LMFDB - Embedded newform 1110.2.x.d.841.3

Newspace parameters

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
Defining polynomial:	$x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416$
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.3
Root			$-0.871333i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.d.751.3

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.435667 + 0.754597i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.435667 + 0.754597i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +1.12820 q^{11} +(0.500000 - 0.866025i) q^{12} +(-5.16160 + 2.98005i) q^{13} -0.871333i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.62062 - 0.935667i) q^{17} +(0.866025 - 0.500000i) q^{18} +(5.64541 - 3.25938i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.435667 - 0.754597i) q^{21} +(-0.977051 - 0.564101i) q^{22} -4.22805i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +5.96011 q^{26} +1.00000 q^{27} +(-0.435667 + 0.754597i) q^{28} -4.16204i q^{29} +(-0.500000 - 0.866025i) q^{30} -5.15096i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.564101 - 0.977051i) q^{33} +(0.935667 + 1.62062i) q^{34} +(-0.754597 - 0.435667i) q^{35} -1.00000 q^{36} +(-2.13754 + 5.69481i) q^{37} -6.51876 q^{38} +(5.16160 + 2.98005i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.31389 - 9.20392i) q^{41} +(-0.754597 + 0.435667i) q^{42} +9.37901i q^{43} +(0.564101 + 0.977051i) q^{44} -1.00000i q^{45} +(-2.11403 + 3.66160i) q^{46} +7.61359 q^{47} +1.00000 q^{48} +(3.12039 - 5.40467i) q^{49} +(-0.866025 + 0.500000i) q^{50} +1.87133i q^{51} +(-5.16160 - 2.98005i) q^{52} +(5.57432 - 9.65501i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.977051 + 0.564101i) q^{55} +(0.754597 - 0.435667i) q^{56} +(-5.64541 - 3.25938i) q^{57} +(-2.08102 + 3.60443i) q^{58} +(-1.96930 - 1.13698i) q^{59} +1.00000i q^{60} +(4.20441 - 2.42742i) q^{61} +(-2.57548 + 4.46086i) q^{62} -0.871333 q^{63} -1.00000 q^{64} +(2.98005 - 5.16160i) q^{65} +1.12820i q^{66} +(-7.07277 - 12.2504i) q^{67} -1.87133i q^{68} +(-3.66160 + 2.11403i) q^{69} +(0.435667 + 0.754597i) q^{70} +(-7.55813 - 13.0911i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.43634 q^{73} +(4.69857 - 3.86308i) q^{74} -1.00000 q^{75} +(5.64541 + 3.25938i) q^{76} +(0.491520 + 0.851337i) q^{77} +(-2.98005 - 5.16160i) q^{78} +(-10.0774 + 5.81817i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +10.6278i q^{82} +(-2.47486 + 4.28659i) q^{83} +0.871333 q^{84} +1.87133 q^{85} +(4.68951 - 8.12246i) q^{86} +(-3.60443 + 2.08102i) q^{87} -1.12820i q^{88} +(7.87663 + 4.54758i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-4.49748 - 2.59662i) q^{91} +(3.66160 - 2.11403i) q^{92} +(-4.46086 + 2.57548i) q^{93} +(-6.59356 - 3.80679i) q^{94} +(-3.25938 + 5.64541i) q^{95} +(-0.866025 - 0.500000i) q^{96} -2.17225i q^{97} +(-5.40467 + 3.12039i) q^{98} +(-0.564101 + 0.977051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) $	$ 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	0.435667	+	0.754597i	0.164666	+	0.285211i	0.936537	−	0.350569i	$-0.114012\pi$
$7$	0.435667	+	0.754597i	0.164666	+	0.285211i	−0.771870	+	0.635780i	$0.780679\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	1.12820			0.340165			0.170083	−	0.985430i	$-0.445597\pi$
$11$	1.12820			0.340165			0.170083	+	0.985430i	$0.445597\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−5.16160	+	2.98005i	−1.43157	+	0.826518i	−0.997241	−	0.0742358i	$-0.976348\pi$
$13$	−5.16160	+	2.98005i	−1.43157	+	0.826518i	−0.434330	+	0.900754i	$0.643015\pi$
$14$		−	0.871333i		−	0.232874i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.62062	−	0.935667i	−0.393059	−	0.226932i	0.290426	−	0.956897i	$-0.406203\pi$
$17$	−1.62062	−	0.935667i	−0.393059	−	0.226932i	−0.683485	+	0.729965i	$0.739536\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	5.64541	−	3.25938i	1.29515	−	0.747753i	0.315585	−	0.948897i	$-0.397799\pi$
$19$	5.64541	−	3.25938i	1.29515	−	0.747753i	0.979562	+	0.201144i	$0.0644659\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	0.435667	−	0.754597i	0.0950702	−	0.164666i
$22$	−0.977051	−	0.564101i	−0.208308	−	0.120267i
$23$		−	4.22805i		−	0.881610i	−0.897603	−	0.440805i	$-0.854693\pi$
$23$		−	4.22805i		−	0.881610i	0.897603	−	0.440805i	$-0.145307\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	5.96011			1.16887
$27$	1.00000			0.192450
$28$	−0.435667	+	0.754597i	−0.0823332	+	0.142605i
$29$		−	4.16204i		−	0.772872i	−0.922316	−	0.386436i	$-0.873706\pi$
$29$		−	4.16204i		−	0.772872i	0.922316	−	0.386436i	$-0.126294\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$		−	5.15096i		−	0.925140i	−0.886583	−	0.462570i	$-0.846927\pi$
$31$		−	5.15096i		−	0.925140i	0.886583	−	0.462570i	$-0.153073\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.564101	−	0.977051i	−0.0981973	−	0.170083i
$34$	0.935667	+	1.62062i	0.160465	+	0.277934i
$35$	−0.754597	−	0.435667i	−0.127550	−	0.0736411i
$36$	−1.00000			−0.166667
$37$	−2.13754	+	5.69481i	−0.351410	+	0.936222i
$37$	−2.13754	+	5.69481i	−0.351410	+	0.936222i
$38$	−6.51876			−1.05748
$39$	5.16160	+	2.98005i	0.826518	+	0.477190i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.31389	−	9.20392i	−0.829890	−	1.43741i	−0.898124	−	0.439742i	$-0.855070\pi$
$41$	−5.31389	−	9.20392i	−0.829890	−	1.43741i	0.0682345	−	0.997669i	$-0.478263\pi$
$42$	−0.754597	+	0.435667i	−0.116437	+	0.0672248i
$43$			9.37901i			1.43029i	0.698978	+	0.715143i	$0.253638\pi$
$43$			9.37901i			1.43029i	−0.698978	+	0.715143i	$0.746362\pi$
$44$	0.564101	+	0.977051i	0.0850414	+	0.147296i
$45$		−	1.00000i		−	0.149071i
$46$	−2.11403	+	3.66160i	−0.311696	+	0.539874i
$47$	7.61359			1.11056			0.555278	−	0.831665i	$-0.312612\pi$
$47$	7.61359			1.11056			0.555278	+	0.831665i	$0.312612\pi$
$48$	1.00000			0.144338
$49$	3.12039	−	5.40467i	0.445770	−	0.772096i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$			1.87133i			0.262039i
$52$	−5.16160	−	2.98005i	−0.715786	−	0.413259i
$53$	5.57432	−	9.65501i	0.765692	−	1.32622i	−0.174188	−	0.984712i	$-0.555730\pi$
$53$	5.57432	−	9.65501i	0.765692	−	1.32622i	0.939880	−	0.341505i	$-0.110937\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−0.977051	+	0.564101i	−0.131746	+	0.0760633i
$56$	0.754597	−	0.435667i	0.100837	−	0.0582184i
$57$	−5.64541	−	3.25938i	−0.747753	−	0.431716i
$58$	−2.08102	+	3.60443i	−0.273251	+	0.473285i
$59$	−1.96930	−	1.13698i	−0.256381	−	0.148022i	0.366301	−	0.930496i	$-0.380624\pi$
$59$	−1.96930	−	1.13698i	−0.256381	−	0.148022i	−0.622683	+	0.782475i	$0.713957\pi$
$60$			1.00000i			0.129099i
$61$	4.20441	−	2.42742i	0.538319	−	0.310799i	−0.206078	−	0.978536i	$-0.566070\pi$
$61$	4.20441	−	2.42742i	0.538319	−	0.310799i	0.744398	+	0.667737i	$0.232737\pi$
$62$	−2.57548	+	4.46086i	−0.327086	+	0.566530i
$63$	−0.871333			−0.109778
$64$	−1.00000			−0.125000
$65$	2.98005	−	5.16160i	0.369630	−	0.640218i
$66$			1.12820i			0.138872i
$67$	−7.07277	−	12.2504i	−0.864076	−	1.49662i	−0.867961	−	0.496632i	$-0.834570\pi$
$67$	−7.07277	−	12.2504i	−0.864076	−	1.49662i	0.00388486	−	0.999992i	$-0.498763\pi$
$68$		−	1.87133i		−	0.226932i
$69$	−3.66160	+	2.11403i	−0.440805	+	0.254499i
$70$	0.435667	+	0.754597i	0.0520721	+	0.0901916i
$71$	−7.55813	−	13.0911i	−0.896985	−	1.55362i	−0.831328	−	0.555782i	$-0.812419\pi$
$71$	−7.55813	−	13.0911i	−0.896985	−	1.55362i	−0.0656567	−	0.997842i	$-0.520914\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−4.43634			−0.519234			−0.259617	−	0.965712i	$-0.583596\pi$
$73$	−4.43634			−0.519234			−0.259617	+	0.965712i	$0.583596\pi$
$74$	4.69857	−	3.86308i	0.546198	−	0.449074i
$75$	−1.00000			−0.115470
$76$	5.64541	+	3.25938i	0.647573	+	0.373877i
$77$	0.491520	+	0.851337i	0.0560139	+	0.0970188i
$78$	−2.98005	−	5.16160i	−0.337425	−	0.584436i
$79$	−10.0774	+	5.81817i	−1.13379	+	0.654596i	−0.944886	−	0.327399i	$-0.893828\pi$
$79$	−10.0774	+	5.81817i	−1.13379	+	0.654596i	−0.188907	+	0.981995i	$0.560494\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			10.6278i			1.17364i
$83$	−2.47486	+	4.28659i	−0.271652	+	0.470515i	−0.969285	−	0.245941i	$-0.920903\pi$
$83$	−2.47486	+	4.28659i	−0.271652	+	0.470515i	0.697633	+	0.716455i	$0.254237\pi$
$84$	0.871333			0.0950702
$85$	1.87133			0.202975
$86$	4.68951	−	8.12246i	0.505683	−	0.875868i
$87$	−3.60443	+	2.08102i	−0.386436	+	0.223109i
$88$		−	1.12820i		−	0.120267i
$89$	7.87663	+	4.54758i	0.834921	+	0.482042i	0.855535	−	0.517745i	$-0.173229\pi$
$89$	7.87663	+	4.54758i	0.834921	+	0.482042i	−0.0206134	+	0.999788i	$0.506562\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−4.49748	−	2.59662i	−0.471464	−	0.272200i
$92$	3.66160	−	2.11403i	0.381748	−	0.220403i
$93$	−4.46086	+	2.57548i	−0.462570	+	0.267065i
$94$	−6.59356	−	3.80679i	−0.680074	−	0.392641i
$95$	−3.25938	+	5.64541i	−0.334405	+	0.579207i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$		−	2.17225i		−	0.220558i	−0.993901	−	0.110279i	$-0.964826\pi$
$97$		−	2.17225i		−	0.220558i	0.993901	−	0.110279i	$-0.0351745\pi$
$98$	−5.40467	+	3.12039i	−0.545954	+	0.315207i
$99$	−0.564101	+	0.977051i	−0.0566942	+	0.0981973i
$100$	1.00000			0.100000
$101$	−4.72751			−0.470405			−0.235202	−	0.971946i	$-0.575575\pi$
$101$	−4.72751			−0.470405			−0.235202	+	0.971946i	$0.575575\pi$
$102$	0.935667	−	1.62062i	0.0926448	−	0.160465i
$103$		−	5.43512i		−	0.535538i	−0.963483	−	0.267769i	$-0.913714\pi$
$103$		−	5.43512i		−	0.535538i	0.963483	−	0.267769i	$-0.0862864\pi$
$104$	2.98005	+	5.16160i	0.292218	+	0.506137i
$105$			0.871333i			0.0850334i
$106$	−9.65501	+	5.57432i	−0.937777	+	0.541426i
$107$	−8.33163	−	14.4308i	−0.805449	−	1.39508i	−0.915988	−	0.401206i	$-0.868591\pi$
$107$	−8.33163	−	14.4308i	−0.805449	−	1.39508i	0.110539	−	0.993872i	$-0.464742\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	14.5230	+	8.38487i	1.39105	+	0.803125i	0.993432	−	0.114424i	$-0.0365023\pi$
$109$	14.5230	+	8.38487i	1.39105	+	0.803125i	0.397622	+	0.917549i	$0.369836\pi$
$110$	1.12820			0.107570
$111$	6.00063	−	0.996242i	0.569554	−	0.0945591i
$112$	−0.871333			−0.0823332
$113$	−7.42944	−	4.28939i	−0.698903	−	0.403512i	0.108036	−	0.994147i	$-0.465544\pi$
$113$	−7.42944	−	4.28939i	−0.698903	−	0.403512i	−0.806939	+	0.590635i	$0.798877\pi$
$114$	3.25938	+	5.64541i	0.305269	+	0.528741i
$115$	2.11403	+	3.66160i	0.197134	+	0.341446i
$116$	3.60443	−	2.08102i	0.334663	−	0.193218i
$117$		−	5.96011i		−	0.551012i
$118$	1.13698	+	1.96930i	0.104667	+	0.181289i
$119$		−	1.63055i		−	0.149473i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−9.72716			−0.884287
$122$	−4.85483			−0.439536
$123$	−5.31389	+	9.20392i	−0.479137	+	0.829890i
$124$	4.46086	−	2.57548i	0.400597	−	0.231285i
$125$			1.00000i			0.0894427i
$126$	0.754597	+	0.435667i	0.0672248	+	0.0388123i
$127$	−8.08310	+	14.0003i	−0.717259	+	1.24233i	0.244823	+	0.969568i	$0.421270\pi$
$127$	−8.08310	+	14.0003i	−0.717259	+	1.24233i	−0.962082	+	0.272761i	$0.912063\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.12246	−	4.68951i	0.715143	−	0.412888i
$130$	−5.16160	+	2.98005i	−0.452703	+	0.261368i
$131$	−4.90282	−	2.83065i	−0.428361	−	0.247315i	0.270287	−	0.962780i	$-0.412881\pi$
$131$	−4.90282	−	2.83065i	−0.428361	−	0.247315i	−0.698648	+	0.715465i	$0.746215\pi$
$132$	0.564101	−	0.977051i	0.0490987	−	0.0850414i
$133$	4.91904	+	2.84001i	0.426535	+	0.246260i
$134$			14.1455i			1.22199i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	−0.935667	+	1.62062i	−0.0802327	+	0.138967i
$137$	−16.5057			−1.41018			−0.705088	−	0.709120i	$-0.749093\pi$
$137$	−16.5057			−1.41018			−0.705088	+	0.709120i	$0.749093\pi$
$138$	4.22805			0.359916
$139$	8.84982	−	15.3283i	0.750632	−	1.30013i	−0.196885	−	0.980427i	$-0.563083\pi$
$139$	8.84982	−	15.3283i	0.750632	−	1.30013i	0.947517	−	0.319706i	$-0.103584\pi$
$140$		−	0.871333i		−	0.0736411i
$141$	−3.80679	−	6.59356i	−0.320590	−	0.555278i
$142$			15.1163i			1.26853i
$143$	−5.82333	+	3.36210i	−0.486971	+	0.281153i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.08102	+	3.60443i	0.172819	+	0.299332i
$146$	3.84198	+	2.21817i	0.317964	+	0.183577i
$147$	−6.24078			−0.514731
$148$	−6.00063	+	0.996242i	−0.493248	+	0.0818906i
$149$	16.5978			1.35975			0.679873	−	0.733330i	$-0.262035\pi$
$149$	16.5978			1.35975			0.679873	+	0.733330i	$0.262035\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	7.15224	+	12.3880i	0.582041	+	1.00812i	0.995237	+	0.0974827i	$0.0310791\pi$
$151$	7.15224	+	12.3880i	0.582041	+	1.00812i	−0.413196	+	0.910642i	$0.635588\pi$
$152$	−3.25938	−	5.64541i	−0.264371	−	0.457903i
$153$	1.62062	−	0.935667i	0.131020	−	0.0756442i
$154$		−	0.983039i		−	0.0792156i
$155$	2.57548	+	4.46086i	0.206868	+	0.358305i
$156$			5.96011i			0.477190i
$157$	9.11409	−	15.7861i	0.727383	−	1.25986i	−0.230602	−	0.973048i	$-0.574070\pi$
$157$	9.11409	−	15.7861i	0.727383	−	1.25986i	0.957985	−	0.286817i	$-0.0925971\pi$
$158$	11.6363			0.925738
$159$	−11.1486			−0.884145
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	3.19048	−	1.84202i	0.251445	−	0.145172i
$162$			1.00000i			0.0785674i
$163$	−5.43671	−	3.13889i	−0.425836	−	0.245857i	0.271735	−	0.962372i	$-0.412403\pi$
$163$	−5.43671	−	3.13889i	−0.425836	−	0.245857i	−0.697571	+	0.716516i	$0.745736\pi$
$164$	5.31389	−	9.20392i	0.414945	−	0.718706i
$165$	0.977051	+	0.564101i	0.0760633	+	0.0439152i
$166$	4.28659	−	2.47486i	0.332704	−	0.192087i
$167$	6.40836	−	3.69987i	0.495894	−	0.286304i	−0.231123	−	0.972925i	$-0.574240\pi$
$167$	6.40836	−	3.69987i	0.495894	−	0.286304i	0.727016	+	0.686620i	$0.240907\pi$
$168$	−0.754597	−	0.435667i	−0.0582184	−	0.0336124i
$169$	11.2614	−	19.5054i	0.866264	−	1.50041i
$170$	−1.62062	−	0.935667i	−0.124296	−	0.0717624i
$171$			6.51876i			0.498502i
$172$	−8.12246	+	4.68951i	−0.619332	+	0.357572i
$173$	5.21856	−	9.03881i	0.396760	−	0.687208i	−0.596564	−	0.802565i	$-0.703468\pi$
$173$	5.21856	−	9.03881i	0.396760	−	0.687208i	0.993324	+	0.115357i	$0.0368012\pi$
$174$	4.16204			0.315523
$175$	0.871333			0.0658666
$176$	−0.564101	+	0.977051i	−0.0425207	+	0.0736480i
$177$			2.27395i			0.170921i
$178$	−4.54758	−	7.87663i	−0.340855	−	0.590379i
$179$			8.74992i			0.653999i	0.945024	+	0.327000i	$0.106038\pi$
$179$			8.74992i			0.653999i	−0.945024	+	0.327000i	$0.893962\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−7.65366	−	13.2565i	−0.568892	−	0.985350i	−0.996676	−	0.0814692i	$-0.974039\pi$
$181$	−7.65366	−	13.2565i	−0.568892	−	0.985350i	0.427784	−	0.903881i	$-0.359295\pi$
$182$	2.59662	+	4.49748i	0.192474	+	0.333375i
$183$	−4.20441	−	2.42742i	−0.310799	−	0.179440i
$184$	−4.22805			−0.311696
$185$	−0.996242	−	6.00063i	−0.0732452	−	0.441175i
$186$	5.15096			0.377687
$187$	−1.82839	−	1.05562i	−0.133705	−	0.0771946i
$188$	3.80679	+	6.59356i	0.277639	+	0.480885i
$189$	0.435667	+	0.754597i	0.0316901	+	0.0548888i
$190$	5.64541	−	3.25938i	0.409561	−	0.236460i
$191$			17.4079i			1.25959i	0.776761	+	0.629796i	$0.216861\pi$
$191$			17.4079i			1.25959i	−0.776761	+	0.629796i	$0.783139\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$		−	18.8491i		−	1.35679i	−0.734698	−	0.678395i	$-0.762676\pi$
$193$		−	18.8491i		−	1.35679i	0.734698	−	0.678395i	$-0.237324\pi$
$194$	−1.08612	+	1.88122i	−0.0779791	+	0.135064i
$195$	−5.96011			−0.426812
$196$	6.24078			0.445770
$197$	0.306829	−	0.531443i	0.0218607	−	0.0378638i	−0.854888	−	0.518812i	$-0.826374\pi$
$197$	0.306829	−	0.531443i	0.0218607	−	0.0378638i	0.876749	+	0.480949i	$0.159708\pi$
$198$	0.977051	−	0.564101i	0.0694360	−	0.0400889i
$199$			23.3952i			1.65844i	0.558920	+	0.829222i	$0.311216\pi$
$199$			23.3952i			1.65844i	−0.558920	+	0.829222i	$0.688784\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−7.07277	+	12.2504i	−0.498875	+	0.864076i
$202$	4.09414	+	2.36375i	0.288063	+	0.166313i
$203$	3.14066	−	1.81326i	0.220431	−	0.127266i
$204$	−1.62062	+	0.935667i	−0.113466	+	0.0655098i
$205$	9.20392	+	5.31389i	0.642830	+	0.371138i
$206$	−2.71756	+	4.70695i	−0.189341	+	0.327949i
$207$	3.66160	+	2.11403i	0.254499	+	0.146935i
$208$		−	5.96011i		−	0.413259i
$209$	6.36916	−	3.67724i	0.440564	−	0.254360i
$210$	0.435667	−	0.754597i	0.0300639	−	0.0520721i
$211$	21.1872			1.45859			0.729295	−	0.684199i	$-0.239848\pi$
$211$	21.1872			1.45859			0.729295	+	0.684199i	$0.239848\pi$
$212$	11.1486			0.765692
$213$	−7.55813	+	13.0911i	−0.517875	+	0.896985i
$214$			16.6633i			1.13908i
$215$	−4.68951	−	8.12246i	−0.319822	−	0.553947i
$216$		−	1.00000i		−	0.0680414i
$217$	3.88690	−	2.24410i	0.263860	−	0.152339i
$218$	−8.38487	−	14.5230i	−0.567895	−	0.983623i
$219$	2.21817	+	3.84198i	0.149890	+	0.259617i
$220$	−0.977051	−	0.564101i	−0.0658728	−	0.0380317i
$221$	11.1533			0.750255
$222$	−5.69481	−	2.13754i	−0.382211	−	0.143462i
$223$	15.4416			1.03405			0.517024	−	0.855971i	$-0.327040\pi$
$223$	15.4416			1.03405			0.517024	+	0.855971i	$0.327040\pi$
$224$	0.754597	+	0.435667i	0.0504186	+	0.0291092i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	4.28939	+	7.42944i	0.285326	+	0.494199i
$227$	3.86623	−	2.23217i	0.256611	−	0.148154i	−0.366177	−	0.930545i	$-0.619333\pi$
$227$	3.86623	−	2.23217i	0.256611	−	0.148154i	0.622788	+	0.782391i	$0.286000\pi$
$228$		−	6.51876i		−	0.431716i
$229$	8.13293	+	14.0866i	0.537439	+	0.930872i	0.999041	+	0.0437847i	$0.0139416\pi$
$229$	8.13293	+	14.0866i	0.537439	+	0.930872i	−0.461602	+	0.887087i	$0.652725\pi$
$230$		−	4.22805i		−	0.278790i
$231$	0.491520	−	0.851337i	0.0323396	−	0.0560139i
$232$	−4.16204			−0.273251
$233$	3.64777			0.238973			0.119487	−	0.992836i	$-0.461875\pi$
$233$	3.64777			0.238973			0.119487	+	0.992836i	$0.461875\pi$
$234$	−2.98005	+	5.16160i	−0.194812	+	0.337425i
$235$	−6.59356	+	3.80679i	−0.430117	+	0.248328i
$236$		−	2.27395i		−	0.148022i
$237$	10.0774	+	5.81817i	0.654596	+	0.377931i
$238$	−0.815277	+	1.41210i	−0.0528466	+	0.0915330i
$239$	6.62403	+	3.82438i	0.428473	+	0.247379i	0.698696	−	0.715419i	$-0.253764\pi$
$239$	6.62403	+	3.82438i	0.428473	+	0.247379i	−0.270223	+	0.962798i	$0.587097\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	−18.8434	+	10.8793i	−1.21381	+	0.700794i	−0.963587	−	0.267394i	$-0.913838\pi$
$241$	−18.8434	+	10.8793i	−1.21381	+	0.700794i	−0.250224	+	0.968188i	$0.580504\pi$
$242$	8.42397	+	4.86358i	0.541513	+	0.312643i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	4.20441	+	2.42742i	0.269160	+	0.155399i
$245$			6.24078i			0.398709i
$246$	9.20392	−	5.31389i	0.586821	−	0.338801i
$247$	−19.4263	+	33.6473i	−1.23606	+	2.14092i
$248$	−5.15096			−0.327086
$249$	4.94973			0.313676
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			0.241710i			0.0152566i	0.999971	+	0.00762829i	$0.00242818\pi$
$251$			0.241710i			0.0152566i	−0.999971	+	0.00762829i	$0.997572\pi$
$252$	−0.435667	−	0.754597i	−0.0274444	−	0.0475351i
$253$		−	4.77010i		−	0.299893i
$254$	14.0003	−	8.08310i	0.878459	−	0.507179i
$255$	−0.935667	−	1.62062i	−0.0585937	−	0.101487i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.5141	+	12.4212i	1.34201	+	0.774810i	0.987102	−	0.160091i	$-0.0511787\pi$
$257$	21.5141	+	12.4212i	1.34201	+	0.774810i	0.354909	+	0.934901i	$0.384512\pi$
$258$	−9.37901			−0.583912
$259$	−5.22854	+	0.868059i	−0.324886	+	0.0539385i
$260$	5.96011			0.369630
$261$	3.60443	+	2.08102i	0.223109	+	0.128812i
$262$	2.83065	+	4.90282i	0.174878	+	0.302897i
$263$	−1.71221	−	2.96564i	−0.105580	−	0.182869i	0.808395	−	0.588640i	$-0.200336\pi$
$263$	−1.71221	−	2.96564i	−0.105580	−	0.182869i	−0.913975	+	0.405771i	$0.867003\pi$
$264$	−0.977051	+	0.564101i	−0.0601333	+	0.0347180i
$265$			11.1486i			0.684856i
$266$	−2.84001	−	4.91904i	−0.174132	−	0.301605i
$267$		−	9.09515i		−	0.556614i
$268$	7.07277	−	12.2504i	0.432038	−	0.748312i
$269$	32.4772			1.98017			0.990084	−	0.140479i	$-0.0448644\pi$
$269$	32.4772			1.98017			0.990084	+	0.140479i	$0.0448644\pi$
$270$	1.00000			0.0608581
$271$	−3.74795	+	6.49164i	−0.227672	+	0.394339i	−0.957118	−	0.289699i	$-0.906445\pi$
$271$	−3.74795	+	6.49164i	−0.227672	+	0.394339i	0.729446	+	0.684039i	$0.239778\pi$
$272$	1.62062	−	0.935667i	0.0982646	−	0.0567331i
$273$			5.19324i			0.314309i
$274$	14.2943	+	8.25285i	0.863553	+	0.498573i
$275$	0.564101	−	0.977051i	0.0340165	−	0.0589184i
$276$	−3.66160	−	2.11403i	−0.220403	−	0.127249i
$277$	−4.86420	+	2.80834i	−0.292261	+	0.168737i	−0.638961	−	0.769239i	$-0.720636\pi$
$277$	−4.86420	+	2.80834i	−0.292261	+	0.168737i	0.346700	+	0.937976i	$0.387302\pi$
$278$	−15.3283	+	8.84982i	−0.919332	+	0.530777i
$279$	4.46086	+	2.57548i	0.267065	+	0.154190i
$280$	−0.435667	+	0.754597i	−0.0260361	+	0.0450958i
$281$	−17.9392	−	10.3572i	−1.07016	−	0.617860i	−0.141938	−	0.989876i	$-0.545333\pi$
$281$	−17.9392	−	10.3572i	−1.07016	−	0.617860i	−0.928226	+	0.372016i	$0.878667\pi$
$282$			7.61359i			0.453383i
$283$	8.44311	−	4.87463i	0.501891	−	0.289767i	−0.227603	−	0.973754i	$-0.573089\pi$
$283$	8.44311	−	4.87463i	0.501891	−	0.289767i	0.729494	+	0.683987i	$0.239756\pi$
$284$	7.55813	−	13.0911i	0.448493	−	0.776812i
$285$	6.51876			0.386138
$286$	6.72420			0.397610
$287$	4.63017	−	8.01968i	0.273310	−	0.473387i
$288$			1.00000i			0.0589256i
$289$	−6.74906	−	11.6897i	−0.397003	−	0.687630i
$290$		−	4.16204i		−	0.244403i
$291$	−1.88122	+	1.08612i	−0.110279	+	0.0636697i
$292$	−2.21817	−	3.84198i	−0.129808	−	0.224835i
$293$	9.36994	+	16.2292i	0.547398	+	0.948121i	0.998452	+	0.0556243i	$0.0177149\pi$
$293$	9.36994	+	16.2292i	0.547398	+	0.948121i	−0.451054	+	0.892497i	$0.648952\pi$
$294$	5.40467	+	3.12039i	0.315207	+	0.181985i
$295$	2.27395			0.132395
$296$	5.69481	+	2.13754i	0.331004	+	0.124242i
$297$	1.12820			0.0654649
$298$	−14.3741	−	8.29891i	−0.832671	−	0.480743i
$299$	12.5998	+	21.8235i	0.728667	+	1.26209i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−7.07737	+	4.08612i	−0.407933	+	0.235520i
$302$		−	14.3045i		−	0.823130i
$303$	2.36375	+	4.09414i	0.135794	+	0.235202i
$304$			6.51876i			0.373877i
$305$	−2.42742	+	4.20441i	−0.138993	+	0.240744i
$306$	−1.87133			−0.106977
$307$	26.2743			1.49955			0.749776	−	0.661692i	$-0.230161\pi$
$307$	26.2743			1.49955			0.749776	+	0.661692i	$0.230161\pi$
$308$	−0.491520	+	0.851337i	−0.0280069	+	0.0485094i
$309$	−4.70695	+	2.71756i	−0.267769	+	0.154597i
$310$		−	5.15096i		−	0.292555i
$311$	−28.9868	−	16.7355i	−1.64369	−	0.948984i	−0.979506	−	0.201414i	$-0.935446\pi$
$311$	−28.9868	−	16.7355i	−1.64369	−	0.948984i	−0.664182	−	0.747571i	$-0.731220\pi$
$312$	2.98005	−	5.16160i	0.168712	−	0.292218i
$313$	−1.72710	−	0.997143i	−0.0976216	−	0.0563619i	0.450394	−	0.892830i	$-0.351283\pi$
$313$	−1.72710	−	0.997143i	−0.0976216	−	0.0563619i	−0.548016	+	0.836468i	$0.684617\pi$
$314$	−15.7861	+	9.11409i	−0.890859	+	0.514338i
$315$	0.754597	−	0.435667i	0.0425167	−	0.0245470i
$316$	−10.0774	−	5.81817i	−0.566897	−	0.327298i
$317$	−2.99369	+	5.18523i	−0.168143	+	0.291232i	−0.937767	−	0.347266i	$-0.887110\pi$
$317$	−2.99369	+	5.18523i	−0.168143	+	0.291232i	0.769624	+	0.638497i	$0.220444\pi$
$318$	9.65501	+	5.57432i	0.541426	+	0.312592i
$319$		−	4.69562i		−	0.262904i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−8.33163	+	14.4308i	−0.465026	+	0.805449i
$322$	−3.68404			−0.205304
$323$	−12.1988			−0.678758
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			5.96011i			0.330607i
$326$	3.13889	+	5.43671i	0.173847	+	0.301112i
$327$		−	16.7697i		−	0.927369i
$328$	−9.20392	+	5.31389i	−0.508202	+	0.293410i
$329$	3.31699	+	5.74519i	0.182871	+	0.316743i
$330$	−0.564101	−	0.977051i	−0.0310527	−	0.0537849i
$331$	−16.1475	−	9.32279i	−0.887549	−	0.512427i	−0.0144090	−	0.999896i	$-0.504587\pi$
$331$	−16.1475	−	9.32279i	−0.887549	−	0.512427i	−0.873140	+	0.487470i	$0.837920\pi$
$332$	−4.94973			−0.271652
$333$	−3.86308	−	4.69857i	−0.211696	−	0.257480i
$334$	−7.39973			−0.404895
$335$	12.2504	+	7.07277i	0.669311	+	0.386427i
$336$	0.435667	+	0.754597i	0.0237676	+	0.0411666i
$337$	0.597607	+	1.03509i	0.0325538	+	0.0563848i	0.881843	−	0.471543i	$-0.156303\pi$
$337$	0.597607	+	1.03509i	0.0325538	+	0.0563848i	−0.849290	+	0.527927i	$0.822969\pi$
$338$	−19.5054	+	11.2614i	−1.06095	+	0.612541i
$339$			8.57878i			0.465935i
$340$	0.935667	+	1.62062i	0.0507436	+	0.0878906i
$341$		−	5.81132i		−	0.314701i
$342$	3.25938	−	5.64541i	0.176247	−	0.305269i
$343$	11.5371			0.622946
$344$	9.37901			0.505683
$345$	2.11403	−	3.66160i	0.113815	−	0.197134i
$346$	−9.03881	+	5.21856i	−0.485930	+	0.280552i
$347$			5.89358i			0.316384i	0.987408	+	0.158192i	$0.0505665\pi$
$347$			5.89358i			0.316384i	−0.987408	+	0.158192i	$0.949434\pi$
$348$	−3.60443	−	2.08102i	−0.193218	−	0.111554i
$349$	7.13276	−	12.3543i	0.381808	−	0.661311i	−0.609513	−	0.792776i	$-0.708635\pi$
$349$	7.13276	−	12.3543i	0.381808	−	0.661311i	0.991321	+	0.131465i	$0.0419682\pi$
$350$	−0.754597	−	0.435667i	−0.0403349	−	0.0232874i
$351$	−5.16160	+	2.98005i	−0.275506	+	0.159063i
$352$	0.977051	−	0.564101i	0.0520770	−	0.0300667i
$353$	14.6158	+	8.43844i	0.777921	+	0.449133i	0.835693	−	0.549197i	$-0.185066\pi$
$353$	14.6158	+	8.43844i	0.777921	+	0.449133i	−0.0577722	+	0.998330i	$0.518400\pi$
$354$	1.13698	−	1.96930i	0.0604296	−	0.104667i
$355$	13.0911	+	7.55813i	0.694802	+	0.401144i
$356$			9.09515i			0.482042i
$357$	−1.41210	+	0.815277i	−0.0747364	+	0.0431491i
$358$	4.37496	−	7.57765i	0.231224	−	0.400491i
$359$	−8.99932			−0.474966			−0.237483	−	0.971392i	$-0.576322\pi$
$359$	−8.99932			−0.474966			−0.237483	+	0.971392i	$0.576322\pi$
$360$	−1.00000			−0.0527046
$361$	11.7471	−	20.3466i	0.618270	−	1.07087i
$362$			15.3073i			0.804535i
$363$	4.86358	+	8.42397i	0.255272	+	0.442144i
$364$		−	5.19324i		−	0.272200i
$365$	3.84198	−	2.21817i	0.201098	−	0.116104i
$366$	2.42742	+	4.20441i	0.126883	+	0.219768i
$367$	6.20181	+	10.7419i	0.323732	+	0.560720i	0.981255	−	0.192714i	$-0.0617290\pi$
$367$	6.20181	+	10.7419i	0.323732	+	0.560720i	−0.657523	+	0.753435i	$0.728396\pi$
$368$	3.66160	+	2.11403i	0.190874	+	0.110201i
$369$	10.6278			0.553260
$370$	−2.13754	+	5.69481i	−0.111126	+	0.296059i
$371$	9.71418			0.504335
$372$	−4.46086	−	2.57548i	−0.231285	−	0.133532i
$373$	−5.45850	−	9.45441i	−0.282631	−	0.489531i	0.689401	−	0.724380i	$-0.257874\pi$
$373$	−5.45850	−	9.45441i	−0.282631	−	0.489531i	−0.972032	+	0.234849i	$0.924540\pi$
$374$	1.05562	+	1.82839i	0.0545848	+	0.0945437i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		−	7.61359i		−	0.392641i
$377$	12.4031	+	21.4828i	0.638792	+	1.10642i
$378$		−	0.871333i		−	0.0448165i
$379$	11.4000	−	19.7454i	0.585578	−	1.01425i	−0.409225	−	0.912434i	$-0.634201\pi$
$379$	11.4000	−	19.7454i	0.585578	−	1.01425i	0.994803	−	0.101818i	$-0.0324659\pi$
$380$	−6.51876			−0.334405
$381$	16.1662			0.828219
$382$	8.70395	−	15.0757i	0.445333	−	0.771339i
$383$	−22.5335	+	13.0097i	−1.15141	+	0.664767i	−0.949230	−	0.314582i	$-0.898136\pi$
$383$	−22.5335	+	13.0097i	−1.15141	+	0.664767i	−0.202180	+	0.979348i	$0.564802\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−0.851337	−	0.491520i	−0.0433881	−	0.0250502i
$386$	−9.42456	+	16.3238i	−0.479697	+	0.830860i
$387$	−8.12246	−	4.68951i	−0.412888	−	0.238381i
$388$	1.88122	−	1.08612i	0.0955045	−	0.0551395i
$389$	−31.1670	+	17.9943i	−1.58023	+	0.912345i	−0.585403	+	0.810743i	$0.699064\pi$
$389$	−31.1670	+	17.9943i	−1.58023	+	0.912345i	−0.994825	+	0.101602i	$0.967603\pi$
$390$	5.16160	+	2.98005i	0.261368	+	0.150901i
$391$	−3.95605	+	6.85208i	−0.200066	+	0.346525i
$392$	−5.40467	−	3.12039i	−0.272977	−	0.157603i
$393$			5.66129i			0.285574i
$394$	−0.531443	+	0.306829i	−0.0267737	+	0.0154578i
$395$	5.81817	−	10.0774i	0.292744	−	0.507048i
$396$	−1.12820			−0.0566942
$397$	−16.2648			−0.816306			−0.408153	−	0.912914i	$-0.633827\pi$
$397$	−16.2648			−0.816306			−0.408153	+	0.912914i	$0.633827\pi$
$398$	11.6976	−	20.2609i	0.586348	−	1.01559i
$399$		−	5.68001i		−	0.284356i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$		−	33.5429i		−	1.67505i	−0.546397	−	0.837527i	$-0.684001\pi$
$401$		−	33.5429i		−	1.67505i	0.546397	−	0.837527i	$-0.315999\pi$
$402$	12.2504	−	7.07277i	0.610994	−	0.352758i
$403$	15.3501	+	26.5872i	0.764644	+	1.32440i
$404$	−2.36375	−	4.09414i	−0.117601	−	0.203691i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−3.62652			−0.179981
$407$	−2.41158	+	6.42490i	−0.119537	+	0.318470i
$408$	1.87133			0.0926448
$409$	−9.51451	−	5.49320i	−0.470462	−	0.271621i	0.245971	−	0.969277i	$-0.420893\pi$
$409$	−9.51451	−	5.49320i	−0.470462	−	0.271621i	−0.716433	+	0.697656i	$0.754227\pi$
$410$	−5.31389	−	9.20392i	−0.262434	−	0.454549i
$411$	8.25285	+	14.2943i	0.407083	+	0.705088i
$412$	4.70695	−	2.71756i	0.231895	−	0.133885i
$413$		−	1.98137i		−	0.0974969i
$414$	−2.11403	−	3.66160i	−0.103899	−	0.179958i
$415$		−	4.94973i		−	0.242973i
$416$	−2.98005	+	5.16160i	−0.146109	+	0.253068i
$417$	−17.6996			−0.866755
$418$	−7.35448			−0.359719
$419$	−16.6045	+	28.7598i	−0.811181	+	1.40501i	0.100858	+	0.994901i	$0.467841\pi$
$419$	−16.6045	+	28.7598i	−0.811181	+	1.40501i	−0.912038	+	0.410105i	$0.865492\pi$
$420$	−0.754597	+	0.435667i	−0.0368205	+	0.0212584i
$421$		−	17.5126i		−	0.853512i	−0.904367	−	0.426756i	$-0.859656\pi$
$421$		−	17.5126i		−	0.853512i	0.904367	−	0.426756i	$-0.140344\pi$
$422$	−18.3487	−	10.5936i	−0.893200	−	0.515689i
$423$	−3.80679	+	6.59356i	−0.185093	+	0.320590i
$424$	−9.65501	−	5.57432i	−0.468889	−	0.270713i
$425$	−1.62062	+	0.935667i	−0.0786117	+	0.0453865i
$426$	13.0911	−	7.55813i	0.634264	−	0.366193i
$427$	3.66344	+	2.11509i	0.177286	+	0.102356i
$428$	8.33163	−	14.4308i	0.402724	−	0.697539i
$429$	5.82333	+	3.36210i	0.281153	+	0.162324i
$430$			9.37901i			0.452296i
$431$	−20.2700	+	11.7029i	−0.976372	+	0.563709i	−0.901173	−	0.433460i	$-0.857293\pi$
$431$	−20.2700	+	11.7029i	−0.976372	+	0.563709i	−0.0751993	+	0.997169i	$0.523959\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	8.47827			0.407439			0.203720	−	0.979029i	$-0.434697\pi$
$433$	8.47827			0.407439			0.203720	+	0.979029i	$0.434697\pi$
$434$	−4.48820			−0.215441
$435$	2.08102	−	3.60443i	0.0997773	−	0.172819i
$436$			16.7697i			0.803125i
$437$	−13.7808	−	23.8691i	−0.659227	−	1.14181i
$438$		−	4.43634i		−	0.211976i
$439$	−2.06183	+	1.19040i	−0.0984056	+	0.0568145i	−0.548395	−	0.836219i	$-0.684761\pi$
$439$	−2.06183	+	1.19040i	−0.0984056	+	0.0568145i	0.449990	+	0.893034i	$0.351428\pi$
$440$	0.564101	+	0.977051i	0.0268924	+	0.0465791i
$441$	3.12039	+	5.40467i	0.148590	+	0.257365i
$442$	−9.65908	−	5.57667i	−0.459436	−	0.265255i
$443$	−3.83814			−0.182355			−0.0911777	−	0.995835i	$-0.529063\pi$
$443$	−3.83814			−0.182355			−0.0911777	+	0.995835i	$0.529063\pi$
$444$	3.86308	+	4.69857i	0.183334	+	0.222984i
$445$	−9.09515			−0.431151
$446$	−13.3728	−	7.72081i	−0.633222	−	0.365591i
$447$	−8.29891	−	14.3741i	−0.392525	−	0.679873i
$448$	−0.435667	−	0.754597i	−0.0205833	−	0.0356513i
$449$	−12.2708	+	7.08457i	−0.579097	+	0.334342i	−0.760774	−	0.649017i	$-0.775181\pi$
$449$	−12.2708	+	7.08457i	−0.579097	+	0.334342i	0.181678	+	0.983358i	$0.441847\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−5.99513	−	10.3839i	−0.282300	−	0.488958i
$452$		−	8.57878i		−	0.403512i
$453$	7.15224	−	12.3880i	0.336042	−	0.582041i
$454$	−4.46434			−0.209522
$455$	5.19324			0.243463
$456$	−3.25938	+	5.64541i	−0.152634	+	0.264371i
$457$	10.7010	−	6.17825i	0.500574	−	0.289006i	−0.228377	−	0.973573i	$-0.573342\pi$
$457$	10.7010	−	6.17825i	0.500574	−	0.289006i	0.728950	+	0.684566i	$0.240008\pi$
$458$		−	16.2659i		−	0.760054i
$459$	−1.62062	−	0.935667i	−0.0756442	−	0.0436732i
$460$	−2.11403	+	3.66160i	−0.0985670	+	0.170723i
$461$	31.2722	+	18.0550i	1.45649	+	0.840905i	0.998837	−	0.0482247i	$-0.0153564\pi$
$461$	31.2722	+	18.0550i	1.45649	+	0.840905i	0.457654	+	0.889130i	$0.348690\pi$
$462$	−0.851337	+	0.491520i	−0.0396078	+	0.0228676i
$463$	−21.4520	+	12.3853i	−0.996960	+	0.575595i	−0.907347	−	0.420382i	$-0.861896\pi$
$463$	−21.4520	+	12.3853i	−0.996960	+	0.575595i	−0.0896122	+	0.995977i	$0.528563\pi$
$464$	3.60443	+	2.08102i	0.167332	+	0.0966089i
$465$	2.57548	−	4.46086i	0.119435	−	0.206868i
$466$	−3.15906	−	1.82389i	−0.146341	−	0.0844899i
$467$			0.754892i			0.0349322i	0.999847	+	0.0174661i	$0.00555992\pi$
$467$			0.754892i			0.0349322i	−0.999847	+	0.0174661i	$0.994440\pi$
$468$	5.16160	−	2.98005i	0.238595	−	0.137753i
$469$	6.16274	−	10.6742i	0.284569	−	0.492888i
$470$	7.61359			0.351189
$471$	−18.2282			−0.839910
$472$	−1.13698	+	1.96930i	−0.0523336	+	0.0906444i
$473$			10.5814i			0.486534i
$474$	−5.81817	−	10.0774i	−0.267238	−	0.462869i
$475$		−	6.51876i		−	0.299101i
$476$	1.41210	−	0.815277i	0.0647236	−	0.0373682i
$477$	5.57432	+	9.65501i	0.255231	+	0.442072i
$478$	−3.82438	−	6.62403i	−0.174923	−	0.302976i
$479$	−13.3889	−	7.73007i	−0.611753	−	0.353196i	0.161898	−	0.986808i	$-0.448238\pi$
$479$	−13.3889	−	7.73007i	−0.611753	−	0.353196i	−0.773651	+	0.633611i	$0.781572\pi$
$480$	1.00000			0.0456435
$481$	−5.93771	−	35.7644i	−0.270736	−	1.63071i
$482$	21.7585			0.991073
$483$	−3.19048	−	1.84202i	−0.145172	−	0.0838149i
$484$	−4.86358	−	8.42397i	−0.221072	−	0.382908i
$485$	1.08612	+	1.88122i	0.0493183	+	0.0854218i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	33.7547i		−	1.52957i	−0.644283	−	0.764787i	$-0.722844\pi$
$487$		−	33.7547i		−	1.52957i	0.644283	−	0.764787i	$-0.277156\pi$
$488$	−2.42742	−	4.20441i	−0.109884	−	0.190325i
$489$			6.27777i			0.283891i
$490$	3.12039	−	5.40467i	0.140965	−	0.244158i
$491$	−9.71651			−0.438500			−0.219250	−	0.975669i	$-0.570361\pi$
$491$	−9.71651			−0.438500			−0.219250	+	0.975669i	$0.570361\pi$
$492$	−10.6278			−0.479137
$493$	−3.89428	+	6.74509i	−0.175390	+	0.303784i
$494$	33.6473	−	19.4263i	1.51386	−	0.874029i
$495$		−	1.12820i		−	0.0507089i
$496$	4.46086	+	2.57548i	0.200299	+	0.115642i
$497$	6.58565	−	11.4067i	0.295407	−	0.511660i
$498$	−4.28659	−	2.47486i	−0.192087	−	0.110901i
$499$	8.26563	−	4.77216i	0.370020	−	0.213631i	−0.303447	−	0.952848i	$-0.598138\pi$
$499$	8.26563	−	4.77216i	0.370020	−	0.213631i	0.673467	+	0.739217i	$0.264804\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−6.40836	−	3.69987i	−0.286304	−	0.165298i
$502$	0.120855	−	0.209327i	0.00539402	−	0.00934271i
$503$	−6.69477	−	3.86523i	−0.298505	−	0.172342i	0.343266	−	0.939238i	$-0.388467\pi$
$503$	−6.69477	−	3.86523i	−0.298505	−	0.172342i	−0.641771	+	0.766896i	$0.721800\pi$
$504$			0.871333i			0.0388123i
$505$	4.09414	−	2.36375i	0.182187	−	0.105186i
$506$	−2.38505	+	4.13102i	−0.106028	+	0.183646i
$507$	−22.5229			−1.00028
$508$	−16.1662			−0.717259
$509$	−10.0860	+	17.4694i	−0.447052	+	0.774317i	−0.998193	−	0.0600954i	$-0.980859\pi$
$509$	−10.0860	+	17.4694i	−0.447052	+	0.774317i	0.551140	+	0.834412i	$0.314193\pi$
$510$			1.87133i			0.0828640i
$511$	−1.93276	−	3.34764i	−0.0855004	−	0.148091i
$512$			1.00000i			0.0441942i
$513$	5.64541	−	3.25938i	0.249251	−	0.143905i
$514$	−12.4212	−	21.5141i	−0.547874	−	0.948945i
$515$	2.71756	+	4.70695i	0.119750	+	0.207413i
$516$	8.12246	+	4.68951i	0.357572	+	0.206444i
$517$	8.58966			0.377773
$518$	4.96208	+	1.86251i	0.218021	+	0.0818340i
$519$	−10.4371			−0.458139
$520$	−5.16160	−	2.98005i	−0.226351	−	0.130684i
$521$	−6.83008	−	11.8301i	−0.299231	−	0.518284i	0.676729	−	0.736232i	$-0.263397\pi$
$521$	−6.83008	−	11.8301i	−0.299231	−	0.518284i	−0.975960	+	0.217948i	$0.930064\pi$
$522$	−2.08102	−	3.60443i	−0.0910838	−	0.157762i
$523$	−16.6298	+	9.60120i	−0.727169	+	0.419831i	−0.817386	−	0.576091i	$-0.804577\pi$
$523$	−16.6298	+	9.60120i	−0.727169	+	0.419831i	0.0902166	+	0.995922i	$0.471244\pi$
$524$		−	5.66129i		−	0.247315i
$525$	−0.435667	−	0.754597i	−0.0190140	−	0.0329333i
$526$			3.42443i			0.149312i
$527$	−4.81958	+	8.34776i	−0.209944	+	0.363634i
$528$	1.12820			0.0490987
$529$	5.12355			0.222763
$530$	5.57432	−	9.65501i	0.242133	−	0.419387i
$531$	1.96930	−	1.13698i	0.0854604	−	0.0493406i
$532$			5.68001i			0.246260i
$533$	54.8563	+	31.6713i	2.37609	+	1.37184i
$534$	−4.54758	+	7.87663i	−0.196793	+	0.340855i
$535$	14.4308	+	8.33163i	0.623898	+	0.360208i
$536$	−12.2504	+	7.07277i	−0.529137	+	0.305497i
$537$	7.57765	−	4.37496i	0.327000	−	0.188793i
$538$	−28.1260	−	16.2386i	−1.21260	−	0.700095i
$539$	3.52043	−	6.09756i	0.151636	−	0.262640i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$			29.5852i			1.27197i	0.771702	+	0.635984i	$0.219406\pi$
$541$			29.5852i			1.27197i	−0.771702	+	0.635984i	$0.780594\pi$
$542$	6.49164	−	3.74795i	0.278840	−	0.160988i
$543$	−7.65366	+	13.2565i	−0.328450	+	0.568892i
$544$	−1.87133			−0.0802327
$545$	−16.7697			−0.718337
$546$	2.59662	−	4.49748i	0.111125	−	0.192474i
$547$			9.36718i			0.400512i	0.979744	+	0.200256i	$0.0641774\pi$
$547$			9.36718i			0.400512i	−0.979744	+	0.200256i	$0.935823\pi$
$548$	−8.25285	−	14.2943i	−0.352544	−	0.610624i
$549$			4.85483i			0.207199i
$550$	−0.977051	+	0.564101i	−0.0416616	+	0.0240533i
$551$	−13.5657	−	23.4964i	−0.577917	−	1.00098i
$552$	2.11403	+	3.66160i	0.0899790	+	0.155848i
$553$	−8.78075	−	5.06957i	−0.373395	−	0.215580i
$554$	5.61669			0.238630
$555$	−4.69857	+	3.86308i	−0.199443	+	0.163979i
$556$	17.6996			0.750632
$557$	−28.3100	−	16.3448i	−1.19953	−	0.692551i	−0.239082	−	0.970999i	$-0.576847\pi$
$557$	−28.3100	−	16.3448i	−1.19953	−	0.692551i	−0.960451	+	0.278448i	$0.910180\pi$
$558$	−2.57548	−	4.46086i	−0.109029	−	0.188843i
$559$	−27.9500	−	48.4107i	−1.18216	−	2.04756i
$560$	0.754597	−	0.435667i	0.0318875	−	0.0184103i
$561$			2.11124i			0.0891366i
$562$	10.3572	+	17.9392i	0.436893	+	0.756721i
$563$		−	29.2451i		−	1.23253i	−0.787538	−	0.616267i	$-0.788644\pi$
$563$		−	29.2451i		−	1.23253i	0.787538	−	0.616267i	$-0.211356\pi$
$564$	3.80679	−	6.59356i	0.160295	−	0.277639i
$565$	8.57878			0.360912
$566$	−9.74927			−0.409792
$567$	0.435667	−	0.754597i	0.0182963	−	0.0316901i
$568$	−13.0911	+	7.55813i	−0.549289	+	0.317132i
$569$		−	2.76558i		−	0.115939i	−0.998318	−	0.0579696i	$-0.981537\pi$
$569$		−	2.76558i		−	0.115939i	0.998318	−	0.0579696i	$-0.0184626\pi$
$570$	−5.64541	−	3.25938i	−0.236460	−	0.136520i
$571$	−8.17459	+	14.1588i	−0.342096	+	0.592528i	−0.984822	−	0.173569i	$-0.944470\pi$
$571$	−8.17459	+	14.1588i	−0.342096	+	0.592528i	0.642726	+	0.766096i	$0.277804\pi$
$572$	−5.82333	−	3.36210i	−0.243486	−	0.140576i
$573$	15.0757	−	8.70395i	0.629796	−	0.363613i
$574$	−8.01968	+	4.63017i	−0.334735	+	0.193259i
$575$	−3.66160	−	2.11403i	−0.152699	−	0.0881610i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	14.5112	+	8.37802i	0.604107	+	0.348782i	0.770656	−	0.637252i	$-0.219929\pi$
$577$	14.5112	+	8.37802i	0.604107	+	0.348782i	−0.166548	+	0.986033i	$0.553262\pi$
$578$			13.4981i			0.561447i
$579$	−16.3238	+	9.42456i	−0.678395	+	0.391671i
$580$	−2.08102	+	3.60443i	−0.0864097	+	0.149666i
$581$	−4.31286			−0.178928
$582$	2.17225			0.0900425
$583$	6.28895	−	10.8928i	0.260462	−	0.451133i
$584$			4.43634i			0.183577i
$585$	2.98005	+	5.16160i	0.123210	+	0.213406i
$586$		−	18.7399i		−	0.774138i
$587$	9.82117	−	5.67026i	0.405363	−	0.234037i	−0.283432	−	0.958992i	$-0.591473\pi$
$587$	9.82117	−	5.67026i	0.405363	−	0.234037i	0.688796	+	0.724956i	$0.258140\pi$
$588$	−3.12039	−	5.40467i	−0.128683	−	0.222885i
$589$	−16.7889	−	29.0793i	−0.691776	−	1.19819i
$590$	−1.96930	−	1.13698i	−0.0810748	−	0.0468086i
$591$	−0.613658			−0.0252425
$592$	−3.86308	−	4.69857i	−0.158772	−	0.193110i
$593$	−37.1864			−1.52706			−0.763531	−	0.645771i	$-0.776536\pi$
$593$	−37.1864			−1.52706			−0.763531	+	0.645771i	$0.776536\pi$
$594$	−0.977051	−	0.564101i	−0.0400889	−	0.0231453i
$595$	0.815277	+	1.41210i	0.0334231	+	0.0578905i
$596$	8.29891	+	14.3741i	0.339937	+	0.588788i
$597$	20.2609	−	11.6976i	0.829222	−	0.478751i
$598$		−	25.1997i		−	1.03049i
$599$	7.12050	+	12.3331i	0.290936	+	0.503915i	0.974031	−	0.226414i	$-0.0727001\pi$
$599$	7.12050	+	12.3331i	0.290936	+	0.503915i	−0.683096	+	0.730329i	$0.739367\pi$
$600$			1.00000i			0.0408248i
$601$	−11.1396	+	19.2944i	−0.454395	+	0.787036i	−0.998653	−	0.0518822i	$-0.983478\pi$
$601$	−11.1396	+	19.2944i	−0.454395	+	0.787036i	0.544258	+	0.838918i	$0.316811\pi$
$602$	8.17225			0.333076
$603$	14.1455			0.576051
$604$	−7.15224	+	12.3880i	−0.291021	+	0.504062i
$605$	8.42397	−	4.86358i	0.342483	−	0.197733i
$606$		−	4.72751i		−	0.192042i
$607$	20.6605	+	11.9284i	0.838585	+	0.484157i	0.856783	−	0.515677i	$-0.172460\pi$
$607$	20.6605	+	11.9284i	0.838585	+	0.484157i	−0.0181978	+	0.999834i	$0.505793\pi$
$608$	3.25938	−	5.64541i	0.132185	−	0.228952i
$609$	−3.14066	−	1.81326i	−0.127266	−	0.0734771i
$610$	4.20441	−	2.42742i	0.170232	−	0.0982832i
$611$	−39.2983	+	22.6889i	−1.58984	+	0.917895i
$612$	1.62062	+	0.935667i	0.0655098	+	0.0378221i
$613$	16.6580	−	28.8526i	0.672812	−	1.16534i	−0.304291	−	0.952579i	$-0.598420\pi$
$613$	16.6580	−	28.8526i	0.672812	−	1.16534i	0.977103	−	0.212765i	$-0.0682470\pi$
$614$	−22.7542	−	13.1371i	−0.918284	−	0.530172i
$615$		−	10.6278i		−	0.428553i
$616$	0.851337	−	0.491520i	0.0343013	−	0.0198039i
$617$	−0.0901992	+	0.156230i	−0.00363128	+	0.00628956i	−0.867835	−	0.496852i	$-0.834489\pi$
$617$	−0.0901992	+	0.156230i	−0.00363128	+	0.00628956i	0.864204	+	0.503141i	$0.167823\pi$
$618$	5.43512			0.218632
$619$	19.6346			0.789181			0.394590	−	0.918857i	$-0.370886\pi$
$619$	19.6346			0.789181			0.394590	+	0.918857i	$0.370886\pi$
$620$	−2.57548	+	4.46086i	−0.103434	+	0.179153i
$621$		−	4.22805i		−	0.169666i
$622$	16.7355	+	28.9868i	0.671033	+	1.16226i
$623$			7.92491i			0.317505i
$624$	−5.16160	+	2.98005i	−0.206629	+	0.119298i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.997143	+	1.72710i	0.0398539	+	0.0690289i
$627$	−6.36916	−	3.67724i	−0.254360	−	0.146855i
$628$	18.2282			0.727383
$629$	8.79260	−	7.22912i	0.350584	−	0.288244i
$630$	−0.871333			−0.0347147
$631$	26.8143	+	15.4812i	1.06746	+	0.616298i	0.927486	−	0.373857i	$-0.121965\pi$
$631$	26.8143	+	15.4812i	1.06746	+	0.616298i	0.139973	+	0.990155i	$0.455298\pi$
$632$	5.81817	+	10.0774i	0.231435	+	0.400856i
$633$	−10.5936	−	18.3487i	−0.421059	−	0.729295i
$634$	5.18523	−	2.99369i	0.205932	−	0.118895i
$635$		−	16.1662i		−	0.641536i
$636$	−5.57432	−	9.65501i	−0.221036	−	0.382846i
$637$			37.1957i			1.47375i
$638$	−2.34781	+	4.06653i	−0.0929507	+	0.160995i
$639$	15.1163			0.597990
$640$	−1.00000			−0.0395285
$641$	5.04530	−	8.73872i	0.199277	−	0.345159i	−0.749017	−	0.662551i	$-0.769474\pi$
$641$	5.04530	−	8.73872i	0.199277	−	0.345159i	0.948294	+	0.317392i	$0.102807\pi$
$642$	14.4308	−	8.33163i	0.569538	−	0.328823i
$643$		−	19.4671i		−	0.767706i	−0.923394	−	0.383853i	$-0.874597\pi$
$643$		−	19.4671i		−	0.767706i	0.923394	−	0.383853i	$-0.125403\pi$
$644$	3.19048	+	1.84202i	0.125722	+	0.0725858i
$645$	−4.68951	+	8.12246i	−0.184649	+	0.319822i
$646$	10.5644	+	6.09939i	0.415653	+	0.239977i
$647$	−11.4187	+	6.59257i	−0.448914	+	0.259181i	−0.707371	−	0.706842i	$-0.750119\pi$
$647$	−11.4187	+	6.59257i	−0.448914	+	0.259181i	0.258458	+	0.966023i	$0.416786\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−2.22177	−	1.28274i	−0.0872120	−	0.0503519i
$650$	2.98005	−	5.16160i	0.116887	−	0.202455i
$651$	−3.88690	−	2.24410i	−0.152339	−	0.0879532i
$652$		−	6.27777i		−	0.245857i
$653$	−20.1410	+	11.6284i	−0.788180	+	0.455056i	−0.839321	−	0.543635i	$-0.817047\pi$
$653$	−20.1410	+	11.6284i	−0.788180	+	0.455056i	0.0511414	+	0.998691i	$0.483714\pi$
$654$	−8.38487	+	14.5230i	−0.327874	+	0.567895i
$655$	5.66129			0.221205
$656$	10.6278			0.414945
$657$	2.21817	−	3.84198i	0.0865390	−	0.149890i
$658$		−	6.63397i		−	0.258619i
$659$	14.9905	+	25.9644i	0.583949	+	1.01143i	0.995006	+	0.0998192i	$0.0318265\pi$
$659$	14.9905	+	25.9644i	0.583949	+	1.01143i	−0.411057	+	0.911610i	$0.634840\pi$
$660$			1.12820i			0.0439152i
$661$	11.5053	−	6.64256i	0.447503	−	0.258366i	−0.259272	−	0.965804i	$-0.583483\pi$
$661$	11.5053	−	6.64256i	0.447503	−	0.258366i	0.706775	+	0.707439i	$0.250149\pi$
$662$	9.32279	+	16.1475i	0.362340	+	0.627592i
$663$	−5.57667	−	9.65908i	−0.216580	−	0.375128i
$664$	4.28659	+	2.47486i	0.166352	+	0.0960434i
$665$	−5.68001			−0.220261
$666$	0.996242	+	6.00063i	0.0386036	+	0.232520i
$667$	−17.5973			−0.681372
$668$	6.40836	+	3.69987i	0.247947	+	0.143152i
$669$	−7.72081	−	13.3728i	−0.298504	−	0.517024i
$670$	−7.07277	−	12.2504i	−0.273245	−	0.473274i
$671$	4.74342	−	2.73861i	0.183118	−	0.105723i
$672$		−	0.871333i		−	0.0336124i
$673$	−6.35737	−	11.0113i	−0.245058	−	0.424454i	0.717090	−	0.696981i	$-0.245474\pi$
$673$	−6.35737	−	11.0113i	−0.245058	−	0.424454i	−0.962148	+	0.272527i	$0.912140\pi$
$674$		−	1.19521i		−	0.0460380i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	22.5229			0.866264
$677$	−12.3800			−0.475801			−0.237901	−	0.971290i	$-0.576459\pi$
$677$	−12.3800			−0.475801			−0.237901	+	0.971290i	$0.576459\pi$
$678$	4.28939	−	7.42944i	0.164733	−	0.285326i
$679$	1.63917	−	0.946375i	0.0629056	−	0.0363185i
$680$		−	1.87133i		−	0.0717624i
$681$	−3.86623	−	2.23217i	−0.148154	−	0.0855370i
$682$	−2.90566	+	5.03275i	−0.111263	+	0.192714i
$683$	−8.49785	−	4.90623i	−0.325161	−	0.187732i	0.328530	−	0.944494i	$-0.393447\pi$
$683$	−8.49785	−	4.90623i	−0.325161	−	0.187732i	−0.653691	+	0.756762i	$0.726780\pi$
$684$	−5.64541	+	3.25938i	−0.215858	+	0.124626i
$685$	14.2943	−	8.25285i	0.546159	−	0.315325i
$686$	−9.99145	−	5.76856i	−0.381475	−	0.220245i
$687$	8.13293	−	14.0866i	0.310291	−	0.537439i
$688$	−8.12246	−	4.68951i	−0.309666	−	0.178786i
$689$			66.4471i			2.53143i
$690$	−3.66160	+	2.11403i	−0.139395	+	0.0804796i
$691$	10.7731	−	18.6595i	0.409828	−	0.709842i	−0.585043	−	0.811003i	$-0.698922\pi$
$691$	10.7731	−	18.6595i	0.409828	−	0.709842i	0.994870	+	0.101160i	$0.0322555\pi$
$692$	10.4371			0.396760
$693$	−0.983039			−0.0373426
$694$	2.94679	−	5.10399i	0.111859	−	0.193745i
$695$			17.6996i			0.671385i
$696$	2.08102	+	3.60443i	0.0788809	+	0.136626i
$697$			19.8881i			0.753316i
$698$	−12.3543	+	7.13276i	−0.467617	+	0.269979i
$699$	−1.82389	−	3.15906i	−0.0689857	−	0.119487i
$700$	0.435667	+	0.754597i	0.0164666	+	0.0285211i
$701$	38.8616	+	22.4368i	1.46778	+	0.847426i	0.999349	−	0.0360723i	$-0.0114847\pi$
$701$	38.8616	+	22.4368i	1.46778	+	0.847426i	0.468435	+	0.883498i	$0.344818\pi$
$702$	5.96011			0.224950
$703$	6.49426	+	39.1166i	0.244936	+	1.47531i
$704$	−1.12820			−0.0425207
$705$	6.59356	+	3.80679i	0.248328	+	0.143372i
$706$	−8.43844	−	14.6158i	−0.317585	−	0.550073i
$707$	−2.05962	−	3.56736i	−0.0774599	−	0.134164i
$708$	−1.96930	+	1.13698i	−0.0740109	+	0.0427302i
$709$			23.4849i			0.881995i	0.897508	+	0.440998i	$0.145375\pi$
$709$			23.4849i			0.881995i	−0.897508	+	0.440998i	$0.854625\pi$
$710$	−7.55813	−	13.0911i	−0.283652	−	0.491299i
$711$		−	11.6363i		−	0.436397i
$712$	4.54758	−	7.87663i	0.170428	−	0.295189i
$713$	−21.7785			−0.815613
$714$	1.63055			0.0610220
$715$	3.36210	−	5.82333i	0.125735	−	0.217780i
$716$	−7.57765	+	4.37496i	−0.283190	+	0.163500i
$717$		−	7.64877i		−	0.285648i
$718$	7.79364	+	4.49966i	0.290856	+	0.167926i
$719$	−14.6060	+	25.2983i	−0.544710	+	0.943466i	0.453915	+	0.891045i	$0.350027\pi$
$719$	−14.6060	+	25.2983i	−0.544710	+	0.943466i	−0.998625	+	0.0524210i	$0.983306\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	4.10132	−	2.36790i	0.152741	−	0.0881852i
$722$	−20.3466	+	11.7471i	−0.757223	+	0.437183i
$723$	18.8434	+	10.8793i	0.700794	+	0.404604i
$724$	7.65366	−	13.2565i	0.284446	−	0.492675i
$725$	−3.60443	−	2.08102i	−0.133865	−	0.0772872i
$726$		−	9.72716i		−	0.361009i
$727$	23.3477	−	13.4798i	0.865917	−	0.499938i	−7.19505e−5	−	1.00000i	$-0.500023\pi$
$727$	23.3477	−	13.4798i	0.865917	−	0.499938i	0.865989	+	0.500062i	$0.166690\pi$
$728$	−2.59662	+	4.49748i	−0.0962371	+	0.166688i
$729$	1.00000			0.0370370
$730$	−4.43634			−0.164196
$731$	8.77563	−	15.1998i	0.324578	−	0.562186i
$732$		−	4.85483i		−	0.179440i
$733$	−15.1833	−	26.2982i	−0.560806	−	0.971345i	−0.997426	−	0.0716990i	$-0.977158\pi$
$733$	−15.1833	−	26.2982i	−0.560806	−	0.971345i	0.436620	−	0.899646i	$-0.356175\pi$
$734$		−	12.4036i		−	0.457826i
$735$	5.40467	−	3.12039i	0.199354	−	0.115097i
$736$	−2.11403	−	3.66160i	−0.0779241	−	0.134968i
$737$	−7.97951	−	13.8209i	−0.293929	−	0.509100i
$738$	−9.20392	−	5.31389i	−0.338801	−	0.195607i
$739$	−13.9985			−0.514942			−0.257471	−	0.966286i	$-0.582889\pi$
$739$	−13.9985			−0.514942			−0.257471	+	0.966286i	$0.582889\pi$
$740$	4.69857	−	3.86308i	0.172723	−	0.142010i
$741$	38.8525			1.42728
$742$	−8.41273	−	4.85709i	−0.308841	−	0.178309i
$743$	10.1124	+	17.5151i	0.370986	+	0.642567i	0.989718	−	0.143036i	$-0.0456864\pi$
$743$	10.1124	+	17.5151i	0.370986	+	0.642567i	−0.618731	+	0.785603i	$0.712353\pi$
$744$	2.57548	+	4.46086i	0.0944217	+	0.163543i
$745$	−14.3741	+	8.29891i	−0.526628	+	0.304049i
$746$			10.9170i			0.399700i
$747$	−2.47486	−	4.28659i	−0.0905506	−	0.156838i
$748$		−	2.11124i		−	0.0771946i
$749$	7.25962	−	12.5740i	0.265261	−	0.459445i
$750$	−1.00000			−0.0365148
$751$	−48.7420			−1.77862			−0.889311	−	0.457302i	$-0.848816\pi$
$751$	−48.7420			−1.77862			−0.889311	+	0.457302i	$0.848816\pi$
$752$	−3.80679	+	6.59356i	−0.138820	+	0.240442i
$753$	0.209327	−	0.120855i	0.00762829	−	0.00440420i
$754$		−	24.8062i		−	0.903389i
$755$	−12.3880	−	7.15224i	−0.450847	−	0.260297i
$756$	−0.435667	+	0.754597i	−0.0158450	+	0.0274444i
$757$	−24.5161	−	14.1544i	−0.891051	−	0.514449i	−0.0167650	−	0.999859i	$-0.505337\pi$
$757$	−24.5161	−	14.1544i	−0.891051	−	0.514449i	−0.874286	+	0.485411i	$0.838670\pi$
$758$	−19.7454	+	11.4000i	−0.717184	+	0.414067i
$759$	−4.13102	+	2.38505i	−0.149947	+	0.0865718i
$760$	5.64541	+	3.25938i	0.204781	+	0.118230i
$761$	14.3149	−	24.7942i	0.518916	−	0.898790i	−0.480842	−	0.876807i	$-0.659669\pi$
$761$	14.3149	−	24.7942i	0.518916	−	0.898790i	0.999758	−	0.0219824i	$-0.00699777\pi$
$762$	−14.0003	−	8.08310i	−0.507179	−	0.292820i
$763$			14.6120i			0.528991i
$764$	−15.0757	+	8.70395i	−0.545419	+	0.314898i
$765$	−0.935667	+	1.62062i	−0.0338291	+	0.0585937i
$766$	26.0195			0.940122
$767$	13.5530			0.489370
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$		−	53.0077i		−	1.91151i	−0.294168	−	0.955754i	$-0.595043\pi$
$769$		−	53.0077i		−	1.91151i	0.294168	−	0.955754i	$-0.404957\pi$
$770$	0.491520	+	0.851337i	0.0177131	+	0.0306801i
$771$		−	24.8423i		−	0.894674i
$772$	16.3238	−	9.42456i	0.587507	−	0.339197i
$773$	4.26473	+	7.38673i	0.153392	+	0.265682i	0.932472	−	0.361242i	$-0.117647\pi$
$773$	4.26473	+	7.38673i	0.153392	+	0.265682i	−0.779080	+	0.626924i	$0.784314\pi$
$774$	4.68951	+	8.12246i	0.168561	+	0.291956i
$775$	−4.46086	−	2.57548i	−0.160239	−	0.0925140i
$776$	−2.17225			−0.0779791

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.435667 + 0.754597i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.435667 + 0.754597i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +1.12820 q^{11} +(0.500000 - 0.866025i) q^{12} +(-5.16160 + 2.98005i) q^{13} -0.871333i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.62062 - 0.935667i) q^{17} +(0.866025 - 0.500000i) q^{18} +(5.64541 - 3.25938i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.435667 - 0.754597i) q^{21} +(-0.977051 - 0.564101i) q^{22} -4.22805i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +5.96011 q^{26} +1.00000 q^{27} +(-0.435667 + 0.754597i) q^{28} -4.16204i q^{29} +(-0.500000 - 0.866025i) q^{30} -5.15096i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.564101 - 0.977051i) q^{33} +(0.935667 + 1.62062i) q^{34} +(-0.754597 - 0.435667i) q^{35} -1.00000 q^{36} +(-2.13754 + 5.69481i) q^{37} -6.51876 q^{38} +(5.16160 + 2.98005i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.31389 - 9.20392i) q^{41} +(-0.754597 + 0.435667i) q^{42} +9.37901i q^{43} +(0.564101 + 0.977051i) q^{44} -1.00000i q^{45} +(-2.11403 + 3.66160i) q^{46} +7.61359 q^{47} +1.00000 q^{48} +(3.12039 - 5.40467i) q^{49} +(-0.866025 + 0.500000i) q^{50} +1.87133i q^{51} +(-5.16160 - 2.98005i) q^{52} +(5.57432 - 9.65501i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.977051 + 0.564101i) q^{55} +(0.754597 - 0.435667i) q^{56} +(-5.64541 - 3.25938i) q^{57} +(-2.08102 + 3.60443i) q^{58} +(-1.96930 - 1.13698i) q^{59} +1.00000i q^{60} +(4.20441 - 2.42742i) q^{61} +(-2.57548 + 4.46086i) q^{62} -0.871333 q^{63} -1.00000 q^{64} +(2.98005 - 5.16160i) q^{65} +1.12820i q^{66} +(-7.07277 - 12.2504i) q^{67} -1.87133i q^{68} +(-3.66160 + 2.11403i) q^{69} +(0.435667 + 0.754597i) q^{70} +(-7.55813 - 13.0911i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.43634 q^{73} +(4.69857 - 3.86308i) q^{74} -1.00000 q^{75} +(5.64541 + 3.25938i) q^{76} +(0.491520 + 0.851337i) q^{77} +(-2.98005 - 5.16160i) q^{78} +(-10.0774 + 5.81817i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +10.6278i q^{82} +(-2.47486 + 4.28659i) q^{83} +0.871333 q^{84} +1.87133 q^{85} +(4.68951 - 8.12246i) q^{86} +(-3.60443 + 2.08102i) q^{87} -1.12820i q^{88} +(7.87663 + 4.54758i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-4.49748 - 2.59662i) q^{91} +(3.66160 - 2.11403i) q^{92} +(-4.46086 + 2.57548i) q^{93} +(-6.59356 - 3.80679i) q^{94} +(-3.25938 + 5.64541i) q^{95} +(-0.866025 - 0.500000i) q^{96} -2.17225i q^{97} +(-5.40467 + 3.12039i) q^{98} +(-0.564101 + 0.977051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \)	\( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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