LMFDB - Embedded newform 1050.3.l.e.757.2

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			757.2
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.e.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +4.18939 q^{11} +(-2.44949 - 2.44949i) q^{12} +(12.9946 - 12.9946i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-23.0622 - 23.0622i) q^{17} +(3.00000 - 3.00000i) q^{18} -32.6732i q^{19} -4.58258 q^{21} +(4.18939 + 4.18939i) q^{22} +(-13.5097 + 13.5097i) q^{23} -4.89898i q^{24} +25.9891 q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -23.2944i q^{29} +32.2818 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-5.13093 + 5.13093i) q^{33} -46.1244i q^{34} +6.00000 q^{36} +(-21.0196 - 21.0196i) q^{37} +(32.6732 - 32.6732i) q^{38} +31.8300i q^{39} -51.9782 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-24.7626 + 24.7626i) q^{43} +8.37878i q^{44} -27.0194 q^{46} +(52.0691 + 52.0691i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +56.4906 q^{51} +(25.9891 + 25.9891i) q^{52} +(26.3788 - 26.3788i) q^{53} +7.34847i q^{54} -7.48331 q^{56} +(40.0163 + 40.0163i) q^{57} +(23.2944 - 23.2944i) q^{58} -103.106i q^{59} +119.719 q^{61} +(32.2818 + 32.2818i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} -10.2619 q^{66} +(-49.4740 - 49.4740i) q^{67} +(46.1244 - 46.1244i) q^{68} -33.0919i q^{69} +94.0594 q^{71} +(6.00000 + 6.00000i) q^{72} +(-15.0771 + 15.0771i) q^{73} -42.0393i q^{74} +65.3463 q^{76} +(7.83763 + 7.83763i) q^{77} +(-31.8300 + 31.8300i) q^{78} -112.890i q^{79} -9.00000 q^{81} +(-51.9782 - 51.9782i) q^{82} +(13.6666 - 13.6666i) q^{83} -9.16515i q^{84} -49.5252 q^{86} +(28.5297 + 28.5297i) q^{87} +(-8.37878 + 8.37878i) q^{88} +35.6390i q^{89} +48.6212 q^{91} +(-27.0194 - 27.0194i) q^{92} +(-39.5370 + 39.5370i) q^{93} +104.138i q^{94} +9.79796 q^{96} +(72.1545 + 72.1545i) q^{97} +(-7.00000 + 7.00000i) q^{98} -12.5682i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.000418908	−	1.00000i	$-0.500133\pi$
$13$	12.9946	−	12.9946i	0.999581	−	0.999581i	1.00000		0.000418908i	$0.000133343\pi$
$14$			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	$-0.841171\pi$
$17$	−23.0622	−	23.0622i	−1.35660	−	1.35660i	−0.478528	−	0.878072i	$-0.658829\pi$
$18$	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	−0.936921	−	0.349542i	$-0.886337\pi$
$23$	−13.5097	+	13.5097i	−0.587379	+	0.587379i	0.349542	+	0.936921i	$0.386337\pi$
$24$		−	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	0.363497	−	0.931595i	$-0.381583\pi$
$37$	−21.0196	−	21.0196i	−0.568098	−	0.568098i	−0.931595	+	0.363497i	$0.881583\pi$
$38$	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	−0.933764	−	0.357889i	$-0.883496\pi$
$43$	−24.7626	+	24.7626i	−0.575874	+	0.575874i	0.357889	+	0.933764i	$0.383496\pi$
$44$			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	$0.0365009\pi$
$47$	52.0691	+	52.0691i	1.10785	+	1.10785i	0.114420	+	0.993432i	$0.463499\pi$
$48$	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	−0.413013	−	0.910725i	$-0.635523\pi$
$53$	26.3788	−	26.3788i	0.497713	−	0.497713i	0.910725	+	0.413013i	$0.135523\pi$
$54$			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	0.233854	−	0.972272i	$-0.424866\pi$
$67$	−49.4740	−	49.4740i	−0.738417	−	0.738417i	−0.972272	+	0.233854i	$0.924866\pi$
$68$	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	−0.802793	−	0.596258i	$-0.796654\pi$
$73$	−15.0771	+	15.0771i	−0.206535	+	0.206535i	0.596258	+	0.802793i	$0.296654\pi$
$74$		−	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	−0.619968	−	0.784627i	$-0.712855\pi$
$83$	13.6666	−	13.6666i	0.164658	−	0.164658i	0.784627	+	0.619968i	$0.212855\pi$
$84$		−	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	0.973319	−	0.229458i	$-0.0736953\pi$
$97$	72.1545	+	72.1545i	0.743861	+	0.743861i	−0.229458	+	0.973319i	$0.573695\pi$
$98$	−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	−0.881518	−	0.472150i	$-0.843478\pi$
$103$	−42.1649	+	42.1649i	−0.409368	+	0.409368i	0.472150	+	0.881518i	$0.343478\pi$
$104$			51.9782i			0.499791i
$105$		0			0
$106$	52.7576			0.497713
$107$	78.0442	+	78.0442i	0.729385	+	0.729385i	0.970497	−	0.241112i	$-0.0775121\pi$
$107$	78.0442	+	78.0442i	0.729385	+	0.729385i	−0.241112	+	0.970497i	$0.577512\pi$
$108$	−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	−0.946004	−	0.324155i	$-0.894920\pi$
$113$	−70.2690	+	70.2690i	−0.621849	+	0.621849i	0.324155	+	0.946004i	$0.394920\pi$
$114$			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	0.765155	−	0.643846i	$-0.222662\pi$
$127$	15.4063	+	15.4063i	0.121309	+	0.121309i	−0.643846	+	0.765155i	$0.722662\pi$
$128$	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	0.507973	−	0.861373i	$-0.330395\pi$
$137$	−48.4157	−	48.4157i	−0.353399	−	0.353399i	−0.861373	+	0.507973i	$0.830395\pi$
$138$	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	0.679419	−	0.733751i	$-0.262232\pi$
$157$	−8.53019	−	8.53019i	−0.0543324	−	0.0543324i	−0.733751	+	0.679419i	$0.762232\pi$
$158$	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	−0.497477	−	0.867477i	$-0.665740\pi$
$163$	60.3100	−	60.3100i	0.370000	−	0.370000i	0.867477	+	0.497477i	$0.165740\pi$
$164$		−	103.956i		−	0.633881i
$165$		0			0
$166$	27.3333			0.164658
$167$	131.125	+	131.125i	0.785181	+	0.785181i	0.980700	−	0.195519i	$-0.0626390\pi$
$167$	131.125	+	131.125i	0.785181	+	0.785181i	−0.195519	+	0.980700i	$0.562639\pi$
$168$	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	−0.895759	−	0.444540i	$-0.853367\pi$
$173$	−78.0609	+	78.0609i	−0.451219	+	0.451219i	0.444540	+	0.895759i	$0.353367\pi$
$174$			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	$0.503225\pi$
$193$	−194.945	+	194.945i	−1.01008	+	1.01008i	−0.999949	+	0.0101307i	$0.996775\pi$
$194$			144.309i			0.743861i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−69.6888	−	69.6888i	−0.353750	−	0.353750i	0.507753	−	0.861503i	$-0.330476\pi$
$197$	−69.6888	−	69.6888i	−0.353750	−	0.353750i	−0.861503	+	0.507753i	$0.830476\pi$
$198$	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	−0.679530	−	0.733648i	$-0.737816\pi$
$223$	12.0682	−	12.0682i	0.0541173	−	0.0541173i	0.733648	+	0.679530i	$0.237816\pi$
$224$		−	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	$-0.982469\pi$
$227$	−239.151	−	239.151i	−1.05353	−	1.05353i	−0.0550464	−	0.998484i	$-0.517531\pi$
$228$	−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	−0.535487	−	0.844544i	$-0.679872\pi$
$233$	72.0103	−	72.0103i	0.309057	−	0.309057i	0.844544	+	0.535487i	$0.179872\pi$
$234$		−	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	0.617528	−	0.786549i	$-0.288134\pi$
$257$	−43.4383	−	43.4383i	−0.169021	−	0.169021i	−0.786549	+	0.617528i	$0.788134\pi$
$258$	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	−0.966089	−	0.258208i	$-0.916868\pi$
$263$	−186.173	+	186.173i	−0.707881	+	0.707881i	0.258208	+	0.966089i	$0.416868\pi$
$264$		−	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	0.146084	−	0.989272i	$-0.453333\pi$
$277$	−233.563	−	233.563i	−0.843188	−	0.843188i	−0.989272	+	0.146084i	$0.953333\pi$
$278$	−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	$-0.482405\pi$
$283$	298.203	−	298.203i	1.05372	−	1.05372i	0.998473	−	0.0552481i	$-0.0175950\pi$
$284$			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	−0.659386	−	0.751805i	$-0.729184\pi$
$293$	27.0786	−	27.0786i	0.0924186	−	0.0924186i	0.751805	+	0.659386i	$0.229184\pi$
$294$		−	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	0.786232	−	0.617932i	$-0.212029\pi$
$307$	51.6680	+	51.6680i	0.168300	+	0.168300i	−0.617932	+	0.786232i	$0.712029\pi$
$308$	−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	$-0.357948\pi$
$313$	417.438	−	417.438i	1.33367	−	1.33367i	0.902064	−	0.431602i	$-0.142052\pi$
$314$		−	17.0604i		−	0.0543324i
$315$		0			0
$316$	225.780			0.714494
$317$	91.5155	+	91.5155i	0.288692	+	0.288692i	0.836563	−	0.547871i	$-0.184561\pi$
$317$	91.5155	+	91.5155i	0.288692	+	0.288692i	−0.547871	+	0.836563i	$0.684561\pi$
$318$	−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	0.148956	−	0.988844i	$-0.452409\pi$
$337$	−283.042	−	283.042i	−0.839888	−	0.839888i	−0.988844	+	0.148956i	$0.952409\pi$
$338$	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	$-0.968540\pi$
$347$	−379.546	−	379.546i	−1.09379	−	1.09379i	−0.0986739	−	0.995120i	$-0.531460\pi$
$348$	−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	−0.862094	−	0.506748i	$-0.830847\pi$
$353$	−125.437	+	125.437i	−0.355346	+	0.355346i	0.506748	+	0.862094i	$0.330847\pi$
$354$			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	0.142210	−	0.989837i	$-0.454579\pi$
$367$	−311.079	−	311.079i	−0.847627	−	0.847627i	−0.989837	+	0.142210i	$0.954579\pi$
$368$	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	−0.902725	−	0.430217i	$-0.858437\pi$
$373$	−176.246	+	176.246i	−0.472508	+	0.472508i	0.430217	+	0.902725i	$0.358437\pi$
$374$		−	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	−0.597844	−	0.801612i	$-0.703976\pi$
$383$	78.0432	−	78.0432i	0.203768	−	0.203768i	0.801612	+	0.597844i	$0.203976\pi$
$384$			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	0.332196	−	0.943210i	$-0.392211\pi$
$397$	−242.573	−	242.573i	−0.611015	−	0.611015i	−0.943210	+	0.332196i	$0.892211\pi$
$398$	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	−0.937199	−	0.348794i	$-0.886591\pi$
$433$	−254.779	+	254.779i	−0.588405	+	0.588405i	0.348794	+	0.937199i	$0.386591\pi$
$434$			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	−0.489802	−	0.871833i	$-0.662931\pi$
$443$	169.240	−	169.240i	0.382031	−	0.382031i	0.871833	+	0.489802i	$0.162931\pi$
$444$			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	$0.0706060\pi$
$457$	546.344	+	546.344i	1.19550	+	1.19550i	0.220001	+	0.975500i	$0.429394\pi$
$458$	−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	−0.538785	−	0.842443i	$-0.681116\pi$
$463$	140.594	−	140.594i	0.303659	−	0.303659i	0.842443	+	0.538785i	$0.181116\pi$
$464$			93.1775i			0.200814i
$465$		0			0
$466$	144.021			0.309057
$467$	−0.0661206	−	0.0661206i	−0.000141586	−	0.000141586i	0.707036	−	0.707178i	$-0.250032\pi$
$467$	−0.0661206	−	0.0661206i	−0.000141586	−	0.000141586i	−0.707178	+	0.707036i	$0.750032\pi$
$468$	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	0.767750	−	0.640749i	$-0.221376\pi$
$487$	61.8493	+	61.8493i	0.127001	+	0.127001i	−0.640749	+	0.767750i	$0.721376\pi$
$488$	−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	$-0.483777\pi$
$503$	527.972	−	527.972i	1.04965	−	1.04965i	0.998701	−	0.0509448i	$-0.0162233\pi$
$504$			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	−0.0544065	−	0.998519i	$-0.517327\pi$
$523$	493.771	−	493.771i	0.944112	−	0.944112i	0.998519	+	0.0544065i	$0.0173267\pi$
$524$		−	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	0.598149	−	0.801385i	$-0.295903\pi$
$547$	−111.170	−	111.170i	−0.203236	−	0.203236i	−0.801385	+	0.598149i	$0.795903\pi$
$548$	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	0.835884	−	0.548907i	$-0.184956\pi$
$557$	159.846	+	159.846i	0.286977	+	0.286977i	−0.548907	+	0.835884i	$0.684956\pi$
$558$	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	−0.741584	−	0.670860i	$-0.765925\pi$
$563$	−39.8174	+	39.8174i	−0.0707237	+	0.0707237i	0.670860	+	0.741584i	$0.265925\pi$
$564$		−	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	$-0.959940\pi$
$577$	−644.862	−	644.862i	−1.11761	−	1.11761i	−0.125521	−	0.992091i	$-0.540060\pi$
$578$	−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	$0.0466920\pi$
$587$	666.493	+	666.493i	1.13542	+	1.13542i	0.146162	+	0.989261i	$0.453308\pi$
$588$	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	−0.107190	−	0.994239i	$-0.534185\pi$
$593$	526.020	−	526.020i	0.887049	−	0.887049i	0.994239	+	0.107190i	$0.0341853\pi$
$594$			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	0.932973	−	0.359945i	$-0.117205\pi$
$607$	347.828	+	347.828i	0.573028	+	0.573028i	−0.359945	+	0.932973i	$0.617205\pi$
$608$	−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	−0.861027	−	0.508560i	$-0.830178\pi$
$613$	−216.062	+	216.062i	−0.352467	+	0.352467i	0.508560	+	0.861027i	$0.330178\pi$
$614$			103.336i			0.168300i
$615$		0			0
$616$	−31.3505			−0.0508937
$617$	432.131	+	432.131i	0.700375	+	0.700375i	0.964491	−	0.264116i	$-0.0850802\pi$
$617$	432.131	+	432.131i	0.700375	+	0.700375i	−0.264116	+	0.964491i	$0.585080\pi$
$618$	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	−0.430060	−	0.902800i	$-0.641508\pi$
$643$	303.972	−	303.972i	0.472741	−	0.472741i	0.902800	+	0.430060i	$0.141508\pi$
$644$		−	101.097i		−	0.156984i
$645$		0			0
$646$	−1507.03			−2.33286
$647$	−88.7310	−	88.7310i	−0.137142	−	0.137142i	0.635203	−	0.772345i	$-0.280916\pi$
$647$	−88.7310	−	88.7310i	−0.137142	−	0.137142i	−0.772345	+	0.635203i	$0.780916\pi$
$648$	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	−0.931250	−	0.364381i	$-0.881281\pi$
$653$	−370.166	+	370.166i	−0.566869	+	0.566869i	0.364381	+	0.931250i	$0.381281\pi$
$654$			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	$0.622031\pi$
$673$	−875.881	+	875.881i	−1.30146	+	1.30146i	−0.927409	+	0.374049i	$0.877969\pi$
$674$		−	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	$0.133378\pi$
$677$	893.879	+	893.879i	1.32035	+	1.32035i	0.406865	+	0.913488i	$0.366622\pi$
$678$	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	−0.725314	−	0.688418i	$-0.758306\pi$
$683$	−25.2004	+	25.2004i	−0.0368966	+	0.0368966i	0.688418	+	0.725314i	$0.258306\pi$
$684$		−	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	0.797330	−	0.603544i	$-0.206245\pi$
$727$	140.883	+	140.883i	0.193786	+	0.193786i	−0.603544	+	0.797330i	$0.706245\pi$
$728$	−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	−0.249122	−	0.968472i	$-0.580142\pi$
$733$	527.284	−	527.284i	0.719351	−	0.719351i	0.968472	+	0.249122i	$0.0801419\pi$
$734$		−	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	−0.413192	−	0.910644i	$-0.635586\pi$
$743$	369.606	−	369.606i	0.497451	−	0.497451i	0.910644	+	0.413192i	$0.135586\pi$
$744$		−	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	$0.0535743\pi$
$757$	873.112	+	873.112i	1.15338	+	1.15338i	0.167515	+	0.985870i	$0.446426\pi$
$758$	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	−0.228090	−	0.973640i	$-0.573248\pi$
$773$	576.310	−	576.310i	0.745550	−	0.745550i	0.973640	+	0.228090i	$0.0732482\pi$
$774$			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	0.635263	−	0.772296i	$-0.280892\pi$
$787$	−107.845	−	107.845i	−0.137033	−	0.137033i	−0.772296	+	0.635263i	$0.780892\pi$
$788$	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	$0.149798\pi$
$797$	1071.74	+	1071.74i	1.34472	+	1.34472i	0.453426	+	0.891294i	$0.350202\pi$
$798$	−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	−0.906335	−	0.422560i	$-0.861131\pi$
$823$	−398.146	+	398.146i	−0.483774	+	0.483774i	0.422560	+	0.906335i	$0.361131\pi$
$824$		−	168.660i		−	0.204684i
$825$		0			0
$826$	385.789			0.467057
$827$	−699.014	−	699.014i	−0.845240	−	0.845240i	0.144294	−	0.989535i	$-0.453909\pi$
$827$	−699.014	−	699.014i	−0.845240	−	0.845240i	−0.989535	+	0.144294i	$0.953909\pi$
$828$	−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	−0.0535608	−	0.998565i	$-0.517057\pi$
$853$	806.088	−	806.088i	0.945004	−	0.945004i	0.998565	+	0.0535608i	$0.0170571\pi$
$854$			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	$-0.878675\pi$
$857$	−1114.29	−	1114.29i	−1.30023	−	1.30023i	−0.371990	−	0.928237i	$-0.621325\pi$
$858$	−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	−0.849036	−	0.528335i	$-0.822816\pi$
$863$	−276.765	+	276.765i	−0.320701	+	0.320701i	0.528335	+	0.849036i	$0.322816\pi$
$864$		−	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	0.700441	−	0.713711i	$-0.252987\pi$
$877$	−11.6377	−	11.6377i	−0.0132699	−	0.0132699i	−0.713711	+	0.700441i	$0.752987\pi$
$878$	−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	−0.434777	−	0.900538i	$-0.643173\pi$
$883$	411.268	−	411.268i	0.465762	−	0.465762i	0.900538	+	0.434777i	$0.143173\pi$
$884$		−	1198.73i		−	1.35603i
$885$		0			0
$886$	338.480			0.382031
$887$	278.003	+	278.003i	0.313419	+	0.313419i	0.846233	−	0.532813i	$-0.178865\pi$
$887$	278.003	+	278.003i	0.313419	+	0.313419i	−0.532813	+	0.846233i	$0.678865\pi$
$888$	−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	0.985090	−	0.172038i	$-0.0550351\pi$
$907$	737.439	+	737.439i	0.813053	+	0.813053i	−0.172038	+	0.985090i	$0.555035\pi$
$908$	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	$0.0959889\pi$
$937$	1173.01	+	1173.01i	1.25188	+	1.25188i	0.297008	+	0.954875i	$0.404011\pi$
$938$	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	0.946574	−	0.322486i	$-0.104519\pi$
$947$	591.011	+	591.011i	0.624088	+	0.624088i	−0.322486	+	0.946574i	$0.604519\pi$
$948$	−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	−0.982919	−	0.184038i	$-0.941083\pi$
$953$	−761.334	+	761.334i	−0.798881	+	0.798881i	0.184038	+	0.982919i	$0.441083\pi$
$954$		−	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	0.527956	−	0.849272i	$-0.322959\pi$
$967$	−310.712	−	310.712i	−0.321316	−	0.321316i	−0.849272	+	0.527956i	$0.822959\pi$
$968$	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	0.726547	−	0.687117i	$-0.241124\pi$
$977$	38.5224	+	38.5224i	0.0394293	+	0.0394293i	−0.687117	+	0.726547i	$0.741124\pi$
$978$	−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	−0.794391	−	0.607407i	$-0.792210\pi$
$983$	−183.804	+	183.804i	−0.186983	+	0.186983i	0.607407	+	0.794391i	$0.292210\pi$
$984$			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	0.964013	−	0.265856i	$-0.0856547\pi$
$997$	696.062	+	696.062i	0.698156	+	0.698156i	−0.265856	+	0.964013i	$0.585655\pi$
$998$	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.e.757.2	yes	8
5.2	odd	4		1050.3.l.a.43.3	✓	8
5.3	odd	4	inner	1050.3.l.e.43.2	yes	8
5.4	even	2		1050.3.l.a.757.3	yes	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
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

Varieties

Fields

Representations

Groups

Database

Properties

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