LMFDB - Embedded newform 522.2.x.a.101.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [522,2,Mod(11,522)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(522, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 75])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("522.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	522.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16819098551$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$30$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.16
Character	$\chi$	$=$	522.101
Dual form			522.2.x.a.491.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.399892 - 0.916562i) q^{2} +(-1.70232 - 0.319518i) q^{3} +(-0.680173 - 0.733052i) q^{4} +(0.658773 + 0.0992940i) q^{5} +(-0.973604 + 1.43251i) q^{6} +(0.208168 + 0.193152i) q^{7} +(-0.943883 + 0.330279i) q^{8} +(2.79582 + 1.08785i) q^{9} +(0.354447 - 0.564099i) q^{10} +(2.39237 - 2.05880i) q^{11} +(0.923651 + 1.46522i) q^{12} +(2.52163 - 3.69855i) q^{13} +(0.260280 - 0.113559i) q^{14} +(-1.08972 - 0.379520i) q^{15} +(-0.0747301 + 0.997204i) q^{16} +(-1.02539 - 1.02539i) q^{17} +(2.11510 - 2.12752i) q^{18} +(-4.57694 - 2.87588i) q^{19} +(-0.375292 - 0.550452i) q^{20} +(-0.292654 - 0.395320i) q^{21} +(-0.930328 - 3.01605i) q^{22} +(-7.17746 - 2.81695i) q^{23} +(1.71233 - 0.260654i) q^{24} +(-4.35374 - 1.34295i) q^{25} +(-2.38157 - 3.79025i) q^{26} +(-4.41180 - 2.74518i) q^{27} -0.283975i q^{28} +(4.35878 + 3.16244i) q^{29} +(-0.783624 + 0.847028i) q^{30} +(6.09734 - 4.50004i) q^{31} +(0.884115 + 0.467269i) q^{32} +(-4.73041 + 2.74034i) q^{33} +(-1.34988 + 0.529788i) q^{34} +(0.117957 + 0.147913i) q^{35} +(-1.10419 - 2.78940i) q^{36} +(1.06483 + 3.04312i) q^{37} +(-4.46621 + 3.04501i) q^{38} +(-5.47438 + 5.49043i) q^{39} +(-0.654599 + 0.123857i) q^{40} +(2.99650 + 0.802909i) q^{41} +(-0.479366 + 0.110150i) q^{42} +(3.54648 - 4.80532i) q^{43} +(-3.13643 - 0.353390i) q^{44} +(1.73379 + 0.994252i) q^{45} +(-5.45212 + 5.45212i) q^{46} +(1.46666 + 1.70429i) q^{47} +(0.445840 - 1.67369i) q^{48} +(-0.517084 - 6.90001i) q^{49} +(-2.97193 + 3.45344i) q^{50} +(1.41791 + 2.07317i) q^{51} +(-4.42637 + 0.667168i) q^{52} +(-2.95033 - 2.35281i) q^{53} +(-4.28037 + 2.94591i) q^{54} +(1.78045 - 1.11873i) q^{55} +(-0.260280 - 0.113559i) q^{56} +(6.87254 + 6.35810i) q^{57} +(4.64162 - 2.73046i) q^{58} +(0.839346 - 0.484597i) q^{59} +(0.462989 + 1.05696i) q^{60} +(4.35248 - 0.162858i) q^{61} +(-1.68629 - 7.38813i) q^{62} +(0.371880 + 0.766472i) q^{63} +(0.781831 - 0.623490i) q^{64} +(2.02842 - 2.18612i) q^{65} +(0.620037 + 5.43155i) q^{66} +(1.17013 - 0.0876893i) q^{67} +(-0.0542216 + 1.44910i) q^{68} +(11.3183 + 7.08869i) q^{69} +(0.182741 - 0.0489654i) q^{70} +(-14.5046 + 6.98504i) q^{71} +(-2.99822 - 0.103401i) q^{72} +(1.43993 - 12.7797i) q^{73} +(3.21503 + 0.240933i) q^{74} +(6.98238 + 3.67724i) q^{75} +(1.00494 + 5.31123i) q^{76} +(0.895674 + 0.0335138i) q^{77} +(2.84315 + 7.21319i) q^{78} +(1.66589 - 8.80444i) q^{79} +(-0.148246 + 0.649510i) q^{80} +(6.63318 + 6.08284i) q^{81} +(1.93419 - 2.42540i) q^{82} +(-1.21176 + 3.92843i) q^{83} +(-0.0907350 + 0.483417i) q^{84} +(-0.573683 - 0.777312i) q^{85} +(-2.98616 - 5.17218i) q^{86} +(-6.40960 - 6.77621i) q^{87} +(-1.57814 + 2.73341i) q^{88} +(8.11748 - 0.914620i) q^{89} +(1.60462 - 1.19153i) q^{90} +(1.23930 - 0.282863i) q^{91} +(2.81695 + 7.17746i) q^{92} +(-11.8175 + 5.71232i) q^{93} +(2.14860 - 0.662755i) q^{94} +(-2.72960 - 2.34901i) q^{95} +(-1.35575 - 1.07793i) q^{96} +(7.39745 + 13.9967i) q^{97} +(-6.53107 - 2.28532i) q^{98} +(8.92827 - 3.15349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 24 q^{11} - 12 q^{14} - 20 q^{15} - 60 q^{16} + 84 q^{21} + 20 q^{24} + 60 q^{25} - 144 q^{27} - 12 q^{29} + 72 q^{30} + 84 q^{33} - 40 q^{36} + 40 q^{39} - 12 q^{41} - 104 q^{45} + 24 q^{46} - 24 q^{47}+ \cdots - 84 q^{99}+O(q^{100}) $ 720 * q + 24 * q^11 - 12 * q^14 - 20 * q^15 - 60 * q^16 + 84 * q^21 + 20 * q^24 + 60 * q^25 - 144 * q^27 - 12 * q^29 + 72 * q^30 + 84 * q^33 - 40 * q^36 + 40 * q^39 - 12 * q^41 - 104 * q^45 + 24 * q^46 - 24 * q^47 + 60 * q^49 + 16 * q^54 - 144 * q^55 + 12 * q^56 + 12 * q^58 + 120 * q^59 - 16 * q^60 - 12 * q^61 + 36 * q^65 - 48 * q^66 - 36 * q^68 + 52 * q^69 - 180 * q^74 - 184 * q^75 - 132 * q^77 - 68 * q^78 + 12 * q^79 - 216 * q^81 + 96 * q^82 - 432 * q^83 - 80 * q^84 - 48 * q^85 - 200 * q^87 - 112 * q^90 - 252 * q^92 - 112 * q^93 + 192 * q^95 + 24 * q^97 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.399892	−	0.916562i	0.282766	−	0.648107i
$2$	0.399892	−	0.916562i	0.282766	−	0.648107i
$3$	−1.70232	−	0.319518i	−0.982837	−	0.184474i
$3$	−1.70232	−	0.319518i	−0.982837	−	0.184474i
$4$	−0.680173	−	0.733052i	−0.340086	−	0.366526i
$5$	0.658773	+	0.0992940i	0.294612	+	0.0444056i	0.294685	−	0.955594i	$-0.404785\pi$
$5$	0.658773	+	0.0992940i	0.294612	+	0.0444056i	−7.31799e−5		1.00000i	$0.500023\pi$
$6$	−0.973604	+	1.43251i	−0.397472	+	0.584821i
$7$	0.208168	+	0.193152i	0.0786801	+	0.0730045i	0.718533	−	0.695493i	$-0.244814\pi$
$7$	0.208168	+	0.193152i	0.0786801	+	0.0730045i	−0.639852	+	0.768498i	$0.721005\pi$
$8$	−0.943883	+	0.330279i	−0.333713	+	0.116771i
$9$	2.79582	+	1.08785i	0.931939	+	0.362616i
$10$	0.354447	−	0.564099i	0.112086	−	0.178384i
$11$	2.39237	−	2.05880i	0.721325	−	0.620751i	−0.213050	−	0.977041i	$-0.568340\pi$
$11$	2.39237	−	2.05880i	0.721325	−	0.620751i	0.934375	+	0.356291i	$0.115959\pi$
$12$	0.923651	+	1.46522i	0.266635	+	0.422972i
$13$	2.52163	−	3.69855i	0.699374	−	1.02579i	−0.298084	−	0.954540i	$-0.596348\pi$
$13$	2.52163	−	3.69855i	0.699374	−	1.02579i	0.997458	−	0.0712536i	$-0.0227000\pi$
$14$	0.260280	−	0.113559i	0.0695629	−	0.0303500i
$15$	−1.08972	−	0.379520i	−0.281364	−	0.0979917i
$16$	−0.0747301	+	0.997204i	−0.0186825	+	0.249301i
$17$	−1.02539	−	1.02539i	−0.248693	−	0.248693i	0.571741	−	0.820434i	$-0.306268\pi$
$17$	−1.02539	−	1.02539i	−0.248693	−	0.248693i	−0.820434	+	0.571741i	$0.806268\pi$
$18$	2.11510	−	2.12752i	0.498535	−	0.501461i
$19$	−4.57694	−	2.87588i	−1.05002	−	0.659772i	−0.107598	−	0.994194i	$-0.534316\pi$
$19$	−4.57694	−	2.87588i	−1.05002	−	0.659772i	−0.942423	+	0.334422i	$0.891459\pi$
$20$	−0.375292	−	0.550452i	−0.0839177	−	0.123085i
$21$	−0.292654	−	0.395320i	−0.0638624	−	0.0862660i
$22$	−0.930328	−	3.01605i	−0.198347	−	0.643024i
$23$	−7.17746	−	2.81695i	−1.49660	−	0.587374i	−0.530996	−	0.847374i	$-0.678182\pi$
$23$	−7.17746	−	2.81695i	−1.49660	−	0.587374i	−0.965608	+	0.260001i	$0.916277\pi$
$24$	1.71233	−	0.260654i	0.349527	−	0.0532058i
$25$	−4.35374	−	1.34295i	−0.870748	−	0.268590i
$26$	−2.38157	−	3.79025i	−0.467065	−	0.743329i
$27$	−4.41180	−	2.74518i	−0.849051	−	0.528311i
$28$		−	0.283975i		−	0.0536661i
$29$	4.35878	+	3.16244i	0.809405	+	0.587251i
$29$	4.35878	+	3.16244i	0.809405	+	0.587251i
$30$	−0.783624	+	0.847028i	−0.143069	+	0.154645i
$31$	6.09734	−	4.50004i	1.09512	−	0.808232i	0.112457	−	0.993657i	$-0.464128\pi$
$31$	6.09734	−	4.50004i	1.09512	−	0.808232i	0.982658	+	0.185425i	$0.0593661\pi$
$32$	0.884115	+	0.467269i	0.156291	+	0.0826022i
$33$	−4.73041	+	2.74034i	−0.823458	+	0.477031i
$34$	−1.34988	+	0.529788i	−0.231502	+	0.0908578i
$35$	0.117957	+	0.147913i	0.0199383	+	0.0250018i
$36$	−1.10419	−	2.78940i	−0.184032	−	0.464900i
$37$	1.06483	+	3.04312i	0.175058	+	0.500286i	0.997663	−	0.0683265i	$-0.0217660\pi$
$37$	1.06483	+	3.04312i	0.175058	+	0.500286i	−0.822605	+	0.568613i	$0.807480\pi$
$38$	−4.46621	+	3.04501i	−0.724514	+	0.493965i
$39$	−5.47438	+	5.49043i	−0.876603	+	0.879172i
$40$	−0.654599	+	0.123857i	−0.103501	+	0.0195835i
$41$	2.99650	+	0.802909i	0.467974	+	0.125393i	0.485098	−	0.874460i	$-0.338784\pi$
$41$	2.99650	+	0.802909i	0.467974	+	0.125393i	−0.0171232	+	0.999853i	$0.505451\pi$
$42$	−0.479366	+	0.110150i	−0.0739678	+	0.0169965i
$43$	3.54648	−	4.80532i	0.540834	−	0.732804i	−0.445912	−	0.895077i	$-0.647121\pi$
$43$	3.54648	−	4.80532i	0.540834	−	0.732804i	0.986746	+	0.162273i	$0.0518825\pi$
$44$	−3.13643	−	0.353390i	−0.472834	−	0.0532756i
$45$	1.73379	+	0.994252i	0.258458	+	0.148214i
$46$	−5.45212	+	5.45212i	−0.803871	+	0.803871i
$47$	1.46666	+	1.70429i	0.213935	+	0.248597i	0.854678	−	0.519158i	$-0.173755\pi$
$47$	1.46666	+	1.70429i	0.213935	+	0.248597i	−0.640743	+	0.767755i	$0.721374\pi$
$48$	0.445840	−	1.67369i	0.0643514	−	0.241576i
$49$	−0.517084	−	6.90001i	−0.0738692	−	0.985716i
$50$	−2.97193	+	3.45344i	−0.420294	+	0.488390i
$51$	1.41791	+	2.07317i	0.198548	+	0.290302i
$52$	−4.42637	+	0.667168i	−0.613827	+	0.0925196i
$53$	−2.95033	−	2.35281i	−0.405259	−	0.323183i	0.399556	−	0.916709i	$-0.369164\pi$
$53$	−2.95033	−	2.35281i	−0.405259	−	0.323183i	−0.804815	+	0.593525i	$0.797736\pi$
$54$	−4.28037	+	2.94591i	−0.582485	+	0.400888i
$55$	1.78045	−	1.11873i	0.240076	−	0.150850i
$56$	−0.260280	−	0.113559i	−0.0347814	−	0.0151750i
$57$	6.87254	+	6.35810i	0.910290	+	0.842151i
$58$	4.64162	−	2.73046i	0.609474	−	0.358526i
$59$	0.839346	−	0.484597i	0.109274	−	0.0630891i	−0.444367	−	0.895845i	$-0.646571\pi$
$59$	0.839346	−	0.484597i	0.109274	−	0.0630891i	0.553641	+	0.832756i	$0.313238\pi$
$60$	0.462989	+	1.05696i	0.0597716	+	0.136453i
$61$	4.35248	−	0.162858i	0.557278	−	0.0208519i	0.242731	−	0.970094i	$-0.421957\pi$
$61$	4.35248	−	0.162858i	0.557278	−	0.0208519i	0.314547	+	0.949242i	$0.398147\pi$
$62$	−1.68629	−	7.38813i	−0.214159	−	0.938293i
$63$	0.371880	+	0.766472i	0.0468525	+	0.0965664i
$64$	0.781831	−	0.623490i	0.0977289	−	0.0779362i
$65$	2.02842	−	2.18612i	0.251595	−	0.271155i
$66$	0.620037	+	5.43155i	0.0763213	+	0.668577i
$67$	1.17013	−	0.0876893i	0.142954	−	0.0107130i	−0.00306066	−	0.999995i	$-0.500974\pi$
$67$	1.17013	−	0.0876893i	0.142954	−	0.0107130i	0.146015	+	0.989282i	$0.453355\pi$
$68$	−0.0542216	+	1.44910i	−0.00657534	+	0.175730i
$69$	11.3183	+	7.08869i	1.36256	+	0.853377i
$70$	0.182741	−	0.0489654i	0.0218418	−	0.00585248i
$71$	−14.5046	+	6.98504i	−1.72138	+	0.828972i	−0.732407	+	0.680868i	$0.761603\pi$
$71$	−14.5046	+	6.98504i	−1.72138	+	0.828972i	−0.988972	+	0.148104i	$0.952683\pi$
$72$	−2.99822	−	0.103401i	−0.353343	−	0.0121860i
$73$	1.43993	−	12.7797i	0.168531	−	1.49576i	−0.570060	−	0.821603i	$-0.693080\pi$
$73$	1.43993	−	12.7797i	0.168531	−	1.49576i	0.738591	−	0.674153i	$-0.235491\pi$
$74$	3.21503	+	0.240933i	0.373740	+	0.0280079i
$75$	6.98238	+	3.67724i	0.806256	+	0.424611i
$76$	1.00494	+	5.31123i	0.115274	+	0.609240i
$77$	0.895674	+	0.0335138i	0.102072	+	0.00381925i
$78$	2.84315	+	7.21319i	0.321924	+	0.816733i
$79$	1.66589	−	8.80444i	0.187427	−	0.990577i	−0.754889	−	0.655853i	$-0.772309\pi$
$79$	1.66589	−	8.80444i	0.187427	−	0.990577i	0.942316	−	0.334724i	$-0.108643\pi$
$80$	−0.148246	+	0.649510i	−0.0165745	+	0.0726175i
$81$	6.63318	+	6.08284i	0.737020	+	0.675871i
$82$	1.93419	−	2.42540i	0.213596	−	0.267841i
$83$	−1.21176	+	3.92843i	−0.133008	+	0.431201i	−0.997437	−	0.0715542i	$-0.977204\pi$
$83$	−1.21176	+	3.92843i	−0.133008	+	0.431201i	0.864429	+	0.502755i	$0.167680\pi$
$84$	−0.0907350	+	0.483417i	−0.00990000	+	0.0527451i
$85$	−0.573683	−	0.777312i	−0.0622246	−	0.0843114i
$86$	−2.98616	−	5.17218i	−0.322006	−	0.557731i
$87$	−6.40960	−	6.77621i	−0.687181	−	0.726486i
$88$	−1.57814	+	2.73341i	−0.168230	+	0.291383i
$89$	8.11748	−	0.914620i	0.860451	−	0.0969496i	0.329299	−	0.944226i	$-0.393188\pi$
$89$	8.11748	−	0.914620i	0.860451	−	0.0969496i	0.531152	+	0.847276i	$0.321759\pi$
$90$	1.60462	−	1.19153i	0.169142	−	0.125599i
$91$	1.23930	−	0.282863i	0.129914	−	0.0296521i
$92$	2.81695	+	7.17746i	0.293687	+	0.748302i
$93$	−11.8175	+	5.71232i	−1.22542	+	0.592340i
$94$	2.14860	−	0.662755i	0.221611	−	0.0683580i
$95$	−2.72960	−	2.34901i	−0.280052	−	0.241004i
$96$	−1.35575	−	1.07793i	−0.138371	−	0.110016i
$97$	7.39745	+	13.9967i	0.751097	+	1.42114i	0.901616	+	0.432538i	$0.142382\pi$
$97$	7.39745	+	13.9967i	0.751097	+	1.42114i	−0.150519	+	0.988607i	$0.548094\pi$
$98$	−6.53107	−	2.28532i	−0.659737	−	0.230852i
$99$	8.92827	−	3.15349i	0.897325	−	0.316938i
$100$	1.97684	+	4.10496i	0.197684	+	0.410496i
$101$	14.1783	+	10.4641i	1.41080	+	1.04122i	0.991038	+	0.133579i	$0.0426471\pi$
$101$	14.1783	+	10.4641i	1.41080	+	1.04122i	0.419758	+	0.907636i	$0.362115\pi$
$102$	2.46720	−	0.470560i	0.244290	−	0.0465924i
$103$	9.52627	+	6.49490i	0.938652	+	0.639962i	0.932944	−	0.360022i	$-0.117231\pi$
$103$	9.52627	+	6.49490i	0.938652	+	0.639962i	0.00570770	+	0.999984i	$0.498183\pi$
$104$	−1.15857	+	4.32384i	−0.113607	+	0.423987i
$105$	−0.153540	−	0.289485i	−0.0149839	−	0.0282508i
$106$	−3.33631	+	1.76329i	−0.324051	+	0.171266i
$107$	−6.49175	+	13.4803i	−0.627581	+	1.30319i	0.308440	+	0.951244i	$0.400193\pi$
$107$	−6.49175	+	13.4803i	−0.627581	+	1.30319i	−0.936022	+	0.351943i	$0.885521\pi$
$108$	0.988424	+	5.10128i	0.0951111	+	0.490871i
$109$	8.78750	+	2.00569i	0.841690	+	0.192110i	0.621566	−	0.783362i	$-0.286497\pi$
$109$	8.78750	+	2.00569i	0.841690	+	0.192110i	0.220124	+	0.975472i	$0.429354\pi$
$110$	−0.313399	−	2.07927i	−0.0298814	−	0.198250i
$111$	−0.840361	−	5.52062i	−0.0797635	−	0.523994i
$112$	−0.208168	+	0.193152i	−0.0196700	+	0.0182511i
$113$	−4.54823	+	8.60567i	−0.427861	+	0.809553i	−0.999943	−	0.0106433i	$-0.996612\pi$
$113$	−4.54823	+	8.60567i	−0.427861	+	0.809553i	0.572082	+	0.820196i	$0.306136\pi$
$114$	8.57587	−	3.75656i	0.803203	−	0.351834i
$115$	−4.44861	−	2.56841i	−0.414835	−	0.239505i
$116$	−0.646486	−	5.34622i	−0.0600247	−	0.496384i
$117$	11.0735	−	7.59732i	1.02374	−	0.702372i
$118$	−0.108515	−	0.963099i	−0.00998963	−	0.0886604i
$119$	−0.0153976	−	0.411509i	−0.00141149	−	0.0377229i
$120$	1.15391	−	0.00168818i	0.105338	−	0.000154109i
$121$	−0.154697	+	1.02635i	−0.0140634	+	0.0933045i
$122$	1.59125	−	4.05445i	0.144065	−	0.367072i
$123$	−4.84447	−	2.32425i	−0.436811	−	0.209570i
$124$	−7.44601	−	1.40886i	−0.668672	−	0.126519i
$125$	−5.73597	−	2.76230i	−0.513041	−	0.247067i
$126$	0.851231	−	0.0343453i	0.0758337	−	0.00305972i
$127$	3.66671	−	10.4789i	0.325368	−	0.929848i	−0.658755	−	0.752358i	$-0.728917\pi$
$127$	3.66671	−	10.4789i	0.325368	−	0.929848i	0.984123	−	0.177490i	$-0.0567978\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−7.57265	+	7.04704i	−0.666735	+	0.620457i
$130$	−1.19257	−	2.73339i	−0.104595	−	0.239734i
$131$	3.10917	+	7.12630i	0.271650	+	0.622628i	0.997898	−	0.0648049i	$-0.0206425\pi$
$131$	3.10917	+	7.12630i	0.271650	+	0.622628i	−0.726248	+	0.687432i	$0.758738\pi$
$132$	5.22630	+	1.60373i	0.454891	+	0.139587i
$133$	−0.397291	−	1.48271i	−0.0344495	−	0.128567i
$134$	0.387554	−	1.10757i	0.0334796	−	0.0956791i
$135$	−2.63379	−	2.24652i	−0.226681	−	0.193349i
$136$	1.30651	+	0.629183i	0.112032	+	0.0539520i
$137$	−3.66473	−	0.693404i	−0.313099	−	0.0592415i	0.0269873	−	0.999636i	$-0.491409\pi$
$137$	−3.66473	−	0.693404i	−0.313099	−	0.0592415i	−0.340086	+	0.940394i	$0.610456\pi$
$138$	11.0233	−	7.53922i	0.938367	−	0.641781i
$139$	−2.29338	+	5.84343i	−0.194522	+	0.495633i	−0.994542	−	0.104340i	$-0.966727\pi$
$139$	−2.29338	+	5.84343i	−0.194522	+	0.495633i	0.800020	+	0.599973i	$0.204822\pi$
$140$	0.0281970	−	0.187075i	0.00238308	−	0.0158107i
$141$	−1.95219	−	3.36989i	−0.164404	−	0.283796i
$142$	0.601956	+	16.0876i	0.0505151	+	1.35004i
$143$	−1.58191	−	14.0398i	−0.132286	−	1.17407i
$144$	−1.29374	+	2.70670i	−0.107811	+	0.225559i
$145$	2.55743	+	2.51613i	0.212383	+	0.208953i
$146$	−11.1376	−	6.43031i	−0.921756	−	0.532176i
$147$	−1.32443	+	11.9113i	−0.109237	+	0.982425i
$148$	1.50650	−	2.85043i	0.123833	−	0.234304i
$149$	−0.571149	+	0.529949i	−0.0467903	+	0.0434151i	−0.703221	−	0.710971i	$-0.748256\pi$
$149$	−0.571149	+	0.529949i	−0.0467903	+	0.0434151i	0.656431	+	0.754386i	$0.272065\pi$
$150$	6.16262	−	4.92929i	0.503176	−	0.402475i
$151$	−2.06562	−	13.7045i	−0.168098	−	1.11526i	−0.900649	−	0.434547i	$-0.856909\pi$
$151$	−2.06562	−	13.7045i	−0.168098	−	1.11526i	0.732551	−	0.680712i	$-0.238329\pi$
$152$	5.26994	+	1.20283i	0.427449	+	0.0975624i
$153$	−1.75133	−	3.98226i	−0.141587	−	0.321947i
$154$	0.388891	−	0.807539i	0.0313377	−	0.0650734i
$155$	4.46359	−	2.35908i	0.358524	−	0.189486i
$156$	7.74829	+	0.278570i	0.620360	+	0.0223034i
$157$	−4.08852	+	15.2586i	−0.326299	+	1.21777i	0.586700	+	0.809804i	$0.300427\pi$
$157$	−4.08852	+	15.2586i	−0.326299	+	1.21777i	−0.912999	+	0.407961i	$0.866240\pi$
$158$	−7.40364	−	5.04772i	−0.589002	−	0.401575i
$159$	4.27065	+	4.94793i	0.338685	+	0.392396i
$160$	0.536034	+	0.395611i	0.0423772	+	0.0312758i
$161$	−0.950020	−	1.97274i	−0.0748721	−	0.155474i
$162$	8.22786	−	3.64724i	0.646442	−	0.286554i
$163$	−1.02164	−	0.357487i	−0.0800209	−	0.0280005i	0.289972	−	0.957035i	$-0.406354\pi$
$163$	−1.02164	−	0.357487i	−0.0800209	−	0.0280005i	−0.369993	+	0.929035i	$0.620640\pi$
$164$	−1.44956	−	2.74271i	−0.113192	−	0.214169i
$165$	−3.38836	+	1.33556i	−0.263783	+	0.103973i
$166$	3.11608	+	2.68160i	0.241854	+	0.208133i
$167$	−11.6180	+	3.58368i	−0.899027	+	0.277313i	−0.709619	−	0.704585i	$-0.751133\pi$
$167$	−11.6180	+	3.58368i	−0.899027	+	0.277313i	−0.189408	+	0.981898i	$0.560657\pi$
$168$	0.406797	+	0.276479i	0.0313851	+	0.0213308i
$169$	−2.57123	−	6.55138i	−0.197787	−	0.503952i
$170$	−0.941866	+	0.214975i	−0.0722379	+	0.0164878i
$171$	−9.66776	−	13.0194i	−0.739312	−	0.995622i
$172$	−5.93477	+	0.668688i	−0.452522	+	0.0509870i
$173$	5.14940	−	8.91903i	0.391502	−	0.678101i	−0.601146	−	0.799139i	$-0.705289\pi$
$173$	5.14940	−	8.91903i	0.391502	−	0.678101i	0.992648	+	0.121038i	$0.0386223\pi$
$174$	−8.77397	+	3.16504i	−0.665153	+	0.239941i
$175$	−0.646917	−	1.12049i	−0.0489023	−	0.0847013i
$176$	1.87426	+	2.53953i	0.141278	+	0.191424i
$177$	−1.58368	+	0.556754i	−0.119036	+	0.0418482i
$178$	2.40781	−	7.80593i	0.180473	−	0.585079i
$179$	6.25402	−	7.84229i	0.467447	−	0.586160i	−0.491097	−	0.871105i	$-0.663404\pi$
$179$	6.25402	−	7.84229i	0.467447	−	0.586160i	0.958544	+	0.284945i	$0.0919753\pi$
$180$	−0.450439	−	1.94722i	−0.0335737	−	0.145137i
$181$	−3.03815	+	13.3110i	−0.225824	+	0.989398i	0.727182	+	0.686445i	$0.240830\pi$
$181$	−3.03815	+	13.3110i	−0.225824	+	0.989398i	−0.953005	+	0.302953i	$0.902027\pi$
$182$	0.236326	−	1.24901i	0.0175177	−	0.0925831i
$183$	−7.46137	−	1.11346i	−0.551560	−	0.0823093i
$184$	7.70507	+	0.288303i	0.568025	+	0.0212540i
$185$	0.399320	+	2.11046i	0.0293586	+	0.155164i
$186$	0.509975	+	13.1158i	0.0373931	+	0.961696i
$187$	−4.56417	−	0.342037i	−0.333765	−	0.0250122i
$188$	0.251751	−	2.23436i	0.0183609	−	0.162957i
$189$	−0.388159	−	1.42361i	−0.0282344	−	0.103552i
$190$	−3.24457	+	1.56250i	−0.235385	+	0.113356i
$191$	3.86356	−	1.03524i	0.279558	−	0.0749073i	−0.116316	−	0.993212i	$-0.537108\pi$
$191$	3.86356	−	1.03524i	0.279558	−	0.0749073i	0.395874	+	0.918305i	$0.370442\pi$
$192$	−1.53015	+	0.811572i	−0.110429	+	0.0585702i
$193$	0.997369	−	26.6552i	0.0717922	−	1.91869i	−0.243858	−	0.969811i	$-0.578413\pi$
$193$	0.997369	−	26.6552i	0.0717922	−	1.91869i	0.315651	−	0.948876i	$-0.397777\pi$
$194$	15.7870	−	1.18307i	1.13344	−	0.0849395i
$195$	−4.15154	+	3.07337i	−0.297298	+	0.220088i
$196$	−4.70636	+	5.07225i	−0.336168	+	0.362303i
$197$	−13.3847	+	10.6739i	−0.953619	+	0.760486i	−0.970930	−	0.239364i	$-0.923061\pi$
$197$	−13.3847	+	10.6739i	−0.953619	+	0.760486i	0.0173108	+	0.999850i	$0.494490\pi$
$198$	0.679974	−	9.44437i	0.0483237	−	0.671182i
$199$	2.78874	+	12.2183i	0.197688	+	0.866129i	0.972308	+	0.233702i	$0.0750841\pi$
$199$	2.78874	+	12.2183i	0.197688	+	0.866129i	−0.774620	+	0.632427i	$0.782059\pi$
$200$	4.55297	−	0.170360i	0.321944	−	0.0120463i
$201$	−2.01996	−	0.224603i	−0.142477	−	0.0158423i
$202$	15.2608	−	8.81082i	1.07375	−	0.619927i
$203$	0.296527	+	1.50023i	0.0208121	+	0.105295i
$204$	0.555318	−	2.44952i	0.0388800	−	0.171501i
$205$	1.89429	+	0.826469i	0.132303	+	0.0577231i
$206$	9.76246	−	6.13416i	0.680183	−	0.427387i
$207$	−17.0025	−	15.6836i	−1.18175	−	1.09009i
$208$	3.49977	+	2.79097i	0.242665	+	0.193519i
$209$	−16.8706	+	2.54283i	−1.16696	+	0.175891i
$210$	−0.326730	+	0.0249658i	−0.0225465	+	0.00172280i
$211$	−13.7330	+	15.9580i	−0.945418	+	1.09860i	0.0495870	+	0.998770i	$0.484209\pi$
$211$	−13.7330	+	15.9580i	−0.945418	+	1.09860i	−0.995005	+	0.0998257i	$0.968171\pi$
$212$	0.282002	+	3.76306i	0.0193680	+	0.258448i
$213$	26.9234	−	7.25633i	1.84476	−	0.497195i
$214$	9.75950	+	11.3407i	0.667146	+	0.775237i
$215$	2.81347	−	2.81347i	0.191877	−	0.191877i
$216$	5.07090	+	1.13401i	0.345031	+	0.0771594i
$217$	2.13846	+	0.240947i	0.145168	+	0.0163565i
$218$	5.35239	−	7.25223i	0.362510	−	0.491183i
$219$	−6.53459	+	21.2952i	−0.441567	+	1.43900i
$220$	−2.03110	−	0.544232i	−0.136937	−	0.0366921i
$221$	−6.37810	+	1.20680i	−0.429037	+	0.0811782i
$222$	−5.39604	−	1.43741i	−0.362159	−	0.0964725i
$223$	−4.10171	+	2.79650i	−0.274671	+	0.187268i	−0.692819	−	0.721111i	$-0.743632\pi$
$223$	−4.10171	+	2.79650i	−0.274671	+	0.187268i	0.418148	+	0.908379i	$0.362679\pi$
$224$	0.0937909	+	0.268039i	0.00626666	+	0.0179091i
$225$	−10.7113	−	8.49085i	−0.714089	−	0.566057i
$226$	6.06883	+	7.61007i	0.403693	+	0.506214i
$227$	27.2483	−	10.6942i	1.80853	−	0.709797i	0.817541	−	0.575870i	$-0.195336\pi$
$227$	27.2483	−	10.6942i	1.80853	−	0.709797i	0.990991	−	0.133927i	$-0.0427587\pi$
$228$	−0.0136974	−	9.36253i	−0.000907135	−	0.620049i
$229$	−6.88387	−	3.63823i	−0.454899	−	0.240421i	0.224092	−	0.974568i	$-0.428059\pi$
$229$	−6.88387	−	3.63823i	−0.454899	−	0.240421i	−0.678991	+	0.734147i	$0.737582\pi$
$230$	−4.13307	+	3.05034i	−0.272526	+	0.201134i
$231$	−1.51402	−	0.343236i	−0.0996152	−	0.0225832i
$232$	−5.15867	−	1.54537i	−0.338683	−	0.101458i
$233$		−	10.0148i		−	0.656091i	−0.944662	−	0.328045i	$-0.893610\pi$
$233$		−	10.0148i		−	0.656091i	0.944662	−	0.328045i	$-0.106390\pi$
$234$	−2.53522	−	13.1876i	−0.165733	−	0.862102i
$235$	0.796972	+	1.26837i	0.0519887	+	0.0827396i
$236$	−0.926135	−	0.285675i	−0.0602862	−	0.0185958i
$237$	−5.64906	+	14.4557i	−0.366946	+	0.939000i
$238$	−0.383331	−	0.150446i	−0.0248476	−	0.00975198i
$239$	8.13469	+	26.3720i	0.526189	+	1.70586i	0.693938	+	0.720035i	$0.255874\pi$
$239$	8.13469	+	26.3720i	0.526189	+	1.70586i	−0.167749	+	0.985830i	$0.553650\pi$
$240$	0.459894	−	1.05831i	0.0296860	−	0.0683136i
$241$	8.49267	+	12.4565i	0.547061	+	0.802391i	0.995827	−	0.0912584i	$-0.0290889\pi$
$241$	8.49267	+	12.4565i	0.547061	+	0.802391i	−0.448767	+	0.893649i	$0.648137\pi$
$242$	0.878851	+	0.552219i	0.0564947	+	0.0354980i
$243$	−9.34824	−	12.4744i	−0.599690	−	0.800232i
$244$	−3.07982	−	3.07982i	−0.197165	−	0.197165i
$245$	0.344489	−	4.59688i	0.0220086	−	0.293684i
$246$	−4.06758	+	3.51081i	−0.259340	+	0.223841i
$247$	−22.1779	+	9.67613i	−1.41115	+	0.615678i
$248$	−4.26891	+	6.26134i	−0.271076	+	0.397596i
$249$	3.31801	−	6.30028i	0.210271	−	0.399264i
$250$	−4.82558	+	4.15275i	−0.305197	+	0.262643i
$251$	−3.16893	+	5.04332i	−0.200021	+	0.318331i	−0.931640	−	0.363382i	$-0.881622\pi$
$251$	−3.16893	+	5.04332i	−0.200021	+	0.318331i	0.731619	+	0.681713i	$0.238765\pi$
$252$	0.308921	−	0.793941i	0.0194602	−	0.0500136i
$253$	−22.9706	+	8.03777i	−1.44415	+	0.505330i
$254$	−8.13823	−	7.55118i	−0.510638	−	0.473803i
$255$	0.728229	+	1.50654i	0.0456034	+	0.0943432i
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	0.701393	+	0.755922i	0.0437517	+	0.0471531i	0.754548	−	0.656244i	$-0.227856\pi$
$257$	0.701393	+	0.755922i	0.0437517	+	0.0471531i	−0.710797	+	0.703397i	$0.751665\pi$
$258$	3.43081	+	9.75886i	0.213593	+	0.607560i
$259$	−0.366120	+	0.839156i	−0.0227496	+	0.0521426i
$260$	−2.98222			−0.184949
$261$	8.74609	+	13.5833i	0.541369	+	0.840785i
$262$	7.77503			0.480343
$263$	7.29916	−	16.7298i	0.450085	−	1.03161i	−0.532607	−	0.846362i	$-0.678788\pi$
$263$	7.29916	−	16.7298i	0.450085	−	1.03161i	0.982693	−	0.185244i	$-0.0593075\pi$
$264$	3.55987	−	4.14891i	0.219095	−	0.255348i
$265$	−1.70998	−	1.84292i	−0.105043	−	0.113209i
$266$	−1.51787	−	0.228782i	−0.0930666	−	0.0140275i
$267$	−14.1108	−	1.03670i	−0.863568	−	0.0634451i
$268$	−0.860173	−	0.798124i	−0.0525434	−	0.0487532i
$269$	11.4389	−	4.00264i	0.697441	−	0.244045i	0.0418089	−	0.999126i	$-0.486688\pi$
$269$	11.4389	−	4.00264i	0.697441	−	0.244045i	0.655632	+	0.755080i	$0.272402\pi$
$270$	−3.11230	+	1.51567i	−0.189409	+	0.0922408i
$271$	9.20529	−	14.6501i	0.559181	−	0.889932i	−0.440789	−	0.897611i	$-0.645301\pi$
$271$	9.20529	−	14.6501i	0.559181	−	0.889932i	0.999971	+	0.00767855i	$0.00244418\pi$
$272$	1.09915	−	0.945894i	0.0666457	−	0.0573532i
$273$	−2.20008	+	0.0855445i	−0.133155	+	0.00517739i
$274$	−2.10104	+	3.08166i	−0.126929	+	0.186170i
$275$	−13.1806	+	5.75064i	−0.794820	+	0.346777i
$276$	−2.50203	−	13.1184i	−0.150604	−	0.789637i
$277$	−0.850574	+	11.3501i	−0.0511060	+	0.681962i	0.911542	+	0.411207i	$0.134893\pi$
$277$	−0.850574	+	11.3501i	−0.0511060	+	0.681962i	−0.962648	+	0.270756i	$0.912726\pi$
$278$	4.43877	+	4.43877i	0.266219	+	0.266219i
$279$	21.9424	−	5.94832i	1.31366	−	0.356117i
$280$	−0.160190	−	0.100654i	−0.00957317	−	0.00601522i
$281$	6.00237	+	8.80386i	0.358071	+	0.525194i	0.962434	−	0.271515i	$-0.0875246\pi$
$281$	6.00237	+	8.80386i	0.358071	+	0.525194i	−0.604363	+	0.796709i	$0.706572\pi$
$282$	−3.86938	+	0.441708i	−0.230418	+	0.0263033i
$283$	0.303968	+	0.985440i	0.0180690	+	0.0585783i	0.964158	−	0.265328i	$-0.0854801\pi$
$283$	0.303968	+	0.985440i	0.0180690	+	0.0585783i	−0.946089	+	0.323906i	$0.895004\pi$
$284$	14.9860	+	5.88158i	0.889257	+	0.349008i
$285$	3.89612	+	4.87094i	0.230786	+	0.288530i
$286$	−13.5009	−	4.16449i	−0.798328	−	0.246251i
$287$	0.468692	+	0.745919i	0.0276660	+	0.0440302i
$288$	1.96351	+	2.26818i	0.115701	+	0.133654i
$289$		−	14.8972i		−	0.876303i
$290$	3.32889	−	1.33786i	0.195479	−	0.0785621i
$291$	−8.12067	−	26.1905i	−0.476042	−	1.53531i
$292$	−10.3476	+	7.63689i	−0.605549	+	0.446915i
$293$	−0.496469	−	0.262392i	−0.0290040	−	0.0153291i	0.452704	−	0.891661i	$-0.350460\pi$
$293$	−0.496469	−	0.262392i	−0.0290040	−	0.0153291i	−0.481708	+	0.876332i	$0.659983\pi$
$294$	10.3878	+	5.97715i	0.605828	+	0.348594i
$295$	0.601056	−	0.235897i	0.0349948	−	0.0137344i
$296$	−2.01016	−	2.52066i	−0.116838	−	0.146510i
$297$	−16.2064	+	2.51552i	−0.940391	+	0.145965i
$298$	0.257333	+	0.735416i	0.0149069	+	0.0426015i
$299$	−28.5175	+	19.4429i	−1.64921	+	1.12441i
$300$	−2.05362	−	7.61961i	−0.118566	−	0.439918i
$301$	1.66642	−	0.315304i	0.0960509	−	0.0181738i
$302$	−13.3871	−	3.58706i	−0.770340	−	0.206412i
$303$	−20.7927	−	22.3435i	−1.19451	−	1.28360i
$304$	3.20988	−	4.34923i	0.184099	−	0.249445i
$305$	2.88347	+	0.324889i	0.165107	+	0.0186031i
$306$	−4.35033	+	0.0127292i	−0.248692	+	0.000727677i
$307$	0.561795	−	0.561795i	0.0320633	−	0.0320633i	−0.690893	−	0.722957i	$-0.742783\pi$
$307$	0.561795	−	0.561795i	0.0320633	−	0.0320633i	0.722957	+	0.690893i	$0.242783\pi$
$308$	−0.584646	−	0.679371i	−0.0333133	−	0.0387108i
$309$	−14.1416	−	14.1002i	−0.804486	−	0.802135i
$310$	−0.377286	−	5.03453i	−0.0214284	−	0.285942i
$311$	3.45147	−	4.01068i	0.195715	−	0.227425i	−0.651536	−	0.758618i	$-0.725875\pi$
$311$	3.45147	−	4.01068i	0.195715	−	0.227425i	0.847251	+	0.531193i	$0.178256\pi$
$312$	3.35381	−	6.99040i	0.189872	−	0.395753i
$313$	2.02625	−	0.305409i	0.114531	−	0.0172627i	−0.0915268	−	0.995803i	$-0.529175\pi$
$313$	2.02625	−	0.305409i	0.114531	−	0.0172627i	0.206057	+	0.978540i	$0.433937\pi$
$314$	12.3504	+	9.84915i	0.696976	+	0.555820i
$315$	0.168878	+	0.541856i	0.00951522	+	0.0305301i
$316$	−7.58720	+	4.76736i	−0.426813	+	0.268185i
$317$	8.36843	+	3.65111i	0.470018	+	0.205067i	0.621533	−	0.783388i	$-0.286510\pi$
$317$	8.36843	+	3.65111i	0.470018	+	0.205067i	−0.151515	+	0.988455i	$0.548415\pi$
$318$	6.24288	−	1.93568i	0.350083	−	0.108548i
$319$	16.9386	−	1.40812i	0.948381	−	0.0788394i
$320$	0.576958	−	0.333107i	0.0322529	−	0.0186212i
$321$	15.3583	−	20.8735i	0.857214	−	1.16505i
$322$	−2.18804	+	0.0818708i	−0.121935	+	0.00456248i
$323$	1.74424	+	7.64203i	0.0970524	+	0.425214i
$324$	−0.0526679	−	8.99985i	−0.00292599	−	0.499991i
$325$	−15.9455	+	12.7161i	−0.884497	+	0.705363i
$326$	−0.736204	+	0.793439i	−0.0407746	+	0.0439445i
$327$	−14.3183	−	6.22210i	−0.791805	−	0.344083i
$328$	−3.09353	+	0.231828i	−0.170812	+	0.0128006i
$329$	−0.0238748	+	0.638069i	−0.00131626	+	0.0351779i
$330$	−0.130857	+	3.63972i	−0.00720342	+	0.200360i
$331$	11.7591	−	3.15083i	0.646337	−	0.173185i	0.0792647	−	0.996854i	$-0.474743\pi$
$331$	11.7591	−	3.15083i	0.646337	−	0.173185i	0.567072	+	0.823668i	$0.308076\pi$
$332$	3.70395	−	1.78373i	0.203281	−	0.0978948i
$333$	−0.333370	+	9.66639i	−0.0182686	+	0.529715i
$334$	−1.36128	+	12.0817i	−0.0744860	+	0.661081i
$335$	0.779558	+	0.0584198i	0.0425918	+	0.00319182i
$336$	0.416085	−	0.262293i	0.0226993	−	0.0143093i
$337$	−2.50077	−	13.2169i	−0.136226	−	0.719971i	−0.982360	−	0.187000i	$-0.940123\pi$
$337$	−2.50077	−	13.2169i	−0.136226	−	0.719971i	0.846134	−	0.532970i	$-0.178924\pi$
$338$	−7.03296	−	0.263155i	−0.382543	−	0.0143137i
$339$	10.4922	−	13.1964i	0.569860	−	0.716730i
$340$	−0.179607	+	0.949246i	−0.00974056	+	0.0514801i
$341$	5.32240	−	23.3189i	0.288224	−	1.26279i
$342$	−15.7992	+	3.65473i	−0.854323	+	0.197625i
$343$	2.46450	−	3.09038i	0.133070	−	0.166865i
$344$	−1.76037	+	5.70699i	−0.0949129	+	0.307700i
$345$	6.75232	+	5.79367i	0.363533	+	0.311921i
$346$	−6.11564	−	8.28640i	−0.328779	−	0.445479i
$347$	3.78303	+	6.55240i	0.203084	+	0.351751i	0.949520	−	0.313705i	$-0.101570\pi$
$347$	3.78303	+	6.55240i	0.203084	+	0.351751i	−0.746437	+	0.665456i	$0.768237\pi$
$348$	−0.607685	+	9.30756i	−0.0325753	+	0.498938i
$349$	14.8180	−	25.6655i	0.793190	−	1.37384i	−0.130793	−	0.991410i	$-0.541752\pi$
$349$	14.8180	−	25.6655i	0.793190	−	1.37384i	0.923982	−	0.382435i	$-0.124914\pi$
$350$	−1.28570	+	0.144863i	−0.0687234	+	0.00774327i
$351$	−21.2781	+	9.39493i	−1.13574	+	0.501464i
$352$	3.07714	−	0.702337i	0.164012	−	0.0374347i
$353$	−4.06537	−	10.3584i	−0.216378	−	0.551322i	0.780932	−	0.624615i	$-0.214744\pi$
$353$	−4.06537	−	10.3584i	−0.216378	−	0.551322i	−0.997310	+	0.0732935i	$0.976649\pi$
$354$	−0.123000	+	1.67418i	−0.00653735	+	0.0889816i
$355$	−10.2488	+	3.16134i	−0.543950	+	0.167786i
$356$	−6.19175	−	5.32843i	−0.328162	−	0.282406i
$357$	−0.105273	+	0.705441i	−0.00557163	+	0.0373359i
$358$	−4.68701	−	8.86826i	−0.247716	−	0.468702i
$359$	21.7579	+	7.61343i	1.14834	+	0.401822i	0.836314	−	0.548252i	$-0.184706\pi$
$359$	21.7579	+	7.61343i	1.14834	+	0.401822i	0.312027	+	0.950073i	$0.398992\pi$
$360$	−1.96488	−	0.365823i	−0.103558	−	0.0192806i
$361$	4.43389	+	9.20706i	0.233363	+	0.484582i
$362$	10.9854	+	8.10761i	0.577381	+	0.426127i
$363$	0.591282	−	1.69775i	0.0310343	−	0.0891088i
$364$	−1.05029	−	0.716078i	−0.0550504	−	0.0375327i
$365$	2.21754	−	8.27597i	0.116071	−	0.433184i
$366$	−4.00430	+	6.39355i	−0.209308	+	0.334196i
$367$	22.4196	−	11.8491i	1.17029	−	0.618517i	0.234861	−	0.972029i	$-0.424536\pi$
$367$	22.4196	−	11.8491i	1.17029	−	0.618517i	0.935430	+	0.353512i	$0.115013\pi$
$368$	3.34544	−	6.94688i	0.174393	−	0.362131i
$369$	7.50422	+	5.50452i	0.390654	+	0.286554i
$370$	2.09405	+	0.477953i	0.108865	+	0.0248476i
$371$	−0.159715	−	1.05964i	−0.00829200	−	0.0550138i
$372$	12.2254	+	4.77748i	0.633856	+	0.247701i
$373$	−21.2838	+	19.7485i	−1.10203	+	1.02254i	−0.102419	+	0.994741i	$0.532658\pi$
$373$	−21.2838	+	19.7485i	−1.10203	+	1.02254i	−0.999614	+	0.0277953i	$0.991151\pi$
$374$	−2.13867	+	4.04657i	−0.110588	+	0.209243i
$375$	8.88187	+	6.53507i	0.458658	+	0.337470i
$376$	−1.94725	−	1.12425i	−0.100422	−	0.0579786i
$377$	22.6877	−	8.14665i	1.16847	−	0.419574i
$378$	−1.46005	−	0.213517i	−0.0750966	−	0.0109821i
$379$	0.306359	+	2.71901i	0.0157366	+	0.139666i	0.999124	−	0.0418546i	$-0.0133266\pi$
$379$	0.306359	+	2.71901i	0.0157366	+	0.139666i	−0.983387	+	0.181521i	$0.941898\pi$
$380$	0.134653	+	3.59868i	0.00690755	+	0.184608i
$381$	−9.59011	+	16.6668i	−0.491316	+	0.853867i
$382$	0.596148	−	3.95518i	0.0305016	−	0.202365i
$383$	4.08150	−	10.3995i	0.208555	−	0.531389i	−0.787873	−	0.615838i	$-0.788818\pi$
$383$	4.08150	−	10.3995i	0.208555	−	0.531389i	0.996428	+	0.0844489i	$0.0269130\pi$
$384$	0.131963	+	1.72702i	0.00673421	+	0.0881314i
$385$	0.586718	+	0.111013i	0.0299019	+	0.00565775i
$386$	−24.0323	−	11.5734i	−1.22321	−	0.589069i
$387$	15.1428	−	9.57675i	0.769750	−	0.486813i
$388$	5.22873	−	14.9429i	0.265449	−	0.758608i
$389$	−2.65622	−	9.91315i	−0.134676	−	0.502616i	−0.999999	−	0.00140240i	$-0.999554\pi$
$389$	−2.65622	−	9.91315i	−0.134676	−	0.502616i	0.865323	−	0.501214i	$-0.167113\pi$
$390$	1.15677	+	5.03416i	0.0585751	+	0.254915i
$391$	4.47122	+	10.2481i	0.226119	+	0.518271i
$392$	2.76700	+	6.34202i	0.139754	+	0.320321i
$393$	−3.01584	−	13.1247i	−0.152129	−	0.662054i
$394$	4.43089	+	16.5363i	0.223225	+	0.833087i
$395$	1.97167	−	5.63471i	0.0992055	−	0.283513i
$396$	−8.38444	−	4.39997i	−0.421334	−	0.221107i
$397$	−14.0274	−	6.75525i	−0.704016	−	0.339036i	0.0473898	−	0.998876i	$-0.484910\pi$
$397$	−14.0274	−	6.75525i	−0.704016	−	0.339036i	−0.751406	+	0.659840i	$0.770624\pi$
$398$	12.3140	+	2.32993i	0.617244	+	0.116789i
$399$	0.202565	+	2.65100i	0.0101410	+	0.132716i
$400$	1.66455	−	4.24121i	0.0832276	−	0.212060i
$401$	5.01333	−	33.2613i	0.250354	−	1.66099i	−0.411539	−	0.911392i	$-0.635009\pi$
$401$	5.01333	−	33.2613i	0.250354	−	1.66099i	0.661893	−	0.749598i	$-0.269753\pi$
$402$	−1.01363	+	1.76161i	−0.0505553	+	0.0878609i
$403$	−1.26840	−	33.8988i	−0.0631836	−	1.68862i
$404$	−1.97300	−	17.5108i	−0.0981603	−	0.871197i
$405$	3.76577	+	4.66584i	0.187122	+	0.231848i
$406$	1.49363	+	0.328143i	0.0741276	+	0.0162855i
$407$	8.81265	+	5.08798i	0.436827	+	0.252202i
$408$	−2.02307	−	1.48853i	−0.100157	−	0.0736931i
$409$	−16.8151	+	31.8156i	−0.831451	+	1.57318i	−0.0120741	+	0.999927i	$0.503843\pi$
$409$	−16.8151	+	31.8156i	−0.831451	+	1.57318i	−0.819377	+	0.573255i	$0.805680\pi$
$410$	1.51502	−	1.40573i	0.0748215	−	0.0694242i
$411$	6.01700	+	2.35135i	0.296797	+	0.115983i
$412$	−1.71841	−	11.4009i	−0.0846600	−	0.561682i
$413$	0.268326	+	0.0612436i	0.0132034	+	0.00301360i
$414$	−21.1742	+	9.31205i	−1.04065	+	0.457662i
$415$	−1.18834	+	2.46762i	−0.0583335	+	0.121131i
$416$	3.95763	−	2.09167i	0.194039	−	0.102552i
$417$	5.77116	−	9.21464i	0.282615	−	0.451243i
$418$	−4.41574	+	16.4798i	−0.215981	+	0.806053i
$419$	21.8859	+	14.9216i	1.06920	+	0.728967i	0.964112	−	0.265496i	$-0.0855358\pi$
$419$	21.8859	+	14.9216i	1.06920	+	0.728967i	0.105086	+	0.994463i	$0.466488\pi$
$420$	−0.107774	+	0.309452i	−0.00525884	+	0.0150997i
$421$	−8.78935	−	6.48683i	−0.428367	−	0.316149i	0.358211	−	0.933641i	$-0.383387\pi$
$421$	−8.78935	−	6.48683i	−0.428367	−	0.316149i	−0.786577	+	0.617492i	$0.788149\pi$
$422$	9.13481	+	18.9686i	0.444675	+	0.923378i
$423$	2.24651	+	6.36040i	0.109229	+	0.309253i
$424$	3.56185	+	1.24635i	0.172979	+	0.0605279i
$425$	3.08723	+	5.84132i	0.149753	+	0.283346i
$426$	4.11556	−	27.5787i	0.199400	−	1.33619i
$427$	0.937504	+	0.806787i	0.0453690	+	0.0390432i
$428$	14.2972	−	4.41012i	0.691084	−	0.213171i
$429$	−1.79306	+	24.4057i	−0.0865695	+	1.17832i
$430$	−1.45363	−	3.70380i	−0.0701005	−	0.178613i
$431$	−6.60113	+	1.50666i	−0.317965	+	0.0725734i	−0.378525	−	0.925591i	$-0.623569\pi$
$431$	−6.60113	+	1.50666i	−0.317965	+	0.0725734i	0.0605598	+	0.998165i	$0.480711\pi$
$432$	3.06720	−	4.19432i	0.147571	−	0.201799i
$433$	−31.2630	+	3.52249i	−1.50240	+	0.169280i	−0.824496	−	0.565867i	$-0.808541\pi$
$433$	−31.2630	+	3.52249i	−1.50240	+	0.169280i	−0.677907	+	0.735148i	$0.737113\pi$
$434$	1.07600	−	1.86368i	0.0516495	−	0.0894596i
$435$	−3.54963	−	5.10042i	−0.170192	−	0.244546i
$436$	−4.50674	−	7.80591i	−0.215834	−	0.373835i
$437$	24.7496	+	33.5345i	1.18393	+	1.60417i
$438$	16.9052	+	14.5051i	0.807763	+	0.693082i
$439$	−2.05746	+	6.67013i	−0.0981973	+	0.318348i	−0.991321	−	0.131463i	$-0.958032\pi$
$439$	−2.05746	+	6.67013i	−0.0981973	+	0.318348i	0.893124	+	0.449811i	$0.148509\pi$
$440$	−1.31104	+	1.64400i	−0.0625016	+	0.0783745i
$441$	6.06048	−	19.8537i	0.288594	−	0.945413i
$442$	−1.44444	+	6.32851i	−0.0687051	+	0.301017i
$443$	−5.33244	+	28.1826i	−0.253352	+	1.33900i	0.592497	+	0.805573i	$0.298142\pi$
$443$	−5.33244	+	28.1826i	−0.253352	+	1.33900i	−0.845849	+	0.533423i	$0.820905\pi$
$444$	−3.47531	+	4.37100i	−0.164931	+	0.207439i
$445$	5.43839	+	0.203490i	0.257804	+	0.00964636i
$446$	0.922925	+	4.87777i	0.0437017	+	0.230969i
$447$	1.14161	−	0.719652i	0.0539962	−	0.0340384i
$448$	0.283181	+	0.0212214i	0.0133790	+	0.00100262i
$449$	−0.0570312	+	0.506166i	−0.00269147	+	0.0238874i	−0.994986	−	0.100013i	$-0.968112\pi$
$449$	−0.0570312	+	0.506166i	−0.00269147	+	0.0238874i	0.992295	+	0.123900i	$0.0395402\pi$
$450$	−12.0658	+	6.42218i	−0.568786	+	0.302745i
$451$	8.82175	−	4.24833i	0.415400	−	0.200046i
$452$	9.40198	−	2.51925i	0.442232	−	0.118496i
$453$	−0.862482	+	23.9896i	−0.0405229	+	1.12713i
$454$	1.09451	−	29.2513i	0.0513677	−	1.37283i
$455$	0.844506	−	0.0632870i	0.0395911	−	0.00296694i
$456$	−8.58682	−	3.73145i	−0.402115	−	0.174741i
$457$	−27.0495	+	29.1525i	−1.26532	+	1.36369i	−0.363498	+	0.931595i	$0.618418\pi$
$457$	−27.0495	+	29.1525i	−1.26532	+	1.36369i	−0.901826	+	0.432100i	$0.857773\pi$
$458$	−6.08747	+	4.85460i	−0.284449	+	0.226840i
$459$	1.70893	+	7.33868i	0.0797660	+	0.342540i
$460$	1.14305	+	5.00802i	0.0532949	+	0.233500i
$461$	33.2843	−	1.24541i	1.55020	−	0.0580046i	0.751502	−	0.659731i	$-0.229330\pi$
$461$	33.2843	−	1.24541i	1.55020	−	0.0580046i	0.798703	+	0.601726i	$0.205520\pi$
$462$	−0.920041	+	1.25044i	−0.0428042	+	0.0581756i
$463$	−11.2218	+	6.47893i	−0.521523	+	0.301102i	−0.737558	−	0.675284i	$-0.764021\pi$
$463$	−11.2218	+	6.47893i	−0.521523	+	0.301102i	0.216034	+	0.976386i	$0.430688\pi$
$464$	−3.47933	+	4.11026i	−0.161524	+	0.190814i
$465$	−8.35225	+	2.58971i	−0.387326	+	0.120095i
$466$	−9.17918	−	4.00484i	−0.425217	−	0.185520i
$467$	−11.6727	+	7.33446i	−0.540149	+	0.339398i	−0.774317	−	0.632798i	$-0.781906\pi$
$467$	−11.6727	+	7.33446i	−0.540149	+	0.339398i	0.234168	+	0.972196i	$0.424764\pi$
$468$	−13.1011	−	2.94994i	−0.605599	−	0.136361i
$469$	0.260522	+	0.207759i	0.0120298	+	0.00959342i
$470$	1.48125	−	0.223262i	0.0683248	−	0.0102983i
$471$	11.8354	−	24.6686i	0.545345	−	1.13667i
$472$	−0.632192	+	0.734621i	−0.0290990	+	0.0338137i
$473$	−1.40868	−	18.7976i	−0.0647713	−	0.864313i
$474$	10.9906	+	10.9584i	0.504813	+	0.503338i
$475$	16.0646	+	18.6675i	0.737096	+	0.856522i
$476$	−0.291184	+	0.291184i	−0.0133464	+	0.0133464i
$477$	−5.68908	−	9.78753i	−0.260485	−	0.448140i
$478$	27.4246	+	3.09001i	1.25437	+	0.141334i
$479$	7.56292	−	10.2474i	0.345559	−	0.468215i	−0.597007	−	0.802236i	$-0.703644\pi$
$479$	7.56292	−	10.2474i	0.345559	−	0.468215i	0.942566	+	0.334021i	$0.108406\pi$
$480$	−0.786099	−	0.844731i	−0.0358803	−	0.0385565i
$481$	13.9403	+	3.73528i	0.635621	+	0.170314i
$482$	14.8133	−	2.80282i	0.674726	−	0.127665i
$483$	0.986917	+	3.66179i	0.0449063	+	0.166617i
$484$	0.857588	−	0.584694i	0.0389813	−	0.0265770i
$485$	3.48345	+	9.95513i	0.158175	+	0.452039i
$486$	−15.1718	+	3.57984i	−0.688209	+	0.162385i
$487$	−16.3590	−	20.5135i	−0.741296	−	0.929556i	0.258035	−	0.966136i	$-0.416925\pi$
$487$	−16.3590	−	20.5135i	−0.741296	−	0.929556i	−0.999331	+	0.0365801i	$0.988354\pi$
$488$	−4.05445	+	1.59125i	−0.183536	+	0.0720326i
$489$	1.62494	+	0.934990i	0.0734821	+	0.0422817i
$490$	−4.07557	−	2.15400i	−0.184115	−	0.0973079i
$491$	−23.9073	+	17.6444i	−1.07892	+	0.796282i	−0.980037	−	0.198817i	$-0.936290\pi$
$491$	−23.9073	+	17.6444i	−1.07892	+	0.796282i	−0.0988868	+	0.995099i	$0.531528\pi$
$492$	1.59128	+	5.13214i	0.0717405	+	0.231375i
$493$	−1.22671	−	7.71217i	−0.0552481	−	0.347339i
$494$			24.1969i			1.08867i
$495$	6.19482	−	1.19091i	0.278437	−	0.0535274i
$496$	4.03181	+	6.41658i	0.181033	+	0.288113i
$497$	−4.36857	−	1.34752i	−0.195957	−	0.0604447i
$498$	−4.44775	−	5.56060i	−0.199309	−	0.249176i
$499$	26.0401	+	10.2200i	1.16571	+	0.457509i	0.867717	−	0.497058i	$-0.165586\pi$
$499$	26.0401	+	10.2200i	1.16571	+	0.457509i	0.297996	+	0.954567i	$0.403682\pi$
$500$	1.87654	+	6.08360i	0.0839215	+	0.272067i
$501$	20.9226	−	2.38842i	0.934755	−	0.106707i
$502$	3.35529	+	4.92130i	0.149754	+	0.219648i
$503$	8.45022	+	5.30963i	0.376777	+	0.236745i	0.707085	−	0.707129i	$-0.250010\pi$
$503$	8.45022	+	5.30963i	0.376777	+	0.236745i	−0.330308	+	0.943873i	$0.607153\pi$
$504$	−0.604161	−	0.600636i	−0.0269115	−	0.0267544i
$505$	8.30127	+	8.30127i	0.369402	+	0.369402i
$506$	−1.81865	+	24.2683i	−0.0808490	+	1.07886i
$507$	2.28378	+	11.9741i	0.101426	+	0.531790i
$508$	−10.1755	+	4.43954i	−0.451467	+	0.196973i
$509$	5.05273	−	7.41100i	0.223959	−	0.328487i	−0.697770	−	0.716321i	$-0.745824\pi$
$509$	5.05273	−	7.41100i	0.223959	−	0.328487i	0.921729	+	0.387835i	$0.126777\pi$
$510$	1.67205	−	0.0650135i	0.0740396	−	0.00287885i
$511$	2.76818	−	2.38221i	0.122457	−	0.105383i
$512$	−0.532032	+	0.846724i	−0.0235127	+	0.0374203i
$513$	12.2977	+	25.2523i	0.542957	+	1.11492i
$514$	0.973331	−	0.340583i	0.0429318	−	0.0150225i
$515$	5.63074	+	5.22457i	0.248120	+	0.230222i
$516$	10.3166	+	0.757943i	0.454161	+	0.0333666i
$517$	7.01759	+	1.05773i	0.308633	+	0.0465190i
$518$	0.622730	+	0.671143i	0.0273612	+	0.0294883i
$519$	−11.6157	+	13.5378i	−0.509875	+	0.594241i
$520$	−1.19257	+	2.73339i	−0.0522975	+	0.119867i
$521$	−0.187718			−0.00822405			−0.00411203	−	0.999992i	$-0.501309\pi$
$521$	−0.187718			−0.00822405			−0.00411203	+	0.999992i	$0.501309\pi$
$522$	15.9474	−	2.58448i	0.698000	−	0.113120i
$523$	9.65513			0.422189			0.211095	−	0.977466i	$-0.432297\pi$
$523$	9.65513			0.422189			0.211095	+	0.977466i	$0.432297\pi$
$524$	3.10917	−	7.12630i	0.135825	−	0.311314i
$525$	0.743244	+	2.11414i	0.0324378	+	0.0922688i
$526$	−12.4151	−	13.3803i	−0.541323	−	0.583407i
$527$	−10.8664	−	1.63785i	−0.473349	−	0.0713459i
$528$	−2.37917	−	4.92196i	−0.103540	−	0.214201i
$529$	26.7206	+	24.7931i	1.16176	+	1.07796i
$530$	−2.37295	+	0.830332i	−0.103074	+	0.0360673i
$531$	2.87382	−	0.441763i	0.124713	−	0.0191709i
$532$	−0.816677	+	1.29973i	−0.0354074	+	0.0563506i
$533$	10.5257	−	9.05806i	0.455917	−	0.392348i
$534$	−6.59301	+	12.5189i	−0.285307	+	0.541745i
$535$	−5.61510	+	8.23584i	−0.242762	+	0.356066i
$536$	−1.07551	+	0.469239i	−0.0464548	+	0.0202680i
$537$	−13.1521	+	11.3518i	−0.567556	+	0.489868i
$538$	0.905651	−	12.0851i	0.0390454	−	0.521025i
$539$	−15.4428	−	15.4428i	−0.665167	−	0.665167i
$540$	0.144621	+	3.45873i	0.00622348	+	0.148840i
$541$	6.53056	+	4.10342i	0.280771	+	0.176420i	0.665054	−	0.746795i	$-0.268409\pi$
$541$	6.53056	+	4.10342i	0.280771	+	0.176420i	−0.384283	+	0.923215i	$0.625551\pi$
$542$	−9.74664	−	14.2957i	−0.418654	−	0.614053i
$543$	9.42502	−	21.6889i	0.404466	−	0.930759i
$544$	−0.427430	−	1.38569i	−0.0183259	−	0.0594111i
$545$	5.58981	+	2.19384i	0.239441	+	0.0939738i
$546$	−0.801387	+	2.05072i	−0.0342962	+	0.0877626i
$547$	27.2551	+	8.40709i	1.16535	+	0.359461i	0.816291	−	0.577641i	$-0.196027\pi$
$547$	27.2551	+	8.40709i	1.16535	+	0.359461i	0.349054	+	0.937102i	$0.386503\pi$
$548$	1.98435	+	3.15807i	0.0847671	+	0.134906i
$549$	12.3459	+	4.27951i	0.526910	+	0.182645i
$550$			14.3805i			0.613186i
$551$	−10.8550	−	27.0096i	−0.462441	−	1.15065i
$552$	−13.0244	−	2.95269i	−0.554355	−	0.125675i
$553$	2.04738	−	1.51103i	0.0870634	−	0.0642557i
$554$	10.0630	+	5.31842i	0.427534	+	0.225958i
$555$	−0.00544278	−	3.72027i	−0.000231033	−	0.157917i
$556$	5.84343	−	2.29338i	0.247817	−	0.0972609i
$557$	−28.8459	−	36.1717i	−1.22224	−	1.53264i	−0.766079	−	0.642746i	$-0.777795\pi$
$557$	−28.8459	−	36.1717i	−1.22224	−	1.53264i	−0.456163	−	0.889896i	$-0.650777\pi$
$558$	3.32259	−	22.4903i	0.140656	−	0.952089i
$559$	−8.82978	−	25.2341i	−0.373460	−	1.06729i
$560$	−0.156314	+	0.106573i	−0.00660548	+	0.00450354i
$561$	7.66041	+	2.04059i	0.323423	+	0.0861539i
$562$	10.4696	−	1.98095i	0.441633	−	0.0835615i
$563$	0.239701	+	0.0642276i	0.0101022	+	0.00270687i	0.263867	−	0.964559i	$-0.415002\pi$
$563$	0.239701	+	0.0642276i	0.0101022	+	0.00270687i	−0.253764	+	0.967266i	$0.581669\pi$
$564$	−1.14248	+	3.72316i	−0.0481071	+	0.156773i
$565$	−3.85074	+	5.21757i	−0.162002	+	0.219505i
$566$	1.02477	+	0.115464i	0.0430744	+	0.00485331i
$567$	0.205904	+	2.54746i	0.00864717	+	0.106983i
$568$	11.3836	−	11.3836i	0.477646	−	0.477646i
$569$	−6.58220	−	7.64865i	−0.275940	−	0.320648i	0.602852	−	0.797853i	$-0.294031\pi$
$569$	−6.58220	−	7.64865i	−0.275940	−	0.320648i	−0.878792	+	0.477205i	$0.841650\pi$
$570$	6.02255	−	1.62318i	0.252257	−	0.0679877i
$571$	2.44652	+	32.6466i	0.102384	+	1.36622i	0.777675	+	0.628666i	$0.216399\pi$
$571$	2.44652	+	32.6466i	0.102384	+	1.36622i	−0.675292	+	0.737551i	$0.735982\pi$
$572$	−9.21594	+	10.7091i	−0.385338	+	0.447770i
$573$	−6.90782	+	0.527833i	−0.288578	+	0.0220506i
$574$	0.871107	−	0.131298i	0.0363593	−	0.00548029i
$575$	27.4658	+	21.9032i	1.14540	+	0.913428i
$576$	2.86412	−	0.892650i	0.119338	−	0.0371937i
$577$	−16.8781	+	10.6052i	−0.702643	+	0.441500i	−0.835395	−	0.549650i	$-0.814761\pi$
$577$	−16.8781	+	10.6052i	−0.702643	+	0.441500i	0.132753	+	0.991149i	$0.457618\pi$
$578$	−13.6542	−	5.95725i	−0.567939	−	0.247789i
$579$	−10.2147	+	45.0572i	−0.424508	+	1.87251i
$580$	0.104960	−	3.58613i	0.00435823	−	0.148906i
$581$	−1.01103	+	0.583720i	−0.0419447	+	0.0242168i
$582$	−27.2526	−	3.03026i	−1.12966	−	0.125608i
$583$	−11.9022	+	0.445350i	−0.492940	+	0.0184445i
$584$	2.86176	+	12.5382i	0.118420	+	0.518833i
$585$	8.04927	−	3.90538i	0.332796	−	0.161467i
$586$	−0.439032	+	0.350117i	−0.0181363	+	0.0144632i
$587$	−8.33928	+	8.98761i	−0.344199	+	0.370958i	−0.881298	−	0.472561i	$-0.843330\pi$
$587$	−8.33928	+	8.98761i	−0.344199	+	0.370958i	0.537099	+	0.843519i	$0.319520\pi$
$588$	9.63243	−	7.13085i	0.397235	−	0.294071i
$589$	−40.8488	+	3.06119i	−1.68314	+	0.126134i
$590$	0.0241431	−	0.645238i	0.000993956	−	0.0265640i
$591$	26.1956	−	13.8938i	1.07754	−	0.571516i
$592$	−3.11419	+	0.834444i	−0.127992	+	0.0342955i
$593$	−19.5819	+	9.43012i	−0.804130	+	0.387249i	−0.790349	−	0.612656i	$-0.790101\pi$
$593$	−19.5819	+	9.43012i	−0.804130	+	0.387249i	−0.0137809	+	0.999905i	$0.504387\pi$
$594$	−4.17519	+	15.8601i	−0.171310	+	0.650749i
$595$	0.0307168	−	0.272619i	0.00125927	−	0.0111763i
$596$	0.776960	+	0.0582251i	0.0318255	+	0.00238499i
$597$	−0.843380	−	21.6905i	−0.0345173	−	0.887733i
$598$	6.41671	+	33.9131i	0.262399	+	1.38681i
$599$	−37.2148	−	1.39248i	−1.52055	−	0.0568951i	−0.736011	−	0.676969i	$-0.763293\pi$
$599$	−37.2148	−	1.39248i	−1.52055	−	0.0568951i	−0.784543	+	0.620074i	$0.787102\pi$
$600$	−7.80507	−	1.16475i	−0.318641	−	0.0475507i
$601$	3.16591	−	16.7322i	0.129140	−	0.682522i	−0.856830	−	0.515599i	$-0.827569\pi$
$601$	3.16591	−	16.7322i	0.129140	−	0.682522i	0.985970	−	0.166923i	$-0.0533831\pi$
$602$	0.377393	−	1.65347i	0.0153814	−	0.0673902i
$603$	3.36687	+	1.02776i	0.137109	+	0.0418537i
$604$	−8.64115	+	10.8357i	−0.351603	+	0.440897i
$605$	−0.203821	+	0.660770i	−0.00828649	+	0.0268641i
$606$	−28.7940	+	10.1228i	−1.16968	+	0.411210i
$607$	8.81328	+	11.9416i	0.357720	+	0.484693i	0.946092	−	0.323897i	$-0.104993\pi$
$607$	8.81328	+	11.9416i	0.357720	+	0.484693i	−0.588373	+	0.808590i	$0.700231\pi$
$608$	−2.70273	−	4.68127i	−0.109610	−	0.189851i
$609$	−0.0254354	−	2.64862i	−0.00103069	−	0.107327i
$610$	1.45086	−	2.51296i	0.0587434	−	0.101747i
$611$	10.0018	−	1.12693i	0.404630	−	0.0455908i
$612$	−1.72800	+	3.99244i	−0.0698501	+	0.161385i
$613$	3.07140	−	0.701028i	0.124053	−	0.0283142i	−0.160044	−	0.987110i	$-0.551164\pi$
$613$	3.07140	−	0.701028i	0.124053	−	0.0283142i	0.284097	+	0.958796i	$0.408306\pi$
$614$	−0.290263	−	0.739578i	−0.0117141	−	0.0298469i
$615$	−2.96062	−	2.01218i	−0.119384	−	0.0811388i
$616$	−0.856481	+	0.264189i	−0.0345086	+	0.0106445i
$617$	15.9457	+	13.7224i	0.641950	+	0.552443i	0.911890	−	0.410434i	$-0.134623\pi$
$617$	15.9457	+	13.7224i	0.641950	+	0.552443i	−0.269940	+	0.962877i	$0.587004\pi$
$618$	−18.5789	+	7.32305i	−0.747351	+	0.294576i
$619$	16.5517	+	31.3173i	0.665268	+	1.25875i	0.953559	+	0.301205i	$0.0973889\pi$
$619$	16.5517	+	31.3173i	0.665268	+	1.25875i	−0.288292	+	0.957543i	$0.593087\pi$
$620$	−4.76534	−	1.66746i	−0.191381	−	0.0669670i
$621$	23.9325	+	32.1312i	0.960378	+	1.28938i
$622$	−2.29582	−	4.76732i	−0.0920541	−	0.191152i
$623$	1.86646	+	1.37751i	0.0747782	+	0.0551888i
$624$	−5.06597	−	5.86938i	−0.202801	−	0.234963i
$625$	15.3180	+	10.4436i	0.612718	+	0.417744i
$626$	0.530357	−	1.97932i	0.0211973	−	0.0791094i
$627$	29.5317	+	1.06173i	1.17938	+	0.0424016i
$628$	13.9662	−	7.38136i	0.557312	−	0.294548i
$629$	2.02851	−	4.21225i	0.0808821	−	0.167953i
$630$	0.564178	+	0.0618964i	0.0224774	+	0.00246601i
$631$	20.1443	+	4.59781i	0.801933	+	0.183036i	0.603796	−	0.797139i	$-0.293654\pi$
$631$	20.1443	+	4.59781i	0.801933	+	0.183036i	0.198136	+	0.980174i	$0.436511\pi$
$632$	1.33552	+	8.86057i	0.0531240	+	0.352455i
$633$	28.4769	−	22.7778i	1.13185	−	0.905336i
$634$	6.69294	−	6.21014i	0.265810	−	0.246636i
$635$	3.45601	−	6.53910i	0.137148	−	0.259496i
$636$	0.722307	−	6.49605i	0.0286413	−	0.257585i
$637$	−26.8239	−	15.4868i	−1.06280	−	0.613609i
$638$	5.48299	−	16.0884i	0.217074	−	0.636946i
$639$	−48.1508	+	3.75012i	−1.90482	+	0.148352i
$640$	−0.0745923	−	0.662025i	−0.00294852	−	0.0261688i
$641$	0.328538	+	8.78037i	0.0129765	+	0.346804i	0.990629	+	0.136578i	$0.0436104\pi$
$641$	0.328538	+	8.78037i	0.0129765	+	0.346804i	−0.977653	+	0.210226i	$0.932580\pi$
$642$	−12.9903	−	22.4240i	−0.512685	−	0.885003i
$643$	5.34949	−	35.4916i	0.210963	−	1.39965i	−0.593110	−	0.805121i	$-0.702100\pi$
$643$	5.34949	−	35.4916i	0.210963	−	1.39965i	0.804074	−	0.594530i	$-0.202662\pi$
$644$	−0.799941	+	2.03822i	−0.0315221	+	0.0803170i
$645$	−5.68838	+	3.89048i	−0.223980	+	0.153187i
$646$	7.70191	+	1.45728i	0.303028	+	0.0573359i
$647$	−9.19166	−	4.42647i	−0.361362	−	0.174023i	0.244389	−	0.969677i	$-0.421413\pi$
$647$	−9.19166	−	4.42647i	−0.361362	−	0.174023i	−0.605750	+	0.795655i	$0.707127\pi$
$648$	−8.26998	−	3.55069i	−0.324876	−	0.139484i
$649$	1.01034	−	2.88737i	0.0396592	−	0.113339i
$650$	5.27863	+	19.7001i	0.207045	+	0.772702i
$651$	−3.56337	−	1.09345i	−0.139660	−	0.0428556i
$652$	0.432834	+	0.992066i	0.0169511	+	0.0388523i
$653$	1.16847	+	2.67816i	0.0457257	+	0.104804i	0.937926	−	0.346836i	$-0.112744\pi$
$653$	1.16847	+	2.67816i	0.0457257	+	0.104804i	−0.892200	+	0.451640i	$0.850839\pi$
$654$	−11.4287	+	10.6355i	−0.446898	+	0.415880i
$655$	1.34064	+	5.00333i	0.0523831	+	0.195496i
$656$	−1.02459	+	2.92812i	−0.0400036	+	0.114324i
$657$	17.9282	−	34.1634i	0.699445	−	1.33284i
$658$	0.575282	+	0.277041i	0.0224268	+	0.0108002i
$659$	−40.6572	−	7.69275i	−1.58378	−	0.299667i	−0.681830	−	0.731510i	$-0.738816\pi$
$659$	−40.6572	−	7.69275i	−1.58378	−	0.299667i	−0.901949	+	0.431843i	$0.857863\pi$
$660$	3.28370	+	1.57543i	0.127818	+	0.0613237i
$661$	13.2152	−	33.6717i	0.514011	−	1.30968i	−0.404593	−	0.914497i	$-0.632587\pi$
$661$	13.2152	−	33.6717i	0.514011	−	1.30968i	0.918603	−	0.395181i	$-0.129318\pi$
$662$	1.81442	−	12.0379i	0.0705195	−	0.467867i
$663$	11.2432	−	0.0164488i	0.436649	−	0.000638820i
$664$	−0.153718	−	4.10820i	−0.00596541	−	0.159429i
$665$	−0.114500	−	1.01622i	−0.00444013	−	0.0394072i
$666$	8.72654	+	4.17107i	0.338146	+	0.161626i
$667$	−22.3765	−	34.9768i	−0.866423	−	1.35431i
$668$	10.5293	+	6.07907i	0.407389	+	0.235206i
$669$	7.87598	−	3.44998i	0.304503	−	0.133384i
$670$	0.365284	−	0.691152i	0.0141122	−	0.0267015i
$671$	10.0774	−	9.35049i	0.389035	−	0.360972i
$672$	−0.0740192	−	0.486257i	−0.00285535	−	0.0187578i
$673$	−0.981112	−	6.50925i	−0.0378191	−	0.250913i	0.961930	−	0.273294i	$-0.0881133\pi$
$673$	−0.981112	−	6.50925i	−0.0378191	−	0.250913i	−0.999750	+	0.0223813i	$0.992875\pi$
$674$	−13.1142	−	2.99322i	−0.505138	−	0.115295i
$675$	15.5212	+	17.8767i	0.597411	+	0.688073i
$676$	−3.05362	+	6.34091i	−0.117447	+	0.243881i
$677$	24.9408	−	13.1816i	0.958553	−	0.506610i	0.0866234	−	0.996241i	$-0.472392\pi$
$677$	24.9408	−	13.1816i	0.958553	−	0.506610i	0.871930	+	0.489631i	$0.162869\pi$
$678$	−7.89956	−	14.8939i	−0.303381	−	0.571997i
$679$	−1.16357	+	4.34249i	−0.0446536	+	0.166649i
$680$	0.798220	+	0.544217i	0.0306103	+	0.0208698i
$681$	−49.8024	+	9.49861i	−1.90843	+	0.363988i
$682$	−19.2449	−	14.2034i	−0.736924	−	0.543875i
$683$	−4.52660	−	9.39958i	−0.173205	−	0.359665i	0.796237	−	0.604985i	$-0.206821\pi$
$683$	−4.52660	−	9.39958i	−0.173205	−	0.359665i	−0.969442	+	0.245321i	$0.921107\pi$
$684$	−2.96818	+	15.9424i	−0.113491	+	0.609575i
$685$	−2.34537	−	0.820681i	−0.0896120	−	0.0313566i
$686$	−1.84699	−	3.49468i	−0.0705185	−	0.133428i
$687$	10.5561	+	8.39298i	0.402741	+	0.320212i
$688$	4.52685	+	3.89567i	0.172585	+	0.148521i
$689$	−16.1416	+	4.97903i	−0.614947	+	0.189686i
$690$	8.01046	−	3.87208i	0.304953	−	0.147408i
$691$	12.7173	+	32.4032i	0.483789	+	1.23268i	0.939500	+	0.342548i	$0.111290\pi$
$691$	12.7173	+	32.4032i	0.483789	+	1.23268i	−0.455711	+	0.890128i	$0.650615\pi$
$692$	−10.0406	+	2.29170i	−0.381686	+	0.0871174i
$693$	2.46768	+	1.06806i	0.0937395	+	0.0405721i
$694$	7.51848	−	0.847130i	0.285398	−	0.0321566i
$695$	−2.09103	+	3.62177i	−0.0793174	+	0.137382i
$696$	8.28795	+	4.27900i	0.314154	+	0.162195i
$697$	−2.24928	−	3.89587i	−0.0851975	−	0.147566i
$698$	−17.5985	−	23.8451i	−0.666112	−	0.902549i
$699$	−3.19991	+	17.0484i	−0.121032	+	0.644831i
$700$	−0.381364	+	1.23635i	−0.0144142	+	0.0467297i
$701$	12.6421	−	15.8527i	0.477487	−	0.598750i	−0.483500	−	0.875345i	$-0.660635\pi$
$701$	12.6421	−	15.8527i	0.477487	−	0.598750i	0.960987	+	0.276595i	$0.0892059\pi$
$702$	0.102088	+	23.2597i	0.00385305	+	0.877880i
$703$	3.87798	−	16.9905i	0.146261	−	0.640810i
$704$	0.586788	−	3.10125i	0.0221154	−	0.116883i
$705$	−0.951436	−	2.41383i	−0.0358332	−	0.0909101i
$706$	−11.1198	−	0.416075i	−0.418500	−	0.0156592i
$707$	0.930320	+	4.91686i	0.0349883	+	0.184917i
$708$	1.48530	+	0.782228i	0.0558211	+	0.0293979i
$709$	19.8677	+	1.48888i	0.746146	+	0.0559159i	0.442376	−	0.896830i	$-0.354136\pi$
$709$	19.8677	+	1.48888i	0.746146	+	0.0559159i	0.303770	+	0.952745i	$0.401755\pi$
$710$	−1.20085	+	10.6579i	−0.0450672	+	0.399982i
$711$	14.2354	−	22.8034i	0.533869	−	0.855193i
$712$	−7.35987	+	3.54433i	−0.275823	+	0.132829i
$713$	−56.4398	+	15.1230i	−2.11369	+	0.566361i
$714$	0.604483	+	0.378589i	0.0226222	+	0.0141683i
$715$	0.351952	−	9.40611i	0.0131623	−	0.351769i
$716$	−10.0026	+	0.749593i	−0.373815	+	0.0280136i
$717$	−5.42154	−	47.4929i	−0.202471	−	1.77366i
$718$	15.6790	−	16.8980i	0.585136	−	0.630626i
$719$	−25.3168	+	20.1895i	−0.944158	+	0.752941i	−0.969080	−	0.246748i	$-0.920638\pi$
$719$	−25.3168	+	20.1895i	−0.944158	+	0.752941i	0.0249212	+	0.999689i	$0.492067\pi$
$720$	−1.12104	+	1.65464i	−0.0417786	+	0.0616649i
$721$	0.728564	+	3.19205i	0.0271331	+	0.118878i
$722$	10.2119	−	0.382103i	0.380048	−	0.0142204i
$723$	−10.4772	−	23.9185i	−0.389652	−	0.889538i
$724$	11.8241	−	6.82666i	0.439440	−	0.253711i
$725$	−14.7300	−	19.6221i	−0.547058	−	0.728746i
$726$	−1.31965	−	1.22086i	−0.0489766	−	0.0453105i
$727$	−16.3972	−	7.15401i	−0.608137	−	0.265328i	0.0731766	−	0.997319i	$-0.476686\pi$
$727$	−16.3972	−	7.15401i	−0.608137	−	0.265328i	−0.681314	+	0.731991i	$0.738591\pi$
$728$	−1.07633	+	0.676306i	−0.0398916	+	0.0250656i
$729$	11.9279	+	24.2224i	0.441776	+	0.897126i
$730$	−6.69867	−	5.34201i	−0.247929	−	0.197717i
$731$	−8.56384	+	1.29079i	−0.316745	+	0.0477416i
$732$	4.25880	+	6.22692i	0.157410	+	0.230153i
$733$	18.4060	−	21.3881i	0.679840	−	0.789989i	−0.306996	−	0.951711i	$-0.599324\pi$
$733$	18.4060	−	21.3881i	0.679840	−	0.789989i	0.986836	+	0.161722i	$0.0517048\pi$
$734$	−1.89502	−	25.2873i	−0.0699464	−	0.933370i
$735$	−2.05522	+	7.71531i	−0.0758079	+	0.284584i
$736$	−5.02943	−	5.84431i	−0.185387	−	0.215424i
$737$	2.61885	−	2.61885i	0.0964666	−	0.0964666i
$738$	8.04611	−	4.67687i	0.296181	−	0.172158i
$739$	31.5916	+	3.55952i	1.16212	+	0.130939i	0.671886	−	0.740654i	$-0.265484\pi$
$739$	31.5916	+	3.55952i	1.16212	+	0.130939i	0.490230	+	0.871593i	$0.336913\pi$
$740$	1.27547	−	1.72820i	0.0468871	−	0.0635298i
$741$	40.8457	−	9.38566i	1.50051	−	0.344791i
$742$	−1.03510	−	0.277353i	−0.0379996	−	0.0101820i
$743$	−17.5672	+	3.32389i	−0.644477	+	0.121942i	−0.497868	−	0.867253i	$-0.665884\pi$
$743$	−17.5672	+	3.32389i	−0.644477	+	0.121942i	−0.146609	+	0.989195i	$0.546836\pi$
$744$	9.26768	−	9.29484i	0.339770	−	0.340765i
$745$	−0.428878	+	0.292404i	−0.0157129	+	0.0107129i
$746$	9.58948	+	27.4052i	0.351096	+	1.00337i
$747$	−7.66139	+	9.66496i	−0.280316	+	0.353622i
$748$	2.85369	+	3.57842i	0.104341	+	0.130840i
$749$	−3.95511	+	1.55227i	−0.144517	+	0.0567186i
$750$	9.54159	−	5.52747i	0.348410	−	0.201835i
$751$	−12.6958	−	6.70993i	−0.463276	−	0.244849i	0.219308	−	0.975656i	$-0.429620\pi$
$751$	−12.6958	−	6.70993i	−0.463276	−	0.244849i	−0.682584	+	0.730807i	$0.739144\pi$
$752$	−1.80913	+	1.33520i	−0.0659723	+	0.0486898i
$753$	7.00597	−	7.57284i	0.255312	−	0.275969i
$754$	1.60571	−	24.0524i	0.0584766	−	0.875939i
$755$		−	9.23327i		−	0.336033i
$756$	−0.779562	+	1.25284i	−0.0283524	+	0.0455653i
$757$	−25.1819	−	40.0768i	−0.915253	−	1.45662i	−0.889493	−	0.456948i	$-0.848942\pi$
$757$	−25.1819	−	40.0768i	−0.915253	−	1.45662i	−0.0257596	−	0.999668i	$-0.508200\pi$
$758$	2.61465	+	0.806513i	0.0949684	+	0.0292939i
$759$	41.6717	−	6.34336i	1.51259	−	0.230249i
$760$	3.35226	+	1.31566i	0.121599	+	0.0477242i
$761$	−10.6594	−	34.5570i	−0.386403	−	1.25269i	−0.914875	−	0.403738i	$-0.867711\pi$
$761$	−10.6594	−	34.5570i	−0.386403	−	1.25269i	0.528472	−	0.848951i	$-0.322765\pi$
$762$	11.4412	+	15.4549i	0.414470	+	0.559871i
$763$	1.44187	+	2.11484i	0.0521994	+	0.0765624i
$764$	−3.38678	−	2.12805i	−0.122529	−	0.0769902i
$765$	−0.758314	−	2.79730i	−0.0274169	−	0.101137i
$766$	−7.89962	−	7.89962i	−0.285425	−	0.285425i
$767$	0.324214	−	4.32633i	0.0117067	−	0.156215i
$768$	1.63569	+	0.569668i	0.0590228	+	0.0205561i
$769$	30.1060	−	13.1351i	1.08565	−	0.473664i	0.220607	−	0.975363i	$-0.429196\pi$
$769$	30.1060	−	13.1351i	1.08565	−	0.473664i	0.865042	+	0.501699i	$0.167291\pi$
$770$	0.336374	−	0.493370i	0.0121221	−	0.0177798i
$771$	−0.952467	−	1.51093i	−0.0343023	−	0.0544149i
$772$	−20.2181	+	17.3990i	−0.727664	+	0.626205i
$773$	−15.7574	+	25.0777i	−0.566753	+	0.901982i	0.433247	+	0.901275i	$0.357368\pi$
$773$	−15.7574	+	25.0777i	−0.566753	+	0.901982i	−1.00000		0.000707038i	$0.999775\pi$
$774$	−2.72221	−	17.7090i	−0.0978479	−	0.636535i
$775$	−32.5896	+	11.4036i	−1.17065	+	0.409629i
$776$	−11.6051	−	10.7680i	−0.416600	−	0.386548i
$777$	0.891380	−	1.31153i	0.0319781	−	0.0470510i
$778$	−10.1482	−	1.52960i	−0.363831	−	0.0548387i
$779$	−11.4057	−	12.2924i	−0.408652	−	0.440422i
$780$	5.07670	+	0.952873i	0.181775	+	0.0341183i
$781$	−20.3195	+	46.5728i	−0.727089	+	1.66651i
$782$	11.1811			0.399834
$783$	−10.5486	−	25.9177i	−0.376975	−	0.926223i
$784$	6.91936			0.247120
$785$	−4.20849	+	9.64595i	−0.150207	+	0.344279i
$786$	−13.2356	−	2.48426i	−0.472099	−	0.0886107i
$787$	−12.7789	−	13.7724i	−0.455519	−	0.490933i	0.462973	−	0.886373i	$-0.346783\pi$
$787$	−12.7789	−	13.7724i	−0.455519	−	0.490933i	−0.918492	+	0.395439i	$0.870592\pi$
$788$	16.9284	+	2.55155i	0.603051	+	0.0908952i
$789$	−17.7710	+	26.1474i	−0.632665	+	0.930872i
$790$	−4.37611	−	4.06043i	−0.155695	−	0.144464i
$791$	−2.60900	+	0.912927i	−0.0927652	+	0.0324600i
$792$	−7.38571	+	5.92535i	−0.262440	+	0.210548i
$793$	10.3730	−	16.5085i	0.368356	−	0.586235i
$794$	−11.8011	+	10.1556i	−0.418804	+	0.360410i
$795$	2.32209	+	3.68361i	0.0823560	+	0.130644i
$796$	7.05979	−	10.3548i	0.250228	−	0.367017i
$797$	50.0666	−	21.8439i	1.77345	−	0.773749i	0.785524	−	0.618831i	$-0.212393\pi$
$797$	50.0666	−	21.8439i	1.77345	−	0.773749i	0.987927	−	0.154918i	$-0.0495114\pi$
$798$	2.51081	+	0.874448i	0.0888816	+	0.0309551i
$799$	0.243664	−	3.25146i	0.00862020	−	0.115029i
$800$	−3.22169	−	3.22169i	−0.113904	−	0.113904i
$801$	23.6900	+	6.27347i	0.837043	+	0.221662i
$802$	−28.4813	−	17.8960i	−1.00571	−	0.631928i
$803$	−22.8661	−	33.5384i	−0.806926	−	1.18354i
$804$	1.20928	+	1.63351i	0.0426480	+	0.0576093i
$805$	−0.429966	−	1.39392i	−0.0151543	−	0.0491291i
$806$	−31.5776	−	12.3933i	−1.11227	−	0.436535i
$807$	−20.7516	+	3.15886i	−0.730491	+	0.111197i
$808$	−16.8388	−	5.19407i	−0.592385	−	0.182727i
$809$	−24.0728	−	38.3116i	−0.846355	−	1.34697i	−0.936366	−	0.351025i	$-0.885833\pi$
$809$	−24.0728	−	38.3116i	−0.846355	−	1.34697i	0.0900113	−	0.995941i	$-0.471310\pi$
$810$	5.78244	−	1.58572i	0.203174	−	0.0557167i
$811$		−	19.6471i		−	0.689902i	−0.938621	−	0.344951i	$-0.887896\pi$
$811$		−	19.6471i		−	0.689902i	0.938621	−	0.344951i	$-0.112104\pi$
$812$	0.898054	−	1.23778i	0.0315155	−	0.0434376i
$813$	−20.3514	+	21.9980i	−0.713754	+	0.771504i
$814$	8.18756	−	6.04269i	0.286974	−	0.211796i
$815$	−0.637531	−	0.336945i	−0.0223317	−	0.0118027i
$816$	−2.17334	+	1.25902i	−0.0760820	+	0.0440745i
$817$	−30.0516	+	11.7944i	−1.05137	+	0.412633i
$818$	22.4368	+	28.1349i	0.784485	+	0.983713i
$819$	3.77258	+	0.557340i	0.131825	+	0.0194750i
$820$	−0.682598	−	1.95075i	−0.0238373	−	0.0681232i
$821$	−44.3538	+	30.2399i	−1.54796	+	1.05538i	−0.576816	+	0.816874i	$0.695705\pi$
$821$	−44.3538	+	30.2399i	−1.54796	+	1.05538i	−0.971141	+	0.238505i	$0.923343\pi$
$822$	4.56131	−	4.57467i	0.159094	−	0.159560i
$823$	52.5180	−	9.93694i	1.83066	−	0.346380i	0.847742	−	0.530410i	$-0.177962\pi$
$823$	52.5180	−	9.93694i	1.83066	−	0.346380i	0.982921	+	0.184030i	$0.0589142\pi$
$824$	−11.1368	−	2.98410i	−0.387970	−	0.103956i
$825$	24.2751	−	5.57801i	0.845151	−	0.194201i
$826$	0.163435	−	0.221446i	0.00568663	−	0.00770510i
$827$	50.9143	+	5.73667i	1.77047	+	0.199484i	0.936101	−	0.351730i	$-0.114407\pi$
$827$	50.9143	+	5.73667i	1.77047	+	0.199484i	0.834364	+	0.551214i	$0.185835\pi$
$828$	0.0676825	+	23.1313i	0.00235213	+	0.803867i
$829$	3.28068	−	3.28068i	0.113943	−	0.113943i	−0.647837	−	0.761779i	$-0.724326\pi$
$829$	3.28068	−	3.28068i	0.113943	−	0.113943i	0.761779	+	0.647837i	$0.224326\pi$
$830$	1.78652	+	2.07597i	0.0620110	+	0.0720581i
$831$	5.07452	−	19.0498i	0.176033	−	0.660830i
$832$	−0.334520	−	4.46385i	−0.0115974	−	0.154756i
$833$	−6.54498	+	7.60540i	−0.226770	+	0.263512i
$834$	−6.13795	−	8.97449i	−0.212540	−	0.310761i
$835$	−8.00945	+	1.20723i	−0.277179	+	0.0417780i
$836$	13.3389	+	10.6374i	0.461336	+	0.367904i
$837$	−39.2537	+	3.11497i	−1.35681	+	0.107669i
$838$	22.4286	−	14.0928i	0.774782	−	0.486828i
$839$	−29.2394	−	12.7570i	−1.00946	−	0.440421i	−0.170930	−	0.985283i	$-0.554677\pi$
$839$	−29.2394	−	12.7570i	−1.00946	−	0.440421i	−0.838526	+	0.544862i	$0.816582\pi$
$840$	0.240534	+	0.222529i	0.00829922	+	0.00767799i
$841$	8.99789	+	27.5688i	0.310272	+	0.950648i
$842$	−9.46038	+	5.46195i	−0.326026	+	0.188231i
$843$	−7.40499	−	16.9049i	−0.255041	−	0.582236i
$844$	21.0389	−	0.787219i	0.724187	−	0.0270972i
$845$	−1.04334	−	4.57118i	−0.0358920	−	0.157253i
$846$	6.72807	+	0.484406i	0.231316	+	0.0166542i
$847$	−0.230444	+	0.183773i	−0.00791816	+	0.00631452i
$848$	2.56671	−	2.76625i	0.0881411	−	0.0949935i
$849$	−0.202586	−	1.77466i	−0.00695274	−	0.0609062i
$850$	6.58849	−	0.493739i	0.225983	−	0.0169351i
$851$	0.929503	−	24.8415i	0.0318629	−	0.851555i
$852$	−23.6318	−	14.8007i	−0.809612	−	0.507063i
$853$	−14.2568	+	3.82009i	−0.488143	+	0.130798i	−0.494492	−	0.869182i	$-0.664646\pi$
$853$	−14.2568	+	3.82009i	−0.488143	+	0.130798i	0.00634876	+	0.999980i	$0.497979\pi$
$854$	1.11437	−	0.536653i	0.0381330	−	0.0183639i
$855$	−5.07610	−	9.53681i	−0.173599	−	0.326152i
$856$	1.67521	−	14.8679i	0.0572574	−	0.508174i
$857$	−3.22119	−	0.241395i	−0.110034	−	0.00824589i	0.0195994	−	0.999808i	$-0.493761\pi$
$857$	−3.22119	−	0.241395i	−0.110034	−	0.00824589i	−0.129633	+	0.991562i	$0.541380\pi$
$858$	21.6524	+	11.4031i	0.739199	+	0.389296i
$859$	7.52023	+	39.7454i	0.256587	+	1.35609i	0.839412	+	0.543496i	$0.182900\pi$
$859$	7.52023	+	39.7454i	0.256587	+	1.35609i	−0.582825	+	0.812598i	$0.698053\pi$
$860$	−3.97606	−	0.148774i	−0.135582	−	0.00507314i
$861$	−0.559531	−	1.41955i	−0.0190688	−	0.0483782i
$862$	−1.25879	+	6.65285i	−0.0428744	+	0.226597i
$863$	−0.372975	+	1.63411i	−0.0126962	+	0.0556257i	−0.980879	−	0.194618i	$-0.937653\pi$
$863$	−0.372975	+	1.63411i	−0.0126962	+	0.0556257i	0.968183	+	0.250243i	$0.0805106\pi$
$864$	−2.61780	−	4.48855i	−0.0890594	−	0.152704i
$865$	4.27789	−	5.36431i	0.145453	−	0.182392i
$866$	−9.27324	+	30.0631i	−0.315117	+	1.02159i
$867$	−4.75991	+	25.3598i	−0.161655	+	0.861264i
$868$	−1.27790	−	1.73149i	−0.0433747	−	0.0587706i
$869$	−14.1411	−	24.4932i	−0.479705	−	0.830874i
$870$	−6.09432	+	1.21384i	−0.206617	+	0.0411530i
$871$	2.62632	−	4.54891i	0.0889893	−	0.154134i
$872$	−8.95681	+	1.00919i	−0.303316	+	0.0341755i
$873$	5.45568	+	47.1794i	0.184647	+	1.59678i
$874$	40.6336	−	9.27436i	1.37445	−	0.313710i
$875$	−0.660503	−	1.68293i	−0.0223291	−	0.0568936i
$876$	20.0551	−	9.69421i	0.677600	−	0.327537i
$877$	−2.92701	+	0.902864i	−0.0988382	+	0.0304876i	−0.343780	−	0.939050i	$-0.611707\pi$
$877$	−2.92701	+	0.902864i	−0.0988382	+	0.0304876i	0.244942	+	0.969538i	$0.421231\pi$
$878$	5.29083	+	4.55312i	0.178557	+	0.153660i
$879$	0.761313	+	0.605306i	0.0256784	+	0.0204165i
$880$	0.982550	+	1.85908i	0.0331218	+	0.0626694i
$881$	−31.4794	−	11.0151i	−1.06057	−	0.371109i	−0.257055	−	0.966397i	$-0.582752\pi$
$881$	−31.4794	−	11.0151i	−1.06057	−	0.371109i	−0.803512	+	0.595288i	$0.797038\pi$
$882$	−15.7736	−	13.4941i	−0.531124	−	0.454371i
$883$	12.0584	+	25.0396i	0.405799	+	0.842650i	0.999285	+	0.0378060i	$0.0120369\pi$
$883$	12.0584	+	25.0396i	0.405799	+	0.842650i	−0.593486	+	0.804844i	$0.702249\pi$
$884$	5.22286	+	3.85464i	0.175664	+	0.129646i
$885$	−1.09856	+	0.209525i	−0.0369279	+	0.00704310i
$886$	23.6987	+	16.1575i	0.796174	+	0.542822i
$887$	11.5052	−	42.9381i	0.386307	−	1.44172i	−0.449788	−	0.893135i	$-0.648501\pi$
$887$	11.5052	−	42.9381i	0.386307	−	1.44172i	0.836096	−	0.548584i	$-0.184833\pi$
$888$	2.61655	+	4.93326i	0.0878056	+	0.165550i
$889$	2.78730	−	1.47313i	0.0934831	−	0.0494072i
$890$	2.36128	−	4.90325i	0.0791503	−	0.164357i
$891$	28.3923	+	0.896015i	0.951178	+	0.0300176i
$892$	4.83985	+	1.10467i	0.162050	+	0.0369869i
$893$	−1.81148	−	12.0184i	−0.0606190	−	0.402181i
$894$	−0.203086	−	1.33414i	−0.00679220	−	0.0446203i
$895$	4.89867	−	4.54530i	0.163744	−	0.151933i
$896$	0.132692	−	0.251066i	0.00443294	−	0.00838754i
$897$	54.7584	−	23.9863i	1.82833	−	0.800878i
$898$	0.441126	+	0.254684i	0.0147206	+	0.00849893i
$899$	40.8081	−	0.332184i	1.36103	−	0.0110790i
$900$	1.06132	+	13.6272i	0.0353775	+	0.454240i
$901$	0.612690	+	5.43777i	0.0204117	+	0.181159i
$902$	−0.366112	−	9.78455i	−0.0121902	−	0.325790i
$903$	−2.93753	+	0.00429763i	−0.0977550	+	0.000143016i
$904$	1.45072	−	9.62493i	0.0482504	−	0.320120i
$905$	−3.32315	+	8.46725i	−0.110465	+	0.281461i
$906$	21.6430	+	10.3837i	0.719041	+	0.344977i
$907$	41.6476	+	7.88016i	1.38289	+	0.261656i	0.823531	−	0.567271i	$-0.192001\pi$
$907$	41.6476	+	7.88016i	1.38289	+	0.261656i	0.559356	+	0.828927i	$0.311048\pi$
$908$	−26.3729	−	12.7005i	−0.875216	−	0.421482i
$909$	28.2567	+	44.6795i	0.937215	+	1.48193i
$910$	0.279705	−	0.799350i	0.00927212	−	0.0264982i
$911$	−0.0109512	−	0.0408704i	−0.000362829	−	0.00135410i	0.965744	−	0.259496i	$-0.0835564\pi$
$911$	−0.0109512	−	0.0408704i	−0.000362829	−	0.00135410i	−0.966107	+	0.258142i	$0.916890\pi$
$912$	−6.85391	+	6.37818i	−0.226955	+	0.211203i
$913$	5.18887	+	11.8930i	0.171726	+	0.393601i
$914$	15.9032	+	36.4504i	0.526030	+	1.20567i
$915$	−4.80479	−	1.47439i	−0.158841	−	0.0487417i
$916$	2.01521	+	7.52086i	0.0665844	+	0.248496i
$917$	−0.729227	+	2.08401i	−0.0240812	+	0.0688201i
$918$	7.40975	+	1.36834i	0.244558	+	0.0451620i
$919$	−7.00316	−	3.37254i	−0.231013	−	0.111250i	0.314797	−	0.949159i	$-0.398064\pi$
$919$	−7.00316	−	3.37254i	−0.231013	−	0.111250i	−0.545810	+	0.837909i	$0.683778\pi$
$920$	5.04726	+	0.954993i	0.166403	+	0.0314852i
$921$	−1.13586	+	0.776854i	−0.0374279	+	0.0255982i
$922$	12.1686	−	31.0052i	0.400753	−	1.02110i
$923$	−10.7407	+	71.2596i	−0.353533	+	2.34554i
$924$	0.778186	+	1.34331i	0.0256004	+	0.0441918i
$925$	−0.549249	−	14.6790i	−0.0180592	−	0.482642i
$926$	1.45082	+	12.8764i	0.0476769	+	0.423144i
$927$	19.5682	+	28.5217i	0.642706	+	0.936775i
$928$	2.37595	+	4.83269i	0.0779944	+	0.158641i
$929$	2.41841	+	1.39627i	0.0793455	+	0.0458101i	0.539148	−	0.842211i	$-0.318746\pi$
$929$	2.41841	+	1.39627i	0.0793455	+	0.0458101i	−0.459802	+	0.888021i	$0.652080\pi$
$930$	−0.966362	+	8.69096i	−0.0316882	+	0.284988i
$931$	−17.4769	+	33.0680i	−0.572784	+	1.08376i
$932$	−7.34136	+	6.81179i	−0.240474	+	0.223128i
$933$	−7.15700	+	5.72467i	−0.234310	+	0.187417i
$934$	2.05466	+	13.6318i	0.0672305	+	0.446045i
$935$	−2.97279	−	0.678519i	−0.0972205	−	0.0221900i
$936$	−7.94283	+	10.8283i	−0.259619	+	0.353935i
$937$	−12.4779	+	25.9107i	−0.407636	+	0.846464i	0.591556	+	0.806264i	$0.298514\pi$
$937$	−12.4779	+	25.9107i	−0.407636	+	0.846464i	−0.999192	+	0.0402003i	$0.987200\pi$
$938$	0.294605	−	0.155703i	0.00961918	−	0.00508389i
$939$	−3.54692	−	0.127520i	−0.115749	−	0.00416147i
$940$	0.387705	−	1.44694i	0.0126455	−	0.0471938i
$941$	−11.1325	−	7.59003i	−0.362910	−	0.247428i	0.368112	−	0.929781i	$-0.380004\pi$
$941$	−11.1325	−	7.59003i	−0.362910	−	0.247428i	−0.731022	+	0.682353i	$0.760957\pi$
$942$	−17.8775	−	20.7126i	−0.582480	−	0.674854i
$943$	−19.2455	−	14.2038i	−0.626720	−	0.462540i
$944$	0.420517	+	0.873213i	0.0136867	+	0.0284207i
$945$	−0.114353	−	0.976375i	−0.00371990	−	0.0317615i
$946$	−17.7925	−	6.22585i	−0.578483	−	0.202420i
$947$	22.0356	+	41.6934i	0.716061	+	1.35485i	0.926144	+	0.377171i	$0.123103\pi$
$947$	22.0356	+	41.6934i	0.716061	+	1.35485i	−0.210082	+	0.977684i	$0.567373\pi$
$948$	14.4391	−	5.69134i	0.468961	−	0.184846i
$949$	−43.6356	−	37.5514i	−1.41647	−	1.21897i
$950$	23.5340	−	7.25928i	0.763544	−	0.235522i
$951$	−13.0792	−	8.88924i	−0.424122	−	0.288253i
$952$	0.150446	+	0.383331i	0.00487599	+	0.0124238i
$953$	−47.8223	+	10.9151i	−1.54912	+	0.353576i	−0.909693	−	0.415280i	$-0.863683\pi$
$953$	−47.8223	+	10.9151i	−1.54912	+	0.353576i	−0.639422	+	0.768856i	$0.720826\pi$
$954$	−11.2459	+	1.30044i	−0.364099	+	0.0421034i
$955$	2.64800	−	0.298358i	0.0856874	−	0.00965465i
$956$	13.7991	−	23.9007i	0.446294	−	0.773003i
$957$	−29.2849	−	3.01513i	−0.946648	−	0.0974652i
$958$	−6.36802	−	11.0297i	−0.205741	−	0.356355i
$959$	−0.628947	−	0.852193i	−0.0203098	−	0.0275188i
$960$	−1.08860	+	0.382707i	−0.0351345	+	0.0123518i
$961$	7.78979	−	25.2539i	0.251283	−	0.814641i
$962$	8.99822	−	11.2834i	0.290114	−	0.363792i
$963$	−32.8142	+	30.6263i	−1.05742	+	0.986919i
$964$	3.35475	−	14.6981i	0.108049	−	0.473394i
$965$	3.30374	−	17.4607i	0.106351	−	0.562080i
$966$	3.75092	+	0.559749i	0.120684	+	0.0180096i
$967$	30.6459	+	1.14669i	0.985505	+	0.0368750i	0.525282	−	0.850928i	$-0.323960\pi$
$967$	30.6459	+	1.14669i	0.985505	+	0.0368750i	0.460223	+	0.887803i	$0.347769\pi$
$968$	−0.192966	−	1.01985i	−0.00620215	−	0.0327791i
$969$	−0.527501	−	13.5665i	−0.0169458	−	0.435820i
$970$	10.5175	+	0.788178i	0.337697	+	0.0253069i
$971$	−5.86624	+	52.0643i	−0.188257	+	1.67082i	0.443971	+	0.896041i	$0.353569\pi$
$971$	−5.86624	+	52.0643i	−0.188257	+	1.67082i	−0.632228	+	0.774783i	$0.717859\pi$
$972$	−2.78596	+	15.3375i	−0.0893596	+	0.491950i
$973$	−1.60608	+	0.773446i	−0.0514885	+	0.0247955i
$974$	−25.3437	+	6.79083i	−0.812065	+	0.217592i
$975$	31.2074	−	16.5521i	0.999438	−	0.530090i
$976$	−0.162858	+	4.35248i	−0.00521297	+	0.139320i
$977$	−21.2147	+	1.58982i	−0.678718	+	0.0508629i	−0.409629	−	0.912252i	$-0.634342\pi$
$977$	−21.2147	+	1.58982i	−0.678718	+	0.0508629i	−0.269089	+	0.963115i	$0.586723\pi$
$978$	1.50678	−	1.11546i	0.0481814	−	0.0356685i
$979$	17.5370	−	18.9004i	0.560484	−	0.604058i
$980$	−3.60406	+	2.87415i	−0.115128	+	0.0918112i
$981$	22.3864	+	15.1670i	0.714741	+	0.484245i
$982$	6.61186	+	28.9684i	0.210993	+	0.924420i
$983$	−40.2493	+	1.50602i	−1.28375	+	0.0480347i	−0.670535	−	0.741878i	$-0.733935\pi$
$983$	−40.2493	+	1.50602i	−1.28375	+	0.0480347i	−0.613219	+	0.789913i	$0.710126\pi$
$984$	5.34026	+	0.593792i	0.170241	+	0.0189294i
$985$	−9.87732	+	5.70267i	−0.314717	+	0.181702i
$986$	−7.55924	−	1.95968i	−0.240735	−	0.0624090i
$987$	0.244517	−	1.07857i	0.00778307	−	0.0343313i
$988$	22.1779	+	9.67613i	0.705574	+	0.307839i
$989$	−38.9911	+	24.4997i	−1.23984	+	0.779046i
$990$	1.38572	−	6.15418i	0.0440410	−	0.195593i
$991$	−33.3341	−	26.5831i	−1.05889	−	0.844440i	−0.0706769	−	0.997499i	$-0.522516\pi$
$991$	−33.3341	−	26.5831i	−1.05889	−	0.844440i	−0.988217	+	0.153060i	$0.951087\pi$
$992$	7.49348	−	1.12946i	0.237918	−	0.0358604i
$993$	−21.0245	+	1.60650i	−0.667192	+	0.0509808i
$994$	−2.98204	+	3.46520i	−0.0945847	+	0.109909i
$995$	0.623944	+	8.32596i	0.0197804	+	0.263951i
$996$	−6.87525	+	1.85300i	−0.217851	+	0.0587147i
$997$	9.06698	+	10.5360i	0.287154	+	0.333679i	0.882959	−	0.469450i	$-0.155548\pi$
$997$	9.06698	+	10.5360i	0.287154	+	0.333679i	−0.595805	+	0.803129i	$0.703167\pi$
$998$	19.7805	−	19.7805i	0.626139	−	0.626139i
$999$	3.65609	−	16.3488i	0.115674	−	0.517254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.2.x.a.101.16	✓	720
9.5	odd	6	inner	522.2.x.a.275.9	yes	720
29.27	odd	28	inner	522.2.x.a.317.9	yes	720
261.230	even	84	inner	522.2.x.a.491.16	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
522.2.x.a.101.16	✓	720	1.1	even	1	trivial
522.2.x.a.275.9	yes	720	9.5	odd	6	inner
522.2.x.a.317.9	yes	720	29.27	odd	28	inner
522.2.x.a.491.16	yes	720	261.230	even	84	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.399892 - 0.916562i) q^{2} +(-1.70232 - 0.319518i) q^{3} +(-0.680173 - 0.733052i) q^{4} +(0.658773 + 0.0992940i) q^{5} +(-0.973604 + 1.43251i) q^{6} +(0.208168 + 0.193152i) q^{7} +(-0.943883 + 0.330279i) q^{8} +(2.79582 + 1.08785i) q^{9} +(0.354447 - 0.564099i) q^{10} +(2.39237 - 2.05880i) q^{11} +(0.923651 + 1.46522i) q^{12} +(2.52163 - 3.69855i) q^{13} +(0.260280 - 0.113559i) q^{14} +(-1.08972 - 0.379520i) q^{15} +(-0.0747301 + 0.997204i) q^{16} +(-1.02539 - 1.02539i) q^{17} +(2.11510 - 2.12752i) q^{18} +(-4.57694 - 2.87588i) q^{19} +(-0.375292 - 0.550452i) q^{20} +(-0.292654 - 0.395320i) q^{21} +(-0.930328 - 3.01605i) q^{22} +(-7.17746 - 2.81695i) q^{23} +(1.71233 - 0.260654i) q^{24} +(-4.35374 - 1.34295i) q^{25} +(-2.38157 - 3.79025i) q^{26} +(-4.41180 - 2.74518i) q^{27} -0.283975i q^{28} +(4.35878 + 3.16244i) q^{29} +(-0.783624 + 0.847028i) q^{30} +(6.09734 - 4.50004i) q^{31} +(0.884115 + 0.467269i) q^{32} +(-4.73041 + 2.74034i) q^{33} +(-1.34988 + 0.529788i) q^{34} +(0.117957 + 0.147913i) q^{35} +(-1.10419 - 2.78940i) q^{36} +(1.06483 + 3.04312i) q^{37} +(-4.46621 + 3.04501i) q^{38} +(-5.47438 + 5.49043i) q^{39} +(-0.654599 + 0.123857i) q^{40} +(2.99650 + 0.802909i) q^{41} +(-0.479366 + 0.110150i) q^{42} +(3.54648 - 4.80532i) q^{43} +(-3.13643 - 0.353390i) q^{44} +(1.73379 + 0.994252i) q^{45} +(-5.45212 + 5.45212i) q^{46} +(1.46666 + 1.70429i) q^{47} +(0.445840 - 1.67369i) q^{48} +(-0.517084 - 6.90001i) q^{49} +(-2.97193 + 3.45344i) q^{50} +(1.41791 + 2.07317i) q^{51} +(-4.42637 + 0.667168i) q^{52} +(-2.95033 - 2.35281i) q^{53} +(-4.28037 + 2.94591i) q^{54} +(1.78045 - 1.11873i) q^{55} +(-0.260280 - 0.113559i) q^{56} +(6.87254 + 6.35810i) q^{57} +(4.64162 - 2.73046i) q^{58} +(0.839346 - 0.484597i) q^{59} +(0.462989 + 1.05696i) q^{60} +(4.35248 - 0.162858i) q^{61} +(-1.68629 - 7.38813i) q^{62} +(0.371880 + 0.766472i) q^{63} +(0.781831 - 0.623490i) q^{64} +(2.02842 - 2.18612i) q^{65} +(0.620037 + 5.43155i) q^{66} +(1.17013 - 0.0876893i) q^{67} +(-0.0542216 + 1.44910i) q^{68} +(11.3183 + 7.08869i) q^{69} +(0.182741 - 0.0489654i) q^{70} +(-14.5046 + 6.98504i) q^{71} +(-2.99822 - 0.103401i) q^{72} +(1.43993 - 12.7797i) q^{73} +(3.21503 + 0.240933i) q^{74} +(6.98238 + 3.67724i) q^{75} +(1.00494 + 5.31123i) q^{76} +(0.895674 + 0.0335138i) q^{77} +(2.84315 + 7.21319i) q^{78} +(1.66589 - 8.80444i) q^{79} +(-0.148246 + 0.649510i) q^{80} +(6.63318 + 6.08284i) q^{81} +(1.93419 - 2.42540i) q^{82} +(-1.21176 + 3.92843i) q^{83} +(-0.0907350 + 0.483417i) q^{84} +(-0.573683 - 0.777312i) q^{85} +(-2.98616 - 5.17218i) q^{86} +(-6.40960 - 6.77621i) q^{87} +(-1.57814 + 2.73341i) q^{88} +(8.11748 - 0.914620i) q^{89} +(1.60462 - 1.19153i) q^{90} +(1.23930 - 0.282863i) q^{91} +(2.81695 + 7.17746i) q^{92} +(-11.8175 + 5.71232i) q^{93} +(2.14860 - 0.662755i) q^{94} +(-2.72960 - 2.34901i) q^{95} +(-1.35575 - 1.07793i) q^{96} +(7.39745 + 13.9967i) q^{97} +(-6.53107 - 2.28532i) q^{98} +(8.92827 - 3.15349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 24 q^{11} - 12 q^{14} - 20 q^{15} - 60 q^{16} + 84 q^{21} + 20 q^{24} + 60 q^{25} - 144 q^{27} - 12 q^{29} + 72 q^{30} + 84 q^{33} - 40 q^{36} + 40 q^{39} - 12 q^{41} - 104 q^{45} + 24 q^{46} - 24 q^{47}+ \cdots - 84 q^{99}+O(q^{100}) \) 720 * q + 24 * q^11 - 12 * q^14 - 20 * q^15 - 60 * q^16 + 84 * q^21 + 20 * q^24 + 60 * q^25 - 144 * q^27 - 12 * q^29 + 72 * q^30 + 84 * q^33 - 40 * q^36 + 40 * q^39 - 12 * q^41 - 104 * q^45 + 24 * q^46 - 24 * q^47 + 60 * q^49 + 16 * q^54 - 144 * q^55 + 12 * q^56 + 12 * q^58 + 120 * q^59 - 16 * q^60 - 12 * q^61 + 36 * q^65 - 48 * q^66 - 36 * q^68 + 52 * q^69 - 180 * q^74 - 184 * q^75 - 132 * q^77 - 68 * q^78 + 12 * q^79 - 216 * q^81 + 96 * q^82 - 432 * q^83 - 80 * q^84 - 48 * q^85 - 200 * q^87 - 112 * q^90 - 252 * q^92 - 112 * q^93 + 192 * q^95 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more