LMFDB - Embedded newform 930.2.d.g.559.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(559,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("930.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.d (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.4
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.g.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} +4.82843i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} +4.82843i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +4.82843 q^{11} -1.00000i q^{12} -0.828427i q^{13} -4.82843 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +4.82843i q^{17} -1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} -4.82843 q^{21} +4.82843i q^{22} -8.48528i q^{23} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +0.828427 q^{26} -1.00000i q^{27} -4.82843i q^{28} +1.65685 q^{29} +(-2.00000 - 1.00000i) q^{30} +1.00000 q^{31} +1.00000i q^{32} +4.82843i q^{33} -4.82843 q^{34} +(-4.82843 + 9.65685i) q^{35} +1.00000 q^{36} -6.48528i q^{37} +0.828427 q^{39} +(1.00000 - 2.00000i) q^{40} -3.65685 q^{41} -4.82843i q^{42} +1.65685i q^{43} -4.82843 q^{44} +(-2.00000 - 1.00000i) q^{45} +8.48528 q^{46} -5.65685i q^{47} +1.00000i q^{48} -16.3137 q^{49} +(-4.00000 + 3.00000i) q^{50} -4.82843 q^{51} +0.828427i q^{52} +11.6569i q^{53} +1.00000 q^{54} +(9.65685 + 4.82843i) q^{55} +4.82843 q^{56} +1.65685i q^{58} -8.82843 q^{59} +(1.00000 - 2.00000i) q^{60} -4.82843 q^{61} +1.00000i q^{62} -4.82843i q^{63} -1.00000 q^{64} +(0.828427 - 1.65685i) q^{65} -4.82843 q^{66} -14.8284i q^{67} -4.82843i q^{68} +8.48528 q^{69} +(-9.65685 - 4.82843i) q^{70} +2.82843 q^{71} +1.00000i q^{72} -2.34315i q^{73} +6.48528 q^{74} +(-4.00000 + 3.00000i) q^{75} +23.3137i q^{77} +0.828427i q^{78} +11.3137 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -3.65685i q^{82} +9.65685i q^{83} +4.82843 q^{84} +(-4.82843 + 9.65685i) q^{85} -1.65685 q^{86} +1.65685i q^{87} -4.82843i q^{88} +0.828427 q^{89} +(1.00000 - 2.00000i) q^{90} +4.00000 q^{91} +8.48528i q^{92} +1.00000i q^{93} +5.65685 q^{94} -1.00000 q^{96} -11.3137i q^{97} -16.3137i q^{98} -4.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{20} - 8 q^{21} + 4 q^{24} + 12 q^{25} - 8 q^{26} - 16 q^{29} - 8 q^{30} + 4 q^{31} - 8 q^{34} - 8 q^{35} + 4 q^{36} - 8 q^{39} + 4 q^{40} + 8 q^{41} - 8 q^{44} - 8 q^{45} - 20 q^{49} - 16 q^{50} - 8 q^{51} + 4 q^{54} + 16 q^{55} + 8 q^{56} - 24 q^{59} + 4 q^{60} - 8 q^{61} - 4 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{70} - 8 q^{74} - 16 q^{75} + 8 q^{80} + 4 q^{81} + 8 q^{84} - 8 q^{85} + 16 q^{86} - 8 q^{89} + 4 q^{90} + 16 q^{91} - 4 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^9 - 4 * q^10 + 8 * q^11 - 8 * q^14 - 4 * q^15 + 4 * q^16 - 8 * q^20 - 8 * q^21 + 4 * q^24 + 12 * q^25 - 8 * q^26 - 16 * q^29 - 8 * q^30 + 4 * q^31 - 8 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^39 + 4 * q^40 + 8 * q^41 - 8 * q^44 - 8 * q^45 - 20 * q^49 - 16 * q^50 - 8 * q^51 + 4 * q^54 + 16 * q^55 + 8 * q^56 - 24 * q^59 + 4 * q^60 - 8 * q^61 - 4 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^70 - 8 * q^74 - 16 * q^75 + 8 * q^80 + 4 * q^81 + 8 * q^84 - 8 * q^85 + 16 * q^86 - 8 * q^89 + 4 * q^90 + 16 * q^91 - 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−1.00000			−0.408248
$7$			4.82843i			1.82497i	0.409106	+	0.912487i	$0.365841\pi$
$7$			4.82843i			1.82497i	−0.409106	+	0.912487i	$0.634159\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	4.82843			1.45583			0.727913	−	0.685670i	$-0.240491\pi$
$11$	4.82843			1.45583			0.727913	+	0.685670i	$0.240491\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	0.828427i		−	0.229764i	−0.993379	−	0.114882i	$-0.963351\pi$
$13$		−	0.828427i		−	0.229764i	0.993379	−	0.114882i	$-0.0366490\pi$
$14$	−4.82843			−1.29045
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$			4.82843i			1.17107i	0.810649	+	0.585533i	$0.199115\pi$
$17$			4.82843i			1.17107i	−0.810649	+	0.585533i	$0.800885\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	−4.82843			−1.05365
$22$			4.82843i			1.02942i
$23$		−	8.48528i		−	1.76930i	−0.466252	−	0.884652i	$-0.654396\pi$
$23$		−	8.48528i		−	1.76930i	0.466252	−	0.884652i	$-0.345604\pi$
$24$	1.00000			0.204124
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	0.828427			0.162468
$27$		−	1.00000i		−	0.192450i
$28$		−	4.82843i		−	0.912487i
$29$	1.65685			0.307670			0.153835	−	0.988097i	$-0.450838\pi$
$29$	1.65685			0.307670			0.153835	+	0.988097i	$0.450838\pi$
$30$	−2.00000	−	1.00000i	−0.365148	−	0.182574i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$			1.00000i			0.176777i
$33$			4.82843i			0.840521i
$34$	−4.82843			−0.828068
$35$	−4.82843	+	9.65685i	−0.816153	+	1.63231i
$36$	1.00000			0.166667
$37$		−	6.48528i		−	1.06617i	−0.846061	−	0.533087i	$-0.821032\pi$
$37$		−	6.48528i		−	1.06617i	0.846061	−	0.533087i	$-0.178968\pi$
$38$		0			0
$39$	0.828427			0.132655
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	−3.65685			−0.571105			−0.285552	−	0.958363i	$-0.592177\pi$
$41$	−3.65685			−0.571105			−0.285552	+	0.958363i	$0.592177\pi$
$42$		−	4.82843i		−	0.745042i
$43$			1.65685i			0.252668i	0.991988	+	0.126334i	$0.0403211\pi$
$43$			1.65685i			0.252668i	−0.991988	+	0.126334i	$0.959679\pi$
$44$	−4.82843			−0.727913
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	8.48528			1.25109
$47$		−	5.65685i		−	0.825137i	−0.910927	−	0.412568i	$-0.864632\pi$
$47$		−	5.65685i		−	0.825137i	0.910927	−	0.412568i	$-0.135368\pi$
$48$			1.00000i			0.144338i
$49$	−16.3137			−2.33053
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	−4.82843			−0.676115
$52$			0.828427i			0.114882i
$53$			11.6569i			1.60119i	0.599204	+	0.800596i	$0.295484\pi$
$53$			11.6569i			1.60119i	−0.599204	+	0.800596i	$0.704516\pi$
$54$	1.00000			0.136083
$55$	9.65685	+	4.82843i	1.30213	+	0.651065i
$56$	4.82843			0.645226
$57$		0			0
$58$			1.65685i			0.217556i
$59$	−8.82843			−1.14936			−0.574682	−	0.818377i	$-0.694874\pi$
$59$	−8.82843			−1.14936			−0.574682	+	0.818377i	$0.694874\pi$
$60$	1.00000	−	2.00000i	0.129099	−	0.258199i
$61$	−4.82843			−0.618217			−0.309108	−	0.951027i	$-0.600031\pi$
$61$	−4.82843			−0.618217			−0.309108	+	0.951027i	$0.600031\pi$
$62$			1.00000i			0.127000i
$63$		−	4.82843i		−	0.608325i
$64$	−1.00000			−0.125000
$65$	0.828427	−	1.65685i	0.102754	−	0.205507i
$66$	−4.82843			−0.594338
$67$		−	14.8284i		−	1.81158i	−0.423726	−	0.905790i	$-0.639278\pi$
$67$		−	14.8284i		−	1.81158i	0.423726	−	0.905790i	$-0.360722\pi$
$68$		−	4.82843i		−	0.585533i
$69$	8.48528			1.02151
$70$	−9.65685	−	4.82843i	−1.15421	−	0.577107i
$71$	2.82843			0.335673			0.167836	−	0.985815i	$-0.446322\pi$
$71$	2.82843			0.335673			0.167836	+	0.985815i	$0.446322\pi$
$72$			1.00000i			0.117851i
$73$		−	2.34315i		−	0.274244i	−0.990554	−	0.137122i	$-0.956215\pi$
$73$		−	2.34315i		−	0.274244i	0.990554	−	0.137122i	$-0.0437853\pi$
$74$	6.48528			0.753899
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$		0			0
$77$			23.3137i			2.65684i
$78$			0.828427i			0.0938009i
$79$	11.3137			1.27289			0.636446	−	0.771321i	$-0.280404\pi$
$79$	11.3137			1.27289			0.636446	+	0.771321i	$0.280404\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	1.00000			0.111111
$82$		−	3.65685i		−	0.403832i
$83$			9.65685i			1.05998i	0.848005	+	0.529989i	$0.177804\pi$
$83$			9.65685i			1.05998i	−0.848005	+	0.529989i	$0.822196\pi$
$84$	4.82843			0.526825
$85$	−4.82843	+	9.65685i	−0.523716	+	1.04743i
$86$	−1.65685			−0.178663
$87$			1.65685i			0.177633i
$88$		−	4.82843i		−	0.514712i
$89$	0.828427			0.0878131			0.0439065	−	0.999036i	$-0.486020\pi$
$89$	0.828427			0.0878131			0.0439065	+	0.999036i	$0.486020\pi$
$90$	1.00000	−	2.00000i	0.105409	−	0.210819i
$91$	4.00000			0.419314
$92$			8.48528i			0.884652i
$93$			1.00000i			0.103695i
$94$	5.65685			0.583460
$95$		0			0
$96$	−1.00000			−0.102062
$97$		−	11.3137i		−	1.14873i	−0.818598	−	0.574367i	$-0.805248\pi$
$97$		−	11.3137i		−	1.14873i	0.818598	−	0.574367i	$-0.194752\pi$
$98$		−	16.3137i		−	1.64793i
$99$	−4.82843			−0.485275
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	−11.3137			−1.12576			−0.562878	−	0.826540i	$-0.690306\pi$
$101$	−11.3137			−1.12576			−0.562878	+	0.826540i	$0.690306\pi$
$102$		−	4.82843i		−	0.478086i
$103$		−	18.4853i		−	1.82141i	−0.413059	−	0.910704i	$-0.635540\pi$
$103$		−	18.4853i		−	1.82141i	0.413059	−	0.910704i	$-0.364460\pi$
$104$	−0.828427			−0.0812340
$105$	−9.65685	−	4.82843i	−0.942412	−	0.471206i
$106$	−11.6569			−1.13221
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$			1.00000i			0.0962250i
$109$	0.343146			0.0328674			0.0164337	−	0.999865i	$-0.494769\pi$
$109$	0.343146			0.0328674			0.0164337	+	0.999865i	$0.494769\pi$
$110$	−4.82843	+	9.65685i	−0.460372	+	0.920745i
$111$	6.48528			0.615556
$112$			4.82843i			0.456243i
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	8.48528	−	16.9706i	0.791257	−	1.58251i
$116$	−1.65685			−0.153835
$117$			0.828427i			0.0765881i
$118$		−	8.82843i		−	0.812723i
$119$	−23.3137			−2.13716
$120$	2.00000	+	1.00000i	0.182574	+	0.0912871i
$121$	12.3137			1.11943
$122$		−	4.82843i		−	0.437145i
$123$		−	3.65685i		−	0.329727i
$124$	−1.00000			−0.0898027
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	4.82843			0.430150
$127$			12.1421i			1.07744i	0.842485	+	0.538720i	$0.181092\pi$
$127$			12.1421i			1.07744i	−0.842485	+	0.538720i	$0.818908\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.65685			−0.145878
$130$	1.65685	+	0.828427i	0.145316	+	0.0726579i
$131$	1.51472			0.132342			0.0661708	−	0.997808i	$-0.478922\pi$
$131$	1.51472			0.132342			0.0661708	+	0.997808i	$0.478922\pi$
$132$		−	4.82843i		−	0.420261i
$133$		0			0
$134$	14.8284			1.28098
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	4.82843			0.414034
$137$		−	10.4853i		−	0.895818i	−0.894079	−	0.447909i	$-0.852169\pi$
$137$		−	10.4853i		−	0.895818i	0.894079	−	0.447909i	$-0.147831\pi$
$138$			8.48528i			0.722315i
$139$	−14.1421			−1.19952			−0.599760	−	0.800180i	$-0.704737\pi$
$139$	−14.1421			−1.19952			−0.599760	+	0.800180i	$0.704737\pi$
$140$	4.82843	−	9.65685i	0.408077	−	0.816153i
$141$	5.65685			0.476393
$142$			2.82843i			0.237356i
$143$		−	4.00000i		−	0.334497i
$144$	−1.00000			−0.0833333
$145$	3.31371	+	1.65685i	0.275189	+	0.137594i
$146$	2.34315			0.193920
$147$		−	16.3137i		−	1.34553i
$148$			6.48528i			0.533087i
$149$	23.3137			1.90993			0.954967	−	0.296713i	$-0.0958905\pi$
$149$	23.3137			1.90993			0.954967	+	0.296713i	$0.0958905\pi$
$150$	−3.00000	−	4.00000i	−0.244949	−	0.326599i
$151$	10.3431			0.841713			0.420857	−	0.907127i	$-0.361730\pi$
$151$	10.3431			0.841713			0.420857	+	0.907127i	$0.361730\pi$
$152$		0			0
$153$		−	4.82843i		−	0.390355i
$154$	−23.3137			−1.87867
$155$	2.00000	+	1.00000i	0.160644	+	0.0803219i
$156$	−0.828427			−0.0663273
$157$			5.31371i			0.424080i	0.977261	+	0.212040i	$0.0680107\pi$
$157$			5.31371i			0.424080i	−0.977261	+	0.212040i	$0.931989\pi$
$158$			11.3137i			0.900070i
$159$	−11.6569			−0.924449
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	40.9706			3.22893
$162$			1.00000i			0.0785674i
$163$		−	9.17157i		−	0.718373i	−0.933266	−	0.359187i	$-0.883054\pi$
$163$		−	9.17157i		−	0.718373i	0.933266	−	0.359187i	$-0.116946\pi$
$164$	3.65685			0.285552
$165$	−4.82843	+	9.65685i	−0.375893	+	0.751785i
$166$	−9.65685			−0.749517
$167$		−	16.4853i		−	1.27567i	−0.770173	−	0.637835i	$-0.779830\pi$
$167$		−	16.4853i		−	1.27567i	0.770173	−	0.637835i	$-0.220170\pi$
$168$			4.82843i			0.372521i
$169$	12.3137			0.947208
$170$	−9.65685	−	4.82843i	−0.740647	−	0.370323i
$171$		0			0
$172$		−	1.65685i		−	0.126334i
$173$			21.3137i			1.62045i	0.586118	+	0.810226i	$0.300655\pi$
$173$			21.3137i			1.62045i	−0.586118	+	0.810226i	$0.699345\pi$
$174$	−1.65685			−0.125606
$175$	−19.3137	+	14.4853i	−1.45998	+	1.09498i
$176$	4.82843			0.363956
$177$		−	8.82843i		−	0.663585i
$178$			0.828427i			0.0620932i
$179$	16.8284			1.25782			0.628908	−	0.777480i	$-0.283502\pi$
$179$	16.8284			1.25782			0.628908	+	0.777480i	$0.283502\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$	19.1716			1.42501			0.712506	−	0.701666i	$-0.247560\pi$
$181$	19.1716			1.42501			0.712506	+	0.701666i	$0.247560\pi$
$182$			4.00000i			0.296500i
$183$		−	4.82843i		−	0.356928i
$184$	−8.48528			−0.625543
$185$	6.48528	−	12.9706i	0.476807	−	0.953615i
$186$	−1.00000			−0.0733236
$187$			23.3137i			1.70487i
$188$			5.65685i			0.412568i
$189$	4.82843			0.351216
$190$		0			0
$191$	16.4853			1.19283			0.596417	−	0.802675i	$-0.296591\pi$
$191$	16.4853			1.19283			0.596417	+	0.802675i	$0.296591\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	7.31371i		−	0.526452i	−0.964734	−	0.263226i	$-0.915213\pi$
$193$		−	7.31371i		−	0.526452i	0.964734	−	0.263226i	$-0.0847865\pi$
$194$	11.3137			0.812277
$195$	1.65685	+	0.828427i	0.118650	+	0.0593249i
$196$	16.3137			1.16526
$197$		−	6.97056i		−	0.496632i	−0.968679	−	0.248316i	$-0.920123\pi$
$197$		−	6.97056i		−	0.496632i	0.968679	−	0.248316i	$-0.0798771\pi$
$198$		−	4.82843i		−	0.343141i
$199$	−2.34315			−0.166101			−0.0830506	−	0.996545i	$-0.526466\pi$
$199$	−2.34315			−0.166101			−0.0830506	+	0.996545i	$0.526466\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$	14.8284			1.04592
$202$		−	11.3137i		−	0.796030i
$203$			8.00000i			0.561490i
$204$	4.82843			0.338058
$205$	−7.31371	−	3.65685i	−0.510812	−	0.255406i
$206$	18.4853			1.28793
$207$			8.48528i			0.589768i
$208$		−	0.828427i		−	0.0574411i
$209$		0			0
$210$	4.82843	−	9.65685i	0.333193	−	0.666386i
$211$	0.686292			0.0472463			0.0236231	−	0.999721i	$-0.492480\pi$
$211$	0.686292			0.0472463			0.0236231	+	0.999721i	$0.492480\pi$
$212$		−	11.6569i		−	0.800596i
$213$			2.82843i			0.193801i
$214$	4.00000			0.273434
$215$	−1.65685	+	3.31371i	−0.112997	+	0.225993i
$216$	−1.00000			−0.0680414
$217$			4.82843i			0.327775i
$218$			0.343146i			0.0232408i
$219$	2.34315			0.158335
$220$	−9.65685	−	4.82843i	−0.651065	−	0.325532i
$221$	4.00000			0.269069
$222$			6.48528i			0.435264i
$223$			21.7990i			1.45977i	0.683571	+	0.729884i	$0.260426\pi$
$223$			21.7990i			1.45977i	−0.683571	+	0.729884i	$0.739574\pi$
$224$	−4.82843			−0.322613
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	−14.0000			−0.931266
$227$		−	6.34315i		−	0.421009i	−0.977593	−	0.210505i	$-0.932489\pi$
$227$		−	6.34315i		−	0.421009i	0.977593	−	0.210505i	$-0.0675107\pi$
$228$		0			0
$229$	−1.51472			−0.100095			−0.0500477	−	0.998747i	$-0.515937\pi$
$229$	−1.51472			−0.100095			−0.0500477	+	0.998747i	$0.515937\pi$
$230$	16.9706	+	8.48528i	1.11901	+	0.559503i
$231$	−23.3137			−1.53393
$232$		−	1.65685i		−	0.108778i
$233$			26.9706i			1.76690i	0.468525	+	0.883450i	$0.344786\pi$
$233$			26.9706i			1.76690i	−0.468525	+	0.883450i	$0.655214\pi$
$234$	−0.828427			−0.0541560
$235$	5.65685	−	11.3137i	0.369012	−	0.738025i
$236$	8.82843			0.574682
$237$			11.3137i			0.734904i
$238$		−	23.3137i		−	1.51120i
$239$	−23.3137			−1.50804			−0.754019	−	0.656852i	$-0.771887\pi$
$239$	−23.3137			−1.50804			−0.754019	+	0.656852i	$0.771887\pi$
$240$	−1.00000	+	2.00000i	−0.0645497	+	0.129099i
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$			12.3137i			0.791555i
$243$			1.00000i			0.0641500i
$244$	4.82843			0.309108
$245$	−32.6274	−	16.3137i	−2.08449	−	1.04224i
$246$	3.65685			0.233153
$247$		0			0
$248$		−	1.00000i		−	0.0635001i
$249$	−9.65685			−0.611978
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	8.82843			0.557245			0.278623	−	0.960401i	$-0.410122\pi$
$251$	8.82843			0.557245			0.278623	+	0.960401i	$0.410122\pi$
$252$			4.82843i			0.304162i
$253$		−	40.9706i		−	2.57580i
$254$	−12.1421			−0.761865
$255$	−9.65685	−	4.82843i	−0.604736	−	0.302368i
$256$	1.00000			0.0625000
$257$			4.34315i			0.270918i	0.990783	+	0.135459i	$0.0432509\pi$
$257$			4.34315i			0.270918i	−0.990783	+	0.135459i	$0.956749\pi$
$258$		−	1.65685i		−	0.103151i
$259$	31.3137			1.94574
$260$	−0.828427	+	1.65685i	−0.0513769	+	0.102754i
$261$	−1.65685			−0.102557
$262$			1.51472i			0.0935796i
$263$			7.51472i			0.463377i	0.972790	+	0.231689i	$0.0744251\pi$
$263$			7.51472i			0.463377i	−0.972790	+	0.231689i	$0.925575\pi$
$264$	4.82843			0.297169
$265$	−11.6569	+	23.3137i	−0.716075	+	1.43215i
$266$		0			0
$267$			0.828427i			0.0506989i
$268$			14.8284i			0.905790i
$269$	−28.9706			−1.76637			−0.883183	−	0.469028i	$-0.844604\pi$
$269$	−28.9706			−1.76637			−0.883183	+	0.469028i	$0.844604\pi$
$270$	2.00000	+	1.00000i	0.121716	+	0.0608581i
$271$	−2.34315			−0.142336			−0.0711680	−	0.997464i	$-0.522673\pi$
$271$	−2.34315			−0.142336			−0.0711680	+	0.997464i	$0.522673\pi$
$272$			4.82843i			0.292766i
$273$			4.00000i			0.242091i
$274$	10.4853			0.633439
$275$	14.4853	+	19.3137i	0.873495	+	1.16466i
$276$	−8.48528			−0.510754
$277$			24.1421i			1.45056i	0.688454	+	0.725280i	$0.258290\pi$
$277$			24.1421i			1.45056i	−0.688454	+	0.725280i	$0.741710\pi$
$278$		−	14.1421i		−	0.848189i
$279$	−1.00000			−0.0598684
$280$	9.65685	+	4.82843i	0.577107	+	0.288554i
$281$	1.31371			0.0783693			0.0391846	−	0.999232i	$-0.487524\pi$
$281$	1.31371			0.0783693			0.0391846	+	0.999232i	$0.487524\pi$
$282$			5.65685i			0.336861i
$283$		−	9.17157i		−	0.545193i	−0.962128	−	0.272597i	$-0.912118\pi$
$283$		−	9.17157i		−	0.545193i	0.962128	−	0.272597i	$-0.0878825\pi$
$284$	−2.82843			−0.167836
$285$		0			0
$286$	4.00000			0.236525
$287$		−	17.6569i		−	1.04225i
$288$		−	1.00000i		−	0.0589256i
$289$	−6.31371			−0.371395
$290$	−1.65685	+	3.31371i	−0.0972938	+	0.194588i
$291$	11.3137			0.663221
$292$			2.34315i			0.137122i
$293$		−	2.00000i		−	0.116841i	−0.998292	−	0.0584206i	$-0.981394\pi$
$293$		−	2.00000i		−	0.116841i	0.998292	−	0.0584206i	$-0.0186065\pi$
$294$	16.3137			0.951435
$295$	−17.6569	−	8.82843i	−1.02802	−	0.514011i
$296$	−6.48528			−0.376949
$297$		−	4.82843i		−	0.280174i
$298$			23.3137i			1.35053i
$299$	−7.02944			−0.406523
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$	−8.00000			−0.461112
$302$			10.3431i			0.595181i
$303$		−	11.3137i		−	0.649956i
$304$		0			0
$305$	−9.65685	−	4.82843i	−0.552950	−	0.276475i
$306$	4.82843			0.276023
$307$		−	16.4853i		−	0.940865i	−0.882436	−	0.470432i	$-0.844098\pi$
$307$		−	16.4853i		−	0.940865i	0.882436	−	0.470432i	$-0.155902\pi$
$308$		−	23.3137i		−	1.32842i
$309$	18.4853			1.05159
$310$	−1.00000	+	2.00000i	−0.0567962	+	0.113592i
$311$	0.485281			0.0275178			0.0137589	−	0.999905i	$-0.495620\pi$
$311$	0.485281			0.0275178			0.0137589	+	0.999905i	$0.495620\pi$
$312$		−	0.828427i		−	0.0469005i
$313$		−	32.9706i		−	1.86361i	−0.362964	−	0.931803i	$-0.618235\pi$
$313$		−	32.9706i		−	1.86361i	0.362964	−	0.931803i	$-0.381765\pi$
$314$	−5.31371			−0.299870
$315$	4.82843	−	9.65685i	0.272051	−	0.544102i
$316$	−11.3137			−0.636446
$317$			9.31371i			0.523110i	0.965189	+	0.261555i	$0.0842353\pi$
$317$			9.31371i			0.523110i	−0.965189	+	0.261555i	$0.915765\pi$
$318$		−	11.6569i		−	0.653684i
$319$	8.00000			0.447914
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	4.00000			0.223258
$322$			40.9706i			2.28320i
$323$		0			0
$324$	−1.00000			−0.0555556
$325$	3.31371	−	2.48528i	0.183811	−	0.137859i
$326$	9.17157			0.507966
$327$			0.343146i			0.0189760i
$328$			3.65685i			0.201916i
$329$	27.3137			1.50585
$330$	−9.65685	−	4.82843i	−0.531592	−	0.265796i
$331$	−4.48528			−0.246533			−0.123267	−	0.992374i	$-0.539337\pi$
$331$	−4.48528			−0.246533			−0.123267	+	0.992374i	$0.539337\pi$
$332$		−	9.65685i		−	0.529989i
$333$			6.48528i			0.355391i
$334$	16.4853			0.902034
$335$	14.8284	−	29.6569i	0.810164	−	1.62033i
$336$	−4.82843			−0.263412
$337$		−	5.65685i		−	0.308148i	−0.988059	−	0.154074i	$-0.950761\pi$
$337$		−	5.65685i		−	0.308148i	0.988059	−	0.154074i	$-0.0492395\pi$
$338$			12.3137i			0.669777i
$339$	−14.0000			−0.760376
$340$	4.82843	−	9.65685i	0.261858	−	0.523716i
$341$	4.82843			0.261474
$342$		0			0
$343$		−	44.9706i		−	2.42818i
$344$	1.65685			0.0893316
$345$	16.9706	+	8.48528i	0.913664	+	0.456832i
$346$	−21.3137			−1.14583
$347$		−	6.34315i		−	0.340518i	−0.985399	−	0.170259i	$-0.945540\pi$
$347$		−	6.34315i		−	0.340518i	0.985399	−	0.170259i	$-0.0544604\pi$
$348$		−	1.65685i		−	0.0888167i
$349$	2.68629			0.143794			0.0718969	−	0.997412i	$-0.477095\pi$
$349$	2.68629			0.143794			0.0718969	+	0.997412i	$0.477095\pi$
$350$	−14.4853	−	19.3137i	−0.774271	−	1.03236i
$351$	−0.828427			−0.0442182
$352$			4.82843i			0.257356i
$353$		−	28.8284i		−	1.53438i	−0.641419	−	0.767191i	$-0.721654\pi$
$353$		−	28.8284i		−	1.53438i	0.641419	−	0.767191i	$-0.278346\pi$
$354$	8.82843			0.469226
$355$	5.65685	+	2.82843i	0.300235	+	0.150117i
$356$	−0.828427			−0.0439065
$357$		−	23.3137i		−	1.23389i
$358$			16.8284i			0.889410i
$359$	18.1421			0.957505			0.478753	−	0.877950i	$-0.341089\pi$
$359$	18.1421			0.957505			0.478753	+	0.877950i	$0.341089\pi$
$360$	−1.00000	+	2.00000i	−0.0527046	+	0.105409i
$361$	−19.0000			−1.00000
$362$			19.1716i			1.00764i
$363$			12.3137i			0.646302i
$364$	−4.00000			−0.209657
$365$	2.34315	−	4.68629i	0.122646	−	0.245292i
$366$	4.82843			0.252386
$367$		−	0.142136i		−	0.00741942i	−0.999993	−	0.00370971i	$-0.998819\pi$
$367$		−	0.142136i		−	0.00741942i	0.999993	−	0.00370971i	$-0.00118084\pi$
$368$		−	8.48528i		−	0.442326i
$369$	3.65685			0.190368
$370$	12.9706	+	6.48528i	0.674307	+	0.337154i
$371$	−56.2843			−2.92213
$372$		−	1.00000i		−	0.0518476i
$373$			11.6569i			0.603569i	0.953376	+	0.301785i	$0.0975823\pi$
$373$			11.6569i			0.603569i	−0.953376	+	0.301785i	$0.902418\pi$
$374$	−23.3137			−1.20552
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	−5.65685			−0.291730
$377$		−	1.37258i		−	0.0706916i
$378$			4.82843i			0.248347i
$379$	−1.65685			−0.0851069			−0.0425534	−	0.999094i	$-0.513549\pi$
$379$	−1.65685			−0.0851069			−0.0425534	+	0.999094i	$0.513549\pi$
$380$		0			0
$381$	−12.1421			−0.622060
$382$			16.4853i			0.843460i
$383$			28.4853i			1.45553i	0.685827	+	0.727765i	$0.259441\pi$
$383$			28.4853i			1.45553i	−0.685827	+	0.727765i	$0.740559\pi$
$384$	1.00000			0.0510310
$385$	−23.3137	+	46.6274i	−1.18818	+	2.37635i
$386$	7.31371			0.372258
$387$		−	1.65685i		−	0.0842226i
$388$			11.3137i			0.574367i
$389$	−35.3137			−1.79048			−0.895238	−	0.445588i	$-0.852995\pi$
$389$	−35.3137			−1.79048			−0.895238	+	0.445588i	$0.852995\pi$
$390$	−0.828427	+	1.65685i	−0.0419490	+	0.0838981i
$391$	40.9706			2.07197
$392$			16.3137i			0.823967i
$393$			1.51472i			0.0764074i
$394$	6.97056			0.351172
$395$	22.6274	+	11.3137i	1.13851	+	0.569254i
$396$	4.82843			0.242638
$397$		−	4.34315i		−	0.217976i	−0.994043	−	0.108988i	$-0.965239\pi$
$397$		−	4.34315i		−	0.217976i	0.994043	−	0.108988i	$-0.0347610\pi$
$398$		−	2.34315i		−	0.117451i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−14.4853			−0.723360			−0.361680	−	0.932302i	$-0.617797\pi$
$401$	−14.4853			−0.723360			−0.361680	+	0.932302i	$0.617797\pi$
$402$			14.8284i			0.739575i
$403$		−	0.828427i		−	0.0412669i
$404$	11.3137			0.562878
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	−8.00000			−0.397033
$407$		−	31.3137i		−	1.55216i
$408$			4.82843i			0.239043i
$409$	−10.6863			−0.528403			−0.264202	−	0.964467i	$-0.585108\pi$
$409$	−10.6863			−0.528403			−0.264202	+	0.964467i	$0.585108\pi$
$410$	3.65685	−	7.31371i	0.180599	−	0.361198i
$411$	10.4853			0.517201
$412$			18.4853i			0.910704i
$413$		−	42.6274i		−	2.09756i
$414$	−8.48528			−0.417029
$415$	−9.65685	+	19.3137i	−0.474036	+	0.948073i
$416$	0.828427			0.0406170
$417$		−	14.1421i		−	0.692543i
$418$		0			0
$419$	−29.7990			−1.45578			−0.727888	−	0.685696i	$-0.759498\pi$
$419$	−29.7990			−1.45578			−0.727888	+	0.685696i	$0.759498\pi$
$420$	9.65685	+	4.82843i	0.471206	+	0.235603i
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$			0.686292i			0.0334081i
$423$			5.65685i			0.275046i
$424$	11.6569			0.566107
$425$	−19.3137	+	14.4853i	−0.936852	+	0.702639i
$426$	−2.82843			−0.137038
$427$		−	23.3137i		−	1.12823i
$428$			4.00000i			0.193347i
$429$	4.00000			0.193122
$430$	−3.31371	−	1.65685i	−0.159801	−	0.0799006i
$431$	−6.82843			−0.328914			−0.164457	−	0.986384i	$-0.552587\pi$
$431$	−6.82843			−0.328914			−0.164457	+	0.986384i	$0.552587\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	2.34315i		−	0.112604i	−0.998414	−	0.0563022i	$-0.982069\pi$
$433$		−	2.34315i		−	0.112604i	0.998414	−	0.0563022i	$-0.0179310\pi$
$434$	−4.82843			−0.231772
$435$	−1.65685	+	3.31371i	−0.0794401	+	0.158880i
$436$	−0.343146			−0.0164337
$437$		0			0
$438$			2.34315i			0.111960i
$439$	−32.9706			−1.57360			−0.786800	−	0.617209i	$-0.788263\pi$
$439$	−32.9706			−1.57360			−0.786800	+	0.617209i	$0.788263\pi$
$440$	4.82843	−	9.65685i	0.230186	−	0.460372i
$441$	16.3137			0.776843
$442$			4.00000i			0.190261i
$443$			17.6569i			0.838902i	0.907778	+	0.419451i	$0.137777\pi$
$443$			17.6569i			0.838902i	−0.907778	+	0.419451i	$0.862223\pi$
$444$	−6.48528			−0.307778
$445$	1.65685	+	0.828427i	0.0785424	+	0.0392712i
$446$	−21.7990			−1.03221
$447$			23.3137i			1.10270i
$448$		−	4.82843i		−	0.228122i
$449$	−16.1421			−0.761794			−0.380897	−	0.924617i	$-0.624385\pi$
$449$	−16.1421			−0.761794			−0.380897	+	0.924617i	$0.624385\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	−17.6569			−0.831429
$452$		−	14.0000i		−	0.658505i
$453$			10.3431i			0.485963i
$454$	6.34315			0.297699
$455$	8.00000	+	4.00000i	0.375046	+	0.187523i
$456$		0			0
$457$			8.68629i			0.406328i	0.979145	+	0.203164i	$0.0651224\pi$
$457$			8.68629i			0.406328i	−0.979145	+	0.203164i	$0.934878\pi$
$458$		−	1.51472i		−	0.0707782i
$459$	4.82843			0.225372
$460$	−8.48528	+	16.9706i	−0.395628	+	0.791257i
$461$	3.31371			0.154335			0.0771674	−	0.997018i	$-0.475412\pi$
$461$	3.31371			0.154335			0.0771674	+	0.997018i	$0.475412\pi$
$462$		−	23.3137i		−	1.08465i
$463$			8.82843i			0.410292i	0.978731	+	0.205146i	$0.0657669\pi$
$463$			8.82843i			0.410292i	−0.978731	+	0.205146i	$0.934233\pi$
$464$	1.65685			0.0769175
$465$	−1.00000	+	2.00000i	−0.0463739	+	0.0927478i
$466$	−26.9706			−1.24939
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		−	0.828427i		−	0.0382941i
$469$	71.5980			3.30609
$470$	11.3137	+	5.65685i	0.521862	+	0.260931i
$471$	−5.31371			−0.244843
$472$			8.82843i			0.406361i
$473$			8.00000i			0.367840i
$474$	−11.3137			−0.519656
$475$		0			0
$476$	23.3137			1.06858
$477$		−	11.6569i		−	0.533731i
$478$		−	23.3137i		−	1.06634i
$479$	−26.8284			−1.22582			−0.612911	−	0.790152i	$-0.710002\pi$
$479$	−26.8284			−1.22582			−0.612911	+	0.790152i	$0.710002\pi$
$480$	−2.00000	−	1.00000i	−0.0912871	−	0.0456435i
$481$	−5.37258			−0.244969
$482$			22.0000i			1.00207i
$483$			40.9706i			1.86423i
$484$	−12.3137			−0.559714
$485$	11.3137	−	22.6274i	0.513729	−	1.02746i
$486$	−1.00000			−0.0453609
$487$			8.14214i			0.368955i	0.982837	+	0.184478i	$0.0590593\pi$
$487$			8.14214i			0.368955i	−0.982837	+	0.184478i	$0.940941\pi$
$488$			4.82843i			0.218573i
$489$	9.17157			0.414753
$490$	16.3137	−	32.6274i	0.736978	−	1.47396i
$491$	7.45584			0.336478			0.168239	−	0.985746i	$-0.446192\pi$
$491$	7.45584			0.336478			0.168239	+	0.985746i	$0.446192\pi$
$492$			3.65685i			0.164864i
$493$			8.00000i			0.360302i
$494$		0			0
$495$	−9.65685	−	4.82843i	−0.434043	−	0.217022i
$496$	1.00000			0.0449013
$497$			13.6569i			0.612594i
$498$		−	9.65685i		−	0.432734i
$499$	10.1421			0.454024			0.227012	−	0.973892i	$-0.427104\pi$
$499$	10.1421			0.454024			0.227012	+	0.973892i	$0.427104\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	16.4853			0.736508
$502$			8.82843i			0.394032i
$503$			35.3137i			1.57456i	0.616595	+	0.787280i	$0.288511\pi$
$503$			35.3137i			1.57456i	−0.616595	+	0.787280i	$0.711489\pi$
$504$	−4.82843			−0.215075
$505$	−22.6274	−	11.3137i	−1.00691	−	0.503453i
$506$	40.9706			1.82136
$507$			12.3137i			0.546871i
$508$		−	12.1421i		−	0.538720i
$509$	12.9706			0.574910			0.287455	−	0.957794i	$-0.407191\pi$
$509$	12.9706			0.574910			0.287455	+	0.957794i	$0.407191\pi$
$510$	4.82843	−	9.65685i	0.213806	−	0.427613i
$511$	11.3137			0.500489
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−4.34315			−0.191568
$515$	18.4853	−	36.9706i	0.814559	−	1.62912i
$516$	1.65685			0.0729389
$517$		−	27.3137i		−	1.20126i
$518$			31.3137i			1.37585i
$519$	−21.3137			−0.935568
$520$	−1.65685	−	0.828427i	−0.0726579	−	0.0363289i
$521$	−22.2843			−0.976292			−0.488146	−	0.872762i	$-0.662327\pi$
$521$	−22.2843			−0.976292			−0.488146	+	0.872762i	$0.662327\pi$
$522$		−	1.65685i		−	0.0725185i
$523$		−	22.6274i		−	0.989428i	−0.869056	−	0.494714i	$-0.835273\pi$
$523$		−	22.6274i		−	0.989428i	0.869056	−	0.494714i	$-0.164727\pi$
$524$	−1.51472			−0.0661708
$525$	−14.4853	−	19.3137i	−0.632190	−	0.842919i
$526$	−7.51472			−0.327657
$527$			4.82843i			0.210330i
$528$			4.82843i			0.210130i
$529$	−49.0000			−2.13043
$530$	−23.3137	−	11.6569i	−1.01268	−	0.506341i
$531$	8.82843			0.383121
$532$		0			0
$533$			3.02944i			0.131219i
$534$	−0.828427			−0.0358495
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$	−14.8284			−0.640490
$537$			16.8284i			0.726200i
$538$		−	28.9706i		−	1.24901i
$539$	−78.7696			−3.39284
$540$	−1.00000	+	2.00000i	−0.0430331	+	0.0860663i
$541$	−34.2843			−1.47400			−0.736998	−	0.675895i	$-0.763757\pi$
$541$	−34.2843			−1.47400			−0.736998	+	0.675895i	$0.763757\pi$
$542$		−	2.34315i		−	0.100647i
$543$			19.1716i			0.822731i
$544$	−4.82843			−0.207017
$545$	0.686292	+	0.343146i	0.0293975	+	0.0146987i
$546$	−4.00000			−0.171184
$547$		−	38.1421i		−	1.63084i	−0.578870	−	0.815420i	$-0.696506\pi$
$547$		−	38.1421i		−	1.63084i	0.578870	−	0.815420i	$-0.303494\pi$
$548$			10.4853i			0.447909i
$549$	4.82843			0.206072
$550$	−19.3137	+	14.4853i	−0.823539	+	0.617654i
$551$		0			0
$552$		−	8.48528i		−	0.361158i
$553$			54.6274i			2.32299i
$554$	−24.1421			−1.02570
$555$	12.9706	+	6.48528i	0.550570	+	0.275285i
$556$	14.1421			0.599760
$557$			5.31371i			0.225149i	0.993643	+	0.112575i	$0.0359097\pi$
$557$			5.31371i			0.225149i	−0.993643	+	0.112575i	$0.964090\pi$
$558$		−	1.00000i		−	0.0423334i
$559$	1.37258			0.0580541
$560$	−4.82843	+	9.65685i	−0.204038	+	0.408077i
$561$	−23.3137			−0.984306
$562$			1.31371i			0.0554154i
$563$		−	28.9706i		−	1.22096i	−0.792030	−	0.610482i	$-0.790976\pi$
$563$		−	28.9706i		−	1.22096i	0.792030	−	0.610482i	$-0.209024\pi$
$564$	−5.65685			−0.238197
$565$	−14.0000	+	28.0000i	−0.588984	+	1.17797i
$566$	9.17157			0.385510
$567$			4.82843i			0.202775i
$568$		−	2.82843i		−	0.118678i
$569$	24.8284			1.04086			0.520431	−	0.853904i	$-0.325771\pi$
$569$	24.8284			1.04086			0.520431	+	0.853904i	$0.325771\pi$
$570$		0			0
$571$	−38.8284			−1.62492			−0.812460	−	0.583018i	$-0.801872\pi$
$571$	−38.8284			−1.62492			−0.812460	+	0.583018i	$0.801872\pi$
$572$			4.00000i			0.167248i
$573$			16.4853i			0.688683i
$574$	17.6569			0.736983
$575$	33.9411	−	25.4558i	1.41544	−	1.06158i
$576$	1.00000			0.0416667
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$		−	6.31371i		−	0.262616i
$579$	7.31371			0.303947
$580$	−3.31371	−	1.65685i	−0.137594	−	0.0687971i
$581$	−46.6274			−1.93443
$582$			11.3137i			0.468968i
$583$			56.2843i			2.33106i
$584$	−2.34315			−0.0969601
$585$	−0.828427	+	1.65685i	−0.0342512	+	0.0685025i
$586$	2.00000			0.0826192
$587$		−	15.3137i		−	0.632064i	−0.948748	−	0.316032i	$-0.897649\pi$
$587$		−	15.3137i		−	0.632064i	0.948748	−	0.316032i	$-0.102351\pi$
$588$			16.3137i			0.672766i
$589$		0			0
$590$	8.82843	−	17.6569i	0.363461	−	0.726921i
$591$	6.97056			0.286731
$592$		−	6.48528i		−	0.266543i
$593$			6.97056i			0.286247i	0.989705	+	0.143123i	$0.0457146\pi$
$593$			6.97056i			0.286247i	−0.989705	+	0.143123i	$0.954285\pi$
$594$	4.82843			0.198113
$595$	−46.6274	−	23.3137i	−1.91154	−	0.955769i
$596$	−23.3137			−0.954967
$597$		−	2.34315i		−	0.0958986i
$598$		−	7.02944i		−	0.287455i
$599$	29.4558			1.20353			0.601767	−	0.798672i	$-0.294464\pi$
$599$	29.4558			1.20353			0.601767	+	0.798672i	$0.294464\pi$
$600$	3.00000	+	4.00000i	0.122474	+	0.163299i
$601$	18.0000			0.734235			0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000			0.734235			0.367118	+	0.930175i	$0.380345\pi$
$602$		−	8.00000i		−	0.326056i
$603$			14.8284i			0.603860i
$604$	−10.3431			−0.420857
$605$	24.6274	+	12.3137i	1.00125	+	0.500623i
$606$	11.3137			0.459588
$607$		−	29.7990i		−	1.20950i	−0.796414	−	0.604752i	$-0.793272\pi$
$607$		−	29.7990i		−	1.20950i	0.796414	−	0.604752i	$-0.206728\pi$
$608$		0			0
$609$	−8.00000			−0.324176
$610$	4.82843	−	9.65685i	0.195497	−	0.390995i
$611$	−4.68629			−0.189587
$612$			4.82843i			0.195178i
$613$			13.1127i			0.529617i	0.964301	+	0.264808i	$0.0853087\pi$
$613$			13.1127i			0.529617i	−0.964301	+	0.264808i	$0.914691\pi$
$614$	16.4853			0.665292
$615$	3.65685	−	7.31371i	0.147459	−	0.294917i
$616$	23.3137			0.939336
$617$			37.5980i			1.51364i	0.653625	+	0.756819i	$0.273248\pi$
$617$			37.5980i			1.51364i	−0.653625	+	0.756819i	$0.726752\pi$
$618$			18.4853i			0.743587i
$619$	32.4853			1.30569			0.652847	−	0.757490i	$-0.273575\pi$
$619$	32.4853			1.30569			0.652847	+	0.757490i	$0.273575\pi$
$620$	−2.00000	−	1.00000i	−0.0803219	−	0.0401610i
$621$	−8.48528			−0.340503
$622$			0.485281i			0.0194580i
$623$			4.00000i			0.160257i
$624$	0.828427			0.0331636
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	32.9706			1.31777
$627$		0			0
$628$		−	5.31371i		−	0.212040i
$629$	31.3137			1.24856
$630$	9.65685	+	4.82843i	0.384738	+	0.192369i
$631$	−30.6274			−1.21926			−0.609629	−	0.792687i	$-0.708682\pi$
$631$	−30.6274			−1.21926			−0.609629	+	0.792687i	$0.708682\pi$
$632$		−	11.3137i		−	0.450035i
$633$			0.686292i			0.0272776i
$634$	−9.31371			−0.369895
$635$	−12.1421	+	24.2843i	−0.481846	+	0.963692i
$636$	11.6569			0.462224
$637$			13.5147i			0.535473i
$638$			8.00000i			0.316723i
$639$	−2.82843			−0.111891
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	31.4558			1.24243			0.621216	−	0.783640i	$-0.286639\pi$
$641$	31.4558			1.24243			0.621216	+	0.783640i	$0.286639\pi$
$642$			4.00000i			0.157867i
$643$		−	8.00000i		−	0.315489i	−0.987480	−	0.157745i	$-0.949578\pi$
$643$		−	8.00000i		−	0.315489i	0.987480	−	0.157745i	$-0.0504223\pi$
$644$	−40.9706			−1.61447
$645$	−3.31371	−	1.65685i	−0.130477	−	0.0652386i
$646$		0			0
$647$			10.1421i			0.398728i	0.979925	+	0.199364i	$0.0638877\pi$
$647$			10.1421i			0.398728i	−0.979925	+	0.199364i	$0.936112\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−42.6274			−1.67327
$650$	2.48528	+	3.31371i	0.0974808	+	0.129974i
$651$	−4.82843			−0.189241
$652$			9.17157i			0.359187i
$653$		−	14.0000i		−	0.547862i	−0.961749	−	0.273931i	$-0.911676\pi$
$653$		−	14.0000i		−	0.547862i	0.961749	−	0.273931i	$-0.0883240\pi$
$654$	−0.343146			−0.0134181
$655$	3.02944	+	1.51472i	0.118370	+	0.0591850i
$656$	−3.65685			−0.142776
$657$			2.34315i			0.0914148i
$658$			27.3137i			1.06480i
$659$	16.8284			0.655542			0.327771	−	0.944757i	$-0.393702\pi$
$659$	16.8284			0.655542			0.327771	+	0.944757i	$0.393702\pi$
$660$	4.82843	−	9.65685i	0.187946	−	0.375893i
$661$	−20.6274			−0.802314			−0.401157	−	0.916009i	$-0.631392\pi$
$661$	−20.6274			−0.802314			−0.401157	+	0.916009i	$0.631392\pi$
$662$		−	4.48528i		−	0.174325i
$663$			4.00000i			0.155347i
$664$	9.65685			0.374759
$665$		0			0
$666$	−6.48528			−0.251300
$667$		−	14.0589i		−	0.544362i
$668$			16.4853i			0.637835i
$669$	−21.7990			−0.842798
$670$	29.6569	+	14.8284i	1.14574	+	0.572872i
$671$	−23.3137			−0.900016
$672$		−	4.82843i		−	0.186261i
$673$			40.9706i			1.57930i	0.613558	+	0.789650i	$0.289738\pi$
$673$			40.9706i			1.57930i	−0.613558	+	0.789650i	$0.710262\pi$
$674$	5.65685			0.217894
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	−12.3137			−0.473604
$677$			38.0000i			1.46046i	0.683202	+	0.730229i	$0.260587\pi$
$677$			38.0000i			1.46046i	−0.683202	+	0.730229i	$0.739413\pi$
$678$		−	14.0000i		−	0.537667i
$679$	54.6274			2.09641
$680$	9.65685	+	4.82843i	0.370323	+	0.185162i
$681$	6.34315			0.243070
$682$			4.82843i			0.184890i
$683$		−	32.2843i		−	1.23532i	−0.786444	−	0.617662i	$-0.788080\pi$
$683$		−	32.2843i		−	1.23532i	0.786444	−	0.617662i	$-0.211920\pi$
$684$		0			0
$685$	10.4853	−	20.9706i	0.400622	−	0.801244i
$686$	44.9706			1.71698
$687$		−	1.51472i		−	0.0577901i
$688$			1.65685i			0.0631670i
$689$	9.65685			0.367897
$690$	−8.48528	+	16.9706i	−0.323029	+	0.646058i
$691$	12.2843			0.467316			0.233658	−	0.972319i	$-0.424930\pi$
$691$	12.2843			0.467316			0.233658	+	0.972319i	$0.424930\pi$
$692$		−	21.3137i		−	0.810226i
$693$		−	23.3137i		−	0.885615i
$694$	6.34315			0.240783
$695$	−28.2843	−	14.1421i	−1.07288	−	0.536442i
$696$	1.65685			0.0628029
$697$		−	17.6569i		−	0.668801i
$698$			2.68629i			0.101678i
$699$	−26.9706			−1.02012
$700$	19.3137	−	14.4853i	0.729990	−	0.547492i
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$		−	0.828427i		−	0.0312670i
$703$		0			0
$704$	−4.82843			−0.181978
$705$	11.3137	+	5.65685i	0.426099	+	0.213049i
$706$	28.8284			1.08497
$707$		−	54.6274i		−	2.05448i
$708$			8.82843i			0.331793i
$709$	35.1716			1.32090			0.660448	−	0.750872i	$-0.270366\pi$
$709$	35.1716			1.32090			0.660448	+	0.750872i	$0.270366\pi$
$710$	−2.82843	+	5.65685i	−0.106149	+	0.212298i
$711$	−11.3137			−0.424297
$712$		−	0.828427i		−	0.0310466i
$713$		−	8.48528i		−	0.317776i
$714$	23.3137			0.872494
$715$	4.00000	−	8.00000i	0.149592	−	0.299183i
$716$	−16.8284			−0.628908
$717$		−	23.3137i		−	0.870666i
$718$			18.1421i			0.677058i
$719$	12.6863			0.473119			0.236559	−	0.971617i	$-0.423980\pi$
$719$	12.6863			0.473119			0.236559	+	0.971617i	$0.423980\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	89.2548			3.32402
$722$		−	19.0000i		−	0.707107i
$723$			22.0000i			0.818189i
$724$	−19.1716			−0.712506
$725$	4.97056	+	6.62742i	0.184602	+	0.246136i
$726$	−12.3137			−0.457005
$727$			46.4853i			1.72404i	0.506871	+	0.862022i	$0.330802\pi$
$727$			46.4853i			1.72404i	−0.506871	+	0.862022i	$0.669198\pi$
$728$		−	4.00000i		−	0.148250i
$729$	−1.00000			−0.0370370
$730$	4.68629	+	2.34315i	0.173447	+	0.0867237i
$731$	−8.00000			−0.295891
$732$			4.82843i			0.178464i
$733$		−	27.6569i		−	1.02153i	−0.859721	−	0.510765i	$-0.829362\pi$
$733$		−	27.6569i		−	1.02153i	0.859721	−	0.510765i	$-0.170638\pi$
$734$	0.142136			0.00524632
$735$	16.3137	−	32.6274i	0.601740	−	1.20348i
$736$	8.48528			0.312772
$737$		−	71.5980i		−	2.63735i
$738$			3.65685i			0.134611i
$739$	20.4853			0.753563			0.376782	−	0.926302i	$-0.377031\pi$
$739$	20.4853			0.753563			0.376782	+	0.926302i	$0.377031\pi$
$740$	−6.48528	+	12.9706i	−0.238404	+	0.476807i
$741$		0			0
$742$		−	56.2843i		−	2.06626i
$743$			29.4558i			1.08063i	0.841463	+	0.540315i	$0.181695\pi$
$743$			29.4558i			1.08063i	−0.841463	+	0.540315i	$0.818305\pi$
$744$	1.00000			0.0366618
$745$	46.6274	+	23.3137i	1.70830	+	0.854148i
$746$	−11.6569			−0.426788
$747$		−	9.65685i		−	0.353326i
$748$		−	23.3137i		−	0.852434i
$749$	19.3137			0.705708
$750$	−2.00000	−	11.0000i	−0.0730297	−	0.401663i
$751$	52.2843			1.90788			0.953940	−	0.299997i	$-0.0969858\pi$
$751$	52.2843			1.90788			0.953940	+	0.299997i	$0.0969858\pi$
$752$		−	5.65685i		−	0.206284i
$753$			8.82843i			0.321726i
$754$	1.37258			0.0499865
$755$	20.6863	+	10.3431i	0.752851	+	0.376426i
$756$	−4.82843			−0.175608
$757$			26.4853i			0.962624i	0.876549	+	0.481312i	$0.159840\pi$
$757$			26.4853i			0.962624i	−0.876549	+	0.481312i	$0.840160\pi$
$758$		−	1.65685i		−	0.0601797i
$759$	40.9706			1.48714
$760$		0			0
$761$	−29.1127			−1.05533			−0.527667	−	0.849451i	$-0.676933\pi$
$761$	−29.1127			−1.05533			−0.527667	+	0.849451i	$0.676933\pi$
$762$		−	12.1421i		−	0.439863i
$763$			1.65685i			0.0599822i
$764$	−16.4853			−0.596417
$765$	4.82843	−	9.65685i	0.174572	−	0.349144i
$766$	−28.4853			−1.02922
$767$			7.31371i			0.264083i
$768$			1.00000i			0.0360844i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$	−46.6274	−	23.3137i	−1.68034	−	0.840168i
$771$	−4.34315			−0.156415
$772$			7.31371i			0.263226i
$773$		−	11.6569i		−	0.419268i	−0.977780	−	0.209634i	$-0.932773\pi$
$773$		−	11.6569i		−	0.419268i	0.977780	−	0.209634i	$-0.0672272\pi$
$774$	1.65685			0.0595544
$775$	3.00000	+	4.00000i	0.107763	+	0.143684i
$776$	−11.3137			−0.406138
$777$			31.3137i			1.12337i
$778$		−	35.3137i		−	1.26606i
$779$		0			0
$780$	−1.65685	−	0.828427i	−0.0593249	−	0.0296624i
$781$	13.6569			0.488681
$782$			40.9706i			1.46510i
$783$		−	1.65685i		−	0.0592111i
$784$	−16.3137			−0.582632
$785$	−5.31371	+	10.6274i	−0.189654	+	0.379309i
$786$	−1.51472			−0.0540282
$787$		−	8.97056i		−	0.319766i	−0.987136	−	0.159883i	$-0.948888\pi$
$787$		−	8.97056i		−	0.319766i	0.987136	−	0.159883i	$-0.0511117\pi$
$788$			6.97056i			0.248316i
$789$	−7.51472			−0.267531
$790$	−11.3137	+	22.6274i	−0.402524	+	0.805047i
$791$	−67.5980			−2.40351
$792$			4.82843i			0.171571i
$793$			4.00000i			0.142044i
$794$	4.34315			0.154132
$795$	−23.3137	−	11.6569i	−0.826852	−	0.413426i
$796$	2.34315			0.0830506
$797$		−	21.3137i		−	0.754970i	−0.926016	−	0.377485i	$-0.876789\pi$
$797$		−	21.3137i		−	0.754970i	0.926016	−	0.377485i	$-0.123211\pi$
$798$		0			0
$799$	27.3137			0.966290
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	−0.828427			−0.0292710
$802$		−	14.4853i		−	0.511493i
$803$		−	11.3137i		−	0.399252i
$804$	−14.8284			−0.522958
$805$	81.9411	+	40.9706i	2.88805	+	1.44402i
$806$	0.828427			0.0291801
$807$		−	28.9706i		−	1.01981i
$808$			11.3137i			0.398015i
$809$	1.51472			0.0532547			0.0266273	−	0.999645i	$-0.491523\pi$
$809$	1.51472			0.0532547			0.0266273	+	0.999645i	$0.491523\pi$
$810$	−1.00000	+	2.00000i	−0.0351364	+	0.0702728i
$811$	12.9706			0.455458			0.227729	−	0.973725i	$-0.426870\pi$
$811$	12.9706			0.455458			0.227729	+	0.973725i	$0.426870\pi$
$812$		−	8.00000i		−	0.280745i
$813$		−	2.34315i		−	0.0821777i
$814$	31.3137			1.09754
$815$	9.17157	−	18.3431i	0.321266	−	0.642532i
$816$	−4.82843			−0.169029
$817$		0			0
$818$		−	10.6863i		−	0.373637i
$819$	−4.00000			−0.139771
$820$	7.31371	+	3.65685i	0.255406	+	0.127703i
$821$	14.3431			0.500579			0.250290	−	0.968171i	$-0.419474\pi$
$821$	14.3431			0.500579			0.250290	+	0.968171i	$0.419474\pi$
$822$			10.4853i			0.365716i
$823$		−	36.8284i		−	1.28376i	−0.766806	−	0.641879i	$-0.778155\pi$
$823$		−	36.8284i		−	1.28376i	0.766806	−	0.641879i	$-0.221845\pi$
$824$	−18.4853			−0.643965
$825$	−19.3137	+	14.4853i	−0.672417	+	0.504313i
$826$	42.6274			1.48320
$827$			16.6863i			0.580239i	0.956990	+	0.290120i	$0.0936951\pi$
$827$			16.6863i			0.580239i	−0.956990	+	0.290120i	$0.906305\pi$
$828$		−	8.48528i		−	0.294884i
$829$	−24.8284			−0.862327			−0.431163	−	0.902274i	$-0.641897\pi$
$829$	−24.8284			−0.862327			−0.431163	+	0.902274i	$0.641897\pi$
$830$	−19.3137	−	9.65685i	−0.670389	−	0.335194i
$831$	−24.1421			−0.837481
$832$			0.828427i			0.0287205i
$833$		−	78.7696i		−	2.72920i
$834$	14.1421			0.489702
$835$	16.4853	−	32.9706i	0.570497	−	1.14099i
$836$		0			0
$837$		−	1.00000i		−	0.0345651i
$838$		−	29.7990i		−	1.02939i
$839$	32.7696			1.13133			0.565665	−	0.824635i	$-0.308619\pi$
$839$	32.7696			1.13133			0.565665	+	0.824635i	$0.308619\pi$
$840$	−4.82843	+	9.65685i	−0.166597	+	0.333193i
$841$	−26.2548			−0.905339
$842$			14.0000i			0.482472i
$843$			1.31371i			0.0452465i
$844$	−0.686292			−0.0236231
$845$	24.6274	+	12.3137i	0.847209	+	0.423604i
$846$	−5.65685			−0.194487
$847$			59.4558i			2.04293i
$848$			11.6569i			0.400298i
$849$	9.17157			0.314768
$850$	−14.4853	−	19.3137i	−0.496841	−	0.662455i
$851$	−55.0294			−1.88638
$852$		−	2.82843i		−	0.0969003i
$853$		−	1.31371i		−	0.0449805i	−0.999747	−	0.0224903i	$-0.992841\pi$
$853$		−	1.31371i		−	0.0449805i	0.999747	−	0.0224903i	$-0.00715948\pi$
$854$	23.3137			0.797779
$855$		0			0
$856$	−4.00000			−0.136717
$857$		−	29.3137i		−	1.00134i	−0.865639	−	0.500669i	$-0.833088\pi$
$857$		−	29.3137i		−	1.00134i	0.865639	−	0.500669i	$-0.166912\pi$
$858$			4.00000i			0.136558i
$859$	−42.4264			−1.44757			−0.723785	−	0.690025i	$-0.757599\pi$
$859$	−42.4264			−1.44757			−0.723785	+	0.690025i	$0.757599\pi$
$860$	1.65685	−	3.31371i	0.0564983	−	0.112997i
$861$	17.6569			0.601744
$862$		−	6.82843i		−	0.232577i
$863$			35.7990i			1.21861i	0.792935	+	0.609306i	$0.208552\pi$
$863$			35.7990i			1.21861i	−0.792935	+	0.609306i	$0.791448\pi$
$864$	1.00000			0.0340207
$865$	−21.3137	+	42.6274i	−0.724688	+	1.44938i
$866$	2.34315			0.0796233
$867$		−	6.31371i		−	0.214425i
$868$		−	4.82843i		−	0.163887i
$869$	54.6274			1.85311
$870$	−3.31371	−	1.65685i	−0.112345	−	0.0561726i
$871$	−12.2843			−0.416237
$872$		−	0.343146i		−	0.0116204i
$873$			11.3137i			0.382911i
$874$		0			0
$875$	−53.1127	+	9.65685i	−1.79554	+	0.326461i
$876$	−2.34315			−0.0791676
$877$			12.3431i			0.416798i	0.978044	+	0.208399i	$0.0668253\pi$
$877$			12.3431i			0.416798i	−0.978044	+	0.208399i	$0.933175\pi$
$878$		−	32.9706i		−	1.11270i
$879$	2.00000			0.0674583
$880$	9.65685	+	4.82843i	0.325532	+	0.162766i
$881$	−7.85786			−0.264738			−0.132369	−	0.991200i	$-0.542258\pi$
$881$	−7.85786			−0.264738			−0.132369	+	0.991200i	$0.542258\pi$
$882$			16.3137i			0.549311i
$883$		−	32.9706i		−	1.10955i	−0.832001	−	0.554774i	$-0.812805\pi$
$883$		−	32.9706i		−	1.10955i	0.832001	−	0.554774i	$-0.187195\pi$
$884$	−4.00000			−0.134535
$885$	8.82843	−	17.6569i	0.296764	−	0.593529i
$886$	−17.6569			−0.593194
$887$			20.0000i			0.671534i	0.941945	+	0.335767i	$0.108996\pi$
$887$			20.0000i			0.671534i	−0.941945	+	0.335767i	$0.891004\pi$
$888$		−	6.48528i		−	0.217632i
$889$	−58.6274			−1.96630
$890$	−0.828427	+	1.65685i	−0.0277689	+	0.0555379i
$891$	4.82843			0.161758
$892$		−	21.7990i		−	0.729884i
$893$		0			0
$894$	−23.3137			−0.779727
$895$	33.6569	+	16.8284i	1.12502	+	0.562512i
$896$	4.82843			0.161306
$897$		−	7.02944i		−	0.234706i
$898$		−	16.1421i		−	0.538670i
$899$	1.65685			0.0552592
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	−56.2843			−1.87510
$902$		−	17.6569i		−	0.587909i
$903$		−	8.00000i		−	0.266223i
$904$	14.0000			0.465633
$905$	38.3431	+	19.1716i	1.27457	+	0.637285i
$906$	−10.3431			−0.343628
$907$		−	9.85786i		−	0.327325i	−0.986516	−	0.163663i	$-0.947669\pi$
$907$		−	9.85786i		−	0.327325i	0.986516	−	0.163663i	$-0.0523308\pi$
$908$			6.34315i			0.210505i
$909$	11.3137			0.375252
$910$	−4.00000	+	8.00000i	−0.132599	+	0.265197i
$911$	17.9411			0.594416			0.297208	−	0.954813i	$-0.403945\pi$
$911$	17.9411			0.594416			0.297208	+	0.954813i	$0.403945\pi$
$912$		0			0
$913$			46.6274i			1.54314i
$914$	−8.68629			−0.287317
$915$	4.82843	−	9.65685i	0.159623	−	0.319246i
$916$	1.51472			0.0500477
$917$			7.31371i			0.241520i
$918$			4.82843i			0.159362i
$919$	−16.9706			−0.559807			−0.279904	−	0.960028i	$-0.590303\pi$
$919$	−16.9706			−0.559807			−0.279904	+	0.960028i	$0.590303\pi$
$920$	−16.9706	−	8.48528i	−0.559503	−	0.279751i
$921$	16.4853			0.543208
$922$			3.31371i			0.109131i
$923$		−	2.34315i		−	0.0771256i
$924$	23.3137			0.766965
$925$	25.9411	−	19.4558i	0.852939	−	0.639704i
$926$	−8.82843			−0.290120
$927$			18.4853i			0.607136i
$928$			1.65685i			0.0543889i
$929$	7.85786			0.257808			0.128904	−	0.991657i	$-0.458854\pi$
$929$	7.85786			0.257808			0.128904	+	0.991657i	$0.458854\pi$
$930$	−2.00000	−	1.00000i	−0.0655826	−	0.0327913i
$931$		0			0
$932$		−	26.9706i		−	0.883450i
$933$			0.485281i			0.0158874i
$934$	36.0000			1.17796
$935$	−23.3137	+	46.6274i	−0.762440	+	1.52488i
$936$	0.828427			0.0270780
$937$		−	22.6274i		−	0.739205i	−0.929190	−	0.369603i	$-0.879494\pi$
$937$		−	22.6274i		−	0.739205i	0.929190	−	0.369603i	$-0.120506\pi$
$938$			71.5980i			2.33776i
$939$	32.9706			1.07595
$940$	−5.65685	+	11.3137i	−0.184506	+	0.369012i
$941$	−40.0000			−1.30396			−0.651981	−	0.758235i	$-0.726062\pi$
$941$	−40.0000			−1.30396			−0.651981	+	0.758235i	$0.726062\pi$
$942$		−	5.31371i		−	0.173130i
$943$			31.0294i			1.01046i
$944$	−8.82843			−0.287341
$945$	9.65685	+	4.82843i	0.314137	+	0.157069i
$946$	−8.00000			−0.260102
$947$			46.9117i			1.52443i	0.647327	+	0.762213i	$0.275887\pi$
$947$			46.9117i			1.52443i	−0.647327	+	0.762213i	$0.724113\pi$
$948$		−	11.3137i		−	0.367452i
$949$	−1.94113			−0.0630116
$950$		0			0
$951$	−9.31371			−0.302018
$952$			23.3137i			0.755602i
$953$		−	33.7990i		−	1.09486i	−0.836853	−	0.547428i	$-0.815607\pi$
$953$		−	33.7990i		−	1.09486i	0.836853	−	0.547428i	$-0.184393\pi$
$954$	11.6569			0.377405
$955$	32.9706	+	16.4853i	1.06690	+	0.533451i
$956$	23.3137			0.754019
$957$			8.00000i			0.258603i
$958$		−	26.8284i		−	0.866787i
$959$	50.6274			1.63484
$960$	1.00000	−	2.00000i	0.0322749	−	0.0645497i
$961$	1.00000			0.0322581
$962$		−	5.37258i		−	0.173219i
$963$			4.00000i			0.128898i
$964$	−22.0000			−0.708572
$965$	7.31371	−	14.6274i	0.235437	−	0.470873i
$966$	−40.9706			−1.31821
$967$		−	12.8284i		−	0.412534i	−0.978496	−	0.206267i	$-0.933868\pi$
$967$		−	12.8284i		−	0.412534i	0.978496	−	0.206267i	$-0.0661316\pi$
$968$		−	12.3137i		−	0.395778i
$969$		0			0
$970$	22.6274	+	11.3137i	0.726523	+	0.363261i
$971$	43.4558			1.39456			0.697282	−	0.716797i	$-0.254392\pi$
$971$	43.4558			1.39456			0.697282	+	0.716797i	$0.254392\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	68.2843i		−	2.18909i
$974$	−8.14214			−0.260891
$975$	2.48528	+	3.31371i	0.0795927	+	0.106124i
$976$	−4.82843			−0.154554
$977$			16.3431i			0.522864i	0.965222	+	0.261432i	$0.0841946\pi$
$977$			16.3431i			0.522864i	−0.965222	+	0.261432i	$0.915805\pi$
$978$			9.17157i			0.293275i
$979$	4.00000			0.127841
$980$	32.6274	+	16.3137i	1.04224	+	0.521122i
$981$	−0.343146			−0.0109558
$982$			7.45584i			0.237926i
$983$			19.5147i			0.622423i	0.950341	+	0.311211i	$0.100735\pi$
$983$			19.5147i			0.622423i	−0.950341	+	0.311211i	$0.899265\pi$
$984$	−3.65685			−0.116576
$985$	6.97056	−	13.9411i	0.222101	−	0.444201i
$986$	−8.00000			−0.254772
$987$			27.3137i			0.869405i
$988$		0			0
$989$	14.0589			0.447046
$990$	4.82843	−	9.65685i	0.153457	−	0.306915i
$991$	33.9411			1.07818			0.539088	−	0.842250i	$-0.318769\pi$
$991$	33.9411			1.07818			0.539088	+	0.842250i	$0.318769\pi$
$992$			1.00000i			0.0317500i
$993$		−	4.48528i		−	0.142336i
$994$	−13.6569			−0.433169
$995$	−4.68629	−	2.34315i	−0.148565	−	0.0742827i
$996$	9.65685			0.305989
$997$			46.2843i			1.46584i	0.680316	+	0.732919i	$0.261842\pi$
$997$			46.2843i			1.46584i	−0.680316	+	0.732919i	$0.738158\pi$
$998$			10.1421i			0.321044i
$999$	−6.48528			−0.205185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.g.559.4	yes	4
3.2	odd	2		2790.2.d.i.559.2		4
5.2	odd	4		4650.2.a.cc.1.1		2
5.3	odd	4		4650.2.a.cf.1.2		2
5.4	even	2	inner	930.2.d.g.559.1	✓	4
15.14	odd	2		2790.2.d.i.559.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.g.559.1	✓	4	5.4	even	2	inner
930.2.d.g.559.4	yes	4	1.1	even	1	trivial
2790.2.d.i.559.2		4	3.2	odd	2
2790.2.d.i.559.3		4	15.14	odd	2
4650.2.a.cc.1.1		2	5.2	odd	4
4650.2.a.cf.1.2		2	5.3	odd	4

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} +4.82843i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} +4.82843i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +4.82843 q^{11} -1.00000i q^{12} -0.828427i q^{13} -4.82843 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +4.82843i q^{17} -1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} -4.82843 q^{21} +4.82843i q^{22} -8.48528i q^{23} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +0.828427 q^{26} -1.00000i q^{27} -4.82843i q^{28} +1.65685 q^{29} +(-2.00000 - 1.00000i) q^{30} +1.00000 q^{31} +1.00000i q^{32} +4.82843i q^{33} -4.82843 q^{34} +(-4.82843 + 9.65685i) q^{35} +1.00000 q^{36} -6.48528i q^{37} +0.828427 q^{39} +(1.00000 - 2.00000i) q^{40} -3.65685 q^{41} -4.82843i q^{42} +1.65685i q^{43} -4.82843 q^{44} +(-2.00000 - 1.00000i) q^{45} +8.48528 q^{46} -5.65685i q^{47} +1.00000i q^{48} -16.3137 q^{49} +(-4.00000 + 3.00000i) q^{50} -4.82843 q^{51} +0.828427i q^{52} +11.6569i q^{53} +1.00000 q^{54} +(9.65685 + 4.82843i) q^{55} +4.82843 q^{56} +1.65685i q^{58} -8.82843 q^{59} +(1.00000 - 2.00000i) q^{60} -4.82843 q^{61} +1.00000i q^{62} -4.82843i q^{63} -1.00000 q^{64} +(0.828427 - 1.65685i) q^{65} -4.82843 q^{66} -14.8284i q^{67} -4.82843i q^{68} +8.48528 q^{69} +(-9.65685 - 4.82843i) q^{70} +2.82843 q^{71} +1.00000i q^{72} -2.34315i q^{73} +6.48528 q^{74} +(-4.00000 + 3.00000i) q^{75} +23.3137i q^{77} +0.828427i q^{78} +11.3137 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -3.65685i q^{82} +9.65685i q^{83} +4.82843 q^{84} +(-4.82843 + 9.65685i) q^{85} -1.65685 q^{86} +1.65685i q^{87} -4.82843i q^{88} +0.828427 q^{89} +(1.00000 - 2.00000i) q^{90} +4.00000 q^{91} +8.48528i q^{92} +1.00000i q^{93} +5.65685 q^{94} -1.00000 q^{96} -11.3137i q^{97} -16.3137i q^{98} -4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{20} - 8 q^{21} + 4 q^{24} + 12 q^{25} - 8 q^{26} - 16 q^{29} - 8 q^{30} + 4 q^{31} - 8 q^{34} - 8 q^{35} + 4 q^{36} - 8 q^{39} + 4 q^{40} + 8 q^{41} - 8 q^{44} - 8 q^{45} - 20 q^{49} - 16 q^{50} - 8 q^{51} + 4 q^{54} + 16 q^{55} + 8 q^{56} - 24 q^{59} + 4 q^{60} - 8 q^{61} - 4 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{70} - 8 q^{74} - 16 q^{75} + 8 q^{80} + 4 q^{81} + 8 q^{84} - 8 q^{85} + 16 q^{86} - 8 q^{89} + 4 q^{90} + 16 q^{91} - 4 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^9 - 4 * q^10 + 8 * q^11 - 8 * q^14 - 4 * q^15 + 4 * q^16 - 8 * q^20 - 8 * q^21 + 4 * q^24 + 12 * q^25 - 8 * q^26 - 16 * q^29 - 8 * q^30 + 4 * q^31 - 8 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^39 + 4 * q^40 + 8 * q^41 - 8 * q^44 - 8 * q^45 - 20 * q^49 - 16 * q^50 - 8 * q^51 + 4 * q^54 + 16 * q^55 + 8 * q^56 - 24 * q^59 + 4 * q^60 - 8 * q^61 - 4 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^70 - 8 * q^74 - 16 * q^75 + 8 * q^80 + 4 * q^81 + 8 * q^84 - 8 * q^85 + 16 * q^86 - 8 * q^89 + 4 * q^90 + 16 * q^91 - 4 * q^96 - 8 * q^99

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