LMFDB - Embedded newform 930.2.i.n.811.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3636603.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 $ x^6 - x^5 + 3x^4 + 4x^3 + 12x^2 - 16x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			811.1
Root			$0.715814 - 1.86751i$ of defining polynomial
Character	$\chi$	$=$	930.811
Dual form			930.2.i.n.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.25941 + 3.91341i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.25941 + 3.91341i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.93163 + 3.34568i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.51882 - 6.09477i) q^{13} +(2.25941 - 3.91341i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-0.240592 + 0.416717i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.95044 - 6.84237i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.25941 + 3.91341i) q^{21} +(-1.93163 - 3.34568i) q^{22} +5.51882 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.51882 + 6.09477i) q^{26} -1.00000 q^{27} +(-2.25941 + 3.91341i) q^{28} +9.38207 q^{29} +1.00000 q^{30} +(5.12266 + 2.18136i) q^{31} -1.00000 q^{32} +3.86325 q^{33} +(0.240592 - 0.416717i) q^{34} +4.51882 q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.24059 - 2.14877i) q^{37} +(-3.95044 + 6.84237i) q^{38} -7.03763 q^{39} +(0.500000 + 0.866025i) q^{40} +(-4.08719 - 7.07922i) q^{41} +(-2.25941 - 3.91341i) q^{42} +(2.19104 - 3.79498i) q^{43} +(1.93163 + 3.34568i) q^{44} +(-0.500000 + 0.866025i) q^{45} -5.51882 q^{46} +10.5565 q^{47} +(0.500000 - 0.866025i) q^{48} +(-6.70985 - 11.6218i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.240592 + 0.416717i) q^{51} +(-3.51882 - 6.09477i) q^{52} +(0.827781 + 1.43376i) q^{53} +1.00000 q^{54} +(1.93163 - 3.34568i) q^{55} +(2.25941 - 3.91341i) q^{56} +(-3.95044 - 6.84237i) q^{57} -9.38207 q^{58} +(-6.77823 + 11.7402i) q^{59} -1.00000 q^{60} +5.90089 q^{61} +(-5.12266 - 2.18136i) q^{62} +4.51882 q^{63} +1.00000 q^{64} +(-3.51882 + 6.09477i) q^{65} -3.86325 q^{66} +(-1.24059 - 2.14877i) q^{67} +(-0.240592 + 0.416717i) q^{68} +(2.75941 - 4.77944i) q^{69} -4.51882 q^{70} +(-1.51882 - 2.63067i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 + 1.73205i) q^{73} +(-1.24059 + 2.14877i) q^{74} +(0.500000 + 0.866025i) q^{75} +(3.95044 - 6.84237i) q^{76} -17.4573 q^{77} +7.03763 q^{78} +(2.19104 - 3.79498i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.08719 + 7.07922i) q^{82} +(0.603846 + 1.04589i) q^{83} +(2.25941 + 3.91341i) q^{84} +0.481183 q^{85} +(-2.19104 + 3.79498i) q^{86} +(4.69104 - 8.12511i) q^{87} +(-1.93163 - 3.34568i) q^{88} -2.96237 q^{89} +(0.500000 - 0.866025i) q^{90} +31.8018 q^{91} +5.51882 q^{92} +(4.45044 - 3.34568i) q^{93} -10.5565 q^{94} -7.90089 q^{95} +(-0.500000 + 0.866025i) q^{96} -11.4573 q^{97} +(6.70985 + 11.6218i) q^{98} +(1.93163 - 3.34568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 14 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} - 6 q^{27} - 4 q^{28} + 24 q^{29} + 6 q^{30} + 8 q^{31} - 6 q^{32} + 10 q^{33} + 11 q^{34} + 8 q^{35} - 3 q^{36} + 17 q^{37} + 2 q^{38} - 4 q^{39} + 3 q^{40} - 12 q^{41} - 4 q^{42} - 3 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} + 6 q^{47} + 3 q^{48} - 5 q^{49} + 3 q^{50} + 11 q^{51} - 2 q^{52} + 2 q^{53} + 6 q^{54} + 5 q^{55} + 4 q^{56} + 2 q^{57} - 24 q^{58} - 12 q^{59} - 6 q^{60} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 6 q^{64} - 2 q^{65} - 10 q^{66} - 17 q^{67} - 11 q^{68} + 7 q^{69} - 8 q^{70} + 10 q^{71} + 3 q^{72} + 6 q^{73} - 17 q^{74} + 3 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{78} - 3 q^{79} - 3 q^{80} - 3 q^{81} + 12 q^{82} + 4 q^{84} + 22 q^{85} + 3 q^{86} + 12 q^{87} - 5 q^{88} - 56 q^{89} + 3 q^{90} + 88 q^{91} + 14 q^{92} + q^{93} - 6 q^{94} + 4 q^{95} - 3 q^{96} + 40 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 6 * q^16 - 11 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 14 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 24 * q^29 + 6 * q^30 + 8 * q^31 - 6 * q^32 + 10 * q^33 + 11 * q^34 + 8 * q^35 - 3 * q^36 + 17 * q^37 + 2 * q^38 - 4 * q^39 + 3 * q^40 - 12 * q^41 - 4 * q^42 - 3 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 + 6 * q^47 + 3 * q^48 - 5 * q^49 + 3 * q^50 + 11 * q^51 - 2 * q^52 + 2 * q^53 + 6 * q^54 + 5 * q^55 + 4 * q^56 + 2 * q^57 - 24 * q^58 - 12 * q^59 - 6 * q^60 - 16 * q^61 - 8 * q^62 + 8 * q^63 + 6 * q^64 - 2 * q^65 - 10 * q^66 - 17 * q^67 - 11 * q^68 + 7 * q^69 - 8 * q^70 + 10 * q^71 + 3 * q^72 + 6 * q^73 - 17 * q^74 + 3 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^78 - 3 * q^79 - 3 * q^80 - 3 * q^81 + 12 * q^82 + 4 * q^84 + 22 * q^85 + 3 * q^86 + 12 * q^87 - 5 * q^88 - 56 * q^89 + 3 * q^90 + 88 * q^91 + 14 * q^92 + q^93 - 6 * q^94 + 4 * q^95 - 3 * q^96 + 40 * q^97 + 5 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.25941	+	3.91341i	−0.853976	+	1.47913i	0.0236156	+	0.999721i	$0.492482\pi$
$7$	−2.25941	+	3.91341i	−0.853976	+	1.47913i	−0.877592	+	0.479409i	$0.840851\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.93163	+	3.34568i	0.582407	+	1.00876i	0.995193	+	0.0979312i	$0.0312225\pi$
$11$	1.93163	+	3.34568i	0.582407	+	1.00876i	−0.412786	+	0.910828i	$0.635444\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.51882	−	6.09477i	−0.975944	−	1.69038i	−0.676784	−	0.736182i	$-0.736627\pi$
$13$	−3.51882	−	6.09477i	−0.975944	−	1.69038i	−0.299161	−	0.954203i	$-0.596707\pi$
$14$	2.25941	−	3.91341i	0.603852	−	1.04590i
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	−0.240592	+	0.416717i	−0.0583520	+	0.101069i	−0.893726	−	0.448614i	$-0.851918\pi$
$17$	−0.240592	+	0.416717i	−0.0583520	+	0.101069i	0.835374	+	0.549682i	$0.185251\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.95044	−	6.84237i	0.906294	−	1.56975i	0.0871232	−	0.996198i	$-0.472233\pi$
$19$	3.95044	−	6.84237i	0.906294	−	1.56975i	0.819171	−	0.573550i	$-0.194434\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	2.25941	+	3.91341i	0.493043	+	0.853976i
$22$	−1.93163	−	3.34568i	−0.411824	−	0.713301i
$23$	5.51882			1.15075			0.575376	−	0.817889i	$-0.304856\pi$
$23$	5.51882			1.15075			0.575376	+	0.817889i	$0.304856\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.51882	+	6.09477i	0.690097	+	1.19528i
$27$	−1.00000			−0.192450
$28$	−2.25941	+	3.91341i	−0.426988	+	0.739565i
$29$	9.38207			1.74221			0.871103	−	0.491100i	$-0.163405\pi$
$29$	9.38207			1.74221			0.871103	+	0.491100i	$0.163405\pi$
$30$	1.00000			0.182574
$31$	5.12266	+	2.18136i	0.920057	+	0.391784i
$31$	5.12266	+	2.18136i	0.920057	+	0.391784i
$32$	−1.00000			−0.176777
$33$	3.86325			0.672506
$34$	0.240592	−	0.416717i	0.0412611	−	0.0714664i
$35$	4.51882			0.763819
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.24059	−	2.14877i	0.203952	−	0.353255i	−0.745846	−	0.666118i	$-0.767955\pi$
$37$	1.24059	−	2.14877i	0.203952	−	0.353255i	0.949798	+	0.312863i	$0.101288\pi$
$38$	−3.95044	+	6.84237i	−0.640847	+	1.10998i
$39$	−7.03763			−1.12692
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−4.08719	−	7.07922i	−0.638312	−	1.10559i	−0.985803	−	0.167905i	$-0.946300\pi$
$41$	−4.08719	−	7.07922i	−0.638312	−	1.10559i	0.347491	−	0.937683i	$-0.387034\pi$
$42$	−2.25941	−	3.91341i	−0.348634	−	0.603852i
$43$	2.19104	−	3.79498i	0.334130	−	0.578730i	−0.649188	−	0.760628i	$-0.724891\pi$
$43$	2.19104	−	3.79498i	0.334130	−	0.578730i	0.983317	+	0.181899i	$0.0582243\pi$
$44$	1.93163	+	3.34568i	0.291204	+	0.504380i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−5.51882			−0.813705
$47$	10.5565			1.53982			0.769908	−	0.638155i	$-0.220302\pi$
$47$	10.5565			1.53982			0.769908	+	0.638155i	$0.220302\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−6.70985	−	11.6218i	−0.958550	−	1.66026i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	0.240592	+	0.416717i	0.0336896	+	0.0583520i
$52$	−3.51882	−	6.09477i	−0.487972	−	0.845192i
$53$	0.827781	+	1.43376i	0.113704	+	0.196942i	0.917261	−	0.398286i	$-0.130395\pi$
$53$	0.827781	+	1.43376i	0.113704	+	0.196942i	−0.803557	+	0.595228i	$0.797062\pi$
$54$	1.00000			0.136083
$55$	1.93163	−	3.34568i	0.260461	−	0.451131i
$56$	2.25941	−	3.91341i	0.301926	−	0.522951i
$57$	−3.95044	−	6.84237i	−0.523249	−	0.906294i
$58$	−9.38207			−1.23193
$59$	−6.77823	+	11.7402i	−0.882450	+	1.52845i	−0.0338407	+	0.999427i	$0.510774\pi$
$59$	−6.77823	+	11.7402i	−0.882450	+	1.52845i	−0.848609	+	0.529021i	$0.822559\pi$
$60$	−1.00000			−0.129099
$61$	5.90089			0.755531			0.377766	−	0.925901i	$-0.376693\pi$
$61$	5.90089			0.755531			0.377766	+	0.925901i	$0.376693\pi$
$62$	−5.12266	−	2.18136i	−0.650579	−	0.277033i
$63$	4.51882			0.569317
$64$	1.00000			0.125000
$65$	−3.51882	+	6.09477i	−0.436455	+	0.755963i
$66$	−3.86325			−0.475534
$67$	−1.24059	−	2.14877i	−0.151562	−	0.262514i	0.780240	−	0.625481i	$-0.215097\pi$
$67$	−1.24059	−	2.14877i	−0.151562	−	0.262514i	−0.931802	+	0.362967i	$0.881764\pi$
$68$	−0.240592	+	0.416717i	−0.0291760	+	0.0505344i
$69$	2.75941	−	4.77944i	0.332194	−	0.575376i
$70$	−4.51882			−0.540102
$71$	−1.51882	−	2.63067i	−0.180250	−	0.312203i	0.761715	−	0.647912i	$-0.224357\pi$
$71$	−1.51882	−	2.63067i	−0.180250	−	0.312203i	−0.941966	+	0.335709i	$0.891024\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	−1.24059	+	2.14877i	−0.144216	+	0.249789i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	3.95044	−	6.84237i	0.453147	−	0.784874i
$77$	−17.4573			−1.98945
$78$	7.03763			0.796855
$79$	2.19104	−	3.79498i	0.246511	−	0.426969i	−0.716045	−	0.698055i	$-0.754049\pi$
$79$	2.19104	−	3.79498i	0.246511	−	0.426969i	0.962555	+	0.271085i	$0.0873826\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.08719	+	7.07922i	0.451355	+	0.781769i
$83$	0.603846	+	1.04589i	0.0662807	+	0.114802i	0.897261	−	0.441500i	$-0.145553\pi$
$83$	0.603846	+	1.04589i	0.0662807	+	0.114802i	−0.830981	+	0.556301i	$0.812220\pi$
$84$	2.25941	+	3.91341i	0.246522	+	0.426988i
$85$	0.481183			0.0521917
$86$	−2.19104	+	3.79498i	−0.236265	+	0.409224i
$87$	4.69104	−	8.12511i	0.502932	−	0.871103i
$88$	−1.93163	−	3.34568i	−0.205912	−	0.356650i
$89$	−2.96237			−0.314010			−0.157005	−	0.987598i	$-0.550184\pi$
$89$	−2.96237			−0.314010			−0.157005	+	0.987598i	$0.550184\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	31.8018			3.33373
$92$	5.51882			0.575376
$93$	4.45044	−	3.34568i	0.461490	−	0.346930i
$94$	−10.5565			−1.08881
$95$	−7.90089			−0.810614
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−11.4573			−1.16332			−0.581658	−	0.813433i	$-0.697596\pi$
$97$	−11.4573			−1.16332			−0.581658	+	0.813433i	$0.697596\pi$
$98$	6.70985	+	11.6218i	0.677797	+	1.17398i
$99$	1.93163	−	3.34568i	0.194136	−	0.336253i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	9.76414			0.971568			0.485784	−	0.874079i	$-0.338534\pi$
$101$	9.76414			0.971568			0.485784	+	0.874079i	$0.338534\pi$
$102$	−0.240592	−	0.416717i	−0.0238221	−	0.0412611i
$103$	−7.77823	−	13.4723i	−0.766411	−	1.32746i	−0.939497	−	0.342557i	$-0.888707\pi$
$103$	−7.77823	−	13.4723i	−0.766411	−	1.32746i	0.173086	−	0.984907i	$-0.444626\pi$
$104$	3.51882	+	6.09477i	0.345048	+	0.597641i
$105$	2.25941	−	3.91341i	0.220496	−	0.381910i
$106$	−0.827781	−	1.43376i	−0.0804012	−	0.139259i
$107$	−2.25941	+	3.91341i	−0.218425	+	0.378324i	−0.954327	−	0.298765i	$-0.903425\pi$
$107$	−2.25941	+	3.91341i	−0.218425	+	0.378324i	0.735901	+	0.677089i	$0.236759\pi$
$108$	−1.00000			−0.0962250
$109$	7.90089			0.756768			0.378384	−	0.925649i	$-0.376480\pi$
$109$	7.90089			0.756768			0.378384	+	0.925649i	$0.376480\pi$
$110$	−1.93163	+	3.34568i	−0.184173	+	0.318998i
$111$	−1.24059	−	2.14877i	−0.117752	−	0.203952i
$112$	−2.25941	+	3.91341i	−0.213494	+	0.369782i
$113$	3.70985	+	6.42565i	0.348994	+	0.604475i	0.986071	−	0.166325i	$-0.0531902\pi$
$113$	3.70985	+	6.42565i	0.348994	+	0.604475i	−0.637077	+	0.770800i	$0.719857\pi$
$114$	3.95044	+	6.84237i	0.369993	+	0.640847i
$115$	−2.75941	−	4.77944i	−0.257316	−	0.445685i
$116$	9.38207			0.871103
$117$	−3.51882	+	6.09477i	−0.325315	+	0.563462i
$118$	6.77823	−	11.7402i	0.623986	−	1.08078i
$119$	−1.08719	−	1.88307i	−0.0996625	−	0.172621i
$120$	1.00000			0.0912871
$121$	−1.96237	+	3.39892i	−0.178397	+	0.308993i
$122$	−5.90089			−0.534241
$123$	−8.17438			−0.737059
$124$	5.12266	+	2.18136i	0.460029	+	0.195892i
$125$	1.00000			0.0894427
$126$	−4.51882			−0.402568
$127$	1.60385	−	2.77794i	0.142318	−	0.246503i	−0.786051	−	0.618162i	$-0.787878\pi$
$127$	1.60385	−	2.77794i	0.142318	−	0.246503i	0.928369	+	0.371659i	$0.121211\pi$
$128$	−1.00000			−0.0883883
$129$	−2.19104	−	3.79498i	−0.192910	−	0.334130i
$130$	3.51882	−	6.09477i	0.308621	−	0.534547i
$131$	3.32778	−	5.76389i	0.290750	−	0.503593i	−0.683238	−	0.730196i	$-0.739429\pi$
$131$	3.32778	−	5.76389i	0.290750	−	0.503593i	0.973987	+	0.226603i	$0.0727620\pi$
$132$	3.86325			0.336253
$133$	17.8513	+	30.9194i	1.54791	+	2.68105i
$134$	1.24059	+	2.14877i	0.107171	+	0.185625i
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	0.240592	−	0.416717i	0.0206306	−	0.0357332i
$137$	2.41497	+	4.18285i	0.206325	+	0.357365i	0.950554	−	0.310559i	$-0.100516\pi$
$137$	2.41497	+	4.18285i	0.206325	+	0.357365i	−0.744229	+	0.667924i	$0.767183\pi$
$138$	−2.75941	+	4.77944i	−0.234896	+	0.406853i
$139$	8.86325			0.751771			0.375886	−	0.926666i	$-0.377339\pi$
$139$	8.86325			0.751771			0.375886	+	0.926666i	$0.377339\pi$
$140$	4.51882			0.381910
$141$	5.27823	−	9.14215i	0.444507	−	0.769908i
$142$	1.51882	+	2.63067i	0.127456	+	0.220761i
$143$	13.5941	−	23.5456i	1.13679	−	1.96899i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.69104	−	8.12511i	−0.389569	−	0.674754i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$	−13.4197			−1.10684
$148$	1.24059	−	2.14877i	0.101976	−	0.176628i
$149$	7.82778	−	13.5581i	0.641277	−	1.11072i	−0.343871	−	0.939017i	$-0.611738\pi$
$149$	7.82778	−	13.5581i	0.641277	−	1.11072i	0.985148	−	0.171707i	$-0.0549283\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−14.9009			−1.21262			−0.606309	−	0.795230i	$-0.707350\pi$
$151$	−14.9009			−1.21262			−0.606309	+	0.795230i	$0.707350\pi$
$152$	−3.95044	+	6.84237i	−0.320423	+	0.554989i
$153$	0.481183			0.0389014
$154$	17.4573			1.40675
$155$	−0.672219	−	5.52704i	−0.0539939	−	0.443942i
$156$	−7.03763			−0.563462
$157$	2.44787			0.195361			0.0976807	−	0.995218i	$-0.468858\pi$
$157$	2.44787			0.195361			0.0976807	+	0.995218i	$0.468858\pi$
$158$	−2.19104	+	3.79498i	−0.174309	+	0.301913i
$159$	1.65556			0.131295
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−12.4693	+	21.5974i	−0.982715	+	1.70211i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−21.3206			−1.66996			−0.834979	−	0.550282i	$-0.814520\pi$
$163$	−21.3206			−1.66996			−0.834979	+	0.550282i	$0.814520\pi$
$164$	−4.08719	−	7.07922i	−0.319156	−	0.552794i
$165$	−1.93163	−	3.34568i	−0.150377	−	0.260461i
$166$	−0.603846	−	1.04589i	−0.0468675	−	0.0811769i
$167$	4.29488	−	7.43895i	0.332348	−	0.575643i	−0.650624	−	0.759400i	$-0.725493\pi$
$167$	4.29488	−	7.43895i	0.332348	−	0.575643i	0.982972	+	0.183757i	$0.0588259\pi$
$168$	−2.25941	−	3.91341i	−0.174317	−	0.301926i
$169$	−18.2641	+	31.6344i	−1.40493	+	2.43342i
$170$	−0.481183			−0.0369051
$171$	−7.90089			−0.604196
$172$	2.19104	−	3.79498i	0.167065	−	0.289365i
$173$	2.69104	+	4.66101i	0.204596	+	0.354370i	0.950004	−	0.312238i	$-0.101079\pi$
$173$	2.69104	+	4.66101i	0.204596	+	0.354370i	−0.745408	+	0.666608i	$0.767745\pi$
$174$	−4.69104	+	8.12511i	−0.355626	+	0.615963i
$175$	−2.25941	−	3.91341i	−0.170795	−	0.295826i
$176$	1.93163	+	3.34568i	0.145602	+	0.252190i
$177$	6.77823	+	11.7402i	0.509483	+	0.882450i
$178$	2.96237			0.222039
$179$	−6.10601	+	10.5759i	−0.456384	+	0.790481i	−0.998767	−	0.0496509i	$-0.984189\pi$
$179$	−6.10601	+	10.5759i	−0.456384	+	0.790481i	0.542382	+	0.840132i	$0.317522\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	5.38207	+	9.32202i	0.400046	+	0.692900i	0.993731	−	0.111797i	$-0.0356607\pi$
$181$	5.38207	+	9.32202i	0.400046	+	0.692900i	−0.593685	+	0.804698i	$0.702327\pi$
$182$	−31.8018			−2.35730
$183$	2.95044	−	5.11032i	0.218103	−	0.377766i
$184$	−5.51882			−0.406853
$185$	−2.48118			−0.182420
$186$	−4.45044	+	3.34568i	−0.326322	+	0.245317i
$187$	−1.85893			−0.135939
$188$	10.5565			0.769908
$189$	2.25941	−	3.91341i	0.164348	−	0.284659i
$190$	7.90089			0.573191
$191$	−4.95044	−	8.57442i	−0.358202	−	0.620423i	0.629459	−	0.777034i	$-0.283277\pi$
$191$	−4.95044	−	8.57442i	−0.358202	−	0.620423i	−0.987660	+	0.156611i	$0.949943\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−10.6910	+	18.5174i	−0.769558	+	1.33291i	0.168245	+	0.985745i	$0.446190\pi$
$193$	−10.6910	+	18.5174i	−0.769558	+	1.33291i	−0.937803	+	0.347168i	$0.887143\pi$
$194$	11.4573			0.822589
$195$	3.51882	+	6.09477i	0.251988	+	0.436455i
$196$	−6.70985	−	11.6218i	−0.479275	−	0.830129i
$197$	−3.65556	−	6.33162i	−0.260448	−	0.451109i	0.705913	−	0.708299i	$-0.250537\pi$
$197$	−3.65556	−	6.33162i	−0.260448	−	0.451109i	−0.966361	+	0.257189i	$0.917204\pi$
$198$	−1.93163	+	3.34568i	−0.137275	+	0.237767i
$199$	−1.39615	−	2.41821i	−0.0989707	−	0.171422i	0.812288	−	0.583256i	$-0.198222\pi$
$199$	−1.39615	−	2.41821i	−0.0989707	−	0.171422i	−0.911259	+	0.411834i	$0.864888\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−2.48118			−0.175009
$202$	−9.76414			−0.687003
$203$	−21.1979	+	36.7159i	−1.48780	+	2.57695i
$204$	0.240592	+	0.416717i	0.0168448	+	0.0291760i
$205$	−4.08719	+	7.07922i	−0.285462	+	0.494434i
$206$	7.77823	+	13.4723i	0.541935	+	0.938658i
$207$	−2.75941	−	4.77944i	−0.191792	−	0.332194i
$208$	−3.51882	−	6.09477i	−0.243986	−	0.422596i
$209$	30.5231			2.11133
$210$	−2.25941	+	3.91341i	−0.155914	+	0.270051i
$211$	0.0495562	−	0.0858338i	0.00341159	−	0.00590905i	−0.864315	−	0.502952i	$-0.832247\pi$
$211$	0.0495562	−	0.0858338i	0.00341159	−	0.00590905i	0.867726	+	0.497043i	$0.165581\pi$
$212$	0.827781	+	1.43376i	0.0568522	+	0.0984710i
$213$	−3.03763			−0.208135
$214$	2.25941	−	3.91341i	0.154450	−	0.267515i
$215$	−4.38207			−0.298855
$216$	1.00000			0.0680414
$217$	−20.1107	+	15.1185i	−1.36521	+	1.02631i
$218$	−7.90089			−0.535116
$219$	2.00000			0.135147
$220$	1.93163	−	3.34568i	0.130230	−	0.225565i
$221$	3.38639			0.227793
$222$	1.24059	+	2.14877i	0.0832631	+	0.144216i
$223$	8.12266	−	14.0689i	0.543934	−	0.942121i	−0.454739	−	0.890625i	$-0.650268\pi$
$223$	8.12266	−	14.0689i	0.543934	−	0.942121i	0.998673	−	0.0514963i	$-0.0163990\pi$
$224$	2.25941	−	3.91341i	0.150963	−	0.261476i
$225$	1.00000			0.0666667
$226$	−3.70985	−	6.42565i	−0.246776	−	0.427428i
$227$	5.64148	+	9.77133i	0.374438	+	0.648546i	0.990243	−	0.139353i	$-0.0445023\pi$
$227$	5.64148	+	9.77133i	0.374438	+	0.648546i	−0.615805	+	0.787899i	$0.711169\pi$
$228$	−3.95044	−	6.84237i	−0.261625	−	0.453147i
$229$	−5.33251	+	9.23619i	−0.352382	+	0.610344i	−0.986666	−	0.162756i	$-0.947962\pi$
$229$	−5.33251	+	9.23619i	−0.352382	+	0.610344i	0.634284	+	0.773100i	$0.281295\pi$
$230$	2.75941	+	4.77944i	0.181950	+	0.315147i
$231$	−8.72867	+	15.1185i	−0.574304	+	0.994724i
$232$	−9.38207			−0.615963
$233$	6.48118			0.424596			0.212298	−	0.977205i	$-0.431905\pi$
$233$	6.48118			0.424596			0.212298	+	0.977205i	$0.431905\pi$
$234$	3.51882	−	6.09477i	0.230032	−	0.398428i
$235$	−5.27823	−	9.14215i	−0.344313	−	0.596368i
$236$	−6.77823	+	11.7402i	−0.441225	+	0.764224i
$237$	−2.19104	−	3.79498i	−0.142323	−	0.246511i
$238$	1.08719	+	1.88307i	0.0704720	+	0.122061i
$239$	10.3821	+	17.9823i	0.671560	+	1.16318i	0.977462	+	0.211113i	$0.0677089\pi$
$239$	10.3821	+	17.9823i	0.671560	+	1.16318i	−0.305901	+	0.952063i	$0.598958\pi$
$240$	−1.00000			−0.0645497
$241$	9.82778	−	17.0222i	0.633063	−	1.09650i	−0.353859	−	0.935299i	$-0.615131\pi$
$241$	9.82778	−	17.0222i	0.633063	−	1.09650i	0.986922	−	0.161199i	$-0.0515360\pi$
$242$	1.96237	−	3.39892i	0.126146	−	0.218491i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	5.90089			0.377766
$245$	−6.70985	+	11.6218i	−0.428677	+	0.742490i
$246$	8.17438			0.521179
$247$	−55.6036			−3.53797
$248$	−5.12266	−	2.18136i	−0.325289	−	0.138516i
$249$	1.20769			0.0765344
$250$	−1.00000			−0.0632456
$251$	0.191035	−	0.330883i	0.0120581	−	0.0208852i	−0.859933	−	0.510406i	$-0.829495\pi$
$251$	0.191035	−	0.330883i	0.0120581	−	0.0208852i	0.871991	+	0.489521i	$0.162828\pi$
$252$	4.51882			0.284659
$253$	10.6603	+	18.4642i	0.670207	+	1.16083i
$254$	−1.60385	+	2.77794i	−0.100634	+	0.174304i
$255$	0.240592	−	0.416717i	0.0150664	−	0.0260958i
$256$	1.00000			0.0625000
$257$	−10.4859	−	18.1621i	−0.654094	−	1.13292i	−0.982120	−	0.188255i	$-0.939717\pi$
$257$	−10.4859	−	18.1621i	−0.654094	−	1.13292i	0.328027	−	0.944668i	$-0.393616\pi$
$258$	2.19104	+	3.79498i	0.136408	+	0.236265i
$259$	5.60601	+	9.70989i	0.348340	+	0.603343i
$260$	−3.51882	+	6.09477i	−0.218228	+	0.377982i
$261$	−4.69104	−	8.12511i	−0.290368	−	0.502932i
$262$	−3.32778	+	5.76389i	−0.205591	+	0.356094i
$263$	2.38207			0.146885			0.0734424	−	0.997299i	$-0.476601\pi$
$263$	2.38207			0.146885			0.0734424	+	0.997299i	$0.476601\pi$
$264$	−3.86325			−0.237767
$265$	0.827781	−	1.43376i	0.0508502	−	0.0880751i
$266$	−17.8513	−	30.9194i	−1.09454	−	1.89579i
$267$	−1.48118	+	2.56548i	−0.0906469	+	0.157005i
$268$	−1.24059	−	2.14877i	−0.0757812	−	0.131257i
$269$	−9.36541	−	16.2214i	−0.571019	−	0.989035i	−0.996462	−	0.0840490i	$-0.973215\pi$
$269$	−9.36541	−	16.2214i	−0.571019	−	0.989035i	0.425442	−	0.904986i	$-0.360119\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−7.82994			−0.475635			−0.237818	−	0.971310i	$-0.576432\pi$
$271$	−7.82994			−0.475635			−0.237818	+	0.971310i	$0.576432\pi$
$272$	−0.240592	+	0.416717i	−0.0145880	+	0.0252672i
$273$	15.9009	−	27.5411i	0.962365	−	1.66687i
$274$	−2.41497	−	4.18285i	−0.145894	−	0.252695i
$275$	−3.86325			−0.232963
$276$	2.75941	−	4.77944i	0.166097	−	0.287688i
$277$	−14.2077			−0.853657			−0.426829	−	0.904332i	$-0.640369\pi$
$277$	−14.2077			−0.853657			−0.426829	+	0.904332i	$0.640369\pi$
$278$	−8.86325			−0.531583
$279$	−0.672219	−	5.52704i	−0.0402447	−	0.330895i
$280$	−4.51882			−0.270051
$281$	4.62225			0.275740			0.137870	−	0.990450i	$-0.455974\pi$
$281$	4.62225			0.275740			0.137870	+	0.990450i	$0.455974\pi$
$282$	−5.27823	+	9.14215i	−0.314314	+	0.544407i
$283$	25.4950			1.51552			0.757759	−	0.652534i	$-0.226294\pi$
$283$	25.4950			1.51552			0.757759	+	0.652534i	$0.226294\pi$
$284$	−1.51882	−	2.63067i	−0.0901252	−	0.156101i
$285$	−3.95044	+	6.84237i	−0.234004	+	0.405307i
$286$	−13.5941	+	23.5456i	−0.803835	+	1.39228i
$287$	36.9385			2.18041
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	8.38423	+	14.5219i	0.493190	+	0.854230i
$290$	4.69104	+	8.12511i	0.275467	+	0.477123i
$291$	−5.72867	+	9.92235i	−0.335821	+	0.581658i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	3.86541	−	6.69509i	0.225820	−	0.391132i	−0.730745	−	0.682650i	$-0.760827\pi$
$293$	3.86541	−	6.69509i	0.225820	−	0.391132i	0.956565	+	0.291519i	$0.0941606\pi$
$294$	13.4197			0.782653
$295$	13.5565			0.789287
$296$	−1.24059	+	2.14877i	−0.0721079	+	0.124895i
$297$	−1.93163	−	3.34568i	−0.112084	−	0.194136i
$298$	−7.82778	+	13.5581i	−0.453451	+	0.785401i
$299$	−19.4197	−	33.6359i	−1.12307	−	1.94522i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	9.90089	+	17.1488i	0.570678	+	0.988443i
$302$	14.9009			0.857450
$303$	4.88207	−	8.45599i	0.280468	−	0.485784i
$304$	3.95044	−	6.84237i	0.226573	−	0.392437i
$305$	−2.95044	−	5.11032i	−0.168942	−	0.292616i
$306$	−0.481183			−0.0275074
$307$	0.223935	−	0.387867i	0.0127807	−	0.0221368i	−0.859564	−	0.511028i	$-0.829265\pi$
$307$	0.223935	−	0.387867i	0.0127807	−	0.0221368i	0.872345	+	0.488891i	$0.162598\pi$
$308$	−17.4573			−0.994724
$309$	−15.5565			−0.884976
$310$	0.672219	+	5.52704i	0.0381795	+	0.313915i
$311$	6.68888			0.379291			0.189646	−	0.981853i	$-0.439266\pi$
$311$	6.68888			0.379291			0.189646	+	0.981853i	$0.439266\pi$
$312$	7.03763			0.398428
$313$	1.48334	−	2.56923i	0.0838435	−	0.145221i	−0.821054	−	0.570850i	$-0.806614\pi$
$313$	1.48334	−	2.56923i	0.0838435	−	0.145221i	0.904898	+	0.425629i	$0.139947\pi$
$314$	−2.44787			−0.138141
$315$	−2.25941	−	3.91341i	−0.127303	−	0.220496i
$316$	2.19104	−	3.79498i	0.123255	−	0.213485i
$317$	−3.34660	+	5.79648i	−0.187964	+	0.325563i	−0.944571	−	0.328307i	$-0.893522\pi$
$317$	−3.34660	+	5.79648i	−0.187964	+	0.325563i	0.756608	+	0.653869i	$0.226855\pi$
$318$	−1.65556			−0.0928393
$319$	18.1227	+	31.3894i	1.01467	+	1.75747i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	2.25941	+	3.91341i	0.126108	+	0.218425i
$322$	12.4693	−	21.5974i	0.694885	−	1.20358i
$323$	1.90089	+	3.29243i	0.105768	+	0.183196i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	7.03763			0.390378
$326$	21.3206			1.18084
$327$	3.95044	−	6.84237i	0.218460	−	0.378384i
$328$	4.08719	+	7.07922i	0.225677	+	0.390885i
$329$	−23.8513	+	41.3117i	−1.31497	+	2.27759i
$330$	1.93163	+	3.34568i	0.106333	+	0.184173i
$331$	3.70512	+	6.41745i	0.203652	+	0.352735i	0.949702	−	0.313154i	$-0.101386\pi$
$331$	3.70512	+	6.41745i	0.203652	+	0.352735i	−0.746051	+	0.665889i	$0.768052\pi$
$332$	0.603846	+	1.04589i	0.0331403	+	0.0574008i
$333$	−2.48118			−0.135968
$334$	−4.29488	+	7.43895i	−0.235005	+	0.407041i
$335$	−1.24059	+	2.14877i	−0.0677808	+	0.117400i
$336$	2.25941	+	3.91341i	0.123261	+	0.213494i
$337$	−15.3821			−0.837915			−0.418957	−	0.908006i	$-0.637604\pi$
$337$	−15.3821			−0.837915			−0.418957	+	0.908006i	$0.637604\pi$
$338$	18.2641	−	31.6344i	0.993438	−	1.72069i
$339$	7.41970			0.402983
$340$	0.481183			0.0260958
$341$	2.59695	+	21.3523i	0.140633	+	1.15629i
$342$	7.90089			0.427231
$343$	29.0095			1.56636
$344$	−2.19104	+	3.79498i	−0.118133	+	0.204612i
$345$	−5.51882			−0.297123
$346$	−2.69104	−	4.66101i	−0.144671	−	0.250577i
$347$	4.64148	−	8.03928i	0.249168	−	0.431571i	−0.714127	−	0.700016i	$-0.753176\pi$
$347$	4.64148	−	8.03928i	0.249168	−	0.431571i	0.963295	+	0.268445i	$0.0865096\pi$
$348$	4.69104	−	8.12511i	0.251466	−	0.435552i
$349$	−18.5898			−0.995087			−0.497544	−	0.867439i	$-0.665765\pi$
$349$	−18.5898			−0.995087			−0.497544	+	0.867439i	$0.665765\pi$
$350$	2.25941	+	3.91341i	0.120770	+	0.209181i
$351$	3.51882	+	6.09477i	0.187821	+	0.325315i
$352$	−1.93163	−	3.34568i	−0.102956	−	0.178325i
$353$	−13.2663	+	22.9779i	−0.706094	+	1.22299i	0.260201	+	0.965554i	$0.416211\pi$
$353$	−13.2663	+	22.9779i	−0.706094	+	1.22299i	−0.966295	+	0.257436i	$0.917122\pi$
$354$	−6.77823	−	11.7402i	−0.360259	−	0.623986i
$355$	−1.51882	+	2.63067i	−0.0806104	+	0.139621i
$356$	−2.96237			−0.157005
$357$	−2.17438			−0.115080
$358$	6.10601	−	10.5759i	0.322712	−	0.558954i
$359$	−4.56837	−	7.91265i	−0.241109	−	0.417614i	0.719921	−	0.694056i	$-0.244178\pi$
$359$	−4.56837	−	7.91265i	−0.241109	−	0.417614i	−0.961031	+	0.276442i	$0.910845\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	−21.7120	−	37.6063i	−1.14274	−	1.97928i
$362$	−5.38207	−	9.32202i	−0.282875	−	0.489955i
$363$	1.96237	+	3.39892i	0.102998	+	0.178397i
$364$	31.8018			1.66687
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$	−2.95044	+	5.11032i	−0.154222	+	0.267121i
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	0.988269	+	0.152721i	$0.0488036\pi$
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	−0.361874	+	0.932227i	$0.617863\pi$
$368$	5.51882			0.287688
$369$	−4.08719	+	7.07922i	−0.212771	+	0.368529i
$370$	2.48118			0.128991
$371$	−7.48118			−0.388404
$372$	4.45044	−	3.34568i	0.230745	−	0.173465i
$373$	25.3959			1.31495			0.657474	−	0.753477i	$-0.271625\pi$
$373$	25.3959			1.31495			0.657474	+	0.753477i	$0.271625\pi$
$374$	1.85893			0.0961232
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−10.5565			−0.544407
$377$	−33.0138	−	57.1816i	−1.70030	−	2.94500i
$378$	−2.25941	+	3.91341i	−0.116211	+	0.201284i
$379$	13.9385	−	24.1422i	0.715974	−	1.24010i	−0.246609	−	0.969115i	$-0.579316\pi$
$379$	13.9385	−	24.1422i	0.715974	−	1.24010i	0.962583	−	0.270988i	$-0.0873503\pi$
$380$	−7.90089			−0.405307
$381$	−1.60385	−	2.77794i	−0.0821675	−	0.142318i
$382$	4.95044	+	8.57442i	0.253287	+	0.438706i
$383$	8.27823	+	14.3383i	0.422998	+	0.732653i	0.996231	−	0.0867388i	$-0.0276446\pi$
$383$	8.27823	+	14.3383i	0.422998	+	0.732653i	−0.573234	+	0.819392i	$0.694311\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	8.72867	+	15.1185i	0.444854	+	0.770510i
$386$	10.6910	−	18.5174i	0.544159	−	0.942512i
$387$	−4.38207			−0.222753
$388$	−11.4573			−0.581658
$389$	−14.8842	+	25.7802i	−0.754660	+	1.30711i	0.190882	+	0.981613i	$0.438865\pi$
$389$	−14.8842	+	25.7802i	−0.754660	+	1.30711i	−0.945543	+	0.325497i	$0.894468\pi$
$390$	−3.51882	−	6.09477i	−0.178182	−	0.308621i
$391$	−1.32778	+	2.29978i	−0.0671488	+	0.116305i
$392$	6.70985	+	11.6218i	0.338899	+	0.586990i
$393$	−3.32778	−	5.76389i	−0.167864	−	0.290750i
$394$	3.65556	+	6.33162i	0.184165	+	0.318982i
$395$	−4.38207			−0.220486
$396$	1.93163	−	3.34568i	0.0970679	−	0.168127i
$397$	10.3278	−	17.8882i	0.518336	−	0.897785i	−0.481437	−	0.876481i	$-0.659885\pi$
$397$	10.3278	−	17.8882i	0.518336	−	0.897785i	0.999773	−	0.0213042i	$-0.00678184\pi$
$398$	1.39615	+	2.41821i	0.0699829	+	0.121214i
$399$	35.7027			1.78737
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−18.8394			−0.940795			−0.470398	−	0.882455i	$-0.655889\pi$
$401$	−18.8394			−0.940795			−0.470398	+	0.882455i	$0.655889\pi$
$402$	2.48118			0.123750
$403$	−4.73083	−	38.8972i	−0.235659	−	1.93761i
$404$	9.76414			0.485784
$405$	1.00000			0.0496904
$406$	21.1979	−	36.7159i	1.05204	−	1.82218i
$407$	9.58544			0.475133
$408$	−0.240592	−	0.416717i	−0.0119111	−	0.0206306i
$409$	−3.67438	+	6.36421i	−0.181686	+	0.314690i	−0.942455	−	0.334333i	$-0.891489\pi$
$409$	−3.67438	+	6.36421i	−0.181686	+	0.314690i	0.760769	+	0.649023i	$0.224822\pi$
$410$	4.08719	−	7.07922i	0.201852	−	0.349618i
$411$	4.82994			0.238243
$412$	−7.77823	−	13.4723i	−0.383206	−	0.663732i
$413$	−30.6296	−	53.0519i	−1.50718	−	2.61052i
$414$	2.75941	+	4.77944i	0.135618	+	0.234896i
$415$	0.603846	−	1.04589i	0.0296416	−	0.0513408i
$416$	3.51882	+	6.09477i	0.172524	+	0.298821i
$417$	4.43163	−	7.67580i	0.217018	−	0.375886i
$418$	−30.5231			−1.49294
$419$	−11.8633			−0.579558			−0.289779	−	0.957094i	$-0.593582\pi$
$419$	−11.8633			−0.579558			−0.289779	+	0.957094i	$0.593582\pi$
$420$	2.25941	−	3.91341i	0.110248	−	0.190955i
$421$	9.81370	+	16.9978i	0.478290	+	0.828423i	0.999690	−	0.0248893i	$-0.00792332\pi$
$421$	9.81370	+	16.9978i	0.478290	+	0.828423i	−0.521400	+	0.853312i	$0.674590\pi$
$422$	−0.0495562	+	0.0858338i	−0.00241236	+	0.00417833i
$423$	−5.27823	−	9.14215i	−0.256636	−	0.444507i
$424$	−0.827781	−	1.43376i	−0.0402006	−	0.0696295i
$425$	−0.240592	−	0.416717i	−0.0116704	−	0.0202137i
$426$	3.03763			0.147174
$427$	−13.3325	+	23.0926i	−0.645206	+	1.11753i
$428$	−2.25941	+	3.91341i	−0.109213	+	0.189162i
$429$	−13.5941	−	23.5456i	−0.656329	−	1.13679i
$430$	4.38207			0.211322
$431$	−15.6436	+	27.0956i	−0.753528	+	1.30515i	0.192575	+	0.981282i	$0.438316\pi$
$431$	−15.6436	+	27.0956i	−0.753528	+	1.30515i	−0.946103	+	0.323866i	$0.895017\pi$
$432$	−1.00000			−0.0481125
$433$	8.68888			0.417561			0.208780	−	0.977963i	$-0.433051\pi$
$433$	8.68888			0.417561			0.208780	+	0.977963i	$0.433051\pi$
$434$	20.1107	−	15.1185i	0.965346	−	0.725711i
$435$	−9.38207			−0.449836
$436$	7.90089			0.378384
$437$	21.8018	−	37.7618i	1.04292	−	1.80639i
$438$	−2.00000			−0.0955637
$439$	−16.6248	−	28.7950i	−0.793460	−	1.37431i	−0.923813	−	0.382845i	$-0.874944\pi$
$439$	−16.6248	−	28.7950i	−0.793460	−	1.37431i	0.130353	−	0.991468i	$-0.458389\pi$
$440$	−1.93163	+	3.34568i	−0.0920867	+	0.159499i
$441$	−6.70985	+	11.6218i	−0.319517	+	0.553419i
$442$	−3.38639			−0.161074
$443$	−7.41970	−	12.8513i	−0.352521	−	0.610584i	0.634170	−	0.773194i	$-0.281342\pi$
$443$	−7.41970	−	12.8513i	−0.352521	−	0.610584i	−0.986690	+	0.162610i	$0.948009\pi$
$444$	−1.24059	−	2.14877i	−0.0588759	−	0.101976i
$445$	1.48118	+	2.56548i	0.0702148	+	0.121616i
$446$	−8.12266	+	14.0689i	−0.384619	+	0.666180i
$447$	−7.82778	−	13.5581i	−0.370241	−	0.641277i
$448$	−2.25941	+	3.91341i	−0.106747	+	0.184891i
$449$	5.80178			0.273803			0.136901	−	0.990585i	$-0.456286\pi$
$449$	5.80178			0.273803			0.136901	+	0.990585i	$0.456286\pi$
$450$	−1.00000			−0.0471405
$451$	15.7899	−	27.3488i	0.743515	−	1.28781i
$452$	3.70985	+	6.42565i	0.174497	+	0.302237i
$453$	−7.45044	+	12.9045i	−0.350052	+	0.606309i
$454$	−5.64148	−	9.77133i	−0.264768	−	0.458591i
$455$	−15.9009	−	27.5411i	−0.745445	−	1.29115i
$456$	3.95044	+	6.84237i	0.184996	+	0.320423i
$457$	29.3864			1.37464			0.687319	−	0.726356i	$-0.258788\pi$
$457$	29.3864			1.37464			0.687319	+	0.726356i	$0.258788\pi$
$458$	5.33251	−	9.23619i	0.249172	−	0.431579i
$459$	0.240592	−	0.416717i	0.0112299	−	0.0194507i
$460$	−2.75941	−	4.77944i	−0.128658	−	0.222842i
$461$	25.4907			1.18722			0.593609	−	0.804754i	$-0.297703\pi$
$461$	25.4907			1.18722			0.593609	+	0.804754i	$0.297703\pi$
$462$	8.72867	−	15.1185i	0.406094	−	0.703376i
$463$	17.3582			0.806705			0.403353	−	0.915045i	$-0.367845\pi$
$463$	17.3582			0.806705			0.403353	+	0.915045i	$0.367845\pi$
$464$	9.38207			0.435552
$465$	−5.12266	−	2.18136i	−0.237558	−	0.101158i
$466$	−6.48118			−0.300235
$467$	31.9718			1.47948			0.739740	−	0.672893i	$-0.234948\pi$
$467$	31.9718			1.47948			0.739740	+	0.672893i	$0.234948\pi$
$468$	−3.51882	+	6.09477i	−0.162657	+	0.281731i
$469$	11.2120			0.517723
$470$	5.27823	+	9.14215i	0.243466	+	0.421696i
$471$	1.22394	−	2.11992i	0.0563960	−	0.0976807i
$472$	6.77823	−	11.7402i	0.311993	−	0.540388i
$473$	16.9291			0.778399
$474$	2.19104	+	3.79498i	0.100638	+	0.174309i
$475$	3.95044	+	6.84237i	0.181259	+	0.313949i
$476$	−1.08719	−	1.88307i	−0.0498313	−	0.0863103i
$477$	0.827781	−	1.43376i	0.0379015	−	0.0656473i
$478$	−10.3821	−	17.9823i	−0.474865	−	0.822490i
$479$	10.3325	−	17.8964i	0.472105	−	0.817709i	−0.527386	−	0.849626i	$-0.676828\pi$
$479$	10.3325	−	17.8964i	0.472105	−	0.817709i	0.999491	+	0.0319166i	$0.0101611\pi$
$480$	1.00000			0.0456435
$481$	−17.4617			−0.796183
$482$	−9.82778	+	17.0222i	−0.447643	+	0.775341i
$483$	12.4693	+	21.5974i	0.567371	+	0.982715i
$484$	−1.96237	+	3.39892i	−0.0891985	+	0.154496i
$485$	5.72867	+	9.92235i	0.260125	+	0.450551i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	11.6415	+	20.1636i	0.527526	+	0.913701i	0.999485	+	0.0320812i	$0.0102135\pi$
$487$	11.6415	+	20.1636i	0.527526	+	0.913701i	−0.471959	+	0.881620i	$0.656453\pi$
$488$	−5.90089			−0.267121
$489$	−10.6603	+	18.4642i	−0.482075	+	0.834979i
$490$	6.70985	−	11.6218i	0.303120	−	0.525020i
$491$	12.8701	+	22.2918i	0.580822	+	1.00601i	0.995382	+	0.0959909i	$0.0306020\pi$
$491$	12.8701	+	22.2918i	0.580822	+	1.00601i	−0.414561	+	0.910022i	$0.636065\pi$
$492$	−8.17438			−0.368529
$493$	−2.25725	+	3.90967i	−0.101661	+	0.176083i
$494$	55.6036			2.50172
$495$	−3.86325			−0.173640
$496$	5.12266	+	2.18136i	0.230014	+	0.0979459i
$497$	13.7265			0.615718
$498$	−1.20769			−0.0541180
$499$	−6.37015	+	11.0334i	−0.285167	+	0.493924i	−0.972650	−	0.232277i	$-0.925382\pi$
$499$	−6.37015	+	11.0334i	−0.285167	+	0.493924i	0.687483	+	0.726201i	$0.258716\pi$
$500$	1.00000			0.0447214
$501$	−4.29488	−	7.43895i	−0.191881	−	0.332348i
$502$	−0.191035	+	0.330883i	−0.00852633	+	0.0147680i
$503$	7.15814	−	12.3983i	0.319165	−	0.552811i	−0.661149	−	0.750255i	$-0.729931\pi$
$503$	7.15814	−	12.3983i	0.319165	−	0.552811i	0.980314	+	0.197444i	$0.0632641\pi$
$504$	−4.51882			−0.201284
$505$	−4.88207	−	8.45599i	−0.217249	−	0.376287i
$506$	−10.6603	−	18.4642i	−0.473908	−	0.820833i
$507$	18.2641	+	31.6344i	0.811139	+	1.40493i
$508$	1.60385	−	2.77794i	0.0711592	−	0.123251i
$509$	11.8488	+	20.5227i	0.525187	+	0.909651i	0.999570	+	0.0293318i	$0.00933795\pi$
$509$	11.8488	+	20.5227i	0.525187	+	0.909651i	−0.474383	+	0.880319i	$0.657329\pi$
$510$	−0.240592	+	0.416717i	−0.0106536	+	0.0184525i
$511$	−9.03763			−0.399801
$512$	−1.00000			−0.0441942
$513$	−3.95044	+	6.84237i	−0.174416	+	0.302098i
$514$	10.4859	+	18.1621i	0.462514	+	0.801098i
$515$	−7.77823	+	13.4723i	−0.342750	+	0.593660i
$516$	−2.19104	−	3.79498i	−0.0964550	−	0.167065i
$517$	20.3911	+	35.3185i	0.896801	+	1.55330i
$518$	−5.60601	−	9.70989i	−0.246314	−	0.426628i
$519$	5.38207			0.236247
$520$	3.51882	−	6.09477i	0.154310	−	0.267273i
$521$	3.82562	−	6.62617i	0.167603	−	0.290298i	−0.769973	−	0.638076i	$-0.779730\pi$
$521$	3.82562	−	6.62617i	0.167603	−	0.290298i	0.937577	+	0.347778i	$0.113064\pi$
$522$	4.69104	+	8.12511i	0.205321	+	0.355626i
$523$	3.07095			0.134283			0.0671415	−	0.997743i	$-0.478612\pi$
$523$	3.07095			0.134283			0.0671415	+	0.997743i	$0.478612\pi$
$524$	3.32778	−	5.76389i	0.145375	−	0.251797i
$525$	−4.51882			−0.197217
$526$	−2.38207			−0.103863
$527$	−2.14148	+	1.60988i	−0.0932843	+	0.0701276i
$528$	3.86325			0.168127
$529$	7.45734			0.324232
$530$	−0.827781	+	1.43376i	−0.0359565	+	0.0622785i
$531$	13.5565			0.588300
$532$	17.8513	+	30.9194i	0.773953	+	1.34053i
$533$	−28.7641	+	49.8210i	−1.24591	+	2.15799i
$534$	1.48118	−	2.56548i	0.0640971	−	0.111019i
$535$	4.51882			0.195365
$536$	1.24059	+	2.14877i	0.0535854	+	0.0928126i
$537$	6.10601	+	10.5759i	0.263494	+	0.456384i
$538$	9.36541	+	16.2214i	0.403772	+	0.699353i
$539$	25.9219	−	44.8980i	1.11653	−	1.93389i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	−7.22394	+	12.5122i	−0.310581	+	0.537942i	−0.978488	−	0.206302i	$-0.933857\pi$
$541$	−7.22394	+	12.5122i	−0.310581	+	0.537942i	0.667907	+	0.744245i	$0.267190\pi$
$542$	7.82994			0.336325
$543$	10.7641			0.461934
$544$	0.240592	−	0.416717i	0.0103153	−	0.0178666i
$545$	−3.95044	−	6.84237i	−0.169218	−	0.293095i
$546$	−15.9009	+	27.5411i	−0.680495	+	1.17865i
$547$	−8.98334	−	15.5596i	−0.384100	−	0.665281i	0.607544	−	0.794286i	$-0.292155\pi$
$547$	−8.98334	−	15.5596i	−0.384100	−	0.665281i	−0.991644	+	0.129005i	$0.958822\pi$
$548$	2.41497	+	4.18285i	0.103162	+	0.178683i
$549$	−2.95044	−	5.11032i	−0.125922	−	0.218103i
$550$	3.86325			0.164730
$551$	37.0633	−	64.1956i	1.57895	−	2.73482i
$552$	−2.75941	+	4.77944i	−0.117448	+	0.203426i
$553$	9.90089	+	17.1488i	0.421029	+	0.729243i
$554$	14.2077			0.603627
$555$	−1.24059	+	2.14877i	−0.0526602	+	0.0912101i
$556$	8.86325			0.375886
$557$	15.1838			0.643360			0.321680	−	0.946848i	$-0.395752\pi$
$557$	15.1838			0.643360			0.321680	+	0.946848i	$0.395752\pi$
$558$	0.672219	+	5.52704i	0.0284573	+	0.233978i
$559$	−30.8394			−1.30437
$560$	4.51882			0.190955
$561$	−0.929467	+	1.60988i	−0.0392421	+	0.0679693i
$562$	−4.62225			−0.194978
$563$	15.8535	+	27.4591i	0.668145	+	1.15726i	0.978422	+	0.206615i	$0.0662448\pi$
$563$	15.8535	+	27.4591i	0.668145	+	1.15726i	−0.310277	+	0.950646i	$0.600422\pi$
$564$	5.27823	−	9.14215i	0.222253	−	0.384954i
$565$	3.70985	−	6.42565i	0.156075	−	0.270329i
$566$	−25.4950			−1.07163
$567$	−2.25941	−	3.91341i	−0.0948862	−	0.164348i
$568$	1.51882	+	2.63067i	0.0637281	+	0.110380i
$569$	−18.9718	−	32.8602i	−0.795341	−	1.37757i	−0.922623	−	0.385704i	$-0.873959\pi$
$569$	−18.9718	−	32.8602i	−0.795341	−	1.37757i	0.127282	−	0.991867i	$-0.459375\pi$
$570$	3.95044	−	6.84237i	0.165466	−	0.286595i
$571$	−9.38207	−	16.2502i	−0.392627	−	0.680051i	0.600168	−	0.799874i	$-0.295100\pi$
$571$	−9.38207	−	16.2502i	−0.392627	−	0.680051i	−0.992795	+	0.119823i	$0.961767\pi$
$572$	13.5941	−	23.5456i	0.568397	−	0.984493i
$573$	−9.90089			−0.413616
$574$	−36.9385			−1.54178
$575$	−2.75941	+	4.77944i	−0.115075	+	0.199316i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.6556	+	20.1880i	−0.485227	+	0.840439i	−0.999856	−	0.0169747i	$-0.994597\pi$
$577$	−11.6556	+	20.1880i	−0.485227	+	0.840439i	0.514629	+	0.857413i	$0.327930\pi$
$578$	−8.38423	−	14.5219i	−0.348738	−	0.604032i
$579$	10.6910	+	18.5174i	0.444304	+	0.769558i
$580$	−4.69104	−	8.12511i	−0.194785	−	0.337377i
$581$	−5.45734			−0.226409
$582$	5.72867	−	9.92235i	0.237461	−	0.411294i
$583$	−3.19793	+	5.53898i	−0.132445	+	0.229401i
$584$	−1.00000	−	1.73205i	−0.0413803	−	0.0716728i
$585$	7.03763			0.290970
$586$	−3.86541	+	6.69509i	−0.159679	+	0.276572i
$587$	−33.4812			−1.38192			−0.690958	−	0.722895i	$-0.742811\pi$
$587$	−33.4812			−1.38192			−0.690958	+	0.722895i	$0.742811\pi$
$588$	−13.4197			−0.553419
$589$	35.1625	−	26.4338i	1.44884	−	1.08919i
$590$	−13.5565			−0.558110
$591$	−7.31112			−0.300739
$592$	1.24059	−	2.14877i	0.0509880	−	0.0883138i
$593$	−31.0891			−1.27667			−0.638337	−	0.769757i	$-0.720377\pi$
$593$	−31.0891			−1.27667			−0.638337	+	0.769757i	$0.720377\pi$
$594$	1.93163	+	3.34568i	0.0792556	+	0.137275i
$595$	−1.08719	+	1.88307i	−0.0445704	+	0.0771982i
$596$	7.82778	−	13.5581i	0.320638	−	0.555362i
$597$	−2.79231			−0.114282
$598$	19.4197	+	33.6359i	0.794131	+	1.37547i
$599$	2.65556	+	4.59957i	0.108503	+	0.187933i	0.915164	−	0.403081i	$-0.132061\pi$
$599$	2.65556	+	4.59957i	0.108503	+	0.187933i	−0.806661	+	0.591015i	$0.798728\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	16.2287	−	28.1089i	0.661981	−	1.14659i	−0.318113	−	0.948053i	$-0.603049\pi$
$601$	16.2287	−	28.1089i	0.661981	−	1.14659i	0.980094	−	0.198532i	$-0.0636175\pi$
$602$	−9.90089	−	17.1488i	−0.403530	−	0.698935i
$603$	−1.24059	+	2.14877i	−0.0505208	+	0.0875046i
$604$	−14.9009			−0.606309
$605$	3.92473			0.159563
$606$	−4.88207	+	8.45599i	−0.198321	+	0.343501i
$607$	12.7641	+	22.1081i	0.518081	+	0.897342i	0.999779	+	0.0210050i	$0.00668659\pi$
$607$	12.7641	+	22.1081i	0.518081	+	0.897342i	−0.481699	+	0.876337i	$0.659980\pi$
$608$	−3.95044	+	6.84237i	−0.160212	+	0.277495i
$609$	21.1979	+	36.7159i	0.858983	+	1.48780i
$610$	2.95044	+	5.11032i	0.119460	+	0.206911i
$611$	−37.1462	−	64.3391i	−1.50277	−	2.60288i
$612$	0.481183			0.0194507
$613$	4.82994	−	8.36570i	0.195080	−	0.337888i	−0.751847	−	0.659338i	$-0.770837\pi$
$613$	4.82994	−	8.36570i	0.195080	−	0.337888i	0.946927	+	0.321450i	$0.104170\pi$
$614$	−0.223935	+	0.387867i	−0.00903730	+	0.0156531i
$615$	4.08719	+	7.07922i	0.164811	+	0.285462i
$616$	17.4573			0.703376
$617$	−2.20296	+	3.81564i	−0.0886878	+	0.153612i	−0.906957	−	0.421224i	$-0.861601\pi$
$617$	−2.20296	+	3.81564i	−0.0886878	+	0.153612i	0.818269	+	0.574836i	$0.194934\pi$
$618$	15.5565			0.625772
$619$	−48.4907			−1.94900			−0.974502	−	0.224379i	$-0.927965\pi$
$619$	−48.4907			−1.94900			−0.974502	+	0.224379i	$0.927965\pi$
$620$	−0.672219	−	5.52704i	−0.0269970	−	0.221971i
$621$	−5.51882			−0.221462
$622$	−6.68888			−0.268199
$623$	6.69320	−	11.5930i	0.268157	−	0.464462i
$624$	−7.03763			−0.281731
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.48334	+	2.56923i	−0.0592863	+	0.102687i
$627$	15.2616	−	26.4338i	0.609488	−	1.05566i
$628$	2.44787			0.0976807
$629$	0.596952	+	1.03395i	0.0238020	+	0.0412263i
$630$	2.25941	+	3.91341i	0.0900170	+	0.155914i
$631$	−6.35133	−	11.0008i	−0.252843	−	0.437936i	0.711465	−	0.702722i	$-0.248032\pi$
$631$	−6.35133	−	11.0008i	−0.252843	−	0.437936i	−0.964307	+	0.264786i	$0.914699\pi$
$632$	−2.19104	+	3.79498i	−0.0871547	+	0.150956i
$633$	−0.0495562	−	0.0858338i	−0.00196968	−	0.00341159i
$634$	3.34660	−	5.79648i	0.132910	−	0.230208i
$635$	−3.20769			−0.127293
$636$	1.65556			0.0656473
$637$	−47.2215	+	81.7900i	−1.87098	+	3.24064i
$638$	−18.1227	−	31.3894i	−0.717483	−	1.24272i
$639$	−1.51882	+	2.63067i	−0.0600835	+	0.104068i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−18.4693	−	31.9897i	−0.729492	−	1.26352i	−0.957098	−	0.289764i	$-0.906423\pi$
$641$	−18.4693	−	31.9897i	−0.729492	−	1.26352i	0.227606	−	0.973753i	$-0.426910\pi$
$642$	−2.25941	−	3.91341i	−0.0891717	−	0.154450i
$643$	−13.2873			−0.523999			−0.262000	−	0.965068i	$-0.584382\pi$
$643$	−13.2873			−0.523999			−0.262000	+	0.965068i	$0.584382\pi$
$644$	−12.4693	+	21.5974i	−0.491358	+	0.851056i
$645$	−2.19104	+	3.79498i	−0.0862719	+	0.149427i
$646$	−1.90089	−	3.29243i	−0.0747894	−	0.129539i
$647$	5.27864			0.207525			0.103762	−	0.994602i	$-0.466912\pi$
$647$	5.27864			0.207525			0.103762	+	0.994602i	$0.466912\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−52.3720			−2.05578
$650$	−7.03763			−0.276039
$651$	3.03763	+	24.9757i	0.119054	+	0.978873i
$652$	−21.3206			−0.834979
$653$	−32.4197			−1.26868			−0.634341	−	0.773054i	$-0.718728\pi$
$653$	−32.4197			−1.26868			−0.634341	+	0.773054i	$0.718728\pi$
$654$	−3.95044	+	6.84237i	−0.154475	+	0.267558i
$655$	−6.65556			−0.260054
$656$	−4.08719	−	7.07922i	−0.159578	−	0.276397i
$657$	1.00000	−	1.73205i	0.0390137	−	0.0675737i
$658$	23.8513	−	41.3117i	0.929822	−	1.61050i
$659$	−13.2496			−0.516133			−0.258066	−	0.966127i	$-0.583085\pi$
$659$	−13.2496			−0.516133			−0.258066	+	0.966127i	$0.583085\pi$
$660$	−1.93163	−	3.34568i	−0.0751885	−	0.130230i
$661$	−17.9881	−	31.1563i	−0.699655	−	1.21184i	−0.968586	−	0.248679i	$-0.920004\pi$
$661$	−17.9881	−	31.1563i	−0.699655	−	1.21184i	0.268931	−	0.963159i	$-0.413330\pi$
$662$	−3.70512	−	6.41745i	−0.144004	−	0.249421i
$663$	1.69320	−	2.93270i	0.0657583	−	0.113897i
$664$	−0.603846	−	1.04589i	−0.0234338	−	0.0405885i
$665$	17.8513	−	30.9194i	0.692245	−	1.19900i
$666$	2.48118			0.0961439
$667$	51.7779			2.00485
$668$	4.29488	−	7.43895i	0.166174	−	0.287822i
$669$	−8.12266	−	14.0689i	−0.314040	−	0.543934i
$670$	1.24059	−	2.14877i	0.0479282	−	0.0830141i
$671$	11.3983	+	19.7425i	0.440027	+	0.762149i
$672$	−2.25941	−	3.91341i	−0.0871586	−	0.150963i
$673$	−6.69104	−	11.5892i	−0.257920	−	0.446731i	0.707764	−	0.706449i	$-0.249704\pi$
$673$	−6.69104	−	11.5892i	−0.257920	−	0.446731i	−0.965685	+	0.259717i	$0.916371\pi$
$674$	15.3821			0.592495
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−18.2641	+	31.6344i	−0.702467	+	1.21671i
$677$	2.10127	+	3.63951i	0.0807585	+	0.139878i	0.903576	−	0.428428i	$-0.140932\pi$
$677$	2.10127	+	3.63951i	0.0807585	+	0.139878i	−0.822817	+	0.568306i	$0.807599\pi$
$678$	−7.41970			−0.284952
$679$	25.8868	−	44.8373i	0.993444	−	1.72070i
$680$	−0.481183			−0.0184525
$681$	11.2830			0.432364
$682$	−2.59695	−	21.3523i	−0.0994424	−	0.817623i
$683$	35.8299			1.37099			0.685497	−	0.728075i	$-0.259585\pi$
$683$	35.8299			1.37099			0.685497	+	0.728075i	$0.259585\pi$
$684$	−7.90089			−0.302098
$685$	2.41497	−	4.18285i	0.0922713	−	0.159819i
$686$	−29.0095			−1.10759
$687$	5.33251	+	9.23619i	0.203448	+	0.352382i
$688$	2.19104	−	3.79498i	0.0835324	−	0.144682i
$689$	5.82562	−	10.0903i	0.221938	−	0.384409i
$690$	5.51882			0.210098
$691$	17.4693	+	30.2576i	0.664562	+	1.15106i	0.979404	+	0.201911i	$0.0647152\pi$
$691$	17.4693	+	30.2576i	0.664562	+	1.15106i	−0.314842	+	0.949144i	$0.601951\pi$
$692$	2.69104	+	4.66101i	0.102298	+	0.177185i
$693$	8.72867	+	15.1185i	0.331575	+	0.574304i
$694$	−4.64148	+	8.03928i	−0.176188	+	0.305167i
$695$	−4.43163	−	7.67580i	−0.168101	−	0.291160i
$696$	−4.69104	+	8.12511i	−0.177813	+	0.307982i
$697$	3.93337			0.148987
$698$	18.5898			0.703633
$699$	3.24059	−	5.61287i	0.122570	−	0.212298i
$700$	−2.25941	−	3.91341i	−0.0853976	−	0.147913i
$701$	−19.5376	+	33.8402i	−0.737926	+	1.27813i	0.215501	+	0.976504i	$0.430861\pi$
$701$	−19.5376	+	33.8402i	−0.737926	+	1.27813i	−0.953428	+	0.301622i	$0.902472\pi$
$702$	−3.51882	−	6.09477i	−0.132809	−	0.230032i
$703$	−9.80178	−	16.9772i	−0.369681	−	0.640306i
$704$	1.93163	+	3.34568i	0.0728009	+	0.126095i
$705$	−10.5565			−0.397579
$706$	13.2663	−	22.9779i	0.499284	−	0.864785i
$707$	−22.0612	+	38.2111i	−0.829696	+	1.43708i
$708$	6.77823	+	11.7402i	0.254741	+	0.441225i
$709$	−45.1557			−1.69586			−0.847929	−	0.530110i	$-0.822150\pi$
$709$	−45.1557			−1.69586			−0.847929	+	0.530110i	$0.822150\pi$
$710$	1.51882	−	2.63067i	0.0570002	−	0.0987272i
$711$	−4.38207			−0.164340
$712$	2.96237			0.111019
$713$	28.2710	+	12.0385i	1.05876	+	0.450846i
$714$	2.17438			0.0813741
$715$	−27.1882			−1.01678
$716$	−6.10601	+	10.5759i	−0.228192	+	0.395240i
$717$	20.7641			0.775451
$718$	4.56837	+	7.91265i	0.170490	+	0.295298i
$719$	−3.18630	+	5.51884i	−0.118829	+	0.205818i	−0.919304	−	0.393548i	$-0.871247\pi$
$719$	−3.18630	+	5.51884i	−0.118829	+	0.205818i	0.800475	+	0.599366i	$0.204581\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	70.2967			2.61799
$722$	21.7120	+	37.6063i	0.808037	+	1.39956i
$723$	−9.82778	−	17.0222i	−0.365499	−	0.633063i
$724$	5.38207	+	9.32202i	0.200023	+	0.346450i
$725$	−4.69104	+	8.12511i	−0.174221	+	0.301759i
$726$	−1.96237	−	3.39892i	−0.0728303	−	0.126146i
$727$	−25.9902	+	45.0164i	−0.963925	+	1.66957i	−0.251447	+	0.967871i	$0.580907\pi$
$727$	−25.9902	+	45.0164i	−0.963925	+	1.66957i	−0.712477	+	0.701695i	$0.752427\pi$
$728$	−31.8018			−1.17865
$729$	1.00000			0.0370370
$730$	−1.00000	+	1.73205i	−0.0370117	+	0.0641061i
$731$	1.05429	+	1.82608i	0.0389943	+	0.0675401i
$732$	2.95044	−	5.11032i	0.109052	−	0.188883i
$733$	15.0586	+	26.0823i	0.556202	+	0.963371i	0.997809	+	0.0661621i	$0.0210754\pi$
$733$	15.0586	+	26.0823i	0.556202	+	0.963371i	−0.441606	+	0.897209i	$0.645591\pi$
$734$	−12.0000	−	20.7846i	−0.442928	−	0.767174i
$735$	6.70985	+	11.6218i	0.247497	+	0.428677i
$736$	−5.51882			−0.203426
$737$	4.79272	−	8.30124i	0.176542	−	0.305780i
$738$	4.08719	−	7.07922i	0.150452	−	0.260590i
$739$	16.6060	+	28.7624i	0.610862	+	1.05804i	0.991095	+	0.133153i	$0.0425102\pi$
$739$	16.6060	+	28.7624i	0.610862	+	1.05804i	−0.380234	+	0.924890i	$0.624156\pi$
$740$	−2.48118			−0.0912101
$741$	−27.8018	+	48.1541i	−1.02132	+	1.76898i
$742$	7.48118			0.274643
$743$	−19.3444			−0.709679			−0.354839	−	0.934927i	$-0.615464\pi$
$743$	−19.3444			−0.709679			−0.354839	+	0.934927i	$0.615464\pi$
$744$	−4.45044	+	3.34568i	−0.163161	+	0.122658i
$745$	−15.6556			−0.573575
$746$	−25.3959			−0.929808
$747$	0.603846	−	1.04589i	0.0220936	−	0.0382672i
$748$	−1.85893			−0.0679693
$749$	−10.2099	−	17.6840i	−0.373060	−	0.646159i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	11.8325	−	20.4945i	0.431775	−	0.747856i	−0.565252	−	0.824919i	$-0.691221\pi$
$751$	11.8325	−	20.4945i	0.431775	−	0.747856i	0.997026	+	0.0770630i	$0.0245543\pi$
$752$	10.5565			0.384954
$753$	−0.191035	−	0.330883i	−0.00696172	−	0.0120581i
$754$	33.0138	+	57.1816i	1.20229	+	2.08243i
$755$	7.45044	+	12.9045i	0.271149	+	0.469645i
$756$	2.25941	−	3.91341i	0.0821739	−	0.142329i
$757$	−17.6107	−	30.5027i	−0.640073	−	1.10864i	−0.985416	−	0.170163i	$-0.945571\pi$
$757$	−17.6107	−	30.5027i	−0.640073	−	1.10864i	0.345343	−	0.938477i	$-0.387763\pi$
$758$	−13.9385	+	24.1422i	−0.506270	+	0.876885i
$759$	21.3206			0.773888
$760$	7.90089			0.286595
$761$	−1.77606	+	3.07623i	−0.0643823	+	0.111513i	−0.896420	−	0.443206i	$-0.853841\pi$
$761$	−1.77606	+	3.07623i	−0.0643823	+	0.111513i	0.832038	+	0.554719i	$0.187174\pi$
$762$	1.60385	+	2.77794i	0.0581012	+	0.100634i
$763$	−17.8513	+	30.9194i	−0.646262	+	1.11936i
$764$	−4.95044	−	8.57442i	−0.179101	−	0.310212i
$765$	−0.240592	−	0.416717i	−0.00869861	−	0.0150664i
$766$	−8.27823	−	14.3383i	−0.299104	−	0.518064i
$767$	95.4053			3.44489
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−8.69104	+	15.0533i	−0.313407	+	0.542836i	−0.979098	−	0.203391i	$-0.934804\pi$
$769$	−8.69104	+	15.0533i	−0.313407	+	0.542836i	0.665691	+	0.746228i	$0.268137\pi$
$770$	−8.72867	−	15.1185i	−0.314559	−	0.544833i
$771$	−20.9718			−0.755282
$772$	−10.6910	+	18.5174i	−0.384779	+	0.666456i
$773$	−28.0753			−1.00980			−0.504899	−	0.863179i	$-0.668470\pi$
$773$	−28.0753			−1.00980			−0.504899	+	0.863179i	$0.668470\pi$
$774$	4.38207			0.157510
$775$	−4.45044	+	3.34568i	−0.159865	+	0.120180i
$776$	11.4573			0.411294
$777$	11.2120			0.402229
$778$	14.8842	−	25.7802i	0.533626	−	0.924267i
$779$	−64.5849			−2.31399
$780$	3.51882	+	6.09477i	0.125994	+	0.218228i
$781$	5.86758	−	10.1629i	0.209958	−	0.363659i
$782$	1.32778	−	2.29978i	0.0474814	−	0.0822401i
$783$	−9.38207			−0.335288
$784$	−6.70985	−	11.6218i	−0.239638	−	0.415064i
$785$	−1.22394	−	2.11992i	−0.0436841	−	0.0756631i
$786$	3.32778	+	5.76389i	0.118698	+	0.205591i
$787$	24.1791	−	41.8795i	0.861892	−	1.49284i	−0.00820790	−	0.999966i	$-0.502613\pi$
$787$	24.1791	−	41.8795i	0.861892	−	1.49284i	0.870100	−	0.492875i	$-0.164054\pi$
$788$	−3.65556	−	6.33162i	−0.130224	−	0.225555i
$789$	1.19104	−	2.06293i	0.0424020	−	0.0734424i
$790$	4.38207			0.155907
$791$	−33.5283			−1.19213
$792$	−1.93163	+	3.34568i	−0.0686374	+	0.118883i
$793$	−20.7641	−	35.9645i	−0.737356	−	1.27714i
$794$	−10.3278	+	17.8882i	−0.366519	+	0.634830i
$795$	−0.827781	−	1.43376i	−0.0293584	−	0.0508502i
$796$	−1.39615	−	2.41821i	−0.0494854	−	0.0857112i
$797$	−10.7287	−	18.5826i	−0.380029	−	0.658229i	0.611037	−	0.791602i	$-0.290753\pi$
$797$	−10.7287	−	18.5826i	−0.380029	−	0.658229i	−0.991066	+	0.133373i	$0.957419\pi$
$798$	−35.7027			−1.26386
$799$	−2.53979	+	4.39905i	−0.0898514	+	0.155627i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	1.48118	+	2.56548i	0.0523350	+	0.0906469i
$802$	18.8394			0.665243
$803$	−3.86325	+	6.69135i	−0.136331	+	0.236133i
$804$	−2.48118			−0.0875046
$805$	24.9385			0.878967
$806$	4.73083	+	38.8972i	0.166636	+	1.37010i
$807$	−18.7308			−0.659356
$808$	−9.76414			−0.343501
$809$	−17.7522	+	30.7477i	−0.624135	+	1.08103i	0.364573	+	0.931175i	$0.381215\pi$
$809$	−17.7522	+	30.7477i	−0.624135	+	1.08103i	−0.988707	+	0.149858i	$0.952118\pi$
$810$	−1.00000			−0.0351364
$811$	−10.3444	−	17.9171i	−0.363242	−	0.629154i	0.625250	−	0.780424i	$-0.284997\pi$
$811$	−10.3444	−	17.9171i	−0.363242	−	0.629154i	−0.988492	+	0.151270i	$0.951664\pi$
$812$	−21.1979	+	36.7159i	−0.743901	+	1.28848i
$813$	−3.91497	+	6.78093i	−0.137304	+	0.237818i
$814$	−9.58544			−0.335970
$815$	10.6603	+	18.4642i	0.373414	+	0.646772i
$816$	0.240592	+	0.416717i	0.00842239	+	0.0145880i
$817$	−17.3111	−	29.9837i	−0.605640	−	1.04900i
$818$	3.67438	−	6.36421i	0.128472	−	0.222519i
$819$	−15.9009	−	27.5411i	−0.555622	−	0.962365i
$820$	−4.08719	+	7.07922i	−0.142731	+	0.247217i
$821$	1.34876			0.0470720			0.0235360	−	0.999723i	$-0.492508\pi$
$821$	1.34876			0.0470720			0.0235360	+	0.999723i	$0.492508\pi$
$822$	−4.82994			−0.168464
$823$	−9.33468	+	16.1681i	−0.325386	+	0.563586i	−0.981590	−	0.190998i	$-0.938828\pi$
$823$	−9.33468	+	16.1681i	−0.325386	+	0.563586i	0.656204	+	0.754583i	$0.272161\pi$
$824$	7.77823	+	13.4723i	0.270967	+	0.469329i
$825$	−1.93163	+	3.34568i	−0.0672506	+	0.116481i
$826$	30.6296	+	53.0519i	1.06574	+	1.84591i
$827$	13.0376	+	22.5818i	0.453363	+	0.785248i	0.998592	−	0.0530392i	$-0.0168908\pi$
$827$	13.0376	+	22.5818i	0.453363	+	0.785248i	−0.545229	+	0.838287i	$0.683557\pi$
$828$	−2.75941	−	4.77944i	−0.0958961	−	0.166097i
$829$	−21.5608			−0.748837			−0.374418	−	0.927260i	$-0.622158\pi$
$829$	−21.5608			−0.748837			−0.374418	+	0.927260i	$0.622158\pi$
$830$	−0.603846	+	1.04589i	−0.0209598	+	0.0363034i
$831$	−7.10385	+	12.3042i	−0.246430	+	0.426829i
$832$	−3.51882	−	6.09477i	−0.121993	−	0.211298i
$833$	6.45734			0.223733
$834$	−4.43163	+	7.67580i	−0.153455	+	0.265791i
$835$	−8.58976			−0.297261
$836$	30.5231			1.05566
$837$	−5.12266	−	2.18136i	−0.177065	−	0.0753988i
$838$	11.8633			0.409809
$839$	−9.56077			−0.330074			−0.165037	−	0.986287i	$-0.552774\pi$
$839$	−9.56077			−0.330074			−0.165037	+	0.986287i	$0.552774\pi$
$840$	−2.25941	+	3.91341i	−0.0779570	+	0.135025i
$841$	59.0233			2.03528
$842$	−9.81370	−	16.9978i	−0.338202	−	0.585784i
$843$	2.31112	−	4.00299i	0.0795994	−	0.137870i
$844$	0.0495562	−	0.0858338i	0.00170579	−	0.00295452i
$845$	36.5283			1.25661
$846$	5.27823	+	9.14215i	0.181469	+	0.314314i
$847$	−8.86758	−	15.3591i	−0.304693	−	0.527745i
$848$	0.827781	+	1.43376i	0.0284261	+	0.0492355i
$849$	12.7475	−	22.0793i	0.437493	−	0.757759i
$850$	0.240592	+	0.416717i	0.00825223	+	0.0142933i
$851$	6.84660	−	11.8587i	0.234698	−	0.406509i
$852$	−3.03763			−0.104068
$853$	−42.6412			−1.46001			−0.730003	−	0.683444i	$-0.760481\pi$
$853$	−42.6412			−1.46001			−0.730003	+	0.683444i	$0.760481\pi$
$854$	13.3325	−	23.0926i	0.456229	−	0.790212i
$855$	3.95044	+	6.84237i	0.135102	+	0.234004i
$856$	2.25941	−	3.91341i	0.0772250	−	0.133758i
$857$	−11.6765	−	20.2244i	−0.398863	−	0.690851i	0.594723	−	0.803931i	$-0.297262\pi$
$857$	−11.6765	−	20.2244i	−0.398863	−	0.690851i	−0.993586	+	0.113080i	$0.963928\pi$
$858$	13.5941	+	23.5456i	0.464094	+	0.803835i
$859$	2.56837	+	4.44855i	0.0876318	+	0.151783i	0.906510	−	0.422185i	$-0.138737\pi$
$859$	2.56837	+	4.44855i	0.0876318	+	0.151783i	−0.818878	+	0.573968i	$0.805403\pi$
$860$	−4.38207			−0.149427
$861$	18.4693	−	31.9897i	0.629431	−	1.09021i
$862$	15.6436	−	27.0956i	0.532824	−	0.922879i
$863$	22.1672	+	38.3947i	0.754580	+	1.30697i	0.945583	+	0.325381i	$0.105493\pi$
$863$	22.1672	+	38.3947i	0.754580	+	1.30697i	−0.191003	+	0.981589i	$0.561174\pi$
$864$	1.00000			0.0340207
$865$	2.69104	−	4.66101i	0.0914980	−	0.158479i
$866$	−8.68888			−0.295260
$867$	16.7685			0.569487
$868$	−20.1107	+	15.1185i	−0.682603	+	0.513155i
$869$	16.9291			0.574279
$870$	9.38207			0.318082
$871$	−8.73083	+	15.1222i	−0.295833	+	0.512398i
$872$	−7.90089			−0.267558
$873$	5.72867	+	9.92235i	0.193886	+	0.335821i
$874$	−21.8018	+	37.7618i	−0.737456	+	1.27731i
$875$	−2.25941	+	3.91341i	−0.0763819	+	0.132297i
$876$	2.00000			0.0675737
$877$	−4.17911	−	7.23844i	−0.141119	−	0.244425i	0.786800	−	0.617209i	$-0.211737\pi$
$877$	−4.17911	−	7.23844i	−0.141119	−	0.244425i	−0.927918	+	0.372784i	$0.878403\pi$
$878$	16.6248	+	28.7950i	0.561061	+	0.971785i
$879$	−3.86541	−	6.69509i	−0.130377	−	0.225820i
$880$	1.93163	−	3.34568i	0.0651151	−	0.112783i
$881$	−2.49311	−	4.31819i	−0.0839949	−	0.145483i	0.820968	−	0.570975i	$-0.193435\pi$
$881$	−2.49311	−	4.31819i	−0.0839949	−	0.145483i	−0.904962	+	0.425491i	$0.860101\pi$
$882$	6.70985	−	11.6218i	0.225932	−	0.391327i
$883$	16.1600			0.543827			0.271914	−	0.962322i	$-0.412343\pi$
$883$	16.1600			0.543827			0.271914	+	0.962322i	$0.412343\pi$
$884$	3.38639			0.113897
$885$	6.77823	−	11.7402i	0.227848	−	0.394644i
$886$	7.41970	+	12.8513i	0.249270	+	0.431748i
$887$	23.0586	−	39.9387i	0.774232	−	1.34101i	−0.160993	−	0.986956i	$-0.551470\pi$
$887$	23.0586	−	39.9387i	0.774232	−	1.34101i	0.935225	−	0.354054i	$-0.115197\pi$
$888$	1.24059	+	2.14877i	0.0416315	+	0.0721079i
$889$	7.24749	+	12.5530i	0.243073	+	0.421015i
$890$	−1.48118	−	2.56548i	−0.0496494	−	0.0859952i
$891$	−3.86325			−0.129424
$892$	8.12266	−	14.0689i	0.271967	−	0.471060i
$893$	41.7027	−	72.2311i	1.39553	−	2.41712i
$894$	7.82778	+	13.5581i	0.261800	+	0.453451i
$895$	12.2120			0.408203
$896$	2.25941	−	3.91341i	0.0754815	−	0.130738i
$897$	−38.8394			−1.29681
$898$	−5.80178			−0.193608
$899$	48.0612	+	20.4657i	1.60293	+	0.682568i
$900$	1.00000			0.0333333
$901$	−0.796629			−0.0265396
$902$	−15.7899	+	27.3488i	−0.525745	+	0.910616i
$903$	19.8018			0.658962
$904$	−3.70985	−	6.42565i	−0.123388	−	0.213714i
$905$	5.38207	−	9.32202i	0.178906	−	0.309874i
$906$	7.45044	−	12.9045i	0.247524	−	0.428725i
$907$	50.0753			1.66272			0.831361	−	0.555733i	$-0.187562\pi$
$907$	50.0753			1.66272			0.831361	+	0.555733i	$0.187562\pi$
$908$	5.64148	+	9.77133i	0.187219	+	0.324273i
$909$	−4.88207	−	8.45599i	−0.161928	−	0.280468i
$910$	15.9009	+	27.5411i	0.527109	+	0.912980i
$911$	−24.7146	+	42.8069i	−0.818831	+	1.41826i	0.0877135	+	0.996146i	$0.472044\pi$
$911$	−24.7146	+	42.8069i	−0.818831	+	1.41826i	−0.906544	+	0.422111i	$0.861289\pi$
$912$	−3.95044	−	6.84237i	−0.130812	−	0.226573i
$913$	−2.33281	+	4.04055i	−0.0772047	+	0.133723i
$914$	−29.3864			−0.972015
$915$	−5.90089			−0.195077
$916$	−5.33251	+	9.23619i	−0.176191	+	0.305172i
$917$	15.0376	+	26.0459i	0.496586	+	0.860113i
$918$	−0.240592	+	0.416717i	−0.00794071	+	0.0137537i
$919$	−10.6958	−	18.5256i	−0.352821	−	0.611104i	0.633922	−	0.773397i	$-0.281444\pi$
$919$	−10.6958	−	18.5256i	−0.352821	−	0.611104i	−0.986743	+	0.162294i	$0.948111\pi$
$920$	2.75941	+	4.77944i	0.0909750	+	0.157573i
$921$	−0.223935	−	0.387867i	−0.00737892	−	0.0127807i
$922$	−25.4907			−0.839490
$923$	−10.6889	+	18.5137i	−0.351829	+	0.609385i
$924$	−8.72867	+	15.1185i	−0.287152	+	0.497362i
$925$	1.24059	+	2.14877i	0.0407904	+	0.0706510i
$926$	−17.3582			−0.570427
$927$	−7.77823	+	13.4723i	−0.255470	+	0.442488i
$928$	−9.38207			−0.307982
$929$	−50.1744			−1.64617			−0.823084	−	0.567920i	$-0.807748\pi$
$929$	−50.1744			−1.64617			−0.823084	+	0.567920i	$0.807748\pi$
$930$	5.12266	+	2.18136i	0.167979	+	0.0715296i
$931$	−106.028			−3.47491
$932$	6.48118			0.212298
$933$	3.34444	−	5.79274i	0.109492	−	0.189646i
$934$	−31.9718			−1.04615
$935$	0.929467	+	1.60988i	0.0303968	+	0.0526488i
$936$	3.51882	−	6.09477i	0.115016	−	0.199214i
$937$	−8.80178	+	15.2451i	−0.287541	+	0.498036i	−0.973222	−	0.229866i	$-0.926171\pi$
$937$	−8.80178	+	15.2451i	−0.287541	+	0.498036i	0.685681	+	0.727902i	$0.259505\pi$
$938$	−11.2120			−0.366085
$939$	−1.48334	−	2.56923i	−0.0484071	−	0.0838435i
$940$	−5.27823	−	9.14215i	−0.172157	−	0.298184i
$941$	−13.0188	−	22.5493i	−0.424401	−	0.735085i	0.571963	−	0.820279i	$-0.306182\pi$
$941$	−13.0188	−	22.5493i	−0.424401	−	0.735085i	−0.996364	+	0.0851948i	$0.972849\pi$
$942$	−1.22394	+	2.11992i	−0.0398780	+	0.0690707i
$943$	−22.5565	−	39.0689i	−0.734539	−	1.27226i
$944$	−6.77823	+	11.7402i	−0.220612	+	0.382112i
$945$	−4.51882			−0.146997
$946$	−16.9291			−0.550411
$947$	−5.44355	+	9.42851i	−0.176892	+	0.306385i	−0.940814	−	0.338923i	$-0.889938\pi$
$947$	−5.44355	+	9.42851i	−0.176892	+	0.306385i	0.763923	+	0.645308i	$0.223271\pi$
$948$	−2.19104	−	3.79498i	−0.0711615	−	0.123255i
$949$	7.03763	−	12.1895i	0.228451	−	0.395689i
$950$	−3.95044	−	6.84237i	−0.128169	−	0.221996i
$951$	3.34660	+	5.79648i	0.108521	+	0.187964i
$952$	1.08719	+	1.88307i	0.0352360	+	0.0610306i
$953$	26.0991			0.845433			0.422717	−	0.906262i	$-0.361077\pi$
$953$	26.0991			0.845433			0.422717	+	0.906262i	$0.361077\pi$
$954$	−0.827781	+	1.43376i	−0.0268004	+	0.0464197i
$955$	−4.95044	+	8.57442i	−0.160193	+	0.277462i
$956$	10.3821	+	17.9823i	0.335780	+	0.581588i
$957$	36.2453			1.17164
$958$	−10.3325	+	17.8964i	−0.333828	+	0.578208i
$959$	−21.8256			−0.704786
$960$	−1.00000			−0.0322749
$961$	21.4833	+	22.3487i	0.693011	+	0.720927i
$962$	17.4617			0.562986
$963$	4.51882			0.145617
$964$	9.82778	−	17.0222i	0.316532	−	0.548249i
$965$	21.3821			0.688313
$966$	−12.4693	−	21.5974i	−0.401192	−	0.694885i
$967$	22.1505	−	38.3658i	0.712313	−	1.23376i	−0.251674	−	0.967812i	$-0.580981\pi$
$967$	22.1505	−	38.3658i	0.712313	−	1.23376i	0.963987	−	0.265950i	$-0.0856857\pi$
$968$	1.96237	−	3.39892i	0.0630729	−	0.109245i
$969$	3.80178			0.122131
$970$	−5.72867	−	9.92235i	−0.183936	−	0.318587i
$971$	9.41281	+	16.3035i	0.302071	+	0.523203i	0.976605	−	0.215041i	$-0.0689885\pi$
$971$	9.41281	+	16.3035i	0.302071	+	0.523203i	−0.674534	+	0.738244i	$0.735655\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−20.0257	+	34.6855i	−0.641995	+	1.11197i
$974$	−11.6415	−	20.1636i	−0.373017	−	0.646084i
$975$	3.51882	−	6.09477i	0.112692	−	0.195189i
$976$	5.90089			0.188883
$977$	−35.0376			−1.12095			−0.560477	−	0.828170i	$-0.689382\pi$
$977$	−35.0376			−1.12095			−0.560477	+	0.828170i	$0.689382\pi$
$978$	10.6603	−	18.4642i	0.340879	−	0.590419i
$979$	−5.72219	−	9.91112i	−0.182882	−	0.316761i
$980$	−6.70985	+	11.6218i	−0.214338	+	0.371245i
$981$	−3.95044	−	6.84237i	−0.126128	−	0.218460i
$982$	−12.8701	−	22.2918i	−0.410703	−	0.711358i
$983$	0.617929	+	1.07028i	0.0197089	+	0.0341368i	0.875712	−	0.482834i	$-0.160393\pi$
$983$	0.617929	+	1.07028i	0.0197089	+	0.0341368i	−0.856003	+	0.516971i	$0.827059\pi$
$984$	8.17438			0.260590
$985$	−3.65556	+	6.33162i	−0.116476	+	0.201742i
$986$	2.25725	−	3.90967i	0.0718854	−	0.124509i
$987$	23.8513	+	41.3117i	0.759196	+	1.31497i
$988$	−55.6036			−1.76898
$989$	12.0919	−	20.9438i	0.384501	−	0.665975i
$990$	3.86325			0.122782
$991$	3.65124			0.115986			0.0579928	−	0.998317i	$-0.481530\pi$
$991$	3.65124			0.115986			0.0579928	+	0.998317i	$0.481530\pi$
$992$	−5.12266	−	2.18136i	−0.162645	−	0.0692582i
$993$	7.41024			0.235157
$994$	−13.7265			−0.435378
$995$	−1.39615	+	2.41821i	−0.0442611	+	0.0766624i
$996$	1.20769			0.0382672
$997$	21.7899	+	37.7411i	0.690092	+	1.19527i	0.971807	+	0.235776i	$0.0757631\pi$
$997$	21.7899	+	37.7411i	0.690092	+	1.19527i	−0.281716	+	0.959498i	$0.590904\pi$
$998$	6.37015	−	11.0334i	0.201644	−	0.349257i
$999$	−1.24059	+	2.14877i	−0.0392506	+	0.0679840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.n.811.1	yes	6
31.25	even	3	inner	930.2.i.n.211.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.n.211.1	✓	6	31.25	even	3	inner
930.2.i.n.811.1	yes	6	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.25941 + 3.91341i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.25941 + 3.91341i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.93163 + 3.34568i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.51882 - 6.09477i) q^{13} +(2.25941 - 3.91341i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-0.240592 + 0.416717i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.95044 - 6.84237i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.25941 + 3.91341i) q^{21} +(-1.93163 - 3.34568i) q^{22} +5.51882 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.51882 + 6.09477i) q^{26} -1.00000 q^{27} +(-2.25941 + 3.91341i) q^{28} +9.38207 q^{29} +1.00000 q^{30} +(5.12266 + 2.18136i) q^{31} -1.00000 q^{32} +3.86325 q^{33} +(0.240592 - 0.416717i) q^{34} +4.51882 q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.24059 - 2.14877i) q^{37} +(-3.95044 + 6.84237i) q^{38} -7.03763 q^{39} +(0.500000 + 0.866025i) q^{40} +(-4.08719 - 7.07922i) q^{41} +(-2.25941 - 3.91341i) q^{42} +(2.19104 - 3.79498i) q^{43} +(1.93163 + 3.34568i) q^{44} +(-0.500000 + 0.866025i) q^{45} -5.51882 q^{46} +10.5565 q^{47} +(0.500000 - 0.866025i) q^{48} +(-6.70985 - 11.6218i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.240592 + 0.416717i) q^{51} +(-3.51882 - 6.09477i) q^{52} +(0.827781 + 1.43376i) q^{53} +1.00000 q^{54} +(1.93163 - 3.34568i) q^{55} +(2.25941 - 3.91341i) q^{56} +(-3.95044 - 6.84237i) q^{57} -9.38207 q^{58} +(-6.77823 + 11.7402i) q^{59} -1.00000 q^{60} +5.90089 q^{61} +(-5.12266 - 2.18136i) q^{62} +4.51882 q^{63} +1.00000 q^{64} +(-3.51882 + 6.09477i) q^{65} -3.86325 q^{66} +(-1.24059 - 2.14877i) q^{67} +(-0.240592 + 0.416717i) q^{68} +(2.75941 - 4.77944i) q^{69} -4.51882 q^{70} +(-1.51882 - 2.63067i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 + 1.73205i) q^{73} +(-1.24059 + 2.14877i) q^{74} +(0.500000 + 0.866025i) q^{75} +(3.95044 - 6.84237i) q^{76} -17.4573 q^{77} +7.03763 q^{78} +(2.19104 - 3.79498i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.08719 + 7.07922i) q^{82} +(0.603846 + 1.04589i) q^{83} +(2.25941 + 3.91341i) q^{84} +0.481183 q^{85} +(-2.19104 + 3.79498i) q^{86} +(4.69104 - 8.12511i) q^{87} +(-1.93163 - 3.34568i) q^{88} -2.96237 q^{89} +(0.500000 - 0.866025i) q^{90} +31.8018 q^{91} +5.51882 q^{92} +(4.45044 - 3.34568i) q^{93} -10.5565 q^{94} -7.90089 q^{95} +(-0.500000 + 0.866025i) q^{96} -11.4573 q^{97} +(6.70985 + 11.6218i) q^{98} +(1.93163 - 3.34568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 14 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} - 6 q^{27} - 4 q^{28} + 24 q^{29} + 6 q^{30} + 8 q^{31} - 6 q^{32} + 10 q^{33} + 11 q^{34} + 8 q^{35} - 3 q^{36} + 17 q^{37} + 2 q^{38} - 4 q^{39} + 3 q^{40} - 12 q^{41} - 4 q^{42} - 3 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} + 6 q^{47} + 3 q^{48} - 5 q^{49} + 3 q^{50} + 11 q^{51} - 2 q^{52} + 2 q^{53} + 6 q^{54} + 5 q^{55} + 4 q^{56} + 2 q^{57} - 24 q^{58} - 12 q^{59} - 6 q^{60} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 6 q^{64} - 2 q^{65} - 10 q^{66} - 17 q^{67} - 11 q^{68} + 7 q^{69} - 8 q^{70} + 10 q^{71} + 3 q^{72} + 6 q^{73} - 17 q^{74} + 3 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{78} - 3 q^{79} - 3 q^{80} - 3 q^{81} + 12 q^{82} + 4 q^{84} + 22 q^{85} + 3 q^{86} + 12 q^{87} - 5 q^{88} - 56 q^{89} + 3 q^{90} + 88 q^{91} + 14 q^{92} + q^{93} - 6 q^{94} + 4 q^{95} - 3 q^{96} + 40 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 6 * q^16 - 11 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 14 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 24 * q^29 + 6 * q^30 + 8 * q^31 - 6 * q^32 + 10 * q^33 + 11 * q^34 + 8 * q^35 - 3 * q^36 + 17 * q^37 + 2 * q^38 - 4 * q^39 + 3 * q^40 - 12 * q^41 - 4 * q^42 - 3 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 + 6 * q^47 + 3 * q^48 - 5 * q^49 + 3 * q^50 + 11 * q^51 - 2 * q^52 + 2 * q^53 + 6 * q^54 + 5 * q^55 + 4 * q^56 + 2 * q^57 - 24 * q^58 - 12 * q^59 - 6 * q^60 - 16 * q^61 - 8 * q^62 + 8 * q^63 + 6 * q^64 - 2 * q^65 - 10 * q^66 - 17 * q^67 - 11 * q^68 + 7 * q^69 - 8 * q^70 + 10 * q^71 + 3 * q^72 + 6 * q^73 - 17 * q^74 + 3 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^78 - 3 * q^79 - 3 * q^80 - 3 * q^81 + 12 * q^82 + 4 * q^84 + 22 * q^85 + 3 * q^86 + 12 * q^87 - 5 * q^88 - 56 * q^89 + 3 * q^90 + 88 * q^91 + 14 * q^92 + q^93 - 6 * q^94 + 4 * q^95 - 3 * q^96 + 40 * q^97 + 5 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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