LMFDB - Embedded newform 74.2.e.a.11.2

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
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			11.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	74.11
Dual form			74.2.e.a.27.2

$q$-expansion

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} -0.732051i q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	−0.740805	−	0.671721i	$-0.765556\pi$
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	0.952129	+	0.305695i	$0.0988889\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$		−	0.732051i		−	0.298858i
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		−	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	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	−5.19615	−	3.00000i	−1.44115	−	0.832050i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$			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	−0.670748	−	0.741685i	$-0.734027\pi$
$17$	−1.50000	+	0.866025i	−0.363803	+	0.210042i	0.306944	+	0.951727i	$0.400693\pi$
$18$	2.13397	+	1.23205i	0.502983	+	0.290397i
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$	−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	$0.0422018\pi$
$23$			1.26795i			0.264386i	−0.991224	+	0.132193i	$0.957798\pi$
$24$	−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	$-0.870305\pi$
$29$		−	4.26795i		−	0.792538i	0.918134	−	0.396269i	$-0.129695\pi$
$30$	−0.633975	+	1.09808i	−0.115747	+	0.200480i
$31$		−	1.26795i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$31$		−	1.26795i		−	0.227730i	0.993496	−	0.113865i	$-0.0363232\pi$
$32$	−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	−0.883577	−	0.468287i	$-0.844871\pi$
$41$	−0.232051	+	0.401924i	−0.0362402	+	0.0627700i	0.847336	+	0.531057i	$0.178205\pi$
$42$	2.53590	+	1.46410i	0.391298	+	0.225916i
$43$			9.46410i			1.44326i	0.692278	+	0.721631i	$0.256607\pi$
$43$			9.46410i			1.44326i	−0.692278	+	0.721631i	$0.743393\pi$
$44$	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	0.939872	−	0.341526i	$-0.110944\pi$
$53$	1.26795	+	2.19615i	0.174166	+	0.301665i	−0.765706	+	0.643191i	$0.777610\pi$
$54$	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	−0.636098	−	0.771608i	$-0.719453\pi$
$59$	−2.19615	+	1.26795i	−0.285915	+	0.165073i	0.350183	+	0.936681i	$0.386119\pi$
$60$			1.26795i			0.163692i
$61$	12.6962	+	7.33013i	1.62558	+	0.938527i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	12.6962	+	7.33013i	1.62558	+	0.938527i	0.640184	+	0.768221i	$0.278858\pi$
$62$	−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	−0.990843	−	0.135020i	$-0.956890\pi$
$67$	−3.09808	+	5.36603i	−0.378490	+	0.655564i	0.612353	+	0.790585i	$0.290223\pi$
$68$			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	−0.931403	−	0.363989i	$-0.881415\pi$
$71$	−1.26795	+	2.19615i	−0.150478	+	0.260635i	0.780925	+	0.624624i	$0.214748\pi$
$72$	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	0.0443840	−	0.999015i	$-0.485867\pi$
$79$	−7.09808	−	4.09808i	−0.798596	−	0.461070i	−0.842980	+	0.537945i	$0.819201\pi$
$80$			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	−0.985446	−	0.169991i	$-0.945626\pi$
$83$	−5.83013	−	10.0981i	−0.639940	−	1.10841i	0.345506	−	0.938417i	$-0.387707\pi$
$84$	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	−0.242166	−	0.970235i	$-0.577858\pi$
$89$	4.50000	−	2.59808i	0.476999	−	0.275396i	0.719165	+	0.694839i	$0.244525\pi$
$90$	−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	$0.0849741\pi$
$97$			5.19615i			0.527589i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	−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	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$	−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	−0.132155	−	0.991229i	$-0.542190\pi$
$107$	8.19615	−	14.1962i	0.792352	−	1.37239i	0.924507	−	0.381165i	$-0.124477\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	−6.69615	+	3.86603i	−0.641375	+	0.370298i	−0.785144	−	0.619313i	$-0.787411\pi$
$109$	−6.69615	+	3.86603i	−0.641375	+	0.370298i	0.143769	+	0.989611i	$0.454078\pi$
$110$	−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	0.630159	−	0.776466i	$-0.282990\pi$
$113$	17.1962	−	9.92820i	1.61768	−	0.933967i	0.987519	−	0.157501i	$-0.0503437\pi$
$114$	−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	0.999403	−	0.0345426i	$-0.0109974\pi$
$127$	5.29423	+	9.16987i	0.469787	+	0.813695i	−0.529616	+	0.848237i	$0.677664\pi$
$128$	−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	−0.776932	−	0.629585i	$-0.783225\pi$
$131$	−7.09808	+	4.09808i	−0.620162	+	0.358051i	0.156770	+	0.987635i	$0.449892\pi$
$132$	−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	0.825237	−	0.564786i	$-0.191041\pi$
$139$	−0.901924	−	1.56218i	−0.0765002	−	0.132502i	−0.901738	+	0.432284i	$0.857708\pi$
$140$		−	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	−0.826991	−	0.562215i	$-0.809949\pi$
$151$	0.901924	−	1.56218i	0.0733975	−	0.127128i	0.900388	+	0.435087i	$0.143282\pi$
$152$	−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	0.990296	−	0.138973i	$-0.0443802\pi$
$157$	4.69615	+	8.13397i	0.374794	+	0.649162i	−0.615502	+	0.788135i	$0.711047\pi$
$158$	−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	−0.583536	−	0.812087i	$-0.698331\pi$
$163$	−2.19615	+	1.26795i	−0.172016	+	0.0993134i	0.411520	+	0.911401i	$0.364998\pi$
$164$	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	0.249554	−	0.968361i	$-0.419716\pi$
$167$	−6.00000	−	3.46410i	−0.464294	−	0.268060i	−0.713848	+	0.700301i	$0.753049\pi$
$168$	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	0.990685	−	0.136173i	$-0.0434802\pi$
$173$	4.96410	+	8.59808i	0.377414	+	0.653700i	−0.613271	+	0.789872i	$0.710147\pi$
$174$	−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	$-0.860953\pi$
$179$		−	11.3205i		−	0.846135i	0.906098	−	0.423067i	$-0.139047\pi$
$180$	−3.69615	−	2.13397i	−0.275495	−	0.159057i
$181$	7.69615	−	13.3301i	0.572051	−	0.990821i	−0.424305	−	0.905519i	$-0.639481\pi$
$181$	7.69615	−	13.3301i	0.572051	−	0.990821i	0.996355	−	0.0853011i	$-0.0271852\pi$
$182$	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	$0.349002\pi$
$191$			24.5885i			1.77916i	−0.456781	+	0.889579i	$0.650998\pi$
$192$	−0.366025	+	0.633975i	−0.0264156	+	0.0457532i
$193$		−	12.1244i		−	0.872730i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$		−	12.1244i		−	0.872730i	0.899770	−	0.436365i	$-0.143734\pi$
$194$	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	−0.769877	−	0.638192i	$-0.779682\pi$
$197$	−13.1603	−	22.7942i	−0.937629	−	1.62402i	−0.167752	−	0.985829i	$-0.553651\pi$
$198$	10.0981	+	5.83013i	0.717639	+	0.414329i
$199$		−	5.07180i		−	0.359530i	−0.983710	−	0.179765i	$-0.942466\pi$
$199$		−	5.07180i		−	0.359530i	0.983710	−	0.179765i	$-0.0575338\pi$
$200$	−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	0.463116	−	0.886298i	$-0.346731\pi$
$227$	−1.09808	−	0.633975i	−0.0728819	−	0.0420784i	−0.535998	+	0.844219i	$0.680065\pi$
$228$			0.928203i			0.0614718i
$229$	9.50000	−	16.4545i	0.627778	−	1.08734i	−0.360219	−	0.932868i	$-0.617298\pi$
$229$	9.50000	−	16.4545i	0.627778	−	1.08734i	0.987997	−	0.154475i	$-0.0493686\pi$
$230$		−	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	−0.635285	−	0.772278i	$-0.719117\pi$
$239$	−4.39230	+	2.53590i	−0.284115	+	0.164034i	0.351170	+	0.936312i	$0.385784\pi$
$240$	1.09808	+	0.633975i	0.0708805	+	0.0409229i
$241$	−15.5885	−	9.00000i	−1.00414	−	0.579741i	−0.0946700	−	0.995509i	$-0.530180\pi$
$241$	−15.5885	−	9.00000i	−1.00414	−	0.579741i	−0.909471	+	0.415768i	$0.863513\pi$
$242$	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	$-0.948830\pi$
$251$		−	5.07180i		−	0.320129i	0.987107	−	0.160064i	$-0.0511702\pi$
$252$	−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	−0.166110	−	0.986107i	$-0.553121\pi$
$257$	9.69615	−	5.59808i	0.604829	−	0.349198i	0.770939	+	0.636909i	$0.219787\pi$
$258$	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	0.242393	+	0.970178i	$0.422068\pi$
$263$	−11.6603	+	20.1962i	−0.719002	+	1.24535i	−0.961396	+	0.275170i	$0.911266\pi$
$264$	−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	0.997917	−	0.0645082i	$-0.0205479\pi$
$271$	7.29423	+	12.6340i	0.443093	+	0.767459i	−0.554824	+	0.831968i	$0.687215\pi$
$272$	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	0.312426	−	0.949942i	$-0.398858\pi$
$277$	−5.89230	−	3.40192i	−0.354034	−	0.204402i	−0.666461	+	0.745540i	$0.732192\pi$
$278$	−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	−0.760507	−	0.649330i	$-0.775049\pi$
$281$	−9.69615	+	5.59808i	−0.578424	+	0.333953i	0.182083	+	0.983283i	$0.441716\pi$
$282$		−	8.53590i		−	0.508305i
$283$	2.19615	+	1.26795i	0.130548	+	0.0753718i	0.563852	−	0.825876i	$-0.309319\pi$
$283$	2.19615	+	1.26795i	0.130548	+	0.0753718i	−0.433304	+	0.901248i	$0.642652\pi$
$284$	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	0.209996	+	0.977702i	$0.432655\pi$
$293$	−12.6962	+	21.9904i	−0.741717	+	1.28469i	−0.951713	+	0.306989i	$0.900678\pi$
$294$	−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	−0.0402231	−	0.999191i	$-0.512807\pi$
$311$	14.1962	−	8.19615i	0.804990	−	0.464761i	0.845213	+	0.534430i	$0.179474\pi$
$312$	2.19615	+	3.80385i	0.124333	+	0.215350i
$313$	18.6962	−	10.7942i	1.05677	−	0.610126i	0.132232	−	0.991219i	$-0.457786\pi$
$313$	18.6962	−	10.7942i	1.05677	−	0.610126i	0.924537	+	0.381093i	$0.124452\pi$
$314$	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	0.711535	−	0.702650i	$-0.248000\pi$
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	−0.964281	+	0.264883i	$0.914667\pi$
$318$	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	−0.999512	−	0.0312377i	$-0.990055\pi$
$331$	−26.7846	+	15.4641i	−1.47222	+	0.849984i	−0.472703	+	0.881222i	$0.656722\pi$
$332$	−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	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	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	$0.0869658\pi$
$347$			10.0526i			0.539650i	−0.962909	+	0.269825i	$0.913034\pi$
$348$	−2.70577	+	1.56218i	−0.145045	+	0.0837415i
$349$	3.30385	+	5.72243i	0.176851	+	0.306315i	0.940800	−	0.338961i	$-0.110076\pi$
$349$	3.30385	+	5.72243i	0.176851	+	0.306315i	−0.763949	+	0.645276i	$0.776742\pi$
$350$	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	0.395397	−	0.918510i	$-0.370607\pi$
$353$	26.0885	−	15.0622i	1.38855	−	0.801679i	0.993152	+	0.116832i	$0.0372738\pi$
$354$	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	−0.871100	−	0.491106i	$-0.836593\pi$
$367$	−0.196152	+	0.339746i	−0.0102391	+	0.0177346i	0.860860	+	0.508841i	$0.169926\pi$
$368$	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	−0.487696	−	0.873014i	$-0.662162\pi$
$373$	9.89230	−	17.1340i	0.512204	−	0.887164i	0.999900	−	0.0141499i	$-0.00450421\pi$
$374$	−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	−0.986184	−	0.165651i	$-0.947028\pi$
$379$	−12.3923	−	21.4641i	−0.636550	−	1.10254i	0.349635	−	0.936886i	$-0.386306\pi$
$380$	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	0.947466	−	0.319858i	$-0.103635\pi$
$383$	22.3923	+	12.9282i	1.14419	+	0.660600i	0.196728	+	0.980458i	$0.436968\pi$
$384$			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	0.517544	−	0.855656i	$-0.326846\pi$
$389$	0.696152	+	0.401924i	0.0352963	+	0.0203783i	−0.482248	+	0.876035i	$0.660180\pi$
$390$	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	$-0.879647\pi$
$401$		−	14.7846i		−	0.738308i	0.929368	−	0.369154i	$-0.120353\pi$
$402$	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	−0.997734	−	0.0672835i	$-0.978567\pi$
$409$	−29.0885	+	16.7942i	−1.43833	+	0.830421i	−0.440598	+	0.897705i	$0.645233\pi$
$410$	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	0.715134	−	0.698987i	$-0.246366\pi$
$419$	−5.07180	−	8.78461i	−0.247773	−	0.429156i	−0.962908	+	0.269831i	$0.913032\pi$
$420$	−4.39230	−	2.53590i	−0.214323	−	0.123739i
$421$			3.33975i			0.162769i	0.996683	+	0.0813846i	$0.0259342\pi$
$421$			3.33975i			0.162769i	−0.996683	+	0.0813846i	$0.974066\pi$
$422$	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	0.883610	−	0.468223i	$-0.155106\pi$
$431$	19.0981	+	11.0263i	0.919922	+	0.531117i	0.0363118	+	0.999341i	$0.488439\pi$
$432$	−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	0.551492	−	0.834180i	$-0.314059\pi$
$439$	2.19615	+	1.26795i	0.104817	+	0.0605159i	−0.446675	+	0.894696i	$0.647392\pi$
$440$	−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	0.708889	−	0.705321i	$-0.249197\pi$
$449$	9.58846	+	5.53590i	0.452507	+	0.261255i	−0.256381	+	0.966576i	$0.582530\pi$
$450$		−	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	0.979636	−	0.200782i	$-0.0643484\pi$
$457$	27.6962	+	15.9904i	1.29557	+	0.747998i	0.315935	+	0.948781i	$0.397682\pi$
$458$		−	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	−0.869266	−	0.494346i	$-0.835408\pi$
$461$	−18.8038	+	10.8564i	−0.875782	+	0.505633i	−0.00651699	+	0.999979i	$0.502074\pi$
$462$	12.0000	+	6.92820i	0.558291	+	0.322329i
$463$	18.5885	+	10.7321i	0.863879	+	0.498761i	0.865309	−	0.501238i	$-0.167122\pi$
$463$	18.5885	+	10.7321i	0.863879	+	0.498761i	−0.00143043	+	0.999999i	$0.500455\pi$
$464$	−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	$-0.861249\pi$
$467$		−	18.2487i		−	0.844450i	0.906491	−	0.422225i	$-0.138751\pi$
$468$	−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	−0.448988	−	0.893538i	$-0.648215\pi$
$479$	2.19615	−	1.26795i	0.100345	−	0.0579341i	0.549333	+	0.835604i	$0.314882\pi$
$480$	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	$-0.926859\pi$
$487$		−	10.0526i		−	0.455525i	0.973717	−	0.227762i	$-0.0731410\pi$
$488$	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	0.650391	−	0.759600i	$-0.274605\pi$
$499$	7.09808	+	4.09808i	0.317754	+	0.183455i	−0.332637	+	0.943055i	$0.607938\pi$
$500$	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	−0.236859	−	0.971544i	$-0.576118\pi$
$503$	10.9019	−	6.29423i	0.486093	−	0.280646i	0.722952	+	0.690898i	$0.242785\pi$
$504$			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	−0.968034	−	0.250818i	$-0.919301\pi$
$509$	−15.8205	−	27.4019i	−0.701232	−	1.21457i	0.266803	−	0.963751i	$-0.414033\pi$
$510$		−	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	0.414049	+	0.910255i	$0.364114\pi$
$521$	−13.2679	+	22.9808i	−0.581279	+	1.00681i	−0.995328	+	0.0965507i	$0.969219\pi$
$522$	5.25833	−	9.10770i	0.230151	−	0.398633i
$523$	10.9019	+	6.29423i	0.476708	+	0.275227i	0.719043	−	0.694965i	$-0.244580\pi$
$523$	10.9019	+	6.29423i	0.476708	+	0.275227i	−0.242336	+	0.970192i	$0.577914\pi$
$524$			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	$0.0245788\pi$
$541$			3.58846i			0.154280i	−0.997020	+	0.0771399i	$0.975421\pi$
$542$	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	$-0.913267\pi$
$547$		−	12.5885i		−	0.538244i	0.963106	−	0.269122i	$-0.0867334\pi$
$548$	−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	−0.294479	−	0.955658i	$-0.595146\pi$
$557$	9.10770	−	5.25833i	0.385905	−	0.222803i	0.680385	+	0.732855i	$0.261813\pi$
$558$	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	$0.0773014\pi$
$563$			11.4115i			0.480939i	−0.970657	+	0.240470i	$0.922699\pi$
$564$	−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	$-0.796065\pi$
$569$		−	28.5167i		−	1.19548i	0.801690	−	0.597740i	$-0.203935\pi$
$570$	1.39230	−	0.803848i	0.0583172	−	0.0336695i
$571$	−7.49038	−	12.9737i	−0.313463	−	0.542933i	0.665647	−	0.746267i	$-0.268156\pi$
$571$	−7.49038	−	12.9737i	−0.313463	−	0.542933i	−0.979110	+	0.203334i	$0.934822\pi$
$572$	−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	−0.423442	−	0.905923i	$-0.639178\pi$
$577$	3.58846	−	2.07180i	0.149389	−	0.0862500i	0.572831	+	0.819673i	$0.305845\pi$
$578$			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	0.839350	−	0.543591i	$-0.182936\pi$
$587$	19.0981	+	11.0263i	0.788262	+	0.455103i	−0.0510884	+	0.998694i	$0.516269\pi$
$588$	−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	−0.910306	−	0.413937i	$-0.864153\pi$
$599$	−2.36603	+	4.09808i	−0.0966732	+	0.167443i	0.813633	+	0.581380i	$0.197487\pi$
$600$			1.46410i			0.0597717i
$601$	12.8923	+	22.3301i	0.525888	+	0.910865i	0.999545	+	0.0301556i	$0.00960027\pi$
$601$	12.8923	+	22.3301i	0.525888	+	0.910865i	−0.473657	+	0.880709i	$0.657066\pi$
$602$	−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	−0.465382	−	0.885110i	$-0.654083\pi$
$607$	1.68653	−	0.973721i	0.0684543	−	0.0395221i	0.533836	+	0.845588i	$0.320750\pi$
$608$	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	0.710180	−	0.704021i	$-0.248614\pi$
$613$	−6.30385	−	10.9186i	−0.254610	−	0.440997i	−0.964790	+	0.263023i	$0.915280\pi$
$614$	−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	0.529965	−	0.848020i	$-0.322205\pi$
$617$	−11.6603	−	20.1962i	−0.469424	−	0.813066i	−0.999389	+	0.0349532i	$0.988872\pi$
$618$	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	−0.914846	−	0.403803i	$-0.867688\pi$
$631$	−25.6865	+	14.8301i	−1.02256	+	0.590378i	−0.107719	+	0.994181i	$0.534355\pi$
$632$	−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	0.990780	−	0.135478i	$-0.0432569\pi$
$641$	9.57180	+	16.5788i	0.378063	+	0.654825i	−0.612717	+	0.790302i	$0.709924\pi$
$642$	−10.3923	−	6.00000i	−0.410152	−	0.236801i
$643$			15.1244i			0.596446i	0.954496	+	0.298223i	$0.0963940\pi$
$643$			15.1244i			0.596446i	−0.954496	+	0.298223i	$0.903606\pi$
$644$	−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	0.542548	−	0.840025i	$-0.317460\pi$
$647$	2.19615	+	1.26795i	0.0863397	+	0.0498482i	−0.456209	+	0.889873i	$0.650793\pi$
$648$	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	0.179457	−	0.983766i	$-0.442566\pi$
$653$	−14.8923	−	8.59808i	−0.582781	−	0.336469i	−0.762238	+	0.647297i	$0.775899\pi$
$654$	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	−0.995744	−	0.0921577i	$-0.970624\pi$
$659$	−10.7321	+	18.5885i	−0.418061	+	0.724103i	0.577683	+	0.816261i	$0.303957\pi$
$660$			6.00000i			0.233550i
$661$	−16.2846	−	9.40192i	−0.633398	−	0.365692i	0.148669	−	0.988887i	$-0.452501\pi$
$661$	−16.2846	−	9.40192i	−0.633398	−	0.365692i	−0.782067	+	0.623195i	$0.785834\pi$
$662$	−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	−0.935496	−	0.353336i	$-0.885047\pi$
$673$	−4.19615	+	7.26795i	−0.161750	+	0.280159i	0.773747	+	0.633495i	$0.218380\pi$
$674$		−	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	−0.755437	−	0.655221i	$-0.772575\pi$
$683$	−14.7846	+	8.53590i	−0.565717	+	0.326617i	0.189720	+	0.981838i	$0.439242\pi$
$684$	−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	0.996153	−	0.0876256i	$-0.0279279\pi$
$691$	11.0981	+	19.2224i	0.422191	+	0.731256i	−0.573963	+	0.818881i	$0.694595\pi$
$692$	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	−0.469332	−	0.883022i	$-0.655505\pi$
$701$	1.60770	−	0.928203i	0.0607218	−	0.0350578i	0.530054	+	0.847964i	$0.322172\pi$
$702$	−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	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	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	0.992052	+	0.125826i	$0.0401581\pi$
$719$	16.2224	+	28.0981i	0.604995	+	1.04788i	−0.387058	+	0.922055i	$0.626509\pi$
$720$	−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	0.469891	−	0.882725i	$-0.344293\pi$
$727$	−1.60770	−	0.928203i	−0.0596261	−	0.0344252i	−0.529517	+	0.848300i	$0.677627\pi$
$728$	−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	−0.973390	−	0.229154i	$-0.926404\pi$
$733$	−7.80385	+	13.5167i	−0.288242	+	0.499249i	0.685148	+	0.728403i	$0.259737\pi$
$734$			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	−0.169498	−	0.985531i	$-0.554215\pi$
$743$	20.9545	−	36.2942i	0.768745	−	1.33151i	0.938244	−	0.345976i	$-0.112452\pi$
$744$	−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	−0.431324	−	0.902197i	$-0.641954\pi$
$757$	3.69615	−	2.13397i	0.134339	−	0.0775606i	0.565663	+	0.824636i	$0.308620\pi$
$758$	−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	−0.994774	−	0.102101i	$-0.967444\pi$
$761$	−16.1603	−	27.9904i	−0.585809	−	1.01465i	0.408965	−	0.912550i	$-0.365890\pi$
$762$	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	$0.128041\pi$
$769$			21.7128i			0.782984i	−0.920181	+	0.391492i	$0.871959\pi$
$770$	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	−0.598667	−	0.800998i

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

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