LMFDB - Embedded newform 930.2.d.f.559.1

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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.f.559.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} -1.00000i q^{12} +2.00000i q^{13} +2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +6.00000i q^{17} +1.00000i q^{18} +8.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -2.00000 q^{21} +2.00000i q^{22} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} -2.00000i q^{28} -4.00000 q^{29} +(2.00000 - 1.00000i) q^{30} +1.00000 q^{31} -1.00000i q^{32} -2.00000i q^{33} +6.00000 q^{34} +(2.00000 + 4.00000i) q^{35} +1.00000 q^{36} +10.0000i q^{37} -8.00000i q^{38} -2.00000 q^{39} +(1.00000 + 2.00000i) q^{40} -6.00000 q^{41} +2.00000i q^{42} +4.00000i q^{43} +2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +1.00000i q^{48} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -6.00000 q^{51} -2.00000i q^{52} +2.00000i q^{53} -1.00000 q^{54} +(-4.00000 + 2.00000i) q^{55} -2.00000 q^{56} +8.00000i q^{57} +4.00000i q^{58} +14.0000 q^{59} +(-1.00000 - 2.00000i) q^{60} -2.00000 q^{61} -1.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(2.00000 + 4.00000i) q^{65} -2.00000 q^{66} -8.00000i q^{67} -6.00000i q^{68} +(4.00000 - 2.00000i) q^{70} +12.0000 q^{71} -1.00000i q^{72} +10.0000 q^{74} +(4.00000 + 3.00000i) q^{75} -8.00000 q^{76} -4.00000i q^{77} +2.00000i q^{78} +16.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +6.00000i q^{82} -12.0000i q^{83} +2.00000 q^{84} +(6.00000 + 12.0000i) q^{85} +4.00000 q^{86} -4.00000i q^{87} -2.00000i q^{88} -6.00000 q^{89} +(1.00000 + 2.00000i) q^{90} -4.00000 q^{91} +1.00000i q^{93} +(16.0000 - 8.00000i) q^{95} +1.00000 q^{96} -3.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 16 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{24} + 6 q^{25} + 4 q^{26} - 8 q^{29} + 4 q^{30} + 2 q^{31} + 12 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{39} + 2 q^{40} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 6 q^{49} - 8 q^{50} - 12 q^{51} - 2 q^{54} - 8 q^{55} - 4 q^{56} + 28 q^{59} - 2 q^{60} - 4 q^{61} - 2 q^{64} + 4 q^{65} - 4 q^{66} + 8 q^{70} + 24 q^{71} + 20 q^{74} + 8 q^{75} - 16 q^{76} + 32 q^{79} + 4 q^{80} + 2 q^{81} + 4 q^{84} + 12 q^{85} + 8 q^{86} - 12 q^{89} + 2 q^{90} - 8 q^{91} + 32 q^{95} + 2 q^{96} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9 - 2 * q^10 - 4 * q^11 + 4 * q^14 + 2 * q^15 + 2 * q^16 + 16 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 8 * q^29 + 4 * q^30 + 2 * q^31 + 12 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^39 + 2 * q^40 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 6 * q^49 - 8 * q^50 - 12 * q^51 - 2 * q^54 - 8 * q^55 - 4 * q^56 + 28 * q^59 - 2 * q^60 - 4 * q^61 - 2 * q^64 + 4 * q^65 - 4 * q^66 + 8 * q^70 + 24 * q^71 + 20 * q^74 + 8 * q^75 - 16 * q^76 + 32 * q^79 + 4 * q^80 + 2 * q^81 + 4 * q^84 + 12 * q^85 + 8 * q^86 - 12 * q^89 + 2 * q^90 - 8 * q^91 + 32 * q^95 + 2 * q^96 + 4 * 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
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		−	1.00000i		−	0.288675i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	2.00000			0.534522
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$			6.00000i			1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$			6.00000i			1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$			1.00000i			0.235702i
$19$	8.00000			1.83533			0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000			1.83533			0.917663	+	0.397360i	$0.130073\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$	−2.00000			−0.436436
$22$			2.00000i			0.426401i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.00000			−0.204124
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	2.00000			0.392232
$27$		−	1.00000i		−	0.192450i
$28$		−	2.00000i		−	0.377964i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$	2.00000	−	1.00000i	0.365148	−	0.182574i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$		−	1.00000i		−	0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	6.00000			1.02899
$35$	2.00000	+	4.00000i	0.338062	+	0.676123i
$36$	1.00000			0.166667
$37$			10.0000i			1.64399i	0.569495	+	0.821995i	$0.307139\pi$
$37$			10.0000i			1.64399i	−0.569495	+	0.821995i	$0.692861\pi$
$38$		−	8.00000i		−	1.29777i
$39$	−2.00000			−0.320256
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$			2.00000i			0.308607i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	2.00000			0.301511
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$			1.00000i			0.144338i
$49$	3.00000			0.428571
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	−6.00000			−0.840168
$52$		−	2.00000i		−	0.277350i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−1.00000			−0.136083
$55$	−4.00000	+	2.00000i	−0.539360	+	0.269680i
$56$	−2.00000			−0.267261
$57$			8.00000i			1.05963i
$58$			4.00000i			0.525226i
$59$	14.0000			1.82264			0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000			1.82264			0.911322	+	0.411693i	$0.135063\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$		−	1.00000i		−	0.127000i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	2.00000	+	4.00000i	0.248069	+	0.496139i
$66$	−2.00000			−0.246183
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		−	6.00000i		−	0.727607i
$69$		0			0
$70$	4.00000	−	2.00000i	0.478091	−	0.239046i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		−	1.00000i		−	0.117851i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	10.0000			1.16248
$75$	4.00000	+	3.00000i	0.461880	+	0.346410i
$76$	−8.00000			−0.917663
$77$		−	4.00000i		−	0.455842i
$78$			2.00000i			0.226455i
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$	1.00000			0.111111
$82$			6.00000i			0.662589i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	2.00000			0.218218
$85$	6.00000	+	12.0000i	0.650791	+	1.30158i
$86$	4.00000			0.431331
$87$		−	4.00000i		−	0.428845i
$88$		−	2.00000i		−	0.213201i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	+	2.00000i	0.105409	+	0.210819i
$91$	−4.00000			−0.419314
$92$		0			0
$93$			1.00000i			0.103695i
$94$		0			0
$95$	16.0000	−	8.00000i	1.64157	−	0.820783i
$96$	1.00000			0.102062
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		−	3.00000i		−	0.303046i
$99$	2.00000			0.201008
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−16.0000			−1.59206			−0.796030	−	0.605257i	$-0.793070\pi$
$101$	−16.0000			−1.59206			−0.796030	+	0.605257i	$0.793070\pi$
$102$			6.00000i			0.594089i
$103$			14.0000i			1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$			14.0000i			1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	−2.00000			−0.196116
$105$	−4.00000	+	2.00000i	−0.390360	+	0.195180i
$106$	2.00000			0.194257
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$			1.00000i			0.0962250i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	2.00000	+	4.00000i	0.190693	+	0.381385i
$111$	−10.0000			−0.949158
$112$			2.00000i			0.188982i
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	8.00000			0.749269
$115$		0			0
$116$	4.00000			0.371391
$117$		−	2.00000i		−	0.184900i
$118$		−	14.0000i		−	1.28880i
$119$	−12.0000			−1.10004
$120$	−2.00000	+	1.00000i	−0.182574	+	0.0912871i
$121$	−7.00000			−0.636364
$122$			2.00000i			0.181071i
$123$		−	6.00000i		−	0.541002i
$124$	−1.00000			−0.0898027
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−2.00000			−0.178174
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$			1.00000i			0.0883883i
$129$	−4.00000			−0.352180
$130$	4.00000	−	2.00000i	0.350823	−	0.175412i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$			2.00000i			0.174078i
$133$			16.0000i			1.38738i
$134$	−8.00000			−0.691095
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$	−6.00000			−0.514496
$137$			10.0000i			0.854358i	0.904167	+	0.427179i	$0.140493\pi$
$137$			10.0000i			0.854358i	−0.904167	+	0.427179i	$0.859507\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$	−2.00000	−	4.00000i	−0.169031	−	0.338062i
$141$		0			0
$142$		−	12.0000i		−	1.00702i
$143$		−	4.00000i		−	0.334497i
$144$	−1.00000			−0.0833333
$145$	−8.00000	+	4.00000i	−0.664364	+	0.332182i
$146$		0			0
$147$			3.00000i			0.247436i
$148$		−	10.0000i		−	0.821995i
$149$	−4.00000			−0.327693			−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000			−0.327693			−0.163846	+	0.986486i	$0.552390\pi$
$150$	3.00000	−	4.00000i	0.244949	−	0.326599i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$			8.00000i			0.648886i
$153$		−	6.00000i		−	0.485071i
$154$	−4.00000			−0.322329
$155$	2.00000	−	1.00000i	0.160644	−	0.0803219i
$156$	2.00000			0.160128
$157$		−	10.0000i		−	0.798087i	−0.916932	−	0.399043i	$-0.869342\pi$
$157$		−	10.0000i		−	0.798087i	0.916932	−	0.399043i	$-0.130658\pi$
$158$		−	16.0000i		−	1.27289i
$159$	−2.00000			−0.158610
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$	6.00000			0.468521
$165$	−2.00000	−	4.00000i	−0.155700	−	0.311400i
$166$	−12.0000			−0.931381
$167$		−	24.0000i		−	1.85718i	−0.371113	−	0.928588i	$-0.621024\pi$
$167$		−	24.0000i		−	1.85718i	0.371113	−	0.928588i	$-0.378976\pi$
$168$		−	2.00000i		−	0.154303i
$169$	9.00000			0.692308
$170$	12.0000	−	6.00000i	0.920358	−	0.460179i
$171$	−8.00000			−0.611775
$172$		−	4.00000i		−	0.304997i
$173$		−	18.0000i		−	1.36851i	−0.729241	−	0.684257i	$-0.760127\pi$
$173$		−	18.0000i		−	1.36851i	0.729241	−	0.684257i	$-0.239873\pi$
$174$	−4.00000			−0.303239
$175$	8.00000	+	6.00000i	0.604743	+	0.453557i
$176$	−2.00000			−0.150756
$177$			14.0000i			1.05230i
$178$			6.00000i			0.449719i
$179$	−14.0000			−1.04641			−0.523205	−	0.852207i	$-0.675264\pi$
$179$	−14.0000			−1.04641			−0.523205	+	0.852207i	$0.675264\pi$
$180$	2.00000	−	1.00000i	0.149071	−	0.0745356i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$			4.00000i			0.296500i
$183$		−	2.00000i		−	0.147844i
$184$		0			0
$185$	10.0000	+	20.0000i	0.735215	+	1.47043i
$186$	1.00000			0.0733236
$187$		−	12.0000i		−	0.877527i
$188$		0			0
$189$	2.00000			0.145479
$190$	−8.00000	−	16.0000i	−0.580381	−	1.16076i
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	4.00000i		−	0.287926i	−0.989583	−	0.143963i	$-0.954015\pi$
$193$		−	4.00000i		−	0.287926i	0.989583	−	0.143963i	$-0.0459847\pi$
$194$		0			0
$195$	−4.00000	+	2.00000i	−0.286446	+	0.143223i
$196$	−3.00000			−0.214286
$197$		−	26.0000i		−	1.85242i	−0.377004	−	0.926212i	$-0.623046\pi$
$197$		−	26.0000i		−	1.85242i	0.377004	−	0.926212i	$-0.376954\pi$
$198$		−	2.00000i		−	0.142134i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$	8.00000			0.564276
$202$			16.0000i			1.12576i
$203$		−	8.00000i		−	0.561490i
$204$	6.00000			0.420084
$205$	−12.0000	+	6.00000i	−0.838116	+	0.419058i
$206$	14.0000			0.975426
$207$		0			0
$208$			2.00000i			0.138675i
$209$	−16.0000			−1.10674
$210$	2.00000	+	4.00000i	0.138013	+	0.276026i
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		−	2.00000i		−	0.137361i
$213$			12.0000i			0.822226i
$214$	4.00000			0.273434
$215$	4.00000	+	8.00000i	0.272798	+	0.545595i
$216$	1.00000			0.0680414
$217$			2.00000i			0.135769i
$218$			10.0000i			0.677285i
$219$		0			0
$220$	4.00000	−	2.00000i	0.269680	−	0.134840i
$221$	−12.0000			−0.807207
$222$			10.0000i			0.671156i
$223$		−	14.0000i		−	0.937509i	−0.883328	−	0.468755i	$-0.844703\pi$
$223$		−	14.0000i		−	0.937509i	0.883328	−	0.468755i	$-0.155297\pi$
$224$	2.00000			0.133631
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	−14.0000			−0.931266
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	8.00000i		−	0.529813i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$		−	4.00000i		−	0.262613i
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$	−2.00000			−0.130744
$235$		0			0
$236$	−14.0000			−0.911322
$237$			16.0000i			1.03931i
$238$			12.0000i			0.777844i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	1.00000	+	2.00000i	0.0645497	+	0.129099i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$			7.00000i			0.449977i
$243$			1.00000i			0.0641500i
$244$	2.00000			0.128037
$245$	6.00000	−	3.00000i	0.383326	−	0.191663i
$246$	−6.00000			−0.382546
$247$			16.0000i			1.01806i
$248$			1.00000i			0.0635001i
$249$	12.0000			0.760469
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−22.0000			−1.38863			−0.694314	−	0.719672i	$-0.744292\pi$
$251$	−22.0000			−1.38863			−0.694314	+	0.719672i	$0.744292\pi$
$252$			2.00000i			0.125988i
$253$		0			0
$254$	−2.00000			−0.125491
$255$	−12.0000	+	6.00000i	−0.751469	+	0.375735i
$256$	1.00000			0.0625000
$257$			22.0000i			1.37232i	0.727450	+	0.686161i	$0.240706\pi$
$257$			22.0000i			1.37232i	−0.727450	+	0.686161i	$0.759294\pi$
$258$			4.00000i			0.249029i
$259$	−20.0000			−1.24274
$260$	−2.00000	−	4.00000i	−0.124035	−	0.248069i
$261$	4.00000			0.247594
$262$		−	6.00000i		−	0.370681i
$263$			16.0000i			0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$			16.0000i			0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$	2.00000			0.123091
$265$	2.00000	+	4.00000i	0.122859	+	0.245718i
$266$	16.0000			0.981023
$267$		−	6.00000i		−	0.367194i
$268$			8.00000i			0.488678i
$269$	28.0000			1.70719			0.853595	−	0.520937i	$-0.174417\pi$
$269$	28.0000			1.70719			0.853595	+	0.520937i	$0.174417\pi$
$270$	−2.00000	+	1.00000i	−0.121716	+	0.0608581i
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$			6.00000i			0.363803i
$273$		−	4.00000i		−	0.242091i
$274$	10.0000			0.604122
$275$	−6.00000	+	8.00000i	−0.361814	+	0.482418i
$276$		0			0
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			16.0000i			0.959616i
$279$	−1.00000			−0.0598684
$280$	−4.00000	+	2.00000i	−0.239046	+	0.119523i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$		−	16.0000i		−	0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$		−	16.0000i		−	0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	−12.0000			−0.712069
$285$	8.00000	+	16.0000i	0.473879	+	0.947758i
$286$	−4.00000			−0.236525
$287$		−	12.0000i		−	0.708338i
$288$			1.00000i			0.0589256i
$289$	−19.0000			−1.11765
$290$	4.00000	+	8.00000i	0.234888	+	0.469776i
$291$		0			0
$292$		0			0
$293$			10.0000i			0.584206i	0.956387	+	0.292103i	$0.0943550\pi$
$293$			10.0000i			0.584206i	−0.956387	+	0.292103i	$0.905645\pi$
$294$	3.00000			0.174964
$295$	28.0000	−	14.0000i	1.63022	−	0.815112i
$296$	−10.0000			−0.581238
$297$			2.00000i			0.116052i
$298$			4.00000i			0.231714i
$299$		0			0
$300$	−4.00000	−	3.00000i	−0.230940	−	0.173205i
$301$	−8.00000			−0.461112
$302$		0			0
$303$		−	16.0000i		−	0.919176i
$304$	8.00000			0.458831
$305$	−4.00000	+	2.00000i	−0.229039	+	0.114520i
$306$	−6.00000			−0.342997
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$			4.00000i			0.227921i
$309$	−14.0000			−0.796432
$310$	−1.00000	−	2.00000i	−0.0567962	−	0.113592i
$311$	−20.0000			−1.13410			−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000			−1.13410			−0.567048	+	0.823685i	$0.691915\pi$
$312$		−	2.00000i		−	0.113228i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−10.0000			−0.564333
$315$	−2.00000	−	4.00000i	−0.112687	−	0.225374i
$316$	−16.0000			−0.900070
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$			2.00000i			0.112154i
$319$	8.00000			0.447914
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$	−4.00000			−0.223258
$322$		0			0
$323$			48.0000i			2.67079i
$324$	−1.00000			−0.0555556
$325$	8.00000	+	6.00000i	0.443760	+	0.332820i
$326$	16.0000			0.886158
$327$		−	10.0000i		−	0.553001i
$328$		−	6.00000i		−	0.331295i
$329$		0			0
$330$	−4.00000	+	2.00000i	−0.220193	+	0.110096i
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$			12.0000i			0.658586i
$333$		−	10.0000i		−	0.547997i
$334$	−24.0000			−1.31322
$335$	−8.00000	−	16.0000i	−0.437087	−	0.874173i
$336$	−2.00000			−0.109109
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$		−	9.00000i		−	0.489535i
$339$	14.0000			0.760376
$340$	−6.00000	−	12.0000i	−0.325396	−	0.650791i
$341$	−2.00000			−0.108306
$342$			8.00000i			0.432590i
$343$			20.0000i			1.07990i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	−18.0000			−0.967686
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$			4.00000i			0.214423i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	6.00000	−	8.00000i	0.320713	−	0.427618i
$351$	2.00000			0.106752
$352$			2.00000i			0.106600i
$353$			2.00000i			0.106449i	0.998583	+	0.0532246i	$0.0169499\pi$
$353$			2.00000i			0.106449i	−0.998583	+	0.0532246i	$0.983050\pi$
$354$	14.0000			0.744092
$355$	24.0000	−	12.0000i	1.27379	−	0.636894i
$356$	6.00000			0.317999
$357$		−	12.0000i		−	0.635107i
$358$			14.0000i			0.739923i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	−1.00000	−	2.00000i	−0.0527046	−	0.105409i
$361$	45.0000			2.36842
$362$			10.0000i			0.525588i
$363$		−	7.00000i		−	0.367405i
$364$	4.00000			0.209657
$365$		0			0
$366$	−2.00000			−0.104542
$367$		−	18.0000i		−	0.939592i	−0.882775	−	0.469796i	$-0.844327\pi$
$367$		−	18.0000i		−	0.939592i	0.882775	−	0.469796i	$-0.155673\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$	20.0000	−	10.0000i	1.03975	−	0.519875i
$371$	−4.00000			−0.207670
$372$		−	1.00000i		−	0.0518476i
$373$			34.0000i			1.76045i	0.474554	+	0.880227i	$0.342610\pi$
$373$			34.0000i			1.76045i	−0.474554	+	0.880227i	$0.657390\pi$
$374$	−12.0000			−0.620505
$375$	11.0000	+	2.00000i	0.568038	+	0.103280i
$376$		0			0
$377$		−	8.00000i		−	0.412021i
$378$		−	2.00000i		−	0.102869i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−16.0000	+	8.00000i	−0.820783	+	0.410391i
$381$	2.00000			0.102463
$382$			4.00000i			0.204658i
$383$		−	12.0000i		−	0.613171i	−0.951843	−	0.306586i	$-0.900813\pi$
$383$		−	12.0000i		−	0.613171i	0.951843	−	0.306586i	$-0.0991866\pi$
$384$	−1.00000			−0.0510310
$385$	−4.00000	−	8.00000i	−0.203859	−	0.407718i
$386$	−4.00000			−0.203595
$387$		−	4.00000i		−	0.203331i
$388$		0			0
$389$	16.0000			0.811232			0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000			0.811232			0.405616	+	0.914044i	$0.367057\pi$
$390$	2.00000	+	4.00000i	0.101274	+	0.202548i
$391$		0			0
$392$			3.00000i			0.151523i
$393$			6.00000i			0.302660i
$394$	−26.0000			−1.30986
$395$	32.0000	−	16.0000i	1.61009	−	0.805047i
$396$	−2.00000			−0.100504
$397$		−	30.0000i		−	1.50566i	−0.658217	−	0.752828i	$-0.728689\pi$
$397$		−	30.0000i		−	1.50566i	0.658217	−	0.752828i	$-0.271311\pi$
$398$		−	8.00000i		−	0.401004i
$399$	−16.0000			−0.801002
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−10.0000			−0.499376			−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000			−0.499376			−0.249688	+	0.968326i	$0.580328\pi$
$402$		−	8.00000i		−	0.399004i
$403$			2.00000i			0.0996271i
$404$	16.0000			0.796030
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	−8.00000			−0.397033
$407$		−	20.0000i		−	0.991363i
$408$		−	6.00000i		−	0.297044i
$409$	−38.0000			−1.87898			−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000			−1.87898			−0.939490	+	0.342578i	$0.888700\pi$
$410$	6.00000	+	12.0000i	0.296319	+	0.592638i
$411$	−10.0000			−0.493264
$412$		−	14.0000i		−	0.689730i
$413$			28.0000i			1.37779i
$414$		0			0
$415$	−12.0000	−	24.0000i	−0.589057	−	1.17811i
$416$	2.00000			0.0980581
$417$		−	16.0000i		−	0.783523i
$418$			16.0000i			0.782586i
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$	4.00000	−	2.00000i	0.195180	−	0.0975900i
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$			4.00000i			0.194717i
$423$		0			0
$424$	−2.00000			−0.0971286
$425$	24.0000	+	18.0000i	1.16417	+	0.873128i
$426$	12.0000			0.581402
$427$		−	4.00000i		−	0.193574i
$428$		−	4.00000i		−	0.193347i
$429$	4.00000			0.193122
$430$	8.00000	−	4.00000i	0.385794	−	0.192897i
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$	2.00000			0.0960031
$435$	−4.00000	−	8.00000i	−0.191785	−	0.383571i
$436$	10.0000			0.478913
$437$		0			0
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	−2.00000	−	4.00000i	−0.0953463	−	0.190693i
$441$	−3.00000			−0.142857
$442$			12.0000i			0.570782i
$443$		−	20.0000i		−	0.950229i	−0.879924	−	0.475114i	$-0.842407\pi$
$443$		−	20.0000i		−	0.950229i	0.879924	−	0.475114i	$-0.157593\pi$
$444$	10.0000			0.474579
$445$	−12.0000	+	6.00000i	−0.568855	+	0.284427i
$446$	−14.0000			−0.662919
$447$		−	4.00000i		−	0.189194i
$448$		−	2.00000i		−	0.0944911i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$	12.0000			0.565058
$452$			14.0000i			0.658505i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	−8.00000	+	4.00000i	−0.375046	+	0.187523i
$456$	−8.00000			−0.374634
$457$		−	20.0000i		−	0.935561i	−0.883845	−	0.467780i	$-0.845054\pi$
$457$		−	20.0000i		−	0.935561i	0.883845	−	0.467780i	$-0.154946\pi$
$458$		−	22.0000i		−	1.02799i
$459$	6.00000			0.280056
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		−	4.00000i		−	0.186097i
$463$			6.00000i			0.278844i	0.990233	+	0.139422i	$0.0445244\pi$
$463$			6.00000i			0.278844i	−0.990233	+	0.139422i	$0.955476\pi$
$464$	−4.00000			−0.185695
$465$	1.00000	+	2.00000i	0.0463739	+	0.0927478i
$466$	−10.0000			−0.463241
$467$			4.00000i			0.185098i	0.995708	+	0.0925490i	$0.0295015\pi$
$467$			4.00000i			0.185098i	−0.995708	+	0.0925490i	$0.970499\pi$
$468$			2.00000i			0.0924500i
$469$	16.0000			0.738811
$470$		0			0
$471$	10.0000			0.460776
$472$			14.0000i			0.644402i
$473$		−	8.00000i		−	0.367840i
$474$	16.0000			0.734904
$475$	24.0000	−	32.0000i	1.10120	−	1.46826i
$476$	12.0000			0.550019
$477$		−	2.00000i		−	0.0915737i
$478$			12.0000i			0.548867i
$479$	12.0000			0.548294			0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000			0.548294			0.274147	+	0.961688i	$0.411605\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$	−20.0000			−0.911922
$482$			18.0000i			0.819878i
$483$		0			0
$484$	7.00000			0.318182
$485$		0			0
$486$	1.00000			0.0453609
$487$			42.0000i			1.90320i	0.307337	+	0.951601i	$0.400562\pi$
$487$			42.0000i			1.90320i	−0.307337	+	0.951601i	$0.599438\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	−16.0000			−0.723545
$490$	−3.00000	−	6.00000i	−0.135526	−	0.271052i
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$			6.00000i			0.270501i
$493$		−	24.0000i		−	1.08091i
$494$	16.0000			0.719874
$495$	4.00000	−	2.00000i	0.179787	−	0.0898933i
$496$	1.00000			0.0449013
$497$			24.0000i			1.07655i
$498$		−	12.0000i		−	0.537733i
$499$	36.0000			1.61158			0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000			1.61158			0.805791	+	0.592200i	$0.201741\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	24.0000			1.07224
$502$			22.0000i			0.981908i
$503$			40.0000i			1.78351i	0.452517	+	0.891756i	$0.350526\pi$
$503$			40.0000i			1.78351i	−0.452517	+	0.891756i	$0.649474\pi$
$504$	2.00000			0.0890871
$505$	−32.0000	+	16.0000i	−1.42398	+	0.711991i
$506$		0			0
$507$			9.00000i			0.399704i
$508$			2.00000i			0.0887357i
$509$	20.0000			0.886484			0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000			0.886484			0.443242	+	0.896402i	$0.353828\pi$
$510$	6.00000	+	12.0000i	0.265684	+	0.531369i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	8.00000i		−	0.353209i
$514$	22.0000			0.970378
$515$	14.0000	+	28.0000i	0.616914	+	1.23383i
$516$	4.00000			0.176090
$517$		0			0
$518$			20.0000i			0.878750i
$519$	18.0000			0.790112
$520$	−4.00000	+	2.00000i	−0.175412	+	0.0877058i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		−	4.00000i		−	0.175075i
$523$			8.00000i			0.349816i	0.984585	+	0.174908i	$0.0559627\pi$
$523$			8.00000i			0.349816i	−0.984585	+	0.174908i	$0.944037\pi$
$524$	−6.00000			−0.262111
$525$	−6.00000	+	8.00000i	−0.261861	+	0.349149i
$526$	16.0000			0.697633
$527$			6.00000i			0.261364i
$528$		−	2.00000i		−	0.0870388i
$529$	23.0000			1.00000
$530$	4.00000	−	2.00000i	0.173749	−	0.0868744i
$531$	−14.0000			−0.607548
$532$		−	16.0000i		−	0.693688i
$533$		−	12.0000i		−	0.519778i
$534$	−6.00000			−0.259645
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$	8.00000			0.345547
$537$		−	14.0000i		−	0.604145i
$538$		−	28.0000i		−	1.20717i
$539$	−6.00000			−0.258438
$540$	1.00000	+	2.00000i	0.0430331	+	0.0860663i
$541$	42.0000			1.80572			0.902861	−	0.429934i	$-0.141463\pi$
$541$	42.0000			1.80572			0.902861	+	0.429934i	$0.141463\pi$
$542$		−	8.00000i		−	0.343629i
$543$		−	10.0000i		−	0.429141i
$544$	6.00000			0.257248
$545$	−20.0000	+	10.0000i	−0.856706	+	0.428353i
$546$	−4.00000			−0.171184
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$		−	10.0000i		−	0.427179i
$549$	2.00000			0.0853579
$550$	8.00000	+	6.00000i	0.341121	+	0.255841i
$551$	−32.0000			−1.36325
$552$		0			0
$553$			32.0000i			1.36078i
$554$	2.00000			0.0849719
$555$	−20.0000	+	10.0000i	−0.848953	+	0.424476i
$556$	16.0000			0.678551
$557$			14.0000i			0.593199i	0.955002	+	0.296600i	$0.0958526\pi$
$557$			14.0000i			0.593199i	−0.955002	+	0.296600i	$0.904147\pi$
$558$			1.00000i			0.0423334i
$559$	−8.00000			−0.338364
$560$	2.00000	+	4.00000i	0.0845154	+	0.169031i
$561$	12.0000			0.506640
$562$		−	6.00000i		−	0.253095i
$563$			4.00000i			0.168580i	0.996441	+	0.0842900i	$0.0268622\pi$
$563$			4.00000i			0.168580i	−0.996441	+	0.0842900i	$0.973138\pi$
$564$		0			0
$565$	−14.0000	−	28.0000i	−0.588984	−	1.17797i
$566$	−16.0000			−0.672530
$567$			2.00000i			0.0839921i
$568$			12.0000i			0.503509i
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$	16.0000	−	8.00000i	0.670166	−	0.335083i
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$			4.00000i			0.167248i
$573$		−	4.00000i		−	0.167102i
$574$	−12.0000			−0.500870
$575$		0			0
$576$	1.00000			0.0416667
$577$		−	16.0000i		−	0.666089i	−0.942911	−	0.333044i	$-0.891924\pi$
$577$		−	16.0000i		−	0.666089i	0.942911	−	0.333044i	$-0.108076\pi$
$578$			19.0000i			0.790296i
$579$	4.00000			0.166234
$580$	8.00000	−	4.00000i	0.332182	−	0.166091i
$581$	24.0000			0.995688
$582$		0			0
$583$		−	4.00000i		−	0.165663i
$584$		0			0
$585$	−2.00000	−	4.00000i	−0.0826898	−	0.165380i
$586$	10.0000			0.413096
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$		−	3.00000i		−	0.123718i
$589$	8.00000			0.329634
$590$	−14.0000	−	28.0000i	−0.576371	−	1.15274i
$591$	26.0000			1.06950
$592$			10.0000i			0.410997i
$593$		−	22.0000i		−	0.903432i	−0.892162	−	0.451716i	$-0.850812\pi$
$593$		−	22.0000i		−	0.903432i	0.892162	−	0.451716i	$-0.149188\pi$
$594$	2.00000			0.0820610
$595$	−24.0000	+	12.0000i	−0.983904	+	0.491952i
$596$	4.00000			0.163846
$597$			8.00000i			0.327418i
$598$		0			0
$599$	−48.0000			−1.96123			−0.980613	−	0.195952i	$-0.937220\pi$
$599$	−48.0000			−1.96123			−0.980613	+	0.195952i	$0.937220\pi$
$600$	−3.00000	+	4.00000i	−0.122474	+	0.163299i
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$			8.00000i			0.326056i
$603$			8.00000i			0.325785i
$604$		0			0
$605$	−14.0000	+	7.00000i	−0.569181	+	0.284590i
$606$	−16.0000			−0.649956
$607$			14.0000i			0.568242i	0.958788	+	0.284121i	$0.0917018\pi$
$607$			14.0000i			0.568242i	−0.958788	+	0.284121i	$0.908298\pi$
$608$		−	8.00000i		−	0.324443i
$609$	8.00000			0.324176
$610$	2.00000	+	4.00000i	0.0809776	+	0.161955i
$611$		0			0
$612$			6.00000i			0.242536i
$613$			22.0000i			0.888572i	0.895885	+	0.444286i	$0.146543\pi$
$613$			22.0000i			0.888572i	−0.895885	+	0.444286i	$0.853457\pi$
$614$	−4.00000			−0.161427
$615$	−6.00000	−	12.0000i	−0.241943	−	0.483887i
$616$	4.00000			0.161165
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$			14.0000i			0.563163i
$619$	8.00000			0.321547			0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000			0.321547			0.160774	+	0.986991i	$0.448601\pi$
$620$	−2.00000	+	1.00000i	−0.0803219	+	0.0401610i
$621$		0			0
$622$			20.0000i			0.801927i
$623$		−	12.0000i		−	0.480770i
$624$	−2.00000			−0.0800641
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$		−	16.0000i		−	0.638978i
$628$			10.0000i			0.399043i
$629$	−60.0000			−2.39236
$630$	−4.00000	+	2.00000i	−0.159364	+	0.0796819i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$			16.0000i			0.636446i
$633$		−	4.00000i		−	0.158986i
$634$	2.00000			0.0794301
$635$	−2.00000	−	4.00000i	−0.0793676	−	0.158735i
$636$	2.00000			0.0793052
$637$			6.00000i			0.237729i
$638$		−	8.00000i		−	0.316723i
$639$	−12.0000			−0.474713
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	−14.0000			−0.552967			−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000			−0.552967			−0.276483	+	0.961019i	$0.589169\pi$
$642$			4.00000i			0.157867i
$643$			16.0000i			0.630978i	0.948929	+	0.315489i	$0.102169\pi$
$643$			16.0000i			0.630978i	−0.948929	+	0.315489i	$0.897831\pi$
$644$		0			0
$645$	−8.00000	+	4.00000i	−0.315000	+	0.157500i
$646$	48.0000			1.88853
$647$			28.0000i			1.10079i	0.834903	+	0.550397i	$0.185524\pi$
$647$			28.0000i			1.10079i	−0.834903	+	0.550397i	$0.814476\pi$
$648$			1.00000i			0.0392837i
$649$	−28.0000			−1.09910
$650$	6.00000	−	8.00000i	0.235339	−	0.313786i
$651$	−2.00000			−0.0783862
$652$		−	16.0000i		−	0.626608i
$653$			6.00000i			0.234798i	0.993085	+	0.117399i	$0.0374557\pi$
$653$			6.00000i			0.234798i	−0.993085	+	0.117399i	$0.962544\pi$
$654$	−10.0000			−0.391031
$655$	12.0000	−	6.00000i	0.468879	−	0.234439i
$656$	−6.00000			−0.234261
$657$		0			0
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	2.00000	+	4.00000i	0.0778499	+	0.155700i
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$		−	12.0000i		−	0.466393i
$663$		−	12.0000i		−	0.466041i
$664$	12.0000			0.465690
$665$	16.0000	+	32.0000i	0.620453	+	1.24091i
$666$	−10.0000			−0.387492
$667$		0			0
$668$			24.0000i			0.928588i
$669$	14.0000			0.541271
$670$	−16.0000	+	8.00000i	−0.618134	+	0.309067i
$671$	4.00000			0.154418
$672$			2.00000i			0.0771517i
$673$		−	16.0000i		−	0.616755i	−0.951264	−	0.308377i	$-0.900214\pi$
$673$		−	16.0000i		−	0.616755i	0.951264	−	0.308377i	$-0.0997859\pi$
$674$	−32.0000			−1.23259
$675$	−4.00000	−	3.00000i	−0.153960	−	0.115470i
$676$	−9.00000			−0.346154
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$		−	14.0000i		−	0.537667i
$679$		0			0
$680$	−12.0000	+	6.00000i	−0.460179	+	0.230089i
$681$	12.0000			0.459841
$682$			2.00000i			0.0765840i
$683$		−	36.0000i		−	1.37750i	−0.724998	−	0.688751i	$-0.758159\pi$
$683$		−	36.0000i		−	1.37750i	0.724998	−	0.688751i	$-0.241841\pi$
$684$	8.00000			0.305888
$685$	10.0000	+	20.0000i	0.382080	+	0.764161i
$686$	20.0000			0.763604
$687$			22.0000i			0.839352i
$688$			4.00000i			0.152499i
$689$	−4.00000			−0.152388
$690$		0			0
$691$	24.0000			0.913003			0.456502	−	0.889723i	$-0.349102\pi$
$691$	24.0000			0.913003			0.456502	+	0.889723i	$0.349102\pi$
$692$			18.0000i			0.684257i
$693$			4.00000i			0.151947i
$694$	−12.0000			−0.455514
$695$	−32.0000	+	16.0000i	−1.21383	+	0.606915i
$696$	4.00000			0.151620
$697$		−	36.0000i		−	1.36360i
$698$		−	14.0000i		−	0.529908i
$699$	10.0000			0.378235
$700$	−8.00000	−	6.00000i	−0.302372	−	0.226779i
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$		−	2.00000i		−	0.0754851i
$703$			80.0000i			3.01726i
$704$	2.00000			0.0753778
$705$		0			0
$706$	2.00000			0.0752710
$707$		−	32.0000i		−	1.20348i
$708$		−	14.0000i		−	0.526152i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−12.0000	−	24.0000i	−0.450352	−	0.900704i
$711$	−16.0000			−0.600047
$712$		−	6.00000i		−	0.224860i
$713$		0			0
$714$	−12.0000			−0.449089
$715$	−4.00000	−	8.00000i	−0.149592	−	0.299183i
$716$	14.0000			0.523205
$717$		−	12.0000i		−	0.448148i
$718$		0			0
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	−2.00000	+	1.00000i	−0.0745356	+	0.0372678i
$721$	−28.0000			−1.04277
$722$		−	45.0000i		−	1.67473i
$723$		−	18.0000i		−	0.669427i
$724$	10.0000			0.371647
$725$	−12.0000	+	16.0000i	−0.445669	+	0.594225i
$726$	−7.00000			−0.259794
$727$		−	10.0000i		−	0.370879i	−0.982656	−	0.185440i	$-0.940629\pi$
$727$		−	10.0000i		−	0.370879i	0.982656	−	0.185440i	$-0.0593710\pi$
$728$		−	4.00000i		−	0.148250i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−24.0000			−0.887672
$732$			2.00000i			0.0739221i
$733$		−	2.00000i		−	0.0738717i	−0.999318	−	0.0369358i	$-0.988240\pi$
$733$		−	2.00000i		−	0.0738717i	0.999318	−	0.0369358i	$-0.0117597\pi$
$734$	−18.0000			−0.664392
$735$	3.00000	+	6.00000i	0.110657	+	0.221313i
$736$		0			0
$737$			16.0000i			0.589368i
$738$		−	6.00000i		−	0.220863i
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−10.0000	−	20.0000i	−0.367607	−	0.735215i
$741$	−16.0000			−0.587775
$742$			4.00000i			0.146845i
$743$		−	28.0000i		−	1.02722i	−0.858024	−	0.513610i	$-0.828308\pi$
$743$		−	28.0000i		−	1.02722i	0.858024	−	0.513610i	$-0.171692\pi$
$744$	−1.00000			−0.0366618
$745$	−8.00000	+	4.00000i	−0.293097	+	0.146549i
$746$	34.0000			1.24483
$747$			12.0000i			0.439057i
$748$			12.0000i			0.438763i
$749$	−8.00000			−0.292314
$750$	2.00000	−	11.0000i	0.0730297	−	0.401663i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$		−	22.0000i		−	0.801725i
$754$	−8.00000			−0.291343
$755$		0			0
$756$	−2.00000			−0.0727393
$757$			50.0000i			1.81728i	0.417579	+	0.908640i	$0.362879\pi$
$757$			50.0000i			1.81728i	−0.417579	+	0.908640i	$0.637121\pi$
$758$		−	20.0000i		−	0.726433i
$759$		0			0
$760$	8.00000	+	16.0000i	0.290191	+	0.580381i
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		−	2.00000i		−	0.0724524i
$763$		−	20.0000i		−	0.724049i
$764$	4.00000			0.144715
$765$	−6.00000	−	12.0000i	−0.216930	−	0.433861i
$766$	−12.0000			−0.433578
$767$			28.0000i			1.01102i
$768$			1.00000i			0.0360844i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$	−8.00000	+	4.00000i	−0.288300	+	0.144150i
$771$	−22.0000			−0.792311
$772$			4.00000i			0.143963i
$773$			6.00000i			0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$			6.00000i			0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$	−4.00000			−0.143777
$775$	3.00000	−	4.00000i	0.107763	−	0.143684i
$776$		0			0
$777$		−	20.0000i		−	0.717496i
$778$		−	16.0000i		−	0.573628i
$779$	−48.0000			−1.71978
$780$	4.00000	−	2.00000i	0.143223	−	0.0716115i
$781$	−24.0000			−0.858788
$782$		0			0
$783$			4.00000i			0.142948i
$784$	3.00000			0.107143
$785$	−10.0000	−	20.0000i	−0.356915	−	0.713831i
$786$	6.00000			0.214013
$787$		−	40.0000i		−	1.42585i	−0.701242	−	0.712923i	$-0.747371\pi$
$787$		−	40.0000i		−	1.42585i	0.701242	−	0.712923i	$-0.252629\pi$
$788$			26.0000i			0.926212i
$789$	−16.0000			−0.569615
$790$	−16.0000	−	32.0000i	−0.569254	−	1.13851i
$791$	28.0000			0.995565
$792$			2.00000i			0.0710669i
$793$		−	4.00000i		−	0.142044i
$794$	−30.0000			−1.06466
$795$	−4.00000	+	2.00000i	−0.141865	+	0.0709327i
$796$	−8.00000			−0.283552
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$			16.0000i			0.566394i
$799$		0			0
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	6.00000			0.212000
$802$			10.0000i			0.353112i
$803$		0			0
$804$	−8.00000			−0.282138
$805$		0			0
$806$	2.00000			0.0704470
$807$			28.0000i			0.985647i
$808$		−	16.0000i		−	0.562878i
$809$	38.0000			1.33601			0.668004	−	0.744157i	$-0.267149\pi$
$809$	38.0000			1.33601			0.668004	+	0.744157i	$0.267149\pi$
$810$	−1.00000	−	2.00000i	−0.0351364	−	0.0702728i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$			8.00000i			0.280745i
$813$			8.00000i			0.280572i
$814$	−20.0000			−0.701000
$815$	16.0000	+	32.0000i	0.560456	+	1.12091i
$816$	−6.00000			−0.210042
$817$			32.0000i			1.11954i
$818$			38.0000i			1.32864i
$819$	4.00000			0.139771
$820$	12.0000	−	6.00000i	0.419058	−	0.209529i
$821$	−20.0000			−0.698005			−0.349002	−	0.937122i	$-0.613479\pi$
$821$	−20.0000			−0.698005			−0.349002	+	0.937122i	$0.613479\pi$
$822$			10.0000i			0.348790i
$823$		−	2.00000i		−	0.0697156i	−0.999392	−	0.0348578i	$-0.988902\pi$
$823$		−	2.00000i		−	0.0697156i	0.999392	−	0.0348578i	$-0.0110978\pi$
$824$	−14.0000			−0.487713
$825$	−8.00000	−	6.00000i	−0.278524	−	0.208893i
$826$	28.0000			0.974245
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$		0			0
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$	−24.0000	+	12.0000i	−0.833052	+	0.416526i
$831$	−2.00000			−0.0693792
$832$		−	2.00000i		−	0.0693375i
$833$			18.0000i			0.623663i
$834$	−16.0000			−0.554035
$835$	−24.0000	−	48.0000i	−0.830554	−	1.66111i
$836$	16.0000			0.553372
$837$		−	1.00000i		−	0.0345651i
$838$		−	18.0000i		−	0.621800i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$	−2.00000	−	4.00000i	−0.0690066	−	0.138013i
$841$	−13.0000			−0.448276
$842$			2.00000i			0.0689246i
$843$			6.00000i			0.206651i
$844$	4.00000			0.137686
$845$	18.0000	−	9.00000i	0.619219	−	0.309609i
$846$		0			0
$847$		−	14.0000i		−	0.481046i
$848$			2.00000i			0.0686803i
$849$	16.0000			0.549119
$850$	18.0000	−	24.0000i	0.617395	−	0.823193i
$851$		0			0
$852$		−	12.0000i		−	0.411113i
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	−4.00000			−0.136877
$855$	−16.0000	+	8.00000i	−0.547188	+	0.273594i
$856$	−4.00000			−0.136717
$857$			2.00000i			0.0683187i	0.999416	+	0.0341593i	$0.0108754\pi$
$857$			2.00000i			0.0683187i	−0.999416	+	0.0341593i	$0.989125\pi$
$858$		−	4.00000i		−	0.136558i
$859$	48.0000			1.63774			0.818869	−	0.573980i	$-0.194601\pi$
$859$	48.0000			1.63774			0.818869	+	0.573980i	$0.194601\pi$
$860$	−4.00000	−	8.00000i	−0.136399	−	0.272798i
$861$	12.0000			0.408959
$862$		−	16.0000i		−	0.544962i
$863$			32.0000i			1.08929i	0.838666	+	0.544646i	$0.183336\pi$
$863$			32.0000i			1.08929i	−0.838666	+	0.544646i	$0.816664\pi$
$864$	−1.00000			−0.0340207
$865$	−18.0000	−	36.0000i	−0.612018	−	1.22404i
$866$	16.0000			0.543702
$867$		−	19.0000i		−	0.645274i
$868$		−	2.00000i		−	0.0678844i
$869$	−32.0000			−1.08553
$870$	−8.00000	+	4.00000i	−0.271225	+	0.135613i
$871$	16.0000			0.542139
$872$		−	10.0000i		−	0.338643i
$873$		0			0
$874$		0			0
$875$	22.0000	+	4.00000i	0.743736	+	0.135225i
$876$		0			0
$877$			6.00000i			0.202606i	0.994856	+	0.101303i	$0.0323011\pi$
$877$			6.00000i			0.202606i	−0.994856	+	0.101303i	$0.967699\pi$
$878$			8.00000i			0.269987i
$879$	−10.0000			−0.337292
$880$	−4.00000	+	2.00000i	−0.134840	+	0.0674200i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$			3.00000i			0.101015i
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$	12.0000			0.403604
$885$	14.0000	+	28.0000i	0.470605	+	0.941210i
$886$	−20.0000			−0.671913
$887$			4.00000i			0.134307i	0.997743	+	0.0671534i	$0.0213917\pi$
$887$			4.00000i			0.134307i	−0.997743	+	0.0671534i	$0.978608\pi$
$888$		−	10.0000i		−	0.335578i
$889$	4.00000			0.134156
$890$	6.00000	+	12.0000i	0.201120	+	0.402241i
$891$	−2.00000			−0.0670025
$892$			14.0000i			0.468755i
$893$		0			0
$894$	−4.00000			−0.133780
$895$	−28.0000	+	14.0000i	−0.935937	+	0.467968i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$		−	18.0000i		−	0.600668i
$899$	−4.00000			−0.133407
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$	−12.0000			−0.399778
$902$		−	12.0000i		−	0.399556i
$903$		−	8.00000i		−	0.266223i
$904$	14.0000			0.465633
$905$	−20.0000	+	10.0000i	−0.664822	+	0.332411i
$906$		0			0
$907$		−	52.0000i		−	1.72663i	−0.504664	−	0.863316i	$-0.668384\pi$
$907$		−	52.0000i		−	1.72663i	0.504664	−	0.863316i	$-0.331616\pi$
$908$			12.0000i			0.398234i
$909$	16.0000			0.530687
$910$	4.00000	+	8.00000i	0.132599	+	0.265197i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$			8.00000i			0.264906i
$913$			24.0000i			0.794284i
$914$	−20.0000			−0.661541
$915$	−2.00000	−	4.00000i	−0.0661180	−	0.132236i
$916$	−22.0000			−0.726900
$917$			12.0000i			0.396275i
$918$		−	6.00000i		−	0.198030i
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$		0			0
$921$	4.00000			0.131804
$922$		0			0
$923$			24.0000i			0.789970i
$924$	−4.00000			−0.131590
$925$	40.0000	+	30.0000i	1.31519	+	0.986394i
$926$	6.00000			0.197172
$927$		−	14.0000i		−	0.459820i
$928$			4.00000i			0.131306i
$929$	26.0000			0.853032			0.426516	−	0.904480i	$-0.359741\pi$
$929$	26.0000			0.853032			0.426516	+	0.904480i	$0.359741\pi$
$930$	2.00000	−	1.00000i	0.0655826	−	0.0327913i
$931$	24.0000			0.786568
$932$			10.0000i			0.327561i
$933$		−	20.0000i		−	0.654771i
$934$	4.00000			0.130884
$935$	−12.0000	−	24.0000i	−0.392442	−	0.784884i
$936$	2.00000			0.0653720
$937$			48.0000i			1.56809i	0.620703	+	0.784046i	$0.286847\pi$
$937$			48.0000i			1.56809i	−0.620703	+	0.784046i	$0.713153\pi$
$938$		−	16.0000i		−	0.522419i
$939$		0			0
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		−	10.0000i		−	0.325818i
$943$		0			0
$944$	14.0000			0.455661
$945$	4.00000	−	2.00000i	0.130120	−	0.0650600i
$946$	−8.00000			−0.260102
$947$		−	20.0000i		−	0.649913i	−0.945729	−	0.324956i	$-0.894650\pi$
$947$		−	20.0000i		−	0.649913i	0.945729	−	0.324956i	$-0.105350\pi$
$948$		−	16.0000i		−	0.519656i
$949$		0			0
$950$	−32.0000	−	24.0000i	−1.03822	−	0.778663i
$951$	−2.00000			−0.0648544
$952$		−	12.0000i		−	0.388922i
$953$		−	58.0000i		−	1.87880i	−0.342817	−	0.939402i	$-0.611381\pi$
$953$		−	58.0000i		−	1.87880i	0.342817	−	0.939402i	$-0.388619\pi$
$954$	−2.00000			−0.0647524
$955$	−8.00000	+	4.00000i	−0.258874	+	0.129437i
$956$	12.0000			0.388108
$957$			8.00000i			0.258603i
$958$		−	12.0000i		−	0.387702i
$959$	−20.0000			−0.645834
$960$	−1.00000	−	2.00000i	−0.0322749	−	0.0645497i
$961$	1.00000			0.0322581
$962$			20.0000i			0.644826i
$963$		−	4.00000i		−	0.128898i
$964$	18.0000			0.579741
$965$	−4.00000	−	8.00000i	−0.128765	−	0.257529i
$966$		0			0
$967$		−	10.0000i		−	0.321578i	−0.986989	−	0.160789i	$-0.948596\pi$
$967$		−	10.0000i		−	0.321578i	0.986989	−	0.160789i	$-0.0514039\pi$
$968$		−	7.00000i		−	0.224989i
$969$	−48.0000			−1.54198
$970$		0			0
$971$	−34.0000			−1.09111			−0.545556	−	0.838074i	$-0.683681\pi$
$971$	−34.0000			−1.09111			−0.545556	+	0.838074i	$0.683681\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	32.0000i		−	1.02587i
$974$	42.0000			1.34577
$975$	−6.00000	+	8.00000i	−0.192154	+	0.256205i
$976$	−2.00000			−0.0640184
$977$		−	22.0000i		−	0.703842i	−0.936030	−	0.351921i	$-0.885529\pi$
$977$		−	22.0000i		−	0.703842i	0.936030	−	0.351921i	$-0.114471\pi$
$978$			16.0000i			0.511624i
$979$	12.0000			0.383522
$980$	−6.00000	+	3.00000i	−0.191663	+	0.0958315i
$981$	10.0000			0.319275
$982$		−	18.0000i		−	0.574403i
$983$		−	4.00000i		−	0.127580i	−0.997963	−	0.0637901i	$-0.979681\pi$
$983$		−	4.00000i		−	0.127580i	0.997963	−	0.0637901i	$-0.0203188\pi$
$984$	6.00000			0.191273
$985$	−26.0000	−	52.0000i	−0.828429	−	1.65686i
$986$	−24.0000			−0.764316
$987$		0			0
$988$		−	16.0000i		−	0.509028i
$989$		0			0
$990$	−2.00000	−	4.00000i	−0.0635642	−	0.127128i
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		−	1.00000i		−	0.0317500i
$993$			12.0000i			0.380808i
$994$	24.0000			0.761234
$995$	16.0000	−	8.00000i	0.507234	−	0.253617i
$996$	−12.0000			−0.380235
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$		−	36.0000i		−	1.13956i
$999$	10.0000			0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.f.559.1	✓	2
3.2	odd	2		2790.2.d.b.559.2		2
5.2	odd	4		4650.2.a.bm.1.1		1
5.3	odd	4		4650.2.a.j.1.1		1
5.4	even	2	inner	930.2.d.f.559.2	yes	2
15.14	odd	2		2790.2.d.b.559.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.f.559.1	✓	2	1.1	even	1	trivial
930.2.d.f.559.2	yes	2	5.4	even	2	inner
2790.2.d.b.559.1		2	15.14	odd	2
2790.2.d.b.559.2		2	3.2	odd	2
4650.2.a.j.1.1		1	5.3	odd	4
4650.2.a.bm.1.1		1	5.2	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} -1.00000i q^{12} +2.00000i q^{13} +2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +6.00000i q^{17} +1.00000i q^{18} +8.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -2.00000 q^{21} +2.00000i q^{22} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} -2.00000i q^{28} -4.00000 q^{29} +(2.00000 - 1.00000i) q^{30} +1.00000 q^{31} -1.00000i q^{32} -2.00000i q^{33} +6.00000 q^{34} +(2.00000 + 4.00000i) q^{35} +1.00000 q^{36} +10.0000i q^{37} -8.00000i q^{38} -2.00000 q^{39} +(1.00000 + 2.00000i) q^{40} -6.00000 q^{41} +2.00000i q^{42} +4.00000i q^{43} +2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +1.00000i q^{48} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -6.00000 q^{51} -2.00000i q^{52} +2.00000i q^{53} -1.00000 q^{54} +(-4.00000 + 2.00000i) q^{55} -2.00000 q^{56} +8.00000i q^{57} +4.00000i q^{58} +14.0000 q^{59} +(-1.00000 - 2.00000i) q^{60} -2.00000 q^{61} -1.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(2.00000 + 4.00000i) q^{65} -2.00000 q^{66} -8.00000i q^{67} -6.00000i q^{68} +(4.00000 - 2.00000i) q^{70} +12.0000 q^{71} -1.00000i q^{72} +10.0000 q^{74} +(4.00000 + 3.00000i) q^{75} -8.00000 q^{76} -4.00000i q^{77} +2.00000i q^{78} +16.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +6.00000i q^{82} -12.0000i q^{83} +2.00000 q^{84} +(6.00000 + 12.0000i) q^{85} +4.00000 q^{86} -4.00000i q^{87} -2.00000i q^{88} -6.00000 q^{89} +(1.00000 + 2.00000i) q^{90} -4.00000 q^{91} +1.00000i q^{93} +(16.0000 - 8.00000i) q^{95} +1.00000 q^{96} -3.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 16 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{24} + 6 q^{25} + 4 q^{26} - 8 q^{29} + 4 q^{30} + 2 q^{31} + 12 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{39} + 2 q^{40} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 6 q^{49} - 8 q^{50} - 12 q^{51} - 2 q^{54} - 8 q^{55} - 4 q^{56} + 28 q^{59} - 2 q^{60} - 4 q^{61} - 2 q^{64} + 4 q^{65} - 4 q^{66} + 8 q^{70} + 24 q^{71} + 20 q^{74} + 8 q^{75} - 16 q^{76} + 32 q^{79} + 4 q^{80} + 2 q^{81} + 4 q^{84} + 12 q^{85} + 8 q^{86} - 12 q^{89} + 2 q^{90} - 8 q^{91} + 32 q^{95} + 2 q^{96} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9 - 2 * q^10 - 4 * q^11 + 4 * q^14 + 2 * q^15 + 2 * q^16 + 16 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 8 * q^29 + 4 * q^30 + 2 * q^31 + 12 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^39 + 2 * q^40 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 6 * q^49 - 8 * q^50 - 12 * q^51 - 2 * q^54 - 8 * q^55 - 4 * q^56 + 28 * q^59 - 2 * q^60 - 4 * q^61 - 2 * q^64 + 4 * q^65 - 4 * q^66 + 8 * q^70 + 24 * q^71 + 20 * q^74 + 8 * q^75 - 16 * q^76 + 32 * q^79 + 4 * q^80 + 2 * q^81 + 4 * q^84 + 12 * q^85 + 8 * q^86 - 12 * q^89 + 2 * q^90 - 8 * q^91 + 32 * q^95 + 2 * q^96 + 4 * q^99

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