LMFDB - Embedded newform 966.2.be.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			61.1
Character	$\chi$	$=$	966.61
Dual form			966.2.be.b.871.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.69832 + 0.520058i) q^{5} +(0.281733 + 0.959493i) q^{6} +(1.79038 - 1.94796i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.69832 + 0.520058i) q^{5} +(0.281733 + 0.959493i) q^{6} +(1.79038 - 1.94796i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(2.44250 + 1.25920i) q^{10} +(0.775323 + 0.985903i) q^{11} +(0.371662 - 0.928368i) q^{12} +(1.31943 + 2.05307i) q^{13} +(-2.61148 + 0.424463i) q^{14} +(2.49965 + 1.14155i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-3.52409 - 3.36022i) q^{17} +(0.327068 - 0.945001i) q^{18} +(2.05799 - 1.96229i) q^{19} +(-1.14155 - 2.49965i) q^{20} +(-2.58833 + 0.548242i) q^{21} -1.25425i q^{22} +(0.0631191 - 4.79542i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(2.36863 - 0.948256i) q^{25} +(0.231983 - 2.42943i) q^{26} +(0.281733 - 0.959493i) q^{27} +(2.31515 + 1.28066i) q^{28} +(5.27378 - 1.54852i) q^{29} +(-1.25920 - 2.44250i) q^{30} +(0.129343 + 1.35454i) q^{31} +(0.981929 + 0.189251i) q^{32} +(-0.0596794 - 1.25282i) q^{33} +(0.692977 + 4.81976i) q^{34} +(-3.81796 + 6.18732i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-6.70584 + 2.32091i) q^{37} +(-2.83070 + 0.270299i) q^{38} +(0.116123 - 2.43772i) q^{39} +(-0.647861 + 2.67052i) q^{40} +(-7.59064 + 6.57733i) q^{41} +(2.37346 + 1.16905i) q^{42} +(2.35599 - 1.07595i) q^{43} +(-0.775323 + 0.985903i) q^{44} +(-1.37399 - 2.37982i) q^{45} +(-3.01394 + 3.73043i) q^{46} +(-9.75328 - 5.63106i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-0.589103 - 6.97517i) q^{49} +(-2.44804 - 0.718810i) q^{50} +(0.921525 + 4.78133i) q^{51} +(-1.68413 + 1.76626i) q^{52} +(-7.97475 - 0.379884i) q^{53} +(-0.814576 + 0.580057i) q^{54} +(-2.60480 - 2.25707i) q^{55} +(-1.02818 - 2.43780i) q^{56} +(-2.81463 + 0.404682i) q^{57} +(-5.10270 - 2.04281i) q^{58} +(-0.493588 + 0.957427i) q^{59} +(-0.520058 + 2.69832i) q^{60} +(-2.10003 - 2.94907i) q^{61} +(0.735652 - 1.14470i) q^{62} +(2.42640 + 1.05479i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-4.62794 - 4.85365i) q^{65} +(-0.727534 + 1.02168i) q^{66} +(-3.48494 - 8.70497i) q^{67} +(2.43466 - 4.21696i) q^{68} +(-2.83303 + 3.86962i) q^{69} +(6.82586 - 2.50346i) q^{70} +(-0.723998 + 5.03552i) q^{71} +(0.995472 + 0.0950560i) q^{72} +(-5.74008 + 1.39253i) q^{73} +(6.70584 + 2.32091i) q^{74} +(-2.47947 - 0.601513i) q^{75} +(2.39216 + 1.53735i) q^{76} +(3.30862 + 0.254840i) q^{77} +(-1.59818 + 1.84439i) q^{78} +(4.28785 - 0.204255i) q^{79} +(2.16006 - 1.69869i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(10.0325 - 0.477906i) q^{82} +(-4.96166 + 5.72606i) q^{83} +(-1.14301 - 2.38611i) q^{84} +(11.2566 + 7.23421i) q^{85} +(-2.51704 - 0.610627i) q^{86} +(-5.19412 - 1.79770i) q^{87} +(1.21889 - 0.295699i) q^{88} +(-16.7290 - 1.59743i) q^{89} +(-0.391078 + 2.72001i) q^{90} +(6.36156 + 1.10557i) q^{91} +(4.67512 - 1.06922i) q^{92} +(0.680352 - 1.17840i) q^{93} +(4.18571 + 10.4554i) q^{94} +(-4.53261 + 6.36516i) q^{95} +(-0.690079 - 0.723734i) q^{96} +(-1.33654 - 1.54245i) q^{97} +(-3.84870 + 5.84701i) q^{98} +(-0.678096 + 1.05514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.786053	−	0.618159i	−0.555823	−	0.437104i
$2$	−0.786053	−	0.618159i	−0.555823	−	0.437104i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$4$	0.235759	+	0.971812i	0.117879	+	0.485906i
$5$	−2.69832	+	0.520058i	−1.20673	+	0.232577i	−0.752671	−	0.658397i	$-0.771235\pi$
$5$	−2.69832	+	0.520058i	−1.20673	+	0.232577i	−0.454054	+	0.890974i	$0.650023\pi$
$6$	0.281733	+	0.959493i	0.115017	+	0.391711i
$7$	1.79038	−	1.94796i	0.676699	−	0.736260i
$7$	1.79038	−	1.94796i	0.676699	−	0.736260i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	2.44250	+	1.25920i	0.772387	+	0.398193i
$11$	0.775323	+	0.985903i	0.233769	+	0.297261i	0.888758	−	0.458377i	$-0.151569\pi$
$11$	0.775323	+	0.985903i	0.233769	+	0.297261i	−0.654989	+	0.755638i	$0.727327\pi$
$12$	0.371662	−	0.928368i	0.107290	−	0.267997i
$13$	1.31943	+	2.05307i	0.365943	+	0.569418i	0.974583	−	0.224029i	$-0.0719209\pi$
$13$	1.31943	+	2.05307i	0.365943	+	0.569418i	−0.608640	+	0.793447i	$0.708285\pi$
$14$	−2.61148	+	0.424463i	−0.697948	+	0.113443i
$15$	2.49965	+	1.14155i	0.645407	+	0.294747i
$16$	−0.888835	+	0.458227i	−0.222209	+	0.114557i
$17$	−3.52409	−	3.36022i	−0.854719	−	0.814972i	0.129564	−	0.991571i	$-0.458642\pi$
$17$	−3.52409	−	3.36022i	−0.854719	−	0.814972i	−0.984283	+	0.176599i	$0.943491\pi$
$18$	0.327068	−	0.945001i	0.0770907	−	0.222739i
$19$	2.05799	−	1.96229i	0.472135	−	0.450180i	−0.416269	−	0.909241i	$-0.636663\pi$
$19$	2.05799	−	1.96229i	0.472135	−	0.450180i	0.888405	+	0.459061i	$0.151814\pi$
$20$	−1.14155	−	2.49965i	−0.255259	−	0.558939i
$21$	−2.58833	+	0.548242i	−0.564819	+	0.119636i
$22$		−	1.25425i		−	0.267406i
$23$	0.0631191	−	4.79542i	0.0131612	−	0.999913i
$23$	0.0631191	−	4.79542i	0.0131612	−	0.999913i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	2.36863	−	0.948256i	0.473726	−	0.189651i
$26$	0.231983	−	2.42943i	0.0454956	−	0.476451i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	2.31515	+	1.28066i	0.437522	+	0.242022i
$29$	5.27378	−	1.54852i	0.979316	−	0.287553i	0.247374	−	0.968920i	$-0.420432\pi$
$29$	5.27378	−	1.54852i	0.979316	−	0.287553i	0.731942	+	0.681367i	$0.238614\pi$
$30$	−1.25920	−	2.44250i	−0.229897	−	0.445938i
$31$	0.129343	+	1.35454i	0.0232307	+	0.243283i	0.999627	+	0.0272978i	$0.00869025\pi$
$31$	0.129343	+	1.35454i	0.0232307	+	0.243283i	−0.976397	+	0.215985i	$0.930704\pi$
$32$	0.981929	+	0.189251i	0.173582	+	0.0334552i
$33$	−0.0596794	−	1.25282i	−0.0103888	−	0.218089i
$34$	0.692977	+	4.81976i	0.118845	+	0.826582i
$35$	−3.81796	+	6.18732i	−0.645352	+	1.04585i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	−6.70584	+	2.32091i	−1.10243	+	0.381556i	−0.816880	−	0.576807i	$-0.804298\pi$
$37$	−6.70584	+	2.32091i	−1.10243	+	0.381556i	−0.285553	+	0.958363i	$0.592177\pi$
$38$	−2.83070	+	0.270299i	−0.459199	+	0.0438482i
$39$	0.116123	−	2.43772i	0.0185945	−	0.390347i
$40$	−0.647861	+	2.67052i	−0.102436	+	0.422246i
$41$	−7.59064	+	6.57733i	−1.18546	+	1.02721i	−0.186460	+	0.982463i	$0.559702\pi$
$41$	−7.59064	+	6.57733i	−1.18546	+	1.02721i	−0.998999	+	0.0447432i	$0.985753\pi$
$42$	2.37346	+	1.16905i	0.366233	+	0.180388i
$43$	2.35599	−	1.07595i	0.359285	−	0.164080i	−0.227591	−	0.973757i	$-0.573085\pi$
$43$	2.35599	−	1.07595i	0.359285	−	0.164080i	0.586876	+	0.809677i	$0.300358\pi$
$44$	−0.775323	+	0.985903i	−0.116884	+	0.148631i
$45$	−1.37399	−	2.37982i	−0.204822	−	0.354763i
$46$	−3.01394	+	3.73043i	−0.444382	+	0.550022i
$47$	−9.75328	−	5.63106i	−1.42266	−	0.821374i	−0.426136	−	0.904659i	$-0.640125\pi$
$47$	−9.75328	−	5.63106i	−1.42266	−	0.821374i	−0.996526	+	0.0832850i	$0.973459\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	−0.589103	−	6.97517i	−0.0841575	−	0.996452i
$50$	−2.44804	−	0.718810i	−0.346205	−	0.101655i
$51$	0.921525	+	4.78133i	0.129039	+	0.669520i
$52$	−1.68413	+	1.76626i	−0.233546	+	0.244936i
$53$	−7.97475	−	0.379884i	−1.09542	−	0.0521811i	−0.507917	−	0.861406i	$-0.669584\pi$
$53$	−7.97475	−	0.379884i	−1.09542	−	0.0521811i	−0.587499	+	0.809225i	$0.699887\pi$
$54$	−0.814576	+	0.580057i	−0.110850	+	0.0789357i
$55$	−2.60480	−	2.25707i	−0.351231	−	0.304343i
$56$	−1.02818	−	2.43780i	−0.137396	−	0.325764i
$57$	−2.81463	+	0.404682i	−0.372807	+	0.0536015i
$58$	−5.10270	−	2.04281i	−0.670017	−	0.268235i
$59$	−0.493588	+	0.957427i	−0.0642597	+	0.124646i	−0.918778	−	0.394776i	$-0.870822\pi$
$59$	−0.493588	+	0.957427i	−0.0642597	+	0.124646i	0.854518	+	0.519422i	$0.173853\pi$
$60$	−0.520058	+	2.69832i	−0.0671393	+	0.348352i
$61$	−2.10003	−	2.94907i	−0.268881	−	0.377590i	0.657955	−	0.753057i	$-0.271422\pi$
$61$	−2.10003	−	2.94907i	−0.268881	−	0.377590i	−0.926836	+	0.375467i	$0.877482\pi$
$62$	0.735652	−	1.14470i	0.0934279	−	0.145377i
$63$	2.42640	+	1.05479i	0.305698	+	0.132891i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−4.62794	−	4.85365i	−0.574026	−	0.602021i
$66$	−0.727534	+	1.02168i	−0.0895532	+	0.125760i
$67$	−3.48494	−	8.70497i	−0.425754	−	1.06348i	−0.973875	−	0.227083i	$-0.927081\pi$
$67$	−3.48494	−	8.70497i	−0.425754	−	1.06348i	0.548122	−	0.836399i	$-0.315343\pi$
$68$	2.43466	−	4.21696i	0.295246	−	0.511381i
$69$	−2.83303	+	3.86962i	−0.341057	+	0.465847i
$70$	6.82586	−	2.50346i	0.815847	−	0.299221i
$71$	−0.723998	+	5.03552i	−0.0859228	+	0.597606i	0.900682	+	0.434479i	$0.143067\pi$
$71$	−0.723998	+	5.03552i	−0.0859228	+	0.597606i	−0.986605	+	0.163128i	$0.947842\pi$
$72$	0.995472	+	0.0950560i	0.117317	+	0.0112025i
$73$	−5.74008	+	1.39253i	−0.671826	+	0.162983i	−0.557140	−	0.830419i	$-0.688101\pi$
$73$	−5.74008	+	1.39253i	−0.671826	+	0.162983i	−0.114686	+	0.993402i	$0.536586\pi$
$74$	6.70584	+	2.32091i	0.779538	+	0.269801i
$75$	−2.47947	−	0.601513i	−0.286305	−	0.0694567i
$76$	2.39216	+	1.53735i	0.274400	+	0.176346i
$77$	3.30862	+	0.254840i	0.377052	+	0.0290417i
$78$	−1.59818	+	1.84439i	−0.180958	+	0.208837i
$79$	4.28785	−	0.204255i	0.482421	−	0.0229805i	0.195037	−	0.980796i	$-0.437517\pi$
$79$	4.28785	−	0.204255i	0.482421	−	0.0229805i	0.287384	+	0.957815i	$0.407214\pi$
$80$	2.16006	−	1.69869i	0.241502	−	0.189919i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	10.0325	−	0.477906i	1.10790	−	0.0527759i
$83$	−4.96166	+	5.72606i	−0.544613	+	0.628517i	−0.959619	−	0.281301i	$-0.909234\pi$
$83$	−4.96166	+	5.72606i	−0.544613	+	0.628517i	0.415006	+	0.909819i	$0.363779\pi$
$84$	−1.14301	−	2.38611i	−0.124712	−	0.260346i
$85$	11.2566	+	7.23421i	1.22095	+	0.784660i
$86$	−2.51704	−	0.610627i	−0.271419	−	0.0658456i
$87$	−5.19412	−	1.79770i	−0.556868	−	0.192734i
$88$	1.21889	−	0.295699i	0.129934	−	0.0315217i
$89$	−16.7290	−	1.59743i	−1.77327	−	0.169327i	−0.843419	−	0.537256i	$-0.819461\pi$
$89$	−16.7290	−	1.59743i	−1.77327	−	0.169327i	−0.929854	+	0.367929i	$0.880067\pi$
$90$	−0.391078	+	2.72001i	−0.0412233	+	0.286714i
$91$	6.36156	+	1.10557i	0.666873	+	0.115895i
$92$	4.67512	−	1.06922i	0.487415	−	0.111474i
$93$	0.680352	−	1.17840i	0.0705492	−	0.122195i
$94$	4.18571	+	10.4554i	0.431723	+	1.07839i
$95$	−4.53261	+	6.36516i	−0.465036	+	0.653051i
$96$	−0.690079	−	0.723734i	−0.0704309	−	0.0738658i
$97$	−1.33654	−	1.54245i	−0.135705	−	0.156612i	0.683829	−	0.729642i	$-0.260313\pi$
$97$	−1.33654	−	1.54245i	−0.135705	−	0.156612i	−0.819535	+	0.573030i	$0.805768\pi$
$98$	−3.84870	+	5.84701i	−0.388777	+	0.590637i
$99$	−0.678096	+	1.05514i	−0.0681512	+	0.106045i
$100$	1.47995	+	2.07830i	0.147995	+	0.207830i
$101$	2.22163	−	11.5269i	0.221060	−	1.14697i	−0.686526	−	0.727105i	$-0.740865\pi$
$101$	2.22163	−	11.5269i	0.221060	−	1.14697i	0.907586	−	0.419865i	$-0.137923\pi$
$102$	2.23125	−	4.32803i	0.220927	−	0.428539i
$103$	−15.8009	−	6.32571i	−1.55691	−	0.623291i	−0.575943	−	0.817490i	$-0.695365\pi$
$103$	−15.8009	−	6.32571i	−1.55691	−	0.623291i	−0.980962	+	0.194199i	$0.937789\pi$
$104$	2.41564	−	0.347317i	0.236873	−	0.0340572i
$105$	6.69901	−	2.82541i	0.653757	−	0.275732i
$106$	6.03375	+	5.22827i	0.586050	+	0.507815i
$107$	−0.944733	+	0.672741i	−0.0913307	+	0.0650363i	−0.624810	−	0.780777i	$-0.714824\pi$
$107$	−0.944733	+	0.672741i	−0.0913307	+	0.0650363i	0.533479	+	0.845813i	$0.320884\pi$
$108$	0.998867	+	0.0475819i	0.0961161	+	0.00457857i
$109$	−5.70025	+	5.97826i	−0.545985	+	0.572613i	−0.937688	−	0.347479i	$-0.887038\pi$
$109$	−5.70025	+	5.97826i	−0.545985	+	0.572613i	0.391702	+	0.920092i	$0.371886\pi$
$110$	0.652281	+	3.38435i	0.0621925	+	0.322686i
$111$	6.80868	+	1.99921i	0.646251	+	0.189756i
$112$	−0.698743	+	2.55181i	−0.0660250	+	0.241124i
$113$	1.37181	+	0.197237i	0.129049	+	0.0185545i	0.206537	−	0.978439i	$-0.433781\pi$
$113$	1.37181	+	0.197237i	0.129049	+	0.0185545i	−0.0774875	+	0.996993i	$0.524690\pi$
$114$	2.46261	+	1.42179i	0.230644	+	0.133162i
$115$	2.32358	+	12.9724i	0.216675	+	1.20968i
$116$	2.74821	+	4.76004i	0.255165	+	0.441959i
$117$	−1.50861	+	1.91835i	−0.139471	+	0.177351i
$118$	0.979828	−	0.447473i	0.0902005	−	0.0411932i
$119$	−12.8550	+	0.848743i	−1.17842	+	0.0778042i
$120$	2.07678	−	1.79954i	0.189584	−	0.164275i
$121$	2.22247	−	9.16114i	0.202043	−	0.832831i
$122$	−0.172265	+	3.61628i	−0.0155961	+	0.327403i
$123$	9.99838	−	0.954729i	0.901523	−	0.0860850i
$124$	−1.28587	+	0.445043i	−0.115474	+	0.0399660i
$125$	5.66057	−	3.63783i	0.506297	−	0.325377i
$126$	−1.25525	−	2.32902i	−0.111827	−	0.207486i
$127$	1.57387	+	10.9465i	0.139659	+	0.971347i	0.932307	+	0.361668i	$0.117793\pi$
$127$	1.57387	+	10.9465i	0.139659	+	0.971347i	−0.792648	+	0.609679i	$0.791298\pi$
$128$	0.0475819	+	0.998867i	0.00420569	+	0.0882882i
$129$	−2.54324	−	0.490170i	−0.223920	−	0.0431571i
$130$	0.637484	+	6.67603i	0.0559110	+	0.585527i
$131$	8.57072	+	16.6249i	0.748827	+	1.45252i	0.886833	+	0.462090i	$0.152900\pi$
$131$	8.57072	+	16.6249i	0.748827	+	1.45252i	−0.138006	+	0.990431i	$0.544069\pi$
$132$	1.20344	−	0.353362i	0.104746	−	0.0307562i
$133$	−0.137886	−	7.52212i	−0.0119562	−	0.652250i
$134$	−2.64170	+	8.99682i	−0.228208	+	0.777207i
$135$	−0.261212	+	2.73554i	−0.0224816	+	0.235437i
$136$	−4.52052	+	1.80974i	−0.387632	+	0.155184i
$137$	18.5685	−	10.7205i	1.58641	−	0.915915i	0.592520	−	0.805556i	$-0.298133\pi$
$137$	18.5685	−	10.7205i	1.58641	−	0.915915i	0.993892	−	0.110360i	$-0.0352003\pi$
$138$	4.61895	−	1.29046i	0.393191	−	0.109851i
$139$		−	22.2847i		−	1.89016i	−0.326837	−	0.945081i	$-0.605983\pi$
$139$		−	22.2847i		−	1.89016i	0.326837	−	0.945081i	$-0.394017\pi$
$140$	−6.91303	−	2.25162i	−0.584257	−	0.190296i
$141$	4.67845	+	10.2444i	0.393997	+	0.862732i
$142$	3.68185	−	3.51064i	0.308974	−	0.294606i
$143$	−1.00114	+	2.89261i	−0.0837198	+	0.241893i
$144$	−0.723734	−	0.690079i	−0.0603112	−	0.0575066i
$145$	−13.4250	+	6.92108i	−1.11489	+	0.574764i
$146$	5.37282	+	2.45368i	0.444657	+	0.203068i
$147$	−3.56613	+	6.02352i	−0.294129	+	0.496811i
$148$	−3.83645	−	5.96964i	−0.315355	−	0.490701i
$149$	3.57100	−	8.91993i	0.292548	−	0.730749i	−0.707171	−	0.707042i	$-0.750029\pi$
$149$	3.57100	−	8.91993i	0.292548	−	0.730749i	0.999719	−	0.0237067i	$-0.00754677\pi$
$150$	1.57716	+	2.00553i	0.128775	+	0.163751i
$151$	11.8809	+	6.12505i	0.966857	+	0.498449i	0.867952	−	0.496648i	$-0.165436\pi$
$151$	11.8809	+	6.12505i	0.966857	+	0.498449i	0.0989045	+	0.995097i	$0.468466\pi$
$152$	−0.930041	−	2.68718i	−0.0754363	−	0.217959i
$153$	2.02279	−	4.42929i	0.163533	−	0.358087i
$154$	−2.44322	−	2.24557i	−0.196880	−	0.180953i
$155$	−1.05345	−	3.58772i	−0.0846152	−	0.288173i
$156$	2.39638	−	0.461865i	0.191864	−	0.0369788i
$157$	−0.427974	−	1.76413i	−0.0341560	−	0.140793i	0.952181	−	0.305536i	$-0.0988357\pi$
$157$	−0.427974	−	1.76413i	−0.0341560	−	0.140793i	−0.986337	+	0.164743i	$0.947321\pi$
$158$	−3.49674	−	2.49002i	−0.278186	−	0.198095i
$159$	6.27569	+	4.93525i	0.497694	+	0.391391i
$160$	−2.74798			−0.217247
$161$	−9.22828	−	8.70855i	−0.727290	−	0.686330i
$162$	1.00000			0.0785674
$163$	−11.1543	−	8.77186i	−0.873674	−	0.687065i	0.0770754	−	0.997025i	$-0.475442\pi$
$163$	−11.1543	−	8.77186i	−0.873674	−	0.687065i	−0.950749	+	0.309960i	$0.899684\pi$
$164$	−8.18148	−	5.82601i	−0.638866	−	0.454935i
$165$	0.812576	+	3.34948i	0.0632590	+	0.260757i
$166$	7.43975	−	1.43389i	0.577436	−	0.111292i
$167$	−3.14143	−	10.6987i	−0.243091	−	0.827891i	−0.987153	−	0.159780i	$-0.948921\pi$
$167$	−3.14143	−	10.6987i	−0.243091	−	0.827891i	0.744062	−	0.668111i	$-0.232897\pi$
$168$	−0.576531	+	2.58217i	−0.0444804	+	0.199219i
$169$	2.92620	−	6.40748i	0.225092	−	0.492883i
$170$	−4.37643	−	12.6449i	−0.335657	−	0.969817i
$171$	2.52747	+	1.30300i	0.193280	+	0.0996429i
$172$	1.60106	+	2.03592i	0.122080	+	0.155237i
$173$	−1.39744	+	3.49064i	−0.106246	+	0.265389i	−0.971959	−	0.235152i	$-0.924441\pi$
$173$	−1.39744	+	3.49064i	−0.106246	+	0.265389i	0.865713	+	0.500541i	$0.166865\pi$
$174$	2.97159	+	4.62388i	0.225276	+	0.350536i
$175$	2.39357	−	6.31173i	0.180937	−	0.477122i
$176$	−1.14090	−	0.521032i	−0.0859987	−	0.0392743i
$177$	0.957427	−	0.493588i	0.0719646	−	0.0371003i
$178$	12.1624	+	11.5969i	0.911613	+	0.869222i
$179$	−6.69538	+	19.3450i	−0.500436	+	1.44592i	0.358353	+	0.933586i	$0.383338\pi$
$179$	−6.69538	+	19.3450i	−0.500436	+	1.44592i	−0.858789	+	0.512329i	$0.828783\pi$
$180$	1.98881	−	1.89632i	0.148237	−	0.141344i
$181$	3.61472	+	7.91513i	0.268680	+	0.588327i	0.995094	−	0.0989300i	$-0.0315420\pi$
$181$	3.61472	+	7.91513i	0.268680	+	0.588327i	−0.726415	+	0.687257i	$0.758815\pi$
$182$	−4.31710	−	4.80149i	−0.320005	−	0.355910i
$183$			3.62038i			0.267626i
$184$	−4.33584	−	2.04950i	−0.319643	−	0.151091i
$185$	16.8875	−	9.75000i	1.24159	−	0.716834i
$186$	−1.26323	+	0.505723i	−0.0926248	+	0.0370814i
$187$	0.580538	−	6.07967i	0.0424532	−	0.444590i
$188$	3.17290	−	10.8059i	0.231408	−	0.788103i
$189$	−1.36465	−	2.26666i	−0.0992635	−	0.164875i
$190$	7.49755	−	2.20148i	0.543929	−	0.159712i
$191$	−1.67056	−	3.24044i	−0.120878	−	0.234470i	0.820631	−	0.571458i	$-0.193622\pi$
$191$	−1.67056	−	3.24044i	−0.120878	−	0.234470i	−0.941509	+	0.336988i	$0.890592\pi$
$192$	0.0950560	+	0.995472i	0.00686008	+	0.0718420i
$193$	−0.694983	−	0.133947i	−0.0500259	−	0.00964171i	0.164177	−	0.986431i	$-0.447503\pi$
$193$	−0.694983	−	0.133947i	−0.0500259	−	0.00964171i	−0.214203	+	0.976789i	$0.568715\pi$
$194$	0.0971127	+	2.03865i	0.00697229	+	0.146366i
$195$	0.954420	+	6.63814i	0.0683474	+	0.475367i
$196$	6.63966	−	2.21695i	0.474262	−	0.158354i
$197$	16.3583	−	10.5129i	1.16548	−	0.749010i	0.192819	−	0.981234i	$-0.438237\pi$
$197$	16.3583	−	10.5129i	1.16548	−	0.749010i	0.972662	+	0.232225i	$0.0746005\pi$
$198$	1.18526	−	0.410223i	0.0842329	−	0.0291533i
$199$	−2.01326	+	0.192243i	−0.142716	+	0.0136277i	−0.166169	−	0.986097i	$-0.553140\pi$
$199$	−2.01326	+	0.192243i	−0.142716	+	0.0136277i	0.0234536	+	0.999725i	$0.492534\pi$
$200$	0.121400	−	2.54850i	0.00858428	−	0.180206i
$201$	−2.21063	+	9.11232i	−0.155926	+	0.642734i
$202$	−8.87178	+	7.68744i	−0.624216	+	0.540887i
$203$	6.42559	−	13.0455i	0.450988	−	0.915618i
$204$	−4.42929	+	2.02279i	−0.310112	+	0.141624i
$205$	17.0614	−	21.6953i	1.19162	−	1.51527i
$206$	8.51002	+	14.7398i	0.592921	+	1.02697i
$207$	4.55232	−	1.50878i	0.316408	−	0.104867i
$208$	−2.11352	−	1.22024i	−0.146546	−	0.0846085i
$209$	3.53023	+	0.507571i	0.244191	+	0.0351094i
$210$	−7.01233	−	1.92013i	−0.483897	−	0.132502i
$211$	−6.19721	−	1.81966i	−0.426633	−	0.125271i	0.0613650	−	0.998115i	$-0.480455\pi$
$211$	−6.19721	−	1.81966i	−0.426633	−	0.125271i	−0.487998	+	0.872845i	$0.662273\pi$
$212$	−1.51094	−	7.83952i	−0.103772	−	0.538420i
$213$	3.51064	−	3.68185i	0.240545	−	0.252276i
$214$	1.15847	+	0.0551848i	0.0791914	+	0.00377235i
$215$	−5.79766	+	4.12850i	−0.395397	+	0.281561i
$216$	−0.755750	−	0.654861i	−0.0514222	−	0.0445576i
$217$	2.87017	+	2.17319i	0.194840	+	0.147526i
$218$	8.17622	−	1.17556i	0.553763	−	0.0796191i
$219$	5.48348	+	2.19525i	0.370539	+	0.148342i
$220$	1.57934	−	3.06350i	0.106479	−	0.206541i
$221$	2.24897	−	11.6688i	0.151282	−	0.784925i
$222$	−4.11615	−	5.78033i	−0.276258	−	0.387950i
$223$	−8.62696	+	13.4238i	−0.577704	+	0.898925i	−0.999972	−	0.00754647i	$-0.997598\pi$
$223$	−8.62696	+	13.4238i	−0.577704	+	0.898925i	0.422268	+	0.906471i	$0.361234\pi$
$224$	2.12668	−	1.57393i	0.142095	−	0.105162i
$225$	1.67081	+	1.92821i	0.111387	+	0.128547i
$226$	−0.956393	−	1.00304i	−0.0636183	−	0.0667210i
$227$	8.13377	−	11.4223i	0.539857	−	0.758123i	−0.451075	−	0.892486i	$-0.648959\pi$
$227$	8.13377	−	11.4223i	0.539857	−	0.758123i	0.990932	+	0.134363i	$0.0428987\pi$
$228$	−1.05685	−	2.63988i	−0.0699915	−	0.174830i
$229$	−7.68636	+	13.3132i	−0.507929	+	0.879759i	0.492029	+	0.870579i	$0.336256\pi$
$229$	−7.68636	+	13.3132i	−0.507929	+	0.879759i	−0.999958	+	0.00918026i	$0.997078\pi$
$230$	6.19254	−	11.6333i	0.408324	−	0.767079i
$231$	−2.54730	−	2.12677i	−0.167600	−	0.139931i
$232$	0.782222	−	5.44048i	0.0513554	−	0.357185i
$233$	−5.32806	−	0.508768i	−0.349053	−	0.0333305i	−0.0809427	−	0.996719i	$-0.525793\pi$
$233$	−5.32806	−	0.508768i	−0.349053	−	0.0333305i	−0.268110	+	0.963388i	$0.586399\pi$
$234$	2.37169	−	0.575366i	0.155042	−	0.0376128i
$235$	29.2459	+	10.1221i	1.90779	+	0.660294i
$236$	−1.04681	−	0.253952i	−0.0681413	−	0.0165309i
$237$	−3.61126	−	2.32082i	−0.234577	−	0.150753i
$238$	10.6294	+	7.27929i	0.689001	+	0.471847i
$239$	−11.7675	+	13.5804i	−0.761174	+	0.878442i	−0.995601	−	0.0936921i	$-0.970133\pi$
$239$	−11.7675	+	13.5804i	−0.761174	+	0.878442i	0.234427	+	0.972134i	$0.424679\pi$
$240$	−2.74487	+	0.130754i	−0.177180	+	0.00844014i
$241$	−3.47977	+	2.73652i	−0.224152	+	0.176275i	−0.723919	−	0.689885i	$-0.757661\pi$
$241$	−3.47977	+	2.73652i	−0.224152	+	0.176275i	0.499768	+	0.866160i	$0.333419\pi$
$242$	−7.41002	+	5.82730i	−0.476334	+	0.374593i
$243$	0.998867	−	0.0475819i	0.0640774	−	0.00305238i
$244$	2.37084	−	2.73610i	0.151778	−	0.175161i
$245$	5.21708	+	18.5149i	0.333307	+	1.18287i
$246$	−8.44943	−	5.43012i	−0.538716	−	0.346212i
$247$	6.74407	+	1.63609i	0.429115	+	0.104102i
$248$	1.28587	+	0.445043i	0.0816526	+	0.0282602i
$249$	7.36309	−	1.78627i	0.466617	−	0.113200i
$250$	−6.69826	−	0.639606i	−0.423635	−	0.0404523i
$251$	2.39486	−	16.6566i	0.151162	−	1.05135i	−0.763114	−	0.646263i	$-0.776331\pi$
$251$	2.39486	−	16.6566i	0.151162	−	1.05135i	0.914276	−	0.405091i	$-0.132760\pi$
$252$	−0.453014	+	2.60668i	−0.0285372	+	0.164205i
$253$	4.77675	−	3.65577i	0.300312	−	0.229836i
$254$	5.52955	−	9.57746i	0.346955	−	0.600943i
$255$	−4.97314	−	12.4223i	−0.311430	−	0.777915i
$256$	0.580057	−	0.814576i	0.0362536	−	0.0509110i
$257$	−7.92883	−	8.31551i	−0.494587	−	0.518707i	0.428374	−	0.903601i	$-0.359087\pi$
$257$	−7.92883	−	8.31551i	−0.494587	−	0.518707i	−0.922961	+	0.384894i	$0.874238\pi$
$258$	1.69612	+	1.95743i	0.105596	+	0.121864i
$259$	−7.48493	+	17.2180i	−0.465091	+	1.06988i
$260$	3.62575	−	5.64178i	0.224860	−	0.349888i
$261$	3.18824	+	4.47725i	0.197347	+	0.277135i
$262$	3.53978	−	18.3661i	0.218688	−	1.13466i
$263$	4.62956	−	8.98009i	0.285471	−	0.553736i	−0.701878	−	0.712297i	$-0.747655\pi$
$263$	4.62956	−	8.98009i	0.285471	−	0.553736i	0.987349	+	0.158561i	$0.0506854\pi$
$264$	−1.16440	−	0.466156i	−0.0716639	−	0.0286899i
$265$	21.7160	−	3.12229i	1.33400	−	0.191801i
$266$	−4.54148	+	5.99802i	−0.278456	+	0.367762i
$267$	12.7005	+	11.0050i	0.777256	+	0.673496i
$268$	7.63798	−	5.43898i	0.466564	−	0.332239i
$269$	22.2102	+	1.05800i	1.35418	+	0.0645075i	0.712071	−	0.702107i	$-0.247757\pi$
$269$	22.2102	+	1.05800i	1.35418	+	0.0645075i	0.642107	+	0.766615i	$0.278060\pi$
$270$	1.89632	−	1.98881i	0.115407	−	0.121035i
$271$	0.291811	+	1.51406i	0.0177263	+	0.0919725i	0.989714	−	0.143057i	$-0.0456933\pi$
$271$	0.291811	+	1.51406i	0.0177263	+	0.0919725i	−0.971988	+	0.235030i	$0.924481\pi$
$272$	4.67208	+	1.37185i	0.283287	+	0.0831804i
$273$	−4.54068	−	4.59064i	−0.274814	−	0.277838i
$274$	−21.2228	−	3.05138i	−1.28212	−	0.184340i
$275$	2.77134	+	1.60003i	0.167118	+	0.0964857i
$276$	−4.42845	−	1.84087i	−0.266561	−	0.110808i
$277$	1.82648	+	3.16356i	0.109743	+	0.190080i	0.915666	−	0.401940i	$-0.131664\pi$
$277$	1.82648	+	3.16356i	0.109743	+	0.190080i	−0.805923	+	0.592020i	$0.798331\pi$
$278$	−13.7755	+	17.5169i	−0.826198	+	1.05060i
$279$	−1.23774	+	0.565257i	−0.0741016	+	0.0338411i
$280$	4.04215	+	6.04324i	0.241565	+	0.361153i
$281$	−9.90934	+	8.58649i	−0.591142	+	0.512227i	−0.898272	−	0.439440i	$-0.855177\pi$
$281$	−9.90934	+	8.58649i	−0.591142	+	0.512227i	0.307130	+	0.951668i	$0.400631\pi$
$282$	2.65514	−	10.9447i	0.158112	−	0.651745i
$283$	−1.03009	+	21.6243i	−0.0612325	+	1.28543i	0.734010	+	0.679138i	$0.237646\pi$
$283$	−1.03009	+	21.6243i	−0.0612325	+	1.28543i	−0.795243	+	0.606291i	$0.792657\pi$
$284$	−5.06426	+	0.483579i	−0.300509	+	0.0286951i
$285$	7.38431	−	2.55573i	0.437409	−	0.151389i
$286$	2.57505	−	1.65488i	0.152266	−	0.0978552i
$287$	−0.777730	+	26.5622i	−0.0459079	+	1.56791i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	0.319289	+	6.70271i	0.0187817	+	0.394277i
$290$	14.8311	+	2.85846i	0.870912	+	0.167855i
$291$	0.194005	+	2.03172i	0.0113728	+	0.119101i
$292$	−2.70655	−	5.24998i	−0.158389	−	0.307232i
$293$	29.4602	−	8.65030i	1.72108	−	0.505356i	0.735934	−	0.677054i	$-0.236744\pi$
$293$	29.4602	−	8.65030i	1.72108	−	0.505356i	0.985150	+	0.171698i	$0.0549253\pi$
$294$	6.52665	−	2.53037i	0.380642	−	0.147574i
$295$	0.833940	−	2.84014i	0.0485539	−	0.165359i
$296$	−0.674529	+	7.06399i	−0.0392062	+	0.410586i
$297$	1.16440	−	0.466156i	0.0675654	−	0.0270491i
$298$	−8.32093	+	4.80409i	−0.482019	+	0.278294i
$299$	9.92858	−	6.19760i	0.574185	−	0.358417i
$300$		−	2.55139i		−	0.147305i
$301$	2.12221	−	6.51573i	0.122322	−	0.375560i
$302$	−5.55279	−	12.1589i	−0.319527	−	0.699667i
$303$	−8.49595	+	8.10087i	−0.488080	+	0.465383i
$304$	−0.930041	+	2.68718i	−0.0533415	+	0.154120i
$305$	7.20023	+	6.86541i	0.412284	+	0.393112i
$306$	−4.32803	+	2.23125i	−0.247417	+	0.127552i
$307$	17.1009	+	7.80970i	0.975997	+	0.445723i	0.838573	−	0.544789i	$-0.183390\pi$
$307$	17.1009	+	7.80970i	0.975997	+	0.445723i	0.137424	+	0.990512i	$0.456118\pi$
$308$	0.532381	+	3.27544i	0.0303352	+	0.186635i
$309$	9.20173	+	14.3182i	0.523468	+	0.814532i
$310$	−1.38972	+	3.47134i	−0.0789305	+	0.197159i
$311$	−14.9610	−	19.0244i	−0.848359	−	1.07878i	−0.995966	−	0.0897303i	$-0.971399\pi$
$311$	−14.9610	−	19.0244i	−0.848359	−	1.07878i	0.147607	−	0.989046i	$-0.452843\pi$
$312$	−2.16919	−	1.11829i	−0.122806	−	0.0633109i
$313$	−9.53106	−	27.5382i	−0.538727	−	1.55655i	−0.805381	−	0.592758i	$-0.798039\pi$
$313$	−9.53106	−	27.5382i	−0.538727	−	1.55655i	0.266653	−	0.963793i	$-0.414082\pi$
$314$	−0.754103	+	1.65126i	−0.0425565	+	0.0931858i
$315$	−7.09575	−	1.58430i	−0.399800	−	0.0892650i
$316$	1.20940	+	4.11883i	0.0680339	+	0.231702i
$317$	14.1943	−	2.73573i	0.797232	−	0.153654i	0.225660	−	0.974206i	$-0.427546\pi$
$317$	14.1943	−	2.73573i	0.797232	−	0.153654i	0.571571	+	0.820552i	$0.306334\pi$
$318$	−1.88225	−	7.75874i	−0.105551	−	0.435089i
$319$	5.61557	+	3.99883i	0.314412	+	0.223892i
$320$	2.16006	+	1.69869i	0.120751	+	0.0949596i
$321$	1.15978			0.0647329
$322$	1.87064	+	12.5499i	0.104247	+	0.699380i
$323$	−13.8463			−0.770427
$324$	−0.786053	−	0.618159i	−0.0436696	−	0.0343422i
$325$	5.07206	+	3.61180i	0.281347	+	0.200346i
$326$	3.34549	+	13.7903i	0.185289	+	0.763774i
$327$	8.11102	−	1.56327i	0.448540	−	0.0864491i
$328$	2.82968	+	9.63701i	0.156243	+	0.532115i
$329$	−28.4311	+	8.91729i	−1.56746	+	0.491626i
$330$	1.43179	−	3.13517i	0.0788172	−	0.172586i
$331$	3.08797	+	8.92209i	0.169730	+	0.490403i	0.997500	−	0.0706648i	$-0.0225121\pi$
$331$	3.08797	+	8.92209i	0.169730	+	0.490403i	−0.827770	+	0.561067i	$0.810391\pi$
$332$	−6.73441	−	3.47183i	−0.369599	−	0.190541i
$333$	−4.38653	−	5.57793i	−0.240380	−	0.305669i
$334$	−4.14418	+	10.3517i	−0.226759	+	0.566417i
$335$	13.9306	+	21.6764i	0.761109	+	1.18431i
$336$	2.04938	−	1.67334i	0.111803	−	0.0912880i
$337$	−1.96477	−	0.897279i	−0.107028	−	0.0488779i	0.361182	−	0.932495i	$-0.382373\pi$
$337$	−1.96477	−	0.897279i	−0.107028	−	0.0488779i	−0.468209	+	0.883618i	$0.655101\pi$
$338$	−6.26099	+	3.22777i	−0.340553	+	0.175567i
$339$	−1.00304	−	0.956393i	−0.0544774	−	0.0519441i
$340$	−4.37643	+	12.6449i	−0.237345	+	0.685764i
$341$	−1.23517	+	1.17773i	−0.0668880	+	0.0637775i
$342$	−1.18126	−	2.58660i	−0.0638753	−	0.139868i
$343$	−14.6421	−	11.3406i	−0.790597	−	0.612336i
$344$		−	2.59005i		−	0.139646i
$345$	5.63199	−	11.9148i	0.303216	−	0.641472i
$346$	3.25624	−	1.87999i	0.175056	−	0.101069i
$347$	−17.1478	+	6.86493i	−0.920540	+	0.368529i	−0.783039	−	0.621973i	$-0.786331\pi$
$347$	−17.1478	+	6.86493i	−0.920540	+	0.368529i	−0.137501	+	0.990502i	$0.543907\pi$
$348$	0.522468	−	5.47153i	0.0280072	−	0.293305i
$349$	0.342014	−	1.16479i	0.0183076	−	0.0623499i	−0.949833	−	0.312759i	$-0.898747\pi$
$349$	0.342014	−	1.16479i	0.0183076	−	0.0623499i	0.968140	+	0.250409i	$0.0805650\pi$
$350$	−5.78313	+	3.48175i	−0.309121	+	0.186107i
$351$	2.34163	−	0.687564i	0.124987	−	0.0366994i
$352$	0.574728	+	1.11482i	0.0306331	+	0.0594200i
$353$	−0.625912	−	6.55484i	−0.0333139	−	0.348879i	−0.996726	−	0.0808543i	$-0.974235\pi$
$353$	−0.625912	−	6.55484i	−0.0333139	−	0.348879i	0.963412	−	0.268025i	$-0.0863709\pi$
$354$	−1.05770	−	0.203856i	−0.0562163	−	0.0108348i
$355$	−0.665186	−	13.9640i	−0.0353044	−	0.741130i
$356$	−2.39162	−	16.6341i	−0.126756	−	0.881604i
$357$	10.9637	+	6.76528i	0.580261	+	0.358057i
$358$	17.2212	−	11.0674i	0.910170	−	0.584931i
$359$	9.47297	−	3.27863i	0.499964	−	0.173039i	−0.0654348	−	0.997857i	$-0.520843\pi$
$359$	9.47297	−	3.27863i	0.499964	−	0.173039i	0.565399	+	0.824818i	$0.308722\pi$
$360$	−2.73554	+	0.261212i	−0.144175	+	0.0137671i
$361$	−0.519314	+	10.9017i	−0.0273323	+	0.573776i
$362$	2.05145	−	8.45618i	0.107822	−	0.444447i
$363$	−7.12435	+	6.17329i	−0.373932	+	0.324014i
$364$	0.425386	+	6.44288i	0.0222963	+	0.337699i
$365$	14.7644	−	6.74267i	0.772803	−	0.352927i
$366$	2.23797	−	2.84581i	0.116981	−	0.148753i
$367$	−2.82842	−	4.89896i	−0.147642	−	0.255724i	0.782713	−	0.622382i	$-0.213835\pi$
$367$	−2.82842	−	4.89896i	−0.147642	−	0.255724i	−0.930356	+	0.366659i	$0.880502\pi$
$368$	2.14128	+	4.29126i	0.111622	+	0.223697i
$369$	−8.69823	−	5.02193i	−0.452812	−	0.261431i
$370$	−19.3015	−	2.77514i	−1.00344	−	0.144273i
$371$	−15.0178	+	14.8544i	−0.779686	+	0.771200i
$372$	1.30559	+	0.383355i	0.0676915	+	0.0198760i
$373$	−5.22563	−	27.1131i	−0.270573	−	1.40386i	−0.821927	−	0.569593i	$-0.807101\pi$
$373$	−5.22563	−	27.1131i	−0.270573	−	1.40386i	0.551354	−	0.834272i	$-0.314111\pi$
$374$	−4.21454	+	4.42008i	−0.217928	+	0.228557i
$375$	−6.72111	−	0.320166i	−0.347077	−	0.0165333i
$376$	−9.17385	+	6.53267i	−0.473105	+	0.336897i
$377$	10.1376	+	8.78425i	0.522111	+	0.452412i
$378$	−0.328470	+	2.62528i	−0.0168947	+	0.135030i
$379$	−25.5761	+	3.67729i	−1.31376	+	0.188890i	−0.763338	−	0.645999i	$-0.776441\pi$
$379$	−25.5761	+	3.67729i	−1.31376	+	0.188890i	−0.550419	+	0.834889i	$0.685532\pi$
$380$	−7.25434	−	2.90420i	−0.372140	−	0.148982i
$381$	5.06757	−	9.82972i	0.259620	−	0.503592i
$382$	−0.689957	+	3.57983i	−0.0353012	+	0.183160i
$383$	12.7568	+	17.9145i	0.651843	+	0.915386i	0.999755	−	0.0221415i	$-0.00704842\pi$
$383$	12.7568	+	17.9145i	0.651843	+	0.915386i	−0.347911	+	0.937527i	$0.613109\pi$
$384$	0.540641	−	0.841254i	0.0275895	−	0.0429300i
$385$	−9.06025	+	1.03304i	−0.461753	+	0.0526485i
$386$	0.463493	+	0.534899i	0.0235912	+	0.0272256i
$387$	1.78734	+	1.87451i	0.0908555	+	0.0952865i
$388$	1.18387	−	1.66252i	0.0601020	−	0.0844014i
$389$	−2.34443	−	5.85609i	−0.118867	−	0.296916i	0.856987	−	0.515337i	$-0.172333\pi$
$389$	−2.34443	−	5.85609i	−0.118867	−	0.296916i	−0.975854	+	0.218422i	$0.929909\pi$
$390$	3.35320	−	5.80791i	0.169796	−	0.294095i
$391$	−16.3361	+	16.6874i	−0.826151	+	0.843918i
$392$	−6.58956	−	2.36172i	−0.332823	−	0.119285i
$393$	2.66187	−	18.5137i	0.134274	−	0.933894i
$394$	−19.3571	−	1.84838i	−0.975197	−	0.0931201i
$395$	−11.4638	+	2.78108i	−0.576805	+	0.139931i
$396$	−1.18526	−	0.410223i	−0.0595617	−	0.0206145i
$397$	12.6199	+	3.06156i	0.633375	+	0.153655i	0.539577	−	0.841936i	$-0.318584\pi$
$397$	12.6199	+	3.06156i	0.633375	+	0.153655i	0.0937978	+	0.995591i	$0.470099\pi$
$398$	1.70136	+	1.09340i	0.0852816	+	0.0548071i
$399$	−4.25094	+	6.20732i	−0.212813	+	0.310755i
$400$	−1.67081	+	1.92821i	−0.0835403	+	0.0964106i
$401$	6.07902	−	0.289579i	0.303572	−	0.0144609i	0.104757	−	0.994498i	$-0.466594\pi$
$401$	6.07902	−	0.289579i	0.303572	−	0.0144609i	0.198815	+	0.980037i	$0.436291\pi$
$402$	7.37053	−	5.79625i	0.367609	−	0.289091i
$403$	−2.61031	+	2.05277i	−0.130029	+	0.102256i
$404$	11.7258	−	0.558566i	0.583378	−	0.0277897i
$405$	1.79954	−	2.07678i	0.0894200	−	0.103196i
$406$	−13.1151	+	6.28246i	−0.650890	+	0.311793i
$407$	−7.48739	−	4.81185i	−0.371136	−	0.238515i
$408$	4.73206	+	1.14799i	0.234272	+	0.0568338i
$409$	−34.2339	−	11.8485i	−1.69276	−	0.585870i	−0.700906	−	0.713253i	$-0.747221\pi$
$409$	−34.2339	−	11.8485i	−1.69276	−	0.585870i	−0.991854	+	0.127384i	$0.959342\pi$
$410$	−26.8223	+	6.50702i	−1.32466	+	0.321359i
$411$	−21.3439	−	2.03810i	−1.05282	−	0.100532i
$412$	2.42221	−	16.8468i	0.119333	−	0.829983i
$413$	0.981322	+	2.67564i	0.0482877	+	0.131660i
$414$	−4.51103	−	1.62807i	−0.221705	−	0.0800155i
$415$	10.4103	−	18.0311i	0.511020	−	0.885112i
$416$	0.907036	+	2.26567i	0.0444711	+	0.111083i
$417$	−12.9264	+	18.1526i	−0.633008	+	0.888935i
$418$	−2.46119	−	2.58122i	−0.120381	−	0.126252i
$419$	2.22870	+	2.57205i	0.108879	+	0.125653i	0.807573	−	0.589767i	$-0.200781\pi$
$419$	2.22870	+	2.57205i	0.108879	+	0.125653i	−0.698694	+	0.715421i	$0.746235\pi$
$420$	4.32512	+	5.84406i	0.211044	+	0.285161i
$421$	12.3391	−	19.2000i	0.601371	−	0.935752i	−0.398456	−	0.917187i	$-0.630454\pi$
$421$	12.3391	−	19.2000i	0.601371	−	0.935752i	0.999828	−	0.0185648i	$-0.00590969\pi$
$422$	3.74649	+	5.26121i	0.182376	+	0.256112i
$423$	2.13137	−	11.0586i	0.103631	−	0.537687i
$424$	−3.65839	+	7.09628i	−0.177667	+	0.344626i
$425$	−11.5336	−	4.61736i	−0.559463	−	0.223975i
$426$	−5.03552	+	0.723998i	−0.243972	+	0.0350778i
$427$	−9.50452	−	1.18919i	−0.459956	−	0.0575487i
$428$	−0.876507	−	0.759497i	−0.0423675	−	0.0367117i
$429$	2.49339	−	1.77553i	0.120382	−	0.0857236i
$430$	7.10934	+	0.338660i	0.342843	+	0.0163316i
$431$	−8.23528	+	8.63692i	−0.396680	+	0.416026i	−0.891537	−	0.452949i	$-0.850372\pi$
$431$	−8.23528	+	8.63692i	−0.396680	+	0.416026i	0.494857	+	0.868975i	$0.335221\pi$
$432$	0.189251	+	0.981929i	0.00910535	+	0.0472431i
$433$	−30.2184	−	8.87291i	−1.45220	−	0.426405i	−0.541932	−	0.840422i	$-0.682307\pi$
$433$	−30.2184	−	8.87291i	−1.45220	−	0.426405i	−0.910269	+	0.414017i	$0.864125\pi$
$434$	−0.912731	−	3.48246i	−0.0438125	−	0.167163i
$435$	14.9503	+	2.14953i	0.716813	+	0.103062i
$436$	−7.15362	−	4.13015i	−0.342596	−	0.197798i
$437$	−9.28009	−	9.99277i	−0.443927	−	0.478019i
$438$	−2.95329	−	5.11525i	−0.141114	−	0.244416i
$439$	1.91723	−	2.43795i	0.0915042	−	0.116357i	−0.738145	−	0.674642i	$-0.764298\pi$
$439$	1.91723	−	2.43795i	0.0915042	−	0.116357i	0.829649	+	0.558285i	$0.188540\pi$
$440$	−3.13517	+	1.43179i	−0.149464	+	0.0682577i
$441$	6.39886	−	2.83806i	0.304708	−	0.135146i
$442$	−8.98095	+	7.78204i	−0.427180	+	0.370154i
$443$	−7.18065	+	29.5990i	−0.341163	+	1.40629i	0.500241	+	0.865886i	$0.333245\pi$
$443$	−7.18065	+	29.5990i	−0.341163	+	1.40629i	−0.841404	+	0.540407i	$0.818270\pi$
$444$	−0.337647	+	7.08808i	−0.0160240	+	0.336386i
$445$	45.9710	−	4.38970i	2.17924	−	0.208092i
$446$	15.0793	−	5.21899i	0.714025	−	0.247127i
$447$	−8.08292	+	5.19458i	−0.382309	+	0.245695i
$448$	−2.64462	−	0.0774334i	−0.124946	−	0.00365838i
$449$	−1.74981	−	12.1702i	−0.0825787	−	0.574347i	−0.988537	−	0.150980i	$-0.951757\pi$
$449$	−1.74981	−	12.1702i	−0.0825787	−	0.574347i	0.905958	−	0.423367i	$-0.139152\pi$
$450$	−0.121400	−	2.54850i	−0.00572285	−	0.120137i
$451$	−12.3698	−	2.38408i	−0.582471	−	0.112262i
$452$	0.131740	+	1.37964i	0.00619652	+	0.0648929i
$453$	−6.12505	−	11.8809i	−0.287780	−	0.558215i
$454$	−13.4544	+	3.95056i	−0.631444	+	0.185409i
$455$	−17.7405	+	0.325195i	−0.831687	+	0.0152454i
$456$	−0.801127	+	2.72839i	−0.0375162	+	0.127768i
$457$	−2.08082	+	21.7914i	−0.0973368	+	1.01936i	0.806429	+	0.591330i	$0.201397\pi$
$457$	−2.08082	+	21.7914i	−0.0973368	+	1.01936i	−0.903766	+	0.428027i	$0.859209\pi$
$458$	14.2715	−	5.71347i	0.666866	−	0.266973i
$459$	−4.21696	+	2.43466i	−0.196831	+	0.113640i
$460$	−12.0589	+	5.31644i	−0.562250	+	0.247880i
$461$			19.2884i			0.898349i	0.893444	+	0.449174i	$0.148282\pi$
$461$			19.2884i			0.898349i	−0.893444	+	0.449174i	$0.851718\pi$
$462$	0.687629	+	3.24640i	0.0319914	+	0.151036i
$463$	5.13309	+	11.2399i	0.238555	+	0.522362i	0.990607	−	0.136742i	$-0.0436630\pi$
$463$	5.13309	+	11.2399i	0.238555	+	0.522362i	−0.752052	+	0.659104i	$0.770936\pi$
$464$	−3.97795	+	3.79296i	−0.184672	+	0.176084i
$465$	−1.22297	+	3.53354i	−0.0567138	+	0.163864i
$466$	3.87364	+	3.69351i	0.179443	+	0.171098i
$467$	7.52251	−	3.87813i	0.348100	−	0.179458i	−0.275305	−	0.961357i	$-0.588779\pi$
$467$	7.52251	−	3.87813i	0.348100	−	0.179458i	0.623406	+	0.781899i	$0.285749\pi$
$468$	−2.21994	−	1.01381i	−0.102617	−	0.0468635i
$469$	−23.1963	−	8.79664i	−1.07111	−	0.406191i
$470$	−16.7318	−	26.0352i	−0.771780	−	1.20091i
$471$	−0.674679	+	1.68527i	−0.0310876	+	0.0776530i
$472$	0.665862	+	0.846713i	0.0306488	+	0.0389731i
$473$	2.88743	+	1.48857i	0.132764	+	0.0684447i
$474$	1.40401	+	4.05662i	0.0644883	+	0.186327i
$475$	3.01386	−	6.59943i	0.138285	−	0.302803i
$476$	−3.85551	−	12.2926i	−0.176717	−	0.563429i
$477$	−2.24929	−	7.66039i	−0.102988	−	0.350745i
$478$	17.6447	−	3.40073i	0.807049	−	0.155546i
$479$	2.23237	+	9.20194i	0.101999	+	0.420447i	0.999801	−	0.0199531i	$-0.00635168\pi$
$479$	2.23237	+	9.20194i	0.101999	+	0.420447i	−0.897802	+	0.440400i	$0.854837\pi$
$480$	2.23844	+	1.59398i	0.102170	+	0.0727551i
$481$	−13.6128	−	10.7053i	−0.620692	−	0.488118i
$482$	4.42689			0.201639
$483$	2.46567	+	12.4467i	0.112192	+	0.566345i
$484$	9.42687			0.428494
$485$	4.40859	+	3.46695i	0.200184	+	0.157426i
$486$	−0.814576	−	0.580057i	−0.0369499	−	0.0263119i
$487$	−6.20107	−	25.5612i	−0.280997	−	1.15829i	−0.920890	−	0.389822i	$-0.872536\pi$
$487$	−6.20107	−	25.5612i	−0.280997	−	1.15829i	0.639893	−	0.768464i	$-0.278979\pi$
$488$	−3.55496	+	0.685161i	−0.160925	+	0.0310158i
$489$	3.99787	+	13.6155i	0.180790	+	0.615714i
$490$	7.34423	−	17.7787i	0.331778	−	0.803158i
$491$	−11.1132	+	24.3345i	−0.501532	+	1.09820i	0.474437	+	0.880290i	$0.342652\pi$
$491$	−11.1132	+	24.3345i	−0.501532	+	1.09820i	−0.975968	+	0.217912i	$0.930076\pi$
$492$	3.28502	+	9.49145i	0.148100	+	0.427908i
$493$	−23.7887	−	12.2639i	−1.07139	−	0.552339i
$494$	−4.28983	−	5.45496i	−0.193009	−	0.245430i
$495$	1.28099	−	3.19975i	0.0575761	−	0.143818i
$496$	−0.735652	−	1.14470i	−0.0330318	−	0.0513984i
$497$	8.51276	+	10.4258i	0.381850	+	0.467661i
$498$	−6.89198	−	3.14746i	−0.308837	−	0.141041i
$499$	11.4696	−	5.91300i	0.513451	−	0.264702i	−0.181971	−	0.983304i	$-0.558248\pi$
$499$	11.4696	−	5.91300i	0.513451	−	0.264702i	0.695422	+	0.718602i	$0.255217\pi$
$500$	4.86981	+	4.64335i	0.217785	+	0.207657i
$501$	−3.64693	+	10.5371i	−0.162933	+	0.470764i
$502$	−12.1789	+	11.6126i	−0.543571	+	0.518294i
$503$	15.2300	+	33.3490i	0.679071	+	1.48696i	0.863624	+	0.504136i	$0.168189\pi$
$503$	15.2300	+	33.3490i	0.679071	+	1.48696i	−0.184553	+	0.982823i	$0.559084\pi$
$504$	1.96744	−	1.76895i	0.0876365	−	0.0787955i
$505$			32.2587i			1.43549i
$506$	−6.01463	−	0.0791668i	−0.267383	−	0.00351939i
$507$	−6.10032	+	3.52202i	−0.270925	+	0.156418i
$508$	−10.2669	+	4.11025i	−0.455520	+	0.182363i
$509$	−4.01542	+	42.0514i	−0.177980	+	1.86390i	0.260921	+	0.965360i	$0.415974\pi$
$509$	−4.01542	+	42.0514i	−0.177980	+	1.86390i	−0.438902	+	0.898535i	$0.644632\pi$
$510$	−3.76981	+	12.8388i	−0.166930	+	0.568511i
$511$	−7.56432	+	13.6746i	−0.334626	+	0.604929i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−1.30300	−	2.52747i	−0.0575288	−	0.111590i
$514$	1.09217	+	11.4377i	0.0481735	+	0.504496i
$515$	45.9255	+	8.85142i	2.02372	+	0.390040i
$516$	−0.123240	−	2.58712i	−0.00542532	−	0.113891i
$517$	−2.01026	−	13.9817i	−0.0884112	−	0.614913i
$518$	16.5270	−	8.90741i	0.726156	−	0.391369i
$519$	3.16309	−	2.03280i	0.138844	−	0.0892299i
$520$	−6.33755	+	2.19345i	−0.277920	+	0.0961891i
$521$	−0.807736	+	0.0771295i	−0.0353876	+	0.00337910i	−0.112735	−	0.993625i	$-0.535961\pi$
$521$	−0.807736	+	0.0771295i	−0.0353876	+	0.00337910i	0.0773472	+	0.997004i	$0.475355\pi$
$522$	0.261530	−	5.49020i	0.0114469	−	0.240299i
$523$	−0.323648	+	1.33410i	−0.0141521	+	0.0583359i	−0.978450	−	0.206485i	$-0.933798\pi$
$523$	−0.323648	+	1.33410i	−0.0141521	+	0.0583359i	0.964298	+	0.264821i	$0.0853128\pi$
$524$	−14.1356	+	12.2486i	−0.617517	+	0.535082i
$525$	−5.61091	+	3.75298i	−0.244880	+	0.163793i
$526$	−9.19020	+	4.19702i	−0.400712	+	0.182999i
$527$	4.09574	−	5.20816i	0.178413	−	0.226871i
$528$	0.627123	+	1.08621i	0.0272920	+	0.0472711i
$529$	−22.9920	−	0.605365i	−0.999654	−	0.0263202i
$530$	−19.0000	−	10.9697i	−0.825307	−	0.476491i
$531$	−1.06621	−	0.153297i	−0.0462694	−	0.00665253i
$532$	7.27757	−	1.90741i	0.315523	−	0.0826965i
$533$	−23.5190	−	6.90579i	−1.01872	−	0.299123i
$534$	−3.18039	−	16.5014i	−0.137629	−	0.714087i
$535$	2.19933	−	2.30659i	0.0950852	−	0.0997224i
$536$	−9.36602	−	0.446158i	−0.404550	−	0.0192711i
$537$	16.6751	−	11.8743i	0.719584	−	0.512414i
$538$	−16.8044	−	14.5611i	−0.724488	−	0.627772i
$539$	6.42010	−	5.98881i	0.276533	−	0.257956i
$540$	−2.72001	+	0.391078i	−0.117051	+	0.0168293i
$541$	−8.55104	−	3.42332i	−0.367638	−	0.147180i	0.180485	−	0.983578i	$-0.442233\pi$
$541$	−8.55104	−	3.42332i	−0.367638	−	0.147180i	−0.548123	+	0.836398i	$0.684657\pi$
$542$	0.706550	−	1.37052i	0.0303489	−	0.0588687i
$543$	1.64676	−	8.54421i	0.0706693	−	0.366667i
$544$	−2.82448	−	3.96643i	−0.121099	−	0.170059i
$545$	12.2721	−	19.0957i	0.525678	−	0.817970i
$546$	0.731469	+	6.41535i	0.0313040	+	0.274551i
$547$	12.6243	+	14.5693i	0.539777	+	0.622936i	0.958471	−	0.285191i	$-0.0920572\pi$
$547$	12.6243	+	14.5693i	0.539777	+	0.622936i	−0.418693	+	0.908128i	$0.637512\pi$
$548$	14.7960	+	15.5176i	0.632054	+	0.662879i
$549$	2.10003	−	2.94907i	0.0896270	−	0.125863i
$550$	−1.18935	−	2.97084i	−0.0507139	−	0.126677i
$551$	7.81473	−	13.5355i	0.332919	−	0.576632i
$552$	2.34305	+	4.18451i	0.0997266	+	0.178105i
$553$	7.27899	−	8.71826i	0.309534	−	0.370738i
$554$	0.519871	−	3.61578i	0.0220872	−	0.153620i
$555$	−19.4117	−	1.85359i	−0.823981	−	0.0786806i
$556$	21.6565	−	5.25381i	0.918440	−	0.222811i
$557$	12.0314	+	4.16412i	0.509789	+	0.176440i	0.569840	−	0.821756i	$-0.307005\pi$
$557$	12.0314	+	4.16412i	0.509789	+	0.176440i	−0.0600512	+	0.998195i	$0.519126\pi$
$558$	1.32235	+	0.320798i	0.0559795	+	0.0135805i
$559$	5.31754	+	3.41738i	0.224908	+	0.144540i
$560$	0.558339	−	7.24900i	0.0235941	−	0.306326i
$561$	−3.99945	+	4.61561i	−0.168857	+	0.194871i
$562$	13.0971	−	0.623891i	0.552467	−	0.0263173i
$563$	24.6059	−	19.3503i	1.03701	−	0.815517i	0.0539065	−	0.998546i	$-0.482833\pi$
$563$	24.6059	−	19.3503i	1.03701	−	0.815517i	0.983107	+	0.183029i	$0.0585903\pi$
$564$	−8.85262	+	6.96178i	−0.372763	+	0.293144i
$565$	−3.80416	+	0.181215i	−0.160042	+	0.00762375i
$566$	14.1769	−	16.3611i	0.595901	−	0.687707i
$567$	−0.203182	+	2.63794i	−0.00853283	+	0.110783i
$568$	4.27971	+	2.75040i	0.179573	+	0.115404i
$569$	16.4238	+	3.98437i	0.688522	+	0.167034i	0.564731	−	0.825275i	$-0.308980\pi$
$569$	16.4238	+	3.98437i	0.688522	+	0.167034i	0.123791	+	0.992308i	$0.460495\pi$
$570$	−7.38431	−	2.55573i	−0.309295	−	0.107048i
$571$	36.7472	−	8.91478i	1.53782	−	0.373072i	0.624736	−	0.780836i	$-0.285207\pi$
$571$	36.7472	−	8.91478i	1.53782	−	0.373072i	0.913087	+	0.407764i	$0.133691\pi$
$572$	−3.04710	−	0.290963i	−0.127406	−	0.0121658i
$573$	−0.518840	+	3.60861i	−0.0216748	+	0.150752i
$574$	17.0310	−	20.3985i	0.710859	−	0.851417i
$575$	−4.39778	−	11.4184i	−0.183400	−	0.476181i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−3.10028	−	7.74413i	−0.129066	−	0.322392i	0.849733	−	0.527213i	$-0.176763\pi$
$577$	−3.10028	−	7.74413i	−0.129066	−	0.322392i	−0.978799	+	0.204821i	$0.934339\pi$
$578$	3.89236	−	5.46605i	0.161901	−	0.227358i
$579$	0.488419	+	0.512239i	0.0202980	+	0.0212879i
$580$	−9.89105	−	11.4149i	−0.410703	−	0.473977i
$581$	2.27090	+	19.9169i	0.0942129	+	0.826294i
$582$	1.10343	−	1.71696i	0.0457385	−	0.0711704i
$583$	−5.80848	−	8.15687i	−0.240563	−	0.337823i
$584$	−1.11783	+	5.79984i	−0.0462561	+	0.239999i
$585$	3.07305	−	5.96088i	0.127055	−	0.246452i
$586$	−28.5045	−	11.4115i	−1.17751	−	0.471405i
$587$	11.6511	−	1.67518i	0.480893	−	0.0691420i	0.102395	−	0.994744i	$-0.467350\pi$
$587$	11.6511	−	1.67518i	0.480893	−	0.0691420i	0.378499	+	0.925602i	$0.376440\pi$
$588$	−6.69447	−	2.04550i	−0.276075	−	0.0843552i
$589$	2.92419	+	2.53383i	0.120489	+	0.104405i
$590$	−2.41118	+	1.71699i	−0.0992666	+	0.0706874i
$591$	−19.4231	−	0.925238i	−0.798961	−	0.0380592i
$592$	4.89689	−	5.13571i	0.201261	−	0.211076i
$593$	1.77785	+	9.22434i	0.0730074	+	0.378798i	0.999993	+	0.00370170i	$0.00117829\pi$
$593$	1.77785	+	9.22434i	0.0730074	+	0.378798i	−0.926986	+	0.375096i	$0.877610\pi$
$594$	−1.20344	−	0.353362i	−0.0493777	−	0.0144986i
$595$	34.2456	−	8.97555i	1.40393	−	0.367962i
$596$	9.51039	+	1.36739i	0.389561	+	0.0560104i
$597$	1.75146	+	1.01121i	0.0716825	+	0.0413859i
$598$	−11.6355	−	1.26580i	−0.475811	−	0.0517623i
$599$	4.15681	+	7.19981i	0.169843	+	0.294176i	0.938364	−	0.345647i	$-0.112341\pi$
$599$	4.15681	+	7.19981i	0.169843	+	0.294176i	−0.768522	+	0.639824i	$0.779007\pi$
$600$	−1.57716	+	2.00553i	−0.0643875	+	0.0818753i
$601$	−38.6854	+	17.6670i	−1.57801	+	0.720654i	−0.995728	−	0.0923326i	$-0.970568\pi$
$601$	−38.6854	+	17.6670i	−1.57801	+	0.720654i	−0.582283	+	0.812986i	$0.697840\pi$
$602$	−5.69593	+	3.80984i	−0.232149	+	0.155278i
$603$	7.08639	−	6.14039i	0.288580	−	0.250056i
$604$	−3.15136	+	12.9901i	−0.128227	+	0.528558i
$605$	−1.23260	+	25.8755i	−0.0501124	+	1.05199i
$606$	11.6859	−	1.11587i	0.474707	−	0.0453290i
$607$	31.7316	−	10.9824i	1.28795	−	0.445762i	0.404604	−	0.914492i	$-0.367409\pi$
$607$	31.7316	−	10.9824i	1.28795	−	0.445762i	0.883342	+	0.468730i	$0.155288\pi$
$608$	2.39216	−	1.53735i	0.0970151	−	0.0623478i
$609$	−12.8013	+	6.89938i	−0.518734	+	0.279577i
$610$	−1.41585	−	9.84747i	−0.0573262	−	0.398712i
$611$	−1.30779	−	27.4539i	−0.0529075	−	1.11066i
$612$	4.78133	+	0.921525i	0.193274	+	0.0372505i
$613$	3.25889	+	34.1286i	0.131625	+	1.37844i	0.784101	+	0.620633i	$0.213124\pi$
$613$	3.25889	+	34.1286i	0.131625	+	1.37844i	−0.652476	+	0.757810i	$0.726270\pi$
$614$	−8.61454	−	16.7099i	−0.347655	−	0.674356i
$615$	−26.4823	+	7.77590i	−1.06787	+	0.313555i
$616$	1.60626	−	2.90376i	0.0647181	−	0.116996i
$617$	6.38875	−	21.7581i	0.257201	−	0.875947i	−0.725101	−	0.688643i	$-0.758207\pi$
$617$	6.38875	−	21.7581i	0.257201	−	0.875947i	0.982302	−	0.187304i	$-0.0599750\pi$
$618$	1.61786	−	16.9430i	0.0650798	−	0.681547i
$619$	18.6751	−	7.47639i	0.750616	−	0.300501i	0.0353701	−	0.999374i	$-0.488739\pi$
$619$	18.6751	−	7.47639i	0.750616	−	0.300501i	0.715246	+	0.698873i	$0.246315\pi$
$620$	3.23823	−	1.86959i	0.130050	−	0.0750847i
$621$	−4.58339	−	1.41159i	−0.183925	−	0.0566450i
$622$			24.2025i			0.970431i
$623$	−33.0630	+	29.7275i	−1.32464	+	1.19101i
$624$	1.01381	+	2.21994i	0.0405850	+	0.0888688i
$625$	−22.6148	+	21.5631i	−0.904591	+	0.862526i
$626$	−9.53106	+	27.5382i	−0.380938	+	1.10065i
$627$	−2.58122	−	2.46119i	−0.103084	−	0.0982905i
$628$	1.61350	−	0.831819i	0.0643858	−	0.0331932i
$629$	31.4308	+	14.3540i	1.25323	+	0.572330i
$630$	4.59829	+	5.63165i	0.183200	+	0.224370i
$631$	−0.973394	−	1.51463i	−0.0387502	−	0.0602965i	0.821338	−	0.570442i	$-0.193228\pi$
$631$	−0.973394	−	1.51463i	−0.0387502	−	0.0602965i	−0.860088	+	0.510145i	$0.829592\pi$
$632$	1.59544	−	3.98522i	0.0634632	−	0.158523i
$633$	3.99259	+	5.07699i	0.158691	+	0.201792i
$634$	−12.8486	−	6.62391i	−0.510283	−	0.263069i
$635$	−9.93965	−	28.7187i	−0.394443	−	1.13967i
$636$	−3.31659	+	7.26231i	−0.131511	+	0.287970i
$637$	13.5432	−	10.4127i	0.536601	−	0.412565i
$638$	−1.94222	−	6.61461i	−0.0768934	−	0.261875i
$639$	−4.99537	+	0.962778i	−0.197614	+	0.0380869i
$640$	−0.647861	−	2.67052i	−0.0256089	−	0.105561i
$641$	7.68066	+	5.46937i	0.303368	+	0.216027i	0.721595	−	0.692315i	$-0.243409\pi$
$641$	7.68066	+	5.46937i	0.303368	+	0.216027i	−0.418228	+	0.908342i	$0.637349\pi$
$642$	−0.911652	−	0.716931i	−0.0359800	−	0.0282950i
$643$	−13.6509			−0.538337			−0.269169	−	0.963093i	$-0.586749\pi$
$643$	−13.6509			−0.538337			−0.269169	+	0.963093i	$0.586749\pi$
$644$	6.28743	−	11.0213i	0.247759	−	0.434299i
$645$	7.11740			0.280247
$646$	10.8839	+	8.55919i	0.428221	+	0.336757i
$647$	22.8024	+	16.2375i	0.896457	+	0.638364i	0.932572	−	0.360984i	$-0.117559\pi$
$647$	22.8024	+	16.2375i	0.896457	+	0.638364i	−0.0361155	+	0.999348i	$0.511498\pi$
$648$	0.235759	+	0.971812i	0.00926149	+	0.0381764i
$649$	−1.32662	+	0.255685i	−0.0520744	+	0.0100365i
$650$	−1.75424	−	5.97440i	−0.0688071	−	0.234335i
$651$	−1.07740	−	3.43509i	−0.0422266	−	0.134632i
$652$	5.89486	−	12.9079i	0.230861	−	0.505514i
$653$	−6.31500	−	18.2460i	−0.247125	−	0.714021i	−0.998531	−	0.0541811i	$-0.982745\pi$
$653$	−6.31500	−	18.2460i	−0.247125	−	0.714021i	0.751406	−	0.659840i	$-0.229376\pi$
$654$	−7.34204	−	3.78509i	−0.287097	−	0.148009i
$655$	−31.7724	−	40.4019i	−1.24145	−	1.57863i
$656$	3.73292	−	9.32439i	0.145746	−	0.364056i
$657$	−3.19334	−	4.96893i	−0.124584	−	0.193857i
$658$	27.8607	+	10.5655i	1.08612	+	0.411886i
$659$	−17.4375	−	7.96345i	−0.679270	−	0.310212i	0.0457375	−	0.998953i	$-0.485436\pi$
$659$	−17.4375	−	7.96345i	−0.679270	−	0.310212i	−0.725007	+	0.688741i	$0.758164\pi$
$660$	−3.06350	+	1.57934i	−0.119246	+	0.0614758i
$661$	−10.1956	−	9.72151i	−0.396564	−	0.378123i	0.465393	−	0.885104i	$-0.345913\pi$
$661$	−10.1956	−	9.72151i	−0.396564	−	0.378123i	−0.861957	+	0.506981i	$0.830761\pi$
$662$	3.08797	−	8.92209i	0.120017	−	0.346767i
$663$	−8.60050	+	8.20056i	−0.334016	+	0.318483i
$664$	3.14746	+	6.89198i	0.122145	+	0.267461i
$665$	4.28400	+	20.2254i	0.166126	+	0.784306i
$666$			7.09612i			0.274969i
$667$	−7.09293	−	25.3877i	−0.274639	−	0.983016i
$668$	9.65651	−	5.57519i	0.373622	−	0.215711i
$669$	14.8139	−	5.93059i	0.572738	−	0.229290i
$670$	2.44929	−	25.6501i	0.0946243	−	0.990951i
$671$	1.27930	−	4.35691i	0.0493870	−	0.168197i
$672$	−2.64531	+	0.0484903i	−0.102045	+	0.00187055i
$673$	−19.5901	+	5.75218i	−0.755144	+	0.221730i	−0.636574	−	0.771215i	$-0.719649\pi$
$673$	−19.5901	+	5.75218i	−0.755144	+	0.221730i	−0.118570	+	0.992946i	$0.537831\pi$
$674$	0.989750	+	1.91985i	0.0381237	+	0.0739497i
$675$	−0.242525	−	2.53984i	−0.00933479	−	0.0977584i
$676$	6.91675	+	1.33309i	0.266029	+	0.0512728i
$677$	1.50740	+	31.6443i	0.0579342	+	1.21619i	0.821405	+	0.570345i	$0.193191\pi$
$677$	1.50740	+	31.6443i	0.0579342	+	1.21619i	−0.763471	+	0.645842i	$0.776506\pi$
$678$	0.197237	+	1.37181i	0.00757483	+	0.0526841i
$679$	−5.39755	−	0.158038i	−0.207139	−	0.00606495i
$680$	11.2566	−	7.23421i	0.431673	−	0.277419i
$681$	−13.2511	+	4.58627i	−0.507785	+	0.175746i
$682$	1.69893	−	0.162228i	0.0650554	−	0.00621203i
$683$	1.52921	−	32.1021i	0.0585136	−	1.22835i	−0.758477	−	0.651700i	$-0.774056\pi$
$683$	1.52921	−	32.1021i	0.0585136	−	1.22835i	0.816990	−	0.576652i	$-0.195641\pi$
$684$	−0.670397	+	2.76342i	−0.0256333	+	0.105662i
$685$	−44.5284	+	38.5841i	−1.70134	+	1.47422i
$686$	4.49913	+	17.9655i	0.171778	+	0.685925i
$687$	13.9835	−	6.38606i	0.533505	−	0.243643i
$688$	−1.60106	+	2.03592i	−0.0610399	+	0.0776186i
$689$	−9.74216	−	16.8739i	−0.371147	−	0.642845i
$690$	−11.7923	+	5.88421i	−0.448925	+	0.224008i
$691$	−2.99964	−	1.73184i	−0.114112	−	0.0658824i	0.441858	−	0.897085i	$-0.354320\pi$
$691$	−2.99964	−	1.73184i	−0.114112	−	0.0658824i	−0.555970	+	0.831203i	$0.687653\pi$
$692$	−3.72171	−	0.535101i	−0.141478	−	0.0203415i
$693$	0.841320	+	3.21000i	0.0319591	+	0.121938i
$694$	17.7227	+	5.20384i	0.672743	+	0.197535i
$695$	11.5893	+	60.1312i	0.439609	+	2.28091i
$696$	−3.79296	+	3.97795i	−0.143772	+	0.150784i
$697$	48.8514	+	2.32708i	1.85038	+	0.0881444i
$698$	−0.988868	+	0.704170i	−0.0374292	+	0.0266532i
$699$	4.04500	+	3.50501i	0.152996	+	0.132572i
$700$	6.69812	+	0.838054i	0.253165	+	0.0316755i
$701$	14.2879	−	2.05429i	0.539646	−	0.0775893i	0.132898	−	0.991130i	$-0.457572\pi$
$701$	14.2879	−	2.05429i	0.539646	−	0.0775893i	0.406748	+	0.913540i	$0.366663\pi$
$702$	−2.26567	−	0.907036i	−0.0855121	−	0.0342339i
$703$	−9.24625	+	17.9352i	−0.348729	+	0.676439i
$704$	0.237367	−	1.23158i	0.00894612	−	0.0464169i
$705$	−17.9516	−	25.2095i	−0.676098	−	0.949446i
$706$	−3.55994	+	5.53937i	−0.133980	+	0.208477i
$707$	−18.4764	−	24.9652i	−0.694877	−	0.938911i
$708$	0.705396	+	0.814071i	0.0265104	+	0.0305947i
$709$	−20.5571	−	21.5596i	−0.772036	−	0.809688i	0.213892	−	0.976857i	$-0.431386\pi$
$709$	−20.5571	−	21.5596i	−0.772036	−	0.809688i	−0.985928	+	0.167169i	$0.946537\pi$
$710$	−8.10908	+	11.3876i	−0.304328	+	0.427369i
$711$	1.59544	+	3.98522i	0.0598337	+	0.149457i
$712$	−8.40256	+	14.5537i	−0.314899	+	0.545422i
$713$	6.50376	−	0.534757i	0.243568	−	0.0200268i
$714$	−4.43604	−	12.0952i	−0.166015	−	0.452651i
$715$	1.19708	−	8.32585i	0.0447681	−	0.311369i
$716$	−20.3782	−	1.94588i	−0.761570	−	0.0727211i
$717$	17.4629	−	4.23645i	0.652163	−	0.158213i
$718$	−9.47297	−	3.27863i	−0.353528	−	0.122357i
$719$	−32.2458	−	7.82275i	−1.20257	−	0.291739i	−0.416069	−	0.909333i	$-0.636593\pi$
$719$	−32.2458	−	7.82275i	−1.20257	−	0.291739i	−0.786497	+	0.617594i	$0.788108\pi$
$720$	2.31175	+	1.48567i	0.0861537	+	0.0553676i
$721$	−40.6117	+	19.4541i	−1.51246	+	0.724507i
$722$	7.14722	−	8.24833i	0.265992	−	0.306971i
$723$	4.42187	−	0.210640i	0.164451	−	0.00783378i
$724$	−6.83981	+	5.37889i	−0.254200	+	0.199905i
$725$	11.0232	−	8.66876i	0.409392	−	0.321950i
$726$	9.41619	−	0.448548i	0.349468	−	0.0166472i
$727$	−10.7214	+	12.3732i	−0.397636	+	0.458896i	−0.918895	−	0.394502i	$-0.870917\pi$
$727$	−10.7214	+	12.3732i	−0.397636	+	0.458896i	0.521259	+	0.853398i	$0.325463\pi$
$728$	3.64835	−	5.32741i	0.135217	−	0.197447i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−15.7736	−	3.82664i	−0.583808	−	0.141630i
$731$	−11.9181	−	4.12491i	−0.440809	−	0.152565i
$732$	−3.51833	+	0.853537i	−0.130041	+	0.0315476i
$733$	10.3869	+	0.991830i	0.383649	+	0.0366341i	0.285099	−	0.958498i	$-0.407973\pi$
$733$	10.3869	+	0.991830i	0.383649	+	0.0366341i	0.0985502	+	0.995132i	$0.468580\pi$
$734$	−0.805051	+	5.59926i	−0.0297150	+	0.206672i
$735$	6.48996	−	18.1080i	0.239386	−	0.667922i
$736$	0.969517	−	4.69681i	0.0357369	−	0.173127i
$737$	5.88030	−	10.1850i	0.216604	−	0.375169i
$738$	3.73292	+	9.32439i	0.137411	+	0.343236i
$739$	−10.1891	+	14.3085i	−0.374811	+	0.526348i	−0.958297	−	0.285775i	$-0.907749\pi$
$739$	−10.1891	+	14.3085i	−0.374811	+	0.526348i	0.583486	+	0.812123i	$0.301688\pi$
$740$	13.4565	+	14.1128i	0.494672	+	0.518797i
$741$	−4.54453	−	5.24467i	−0.166947	−	0.192668i
$742$	20.9872	−	2.39293i	0.770463	−	0.0878472i
$743$	8.91549	−	13.8728i	0.327078	−	0.508943i	−0.638304	−	0.769784i	$-0.720364\pi$
$743$	8.91549	−	13.8728i	0.327078	−	0.508943i	0.965382	+	0.260842i	$0.0840001\pi$
$744$	−0.789286	−	1.10840i	−0.0289366	−	0.0406358i
$745$	−4.99682	+	25.9259i	−0.183069	+	0.949853i
$746$	−12.6526	+	24.5426i	−0.463245	+	0.898570i
$747$	−7.03394	−	2.81596i	−0.257358	−	0.103031i
$748$	6.04516	−	0.869163i	0.221033	−	0.0317797i
$749$	−0.380954	+	3.04476i	−0.0139198	+	0.111253i
$750$	5.08523	+	4.40638i	0.185687	+	0.160898i
$751$	28.8421	−	20.5384i	1.05246	−	0.749456i	0.0834620	−	0.996511i	$-0.473402\pi$
$751$	28.8421	−	20.5384i	1.05246	−	0.749456i	0.969001	+	0.247055i	$0.0794629\pi$
$752$	11.2494	+	0.535873i	0.410222	+	0.0195413i
$753$	−11.6126	+	12.1789i	−0.423185	+	0.443824i
$754$	−2.53860	−	13.1715i	−0.0924504	−	0.479678i
$755$	−35.2439	−	10.3486i	−1.28266	−	0.376623i
$756$	1.88104	−	1.86056i	0.0684126	−	0.0676681i
$757$	37.2975	+	5.36257i	1.35560	+	0.194906i	0.781513	−	0.623889i	$-0.214448\pi$
$757$	37.2975	+	5.36257i	1.35560	+	0.194906i	0.574086	+	0.818795i	$0.305357\pi$
$758$	22.3773	+	12.9196i	0.812781	+	0.469260i
$759$	−6.01158	+	0.207110i	−0.218207	+	0.00751763i
$760$	3.90704	+	6.76719i	0.141723	+	0.245472i
$761$	−0.774627	+	0.985019i	−0.0280802	+	0.0357069i	−0.799890	−	0.600146i	$-0.795109\pi$
$761$	−0.774627	+	0.985019i	−0.0280802	+	0.0357069i	0.771810	+	0.635853i	$0.219352\pi$
$762$	−10.0597	+	4.59411i	−0.364425	+	0.166427i
$763$	1.43980	+	21.8072i	0.0521244	+	0.789474i
$764$	2.75525	−	2.38744i	0.0996814	−	0.0863744i
$765$	−3.15464	+	13.0036i	−0.114056	+	0.470147i
$766$	1.04644	−	21.9675i	0.0378094	−	0.793717i
$767$	−2.61691	+	0.249885i	−0.0944912	+	0.00902282i
$768$	−0.945001	+	0.327068i	−0.0340998	+	0.0118020i
$769$	25.0719	−	16.1127i	0.904114	−	0.581039i	−0.00389346	−	0.999992i	$-0.501239\pi$
$769$	25.0719	−	16.1127i	0.904114	−	0.581039i	0.908008	+	0.418953i	$0.137603\pi$
$770$	7.76042	+	4.78865i	0.279666	+	0.172571i
$771$	1.63516	+	11.3728i	0.0588888	+	0.409581i
$772$	−0.0336772	−	0.706971i	−0.00121207	−	0.0254445i
$773$	−15.1976	−	2.92910i	−0.546620	−	0.105352i	−0.0915377	−	0.995802i	$-0.529178\pi$
$773$	−15.1976	−	2.92910i	−0.546620	−	0.105352i	−0.455083	+	0.890449i	$0.650390\pi$
$774$	−0.246200	−	2.57832i	−0.00884947	−	0.0926759i
$775$	1.59082	+	3.08576i	0.0571439	+	0.110844i
$776$	−1.95829	+	0.575004i	−0.0702983	+	0.0206415i
$777$	16.0845	−	9.68370i	0.577028	−	0.347401i
$778$	−1.77715	+	6.05243i	−0.0637140	+	0.216990i
$779$	−2.71484	+	28.4311i	−0.0972692	+	1.01865i
$780$	−6.22600	+	2.49252i	−0.222927	+	0.0892464i
$781$	−5.52587	+	3.19036i	−0.197731	+	0.114160i
$782$	23.1565	−	3.01889i	0.828075	−	0.107955i
$783$		−	5.49642i		−	0.196426i
$784$	3.71982	+	5.92983i	0.132851	+	0.211780i
$785$	2.07226	+	4.53762i	0.0739622	+	0.161955i
$786$	−13.5368	+	12.9073i	−0.482842	+	0.460388i
$787$	6.65822	−	19.2377i	0.237340	−	0.685749i	−0.761934	−	0.647655i	$-0.775750\pi$
$787$	6.65822	−	19.2377i	0.237340	−	0.685749i	0.999274	−	0.0380945i	$-0.0121288\pi$
$788$	14.0731	+	13.4187i	0.501334	+	0.478021i
$789$	−8.98009	+	4.62956i	−0.319700	+	0.164817i
$790$	10.7303	+	4.90035i	0.381766	+	0.174347i
$791$	2.84027	−	2.31911i	0.100988	−	0.0824580i
$792$	0.678096	+	1.05514i	0.0240951	+	0.0374927i
$793$	3.28382	−	8.20257i	0.116612	−	0.291282i
$794$	−8.02739	−	10.2077i	−0.284881	−	0.362256i
$795$	−19.5004	−	10.0532i	−0.691609	−	0.356549i
$796$	−0.661467	−	1.91118i	−0.0234451	−	0.0677400i
$797$	14.1366	−	30.9548i	0.500744	−	1.09648i	−0.475483	−	0.879725i	$-0.657727\pi$
$797$	14.1366	−	30.9548i	0.500744	−	1.09648i	0.976227	−	0.216751i	$-0.0695461\pi$
$798$	7.17857	−	2.25153i	0.254119	−	0.0797032i
$799$	15.4499	+	52.6175i	0.546578	+	1.86147i
$800$	2.50528	−	0.482854i	0.0885751	−	0.0170715i
$801$	−3.96196	−	16.3314i	−0.139989	−	0.577042i
$802$	−4.95744	−	3.53018i	−0.175053	−	0.124655i
$803$	−5.82332	−	4.57951i	−0.205500	−	0.161607i
$804$	−9.37664			−0.330688
$805$	29.4298	+	18.6992i	1.03726	+	0.659061i
$806$	3.32078			0.116969
$807$	−17.4782	−	13.7450i	−0.615261	−	0.483847i
$808$	−9.56235	−	6.80932i	−0.336402	−	0.239551i
$809$	−12.0868	−	49.8225i	−0.424950	−	1.75167i	−0.633585	−	0.773673i	$-0.718417\pi$
$809$	−12.0868	−	49.8225i	−0.424950	−	1.75167i	0.208635	−	0.977994i	$-0.433098\pi$
$810$	−2.69832	+	0.520058i	−0.0948093	+	0.0182730i
$811$	−2.01565	−	6.86469i	−0.0707792	−	0.241052i	0.916503	−	0.400027i	$-0.130999\pi$
$811$	−2.01565	−	6.86469i	−0.0707792	−	0.241052i	−0.987283	+	0.158975i	$0.949181\pi$
$812$	14.1927	+	3.16886i	0.498066	+	0.111205i
$813$	0.640538	−	1.40258i	0.0224647	−	0.0491907i
$814$	2.91100	+	8.41077i	0.102030	+	0.294797i
$815$	34.6598	+	17.8684i	1.21408	+	0.625902i
$816$	−3.01002	−	3.82755i	−0.105372	−	0.133991i
$817$	2.73729	−	6.83742i	0.0957657	−	0.239211i
$818$	19.5855	+	30.4756i	0.684789	+	1.06555i
$819$	1.03590	+	6.37328i	0.0361971	+	0.222700i
$820$	25.1061	+	11.4656i	0.876744	+	0.400395i
$821$	50.2827	−	25.9225i	1.75488	−	0.904702i	0.804294	−	0.594231i	$-0.202544\pi$
$821$	50.2827	−	25.9225i	1.75488	−	0.904702i	0.950583	−	0.310471i	$-0.100487\pi$
$822$	15.5176	+	14.7960i	0.541239	+	0.516070i
$823$	8.74762	−	25.2746i	0.304923	−	0.881017i	−0.683588	−	0.729868i	$-0.739581\pi$
$823$	8.74762	−	25.2746i	0.304923	−	0.881017i	0.988511	−	0.151149i	$-0.0482973\pi$
$824$	−12.3180	+	11.7452i	−0.429117	+	0.409163i
$825$	−1.32936	−	2.91088i	−0.0462823	−	0.101344i
$826$	0.882603	−	2.70981i	0.0307097	−	0.0942864i
$827$		−	42.8896i		−	1.49142i	−0.666273	−	0.745708i	$-0.732111\pi$
$827$		−	42.8896i		−	1.49142i	0.666273	−	0.745708i	$-0.267889\pi$
$828$	2.53950	+	4.06829i	0.0882537	+	0.141383i
$829$	10.2146	−	5.89739i	0.354767	−	0.204825i	−0.312016	−	0.950077i	$-0.601004\pi$
$829$	10.2146	−	5.89739i	0.354767	−	0.204825i	0.666783	+	0.745252i	$0.267671\pi$
$830$	−19.3291	+	7.73821i	−0.670923	+	0.268597i
$831$	0.347236	−	3.63642i	0.0120455	−	0.126146i
$832$	0.687564	−	2.34163i	0.0238370	−	0.0811813i
$833$	−21.3620	+	26.5607i	−0.740150	+	0.920272i
$834$	21.3820	−	6.27832i	0.740398	−	0.217400i
$835$	14.0405	+	27.2348i	0.485892	+	0.942500i
$836$	0.339021	+	3.55039i	0.0117253	+	0.122793i
$837$	1.33611	+	0.257515i	0.0461829	+	0.00890102i
$838$	−0.161936	−	3.39946i	−0.00559400	−	0.117432i
$839$	−3.47778	−	24.1885i	−0.120066	−	0.835078i	−0.957478	−	0.288506i	$-0.906841\pi$
$839$	−3.47778	−	24.1885i	−0.120066	−	0.835078i	0.837412	−	0.546572i	$-0.184068\pi$
$840$	0.212785	−	7.26736i	0.00734179	−	0.250748i
$841$	1.01846	−	0.654523i	0.0351192	−	0.0225697i
$842$	−21.5679	+	7.46471i	−0.743278	+	0.257251i
$843$	13.0526	−	1.24637i	0.449554	−	0.0429272i
$844$	0.307324	−	6.45152i	0.0105785	−	0.222071i
$845$	−4.56356	+	18.8112i	−0.156991	+	0.647126i
$846$	−8.51134	+	7.37512i	−0.292626	+	0.253562i
$847$	−13.8665	−	20.7312i	−0.476458	−	0.712332i
$848$	7.26231	−	3.31659i	0.249389	−	0.113892i
$849$	13.3824	−	17.0171i	0.459282	−	0.584025i
$850$	6.21177	+	10.7591i	0.213062	+	0.369034i
$851$	10.7065	+	32.3038i	0.367014	+	1.10736i
$852$	4.40573	+	2.54365i	0.150938	+	0.0871440i
$853$	30.4539	+	4.37861i	1.04272	+	0.149921i	0.642334	−	0.766425i	$-0.277966\pi$
$853$	30.4539	+	4.37861i	1.04272	+	0.149921i	0.400388	+	0.916346i	$0.368875\pi$
$854$	6.73595	+	6.81007i	0.230500	+	0.233036i
$855$	−7.49755	−	2.20148i	−0.256411	−	0.0752890i
$856$	0.219491	+	1.13883i	0.00750204	+	0.0389243i
$857$	−19.7923	+	20.7576i	−0.676092	+	0.709065i	−0.968996	−	0.247077i	$-0.920530\pi$
$857$	−19.7923	+	20.7576i	−0.676092	+	0.709065i	0.292904	+	0.956142i	$0.405378\pi$
$858$	−3.05750	−	0.145647i	−0.104381	−	0.00497229i
$859$	28.3008	−	20.1529i	0.965612	−	0.687609i	0.0156183	−	0.999878i	$-0.495028\pi$
$859$	28.3008	−	20.1529i	0.965612	−	0.687609i	0.949994	+	0.312269i	$0.101089\pi$
$860$	−5.37897	−	4.66091i	−0.183421	−	0.158936i
$861$	16.0411	−	21.1858i	0.546679	−	0.722009i
$862$	11.8124	−	1.69836i	0.402331	−	0.0578464i
$863$	52.1912	+	20.8942i	1.77661	+	0.711246i	0.996309	+	0.0858392i	$0.0273571\pi$
$863$	52.1912	+	20.8942i	1.77661	+	0.711246i	0.780299	+	0.625407i	$0.215067\pi$
$864$	0.458227	−	0.888835i	0.0155892	−	0.0302388i
$865$	1.95541	−	10.1456i	0.0664859	−	0.344961i
$866$	18.2684	+	25.6543i	0.620784	+	0.871769i
$867$	3.62787	−	5.64507i	0.123209	−	0.191717i
$868$	−1.43526	+	3.30161i	−0.0487159	+	0.112064i
$869$	3.52584	+	4.06904i	0.119606	+	0.138033i
$870$	−10.4230	−	10.9313i	−0.353372	−	0.370606i
$871$	13.2737	−	18.6404i	0.449764	−	0.631605i
$872$	3.07004	+	7.66859i	0.103965	+	0.259691i
$873$	1.02048	−	1.76752i	0.0345380	−	0.0598215i
$874$	1.11752	+	13.5914i	0.0378008	+	0.459737i
$875$	3.04821	−	17.5396i	0.103048	−	0.592948i
$876$	−0.840594	+	5.84646i	−0.0284010	+	0.197534i
$877$	−42.3509	−	4.04402i	−1.43009	−	0.136557i	−0.648909	−	0.760866i	$-0.724775\pi$
$877$	−42.3509	−	4.04402i	−1.43009	−	0.136557i	−0.781177	+	0.624309i	$0.785381\pi$
$878$	−3.01408	+	0.731209i	−0.101720	+	0.0246771i
$879$	−29.0152	−	10.0423i	−0.978660	−	0.338717i
$880$	3.34948	+	0.812576i	0.112911	+	0.0273919i
$881$	−18.3713	−	11.8065i	−0.618944	−	0.397771i	0.193257	−	0.981148i	$-0.438095\pi$
$881$	−18.3713	−	11.8065i	−0.618944	−	0.397771i	−0.812202	+	0.583377i	$0.801731\pi$
$882$	−6.78422	−	1.72465i	−0.228436	−	0.0580720i
$883$	−35.3762	+	40.8264i	−1.19051	+	1.37392i	−0.280220	+	0.959936i	$0.590407\pi$
$883$	−35.3762	+	40.8264i	−1.19051	+	1.37392i	−0.910286	+	0.413980i	$0.864138\pi$
$884$	11.8700	−	0.565440i	0.399233	−	0.0190178i
$885$	−2.32675	+	1.82978i	−0.0782128	+	0.0615072i
$886$	23.9413	−	18.8276i	0.804323	−	0.632527i
$887$	10.4868	−	0.499549i	0.352113	−	0.0167732i	0.129220	−	0.991616i	$-0.458753\pi$
$887$	10.4868	−	0.499549i	0.352113	−	0.0167732i	0.222894	+	0.974843i	$0.428450\pi$
$888$	4.64697	−	5.36289i	0.155942	−	0.179967i
$889$	24.1412	+	16.5326i	0.809671	+	0.554485i
$890$	−38.8492	−	24.9669i	−1.30223	−	0.836891i
$891$	−1.21889	−	0.295699i	−0.0408343	−	0.00990631i
$892$	−15.0793	−	5.21899i	−0.504892	−	0.174745i
$893$	−31.1219	+	7.55009i	−1.04145	+	0.252654i
$894$	9.56468	+	0.913316i	0.319891	+	0.0305459i
$895$	8.00573	−	55.6811i	0.267602	−	1.86121i
$896$	2.03094	+	1.69566i	0.0678491	+	0.0566481i
$897$	−11.6825	−	0.710724i	−0.390069	−	0.0237304i
$898$	−6.14768	+	10.6481i	−0.205151	+	0.355331i
$899$	2.77966	+	6.94327i	0.0927070	+	0.231571i
$900$	−1.47995	+	2.07830i	−0.0493317	+	0.0692767i
$901$	26.8273	+	28.1356i	0.893746	+	0.937334i
$902$	8.24958	+	9.52052i	0.274681	+	0.316999i
$903$	−5.50820	+	4.07655i	−0.183301	+	0.135659i
$904$	0.749284	−	1.16591i	0.0249208	−	0.0387775i
$905$	−13.8700	−	19.4777i	−0.461054	−	0.647460i
$906$	−2.52969	+	13.1253i	−0.0840435	+	0.436059i
$907$	24.2410	−	47.0210i	0.804910	−	1.56131i	−0.0225252	−	0.999746i	$-0.507171\pi$
$907$	24.2410	−	47.0210i	0.804910	−	1.56131i	0.827435	−	0.561561i	$-0.189799\pi$
$908$	13.0179	+	5.21159i	0.432015	+	0.172953i
$909$	11.6196	−	1.67064i	0.385397	−	0.0554117i
$910$	14.1460	+	10.7108i	0.468935	+	0.355060i
$911$	−9.60670	−	8.32425i	−0.318284	−	0.275795i	0.481035	−	0.876701i	$-0.340261\pi$
$911$	−9.60670	−	8.32425i	−0.318284	−	0.275795i	−0.799319	+	0.600906i	$0.794806\pi$
$912$	2.31630	−	1.64943i	0.0767005	−	0.0546182i
$913$	−9.49224	−	0.452171i	−0.314147	−	0.0149647i
$914$	15.1062	−	15.8429i	0.499667	−	0.524036i
$915$	−1.88281	−	9.76894i	−0.0622438	−	0.322951i
$916$	−14.7500	−	4.33100i	−0.487355	−	0.143100i
$917$	47.7294	+	13.0694i	1.57616	+	0.431588i
$918$	4.81976	+	0.692977i	0.159076	+	0.0228716i
$919$	47.2876	+	27.3015i	1.55987	+	0.900593i	0.997268	+	0.0738668i	$0.0235340\pi$
$919$	47.2876	+	27.3015i	1.55987	+	0.900593i	0.562605	+	0.826726i	$0.309799\pi$
$920$	12.7654	+	3.27532i	0.420861	+	0.107984i
$921$	−9.39988	−	16.2811i	−0.309736	−	0.536479i
$922$	11.9233	−	15.1617i	0.392672	−	0.499323i
$923$	−11.2935	+	5.15757i	−0.371730	+	0.169764i
$924$	1.46628	−	2.97690i	0.0482369	−	0.0979329i
$925$	−13.6828	+	11.8562i	−0.449889	+	0.389831i
$926$	2.91316	−	12.0082i	0.0957325	−	0.394615i
$927$	0.809846	−	17.0008i	0.0265988	−	0.558378i
$928$	5.47153	−	0.522468i	0.179612	−	0.0171509i
$929$	17.5954	−	6.08982i	0.577285	−	0.199800i	−0.0227949	−	0.999740i	$-0.507256\pi$
$929$	17.5954	−	6.08982i	0.577285	−	0.199800i	0.600080	+	0.799940i	$0.295135\pi$
$930$	3.14560	−	2.02156i	0.103148	−	0.0662895i
$931$	−14.8997	−	13.1988i	−0.488317	−	0.432574i
$932$	−0.761712	−	5.29782i	−0.0249507	−	0.173536i
$933$	1.15160	+	24.1751i	0.0377017	+	0.791456i
$934$	−8.31039	−	1.60170i	−0.271924	−	0.0524091i
$935$	1.59531	+	16.7068i	0.0521721	+	0.546371i
$936$	1.11829	+	2.16919i	0.0365526	+	0.0709021i
$937$	28.6429	−	8.41032i	0.935723	−	0.274753i	0.221892	−	0.975071i	$-0.428777\pi$
$937$	28.6429	−	8.41032i	0.935723	−	0.274753i	0.713831	+	0.700318i	$0.246958\pi$
$938$	12.7958	+	21.2536i	0.417798	+	0.693956i
$939$	−8.20995	+	27.9605i	−0.267921	+	0.912457i
$940$	−2.94180	+	30.8079i	−0.0959509	+	1.00484i
$941$	−23.6470	+	9.46684i	−0.770871	+	0.308610i	−0.723552	−	0.690270i	$-0.757492\pi$
$941$	−23.6470	+	9.46684i	−0.770871	+	0.308610i	−0.0473188	+	0.998880i	$0.515068\pi$
$942$	1.57210	−	0.907651i	0.0512217	−	0.0295729i
$943$	31.0619	+	36.8154i	1.01151	+	1.19888i
$944$		−	1.07717i		−	0.0350589i
$945$	4.86105	+	5.40647i	0.158130	+	0.175873i
$946$	−1.34950	−	2.95499i	−0.0438760	−	0.0960751i
$947$	0.257096	−	0.245141i	0.00835450	−	0.00796600i	−0.685890	−	0.727705i	$-0.740587\pi$
$947$	0.257096	−	0.245141i	0.00835450	−	0.00796600i	0.694245	+	0.719739i	$0.255739\pi$
$948$	1.40401	−	4.05662i	0.0456001	−	0.131753i
$949$	−10.4326	−	9.94743i	−0.338655	−	0.322907i
$950$	−6.44855	+	3.32446i	−0.209219	+	0.107860i
$951$	−13.1492	−	6.00505i	−0.426393	−	0.194727i
$952$	−4.56813	+	12.0459i	−0.148054	+	0.390411i
$953$	−32.6130	−	50.7468i	−1.05644	−	1.64385i	−0.707514	−	0.706700i	$-0.750183\pi$
$953$	−32.6130	−	50.7468i	−1.05644	−	1.64385i	−0.348925	−	0.937151i	$-0.613453\pi$
$954$	−2.96728	+	7.41190i	−0.0960691	+	0.239969i
$955$	6.19294	+	7.87496i	0.200399	+	0.254828i
$956$	−15.9719	−	8.23406i	−0.516567	−	0.266309i
$957$	−2.25476	−	6.51470i	−0.0728861	−	0.210590i
$958$	3.93350	−	8.61317i	0.127086	−	0.278279i
$959$	12.3614	−	55.3644i	0.399171	−	1.78781i
$960$	−0.774195	−	2.63667i	−0.0249870	−	0.0850981i
$961$	28.6217	−	5.51639i	0.923282	−	0.177948i
$962$	4.08287	+	16.8298i	0.131637	+	0.542615i
$963$	−0.944733	−	0.672741i	−0.0304436	−	0.0216788i
$964$	−3.47977	−	2.73652i	−0.112076	−	0.0881374i
$965$	1.94495			0.0626100
$966$	5.75589	−	11.3079i	0.185193	−	0.363827i
$967$	51.0406			1.64136			0.820678	−	0.571391i	$-0.193596\pi$
$967$	51.0406			1.64136			0.820678	+	0.571391i	$0.193596\pi$
$968$	−7.41002	−	5.82730i	−0.238167	−	0.187297i
$969$	11.2788	+	8.03162i	0.362328	+	0.258013i
$970$	−1.32226	−	5.45042i	−0.0424551	−	0.175002i
$971$	48.6782	−	9.38195i	1.56216	−	0.301081i	0.666390	−	0.745603i	$-0.267839\pi$
$971$	48.6782	−	9.38195i	1.56216	−	0.301081i	0.895768	+	0.444522i	$0.146627\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	−43.4097	−	39.8980i	−1.39165	−	1.27907i
$974$	−10.9265	+	23.9257i	−0.350107	+	0.766628i
$975$	−2.03653	−	5.88417i	−0.0652211	−	0.188444i
$976$	3.21792	+	1.65895i	0.103003	+	0.0531018i
$977$	−10.1262	−	12.8765i	−0.323966	−	0.411956i	0.596603	−	0.802537i	$-0.296517\pi$
$977$	−10.1262	−	12.8765i	−0.323966	−	0.411956i	−0.920569	+	0.390580i	$0.872274\pi$
$978$	5.27400	−	13.1738i	0.168644	−	0.421252i
$979$	−11.3955	−	17.7317i	−0.364201	−	0.566708i
$980$	−16.7630	+	9.43507i	−0.535474	+	0.301392i
$981$	−7.51383	−	3.43145i	−0.239898	−	0.109558i
$982$	23.7782	−	12.2585i	0.758792	−	0.391184i
$983$	33.5164	+	31.9579i	1.06901	+	1.01930i	0.999765	+	0.0216980i	$0.00690722\pi$
$983$	33.5164	+	31.9579i	1.06901	+	1.01930i	0.0692441	+	0.997600i	$0.477941\pi$
$984$	3.28502	−	9.49145i	0.104723	−	0.302576i
$985$	−38.6727	+	36.8743i	−1.23221	+	1.17491i
$986$	11.1181	+	24.3453i	0.354073	+	0.775311i
$987$	28.3318	+	9.22786i	0.901812	+	0.293726i
$988$			6.93969i			0.220781i
$989$	−5.01090	−	11.3659i	−0.159337	−	0.361414i
$990$	−2.98488	+	1.72332i	−0.0948656	+	0.0547707i
$991$	−20.3374	+	8.14187i	−0.646039	+	0.258635i	−0.671459	−	0.741042i	$-0.734332\pi$
$991$	−20.3374	+	8.14187i	−0.646039	+	0.258635i	0.0254200	+	0.999677i	$0.491908\pi$
$992$	−0.129343	+	1.35454i	−0.00410665	+	0.0430068i
$993$	2.65994	−	9.05892i	0.0844106	−	0.287476i
$994$	−0.246685	−	13.4575i	−0.00782437	−	0.426845i
$995$	5.33243	−	1.56574i	0.169049	−	0.0496374i
$996$	3.47183	+	6.73441i	0.110009	+	0.213388i
$997$	−0.0616744	−	0.645884i	−0.00195325	−	0.0204553i	0.994443	−	0.105279i	$-0.0335735\pi$
$997$	−0.0616744	−	0.645884i	−0.00195325	−	0.0204553i	−0.996396	+	0.0848234i	$0.972967\pi$
$998$	−12.6709	−	2.44212i	−0.401091	−	0.0773039i
$999$	0.337647	+	7.08808i	0.0106827	+	0.224257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.61.1	✓	320
7.3	odd	6	inner	966.2.be.b.199.9	yes	320
23.20	odd	22	inner	966.2.be.b.733.9	yes	320
161.66	even	66	inner	966.2.be.b.871.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.61.1	✓	320	1.1	even	1	trivial
966.2.be.b.199.9	yes	320	7.3	odd	6	inner
966.2.be.b.733.9	yes	320	23.20	odd	22	inner
966.2.be.b.871.1	yes	320	161.66	even	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.69832 + 0.520058i) q^{5} +(0.281733 + 0.959493i) q^{6} +(1.79038 - 1.94796i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.69832 + 0.520058i) q^{5} +(0.281733 + 0.959493i) q^{6} +(1.79038 - 1.94796i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(2.44250 + 1.25920i) q^{10} +(0.775323 + 0.985903i) q^{11} +(0.371662 - 0.928368i) q^{12} +(1.31943 + 2.05307i) q^{13} +(-2.61148 + 0.424463i) q^{14} +(2.49965 + 1.14155i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-3.52409 - 3.36022i) q^{17} +(0.327068 - 0.945001i) q^{18} +(2.05799 - 1.96229i) q^{19} +(-1.14155 - 2.49965i) q^{20} +(-2.58833 + 0.548242i) q^{21} -1.25425i q^{22} +(0.0631191 - 4.79542i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(2.36863 - 0.948256i) q^{25} +(0.231983 - 2.42943i) q^{26} +(0.281733 - 0.959493i) q^{27} +(2.31515 + 1.28066i) q^{28} +(5.27378 - 1.54852i) q^{29} +(-1.25920 - 2.44250i) q^{30} +(0.129343 + 1.35454i) q^{31} +(0.981929 + 0.189251i) q^{32} +(-0.0596794 - 1.25282i) q^{33} +(0.692977 + 4.81976i) q^{34} +(-3.81796 + 6.18732i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-6.70584 + 2.32091i) q^{37} +(-2.83070 + 0.270299i) q^{38} +(0.116123 - 2.43772i) q^{39} +(-0.647861 + 2.67052i) q^{40} +(-7.59064 + 6.57733i) q^{41} +(2.37346 + 1.16905i) q^{42} +(2.35599 - 1.07595i) q^{43} +(-0.775323 + 0.985903i) q^{44} +(-1.37399 - 2.37982i) q^{45} +(-3.01394 + 3.73043i) q^{46} +(-9.75328 - 5.63106i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-0.589103 - 6.97517i) q^{49} +(-2.44804 - 0.718810i) q^{50} +(0.921525 + 4.78133i) q^{51} +(-1.68413 + 1.76626i) q^{52} +(-7.97475 - 0.379884i) q^{53} +(-0.814576 + 0.580057i) q^{54} +(-2.60480 - 2.25707i) q^{55} +(-1.02818 - 2.43780i) q^{56} +(-2.81463 + 0.404682i) q^{57} +(-5.10270 - 2.04281i) q^{58} +(-0.493588 + 0.957427i) q^{59} +(-0.520058 + 2.69832i) q^{60} +(-2.10003 - 2.94907i) q^{61} +(0.735652 - 1.14470i) q^{62} +(2.42640 + 1.05479i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-4.62794 - 4.85365i) q^{65} +(-0.727534 + 1.02168i) q^{66} +(-3.48494 - 8.70497i) q^{67} +(2.43466 - 4.21696i) q^{68} +(-2.83303 + 3.86962i) q^{69} +(6.82586 - 2.50346i) q^{70} +(-0.723998 + 5.03552i) q^{71} +(0.995472 + 0.0950560i) q^{72} +(-5.74008 + 1.39253i) q^{73} +(6.70584 + 2.32091i) q^{74} +(-2.47947 - 0.601513i) q^{75} +(2.39216 + 1.53735i) q^{76} +(3.30862 + 0.254840i) q^{77} +(-1.59818 + 1.84439i) q^{78} +(4.28785 - 0.204255i) q^{79} +(2.16006 - 1.69869i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(10.0325 - 0.477906i) q^{82} +(-4.96166 + 5.72606i) q^{83} +(-1.14301 - 2.38611i) q^{84} +(11.2566 + 7.23421i) q^{85} +(-2.51704 - 0.610627i) q^{86} +(-5.19412 - 1.79770i) q^{87} +(1.21889 - 0.295699i) q^{88} +(-16.7290 - 1.59743i) q^{89} +(-0.391078 + 2.72001i) q^{90} +(6.36156 + 1.10557i) q^{91} +(4.67512 - 1.06922i) q^{92} +(0.680352 - 1.17840i) q^{93} +(4.18571 + 10.4554i) q^{94} +(-4.53261 + 6.36516i) q^{95} +(-0.690079 - 0.723734i) q^{96} +(-1.33654 - 1.54245i) q^{97} +(-3.84870 + 5.84701i) q^{98} +(-0.678096 + 1.05514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

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