LMFDB - Embedded newform 1218.2.m.b.307.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(307,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.11
Character	$\chi$	$=$	1218.307
Dual form			1218.2.m.b.853.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +3.88041 q^{5} +1.00000 q^{6} +(-0.687128 + 2.55497i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.74387 - 2.74387i) q^{10} +(-2.40290 + 2.40290i) q^{11} +(0.707107 - 0.707107i) q^{12} +1.76810 q^{13} +(1.32076 + 2.29251i) q^{14} +(2.74387 + 2.74387i) q^{15} -1.00000 q^{16} +(-2.16662 - 2.16662i) q^{17} +(0.707107 + 0.707107i) q^{18} +(1.23644 + 1.23644i) q^{19} -3.88041i q^{20} +(-2.29251 + 1.32076i) q^{21} +3.39821i q^{22} +7.16005 q^{23} -1.00000i q^{24} +10.0576 q^{25} +(1.25024 - 1.25024i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.55497 + 0.687128i) q^{28} +(3.09777 + 4.40498i) q^{29} +3.88041 q^{30} +(-0.785278 - 0.785278i) q^{31} +(-0.707107 + 0.707107i) q^{32} -3.39821 q^{33} -3.06407 q^{34} +(-2.66634 + 9.91432i) q^{35} +1.00000 q^{36} +(-6.21199 - 6.21199i) q^{37} +1.74860 q^{38} +(1.25024 + 1.25024i) q^{39} +(-2.74387 - 2.74387i) q^{40} +(0.510951 - 0.510951i) q^{41} +(-0.687128 + 2.55497i) q^{42} +(-1.06007 + 1.06007i) q^{43} +(2.40290 + 2.40290i) q^{44} +3.88041i q^{45} +(5.06292 - 5.06292i) q^{46} +(-1.53254 + 1.53254i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.05571 - 3.51118i) q^{49} +(7.11180 - 7.11180i) q^{50} -3.06407i q^{51} -1.76810i q^{52} -4.74736 q^{53} +1.00000i q^{54} +(-9.32424 + 9.32424i) q^{55} +(2.29251 - 1.32076i) q^{56} +1.74860i q^{57} +(5.30524 + 0.924337i) q^{58} -9.85641i q^{59} +(2.74387 - 2.74387i) q^{60} +(-3.88401 - 3.88401i) q^{61} -1.11055 q^{62} +(-2.55497 - 0.687128i) q^{63} +1.00000i q^{64} +6.86097 q^{65} +(-2.40290 + 2.40290i) q^{66} +1.35982i q^{67} +(-2.16662 + 2.16662i) q^{68} +(5.06292 + 5.06292i) q^{69} +(5.12510 + 8.89587i) q^{70} +11.6097i q^{71} +(0.707107 - 0.707107i) q^{72} +(11.0505 - 11.0505i) q^{73} -8.78507 q^{74} +(7.11180 + 7.11180i) q^{75} +(1.23644 - 1.23644i) q^{76} +(-4.48823 - 7.79042i) q^{77} +1.76810 q^{78} +(7.92623 - 7.92623i) q^{79} -3.88041 q^{80} -1.00000 q^{81} -0.722594i q^{82} +4.45629i q^{83} +(1.32076 + 2.29251i) q^{84} +(-8.40739 - 8.40739i) q^{85} +1.49917i q^{86} +(-0.924337 + 5.30524i) q^{87} +3.39821 q^{88} +(-5.59795 - 5.59795i) q^{89} +(2.74387 + 2.74387i) q^{90} +(-1.21491 + 4.51745i) q^{91} -7.16005i q^{92} -1.11055i q^{93} +2.16733i q^{94} +(4.79791 + 4.79791i) q^{95} -1.00000 q^{96} +(5.97411 - 5.97411i) q^{97} +(-6.76481 + 1.79926i) q^{98} +(-2.40290 - 2.40290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{6} - 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} - 8 q^{19} + 4 q^{21} + 24 q^{25} + 12 q^{28} + 8 q^{29} + 24 q^{31} + 12 q^{35} + 40 q^{36} - 16 q^{37} + 4 q^{40} - 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 24 q^{98}+O(q^{100}) $ 40 * q + 40 * q^6 - 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 - 8 * q^19 + 4 * q^21 + 24 * q^25 + 12 * q^28 + 8 * q^29 + 24 * q^31 + 12 * q^35 + 40 * q^36 - 16 * q^37 + 4 * q^40 - 16 * q^41 - 20 * q^43 + 4 * q^46 + 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 + 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 + 44 * q^61 - 12 * q^63 + 4 * q^69 + 20 * q^70 + 52 * q^73 + 32 * q^75 - 8 * q^76 + 20 * q^77 + 4 * q^79 - 40 * q^81 + 4 * q^84 - 24 * q^85 + 12 * q^87 - 24 * q^89 - 4 * q^90 - 16 * q^95 - 40 * q^96 + 68 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	3.88041			1.73537			0.867687	−	0.497112i	$-0.165606\pi$
$5$	3.88041			1.73537			0.867687	+	0.497112i	$0.165606\pi$
$6$	1.00000			0.408248
$7$	−0.687128	+	2.55497i	−0.259710	+	0.965687i
$7$	−0.687128	+	2.55497i	−0.259710	+	0.965687i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	2.74387	−	2.74387i	0.867687	−	0.867687i
$11$	−2.40290	+	2.40290i	−0.724501	+	0.724501i	−0.969519	−	0.245017i	$-0.921206\pi$
$11$	−2.40290	+	2.40290i	−0.724501	+	0.724501i	0.245017	+	0.969519i	$0.421206\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	1.76810			0.490384			0.245192	−	0.969475i	$-0.421149\pi$
$13$	1.76810			0.490384			0.245192	+	0.969475i	$0.421149\pi$
$14$	1.32076	+	2.29251i	0.352988	+	0.612698i
$15$	2.74387	+	2.74387i	0.708463	+	0.708463i
$16$	−1.00000			−0.250000
$17$	−2.16662	−	2.16662i	−0.525483	−	0.525483i	0.393739	−	0.919222i	$-0.371181\pi$
$17$	−2.16662	−	2.16662i	−0.525483	−	0.525483i	−0.919222	+	0.393739i	$0.871181\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	1.23644	+	1.23644i	0.283660	+	0.283660i	0.834567	−	0.550907i	$-0.185718\pi$
$19$	1.23644	+	1.23644i	0.283660	+	0.283660i	−0.550907	+	0.834567i	$0.685718\pi$
$20$		−	3.88041i		−	0.867687i
$21$	−2.29251	+	1.32076i	−0.500266	+	0.288214i
$22$			3.39821i			0.724501i
$23$	7.16005			1.49297			0.746487	−	0.665400i	$-0.231739\pi$
$23$	7.16005			1.49297			0.746487	+	0.665400i	$0.231739\pi$
$24$		−	1.00000i		−	0.204124i
$25$	10.0576			2.01152
$26$	1.25024	−	1.25024i	0.245192	−	0.245192i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	2.55497	+	0.687128i	0.482843	+	0.129855i
$29$	3.09777	+	4.40498i	0.575241	+	0.817984i
$29$	3.09777	+	4.40498i	0.575241	+	0.817984i
$30$	3.88041			0.708463
$31$	−0.785278	−	0.785278i	−0.141040	−	0.141040i	0.633061	−	0.774102i	$-0.281798\pi$
$31$	−0.785278	−	0.785278i	−0.141040	−	0.141040i	−0.774102	+	0.633061i	$0.781798\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.39821			−0.591553
$34$	−3.06407			−0.525483
$35$	−2.66634	+	9.91432i	−0.450694	+	1.67583i
$36$	1.00000			0.166667
$37$	−6.21199	−	6.21199i	−1.02124	−	1.02124i	−0.999769	−	0.0214747i	$-0.993164\pi$
$37$	−6.21199	−	6.21199i	−1.02124	−	1.02124i	−0.0214747	−	0.999769i	$-0.506836\pi$
$38$	1.74860			0.283660
$39$	1.25024	+	1.25024i	0.200198	+	0.200198i
$40$	−2.74387	−	2.74387i	−0.433843	−	0.433843i
$41$	0.510951	−	0.510951i	0.0797972	−	0.0797972i	−0.666082	−	0.745879i	$-0.732030\pi$
$41$	0.510951	−	0.510951i	0.0797972	−	0.0797972i	0.745879	+	0.666082i	$0.232030\pi$
$42$	−0.687128	+	2.55497i	−0.106026	+	0.394240i
$43$	−1.06007	+	1.06007i	−0.161659	+	0.161659i	−0.783301	−	0.621642i	$-0.786466\pi$
$43$	−1.06007	+	1.06007i	−0.161659	+	0.161659i	0.621642	+	0.783301i	$0.286466\pi$
$44$	2.40290	+	2.40290i	0.362251	+	0.362251i
$45$			3.88041i			0.578458i
$46$	5.06292	−	5.06292i	0.746487	−	0.746487i
$47$	−1.53254	+	1.53254i	−0.223543	+	0.223543i	−0.809989	−	0.586445i	$-0.800527\pi$
$47$	−1.53254	+	1.53254i	−0.223543	+	0.223543i	0.586445	+	0.809989i	$0.300527\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−6.05571	−	3.51118i	−0.865101	−	0.501597i
$50$	7.11180	−	7.11180i	1.00576	−	1.00576i
$51$		−	3.06407i		−	0.429055i
$52$		−	1.76810i		−	0.245192i
$53$	−4.74736			−0.652100			−0.326050	−	0.945353i	$-0.605718\pi$
$53$	−4.74736			−0.652100			−0.326050	+	0.945353i	$0.605718\pi$
$54$			1.00000i			0.136083i
$55$	−9.32424	+	9.32424i	−1.25728	+	1.25728i
$56$	2.29251	−	1.32076i	0.306349	−	0.176494i
$57$			1.74860i			0.231607i
$58$	5.30524	+	0.924337i	0.696613	+	0.121371i
$59$		−	9.85641i		−	1.28320i	−0.767041	−	0.641598i	$-0.778272\pi$
$59$		−	9.85641i		−	1.28320i	0.767041	−	0.641598i	$-0.221728\pi$
$60$	2.74387	−	2.74387i	0.354232	−	0.354232i
$61$	−3.88401	−	3.88401i	−0.497297	−	0.497297i	0.413299	−	0.910596i	$-0.364377\pi$
$61$	−3.88401	−	3.88401i	−0.497297	−	0.497297i	−0.910596	+	0.413299i	$0.864377\pi$
$62$	−1.11055			−0.141040
$63$	−2.55497	−	0.687128i	−0.321896	−	0.0865700i
$64$			1.00000i			0.125000i
$65$	6.86097			0.850999
$66$	−2.40290	+	2.40290i	−0.295776	+	0.295776i
$67$			1.35982i			0.166128i	0.996544	+	0.0830640i	$0.0264706\pi$
$67$			1.35982i			0.166128i	−0.996544	+	0.0830640i	$0.973529\pi$
$68$	−2.16662	+	2.16662i	−0.262742	+	0.262742i
$69$	5.06292	+	5.06292i	0.609504	+	0.609504i
$70$	5.12510	+	8.89587i	0.612566	+	1.06326i
$71$			11.6097i			1.37782i	0.724848	+	0.688909i	$0.241910\pi$
$71$			11.6097i			1.37782i	−0.724848	+	0.688909i	$0.758090\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	11.0505	−	11.0505i	1.29336	−	1.29336i	0.360666	−	0.932695i	$-0.382550\pi$
$73$	11.0505	−	11.0505i	1.29336	−	1.29336i	0.932695	−	0.360666i	$-0.117450\pi$
$74$	−8.78507			−1.02124
$75$	7.11180	+	7.11180i	0.821199	+	0.821199i
$76$	1.23644	−	1.23644i	0.141830	−	0.141830i
$77$	−4.48823	−	7.79042i	−0.511481	−	0.887801i
$78$	1.76810			0.200198
$79$	7.92623	−	7.92623i	0.891770	−	0.891770i	−0.102920	−	0.994690i	$-0.532818\pi$
$79$	7.92623	−	7.92623i	0.891770	−	0.891770i	0.994690	+	0.102920i	$0.0328184\pi$
$80$	−3.88041			−0.433843
$81$	−1.00000			−0.111111
$82$		−	0.722594i		−	0.0797972i
$83$			4.45629i			0.489141i	0.969631	+	0.244571i	$0.0786470\pi$
$83$			4.45629i			0.489141i	−0.969631	+	0.244571i	$0.921353\pi$
$84$	1.32076	+	2.29251i	0.144107	+	0.250133i
$85$	−8.40739	−	8.40739i	−0.911910	−	0.911910i
$86$			1.49917i			0.161659i
$87$	−0.924337	+	5.30524i	−0.0990994	+	0.568782i
$88$	3.39821			0.362251
$89$	−5.59795	−	5.59795i	−0.593382	−	0.593382i	0.345161	−	0.938543i	$-0.387824\pi$
$89$	−5.59795	−	5.59795i	−0.593382	−	0.593382i	−0.938543	+	0.345161i	$0.887824\pi$
$90$	2.74387	+	2.74387i	0.289229	+	0.289229i
$91$	−1.21491	+	4.51745i	−0.127358	+	0.473557i
$92$		−	7.16005i		−	0.746487i
$93$		−	1.11055i		−	0.115159i
$94$			2.16733i			0.223543i
$95$	4.79791	+	4.79791i	0.492256	+	0.492256i
$96$	−1.00000			−0.102062
$97$	5.97411	−	5.97411i	0.606579	−	0.606579i	−0.335472	−	0.942050i	$-0.608896\pi$
$97$	5.97411	−	5.97411i	0.606579	−	0.606579i	0.942050	+	0.335472i	$0.108896\pi$
$98$	−6.76481	+	1.79926i	−0.683349	+	0.181752i
$99$	−2.40290	−	2.40290i	−0.241500	−	0.241500i
$100$		−	10.0576i		−	1.00576i
$101$	−7.21936	−	7.21936i	−0.718354	−	0.718354i	0.249914	−	0.968268i	$-0.419598\pi$
$101$	−7.21936	−	7.21936i	−0.718354	−	0.718354i	−0.968268	+	0.249914i	$0.919598\pi$
$102$	−2.16662	−	2.16662i	−0.214528	−	0.214528i
$103$			0.782210i			0.0770734i	0.999257	+	0.0385367i	$0.0122697\pi$
$103$			0.782210i			0.0770734i	−0.999257	+	0.0385367i	$0.987730\pi$
$104$	−1.25024	−	1.25024i	−0.122596	−	0.122596i
$105$	−8.89587	+	5.12510i	−0.868148	+	0.500158i
$106$	−3.35689	+	3.35689i	−0.326050	+	0.326050i
$107$	−11.5937			−1.12081			−0.560404	−	0.828220i	$-0.689354\pi$
$107$	−11.5937			−1.12081			−0.560404	+	0.828220i	$0.689354\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			14.2977i			1.36947i	0.728793	+	0.684734i	$0.240082\pi$
$109$			14.2977i			1.36947i	−0.728793	+	0.684734i	$0.759918\pi$
$110$			13.1865i			1.25728i
$111$		−	8.78507i		−	0.833842i
$112$	0.687128	−	2.55497i	0.0649275	−	0.241422i
$113$	−6.59090	−	6.59090i	−0.620019	−	0.620019i	0.325517	−	0.945536i	$-0.394462\pi$
$113$	−6.59090	−	6.59090i	−0.620019	−	0.620019i	−0.945536	+	0.325517i	$0.894462\pi$
$114$	1.23644	+	1.23644i	0.115804	+	0.115804i
$115$	27.7840			2.59087
$116$	4.40498	−	3.09777i	0.408992	−	0.287621i
$117$			1.76810i			0.163461i
$118$	−6.96953	−	6.96953i	−0.641598	−	0.641598i
$119$	7.02440	−	4.04690i	0.643925	−	0.370979i
$120$		−	3.88041i		−	0.354232i
$121$		−	0.547843i		−	0.0498039i
$122$	−5.49282			−0.497297
$123$	0.722594			0.0651541
$124$	−0.785278	+	0.785278i	−0.0705201	+	0.0705201i
$125$	19.6256			1.75536
$126$	−2.29251	+	1.32076i	−0.204233	+	0.117663i
$127$	0.338185	−	0.338185i	0.0300090	−	0.0300090i	−0.691943	−	0.721952i	$-0.743245\pi$
$127$	0.338185	−	0.338185i	0.0300090	−	0.0300090i	0.721952	+	0.691943i	$0.243245\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−1.49917			−0.131994
$130$	4.85144	−	4.85144i	0.425500	−	0.425500i
$131$	14.5792	−	14.5792i	1.27379	−	1.27379i	0.329705	−	0.944084i	$-0.393051\pi$
$131$	14.5792	−	14.5792i	1.27379	−	1.27379i	0.944084	−	0.329705i	$-0.106949\pi$
$132$			3.39821i			0.295776i
$133$	−4.00867	+	2.30948i	−0.347596	+	0.200257i
$134$	0.961535	+	0.961535i	0.0830640	+	0.0830640i
$135$	−2.74387	+	2.74387i	−0.236154	+	0.236154i
$136$			3.06407i			0.262742i
$137$	8.26353	−	8.26353i	0.706001	−	0.706001i	−0.259691	−	0.965692i	$-0.583621\pi$
$137$	8.26353	−	8.26353i	0.706001	−	0.706001i	0.965692	+	0.259691i	$0.0836206\pi$
$138$	7.16005			0.609504
$139$			17.5372i			1.48749i	0.668466	+	0.743743i	$0.266951\pi$
$139$			17.5372i			1.48749i	−0.668466	+	0.743743i	$0.733049\pi$
$140$	9.91432	+	2.66634i	0.837913	+	0.225347i
$141$	−2.16733			−0.182522
$142$	8.20930	+	8.20930i	0.688909	+	0.688909i
$143$	−4.24858	+	4.24858i	−0.355284	+	0.355284i
$144$		−	1.00000i		−	0.0833333i
$145$	12.0206	+	17.0931i	0.998258	+	1.41951i
$146$		−	15.6277i		−	1.29336i
$147$	−1.79926	−	6.76481i	−0.148400	−	0.557952i
$148$	−6.21199	+	6.21199i	−0.510622	+	0.510622i
$149$		−	18.4592i		−	1.51224i	−0.654435	−	0.756118i	$-0.727093\pi$
$149$		−	18.4592i		−	1.51224i	0.654435	−	0.756118i	$-0.272907\pi$
$150$	10.0576			0.821199
$151$			15.7405i			1.28094i	0.767982	+	0.640471i	$0.221261\pi$
$151$			15.7405i			1.28094i	−0.767982	+	0.640471i	$0.778739\pi$
$152$		−	1.74860i		−	0.141830i
$153$	2.16662	−	2.16662i	0.175161	−	0.175161i
$154$	−8.68232	−	2.33501i	−0.699641	−	0.188160i
$155$	−3.04720	−	3.04720i	−0.244757	−	0.244757i
$156$	1.25024	−	1.25024i	0.100099	−	0.100099i
$157$	−1.45145	+	1.45145i	−0.115838	+	0.115838i	−0.762650	−	0.646812i	$-0.776102\pi$
$157$	−1.45145	+	1.45145i	−0.115838	+	0.115838i	0.646812	+	0.762650i	$0.276102\pi$
$158$		−	11.2094i		−	0.891770i
$159$	−3.35689	−	3.35689i	−0.266219	−	0.266219i
$160$	−2.74387	+	2.74387i	−0.216922	+	0.216922i
$161$	−4.91987	+	18.2937i	−0.387740	+	1.44175i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−4.55608	−	4.55608i	−0.356859	−	0.356859i	0.505795	−	0.862654i	$-0.331199\pi$
$163$	−4.55608	−	4.55608i	−0.356859	−	0.356859i	−0.862654	+	0.505795i	$0.831199\pi$
$164$	−0.510951	−	0.510951i	−0.0398986	−	0.0398986i
$165$	−13.1865			−1.02656
$166$	3.15107	+	3.15107i	0.244571	+	0.244571i
$167$	−18.2313			−1.41078			−0.705392	−	0.708817i	$-0.749229\pi$
$167$	−18.2313			−1.41078			−0.705392	+	0.708817i	$0.749229\pi$
$168$	2.55497	+	0.687128i	0.197120	+	0.0530131i
$169$	−9.87381			−0.759524
$170$	−11.8898			−0.911910
$171$	−1.23644	+	1.23644i	−0.0945533	+	0.0945533i
$172$	1.06007	+	1.06007i	0.0808296	+	0.0808296i
$173$	5.05323			0.384190			0.192095	−	0.981376i	$-0.438472\pi$
$173$	5.05323			0.384190			0.192095	+	0.981376i	$0.438472\pi$
$174$	3.09777	+	4.40498i	0.234841	+	0.333941i
$175$	−6.91086	+	25.6968i	−0.522412	+	1.94250i
$176$	2.40290	−	2.40290i	0.181125	−	0.181125i
$177$	6.96953	−	6.96953i	0.523862	−	0.523862i
$178$	−7.91670			−0.593382
$179$		−	0.891530i		−	0.0666361i	−0.999445	−	0.0333181i	$-0.989393\pi$
$179$		−	0.891530i		−	0.0666361i	0.999445	−	0.0333181i	$-0.0106074\pi$
$180$	3.88041			0.289229
$181$			6.24425i			0.464131i	0.972700	+	0.232066i	$0.0745484\pi$
$181$			6.24425i			0.464131i	−0.972700	+	0.232066i	$0.925452\pi$
$182$	2.33524	+	4.05339i	0.173100	+	0.300457i
$183$		−	5.49282i		−	0.406041i
$184$	−5.06292	−	5.06292i	−0.373244	−	0.373244i
$185$	−24.1051	−	24.1051i	−1.77224	−	1.77224i
$186$	−0.785278	−	0.785278i	−0.0575794	−	0.0575794i
$187$	10.4124			0.761427
$188$	1.53254	+	1.53254i	0.111772	+	0.111772i
$189$	−1.32076	−	2.29251i	−0.0960713	−	0.166755i
$190$	6.78527			0.492256
$191$	−10.9753	+	10.9753i	−0.794144	+	0.794144i	−0.982165	−	0.188021i	$-0.939793\pi$
$191$	−10.9753	+	10.9753i	−0.794144	+	0.794144i	0.188021	+	0.982165i	$0.439793\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	6.10050	−	6.10050i	0.439124	−	0.439124i	−0.452593	−	0.891717i	$-0.649501\pi$
$193$	6.10050	−	6.10050i	0.439124	−	0.439124i	0.891717	+	0.452593i	$0.149501\pi$
$194$		−	8.44867i		−	0.606579i
$195$	4.85144	+	4.85144i	0.347419	+	0.347419i
$196$	−3.51118	+	6.05571i	−0.250798	+	0.432551i
$197$	−20.1298			−1.43419			−0.717095	−	0.696976i	$-0.754529\pi$
$197$	−20.1298			−1.43419			−0.717095	+	0.696976i	$0.754529\pi$
$198$	−3.39821			−0.241500
$199$		−	25.5990i		−	1.81466i	−0.420415	−	0.907332i	$-0.638115\pi$
$199$		−	25.5990i		−	1.81466i	0.420415	−	0.907332i	$-0.361885\pi$
$200$	−7.11180	−	7.11180i	−0.502880	−	0.502880i
$201$	−0.961535	+	0.961535i	−0.0678215	+	0.0678215i
$202$	−10.2097			−0.718354
$203$	−13.3831	+	4.88791i	−0.939312	+	0.343064i
$204$	−3.06407			−0.214528
$205$	1.98270	−	1.98270i	0.138478	−	0.138478i
$206$	0.553106	+	0.553106i	0.0385367	+	0.0385367i
$207$			7.16005i			0.497658i
$208$	−1.76810			−0.122596
$209$	−5.94210			−0.411024
$210$	−2.66634	+	9.91432i	−0.183995	+	0.684153i
$211$	1.07647	+	1.07647i	0.0741069	+	0.0741069i	0.743189	−	0.669082i	$-0.233312\pi$
$211$	1.07647	+	1.07647i	0.0741069	+	0.0741069i	−0.669082	+	0.743189i	$0.733312\pi$
$212$			4.74736i			0.326050i
$213$	−8.20930	+	8.20930i	−0.562492	+	0.562492i
$214$	−8.19800	+	8.19800i	−0.560404	+	0.560404i
$215$	−4.11351	+	4.11351i	−0.280539	+	0.280539i
$216$	1.00000			0.0680414
$217$	2.54595	−	1.46677i	0.172830	−	0.0995710i
$218$	10.1100	+	10.1100i	0.684734	+	0.684734i
$219$	15.6277			1.05602
$220$	9.32424	+	9.32424i	0.628640	+	0.628640i
$221$	−3.83082	−	3.83082i	−0.257689	−	0.257689i
$222$	−6.21199	−	6.21199i	−0.416921	−	0.416921i
$223$		−	10.9392i		−	0.732540i	−0.930509	−	0.366270i	$-0.880635\pi$
$223$		−	10.9392i		−	0.732540i	0.930509	−	0.366270i	$-0.119365\pi$
$224$	−1.32076	−	2.29251i	−0.0882471	−	0.153175i
$225$			10.0576i			0.670506i
$226$	−9.32093			−0.620019
$227$		−	17.7624i		−	1.17893i	−0.807794	−	0.589465i	$-0.799339\pi$
$227$		−	17.7624i		−	1.17893i	0.807794	−	0.589465i	$-0.200661\pi$
$228$	1.74860			0.115804
$229$	−3.14767	+	3.14767i	−0.208004	+	0.208004i	−0.803419	−	0.595414i	$-0.796988\pi$
$229$	−3.14767	+	3.14767i	−0.208004	+	0.208004i	0.595414	+	0.803419i	$0.296988\pi$
$230$	19.6462	−	19.6462i	1.29543	−	1.29543i
$231$	2.33501	−	8.68232i	0.153632	−	0.571255i
$232$	0.924337	−	5.30524i	0.0606857	−	0.348306i
$233$	−19.9854			−1.30929			−0.654643	−	0.755938i	$-0.727181\pi$
$233$	−19.9854			−1.30929			−0.654643	+	0.755938i	$0.727181\pi$
$234$	1.25024	+	1.25024i	0.0817307	+	0.0817307i
$235$	−5.94687	+	5.94687i	−0.387931	+	0.387931i
$236$	−9.85641			−0.641598
$237$	11.2094			0.728127
$238$	2.10541	−	7.82859i	0.136473	−	0.507452i
$239$	11.0084			0.712073			0.356036	−	0.934472i	$-0.384128\pi$
$239$	11.0084			0.712073			0.356036	+	0.934472i	$0.384128\pi$
$240$	−2.74387	−	2.74387i	−0.177116	−	0.177116i
$241$	20.2704			1.30573			0.652866	−	0.757473i	$-0.273566\pi$
$241$	20.2704			1.30573			0.652866	+	0.757473i	$0.273566\pi$
$242$	−0.387383	−	0.387383i	−0.0249019	−	0.0249019i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−3.88401	+	3.88401i	−0.248648	+	0.248648i
$245$	−23.4987	−	13.6248i	−1.50127	−	0.870458i
$246$	0.510951	−	0.510951i	0.0325771	−	0.0325771i
$247$	2.18616	+	2.18616i	0.139102	+	0.139102i
$248$			1.11055i			0.0705201i
$249$	−3.15107	+	3.15107i	−0.199691	+	0.199691i
$250$	13.8774	−	13.8774i	0.877682	−	0.877682i
$251$	−21.1985	−	21.1985i	−1.33804	−	1.33804i	−0.897958	−	0.440081i	$-0.854950\pi$
$251$	−21.1985	−	21.1985i	−1.33804	−	1.33804i	−0.440081	−	0.897958i	$-0.645050\pi$
$252$	−0.687128	+	2.55497i	−0.0432850	+	0.160948i
$253$	−17.2049	+	17.2049i	−1.08166	+	1.08166i
$254$		−	0.478265i		−	0.0300090i
$255$		−	11.8898i		−	0.744571i
$256$	1.00000			0.0625000
$257$			10.3926i			0.648275i	0.946010	+	0.324137i	$0.105074\pi$
$257$			10.3926i			0.648275i	−0.946010	+	0.324137i	$0.894926\pi$
$258$	−1.06007	+	1.06007i	−0.0659971	+	0.0659971i
$259$	20.1398	−	11.6030i	1.25143	−	0.720975i
$260$		−	6.86097i		−	0.425500i
$261$	−4.40498	+	3.09777i	−0.272661	+	0.191747i
$262$		−	20.6181i		−	1.27379i
$263$	−9.73225	+	9.73225i	−0.600116	+	0.600116i	−0.940343	−	0.340227i	$-0.889496\pi$
$263$	−9.73225	+	9.73225i	−0.600116	+	0.600116i	0.340227	+	0.940343i	$0.389496\pi$
$264$	2.40290	+	2.40290i	0.147888	+	0.147888i
$265$	−18.4217			−1.13164
$266$	−1.20151	+	4.46761i	−0.0736693	+	0.273926i
$267$		−	7.91670i		−	0.484494i
$268$	1.35982			0.0830640
$269$	8.63324	−	8.63324i	0.526378	−	0.526378i	−0.393112	−	0.919490i	$-0.628602\pi$
$269$	8.63324	−	8.63324i	0.526378	−	0.526378i	0.919490	+	0.393112i	$0.128602\pi$
$270$			3.88041i			0.236154i
$271$	−18.4083	+	18.4083i	−1.11823	+	1.11823i	−0.126223	+	0.992002i	$0.540286\pi$
$271$	−18.4083	+	18.4083i	−1.11823	+	1.11823i	−0.992002	+	0.126223i	$0.959714\pi$
$272$	2.16662	+	2.16662i	0.131371	+	0.131371i
$273$	−4.05339	+	2.33524i	−0.245322	+	0.141335i
$274$		−	11.6864i		−	0.706001i
$275$	−24.1674	+	24.1674i	−1.45735	+	1.45735i
$276$	5.06292	−	5.06292i	0.304752	−	0.304752i
$277$	31.0879			1.86789			0.933944	−	0.357418i	$-0.116343\pi$
$277$	31.0879			1.86789			0.933944	+	0.357418i	$0.116343\pi$
$278$	12.4007	+	12.4007i	0.743743	+	0.743743i
$279$	0.785278	−	0.785278i	0.0470134	−	0.0470134i
$280$	8.89587	−	5.12510i	0.531630	−	0.306283i
$281$	−23.9949			−1.43142			−0.715709	−	0.698398i	$-0.753896\pi$
$281$	−23.9949			−1.43142			−0.715709	+	0.698398i	$0.753896\pi$
$282$	−1.53254	+	1.53254i	−0.0912612	+	0.0912612i
$283$	−9.79920			−0.582502			−0.291251	−	0.956647i	$-0.594071\pi$
$283$	−9.79920			−0.582502			−0.291251	+	0.956647i	$0.594071\pi$
$284$	11.6097			0.688909
$285$			6.78527i			0.401925i
$286$			6.00839i			0.355284i
$287$	0.954374	+	1.65655i	0.0563349	+	0.0977832i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	7.61149i		−	0.447735i
$290$	20.5865	+	3.58681i	1.20888	+	0.210625i
$291$	8.44867			0.495270
$292$	−11.0505	−	11.0505i	−0.646680	−	0.646680i
$293$	10.0604	+	10.0604i	0.587735	+	0.587735i	0.937017	−	0.349283i	$-0.113575\pi$
$293$	10.0604	+	10.0604i	0.587735	+	0.587735i	−0.349283	+	0.937017i	$0.613575\pi$
$294$	−6.05571	−	3.51118i	−0.353176	−	0.204776i
$295$		−	38.2469i		−	2.22682i
$296$			8.78507i			0.510622i
$297$		−	3.39821i		−	0.197184i
$298$	−13.0526	−	13.0526i	−0.756118	−	0.756118i
$299$	12.6597			0.732131
$300$	7.11180	−	7.11180i	0.410600	−	0.410600i
$301$	−1.98004	−	3.43685i	−0.114128	−	0.198097i
$302$	11.1302	+	11.1302i	0.640471	+	0.640471i
$303$		−	10.2097i		−	0.586533i
$304$	−1.23644	−	1.23644i	−0.0709149	−	0.0709149i
$305$	−15.0716	−	15.0716i	−0.862996	−	0.862996i
$306$		−	3.06407i		−	0.175161i
$307$	2.73053	+	2.73053i	0.155839	+	0.155839i	0.780720	−	0.624881i	$-0.214852\pi$
$307$	2.73053	+	2.73053i	0.155839	+	0.155839i	−0.624881	+	0.780720i	$0.714852\pi$
$308$	−7.79042	+	4.48823i	−0.443901	+	0.255740i
$309$	−0.553106	+	0.553106i	−0.0314651	+	0.0314651i
$310$	−4.30940			−0.244757
$311$	11.4930	+	11.4930i	0.651709	+	0.651709i	0.953404	−	0.301695i	$-0.0975525\pi$
$311$	11.4930	+	11.4930i	0.651709	+	0.651709i	−0.301695	+	0.953404i	$0.597553\pi$
$312$		−	1.76810i		−	0.100099i
$313$			21.8401i			1.23448i	0.786777	+	0.617238i	$0.211748\pi$
$313$			21.8401i			1.23448i	−0.786777	+	0.617238i	$0.788252\pi$
$314$			2.05266i			0.115838i
$315$	−9.91432	−	2.66634i	−0.558609	−	0.150231i
$316$	−7.92623	−	7.92623i	−0.445885	−	0.445885i
$317$	11.4335	+	11.4335i	0.642171	+	0.642171i	0.951089	−	0.308918i	$-0.0999668\pi$
$317$	11.4335	+	11.4335i	0.642171	+	0.642171i	−0.308918	+	0.951089i	$0.599967\pi$
$318$	−4.74736			−0.266219
$319$	−18.0283	−	3.14109i	−1.00939	−	0.175867i
$320$			3.88041i			0.216922i
$321$	−8.19800	−	8.19800i	−0.457568	−	0.457568i
$322$	9.45672	+	16.4145i	0.527002	+	0.914743i
$323$		−	5.35782i		−	0.298117i
$324$			1.00000i			0.0555556i
$325$	17.7829			0.986417
$326$	−6.44326			−0.356859
$327$	−10.1100	+	10.1100i	−0.559083	+	0.559083i
$328$	−0.722594			−0.0398986
$329$	−2.86253	−	4.96862i	−0.157816	−	0.273929i
$330$	−9.32424	+	9.32424i	−0.513282	+	0.513282i
$331$	−4.83645	−	4.83645i	−0.265836	−	0.265836i	0.561584	−	0.827420i	$-0.310192\pi$
$331$	−4.83645	−	4.83645i	−0.265836	−	0.265836i	−0.827420	+	0.561584i	$0.810192\pi$
$332$	4.45629			0.244571
$333$	6.21199	−	6.21199i	0.340415	−	0.340415i
$334$	−12.8915	+	12.8915i	−0.705392	+	0.705392i
$335$			5.27665i			0.288294i
$336$	2.29251	−	1.32076i	0.125067	−	0.0720534i
$337$	22.2007	+	22.2007i	1.20935	+	1.20935i	0.971238	+	0.238109i	$0.0765277\pi$
$337$	22.2007	+	22.2007i	1.20935	+	1.20935i	0.238109	+	0.971238i	$0.423472\pi$
$338$	−6.98184	+	6.98184i	−0.379762	+	0.379762i
$339$		−	9.32093i		−	0.506244i
$340$	−8.40739	+	8.40739i	−0.455955	+	0.455955i
$341$	3.77389			0.204367
$342$			1.74860i			0.0945533i
$343$	13.1320	−	13.0595i	0.709061	−	0.705147i
$344$	1.49917			0.0808296
$345$	19.6462	+	19.6462i	1.05772	+	1.05772i
$346$	3.57317	−	3.57317i	0.192095	−	0.192095i
$347$			29.9840i			1.60962i	0.593531	+	0.804811i	$0.297734\pi$
$347$			29.9840i			1.60962i	−0.593531	+	0.804811i	$0.702266\pi$
$348$	5.30524	+	0.924337i	0.284391	+	0.0495497i
$349$			23.4820i			1.25696i	0.777824	+	0.628482i	$0.216323\pi$
$349$			23.4820i			1.25696i	−0.777824	+	0.628482i	$0.783677\pi$
$350$	13.2837	+	23.0571i	0.710043	+	1.23245i
$351$	−1.25024	+	1.25024i	−0.0667328	+	0.0667328i
$352$		−	3.39821i		−	0.181125i
$353$	−17.7191			−0.943090			−0.471545	−	0.881842i	$-0.656304\pi$
$353$	−17.7191			−0.943090			−0.471545	+	0.881842i	$0.656304\pi$
$354$		−	9.85641i		−	0.523862i
$355$			45.0504i			2.39103i
$356$	−5.59795	+	5.59795i	−0.296691	+	0.296691i
$357$	7.82859	+	2.10541i	0.414333	+	0.111430i
$358$	−0.630407	−	0.630407i	−0.0333181	−	0.0333181i
$359$	−21.1072	+	21.1072i	−1.11400	+	1.11400i	−0.121391	+	0.992605i	$0.538736\pi$
$359$	−21.1072	+	21.1072i	−1.11400	+	1.11400i	−0.992605	+	0.121391i	$0.961264\pi$
$360$	2.74387	−	2.74387i	0.144614	−	0.144614i
$361$		−	15.9424i		−	0.839074i
$362$	4.41535	+	4.41535i	0.232066	+	0.232066i
$363$	0.387383	−	0.387383i	0.0203323	−	0.0203323i
$364$	4.51745	+	1.21491i	0.236779	+	0.0636788i
$365$	42.8804	−	42.8804i	2.24446	−	2.24446i
$366$	−3.88401	−	3.88401i	−0.203021	−	0.203021i
$367$	1.25748	+	1.25748i	0.0656401	+	0.0656401i	0.739165	−	0.673525i	$-0.235220\pi$
$367$	1.25748	+	1.25748i	0.0656401	+	0.0656401i	−0.673525	+	0.739165i	$0.735220\pi$
$368$	−7.16005			−0.373244
$369$	0.510951	+	0.510951i	0.0265991	+	0.0265991i
$370$	−34.0897			−1.77224
$371$	3.26204	−	12.1293i	0.169357	−	0.629724i
$372$	−1.11055			−0.0575794
$373$	23.0732			1.19468			0.597342	−	0.801987i	$-0.296224\pi$
$373$	23.0732			1.19468			0.597342	+	0.801987i	$0.296224\pi$
$374$	7.36264	−	7.36264i	0.380713	−	0.380713i
$375$	13.8774	+	13.8774i	0.716624	+	0.716624i
$376$	2.16733			0.111772
$377$	5.47718	+	7.78846i	0.282089	+	0.401126i
$378$	−2.55497	−	0.687128i	−0.131413	−	0.0353420i
$379$	7.79108	−	7.79108i	0.400201	−	0.400201i	−0.478103	−	0.878304i	$-0.658675\pi$
$379$	7.79108	−	7.79108i	0.400201	−	0.400201i	0.878304	+	0.478103i	$0.158675\pi$
$380$	4.79791	−	4.79791i	0.246128	−	0.246128i
$381$	0.478265			0.0245023
$382$			15.5214i			0.794144i
$383$	−12.5525			−0.641405			−0.320702	−	0.947180i	$-0.603919\pi$
$383$	−12.5525			−0.641405			−0.320702	+	0.947180i	$0.603919\pi$
$384$			1.00000i			0.0510310i
$385$	−17.4162	−	30.2301i	−0.887610	−	1.54067i
$386$		−	8.62741i		−	0.439124i
$387$	−1.06007	−	1.06007i	−0.0538864	−	0.0538864i
$388$	−5.97411	−	5.97411i	−0.303289	−	0.303289i
$389$	10.5528	+	10.5528i	0.535048	+	0.535048i	0.922070	−	0.387022i	$-0.126496\pi$
$389$	10.5528	+	10.5528i	0.535048	+	0.535048i	−0.387022	+	0.922070i	$0.626496\pi$
$390$	6.86097			0.347419
$391$	−15.5131	−	15.5131i	−0.784533	−	0.784533i
$392$	1.79926	+	6.76481i	0.0908761	+	0.341675i
$393$	20.6181			1.04004
$394$	−14.2339	+	14.2339i	−0.717095	+	0.717095i
$395$	30.7570	−	30.7570i	1.54755	−	1.54755i
$396$	−2.40290	+	2.40290i	−0.120750	+	0.120750i
$397$			3.99122i			0.200314i	0.994972	+	0.100157i	$0.0319344\pi$
$397$			3.99122i			0.200314i	−0.994972	+	0.100157i	$0.968066\pi$
$398$	−18.1012	−	18.1012i	−0.907332	−	0.907332i
$399$	−4.46761	−	1.20151i	−0.223660	−	0.0601507i
$400$	−10.0576			−0.502880
$401$	4.52848			0.226142			0.113071	−	0.993587i	$-0.463931\pi$
$401$	4.52848			0.226142			0.113071	+	0.993587i	$0.463931\pi$
$402$			1.35982i			0.0678215i
$403$	−1.38845	−	1.38845i	−0.0691638	−	0.0691638i
$404$	−7.21936	+	7.21936i	−0.359177	+	0.359177i
$405$	−3.88041			−0.192819
$406$	−6.00703	+	12.9196i	−0.298124	+	0.641188i
$407$	29.8535			1.47979
$408$	−2.16662	+	2.16662i	−0.107264	+	0.107264i
$409$	9.49565	+	9.49565i	0.469530	+	0.469530i	0.901762	−	0.432232i	$-0.142274\pi$
$409$	9.49565	+	9.49565i	0.469530	+	0.469530i	−0.432232	+	0.901762i	$0.642274\pi$
$410$		−	2.80396i		−	0.138478i
$411$	11.6864			0.576448
$412$	0.782210			0.0385367
$413$	25.1828	+	6.77261i	1.23916	+	0.333259i
$414$	5.06292	+	5.06292i	0.248829	+	0.248829i
$415$			17.2922i			0.848843i
$416$	−1.25024	+	1.25024i	−0.0612980	+	0.0612980i
$417$	−12.4007	+	12.4007i	−0.607264	+	0.607264i
$418$	−4.20170	+	4.20170i	−0.205512	+	0.205512i
$419$	17.6136			0.860480			0.430240	−	0.902715i	$-0.358429\pi$
$419$	17.6136			0.860480			0.430240	+	0.902715i	$0.358429\pi$
$420$	5.12510	+	8.89587i	0.250079	+	0.434074i
$421$	−22.3294	−	22.3294i	−1.08827	−	1.08827i	−0.995707	−	0.0925634i	$-0.970494\pi$
$421$	−22.3294	−	22.3294i	−1.08827	−	1.08827i	−0.0925634	−	0.995707i	$-0.529506\pi$
$422$	1.52235			0.0741069
$423$	−1.53254	−	1.53254i	−0.0745144	−	0.0745144i
$424$	3.35689	+	3.35689i	0.163025	+	0.163025i
$425$	−21.7910	−	21.7910i	−1.05702	−	1.05702i
$426$			11.6097i			0.562492i
$427$	12.5923	−	7.25471i	0.609386	−	0.351080i
$428$			11.5937i			0.560404i
$429$	−6.00839			−0.290088
$430$			5.81738i			0.280539i
$431$	−40.2666			−1.93958			−0.969788	−	0.243950i	$-0.921557\pi$
$431$	−40.2666			−1.93958			−0.969788	+	0.243950i	$0.921557\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−11.3274	+	11.3274i	−0.544360	+	0.544360i	−0.924804	−	0.380444i	$-0.875771\pi$
$433$	−11.3274	+	11.3274i	−0.544360	+	0.544360i	0.380444	+	0.924804i	$0.375771\pi$
$434$	0.763091	−	2.83742i	0.0366295	−	0.136201i
$435$	−3.58681	+	20.5865i	−0.171974	+	0.987048i
$436$	14.2977			0.684734
$437$	8.85301	+	8.85301i	0.423497	+	0.423497i
$438$	11.0505	−	11.0505i	0.528012	−	0.528012i
$439$	16.5852			0.791570			0.395785	−	0.918343i	$-0.370473\pi$
$439$	16.5852			0.791570			0.395785	+	0.918343i	$0.370473\pi$
$440$	13.1865			0.628640
$441$	3.51118	−	6.05571i	0.167199	−	0.288367i
$442$	−5.41759			−0.257689
$443$	6.90021	+	6.90021i	0.327839	+	0.327839i	0.851764	−	0.523925i	$-0.175533\pi$
$443$	6.90021	+	6.90021i	0.327839	+	0.327839i	−0.523925	+	0.851764i	$0.675533\pi$
$444$	−8.78507			−0.416921
$445$	−21.7224	−	21.7224i	−1.02974	−	1.02974i
$446$	−7.73515	−	7.73515i	−0.366270	−	0.366270i
$447$	13.0526	−	13.0526i	0.617368	−	0.617368i
$448$	−2.55497	−	0.687128i	−0.120711	−	0.0324637i
$449$	−7.35642	+	7.35642i	−0.347171	+	0.347171i	−0.859055	−	0.511884i	$-0.828948\pi$
$449$	−7.35642	+	7.35642i	−0.347171	+	0.347171i	0.511884	+	0.859055i	$0.328948\pi$
$450$	7.11180	+	7.11180i	0.335253	+	0.335253i
$451$			2.45553i			0.115626i
$452$	−6.59090	+	6.59090i	−0.310010	+	0.310010i
$453$	−11.1302	+	11.1302i	−0.522943	+	0.522943i
$454$	−12.5599	−	12.5599i	−0.589465	−	0.589465i
$455$	−4.71437	+	17.5296i	−0.221013	+	0.821798i
$456$	1.23644	−	1.23644i	0.0579018	−	0.0579018i
$457$			20.0788i			0.939248i	0.882866	+	0.469624i	$0.155611\pi$
$457$			20.0788i			0.939248i	−0.882866	+	0.469624i	$0.844389\pi$
$458$			4.45148i			0.208004i
$459$	3.06407			0.143018
$460$		−	27.7840i		−	1.29543i
$461$	−7.14248	+	7.14248i	−0.332658	+	0.332658i	−0.853595	−	0.520937i	$-0.825583\pi$
$461$	−7.14248	+	7.14248i	−0.332658	+	0.332658i	0.520937	+	0.853595i	$0.325583\pi$
$462$	−4.48823	−	7.79042i	−0.208811	−	0.362443i
$463$			8.83408i			0.410554i	0.978704	+	0.205277i	$0.0658096\pi$
$463$			8.83408i			0.410554i	−0.978704	+	0.205277i	$0.934190\pi$
$464$	−3.09777	−	4.40498i	−0.143810	−	0.204496i
$465$		−	4.30940i		−	0.199843i
$466$	−14.1318	+	14.1318i	−0.654643	+	0.654643i
$467$	−4.91709	−	4.91709i	−0.227536	−	0.227536i	0.584127	−	0.811662i	$-0.301437\pi$
$467$	−4.91709	−	4.91709i	−0.227536	−	0.227536i	−0.811662	+	0.584127i	$0.801437\pi$
$468$	1.76810			0.0817307
$469$	−3.47429	−	0.934368i	−0.160428	−	0.0431451i
$470$			8.41014i			0.387931i
$471$	−2.05266			−0.0945814
$472$	−6.96953	+	6.96953i	−0.320799	+	0.320799i
$473$		−	5.09448i		−	0.234245i
$474$	7.92623	−	7.92623i	0.364064	−	0.364064i
$475$	12.4357	+	12.4357i	0.570587	+	0.570587i
$476$	−4.04690	−	7.02440i	−0.185489	−	0.321963i
$477$		−	4.74736i		−	0.217367i
$478$	7.78410	−	7.78410i	0.356036	−	0.356036i
$479$	28.3303	−	28.3303i	1.29445	−	1.29445i	0.362438	−	0.932008i	$-0.381945\pi$
$479$	28.3303	−	28.3303i	1.29445	−	1.29445i	0.932008	−	0.362438i	$-0.118055\pi$
$480$	−3.88041			−0.177116
$481$	−10.9834	−	10.9834i	−0.500802	−	0.500802i
$482$	14.3333	−	14.3333i	0.652866	−	0.652866i
$483$	−16.4145	+	9.45672i	−0.746884	+	0.430296i
$484$	−0.547843			−0.0249019
$485$	23.1820	−	23.1820i	1.05264	−	1.05264i
$486$	−1.00000			−0.0453609
$487$	20.9227			0.948098			0.474049	−	0.880498i	$-0.342792\pi$
$487$	20.9227			0.948098			0.474049	+	0.880498i	$0.342792\pi$
$488$			5.49282i			0.248648i
$489$		−	6.44326i		−	0.291374i
$490$	−26.2503	+	6.98185i	−1.18587	+	0.315408i
$491$	5.00624	+	5.00624i	0.225928	+	0.225928i	0.810989	−	0.585061i	$-0.198929\pi$
$491$	5.00624	+	5.00624i	0.225928	+	0.225928i	−0.585061	+	0.810989i	$0.698929\pi$
$492$		−	0.722594i		−	0.0325771i
$493$	2.83223	−	16.2556i	0.127557	−	0.732116i
$494$	3.09170			0.139102
$495$	−9.32424	−	9.32424i	−0.419093	−	0.419093i
$496$	0.785278	+	0.785278i	0.0352600	+	0.0352600i
$497$	−29.6624	−	7.97735i	−1.33054	−	0.357833i
$498$			4.45629i			0.199691i
$499$			23.0218i			1.03060i	0.857010	+	0.515300i	$0.172319\pi$
$499$			23.0218i			1.03060i	−0.857010	+	0.515300i	$0.827681\pi$
$500$		−	19.6256i		−	0.877682i
$501$	−12.8915	−	12.8915i	−0.575950	−	0.575950i
$502$	−29.9792			−1.33804
$503$	8.96664	−	8.96664i	0.399803	−	0.399803i	−0.478361	−	0.878163i	$-0.658769\pi$
$503$	8.96664	−	8.96664i	0.399803	−	0.399803i	0.878163	+	0.478361i	$0.158769\pi$
$504$	1.32076	+	2.29251i	0.0588314	+	0.102116i
$505$	−28.0141	−	28.0141i	−1.24661	−	1.24661i
$506$			24.3314i			1.08166i
$507$	−6.98184	−	6.98184i	−0.310074	−	0.310074i
$508$	−0.338185	−	0.338185i	−0.0150045	−	0.0150045i
$509$		−	20.3233i		−	0.900813i	−0.892824	−	0.450407i	$-0.851279\pi$
$509$		−	20.3233i		−	0.900813i	0.892824	−	0.450407i	$-0.148721\pi$
$510$	−8.40739	−	8.40739i	−0.372286	−	0.372286i
$511$	20.6405	+	35.8267i	0.913083	+	1.58488i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.74860			−0.0772024
$514$	7.34870	+	7.34870i	0.324137	+	0.324137i
$515$			3.03530i			0.133751i
$516$			1.49917i			0.0659971i
$517$		−	7.36505i		−	0.323915i
$518$	6.03647	−	22.4456i	0.265227	−	0.986202i
$519$	3.57317	+	3.57317i	0.156845	+	0.156845i
$520$	−4.85144	−	4.85144i	−0.212750	−	0.212750i
$521$	11.3986			0.499382			0.249691	−	0.968326i	$-0.419671\pi$
$521$	11.3986			0.499382			0.249691	+	0.968326i	$0.419671\pi$
$522$	−0.924337	+	5.30524i	−0.0404571	+	0.232204i
$523$		−	22.2814i		−	0.974300i	−0.873318	−	0.487150i	$-0.838037\pi$
$523$		−	22.2814i		−	0.974300i	0.873318	−	0.487150i	$-0.161963\pi$
$524$	−14.5792	−	14.5792i	−0.636894	−	0.636894i
$525$	−23.0571	+	13.2837i	−1.00629	+	0.579748i
$526$			13.7635i			0.600116i
$527$			3.40280i			0.148228i
$528$	3.39821			0.147888
$529$	28.2663			1.22897
$530$	−13.0261	+	13.0261i	−0.565818	+	0.565818i
$531$	9.85641			0.427732
$532$	2.30948	+	4.00867i	0.100129	+	0.173798i
$533$	0.903415	−	0.903415i	0.0391312	−	0.0391312i
$534$	−5.59795	−	5.59795i	−0.242247	−	0.242247i
$535$	−44.9884			−1.94502
$536$	0.961535	−	0.961535i	0.0415320	−	0.0415320i
$537$	0.630407	−	0.630407i	0.0272041	−	0.0272041i
$538$		−	12.2092i		−	0.526378i
$539$	22.9883	−	6.11425i	0.990175	−	0.263359i
$540$	2.74387	+	2.74387i	0.118077	+	0.118077i
$541$	−1.68034	+	1.68034i	−0.0722434	+	0.0722434i	−0.742305	−	0.670062i	$-0.766268\pi$
$541$	−1.68034	+	1.68034i	−0.0722434	+	0.0722434i	0.670062	+	0.742305i	$0.266268\pi$
$542$			26.0333i			1.11823i
$543$	−4.41535	+	4.41535i	−0.189481	+	0.189481i
$544$	3.06407			0.131371
$545$			55.4808i			2.37654i
$546$	−1.21491	+	4.51745i	−0.0519935	+	0.193329i
$547$	2.50454			0.107087			0.0535433	−	0.998566i	$-0.482948\pi$
$547$	2.50454			0.107087			0.0535433	+	0.998566i	$0.482948\pi$
$548$	−8.26353	−	8.26353i	−0.353001	−	0.353001i
$549$	3.88401	−	3.88401i	0.165766	−	0.165766i
$550$			34.1778i			1.45735i
$551$	−1.61629	+	9.27673i	−0.0688564	+	0.395202i
$552$		−	7.16005i		−	0.304752i
$553$	14.8049	+	25.6976i	0.629569	+	1.09277i
$554$	21.9824	−	21.9824i	0.933944	−	0.933944i
$555$		−	34.0897i		−	1.44703i
$556$	17.5372			0.743743
$557$		−	9.74487i		−	0.412904i	−0.978457	−	0.206452i	$-0.933808\pi$
$557$		−	9.74487i		−	0.412904i	0.978457	−	0.206452i	$-0.0661917\pi$
$558$		−	1.11055i		−	0.0470134i
$559$	−1.87432	+	1.87432i	−0.0792751	+	0.0792751i
$560$	2.66634	−	9.91432i	0.112673	−	0.418957i
$561$	7.36264	+	7.36264i	0.310851	+	0.310851i
$562$	−16.9670	+	16.9670i	−0.715709	+	0.715709i
$563$	−19.3437	+	19.3437i	−0.815238	+	0.815238i	−0.985414	−	0.170176i	$-0.945566\pi$
$563$	−19.3437	+	19.3437i	−0.815238	+	0.815238i	0.170176	+	0.985414i	$0.445566\pi$
$564$			2.16733i			0.0912612i
$565$	−25.5754	−	25.5754i	−1.07596	−	1.07596i
$566$	−6.92908	+	6.92908i	−0.291251	+	0.291251i
$567$	0.687128	−	2.55497i	0.0288567	−	0.107299i
$568$	8.20930	−	8.20930i	0.344455	−	0.344455i
$569$	−15.2343	−	15.2343i	−0.638656	−	0.638656i	0.311568	−	0.950224i	$-0.399146\pi$
$569$	−15.2343	−	15.2343i	−0.638656	−	0.638656i	−0.950224	+	0.311568i	$0.899146\pi$
$570$	4.79791	+	4.79791i	0.200962	+	0.200962i
$571$	17.0054			0.711653			0.355827	−	0.934552i	$-0.384199\pi$
$571$	17.0054			0.711653			0.355827	+	0.934552i	$0.384199\pi$
$572$	4.24858	+	4.24858i	0.177642	+	0.177642i
$573$	−15.5214			−0.648416
$574$	1.84620	+	0.496515i	0.0770591	+	0.0207241i
$575$	72.0129			3.00315
$576$	−1.00000			−0.0416667
$577$	21.7073	−	21.7073i	0.903686	−	0.903686i	−0.0920667	−	0.995753i	$-0.529347\pi$
$577$	21.7073	−	21.7073i	0.903686	−	0.903686i	0.995753	+	0.0920667i	$0.0293473\pi$
$578$	−5.38213	−	5.38213i	−0.223867	−	0.223867i
$579$	8.62741			0.358543
$580$	17.0931	−	12.0206i	0.709754	−	0.499129i
$581$	−11.3857	−	3.06204i	−0.472357	−	0.127035i
$582$	5.97411	−	5.97411i	0.247635	−	0.247635i
$583$	11.4074	−	11.4074i	0.472447	−	0.472447i
$584$	−15.6277			−0.646680
$585$			6.86097i			0.283666i
$586$	14.2276			0.587735
$587$		−	35.2646i		−	1.45553i	−0.685828	−	0.727764i	$-0.740560\pi$
$587$		−	35.2646i		−	1.45553i	0.685828	−	0.727764i	$-0.259440\pi$
$588$	−6.76481	+	1.79926i	−0.278976	+	0.0742001i
$589$		−	1.94191i		−	0.0800148i
$590$	−27.0447	−	27.0447i	−1.11341	−	1.11341i
$591$	−14.2339	−	14.2339i	−0.585505	−	0.585505i
$592$	6.21199	+	6.21199i	0.255311	+	0.255311i
$593$	38.8278			1.59447			0.797234	−	0.603670i	$-0.206296\pi$
$593$	38.8278			1.59447			0.797234	+	0.603670i	$0.206296\pi$
$594$	−2.40290	−	2.40290i	−0.0985921	−	0.0985921i
$595$	27.2576	−	15.7037i	1.11745	−	0.643787i
$596$	−18.4592			−0.756118
$597$	18.1012	−	18.1012i	0.740834	−	0.740834i
$598$	8.95177	−	8.95177i	0.366065	−	0.366065i
$599$	23.2214	−	23.2214i	0.948800	−	0.948800i	−0.0499516	−	0.998752i	$-0.515907\pi$
$599$	23.2214	−	23.2214i	0.948800	−	0.948800i	0.998752	+	0.0499516i	$0.0159067\pi$
$600$		−	10.0576i		−	0.410600i
$601$	−11.1708	−	11.1708i	−0.455665	−	0.455665i	0.441564	−	0.897230i	$-0.354424\pi$
$601$	−11.1708	−	11.1708i	−0.455665	−	0.455665i	−0.897230	+	0.441564i	$0.854424\pi$
$602$	−3.83032	−	1.03012i	−0.156112	−	0.0419845i
$603$	−1.35982			−0.0553760
$604$	15.7405			0.640471
$605$		−	2.12586i		−	0.0864283i
$606$	−7.21936	−	7.21936i	−0.293267	−	0.293267i
$607$	−20.1281	+	20.1281i	−0.816976	+	0.816976i	−0.985669	−	0.168692i	$-0.946046\pi$
$607$	−20.1281	+	20.1281i	−0.816976	+	0.816976i	0.168692	+	0.985669i	$0.446046\pi$
$608$	−1.74860			−0.0709149
$609$	−12.9196	−	6.00703i	−0.523528	−	0.243417i
$610$	−21.3144			−0.862996
$611$	−2.70968	+	2.70968i	−0.109622	+	0.109622i
$612$	−2.16662	−	2.16662i	−0.0875806	−	0.0875806i
$613$		−	23.9316i		−	0.966590i	−0.875458	−	0.483295i	$-0.839440\pi$
$613$		−	23.9316i		−	0.966590i	0.875458	−	0.483295i	$-0.160560\pi$
$614$	3.86155			0.155839
$615$	2.80396			0.113067
$616$	−2.33501	+	8.68232i	−0.0940801	+	0.349821i
$617$	17.8937	+	17.8937i	0.720374	+	0.720374i	0.968681	−	0.248307i	$-0.0798743\pi$
$617$	17.8937	+	17.8937i	0.720374	+	0.720374i	−0.248307	+	0.968681i	$0.579874\pi$
$618$			0.782210i			0.0314651i
$619$	−27.0456	+	27.0456i	−1.08705	+	1.08705i	−0.0912240	+	0.995830i	$0.529078\pi$
$619$	−27.0456	+	27.0456i	−1.08705	+	1.08705i	−0.995830	+	0.0912240i	$0.970922\pi$
$620$	−3.04720	+	3.04720i	−0.122379	+	0.122379i
$621$	−5.06292	+	5.06292i	−0.203168	+	0.203168i
$622$	16.2536			0.651709
$623$	18.1491	−	10.4561i	0.727128	−	0.418914i
$624$	−1.25024	−	1.25024i	−0.0500496	−	0.0500496i
$625$	25.8673			1.03469
$626$	15.4433	+	15.4433i	0.617238	+	0.617238i
$627$	−4.20170	−	4.20170i	−0.167800	−	0.167800i
$628$	1.45145	+	1.45145i	0.0579191	+	0.0579191i
$629$			26.9181i			1.07329i
$630$	−8.89587	+	5.12510i	−0.354420	+	0.204189i
$631$			16.7392i			0.666379i	0.942860	+	0.333189i	$0.108125\pi$
$631$			16.7392i			0.666379i	−0.942860	+	0.333189i	$0.891875\pi$
$632$	−11.2094			−0.445885
$633$			1.52235i			0.0605080i
$634$	16.1694			0.642171
$635$	1.31230	−	1.31230i	0.0520769	−	0.0520769i
$636$	−3.35689	+	3.35689i	−0.133109	+	0.133109i
$637$	−10.7071	−	6.20813i	−0.424232	−	0.245975i
$638$	−14.9690	+	10.5269i	−0.592630	+	0.416763i
$639$	−11.6097			−0.459273
$640$	2.74387	+	2.74387i	0.108461	+	0.108461i
$641$	20.3165	−	20.3165i	0.802454	−	0.802454i	−0.181025	−	0.983479i	$-0.557941\pi$
$641$	20.3165	−	20.3165i	0.802454	−	0.802454i	0.983479	+	0.181025i	$0.0579413\pi$
$642$	−11.5937			−0.457568
$643$	36.0097			1.42008			0.710041	−	0.704160i	$-0.248676\pi$
$643$	36.0097			1.42008			0.710041	+	0.704160i	$0.248676\pi$
$644$	18.2937	+	4.91987i	0.720873	+	0.193870i
$645$	−5.81738			−0.229059
$646$	−3.78855	−	3.78855i	−0.149058	−	0.149058i
$647$	18.3194			0.720211			0.360106	−	0.932912i	$-0.382741\pi$
$647$	18.3194			0.720211			0.360106	+	0.932912i	$0.382741\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	23.6840	+	23.6840i	0.929676	+	0.929676i
$650$	12.5744	−	12.5744i	0.493208	−	0.493208i
$651$	2.83742	+	0.763091i	0.111207	+	0.0299079i
$652$	−4.55608	+	4.55608i	−0.178430	+	0.178430i
$653$	0.221855	+	0.221855i	0.00868187	+	0.00868187i	0.711434	−	0.702753i	$-0.248046\pi$
$653$	0.221855	+	0.221855i	0.00868187	+	0.00868187i	−0.702753	+	0.711434i	$0.748046\pi$
$654$			14.2977i			0.559083i
$655$	56.5732	−	56.5732i	2.21050	−	2.21050i
$656$	−0.510951	+	0.510951i	−0.0199493	+	0.0199493i
$657$	11.0505	+	11.0505i	0.431120	+	0.431120i
$658$	−5.53746	−	1.48923i	−0.215873	−	0.0580564i
$659$	11.2380	−	11.2380i	0.437770	−	0.437770i	−0.453491	−	0.891261i	$-0.649822\pi$
$659$	11.2380	−	11.2380i	0.437770	−	0.437770i	0.891261	+	0.453491i	$0.149822\pi$
$660$			13.1865i			0.513282i
$661$		−	35.6931i		−	1.38830i	−0.719830	−	0.694151i	$-0.755780\pi$
$661$		−	35.6931i		−	1.38830i	0.719830	−	0.694151i	$-0.244220\pi$
$662$	−6.83978			−0.265836
$663$		−	5.41759i		−	0.210402i
$664$	3.15107	−	3.15107i	0.122285	−	0.122285i
$665$	−15.5553	+	8.96173i	−0.603208	+	0.347521i
$666$		−	8.78507i		−	0.340415i
$667$	22.1802	+	31.5399i	0.858820	+	1.22123i
$668$			18.2313i			0.705392i
$669$	7.73515	−	7.73515i	0.299058	−	0.299058i
$670$	3.73115	+	3.73115i	0.144147	+	0.144147i
$671$	18.6658			0.720584
$672$	0.687128	−	2.55497i	0.0265065	−	0.0985600i
$673$			30.8589i			1.18952i	0.803902	+	0.594761i	$0.202753\pi$
$673$			30.8589i			1.18952i	−0.803902	+	0.594761i	$0.797247\pi$
$674$	31.3965			1.20935
$675$	−7.11180	+	7.11180i	−0.273733	+	0.273733i
$676$			9.87381i			0.379762i
$677$	−32.9228	+	32.9228i	−1.26533	+	1.26533i	−0.316850	+	0.948476i	$0.602625\pi$
$677$	−32.9228	+	32.9228i	−1.26533	+	1.26533i	−0.948476	+	0.316850i	$0.897375\pi$
$678$	−6.59090	−	6.59090i	−0.253122	−	0.253122i
$679$	11.1587	+	19.3686i	0.428231	+	0.743300i
$680$			11.8898i			0.455955i
$681$	12.5599	−	12.5599i	0.481296	−	0.481296i
$682$	2.66854	−	2.66854i	0.102184	−	0.102184i
$683$	−43.0568			−1.64752			−0.823761	−	0.566938i	$-0.808128\pi$
$683$	−43.0568			−1.64752			−0.823761	+	0.566938i	$0.808128\pi$
$684$	1.23644	+	1.23644i	0.0472766	+	0.0472766i
$685$	32.0659	−	32.0659i	1.22518	−	1.22518i
$686$	0.0512525	−	18.5202i	0.00195683	−	0.707104i
$687$	−4.45148			−0.169835
$688$	1.06007	−	1.06007i	0.0404148	−	0.0404148i
$689$	−8.39382			−0.319779
$690$	27.7840			1.05772
$691$			5.39638i			0.205288i	0.994718	+	0.102644i	$0.0327303\pi$
$691$			5.39638i			0.205288i	−0.994718	+	0.102644i	$0.967270\pi$
$692$		−	5.05323i		−	0.192095i
$693$	7.79042	−	4.48823i	0.295934	−	0.170494i
$694$	21.2019	+	21.2019i	0.804811	+	0.804811i
$695$			68.0516i			2.58134i
$696$	4.40498	−	3.09777i	0.166970	−	0.117421i
$697$	−2.21408			−0.0838641
$698$	16.6043	+	16.6043i	0.628482	+	0.628482i
$699$	−14.1318	−	14.1318i	−0.534514	−	0.534514i
$700$	25.6968	+	6.91086i	0.971249	+	0.261206i
$701$			14.4183i			0.544571i	0.962217	+	0.272285i	$0.0877795\pi$
$701$			14.4183i			0.544571i	−0.962217	+	0.272285i	$0.912221\pi$
$702$			1.76810i			0.0667328i
$703$		−	15.3615i		−	0.579372i
$704$	−2.40290	−	2.40290i	−0.0905626	−	0.0905626i
$705$	−8.41014			−0.316744
$706$	−12.5293	+	12.5293i	−0.471545	+	0.471545i
$707$	23.4059	−	13.4846i	0.880268	−	0.507141i
$708$	−6.96953	−	6.96953i	−0.261931	−	0.261931i
$709$		−	11.3698i		−	0.427000i	−0.976943	−	0.213500i	$-0.931514\pi$
$709$		−	11.3698i		−	0.427000i	0.976943	−	0.213500i	$-0.0684863\pi$
$710$	31.8555	+	31.8555i	1.19551	+	1.19551i
$711$	7.92623	+	7.92623i	0.297257	+	0.297257i
$712$			7.91670i			0.296691i
$713$	−5.62263	−	5.62263i	−0.210569	−	0.210569i
$714$	7.02440	−	4.04690i	0.262881	−	0.151452i
$715$	−16.4862	+	16.4862i	−0.616550	+	0.616550i
$716$	−0.891530			−0.0333181
$717$	7.78410	+	7.78410i	0.290702	+	0.290702i
$718$			29.8501i			1.11400i
$719$		−	44.8233i		−	1.67163i	−0.549013	−	0.835814i	$-0.684996\pi$
$719$		−	44.8233i		−	1.67163i	0.549013	−	0.835814i	$-0.315004\pi$
$720$		−	3.88041i		−	0.144614i
$721$	−1.99852	−	0.537478i	−0.0744288	−	0.0200167i
$722$	−11.2730	−	11.2730i	−0.419537	−	0.419537i
$723$	14.3333	+	14.3333i	0.533063	+	0.533063i
$724$	6.24425			0.232066
$725$	31.1561	+	44.3035i	1.15711	+	1.64539i
$726$		−	0.547843i		−	0.0203323i
$727$	26.5082	+	26.5082i	0.983133	+	0.983133i	0.999860	−	0.0167272i	$-0.00532467\pi$
$727$	26.5082	+	26.5082i	0.983133	+	0.983133i	−0.0167272	+	0.999860i	$0.505325\pi$
$728$	4.05339	−	2.33524i	0.150229	−	0.0865499i
$729$		−	1.00000i		−	0.0370370i
$730$		−	60.6421i		−	2.24446i
$731$	4.59355			0.169898
$732$	−5.49282			−0.203021
$733$	20.4703	−	20.4703i	0.756087	−	0.756087i	−0.219521	−	0.975608i	$-0.570449\pi$
$733$	20.4703	−	20.4703i	0.756087	−	0.756087i	0.975608	+	0.219521i	$0.0704494\pi$
$734$	1.77835			0.0656401
$735$	−6.98185	−	26.2503i	−0.257530	−	0.968255i
$736$	−5.06292	+	5.06292i	−0.186622	+	0.186622i
$737$	−3.26750	−	3.26750i	−0.120360	−	0.120360i
$738$	0.722594			0.0265991
$739$	−37.2012	+	37.2012i	−1.36847	+	1.36847i	−0.505840	+	0.862627i	$0.668818\pi$
$739$	−37.2012	+	37.2012i	−1.36847	+	1.36847i	−0.862627	+	0.505840i	$0.831182\pi$
$740$	−24.1051	+	24.1051i	−0.886120	+	0.886120i
$741$			3.09170i			0.113576i
$742$	−6.27013	−	10.8833i	−0.230184	−	0.399540i
$743$	−7.00263	−	7.00263i	−0.256901	−	0.256901i	0.566891	−	0.823793i	$-0.308146\pi$
$743$	−7.00263	−	7.00263i	−0.256901	−	0.256901i	−0.823793	+	0.566891i	$0.808146\pi$
$744$	−0.785278	+	0.785278i	−0.0287897	+	0.0287897i
$745$		−	71.6293i		−	2.62429i
$746$	16.3152	−	16.3152i	0.597342	−	0.597342i
$747$	−4.45629			−0.163047
$748$		−	10.4124i		−	0.380713i
$749$	7.96637	−	29.6216i	0.291085	−	1.08235i
$750$	19.6256			0.716624
$751$	−10.2481	−	10.2481i	−0.373959	−	0.373959i	0.494958	−	0.868917i	$-0.335183\pi$
$751$	−10.2481	−	10.2481i	−0.373959	−	0.373959i	−0.868917	+	0.494958i	$0.835183\pi$
$752$	1.53254	−	1.53254i	0.0558858	−	0.0558858i
$753$		−	29.9792i		−	1.09250i
$754$	9.38022	+	1.63432i	0.341608	+	0.0595186i
$755$			61.0796i			2.22291i
$756$	−2.29251	+	1.32076i	−0.0833777	+	0.0480356i
$757$	−12.1461	+	12.1461i	−0.441457	+	0.441457i	−0.892501	−	0.451045i	$-0.851052\pi$
$757$	−12.1461	+	12.1461i	−0.441457	+	0.441457i	0.451045	+	0.892501i	$0.351052\pi$
$758$		−	11.0183i		−	0.400201i
$759$	−24.3314			−0.883173
$760$		−	6.78527i		−	0.246128i
$761$			47.5299i			1.72296i	0.507795	+	0.861478i	$0.330461\pi$
$761$			47.5299i			1.72296i	−0.507795	+	0.861478i	$0.669539\pi$
$762$	0.338185	−	0.338185i	0.0122511	−	0.0122511i
$763$	−36.5301	−	9.82433i	−1.32248	−	0.355664i
$764$	10.9753	+	10.9753i	0.397072	+	0.397072i
$765$	8.40739	−	8.40739i	0.303970	−	0.303970i
$766$	−8.87599	+	8.87599i	−0.320702	+	0.320702i
$767$		−	17.4272i		−	0.629258i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	2.93648	−	2.93648i	0.105892	−	0.105892i	−0.652176	−	0.758068i	$-0.726144\pi$
$769$	2.93648	−	2.93648i	0.105892	−	0.105892i	0.758068	+	0.652176i	$0.226144\pi$
$770$	−33.6910	−	9.06079i	−1.21414	−	0.326528i
$771$	−7.34870	+	7.34870i	−0.264657	+	0.264657i
$772$	−6.10050	−	6.10050i	−0.219562	−	0.219562i
$773$	20.7552	+	20.7552i	0.746513	+	0.746513i	0.973823	−	0.227309i	$-0.0729928\pi$
$773$	20.7552	+	20.7552i	0.746513	+	0.746513i	−0.227309	+	0.973823i	$0.572993\pi$
$774$	−1.49917			−0.0538864
$775$	−7.89801	−	7.89801i	−0.283705	−	0.283705i
$776$	−8.44867			−0.303289
$777$	22.4456	+	6.03647i	0.805230	+	0.216557i
$778$	14.9239			0.535048
$779$	1.26353			0.0452705
$780$	4.85144	−	4.85144i	0.173709	−	0.173709i
$781$	−27.8969	−	27.8969i	−0.998231	−	0.998231i
$782$	−21.9389			−0.784533
$783$	−5.30524	−	0.924337i	−0.189594	−	0.0330331i
$784$	6.05571	+	3.51118i	0.216275	+	0.125399i
$785$	−5.63221	+	5.63221i	−0.201022	+	0.201022i
$786$	14.5792	−	14.5792i	0.520022	−	0.520022i
$787$	0.190626			0.00679510			0.00339755	−	0.999994i	$-0.498919\pi$
$787$	0.190626			0.00679510			0.00339755	+	0.999994i	$0.498919\pi$
$788$			20.1298i			0.717095i
$789$	−13.7635			−0.489993
$790$		−	43.4970i		−	1.54755i
$791$	21.3683	−	12.3107i	0.759770	−	0.437719i
$792$			3.39821i			0.120750i
$793$	−6.86734	−	6.86734i	−0.243866	−	0.243866i
$794$	2.82222	+	2.82222i	0.100157	+	0.100157i
$795$	−13.0261	−	13.0261i	−0.461988	−	0.461988i
$796$	−25.5990			−0.907332
$797$	−14.2877	−	14.2877i	−0.506097	−	0.506097i	0.407229	−	0.913326i	$-0.366495\pi$
$797$	−14.2877	−	14.2877i	−0.506097	−	0.506097i	−0.913326	+	0.407229i	$0.866495\pi$
$798$	−4.00867	+	2.30948i	−0.141905	+	0.0817547i
$799$	6.64085			0.234937
$800$	−7.11180	+	7.11180i	−0.251440	+	0.251440i
$801$	5.59795	−	5.59795i	0.197794	−	0.197794i
$802$	3.20212	−	3.20212i	0.113071	−	0.113071i
$803$			53.1064i			1.87408i
$804$	0.961535	+	0.961535i	0.0339107	+	0.0339107i
$805$	−19.0911	+	70.9871i	−0.672874	+	2.50197i
$806$	−1.96357			−0.0691638
$807$	12.2092			0.429786
$808$			10.2097i			0.359177i
$809$	−1.77372	−	1.77372i	−0.0623608	−	0.0623608i	0.675239	−	0.737599i	$-0.264041\pi$
$809$	−1.77372	−	1.77372i	−0.0623608	−	0.0623608i	−0.737599	+	0.675239i	$0.764041\pi$
$810$	−2.74387	+	2.74387i	−0.0964096	+	0.0964096i
$811$	8.91151			0.312925			0.156463	−	0.987684i	$-0.449991\pi$
$811$	8.91151			0.312925			0.156463	+	0.987684i	$0.449991\pi$
$812$	4.88791	+	13.3831i	0.171532	+	0.469656i
$813$	−26.0333			−0.913027
$814$	21.1096	−	21.1096i	0.739893	−	0.739893i
$815$	−17.6794	−	17.6794i	−0.619284	−	0.619284i
$816$			3.06407i			0.107264i
$817$	−2.62144			−0.0917125
$818$	13.4289			0.469530
$819$	−4.51745	−	1.21491i	−0.157852	−	0.0424525i
$820$	−1.98270	−	1.98270i	−0.0692389	−	0.0692389i
$821$			5.40991i			0.188807i	0.995534	+	0.0944036i	$0.0300944\pi$
$821$			5.40991i			0.188807i	−0.995534	+	0.0944036i	$0.969906\pi$
$822$	8.26353	−	8.26353i	0.288224	−	0.288224i
$823$	11.9186	−	11.9186i	0.415458	−	0.415458i	−0.468177	−	0.883635i	$-0.655089\pi$
$823$	11.9186	−	11.9186i	0.415458	−	0.415458i	0.883635	+	0.468177i	$0.155089\pi$
$824$	0.553106	−	0.553106i	0.0192684	−	0.0192684i
$825$	−34.1778			−1.18992
$826$	22.5959	−	13.0180i	0.786212	−	0.452953i
$827$	31.9286	+	31.9286i	1.11027	+	1.11027i	0.993114	+	0.117154i	$0.0373771\pi$
$827$	31.9286	+	31.9286i	1.11027	+	1.11027i	0.117154	+	0.993114i	$0.462623\pi$
$828$	7.16005			0.248829
$829$	−21.5126	−	21.5126i	−0.747165	−	0.747165i	0.226781	−	0.973946i	$-0.427180\pi$
$829$	−21.5126	−	21.5126i	−0.747165	−	0.747165i	−0.973946	+	0.226781i	$0.927180\pi$
$830$	12.2275	+	12.2275i	0.424421	+	0.424421i
$831$	21.9824	+	21.9824i	0.762562	+	0.762562i
$832$			1.76810i			0.0612980i
$833$	5.51304	+	20.7278i	0.191016	+	0.718177i
$834$			17.5372i			0.607264i
$835$	−70.7451			−2.44824
$836$			5.94210i			0.205512i
$837$	1.11055			0.0383863
$838$	12.4547	−	12.4547i	0.430240	−	0.430240i
$839$	−8.26833	+	8.26833i	−0.285455	+	0.285455i	−0.835280	−	0.549825i	$-0.814694\pi$
$839$	−8.26833	+	8.26833i	−0.285455	+	0.285455i	0.549825	+	0.835280i	$0.314694\pi$
$840$	9.91432	+	2.66634i	0.342077	+	0.0919975i
$841$	−9.80767	+	27.2912i	−0.338195	+	0.941076i
$842$	−31.5786			−1.08827
$843$	−16.9670	−	16.9670i	−0.584374	−	0.584374i
$844$	1.07647	−	1.07647i	0.0370535	−	0.0370535i
$845$	−38.3144			−1.31806
$846$	−2.16733			−0.0745144
$847$	1.39972	+	0.376438i	0.0480949	+	0.0129346i
$848$	4.74736			0.163025
$849$	−6.92908	−	6.92908i	−0.237805	−	0.237805i
$850$	−30.8172			−1.05702
$851$	−44.4781	−	44.4781i	−1.52469	−	1.52469i
$852$	8.20930	+	8.20930i	0.281246	+	0.281246i
$853$	34.4054	−	34.4054i	1.17802	−	1.17802i	0.197770	−	0.980248i	$-0.436630\pi$
$853$	34.4054	−	34.4054i	1.17802	−	1.17802i	0.980248	−	0.197770i	$-0.0633699\pi$
$854$	3.77427	−	14.0340i	0.129153	−	0.480233i
$855$	−4.79791	+	4.79791i	−0.164085	+	0.164085i
$856$	8.19800	+	8.19800i	0.280202	+	0.280202i
$857$		−	14.3116i		−	0.488875i	−0.969665	−	0.244438i	$-0.921397\pi$
$857$		−	14.3116i		−	0.488875i	0.969665	−	0.244438i	$-0.0786033\pi$
$858$	−4.24858	+	4.24858i	−0.145044	+	0.145044i
$859$	1.18430	−	1.18430i	0.0404077	−	0.0404077i	−0.686614	−	0.727022i	$-0.740904\pi$
$859$	1.18430	−	1.18430i	0.0404077	−	0.0404077i	0.727022	+	0.686614i	$0.240904\pi$
$860$	4.11351	+	4.11351i	0.140270	+	0.140270i
$861$	−0.496515	+	1.84620i	−0.0169212	+	0.0629185i
$862$	−28.4728	+	28.4728i	−0.969788	+	0.969788i
$863$		−	52.4294i		−	1.78472i	−0.451328	−	0.892358i	$-0.649049\pi$
$863$		−	52.4294i		−	1.78472i	0.451328	−	0.892358i	$-0.350951\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	19.6086			0.666712
$866$			16.0194i			0.544360i
$867$	5.38213	−	5.38213i	0.182787	−	0.182787i
$868$	−1.46677	−	2.54595i	−0.0497855	−	0.0864150i
$869$			38.0918i			1.29218i
$870$	12.0206	+	17.0931i	0.407537	+	0.579511i
$871$			2.40430i			0.0814665i
$872$	10.1100	−	10.1100i	0.342367	−	0.342367i
$873$	5.97411	+	5.97411i	0.202193	+	0.202193i
$874$	12.5200			0.423497
$875$	−13.4853	+	50.1427i	−0.455885	+	1.69513i
$876$		−	15.6277i		−	0.528012i
$877$	47.4101			1.60093			0.800463	−	0.599383i	$-0.204587\pi$
$877$	47.4101			1.60093			0.800463	+	0.599383i	$0.204587\pi$
$878$	11.7275	−	11.7275i	0.395785	−	0.395785i
$879$			14.2276i			0.479883i
$880$	9.32424	−	9.32424i	0.314320	−	0.314320i
$881$	16.9873	+	16.9873i	0.572315	+	0.572315i	0.932775	−	0.360460i	$-0.117380\pi$
$881$	16.9873	+	16.9873i	0.572315	+	0.572315i	−0.360460	+	0.932775i	$0.617380\pi$
$882$	−1.79926	−	6.76481i	−0.0605841	−	0.227783i
$883$			6.73111i			0.226520i	0.993565	+	0.113260i	$0.0361293\pi$
$883$			6.73111i			0.226520i	−0.993565	+	0.113260i	$0.963871\pi$
$884$	−3.83082	+	3.83082i	−0.128844	+	0.128844i
$885$	27.0447	−	27.0447i	0.909096	−	0.909096i
$886$	9.75837			0.327839
$887$	−2.89190	−	2.89190i	−0.0971006	−	0.0971006i	0.656888	−	0.753988i	$-0.271873\pi$
$887$	−2.89190	−	2.89190i	−0.0971006	−	0.0971006i	−0.753988	+	0.656888i	$0.771873\pi$
$888$	−6.21199	+	6.21199i	−0.208461	+	0.208461i
$889$	0.631674	+	1.09643i	0.0211857	+	0.0367730i
$890$	−30.7201			−1.02974
$891$	2.40290	−	2.40290i	0.0805001	−	0.0805001i
$892$	−10.9392			−0.366270
$893$	−3.78979			−0.126820
$894$		−	18.4592i		−	0.617368i
$895$		−	3.45950i		−	0.115638i
$896$	−2.29251	+	1.32076i	−0.0765873	+	0.0441235i
$897$	8.95177	+	8.95177i	0.298891	+	0.298891i
$898$			10.4036i			0.347171i
$899$	1.02652	−	5.89174i	0.0342365	−	0.196501i
$900$	10.0576			0.335253
$901$	10.2857	+	10.2857i	0.342667	+	0.342667i
$902$	1.73632	+	1.73632i	0.0578131	+	0.0578131i
$903$	1.03012	−	3.83032i	0.0342802	−	0.127465i
$904$			9.32093i			0.310010i
$905$			24.2302i			0.805441i
$906$			15.7405i			0.522943i
$907$	−8.96822	−	8.96822i	−0.297785	−	0.297785i	0.542361	−	0.840146i	$-0.317531\pi$
$907$	−8.96822	−	8.96822i	−0.297785	−	0.297785i	−0.840146	+	0.542361i	$0.817531\pi$
$908$	−17.7624			−0.589465
$909$	7.21936	−	7.21936i	0.239451	−	0.239451i
$910$	9.06171	+	15.7288i	0.300393	+	0.521406i
$911$	7.57665	+	7.57665i	0.251026	+	0.251026i	0.821391	−	0.570365i	$-0.193198\pi$
$911$	7.57665	+	7.57665i	0.251026	+	0.251026i	−0.570365	+	0.821391i	$0.693198\pi$
$912$		−	1.74860i		−	0.0579018i
$913$	−10.7080	−	10.7080i	−0.354383	−	0.354383i
$914$	14.1979	+	14.1979i	0.469624	+	0.469624i
$915$		−	21.3144i		−	0.704633i
$916$	3.14767	+	3.14767i	0.104002	+	0.104002i
$917$	27.2316	+	47.2671i	0.899265	+	1.56090i
$918$	2.16662	−	2.16662i	0.0715092	−	0.0715092i
$919$	53.3016			1.75826			0.879128	−	0.476586i	$-0.158126\pi$
$919$	53.3016			1.75826			0.879128	+	0.476586i	$0.158126\pi$
$920$	−19.6462	−	19.6462i	−0.647717	−	0.647717i
$921$			3.86155i			0.127242i
$922$			10.1010i			0.332658i
$923$			20.5272i			0.675660i
$924$	−8.68232	−	2.33501i	−0.285627	−	0.0768161i
$925$	−62.4776	−	62.4776i	−2.05425	−	2.05425i
$926$	6.24664	+	6.24664i	0.205277	+	0.205277i
$927$	−0.782210			−0.0256911
$928$	−5.30524	−	0.924337i	−0.174153	−	0.0303429i
$929$			22.7690i			0.747028i	0.927625	+	0.373514i	$0.121847\pi$
$929$			22.7690i			0.747028i	−0.927625	+	0.373514i	$0.878153\pi$
$930$	−3.04720	−	3.04720i	−0.0999217	−	0.0999217i
$931$	−3.14617	−	11.8289i	−0.103112	−	0.387677i
$932$			19.9854i			0.654643i
$933$			16.2536i			0.532118i
$934$	−6.95381			−0.227536
$935$	40.4042			1.32136
$936$	1.25024	−	1.25024i	0.0408653	−	0.0408653i
$937$	9.74666			0.318410			0.159205	−	0.987246i	$-0.449107\pi$
$937$	9.74666			0.318410			0.159205	+	0.987246i	$0.449107\pi$
$938$	−3.11739	+	1.79599i	−0.101786	+	0.0586412i
$939$	−15.4433	+	15.4433i	−0.503972	+	0.503972i
$940$	5.94687	+	5.94687i	0.193965	+	0.193965i
$941$	−10.3962			−0.338907			−0.169453	−	0.985538i	$-0.554200\pi$
$941$	−10.3962			−0.338907			−0.169453	+	0.985538i	$0.554200\pi$
$942$	−1.45145	+	1.45145i	−0.0472907	+	0.0472907i
$943$	3.65844	−	3.65844i	0.119135	−	0.119135i
$944$			9.85641i			0.320799i
$945$	−5.12510	−	8.89587i	−0.166719	−	0.289383i
$946$	−3.60234	−	3.60234i	−0.117122	−	0.117122i
$947$	−14.0961	+	14.0961i	−0.458063	+	0.458063i	−0.898019	−	0.439956i	$-0.854994\pi$
$947$	−14.0961	+	14.0961i	−0.458063	+	0.458063i	0.439956	+	0.898019i	$0.354994\pi$
$948$		−	11.2094i		−	0.364064i
$949$	19.5384	−	19.5384i	0.634243	−	0.634243i
$950$	17.5867			0.570587
$951$			16.1694i			0.524330i
$952$	−7.82859	−	2.10541i	−0.253726	−	0.0682366i
$953$	−11.5308			−0.373520			−0.186760	−	0.982406i	$-0.559799\pi$
$953$	−11.5308			−0.373520			−0.186760	+	0.982406i	$0.559799\pi$
$954$	−3.35689	−	3.35689i	−0.108683	−	0.108683i
$955$	−42.5887	+	42.5887i	−1.37814	+	1.37814i
$956$		−	11.0084i		−	0.356036i
$957$	−10.5269	−	14.9690i	−0.340285	−	0.483881i
$958$		−	40.0651i		−	1.29445i
$959$	15.4349	+	26.7912i	0.498420	+	0.865132i
$960$	−2.74387	+	2.74387i	−0.0885579	+	0.0885579i
$961$		−	29.7667i		−	0.960215i
$962$	−15.5329			−0.500802
$963$		−	11.5937i		−	0.373602i
$964$		−	20.2704i		−	0.652866i
$965$	23.6725	−	23.6725i	0.762043	−	0.762043i
$966$	−4.91987	+	18.2937i	−0.158294	+	0.588590i
$967$	21.2133	+	21.2133i	0.682173	+	0.682173i	0.960489	−	0.278316i	$-0.0897763\pi$
$967$	21.2133	+	21.2133i	0.682173	+	0.682173i	−0.278316	+	0.960489i	$0.589776\pi$
$968$	−0.387383	+	0.387383i	−0.0124510	+	0.0124510i
$969$	3.78855	−	3.78855i	0.121706	−	0.121706i
$970$		−	32.7843i		−	1.05264i
$971$	1.28115	+	1.28115i	0.0411142	+	0.0411142i	0.727365	−	0.686251i	$-0.240745\pi$
$971$	1.28115	+	1.28115i	0.0411142	+	0.0411142i	−0.686251	+	0.727365i	$0.740745\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−44.8070	−	12.0503i	−1.43645	−	0.386315i
$974$	14.7946	−	14.7946i	0.474049	−	0.474049i
$975$	12.5744	+	12.5744i	0.402703	+	0.402703i
$976$	3.88401	+	3.88401i	0.124324	+	0.124324i
$977$	−24.4587			−0.782504			−0.391252	−	0.920283i	$-0.627958\pi$
$977$	−24.4587			−0.782504			−0.391252	+	0.920283i	$0.627958\pi$
$978$	−4.55608	−	4.55608i	−0.145687	−	0.145687i
$979$	26.9026			0.859812
$980$	−13.6248	+	23.4987i	−0.435229	+	0.750637i
$981$	−14.2977			−0.456489
$982$	7.07989			0.225928
$983$	−30.1694	+	30.1694i	−0.962253	+	0.962253i	−0.999313	−	0.0370597i	$-0.988201\pi$
$983$	−30.1694	+	30.1694i	−0.962253	+	0.962253i	0.0370597	+	0.999313i	$0.488201\pi$
$984$	−0.510951	−	0.510951i	−0.0162885	−	0.0162885i
$985$	−78.1120			−2.48885
$986$	−9.49177	−	13.4972i	−0.302280	−	0.429837i
$987$	1.48923	−	5.53746i	0.0474029	−	0.176259i
$988$	2.18616	−	2.18616i	0.0695511	−	0.0695511i
$989$	−7.59016	+	7.59016i	−0.241353	+	0.241353i
$990$	−13.1865			−0.419093
$991$			52.3974i			1.66446i	0.554432	+	0.832229i	$0.312936\pi$
$991$			52.3974i			1.66446i	−0.554432	+	0.832229i	$0.687064\pi$
$992$	1.11055			0.0352600
$993$		−	6.83978i		−	0.217054i
$994$	−26.6153	+	15.3336i	−0.844187	+	0.486354i
$995$		−	99.3346i		−	3.14912i
$996$	3.15107	+	3.15107i	0.0998455	+	0.0998455i
$997$	38.8636	+	38.8636i	1.23082	+	1.23082i	0.963648	+	0.267174i	$0.0860898\pi$
$997$	38.8636	+	38.8636i	1.23082	+	1.23082i	0.267174	+	0.963648i	$0.413910\pi$
$998$	16.2789	+	16.2789i	0.515300	+	0.515300i
$999$	8.78507			0.277947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.m.b.307.11	yes	40
7.6	odd	2		1218.2.m.a.307.11	✓	40
29.12	odd	4		1218.2.m.a.853.11	yes	40
203.41	even	4	inner	1218.2.m.b.853.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.m.a.307.11	✓	40	7.6	odd	2
1218.2.m.a.853.11	yes	40	29.12	odd	4
1218.2.m.b.307.11	yes	40	1.1	even	1	trivial
1218.2.m.b.853.11	yes	40	203.41	even	4	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:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +3.88041 q^{5} +1.00000 q^{6} +(-0.687128 + 2.55497i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.74387 - 2.74387i) q^{10} +(-2.40290 + 2.40290i) q^{11} +(0.707107 - 0.707107i) q^{12} +1.76810 q^{13} +(1.32076 + 2.29251i) q^{14} +(2.74387 + 2.74387i) q^{15} -1.00000 q^{16} +(-2.16662 - 2.16662i) q^{17} +(0.707107 + 0.707107i) q^{18} +(1.23644 + 1.23644i) q^{19} -3.88041i q^{20} +(-2.29251 + 1.32076i) q^{21} +3.39821i q^{22} +7.16005 q^{23} -1.00000i q^{24} +10.0576 q^{25} +(1.25024 - 1.25024i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.55497 + 0.687128i) q^{28} +(3.09777 + 4.40498i) q^{29} +3.88041 q^{30} +(-0.785278 - 0.785278i) q^{31} +(-0.707107 + 0.707107i) q^{32} -3.39821 q^{33} -3.06407 q^{34} +(-2.66634 + 9.91432i) q^{35} +1.00000 q^{36} +(-6.21199 - 6.21199i) q^{37} +1.74860 q^{38} +(1.25024 + 1.25024i) q^{39} +(-2.74387 - 2.74387i) q^{40} +(0.510951 - 0.510951i) q^{41} +(-0.687128 + 2.55497i) q^{42} +(-1.06007 + 1.06007i) q^{43} +(2.40290 + 2.40290i) q^{44} +3.88041i q^{45} +(5.06292 - 5.06292i) q^{46} +(-1.53254 + 1.53254i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.05571 - 3.51118i) q^{49} +(7.11180 - 7.11180i) q^{50} -3.06407i q^{51} -1.76810i q^{52} -4.74736 q^{53} +1.00000i q^{54} +(-9.32424 + 9.32424i) q^{55} +(2.29251 - 1.32076i) q^{56} +1.74860i q^{57} +(5.30524 + 0.924337i) q^{58} -9.85641i q^{59} +(2.74387 - 2.74387i) q^{60} +(-3.88401 - 3.88401i) q^{61} -1.11055 q^{62} +(-2.55497 - 0.687128i) q^{63} +1.00000i q^{64} +6.86097 q^{65} +(-2.40290 + 2.40290i) q^{66} +1.35982i q^{67} +(-2.16662 + 2.16662i) q^{68} +(5.06292 + 5.06292i) q^{69} +(5.12510 + 8.89587i) q^{70} +11.6097i q^{71} +(0.707107 - 0.707107i) q^{72} +(11.0505 - 11.0505i) q^{73} -8.78507 q^{74} +(7.11180 + 7.11180i) q^{75} +(1.23644 - 1.23644i) q^{76} +(-4.48823 - 7.79042i) q^{77} +1.76810 q^{78} +(7.92623 - 7.92623i) q^{79} -3.88041 q^{80} -1.00000 q^{81} -0.722594i q^{82} +4.45629i q^{83} +(1.32076 + 2.29251i) q^{84} +(-8.40739 - 8.40739i) q^{85} +1.49917i q^{86} +(-0.924337 + 5.30524i) q^{87} +3.39821 q^{88} +(-5.59795 - 5.59795i) q^{89} +(2.74387 + 2.74387i) q^{90} +(-1.21491 + 4.51745i) q^{91} -7.16005i q^{92} -1.11055i q^{93} +2.16733i q^{94} +(4.79791 + 4.79791i) q^{95} -1.00000 q^{96} +(5.97411 - 5.97411i) q^{97} +(-6.76481 + 1.79926i) q^{98} +(-2.40290 - 2.40290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{6} - 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} - 8 q^{19} + 4 q^{21} + 24 q^{25} + 12 q^{28} + 8 q^{29} + 24 q^{31} + 12 q^{35} + 40 q^{36} - 16 q^{37} + 4 q^{40} - 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 24 q^{98}+O(q^{100}) \) 40 * q + 40 * q^6 - 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 - 8 * q^19 + 4 * q^21 + 24 * q^25 + 12 * q^28 + 8 * q^29 + 24 * q^31 + 12 * q^35 + 40 * q^36 - 16 * q^37 + 4 * q^40 - 16 * q^41 - 20 * q^43 + 4 * q^46 + 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 + 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 + 44 * q^61 - 12 * q^63 + 4 * q^69 + 20 * q^70 + 52 * q^73 + 32 * q^75 - 8 * q^76 + 20 * q^77 + 4 * q^79 - 40 * q^81 + 4 * q^84 - 24 * q^85 + 12 * q^87 - 24 * q^89 - 4 * q^90 - 16 * q^95 - 40 * q^96 + 68 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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