LMFDB - Embedded newform 1050.3.l.b.757.1

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:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			757.1
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +2.92322 q^{11} +(-2.44949 - 2.44949i) q^{12} +(1.13309 - 1.13309i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-1.54506 - 1.54506i) q^{17} +(-3.00000 + 3.00000i) q^{18} +3.35199i q^{19} +4.58258 q^{21} +(-2.92322 - 2.92322i) q^{22} +(-7.90681 + 7.90681i) q^{23} +4.89898i q^{24} -2.26617 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -13.5474i q^{29} +15.7936 q^{31} +(4.00000 + 4.00000i) q^{32} +(-3.58019 + 3.58019i) q^{33} +3.09013i q^{34} +6.00000 q^{36} +(16.8305 + 16.8305i) q^{37} +(3.35199 - 3.35199i) q^{38} +2.77548i q^{39} -72.6227 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-20.3749 + 20.3749i) q^{43} +5.84643i q^{44} +15.8136 q^{46} +(52.3194 + 52.3194i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +3.78462 q^{51} +(2.26617 + 2.26617i) q^{52} +(40.5379 - 40.5379i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(-4.10533 - 4.10533i) q^{57} +(-13.5474 + 13.5474i) q^{58} -117.165i q^{59} -45.4373 q^{61} +(-15.7936 - 15.7936i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +7.16039 q^{66} +(-57.7773 - 57.7773i) q^{67} +(3.09013 - 3.09013i) q^{68} -19.3676i q^{69} -51.7217 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-72.3851 + 72.3851i) q^{73} -33.6610i q^{74} -6.70398 q^{76} +(-5.46884 - 5.46884i) q^{77} +(2.77548 - 2.77548i) q^{78} -37.1850i q^{79} -9.00000 q^{81} +(72.6227 + 72.6227i) q^{82} +(21.3331 - 21.3331i) q^{83} +9.16515i q^{84} +40.7498 q^{86} +(16.5922 + 16.5922i) q^{87} +(5.84643 - 5.84643i) q^{88} -100.951i q^{89} -4.23962 q^{91} +(-15.8136 - 15.8136i) q^{92} +(-19.3432 + 19.3432i) q^{93} -104.639i q^{94} -9.79796 q^{96} +(-52.5887 - 52.5887i) q^{97} +(7.00000 - 7.00000i) q^{98} -8.76965i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * 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
$11$	2.92322			0.265747			0.132873	−	0.991133i	$-0.457580\pi$
$11$	2.92322			0.265747			0.132873	+	0.991133i	$0.457580\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	1.13309	−	1.13309i	0.0871605	−	0.0871605i	−0.662182	−	0.749343i	$-0.730370\pi$
$13$	1.13309	−	1.13309i	0.0871605	−	0.0871605i	0.749343	+	0.662182i	$0.230370\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−1.54506	−	1.54506i	−0.0908861	−	0.0908861i	0.660202	−	0.751088i	$-0.270471\pi$
$17$	−1.54506	−	1.54506i	−0.0908861	−	0.0908861i	−0.751088	+	0.660202i	$0.770471\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			3.35199i			0.176420i	0.996102	+	0.0882102i	$0.0281147\pi$
$19$			3.35199i			0.176420i	−0.996102	+	0.0882102i	$0.971885\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	−2.92322	−	2.92322i	−0.132873	−	0.132873i
$23$	−7.90681	+	7.90681i	−0.343774	+	0.343774i	−0.857784	−	0.514010i	$-0.828159\pi$
$23$	−7.90681	+	7.90681i	−0.343774	+	0.343774i	0.514010	+	0.857784i	$0.328159\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	−2.26617			−0.0871605
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$		−	13.5474i		−	0.467153i	−0.972338	−	0.233577i	$-0.924957\pi$
$29$		−	13.5474i		−	0.467153i	0.972338	−	0.233577i	$-0.0750430\pi$
$30$		0			0
$31$	15.7936			0.509473			0.254736	−	0.967011i	$-0.418011\pi$
$31$	15.7936			0.509473			0.254736	+	0.967011i	$0.418011\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−3.58019	+	3.58019i	−0.108491	+	0.108491i
$34$			3.09013i			0.0908861i
$35$		0			0
$36$	6.00000			0.166667
$37$	16.8305	+	16.8305i	0.454878	+	0.454878i	0.896970	−	0.442092i	$-0.145764\pi$
$37$	16.8305	+	16.8305i	0.454878	+	0.454878i	−0.442092	+	0.896970i	$0.645764\pi$
$38$	3.35199	−	3.35199i	0.0882102	−	0.0882102i
$39$			2.77548i			0.0711662i
$40$		0			0
$41$	−72.6227			−1.77129			−0.885643	−	0.464367i	$-0.846282\pi$
$41$	−72.6227			−1.77129			−0.885643	+	0.464367i	$0.846282\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	−20.3749	+	20.3749i	−0.473835	+	0.473835i	−0.903153	−	0.429318i	$-0.858754\pi$
$43$	−20.3749	+	20.3749i	−0.473835	+	0.473835i	0.429318	+	0.903153i	$0.358754\pi$
$44$			5.84643i			0.132873i
$45$		0			0
$46$	15.8136			0.343774
$47$	52.3194	+	52.3194i	1.11318	+	1.11318i	0.992718	+	0.120461i	$0.0384372\pi$
$47$	52.3194	+	52.3194i	1.11318	+	1.11318i	0.120461	+	0.992718i	$0.461563\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	3.78462			0.0742082
$52$	2.26617	+	2.26617i	0.0435802	+	0.0435802i
$53$	40.5379	−	40.5379i	0.764865	−	0.764865i	−0.212332	−	0.977198i	$-0.568106\pi$
$53$	40.5379	−	40.5379i	0.764865	−	0.764865i	0.977198	+	0.212332i	$0.0681059\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−7.48331			−0.133631
$57$	−4.10533	−	4.10533i	−0.0720233	−	0.0720233i
$58$	−13.5474	+	13.5474i	−0.233577	+	0.233577i
$59$		−	117.165i		−	1.98585i	−0.118752	−	0.992924i	$-0.537889\pi$
$59$		−	117.165i		−	1.98585i	0.118752	−	0.992924i	$-0.462111\pi$
$60$		0			0
$61$	−45.4373			−0.744874			−0.372437	−	0.928057i	$-0.621478\pi$
$61$	−45.4373			−0.744874			−0.372437	+	0.928057i	$0.621478\pi$
$62$	−15.7936	−	15.7936i	−0.254736	−	0.254736i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	7.16039			0.108491
$67$	−57.7773	−	57.7773i	−0.862348	−	0.862348i	0.129263	−	0.991610i	$-0.458739\pi$
$67$	−57.7773	−	57.7773i	−0.862348	−	0.862348i	−0.991610	+	0.129263i	$0.958739\pi$
$68$	3.09013	−	3.09013i	0.0454430	−	0.0454430i
$69$		−	19.3676i		−	0.280691i
$70$		0			0
$71$	−51.7217			−0.728475			−0.364238	−	0.931306i	$-0.618670\pi$
$71$	−51.7217			−0.728475			−0.364238	+	0.931306i	$0.618670\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−72.3851	+	72.3851i	−0.991576	+	0.991576i	−0.999965	−	0.00838858i	$-0.997330\pi$
$73$	−72.3851	+	72.3851i	−0.991576	+	0.991576i	0.00838858	+	0.999965i	$0.497330\pi$
$74$		−	33.6610i		−	0.454878i
$75$		0			0
$76$	−6.70398			−0.0882102
$77$	−5.46884	−	5.46884i	−0.0710238	−	0.0710238i
$78$	2.77548	−	2.77548i	0.0355831	−	0.0355831i
$79$		−	37.1850i		−	0.470696i	−0.971911	−	0.235348i	$-0.924377\pi$
$79$		−	37.1850i		−	0.470696i	0.971911	−	0.235348i	$-0.0756230\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	72.6227	+	72.6227i	0.885643	+	0.885643i
$83$	21.3331	−	21.3331i	0.257026	−	0.257026i	−0.566818	−	0.823843i	$-0.691826\pi$
$83$	21.3331	−	21.3331i	0.257026	−	0.257026i	0.823843	+	0.566818i	$0.191826\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	40.7498			0.473835
$87$	16.5922	+	16.5922i	0.190715	+	0.190715i
$88$	5.84643	−	5.84643i	0.0664367	−	0.0664367i
$89$		−	100.951i		−	1.13428i	−0.823620	−	0.567141i	$-0.808049\pi$
$89$		−	100.951i		−	1.13428i	0.823620	−	0.567141i	$-0.191951\pi$
$90$		0			0
$91$	−4.23962			−0.0465892
$92$	−15.8136	−	15.8136i	−0.171887	−	0.171887i
$93$	−19.3432	+	19.3432i	−0.207991	+	0.207991i
$94$		−	104.639i		−	1.11318i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	−52.5887	−	52.5887i	−0.542151	−	0.542151i	0.382008	−	0.924159i	$-0.375233\pi$
$97$	−52.5887	−	52.5887i	−0.542151	−	0.542151i	−0.924159	+	0.382008i	$0.875233\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		−	8.76965i		−	0.0885823i
$100$		0			0
$101$	−129.417			−1.28136			−0.640679	−	0.767808i	$-0.721347\pi$
$101$	−129.417			−1.28136			−0.640679	+	0.767808i	$0.721347\pi$
$102$	−3.78462	−	3.78462i	−0.0371041	−	0.0371041i
$103$	−31.0447	+	31.0447i	−0.301405	+	0.301405i	−0.841563	−	0.540158i	$-0.818364\pi$
$103$	−31.0447	+	31.0447i	−0.301405	+	0.301405i	0.540158	+	0.841563i	$0.318364\pi$
$104$		−	4.53234i		−	0.0435802i
$105$		0			0
$106$	−81.0757			−0.764865
$107$	−109.421	−	109.421i	−1.02263	−	1.02263i	−0.999738	−	0.0228904i	$-0.992713\pi$
$107$	−109.421	−	109.421i	−1.02263	−	1.02263i	−0.0228904	−	0.999738i	$-0.507287\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			68.6170i			0.629514i	0.949172	+	0.314757i	$0.101923\pi$
$109$			68.6170i			0.629514i	−0.949172	+	0.314757i	$0.898077\pi$
$110$		0			0
$111$	−41.2261			−0.371406
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	68.0366	−	68.0366i	0.602094	−	0.602094i	−0.338774	−	0.940868i	$-0.610012\pi$
$113$	68.0366	−	68.0366i	0.602094	−	0.602094i	0.940868	+	0.338774i	$0.110012\pi$
$114$			8.21066i			0.0720233i
$115$		0			0
$116$	27.0949			0.233577
$117$	−3.39926	−	3.39926i	−0.0290535	−	0.0290535i
$118$	−117.165	+	117.165i	−0.992924	+	0.992924i
$119$			5.78110i			0.0485807i
$120$		0			0
$121$	−112.455			−0.929379
$122$	45.4373	+	45.4373i	0.372437	+	0.372437i
$123$	88.9443	−	88.9443i	0.723124	−	0.723124i
$124$			31.5873i			0.254736i
$125$		0			0
$126$	11.2250			0.0890871
$127$	−142.963	−	142.963i	−1.12569	−	1.12569i	−0.990870	−	0.134824i	$-0.956953\pi$
$127$	−142.963	−	142.963i	−1.12569	−	1.12569i	−0.134824	−	0.990870i	$-0.543047\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	49.9082i		−	0.386885i
$130$		0			0
$131$	3.55384			0.0271285			0.0135643	−	0.999908i	$-0.495682\pi$
$131$	3.55384			0.0271285			0.0135643	+	0.999908i	$0.495682\pi$
$132$	−7.16039	−	7.16039i	−0.0542454	−	0.0542454i
$133$	6.27100	−	6.27100i	0.0471503	−	0.0471503i
$134$			115.555i			0.862348i
$135$		0			0
$136$	−6.18025			−0.0454430
$137$	−75.1054	−	75.1054i	−0.548214	−	0.548214i	0.377710	−	0.925924i	$-0.376712\pi$
$137$	−75.1054	−	75.1054i	−0.548214	−	0.548214i	−0.925924	+	0.377710i	$0.876712\pi$
$138$	−19.3676	+	19.3676i	−0.140345	+	0.140345i
$139$			192.352i			1.38383i	0.721980	+	0.691914i	$0.243232\pi$
$139$			192.352i			1.38383i	−0.721980	+	0.691914i	$0.756768\pi$
$140$		0			0
$141$	−128.156			−0.908907
$142$	51.7217	+	51.7217i	0.364238	+	0.364238i
$143$	3.31225	−	3.31225i	0.0231626	−	0.0231626i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	144.770			0.991576
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	−33.6610	+	33.6610i	−0.227439	+	0.227439i
$149$		−	77.5005i		−	0.520138i	−0.965590	−	0.260069i	$-0.916255\pi$
$149$		−	77.5005i		−	0.520138i	0.965590	−	0.260069i	$-0.0837453\pi$
$150$		0			0
$151$	36.8195			0.243837			0.121919	−	0.992540i	$-0.461095\pi$
$151$	36.8195			0.243837			0.121919	+	0.992540i	$0.461095\pi$
$152$	6.70398	+	6.70398i	0.0441051	+	0.0441051i
$153$	−4.63519	+	4.63519i	−0.0302954	+	0.0302954i
$154$			10.9377i			0.0710238i
$155$		0			0
$156$	−5.55096			−0.0355831
$157$	−75.7654	−	75.7654i	−0.482582	−	0.482582i	0.423373	−	0.905955i	$-0.360846\pi$
$157$	−75.7654	−	75.7654i	−0.482582	−	0.482582i	−0.905955	+	0.423373i	$0.860846\pi$
$158$	−37.1850	+	37.1850i	−0.235348	+	0.235348i
$159$			99.2971i			0.624510i
$160$		0			0
$161$	29.5846			0.183755
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−174.453	+	174.453i	−1.07026	+	1.07026i	−0.0729236	+	0.997338i	$0.523233\pi$
$163$	−174.453	+	174.453i	−1.07026	+	1.07026i	−0.997338	+	0.0729236i	$0.976767\pi$
$164$		−	145.245i		−	0.885643i
$165$		0			0
$166$	−42.6663			−0.257026
$167$	−119.275	−	119.275i	−0.714222	−	0.714222i	0.253194	−	0.967416i	$-0.418519\pi$
$167$	−119.275	−	119.275i	−0.714222	−	0.714222i	−0.967416	+	0.253194i	$0.918519\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$			166.432i			0.984806i
$170$		0			0
$171$	10.0560			0.0588068
$172$	−40.7498	−	40.7498i	−0.236918	−	0.236918i
$173$	−110.021	+	110.021i	−0.635957	+	0.635957i	−0.949556	−	0.313599i	$-0.898465\pi$
$173$	−110.021	+	110.021i	−0.635957	+	0.635957i	0.313599	+	0.949556i	$0.398465\pi$
$174$		−	33.1843i		−	0.190715i
$175$		0			0
$176$	−11.6929			−0.0664367
$177$	143.497	+	143.497i	0.810719	+	0.810719i
$178$	−100.951	+	100.951i	−0.567141	+	0.567141i
$179$		−	49.0357i		−	0.273943i	−0.990575	−	0.136971i	$-0.956263\pi$
$179$		−	49.0357i		−	0.273943i	0.990575	−	0.136971i	$-0.0437368\pi$
$180$		0			0
$181$	−327.143			−1.80742			−0.903709	−	0.428148i	$-0.859166\pi$
$181$	−327.143			−1.80742			−0.903709	+	0.428148i	$0.859166\pi$
$182$	4.23962	+	4.23962i	0.0232946	+	0.0232946i
$183$	55.6491	−	55.6491i	0.304094	−	0.304094i
$184$			31.6272i			0.171887i
$185$		0			0
$186$	38.6864			0.207991
$187$	−4.51655	−	4.51655i	−0.0241527	−	0.0241527i
$188$	−104.639	+	104.639i	−0.556589	+	0.556589i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	289.078			1.51350			0.756749	−	0.653705i	$-0.226786\pi$
$191$	289.078			1.51350			0.756749	+	0.653705i	$0.226786\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	131.213	−	131.213i	0.679858	−	0.679858i	−0.280110	−	0.959968i	$-0.590371\pi$
$193$	131.213	−	131.213i	0.679858	−	0.679858i	0.959968	+	0.280110i	$0.0903710\pi$
$194$			105.177i			0.542151i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−111.798	−	111.798i	−0.567504	−	0.567504i	0.363924	−	0.931429i	$-0.381437\pi$
$197$	−111.798	−	111.798i	−0.567504	−	0.567504i	−0.931429	+	0.363924i	$0.881437\pi$
$198$	−8.76965	+	8.76965i	−0.0442911	+	0.0442911i
$199$		−	58.3715i		−	0.293324i	−0.989187	−	0.146662i	$-0.953147\pi$
$199$		−	58.3715i		−	0.293324i	0.989187	−	0.146662i	$-0.0468530\pi$
$200$		0			0
$201$	141.525			0.704104
$202$	129.417	+	129.417i	0.640679	+	0.640679i
$203$	−25.3450	+	25.3450i	−0.124852	+	0.124852i
$204$			7.56923i			0.0371041i
$205$		0			0
$206$	62.0894			0.301405
$207$	23.7204	+	23.7204i	0.114591	+	0.114591i
$208$	−4.53234	+	4.53234i	−0.0217901	+	0.0217901i
$209$			9.79858i			0.0468832i
$210$		0			0
$211$	55.0602			0.260949			0.130474	−	0.991452i	$-0.458350\pi$
$211$	55.0602			0.260949			0.130474	+	0.991452i	$0.458350\pi$
$212$	81.0757	+	81.0757i	0.382433	+	0.382433i
$213$	63.3459	−	63.3459i	0.297399	−	0.297399i
$214$			218.842i			1.02263i
$215$		0			0
$216$	14.6969			0.0680414
$217$	−29.5472	−	29.5472i	−0.136162	−	0.136162i
$218$	68.6170	−	68.6170i	0.314757	−	0.314757i
$219$		−	177.306i		−	0.809619i
$220$		0			0
$221$	−3.50138			−0.0158433
$222$	41.2261	+	41.2261i	0.185703	+	0.185703i
$223$	101.768	−	101.768i	0.456360	−	0.456360i	−0.441099	−	0.897459i	$-0.645411\pi$
$223$	101.768	−	101.768i	0.456360	−	0.456360i	0.897459	+	0.441099i	$0.145411\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−136.073			−0.602094
$227$	25.0589	+	25.0589i	0.110392	+	0.110392i	0.760145	−	0.649753i	$-0.225128\pi$
$227$	25.0589	+	25.0589i	0.110392	+	0.110392i	−0.649753	+	0.760145i	$0.725128\pi$
$228$	8.21066	−	8.21066i	0.0360117	−	0.0360117i
$229$			283.497i			1.23798i	0.785399	+	0.618990i	$0.212458\pi$
$229$			283.497i			1.23798i	−0.785399	+	0.618990i	$0.787542\pi$
$230$		0			0
$231$	13.3959			0.0579907
$232$	−27.0949	−	27.0949i	−0.116788	−	0.116788i
$233$	−139.119	+	139.119i	−0.597077	+	0.597077i	−0.939534	−	0.342457i	$-0.888741\pi$
$233$	−139.119	+	139.119i	−0.597077	+	0.597077i	0.342457	+	0.939534i	$0.388741\pi$
$234$			6.79852i			0.0290535i
$235$		0			0
$236$	234.330			0.992924
$237$	45.5421	+	45.5421i	0.192161	+	0.192161i
$238$	5.78110	−	5.78110i	0.0242903	−	0.0242903i
$239$		−	183.280i		−	0.766864i	−0.923569	−	0.383432i	$-0.874742\pi$
$239$		−	183.280i		−	0.766864i	0.923569	−	0.383432i	$-0.125258\pi$
$240$		0			0
$241$	−280.094			−1.16222			−0.581108	−	0.813827i	$-0.697380\pi$
$241$	−280.094			−1.16222			−0.581108	+	0.813827i	$0.697380\pi$
$242$	112.455	+	112.455i	0.464689	+	0.464689i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	90.8747i		−	0.372437i
$245$		0			0
$246$	−177.889			−0.723124
$247$	3.79809	+	3.79809i	0.0153769	+	0.0153769i
$248$	31.5873	−	31.5873i	0.127368	−	0.127368i
$249$			52.2553i			0.209861i
$250$		0			0
$251$	148.745			0.592611			0.296305	−	0.955093i	$-0.404245\pi$
$251$	148.745			0.592611			0.296305	+	0.955093i	$0.404245\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	−23.1133	+	23.1133i	−0.0913569	+	0.0913569i
$254$			285.926i			1.12569i
$255$		0			0
$256$	16.0000			0.0625000
$257$	241.684	+	241.684i	0.940404	+	0.940404i	0.998321	−	0.0579178i	$-0.0184461\pi$
$257$	241.684	+	241.684i	0.940404	+	0.940404i	−0.0579178	+	0.998321i	$0.518446\pi$
$258$	−49.9082	+	49.9082i	−0.193442	+	0.193442i
$259$		−	62.9739i		−	0.243142i
$260$		0			0
$261$	−40.6423			−0.155718
$262$	−3.55384	−	3.55384i	−0.0135643	−	0.0135643i
$263$	234.607	−	234.607i	0.892042	−	0.892042i	−0.102673	−	0.994715i	$-0.532740\pi$
$263$	234.607	−	234.607i	0.892042	−	0.892042i	0.994715	+	0.102673i	$0.0327395\pi$
$264$			14.3208i			0.0542454i
$265$		0			0
$266$	−12.5420			−0.0471503
$267$	123.639	+	123.639i	0.463069	+	0.463069i
$268$	115.555	−	115.555i	0.431174	−	0.431174i
$269$		−	357.902i		−	1.33049i	−0.746625	−	0.665245i	$-0.768327\pi$
$269$		−	357.902i		−	1.33049i	0.746625	−	0.665245i	$-0.231673\pi$
$270$		0			0
$271$	178.869			0.660035			0.330017	−	0.943975i	$-0.392945\pi$
$271$	178.869			0.660035			0.330017	+	0.943975i	$0.392945\pi$
$272$	6.18025	+	6.18025i	0.0227215	+	0.0227215i
$273$	5.19245	−	5.19245i	0.0190200	−	0.0190200i
$274$			150.211i			0.548214i
$275$		0			0
$276$	38.7353			0.140345
$277$	119.355	+	119.355i	0.430883	+	0.430883i	0.888929	−	0.458045i	$-0.151450\pi$
$277$	119.355	+	119.355i	0.430883	+	0.430883i	−0.458045	+	0.888929i	$0.651450\pi$
$278$	192.352	−	192.352i	0.691914	−	0.691914i
$279$		−	47.3809i		−	0.169824i
$280$		0			0
$281$	−42.3632			−0.150759			−0.0753793	−	0.997155i	$-0.524017\pi$
$281$	−42.3632			−0.150759			−0.0753793	+	0.997155i	$0.524017\pi$
$282$	128.156	+	128.156i	0.454453	+	0.454453i
$283$	−3.43964	+	3.43964i	−0.0121542	+	0.0121542i	−0.713158	−	0.701004i	$-0.752736\pi$
$283$	−3.43964	+	3.43964i	−0.0121542	+	0.0121542i	0.701004	+	0.713158i	$0.252736\pi$
$284$		−	103.443i		−	0.364238i
$285$		0			0
$286$	−6.62451			−0.0231626
$287$	135.865	+	135.865i	0.473396	+	0.473396i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	284.226i		−	0.983479i
$290$		0			0
$291$	128.815			0.442665
$292$	−144.770	−	144.770i	−0.495788	−	0.495788i
$293$	25.3982	−	25.3982i	0.0866834	−	0.0866834i	−0.662436	−	0.749119i	$-0.730477\pi$
$293$	25.3982	−	25.3982i	0.0866834	−	0.0866834i	0.749119	+	0.662436i	$0.230477\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	67.3219			0.227439
$297$	10.7406	+	10.7406i	0.0361636	+	0.0361636i
$298$	−77.5005	+	77.5005i	−0.260069	+	0.260069i
$299$			17.9182i			0.0599270i
$300$		0			0
$301$	76.2360			0.253276
$302$	−36.8195	−	36.8195i	−0.121919	−	0.121919i
$303$	158.503	−	158.503i	0.523113	−	0.523113i
$304$		−	13.4080i		−	0.0441051i
$305$		0			0
$306$	9.27038			0.0302954
$307$	323.839	+	323.839i	1.05485	+	1.05485i	0.998406	+	0.0564445i	$0.0179764\pi$
$307$	323.839	+	323.839i	1.05485	+	1.05485i	0.0564445	+	0.998406i	$0.482024\pi$
$308$	10.9377	−	10.9377i	0.0355119	−	0.0355119i
$309$		−	76.0437i		−	0.246096i
$310$		0			0
$311$	−284.428			−0.914561			−0.457280	−	0.889323i	$-0.651176\pi$
$311$	−284.428			−0.914561			−0.457280	+	0.889323i	$0.651176\pi$
$312$	5.55096	+	5.55096i	0.0177916	+	0.0177916i
$313$	−178.964	+	178.964i	−0.571771	+	0.571771i	−0.932623	−	0.360852i	$-0.882486\pi$
$313$	−178.964	+	178.964i	−0.571771	+	0.571771i	0.360852	+	0.932623i	$0.382486\pi$
$314$			151.531i			0.482582i
$315$		0			0
$316$	74.3700			0.235348
$317$	−335.800	−	335.800i	−1.05931	−	1.05931i	−0.998127	−	0.0611787i	$-0.980514\pi$
$317$	−335.800	−	335.800i	−1.05931	−	1.05931i	−0.0611787	−	0.998127i	$-0.519486\pi$
$318$	99.2971	−	99.2971i	0.312255	−	0.312255i
$319$		−	39.6021i		−	0.124145i
$320$		0			0
$321$	268.026			0.834973
$322$	−29.5846	−	29.5846i	−0.0918775	−	0.0918775i
$323$	5.17903	−	5.17903i	0.0160342	−	0.0160342i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	348.905			1.07026
$327$	−84.0384	−	84.0384i	−0.256998	−	0.256998i
$328$	−145.245	+	145.245i	−0.442821	+	0.442821i
$329$		−	195.761i		−	0.595019i
$330$		0			0
$331$	444.301			1.34230			0.671150	−	0.741322i	$-0.265801\pi$
$331$	444.301			1.34230			0.671150	+	0.741322i	$0.265801\pi$
$332$	42.6663	+	42.6663i	0.128513	+	0.128513i
$333$	50.4914	−	50.4914i	0.151626	−	0.151626i
$334$			238.550i			0.714222i
$335$		0			0
$336$	−18.3303			−0.0545545
$337$	−431.469	−	431.469i	−1.28032	−	1.28032i	−0.940483	−	0.339842i	$-0.889626\pi$
$337$	−431.469	−	431.469i	−1.28032	−	1.28032i	−0.339842	−	0.940483i	$-0.610374\pi$
$338$	166.432	−	166.432i	0.492403	−	0.492403i
$339$			166.655i			0.491608i
$340$		0			0
$341$	46.1682			0.135391
$342$	−10.0560	−	10.0560i	−0.0294034	−	0.0294034i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			81.4997i			0.236918i
$345$		0			0
$346$	220.041			0.635957
$347$	227.893	+	227.893i	0.656751	+	0.656751i	0.954610	−	0.297859i	$-0.0962725\pi$
$347$	227.893	+	227.893i	0.656751	+	0.656751i	−0.297859	+	0.954610i	$0.596272\pi$
$348$	−33.1843	+	33.1843i	−0.0953573	+	0.0953573i
$349$			280.016i			0.802337i	0.916004	+	0.401168i	$0.131396\pi$
$349$			280.016i			0.802337i	−0.916004	+	0.401168i	$0.868604\pi$
$350$		0			0
$351$	8.32645			0.0237221
$352$	11.6929	+	11.6929i	0.0332184	+	0.0332184i
$353$	114.469	−	114.469i	0.324276	−	0.324276i	−0.526129	−	0.850405i	$-0.676357\pi$
$353$	114.469	−	114.469i	0.324276	−	0.324276i	0.850405	+	0.526129i	$0.176357\pi$
$354$		−	286.995i		−	0.810719i
$355$		0			0
$356$	201.902			0.567141
$357$	−7.08037	−	7.08037i	−0.0198330	−	0.0198330i
$358$	−49.0357	+	49.0357i	−0.136971	+	0.136971i
$359$			700.748i			1.95195i	0.217893	+	0.975973i	$0.430082\pi$
$359$			700.748i			1.95195i	−0.217893	+	0.975973i	$0.569918\pi$
$360$		0			0
$361$	349.764			0.968876
$362$	327.143	+	327.143i	0.903709	+	0.903709i
$363$	137.728	−	137.728i	0.379417	−	0.379417i
$364$		−	8.47924i		−	0.0232946i
$365$		0			0
$366$	−111.298			−0.304094
$367$	−412.257	−	412.257i	−1.12332	−	1.12332i	−0.991240	−	0.132075i	$-0.957836\pi$
$367$	−412.257	−	412.257i	−1.12332	−	1.12332i	−0.132075	−	0.991240i	$-0.542164\pi$
$368$	31.6272	−	31.6272i	0.0859436	−	0.0859436i
$369$			217.868i			0.590428i
$370$		0			0
$371$	−151.679			−0.408838
$372$	−38.6864	−	38.6864i	−0.103996	−	0.103996i
$373$	121.669	−	121.669i	0.326191	−	0.326191i	−0.524945	−	0.851136i	$-0.675914\pi$
$373$	121.669	−	121.669i	0.326191	−	0.326191i	0.851136	+	0.524945i	$0.175914\pi$
$374$			9.03311i			0.0241527i
$375$		0			0
$376$	209.278			0.556589
$377$	−15.3504	−	15.3504i	−0.0407173	−	0.0407173i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$		−	709.113i		−	1.87101i	−0.353312	−	0.935506i	$-0.614945\pi$
$379$		−	709.113i		−	1.87101i	0.353312	−	0.935506i	$-0.385055\pi$
$380$		0			0
$381$	350.187			0.919125
$382$	−289.078	−	289.078i	−0.756749	−	0.756749i
$383$	476.611	−	476.611i	1.24441	−	1.24441i	0.286264	−	0.958151i	$-0.407587\pi$
$383$	476.611	−	476.611i	1.24441	−	1.24441i	0.958151	−	0.286264i	$-0.0924134\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−262.425			−0.679858
$387$	61.1248	+	61.1248i	0.157945	+	0.157945i
$388$	105.177	−	105.177i	0.271076	−	0.271076i
$389$			270.210i			0.694627i	0.937749	+	0.347313i	$0.112906\pi$
$389$			270.210i			0.694627i	−0.937749	+	0.347313i	$0.887094\pi$
$390$		0			0
$391$	24.4330			0.0624886
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	−4.35255	+	4.35255i	−0.0110752	+	0.0110752i
$394$			223.597i			0.567504i
$395$		0			0
$396$	17.5393			0.0442911
$397$	169.270	+	169.270i	0.426374	+	0.426374i	0.887391	−	0.461017i	$-0.152515\pi$
$397$	169.270	+	169.270i	0.426374	+	0.426374i	−0.461017	+	0.887391i	$0.652515\pi$
$398$	−58.3715	+	58.3715i	−0.146662	+	0.146662i
$399$			15.3607i			0.0384981i
$400$		0			0
$401$	397.414			0.991058			0.495529	−	0.868592i	$-0.334974\pi$
$401$	397.414			0.991058			0.495529	+	0.868592i	$0.334974\pi$
$402$	−141.525	−	141.525i	−0.352052	−	0.352052i
$403$	17.8956	−	17.8956i	0.0444059	−	0.0444059i
$404$		−	258.834i		−	0.640679i
$405$		0			0
$406$	50.6899			0.124852
$407$	49.1991	+	49.1991i	0.120882	+	0.120882i
$408$	7.56923	−	7.56923i	0.0185520	−	0.0185520i
$409$			787.478i			1.92537i	0.270616	+	0.962687i	$0.412773\pi$
$409$			787.478i			1.92537i	−0.270616	+	0.962687i	$0.587227\pi$
$410$		0			0
$411$	183.970			0.447615
$412$	−62.0894	−	62.0894i	−0.150703	−	0.150703i
$413$	−219.196	+	219.196i	−0.530740	+	0.530740i
$414$		−	47.4409i		−	0.114591i
$415$		0			0
$416$	9.06469			0.0217901
$417$	−235.582	−	235.582i	−0.564945	−	0.564945i
$418$	9.79858	−	9.79858i	0.0234416	−	0.0234416i
$419$		−	293.606i		−	0.700730i	−0.936613	−	0.350365i	$-0.886058\pi$
$419$		−	293.606i		−	0.700730i	0.936613	−	0.350365i	$-0.113942\pi$
$420$		0			0
$421$	−294.797			−0.700230			−0.350115	−	0.936707i	$-0.613857\pi$
$421$	−294.797			−0.700230			−0.350115	+	0.936707i	$0.613857\pi$
$422$	−55.0602	−	55.0602i	−0.130474	−	0.130474i
$423$	156.958	−	156.958i	0.371060	−	0.371060i
$424$		−	162.151i		−	0.382433i
$425$		0			0
$426$	−126.692			−0.297399
$427$	85.0055	+	85.0055i	0.199076	+	0.199076i
$428$	218.842	−	218.842i	0.511314	−	0.511314i
$429$			8.11333i			0.0189122i
$430$		0			0
$431$	−314.916			−0.730663			−0.365332	−	0.930877i	$-0.619044\pi$
$431$	−314.916			−0.730663			−0.365332	+	0.930877i	$0.619044\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−236.366	+	236.366i	−0.545880	+	0.545880i	−0.925246	−	0.379367i	$-0.876142\pi$
$433$	−236.366	+	236.366i	−0.545880	+	0.545880i	0.379367	+	0.925246i	$0.376142\pi$
$434$			59.0944i			0.136162i
$435$		0			0
$436$	−137.234			−0.314757
$437$	−26.5035	−	26.5035i	−0.0606488	−	0.0606488i
$438$	−177.306	+	177.306i	−0.404809	+	0.404809i
$439$			254.993i			0.580850i	0.956898	+	0.290425i	$0.0937967\pi$
$439$			254.993i			0.580850i	−0.956898	+	0.290425i	$0.906203\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	3.50138	+	3.50138i	0.00792167	+	0.00792167i
$443$	292.628	−	292.628i	0.660559	−	0.660559i	−0.294953	−	0.955512i	$-0.595304\pi$
$443$	292.628	−	292.628i	0.660559	−	0.660559i	0.955512	+	0.294953i	$0.0953039\pi$
$444$		−	82.4522i		−	0.185703i
$445$		0			0
$446$	−203.537			−0.456360
$447$	94.9184	+	94.9184i	0.212345	+	0.212345i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$		−	400.989i		−	0.893072i	−0.894766	−	0.446536i	$-0.852657\pi$
$449$		−	400.989i		−	0.893072i	0.894766	−	0.446536i	$-0.147343\pi$
$450$		0			0
$451$	−212.292			−0.470714
$452$	136.073	+	136.073i	0.301047	+	0.301047i
$453$	−45.0944	+	45.0944i	−0.0995462	+	0.0995462i
$454$		−	50.1179i		−	0.110392i
$455$		0			0
$456$	−16.4213			−0.0360117
$457$	172.040	+	172.040i	0.376454	+	0.376454i	0.869821	−	0.493367i	$-0.164234\pi$
$457$	172.040	+	172.040i	0.376454	+	0.376454i	−0.493367	+	0.869821i	$0.664234\pi$
$458$	283.497	−	283.497i	0.618990	−	0.618990i
$459$		−	11.3539i		−	0.0247361i
$460$		0			0
$461$	153.918			0.333878			0.166939	−	0.985967i	$-0.446612\pi$
$461$	153.918			0.333878			0.166939	+	0.985967i	$0.446612\pi$
$462$	−13.3959	−	13.3959i	−0.0289954	−	0.0289954i
$463$	291.763	−	291.763i	0.630158	−	0.630158i	−0.317949	−	0.948108i	$-0.602994\pi$
$463$	291.763	−	291.763i	0.630158	−	0.630158i	0.948108	+	0.317949i	$0.102994\pi$
$464$			54.1898i			0.116788i
$465$		0			0
$466$	278.238			0.597077
$467$	503.234	+	503.234i	1.07759	+	1.07759i	0.996725	+	0.0808645i	$0.0257681\pi$
$467$	503.234	+	503.234i	1.07759	+	1.07759i	0.0808645	+	0.996725i	$0.474232\pi$
$468$	6.79852	−	6.79852i	0.0145267	−	0.0145267i
$469$			216.183i			0.460944i
$470$		0			0
$471$	185.586			0.394026
$472$	−234.330	−	234.330i	−0.496462	−	0.496462i
$473$	−59.5603	+	59.5603i	−0.125920	+	0.125920i
$474$		−	91.0843i		−	0.192161i
$475$		0			0
$476$	−11.5622			−0.0242903
$477$	−121.614	−	121.614i	−0.254955	−	0.254955i
$478$	−183.280	+	183.280i	−0.383432	+	0.383432i
$479$			670.857i			1.40054i	0.713880	+	0.700268i	$0.246936\pi$
$479$			670.857i			1.40054i	−0.713880	+	0.700268i	$0.753064\pi$
$480$		0			0
$481$	38.1408			0.0792947
$482$	280.094	+	280.094i	0.581108	+	0.581108i
$483$	−36.2335	+	36.2335i	−0.0750177	+	0.0750177i
$484$		−	224.910i		−	0.464689i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	431.350	+	431.350i	0.885729	+	0.885729i	0.994110	−	0.108380i	$-0.0345664\pi$
$487$	431.350	+	431.350i	0.885729	+	0.885729i	−0.108380	+	0.994110i	$0.534566\pi$
$488$	−90.8747	+	90.8747i	−0.186219	+	0.186219i
$489$		−	427.320i		−	0.873865i
$490$		0			0
$491$	−643.019			−1.30961			−0.654806	−	0.755797i	$-0.727250\pi$
$491$	−643.019			−1.30961			−0.654806	+	0.755797i	$0.727250\pi$
$492$	177.889	+	177.889i	0.361562	+	0.361562i
$493$	−20.9317	+	20.9317i	−0.0424577	+	0.0424577i
$494$		−	7.59618i		−	0.0153769i
$495$		0			0
$496$	−63.1746			−0.127368
$497$	96.7625	+	96.7625i	0.194693	+	0.194693i
$498$	52.2553	−	52.2553i	0.104930	−	0.104930i
$499$		−	350.058i		−	0.701520i	−0.936465	−	0.350760i	$-0.885923\pi$
$499$		−	350.058i		−	0.701520i	0.936465	−	0.350760i	$-0.114077\pi$
$500$		0			0
$501$	292.163			0.583160
$502$	−148.745	−	148.745i	−0.296305	−	0.296305i
$503$	−160.423	+	160.423i	−0.318932	+	0.318932i	−0.848357	−	0.529425i	$-0.822408\pi$
$503$	−160.423	+	160.423i	−0.318932	+	0.318932i	0.529425	+	0.848357i	$0.322408\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	46.2266			0.0913569
$507$	−203.837	−	203.837i	−0.402045	−	0.402045i
$508$	285.926	−	285.926i	0.562847	−	0.562847i
$509$			402.935i			0.791620i	0.918332	+	0.395810i	$0.129536\pi$
$509$			402.935i			0.791620i	−0.918332	+	0.395810i	$0.870464\pi$
$510$		0			0
$511$	270.840			0.530020
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−12.3160	+	12.3160i	−0.0240078	+	0.0240078i
$514$		−	483.367i		−	0.940404i
$515$		0			0
$516$	99.8163			0.193442
$517$	152.941	+	152.941i	0.295824	+	0.295824i
$518$	−62.9739	+	62.9739i	−0.121571	+	0.121571i
$519$		−	269.494i		−	0.519257i
$520$		0			0
$521$	−725.448			−1.39241			−0.696207	−	0.717841i	$-0.745131\pi$
$521$	−725.448			−1.39241			−0.696207	+	0.717841i	$0.745131\pi$
$522$	40.6423	+	40.6423i	0.0778589	+	0.0778589i
$523$	−454.490	+	454.490i	−0.869005	+	0.869005i	−0.992362	−	0.123357i	$-0.960634\pi$
$523$	−454.490	+	454.490i	−0.869005	+	0.869005i	0.123357	+	0.992362i	$0.460634\pi$
$524$			7.10768i			0.0135643i
$525$		0			0
$526$	−469.214			−0.892042
$527$	−24.4022	−	24.4022i	−0.0463040	−	0.0463040i
$528$	14.3208	−	14.3208i	0.0271227	−	0.0271227i
$529$			403.965i			0.763638i
$530$		0			0
$531$	−351.495			−0.661949
$532$	12.5420	+	12.5420i	0.0235752	+	0.0235752i
$533$	−82.2878	+	82.2878i	−0.154386	+	0.154386i
$534$		−	247.279i		−	0.463069i
$535$		0			0
$536$	−231.109			−0.431174
$537$	60.0563	+	60.0563i	0.111837	+	0.111837i
$538$	−357.902	+	357.902i	−0.665245	+	0.665245i
$539$			20.4625i			0.0379638i
$540$		0			0
$541$	−173.852			−0.321354			−0.160677	−	0.987007i	$-0.551368\pi$
$541$	−173.852			−0.321354			−0.160677	+	0.987007i	$0.551368\pi$
$542$	−178.869	−	178.869i	−0.330017	−	0.330017i
$543$	400.666	−	400.666i	0.737875	−	0.737875i
$544$		−	12.3605i		−	0.0227215i
$545$		0			0
$546$	−10.3849			−0.0190200
$547$	293.440	+	293.440i	0.536453	+	0.536453i	0.922485	−	0.386032i	$-0.126155\pi$
$547$	293.440	+	293.440i	0.536453	+	0.536453i	−0.386032	+	0.922485i	$0.626155\pi$
$548$	150.211	−	150.211i	0.274107	−	0.274107i
$549$			136.312i			0.248291i
$550$		0			0
$551$	45.4109			0.0824154
$552$	−38.7353	−	38.7353i	−0.0701726	−	0.0701726i
$553$	−69.5668	+	69.5668i	−0.125799	+	0.125799i
$554$		−	238.709i		−	0.430883i
$555$		0			0
$556$	−384.704			−0.691914
$557$	−234.581	−	234.581i	−0.421151	−	0.421151i	0.464449	−	0.885600i	$-0.346253\pi$
$557$	−234.581	−	234.581i	−0.421151	−	0.421151i	−0.885600	+	0.464449i	$0.846253\pi$
$558$	−47.3809	+	47.3809i	−0.0849121	+	0.0849121i
$559$			46.1731i			0.0825994i
$560$		0			0
$561$	11.0633			0.0197206
$562$	42.3632	+	42.3632i	0.0753793	+	0.0753793i
$563$	−177.541	+	177.541i	−0.315348	+	0.315348i	−0.846977	−	0.531629i	$-0.821580\pi$
$563$	−177.541	+	177.541i	−0.315348	+	0.315348i	0.531629	+	0.846977i	$0.321580\pi$
$564$		−	256.312i		−	0.454453i
$565$		0			0
$566$	6.87928			0.0121542
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	−103.443	+	103.443i	−0.182119	+	0.182119i
$569$			253.619i			0.445727i	0.974850	+	0.222864i	$0.0715405\pi$
$569$			253.619i			0.445727i	−0.974850	+	0.222864i	$0.928460\pi$
$570$		0			0
$571$	219.857			0.385038			0.192519	−	0.981293i	$-0.438334\pi$
$571$	219.857			0.385038			0.192519	+	0.981293i	$0.438334\pi$
$572$	6.62451	+	6.62451i	0.0115813	+	0.0115813i
$573$	−354.047	+	354.047i	−0.617883	+	0.617883i
$574$		−	271.729i		−	0.473396i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−419.350	−	419.350i	−0.726776	−	0.726776i	0.243200	−	0.969976i	$-0.421803\pi$
$577$	−419.350	−	419.350i	−0.726776	−	0.726776i	−0.969976	+	0.243200i	$0.921803\pi$
$578$	−284.226	+	284.226i	−0.491740	+	0.491740i
$579$			321.404i			0.555101i
$580$		0			0
$581$	−79.8213			−0.137386
$582$	−128.815	−	128.815i	−0.221332	−	0.221332i
$583$	118.501	−	118.501i	0.203261	−	0.203261i
$584$			289.540i			0.495788i
$585$		0			0
$586$	−50.7965			−0.0866834
$587$	493.116	+	493.116i	0.840061	+	0.840061i	0.988867	−	0.148805i	$-0.0475427\pi$
$587$	493.116	+	493.116i	0.840061	+	0.840061i	−0.148805	+	0.988867i	$0.547543\pi$
$588$	17.1464	−	17.1464i	0.0291606	−	0.0291606i
$589$			52.9401i			0.0898814i
$590$		0			0
$591$	273.849			0.463365
$592$	−67.3219	−	67.3219i	−0.113719	−	0.113719i
$593$	−528.205	+	528.205i	−0.890733	+	0.890733i	−0.994592	−	0.103859i	$-0.966881\pi$
$593$	−528.205	+	528.205i	−0.890733	+	0.890733i	0.103859	+	0.994592i	$0.466881\pi$
$594$		−	21.4812i		−	0.0361636i
$595$		0			0
$596$	155.001			0.260069
$597$	71.4902	+	71.4902i	0.119749	+	0.119749i
$598$	17.9182	−	17.9182i	0.0299635	−	0.0299635i
$599$		−	436.395i		−	0.728540i	−0.931293	−	0.364270i	$-0.881319\pi$
$599$		−	436.395i		−	0.728540i	0.931293	−	0.364270i	$-0.118681\pi$
$600$		0			0
$601$	907.900			1.51065			0.755324	−	0.655351i	$-0.227479\pi$
$601$	907.900			1.51065			0.755324	+	0.655351i	$0.227479\pi$
$602$	−76.2360	−	76.2360i	−0.126638	−	0.126638i
$603$	−173.332	+	173.332i	−0.287449	+	0.287449i
$604$			73.6389i			0.121919i
$605$		0			0
$606$	−317.006			−0.523113
$607$	46.6746	+	46.6746i	0.0768939	+	0.0768939i	0.744508	−	0.667614i	$-0.232684\pi$
$607$	46.6746	+	46.6746i	0.0768939	+	0.0768939i	−0.667614	+	0.744508i	$0.732684\pi$
$608$	−13.4080	+	13.4080i	−0.0220526	+	0.0220526i
$609$		−	62.0822i		−	0.101941i
$610$		0			0
$611$	118.565			0.194050
$612$	−9.27038	−	9.27038i	−0.0151477	−	0.0151477i
$613$	−404.981	+	404.981i	−0.660653	+	0.660653i	−0.955534	−	0.294881i	$-0.904720\pi$
$613$	−404.981	+	404.981i	−0.660653	+	0.660653i	0.294881	+	0.955534i	$0.404720\pi$
$614$		−	647.678i		−	1.05485i
$615$		0			0
$616$	−21.8753			−0.0355119
$617$	−821.889	−	821.889i	−1.33207	−	1.33207i	−0.903514	−	0.428558i	$-0.859022\pi$
$617$	−821.889	−	821.889i	−1.33207	−	1.33207i	−0.428558	−	0.903514i	$-0.640978\pi$
$618$	−76.0437	+	76.0437i	−0.123048	+	0.123048i
$619$			355.855i			0.574886i	0.957798	+	0.287443i	$0.0928052\pi$
$619$			355.855i			0.574886i	−0.957798	+	0.287443i	$0.907195\pi$
$620$		0			0
$621$	−58.1029			−0.0935635
$622$	284.428	+	284.428i	0.457280	+	0.457280i
$623$	−188.862	+	188.862i	−0.303150	+	0.303150i
$624$		−	11.1019i		−	0.0177916i
$625$		0			0
$626$	357.929			0.571771
$627$	−12.0008	−	12.0008i	−0.0191400	−	0.0191400i
$628$	151.531	−	151.531i	0.241291	−	0.241291i
$629$		−	52.0083i		−	0.0826841i
$630$		0			0
$631$	−588.910			−0.933297			−0.466648	−	0.884443i	$-0.654539\pi$
$631$	−588.910			−0.933297			−0.466648	+	0.884443i	$0.654539\pi$
$632$	−74.3700	−	74.3700i	−0.117674	−	0.117674i
$633$	−67.4347	+	67.4347i	−0.106532	+	0.106532i
$634$			671.600i			1.05931i
$635$		0			0
$636$	−198.594			−0.312255
$637$	7.93160	+	7.93160i	0.0124515	+	0.0124515i
$638$	−39.6021	+	39.6021i	−0.0620723	+	0.0620723i
$639$			155.165i			0.242825i
$640$		0			0
$641$	−703.566			−1.09761			−0.548804	−	0.835951i	$-0.684917\pi$
$641$	−703.566			−1.09761			−0.548804	+	0.835951i	$0.684917\pi$
$642$	−268.026	−	268.026i	−0.417486	−	0.417486i
$643$	−75.8005	+	75.8005i	−0.117886	+	0.117886i	−0.763589	−	0.645703i	$-0.776564\pi$
$643$	−75.8005	+	75.8005i	−0.117886	+	0.117886i	0.645703	+	0.763589i	$0.276564\pi$
$644$			59.1691i			0.0918775i
$645$		0			0
$646$	−10.3581			−0.0160342
$647$	−362.070	−	362.070i	−0.559613	−	0.559613i	0.369584	−	0.929197i	$-0.379500\pi$
$647$	−362.070	−	362.070i	−0.559613	−	0.559613i	−0.929197	+	0.369584i	$0.879500\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	342.499i		−	0.527733i
$650$		0			0
$651$	72.3756			0.111176
$652$	−348.905	−	348.905i	−0.535131	−	0.535131i
$653$	−804.153	+	804.153i	−1.23147	+	1.23147i	−0.268077	+	0.963397i	$0.586388\pi$
$653$	−804.153	+	804.153i	−1.23147	+	1.23147i	−0.963397	+	0.268077i	$0.913612\pi$
$654$			168.077i			0.256998i
$655$		0			0
$656$	290.491			0.442821
$657$	217.155	+	217.155i	0.330525	+	0.330525i
$658$	−195.761	+	195.761i	−0.297510	+	0.297510i
$659$		−	803.984i		−	1.22001i	−0.792399	−	0.610003i	$-0.791168\pi$
$659$		−	803.984i		−	1.22001i	0.792399	−	0.610003i	$-0.208832\pi$
$660$		0			0
$661$	−923.281			−1.39679			−0.698397	−	0.715710i	$-0.746103\pi$
$661$	−923.281			−1.39679			−0.698397	+	0.715710i	$0.746103\pi$
$662$	−444.301	−	444.301i	−0.671150	−	0.671150i
$663$	4.28830	−	4.28830i	0.00646802	−	0.00646802i
$664$		−	85.3325i		−	0.128513i
$665$		0			0
$666$	−100.983			−0.151626
$667$	107.117	+	107.117i	0.160595	+	0.160595i
$668$	238.550	−	238.550i	0.357111	−	0.357111i
$669$			249.280i			0.372616i
$670$		0			0
$671$	−132.823			−0.197948
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	750.322	−	750.322i	1.11489	−	1.11489i	0.122413	−	0.992479i	$-0.460937\pi$
$673$	750.322	−	750.322i	1.11489	−	1.11489i	0.992479	−	0.122413i	$-0.0390631\pi$
$674$			862.939i			1.28032i
$675$		0			0
$676$	−332.864			−0.492403
$677$	405.042	+	405.042i	0.598290	+	0.598290i	0.939857	−	0.341567i	$-0.110958\pi$
$677$	405.042	+	405.042i	0.598290	+	0.598290i	−0.341567	+	0.939857i	$0.610958\pi$
$678$	166.655	−	166.655i	0.245804	−	0.245804i
$679$			196.769i			0.289792i
$680$		0			0
$681$	−61.3816			−0.0901345
$682$	−46.1682	−	46.1682i	−0.0676954	−	0.0676954i
$683$	−666.271	+	666.271i	−0.975506	+	0.975506i	−0.999707	−	0.0242009i	$-0.992296\pi$
$683$	−666.271	+	666.271i	−0.975506	+	0.975506i	0.0242009	+	0.999707i	$0.492296\pi$
$684$			20.1119i			0.0294034i
$685$		0			0
$686$	−26.1916			−0.0381802
$687$	−347.212	−	347.212i	−0.505403	−	0.505403i
$688$	81.4997	−	81.4997i	0.118459	−	0.118459i
$689$		−	91.8658i		−	0.133332i
$690$		0			0
$691$	521.895			0.755275			0.377637	−	0.925954i	$-0.376737\pi$
$691$	521.895			0.755275			0.377637	+	0.925954i	$0.376737\pi$
$692$	−220.041	−	220.041i	−0.317978	−	0.317978i
$693$	−16.4065	+	16.4065i	−0.0236746	+	0.0236746i
$694$		−	455.785i		−	0.656751i
$695$		0			0
$696$	66.3687			0.0953573
$697$	112.207	+	112.207i	0.160985	+	0.160985i
$698$	280.016	−	280.016i	0.401168	−	0.401168i
$699$		−	340.771i		−	0.487511i
$700$		0			0
$701$	525.400			0.749501			0.374750	−	0.927126i	$-0.377728\pi$
$701$	525.400			0.749501			0.374750	+	0.927126i	$0.377728\pi$
$702$	−8.32645	−	8.32645i	−0.0118610	−	0.0118610i
$703$	−56.4156	+	56.4156i	−0.0802497	+	0.0802497i
$704$		−	23.3857i		−	0.0332184i
$705$		0			0
$706$	−228.939			−0.324276
$707$	242.117	+	242.117i	0.342458	+	0.342458i
$708$	−286.995	+	286.995i	−0.405360	+	0.405360i
$709$		−	269.858i		−	0.380618i	−0.981724	−	0.190309i	$-0.939051\pi$
$709$		−	269.858i		−	0.380618i	0.981724	−	0.190309i	$-0.0609489\pi$
$710$		0			0
$711$	−111.555			−0.156899
$712$	−201.902	−	201.902i	−0.283571	−	0.283571i
$713$	−124.877	+	124.877i	−0.175144	+	0.175144i
$714$			14.1607i			0.0198330i
$715$		0			0
$716$	98.0715			0.136971
$717$	224.472	+	224.472i	0.313071	+	0.313071i
$718$	700.748	−	700.748i	0.975973	−	0.975973i
$719$		−	42.9232i		−	0.0596985i	−0.999554	−	0.0298493i	$-0.990497\pi$
$719$		−	42.9232i		−	0.0596985i	0.999554	−	0.0298493i	$-0.00950273\pi$
$720$		0			0
$721$	116.159			0.161108
$722$	−349.764	−	349.764i	−0.484438	−	0.484438i
$723$	343.044	−	343.044i	0.474472	−	0.474472i
$724$		−	654.285i		−	0.903709i
$725$		0			0
$726$	−275.457			−0.379417
$727$	−109.192	−	109.192i	−0.150195	−	0.150195i	0.628010	−	0.778205i	$-0.283870\pi$
$727$	−109.192	−	109.192i	−0.150195	−	0.150195i	−0.778205	+	0.628010i	$0.783870\pi$
$728$	−8.47924	+	8.47924i	−0.0116473	+	0.0116473i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	62.9611			0.0861301
$732$	111.298	+	111.298i	0.152047	+	0.152047i
$733$	−414.682	+	414.682i	−0.565733	+	0.565733i	−0.930930	−	0.365197i	$-0.881001\pi$
$733$	−414.682	+	414.682i	−0.565733	+	0.565733i	0.365197	+	0.930930i	$0.381001\pi$
$734$			824.513i			1.12332i
$735$		0			0
$736$	−63.2545			−0.0859436
$737$	−168.895	−	168.895i	−0.229166	−	0.229166i
$738$	217.868	−	217.868i	0.295214	−	0.295214i
$739$		−	1042.54i		−	1.41074i	−0.708838	−	0.705372i	$-0.750780\pi$
$739$		−	1042.54i		−	1.41074i	0.708838	−	0.705372i	$-0.249220\pi$
$740$		0			0
$741$	−9.30338			−0.0125552
$742$	151.679	+	151.679i	0.204419	+	0.204419i
$743$	403.117	−	403.117i	0.542553	−	0.542553i	−0.381724	−	0.924277i	$-0.624669\pi$
$743$	403.117	−	403.117i	0.542553	−	0.542553i	0.924277	+	0.381724i	$0.124669\pi$
$744$			77.3728i			0.103996i
$745$		0			0
$746$	−243.338			−0.326191
$747$	−63.9994	−	63.9994i	−0.0856752	−	0.0856752i
$748$	9.03311	−	9.03311i	0.0120763	−	0.0120763i
$749$			409.417i			0.546618i
$750$		0			0
$751$	346.283			0.461096			0.230548	−	0.973061i	$-0.425948\pi$
$751$	346.283			0.461096			0.230548	+	0.973061i	$0.425948\pi$
$752$	−209.278	−	209.278i	−0.278295	−	0.278295i
$753$	−182.175	+	182.175i	−0.241932	+	0.241932i
$754$			30.7008i			0.0407173i
$755$		0			0
$756$	27.4955			0.0363696
$757$	−284.836	−	284.836i	−0.376270	−	0.376270i	0.493485	−	0.869754i	$-0.335723\pi$
$757$	−284.836	−	284.836i	−0.376270	−	0.376270i	−0.869754	+	0.493485i	$0.835723\pi$
$758$	−709.113	+	709.113i	−0.935506	+	0.935506i
$759$		−	56.6158i		−	0.0745926i
$760$		0			0
$761$	321.609			0.422614			0.211307	−	0.977420i	$-0.432228\pi$
$761$	321.609			0.422614			0.211307	+	0.977420i	$0.432228\pi$
$762$	−350.187	−	350.187i	−0.459563	−	0.459563i
$763$	128.371	−	128.371i	0.168245	−	0.168245i
$764$			578.156i			0.756749i
$765$		0			0
$766$	−953.222			−1.24441
$767$	−132.758	−	132.758i	−0.173087	−	0.173087i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			634.413i			0.824984i	0.910961	+	0.412492i	$0.135342\pi$
$769$			634.413i			0.824984i	−0.910961	+	0.412492i	$0.864658\pi$
$770$		0			0
$771$	−592.002			−0.767836
$772$	262.425	+	262.425i	0.339929	+	0.339929i
$773$	−793.682	+	793.682i	−1.02676	+	1.02676i	−0.0271240	+	0.999632i	$0.508635\pi$
$773$	−793.682	+	793.682i	−1.02676	+	1.02676i	−0.999632	+	0.0271240i	$0.991365\pi$
$774$		−	122.250i		−	0.157945i
$775$		0			0
$776$	−210.355			−0.271076
$777$	77.1269	+	77.1269i	0.0992625	+	0.0992625i
$778$	270.210	−	270.210i	0.347313	−	0.347313i
$779$		−	243.430i		−	0.312491i
$780$		0			0
$781$	−151.194			−0.193590
$782$	−24.4330	−	24.4330i	−0.0312443	−	0.0312443i
$783$	49.7765	−	49.7765i	0.0635715	−	0.0635715i
$784$		−	28.0000i		−	0.0357143i
$785$		0			0
$786$	8.70509			0.0110752
$787$	−30.7537	−	30.7537i	−0.0390771	−	0.0390771i	0.687298	−	0.726375i	$-0.258797\pi$
$787$	−30.7537	−	30.7537i	−0.0390771	−	0.0390771i	−0.726375	+	0.687298i	$0.758797\pi$
$788$	223.597	−	223.597i	0.283752	−	0.283752i
$789$			574.668i			0.728349i
$790$		0			0
$791$	−254.570			−0.321833
$792$	−17.5393	−	17.5393i	−0.0221456	−	0.0221456i
$793$	−51.4844	+	51.4844i	−0.0649236	+	0.0649236i
$794$		−	338.541i		−	0.426374i
$795$		0			0
$796$	116.743			0.146662
$797$	−613.430	−	613.430i	−0.769674	−	0.769674i	0.208375	−	0.978049i	$-0.433183\pi$
$797$	−613.430	−	613.430i	−0.769674	−	0.769674i	−0.978049	+	0.208375i	$0.933183\pi$
$798$	15.3607	−	15.3607i	0.0192490	−	0.0192490i
$799$		−	161.674i		−	0.202345i
$800$		0			0
$801$	−302.854			−0.378094
$802$	−397.414	−	397.414i	−0.495529	−	0.495529i
$803$	−211.597	+	211.597i	−0.263508	+	0.263508i
$804$			283.050i			0.352052i
$805$		0			0
$806$	−35.7911			−0.0444059
$807$	438.338	+	438.338i	0.543170	+	0.543170i
$808$	−258.834	+	258.834i	−0.320340	+	0.320340i
$809$			23.8289i			0.0294548i	0.999892	+	0.0147274i	$0.00468804\pi$
$809$			23.8289i			0.0294548i	−0.999892	+	0.0147274i	$0.995312\pi$
$810$		0			0
$811$	676.685			0.834383			0.417192	−	0.908819i	$-0.363014\pi$
$811$	676.685			0.834383			0.417192	+	0.908819i	$0.363014\pi$
$812$	−50.6899	−	50.6899i	−0.0624260	−	0.0624260i
$813$	−219.069	+	219.069i	−0.269458	+	0.269458i
$814$		−	98.3982i		−	0.120882i
$815$		0			0
$816$	−15.1385			−0.0185520
$817$	−68.2965	−	68.2965i	−0.0835942	−	0.0835942i
$818$	787.478	−	787.478i	0.962687	−	0.962687i
$819$			12.7189i			0.0155297i
$820$		0			0
$821$	−7.29733			−0.00888834			−0.00444417	−	0.999990i	$-0.501415\pi$
$821$	−7.29733			−0.00888834			−0.00444417	+	0.999990i	$0.501415\pi$
$822$	−183.970	−	183.970i	−0.223808	−	0.223808i
$823$	−3.19071	+	3.19071i	−0.00387692	+	0.00387692i	−0.709043	−	0.705166i	$-0.750873\pi$
$823$	−3.19071	+	3.19071i	−0.00387692	+	0.00387692i	0.705166	+	0.709043i	$0.250873\pi$
$824$			124.179i			0.150703i
$825$		0			0
$826$	438.391			0.530740
$827$	−355.496	−	355.496i	−0.429863	−	0.429863i	0.458719	−	0.888581i	$-0.348309\pi$
$827$	−355.496	−	355.496i	−0.429863	−	0.429863i	−0.888581	+	0.458719i	$0.848309\pi$
$828$	−47.4409	+	47.4409i	−0.0572957	+	0.0572957i
$829$		−	1466.78i		−	1.76933i	−0.466225	−	0.884666i	$-0.654386\pi$
$829$		−	1466.78i		−	1.76933i	0.466225	−	0.884666i	$-0.345614\pi$
$830$		0			0
$831$	−292.358			−0.351815
$832$	−9.06469	−	9.06469i	−0.0108951	−	0.0108951i
$833$	10.8154	−	10.8154i	0.0129837	−	0.0129837i
$834$			471.164i			0.564945i
$835$		0			0
$836$	−19.5972			−0.0234416
$837$	58.0296	+	58.0296i	0.0693304	+	0.0693304i
$838$	−293.606	+	293.606i	−0.350365	+	0.350365i
$839$		−	807.662i		−	0.962648i	−0.876543	−	0.481324i	$-0.840156\pi$
$839$		−	807.662i		−	0.962648i	0.876543	−	0.481324i	$-0.159844\pi$
$840$		0			0
$841$	657.467			0.781768
$842$	294.797	+	294.797i	0.350115	+	0.350115i
$843$	51.8841	−	51.8841i	0.0615470	−	0.0615470i
$844$			110.120i			0.130474i
$845$		0			0
$846$	−313.916			−0.371060
$847$	210.384	+	210.384i	0.248387	+	0.248387i
$848$	−162.151	+	162.151i	−0.191216	+	0.191216i
$849$		−	8.42536i		−	0.00992387i
$850$		0			0
$851$	−266.151			−0.312751
$852$	126.692	+	126.692i	0.148699	+	0.148699i
$853$	−34.4347	+	34.4347i	−0.0403690	+	0.0403690i	−0.727003	−	0.686634i	$-0.759087\pi$
$853$	−34.4347	+	34.4347i	−0.0403690	+	0.0403690i	0.686634	+	0.727003i	$0.259087\pi$
$854$		−	170.011i		−	0.199076i
$855$		0			0
$856$	−437.685			−0.511314
$857$	795.023	+	795.023i	0.927681	+	0.927681i	0.997556	−	0.0698747i	$-0.0222599\pi$
$857$	795.023	+	795.023i	0.927681	+	0.927681i	−0.0698747	+	0.997556i	$0.522260\pi$
$858$	8.11333	−	8.11333i	0.00945610	−	0.00945610i
$859$		−	367.334i		−	0.427629i	−0.976874	−	0.213815i	$-0.931411\pi$
$859$		−	367.334i		−	0.427629i	0.976874	−	0.213815i	$-0.0685889\pi$
$860$		0			0
$861$	−332.799			−0.386526
$862$	314.916	+	314.916i	0.365332	+	0.365332i
$863$	97.5396	−	97.5396i	0.113024	−	0.113024i	−0.648333	−	0.761357i	$-0.724534\pi$
$863$	97.5396	−	97.5396i	0.113024	−	0.113024i	0.761357	+	0.648333i	$0.224534\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	472.732			0.545880
$867$	348.104	+	348.104i	0.401504	+	0.401504i
$868$	59.0944	−	59.0944i	0.0680811	−	0.0680811i
$869$		−	108.700i		−	0.125086i
$870$		0			0
$871$	−130.933			−0.150325
$872$	137.234	+	137.234i	0.157379	+	0.157379i
$873$	−157.766	+	157.766i	−0.180717	+	0.180717i
$874$			53.0071i			0.0606488i
$875$		0			0
$876$	354.613			0.404809
$877$	326.965	+	326.965i	0.372822	+	0.372822i	0.868504	−	0.495682i	$-0.165082\pi$
$877$	326.965	+	326.965i	0.372822	+	0.372822i	−0.495682	+	0.868504i	$0.665082\pi$
$878$	254.993	−	254.993i	0.290425	−	0.290425i
$879$			62.2127i			0.0707767i
$880$		0			0
$881$	538.293			0.611003			0.305501	−	0.952192i	$-0.401176\pi$
$881$	538.293			0.611003			0.305501	+	0.952192i	$0.401176\pi$
$882$	−21.0000	−	21.0000i	−0.0238095	−	0.0238095i
$883$	951.591	−	951.591i	1.07768	−	1.07768i	0.0809620	−	0.996717i	$-0.474201\pi$
$883$	951.591	−	951.591i	1.07768	−	1.07768i	0.996717	−	0.0809620i	$-0.0257992\pi$
$884$		−	7.00276i		−	0.00792167i
$885$		0			0
$886$	−585.255			−0.660559
$887$	−300.730	−	300.730i	−0.339042	−	0.339042i	0.516965	−	0.856007i	$-0.327062\pi$
$887$	−300.730	−	300.730i	−0.339042	−	0.339042i	−0.856007	+	0.516965i	$0.827062\pi$
$888$	−82.4522	+	82.4522i	−0.0928515	+	0.0928515i
$889$			534.919i			0.601709i
$890$		0			0
$891$	−26.3089			−0.0295274
$892$	203.537	+	203.537i	0.228180	+	0.228180i
$893$	−175.374	+	175.374i	−0.196388	+	0.196388i
$894$		−	189.837i		−	0.212345i
$895$		0			0
$896$	29.9333			0.0334077
$897$	−21.9452	−	21.9452i	−0.0244651	−	0.0244651i
$898$	−400.989	+	400.989i	−0.446536	+	0.446536i
$899$		−	213.964i		−	0.238002i
$900$		0			0
$901$	−125.267			−0.139031
$902$	212.292	+	212.292i	0.235357	+	0.235357i
$903$	−93.3696	+	93.3696i	−0.103399	+	0.103399i
$904$		−	272.147i		−	0.301047i
$905$		0			0
$906$	90.1889			0.0995462
$907$	801.951	+	801.951i	0.884179	+	0.884179i	0.993956	−	0.109777i	$-0.0350136\pi$
$907$	801.951	+	801.951i	0.884179	+	0.884179i	−0.109777	+	0.993956i	$0.535014\pi$
$908$	−50.1179	+	50.1179i	−0.0551959	+	0.0551959i
$909$			388.252i			0.427120i
$910$		0			0
$911$	−1437.85			−1.57832			−0.789160	−	0.614187i	$-0.789484\pi$
$911$	−1437.85			−1.57832			−0.789160	+	0.614187i	$0.789484\pi$
$912$	16.4213	+	16.4213i	0.0180058	+	0.0180058i
$913$	62.3613	−	62.3613i	0.0683038	−	0.0683038i
$914$		−	344.079i		−	0.376454i
$915$		0			0
$916$	−566.995			−0.618990
$917$	−6.64862	−	6.64862i	−0.00725041	−	0.00725041i
$918$	−11.3539	+	11.3539i	−0.0123680	+	0.0123680i
$919$		−	1282.30i		−	1.39532i	−0.716428	−	0.697661i	$-0.754224\pi$
$919$		−	1282.30i		−	1.39532i	0.716428	−	0.697661i	$-0.245776\pi$
$920$		0			0
$921$	−793.240			−0.861282
$922$	−153.918	−	153.918i	−0.166939	−	0.166939i
$923$	−58.6052	+	58.6052i	−0.0634942	+	0.0634942i
$924$			26.7917i			0.0289954i
$925$		0			0
$926$	−583.527			−0.630158
$927$	93.1342	+	93.1342i	0.100468	+	0.100468i
$928$	54.1898	−	54.1898i	0.0583942	−	0.0583942i
$929$		−	520.920i		−	0.560732i	−0.959893	−	0.280366i	$-0.909544\pi$
$929$		−	520.920i		−	0.560732i	0.959893	−	0.280366i	$-0.0904558\pi$
$930$		0			0
$931$	−23.4639			−0.0252029
$932$	−278.238	−	278.238i	−0.298539	−	0.298539i
$933$	348.352	−	348.352i	0.373368	−	0.373368i
$934$		−	1006.47i		−	1.07759i
$935$		0			0
$936$	−13.5970			−0.0145267
$937$	49.7102	+	49.7102i	0.0530525	+	0.0530525i	0.733135	−	0.680083i	$-0.238056\pi$
$937$	49.7102	+	49.7102i	0.0530525	+	0.0530525i	−0.680083	+	0.733135i	$0.738056\pi$
$938$	216.183	−	216.183i	0.230472	−	0.230472i
$939$		−	438.371i		−	0.466849i
$940$		0			0
$941$	−163.591			−0.173848			−0.0869242	−	0.996215i	$-0.527704\pi$
$941$	−163.591			−0.173848			−0.0869242	+	0.996215i	$0.527704\pi$
$942$	−185.586	−	185.586i	−0.197013	−	0.197013i
$943$	574.214	−	574.214i	0.608922	−	0.608922i
$944$			468.660i			0.496462i
$945$		0			0
$946$	119.121			0.125920
$947$	1003.15	+	1003.15i	1.05929	+	1.05929i	0.998128	+	0.0611651i	$0.0194816\pi$
$947$	1003.15	+	1003.15i	1.05929	+	1.05929i	0.0611651	+	0.998128i	$0.480518\pi$
$948$	−91.0843	+	91.0843i	−0.0960805	+	0.0960805i
$949$			164.037i			0.172852i
$950$		0			0
$951$	822.538			0.864919
$952$	11.5622	+	11.5622i	0.0121452	+	0.0121452i
$953$	265.856	−	265.856i	0.278967	−	0.278967i	−0.553729	−	0.832697i	$-0.686796\pi$
$953$	265.856	−	265.856i	0.278967	−	0.278967i	0.832697	+	0.553729i	$0.186796\pi$
$954$			243.227i			0.254955i
$955$		0			0
$956$	366.561			0.383432
$957$	48.5025	+	48.5025i	0.0506818	+	0.0506818i
$958$	670.857	−	670.857i	0.700268	−	0.700268i
$959$			281.019i			0.293033i
$960$		0			0
$961$	−711.561			−0.740438
$962$	−38.1408	−	38.1408i	−0.0396474	−	0.0396474i
$963$	−328.264	+	328.264i	−0.340876	+	0.340876i
$964$		−	560.188i		−	0.581108i
$965$		0			0
$966$	72.4671			0.0750177
$967$	−662.074	−	662.074i	−0.684668	−	0.684668i	0.276380	−	0.961048i	$-0.410865\pi$
$967$	−662.074	−	662.074i	−0.684668	−	0.684668i	−0.961048	+	0.276380i	$0.910865\pi$
$968$	−224.910	+	224.910i	−0.232345	+	0.232345i
$969$			12.6860i			0.0130918i
$970$		0			0
$971$	562.832			0.579642			0.289821	−	0.957081i	$-0.406404\pi$
$971$	562.832			0.579642			0.289821	+	0.957081i	$0.406404\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	359.858	−	359.858i	0.369844	−	0.369844i
$974$		−	862.700i		−	0.885729i
$975$		0			0
$976$	181.749			0.186219
$977$	−1319.92	−	1319.92i	−1.35099	−	1.35099i	−0.884556	−	0.466433i	$-0.845539\pi$
$977$	−1319.92	−	1319.92i	−1.35099	−	1.35099i	−0.466433	−	0.884556i	$-0.654461\pi$
$978$	−427.320	+	427.320i	−0.436932	+	0.436932i
$979$		−	295.102i		−	0.301432i
$980$		0			0
$981$	205.851			0.209838
$982$	643.019	+	643.019i	0.654806	+	0.654806i
$983$	−117.249	+	117.249i	−0.119277	+	0.119277i	−0.764226	−	0.644949i	$-0.776879\pi$
$983$	−117.249	+	117.249i	−0.119277	+	0.119277i	0.644949	+	0.764226i	$0.276879\pi$
$984$		−	355.777i		−	0.361562i
$985$		0			0
$986$	41.8633			0.0424577
$987$	239.758	+	239.758i	0.242916	+	0.242916i
$988$	−7.59618	+	7.59618i	−0.00768844	+	0.00768844i
$989$		−	322.201i		−	0.325785i
$990$		0			0
$991$	−354.972			−0.358196			−0.179098	−	0.983831i	$-0.557318\pi$
$991$	−354.972			−0.358196			−0.179098	+	0.983831i	$0.557318\pi$
$992$	63.1746	+	63.1746i	0.0636841	+	0.0636841i
$993$	−544.156	+	544.156i	−0.547991	+	0.547991i
$994$		−	193.525i		−	0.194693i
$995$		0			0
$996$	−104.511			−0.104930
$997$	913.231	+	913.231i	0.915979	+	0.915979i	0.996734	−	0.0807549i	$-0.0257331\pi$
$997$	913.231	+	913.231i	0.915979	+	0.915979i	−0.0807549	+	0.996734i	$0.525733\pi$
$998$	−350.058	+	350.058i	−0.350760	+	0.350760i
$999$			123.678i			0.123802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.b.757.1		8
5.2	odd	4		210.3.l.a.43.4	✓	8
5.3	odd	4	inner	1050.3.l.b.43.1		8
5.4	even	2		210.3.l.a.127.4	yes	8
15.2	even	4		630.3.o.b.253.1		8
15.14	odd	2		630.3.o.b.127.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.4	✓	8	5.2	odd	4
210.3.l.a.127.4	yes	8	5.4	even	2
630.3.o.b.127.1		8	15.14	odd	2
630.3.o.b.253.1		8	15.2	even	4
1050.3.l.b.43.1		8	5.3	odd	4	inner
1050.3.l.b.757.1		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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +2.92322 q^{11} +(-2.44949 - 2.44949i) q^{12} +(1.13309 - 1.13309i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-1.54506 - 1.54506i) q^{17} +(-3.00000 + 3.00000i) q^{18} +3.35199i q^{19} +4.58258 q^{21} +(-2.92322 - 2.92322i) q^{22} +(-7.90681 + 7.90681i) q^{23} +4.89898i q^{24} -2.26617 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -13.5474i q^{29} +15.7936 q^{31} +(4.00000 + 4.00000i) q^{32} +(-3.58019 + 3.58019i) q^{33} +3.09013i q^{34} +6.00000 q^{36} +(16.8305 + 16.8305i) q^{37} +(3.35199 - 3.35199i) q^{38} +2.77548i q^{39} -72.6227 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-20.3749 + 20.3749i) q^{43} +5.84643i q^{44} +15.8136 q^{46} +(52.3194 + 52.3194i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +3.78462 q^{51} +(2.26617 + 2.26617i) q^{52} +(40.5379 - 40.5379i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(-4.10533 - 4.10533i) q^{57} +(-13.5474 + 13.5474i) q^{58} -117.165i q^{59} -45.4373 q^{61} +(-15.7936 - 15.7936i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +7.16039 q^{66} +(-57.7773 - 57.7773i) q^{67} +(3.09013 - 3.09013i) q^{68} -19.3676i q^{69} -51.7217 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-72.3851 + 72.3851i) q^{73} -33.6610i q^{74} -6.70398 q^{76} +(-5.46884 - 5.46884i) q^{77} +(2.77548 - 2.77548i) q^{78} -37.1850i q^{79} -9.00000 q^{81} +(72.6227 + 72.6227i) q^{82} +(21.3331 - 21.3331i) q^{83} +9.16515i q^{84} +40.7498 q^{86} +(16.5922 + 16.5922i) q^{87} +(5.84643 - 5.84643i) q^{88} -100.951i q^{89} -4.23962 q^{91} +(-15.8136 - 15.8136i) q^{92} +(-19.3432 + 19.3432i) q^{93} -104.639i q^{94} -9.79796 q^{96} +(-52.5887 - 52.5887i) q^{97} +(7.00000 - 7.00000i) q^{98} -8.76965i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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