LMFDB - Embedded newform 804.2.bd.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, 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:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	804.23
Dual form			804.2.bd.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41084 + 0.0976039i) q^{2} +(0.479660 - 1.66431i) q^{3} +(1.98095 - 0.275407i) q^{4} +(2.88456 - 1.31734i) q^{5} +(-0.514280 + 2.39489i) q^{6} +(1.85789 + 1.94850i) q^{7} +(-2.76792 + 0.581904i) q^{8} +(-2.53985 - 1.59660i) q^{9} +O(q^{10})$	\(q+(-1.41084 + 0.0976039i) q^{2} +(0.479660 - 1.66431i) q^{3} +(1.98095 - 0.275407i) q^{4} +(2.88456 - 1.31734i) q^{5} +(-0.514280 + 2.39489i) q^{6} +(1.85789 + 1.94850i) q^{7} +(-2.76792 + 0.581904i) q^{8} +(-2.53985 - 1.59660i) q^{9} +(-3.94108 + 2.14010i) q^{10} +(-0.725043 - 0.0692332i) q^{11} +(0.491817 - 3.42901i) q^{12} +(-0.625573 - 0.120569i) q^{13} +(-2.81137 - 2.56768i) q^{14} +(-0.808847 - 5.43268i) q^{15} +(3.84830 - 1.09113i) q^{16} +(2.55706 - 4.96000i) q^{17} +(3.73917 + 2.00466i) q^{18} +(0.463180 - 0.485769i) q^{19} +(5.35136 - 3.40400i) q^{20} +(4.13406 - 2.15749i) q^{21} +(1.02968 + 0.0269101i) q^{22} +(3.17927 - 1.27279i) q^{23} +(-0.359191 + 4.88579i) q^{24} +(3.31103 - 3.82113i) q^{25} +(0.894353 + 0.109046i) q^{26} +(-3.87551 + 3.46128i) q^{27} +(4.21701 + 3.34819i) q^{28} +(-2.31618 - 1.33725i) q^{29} +(1.67141 + 7.58570i) q^{30} +(0.712251 + 3.69551i) q^{31} +(-5.32284 + 1.91503i) q^{32} +(-0.462999 + 1.17349i) q^{33} +(-3.12349 + 7.24736i) q^{34} +(7.92602 + 3.17310i) q^{35} +(-5.47103 - 2.46329i) q^{36} +(-5.19757 - 9.00245i) q^{37} +(-0.606061 + 0.730551i) q^{38} +(-0.500727 + 0.983316i) q^{39} +(-7.21768 + 5.32482i) q^{40} +(5.15363 - 0.245498i) q^{41} +(-5.62192 + 3.44737i) q^{42} +(6.81001 + 10.5966i) q^{43} +(-1.45534 + 0.0625347i) q^{44} +(-9.42963 - 1.25967i) q^{45} +(-4.36121 + 2.10601i) q^{46} +(-2.67511 - 2.10373i) q^{47} +(0.0298899 - 6.92814i) q^{48} +(-0.0118191 + 0.248113i) q^{49} +(-4.29838 + 5.71418i) q^{50} +(-7.02847 - 6.63485i) q^{51} +(-1.27243 - 0.0665542i) q^{52} +(-2.69922 + 4.20007i) q^{53} +(5.12989 - 5.26158i) q^{54} +(-2.18263 + 0.755417i) q^{55} +(-6.27633 - 4.31218i) q^{56} +(-0.586302 - 1.00388i) q^{57} +(3.39828 + 1.66058i) q^{58} +(-2.59006 - 2.98909i) q^{59} +(-3.09848 - 10.5391i) q^{60} +(14.0631 - 1.34286i) q^{61} +(-1.36557 - 5.14426i) q^{62} +(-1.60779 - 7.91521i) q^{63} +(7.32278 - 3.22133i) q^{64} +(-1.96334 + 0.476300i) q^{65} +(0.538681 - 1.70079i) q^{66} +(7.24286 - 3.81326i) q^{67} +(3.69938 - 10.5297i) q^{68} +(-0.593345 - 5.90179i) q^{69} +(-11.4921 - 3.70313i) q^{70} +(-7.73502 + 3.98768i) q^{71} +(7.95918 + 2.94132i) q^{72} +(4.36934 - 0.417221i) q^{73} +(8.21162 + 12.1937i) q^{74} +(-4.77138 - 7.34342i) q^{75} +(0.783751 - 1.08985i) q^{76} +(-1.21215 - 1.54137i) q^{77} +(0.610471 - 1.43618i) q^{78} +(-13.8455 + 4.79198i) q^{79} +(9.66328 - 8.21695i) q^{80} +(3.90171 + 8.11028i) q^{81} +(-7.24699 + 0.849373i) q^{82} +(-0.456515 + 0.641086i) q^{83} +(7.59516 - 5.41242i) q^{84} +(0.842010 - 17.6760i) q^{85} +(-10.6421 - 14.2854i) q^{86} +(-3.33657 + 3.21342i) q^{87} +(2.04715 - 0.230273i) q^{88} +(-3.02104 + 0.434359i) q^{89} +(13.4267 + 0.856819i) q^{90} +(-0.927317 - 1.44293i) q^{91} +(5.94742 - 3.39692i) q^{92} +(6.49211 + 0.587180i) q^{93} +(3.97949 + 2.70693i) q^{94} +(0.696151 - 2.01140i) q^{95} +(0.634043 + 9.77742i) q^{96} +(5.40049 + 9.35392i) q^{97} +(-0.00754195 - 0.351202i) q^{98} +(1.73096 + 1.33345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{14}{33}\right)$	$-1$

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 $

$2$	−1.41084	+	0.0976039i	−0.997616	+	0.0690164i
$2$	−1.41084	+	0.0976039i	−0.997616	+	0.0690164i
$3$	0.479660	−	1.66431i	0.276932	−	0.960890i
$3$	0.479660	−	1.66431i	0.276932	−	0.960890i
$4$	1.98095	−	0.275407i	0.990473	−	0.137704i
$5$	2.88456	−	1.31734i	1.29002	−	0.589131i	0.352090	−	0.935966i	$-0.385471\pi$
$5$	2.88456	−	1.31734i	1.29002	−	0.589131i	0.937926	+	0.346836i	$0.112744\pi$
$6$	−0.514280	+	2.39489i	−0.209954	+	0.977711i
$7$	1.85789	+	1.94850i	0.702216	+	0.736463i	0.974162	−	0.225850i	$-0.0725158\pi$
$7$	1.85789	+	1.94850i	0.702216	+	0.736463i	−0.271946	+	0.962312i	$0.587667\pi$
$8$	−2.76792	+	0.581904i	−0.978608	+	0.205734i
$9$	−2.53985	−	1.59660i	−0.846618	−	0.532201i
$10$	−3.94108	+	2.14010i	−1.24628	+	0.676758i
$11$	−0.725043	−	0.0692332i	−0.218609	−	0.0208746i	−0.0148230	−	0.999890i	$-0.504718\pi$
$11$	−0.725043	−	0.0692332i	−0.218609	−	0.0208746i	−0.203786	+	0.979016i	$0.565325\pi$
$12$	0.491817	−	3.42901i	0.141975	−	0.989870i
$13$	−0.625573	−	0.120569i	−0.173503	−	0.0334399i	0.101760	−	0.994809i	$-0.467553\pi$
$13$	−0.625573	−	0.120569i	−0.173503	−	0.0334399i	−0.275263	+	0.961369i	$0.588765\pi$
$14$	−2.81137	−	2.56768i	−0.751370	−	0.686242i
$15$	−0.808847	−	5.43268i	−0.208843	−	1.40271i
$16$	3.84830	−	1.09113i	0.962075	−	0.272783i
$17$	2.55706	−	4.96000i	0.620178	−	1.20298i	−0.344311	−	0.938856i	$-0.611887\pi$
$17$	2.55706	−	4.96000i	0.620178	−	1.20298i	0.964489	−	0.264122i	$-0.0850822\pi$
$18$	3.73917	+	2.00466i	0.881330	+	0.472502i
$19$	0.463180	−	0.485769i	0.106261	−	0.111443i	−0.668455	−	0.743752i	$-0.733044\pi$
$19$	0.463180	−	0.485769i	0.106261	−	0.111443i	0.774716	+	0.632309i	$0.217893\pi$
$20$	5.35136	−	3.40400i	1.19660	−	0.761158i
$21$	4.13406	−	2.15749i	0.902125	−	0.470802i
$22$	1.02968	+	0.0269101i	0.219528	+	0.00573725i
$23$	3.17927	−	1.27279i	0.662923	−	0.265394i	−0.0157049	−	0.999877i	$-0.504999\pi$
$23$	3.17927	−	1.27279i	0.662923	−	0.265394i	0.678628	+	0.734482i	$0.262575\pi$
$24$	−0.359191	+	4.88579i	−0.0733197	+	0.997308i
$25$	3.31103	−	3.82113i	0.662206	−	0.764226i
$26$	0.894353	+	0.109046i	0.175397	+	0.0213857i
$27$	−3.87551	+	3.46128i	−0.745842	+	0.666123i
$28$	4.21701	+	3.34819i	0.796940	+	0.632749i
$29$	−2.31618	−	1.33725i	−0.430104	−	0.248321i	0.269287	−	0.963060i	$-0.413212\pi$
$29$	−2.31618	−	1.33725i	−0.430104	−	0.248321i	−0.699391	+	0.714739i	$0.746545\pi$
$30$	1.67141	+	7.58570i	0.305155	+	1.38495i
$31$	0.712251	+	3.69551i	0.127924	+	0.663733i	0.988110	+	0.153752i	$0.0491356\pi$
$31$	0.712251	+	3.69551i	0.127924	+	0.663733i	−0.860185	+	0.509981i	$0.829652\pi$
$32$	−5.32284	+	1.91503i	−0.940955	+	0.338532i
$33$	−0.462999	+	1.17349i	−0.0805978	+	0.204278i
$34$	−3.12349	+	7.24736i	−0.535674	+	1.24291i
$35$	7.92602	+	3.17310i	1.33974	+	0.536352i
$36$	−5.47103	−	2.46329i	−0.911839	−	0.410549i
$37$	−5.19757	−	9.00245i	−0.854475	−	1.47999i	−0.877131	−	0.480251i	$-0.840546\pi$
$37$	−5.19757	−	9.00245i	−0.854475	−	1.47999i	0.0226564	−	0.999743i	$-0.492788\pi$
$38$	−0.606061	+	0.730551i	−0.0983160	+	0.118511i
$39$	−0.500727	+	0.983316i	−0.0801805	+	0.157457i
$40$	−7.21768	+	5.32482i	−1.14122	+	0.841928i
$41$	5.15363	−	0.245498i	0.804862	−	0.0383403i	0.358882	−	0.933383i	$-0.383158\pi$
$41$	5.15363	−	0.245498i	0.804862	−	0.0383403i	0.445980	+	0.895043i	$0.352855\pi$
$42$	−5.62192	+	3.44737i	−0.867481	+	0.531941i
$43$	6.81001	+	10.5966i	1.03852	+	1.61596i	0.753508	+	0.657439i	$0.228360\pi$
$43$	6.81001	+	10.5966i	1.03852	+	1.61596i	0.285009	+	0.958525i	$0.408003\pi$
$44$	−1.45534	+	0.0625347i	−0.219400	+	0.00942746i
$45$	−9.42963	−	1.25967i	−1.40569	−	0.187780i
$46$	−4.36121	+	2.10601i	−0.643026	+	0.310514i
$47$	−2.67511	−	2.10373i	−0.390205	−	0.306861i	0.403712	−	0.914886i	$-0.367720\pi$
$47$	−2.67511	−	2.10373i	−0.390205	−	0.306861i	−0.793918	+	0.608025i	$0.791962\pi$
$48$	0.0298899	−	6.92814i	0.00431423	−	0.999991i
$49$	−0.0118191	+	0.248113i	−0.00168844	+	0.0354448i
$50$	−4.29838	+	5.71418i	−0.607883	+	0.808107i
$51$	−7.02847	−	6.63485i	−0.984182	−	0.929065i
$52$	−1.27243	−	0.0665542i	−0.176455	−	0.00922941i
$53$	−2.69922	+	4.20007i	−0.370767	+	0.576925i	−0.975635	−	0.219401i	$-0.929590\pi$
$53$	−2.69922	+	4.20007i	−0.370767	+	0.576925i	0.604868	+	0.796326i	$0.293226\pi$
$54$	5.12989	−	5.26158i	0.698090	−	0.716010i
$55$	−2.18263	+	0.755417i	−0.294306	+	0.101860i
$56$	−6.27633	−	4.31218i	−0.838710	−	0.576239i
$57$	−0.586302	−	1.00388i	−0.0776575	−	0.132967i
$58$	3.39828	+	1.66058i	0.446217	+	0.218044i
$59$	−2.59006	−	2.98909i	−0.337197	−	0.389146i	0.561674	−	0.827358i	$-0.310157\pi$
$59$	−2.59006	−	2.98909i	−0.337197	−	0.389146i	−0.898872	+	0.438212i	$0.855612\pi$
$60$	−3.09848	−	10.5391i	−0.400012	−	1.36059i
$61$	14.0631	−	1.34286i	1.80059	−	0.171936i	0.859735	−	0.510740i	$-0.170629\pi$
$61$	14.0631	−	1.34286i	1.80059	−	0.171936i	0.940857	+	0.338804i	$0.110022\pi$
$62$	−1.36557	−	5.14426i	−0.173427	−	0.653322i
$63$	−1.60779	−	7.91521i	−0.202562	−	0.997223i
$64$	7.32278	−	3.22133i	0.915347	−	0.402666i
$65$	−1.96334	+	0.476300i	−0.243522	+	0.0590778i
$66$	0.538681	−	1.70079i	0.0663071	−	0.209353i
$67$	7.24286	−	3.81326i	0.884856	−	0.465864i
$67$	7.24286	−	3.81326i	0.884856	−	0.465864i
$68$	3.69938	−	10.5297i	0.448616	−	1.27692i
$69$	−0.593345	−	5.90179i	−0.0714304	−	0.710492i
$70$	−11.4921	−	3.70313i	−1.37357	−	0.442609i
$71$	−7.73502	+	3.98768i	−0.917978	+	0.473250i	−0.851392	−	0.524530i	$-0.824241\pi$
$71$	−7.73502	+	3.98768i	−0.917978	+	0.473250i	−0.0665860	+	0.997781i	$0.521211\pi$
$72$	7.95918	+	2.94132i	0.937999	+	0.346638i
$73$	4.36934	−	0.417221i	0.511392	−	0.0488320i	0.163829	−	0.986489i	$-0.447615\pi$
$73$	4.36934	−	0.417221i	0.511392	−	0.0488320i	0.347563	+	0.937657i	$0.387009\pi$
$74$	8.21162	+	12.1937i	0.954581	+	1.41749i
$75$	−4.77138	−	7.34342i	−0.550951	−	0.847945i
$76$	0.783751	−	1.08985i	0.0899024	−	0.125014i
$77$	−1.21215	−	1.54137i	−0.138137	−	0.175656i
$78$	0.610471	−	1.43618i	0.0691222	−	0.162615i
$79$	−13.8455	+	4.79198i	−1.55774	+	0.539140i	−0.964089	−	0.265581i	$-0.914436\pi$
$79$	−13.8455	+	4.79198i	−1.55774	+	0.539140i	−0.593654	+	0.804721i	$0.702315\pi$
$80$	9.66328	−	8.21695i	1.08039	−	0.918683i
$81$	3.90171	+	8.11028i	0.433523	+	0.901142i
$82$	−7.24699	+	0.849373i	−0.800297	+	0.0937975i
$83$	−0.456515	+	0.641086i	−0.0501090	+	0.0703683i	−0.838870	−	0.544331i	$-0.816783\pi$
$83$	−0.456515	+	0.641086i	−0.0501090	+	0.0703683i	0.788761	+	0.614700i	$0.210723\pi$
$84$	7.59516	−	5.41242i	0.828700	−	0.590543i
$85$	0.842010	−	17.6760i	0.0913288	−	1.91723i
$86$	−10.6421	−	14.2854i	−1.14757	−	1.54044i
$87$	−3.33657	+	3.21342i	−0.357718	+	0.344515i
$88$	2.04715	−	0.230273i	0.218227	−	0.0245472i
$89$	−3.02104	+	0.434359i	−0.320229	+	0.0460420i	−0.300555	−	0.953764i	$-0.597172\pi$
$89$	−3.02104	+	0.434359i	−0.320229	+	0.0460420i	−0.0196740	+	0.999806i	$0.506263\pi$
$90$	13.4267	+	0.856819i	1.41529	+	0.0903167i
$91$	−0.927317	−	1.44293i	−0.0972092	−	0.151260i
$92$	5.94742	−	3.39692i	0.620062	−	0.354153i
$93$	6.49211	+	0.587180i	0.673200	+	0.0608877i
$94$	3.97949	+	2.70693i	0.410453	+	0.279199i
$95$	0.696151	−	2.01140i	0.0714236	−	0.206365i
$96$	0.634043	+	9.77742i	0.0647118	+	0.997904i
$97$	5.40049	+	9.35392i	0.548336	+	0.949746i	0.998389	+	0.0567442i	$0.0180720\pi$
$97$	5.40049	+	9.35392i	0.548336	+	0.949746i	−0.450052	+	0.893002i	$0.648595\pi$
$98$	−0.00754195	−	0.351202i	−0.000761852	−	0.0354768i
$99$	1.73096	+	1.33345i	0.173968	+	0.134017i
$100$	5.50661	−	8.48134i	0.550661	−	0.848134i
$101$	−5.58738	−	1.35548i	−0.555965	−	0.134876i	−0.0520745	−	0.998643i	$-0.516583\pi$
$101$	−5.58738	−	1.35548i	−0.555965	−	0.134876i	−0.503890	+	0.863768i	$0.668098\pi$
$102$	10.5636	+	8.67472i	1.04596	+	0.858925i
$103$	−1.95650	−	10.1513i	−0.192780	−	1.00024i	−0.941414	−	0.337253i	$-0.890502\pi$
$103$	−1.95650	−	10.1513i	−0.192780	−	1.00024i	0.748634	−	0.662983i	$-0.230710\pi$
$104$	1.80170	−	0.0302970i	0.176671	−	0.00297087i
$105$	9.08282	−	11.6694i	0.886392	−	1.13881i
$106$	3.39823	−	6.18909i	0.330066	−	0.601138i
$107$	−4.94819	+	10.8350i	−0.478359	+	1.04746i	0.504552	+	0.863381i	$0.331658\pi$
$107$	−4.94819	+	10.8350i	−0.478359	+	1.04746i	−0.982911	+	0.184079i	$0.941070\pi$
$108$	−6.72392	+	7.92395i	−0.647009	+	0.762482i
$109$	3.93036	−	4.53587i	0.376460	−	0.434458i	−0.535627	−	0.844455i	$-0.679925\pi$
$109$	3.93036	−	4.53587i	0.376460	−	0.434458i	0.912087	+	0.409997i	$0.134470\pi$
$110$	3.00562	−	1.27881i	0.286575	−	0.121930i
$111$	−17.4759	+	4.33225i	−1.65874	+	0.411199i
$112$	9.27579	+	5.47120i	0.876480	+	0.516980i
$113$	−5.89046	+	4.19458i	−0.554128	+	0.394592i	−0.822536	−	0.568713i	$-0.807442\pi$
$113$	−5.89046	+	4.19458i	−0.554128	+	0.394592i	0.268409	+	0.963305i	$0.413502\pi$
$114$	0.925161	+	1.35909i	0.0866493	+	0.127290i
$115$	7.49411	−	7.85960i	0.698829	−	0.732911i
$116$	−4.95652	−	2.01112i	−0.460201	−	0.186728i
$117$	1.39636	+	1.30502i	0.129094	+	0.120649i
$118$	3.94591	+	3.96433i	0.363251	+	0.364946i
$119$	14.4153	−	4.23271i	1.32145	−	0.388012i
$120$	5.40012	+	14.5666i	0.492961	+	1.32974i
$121$	−10.2803	−	1.98137i	−0.934575	−	0.180125i
$122$	−19.7097	+	3.26717i	−1.78443	+	0.295796i
$123$	2.06340	−	8.69499i	0.186051	−	0.784001i
$124$	2.42870	+	7.12445i	0.218104	+	0.639794i
$125$	0.0501037	−	0.170638i	0.00448142	−	0.0152623i
$126$	3.04089	+	11.0102i	0.270904	+	0.980865i
$127$	−0.230243	−	0.241472i	−0.0204308	−	0.0214272i	0.713439	−	0.700717i	$-0.247136\pi$
$127$	−0.230243	−	0.241472i	−0.0204308	−	0.0214272i	−0.733870	+	0.679290i	$0.762288\pi$
$128$	−10.0169	+	5.25951i	−0.885374	+	0.464880i
$129$	20.9025	−	6.25121i	1.84036	−	0.550389i
$130$	2.72347	−	0.863614i	0.238864	−	0.0757439i
$131$	2.76286	−	19.2161i	0.241392	−	1.67892i	−0.403759	−	0.914865i	$-0.632297\pi$
$131$	2.76286	−	19.2161i	0.241392	−	1.67892i	0.645151	−	0.764055i	$-0.276794\pi$
$132$	−0.593990	+	2.45213i	−0.0517002	+	0.213430i
$133$	1.80706			0.156692
$134$	−9.84634	+	6.08684i	−0.850594	+	0.525823i
$135$	−6.61949	+	15.0896i	−0.569715	+	1.29871i
$136$	−4.19149	+	15.2169i	−0.359418	+	1.30484i
$137$	−7.33284	−	1.05430i	−0.626487	−	0.0900753i	−0.178243	−	0.983986i	$-0.557041\pi$
$137$	−7.33284	−	1.05430i	−0.626487	−	0.0900753i	−0.448244	+	0.893911i	$0.647950\pi$
$138$	1.41315	+	8.26857i	0.120296	+	0.703868i
$139$	5.14453	−	2.34943i	0.436353	−	0.199276i	−0.185112	−	0.982717i	$-0.559265\pi$
$139$	5.14453	−	2.34943i	0.436353	−	0.199276i	0.621465	+	0.783442i	$0.286538\pi$
$140$	16.5749	+	4.10286i	1.40084	+	0.346755i
$141$	−4.78441	+	3.44314i	−0.402920	+	0.289965i
$142$	10.5237	−	6.38095i	0.883127	−	0.535477i
$143$	0.445220	+	0.130728i	0.0372312	+	0.0109321i
$144$	−11.5162	−	3.37289i	−0.959686	−	0.281074i
$145$	−8.44277	−	0.806187i	−0.701134	−	0.0669502i
$146$	−6.12372	+	1.01510i	−0.506802	+	0.0840100i
$147$	0.407268	+	0.138681i	0.0335909	+	0.0114382i
$148$	−12.7754	−	16.4019i	−1.05014	−	1.34823i
$149$	2.04147	+	6.95259i	0.167243	+	0.569578i	0.999876	+	0.0157527i	$0.00501445\pi$
$149$	2.04147	+	6.95259i	0.167243	+	0.569578i	−0.832633	+	0.553826i	$0.813167\pi$
$150$	7.44841	+	9.89470i	0.608160	+	0.807899i
$151$	−8.86541	+	17.1965i	−0.721457	+	1.39943i	0.187383	+	0.982287i	$0.439999\pi$
$151$	−8.86541	+	17.1965i	−0.721457	+	1.39943i	−0.908840	+	0.417145i	$0.863031\pi$
$152$	−0.999375	+	1.61410i	−0.0810600	+	0.130921i
$153$	−14.4137	+	8.51507i	−1.16528	+	0.688403i
$154$	1.86059	+	2.05632i	0.149931	+	0.165703i
$155$	6.92276	+	9.72166i	0.556050	+	0.780862i
$156$	−0.721102	+	2.08580i	−0.0577343	+	0.166998i
$157$	−2.47408	+	0.990474i	−0.197453	+	0.0790484i	−0.468282	−	0.883579i	$-0.655127\pi$
$157$	−2.47408	+	0.990474i	−0.197453	+	0.0790484i	0.270828	+	0.962628i	$0.412702\pi$
$158$	19.0661	−	8.11210i	1.51682	−	0.645364i
$159$	5.69552	+	6.50695i	0.451684	+	0.516035i
$160$	−12.8314	+	12.5360i	−1.01441	+	0.991057i
$161$	8.38675	+	3.83010i	0.660968	+	0.301854i
$162$	−6.29629	−	11.0615i	−0.494683	−	0.869073i
$163$	13.1328	+	7.58225i	1.02864	+	0.593888i	0.916596	−	0.399815i	$-0.130926\pi$
$163$	13.1328	+	7.58225i	1.02864	+	0.593888i	0.112048	+	0.993703i	$0.464259\pi$
$164$	10.1415	−	1.90566i	0.791915	−	0.148807i
$165$	0.210327	+	3.99492i	0.0163739	+	0.311004i
$166$	0.581498	−	0.949028i	0.0451330	−	0.0736589i
$167$	0.513521	−	2.11676i	0.0397374	−	0.163800i	−0.948486	−	0.316820i	$-0.897385\pi$
$167$	0.513521	−	2.11676i	0.0397374	−	0.163800i	0.988223	+	0.153020i	$0.0489000\pi$
$168$	−10.1873	+	8.37738i	−0.785967	+	0.646329i
$169$	−11.6920	−	4.68076i	−0.899383	−	0.360059i
$170$	0.537300	+	25.0202i	0.0412090	+	1.91896i
$171$	−1.95199	+	0.494268i	−0.149272	+	0.0377976i
$172$	16.4086	+	19.1157i	1.25115	+	1.45756i
$173$	12.1469	+	4.20410i	0.923515	+	0.319632i	0.747121	−	0.664688i	$-0.231435\pi$
$173$	12.1469	+	4.20410i	0.923515	+	0.319632i	0.176394	+	0.984320i	$0.443557\pi$
$174$	4.39373	−	4.85929i	0.333088	−	0.368381i
$175$	13.5970	−	0.647704i	1.02784	−	0.0489619i
$176$	−2.86573	+	0.524688i	−0.216012	+	0.0395499i
$177$	−6.21712	+	2.87692i	−0.467307	+	0.216242i
$178$	4.21981	−	0.907677i	0.316288	−	0.0680333i
$179$	1.51141	+	10.5121i	0.112968	+	0.785709i	0.965006	+	0.262229i	$0.0844575\pi$
$179$	1.51141	+	10.5121i	0.112968	+	0.785709i	−0.852038	+	0.523480i	$0.824633\pi$
$180$	−19.0265	+	0.101658i	−1.41815	+	0.00757717i
$181$	0.864935	+	0.680192i	0.0642901	+	0.0505583i	0.649787	−	0.760116i	$-0.274858\pi$
$181$	0.864935	+	0.680192i	0.0642901	+	0.0505583i	−0.585497	+	0.810675i	$0.699101\pi$
$182$	1.44913	+	1.94524i	0.107417	+	0.144191i
$183$	4.51055	−	24.0494i	0.333430	−	1.77778i
$184$	−8.05932	+	5.37300i	−0.594141	+	0.396103i
$185$	−26.8520	−	19.1212i	−1.97420	−	1.40582i
$186$	−9.21665	−	0.194763i	−0.675797	−	0.0142807i
$187$	−2.19737	+	3.41918i	−0.160688	+	0.250035i
$188$	−5.87864	−	3.43064i	−0.428744	−	0.250205i
$189$	−13.9446	−	1.12075i	−1.01432	−	0.0815228i
$190$	−0.785838	+	2.90571i	−0.0570107	+	0.210802i
$191$	−11.5207	+	9.05997i	−0.833608	+	0.655557i	−0.940905	−	0.338670i	$-0.890023\pi$
$191$	−11.5207	+	9.05997i	−0.833608	+	0.655557i	0.107297	+	0.994227i	$0.465780\pi$
$192$	−1.84885	−	13.7325i	−0.133429	−	0.991058i
$193$	13.6591	+	15.7634i	0.983201	+	1.13467i	0.990886	+	0.134704i	$0.0430084\pi$
$193$	13.6591	+	15.7634i	0.983201	+	1.13467i	−0.00768468	+	0.999970i	$0.502446\pi$
$194$	−8.53221	−	12.6698i	−0.612577	−	0.909638i
$195$	−0.149022	+	3.49606i	−0.0106717	+	0.250358i
$196$	0.0449192	+	0.494754i	0.00320851	+	0.0353396i
$197$	7.76422	+	15.0605i	0.553178	+	1.07302i	0.985241	+	0.171172i	$0.0547554\pi$
$197$	7.76422	+	15.0605i	0.553178	+	1.07302i	−0.432063	+	0.901843i	$0.642214\pi$
$198$	−2.57227	−	1.71233i	−0.182803	−	0.121690i
$199$	−14.8582	+	3.60455i	−1.05327	+	0.255520i	−0.724774	−	0.688987i	$-0.758056\pi$
$199$	−14.8582	+	3.60455i	−1.05327	+	0.255520i	−0.328493	+	0.944506i	$0.606541\pi$
$200$	−6.94114	+	12.5033i	−0.490812	+	0.884116i
$201$	−2.87234	−	13.8834i	−0.202599	−	0.979262i
$202$	8.01521	+	1.36702i	0.563948	+	0.0961834i
$203$	−1.69758	−	6.99753i	−0.119147	−	0.491130i
$204$	−15.7503	−	11.2076i	−1.10274	−	0.784689i
$205$	14.5426	−	7.49722i	1.01570	−	0.523628i
$206$	3.75112	+	14.1309i	0.261353	+	0.984547i
$207$	−10.1070	−	1.84334i	−0.702486	−	0.128121i
$208$	−2.53895	+	0.218597i	−0.176045	+	0.0151570i
$209$	−0.369457	+	0.320136i	−0.0255558	+	0.0221443i
$210$	−11.6754	+	17.3501i	−0.805682	+	1.19727i
$211$	−10.6534	−	13.5469i	−0.733408	−	0.932605i	0.266100	−	0.963945i	$-0.414265\pi$
$211$	−10.6534	−	13.5469i	−0.733408	−	0.932605i	−0.999509	+	0.0313408i	$0.990022\pi$
$212$	−4.19029	+	9.06351i	−0.287790	+	0.622484i
$213$	2.92656	+	14.7862i	0.200524	+	1.01313i
$214$	5.92357	−	15.7695i	0.404927	−	1.07798i
$215$	33.6032	+	21.5954i	2.29172	+	1.47280i
$216$	8.71297	−	11.8357i	0.592843	−	0.805318i
$217$	−5.87741	+	8.25366i	−0.398984	+	0.560295i
$218$	−5.10239	+	6.78302i	−0.345577	+	0.459404i
$219$	1.40141	−	7.47205i	0.0946984	−	0.504915i
$220$	−4.11564	+	2.09755i	−0.277476	+	0.141417i
$221$	−2.19765	+	2.79454i	−0.147830	+	0.187981i
$222$	24.2329	−	7.81784i	1.62641	−	0.524699i
$223$	12.3151	−	1.77065i	0.824681	−	0.118571i	0.282962	−	0.959131i	$-0.408683\pi$
$223$	12.3151	−	1.77065i	0.824681	−	0.118571i	0.541719	+	0.840560i	$0.317774\pi$
$224$	−13.6207	−	6.81365i	−0.910070	−	0.455256i
$225$	−14.5104	+	4.41871i	−0.967358	+	0.294581i
$226$	7.90109	−	6.49281i	0.525573	−	0.431895i
$227$	0.425480	+	8.93192i	0.0282401	+	0.592832i	0.967993	+	0.250978i	$0.0807521\pi$
$227$	0.425480	+	8.93192i	0.0282401	+	0.592832i	−0.939753	+	0.341855i	$0.888945\pi$
$228$	−1.43791	−	1.82716i	−0.0952278	−	0.121007i
$229$	3.65009	−	10.5462i	0.241205	−	0.696915i	−0.757808	−	0.652478i	$-0.773729\pi$
$229$	3.65009	−	10.5462i	0.241205	−	0.696915i	0.999012	−	0.0444369i	$-0.0141494\pi$
$230$	−9.80587	+	11.8201i	−0.646580	+	0.779394i
$231$	−3.14674	+	1.27806i	−0.207040	+	0.0840899i
$232$	7.18915	+	2.35360i	0.471991	+	0.154521i
$233$	5.24442	−	13.0999i	0.343573	−	0.858204i	−0.651462	−	0.758681i	$-0.725844\pi$
$233$	5.24442	−	13.0999i	0.343573	−	0.858204i	0.995035	−	0.0995231i	$-0.0317317\pi$
$234$	−2.09742	−	1.70489i	−0.137113	−	0.111452i
$235$	−10.4879	−	2.54433i	−0.684153	−	0.165974i
$236$	−5.95399	−	5.20791i	−0.387572	−	0.339006i
$237$	1.33420	+	25.3417i	0.0866659	+	1.64612i
$238$	−19.9246	+	7.37867i	−1.29152	+	0.478288i
$239$	0.451058	−	0.781255i	0.0291765	−	0.0505352i	−0.851068	−	0.525055i	$-0.824045\pi$
$239$	0.451058	−	0.781255i	0.0291765	−	0.0505352i	0.880245	+	0.474520i	$0.157378\pi$
$240$	−9.04047	−	20.0240i	−0.583560	−	1.29255i
$241$	−12.5138	+	27.4014i	−0.806085	+	1.76508i	−0.182695	+	0.983170i	$0.558482\pi$
$241$	−12.5138	+	27.4014i	−0.806085	+	1.76508i	−0.623390	+	0.781911i	$0.714245\pi$
$242$	14.6973	+	1.79200i	0.944778	+	0.115194i
$243$	15.3695	−	2.60348i	0.985955	−	0.167013i
$244$	27.4884	−	6.53321i	1.75976	−	0.418246i
$245$	0.292756	+	0.731268i	0.0187035	+	0.0467190i
$246$	−2.06247	+	12.4687i	−0.131498	+	0.794972i
$247$	−0.348322	+	0.248039i	−0.0221632	+	0.0157823i
$248$	−4.12189	−	9.81442i	−0.261740	−	0.623216i
$249$	0.847993	+	1.06729i	0.0537394	+	0.0676365i
$250$	−0.0540335	+	0.245633i	−0.00341738	+	0.0155352i
$251$	24.5706	+	12.6670i	1.55088	+	0.799536i	0.999399	−	0.0346503i	$-0.0110317\pi$
$251$	24.5706	+	12.6670i	1.55088	+	0.799536i	0.551483	+	0.834186i	$0.314062\pi$
$252$	−5.36485	−	15.2368i	−0.337953	−	0.959829i
$253$	−2.39322	+	0.702714i	−0.150461	+	0.0441792i
$254$	0.348405	+	0.318206i	0.0218609	+	0.0199660i
$255$	−29.0144	−	9.87981i	−1.81695	−	0.618697i
$256$	13.6189	−	8.39803i	0.851178	−	0.524877i
$257$	−1.36277	+	14.2716i	−0.0850072	+	0.890236i	0.847909	+	0.530142i	$0.177861\pi$
$257$	−1.36277	+	14.2716i	−0.0850072	+	0.890236i	−0.932916	+	0.360094i	$0.882745\pi$
$258$	−28.8799	+	10.8596i	−1.79799	+	0.676091i
$259$	7.88475	−	26.8530i	0.489935	−	1.66856i
$260$	−3.75809	+	1.48424i	−0.233067	+	0.0920488i
$261$	3.74770	+	7.09444i	0.231977	+	0.439135i
$262$	−2.02239	+	27.3806i	−0.124944	+	1.69158i
$263$	12.9361	+	28.3262i	0.797676	+	1.74667i	0.653239	+	0.757152i	$0.273410\pi$
$263$	12.9361	+	28.3262i	0.797676	+	1.74667i	0.144436	+	0.989514i	$0.453863\pi$
$264$	0.598688	−	3.51754i	0.0368467	−	0.216490i
$265$	−2.25317	+	15.6712i	−0.138411	+	0.962672i
$266$	−2.54947	+	0.176376i	−0.156318	+	0.0108143i
$267$	−0.726160	+	5.23628i	−0.0444403	+	0.320455i
$268$	13.2975	−	9.54861i	0.812276	−	0.583274i
$269$		−	5.94192i		−	0.362285i	−0.983457	−	0.181143i	$-0.942020\pi$
$269$		−	5.94192i		−	0.362285i	0.983457	−	0.181143i	$-0.0579795\pi$
$270$	7.86624	−	21.9351i	0.478724	−	1.33493i
$271$	−18.1727	−	2.61284i	−1.10391	−	0.158719i	−0.433824	−	0.900998i	$-0.642836\pi$
$271$	−18.1727	−	2.61284i	−1.10391	−	0.158719i	−0.670091	+	0.742279i	$0.733745\pi$
$272$	4.42831	−	21.8777i	0.268506	−	1.32653i
$273$	−2.84628	+	0.851226i	−0.172265	+	0.0515185i
$274$	10.4484	+	0.771742i	0.631210	+	0.0466226i
$275$	−2.66519	+	2.54125i	−0.160717	+	0.153243i
$276$	−2.80078	−	11.5277i	−0.168587	−	0.693887i
$277$	−1.06720	−	0.313358i	−0.0641218	−	0.0188279i	0.249514	−	0.968371i	$-0.419729\pi$
$277$	−1.06720	−	0.313358i	−0.0641218	−	0.0188279i	−0.313636	+	0.949543i	$0.601547\pi$
$278$	−7.02880	+	3.81679i	−0.421559	+	0.228916i
$279$	4.09125	−	10.5232i	0.244937	−	0.630010i
$280$	−23.7851	−	4.17071i	−1.42143	−	0.249248i
$281$	0.866962	−	4.49823i	0.0517186	−	0.268342i	−0.946860	−	0.321647i	$-0.895764\pi$
$281$	0.866962	−	4.49823i	0.0517186	−	0.268342i	0.998578	+	0.0533054i	$0.0169757\pi$
$282$	6.41398	−	5.32470i	0.381947	−	0.317082i
$283$	4.46968	+	15.2223i	0.265695	+	0.904873i	0.978973	+	0.203992i	$0.0653916\pi$
$283$	4.46968	+	15.2223i	0.265695	+	0.904873i	−0.713278	+	0.700881i	$0.752790\pi$
$284$	−14.2244	+	10.0297i	−0.844064	+	0.595151i
$285$	−3.01367	−	2.12340i	−0.178514	−	0.125779i
$286$	−0.640894	−	0.140982i	−0.0378969	−	0.00833643i
$287$	10.0532	+	9.58573i	0.593423	+	0.565828i
$288$	16.5768	+	3.63459i	0.976796	+	0.214170i
$289$	−8.20212	−	11.5183i	−0.482478	−	0.677545i
$290$	11.9901	+	0.313355i	0.704083	+	0.0184008i
$291$	18.1582	−	4.50139i	1.06445	−	0.263876i
$292$	8.54052	−	2.02984i	0.499796	−	0.118787i
$293$	19.4930	+	16.8908i	1.13880	+	0.986772i	0.999994	−	0.00354794i	$-0.00112935\pi$
$293$	19.4930	+	16.8908i	1.13880	+	0.986772i	0.138802	+	0.990320i	$0.455675\pi$
$294$	−0.588127	−	0.155905i	−0.0343002	−	0.00909258i
$295$	−11.4088	−	5.21024i	−0.664248	−	0.303352i
$296$	19.6250	+	21.8936i	1.14068	+	1.27254i
$297$	3.04954	−	2.24126i	0.176952	−	0.130051i
$298$	−3.55878	−	9.60975i	−0.206155	−	0.556678i
$299$	−2.14232	+	0.412899i	−0.123894	+	0.0238786i
$300$	−11.4743	−	13.2329i	−0.662468	−	0.763999i
$301$	−7.99518	+	32.9566i	−0.460834	+	1.89958i
$302$	10.8292	−	25.1268i	0.623153	−	1.44589i
$303$	−4.93598	+	8.64896i	−0.283565	+	0.496870i
$304$	1.25242	−	2.37478i	0.0718310	−	0.136203i
$305$	38.7968	−	22.3994i	2.22150	−	1.28258i
$306$	19.5044	−	13.4203i	1.11499	−	0.767185i
$307$	23.3034	+	8.06540i	1.33000	+	0.460317i	0.897379	−	0.441260i	$-0.145468\pi$
$307$	23.3034	+	8.06540i	1.33000	+	0.460317i	0.432619	+	0.901577i	$0.357590\pi$
$308$	−2.82571	−	2.71954i	−0.161009	−	0.154960i
$309$	−17.8333	−	1.61294i	−1.01450	−	0.0917570i
$310$	−10.7158	−	13.0400i	−0.608616	−	0.740624i
$311$	3.88873	−	2.49913i	0.220509	−	0.141713i	−0.425723	−	0.904854i	$-0.639980\pi$
$311$	3.88873	−	2.49913i	0.220509	−	0.141713i	0.646232	+	0.763141i	$0.276344\pi$
$312$	0.813778	−	3.01312i	0.0460711	−	0.170584i
$313$	1.06213	+	7.38729i	0.0600353	+	0.417554i	0.997571	+	0.0696641i	$0.0221927\pi$
$313$	1.06213	+	7.38729i	0.0600353	+	0.417554i	−0.937535	+	0.347890i	$0.886898\pi$
$314$	3.39387	−	1.63888i	0.191527	−	0.0924874i
$315$	−15.0648	−	20.7139i	−0.848803	−	1.16710i
$316$	−26.1075	+	13.3058i	−1.46866	+	0.748510i
$317$	−17.1881	−	0.818771i	−0.965381	−	0.0459868i	−0.441033	−	0.897491i	$-0.645388\pi$
$317$	−17.1881	−	0.818771i	−0.965381	−	0.0459868i	−0.524348	+	0.851504i	$0.675691\pi$
$318$	−8.67057	−	8.62437i	−0.486222	−	0.483631i
$319$	1.58675	+	1.12992i	0.0888408	+	0.0632632i
$320$	16.8794	−	18.9387i	0.943589	−	1.05870i
$321$	15.6594	+	13.4324i	0.874021	+	0.749725i
$322$	−12.2062	−	4.58508i	−0.680225	−	0.255517i
$323$	−1.22504	−	3.53952i	−0.0681630	−	0.196944i
$324$	9.96271	+	14.9915i	0.553484	+	0.832860i
$325$	−2.53200	+	1.99119i	−0.140450	+	0.110451i
$326$	−19.2684	−	9.41554i	−1.06718	−	0.521478i
$327$	−5.66386	−	8.71700i	−0.313212	−	0.482051i
$328$	−14.1220	+	3.67844i	−0.779756	+	0.203108i
$329$	−0.870946	−	9.12096i	−0.0480168	−	0.502855i
$330$	−0.686657	−	5.61567i	−0.0377992	−	0.309133i
$331$	−0.439441	−	0.852396i	−0.0241538	−	0.0468519i	0.876450	−	0.481493i	$-0.159905\pi$
$331$	−0.439441	−	0.852396i	−0.0241538	−	0.0468519i	−0.900604	+	0.434641i	$0.856875\pi$
$332$	−0.727773	+	1.39568i	−0.0399417	+	0.0765981i
$333$	−1.17229	+	31.1634i	−0.0642411	+	1.70774i
$334$	−0.517892	+	3.03654i	−0.0283378	+	0.166152i
$335$	15.8691	−	20.5409i	0.867024	−	1.12227i
$336$	13.5550	−	12.8135i	0.739486	−	0.699032i
$337$	−5.11053	−	21.0659i	−0.278388	−	1.14753i	−0.923547	−	0.383484i	$-0.874724\pi$
$337$	−5.11053	−	21.0659i	−0.278388	−	1.14753i	0.645159	−	0.764048i	$-0.276791\pi$
$338$	16.9524	+	5.46263i	0.922088	+	0.297128i
$339$	4.15566	+	11.8155i	0.225704	+	0.641731i
$340$	−3.20011	−	35.2470i	−0.173550	−	1.91154i
$341$	−0.260560	−	2.72871i	−0.0141101	−	0.147768i
$342$	2.70571	−	0.887855i	0.146308	−	0.0480097i
$343$	13.7374	−	11.9036i	0.741752	−	0.642732i
$344$	−25.0158	−	25.3677i	−1.34876	−	1.36774i
$345$	−9.48618	−	16.2424i	−0.510719	−	0.874464i
$346$	−17.5478	−	4.74573i	−0.943373	−	0.255132i
$347$	−7.96307	−	23.0078i	−0.427480	−	1.23512i	−0.929034	−	0.369995i	$-0.879359\pi$
$347$	−7.96307	−	23.0078i	−0.427480	−	1.23512i	0.501554	−	0.865126i	$-0.332762\pi$
$348$	−5.72457	+	7.28453i	−0.306869	+	0.390492i
$349$	−24.2672	−	15.5956i	−1.29899	−	0.834812i	−0.305891	−	0.952067i	$-0.598954\pi$
$349$	−24.2672	−	15.5956i	−1.29899	−	0.834812i	−0.993102	+	0.117255i	$0.962591\pi$
$350$	−19.1200	+	2.24093i	−1.02201	+	0.119783i
$351$	2.84174	−	1.69801i	0.151681	−	0.0906333i
$352$	3.99187	−	1.01996i	0.212767	−	0.0543639i
$353$	2.53073	+	0.120554i	0.134697	+	0.00641642i	0.114822	−	0.993386i	$-0.463370\pi$
$353$	2.53073	+	0.120554i	0.134697	+	0.00641642i	0.0198750	+	0.999802i	$0.493673\pi$
$354$	8.49057	−	4.66569i	0.451269	−	0.247979i
$355$	−17.0590	+	21.6923i	−0.905400	+	1.15131i
$356$	−5.86489	+	1.69246i	−0.310838	+	0.0897001i
$357$	−0.130111	−	26.0218i	−0.00688619	−	1.37722i
$358$	−3.15837	−	14.6833i	−0.166925	−	0.776039i
$359$	19.6213	−	12.6098i	1.03557	−	0.665522i	0.0916842	−	0.995788i	$-0.470775\pi$
$359$	19.6213	−	12.6098i	1.03557	−	0.665522i	0.943888	+	0.330266i	$0.107139\pi$
$360$	26.8335	−	2.00049i	1.41425	−	0.105435i
$361$	0.882620	+	18.5285i	0.0464537	+	0.975183i
$362$	−1.28667	−	0.875222i	−0.0676261	−	0.0460007i
$363$	−8.22867	+	16.1593i	−0.431893	+	0.848141i
$364$	−2.23436	−	2.60298i	−0.117112	−	0.136433i
$365$	12.0540	−	6.95938i	0.630936	−	0.364271i
$366$	−4.01636	+	34.3702i	−0.209938	+	1.79656i
$367$	1.60296	−	4.00400i	0.0836738	−	0.209007i	−0.880630	−	0.473804i	$-0.842881\pi$
$367$	1.60296	−	4.00400i	0.0836738	−	0.209007i	0.964304	+	0.264797i	$0.0853048\pi$
$368$	10.8460	−	8.36707i	0.565387	−	0.436164i
$369$	−13.4814	−	7.60478i	−0.701815	−	0.395889i
$370$	39.7502	+	24.3561i	2.06651	+	1.26621i
$371$	−13.1987	+	2.54384i	−0.685242	+	0.132070i
$372$	13.0222	−	0.624801i	0.675172	−	0.0323944i
$373$	−2.84896	+	4.93454i	−0.147513	+	0.255501i	−0.930308	−	0.366780i	$-0.880460\pi$
$373$	−2.84896	+	4.93454i	−0.147513	+	0.255501i	0.782794	+	0.622280i	$0.213794\pi$
$374$	2.76642	−	5.03839i	0.143048	−	0.260529i
$375$	−0.259961	−	0.165236i	−0.0134243	−	0.00853276i
$376$	8.62868	+	4.26631i	0.444990	+	0.220018i
$377$	1.28771	+	1.11581i	0.0663204	+	0.0574670i
$378$	19.7829	+	0.220162i	1.01752	+	0.0113239i
$379$	−8.51672	−	21.2737i	−0.437474	−	1.09276i	−0.969295	−	0.245901i	$-0.920916\pi$
$379$	−8.51672	−	21.2737i	−0.437474	−	1.09276i	0.531820	−	0.846857i	$-0.321508\pi$
$380$	0.825085	−	4.17619i	0.0423260	−	0.214234i
$381$	−0.512323	+	0.267372i	−0.0262471	+	0.0136979i
$382$	15.3696	−	13.9066i	0.786376	−	0.711526i
$383$	6.57162	+	6.26602i	0.335794	+	0.320179i	0.839150	−	0.543900i	$-0.183053\pi$
$383$	6.57162	+	6.26602i	0.335794	+	0.320179i	−0.503356	+	0.864079i	$0.667902\pi$
$384$	3.94878	+	19.1939i	0.201510	+	0.979486i
$385$	−5.52702	−	2.84938i	−0.281683	−	0.145218i
$386$	−20.8093	−	20.9065i	−1.05917	−	1.06411i
$387$	−0.377882	−	37.7867i	−0.0192088	−	1.92080i
$388$	13.2742	+	17.0423i	0.673896	+	0.865191i
$389$	−5.98210	+	31.0381i	−0.303304	+	1.57369i	0.435764	+	0.900061i	$0.356478\pi$
$389$	−5.98210	+	31.0381i	−0.303304	+	1.57369i	−0.739068	+	0.673631i	$0.764734\pi$
$390$	−0.130983	−	4.94694i	−0.00663258	−	0.250498i
$391$	1.81655	−	19.0238i	0.0918669	−	0.962073i
$392$	−0.111664	−	0.693636i	−0.00563987	−	0.0350339i
$393$	−30.6563	−	13.8155i	−1.54641	−	0.696897i
$394$	−12.4240	−	20.4901i	−0.625914	−	1.03228i
$395$	−33.6256	+	32.0620i	−1.69189	+	1.61321i
$396$	3.79619	+	2.16477i	0.190766	+	0.108784i
$397$	13.3673	+	29.2703i	0.670885	+	1.46903i	0.872021	+	0.489469i	$0.162809\pi$
$397$	13.3673	+	29.2703i	0.670885	+	1.46903i	−0.201136	+	0.979563i	$0.564463\pi$
$398$	20.6107	−	6.53566i	1.03312	−	0.327603i
$399$	0.866772	−	3.00750i	0.0433929	−	0.150563i
$400$	8.57247	−	18.3176i	0.428624	−	0.915882i
$401$		−	13.4358i		−	0.670951i	−0.942049	−	0.335476i	$-0.891103\pi$
$401$		−	13.4358i		−	0.670951i	0.942049	−	0.335476i	$-0.108897\pi$
$402$	5.40750	+	19.3070i	0.269701	+	0.962944i
$403$		−	2.39769i		−	0.119437i
$404$	−11.4416	−	1.14634i	−0.569241	−	0.0570324i
$405$	21.9387	+	18.2548i	1.09014	+	0.907086i
$406$	3.07801	+	9.70671i	0.152759	+	0.481736i
$407$	3.14519	+	6.88700i	0.155901	+	0.341376i
$408$	23.3151	+	14.2749i	1.15427	+	0.706711i
$409$	21.1568	−	20.1730i	1.04614	−	0.997491i	0.0461398	−	0.998935i	$-0.485308\pi$
$409$	21.1568	−	20.1730i	1.04614	−	0.997491i	0.999999	+	0.00144373i	$0.000459555\pi$
$410$	−19.7855	+	11.9968i	−0.977136	+	0.592479i
$411$	−5.27196	+	11.6984i	−0.260046	+	0.577040i
$412$	−6.67146	−	19.5703i	−0.328679	−	0.964161i
$413$	1.01219	−	10.6001i	0.0498066	−	0.521598i
$414$	14.4393	+	1.61418i	0.709653	+	0.0793324i
$415$	−0.472321	+	2.45064i	−0.0231853	+	0.120297i
$416$	3.56072	−	0.556217i	0.174579	−	0.0272708i
$417$	−1.44255	−	9.68901i	−0.0706421	−	0.474473i
$418$	0.489998	−	0.487721i	0.0239666	−	0.0238552i
$419$	−22.8503	−	11.7801i	−1.11631	−	0.575497i	−0.201542	−	0.979480i	$-0.564595\pi$
$419$	−22.8503	−	11.7801i	−1.11631	−	0.575497i	−0.914767	+	0.403983i	$0.867626\pi$
$420$	14.7788	−	25.6178i	0.721129	−	1.25002i
$421$	6.26850	+	5.97700i	0.305508	+	0.291301i	0.827287	−	0.561779i	$-0.189883\pi$
$421$	6.26850	+	5.97700i	0.305508	+	0.291301i	−0.521779	+	0.853081i	$0.674731\pi$
$422$	16.3524	+	18.0727i	0.796024	+	0.879764i
$423$	3.43557	+	9.61427i	0.167043	+	0.467462i
$424$	5.02720	−	13.1962i	0.244142	−	0.640862i
$425$	−10.4863	−	26.1936i	−0.508662	−	1.27058i
$426$	−5.57210	−	20.5753i	−0.269969	−	0.996878i
$427$	28.7442	+	24.9070i	1.39103	+	1.20533i
$428$	−6.81805	+	22.8264i	−0.329563	+	1.10335i
$429$	0.431127	−	0.678279i	0.0208150	−	0.0327476i
$430$	−49.5165	−	27.1880i	−2.38790	−	1.31112i
$431$	−13.4206	+	23.2451i	−0.646446	+	1.11968i	0.337519	+	0.941319i	$0.390412\pi$
$431$	−13.4206	+	23.2451i	−0.646446	+	1.11968i	−0.983965	+	0.178359i	$0.942921\pi$
$432$	−11.1374	+	17.5487i	−0.535849	+	0.844314i
$433$	25.5887	−	4.93183i	1.22972	−	0.237008i	0.467302	−	0.884098i	$-0.345226\pi$
$433$	25.5887	−	4.93183i	1.22972	−	0.237008i	0.762414	+	0.647089i	$0.224014\pi$
$434$	7.48650	−	12.2183i	0.359364	−	0.586496i
$435$	−5.39140	+	13.6647i	−0.258498	+	0.655172i
$436$	6.53662	−	10.0678i	0.313047	−	0.482159i
$437$	0.854292	−	2.13392i	0.0408663	−	0.102079i
$438$	−1.24786	+	10.6787i	−0.0596253	+	0.510246i
$439$	−22.4618	+	12.9683i	−1.07204	+	0.618943i	−0.928738	−	0.370736i	$-0.879106\pi$
$439$	−22.4618	+	12.9683i	−1.07204	+	0.618943i	−0.143303	+	0.989679i	$0.545772\pi$
$440$	5.60178	−	3.36102i	0.267054	−	0.160230i
$441$	0.426157	−	0.611301i	0.0202932	−	0.0291096i
$442$	2.82778	−	4.15716i	0.134504	−	0.197736i
$443$	−1.61442	−	33.8908i	−0.0767034	−	1.61020i	−0.629578	−	0.776938i	$-0.716772\pi$
$443$	−1.61442	−	33.8908i	−0.0767034	−	1.61020i	0.552874	−	0.833265i	$-0.313531\pi$
$444$	−33.4258	+	13.3950i	−1.58632	+	0.635696i
$445$	−8.14217	+	5.23266i	−0.385976	+	0.248052i
$446$	−17.2019	+	3.70011i	−0.814532	+	0.175205i
$447$	12.5505	−	0.0627533i	0.593617	−	0.00296813i
$448$	19.8817	+	8.28354i	0.939320	+	0.391361i
$449$	−4.85458	+	6.17310i	−0.229102	+	0.291327i	−0.886990	−	0.461789i	$-0.847208\pi$
$449$	−4.85458	+	6.17310i	−0.229102	+	0.291327i	0.657888	+	0.753116i	$0.271450\pi$
$450$	20.0405	−	7.65037i	0.944720	−	0.360642i
$451$	−3.75360	−	0.178806i	−0.176750	−	0.00841964i
$452$	−10.5135	+	9.93151i	−0.494512	+	0.467139i
$453$	24.3679	+	23.0033i	1.14490	+	1.08079i
$454$	−1.47207	−	12.5600i	−0.0690879	−	0.589470i
$455$	−4.57573	−	2.94064i	−0.214514	−	0.137860i
$456$	2.20700	+	2.43749i	0.103352	+	0.114146i
$457$	−9.45708	−	27.3244i	−0.442384	−	1.27818i	−0.917316	−	0.398161i	$-0.869649\pi$
$457$	−9.45708	−	27.3244i	−0.442384	−	1.27818i	0.474932	−	0.880023i	$-0.342473\pi$
$458$	−4.12034	+	15.2353i	−0.192531	+	0.711900i
$459$	7.25804	+	28.0732i	0.338776	+	1.31035i
$460$	12.6808	−	17.6334i	0.591247	−	0.822160i
$461$	11.1337	−	9.64743i	0.518550	−	0.449326i	−0.355842	−	0.934546i	$-0.615806\pi$
$461$	11.1337	−	9.64743i	0.518550	−	0.449326i	0.874392	+	0.485220i	$0.161261\pi$
$462$	4.31480	−	2.11027i	0.200743	−	0.0981785i
$463$	3.08264	+	32.2828i	0.143262	+	1.50031i	0.726025	+	0.687668i	$0.241366\pi$
$463$	3.08264	+	32.2828i	0.143262	+	1.50031i	−0.582763	+	0.812642i	$0.698028\pi$
$464$	−10.3725	−	2.61887i	−0.481530	−	0.121578i
$465$	19.5004	−	6.85853i	0.904310	−	0.318057i
$466$	−6.12044	+	18.9938i	−0.283524	+	0.879870i
$467$	−2.60824	−	10.7513i	−0.120695	−	0.497511i	−0.999783	−	0.0208511i	$-0.993362\pi$
$467$	−2.60824	−	10.7513i	−0.120695	−	0.497511i	0.879088	−	0.476660i	$-0.158153\pi$
$468$	3.12553	+	2.20061i	0.144478	+	0.101723i
$469$	20.8866	+	7.02808i	0.964452	+	0.324527i
$470$	15.0450	+	2.56599i	0.693976	+	0.118360i
$471$	0.461737	+	4.59273i	0.0212757	+	0.211622i
$472$	8.90845	+	6.76640i	0.410045	+	0.311449i
$473$	−4.20391	−	8.15445i	−0.193296	−	0.374942i
$474$	−4.35580	−	35.6230i	−0.200069	−	1.63622i
$475$	−0.322585	−	3.37827i	−0.0148012	−	0.155006i
$476$	27.3902	−	12.3549i	1.25543	−	0.566284i
$477$	13.5615	−	6.35798i	0.620938	−	0.291112i
$478$	−0.560118	+	1.14625i	−0.0256192	+	0.0524284i
$479$	8.79334	−	6.91516i	0.401778	−	0.315962i	−0.396742	−	0.917930i	$-0.629859\pi$
$479$	8.79334	−	6.91516i	0.401778	−	0.315962i	0.798520	+	0.601968i	$0.205617\pi$
$480$	14.7091	+	27.3683i	0.671375	+	1.24919i
$481$	2.16604	+	6.25836i	0.0987629	+	0.285357i
$482$	14.9805	−	39.8804i	0.682344	−	1.81650i
$483$	10.3973	−	12.1210i	0.473091	−	0.551525i
$484$	−20.9105	−	1.09371i	−0.950475	−	0.0497143i
$485$	27.9003	+	19.8677i	1.26689	+	0.902146i
$486$	−21.4298	+	5.17322i	−0.972077	+	0.234662i
$487$	−10.7486	−	0.512017i	−0.487063	−	0.0232017i	−0.197386	−	0.980326i	$-0.563245\pi$
$487$	−10.7486	−	0.512017i	−0.487063	−	0.0232017i	−0.289678	+	0.957124i	$0.593548\pi$
$488$	−38.1441	+	11.9003i	−1.72670	+	0.538701i
$489$	18.9185	−	18.2202i	0.855525	−	0.823947i
$490$	−0.484406	−	1.00313i	−0.0218833	−	0.0453168i
$491$	−5.06161	−	35.2043i	−0.228427	−	1.58875i	−0.704737	−	0.709469i	$-0.748935\pi$
$491$	−5.06161	−	35.2043i	−0.228427	−	1.58875i	0.476310	−	0.879278i	$-0.341974\pi$
$492$	1.69283	−	17.7926i	0.0763187	−	0.802152i
$493$	−12.5554	+	8.06884i	−0.565465	+	0.363402i
$494$	0.467218	−	0.383941i	0.0210211	−	0.0172743i
$495$	6.74967	+	1.56615i	0.303375	+	0.0703934i
$496$	6.77325	+	13.4443i	0.304128	+	0.603666i
$497$	−22.1408	−	7.66300i	−0.993150	−	0.343733i
$498$	−1.30056	−	1.42300i	−0.0582793	−	0.0637663i
$499$	−7.75593	+	4.47789i	−0.347203	+	0.200458i	−0.663453	−	0.748218i	$-0.730910\pi$
$499$	−7.75593	+	4.47789i	−0.347203	+	0.200458i	0.316250	+	0.948676i	$0.397576\pi$
$500$	0.0522580	−	0.351823i	0.00233705	−	0.0157340i
$501$	−3.27663	−	1.86998i	−0.146389	−	0.0835446i
$502$	−35.9016	−	15.4730i	−1.60237	−	0.690593i
$503$	2.95059	−	12.1625i	0.131560	−	0.542299i	−0.867438	−	0.497546i	$-0.834235\pi$
$503$	2.95059	−	12.1625i	0.131560	−	0.542299i	0.998998	−	0.0447533i	$-0.0142502\pi$
$504$	9.05612	+	20.9731i	0.403392	+	0.934216i
$505$	−17.9028	+	3.45048i	−0.796663	+	0.153544i
$506$	3.30787	−	1.22501i	0.147053	−	0.0544581i
$507$	−13.3984	+	17.2139i	−0.595044	+	0.764496i
$508$	−0.522603	−	0.414933i	−0.0231868	−	0.0184097i
$509$	32.6428	+	14.9075i	1.44687	+	0.660762i	0.975263	−	0.221048i	$-0.0709477\pi$
$509$	32.6428	+	14.9075i	1.44687	+	0.660762i	0.471605	+	0.881810i	$0.343675\pi$
$510$	41.8990	+	11.1069i	1.85532	+	0.491823i
$511$	8.93069	+	7.73849i	0.395071	+	0.342331i
$512$	−18.3944	+	13.1775i	−0.812924	+	0.582370i
$513$	−0.113676	+	3.48580i	−0.00501894	+	0.153902i
$514$	0.529691	−	20.2679i	0.0233637	−	0.893980i
$515$	−19.0163	−	26.7047i	−0.837959	−	1.17675i
$516$	39.6851	−	18.1400i	1.74704	−	0.798570i
$517$	1.79392	+	1.71050i	0.0788967	+	0.0752278i
$518$	−8.50318	+	38.6549i	−0.373608	+	1.69840i
$519$	12.8233	−	18.1997i	0.562881	−	0.798880i
$520$	5.15720	−	2.46084i	0.226158	−	0.107915i
$521$	−7.28919	−	24.8247i	−0.319345	−	1.08759i	−0.950188	−	0.311679i	$-0.899109\pi$
$521$	−7.28919	−	24.8247i	−0.319345	−	1.08759i	0.630842	−	0.775911i	$-0.282709\pi$
$522$	−5.97986	−	9.64333i	−0.261731	−	0.422077i
$523$	7.00920	−	36.3672i	0.306491	−	1.59023i	−0.422931	−	0.906162i	$-0.638999\pi$
$523$	7.00920	−	36.3672i	0.306491	−	1.59023i	0.729422	−	0.684064i	$-0.239789\pi$
$524$	0.180824	−	38.8270i	0.00789934	−	1.69617i
$525$	5.44395	−	22.9403i	0.237593	−	1.00120i
$526$	−21.0156	−	38.7011i	−0.916322	−	1.68745i
$527$	20.1510	+	5.91687i	0.877792	+	0.257743i
$528$	−0.501328	+	5.02113i	−0.0218175	+	0.218516i
$529$	−8.15813	+	7.77876i	−0.354701	+	0.338207i
$530$	1.64930	−	22.3294i	0.0716412	−	0.969929i
$531$	1.80598	+	11.7272i	0.0783730	+	0.508915i
$532$	3.57968	−	0.497676i	0.155199	−	0.0215770i
$533$	−3.25357	−	0.467793i	−0.140928	−	0.0202624i
$534$	0.513415	−	7.45844i	0.0222176	−	0.322758i
$535$			37.7727i			1.63306i
$536$	−17.8287	+	14.7695i	−0.770083	+	0.637943i
$537$	18.2203	+	2.52676i	0.786264	+	0.109038i
$538$	0.579954	+	8.38310i	0.0250036	+	0.361421i
$539$	0.0257470	−	0.179074i	0.00110900	−	0.00771328i
$540$	−8.95706	+	31.7148i	−0.385451	+	1.36479i
$541$	6.65834	+	14.5797i	0.286264	+	0.626832i	0.997065	−	0.0765621i	$-0.0243943\pi$
$541$	6.65834	+	14.5797i	0.286264	+	0.626832i	−0.710800	+	0.703394i	$0.751667\pi$
$542$	25.8939	+	1.91258i	1.11224	+	0.0821524i
$543$	1.54692	−	1.11326i	0.0663849	−	0.0477745i
$544$	−4.11230	+	31.2982i	−0.176313	+	1.34190i
$545$	5.36209	−	18.2616i	0.229687	−	0.782242i
$546$	3.93257	−	1.47875i	0.168299	−	0.0632848i
$547$	−0.0934971	+	0.979146i	−0.00399765	+	0.0418653i	−0.997251	−	0.0741024i	$-0.976391\pi$
$547$	−0.0934971	+	0.979146i	−0.00399765	+	0.0418653i	0.993253	+	0.115968i	$0.0369969\pi$
$548$	−14.8163	−	0.0690023i	−0.632923	−	0.00294763i
$549$	−37.8622	−	19.0425i	−1.61592	−	0.812714i
$550$	3.51212	−	3.84543i	0.149757	−	0.163970i
$551$	−1.72240	+	0.505743i	−0.0733768	+	0.0215454i
$552$	5.07661	+	15.9904i	0.216075	+	0.680597i
$553$	−35.0606	−	18.0750i	−1.49093	−	0.768627i
$554$	1.53623	+	0.337936i	0.0652683	+	0.0143575i
$555$	−44.7034	+	35.5183i	−1.89755	+	1.50767i
$556$	9.54398	−	6.07093i	0.404755	−	0.257465i
$557$	4.51883	−	3.21785i	0.191469	−	0.136345i	−0.480302	−	0.877103i	$-0.659473\pi$
$557$	4.51883	−	3.21785i	0.191469	−	0.136345i	0.671772	+	0.740758i	$0.265534\pi$
$558$	−4.74500	+	15.2459i	−0.200872	+	0.645412i
$559$	−2.98254	−	7.45002i	−0.126148	−	0.315102i
$560$	33.9640	+	3.56270i	1.43524	+	0.150551i
$561$	4.63658	+	5.29715i	0.195757	+	0.223646i
$562$	−0.784102	+	6.43090i	−0.0330753	+	0.271271i
$563$	−4.13840	+	9.06183i	−0.174413	+	0.381911i	−0.976569	−	0.215203i	$-0.930959\pi$
$563$	−4.13840	+	9.06183i	−0.174413	+	0.381911i	0.802157	+	0.597114i	$0.203686\pi$
$564$	−8.52939	+	8.13834i	−0.359152	+	0.342686i
$565$	−11.4657	+	19.8592i	−0.482367	+	0.835484i
$566$	−7.79176	−	21.0400i	−0.327512	−	0.884378i
$567$	−8.55392	+	22.6705i	−0.359231	+	0.952070i
$568$	19.0895	−	15.5386i	0.800977	−	0.651986i
$569$	−1.09226	−	0.264978i	−0.0457897	−	0.0111085i	0.212799	−	0.977096i	$-0.431742\pi$
$569$	−1.09226	−	0.264978i	−0.0457897	−	0.0111085i	−0.258588	+	0.965988i	$0.583257\pi$
$570$	4.45906	+	2.70163i	0.186770	+	0.113159i
$571$	−9.78124	+	24.4323i	−0.409332	+	1.02246i	0.570260	+	0.821464i	$0.306843\pi$
$571$	−9.78124	+	24.4323i	−0.409332	+	1.02246i	−0.979592	+	0.200998i	$0.935582\pi$
$572$	0.917961	+	0.136349i	0.0383819	+	0.00570105i
$573$	9.55259	+	23.5197i	0.399065	+	0.982550i
$574$	−15.1191	−	12.5427i	−0.631059	−	0.523523i
$575$	5.66316	−	16.3626i	0.236170	−	0.682369i
$576$	−23.7420	−	3.50987i	−0.989248	−	0.146245i
$577$	−1.15975	−	24.3461i	−0.0482809	−	1.01354i	−0.884907	−	0.465767i	$-0.845778\pi$
$577$	−1.15975	−	24.3461i	−0.0482809	−	1.01354i	0.836626	−	0.547774i	$-0.184525\pi$
$578$	12.6961	+	15.4499i	0.528089	+	0.642631i
$579$	32.7869	−	15.1719i	1.36258	−	0.630521i
$580$	−16.9467	+	0.728186i	−0.703674	+	0.0302363i
$581$	−2.09731	+	0.301547i	−0.0870110	+	0.0125103i
$582$	−25.1790	+	8.12305i	−1.04370	+	0.336711i
$583$	2.24784	−	2.85836i	0.0930959	−	0.118381i
$584$	−11.8512	+	3.69737i	−0.490406	+	0.152998i
$585$	5.74705	+	1.92494i	0.237611	+	0.0795864i
$586$	−29.1502	−	21.9277i	−1.20418	−	0.905824i
$587$	−24.2913	+	34.1124i	−1.00261	+	1.40797i	−0.0914989	+	0.995805i	$0.529166\pi$
$587$	−24.2913	+	34.1124i	−1.00261	+	1.40797i	−0.911110	+	0.412163i	$0.864774\pi$
$588$	0.844970	+	0.162554i	0.0348460	+	0.00670362i
$589$	2.12506	+	1.36570i	0.0875618	+	0.0562725i
$590$	16.6046	+	6.23727i	0.683600	+	0.256785i
$591$	28.7895	−	5.69816i	1.18424	−	0.234391i
$592$	−29.8247	−	28.9729i	−1.22579	−	1.19078i
$593$	26.1989	+	33.3146i	1.07586	+	1.36807i	0.925199	+	0.379483i	$0.123898\pi$
$593$	26.1989	+	33.3146i	1.07586	+	1.36807i	0.150662	+	0.988585i	$0.451859\pi$
$594$	−4.08367	+	3.45971i	−0.167555	+	0.141954i
$595$	36.0059	−	31.1993i	1.47610	−	1.27905i
$596$	5.95883	+	13.2105i	0.244083	+	0.541122i
$597$	−1.12777	+	26.4575i	−0.0461565	+	1.08283i
$598$	2.98218	−	0.791634i	0.121950	−	0.0323723i
$599$	−25.1009	+	12.9404i	−1.02560	+	0.528731i	−0.887073	−	0.461628i	$-0.847265\pi$
$599$	−25.1009	+	12.9404i	−1.02560	+	0.528731i	−0.138522	+	0.990359i	$0.544235\pi$
$600$	17.4800	+	17.5495i	0.713617	+	0.716456i
$601$	4.83990	+	19.9503i	0.197424	+	0.813792i	0.981239	+	0.192797i	$0.0617559\pi$
$601$	4.83990	+	19.9503i	0.197424	+	0.813792i	−0.783815	+	0.620994i	$0.786729\pi$
$602$	8.06324	−	47.2768i	0.328633	−	1.92686i
$603$	−24.4841	−	1.87885i	−0.997069	−	0.0765128i
$604$	−12.8259	+	36.5070i	−0.521877	+	1.48545i
$605$	−32.2644	+	7.82725i	−1.31173	+	0.318223i
$606$	6.11972	−	12.6841i	0.248597	−	0.515256i
$607$	−13.0368	−	25.2880i	−0.529149	−	1.02641i	−0.990282	−	0.139075i	$-0.955587\pi$
$607$	−13.0368	−	25.2880i	−0.529149	−	1.02641i	0.461133	−	0.887331i	$-0.347443\pi$
$608$	−1.53517	+	3.47268i	−0.0622595	+	0.140836i
$609$	−12.4603	−	0.531129i	−0.504918	−	0.0215224i
$610$	−52.5499	+	35.3887i	−2.12768	+	1.43285i
$611$	1.41983	+	1.63858i	0.0574404	+	0.0662897i
$612$	−26.2077	+	20.8375i	−1.05938	+	0.842308i
$613$	−7.19186	+	5.65574i	−0.290476	+	0.228433i	−0.752754	−	0.658302i	$-0.771275\pi$
$613$	−7.19186	+	5.65574i	−0.290476	+	0.228433i	0.462277	+	0.886735i	$0.347032\pi$
$614$	−33.6647	−	9.10450i	−1.35860	−	0.367428i
$615$	−5.50221	−	27.7995i	−0.221870	−	1.12098i
$616$	4.25206	+	3.56104i	0.171320	+	0.143478i
$617$	−14.6781	+	22.8396i	−0.590918	+	0.919487i	0.409057	+	0.912509i	$0.365858\pi$
$617$	−14.6781	+	22.8396i	−0.590918	+	0.919487i	−0.999976	+	0.00697814i	$0.997779\pi$
$618$	25.3175	+	0.534999i	1.01842	+	0.0215208i
$619$	−18.8152	−	13.3982i	−0.756246	−	0.538520i	0.135652	−	0.990756i	$-0.456687\pi$
$619$	−18.8152	−	13.3982i	−0.756246	−	0.538520i	−0.891898	+	0.452236i	$0.850626\pi$
$620$	16.3910	+	17.3515i	0.658280	+	0.696853i
$621$	−7.91581	+	15.9370i	−0.317650	+	0.639530i
$622$	−5.24245	+	3.90543i	−0.210203	+	0.156594i
$623$	−6.45910	−	5.07949i	−0.258778	−	0.203505i
$624$	−0.854020	+	4.33046i	−0.0341882	+	0.173357i
$625$	3.51752	+	24.4649i	0.140701	+	0.978595i
$626$	−2.21953	−	10.3186i	−0.0887102	−	0.412415i
$627$	0.355592	+	0.768446i	0.0142010	+	0.0306888i
$628$	−4.62825	+	2.64346i	−0.184687	+	0.105485i
$629$	−57.9427	+	2.76015i	−2.31033	+	0.110054i
$630$	23.2757	+	27.7537i	0.927328	+	1.10573i
$631$	−12.6954	−	4.39392i	−0.505396	−	0.174919i	0.0624595	−	0.998048i	$-0.480106\pi$
$631$	−12.6954	−	4.39392i	−0.505396	−	0.174919i	−0.567856	+	0.823128i	$0.692227\pi$
$632$	35.5348	−	21.3206i	1.41350	−	0.848087i
$633$	−27.6562	+	11.2326i	−1.09923	+	0.446457i
$634$	24.3296	−	0.522471i	0.966253	−	0.0207500i
$635$	−0.982251	−	0.393234i	−0.0389795	−	0.0156050i
$636$	13.0746	+	11.3213i	0.518441	+	0.448920i
$637$	0.0373086	−	0.153788i	0.00147822	−	0.00609331i
$638$	−2.34893	−	1.43926i	−0.0929952	−	0.0569809i
$639$	26.0126	+	2.22164i	1.02904	+	0.0878867i
$640$	−21.9657	+	28.3670i	−0.868272	+	1.12130i
$641$	−24.7123	−	14.2677i	−0.976078	−	0.563539i	−0.0749942	−	0.997184i	$-0.523894\pi$
$641$	−24.7123	−	14.2677i	−0.976078	−	0.563539i	−0.901084	+	0.433645i	$0.857227\pi$
$642$	−23.4040	−	17.4226i	−0.923681	−	0.687616i
$643$	−2.33112	−	1.06459i	−0.0919305	−	0.0419833i	0.368919	−	0.929462i	$-0.379728\pi$
$643$	−2.33112	−	1.06459i	−0.0919305	−	0.0419833i	−0.460850	+	0.887478i	$0.652455\pi$
$644$	17.6685	+	5.27745i	0.696238	+	0.207961i
$645$	52.0596	−	45.5676i	2.04984	−	1.79422i
$646$	2.07381	+	4.87413i	0.0815928	+	0.191770i
$647$	−29.4188	+	11.7775i	−1.15657	+	0.463022i	−0.869036	−	0.494748i	$-0.835260\pi$
$647$	−29.4188	+	11.7775i	−1.15657	+	0.463022i	−0.287536	+	0.957770i	$0.592836\pi$
$648$	−15.5190	−	20.1782i	−0.609645	−	0.792674i
$649$	1.67096	+	2.34654i	0.0655909	+	0.0921096i
$650$	3.37791	−	3.05639i	0.132492	−	0.119881i
$651$	10.9175	+	13.7408i	0.427891	+	0.538543i
$652$	28.1037	+	11.4032i	1.10062	+	0.446582i
$653$	−16.8821	+	32.7466i	−0.660646	+	1.28147i	0.285700	+	0.958319i	$0.407774\pi$
$653$	−16.8821	+	32.7466i	−0.660646	+	1.28147i	−0.946346	+	0.323155i	$0.895256\pi$
$654$	8.84163	+	11.7455i	0.345735	+	0.459285i
$655$	−17.3444	−	59.0697i	−0.677703	−	2.30805i
$656$	19.5649	−	6.56805i	0.763879	−	0.256439i
$657$	−11.7636	−	5.91642i	−0.458942	−	0.230821i
$658$	2.11901	+	12.7832i	0.0826075	+	0.498342i
$659$	−4.60951	−	0.440154i	−0.179561	−	0.0171460i	0.00488822	−	0.999988i	$-0.498444\pi$
$659$	−4.60951	−	0.440154i	−0.179561	−	0.0171460i	−0.184449	+	0.982842i	$0.559050\pi$
$660$	1.51688	+	7.85581i	0.0590443	+	0.305787i
$661$	−11.2048	−	3.29003i	−0.435817	−	0.127967i	0.0564623	−	0.998405i	$-0.482018\pi$
$661$	−11.2048	−	3.29003i	−0.435817	−	0.127967i	−0.492279	+	0.870437i	$0.663836\pi$
$662$	0.703178	+	1.15970i	0.0273298	+	0.0450732i
$663$	3.59686	+	4.99801i	0.139691	+	0.194106i
$664$	0.890548	−	2.04012i	0.0345599	−	0.0791721i
$665$	5.21257	−	2.38050i	0.202135	−	0.0923119i
$666$	−1.38775	−	44.0810i	−0.0537742	−	1.70810i
$667$	−9.06579	−	1.30346i	−0.351029	−	0.0504703i
$668$	0.434286	−	4.33462i	0.0168030	−	0.167711i
$669$	2.96016	−	21.3455i	0.114446	−	0.825264i
$670$	−20.3840	+	30.5288i	−0.787502	+	1.17943i
$671$	−10.2893			−0.397214
$672$	−17.8733	+	19.4008i	−0.689478	+	0.748402i
$673$	2.76286	−	19.2161i	0.106500	−	0.740726i	−0.864670	−	0.502340i	$-0.832473\pi$
$673$	2.76286	−	19.2161i	0.106500	−	0.740726i	0.971171	−	0.238386i	$-0.0766183\pi$
$674$	9.26626	+	29.2218i	0.356923	+	1.12558i
$675$	0.394070	+	26.2692i	0.0151678	+	1.01110i
$676$	−24.4503	−	6.05229i	−0.940396	−	0.232780i
$677$	24.2581	+	25.4411i	0.932314	+	0.977783i	0.999801	−	0.0199375i	$-0.00634672\pi$
$677$	24.2581	+	25.4411i	0.932314	+	0.977783i	−0.0674874	+	0.997720i	$0.521498\pi$
$678$	−7.01622	−	16.2642i	−0.269456	−	0.624623i
$679$	−8.19258	+	27.9014i	−0.314402	+	1.07076i
$680$	7.95509	+	49.4156i	0.305064	+	1.89500i
$681$	15.0696	+	3.57615i	0.577467	+	0.137038i
$682$	0.633942	+	3.82435i	0.0242749	+	0.146442i
$683$	39.1945	+	7.55413i	1.49974	+	0.289051i	0.872051	−	0.489415i	$-0.162790\pi$
$683$	39.1945	+	7.55413i	1.49974	+	0.289051i	0.627687	+	0.778466i	$0.284002\pi$
$684$	−3.73066	+	1.51671i	−0.142646	+	0.0579928i
$685$	−22.5409	+	6.61861i	−0.861245	+	0.252884i
$686$	−18.2195	+	18.1349i	−0.695624	+	0.692392i
$687$	−15.8014	−	11.1335i	−0.602861	−	0.424769i
$688$	37.7693	+	33.3482i	1.43994	+	1.27139i
$689$	2.19496	−	2.30201i	0.0836214	−	0.0876996i
$690$	14.9688	+	21.9896i	0.569853	+	0.837131i
$691$	11.9005	−	8.47430i	0.452716	−	0.322377i	−0.330853	−	0.943682i	$-0.607336\pi$
$691$	11.9005	−	8.47430i	0.452716	−	0.322377i	0.783569	+	0.621305i	$0.213397\pi$
$692$	25.2203	+	4.98274i	0.958732	+	0.189415i
$693$	0.617718	+	5.85018i	0.0234652	+	0.222230i
$694$	13.4803	+	31.6831i	0.511704	+	1.20267i
$695$	11.7447	−	13.5541i	0.445503	−	0.514138i
$696$	7.36547	−	10.8361i	0.279187	−	0.410740i
$697$	11.9605	−	26.1898i	0.453035	−	0.992009i
$698$	35.7593	+	19.6343i	1.35351	+	0.743170i
$699$	−19.2868	−	15.0118i	−0.729493	−	0.567800i
$700$	26.7565	−	5.02778i	1.01130	−	0.190032i
$701$	3.16019	+	16.3966i	0.119359	+	0.619292i	0.991507	+	0.130051i	$0.0415140\pi$
$701$	3.16019	+	16.3966i	0.119359	+	0.619292i	−0.872149	+	0.489241i	$0.837274\pi$
$702$	−3.84351	+	2.67299i	−0.145064	+	0.100886i
$703$	−6.78052	−	1.64494i	−0.255732	−	0.0620400i
$704$	−5.53235	+	1.82862i	−0.208508	+	0.0689187i
$705$	−9.26515	+	16.2346i	−0.348946	+	0.611432i
$706$	−3.58223	+	0.0769272i	−0.134819	+	0.00289519i
$707$	−7.73957	−	13.4053i	−0.291077	−	0.504159i
$708$	−11.5235	+	7.41126i	−0.433078	+	0.278532i
$709$	6.75902	−	19.5289i	0.253840	−	0.733424i	−0.744027	−	0.668150i	$-0.767087\pi$
$709$	6.75902	−	19.5289i	0.253840	−	0.733424i	0.997867	−	0.0652743i	$-0.0207922\pi$
$710$	21.9503	−	32.2695i	0.823782	−	1.21105i
$711$	42.8165	+	9.93488i	1.60574	+	0.372587i
$712$	8.10923	−	2.96023i	0.303906	−	0.110939i
$713$	6.96803	+	10.8425i	0.260955	+	0.406054i
$714$	2.72339	+	36.6999i	0.101920	+	1.37346i
$715$	1.45648	−	0.209410i	0.0544692	−	0.00783149i
$716$	5.88912	+	20.4076i	0.220087	+	0.762668i
$717$	−1.08390	−	1.12544i	−0.0404789	−	0.0420302i
$718$	−26.4518	+	19.7056i	−0.987171	+	0.735406i
$719$	0.0411406	−	0.863647i	0.00153428	−	0.0322086i	−0.997970	−	0.0636800i	$-0.979716\pi$
$719$	0.0411406	−	0.863647i	0.00153428	−	0.0322086i	0.999505	+	0.0314714i	$0.0100193\pi$
$720$	−37.6625	+	5.44142i	−1.40360	+	0.202790i
$721$	16.1448	−	22.6722i	0.601264	−	0.844357i
$722$	−3.05369	−	26.0546i	−0.113647	−	0.969652i
$723$	39.6021	+	33.9702i	1.47282	+	1.26337i
$724$	1.90072	+	1.10922i	0.0706397	+	0.0412237i
$725$	−12.7787	+	4.42276i	−0.474590	+	0.164257i
$726$	10.0321	−	23.6013i	0.372328	−	0.875926i
$727$	−0.557914	−	0.709446i	−0.0206919	−	0.0263119i	0.775597	−	0.631228i	$-0.217449\pi$
$727$	−0.557914	−	0.709446i	−0.0206919	−	0.0263119i	−0.796289	+	0.604916i	$0.793206\pi$
$728$	3.40639	+	3.45432i	0.126249	+	0.128025i
$729$	3.03913	−	26.8284i	0.112560	−	0.993645i
$730$	−16.3270	+	10.9951i	−0.604290	+	0.406947i
$731$	69.9727	−	6.68158i	2.58803	−	0.247127i
$732$	2.31178	−	48.8829i	0.0854458	−	1.80676i
$733$	40.1467	−	20.6971i	1.48285	−	0.764464i	0.488701	−	0.872451i	$-0.337471\pi$
$733$	40.1467	−	20.6971i	1.48285	−	0.764464i	0.994152	+	0.107987i	$0.0344406\pi$
$734$	−1.87072	+	5.80546i	−0.0690494	+	0.214284i
$735$	1.35748	−	0.136476i	0.0500714	−	0.00503400i
$736$	−14.4853	+	12.8632i	−0.533936	+	0.474145i
$737$	−5.51539	+	2.26333i	−0.203162	+	0.0833709i
$738$	19.7624	+	9.41330i	0.727464	+	0.346508i
$739$	−16.4468	+	3.98994i	−0.605004	+	0.146772i	−0.526548	−	0.850145i	$-0.676514\pi$
$739$	−16.4468	+	3.98994i	−0.605004	+	0.146772i	−0.0784557	+	0.996918i	$0.524999\pi$
$740$	−58.4584	−	30.4829i	−2.14898	−	1.12057i
$741$	0.245738	+	0.698690i	0.00902740	+	0.0256670i
$742$	18.3730	−	4.87720i	0.674493	−	0.179048i
$743$	−22.8843	+	2.18518i	−0.839542	+	0.0801665i	−0.505962	−	0.862556i	$-0.668863\pi$
$743$	−22.8843	+	2.18518i	−0.839542	+	0.0801665i	−0.333579	+	0.942722i	$0.608257\pi$
$744$	−18.3113	+	2.15252i	−0.671326	+	0.0789151i
$745$	15.0476	+	17.3659i	0.551303	+	0.636237i
$746$	3.53780	−	7.23992i	0.129528	−	0.265072i
$747$	2.18304	−	0.899390i	0.0798733	−	0.0329070i
$748$	−3.41121	+	7.37839i	−0.124726	+	0.269781i
$749$	−30.3052	+	10.4887i	−1.10733	+	0.383250i
$750$	0.382892	+	0.207749i	0.0139812	+	0.00758591i
$751$	22.3934	−	34.8447i	0.817145	−	1.27150i	−0.142361	−	0.989815i	$-0.545469\pi$
$751$	22.3934	−	34.8447i	0.817145	−	1.27150i	0.959506	−	0.281688i	$-0.0908942\pi$
$752$	−12.5901	−	5.17689i	−0.459114	−	0.188782i
$753$	32.8674	−	34.8172i	1.19775	−	1.26881i
$754$	−1.92566	−	1.44854i	−0.0701285	−	0.0527528i
$755$	−2.91928	+	61.2831i	−0.106243	+	2.23032i
$756$	−27.9321	+	1.62028i	−1.01588	+	0.0589290i
$757$	−37.5116	−	29.4994i	−1.36338	−	1.07217i	−0.989474	−	0.144709i	$-0.953775\pi$
$757$	−37.5116	−	29.4994i	−1.36338	−	1.07217i	−0.373907	−	0.927466i	$-0.621982\pi$
$758$	14.0921	+	29.1826i	0.511850	+	1.05996i
$759$	0.0216010	+	4.32013i	0.000784065	+	0.156811i
$760$	−0.756452	+	5.97248i	−0.0274394	+	0.216645i
$761$	−1.03225	−	1.60622i	−0.0374192	−	0.0582254i	0.822040	−	0.569430i	$-0.192836\pi$
$761$	−1.03225	−	1.60622i	−0.0374192	−	0.0582254i	−0.859459	+	0.511204i	$0.829200\pi$
$762$	0.696710	−	0.427224i	0.0252391	−	0.0154767i
$763$	16.1403	−	0.768857i	0.584318	−	0.0278345i
$764$	−20.3267	+	21.1202i	−0.735394	+	0.764102i
$765$	−30.3601	+	43.5500i	−1.09767	+	1.57455i
$766$	−9.88310	−	8.19895i	−0.357091	−	0.296240i
$767$	1.25988	+	2.18218i	0.0454917	+	0.0787939i
$768$	−7.44450	−	26.6942i	−0.268630	−	0.963243i
$769$	−16.6202	−	6.65372i	−0.599339	−	0.239939i	0.0520978	−	0.998642i	$-0.483409\pi$
$769$	−16.6202	−	6.65372i	−0.599339	−	0.239939i	−0.651437	+	0.758703i	$0.725833\pi$
$770$	8.07586	+	3.48056i	0.291034	+	0.125431i
$771$	23.0986	+	9.11356i	0.831877	+	0.328217i
$772$	31.3992	+	27.4647i	1.13008	+	0.988475i
$773$	−3.18149	−	16.5071i	−0.114430	−	0.593721i	−0.993195	−	0.116465i	$-0.962844\pi$
$773$	−3.18149	−	16.5071i	−0.114430	−	0.593721i	0.878765	−	0.477256i	$-0.158368\pi$
$774$	4.22126	+	53.2741i	0.151730	+	1.91490i
$775$	16.4793	+	9.51433i	0.591954	+	0.341765i
$776$	−20.3912	−	22.7483i	−0.732001	−	0.816618i
$777$	−40.9097	−	26.0030i	−1.46763	−	0.932851i
$778$	5.41035	−	44.3737i	0.193971	−	1.59087i
$779$	2.26780	−	2.61718i	0.0812525	−	0.0937704i
$780$	0.667636	+	6.96656i	0.0239052	+	0.249443i
$781$	5.88430	−	2.35572i	0.210557	−	0.0842942i
$782$	−0.706070	+	27.0168i	−0.0252490	+	0.966120i
$783$	13.6050	−	2.83443i	0.486202	−	0.101294i
$784$	0.225241	+	0.967711i	0.00804434	+	0.0345611i
$785$	−5.83187	+	6.11628i	−0.208148	+	0.218300i
$786$	44.5997	+	16.4992i	1.59082	+	0.588508i
$787$	−19.6167	+	38.0511i	−0.699260	+	1.35637i	0.224905	+	0.974381i	$0.427793\pi$
$787$	−19.6167	+	38.0511i	−0.699260	+	1.35637i	−0.924165	+	0.381994i	$0.875237\pi$
$788$	19.5283	+	27.6957i	0.695666	+	0.986619i
$789$	53.3484	−	7.94280i	1.89925	−	0.282771i
$790$	44.3110	−	48.5163i	1.57652	−	1.72613i
$791$	−19.1169	−	3.68449i	−0.679720	−	0.131005i
$792$	−5.56711	−	2.68362i	−0.197819	−	0.0953584i
$793$	−8.95939	−	0.855518i	−0.318157	−	0.0303803i
$794$	−21.7160	−	39.9910i	−0.770672	−	1.41923i
$795$	25.0009	+	11.2668i	0.886691	+	0.399592i
$796$	−28.4405	+	11.2325i	−1.00805	+	0.398124i
$797$	−4.44128	−	4.65788i	−0.157318	−	0.164991i	0.640358	−	0.768077i	$-0.278786\pi$
$797$	−4.44128	−	4.65788i	−0.157318	−	0.164991i	−0.797676	+	0.603086i	$0.793938\pi$
$798$	−0.929334	+	4.32771i	−0.0328981	+	0.153199i
$799$	−17.2750	+	7.88921i	−0.611144	+	0.279100i
$800$	−10.3065	+	26.6800i	−0.364391	+	0.943280i
$801$	8.36649	+	3.72019i	0.295615	+	0.131446i
$802$	1.31138	+	18.9558i	0.0463066	+	0.669351i
$803$	−3.19684			−0.112814
$804$	−9.51355	−	26.7113i	−0.335517	−	0.942034i
$805$	29.2376			1.03049
$806$	0.234024	+	3.38276i	0.00824313	+	0.119153i
$807$	−9.88919	−	2.85010i	−0.348116	−	0.100328i
$808$	16.2542	+	0.500554i	0.571820	+	0.0176094i
$809$	−33.5521	+	15.3227i	−1.17963	+	0.538718i	−0.906066	−	0.423137i	$-0.860929\pi$
$809$	−33.5521	+	15.3227i	−1.17963	+	0.538718i	−0.273562	+	0.961854i	$0.588202\pi$
$810$	−32.7338	−	23.6133i	−1.15015	−	0.829685i
$811$	19.4104	+	20.3570i	0.681590	+	0.714832i	0.970116	−	0.242641i	$-0.0780136\pi$
$811$	19.4104	+	20.3570i	0.681590	+	0.714832i	−0.288526	+	0.957472i	$0.593165\pi$
$812$	−5.28999	−	13.3942i	−0.185642	−	0.470045i
$813$	−13.0653	+	28.9918i	−0.458220	+	1.01679i
$814$	−5.10956	−	9.40949i	−0.179090	−	0.329802i
$815$	47.8709	+	4.57112i	1.67684	+	0.160119i
$816$	−34.2872	−	17.8639i	−1.20029	−	0.625362i
$817$	8.30175	+	1.60003i	0.290442	+	0.0559780i
$818$	−27.8800	+	30.5259i	−0.974801	+	1.06731i
$819$	0.0514560	+	5.14540i	0.00179802	+	0.179795i
$820$	26.7433	−	18.8567i	0.933916	−	0.658505i
$821$	1.54563	−	2.99811i	0.0539429	−	0.104635i	−0.860323	−	0.509749i	$-0.829738\pi$
$821$	1.54563	−	2.99811i	0.0539429	−	0.104635i	0.914266	+	0.405115i	$0.132768\pi$
$822$	6.29608	−	17.0192i	0.219601	−	0.593612i
$823$	4.57756	−	4.80080i	0.159564	−	0.167345i	−0.639099	−	0.769124i	$-0.720693\pi$
$823$	4.57756	−	4.80080i	0.159564	−	0.167345i	0.798663	+	0.601779i	$0.205541\pi$
$824$	11.3225	+	26.9595i	0.394439	+	0.939178i
$825$	2.95104	+	5.65463i	0.102742	+	0.196869i
$826$	−0.393425	+	15.0539i	−0.0136890	+	0.523792i
$827$	45.4726	−	18.2045i	1.58124	−	0.633032i	0.595810	−	0.803126i	$-0.296831\pi$
$827$	45.4726	−	18.2045i	1.58124	−	0.633032i	0.985428	+	0.170094i	$0.0544071\pi$
$828$	−20.5291	−	0.868015i	−0.713436	−	0.0301656i
$829$	26.5133	−	30.5980i	0.920846	−	1.06271i	−0.0769947	−	0.997031i	$-0.524532\pi$
$829$	26.5133	−	30.5980i	0.920846	−	1.06271i	0.997841	−	0.0656813i	$-0.0209221\pi$
$830$	0.427179	−	3.50356i	0.0148276	−	0.121610i
$831$	−1.03342	+	1.62584i	−0.0358488	+	0.0563999i
$832$	−4.96933	+	1.13227i	−0.172280	+	0.0392546i
$833$	1.20042	+	0.693063i	0.0415921	+	0.0240132i
$834$	2.98090	+	13.5289i	0.103220	+	0.468466i
$835$	−1.30720	−	6.78241i	−0.0452376	−	0.234715i
$836$	−0.643706	+	0.735923i	−0.0222630	+	0.0254524i
$837$	−15.5515	−	11.8567i	−0.537539	−	0.409827i
$838$	33.3879	+	14.3896i	1.15337	+	0.497081i
$839$	−1.45491	−	0.582458i	−0.0502291	−	0.0201087i	0.346412	−	0.938083i	$-0.387400\pi$
$839$	−1.45491	−	0.582458i	−0.0502291	−	0.0201087i	−0.396641	+	0.917974i	$0.629824\pi$
$840$	−18.3501	+	37.5852i	−0.633138	+	1.29681i
$841$	−10.9235	−	18.9201i	−0.376674	−	0.652418i
$842$	−9.42724	−	7.82077i	−0.324884	−	0.269522i
$843$	−7.07059	−	3.60051i	−0.243524	−	0.124008i
$844$	−24.8347	−	23.9016i	−0.854844	−	0.822727i
$845$	−39.8924	+	1.90031i	−1.37234	+	0.0653726i
$846$	−5.78543	−	13.2289i	−0.198907	−	0.454819i
$847$	−15.2390	−	23.7123i	−0.523618	−	0.814766i
$848$	−5.80458	+	19.1084i	−0.199330	+	0.656184i
$849$	27.4786	−	0.137395i	0.943062	−	0.00471538i
$850$	17.3511	+	35.9315i	0.595139	+	1.23244i
$851$	−27.9827	−	22.0058i	−0.959233	−	0.754349i
$852$	9.86958	+	28.4847i	0.338126	+	0.975869i
$853$	0.817198	−	17.1551i	0.0279803	−	0.587380i	−0.940726	−	0.339168i	$-0.889854\pi$
$853$	0.817198	−	17.1551i	0.0279803	−	0.587380i	0.968706	−	0.248211i	$-0.0798426\pi$
$854$	−42.9845	−	32.3343i	−1.47090	−	1.10646i
$855$	−4.97952	+	3.99717i	−0.170296	+	0.136700i
$856$	7.39125	−	32.8698i	0.252628	−	1.12347i
$857$	25.5034	−	39.6840i	0.871179	−	1.35558i	−0.0627151	−	0.998031i	$-0.519976\pi$
$857$	25.5034	−	39.6840i	0.871179	−	1.35558i	0.933894	−	0.357550i	$-0.116388\pi$
$858$	−0.542048	+	0.999023i	−0.0185052	+	0.0341061i
$859$	11.0023	−	3.80795i	0.375395	−	0.129925i	−0.132854	−	0.991136i	$-0.542414\pi$
$859$	11.0023	−	3.80795i	0.375395	−	0.129925i	0.508249	+	0.861210i	$0.330293\pi$
$860$	72.5136	+	33.5249i	2.47269	+	1.14319i
$861$	20.7757	−	12.1338i	0.708036	−	0.413519i
$862$	16.6655	−	34.1051i	0.567629	−	1.16162i
$863$	−28.1077	−	32.4381i	−0.956799	−	1.10420i	−0.994481	−	0.104915i	$-0.966543\pi$
$863$	−28.1077	−	32.4381i	−0.956799	−	1.10420i	0.0376824	−	0.999290i	$-0.488002\pi$
$864$	14.0003	−	25.8455i	0.476300	−	0.879283i
$865$	40.5769	−	3.87462i	1.37965	−	0.131741i
$866$	−35.6203	+	9.45559i	−1.21043	+	0.321314i
$867$	−23.1042	+	8.12602i	−0.784659	+	0.275974i
$868$	−9.36972	+	17.9688i	−0.318029	+	0.609899i
$869$	10.3704	−	2.51582i	0.351790	−	0.0853433i
$870$	6.27269	−	19.8049i	0.212664	−	0.671450i
$871$	−4.99070	+	1.51221i	−0.169104	+	0.0512392i
$872$	−8.23947	+	14.8420i	−0.279024	+	0.502615i
$873$	1.21806	−	32.3800i	0.0412250	−	1.09590i
$874$	−0.996992	+	3.09400i	−0.0337238	+	0.104656i
$875$	0.425574	−	0.219399i	0.0143870	−	0.00741703i
$876$	0.718260	−	15.1877i	0.0242677	−	0.513145i
$877$	46.8458	−	4.47323i	1.58187	−	0.151050i	0.733215	−	0.679997i	$-0.238019\pi$
$877$	46.8458	−	4.47323i	1.58187	−	0.151050i	0.848655	+	0.528947i	$0.177413\pi$
$878$	30.4242	−	20.4886i	1.02677	−	0.691456i
$879$	37.4616	−	24.3406i	1.26355	−	0.820989i
$880$	−7.57518	+	5.28862i	−0.255359	+	0.178279i
$881$	−11.8410	−	15.0571i	−0.398934	−	0.507285i	0.544539	−	0.838735i	$-0.316705\pi$
$881$	−11.8410	−	15.0571i	−0.398934	−	0.507285i	−0.943473	+	0.331450i	$0.892462\pi$
$882$	−0.541575	+	0.904043i	−0.0182358	+	0.0304407i
$883$	−24.7559	+	8.56810i	−0.833103	+	0.288340i	−0.710130	−	0.704070i	$-0.751364\pi$
$883$	−24.7559	+	8.56810i	−0.833103	+	0.288340i	−0.122973	+	0.992410i	$0.539243\pi$
$884$	−3.58380	+	6.14109i	−0.120536	+	0.206547i
$885$	−14.1438	+	16.4887i	−0.475439	+	0.554261i
$886$	5.58557	+	47.6570i	0.187651	+	1.60107i
$887$	−26.5007	+	37.2151i	−0.889808	+	1.24956i	0.0777656	+	0.996972i	$0.475221\pi$
$887$	−26.5007	+	37.2151i	−0.889808	+	1.24956i	−0.967574	+	0.252589i	$0.918718\pi$
$888$	45.8510	−	22.1606i	1.53866	−	0.743662i
$889$	0.0427416	−	0.897257i	0.00143351	−	0.0300930i
$890$	10.9766	−	8.17716i	0.367936	−	0.274099i
$891$	−2.26741	−	6.15043i	−0.0759610	−	0.206047i
$892$	23.9079	−	6.89923i	0.800497	−	0.231003i
$893$	−2.26099	+	0.325081i	−0.0756611	+	0.0108784i
$894$	−17.7006	+	1.31351i	−0.591997	+	0.0439303i
$895$	18.2077	+	28.3317i	0.608615	+	0.947024i
$896$	−28.8584	−	9.74624i	−0.964090	−	0.325599i
$897$	−0.340394	+	3.76354i	−0.0113654	+	0.125661i
$898$	6.24653	−	9.18310i	0.208449	−	0.306444i
$899$	3.29211	−	9.51192i	0.109798	−	0.317240i
$900$	−27.5273	+	12.7495i	−0.917577	+	0.424983i
$901$	13.9303	+	24.1280i	0.464086	+	0.803820i
$902$	5.31318	−	0.114099i	0.176910	−	0.00379908i
$903$	51.0150	+	29.1144i	1.69767	+	0.968866i
$904$	13.8635	−	15.0379i	0.461093	−	0.500154i
$905$	3.39100	+	0.822648i	0.112721	+	0.0273457i
$906$	−36.6245	−	30.0755i	−1.21677	−	0.999193i
$907$	−3.36003	−	17.4335i	−0.111568	−	0.578869i	−0.994086	−	0.108592i	$-0.965366\pi$
$907$	−3.36003	−	17.4335i	−0.111568	−	0.578869i	0.882518	−	0.470278i	$-0.155846\pi$
$908$	3.30277	+	17.5765i	0.109606	+	0.583296i
$909$	12.0270	+	12.3636i	0.398909	+	0.410073i
$910$	6.74265	+	3.70217i	0.223517	+	0.122726i
$911$	14.9652	−	32.7693i	0.495820	−	1.08569i	−0.481985	−	0.876179i	$-0.660084\pi$
$911$	14.9652	−	32.7693i	0.495820	−	1.08569i	0.977805	−	0.209515i	$-0.0671885\pi$
$912$	−3.35163	−	3.22349i	−0.110984	−	0.106741i
$913$	0.375377	−	0.433208i	0.0124232	−	0.0143371i
$914$	16.0094	+	37.6274i	0.529544	+	1.24460i
$915$	−18.6702	−	75.3140i	−0.617218	−	2.48980i
$916$	4.32612	−	21.8968i	0.142939	−	0.723491i
$917$	42.5757	−	30.3180i	1.40597	−	1.00119i
$918$	−12.9800	−	38.8985i	−0.428404	−	1.28384i
$919$	14.1584	−	14.8489i	0.467044	−	0.489822i	−0.447514	−	0.894277i	$-0.647690\pi$
$919$	14.1584	−	14.8489i	0.467044	−	0.489822i	0.914558	+	0.404455i	$0.132539\pi$
$920$	−16.1696	+	26.1156i	−0.533095	+	0.861006i
$921$	24.6010	−	34.9155i	0.810632	−	1.15051i
$922$	−14.7663	+	14.6977i	−0.486302	+	0.484043i
$923$	5.31961	−	1.56198i	0.175097	−	0.0514132i
$924$	−5.88153	+	3.39839i	−0.193488	+	0.111799i
$925$	−51.6089	−	9.94679i	−1.69689	−	0.327048i
$926$	−7.50004	−	45.2451i	−0.246467	−	1.48685i
$927$	−11.2384	+	28.9066i	−0.369116	+	0.949416i
$928$	14.8895	+	2.68241i	0.488773	+	0.0880546i
$929$	−3.86555	+	13.1649i	−0.126825	+	0.431925i	−0.998285	−	0.0585408i	$-0.981355\pi$
$929$	−3.86555	+	13.1649i	−0.126825	+	0.431925i	0.871460	+	0.490466i	$0.163173\pi$
$930$	−26.8426	+	11.5796i	−0.880203	+	0.379711i
$931$	0.115051	+	0.120662i	0.00377066	+	0.00395455i
$932$	6.78110	−	27.3946i	0.222122	−	0.897340i
$933$	−2.29407	−	7.67078i	−0.0751044	−	0.251130i
$934$	4.72918	+	14.9138i	0.154744	+	0.487995i
$935$	−1.83426	+	12.7575i	−0.0599866	+	0.417216i
$936$	−4.62442	−	2.79965i	−0.151154	−	0.0915094i
$937$	−17.6806			−0.577599			−0.288800	−	0.957390i	$-0.593256\pi$
$937$	−17.6806			−0.577599			−0.288800	+	0.957390i	$0.593256\pi$
$938$	−30.1536	−	7.87690i	−0.984550	−	0.257190i
$939$	12.8042	+	1.77567i	0.417849	+	0.0579467i
$940$	−21.4766	−	2.15175i	−0.700490	−	0.0701822i
$941$	−1.13894	−	0.163755i	−0.0371284	−	0.00533825i	0.123726	−	0.992316i	$-0.460516\pi$
$941$	−1.13894	−	0.163755i	−0.0371284	−	0.00533825i	−0.160854	+	0.986978i	$0.551425\pi$
$942$	−1.09971	−	6.43455i	−0.0358304	−	0.209649i
$943$	16.0723	−	7.33997i	0.523386	−	0.239022i
$944$	−13.2288	−	8.67682i	−0.430562	−	0.282406i
$945$	−41.7004	+	15.1368i	−1.35651	+	0.492400i
$946$	6.72696	+	11.0943i	0.218712	+	0.360707i
$947$	−23.0150	−	6.75780i	−0.747886	−	0.219599i	−0.114487	−	0.993425i	$-0.536523\pi$
$947$	−23.0150	−	6.75780i	−0.747886	−	0.219599i	−0.633399	+	0.773826i	$0.718341\pi$
$948$	9.62229	+	49.8332i	0.312517	+	1.61851i
$949$	−2.78364	−	0.265806i	−0.0903609	−	0.00862842i
$950$	0.784849	+	4.73471i	0.0254639	+	0.153614i
$951$	−9.60714	+	28.2136i	−0.311533	+	0.914890i
$952$	−37.4374	+	20.1041i	−1.21335	+	0.651578i
$953$	4.63376	+	15.7812i	0.150102	+	0.511202i	0.999873	−	0.0159513i	$-0.00507767\pi$
$953$	4.63376	+	15.7812i	0.150102	+	0.511202i	−0.849770	+	0.527153i	$0.823259\pi$
$954$	−18.5125	+	10.2938i	−0.599366	+	0.333273i
$955$	−21.2971	+	41.3107i	−0.689159	+	1.33678i
$956$	0.678359	−	1.67185i	0.0219397	−	0.0540715i
$957$	2.64163	−	2.09886i	0.0853918	−	0.0678466i
$958$	−11.7311	+	10.6145i	−0.379014	+	0.342938i
$959$	−11.5693	−	16.2468i	−0.373592	−	0.524637i
$960$	−23.4234	−	37.1767i	−0.755989	−	1.19987i
$961$	15.6299	−	6.25728i	0.504191	−	0.201848i
$962$	−3.66678	−	8.61814i	−0.118222	−	0.277860i
$963$	29.8669	−	19.6191i	0.962447	−	0.632215i
$964$	−17.2426	+	57.7271i	−0.555348	+	1.85927i
$965$	60.1661	+	27.4770i	1.93682	+	0.884515i
$966$	−13.4858	+	18.1156i	−0.433899	+	0.582860i
$967$	−29.2697	−	16.8989i	−0.941251	−	0.543431i	−0.0508984	−	0.998704i	$-0.516208\pi$
$967$	−29.2697	−	16.8989i	−0.941251	−	0.543431i	−0.890352	+	0.455273i	$0.849542\pi$
$968$	29.6081	−	0.497884i	0.951640	−	0.0160026i
$969$	−6.47845	+	0.341081i	−0.208118	+	0.0109571i
$970$	−41.3021	−	25.3070i	−1.32613	−	0.812559i
$971$	−8.09709	+	33.3767i	−0.259848	+	1.07111i	0.681001	+	0.732282i	$0.261545\pi$
$971$	−8.09709	+	33.3767i	−0.259848	+	1.07111i	−0.940849	+	0.338826i	$0.889970\pi$
$972$	29.7292	−	9.39023i	0.953564	−	0.301192i
$973$	14.1358	+	5.65912i	0.453173	+	0.181423i
$974$	15.2145	−	0.326726i	0.487503	−	0.0104690i
$975$	2.09946	+	5.16913i	0.0672364	+	0.165545i
$976$	52.6537	−	20.5124i	1.68540	−	0.656587i
$977$	6.70974	+	2.32226i	0.214664	+	0.0742958i	0.432283	−	0.901738i	$-0.357708\pi$
$977$	6.70974	+	2.32226i	0.214664	+	0.0742958i	−0.217620	+	0.976034i	$0.569829\pi$
$978$	−24.9127	+	27.5524i	−0.796619	+	0.881027i
$979$	2.22045	−	0.105773i	0.0709659	−	0.00338052i
$980$	0.781330	+	1.36798i	0.0249587	+	0.0436984i
$981$	−17.2245	+	5.24523i	−0.549937	+	0.167467i
$982$	10.5772	+	49.1736i	0.337532	+	1.56919i
$983$	−5.71924	−	39.7782i	−0.182416	−	1.26873i	−0.851029	−	0.525118i	$-0.824021\pi$
$983$	−5.71924	−	39.7782i	−0.182416	−	1.26873i	0.668614	−	0.743610i	$-0.266888\pi$
$984$	−0.651689	+	25.2678i	−0.0207751	+	0.805507i
$985$	42.2361	+	33.2148i	1.34575	+	1.05831i
$986$	16.9261	−	12.6093i	0.539036	−	0.401562i
$987$	−15.5979	−	2.92543i	−0.496485	−	0.0931175i
$988$	−0.621696	+	0.587282i	−0.0197788	+	0.0186839i
$989$	35.1380	+	25.0217i	1.11732	+	0.795643i
$990$	−9.67558	−	1.55080i	−0.307510	−	0.0492877i
$991$	5.61668	−	8.73973i	0.178420	−	0.277627i	−0.740512	−	0.672043i	$-0.765417\pi$
$991$	5.61668	−	8.73973i	0.178420	−	0.277627i	0.918932	+	0.394416i	$0.129053\pi$
$992$	−10.8682	−	18.3066i	−0.345066	−	0.581236i
$993$	−1.62943	+	0.322506i	−0.0517085	+	0.0102344i
$994$	31.9851	+	8.65025i	1.01451	+	0.274369i
$995$	−38.1109	+	29.9707i	−1.20820	+	0.950136i
$996$	1.97377	+	1.88069i	0.0625412	+	0.0595920i
$997$	−30.1199	−	34.7602i	−0.953908	−	1.10087i	−0.994815	−	0.101705i	$-0.967570\pi$
$997$	−30.1199	−	34.7602i	−0.953908	−	1.10087i	0.0409070	−	0.999163i	$-0.486975\pi$
$998$	10.5053	−	7.07460i	0.332540	−	0.223943i
$999$	51.3032	+	16.8989i	1.62316	+	0.534656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.23.2	✓	2640
3.2	odd	2	inner	804.2.bd.a.23.131	yes	2640
4.3	odd	2	inner	804.2.bd.a.23.18	yes	2640
12.11	even	2	inner	804.2.bd.a.23.115	yes	2640
67.35	even	33	inner	804.2.bd.a.35.115	yes	2640
201.35	odd	66	inner	804.2.bd.a.35.18	yes	2640
268.35	odd	66	inner	804.2.bd.a.35.131	yes	2640
804.35	even	66	inner	804.2.bd.a.35.2	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.2	✓	2640	1.1	even	1	trivial
804.2.bd.a.23.18	yes	2640	4.3	odd	2	inner
804.2.bd.a.23.115	yes	2640	12.11	even	2	inner
804.2.bd.a.23.131	yes	2640	3.2	odd	2	inner
804.2.bd.a.35.2	yes	2640	804.35	even	66	inner
804.2.bd.a.35.18	yes	2640	201.35	odd	66	inner
804.2.bd.a.35.115	yes	2640	67.35	even	33	inner
804.2.bd.a.35.131	yes	2640	268.35	odd	66	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.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41084 + 0.0976039i) q^{2} +(0.479660 - 1.66431i) q^{3} +(1.98095 - 0.275407i) q^{4} +(2.88456 - 1.31734i) q^{5} +(-0.514280 + 2.39489i) q^{6} +(1.85789 + 1.94850i) q^{7} +(-2.76792 + 0.581904i) q^{8} +(-2.53985 - 1.59660i) q^{9} +O(q^{10})\)	\(q+(-1.41084 + 0.0976039i) q^{2} +(0.479660 - 1.66431i) q^{3} +(1.98095 - 0.275407i) q^{4} +(2.88456 - 1.31734i) q^{5} +(-0.514280 + 2.39489i) q^{6} +(1.85789 + 1.94850i) q^{7} +(-2.76792 + 0.581904i) q^{8} +(-2.53985 - 1.59660i) q^{9} +(-3.94108 + 2.14010i) q^{10} +(-0.725043 - 0.0692332i) q^{11} +(0.491817 - 3.42901i) q^{12} +(-0.625573 - 0.120569i) q^{13} +(-2.81137 - 2.56768i) q^{14} +(-0.808847 - 5.43268i) q^{15} +(3.84830 - 1.09113i) q^{16} +(2.55706 - 4.96000i) q^{17} +(3.73917 + 2.00466i) q^{18} +(0.463180 - 0.485769i) q^{19} +(5.35136 - 3.40400i) q^{20} +(4.13406 - 2.15749i) q^{21} +(1.02968 + 0.0269101i) q^{22} +(3.17927 - 1.27279i) q^{23} +(-0.359191 + 4.88579i) q^{24} +(3.31103 - 3.82113i) q^{25} +(0.894353 + 0.109046i) q^{26} +(-3.87551 + 3.46128i) q^{27} +(4.21701 + 3.34819i) q^{28} +(-2.31618 - 1.33725i) q^{29} +(1.67141 + 7.58570i) q^{30} +(0.712251 + 3.69551i) q^{31} +(-5.32284 + 1.91503i) q^{32} +(-0.462999 + 1.17349i) q^{33} +(-3.12349 + 7.24736i) q^{34} +(7.92602 + 3.17310i) q^{35} +(-5.47103 - 2.46329i) q^{36} +(-5.19757 - 9.00245i) q^{37} +(-0.606061 + 0.730551i) q^{38} +(-0.500727 + 0.983316i) q^{39} +(-7.21768 + 5.32482i) q^{40} +(5.15363 - 0.245498i) q^{41} +(-5.62192 + 3.44737i) q^{42} +(6.81001 + 10.5966i) q^{43} +(-1.45534 + 0.0625347i) q^{44} +(-9.42963 - 1.25967i) q^{45} +(-4.36121 + 2.10601i) q^{46} +(-2.67511 - 2.10373i) q^{47} +(0.0298899 - 6.92814i) q^{48} +(-0.0118191 + 0.248113i) q^{49} +(-4.29838 + 5.71418i) q^{50} +(-7.02847 - 6.63485i) q^{51} +(-1.27243 - 0.0665542i) q^{52} +(-2.69922 + 4.20007i) q^{53} +(5.12989 - 5.26158i) q^{54} +(-2.18263 + 0.755417i) q^{55} +(-6.27633 - 4.31218i) q^{56} +(-0.586302 - 1.00388i) q^{57} +(3.39828 + 1.66058i) q^{58} +(-2.59006 - 2.98909i) q^{59} +(-3.09848 - 10.5391i) q^{60} +(14.0631 - 1.34286i) q^{61} +(-1.36557 - 5.14426i) q^{62} +(-1.60779 - 7.91521i) q^{63} +(7.32278 - 3.22133i) q^{64} +(-1.96334 + 0.476300i) q^{65} +(0.538681 - 1.70079i) q^{66} +(7.24286 - 3.81326i) q^{67} +(3.69938 - 10.5297i) q^{68} +(-0.593345 - 5.90179i) q^{69} +(-11.4921 - 3.70313i) q^{70} +(-7.73502 + 3.98768i) q^{71} +(7.95918 + 2.94132i) q^{72} +(4.36934 - 0.417221i) q^{73} +(8.21162 + 12.1937i) q^{74} +(-4.77138 - 7.34342i) q^{75} +(0.783751 - 1.08985i) q^{76} +(-1.21215 - 1.54137i) q^{77} +(0.610471 - 1.43618i) q^{78} +(-13.8455 + 4.79198i) q^{79} +(9.66328 - 8.21695i) q^{80} +(3.90171 + 8.11028i) q^{81} +(-7.24699 + 0.849373i) q^{82} +(-0.456515 + 0.641086i) q^{83} +(7.59516 - 5.41242i) q^{84} +(0.842010 - 17.6760i) q^{85} +(-10.6421 - 14.2854i) q^{86} +(-3.33657 + 3.21342i) q^{87} +(2.04715 - 0.230273i) q^{88} +(-3.02104 + 0.434359i) q^{89} +(13.4267 + 0.856819i) q^{90} +(-0.927317 - 1.44293i) q^{91} +(5.94742 - 3.39692i) q^{92} +(6.49211 + 0.587180i) q^{93} +(3.97949 + 2.70693i) q^{94} +(0.696151 - 2.01140i) q^{95} +(0.634043 + 9.77742i) q^{96} +(5.40049 + 9.35392i) q^{97} +(-0.00754195 - 0.351202i) q^{98} +(1.73096 + 1.33345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

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