LMFDB - Embedded newform 287.2.f.a.50.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.15
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.38058i q^{2} +(1.24569 + 1.24569i) q^{3} +0.0939893 q^{4} +1.25269i q^{5} +(-1.71978 + 1.71978i) q^{6} +(-0.707107 - 0.707107i) q^{7} +2.89093i q^{8} +0.103480i q^{9} +O(q^{10})$	\(q+1.38058i q^{2} +(1.24569 + 1.24569i) q^{3} +0.0939893 q^{4} +1.25269i q^{5} +(-1.71978 + 1.71978i) q^{6} +(-0.707107 - 0.707107i) q^{7} +2.89093i q^{8} +0.103480i q^{9} -1.72944 q^{10} +(-0.995238 - 0.995238i) q^{11} +(0.117081 + 0.117081i) q^{12} +(1.16696 + 1.16696i) q^{13} +(0.976220 - 0.976220i) q^{14} +(-1.56046 + 1.56046i) q^{15} -3.80319 q^{16} +(-0.885409 + 0.885409i) q^{17} -0.142863 q^{18} +(4.74103 - 4.74103i) q^{19} +0.117739i q^{20} -1.76167i q^{21} +(1.37401 - 1.37401i) q^{22} -5.26379 q^{23} +(-3.60119 + 3.60119i) q^{24} +3.43078 q^{25} +(-1.61109 + 1.61109i) q^{26} +(3.60816 - 3.60816i) q^{27} +(-0.0664604 - 0.0664604i) q^{28} +(-0.807329 - 0.807329i) q^{29} +(-2.15434 - 2.15434i) q^{30} +0.629394 q^{31} +0.531236i q^{32} -2.47951i q^{33} +(-1.22238 - 1.22238i) q^{34} +(0.885783 - 0.885783i) q^{35} +0.00972599i q^{36} -4.95636 q^{37} +(6.54538 + 6.54538i) q^{38} +2.90734i q^{39} -3.62143 q^{40} +(-5.50687 - 3.26717i) q^{41} +2.43213 q^{42} -0.969443i q^{43} +(-0.0935417 - 0.0935417i) q^{44} -0.129628 q^{45} -7.26710i q^{46} +(0.979177 - 0.979177i) q^{47} +(-4.73759 - 4.73759i) q^{48} +1.00000i q^{49} +4.73647i q^{50} -2.20589 q^{51} +(0.109682 + 0.109682i) q^{52} +(7.56408 + 7.56408i) q^{53} +(4.98137 + 4.98137i) q^{54} +(1.24672 - 1.24672i) q^{55} +(2.04419 - 2.04419i) q^{56} +11.8117 q^{57} +(1.11458 - 1.11458i) q^{58} +8.26662 q^{59} +(-0.146666 + 0.146666i) q^{60} -10.3523i q^{61} +0.868931i q^{62} +(0.0731713 - 0.0731713i) q^{63} -8.33979 q^{64} +(-1.46184 + 1.46184i) q^{65} +3.42317 q^{66} +(1.91163 - 1.91163i) q^{67} +(-0.0832190 + 0.0832190i) q^{68} +(-6.55704 - 6.55704i) q^{69} +(1.22290 + 1.22290i) q^{70} +(5.24190 + 5.24190i) q^{71} -0.299153 q^{72} +2.81279i q^{73} -6.84267i q^{74} +(4.27368 + 4.27368i) q^{75} +(0.445606 - 0.445606i) q^{76} +1.40748i q^{77} -4.01383 q^{78} +(-1.50331 - 1.50331i) q^{79} -4.76420i q^{80} +9.29973 q^{81} +(4.51060 - 7.60269i) q^{82} +6.52174 q^{83} -0.165578i q^{84} +(-1.10914 - 1.10914i) q^{85} +1.33840 q^{86} -2.01136i q^{87} +(2.87716 - 2.87716i) q^{88} +(-4.71425 - 4.71425i) q^{89} -0.178962i q^{90} -1.65033i q^{91} -0.494740 q^{92} +(0.784029 + 0.784029i) q^{93} +(1.35184 + 1.35184i) q^{94} +(5.93902 + 5.93902i) q^{95} +(-0.661755 + 0.661755i) q^{96} +(-3.61017 + 3.61017i) q^{97} -1.38058 q^{98} +(0.102987 - 0.102987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.38058i			0.976220i	0.872782	+	0.488110i	$0.162314\pi$
$2$			1.38058i			0.976220i	−0.872782	+	0.488110i	$0.837686\pi$
$3$	1.24569	+	1.24569i	0.719199	+	0.719199i	0.968441	−	0.249242i	$-0.0801816\pi$
$3$	1.24569	+	1.24569i	0.719199	+	0.719199i	−0.249242	+	0.968441i	$0.580182\pi$
$4$	0.0939893			0.0469946
$5$			1.25269i			0.560219i	0.959968	+	0.280109i	$0.0903707\pi$
$5$			1.25269i			0.560219i	−0.959968	+	0.280109i	$0.909629\pi$
$6$	−1.71978	+	1.71978i	−0.702096	+	0.702096i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$			2.89093i			1.02210i
$9$			0.103480i			0.0344933i
$10$	−1.72944			−0.546897
$11$	−0.995238	−	0.995238i	−0.300076	−	0.300076i	0.540968	−	0.841043i	$-0.318058\pi$
$11$	−0.995238	−	0.995238i	−0.300076	−	0.300076i	−0.841043	+	0.540968i	$0.818058\pi$
$12$	0.117081	+	0.117081i	0.0337985	+	0.0337985i
$13$	1.16696	+	1.16696i	0.323657	+	0.323657i	0.850168	−	0.526511i	$-0.176500\pi$
$13$	1.16696	+	1.16696i	0.323657	+	0.323657i	−0.526511	+	0.850168i	$0.676500\pi$
$14$	0.976220	−	0.976220i	0.260906	−	0.260906i
$15$	−1.56046	+	1.56046i	−0.402908	+	0.402908i
$16$	−3.80319			−0.950797
$17$	−0.885409	+	0.885409i	−0.214743	+	0.214743i	−0.806279	−	0.591536i	$-0.798522\pi$
$17$	−0.885409	+	0.885409i	−0.214743	+	0.214743i	0.591536	+	0.806279i	$0.298522\pi$
$18$	−0.142863			−0.0336730
$19$	4.74103	−	4.74103i	1.08767	−	1.08767i	0.0918974	−	0.995768i	$-0.470707\pi$
$19$	4.74103	−	4.74103i	1.08767	−	1.08767i	0.995768	−	0.0918974i	$-0.0292932\pi$
$20$			0.117739i			0.0263273i
$21$		−	1.76167i		−	0.384428i
$22$	1.37401	−	1.37401i	0.292940	−	0.292940i
$23$	−5.26379			−1.09758			−0.548788	−	0.835961i	$-0.684911\pi$
$23$	−5.26379			−1.09758			−0.548788	+	0.835961i	$0.684911\pi$
$24$	−3.60119	+	3.60119i	−0.735091	+	0.735091i
$25$	3.43078			0.686155
$26$	−1.61109	+	1.61109i	−0.315960	+	0.315960i
$27$	3.60816	−	3.60816i	0.694391	−	0.694391i
$28$	−0.0664604	−	0.0664604i	−0.0125598	−	0.0125598i
$29$	−0.807329	−	0.807329i	−0.149917	−	0.149917i	0.628164	−	0.778081i	$-0.283807\pi$
$29$	−0.807329	−	0.807329i	−0.149917	−	0.149917i	−0.778081	+	0.628164i	$0.783807\pi$
$30$	−2.15434	−	2.15434i	−0.393327	−	0.393327i
$31$	0.629394			0.113042			0.0565212	−	0.998401i	$-0.481999\pi$
$31$	0.629394			0.113042			0.0565212	+	0.998401i	$0.481999\pi$
$32$			0.531236i			0.0939102i
$33$		−	2.47951i		−	0.431628i
$34$	−1.22238	−	1.22238i	−0.209637	−	0.209637i
$35$	0.885783	−	0.885783i	0.149725	−	0.149725i
$36$			0.00972599i			0.00162100i
$37$	−4.95636			−0.814820			−0.407410	−	0.913245i	$-0.633568\pi$
$37$	−4.95636			−0.814820			−0.407410	+	0.913245i	$0.633568\pi$
$38$	6.54538	+	6.54538i	1.06180	+	1.06180i
$39$			2.90734i			0.465547i
$40$	−3.62143			−0.572598
$41$	−5.50687	−	3.26717i	−0.860028	−	0.510246i
$41$	−5.50687	−	3.26717i	−0.860028	−	0.510246i
$42$	2.43213			0.375286
$43$		−	0.969443i		−	0.147839i	−0.997264	−	0.0739194i	$-0.976449\pi$
$43$		−	0.969443i		−	0.147839i	0.997264	−	0.0739194i	$-0.0235507\pi$
$44$	−0.0935417	−	0.0935417i	−0.0141019	−	0.0141019i
$45$	−0.129628			−0.0193238
$46$		−	7.26710i		−	1.07148i
$47$	0.979177	−	0.979177i	0.142828	−	0.142828i	−0.632078	−	0.774905i	$-0.717798\pi$
$47$	0.979177	−	0.979177i	0.142828	−	0.142828i	0.774905	+	0.632078i	$0.217798\pi$
$48$	−4.73759	−	4.73759i	−0.683812	−	0.683812i
$49$			1.00000i			0.142857i
$50$			4.73647i			0.669838i
$51$	−2.20589			−0.308886
$52$	0.109682	+	0.109682i	0.0152101	+	0.0152101i
$53$	7.56408	+	7.56408i	1.03901	+	1.03901i	0.999208	+	0.0397992i	$0.0126718\pi$
$53$	7.56408	+	7.56408i	1.03901	+	1.03901i	0.0397992	+	0.999208i	$0.487328\pi$
$54$	4.98137	+	4.98137i	0.677878	+	0.677878i
$55$	1.24672	−	1.24672i	0.168108	−	0.168108i
$56$	2.04419	−	2.04419i	0.273167	−	0.273167i
$57$	11.8117			1.56450
$58$	1.11458	−	1.11458i	0.146352	−	0.146352i
$59$	8.26662			1.07622			0.538111	−	0.842874i	$-0.319138\pi$
$59$	8.26662			1.07622			0.538111	+	0.842874i	$0.319138\pi$
$60$	−0.146666	+	0.146666i	−0.0189345	+	0.0189345i
$61$		−	10.3523i		−	1.32548i	−0.748852	−	0.662738i	$-0.769394\pi$
$61$		−	10.3523i		−	1.32548i	0.748852	−	0.662738i	$-0.230606\pi$
$62$			0.868931i			0.110354i
$63$	0.0731713	−	0.0731713i	0.00921872	−	0.00921872i
$64$	−8.33979			−1.04247
$65$	−1.46184	+	1.46184i	−0.181319	+	0.181319i
$66$	3.42317			0.421364
$67$	1.91163	−	1.91163i	0.233543	−	0.233543i	−0.580627	−	0.814170i	$-0.697192\pi$
$67$	1.91163	−	1.91163i	0.233543	−	0.233543i	0.814170	+	0.580627i	$0.197192\pi$
$68$	−0.0832190	+	0.0832190i	−0.0100918	+	0.0100918i
$69$	−6.55704	−	6.55704i	−0.789375	−	0.789375i
$70$	1.22290	+	1.22290i	0.146164	+	0.146164i
$71$	5.24190	+	5.24190i	0.622099	+	0.622099i	0.946068	−	0.323968i	$-0.105017\pi$
$71$	5.24190	+	5.24190i	0.622099	+	0.622099i	−0.323968	+	0.946068i	$0.605017\pi$
$72$	−0.299153			−0.0352555
$73$			2.81279i			0.329212i	0.986359	+	0.164606i	$0.0526353\pi$
$73$			2.81279i			0.329212i	−0.986359	+	0.164606i	$0.947365\pi$
$74$		−	6.84267i		−	0.795444i
$75$	4.27368	+	4.27368i	0.493482	+	0.493482i
$76$	0.445606	−	0.445606i	0.0511145	−	0.0511145i
$77$			1.40748i			0.160397i
$78$	−4.01383			−0.454477
$79$	−1.50331	−	1.50331i	−0.169136	−	0.169136i	0.617464	−	0.786600i	$-0.288160\pi$
$79$	−1.50331	−	1.50331i	−0.169136	−	0.169136i	−0.786600	+	0.617464i	$0.788160\pi$
$80$		−	4.76420i		−	0.532654i
$81$	9.29973			1.03330
$82$	4.51060	−	7.60269i	0.498113	−	0.839577i
$83$	6.52174			0.715854			0.357927	−	0.933749i	$-0.383484\pi$
$83$	6.52174			0.715854			0.357927	+	0.933749i	$0.383484\pi$
$84$		−	0.165578i		−	0.0180660i
$85$	−1.10914	−	1.10914i	−0.120303	−	0.120303i
$86$	1.33840			0.144323
$87$		−	2.01136i		−	0.215640i
$88$	2.87716	−	2.87716i	0.306706	−	0.306706i
$89$	−4.71425	−	4.71425i	−0.499710	−	0.499710i	0.411638	−	0.911348i	$-0.364957\pi$
$89$	−4.71425	−	4.71425i	−0.499710	−	0.499710i	−0.911348	+	0.411638i	$0.864957\pi$
$90$		−	0.178962i		−	0.0188643i
$91$		−	1.65033i		−	0.173002i
$92$	−0.494740			−0.0515802
$93$	0.784029	+	0.784029i	0.0813000	+	0.0813000i
$94$	1.35184	+	1.35184i	0.139431	+	0.139431i
$95$	5.93902	+	5.93902i	0.609331	+	0.609331i
$96$	−0.661755	+	0.661755i	−0.0675401	+	0.0675401i
$97$	−3.61017	+	3.61017i	−0.366558	+	0.366558i	−0.866220	−	0.499662i	$-0.833457\pi$
$97$	−3.61017	+	3.61017i	−0.366558	+	0.366558i	0.499662	+	0.866220i	$0.333457\pi$
$98$	−1.38058			−0.139460
$99$	0.102987	−	0.102987i	0.0103506	−	0.0103506i
$100$	0.322456			0.0322456
$101$	9.97579	−	9.97579i	0.992628	−	0.992628i	−0.00734499	−	0.999973i	$-0.502338\pi$
$101$	9.97579	−	9.97579i	0.992628	−	0.992628i	0.999973	+	0.00734499i	$0.00233801\pi$
$102$		−	3.04541i		−	0.301541i
$103$			1.79490i			0.176857i	0.996083	+	0.0884286i	$0.0281845\pi$
$103$			1.79490i			0.176857i	−0.996083	+	0.0884286i	$0.971815\pi$
$104$	−3.37360	+	3.37360i	−0.330809	+	0.330809i
$105$	2.20682			0.215364
$106$	−10.4428	+	10.4428i	−1.01430	+	1.01430i
$107$	−16.6043			−1.60520			−0.802602	−	0.596516i	$-0.796551\pi$
$107$	−16.6043			−1.60520			−0.802602	+	0.596516i	$0.796551\pi$
$108$	0.339128	−	0.339128i	0.0326327	−	0.0326327i
$109$	−13.0476	+	13.0476i	−1.24973	+	1.24973i	−0.293893	+	0.955838i	$0.594951\pi$
$109$	−13.0476	+	13.0476i	−1.24973	+	1.24973i	−0.955838	+	0.293893i	$0.905049\pi$
$110$	1.72120	+	1.72120i	0.164110	+	0.164110i
$111$	−6.17408	−	6.17408i	−0.586018	−	0.586018i
$112$	2.68926	+	2.68926i	0.254111	+	0.254111i
$113$	−16.8371			−1.58390			−0.791948	−	0.610588i	$-0.790933\pi$
$113$	−16.8371			−1.58390			−0.791948	+	0.610588i	$0.790933\pi$
$114$			16.3070i			1.52729i
$115$		−	6.59388i		−	0.614883i
$116$	−0.0758802	−	0.0758802i	−0.00704530	−	0.00704530i
$117$	−0.120757	+	0.120757i	−0.0111640	+	0.0111640i
$118$			11.4128i			1.05063i
$119$	1.25216			0.114785
$120$	−4.51117	−	4.51117i	−0.411811	−	0.411811i
$121$		−	9.01900i		−	0.819909i
$122$	14.2922			1.29396
$123$	−2.78996	−	10.9297i	−0.251563	−	0.985500i
$124$	0.0591562			0.00531239
$125$			10.5611i			0.944615i
$126$	0.101019	+	0.101019i	0.00899949	+	0.00899949i
$127$	5.07274			0.450133			0.225067	−	0.974343i	$-0.427740\pi$
$127$	5.07274			0.450133			0.225067	+	0.974343i	$0.427740\pi$
$128$		−	10.4513i		−	0.923774i
$129$	1.20762	−	1.20762i	0.106325	−	0.106325i
$130$	−2.01819	−	2.01819i	−0.177007	−	0.177007i
$131$		−	6.48647i		−	0.566725i	−0.959013	−	0.283363i	$-0.908550\pi$
$131$		−	6.48647i		−	0.566725i	0.959013	−	0.283363i	$-0.0914500\pi$
$132$		−	0.233048i		−	0.0202842i
$133$	−6.70482			−0.581382
$134$	2.63917	+	2.63917i	0.227989	+	0.227989i
$135$	4.51990	+	4.51990i	0.389011	+	0.389011i
$136$	−2.55965	−	2.55965i	−0.219488	−	0.219488i
$137$	−10.3462	+	10.3462i	−0.883934	+	0.883934i	−0.993932	−	0.109998i	$-0.964916\pi$
$137$	−10.3462	+	10.3462i	−0.883934	+	0.883934i	0.109998	+	0.993932i	$0.464916\pi$
$138$	9.05255	−	9.05255i	0.770604	−	0.770604i
$139$	−9.35282			−0.793296			−0.396648	−	0.917971i	$-0.629827\pi$
$139$	−9.35282			−0.793296			−0.396648	+	0.917971i	$0.629827\pi$
$140$	0.0832541	−	0.0832541i	0.00703626	−	0.00703626i
$141$	2.43950			0.205443
$142$	−7.23688	+	7.23688i	−0.607306	+	0.607306i
$143$		−	2.32281i		−	0.194243i
$144$		−	0.393553i		−	0.0327961i
$145$	1.01133	−	1.01133i	0.0839864	−	0.0839864i
$146$	−3.88329			−0.321384
$147$	−1.24569	+	1.24569i	−0.102743	+	0.102743i
$148$	−0.465844			−0.0382922
$149$	−13.6883	+	13.6883i	−1.12139	+	1.12139i	−0.129858	+	0.991533i	$0.541452\pi$
$149$	−13.6883	+	13.6883i	−1.12139	+	1.12139i	−0.991533	+	0.129858i	$0.958548\pi$
$150$	−5.90017	+	5.90017i	−0.481747	+	0.481747i
$151$	−0.958487	−	0.958487i	−0.0780006	−	0.0780006i	0.667030	−	0.745031i	$-0.267565\pi$
$151$	−0.958487	−	0.958487i	−0.0780006	−	0.0780006i	−0.745031	+	0.667030i	$0.767565\pi$
$152$	13.7060	+	13.7060i	1.11170	+	1.11170i
$153$	−0.0916220	−	0.0916220i	−0.00740720	−	0.00740720i
$154$	−1.94314			−0.156583
$155$			0.788433i			0.0633285i
$156$			0.273259i			0.0218782i
$157$	−8.99994	−	8.99994i	−0.718273	−	0.718273i	0.249978	−	0.968251i	$-0.419577\pi$
$157$	−8.99994	−	8.99994i	−0.718273	−	0.718273i	−0.968251	+	0.249978i	$0.919577\pi$
$158$	2.07545	−	2.07545i	0.165114	−	0.165114i
$159$			18.8450i			1.49450i
$160$	−0.665472			−0.0526102
$161$	3.72206	+	3.72206i	0.293340	+	0.293340i
$162$			12.8391i			1.00873i
$163$	−7.07020			−0.553780			−0.276890	−	0.960902i	$-0.589304\pi$
$163$	−7.07020			−0.553780			−0.276890	+	0.960902i	$0.589304\pi$
$164$	−0.517586	−	0.307079i	−0.0404167	−	0.0239788i
$165$	3.10605			0.241806
$166$			9.00381i			0.698831i
$167$	5.24363	+	5.24363i	0.405765	+	0.405765i	0.880259	−	0.474494i	$-0.157369\pi$
$167$	5.24363	+	5.24363i	0.405765	+	0.405765i	−0.474494	+	0.880259i	$0.657369\pi$
$168$	5.09286			0.392923
$169$		−	10.2764i		−	0.790492i
$170$	1.53126	−	1.53126i	0.117442	−	0.117442i
$171$	0.490600	+	0.490600i	0.0375172	+	0.0375172i
$172$		−	0.0911173i		−	0.00694763i
$173$			3.02228i			0.229780i	0.993378	+	0.114890i	$0.0366515\pi$
$173$			3.02228i			0.229780i	−0.993378	+	0.114890i	$0.963348\pi$
$174$	2.77685			0.210512
$175$	−2.42592	−	2.42592i	−0.183383	−	0.183383i
$176$	3.78508	+	3.78508i	0.285311	+	0.285311i
$177$	10.2976	+	10.2976i	0.774017	+	0.774017i
$178$	6.50842	−	6.50842i	0.487827	−	0.487827i
$179$	−6.54440	+	6.54440i	−0.489151	+	0.489151i	−0.908038	−	0.418887i	$-0.862420\pi$
$179$	−6.54440	+	6.54440i	−0.489151	+	0.489151i	0.418887	+	0.908038i	$0.362420\pi$
$180$	−0.0121836			−0.000908114
$181$	−10.2808	+	10.2808i	−0.764169	+	0.764169i	−0.977073	−	0.212904i	$-0.931708\pi$
$181$	−10.2808	+	10.2808i	−0.764169	+	0.764169i	0.212904	+	0.977073i	$0.431708\pi$
$182$	2.27842			0.168888
$183$	12.8957	−	12.8957i	0.953280	−	0.953280i
$184$		−	15.2172i		−	1.12183i
$185$		−	6.20876i		−	0.456477i
$186$	−1.08242	+	1.08242i	−0.0793667	+	0.0793667i
$187$	1.76239			0.128878
$188$	0.0920321	−	0.0920321i	0.00671213	−	0.00671213i
$189$	−5.10271			−0.371168
$190$	−8.19931	+	8.19931i	−0.594841	+	0.594841i
$191$	0.0689612	−	0.0689612i	0.00498986	−	0.00498986i	−0.704607	−	0.709597i	$-0.748877\pi$
$191$	0.0689612	−	0.0689612i	0.00498986	−	0.00498986i	0.709597	+	0.704607i	$0.248877\pi$
$192$	−10.3888	−	10.3888i	−0.749746	−	0.749746i
$193$	0.639833	+	0.639833i	0.0460562	+	0.0460562i	0.729760	−	0.683704i	$-0.239632\pi$
$193$	0.639833	+	0.639833i	0.0460562	+	0.0460562i	−0.683704	+	0.729760i	$0.739632\pi$
$194$	−4.98415	−	4.98415i	−0.357841	−	0.357841i
$195$	−3.64199			−0.260808
$196$			0.0939893i			0.00671352i
$197$		−	14.9467i		−	1.06491i	−0.846460	−	0.532453i	$-0.821270\pi$
$197$		−	14.9467i		−	1.06491i	0.846460	−	0.532453i	$-0.178730\pi$
$198$	0.142182	+	0.142182i	0.0101044	+	0.0101044i
$199$	5.77133	−	5.77133i	0.409119	−	0.409119i	−0.472312	−	0.881431i	$-0.656581\pi$
$199$	5.77133	−	5.77133i	0.409119	−	0.409119i	0.881431	+	0.472312i	$0.156581\pi$
$200$			9.91812i			0.701317i
$201$	4.76260			0.335928
$202$	13.7724	+	13.7724i	0.969023	+	0.969023i
$203$			1.14174i			0.0801341i
$204$	−0.207330			−0.0145160
$205$	4.09274	−	6.89838i	0.285850	−	0.481804i
$206$	−2.47802			−0.172651
$207$		−	0.544696i		−	0.0378590i
$208$	−4.43817	−	4.43817i	−0.307732	−	0.307732i
$209$	−9.43690			−0.652764
$210$			3.04670i			0.210242i
$211$	4.75996	−	4.75996i	0.327689	−	0.327689i	−0.524018	−	0.851707i	$-0.675568\pi$
$211$	4.75996	−	4.75996i	0.327689	−	0.327689i	0.851707	+	0.524018i	$0.175568\pi$
$212$	0.710943	+	0.710943i	0.0488277	+	0.0488277i
$213$			13.0596i			0.894826i
$214$		−	22.9237i		−	1.56703i
$215$	1.21441			0.0828220
$216$	10.4309	+	10.4309i	0.709735	+	0.709735i
$217$	−0.445049	−	0.445049i	−0.0302119	−	0.0302119i
$218$	−18.0133	−	18.0133i	−1.22001	−	1.22001i
$219$	−3.50386	+	3.50386i	−0.236769	+	0.236769i
$220$	0.117178	−	0.117178i	0.00790017	−	0.00790017i
$221$	−2.06648			−0.139006
$222$	8.52383	−	8.52383i	0.572082	−	0.572082i
$223$	22.5871			1.51255			0.756273	−	0.654256i	$-0.227018\pi$
$223$	22.5871			1.51255			0.756273	+	0.654256i	$0.227018\pi$
$224$	0.375641	−	0.375641i	0.0250985	−	0.0250985i
$225$			0.355016i			0.0236677i
$226$		−	23.2450i		−	1.54623i
$227$	9.21968	−	9.21968i	0.611932	−	0.611932i	−0.331518	−	0.943449i	$-0.607561\pi$
$227$	9.21968	−	9.21968i	0.611932	−	0.611932i	0.943449	+	0.331518i	$0.107561\pi$
$228$	1.11017			0.0735229
$229$	−15.9433	+	15.9433i	−1.05356	+	1.05356i	−0.0550787	+	0.998482i	$0.517541\pi$
$229$	−15.9433	+	15.9433i	−1.05356	+	1.05356i	−0.998482	+	0.0550787i	$0.982459\pi$
$230$	9.10340			0.600261
$231$	−1.75328	+	1.75328i	−0.115357	+	0.115357i
$232$	2.33393	−	2.33393i	0.153230	−	0.153230i
$233$	0.255543	+	0.255543i	0.0167412	+	0.0167412i	0.715428	−	0.698687i	$-0.246232\pi$
$233$	0.255543	+	0.255543i	0.0167412	+	0.0167412i	−0.698687	+	0.715428i	$0.746232\pi$
$234$	−0.166715	−	0.166715i	−0.0108985	−	0.0108985i
$235$	1.22660	+	1.22660i	0.0800147	+	0.0800147i
$236$	0.776973			0.0505766
$237$		−	3.74532i		−	0.243285i
$238$			1.72871i			0.112056i
$239$	−8.38240	−	8.38240i	−0.542213	−	0.542213i	0.381964	−	0.924177i	$-0.375248\pi$
$239$	−8.38240	−	8.38240i	−0.542213	−	0.542213i	−0.924177	+	0.381964i	$0.875248\pi$
$240$	5.93471	−	5.93471i	0.383084	−	0.383084i
$241$			24.2378i			1.56130i	0.624970	+	0.780649i	$0.285111\pi$
$241$			24.2378i			1.56130i	−0.624970	+	0.780649i	$0.714889\pi$
$242$	12.4515			0.800412
$243$	0.760083	+	0.760083i	0.0487593	+	0.0487593i
$244$		−	0.973004i		−	0.0622902i
$245$	−1.25269			−0.0800312
$246$	15.0894	−	3.85178i	0.962064	−	0.245580i
$247$	11.0652			0.704061
$248$			1.81953i			0.115540i
$249$	8.12406	+	8.12406i	0.514841	+	0.514841i
$250$	−14.5805			−0.922152
$251$		−	21.3514i		−	1.34769i	−0.738872	−	0.673845i	$-0.764641\pi$
$251$		−	21.3514i		−	1.34769i	0.738872	−	0.673845i	$-0.235359\pi$
$252$	0.00687731	−	0.00687731i	0.000433230	−	0.000433230i
$253$	5.23872	+	5.23872i	0.329356	+	0.329356i
$254$			7.00335i			0.439429i
$255$		−	2.76329i		−	0.173044i
$256$	−2.25068			−0.140668
$257$	16.9206	+	16.9206i	1.05548	+	1.05548i	0.998368	+	0.0571070i	$0.0181876\pi$
$257$	16.9206	+	16.9206i	1.05548	+	1.05548i	0.0571070	+	0.998368i	$0.481812\pi$
$258$	1.66723	+	1.66723i	0.103797	+	0.103797i
$259$	3.50467	+	3.50467i	0.217770	+	0.217770i
$260$	−0.137397	+	0.137397i	−0.00852100	+	0.00852100i
$261$	0.0835422	−	0.0835422i	0.00517113	−	0.00517113i
$262$	8.95511			0.553249
$263$	9.27761	−	9.27761i	0.572082	−	0.572082i	−0.360628	−	0.932710i	$-0.617438\pi$
$263$	9.27761	−	9.27761i	0.572082	−	0.572082i	0.932710	+	0.360628i	$0.117438\pi$
$264$	7.16809			0.441165
$265$	−9.47543	+	9.47543i	−0.582071	+	0.582071i
$266$		−	9.25657i		−	0.567557i
$267$		−	11.7450i		−	0.718781i
$268$	0.179673	−	0.179673i	0.0109753	−	0.0109753i
$269$	−6.56253			−0.400124			−0.200062	−	0.979783i	$-0.564114\pi$
$269$	−6.56253			−0.400124			−0.200062	+	0.979783i	$0.564114\pi$
$270$	−6.24009	+	6.24009i	−0.379760	+	0.379760i
$271$	−11.1521			−0.677441			−0.338720	−	0.940887i	$-0.609994\pi$
$271$	−11.1521			−0.677441			−0.338720	+	0.940887i	$0.609994\pi$
$272$	3.36738	−	3.36738i	0.204177	−	0.204177i
$273$	2.05580	−	2.05580i	0.124423	−	0.124423i
$274$	−14.2838	−	14.2838i	−0.862914	−	0.862914i
$275$	−3.41444	−	3.41444i	−0.205898	−	0.205898i
$276$	−0.616292	−	0.616292i	−0.0370964	−	0.0370964i
$277$	4.21059			0.252990			0.126495	−	0.991967i	$-0.459627\pi$
$277$	4.21059			0.252990			0.126495	+	0.991967i	$0.459627\pi$
$278$		−	12.9124i		−	0.774431i
$279$			0.0651295i			0.00389920i
$280$	2.56073	+	2.56073i	0.153033	+	0.153033i
$281$	11.4110	−	11.4110i	0.680725	−	0.680725i	−0.279439	−	0.960164i	$-0.590148\pi$
$281$	11.4110	−	11.4110i	0.680725	−	0.680725i	0.960164	+	0.279439i	$0.0901484\pi$
$282$			3.36793i			0.200557i
$283$	−0.853556			−0.0507386			−0.0253693	−	0.999678i	$-0.508076\pi$
$283$	−0.853556			−0.0507386			−0.0253693	+	0.999678i	$0.508076\pi$
$284$	0.492683	+	0.492683i	0.0292353	+	0.0292353i
$285$			14.7963i			0.876459i
$286$	3.20683			0.189624
$287$	1.58370	+	6.20418i	0.0934831	+	0.366221i
$288$	−0.0549722			−0.00323927
$289$			15.4321i			0.907771i
$290$	1.39623	+	1.39623i	0.0819892	+	0.0819892i
$291$	−8.99431			−0.527256
$292$			0.264372i			0.0154712i
$293$	−16.8451	+	16.8451i	−0.984103	+	0.984103i	−0.999876	−	0.0157729i	$-0.994979\pi$
$293$	−16.8451	+	16.8451i	−0.984103	+	0.984103i	0.0157729	+	0.999876i	$0.494979\pi$
$294$	−1.71978	−	1.71978i	−0.100299	−	0.100299i
$295$			10.3555i			0.602919i
$296$		−	14.3285i		−	0.832825i
$297$	−7.18196			−0.416740
$298$	−18.8979	−	18.8979i	−1.09472	−	1.09472i
$299$	−6.14264	−	6.14264i	−0.355238	−	0.355238i
$300$	0.401680	+	0.401680i	0.0231910	+	0.0231910i
$301$	−0.685500	+	0.685500i	−0.0395116	+	0.0395116i
$302$	1.32327	−	1.32327i	0.0761457	−	0.0761457i
$303$	24.8534			1.42779
$304$	−18.0310	+	18.0310i	−1.03415	+	1.03415i
$305$	12.9682			0.742556
$306$	0.126492	−	0.126492i	0.00723106	−	0.00723106i
$307$		−	19.4990i		−	1.11286i	−0.830893	−	0.556432i	$-0.812170\pi$
$307$		−	19.4990i		−	1.11286i	0.830893	−	0.556432i	$-0.187830\pi$
$308$			0.132288i			0.00753780i
$309$	−2.23589	+	2.23589i	−0.127195	+	0.127195i
$310$	−1.08850			−0.0618225
$311$	8.58428	−	8.58428i	0.486770	−	0.486770i	−0.420516	−	0.907285i	$-0.638151\pi$
$311$	8.58428	−	8.58428i	0.486770	−	0.486770i	0.907285	+	0.420516i	$0.138151\pi$
$312$	−8.40491			−0.475834
$313$	16.2782	−	16.2782i	0.920097	−	0.920097i	−0.0769390	−	0.997036i	$-0.524515\pi$
$313$	16.2782	−	16.2782i	0.920097	−	0.920097i	0.997036	+	0.0769390i	$0.0245147\pi$
$314$	12.4252	−	12.4252i	0.701193	−	0.701193i
$315$	0.0916607	+	0.0916607i	0.00516450	+	0.00516450i
$316$	−0.141295	−	0.141295i	−0.00794848	−	0.00794848i
$317$	6.44770	+	6.44770i	0.362139	+	0.362139i	0.864600	−	0.502461i	$-0.167572\pi$
$317$	6.44770	+	6.44770i	0.362139	+	0.362139i	−0.502461	+	0.864600i	$0.667572\pi$
$318$	−26.0171			−1.45897
$319$			1.60697i			0.0899729i
$320$		−	10.4471i		−	0.584013i
$321$	−20.6838	−	20.6838i	−1.15446	−	1.15446i
$322$	−5.13862	+	5.13862i	−0.286364	+	0.286364i
$323$			8.39550i			0.467138i
$324$	0.874075			0.0485597
$325$	4.00358	+	4.00358i	0.222079	+	0.222079i
$326$		−	9.76100i		−	0.540612i
$327$	−32.5064			−1.79761
$328$	9.44515	−	15.9200i	0.521521	−	0.879032i
$329$	−1.38477			−0.0763446
$330$			4.28817i			0.236056i
$331$	22.9416	+	22.9416i	1.26099	+	1.26099i	0.950616	+	0.310371i	$0.100453\pi$
$331$	22.9416	+	22.9416i	1.26099	+	1.26099i	0.310371	+	0.950616i	$0.399547\pi$
$332$	0.612974			0.0336413
$333$		−	0.512883i		−	0.0281058i
$334$	−7.23927	+	7.23927i	−0.396115	+	0.396115i
$335$	2.39468	+	2.39468i	0.130835	+	0.130835i
$336$			6.69996i			0.365513i
$337$		−	8.09349i		−	0.440881i	−0.975400	−	0.220440i	$-0.929251\pi$
$337$		−	8.09349i		−	0.440881i	0.975400	−	0.220440i	$-0.0707494\pi$
$338$	14.1874			0.771694
$339$	−20.9737	−	20.9737i	−1.13914	−	1.13914i
$340$	−0.104247	−	0.104247i	−0.00565360	−	0.00565360i
$341$	−0.626396	−	0.626396i	−0.0339213	−	0.0339213i
$342$	−0.677315	+	0.677315i	−0.0366250	+	0.0366250i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	2.80259			0.151106
$345$	8.21392	−	8.21392i	0.442223	−	0.442223i
$346$	−4.17251			−0.224316
$347$	9.61156	−	9.61156i	0.515975	−	0.515975i	−0.400376	−	0.916351i	$-0.631120\pi$
$347$	9.61156	−	9.61156i	0.515975	−	0.515975i	0.916351	+	0.400376i	$0.131120\pi$
$348$		−	0.189046i		−	0.0101339i
$349$			26.5931i			1.42349i	0.702435	+	0.711747i	$0.252096\pi$
$349$			26.5931i			1.42349i	−0.702435	+	0.711747i	$0.747904\pi$
$350$	3.34919	−	3.34919i	0.179022	−	0.179022i
$351$	8.42117			0.449489
$352$	0.528706	−	0.528706i	0.0281801	−	0.0281801i
$353$	−4.57042			−0.243259			−0.121629	−	0.992576i	$-0.538812\pi$
$353$	−4.57042			−0.243259			−0.121629	+	0.992576i	$0.538812\pi$
$354$	−14.2167	+	14.2167i	−0.755611	+	0.755611i
$355$	−6.56646	+	6.56646i	−0.348512	+	0.348512i
$356$	−0.443089	−	0.443089i	−0.0234837	−	0.0234837i
$357$	1.55980	+	1.55980i	0.0825533	+	0.0825533i
$358$	−9.03509	−	9.03509i	−0.477519	−	0.477519i
$359$	−32.4432			−1.71228			−0.856142	−	0.516741i	$-0.827145\pi$
$359$	−32.4432			−1.71228			−0.856142	+	0.516741i	$0.827145\pi$
$360$		−	0.374745i		−	0.0197508i
$361$		−	25.9546i		−	1.36603i
$362$	−14.1936	−	14.1936i	−0.745997	−	0.745997i
$363$	11.2349	−	11.2349i	0.589678	−	0.589678i
$364$		−	0.155114i		−	0.00813016i
$365$	−3.52355			−0.184431
$366$	17.8036	+	17.8036i	0.930611	+	0.930611i
$367$			32.5263i			1.69786i	0.528504	+	0.848931i	$0.322753\pi$
$367$			32.5263i			1.69786i	−0.528504	+	0.848931i	$0.677247\pi$
$368$	20.0192			1.04357
$369$	0.338086	−	0.569850i	0.0176001	−	0.0296652i
$370$	8.57172			0.445622
$371$		−	10.6972i		−	0.555373i
$372$	0.0736903	+	0.0736903i	0.00382066	+	0.00382066i
$373$	−9.29490			−0.481271			−0.240636	−	0.970615i	$-0.577356\pi$
$373$	−9.29490			−0.481271			−0.240636	+	0.970615i	$0.577356\pi$
$374$			2.43312i			0.125814i
$375$	−13.1559	+	13.1559i	−0.679366	+	0.679366i
$376$	2.83073	+	2.83073i	0.145984	+	0.145984i
$377$		−	1.88424i		−	0.0970435i
$378$		−	7.04472i		−	0.362341i
$379$	27.7966			1.42781			0.713907	−	0.700240i	$-0.246924\pi$
$379$	27.7966			1.42781			0.713907	+	0.700240i	$0.246924\pi$
$380$	0.558204	+	0.558204i	0.0286353	+	0.0286353i
$381$	6.31906	+	6.31906i	0.323735	+	0.323735i
$382$	0.0952067	+	0.0952067i	0.00487120	+	0.00487120i
$383$	−13.2326	+	13.2326i	−0.676155	+	0.676155i	−0.959128	−	0.282973i	$-0.908679\pi$
$383$	−13.2326	+	13.2326i	−0.676155	+	0.676155i	0.282973	+	0.959128i	$0.408679\pi$
$384$	13.0191	−	13.0191i	0.664377	−	0.664377i
$385$	−1.76313			−0.0898574
$386$	−0.883343	+	0.883343i	−0.0449610	+	0.0449610i
$387$	0.100318			0.00509944
$388$	−0.339318	+	0.339318i	−0.0172262	+	0.0172262i
$389$			28.9083i			1.46571i	0.680386	+	0.732854i	$0.261812\pi$
$389$			28.9083i			1.46571i	−0.680386	+	0.732854i	$0.738188\pi$
$390$		−	5.02807i		−	0.254606i
$391$	4.66061	−	4.66061i	0.235697	−	0.235697i
$392$	−2.89093			−0.146014
$393$	8.08012	−	8.08012i	0.407588	−	0.407588i
$394$	20.6351			1.03958
$395$	1.88318	−	1.88318i	0.0947531	−	0.0947531i
$396$	0.00967968	−	0.00967968i	0.000486422	−	0.000486422i
$397$	−9.06698	−	9.06698i	−0.455059	−	0.455059i	0.441971	−	0.897029i	$-0.354279\pi$
$397$	−9.06698	−	9.06698i	−0.455059	−	0.455059i	−0.897029	+	0.441971i	$0.854279\pi$
$398$	7.96781	+	7.96781i	0.399390	+	0.399390i
$399$	−8.35212	−	8.35212i	−0.418129	−	0.418129i
$400$	−13.0479			−0.652394
$401$			27.9752i			1.39701i	0.715604	+	0.698506i	$0.246152\pi$
$401$			27.9752i			1.39701i	−0.715604	+	0.698506i	$0.753848\pi$
$402$			6.57516i			0.327939i
$403$	0.734478	+	0.734478i	0.0365870	+	0.0365870i
$404$	0.937617	−	0.937617i	0.0466482	−	0.0466482i
$405$			11.6497i			0.578876i
$406$	−1.57626			−0.0782285
$407$	4.93275	+	4.93275i	0.244508	+	0.244508i
$408$		−	6.37706i		−	0.315712i
$409$	−9.42336			−0.465955			−0.232978	−	0.972482i	$-0.574847\pi$
$409$	−9.42336			−0.465955			−0.232978	+	0.972482i	$0.574847\pi$
$410$	9.52379	+	5.65037i	0.470346	+	0.279052i
$411$	−25.7763			−1.27145
$412$			0.168702i			0.00831134i
$413$	−5.84538	−	5.84538i	−0.287632	−	0.287632i
$414$	0.751999			0.0369587
$415$			8.16970i			0.401035i
$416$	−0.619932	+	0.619932i	−0.0303947	+	0.0303947i
$417$	−11.6507	−	11.6507i	−0.570537	−	0.570537i
$418$		−	13.0284i		−	0.637241i
$419$		−	8.77076i		−	0.428479i	−0.976781	−	0.214240i	$-0.931273\pi$
$419$		−	8.77076i		−	0.428479i	0.976781	−	0.214240i	$-0.0687274\pi$
$420$	0.207417			0.0101209
$421$	26.7073	+	26.7073i	1.30163	+	1.30163i	0.927291	+	0.374341i	$0.122131\pi$
$421$	26.7073	+	26.7073i	1.30163	+	1.30163i	0.374341	+	0.927291i	$0.377869\pi$
$422$	6.57153	+	6.57153i	0.319897	+	0.319897i
$423$	0.101325	+	0.101325i	0.00492659	+	0.00492659i
$424$	−21.8672	+	21.8672i	−1.06197	+	1.06197i
$425$	−3.03764	+	3.03764i	−0.147347	+	0.147347i
$426$	−18.0298			−0.873547
$427$	−7.32018	+	7.32018i	−0.354248	+	0.354248i
$428$	−1.56063			−0.0754359
$429$	2.89350	−	2.89350i	0.139699	−	0.139699i
$430$			1.67659i			0.0808525i
$431$		−	24.1548i		−	1.16350i	−0.813369	−	0.581749i	$-0.802369\pi$
$431$		−	24.1548i		−	1.16350i	0.813369	−	0.581749i	$-0.197631\pi$
$432$	−13.7225	+	13.7225i	−0.660225	+	0.660225i
$433$	35.7346			1.71730			0.858648	−	0.512566i	$-0.171305\pi$
$433$	35.7346			1.71730			0.858648	+	0.512566i	$0.171305\pi$
$434$	0.614427	−	0.614427i	0.0294934	−	0.0294934i
$435$	2.51960			0.120806
$436$	−1.22633	+	1.22633i	−0.0587307	+	0.0587307i
$437$	−24.9558	+	24.9558i	−1.19380	+	1.19380i
$438$	−4.83737	−	4.83737i	−0.231139	−	0.231139i
$439$	13.7200	+	13.7200i	0.654820	+	0.654820i	0.954150	−	0.299330i	$-0.0967631\pi$
$439$	13.7200	+	13.7200i	0.654820	+	0.654820i	−0.299330	+	0.954150i	$0.596763\pi$
$440$	3.60418	+	3.60418i	0.171823	+	0.171823i
$441$	−0.103480			−0.00492761
$442$		−	2.85294i		−	0.135701i
$443$		−	20.1857i		−	0.959051i	−0.877528	−	0.479526i	$-0.840809\pi$
$443$		−	20.1857i		−	0.959051i	0.877528	−	0.479526i	$-0.159191\pi$
$444$	−0.580297	−	0.580297i	−0.0275397	−	0.0275397i
$445$	5.90548	−	5.90548i	0.279947	−	0.279947i
$446$			31.1834i			1.47658i
$447$	−34.1028			−1.61300
$448$	5.89712	+	5.89712i	0.278613	+	0.278613i
$449$			24.7485i			1.16795i	0.811770	+	0.583977i	$0.198504\pi$
$449$			24.7485i			1.16795i	−0.811770	+	0.583977i	$0.801496\pi$
$450$	−0.490129			−0.0231049
$451$	2.22903	+	8.73226i	0.104961	+	0.411186i
$452$	−1.58250			−0.0744346
$453$		−	2.38795i		−	0.112196i
$454$	12.7285	+	12.7285i	0.597380	+	0.597380i
$455$	2.06735			0.0969189
$456$			34.1467i			1.59907i
$457$	6.42851	−	6.42851i	0.300713	−	0.300713i	−0.540580	−	0.841293i	$-0.681795\pi$
$457$	6.42851	−	6.42851i	0.300713	−	0.300713i	0.841293	+	0.540580i	$0.181795\pi$
$458$	−22.0110	−	22.0110i	−1.02851	−	1.02851i
$459$			6.38940i			0.298232i
$460$		−	0.619754i		−	0.0288962i
$461$	20.3037			0.945638			0.472819	−	0.881160i	$-0.343236\pi$
$461$	20.3037			0.945638			0.472819	+	0.881160i	$0.343236\pi$
$462$	−2.42055	−	2.42055i	−0.112614	−	0.112614i
$463$	15.8015	+	15.8015i	0.734356	+	0.734356i	0.971479	−	0.237124i	$-0.0762047\pi$
$463$	15.8015	+	15.8015i	0.734356	+	0.734356i	−0.237124	+	0.971479i	$0.576205\pi$
$464$	3.07042	+	3.07042i	0.142541	+	0.142541i
$465$	−0.982142	+	0.982142i	−0.0455458	+	0.0455458i
$466$	−0.352799	+	0.352799i	−0.0163431	+	0.0163431i
$467$	13.9099			0.643673			0.321836	−	0.946795i	$-0.395700\pi$
$467$	13.9099			0.643673			0.321836	+	0.946795i	$0.395700\pi$
$468$	−0.0113499	+	0.0113499i	−0.000524647	+	0.000524647i
$469$	−2.70346			−0.124834
$470$	−1.69343	+	1.69343i	−0.0781119	+	0.0781119i
$471$		−	22.4222i		−	1.03316i
$472$			23.8982i			1.10000i
$473$	−0.964827	+	0.964827i	−0.0443628	+	0.0443628i
$474$	5.17073			0.237499
$475$	16.2654	−	16.2654i	0.746308	−	0.746308i
$476$	0.117689			0.00539428
$477$	−0.782730	+	0.782730i	−0.0358387	+	0.0358387i
$478$	11.5726	−	11.5726i	0.529319	−	0.529319i
$479$	−2.94814	−	2.94814i	−0.134704	−	0.134704i	0.636540	−	0.771244i	$-0.280365\pi$
$479$	−2.94814	−	2.94814i	−0.134704	−	0.134704i	−0.771244	+	0.636540i	$0.780365\pi$
$480$	−0.828971	−	0.828971i	−0.0378372	−	0.0378372i
$481$	−5.78388	−	5.78388i	−0.263722	−	0.263722i
$482$	−33.4624			−1.52417
$483$			9.27306i			0.421939i
$484$		−	0.847689i		−	0.0385313i
$485$	−4.52242	−	4.52242i	−0.205352	−	0.205352i
$486$	−1.04936	+	1.04936i	−0.0475998	+	0.0475998i
$487$			5.25945i			0.238328i	0.992875	+	0.119164i	$0.0380215\pi$
$487$			5.25945i			0.238328i	−0.992875	+	0.119164i	$0.961979\pi$
$488$	29.9277			1.35476
$489$	−8.80726	−	8.80726i	−0.398278	−	0.398278i
$490$		−	1.72944i		−	0.0781281i
$491$	−23.0443			−1.03997			−0.519987	−	0.854174i	$-0.674063\pi$
$491$	−23.0443			−1.03997			−0.519987	+	0.854174i	$0.674063\pi$
$492$	−0.262227	−	1.02728i	−0.0118221	−	0.0463132i
$493$	1.42963			0.0643874
$494$			15.2764i			0.687319i
$495$	0.129011	+	0.129011i	0.00579859	+	0.00579859i
$496$	−2.39370			−0.107480
$497$		−	7.41317i		−	0.332526i
$498$	−11.2159	+	11.2159i	−0.502599	+	0.502599i
$499$	10.8549	+	10.8549i	0.485932	+	0.485932i	0.907020	−	0.421088i	$-0.138352\pi$
$499$	10.8549	+	10.8549i	0.485932	+	0.485932i	−0.421088	+	0.907020i	$0.638352\pi$
$500$			0.992632i			0.0443919i
$501$			13.0639i			0.583651i
$502$	29.4774			1.31564
$503$	11.6760	+	11.6760i	0.520609	+	0.520609i	0.917755	−	0.397147i	$-0.130000\pi$
$503$	11.6760	+	11.6760i	0.520609	+	0.520609i	−0.397147	+	0.917755i	$0.630000\pi$
$504$	0.211533	+	0.211533i	0.00942242	+	0.00942242i
$505$	12.4965	+	12.4965i	0.556089	+	0.556089i
$506$	−7.23250	+	7.23250i	−0.321524	+	0.321524i
$507$	12.8012	−	12.8012i	0.568521	−	0.568521i
$508$	0.476783			0.0211538
$509$	−0.417247	+	0.417247i	−0.0184941	+	0.0184941i	−0.716293	−	0.697799i	$-0.754163\pi$
$509$	−0.417247	+	0.417247i	−0.0184941	+	0.0184941i	0.697799	+	0.716293i	$0.254163\pi$
$510$	3.81495			0.168929
$511$	1.98894	−	1.98894i	0.0879857	−	0.0879857i
$512$		−	24.0099i		−	1.06110i
$513$		−	34.2128i		−	1.51053i
$514$	−23.3602	+	23.3602i	−1.03038	+	1.03038i
$515$	−2.24845			−0.0990787
$516$	0.113504	−	0.113504i	0.00499672	−	0.00499672i
$517$	−1.94903			−0.0857182
$518$	−4.83849	+	4.83849i	−0.212591	+	0.212591i
$519$	−3.76482	+	3.76482i	−0.165257	+	0.165257i
$520$	−4.22607	−	4.22607i	−0.185325	−	0.185325i
$521$	−4.32791	−	4.32791i	−0.189609	−	0.189609i	0.605918	−	0.795527i	$-0.292806\pi$
$521$	−4.32791	−	4.32791i	−0.189609	−	0.189609i	−0.795527	+	0.605918i	$0.792806\pi$
$522$	0.115337	+	0.115337i	0.00504816	+	0.00504816i
$523$	−10.8230			−0.473257			−0.236628	−	0.971600i	$-0.576042\pi$
$523$	−10.8230			−0.473257			−0.236628	+	0.971600i	$0.576042\pi$
$524$		−	0.609658i		−	0.0266331i
$525$		−	6.04389i		−	0.263777i
$526$	12.8085	+	12.8085i	0.558478	+	0.558478i
$527$	−0.557271	+	0.557271i	−0.0242751	+	0.0242751i
$528$			9.43005i			0.410390i
$529$	4.70750			0.204674
$530$	−13.0816	−	13.0816i	−0.568229	−	0.568229i
$531$			0.855428i			0.0371224i
$532$	−0.630181			−0.0273218
$533$	−2.61364	−	10.2390i	−0.113209	−	0.443499i
$534$	16.2149			0.701689
$535$		−	20.8000i		−	0.899265i
$536$	5.52639	+	5.52639i	0.238704	+	0.238704i
$537$	−16.3046			−0.703594
$538$		−	9.06012i		−	0.390609i
$539$	0.995238	−	0.995238i	0.0428679	−	0.0428679i
$540$	0.424822	+	0.424822i	0.0182814	+	0.0182814i
$541$		−	40.3486i		−	1.73472i	−0.497681	−	0.867360i	$-0.665815\pi$
$541$		−	40.3486i		−	1.73472i	0.497681	−	0.867360i	$-0.334185\pi$
$542$		−	15.3964i		−	0.661331i
$543$	−25.6135			−1.09918
$544$	−0.470361	−	0.470361i	−0.0201666	−	0.0201666i
$545$	−16.3445	−	16.3445i	−0.700123	−	0.700123i
$546$	2.83820	+	2.83820i	0.121464	+	0.121464i
$547$	11.0533	−	11.0533i	0.472605	−	0.472605i	−0.430152	−	0.902757i	$-0.641540\pi$
$547$	11.0533	−	11.0533i	0.472605	−	0.472605i	0.902757	+	0.430152i	$0.141540\pi$
$548$	−0.972430	+	0.972430i	−0.0415402	+	0.0415402i
$549$	1.07125			0.0457200
$550$	4.71392	−	4.71392i	0.201002	−	0.201002i
$551$	−7.65513			−0.326120
$552$	18.9559	−	18.9559i	0.806818	−	0.806818i
$553$			2.12601i			0.0904070i
$554$			5.81307i			0.246974i
$555$	7.73419	−	7.73419i	0.328298	−	0.328298i
$556$	−0.879065			−0.0372807
$557$	−17.4836	+	17.4836i	−0.740805	+	0.740805i	−0.972733	−	0.231928i	$-0.925497\pi$
$557$	−17.4836	+	17.4836i	−0.740805	+	0.740805i	0.231928	+	0.972733i	$0.425497\pi$
$558$	−0.0899168			−0.00380648
$559$	1.13130	−	1.13130i	0.0478490	−	0.0478490i
$560$	−3.36880	+	3.36880i	−0.142358	+	0.142358i
$561$	2.19538	+	2.19538i	0.0926892	+	0.0926892i
$562$	15.7539	+	15.7539i	0.664537	+	0.664537i
$563$	7.19127	+	7.19127i	0.303076	+	0.303076i	0.842216	−	0.539140i	$-0.181251\pi$
$563$	7.19127	+	7.19127i	0.303076	+	0.303076i	−0.539140	+	0.842216i	$0.681251\pi$
$564$	0.229287			0.00965471
$565$		−	21.0916i		−	0.887328i
$566$		−	1.17840i		−	0.0495320i
$567$	−6.57590	−	6.57590i	−0.276162	−	0.276162i
$568$	−15.1540	+	15.1540i	−0.635846	+	0.635846i
$569$		−	37.4572i		−	1.57029i	−0.619314	−	0.785143i	$-0.712589\pi$
$569$		−	37.4572i		−	1.57029i	0.619314	−	0.785143i	$-0.287411\pi$
$570$	−20.4276			−0.855617
$571$	−26.5343	−	26.5343i	−1.11042	−	1.11042i	−0.993093	−	0.117331i	$-0.962566\pi$
$571$	−26.5343	−	26.5343i	−1.11042	−	1.11042i	−0.117331	−	0.993093i	$-0.537434\pi$
$572$		−	0.218319i		−	0.00912838i
$573$	0.171808			0.00717740
$574$	−8.56539	+	2.18644i	−0.357513	+	0.0912601i
$575$	−18.0589			−0.753108
$576$		−	0.863000i		−	0.0359583i
$577$	9.02107	+	9.02107i	0.375552	+	0.375552i	0.869495	−	0.493942i	$-0.164445\pi$
$577$	9.02107	+	9.02107i	0.375552	+	0.375552i	−0.493942	+	0.869495i	$0.664445\pi$
$578$	−21.3053			−0.886184
$579$			1.59406i			0.0662471i
$580$	0.0950541	−	0.0950541i	0.00394691	−	0.00394691i
$581$	−4.61157	−	4.61157i	−0.191320	−	0.191320i
$582$		−	12.4174i		−	0.514717i
$583$		−	15.0561i		−	0.623561i
$584$	−8.13157			−0.336487
$585$	−0.151271	−	0.151271i	−0.00625427	−	0.00625427i
$586$	−23.2561	−	23.2561i	−0.960701	−	0.960701i
$587$	−16.6602	−	16.6602i	−0.687639	−	0.687639i	0.274071	−	0.961710i	$-0.411630\pi$
$587$	−16.6602	−	16.6602i	−0.687639	−	0.687639i	−0.961710	+	0.274071i	$0.911630\pi$
$588$	−0.117081	+	0.117081i	−0.00482835	+	0.00482835i
$589$	2.98397	−	2.98397i	0.122952	−	0.122952i
$590$	−14.2966			−0.588582
$591$	18.6189	−	18.6189i	0.765879	−	0.765879i
$592$	18.8500			0.774728
$593$	18.7395	−	18.7395i	0.769540	−	0.769540i	−0.208485	−	0.978026i	$-0.566853\pi$
$593$	18.7395	−	18.7395i	0.769540	−	0.769540i	0.978026	+	0.208485i	$0.0668533\pi$
$594$		−	9.91529i		−	0.406829i
$595$			1.56856i			0.0643047i
$596$	−1.28655	+	1.28655i	−0.0526993	+	0.0526993i
$597$	14.3786			0.588476
$598$	8.48043	−	8.48043i	0.346791	−	0.346791i
$599$	27.1446			1.10910			0.554549	−	0.832151i	$-0.312891\pi$
$599$	27.1446			1.10910			0.554549	+	0.832151i	$0.312891\pi$
$600$	−12.3549	+	12.3549i	−0.504386	+	0.504386i
$601$	−30.2540	+	30.2540i	−1.23408	+	1.23408i	−0.271704	+	0.962381i	$0.587587\pi$
$601$	−30.2540	+	30.2540i	−1.23408	+	1.23408i	−0.962381	+	0.271704i	$0.912413\pi$
$602$	−0.946390	−	0.946390i	−0.0385720	−	0.0385720i
$603$	0.197815	+	0.197815i	0.00805567	+	0.00805567i
$604$	−0.0900875	−	0.0900875i	−0.00366561	−	0.00366561i
$605$	11.2980			0.459328
$606$			34.3123i			1.39384i
$607$		−	38.4255i		−	1.55964i	−0.626001	−	0.779822i	$-0.715309\pi$
$607$		−	38.4255i		−	1.55964i	0.626001	−	0.779822i	$-0.284691\pi$
$608$	2.51860	+	2.51860i	0.102143	+	0.102143i
$609$	−1.42225	+	1.42225i	−0.0576323	+	0.0576323i
$610$			17.9037i			0.724898i
$611$	2.28532			0.0924543
$612$	−0.00861148	−	0.00861148i	−0.000348099	−	0.000348099i
$613$		−	35.5689i		−	1.43662i	−0.695725	−	0.718308i	$-0.744917\pi$
$613$		−	35.5689i		−	1.43662i	0.695725	−	0.718308i	$-0.255083\pi$
$614$	26.9200			1.08640
$615$	13.6915	−	3.49495i	0.552095	−	0.140930i
$616$	−4.06892			−0.163941
$617$		−	7.26366i		−	0.292424i	−0.989253	−	0.146212i	$-0.953292\pi$
$617$		−	7.26366i		−	0.292424i	0.989253	−	0.146212i	$-0.0467082\pi$
$618$	−3.08684	−	3.08684i	−0.124171	−	0.124171i
$619$	38.4134			1.54396			0.771982	−	0.635644i	$-0.219266\pi$
$619$	38.4134			1.54396			0.771982	+	0.635644i	$0.219266\pi$
$620$			0.0741042i			0.00297610i
$621$	−18.9926	+	18.9926i	−0.762147	+	0.762147i
$622$	11.8513	+	11.8513i	0.475194	+	0.475194i
$623$			6.66696i			0.267106i
$624$		−	11.0572i		−	0.442641i
$625$	3.92410			0.156964
$626$	22.4734	+	22.4734i	0.898217	+	0.898217i
$627$	−11.7554	−	11.7554i	−0.469467	−	0.469467i
$628$	−0.845898	−	0.845898i	−0.0337550	−	0.0337550i
$629$	4.38840	−	4.38840i	0.174977	−	0.174977i
$630$	−0.126545	+	0.126545i	−0.00504168	+	0.00504168i
$631$	16.4526			0.654968			0.327484	−	0.944857i	$-0.393799\pi$
$631$	16.4526			0.654968			0.327484	+	0.944857i	$0.393799\pi$
$632$	4.34597	−	4.34597i	0.172873	−	0.172873i
$633$	11.8589			0.471347
$634$	−8.90158	+	8.90158i	−0.353527	+	0.353527i
$635$			6.35456i			0.252173i
$636$			1.77123i			0.0702337i
$637$	−1.16696	+	1.16696i	−0.0462367	+	0.0462367i
$638$	−2.21855			−0.0878334
$639$	−0.542431	+	0.542431i	−0.0214582	+	0.0214582i
$640$	13.0922			0.517515
$641$	34.6147	−	34.6147i	1.36720	−	1.36720i	0.502790	−	0.864408i	$-0.332307\pi$
$641$	34.6147	−	34.6147i	1.36720	−	1.36720i	0.864408	−	0.502790i	$-0.167693\pi$
$642$	28.5558	−	28.5558i	1.12701	−	1.12701i
$643$	23.8464	+	23.8464i	0.940410	+	0.940410i	0.998322	−	0.0579116i	$-0.0184442\pi$
$643$	23.8464	+	23.8464i	0.940410	+	0.940410i	−0.0579116	+	0.998322i	$0.518444\pi$
$644$	0.349834	+	0.349834i	0.0137854	+	0.0137854i
$645$	1.51278	+	1.51278i	0.0595655	+	0.0595655i
$646$	−11.5907			−0.456029
$647$			3.20208i			0.125887i	0.998017	+	0.0629434i	$0.0200488\pi$
$647$			3.20208i			0.125887i	−0.998017	+	0.0629434i	$0.979951\pi$
$648$			26.8848i			1.05614i
$649$	−8.22725	−	8.22725i	−0.322948	−	0.322948i
$650$	−5.52728	+	5.52728i	−0.216798	+	0.216798i
$651$		−	1.10878i		−	0.0434567i
$652$	−0.664523			−0.0260247
$653$	−11.9509	−	11.9509i	−0.467676	−	0.467676i	0.433485	−	0.901161i	$-0.357284\pi$
$653$	−11.9509	−	11.9509i	−0.467676	−	0.467676i	−0.901161	+	0.433485i	$0.857284\pi$
$654$		−	44.8779i		−	1.75486i
$655$	8.12551			0.317490
$656$	20.9437	+	12.4257i	0.817712	+	0.485141i
$657$	−0.291067			−0.0113556
$658$		−	1.91178i		−	0.0745291i
$659$	10.3894	+	10.3894i	0.404715	+	0.404715i	0.879891	−	0.475176i	$-0.157616\pi$
$659$	10.3894	+	10.3894i	0.404715	+	0.404715i	−0.475176	+	0.879891i	$0.657616\pi$
$660$	0.291936			0.0113636
$661$		−	30.7257i		−	1.19509i	−0.801835	−	0.597545i	$-0.796143\pi$
$661$		−	30.7257i		−	1.19509i	0.801835	−	0.597545i	$-0.203857\pi$
$662$	−31.6728	+	31.6728i	−1.23100	+	1.23100i
$663$	−2.57419	−	2.57419i	−0.0999731	−	0.0999731i
$664$			18.8539i			0.731673i
$665$		−	8.39904i		−	0.325701i
$666$	0.708078			0.0274375
$667$	4.24961	+	4.24961i	0.164546	+	0.164546i
$668$	0.492845	+	0.492845i	0.0190688	+	0.0190688i
$669$	28.1365	+	28.1365i	1.08782	+	1.08782i
$670$	−3.30605	+	3.30605i	−0.127724	+	0.127724i
$671$	−10.3030	+	10.3030i	−0.397743	+	0.397743i
$672$	0.935863			0.0361017
$673$	8.93380	−	8.93380i	0.344373	−	0.344373i	−0.513636	−	0.858008i	$-0.671702\pi$
$673$	8.93380	−	8.93380i	0.344373	−	0.344373i	0.858008	+	0.513636i	$0.171702\pi$
$674$	11.1737			0.430397
$675$	12.3788	−	12.3788i	0.476460	−	0.476460i
$676$		−	0.965871i		−	0.0371489i
$677$		−	18.9961i		−	0.730078i	−0.930992	−	0.365039i	$-0.881056\pi$
$677$		−	18.9961i		−	0.730078i	0.930992	−	0.365039i	$-0.118944\pi$
$678$	28.9560	−	28.9560i	1.11205	−	1.11205i
$679$	5.10556			0.195933
$680$	3.20644	−	3.20644i	0.122962	−	0.122962i
$681$	22.9697			0.880201
$682$	0.864793	−	0.864793i	0.0331146	−	0.0331146i
$683$	−34.2788	+	34.2788i	−1.31164	+	1.31164i	−0.391437	+	0.920205i	$0.628022\pi$
$683$	−34.2788	+	34.2788i	−1.31164	+	1.31164i	−0.920205	+	0.391437i	$0.871978\pi$
$684$	0.0461112	+	0.0461112i	0.00176310	+	0.00176310i
$685$	−12.9605	−	12.9605i	−0.495196	−	0.495196i
$686$	0.976220	+	0.976220i	0.0372723	+	0.0372723i
$687$	−39.7207			−1.51544
$688$			3.68697i			0.140565i
$689$			17.6540i			0.672564i
$690$	11.3400	+	11.3400i	0.431707	+	0.431707i
$691$	−30.8882	+	30.8882i	−1.17504	+	1.17504i	−0.194050	+	0.980992i	$0.562162\pi$
$691$	−30.8882	+	30.8882i	−1.17504	+	1.17504i	−0.980992	+	0.194050i	$0.937838\pi$
$692$			0.284062i			0.0107984i
$693$	−0.145646			−0.00553262
$694$	13.2696	+	13.2696i	0.503706	+	0.503706i
$695$		−	11.7162i		−	0.444419i
$696$	5.81469			0.220405
$697$	7.76862	−	1.98305i	0.294257	−	0.0751133i
$698$	−36.7140			−1.38964
$699$			0.636655i			0.0240805i
$700$	−0.228011	−	0.228011i	−0.00861800	−	0.00861800i
$701$	−8.50574			−0.321257			−0.160629	−	0.987015i	$-0.551352\pi$
$701$	−8.50574			−0.321257			−0.160629	+	0.987015i	$0.551352\pi$
$702$			11.6261i			0.438800i
$703$	−23.4982	+	23.4982i	−0.886252	+	0.886252i
$704$	8.30008	+	8.30008i	0.312821	+	0.312821i
$705$			3.05593i			0.115093i
$706$		−	6.30984i		−	0.237474i
$707$	−14.1079			−0.530582
$708$	0.967867	+	0.967867i	0.0363747	+	0.0363747i
$709$	34.8522	+	34.8522i	1.30890	+	1.30890i	0.922209	+	0.386693i	$0.126383\pi$
$709$	34.8522	+	34.8522i	1.30890	+	1.30890i	0.386693	+	0.922209i	$0.373617\pi$
$710$	−9.06555	−	9.06555i	−0.340224	−	0.340224i
$711$	0.155563	−	0.155563i	0.00583405	−	0.00583405i
$712$	13.6286	−	13.6286i	0.510752	−	0.510752i
$713$	−3.31300			−0.124073
$714$	−2.15343	+	2.15343i	−0.0805902	+	0.0805902i
$715$	2.90975			0.108819
$716$	−0.615103	+	0.615103i	−0.0229875	+	0.0229875i
$717$		−	20.8837i		−	0.779917i
$718$		−	44.7905i		−	1.67157i
$719$	−4.71261	+	4.71261i	−0.175751	+	0.175751i	−0.789501	−	0.613750i	$-0.789660\pi$
$719$	−4.71261	+	4.71261i	−0.175751	+	0.175751i	0.613750	+	0.789501i	$0.289660\pi$
$720$	0.492999			0.0183730
$721$	1.26919	−	1.26919i	0.0472671	−	0.0472671i
$722$	35.8326			1.33355
$723$	−30.1928	+	30.1928i	−1.12288	+	1.12288i
$724$	−0.966289	+	0.966289i	−0.0359119	+	0.0359119i
$725$	−2.76976	−	2.76976i	−0.102866	−	0.102866i
$726$	15.5107	+	15.5107i	0.575655	+	0.575655i
$727$	29.8059	+	29.8059i	1.10544	+	1.10544i	0.993742	+	0.111698i	$0.0356291\pi$
$727$	29.8059	+	29.8059i	1.10544	+	1.10544i	0.111698	+	0.993742i	$0.464371\pi$
$728$	4.77099			0.176825
$729$		−	26.0055i		−	0.963168i
$730$		−	4.86455i		−	0.180045i
$731$	0.858354	+	0.858354i	0.0317474	+	0.0317474i
$732$	1.21206	−	1.21206i	0.0447990	−	0.0447990i
$733$		−	13.5635i		−	0.500978i	−0.968120	−	0.250489i	$-0.919409\pi$
$733$		−	13.5635i		−	0.500978i	0.968120	−	0.250489i	$-0.0805913\pi$
$734$	−44.9053			−1.65749
$735$	−1.56046	−	1.56046i	−0.0575583	−	0.0575583i
$736$		−	2.79632i		−	0.103074i
$737$	−3.80506			−0.140161
$738$	0.786725	+	0.466756i	0.0289597	+	0.0171815i
$739$	45.7499			1.68294			0.841469	−	0.540305i	$-0.181691\pi$
$739$	45.7499			1.68294			0.841469	+	0.540305i	$0.181691\pi$
$740$		−	0.583557i		−	0.0214520i
$741$	13.7838	+	13.7838i	0.506360	+	0.506360i
$742$	14.7684			0.542166
$743$			15.1962i			0.557495i	0.960364	+	0.278747i	$0.0899192\pi$
$743$			15.1962i			0.557495i	−0.960364	+	0.278747i	$0.910081\pi$
$744$	−2.26657	+	2.26657i	−0.0830965	+	0.0830965i
$745$	−17.1472	−	17.1472i	−0.628224	−	0.628224i
$746$		−	12.8324i		−	0.469827i
$747$			0.674869i			0.0246922i
$748$	0.165645			0.00605659
$749$	11.7410	+	11.7410i	0.429009	+	0.429009i
$750$	−18.1628	−	18.1628i	−0.663211	−	0.663211i
$751$	2.68399	+	2.68399i	0.0979403	+	0.0979403i	0.754379	−	0.656439i	$-0.227938\pi$
$751$	2.68399	+	2.68399i	0.0979403	+	0.0979403i	−0.656439	+	0.754379i	$0.727938\pi$
$752$	−3.72399	+	3.72399i	−0.135800	+	0.135800i
$753$	26.5972	−	26.5972i	0.969257	−	0.969257i
$754$	2.60136			0.0947358
$755$	1.20068	−	1.20068i	0.0436974	−	0.0436974i
$756$	−0.479600			−0.0174429
$757$	−32.6417	+	32.6417i	−1.18638	+	1.18638i	−0.208325	+	0.978060i	$0.566801\pi$
$757$	−32.6417	+	32.6417i	−1.18638	+	1.18638i	−0.978060	+	0.208325i	$0.933199\pi$
$758$			38.3755i			1.39386i
$759$			13.0516i			0.473744i
$760$	−17.1693	+	17.1693i	−0.622795	+	0.622795i
$761$	−3.73218			−0.135292			−0.0676458	−	0.997709i	$-0.521549\pi$
$761$	−3.73218			−0.135292			−0.0676458	+	0.997709i	$0.521549\pi$
$762$	−8.72399	+	8.72399i	−0.316037	+	0.316037i
$763$	18.4521			0.668010
$764$	0.00648161	−	0.00648161i	0.000234497	−	0.000234497i
$765$	0.114774	−	0.114774i	0.00414965	−	0.00414965i
$766$	−18.2687	−	18.2687i	−0.660076	−	0.660076i
$767$	9.64683	+	9.64683i	0.348327	+	0.348327i
$768$	−2.80365	−	2.80365i	−0.101168	−	0.101168i
$769$	6.51059			0.234778			0.117389	−	0.993086i	$-0.462548\pi$
$769$	6.51059			0.234778			0.117389	+	0.993086i	$0.462548\pi$
$770$		−	2.43415i		−	0.0877206i
$771$			42.1555i			1.51819i
$772$	0.0601374	+	0.0601374i	0.00216439	+	0.00216439i
$773$	−2.90881	+	2.90881i	−0.104623	+	0.104623i	−0.757480	−	0.652858i	$-0.773570\pi$
$773$	−2.90881	+	2.90881i	−0.104623	+	0.104623i	0.652858	+	0.757480i	$0.273570\pi$
$774$			0.138497i			0.00497818i
$775$	2.15931			0.0775647
$776$	−10.4368	−	10.4368i	−0.374658	−	0.374658i
$777$			8.73146i			0.313240i
$778$	−39.9103			−1.43085
$779$	−41.5979	+	10.6185i	−1.49040	+	0.380446i
$780$	−0.342308			−0.0122566
$781$		−	10.4339i		−	0.373354i
$782$	6.43436	+	6.43436i	0.230092	+	0.230092i
$783$	−5.82594			−0.208202
$784$		−	3.80319i		−	0.135828i
$785$	11.2741	−	11.2741i	0.402390	−	0.402390i
$786$	11.1553	+	11.1553i	0.397896	+	0.397896i
$787$			38.6622i			1.37816i	0.724687	+	0.689079i	$0.241985\pi$
$787$			38.6622i			1.37816i	−0.724687	+	0.689079i	$0.758015\pi$
$788$		−	1.40483i		−	0.0500449i
$789$	23.1140			0.822881
$790$	2.59989	+	2.59989i	0.0924999	+	0.0924999i
$791$	11.9056	+	11.9056i	0.423314	+	0.423314i
$792$	0.297728	+	0.297728i	0.0105793	+	0.0105793i
$793$	12.0807	−	12.0807i	0.428999	−	0.428999i
$794$	12.5177	−	12.5177i	0.444237	−	0.444237i
$795$	−23.6069			−0.837249
$796$	0.542443	−	0.542443i	0.0192264	−	0.0192264i
$797$	−37.0825			−1.31353			−0.656765	−	0.754095i	$-0.728076\pi$
$797$	−37.0825			−1.31353			−0.656765	+	0.754095i	$0.728076\pi$
$798$	11.5308	−	11.5308i	0.408186	−	0.408186i
$799$			1.73394i			0.0613426i
$800$			1.82255i			0.0644369i
$801$	0.487830	−	0.487830i	0.0172366	−	0.0172366i
$802$	−38.6220			−1.36379
$803$	2.79940	−	2.79940i	0.0987885	−	0.0987885i
$804$	0.447633			0.0157868
$805$	−4.66258	+	4.66258i	−0.164334	+	0.164334i
$806$	−1.01401	+	1.01401i	−0.0357169	+	0.0357169i
$807$	−8.17487	−	8.17487i	−0.287769	−	0.287769i
$808$	28.8393	+	28.8393i	1.01456	+	1.01456i
$809$	16.1791	+	16.1791i	0.568826	+	0.568826i	0.931799	−	0.362974i	$-0.118239\pi$
$809$	16.1791	+	16.1791i	0.568826	+	0.568826i	−0.362974	+	0.931799i	$0.618239\pi$
$810$	−16.0833			−0.565110
$811$			21.7333i			0.763160i	0.924336	+	0.381580i	$0.124620\pi$
$811$			21.7333i			0.763160i	−0.924336	+	0.381580i	$0.875380\pi$
$812$			0.107311i			0.00376587i
$813$	−13.8920	−	13.8920i	−0.487214	−	0.487214i
$814$	−6.81008	+	6.81008i	−0.238693	+	0.238693i
$815$		−	8.85674i		−	0.310238i
$816$	8.38941			0.293688
$817$	−4.59616	−	4.59616i	−0.160799	−	0.160799i
$818$		−	13.0097i		−	0.454875i
$819$	0.170776			0.00596740
$820$	0.384674	−	0.648374i	0.0134334	−	0.0226422i
$821$	19.1712			0.669079			0.334540	−	0.942382i	$-0.391419\pi$
$821$	19.1712			0.669079			0.334540	+	0.942382i	$0.391419\pi$
$822$		−	35.5863i		−	1.24121i
$823$	−5.36365	−	5.36365i	−0.186965	−	0.186965i	0.607418	−	0.794383i	$-0.292206\pi$
$823$	−5.36365	−	5.36365i	−0.186965	−	0.186965i	−0.794383	+	0.607418i	$0.792206\pi$
$824$	−5.18894			−0.180765
$825$		−	8.50665i		−	0.296164i
$826$	8.07004	−	8.07004i	0.280792	−	0.280792i
$827$	−3.17615	−	3.17615i	−0.110445	−	0.110445i	0.649724	−	0.760170i	$-0.274884\pi$
$827$	−3.17615	−	3.17615i	−0.110445	−	0.110445i	−0.760170	+	0.649724i	$0.774884\pi$
$828$		−	0.0511956i		−	0.00177917i
$829$		−	21.4621i		−	0.745408i	−0.927950	−	0.372704i	$-0.878431\pi$
$829$		−	21.4621i		−	0.745408i	0.927950	−	0.372704i	$-0.121569\pi$
$830$	−11.2790			−0.391498
$831$	5.24508	+	5.24508i	0.181950	+	0.181950i
$832$	−9.73222	−	9.73222i	−0.337404	−	0.337404i
$833$	−0.885409	−	0.885409i	−0.0306776	−	0.0306776i
$834$	16.0848	−	16.0848i	0.556970	−	0.556970i
$835$	−6.56863	+	6.56863i	−0.227317	+	0.227317i
$836$	−0.886967			−0.0306764
$837$	2.27095	−	2.27095i	0.0784957	−	0.0784957i
$838$	12.1088			0.418290
$839$	30.4459	−	30.4459i	1.05111	−	1.05111i	0.0524883	−	0.998622i	$-0.483285\pi$
$839$	30.4459	−	30.4459i	1.05111	−	1.05111i	0.998622	−	0.0524883i	$-0.0167152\pi$
$840$			6.37976i			0.220122i
$841$		−	27.6964i		−	0.955050i
$842$	−36.8716	+	36.8716i	−1.27068	+	1.27068i
$843$	28.4292			0.979153
$844$	0.447385	−	0.447385i	0.0153996	−	0.0153996i
$845$	12.8731			0.442848
$846$	−0.139888	+	0.139888i	−0.00480944	+	0.00480944i
$847$	−6.37740	+	6.37740i	−0.219130	+	0.219130i
$848$	−28.7676	−	28.7676i	−0.987885	−	0.987885i
$849$	−1.06326	−	1.06326i	−0.0364911	−	0.0364911i
$850$	−4.19372	−	4.19372i	−0.143843	−	0.143843i
$851$	26.0892			0.894327
$852$			1.22746i			0.0420520i
$853$			50.6245i			1.73335i	0.498874	+	0.866675i	$0.333747\pi$
$853$			50.6245i			1.73335i	−0.498874	+	0.866675i	$0.666253\pi$
$854$	−10.1061	−	10.1061i	−0.345824	−	0.345824i
$855$	−0.614569	+	0.614569i	−0.0210178	+	0.0210178i
$856$		−	48.0020i		−	1.64067i
$857$	−20.4749			−0.699409			−0.349705	−	0.936860i	$-0.613718\pi$
$857$	−20.4749			−0.699409			−0.349705	+	0.936860i	$0.613718\pi$
$858$	3.99471	+	3.99471i	0.136377	+	0.136377i
$859$			40.7861i			1.39161i	0.718233	+	0.695803i	$0.244951\pi$
$859$			40.7861i			1.39161i	−0.718233	+	0.695803i	$0.755049\pi$
$860$	0.114141			0.00389219
$861$	−5.75568	+	9.70128i	−0.196153	+	0.330619i
$862$	33.3478			1.13583
$863$			32.8565i			1.11845i	0.829017	+	0.559224i	$0.188901\pi$
$863$			32.8565i			1.11845i	−0.829017	+	0.559224i	$0.811099\pi$
$864$	1.91679	+	1.91679i	0.0652104	+	0.0652104i
$865$	−3.78597			−0.128727
$866$			49.3346i			1.67646i
$867$	−19.2236	+	19.2236i	−0.652867	+	0.652867i
$868$	−0.0418298	−	0.0418298i	−0.00141980	−	0.00141980i
$869$			2.99231i			0.101507i
$870$			3.47852i			0.117933i
$871$	4.46160			0.151176
$872$	−37.7196	−	37.7196i	−1.27735	−	1.27735i
$873$	−0.373580	−	0.373580i	−0.0126438	−	0.0126438i
$874$	−34.4535	−	34.4535i	−1.16541	−	1.16541i
$875$	7.46784	−	7.46784i	0.252459	−	0.252459i
$876$	−0.329325	+	0.329325i	−0.0111269	+	0.0111269i
$877$	−8.41967			−0.284312			−0.142156	−	0.989844i	$-0.545403\pi$
$877$	−8.41967			−0.284312			−0.142156	+	0.989844i	$0.545403\pi$
$878$	−18.9416	+	18.9416i	−0.639248	+	0.639248i
$879$	−41.9676			−1.41553
$880$	−4.74152	+	4.74152i	−0.159836	+	0.159836i
$881$			3.67685i			0.123876i	0.998080	+	0.0619381i	$0.0197281\pi$
$881$			3.67685i			0.123876i	−0.998080	+	0.0619381i	$0.980272\pi$
$882$		−	0.142863i		−	0.00481043i
$883$	−32.3765	+	32.3765i	−1.08956	+	1.08956i	−0.0939834	+	0.995574i	$0.529960\pi$
$883$	−32.3765	+	32.3765i	−1.08956	+	1.08956i	−0.995574	+	0.0939834i	$0.970040\pi$
$884$	−0.194227			−0.00653255
$885$	−12.8997	+	12.8997i	−0.433619	+	0.433619i
$886$	27.8680			0.936245
$887$	7.03511	−	7.03511i	0.236216	−	0.236216i	−0.579065	−	0.815281i	$-0.696582\pi$
$887$	7.03511	−	7.03511i	0.236216	−	0.236216i	0.815281	+	0.579065i	$0.196582\pi$
$888$	17.8488	−	17.8488i	0.598967	−	0.598967i
$889$	−3.58697	−	3.58697i	−0.120303	−	0.120303i
$890$	8.15301	+	8.15301i	0.273290	+	0.273290i
$891$	−9.25545	−	9.25545i	−0.310069	−	0.310069i
$892$	2.12295			0.0710816
$893$		−	9.28461i		−	0.310698i
$894$		−	47.0817i		−	1.57465i
$895$	−8.19808	−	8.19808i	−0.274032	−	0.274032i
$896$	−7.39019	+	7.39019i	−0.246889	+	0.246889i
$897$		−	15.3036i		−	0.510974i
$898$	−34.1674			−1.14018
$899$	−0.508128	−	0.508128i	−0.0169470	−	0.0169470i
$900$			0.0333677i			0.00111226i
$901$	−13.3946			−0.446239
$902$	−12.0556	+	3.07736i	−0.401408	+	0.102465i
$903$	−1.70784			−0.0568333
$904$		−	48.6747i		−	1.61890i
$905$	−12.8787	−	12.8787i	−0.428102	−	0.428102i
$906$	3.29677			0.109528
$907$		−	37.5232i		−	1.24594i	−0.782246	−	0.622969i	$-0.785926\pi$
$907$		−	37.5232i		−	1.24594i	0.782246	−	0.622969i	$-0.214074\pi$
$908$	0.866551	−	0.866551i	0.0287575	−	0.0287575i
$909$	1.03229	+	1.03229i	0.0342390	+	0.0342390i
$910$			2.85415i			0.0946141i
$911$		−	32.4058i		−	1.07365i	−0.843693	−	0.536826i	$-0.819623\pi$
$911$		−	32.4058i		−	1.07365i	0.843693	−	0.536826i	$-0.180377\pi$
$912$	−44.9220			−1.48752
$913$	−6.49069	−	6.49069i	−0.214810	−	0.214810i
$914$	8.87510	+	8.87510i	0.293562	+	0.293562i
$915$	16.1543	+	16.1543i	0.534045	+	0.534045i
$916$	−1.49850	+	1.49850i	−0.0495117	+	0.0495117i
$917$	−4.58663	+	4.58663i	−0.151464	+	0.151464i
$918$	−8.82110			−0.291140
$919$	−37.7760	+	37.7760i	−1.24611	+	1.24611i	−0.288693	+	0.957422i	$0.593221\pi$
$919$	−37.7760	+	37.7760i	−1.24611	+	1.24611i	−0.957422	+	0.288693i	$0.906779\pi$
$920$	19.0624			0.628470
$921$	24.2896	−	24.2896i	0.800371	−	0.800371i
$922$			28.0310i			0.923151i
$923$			12.2342i			0.402694i
$924$	−0.164790	+	0.164790i	−0.00542118	+	0.00542118i
$925$	−17.0042			−0.559093
$926$	−21.8152	+	21.8152i	−0.716893	+	0.716893i
$927$	−0.185736			−0.00610038
$928$	0.428882	−	0.428882i	0.0140787	−	0.0140787i
$929$	−2.05199	+	2.05199i	−0.0673236	+	0.0673236i	−0.739967	−	0.672643i	$-0.765159\pi$
$929$	−2.05199	+	2.05199i	−0.0673236	+	0.0673236i	0.672643	+	0.739967i	$0.265159\pi$
$930$	−1.35593	−	1.35593i	−0.0444627	−	0.0444627i
$931$	4.74103	+	4.74103i	0.155381	+	0.155381i
$932$	0.0240183	+	0.0240183i	0.000786747	+	0.000786747i
$933$	21.3867			0.700168
$934$			19.2038i			0.628366i
$935$			2.20772i			0.0722001i
$936$	−0.349100	−	0.349100i	−0.0114107	−	0.0114107i
$937$	4.85205	−	4.85205i	0.158510	−	0.158510i	−0.623396	−	0.781906i	$-0.714248\pi$
$937$	4.85205	−	4.85205i	0.158510	−	0.158510i	0.781906	+	0.623396i	$0.214248\pi$
$938$		−	3.73235i		−	0.121865i
$939$	40.5551			1.32346
$940$	0.115287	+	0.115287i	0.00376026	+	0.00376026i
$941$			0.700203i			0.0228260i	0.999935	+	0.0114130i	$0.00363294\pi$
$941$			0.700203i			0.0228260i	−0.999935	+	0.0114130i	$0.996367\pi$
$942$	30.9558			1.00859
$943$	28.9870	+	17.1977i	0.943947	+	0.560034i
$944$	−31.4395			−1.02327
$945$		−	6.39210i		−	0.207935i
$946$	−1.33202	−	1.33202i	−0.0433078	−	0.0433078i
$947$	−50.1782			−1.63057			−0.815287	−	0.579058i	$-0.803421\pi$
$947$	−50.1782			−1.63057			−0.815287	+	0.579058i	$0.803421\pi$
$948$		−	0.352020i		−	0.0114331i
$949$	−3.28242	+	3.28242i	−0.106552	+	0.106552i
$950$	22.4557	+	22.4557i	0.728560	+	0.728560i
$951$			16.0636i			0.520899i
$952$			3.61990i			0.117322i
$953$	−7.25555			−0.235030			−0.117515	−	0.993071i	$-0.537493\pi$
$953$	−7.25555			−0.235030			−0.117515	+	0.993071i	$0.537493\pi$
$954$	−1.08062	−	1.08062i	−0.0349865	−	0.0349865i
$955$	0.0863868	+	0.0863868i	0.00279541	+	0.00279541i
$956$	−0.787856	−	0.787856i	−0.0254811	−	0.0254811i
$957$	−2.00178	+	2.00178i	−0.0647084	+	0.0647084i
$958$	4.07016	−	4.07016i	0.131501	−	0.131501i
$959$	14.6317			0.472483
$960$	13.0139	−	13.0139i	0.420021	−	0.420021i
$961$	−30.6039			−0.987221
$962$	7.98513	−	7.98513i	0.257451	−	0.257451i
$963$		−	1.71822i		−	0.0553687i
$964$			2.27810i			0.0733726i
$965$	−0.801510	+	0.801510i	−0.0258015	+	0.0258015i
$966$	−12.8022			−0.411905
$967$	36.2118	−	36.2118i	1.16449	−	1.16449i	0.181014	−	0.983481i	$-0.442062\pi$
$967$	36.2118	−	36.2118i	1.16449	−	1.16449i	0.983481	−	0.181014i	$-0.0579379\pi$
$968$	26.0733			0.838027
$969$	−10.4582	+	10.4582i	−0.335965	+	0.335965i
$970$	6.24358	−	6.24358i	0.200469	−	0.200469i
$971$	−2.46826	−	2.46826i	−0.0792104	−	0.0792104i	0.666392	−	0.745602i	$-0.267838\pi$
$971$	−2.46826	−	2.46826i	−0.0792104	−	0.0792104i	−0.745602	+	0.666392i	$0.767838\pi$
$972$	0.0714396	+	0.0714396i	0.00229143	+	0.00229143i
$973$	6.61344	+	6.61344i	0.212017	+	0.212017i
$974$	−7.26111			−0.232661
$975$			9.97444i			0.319438i
$976$			39.3717i			1.26026i
$977$	13.9458	+	13.9458i	0.446167	+	0.446167i	0.894078	−	0.447911i	$-0.147832\pi$
$977$	13.9458	+	13.9458i	0.446167	+	0.446167i	−0.447911	+	0.894078i	$0.647832\pi$
$978$	12.1592	−	12.1592i	0.388807	−	0.388807i
$979$			9.38361i			0.299901i
$980$	−0.117739			−0.00376104
$981$	−1.35016	−	1.35016i	−0.0431073	−	0.0431073i
$982$		−	31.8146i		−	1.01524i
$983$	0.602898			0.0192294			0.00961472	−	0.999954i	$-0.496939\pi$
$983$	0.602898			0.0192294			0.00961472	+	0.999954i	$0.496939\pi$
$984$	31.5970	−	8.06558i	1.00728	−	0.257121i
$985$	18.7235			0.596580
$986$			1.97373i			0.0628563i
$987$	−1.72499	−	1.72499i	−0.0549069	−	0.0549069i
$988$	1.04001			0.0330871
$989$			5.10295i			0.162264i
$990$	−0.178110	+	0.178110i	−0.00566070	+	0.00566070i
$991$	−6.04747	−	6.04747i	−0.192104	−	0.192104i	0.604500	−	0.796605i	$-0.293373\pi$
$991$	−6.04747	−	6.04747i	−0.192104	−	0.192104i	−0.796605	+	0.604500i	$0.793373\pi$
$992$			0.334357i			0.0106158i
$993$			57.1563i			1.81380i
$994$	10.2345			0.324619
$995$	7.22967	+	7.22967i	0.229196	+	0.229196i
$996$	0.763575	+	0.763575i	0.0241948	+	0.0241948i
$997$	21.2095	+	21.2095i	0.671710	+	0.671710i	0.958110	−	0.286400i	$-0.0924586\pi$
$997$	21.2095	+	21.2095i	0.671710	+	0.671710i	−0.286400	+	0.958110i	$0.592459\pi$
$998$	−14.9861	+	14.9861i	−0.474376	+	0.474376i
$999$	−17.8833	+	17.8833i	−0.565804	+	0.565804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.15	✓	40
41.32	even	4	inner	287.2.f.a.155.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.15	✓	40	1.1	even	1	trivial
287.2.f.a.155.6	yes	40	41.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.38058i q^{2} +(1.24569 + 1.24569i) q^{3} +0.0939893 q^{4} +1.25269i q^{5} +(-1.71978 + 1.71978i) q^{6} +(-0.707107 - 0.707107i) q^{7} +2.89093i q^{8} +0.103480i q^{9} +O(q^{10})\)	\(q+1.38058i q^{2} +(1.24569 + 1.24569i) q^{3} +0.0939893 q^{4} +1.25269i q^{5} +(-1.71978 + 1.71978i) q^{6} +(-0.707107 - 0.707107i) q^{7} +2.89093i q^{8} +0.103480i q^{9} -1.72944 q^{10} +(-0.995238 - 0.995238i) q^{11} +(0.117081 + 0.117081i) q^{12} +(1.16696 + 1.16696i) q^{13} +(0.976220 - 0.976220i) q^{14} +(-1.56046 + 1.56046i) q^{15} -3.80319 q^{16} +(-0.885409 + 0.885409i) q^{17} -0.142863 q^{18} +(4.74103 - 4.74103i) q^{19} +0.117739i q^{20} -1.76167i q^{21} +(1.37401 - 1.37401i) q^{22} -5.26379 q^{23} +(-3.60119 + 3.60119i) q^{24} +3.43078 q^{25} +(-1.61109 + 1.61109i) q^{26} +(3.60816 - 3.60816i) q^{27} +(-0.0664604 - 0.0664604i) q^{28} +(-0.807329 - 0.807329i) q^{29} +(-2.15434 - 2.15434i) q^{30} +0.629394 q^{31} +0.531236i q^{32} -2.47951i q^{33} +(-1.22238 - 1.22238i) q^{34} +(0.885783 - 0.885783i) q^{35} +0.00972599i q^{36} -4.95636 q^{37} +(6.54538 + 6.54538i) q^{38} +2.90734i q^{39} -3.62143 q^{40} +(-5.50687 - 3.26717i) q^{41} +2.43213 q^{42} -0.969443i q^{43} +(-0.0935417 - 0.0935417i) q^{44} -0.129628 q^{45} -7.26710i q^{46} +(0.979177 - 0.979177i) q^{47} +(-4.73759 - 4.73759i) q^{48} +1.00000i q^{49} +4.73647i q^{50} -2.20589 q^{51} +(0.109682 + 0.109682i) q^{52} +(7.56408 + 7.56408i) q^{53} +(4.98137 + 4.98137i) q^{54} +(1.24672 - 1.24672i) q^{55} +(2.04419 - 2.04419i) q^{56} +11.8117 q^{57} +(1.11458 - 1.11458i) q^{58} +8.26662 q^{59} +(-0.146666 + 0.146666i) q^{60} -10.3523i q^{61} +0.868931i q^{62} +(0.0731713 - 0.0731713i) q^{63} -8.33979 q^{64} +(-1.46184 + 1.46184i) q^{65} +3.42317 q^{66} +(1.91163 - 1.91163i) q^{67} +(-0.0832190 + 0.0832190i) q^{68} +(-6.55704 - 6.55704i) q^{69} +(1.22290 + 1.22290i) q^{70} +(5.24190 + 5.24190i) q^{71} -0.299153 q^{72} +2.81279i q^{73} -6.84267i q^{74} +(4.27368 + 4.27368i) q^{75} +(0.445606 - 0.445606i) q^{76} +1.40748i q^{77} -4.01383 q^{78} +(-1.50331 - 1.50331i) q^{79} -4.76420i q^{80} +9.29973 q^{81} +(4.51060 - 7.60269i) q^{82} +6.52174 q^{83} -0.165578i q^{84} +(-1.10914 - 1.10914i) q^{85} +1.33840 q^{86} -2.01136i q^{87} +(2.87716 - 2.87716i) q^{88} +(-4.71425 - 4.71425i) q^{89} -0.178962i q^{90} -1.65033i q^{91} -0.494740 q^{92} +(0.784029 + 0.784029i) q^{93} +(1.35184 + 1.35184i) q^{94} +(5.93902 + 5.93902i) q^{95} +(-0.661755 + 0.661755i) q^{96} +(-3.61017 + 3.61017i) q^{97} -1.38058 q^{98} +(0.102987 - 0.102987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

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