LMFDB - Embedded newform 525.3.l.e.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(43,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	525.43
Dual form			525.3.l.e.232.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.408558 + 0.408558i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.66616i q^{4} -1.00076 q^{6} +(1.87083 - 1.87083i) q^{7} +(-3.13207 - 3.13207i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-0.408558 + 0.408558i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.66616i q^{4} -1.00076 q^{6} +(1.87083 - 1.87083i) q^{7} +(-3.13207 - 3.13207i) q^{8} +3.00000i q^{9} -6.25808 q^{11} +(-4.49011 + 4.49011i) q^{12} +(-16.4621 - 16.4621i) q^{13} +1.52868i q^{14} -12.1054 q^{16} +(-20.4811 + 20.4811i) q^{17} +(-1.22567 - 1.22567i) q^{18} +7.15227i q^{19} +4.58258 q^{21} +(2.55679 - 2.55679i) q^{22} +(12.0129 + 12.0129i) q^{23} -7.67197i q^{24} +13.4514 q^{26} +(-3.67423 + 3.67423i) q^{27} +(6.85876 + 6.85876i) q^{28} -18.1286i q^{29} -33.3500 q^{31} +(17.4740 - 17.4740i) q^{32} +(-7.66455 - 7.66455i) q^{33} -16.7354i q^{34} -10.9985 q^{36} +(-18.8529 + 18.8529i) q^{37} +(-2.92211 - 2.92211i) q^{38} -40.3237i q^{39} +50.8319 q^{41} +(-1.87225 + 1.87225i) q^{42} +(-53.3589 - 53.3589i) q^{43} -22.9431i q^{44} -9.81596 q^{46} +(-46.9338 + 46.9338i) q^{47} +(-14.8260 - 14.8260i) q^{48} -7.00000i q^{49} -50.1682 q^{51} +(60.3527 - 60.3527i) q^{52} +(28.9805 + 28.9805i) q^{53} -3.00227i q^{54} -11.7191 q^{56} +(-8.75971 + 8.75971i) q^{57} +(7.40656 + 7.40656i) q^{58} +10.0079i q^{59} +85.6806 q^{61} +(13.6254 - 13.6254i) q^{62} +(5.61249 + 5.61249i) q^{63} -34.1432i q^{64} +6.26283 q^{66} +(-11.9931 + 11.9931i) q^{67} +(-75.0869 - 75.0869i) q^{68} +29.4256i q^{69} -20.8660 q^{71} +(9.39621 - 9.39621i) q^{72} +(-35.2913 - 35.2913i) q^{73} -15.4050i q^{74} -26.2214 q^{76} +(-11.7078 + 11.7078i) q^{77} +(16.4746 + 16.4746i) q^{78} -31.9858i q^{79} -9.00000 q^{81} +(-20.7677 + 20.7677i) q^{82} +(-6.49178 - 6.49178i) q^{83} +16.8005i q^{84} +43.6003 q^{86} +(22.2029 - 22.2029i) q^{87} +(19.6007 + 19.6007i) q^{88} +145.472i q^{89} -61.5955 q^{91} +(-44.0414 + 44.0414i) q^{92} +(-40.8453 - 40.8453i) q^{93} -38.3503i q^{94} +42.8024 q^{96} +(-31.5344 + 31.5344i) q^{97} +(2.85990 + 2.85990i) q^{98} -18.7742i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8	$ 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8 + 48 * q^12 - 64 * q^13 - 184 * q^16 - 24 * q^17 - 24 * q^18 - 8 * q^22 - 8 * q^23 - 80 * q^26 + 96 * q^31 - 56 * q^32 + 72 * q^33 + 168 * q^36 - 8 * q^37 - 56 * q^38 + 320 * q^41 + 112 * q^43 + 320 * q^46 - 64 * q^47 - 192 * q^48 - 192 * q^51 - 96 * q^52 + 72 * q^53 - 336 * q^56 - 48 * q^57 + 512 * q^58 - 496 * q^61 + 776 * q^62 - 192 * q^66 + 192 * q^67 - 568 * q^68 - 144 * q^71 - 144 * q^72 - 224 * q^73 + 416 * q^76 - 112 * q^77 + 216 * q^78 - 216 * q^81 - 352 * q^82 + 32 * q^83 + 240 * q^86 - 384 * q^87 - 216 * q^88 - 1304 * q^92 + 168 * q^96 + 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.408558	+	0.408558i	−0.204279	+	0.204279i	−0.801830	−	0.597552i	$-0.796140\pi$
$2$	−0.408558	+	0.408558i	−0.204279	+	0.204279i	0.597552	+	0.801830i	$0.296140\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$			3.66616i			0.916540i
$5$		0			0
$5$		0			0
$6$	−1.00076			−0.166793
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	−3.13207	−	3.13207i	−0.391509	−	0.391509i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	−6.25808			−0.568917			−0.284458	−	0.958688i	$-0.591814\pi$
$11$	−6.25808			−0.568917			−0.284458	+	0.958688i	$0.591814\pi$
$12$	−4.49011	+	4.49011i	−0.374176	+	0.374176i
$13$	−16.4621	−	16.4621i	−1.26631	−	1.26631i	−0.947978	−	0.318337i	$-0.896876\pi$
$13$	−16.4621	−	16.4621i	−1.26631	−	1.26631i	−0.318337	−	0.947978i	$-0.603124\pi$
$14$			1.52868i			0.109192i
$15$		0			0
$16$	−12.1054			−0.756586
$17$	−20.4811	+	20.4811i	−1.20477	+	1.20477i	−0.232071	+	0.972699i	$0.574550\pi$
$17$	−20.4811	+	20.4811i	−1.20477	+	1.20477i	−0.972699	+	0.232071i	$0.925450\pi$
$18$	−1.22567	−	1.22567i	−0.0680929	−	0.0680929i
$19$			7.15227i			0.376435i	0.982127	+	0.188218i	$0.0602710\pi$
$19$			7.15227i			0.376435i	−0.982127	+	0.188218i	$0.939729\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	2.55679	−	2.55679i	0.116218	−	0.116218i
$23$	12.0129	+	12.0129i	0.522302	+	0.522302i	0.918266	−	0.395964i	$-0.129590\pi$
$23$	12.0129	+	12.0129i	0.522302	+	0.522302i	−0.395964	+	0.918266i	$0.629590\pi$
$24$		−	7.67197i		−	0.319665i
$25$		0			0
$26$	13.4514			0.517362
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	6.85876	+	6.85876i	0.244956	+	0.244956i
$29$		−	18.1286i		−	0.625123i	−0.949898	−	0.312561i	$-0.898813\pi$
$29$		−	18.1286i		−	0.625123i	0.949898	−	0.312561i	$-0.101187\pi$
$30$		0			0
$31$	−33.3500			−1.07581			−0.537904	−	0.843006i	$-0.680784\pi$
$31$	−33.3500			−1.07581			−0.537904	+	0.843006i	$0.680784\pi$
$32$	17.4740	−	17.4740i	0.546063	−	0.546063i
$33$	−7.66455	−	7.66455i	−0.232259	−	0.232259i
$34$		−	16.7354i		−	0.492218i
$35$		0			0
$36$	−10.9985			−0.305513
$37$	−18.8529	+	18.8529i	−0.509538	+	0.509538i	−0.914384	−	0.404847i	$-0.867325\pi$
$37$	−18.8529	+	18.8529i	−0.509538	+	0.509538i	0.404847	+	0.914384i	$0.367325\pi$
$38$	−2.92211	−	2.92211i	−0.0768978	−	0.0768978i
$39$		−	40.3237i		−	1.03394i
$40$		0			0
$41$	50.8319			1.23980			0.619901	−	0.784680i	$-0.287173\pi$
$41$	50.8319			1.23980			0.619901	+	0.784680i	$0.287173\pi$
$42$	−1.87225	+	1.87225i	−0.0445773	+	0.0445773i
$43$	−53.3589	−	53.3589i	−1.24090	−	1.24090i	−0.959627	−	0.281277i	$-0.909242\pi$
$43$	−53.3589	−	53.3589i	−1.24090	−	1.24090i	−0.281277	−	0.959627i	$-0.590758\pi$
$44$		−	22.9431i		−	0.521435i
$45$		0			0
$46$	−9.81596			−0.213390
$47$	−46.9338	+	46.9338i	−0.998592	+	0.998592i	−0.999999	−	0.00140698i	$-0.999552\pi$
$47$	−46.9338	+	46.9338i	−0.998592	+	0.998592i	0.00140698	+	0.999999i	$0.499552\pi$
$48$	−14.8260	−	14.8260i	−0.308875	−	0.308875i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	−50.1682			−0.983690
$52$	60.3527	−	60.3527i	1.16063	−	1.16063i
$53$	28.9805	+	28.9805i	0.546801	+	0.546801i	0.925514	−	0.378713i	$-0.123633\pi$
$53$	28.9805	+	28.9805i	0.546801	+	0.546801i	−0.378713	+	0.925514i	$0.623633\pi$
$54$		−	3.00227i		−	0.0555977i
$55$		0			0
$56$	−11.7191			−0.209270
$57$	−8.75971	+	8.75971i	−0.153679	+	0.153679i
$58$	7.40656	+	7.40656i	0.127699	+	0.127699i
$59$			10.0079i			0.169626i	0.996397	+	0.0848128i	$0.0270292\pi$
$59$			10.0079i			0.169626i	−0.996397	+	0.0848128i	$0.972971\pi$
$60$		0			0
$61$	85.6806			1.40460			0.702300	−	0.711881i	$-0.252157\pi$
$61$	85.6806			1.40460			0.702300	+	0.711881i	$0.252157\pi$
$62$	13.6254	−	13.6254i	0.219765	−	0.219765i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$		−	34.1432i		−	0.533488i
$65$		0			0
$66$	6.26283			0.0948913
$67$	−11.9931	+	11.9931i	−0.179001	+	0.179001i	−0.790920	−	0.611919i	$-0.790398\pi$
$67$	−11.9931	+	11.9931i	−0.179001	+	0.179001i	0.611919	+	0.790920i	$0.290398\pi$
$68$	−75.0869	−	75.0869i	−1.10422	−	1.10422i
$69$			29.4256i			0.426458i
$70$		0			0
$71$	−20.8660			−0.293887			−0.146943	−	0.989145i	$-0.546944\pi$
$71$	−20.8660			−0.293887			−0.146943	+	0.989145i	$0.546944\pi$
$72$	9.39621	−	9.39621i	0.130503	−	0.130503i
$73$	−35.2913	−	35.2913i	−0.483443	−	0.483443i	0.422787	−	0.906229i	$-0.361052\pi$
$73$	−35.2913	−	35.2913i	−0.483443	−	0.483443i	−0.906229	+	0.422787i	$0.861052\pi$
$74$		−	15.4050i		−	0.208176i
$75$		0			0
$76$	−26.2214			−0.345018
$77$	−11.7078	+	11.7078i	−0.152049	+	0.152049i
$78$	16.4746	+	16.4746i	0.211212	+	0.211212i
$79$		−	31.9858i		−	0.404884i	−0.979294	−	0.202442i	$-0.935112\pi$
$79$		−	31.9858i		−	0.404884i	0.979294	−	0.202442i	$-0.0648877\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−20.7677	+	20.7677i	−0.253265	+	0.253265i
$83$	−6.49178	−	6.49178i	−0.0782142	−	0.0782142i	0.666917	−	0.745132i	$-0.267613\pi$
$83$	−6.49178	−	6.49178i	−0.0782142	−	0.0782142i	−0.745132	+	0.666917i	$0.767613\pi$
$84$			16.8005i			0.200005i
$85$		0			0
$86$	43.6003			0.506981
$87$	22.2029	−	22.2029i	0.255205	−	0.255205i
$88$	19.6007	+	19.6007i	0.222736	+	0.222736i
$89$			145.472i			1.63452i	0.576273	+	0.817258i	$0.304507\pi$
$89$			145.472i			1.63452i	−0.576273	+	0.817258i	$0.695493\pi$
$90$		0			0
$91$	−61.5955			−0.676873
$92$	−44.0414	+	44.0414i	−0.478711	+	0.478711i
$93$	−40.8453	−	40.8453i	−0.439197	−	0.439197i
$94$		−	38.3503i		−	0.407982i
$95$		0			0
$96$	42.8024			0.445859
$97$	−31.5344	+	31.5344i	−0.325097	+	0.325097i	−0.850719	−	0.525621i	$-0.823833\pi$
$97$	−31.5344	+	31.5344i	−0.325097	+	0.325097i	0.525621	+	0.850719i	$0.323833\pi$
$98$	2.85990	+	2.85990i	0.0291827	+	0.0291827i
$99$		−	18.7742i		−	0.189639i
$100$		0			0
$101$	−128.207			−1.26938			−0.634688	−	0.772768i	$-0.718871\pi$
$101$	−128.207			−1.26938			−0.634688	+	0.772768i	$0.718871\pi$
$102$	20.4966	−	20.4966i	0.200947	−	0.200947i
$103$	89.6356	+	89.6356i	0.870248	+	0.870248i	0.992499	−	0.122251i	$-0.0390112\pi$
$103$	89.6356	+	89.6356i	0.870248	+	0.870248i	−0.122251	+	0.992499i	$0.539011\pi$
$104$			103.121i			0.991546i
$105$		0			0
$106$	−23.6804			−0.223400
$107$	−32.4213	+	32.4213i	−0.303003	+	0.303003i	−0.842188	−	0.539185i	$-0.818732\pi$
$107$	−32.4213	+	32.4213i	−0.303003	+	0.303003i	0.539185	+	0.842188i	$0.318732\pi$
$108$	−13.4703	−	13.4703i	−0.124725	−	0.124725i
$109$		−	87.2642i		−	0.800589i	−0.916387	−	0.400294i	$-0.868908\pi$
$109$		−	87.2642i		−	0.800589i	0.916387	−	0.400294i	$-0.131092\pi$
$110$		0			0
$111$	−46.1800			−0.416036
$112$	−22.6471	+	22.6471i	−0.202206	+	0.202206i
$113$	14.4360	+	14.4360i	0.127752	+	0.127752i	0.768092	−	0.640340i	$-0.221206\pi$
$113$	14.4360	+	14.4360i	0.127752	+	0.127752i	−0.640340	+	0.768092i	$0.721206\pi$
$114$		−	7.15769i		−	0.0627868i
$115$		0			0
$116$	66.4622			0.572950
$117$	49.3863	−	49.3863i	0.422105	−	0.422105i
$118$	−4.08881	−	4.08881i	−0.0346509	−	0.0346509i
$119$			76.6332i			0.643976i
$120$		0			0
$121$	−81.8364			−0.676334
$122$	−35.0055	+	35.0055i	−0.286930	+	0.286930i
$123$	62.2561	+	62.2561i	0.506147	+	0.506147i
$124$		−	122.267i		−	0.986021i
$125$		0			0
$126$	−4.58605			−0.0363972
$127$	54.2946	−	54.2946i	0.427517	−	0.427517i	−0.460265	−	0.887782i	$-0.652246\pi$
$127$	54.2946	−	54.2946i	0.427517	−	0.427517i	0.887782	+	0.460265i	$0.152246\pi$
$128$	83.8456	+	83.8456i	0.655044	+	0.655044i
$129$		−	130.702i		−	1.01319i
$130$		0			0
$131$	36.7377			0.280440			0.140220	−	0.990120i	$-0.455219\pi$
$131$	36.7377			0.280440			0.140220	+	0.990120i	$0.455219\pi$
$132$	28.0995	−	28.0995i	0.212875	−	0.212875i
$133$	13.3807	+	13.3807i	0.100607	+	0.100607i
$134$		−	9.79973i		−	0.0731323i
$135$		0			0
$136$	128.296			0.943355
$137$	90.1192	−	90.1192i	0.657804	−	0.657804i	−0.297056	−	0.954860i	$-0.596005\pi$
$137$	90.1192	−	90.1192i	0.657804	−	0.657804i	0.954860	+	0.297056i	$0.0960048\pi$
$138$	−12.0220	−	12.0220i	−0.0871163	−	0.0871163i
$139$		−	88.5028i		−	0.636711i	−0.947971	−	0.318355i	$-0.896869\pi$
$139$		−	88.5028i		−	0.636711i	0.947971	−	0.318355i	$-0.103131\pi$
$140$		0			0
$141$	−114.964			−0.815347
$142$	8.52495	−	8.52495i	0.0600349	−	0.0600349i
$143$	103.021	+	103.021i	0.720427	+	0.720427i
$144$		−	36.3161i		−	0.252195i
$145$		0			0
$146$	28.8371			0.197514
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	−69.1177	−	69.1177i	−0.467012	−	0.467012i
$149$			205.375i			1.37835i	0.724594	+	0.689176i	$0.242027\pi$
$149$			205.375i			1.37835i	−0.724594	+	0.689176i	$0.757973\pi$
$150$		0			0
$151$	175.527			1.16243			0.581214	−	0.813751i	$-0.302578\pi$
$151$	175.527			1.16243			0.581214	+	0.813751i	$0.302578\pi$
$152$	22.4014	−	22.4014i	0.147378	−	0.147378i
$153$	−61.4432	−	61.4432i	−0.401590	−	0.401590i
$154$		−	9.56662i		−	0.0621209i
$155$		0			0
$156$	147.833			0.947649
$157$	−22.5653	+	22.5653i	−0.143728	+	0.143728i	−0.775310	−	0.631581i	$-0.782406\pi$
$157$	−22.5653	+	22.5653i	−0.143728	+	0.143728i	0.631581	+	0.775310i	$0.282406\pi$
$158$	13.0681	+	13.0681i	0.0827092	+	0.0827092i
$159$			70.9874i			0.446461i
$160$		0			0
$161$	44.9483			0.279182
$162$	3.67702	−	3.67702i	0.0226976	−	0.0226976i
$163$	6.70761	+	6.70761i	0.0411510	+	0.0411510i	0.727383	−	0.686232i	$-0.240736\pi$
$163$	6.70761	+	6.70761i	0.0411510	+	0.0411510i	−0.686232	+	0.727383i	$0.740736\pi$
$164$			186.358i			1.13633i
$165$		0			0
$166$	5.30453			0.0319550
$167$	−105.816	+	105.816i	−0.633630	+	0.633630i	−0.948977	−	0.315347i	$-0.897879\pi$
$167$	−105.816	+	105.816i	−0.633630	+	0.633630i	0.315347	+	0.948977i	$0.397879\pi$
$168$	−14.3529	−	14.3529i	−0.0854342	−	0.0854342i
$169$			373.001i			2.20710i
$170$		0			0
$171$	−21.4568			−0.125478
$172$	195.622	−	195.622i	1.13734	−	1.13734i
$173$	174.772	+	174.772i	1.01024	+	1.01024i	0.999947	+	0.0102943i	$0.00327684\pi$
$173$	174.772	+	174.772i	1.01024	+	1.01024i	0.0102943	+	0.999947i	$0.496723\pi$
$174$			18.1423i			0.104266i
$175$		0			0
$176$	75.7565			0.430435
$177$	−12.2571	+	12.2571i	−0.0692494	+	0.0692494i
$178$	−59.4336	−	59.4336i	−0.333897	−	0.333897i
$179$			18.1770i			0.101547i	0.998710	+	0.0507736i	$0.0161687\pi$
$179$			18.1770i			0.101547i	−0.998710	+	0.0507736i	$0.983831\pi$
$180$		0			0
$181$	−120.550			−0.666021			−0.333010	−	0.942923i	$-0.608064\pi$
$181$	−120.550			−0.666021			−0.333010	+	0.942923i	$0.608064\pi$
$182$	25.1653	−	25.1653i	0.138271	−	0.138271i
$183$	104.937	+	104.937i	0.573425	+	0.573425i
$184$		−	75.2507i		−	0.408971i
$185$		0			0
$186$	33.3753			0.179437
$187$	128.172	−	128.172i	0.685413	−	0.685413i
$188$	−172.067	−	172.067i	−0.915250	−	0.915250i
$189$			13.7477i			0.0727393i
$190$		0			0
$191$	58.8671			0.308205			0.154102	−	0.988055i	$-0.450751\pi$
$191$	58.8671			0.308205			0.154102	+	0.988055i	$0.450751\pi$
$192$	41.8168	−	41.8168i	0.217796	−	0.217796i
$193$	−3.25902	−	3.25902i	−0.0168861	−	0.0168861i	0.698613	−	0.715499i	$-0.253801\pi$
$193$	−3.25902	−	3.25902i	−0.0168861	−	0.0168861i	−0.715499	+	0.698613i	$0.753801\pi$
$194$		−	25.7673i		−	0.132821i
$195$		0			0
$196$	25.6631			0.130934
$197$	12.5485	−	12.5485i	0.0636980	−	0.0636980i	−0.674540	−	0.738238i	$-0.735658\pi$
$197$	12.5485	−	12.5485i	0.0636980	−	0.0636980i	0.738238	+	0.674540i	$0.235658\pi$
$198$	7.67036	+	7.67036i	0.0387392	+	0.0387392i
$199$			391.240i			1.96603i	0.183526	+	0.983015i	$0.441249\pi$
$199$			391.240i			1.96603i	−0.183526	+	0.983015i	$0.558751\pi$
$200$		0			0
$201$	−29.3769			−0.146154
$202$	52.3800	−	52.3800i	0.259307	−	0.259307i
$203$	−33.9154	−	33.9154i	−0.167071	−	0.167071i
$204$		−	183.925i		−	0.901592i
$205$		0			0
$206$	−73.2426			−0.355547
$207$	−36.0388	+	36.0388i	−0.174101	+	0.174101i
$208$	199.280	+	199.280i	0.958076	+	0.958076i
$209$		−	44.7595i		−	0.214160i
$210$		0			0
$211$	−80.9281			−0.383546			−0.191773	−	0.981439i	$-0.561424\pi$
$211$	−80.9281			−0.383546			−0.191773	+	0.981439i	$0.561424\pi$
$212$	−106.247	+	106.247i	−0.501166	+	0.501166i
$213$	−25.5555	−	25.5555i	−0.119979	−	0.119979i
$214$		−	26.4919i		−	0.123794i
$215$		0			0
$216$	23.0159			0.106555
$217$	−62.3922	+	62.3922i	−0.287522	+	0.287522i
$218$	35.6525	+	35.6525i	0.163543	+	0.163543i
$219$		−	86.4457i		−	0.394729i
$220$		0			0
$221$	674.323			3.05123
$222$	18.8672	−	18.8672i	0.0849873	−	0.0849873i
$223$	227.428	+	227.428i	1.01986	+	1.01986i	0.999799	+	0.0200565i	$0.00638461\pi$
$223$	227.428	+	227.428i	1.01986	+	1.01986i	0.0200565	+	0.999799i	$0.493615\pi$
$224$		−	65.3818i		−	0.291883i
$225$		0			0
$226$	−11.7959			−0.0521941
$227$	−186.163	+	186.163i	−0.820101	+	0.820101i	−0.986122	−	0.166022i	$-0.946908\pi$
$227$	−186.163	+	186.163i	−0.820101	+	0.820101i	0.166022	+	0.986122i	$0.446908\pi$
$228$	−32.1145	−	32.1145i	−0.140853	−	0.140853i
$229$		−	299.882i		−	1.30953i	−0.755832	−	0.654765i	$-0.772768\pi$
$229$		−	299.882i		−	1.30953i	0.755832	−	0.654765i	$-0.227232\pi$
$230$		0			0
$231$	−28.6781			−0.124148
$232$	−56.7799	+	56.7799i	−0.244741	+	0.244741i
$233$	−46.9263	−	46.9263i	−0.201400	−	0.201400i	0.599199	−	0.800600i	$-0.295486\pi$
$233$	−46.9263	−	46.9263i	−0.201400	−	0.201400i	−0.800600	+	0.599199i	$0.795486\pi$
$234$			40.3543i			0.172454i
$235$		0			0
$236$	−36.6906			−0.155469
$237$	39.1745	−	39.1745i	0.165293	−	0.165293i
$238$	−31.3091	−	31.3091i	−0.131551	−	0.131551i
$239$		−	155.118i		−	0.649030i	−0.945881	−	0.324515i	$-0.894799\pi$
$239$		−	155.118i		−	0.649030i	0.945881	−	0.324515i	$-0.105201\pi$
$240$		0			0
$241$	−113.600			−0.471370			−0.235685	−	0.971829i	$-0.575733\pi$
$241$	−113.600			−0.471370			−0.235685	+	0.971829i	$0.575733\pi$
$242$	33.4349	−	33.4349i	0.138161	−	0.138161i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			314.119i			1.28737i
$245$		0			0
$246$	−50.8704			−0.206790
$247$	117.741	−	117.741i	0.476685	−	0.476685i
$248$	104.455	+	104.455i	0.421188	+	0.421188i
$249$		−	15.9015i		−	0.0638616i
$250$		0			0
$251$	−295.062			−1.17554			−0.587772	−	0.809027i	$-0.699995\pi$
$251$	−295.062			−1.17554			−0.587772	+	0.809027i	$0.699995\pi$
$252$	−20.5763	+	20.5763i	−0.0816519	+	0.0816519i
$253$	−75.1780	−	75.1780i	−0.297146	−	0.297146i
$254$			44.3650i			0.174665i
$255$		0			0
$256$	68.0615			0.265865
$257$	−18.1666	+	18.1666i	−0.0706872	+	0.0706872i	−0.741567	−	0.670879i	$-0.765917\pi$
$257$	−18.1666	+	18.1666i	−0.0706872	+	0.0706872i	0.670879	+	0.741567i	$0.265917\pi$
$258$	53.3993	+	53.3993i	0.206974	+	0.206974i
$259$			70.5411i			0.272359i
$260$		0			0
$261$	54.3857			0.208374
$262$	−15.0095	+	15.0095i	−0.0572880	+	0.0572880i
$263$	364.409	+	364.409i	1.38559	+	1.38559i	0.834349	+	0.551237i	$0.185844\pi$
$263$	364.409	+	364.409i	1.38559	+	1.38559i	0.551237	+	0.834349i	$0.314156\pi$
$264$			48.0118i			0.181863i
$265$		0			0
$266$	−10.9336			−0.0411036
$267$	−178.166	+	178.166i	−0.667288	+	0.667288i
$268$	−43.9686	−	43.9686i	−0.164062	−	0.164062i
$269$			0.809793i			0.00301038i	0.999999	+	0.00150519i	$0.000479118\pi$
$269$			0.809793i			0.00301038i	−0.999999	+	0.00150519i	$0.999521\pi$
$270$		0			0
$271$	−341.910			−1.26166			−0.630831	−	0.775921i	$-0.717286\pi$
$271$	−341.910			−1.26166			−0.630831	+	0.775921i	$0.717286\pi$
$272$	247.931	−	247.931i	0.911512	−	0.911512i
$273$	−75.4388	−	75.4388i	−0.276332	−	0.276332i
$274$			73.6378i			0.268751i
$275$		0			0
$276$	−107.879			−0.390866
$277$	−279.570	+	279.570i	−1.00928	+	1.00928i	−0.00932280	+	0.999957i	$0.502968\pi$
$277$	−279.570	+	279.570i	−1.00928	+	1.00928i	−0.999957	+	0.00932280i	$0.997032\pi$
$278$	36.1585	+	36.1585i	0.130067	+	0.130067i
$279$		−	100.050i		−	0.358602i
$280$		0			0
$281$	−383.827			−1.36593			−0.682967	−	0.730449i	$-0.739311\pi$
$281$	−383.827			−1.36593			−0.682967	+	0.730449i	$0.739311\pi$
$282$	46.9694	−	46.9694i	0.166558	−	0.166558i
$283$	−335.505	−	335.505i	−1.18553	−	1.18553i	−0.978291	−	0.207238i	$-0.933553\pi$
$283$	−335.505	−	335.505i	−1.18553	−	1.18553i	−0.207238	−	0.978291i	$-0.566447\pi$
$284$		−	76.4980i		−	0.269359i
$285$		0			0
$286$	−84.1801			−0.294336
$287$	95.0977	−	95.0977i	0.331351	−	0.331351i
$288$	52.4221	+	52.4221i	0.182021	+	0.182021i
$289$		−	549.949i		−	1.90294i
$290$		0			0
$291$	−77.2432			−0.265441
$292$	129.384	−	129.384i	0.443095	−	0.443095i
$293$	−222.379	−	222.379i	−0.758972	−	0.758972i	0.217163	−	0.976135i	$-0.430320\pi$
$293$	−222.379	−	222.379i	−0.758972	−	0.758972i	−0.976135	+	0.217163i	$0.930320\pi$
$294$			7.00530i			0.0238276i
$295$		0			0
$296$	118.097			0.398977
$297$	22.9937	−	22.9937i	0.0774197	−	0.0774197i
$298$	−83.9073	−	83.9073i	−0.281568	−	0.281568i
$299$		−	395.516i		−	1.32280i
$300$		0			0
$301$	−199.651			−0.663291
$302$	−71.7128	+	71.7128i	−0.237460	+	0.237460i
$303$	−157.021	−	157.021i	−0.518221	−	0.518221i
$304$		−	86.5810i		−	0.284806i
$305$		0			0
$306$	50.2062			0.164073
$307$	−264.406	+	264.406i	−0.861257	+	0.861257i	−0.991484	−	0.130227i	$-0.958429\pi$
$307$	−264.406	+	264.406i	−0.861257	+	0.861257i	0.130227	+	0.991484i	$0.458429\pi$
$308$	−42.9227	−	42.9227i	−0.139359	−	0.139359i
$309$			219.561i			0.710555i
$310$		0			0
$311$	307.452			0.988592			0.494296	−	0.869294i	$-0.335426\pi$
$311$	307.452			0.988592			0.494296	+	0.869294i	$0.335426\pi$
$312$	−126.297	+	126.297i	−0.404797	+	0.404797i
$313$	67.0805	+	67.0805i	0.214315	+	0.214315i	0.806098	−	0.591783i	$-0.201576\pi$
$313$	67.0805	+	67.0805i	0.214315	+	0.214315i	−0.591783	+	0.806098i	$0.701576\pi$
$314$		−	18.4385i		−	0.0587213i
$315$		0			0
$316$	117.265			0.371092
$317$	96.9267	−	96.9267i	0.305762	−	0.305762i	−0.537501	−	0.843263i	$-0.680631\pi$
$317$	96.9267	−	96.9267i	0.305762	−	0.305762i	0.843263	+	0.537501i	$0.180631\pi$
$318$	−29.0024	−	29.0024i	−0.0912026	−	0.0912026i
$319$			113.450i			0.355643i
$320$		0			0
$321$	−79.4157			−0.247401
$322$	−18.3640	+	18.3640i	−0.0570310	+	0.0570310i
$323$	−146.486	−	146.486i	−0.453518	−	0.453518i
$324$		−	32.9955i		−	0.101838i
$325$		0			0
$326$	−5.48089			−0.0168126
$327$	106.876	−	106.876i	0.326839	−	0.326839i
$328$	−159.209	−	159.209i	−0.485393	−	0.485393i
$329$			175.610i			0.533770i
$330$		0			0
$331$	300.702			0.908464			0.454232	−	0.890883i	$-0.349914\pi$
$331$	300.702			0.908464			0.454232	+	0.890883i	$0.349914\pi$
$332$	23.7999	−	23.7999i	0.0716864	−	0.0716864i
$333$	−56.5587	−	56.5587i	−0.169846	−	0.169846i
$334$		−	86.4640i		−	0.258874i
$335$		0			0
$336$	−55.4738			−0.165101
$337$	43.5765	−	43.5765i	0.129307	−	0.129307i	−0.639491	−	0.768798i	$-0.720855\pi$
$337$	43.5765	−	43.5765i	0.129307	−	0.129307i	0.768798	+	0.639491i	$0.220855\pi$
$338$	−152.392	−	152.392i	−0.450865	−	0.450865i
$339$			35.3608i			0.104309i
$340$		0			0
$341$	208.707			0.612045
$342$	8.76634	−	8.76634i	0.0256326	−	0.0256326i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			334.247i			0.971649i
$345$		0			0
$346$	−142.809			−0.412742
$347$	190.647	−	190.647i	0.549416	−	0.549416i	−0.376856	−	0.926272i	$-0.622995\pi$
$347$	190.647	−	190.647i	0.549416	−	0.549416i	0.926272	+	0.376856i	$0.122995\pi$
$348$	81.3992	+	81.3992i	0.233906	+	0.233906i
$349$		−	186.770i		−	0.535158i	−0.963536	−	0.267579i	$-0.913776\pi$
$349$		−	186.770i		−	0.535158i	0.963536	−	0.267579i	$-0.0862237\pi$
$350$		0			0
$351$	120.971			0.344647
$352$	−109.354	+	109.354i	−0.310664	+	0.310664i
$353$	−105.217	−	105.217i	−0.298066	−	0.298066i	0.542190	−	0.840256i	$-0.317595\pi$
$353$	−105.217	−	105.217i	−0.298066	−	0.298066i	−0.840256	+	0.542190i	$0.817595\pi$
$354$		−	10.0155i		−	0.0282924i
$355$		0			0
$356$	−533.323			−1.49810
$357$	−93.8561	+	93.8561i	−0.262902	+	0.262902i
$358$	−7.42633	−	7.42633i	−0.0207440	−	0.0207440i
$359$		−	44.2544i		−	0.123271i	−0.998099	−	0.0616356i	$-0.980368\pi$
$359$		−	44.2544i		−	0.123271i	0.998099	−	0.0616356i	$-0.0196317\pi$
$360$		0			0
$361$	309.845			0.858297
$362$	49.2515	−	49.2515i	0.136054	−	0.136054i
$363$	−100.229	−	100.229i	−0.276112	−	0.276112i
$364$		−	225.819i		−	0.620382i
$365$		0			0
$366$	−85.7455			−0.234277
$367$	−133.204	+	133.204i	−0.362953	+	0.362953i	−0.864899	−	0.501946i	$-0.832618\pi$
$367$	−133.204	+	133.204i	−0.362953	+	0.362953i	0.501946	+	0.864899i	$0.332618\pi$
$368$	−145.421	−	145.421i	−0.395167	−	0.395167i
$369$			152.496i			0.413267i
$370$		0			0
$371$	108.435			0.292278
$372$	149.745	−	149.745i	0.402541	−	0.402541i
$373$	−54.6349	−	54.6349i	−0.146474	−	0.146474i	0.630067	−	0.776541i	$-0.283028\pi$
$373$	−54.6349	−	54.6349i	−0.146474	−	0.146474i	−0.776541	+	0.630067i	$0.783028\pi$
$374$			104.732i			0.280031i
$375$		0			0
$376$	294.000			0.781915
$377$	−298.434	+	298.434i	−0.791602	+	0.791602i
$378$	−5.61674	−	5.61674i	−0.0148591	−	0.0148591i
$379$			189.045i			0.498799i	0.968401	+	0.249400i	$0.0802333\pi$
$379$			189.045i			0.498799i	−0.968401	+	0.249400i	$0.919767\pi$
$380$		0			0
$381$	132.994			0.349066
$382$	−24.0506	+	24.0506i	−0.0629597	+	0.0629597i
$383$	−477.999	−	477.999i	−1.24804	−	1.24804i	−0.956585	−	0.291455i	$-0.905861\pi$
$383$	−477.999	−	477.999i	−1.24804	−	1.24804i	−0.291455	−	0.956585i	$-0.594139\pi$
$384$			205.379i			0.534841i
$385$		0			0
$386$	2.66300			0.00689896
$387$	160.077	−	160.077i	0.413635	−	0.413635i
$388$	−115.610	−	115.610i	−0.297965	−	0.297965i
$389$		−	667.365i		−	1.71559i	−0.513990	−	0.857796i	$-0.671833\pi$
$389$		−	667.365i		−	1.71559i	0.513990	−	0.857796i	$-0.328167\pi$
$390$		0			0
$391$	−492.076			−1.25851
$392$	−21.9245	+	21.9245i	−0.0559298	+	0.0559298i
$393$	44.9943	+	44.9943i	0.114489	+	0.114489i
$394$			10.2536i			0.0260243i
$395$		0			0
$396$	68.8294			0.173812
$397$	−98.8649	+	98.8649i	−0.249030	+	0.249030i	−0.820572	−	0.571543i	$-0.806345\pi$
$397$	−98.8649	+	98.8649i	−0.249030	+	0.249030i	0.571543	+	0.820572i	$0.306345\pi$
$398$	−159.844	−	159.844i	−0.401618	−	0.401618i
$399$			32.7758i			0.0821449i
$400$		0			0
$401$	−505.616			−1.26089			−0.630444	−	0.776235i	$-0.717127\pi$
$401$	−505.616			−1.26089			−0.630444	+	0.776235i	$0.717127\pi$
$402$	12.0022	−	12.0022i	0.0298561	−	0.0298561i
$403$	549.011	+	549.011i	1.36231	+	1.36231i
$404$		−	470.028i		−	1.16343i
$405$		0			0
$406$	27.7128			0.0682581
$407$	117.983	−	117.983i	0.289884	−	0.289884i
$408$	157.130	+	157.130i	0.385123	+	0.385123i
$409$		−	173.212i		−	0.423502i	−0.977324	−	0.211751i	$-0.932083\pi$
$409$		−	173.212i		−	0.423502i	0.977324	−	0.211751i	$-0.0679166\pi$
$410$		0			0
$411$	220.746			0.537095
$412$	−328.619	+	328.619i	−0.797618	+	0.797618i
$413$	18.7231	+	18.7231i	0.0453344	+	0.0453344i
$414$		−	29.4479i		−	0.0711301i
$415$		0			0
$416$	−575.318			−1.38298
$417$	108.393	−	108.393i	0.259936	−	0.259936i
$418$	18.2868	+	18.2868i	0.0437484	+	0.0437484i
$419$			69.3107i			0.165419i	0.996574	+	0.0827096i	$0.0263574\pi$
$419$			69.3107i			0.165419i	−0.996574	+	0.0827096i	$0.973643\pi$
$420$		0			0
$421$	153.026			0.363483			0.181742	−	0.983346i	$-0.441827\pi$
$421$	153.026			0.363483			0.181742	+	0.983346i	$0.441827\pi$
$422$	33.0638	−	33.0638i	0.0783502	−	0.0783502i
$423$	−140.801	−	140.801i	−0.332864	−	0.332864i
$424$		−	181.538i		−	0.428155i
$425$		0			0
$426$	20.8818			0.0490183
$427$	160.294	−	160.294i	0.375395	−	0.375395i
$428$	−118.862	−	118.862i	−0.277714	−	0.277714i
$429$			252.349i			0.588226i
$430$		0			0
$431$	−138.173			−0.320588			−0.160294	−	0.987069i	$-0.551244\pi$
$431$	−138.173			−0.320588			−0.160294	+	0.987069i	$0.551244\pi$
$432$	44.4780	−	44.4780i	0.102958	−	0.102958i
$433$	−79.3560	−	79.3560i	−0.183270	−	0.183270i	0.609509	−	0.792779i	$-0.291367\pi$
$433$	−79.3560	−	79.3560i	−0.183270	−	0.183270i	−0.792779	+	0.609509i	$0.791367\pi$
$434$		−	50.9816i		−	0.117469i
$435$		0			0
$436$	319.925			0.733772
$437$	−85.9198	+	85.9198i	−0.196613	+	0.196613i
$438$	35.3180	+	35.3180i	0.0806348	+	0.0806348i
$439$			541.986i			1.23459i	0.786731	+	0.617296i	$0.211772\pi$
$439$			541.986i			1.23459i	−0.786731	+	0.617296i	$0.788228\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	−275.500	+	275.500i	−0.623302	+	0.623302i
$443$	395.555	+	395.555i	0.892901	+	0.892901i	0.994795	−	0.101894i	$-0.0324903\pi$
$443$	395.555	+	395.555i	0.892901	+	0.892901i	−0.101894	+	0.994795i	$0.532490\pi$
$444$		−	169.303i		−	0.381314i
$445$		0			0
$446$	−185.835			−0.416670
$447$	−251.531	+	251.531i	−0.562710	+	0.562710i
$448$	−63.8762	−	63.8762i	−0.142581	−	0.142581i
$449$		−	478.107i		−	1.06483i	−0.846485	−	0.532413i	$-0.821285\pi$
$449$		−	478.107i		−	1.06483i	0.846485	−	0.532413i	$-0.178715\pi$
$450$		0			0
$451$	−318.110			−0.705344
$452$	−52.9246	+	52.9246i	−0.117090	+	0.117090i
$453$	214.975	+	214.975i	0.474560	+	0.474560i
$454$		−	152.117i		−	0.335058i
$455$		0			0
$456$	54.8720			0.120333
$457$	6.40164	−	6.40164i	0.0140080	−	0.0140080i	−0.700068	−	0.714076i	$-0.746847\pi$
$457$	6.40164	−	6.40164i	0.0140080	−	0.0140080i	0.714076	+	0.700068i	$0.246847\pi$
$458$	122.519	+	122.519i	0.267509	+	0.267509i
$459$		−	150.505i		−	0.327897i
$460$		0			0
$461$	227.575			0.493655			0.246828	−	0.969059i	$-0.420612\pi$
$461$	227.575			0.493655			0.246828	+	0.969059i	$0.420612\pi$
$462$	11.7167	−	11.7167i	0.0253608	−	0.0253608i
$463$	5.28403	+	5.28403i	0.0114126	+	0.0114126i	0.712790	−	0.701377i	$-0.247431\pi$
$463$	5.28403	+	5.28403i	0.0114126	+	0.0114126i	−0.701377	+	0.712790i	$0.747431\pi$
$464$			219.453i			0.472959i
$465$		0			0
$466$	38.3442			0.0822836
$467$	−176.806	+	176.806i	−0.378599	+	0.378599i	−0.870597	−	0.491997i	$-0.836267\pi$
$467$	−176.806	+	176.806i	−0.378599	+	0.378599i	0.491997	+	0.870597i	$0.336267\pi$
$468$	181.058	+	181.058i	0.386876	+	0.386876i
$469$			44.8740i			0.0956802i
$470$		0			0
$471$	−55.2735			−0.117354
$472$	31.3455	−	31.3455i	0.0664099	−	0.0664099i
$473$	333.924	+	333.924i	0.705971	+	0.705971i
$474$			32.0101i			0.0675318i
$475$		0			0
$476$	−280.950			−0.590230
$477$	−86.9414	+	86.9414i	−0.182267	+	0.182267i
$478$	63.3747	+	63.3747i	0.132583	+	0.132583i
$479$			355.453i			0.742074i	0.928618	+	0.371037i	$0.120998\pi$
$479$			355.453i			0.742074i	−0.928618	+	0.371037i	$0.879002\pi$
$480$		0			0
$481$	620.716			1.29047
$482$	46.4123	−	46.4123i	0.0962910	−	0.0962910i
$483$	55.0502	+	55.0502i	0.113976	+	0.113976i
$484$		−	300.025i		−	0.619887i
$485$		0			0
$486$	9.00682			0.0185326
$487$	261.155	−	261.155i	0.536253	−	0.536253i	−0.386173	−	0.922426i	$-0.626203\pi$
$487$	261.155	−	261.155i	0.536253	−	0.536253i	0.922426	+	0.386173i	$0.126203\pi$
$488$	−268.358	−	268.358i	−0.549913	−	0.549913i
$489$			16.4302i			0.0335997i
$490$		0			0
$491$	648.152			1.32006			0.660032	−	0.751237i	$-0.270543\pi$
$491$	648.152			1.32006			0.660032	+	0.751237i	$0.270543\pi$
$492$	−228.241	+	228.241i	−0.463904	+	0.463904i
$493$	371.292	+	371.292i	0.753129	+	0.753129i
$494$			96.2082i			0.194753i
$495$		0			0
$496$	403.715			0.813941
$497$	−39.0367	+	39.0367i	−0.0785446	+	0.0785446i
$498$	6.49670	+	6.49670i	0.0130456	+	0.0130456i
$499$			177.417i			0.355545i	0.984072	+	0.177772i	$0.0568891\pi$
$499$			177.417i			0.355545i	−0.984072	+	0.177772i	$0.943111\pi$
$500$		0			0
$501$	−259.196			−0.517357
$502$	120.550	−	120.550i	0.240139	−	0.240139i
$503$	336.836	+	336.836i	0.669654	+	0.669654i	0.957636	−	0.287982i	$-0.0929844\pi$
$503$	336.836	+	336.836i	0.669654	+	0.669654i	−0.287982	+	0.957636i	$0.592984\pi$
$504$		−	35.1574i		−	0.0697567i
$505$		0			0
$506$	61.4291			0.121401
$507$	−456.831	+	456.831i	−0.901046	+	0.901046i
$508$	199.053	+	199.053i	0.391836	+	0.391836i
$509$		−	315.435i		−	0.619715i	−0.950783	−	0.309857i	$-0.899719\pi$
$509$		−	315.435i		−	0.619715i	0.950783	−	0.309857i	$-0.100281\pi$
$510$		0			0
$511$	−132.048			−0.258411
$512$	−363.189	+	363.189i	−0.709354	+	0.709354i
$513$	−26.2791	−	26.2791i	−0.0512263	−	0.0512263i
$514$		−	14.8442i		−	0.0288798i
$515$		0			0
$516$	479.175			0.928633
$517$	293.716	−	293.716i	0.568116	−	0.568116i
$518$	−28.8201	−	28.8201i	−0.0556372	−	0.0556372i
$519$			428.102i			0.824859i
$520$		0			0
$521$	−999.113			−1.91768			−0.958842	−	0.283940i	$-0.908358\pi$
$521$	−999.113			−1.91768			−0.958842	+	0.283940i	$0.908358\pi$
$522$	−22.2197	+	22.2197i	−0.0425664	+	0.0425664i
$523$	−284.638	−	284.638i	−0.544241	−	0.544241i	0.380529	−	0.924769i	$-0.375742\pi$
$523$	−284.638	−	284.638i	−0.544241	−	0.544241i	−0.924769	+	0.380529i	$0.875742\pi$
$524$			134.686i			0.257035i
$525$		0			0
$526$	−297.764			−0.566092
$527$	683.045	−	683.045i	1.29610	−	1.29610i
$528$	92.7824	+	92.7824i	0.175724	+	0.175724i
$529$		−	240.378i		−	0.454402i
$530$		0			0
$531$	−30.0237			−0.0565419
$532$	−49.0557	+	49.0557i	−0.0922100	+	0.0922100i
$533$	−836.799	−	836.799i	−1.56998	−	1.56998i
$534$		−	145.582i		−	0.272626i
$535$		0			0
$536$	75.1263			0.140161
$537$	−22.2621	+	22.2621i	−0.0414565	+	0.0414565i
$538$	−0.330847	−	0.330847i	−0.000614958	−	0.000614958i
$539$			43.8066i			0.0812738i
$540$		0			0
$541$	−662.246			−1.22411			−0.612057	−	0.790814i	$-0.709658\pi$
$541$	−662.246			−1.22411			−0.612057	+	0.790814i	$0.709658\pi$
$542$	139.690	−	139.690i	0.257731	−	0.257731i
$543$	−147.643	−	147.643i	−0.271902	−	0.271902i
$544$			715.774i			1.31576i
$545$		0			0
$546$	61.6422			0.112898
$547$	596.362	−	596.362i	1.09024	−	1.09024i	0.0947395	−	0.995502i	$-0.469798\pi$
$547$	596.362	−	596.362i	1.09024	−	1.09024i	0.995502	−	0.0947395i	$-0.0302018\pi$
$548$	330.391	+	330.391i	0.602904	+	0.602904i
$549$			257.042i			0.468200i
$550$		0			0
$551$	129.660			0.235318
$552$	92.1629	−	92.1629i	0.166962	−	0.166962i
$553$	−59.8400	−	59.8400i	−0.108210	−	0.108210i
$554$		−	228.441i		−	0.412349i
$555$		0			0
$556$	324.465			0.583571
$557$	703.702	−	703.702i	1.26338	−	1.26338i	0.313935	−	0.949444i	$-0.398353\pi$
$557$	703.702	−	703.702i	1.26338	−	1.26338i	0.949444	−	0.313935i	$-0.101647\pi$
$558$	40.8762	+	40.8762i	0.0732549	+	0.0732549i
$559$			1756.80i			3.14275i
$560$		0			0
$561$	313.957			0.559638
$562$	156.816	−	156.816i	0.279031	−	0.279031i
$563$	−30.9148	−	30.9148i	−0.0549109	−	0.0549109i	0.679118	−	0.734029i	$-0.262362\pi$
$563$	−30.9148	−	30.9148i	−0.0549109	−	0.0549109i	−0.734029	+	0.679118i	$0.762362\pi$
$564$		−	421.476i		−	0.747298i
$565$		0			0
$566$	274.146			0.484357
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	65.3537	+	65.3537i	0.115059	+	0.115059i
$569$		−	661.719i		−	1.16295i	−0.813564	−	0.581475i	$-0.802476\pi$
$569$		−	661.719i		−	1.16295i	0.813564	−	0.581475i	$-0.197524\pi$
$570$		0			0
$571$	862.831			1.51109			0.755544	−	0.655098i	$-0.227373\pi$
$571$	862.831			1.51109			0.755544	+	0.655098i	$0.227373\pi$
$572$	−377.692	+	377.692i	−0.660301	+	0.660301i
$573$	72.0972	+	72.0972i	0.125824	+	0.125824i
$574$			77.7058i			0.135376i
$575$		0			0
$576$	102.430			0.177829
$577$	−110.827	+	110.827i	−0.192074	+	0.192074i	−0.796592	−	0.604518i	$-0.793366\pi$
$577$	−110.827	+	110.827i	−0.192074	+	0.192074i	0.604518	+	0.796592i	$0.293366\pi$
$578$	224.686	+	224.686i	0.388730	+	0.388730i
$579$		−	7.98294i		−	0.0137875i
$580$		0			0
$581$	−24.2900			−0.0418072
$582$	31.5583	−	31.5583i	0.0542239	−	0.0542239i
$583$	−181.362	−	181.362i	−0.311084	−	0.311084i
$584$			221.070i			0.378544i
$585$		0			0
$586$	181.709			0.310084
$587$	224.917	−	224.917i	0.383164	−	0.383164i	−0.489077	−	0.872241i	$-0.662666\pi$
$587$	224.917	−	224.917i	0.383164	−	0.383164i	0.872241	+	0.489077i	$0.162666\pi$
$588$	31.4308	+	31.4308i	0.0534537	+	0.0534537i
$589$		−	238.528i		−	0.404972i
$590$		0			0
$591$	30.7374			0.0520092
$592$	228.221	−	228.221i	0.385509	−	0.385509i
$593$	−456.305	−	456.305i	−0.769485	−	0.769485i	0.208531	−	0.978016i	$-0.433132\pi$
$593$	−456.305	−	456.305i	−0.769485	−	0.769485i	−0.978016	+	0.208531i	$0.933132\pi$
$594$			18.7885i			0.0316304i
$595$		0			0
$596$	−752.936			−1.26332
$597$	−479.169	+	479.169i	−0.802628	+	0.802628i
$598$	161.591	+	161.591i	0.270219	+	0.270219i
$599$			507.846i			0.847823i	0.905704	+	0.423911i	$0.139343\pi$
$599$			507.846i			0.847823i	−0.905704	+	0.423911i	$0.860657\pi$
$600$		0			0
$601$	382.086			0.635751			0.317875	−	0.948132i	$-0.397031\pi$
$601$	382.086			0.635751			0.317875	+	0.948132i	$0.397031\pi$
$602$	81.5688	−	81.5688i	0.135496	−	0.135496i
$603$	−35.9792	−	35.9792i	−0.0596671	−	0.0596671i
$604$			643.509i			1.06541i
$605$		0			0
$606$	128.304			0.211723
$607$	−138.297	+	138.297i	−0.227837	+	0.227837i	−0.811788	−	0.583952i	$-0.801506\pi$
$607$	−138.297	+	138.297i	−0.227837	+	0.227837i	0.583952	+	0.811788i	$0.301506\pi$
$608$	124.979	+	124.979i	0.205557	+	0.205557i
$609$		−	83.0755i		−	0.136413i
$610$		0			0
$611$	1545.26			2.52906
$612$	225.261	−	225.261i	0.368073	−	0.368073i
$613$	−438.734	−	438.734i	−0.715715	−	0.715715i	0.252009	−	0.967725i	$-0.418909\pi$
$613$	−438.734	−	438.734i	−0.715715	−	0.715715i	−0.967725	+	0.252009i	$0.918909\pi$
$614$		−	216.050i		−	0.351873i
$615$		0			0
$616$	73.3393			0.119057
$617$	442.672	−	442.672i	0.717458	−	0.717458i	−0.250626	−	0.968084i	$-0.580636\pi$
$617$	442.672	−	442.672i	0.717458	−	0.717458i	0.968084	+	0.250626i	$0.0806363\pi$
$618$	−89.7035	−	89.7035i	−0.145151	−	0.145151i
$619$		−	186.618i		−	0.301483i	−0.988573	−	0.150741i	$-0.951834\pi$
$619$		−	186.618i		−	0.301483i	0.988573	−	0.150741i	$-0.0481661\pi$
$620$		0			0
$621$	−88.2767			−0.142153
$622$	−125.612	+	125.612i	−0.201948	+	0.201948i
$623$	272.153	+	272.153i	0.436843	+	0.436843i
$624$			488.134i			0.782266i
$625$		0			0
$626$	−54.8125			−0.0875600
$627$	54.8190	−	54.8190i	0.0874306	−	0.0874306i
$628$	−82.7281	−	82.7281i	−0.131733	−	0.131733i
$629$		−	772.255i		−	1.22775i
$630$		0			0
$631$	−973.263			−1.54241			−0.771207	−	0.636585i	$-0.780346\pi$
$631$	−973.263			−1.54241			−0.771207	+	0.636585i	$0.780346\pi$
$632$	−100.182	+	100.182i	−0.158516	+	0.158516i
$633$	−99.1163	−	99.1163i	−0.156582	−	0.156582i
$634$			79.2003i			0.124922i
$635$		0			0
$636$	−260.251			−0.409200
$637$	−115.235	+	115.235i	−0.180902	+	0.180902i
$638$	−46.3509	−	46.3509i	−0.0726502	−	0.0726502i
$639$		−	62.5979i		−	0.0979623i
$640$		0			0
$641$	11.4492			0.0178614			0.00893072	−	0.999960i	$-0.497157\pi$
$641$	11.4492			0.0178614			0.00893072	+	0.999960i	$0.497157\pi$
$642$	32.4459	−	32.4459i	0.0505388	−	0.0505388i
$643$	−132.472	−	132.472i	−0.206021	−	0.206021i	0.596553	−	0.802574i	$-0.296537\pi$
$643$	−132.472	−	132.472i	−0.206021	−	0.206021i	−0.802574	+	0.596553i	$0.796537\pi$
$644$			164.788i			0.255882i
$645$		0			0
$646$	119.696			0.185288
$647$	488.968	−	488.968i	0.755746	−	0.755746i	−0.219799	−	0.975545i	$-0.570540\pi$
$647$	488.968	−	488.968i	0.755746	−	0.755746i	0.975545	+	0.219799i	$0.0705402\pi$
$648$	28.1886	+	28.1886i	0.0435010	+	0.0435010i
$649$		−	62.6304i		−	0.0965029i
$650$		0			0
$651$	−152.829			−0.234760
$652$	−24.5912	+	24.5912i	−0.0377166	+	0.0377166i
$653$	866.784	+	866.784i	1.32739	+	1.32739i	0.907642	+	0.419745i	$0.137880\pi$
$653$	866.784	+	866.784i	1.32739	+	1.32739i	0.419745	+	0.907642i	$0.362120\pi$
$654$			87.3303i			0.133533i
$655$		0			0
$656$	−615.339			−0.938017
$657$	105.874	−	105.874i	0.161148	−	0.161148i
$658$	−71.7469	−	71.7469i	−0.109038	−	0.109038i
$659$			32.6504i			0.0495454i	0.999693	+	0.0247727i	$0.00788620\pi$
$659$			32.6504i			0.0495454i	−0.999693	+	0.0247727i	$0.992114\pi$
$660$		0			0
$661$	−417.442			−0.631532			−0.315766	−	0.948837i	$-0.602261\pi$
$661$	−417.442			−0.631532			−0.315766	+	0.948837i	$0.602261\pi$
$662$	−122.854	+	122.854i	−0.185580	+	0.185580i
$663$	825.873	+	825.873i	1.24566	+	1.24566i
$664$			40.6654i			0.0612430i
$665$		0			0
$666$	46.2150			0.0693918
$667$	217.777	−	217.777i	0.326503	−	0.326503i
$668$	−387.939	−	387.939i	−0.580747	−	0.580747i
$669$			557.082i			0.832708i
$670$		0			0
$671$	−536.196			−0.799100
$672$	80.0760	−	80.0760i	0.119161	−	0.119161i
$673$	668.058	+	668.058i	0.992657	+	0.992657i	0.999973	−	0.00731589i	$-0.00232874\pi$
$673$	668.058	+	668.058i	0.992657	+	0.992657i	−0.00731589	+	0.999973i	$0.502329\pi$
$674$			35.6070i			0.0528294i
$675$		0			0
$676$	−1367.48			−2.02290
$677$	−287.193	+	287.193i	−0.424214	+	0.424214i	−0.886652	−	0.462438i	$-0.846975\pi$
$677$	−287.193	+	287.193i	−0.424214	+	0.424214i	0.462438	+	0.886652i	$0.346975\pi$
$678$	−14.4469	−	14.4469i	−0.0213081	−	0.0213081i
$679$			117.991i			0.173772i
$680$		0			0
$681$	−456.004			−0.669609
$682$	−85.2689	+	85.2689i	−0.125028	+	0.125028i
$683$	142.312	+	142.312i	0.208364	+	0.208364i	0.803572	−	0.595208i	$-0.202930\pi$
$683$	142.312	+	142.312i	0.208364	+	0.208364i	−0.595208	+	0.803572i	$0.702930\pi$
$684$		−	78.6641i		−	0.115006i
$685$		0			0
$686$	10.7008			0.0155988
$687$	367.279	−	367.279i	0.534613	−	0.534613i
$688$	645.930	+	645.930i	0.938851	+	0.938851i
$689$		−	954.158i		−	1.38484i
$690$		0			0
$691$	1281.91			1.85515			0.927577	−	0.373632i	$-0.121888\pi$
$691$	1281.91			1.85515			0.927577	+	0.373632i	$0.121888\pi$
$692$	−640.741	+	640.741i	−0.925927	+	0.925927i
$693$	−35.1234	−	35.1234i	−0.0506831	−	0.0506831i
$694$			155.781i			0.224468i
$695$		0			0
$696$	−139.082			−0.199830
$697$	−1041.09	+	1041.09i	−1.49368	+	1.49368i
$698$	76.3064	+	76.3064i	0.109322	+	0.109322i
$699$		−	114.945i		−	0.164443i
$700$		0			0
$701$	−122.572			−0.174854			−0.0874268	−	0.996171i	$-0.527864\pi$
$701$	−122.572			−0.174854			−0.0874268	+	0.996171i	$0.527864\pi$
$702$	−49.4237	+	49.4237i	−0.0704041	+	0.0704041i
$703$	−134.841	−	134.841i	−0.191808	−	0.191808i
$704$			213.671i			0.303510i
$705$		0			0
$706$	85.9748			0.121777
$707$	−239.853	+	239.853i	−0.339255	+	0.339255i
$708$	−44.9367	−	44.9367i	−0.0634699	−	0.0634699i
$709$			140.031i			0.197504i	0.995112	+	0.0987522i	$0.0314851\pi$
$709$			140.031i			0.197504i	−0.995112	+	0.0987522i	$0.968515\pi$
$710$		0			0
$711$	95.9575			0.134961
$712$	455.628	−	455.628i	0.639927	−	0.639927i
$713$	−400.632	−	400.632i	−0.561896	−	0.561896i
$714$		−	76.6913i		−	0.107411i
$715$		0			0
$716$	−66.6396			−0.0930721
$717$	189.980	−	189.980i	0.264965	−	0.264965i
$718$	18.0805	+	18.0805i	0.0251817	+	0.0251817i
$719$			247.009i			0.343545i	0.985137	+	0.171773i	$0.0549494\pi$
$719$			247.009i			0.343545i	−0.985137	+	0.171773i	$0.945051\pi$
$720$		0			0
$721$	335.386			0.465167
$722$	−126.590	+	126.590i	−0.175332	+	0.175332i
$723$	−139.131	−	139.131i	−0.192436	−	0.192436i
$724$		−	441.955i		−	0.610435i
$725$		0			0
$726$	81.8984			0.112808
$727$	663.212	−	663.212i	0.912259	−	0.912259i	−0.0841908	−	0.996450i	$-0.526831\pi$
$727$	663.212	−	663.212i	0.912259	−	0.912259i	0.996450	+	0.0841908i	$0.0268305\pi$
$728$	192.921	+	192.921i	0.265002	+	0.265002i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	2185.69			2.99001
$732$	−384.715	+	384.715i	−0.525568	+	0.525568i
$733$	648.037	+	648.037i	0.884089	+	0.884089i	0.993947	−	0.109858i	$-0.0350397\pi$
$733$	648.037	+	648.037i	0.884089	+	0.884089i	−0.109858	+	0.993947i	$0.535040\pi$
$734$		−	108.843i		−	0.148287i
$735$		0			0
$736$	419.829			0.570420
$737$	75.0537	−	75.0537i	0.101837	−	0.101837i
$738$	−62.3032	−	62.3032i	−0.0844217	−	0.0844217i
$739$		−	1233.42i		−	1.66904i	−0.550980	−	0.834519i	$-0.685746\pi$
$739$		−	1233.42i		−	1.66904i	0.550980	−	0.834519i	$-0.314254\pi$
$740$		0			0
$741$	288.406			0.389212
$742$	−44.3020	+	44.3020i	−0.0597061	+	0.0597061i
$743$	877.884	+	877.884i	1.18154	+	1.18154i	0.979345	+	0.202195i	$0.0648074\pi$
$743$	877.884	+	877.884i	1.18154	+	1.18154i	0.202195	+	0.979345i	$0.435193\pi$
$744$			255.860i			0.343898i
$745$		0			0
$746$	44.6430			0.0598431
$747$	19.4753	−	19.4753i	0.0260714	−	0.0260714i
$748$	469.900	+	469.900i	0.628209	+	0.628209i
$749$			121.309i			0.161962i
$750$		0			0
$751$	−495.029			−0.659160			−0.329580	−	0.944128i	$-0.606907\pi$
$751$	−495.029			−0.659160			−0.329580	+	0.944128i	$0.606907\pi$
$752$	568.152	−	568.152i	0.755521	−	0.755521i
$753$	−361.375	−	361.375i	−0.479914	−	0.479914i
$754$		−	243.855i		−	0.323415i
$755$		0			0
$756$	−50.4014			−0.0666685
$757$	−700.188	+	700.188i	−0.924951	+	0.924951i	−0.997374	−	0.0724227i	$-0.976927\pi$
$757$	−700.188	+	700.188i	−0.924951	+	0.924951i	0.0724227	+	0.997374i	$0.476927\pi$
$758$	−77.2358	−	77.2358i	−0.101894	−	0.101894i
$759$		−	184.148i		−	0.242619i
$760$		0			0
$761$	−658.430			−0.865216			−0.432608	−	0.901582i	$-0.642407\pi$
$761$	−658.430			−0.865216			−0.432608	+	0.901582i	$0.642407\pi$
$762$	−54.3358	+	54.3358i	−0.0713068	+	0.0713068i
$763$	−163.256	−	163.256i	−0.213966	−	0.213966i
$764$			215.816i			0.282482i
$765$		0			0
$766$	390.580			0.509896
$767$	164.751	−	164.751i	0.214799	−	0.214799i
$768$	83.3579	+	83.3579i	0.108539	+	0.108539i
$769$			121.021i			0.157375i	0.996899	+	0.0786873i	$0.0250729\pi$
$769$			121.021i			0.157375i	−0.996899	+	0.0786873i	$0.974927\pi$
$770$		0			0
$771$	−44.4990			−0.0577159
$772$	11.9481	−	11.9481i	0.0154768	−	0.0154768i
$773$	−191.617	−	191.617i	−0.247888	−	0.247888i	0.572215	−	0.820103i	$-0.306084\pi$
$773$	−191.617	−	191.617i	−0.247888	−	0.247888i	−0.820103	+	0.572215i	$0.806084\pi$
$774$			130.801i			0.168994i
$775$		0			0
$776$	197.536			0.254557
$777$	−86.3948	+	86.3948i	−0.111190	+	0.111190i
$778$	272.657	+	272.657i	0.350459	+	0.350459i
$779$			363.563i			0.466705i
$780$		0			0
$781$	130.581			0.167197
$782$	201.041	−	201.041i	0.257086	−	0.257086i
$783$	66.6086	+	66.6086i	0.0850684	+	0.0850684i
$784$			84.7377i			0.108084i
$785$		0			0
$786$	−36.7655			−0.0467755
$787$	−52.6931	+	52.6931i	−0.0669544	+	0.0669544i	−0.739791	−	0.672837i	$-0.765076\pi$
$787$	−52.6931	+	52.6931i	−0.0669544	+	0.0669544i	0.672837	+	0.739791i	$0.265076\pi$
$788$	46.0048	+	46.0048i	0.0583818	+	0.0583818i
$789$			892.616i			1.13133i
$790$		0			0
$791$	54.0145			0.0682863
$792$	−58.8022	+	58.8022i	−0.0742453	+	0.0742453i
$793$	−1410.48	−	1410.48i	−1.77866	−	1.77866i
$794$		−	80.7840i		−	0.101743i
$795$		0			0
$796$	−1434.35			−1.80195
$797$	369.849	−	369.849i	0.464051	−	0.464051i	−0.435930	−	0.899981i	$-0.643580\pi$
$797$	369.849	−	369.849i	0.464051	−	0.464051i	0.899981	+	0.435930i	$0.143580\pi$
$798$	−13.3908	−	13.3908i	−0.0167805	−	0.0167805i
$799$		−	1922.51i		−	2.40615i
$800$		0			0
$801$	−436.416			−0.544838
$802$	206.573	−	206.573i	0.257573	−	0.257573i
$803$	220.856	+	220.856i	0.275038	+	0.275038i
$804$		−	107.701i		−	0.133956i
$805$		0			0
$806$	−448.605			−0.556582
$807$	−0.991790	+	0.991790i	−0.00122898	+	0.00122898i
$808$	401.553	+	401.553i	0.496972	+	0.496972i
$809$			1351.17i			1.67017i	0.550121	+	0.835085i	$0.314582\pi$
$809$			1351.17i			1.67017i	−0.550121	+	0.835085i	$0.685418\pi$
$810$		0			0
$811$	509.726			0.628516			0.314258	−	0.949338i	$-0.398244\pi$
$811$	509.726			0.628516			0.314258	+	0.949338i	$0.398244\pi$
$812$	124.339	−	124.339i	0.153127	−	0.153127i
$813$	−418.753	−	418.753i	−0.515071	−	0.515071i
$814$			96.4057i			0.118434i
$815$		0			0
$816$	607.305			0.744247
$817$	381.637	−	381.637i	0.467120	−	0.467120i
$818$	70.7672	+	70.7672i	0.0865125	+	0.0865125i
$819$		−	184.786i		−	0.225624i
$820$		0			0
$821$	−220.673			−0.268785			−0.134393	−	0.990928i	$-0.542908\pi$
$821$	−220.673			−0.268785			−0.134393	+	0.990928i	$0.542908\pi$
$822$	−90.1875	+	90.1875i	−0.109717	+	0.109717i
$823$	−864.049	−	864.049i	−1.04988	−	1.04988i	−0.998689	−	0.0511881i	$-0.983699\pi$
$823$	−864.049	−	864.049i	−1.04988	−	1.04988i	−0.0511881	−	0.998689i	$-0.516301\pi$
$824$		−	561.490i		−	0.681420i
$825$		0			0
$826$	−15.2989			−0.0185217
$827$	−289.315	+	289.315i	−0.349837	+	0.349837i	−0.860049	−	0.510212i	$-0.829567\pi$
$827$	−289.315	+	289.315i	−0.349837	+	0.349837i	0.510212	+	0.860049i	$0.329567\pi$
$828$	−132.124	−	132.124i	−0.159570	−	0.159570i
$829$			460.234i			0.555167i	0.960701	+	0.277584i	$0.0895336\pi$
$829$			460.234i			0.555167i	−0.960701	+	0.277584i	$0.910466\pi$
$830$		0			0
$831$	−684.805			−0.824073
$832$	−562.069	+	562.069i	−0.675564	+	0.675564i
$833$	143.368	+	143.368i	0.172110	+	0.172110i
$834$			88.5699i			0.106199i
$835$		0			0
$836$	164.096			0.196287
$837$	122.536	−	122.536i	0.146399	−	0.146399i
$838$	−28.3174	−	28.3174i	−0.0337917	−	0.0337917i
$839$		−	859.488i		−	1.02442i	−0.858860	−	0.512210i	$-0.828827\pi$
$839$		−	859.488i		−	1.02442i	0.858860	−	0.512210i	$-0.171173\pi$
$840$		0			0
$841$	512.356			0.609222
$842$	−62.5201	+	62.5201i	−0.0742519	+	0.0742519i
$843$	−470.091	−	470.091i	−0.557640	−	0.557640i
$844$		−	296.696i		−	0.351535i
$845$		0			0
$846$	115.051			0.135994
$847$	−153.102	+	153.102i	−0.180758	+	0.180758i
$848$	−350.820	−	350.820i	−0.413703	−	0.413703i
$849$		−	821.815i		−	0.967980i
$850$		0			0
$851$	−452.957			−0.532265
$852$	93.6906	−	93.6906i	0.109965	−	0.109965i
$853$	−717.258	−	717.258i	−0.840865	−	0.840865i	0.148107	−	0.988971i	$-0.452682\pi$
$853$	−717.258	−	717.258i	−0.840865	−	0.840865i	−0.988971	+	0.148107i	$0.952682\pi$
$854$			130.978i			0.153371i
$855$		0			0
$856$	203.092			0.237256
$857$	36.5861	−	36.5861i	0.0426909	−	0.0426909i	−0.685439	−	0.728130i	$-0.740390\pi$
$857$	36.5861	−	36.5861i	0.0426909	−	0.0426909i	0.728130	+	0.685439i	$0.240390\pi$
$858$	−103.099	−	103.099i	−0.120162	−	0.120162i
$859$			1379.61i			1.60607i	0.595935	+	0.803033i	$0.296782\pi$
$859$			1379.61i			1.60607i	−0.595935	+	0.803033i	$0.703218\pi$
$860$		0			0
$861$	232.941			0.270547
$862$	56.4518	−	56.4518i	0.0654893	−	0.0654893i
$863$	−914.825	−	914.825i	−1.06005	−	1.06005i	−0.998078	−	0.0619741i	$-0.980260\pi$
$863$	−914.825	−	914.825i	−1.06005	−	1.06005i	−0.0619741	−	0.998078i	$-0.519740\pi$
$864$			128.407i			0.148620i
$865$		0			0
$866$	64.8430			0.0748765
$867$	673.548	−	673.548i	0.776872	−	0.776872i
$868$	−228.740	−	228.740i	−0.263525	−	0.263525i
$869$			200.170i			0.230345i
$870$		0			0
$871$	394.862			0.453344
$872$	−273.317	+	273.317i	−0.313437	+	0.313437i
$873$	−94.6033	−	94.6033i	−0.108366	−	0.108366i
$874$		−	70.2064i		−	0.0803277i
$875$		0			0
$876$	316.924			0.361785
$877$	−1008.35	+	1008.35i	−1.14977	+	1.14977i	−0.163175	+	0.986597i	$0.552174\pi$
$877$	−1008.35	+	1008.35i	−1.14977	+	1.14977i	−0.986597	+	0.163175i	$0.947826\pi$
$878$	−221.432	−	221.432i	−0.252201	−	0.252201i
$879$		−	544.715i		−	0.619698i
$880$		0			0
$881$	−199.243			−0.226155			−0.113077	−	0.993586i	$-0.536071\pi$
$881$	−199.243			−0.226155			−0.113077	+	0.993586i	$0.536071\pi$
$882$	−8.57971	+	8.57971i	−0.00972756	+	0.00972756i
$883$	555.536	+	555.536i	0.629146	+	0.629146i	0.947853	−	0.318707i	$-0.103249\pi$
$883$	555.536	+	555.536i	0.629146	+	0.629146i	−0.318707	+	0.947853i	$0.603249\pi$
$884$			2472.18i			2.79658i
$885$		0			0
$886$	−323.214			−0.364802
$887$	−633.737	+	633.737i	−0.714473	+	0.714473i	−0.967468	−	0.252995i	$-0.918584\pi$
$887$	−633.737	+	633.737i	−0.714473	+	0.714473i	0.252995	+	0.967468i	$0.418584\pi$
$888$	144.639	+	144.639i	0.162882	+	0.162882i
$889$		−	203.152i		−	0.228517i
$890$		0			0
$891$	56.3227			0.0632130
$892$	−833.787	+	833.787i	−0.934739	+	0.934739i
$893$	−335.683	−	335.683i	−0.375905	−	0.375905i
$894$		−	205.530i		−	0.229899i
$895$		0			0
$896$	313.721			0.350136
$897$	484.406	−	484.406i	0.540029	−	0.540029i
$898$	195.334	+	195.334i	0.217522	+	0.217522i
$899$			604.588i			0.672511i
$900$		0			0
$901$	−1187.10			−1.31754
$902$	129.966	−	129.966i	0.144087	−	0.144087i
$903$	−244.521	−	244.521i	−0.270787	−	0.270787i
$904$		−	90.4289i		−	0.100032i
$905$		0			0
$906$	−175.660			−0.193885
$907$	54.4248	−	54.4248i	0.0600053	−	0.0600053i	−0.676467	−	0.736473i	$-0.736490\pi$
$907$	54.4248	−	54.4248i	0.0600053	−	0.0600053i	0.736473	+	0.676467i	$0.236490\pi$
$908$	−682.503	−	682.503i	−0.751655	−	0.751655i
$909$		−	384.621i		−	0.423125i
$910$		0			0
$911$	413.285			0.453660			0.226830	−	0.973934i	$-0.427164\pi$
$911$	413.285			0.453660			0.226830	+	0.973934i	$0.427164\pi$
$912$	106.040	−	106.040i	0.116271	−	0.116271i
$913$	40.6261	+	40.6261i	0.0444973	+	0.0444973i
$914$			5.23088i			0.00572307i
$915$		0			0
$916$	1099.42			1.20024
$917$	68.7299	−	68.7299i	0.0749508	−	0.0749508i
$918$	61.4898	+	61.4898i	0.0669824	+	0.0669824i
$919$		−	1275.48i		−	1.38790i	−0.720023	−	0.693951i	$-0.755869\pi$
$919$		−	1275.48i		−	1.38790i	0.720023	−	0.693951i	$-0.244131\pi$
$920$		0			0
$921$	−647.660			−0.703214
$922$	−92.9775	+	92.9775i	−0.100843	+	0.100843i
$923$	343.497	+	343.497i	0.372153	+	0.372153i
$924$		−	105.139i		−	0.113786i
$925$		0			0
$926$	−4.31766			−0.00466270
$927$	−268.907	+	268.907i	−0.290083	+	0.290083i
$928$	−316.779	−	316.779i	−0.341356	−	0.341356i
$929$		−	1580.92i		−	1.70174i	−0.525375	−	0.850871i	$-0.676075\pi$
$929$		−	1580.92i		−	1.70174i	0.525375	−	0.850871i	$-0.323925\pi$
$930$		0			0
$931$	50.0659			0.0537765
$932$	172.039	−	172.039i	0.184592	−	0.184592i
$933$	376.550	+	376.550i	0.403591	+	0.403591i
$934$		−	144.471i		−	0.154680i
$935$		0			0
$936$	−309.362			−0.330515
$937$	716.815	−	716.815i	0.765010	−	0.765010i	−0.212213	−	0.977223i	$-0.568067\pi$
$937$	716.815	−	716.815i	0.765010	−	0.765010i	0.977223	+	0.212213i	$0.0680671\pi$
$938$	−18.3336	−	18.3336i	−0.0195454	−	0.0195454i
$939$			164.313i			0.174987i
$940$		0			0
$941$	1118.51			1.18864			0.594321	−	0.804228i	$-0.297421\pi$
$941$	1118.51			1.18864			0.594321	+	0.804228i	$0.297421\pi$
$942$	22.5824	−	22.5824i	0.0239729	−	0.0239729i
$943$	610.640	+	610.640i	0.647551	+	0.647551i
$944$		−	121.150i		−	0.128336i
$945$		0			0
$946$	−272.855			−0.288430
$947$	61.6150	−	61.6150i	0.0650633	−	0.0650633i	−0.673826	−	0.738890i	$-0.735350\pi$
$947$	61.6150	−	61.6150i	0.0650633	−	0.0650633i	0.738890	+	0.673826i	$0.235350\pi$
$948$	143.620	+	143.620i	0.151498	+	0.151498i
$949$			1161.94i			1.22438i
$950$		0			0
$951$	237.421			0.249654
$952$	240.020	−	240.020i	0.252122	−	0.252122i
$953$	−984.214	−	984.214i	−1.03275	−	1.03275i	−0.999445	−	0.0333085i	$-0.989396\pi$
$953$	−984.214	−	984.214i	−1.03275	−	1.03275i	−0.0333085	−	0.999445i	$-0.510604\pi$
$954$		−	71.0412i		−	0.0744666i
$955$		0			0
$956$	568.688			0.594862
$957$	−138.947	+	138.947i	−0.145190	+	0.145190i
$958$	−145.223	−	145.223i	−0.151590	−	0.151590i
$959$		−	337.195i		−	0.351611i
$960$		0			0
$961$	151.224			0.157361
$962$	−253.598	+	253.598i	−0.263616	+	0.263616i
$963$	−97.2639	−	97.2639i	−0.101001	−	0.101001i
$964$		−	416.477i		−	0.432030i
$965$		0			0
$966$	−44.9824			−0.0465656
$967$	822.841	−	822.841i	0.850921	−	0.850921i	−0.139325	−	0.990247i	$-0.544493\pi$
$967$	822.841	−	822.841i	0.850921	−	0.850921i	0.990247	+	0.139325i	$0.0444933\pi$
$968$	256.317	+	256.317i	0.264791	+	0.264791i
$969$		−	358.816i		−	0.370296i
$970$		0			0
$971$	−1691.65			−1.74217			−0.871086	−	0.491131i	$-0.836584\pi$
$971$	−1691.65			−1.74217			−0.871086	+	0.491131i	$0.836584\pi$
$972$	40.4110	−	40.4110i	0.0415751	−	0.0415751i
$973$	−165.574	−	165.574i	−0.170168	−	0.170168i
$974$			213.394i			0.219090i
$975$		0			0
$976$	−1037.20			−1.06270
$977$	−926.154	+	926.154i	−0.947957	+	0.947957i	−0.998711	−	0.0507539i	$-0.983838\pi$
$977$	−926.154	+	926.154i	−0.947957	+	0.947957i	0.0507539	+	0.998711i	$0.483838\pi$
$978$	−6.71270	−	6.71270i	−0.00686370	−	0.00686370i
$979$		−	910.375i		−	0.929903i
$980$		0			0
$981$	261.793			0.266863
$982$	−264.807	+	264.807i	−0.269661	+	0.269661i
$983$	821.842	+	821.842i	0.836055	+	0.836055i	0.988337	−	0.152282i	$-0.0486622\pi$
$983$	821.842	+	821.842i	0.836055	+	0.836055i	−0.152282	+	0.988337i	$0.548662\pi$
$984$		−	389.981i		−	0.396322i
$985$		0			0
$986$	−303.389			−0.307696
$987$	−215.078	+	215.078i	−0.217911	+	0.217911i
$988$	431.659	+	431.659i	0.436901	+	0.436901i
$989$		−	1281.99i		−	1.29625i
$990$		0			0
$991$	−765.742			−0.772696			−0.386348	−	0.922353i	$-0.626264\pi$
$991$	−765.742			−0.772696			−0.386348	+	0.922353i	$0.626264\pi$
$992$	−582.759	+	582.759i	−0.587459	+	0.587459i
$993$	368.283	+	368.283i	0.370879	+	0.370879i
$994$		−	31.8975i		−	0.0320900i
$995$		0			0
$996$	58.2976			0.0585317
$997$	406.099	−	406.099i	0.407321	−	0.407321i	−0.473483	−	0.880803i	$-0.657003\pi$
$997$	406.099	−	406.099i	0.407321	−	0.407321i	0.880803	+	0.473483i	$0.157003\pi$
$998$	−72.4850	−	72.4850i	−0.0726303	−	0.0726303i
$999$		−	138.540i		−	0.138679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.l.e.43.7		24
5.2	odd	4	inner	525.3.l.e.232.7		24
5.3	odd	4		105.3.l.a.22.6	✓	24
5.4	even	2		105.3.l.a.43.6	yes	24
15.8	even	4		315.3.o.b.127.7		24
15.14	odd	2		315.3.o.b.253.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.6	✓	24	5.3	odd	4
105.3.l.a.43.6	yes	24	5.4	even	2
315.3.o.b.127.7		24	15.8	even	4
315.3.o.b.253.7		24	15.14	odd	2
525.3.l.e.43.7		24	1.1	even	1	trivial
525.3.l.e.232.7		24	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.408558 + 0.408558i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.66616i q^{4} -1.00076 q^{6} +(1.87083 - 1.87083i) q^{7} +(-3.13207 - 3.13207i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-0.408558 + 0.408558i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.66616i q^{4} -1.00076 q^{6} +(1.87083 - 1.87083i) q^{7} +(-3.13207 - 3.13207i) q^{8} +3.00000i q^{9} -6.25808 q^{11} +(-4.49011 + 4.49011i) q^{12} +(-16.4621 - 16.4621i) q^{13} +1.52868i q^{14} -12.1054 q^{16} +(-20.4811 + 20.4811i) q^{17} +(-1.22567 - 1.22567i) q^{18} +7.15227i q^{19} +4.58258 q^{21} +(2.55679 - 2.55679i) q^{22} +(12.0129 + 12.0129i) q^{23} -7.67197i q^{24} +13.4514 q^{26} +(-3.67423 + 3.67423i) q^{27} +(6.85876 + 6.85876i) q^{28} -18.1286i q^{29} -33.3500 q^{31} +(17.4740 - 17.4740i) q^{32} +(-7.66455 - 7.66455i) q^{33} -16.7354i q^{34} -10.9985 q^{36} +(-18.8529 + 18.8529i) q^{37} +(-2.92211 - 2.92211i) q^{38} -40.3237i q^{39} +50.8319 q^{41} +(-1.87225 + 1.87225i) q^{42} +(-53.3589 - 53.3589i) q^{43} -22.9431i q^{44} -9.81596 q^{46} +(-46.9338 + 46.9338i) q^{47} +(-14.8260 - 14.8260i) q^{48} -7.00000i q^{49} -50.1682 q^{51} +(60.3527 - 60.3527i) q^{52} +(28.9805 + 28.9805i) q^{53} -3.00227i q^{54} -11.7191 q^{56} +(-8.75971 + 8.75971i) q^{57} +(7.40656 + 7.40656i) q^{58} +10.0079i q^{59} +85.6806 q^{61} +(13.6254 - 13.6254i) q^{62} +(5.61249 + 5.61249i) q^{63} -34.1432i q^{64} +6.26283 q^{66} +(-11.9931 + 11.9931i) q^{67} +(-75.0869 - 75.0869i) q^{68} +29.4256i q^{69} -20.8660 q^{71} +(9.39621 - 9.39621i) q^{72} +(-35.2913 - 35.2913i) q^{73} -15.4050i q^{74} -26.2214 q^{76} +(-11.7078 + 11.7078i) q^{77} +(16.4746 + 16.4746i) q^{78} -31.9858i q^{79} -9.00000 q^{81} +(-20.7677 + 20.7677i) q^{82} +(-6.49178 - 6.49178i) q^{83} +16.8005i q^{84} +43.6003 q^{86} +(22.2029 - 22.2029i) q^{87} +(19.6007 + 19.6007i) q^{88} +145.472i q^{89} -61.5955 q^{91} +(-44.0414 + 44.0414i) q^{92} +(-40.8453 - 40.8453i) q^{93} -38.3503i q^{94} +42.8024 q^{96} +(-31.5344 + 31.5344i) q^{97} +(2.85990 + 2.85990i) q^{98} -18.7742i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8 + 48 * q^12 - 64 * q^13 - 184 * q^16 - 24 * q^17 - 24 * q^18 - 8 * q^22 - 8 * q^23 - 80 * q^26 + 96 * q^31 - 56 * q^32 + 72 * q^33 + 168 * q^36 - 8 * q^37 - 56 * q^38 + 320 * q^41 + 112 * q^43 + 320 * q^46 - 64 * q^47 - 192 * q^48 - 192 * q^51 - 96 * q^52 + 72 * q^53 - 336 * q^56 - 48 * q^57 + 512 * q^58 - 496 * q^61 + 776 * q^62 - 192 * q^66 + 192 * q^67 - 568 * q^68 - 144 * q^71 - 144 * q^72 - 224 * q^73 + 416 * q^76 - 112 * q^77 + 216 * q^78 - 216 * q^81 - 352 * q^82 + 32 * q^83 + 240 * q^86 - 384 * q^87 - 216 * q^88 - 1304 * q^92 + 168 * q^96 + 816 * q^97 + 56 * q^98

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