LMFDB - Embedded newform 804.2.bd.a.35.2

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			35.2
Character	$\chi$	$=$	804.35
Dual form			804.2.bd.a.23.2

$q$-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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{19}{33}\right)$	$-1$

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	0.937926	−	0.346836i	$-0.112744\pi$
$5$	2.88456	+	1.31734i	1.29002	+	0.589131i	0.352090	+	0.935966i	$0.385471\pi$
$6$	−0.514280	−	2.39489i	−0.209954	−	0.977711i
$7$	1.85789	−	1.94850i	0.702216	−	0.736463i	−0.271946	−	0.962312i	$-0.587667\pi$
$7$	1.85789	−	1.94850i	0.702216	−	0.736463i	0.974162	+	0.225850i	$0.0725158\pi$
$8$	−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	−0.203786	−	0.979016i	$-0.565325\pi$
$11$	−0.725043	+	0.0692332i	−0.218609	+	0.0208746i	−0.0148230	+	0.999890i	$0.504718\pi$
$12$	0.491817	+	3.42901i	0.141975	+	0.989870i
$13$	−0.625573	+	0.120569i	−0.173503	+	0.0334399i	−0.275263	−	0.961369i	$-0.588765\pi$
$13$	−0.625573	+	0.120569i	−0.173503	+	0.0334399i	0.101760	+	0.994809i	$0.467553\pi$
$14$	−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	0.964489	+	0.264122i	$0.0850822\pi$
$17$	2.55706	+	4.96000i	0.620178	+	1.20298i	−0.344311	+	0.938856i	$0.611887\pi$
$18$	3.73917	−	2.00466i	0.881330	−	0.472502i
$19$	0.463180	+	0.485769i	0.106261	+	0.111443i	0.774716	−	0.632309i	$-0.217893\pi$
$19$	0.463180	+	0.485769i	0.106261	+	0.111443i	−0.668455	+	0.743752i	$0.733044\pi$
$20$	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	0.678628	−	0.734482i	$-0.262575\pi$
$23$	3.17927	+	1.27279i	0.662923	+	0.265394i	−0.0157049	+	0.999877i	$0.504999\pi$
$24$	−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	−0.699391	−	0.714739i	$-0.746545\pi$
$29$	−2.31618	+	1.33725i	−0.430104	+	0.248321i	0.269287	+	0.963060i	$0.413212\pi$
$30$	1.67141	−	7.58570i	0.305155	−	1.38495i
$31$	0.712251	−	3.69551i	0.127924	−	0.663733i	−0.860185	−	0.509981i	$-0.829652\pi$
$31$	0.712251	−	3.69551i	0.127924	−	0.663733i	0.988110	−	0.153752i	$-0.0491356\pi$
$32$	−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	0.0226564	+	0.999743i	$0.492788\pi$
$37$	−5.19757	+	9.00245i	−0.854475	+	1.47999i	−0.877131	+	0.480251i	$0.840546\pi$
$38$	−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	0.445980	−	0.895043i	$-0.352855\pi$
$41$	5.15363	+	0.245498i	0.804862	+	0.0383403i	0.358882	+	0.933383i	$0.383158\pi$
$42$	−5.62192	−	3.44737i	−0.867481	−	0.531941i
$43$	6.81001	−	10.5966i	1.03852	−	1.61596i	0.285009	−	0.958525i	$-0.408003\pi$
$43$	6.81001	−	10.5966i	1.03852	−	1.61596i	0.753508	−	0.657439i	$-0.228360\pi$
$44$	−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	−0.793918	−	0.608025i	$-0.791962\pi$
$47$	−2.67511	+	2.10373i	−0.390205	+	0.306861i	0.403712	+	0.914886i	$0.367720\pi$
$48$	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	0.604868	−	0.796326i	$-0.293226\pi$
$53$	−2.69922	−	4.20007i	−0.370767	−	0.576925i	−0.975635	+	0.219401i	$0.929590\pi$
$54$	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	−0.898872	−	0.438212i	$-0.855612\pi$
$59$	−2.59006	+	2.98909i	−0.337197	+	0.389146i	0.561674	+	0.827358i	$0.310157\pi$
$60$	−3.09848	+	10.5391i	−0.400012	+	1.36059i
$61$	14.0631	+	1.34286i	1.80059	+	0.171936i	0.940857	−	0.338804i	$-0.110022\pi$
$61$	14.0631	+	1.34286i	1.80059	+	0.171936i	0.859735	+	0.510740i	$0.170629\pi$
$62$	−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	−0.0665860	−	0.997781i	$-0.521211\pi$
$71$	−7.73502	−	3.98768i	−0.917978	−	0.473250i	−0.851392	+	0.524530i	$0.824241\pi$
$72$	7.95918	−	2.94132i	0.937999	−	0.346638i
$73$	4.36934	+	0.417221i	0.511392	+	0.0488320i	0.347563	−	0.937657i	$-0.387009\pi$
$73$	4.36934	+	0.417221i	0.511392	+	0.0488320i	0.163829	+	0.986489i	$0.447615\pi$
$74$	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	−0.593654	−	0.804721i	$-0.702315\pi$
$79$	−13.8455	−	4.79198i	−1.55774	−	0.539140i	−0.964089	+	0.265581i	$0.914436\pi$
$80$	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	0.788761	−	0.614700i	$-0.210723\pi$
$83$	−0.456515	−	0.641086i	−0.0501090	−	0.0703683i	−0.838870	+	0.544331i	$0.816783\pi$
$84$	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	−0.0196740	−	0.999806i	$-0.506263\pi$
$89$	−3.02104	−	0.434359i	−0.320229	−	0.0460420i	−0.300555	+	0.953764i	$0.597172\pi$
$90$	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	−0.450052	−	0.893002i	$-0.648595\pi$
$97$	5.40049	−	9.35392i	0.548336	−	0.949746i	0.998389	−	0.0567442i	$-0.0180720\pi$
$98$	−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	−0.503890	−	0.863768i	$-0.668098\pi$
$101$	−5.58738	+	1.35548i	−0.555965	+	0.134876i	−0.0520745	+	0.998643i	$0.516583\pi$
$102$	10.5636	−	8.67472i	1.04596	−	0.858925i
$103$	−1.95650	+	10.1513i	−0.192780	+	1.00024i	0.748634	+	0.662983i	$0.230710\pi$
$103$	−1.95650	+	10.1513i	−0.192780	+	1.00024i	−0.941414	+	0.337253i	$0.890502\pi$
$104$	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	−0.982911	−	0.184079i	$-0.941070\pi$
$107$	−4.94819	−	10.8350i	−0.478359	−	1.04746i	0.504552	−	0.863381i	$-0.331658\pi$
$108$	−6.72392	−	7.92395i	−0.647009	−	0.762482i
$109$	3.93036	+	4.53587i	0.376460	+	0.434458i	0.912087	−	0.409997i	$-0.134470\pi$
$109$	3.93036	+	4.53587i	0.376460	+	0.434458i	−0.535627	+	0.844455i	$0.679925\pi$
$110$	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	0.268409	−	0.963305i	$-0.413502\pi$
$113$	−5.89046	−	4.19458i	−0.554128	−	0.394592i	−0.822536	+	0.568713i	$0.807442\pi$
$114$	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	−0.733870	−	0.679290i	$-0.762288\pi$
$127$	−0.230243	+	0.241472i	−0.0204308	+	0.0214272i	0.713439	+	0.700717i	$0.247136\pi$
$128$	−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	0.645151	+	0.764055i	$0.276794\pi$
$131$	2.76286	+	19.2161i	0.241392	+	1.67892i	−0.403759	+	0.914865i	$0.632297\pi$
$132$	−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	−0.448244	−	0.893911i	$-0.647950\pi$
$137$	−7.33284	+	1.05430i	−0.626487	+	0.0900753i	−0.178243	+	0.983986i	$0.557041\pi$
$138$	1.41315	−	8.26857i	0.120296	−	0.703868i
$139$	5.14453	+	2.34943i	0.436353	+	0.199276i	0.621465	−	0.783442i	$-0.286538\pi$
$139$	5.14453	+	2.34943i	0.436353	+	0.199276i	−0.185112	+	0.982717i	$0.559265\pi$
$140$	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	−0.832633	−	0.553826i	$-0.813167\pi$
$149$	2.04147	−	6.95259i	0.167243	−	0.569578i	0.999876	−	0.0157527i	$-0.00501445\pi$
$150$	7.44841	−	9.89470i	0.608160	−	0.807899i
$151$	−8.86541	−	17.1965i	−0.721457	−	1.39943i	−0.908840	−	0.417145i	$-0.863031\pi$
$151$	−8.86541	−	17.1965i	−0.721457	−	1.39943i	0.187383	−	0.982287i	$-0.439999\pi$
$152$	−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	0.270828	−	0.962628i	$-0.412702\pi$
$157$	−2.47408	−	0.990474i	−0.197453	−	0.0790484i	−0.468282	+	0.883579i	$0.655127\pi$
$158$	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	0.112048	−	0.993703i	$-0.464259\pi$
$163$	13.1328	−	7.58225i	1.02864	−	0.593888i	0.916596	+	0.399815i	$0.130926\pi$
$164$	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	0.988223	−	0.153020i	$-0.0489000\pi$
$167$	0.513521	+	2.11676i	0.0397374	+	0.163800i	−0.948486	+	0.316820i	$0.897385\pi$
$168$	−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	0.176394	−	0.984320i	$-0.443557\pi$
$173$	12.1469	−	4.20410i	0.923515	−	0.319632i	0.747121	+	0.664688i	$0.231435\pi$
$174$	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	−0.852038	−	0.523480i	$-0.824633\pi$
$179$	1.51141	−	10.5121i	0.112968	−	0.785709i	0.965006	−	0.262229i	$-0.0844575\pi$
$180$	−19.0265	−	0.101658i	−1.41815	−	0.00757717i
$181$	0.864935	−	0.680192i	0.0642901	−	0.0505583i	−0.585497	−	0.810675i	$-0.699101\pi$
$181$	0.864935	−	0.680192i	0.0642901	−	0.0505583i	0.649787	+	0.760116i	$0.274858\pi$
$182$	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	0.107297	−	0.994227i	$-0.465780\pi$
$191$	−11.5207	−	9.05997i	−0.833608	−	0.655557i	−0.940905	+	0.338670i	$0.890023\pi$
$192$	−1.84885	+	13.7325i	−0.133429	+	0.991058i
$193$	13.6591	−	15.7634i	0.983201	−	1.13467i	−0.00768468	−	0.999970i	$-0.502446\pi$
$193$	13.6591	−	15.7634i	0.983201	−	1.13467i	0.990886	−	0.134704i	$-0.0430084\pi$
$194$	−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	−0.432063	−	0.901843i	$-0.642214\pi$
$197$	7.76422	−	15.0605i	0.553178	−	1.07302i	0.985241	−	0.171172i	$-0.0547554\pi$
$198$	−2.57227	+	1.71233i	−0.182803	+	0.121690i
$199$	−14.8582	−	3.60455i	−1.05327	−	0.255520i	−0.328493	−	0.944506i	$-0.606541\pi$
$199$	−14.8582	−	3.60455i	−1.05327	−	0.255520i	−0.724774	+	0.688987i	$0.758056\pi$
$200$	−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	−0.999509	−	0.0313408i	$-0.990022\pi$
$211$	−10.6534	+	13.5469i	−0.733408	+	0.932605i	0.266100	+	0.963945i	$0.414265\pi$
$212$	−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	0.541719	−	0.840560i	$-0.317774\pi$
$223$	12.3151	+	1.77065i	0.824681	+	0.118571i	0.282962	+	0.959131i	$0.408683\pi$
$224$	−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	−0.939753	−	0.341855i	$-0.888945\pi$
$227$	0.425480	−	8.93192i	0.0282401	−	0.592832i	0.967993	−	0.250978i	$-0.0807521\pi$
$228$	−1.43791	+	1.82716i	−0.0952278	+	0.121007i
$229$	3.65009	+	10.5462i	0.241205	+	0.696915i	0.999012	+	0.0444369i	$0.0141494\pi$
$229$	3.65009	+	10.5462i	0.241205	+	0.696915i	−0.757808	+	0.652478i	$0.773729\pi$
$230$	−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	0.995035	+	0.0995231i	$0.0317317\pi$
$233$	5.24442	+	13.0999i	0.343573	+	0.858204i	−0.651462	+	0.758681i	$0.725844\pi$
$234$	−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	0.880245	−	0.474520i	$-0.157378\pi$
$239$	0.451058	+	0.781255i	0.0291765	+	0.0505352i	−0.851068	+	0.525055i	$0.824045\pi$
$240$	−9.04047	+	20.0240i	−0.583560	+	1.29255i
$241$	−12.5138	−	27.4014i	−0.806085	−	1.76508i	−0.623390	−	0.781911i	$-0.714245\pi$
$241$	−12.5138	−	27.4014i	−0.806085	−	1.76508i	−0.182695	−	0.983170i	$-0.558482\pi$
$242$	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	0.551483	−	0.834186i	$-0.314062\pi$
$251$	24.5706	−	12.6670i	1.55088	−	0.799536i	0.999399	+	0.0346503i	$0.0110317\pi$
$252$	−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	−0.932916	−	0.360094i	$-0.882745\pi$
$257$	−1.36277	−	14.2716i	−0.0850072	−	0.890236i	0.847909	−	0.530142i	$-0.177861\pi$
$258$	−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	0.144436	−	0.989514i	$-0.453863\pi$
$263$	12.9361	−	28.3262i	0.797676	−	1.74667i	0.653239	−	0.757152i	$-0.273410\pi$
$264$	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	$0.0579795\pi$
$269$			5.94192i			0.362285i	−0.983457	+	0.181143i	$0.942020\pi$
$270$	7.86624	+	21.9351i	0.478724	+	1.33493i
$271$	−18.1727	+	2.61284i	−1.10391	+	0.158719i	−0.670091	−	0.742279i	$-0.733745\pi$
$271$	−18.1727	+	2.61284i	−1.10391	+	0.158719i	−0.433824	+	0.900998i	$0.642836\pi$
$272$	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	−0.313636	−	0.949543i	$-0.601547\pi$
$277$	−1.06720	+	0.313358i	−0.0641218	+	0.0188279i	0.249514	+	0.968371i	$0.419729\pi$
$278$	−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	0.998578	−	0.0533054i	$-0.0169757\pi$
$281$	0.866962	+	4.49823i	0.0517186	+	0.268342i	−0.946860	+	0.321647i	$0.895764\pi$
$282$	6.41398	+	5.32470i	0.381947	+	0.317082i
$283$	4.46968	−	15.2223i	0.265695	−	0.904873i	−0.713278	−	0.700881i	$-0.752790\pi$
$283$	4.46968	−	15.2223i	0.265695	−	0.904873i	0.978973	−	0.203992i	$-0.0653916\pi$
$284$	−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	0.138802	−	0.990320i	$-0.455675\pi$
$293$	19.4930	−	16.8908i	1.13880	−	0.986772i	0.999994	+	0.00354794i	$0.00112935\pi$
$294$	−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	0.432619	−	0.901577i	$-0.357590\pi$
$307$	23.3034	−	8.06540i	1.33000	−	0.460317i	0.897379	+	0.441260i	$0.145468\pi$
$308$	−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	0.646232	−	0.763141i	$-0.276344\pi$
$311$	3.88873	+	2.49913i	0.220509	+	0.141713i	−0.425723	+	0.904854i	$0.639980\pi$
$312$	0.813778	+	3.01312i	0.0460711	+	0.170584i
$313$	1.06213	−	7.38729i	0.0600353	−	0.417554i	−0.937535	−	0.347890i	$-0.886898\pi$
$313$	1.06213	−	7.38729i	0.0600353	−	0.417554i	0.997571	−	0.0696641i	$-0.0221927\pi$
$314$	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	−0.524348	−	0.851504i	$-0.675691\pi$
$317$	−17.1881	+	0.818771i	−0.965381	+	0.0459868i	−0.441033	+	0.897491i	$0.645388\pi$
$318$	−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	−0.900604	−	0.434641i	$-0.856875\pi$
$331$	−0.439441	+	0.852396i	−0.0241538	+	0.0468519i	0.876450	+	0.481493i	$0.159905\pi$
$332$	−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	0.645159	+	0.764048i	$0.276791\pi$
$337$	−5.11053	+	21.0659i	−0.278388	+	1.14753i	−0.923547	+	0.383484i	$0.874724\pi$
$338$	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	0.501554	+	0.865126i	$0.332762\pi$
$347$	−7.96307	+	23.0078i	−0.427480	+	1.23512i	−0.929034	+	0.369995i	$0.879359\pi$
$348$	−5.72457	−	7.28453i	−0.306869	−	0.390492i
$349$	−24.2672	+	15.5956i	−1.29899	+	0.834812i	−0.993102	−	0.117255i	$-0.962591\pi$
$349$	−24.2672	+	15.5956i	−1.29899	+	0.834812i	−0.305891	+	0.952067i	$0.598954\pi$
$350$	−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	0.0198750	−	0.999802i	$-0.493673\pi$
$353$	2.53073	−	0.120554i	0.134697	−	0.00641642i	0.114822	+	0.993386i	$0.463370\pi$
$354$	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	0.943888	−	0.330266i	$-0.107139\pi$
$359$	19.6213	+	12.6098i	1.03557	+	0.665522i	0.0916842	+	0.995788i	$0.470775\pi$
$360$	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	0.964304	−	0.264797i	$-0.0853048\pi$
$367$	1.60296	+	4.00400i	0.0836738	+	0.209007i	−0.880630	+	0.473804i	$0.842881\pi$
$368$	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	0.782794	−	0.622280i	$-0.213794\pi$
$373$	−2.84896	−	4.93454i	−0.147513	−	0.255501i	−0.930308	+	0.366780i	$0.880460\pi$
$374$	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	0.531820	+	0.846857i	$0.321508\pi$
$379$	−8.51672	+	21.2737i	−0.437474	+	1.09276i	−0.969295	+	0.245901i	$0.920916\pi$
$380$	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	−0.503356	−	0.864079i	$-0.667902\pi$
$383$	6.57162	−	6.26602i	0.335794	−	0.320179i	0.839150	+	0.543900i	$0.183053\pi$
$384$	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	−0.739068	−	0.673631i	$-0.764734\pi$
$389$	−5.98210	−	31.0381i	−0.303304	−	1.57369i	0.435764	−	0.900061i	$-0.356478\pi$
$390$	−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	−0.201136	−	0.979563i	$-0.564463\pi$
$397$	13.3673	−	29.2703i	0.670885	−	1.46903i	0.872021	−	0.489469i	$-0.162809\pi$
$398$	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	$0.108897\pi$
$401$			13.4358i			0.670951i	−0.942049	+	0.335476i	$0.891103\pi$
$402$	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	0.999999	−	0.00144373i	$-0.000459555\pi$
$409$	21.1568	+	20.1730i	1.04614	+	0.997491i	0.0461398	+	0.998935i	$0.485308\pi$
$410$	−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	−0.914767	−	0.403983i	$-0.867626\pi$
$419$	−22.8503	+	11.7801i	−1.11631	+	0.575497i	−0.201542	+	0.979480i	$0.564595\pi$
$420$	14.7788	+	25.6178i	0.721129	+	1.25002i
$421$	6.26850	−	5.97700i	0.305508	−	0.291301i	−0.521779	−	0.853081i	$-0.674731\pi$
$421$	6.26850	−	5.97700i	0.305508	−	0.291301i	0.827287	+	0.561779i	$0.189883\pi$
$422$	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	−0.983965	−	0.178359i	$-0.942921\pi$
$431$	−13.4206	−	23.2451i	−0.646446	−	1.11968i	0.337519	−	0.941319i	$-0.390412\pi$
$432$	−11.1374	−	17.5487i	−0.535849	−	0.844314i
$433$	25.5887	+	4.93183i	1.22972	+	0.237008i	0.762414	−	0.647089i	$-0.224014\pi$
$433$	25.5887	+	4.93183i	1.22972	+	0.237008i	0.467302	+	0.884098i	$0.345226\pi$
$434$	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	−0.143303	−	0.989679i	$-0.545772\pi$
$439$	−22.4618	−	12.9683i	−1.07204	−	0.618943i	−0.928738	+	0.370736i	$0.879106\pi$
$440$	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	0.552874	+	0.833265i	$0.313531\pi$
$443$	−1.61442	+	33.8908i	−0.0767034	+	1.61020i	−0.629578	+	0.776938i	$0.716772\pi$
$444$	−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	0.657888	−	0.753116i	$-0.271450\pi$
$449$	−4.85458	−	6.17310i	−0.229102	−	0.291327i	−0.886990	+	0.461789i	$0.847208\pi$
$450$	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	0.474932	+	0.880023i	$0.342473\pi$
$457$	−9.45708	+	27.3244i	−0.442384	+	1.27818i	−0.917316	+	0.398161i	$0.869649\pi$
$458$	−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	0.874392	−	0.485220i	$-0.161261\pi$
$461$	11.1337	+	9.64743i	0.518550	+	0.449326i	−0.355842	+	0.934546i	$0.615806\pi$
$462$	4.31480	+	2.11027i	0.200743	+	0.0981785i
$463$	3.08264	−	32.2828i	0.143262	−	1.50031i	−0.582763	−	0.812642i	$-0.698028\pi$
$463$	3.08264	−	32.2828i	0.143262	−	1.50031i	0.726025	−	0.687668i	$-0.241366\pi$
$464$	−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	0.879088	+	0.476660i	$0.158153\pi$
$467$	−2.60824	+	10.7513i	−0.120695	+	0.497511i	−0.999783	+	0.0208511i	$0.993362\pi$
$468$	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	0.798520	−	0.601968i	$-0.205617\pi$
$479$	8.79334	+	6.91516i	0.401778	+	0.315962i	−0.396742	+	0.917930i	$0.629859\pi$
$480$	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	−0.289678	−	0.957124i	$-0.593548\pi$
$487$	−10.7486	+	0.512017i	−0.487063	+	0.0232017i	−0.197386	+	0.980326i	$0.563245\pi$
$488$	−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	0.476310	+	0.879278i	$0.341974\pi$
$491$	−5.06161	+	35.2043i	−0.228427	+	1.58875i	−0.704737	+	0.709469i	$0.748935\pi$
$492$	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	0.316250	−	0.948676i	$-0.397576\pi$
$499$	−7.75593	−	4.47789i	−0.347203	−	0.200458i	−0.663453	+	0.748218i	$0.730910\pi$
$500$	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	0.998998	+	0.0447533i	$0.0142502\pi$
$503$	2.95059	+	12.1625i	0.131560	+	0.542299i	−0.867438	+	0.497546i	$0.834235\pi$
$504$	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	0.471605	−	0.881810i	$-0.343675\pi$
$509$	32.6428	−	14.9075i	1.44687	−	0.660762i	0.975263	+	0.221048i	$0.0709477\pi$
$510$	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	0.630842	+	0.775911i	$0.282709\pi$
$521$	−7.28919	+	24.8247i	−0.319345	+	1.08759i	−0.950188	+	0.311679i	$0.899109\pi$
$522$	−5.97986	+	9.64333i	−0.261731	+	0.422077i
$523$	7.00920	+	36.3672i	0.306491	+	1.59023i	0.729422	+	0.684064i	$0.239789\pi$
$523$	7.00920	+	36.3672i	0.306491	+	1.59023i	−0.422931	+	0.906162i	$0.638999\pi$
$524$	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	−0.710800	−	0.703394i	$-0.751667\pi$
$541$	6.65834	−	14.5797i	0.286264	−	0.626832i	0.997065	+	0.0765621i	$0.0243943\pi$
$542$	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	0.993253	−	0.115968i	$-0.0369969\pi$
$547$	−0.0934971	−	0.979146i	−0.00399765	−	0.0418653i	−0.997251	+	0.0741024i	$0.976391\pi$
$548$	−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	0.671772	−	0.740758i	$-0.265534\pi$
$557$	4.51883	+	3.21785i	0.191469	+	0.136345i	−0.480302	+	0.877103i	$0.659473\pi$
$558$	−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	0.802157	−	0.597114i	$-0.203686\pi$
$563$	−4.13840	−	9.06183i	−0.174413	−	0.381911i	−0.976569	+	0.215203i	$0.930959\pi$
$564$	−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	−0.258588	−	0.965988i	$-0.583257\pi$
$569$	−1.09226	+	0.264978i	−0.0457897	+	0.0111085i	0.212799	+	0.977096i	$0.431742\pi$
$570$	4.45906	−	2.70163i	0.186770	−	0.113159i
$571$	−9.78124	−	24.4323i	−0.409332	−	1.02246i	−0.979592	−	0.200998i	$-0.935582\pi$
$571$	−9.78124	−	24.4323i	−0.409332	−	1.02246i	0.570260	−	0.821464i	$-0.306843\pi$
$572$	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	0.836626	+	0.547774i	$0.184525\pi$
$577$	−1.15975	+	24.3461i	−0.0482809	+	1.01354i	−0.884907	+	0.465767i	$0.845778\pi$
$578$	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	−0.911110	−	0.412163i	$-0.864774\pi$
$587$	−24.2913	−	34.1124i	−1.00261	−	1.40797i	−0.0914989	−	0.995805i	$-0.529166\pi$
$588$	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	0.150662	−	0.988585i	$-0.451859\pi$
$593$	26.1989	−	33.3146i	1.07586	−	1.36807i	0.925199	−	0.379483i	$-0.123898\pi$
$594$	−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	−0.138522	−	0.990359i	$-0.544235\pi$
$599$	−25.1009	−	12.9404i	−1.02560	−	0.528731i	−0.887073	+	0.461628i	$0.847265\pi$
$600$	17.4800	−	17.5495i	0.713617	−	0.716456i
$601$	4.83990	−	19.9503i	0.197424	−	0.813792i	−0.783815	−	0.620994i	$-0.786729\pi$
$601$	4.83990	−	19.9503i	0.197424	−	0.813792i	0.981239	−	0.192797i	$-0.0617559\pi$
$602$	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	0.461133	+	0.887331i	$0.347443\pi$
$607$	−13.0368	+	25.2880i	−0.529149	+	1.02641i	−0.990282	+	0.139075i	$0.955587\pi$
$608$	−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	0.462277	−	0.886735i	$-0.347032\pi$
$613$	−7.19186	−	5.65574i	−0.290476	−	0.228433i	−0.752754	+	0.658302i	$0.771275\pi$
$614$	−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	−0.999976	−	0.00697814i	$-0.997779\pi$
$617$	−14.6781	−	22.8396i	−0.590918	−	0.919487i	0.409057	−	0.912509i	$-0.365858\pi$
$618$	25.3175	−	0.534999i	1.01842	−	0.0215208i
$619$	−18.8152	+	13.3982i	−0.756246	+	0.538520i	−0.891898	−	0.452236i	$-0.850626\pi$
$619$	−18.8152	+	13.3982i	−0.756246	+	0.538520i	0.135652	+	0.990756i	$0.456687\pi$
$620$	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	−0.567856	−	0.823128i	$-0.692227\pi$
$631$	−12.6954	+	4.39392i	−0.505396	+	0.174919i	0.0624595	+	0.998048i	$0.480106\pi$
$632$	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	−0.901084	−	0.433645i	$-0.857227\pi$
$641$	−24.7123	+	14.2677i	−0.976078	+	0.563539i	−0.0749942	+	0.997184i	$0.523894\pi$
$642$	−23.4040	+	17.4226i	−0.923681	+	0.687616i
$643$	−2.33112	+	1.06459i	−0.0919305	+	0.0419833i	−0.460850	−	0.887478i	$-0.652455\pi$
$643$	−2.33112	+	1.06459i	−0.0919305	+	0.0419833i	0.368919	+	0.929462i	$0.379728\pi$
$644$	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	−0.287536	−	0.957770i	$-0.592836\pi$
$647$	−29.4188	−	11.7775i	−1.15657	−	0.463022i	−0.869036	+	0.494748i	$0.835260\pi$
$648$	−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	−0.946346	−	0.323155i	$-0.895256\pi$
$653$	−16.8821	−	32.7466i	−0.660646	−	1.28147i	0.285700	−	0.958319i	$-0.407774\pi$
$654$	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	−0.184449	−	0.982842i	$-0.559050\pi$
$659$	−4.60951	+	0.440154i	−0.179561	+	0.0171460i	0.00488822	+	0.999988i	$0.498444\pi$
$660$	1.51688	−	7.85581i	0.0590443	−	0.305787i
$661$	−11.2048	+	3.29003i	−0.435817	+	0.127967i	−0.492279	−	0.870437i	$-0.663836\pi$
$661$	−11.2048	+	3.29003i	−0.435817	+	0.127967i	0.0564623	+	0.998405i	$0.482018\pi$
$662$	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	0.971171	+	0.238386i	$0.0766183\pi$
$673$	2.76286	+	19.2161i	0.106500	+	0.740726i	−0.864670	+	0.502340i	$0.832473\pi$
$674$	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	−0.0674874	−	0.997720i	$-0.521498\pi$
$677$	24.2581	−	25.4411i	0.932314	−	0.977783i	0.999801	+	0.0199375i	$0.00634672\pi$
$678$	−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	0.627687	−	0.778466i	$-0.284002\pi$
$683$	39.1945	−	7.55413i	1.49974	−	0.289051i	0.872051	+	0.489415i	$0.162790\pi$
$684$	−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	0.783569	−	0.621305i	$-0.213397\pi$
$691$	11.9005	+	8.47430i	0.452716	+	0.322377i	−0.330853	+	0.943682i	$0.607336\pi$
$692$	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	−0.872149	−	0.489241i	$-0.837274\pi$
$701$	3.16019	−	16.3966i	0.119359	−	0.619292i	0.991507	−	0.130051i	$-0.0415140\pi$
$702$	−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	0.997867	+	0.0652743i	$0.0207922\pi$
$709$	6.75902	+	19.5289i	0.253840	+	0.733424i	−0.744027	+	0.668150i	$0.767087\pi$
$710$	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	0.999505	−	0.0314714i	$-0.0100193\pi$
$719$	0.0411406	+	0.863647i	0.00153428	+	0.0322086i	−0.997970	+	0.0636800i	$0.979716\pi$
$720$	−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	−0.796289	−	0.604916i	$-0.793206\pi$
$727$	−0.557914	+	0.709446i	−0.0206919	+	0.0263119i	0.775597	+	0.631228i	$0.217449\pi$
$728$	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	0.994152	−	0.107987i	$-0.0344406\pi$
$733$	40.1467	+	20.6971i	1.48285	+	0.764464i	0.488701	+	0.872451i	$0.337471\pi$
$734$	−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	−0.0784557	−	0.996918i	$-0.524999\pi$
$739$	−16.4468	−	3.98994i	−0.605004	−	0.146772i	−0.526548	+	0.850145i	$0.676514\pi$
$740$	−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	−0.333579	−	0.942722i	$-0.608257\pi$
$743$	−22.8843	−	2.18518i	−0.839542	−	0.0801665i	−0.505962	+	0.862556i	$0.668863\pi$
$744$	−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	0.959506	+	0.281688i	$0.0908942\pi$
$751$	22.3934	+	34.8447i	0.817145	+	1.27150i	−0.142361	+	0.989815i	$0.545469\pi$
$752$	−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	−0.373907	+	0.927466i	$0.621982\pi$
$757$	−37.5116	+	29.4994i	−1.36338	+	1.07217i	−0.989474	+	0.144709i	$0.953775\pi$
$758$	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	−0.859459	−	0.511204i	$-0.829200\pi$
$761$	−1.03225	+	1.60622i	−0.0374192	+	0.0582254i	0.822040	+	0.569430i	$0.192836\pi$
$762$	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	−0.651437	−	0.758703i	$-0.725833\pi$
$769$	−16.6202	+	6.65372i	−0.599339	+	0.239939i	0.0520978	+	0.998642i	$0.483409\pi$
$770$	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	0.878765	+	0.477256i	$0.158368\pi$
$773$	−3.18149	+	16.5071i	−0.114430	+	0.593721i	−0.993195	+	0.116465i	$0.962844\pi$
$774$	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	−0.924165	−	0.381994i	$-0.875237\pi$
$787$	−19.6167	−	38.0511i	−0.699260	−	1.35637i	0.224905	−	0.974381i	$-0.427793\pi$
$788$	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	−0.797676	−	0.603086i	$-0.793938\pi$
$797$	−4.44128	+	4.65788i	−0.157318	+	0.164991i	0.640358	+	0.768077i	$0.278786\pi$
$798$	−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	−0.273562	−	0.961854i	$-0.588202\pi$
$809$	−33.5521	−	15.3227i	−1.17963	−	0.538718i	−0.906066	+	0.423137i	$0.860929\pi$
$810$	−32.7338	+	23.6133i	−1.15015	+	0.829685i
$811$	19.4104	−	20.3570i	0.681590	−	0.714832i	−0.288526	−	0.957472i	$-0.593165\pi$
$811$	19.4104	−	20.3570i	0.681590	−	0.714832i	0.970116	+	0.242641i	$0.0780136\pi$
$812$	−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	0.914266	−	0.405115i	$-0.132768\pi$
$821$	1.54563	+	2.99811i	0.0539429	+	0.104635i	−0.860323	+	0.509749i	$0.829738\pi$
$822$	6.29608	+	17.0192i	0.219601	+	0.593612i
$823$	4.57756	+	4.80080i	0.159564	+	0.167345i	0.798663	−	0.601779i	$-0.205541\pi$
$823$	4.57756	+	4.80080i	0.159564	+	0.167345i	−0.639099	+	0.769124i	$0.720693\pi$
$824$	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	0.985428	−	0.170094i	$-0.0544071\pi$
$827$	45.4726	+	18.2045i	1.58124	+	0.633032i	0.595810	+	0.803126i	$0.296831\pi$
$828$	−20.5291	+	0.868015i	−0.713436	+	0.0301656i
$829$	26.5133	+	30.5980i	0.920846	+	1.06271i	0.997841	+	0.0656813i	$0.0209221\pi$
$829$	26.5133	+	30.5980i	0.920846	+	1.06271i	−0.0769947	+	0.997031i	$0.524532\pi$
$830$	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	−0.396641	−	0.917974i	$-0.629824\pi$
$839$	−1.45491	+	0.582458i	−0.0502291	+	0.0201087i	0.346412	+	0.938083i	$0.387400\pi$
$840$	−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	0.968706	+	0.248211i	$0.0798426\pi$
$853$	0.817198	+	17.1551i	0.0279803	+	0.587380i	−0.940726	+	0.339168i	$0.889854\pi$
$854$	−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	0.933894	+	0.357550i	$0.116388\pi$
$857$	25.5034	+	39.6840i	0.871179	+	1.35558i	−0.0627151	+	0.998031i	$0.519976\pi$
$858$	−0.542048	−	0.999023i	−0.0185052	−	0.0341061i
$859$	11.0023	+	3.80795i	0.375395	+	0.129925i	0.508249	−	0.861210i	$-0.330293\pi$
$859$	11.0023	+	3.80795i	0.375395	+	0.129925i	−0.132854	+	0.991136i	$0.542414\pi$
$860$	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	0.0376824	+	0.999290i	$0.488002\pi$
$863$	−28.1077	+	32.4381i	−0.956799	+	1.10420i	−0.994481	+	0.104915i	$0.966543\pi$
$864$	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	0.848655	−	0.528947i	$-0.177413\pi$
$877$	46.8458	+	4.47323i	1.58187	+	0.151050i	0.733215	+	0.679997i	$0.238019\pi$
$878$	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	−0.943473	−	0.331450i	$-0.892462\pi$
$881$	−11.8410	+	15.0571i	−0.398934	+	0.507285i	0.544539	+	0.838735i	$0.316705\pi$
$882$	−0.541575	−	0.904043i	−0.0182358	−	0.0304407i
$883$	−24.7559	−	8.56810i	−0.833103	−	0.288340i	−0.122973	−	0.992410i	$-0.539243\pi$
$883$	−24.7559	−	8.56810i	−0.833103	−	0.288340i	−0.710130	+	0.704070i	$0.751364\pi$
$884$	−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	−0.967574	−	0.252589i	$-0.918718\pi$
$887$	−26.5007	−	37.2151i	−0.889808	−	1.24956i	0.0777656	−	0.996972i	$-0.475221\pi$
$888$	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	0.882518	+	0.470278i	$0.155846\pi$
$907$	−3.36003	+	17.4335i	−0.111568	+	0.578869i	−0.994086	+	0.108592i	$0.965366\pi$
$908$	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	0.977805	+	0.209515i	$0.0671885\pi$
$911$	14.9652	+	32.7693i	0.495820	+	1.08569i	−0.481985	+	0.876179i	$0.660084\pi$
$912$	−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	0.914558	−	0.404455i	$-0.132539\pi$
$919$	14.1584	+	14.8489i	0.467044	+	0.489822i	−0.447514	+	0.894277i	$0.647690\pi$
$920$	−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	0.871460	−	0.490466i	$-0.163173\pi$
$929$	−3.86555	−	13.1649i	−0.126825	−	0.431925i	−0.998285	+	0.0585408i	$0.981355\pi$
$930$	−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	−0.160854	−	0.986978i	$-0.551425\pi$
$941$	−1.13894	+	0.163755i	−0.0371284	+	0.00533825i	0.123726	+	0.992316i	$0.460516\pi$
$942$	−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	−0.633399	−	0.773826i	$-0.718341\pi$
$947$	−23.0150	+	6.75780i	−0.747886	+	0.219599i	−0.114487	+	0.993425i	$0.536523\pi$
$948$	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	−0.849770	−	0.527153i	$-0.823259\pi$
$953$	4.63376	−	15.7812i	0.150102	−	0.511202i	0.999873	+	0.0159513i	$0.00507767\pi$
$954$	−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	−0.890352	−	0.455273i	$-0.849542\pi$
$967$	−29.2697	+	16.8989i	−0.941251	+	0.543431i	−0.0508984	+	0.998704i	$0.516208\pi$
$968$	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	−0.940849	−	0.338826i	$-0.889970\pi$
$971$	−8.09709	−	33.3767i	−0.259848	−	1.07111i	0.681001	−	0.732282i	$-0.261545\pi$
$972$	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	−0.217620	−	0.976034i	$-0.569829\pi$
$977$	6.70974	−	2.32226i	0.214664	−	0.0742958i	0.432283	+	0.901738i	$0.357708\pi$
$978$	−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	0.668614	+	0.743610i	$0.266888\pi$
$983$	−5.71924	+	39.7782i	−0.182416	+	1.26873i	−0.851029	+	0.525118i	$0.824021\pi$
$984$	−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	0.918932	−	0.394416i	$-0.129053\pi$
$991$	5.61668	+	8.73973i	0.178420	+	0.277627i	−0.740512	+	0.672043i	$0.765417\pi$
$992$	−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	0.0409070	+	0.999163i	$0.486975\pi$
$997$	−30.1199	+	34.7602i	−0.953908	+	1.10087i	−0.994815	+	0.101705i	$0.967570\pi$
$998$	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.35.2	yes	2640
3.2	odd	2	inner	804.2.bd.a.35.131	yes	2640
4.3	odd	2	inner	804.2.bd.a.35.18	yes	2640
12.11	even	2	inner	804.2.bd.a.35.115	yes	2640
67.23	even	33	inner	804.2.bd.a.23.115	yes	2640
201.23	odd	66	inner	804.2.bd.a.23.18	yes	2640
268.23	odd	66	inner	804.2.bd.a.23.131	yes	2640
804.23	even	66	inner	804.2.bd.a.23.2	✓	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.2	✓	2640	804.23	even	66	inner
804.2.bd.a.23.18	yes	2640	201.23	odd	66	inner
804.2.bd.a.23.115	yes	2640	67.23	even	33	inner
804.2.bd.a.23.131	yes	2640	268.23	odd	66	inner
804.2.bd.a.35.2	yes	2640	1.1	even	1	trivial
804.2.bd.a.35.18	yes	2640	4.3	odd	2	inner
804.2.bd.a.35.115	yes	2640	12.11	even	2	inner
804.2.bd.a.35.131	yes	2640	3.2	odd	2	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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