LMFDB - Embedded newform 74.2.e.a.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(11,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("74.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	74.27
Dual form			74.2.e.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} -1.73205 q^{10} +4.73205 q^{11} +(-0.366025 + 0.633975i) q^{12} +(-5.19615 + 3.00000i) q^{13} -4.00000i q^{14} +(-1.09808 - 0.633975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(2.13397 - 1.23205i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(1.46410 - 2.53590i) q^{21} +(4.09808 + 2.36603i) q^{22} -1.26795i q^{23} +(-0.633975 + 0.366025i) q^{24} +(-1.00000 + 1.73205i) q^{25} -6.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +4.26795i q^{29} +(-0.633975 - 1.09808i) q^{30} +1.26795i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 3.00000i) q^{33} +(-0.866025 - 1.50000i) q^{34} +(6.00000 + 3.46410i) q^{35} +2.46410 q^{36} +(-0.500000 + 6.06218i) q^{37} -1.26795 q^{38} +(-3.80385 - 2.19615i) q^{39} +(-0.866025 - 1.50000i) q^{40} +(-0.232051 - 0.401924i) q^{41} +(2.53590 - 1.46410i) q^{42} -9.46410i q^{43} +(2.36603 + 4.09808i) q^{44} +4.26795i q^{45} +(0.633975 - 1.09808i) q^{46} +11.6603 q^{47} -0.732051 q^{48} +(-4.50000 + 7.79423i) q^{49} +(-1.73205 + 1.00000i) q^{50} -1.26795i q^{51} +(-5.19615 - 3.00000i) q^{52} +(1.26795 - 2.19615i) q^{53} +(3.46410 + 2.00000i) q^{54} +(-7.09808 + 4.09808i) q^{55} +(3.46410 - 2.00000i) q^{56} +(-0.803848 - 0.464102i) q^{57} +(-2.13397 + 3.69615i) q^{58} +(-2.19615 - 1.26795i) q^{59} -1.26795i q^{60} +(12.6962 - 7.33013i) q^{61} +(-0.633975 + 1.09808i) q^{62} -9.85641 q^{63} -1.00000 q^{64} +(5.19615 - 9.00000i) q^{65} +3.46410i q^{66} +(-3.09808 - 5.36603i) q^{67} -1.73205i q^{68} +(0.803848 - 0.464102i) q^{69} +(3.46410 + 6.00000i) q^{70} +(-1.26795 - 2.19615i) q^{71} +(2.13397 + 1.23205i) q^{72} -12.3923 q^{73} +(-3.46410 + 5.00000i) q^{74} -1.46410 q^{75} +(-1.09808 - 0.633975i) q^{76} +(-9.46410 - 16.3923i) q^{77} +(-2.19615 - 3.80385i) q^{78} +(-7.09808 + 4.09808i) q^{79} -1.73205i q^{80} +(-2.23205 - 3.86603i) q^{81} -0.464102i q^{82} +(-5.83013 + 10.0981i) q^{83} +2.92820 q^{84} +3.00000 q^{85} +(4.73205 - 8.19615i) q^{86} +(-2.70577 + 1.56218i) q^{87} +4.73205i q^{88} +(4.50000 + 2.59808i) q^{89} +(-2.13397 + 3.69615i) q^{90} +(20.7846 + 12.0000i) q^{91} +(1.09808 - 0.633975i) q^{92} +(-0.803848 + 0.464102i) q^{93} +(10.0981 + 5.83013i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.633975 - 0.366025i) q^{96} -5.19615i q^{97} +(-7.79423 + 4.50000i) q^{98} +(5.83013 - 10.0981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9} + 12 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{18} + 6 q^{19} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 6 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{27} + 8 q^{28} - 6 q^{30} + 24 q^{35} - 4 q^{36} - 2 q^{37} - 12 q^{38} - 36 q^{39} + 6 q^{41} + 24 q^{42} + 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} - 18 q^{49} + 12 q^{53} - 18 q^{55} - 24 q^{57} - 12 q^{58} + 12 q^{59} + 30 q^{61} - 6 q^{62} + 16 q^{63} - 4 q^{64} - 2 q^{67} + 24 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} + 8 q^{75} + 6 q^{76} - 24 q^{77} + 12 q^{78} - 18 q^{79} - 2 q^{81} - 6 q^{83} - 16 q^{84} + 12 q^{85} + 12 q^{86} - 42 q^{87} + 18 q^{89} - 12 q^{90} - 6 q^{92} - 24 q^{93} + 30 q^{94} - 6 q^{95} - 6 q^{96} + 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9 + 12 * q^11 + 2 * q^12 + 6 * q^15 - 2 * q^16 - 6 * q^17 + 12 * q^18 + 6 * q^19 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 6 * q^24 - 4 * q^25 - 24 * q^26 + 16 * q^27 + 8 * q^28 - 6 * q^30 + 24 * q^35 - 4 * q^36 - 2 * q^37 - 12 * q^38 - 36 * q^39 + 6 * q^41 + 24 * q^42 + 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 - 18 * q^49 + 12 * q^53 - 18 * q^55 - 24 * q^57 - 12 * q^58 + 12 * q^59 + 30 * q^61 - 6 * q^62 + 16 * q^63 - 4 * q^64 - 2 * q^67 + 24 * q^69 - 12 * q^71 + 12 * q^72 - 8 * q^73 + 8 * q^75 + 6 * q^76 - 24 * q^77 + 12 * q^78 - 18 * q^79 - 2 * q^81 - 6 * q^83 - 16 * q^84 + 12 * q^85 + 12 * q^86 - 42 * q^87 + 18 * q^89 - 12 * q^90 - 6 * q^92 - 24 * q^93 + 30 * q^94 - 6 * q^95 - 6 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$			0.732051i			0.298858i
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$			1.00000i			0.353553i
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	−1.73205			−0.547723
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$	−0.366025	+	0.633975i	−0.105662	+	0.183013i
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.443227	+	0.896410i	$0.646166\pi$
$14$		−	4.00000i		−	1.06904i
$15$	−1.09808	−	0.633975i	−0.283522	−	0.163692i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	0.306944	−	0.951727i	$-0.400693\pi$
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	−0.670748	+	0.741685i	$0.734027\pi$
$18$	2.13397	−	1.23205i	0.502983	−	0.290397i
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	−0.620641	−	0.784095i	$-0.713128\pi$
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	0.368725	+	0.929538i	$0.379794\pi$
$20$	−1.50000	−	0.866025i	−0.335410	−	0.193649i
$21$	1.46410	−	2.53590i	0.319493	−	0.553378i
$22$	4.09808	+	2.36603i	0.873713	+	0.504438i
$23$		−	1.26795i		−	0.264386i	−0.991224	−	0.132193i	$-0.957798\pi$
$23$		−	1.26795i		−	0.264386i	0.991224	−	0.132193i	$-0.0422018\pi$
$24$	−0.633975	+	0.366025i	−0.129410	+	0.0747146i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−6.00000			−1.17670
$27$	4.00000			0.769800
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$			4.26795i			0.792538i	0.918134	+	0.396269i	$0.129695\pi$
$29$			4.26795i			0.792538i	−0.918134	+	0.396269i	$0.870305\pi$
$30$	−0.633975	−	1.09808i	−0.115747	−	0.200480i
$31$			1.26795i			0.227730i	0.993496	+	0.113865i	$0.0363232\pi$
$31$			1.26795i			0.227730i	−0.993496	+	0.113865i	$0.963677\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.73205	+	3.00000i	0.301511	+	0.522233i
$34$	−0.866025	−	1.50000i	−0.148522	−	0.257248i
$35$	6.00000	+	3.46410i	1.01419	+	0.585540i
$36$	2.46410			0.410684
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$38$	−1.26795			−0.205689
$39$	−3.80385	−	2.19615i	−0.609103	−	0.351666i
$40$	−0.866025	−	1.50000i	−0.136931	−	0.237171i
$41$	−0.232051	−	0.401924i	−0.0362402	−	0.0627700i	0.847336	−	0.531057i	$-0.178205\pi$
$41$	−0.232051	−	0.401924i	−0.0362402	−	0.0627700i	−0.883577	+	0.468287i	$0.844871\pi$
$42$	2.53590	−	1.46410i	0.391298	−	0.225916i
$43$		−	9.46410i		−	1.44326i	−0.692278	−	0.721631i	$-0.743393\pi$
$43$		−	9.46410i		−	1.44326i	0.692278	−	0.721631i	$-0.256607\pi$
$44$	2.36603	+	4.09808i	0.356692	+	0.617808i
$45$			4.26795i			0.636228i
$46$	0.633975	−	1.09808i	0.0934745	−	0.161903i
$47$	11.6603			1.70082			0.850411	−	0.526118i	$-0.176353\pi$
$47$	11.6603			1.70082			0.850411	+	0.526118i	$0.176353\pi$
$48$	−0.732051			−0.105662
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−1.73205	+	1.00000i	−0.244949	+	0.141421i
$51$		−	1.26795i		−	0.177548i
$52$	−5.19615	−	3.00000i	−0.720577	−	0.416025i
$53$	1.26795	−	2.19615i	0.174166	−	0.301665i	−0.765706	−	0.643191i	$-0.777610\pi$
$53$	1.26795	−	2.19615i	0.174166	−	0.301665i	0.939872	+	0.341526i	$0.110944\pi$
$54$	3.46410	+	2.00000i	0.471405	+	0.272166i
$55$	−7.09808	+	4.09808i	−0.957104	+	0.552584i
$56$	3.46410	−	2.00000i	0.462910	−	0.267261i
$57$	−0.803848	−	0.464102i	−0.106472	−	0.0614718i
$58$	−2.13397	+	3.69615i	−0.280205	+	0.485329i
$59$	−2.19615	−	1.26795i	−0.285915	−	0.165073i	0.350183	−	0.936681i	$-0.386119\pi$
$59$	−2.19615	−	1.26795i	−0.285915	−	0.165073i	−0.636098	+	0.771608i	$0.719453\pi$
$60$		−	1.26795i		−	0.163692i
$61$	12.6962	−	7.33013i	1.62558	−	0.938527i	0.640184	−	0.768221i	$-0.278858\pi$
$61$	12.6962	−	7.33013i	1.62558	−	0.938527i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	−0.633975	+	1.09808i	−0.0805149	+	0.139456i
$63$	−9.85641			−1.24179
$64$	−1.00000			−0.125000
$65$	5.19615	−	9.00000i	0.644503	−	1.11631i
$66$			3.46410i			0.426401i
$67$	−3.09808	−	5.36603i	−0.378490	−	0.655564i	0.612353	−	0.790585i	$-0.290223\pi$
$67$	−3.09808	−	5.36603i	−0.378490	−	0.655564i	−0.990843	+	0.135020i	$0.956890\pi$
$68$		−	1.73205i		−	0.210042i
$69$	0.803848	−	0.464102i	0.0967719	−	0.0558713i
$70$	3.46410	+	6.00000i	0.414039	+	0.717137i
$71$	−1.26795	−	2.19615i	−0.150478	−	0.260635i	0.780925	−	0.624624i	$-0.214748\pi$
$71$	−1.26795	−	2.19615i	−0.150478	−	0.260635i	−0.931403	+	0.363989i	$0.881415\pi$
$72$	2.13397	+	1.23205i	0.251491	+	0.145199i
$73$	−12.3923			−1.45041			−0.725205	−	0.688533i	$-0.758255\pi$
$73$	−12.3923			−1.45041			−0.725205	+	0.688533i	$0.758255\pi$
$74$	−3.46410	+	5.00000i	−0.402694	+	0.581238i
$75$	−1.46410			−0.169060
$76$	−1.09808	−	0.633975i	−0.125958	−	0.0727219i
$77$	−9.46410	−	16.3923i	−1.07853	−	1.86808i
$78$	−2.19615	−	3.80385i	−0.248665	−	0.430701i
$79$	−7.09808	+	4.09808i	−0.798596	+	0.461070i	−0.842980	−	0.537945i	$-0.819201\pi$
$79$	−7.09808	+	4.09808i	−0.798596	+	0.461070i	0.0443840	+	0.999015i	$0.485867\pi$
$80$		−	1.73205i		−	0.193649i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$		−	0.464102i		−	0.0512514i
$83$	−5.83013	+	10.0981i	−0.639940	+	1.10841i	0.345506	+	0.938417i	$0.387707\pi$
$83$	−5.83013	+	10.0981i	−0.639940	+	1.10841i	−0.985446	+	0.169991i	$0.945626\pi$
$84$	2.92820			0.319493
$85$	3.00000			0.325396
$86$	4.73205	−	8.19615i	0.510270	−	0.883814i
$87$	−2.70577	+	1.56218i	−0.290089	+	0.167483i
$88$			4.73205i			0.504438i
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	0.719165	−	0.694839i	$-0.244525\pi$
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	−0.242166	+	0.970235i	$0.577858\pi$
$90$	−2.13397	+	3.69615i	−0.224941	+	0.389609i
$91$	20.7846	+	12.0000i	2.17882	+	1.25794i
$92$	1.09808	−	0.633975i	0.114482	−	0.0660964i
$93$	−0.803848	+	0.464102i	−0.0833551	+	0.0481251i
$94$	10.0981	+	5.83013i	1.04154	+	0.601332i
$95$	1.09808	−	1.90192i	0.112660	−	0.195133i
$96$	−0.633975	−	0.366025i	−0.0647048	−	0.0373573i
$97$		−	5.19615i		−	0.527589i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$		−	5.19615i		−	0.527589i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$	−7.79423	+	4.50000i	−0.787336	+	0.454569i
$99$	5.83013	−	10.0981i	0.585950	−	1.01489i
$100$	−2.00000			−0.200000
$101$	−0.464102			−0.0461798			−0.0230899	−	0.999733i	$-0.507350\pi$
$101$	−0.464102			−0.0461798			−0.0230899	+	0.999733i	$0.507350\pi$
$102$	0.633975	−	1.09808i	0.0627728	−	0.108726i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$			5.07180i			0.494957i
$106$	2.19615	−	1.26795i	0.213309	−	0.123154i
$107$	8.19615	+	14.1962i	0.792352	+	1.37239i	0.924507	+	0.381165i	$0.124477\pi$
$107$	8.19615	+	14.1962i	0.792352	+	1.37239i	−0.132155	+	0.991229i	$0.542190\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	−6.69615	−	3.86603i	−0.641375	−	0.370298i	0.143769	−	0.989611i	$-0.454078\pi$
$109$	−6.69615	−	3.86603i	−0.641375	−	0.370298i	−0.785144	+	0.619313i	$0.787411\pi$
$110$	−8.19615			−0.781472
$111$	−4.02628	+	1.90192i	−0.382158	+	0.180523i
$112$	4.00000			0.377964
$113$	17.1962	+	9.92820i	1.61768	+	0.933967i	0.987519	+	0.157501i	$0.0503437\pi$
$113$	17.1962	+	9.92820i	1.61768	+	0.933967i	0.630159	+	0.776466i	$0.282990\pi$
$114$	−0.464102	−	0.803848i	−0.0434671	−	0.0752872i
$115$	1.09808	+	1.90192i	0.102396	+	0.177355i
$116$	−3.69615	+	2.13397i	−0.343179	+	0.198135i
$117$			14.7846i			1.36684i
$118$	−1.26795	−	2.19615i	−0.116724	−	0.202172i
$119$			6.92820i			0.635107i
$120$	0.633975	−	1.09808i	0.0578737	−	0.100240i
$121$	11.3923			1.03566
$122$	14.6603			1.32728
$123$	0.169873	−	0.294229i	0.0153169	−	0.0265297i
$124$	−1.09808	+	0.633975i	−0.0986102	+	0.0569326i
$125$		−	12.1244i		−	1.08444i
$126$	−8.53590	−	4.92820i	−0.760438	−	0.439039i
$127$	5.29423	−	9.16987i	0.469787	−	0.813695i	−0.529616	−	0.848237i	$-0.677664\pi$
$127$	5.29423	−	9.16987i	0.469787	−	0.813695i	0.999403	+	0.0345426i	$0.0109974\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	6.00000	−	3.46410i	0.528271	−	0.304997i
$130$	9.00000	−	5.19615i	0.789352	−	0.455733i
$131$	−7.09808	−	4.09808i	−0.620162	−	0.358051i	0.156770	−	0.987635i	$-0.449892\pi$
$131$	−7.09808	−	4.09808i	−0.620162	−	0.358051i	−0.776932	+	0.629585i	$0.783225\pi$
$132$	−1.73205	+	3.00000i	−0.150756	+	0.261116i
$133$	4.39230	+	2.53590i	0.380861	+	0.219890i
$134$		−	6.19615i		−	0.535266i
$135$	−6.00000	+	3.46410i	−0.516398	+	0.298142i
$136$	0.866025	−	1.50000i	0.0742611	−	0.128624i
$137$	−13.3923			−1.14418			−0.572091	−	0.820190i	$-0.693868\pi$
$137$	−13.3923			−1.14418			−0.572091	+	0.820190i	$0.693868\pi$
$138$	0.928203			0.0790139
$139$	−0.901924	+	1.56218i	−0.0765002	+	0.132502i	−0.901738	−	0.432284i	$-0.857708\pi$
$139$	−0.901924	+	1.56218i	−0.0765002	+	0.132502i	0.825237	+	0.564786i	$0.191041\pi$
$140$			6.92820i			0.585540i
$141$	4.26795	+	7.39230i	0.359426	+	0.622544i
$142$		−	2.53590i		−	0.212808i
$143$	−24.5885	+	14.1962i	−2.05619	+	1.18714i
$144$	1.23205	+	2.13397i	0.102671	+	0.177831i
$145$	−3.69615	−	6.40192i	−0.306949	−	0.531651i
$146$	−10.7321	−	6.19615i	−0.888191	−	0.512797i
$147$	−6.58846			−0.543407
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	3.92820			0.321811			0.160905	−	0.986970i	$-0.448559\pi$
$149$	3.92820			0.321811			0.160905	+	0.986970i	$0.448559\pi$
$150$	−1.26795	−	0.732051i	−0.103528	−	0.0597717i
$151$	0.901924	+	1.56218i	0.0733975	+	0.127128i	0.900388	−	0.435087i	$-0.143282\pi$
$151$	0.901924	+	1.56218i	0.0733975	+	0.127128i	−0.826991	+	0.562215i	$0.809949\pi$
$152$	−0.633975	−	1.09808i	−0.0514221	−	0.0890657i
$153$	−3.69615	+	2.13397i	−0.298816	+	0.172522i
$154$		−	18.9282i		−	1.52528i
$155$	−1.09808	−	1.90192i	−0.0881996	−	0.152766i
$156$		−	4.39230i		−	0.351666i
$157$	4.69615	−	8.13397i	0.374794	−	0.649162i	−0.615502	−	0.788135i	$-0.711047\pi$
$157$	4.69615	−	8.13397i	0.374794	−	0.649162i	0.990296	+	0.138973i	$0.0443802\pi$
$158$	−8.19615			−0.652051
$159$	1.85641			0.147223
$160$	0.866025	−	1.50000i	0.0684653	−	0.118585i
$161$	−4.39230	+	2.53590i	−0.346162	+	0.199857i
$162$		−	4.46410i		−	0.350733i
$163$	−2.19615	−	1.26795i	−0.172016	−	0.0993134i	0.411520	−	0.911401i	$-0.364998\pi$
$163$	−2.19615	−	1.26795i	−0.172016	−	0.0993134i	−0.583536	+	0.812087i	$0.698331\pi$
$164$	0.232051	−	0.401924i	0.0181201	−	0.0313850i
$165$	−5.19615	−	3.00000i	−0.404520	−	0.233550i
$166$	−10.0981	+	5.83013i	−0.783763	+	0.452506i
$167$	−6.00000	+	3.46410i	−0.464294	+	0.268060i	−0.713848	−	0.700301i	$-0.753049\pi$
$167$	−6.00000	+	3.46410i	−0.464294	+	0.268060i	0.249554	+	0.968361i	$0.419716\pi$
$168$	2.53590	+	1.46410i	0.195649	+	0.112958i
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$	2.59808	+	1.50000i	0.199263	+	0.115045i
$171$			3.12436i			0.238925i
$172$	8.19615	−	4.73205i	0.624951	−	0.360815i
$173$	4.96410	−	8.59808i	0.377414	−	0.653700i	−0.613271	−	0.789872i	$-0.710147\pi$
$173$	4.96410	−	8.59808i	0.377414	−	0.653700i	0.990685	+	0.136173i	$0.0434802\pi$
$174$	−3.12436			−0.236857
$175$	8.00000			0.604743
$176$	−2.36603	+	4.09808i	−0.178346	+	0.308904i
$177$		−	1.85641i		−	0.139536i
$178$	2.59808	+	4.50000i	0.194734	+	0.337289i
$179$			11.3205i			0.846135i	0.906098	+	0.423067i	$0.139047\pi$
$179$			11.3205i			0.846135i	−0.906098	+	0.423067i	$0.860953\pi$
$180$	−3.69615	+	2.13397i	−0.275495	+	0.159057i
$181$	7.69615	+	13.3301i	0.572051	+	0.990821i	0.996355	+	0.0853011i	$0.0271852\pi$
$181$	7.69615	+	13.3301i	0.572051	+	0.990821i	−0.424305	+	0.905519i	$0.639481\pi$
$182$	12.0000	+	20.7846i	0.889499	+	1.54066i
$183$	9.29423	+	5.36603i	0.687049	+	0.396668i
$184$	1.26795			0.0934745
$185$	−4.50000	−	9.52628i	−0.330847	−	0.700386i
$186$	−0.928203			−0.0680592
$187$	−7.09808	−	4.09808i	−0.519063	−	0.299681i
$188$	5.83013	+	10.0981i	0.425206	+	0.736478i
$189$	−8.00000	−	13.8564i	−0.581914	−	1.00791i
$190$	1.90192	−	1.09808i	0.137980	−	0.0796628i
$191$		−	24.5885i		−	1.77916i	−0.456781	−	0.889579i	$-0.650998\pi$
$191$		−	24.5885i		−	1.77916i	0.456781	−	0.889579i	$-0.349002\pi$
$192$	−0.366025	−	0.633975i	−0.0264156	−	0.0457532i
$193$			12.1244i			0.872730i	0.899770	+	0.436365i	$0.143734\pi$
$193$			12.1244i			0.872730i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	2.59808	−	4.50000i	0.186531	−	0.323081i
$195$	7.60770			0.544798
$196$	−9.00000			−0.642857
$197$	−13.1603	+	22.7942i	−0.937629	+	1.62402i	−0.167752	+	0.985829i	$0.553651\pi$
$197$	−13.1603	+	22.7942i	−0.937629	+	1.62402i	−0.769877	+	0.638192i	$0.779682\pi$
$198$	10.0981	−	5.83013i	0.717639	−	0.414329i
$199$			5.07180i			0.359530i	0.983710	+	0.179765i	$0.0575338\pi$
$199$			5.07180i			0.359530i	−0.983710	+	0.179765i	$0.942466\pi$
$200$	−1.73205	−	1.00000i	−0.122474	−	0.0707107i
$201$	2.26795	−	3.92820i	0.159969	−	0.277074i
$202$	−0.401924	−	0.232051i	−0.0282793	−	0.0163270i
$203$	14.7846	−	8.53590i	1.03768	−	0.599103i
$204$	1.09808	−	0.633975i	0.0768807	−	0.0443871i
$205$	0.696152	+	0.401924i	0.0486214	+	0.0280716i
$206$	3.46410	−	6.00000i	0.241355	−	0.418040i
$207$	−2.70577	−	1.56218i	−0.188064	−	0.108579i
$208$		−	6.00000i		−	0.416025i
$209$	−5.19615	+	3.00000i	−0.359425	+	0.207514i
$210$	−2.53590	+	4.39230i	−0.174994	+	0.303098i
$211$	12.3923			0.853121			0.426561	−	0.904459i	$-0.359725\pi$
$211$	12.3923			0.853121			0.426561	+	0.904459i	$0.359725\pi$
$212$	2.53590			0.174166
$213$	0.928203	−	1.60770i	0.0635994	−	0.110157i
$214$			16.3923i			1.12055i
$215$	8.19615	+	14.1962i	0.558973	+	0.968170i
$216$			4.00000i			0.272166i
$217$	4.39230	−	2.53590i	0.298169	−	0.172148i
$218$	−3.86603	−	6.69615i	−0.261840	−	0.453521i
$219$	−4.53590	−	7.85641i	−0.306508	−	0.530887i
$220$	−7.09808	−	4.09808i	−0.478552	−	0.276292i
$221$	10.3923			0.699062
$222$	−4.43782	−	0.366025i	−0.297847	−	0.0245660i
$223$	−22.5885			−1.51263			−0.756317	−	0.654205i	$-0.773003\pi$
$223$	−22.5885			−1.51263			−0.756317	+	0.654205i	$0.773003\pi$
$224$	3.46410	+	2.00000i	0.231455	+	0.133631i
$225$	2.46410	+	4.26795i	0.164273	+	0.284530i
$226$	9.92820	+	17.1962i	0.660414	+	1.14387i
$227$	−1.09808	+	0.633975i	−0.0728819	+	0.0420784i	−0.535998	−	0.844219i	$-0.680065\pi$
$227$	−1.09808	+	0.633975i	−0.0728819	+	0.0420784i	0.463116	+	0.886298i	$0.346731\pi$
$228$		−	0.928203i		−	0.0614718i
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$			2.19615i			0.144810i
$231$	6.92820	−	12.0000i	0.455842	−	0.789542i
$232$	−4.26795			−0.280205
$233$	−4.60770			−0.301860			−0.150930	−	0.988544i	$-0.548227\pi$
$233$	−4.60770			−0.301860			−0.150930	+	0.988544i	$0.548227\pi$
$234$	−7.39230	+	12.8038i	−0.483250	+	0.837014i
$235$	−17.4904	+	10.0981i	−1.14095	+	0.658726i
$236$		−	2.53590i		−	0.165073i
$237$	−5.19615	−	3.00000i	−0.337526	−	0.194871i
$238$	−3.46410	+	6.00000i	−0.224544	+	0.388922i
$239$	−4.39230	−	2.53590i	−0.284115	−	0.164034i	0.351170	−	0.936312i	$-0.385784\pi$
$239$	−4.39230	−	2.53590i	−0.284115	−	0.164034i	−0.635285	+	0.772278i	$0.719117\pi$
$240$	1.09808	−	0.633975i	0.0708805	−	0.0409229i
$241$	−15.5885	+	9.00000i	−1.00414	+	0.579741i	−0.909471	−	0.415768i	$-0.863513\pi$
$241$	−15.5885	+	9.00000i	−1.00414	+	0.579741i	−0.0946700	+	0.995509i	$0.530180\pi$
$242$	9.86603	+	5.69615i	0.634212	+	0.366163i
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$	12.6962	+	7.33013i	0.812788	+	0.469263i
$245$		−	15.5885i		−	0.995910i
$246$	0.294229	−	0.169873i	0.0187593	−	0.0108307i
$247$	3.80385	−	6.58846i	0.242033	−	0.419213i
$248$	−1.26795			−0.0805149
$249$	−8.53590			−0.540941
$250$	6.06218	−	10.5000i	0.383406	−	0.664078i
$251$			5.07180i			0.320129i	0.987107	+	0.160064i	$0.0511702\pi$
$251$			5.07180i			0.320129i	−0.987107	+	0.160064i	$0.948830\pi$
$252$	−4.92820	−	8.53590i	−0.310448	−	0.537711i
$253$		−	6.00000i		−	0.377217i
$254$	9.16987	−	5.29423i	0.575369	−	0.332189i
$255$	1.09808	+	1.90192i	0.0687642	+	0.119103i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.69615	+	5.59808i	0.604829	+	0.349198i	0.770939	−	0.636909i	$-0.219787\pi$
$257$	9.69615	+	5.59808i	0.604829	+	0.349198i	−0.166110	+	0.986107i	$0.553121\pi$
$258$	6.92820			0.431331
$259$	22.0000	−	10.3923i	1.36701	−	0.645746i
$260$	10.3923			0.644503
$261$	9.10770	+	5.25833i	0.563752	+	0.325482i
$262$	−4.09808	−	7.09808i	−0.253180	−	0.438521i
$263$	−11.6603	−	20.1962i	−0.719002	−	1.24535i	−0.961396	−	0.275170i	$-0.911266\pi$
$263$	−11.6603	−	20.1962i	−0.719002	−	1.24535i	0.242393	−	0.970178i	$-0.422068\pi$
$264$	−3.00000	+	1.73205i	−0.184637	+	0.106600i
$265$			4.39230i			0.269817i
$266$	2.53590	+	4.39230i	0.155486	+	0.269309i
$267$			3.80385i			0.232792i
$268$	3.09808	−	5.36603i	0.189245	−	0.327782i
$269$	−7.60770			−0.463849			−0.231925	−	0.972734i	$-0.574502\pi$
$269$	−7.60770			−0.463849			−0.231925	+	0.972734i	$0.574502\pi$
$270$	−6.92820			−0.421637
$271$	7.29423	−	12.6340i	0.443093	−	0.767459i	−0.554824	−	0.831968i	$-0.687215\pi$
$271$	7.29423	−	12.6340i	0.443093	−	0.767459i	0.997917	+	0.0645082i	$0.0205479\pi$
$272$	1.50000	−	0.866025i	0.0909509	−	0.0525105i
$273$			17.5692i			1.06334i
$274$	−11.5981	−	6.69615i	−0.700665	−	0.404529i
$275$	−4.73205	+	8.19615i	−0.285353	+	0.494247i
$276$	0.803848	+	0.464102i	0.0483859	+	0.0279356i
$277$	−5.89230	+	3.40192i	−0.354034	+	0.204402i	−0.666461	−	0.745540i	$-0.732192\pi$
$277$	−5.89230	+	3.40192i	−0.354034	+	0.204402i	0.312426	+	0.949942i	$0.398858\pi$
$278$	−1.56218	+	0.901924i	−0.0936932	+	0.0540938i
$279$	2.70577	+	1.56218i	0.161990	+	0.0935251i
$280$	−3.46410	+	6.00000i	−0.207020	+	0.358569i
$281$	−9.69615	−	5.59808i	−0.578424	−	0.333953i	0.182083	−	0.983283i	$-0.441716\pi$
$281$	−9.69615	−	5.59808i	−0.578424	−	0.333953i	−0.760507	+	0.649330i	$0.775049\pi$
$282$			8.53590i			0.508305i
$283$	2.19615	−	1.26795i	0.130548	−	0.0753718i	−0.433304	−	0.901248i	$-0.642652\pi$
$283$	2.19615	−	1.26795i	0.130548	−	0.0753718i	0.563852	+	0.825876i	$0.309319\pi$
$284$	1.26795	−	2.19615i	0.0752389	−	0.130318i
$285$	1.60770			0.0952316
$286$	−28.3923			−1.67887
$287$	−0.928203	+	1.60770i	−0.0547901	+	0.0948992i
$288$			2.46410i			0.145199i
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$		−	7.39230i		−	0.434091i
$291$	3.29423	−	1.90192i	0.193111	−	0.111493i
$292$	−6.19615	−	10.7321i	−0.362602	−	0.628046i
$293$	−12.6962	−	21.9904i	−0.741717	−	1.28469i	−0.951713	−	0.306989i	$-0.900678\pi$
$293$	−12.6962	−	21.9904i	−0.741717	−	1.28469i	0.209996	−	0.977702i	$-0.432655\pi$
$294$	−5.70577	−	3.29423i	−0.332767	−	0.192123i
$295$	4.39230			0.255730
$296$	−6.06218	−	0.500000i	−0.352357	−	0.0290619i
$297$	18.9282			1.09833
$298$	3.40192	+	1.96410i	0.197068	+	0.113777i
$299$	3.80385	+	6.58846i	0.219982	+	0.381020i
$300$	−0.732051	−	1.26795i	−0.0422650	−	0.0732051i
$301$	−32.7846	+	18.9282i	−1.88967	+	1.09100i
$302$			1.80385i			0.103800i
$303$	−0.169873	−	0.294229i	−0.00975895	−	0.0169030i
$304$		−	1.26795i		−	0.0727219i
$305$	−12.6962	+	21.9904i	−0.726980	+	1.25917i
$306$	−4.26795			−0.243982
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	9.46410	−	16.3923i	0.539267	−	0.934038i
$309$	4.39230	−	2.53590i	0.249869	−	0.144262i
$310$		−	2.19615i		−	0.124733i
$311$	14.1962	+	8.19615i	0.804990	+	0.464761i	0.845213	−	0.534430i	$-0.179474\pi$
$311$	14.1962	+	8.19615i	0.804990	+	0.464761i	−0.0402231	+	0.999191i	$0.512807\pi$
$312$	2.19615	−	3.80385i	0.124333	−	0.215350i
$313$	18.6962	+	10.7942i	1.05677	+	0.610126i	0.924537	−	0.381093i	$-0.124452\pi$
$313$	18.6962	+	10.7942i	1.05677	+	0.610126i	0.132232	+	0.991219i	$0.457786\pi$
$314$	8.13397	−	4.69615i	0.459027	−	0.265019i
$315$	14.7846	−	8.53590i	0.833018	−	0.480943i
$316$	−7.09808	−	4.09808i	−0.399298	−	0.230535i
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	−0.964281	−	0.264883i	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$	1.60770	+	0.928203i	0.0901551	+	0.0520511i
$319$			20.1962i			1.13077i
$320$	1.50000	−	0.866025i	0.0838525	−	0.0484123i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	−5.07180			−0.282640
$323$	2.19615			0.122197
$324$	2.23205	−	3.86603i	0.124003	−	0.214779i
$325$		−	12.0000i		−	0.665640i
$326$	−1.26795	−	2.19615i	−0.0702252	−	0.121634i
$327$		−	5.66025i		−	0.313013i
$328$	0.401924	−	0.232051i	0.0221925	−	0.0128129i
$329$	−23.3205	−	40.3923i	−1.28570	−	2.22690i
$330$	−3.00000	−	5.19615i	−0.165145	−	0.286039i
$331$	−26.7846	−	15.4641i	−1.47222	−	0.849984i	−0.472703	−	0.881222i	$-0.656722\pi$
$331$	−26.7846	−	15.4641i	−1.47222	−	0.849984i	−0.999512	+	0.0312377i	$0.990055\pi$
$332$	−11.6603			−0.639940
$333$	12.3205	+	8.53590i	0.675160	+	0.467764i
$334$	−6.92820			−0.379094
$335$	9.29423	+	5.36603i	0.507798	+	0.293177i
$336$	1.46410	+	2.53590i	0.0798733	+	0.138345i
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	19.9186	−	11.5000i	1.08343	−	0.625518i
$339$			14.5359i			0.789482i
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$			6.00000i			0.324918i
$342$	−1.56218	+	2.70577i	−0.0844729	+	0.146311i
$343$	8.00000			0.431959
$344$	9.46410			0.510270
$345$	−0.803848	+	1.39230i	−0.0432777	+	0.0749592i
$346$	8.59808	−	4.96410i	0.462235	−	0.266872i
$347$		−	10.0526i		−	0.539650i	−0.962909	−	0.269825i	$-0.913034\pi$
$347$		−	10.0526i		−	0.539650i	0.962909	−	0.269825i	$-0.0869658\pi$
$348$	−2.70577	−	1.56218i	−0.145045	−	0.0837415i
$349$	3.30385	−	5.72243i	0.176851	−	0.306315i	−0.763949	−	0.645276i	$-0.776742\pi$
$349$	3.30385	−	5.72243i	0.176851	−	0.306315i	0.940800	+	0.338961i	$0.110076\pi$
$350$	6.92820	+	4.00000i	0.370328	+	0.213809i
$351$	−20.7846	+	12.0000i	−1.10940	+	0.640513i
$352$	−4.09808	+	2.36603i	−0.218428	+	0.126110i
$353$	26.0885	+	15.0622i	1.38855	+	0.801679i	0.993152	−	0.116832i	$-0.0372738\pi$
$353$	26.0885	+	15.0622i	1.38855	+	0.801679i	0.395397	+	0.918510i	$0.370607\pi$
$354$	0.928203	−	1.60770i	0.0493334	−	0.0854480i
$355$	3.80385	+	2.19615i	0.201887	+	0.116560i
$356$			5.19615i			0.275396i
$357$	−4.39230	+	2.53590i	−0.232465	+	0.134214i
$358$	−5.66025	+	9.80385i	−0.299154	+	0.518149i
$359$	33.4641			1.76617			0.883084	−	0.469215i	$-0.155463\pi$
$359$	33.4641			1.76617			0.883084	+	0.469215i	$0.155463\pi$
$360$	−4.26795			−0.224941
$361$	−8.69615	+	15.0622i	−0.457692	+	0.792746i
$362$			15.3923i			0.809002i
$363$	4.16987	+	7.22243i	0.218862	+	0.379079i
$364$			24.0000i			1.25794i
$365$	18.5885	−	10.7321i	0.972964	−	0.561741i
$366$	5.36603	+	9.29423i	0.280487	+	0.485817i
$367$	−0.196152	−	0.339746i	−0.0102391	−	0.0177346i	0.860860	−	0.508841i	$-0.169926\pi$
$367$	−0.196152	−	0.339746i	−0.0102391	−	0.0177346i	−0.871100	+	0.491106i	$0.836593\pi$
$368$	1.09808	+	0.633975i	0.0572412	+	0.0330482i
$369$	−1.14359			−0.0595331
$370$	0.866025	−	10.5000i	0.0450225	−	0.545869i
$371$	−10.1436			−0.526629
$372$	−0.803848	−	0.464102i	−0.0416776	−	0.0240625i
$373$	9.89230	+	17.1340i	0.512204	+	0.887164i	0.999900	+	0.0141499i	$0.00450421\pi$
$373$	9.89230	+	17.1340i	0.512204	+	0.887164i	−0.487696	+	0.873014i	$0.662162\pi$
$374$	−4.09808	−	7.09808i	−0.211906	−	0.367033i
$375$	7.68653	−	4.43782i	0.396931	−	0.229168i
$376$			11.6603i			0.601332i
$377$	−12.8038	−	22.1769i	−0.659432	−	1.14217i
$378$		−	16.0000i		−	0.822951i
$379$	−12.3923	+	21.4641i	−0.636550	+	1.10254i	0.349635	+	0.936886i	$0.386306\pi$
$379$	−12.3923	+	21.4641i	−0.636550	+	1.10254i	−0.986184	+	0.165651i	$0.947028\pi$
$380$	2.19615			0.112660
$381$	7.75129			0.397111
$382$	12.2942	−	21.2942i	0.629027	−	1.08951i
$383$	22.3923	−	12.9282i	1.14419	−	0.660600i	0.196728	−	0.980458i	$-0.436968\pi$
$383$	22.3923	−	12.9282i	1.14419	−	0.660600i	0.947466	+	0.319858i	$0.103635\pi$
$384$		−	0.732051i		−	0.0373573i
$385$	28.3923	+	16.3923i	1.44701	+	0.835429i
$386$	−6.06218	+	10.5000i	−0.308557	+	0.534436i
$387$	−20.1962	−	11.6603i	−1.02663	−	0.592724i
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$	0.696152	−	0.401924i	0.0352963	−	0.0203783i	−0.482248	−	0.876035i	$-0.660180\pi$
$389$	0.696152	−	0.401924i	0.0352963	−	0.0203783i	0.517544	+	0.855656i	$0.326846\pi$
$390$	6.58846	+	3.80385i	0.333620	+	0.192615i
$391$	−1.09808	+	1.90192i	−0.0555321	+	0.0961844i
$392$	−7.79423	−	4.50000i	−0.393668	−	0.227284i
$393$		−	6.00000i		−	0.302660i
$394$	−22.7942	+	13.1603i	−1.14836	+	0.663004i
$395$	7.09808	−	12.2942i	0.357143	−	0.618590i
$396$	11.6603			0.585950
$397$	−5.00000			−0.250943			−0.125471	−	0.992097i	$-0.540044\pi$
$397$	−5.00000			−0.250943			−0.125471	+	0.992097i	$0.540044\pi$
$398$	−2.53590	+	4.39230i	−0.127113	+	0.220166i
$399$			3.71281i			0.185873i
$400$	−1.00000	−	1.73205i	−0.0500000	−	0.0866025i
$401$			14.7846i			0.738308i	0.929368	+	0.369154i	$0.120353\pi$
$401$			14.7846i			0.738308i	−0.929368	+	0.369154i	$0.879647\pi$
$402$	3.92820	−	2.26795i	0.195921	−	0.113115i
$403$	−3.80385	−	6.58846i	−0.189483	−	0.328194i
$404$	−0.232051	−	0.401924i	−0.0115450	−	0.0199965i
$405$	6.69615	+	3.86603i	0.332734	+	0.192104i
$406$	17.0718			0.847259
$407$	−2.36603	+	28.6865i	−0.117280	+	1.42194i
$408$	1.26795			0.0627728
$409$	−29.0885	−	16.7942i	−1.43833	−	0.830421i	−0.440598	−	0.897705i	$-0.645233\pi$
$409$	−29.0885	−	16.7942i	−1.43833	−	0.830421i	−0.997734	+	0.0672835i	$0.978567\pi$
$410$	0.401924	+	0.696152i	0.0198496	+	0.0343805i
$411$	−4.90192	−	8.49038i	−0.241794	−	0.418800i
$412$	6.00000	−	3.46410i	0.295599	−	0.170664i
$413$			10.1436i			0.499134i
$414$	−1.56218	−	2.70577i	−0.0767769	−	0.132981i
$415$		−	20.1962i		−	0.991390i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	−1.32051			−0.0646656
$418$	−6.00000			−0.293470
$419$	−5.07180	+	8.78461i	−0.247773	+	0.429156i	−0.962908	−	0.269831i	$-0.913032\pi$
$419$	−5.07180	+	8.78461i	−0.247773	+	0.429156i	0.715134	+	0.698987i	$0.246366\pi$
$420$	−4.39230	+	2.53590i	−0.214323	+	0.123739i
$421$		−	3.33975i		−	0.162769i	−0.996683	−	0.0813846i	$-0.974066\pi$
$421$		−	3.33975i		−	0.162769i	0.996683	−	0.0813846i	$-0.0259342\pi$
$422$	10.7321	+	6.19615i	0.522428	+	0.301624i
$423$	14.3660	−	24.8827i	0.698500	−	1.20984i
$424$	2.19615	+	1.26795i	0.106655	+	0.0615771i
$425$	3.00000	−	1.73205i	0.145521	−	0.0840168i
$426$	1.60770	−	0.928203i	0.0778931	−	0.0449716i
$427$	−50.7846	−	29.3205i	−2.45764	−	1.41892i
$428$	−8.19615	+	14.1962i	−0.396176	+	0.686197i
$429$	−18.0000	−	10.3923i	−0.869048	−	0.501745i
$430$			16.3923i			0.790507i
$431$	19.0981	−	11.0263i	0.919922	−	0.531117i	0.0363118	−	0.999341i	$-0.488439\pi$
$431$	19.0981	−	11.0263i	0.919922	−	0.531117i	0.883610	+	0.468223i	$0.155106\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	−12.6077			−0.605887			−0.302944	−	0.953008i	$-0.597969\pi$
$433$	−12.6077			−0.605887			−0.302944	+	0.953008i	$0.597969\pi$
$434$	5.07180			0.243454
$435$	2.70577	−	4.68653i	0.129732	−	0.224702i
$436$		−	7.73205i		−	0.370298i
$437$	0.803848	+	1.39230i	0.0384532	+	0.0666030i
$438$		−	9.07180i		−	0.433467i
$439$	2.19615	−	1.26795i	0.104817	−	0.0605159i	−0.446675	−	0.894696i	$-0.647392\pi$
$439$	2.19615	−	1.26795i	0.104817	−	0.0605159i	0.551492	+	0.834180i	$0.314059\pi$
$440$	−4.09808	−	7.09808i	−0.195368	−	0.338388i
$441$	11.0885	+	19.2058i	0.528022	+	0.914561i
$442$	9.00000	+	5.19615i	0.428086	+	0.247156i
$443$	−9.46410			−0.449653			−0.224827	−	0.974399i	$-0.572182\pi$
$443$	−9.46410			−0.449653			−0.224827	+	0.974399i	$0.572182\pi$
$444$	−3.66025	−	2.53590i	−0.173708	−	0.120348i
$445$	−9.00000			−0.426641
$446$	−19.5622	−	11.2942i	−0.926296	−	0.534797i
$447$	1.43782	+	2.49038i	0.0680067	+	0.117791i
$448$	2.00000	+	3.46410i	0.0944911	+	0.163663i
$449$	9.58846	−	5.53590i	0.452507	−	0.261255i	−0.256381	−	0.966576i	$-0.582530\pi$
$449$	9.58846	−	5.53590i	0.452507	−	0.261255i	0.708889	+	0.705321i	$0.249197\pi$
$450$			4.92820i			0.232318i
$451$	−1.09808	−	1.90192i	−0.0517064	−	0.0895581i
$452$			19.8564i			0.933967i
$453$	−0.660254	+	1.14359i	−0.0310214	+	0.0537307i
$454$	−1.26795			−0.0595078
$455$	−41.5692			−1.94880
$456$	0.464102	−	0.803848i	0.0217335	−	0.0376436i
$457$	27.6962	−	15.9904i	1.29557	−	0.747998i	0.315935	−	0.948781i	$-0.397682\pi$
$457$	27.6962	−	15.9904i	1.29557	−	0.747998i	0.979636	+	0.200782i	$0.0643484\pi$
$458$			19.0000i			0.887812i
$459$	−6.00000	−	3.46410i	−0.280056	−	0.161690i
$460$	−1.09808	+	1.90192i	−0.0511981	+	0.0886777i
$461$	−18.8038	−	10.8564i	−0.875782	−	0.505633i	−0.00651699	−	0.999979i	$-0.502074\pi$
$461$	−18.8038	−	10.8564i	−0.875782	−	0.505633i	−0.869266	+	0.494346i	$0.835408\pi$
$462$	12.0000	−	6.92820i	0.558291	−	0.322329i
$463$	18.5885	−	10.7321i	0.863879	−	0.498761i	−0.00143043	−	0.999999i	$-0.500455\pi$
$463$	18.5885	−	10.7321i	0.863879	−	0.498761i	0.865309	+	0.501238i	$0.167122\pi$
$464$	−3.69615	−	2.13397i	−0.171590	−	0.0990673i
$465$	0.803848	−	1.39230i	0.0372775	−	0.0645666i
$466$	−3.99038	−	2.30385i	−0.184851	−	0.106724i
$467$			18.2487i			0.844450i	0.906491	+	0.422225i	$0.138751\pi$
$467$			18.2487i			0.844450i	−0.906491	+	0.422225i	$0.861249\pi$
$468$	−12.8038	+	7.39230i	−0.591858	+	0.341709i
$469$	−12.3923	+	21.4641i	−0.572223	+	0.991120i
$470$	−20.1962			−0.931579
$471$	6.87564			0.316813
$472$	1.26795	−	2.19615i	0.0583621	−	0.101086i
$473$		−	44.7846i		−	2.05920i
$474$	−3.00000	−	5.19615i	−0.137795	−	0.238667i
$475$		−	2.53590i		−	0.116355i
$476$	−6.00000	+	3.46410i	−0.275010	+	0.158777i
$477$	−3.12436	−	5.41154i	−0.143054	−	0.247778i
$478$	−2.53590	−	4.39230i	−0.115989	−	0.200899i
$479$	2.19615	+	1.26795i	0.100345	+	0.0579341i	0.549333	−	0.835604i	$-0.314882\pi$
$479$	2.19615	+	1.26795i	0.100345	+	0.0579341i	−0.448988	+	0.893538i	$0.648215\pi$
$480$	1.26795			0.0578737
$481$	−15.5885	−	33.0000i	−0.710772	−	1.50467i
$482$	−18.0000			−0.819878
$483$	−3.21539	−	1.85641i	−0.146305	−	0.0844694i
$484$	5.69615	+	9.86603i	0.258916	+	0.448456i
$485$	4.50000	+	7.79423i	0.204334	+	0.353918i
$486$	13.2224	−	7.63397i	0.599782	−	0.346284i
$487$			10.0526i			0.455525i	0.973717	+	0.227762i	$0.0731410\pi$
$487$			10.0526i			0.455525i	−0.973717	+	0.227762i	$0.926859\pi$
$488$	7.33013	+	12.6962i	0.331819	+	0.574728i
$489$		−	1.85641i		−	0.0839496i
$490$	7.79423	−	13.5000i	0.352107	−	0.609868i
$491$	−22.9808			−1.03711			−0.518554	−	0.855045i	$-0.673529\pi$
$491$	−22.9808			−1.03711			−0.518554	+	0.855045i	$0.673529\pi$
$492$	0.339746			0.0153169
$493$	3.69615	−	6.40192i	0.166466	−	0.288328i
$494$	6.58846	−	3.80385i	0.296429	−	0.171143i
$495$			20.1962i			0.907750i
$496$	−1.09808	−	0.633975i	−0.0493051	−	0.0284663i
$497$	−5.07180	+	8.78461i	−0.227501	+	0.394044i
$498$	−7.39230	−	4.26795i	−0.331257	−	0.191251i
$499$	7.09808	−	4.09808i	0.317754	−	0.183455i	−0.332637	−	0.943055i	$-0.607938\pi$
$499$	7.09808	−	4.09808i	0.317754	−	0.183455i	0.650391	+	0.759600i	$0.274605\pi$
$500$	10.5000	−	6.06218i	0.469574	−	0.271109i
$501$	−4.39230	−	2.53590i	−0.196234	−	0.113296i
$502$	−2.53590	+	4.39230i	−0.113183	+	0.196038i
$503$	10.9019	+	6.29423i	0.486093	+	0.280646i	0.722952	−	0.690898i	$-0.242785\pi$
$503$	10.9019	+	6.29423i	0.486093	+	0.280646i	−0.236859	+	0.971544i	$0.576118\pi$
$504$		−	9.85641i		−	0.439039i
$505$	0.696152	−	0.401924i	0.0309784	−	0.0178854i
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	16.8372			0.747765
$508$	10.5885			0.469787
$509$	−15.8205	+	27.4019i	−0.701232	+	1.21457i	0.266803	+	0.963751i	$0.414033\pi$
$509$	−15.8205	+	27.4019i	−0.701232	+	1.21457i	−0.968034	+	0.250818i	$0.919301\pi$
$510$			2.19615i			0.0972473i
$511$	24.7846	+	42.9282i	1.09641	+	1.89903i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.39230	+	2.53590i	−0.193925	+	0.111963i
$514$	5.59808	+	9.69615i	0.246921	+	0.427679i
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$	6.00000	+	3.46410i	0.264135	+	0.152499i
$517$	55.1769			2.42668
$518$	24.2487	+	2.00000i	1.06543	+	0.0878750i
$519$	7.26795			0.319028
$520$	9.00000	+	5.19615i	0.394676	+	0.227866i
$521$	−13.2679	−	22.9808i	−0.581279	−	1.00681i	−0.995328	−	0.0965507i	$-0.969219\pi$
$521$	−13.2679	−	22.9808i	−0.581279	−	1.00681i	0.414049	−	0.910255i	$-0.364114\pi$
$522$	5.25833	+	9.10770i	0.230151	+	0.398633i
$523$	10.9019	−	6.29423i	0.476708	−	0.275227i	−0.242336	−	0.970192i	$-0.577914\pi$
$523$	10.9019	−	6.29423i	0.476708	−	0.275227i	0.719043	+	0.694965i	$0.244580\pi$
$524$		−	8.19615i		−	0.358051i
$525$	2.92820	+	5.07180i	0.127797	+	0.221351i
$526$		−	23.3205i		−	1.01682i
$527$	1.09808	−	1.90192i	0.0478330	−	0.0828491i
$528$	−3.46410			−0.150756
$529$	21.3923			0.930100
$530$	−2.19615	+	3.80385i	−0.0953948	+	0.165229i
$531$	−5.41154	+	3.12436i	−0.234841	+	0.135585i
$532$			5.07180i			0.219890i
$533$	2.41154	+	1.39230i	0.104456	+	0.0603074i
$534$	−1.90192	+	3.29423i	−0.0823043	+	0.142555i
$535$	−24.5885	−	14.1962i	−1.06305	−	0.613753i
$536$	5.36603	−	3.09808i	0.231777	−	0.133817i
$537$	−7.17691	+	4.14359i	−0.309707	+	0.178809i
$538$	−6.58846	−	3.80385i	−0.284049	−	0.163996i
$539$	−21.2942	+	36.8827i	−0.917207	+	1.58865i
$540$	−6.00000	−	3.46410i	−0.258199	−	0.149071i
$541$		−	3.58846i		−	0.154280i	−0.997020	−	0.0771399i	$-0.975421\pi$
$541$		−	3.58846i		−	0.154280i	0.997020	−	0.0771399i	$-0.0245788\pi$
$542$	12.6340	−	7.29423i	0.542676	−	0.313314i
$543$	−5.63397	+	9.75833i	−0.241777	+	0.418770i
$544$	1.73205			0.0742611
$545$	13.3923			0.573663
$546$	−8.78461	+	15.2154i	−0.375947	+	0.651159i
$547$			12.5885i			0.538244i	0.963106	+	0.269122i	$0.0867334\pi$
$547$			12.5885i			0.538244i	−0.963106	+	0.269122i	$0.913267\pi$
$548$	−6.69615	−	11.5981i	−0.286045	−	0.495445i
$549$		−	36.1244i		−	1.54175i
$550$	−8.19615	+	4.73205i	−0.349485	+	0.201775i
$551$	−2.70577	−	4.68653i	−0.115270	−	0.199653i
$552$	0.464102	+	0.803848i	0.0197535	+	0.0342140i
$553$	28.3923	+	16.3923i	1.20736	+	0.697072i
$554$	−6.80385			−0.289068
$555$	4.39230	−	6.33975i	0.186443	−	0.269107i
$556$	−1.80385			−0.0765002
$557$	9.10770	+	5.25833i	0.385905	+	0.222803i	0.680385	−	0.732855i	$-0.261813\pi$
$557$	9.10770	+	5.25833i	0.385905	+	0.222803i	−0.294479	+	0.955658i	$0.595146\pi$
$558$	1.56218	+	2.70577i	0.0661323	+	0.114544i
$559$	28.3923	+	49.1769i	1.20087	+	2.07996i
$560$	−6.00000	+	3.46410i	−0.253546	+	0.146385i
$561$		−	6.00000i		−	0.253320i
$562$	−5.59808	−	9.69615i	−0.236141	−	0.409008i
$563$		−	11.4115i		−	0.480939i	−0.970657	−	0.240470i	$-0.922699\pi$
$563$		−	11.4115i		−	0.480939i	0.970657	−	0.240470i	$-0.0773014\pi$
$564$	−4.26795	+	7.39230i	−0.179713	+	0.311272i
$565$	−34.3923			−1.44690
$566$	2.53590			0.106592
$567$	−8.92820	+	15.4641i	−0.374949	+	0.649431i
$568$	2.19615	−	1.26795i	0.0921485	−	0.0532020i
$569$			28.5167i			1.19548i	0.801690	+	0.597740i	$0.203935\pi$
$569$			28.5167i			1.19548i	−0.801690	+	0.597740i	$0.796065\pi$
$570$	1.39230	+	0.803848i	0.0583172	+	0.0336695i
$571$	−7.49038	+	12.9737i	−0.313463	+	0.542933i	−0.979110	−	0.203334i	$-0.934822\pi$
$571$	−7.49038	+	12.9737i	−0.313463	+	0.542933i	0.665647	+	0.746267i	$0.268156\pi$
$572$	−24.5885	−	14.1962i	−1.02810	−	0.593571i
$573$	15.5885	−	9.00000i	0.651217	−	0.375980i
$574$	−1.60770	+	0.928203i	−0.0671039	+	0.0387425i
$575$	2.19615	+	1.26795i	0.0915859	+	0.0528771i
$576$	−1.23205	+	2.13397i	−0.0513355	+	0.0889156i
$577$	3.58846	+	2.07180i	0.149389	+	0.0862500i	0.572831	−	0.819673i	$-0.305845\pi$
$577$	3.58846	+	2.07180i	0.149389	+	0.0862500i	−0.423442	+	0.905923i	$0.639178\pi$
$578$		−	14.0000i		−	0.582323i
$579$	−7.68653	+	4.43782i	−0.319441	+	0.184430i
$580$	3.69615	−	6.40192i	0.153474	−	0.265825i
$581$	46.6410			1.93500
$582$	3.80385			0.157675
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$		−	12.3923i		−	0.512797i
$585$	−12.8038	−	22.1769i	−0.529374	−	0.916903i
$586$		−	25.3923i		−	1.04895i
$587$	19.0981	−	11.0263i	0.788262	−	0.455103i	−0.0510884	−	0.998694i	$-0.516269\pi$
$587$	19.0981	−	11.0263i	0.788262	−	0.455103i	0.839350	+	0.543591i	$0.182936\pi$
$588$	−3.29423	−	5.70577i	−0.135852	−	0.235302i
$589$	−0.803848	−	1.39230i	−0.0331220	−	0.0573689i
$590$	3.80385	+	2.19615i	0.156602	+	0.0904142i
$591$	−19.2679			−0.792578
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	23.5359			0.966504			0.483252	−	0.875481i	$-0.339456\pi$
$593$	23.5359			0.966504			0.483252	+	0.875481i	$0.339456\pi$
$594$	16.3923	+	9.46410i	0.672584	+	0.388317i
$595$	−6.00000	−	10.3923i	−0.245976	−	0.426043i
$596$	1.96410	+	3.40192i	0.0804527	+	0.139348i
$597$	−3.21539	+	1.85641i	−0.131597	+	0.0759777i
$598$			7.60770i			0.311102i
$599$	−2.36603	−	4.09808i	−0.0966732	−	0.167443i	0.813633	−	0.581380i	$-0.197487\pi$
$599$	−2.36603	−	4.09808i	−0.0966732	−	0.167443i	−0.910306	+	0.413937i	$0.864153\pi$
$600$		−	1.46410i		−	0.0597717i
$601$	12.8923	−	22.3301i	0.525888	−	0.910865i	−0.473657	−	0.880709i	$-0.657066\pi$
$601$	12.8923	−	22.3301i	0.525888	−	0.910865i	0.999545	−	0.0301556i	$-0.00960027\pi$
$602$	−37.8564			−1.54291
$603$	−15.2679			−0.621759
$604$	−0.901924	+	1.56218i	−0.0366988	+	0.0635641i
$605$	−17.0885	+	9.86603i	−0.694745	+	0.401111i
$606$		−	0.339746i		−	0.0138012i
$607$	1.68653	+	0.973721i	0.0684543	+	0.0395221i	0.533836	−	0.845588i	$-0.320750\pi$
$607$	1.68653	+	0.973721i	0.0684543	+	0.0395221i	−0.465382	+	0.885110i	$0.654083\pi$
$608$	0.633975	−	1.09808i	0.0257111	−	0.0445329i
$609$	10.8231	+	6.24871i	0.438574	+	0.253211i
$610$	−21.9904	+	12.6962i	−0.890365	+	0.514052i
$611$	−60.5885	+	34.9808i	−2.45115	+	1.41517i
$612$	−3.69615	−	2.13397i	−0.149408	−	0.0862608i
$613$	−6.30385	+	10.9186i	−0.254610	+	0.440997i	−0.964790	−	0.263023i	$-0.915280\pi$
$613$	−6.30385	+	10.9186i	−0.254610	+	0.440997i	0.710180	+	0.704021i	$0.248614\pi$
$614$	−3.46410	−	2.00000i	−0.139800	−	0.0807134i
$615$			0.588457i			0.0237289i
$616$	16.3923	−	9.46410i	0.660465	−	0.381320i
$617$	−11.6603	+	20.1962i	−0.469424	+	0.813066i	−0.999389	−	0.0349532i	$-0.988872\pi$
$617$	−11.6603	+	20.1962i	−0.469424	+	0.813066i	0.529965	+	0.848020i	$0.322205\pi$
$618$	5.07180			0.204018
$619$	21.1769			0.851172			0.425586	−	0.904918i	$-0.360068\pi$
$619$	21.1769			0.851172			0.425586	+	0.904918i	$0.360068\pi$
$620$	1.09808	−	1.90192i	0.0440998	−	0.0763831i
$621$		−	5.07180i		−	0.203524i
$622$	8.19615	+	14.1962i	0.328636	+	0.569214i
$623$		−	20.7846i		−	0.832718i
$624$	3.80385	−	2.19615i	0.152276	−	0.0879165i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	10.7942	+	18.6962i	0.431424	+	0.747249i
$627$	−3.80385	−	2.19615i	−0.151911	−	0.0877059i
$628$	9.39230			0.374794
$629$	6.00000	−	8.66025i	0.239236	−	0.345307i
$630$	17.0718			0.680157
$631$	−25.6865	−	14.8301i	−1.02256	−	0.590378i	−0.107719	−	0.994181i	$-0.534355\pi$
$631$	−25.6865	−	14.8301i	−1.02256	−	0.590378i	−0.914846	+	0.403803i	$0.867688\pi$
$632$	−4.09808	−	7.09808i	−0.163013	−	0.282346i
$633$	4.53590	+	7.85641i	0.180286	+	0.312264i
$634$	−7.79423	+	4.50000i	−0.309548	+	0.178718i
$635$			18.3397i			0.727791i
$636$	0.928203	+	1.60770i	0.0368057	+	0.0637493i
$637$		−	54.0000i		−	2.13956i
$638$	−10.0981	+	17.4904i	−0.399787	+	0.692451i
$639$	−6.24871			−0.247195
$640$	1.73205			0.0684653
$641$	9.57180	−	16.5788i	0.378063	−	0.654825i	−0.612717	−	0.790302i	$-0.709924\pi$
$641$	9.57180	−	16.5788i	0.378063	−	0.654825i	0.990780	+	0.135478i	$0.0432569\pi$
$642$	−10.3923	+	6.00000i	−0.410152	+	0.236801i
$643$		−	15.1244i		−	0.596446i	−0.954496	−	0.298223i	$-0.903606\pi$
$643$		−	15.1244i		−	0.596446i	0.954496	−	0.298223i	$-0.0963940\pi$
$644$	−4.39230	−	2.53590i	−0.173081	−	0.0999284i
$645$	−6.00000	+	10.3923i	−0.236250	+	0.409197i
$646$	1.90192	+	1.09808i	0.0748302	+	0.0432032i
$647$	2.19615	−	1.26795i	0.0863397	−	0.0498482i	−0.456209	−	0.889873i	$-0.650793\pi$
$647$	2.19615	−	1.26795i	0.0863397	−	0.0498482i	0.542548	+	0.840025i	$0.317460\pi$
$648$	3.86603	−	2.23205i	0.151872	−	0.0876832i
$649$	−10.3923	−	6.00000i	−0.407934	−	0.235521i
$650$	6.00000	−	10.3923i	0.235339	−	0.407620i
$651$	3.21539	+	1.85641i	0.126021	+	0.0727583i
$652$		−	2.53590i		−	0.0993134i
$653$	−14.8923	+	8.59808i	−0.582781	+	0.336469i	−0.762238	−	0.647297i	$-0.775899\pi$
$653$	−14.8923	+	8.59808i	−0.582781	+	0.336469i	0.179457	+	0.983766i	$0.442566\pi$
$654$	2.83013	−	4.90192i	0.110667	−	0.191680i
$655$	14.1962			0.554690
$656$	0.464102			0.0181201
$657$	−15.2679	+	26.4449i	−0.595659	+	1.03171i
$658$		−	46.6410i		−	1.81826i
$659$	−10.7321	−	18.5885i	−0.418061	−	0.724103i	0.577683	−	0.816261i	$-0.303957\pi$
$659$	−10.7321	−	18.5885i	−0.418061	−	0.724103i	−0.995744	+	0.0921577i	$0.970624\pi$
$660$		−	6.00000i		−	0.233550i
$661$	−16.2846	+	9.40192i	−0.633398	+	0.365692i	−0.782067	−	0.623195i	$-0.785834\pi$
$661$	−16.2846	+	9.40192i	−0.633398	+	0.365692i	0.148669	+	0.988887i	$0.452501\pi$
$662$	−15.4641	−	26.7846i	−0.601029	−	1.04101i
$663$	3.80385	+	6.58846i	0.147729	+	0.255874i
$664$	−10.0981	−	5.83013i	−0.391881	−	0.226253i
$665$	−8.78461			−0.340653
$666$	6.40192	+	13.5526i	0.248070	+	0.525151i
$667$	5.41154			0.209536
$668$	−6.00000	−	3.46410i	−0.232147	−	0.134030i
$669$	−8.26795	−	14.3205i	−0.319657	−	0.553663i
$670$	5.36603	+	9.29423i	0.207308	+	0.359067i
$671$	60.0788	−	34.6865i	2.31932	−	1.33906i
$672$			2.92820i			0.112958i
$673$	−4.19615	−	7.26795i	−0.161750	−	0.280159i	0.773747	−	0.633495i	$-0.218380\pi$
$673$	−4.19615	−	7.26795i	−0.161750	−	0.280159i	−0.935496	+	0.353336i	$0.885047\pi$
$674$			7.00000i			0.269630i
$675$	−4.00000	+	6.92820i	−0.153960	+	0.266667i
$676$	23.0000			0.884615
$677$	34.8564			1.33964			0.669820	−	0.742523i	$-0.266371\pi$
$677$	34.8564			1.33964			0.669820	+	0.742523i	$0.266371\pi$
$678$	−7.26795	+	12.5885i	−0.279124	+	0.483457i
$679$	−18.0000	+	10.3923i	−0.690777	+	0.398820i
$680$			3.00000i			0.115045i
$681$	−0.803848	−	0.464102i	−0.0308035	−	0.0177844i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	−14.7846	−	8.53590i	−0.565717	−	0.326617i	0.189720	−	0.981838i	$-0.439242\pi$
$683$	−14.7846	−	8.53590i	−0.565717	−	0.326617i	−0.755437	+	0.655221i	$0.772575\pi$
$684$	−2.70577	+	1.56218i	−0.103458	+	0.0597314i
$685$	20.0885	−	11.5981i	0.767540	−	0.443140i
$686$	6.92820	+	4.00000i	0.264520	+	0.152721i
$687$	−6.95448	+	12.0455i	−0.265330	+	0.459565i
$688$	8.19615	+	4.73205i	0.312475	+	0.180408i
$689$			15.2154i			0.579660i
$690$	−1.39230	+	0.803848i	−0.0530041	+	0.0306020i
$691$	11.0981	−	19.2224i	0.422191	−	0.731256i	−0.573963	−	0.818881i	$-0.694595\pi$
$691$	11.0981	−	19.2224i	0.422191	−	0.731256i	0.996153	+	0.0876256i	$0.0279279\pi$
$692$	9.92820			0.377414
$693$	−46.6410			−1.77175
$694$	5.02628	−	8.70577i	0.190795	−	0.330467i
$695$		−	3.12436i		−	0.118514i
$696$	−1.56218	−	2.70577i	−0.0592142	−	0.102562i
$697$			0.803848i			0.0304479i
$698$	5.72243	−	3.30385i	0.216597	−	0.125052i
$699$	−1.68653	−	2.92116i	−0.0637906	−	0.110488i
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	1.60770	+	0.928203i	0.0607218	+	0.0350578i	0.530054	−	0.847964i	$-0.322172\pi$
$701$	1.60770	+	0.928203i	0.0607218	+	0.0350578i	−0.469332	+	0.883022i	$0.655505\pi$
$702$	−24.0000			−0.905822
$703$	−3.29423	−	6.97372i	−0.124244	−	0.263019i
$704$	−4.73205			−0.178346
$705$	−12.8038	−	7.39230i	−0.482221	−	0.278410i
$706$	15.0622	+	26.0885i	0.566873	+	0.981852i
$707$	0.928203	+	1.60770i	0.0349087	+	0.0604636i
$708$	1.60770	−	0.928203i	0.0604209	−	0.0348840i
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$	2.19615	+	3.80385i	0.0824201	+	0.142756i
$711$			20.1962i			0.757415i
$712$	−2.59808	+	4.50000i	−0.0973670	+	0.168645i
$713$	1.60770			0.0602087
$714$	−5.07180			−0.189807
$715$	24.5885	−	42.5885i	0.919556	−	1.59272i
$716$	−9.80385	+	5.66025i	−0.366387	+	0.211534i
$717$		−	3.71281i		−	0.138658i
$718$	28.9808	+	16.7321i	1.08155	+	0.624435i
$719$	16.2224	−	28.0981i	0.604995	−	1.04788i	−0.387058	−	0.922055i	$-0.626509\pi$
$719$	16.2224	−	28.0981i	0.604995	−	1.04788i	0.992052	−	0.125826i	$-0.0401581\pi$
$720$	−3.69615	−	2.13397i	−0.137747	−	0.0795285i
$721$	−24.0000	+	13.8564i	−0.893807	+	0.516040i
$722$	−15.0622	+	8.69615i	−0.560556	+	0.323637i
$723$	−11.4115	−	6.58846i	−0.424400	−	0.245027i
$724$	−7.69615	+	13.3301i	−0.286025	+	0.495410i
$725$	−7.39230	−	4.26795i	−0.274543	−	0.158508i
$726$			8.33975i			0.309517i
$727$	−1.60770	+	0.928203i	−0.0596261	+	0.0344252i	−0.529517	−	0.848300i	$-0.677627\pi$
$727$	−1.60770	+	0.928203i	−0.0596261	+	0.0344252i	0.469891	+	0.882725i	$0.344293\pi$
$728$	−12.0000	+	20.7846i	−0.444750	+	0.770329i
$729$	−2.21539			−0.0820515
$730$	21.4641			0.794422
$731$	−8.19615	+	14.1962i	−0.303146	+	0.525064i
$732$			10.7321i			0.396668i
$733$	−7.80385	−	13.5167i	−0.288242	−	0.499249i	0.685148	−	0.728403i	$-0.259737\pi$
$733$	−7.80385	−	13.5167i	−0.288242	−	0.499249i	−0.973390	+	0.229154i	$0.926404\pi$
$734$		−	0.392305i		−	0.0144802i
$735$	9.88269	−	5.70577i	0.364528	−	0.210461i
$736$	0.633975	+	1.09808i	0.0233686	+	0.0404756i
$737$	−14.6603	−	25.3923i	−0.540017	−	0.935338i
$738$	−0.990381	−	0.571797i	−0.0364564	−	0.0210481i
$739$	6.98076			0.256791			0.128396	−	0.991723i	$-0.459017\pi$
$739$	6.98076			0.256791			0.128396	+	0.991723i	$0.459017\pi$
$740$	6.00000	−	8.66025i	0.220564	−	0.318357i
$741$	5.56922			0.204590
$742$	−8.78461	−	5.07180i	−0.322493	−	0.186192i
$743$	20.9545	+	36.2942i	0.768745	+	1.33151i	0.938244	+	0.345976i	$0.112452\pi$
$743$	20.9545	+	36.2942i	0.768745	+	1.33151i	−0.169498	+	0.985531i	$0.554215\pi$
$744$	−0.464102	−	0.803848i	−0.0170148	−	0.0294705i
$745$	−5.89230	+	3.40192i	−0.215877	+	0.124637i
$746$			19.7846i			0.724366i
$747$	14.3660	+	24.8827i	0.525625	+	0.910410i
$748$		−	8.19615i		−	0.299681i
$749$	32.7846	−	56.7846i	1.19792	−	2.07486i
$750$	8.87564			0.324093
$751$	−36.3923			−1.32797			−0.663987	−	0.747744i	$-0.731137\pi$
$751$	−36.3923			−1.32797			−0.663987	+	0.747744i	$0.731137\pi$
$752$	−5.83013	+	10.0981i	−0.212603	+	0.368239i
$753$	−3.21539	+	1.85641i	−0.117175	+	0.0676512i
$754$		−	25.6077i		−	0.932577i
$755$	−2.70577	−	1.56218i	−0.0984731	−	0.0568535i
$756$	8.00000	−	13.8564i	0.290957	−	0.503953i
$757$	3.69615	+	2.13397i	0.134339	+	0.0775606i	0.565663	−	0.824636i	$-0.308620\pi$
$757$	3.69615	+	2.13397i	0.134339	+	0.0775606i	−0.431324	+	0.902197i	$0.641954\pi$
$758$	−21.4641	+	12.3923i	−0.779611	+	0.450109i
$759$	3.80385	−	2.19615i	0.138071	−	0.0797153i
$760$	1.90192	+	1.09808i	0.0689900	+	0.0398314i
$761$	−16.1603	+	27.9904i	−0.585809	+	1.01465i	0.408965	+	0.912550i	$0.365890\pi$
$761$	−16.1603	+	27.9904i	−0.585809	+	1.01465i	−0.994774	+	0.102101i	$0.967444\pi$
$762$	6.71281	+	3.87564i	0.243180	+	0.140400i
$763$			30.9282i			1.11968i
$764$	21.2942	−	12.2942i	0.770398	−	0.444790i
$765$	3.69615	−	6.40192i	0.133635	−	0.231462i
$766$	25.8564			0.934230
$767$	15.2154			0.549396
$768$	0.366025	−	0.633975i	0.0132078	−	0.0228766i
$769$		−	21.7128i		−	0.782984i	−0.920181	−	0.391492i	$-0.871959\pi$
$769$		−	21.7128i		−	0.782984i	0.920181	−	0.391492i	$-0.128041\pi$
$770$	16.3923	+	28.3923i	0.590738	+	1.02319i
$771$			8.19615i			0.295177i
$772$	−10.5000	+	6.06218i	−0.377903	+	0.218183i
$773$	10.9641	+	18.9904i	0.394351	+	0.683037i	0.993018	−	0.117962i	$-0.0376360\pi$
$773$	10.9641	+	18.9904i	0.394351	+	0.683037i	−0.598667	+	0.800998i	$0.704303\pi$
$774$	−11.6603	−	20.1962i	−0.419119	−	0.725936i
$775$	−2.19615	−	1.26795i	−0.0788881	−	0.0455461i
$776$	5.19615			0.186531
$777$	14.6410	+	10.1436i	0.525244	+	0.363899i
$778$	0.803848			0.0288193
$779$	0.509619	+	0.294229i	0.0182590	+	0.0105418i
$780$	3.80385	+	6.58846i	0.136200	+	0.235905i
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	−1.90192	+	1.09808i	−0.0680127	+	0.0392671i
$783$			17.0718i			0.610096i
$784$	−4.50000	−	7.79423i	−0.160714	−	0.278365i
$785$			16.2679i			0.580628i
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$	33.1769			1.18263			0.591315	−	0.806441i	$-0.298609\pi$
$787$	33.1769			1.18263			0.591315	+	0.806441i	$0.298609\pi$
$788$	−26.3205			−0.937629
$789$	8.53590	−	14.7846i	0.303886	−	0.526346i
$790$	12.2942	−	7.09808i	0.437409	−	0.252538i
$791$		−	79.4256i		−	2.82405i
$792$	10.0981	+	5.83013i	0.358820	+	0.207165i
$793$	−43.9808	+	76.1769i	−1.56180	+	2.70512i
$794$	−4.33013	−	2.50000i	−0.153670	−	0.0887217i
$795$	−2.78461	+	1.60770i	−0.0987599	+	0.0570191i
$796$	−4.39230	+	2.53590i	−0.155681	+	0.0898825i
$797$	18.0000	+	10.3923i	0.637593	+	0.368114i	0.783687	−	0.621156i	$-0.213337\pi$
$797$	18.0000	+	10.3923i	0.637593	+	0.368114i	−0.146094	+	0.989271i	$0.546670\pi$
$798$	−1.85641	+	3.21539i	−0.0657161	+	0.113824i
$799$	−17.4904	−	10.0981i	−0.618765	−	0.357244i
$800$		−	2.00000i		−	0.0707107i
$801$	11.0885	−	6.40192i	0.391791	−	0.226201i
$802$	−7.39230	+	12.8038i	−0.261031	+	0.452120i
$803$	−58.6410			−2.06940
$804$	4.53590			0.159969
$805$	4.39230	−	7.60770i	0.154808	−	0.268136i
$806$		−	7.60770i		−	0.267970i
$807$	−2.78461	−	4.82309i	−0.0980229	−	0.169781i
$808$		−	0.464102i		−	0.0163270i
$809$	25.1769	−	14.5359i	0.885173	−	0.511055i	0.0128126	−	0.999918i	$-0.495922\pi$
$809$	25.1769	−	14.5359i	0.885173	−	0.511055i	0.872361	+	0.488863i	$0.162588\pi$
$810$	3.86603	+	6.69615i	0.135838	+	0.235279i
$811$	18.1962	+	31.5167i	0.638953	+	1.10670i	0.985663	+	0.168727i	$0.0539656\pi$
$811$	18.1962	+	31.5167i	0.638953	+	1.10670i	−0.346709	+	0.937973i	$0.612701\pi$
$812$	14.7846	+	8.53590i	0.518838	+	0.299551i
$813$	10.6795			0.374546
$814$	−16.3923	+	23.6603i	−0.574550	+	0.829291i
$815$	4.39230			0.153856
$816$	1.09808	+	0.633975i	0.0384404	+	0.0221936i
$817$	6.00000	+	10.3923i	0.209913	+	0.363581i
$818$	−16.7942	−	29.0885i	−0.587196	−	1.01705i
$819$	51.2154	−	29.5692i	1.78961	−	1.03323i
$820$			0.803848i			0.0280716i
$821$	19.2679	+	33.3731i	0.672456	+	1.16473i	0.977206	+	0.212296i	$0.0680939\pi$
$821$	19.2679	+	33.3731i	0.672456	+	1.16473i	−0.304749	+	0.952433i	$0.598573\pi$
$822$		−	9.80385i		−	0.341948i
$823$	−19.2942	+	33.4186i	−0.672555	+	1.16490i	0.304623	+	0.952473i	$0.401470\pi$
$823$	−19.2942	+	33.4186i	−0.672555	+	1.16490i	−0.977177	+	0.212426i	$0.931864\pi$
$824$	6.92820			0.241355
$825$	−6.92820			−0.241209
$826$	−5.07180	+	8.78461i	−0.176470	+	0.305656i
$827$	40.3923	−	23.3205i	1.40458	−	0.810934i	0.409720	−	0.912211i	$-0.365626\pi$
$827$	40.3923	−	23.3205i	1.40458	−	0.810934i	0.994858	+	0.101278i	$0.0322931\pi$
$828$		−	3.12436i		−	0.108579i
$829$	19.9808	+	11.5359i	0.693961	+	0.400658i	0.805094	−	0.593147i	$-0.202115\pi$
$829$	19.9808	+	11.5359i	0.693961	+	0.400658i	−0.111133	+	0.993805i	$0.535448\pi$
$830$	10.0981	−	17.4904i	0.350509	−	0.607100i
$831$	−4.31347	−	2.49038i	−0.149632	−	0.0863904i
$832$	5.19615	−	3.00000i	0.180144	−	0.104006i
$833$	13.5000	−	7.79423i	0.467747	−	0.270054i
$834$	−1.14359	−	0.660254i	−0.0395994	−	0.0228627i
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$	−5.19615	−	3.00000i	−0.179713	−	0.103757i
$837$			5.07180i			0.175307i
$838$	−8.78461	+	5.07180i	−0.303459	+	0.175202i
$839$	−4.90192	+	8.49038i	−0.169233	+	0.293121i	−0.938150	−	0.346228i	$-0.887462\pi$
$839$	−4.90192	+	8.49038i	−0.169233	+	0.293121i	0.768917	+	0.639348i	$0.220796\pi$
$840$	−5.07180			−0.174994
$841$	10.7846			0.371883
$842$	1.66987	−	2.89230i	0.0575476	−	0.0996754i
$843$		−	8.19615i		−	0.282290i
$844$	6.19615	+	10.7321i	0.213280	+	0.369412i
$845$			39.8372i			1.37044i
$846$	24.8827	−	14.3660i	0.855484	−	0.493914i
$847$	−22.7846	−	39.4641i	−0.782888	−	1.35600i
$848$	1.26795	+	2.19615i	0.0435416	+	0.0754162i
$849$	1.60770	+	0.928203i	0.0551760	+	0.0318559i
$850$	3.46410			0.118818
$851$	7.68653	+	0.633975i	0.263491	+	0.0217324i
$852$	1.85641			0.0635994
$853$	−22.2846	−	12.8660i	−0.763011	−	0.440524i	0.0673651	−	0.997728i	$-0.478541\pi$
$853$	−22.2846	−	12.8660i	−0.763011	−	0.440524i	−0.830376	+	0.557204i	$0.811874\pi$
$854$	−29.3205	−	50.7846i	−1.00333	−	1.73781i
$855$	−2.70577	−	4.68653i	−0.0925354	−	0.160276i
$856$	−14.1962	+	8.19615i	−0.485215	+	0.280139i
$857$			1.05256i			0.0359547i	0.999838	+	0.0179774i	$0.00572268\pi$
$857$			1.05256i			0.0359547i	−0.999838	+	0.0179774i	$0.994277\pi$
$858$	−10.3923	−	18.0000i	−0.354787	−	0.614510i
$859$		−	14.5359i		−	0.495958i	−0.968765	−	0.247979i	$-0.920234\pi$
$859$		−	14.5359i		−	0.495958i	0.968765	−	0.247979i	$-0.0797665\pi$
$860$	−8.19615	+	14.1962i	−0.279486	+	0.484085i
$861$	−1.35898			−0.0463140
$862$	22.0526			0.751113
$863$	−2.19615	+	3.80385i	−0.0747579	+	0.129484i	−0.900981	−	0.433859i	$-0.857152\pi$
$863$	−2.19615	+	3.80385i	−0.0747579	+	0.129484i	0.826223	+	0.563343i	$0.190485\pi$
$864$	−3.46410	+	2.00000i	−0.117851	+	0.0680414i
$865$			17.1962i			0.584687i
$866$	−10.9186	−	6.30385i	−0.371029	−	0.214213i
$867$	5.12436	−	8.87564i	0.174032	−	0.301433i
$868$	4.39230	+	2.53590i	0.149085	+	0.0860740i
$869$	−33.5885	+	19.3923i	−1.13941	+	0.657839i
$870$	4.68653	−	2.70577i	0.158888	−	0.0917342i
$871$	32.1962	+	18.5885i	1.09093	+	0.629846i
$872$	3.86603	−	6.69615i	0.130920	−	0.226760i
$873$	−11.0885	−	6.40192i	−0.375287	−	0.216672i
$874$			1.60770i			0.0543811i
$875$	−42.0000	+	24.2487i	−1.41986	+	0.819756i
$876$	4.53590	−	7.85641i	0.153254	−	0.265443i
$877$	−18.1769			−0.613791			−0.306895	−	0.951743i	$-0.599290\pi$
$877$	−18.1769			−0.613791			−0.306895	+	0.951743i	$0.599290\pi$
$878$	2.53590			0.0855824
$879$	9.29423	−	16.0981i	0.313487	−	0.542975i
$880$		−	8.19615i		−	0.276292i
$881$	−27.4808	−	47.5981i	−0.925850	−	1.60362i	−0.790188	−	0.612865i	$-0.790017\pi$
$881$	−27.4808	−	47.5981i	−0.925850	−	1.60362i	−0.135663	−	0.990755i	$-0.543316\pi$
$882$			22.1769i			0.746736i
$883$	−15.8827	+	9.16987i	−0.534495	+	0.308591i	−0.742845	−	0.669464i	$-0.766524\pi$
$883$	−15.8827	+	9.16987i	−0.534495	+	0.308591i	0.208350	+	0.978054i	$0.433191\pi$
$884$	5.19615	+	9.00000i	0.174766	+	0.302703i
$885$	1.60770	+	2.78461i	0.0540421	+	0.0936036i
$886$	−8.19615	−	4.73205i	−0.275355	−	0.158976i
$887$	2.87564			0.0965547			0.0482773	−	0.998834i	$-0.484627\pi$
$887$	2.87564			0.0965547			0.0482773	+	0.998834i	$0.484627\pi$
$888$	−1.90192	−	4.02628i	−0.0638244	−	0.135113i
$889$	−42.3538			−1.42050
$890$	−7.79423	−	4.50000i	−0.261263	−	0.150840i
$891$	−10.5622	−	18.2942i	−0.353846	−	0.612880i
$892$	−11.2942	−	19.5622i	−0.378159	−	0.654990i
$893$	−12.8038	+	7.39230i	−0.428464	+	0.247374i
$894$			2.87564i			0.0961759i
$895$	−9.80385	−	16.9808i	−0.327706	−	0.567604i
$896$			4.00000i			0.133631i
$897$	−2.78461	+	4.82309i	−0.0929754	+	0.161038i
$898$	11.0718			0.369471
$899$	−5.41154			−0.180485
$900$	−2.46410	+	4.26795i	−0.0821367	+	0.142265i
$901$	−3.80385	+	2.19615i	−0.126725	+	0.0731644i
$902$		−	2.19615i		−	0.0731239i
$903$	−24.0000	−	13.8564i	−0.798670	−	0.461112i
$904$	−9.92820	+	17.1962i	−0.330207	+	0.571936i
$905$	−23.0885	−	13.3301i	−0.767486	−	0.443108i
$906$	−1.14359	+	0.660254i	−0.0379934	+	0.0219355i
$907$	34.9019	−	20.1506i	1.15890	−	0.669091i	0.207859	−	0.978159i	$-0.433350\pi$
$907$	34.9019	−	20.1506i	1.15890	−	0.669091i	0.951040	+	0.309068i	$0.100017\pi$
$908$	−1.09808	−	0.633975i	−0.0364409	−	0.0210392i
$909$	−0.571797	+	0.990381i	−0.0189653	+	0.0328489i
$910$	−36.0000	−	20.7846i	−1.19339	−	0.689003i
$911$		−	27.1244i		−	0.898670i	−0.893363	−	0.449335i	$-0.851661\pi$
$911$		−	27.1244i		−	0.898670i	0.893363	−	0.449335i	$-0.148339\pi$
$912$	0.803848	−	0.464102i	0.0266181	−	0.0153679i
$913$	−27.5885	+	47.7846i	−0.913045	+	1.58144i
$914$	31.9808			1.05783
$915$	−18.5885			−0.614515
$916$	−9.50000	+	16.4545i	−0.313889	+	0.543671i
$917$			32.7846i			1.08264i
$918$	−3.46410	−	6.00000i	−0.114332	−	0.198030i
$919$		−	10.0526i		−	0.331603i	−0.986159	−	0.165802i	$-0.946979\pi$
$919$		−	10.0526i		−	0.331603i	0.986159	−	0.165802i	$-0.0530212\pi$
$920$	−1.90192	+	1.09808i	−0.0627046	+	0.0362025i
$921$	−1.46410	−	2.53590i	−0.0482438	−	0.0835607i
$922$	−10.8564	−	18.8038i	−0.357537	−	0.619272i
$923$	13.1769	+	7.60770i	0.433723	+	0.250410i
$924$	13.8564			0.455842
$925$	−10.0000	−	6.92820i	−0.328798	−	0.227798i
$926$	21.4641			0.705354
$927$	−14.7846	−	8.53590i	−0.485590	−	0.280356i
$928$	−2.13397	−	3.69615i	−0.0700511	−	0.121332i
$929$	8.30385	+	14.3827i	0.272440	+	0.471881i	0.969486	−	0.245146i	$-0.0788359\pi$
$929$	8.30385	+	14.3827i	0.272440	+	0.471881i	−0.697046	+	0.717027i	$0.745503\pi$
$930$	1.39230	−	0.803848i	0.0456555	−	0.0263592i
$931$		−	11.4115i		−	0.373998i
$932$	−2.30385	−	3.99038i	−0.0754650	−	0.130709i
$933$			12.0000i			0.392862i
$934$	−9.12436	+	15.8038i	−0.298558	+	0.517118i
$935$	14.1962			0.464264
$936$	−14.7846			−0.483250
$937$	13.0885	−	22.6699i	0.427581	−	0.740592i	−0.569076	−	0.822285i	$-0.692699\pi$
$937$	13.0885	−	22.6699i	0.427581	−	0.740592i	0.996658	+	0.0816922i	$0.0260325\pi$
$938$	−21.4641	+	12.3923i	−0.700828	+	0.404623i
$939$			15.8038i			0.515739i
$940$	−17.4904	−	10.0981i	−0.570473	−	0.329363i
$941$	−9.10770	+	15.7750i	−0.296902	+	0.514250i	−0.975426	−	0.220329i	$-0.929287\pi$
$941$	−9.10770	+	15.7750i	−0.296902	+	0.514250i	0.678523	+	0.734579i	$0.262620\pi$
$942$	5.95448	+	3.43782i	0.194008	+	0.112010i
$943$	−0.509619	+	0.294229i	−0.0165955	+	0.00958140i
$944$	2.19615	−	1.26795i	0.0714787	−	0.0412682i
$945$	24.0000	+	13.8564i	0.780720	+	0.450749i
$946$	22.3923	−	38.7846i	0.728037	−	1.26100i
$947$	27.3731	+	15.8038i	0.889505	+	0.513556i	0.873781	−	0.486320i	$-0.161661\pi$
$947$	27.3731	+	15.8038i	0.889505	+	0.513556i	0.0157246	+	0.999876i	$0.494995\pi$
$948$		−	6.00000i		−	0.194871i
$949$	64.3923	−	37.1769i	2.09026	−	1.20681i
$950$	1.26795	−	2.19615i	0.0411377	−	0.0712526i
$951$	−6.58846			−0.213645
$952$	−6.92820			−0.224544
$953$	9.92820	−	17.1962i	0.321606	−	0.557038i	−0.659214	−	0.751956i	$-0.729111\pi$
$953$	9.92820	−	17.1962i	0.321606	−	0.557038i	0.980820	+	0.194918i	$0.0624440\pi$
$954$		−	6.24871i		−	0.202309i
$955$	21.2942	+	36.8827i	0.689065	+	1.19350i
$956$		−	5.07180i		−	0.164034i
$957$	−12.8038	+	7.39230i	−0.413890	+	0.238959i
$958$	1.26795	+	2.19615i	0.0409656	+	0.0709545i
$959$	26.7846	+	46.3923i	0.864920	+	1.49809i
$960$	1.09808	+	0.633975i	0.0354403	+	0.0204614i
$961$	29.3923			0.948139
$962$	3.00000	−	36.3731i	0.0967239	−	1.17271i
$963$	40.3923			1.30162
$964$	−15.5885	−	9.00000i	−0.502070	−	0.289870i
$965$	−10.5000	−	18.1865i	−0.338007	−	0.585445i
$966$	−1.85641	−	3.21539i	−0.0597289	−	0.103453i
$967$	−50.7846	+	29.3205i	−1.63312	+	0.942884i	−0.650001	+	0.759934i	$0.725231\pi$
$967$	−50.7846	+	29.3205i	−1.63312	+	0.942884i	−0.983122	+	0.182950i	$0.941435\pi$
$968$			11.3923i			0.366163i
$969$	0.803848	+	1.39230i	0.0258233	+	0.0447273i
$970$			9.00000i			0.288973i
$971$	−9.29423	+	16.0981i	−0.298266	+	0.516612i	−0.975739	−	0.218935i	$-0.929742\pi$
$971$	−9.29423	+	16.0981i	−0.298266	+	0.516612i	0.677473	+	0.735547i	$0.263075\pi$
$972$	15.2679			0.489720
$973$	7.21539			0.231315
$974$	−5.02628	+	8.70577i	−0.161052	+	0.278951i
$975$	7.60770	−	4.39230i	0.243641	−	0.140666i
$976$			14.6603i			0.469263i
$977$	1.98076	+	1.14359i	0.0633702	+	0.0365868i	0.531350	−	0.847152i	$-0.321685\pi$
$977$	1.98076	+	1.14359i	0.0633702	+	0.0365868i	−0.467980	+	0.883739i	$0.655018\pi$
$978$	0.928203	−	1.60770i	0.0296807	−	0.0514084i
$979$	21.2942	+	12.2942i	0.680566	+	0.392925i
$980$	13.5000	−	7.79423i	0.431242	−	0.248978i
$981$	−16.5000	+	9.52628i	−0.526804	+	0.304151i
$982$	−19.9019	−	11.4904i	−0.635096	−	0.366673i
$983$	12.7583	−	22.0981i	0.406928	−	0.704819i	−0.587616	−	0.809140i	$-0.699933\pi$
$983$	12.7583	−	22.0981i	0.406928	−	0.704819i	0.994544	+	0.104321i	$0.0332668\pi$
$984$	0.294229	+	0.169873i	0.00937967	+	0.00541535i
$985$		−	45.5885i		−	1.45257i
$986$	6.40192	−	3.69615i	0.203879	−	0.117709i
$987$	17.0718	−	29.5692i	0.543401	−	0.941199i
$988$	7.60770			0.242033
$989$	−12.0000			−0.381578
$990$	−10.0981	+	17.4904i	−0.320938	+	0.555881i
$991$			32.1051i			1.01985i	0.860218	+	0.509926i	$0.170327\pi$
$991$			32.1051i			1.01985i	−0.860218	+	0.509926i	$0.829673\pi$
$992$	−0.633975	−	1.09808i	−0.0201287	−	0.0348640i
$993$		−	22.6410i		−	0.718491i
$994$	−8.78461	+	5.07180i	−0.278631	+	0.160868i
$995$	−4.39230	−	7.60770i	−0.139245	−	0.241180i
$996$	−4.26795	−	7.39230i	−0.135235	−	0.234234i
$997$	−51.5885	−	29.7846i	−1.63382	−	0.943288i	−0.982899	−	0.184145i	$-0.941048\pi$
$997$	−51.5885	−	29.7846i	−1.63382	−	0.943288i	−0.650924	−	0.759143i	$-0.725618\pi$
$998$	8.19615			0.259445
$999$	−2.00000	+	24.2487i	−0.0632772	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.e.a.27.2	yes	4
3.2	odd	2		666.2.s.e.397.1		4
4.3	odd	2		592.2.w.d.545.1		4
37.11	even	6	inner	74.2.e.a.11.2	✓	4
37.14	odd	12		2738.2.a.j.1.2		2
37.23	odd	12		2738.2.a.f.1.2		2
111.11	odd	6		666.2.s.e.307.1		4
148.11	odd	6		592.2.w.d.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.e.a.11.2	✓	4	37.11	even	6	inner
74.2.e.a.27.2	yes	4	1.1	even	1	trivial
592.2.w.d.529.1		4	148.11	odd	6
592.2.w.d.545.1		4	4.3	odd	2
666.2.s.e.307.1		4	111.11	odd	6
666.2.s.e.397.1		4	3.2	odd	2
2738.2.a.f.1.2		2	37.23	odd	12
2738.2.a.j.1.2		2	37.14	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} -1.73205 q^{10} +4.73205 q^{11} +(-0.366025 + 0.633975i) q^{12} +(-5.19615 + 3.00000i) q^{13} -4.00000i q^{14} +(-1.09808 - 0.633975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 0.866025i) q^{17} +(2.13397 - 1.23205i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(1.46410 - 2.53590i) q^{21} +(4.09808 + 2.36603i) q^{22} -1.26795i q^{23} +(-0.633975 + 0.366025i) q^{24} +(-1.00000 + 1.73205i) q^{25} -6.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +4.26795i q^{29} +(-0.633975 - 1.09808i) q^{30} +1.26795i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 3.00000i) q^{33} +(-0.866025 - 1.50000i) q^{34} +(6.00000 + 3.46410i) q^{35} +2.46410 q^{36} +(-0.500000 + 6.06218i) q^{37} -1.26795 q^{38} +(-3.80385 - 2.19615i) q^{39} +(-0.866025 - 1.50000i) q^{40} +(-0.232051 - 0.401924i) q^{41} +(2.53590 - 1.46410i) q^{42} -9.46410i q^{43} +(2.36603 + 4.09808i) q^{44} +4.26795i q^{45} +(0.633975 - 1.09808i) q^{46} +11.6603 q^{47} -0.732051 q^{48} +(-4.50000 + 7.79423i) q^{49} +(-1.73205 + 1.00000i) q^{50} -1.26795i q^{51} +(-5.19615 - 3.00000i) q^{52} +(1.26795 - 2.19615i) q^{53} +(3.46410 + 2.00000i) q^{54} +(-7.09808 + 4.09808i) q^{55} +(3.46410 - 2.00000i) q^{56} +(-0.803848 - 0.464102i) q^{57} +(-2.13397 + 3.69615i) q^{58} +(-2.19615 - 1.26795i) q^{59} -1.26795i q^{60} +(12.6962 - 7.33013i) q^{61} +(-0.633975 + 1.09808i) q^{62} -9.85641 q^{63} -1.00000 q^{64} +(5.19615 - 9.00000i) q^{65} +3.46410i q^{66} +(-3.09808 - 5.36603i) q^{67} -1.73205i q^{68} +(0.803848 - 0.464102i) q^{69} +(3.46410 + 6.00000i) q^{70} +(-1.26795 - 2.19615i) q^{71} +(2.13397 + 1.23205i) q^{72} -12.3923 q^{73} +(-3.46410 + 5.00000i) q^{74} -1.46410 q^{75} +(-1.09808 - 0.633975i) q^{76} +(-9.46410 - 16.3923i) q^{77} +(-2.19615 - 3.80385i) q^{78} +(-7.09808 + 4.09808i) q^{79} -1.73205i q^{80} +(-2.23205 - 3.86603i) q^{81} -0.464102i q^{82} +(-5.83013 + 10.0981i) q^{83} +2.92820 q^{84} +3.00000 q^{85} +(4.73205 - 8.19615i) q^{86} +(-2.70577 + 1.56218i) q^{87} +4.73205i q^{88} +(4.50000 + 2.59808i) q^{89} +(-2.13397 + 3.69615i) q^{90} +(20.7846 + 12.0000i) q^{91} +(1.09808 - 0.633975i) q^{92} +(-0.803848 + 0.464102i) q^{93} +(10.0981 + 5.83013i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-0.633975 - 0.366025i) q^{96} -5.19615i q^{97} +(-7.79423 + 4.50000i) q^{98} +(5.83013 - 10.0981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 8 q^{7} - 2 q^{9} + 12 q^{11} + 2 q^{12} + 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{18} + 6 q^{19} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 6 q^{24} - 4 q^{25} - 24 q^{26} + 16 q^{27} + 8 q^{28} - 6 q^{30} + 24 q^{35} - 4 q^{36} - 2 q^{37} - 12 q^{38} - 36 q^{39} + 6 q^{41} + 24 q^{42} + 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} - 18 q^{49} + 12 q^{53} - 18 q^{55} - 24 q^{57} - 12 q^{58} + 12 q^{59} + 30 q^{61} - 6 q^{62} + 16 q^{63} - 4 q^{64} - 2 q^{67} + 24 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} + 8 q^{75} + 6 q^{76} - 24 q^{77} + 12 q^{78} - 18 q^{79} - 2 q^{81} - 6 q^{83} - 16 q^{84} + 12 q^{85} + 12 q^{86} - 42 q^{87} + 18 q^{89} - 12 q^{90} - 6 q^{92} - 24 q^{93} + 30 q^{94} - 6 q^{95} - 6 q^{96} + 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 8 * q^7 - 2 * q^9 + 12 * q^11 + 2 * q^12 + 6 * q^15 - 2 * q^16 - 6 * q^17 + 12 * q^18 + 6 * q^19 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 6 * q^24 - 4 * q^25 - 24 * q^26 + 16 * q^27 + 8 * q^28 - 6 * q^30 + 24 * q^35 - 4 * q^36 - 2 * q^37 - 12 * q^38 - 36 * q^39 + 6 * q^41 + 24 * q^42 + 6 * q^44 + 6 * q^46 + 12 * q^47 + 4 * q^48 - 18 * q^49 + 12 * q^53 - 18 * q^55 - 24 * q^57 - 12 * q^58 + 12 * q^59 + 30 * q^61 - 6 * q^62 + 16 * q^63 - 4 * q^64 - 2 * q^67 + 24 * q^69 - 12 * q^71 + 12 * q^72 - 8 * q^73 + 8 * q^75 + 6 * q^76 - 24 * q^77 + 12 * q^78 - 18 * q^79 - 2 * q^81 - 6 * q^83 - 16 * q^84 + 12 * q^85 + 12 * q^86 - 42 * q^87 + 18 * q^89 - 12 * q^90 - 6 * q^92 - 24 * q^93 + 30 * q^94 - 6 * q^95 - 6 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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