LMFDB - Embedded newform 804.2.y.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	804.49
Dual form			804.2.y.a.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{3} +(-0.138288 - 0.961813i) q^{5} +(4.23021 + 0.403936i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{3} +(-0.138288 - 0.961813i) q^{5} +(4.23021 + 0.403936i) q^{7} +(0.415415 + 0.909632i) q^{9} +(-2.05350 - 0.822096i) q^{11} +(1.78779 + 1.70466i) q^{13} +(0.403660 - 0.883893i) q^{15} +(0.348908 - 1.00810i) q^{17} +(1.68813 - 0.161197i) q^{19} +(3.34029 + 2.62684i) q^{21} +(0.107372 - 2.25401i) q^{23} +(3.89150 - 1.14265i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(-1.55560 + 2.69437i) q^{29} +(-2.82315 + 2.69187i) q^{31} +(-1.28305 - 1.80179i) q^{33} +(-0.196476 - 4.12453i) q^{35} +(-1.27971 - 2.21653i) q^{37} +(0.582379 + 2.40060i) q^{39} +(4.33963 - 0.836395i) q^{41} +(-0.666868 - 0.769607i) q^{43} +(0.817449 - 0.525343i) q^{45} +(1.82266 - 0.939646i) q^{47} +(10.8580 + 2.09271i) q^{49} +(0.838541 - 0.659436i) q^{51} +(-1.57732 + 1.82032i) q^{53} +(-0.506729 + 2.08876i) q^{55} +(1.50729 + 0.777063i) q^{57} +(6.45019 + 1.89395i) q^{59} +(3.63792 - 1.45641i) q^{61} +(1.38986 + 4.01573i) q^{63} +(1.39233 - 1.95525i) q^{65} +(-4.51993 + 6.82424i) q^{67} +(1.30894 - 1.83814i) q^{69} +(0.231622 + 0.669229i) q^{71} +(-2.56007 + 1.02490i) q^{73} +(3.89150 + 1.14265i) q^{75} +(-8.35464 - 4.30712i) q^{77} +(1.04259 - 4.29763i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-6.64404 + 5.22493i) q^{83} +(-1.01786 - 0.196176i) q^{85} +(-2.76534 + 1.42563i) q^{87} +(3.77032 - 2.42304i) q^{89} +(6.87416 + 7.93320i) q^{91} +(-3.83032 + 0.738235i) q^{93} +(-0.388488 - 1.60137i) q^{95} +(-3.73608 - 6.47107i) q^{97} +(-0.105248 - 2.20944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{23}{33}\right)$	$1$

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
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$		0			0
$5$	−0.138288	−	0.961813i	−0.0618442	−	0.430136i	−0.997096	−	0.0761531i	$-0.975736\pi$
$5$	−0.138288	−	0.961813i	−0.0618442	−	0.430136i	0.935252	−	0.353983i	$-0.115173\pi$
$6$		0			0
$7$	4.23021	+	0.403936i	1.59887	+	0.152673i	0.856077	−	0.516849i	$-0.172895\pi$
$7$	4.23021	+	0.403936i	1.59887	+	0.152673i	0.742792	+	0.669522i	$0.233501\pi$
$8$		0			0
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$		0			0
$11$	−2.05350	−	0.822096i	−0.619152	−	0.247871i	0.0408136	−	0.999167i	$-0.487005\pi$
$11$	−2.05350	−	0.822096i	−0.619152	−	0.247871i	−0.659966	+	0.751296i	$0.729429\pi$
$12$		0			0
$13$	1.78779	+	1.70466i	0.495844	+	0.472786i	0.896249	−	0.443552i	$-0.146282\pi$
$13$	1.78779	+	1.70466i	0.495844	+	0.472786i	−0.400405	+	0.916338i	$0.631130\pi$
$14$		0			0
$15$	0.403660	−	0.883893i	0.104225	−	0.228220i
$16$		0			0
$17$	0.348908	−	1.00810i	0.0846225	−	0.244501i	−0.894749	−	0.446570i	$-0.852645\pi$
$17$	0.348908	−	1.00810i	0.0846225	−	0.244501i	0.979371	+	0.202069i	$0.0647666\pi$
$18$		0			0
$19$	1.68813	−	0.161197i	0.387283	−	0.0369810i	0.100401	−	0.994947i	$-0.467987\pi$
$19$	1.68813	−	0.161197i	0.387283	−	0.0369810i	0.286882	+	0.957966i	$0.407381\pi$
$20$		0			0
$21$	3.34029	+	2.62684i	0.728912	+	0.573223i
$22$		0			0
$23$	0.107372	−	2.25401i	0.0223885	−	0.469993i	−0.959637	−	0.281243i	$-0.909253\pi$
$23$	0.107372	−	2.25401i	0.0223885	−	0.469993i	0.982025	−	0.188750i	$-0.0604437\pi$
$24$		0			0
$25$	3.89150	−	1.14265i	0.778301	−	0.228530i
$26$		0			0
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$		0			0
$29$	−1.55560	+	2.69437i	−0.288867	+	0.500333i	−0.973540	−	0.228518i	$-0.926612\pi$
$29$	−1.55560	+	2.69437i	−0.288867	+	0.500333i	0.684672	+	0.728851i	$0.259945\pi$
$30$		0			0
$31$	−2.82315	+	2.69187i	−0.507054	+	0.483475i	−0.899880	−	0.436138i	$-0.856346\pi$
$31$	−2.82315	+	2.69187i	−0.507054	+	0.483475i	0.392826	+	0.919613i	$0.371497\pi$
$32$		0			0
$33$	−1.28305	−	1.80179i	−0.223351	−	0.313652i
$34$		0			0
$35$	−0.196476	−	4.12453i	−0.0332104	−	0.697173i
$36$		0			0
$37$	−1.27971	−	2.21653i	−0.210384	−	0.364395i	0.741451	−	0.671007i	$-0.234138\pi$
$37$	−1.27971	−	2.21653i	−0.210384	−	0.364395i	−0.951835	+	0.306612i	$0.900805\pi$
$38$		0			0
$39$	0.582379	+	2.40060i	0.0932553	+	0.384404i
$40$		0			0
$41$	4.33963	−	0.836395i	0.677737	−	0.130623i	0.161244	−	0.986915i	$-0.448449\pi$
$41$	4.33963	−	0.836395i	0.677737	−	0.130623i	0.516493	+	0.856292i	$0.327237\pi$
$42$		0			0
$43$	−0.666868	−	0.769607i	−0.101696	−	0.117364i	0.702620	−	0.711566i	$-0.252014\pi$
$43$	−0.666868	−	0.769607i	−0.101696	−	0.117364i	−0.804316	+	0.594202i	$0.797468\pi$
$44$		0			0
$45$	0.817449	−	0.525343i	0.121858	−	0.0783134i
$46$		0			0
$47$	1.82266	−	0.939646i	0.265862	−	0.137062i	−0.320142	−	0.947370i	$-0.603731\pi$
$47$	1.82266	−	0.939646i	0.265862	−	0.137062i	0.586004	+	0.810308i	$0.300700\pi$
$48$		0			0
$49$	10.8580	+	2.09271i	1.55114	+	0.298958i
$50$		0			0
$51$	0.838541	−	0.659436i	0.117419	−	0.0923395i
$52$		0			0
$53$	−1.57732	+	1.82032i	−0.216661	+	0.250040i	−0.853668	−	0.520818i	$-0.825627\pi$
$53$	−1.57732	+	1.82032i	−0.216661	+	0.250040i	0.637007	+	0.770858i	$0.280172\pi$
$54$		0			0
$55$	−0.506729	+	2.08876i	−0.0683273	+	0.281649i
$56$		0			0
$57$	1.50729	+	0.777063i	0.199646	+	0.102925i
$58$		0			0
$59$	6.45019	+	1.89395i	0.839743	+	0.246571i	0.673197	−	0.739463i	$-0.264920\pi$
$59$	6.45019	+	1.89395i	0.839743	+	0.246571i	0.166546	+	0.986034i	$0.446739\pi$
$60$		0			0
$61$	3.63792	−	1.45641i	0.465788	−	0.186474i	−0.126883	−	0.991918i	$-0.540497\pi$
$61$	3.63792	−	1.45641i	0.465788	−	0.186474i	0.592672	+	0.805444i	$0.298073\pi$
$62$		0			0
$63$	1.38986	+	4.01573i	0.175106	+	0.505935i
$64$		0			0
$65$	1.39233	−	1.95525i	0.172697	−	0.242519i
$66$		0			0
$67$	−4.51993	+	6.82424i	−0.552197	+	0.833714i
$67$	−4.51993	+	6.82424i	−0.552197	+	0.833714i
$68$		0			0
$69$	1.30894	−	1.83814i	0.157577	−	0.221286i
$70$		0			0
$71$	0.231622	+	0.669229i	0.0274885	+	0.0794228i	0.957910	−	0.287068i	$-0.0926804\pi$
$71$	0.231622	+	0.669229i	0.0274885	+	0.0794228i	−0.930422	+	0.366490i	$0.880559\pi$
$72$		0			0
$73$	−2.56007	+	1.02490i	−0.299634	+	0.119955i	−0.516608	−	0.856222i	$-0.672806\pi$
$73$	−2.56007	+	1.02490i	−0.299634	+	0.119955i	0.216974	+	0.976177i	$0.430381\pi$
$74$		0			0
$75$	3.89150	+	1.14265i	0.449352	+	0.131942i
$76$		0			0
$77$	−8.35464	−	4.30712i	−0.952100	−	0.490842i
$78$		0			0
$79$	1.04259	−	4.29763i	0.117301	−	0.483522i	−0.882609	−	0.470108i	$-0.844215\pi$
$79$	1.04259	−	4.29763i	0.117301	−	0.483522i	0.999910	−	0.0134137i	$-0.00426985\pi$
$80$		0			0
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$		0			0
$83$	−6.64404	+	5.22493i	−0.729278	+	0.573510i	−0.912263	−	0.409605i	$-0.865666\pi$
$83$	−6.64404	+	5.22493i	−0.729278	+	0.573510i	0.182985	+	0.983116i	$0.441424\pi$
$84$		0			0
$85$	−1.01786	−	0.196176i	−0.110402	−	0.0212782i
$86$		0			0
$87$	−2.76534	+	1.42563i	−0.296476	+	0.152844i
$88$		0			0
$89$	3.77032	−	2.42304i	0.399653	−	0.256842i	−0.325341	−	0.945597i	$-0.605479\pi$
$89$	3.77032	−	2.42304i	0.399653	−	0.256842i	0.724994	+	0.688755i	$0.241843\pi$
$90$		0			0
$91$	6.87416	+	7.93320i	0.720607	+	0.831625i
$92$		0			0
$93$	−3.83032	+	0.738235i	−0.397186	+	0.0765514i
$94$		0			0
$95$	−0.388488	−	1.60137i	−0.0398581	−	0.164297i
$96$		0			0
$97$	−3.73608	−	6.47107i	−0.379341	−	0.657038i	0.611625	−	0.791147i	$-0.290516\pi$
$97$	−3.73608	−	6.47107i	−0.379341	−	0.657038i	−0.990967	+	0.134109i	$0.957183\pi$
$98$		0			0
$99$	−0.105248	−	2.20944i	−0.0105779	−	0.222057i
$100$		0			0
$101$	−6.48021	−	9.10018i	−0.644805	−	0.905502i	0.354761	−	0.934957i	$-0.384562\pi$
$101$	−6.48021	−	9.10018i	−0.644805	−	0.905502i	−0.999566	+	0.0294550i	$0.990623\pi$
$102$		0			0
$103$	−3.34232	+	3.18689i	−0.329328	+	0.314014i	−0.836645	−	0.547746i	$-0.815486\pi$
$103$	−3.34232	+	3.18689i	−0.329328	+	0.314014i	0.507316	+	0.861760i	$0.330638\pi$
$104$		0			0
$105$	2.06460	−	3.57600i	0.201485	−	0.348982i
$106$		0			0
$107$	−2.66239	+	18.5173i	−0.257383	+	1.79014i	0.293918	+	0.955831i	$0.405041\pi$
$107$	−2.66239	+	18.5173i	−0.257383	+	1.79014i	−0.551301	+	0.834306i	$0.685868\pi$
$108$		0			0
$109$	−10.8059	+	3.17289i	−1.03501	+	0.303907i	−0.754748	−	0.656015i	$-0.772241\pi$
$109$	−10.8059	+	3.17289i	−1.03501	+	0.303907i	−0.280265	+	0.959923i	$0.590423\pi$
$110$		0			0
$111$	0.121782	−	2.55653i	0.0115591	−	0.242655i
$112$		0			0
$113$	−6.27040	−	4.93110i	−0.589870	−	0.463879i	0.278061	−	0.960563i	$-0.410308\pi$
$113$	−6.27040	−	4.93110i	−0.589870	−	0.463879i	−0.867931	+	0.496685i	$0.834551\pi$
$114$		0			0
$115$	−2.18278	+	0.208431i	−0.203546	+	0.0194362i
$116$		0			0
$117$	−0.807934	+	2.33437i	−0.0746935	+	0.215813i
$118$		0			0
$119$	1.88316	−	4.12355i	0.172629	−	0.378005i
$120$		0			0
$121$	−4.42007	−	4.21453i	−0.401825	−	0.383139i
$122$		0			0
$123$	4.10292	+	1.64256i	0.369948	+	0.148105i
$124$		0			0
$125$	−3.65546	−	8.00435i	−0.326955	−	0.715931i
$126$		0			0
$127$	7.41464	+	0.708013i	0.657943	+	0.0628260i	0.418687	−	0.908131i	$-0.362490\pi$
$127$	7.41464	+	0.708013i	0.657943	+	0.0628260i	0.239256	+	0.970957i	$0.423096\pi$
$128$		0			0
$129$	−0.144924	−	1.00797i	−0.0127599	−	0.0887469i
$130$		0			0
$131$	−18.1940	−	11.6925i	−1.58961	−	1.02158i	−0.971964	−	0.235129i	$-0.924449\pi$
$131$	−18.1940	−	11.6925i	−1.58961	−	1.02158i	−0.617649	−	0.786454i	$-0.711915\pi$
$132$		0			0
$133$	7.20624			0.624860
$134$		0			0
$135$	0.971703			0.0836309
$136$		0			0
$137$	−12.5298	−	8.05242i	−1.07049	−	0.687965i	−0.118152	−	0.992996i	$-0.537697\pi$
$137$	−12.5298	−	8.05242i	−1.07049	−	0.687965i	−0.952342	+	0.305031i	$0.901333\pi$
$138$		0			0
$139$	1.54789	+	10.7658i	0.131290	+	0.913144i	0.943876	+	0.330301i	$0.107150\pi$
$139$	1.54789	+	10.7658i	0.131290	+	0.913144i	−0.812585	+	0.582842i	$0.801941\pi$
$140$		0			0
$141$	2.04133	+	0.194923i	0.171911	+	0.0164155i
$142$		0			0
$143$	−2.26983	−	4.97024i	−0.189813	−	0.415632i
$144$		0			0
$145$	2.80660	+	1.12359i	0.233076	+	0.0933095i
$146$		0			0
$147$	8.00293	+	7.63078i	0.660070	+	0.629376i
$148$		0			0
$149$	3.29038	−	7.20493i	0.269559	−	0.590251i	−0.725646	−	0.688068i	$-0.758459\pi$
$149$	3.29038	−	7.20493i	0.269559	−	0.590251i	0.995204	+	0.0978175i	$0.0311862\pi$
$150$		0			0
$151$	0.0549162	−	0.158670i	0.00446902	−	0.0129124i	−0.942744	−	0.333517i	$-0.891765\pi$
$151$	0.0549162	−	0.158670i	0.00446902	−	0.0129124i	0.947213	+	0.320604i	$0.103886\pi$
$152$		0			0
$153$	1.06194	−	0.101403i	0.0858531	−	0.00819797i
$154$		0			0
$155$	2.97949	+	2.34309i	0.239318	+	0.188202i
$156$		0			0
$157$	−0.0590070	+	1.23871i	−0.00470927	+	0.0988598i	0.995289	+	0.0969535i	$0.0309098\pi$
$157$	−0.0590070	+	1.23871i	−0.00470927	+	0.0988598i	−0.999998	+	0.00190627i	$0.999393\pi$
$158$		0			0
$159$	−2.31106	+	0.678589i	−0.183279	+	0.0538156i
$160$		0			0
$161$	1.36468	−	9.49156i	0.107552	−	0.748039i
$162$		0			0
$163$	−1.33295	+	2.30874i	−0.104405	+	0.180835i	−0.913495	−	0.406850i	$-0.866627\pi$
$163$	−1.33295	+	2.30874i	−0.104405	+	0.180835i	0.809090	+	0.587685i	$0.199960\pi$
$164$		0			0
$165$	−1.55556	+	1.48322i	−0.121100	+	0.115469i
$166$		0			0
$167$	1.31224	+	1.84279i	0.101544	+	0.142599i	0.862222	−	0.506531i	$-0.169072\pi$
$167$	1.31224	+	1.84279i	0.101544	+	0.142599i	−0.760677	+	0.649130i	$0.775133\pi$
$168$		0			0
$169$	−0.328218	−	6.89014i	−0.0252475	−	0.530011i
$170$		0			0
$171$	0.847903	+	1.46861i	0.0648407	+	0.112307i
$172$		0			0
$173$	0.0688608	+	0.283848i	0.00523539	+	0.0215806i	0.974369	−	0.224954i	$-0.0722232\pi$
$173$	0.0688608	+	0.283848i	0.00523539	+	0.0215806i	−0.969134	+	0.246535i	$0.920708\pi$
$174$		0			0
$175$	16.9234	−	3.26172i	1.27929	−	0.246563i
$176$		0			0
$177$	4.40230	+	5.08052i	0.330897	+	0.381876i
$178$		0			0
$179$	−8.46024	+	5.43707i	−0.632348	+	0.406385i	−0.817178	−	0.576385i	$-0.804463\pi$
$179$	−8.46024	+	5.43707i	−0.632348	+	0.406385i	0.184830	+	0.982770i	$0.440826\pi$
$180$		0			0
$181$	−5.40113	+	2.78448i	−0.401463	+	0.206969i	−0.647120	−	0.762388i	$-0.724027\pi$
$181$	−5.40113	+	2.78448i	−0.401463	+	0.206969i	0.245657	+	0.969357i	$0.420996\pi$
$182$		0			0
$183$	3.84781	+	0.741604i	0.284438	+	0.0548210i
$184$		0			0
$185$	−1.95492	+	1.53736i	−0.143728	+	0.113029i
$186$		0			0
$187$	−1.54524	+	1.78330i	−0.112999	+	0.130408i
$188$		0			0
$189$	−1.00185	+	4.12967i	−0.0728736	+	0.300389i
$190$		0			0
$191$	1.90580	+	0.982509i	0.137899	+	0.0710918i	0.525795	−	0.850611i	$-0.323768\pi$
$191$	1.90580	+	0.982509i	0.137899	+	0.0710918i	−0.387896	+	0.921703i	$0.626798\pi$
$192$		0			0
$193$	−15.1385	−	4.44506i	−1.08969	−	0.319962i	−0.312942	−	0.949772i	$-0.601315\pi$
$193$	−15.1385	−	4.44506i	−1.08969	−	0.319962i	−0.776749	+	0.629810i	$0.783133\pi$
$194$		0			0
$195$	2.22839	−	0.892114i	0.159578	−	0.0638856i
$196$		0			0
$197$	−8.87557	−	25.6443i	−0.632358	−	1.82708i	−0.557991	−	0.829847i	$-0.688428\pi$
$197$	−8.87557	−	25.6443i	−0.632358	−	1.82708i	−0.0743670	−	0.997231i	$-0.523694\pi$
$198$		0			0
$199$	8.77791	−	12.3269i	0.622250	−	0.873827i	−0.376364	−	0.926472i	$-0.622826\pi$
$199$	8.77791	−	12.3269i	0.622250	−	0.873827i	0.998613	+	0.0526447i	$0.0167651\pi$
$200$		0			0
$201$	−7.49187	+	3.29726i	−0.528436	+	0.232571i
$202$		0			0
$203$	−7.66886	+	10.7694i	−0.538248	+	0.755864i
$204$		0			0
$205$	−1.40457	−	4.05825i	−0.0980997	−	0.283441i
$206$		0			0
$207$	2.09492	−	0.838680i	0.145607	−	0.0582923i
$208$		0			0
$209$	−3.59908	−	1.05679i	−0.248954	−	0.0730994i
$210$		0			0
$211$	−9.88252	−	5.09480i	−0.680341	−	0.350740i	0.0831696	−	0.996535i	$-0.473496\pi$
$211$	−9.88252	−	5.09480i	−0.680341	−	0.350740i	−0.763511	+	0.645795i	$0.776526\pi$
$212$		0			0
$213$	−0.166959	+	0.688216i	−0.0114399	+	0.0471558i
$214$		0			0
$215$	−0.647998	+	0.747830i	−0.0441931	+	0.0510016i
$216$		0			0
$217$	−13.0299	+	10.2468i	−0.884526	+	0.695599i
$218$		0			0
$219$	−2.70777	−	0.521880i	−0.182974	−	0.0352654i
$220$		0			0
$221$	2.34224	−	1.20751i	0.157556	−	0.0812259i
$222$		0			0
$223$	−10.3736	+	6.66669i	−0.694666	+	0.446435i	−0.839742	−	0.542986i	$-0.817294\pi$
$223$	−10.3736	+	6.66669i	−0.694666	+	0.446435i	0.145076	+	0.989421i	$0.453657\pi$
$224$		0			0
$225$	2.65598	+	3.06516i	0.177065	+	0.204344i
$226$		0			0
$227$	−23.5229	+	4.53366i	−1.56127	+	0.300910i	−0.895436	−	0.445191i	$-0.853136\pi$
$227$	−23.5229	+	4.53366i	−1.56127	+	0.300910i	−0.665833	+	0.746101i	$0.731924\pi$
$228$		0			0
$229$	3.55789	+	14.6658i	0.235112	+	0.969145i	0.959938	+	0.280213i	$0.0904050\pi$
$229$	3.55789	+	14.6658i	0.235112	+	0.969145i	−0.724826	+	0.688932i	$0.758080\pi$
$230$		0			0
$231$	−4.69977	−	8.14024i	−0.309222	−	0.535588i
$232$		0			0
$233$	0.664197	+	13.9432i	0.0435130	+	0.913450i	0.910091	+	0.414408i	$0.136011\pi$
$233$	0.664197	+	13.9432i	0.0435130	+	0.913450i	−0.866578	+	0.499042i	$0.833686\pi$
$234$		0			0
$235$	−1.15582	−	1.62312i	−0.0753971	−	0.105880i
$236$		0			0
$237$	3.20056	−	3.05173i	0.207899	−	0.198231i
$238$		0			0
$239$	−7.53680	+	13.0541i	−0.487515	+	0.844401i	−0.999897	−	0.0143566i	$-0.995430\pi$
$239$	−7.53680	+	13.0541i	−0.487515	+	0.844401i	0.512382	+	0.858758i	$0.328763\pi$
$240$		0			0
$241$	−1.43229	+	9.96179i	−0.0922619	+	0.641696i	0.890247	+	0.455479i	$0.150532\pi$
$241$	−1.43229	+	9.96179i	−0.0922619	+	0.641696i	−0.982509	+	0.186217i	$0.940377\pi$
$242$		0			0
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$		0			0
$245$	0.511265	−	10.7328i	0.0326635	−	0.685691i
$246$		0			0
$247$	3.29280	+	2.58949i	0.209516	+	0.164765i
$248$		0			0
$249$	−8.41413	+	0.803452i	−0.533224	+	0.0509167i
$250$		0			0
$251$	−3.68570	+	10.6491i	−0.232639	+	0.672168i	0.766898	+	0.641769i	$0.221799\pi$
$251$	−3.68570	+	10.6491i	−0.232639	+	0.672168i	−0.999538	+	0.0303990i	$0.990322\pi$
$252$		0			0
$253$	−2.07350	+	4.54033i	−0.130360	+	0.285448i
$254$		0			0
$255$	−0.750214	−	0.715328i	−0.0469802	−	0.0447956i
$256$		0			0
$257$	−21.7816	−	8.72004i	−1.35870	−	0.543941i	−0.426042	−	0.904703i	$-0.640092\pi$
$257$	−21.7816	−	8.72004i	−1.35870	−	0.543941i	−0.932658	+	0.360762i	$0.882517\pi$
$258$		0			0
$259$	−4.51812	−	9.89331i	−0.280742	−	0.614740i
$260$		0			0
$261$	−3.09711	−	0.295738i	−0.191706	−	0.0183057i
$262$		0			0
$263$	0.826807	+	5.75057i	0.0509831	+	0.354595i	0.999305	+	0.0372845i	$0.0118708\pi$
$263$	0.826807	+	5.75057i	0.0509831	+	0.354595i	−0.948322	+	0.317311i	$0.897220\pi$
$264$		0			0
$265$	1.96893	+	1.26536i	0.120950	+	0.0777302i
$266$		0			0
$267$	4.48179			0.274281
$268$		0			0
$269$	8.26131			0.503701			0.251851	−	0.967766i	$-0.418961\pi$
$269$	8.26131			0.503701			0.251851	+	0.967766i	$0.418961\pi$
$270$		0			0
$271$	−21.0138	−	13.5048i	−1.27650	−	0.820355i	−0.286046	−	0.958216i	$-0.592341\pi$
$271$	−21.0138	−	13.5048i	−1.27650	−	0.820355i	−0.990452	+	0.137861i	$0.955977\pi$
$272$		0			0
$273$	1.49390	+	10.3903i	0.0904148	+	0.628848i
$274$		0			0
$275$	−8.93055	−	0.852765i	−0.538533	−	0.0514236i
$276$		0			0
$277$	−2.50159	−	5.47771i	−0.150306	−	0.329124i	0.819470	−	0.573122i	$-0.194268\pi$
$277$	−2.50159	−	5.47771i	−0.150306	−	0.329124i	−0.969776	+	0.243999i	$0.921541\pi$
$278$		0			0
$279$	−3.62139	−	1.44979i	−0.216807	−	0.0867965i
$280$		0			0
$281$	10.7565	+	10.2563i	0.641682	+	0.611842i	0.939405	−	0.342810i	$-0.111379\pi$
$281$	10.7565	+	10.2563i	0.641682	+	0.611842i	−0.297723	+	0.954652i	$0.596227\pi$
$282$		0			0
$283$	10.4980	−	22.9874i	0.624041	−	1.36646i	−0.288502	−	0.957479i	$-0.593157\pi$
$283$	10.4980	−	22.9874i	0.624041	−	1.36646i	0.912543	−	0.408980i	$-0.134116\pi$
$284$		0			0
$285$	0.538949	−	1.55719i	0.0319246	−	0.0922401i
$286$		0			0
$287$	18.6954	−	1.78519i	1.10355	−	0.105377i
$288$		0			0
$289$	12.4684	+	9.80523i	0.733433	+	0.576778i
$290$		0			0
$291$	0.355539	−	7.46369i	0.0208421	−	0.437529i
$292$		0			0
$293$	28.5379	−	8.37948i	1.66720	−	0.489534i	0.694093	−	0.719885i	$-0.255806\pi$
$293$	28.5379	−	8.37948i	1.66720	−	0.489534i	0.973108	+	0.230351i	$0.0739874\pi$
$294$		0			0
$295$	0.929639	−	6.46578i	0.0541257	−	0.376453i
$296$		0			0
$297$	1.10597	−	1.91560i	0.0641749	−	0.111154i
$298$		0			0
$299$	4.03427	−	3.84666i	0.233308	−	0.222458i
$300$		0			0
$301$	−2.51012	−	3.52497i	−0.144681	−	0.203176i
$302$		0			0
$303$	−0.531570	−	11.1590i	−0.0305379	−	0.641069i
$304$		0			0
$305$	−1.90387	−	3.29760i	−0.109015	−	0.188820i
$306$		0			0
$307$	5.24548	+	21.6222i	0.299376	+	1.23404i	0.900489	+	0.434879i	$0.143209\pi$
$307$	5.24548	+	21.6222i	0.299376	+	1.23404i	−0.601113	+	0.799164i	$0.705276\pi$
$308$		0			0
$309$	−4.53470	+	0.873992i	−0.257970	+	0.0497196i
$310$		0			0
$311$	20.6607	+	23.8437i	1.17156	+	1.35205i	0.923636	+	0.383271i	$0.125202\pi$
$311$	20.6607	+	23.8437i	1.17156	+	1.35205i	0.247922	+	0.968780i	$0.420252\pi$
$312$		0			0
$313$	9.35048	−	6.00919i	0.528520	−	0.339659i	−0.249014	−	0.968500i	$-0.580106\pi$
$313$	9.35048	−	6.00919i	0.528520	−	0.339659i	0.777534	+	0.628840i	$0.216470\pi$
$314$		0			0
$315$	3.67018	−	1.89211i	0.206791	−	0.106608i
$316$		0			0
$317$	1.04106	+	0.200647i	0.0584715	+	0.0112695i	0.218403	−	0.975859i	$-0.429915\pi$
$317$	1.04106	+	0.200647i	0.0584715	+	0.0112695i	−0.159932	+	0.987128i	$0.551127\pi$
$318$		0			0
$319$	5.40945	−	4.25404i	0.302871	−	0.238180i
$320$		0			0
$321$	−12.2510	+	14.1384i	−0.683782	+	0.789127i
$322$		0			0
$323$	0.426498	−	1.75805i	0.0237310	−	0.0978204i
$324$		0			0
$325$	8.90502	+	4.59086i	0.493961	+	0.254655i
$326$		0			0
$327$	−10.8059	−	3.17289i	−0.597565	−	0.175461i
$328$		0			0
$329$	8.08979	−	3.23866i	0.446005	−	0.178553i
$330$		0			0
$331$	−0.202406	−	0.584815i	−0.0111253	−	0.0321443i	0.939302	−	0.343093i	$-0.111475\pi$
$331$	−0.202406	−	0.584815i	−0.0111253	−	0.0321443i	−0.950427	+	0.310948i	$0.899353\pi$
$332$		0			0
$333$	1.48461	−	2.08485i	0.0813563	−	0.114249i
$334$		0			0
$335$	7.18869	+	3.40361i	0.392760	+	0.185959i
$336$		0			0
$337$	0.487642	−	0.684797i	0.0265635	−	0.0373033i	−0.801081	−	0.598556i	$-0.795741\pi$
$337$	0.487642	−	0.684797i	0.0265635	−	0.0373033i	0.827644	+	0.561253i	$0.189681\pi$
$338$		0			0
$339$	−2.60904	−	7.53834i	−0.141704	−	0.409426i
$340$		0			0
$341$	8.01031	−	3.20685i	0.433783	−	0.173660i
$342$		0			0
$343$	16.5451	+	4.85807i	0.893350	+	0.262311i
$344$		0			0
$345$	−1.94896	−	1.00476i	−0.104928	−	0.0540944i
$346$		0			0
$347$	−3.88834	+	16.0279i	−0.208737	+	0.860425i	0.767030	+	0.641612i	$0.221734\pi$
$347$	−3.88834	+	16.0279i	−0.208737	+	0.860425i	−0.975767	+	0.218814i	$0.929781\pi$
$348$		0			0
$349$	12.6898	−	14.6448i	0.679267	−	0.783916i	−0.306529	−	0.951861i	$-0.599168\pi$
$349$	12.6898	−	14.6448i	0.679267	−	0.783916i	0.985796	+	0.167945i	$0.0537131\pi$
$350$		0			0
$351$	−1.94173	+	1.52700i	−0.103642	+	0.0815050i
$352$		0			0
$353$	29.8234	+	5.74799i	1.58734	+	0.305935i	0.905102	−	0.425195i	$-0.139794\pi$
$353$	29.8234	+	5.74799i	1.58734	+	0.305935i	0.682239	+	0.731130i	$0.261007\pi$
$354$		0			0
$355$	0.611642	−	0.315324i	0.0324626	−	0.0167356i
$356$		0			0
$357$	3.81357	−	2.45084i	0.201836	−	0.129712i
$358$		0			0
$359$	17.1375	+	19.7777i	0.904482	+	1.04383i	0.998833	+	0.0482893i	$0.0153770\pi$
$359$	17.1375	+	19.7777i	0.904482	+	1.04383i	−0.0943510	+	0.995539i	$0.530078\pi$
$360$		0			0
$361$	−15.8329	+	3.05153i	−0.833308	+	0.160607i
$362$		0			0
$363$	−1.43985	−	5.93516i	−0.0755727	−	0.311515i
$364$		0			0
$365$	1.33979	+	2.32058i	0.0701277	+	0.121465i
$366$		0			0
$367$	−0.409871	−	8.60425i	−0.0213951	−	0.449138i	−0.983993	−	0.178205i	$-0.942971\pi$
$367$	−0.409871	−	8.60425i	−0.0213951	−	0.449138i	0.962598	−	0.270933i	$-0.0873321\pi$
$368$		0			0
$369$	2.56356	+	3.60002i	0.133454	+	0.187409i
$370$		0			0
$371$	−7.40767	+	7.06320i	−0.384587	+	0.366703i
$372$		0			0
$373$	14.6343	−	25.3473i	0.757734	−	1.31243i	−0.186270	−	0.982499i	$-0.559640\pi$
$373$	14.6343	−	25.3473i	0.757734	−	1.31243i	0.944004	−	0.329935i	$-0.107027\pi$
$374$		0			0
$375$	1.25231	−	8.70998i	0.0646688	−	0.449781i
$376$		0			0
$377$	−7.37406	+	2.16522i	−0.379783	+	0.111514i
$378$		0			0
$379$	−0.770748	+	16.1800i	−0.0395906	+	0.831110i	0.888527	+	0.458824i	$0.151729\pi$
$379$	−0.770748	+	16.1800i	−0.0395906	+	0.831110i	−0.928118	+	0.372286i	$0.878574\pi$
$380$		0			0
$381$	5.85481	+	4.60428i	0.299951	+	0.235884i
$382$		0			0
$383$	38.3856	−	3.66538i	1.96141	−	0.187292i	0.964396	−	0.264464i	$-0.0851950\pi$
$383$	38.3856	−	3.66538i	1.96141	−	0.187292i	0.997018	+	0.0771716i	$0.0245889\pi$
$384$		0			0
$385$	−2.98730	+	8.63123i	−0.152247	+	0.439888i
$386$		0			0
$387$	0.423032	−	0.926311i	0.0215039	−	0.0470870i
$388$		0			0
$389$	−19.6331	−	18.7201i	−0.995438	−	0.949148i	0.00326854	−	0.999995i	$-0.498960\pi$
$389$	−19.6331	−	18.7201i	−0.995438	−	0.949148i	−0.998706	+	0.0508465i	$0.983808\pi$
$390$		0			0
$391$	−2.23481	−	0.894683i	−0.113019	−	0.0452460i
$392$		0			0
$393$	−8.98426	−	19.6728i	−0.453196	−	0.992361i
$394$		0			0
$395$	−4.27770	−	0.408471i	−0.215234	−	0.0205524i
$396$		0			0
$397$	0.703145	+	4.89048i	0.0352898	+	0.245446i	0.999829	−	0.0184936i	$-0.00588704\pi$
$397$	0.703145	+	4.89048i	0.0352898	+	0.245446i	−0.964539	+	0.263940i	$0.914978\pi$
$398$		0			0
$399$	6.06228	+	3.89599i	0.303493	+	0.195043i
$400$		0			0
$401$	31.8465			1.59034			0.795169	−	0.606389i	$-0.207382\pi$
$401$	31.8465			1.59034			0.795169	+	0.606389i	$0.207382\pi$
$402$		0			0
$403$	−9.63592			−0.480000
$404$		0			0
$405$	0.817449	+	0.525343i	0.0406194	+	0.0261045i
$406$		0			0
$407$	0.805688	+	5.60368i	0.0399365	+	0.277764i
$408$		0			0
$409$	−28.2343	−	2.69605i	−1.39609	−	0.133311i	−0.630278	−	0.776370i	$-0.717059\pi$
$409$	−28.2343	−	2.69605i	−1.39609	−	0.133311i	−0.765817	+	0.643059i	$0.777665\pi$
$410$		0			0
$411$	−6.18728	−	13.5483i	−0.305196	−	0.668286i
$412$		0			0
$413$	26.5206	+	10.6173i	1.30499	+	0.522441i
$414$		0			0
$415$	5.94419	+	5.66778i	0.291789	+	0.278220i
$416$		0			0
$417$	−4.51827	+	9.89362i	−0.221260	+	0.484493i
$418$		0			0
$419$	−3.71888	+	10.7450i	−0.181679	+	0.524928i	−0.998661	−	0.0517359i	$-0.983525\pi$
$419$	−3.71888	+	10.7450i	−0.181679	+	0.524928i	0.816981	+	0.576664i	$0.195646\pi$
$420$		0			0
$421$	21.7329	−	2.07524i	1.05920	−	0.101141i	0.449110	−	0.893476i	$-0.351741\pi$
$421$	21.7329	−	2.07524i	1.05920	−	0.101141i	0.610086	+	0.792335i	$0.291135\pi$
$422$		0			0
$423$	1.61189	+	1.26761i	0.0783729	+	0.0616331i
$424$		0			0
$425$	0.205869	−	4.32171i	0.00998609	−	0.209634i
$426$		0			0
$427$	15.9775	−	4.69141i	0.773204	−	0.227033i
$428$		0			0
$429$	0.777610	−	5.40839i	0.0375433	−	0.261120i
$430$		0			0
$431$	−0.206034	+	0.356861i	−0.00992429	+	0.0171894i	−0.870945	−	0.491381i	$-0.836492\pi$
$431$	−0.206034	+	0.356861i	−0.00992429	+	0.0171894i	0.861021	+	0.508570i	$0.169826\pi$
$432$		0			0
$433$	−15.0312	+	14.3323i	−0.722355	+	0.688764i	−0.959183	−	0.282787i	$-0.908741\pi$
$433$	−15.0312	+	14.3323i	−0.722355	+	0.688764i	0.236827	+	0.971552i	$0.423892\pi$
$434$		0			0
$435$	1.75360	+	2.46259i	0.0840789	+	0.118072i
$436$		0			0
$437$	−0.182081	−	3.82236i	−0.00871014	−	0.182848i
$438$		0			0
$439$	−4.05568	−	7.02465i	−0.193567	−	0.335268i	0.752863	−	0.658178i	$-0.228672\pi$
$439$	−4.05568	−	7.02465i	−0.193567	−	0.335268i	−0.946430	+	0.322909i	$0.895339\pi$
$440$		0			0
$441$	2.60698	+	10.7461i	0.124142	+	0.511720i
$442$		0			0
$443$	37.6368	−	7.25390i	1.78818	−	0.344643i	0.815850	−	0.578263i	$-0.196269\pi$
$443$	37.6368	−	7.25390i	1.78818	−	0.344643i	0.972328	+	0.233620i	$0.0750572\pi$
$444$		0			0
$445$	−2.85190	−	3.29127i	−0.135193	−	0.156021i
$446$		0			0
$447$	6.66332	−	4.28226i	0.315164	−	0.202544i
$448$		0			0
$449$	21.6743	−	11.1739i	1.02287	−	0.527328i	0.136666	−	0.990617i	$-0.456361\pi$
$449$	21.6743	−	11.1739i	1.02287	−	0.527328i	0.886207	+	0.463289i	$0.153331\pi$
$450$		0			0
$451$	−9.59901	−	1.85006i	−0.452000	−	0.0871158i
$452$		0			0
$453$	0.131982	−	0.103792i	0.00620105	−	0.00487656i
$454$		0			0
$455$	6.67964	−	7.70872i	0.313146	−	0.361390i
$456$		0			0
$457$	3.05269	−	12.5834i	0.142799	−	0.588625i	−0.854774	−	0.519000i	$-0.826305\pi$
$457$	3.05269	−	12.5834i	0.142799	−	0.588625i	0.997573	−	0.0696251i	$-0.0221803\pi$
$458$		0			0
$459$	0.948187	+	0.488824i	0.0442576	+	0.0228164i
$460$		0			0
$461$	−5.92734	−	1.74042i	−0.276064	−	0.0810596i	0.140770	−	0.990042i	$-0.455042\pi$
$461$	−5.92734	−	1.74042i	−0.276064	−	0.0810596i	−0.416834	+	0.908983i	$0.636860\pi$
$462$		0			0
$463$	16.7723	−	6.71463i	0.779477	−	0.312055i	0.0524132	−	0.998625i	$-0.483309\pi$
$463$	16.7723	−	6.71463i	0.779477	−	0.312055i	0.727064	+	0.686570i	$0.240884\pi$
$464$		0			0
$465$	1.23973	+	3.58197i	0.0574911	+	0.166110i
$466$		0			0
$467$	−19.7468	+	27.7305i	−0.913772	+	1.28321i	0.0449860	+	0.998988i	$0.485676\pi$
$467$	−19.7468	+	27.7305i	−0.913772	+	1.28321i	−0.958758	+	0.284225i	$0.908264\pi$
$468$		0			0
$469$	−21.8768	+	27.0422i	−1.01018	+	1.24869i
$470$		0			0
$471$	−0.719337	+	1.01017i	−0.0331453	+	0.0465460i
$472$		0			0
$473$	0.736721	+	2.12861i	0.0338744	+	0.0978738i
$474$		0			0
$475$	6.38516	−	2.55623i	0.292971	−	0.117288i
$476$		0			0
$477$	−2.31106	−	0.678589i	−0.105816	−	0.0310705i
$478$		0			0
$479$	−20.0616	−	10.3425i	−0.916640	−	0.472561i	−0.0657094	−	0.997839i	$-0.520931\pi$
$479$	−20.0616	−	10.3425i	−0.916640	−	0.472561i	−0.850931	+	0.525278i	$0.823961\pi$
$480$		0			0
$481$	1.49056	−	6.14416i	0.0679636	−	0.280150i
$482$		0			0
$483$	6.27956	−	7.24700i	0.285730	−	0.329750i
$484$		0			0
$485$	−5.70731	+	4.48828i	−0.259156	+	0.203802i
$486$		0			0
$487$	4.95300	+	0.954613i	0.224442	+	0.0432576i	0.300232	−	0.953866i	$-0.402936\pi$
$487$	4.95300	+	0.954613i	0.224442	+	0.0432576i	−0.0757902	+	0.997124i	$0.524148\pi$
$488$		0			0
$489$	−2.36955	+	1.22159i	−0.107155	+	0.0552422i
$490$		0			0
$491$	−16.6813	+	10.7204i	−0.752814	+	0.483804i	−0.859911	−	0.510444i	$-0.829481\pi$
$491$	−16.6813	+	10.7204i	−0.752814	+	0.483804i	0.107097	+	0.994249i	$0.465845\pi$
$492$		0			0
$493$	2.17344	+	2.50829i	0.0978870	+	0.112968i
$494$		0			0
$495$	−2.11051	+	0.406767i	−0.0948604	+	0.0182828i
$496$		0			0
$497$	0.709485	+	2.92454i	0.0318248	+	0.131183i
$498$		0			0
$499$	−8.72748	−	15.1164i	−0.390696	−	0.676705i	0.601846	−	0.798612i	$-0.294432\pi$
$499$	−8.72748	−	15.1164i	−0.390696	−	0.676705i	−0.992541	+	0.121907i	$0.961099\pi$
$500$		0			0
$501$	0.107643	+	2.25970i	0.00480913	+	0.100956i
$502$		0			0
$503$	−1.84550	−	2.59165i	−0.0822870	−	0.115556i	0.771381	−	0.636374i	$-0.219566\pi$
$503$	−1.84550	−	2.59165i	−0.0822870	−	0.115556i	−0.853668	+	0.520818i	$0.825627\pi$
$504$		0			0
$505$	−7.85654	+	7.49119i	−0.349611	+	0.333354i
$506$		0			0
$507$	3.44898	−	5.97380i	0.153174	−	0.265306i
$508$		0			0
$509$	−1.40556	+	9.77591i	−0.0623005	+	0.433309i	0.934669	+	0.355519i	$0.115696\pi$
$509$	−1.40556	+	9.77591i	−0.0623005	+	0.433309i	−0.996970	+	0.0777908i	$0.975213\pi$
$510$		0			0
$511$	−11.2436	+	3.30143i	−0.497389	+	0.146047i
$512$		0			0
$513$	−0.0806897	+	1.69388i	−0.00356254	+	0.0747868i
$514$		0			0
$515$	3.52740	+	2.77397i	0.155436	+	0.122236i
$516$		0			0
$517$	−4.51530	+	0.431159i	−0.198583	+	0.0189624i
$518$		0			0
$519$	−0.0955305	+	0.276017i	−0.00419332	+	0.0121158i
$520$		0			0
$521$	7.46005	−	16.3352i	0.326831	−	0.715659i	−0.672879	−	0.739752i	$-0.734943\pi$
$521$	7.46005	−	16.3352i	0.326831	−	0.715659i	0.999710	+	0.0240933i	$0.00766987\pi$
$522$		0			0
$523$	19.1585	+	18.2676i	0.837741	+	0.798784i	0.981627	−	0.190810i	$-0.0611114\pi$
$523$	19.1585	+	18.2676i	0.837741	+	0.798784i	−0.143886	+	0.989594i	$0.545960\pi$
$524$		0			0
$525$	16.0003	+	6.40556i	0.698311	+	0.279562i
$526$		0			0
$527$	1.72866	+	3.78524i	0.0753017	+	0.164888i
$528$		0			0
$529$	17.8268	+	1.70226i	0.775079	+	0.0740111i
$530$		0			0
$531$	0.956711	+	6.65407i	0.0415177	+	0.288762i
$532$		0			0
$533$	9.18412	+	5.90228i	0.397808	+	0.255656i
$534$		0			0
$535$	18.1784			0.785920
$536$		0			0
$537$	−10.0567			−0.433979
$538$		0			0
$539$	−20.5765	−	13.2237i	−0.886291	−	0.569584i
$540$		0			0
$541$	2.88234	+	20.0471i	0.123921	+	0.861893i	0.953045	+	0.302828i	$0.0979307\pi$
$541$	2.88234	+	20.0471i	0.123921	+	0.861893i	−0.829124	+	0.559065i	$0.811160\pi$
$542$		0			0
$543$	−6.04913	−	0.577622i	−0.259593	−	0.0247881i
$544$		0			0
$545$	4.54604	+	9.95444i	0.194731	+	0.426401i
$546$		0			0
$547$	−19.4038	−	7.76810i	−0.829646	−	0.332140i	−0.0823266	−	0.996605i	$-0.526235\pi$
$547$	−19.4038	−	7.76810i	−0.829646	−	0.332140i	−0.747319	+	0.664465i	$0.768659\pi$
$548$		0			0
$549$	2.83604	+	2.70416i	0.121039	+	0.115411i
$550$		0			0
$551$	−2.19172	+	4.79920i	−0.0933705	+	0.204453i
$552$		0			0
$553$	6.14636	−	17.7587i	0.261370	−	0.755179i
$554$		0			0
$555$	−2.47574	+	0.236405i	−0.105089	+	0.0100348i
$556$		0			0
$557$	15.1851	+	11.9417i	0.643411	+	0.505984i	0.885723	−	0.464214i	$-0.153663\pi$
$557$	15.1851	+	11.9417i	0.643411	+	0.505984i	−0.242312	+	0.970198i	$0.577906\pi$
$558$		0			0
$559$	0.119694	−	2.51268i	0.00506250	−	0.106275i
$560$		0			0
$561$	−2.26406	+	0.664788i	−0.0955887	+	0.0280674i
$562$		0			0
$563$	1.00195	−	6.96868i	0.0422270	−	0.293695i	−0.957754	−	0.287587i	$-0.907147\pi$
$563$	1.00195	−	6.96868i	0.0422270	−	0.293695i	0.999981	−	0.00610752i	$-0.00194410\pi$
$564$		0			0
$565$	−3.87567	+	6.71286i	−0.163051	+	0.282412i
$566$		0			0
$567$	−3.07547	+	2.93246i	−0.129158	+	0.123152i
$568$		0			0
$569$	8.89072	+	12.4853i	0.372718	+	0.523410i	0.957750	−	0.287600i	$-0.0928575\pi$
$569$	8.89072	+	12.4853i	0.372718	+	0.523410i	−0.585032	+	0.811010i	$0.698918\pi$
$570$		0			0
$571$	−1.78755	−	37.5253i	−0.0748066	−	1.57038i	−0.654825	−	0.755781i	$-0.727258\pi$
$571$	−1.78755	−	37.5253i	−0.0748066	−	1.57038i	0.580018	−	0.814604i	$-0.303046\pi$
$572$		0			0
$573$	1.07208	+	1.85689i	0.0447867	+	0.0775728i
$574$		0			0
$575$	−2.15770	−	8.89417i	−0.0899824	−	0.370913i
$576$		0			0
$577$	−9.46473	+	1.82418i	−0.394022	+	0.0759415i	−0.382414	−	0.923991i	$-0.624907\pi$
$577$	−9.46473	+	1.82418i	−0.394022	+	0.0759415i	−0.0116079	+	0.999933i	$0.503695\pi$
$578$		0			0
$579$	−10.3321	−	11.9239i	−0.429388	−	0.495540i
$580$		0			0
$581$	−30.2162	+	19.4188i	−1.25358	+	0.805627i
$582$		0			0
$583$	4.73549	−	2.44131i	0.196124	−	0.101109i
$584$		0			0
$585$	2.35696	+	0.454266i	0.0974481	+	0.0187816i
$586$		0			0
$587$	1.07237	−	0.843319i	0.0442614	−	0.0348075i	−0.595783	−	0.803145i	$-0.703158\pi$
$587$	1.07237	−	0.843319i	0.0442614	−	0.0348075i	0.640045	+	0.768338i	$0.278916\pi$
$588$		0			0
$589$	−4.33192	+	4.99930i	−0.178494	+	0.205993i
$590$		0			0
$591$	6.39773	−	26.3718i	0.263168	−	1.08479i
$592$		0			0
$593$	30.6995	+	15.8267i	1.26068	+	0.649925i	0.953404	−	0.301696i	$-0.0975527\pi$
$593$	30.6995	+	15.8267i	1.26068	+	0.649925i	0.307274	+	0.951621i	$0.400583\pi$
$594$		0			0
$595$	−4.22650	−	1.24101i	−0.173270	−	0.0508765i
$596$		0			0
$597$	14.0488	−	5.62431i	0.574981	−	0.230188i
$598$		0			0
$599$	−2.36893	−	6.84457i	−0.0967919	−	0.279662i	0.886202	−	0.463298i	$-0.153334\pi$
$599$	−2.36893	−	6.84457i	−0.0967919	−	0.279662i	−0.982994	+	0.183637i	$0.941213\pi$
$600$		0			0
$601$	−16.5031	+	23.1754i	−0.673177	+	0.945345i	0.326823	+	0.945086i	$0.394022\pi$
$601$	−16.5031	+	23.1754i	−0.673177	+	0.945345i	−1.00000		0.000259067i	$0.999918\pi$
$602$		0			0
$603$	−8.08519	−	1.27658i	−0.329255	−	0.0519862i
$604$		0			0
$605$	−3.44235	+	4.83410i	−0.139951	+	0.196534i
$606$		0			0
$607$	−3.56280	−	10.2940i	−0.144609	−	0.417821i	0.849315	−	0.527886i	$-0.177015\pi$
$607$	−3.56280	−	10.2940i	−0.144609	−	0.417821i	−0.993924	+	0.110065i	$0.964894\pi$
$608$		0			0
$609$	−12.2738	+	4.91370i	−0.497361	+	0.199113i
$610$		0			0
$611$	4.86031	+	1.42712i	0.196627	+	0.0577349i
$612$		0			0
$613$	15.1879	+	7.82991i	0.613434	+	0.316247i	0.736796	−	0.676115i	$-0.236338\pi$
$613$	15.1879	+	7.82991i	0.613434	+	0.316247i	−0.123363	+	0.992362i	$0.539368\pi$
$614$		0			0
$615$	1.01245	−	4.17339i	0.0408260	−	0.168287i
$616$		0			0
$617$	−13.3986	+	15.4629i	−0.539409	+	0.622511i	−0.958383	−	0.285487i	$-0.907845\pi$
$617$	−13.3986	+	15.4629i	−0.539409	+	0.622511i	0.418973	+	0.907998i	$0.362390\pi$
$618$		0			0
$619$	−35.6325	+	28.0217i	−1.43219	+	1.12629i	−0.461163	+	0.887315i	$0.652568\pi$
$619$	−35.6325	+	28.0217i	−1.43219	+	1.12629i	−0.971027	+	0.238971i	$0.923190\pi$
$620$		0			0
$621$	2.21579	+	0.427058i	0.0889164	+	0.0171372i
$622$		0			0
$623$	16.9280	−	8.72699i	0.678206	−	0.349640i
$624$		0			0
$625$	9.86657	−	6.34086i	0.394663	−	0.253634i
$626$		0			0
$627$	−2.45640	−	2.83483i	−0.0980991	−	0.113212i
$628$		0			0
$629$	−2.68099	+	0.516719i	−0.106898	+	0.0206029i
$630$		0			0
$631$	−5.79623	−	23.8924i	−0.230744	−	0.951140i	−0.962869	−	0.269970i	$-0.912986\pi$
$631$	−5.79623	−	23.8924i	−0.230744	−	0.951140i	0.732125	−	0.681171i	$-0.238529\pi$
$632$		0			0
$633$	−5.55925	−	9.62891i	−0.220961	−	0.382715i
$634$		0			0
$635$	−0.344379	−	7.22941i	−0.0136663	−	0.286890i
$636$		0			0
$637$	15.8445	+	22.2505i	0.627782	+	0.881596i
$638$		0			0
$639$	−0.512532	+	0.488699i	−0.0202755	+	0.0193326i
$640$		0			0
$641$	−0.891953	+	1.54491i	−0.0352300	+	0.0610202i	−0.883103	−	0.469180i	$-0.844550\pi$
$641$	−0.891953	+	1.54491i	−0.0352300	+	0.0610202i	0.847873	+	0.530200i	$0.177883\pi$
$642$		0			0
$643$	5.96151	−	41.4632i	0.235099	−	1.63515i	−0.440410	−	0.897797i	$-0.645167\pi$
$643$	5.96151	−	41.4632i	0.235099	−	1.63515i	0.675509	−	0.737352i	$-0.263924\pi$
$644$		0			0
$645$	−0.949438	+	0.278780i	−0.0373841	+	0.0109770i
$646$		0			0
$647$	0.524459	−	11.0098i	0.0206186	−	0.432838i	−0.964831	−	0.262871i	$-0.915331\pi$
$647$	0.524459	−	11.0098i	0.0206186	−	0.432838i	0.985450	−	0.169967i	$-0.0543663\pi$
$648$		0			0
$649$	−11.6884	−	9.19188i	−0.458811	−	0.360813i
$650$		0			0
$651$	−16.5013	+	1.57568i	−0.646736	+	0.0617558i
$652$		0			0
$653$	2.47318	−	7.14577i	0.0967828	−	0.279636i	−0.886209	−	0.463286i	$-0.846670\pi$
$653$	2.47318	−	7.14577i	0.0967828	−	0.279636i	0.982992	+	0.183650i	$0.0587915\pi$
$654$		0			0
$655$	−8.73004	+	19.1161i	−0.341111	+	0.746929i
$656$		0			0
$657$	−1.99577	−	1.90297i	−0.0778625	−	0.0742417i
$658$		0			0
$659$	3.83279	+	1.53442i	0.149304	+	0.0597724i	0.445111	−	0.895475i	$-0.353164\pi$
$659$	3.83279	+	1.53442i	0.149304	+	0.0597724i	−0.295807	+	0.955248i	$0.595588\pi$
$660$		0			0
$661$	−10.9957	−	24.0773i	−0.427684	−	0.936497i	−0.993697	−	0.112101i	$-0.964242\pi$
$661$	−10.9957	−	24.0773i	−0.427684	−	0.936497i	0.566013	−	0.824396i	$-0.308485\pi$
$662$		0			0
$663$	2.62325	+	0.250490i	0.101878	+	0.00972821i
$664$		0			0
$665$	−0.996536	−	6.93106i	−0.0386440	−	0.268775i
$666$		0			0
$667$	5.90612	+	3.79563i	0.228686	+	0.146967i
$668$		0			0
$669$	−12.3311			−0.476748
$670$		0			0
$671$	−8.66777			−0.334615
$672$		0			0
$673$	12.3770	+	7.95420i	0.477097	+	0.306612i	0.756998	−	0.653417i	$-0.226665\pi$
$673$	12.3770	+	7.95420i	0.477097	+	0.306612i	−0.279901	+	0.960029i	$0.590302\pi$
$674$		0			0
$675$	0.577199	+	4.01451i	0.0222164	+	0.154519i
$676$		0			0
$677$	−12.6847	−	1.21124i	−0.487512	−	0.0465518i	−0.151594	−	0.988443i	$-0.548441\pi$
$677$	−12.6847	−	1.21124i	−0.487512	−	0.0465518i	−0.335918	+	0.941891i	$0.609047\pi$
$678$		0			0
$679$	−13.1905	−	28.8831i	−0.506204	−	1.10843i
$680$		0			0
$681$	−22.2398	−	8.90347i	−0.852231	−	0.341182i
$682$		0			0
$683$	7.69941	+	7.34137i	0.294610	+	0.280910i	0.822939	−	0.568130i	$-0.192333\pi$
$683$	7.69941	+	7.34137i	0.294610	+	0.280910i	−0.528329	+	0.849040i	$0.677181\pi$
$684$		0			0
$685$	−6.01220	+	13.1649i	−0.229714	+	0.503004i
$686$		0			0
$687$	−4.93585	+	14.2612i	−0.188315	+	0.544099i
$688$		0			0
$689$	−5.92293	+	0.565571i	−0.225646	+	0.0215465i
$690$		0			0
$691$	−15.5029	−	12.1916i	−0.589760	−	0.463792i	0.278134	−	0.960542i	$-0.410284\pi$
$691$	−15.5029	−	12.1916i	−0.589760	−	0.463792i	−0.867894	+	0.496750i	$0.834527\pi$
$692$		0			0
$693$	0.447248	−	9.38889i	0.0169895	−	0.356654i
$694$		0			0
$695$	10.1406	−	2.97756i	0.384656	−	0.112945i
$696$		0			0
$697$	0.670958	−	4.66662i	0.0254144	−	0.176761i
$698$		0			0
$699$	−6.97951	+	12.0889i	−0.263989	+	0.457243i
$700$		0			0
$701$	−15.7575	+	15.0248i	−0.595153	+	0.567477i	−0.926625	−	0.375988i	$-0.877303\pi$
$701$	−15.7575	+	15.0248i	−0.595153	+	0.567477i	0.331472	+	0.943465i	$0.392455\pi$
$702$		0			0
$703$	−2.51762	−	3.53550i	−0.0949537	−	0.133344i
$704$		0			0
$705$	−0.0948113	−	1.99033i	−0.00357080	−	0.0749603i
$706$		0			0
$707$	−23.7368	−	41.1133i	−0.892712	−	1.54622i
$708$		0			0
$709$	4.03645	+	16.6385i	0.151592	+	0.624871i	0.996014	+	0.0891927i	$0.0284287\pi$
$709$	4.03645	+	16.6385i	0.151592	+	0.624871i	−0.844422	+	0.535678i	$0.820056\pi$
$710$		0			0
$711$	4.34238	−	0.836924i	0.162852	−	0.0313871i
$712$		0			0
$713$	5.76438	+	6.65245i	0.215878	+	0.249136i
$714$		0			0
$715$	−4.46655	+	2.87048i	−0.167039	+	0.107350i
$716$		0			0
$717$	−13.3980	+	6.90713i	−0.500356	+	0.257951i
$718$		0			0
$719$	−35.5847	−	6.85839i	−1.32708	−	0.255775i	−0.524040	−	0.851694i	$-0.675576\pi$
$719$	−35.5847	−	6.85839i	−1.32708	−	0.255775i	−0.803045	+	0.595919i	$0.796788\pi$
$720$		0			0
$721$	−15.4260	+	12.1311i	−0.574494	+	0.451787i
$722$		0			0
$723$	−6.59067	+	7.60604i	−0.245110	+	0.282872i
$724$		0			0
$725$	−2.97489	+	12.2627i	−0.110485	+	0.455424i
$726$		0			0
$727$	−1.37277	−	0.707712i	−0.0509132	−	0.0262476i	0.432582	−	0.901595i	$-0.357603\pi$
$727$	−1.37277	−	0.707712i	−0.0509132	−	0.0262476i	−0.483495	+	0.875347i	$0.660633\pi$
$728$		0			0
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$		0			0
$731$	−1.00852	+	0.403750i	−0.0373014	+	0.0149332i
$732$		0			0
$733$	−15.6348	−	45.1738i	−0.577484	−	1.66853i	−0.732620	−	0.680638i	$-0.761703\pi$
$733$	−15.6348	−	45.1738i	−0.577484	−	1.66853i	0.155136	−	0.987893i	$-0.450418\pi$
$734$		0			0
$735$	6.23267	−	8.75256i	0.229896	−	0.322843i
$736$		0			0
$737$	14.8918	−	10.2977i	0.548548	−	0.379322i
$738$		0			0
$739$	−11.6331	+	16.3365i	−0.427932	+	0.600946i	−0.971099	−	0.238679i	$-0.923286\pi$
$739$	−11.6331	+	16.3365i	−0.427932	+	0.600946i	0.543167	+	0.839625i	$0.317225\pi$
$740$		0			0
$741$	1.37010	+	3.95864i	0.0503318	+	0.145424i
$742$		0			0
$743$	37.9008	−	15.1732i	1.39044	−	0.556650i	0.448913	−	0.893576i	$-0.351811\pi$
$743$	37.9008	−	15.1732i	1.39044	−	0.556650i	0.941531	+	0.336926i	$0.109387\pi$
$744$		0			0
$745$	−7.38481	−	2.16838i	−0.270559	−	0.0794432i
$746$		0			0
$747$	−7.51280	−	3.87312i	−0.274879	−	0.141710i
$748$		0			0
$749$	−18.7423	+	77.2567i	−0.684828	+	2.82290i
$750$		0			0
$751$	28.8351	−	33.2775i	1.05221	−	1.21431i	0.0760830	−	0.997101i	$-0.475759\pi$
$751$	28.8351	−	33.2775i	1.05221	−	1.21431i	0.976125	−	0.217211i	$-0.0696960\pi$
$752$		0			0
$753$	−8.85797	+	6.96598i	−0.322802	+	0.253855i
$754$		0			0
$755$	−0.160205	−	0.0308770i	−0.00583046	−	0.00112373i
$756$		0			0
$757$	−32.5301	+	16.7704i	−1.18233	+	0.609531i	−0.933346	−	0.358978i	$-0.883125\pi$
$757$	−32.5301	+	16.7704i	−1.18233	+	0.609531i	−0.248979	+	0.968509i	$0.580095\pi$
$758$		0			0
$759$	−4.19902	+	2.69855i	−0.152415	+	0.0979511i
$760$		0			0
$761$	35.1774	+	40.5968i	1.27518	+	1.47163i	0.810015	+	0.586409i	$0.199459\pi$
$761$	35.1774	+	40.5968i	1.27518	+	1.47163i	0.465163	+	0.885225i	$0.345996\pi$
$762$		0			0
$763$	−46.9927	+	9.05709i	−1.70125	+	0.327889i
$764$		0			0
$765$	−0.244385	−	1.00737i	−0.00883576	−	0.0364215i
$766$		0			0
$767$	8.30306	+	14.3813i	0.299806	+	0.519280i
$768$		0			0
$769$	−1.70671	−	35.8283i	−0.0615457	−	1.29200i	−0.792625	−	0.609710i	$-0.791286\pi$
$769$	−1.70671	−	35.8283i	−0.0615457	−	1.29200i	0.731079	−	0.682293i	$-0.239017\pi$
$770$		0			0
$771$	−13.6095	−	19.1118i	−0.490132	−	0.688295i
$772$		0			0
$773$	−20.6397	+	19.6799i	−0.742360	+	0.707838i	−0.963590	−	0.267383i	$-0.913841\pi$
$773$	−20.6397	+	19.6799i	−0.742360	+	0.707838i	0.221231	+	0.975221i	$0.428993\pi$
$774$		0			0
$775$	−7.91045	+	13.7013i	−0.284152	+	0.492165i
$776$		0			0
$777$	1.54784	−	10.7655i	0.0555284	−	0.386209i
$778$		0			0
$779$	7.19102	−	2.11148i	0.257645	−	0.0756515i
$780$		0			0
$781$	0.0745346	−	1.56467i	0.00266706	−	0.0559884i
$782$		0			0
$783$	−2.44556	−	1.92321i	−0.0873973	−	0.0687300i
$784$		0			0
$785$	1.19957	−	0.114545i	0.0428144	−	0.00408828i
$786$		0			0
$787$	−2.66230	+	7.69222i	−0.0949009	+	0.274198i	−0.982453	−	0.186509i	$-0.940283\pi$
$787$	−2.66230	+	7.69222i	−0.0949009	+	0.274198i	0.887552	+	0.460707i	$0.152404\pi$
$788$		0			0
$789$	−2.41344	+	5.28469i	−0.0859207	+	0.188140i
$790$		0			0
$791$	−24.5333	−	23.3924i	−0.872302	−	0.831738i
$792$		0			0
$793$	8.98652	+	3.59766i	0.319121	+	0.127757i
$794$		0			0
$795$	0.972268	+	2.12897i	0.0344828	+	0.0755068i
$796$		0			0
$797$	3.76784	+	0.359785i	0.133464	+	0.0127442i	0.161574	−	0.986861i	$-0.448343\pi$
$797$	3.76784	+	0.359785i	0.133464	+	0.0127442i	−0.0281104	+	0.999605i	$0.508949\pi$
$798$		0			0
$799$	−0.311320	−	2.16528i	−0.0110137	−	0.0766020i
$800$		0			0
$801$	3.77032	+	2.42304i	0.133218	+	0.0856139i
$802$		0			0
$803$	6.09966			0.215252
$804$		0			0
$805$	−9.31782			−0.328410
$806$		0			0
$807$	6.94986	+	4.46640i	0.244647	+	0.157225i
$808$		0			0
$809$	0.767170	+	5.33578i	0.0269723	+	0.187596i	0.998853	−	0.0478763i	$-0.0152453\pi$
$809$	0.767170	+	5.33578i	0.0269723	+	0.187596i	−0.971881	+	0.235472i	$0.924336\pi$
$810$		0			0
$811$	4.68196	+	0.447073i	0.164406	+	0.0156988i	0.176934	−	0.984223i	$-0.443382\pi$
$811$	4.68196	+	0.447073i	0.164406	+	0.0156988i	−0.0125285	+	0.999922i	$0.503988\pi$
$812$		0			0
$813$	−10.3767	−	22.7218i	−0.363927	−	0.796890i
$814$		0			0
$815$	2.40491	+	0.962781i	0.0842403	+	0.0337247i
$816$		0			0
$817$	−1.24982	−	1.19170i	−0.0437255	−	0.0416922i
$818$		0			0
$819$	−4.36066	+	9.54852i	−0.152374	+	0.333652i
$820$		0			0
$821$	12.0533	−	34.8258i	0.420664	−	1.21543i	−0.513345	−	0.858182i	$-0.671594\pi$
$821$	12.0533	−	34.8258i	0.420664	−	1.21543i	0.934010	−	0.357248i	$-0.116285\pi$
$822$		0			0
$823$	25.1258	−	2.39923i	0.875831	−	0.0836318i	0.352551	−	0.935792i	$-0.385314\pi$
$823$	25.1258	−	2.39923i	0.875831	−	0.0836318i	0.523280	+	0.852161i	$0.324708\pi$
$824$		0			0
$825$	−7.05182	−	5.54561i	−0.245513	−	0.193073i
$826$		0			0
$827$	−2.16757	+	45.5028i	−0.0753736	+	1.58229i	0.572090	+	0.820191i	$0.306133\pi$
$827$	−2.16757	+	45.5028i	−0.0753736	+	1.58229i	−0.647463	+	0.762097i	$0.724170\pi$
$828$		0			0
$829$	−2.01631	+	0.592042i	−0.0700294	+	0.0205625i	−0.316560	−	0.948573i	$-0.602528\pi$
$829$	−2.01631	+	0.592042i	−0.0700294	+	0.0205625i	0.246530	+	0.969135i	$0.420710\pi$
$830$		0			0
$831$	0.857006	−	5.96060i	0.0297292	−	0.206771i
$832$		0			0
$833$	5.89810	−	10.2158i	0.204357	−	0.353957i
$834$		0			0
$835$	1.59095	−	1.51697i	0.0550571	−	0.0524968i
$836$		0			0
$837$	−2.26270	−	3.17751i	−0.0782102	−	0.109831i
$838$		0			0
$839$	−0.977497	−	20.5202i	−0.0337469	−	0.708435i	−0.950825	−	0.309728i	$-0.899762\pi$
$839$	−0.977497	−	20.5202i	−0.0337469	−	0.708435i	0.917078	−	0.398707i	$-0.130541\pi$
$840$		0			0
$841$	9.66023	+	16.7320i	0.333112	+	0.576966i
$842$		0			0
$843$	3.50398	+	14.4436i	0.120684	+	0.497465i
$844$		0			0
$845$	−6.58164	+	1.26851i	−0.226415	+	0.0436380i
$846$		0			0
$847$	−16.9954	−	19.6138i	−0.583970	−	0.673937i
$848$		0			0
$849$	21.2594	−	13.6626i	0.729621	−	0.468899i
$850$		0			0
$851$	−5.13348	+	2.64649i	−0.175974	+	0.0907207i
$852$		0			0
$853$	46.6304	+	8.98727i	1.59659	+	0.307718i	0.908494	−	0.417897i	$-0.137233\pi$
$853$	46.6304	+	8.98727i	1.59659	+	0.307718i	0.688100	+	0.725616i	$0.258445\pi$
$854$		0			0
$855$	1.29527	−	1.01861i	0.0442974	−	0.0348359i
$856$		0			0
$857$	24.1971	−	27.9250i	0.826558	−	0.953899i	−0.172960	−	0.984929i	$-0.555333\pi$
$857$	24.1971	−	27.9250i	0.826558	−	0.953899i	0.999518	+	0.0310300i	$0.00987873\pi$
$858$		0			0
$859$	9.27212	−	38.2202i	0.316361	−	1.30406i	−0.562428	−	0.826846i	$-0.690133\pi$
$859$	9.27212	−	38.2202i	0.316361	−	1.30406i	0.878789	−	0.477211i	$-0.158352\pi$
$860$		0			0
$861$	16.6927	+	8.60570i	0.568886	+	0.293281i
$862$		0			0
$863$	42.9166	+	12.6014i	1.46090	+	0.428958i	0.913128	−	0.407672i	$-0.133659\pi$
$863$	42.9166	+	12.6014i	1.46090	+	0.428958i	0.547768	+	0.836630i	$0.315478\pi$
$864$		0			0
$865$	0.263486	−	0.105484i	0.00895880	−	0.00358656i
$866$		0			0
$867$	5.18795	+	14.9896i	0.176192	+	0.509073i
$868$		0			0
$869$	−5.67403	+	7.96806i	−0.192478	+	0.270298i
$870$		0			0
$871$	−19.7137	+	4.49540i	−0.667972	+	0.152321i
$872$		0			0
$873$	4.33427	−	6.08664i	0.146693	−	0.206001i
$874$		0			0
$875$	−12.2301	−	35.3366i	−0.413454	−	1.19460i
$876$		0			0
$877$	−13.3216	+	5.33315i	−0.449837	+	0.180088i	−0.585508	−	0.810666i	$-0.699105\pi$
$877$	−13.3216	+	5.33315i	−0.449837	+	0.180088i	0.135671	+	0.990754i	$0.456681\pi$
$878$		0			0
$879$	28.5379	+	8.37948i	0.962559	+	0.282633i
$880$		0			0
$881$	−9.80887	−	5.05682i	−0.330469	−	0.170369i	0.285004	−	0.958526i	$-0.408005\pi$
$881$	−9.80887	−	5.05682i	−0.330469	−	0.170369i	−0.615474	+	0.788157i	$0.711035\pi$
$882$		0			0
$883$	−10.8327	+	44.6531i	−0.364551	+	1.50270i	0.434079	+	0.900875i	$0.357074\pi$
$883$	−10.8327	+	44.6531i	−0.364551	+	1.50270i	−0.798629	+	0.601823i	$0.794441\pi$
$884$		0			0
$885$	4.27773	−	4.93676i	0.143794	−	0.165947i
$886$		0			0
$887$	−6.95419	+	5.46883i	−0.233499	+	0.183625i	−0.728052	−	0.685522i	$-0.759574\pi$
$887$	−6.95419	+	5.46883i	−0.233499	+	0.183625i	0.494553	+	0.869147i	$0.335332\pi$
$888$		0			0
$889$	31.0795	+	5.99008i	1.04237	+	0.200901i
$890$		0			0
$891$	1.96605	−	1.01357i	0.0658652	−	0.0339559i
$892$		0			0
$893$	2.92541	−	1.88005i	0.0978952	−	0.0629134i
$894$		0			0
$895$	6.39939	+	7.38529i	0.213908	+	0.246863i
$896$		0			0
$897$	5.47350	−	1.05493i	0.182755	−	0.0352231i
$898$		0			0
$899$	−2.86122	−	11.7941i	−0.0954270	−	0.393355i
$900$		0			0
$901$	1.28473	+	2.22522i	0.0428006	+	0.0741328i
$902$		0			0
$903$	−0.205904	−	4.32247i	−0.00685207	−	0.143843i
$904$		0			0
$905$	3.42506	+	4.80982i	0.113853	+	0.159884i
$906$		0			0
$907$	0.162077	−	0.154540i	0.00538168	−	0.00513142i	−0.687383	−	0.726295i	$-0.741241\pi$
$907$	0.162077	−	0.154540i	0.00538168	−	0.00513142i	0.692765	+	0.721163i	$0.256392\pi$
$908$		0			0
$909$	5.58584	−	9.67496i	0.185271	−	0.320898i
$910$		0			0
$911$	−0.0569818	+	0.396317i	−0.00188789	+	0.0131306i	−0.990744	−	0.135746i	$-0.956657\pi$
$911$	−0.0569818	+	0.396317i	−0.00188789	+	0.0131306i	0.988856	+	0.148877i	$0.0475658\pi$
$912$		0			0
$913$	17.9389	−	5.26734i	0.593691	−	0.174323i
$914$		0			0
$915$	0.181180	−	3.80343i	0.00598961	−	0.125737i
$916$		0			0
$917$	−72.2412	−	56.8111i	−2.38561	−	1.87607i
$918$		0			0
$919$	0.0475885	−	0.00454415i	0.00156980	−	0.000149898i	−0.0942711	−	0.995547i	$-0.530052\pi$
$919$	0.0475885	−	0.00454415i	0.00156980	−	0.000149898i	0.0958409	+	0.995397i	$0.469446\pi$
$920$		0			0
$921$	−7.27705	+	21.0257i	−0.239787	+	0.692819i
$922$		0			0
$923$	−0.726712	+	1.59128i	−0.0239200	+	0.0523775i
$924$		0			0
$925$	−7.51273	−	7.16337i	−0.247017	−	0.235530i
$926$		0			0
$927$	−4.28735	−	1.71639i	−0.140815	−	0.0563738i
$928$		0			0
$929$	−0.148286	−	0.324701i	−0.00486511	−	0.0106531i	0.907184	−	0.420734i	$-0.138228\pi$
$929$	−0.148286	−	0.324701i	−0.00486511	−	0.0106531i	−0.912049	+	0.410081i	$0.865500\pi$
$930$		0			0
$931$	18.6670	+	1.78248i	0.611787	+	0.0584186i
$932$		0			0
$933$	4.48999	+	31.2286i	0.146996	+	1.02238i
$934$		0			0
$935$	1.92889	+	1.23962i	0.0630814	+	0.0405399i
$936$		0			0
$937$	−19.9664			−0.652273			−0.326137	−	0.945323i	$-0.605747\pi$
$937$	−19.9664			−0.652273			−0.326137	+	0.945323i	$0.605747\pi$
$938$		0			0
$939$	11.1149			0.362722
$940$		0			0
$941$	−8.79777	−	5.65398i	−0.286799	−	0.184315i	0.389329	−	0.921099i	$-0.372707\pi$
$941$	−8.79777	−	5.65398i	−0.286799	−	0.184315i	−0.676128	+	0.736784i	$0.736343\pi$
$942$		0			0
$943$	−1.41929	−	9.87137i	−0.0462184	−	0.321456i
$944$		0			0
$945$	4.11051	+	0.392506i	0.133715	+	0.0127682i
$946$		0			0
$947$	17.1862	+	37.6325i	0.558477	+	1.22289i	0.952710	+	0.303883i	$0.0982830\pi$
$947$	17.1862	+	37.6325i	0.558477	+	1.22289i	−0.394233	+	0.919011i	$0.628990\pi$
$948$		0			0
$949$	−6.32397	−	2.53174i	−0.205285	−	0.0821836i
$950$		0			0
$951$	0.767313	+	0.731632i	0.0248818	+	0.0237248i
$952$		0			0
$953$	5.53430	−	12.1184i	0.179274	−	0.392554i	−0.798567	−	0.601906i	$-0.794408\pi$
$953$	5.53430	−	12.1184i	0.179274	−	0.392554i	0.977840	+	0.209352i	$0.0671354\pi$
$954$		0			0
$955$	0.681440	−	1.96889i	0.0220509	−	0.0637119i
$956$		0			0
$957$	6.85062	−	0.654155i	0.221449	−	0.0211458i
$958$		0			0
$959$	−49.7511	−	39.1247i	−1.60655	−	1.26340i
$960$		0			0
$961$	−0.751015	+	15.7657i	−0.0242263	+	0.508572i
$962$		0			0
$963$	−17.9499	+	5.27058i	−0.578429	+	0.169842i
$964$		0			0
$965$	−2.18185	+	15.1751i	−0.0702362	+	0.488503i
$966$		0			0
$967$	0.431400	−	0.747207i	0.0138729	−	0.0240286i	−0.859006	−	0.511966i	$-0.828917\pi$
$967$	0.431400	−	0.747207i	0.0138729	−	0.0240286i	0.872879	+	0.487938i	$0.162251\pi$
$968$		0			0
$969$	1.30926	−	1.24838i	0.0420596	−	0.0401038i
$970$		0			0
$971$	−1.20905	−	1.69787i	−0.0388001	−	0.0544872i	0.794720	−	0.606976i	$-0.207618\pi$
$971$	−1.20905	−	1.69787i	−0.0388001	−	0.0544872i	−0.833520	+	0.552489i	$0.813678\pi$
$972$		0			0
$973$	2.19920	+	46.1668i	0.0705030	+	1.48004i
$974$		0			0
$975$	5.00937	+	8.67649i	0.160428	+	0.277870i
$976$		0			0
$977$	−11.7282	−	48.3443i	−0.375218	−	1.54667i	−0.776141	−	0.630559i	$-0.782826\pi$
$977$	−11.7282	−	48.3443i	−0.375218	−	1.54667i	0.400923	−	0.916112i	$-0.368690\pi$
$978$		0			0
$979$	−9.73431	+	1.87613i	−0.311110	+	0.0599615i
$980$		0			0
$981$	−7.37507	−	8.51129i	−0.235468	−	0.271744i
$982$		0			0
$983$	−44.0463	+	28.3069i	−1.40486	+	0.902849i	−0.999934	−	0.0115008i	$-0.996339\pi$
$983$	−44.0463	+	28.3069i	−1.40486	+	0.902849i	−0.404926	+	0.914349i	$0.632703\pi$
$984$		0			0
$985$	−23.4376	+	12.0829i	−0.746784	+	0.384994i
$986$		0			0
$987$	8.55652	+	1.64913i	0.272357	+	0.0524925i
$988$		0			0
$989$	−1.80630	+	1.42049i	−0.0574371	+	0.0451690i
$990$		0			0
$991$	−6.09225	+	7.03084i	−0.193527	+	0.223342i	−0.844217	−	0.536001i	$-0.819934\pi$
$991$	−6.09225	+	7.03084i	−0.193527	+	0.223342i	0.650690	+	0.759343i	$0.274480\pi$
$992$		0			0
$993$	0.145900	−	0.601407i	0.00462999	−	0.0190851i
$994$		0			0
$995$	−13.0700	−	6.73806i	−0.414347	−	0.213611i
$996$		0			0
$997$	27.0726	+	7.94924i	0.857399	+	0.251755i	0.680747	−	0.732518i	$-0.261655\pi$
$997$	27.0726	+	7.94924i	0.857399	+	0.251755i	0.176652	+	0.984273i	$0.443473\pi$
$998$		0			0
$999$	2.37609	−	0.951243i	0.0751762	−	0.0300960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.49.3	✓	100
67.26	even	33	inner	804.2.y.a.361.3	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.49.3	✓	100	1.1	even	1	trivial
804.2.y.a.361.3	yes	100	67.26	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{3} +(-0.138288 - 0.961813i) q^{5} +(4.23021 + 0.403936i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{3} +(-0.138288 - 0.961813i) q^{5} +(4.23021 + 0.403936i) q^{7} +(0.415415 + 0.909632i) q^{9} +(-2.05350 - 0.822096i) q^{11} +(1.78779 + 1.70466i) q^{13} +(0.403660 - 0.883893i) q^{15} +(0.348908 - 1.00810i) q^{17} +(1.68813 - 0.161197i) q^{19} +(3.34029 + 2.62684i) q^{21} +(0.107372 - 2.25401i) q^{23} +(3.89150 - 1.14265i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(-1.55560 + 2.69437i) q^{29} +(-2.82315 + 2.69187i) q^{31} +(-1.28305 - 1.80179i) q^{33} +(-0.196476 - 4.12453i) q^{35} +(-1.27971 - 2.21653i) q^{37} +(0.582379 + 2.40060i) q^{39} +(4.33963 - 0.836395i) q^{41} +(-0.666868 - 0.769607i) q^{43} +(0.817449 - 0.525343i) q^{45} +(1.82266 - 0.939646i) q^{47} +(10.8580 + 2.09271i) q^{49} +(0.838541 - 0.659436i) q^{51} +(-1.57732 + 1.82032i) q^{53} +(-0.506729 + 2.08876i) q^{55} +(1.50729 + 0.777063i) q^{57} +(6.45019 + 1.89395i) q^{59} +(3.63792 - 1.45641i) q^{61} +(1.38986 + 4.01573i) q^{63} +(1.39233 - 1.95525i) q^{65} +(-4.51993 + 6.82424i) q^{67} +(1.30894 - 1.83814i) q^{69} +(0.231622 + 0.669229i) q^{71} +(-2.56007 + 1.02490i) q^{73} +(3.89150 + 1.14265i) q^{75} +(-8.35464 - 4.30712i) q^{77} +(1.04259 - 4.29763i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-6.64404 + 5.22493i) q^{83} +(-1.01786 - 0.196176i) q^{85} +(-2.76534 + 1.42563i) q^{87} +(3.77032 - 2.42304i) q^{89} +(6.87416 + 7.93320i) q^{91} +(-3.83032 + 0.738235i) q^{93} +(-0.388488 - 1.60137i) q^{95} +(-3.73608 - 6.47107i) q^{97} +(-0.105248 - 2.20944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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