LMFDB - Embedded newform 370.2.e.e.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(121,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.e (of order $3$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	370.211
Dual form			370.2.e.e.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.581139 - 1.00656i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.581139 - 1.00656i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -1.00000 q^{10} +5.16228 q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.08114 + 1.87259i) q^{13} +1.16228 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.58114 + 4.47066i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(2.16228 - 3.74517i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.581139 - 1.00656i) q^{21} +(2.58114 + 4.47066i) q^{22} -3.16228 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.16228 q^{26} +5.00000 q^{27} +(0.581139 + 1.00656i) q^{28} -4.32456 q^{29} +(-0.500000 + 0.866025i) q^{30} -2.16228 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.58114 - 4.47066i) q^{33} +(-2.58114 + 4.47066i) q^{34} +(0.581139 + 1.00656i) q^{35} -2.00000 q^{36} +(-2.91886 - 5.33669i) q^{37} +4.32456 q^{38} +(1.08114 + 1.87259i) q^{39} +(0.500000 - 0.866025i) q^{40} +(3.66228 - 6.34325i) q^{41} +(0.581139 - 1.00656i) q^{42} -5.32456 q^{43} +(-2.58114 + 4.47066i) q^{44} -2.00000 q^{45} +(-1.58114 - 2.73861i) q^{46} -1.16228 q^{47} -1.00000 q^{48} +(2.82456 + 4.89227i) q^{49} +(0.500000 - 0.866025i) q^{50} +5.16228 q^{51} +(-1.08114 - 1.87259i) q^{52} +(-3.91886 - 6.78767i) q^{53} +(2.50000 + 4.33013i) q^{54} +(-2.58114 + 4.47066i) q^{55} +(-0.581139 + 1.00656i) q^{56} +(-2.16228 - 3.74517i) q^{57} +(-2.16228 - 3.74517i) q^{58} +(-2.58114 - 4.47066i) q^{59} -1.00000 q^{60} +(-2.16228 + 3.74517i) q^{61} +(-1.08114 - 1.87259i) q^{62} +2.32456 q^{63} +1.00000 q^{64} +(-1.08114 - 1.87259i) q^{65} +5.16228 q^{66} +(-2.16228 + 3.74517i) q^{67} -5.16228 q^{68} +(-1.58114 + 2.73861i) q^{69} +(-0.581139 + 1.00656i) q^{70} +(3.16228 - 5.47723i) q^{71} +(-1.00000 - 1.73205i) q^{72} -15.4868 q^{73} +(3.16228 - 5.19615i) q^{74} -1.00000 q^{75} +(2.16228 + 3.74517i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-1.08114 + 1.87259i) q^{78} +(1.00000 - 1.73205i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +7.32456 q^{82} +(2.00000 + 3.46410i) q^{83} +1.16228 q^{84} -5.16228 q^{85} +(-2.66228 - 4.61120i) q^{86} +(-2.16228 + 3.74517i) q^{87} -5.16228 q^{88} +(-4.32456 - 7.49035i) q^{89} +(-1.00000 - 1.73205i) q^{90} +(1.25658 + 2.17647i) q^{91} +(1.58114 - 2.73861i) q^{92} +(-1.08114 + 1.87259i) q^{93} +(-0.581139 - 1.00656i) q^{94} +(2.16228 + 3.74517i) q^{95} +(-0.500000 - 0.866025i) q^{96} +0.324555 q^{97} +(-2.82456 + 4.89227i) q^{98} +(5.16228 + 8.94133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} - 2 q^{20} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 20 q^{27} - 4 q^{28} + 8 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} - 4 q^{34} - 4 q^{35} - 8 q^{36} - 18 q^{37} - 8 q^{38} - 2 q^{39} + 2 q^{40} + 2 q^{41} - 4 q^{42} + 4 q^{43} - 4 q^{44} - 8 q^{45} + 8 q^{47} - 4 q^{48} - 14 q^{49} + 2 q^{50} + 8 q^{51} + 2 q^{52} - 22 q^{53} + 10 q^{54} - 4 q^{55} + 4 q^{56} + 4 q^{57} + 4 q^{58} - 4 q^{59} - 4 q^{60} + 4 q^{61} + 2 q^{62} - 16 q^{63} + 4 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} - 8 q^{68} + 4 q^{70} - 4 q^{72} - 24 q^{73} - 4 q^{75} - 4 q^{76} + 12 q^{77} + 2 q^{78} + 4 q^{79} + 4 q^{80} - 2 q^{81} + 4 q^{82} + 8 q^{83} - 8 q^{84} - 8 q^{85} + 2 q^{86} + 4 q^{87} - 8 q^{88} + 8 q^{89} - 4 q^{90} + 24 q^{91} + 2 q^{93} + 4 q^{94} - 4 q^{95} - 2 q^{96} - 24 q^{97} + 14 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 + 8 * q^11 + 2 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 2 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 - 2 * q^20 + 4 * q^21 + 4 * q^22 - 2 * q^24 - 2 * q^25 + 4 * q^26 + 20 * q^27 - 4 * q^28 + 8 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^33 - 4 * q^34 - 4 * q^35 - 8 * q^36 - 18 * q^37 - 8 * q^38 - 2 * q^39 + 2 * q^40 + 2 * q^41 - 4 * q^42 + 4 * q^43 - 4 * q^44 - 8 * q^45 + 8 * q^47 - 4 * q^48 - 14 * q^49 + 2 * q^50 + 8 * q^51 + 2 * q^52 - 22 * q^53 + 10 * q^54 - 4 * q^55 + 4 * q^56 + 4 * q^57 + 4 * q^58 - 4 * q^59 - 4 * q^60 + 4 * q^61 + 2 * q^62 - 16 * q^63 + 4 * q^64 + 2 * q^65 + 8 * q^66 + 4 * q^67 - 8 * q^68 + 4 * q^70 - 4 * q^72 - 24 * q^73 - 4 * q^75 - 4 * q^76 + 12 * q^77 + 2 * q^78 + 4 * q^79 + 4 * q^80 - 2 * q^81 + 4 * q^82 + 8 * q^83 - 8 * q^84 - 8 * q^85 + 2 * q^86 + 4 * q^87 - 8 * q^88 + 8 * q^89 - 4 * q^90 + 24 * q^91 + 2 * q^93 + 4 * q^94 - 4 * q^95 - 2 * q^96 - 24 * q^97 + 14 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.00000			0.408248
$7$	0.581139	−	1.00656i	0.219650	−	0.380445i	−0.735051	−	0.678012i	$-0.762842\pi$
$7$	0.581139	−	1.00656i	0.219650	−	0.380445i	0.954701	+	0.297567i	$0.0961752\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.00000			−0.316228
$11$	5.16228			1.55649			0.778243	−	0.627964i	$-0.216111\pi$
$11$	5.16228			1.55649			0.778243	+	0.627964i	$0.216111\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−1.08114	+	1.87259i	−0.299854	+	0.519362i	−0.976102	−	0.217311i	$-0.930271\pi$
$13$	−1.08114	+	1.87259i	−0.299854	+	0.519362i	0.676248	+	0.736674i	$0.263605\pi$
$14$	1.16228			0.310632
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.58114	+	4.47066i	0.626018	+	1.08430i	0.988343	+	0.152243i	$0.0486497\pi$
$17$	2.58114	+	4.47066i	0.626018	+	1.08430i	−0.362325	+	0.932052i	$0.618017\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	2.16228	−	3.74517i	0.496061	−	0.859202i	−0.503929	−	0.863745i	$-0.668113\pi$
$19$	2.16228	−	3.74517i	0.496061	−	0.859202i	0.999990	+	0.00454297i	$0.00144608\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−0.581139	−	1.00656i	−0.126815	−	0.219650i
$22$	2.58114	+	4.47066i	0.550301	+	0.953149i
$23$	−3.16228			−0.659380			−0.329690	−	0.944089i	$-0.606944\pi$
$23$	−3.16228			−0.659380			−0.329690	+	0.944089i	$0.606944\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.16228			−0.424058
$27$	5.00000			0.962250
$28$	0.581139	+	1.00656i	0.109825	+	0.190222i
$29$	−4.32456			−0.803050			−0.401525	−	0.915848i	$-0.631520\pi$
$29$	−4.32456			−0.803050			−0.401525	+	0.915848i	$0.631520\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−2.16228			−0.388357			−0.194178	−	0.980966i	$-0.562204\pi$
$31$	−2.16228			−0.388357			−0.194178	+	0.980966i	$0.562204\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.58114	−	4.47066i	0.449319	−	0.778243i
$34$	−2.58114	+	4.47066i	−0.442662	+	0.766712i
$35$	0.581139	+	1.00656i	0.0982304	+	0.170140i
$36$	−2.00000			−0.333333
$37$	−2.91886	−	5.33669i	−0.479858	−	0.877346i
$37$	−2.91886	−	5.33669i	−0.479858	−	0.877346i
$38$	4.32456			0.701536
$39$	1.08114	+	1.87259i	0.173121	+	0.299854i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	3.66228	−	6.34325i	0.571952	−	0.990649i	−0.424414	−	0.905468i	$-0.639520\pi$
$41$	3.66228	−	6.34325i	0.571952	−	0.990649i	0.996365	−	0.0851810i	$-0.0271469\pi$
$42$	0.581139	−	1.00656i	0.0896717	−	0.155316i
$43$	−5.32456			−0.811987			−0.405994	−	0.913876i	$-0.633074\pi$
$43$	−5.32456			−0.811987			−0.405994	+	0.913876i	$0.633074\pi$
$44$	−2.58114	+	4.47066i	−0.389121	+	0.673978i
$45$	−2.00000			−0.298142
$46$	−1.58114	−	2.73861i	−0.233126	−	0.403786i
$47$	−1.16228			−0.169536			−0.0847678	−	0.996401i	$-0.527015\pi$
$47$	−1.16228			−0.169536			−0.0847678	+	0.996401i	$0.527015\pi$
$48$	−1.00000			−0.144338
$49$	2.82456	+	4.89227i	0.403508	+	0.698896i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	5.16228			0.722863
$52$	−1.08114	−	1.87259i	−0.149927	−	0.259681i
$53$	−3.91886	−	6.78767i	−0.538297	−	0.932358i	−0.998996	−	0.0448012i	$-0.985735\pi$
$53$	−3.91886	−	6.78767i	−0.538297	−	0.932358i	0.460699	−	0.887556i	$-0.347599\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$	−2.58114	+	4.47066i	−0.348041	+	0.602824i
$56$	−0.581139	+	1.00656i	−0.0776579	+	0.134508i
$57$	−2.16228	−	3.74517i	−0.286401	−	0.496061i
$58$	−2.16228	−	3.74517i	−0.283921	−	0.491766i
$59$	−2.58114	−	4.47066i	−0.336036	−	0.582031i	0.647648	−	0.761940i	$-0.275753\pi$
$59$	−2.58114	−	4.47066i	−0.336036	−	0.582031i	−0.983683	+	0.179909i	$0.942420\pi$
$60$	−1.00000			−0.129099
$61$	−2.16228	+	3.74517i	−0.276851	+	0.479520i	−0.970601	−	0.240696i	$-0.922624\pi$
$61$	−2.16228	+	3.74517i	−0.276851	+	0.479520i	0.693749	+	0.720217i	$0.255958\pi$
$62$	−1.08114	−	1.87259i	−0.137305	−	0.237819i
$63$	2.32456			0.292866
$64$	1.00000			0.125000
$65$	−1.08114	−	1.87259i	−0.134099	−	0.232266i
$66$	5.16228			0.635432
$67$	−2.16228	+	3.74517i	−0.264164	+	0.457546i	−0.967344	−	0.253466i	$-0.918429\pi$
$67$	−2.16228	+	3.74517i	−0.264164	+	0.457546i	0.703180	+	0.711012i	$0.251763\pi$
$68$	−5.16228			−0.626018
$69$	−1.58114	+	2.73861i	−0.190347	+	0.329690i
$70$	−0.581139	+	1.00656i	−0.0694594	+	0.120307i
$71$	3.16228	−	5.47723i	0.375293	−	0.650027i	−0.615078	−	0.788467i	$-0.710875\pi$
$71$	3.16228	−	5.47723i	0.375293	−	0.650027i	0.990371	+	0.138440i	$0.0442087\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	−15.4868			−1.81260			−0.906298	−	0.422639i	$-0.861104\pi$
$73$	−15.4868			−1.81260			−0.906298	+	0.422639i	$0.861104\pi$
$74$	3.16228	−	5.19615i	0.367607	−	0.604040i
$75$	−1.00000			−0.115470
$76$	2.16228	+	3.74517i	0.248030	+	0.429601i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$	−1.08114	+	1.87259i	−0.122415	+	0.212029i
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$	1.00000			0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.32456			0.808862
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	0.954664	−	0.297686i	$-0.0962148\pi$
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	−0.735135	+	0.677920i	$0.762881\pi$
$84$	1.16228			0.126815
$85$	−5.16228			−0.559928
$86$	−2.66228	−	4.61120i	−0.287081	−	0.497239i
$87$	−2.16228	+	3.74517i	−0.231820	+	0.401525i
$88$	−5.16228			−0.550301
$89$	−4.32456	−	7.49035i	−0.458402	−	0.793975i	0.540475	−	0.841360i	$-0.318245\pi$
$89$	−4.32456	−	7.49035i	−0.458402	−	0.793975i	−0.998877	+	0.0473848i	$0.984911\pi$
$90$	−1.00000	−	1.73205i	−0.105409	−	0.182574i
$91$	1.25658	+	2.17647i	0.131726	+	0.228156i
$92$	1.58114	−	2.73861i	0.164845	−	0.285520i
$93$	−1.08114	+	1.87259i	−0.112109	+	0.194178i
$94$	−0.581139	−	1.00656i	−0.0599399	−	0.103819i
$95$	2.16228	+	3.74517i	0.221845	+	0.384247i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	0.324555			0.0329536			0.0164768	−	0.999864i	$-0.494755\pi$
$97$	0.324555			0.0329536			0.0164768	+	0.999864i	$0.494755\pi$
$98$	−2.82456	+	4.89227i	−0.285323	+	0.494194i
$99$	5.16228	+	8.94133i	0.518828	+	0.898637i
$100$	1.00000			0.100000
$101$	19.1623			1.90672			0.953359	−	0.301839i	$-0.0976005\pi$
$101$	19.1623			1.90672			0.953359	+	0.301839i	$0.0976005\pi$
$102$	2.58114	+	4.47066i	0.255571	+	0.442662i
$103$	5.48683			0.540634			0.270317	−	0.962771i	$-0.412872\pi$
$103$	5.48683			0.540634			0.270317	+	0.962771i	$0.412872\pi$
$104$	1.08114	−	1.87259i	0.106014	−	0.183622i
$105$	1.16228			0.113427
$106$	3.91886	−	6.78767i	0.380633	−	0.659276i
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	−0.645766	−	0.763535i	$-0.723462\pi$
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	0.984124	+	0.177482i	$0.0567953\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	−8.16228	−	14.1375i	−0.781804	−	1.35412i	−0.930890	−	0.365301i	$-0.880966\pi$
$109$	−8.16228	−	14.1375i	−0.781804	−	1.35412i	0.149085	−	0.988824i	$-0.452367\pi$
$110$	−5.16228			−0.492204
$111$	−6.08114	−	0.140537i	−0.577196	−	0.0133391i
$112$	−1.16228			−0.109825
$113$	−3.16228	−	5.47723i	−0.297482	−	0.515254i	0.678077	−	0.734991i	$-0.262814\pi$
$113$	−3.16228	−	5.47723i	−0.297482	−	0.515254i	−0.975559	+	0.219737i	$0.929480\pi$
$114$	2.16228	−	3.74517i	0.202516	−	0.350768i
$115$	1.58114	−	2.73861i	0.147442	−	0.255377i
$116$	2.16228	−	3.74517i	0.200762	−	0.347731i
$117$	−4.32456			−0.399805
$118$	2.58114	−	4.47066i	0.237613	−	0.411558i
$119$	6.00000			0.550019
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	15.6491			1.42265
$122$	−4.32456			−0.391527
$123$	−3.66228	−	6.34325i	−0.330216	−	0.571952i
$124$	1.08114	−	1.87259i	0.0970891	−	0.168163i
$125$	1.00000			0.0894427
$126$	1.16228	+	2.01312i	0.103544	+	0.179343i
$127$	−9.16228	−	15.8695i	−0.813021	−	1.40819i	−0.910740	−	0.412979i	$-0.864488\pi$
$127$	−9.16228	−	15.8695i	−0.813021	−	1.40819i	0.0977198	−	0.995214i	$-0.468845\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.66228	+	4.61120i	−0.234400	+	0.405994i
$130$	1.08114	−	1.87259i	0.0948221	−	0.164237i
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$	2.58114	+	4.47066i	0.224659	+	0.389121i
$133$	−2.51317	−	4.35293i	−0.217919	−	0.377447i
$134$	−4.32456			−0.373585
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$	−2.58114	−	4.47066i	−0.221331	−	0.383356i
$137$	−7.48683			−0.639643			−0.319822	−	0.947478i	$-0.603623\pi$
$137$	−7.48683			−0.639643			−0.319822	+	0.947478i	$0.603623\pi$
$138$	−3.16228			−0.269191
$139$	−1.74342	−	3.01969i	−0.147875	−	0.256126i	0.782567	−	0.622566i	$-0.213910\pi$
$139$	−1.74342	−	3.01969i	−0.147875	−	0.256126i	−0.930442	+	0.366440i	$0.880577\pi$
$140$	−1.16228			−0.0982304
$141$	−0.581139	+	1.00656i	−0.0489407	+	0.0847678i
$142$	6.32456			0.530745
$143$	−5.58114	+	9.66682i	−0.466718	+	0.808380i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	2.16228	−	3.74517i	0.179567	−	0.311020i
$146$	−7.74342	−	13.4120i	−0.640850	−	1.10998i
$147$	5.64911			0.465931
$148$	6.08114	+	0.140537i	0.499867	+	0.0115520i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−11.2434	+	19.4742i	−0.914976	+	1.58479i	−0.108040	+	0.994147i	$0.534458\pi$
$151$	−11.2434	+	19.4742i	−0.914976	+	1.58479i	−0.806936	+	0.590639i	$0.798876\pi$
$152$	−2.16228	+	3.74517i	−0.175384	+	0.303774i
$153$	−5.16228	+	8.94133i	−0.417345	+	0.722863i
$154$	6.00000			0.483494
$155$	1.08114	−	1.87259i	0.0868392	−	0.150410i
$156$	−2.16228			−0.173121
$157$	1.91886	+	3.32357i	0.153142	+	0.265249i	0.932381	−	0.361477i	$-0.117728\pi$
$157$	1.91886	+	3.32357i	0.153142	+	0.265249i	−0.779239	+	0.626727i	$0.784394\pi$
$158$	2.00000			0.159111
$159$	−7.83772			−0.621572
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−1.83772	+	3.18303i	−0.144833	+	0.250858i
$162$	−1.00000			−0.0785674
$163$	9.82456	+	17.0166i	0.769519	+	1.33285i	0.937824	+	0.347110i	$0.112837\pi$
$163$	9.82456	+	17.0166i	0.769519	+	1.33285i	−0.168306	+	0.985735i	$0.553830\pi$
$164$	3.66228	+	6.34325i	0.285976	+	0.495325i
$165$	2.58114	+	4.47066i	0.200941	+	0.348041i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−2.16228	+	3.74517i	−0.167322	+	0.289810i	−0.937477	−	0.348046i	$-0.886845\pi$
$167$	−2.16228	+	3.74517i	−0.167322	+	0.289810i	0.770155	+	0.637856i	$0.220179\pi$
$168$	0.581139	+	1.00656i	0.0448358	+	0.0776579i
$169$	4.16228	+	7.20928i	0.320175	+	0.554560i
$170$	−2.58114	−	4.47066i	−0.197964	−	0.342884i
$171$	8.64911			0.661414
$172$	2.66228	−	4.61120i	0.202997	−	0.351601i
$173$	5.16228	+	8.94133i	0.392481	+	0.679797i	0.992776	−	0.119982i	$-0.0382836\pi$
$173$	5.16228	+	8.94133i	0.392481	+	0.679797i	−0.600295	+	0.799778i	$0.704950\pi$
$174$	−4.32456			−0.327844
$175$	−1.16228			−0.0878599
$176$	−2.58114	−	4.47066i	−0.194561	−	0.336989i
$177$	−5.16228			−0.388021
$178$	4.32456	−	7.49035i	0.324139	−	0.561425i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−11.7434	+	20.3402i	−0.872881	+	1.51187i	−0.0138786	+	0.999904i	$0.504418\pi$
$181$	−11.7434	+	20.3402i	−0.872881	+	1.51187i	−0.859003	+	0.511971i	$0.828916\pi$
$182$	−1.25658	+	2.17647i	−0.0931442	+	0.161330i
$183$	2.16228	+	3.74517i	0.159840	+	0.276851i
$184$	3.16228			0.233126
$185$	6.08114	+	0.140537i	0.447094	+	0.0103325i
$186$	−2.16228			−0.158546
$187$	13.3246	+	23.0788i	0.974388	+	1.68769i
$188$	0.581139	−	1.00656i	0.0423839	−	0.0734111i
$189$	2.90569	−	5.03281i	0.211358	−	0.366083i
$190$	−2.16228	+	3.74517i	−0.156868	+	0.271704i
$191$	22.8114			1.65057			0.825287	−	0.564713i	$-0.191013\pi$
$191$	22.8114			1.65057			0.825287	+	0.564713i	$0.191013\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−19.4868			−1.40269			−0.701346	−	0.712821i	$-0.747417\pi$
$193$	−19.4868			−1.40269			−0.701346	+	0.712821i	$0.747417\pi$
$194$	0.162278	+	0.281073i	0.0116509	+	0.0201799i
$195$	−2.16228			−0.154844
$196$	−5.64911			−0.403508
$197$	−10.0811	−	17.4610i	−0.718251	−	1.24405i	−0.961692	−	0.274132i	$-0.911609\pi$
$197$	−10.0811	−	17.4610i	−0.718251	−	1.24405i	0.243441	−	0.969916i	$-0.421724\pi$
$198$	−5.16228	+	8.94133i	−0.366867	+	0.635432i
$199$	−12.1623			−0.862161			−0.431081	−	0.902313i	$-0.641868\pi$
$199$	−12.1623			−0.862161			−0.431081	+	0.902313i	$0.641868\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	2.16228	+	3.74517i	0.152515	+	0.264164i
$202$	9.58114	+	16.5950i	0.674127	+	1.16762i
$203$	−2.51317	+	4.35293i	−0.176390	+	0.305516i
$204$	−2.58114	+	4.47066i	−0.180716	+	0.313009i
$205$	3.66228	+	6.34325i	0.255785	+	0.443032i
$206$	2.74342	+	4.75174i	0.191143	+	0.331069i
$207$	−3.16228	−	5.47723i	−0.219793	−	0.380693i
$208$	2.16228			0.149927
$209$	11.1623	−	19.3336i	0.772111	−	1.33734i
$210$	0.581139	+	1.00656i	0.0401024	+	0.0694594i
$211$	4.32456			0.297715			0.148857	−	0.988859i	$-0.452440\pi$
$211$	4.32456			0.297715			0.148857	+	0.988859i	$0.452440\pi$
$212$	7.83772			0.538297
$213$	−3.16228	−	5.47723i	−0.216676	−	0.375293i
$214$	7.00000			0.478510
$215$	2.66228	−	4.61120i	0.181566	−	0.314481i
$216$	−5.00000			−0.340207
$217$	−1.25658	+	2.17647i	−0.0853024	+	0.147748i
$218$	8.16228	−	14.1375i	0.552819	−	0.957511i
$219$	−7.74342	+	13.4120i	−0.523252	+	0.906298i
$220$	−2.58114	−	4.47066i	−0.174020	−	0.301412i
$221$	−11.1623			−0.750856
$222$	−2.91886	−	5.33669i	−0.195901	−	0.358175i
$223$	7.16228			0.479622			0.239811	−	0.970820i	$-0.422915\pi$
$223$	7.16228			0.479622			0.239811	+	0.970820i	$0.422915\pi$
$224$	−0.581139	−	1.00656i	−0.0388290	−	0.0672538i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$	3.16228	−	5.47723i	0.210352	−	0.364340i
$227$	7.66228	−	13.2715i	0.508563	−	0.880857i	−0.491388	−	0.870941i	$-0.663510\pi$
$227$	7.66228	−	13.2715i	0.508563	−	0.880857i	0.999951	−	0.00991635i	$-0.00315653\pi$
$228$	4.32456			0.286401
$229$	8.58114	−	14.8630i	0.567058	−	0.982173i	−0.429797	−	0.902925i	$-0.641415\pi$
$229$	8.58114	−	14.8630i	0.567058	−	0.982173i	0.996855	−	0.0792472i	$-0.0252517\pi$
$230$	3.16228			0.208514
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$	4.32456			0.283921
$233$	−5.48683			−0.359454			−0.179727	−	0.983716i	$-0.557521\pi$
$233$	−5.48683			−0.359454			−0.179727	+	0.983716i	$0.557521\pi$
$234$	−2.16228	−	3.74517i	−0.141353	−	0.244830i
$235$	0.581139	−	1.00656i	0.0379093	−	0.0656609i
$236$	5.16228			0.336036
$237$	−1.00000	−	1.73205i	−0.0649570	−	0.112509i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	7.32456	+	12.6865i	0.473786	+	0.820622i	0.999550	−	0.0300092i	$-0.00955365\pi$
$239$	7.32456	+	12.6865i	0.473786	+	0.820622i	−0.525764	+	0.850631i	$0.676220\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−7.32456	+	12.6865i	−0.471816	+	0.817209i	−0.999480	−	0.0322438i	$-0.989735\pi$
$241$	−7.32456	+	12.6865i	−0.471816	+	0.817209i	0.527664	+	0.849453i	$0.323068\pi$
$242$	7.82456	+	13.5525i	0.502981	+	0.871189i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−2.16228	−	3.74517i	−0.138426	−	0.239760i
$245$	−5.64911			−0.360908
$246$	3.66228	−	6.34325i	0.233498	−	0.404431i
$247$	4.67544	+	8.09811i	0.297491	+	0.515270i
$248$	2.16228			0.137305
$249$	4.00000			0.253490
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$	−1.16228	+	2.01312i	−0.0732166	+	0.126815i
$253$	−16.3246			−1.02632
$254$	9.16228	−	15.8695i	0.574892	−	0.995743i
$255$	−2.58114	+	4.47066i	−0.161637	+	0.279964i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.743416	+	1.28764i	0.0463730	+	0.0803205i	0.888280	−	0.459302i	$-0.151900\pi$
$257$	0.743416	+	1.28764i	0.0463730	+	0.0803205i	−0.841907	+	0.539622i	$0.818567\pi$
$258$	−5.32456			−0.331492
$259$	−7.06797	−	0.163343i	−0.439182	−	0.0101496i
$260$	2.16228			0.134099
$261$	−4.32456	−	7.49035i	−0.267683	−	0.463641i
$262$	−9.00000	+	15.5885i	−0.556022	+	0.963058i
$263$	−5.74342	+	9.94789i	−0.354154	+	0.613413i	−0.986973	−	0.160887i	$-0.948565\pi$
$263$	−5.74342	+	9.94789i	−0.354154	+	0.613413i	0.632819	+	0.774300i	$0.281898\pi$
$264$	−2.58114	+	4.47066i	−0.158858	+	0.275150i
$265$	7.83772			0.481467
$266$	2.51317	−	4.35293i	0.154092	−	0.266895i
$267$	−8.64911			−0.529317
$268$	−2.16228	−	3.74517i	−0.132082	−	0.228773i
$269$	20.8377			1.27050			0.635249	−	0.772307i	$-0.280897\pi$
$269$	20.8377			1.27050			0.635249	+	0.772307i	$0.280897\pi$
$270$	−5.00000			−0.304290
$271$	−3.75658	−	6.50659i	−0.228196	−	0.395247i	0.729077	−	0.684431i	$-0.239949\pi$
$271$	−3.75658	−	6.50659i	−0.228196	−	0.395247i	−0.957274	+	0.289184i	$0.906616\pi$
$272$	2.58114	−	4.47066i	0.156505	−	0.271074i
$273$	2.51317			0.152104
$274$	−3.74342	−	6.48379i	−0.226148	−	0.391700i
$275$	−2.58114	−	4.47066i	−0.155649	−	0.269591i
$276$	−1.58114	−	2.73861i	−0.0951734	−	0.164845i
$277$	−5.24342	+	9.08186i	−0.315046	+	0.545676i	−0.979447	−	0.201700i	$-0.935353\pi$
$277$	−5.24342	+	9.08186i	−0.315046	+	0.545676i	0.664401	+	0.747376i	$0.268687\pi$
$278$	1.74342	−	3.01969i	0.104563	−	0.181109i
$279$	−2.16228	−	3.74517i	−0.129452	−	0.224218i
$280$	−0.581139	−	1.00656i	−0.0347297	−	0.0601536i
$281$	−11.8246	−	20.4807i	−0.705394	−	1.22178i	−0.966549	−	0.256481i	$-0.917437\pi$
$281$	−11.8246	−	20.4807i	−0.705394	−	1.22178i	0.261155	−	0.965297i	$-0.415896\pi$
$282$	−1.16228			−0.0692126
$283$	16.3114	−	28.2522i	0.969611	−	1.67942i	0.272932	−	0.962033i	$-0.412006\pi$
$283$	16.3114	−	28.2522i	0.969611	−	1.67942i	0.696679	−	0.717383i	$-0.254660\pi$
$284$	3.16228	+	5.47723i	0.187647	+	0.325014i
$285$	4.32456			0.256165
$286$	−11.1623			−0.660039
$287$	−4.25658	−	7.37262i	−0.251258	−	0.435192i
$288$	2.00000			0.117851
$289$	−4.82456	+	8.35637i	−0.283797	+	0.491551i
$290$	4.32456			0.253947
$291$	0.162278	−	0.281073i	0.00951288	−	0.0164768i
$292$	7.74342	−	13.4120i	0.453149	−	0.784877i
$293$	9.24342	−	16.0101i	0.540006	−	0.935318i	−0.458897	−	0.888490i	$-0.651755\pi$
$293$	9.24342	−	16.0101i	0.540006	−	0.935318i	0.998903	−	0.0468285i	$-0.0149114\pi$
$294$	2.82456	+	4.89227i	0.164731	+	0.285323i
$295$	5.16228			0.300559
$296$	2.91886	+	5.33669i	0.169655	+	0.310189i
$297$	25.8114			1.49773
$298$	6.00000	+	10.3923i	0.347571	+	0.602010i
$299$	3.41886	−	5.92164i	0.197718	−	0.342457i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−3.09431	+	5.35949i	−0.178353	+	0.308916i
$302$	−22.4868			−1.29397
$303$	9.58114	−	16.5950i	0.550422	−	0.953359i
$304$	−4.32456			−0.248030
$305$	−2.16228	−	3.74517i	−0.123812	−	0.214448i
$306$	−10.3246			−0.590216
$307$	24.2982			1.38677			0.693386	−	0.720566i	$-0.256118\pi$
$307$	24.2982			1.38677			0.693386	+	0.720566i	$0.256118\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	2.74342	−	4.75174i	0.156068	−	0.270317i
$310$	2.16228			0.122809
$311$	−0.918861	−	1.59151i	−0.0521038	−	0.0902465i	0.838797	−	0.544444i	$-0.183259\pi$
$311$	−0.918861	−	1.59151i	−0.0521038	−	0.0902465i	−0.890901	+	0.454198i	$0.849926\pi$
$312$	−1.08114	−	1.87259i	−0.0612074	−	0.106014i
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$	−1.91886	+	3.32357i	−0.108288	+	0.187560i
$315$	−1.16228	+	2.01312i	−0.0654869	+	0.113427i
$316$	1.00000	+	1.73205i	0.0562544	+	0.0974355i
$317$	−6.24342	−	10.8139i	−0.350665	−	0.607370i	0.635701	−	0.771935i	$-0.280711\pi$
$317$	−6.24342	−	10.8139i	−0.350665	−	0.607370i	−0.986366	+	0.164565i	$0.947378\pi$
$318$	−3.91886	−	6.78767i	−0.219759	−	0.380633i
$319$	−22.3246			−1.24994
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−3.50000	−	6.06218i	−0.195351	−	0.338358i
$322$	−3.67544			−0.204825
$323$	22.3246			1.24217
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.16228			0.119942
$326$	−9.82456	+	17.0166i	−0.544132	+	0.942464i
$327$	−16.3246			−0.902750
$328$	−3.66228	+	6.34325i	−0.202215	+	0.350247i
$329$	−0.675445	+	1.16990i	−0.0372385	+	0.0644989i
$330$	−2.58114	+	4.47066i	−0.142087	+	0.246102i
$331$	−16.7434	−	29.0004i	−0.920301	−	1.59401i	−0.798949	−	0.601399i	$-0.794610\pi$
$331$	−16.7434	−	29.0004i	−0.920301	−	1.59401i	−0.121353	−	0.992609i	$-0.538723\pi$
$332$	−4.00000			−0.219529
$333$	6.32456	−	10.3923i	0.346583	−	0.569495i
$334$	−4.32456			−0.236629
$335$	−2.16228	−	3.74517i	−0.118138	−	0.204621i
$336$	−0.581139	+	1.00656i	−0.0317037	+	0.0549125i
$337$	−11.6491	+	20.1769i	−0.634567	+	1.09910i	0.352039	+	0.935985i	$0.385488\pi$
$337$	−11.6491	+	20.1769i	−0.634567	+	1.09910i	−0.986607	+	0.163118i	$0.947845\pi$
$338$	−4.16228	+	7.20928i	−0.226398	+	0.392133i
$339$	−6.32456			−0.343503
$340$	2.58114	−	4.47066i	0.139982	−	0.242456i
$341$	−11.1623			−0.604471
$342$	4.32456	+	7.49035i	0.233845	+	0.405032i
$343$	14.7018			0.793821
$344$	5.32456			0.287081
$345$	−1.58114	−	2.73861i	−0.0851257	−	0.147442i
$346$	−5.16228	+	8.94133i	−0.277526	+	0.480689i
$347$	−20.3246			−1.09108			−0.545540	−	0.838085i	$-0.683675\pi$
$347$	−20.3246			−1.09108			−0.545540	+	0.838085i	$0.683675\pi$
$348$	−2.16228	−	3.74517i	−0.115910	−	0.200762i
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$	−0.581139	−	1.00656i	−0.0310632	−	0.0538030i
$351$	−5.40569	+	9.36294i	−0.288535	+	0.499757i
$352$	2.58114	−	4.47066i	0.137575	−	0.238287i
$353$	7.90569	+	13.6931i	0.420778	+	0.728808i	0.996016	−	0.0891778i	$-0.0284239\pi$
$353$	7.90569	+	13.6931i	0.420778	+	0.728808i	−0.575238	+	0.817986i	$0.695091\pi$
$354$	−2.58114	−	4.47066i	−0.137186	−	0.237613i
$355$	3.16228	+	5.47723i	0.167836	+	0.290701i
$356$	8.64911			0.458402
$357$	3.00000	−	5.19615i	0.158777	−	0.275010i
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−14.4868			−0.764586			−0.382293	−	0.924041i	$-0.624865\pi$
$359$	−14.4868			−0.764586			−0.382293	+	0.924041i	$0.624865\pi$
$360$	2.00000			0.105409
$361$	0.149111	+	0.258267i	0.00784793	+	0.0135930i
$362$	−23.4868			−1.23444
$363$	7.82456	−	13.5525i	0.410683	−	0.711323i
$364$	−2.51317			−0.131726
$365$	7.74342	−	13.4120i	0.405309	−	0.702016i
$366$	−2.16228	+	3.74517i	−0.113024	+	0.195763i
$367$	−9.32456	+	16.1506i	−0.486738	+	0.843055i	−0.999884	−	0.0152467i	$-0.995147\pi$
$367$	−9.32456	+	16.1506i	−0.486738	+	0.843055i	0.513146	+	0.858301i	$0.328480\pi$
$368$	1.58114	+	2.73861i	0.0824226	+	0.142760i
$369$	14.6491			0.762602
$370$	2.91886	+	5.33669i	0.151744	+	0.277441i
$371$	−9.10961			−0.472947
$372$	−1.08114	−	1.87259i	−0.0560544	−	0.0970891i
$373$	4.24342	−	7.34981i	0.219716	−	0.380559i	−0.735005	−	0.678061i	$-0.762820\pi$
$373$	4.24342	−	7.34981i	0.219716	−	0.380559i	0.954721	+	0.297503i	$0.0961537\pi$
$374$	−13.3246	+	23.0788i	−0.688996	+	1.19338i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	1.16228			0.0599399
$377$	4.67544	−	8.09811i	0.240798	−	0.417074i
$378$	5.81139			0.298906
$379$	−6.25658	−	10.8367i	−0.321379	−	0.556645i	0.659394	−	0.751798i	$-0.270813\pi$
$379$	−6.25658	−	10.8367i	−0.321379	−	0.556645i	−0.980773	+	0.195153i	$0.937480\pi$
$380$	−4.32456			−0.221845
$381$	−18.3246			−0.938795
$382$	11.4057	+	19.7552i	0.583566	+	1.01077i
$383$	−2.58114	+	4.47066i	−0.131890	+	0.228440i	−0.924405	−	0.381412i	$-0.875438\pi$
$383$	−2.58114	+	4.47066i	−0.131890	+	0.228440i	0.792515	+	0.609852i	$0.208771\pi$
$384$	1.00000			0.0510310
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$	−9.74342	−	16.8761i	−0.495927	−	0.858970i
$387$	−5.32456	−	9.22240i	−0.270662	−	0.468801i
$388$	−0.162278	+	0.281073i	−0.00823840	+	0.0142693i
$389$	−1.67544	+	2.90196i	−0.0849484	+	0.147135i	−0.905369	−	0.424625i	$-0.860406\pi$
$389$	−1.67544	+	2.90196i	−0.0849484	+	0.147135i	0.820421	+	0.571760i	$0.193739\pi$
$390$	−1.08114	−	1.87259i	−0.0547456	−	0.0948221i
$391$	−8.16228	−	14.1375i	−0.412784	−	0.714963i
$392$	−2.82456	−	4.89227i	−0.142662	−	0.247097i
$393$	18.0000			0.907980
$394$	10.0811	−	17.4610i	0.507880	−	0.879675i
$395$	1.00000	+	1.73205i	0.0503155	+	0.0871489i
$396$	−10.3246			−0.518828
$397$	−2.16228			−0.108522			−0.0542608	−	0.998527i	$-0.517280\pi$
$397$	−2.16228			−0.108522			−0.0542608	+	0.998527i	$0.517280\pi$
$398$	−6.08114	−	10.5328i	−0.304820	−	0.527964i
$399$	−5.02633			−0.251631
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−8.00000			−0.399501			−0.199750	−	0.979847i	$-0.564013\pi$
$401$	−8.00000			−0.399501			−0.199750	+	0.979847i	$0.564013\pi$
$402$	−2.16228	+	3.74517i	−0.107845	+	0.186792i
$403$	2.33772	−	4.04905i	0.116450	−	0.201698i
$404$	−9.58114	+	16.5950i	−0.476679	+	0.825633i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−5.02633			−0.249453
$407$	−15.0680	−	27.5495i	−0.746892	−	1.36558i
$408$	−5.16228			−0.255571
$409$	−2.82456	−	4.89227i	−0.139665	−	0.241907i	0.787705	−	0.616053i	$-0.211269\pi$
$409$	−2.82456	−	4.89227i	−0.139665	−	0.241907i	−0.927370	+	0.374146i	$0.877936\pi$
$410$	−3.66228	+	6.34325i	−0.180867	+	0.313271i
$411$	−3.74342	+	6.48379i	−0.184649	+	0.319822i
$412$	−2.74342	+	4.75174i	−0.135158	+	0.234101i
$413$	−6.00000			−0.295241
$414$	3.16228	−	5.47723i	0.155417	−	0.269191i
$415$	−4.00000			−0.196352
$416$	1.08114	+	1.87259i	0.0530072	+	0.0918112i
$417$	−3.48683			−0.170751
$418$	22.3246			1.09193
$419$	−6.90569	−	11.9610i	−0.337365	−	0.584334i	0.646571	−	0.762854i	$-0.276202\pi$
$419$	−6.90569	−	11.9610i	−0.337365	−	0.584334i	−0.983936	+	0.178520i	$0.942869\pi$
$420$	−0.581139	+	1.00656i	−0.0283567	+	0.0491152i
$421$	7.48683			0.364886			0.182443	−	0.983216i	$-0.441600\pi$
$421$	7.48683			0.364886			0.182443	+	0.983216i	$0.441600\pi$
$422$	2.16228	+	3.74517i	0.105258	+	0.182312i
$423$	−1.16228	−	2.01312i	−0.0565119	−	0.0978814i
$424$	3.91886	+	6.78767i	0.190317	+	0.329638i
$425$	2.58114	−	4.47066i	0.125204	−	0.216859i
$426$	3.16228	−	5.47723i	0.153213	−	0.265372i
$427$	2.51317	+	4.35293i	0.121621	+	0.210653i
$428$	3.50000	+	6.06218i	0.169179	+	0.293026i
$429$	5.58114	+	9.66682i	0.269460	+	0.466718i
$430$	5.32456			0.256773
$431$	−8.56797	+	14.8402i	−0.412705	+	0.714825i	−0.995184	−	0.0980197i	$-0.968749\pi$
$431$	−8.56797	+	14.8402i	−0.412705	+	0.714825i	0.582480	+	0.812845i	$0.302083\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	−2.51317			−0.120636
$435$	−2.16228	−	3.74517i	−0.103673	−	0.179567i
$436$	16.3246			0.781804
$437$	−6.83772	+	11.8433i	−0.327093	+	0.566541i
$438$	−15.4868			−0.739990
$439$	−13.4057	+	23.2193i	−0.639819	+	1.10820i	0.345653	+	0.938362i	$0.387657\pi$
$439$	−13.4057	+	23.2193i	−0.639819	+	1.10820i	−0.985472	+	0.169837i	$0.945676\pi$
$440$	2.58114	−	4.47066i	0.123051	−	0.213131i
$441$	−5.64911	+	9.78455i	−0.269005	+	0.465931i
$442$	−5.58114	−	9.66682i	−0.265468	−	0.459804i
$443$	24.6754			1.17237			0.586183	−	0.810179i	$-0.300630\pi$
$443$	24.6754			1.17237			0.586183	+	0.810179i	$0.300630\pi$
$444$	3.16228	−	5.19615i	0.150075	−	0.246598i
$445$	8.64911			0.410007
$446$	3.58114	+	6.20271i	0.169572	+	0.293707i
$447$	6.00000	−	10.3923i	0.283790	−	0.491539i
$448$	0.581139	−	1.00656i	0.0274562	−	0.0475556i
$449$	−15.8246	+	27.4089i	−0.746807	+	1.29351i	0.202539	+	0.979274i	$0.435081\pi$
$449$	−15.8246	+	27.4089i	−0.746807	+	1.29351i	−0.949346	+	0.314233i	$0.898253\pi$
$450$	2.00000			0.0942809
$451$	18.9057	−	32.7456i	0.890234	−	1.54193i
$452$	6.32456			0.297482
$453$	11.2434	+	19.4742i	0.528262	+	0.914976i
$454$	15.3246			0.719217
$455$	−2.51317			−0.117819
$456$	2.16228	+	3.74517i	0.101258	+	0.175384i
$457$	15.4868	−	26.8240i	0.724443	−	1.25477i	−0.234759	−	0.972054i	$-0.575430\pi$
$457$	15.4868	−	26.8240i	0.724443	−	1.25477i	0.959203	−	0.282719i	$-0.0912365\pi$
$458$	17.1623			0.801941
$459$	12.9057	+	22.3533i	0.602386	+	1.04336i
$460$	1.58114	+	2.73861i	0.0737210	+	0.127688i
$461$	10.1623	+	17.6016i	0.473304	+	0.819787i	0.999533	−	0.0305558i	$-0.00972772\pi$
$461$	10.1623	+	17.6016i	0.473304	+	0.819787i	−0.526229	+	0.850343i	$0.676394\pi$
$462$	3.00000	−	5.19615i	0.139573	−	0.241747i
$463$	9.48683	−	16.4317i	0.440891	−	0.763645i	−0.556865	−	0.830603i	$-0.687996\pi$
$463$	9.48683	−	16.4317i	0.440891	−	0.763645i	0.997756	+	0.0669581i	$0.0213294\pi$
$464$	2.16228	+	3.74517i	0.100381	+	0.173865i
$465$	−1.08114	−	1.87259i	−0.0501366	−	0.0868392i
$466$	−2.74342	−	4.75174i	−0.127086	−	0.220120i
$467$	−16.3509			−0.756629			−0.378314	−	0.925677i	$-0.623496\pi$
$467$	−16.3509			−0.756629			−0.378314	+	0.925677i	$0.623496\pi$
$468$	2.16228	−	3.74517i	0.0999513	−	0.173121i
$469$	2.51317	+	4.35293i	0.116047	+	0.201000i
$470$	1.16228			0.0536119
$471$	3.83772			0.176833
$472$	2.58114	+	4.47066i	0.118807	+	0.205779i
$473$	−27.4868			−1.26385
$474$	1.00000	−	1.73205i	0.0459315	−	0.0795557i
$475$	−4.32456			−0.198424
$476$	−3.00000	+	5.19615i	−0.137505	+	0.238165i
$477$	7.83772	−	13.5753i	0.358865	−	0.621572i
$478$	−7.32456	+	12.6865i	−0.335017	+	0.580267i
$479$	−12.9189	−	22.3761i	−0.590278	−	1.02239i	−0.994195	−	0.107596i	$-0.965685\pi$
$479$	−12.9189	−	22.3761i	−0.590278	−	1.02239i	0.403917	−	0.914796i	$-0.367648\pi$
$480$	1.00000			0.0456435
$481$	13.1491	+	0.303879i	0.599548	+	0.0138557i
$482$	−14.6491			−0.667249
$483$	1.83772	+	3.18303i	0.0836193	+	0.144833i
$484$	−7.82456	+	13.5525i	−0.355662	+	0.616024i
$485$	−0.162278	+	0.281073i	−0.00736865	+	0.0127629i
$486$	−8.00000	+	13.8564i	−0.362887	+	0.628539i
$487$	27.2982			1.23700			0.618500	−	0.785785i	$-0.287741\pi$
$487$	27.2982			1.23700			0.618500	+	0.785785i	$0.287741\pi$
$488$	2.16228	−	3.74517i	0.0978817	−	0.169536i
$489$	19.6491			0.888563
$490$	−2.82456	−	4.89227i	−0.127600	−	0.221010i
$491$	31.4868			1.42098			0.710490	−	0.703707i	$-0.248473\pi$
$491$	31.4868			1.42098			0.710490	+	0.703707i	$0.248473\pi$
$492$	7.32456			0.330216
$493$	−11.1623	−	19.3336i	−0.502724	−	0.870743i
$494$	−4.67544	+	8.09811i	−0.210358	+	0.364351i
$495$	−10.3246			−0.464054
$496$	1.08114	+	1.87259i	0.0485446	+	0.0840817i
$497$	−3.67544	−	6.36606i	−0.164866	−	0.285557i
$498$	2.00000	+	3.46410i	0.0896221	+	0.155230i
$499$	18.3246	−	31.7391i	0.820320	−	1.42084i	−0.0851245	−	0.996370i	$-0.527129\pi$
$499$	18.3246	−	31.7391i	0.820320	−	1.42084i	0.905444	−	0.424465i	$-0.139538\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	2.16228	+	3.74517i	0.0966034	+	0.167322i
$502$	3.00000	+	5.19615i	0.133897	+	0.231916i
$503$	−7.74342	−	13.4120i	−0.345262	−	0.598011i	0.640139	−	0.768259i	$-0.278877\pi$
$503$	−7.74342	−	13.4120i	−0.345262	−	0.598011i	−0.985401	+	0.170248i	$0.945543\pi$
$504$	−2.32456			−0.103544
$505$	−9.58114	+	16.5950i	−0.426355	+	0.738469i
$506$	−8.16228	−	14.1375i	−0.362858	−	0.628488i
$507$	8.32456			0.369706
$508$	18.3246			0.813021
$509$	16.3925	+	28.3927i	0.726586	+	1.25848i	0.958318	+	0.285704i	$0.0922275\pi$
$509$	16.3925	+	28.3927i	0.726586	+	1.25848i	−0.231732	+	0.972780i	$0.574439\pi$
$510$	−5.16228			−0.228589
$511$	−9.00000	+	15.5885i	−0.398137	+	0.689593i
$512$	−1.00000			−0.0441942
$513$	10.8114	−	18.7259i	0.477334	−	0.826768i
$514$	−0.743416	+	1.28764i	−0.0327907	+	0.0567952i
$515$	−2.74342	+	4.75174i	−0.120889	+	0.209387i
$516$	−2.66228	−	4.61120i	−0.117200	−	0.202997i
$517$	−6.00000			−0.263880
$518$	−3.39253	−	6.20271i	−0.149059	−	0.272532i
$519$	10.3246			0.453198
$520$	1.08114	+	1.87259i	0.0474111	+	0.0821184i
$521$	0.824555	−	1.42817i	0.0361244	−	0.0625693i	−0.847398	−	0.530958i	$-0.821832\pi$
$521$	0.824555	−	1.42817i	0.0361244	−	0.0625693i	0.883522	+	0.468389i	$0.155165\pi$
$522$	4.32456	−	7.49035i	0.189281	−	0.327844i
$523$	−6.98683	+	12.1015i	−0.305513	+	0.529164i	−0.977375	−	0.211512i	$-0.932161\pi$
$523$	−6.98683	+	12.1015i	−0.305513	+	0.529164i	0.671863	+	0.740676i	$0.265495\pi$
$524$	−18.0000			−0.786334
$525$	−0.581139	+	1.00656i	−0.0253630	+	0.0439300i
$526$	−11.4868			−0.500850
$527$	−5.58114	−	9.66682i	−0.243118	−	0.421093i
$528$	−5.16228			−0.224659
$529$	−13.0000			−0.565217
$530$	3.91886	+	6.78767i	0.170224	+	0.294837i
$531$	5.16228	−	8.94133i	0.224024	−	0.388021i
$532$	5.02633			0.217919
$533$	7.91886	+	13.7159i	0.343004	+	0.594100i
$534$	−4.32456	−	7.49035i	−0.187142	−	0.324139i
$535$	3.50000	+	6.06218i	0.151318	+	0.262091i
$536$	2.16228	−	3.74517i	0.0933962	−	0.161767i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	10.4189	+	18.0460i	0.449189	+	0.778018i
$539$	14.5811	+	25.2553i	0.628054	+	1.08782i
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	−29.6228			−1.27358			−0.636791	−	0.771036i	$-0.719739\pi$
$541$	−29.6228			−1.27358			−0.636791	+	0.771036i	$0.719739\pi$
$542$	3.75658	−	6.50659i	0.161359	−	0.279482i
$543$	11.7434	+	20.3402i	0.503958	+	0.872881i
$544$	5.16228			0.221331
$545$	16.3246			0.699267
$546$	1.25658	+	2.17647i	0.0537768	+	0.0931442i
$547$	−13.9737			−0.597471			−0.298735	−	0.954336i	$-0.596565\pi$
$547$	−13.9737			−0.597471			−0.298735	+	0.954336i	$0.596565\pi$
$548$	3.74342	−	6.48379i	0.159911	−	0.276974i
$549$	−8.64911			−0.369135
$550$	2.58114	−	4.47066i	0.110060	−	0.190630i
$551$	−9.35089	+	16.1962i	−0.398361	+	0.689982i
$552$	1.58114	−	2.73861i	0.0672977	−	0.116563i
$553$	−1.16228	−	2.01312i	−0.0494251	−	0.0856067i
$554$	−10.4868			−0.445543
$555$	3.16228	−	5.19615i	0.134231	−	0.220564i
$556$	3.48683			0.147875
$557$	19.4057	+	33.6116i	0.822246	+	1.42417i	0.904006	+	0.427519i	$0.140612\pi$
$557$	19.4057	+	33.6116i	0.822246	+	1.42417i	−0.0817606	+	0.996652i	$0.526054\pi$
$558$	2.16228	−	3.74517i	0.0915365	−	0.158546i
$559$	5.75658	−	9.97070i	0.243478	−	0.421715i
$560$	0.581139	−	1.00656i	0.0245576	−	0.0425350i
$561$	26.6491			1.12513
$562$	11.8246	−	20.4807i	0.498789	−	0.863927i
$563$	39.2982			1.65622			0.828111	−	0.560564i	$-0.189416\pi$
$563$	39.2982			1.65622			0.828111	+	0.560564i	$0.189416\pi$
$564$	−0.581139	−	1.00656i	−0.0244704	−	0.0423839i
$565$	6.32456			0.266076
$566$	32.6228			1.37124
$567$	0.581139	+	1.00656i	0.0244055	+	0.0422716i
$568$	−3.16228	+	5.47723i	−0.132686	+	0.229819i
$569$	14.6754			0.615227			0.307613	−	0.951511i	$-0.400470\pi$
$569$	14.6754			0.615227			0.307613	+	0.951511i	$0.400470\pi$
$570$	2.16228	+	3.74517i	0.0905678	+	0.156868i
$571$	−4.83772	−	8.37918i	−0.202452	−	0.350658i	0.746866	−	0.664975i	$-0.231558\pi$
$571$	−4.83772	−	8.37918i	−0.202452	−	0.350658i	−0.949318	+	0.314317i	$0.898224\pi$
$572$	−5.58114	−	9.66682i	−0.233359	−	0.404190i
$573$	11.4057	−	19.7552i	0.476480	−	0.825287i
$574$	4.25658	−	7.37262i	0.177666	−	0.307727i
$575$	1.58114	+	2.73861i	0.0659380	+	0.114208i
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	18.4189	+	31.9024i	0.766787	+	1.32811i	0.939296	+	0.343107i	$0.111479\pi$
$577$	18.4189	+	31.9024i	0.766787	+	1.32811i	−0.172509	+	0.985008i	$0.555187\pi$
$578$	−9.64911			−0.401350
$579$	−9.74342	+	16.8761i	−0.404923	+	0.701346i
$580$	2.16228	+	3.74517i	0.0897837	+	0.155510i
$581$	4.64911			0.192878
$582$	0.324555			0.0134533
$583$	−20.2302	−	35.0398i	−0.837851	−	1.45120i
$584$	15.4868			0.640850
$585$	2.16228	−	3.74517i	0.0893992	−	0.154844i
$586$	18.4868			0.763684
$587$	−22.3114	+	38.6445i	−0.920890	+	1.59503i	−0.122848	+	0.992426i	$0.539203\pi$
$587$	−22.3114	+	38.6445i	−0.920890	+	1.59503i	−0.798042	+	0.602602i	$0.794131\pi$
$588$	−2.82456	+	4.89227i	−0.116483	+	0.201754i
$589$	−4.67544	+	8.09811i	−0.192648	+	0.333677i
$590$	2.58114	+	4.47066i	0.106264	+	0.184054i
$591$	−20.1623			−0.829365
$592$	−3.16228	+	5.19615i	−0.129969	+	0.213561i
$593$	0.135944			0.00558254			0.00279127	−	0.999996i	$-0.499112\pi$
$593$	0.135944			0.00558254			0.00279127	+	0.999996i	$0.499112\pi$
$594$	12.9057	+	22.3533i	0.529527	+	0.917168i
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$	−6.08114	+	10.5328i	−0.248884	+	0.431081i
$598$	6.83772			0.279615
$599$	−6.73025	+	11.6571i	−0.274991	+	0.476298i	−0.970133	−	0.242575i	$-0.922008\pi$
$599$	−6.73025	+	11.6571i	−0.274991	+	0.476298i	0.695142	+	0.718872i	$0.255341\pi$
$600$	1.00000			0.0408248
$601$	8.82456	+	15.2846i	0.359961	+	0.623471i	0.987954	−	0.154748i	$-0.0494566\pi$
$601$	8.82456	+	15.2846i	0.359961	+	0.623471i	−0.627993	+	0.778219i	$0.716123\pi$
$602$	−6.18861			−0.252229
$603$	−8.64911			−0.352219
$604$	−11.2434	−	19.4742i	−0.457488	−	0.792393i
$605$	−7.82456	+	13.5525i	−0.318113	+	0.550989i
$606$	19.1623			0.778414
$607$	17.7434	+	30.7325i	0.720183	+	1.24739i	0.960926	+	0.276805i	$0.0892755\pi$
$607$	17.7434	+	30.7325i	0.720183	+	1.24739i	−0.240743	+	0.970589i	$0.577391\pi$
$608$	−2.16228	−	3.74517i	−0.0876919	−	0.151887i
$609$	2.51317	+	4.35293i	0.101839	+	0.176390i
$610$	2.16228	−	3.74517i	0.0875481	−	0.151638i
$611$	1.25658	−	2.17647i	0.0508359	−	0.0880504i
$612$	−5.16228	−	8.94133i	−0.208673	−	0.361432i
$613$	5.83772	+	10.1112i	0.235783	+	0.408389i	0.959500	−	0.281708i	$-0.0909011\pi$
$613$	5.83772	+	10.1112i	0.235783	+	0.408389i	−0.723717	+	0.690097i	$0.757568\pi$
$614$	12.1491	+	21.0429i	0.490298	+	0.849221i
$615$	7.32456			0.295355
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	18.4868	+	32.0201i	0.744252	+	1.28908i	0.950543	+	0.310591i	$0.100527\pi$
$617$	18.4868	+	32.0201i	0.744252	+	1.28908i	−0.206292	+	0.978491i	$0.566140\pi$
$618$	5.48683			0.220713
$619$	−34.0000			−1.36658			−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000			−1.36658			−0.683288	+	0.730149i	$0.739451\pi$
$620$	1.08114	+	1.87259i	0.0434196	+	0.0752049i
$621$	−15.8114			−0.634489
$622$	0.918861	−	1.59151i	0.0368430	−	0.0638139i
$623$	−10.0527			−0.402752
$624$	1.08114	−	1.87259i	0.0432802	−	0.0749635i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.00000	+	8.66025i	−0.199840	+	0.346133i
$627$	−11.1623	−	19.3336i	−0.445778	−	0.772111i
$628$	−3.83772			−0.153142
$629$	16.3246	−	26.8240i	0.650903	−	1.06954i
$630$	−2.32456			−0.0926125
$631$	−9.08114	−	15.7290i	−0.361514	−	0.626161i	0.626696	−	0.779264i	$-0.284407\pi$
$631$	−9.08114	−	15.7290i	−0.361514	−	0.626161i	−0.988210	+	0.153103i	$0.951074\pi$
$632$	−1.00000	+	1.73205i	−0.0397779	+	0.0688973i
$633$	2.16228	−	3.74517i	0.0859428	−	0.148857i
$634$	6.24342	−	10.8139i	0.247958	−	0.429475i
$635$	18.3246			0.727188
$636$	3.91886	−	6.78767i	0.155393	−	0.269148i
$637$	−12.2149			−0.483974
$638$	−11.1623	−	19.3336i	−0.441919	−	0.765426i
$639$	12.6491			0.500391
$640$	−1.00000			−0.0395285
$641$	−15.6623	−	27.1279i	−0.618623	−	1.07149i	−0.989737	−	0.142899i	$-0.954358\pi$
$641$	−15.6623	−	27.1279i	−0.618623	−	1.07149i	0.371115	−	0.928587i	$-0.378976\pi$
$642$	3.50000	−	6.06218i	0.138134	−	0.239255i
$643$	47.9737			1.89190			0.945948	−	0.324317i	$-0.105135\pi$
$643$	47.9737			1.89190			0.945948	+	0.324317i	$0.105135\pi$
$644$	−1.83772	−	3.18303i	−0.0724164	−	0.125429i
$645$	−2.66228	−	4.61120i	−0.104827	−	0.181566i
$646$	11.1623	+	19.3336i	0.439174	+	0.760672i
$647$	−6.83772	+	11.8433i	−0.268819	+	0.465607i	−0.968557	−	0.248792i	$-0.919967\pi$
$647$	−6.83772	+	11.8433i	−0.268819	+	0.465607i	0.699738	+	0.714399i	$0.253300\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−13.3246	−	23.0788i	−0.523035	−	0.905922i
$650$	1.08114	+	1.87259i	0.0424058	+	0.0734489i
$651$	1.25658	+	2.17647i	0.0492494	+	0.0853024i
$652$	−19.6491			−0.769519
$653$	−18.7302	+	32.4417i	−0.732971	+	1.26954i	0.222636	+	0.974902i	$0.428534\pi$
$653$	−18.7302	+	32.4417i	−0.732971	+	1.26954i	−0.955608	+	0.294642i	$0.904800\pi$
$654$	−8.16228	−	14.1375i	−0.319170	−	0.552819i
$655$	−18.0000			−0.703318
$656$	−7.32456			−0.285976
$657$	−15.4868	−	26.8240i	−0.604199	−	1.04650i
$658$	−1.35089			−0.0526632
$659$	−2.51317	+	4.35293i	−0.0978991	+	0.169566i	−0.910815	−	0.412815i	$-0.864546\pi$
$659$	−2.51317	+	4.35293i	−0.0978991	+	0.169566i	0.812916	+	0.582381i	$0.197879\pi$
$660$	−5.16228			−0.200941
$661$	−16.9057	+	29.2815i	−0.657555	+	1.13892i	0.323691	+	0.946163i	$0.395076\pi$
$661$	−16.9057	+	29.2815i	−0.657555	+	1.13892i	−0.981247	+	0.192756i	$0.938257\pi$
$662$	16.7434	−	29.0004i	0.650751	−	1.12713i
$663$	−5.58114	+	9.66682i	−0.216753	+	0.375428i
$664$	−2.00000	−	3.46410i	−0.0776151	−	0.134433i
$665$	5.02633			0.194913
$666$	12.1623	+	0.281073i	0.471279	+	0.0108914i
$667$	13.6754			0.529515
$668$	−2.16228	−	3.74517i	−0.0836610	−	0.144905i
$669$	3.58114	−	6.20271i	0.138455	−	0.239811i
$670$	2.16228	−	3.74517i	0.0835361	−	0.144689i
$671$	−11.1623	+	19.3336i	−0.430915	+	0.746367i
$672$	−1.16228			−0.0448358
$673$	−7.90569	+	13.6931i	−0.304742	+	0.527829i	−0.977204	−	0.212303i	$-0.931904\pi$
$673$	−7.90569	+	13.6931i	−0.304742	+	0.527829i	0.672462	+	0.740132i	$0.265237\pi$
$674$	−23.2982			−0.897414
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	−8.32456			−0.320175
$677$	−41.6228			−1.59969			−0.799847	−	0.600204i	$-0.795086\pi$
$677$	−41.6228			−1.59969			−0.799847	+	0.600204i	$0.795086\pi$
$678$	−3.16228	−	5.47723i	−0.121447	−	0.210352i
$679$	0.188612	−	0.326685i	0.00723825	−	0.0125370i
$680$	5.16228			0.197964
$681$	−7.66228	−	13.2715i	−0.293619	−	0.508563i
$682$	−5.58114	−	9.66682i	−0.213713	−	0.370162i
$683$	−1.17544	−	2.03593i	−0.0449771	−	0.0779027i	0.842660	−	0.538445i	$-0.180988\pi$
$683$	−1.17544	−	2.03593i	−0.0449771	−	0.0779027i	−0.887638	+	0.460543i	$0.847655\pi$
$684$	−4.32456	+	7.49035i	−0.165354	+	0.286401i
$685$	3.74342	−	6.48379i	0.143029	−	0.247733i
$686$	7.35089	+	12.7321i	0.280658	+	0.486114i
$687$	−8.58114	−	14.8630i	−0.327391	−	0.567058i
$688$	2.66228	+	4.61120i	0.101498	+	0.175800i
$689$	16.9473			0.645642
$690$	1.58114	−	2.73861i	0.0601929	−	0.104257i
$691$	−13.9057	−	24.0854i	−0.528998	−	0.916251i	−0.999428	−	0.0338136i	$-0.989235\pi$
$691$	−13.9057	−	24.0854i	−0.528998	−	0.916251i	0.470431	−	0.882437i	$-0.344099\pi$
$692$	−10.3246			−0.392481
$693$	12.0000			0.455842
$694$	−10.1623	−	17.6016i	−0.385755	−	0.668147i
$695$	3.48683			0.132263
$696$	2.16228	−	3.74517i	0.0819609	−	0.141960i
$697$	37.8114			1.43221
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$	−2.74342	+	4.75174i	−0.103766	+	0.179727i
$700$	0.581139	−	1.00656i	0.0219650	−	0.0380445i
$701$	14.4868	+	25.0919i	0.547160	+	0.947709i	0.998468	+	0.0553406i	$0.0176245\pi$
$701$	14.4868	+	25.0919i	0.547160	+	0.947709i	−0.451307	+	0.892369i	$0.649042\pi$
$702$	−10.8114			−0.408050
$703$	−26.2982	−	0.607758i	−0.991856	−	0.0229220i
$704$	5.16228			0.194561
$705$	−0.581139	−	1.00656i	−0.0218870	−	0.0379093i
$706$	−7.90569	+	13.6931i	−0.297535	+	0.515345i
$707$	11.1359	−	19.2880i	0.418810	−	0.725401i
$708$	2.58114	−	4.47066i	0.0970051	−	0.168018i
$709$	28.6491			1.07594			0.537970	−	0.842964i	$-0.319191\pi$
$709$	28.6491			1.07594			0.537970	+	0.842964i	$0.319191\pi$
$710$	−3.16228	+	5.47723i	−0.118678	+	0.205557i
$711$	4.00000			0.150012
$712$	4.32456	+	7.49035i	0.162070	+	0.280713i
$713$	6.83772			0.256075
$714$	6.00000			0.224544
$715$	−5.58114	−	9.66682i	−0.208723	−	0.361518i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	14.6491			0.547081
$718$	−7.24342	−	12.5460i	−0.270322	−	0.468211i
$719$	−19.5680	−	33.8927i	−0.729762	−	1.26399i	−0.956984	−	0.290142i	$-0.906297\pi$
$719$	−19.5680	−	33.8927i	−0.729762	−	1.26399i	0.227221	−	0.973843i	$-0.427036\pi$
$720$	1.00000	+	1.73205i	0.0372678	+	0.0645497i
$721$	3.18861	−	5.52284i	0.118750	−	0.205681i
$722$	−0.149111	+	0.258267i	−0.00554932	+	0.00961171i
$723$	7.32456	+	12.6865i	0.272403	+	0.471816i
$724$	−11.7434	−	20.3402i	−0.436441	−	0.755937i
$725$	2.16228	+	3.74517i	0.0803050	+	0.139092i
$726$	15.6491			0.580793
$727$	−7.16228	+	12.4054i	−0.265634	+	0.460092i	−0.967730	−	0.251991i	$-0.918915\pi$
$727$	−7.16228	+	12.4054i	−0.265634	+	0.460092i	0.702095	+	0.712083i	$0.252248\pi$
$728$	−1.25658	−	2.17647i	−0.0465721	−	0.0806652i
$729$	13.0000			0.481481
$730$	15.4868			0.573193
$731$	−13.7434	−	23.8043i	−0.508319	−	0.880434i
$732$	−4.32456			−0.159840
$733$	−9.32456	+	16.1506i	−0.344410	+	0.596536i	−0.985246	−	0.171142i	$-0.945254\pi$
$733$	−9.32456	+	16.1506i	−0.344410	+	0.596536i	0.640836	+	0.767678i	$0.278588\pi$
$734$	−18.6491			−0.688351
$735$	−2.82456	+	4.89227i	−0.104185	+	0.180454i
$736$	−1.58114	+	2.73861i	−0.0582816	+	0.100947i
$737$	−11.1623	+	19.3336i	−0.411168	+	0.712163i
$738$	7.32456	+	12.6865i	0.269621	+	0.466997i
$739$	−3.48683			−0.128265			−0.0641326	−	0.997941i	$-0.520428\pi$
$739$	−3.48683			−0.128265			−0.0641326	+	0.997941i	$0.520428\pi$
$740$	−3.16228	+	5.19615i	−0.116248	+	0.191014i
$741$	9.35089			0.343514
$742$	−4.55480	−	7.88915i	−0.167212	−	0.289620i
$743$	5.58114	−	9.66682i	0.204752	−	0.354641i	−0.745302	−	0.666727i	$-0.767695\pi$
$743$	5.58114	−	9.66682i	0.204752	−	0.354641i	0.950054	+	0.312086i	$0.101028\pi$
$744$	1.08114	−	1.87259i	0.0396365	−	0.0686524i
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	8.48683			0.310725
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$	−26.6491			−0.974388
$749$	−4.06797	−	7.04593i	−0.148640	−	0.257453i
$750$	1.00000			0.0365148
$751$	−4.48683			−0.163727			−0.0818634	−	0.996644i	$-0.526087\pi$
$751$	−4.48683			−0.163727			−0.0818634	+	0.996644i	$0.526087\pi$
$752$	0.581139	+	1.00656i	0.0211920	+	0.0367055i
$753$	3.00000	−	5.19615i	0.109326	−	0.189358i
$754$	9.35089			0.340539
$755$	−11.2434	−	19.4742i	−0.409190	−	0.708738i
$756$	2.90569	+	5.03281i	0.105679	+	0.183042i
$757$	−1.75658	−	3.04249i	−0.0638441	−	0.110581i	0.832337	−	0.554271i	$-0.187003\pi$
$757$	−1.75658	−	3.04249i	−0.0638441	−	0.110581i	−0.896181	+	0.443689i	$0.853669\pi$
$758$	6.25658	−	10.8367i	0.227249	−	0.393607i
$759$	−8.16228	+	14.1375i	−0.296272	+	0.513158i
$760$	−2.16228	−	3.74517i	−0.0784341	−	0.135852i
$761$	−0.837722	−	1.45098i	−0.0303674	−	0.0525979i	0.850442	−	0.526068i	$-0.176334\pi$
$761$	−0.837722	−	1.45098i	−0.0303674	−	0.0525979i	−0.880810	+	0.473470i	$0.843001\pi$
$762$	−9.16228	−	15.8695i	−0.331914	−	0.574892i
$763$	−18.9737			−0.686893
$764$	−11.4057	+	19.7552i	−0.412644	+	0.714720i
$765$	−5.16228	−	8.94133i	−0.186643	−	0.323274i
$766$	−5.16228			−0.186521
$767$	11.1623			0.403046
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−22.9737			−0.828452			−0.414226	−	0.910174i	$-0.635948\pi$
$769$	−22.9737			−0.828452			−0.414226	+	0.910174i	$0.635948\pi$
$770$	−3.00000	+	5.19615i	−0.108112	+	0.187256i
$771$	1.48683			0.0535470
$772$	9.74342	−	16.8761i	0.350673	−	0.607384i
$773$	−19.8925	+	34.4549i	−0.715484	+	1.23926i	0.247288	+	0.968942i	$0.420461\pi$
$773$	−19.8925	+	34.4549i	−0.715484	+	1.23926i	−0.962772	+	0.270313i	$0.912873\pi$
$774$	5.32456	−	9.22240i	0.191387	−	0.331492i
$775$	1.08114	+	1.87259i	0.0388357	+	0.0672653i
$776$	−0.324555			−0.0116509
$777$	−3.67544	+	6.03937i	−0.131856	+	0.216661i
$778$	−3.35089			−0.120135
$779$	−15.8377	−	27.4317i	−0.567445	−	0.982844i
$780$	1.08114	−	1.87259i	0.0387110	−	0.0670494i
$781$	16.3246	−	28.2750i	0.584139	−	1.01176i
$782$	8.16228	−	14.1375i	0.291882	−	0.505555i
$783$	−21.6228			−0.772735
$784$	2.82456	−	4.89227i	0.100877	−	0.174724i
$785$	−3.83772			−0.136974
$786$	9.00000	+	15.5885i	0.321019	+	0.556022i
$787$	29.9737			1.06845			0.534223	−	0.845344i	$-0.320604\pi$
$787$	29.9737			1.06845			0.534223	+	0.845344i	$0.320604\pi$
$788$	20.1623			0.718251
$789$	5.74342	+	9.94789i	0.204471	+	0.354154i
$790$	−1.00000	+	1.73205i	−0.0355784	+	0.0616236i
$791$	−7.35089			−0.261368
$792$	−5.16228	−	8.94133i	−0.183434	−	0.317716i
$793$	−4.67544	−	8.09811i	−0.166030	−	0.287572i
$794$	−1.08114	−	1.87259i	−0.0383682	−	0.0664556i
$795$	3.91886	−	6.78767i	0.138988	−	0.240734i
$796$	6.08114	−	10.5328i	0.215540	−	0.373327i
$797$	14.9189	+	25.8402i	0.528453	+	0.915308i	0.999450	+	0.0331726i	$0.0105611\pi$
$797$	14.9189	+	25.8402i	0.528453	+	0.915308i	−0.470996	+	0.882135i	$0.656106\pi$
$798$	−2.51317	−	4.35293i	−0.0889651	−	0.154092i
$799$	−3.00000	−	5.19615i	−0.106132	−	0.183827i
$800$	−1.00000			−0.0353553
$801$	8.64911	−	14.9807i	0.305601	−	0.529317i
$802$	−4.00000	−	6.92820i	−0.141245	−	0.244643i
$803$	−79.9473			−2.82128
$804$	−4.32456			−0.152515
$805$	−1.83772	−	3.18303i	−0.0647712	−	0.112187i
$806$	4.67544			0.164686
$807$	10.4189	−	18.0460i	0.366761	−	0.635249i
$808$	−19.1623			−0.674127
$809$	5.14911	−	8.91852i	0.181033	−	0.313559i	−0.761200	−	0.648518i	$-0.775389\pi$
$809$	5.14911	−	8.91852i	0.181033	−	0.313559i	0.942233	+	0.334959i	$0.108723\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	20.9737	−	36.3275i	0.736485	−	1.27563i	−0.217584	−	0.976042i	$-0.569818\pi$
$811$	20.9737	−	36.3275i	0.736485	−	1.27563i	0.954069	−	0.299588i	$-0.0968492\pi$
$812$	−2.51317	−	4.35293i	−0.0881949	−	0.152758i
$813$	−7.51317			−0.263498
$814$	16.3246	−	26.8240i	0.572175	−	0.940180i
$815$	−19.6491			−0.688278
$816$	−2.58114	−	4.47066i	−0.0903579	−	0.156505i
$817$	−11.5132	+	19.9414i	−0.402795	+	0.697661i
$818$	2.82456	−	4.89227i	0.0987583	−	0.171054i
$819$	−2.51317	+	4.35293i	−0.0878172	+	0.152104i
$820$	−7.32456			−0.255785
$821$	22.1623	−	38.3862i	0.773469	−	1.33969i	−0.162182	−	0.986761i	$-0.551853\pi$
$821$	22.1623	−	38.3862i	0.773469	−	1.33969i	0.935651	−	0.352926i	$-0.114813\pi$
$822$	−7.48683			−0.261133
$823$	−24.0680	−	41.6870i	−0.838957	−	1.45312i	−0.890768	−	0.454459i	$-0.849833\pi$
$823$	−24.0680	−	41.6870i	−0.838957	−	1.45312i	0.0518110	−	0.998657i	$-0.483501\pi$
$824$	−5.48683			−0.191143
$825$	−5.16228			−0.179727
$826$	−3.00000	−	5.19615i	−0.104383	−	0.180797i
$827$	7.83772	−	13.5753i	0.272544	−	0.472061i	−0.696968	−	0.717102i	$-0.745468\pi$
$827$	7.83772	−	13.5753i	0.272544	−	0.472061i	0.969513	+	0.245041i	$0.0788015\pi$
$828$	6.32456			0.219793
$829$	21.5548	+	37.3340i	0.748629	+	1.29666i	0.948480	+	0.316838i	$0.102621\pi$
$829$	21.5548	+	37.3340i	0.748629	+	1.29666i	−0.199850	+	0.979826i	$0.564046\pi$
$830$	−2.00000	−	3.46410i	−0.0694210	−	0.120241i
$831$	5.24342	+	9.08186i	0.181892	+	0.315046i
$832$	−1.08114	+	1.87259i	−0.0374817	+	0.0649203i
$833$	−14.5811	+	25.2553i	−0.505207	+	0.875043i
$834$	−1.74342	−	3.01969i	−0.0603696	−	0.104563i
$835$	−2.16228	−	3.74517i	−0.0748287	−	0.129607i
$836$	11.1623	+	19.3336i	0.386055	+	0.668668i
$837$	−10.8114			−0.373696
$838$	6.90569	−	11.9610i	0.238553	−	0.413186i
$839$	18.2434	+	31.5985i	0.629833	+	1.09090i	0.987585	+	0.157086i	$0.0502099\pi$
$839$	18.2434	+	31.5985i	0.629833	+	1.09090i	−0.357752	+	0.933817i	$0.616457\pi$
$840$	−1.16228			−0.0401024
$841$	−10.2982			−0.355111
$842$	3.74342	+	6.48379i	0.129007	+	0.223446i
$843$	−23.6491			−0.814519
$844$	−2.16228	+	3.74517i	−0.0744287	+	0.128914i
$845$	−8.32456			−0.286373
$846$	1.16228	−	2.01312i	0.0399599	−	0.0692126i
$847$	9.09431	−	15.7518i	0.312484	−	0.541238i
$848$	−3.91886	+	6.78767i	−0.134574	+	0.233089i
$849$	−16.3114	−	28.2522i	−0.559805	−	0.969611i
$850$	5.16228			0.177065
$851$	9.23025	+	16.8761i	0.316409	+	0.578505i
$852$	6.32456			0.216676
$853$	−0.432028	−	0.748295i	−0.0147924	−	0.0256211i	0.858534	−	0.512756i	$-0.171375\pi$
$853$	−0.432028	−	0.748295i	−0.0147924	−	0.0256211i	−0.873327	+	0.487135i	$0.838042\pi$
$854$	−2.51317	+	4.35293i	−0.0859988	+	0.148954i
$855$	−4.32456	+	7.49035i	−0.147897	+	0.256165i
$856$	−3.50000	+	6.06218i	−0.119628	+	0.207201i
$857$	27.4868			0.938932			0.469466	−	0.882950i	$-0.344446\pi$
$857$	27.4868			0.938932			0.469466	+	0.882950i	$0.344446\pi$
$858$	−5.58114	+	9.66682i	−0.190537	+	0.330020i
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$	2.66228	+	4.61120i	0.0907829	+	0.157241i
$861$	−8.51317			−0.290128
$862$	−17.1359			−0.583653
$863$	18.9737	+	32.8634i	0.645871	+	1.11868i	0.984100	+	0.177618i	$0.0568390\pi$
$863$	18.9737	+	32.8634i	0.645871	+	1.11868i	−0.338228	+	0.941064i	$0.609828\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$	−10.3246			−0.351045
$866$	−8.00000	−	13.8564i	−0.271851	−	0.470860i
$867$	4.82456	+	8.35637i	0.163850	+	0.283797i
$868$	−1.25658	−	2.17647i	−0.0426512	−	0.0738741i
$869$	5.16228	−	8.94133i	0.175118	−	0.303314i
$870$	2.16228	−	3.74517i	0.0733081	−	0.126973i
$871$	−4.67544	−	8.09811i	−0.158421	−	0.274394i
$872$	8.16228	+	14.1375i	0.276410	+	0.478755i
$873$	0.324555	+	0.562146i	0.0109845	+	0.0190258i
$874$	−13.6754			−0.462579
$875$	0.581139	−	1.00656i	0.0196461	−	0.0340280i
$876$	−7.74342	−	13.4120i	−0.261626	−	0.453149i
$877$	40.1623			1.35618			0.678092	−	0.734977i	$-0.262807\pi$
$877$	40.1623			1.35618			0.678092	+	0.734977i	$0.262807\pi$
$878$	−26.8114			−0.904841
$879$	−9.24342	−	16.0101i	−0.311773	−	0.540006i
$880$	5.16228			0.174020
$881$	−27.4868	+	47.6086i	−0.926055	+	1.60397i	−0.136199	+	0.990681i	$0.543489\pi$
$881$	−27.4868	+	47.6086i	−0.926055	+	1.60397i	−0.789856	+	0.613293i	$0.789845\pi$
$882$	−11.2982			−0.380431
$883$	3.50000	−	6.06218i	0.117784	−	0.204009i	−0.801105	−	0.598524i	$-0.795754\pi$
$883$	3.50000	−	6.06218i	0.117784	−	0.204009i	0.918889	+	0.394515i	$0.129088\pi$
$884$	5.58114	−	9.66682i	0.187714	−	0.325130i
$885$	2.58114	−	4.47066i	0.0867640	−	0.150280i
$886$	12.3377	+	21.3696i	0.414494	+	0.717924i
$887$	24.9737			0.838534			0.419267	−	0.907863i	$-0.362287\pi$
$887$	24.9737			0.838534			0.419267	+	0.907863i	$0.362287\pi$
$888$	6.08114	+	0.140537i	0.204070	+	0.00471610i
$889$	−21.2982			−0.714319
$890$	4.32456	+	7.49035i	0.144959	+	0.251077i
$891$	−2.58114	+	4.47066i	−0.0864714	+	0.149773i
$892$	−3.58114	+	6.20271i	−0.119905	+	0.207682i
$893$	−2.51317	+	4.35293i	−0.0840999	+	0.145665i
$894$	12.0000			0.401340
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$	1.16228			0.0388290
$897$	−3.41886	−	5.92164i	−0.114152	−	0.197718i
$898$	−31.6491			−1.05614
$899$	9.35089			0.311870
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	20.2302	−	35.0398i	0.673967	−	1.16735i
$902$	37.8114			1.25898
$903$	3.09431	+	5.35949i	0.102972	+	0.178353i
$904$	3.16228	+	5.47723i	0.105176	+	0.182170i
$905$	−11.7434	−	20.3402i	−0.390364	−	0.676131i
$906$	−11.2434	+	19.4742i	−0.373537	+	0.646986i
$907$	−5.51317	+	9.54909i	−0.183062	+	0.317072i	−0.942922	−	0.333015i	$-0.891934\pi$
$907$	−5.51317	+	9.54909i	−0.183062	+	0.317072i	0.759860	+	0.650087i	$0.225267\pi$
$908$	7.66228	+	13.2715i	0.254282	+	0.440429i
$909$	19.1623	+	33.1900i	0.635573	+	1.10084i
$910$	−1.25658	−	2.17647i	−0.0416553	−	0.0721492i
$911$	21.8377			0.723516			0.361758	−	0.932272i	$-0.382177\pi$
$911$	21.8377			0.723516			0.361758	+	0.932272i	$0.382177\pi$
$912$	−2.16228	+	3.74517i	−0.0716002	+	0.124015i
$913$	10.3246	+	17.8827i	0.341693	+	0.591829i
$914$	30.9737			1.02452
$915$	−4.32456			−0.142965
$916$	8.58114	+	14.8630i	0.283529	+	0.491086i
$917$	20.9210			0.690872
$918$	−12.9057	+	22.3533i	−0.425951	+	0.737769i
$919$	9.67544			0.319163			0.159582	−	0.987185i	$-0.448985\pi$
$919$	9.67544			0.319163			0.159582	+	0.987185i	$0.448985\pi$
$920$	−1.58114	+	2.73861i	−0.0521286	+	0.0902894i
$921$	12.1491	−	21.0429i	0.400327	−	0.693386i
$922$	−10.1623	+	17.6016i	−0.334677	+	0.579677i
$923$	6.83772	+	11.8433i	0.225066	+	0.389826i
$924$	6.00000			0.197386
$925$	−3.16228	+	5.19615i	−0.103975	+	0.170848i
$926$	18.9737			0.623513
$927$	5.48683	+	9.50347i	0.180211	+	0.312135i
$928$	−2.16228	+	3.74517i	−0.0709802	+	0.122941i
$929$	−2.82456	+	4.89227i	−0.0926707	+	0.160510i	−0.908634	−	0.417593i	$-0.862874\pi$
$929$	−2.82456	+	4.89227i	−0.0926707	+	0.160510i	0.815963	+	0.578104i	$0.196207\pi$
$930$	1.08114	−	1.87259i	0.0354519	−	0.0614046i
$931$	24.4299			0.800657
$932$	2.74342	−	4.75174i	0.0898636	−	0.155648i
$933$	−1.83772			−0.0601643
$934$	−8.17544	−	14.1603i	−0.267509	−	0.463339i
$935$	−26.6491			−0.871519
$936$	4.32456			0.141353
$937$	−28.2982	−	49.0140i	−0.924463	−	1.60122i	−0.792423	−	0.609972i	$-0.791181\pi$
$937$	−28.2982	−	49.0140i	−0.924463	−	1.60122i	−0.132039	−	0.991244i	$-0.542153\pi$
$938$	−2.51317	+	4.35293i	−0.0820578	+	0.142128i
$939$	10.0000			0.326338
$940$	0.581139	+	1.00656i	0.0189547	+	0.0328304i
$941$	−14.2302	−	24.6475i	−0.463893	−	0.803486i	0.535258	−	0.844689i	$-0.320214\pi$
$941$	−14.2302	−	24.6475i	−0.463893	−	0.803486i	−0.999151	+	0.0412026i	$0.986881\pi$
$942$	1.91886	+	3.32357i	0.0625199	+	0.108288i
$943$	−11.5811	+	20.0591i	−0.377134	+	0.653215i
$944$	−2.58114	+	4.47066i	−0.0840089	+	0.145508i
$945$	2.90569	+	5.03281i	0.0945222	+	0.163717i
$946$	−13.7434	−	23.8043i	−0.446837	−	0.773944i
$947$	24.6623	+	42.7163i	0.801416	+	1.38809i	0.918684	+	0.394993i	$0.129253\pi$
$947$	24.6623	+	42.7163i	0.801416	+	1.38809i	−0.117268	+	0.993100i	$0.537414\pi$
$948$	2.00000			0.0649570
$949$	16.7434	−	29.0004i	0.543514	−	0.941394i
$950$	−2.16228	−	3.74517i	−0.0701536	−	0.121510i
$951$	−12.4868			−0.404913
$952$	−6.00000			−0.194461
$953$	−15.4189	−	26.7063i	−0.499466	−	0.865100i	0.500534	−	0.865717i	$-0.333137\pi$
$953$	−15.4189	−	26.7063i	−0.499466	−	0.865100i	−1.00000		0.000616609i	$0.999804\pi$
$954$	15.6754			0.507511
$955$	−11.4057	+	19.7552i	−0.369080	+	0.639265i
$956$	−14.6491			−0.473786
$957$	−11.1623	+	19.3336i	−0.360825	+	0.624968i
$958$	12.9189	−	22.3761i	0.417389	−	0.722940i
$959$	−4.35089	+	7.53596i	−0.140498	+	0.243349i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−26.3246			−0.849179
$962$	6.31139	+	11.5394i	0.203487	+	0.372045i
$963$	14.0000			0.451144
$964$	−7.32456	−	12.6865i	−0.235908	−	0.408605i
$965$	9.74342	−	16.8761i	0.313652	−	0.543261i
$966$	−1.83772	+	3.18303i	−0.0591277	+	0.102412i
$967$	10.3246	−	17.8827i	0.332015	−	0.575067i	−0.650892	−	0.759171i	$-0.725605\pi$
$967$	10.3246	−	17.8827i	0.332015	−	0.575067i	0.982907	+	0.184103i	$0.0589381\pi$
$968$	−15.6491			−0.502981
$969$	11.1623	−	19.3336i	0.358584	−	0.621086i
$970$	−0.324555			−0.0104208
$971$	24.0680	+	41.6870i	0.772378	+	1.33780i	0.936256	+	0.351317i	$0.114266\pi$
$971$	24.0680	+	41.6870i	0.772378	+	1.33780i	−0.163878	+	0.986481i	$0.552400\pi$
$972$	−16.0000			−0.513200
$973$	−4.05267			−0.129923
$974$	13.6491	+	23.6410i	0.437346	+	0.757505i
$975$	1.08114	−	1.87259i	0.0346242	−	0.0599708i
$976$	4.32456			0.138426
$977$	−13.9737	−	24.2031i	−0.447057	−	0.774326i	0.551136	−	0.834416i	$-0.314195\pi$
$977$	−13.9737	−	24.2031i	−0.447057	−	0.774326i	−0.998193	+	0.0600898i	$0.980861\pi$
$978$	9.82456	+	17.0166i	0.314155	+	0.544132i
$979$	−22.3246	−	38.6673i	−0.713496	−	1.23581i
$980$	2.82456	−	4.89227i	0.0902271	−	0.156278i
$981$	16.3246	−	28.2750i	0.521203	−	0.902750i
$982$	15.7434	+	27.2684i	0.502393	+	0.870170i
$983$	12.4868	+	21.6278i	0.398268	+	0.689821i	0.993512	−	0.113724i	$-0.0362780\pi$
$983$	12.4868	+	21.6278i	0.398268	+	0.689821i	−0.595244	+	0.803545i	$0.702945\pi$
$984$	3.66228	+	6.34325i	0.116749	+	0.202215i
$985$	20.1623			0.642424
$986$	11.1623	−	19.3336i	0.355479	−	0.615708i
$987$	0.675445	+	1.16990i	0.0214996	+	0.0372385i
$988$	−9.35089			−0.297491
$989$	16.8377			0.535408
$990$	−5.16228	−	8.94133i	−0.164068	−	0.284174i
$991$	−3.83772			−0.121909			−0.0609546	−	0.998141i	$-0.519414\pi$
$991$	−3.83772			−0.121909			−0.0609546	+	0.998141i	$0.519414\pi$
$992$	−1.08114	+	1.87259i	−0.0343262	+	0.0594547i
$993$	−33.4868			−1.06267
$994$	3.67544	−	6.36606i	0.116578	−	0.201919i
$995$	6.08114	−	10.5328i	0.192785	−	0.333914i
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	−6.73025	−	11.6571i	−0.213149	−	0.369185i	0.739549	−	0.673102i	$-0.235039\pi$
$997$	−6.73025	−	11.6571i	−0.213149	−	0.369185i	−0.952698	+	0.303917i	$0.901705\pi$
$998$	36.6491			1.16011
$999$	−14.5943	−	26.6834i	−0.461743	−	0.844227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.e.211.2	yes	4
37.10	even	3	inner	370.2.e.e.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.e.121.2	✓	4	37.10	even	3	inner
370.2.e.e.211.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.581139 - 1.00656i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.581139 - 1.00656i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -1.00000 q^{10} +5.16228 q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.08114 + 1.87259i) q^{13} +1.16228 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.58114 + 4.47066i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(2.16228 - 3.74517i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.581139 - 1.00656i) q^{21} +(2.58114 + 4.47066i) q^{22} -3.16228 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.16228 q^{26} +5.00000 q^{27} +(0.581139 + 1.00656i) q^{28} -4.32456 q^{29} +(-0.500000 + 0.866025i) q^{30} -2.16228 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.58114 - 4.47066i) q^{33} +(-2.58114 + 4.47066i) q^{34} +(0.581139 + 1.00656i) q^{35} -2.00000 q^{36} +(-2.91886 - 5.33669i) q^{37} +4.32456 q^{38} +(1.08114 + 1.87259i) q^{39} +(0.500000 - 0.866025i) q^{40} +(3.66228 - 6.34325i) q^{41} +(0.581139 - 1.00656i) q^{42} -5.32456 q^{43} +(-2.58114 + 4.47066i) q^{44} -2.00000 q^{45} +(-1.58114 - 2.73861i) q^{46} -1.16228 q^{47} -1.00000 q^{48} +(2.82456 + 4.89227i) q^{49} +(0.500000 - 0.866025i) q^{50} +5.16228 q^{51} +(-1.08114 - 1.87259i) q^{52} +(-3.91886 - 6.78767i) q^{53} +(2.50000 + 4.33013i) q^{54} +(-2.58114 + 4.47066i) q^{55} +(-0.581139 + 1.00656i) q^{56} +(-2.16228 - 3.74517i) q^{57} +(-2.16228 - 3.74517i) q^{58} +(-2.58114 - 4.47066i) q^{59} -1.00000 q^{60} +(-2.16228 + 3.74517i) q^{61} +(-1.08114 - 1.87259i) q^{62} +2.32456 q^{63} +1.00000 q^{64} +(-1.08114 - 1.87259i) q^{65} +5.16228 q^{66} +(-2.16228 + 3.74517i) q^{67} -5.16228 q^{68} +(-1.58114 + 2.73861i) q^{69} +(-0.581139 + 1.00656i) q^{70} +(3.16228 - 5.47723i) q^{71} +(-1.00000 - 1.73205i) q^{72} -15.4868 q^{73} +(3.16228 - 5.19615i) q^{74} -1.00000 q^{75} +(2.16228 + 3.74517i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-1.08114 + 1.87259i) q^{78} +(1.00000 - 1.73205i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +7.32456 q^{82} +(2.00000 + 3.46410i) q^{83} +1.16228 q^{84} -5.16228 q^{85} +(-2.66228 - 4.61120i) q^{86} +(-2.16228 + 3.74517i) q^{87} -5.16228 q^{88} +(-4.32456 - 7.49035i) q^{89} +(-1.00000 - 1.73205i) q^{90} +(1.25658 + 2.17647i) q^{91} +(1.58114 - 2.73861i) q^{92} +(-1.08114 + 1.87259i) q^{93} +(-0.581139 - 1.00656i) q^{94} +(2.16228 + 3.74517i) q^{95} +(-0.500000 - 0.866025i) q^{96} +0.324555 q^{97} +(-2.82456 + 4.89227i) q^{98} +(5.16228 + 8.94133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} - 4 q^{19} - 2 q^{20} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 2 q^{25} + 4 q^{26} + 20 q^{27} - 4 q^{28} + 8 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} - 4 q^{34} - 4 q^{35} - 8 q^{36} - 18 q^{37} - 8 q^{38} - 2 q^{39} + 2 q^{40} + 2 q^{41} - 4 q^{42} + 4 q^{43} - 4 q^{44} - 8 q^{45} + 8 q^{47} - 4 q^{48} - 14 q^{49} + 2 q^{50} + 8 q^{51} + 2 q^{52} - 22 q^{53} + 10 q^{54} - 4 q^{55} + 4 q^{56} + 4 q^{57} + 4 q^{58} - 4 q^{59} - 4 q^{60} + 4 q^{61} + 2 q^{62} - 16 q^{63} + 4 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} - 8 q^{68} + 4 q^{70} - 4 q^{72} - 24 q^{73} - 4 q^{75} - 4 q^{76} + 12 q^{77} + 2 q^{78} + 4 q^{79} + 4 q^{80} - 2 q^{81} + 4 q^{82} + 8 q^{83} - 8 q^{84} - 8 q^{85} + 2 q^{86} + 4 q^{87} - 8 q^{88} + 8 q^{89} - 4 q^{90} + 24 q^{91} + 2 q^{93} + 4 q^{94} - 4 q^{95} - 2 q^{96} - 24 q^{97} + 14 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 + 8 * q^11 + 2 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 2 * q^16 + 4 * q^17 - 4 * q^18 - 4 * q^19 - 2 * q^20 + 4 * q^21 + 4 * q^22 - 2 * q^24 - 2 * q^25 + 4 * q^26 + 20 * q^27 - 4 * q^28 + 8 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^33 - 4 * q^34 - 4 * q^35 - 8 * q^36 - 18 * q^37 - 8 * q^38 - 2 * q^39 + 2 * q^40 + 2 * q^41 - 4 * q^42 + 4 * q^43 - 4 * q^44 - 8 * q^45 + 8 * q^47 - 4 * q^48 - 14 * q^49 + 2 * q^50 + 8 * q^51 + 2 * q^52 - 22 * q^53 + 10 * q^54 - 4 * q^55 + 4 * q^56 + 4 * q^57 + 4 * q^58 - 4 * q^59 - 4 * q^60 + 4 * q^61 + 2 * q^62 - 16 * q^63 + 4 * q^64 + 2 * q^65 + 8 * q^66 + 4 * q^67 - 8 * q^68 + 4 * q^70 - 4 * q^72 - 24 * q^73 - 4 * q^75 - 4 * q^76 + 12 * q^77 + 2 * q^78 + 4 * q^79 + 4 * q^80 - 2 * q^81 + 4 * q^82 + 8 * q^83 - 8 * q^84 - 8 * q^85 + 2 * q^86 + 4 * q^87 - 8 * q^88 + 8 * q^89 - 4 * q^90 + 24 * q^91 + 2 * q^93 + 4 * q^94 - 4 * q^95 - 2 * q^96 - 24 * q^97 + 14 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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