LMFDB - Embedded newform 1050.3.l.a.757.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(43,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			757.3
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +4.18939 q^{11} +(2.44949 + 2.44949i) q^{12} +(-12.9946 + 12.9946i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(23.0622 + 23.0622i) q^{17} +(-3.00000 + 3.00000i) q^{18} -32.6732i q^{19} -4.58258 q^{21} +(-4.18939 - 4.18939i) q^{22} +(13.5097 - 13.5097i) q^{23} -4.89898i q^{24} +25.9891 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -23.2944i q^{29} +32.2818 q^{31} +(4.00000 + 4.00000i) q^{32} +(5.13093 - 5.13093i) q^{33} -46.1244i q^{34} +6.00000 q^{36} +(21.0196 + 21.0196i) q^{37} +(-32.6732 + 32.6732i) q^{38} +31.8300i q^{39} -51.9782 q^{41} +(4.58258 + 4.58258i) q^{42} +(24.7626 - 24.7626i) q^{43} +8.37878i q^{44} -27.0194 q^{46} +(-52.0691 - 52.0691i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +56.4906 q^{51} +(-25.9891 - 25.9891i) q^{52} +(-26.3788 + 26.3788i) q^{53} +7.34847i q^{54} -7.48331 q^{56} +(-40.0163 - 40.0163i) q^{57} +(-23.2944 + 23.2944i) q^{58} -103.106i q^{59} +119.719 q^{61} +(-32.2818 - 32.2818i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} -10.2619 q^{66} +(49.4740 + 49.4740i) q^{67} +(-46.1244 + 46.1244i) q^{68} -33.0919i q^{69} +94.0594 q^{71} +(-6.00000 - 6.00000i) q^{72} +(15.0771 - 15.0771i) q^{73} -42.0393i q^{74} +65.3463 q^{76} +(-7.83763 - 7.83763i) q^{77} +(31.8300 - 31.8300i) q^{78} -112.890i q^{79} -9.00000 q^{81} +(51.9782 + 51.9782i) q^{82} +(-13.6666 + 13.6666i) q^{83} -9.16515i q^{84} -49.5252 q^{86} +(-28.5297 - 28.5297i) q^{87} +(8.37878 - 8.37878i) q^{88} +35.6390i q^{89} +48.6212 q^{91} +(27.0194 + 27.0194i) q^{92} +(39.5370 - 39.5370i) q^{93} +104.138i q^{94} +9.79796 q^{96} +(-72.1545 - 72.1545i) q^{97} +(7.00000 - 7.00000i) q^{98} -12.5682i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} - 32 q^{11} - 40 q^{13} - 32 q^{16} + 40 q^{17} - 24 q^{18} + 32 q^{22} + 8 q^{23} + 80 q^{26} + 96 q^{31} + 32 q^{32} + 72 q^{33} + 48 q^{36} - 112 q^{37} + 24 q^{38} - 160 q^{41} + 64 q^{43} - 16 q^{46} - 64 q^{47} + 24 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{57} - 32 q^{58} - 128 q^{61} - 96 q^{62} - 144 q^{66} + 304 q^{67} - 80 q^{68} + 240 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{76} + 56 q^{77} + 120 q^{78} - 72 q^{81} + 160 q^{82} - 64 q^{83} - 128 q^{86} + 96 q^{87} - 64 q^{88} + 56 q^{91} + 16 q^{92} - 144 q^{93} - 272 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 32 * q^11 - 40 * q^13 - 32 * q^16 + 40 * q^17 - 24 * q^18 + 32 * q^22 + 8 * q^23 + 80 * q^26 + 96 * q^31 + 32 * q^32 + 72 * q^33 + 48 * q^36 - 112 * q^37 + 24 * q^38 - 160 * q^41 + 64 * q^43 - 16 * q^46 - 64 * q^47 + 24 * q^51 - 80 * q^52 - 80 * q^53 - 48 * q^57 - 32 * q^58 - 128 * q^61 - 96 * q^62 - 144 * q^66 + 304 * q^67 - 80 * q^68 + 240 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^76 + 56 * q^77 + 120 * q^78 - 72 * q^81 + 160 * q^82 - 64 * q^83 - 128 * q^86 + 96 * q^87 - 64 * q^88 + 56 * q^91 + 16 * q^92 - 144 * q^93 - 272 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−2.44949			−0.408248
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	4.18939			0.380853			0.190427	−	0.981701i	$-0.439013\pi$
$11$	4.18939			0.380853			0.190427	+	0.981701i	$0.439013\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−12.9946	+	12.9946i	−0.999581	+	0.999581i	−1.00000		0.000418908i	$-0.999867\pi$
$13$	−12.9946	+	12.9946i	−0.999581	+	0.999581i	0.000418908		1.00000i	$0.499867\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	23.0622	+	23.0622i	1.35660	+	1.35660i	0.878072	+	0.478528i	$0.158829\pi$
$17$	23.0622	+	23.0622i	1.35660	+	1.35660i	0.478528	+	0.878072i	$0.341171\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	32.6732i		−	1.71964i	−0.510597	−	0.859820i	$-0.670576\pi$
$19$		−	32.6732i		−	1.71964i	0.510597	−	0.859820i	$-0.329424\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	−4.18939	−	4.18939i	−0.190427	−	0.190427i
$23$	13.5097	−	13.5097i	0.587379	−	0.587379i	−0.349542	−	0.936921i	$-0.613663\pi$
$23$	13.5097	−	13.5097i	0.587379	−	0.587379i	0.936921	+	0.349542i	$0.113663\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$	25.9891			0.999581
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$		−	23.2944i		−	0.803255i	−0.915803	−	0.401627i	$-0.868445\pi$
$29$		−	23.2944i		−	0.803255i	0.915803	−	0.401627i	$-0.131555\pi$
$30$		0			0
$31$	32.2818			1.04135			0.520675	−	0.853755i	$-0.325680\pi$
$31$	32.2818			1.04135			0.520675	+	0.853755i	$0.325680\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	5.13093	−	5.13093i	0.155483	−	0.155483i
$34$		−	46.1244i		−	1.35660i
$35$		0			0
$36$	6.00000			0.166667
$37$	21.0196	+	21.0196i	0.568098	+	0.568098i	0.931595	−	0.363497i	$-0.118417\pi$
$37$	21.0196	+	21.0196i	0.568098	+	0.568098i	−0.363497	+	0.931595i	$0.618417\pi$
$38$	−32.6732	+	32.6732i	−0.859820	+	0.859820i
$39$			31.8300i			0.816154i
$40$		0			0
$41$	−51.9782			−1.26776			−0.633881	−	0.773431i	$-0.718539\pi$
$41$	−51.9782			−1.26776			−0.633881	+	0.773431i	$0.718539\pi$
$42$	4.58258	+	4.58258i	0.109109	+	0.109109i
$43$	24.7626	−	24.7626i	0.575874	−	0.575874i	−0.357889	−	0.933764i	$-0.616504\pi$
$43$	24.7626	−	24.7626i	0.575874	−	0.575874i	0.933764	+	0.357889i	$0.116504\pi$
$44$			8.37878i			0.190427i
$45$		0			0
$46$	−27.0194			−0.587379
$47$	−52.0691	−	52.0691i	−1.10785	−	1.10785i	−0.993432	−	0.114420i	$-0.963499\pi$
$47$	−52.0691	−	52.0691i	−1.10785	−	1.10785i	−0.114420	−	0.993432i	$-0.536501\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	56.4906			1.10766
$52$	−25.9891	−	25.9891i	−0.499791	−	0.499791i
$53$	−26.3788	+	26.3788i	−0.497713	+	0.497713i	−0.910725	−	0.413013i	$-0.864477\pi$
$53$	−26.3788	+	26.3788i	−0.497713	+	0.497713i	0.413013	+	0.910725i	$0.364477\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	−7.48331			−0.133631
$57$	−40.0163	−	40.0163i	−0.702040	−	0.702040i
$58$	−23.2944	+	23.2944i	−0.401627	+	0.401627i
$59$		−	103.106i		−	1.74757i	−0.486316	−	0.873783i	$-0.661659\pi$
$59$		−	103.106i		−	1.74757i	0.486316	−	0.873783i	$-0.338341\pi$
$60$		0			0
$61$	119.719			1.96261			0.981303	−	0.192470i	$-0.0616497\pi$
$61$	119.719			1.96261			0.981303	+	0.192470i	$0.0616497\pi$
$62$	−32.2818	−	32.2818i	−0.520675	−	0.520675i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−10.2619			−0.155483
$67$	49.4740	+	49.4740i	0.738417	+	0.738417i	0.972272	−	0.233854i	$-0.0751339\pi$
$67$	49.4740	+	49.4740i	0.738417	+	0.738417i	−0.233854	+	0.972272i	$0.575134\pi$
$68$	−46.1244	+	46.1244i	−0.678300	+	0.678300i
$69$		−	33.0919i		−	0.479593i
$70$		0			0
$71$	94.0594			1.32478			0.662390	−	0.749159i	$-0.269542\pi$
$71$	94.0594			1.32478			0.662390	+	0.749159i	$0.269542\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	15.0771	−	15.0771i	0.206535	−	0.206535i	−0.596258	−	0.802793i	$-0.703346\pi$
$73$	15.0771	−	15.0771i	0.206535	−	0.206535i	0.802793	+	0.596258i	$0.203346\pi$
$74$		−	42.0393i		−	0.568098i
$75$		0			0
$76$	65.3463			0.859820
$77$	−7.83763	−	7.83763i	−0.101787	−	0.101787i
$78$	31.8300	−	31.8300i	0.408077	−	0.408077i
$79$		−	112.890i		−	1.42899i	−0.699642	−	0.714494i	$-0.746657\pi$
$79$		−	112.890i		−	1.42899i	0.699642	−	0.714494i	$-0.253343\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	51.9782	+	51.9782i	0.633881	+	0.633881i
$83$	−13.6666	+	13.6666i	−0.164658	+	0.164658i	−0.784627	−	0.619968i	$-0.787145\pi$
$83$	−13.6666	+	13.6666i	−0.164658	+	0.164658i	0.619968	+	0.784627i	$0.287145\pi$
$84$		−	9.16515i		−	0.109109i
$85$		0			0
$86$	−49.5252			−0.575874
$87$	−28.5297	−	28.5297i	−0.327927	−	0.327927i
$88$	8.37878	−	8.37878i	0.0952134	−	0.0952134i
$89$			35.6390i			0.400438i	0.979751	+	0.200219i	$0.0641654\pi$
$89$			35.6390i			0.400438i	−0.979751	+	0.200219i	$0.935835\pi$
$90$		0			0
$91$	48.6212			0.534299
$92$	27.0194	+	27.0194i	0.293689	+	0.293689i
$93$	39.5370	−	39.5370i	0.425129	−	0.425129i
$94$			104.138i			1.10785i
$95$		0			0
$96$	9.79796			0.102062
$97$	−72.1545	−	72.1545i	−0.743861	−	0.743861i	0.229458	−	0.973319i	$-0.426305\pi$
$97$	−72.1545	−	72.1545i	−0.743861	−	0.743861i	−0.973319	+	0.229458i	$0.926305\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		−	12.5682i		−	0.126951i
$100$		0			0
$101$	27.1945			0.269253			0.134626	−	0.990896i	$-0.457017\pi$
$101$	27.1945			0.269253			0.134626	+	0.990896i	$0.457017\pi$
$102$	−56.4906	−	56.4906i	−0.553830	−	0.553830i
$103$	42.1649	−	42.1649i	0.409368	−	0.409368i	−0.472150	−	0.881518i	$-0.656522\pi$
$103$	42.1649	−	42.1649i	0.409368	−	0.409368i	0.881518	+	0.472150i	$0.156522\pi$
$104$			51.9782i			0.499791i
$105$		0			0
$106$	52.7576			0.497713
$107$	−78.0442	−	78.0442i	−0.729385	−	0.729385i	0.241112	−	0.970497i	$-0.422488\pi$
$107$	−78.0442	−	78.0442i	−0.729385	−	0.729385i	−0.970497	+	0.241112i	$0.922488\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	115.318i		−	1.05796i	−0.848634	−	0.528981i	$-0.822574\pi$
$109$		−	115.318i		−	1.05796i	0.848634	−	0.528981i	$-0.177426\pi$
$110$		0			0
$111$	51.4874			0.463850
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	70.2690	−	70.2690i	0.621849	−	0.621849i	−0.324155	−	0.946004i	$-0.605080\pi$
$113$	70.2690	−	70.2690i	0.621849	−	0.621849i	0.946004	+	0.324155i	$0.105080\pi$
$114$			80.0326i			0.702040i
$115$		0			0
$116$	46.5888			0.401627
$117$	38.9837	+	38.9837i	0.333194	+	0.333194i
$118$	−103.106	+	103.106i	−0.873783	+	0.873783i
$119$		−	86.2909i		−	0.725133i
$120$		0			0
$121$	−103.449			−0.854951
$122$	−119.719	−	119.719i	−0.981303	−	0.981303i
$123$	−63.6600	+	63.6600i	−0.517561	+	0.517561i
$124$			64.5637i			0.520675i
$125$		0			0
$126$	11.2250			0.0890871
$127$	−15.4063	−	15.4063i	−0.121309	−	0.121309i	0.643846	−	0.765155i	$-0.277338\pi$
$127$	−15.4063	−	15.4063i	−0.121309	−	0.121309i	−0.765155	+	0.643846i	$0.777338\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	60.6557i		−	0.470200i
$130$		0			0
$131$	−237.306			−1.81150			−0.905750	−	0.423812i	$-0.860692\pi$
$131$	−237.306			−1.81150			−0.905750	+	0.423812i	$0.860692\pi$
$132$	10.2619	+	10.2619i	0.0777414	+	0.0777414i
$133$	−61.1259	+	61.1259i	−0.459593	+	0.459593i
$134$		−	98.9479i		−	0.738417i
$135$		0			0
$136$	92.2488			0.678300
$137$	48.4157	+	48.4157i	0.353399	+	0.353399i	0.861373	−	0.507973i	$-0.169605\pi$
$137$	48.4157	+	48.4157i	0.353399	+	0.353399i	−0.507973	+	0.861373i	$0.669605\pi$
$138$	−33.0919	+	33.0919i	−0.239796	+	0.239796i
$139$			106.547i			0.766523i	0.923640	+	0.383262i	$0.125199\pi$
$139$			106.547i			0.766523i	−0.923640	+	0.383262i	$0.874801\pi$
$140$		0			0
$141$	−127.543			−0.904558
$142$	−94.0594	−	94.0594i	−0.662390	−	0.662390i
$143$	−54.4392	+	54.4392i	−0.380694	+	0.380694i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	−30.1541			−0.206535
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	−42.0393	+	42.0393i	−0.284049	+	0.284049i
$149$		−	30.2575i		−	0.203070i	−0.994832	−	0.101535i	$-0.967625\pi$
$149$		−	30.2575i		−	0.203070i	0.994832	−	0.101535i	$-0.0323755\pi$
$150$		0			0
$151$	181.315			1.20076			0.600379	−	0.799715i	$-0.295016\pi$
$151$	181.315			1.20076			0.600379	+	0.799715i	$0.295016\pi$
$152$	−65.3463	−	65.3463i	−0.429910	−	0.429910i
$153$	69.1866	−	69.1866i	0.452200	−	0.452200i
$154$			15.6753i			0.101787i
$155$		0			0
$156$	−63.6600			−0.408077
$157$	8.53019	+	8.53019i	0.0543324	+	0.0543324i	0.733751	−	0.679419i	$-0.237768\pi$
$157$	8.53019	+	8.53019i	0.0543324	+	0.0543324i	−0.679419	+	0.733751i	$0.737768\pi$
$158$	−112.890	+	112.890i	−0.714494	+	0.714494i
$159$			64.6145i			0.406381i
$160$		0			0
$161$	−50.5487			−0.313967
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−60.3100	+	60.3100i	−0.370000	+	0.370000i	−0.867477	−	0.497477i	$-0.834260\pi$
$163$	−60.3100	+	60.3100i	−0.370000	+	0.370000i	0.497477	+	0.867477i	$0.334260\pi$
$164$		−	103.956i		−	0.633881i
$165$		0			0
$166$	27.3333			0.164658
$167$	−131.125	−	131.125i	−0.785181	−	0.785181i	0.195519	−	0.980700i	$-0.437361\pi$
$167$	−131.125	−	131.125i	−0.785181	−	0.785181i	−0.980700	+	0.195519i	$0.937361\pi$
$168$	−9.16515	+	9.16515i	−0.0545545	+	0.0545545i
$169$		−	168.717i		−	0.998324i
$170$		0			0
$171$	−98.0195			−0.573213
$172$	49.5252	+	49.5252i	0.287937	+	0.287937i
$173$	78.0609	−	78.0609i	0.451219	−	0.451219i	−0.444540	−	0.895759i	$-0.646633\pi$
$173$	78.0609	−	78.0609i	0.451219	−	0.451219i	0.895759	+	0.444540i	$0.146633\pi$
$174$			57.0593i			0.327927i
$175$		0			0
$176$	−16.7576			−0.0952134
$177$	−126.279	−	126.279i	−0.713441	−	0.713441i
$178$	35.6390	−	35.6390i	0.200219	−	0.200219i
$179$			116.492i			0.650796i	0.945577	+	0.325398i	$0.105498\pi$
$179$			116.492i			0.650796i	−0.945577	+	0.325398i	$0.894502\pi$
$180$		0			0
$181$	256.478			1.41701			0.708503	−	0.705708i	$-0.249371\pi$
$181$	256.478			1.41701			0.708503	+	0.705708i	$0.249371\pi$
$182$	−48.6212	−	48.6212i	−0.267149	−	0.267149i
$183$	146.625	−	146.625i	0.801231	−	0.801231i
$184$		−	54.0388i		−	0.293689i
$185$		0			0
$186$	−79.0740			−0.425129
$187$	96.6165	+	96.6165i	0.516666	+	0.516666i
$188$	104.138	−	104.138i	0.553926	−	0.553926i
$189$			13.7477i			0.0727393i
$190$		0			0
$191$	−134.669			−0.705072			−0.352536	−	0.935798i	$-0.614681\pi$
$191$	−134.669			−0.705072			−0.352536	+	0.935798i	$0.614681\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	194.945	−	194.945i	1.01008	−	1.01008i	0.0101307	−	0.999949i	$-0.496775\pi$
$193$	194.945	−	194.945i	1.01008	−	1.01008i	0.999949	−	0.0101307i	$-0.00322475\pi$
$194$			144.309i			0.743861i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	69.6888	+	69.6888i	0.353750	+	0.353750i	0.861503	−	0.507753i	$-0.169524\pi$
$197$	69.6888	+	69.6888i	0.353750	+	0.353750i	−0.507753	+	0.861503i	$0.669524\pi$
$198$	−12.5682	+	12.5682i	−0.0634756	+	0.0634756i
$199$		−	346.988i		−	1.74366i	−0.489809	−	0.871830i	$-0.662934\pi$
$199$		−	346.988i		−	1.74366i	0.489809	−	0.871830i	$-0.337066\pi$
$200$		0			0
$201$	121.186			0.602915
$202$	−27.1945	−	27.1945i	−0.134626	−	0.134626i
$203$	−43.5798	+	43.5798i	−0.214679	+	0.214679i
$204$			112.981i			0.553830i
$205$		0			0
$206$	−84.3298			−0.409368
$207$	−40.5291	−	40.5291i	−0.195793	−	0.195793i
$208$	51.9782	−	51.9782i	0.249895	−	0.249895i
$209$		−	136.881i		−	0.654931i
$210$		0			0
$211$	−59.3269			−0.281170			−0.140585	−	0.990069i	$-0.544898\pi$
$211$	−59.3269			−0.281170			−0.140585	+	0.990069i	$0.544898\pi$
$212$	−52.7576	−	52.7576i	−0.248856	−	0.248856i
$213$	115.199	−	115.199i	0.540839	−	0.540839i
$214$			156.088i			0.729385i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−60.3938	−	60.3938i	−0.278312	−	0.278312i
$218$	−115.318	+	115.318i	−0.528981	+	0.528981i
$219$		−	36.9311i		−	0.168635i
$220$		0			0
$221$	−599.366			−2.71206
$222$	−51.4874	−	51.4874i	−0.231925	−	0.231925i
$223$	−12.0682	+	12.0682i	−0.0541173	+	0.0541173i	−0.733648	−	0.679530i	$-0.762184\pi$
$223$	−12.0682	+	12.0682i	−0.0541173	+	0.0541173i	0.679530	+	0.733648i	$0.262184\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−140.538			−0.621849
$227$	239.151	+	239.151i	1.05353	+	1.05353i	0.998484	+	0.0550464i	$0.0175307\pi$
$227$	239.151	+	239.151i	1.05353	+	1.05353i	0.0550464	+	0.998484i	$0.482469\pi$
$228$	80.0326	−	80.0326i	0.351020	−	0.351020i
$229$			85.4596i			0.373186i	0.982437	+	0.186593i	$0.0597446\pi$
$229$			85.4596i			0.373186i	−0.982437	+	0.186593i	$0.940255\pi$
$230$		0			0
$231$	−19.1982			−0.0831090
$232$	−46.5888	−	46.5888i	−0.200814	−	0.200814i
$233$	−72.0103	+	72.0103i	−0.309057	+	0.309057i	−0.844544	−	0.535487i	$-0.820128\pi$
$233$	−72.0103	+	72.0103i	−0.309057	+	0.309057i	0.535487	+	0.844544i	$0.320128\pi$
$234$		−	77.9673i		−	0.333194i
$235$		0			0
$236$	206.213			0.873783
$237$	−138.261	−	138.261i	−0.583382	−	0.583382i
$238$	−86.2909	+	86.2909i	−0.362567	+	0.362567i
$239$		−	260.366i		−	1.08940i	−0.838632	−	0.544699i	$-0.816644\pi$
$239$		−	260.366i		−	1.08940i	0.838632	−	0.544699i	$-0.183356\pi$
$240$		0			0
$241$	69.8087			0.289663			0.144831	−	0.989456i	$-0.453736\pi$
$241$	69.8087			0.289663			0.144831	+	0.989456i	$0.453736\pi$
$242$	103.449	+	103.449i	0.427475	+	0.427475i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			239.438i			0.981303i
$245$		0			0
$246$	127.320			0.517561
$247$	424.573	+	424.573i	1.71892	+	1.71892i
$248$	64.5637	−	64.5637i	0.260337	−	0.260337i
$249$			33.4763i			0.134443i
$250$		0			0
$251$	−39.4536			−0.157186			−0.0785928	−	0.996907i	$-0.525043\pi$
$251$	−39.4536			−0.157186			−0.0785928	+	0.996907i	$0.525043\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	56.5974	−	56.5974i	0.223705	−	0.223705i
$254$			30.8126i			0.121309i
$255$		0			0
$256$	16.0000			0.0625000
$257$	43.4383	+	43.4383i	0.169021	+	0.169021i	0.786549	−	0.617528i	$-0.211866\pi$
$257$	43.4383	+	43.4383i	0.169021	+	0.169021i	−0.617528	+	0.786549i	$0.711866\pi$
$258$	−60.6557	+	60.6557i	−0.235100	+	0.235100i
$259$		−	78.6483i		−	0.303661i
$260$		0			0
$261$	−69.8831			−0.267752
$262$	237.306	+	237.306i	0.905750	+	0.905750i
$263$	186.173	−	186.173i	0.707881	−	0.707881i	−0.258208	−	0.966089i	$-0.583132\pi$
$263$	186.173	−	186.173i	0.707881	−	0.707881i	0.966089	+	0.258208i	$0.0831321\pi$
$264$		−	20.5237i		−	0.0777414i
$265$		0			0
$266$	122.252			0.459593
$267$	43.6487	+	43.6487i	0.163478	+	0.163478i
$268$	−98.9479	+	98.9479i	−0.369209	+	0.369209i
$269$			166.391i			0.618555i	0.950972	+	0.309278i	$0.100087\pi$
$269$			166.391i			0.618555i	−0.950972	+	0.309278i	$0.899913\pi$
$270$		0			0
$271$	335.279			1.23719			0.618597	−	0.785709i	$-0.287702\pi$
$271$	335.279			1.23719			0.618597	+	0.785709i	$0.287702\pi$
$272$	−92.2488	−	92.2488i	−0.339150	−	0.339150i
$273$	59.5485	−	59.5485i	0.218126	−	0.218126i
$274$		−	96.8314i		−	0.353399i
$275$		0			0
$276$	66.1838			0.239796
$277$	233.563	+	233.563i	0.843188	+	0.843188i	0.989272	−	0.146084i	$-0.0466670\pi$
$277$	233.563	+	233.563i	0.843188	+	0.843188i	−0.146084	+	0.989272i	$0.546667\pi$
$278$	106.547	−	106.547i	0.383262	−	0.383262i
$279$		−	96.8455i		−	0.347116i
$280$		0			0
$281$	−333.559			−1.18704			−0.593522	−	0.804818i	$-0.702263\pi$
$281$	−333.559			−1.18704			−0.593522	+	0.804818i	$0.702263\pi$
$282$	127.543	+	127.543i	0.452279	+	0.452279i
$283$	−298.203	+	298.203i	−1.05372	+	1.05372i	−0.0552481	+	0.998473i	$0.517595\pi$
$283$	−298.203	+	298.203i	−1.05372	+	1.05372i	−0.998473	+	0.0552481i	$0.982405\pi$
$284$			188.119i			0.662390i
$285$		0			0
$286$	108.878			0.380694
$287$	97.2423	+	97.2423i	0.338823	+	0.338823i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			774.730i			2.68073i
$290$		0			0
$291$	−176.742			−0.607360
$292$	30.1541	+	30.1541i	0.103268	+	0.103268i
$293$	−27.0786	+	27.0786i	−0.0924186	+	0.0924186i	−0.751805	−	0.659386i	$-0.770816\pi$
$293$	−27.0786	+	27.0786i	−0.0924186	+	0.0924186i	0.659386	+	0.751805i	$0.270816\pi$
$294$		−	17.1464i		−	0.0583212i
$295$		0			0
$296$	84.0786			0.284049
$297$	−15.3928	−	15.3928i	−0.0518276	−	0.0518276i
$298$	−30.2575	+	30.2575i	−0.101535	+	0.101535i
$299$			351.105i			1.17426i
$300$		0			0
$301$	−92.6532			−0.307818
$302$	−181.315	−	181.315i	−0.600379	−	0.600379i
$303$	33.3064	−	33.3064i	0.109922	−	0.109922i
$304$			130.693i			0.429910i
$305$		0			0
$306$	−138.373			−0.452200
$307$	−51.6680	−	51.6680i	−0.168300	−	0.168300i	0.617932	−	0.786232i	$-0.287971\pi$
$307$	−51.6680	−	51.6680i	−0.168300	−	0.168300i	−0.786232	+	0.617932i	$0.787971\pi$
$308$	15.6753	−	15.6753i	0.0508937	−	0.0508937i
$309$		−	103.282i		−	0.334247i
$310$		0			0
$311$	190.936			0.613942			0.306971	−	0.951719i	$-0.400685\pi$
$311$	190.936			0.613942			0.306971	+	0.951719i	$0.400685\pi$
$312$	63.6600	+	63.6600i	0.204039	+	0.204039i
$313$	−417.438	+	417.438i	−1.33367	+	1.33367i	−0.431602	+	0.902064i	$0.642052\pi$
$313$	−417.438	+	417.438i	−1.33367	+	1.33367i	−0.902064	+	0.431602i	$0.857948\pi$
$314$		−	17.0604i		−	0.0543324i
$315$		0			0
$316$	225.780			0.714494
$317$	−91.5155	−	91.5155i	−0.288692	−	0.288692i	0.547871	−	0.836563i	$-0.315439\pi$
$317$	−91.5155	−	91.5155i	−0.288692	−	0.288692i	−0.836563	+	0.547871i	$0.815439\pi$
$318$	64.6145	−	64.6145i	0.203190	−	0.203190i
$319$		−	97.5892i		−	0.305922i
$320$		0			0
$321$	−191.169			−0.595541
$322$	50.5487	+	50.5487i	0.156984	+	0.156984i
$323$	753.515	−	753.515i	2.33286	−	2.33286i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	120.620			0.370000
$327$	−141.235	−	141.235i	−0.431911	−	0.431911i
$328$	−103.956	+	103.956i	−0.316940	+	0.316940i
$329$			194.825i			0.592172i
$330$		0			0
$331$	172.125			0.520016			0.260008	−	0.965606i	$-0.416275\pi$
$331$	172.125			0.520016			0.260008	+	0.965606i	$0.416275\pi$
$332$	−27.3333	−	27.3333i	−0.0823291	−	0.0823291i
$333$	63.0589	−	63.0589i	0.189366	−	0.189366i
$334$			262.251i			0.785181i
$335$		0			0
$336$	18.3303			0.0545545
$337$	283.042	+	283.042i	0.839888	+	0.839888i	0.988844	−	0.148956i	$-0.0475912\pi$
$337$	283.042	+	283.042i	0.839888	+	0.839888i	−0.148956	+	0.988844i	$0.547591\pi$
$338$	−168.717	+	168.717i	−0.499162	+	0.499162i
$339$		−	172.123i		−	0.507738i
$340$		0			0
$341$	135.241			0.396601
$342$	98.0195	+	98.0195i	0.286607	+	0.286607i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	99.0504i		−	0.287937i
$345$		0			0
$346$	−156.122			−0.451219
$347$	379.546	+	379.546i	1.09379	+	1.09379i	0.995120	+	0.0986739i	$0.0314601\pi$
$347$	379.546	+	379.546i	1.09379	+	1.09379i	0.0986739	+	0.995120i	$0.468540\pi$
$348$	57.0593	−	57.0593i	0.163964	−	0.163964i
$349$		−	112.412i		−	0.322097i	−0.986947	−	0.161048i	$-0.948513\pi$
$349$		−	112.412i		−	0.322097i	0.986947	−	0.161048i	$-0.0514875\pi$
$350$		0			0
$351$	95.4901			0.272051
$352$	16.7576	+	16.7576i	0.0476067	+	0.0476067i
$353$	125.437	−	125.437i	0.355346	−	0.355346i	−0.506748	−	0.862094i	$-0.669153\pi$
$353$	125.437	−	125.437i	0.355346	−	0.355346i	0.862094	+	0.506748i	$0.169153\pi$
$354$			252.558i			0.713441i
$355$		0			0
$356$	−71.2780			−0.200219
$357$	−105.684	−	105.684i	−0.296034	−	0.296034i
$358$	116.492	−	116.492i	0.325398	−	0.325398i
$359$			427.225i			1.19004i	0.803710	+	0.595021i	$0.202856\pi$
$359$			427.225i			1.19004i	−0.803710	+	0.595021i	$0.797144\pi$
$360$		0			0
$361$	−706.535			−1.95716
$362$	−256.478	−	256.478i	−0.708503	−	0.708503i
$363$	−126.699	+	126.699i	−0.349032	+	0.349032i
$364$			97.2423i			0.267149i
$365$		0			0
$366$	−293.250			−0.801231
$367$	311.079	+	311.079i	0.847627	+	0.847627i	0.989837	−	0.142210i	$-0.0454207\pi$
$367$	311.079	+	311.079i	0.847627	+	0.847627i	−0.142210	+	0.989837i	$0.545421\pi$
$368$	−54.0388	+	54.0388i	−0.146845	+	0.146845i
$369$			155.935i			0.422587i
$370$		0			0
$371$	98.7003			0.266039
$372$	79.0740	+	79.0740i	0.212565	+	0.212565i
$373$	176.246	−	176.246i	0.472508	−	0.472508i	−0.430217	−	0.902725i	$-0.641563\pi$
$373$	176.246	−	176.246i	0.472508	−	0.472508i	0.902725	+	0.430217i	$0.141563\pi$
$374$		−	193.233i		−	0.516666i
$375$		0			0
$376$	−208.276			−0.553926
$377$	302.700	+	302.700i	0.802918	+	0.802918i
$378$	13.7477	−	13.7477i	0.0363696	−	0.0363696i
$379$		−	486.127i		−	1.28266i	−0.767266	−	0.641329i	$-0.778383\pi$
$379$		−	486.127i		−	1.28266i	0.767266	−	0.641329i	$-0.221617\pi$
$380$		0			0
$381$	−37.7376			−0.0990488
$382$	134.669	+	134.669i	0.352536	+	0.352536i
$383$	−78.0432	+	78.0432i	−0.203768	+	0.203768i	−0.801612	−	0.597844i	$-0.796024\pi$
$383$	−78.0432	+	78.0432i	−0.203768	+	0.203768i	0.597844	+	0.801612i	$0.296024\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−389.891			−1.01008
$387$	−74.2878	−	74.2878i	−0.191958	−	0.191958i
$388$	144.309	−	144.309i	0.371930	−	0.371930i
$389$			283.465i			0.728702i	0.931262	+	0.364351i	$0.118709\pi$
$389$			283.465i			0.728702i	−0.931262	+	0.364351i	$0.881291\pi$
$390$		0			0
$391$	623.127			1.59368
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	−290.640	+	290.640i	−0.739542	+	0.739542i
$394$		−	139.378i		−	0.353750i
$395$		0			0
$396$	25.1363			0.0634756
$397$	242.573	+	242.573i	0.611015	+	0.611015i	0.943210	−	0.332196i	$-0.107789\pi$
$397$	242.573	+	242.573i	0.611015	+	0.611015i	−0.332196	+	0.943210i	$0.607789\pi$
$398$	−346.988	+	346.988i	−0.871830	+	0.871830i
$399$			149.727i			0.375256i
$400$		0			0
$401$	263.635			0.657445			0.328723	−	0.944427i	$-0.393382\pi$
$401$	263.635			0.657445			0.328723	+	0.944427i	$0.393382\pi$
$402$	−121.186	−	121.186i	−0.301458	−	0.301458i
$403$	−419.488	+	419.488i	−1.04091	+	1.04091i
$404$			54.3890i			0.134626i
$405$		0			0
$406$	87.1596			0.214679
$407$	88.0594	+	88.0594i	0.216362	+	0.216362i
$408$	112.981	−	112.981i	0.276915	−	0.276915i
$409$		−	202.287i		−	0.494590i	−0.968940	−	0.247295i	$-0.920458\pi$
$409$		−	202.287i		−	0.494590i	0.968940	−	0.247295i	$-0.0795417\pi$
$410$		0			0
$411$	118.594			0.288549
$412$	84.3298	+	84.3298i	0.204684	+	0.204684i
$413$	−192.894	+	192.894i	−0.467057	+	0.467057i
$414$			81.0582i			0.195793i
$415$		0			0
$416$	−103.956			−0.249895
$417$	130.493	+	130.493i	0.312932	+	0.312932i
$418$	−136.881	+	136.881i	−0.327465	+	0.327465i
$419$			498.267i			1.18918i	0.804029	+	0.594591i	$0.202686\pi$
$419$			498.267i			1.18918i	−0.804029	+	0.594591i	$0.797314\pi$
$420$		0			0
$421$	662.760			1.57425			0.787126	−	0.616793i	$-0.211568\pi$
$421$	662.760			1.57425			0.787126	+	0.616793i	$0.211568\pi$
$422$	59.3269	+	59.3269i	0.140585	+	0.140585i
$423$	−156.207	+	156.207i	−0.369284	+	0.369284i
$424$			105.515i			0.248856i
$425$		0			0
$426$	−230.398			−0.540839
$427$	−223.974	−	223.974i	−0.524528	−	0.524528i
$428$	156.088	−	156.088i	0.364693	−	0.364693i
$429$			133.348i			0.310835i
$430$		0			0
$431$	73.7144			0.171031			0.0855155	−	0.996337i	$-0.472746\pi$
$431$	73.7144			0.171031			0.0855155	+	0.996337i	$0.472746\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	254.779	−	254.779i	0.588405	−	0.588405i	−0.348794	−	0.937199i	$-0.613409\pi$
$433$	254.779	−	254.779i	0.588405	−	0.588405i	0.937199	+	0.348794i	$0.113409\pi$
$434$			120.788i			0.278312i
$435$		0			0
$436$	230.636			0.528981
$437$	−441.405	−	441.405i	−1.01008	−	1.01008i
$438$	−36.9311	+	36.9311i	−0.0843176	+	0.0843176i
$439$			596.437i			1.35863i	0.733848	+	0.679314i	$0.237722\pi$
$439$			596.437i			1.35863i	−0.733848	+	0.679314i	$0.762278\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	599.366	+	599.366i	1.35603	+	1.35603i
$443$	−169.240	+	169.240i	−0.382031	+	0.382031i	−0.871833	−	0.489802i	$-0.837069\pi$
$443$	−169.240	+	169.240i	−0.382031	+	0.382031i	0.489802	+	0.871833i	$0.337069\pi$
$444$			102.975i			0.231925i
$445$		0			0
$446$	24.1363			0.0541173
$447$	−37.0577	−	37.0577i	−0.0829032	−	0.0829032i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$			286.986i			0.639167i	0.947558	+	0.319583i	$0.103543\pi$
$449$			286.986i			0.639167i	−0.947558	+	0.319583i	$0.896457\pi$
$450$		0			0
$451$	−217.757			−0.482831
$452$	140.538	+	140.538i	0.310925	+	0.310925i
$453$	222.064	−	222.064i	0.490208	−	0.490208i
$454$		−	478.303i		−	1.05353i
$455$		0			0
$456$	−160.065			−0.351020
$457$	−546.344	−	546.344i	−1.19550	−	1.19550i	−0.975500	−	0.220001i	$-0.929394\pi$
$457$	−546.344	−	546.344i	−1.19550	−	1.19550i	−0.220001	−	0.975500i	$-0.570606\pi$
$458$	85.4596	−	85.4596i	0.186593	−	0.186593i
$459$		−	169.472i		−	0.369220i
$460$		0			0
$461$	−208.632			−0.452565			−0.226282	−	0.974062i	$-0.572657\pi$
$461$	−208.632			−0.452565			−0.226282	+	0.974062i	$0.572657\pi$
$462$	19.1982	+	19.1982i	0.0415545	+	0.0415545i
$463$	−140.594	+	140.594i	−0.303659	+	0.303659i	−0.842443	−	0.538785i	$-0.818884\pi$
$463$	−140.594	+	140.594i	−0.303659	+	0.303659i	0.538785	+	0.842443i	$0.318884\pi$
$464$			93.1775i			0.200814i
$465$		0			0
$466$	144.021			0.309057
$467$	0.0661206	+	0.0661206i	0.000141586	+	0.000141586i	0.707178	−	0.707036i	$-0.249968\pi$
$467$	0.0661206	+	0.0661206i	0.000141586	+	0.000141586i	−0.707036	+	0.707178i	$0.749968\pi$
$468$	−77.9673	+	77.9673i	−0.166597	+	0.166597i
$469$		−	185.115i		−	0.394701i
$470$		0			0
$471$	20.8946			0.0443622
$472$	−206.213	−	206.213i	−0.436892	−	0.436892i
$473$	103.740	−	103.740i	0.219324	−	0.219324i
$474$			276.523i			0.583382i
$475$		0			0
$476$	172.582			0.362567
$477$	79.1363	+	79.1363i	0.165904	+	0.165904i
$478$	−260.366	+	260.366i	−0.544699	+	0.544699i
$479$		−	539.039i		−	1.12534i	−0.826681	−	0.562672i	$-0.809774\pi$
$479$		−	539.039i		−	1.12534i	0.826681	−	0.562672i	$-0.190226\pi$
$480$		0			0
$481$	−546.282			−1.13572
$482$	−69.8087	−	69.8087i	−0.144831	−	0.144831i
$483$	−61.9093	+	61.9093i	−0.128177	+	0.128177i
$484$		−	206.898i		−	0.427475i
$485$		0			0
$486$	22.0454			0.0453609
$487$	−61.8493	−	61.8493i	−0.127001	−	0.127001i	0.640749	−	0.767750i	$-0.278624\pi$
$487$	−61.8493	−	61.8493i	−0.127001	−	0.127001i	−0.767750	+	0.640749i	$0.778624\pi$
$488$	239.438	−	239.438i	0.490651	−	0.490651i
$489$			147.729i			0.302104i
$490$		0			0
$491$	191.070			0.389145			0.194573	−	0.980888i	$-0.437668\pi$
$491$	191.070			0.389145			0.194573	+	0.980888i	$0.437668\pi$
$492$	−127.320	−	127.320i	−0.258781	−	0.258781i
$493$	537.220	−	537.220i	1.08970	−	1.08970i
$494$		−	849.146i		−	1.71892i
$495$		0			0
$496$	−129.127			−0.260337
$497$	−175.969	−	175.969i	−0.354063	−	0.354063i
$498$	33.4763	−	33.4763i	0.0672214	−	0.0672214i
$499$		−	190.849i		−	0.382463i	−0.981545	−	0.191232i	$-0.938752\pi$
$499$		−	190.849i		−	0.382463i	0.981545	−	0.191232i	$-0.0612481\pi$
$500$		0			0
$501$	−321.190			−0.641098
$502$	39.4536	+	39.4536i	0.0785928	+	0.0785928i
$503$	−527.972	+	527.972i	−1.04965	+	1.04965i	−0.0509448	+	0.998701i	$0.516223\pi$
$503$	−527.972	+	527.972i	−1.04965	+	1.04965i	−0.998701	+	0.0509448i	$0.983777\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	−113.195			−0.223705
$507$	−206.635	−	206.635i	−0.407564	−	0.407564i
$508$	30.8126	−	30.8126i	0.0606547	−	0.0606547i
$509$			861.064i			1.69168i	0.533438	+	0.845839i	$0.320900\pi$
$509$			861.064i			1.69168i	−0.533438	+	0.845839i	$0.679100\pi$
$510$		0			0
$511$	−56.4132			−0.110398
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−120.049	+	120.049i	−0.234013	+	0.234013i
$514$		−	86.8766i		−	0.169021i
$515$		0			0
$516$	121.311			0.235100
$517$	−218.137	−	218.137i	−0.421929	−	0.421929i
$518$	−78.6483	+	78.6483i	−0.151831	+	0.151831i
$519$		−	191.209i		−	0.368419i
$520$		0			0
$521$	−550.681			−1.05697			−0.528485	−	0.848943i	$-0.677240\pi$
$521$	−550.681			−1.05697			−0.528485	+	0.848943i	$0.677240\pi$
$522$	69.8831	+	69.8831i	0.133876	+	0.133876i
$523$	−493.771	+	493.771i	−0.944112	+	0.944112i	−0.998519	−	0.0544065i	$-0.982673\pi$
$523$	−493.771	+	493.771i	−0.944112	+	0.944112i	0.0544065	+	0.998519i	$0.482673\pi$
$524$		−	474.613i		−	0.905750i
$525$		0			0
$526$	−372.345			−0.707881
$527$	744.490	+	744.490i	1.41269	+	1.41269i
$528$	−20.5237	+	20.5237i	−0.0388707	+	0.0388707i
$529$			163.976i			0.309973i
$530$		0			0
$531$	−309.319			−0.582522
$532$	−122.252	−	122.252i	−0.229797	−	0.229797i
$533$	675.434	−	675.434i	1.26723	−	1.26723i
$534$		−	87.2974i		−	0.163478i
$535$		0			0
$536$	197.896			0.369209
$537$	142.673	+	142.673i	0.265686	+	0.265686i
$538$	166.391	−	166.391i	0.309278	−	0.309278i
$539$			29.3257i			0.0544076i
$540$		0			0
$541$	278.337			0.514486			0.257243	−	0.966347i	$-0.417186\pi$
$541$	278.337			0.514486			0.257243	+	0.966347i	$0.417186\pi$
$542$	−335.279	−	335.279i	−0.618597	−	0.618597i
$543$	314.120	−	314.120i	0.578490	−	0.578490i
$544$			184.498i			0.339150i
$545$		0			0
$546$	−119.097			−0.218126
$547$	111.170	+	111.170i	0.203236	+	0.203236i	0.801385	−	0.598149i	$-0.204097\pi$
$547$	111.170	+	111.170i	0.203236	+	0.203236i	−0.598149	+	0.801385i	$0.704097\pi$
$548$	−96.8314	+	96.8314i	−0.176700	+	0.176700i
$549$		−	359.157i		−	0.654202i
$550$		0			0
$551$	−761.101			−1.38131
$552$	−66.1838	−	66.1838i	−0.119898	−	0.119898i
$553$	−211.198	+	211.198i	−0.381913	+	0.381913i
$554$		−	467.126i		−	0.843188i
$555$		0			0
$556$	−213.093			−0.383262
$557$	−159.846	−	159.846i	−0.286977	−	0.286977i	0.548907	−	0.835884i	$-0.315044\pi$
$557$	−159.846	−	159.846i	−0.286977	−	0.286977i	−0.835884	+	0.548907i	$0.815044\pi$
$558$	−96.8455	+	96.8455i	−0.173558	+	0.173558i
$559$			643.558i			1.15127i
$560$		0			0
$561$	236.661			0.421856
$562$	333.559	+	333.559i	0.593522	+	0.593522i
$563$	39.8174	−	39.8174i	0.0707237	−	0.0707237i	−0.670860	−	0.741584i	$-0.734075\pi$
$563$	39.8174	−	39.8174i	0.0707237	−	0.0707237i	0.741584	+	0.670860i	$0.234075\pi$
$564$		−	255.085i		−	0.452279i
$565$		0			0
$566$	596.406			1.05372
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	188.119	−	188.119i	0.331195	−	0.331195i
$569$		−	166.511i		−	0.292638i	−0.989237	−	0.146319i	$-0.953257\pi$
$569$		−	166.511i		−	0.292638i	0.989237	−	0.146319i	$-0.0467426\pi$
$570$		0			0
$571$	602.196			1.05463			0.527317	−	0.849668i	$-0.323198\pi$
$571$	602.196			1.05463			0.527317	+	0.849668i	$0.323198\pi$
$572$	−108.878	−	108.878i	−0.190347	−	0.190347i
$573$	−164.935	+	164.935i	−0.287844	+	0.287844i
$574$		−	194.485i		−	0.338823i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	644.862	+	644.862i	1.11761	+	1.11761i	0.992091	+	0.125521i	$0.0400602\pi$
$577$	644.862	+	644.862i	1.11761	+	1.11761i	0.125521	+	0.992091i	$0.459940\pi$
$578$	774.730	−	774.730i	1.34036	−	1.34036i
$579$		−	477.517i		−	0.824726i
$580$		0			0
$581$	51.1359			0.0880135
$582$	176.742	+	176.742i	0.303680	+	0.303680i
$583$	−110.511	+	110.511i	−0.189556	+	0.189556i
$584$		−	60.3083i		−	0.103268i
$585$		0			0
$586$	54.1573			0.0924186
$587$	−666.493	−	666.493i	−1.13542	−	1.13542i	−0.989261	−	0.146162i	$-0.953308\pi$
$587$	−666.493	−	666.493i	−1.13542	−	1.13542i	−0.146162	−	0.989261i	$-0.546692\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$		−	1054.75i		−	1.79075i
$590$		0			0
$591$	170.702			0.288836
$592$	−84.0786	−	84.0786i	−0.142025	−	0.142025i
$593$	−526.020	+	526.020i	−0.887049	+	0.887049i	−0.994239	−	0.107190i	$-0.965815\pi$
$593$	−526.020	+	526.020i	−0.887049	+	0.887049i	0.107190	+	0.994239i	$0.465815\pi$
$594$			30.7856i			0.0518276i
$595$		0			0
$596$	60.5150			0.101535
$597$	−424.972	−	424.972i	−0.711846	−	0.711846i
$598$	351.105	−	351.105i	0.587132	−	0.587132i
$599$			637.374i			1.06406i	0.846724	+	0.532032i	$0.178571\pi$
$599$			637.374i			1.06406i	−0.846724	+	0.532032i	$0.821429\pi$
$600$		0			0
$601$	203.010			0.337786			0.168893	−	0.985634i	$-0.445981\pi$
$601$	203.010			0.337786			0.168893	+	0.985634i	$0.445981\pi$
$602$	92.6532	+	92.6532i	0.153909	+	0.153909i
$603$	148.422	−	148.422i	0.246139	−	0.246139i
$604$			362.629i			0.600379i
$605$		0			0
$606$	−66.6127			−0.109922
$607$	−347.828	−	347.828i	−0.573028	−	0.573028i	0.359945	−	0.932973i	$-0.382795\pi$
$607$	−347.828	−	347.828i	−0.573028	−	0.573028i	−0.932973	+	0.359945i	$0.882795\pi$
$608$	130.693	−	130.693i	0.214955	−	0.214955i
$609$			106.748i			0.175285i
$610$		0			0
$611$	1353.23			2.21478
$612$	138.373	+	138.373i	0.226100	+	0.226100i
$613$	216.062	−	216.062i	0.352467	−	0.352467i	−0.508560	−	0.861027i	$-0.669822\pi$
$613$	216.062	−	216.062i	0.352467	−	0.352467i	0.861027	+	0.508560i	$0.169822\pi$
$614$			103.336i			0.168300i
$615$		0			0
$616$	−31.3505			−0.0508937
$617$	−432.131	−	432.131i	−0.700375	−	0.700375i	0.264116	−	0.964491i	$-0.414920\pi$
$617$	−432.131	−	432.131i	−0.700375	−	0.700375i	−0.964491	+	0.264116i	$0.914920\pi$
$618$	−103.282	+	103.282i	−0.167124	+	0.167124i
$619$		−	134.611i		−	0.217465i	−0.994071	−	0.108732i	$-0.965321\pi$
$619$		−	134.611i		−	0.217465i	0.994071	−	0.108732i	$-0.0346792\pi$
$620$		0			0
$621$	−99.2757			−0.159864
$622$	−190.936	−	190.936i	−0.306971	−	0.306971i
$623$	66.6745	−	66.6745i	0.107022	−	0.107022i
$624$		−	127.320i		−	0.204039i
$625$		0			0
$626$	834.875			1.33367
$627$	−167.644	−	167.644i	−0.267374	−	0.267374i
$628$	−17.0604	+	17.0604i	−0.0271662	+	0.0271662i
$629$			969.518i			1.54136i
$630$		0			0
$631$	−911.796			−1.44500			−0.722500	−	0.691370i	$-0.757007\pi$
$631$	−911.796			−1.44500			−0.722500	+	0.691370i	$0.757007\pi$
$632$	−225.780	−	225.780i	−0.357247	−	0.357247i
$633$	−72.6603	+	72.6603i	−0.114787	+	0.114787i
$634$			183.031i			0.288692i
$635$		0			0
$636$	−129.229			−0.203190
$637$	−90.9619	−	90.9619i	−0.142797	−	0.142797i
$638$	−97.5892	+	97.5892i	−0.152961	+	0.152961i
$639$		−	282.178i		−	0.441594i
$640$		0			0
$641$	277.395			0.432754			0.216377	−	0.976310i	$-0.430576\pi$
$641$	277.395			0.432754			0.216377	+	0.976310i	$0.430576\pi$
$642$	191.169	+	191.169i	0.297770	+	0.297770i
$643$	−303.972	+	303.972i	−0.472741	+	0.472741i	−0.902800	−	0.430060i	$-0.858492\pi$
$643$	−303.972	+	303.972i	−0.472741	+	0.472741i	0.430060	+	0.902800i	$0.358492\pi$
$644$		−	101.097i		−	0.156984i
$645$		0			0
$646$	−1507.03			−2.33286
$647$	88.7310	+	88.7310i	0.137142	+	0.137142i	0.772345	−	0.635203i	$-0.219084\pi$
$647$	88.7310	+	88.7310i	0.137142	+	0.137142i	−0.635203	+	0.772345i	$0.719084\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	431.953i		−	0.665567i
$650$		0			0
$651$	−147.934			−0.227241
$652$	−120.620	−	120.620i	−0.185000	−	0.185000i
$653$	370.166	−	370.166i	0.566869	−	0.566869i	−0.364381	−	0.931250i	$-0.618719\pi$
$653$	370.166	−	370.166i	0.566869	−	0.566869i	0.931250	+	0.364381i	$0.118719\pi$
$654$			282.470i			0.431911i
$655$		0			0
$656$	207.913			0.316940
$657$	−45.2312	−	45.2312i	−0.0688451	−	0.0688451i
$658$	194.825	−	194.825i	0.296086	−	0.296086i
$659$		−	89.6092i		−	0.135978i	−0.997686	−	0.0679888i	$-0.978342\pi$
$659$		−	89.6092i		−	0.135978i	0.997686	−	0.0679888i	$-0.0216582\pi$
$660$		0			0
$661$	−179.575			−0.271671			−0.135836	−	0.990731i	$-0.543372\pi$
$661$	−179.575			−0.271671			−0.135836	+	0.990731i	$0.543372\pi$
$662$	−172.125	−	172.125i	−0.260008	−	0.260008i
$663$	−734.070	+	734.070i	−1.10720	+	1.10720i
$664$			54.6665i			0.0823291i
$665$		0			0
$666$	−126.118			−0.189366
$667$	−314.700	−	314.700i	−0.471814	−	0.471814i
$668$	262.251	−	262.251i	0.392591	−	0.392591i
$669$			29.5608i			0.0441866i
$670$		0			0
$671$	501.549			0.747465
$672$	−18.3303	−	18.3303i	−0.0272772	−	0.0272772i
$673$	875.881	−	875.881i	1.30146	−	1.30146i	0.374049	−	0.927409i	$-0.377969\pi$
$673$	875.881	−	875.881i	1.30146	−	1.30146i	0.927409	−	0.374049i	$-0.122031\pi$
$674$		−	566.085i		−	0.839888i
$675$		0			0
$676$	337.434			0.499162
$677$	−893.879	−	893.879i	−1.32035	−	1.32035i	−0.913488	−	0.406865i	$-0.866622\pi$
$677$	−893.879	−	893.879i	−1.32035	−	1.32035i	−0.406865	−	0.913488i	$-0.633378\pi$
$678$	−172.123	+	172.123i	−0.253869	+	0.253869i
$679$			269.977i			0.397610i
$680$		0			0
$681$	585.799			0.860204
$682$	−135.241	−	135.241i	−0.198301	−	0.198301i
$683$	25.2004	−	25.2004i	0.0368966	−	0.0368966i	−0.688418	−	0.725314i	$-0.741694\pi$
$683$	25.2004	−	25.2004i	0.0368966	−	0.0368966i	0.725314	+	0.688418i	$0.241694\pi$
$684$		−	196.039i		−	0.286607i
$685$		0			0
$686$	−26.1916			−0.0381802
$687$	104.666	+	104.666i	0.152353	+	0.152353i
$688$	−99.0504	+	99.0504i	−0.143969	+	0.143969i
$689$		−	685.561i		−	0.995008i
$690$		0			0
$691$	301.682			0.436588			0.218294	−	0.975883i	$-0.429951\pi$
$691$	301.682			0.436588			0.218294	+	0.975883i	$0.429951\pi$
$692$	156.122	+	156.122i	0.225610	+	0.225610i
$693$	−23.5129	+	23.5129i	−0.0339291	+	0.0339291i
$694$		−	759.093i		−	1.09379i
$695$		0			0
$696$	−114.119			−0.163964
$697$	−1198.73	−	1198.73i	−1.71985	−	1.71985i
$698$	−112.412	+	112.412i	−0.161048	+	0.161048i
$699$			176.389i			0.252344i
$700$		0			0
$701$	−1292.71			−1.84409			−0.922045	−	0.387084i	$-0.873483\pi$
$701$	−1292.71			−1.84409			−0.922045	+	0.387084i	$0.873483\pi$
$702$	−95.4901	−	95.4901i	−0.136026	−	0.136026i
$703$	686.778	−	686.778i	0.976925	−	0.976925i
$704$		−	33.5151i		−	0.0476067i
$705$		0			0
$706$	−250.874			−0.355346
$707$	−50.8763	−	50.8763i	−0.0719608	−	0.0719608i
$708$	252.558	−	252.558i	0.356720	−	0.356720i
$709$			137.796i			0.194353i	0.995267	+	0.0971764i	$0.0309811\pi$
$709$			137.796i			0.194353i	−0.995267	+	0.0971764i	$0.969019\pi$
$710$		0			0
$711$	−338.670			−0.476329
$712$	71.2780	+	71.2780i	0.100110	+	0.100110i
$713$	436.118	−	436.118i	0.611666	−	0.611666i
$714$			211.369i			0.296034i
$715$		0			0
$716$	−232.985			−0.325398
$717$	−318.882	−	318.882i	−0.444745	−	0.444745i
$718$	427.225	−	427.225i	0.595021	−	0.595021i
$719$		−	848.625i		−	1.18028i	−0.807299	−	0.590142i	$-0.799072\pi$
$719$		−	848.625i		−	1.18028i	0.807299	−	0.590142i	$-0.200928\pi$
$720$		0			0
$721$	−157.767			−0.218816
$722$	706.535	+	706.535i	0.978581	+	0.978581i
$723$	85.4978	−	85.4978i	0.118254	−	0.118254i
$724$			512.956i			0.708503i
$725$		0			0
$726$	253.397			0.349032
$727$	−140.883	−	140.883i	−0.193786	−	0.193786i	0.603544	−	0.797330i	$-0.293755\pi$
$727$	−140.883	−	140.883i	−0.193786	−	0.193786i	−0.797330	+	0.603544i	$0.793755\pi$
$728$	97.2423	−	97.2423i	0.133575	−	0.133575i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	1142.16			1.56246
$732$	293.250	+	293.250i	0.400615	+	0.400615i
$733$	−527.284	+	527.284i	−0.719351	+	0.719351i	−0.968472	−	0.249122i	$-0.919858\pi$
$733$	−527.284	+	527.284i	−0.719351	+	0.719351i	0.249122	+	0.968472i	$0.419858\pi$
$734$		−	622.158i		−	0.847627i
$735$		0			0
$736$	108.078			0.146845
$737$	207.266	+	207.266i	0.281229	+	0.281229i
$738$	155.935	−	155.935i	0.211294	−	0.211294i
$739$		−	546.536i		−	0.739562i	−0.929119	−	0.369781i	$-0.879433\pi$
$739$		−	546.536i		−	0.739562i	0.929119	−	0.369781i	$-0.120567\pi$
$740$		0			0
$741$	1039.99			1.40349
$742$	−98.7003	−	98.7003i	−0.133019	−	0.133019i
$743$	−369.606	+	369.606i	−0.497451	+	0.497451i	−0.910644	−	0.413192i	$-0.864414\pi$
$743$	−369.606	+	369.606i	−0.497451	+	0.497451i	0.413192	+	0.910644i	$0.364414\pi$
$744$		−	158.148i		−	0.212565i
$745$		0			0
$746$	−352.491			−0.472508
$747$	40.9999	+	40.9999i	0.0548861	+	0.0548861i
$748$	−193.233	+	193.233i	−0.258333	+	0.258333i
$749$			292.015i			0.389873i
$750$		0			0
$751$	300.340			0.399920			0.199960	−	0.979804i	$-0.435919\pi$
$751$	300.340			0.399920			0.199960	+	0.979804i	$0.435919\pi$
$752$	208.276	+	208.276i	0.276963	+	0.276963i
$753$	−48.3206	+	48.3206i	−0.0641708	+	0.0641708i
$754$		−	605.400i		−	0.802918i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	−873.112	−	873.112i	−1.15338	−	1.15338i	−0.985870	−	0.167515i	$-0.946426\pi$
$757$	−873.112	−	873.112i	−1.15338	−	1.15338i	−0.167515	−	0.985870i	$-0.553574\pi$
$758$	−486.127	+	486.127i	−0.641329	+	0.641329i
$759$		−	138.635i		−	0.182654i
$760$		0			0
$761$	−928.459			−1.22005			−0.610026	−	0.792382i	$-0.708841\pi$
$761$	−928.459			−1.22005			−0.610026	+	0.792382i	$0.708841\pi$
$762$	37.7376	+	37.7376i	0.0495244	+	0.0495244i
$763$	−215.740	+	215.740i	−0.282752	+	0.282752i
$764$		−	269.337i		−	0.352536i
$765$		0			0
$766$	156.086			0.203768
$767$	1339.82	+	1339.82i	1.74683	+	1.74683i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	978.370i		−	1.27226i	−0.771581	−	0.636131i	$-0.780534\pi$
$769$		−	978.370i		−	1.27226i	0.771581	−	0.636131i	$-0.219466\pi$
$770$		0			0
$771$	106.402			0.138005
$772$	389.891	+	389.891i	0.505040	+	0.505040i
$773$	−576.310	+	576.310i	−0.745550	+	0.745550i	−0.973640	−	0.228090i	$-0.926752\pi$
$773$	−576.310	+	576.310i	−0.745550	+	0.745550i	0.228090	+	0.973640i	$0.426752\pi$
$774$			148.576i			0.191958i
$775$		0			0
$776$	−288.618			−0.371930
$777$	−96.3241	−	96.3241i	−0.123969	−	0.123969i
$778$	283.465	−	283.465i	0.364351	−	0.364351i
$779$			1698.29i			2.18009i
$780$		0			0
$781$	394.051			0.504547
$782$	−623.127	−	623.127i	−0.796838	−	0.796838i
$783$	−85.5890	+	85.5890i	−0.109309	+	0.109309i
$784$		−	28.0000i		−	0.0357143i
$785$		0			0
$786$	581.280			0.739542
$787$	107.845	+	107.845i	0.137033	+	0.137033i	0.772296	−	0.635263i	$-0.219108\pi$
$787$	107.845	+	107.845i	0.137033	+	0.137033i	−0.635263	+	0.772296i	$0.719108\pi$
$788$	−139.378	+	139.378i	−0.176875	+	0.176875i
$789$		−	456.028i		−	0.577982i
$790$		0			0
$791$	−262.922			−0.332392
$792$	−25.1363	−	25.1363i	−0.0317378	−	0.0317378i
$793$	−1555.69	+	1555.69i	−1.96178	+	1.96178i
$794$		−	485.146i		−	0.611015i
$795$		0			0
$796$	693.976			0.871830
$797$	−1071.74	−	1071.74i	−1.34472	−	1.34472i	−0.891294	−	0.453426i	$-0.850202\pi$
$797$	−1071.74	−	1071.74i	−1.34472	−	1.34472i	−0.453426	−	0.891294i	$-0.649798\pi$
$798$	149.727	−	149.727i	0.187628	−	0.187628i
$799$		−	2401.65i		−	3.00583i
$800$		0			0
$801$	106.917			0.133479
$802$	−263.635	−	263.635i	−0.328723	−	0.328723i
$803$	63.1637	−	63.1637i	0.0786596	−	0.0786596i
$804$			242.372i			0.301458i
$805$		0			0
$806$	838.976			1.04091
$807$	203.787	+	203.787i	0.252524	+	0.252524i
$808$	54.3890	−	54.3890i	0.0673132	−	0.0673132i
$809$		−	1544.59i		−	1.90926i	−0.297790	−	0.954631i	$-0.596250\pi$
$809$		−	1544.59i		−	1.90926i	0.297790	−	0.954631i	$-0.403750\pi$
$810$		0			0
$811$	664.090			0.818853			0.409426	−	0.912343i	$-0.365729\pi$
$811$	664.090			0.818853			0.409426	+	0.912343i	$0.365729\pi$
$812$	−87.1596	−	87.1596i	−0.107339	−	0.107339i
$813$	410.632	−	410.632i	0.505082	−	0.505082i
$814$		−	176.119i		−	0.216362i
$815$		0			0
$816$	−225.963			−0.276915
$817$	−809.072	−	809.072i	−0.990297	−	0.990297i
$818$	−202.287	+	202.287i	−0.247295	+	0.247295i
$819$		−	145.863i		−	0.178100i
$820$		0			0
$821$	300.711			0.366274			0.183137	−	0.983087i	$-0.441375\pi$
$821$	300.711			0.366274			0.183137	+	0.983087i	$0.441375\pi$
$822$	−118.594	−	118.594i	−0.144275	−	0.144275i
$823$	398.146	−	398.146i	0.483774	−	0.483774i	−0.422560	−	0.906335i	$-0.638869\pi$
$823$	398.146	−	398.146i	0.483774	−	0.483774i	0.906335	+	0.422560i	$0.138869\pi$
$824$		−	168.660i		−	0.204684i
$825$		0			0
$826$	385.789			0.467057
$827$	699.014	+	699.014i	0.845240	+	0.845240i	0.989535	−	0.144294i	$-0.0460912\pi$
$827$	699.014	+	699.014i	0.845240	+	0.845240i	−0.144294	+	0.989535i	$0.546091\pi$
$828$	81.0582	−	81.0582i	0.0978964	−	0.0978964i
$829$			1480.53i			1.78593i	0.450128	+	0.892964i	$0.351378\pi$
$829$			1480.53i			1.78593i	−0.450128	+	0.892964i	$0.648622\pi$
$830$		0			0
$831$	572.110			0.688460
$832$	103.956	+	103.956i	0.124948	+	0.124948i
$833$	−161.435	+	161.435i	−0.193800	+	0.193800i
$834$		−	260.985i		−	0.312932i
$835$		0			0
$836$	273.761			0.327465
$837$	−118.611	−	118.611i	−0.141710	−	0.141710i
$838$	498.267	−	498.267i	0.594591	−	0.594591i
$839$			925.220i			1.10277i	0.834252	+	0.551383i	$0.185900\pi$
$839$			925.220i			1.10277i	−0.834252	+	0.551383i	$0.814100\pi$
$840$		0			0
$841$	298.372			0.354782
$842$	−662.760	−	662.760i	−0.787126	−	0.787126i
$843$	−408.525	+	408.525i	−0.484609	+	0.484609i
$844$		−	118.654i		−	0.140585i
$845$		0			0
$846$	312.414			0.369284
$847$	193.535	+	193.535i	0.228495	+	0.228495i
$848$	105.515	−	105.515i	0.124428	−	0.124428i
$849$			730.445i			0.860359i
$850$		0			0
$851$	567.938			0.667378
$852$	230.398	+	230.398i	0.270420	+	0.270420i
$853$	−806.088	+	806.088i	−0.945004	+	0.945004i	−0.998565	−	0.0535608i	$-0.982943\pi$
$853$	−806.088	+	806.088i	−0.945004	+	0.945004i	0.0535608	+	0.998565i	$0.482943\pi$
$854$			447.947i			0.524528i
$855$		0			0
$856$	−312.177			−0.364693
$857$	1114.29	+	1114.29i	1.30023	+	1.30023i	0.928237	+	0.371990i	$0.121325\pi$
$857$	1114.29	+	1114.29i	1.30023	+	1.30023i	0.371990	+	0.928237i	$0.378675\pi$
$858$	133.348	−	133.348i	0.155418	−	0.155418i
$859$			1548.40i			1.80257i	0.433231	+	0.901283i	$0.357373\pi$
$859$			1548.40i			1.80257i	−0.433231	+	0.901283i	$0.642627\pi$
$860$		0			0
$861$	238.194			0.276648
$862$	−73.7144	−	73.7144i	−0.0855155	−	0.0855155i
$863$	276.765	−	276.765i	0.320701	−	0.320701i	−0.528335	−	0.849036i	$-0.677184\pi$
$863$	276.765	−	276.765i	0.320701	−	0.320701i	0.849036	+	0.528335i	$0.177184\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$	−509.559			−0.588405
$867$	948.847	+	948.847i	1.09440	+	1.09440i
$868$	120.788	−	120.788i	0.139156	−	0.139156i
$869$		−	472.940i		−	0.544235i
$870$		0			0
$871$	−1285.78			−1.47622
$872$	−230.636	−	230.636i	−0.264490	−	0.264490i
$873$	−216.463	+	216.463i	−0.247954	+	0.247954i
$874$			882.809i			1.01008i
$875$		0			0
$876$	73.8623			0.0843176
$877$	11.6377	+	11.6377i	0.0132699	+	0.0132699i	0.713711	−	0.700441i	$-0.247013\pi$
$877$	11.6377	+	11.6377i	0.0132699	+	0.0132699i	−0.700441	+	0.713711i	$0.747013\pi$
$878$	596.437	−	596.437i	0.679314	−	0.679314i
$879$			66.3289i			0.0754594i
$880$		0			0
$881$	−745.486			−0.846182			−0.423091	−	0.906087i	$-0.639055\pi$
$881$	−745.486			−0.846182			−0.423091	+	0.906087i	$0.639055\pi$
$882$	−21.0000	−	21.0000i	−0.0238095	−	0.0238095i
$883$	−411.268	+	411.268i	−0.465762	+	0.465762i	−0.900538	−	0.434777i	$-0.856827\pi$
$883$	−411.268	+	411.268i	−0.465762	+	0.465762i	0.434777	+	0.900538i	$0.356827\pi$
$884$		−	1198.73i		−	1.35603i
$885$		0			0
$886$	338.480			0.382031
$887$	−278.003	−	278.003i	−0.313419	−	0.313419i	0.532813	−	0.846233i	$-0.321135\pi$
$887$	−278.003	−	278.003i	−0.313419	−	0.313419i	−0.846233	+	0.532813i	$0.821135\pi$
$888$	102.975	−	102.975i	0.115963	−	0.115963i
$889$			57.6451i			0.0648426i
$890$		0			0
$891$	−37.7045			−0.0423170
$892$	−24.1363	−	24.1363i	−0.0270586	−	0.0270586i
$893$	−1701.26	+	1701.26i	−1.90511	+	1.90511i
$894$			74.1154i			0.0829032i
$895$		0			0
$896$	29.9333			0.0334077
$897$	430.014	+	430.014i	0.479392	+	0.479392i
$898$	286.986	−	286.986i	0.319583	−	0.319583i
$899$		−	751.985i		−	0.836469i
$900$		0			0
$901$	−1216.71			−1.35039
$902$	217.757	+	217.757i	0.241416	+	0.241416i
$903$	−113.476	+	113.476i	−0.125666	+	0.125666i
$904$		−	281.076i		−	0.310925i
$905$		0			0
$906$	−444.128			−0.490208
$907$	−737.439	−	737.439i	−0.813053	−	0.813053i	0.172038	−	0.985090i	$-0.444965\pi$
$907$	−737.439	−	737.439i	−0.813053	−	0.813053i	−0.985090	+	0.172038i	$0.944965\pi$
$908$	−478.303	+	478.303i	−0.526765	+	0.526765i
$909$		−	81.5836i		−	0.0897509i
$910$		0			0
$911$	1367.27			1.50084			0.750422	−	0.660959i	$-0.229850\pi$
$911$	1367.27			1.50084			0.750422	+	0.660959i	$0.229850\pi$
$912$	160.065	+	160.065i	0.175510	+	0.175510i
$913$	−57.2548	+	57.2548i	−0.0627106	+	0.0627106i
$914$			1092.69i			1.19550i
$915$		0			0
$916$	−170.919			−0.186593
$917$	443.960	+	443.960i	0.484144	+	0.484144i
$918$	−169.472	+	169.472i	−0.184610	+	0.184610i
$919$			1127.32i			1.22668i	0.789819	+	0.613340i	$0.210174\pi$
$919$			1127.32i			1.22668i	−0.789819	+	0.613340i	$0.789826\pi$
$920$		0			0
$921$	−126.560			−0.137416
$922$	208.632	+	208.632i	0.226282	+	0.226282i
$923$	−1222.26	+	1222.26i	−1.32423	+	1.32423i
$924$		−	38.3964i		−	0.0415545i
$925$		0			0
$926$	281.188			0.303659
$927$	−126.495	−	126.495i	−0.136456	−	0.136456i
$928$	93.1775	−	93.1775i	0.100407	−	0.100407i
$929$		−	533.383i		−	0.574147i	−0.957909	−	0.287074i	$-0.907318\pi$
$929$		−	533.383i		−	0.574147i	0.957909	−	0.287074i	$-0.0926824\pi$
$930$		0			0
$931$	228.712			0.245663
$932$	−144.021	−	144.021i	−0.154529	−	0.154529i
$933$	233.848	−	233.848i	0.250641	−	0.250641i
$934$		−	0.132241i		−	0.000141586i
$935$		0			0
$936$	155.935			0.166597
$937$	−1173.01	−	1173.01i	−1.25188	−	1.25188i	−0.954875	−	0.297008i	$-0.904011\pi$
$937$	−1173.01	−	1173.01i	−1.25188	−	1.25188i	−0.297008	−	0.954875i	$-0.595989\pi$
$938$	−185.115	+	185.115i	−0.197350	+	0.197350i
$939$			1022.51i			1.08893i
$940$		0			0
$941$	−704.024			−0.748166			−0.374083	−	0.927395i	$-0.622042\pi$
$941$	−704.024			−0.748166			−0.374083	+	0.927395i	$0.622042\pi$
$942$	−20.8946	−	20.8946i	−0.0221811	−	0.0221811i
$943$	−702.210	+	702.210i	−0.744656	+	0.744656i
$944$			412.426i			0.436892i
$945$		0			0
$946$	−207.480			−0.219324
$947$	−591.011	−	591.011i	−0.624088	−	0.624088i	0.322486	−	0.946574i	$-0.395481\pi$
$947$	−591.011	−	591.011i	−0.624088	−	0.624088i	−0.946574	+	0.322486i	$0.895481\pi$
$948$	276.523	−	276.523i	0.291691	−	0.291691i
$949$			391.840i			0.412897i
$950$		0			0
$951$	−224.166			−0.235716
$952$	−172.582	−	172.582i	−0.181283	−	0.181283i
$953$	761.334	−	761.334i	0.798881	−	0.798881i	−0.184038	−	0.982919i	$-0.558917\pi$
$953$	761.334	−	761.334i	0.798881	−	0.798881i	0.982919	+	0.184038i	$0.0589169\pi$
$954$		−	158.273i		−	0.165904i
$955$		0			0
$956$	520.732			0.544699
$957$	−119.522	−	119.522i	−0.124892	−	0.124892i
$958$	−539.039	+	539.039i	−0.562672	+	0.562672i
$959$		−	181.155i		−	0.188900i
$960$		0			0
$961$	81.1166			0.0844085
$962$	546.282	+	546.282i	0.567860	+	0.567860i
$963$	−234.133	+	234.133i	−0.243128	+	0.243128i
$964$			139.617i			0.144831i
$965$		0			0
$966$	123.819			0.128177
$967$	310.712	+	310.712i	0.321316	+	0.321316i	0.849272	−	0.527956i	$-0.177041\pi$
$967$	310.712	+	310.712i	0.321316	+	0.321316i	−0.527956	+	0.849272i	$0.677041\pi$
$968$	−206.898	+	206.898i	−0.213738	+	0.213738i
$969$		−	1845.73i		−	1.90478i
$970$		0			0
$971$	198.336			0.204259			0.102130	−	0.994771i	$-0.467434\pi$
$971$	198.336			0.204259			0.102130	+	0.994771i	$0.467434\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	199.331	−	199.331i	0.204862	−	0.204862i
$974$			123.699i			0.127001i
$975$		0			0
$976$	−478.876			−0.490651
$977$	−38.5224	−	38.5224i	−0.0394293	−	0.0394293i	0.687117	−	0.726547i	$-0.258876\pi$
$977$	−38.5224	−	38.5224i	−0.0394293	−	0.0394293i	−0.726547	+	0.687117i	$0.758876\pi$
$978$	147.729	−	147.729i	0.151052	−	0.151052i
$979$			149.306i			0.152508i
$980$		0			0
$981$	−345.954			−0.352654
$982$	−191.070	−	191.070i	−0.194573	−	0.194573i
$983$	183.804	−	183.804i	0.186983	−	0.186983i	−0.607407	−	0.794391i	$-0.707790\pi$
$983$	183.804	−	183.804i	0.186983	−	0.186983i	0.794391	+	0.607407i	$0.207790\pi$
$984$			254.640i			0.258781i
$985$		0			0
$986$	−1074.44			−1.08970
$987$	238.610	+	238.610i	0.241753	+	0.241753i
$988$	−849.146	+	849.146i	−0.859460	+	0.859460i
$989$		−	669.071i		−	0.676513i
$990$		0			0
$991$	−1218.07			−1.22913			−0.614567	−	0.788865i	$-0.710669\pi$
$991$	−1218.07			−1.22913			−0.614567	+	0.788865i	$0.710669\pi$
$992$	129.127	+	129.127i	0.130169	+	0.130169i
$993$	210.810	−	210.810i	0.212296	−	0.212296i
$994$			351.938i			0.354063i
$995$		0			0
$996$	−66.9526			−0.0672214
$997$	−696.062	−	696.062i	−0.698156	−	0.698156i	0.265856	−	0.964013i	$-0.414345\pi$
$997$	−696.062	−	696.062i	−0.698156	−	0.698156i	−0.964013	+	0.265856i	$0.914345\pi$
$998$	−190.849	+	190.849i	−0.191232	+	0.191232i
$999$		−	154.462i		−	0.154617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.a.757.3	yes	8
5.2	odd	4		1050.3.l.e.43.2	yes	8
5.3	odd	4	inner	1050.3.l.a.43.3	✓	8
5.4	even	2		1050.3.l.e.757.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.l.a.43.3	✓	8	5.3	odd	4	inner
1050.3.l.a.757.3	yes	8	1.1	even	1	trivial
1050.3.l.e.43.2	yes	8	5.2	odd	4
1050.3.l.e.757.2	yes	8	5.4	even	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +4.18939 q^{11} +(2.44949 + 2.44949i) q^{12} +(-12.9946 + 12.9946i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(23.0622 + 23.0622i) q^{17} +(-3.00000 + 3.00000i) q^{18} -32.6732i q^{19} -4.58258 q^{21} +(-4.18939 - 4.18939i) q^{22} +(13.5097 - 13.5097i) q^{23} -4.89898i q^{24} +25.9891 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -23.2944i q^{29} +32.2818 q^{31} +(4.00000 + 4.00000i) q^{32} +(5.13093 - 5.13093i) q^{33} -46.1244i q^{34} +6.00000 q^{36} +(21.0196 + 21.0196i) q^{37} +(-32.6732 + 32.6732i) q^{38} +31.8300i q^{39} -51.9782 q^{41} +(4.58258 + 4.58258i) q^{42} +(24.7626 - 24.7626i) q^{43} +8.37878i q^{44} -27.0194 q^{46} +(-52.0691 - 52.0691i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +56.4906 q^{51} +(-25.9891 - 25.9891i) q^{52} +(-26.3788 + 26.3788i) q^{53} +7.34847i q^{54} -7.48331 q^{56} +(-40.0163 - 40.0163i) q^{57} +(-23.2944 + 23.2944i) q^{58} -103.106i q^{59} +119.719 q^{61} +(-32.2818 - 32.2818i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} -10.2619 q^{66} +(49.4740 + 49.4740i) q^{67} +(-46.1244 + 46.1244i) q^{68} -33.0919i q^{69} +94.0594 q^{71} +(-6.00000 - 6.00000i) q^{72} +(15.0771 - 15.0771i) q^{73} -42.0393i q^{74} +65.3463 q^{76} +(-7.83763 - 7.83763i) q^{77} +(31.8300 - 31.8300i) q^{78} -112.890i q^{79} -9.00000 q^{81} +(51.9782 + 51.9782i) q^{82} +(-13.6666 + 13.6666i) q^{83} -9.16515i q^{84} -49.5252 q^{86} +(-28.5297 - 28.5297i) q^{87} +(8.37878 - 8.37878i) q^{88} +35.6390i q^{89} +48.6212 q^{91} +(27.0194 + 27.0194i) q^{92} +(39.5370 - 39.5370i) q^{93} +104.138i q^{94} +9.79796 q^{96} +(-72.1545 - 72.1545i) q^{97} +(7.00000 - 7.00000i) q^{98} -12.5682i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 32 q^{11} - 40 q^{13} - 32 q^{16} + 40 q^{17} - 24 q^{18} + 32 q^{22} + 8 q^{23} + 80 q^{26} + 96 q^{31} + 32 q^{32} + 72 q^{33} + 48 q^{36} - 112 q^{37} + 24 q^{38} - 160 q^{41} + 64 q^{43} - 16 q^{46} - 64 q^{47} + 24 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{57} - 32 q^{58} - 128 q^{61} - 96 q^{62} - 144 q^{66} + 304 q^{67} - 80 q^{68} + 240 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{76} + 56 q^{77} + 120 q^{78} - 72 q^{81} + 160 q^{82} - 64 q^{83} - 128 q^{86} + 96 q^{87} - 64 q^{88} + 56 q^{91} + 16 q^{92} - 144 q^{93} - 272 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 32 * q^11 - 40 * q^13 - 32 * q^16 + 40 * q^17 - 24 * q^18 + 32 * q^22 + 8 * q^23 + 80 * q^26 + 96 * q^31 + 32 * q^32 + 72 * q^33 + 48 * q^36 - 112 * q^37 + 24 * q^38 - 160 * q^41 + 64 * q^43 - 16 * q^46 - 64 * q^47 + 24 * q^51 - 80 * q^52 - 80 * q^53 - 48 * q^57 - 32 * q^58 - 128 * q^61 - 96 * q^62 - 144 * q^66 + 304 * q^67 - 80 * q^68 + 240 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^76 + 56 * q^77 + 120 * q^78 - 72 * q^81 + 160 * q^82 - 64 * q^83 - 128 * q^86 + 96 * q^87 - 64 * q^88 + 56 * q^91 + 16 * q^92 - 144 * q^93 - 272 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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