8148i	−0.360691	−	0.624736i	−0.988075	+	0.153975i	$0.950793\pi$
$908$	33.8056	+	12.4316i	1.12188	+	0.412558i
$909$		0			0
$910$	28.1595	+	16.1185i	0.933478	+	0.534322i
$911$		−	8.27670i		−	0.274219i	−0.990556	−	0.137110i	$-0.956219\pi$
$911$		−	8.27670i		−	0.274219i	0.990556	−	0.137110i	$-0.0437813\pi$
$912$		0			0
$913$	−16.3054	+	9.41395i	−0.539632	+	0.311556i
$914$	−4.58932	−	6.57747i	−0.151801	−	0.217563i
$915$		0			0
$916$	−23.6554	+	4.09006i	−0.781597	+	0.135139i
$917$	−21.3655	−	1.75339i	−0.705550	−	0.0579020i
$918$		0			0
$919$	48.2363	+	27.8492i	1.59117	+	0.918661i	0.993107	+	0.117211i	$0.0373953\pi$
$919$	48.2363	+	27.8492i	1.59117	+	0.918661i	0.598061	+	0.801451i	$0.295938\pi$
$920$	25.4374	−	25.1850i	0.838645	−	0.830323i
$921$		0			0
$922$	18.1887	−	38.8371i	0.599012	−	1.27903i
$923$			39.6702i			1.30576i
$924$		0			0
$925$		−	3.05316i		−	0.100387i
$926$	−10.7743	−	5.04594i	−0.354064	−	0.165820i
$927$		0			0
$928$	−20.8465	+	29.2515i	−0.684320	+	0.960227i
$929$	−0.357266	−	0.206268i	−0.0117215	−	0.00676743i	0.494128	−	0.869389i	$-0.335487\pi$
$929$	−0.357266	−	0.206268i	−0.0117215	−	0.00676743i	−0.505849	+	0.862622i	$0.668821\pi$
$930$		0			0
$931$	−33.0432	+	12.4312i	−1.08295	+	0.407418i
$932$	−18.9482	+	3.27618i	−0.620670	+	0.107315i
$933$		0			0
$934$	−37.7069	+	26.3093i	−1.23381	+	0.860868i
$935$	12.5653	−	7.25459i	0.410930	−	0.237250i
$936$		0			0
$937$			30.5249i			0.997204i	0.866831	+	0.498602i	$0.166153\pi$
$937$			30.5249i			0.997204i	−0.866831	+	0.498602i	$0.833847\pi$
$938$	−17.9370	+	10.4451i	−0.585664	+	0.341045i
$939$		0			0
$940$	13.9203	−	37.8536i	0.454029	−	1.23465i
$941$	−20.5887	−	35.6607i	−0.671173	−	1.16251i	−0.977572	−	0.210602i	$-0.932457\pi$
$941$	−20.5887	−	35.6607i	−0.671173	−	1.16251i	0.306399	−	0.951903i	$-0.400876\pi$
$942$		0			0
$943$	7.53877	−	13.0575i	0.245496	−	0.425212i
$944$	−9.57133	−	26.8511i	−0.311520	−	0.873929i
$945$		0			0
$946$	12.0000	−	1.02977i	0.390154	−	0.0334807i
$947$	0.870237	−	1.50729i	0.0282789	−	0.0489805i	−0.851540	−	0.524290i	$-0.824331\pi$
$947$	0.870237	−	1.50729i	0.0282789	−	0.0489805i	0.879819	+	0.475310i	$0.157664\pi$
$948$		0			0
$949$	45.0148	−	25.9893i	1.46124	−	0.843648i
$950$	−4.78988	−	2.24326i	−0.155404	−	0.0727808i
$951$		0			0
$952$	−9.15120	+	25.1738i	−0.296592	+	0.815889i
$953$	−11.1171			−0.360119			−0.180059	−	0.983656i	$-0.557629\pi$
$953$	−11.1171			−0.360119			−0.180059	+	0.983656i	$0.557629\pi$
$954$		0			0
$955$	0.688919	−	0.397747i	0.0222929	−	0.0128708i
$956$	33.4659	−	27.8922i	1.08237	−	0.902098i
$957$		0			0
$958$	−40.5896	+	3.48316i	−1.31139	+	0.112536i
$959$	−15.2584	−	10.5621i	−0.492720	−	0.341068i
$960$		0			0
$961$	−7.94152	+	13.7551i	−0.256178	+	0.443713i
$962$	20.0663	−	14.0009i	0.646962	−	0.451407i
$963$		0			0
$964$	14.2311	+	5.23334i	0.458354	+	0.168555i
$965$	−53.3177			−1.71636
$966$		0			0
$967$			6.95681i			0.223716i	0.993724	+	0.111858i	$0.0356801\pi$
$967$			6.95681i			0.223716i	−0.993724	+	0.111858i	$0.964320\pi$
$968$	−5.32515	+	19.4846i	−0.171157	+	0.626258i
$969$		0			0
$970$	1.31740	−	0.919197i	0.0422993	−	0.0295136i
$971$	−21.5086	−	12.4180i	−0.690245	−	0.398513i	0.113459	−	0.993543i	$-0.463807\pi$
$971$	−21.5086	−	12.4180i	−0.690245	−	0.398513i	−0.803704	+	0.595030i	$0.797140\pi$
$972$		0			0
$973$	5.82060	+	12.3089i	0.186600	+	0.394604i
$974$	3.05545	+	35.6054i	0.0979028	+	1.14087i
$975$		0			0
$976$	6.28751	+	5.34748i	0.201258	+	0.171169i
$977$	−5.38526	−	9.32755i	−0.172290	−	0.298415i	0.766930	−	0.641731i	$-0.221783\pi$
$977$	−5.38526	−	9.32755i	−0.172290	−	0.298415i	−0.939220	+	0.343316i	$0.888450\pi$
$978$		0			0
$979$			28.6930i			0.917033i
$980$	14.2586	−	25.1266i	0.455474	−	0.802641i
$981$		0			0
$982$	15.4797	−	33.0528i	0.493977	−	1.05476i
$983$	−20.3158	−	35.1881i	−0.647974	−	1.12232i	−0.983606	−	0.180331i	$-0.942283\pi$
$983$	−20.3158	−	35.1881i	−0.647974	−	1.12232i	0.335631	−	0.941993i	$-0.391050\pi$
$984$		0			0
$985$	13.5533	+	7.82499i	0.431844	+	0.249325i
$986$	−32.0248	+	2.74818i	−1.01988	+	0.0875199i
$987$		0			0
$988$	−7.22165	−	41.7674i	−0.229751	−	1.32880i
$989$	23.0272	+	13.2948i	0.732223	+	0.422749i
$990$		0			0
$991$	30.4544	−	17.5829i	0.967417	−	0.558538i	0.0689690	−	0.997619i	$-0.478029\pi$
$991$	30.4544	−	17.5829i	0.967417	−	0.558538i	0.898448	+	0.439080i	$0.144696\pi$
$992$	3.69636	−	38.5564i	0.117359	−	1.22417i
$993$		0			0
$994$	35.3224	−	0.131449i	1.12036	−	0.00416931i
$995$	5.48512			0.173890
$996$		0			0
$997$	26.8018	+	46.4221i	0.848822	+	1.47020i	0.882260	+	0.470762i	$0.156021\pi$
$997$	26.8018	+	46.4221i	0.848822	+	1.47020i	−0.0334384	+	0.999441i	$0.510646\pi$
$998$	−18.3037	−	26.2331i	−0.579393	−	0.830393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.b.19.10	yes	32
3.2	odd	2	inner	504.2.bk.b.19.7	yes	32
4.3	odd	2		2016.2.bs.b.271.5		32
7.3	odd	6	inner	504.2.bk.b.451.11	yes	32
8.3	odd	2	inner	504.2.bk.b.19.11	yes	32
8.5	even	2		2016.2.bs.b.271.11		32
12.11	even	2		2016.2.bs.b.271.12		32
21.17	even	6	inner	504.2.bk.b.451.6	yes	32
24.5	odd	2		2016.2.bs.b.271.6		32
24.11	even	2	inner	504.2.bk.b.19.6	✓	32
28.3	even	6		2016.2.bs.b.1711.11		32
56.3	even	6	inner	504.2.bk.b.451.10	yes	32
56.45	odd	6		2016.2.bs.b.1711.5		32
84.59	odd	6		2016.2.bs.b.1711.6		32
168.59	odd	6	inner	504.2.bk.b.451.7	yes	32
168.101	even	6		2016.2.bs.b.1711.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bk.b.19.6	✓	32	24.11	even	2	inner
504.2.bk.b.19.7	yes	32	3.2	odd	2	inner
504.2.bk.b.19.10	yes	32	1.1	even	1	trivial
504.2.bk.b.19.11	yes	32	8.3	odd	2	inner
504.2.bk.b.451.6	yes	32	21.17	even	6	inner
504.2.bk.b.451.7	yes	32	168.59	odd	6	inner
504.2.bk.b.451.10	yes	32	56.3	even	6	inner
504.2.bk.b.451.11	yes	32	7.3	odd	6	inner
2016.2.bs.b.271.5		32	4.3	odd	2
2016.2.bs.b.271.6		32	24.5	odd	2
2016.2.bs.b.271.11		32	8.5	even	2
2016.2.bs.b.271.12		32	12.11	even	2
2016.2.bs.b.1711.5		32	56.45	odd	6
2016.2.bs.b.1711.6		32	84.59	odd	6
2016.2.bs.b.1711.11		32	28.3	even	6
2016.2.bs.b.1711.12		32	168.101	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599802 - 1.28072i) q^{2} +(-1.28048 - 1.53635i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(-2.39181 + 1.13104i) q^{7} +(-2.73567 + 0.718419i) q^{8} +O(q^{10})\)	\(q+(0.599802 - 1.28072i) q^{2} +(-1.28048 - 1.53635i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(-2.39181 + 1.13104i) q^{7} +(-2.73567 + 0.718419i) q^{8} +(1.66993 + 2.39337i) q^{10} +(0.982155 + 1.70114i) q^{11} -4.20219 q^{13} +(0.0139241 + 3.74163i) q^{14} +(-0.720766 + 3.93453i) q^{16} +(-3.09983 + 1.78969i) q^{17} +(-4.36777 - 2.52173i) q^{19} +(4.06686 - 0.703166i) q^{20} +(2.76778 - 0.237515i) q^{22} +(5.31120 + 3.06642i) q^{23} +(0.370777 + 0.642204i) q^{25} +(-2.52048 + 5.38182i) q^{26} +(4.80033 + 2.22640i) q^{28} +6.34977i q^{29} +(-3.42356 - 5.92978i) q^{31} +(4.60670 + 3.28303i) q^{32} +(0.432800 + 5.04346i) q^{34} +(0.446563 - 5.44148i) q^{35} +(-3.56564 - 2.05862i) q^{37} +(-5.84942 + 4.08133i) q^{38} +(1.53875 - 5.63026i) q^{40} -2.45849i q^{41} +4.33560 q^{43} +(1.35593 - 3.68721i) q^{44} +(7.11289 - 4.96290i) q^{46} +(4.88612 - 8.46301i) q^{47} +(4.44152 - 5.41045i) q^{49} +(1.04487 - 0.0896650i) q^{50} +(5.38080 + 6.45605i) q^{52} +(-11.2291 + 6.48313i) q^{53} -4.05355 q^{55} +(5.73064 - 4.81246i) q^{56} +(8.13226 + 3.80860i) q^{58} +(-6.17173 + 3.56325i) q^{59} +(1.03175 - 1.78704i) q^{61} +(-9.64783 + 0.827920i) q^{62} +(6.96775 - 3.93071i) q^{64} +(4.33582 - 7.50986i) q^{65} +(2.77372 + 4.80422i) q^{67} +(6.71884 + 2.47078i) q^{68} +(-6.70115 - 3.83573i) q^{70} -9.44037i q^{71} +(-10.7122 + 6.18471i) q^{73} +(-4.77520 + 3.33181i) q^{74} +(1.71855 + 9.93945i) q^{76} +(-4.27318 - 2.95796i) q^{77} +(-0.778628 - 0.449541i) q^{79} +(-6.28782 - 5.34775i) q^{80} +(-3.14863 - 1.47461i) q^{82} +9.58499i q^{83} -7.38639i q^{85} +(2.60050 - 5.55268i) q^{86} +(-3.90898 - 3.94816i) q^{88} +(12.6502 + 7.30359i) q^{89} +(10.0508 - 4.75282i) q^{91} +(-2.08975 - 12.0864i) q^{92} +(-7.90802 - 11.3339i) q^{94} +(9.01332 - 5.20384i) q^{95} -0.550439i q^{97} +(-4.26522 - 8.93353i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 32 * q + 2 * q^4	\( 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) \) 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

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