LMFDB - Embedded newform 912.2.cs.a.773.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(29,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 18, 34]))

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

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

chi := DirichletCharacter("912.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cs (of order $36$, degree $12$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$1872$
Relative dimension:	$156$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			773.51
Character	$\chi$	$=$	912.773
Dual form			912.2.cs.a.269.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.741028 - 1.20452i) q^{2} +(-0.635489 + 1.61126i) q^{3} +(-0.901756 + 1.78517i) q^{4} +(-1.65579 - 1.15939i) q^{5} +(2.41171 - 0.428526i) q^{6} +(3.66991 + 2.11883i) q^{7} +(2.81851 - 0.236675i) q^{8} +(-2.19231 - 2.04787i) q^{9} +O(q^{10})$	\(q+(-0.741028 - 1.20452i) q^{2} +(-0.635489 + 1.61126i) q^{3} +(-0.901756 + 1.78517i) q^{4} +(-1.65579 - 1.15939i) q^{5} +(2.41171 - 0.428526i) q^{6} +(3.66991 + 2.11883i) q^{7} +(2.81851 - 0.236675i) q^{8} +(-2.19231 - 2.04787i) q^{9} +(-0.169534 + 2.85358i) q^{10} +(3.98641 + 1.06815i) q^{11} +(-2.30332 - 2.58742i) q^{12} +(-1.59628 - 0.744358i) q^{13} +(-0.167332 - 5.99061i) q^{14} +(2.92032 - 1.93112i) q^{15} +(-2.37367 - 3.21958i) q^{16} +(-0.339685 - 0.404821i) q^{17} +(-0.842151 + 4.15822i) q^{18} +(-0.601479 - 4.31720i) q^{19} +(3.56283 - 1.91037i) q^{20} +(-5.74617 + 4.56669i) q^{21} +(-1.66742 - 5.59325i) q^{22} +(-1.23124 + 6.98271i) q^{23} +(-1.40978 + 4.69175i) q^{24} +(-0.312668 - 0.859049i) q^{25} +(0.286291 + 2.47435i) q^{26} +(4.69284 - 2.23098i) q^{27} +(-7.09183 + 4.64076i) q^{28} +(2.99492 - 0.262022i) q^{29} +(-4.49011 - 2.08658i) q^{30} +(6.14986 + 3.55062i) q^{31} +(-2.11910 + 5.24494i) q^{32} +(-4.25439 + 5.74433i) q^{33} +(-0.235901 + 0.709143i) q^{34} +(-3.62004 - 7.76320i) q^{35} +(5.63273 - 2.06696i) q^{36} +(3.28232 - 3.28232i) q^{37} +(-4.75446 + 3.92366i) q^{38} +(2.21377 - 2.09899i) q^{39} +(-4.94124 - 2.87588i) q^{40} +(-3.54251 + 9.73297i) q^{41} +(9.75876 + 3.53735i) q^{42} +(-1.19021 + 1.69980i) q^{43} +(-5.50160 + 6.15320i) q^{44} +(1.25570 + 5.93259i) q^{45} +(9.32322 - 3.69132i) q^{46} +(-3.06591 + 3.65381i) q^{47} +(6.69601 - 1.77860i) q^{48} +(5.47885 + 9.48965i) q^{49} +(-0.803049 + 1.01320i) q^{50} +(0.868138 - 0.290062i) q^{51} +(2.76826 - 2.17841i) q^{52} +(9.97938 - 6.98764i) q^{53} +(-6.16479 - 3.99942i) q^{54} +(-5.36222 - 6.39045i) q^{55} +(10.8452 + 5.10335i) q^{56} +(7.33836 + 1.77439i) q^{57} +(-2.53493 - 3.41329i) q^{58} +(13.0264 + 1.13966i) q^{59} +(0.813964 + 6.95466i) q^{60} +(-0.519009 - 0.741222i) q^{61} +(-0.280406 - 10.0388i) q^{62} +(-3.70650 - 12.1606i) q^{63} +(7.88797 - 1.33414i) q^{64} +(1.78009 + 3.08321i) q^{65} +(10.0718 + 0.867804i) q^{66} +(1.31653 + 15.0480i) q^{67} +(1.02899 - 0.241347i) q^{68} +(-10.4685 - 6.42128i) q^{69} +(-6.66841 + 10.1132i) q^{70} +(3.87242 - 0.682813i) q^{71} +(-6.66372 - 5.25308i) q^{72} +(-4.58071 + 12.5854i) q^{73} +(-6.38592 - 1.52134i) q^{74} +(1.58285 + 0.0421265i) q^{75} +(8.24933 + 2.81932i) q^{76} +(12.3665 + 12.3665i) q^{77} +(-4.16875 - 1.11113i) q^{78} +(-0.863449 + 2.37231i) q^{79} +(0.197538 + 8.08295i) q^{80} +(0.612431 + 8.97914i) q^{81} +(14.3487 - 2.94536i) q^{82} +(-11.7517 + 3.14886i) q^{83} +(-2.97069 - 14.3759i) q^{84} +(0.0930990 + 1.06413i) q^{85} +(2.92943 + 0.174040i) q^{86} +(-1.48105 + 4.99210i) q^{87} +(11.4885 + 2.06712i) q^{88} +(1.36686 + 3.75542i) q^{89} +(6.21543 - 5.90873i) q^{90} +(-4.28105 - 6.11397i) q^{91} +(-11.3551 - 8.49467i) q^{92} +(-9.62913 + 7.65263i) q^{93} +(6.67302 + 0.985386i) q^{94} +(-4.00942 + 7.84571i) q^{95} +(-7.10429 - 6.74752i) q^{96} +(6.02925 + 7.18538i) q^{97} +(7.37053 - 13.6315i) q^{98} +(-6.55199 - 10.5054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1872 q - 12 q^{3} - 24 q^{4} - 12 q^{6}+O(q^{10}) $ 1872 * q - 12 * q^3 - 24 * q^4 - 12 * q^6	$ 1872 q - 12 q^{3} - 24 q^{4} - 12 q^{6} - 12 q^{10} - 18 q^{12} - 24 q^{13} - 24 q^{15} - 36 q^{16} - 24 q^{19} - 30 q^{21} - 24 q^{22} - 12 q^{24} - 18 q^{27} - 72 q^{28} - 48 q^{30} - 72 q^{31} - 24 q^{33} - 24 q^{34} - 12 q^{36} - 24 q^{40} + 72 q^{42} - 24 q^{43} - 6 q^{45} - 36 q^{46} - 12 q^{48} + 768 q^{49} - 12 q^{51} - 72 q^{52} - 78 q^{54} - 48 q^{58} + 30 q^{60} - 24 q^{61} - 108 q^{63} - 12 q^{64} + 48 q^{66} - 24 q^{67} - 18 q^{69} - 180 q^{70} - 144 q^{72} - 72 q^{76} - 36 q^{78} - 48 q^{79} - 24 q^{81} - 24 q^{82} - 18 q^{84} - 120 q^{85} - 36 q^{88} + 96 q^{90} - 108 q^{91} - 30 q^{93} - 324 q^{96} - 48 q^{97} + 42 q^{99}+O(q^{100}) $ 1872 * q - 12 * q^3 - 24 * q^4 - 12 * q^6 - 12 * q^10 - 18 * q^12 - 24 * q^13 - 24 * q^15 - 36 * q^16 - 24 * q^19 - 30 * q^21 - 24 * q^22 - 12 * q^24 - 18 * q^27 - 72 * q^28 - 48 * q^30 - 72 * q^31 - 24 * q^33 - 24 * q^34 - 12 * q^36 - 24 * q^40 + 72 * q^42 - 24 * q^43 - 6 * q^45 - 36 * q^46 - 12 * q^48 + 768 * q^49 - 12 * q^51 - 72 * q^52 - 78 * q^54 - 48 * q^58 + 30 * q^60 - 24 * q^61 - 108 * q^63 - 12 * q^64 + 48 * q^66 - 24 * q^67 - 18 * q^69 - 180 * q^70 - 144 * q^72 - 72 * q^76 - 36 * q^78 - 48 * q^79 - 24 * q^81 - 24 * q^82 - 18 * q^84 - 120 * q^85 - 36 * q^88 + 96 * q^90 - 108 * q^91 - 30 * q^93 - 324 * q^96 - 48 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.741028	−	1.20452i	−0.523986	−	0.851727i
$2$	−0.741028	−	1.20452i	−0.523986	−	0.851727i
$3$	−0.635489	+	1.61126i	−0.366900	+	0.930261i
$3$	−0.635489	+	1.61126i	−0.366900	+	0.930261i
$4$	−0.901756	+	1.78517i	−0.450878	+	0.892586i
$5$	−1.65579	−	1.15939i	−0.740490	−	0.518497i	0.141400	−	0.989953i	$-0.454840\pi$
$5$	−1.65579	−	1.15939i	−0.740490	−	0.518497i	−0.881890	+	0.471456i	$0.843729\pi$
$6$	2.41171	−	0.428526i	0.984578	−	0.174945i
$7$	3.66991	+	2.11883i	1.38710	+	0.800841i	0.992987	−	0.118222i	$-0.0377195\pi$
$7$	3.66991	+	2.11883i	1.38710	+	0.800841i	0.394110	+	0.919063i	$0.371053\pi$
$8$	2.81851	−	0.236675i	0.996493	−	0.0836774i
$9$	−2.19231	−	2.04787i	−0.730769	−	0.682624i
$10$	−0.169534	+	2.85358i	−0.0536114	+	0.902380i
$11$	3.98641	+	1.06815i	1.20195	+	0.322061i	0.803597	−	0.595173i	$-0.202917\pi$
$11$	3.98641	+	1.06815i	1.20195	+	0.322061i	0.398349	+	0.917234i	$0.369583\pi$
$12$	−2.30332	−	2.58742i	−0.664910	−	0.746923i
$13$	−1.59628	−	0.744358i	−0.442729	−	0.206448i	0.188454	−	0.982082i	$-0.439652\pi$
$13$	−1.59628	−	0.744358i	−0.442729	−	0.206448i	−0.631183	+	0.775634i	$0.717430\pi$
$14$	−0.167332	−	5.99061i	−0.0447214	−	1.60106i
$15$	2.92032	−	1.93112i	0.754022	−	0.498612i
$16$	−2.37367	−	3.21958i	−0.593418	−	0.804894i
$17$	−0.339685	−	0.404821i	−0.0823858	−	0.0981836i	0.723277	−	0.690558i	$-0.242635\pi$
$17$	−0.339685	−	0.404821i	−0.0823858	−	0.0981836i	−0.805663	+	0.592375i	$0.798191\pi$
$18$	−0.842151	+	4.15822i	−0.198497	+	0.980102i
$19$	−0.601479	−	4.31720i	−0.137989	−	0.990434i
$19$	−0.601479	−	4.31720i	−0.137989	−	0.990434i
$20$	3.56283	−	1.91037i	0.796673	−	0.427172i
$21$	−5.74617	+	4.56669i	−1.25392	+	0.996534i
$22$	−1.66742	−	5.59325i	−0.355495	−	1.19249i
$23$	−1.23124	+	6.98271i	−0.256731	+	1.45600i	0.534858	+	0.844942i	$0.320365\pi$
$23$	−1.23124	+	6.98271i	−0.256731	+	1.45600i	−0.791589	+	0.611053i	$0.790746\pi$
$24$	−1.40978	+	4.69175i	−0.287771	+	0.957699i
$25$	−0.312668	−	0.859049i	−0.0625336	−	0.171810i
$26$	0.286291	+	2.47435i	0.0561464	+	0.485260i
$27$	4.69284	−	2.23098i	0.903138	−	0.429351i
$28$	−7.09183	+	4.64076i	−1.34023	+	0.877022i
$29$	2.99492	−	0.262022i	0.556143	−	0.0486562i	0.194380	−	0.980926i	$-0.437731\pi$
$29$	2.99492	−	0.262022i	0.556143	−	0.0486562i	0.361763	+	0.932270i	$0.382175\pi$
$30$	−4.49011	−	2.08658i	−0.819779	−	0.380955i
$31$	6.14986	+	3.55062i	1.10455	+	0.637710i	0.937412	−	0.348224i	$-0.113215\pi$
$31$	6.14986	+	3.55062i	1.10455	+	0.637710i	0.167135	+	0.985934i	$0.446548\pi$
$32$	−2.11910	+	5.24494i	−0.374607	+	0.927184i
$33$	−4.25439	+	5.74433i	−0.740594	+	0.999960i
$34$	−0.235901	+	0.709143i	−0.0404566	+	0.121617i
$35$	−3.62004	−	7.76320i	−0.611898	−	1.31222i
$36$	5.63273	−	2.06696i	0.938788	−	0.344494i
$37$	3.28232	−	3.28232i	0.539610	−	0.539610i	−0.383805	−	0.923414i	$-0.625386\pi$
$37$	3.28232	−	3.28232i	0.539610	−	0.539610i	0.923414	+	0.383805i	$0.125386\pi$
$38$	−4.75446	+	3.92366i	−0.771275	+	0.636502i
$39$	2.21377	−	2.09899i	0.354487	−	0.336107i
$40$	−4.94124	−	2.87588i	−0.781279	−	0.454716i
$41$	−3.54251	+	9.73297i	−0.553247	+	1.52003i	0.276003	+	0.961157i	$0.410990\pi$
$41$	−3.54251	+	9.73297i	−0.553247	+	1.52003i	−0.829250	+	0.558877i	$0.811232\pi$
$42$	9.75876	+	3.53735i	1.50581	+	0.545825i
$43$	−1.19021	+	1.69980i	−0.181506	+	0.259217i	−0.899586	−	0.436743i	$-0.856132\pi$
$43$	−1.19021	+	1.69980i	−0.181506	+	0.259217i	0.718081	+	0.695960i	$0.245021\pi$
$44$	−5.50160	+	6.15320i	−0.829398	+	0.927630i
$45$	1.25570	+	5.93259i	0.187189	+	0.884378i
$46$	9.32322	−	3.69132i	1.37463	−	0.544256i
$47$	−3.06591	+	3.65381i	−0.447208	+	0.532962i	−0.941805	−	0.336161i	$-0.890871\pi$
$47$	−3.06591	+	3.65381i	−0.447208	+	0.532962i	0.494596	+	0.869123i	$0.335316\pi$
$48$	6.69601	−	1.77860i	0.966486	−	0.256718i
$49$	5.47885	+	9.48965i	0.782693	+	1.35566i
$50$	−0.803049	+	1.01320i	−0.113568	+	0.143287i
$51$	0.868138	−	0.290062i	0.121564	−	0.0406168i
$52$	2.76826	−	2.17841i	0.383889	−	0.302090i
$53$	9.97938	−	6.98764i	1.37077	−	0.959826i	0.371263	−	0.928528i	$-0.378925\pi$
$53$	9.97938	−	6.98764i	1.37077	−	0.959826i	0.999510	−	0.0312983i	$-0.00996420\pi$
$54$	−6.16479	−	3.99942i	−0.838921	−	0.544253i
$55$	−5.36222	−	6.39045i	−0.723042	−	0.861688i
$56$	10.8452	+	5.10335i	1.44925	+	0.681964i
$57$	7.33836	+	1.77439i	0.971989	+	0.235024i
$58$	−2.53493	−	3.41329i	−0.332853	−	0.448187i
$59$	13.0264	+	1.13966i	1.69589	+	0.148371i	0.893689	−	0.448687i	$-0.148108\pi$
$59$	13.0264	+	1.13966i	1.69589	+	0.148371i	0.802198	+	0.597058i	$0.203664\pi$
$60$	0.813964	+	6.95466i	0.105082	+	0.897843i
$61$	−0.519009	−	0.741222i	−0.0664523	−	0.0949038i	0.784550	−	0.620065i	$-0.212894\pi$
$61$	−0.519009	−	0.741222i	−0.0664523	−	0.0949038i	−0.851003	+	0.525161i	$0.824005\pi$
$62$	−0.280406	−	10.0388i	−0.0356117	−	1.27492i
$63$	−3.70650	−	12.1606i	−0.466975	−	1.53210i
$64$	7.88797	−	1.33414i	0.985996	−	0.166768i
$65$	1.78009	+	3.08321i	0.220794	+	0.382426i
$66$	10.0718	+	0.867804i	1.23975	+	0.106819i
$67$	1.31653	+	15.0480i	0.160840	+	1.83841i	0.464439	+	0.885605i	$0.346256\pi$
$67$	1.31653	+	15.0480i	0.160840	+	1.83841i	−0.303599	+	0.952800i	$0.598188\pi$
$68$	1.02899	−	0.241347i	0.124783	−	0.0292676i
$69$	−10.4685	−	6.42128i	−1.26026	−	0.773031i
$70$	−6.66841	+	10.1132i	−0.797027	+	1.20875i
$71$	3.87242	−	0.682813i	0.459572	−	0.0810350i	0.0609310	−	0.998142i	$-0.480593\pi$
$71$	3.87242	−	0.682813i	0.459572	−	0.0810350i	0.398641	+	0.917107i	$0.369482\pi$
$72$	−6.66372	−	5.25308i	−0.785327	−	0.619081i
$73$	−4.58071	+	12.5854i	−0.536132	+	1.47301i	0.315529	+	0.948916i	$0.397818\pi$
$73$	−4.58071	+	12.5854i	−0.536132	+	1.47301i	−0.851661	+	0.524094i	$0.824404\pi$
$74$	−6.38592	−	1.52134i	−0.742348	−	0.176852i
$75$	1.58285	+	0.0421265i	0.182771	+	0.00486435i
$76$	8.24933	+	2.81932i	0.946263	+	0.323398i
$77$	12.3665	+	12.3665i	1.40930	+	1.40930i
$78$	−4.16875	−	1.11113i	−0.472018	−	0.125811i
$79$	−0.863449	+	2.37231i	−0.0971456	+	0.266905i	−0.978741	−	0.205101i	$-0.934248\pi$
$79$	−0.863449	+	2.37231i	−0.0971456	+	0.266905i	0.881595	+	0.472006i	$0.156470\pi$
$80$	0.197538	+	8.08295i	0.0220855	+	0.903701i
$81$	0.612431	+	8.97914i	0.0680479	+	0.997682i
$82$	14.3487	−	2.94536i	1.58455	−	0.325261i
$83$	−11.7517	+	3.14886i	−1.28992	+	0.345632i	−0.837629	−	0.546239i	$-0.816059\pi$
$83$	−11.7517	+	3.14886i	−1.28992	+	0.345632i	−0.452289	+	0.891872i	$0.649392\pi$
$84$	−2.97069	−	14.3759i	−0.324129	−	1.56854i
$85$	0.0930990	+	1.06413i	0.0100980	+	0.115421i
$86$	2.92943	+	0.174040i	0.315888	+	0.0187673i
$87$	−1.48105	+	4.99210i	−0.158786	+	0.535210i
$88$	11.4885	+	2.06712i	1.22468	+	0.220355i
$89$	1.36686	+	3.75542i	0.144887	+	0.398074i	0.990815	−	0.135223i	$-0.0431751\pi$
$89$	1.36686	+	3.75542i	0.144887	+	0.398074i	−0.845928	+	0.533297i	$0.820953\pi$
$90$	6.21543	−	5.90873i	0.655164	−	0.622835i
$91$	−4.28105	−	6.11397i	−0.448776	−	0.640918i
$92$	−11.3551	−	8.49467i	−1.18385	−	0.885631i
$93$	−9.62913	+	7.65263i	−0.998495	+	0.793541i
$94$	6.67302	+	0.985386i	0.688269	+	0.101635i
$95$	−4.00942	+	7.84571i	−0.411357	+	0.804953i
$96$	−7.10429	−	6.74752i	−0.725079	−	0.688666i
$97$	6.02925	+	7.18538i	0.612177	+	0.729565i	0.979704	−	0.200448i	$-0.0642399\pi$
$97$	6.02925	+	7.18538i	0.612177	+	0.729565i	−0.367527	+	0.930013i	$0.619795\pi$
$98$	7.37053	−	13.6315i	0.744536	−	1.37699i
$99$	−6.55199	−	10.5054i	−0.658499	−	1.05583i
$100$	1.81550	+	0.216486i	0.181550	+	0.0216486i
$101$	2.04627	−	4.38824i	0.203611	−	0.436646i	−0.777813	−	0.628496i	$-0.783671\pi$
$101$	2.04627	−	4.38824i	0.203611	−	0.436646i	0.981424	+	0.191850i	$0.0614487\pi$
$102$	−0.992701	−	0.830749i	−0.0982920	−	0.0822564i
$103$	−3.90704	−	6.76720i	−0.384973	−	0.666792i	0.606793	−	0.794860i	$-0.292456\pi$
$103$	−3.90704	−	6.76720i	−0.384973	−	0.666792i	−0.991765	+	0.128068i	$0.959122\pi$
$104$	−4.67530	−	1.72018i	−0.458451	−	0.168677i
$105$	14.8090	−	0.899394i	1.44521	−	0.0877718i
$106$	−15.8118	−	6.84237i	−1.53578	−	0.664590i
$107$	−9.35093	+	2.50557i	−0.903988	+	0.242223i	−0.680728	−	0.732536i	$-0.738337\pi$
$107$	−9.35093	+	2.50557i	−0.903988	+	0.242223i	−0.223260	+	0.974759i	$0.571670\pi$
$108$	−0.249122	+	10.3893i	−0.0239718	+	0.999713i
$109$	−0.114748	+	0.163877i	−0.0109909	+	0.0156966i	−0.824610	−	0.565702i	$-0.808605\pi$
$109$	−0.114748	+	0.163877i	−0.0109909	+	0.0156966i	0.813619	+	0.581398i	$0.197494\pi$
$110$	−3.72389	+	11.1944i	−0.355059	+	1.06735i
$111$	3.20279	+	7.37454i	0.303995	+	0.699960i
$112$	−1.88946	−	16.8450i	−0.178537	−	1.59170i
$113$	11.2238			1.05585			0.527923	−	0.849292i	$-0.322971\pi$
$113$	11.2238			1.05585			0.527923	+	0.849292i	$0.322971\pi$
$114$	−3.30063	−	10.1541i	−0.309132	−	0.951019i
$115$	10.1344	−	10.1344i	0.945035	−	0.945035i
$116$	−2.23293	+	5.58273i	−0.207323	+	0.518343i
$117$	1.97519	+	4.90084i	0.182606	+	0.453083i
$118$	−8.28015	−	16.5351i	−0.762249	−	1.52218i
$119$	−0.388871	−	2.20539i	−0.0356477	−	0.202168i
$120$	7.77388	−	6.13404i	0.709655	−	0.559958i
$121$	5.22420	+	3.01619i	0.474927	+	0.274199i
$122$	−0.508219	+	1.17443i	−0.0460120	+	0.106327i
$123$	−13.4311	−	11.8931i	−1.21104	−	1.07236i
$124$	−11.8841	+	7.77676i	−1.06723	+	0.698373i
$125$	−3.09407	+	11.5472i	−0.276742	+	1.03282i
$126$	−11.9012	+	13.4759i	−1.06024	+	1.20053i
$127$	−3.36572	−	9.24724i	−0.298659	−	0.820560i	−0.994725	−	0.102581i	$-0.967290\pi$
$127$	−3.36572	−	9.24724i	−0.298659	−	0.820560i	0.696065	−	0.717979i	$-0.254932\pi$
$128$	−7.45221	−	8.51261i	−0.658689	−	0.752416i
$129$	−1.98245	−	2.99794i	−0.174545	−	0.263954i
$130$	2.39471	−	4.42891i	0.210030	−	0.388441i
$131$	−8.41784	−	0.736466i	−0.735470	−	0.0643453i	−0.286735	−	0.958010i	$-0.592570\pi$
$131$	−8.41784	−	0.736466i	−0.735470	−	0.0643453i	−0.448735	+	0.893665i	$0.648125\pi$
$132$	−6.41820	−	12.7748i	−0.558632	−	1.11190i
$133$	6.94002	−	17.1182i	0.601776	−	1.48434i
$134$	17.1501	−	12.7368i	1.48154	−	1.10029i
$135$	−10.3569	−	1.74683i	−0.891381	−	0.150343i
$136$	−1.05322	−	1.06060i	−0.0903126	−	0.0909454i
$137$	2.60157	−	14.7542i	0.222267	−	1.26054i	−0.645574	−	0.763698i	$-0.723382\pi$
$137$	2.60157	−	14.7542i	0.222267	−	1.26054i	0.867841	−	0.496842i	$-0.165507\pi$
$138$	0.0228738	+	17.3679i	0.00194715	+	1.47845i
$139$	6.20267	+	2.89235i	0.526104	+	0.245326i	0.667477	−	0.744630i	$-0.267374\pi$
$139$	6.20267	+	2.89235i	0.526104	+	0.245326i	−0.141374	+	0.989956i	$0.545152\pi$
$140$	17.1230	+	0.538118i	1.44716	+	0.0454793i
$141$	−3.93888	−	7.26192i	−0.331713	−	0.611564i
$142$	−3.69204	−	4.15844i	−0.309829	−	0.348969i
$143$	−5.56833	−	4.67239i	−0.465647	−	0.390725i
$144$	−1.38946	+	11.9193i	−0.115788	+	0.993274i
$145$	−5.26273	−	3.03844i	−0.437046	−	0.252329i
$146$	18.5539	−	3.80856i	1.53553	−	0.315198i
$147$	−18.7720	+	2.79728i	−1.54829	+	0.230716i
$148$	2.89965	+	8.81935i	0.238350	+	0.724946i
$149$	9.99743	−	4.66188i	0.819021	−	0.381916i	0.0324944	−	0.999472i	$-0.489655\pi$
$149$	9.99743	−	4.66188i	0.819021	−	0.381916i	0.786527	+	0.617556i	$0.211877\pi$
$150$	−1.12219	−	1.93779i	−0.0916265	−	0.158220i
$151$	9.98921			0.812911			0.406455	−	0.913671i	$-0.366765\pi$
$151$	9.98921			0.812911			0.406455	+	0.913671i	$0.366765\pi$
$152$	−2.71705	−	12.0257i	−0.220382	−	0.975414i
$153$	−0.0843276	+	1.58313i	−0.00681748	+	0.127988i
$154$	5.73184	−	24.0597i	0.461885	−	1.93879i
$155$	−6.06628	−	13.0092i	−0.487255	−	1.04492i
$156$	1.75078	+	5.84474i	0.140174	+	0.467953i
$157$	−11.2563	−	7.88177i	−0.898353	−	0.629034i	0.0304785	−	0.999535i	$-0.490297\pi$
$157$	−11.2563	−	7.88177i	−0.898353	−	0.629034i	−0.928832	+	0.370502i	$0.879186\pi$
$158$	3.49734	−	0.717900i	0.278233	−	0.0571131i
$159$	4.91711	+	20.5199i	0.389952	+	1.62734i
$160$	9.58973	−	6.22763i	0.758134	−	0.492337i
$161$	−19.3137	+	23.0172i	−1.52213	+	1.81401i
$162$	10.3618	−	7.39148i	0.814097	−	0.580729i
$163$	14.5692	+	3.90380i	1.14115	+	0.305770i	0.779412	−	0.626511i	$-0.215518\pi$
$163$	14.5692	+	3.90380i	1.14115	+	0.305770i	0.361735	+	0.932281i	$0.382184\pi$
$164$	−14.1805	−	15.1007i	−1.10731	−	1.17917i
$165$	13.7043	−	4.57887i	1.06688	−	0.356464i
$166$	12.5012	+	11.8218i	0.970283	+	0.917551i
$167$	−5.76172	−	1.01595i	−0.445855	−	0.0786163i	−0.0537870	−	0.998552i	$-0.517129\pi$
$167$	−5.76172	−	1.01595i	−0.445855	−	0.0786163i	−0.392068	+	0.919936i	$0.628240\pi$
$168$	−15.1148	+	14.2312i	−1.16613	+	1.09796i
$169$	−6.36220	−	7.58217i	−0.489400	−	0.583244i
$170$	1.21278	−	0.900687i	0.0930157	−	0.0690796i
$171$	−7.52245	+	10.6964i	−0.575256	+	0.817973i
$172$	−1.96115	−	3.65753i	−0.149536	−	0.278884i
$173$	−0.0686373	+	0.784528i	−0.00521840	+	0.0596465i	−0.998357	−	0.0572934i	$-0.981753\pi$
$173$	−0.0686373	+	0.784528i	−0.00521840	+	0.0596465i	0.993139	+	0.116940i	$0.0373085\pi$
$174$	7.11061	−	1.91532i	0.539054	−	0.145200i
$175$	0.672709	−	3.81513i	0.0508521	−	0.288396i
$176$	−6.02342	−	15.3700i	−0.454033	−	1.15856i
$177$	−10.1144	+	20.2646i	−0.760244	+	1.52318i
$178$	3.51061	−	4.42929i	0.263132	−	0.331989i
$179$	1.34005	+	0.359065i	0.100160	+	0.0268378i	0.308551	−	0.951208i	$-0.400156\pi$
$179$	1.34005	+	0.359065i	0.100160	+	0.0268378i	−0.208391	+	0.978046i	$0.566823\pi$
$180$	−11.7230	−	3.10810i	−0.873782	−	0.231664i
$181$	−5.69198	+	0.497983i	−0.423081	+	0.0370148i	−0.296709	−	0.954968i	$-0.595889\pi$
$181$	−5.69198	+	0.497983i	−0.423081	+	0.0370148i	−0.126373	+	0.991983i	$0.540333\pi$
$182$	−4.19205	+	9.68725i	−0.310735	+	0.718067i
$183$	1.52412	−	0.365220i	0.112667	−	0.0269978i
$184$	−1.81762	+	19.9722i	−0.133997	+	1.47237i
$185$	−9.24031	+	1.62932i	−0.679361	+	0.119790i
$186$	16.3532	+	5.92771i	1.19908	+	0.434641i
$187$	−0.921712	−	1.97662i	−0.0674023	−	0.144545i
$188$	−3.75797	−	8.76801i	−0.274078	−	0.639473i
$189$	21.9494	+	1.75582i	1.59658	+	0.127717i
$190$	12.4214	−	0.984453i	0.901145	−	0.0714197i
$191$			1.98137i			0.143367i	0.997427	+	0.0716836i	$0.0228372\pi$
$191$			1.98137i			0.143367i	−0.997427	+	0.0716836i	$0.977163\pi$
$192$	−2.86307	+	13.5574i	−0.206624	+	0.978420i
$193$	−6.39346	+	17.5659i	−0.460211	+	1.26442i	0.465115	+	0.885250i	$0.346013\pi$
$193$	−6.39346	+	17.5659i	−0.460211	+	1.26442i	−0.925327	+	0.379170i	$0.876209\pi$
$194$	4.18712	−	12.5869i	0.300618	−	0.903689i
$195$	−6.09909	+	0.908845i	−0.436765	+	0.0650837i
$196$	−21.8812	+	1.22334i	−1.56295	+	0.0873817i
$197$	1.63083	+	6.08633i	0.116192	+	0.433633i	0.999373	−	0.0353982i	$-0.0112699\pi$
$197$	1.63083	+	6.08633i	0.116192	+	0.433633i	−0.883182	+	0.469031i	$0.844603\pi$
$198$	−7.79877	+	15.6768i	−0.554235	+	1.11410i
$199$	5.78680	−	6.89644i	0.410215	−	0.488876i	−0.520891	−	0.853623i	$-0.674400\pi$
$199$	5.78680	−	6.89644i	0.410215	−	0.488876i	0.931106	+	0.364748i	$0.118845\pi$
$200$	−1.08457	−	2.34723i	−0.0766909	−	0.165975i
$201$	−25.0829	−	7.44156i	−1.76921	−	0.524887i
$202$	−6.80208	+	0.787027i	−0.478593	+	0.0553750i
$203$	11.5463	+	5.38412i	0.810390	+	0.377891i
$204$	−0.265039	+	1.81134i	−0.0185564	+	0.126819i
$205$	17.1500	−	12.0085i	1.19781	−	0.838713i
$206$	−5.25602	+	9.72081i	−0.366205	+	0.677281i
$207$	16.9990	−	12.7868i	1.18151	−	0.888746i
$208$	1.39253	+	6.90621i	0.0965547	+	0.478859i
$209$	2.21370	−	17.8526i	0.153125	−	1.23489i
$210$	−12.0572	−	17.1713i	−0.832028	−	1.18493i
$211$	−19.0694	−	1.66836i	−1.31279	−	0.114855i	−0.590836	−	0.806792i	$-0.701202\pi$
$211$	−19.0694	−	1.66836i	−1.31279	−	0.114855i	−0.721958	+	0.691937i	$0.756758\pi$
$212$	3.47517	+	24.1160i	0.238676	+	1.65630i
$213$	−1.36069	+	6.67340i	−0.0932332	+	0.457254i
$214$	9.94732	+	9.40672i	0.679985	+	0.643030i
$215$	3.94147	−	1.43458i	0.268806	−	0.0978374i
$216$	12.6988	−	7.39870i	0.864043	−	0.503418i
$217$	15.0463	+	26.0610i	1.02141	+	1.76913i
$218$	0.282426	+	0.0167792i	0.0191283	+	0.00113643i
$219$	−17.3673	−	15.3786i	−1.17358	−	1.03919i
$220$	16.2435	−	3.80986i	1.09513	−	0.256861i
$221$	0.240901	+	0.899056i	0.0162048	+	0.0604770i
$222$	6.50945	−	9.32257i	0.436886	−	0.625690i
$223$	18.4325	−	3.25015i	1.23433	−	0.217646i	0.481848	−	0.876255i	$-0.339966\pi$
$223$	18.4325	−	3.25015i	1.23433	−	0.217646i	0.752486	+	0.658608i	$0.228855\pi$
$224$	−18.8900	+	14.7585i	−1.26214	+	0.986093i
$225$	−1.07376	+	2.52360i	−0.0715839	+	0.168240i
$226$	−8.31714	−	13.5193i	−0.553248	−	0.899292i
$227$	−2.42743	+	2.42743i	−0.161114	+	0.161114i	−0.783060	−	0.621946i	$-0.786342\pi$
$227$	−2.42743	+	2.42743i	−0.161114	+	0.161114i	0.621946	+	0.783060i	$0.286342\pi$
$228$	−9.78501	+	11.5002i	−0.648028	+	0.761617i
$229$	−16.5404	−	16.5404i	−1.09302	−	1.09302i	−0.995205	−	0.0978154i	$-0.968815\pi$
$229$	−16.5404	−	16.5404i	−1.09302	−	1.09302i	−0.0978154	−	0.995205i	$-0.531185\pi$
$230$	−19.7170	−	4.69724i	−1.30010	−	0.309727i
$231$	−27.7845	+	12.0669i	−1.82808	+	0.793943i
$232$	8.37919	−	1.44733i	0.550121	−	0.0950221i
$233$	−0.616658	−	3.49724i	−0.0403986	−	0.229112i	0.957923	−	0.287025i	$-0.0926664\pi$
$233$	−0.616658	−	3.49724i	−0.0403986	−	0.229112i	−0.998322	+	0.0579133i	$0.981555\pi$
$234$	4.43951	−	6.01082i	0.290220	−	0.392940i
$235$	9.31268	−	2.49533i	0.607492	−	0.162777i
$236$	−13.7811	+	22.2266i	−0.897072	+	1.44683i
$237$	−3.27369	−	2.89881i	−0.212649	−	0.188298i
$238$	−2.36829	+	2.10266i	−0.153513	+	0.136295i
$239$	−4.27493	+	2.46813i	−0.276522	+	0.159650i	−0.631848	−	0.775092i	$-0.717703\pi$
$239$	−4.27493	+	2.46813i	−0.276522	+	0.159650i	0.355326	+	0.934743i	$0.384370\pi$
$240$	−13.1493	−	4.81834i	−0.848781	−	0.311022i
$241$	2.18953	+	6.01569i	0.141040	+	0.387505i	0.990021	−	0.140919i	$-0.0450056\pi$
$241$	2.18953	+	6.01569i	0.141040	+	0.387505i	−0.848981	+	0.528423i	$0.822783\pi$
$242$	−0.238200	−	8.52775i	−0.0153121	−	0.548185i
$243$	−14.8569	−	4.71936i	−0.953071	−	0.302747i
$244$	1.79123	−	0.258119i	0.114672	−	0.0165244i
$245$	1.93043	−	22.0650i	0.123331	−	1.40968i
$246$	−4.37269	+	24.9912i	−0.278793	+	1.59338i
$247$	−2.25341	+	7.33918i	−0.143381	+	0.466981i
$248$	18.1738	+	8.55193i	1.15404	+	0.543048i
$249$	2.39445	−	20.9361i	0.151742	−	1.32677i
$250$	16.2017	−	4.82994i	1.02469	−	0.305472i
$251$	5.70708	+	8.15055i	0.360228	+	0.514458i	0.957830	−	0.287334i	$-0.0927689\pi$
$251$	5.70708	+	8.15055i	0.360228	+	0.514458i	−0.597603	+	0.801792i	$0.703880\pi$
$252$	25.0512	+	4.34919i	1.57808	+	0.273973i
$253$	−12.3668	+	26.5208i	−0.777496	+	1.66735i
$254$	−8.64443	+	10.9066i	−0.542400	+	0.684338i
$255$	−1.77375	−	0.526234i	−0.111076	−	0.0329540i
$256$	−4.73135	+	15.2844i	−0.295709	+	0.955278i
$257$	0.411627	+	0.345396i	0.0256766	+	0.0215452i	0.655536	−	0.755164i	$-0.272443\pi$
$257$	0.411627	+	0.345396i	0.0256766	+	0.0215452i	−0.629859	+	0.776709i	$0.716887\pi$
$258$	−2.14204	+	4.60946i	−0.133358	+	0.286973i
$259$	19.0005	−	5.09117i	1.18063	−	0.316350i
$260$	−7.10928	+	0.397468i	−0.440899	+	0.0246499i
$261$	−7.10238	−	5.55879i	−0.439626	−	0.344080i
$262$	5.35076	+	10.6852i	0.330571	+	0.660136i
$263$	17.1824	+	6.25387i	1.05951	+	0.385630i	0.812245	−	0.583317i	$-0.198245\pi$
$263$	17.1824	+	6.25387i	1.05951	+	0.385630i	0.247266	+	0.968948i	$0.420468\pi$
$264$	−10.6315	+	17.1973i	−0.654323	+	1.05842i
$265$	−24.6251			−1.51271
$266$	−25.7620	+	4.32563i	−1.57957	+	0.265221i
$267$	−6.91958	−	0.184160i	−0.423472	−	0.0112704i
$268$	−28.0504	−	11.2194i	−1.71345	−	0.685333i
$269$	19.0169	−	8.86772i	1.15948	−	0.540674i	0.254895	−	0.966969i	$-0.417959\pi$
$269$	19.0169	−	8.86772i	1.15948	−	0.540674i	0.904584	+	0.426294i	$0.140181\pi$
$270$	5.57066	+	13.7696i	0.339020	+	0.837991i
$271$	−5.06290	−	28.7132i	−0.307550	−	1.74420i	−0.611255	−	0.791434i	$-0.709335\pi$
$271$	−5.06290	−	28.7132i	−0.307550	−	1.74420i	0.303705	−	0.952766i	$-0.401776\pi$
$272$	−0.497051	+	2.05456i	−0.0301381	+	0.124576i
$273$	12.5717	−	3.01252i	0.760877	−	0.182326i
$274$	−19.6997	+	7.79965i	−1.19010	+	0.471194i
$275$	−0.328826	−	3.75849i	−0.0198289	−	0.226646i
$276$	20.9031	−	12.8977i	1.25822	−	0.776348i
$277$	2.64286	−	9.86330i	0.158794	−	0.592628i	−0.839956	−	0.542654i	$-0.817419\pi$
$277$	2.64286	−	9.86330i	0.158794	−	0.592628i	0.998751	−	0.0499741i	$-0.0159139\pi$
$278$	−1.11244	−	9.61458i	−0.0667199	−	0.576644i
$279$	−6.21116	−	20.3782i	−0.371852	−	1.22001i
$280$	−12.0405	−	21.0239i	−0.719555	−	1.25642i
$281$	−2.02734	−	0.357475i	−0.120941	−	0.0213252i	0.112850	−	0.993612i	$-0.464002\pi$
$281$	−2.02734	−	0.357475i	−0.120941	−	0.0213252i	−0.233791	+	0.972287i	$0.575113\pi$
$282$	−5.82834	+	10.1258i	−0.347073	+	0.602980i
$283$	26.9279	+	2.35588i	1.60069	+	0.140043i	0.852243	−	0.523146i	$-0.175242\pi$
$283$	26.9279	+	2.35588i	1.60069	+	0.140043i	0.748452	+	0.663189i	$0.230797\pi$
$284$	−2.27304	+	7.52867i	−0.134880	+	0.446744i
$285$	−10.0935	−	11.4461i	−0.597889	−	0.678006i
$286$	−1.50171	+	10.1696i	−0.0887980	+	0.601339i
$287$	−33.6232	+	28.2132i	−1.98471	+	1.66537i
$288$	15.3867	−	7.15888i	0.906670	−	0.421841i
$289$	2.90352	−	16.4667i	0.170796	−	0.968630i
$290$	0.239957	+	8.59066i	0.0140908	+	0.504461i
$291$	−15.4090	+	5.14845i	−0.903293	+	0.301808i
$292$	−18.3364	−	19.5263i	−1.07306	−	1.14269i
$293$	1.09387	−	4.08238i	0.0639047	−	0.238495i	−0.926584	−	0.376087i	$-0.877269\pi$
$293$	1.09387	−	4.08238i	0.0639047	−	0.238495i	0.990489	+	0.137591i	$0.0439361\pi$
$294$	17.2800	+	20.5385i	1.00779	+	1.19783i
$295$	−20.2475	−	16.9897i	−1.17886	−	0.989179i
$296$	8.47439	−	10.0281i	0.492564	−	0.582870i
$297$	21.0906	−	3.88090i	1.22380	−	0.225192i
$298$	−13.0237	−	8.58756i	−0.754444	−	0.497464i
$299$	7.16304	−	10.2299i	0.414249	−	0.591609i
$300$	−1.50254	+	2.78766i	−0.0867494	+	0.160946i
$301$	−7.96955	+	3.71626i	−0.459357	+	0.214202i
$302$	−7.40228	−	12.0322i	−0.425954	−	0.692378i
$303$	5.77021	+	6.08575i	0.331490	+	0.349617i
$304$	−12.4718	+	12.1841i	−0.715309	+	0.698808i
$305$			1.82904i			0.104731i
$306$	1.96940	−	1.07157i	0.112583	−	0.0612573i
$307$	3.91176	+	8.38880i	0.223256	+	0.478774i	0.985749	−	0.168222i	$-0.0538027\pi$
$307$	3.91176	+	8.38880i	0.223256	+	0.478774i	−0.762493	+	0.646996i	$0.776025\pi$
$308$	−33.2280	+	10.9248i	−1.89334	+	0.622498i
$309$	13.3866	−	1.99478i	0.761537	−	0.113479i
$310$	−11.1746	+	16.9471i	−0.634673	+	0.962533i
$311$	−6.48336	+	11.2295i	−0.367638	+	0.636767i	−0.989196	−	0.146601i	$-0.953167\pi$
$311$	−6.48336	+	11.2295i	−0.367638	+	0.636767i	0.621558	+	0.783368i	$0.286500\pi$
$312$	5.74275	−	6.43996i	0.325119	−	0.364591i
$313$	−17.1871	+	20.4828i	−0.971475	+	1.15776i	0.0159828	+	0.999872i	$0.494912\pi$
$313$	−17.1871	+	20.4828i	−0.971475	+	1.15776i	−0.987457	+	0.157886i	$0.949532\pi$
$314$	−1.15252	+	19.3991i	−0.0650407	+	1.09476i
$315$	−7.96180	+	24.4327i	−0.448597	+	1.37663i
$316$	−3.45635	−	3.68064i	−0.194435	−	0.207052i
$317$	5.73048	−	12.2891i	0.321856	−	0.690222i	−0.677101	−	0.735890i	$-0.736764\pi$
$317$	5.73048	−	12.2891i	0.321856	−	0.690222i	0.998957	+	0.0456681i	$0.0145417\pi$
$318$	21.0730	−	21.1286i	1.18172	−	1.18483i
$319$	12.2188	+	2.15451i	0.684124	+	0.120630i
$320$	−14.6076	−	6.93621i	−0.816589	−	0.387746i
$321$	1.90528	−	16.6590i	0.106342	−	0.929816i
$322$	42.0367	+	6.20745i	2.34261	+	0.345927i
$323$	−1.54338	+	1.70998i	−0.0858760	+	0.0951459i
$324$	−16.5816	−	7.00369i	−0.921198	−	0.389094i
$325$	−0.140334	+	1.60402i	−0.00778430	+	0.0889750i
$326$	−6.09395	−	20.4418i	−0.337513	−	1.13216i
$327$	−0.191128	−	0.289031i	−0.0105694	−	0.0159835i
$328$	−7.68104	+	28.2709i	−0.424114	+	1.56100i
$329$	−18.9934	+	6.91303i	−1.04714	+	0.381128i
$330$	−15.6706	−	13.1141i	−0.862639	−	0.721906i
$331$	−25.1728	−	6.74502i	−1.38362	−	0.370740i	−0.511186	−	0.859470i	$-0.670794\pi$
$331$	−25.1728	−	6.74502i	−1.38362	−	0.370740i	−0.872435	+	0.488730i	$0.837460\pi$
$332$	4.97591	−	23.8183i	0.273089	−	1.30720i
$333$	−13.9176	+	0.474082i	−0.762681	+	0.0259795i
$334$	3.04586	+	7.69297i	0.166662	+	0.420941i
$335$	15.2667	−	26.4426i	0.834107	−	1.44472i
$336$	28.3423	+	7.66039i	1.54620	+	0.417908i
$337$	30.9419	−	5.45589i	1.68551	−	0.297201i	0.752914	−	0.658119i	$-0.228648\pi$
$337$	30.9419	−	5.45589i	1.68551	−	0.297201i	0.932598	+	0.360918i	$0.117536\pi$
$338$	−4.41834	+	13.2820i	−0.240326	+	0.722446i
$339$	−7.13259	+	18.0844i	−0.387389	+	0.982211i
$340$	−1.98360	−	0.793384i	−0.107576	−	0.0430273i
$341$	20.7232	+	20.7232i	1.12222	+	1.12222i
$342$	18.4584	+	1.13465i	0.998116	+	0.0613551i
$343$			16.7714i			0.905569i
$344$	−2.95232	+	5.07259i	−0.159178	+	0.273496i
$345$	9.88882	+	22.7694i	0.532396	+	1.22586i
$346$	0.995844	−	0.498682i	0.0535369	−	0.0268093i
$347$	−8.61621	−	6.03314i	−0.462543	−	0.323876i	0.318971	−	0.947765i	$-0.396663\pi$
$347$	−8.61621	−	6.03314i	−0.462543	−	0.323876i	−0.781513	+	0.623889i	$0.785552\pi$
$348$	−7.57621	−	7.14559i	−0.406128	−	0.383044i
$349$	2.01974	+	7.53777i	0.108114	+	0.403488i	0.998680	−	0.0513671i	$-0.0163578\pi$
$349$	2.01974	+	7.53777i	0.108114	+	0.403488i	−0.890566	+	0.454855i	$0.849691\pi$
$350$	−5.09391	+	2.01682i	−0.272281	+	0.107804i
$351$	−9.15173	+	0.0681097i	−0.488483	+	0.00363543i
$352$	−14.0500	+	18.6449i	−0.748867	+	0.993779i
$353$	−19.5538	+	11.2894i	−1.04074	+	0.600873i	−0.920043	−	0.391816i	$-0.871847\pi$
$353$	−19.5538	+	11.2894i	−1.04074	+	0.600873i	−0.120699	+	0.992689i	$0.538514\pi$
$354$	31.9042	−	2.83360i	1.69569	−	0.150604i
$355$	−7.20355	−	3.35907i	−0.382325	−	0.178281i
$356$	−7.93665	−	0.946390i	−0.420642	−	0.0501586i
$357$	3.80058	+	0.774932i	0.201148	+	0.0410138i
$358$	−0.560512	−	1.88020i	−0.0296240	−	0.0993717i
$359$	9.38641	−	7.87614i	0.495396	−	0.415687i	−0.360559	−	0.932736i	$-0.617414\pi$
$359$	9.38641	−	7.87614i	0.495396	−	0.415687i	0.855955	+	0.517050i	$0.172970\pi$
$360$	4.94330	+	16.4238i	0.260535	+	0.865613i
$361$	−18.2764	+	5.19341i	−0.961918	+	0.273337i
$362$	4.81775	+	6.48710i	0.253215	+	0.340955i
$363$	−8.17978	+	6.50078i	−0.429327	+	0.341202i
$364$	14.7749	−	2.12910i	0.774418	−	0.111595i
$365$	22.1761	−	15.5279i	1.16075	−	0.812766i
$366$	−1.56933	−	1.56521i	−0.0820304	−	0.0818147i
$367$	29.7584	−	10.8312i	1.55338	−	0.565382i	0.584169	−	0.811632i	$-0.301421\pi$
$367$	29.7584	−	10.8312i	1.55338	−	0.565382i	0.969206	+	0.246250i	$0.0791983\pi$
$368$	25.4039	−	12.6106i	1.32427	−	0.657373i
$369$	27.6982	−	14.0831i	1.44191	−	0.733134i
$370$	8.80988	+	9.92281i	0.458004	+	0.515862i
$371$	51.4291	−	4.49946i	2.67006	−	0.233600i
$372$	−4.97813	−	24.0905i	−0.258104	−	1.24903i
$373$	−0.692357	−	2.58391i	−0.0358489	−	0.133790i	0.945682	−	0.325093i	$-0.105395\pi$
$373$	−0.692357	−	2.58391i	−0.0358489	−	0.133790i	−0.981531	+	0.191303i	$0.938729\pi$
$374$	−1.69787	+	2.57495i	−0.0877948	+	0.133148i
$375$	−16.6393	−	12.3235i	−0.859251	−	0.636382i
$376$	−7.77651	+	11.0239i	−0.401043	+	0.568514i
$377$	−4.97577	−	1.81103i	−0.256265	−	0.0932729i
$378$	−14.1502	−	27.7397i	−0.727806	−	1.42677i
$379$	18.7925	−	18.7925i	0.965304	−	0.965304i	−0.0341136	−	0.999418i	$-0.510861\pi$
$379$	18.7925	−	18.7925i	0.965304	−	0.965304i	0.999418	+	0.0341136i	$0.0108608\pi$
$380$	−10.3904	−	14.2324i	−0.533017	−	0.730107i
$381$	17.0386	+	0.453471i	0.872912	+	0.0232320i
$382$	2.38661	−	1.46825i	0.122110	−	0.0751223i
$383$	1.22091	+	0.444375i	0.0623857	+	0.0227065i	0.373024	−	0.927821i	$-0.378321\pi$
$383$	1.22091	+	0.444375i	0.0623857	+	0.0227065i	−0.310639	+	0.950528i	$0.600543\pi$
$384$	18.4518	−	6.59777i	0.941615	−	0.336691i
$385$	−6.13865	−	34.8140i	−0.312855	−	1.77429i
$386$	25.8963	−	5.31574i	1.31809	−	0.270564i
$387$	6.09028	−	1.28908i	0.309586	−	0.0655276i
$388$	−18.2640	+	4.28379i	−0.927216	+	0.217476i
$389$	−12.0939	+	1.05808i	−0.613186	+	0.0536468i	−0.389518	−	0.921019i	$-0.627358\pi$
$389$	−12.0939	+	1.05808i	−0.613186	+	0.0536468i	−0.223667	+	0.974666i	$0.571803\pi$
$390$	5.61432	+	6.67301i	0.284292	+	0.337901i
$391$	3.24498	−	1.87349i	0.164106	−	0.0947466i
$392$	17.6881	+	25.4499i	0.893386	+	1.28542i
$393$	6.53608	−	13.0953i	0.329702	−	0.660570i
$394$	6.12264	−	6.47451i	0.308454	−	0.326181i
$395$	4.18012	−	2.92695i	0.210325	−	0.147271i
$396$	24.6622	−	2.22314i	1.23932	−	0.111717i
$397$	0.171064	−	1.95527i	0.00858547	−	0.0981324i	−0.990693	−	0.136116i	$-0.956538\pi$
$397$	0.171064	−	1.95527i	0.00858547	−	0.0981324i	0.999278	+	0.0379838i	$0.0120935\pi$
$398$	−12.5951	−	1.85989i	−0.631336	−	0.0932276i
$399$	23.1715	+	22.0606i	1.16003	+	1.10441i
$400$	−2.02360	+	3.04576i	−0.101180	+	0.152288i
$401$	27.9962	−	23.4916i	1.39806	−	1.17311i	0.436111	−	0.899893i	$-0.356355\pi$
$401$	27.9962	−	23.4916i	1.39806	−	1.17311i	0.961951	−	0.273221i	$-0.0880891\pi$
$402$	9.62355	+	35.7273i	0.479979	+	1.78192i
$403$	−7.17396	−	10.2455i	−0.357361	−	0.510364i
$404$	5.98852	+	7.61006i	0.297940	+	0.378615i
$405$	9.39630	−	15.5776i	0.466906	−	0.774056i
$406$	−2.07082	−	17.8976i	−0.102773	−	0.888241i
$407$	16.5907	−	9.57863i	0.822369	−	0.474795i
$408$	2.37820	−	1.02301i	0.117739	−	0.0506464i
$409$	−15.4366	−	12.9528i	−0.763290	−	0.640477i	0.175691	−	0.984445i	$-0.443784\pi$
$409$	−15.4366	−	12.9528i	−0.763290	−	0.640477i	−0.938981	+	0.343969i	$0.888229\pi$
$410$	−27.1732	−	11.7589i	−1.34199	−	0.580730i
$411$	22.1196	+	13.5680i	1.09108	+	0.669258i
$412$	15.6038	−	0.872384i	0.768745	−	0.0429793i
$413$	45.3909	+	31.7830i	2.23354	+	1.56394i
$414$	−27.9987	−	11.0003i	−1.37606	−	0.540633i
$415$	23.1091	+	8.41102i	1.13438	+	0.412881i
$416$	7.28679	−	6.79503i	0.357264	−	0.333154i
$417$	−8.60206	+	8.15605i	−0.421245	+	0.399404i
$418$	−23.1443	+	10.5628i	−1.13202	+	0.516644i
$419$	−13.5505	−	13.5505i	−0.661986	−	0.661986i	0.293862	−	0.955848i	$-0.405059\pi$
$419$	−13.5505	−	13.5505i	−0.661986	−	0.661986i	−0.955848	+	0.293862i	$0.905059\pi$
$420$	−11.7485	+	27.2477i	−0.573270	+	1.32955i
$421$	−20.2597	+	9.44726i	−0.987398	+	0.460431i	−0.848110	−	0.529820i	$-0.822259\pi$
$421$	−20.2597	+	9.44726i	−0.987398	+	0.460431i	−0.139289	+	0.990252i	$0.544482\pi$
$422$	12.1214	+	24.2059i	0.590061	+	1.17832i
$423$	14.2039	−	1.73168i	0.690619	−	0.0841971i
$424$	26.4732	−	22.0566i	1.28565	−	1.07116i
$425$	−0.241552	+	0.418381i	−0.0117170	+	0.0202945i
$426$	9.04658	−	3.30618i	0.438308	−	0.160185i
$427$	−0.334199	−	3.81991i	−0.0161730	−	0.184859i
$428$	3.95937	−	18.9524i	0.191384	−	0.916100i
$429$	11.0670	−	6.00278i	0.534321	−	0.289817i
$430$	−4.64872	−	3.68453i	−0.224181	−	0.177684i
$431$	34.1444	−	12.4275i	1.64468	−	0.598614i	0.656830	−	0.754039i	$-0.271897\pi$
$431$	34.1444	−	12.4275i	1.64468	−	0.598614i	0.987848	+	0.155425i	$0.0496746\pi$
$432$	−18.3221	−	9.81335i	−0.881521	−	0.472145i
$433$	−8.42924	−	1.48630i	−0.405083	−	0.0714271i	−0.0326056	−	0.999468i	$-0.510381\pi$
$433$	−8.42924	−	1.48630i	−0.405083	−	0.0714271i	−0.372478	+	0.928041i	$0.621492\pi$
$434$	20.2413	−	37.4355i	0.971614	−	1.79696i
$435$	8.24012	−	6.54873i	0.395083	−	0.313988i
$436$	−0.189074	−	0.352622i	−0.00905502	−	0.0168876i
$437$	30.8863	+	1.11556i	1.47749	+	0.0533644i
$438$	−5.65419	+	32.3153i	−0.270168	+	1.54409i
$439$	9.53992	−	8.00494i	0.455316	−	0.382055i	−0.386088	−	0.922462i	$-0.626174\pi$
$439$	9.53992	−	8.00494i	0.455316	−	0.382055i	0.841404	+	0.540407i	$0.181730\pi$
$440$	−16.6259	−	16.7424i	−0.792610	−	0.798163i
$441$	7.42227	−	32.0242i	0.353441	−	1.52496i
$442$	0.904420	−	0.956397i	0.0430189	−	0.0454912i
$443$	−0.126608	+	0.271511i	−0.00601531	+	0.0128999i	−0.909292	−	0.416158i	$-0.863376\pi$
$443$	−0.126608	+	0.271511i	−0.00601531	+	0.0128999i	0.903277	+	0.429057i	$0.141154\pi$
$444$	−16.0529	−	0.932508i	−0.761839	−	0.0442549i
$445$	2.09078	−	7.80291i	0.0991126	−	0.369893i
$446$	−17.5739	−	19.7940i	−0.832149	−	0.937272i
$447$	1.15824	+	19.0710i	0.0547827	+	0.902028i
$448$	31.7750	+	11.8170i	1.50123	+	0.558303i
$449$	−1.93426	+	3.35024i	−0.0912836	+	0.158108i	−0.908051	−	0.418859i	$-0.862430\pi$
$449$	−1.93426	+	3.35024i	−0.0912836	+	0.158108i	0.816768	+	0.576966i	$0.195764\pi$
$450$	3.83543	−	0.576694i	0.180804	−	0.0271856i
$451$	−24.5182	+	35.0156i	−1.15452	+	1.64882i
$452$	−10.1211	+	20.0364i	−0.476057	+	0.942433i
$453$	−6.34803	+	16.0952i	−0.298257	+	0.756219i
$454$	4.72268	+	1.12510i	0.221646	+	0.0528037i
$455$			15.0868i			0.707282i
$456$	21.1032	+	3.26433i	0.988247	+	0.152866i
$457$			7.39536i			0.345940i	0.984927	+	0.172970i	$0.0553364\pi$
$457$			7.39536i			0.345940i	−0.984927	+	0.172970i	$0.944664\pi$
$458$	−7.66641	+	32.1802i	−0.358228	+	1.50368i
$459$	−2.49724	−	1.14193i	−0.116561	−	0.0533008i
$460$	8.95287	+	27.2303i	0.417430	+	1.26962i
$461$	−4.94748	+	7.06574i	−0.230427	+	0.329084i	−0.917670	−	0.397344i	$-0.869932\pi$
$461$	−4.94748	+	7.06574i	−0.230427	+	0.329084i	0.687243	+	0.726428i	$0.258821\pi$
$462$	35.1239	+	24.5252i	1.63411	+	1.14101i
$463$	−20.4675	+	35.4508i	−0.951207	+	1.64754i	−0.208387	+	0.978046i	$0.566821\pi$
$463$	−20.4675	+	35.4508i	−0.951207	+	1.64754i	−0.742819	+	0.669492i	$0.766512\pi$
$464$	−7.95256	−	9.02042i	−0.369188	−	0.418763i
$465$	24.8162	−	1.50716i	1.15082	−	0.0698928i
$466$	−3.75555	+	3.33433i	−0.173973	+	0.154460i
$467$	9.69357	−	36.1769i	0.448565	−	1.67407i	−0.257783	−	0.966203i	$-0.582992\pi$
$467$	9.69357	−	36.1769i	0.448565	−	1.67407i	0.706348	−	0.707865i	$-0.250341\pi$
$468$	−10.5300	−	0.893312i	−0.486748	−	0.0412933i
$469$	−27.0525	+	58.0144i	−1.24917	+	2.67885i
$470$	−9.90664	−	9.36824i	−0.456959	−	0.432125i
$471$	19.8528	−	13.1281i	0.914771	−	0.604910i
$472$	36.9846	+	0.129117i	1.70236	+	0.00594311i
$473$	−6.56031	+	5.50475i	−0.301643	+	0.253109i
$474$	−1.06580	+	6.09133i	−0.0489537	+	0.279784i
$475$	−3.52062	+	1.86655i	−0.161537	+	0.0856432i
$476$	4.28767	+	1.29453i	0.196525	+	0.0593345i
$477$	−36.1877	−	5.11745i	−1.65692	−	0.234312i
$478$	6.14077	+	3.32030i	0.280872	+	0.151867i
$479$	−38.8650	−	6.85295i	−1.77579	−	0.313119i	−0.812775	−	0.582578i	$-0.802044\pi$
$479$	−38.8650	−	6.85295i	−1.77579	−	0.313119i	−0.963012	+	0.269459i	$0.913155\pi$
$480$	3.94016	+	19.4091i	0.179843	+	0.885901i
$481$	−7.68272	+	2.79628i	−0.350302	+	0.127499i
$482$	5.62354	−	7.09514i	0.256145	−	0.323175i
$483$	−24.8130	−	45.7465i	−1.12903	−	2.08154i
$484$	−10.0954	+	6.60622i	−0.458880	+	0.300283i
$485$	−1.65246	−	18.8877i	−0.0750344	−	0.857647i
$486$	5.32480	+	21.3927i	0.241538	+	0.970391i
$487$	15.3607	−	26.6054i	0.696058	−	1.20561i	−0.273765	−	0.961797i	$-0.588269\pi$
$487$	15.3607	−	26.6054i	0.696058	−	1.20561i	0.969823	−	0.243811i	$-0.0783977\pi$
$488$	−1.63826	−	1.96630i	−0.0741606	−	0.0890104i
$489$	−15.5486	+	20.9939i	−0.703132	+	0.949378i
$490$	−28.0083	+	14.0255i	−1.26529	+	0.633607i
$491$	2.07516	−	0.967662i	0.0936505	−	0.0436700i	−0.375229	−	0.926932i	$-0.622436\pi$
$491$	2.07516	−	0.967662i	0.0936505	−	0.0436700i	0.468879	+	0.883262i	$0.344658\pi$
$492$	33.3428	−	13.2522i	1.50321	−	0.597453i
$493$	−1.12340	−	1.12340i	−0.0505955	−	0.0505955i
$494$	10.5101	−	2.72425i	0.472870	−	0.122570i
$495$	−1.33118	+	24.9910i	−0.0598322	+	1.12326i
$496$	−3.16626	−	28.2280i	−0.142169	−	1.26747i
$497$	15.6582	+	5.69913i	0.702367	+	0.255641i
$498$	−26.9924	+	12.6301i	−1.20956	+	0.565967i
$499$	−21.5509	−	15.0901i	−0.964749	−	0.675525i	−0.0187943	−	0.999823i	$-0.505983\pi$
$499$	−21.5509	−	15.0901i	−0.964749	−	0.675525i	−0.945955	+	0.324299i	$0.894872\pi$
$500$	−17.8237	−	15.9362i	−0.797100	−	0.712690i
$501$	5.29846	−	8.63800i	0.236718	−	0.385917i
$502$	5.58843	−	12.9141i	0.249424	−	0.576385i
$503$	17.0816	+	14.3332i	0.761633	+	0.639086i	0.938551	−	0.345140i	$-0.112168\pi$
$503$	17.0816	+	14.3332i	0.761633	+	0.639086i	−0.176918	+	0.984226i	$0.556613\pi$
$504$	−13.3249	−	33.3976i	−0.593539	−	1.48765i
$505$	−8.47588	+	4.89355i	−0.377172	+	0.217760i
$506$	41.1090	−	4.75647i	1.82752	−	0.211451i
$507$	16.2599	−	5.43276i	0.722129	−	0.241277i
$508$	19.5430	+	2.33036i	0.867079	+	0.103393i
$509$	−9.72296	−	13.8858i	−0.430963	−	0.615478i	0.543667	−	0.839301i	$-0.317035\pi$
$509$	−9.72296	−	13.8858i	−0.430963	−	0.615478i	−0.974630	+	0.223822i	$0.928146\pi$
$510$	0.680534	+	2.52647i	0.0301346	+	0.111874i
$511$	−43.4771	+	36.4816i	−1.92331	+	1.61385i
$512$	21.9165	−	5.62718i	0.968583	−	0.248689i
$513$	−12.4542	−	18.9181i	−0.549867	−	0.835252i
$514$	0.111011	−	0.751763i	0.00489648	−	0.0331588i
$515$	−1.37662	+	15.7348i	−0.0606611	+	0.693360i
$516$	7.13952	−	0.835600i	0.314300	−	0.0367852i
$517$	−16.1248	+	11.2907i	−0.709167	+	0.496564i
$518$	−20.2123	−	19.1138i	−0.888078	−	0.839814i
$519$	−1.22046	−	0.609151i	−0.0535722	−	0.0267388i
$520$	5.74693	+	8.26876i	0.252020	+	0.362609i
$521$	16.1519	−	9.32530i	0.707628	−	0.408549i	−0.102554	−	0.994727i	$-0.532702\pi$
$521$	16.1519	−	9.32530i	0.707628	−	0.408549i	0.810182	+	0.586178i	$0.199368\pi$
$522$	−1.43263	+	12.6742i	−0.0627046	+	0.554734i
$523$	−34.4632	+	3.01514i	−1.50697	+	0.131843i	−0.810498	−	0.585742i	$-0.800803\pi$
$523$	−34.4632	+	3.01514i	−1.50697	+	0.131843i	−0.696471	+	0.717585i	$0.745248\pi$
$524$	8.90555	−	14.3632i	0.389041	−	0.627458i
$525$	5.71965	+	3.50838i	0.249626	+	0.153118i
$526$	−5.19968	−	25.3309i	−0.226717	−	1.10448i
$527$	−0.651649	−	3.69569i	−0.0283863	−	0.160987i
$528$	28.5928	+	0.0621633i	1.24434	+	0.00270531i
$529$	−25.6293	−	9.32831i	−1.11432	−	0.405579i
$530$	18.2479	+	29.6616i	0.792639	+	1.28842i
$531$	−26.2239	−	29.1748i	−1.13802	−	1.26608i
$532$	24.3007	+	27.8256i	1.05357	+	1.20639i
$533$	12.8997	−	12.8997i	0.558746	−	0.558746i
$534$	4.90578	+	8.47127i	0.212294	+	0.366588i
$535$	18.3881	+	6.69271i	0.794986	+	0.289351i
$536$	7.27214	+	42.1013i	0.314109	+	1.81850i
$537$	−1.43013	+	1.93099i	−0.0617148	+	0.0833282i
$538$	−24.7734	−	16.3351i	−1.06806	−	0.704255i
$539$	11.7045	+	43.6818i	0.504149	+	1.88151i
$540$	12.4578	−	16.9137i	0.536098	−	0.727848i
$541$	20.3190	−	1.77768i	0.873583	−	0.0764286i	0.358460	−	0.933545i	$-0.383302\pi$
$541$	20.3190	−	1.77768i	0.873583	−	0.0764286i	0.515123	+	0.857116i	$0.327746\pi$
$542$	−30.8339	+	27.3756i	−1.32443	+	1.17588i
$543$	2.81481	−	9.48771i	0.120795	−	0.407157i
$544$	2.84309	−	0.923774i	0.121897	−	0.0396065i
$545$	0.379997	−	0.138307i	0.0162773	−	0.00592444i
$546$	−12.9447	−	12.9106i	−0.553980	−	0.552523i
$547$	−9.80654	+	6.86662i	−0.419298	+	0.293595i	−0.764122	−	0.645072i	$-0.776827\pi$
$547$	−9.80654	+	6.86662i	−0.419298	+	0.293595i	0.344824	+	0.938667i	$0.387938\pi$
$548$	23.9929	+	17.9490i	1.02492	+	0.766742i
$549$	−0.380100	+	2.68785i	−0.0162223	+	0.114715i
$550$	−4.28353	+	3.18123i	−0.182650	+	0.135648i
$551$	−2.93258	−	12.7721i	−0.124932	−	0.544109i
$552$	−31.0253	−	15.6208i	−1.32053	−	0.664865i
$553$	−8.19529	+	6.87666i	−0.348499	+	0.292425i
$554$	−13.8390	+	4.12559i	−0.587963	+	0.175279i
$555$	3.24686	−	15.9239i	0.137822	−	0.675934i
$556$	−10.7566	+	8.46464i	−0.456183	+	0.358981i
$557$	−31.7469	−	14.8038i	−1.34516	−	0.627259i	−0.389309	−	0.921107i	$-0.627286\pi$
$557$	−31.7469	−	14.8038i	−1.34516	−	0.627259i	−0.955852	+	0.293848i	$0.905064\pi$
$558$	−19.9434	+	22.5823i	−0.844270	+	0.955985i
$559$	3.16517	−	1.82741i	0.133872	−	0.0772912i
$560$	−16.4014	+	30.0823i	−0.693087	+	1.27121i
$561$	3.77058	−	0.228998i	0.159194	−	0.00966831i
$562$	1.07173	+	2.70688i	0.0452082	+	0.114183i
$563$	−1.57023	−	5.86016i	−0.0661771	−	0.246976i	0.924911	−	0.380183i	$-0.124139\pi$
$563$	−1.57023	−	5.86016i	−0.0661771	−	0.246976i	−0.991088	+	0.133207i	$0.957472\pi$
$564$	16.5157	−	0.483091i	0.695435	−	0.0203418i
$565$	−18.5842	−	13.0128i	−0.781843	−	0.547452i
$566$	−17.1166	−	34.1810i	−0.719463	−	1.43674i
$567$	−16.7777	+	34.2503i	−0.704596	+	1.43838i
$568$	10.7528	−	2.84102i	0.451180	−	0.119207i
$569$			20.6614i			0.866172i	0.901353	+	0.433086i	$0.142575\pi$
$569$			20.6614i			0.866172i	−0.901353	+	0.433086i	$0.857425\pi$
$570$	−6.30747	+	20.6397i	−0.264191	+	0.864504i
$571$	−9.47287	−	9.47287i	−0.396427	−	0.396427i	0.480544	−	0.876971i	$-0.340439\pi$
$571$	−9.47287	−	9.47287i	−0.396427	−	0.396427i	−0.876971	+	0.480544i	$0.840439\pi$
$572$	13.3623	−	5.72708i	0.558705	−	0.239461i
$573$	−3.19250	−	1.25914i	−0.133369	−	0.0526013i
$574$	58.8992	+	19.5932i	2.45840	+	0.817803i
$575$	6.38346	−	1.12558i	0.266208	−	0.0469397i
$576$	−20.0250	−	13.2287i	−0.834376	−	0.551196i
$577$	−8.92907	+	15.4656i	−0.371722	+	0.643841i	−0.989831	−	0.142251i	$-0.954566\pi$
$577$	−8.92907	+	15.4656i	−0.371722	+	0.643841i	0.618109	+	0.786093i	$0.287899\pi$
$578$	−21.9861	+	8.70492i	−0.914503	+	0.362077i
$579$	−24.2402	−	21.4644i	−1.00739	−	0.892032i
$580$	10.1698	−	6.65495i	0.422279	−	0.276332i
$581$	−49.7997	−	13.3438i	−2.06604	−	0.553593i
$582$	17.6199	+	14.7454i	0.730370	+	0.611216i
$583$	47.2457	−	17.1960i	1.95672	−	0.712187i
$584$	−9.93211	+	36.5562i	−0.410994	+	1.51271i
$585$	2.41152	−	10.4048i	0.0997039	−	0.430184i
$586$	−5.72792	+	1.70757i	−0.236618	+	0.0705389i
$587$	−1.00090	+	11.4403i	−0.0413115	+	0.472193i	0.947157	+	0.320769i	$0.103941\pi$
$587$	−1.00090	+	11.4403i	−0.0413115	+	0.472193i	−0.988469	+	0.151424i	$0.951614\pi$
$588$	11.9342	−	36.0337i	0.492156	−	1.48601i
$589$	11.6297	−	28.6858i	0.479195	−	1.18198i
$590$	−5.46051	+	36.9785i	−0.224806	+	1.52238i
$591$	−10.8430	−	1.24011i	−0.446022	−	0.0510113i
$592$	−18.3588	−	2.77652i	−0.754543	−	0.114114i
$593$	−13.8241	−	2.43756i	−0.567688	−	0.100099i	−0.117565	−	0.993065i	$-0.537509\pi$
$593$	−13.8241	−	2.43756i	−0.567688	−	0.100099i	−0.450123	+	0.892966i	$0.648620\pi$
$594$	−20.3033	−	22.5283i	−0.833056	−	0.924346i
$595$	−1.91303	+	4.10251i	−0.0784267	+	0.168187i
$596$	−0.692987	+	22.0510i	−0.0283859	+	0.903244i
$597$	7.43450	+	13.7066i	0.304274	+	0.560975i
$598$	−17.6301	−	1.04743i	−0.720950	−	0.0428324i
$599$	26.2329	−	31.2632i	1.07185	−	1.27738i	0.112959	−	0.993600i	$-0.463967\pi$
$599$	26.2329	−	31.2632i	1.07185	−	1.27738i	0.958889	−	0.283780i	$-0.0915885\pi$
$600$	4.47124	−	0.255887i	0.182537	−	0.0104465i
$601$	13.3577	−	23.1361i	0.544870	−	0.943743i	−0.453745	−	0.891132i	$-0.649912\pi$
$601$	13.3577	−	23.1361i	0.544870	−	0.943743i	0.998615	−	0.0526112i	$-0.0167544\pi$
$602$	10.3820	+	6.84566i	0.423138	+	0.279008i
$603$	27.9301	−	35.6859i	1.13740	−	1.45324i
$604$	−9.00783	+	17.8325i	−0.366523	+	0.725592i
$605$	−5.15320	−	11.0511i	−0.209507	−	0.449290i
$606$	3.05454	−	11.4601i	0.124082	−	0.465533i
$607$			20.8745i			0.847272i	0.905833	+	0.423636i	$0.139246\pi$
$607$			20.8745i			0.847272i	−0.905833	+	0.423636i	$0.860754\pi$
$608$	23.9181	+	5.99385i	0.970006	+	0.243083i
$609$	−16.0127	+	15.1825i	−0.648869	+	0.615226i
$610$	2.20312	−	1.35537i	0.0892019	−	0.0548773i
$611$	7.61378	−	3.55037i	0.308021	−	0.143632i
$612$	−2.75011	−	1.57813i	−0.111167	−	0.0637922i
$613$	−3.79994	+	5.42688i	−0.153478	+	0.219190i	−0.888527	−	0.458825i	$-0.848270\pi$
$613$	−3.79994	+	5.42688i	−0.153478	+	0.219190i	0.735048	+	0.678015i	$0.237159\pi$
$614$	7.20578	−	10.9281i	0.290802	−	0.441024i
$615$	8.45025	+	35.2643i	0.340747	+	1.42200i
$616$	37.7820	+	31.9283i	1.52228	+	1.28643i
$617$	29.0218	+	24.3522i	1.16838	+	0.980383i	0.999986	−	0.00533726i	$-0.00169891\pi$
$617$	29.0218	+	24.3522i	1.16838	+	0.980383i	0.168390	+	0.985721i	$0.446143\pi$
$618$	−12.3226	−	14.6463i	−0.495687	−	0.589160i
$619$	9.59912	−	35.8244i	0.385821	−	1.43991i	−0.451047	−	0.892500i	$-0.648949\pi$
$619$	9.59912	−	35.8244i	0.385821	−	1.43991i	0.836868	−	0.547405i	$-0.184384\pi$
$620$	28.6939	+	0.901751i	1.15237	+	0.0362152i
$621$	9.80024	+	35.5156i	0.393270	+	1.42519i
$622$	18.3306	−	0.512017i	0.734989	−	0.0205300i
$623$	−2.94082	+	16.6782i	−0.117822	+	0.668199i
$624$	−12.0126	−	2.14509i	−0.480890	−	0.0858723i
$625$	15.0094	−	12.5944i	0.600376	−	0.503775i
$626$	37.4082	+	5.52397i	1.49513	+	0.220782i
$627$	27.3584	+	14.9120i	1.09259	+	0.595526i
$628$	24.2208	−	12.9871i	0.966514	−	0.518240i
$629$	−2.44371	−	0.213797i	−0.0974370	−	0.00852463i
$630$	35.3297	−	8.51513i	1.40757	−	0.339251i
$631$	−11.7568	−	2.07304i	−0.468032	−	0.0825266i	−0.0653415	−	0.997863i	$-0.520814\pi$
$631$	−11.7568	−	2.07304i	−0.468032	−	0.0825266i	−0.402690	+	0.915336i	$0.631925\pi$
$632$	−1.87217	+	6.89072i	−0.0744709	+	0.274098i
$633$	14.8066	−	29.6656i	0.588508	−	1.17910i
$634$	−19.0489	+	2.20403i	−0.756529	+	0.0875333i
$635$	−5.14828	+	19.2136i	−0.204303	+	0.762470i
$636$	−41.0656	−	9.72608i	−1.62836	−	0.385664i
$637$	−1.68209	−	19.2264i	−0.0666468	−	0.761776i
$638$	−6.45934	−	16.3144i	−0.255728	−	0.645895i
$639$	−9.88786	−	6.43330i	−0.391158	−	0.254497i
$640$	2.46980	+	22.7351i	0.0976274	+	0.898684i
$641$	−2.08763	−	11.8395i	−0.0824564	−	0.467633i	−0.997877	−	0.0651338i	$-0.979253\pi$
$641$	−2.08763	−	11.8395i	−0.0824564	−	0.467633i	0.915420	−	0.402500i	$-0.131859\pi$
$642$	−21.4781	+	10.0498i	−0.847671	+	0.396636i
$643$	−4.87098	+	2.27137i	−0.192093	+	0.0895742i	−0.516285	−	0.856417i	$-0.672685\pi$
$643$	−4.87098	+	2.27137i	−0.192093	+	0.0895742i	0.324192	+	0.945991i	$0.394908\pi$
$644$	−23.6733	−	55.2341i	−0.932861	−	2.17653i
$645$	−0.193284	+	7.26238i	−0.00761055	+	0.285956i
$646$	3.20340	+	0.591896i	0.126036	+	0.0232878i
$647$	−28.3349			−1.11396			−0.556981	−	0.830525i	$-0.688040\pi$
$647$	−28.3349			−1.11396			−0.556981	+	0.830525i	$0.688040\pi$
$648$	3.85128	+	25.1628i	0.151293	+	0.988489i
$649$	50.7110	+	18.4573i	1.99058	+	0.724512i
$650$	2.03607	−	1.01959i	0.0798613	−	0.0399915i
$651$	−51.5527	+	7.68204i	−2.02051	+	0.301083i
$652$	−20.1068	+	22.4882i	−0.787444	+	0.880707i
$653$	−8.99636	+	2.41057i	−0.352055	+	0.0943328i	−0.430512	−	0.902585i	$-0.641667\pi$
$653$	−8.99636	+	2.41057i	−0.352055	+	0.0943328i	0.0784577	+	0.996917i	$0.475000\pi$
$654$	−0.206514	+	0.444398i	−0.00807534	+	0.0173773i
$655$	13.0843	+	10.9790i	0.511245	+	0.428986i
$656$	39.7448	−	11.6975i	1.55177	−	0.456711i
$657$	35.8156	−	18.2104i	1.39730	−	0.710454i
$658$	22.4015	+	17.7553i	0.873303	+	0.692172i
$659$	0.669374	−	1.43548i	0.0260751	−	0.0559183i	−0.892839	−	0.450376i	$-0.851290\pi$
$659$	0.669374	−	1.43548i	0.0260751	−	0.0559183i	0.918914	+	0.394458i	$0.129068\pi$
$660$	−4.18386	+	28.5935i	−0.162856	+	1.11300i
$661$	−7.41311	−	10.5870i	−0.288336	−	0.411787i	0.648686	−	0.761056i	$-0.275319\pi$
$661$	−7.41311	−	10.5870i	−0.288336	−	0.411787i	−0.937022	+	0.349269i	$0.886430\pi$
$662$	10.5292	+	35.3194i	0.409228	+	1.37273i
$663$	−1.60170	−	0.183186i	−0.0622049	−	0.00711434i
$664$	−32.3770	+	11.6564i	−1.25647	+	0.452357i
$665$	−31.3379	+	20.2978i	−1.21523	+	0.787116i
$666$	10.8844	+	16.4128i	0.421762	+	0.635983i
$667$	−1.85785	+	21.2353i	−0.0719360	+	0.822233i
$668$	7.00930	−	9.36952i	0.271198	−	0.362518i
$669$	−6.47683	+	31.7650i	−0.250409	+	1.22811i
$670$	−43.1638	+	1.20567i	−1.66756	+	0.0465790i
$671$	−1.27724	−	3.50919i	−0.0493074	−	0.135471i
$672$	−11.7753	−	39.8156i	−0.454244	−	1.53592i
$673$	2.39351	−	1.38190i	0.0922631	−	0.0532682i	−0.453159	−	0.891430i	$-0.649703\pi$
$673$	2.39351	−	1.38190i	0.0922631	−	0.0532682i	0.545422	+	0.838162i	$0.316370\pi$
$674$	−29.5005	−	33.2273i	−1.13632	−	1.27987i
$675$	−3.38382	−	3.33382i	−0.130243	−	0.128319i
$676$	19.2726	−	4.52035i	0.741255	−	0.173859i
$677$	−30.9665	+	8.29745i	−1.19014	+	0.318897i	−0.798941	−	0.601410i	$-0.794606\pi$
$677$	−30.9665	+	8.29745i	−1.19014	+	0.318897i	−0.391198	+	0.920306i	$0.627939\pi$
$678$	27.0686	−	4.80969i	1.03956	−	0.184715i
$679$	6.90226	+	39.1447i	0.264884	+	1.50223i
$680$	0.514253	+	2.97721i	0.0197207	+	0.114171i
$681$	−2.36861	−	5.45381i	−0.0907653	−	0.208990i
$682$	9.60513	−	40.3181i	0.367799	−	1.54386i
$683$	−6.31870	−	6.31870i	−0.241778	−	0.241778i	0.575807	−	0.817585i	$-0.304688\pi$
$683$	−6.31870	−	6.31870i	−0.241778	−	0.241778i	−0.817585	+	0.575807i	$0.804688\pi$
$684$	−12.3115	−	23.0744i	−0.470741	−	0.882272i
$685$	−21.4136	+	21.4136i	−0.818172	+	0.818172i
$686$	20.2015	−	12.4280i	0.771297	−	0.474505i
$687$	37.1621	−	16.1396i	1.41782	−	0.615765i
$688$	8.29780	−	0.202789i	0.316351	−	0.00773126i
$689$	−21.1312	+	3.72600i	−0.805034	+	0.141949i
$690$	20.0984	−	28.7841i	0.765132	−	1.09579i
$691$	0.814388	+	3.03934i	0.0309808	+	0.115622i	0.979685	−	0.200544i	$-0.0642710\pi$
$691$	0.814388	+	3.03934i	0.0309808	+	0.115622i	−0.948704	+	0.316166i	$0.897604\pi$
$692$	−1.33862	−	0.829981i	−0.0508868	−	0.0315512i
$693$	−1.78616	−	52.4364i	−0.0678507	−	1.99189i
$694$	−0.882205	+	14.8492i	−0.0334880	+	0.563666i
$695$	−6.91692	−	11.9805i	−0.262374	−	0.454445i
$696$	−2.99285	+	14.4208i	−0.113444	+	0.546619i
$697$	5.14345	−	1.87206i	0.194822	−	0.0709095i
$698$	7.58274	−	8.01852i	0.287011	−	0.303506i
$699$	6.02684	+	1.22886i	0.227956	+	0.0464799i
$700$	6.20403	+	4.64121i	0.234490	+	0.175421i
$701$	−24.3201	−	2.12773i	−0.918556	−	0.0803632i	−0.381937	−	0.924188i	$-0.624743\pi$
$701$	−24.3201	−	2.12773i	−0.918556	−	0.0803632i	−0.536619	+	0.843825i	$0.680299\pi$
$702$	6.86373	+	10.9730i	0.259055	+	0.414150i
$703$	−16.1447	−	12.1962i	−0.608908	−	0.459988i
$704$	32.8697	+	3.10713i	1.23882	+	0.117104i
$705$	−1.89749	+	16.5909i	−0.0714636	+	0.624849i
$706$	28.0882	+	15.1872i	1.05711	+	0.571580i
$707$	16.8076	−	11.7688i	0.632113	−	0.442610i
$708$	−27.0551	−	36.3296i	−1.01679	−	1.36535i
$709$	14.9562	+	6.97418i	0.561691	+	0.261921i	0.682661	−	0.730735i	$-0.260823\pi$
$709$	14.9562	+	6.97418i	0.561691	+	0.261921i	−0.120970	+	0.992656i	$0.538600\pi$
$710$	1.29195	+	11.1660i	0.0484860	+	0.419053i
$711$	6.75113	−	3.43259i	0.253187	−	0.128732i
$712$	4.74133	+	10.2612i	0.177689	+	0.384554i
$713$	−32.3649	+	38.5710i	−1.21208	+	1.44449i
$714$	−1.88291	−	5.15214i	−0.0704663	−	0.192814i
$715$	3.80283	+	14.1924i	0.142218	+	0.530764i
$716$	−1.84939	+	2.06843i	−0.0691150	+	0.0773009i
$717$	−1.26013	−	8.45649i	−0.0470604	−	0.315813i
$718$	−16.4426	−	5.46972i	−0.613632	−	0.204128i
$719$	3.87726	−	10.6527i	0.144597	−	0.397278i	−0.846159	−	0.532930i	$-0.821091\pi$
$719$	3.87726	−	10.6527i	0.144597	−	0.397278i	0.990756	+	0.135652i	$0.0433130\pi$
$720$	16.1198	−	18.1249i	0.600749	−	0.675473i
$721$		−	33.1134i		−	1.23321i
$722$	19.7989	+	18.1660i	0.736840	+	0.676067i
$723$	−11.0843	−	0.295001i	−0.412228	−	0.0109712i
$724$	4.24379	−	10.6102i	0.157719	−	0.394325i
$725$	−1.16151	−	2.49086i	−0.0431372	−	0.0925081i
$726$	13.8918	+	5.03549i	0.515573	+	0.186885i
$727$	−0.598679	+	0.105563i	−0.0222038	+	0.00391512i	−0.184739	−	0.982788i	$-0.559144\pi$
$727$	−0.598679	+	0.105563i	−0.0222038	+	0.00391512i	0.162535	+	0.986703i	$0.448033\pi$
$728$	−13.5132	−	16.2191i	−0.500832	−	0.601118i
$729$	17.0455	−	20.9392i	0.631315	−	0.775527i
$730$	−35.1368	−	15.2051i	−1.30047	−	0.562765i
$731$	1.09241	−	0.0955737i	0.0404043	−	0.00353492i
$732$	−0.722408	+	3.05016i	−0.0267010	+	0.112737i
$733$	−28.0416	−	7.51373i	−1.03574	−	0.277526i	−0.299393	−	0.954130i	$-0.596784\pi$
$733$	−28.0416	−	7.51373i	−1.03574	−	0.277526i	−0.736347	+	0.676604i	$0.763451\pi$
$734$	−35.0982	−	27.8185i	−1.29550	−	1.02680i
$735$	34.3256	+	17.1325i	1.26612	+	0.631941i
$736$	−34.0148	−	21.2548i	−1.25380	−	0.783463i
$737$	−10.8254	+	61.3937i	−0.398757	+	2.26146i
$738$	−37.4885	−	22.9272i	−1.37997	−	0.843960i
$739$	−0.854239	+	9.76400i	−0.0314237	+	0.359174i	0.964162	+	0.265315i	$0.0854760\pi$
$739$	−0.854239	+	9.76400i	−0.0314237	+	0.359174i	−0.995585	+	0.0938594i	$0.970080\pi$
$740$	5.42390	−	17.9648i	0.199386	−	0.660399i
$741$	−10.3933	−	8.29480i	−0.381807	−	0.304717i
$742$	−43.5301	−	58.6133i	−1.59804	−	2.15176i
$743$	−1.47351	−	1.75606i	−0.0540579	−	0.0644236i	0.738338	−	0.674431i	$-0.235611\pi$
$743$	−1.47351	−	1.75606i	−0.0540579	−	0.0644236i	−0.792396	+	0.610007i	$0.791167\pi$
$744$	−25.3286	+	23.8480i	−0.928591	+	0.874309i
$745$	−21.9586	−	3.87188i	−0.804499	−	0.141855i
$746$	−2.59933	+	2.74871i	−0.0951682	+	0.100637i
$747$	32.2118	+	17.1627i	1.17857	+	0.627952i
$748$	4.35976	+	0.137012i	0.159409	+	0.00500967i
$749$	−39.6260	−	10.6178i	−1.44790	−	0.387964i
$750$	−2.51373	+	29.1745i	−0.0917883	+	1.06530i
$751$	−5.72929	+	6.82790i	−0.209065	+	0.249154i	−0.860379	−	0.509654i	$-0.829773\pi$
$751$	−5.72929	+	6.82790i	−0.209065	+	0.249154i	0.651315	+	0.758808i	$0.274218\pi$
$752$	19.0412	+	1.19798i	0.694360	+	0.0436858i
$753$	−16.7594	+	4.01600i	−0.610748	+	0.146351i
$754$	1.50575	+	7.33546i	0.0548363	+	0.267142i
$755$	−16.5400	−	11.5814i	−0.601952	−	0.421491i
$756$	−22.9274	+	37.6001i	−0.833862	+	1.36750i
$757$	2.32270	+	4.98105i	0.0844201	+	0.181039i	0.943986	−	0.329985i	$-0.107044\pi$
$757$	2.32270	+	4.98105i	0.0844201	+	0.181039i	−0.859566	+	0.511025i	$0.829266\pi$
$758$	−36.5617	−	8.71024i	−1.32798	−	0.316370i
$759$	−34.8728	−	36.7798i	−1.26580	−	1.33502i
$760$	−9.44368	+	23.0621i	−0.342558	+	0.836551i
$761$	−5.70626			−0.206852			−0.103426	−	0.994637i	$-0.532980\pi$
$761$	−5.70626			−0.206852			−0.103426	+	0.994637i	$0.532980\pi$
$762$	−12.0798	−	20.8594i	−0.437606	−	0.755656i
$763$	−0.768344	+	0.358284i	−0.0278159	+	0.0129708i
$764$	−3.53709	−	1.78671i	−0.127967	−	0.0646410i
$765$	1.97509	−	2.52355i	0.0714097	−	0.0912391i
$766$	−0.369468	−	1.79991i	−0.0133494	−	0.0650334i
$767$	−19.9454	−	11.5155i	−0.720187	−	0.415800i
$768$	−21.6205	−	17.3365i	−0.780162	−	0.625578i
$769$	24.0282	+	20.1621i	0.866481	+	0.727064i	0.963354	−	0.268233i	$-0.0864398\pi$
$769$	24.0282	+	20.1621i	0.866481	+	0.727064i	−0.0968734	+	0.995297i	$0.530884\pi$
$770$	−37.3854	+	33.1923i	−1.34728	+	1.19617i
$771$	−0.818107	+	0.443742i	−0.0294634	+	0.0159810i
$772$	−25.5928	−	27.2536i	−0.921105	−	0.980877i
$773$	16.5811	+	7.73191i	0.596382	+	0.278098i	0.697280	−	0.716799i	$-0.254394\pi$
$773$	16.5811	+	7.73191i	0.596382	+	0.278098i	−0.100897	+	0.994897i	$0.532171\pi$
$774$	−6.06579	−	6.38064i	−0.218030	−	0.229348i
$775$	1.12729	−	6.39319i	0.0404935	−	0.229650i
$776$	18.6941	+	18.8251i	0.671078	+	0.675780i
$777$	−3.87141	+	33.8501i	−0.138886	+	1.21436i
$778$	10.2364	+	13.7833i	0.366993	+	0.494157i
$779$	44.1499	+	9.43956i	1.58184	+	0.338207i
$780$	3.87744	−	11.7075i	0.138835	−	0.419195i
$781$	16.1664	+	1.41438i	0.578479	+	0.0506104i
$782$	−4.66129	−	2.52035i	−0.166687	−	0.0901275i
$783$	13.4701	−	7.91122i	0.481383	−	0.282724i
$784$	17.5476	−	40.1649i	0.626702	−	1.43446i
$785$	9.50000	+	26.1010i	0.339070	+	0.931586i
$786$	−20.6170	+	1.83112i	−0.735385	+	0.0653139i
$787$	−11.7075	+	43.6931i	−0.417328	+	1.55749i	0.362797	+	0.931868i	$0.381822\pi$
$787$	−11.7075	+	43.6931i	−0.417328	+	1.55749i	−0.780126	+	0.625623i	$0.784845\pi$
$788$	−12.3357	−	2.57707i	−0.439443	−	0.0918045i
$789$	−20.9958	+	23.7110i	−0.747471	+	0.844134i
$790$	−6.62317	−	2.86610i	−0.235642	−	0.101971i
$791$	41.1904	+	23.7813i	1.46456	+	0.845564i
$792$	−20.9532	−	28.0588i	−0.744539	−	0.997026i
$793$	0.276750	+	1.56953i	0.00982768	+	0.0557355i
$794$	−2.48194	+	1.24286i	−0.0880807	+	0.0441075i
$795$	15.6490	−	39.6775i	0.555013	−	1.40721i
$796$	7.09305	+	16.5493i	0.251406	+	0.586576i
$797$	−4.73581	+	4.73581i	−0.167751	+	0.167751i	−0.785990	−	0.618239i	$-0.787846\pi$
$797$	−4.73581	+	4.73581i	−0.167751	+	0.167751i	0.618239	+	0.785990i	$0.287846\pi$
$798$	9.40176	−	44.2582i	0.332819	−	1.56672i
$799$	2.52058			0.0891718
$800$	5.16824	+	0.180483i	0.182725	+	0.00638102i
$801$	4.69405	−	11.0322i	0.165856	−	0.389804i
$802$	−49.0421	−	16.3142i	−1.73174	−	0.576073i
$803$	−31.7037	+	45.2776i	−1.11880	+	1.59781i
$804$	35.9031	−	38.0667i	1.26620	−	1.34251i
$805$	58.6653	−	15.7193i	2.06768	−	0.554033i
$806$	−7.02482	+	16.2334i	−0.247439	+	0.571797i
$807$	2.20317	+	36.2764i	0.0775553	+	1.27699i
$808$	4.72884	−	12.8526i	0.166360	−	0.452152i
$809$	−9.41041	−	16.2993i	−0.330852	−	0.573053i	0.651827	−	0.758368i	$-0.274003\pi$
$809$	−9.41041	−	16.2993i	−0.330852	−	0.573053i	−0.982679	+	0.185315i	$0.940670\pi$
$810$	−25.7265	+	0.225348i	−0.903937	+	0.00791792i
$811$	−12.1055	+	25.9603i	−0.425080	+	0.911588i	0.570815	+	0.821079i	$0.306627\pi$
$811$	−12.1055	+	25.9603i	−0.425080	+	0.911588i	−0.995896	+	0.0905093i	$0.971151\pi$
$812$	−20.0235	+	15.7569i	−0.702687	+	0.552960i
$813$	49.4817	+	10.0892i	1.73540	+	0.353845i
$814$	−23.8318	−	12.8858i	−0.835306	−	0.451648i
$815$	−19.5974	−	23.3553i	−0.686468	−	0.818100i
$816$	−2.99455	−	2.10653i	−0.104830	−	0.0737431i
$817$	8.05426	+	4.11599i	0.281783	+	0.144000i
$818$	−4.16306	+	28.1922i	−0.145558	+	0.985716i
$819$	−3.13526	+	22.1708i	−0.109555	+	0.774709i
$820$	5.97222	+	41.4444i	0.208559	+	1.44730i
$821$	−5.66067	−	8.08427i	−0.197559	−	0.282143i	0.708134	−	0.706078i	$-0.249537\pi$
$821$	−5.66067	−	8.08427i	−0.197559	−	0.282143i	−0.905693	+	0.423935i	$0.860648\pi$
$822$	−0.0483316	−	36.6978i	−0.00168576	−	1.27998i
$823$	18.9590	+	52.0895i	0.660870	+	1.81573i	0.572938	+	0.819599i	$0.305804\pi$
$823$	18.9590	+	52.0895i	0.660870	+	1.81573i	0.0879324	+	0.996126i	$0.471974\pi$
$824$	−12.6137	−	18.1487i	−0.439418	−	0.632240i
$825$	6.26487	+	1.85866i	0.218115	+	0.0647101i
$826$	4.64752	−	78.2265i	0.161708	−	2.72185i
$827$	0.596252	+	6.81519i	0.0207337	+	0.236987i	0.999489	+	0.0319566i	$0.0101738\pi$
$827$	0.596252	+	6.81519i	0.0207337	+	0.236987i	−0.978756	+	0.205031i	$0.934271\pi$
$828$	7.49777	+	41.8766i	0.260565	+	1.45531i
$829$	−5.52291	+	1.47986i	−0.191818	+	0.0513976i	−0.353449	−	0.935454i	$-0.614991\pi$
$829$	−5.52291	+	1.47986i	−0.191818	+	0.0513976i	0.161631	+	0.986851i	$0.448325\pi$
$830$	−6.99320	−	34.0682i	−0.242738	−	1.18253i
$831$	14.2128	+	10.5263i	0.493037	+	0.365155i
$832$	−13.5845	−	3.74181i	−0.470957	−	0.129724i
$833$	1.98053	−	5.44145i	0.0686212	−	0.188535i
$834$	16.1985	+	4.31752i	0.560909	+	0.149504i
$835$	8.36229	+	8.36229i	0.289389	+	0.289389i
$836$	29.8737	+	20.0505i	1.03320	+	0.693461i
$837$	36.7816	+	2.94232i	1.27136	+	0.101702i
$838$	−6.28061	+	26.3632i	−0.216960	+	0.910702i
$839$	0.518396	−	1.42428i	0.0178970	−	0.0491717i	−0.930422	−	0.366489i	$-0.880560\pi$
$839$	0.518396	−	1.42428i	0.0178970	−	0.0491717i	0.948319	+	0.317317i	$0.102782\pi$
$840$	41.5265	−	6.03988i	1.43280	−	0.208396i
$841$	−19.6585	+	3.46633i	−0.677880	+	0.119529i
$842$	26.3925	+	17.4026i	0.909545	+	0.599734i
$843$	1.86434	−	3.03940i	0.0642112	−	0.104682i
$844$	20.1743	−	32.5377i	0.694427	−	1.12000i
$845$	1.74371	+	19.9307i	0.0599856	+	0.685638i
$846$	−12.6114	−	15.8258i	−0.433588	−	0.544101i
$847$	12.7816	+	22.1383i	0.439180	+	0.760682i
$848$	−46.1850	−	15.5430i	−1.58600	−	0.533749i
$849$	−20.9083	+	41.8906i	−0.717570	+	1.43768i
$850$	0.682947	−	0.0190763i	0.0234249	−	0.000654313i
$851$	18.8781	+	26.9608i	0.647135	+	0.924204i
$852$	−10.6861	−	8.44684i	−0.366101	−	0.289384i
$853$	30.4494	+	2.66398i	1.04257	+	0.0912130i	0.595555	−	0.803314i	$-0.296932\pi$
$853$	30.4494	+	2.66398i	1.04257	+	0.0912130i	0.447014	+	0.894527i	$0.352488\pi$
$854$	−4.35352	+	3.23321i	−0.148975	+	0.110638i
$855$	24.8569	−	8.98944i	0.850088	−	0.307432i
$856$	−25.7627	+	9.27511i	−0.880549	+	0.317017i
$857$	0.932375	+	1.11116i	0.0318493	+	0.0379566i	0.781734	−	0.623612i	$-0.214335\pi$
$857$	0.932375	+	1.11116i	0.0318493	+	0.0379566i	−0.749885	+	0.661569i	$0.769891\pi$
$858$	−15.4315	−	8.88228i	−0.526822	−	0.303236i
$859$	−7.39324	+	5.17680i	−0.252254	+	0.176630i	−0.692864	−	0.721069i	$-0.743651\pi$
$859$	−7.39324	+	5.17680i	−0.252254	+	0.176630i	0.440610	+	0.897699i	$0.354762\pi$
$860$	−0.993275	+	8.32984i	−0.0338704	+	0.284045i
$861$	−24.0916	−	72.1048i	−0.821040	−	2.45733i
$862$	−40.2712	−	31.9186i	−1.37164	−	1.08715i
$863$	21.7423	+	37.6587i	0.740115	+	1.28192i	0.952443	+	0.304718i	$0.0985623\pi$
$863$	21.7423	+	37.6587i	0.740115	+	1.28192i	−0.212328	+	0.977199i	$0.568104\pi$
$864$	1.75674	+	29.3413i	0.0597656	+	0.998212i
$865$	1.02322	−	1.21943i	0.0347907	−	0.0414619i
$866$	4.45601	+	11.2546i	0.151421	+	0.382447i
$867$	24.6870	+	15.1427i	0.838413	+	0.514274i
$868$	−60.0914	+	3.35961i	−2.03963	+	0.114033i
$869$	−5.97605	+	8.53468i	−0.202723	+	0.289519i
$870$	−13.9943	−	5.07263i	−0.474450	−	0.171978i
$871$	9.09954	−	25.0008i	0.308326	−	0.847119i
$872$	−0.284633	+	0.489048i	−0.00963888	+	0.0165612i
$873$	1.49677	−	28.0997i	0.0506581	−	0.951031i
$874$	−21.5439	−	38.0300i	−0.728733	−	1.28638i
$875$	−35.8216	+	35.8216i	−1.21099	+	1.21099i
$876$	43.1145	−	17.1360i	1.45670	−	0.578970i
$877$	−10.7458	−	23.0444i	−0.362859	−	0.778153i	−0.999973	−	0.00738360i	$-0.997650\pi$
$877$	−10.7458	−	23.0444i	−0.362859	−	0.778153i	0.637114	−	0.770770i	$-0.280128\pi$
$878$	−16.7115	−	5.55918i	−0.563986	−	0.187613i
$879$	5.88263	+	4.35682i	0.198416	+	0.146952i
$880$	−7.84637	+	32.4329i	−0.264501	+	1.09331i
$881$	−20.7044	−	11.9537i	−0.697548	−	0.402729i	0.108886	−	0.994054i	$-0.465272\pi$
$881$	−20.7044	−	11.9537i	−0.697548	−	0.402729i	−0.806433	+	0.591325i	$0.798605\pi$
$882$	−44.0740	+	14.7905i	−1.48405	+	0.498024i
$883$	33.2551	−	2.90945i	1.11912	−	0.0979106i	0.487454	−	0.873148i	$-0.337926\pi$
$883$	33.2551	−	2.90945i	1.11912	−	0.0979106i	0.631669	+	0.775238i	$0.282370\pi$
$884$	−1.82220	−	0.380679i	−0.0612873	−	0.0128036i
$885$	40.2419	−	21.8273i	1.35272	−	0.733715i
$886$	0.420861	−	0.0486952i	0.0141391	−	0.00163595i
$887$	−19.0912	−	52.4526i	−0.641020	−	1.76119i	−0.648499	−	0.761216i	$-0.724603\pi$
$887$	−19.0912	−	52.4526i	−0.641020	−	1.76119i	0.00747905	−	0.999972i	$-0.497619\pi$
$888$	10.7725	+	20.0272i	0.361500	+	0.672068i
$889$	7.24139	−	41.0680i	0.242868	−	1.37738i
$890$	−10.9481	+	3.26377i	−0.366982	+	0.109402i
$891$	−7.14971	+	36.4487i	−0.239524	+	1.22108i
$892$	−10.8196	+	35.8361i	−0.362266	+	1.19988i
$893$	17.6183	+	11.0384i	0.589574	+	0.369388i
$894$	22.1132	−	15.5273i	0.739576	−	0.519310i
$895$	−1.80254	−	2.14818i	−0.0602522	−	0.0718058i
$896$	−9.31224	−	47.0305i	−0.311100	−	1.57118i
$897$	11.9309	+	18.0425i	0.398363	+	0.602421i
$898$	5.46879	−	0.152756i	0.182496	−	0.00509755i
$899$	19.3487	+	9.02243i	0.645314	+	0.300915i
$900$	−3.53680	−	4.19252i	−0.117893	−	0.139751i
$901$	−6.21860	−	1.66627i	−0.207171	−	0.0555114i
$902$	60.3458	+	3.58521i	2.00930	+	0.119374i
$903$	−0.923300	−	15.2026i	−0.0307255	−	0.505912i
$904$	31.6343	−	2.65640i	1.05214	−	0.0883504i
$905$	10.0021	+	5.77469i	0.332479	+	0.191957i
$906$	24.0911	−	4.28064i	0.800374	−	0.142215i
$907$	−7.16918	−	5.01991i	−0.238049	−	0.166683i	0.448465	−	0.893800i	$-0.351971\pi$
$907$	−7.16918	−	5.01991i	−0.238049	−	0.166683i	−0.686514	+	0.727117i	$0.740860\pi$
$908$	−2.14443	−	6.52231i	−0.0711653	−	0.216451i
$909$	−13.4726	+	5.42987i	−0.446858	+	0.180097i
$910$	18.1725	−	11.1798i	0.602411	−	0.370606i
$911$	−41.2512			−1.36671			−0.683357	−	0.730085i	$-0.739481\pi$
$911$	−41.2512			−1.36671			−0.683357	+	0.730085i	$0.739481\pi$
$912$	−11.7061	−	27.8382i	−0.387627	−	0.921816i
$913$	−50.2106			−1.66173
$914$	8.90788	−	5.48017i	0.294647	−	0.181268i
$915$	−2.94706	−	1.16233i	−0.0974267	−	0.0384256i
$916$	44.4428	−	14.6120i	1.46843	−	0.482796i
$917$	−29.3323	−	20.5387i	−0.968638	−	0.678248i
$918$	0.475037	+	3.85418i	0.0156785	+	0.127207i
$919$	23.7996	+	13.7407i	0.785075	+	0.453263i	0.838226	−	0.545323i	$-0.183593\pi$
$919$	23.7996	+	13.7407i	0.785075	+	0.453263i	−0.0531510	+	0.998586i	$0.516926\pi$
$920$	26.1653	−	30.9624i	0.862643	−	1.02080i
$921$	−16.0024	+	0.971872i	−0.527297	+	0.0320243i
$922$	12.1771	+	0.723453i	0.401030	+	0.0238257i
$923$	−6.68973	−	1.79251i	−0.220195	−	0.0590011i
$924$	3.51334	−	60.4815i	0.115580	−	1.98969i
$925$	−3.84595	−	1.79339i	−0.126454	−	0.0589665i
$926$	57.8683	−	1.61640i	1.90167	−	0.0531182i
$927$	−5.29292	+	22.8369i	−0.173842	+	0.750063i
$928$	−4.97224	+	16.2634i	−0.163222	+	0.533873i
$929$	−22.9673	−	27.3714i	−0.753533	−	0.898026i	0.243888	−	0.969803i	$-0.421577\pi$
$929$	−22.9673	−	27.3714i	−0.753533	−	0.898026i	−0.997421	+	0.0717780i	$0.977133\pi$
$930$	−20.2049	−	28.7748i	−0.662545	−	0.943564i
$931$	37.6733	−	29.3611i	1.23469	−	0.962272i
$932$	6.79925	+	2.05282i	0.222717	+	0.0672423i
$933$	−13.9735	−	17.5826i	−0.457473	−	0.575629i
$934$	−50.7592	+	15.1320i	−1.66089	+	0.495133i
$935$	−0.765521	+	4.34148i	−0.0250352	+	0.141982i
$936$	6.72699	+	13.3456i	0.219879	+	0.436214i
$937$	−6.50796	−	17.8805i	−0.212606	−	0.584130i	0.786849	−	0.617146i	$-0.211711\pi$
$937$	−6.50796	−	17.8805i	−0.212606	−	0.584130i	−0.999455	+	0.0330157i	$0.989489\pi$
$938$	89.9264	−	10.4048i	2.93620	−	0.339729i
$939$	−22.0809	−	40.7095i	−0.720583	−	1.32851i
$940$	−3.94318	+	18.8749i	−0.128612	+	0.615632i
$941$	32.2254	−	2.81936i	1.05052	−	0.0919085i	0.451203	−	0.892421i	$-0.350995\pi$
$941$	32.2254	−	2.81936i	1.05052	−	0.0919085i	0.599316	+	0.800513i	$0.295439\pi$
$942$	−30.5246	−	14.1849i	−0.994545	−	0.462170i
$943$	−63.6008	−	36.7199i	−2.07113	−	1.19577i
$944$	−27.2511	−	44.6445i	−0.886948	−	1.45306i
$945$	−34.3078	−	28.3552i	−1.11603	−	0.922396i
$946$	11.4920	+	3.82288i	0.373637	+	0.124292i
$947$	13.9294	+	29.8717i	0.452644	+	0.970698i	0.991717	+	0.128439i	$0.0409968\pi$
$947$	13.9294	+	29.8717i	0.452644	+	0.970698i	−0.539073	+	0.842259i	$0.681225\pi$
$948$	8.12694	−	3.23007i	0.263951	−	0.104908i
$949$	16.6801	−	16.6801i	0.541460	−	0.541460i
$950$	4.85718	+	2.85751i	0.157588	+	0.0927098i
$951$	16.1592	+	17.0428i	0.523998	+	0.552652i
$952$	−1.61800	−	6.12388i	−0.0524396	−	0.198476i
$953$	−10.9621	+	30.1181i	−0.355097	+	0.975622i	0.625609	+	0.780137i	$0.284850\pi$
$953$	−10.9621	+	30.1181i	−0.355097	+	0.975622i	−0.980707	+	0.195485i	$0.937372\pi$
$954$	20.6520	+	47.3811i	0.668633	+	1.53402i
$955$	2.29719	−	3.28073i	0.0743354	−	0.106162i
$956$	−0.551097	−	9.85714i	−0.0178237	−	0.318803i
$957$	−11.2364	+	18.3186i	−0.363222	+	0.592155i
$958$	20.5455	+	51.8920i	0.663795	+	1.67656i
$959$	40.8092	−	48.6345i	1.31780	−	1.57049i
$960$	20.4590	−	19.1287i	0.660311	−	0.617377i
$961$	9.71383	+	16.8248i	0.313349	+	0.542737i
$962$	9.06130	+	7.18190i	0.292148	+	0.231554i
$963$	25.6312	+	13.6565i	0.825954	+	0.440075i
$964$	−12.7135	−	1.51599i	−0.409473	−	0.0488268i
$965$	30.9520	−	21.6728i	0.996380	−	0.697672i
$966$	−36.7156	+	63.7872i	−1.18131	+	2.05232i
$967$	−15.0203	−	17.9005i	−0.483021	−	0.575642i	0.468407	−	0.883513i	$-0.344828\pi$
$967$	−15.0203	−	17.9005i	−0.483021	−	0.575642i	−0.951428	+	0.307871i	$0.900384\pi$
$968$	15.4383	+	7.26472i	0.496206	+	0.233497i
$969$	−1.77442	−	3.57346i	−0.0570026	−	0.114796i
$970$	−21.5262	+	15.9868i	−0.691164	+	0.513304i
$971$	−51.5852	−	4.51312i	−1.65545	−	0.144833i	−0.779227	−	0.626741i	$-0.784388\pi$
$971$	−51.5852	−	4.51312i	−1.65545	−	0.144833i	−0.876222	+	0.481908i	$0.839944\pi$
$972$	21.8222	−	22.2664i	0.699946	−	0.714196i
$973$	16.6349	+	23.7571i	0.533290	+	0.761617i
$974$	−43.4296	+	1.21309i	−1.39157	+	0.0388700i
$975$	−2.49531	−	1.24545i	−0.0799139	−	0.0398863i
$976$	−1.15446	+	3.43041i	−0.0369534	+	0.109805i
$977$	−20.6805	−	35.8197i	−0.661629	−	1.14598i	−0.980187	−	0.198072i	$-0.936532\pi$
$977$	−20.6805	−	35.8197i	−0.661629	−	1.14598i	0.318558	−	0.947903i	$-0.396801\pi$
$978$	36.8096	+	3.17158i	1.17704	+	0.101416i
$979$	1.43750	+	16.4307i	0.0459426	+	0.525126i
$980$	37.6490	+	23.3434i	1.20265	+	0.745676i
$981$	0.587163	−	0.124280i	0.0187467	−	0.00396795i
$982$	−2.70332	−	1.78251i	−0.0862664	−	0.0568822i
$983$	−7.40050	+	1.30491i	−0.236039	+	0.0416201i	−0.290416	−	0.956900i	$-0.593794\pi$
$983$	−7.40050	+	1.30491i	−0.236039	+	0.0416201i	0.0543772	+	0.998520i	$0.482683\pi$
$984$	−40.6705	−	30.3420i	−1.29653	−	0.967266i
$985$	4.35615	−	11.9684i	0.138798	−	0.381346i
$986$	−0.520693	+	2.18564i	−0.0165822	+	0.0696049i
$987$	0.931408	−	34.9964i	0.0296471	−	1.11395i
$988$	−11.0697	−	10.6409i	−0.352173	−	0.338531i
$989$	−10.4038	−	10.4038i	−0.330820	−	0.330820i
$990$	31.0887	−	16.9156i	0.988063	−	0.537612i
$991$	12.0162	−	33.0142i	0.381706	−	1.04873i	−0.588931	−	0.808183i	$-0.700451\pi$
$991$	12.0162	−	33.0142i	0.381706	−	1.04873i	0.970638	−	0.240546i	$-0.0773266\pi$
$992$	−31.6550	+	24.7315i	−1.00505	+	0.785227i
$993$	26.8650	−	36.2735i	0.852535	−	1.15110i
$994$	−4.73844	−	23.0839i	−0.150294	−	0.732178i
$995$	−17.5774	+	4.70985i	−0.557241	+	0.149312i
$996$	35.2153	+	23.1538i	1.11584	+	0.733655i
$997$	−2.21440	−	25.3107i	−0.0701306	−	0.801597i	−0.947077	−	0.321008i	$-0.895978\pi$
$997$	−2.21440	−	25.3107i	−0.0701306	−	0.801597i	0.876946	−	0.480589i	$-0.159577\pi$
$998$	−2.20657	+	37.1407i	−0.0698477	+	1.17567i
$999$	8.08062	−	22.7262i	0.255660	−	0.719024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cs.a.773.51	yes	1872
3.2	odd	2	inner	912.2.cs.a.773.106	yes	1872
16.13	even	4	inner	912.2.cs.a.317.120	yes	1872
19.3	odd	18	inner	912.2.cs.a.725.37	yes	1872
48.29	odd	4	inner	912.2.cs.a.317.37	yes	1872
57.41	even	18	inner	912.2.cs.a.725.120	yes	1872
304.269	odd	36	inner	912.2.cs.a.269.106	yes	1872
912.269	even	36	inner	912.2.cs.a.269.51	✓	1872

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.cs.a.269.51	✓	1872	912.269	even	36	inner
912.2.cs.a.269.106	yes	1872	304.269	odd	36	inner
912.2.cs.a.317.37	yes	1872	48.29	odd	4	inner
912.2.cs.a.317.120	yes	1872	16.13	even	4	inner
912.2.cs.a.725.37	yes	1872	19.3	odd	18	inner
912.2.cs.a.725.120	yes	1872	57.41	even	18	inner
912.2.cs.a.773.51	yes	1872	1.1	even	1	trivial
912.2.cs.a.773.106	yes	1872	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.741028 - 1.20452i) q^{2} +(-0.635489 + 1.61126i) q^{3} +(-0.901756 + 1.78517i) q^{4} +(-1.65579 - 1.15939i) q^{5} +(2.41171 - 0.428526i) q^{6} +(3.66991 + 2.11883i) q^{7} +(2.81851 - 0.236675i) q^{8} +(-2.19231 - 2.04787i) q^{9} +O(q^{10})\)	\(q+(-0.741028 - 1.20452i) q^{2} +(-0.635489 + 1.61126i) q^{3} +(-0.901756 + 1.78517i) q^{4} +(-1.65579 - 1.15939i) q^{5} +(2.41171 - 0.428526i) q^{6} +(3.66991 + 2.11883i) q^{7} +(2.81851 - 0.236675i) q^{8} +(-2.19231 - 2.04787i) q^{9} +(-0.169534 + 2.85358i) q^{10} +(3.98641 + 1.06815i) q^{11} +(-2.30332 - 2.58742i) q^{12} +(-1.59628 - 0.744358i) q^{13} +(-0.167332 - 5.99061i) q^{14} +(2.92032 - 1.93112i) q^{15} +(-2.37367 - 3.21958i) q^{16} +(-0.339685 - 0.404821i) q^{17} +(-0.842151 + 4.15822i) q^{18} +(-0.601479 - 4.31720i) q^{19} +(3.56283 - 1.91037i) q^{20} +(-5.74617 + 4.56669i) q^{21} +(-1.66742 - 5.59325i) q^{22} +(-1.23124 + 6.98271i) q^{23} +(-1.40978 + 4.69175i) q^{24} +(-0.312668 - 0.859049i) q^{25} +(0.286291 + 2.47435i) q^{26} +(4.69284 - 2.23098i) q^{27} +(-7.09183 + 4.64076i) q^{28} +(2.99492 - 0.262022i) q^{29} +(-4.49011 - 2.08658i) q^{30} +(6.14986 + 3.55062i) q^{31} +(-2.11910 + 5.24494i) q^{32} +(-4.25439 + 5.74433i) q^{33} +(-0.235901 + 0.709143i) q^{34} +(-3.62004 - 7.76320i) q^{35} +(5.63273 - 2.06696i) q^{36} +(3.28232 - 3.28232i) q^{37} +(-4.75446 + 3.92366i) q^{38} +(2.21377 - 2.09899i) q^{39} +(-4.94124 - 2.87588i) q^{40} +(-3.54251 + 9.73297i) q^{41} +(9.75876 + 3.53735i) q^{42} +(-1.19021 + 1.69980i) q^{43} +(-5.50160 + 6.15320i) q^{44} +(1.25570 + 5.93259i) q^{45} +(9.32322 - 3.69132i) q^{46} +(-3.06591 + 3.65381i) q^{47} +(6.69601 - 1.77860i) q^{48} +(5.47885 + 9.48965i) q^{49} +(-0.803049 + 1.01320i) q^{50} +(0.868138 - 0.290062i) q^{51} +(2.76826 - 2.17841i) q^{52} +(9.97938 - 6.98764i) q^{53} +(-6.16479 - 3.99942i) q^{54} +(-5.36222 - 6.39045i) q^{55} +(10.8452 + 5.10335i) q^{56} +(7.33836 + 1.77439i) q^{57} +(-2.53493 - 3.41329i) q^{58} +(13.0264 + 1.13966i) q^{59} +(0.813964 + 6.95466i) q^{60} +(-0.519009 - 0.741222i) q^{61} +(-0.280406 - 10.0388i) q^{62} +(-3.70650 - 12.1606i) q^{63} +(7.88797 - 1.33414i) q^{64} +(1.78009 + 3.08321i) q^{65} +(10.0718 + 0.867804i) q^{66} +(1.31653 + 15.0480i) q^{67} +(1.02899 - 0.241347i) q^{68} +(-10.4685 - 6.42128i) q^{69} +(-6.66841 + 10.1132i) q^{70} +(3.87242 - 0.682813i) q^{71} +(-6.66372 - 5.25308i) q^{72} +(-4.58071 + 12.5854i) q^{73} +(-6.38592 - 1.52134i) q^{74} +(1.58285 + 0.0421265i) q^{75} +(8.24933 + 2.81932i) q^{76} +(12.3665 + 12.3665i) q^{77} +(-4.16875 - 1.11113i) q^{78} +(-0.863449 + 2.37231i) q^{79} +(0.197538 + 8.08295i) q^{80} +(0.612431 + 8.97914i) q^{81} +(14.3487 - 2.94536i) q^{82} +(-11.7517 + 3.14886i) q^{83} +(-2.97069 - 14.3759i) q^{84} +(0.0930990 + 1.06413i) q^{85} +(2.92943 + 0.174040i) q^{86} +(-1.48105 + 4.99210i) q^{87} +(11.4885 + 2.06712i) q^{88} +(1.36686 + 3.75542i) q^{89} +(6.21543 - 5.90873i) q^{90} +(-4.28105 - 6.11397i) q^{91} +(-11.3551 - 8.49467i) q^{92} +(-9.62913 + 7.65263i) q^{93} +(6.67302 + 0.985386i) q^{94} +(-4.00942 + 7.84571i) q^{95} +(-7.10429 - 6.74752i) q^{96} +(6.02925 + 7.18538i) q^{97} +(7.37053 - 13.6315i) q^{98} +(-6.55199 - 10.5054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1872 q - 12 q^{3} - 24 q^{4} - 12 q^{6}+O(q^{10}) \) 1872 * q - 12 * q^3 - 24 * q^4 - 12 * q^6	\( 1872 q - 12 q^{3} - 24 q^{4} - 12 q^{6} - 12 q^{10} - 18 q^{12} - 24 q^{13} - 24 q^{15} - 36 q^{16} - 24 q^{19} - 30 q^{21} - 24 q^{22} - 12 q^{24} - 18 q^{27} - 72 q^{28} - 48 q^{30} - 72 q^{31} - 24 q^{33} - 24 q^{34} - 12 q^{36} - 24 q^{40} + 72 q^{42} - 24 q^{43} - 6 q^{45} - 36 q^{46} - 12 q^{48} + 768 q^{49} - 12 q^{51} - 72 q^{52} - 78 q^{54} - 48 q^{58} + 30 q^{60} - 24 q^{61} - 108 q^{63} - 12 q^{64} + 48 q^{66} - 24 q^{67} - 18 q^{69} - 180 q^{70} - 144 q^{72} - 72 q^{76} - 36 q^{78} - 48 q^{79} - 24 q^{81} - 24 q^{82} - 18 q^{84} - 120 q^{85} - 36 q^{88} + 96 q^{90} - 108 q^{91} - 30 q^{93} - 324 q^{96} - 48 q^{97} + 42 q^{99}+O(q^{100}) \) 1872 * q - 12 * q^3 - 24 * q^4 - 12 * q^6 - 12 * q^10 - 18 * q^12 - 24 * q^13 - 24 * q^15 - 36 * q^16 - 24 * q^19 - 30 * q^21 - 24 * q^22 - 12 * q^24 - 18 * q^27 - 72 * q^28 - 48 * q^30 - 72 * q^31 - 24 * q^33 - 24 * q^34 - 12 * q^36 - 24 * q^40 + 72 * q^42 - 24 * q^43 - 6 * q^45 - 36 * q^46 - 12 * q^48 + 768 * q^49 - 12 * q^51 - 72 * q^52 - 78 * q^54 - 48 * q^58 + 30 * q^60 - 24 * q^61 - 108 * q^63 - 12 * q^64 + 48 * q^66 - 24 * q^67 - 18 * q^69 - 180 * q^70 - 144 * q^72 - 72 * q^76 - 36 * q^78 - 48 * q^79 - 24 * q^81 - 24 * q^82 - 18 * q^84 - 120 * q^85 - 36 * q^88 + 96 * q^90 - 108 * q^91 - 30 * q^93 - 324 * q^96 - 48 * q^97 + 42 * q^99

Introduction

L-functions

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