LMFDB - Embedded newform 804.2.y.b.505.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			505.4
Character	$\chi$	$=$	804.505
Dual form			804.2.y.b.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-0.192294 - 0.123580i) q^{5} +(-3.39999 + 1.36115i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-0.192294 - 0.123580i) q^{5} +(-3.39999 + 1.36115i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.270673 - 5.68213i) q^{11} +(-7.01139 - 0.669507i) q^{13} +(-0.0325305 - 0.226254i) q^{15} +(-0.521840 + 2.15105i) q^{17} +(3.17314 + 1.27033i) q^{19} +(-3.25521 - 1.67818i) q^{21} +(-5.32369 + 1.02606i) q^{23} +(-2.05537 - 4.50063i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-2.03892 - 3.53152i) q^{29} +(-4.18895 + 0.399996i) q^{31} +(4.47152 - 3.51644i) q^{33} +(0.822011 + 0.158430i) q^{35} +(5.38316 - 9.32391i) q^{37} +(-4.08551 - 5.73729i) q^{39} +(6.45714 + 6.15688i) q^{41} +(-0.315331 + 0.0925896i) q^{43} +(0.149689 - 0.172750i) q^{45} +(-3.08261 + 8.90661i) q^{47} +(4.64107 - 4.42526i) q^{49} +(-1.96739 + 1.01426i) q^{51} +(-4.04631 - 1.18810i) q^{53} +(-0.754248 + 1.05919i) q^{55} +(1.11791 + 3.22999i) q^{57} +(-4.67990 + 10.2476i) q^{59} +(-0.371752 - 7.80404i) q^{61} +(-0.863428 - 3.55910i) q^{63} +(1.26551 + 0.995212i) q^{65} +(-4.45180 - 6.86888i) q^{67} +(-4.26172 - 3.35145i) q^{69} +(0.0517593 + 0.213355i) q^{71} +(0.400351 + 8.40440i) q^{73} +(2.05537 - 4.50063i) q^{75} +(6.81396 + 19.6876i) q^{77} +(-0.176501 + 0.247860i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-11.5927 + 5.97647i) q^{83} +(0.366174 - 0.349146i) q^{85} +(1.33373 - 3.85356i) q^{87} +(10.8214 - 12.4886i) q^{89} +(24.7500 - 7.26725i) q^{91} +(-3.04547 - 2.90385i) q^{93} +(-0.453190 - 0.636416i) q^{95} +(-5.87348 + 10.1732i) q^{97} +(5.58578 + 1.07657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.192294	−	0.123580i	−0.0859967	−	0.0552667i	0.496936	−	0.867787i	$-0.334458\pi$
$5$	−0.192294	−	0.123580i	−0.0859967	−	0.0552667i	−0.582933	+	0.812521i	$0.698095\pi$
$6$		0			0
$7$	−3.39999	+	1.36115i	−1.28508	+	0.514467i	−0.910799	−	0.412850i	$-0.864533\pi$
$7$	−3.39999	+	1.36115i	−1.28508	+	0.514467i	−0.374277	+	0.927317i	$0.622109\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	0.270673	−	5.68213i	0.0816111	−	1.71323i	−0.472954	−	0.881087i	$-0.656812\pi$
$11$	0.270673	−	5.68213i	0.0816111	−	1.71323i	0.554565	−	0.832140i	$-0.312885\pi$
$12$		0			0
$13$	−7.01139	−	0.669507i	−1.94461	−	0.185688i	−0.951917	−	0.306355i	$-0.900891\pi$
$13$	−7.01139	−	0.669507i	−1.94461	−	0.185688i	−0.992693	+	0.120667i	$0.961497\pi$
$14$		0			0
$15$	−0.0325305	−	0.226254i	−0.00839933	−	0.0584186i
$16$		0			0
$17$	−0.521840	+	2.15105i	−0.126565	+	0.521707i	0.872866	+	0.487960i	$0.162259\pi$
$17$	−0.521840	+	2.15105i	−0.126565	+	0.521707i	−0.999430	+	0.0337463i	$0.989256\pi$
$18$		0			0
$19$	3.17314	+	1.27033i	0.727969	+	0.291435i	0.705890	−	0.708321i	$-0.250547\pi$
$19$	3.17314	+	1.27033i	0.727969	+	0.291435i	0.0220789	+	0.999756i	$0.492971\pi$
$20$		0			0
$21$	−3.25521	−	1.67818i	−0.710345	−	0.366208i
$22$		0			0
$23$	−5.32369	+	1.02606i	−1.11007	+	0.213948i	−0.711150	−	0.703040i	$-0.751825\pi$
$23$	−5.32369	+	1.02606i	−1.11007	+	0.213948i	−0.398916	+	0.916988i	$0.630613\pi$
$24$		0			0
$25$	−2.05537	−	4.50063i	−0.411074	−	0.900126i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−2.03892	−	3.53152i	−0.378618	−	0.655786i	0.612243	−	0.790669i	$-0.290267\pi$
$29$	−2.03892	−	3.53152i	−0.378618	−	0.655786i	−0.990861	+	0.134883i	$0.956934\pi$
$30$		0			0
$31$	−4.18895	+	0.399996i	−0.752357	+	0.0718414i	−0.464186	−	0.885738i	$-0.653653\pi$
$31$	−4.18895	+	0.399996i	−0.752357	+	0.0718414i	−0.288171	+	0.957579i	$0.593047\pi$
$32$		0			0
$33$	4.47152	−	3.51644i	0.778392	−	0.612134i
$34$		0			0
$35$	0.822011	+	0.158430i	0.138945	+	0.0267795i
$36$		0			0
$37$	5.38316	−	9.32391i	0.884986	−	1.53284i	0.0392567	−	0.999229i	$-0.487501\pi$
$37$	5.38316	−	9.32391i	0.884986	−	1.53284i	0.845729	−	0.533612i	$-0.179166\pi$
$38$		0			0
$39$	−4.08551	−	5.73729i	−0.654205	−	0.918702i
$40$		0			0
$41$	6.45714	+	6.15688i	1.00844	+	0.961542i	0.999262	−	0.0384156i	$-0.0122311\pi$
$41$	6.45714	+	6.15688i	1.00844	+	0.961542i	0.00917473	+	0.999958i	$0.497080\pi$
$42$		0			0
$43$	−0.315331	+	0.0925896i	−0.0480876	+	0.0141198i	−0.305688	−	0.952132i	$-0.598886\pi$
$43$	−0.315331	+	0.0925896i	−0.0480876	+	0.0141198i	0.257600	+	0.966252i	$0.417068\pi$
$44$		0			0
$45$	0.149689	−	0.172750i	0.0223143	−	0.0257520i
$46$		0			0
$47$	−3.08261	+	8.90661i	−0.449644	+	1.29916i	0.461524	+	0.887128i	$0.347303\pi$
$47$	−3.08261	+	8.90661i	−0.449644	+	1.29916i	−0.911168	+	0.412034i	$0.864818\pi$
$48$		0			0
$49$	4.64107	−	4.42526i	0.663011	−	0.632179i
$50$		0			0
$51$	−1.96739	+	1.01426i	−0.275490	+	0.142025i
$52$		0			0
$53$	−4.04631	−	1.18810i	−0.555804	−	0.163199i	−0.00824496	−	0.999966i	$-0.502624\pi$
$53$	−4.04631	−	1.18810i	−0.555804	−	0.163199i	−0.547559	+	0.836767i	$0.684443\pi$
$54$		0			0
$55$	−0.754248	+	1.05919i	−0.101703	+	0.142822i
$56$		0			0
$57$	1.11791	+	3.22999i	0.148071	+	0.427823i
$58$		0			0
$59$	−4.67990	+	10.2476i	−0.609271	+	1.33412i	0.313800	+	0.949489i	$0.398398\pi$
$59$	−4.67990	+	10.2476i	−0.609271	+	1.33412i	−0.923071	+	0.384629i	$0.874329\pi$
$60$		0			0
$61$	−0.371752	−	7.80404i	−0.0475980	−	0.999205i	−0.888746	−	0.458400i	$-0.848423\pi$
$61$	−0.371752	−	7.80404i	−0.0475980	−	0.999205i	0.841148	−	0.540805i	$-0.181880\pi$
$62$		0			0
$63$	−0.863428	−	3.55910i	−0.108782	−	0.448404i
$64$		0			0
$65$	1.26551	+	0.995212i	0.156968	+	0.123441i
$66$		0			0
$67$	−4.45180	−	6.86888i	−0.543874	−	0.839167i
$67$	−4.45180	−	6.86888i	−0.543874	−	0.839167i
$68$		0			0
$69$	−4.26172	−	3.35145i	−0.513050	−	0.403467i
$70$		0			0
$71$	0.0517593	+	0.213355i	0.00614270	+	0.0253206i	0.974800	−	0.223079i	$-0.0716107\pi$
$71$	0.0517593	+	0.213355i	0.00614270	+	0.0253206i	−0.968658	+	0.248399i	$0.920096\pi$
$72$		0			0
$73$	0.400351	+	8.40440i	0.0468575	+	0.983661i	0.892819	+	0.450416i	$0.148724\pi$
$73$	0.400351	+	8.40440i	0.0468575	+	0.983661i	−0.845961	+	0.533245i	$0.820973\pi$
$74$		0			0
$75$	2.05537	−	4.50063i	0.237334	−	0.519688i
$76$		0			0
$77$	6.81396	+	19.6876i	0.776522	+	2.24361i
$78$		0			0
$79$	−0.176501	+	0.247860i	−0.0198579	+	0.0278865i	−0.824386	−	0.566029i	$-0.808479\pi$
$79$	−0.176501	+	0.247860i	−0.0198579	+	0.0278865i	0.804528	+	0.593915i	$0.202419\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−11.5927	+	5.97647i	−1.27247	+	0.656002i	−0.956213	−	0.292672i	$-0.905456\pi$
$83$	−11.5927	+	5.97647i	−1.27247	+	0.656002i	−0.316254	+	0.948675i	$0.602425\pi$
$84$		0			0
$85$	0.366174	−	0.349146i	0.0397172	−	0.0378702i
$86$		0			0
$87$	1.33373	−	3.85356i	0.142991	−	0.413146i
$88$		0			0
$89$	10.8214	−	12.4886i	1.14707	−	1.32379i	0.208773	−	0.977964i	$-0.433053\pi$
$89$	10.8214	−	12.4886i	1.14707	−	1.32379i	0.938298	−	0.345826i	$-0.112401\pi$
$90$		0			0
$91$	24.7500	−	7.26725i	2.59450	−	0.761815i
$92$		0			0
$93$	−3.04547	−	2.90385i	−0.315801	−	0.301115i
$94$		0			0
$95$	−0.453190	−	0.636416i	−0.0464963	−	0.0652949i
$96$		0			0
$97$	−5.87348	+	10.1732i	−0.596361	+	1.03293i	0.396992	+	0.917822i	$0.370054\pi$
$97$	−5.87348	+	10.1732i	−0.596361	+	1.03293i	−0.993353	+	0.115106i	$0.963279\pi$
$98$		0			0
$99$	5.58578	+	1.07657i	0.561392	+	0.108199i
$100$		0			0
$101$	9.35267	−	7.35502i	0.930626	−	0.731852i	−0.0329027	−	0.999459i	$-0.510475\pi$
$101$	9.35267	−	7.35502i	0.930626	−	0.731852i	0.963528	+	0.267607i	$0.0862327\pi$
$102$		0			0
$103$	−12.9779	+	1.23924i	−1.27875	+	0.122106i	−0.712231	−	0.701945i	$-0.752315\pi$
$103$	−12.9779	+	1.23924i	−1.27875	+	0.122106i	−0.566516	+	0.824051i	$0.691709\pi$
$104$		0			0
$105$	0.418570	+	0.724984i	0.0408482	+	0.0707512i
$106$		0			0
$107$	1.31009	−	0.841943i	0.126651	−	0.0813937i	−0.475781	−	0.879564i	$-0.657835\pi$
$107$	1.31009	−	0.841943i	0.126651	−	0.0813937i	0.602432	+	0.798170i	$0.294198\pi$
$108$		0			0
$109$	−1.31313	−	2.87536i	−0.125775	−	0.275409i	0.836261	−	0.548332i	$-0.184737\pi$
$109$	−1.31313	−	2.87536i	−0.125775	−	0.275409i	−0.962036	+	0.272923i	$0.912010\pi$
$110$		0			0
$111$	10.5718	−	2.03754i	1.00343	−	0.193395i
$112$		0			0
$113$	−3.85416	−	1.98696i	−0.362569	−	0.186917i	0.267310	−	0.963611i	$-0.413865\pi$
$113$	−3.85416	−	1.98696i	−0.362569	−	0.186917i	−0.629879	+	0.776693i	$0.716896\pi$
$114$		0			0
$115$	1.15052	+	0.460597i	0.107286	+	0.0429509i
$116$		0			0
$117$	1.66052	−	6.84475i	0.153515	−	0.632797i
$118$		0			0
$119$	−1.15366	−	8.02386i	−0.105756	−	0.735546i
$120$		0			0
$121$	−21.2632	−	2.03039i	−1.93302	−	0.184581i
$122$		0			0
$123$	−0.424525	+	8.91188i	−0.0382781	+	0.803557i
$124$		0			0
$125$	−0.323605	+	2.25072i	−0.0289441	+	0.201311i
$126$		0			0
$127$	5.98973	−	2.39792i	0.531502	−	0.212781i	−0.0903584	−	0.995909i	$-0.528801\pi$
$127$	5.98973	−	2.39792i	0.531502	−	0.212781i	0.621861	+	0.783128i	$0.286377\pi$
$128$		0			0
$129$	−0.276473	−	0.177678i	−0.0243421	−	0.0156437i
$130$		0			0
$131$	3.82785	+	4.41758i	0.334441	+	0.385965i	0.897915	−	0.440168i	$-0.145081\pi$
$131$	3.82785	+	4.41758i	0.334441	+	0.385965i	−0.563474	+	0.826133i	$0.690536\pi$
$132$		0			0
$133$	−12.5178			−1.08543
$134$		0			0
$135$	0.228581			0.0196731
$136$		0			0
$137$	−1.14328	−	1.31942i	−0.0976771	−	0.112725i	0.704806	−	0.709400i	$-0.251034\pi$
$137$	−1.14328	−	1.31942i	−0.0976771	−	0.112725i	−0.802483	+	0.596674i	$0.796488\pi$
$138$		0			0
$139$	0.395379	+	0.254094i	0.0335356	+	0.0215520i	0.557301	−	0.830310i	$-0.311837\pi$
$139$	0.395379	+	0.254094i	0.0335356	+	0.0215520i	−0.523766	+	0.851862i	$0.675473\pi$
$140$		0			0
$141$	−8.74984	+	3.50291i	−0.736870	+	0.294998i
$142$		0			0
$143$	−5.70202	+	39.6584i	−0.476827	+	3.31641i
$144$		0			0
$145$	−0.0443519	+	0.931061i	−0.00368323	+	0.0773204i
$146$		0			0
$147$	6.38364	+	0.609564i	0.526514	+	0.0502760i
$148$		0			0
$149$	0.596556	+	4.14914i	0.0488718	+	0.339911i	0.999557	+	0.0297541i	$0.00947241\pi$
$149$	0.596556	+	4.14914i	0.0488718	+	0.339911i	−0.950685	+	0.310157i	$0.899618\pi$
$150$		0			0
$151$	−1.95586	+	8.06216i	−0.159165	+	0.656089i	0.835187	+	0.549965i	$0.185359\pi$
$151$	−1.95586	+	8.06216i	−0.159165	+	0.656089i	−0.994353	+	0.106124i	$0.966156\pi$
$152$		0			0
$153$	−2.05489	−	0.822655i	−0.166128	−	0.0665077i
$154$		0			0
$155$	0.854943	+	0.440754i	0.0686706	+	0.0354022i
$156$		0			0
$157$	6.76380	−	1.30362i	0.539810	−	0.104040i	0.0879436	−	0.996125i	$-0.471970\pi$
$157$	6.76380	−	1.30362i	0.539810	−	0.104040i	0.451866	+	0.892086i	$0.350758\pi$
$158$		0			0
$159$	−1.75186	−	3.83604i	−0.138932	−	0.304218i
$160$		0			0
$161$	16.7039	−	10.7349i	1.31645	−	0.846031i
$162$		0			0
$163$	−3.51253	−	6.08388i	−0.275123	−	0.476527i	0.695043	−	0.718968i	$-0.255385\pi$
$163$	−3.51253	−	6.08388i	−0.275123	−	0.476527i	−0.970166	+	0.242441i	$0.922052\pi$
$164$		0			0
$165$	−1.29441	+	0.123601i	−0.100770	+	0.00962235i
$166$		0			0
$167$	6.71923	−	5.28406i	0.519950	−	0.408893i	−0.323397	−	0.946264i	$-0.604825\pi$
$167$	6.71923	−	5.28406i	0.519950	−	0.408893i	0.843346	+	0.537371i	$0.180582\pi$
$168$		0			0
$169$	35.9463	+	6.92809i	2.76510	+	0.532930i
$170$		0			0
$171$	−1.70899	+	2.96006i	−0.130690	+	0.226361i
$172$		0			0
$173$	14.2849	+	20.0603i	1.08606	+	1.52516i	0.829401	+	0.558653i	$0.188682\pi$
$173$	14.2849	+	20.0603i	1.08606	+	1.52516i	0.256657	+	0.966503i	$0.417379\pi$
$174$		0			0
$175$	13.1143	+	12.5044i	0.991347	+	0.945247i
$176$		0			0
$177$	−10.8093	+	3.17389i	−0.812475	+	0.238564i
$178$		0			0
$179$	−11.8448	+	13.6696i	−0.885321	+	1.02172i	0.114279	+	0.993449i	$0.463544\pi$
$179$	−11.8448	+	13.6696i	−0.885321	+	1.02172i	−0.999600	+	0.0282665i	$0.991001\pi$
$180$		0			0
$181$	−3.72342	+	10.7581i	−0.276759	+	0.799644i	0.717873	+	0.696174i	$0.245116\pi$
$181$	−3.72342	+	10.7581i	−0.276759	+	0.799644i	−0.994633	+	0.103470i	$0.967005\pi$
$182$		0			0
$183$	5.65445	−	5.39151i	0.417989	−	0.398552i
$184$		0			0
$185$	−2.18740	+	1.12768i	−0.160821	+	0.0829090i
$186$		0			0
$187$	12.0813	+	3.54739i	0.883473	+	0.259411i
$188$		0			0
$189$	2.12436	−	2.98325i	0.154525	−	0.216999i
$190$		0			0
$191$	7.76347	+	22.4311i	0.561745	+	1.62306i	0.765072	+	0.643945i	$0.222703\pi$
$191$	7.76347	+	22.4311i	0.561745	+	1.62306i	−0.203327	+	0.979111i	$0.565176\pi$
$192$		0			0
$193$	6.46555	−	14.1576i	0.465401	−	1.01909i	−0.520823	−	0.853665i	$-0.674375\pi$
$193$	6.46555	−	14.1576i	0.465401	−	1.01909i	0.986223	−	0.165420i	$-0.0528981\pi$
$194$		0			0
$195$	0.0766050	+	1.60814i	0.00548580	+	0.115161i
$196$		0			0
$197$	−1.93808	−	7.98889i	−0.138083	−	0.569185i	−0.998248	−	0.0591694i	$-0.981155\pi$
$197$	−1.93808	−	7.98889i	−0.138083	−	0.569185i	0.860165	−	0.510016i	$-0.170360\pi$
$198$		0			0
$199$	−13.5724	−	10.6734i	−0.962121	−	0.756620i	0.00781775	−	0.999969i	$-0.497512\pi$
$199$	−13.5724	−	10.6734i	−0.962121	−	0.756620i	−0.969939	+	0.243349i	$0.921754\pi$
$200$		0			0
$201$	2.27584	−	7.86260i	0.160525	−	0.554585i
$202$		0			0
$203$	11.7392	+	9.23184i	0.823933	+	0.647948i
$204$		0			0
$205$	−0.480806	−	1.98191i	−0.0335809	−	0.138422i
$206$		0			0
$207$	−0.257973	−	5.41552i	−0.0179304	−	0.376405i
$208$		0			0
$209$	8.07710	−	17.6864i	0.558704	−	1.22339i
$210$		0			0
$211$	5.76778	+	16.6649i	0.397071	+	1.14726i	0.949518	+	0.313712i	$0.101573\pi$
$211$	5.76778	+	16.6649i	0.397071	+	1.14726i	−0.552448	+	0.833548i	$0.686306\pi$
$212$		0			0
$213$	−0.127348	+	0.178835i	−0.00872572	+	0.0122536i
$214$		0			0
$215$	0.0720787	+	0.0211642i	0.00491573	+	0.00144339i
$216$		0			0
$217$	13.6979	−	7.06177i	0.929876	−	0.479384i
$218$		0			0
$219$	−6.08945	+	5.80628i	−0.411487	+	0.392352i
$220$		0			0
$221$	5.09897	−	14.7325i	0.342994	−	0.991015i
$222$		0			0
$223$	12.0872	−	13.9493i	0.809416	−	0.934116i	−0.189442	−	0.981892i	$-0.560668\pi$
$223$	12.0872	−	13.9493i	0.809416	−	0.934116i	0.998858	+	0.0477763i	$0.0152134\pi$
$224$		0			0
$225$	4.74733	−	1.39394i	0.316489	−	0.0929295i
$226$		0			0
$227$	−12.0572	−	11.4965i	−0.800266	−	0.763052i	0.174886	−	0.984589i	$-0.444044\pi$
$227$	−12.0572	−	11.4965i	−0.800266	−	0.763052i	−0.975152	+	0.221537i	$0.928893\pi$
$228$		0			0
$229$	−13.8206	−	19.4083i	−0.913291	−	1.28254i	−0.958948	−	0.283581i	$-0.908477\pi$
$229$	−13.8206	−	19.4083i	−0.913291	−	1.28254i	0.0456568	−	0.998957i	$-0.485462\pi$
$230$		0			0
$231$	−10.4167	+	18.0423i	−0.685370	+	1.18710i
$232$		0			0
$233$	−10.9347	−	2.10748i	−0.716353	−	0.138066i	−0.181965	−	0.983305i	$-0.558246\pi$
$233$	−10.9347	−	2.10748i	−0.716353	−	0.138066i	−0.534388	+	0.845239i	$0.679458\pi$
$234$		0			0
$235$	1.69345	−	1.33174i	0.110468	−	0.0868733i
$236$		0			0
$237$	−0.302904	+	0.0289238i	−0.0196757	+	0.00187880i
$238$		0			0
$239$	−1.39913	−	2.42337i	−0.0905025	−	0.156755i	0.817220	−	0.576326i	$-0.195514\pi$
$239$	−1.39913	−	2.42337i	−0.0905025	−	0.156755i	−0.907723	+	0.419571i	$0.862181\pi$
$240$		0			0
$241$	3.42546	−	2.20141i	0.220653	−	0.141805i	−0.425645	−	0.904890i	$-0.639953\pi$
$241$	3.42546	−	2.20141i	0.220653	−	0.141805i	0.646298	+	0.763085i	$0.276316\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−1.43933	+	0.277407i	−0.0919552	+	0.0177229i
$246$		0			0
$247$	−21.3977	−	11.0313i	−1.36150	−	0.701902i
$248$		0			0
$249$	−12.1083	−	4.84744i	−0.767334	−	0.307194i
$250$		0			0
$251$	2.88084	−	11.8750i	0.181837	−	0.749543i	−0.805722	−	0.592294i	$-0.798222\pi$
$251$	2.88084	−	11.8750i	0.181837	−	0.749543i	0.987559	−	0.157249i	$-0.0502625\pi$
$252$		0			0
$253$	4.38921	+	30.5276i	0.275947	+	1.91926i
$254$		0			0
$255$	0.503660	+	0.0480937i	0.0315404	+	0.00301175i
$256$		0			0
$257$	1.09210	−	22.9260i	0.0681233	−	1.43008i	−0.663399	−	0.748266i	$-0.730887\pi$
$257$	1.09210	−	22.9260i	0.0681233	−	1.43008i	0.731522	−	0.681817i	$-0.238810\pi$
$258$		0			0
$259$	−5.61145	+	39.0285i	−0.348679	+	2.42511i
$260$		0			0
$261$	3.78574	−	1.51558i	0.234331	−	0.0938121i
$262$		0			0
$263$	17.3623	+	11.1581i	1.07061	+	0.688036i	0.952369	−	0.304949i	$-0.0986394\pi$
$263$	17.3623	+	11.1581i	1.07061	+	0.688036i	0.118237	+	0.992985i	$0.462276\pi$
$264$		0			0
$265$	0.631257	+	0.728510i	0.0387778	+	0.0447520i
$266$		0			0
$267$	16.5248			1.01130
$268$		0			0
$269$	23.7344			1.44711			0.723555	−	0.690266i	$-0.242507\pi$
$269$	23.7344			1.44711			0.723555	+	0.690266i	$0.242507\pi$
$270$		0			0
$271$	−1.86909	−	2.15705i	−0.113539	−	0.131031i	0.696135	−	0.717911i	$-0.254902\pi$
$271$	−1.86909	−	2.15705i	−0.113539	−	0.131031i	−0.809674	+	0.586880i	$0.800356\pi$
$272$		0			0
$273$	21.7000	+	13.9458i	1.31334	+	0.844035i
$274$		0			0
$275$	−26.1295	+	10.4607i	−1.57567	+	0.630803i
$276$		0			0
$277$	2.46889	−	17.1715i	0.148342	−	1.03174i	−0.770593	−	0.637328i	$-0.780040\pi$
$277$	2.46889	−	17.1715i	0.148342	−	1.03174i	0.918934	−	0.394410i	$-0.129051\pi$
$278$		0			0
$279$	0.200225	−	4.20323i	0.0119871	−	0.251641i
$280$		0			0
$281$	−28.1409	−	2.68713i	−1.67875	−	0.160301i	−0.788270	−	0.615329i	$-0.789023\pi$
$281$	−28.1409	−	2.68713i	−1.67875	−	0.160301i	−0.890477	+	0.455028i	$0.849629\pi$
$282$		0			0
$283$	−1.10135	−	7.66009i	−0.0654687	−	0.455345i	−0.996016	−	0.0891736i	$-0.971577\pi$
$283$	−1.10135	−	7.66009i	−0.0654687	−	0.455345i	0.930547	−	0.366172i	$-0.119332\pi$
$284$		0			0
$285$	0.184195	−	0.759262i	0.0109108	−	0.0449748i
$286$		0			0
$287$	−30.3347	−	12.1442i	−1.79060	−	0.716848i
$288$		0			0
$289$	10.7555	+	5.54484i	0.632676	+	0.326167i
$290$		0			0
$291$	−11.5347	+	2.22313i	−0.676174	+	0.130322i
$292$		0			0
$293$	6.67704	+	14.6207i	0.390077	+	0.854149i	0.998181	+	0.0602914i	$0.0192030\pi$
$293$	6.67704	+	14.6207i	0.390077	+	0.854149i	−0.608104	+	0.793857i	$0.708070\pi$
$294$		0			0
$295$	2.16631	−	1.39221i	0.126128	−	0.0810573i
$296$		0			0
$297$	2.84429	+	4.92645i	0.165042	+	0.285862i
$298$		0			0
$299$	38.0134	−	3.62984i	2.19837	−	0.209919i
$300$		0			0
$301$	0.946095	−	0.744017i	0.0545320	−	0.0428845i
$302$		0			0
$303$	11.6833	+	2.25176i	0.671185	+	0.129360i
$304$		0			0
$305$	−0.892938	+	1.54661i	−0.0511295	+	0.0885589i
$306$		0			0
$307$	−1.84084	−	2.58510i	−0.105062	−	0.147539i	0.758698	−	0.651443i	$-0.225836\pi$
$307$	−1.84084	−	2.58510i	−0.105062	−	0.147539i	−0.863760	+	0.503904i	$0.831897\pi$
$308$		0			0
$309$	−9.43524	−	8.99649i	−0.536752	−	0.511792i
$310$		0			0
$311$	−5.21350	+	1.53082i	−0.295631	+	0.0868050i	−0.426185	−	0.904636i	$-0.640143\pi$
$311$	−5.21350	+	1.53082i	−0.295631	+	0.0868050i	0.130554	+	0.991441i	$0.458324\pi$
$312$		0			0
$313$	7.22066	−	8.33309i	0.408136	−	0.471014i	−0.514050	−	0.857760i	$-0.671856\pi$
$313$	7.22066	−	8.33309i	0.408136	−	0.471014i	0.922186	+	0.386746i	$0.126401\pi$
$314$		0			0
$315$	−0.273801	+	0.791097i	−0.0154270	+	0.0445733i
$316$		0			0
$317$	−15.8346	+	15.0982i	−0.889359	+	0.848002i	−0.989135	−	0.147008i	$-0.953036\pi$
$317$	−15.8346	+	15.0982i	−0.889359	+	0.848002i	0.0997768	+	0.995010i	$0.468187\pi$
$318$		0			0
$319$	−20.6184	+	10.6295i	−1.15441	+	0.595140i
$320$		0			0
$321$	1.49422	+	0.438744i	0.0833995	+	0.0244883i
$322$		0			0
$323$	−4.38843	+	6.16269i	−0.244179	+	0.342901i
$324$		0			0
$325$	11.3978	+	32.9318i	0.632236	+	1.82673i
$326$		0			0
$327$	1.31313	−	2.87536i	0.0726163	−	0.159008i
$328$		0			0
$329$	−1.64240	−	34.4783i	−0.0905486	−	1.90085i
$330$		0			0
$331$	−2.93978	−	12.1179i	−0.161585	−	0.666062i	−0.993759	−	0.111548i	$-0.964419\pi$
$331$	−2.93978	−	12.1179i	−0.161585	−	0.666062i	0.832174	−	0.554515i	$-0.187096\pi$
$332$		0			0
$333$	8.46290	+	6.65530i	0.463764	+	0.364708i
$334$		0			0
$335$	0.00720021	+	1.87100i	0.000393390	+	0.102224i
$336$		0			0
$337$	−25.7858	−	20.2782i	−1.40464	−	1.10462i	−0.979941	−	0.199289i	$-0.936137\pi$
$337$	−25.7858	−	20.2782i	−1.40464	−	1.10462i	−0.424702	−	0.905333i	$-0.639621\pi$
$338$		0			0
$339$	−1.02230	−	4.21396i	−0.0555235	−	0.228871i
$340$		0			0
$341$	1.13899	+	23.9104i	0.0616799	+	1.29482i
$342$		0			0
$343$	0.893543	−	1.95659i	0.0482468	−	0.105646i
$344$		0			0
$345$	0.405332	+	1.17113i	0.0218223	+	0.0630515i
$346$		0			0
$347$	16.8965	−	23.7278i	0.907050	−	1.27377i	−0.0543233	−	0.998523i	$-0.517300\pi$
$347$	16.8965	−	23.7278i	0.907050	−	1.27377i	0.961373	−	0.275249i	$-0.0887604\pi$
$348$		0			0
$349$	−23.7187	−	6.96445i	−1.26964	−	0.372798i	−0.423563	−	0.905867i	$-0.639221\pi$
$349$	−23.7187	−	6.96445i	−1.26964	−	0.372798i	−0.846072	+	0.533068i	$0.821039\pi$
$350$		0			0
$351$	6.26032	−	3.22742i	0.334151	−	0.172267i
$352$		0			0
$353$	−14.7119	+	14.0278i	−0.783037	+	0.746624i	−0.971904	−	0.235378i	$-0.924367\pi$
$353$	−14.7119	+	14.0278i	−0.783037	+	0.746624i	0.188867	+	0.982003i	$0.439519\pi$
$354$		0			0
$355$	0.0164134	−	0.0474234i	0.000871133	−	0.00251697i
$356$		0			0
$357$	5.30855	−	6.12639i	0.280958	−	0.324243i
$358$		0			0
$359$	9.95788	−	2.92390i	0.525557	−	0.154317i	−0.00818237	−	0.999967i	$-0.502605\pi$
$359$	9.95788	−	2.92390i	0.525557	−	0.154317i	0.533739	+	0.845649i	$0.320786\pi$
$360$		0			0
$361$	−5.29586	−	5.04959i	−0.278729	−	0.265768i
$362$		0			0
$363$	−12.3900	−	17.3993i	−0.650304	−	0.913224i
$364$		0			0
$365$	0.961632	−	1.66560i	0.0503341	−	0.0871813i
$366$		0			0
$367$	−3.80279	−	0.732928i	−0.198504	−	0.0382585i	0.0890299	−	0.996029i	$-0.471623\pi$
$367$	−3.80279	−	0.732928i	−0.198504	−	0.0382585i	−0.287534	+	0.957770i	$0.592835\pi$
$368$		0			0
$369$	−7.01315	+	5.51521i	−0.365090	+	0.287110i
$370$		0			0
$371$	15.3746	−	1.46810i	0.798210	−	0.0762198i
$372$		0			0
$373$	−2.17804	−	3.77248i	−0.112775	−	0.195332i	0.804113	−	0.594476i	$-0.202641\pi$
$373$	−2.17804	−	3.77248i	−0.112775	−	0.195332i	−0.916888	+	0.399144i	$0.869307\pi$
$374$		0			0
$375$	−1.91290	+	1.22934i	−0.0987816	+	0.0634831i
$376$		0			0
$377$	11.9313	+	26.1259i	0.614494	+	1.34555i
$378$		0			0
$379$	−9.54134	+	1.83894i	−0.490106	+	0.0944601i	−0.428316	−	0.903629i	$-0.640893\pi$
$379$	−9.54134	+	1.83894i	−0.490106	+	0.0944601i	−0.0617898	+	0.998089i	$0.519681\pi$
$380$		0			0
$381$	5.73467	+	2.95643i	0.293796	+	0.151462i
$382$		0			0
$383$	−21.6934	−	8.68471i	−1.10848	−	0.443768i	−0.256077	−	0.966656i	$-0.582430\pi$
$383$	−21.6934	−	8.68471i	−1.10848	−	0.443768i	−0.852401	+	0.522888i	$0.824854\pi$
$384$		0			0
$385$	1.12271	−	4.62789i	0.0572188	−	0.235859i
$386$		0			0
$387$	−0.0467709	−	0.325298i	−0.00237750	−	0.0165358i
$388$		0			0
$389$	4.49564	+	0.429282i	0.227938	+	0.0217655i	0.208400	−	0.978044i	$-0.433174\pi$
$389$	4.49564	+	0.429282i	0.227938	+	0.0217655i	0.0195381	+	0.999809i	$0.493780\pi$
$390$		0			0
$391$	0.571010	−	11.9870i	0.0288772	−	0.606207i
$392$		0			0
$393$	−0.831872	+	5.78580i	−0.0419624	+	0.291855i
$394$		0			0
$395$	0.0645707	−	0.0258502i	0.00324890	−	0.00130067i
$396$		0			0
$397$	−17.5893	−	11.3040i	−0.882782	−	0.567329i	0.0188555	−	0.999822i	$-0.493998\pi$
$397$	−17.5893	−	11.3040i	−0.882782	−	0.567329i	−0.901637	+	0.432493i	$0.857634\pi$
$398$		0			0
$399$	−8.19740	−	9.46031i	−0.410383	−	0.473608i
$400$		0			0
$401$	−24.4977			−1.22336			−0.611680	−	0.791106i	$-0.709506\pi$
$401$	−24.4977			−1.22336			−0.611680	+	0.791106i	$0.709506\pi$
$402$		0			0
$403$	29.6381			1.47638
$404$		0			0
$405$	0.149689	+	0.172750i	0.00743809	+	0.00858401i
$406$		0			0
$407$	−51.5226	−	33.1116i	−2.55388	−	1.64128i
$408$		0			0
$409$	−21.1623	+	8.47213i	−1.04641	+	0.418920i	−0.830223	−	0.557432i	$-0.811787\pi$
$409$	−21.1623	+	8.47213i	−1.04641	+	0.418920i	−0.216188	+	0.976352i	$0.569362\pi$
$410$		0			0
$411$	0.248459	−	1.72807i	0.0122556	−	0.0852393i
$412$		0			0
$413$	1.96315	−	41.2117i	0.0966005	−	2.02789i
$414$		0			0
$415$	2.96779	+	0.283390i	0.145683	+	0.0139110i
$416$		0			0
$417$	0.0668862	+	0.465204i	0.00327543	+	0.0227811i
$418$		0			0
$419$	0.737170	−	3.03866i	0.0360131	−	0.148448i	−0.950966	−	0.309294i	$-0.899907\pi$
$419$	0.737170	−	3.03866i	0.0360131	−	0.148448i	0.986979	+	0.160846i	$0.0514223\pi$
$420$		0			0
$421$	−13.4190	−	5.37215i	−0.654001	−	0.261822i	0.0208434	−	0.999783i	$-0.493365\pi$
$421$	−13.4190	−	5.37215i	−0.654001	−	0.261822i	−0.674844	+	0.737960i	$0.735789\pi$
$422$		0			0
$423$	−8.37725	−	4.31877i	−0.407316	−	0.209986i
$424$		0			0
$425$	10.7537	−	2.07260i	0.521629	−	0.100536i
$426$		0			0
$427$	11.8864	+	26.0277i	0.575225	+	1.25957i
$428$		0			0
$429$	−33.7059	+	21.6615i	−1.62734	+	1.04582i
$430$		0			0
$431$	0.380773	+	0.659518i	0.0183412	+	0.0317679i	0.875050	−	0.484032i	$-0.160828\pi$
$431$	0.380773	+	0.659518i	0.0183412	+	0.0317679i	−0.856709	+	0.515800i	$0.827495\pi$
$432$		0			0
$433$	−15.8036	+	1.50906i	−0.759472	+	0.0725208i	−0.467604	−	0.883938i	$-0.654883\pi$
$433$	−15.8036	+	1.50906i	−0.759472	+	0.0725208i	−0.291868	+	0.956459i	$0.594277\pi$
$434$		0			0
$435$	−0.732693	+	0.576197i	−0.0351300	+	0.0276265i
$436$		0			0
$437$	−18.1963	−	3.50704i	−0.870445	−	0.167765i
$438$		0			0
$439$	−17.3067	+	29.9760i	−0.826002	+	1.43068i	0.0751496	+	0.997172i	$0.476057\pi$
$439$	−17.3067	+	29.9760i	−0.826002	+	1.43068i	−0.901151	+	0.433505i	$0.857277\pi$
$440$		0			0
$441$	3.71972	+	5.22361i	0.177129	+	0.248744i
$442$		0			0
$443$	5.91125	+	5.63636i	0.280852	+	0.267792i	0.817390	−	0.576084i	$-0.195420\pi$
$443$	5.91125	+	5.63636i	0.280852	+	0.267792i	−0.536539	+	0.843876i	$0.680268\pi$
$444$		0			0
$445$	−3.62425	+	1.06418i	−0.171806	+	0.0504468i
$446$		0			0
$447$	−2.74505	+	3.16796i	−0.129836	+	0.149839i
$448$		0			0
$449$	2.57737	−	7.44683i	0.121634	−	0.351438i	−0.867703	−	0.497083i	$-0.834405\pi$
$449$	2.57737	−	7.44683i	0.121634	−	0.351438i	0.989337	+	0.145645i	$0.0465258\pi$
$450$		0			0
$451$	36.7320	−	35.0238i	1.72964	−	1.64921i
$452$		0			0
$453$	−7.37379	+	3.80145i	−0.346451	+	0.178608i
$454$		0			0
$455$	−5.65737	−	1.66115i	−0.265222	−	0.0778761i
$456$		0			0
$457$	5.15137	−	7.23408i	0.240971	−	0.338396i	−0.676325	−	0.736604i	$-0.736428\pi$
$457$	5.15137	−	7.23408i	0.240971	−	0.338396i	0.917295	+	0.398208i	$0.130368\pi$
$458$		0			0
$459$	−0.723947	−	2.09171i	−0.0337910	−	0.0976326i
$460$		0			0
$461$	−6.47087	+	14.1692i	−0.301379	+	0.659927i	−0.998365	−	0.0571572i	$-0.981796\pi$
$461$	−6.47087	+	14.1692i	−0.301379	+	0.659927i	0.696987	+	0.717084i	$0.254524\pi$
$462$		0			0
$463$	0.264913	+	5.56121i	0.0123116	+	0.258451i	0.996629	+	0.0820436i	$0.0261447\pi$
$463$	0.264913	+	5.56121i	0.0123116	+	0.258451i	−0.984317	+	0.176408i	$0.943552\pi$
$464$		0			0
$465$	0.226769	+	0.934755i	0.0105162	+	0.0433482i
$466$		0			0
$467$	−27.4547	−	21.5906i	−1.27045	−	0.999094i	−0.999332	−	0.0365483i	$-0.988364\pi$
$467$	−27.4547	−	21.5906i	−1.27045	−	0.999094i	−0.271119	−	0.962546i	$-0.587394\pi$
$468$		0			0
$469$	24.4857	+	17.2945i	1.13064	+	0.798588i
$470$		0			0
$471$	5.41456	+	4.25805i	0.249490	+	0.196201i
$472$		0			0
$473$	0.440755	+	1.81682i	0.0202659	+	0.0835372i
$474$		0			0
$475$	−0.804673	−	16.8922i	−0.0369209	−	0.775065i
$476$		0			0
$477$	1.75186	−	3.83604i	0.0802122	−	0.175640i
$478$		0			0
$479$	−7.98142	−	23.0608i	−0.364680	−	1.05367i	−0.966858	−	0.255313i	$-0.917821\pi$
$479$	−7.98142	−	23.0608i	−0.364680	−	1.05367i	0.602178	−	0.798362i	$-0.294300\pi$
$480$		0			0
$481$	−43.9859	+	61.7695i	−2.00558	+	2.81645i
$482$		0			0
$483$	19.0516	+	5.59406i	0.866879	+	0.254539i
$484$		0			0
$485$	2.38664	−	1.23040i	0.108372	−	0.0558695i
$486$		0			0
$487$	18.9213	−	18.0414i	0.857404	−	0.817533i	−0.127283	−	0.991866i	$-0.540626\pi$
$487$	18.9213	−	18.0414i	0.857404	−	0.817533i	0.984687	+	0.174333i	$0.0557770\pi$
$488$		0			0
$489$	2.29767	−	6.63869i	0.103904	−	0.300212i
$490$		0			0
$491$	0.739602	−	0.853546i	0.0333778	−	0.0385200i	−0.738815	−	0.673908i	$-0.764614\pi$
$491$	0.739602	−	0.853546i	0.0333778	−	0.0385200i	0.772193	+	0.635388i	$0.219160\pi$
$492$		0			0
$493$	8.66046	−	2.54294i	0.390048	−	0.114528i
$494$		0			0
$495$	−0.941071	−	0.897309i	−0.0422980	−	0.0403311i
$496$		0			0
$497$	−0.466390	−	0.654953i	−0.0209204	−	0.0293786i
$498$		0			0
$499$	2.73128	−	4.73072i	0.122269	−	0.211776i	−0.798393	−	0.602137i	$-0.794316\pi$
$499$	2.73128	−	4.73072i	0.122269	−	0.211776i	0.920662	+	0.390360i	$0.127650\pi$
$500$		0			0
$501$	8.39359	+	1.61773i	0.374998	+	0.0722749i
$502$		0			0
$503$	1.73112	−	1.36137i	0.0771869	−	0.0607005i	−0.578820	−	0.815455i	$-0.696487\pi$
$503$	1.73112	−	1.36137i	0.0771869	−	0.0607005i	0.656007	+	0.754755i	$0.272244\pi$
$504$		0			0
$505$	−2.70740	+	0.258526i	−0.120478	+	0.0115042i
$506$		0			0
$507$	18.3039	+	31.7033i	0.812906	+	1.40800i
$508$		0			0
$509$	17.6650	−	11.3526i	0.782988	−	0.503196i	−0.0870359	−	0.996205i	$-0.527739\pi$
$509$	17.6650	−	11.3526i	0.782988	−	0.503196i	0.870024	+	0.493009i	$0.164103\pi$
$510$		0			0
$511$	−12.8009	−	28.0300i	−0.566276	−	1.23997i
$512$		0			0
$513$	−3.35621	+	0.646857i	−0.148180	+	0.0285594i
$514$		0			0
$515$	2.64872	+	1.36551i	0.116716	+	0.0601715i
$516$		0			0
$517$	49.7741	+	19.9266i	2.18906	+	0.876369i
$518$		0			0
$519$	−5.80596	+	23.9325i	−0.254853	+	1.05052i
$520$		0			0
$521$	−5.76208	−	40.0761i	−0.252441	−	1.75577i	−0.583458	−	0.812143i	$-0.698301\pi$
$521$	−5.76208	−	40.0761i	−0.252441	−	1.75577i	0.331017	−	0.943625i	$-0.392608\pi$
$522$		0			0
$523$	−5.01652	−	0.479019i	−0.219357	−	0.0209461i	−0.0152012	−	0.999884i	$-0.504839\pi$
$523$	−5.01652	−	0.479019i	−0.219357	−	0.0209461i	−0.204156	+	0.978938i	$0.565445\pi$
$524$		0			0
$525$	−0.862199	+	18.0998i	−0.0376294	+	0.789939i
$526$		0			0
$527$	1.32555	−	9.21937i	0.0577417	−	0.401602i
$528$		0			0
$529$	5.93640	−	2.37658i	0.258104	−	0.103329i
$530$		0			0
$531$	−9.47723	−	6.09065i	−0.411277	−	0.264312i
$532$		0			0
$533$	−41.1515	−	47.4914i	−1.78247	−	2.05708i
$534$		0			0
$535$	−0.355970			−0.0153899
$536$		0			0
$537$	−18.0875			−0.780533
$538$		0			0
$539$	−23.8887	−	27.5690i	−1.02896	−	1.18748i
$540$		0			0
$541$	1.60667	+	1.03254i	0.0690760	+	0.0443925i	0.574723	−	0.818348i	$-0.305110\pi$
$541$	1.60667	+	1.03254i	0.0690760	+	0.0443925i	−0.505647	+	0.862740i	$0.668746\pi$
$542$		0			0
$543$	−10.5688	+	4.23109i	−0.453549	+	0.181573i
$544$		0			0
$545$	−0.102829	+	0.715192i	−0.00440471	+	0.0306355i
$546$		0			0
$547$	−1.06223	+	22.2990i	−0.0454178	+	0.953436i	0.855059	+	0.518531i	$0.173521\pi$
$547$	−1.06223	+	22.2990i	−0.0454178	+	0.953436i	−0.900476	+	0.434905i	$0.856782\pi$
$548$		0			0
$549$	7.77751	+	0.742662i	0.331936	+	0.0316960i
$550$		0			0
$551$	−1.98358	−	13.7961i	−0.0845034	−	0.587734i
$552$		0			0
$553$	0.262725	−	1.08297i	0.0111722	−	0.0460524i
$554$		0			0
$555$	−2.28469	−	0.914652i	−0.0969797	−	0.0388248i
$556$		0			0
$557$	27.8732	+	14.3696i	1.18103	+	0.608861i	0.932994	−	0.359891i	$-0.117186\pi$
$557$	27.8732	+	14.3696i	1.18103	+	0.608861i	0.248031	+	0.968752i	$0.420217\pi$
$558$		0			0
$559$	2.27290	−	0.438066i	0.0961334	−	0.0185282i
$560$		0			0
$561$	5.23064	+	11.4535i	0.220838	+	0.483567i
$562$		0			0
$563$	34.5485	−	22.2030i	1.45604	−	0.935743i	0.457119	−	0.889406i	$-0.348881\pi$
$563$	34.5485	−	22.2030i	1.45604	−	0.935743i	0.998926	−	0.0463377i	$-0.0147550\pi$
$564$		0			0
$565$	0.495585	+	0.858379i	0.0208494	+	0.0361123i
$566$		0			0
$567$	3.64575	−	0.348127i	0.153107	−	0.0146200i
$568$		0			0
$569$	7.05286	−	5.54643i	0.295671	−	0.232518i	−0.459292	−	0.888285i	$-0.651897\pi$
$569$	7.05286	−	5.54643i	0.295671	−	0.232518i	0.754964	+	0.655767i	$0.227655\pi$
$570$		0			0
$571$	26.7533	+	5.15628i	1.11959	+	0.215784i	0.715280	−	0.698838i	$-0.246299\pi$
$571$	26.7533	+	5.15628i	1.11959	+	0.215784i	0.404311	+	0.914621i	$0.367511\pi$
$572$		0			0
$573$	−11.8683	+	20.5565i	−0.495805	+	0.858759i
$574$		0			0
$575$	15.5601	+	21.8510i	0.648899	+	0.911251i
$576$		0			0
$577$	−12.8764	−	12.2776i	−0.536051	−	0.511123i	0.372987	−	0.927836i	$-0.378333\pi$
$577$	−12.8764	−	12.2776i	−0.536051	−	0.511123i	−0.909038	+	0.416713i	$0.863182\pi$
$578$		0			0
$579$	14.9336	−	4.38491i	0.620620	−	0.182231i
$580$		0			0
$581$	31.2803	−	36.0994i	1.29773	−	1.49766i
$582$		0			0
$583$	−7.84619	+	22.6701i	−0.324956	+	0.938899i
$584$		0			0
$585$	−1.16518	+	1.11100i	−0.0481744	+	0.0459342i
$586$		0			0
$587$	0.313976	−	0.161866i	0.0129592	−	0.00668093i	−0.451735	−	0.892152i	$-0.649195\pi$
$587$	0.313976	−	0.161866i	0.0129592	−	0.00668093i	0.464694	+	0.885471i	$0.346164\pi$
$588$		0			0
$589$	−13.8003	−	4.05212i	−0.568629	−	0.166965i
$590$		0			0
$591$	4.76843	−	6.69632i	0.196147	−	0.275450i
$592$		0			0
$593$	10.7471	+	31.0517i	0.441331	+	1.27514i	0.918182	+	0.396158i	$0.129657\pi$
$593$	10.7471	+	31.0517i	0.441331	+	1.27514i	−0.476851	+	0.878984i	$0.658222\pi$
$594$		0			0
$595$	−0.769748	+	1.68551i	−0.0315566	+	0.0690993i
$596$		0			0
$597$	−0.821573	−	17.2469i	−0.0336248	−	0.705870i
$598$		0			0
$599$	−4.80614	−	19.8112i	−0.196374	−	0.809464i	−0.981708	−	0.190392i	$-0.939024\pi$
$599$	−4.80614	−	19.8112i	−0.196374	−	0.809464i	0.785334	−	0.619072i	$-0.212491\pi$
$600$		0			0
$601$	−13.4079	−	10.5441i	−0.546919	−	0.430102i	0.306086	−	0.952004i	$-0.400980\pi$
$601$	−13.4079	−	10.5441i	−0.546919	−	0.430102i	−0.853006	+	0.521902i	$0.825223\pi$
$602$		0			0
$603$	7.43252	−	3.42895i	0.302676	−	0.139637i
$604$		0			0
$605$	3.83787	+	3.01814i	0.156032	+	0.122705i
$606$		0			0
$607$	9.42281	+	38.8414i	0.382460	+	1.57652i	0.759615	+	0.650373i	$0.225387\pi$
$607$	9.42281	+	38.8414i	0.382460	+	1.57652i	−0.377155	+	0.926150i	$0.623098\pi$
$608$		0			0
$609$	0.710608	+	14.9175i	0.0287953	+	0.604488i
$610$		0			0
$611$	27.5764	−	60.3839i	1.11562	−	2.44287i
$612$		0			0
$613$	8.47496	+	24.4868i	0.342301	+	0.989012i	0.976439	+	0.215793i	$0.0692336\pi$
$613$	8.47496	+	24.4868i	0.342301	+	0.989012i	−0.634139	+	0.773219i	$0.718645\pi$
$614$		0			0
$615$	1.18297	−	1.66124i	0.0477018	−	0.0669878i
$616$		0			0
$617$	23.4726	+	6.89218i	0.944972	+	0.277469i	0.717692	−	0.696361i	$-0.245199\pi$
$617$	23.4726	+	6.89218i	0.944972	+	0.277469i	0.227280	+	0.973829i	$0.427017\pi$
$618$		0			0
$619$	−16.0169	+	8.25728i	−0.643773	+	0.331888i	−0.749010	−	0.662559i	$-0.769470\pi$
$619$	−16.0169	+	8.25728i	−0.643773	+	0.331888i	0.105237	+	0.994447i	$0.466440\pi$
$620$		0			0
$621$	3.92384	−	3.74138i	0.157458	−	0.150136i
$622$		0			0
$623$	−19.7939	+	57.1908i	−0.793027	+	2.29130i
$624$		0			0
$625$	−15.8601	+	18.3035i	−0.634403	+	0.732140i
$626$		0			0
$627$	18.6558	−	5.47785i	0.745043	−	0.218764i
$628$		0			0
$629$	17.2471	+	16.4450i	0.687685	+	0.655707i
$630$		0			0
$631$	−16.0708	−	22.5683i	−0.639768	−	0.898429i	0.359631	−	0.933095i	$-0.382903\pi$
$631$	−16.0708	−	22.5683i	−0.639768	−	0.898429i	−0.999399	+	0.0346661i	$0.988963\pi$
$632$		0			0
$633$	−8.81741	+	15.2722i	−0.350460	+	0.607015i
$634$		0			0
$635$	−1.44813	−	0.279104i	−0.0574672	−	0.0110759i
$636$		0			0
$637$	−35.5031	+	27.9200i	−1.40669	+	1.10623i
$638$		0			0
$639$	−0.218549	+	0.0208689i	−0.00864568	+	0.000825562i
$640$		0			0
$641$	15.0278	+	26.0290i	0.593563	+	1.02808i	0.993748	+	0.111647i	$0.0356127\pi$
$641$	15.0278	+	26.0290i	0.593563	+	1.02808i	−0.400185	+	0.916435i	$0.631054\pi$
$642$		0			0
$643$	−18.7388	+	12.0427i	−0.738988	+	0.474919i	−0.855195	−	0.518306i	$-0.826563\pi$
$643$	−18.7388	+	12.0427i	−0.738988	+	0.474919i	0.116207	+	0.993225i	$0.462926\pi$
$644$		0			0
$645$	0.0312067	+	0.0683331i	0.00122876	+	0.00269061i
$646$		0			0
$647$	−29.1811	+	5.62419i	−1.14723	+	0.221110i	−0.727216	−	0.686409i	$-0.759186\pi$
$647$	−29.1811	+	5.62419i	−1.14723	+	0.221110i	−0.420011	+	0.907519i	$0.637974\pi$
$648$		0			0
$649$	56.9612	+	29.3656i	2.23592	+	1.15270i
$650$		0			0
$651$	14.3072	+	5.72772i	0.560742	+	0.224487i
$652$		0			0
$653$	0.444747	−	1.83327i	0.0174043	−	0.0717415i	−0.962447	−	0.271469i	$-0.912491\pi$
$653$	0.444747	−	1.83327i	0.0174043	−	0.0717415i	0.979851	+	0.199728i	$0.0640057\pi$
$654$		0			0
$655$	−0.190150	−	1.32252i	−0.00742978	−	0.0516752i
$656$		0			0
$657$	−8.37583	−	0.799795i	−0.326772	−	0.0312030i
$658$		0			0
$659$	−1.95056	+	40.9473i	−0.0759830	+	1.59508i	0.563396	+	0.826187i	$0.309495\pi$
$659$	−1.95056	+	40.9473i	−0.0759830	+	1.59508i	−0.639379	+	0.768892i	$0.720808\pi$
$660$		0			0
$661$	6.06496	−	42.1827i	0.235899	−	1.64072i	−0.435908	−	0.899991i	$-0.643573\pi$
$661$	6.06496	−	42.1827i	0.235899	−	1.64072i	0.671808	−	0.740725i	$-0.265518\pi$
$662$		0			0
$663$	14.4732	−	5.79419i	0.562092	−	0.225028i
$664$		0			0
$665$	2.40710	+	1.54695i	0.0933433	+	0.0599881i
$666$		0			0
$667$	14.4781	+	16.7086i	0.560595	+	0.646961i
$668$		0			0
$669$	18.4576			0.713612
$670$		0			0
$671$	−44.4442			−1.71575
$672$		0			0
$673$	11.4697	+	13.2367i	0.442125	+	0.510239i	0.932449	−	0.361301i	$-0.117667\pi$
$673$	11.4697	+	13.2367i	0.442125	+	0.510239i	−0.490325	+	0.871540i	$0.663122\pi$
$674$		0			0
$675$	4.16231	+	2.67496i	0.160207	+	0.102959i
$676$		0			0
$677$	21.4876	−	8.60235i	0.825837	−	0.330615i	0.0800424	−	0.996791i	$-0.474494\pi$
$677$	21.4876	−	8.60235i	0.825837	−	0.330615i	0.745794	+	0.666176i	$0.232070\pi$
$678$		0			0
$679$	6.12256	−	42.5834i	0.234962	−	1.63420i
$680$		0			0
$681$	0.792702	−	16.6409i	0.0303764	−	0.637680i
$682$		0			0
$683$	−16.1770	−	1.54472i	−0.618996	−	0.0591069i	−0.219153	−	0.975691i	$-0.570329\pi$
$683$	−16.1770	−	1.54472i	−0.618996	−	0.0591069i	−0.399843	+	0.916584i	$0.630935\pi$
$684$		0			0
$685$	0.0567929	+	0.395003i	0.00216995	+	0.0150923i
$686$		0			0
$687$	5.61726	−	23.1547i	0.214312	−	0.883406i
$688$		0			0
$689$	27.5748	+	11.0393i	1.05052	+	0.420564i
$690$		0			0
$691$	−7.35152	−	3.78997i	−0.279665	−	0.144177i	0.312688	−	0.949856i	$-0.398771\pi$
$691$	−7.35152	−	3.78997i	−0.279665	−	0.144177i	−0.592353	+	0.805679i	$0.701801\pi$
$692$		0			0
$693$	−20.4570	+	3.94276i	−0.777096	+	0.149773i
$694$		0			0
$695$	−0.0446281	−	0.0977219i	−0.00169284	−	0.00370680i
$696$		0			0
$697$	−16.6134	+	10.6768i	−0.629276	+	0.404411i
$698$		0			0
$699$	−5.56795	−	9.64397i	−0.210599	−	0.364768i
$700$		0			0
$701$	25.1333	−	2.39994i	0.949271	−	0.0906444i	0.391080	−	0.920357i	$-0.372102\pi$
$701$	25.1333	−	2.39994i	0.949271	−	0.0906444i	0.558191	+	0.829712i	$0.311496\pi$
$702$		0			0
$703$	28.9260	−	22.7477i	1.09097	−	0.857945i
$704$		0			0
$705$	2.11544	+	0.407717i	0.0796719	+	0.0153555i
$706$		0			0
$707$	−21.7877	+	37.7374i	−0.819411	+	1.41926i
$708$		0			0
$709$	−2.11022	−	2.96339i	−0.0792509	−	0.111292i	0.773048	−	0.634348i	$-0.218731\pi$
$709$	−2.11022	−	2.96339i	−0.0792509	−	0.111292i	−0.852299	+	0.523056i	$0.824792\pi$
$710$		0			0
$711$	−0.220219	−	0.209978i	−0.00825885	−	0.00787480i
$712$		0			0
$713$	21.8902	−	6.42755i	0.819795	−	0.240714i
$714$		0			0
$715$	5.99746	−	6.92144i	0.224292	−	0.258847i
$716$		0			0
$717$	0.915224	−	2.64437i	0.0341797	−	0.0987557i
$718$		0			0
$719$	−19.7626	+	18.8436i	−0.737019	+	0.702747i	−0.962434	−	0.271516i	$-0.912475\pi$
$719$	−19.7626	+	18.8436i	−0.737019	+	0.702747i	0.225414	+	0.974263i	$0.427626\pi$
$720$		0			0
$721$	42.4378	−	21.8782i	1.58047	−	0.814788i
$722$		0			0
$723$	3.90692	+	1.14717i	0.145300	+	0.0426639i
$724$		0			0
$725$	−11.7033	+	16.4350i	−0.434650	+	0.610381i
$726$		0			0
$727$	−14.5109	−	41.9264i	−0.538179	−	1.55496i	−0.806256	−	0.591567i	$-0.798509\pi$
$727$	−14.5109	−	41.9264i	−0.538179	−	1.55496i	0.268077	−	0.963398i	$-0.413612\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−0.0346127	−	0.726611i	−0.00128020	−	0.0268747i
$732$		0			0
$733$	−2.33023	−	9.60532i	−0.0860689	−	0.354781i	0.912450	−	0.409188i	$-0.134188\pi$
$733$	−2.33023	−	9.60532i	−0.0860689	−	0.354781i	−0.998519	+	0.0544076i	$0.982673\pi$
$734$		0			0
$735$	−1.15221	−	0.906107i	−0.0424999	−	0.0334223i
$736$		0			0
$737$	−40.2348	+	23.4365i	−1.48207	+	0.863295i
$738$		0			0
$739$	−6.62363	−	5.20888i	−0.243654	−	0.191612i	0.488862	−	0.872361i	$-0.337412\pi$
$739$	−6.62363	−	5.20888i	−0.243654	−	0.191612i	−0.732517	+	0.680749i	$0.761654\pi$
$740$		0			0
$741$	−5.67562	−	23.3952i	−0.208499	−	0.859444i
$742$		0			0
$743$	−1.12796	−	23.6787i	−0.0413807	−	0.868688i	−0.920180	−	0.391496i	$-0.871958\pi$
$743$	−1.12796	−	23.6787i	−0.0413807	−	0.868688i	0.878799	−	0.477192i	$-0.158345\pi$
$744$		0			0
$745$	0.398037	−	0.871579i	0.0145829	−	0.0319322i
$746$		0			0
$747$	−4.26582	−	12.3253i	−0.156078	−	0.450958i
$748$		0			0
$749$	−3.30828	+	4.64583i	−0.120882	+	0.169755i
$750$		0			0
$751$	−7.00887	−	2.05799i	−0.255757	−	0.0750971i	0.151341	−	0.988482i	$-0.451641\pi$
$751$	−7.00887	−	2.05799i	−0.255757	−	0.0750971i	−0.407098	+	0.913385i	$0.633459\pi$
$752$		0			0
$753$	10.8611	−	5.59927i	0.395800	−	0.204049i
$754$		0			0
$755$	1.37242	−	1.30860i	0.0499476	−	0.0476249i
$756$		0			0
$757$	0.805633	−	2.32772i	0.0292812	−	0.0846026i	−0.929413	−	0.369041i	$-0.879686\pi$
$757$	0.805633	−	2.32772i	0.0292812	−	0.0846026i	0.958694	+	0.284439i	$0.0918073\pi$
$758$		0			0
$759$	−20.1969	+	23.3085i	−0.733102	+	0.846044i
$760$		0			0
$761$	−31.9093	+	9.36941i	−1.15671	+	0.339641i	−0.803153	−	0.595772i	$-0.796846\pi$
$761$	−31.9093	+	9.36941i	−1.15671	+	0.339641i	−0.353557	+	0.935413i	$0.615028\pi$
$762$		0			0
$763$	8.37843	+	7.98882i	0.303320	+	0.289215i
$764$		0			0
$765$	0.293481	+	0.412136i	0.0106108	+	0.0149008i
$766$		0			0
$767$	39.6734	−	68.7164i	1.43252	−	2.48121i
$768$		0			0
$769$	−23.7915	−	4.58544i	−0.857944	−	0.165355i	−0.258735	−	0.965948i	$-0.583306\pi$
$769$	−23.7915	−	4.58544i	−0.857944	−	0.165355i	−0.599208	+	0.800593i	$0.704518\pi$
$770$		0			0
$771$	18.0415	−	14.1880i	0.649748	−	0.510967i
$772$		0			0
$773$	1.15417	−	0.110210i	0.0415126	−	0.00396398i	−0.0742791	−	0.997237i	$-0.523666\pi$
$773$	1.15417	−	0.110210i	0.0415126	−	0.00396398i	0.115792	+	0.993274i	$0.463059\pi$
$774$		0			0
$775$	10.4101	+	18.0308i	0.373941	+	0.647684i
$776$		0			0
$777$	−33.1705	+	21.3174i	−1.18999	+	0.764757i
$778$		0			0
$779$	12.6682	+	27.7394i	0.453884	+	0.993867i
$780$		0			0
$781$	1.22632	−	0.236354i	0.0438812	−	0.00845741i
$782$		0			0
$783$	3.62453	+	1.86858i	0.129530	+	0.0667775i
$784$		0			0
$785$	−1.46174	−	0.585194i	−0.0521718	−	0.0208865i
$786$		0			0
$787$	1.96522	−	8.10076i	0.0700526	−	0.288761i	−0.926000	−	0.377523i	$-0.876776\pi$
$787$	1.96522	−	8.10076i	0.0700526	−	0.288761i	0.996053	+	0.0887621i	$0.0282911\pi$
$788$		0			0
$789$	2.93718	+	20.4285i	0.104566	+	0.727275i
$790$		0			0
$791$	15.8087	+	1.50955i	0.562092	+	0.0536732i
$792$		0			0
$793$	−2.61836	+	54.9661i	−0.0929806	+	1.95190i
$794$		0			0
$795$	−0.137185	+	0.954145i	−0.00486546	+	0.0338400i
$796$		0			0
$797$	19.7523	−	7.90764i	0.699663	−	0.280103i	0.00556638	−	0.999985i	$-0.498228\pi$
$797$	19.7523	−	7.90764i	0.699663	−	0.280103i	0.694097	+	0.719882i	$0.255804\pi$
$798$		0			0
$799$	−17.5499	−	11.2787i	−0.620872	−	0.399010i
$800$		0			0
$801$	10.8214	+	12.4886i	0.382357	+	0.441264i
$802$		0			0
$803$	47.8633			1.68906
$804$		0			0
$805$	−4.53869			−0.159968
$806$		0			0
$807$	15.5427	+	17.9372i	0.547129	+	0.631421i
$808$		0			0
$809$	1.89040	+	1.21488i	0.0664628	+	0.0427131i	0.573450	−	0.819240i	$-0.305605\pi$
$809$	1.89040	+	1.21488i	0.0664628	+	0.0427131i	−0.506987	+	0.861953i	$0.669241\pi$
$810$		0			0
$811$	31.2253	−	12.5007i	1.09647	−	0.438960i	0.248298	−	0.968684i	$-0.420129\pi$
$811$	31.2253	−	12.5007i	1.09647	−	0.438960i	0.848170	+	0.529724i	$0.177705\pi$
$812$		0			0
$813$	0.406192	−	2.82513i	0.0142458	−	0.0990816i
$814$		0			0
$815$	−0.0764068	+	1.60398i	−0.00267641	+	0.0561848i
$816$		0			0
$817$	−1.11821	−	0.106776i	−0.0391212	−	0.00373563i
$818$		0			0
$819$	3.67099	+	25.5323i	0.128275	+	0.892171i
$820$		0			0
$821$	−6.25475	+	25.7825i	−0.218292	+	0.899814i	0.752249	+	0.658879i	$0.228969\pi$
$821$	−6.25475	+	25.7825i	−0.218292	+	0.899814i	−0.970541	+	0.240935i	$0.922546\pi$
$822$		0			0
$823$	28.0559	+	11.2319i	0.977968	+	0.391519i	0.804913	−	0.593393i	$-0.202212\pi$
$823$	28.0559	+	11.2319i	0.977968	+	0.391519i	0.173055	+	0.984912i	$0.444636\pi$
$824$		0			0
$825$	−25.0169	−	12.8971i	−0.870975	−	0.449019i
$826$		0			0
$827$	−10.9772	+	2.11568i	−0.381715	+	0.0735695i	−0.376499	−	0.926417i	$-0.622872\pi$
$827$	−10.9772	+	2.11568i	−0.381715	+	0.0735695i	−0.00521556	+	0.999986i	$0.501660\pi$
$828$		0			0
$829$	16.2932	+	35.6771i	0.565886	+	1.23912i	0.948959	+	0.315399i	$0.102138\pi$
$829$	16.2932	+	35.6771i	0.565886	+	1.23912i	−0.383073	+	0.923718i	$0.625134\pi$
$830$		0			0
$831$	14.5942	−	9.37910i	0.506266	−	0.325357i
$832$		0			0
$833$	7.09706	+	12.2925i	0.245898	+	0.425909i
$834$		0			0
$835$	−1.94508	+	0.185732i	−0.0673121	+	0.00642753i
$836$		0			0
$837$	3.30771	−	2.60121i	0.114331	−	0.0899111i
$838$		0			0
$839$	−21.0807	−	4.06296i	−0.727785	−	0.140269i	−0.188117	−	0.982147i	$-0.560238\pi$
$839$	−21.0807	−	4.06296i	−0.727785	−	0.140269i	−0.539668	+	0.841878i	$0.681450\pi$
$840$		0			0
$841$	6.18560	−	10.7138i	0.213296	−	0.369440i
$842$		0			0
$843$	−16.3976	−	23.0272i	−0.564763	−	0.793099i
$844$		0			0
$845$	−6.05611	−	5.77448i	−0.208336	−	0.198648i
$846$		0			0
$847$	75.0583	−	22.0391i	2.57903	−	0.757272i
$848$		0			0
$849$	5.06788	−	5.84864i	0.173929	−	0.200725i
$850$		0			0
$851$	−19.0914	+	55.1610i	−0.654445	+	1.89090i
$852$		0			0
$853$	−26.7928	+	25.5468i	−0.917367	+	0.874707i	−0.992472	−	0.122468i	$-0.960919\pi$
$853$	−26.7928	+	25.5468i	−0.917367	+	0.874707i	0.0751058	+	0.997176i	$0.476071\pi$
$854$		0			0
$855$	0.694434	−	0.358006i	0.0237491	−	0.0122435i
$856$		0			0
$857$	51.0765	+	14.9974i	1.74474	+	0.512302i	0.989673	−	0.143344i	$-0.0457855\pi$
$857$	51.0765	+	14.9974i	1.74474	+	0.512302i	0.755068	+	0.655646i	$0.227604\pi$
$858$		0			0
$859$	−6.36746	+	8.94185i	−0.217255	+	0.305092i	−0.908792	−	0.417249i	$-0.862994\pi$
$859$	−6.36746	+	8.94185i	−0.217255	+	0.305092i	0.691537	+	0.722341i	$0.256934\pi$
$860$		0			0
$861$	−10.6870	−	30.8782i	−0.364213	−	1.05233i
$862$		0			0
$863$	−14.9831	+	32.8083i	−0.510029	+	1.11681i	0.463049	+	0.886333i	$0.346755\pi$
$863$	−14.9831	+	32.8083i	−0.510029	+	1.11681i	−0.973078	+	0.230475i	$0.925972\pi$
$864$		0			0
$865$	−0.267847	−	5.62281i	−0.00910709	−	0.191181i
$866$		0			0
$867$	2.85284	+	11.7596i	0.0968875	+	0.399376i
$868$		0			0
$869$	1.36060	+	1.06999i	0.0461552	+	0.0362969i
$870$		0			0
$871$	26.6146	+	51.1409i	0.901801	+	1.73284i
$872$		0			0
$873$	−9.23373	−	7.26148i	−0.312514	−	0.245764i
$874$		0			0
$875$	−1.96332	−	8.09291i	−0.0663723	−	0.273590i
$876$		0			0
$877$	−0.692164	−	14.5303i	−0.0233727	−	0.490654i	−0.979958	−	0.199202i	$-0.936165\pi$
$877$	−0.692164	−	14.5303i	−0.0233727	−	0.490654i	0.956586	−	0.291451i	$-0.0941381\pi$
$878$		0			0
$879$	−6.67704	+	14.6207i	−0.225211	+	0.493143i
$880$		0			0
$881$	−2.43248	−	7.02820i	−0.0819525	−	0.236786i	0.896579	−	0.442884i	$-0.146045\pi$
$881$	−2.43248	−	7.02820i	−0.0819525	−	0.236786i	−0.978531	+	0.206098i	$0.933923\pi$
$882$		0			0
$883$	9.11023	−	12.7935i	0.306584	−	0.430536i	−0.632325	−	0.774703i	$-0.717899\pi$
$883$	9.11023	−	12.7935i	0.306584	−	0.430536i	0.938908	+	0.344167i	$0.111839\pi$
$884$		0			0
$885$	2.47079	+	0.725490i	0.0830548	+	0.0243871i
$886$		0			0
$887$	7.25877	−	3.74216i	0.243726	−	0.125649i	−0.332037	−	0.943267i	$-0.607736\pi$
$887$	7.25877	−	3.74216i	0.243726	−	0.125649i	0.575762	+	0.817617i	$0.304705\pi$
$888$		0			0
$889$	−17.1011	+	16.3058i	−0.573552	+	0.546881i
$890$		0			0
$891$	−1.86055	+	5.37571i	−0.0623308	+	0.180093i
$892$		0			0
$893$	−21.0959	+	24.3460i	−0.705948	+	0.814708i
$894$		0			0
$895$	3.96698	−	1.16481i	0.132602	−	0.0389353i
$896$		0			0
$897$	27.6368	+	26.3516i	0.922764	+	0.879854i
$898$		0			0
$899$	9.95352	+	13.9778i	0.331969	+	0.466185i
$900$		0			0
$901$	4.66720	−	8.08382i	0.155487	−	0.269311i
$902$		0			0
$903$	1.18185	+	0.227783i	0.0393296	+	0.00758015i
$904$		0			0
$905$	2.04548	−	1.60858i	0.0679941	−	0.0534711i
$906$		0			0
$907$	−17.8034	+	1.70002i	−0.591153	+	0.0564483i	−0.386346	−	0.922354i	$-0.626263\pi$
$907$	−17.8034	+	1.70002i	−0.591153	+	0.0564483i	−0.204807	+	0.978802i	$0.565657\pi$
$908$		0			0
$909$	5.94913	+	10.3042i	0.197320	+	0.341769i
$910$		0			0
$911$	3.25855	−	2.09414i	0.107961	−	0.0693820i	−0.485546	−	0.874211i	$-0.661379\pi$
$911$	3.25855	−	2.09414i	0.107961	−	0.0693820i	0.593507	+	0.804829i	$0.297743\pi$
$912$		0			0
$913$	30.8212	+	67.4891i	1.02003	+	2.23356i
$914$		0			0
$915$	−1.75360	+	0.337979i	−0.0579723	+	0.0111733i
$916$		0			0
$917$	−19.0277	−	9.80944i	−0.628349	−	0.323936i
$918$		0			0
$919$	7.62107	+	3.05102i	0.251396	+	0.100644i	0.493938	−	0.869497i	$-0.335557\pi$
$919$	7.62107	+	3.05102i	0.251396	+	0.100644i	−0.242542	+	0.970141i	$0.577981\pi$
$920$		0			0
$921$	0.748193	−	3.08410i	0.0246538	−	0.101624i
$922$		0			0
$923$	−0.220063	−	1.53057i	−0.00724345	−	0.0503793i
$924$		0			0
$925$	−53.0279	−	5.06355i	−1.74355	−	0.166488i
$926$		0			0
$927$	0.620320	−	13.0221i	0.0203740	−	0.427703i
$928$		0			0
$929$	0.876990	−	6.09960i	0.0287731	−	0.200121i	−0.970364	−	0.241646i	$-0.922313\pi$
$929$	0.876990	−	6.09960i	0.0287731	−	0.200121i	0.999137	+	0.0415251i	$0.0132217\pi$
$930$		0			0
$931$	20.3484	−	8.14625i	0.666890	−	0.266983i
$932$		0			0
$933$	−4.57104	−	2.93763i	−0.149649	−	0.0961736i
$934$		0			0
$935$	−1.88478	−	2.17515i	−0.0616390	−	0.0711352i
$936$		0			0
$937$	−6.25646			−0.204390			−0.102195	−	0.994764i	$-0.532587\pi$
$937$	−6.25646			−0.204390			−0.102195	+	0.994764i	$0.532587\pi$
$938$		0			0
$939$	11.0263			0.359828
$940$		0			0
$941$	−24.3306	−	28.0791i	−0.793156	−	0.915351i	0.204829	−	0.978798i	$-0.434336\pi$
$941$	−24.3306	−	28.0791i	−0.793156	−	0.915351i	−0.997985	+	0.0634466i	$0.979791\pi$
$942$		0			0
$943$	−40.6931	−	26.1519i	−1.32515	−	0.851623i
$944$		0			0
$945$	−0.777173	+	0.311133i	−0.0252814	+	0.0101212i
$946$		0			0
$947$	7.36105	−	51.1973i	0.239202	−	1.66369i	−0.416853	−	0.908974i	$-0.636867\pi$
$947$	7.36105	−	51.1973i	0.239202	−	1.66369i	0.656055	−	0.754713i	$-0.272224\pi$
$948$		0			0
$949$	2.81979	−	59.1946i	0.0915341	−	1.92154i
$950$		0			0
$951$	−21.7799	−	2.07973i	−0.706263	−	0.0674399i
$952$		0			0
$953$	−4.16364	−	28.9587i	−0.134873	−	0.938065i	−0.939076	−	0.343710i	$-0.888316\pi$
$953$	−4.16364	−	28.9587i	−0.134873	−	0.938065i	0.804202	−	0.594355i	$-0.202593\pi$
$954$		0			0
$955$	1.27916	−	5.27278i	0.0413927	−	0.170623i
$956$		0			0
$957$	−21.5355	−	8.62150i	−0.696143	−	0.278693i
$958$		0			0
$959$	5.68307	+	2.92983i	0.183516	+	0.0946091i
$960$		0			0
$961$	−13.0525	+	2.51567i	−0.421049	+	0.0811506i
$962$		0			0
$963$	0.646928	+	1.41658i	0.0208470	+	0.0456485i
$964$		0			0
$965$	−2.99289	+	1.92341i	−0.0963444	+	0.0619168i
$966$		0			0
$967$	16.1242	+	27.9280i	0.518520	+	0.898103i	0.999768	+	0.0215191i	$0.00685026\pi$
$967$	16.1242	+	27.9280i	0.518520	+	0.898103i	−0.481248	+	0.876584i	$0.659816\pi$
$968$		0			0
$969$	−7.53126	+	0.719148i	−0.241939	+	0.0231024i
$970$		0			0
$971$	5.82180	−	4.57831i	0.186830	−	0.146925i	−0.520363	−	0.853945i	$-0.674203\pi$
$971$	5.82180	−	4.57831i	0.186830	−	0.146925i	0.707193	+	0.707020i	$0.249961\pi$
$972$		0			0
$973$	−1.69014	−	0.325749i	−0.0541836	−	0.0104430i
$974$		0			0
$975$	−17.4242	+	30.1796i	−0.558021	+	0.966521i
$976$		0			0
$977$	33.7572	+	47.4054i	1.07999	+	1.51663i	0.837467	+	0.546487i	$0.184035\pi$
$977$	33.7572	+	47.4054i	1.07999	+	1.51663i	0.242522	+	0.970146i	$0.422025\pi$
$978$		0			0
$979$	−68.0329	−	64.8692i	−2.17434	−	2.07323i
$980$		0			0
$981$	3.03297	−	0.890559i	0.0968352	−	0.0284334i
$982$		0			0
$983$	−20.5168	+	23.6777i	−0.654385	+	0.755201i	−0.981849	−	0.189663i	$-0.939261\pi$
$983$	−20.5168	+	23.6777i	−0.654385	+	0.755201i	0.327464	+	0.944864i	$0.393806\pi$
$984$		0			0
$985$	−0.614586	+	1.77573i	−0.0195823	+	0.0565794i
$986$		0			0
$987$	24.9814	−	23.8197i	0.795167	−	0.758190i
$988$		0			0
$989$	1.58372	−	0.816466i	0.0503595	−	0.0259621i
$990$		0			0
$991$	49.5236	+	14.5414i	1.57317	+	0.461924i	0.947922	−	0.318502i	$-0.103180\pi$
$991$	49.5236	+	14.5414i	1.57317	+	0.461924i	0.625247	+	0.780427i	$0.284998\pi$
$992$		0			0
$993$	7.23298	−	10.1573i	0.229532	−	0.322332i
$994$		0			0
$995$	1.29087	+	3.72972i	0.0409233	+	0.118240i
$996$		0			0
$997$	3.21346	−	7.03649i	0.101771	−	0.222848i	−0.851896	−	0.523711i	$-0.824547\pi$
$997$	3.21346	−	7.03649i	0.101771	−	0.222848i	0.953667	+	0.300863i	$0.0972746\pi$
$998$		0			0
$999$	0.512282	+	10.7541i	0.0162079	+	0.340246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.505.4	yes	120
67.54	even	33	inner	804.2.y.b.121.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.4	✓	120	67.54	even	33	inner
804.2.y.b.505.4	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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.192294 - 0.123580i) q^{5} +(-3.39999 + 1.36115i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.192294 - 0.123580i) q^{5} +(-3.39999 + 1.36115i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.270673 - 5.68213i) q^{11} +(-7.01139 - 0.669507i) q^{13} +(-0.0325305 - 0.226254i) q^{15} +(-0.521840 + 2.15105i) q^{17} +(3.17314 + 1.27033i) q^{19} +(-3.25521 - 1.67818i) q^{21} +(-5.32369 + 1.02606i) q^{23} +(-2.05537 - 4.50063i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-2.03892 - 3.53152i) q^{29} +(-4.18895 + 0.399996i) q^{31} +(4.47152 - 3.51644i) q^{33} +(0.822011 + 0.158430i) q^{35} +(5.38316 - 9.32391i) q^{37} +(-4.08551 - 5.73729i) q^{39} +(6.45714 + 6.15688i) q^{41} +(-0.315331 + 0.0925896i) q^{43} +(0.149689 - 0.172750i) q^{45} +(-3.08261 + 8.90661i) q^{47} +(4.64107 - 4.42526i) q^{49} +(-1.96739 + 1.01426i) q^{51} +(-4.04631 - 1.18810i) q^{53} +(-0.754248 + 1.05919i) q^{55} +(1.11791 + 3.22999i) q^{57} +(-4.67990 + 10.2476i) q^{59} +(-0.371752 - 7.80404i) q^{61} +(-0.863428 - 3.55910i) q^{63} +(1.26551 + 0.995212i) q^{65} +(-4.45180 - 6.86888i) q^{67} +(-4.26172 - 3.35145i) q^{69} +(0.0517593 + 0.213355i) q^{71} +(0.400351 + 8.40440i) q^{73} +(2.05537 - 4.50063i) q^{75} +(6.81396 + 19.6876i) q^{77} +(-0.176501 + 0.247860i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-11.5927 + 5.97647i) q^{83} +(0.366174 - 0.349146i) q^{85} +(1.33373 - 3.85356i) q^{87} +(10.8214 - 12.4886i) q^{89} +(24.7500 - 7.26725i) q^{91} +(-3.04547 - 2.90385i) q^{93} +(-0.453190 - 0.636416i) q^{95} +(-5.87348 + 10.1732i) q^{97} +(5.58578 + 1.07657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 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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