LMFDB - Embedded newform 525.3.l.e.43.10

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			43.10
Character	$\chi$	$=$	525.43
Dual form			525.3.l.e.232.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36784 - 1.36784i) q^{2} +(1.22474 + 1.22474i) q^{3} +0.258033i q^{4} +3.35051 q^{6} +(-1.87083 + 1.87083i) q^{7} +(5.82430 + 5.82430i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.36784 - 1.36784i) q^{2} +(1.22474 + 1.22474i) q^{3} +0.258033i q^{4} +3.35051 q^{6} +(-1.87083 + 1.87083i) q^{7} +(5.82430 + 5.82430i) q^{8} +3.00000i q^{9} +17.6130 q^{11} +(-0.316024 + 0.316024i) q^{12} +(-12.1245 - 12.1245i) q^{13} +5.11799i q^{14} +14.9013 q^{16} +(-13.8772 + 13.8772i) q^{17} +(4.10352 + 4.10352i) q^{18} +18.3068i q^{19} -4.58258 q^{21} +(24.0917 - 24.0917i) q^{22} +(26.3956 + 26.3956i) q^{23} +14.2666i q^{24} -33.1686 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.482735 - 0.482735i) q^{28} +2.87815i q^{29} +16.1149 q^{31} +(-2.91465 + 2.91465i) q^{32} +(21.5714 + 21.5714i) q^{33} +37.9637i q^{34} -0.774098 q^{36} +(-2.52440 + 2.52440i) q^{37} +(25.0408 + 25.0408i) q^{38} -29.6988i q^{39} -1.89828 q^{41} +(-6.26823 + 6.26823i) q^{42} +(42.5974 + 42.5974i) q^{43} +4.54472i q^{44} +72.2098 q^{46} +(57.7457 - 57.7457i) q^{47} +(18.2503 + 18.2503i) q^{48} -7.00000i q^{49} -33.9922 q^{51} +(3.12851 - 3.12851i) q^{52} +(-66.5567 - 66.5567i) q^{53} +10.0515i q^{54} -21.7925 q^{56} +(-22.4212 + 22.4212i) q^{57} +(3.93685 + 3.93685i) q^{58} -16.4673i q^{59} -7.37026 q^{61} +(22.0426 - 22.0426i) q^{62} +(-5.61249 - 5.61249i) q^{63} +67.5787i q^{64} +59.0124 q^{66} +(27.2024 - 27.2024i) q^{67} +(-3.58078 - 3.58078i) q^{68} +64.6557i q^{69} -79.5984 q^{71} +(-17.4729 + 17.4729i) q^{72} +(-63.3051 - 63.3051i) q^{73} +6.90594i q^{74} -4.72376 q^{76} +(-32.9508 + 32.9508i) q^{77} +(-40.6231 - 40.6231i) q^{78} -2.48684i q^{79} -9.00000 q^{81} +(-2.59655 + 2.59655i) q^{82} +(29.0421 + 29.0421i) q^{83} -1.18245i q^{84} +116.533 q^{86} +(-3.52500 + 3.52500i) q^{87} +(102.583 + 102.583i) q^{88} -29.3345i q^{89} +45.3656 q^{91} +(-6.81092 + 6.81092i) q^{92} +(19.7367 + 19.7367i) q^{93} -157.974i q^{94} -7.13941 q^{96} +(89.1223 - 89.1223i) q^{97} +(-9.57487 - 9.57487i) q^{98} +52.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36784	−	1.36784i	0.683920	−	0.683920i	−0.276961	−	0.960881i	$-0.589327\pi$
$2$	1.36784	−	1.36784i	0.683920	−	0.683920i	0.960881	+	0.276961i	$0.0893274\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$			0.258033i			0.0645082i
$5$		0			0
$5$		0			0
$6$	3.35051			0.558418
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	5.82430	+	5.82430i	0.728038	+	0.728038i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	17.6130			1.60118			0.800589	−	0.599213i	$-0.204520\pi$
$11$	17.6130			1.60118			0.800589	+	0.599213i	$0.204520\pi$
$12$	−0.316024	+	0.316024i	−0.0263354	+	0.0263354i
$13$	−12.1245	−	12.1245i	−0.932651	−	0.932651i	0.0652196	−	0.997871i	$-0.479225\pi$
$13$	−12.1245	−	12.1245i	−0.932651	−	0.932651i	−0.997871	+	0.0652196i	$0.979225\pi$
$14$			5.11799i			0.365570i
$15$		0			0
$16$	14.9013			0.931331
$17$	−13.8772	+	13.8772i	−0.816309	+	0.816309i	−0.985571	−	0.169262i	$-0.945862\pi$
$17$	−13.8772	+	13.8772i	−0.816309	+	0.816309i	0.169262	+	0.985571i	$0.445862\pi$
$18$	4.10352	+	4.10352i	0.227973	+	0.227973i
$19$			18.3068i			0.963516i	0.876304	+	0.481758i	$0.160002\pi$
$19$			18.3068i			0.963516i	−0.876304	+	0.481758i	$0.839998\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	24.0917	−	24.0917i	1.09508	−	1.09508i
$23$	26.3956	+	26.3956i	1.14763	+	1.14763i	0.987017	+	0.160617i	$0.0513483\pi$
$23$	26.3956	+	26.3956i	1.14763	+	1.14763i	0.160617	+	0.987017i	$0.448652\pi$
$24$			14.2666i			0.594440i
$25$		0			0
$26$	−33.1686			−1.27572
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−0.482735	−	0.482735i	−0.0172405	−	0.0172405i
$29$			2.87815i			0.0992467i	0.998768	+	0.0496234i	$0.0158021\pi$
$29$			2.87815i			0.0992467i	−0.998768	+	0.0496234i	$0.984198\pi$
$30$		0			0
$31$	16.1149			0.519836			0.259918	−	0.965631i	$-0.416304\pi$
$31$	16.1149			0.519836			0.259918	+	0.965631i	$0.416304\pi$
$32$	−2.91465	+	2.91465i	−0.0910828	+	0.0910828i
$33$	21.5714	+	21.5714i	0.653679	+	0.653679i
$34$			37.9637i			1.11658i
$35$		0			0
$36$	−0.774098			−0.0215027
$37$	−2.52440	+	2.52440i	−0.0682270	+	0.0682270i	−0.740397	−	0.672170i	$-0.765362\pi$
$37$	−2.52440	+	2.52440i	−0.0682270	+	0.0682270i	0.672170	+	0.740397i	$0.265362\pi$
$38$	25.0408	+	25.0408i	0.658968	+	0.658968i
$39$		−	29.6988i		−	0.761507i
$40$		0			0
$41$	−1.89828			−0.0462996			−0.0231498	−	0.999732i	$-0.507369\pi$
$41$	−1.89828			−0.0462996			−0.0231498	+	0.999732i	$0.507369\pi$
$42$	−6.26823	+	6.26823i	−0.149243	+	0.149243i
$43$	42.5974	+	42.5974i	0.990637	+	0.990637i	0.999957	−	0.00931954i	$-0.00296654\pi$
$43$	42.5974	+	42.5974i	0.990637	+	0.990637i	−0.00931954	+	0.999957i	$0.502967\pi$
$44$			4.54472i			0.103289i
$45$		0			0
$46$	72.2098			1.56978
$47$	57.7457	−	57.7457i	1.22863	−	1.22863i	0.264150	−	0.964482i	$-0.414909\pi$
$47$	57.7457	−	57.7457i	1.22863	−	1.22863i	0.964482	−	0.264150i	$-0.0850913\pi$
$48$	18.2503	+	18.2503i	0.380214	+	0.380214i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	−33.9922			−0.666513
$52$	3.12851	−	3.12851i	0.0601636	−	0.0601636i
$53$	−66.5567	−	66.5567i	−1.25579	−	1.25579i	−0.953086	−	0.302701i	$-0.902112\pi$
$53$	−66.5567	−	66.5567i	−1.25579	−	1.25579i	−0.302701	−	0.953086i	$-0.597888\pi$
$54$			10.0515i			0.186139i
$55$		0			0
$56$	−21.7925			−0.389153
$57$	−22.4212	+	22.4212i	−0.393354	+	0.393354i
$58$	3.93685	+	3.93685i	0.0678768	+	0.0678768i
$59$		−	16.4673i		−	0.279107i	−0.990215	−	0.139554i	$-0.955433\pi$
$59$		−	16.4673i		−	0.279107i	0.990215	−	0.139554i	$-0.0445668\pi$
$60$		0			0
$61$	−7.37026			−0.120824			−0.0604119	−	0.998174i	$-0.519241\pi$
$61$	−7.37026			−0.120824			−0.0604119	+	0.998174i	$0.519241\pi$
$62$	22.0426	−	22.0426i	0.355526	−	0.355526i
$63$	−5.61249	−	5.61249i	−0.0890871	−	0.0890871i
$64$			67.5787i			1.05592i
$65$		0			0
$66$	59.0124			0.894127
$67$	27.2024	−	27.2024i	0.406006	−	0.406006i	−0.474337	−	0.880343i	$-0.657312\pi$
$67$	27.2024	−	27.2024i	0.406006	−	0.406006i	0.880343	+	0.474337i	$0.157312\pi$
$68$	−3.58078	−	3.58078i	−0.0526586	−	0.0526586i
$69$			64.6557i			0.937039i
$70$		0			0
$71$	−79.5984			−1.12110			−0.560552	−	0.828119i	$-0.689411\pi$
$71$	−79.5984			−1.12110			−0.560552	+	0.828119i	$0.689411\pi$
$72$	−17.4729	+	17.4729i	−0.242679	+	0.242679i
$73$	−63.3051	−	63.3051i	−0.867193	−	0.867193i	0.124968	−	0.992161i	$-0.460117\pi$
$73$	−63.3051	−	63.3051i	−0.867193	−	0.867193i	−0.992161	+	0.124968i	$0.960117\pi$
$74$			6.90594i			0.0933235i
$75$		0			0
$76$	−4.72376			−0.0621547
$77$	−32.9508	+	32.9508i	−0.427933	+	0.427933i
$78$	−40.6231	−	40.6231i	−0.520809	−	0.520809i
$79$		−	2.48684i		−	0.0314790i	−0.999876	−	0.0157395i	$-0.994990\pi$
$79$		−	2.48684i		−	0.0314790i	0.999876	−	0.0157395i	$-0.00501024\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−2.59655	+	2.59655i	−0.0316652	+	0.0316652i
$83$	29.0421	+	29.0421i	0.349905	+	0.349905i	0.860074	−	0.510169i	$-0.170417\pi$
$83$	29.0421	+	29.0421i	0.349905	+	0.349905i	−0.510169	+	0.860074i	$0.670417\pi$
$84$		−	1.18245i		−	0.0140768i
$85$		0			0
$86$	116.533			1.35503
$87$	−3.52500	+	3.52500i	−0.0405173	+	0.0405173i
$88$	102.583	+	102.583i	1.16572	+	1.16572i
$89$		−	29.3345i		−	0.329601i	−0.986327	−	0.164800i	$-0.947302\pi$
$89$		−	29.3345i		−	0.329601i	0.986327	−	0.164800i	$-0.0526980\pi$
$90$		0			0
$91$	45.3656			0.498523
$92$	−6.81092	+	6.81092i	−0.0740318	+	0.0740318i
$93$	19.7367	+	19.7367i	0.212222	+	0.212222i
$94$		−	157.974i		−	1.68057i
$95$		0			0
$96$	−7.13941			−0.0743688
$97$	89.1223	−	89.1223i	0.918786	−	0.918786i	−0.0781549	−	0.996941i	$-0.524903\pi$
$97$	89.1223	−	89.1223i	0.918786	−	0.918786i	0.996941	+	0.0781549i	$0.0249029\pi$
$98$	−9.57487	−	9.57487i	−0.0977028	−	0.0977028i
$99$			52.8389i			0.533726i
$100$		0			0
$101$	−87.3306			−0.864660			−0.432330	−	0.901716i	$-0.642308\pi$
$101$	−87.3306			−0.864660			−0.432330	+	0.901716i	$0.642308\pi$
$102$	−46.4958	+	46.4958i	−0.455841	+	0.455841i
$103$	−36.7417	−	36.7417i	−0.356715	−	0.356715i	0.505885	−	0.862601i	$-0.331166\pi$
$103$	−36.7417	−	36.7417i	−0.356715	−	0.356715i	−0.862601	+	0.505885i	$0.831166\pi$
$104$		−	141.233i		−	1.35801i
$105$		0			0
$106$	−182.078			−1.71771
$107$	91.9855	−	91.9855i	0.859677	−	0.859677i	−0.131622	−	0.991300i	$-0.542019\pi$
$107$	91.9855	−	91.9855i	0.859677	−	0.859677i	0.991300	+	0.131622i	$0.0420187\pi$
$108$	−0.948073	−	0.948073i	−0.00877845	−	0.00877845i
$109$		−	144.628i		−	1.32686i	−0.748237	−	0.663432i	$-0.769099\pi$
$109$		−	144.628i		−	1.32686i	0.748237	−	0.663432i	$-0.230901\pi$
$110$		0			0
$111$	−6.18349			−0.0557071
$112$	−27.8778	+	27.8778i	−0.248909	+	0.248909i
$113$	−28.6801	−	28.6801i	−0.253806	−	0.253806i	0.568723	−	0.822529i	$-0.307438\pi$
$113$	−28.6801	−	28.6801i	−0.253806	−	0.253806i	−0.822529	+	0.568723i	$0.807438\pi$
$114$			61.3371i			0.538045i
$115$		0			0
$116$	−0.742658			−0.00640222
$117$	36.3734	−	36.3734i	0.310884	−	0.310884i
$118$	−22.5247	−	22.5247i	−0.190887	−	0.190887i
$119$		−	51.9239i		−	0.436335i
$120$		0			0
$121$	189.217			1.56377
$122$	−10.0813	+	10.0813i	−0.0826338	+	0.0826338i
$123$	−2.32491	−	2.32491i	−0.0189017	−	0.0189017i
$124$			4.15818i			0.0335337i
$125$		0			0
$126$	−15.3540			−0.121857
$127$	−12.2062	+	12.2062i	−0.0961116	+	0.0961116i	−0.753528	−	0.657416i	$-0.771649\pi$
$127$	−12.2062	+	12.2062i	−0.0961116	+	0.0961116i	0.657416	+	0.753528i	$0.271649\pi$
$128$	80.7782	+	80.7782i	0.631080	+	0.631080i
$129$			104.342i			0.808852i
$130$		0			0
$131$	−23.2249			−0.177290			−0.0886448	−	0.996063i	$-0.528254\pi$
$131$	−23.2249			−0.177290			−0.0886448	+	0.996063i	$0.528254\pi$
$132$	−5.56613	+	5.56613i	−0.0421676	+	0.0421676i
$133$	−34.2489	−	34.2489i	−0.257511	−	0.257511i
$134$		−	74.4170i		−	0.555351i
$135$		0			0
$136$	−161.651			−1.18861
$137$	17.2588	−	17.2588i	0.125977	−	0.125977i	−0.641307	−	0.767284i	$-0.721608\pi$
$137$	17.2588	−	17.2588i	0.125977	−	0.125977i	0.767284	+	0.641307i	$0.221608\pi$
$138$	88.4386	+	88.4386i	0.640859	+	0.640859i
$139$			29.4799i			0.212085i	0.994362	+	0.106043i	$0.0338180\pi$
$139$			29.4799i			0.212085i	−0.994362	+	0.106043i	$0.966182\pi$
$140$		0			0
$141$	141.447			1.00317
$142$	−108.878	+	108.878i	−0.766745	+	0.766745i
$143$	−213.548	−	213.548i	−1.49334	−	1.49334i
$144$			44.7039i			0.310444i
$145$		0			0
$146$	−173.182			−1.18618
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	−0.651377	−	0.651377i	−0.00440120	−	0.00440120i
$149$			14.3848i			0.0965421i	0.998834	+	0.0482710i	$0.0153711\pi$
$149$			14.3848i			0.0965421i	−0.998834	+	0.0482710i	$0.984629\pi$
$150$		0			0
$151$	15.3569			0.101701			0.0508506	−	0.998706i	$-0.483807\pi$
$151$	15.3569			0.101701			0.0508506	+	0.998706i	$0.483807\pi$
$152$	−106.624	+	106.624i	−0.701476	+	0.701476i
$153$	−41.6317	−	41.6317i	−0.272103	−	0.272103i
$154$			90.1429i			0.585344i
$155$		0			0
$156$	7.66325			0.0491234
$157$	−63.2769	+	63.2769i	−0.403037	+	0.403037i	−0.879302	−	0.476265i	$-0.841990\pi$
$157$	−63.2769	+	63.2769i	−0.403037	+	0.403037i	0.476265	+	0.879302i	$0.341990\pi$
$158$	−3.40160	−	3.40160i	−0.0215291	−	0.0215291i
$159$		−	163.030i		−	1.02535i
$160$		0			0
$161$	−98.7632			−0.613436
$162$	−12.3106	+	12.3106i	−0.0759911	+	0.0759911i
$163$	121.254	+	121.254i	0.743890	+	0.743890i	0.973324	−	0.229434i	$-0.0736876\pi$
$163$	121.254	+	121.254i	0.743890	+	0.743890i	−0.229434	+	0.973324i	$0.573688\pi$
$164$		−	0.489819i		−	0.00298670i
$165$		0			0
$166$	79.4498			0.478613
$167$	51.2223	−	51.2223i	0.306720	−	0.306720i	−0.536916	−	0.843636i	$-0.680411\pi$
$167$	51.2223	−	51.2223i	0.306720	−	0.306720i	0.843636	+	0.536916i	$0.180411\pi$
$168$	−26.6903	−	26.6903i	−0.158871	−	0.158871i
$169$			125.005i			0.739677i
$170$		0			0
$171$	−54.9204			−0.321172
$172$	−10.9915	+	10.9915i	−0.0639042	+	0.0639042i
$173$	−78.5418	−	78.5418i	−0.453999	−	0.453999i	0.442681	−	0.896679i	$-0.354028\pi$
$173$	−78.5418	−	78.5418i	−0.453999	−	0.453999i	−0.896679	+	0.442681i	$0.854028\pi$
$174$			9.64328i			0.0554211i
$175$		0			0
$176$	262.456			1.49123
$177$	20.1683	−	20.1683i	0.113945	−	0.113945i
$178$	−40.1248	−	40.1248i	−0.225420	−	0.225420i
$179$		−	162.375i		−	0.907125i	−0.891224	−	0.453563i	$-0.850153\pi$
$179$		−	162.375i		−	0.907125i	0.891224	−	0.453563i	$-0.149847\pi$
$180$		0			0
$181$	257.224			1.42113			0.710564	−	0.703633i	$-0.248440\pi$
$181$	257.224			1.42113			0.710564	+	0.703633i	$0.248440\pi$
$182$	62.0528	−	62.0528i	0.340950	−	0.340950i
$183$	−9.02668	−	9.02668i	−0.0493261	−	0.0493261i
$184$			307.472i			1.67104i
$185$		0			0
$186$	53.9932			0.290286
$187$	−244.420	+	244.420i	−1.30706	+	1.30706i
$188$	14.9003	+	14.9003i	0.0792568	+	0.0792568i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	−334.101			−1.74922			−0.874610	−	0.484827i	$-0.838883\pi$
$191$	−334.101			−1.74922			−0.874610	+	0.484827i	$0.838883\pi$
$192$	−82.7667	+	82.7667i	−0.431076	+	0.431076i
$193$	−19.9582	−	19.9582i	−0.103410	−	0.103410i	0.653509	−	0.756919i	$-0.273296\pi$
$193$	−19.9582	−	19.9582i	−0.103410	−	0.103410i	−0.756919	+	0.653509i	$0.773296\pi$
$194$		−	243.810i		−	1.25675i
$195$		0			0
$196$	1.80623			0.00921545
$197$	−36.5252	+	36.5252i	−0.185407	+	0.185407i	−0.793707	−	0.608300i	$-0.791852\pi$
$197$	−36.5252	+	36.5252i	−0.185407	+	0.185407i	0.608300	+	0.793707i	$0.291852\pi$
$198$	72.2751	+	72.2751i	0.365026	+	0.365026i
$199$			187.619i			0.942810i	0.881917	+	0.471405i	$0.156253\pi$
$199$			187.619i			0.942810i	−0.881917	+	0.471405i	$0.843747\pi$
$200$		0			0
$201$	66.6320			0.331502
$202$	−119.454	+	119.454i	−0.591358	+	0.591358i
$203$	−5.38453	−	5.38453i	−0.0265248	−	0.0265248i
$204$		−	8.77110i		−	0.0429956i
$205$		0			0
$206$	−100.513			−0.487929
$207$	−79.1867	+	79.1867i	−0.382545	+	0.382545i
$208$	−180.670	−	180.670i	−0.868607	−	0.868607i
$209$			322.437i			1.54276i
$210$		0			0
$211$	−73.6409			−0.349009			−0.174505	−	0.984656i	$-0.555832\pi$
$211$	−73.6409			−0.349009			−0.174505	+	0.984656i	$0.555832\pi$
$212$	17.1738	−	17.1738i	0.0810085	−	0.0810085i
$213$	−97.4878	−	97.4878i	−0.457689	−	0.457689i
$214$		−	251.643i		−	1.17590i
$215$		0			0
$216$	−42.7997			−0.198147
$217$	−30.1483	+	30.1483i	−0.138932	+	0.138932i
$218$	−197.828	−	197.828i	−0.907468	−	0.907468i
$219$		−	155.065i		−	0.708060i
$220$		0			0
$221$	336.509			1.52266
$222$	−8.45801	+	8.45801i	−0.0380992	+	0.0380992i
$223$	−258.221	−	258.221i	−1.15794	−	1.15794i	−0.984917	−	0.173025i	$-0.944646\pi$
$223$	−258.221	−	258.221i	−1.15794	−	1.15794i	−0.173025	−	0.984917i	$-0.555354\pi$
$224$		−	10.9056i		−	0.0486858i
$225$		0			0
$226$	−78.4596			−0.347166
$227$	9.72923	−	9.72923i	0.0428601	−	0.0428601i	−0.685352	−	0.728212i	$-0.740352\pi$
$227$	9.72923	−	9.72923i	0.0428601	−	0.0428601i	0.728212	+	0.685352i	$0.240352\pi$
$228$	−5.78540	−	5.78540i	−0.0253745	−	0.0253745i
$229$			108.047i			0.471822i	0.971775	+	0.235911i	$0.0758074\pi$
$229$			108.047i			0.471822i	−0.971775	+	0.235911i	$0.924193\pi$
$230$		0			0
$231$	−80.7128			−0.349406
$232$	−16.7632	+	16.7632i	−0.0722554	+	0.0722554i
$233$	2.47323	+	2.47323i	0.0106147	+	0.0106147i	0.712394	−	0.701779i	$-0.247611\pi$
$233$	2.47323	+	2.47323i	0.0106147	+	0.0106147i	−0.701779	+	0.712394i	$0.747611\pi$
$234$		−	99.5059i		−	0.425239i
$235$		0			0
$236$	4.24911			0.0180047
$237$	3.04574	−	3.04574i	0.0128512	−	0.0128512i
$238$	−71.0236	−	71.0236i	−0.298418	−	0.298418i
$239$		−	230.974i		−	0.966417i	−0.875505	−	0.483209i	$-0.839471\pi$
$239$		−	230.974i		−	0.966417i	0.875505	−	0.483209i	$-0.160529\pi$
$240$		0			0
$241$	−280.404			−1.16350			−0.581752	−	0.813366i	$-0.697633\pi$
$241$	−280.404			−1.16350			−0.581752	+	0.813366i	$0.697633\pi$
$242$	258.818	−	258.818i	1.06950	−	1.06950i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	1.90177i		−	0.00779413i
$245$		0			0
$246$	−6.36022			−0.0258545
$247$	221.960	−	221.960i	0.898625	−	0.898625i
$248$	93.8582	+	93.8582i	0.378460	+	0.378460i
$249$			71.1383i			0.285696i
$250$		0			0
$251$	53.4737			0.213043			0.106521	−	0.994310i	$-0.466029\pi$
$251$	53.4737			0.213043			0.106521	+	0.994310i	$0.466029\pi$
$252$	1.44821	−	1.44821i	0.00574685	−	0.00574685i
$253$	464.904	+	464.904i	1.83757	+	1.83757i
$254$			33.3921i			0.131465i
$255$		0			0
$256$	−49.3317			−0.192702
$257$	−78.9368	+	78.9368i	−0.307147	+	0.307147i	−0.843802	−	0.536655i	$-0.819688\pi$
$257$	−78.9368	+	78.9368i	−0.307147	+	0.307147i	0.536655	+	0.843802i	$0.319688\pi$
$258$	142.723	+	142.723i	0.553189	+	0.553189i
$259$		−	9.44543i		−	0.0364688i
$260$		0			0
$261$	−8.63446			−0.0330822
$262$	−31.7680	+	31.7680i	−0.121252	+	0.121252i
$263$	323.863	+	323.863i	1.23142	+	1.23142i	0.963418	+	0.268002i	$0.0863632\pi$
$263$	323.863	+	323.863i	1.23142	+	1.23142i	0.268002	+	0.963418i	$0.413637\pi$
$264$			251.277i			0.951806i
$265$		0			0
$266$	−93.6940			−0.352233
$267$	35.9272	−	35.9272i	0.134559	−	0.134559i
$268$	7.01911	+	7.01911i	0.0261907	+	0.0261907i
$269$		−	119.052i		−	0.442573i	−0.975209	−	0.221286i	$-0.928974\pi$
$269$		−	119.052i		−	0.442573i	0.975209	−	0.221286i	$-0.0710256\pi$
$270$		0			0
$271$	380.174			1.40286			0.701429	−	0.712740i	$-0.252546\pi$
$271$	380.174			1.40286			0.701429	+	0.712740i	$0.252546\pi$
$272$	−206.789	+	206.789i	−0.760253	+	0.760253i
$273$	55.5613	+	55.5613i	0.203521	+	0.203521i
$274$		−	47.2146i		−	0.172316i
$275$		0			0
$276$	−16.6833			−0.0604467
$277$	374.455	−	374.455i	1.35182	−	1.35182i	0.468198	−	0.883624i	$-0.344903\pi$
$277$	374.455	−	374.455i	1.35182	−	1.35182i	0.883624	−	0.468198i	$-0.155097\pi$
$278$	40.3237	+	40.3237i	0.145049	+	0.145049i
$279$			48.3448i			0.173279i
$280$		0			0
$281$	−300.844			−1.07062			−0.535309	−	0.844656i	$-0.679805\pi$
$281$	−300.844			−1.07062			−0.535309	+	0.844656i	$0.679805\pi$
$282$	193.477	−	193.477i	0.686090	−	0.686090i
$283$	137.166	+	137.166i	0.484686	+	0.484686i	0.906624	−	0.421938i	$-0.138650\pi$
$283$	137.166	+	137.166i	0.484686	+	0.484686i	−0.421938	+	0.906624i	$0.638650\pi$
$284$		−	20.5390i		−	0.0723204i
$285$		0			0
$286$	−584.198			−2.04265
$287$	3.55136	−	3.55136i	0.0123741	−	0.0123741i
$288$	−8.74395	−	8.74395i	−0.0303609	−	0.0303609i
$289$		−	96.1561i		−	0.332720i
$290$		0			0
$291$	218.304			0.750186
$292$	16.3348	−	16.3348i	0.0559411	−	0.0559411i
$293$	−193.498	−	193.498i	−0.660403	−	0.660403i	0.295072	−	0.955475i	$-0.404656\pi$
$293$	−193.498	−	193.498i	−0.660403	−	0.660403i	−0.955475	+	0.295072i	$0.904656\pi$
$294$		−	23.4536i		−	0.0797740i
$295$		0			0
$296$	−29.4057			−0.0993436
$297$	−64.7142	+	64.7142i	−0.217893	+	0.217893i
$298$	19.6761	+	19.6761i	0.0660270	+	0.0660270i
$299$		−	640.065i		−	2.14068i
$300$		0			0
$301$	−159.385			−0.529518
$302$	21.0057	−	21.0057i	0.0695554	−	0.0695554i
$303$	−106.958	−	106.958i	−0.352996	−	0.352996i
$304$			272.795i			0.897352i
$305$		0			0
$306$	−113.891			−0.372193
$307$	−122.528	+	122.528i	−0.399115	+	0.399115i	−0.877921	−	0.478806i	$-0.841070\pi$
$307$	−122.528	+	122.528i	−0.399115	+	0.399115i	0.478806	+	0.877921i	$0.341070\pi$
$308$	−8.50240	−	8.50240i	−0.0276052	−	0.0276052i
$309$		−	89.9984i		−	0.291257i
$310$		0			0
$311$	118.050			0.379582			0.189791	−	0.981825i	$-0.439219\pi$
$311$	118.050			0.379582			0.189791	+	0.981825i	$0.439219\pi$
$312$	172.975	−	172.975i	0.554406	−	0.554406i
$313$	289.482	+	289.482i	0.924861	+	0.924861i	0.997368	−	0.0725069i	$-0.0230999\pi$
$313$	289.482	+	289.482i	0.924861	+	0.924861i	−0.0725069	+	0.997368i	$0.523100\pi$
$314$			173.105i			0.551290i
$315$		0			0
$316$	0.641686			0.00203065
$317$	292.255	−	292.255i	0.921942	−	0.921942i	−0.0752250	−	0.997167i	$-0.523968\pi$
$317$	292.255	−	292.255i	0.921942	−	0.921942i	0.997167	+	0.0752250i	$0.0239675\pi$
$318$	−222.999	−	222.999i	−0.701254	−	0.701254i
$319$			50.6928i			0.158912i
$320$		0			0
$321$	225.318			0.701924
$322$	−135.092	+	135.092i	−0.419541	+	0.419541i
$323$	−254.048	−	254.048i	−0.786527	−	0.786527i
$324$		−	2.32229i		−	0.00716758i
$325$		0			0
$326$	331.712			1.01752
$327$	177.133	−	177.133i	0.541690	−	0.541690i
$328$	−11.0562	−	11.0562i	−0.0337079	−	0.0337079i
$329$			216.065i			0.656731i
$330$		0			0
$331$	580.718			1.75443			0.877217	−	0.480093i	$-0.159397\pi$
$331$	580.718			1.75443			0.877217	+	0.480093i	$0.159397\pi$
$332$	−7.49381	+	7.49381i	−0.0225717	+	0.0225717i
$333$	−7.57319	−	7.57319i	−0.0227423	−	0.0227423i
$334$		−	140.128i		−	0.419544i
$335$		0			0
$336$	−68.2863			−0.203233
$337$	−253.637	+	253.637i	−0.752631	+	0.752631i	−0.974970	−	0.222339i	$-0.928631\pi$
$337$	−253.637	+	253.637i	−0.752631	+	0.752631i	0.222339	+	0.974970i	$0.428631\pi$
$338$	170.987	+	170.987i	0.505880	+	0.505880i
$339$		−	70.2516i		−	0.207232i
$340$		0			0
$341$	283.832			0.832351
$342$	−75.1223	+	75.1223i	−0.219656	+	0.219656i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$			496.200i			1.44244i
$345$		0			0
$346$	−214.865			−0.620997
$347$	−60.2580	+	60.2580i	−0.173654	+	0.173654i	−0.788583	−	0.614929i	$-0.789185\pi$
$347$	−60.2580	+	60.2580i	−0.173654	+	0.173654i	0.614929	+	0.788583i	$0.289185\pi$
$348$	−0.909567	−	0.909567i	−0.00261370	−	0.00261370i
$349$		−	348.191i		−	0.997681i	−0.866694	−	0.498841i	$-0.833759\pi$
$349$		−	348.191i		−	0.997681i	0.866694	−	0.498841i	$-0.166241\pi$
$350$		0			0
$351$	89.0963			0.253836
$352$	−51.3356	+	51.3356i	−0.145840	+	0.145840i
$353$	−113.128	−	113.128i	−0.320476	−	0.320476i	0.528474	−	0.848950i	$-0.322765\pi$
$353$	−113.128	−	113.128i	−0.320476	−	0.320476i	−0.848950	+	0.528474i	$0.822765\pi$
$354$		−	55.1740i		−	0.155859i
$355$		0			0
$356$	7.56925			0.0212619
$357$	63.5935	−	63.5935i	0.178133	−	0.178133i
$358$	−222.103	−	222.103i	−0.620401	−	0.620401i
$359$		−	105.651i		−	0.294293i	−0.989115	−	0.147147i	$-0.952991\pi$
$359$		−	105.651i		−	0.294293i	0.989115	−	0.147147i	$-0.0470089\pi$
$360$		0			0
$361$	25.8608			0.0716365
$362$	351.841	−	351.841i	0.971937	−	0.971937i
$363$	231.742	+	231.742i	0.638408	+	0.638408i
$364$			11.7058i			0.0321588i
$365$		0			0
$366$	−24.6941			−0.0674702
$367$	230.168	−	230.168i	0.627161	−	0.627161i	−0.320191	−	0.947353i	$-0.603747\pi$
$367$	230.168	−	230.168i	0.627161	−	0.627161i	0.947353	+	0.320191i	$0.103747\pi$
$368$	393.328	+	393.328i	1.06883	+	1.06883i
$369$		−	5.69485i		−	0.0154332i
$370$		0			0
$371$	249.032			0.671246
$372$	−5.09271	+	5.09271i	−0.0136901	+	0.0136901i
$373$	211.456	+	211.456i	0.566906	+	0.566906i	0.931260	−	0.364355i	$-0.118710\pi$
$373$	211.456	+	211.456i	0.566906	+	0.566906i	−0.364355	+	0.931260i	$0.618710\pi$
$374$			668.653i			1.78784i
$375$		0			0
$376$	672.657			1.78898
$377$	34.8961	−	34.8961i	0.0925626	−	0.0925626i
$378$	−18.8047	−	18.8047i	−0.0497478	−	0.0497478i
$379$			132.280i			0.349024i	0.984655	+	0.174512i	$0.0558347\pi$
$379$			132.280i			0.349024i	−0.984655	+	0.174512i	$0.944165\pi$
$380$		0			0
$381$	−29.8989			−0.0784748
$382$	−456.997	+	456.997i	−1.19633	+	1.19633i
$383$	−149.538	−	149.538i	−0.390438	−	0.390438i	0.484406	−	0.874844i	$-0.339036\pi$
$383$	−149.538	−	149.538i	−0.390438	−	0.390438i	−0.874844	+	0.484406i	$0.839036\pi$
$384$			197.865i			0.515274i
$385$		0			0
$386$	−54.5991			−0.141448
$387$	−127.792	+	127.792i	−0.330212	+	0.330212i
$388$	22.9965	+	22.9965i	0.0592692	+	0.0592692i
$389$			289.081i			0.743140i	0.928405	+	0.371570i	$0.121180\pi$
$389$			289.081i			0.743140i	−0.928405	+	0.371570i	$0.878820\pi$
$390$		0			0
$391$	−732.596			−1.87365
$392$	40.7701	−	40.7701i	0.104005	−	0.104005i
$393$	−28.4446	−	28.4446i	−0.0723781	−	0.0723781i
$394$			99.9213i			0.253607i
$395$		0			0
$396$	−13.6342			−0.0344297
$397$	502.891	−	502.891i	1.26673	−	1.26673i	0.318961	−	0.947768i	$-0.396666\pi$
$397$	502.891	−	502.891i	1.26673	−	1.26673i	0.947768	−	0.318961i	$-0.103334\pi$
$398$	256.633	+	256.633i	0.644806	+	0.644806i
$399$		−	83.8923i		−	0.210256i
$400$		0			0
$401$	405.912			1.01225			0.506125	−	0.862460i	$-0.331078\pi$
$401$	405.912			1.01225			0.506125	+	0.862460i	$0.331078\pi$
$402$	91.1418	−	91.1418i	0.226721	−	0.226721i
$403$	−195.385	−	195.385i	−0.484826	−	0.484826i
$404$		−	22.5342i		−	0.0557776i
$405$		0			0
$406$	−14.7304			−0.0362817
$407$	−44.4621	+	44.4621i	−0.109244	+	0.109244i
$408$	−197.981	−	197.981i	−0.485247	−	0.485247i
$409$		−	505.400i		−	1.23570i	−0.786297	−	0.617849i	$-0.788004\pi$
$409$		−	505.400i		−	1.23570i	0.786297	−	0.617849i	$-0.211996\pi$
$410$		0			0
$411$	42.2753			0.102860
$412$	9.48056	−	9.48056i	0.0230111	−	0.0230111i
$413$	30.8076	+	30.8076i	0.0745946	+	0.0745946i
$414$			216.629i			0.523259i
$415$		0			0
$416$	70.6772			0.169897
$417$	−36.1053	+	36.1053i	−0.0865834	+	0.0865834i
$418$	441.042	+	441.042i	1.05512	+	1.05512i
$419$			553.591i			1.32122i	0.750729	+	0.660610i	$0.229702\pi$
$419$			553.591i			1.32122i	−0.750729	+	0.660610i	$0.770298\pi$
$420$		0			0
$421$	−320.444			−0.761150			−0.380575	−	0.924750i	$-0.624274\pi$
$421$	−320.444			−0.761150			−0.380575	+	0.924750i	$0.624274\pi$
$422$	−100.729	+	100.729i	−0.238694	+	0.238694i
$423$	173.237	+	173.237i	0.409544	+	0.409544i
$424$		−	775.293i		−	1.82852i
$425$		0			0
$426$	−266.695			−0.626045
$427$	13.7885	−	13.7885i	0.0322915	−	0.0322915i
$428$	23.7353	+	23.7353i	0.0554562	+	0.0554562i
$429$		−	523.083i		−	1.21931i
$430$		0			0
$431$	221.870			0.514780			0.257390	−	0.966308i	$-0.417138\pi$
$431$	221.870			0.514780			0.257390	+	0.966308i	$0.417138\pi$
$432$	−54.7508	+	54.7508i	−0.126738	+	0.126738i
$433$	162.133	+	162.133i	0.374440	+	0.374440i	0.869091	−	0.494651i	$-0.164704\pi$
$433$	162.133	+	162.133i	0.374440	+	0.374440i	−0.494651	+	0.869091i	$0.664704\pi$
$434$			82.4759i			0.190037i
$435$		0			0
$436$	37.3188			0.0855936
$437$	−483.219	+	483.219i	−1.10576	+	1.10576i
$438$	−212.104	−	212.104i	−0.484256	−	0.484256i
$439$			606.504i			1.38156i	0.723066	+	0.690779i	$0.242732\pi$
$439$			606.504i			1.38156i	−0.723066	+	0.690779i	$0.757268\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	460.289	−	460.289i	1.04138	−	1.04138i
$443$	9.75385	+	9.75385i	0.0220177	+	0.0220177i	0.718030	−	0.696012i	$-0.245044\pi$
$443$	9.75385	+	9.75385i	0.0220177	+	0.0220177i	−0.696012	+	0.718030i	$0.745044\pi$
$444$		−	1.59554i		−	0.00359356i
$445$		0			0
$446$	−706.410			−1.58388
$447$	−17.6177	+	17.6177i	−0.0394131	+	0.0394131i
$448$	−126.428	−	126.428i	−0.282206	−	0.282206i
$449$			448.959i			0.999908i	0.866052	+	0.499954i	$0.166650\pi$
$449$			448.959i			0.999908i	−0.866052	+	0.499954i	$0.833350\pi$
$450$		0			0
$451$	−33.4344			−0.0741340
$452$	7.40041	−	7.40041i	0.0163726	−	0.0163726i
$453$	18.8083	+	18.8083i	0.0415193	+	0.0415193i
$454$		−	26.6161i		−	0.0586257i
$455$		0			0
$456$	−261.175			−0.572753
$457$	−368.860	+	368.860i	−0.807133	+	0.807133i	−0.984199	−	0.177066i	$-0.943339\pi$
$457$	−368.860	+	368.860i	−0.807133	+	0.807133i	0.177066	+	0.984199i	$0.443339\pi$
$458$	147.791	+	147.791i	0.322688	+	0.322688i
$459$		−	101.977i		−	0.222171i
$460$		0			0
$461$	−507.955			−1.10186			−0.550928	−	0.834553i	$-0.685726\pi$
$461$	−507.955			−1.10186			−0.550928	+	0.834553i	$0.685726\pi$
$462$	−110.402	+	110.402i	−0.238966	+	0.238966i
$463$	−255.428	−	255.428i	−0.551681	−	0.551681i	0.375245	−	0.926926i	$-0.377559\pi$
$463$	−255.428	−	255.428i	−0.551681	−	0.551681i	−0.926926	+	0.375245i	$0.877559\pi$
$464$			42.8882i			0.0924315i
$465$		0			0
$466$	6.76597			0.0145192
$467$	−408.350	+	408.350i	−0.874411	+	0.874411i	−0.992950	−	0.118538i	$-0.962179\pi$
$467$	−408.350	+	408.350i	−0.874411	+	0.874411i	0.118538	+	0.992950i	$0.462179\pi$
$468$	9.38553	+	9.38553i	0.0200545	+	0.0200545i
$469$			101.782i			0.217019i
$470$		0			0
$471$	−154.996			−0.329079
$472$	95.9108	−	95.9108i	0.203201	−	0.203201i
$473$	750.267	+	750.267i	1.58619	+	1.58619i
$474$		−	8.33218i		−	0.0175784i
$475$		0			0
$476$	13.3981			0.0281472
$477$	199.670	−	199.670i	0.418595	−	0.418595i
$478$	−315.935	−	315.935i	−0.660952	−	0.660952i
$479$			664.740i			1.38777i	0.720087	+	0.693883i	$0.244102\pi$
$479$			664.740i			1.38777i	−0.720087	+	0.693883i	$0.755898\pi$
$480$		0			0
$481$	61.2140			0.127264
$482$	−383.548	+	383.548i	−0.795743	+	0.795743i
$483$	−120.960	−	120.960i	−0.250434	−	0.250434i
$484$			48.8241i			0.100876i
$485$		0			0
$486$	−30.1546			−0.0620464
$487$	334.715	−	334.715i	0.687300	−	0.687300i	−0.274334	−	0.961634i	$-0.588457\pi$
$487$	334.715	−	334.715i	0.687300	−	0.687300i	0.961634	+	0.274334i	$0.0884575\pi$
$488$	−42.9266	−	42.9266i	−0.0879643	−	0.0879643i
$489$			297.010i			0.607383i
$490$		0			0
$491$	−312.255			−0.635958			−0.317979	−	0.948098i	$-0.603004\pi$
$491$	−312.255			−0.635958			−0.317979	+	0.948098i	$0.603004\pi$
$492$	0.599904	−	0.599904i	0.00121932	−	0.00121932i
$493$	−39.9409	−	39.9409i	−0.0810160	−	0.0810160i
$494$		−	607.212i		−	1.22917i
$495$		0			0
$496$	240.133			0.484139
$497$	148.915	−	148.915i	0.299628	−	0.299628i
$498$	97.3057	+	97.3057i	0.195393	+	0.195393i
$499$		−	89.3669i		−	0.179092i	−0.995983	−	0.0895460i	$-0.971458\pi$
$499$		−	89.3669i		−	0.179092i	0.995983	−	0.0895460i	$-0.0285416\pi$
$500$		0			0
$501$	125.469			0.250436
$502$	73.1434	−	73.1434i	0.145704	−	0.145704i
$503$	−627.521	−	627.521i	−1.24756	−	1.24756i	−0.956796	−	0.290761i	$-0.906092\pi$
$503$	−627.521	−	627.521i	−1.24756	−	1.24756i	−0.290761	−	0.956796i	$-0.593908\pi$
$504$		−	65.3776i		−	0.129718i
$505$		0			0
$506$	1271.83			2.51350
$507$	−153.100	+	153.100i	−0.301972	+	0.301972i
$508$	−3.14959	−	3.14959i	−0.00619998	−	0.00619998i
$509$			556.945i			1.09420i	0.837069	+	0.547098i	$0.184267\pi$
$509$			556.945i			1.09420i	−0.837069	+	0.547098i	$0.815733\pi$
$510$		0			0
$511$	236.866			0.463534
$512$	−390.591	+	390.591i	−0.762872	+	0.762872i
$513$	−67.2635	−	67.2635i	−0.131118	−	0.131118i
$514$			215.946i			0.420128i
$515$		0			0
$516$	−26.9236			−0.0521776
$517$	1017.07	−	1017.07i	1.96726	−	1.96726i
$518$	−12.9198	−	12.9198i	−0.0249418	−	0.0249418i
$519$		−	192.387i		−	0.370688i
$520$		0			0
$521$	−64.5705			−0.123936			−0.0619679	−	0.998078i	$-0.519738\pi$
$521$	−64.5705			−0.123936			−0.0619679	+	0.998078i	$0.519738\pi$
$522$	−11.8106	+	11.8106i	−0.0226256	+	0.0226256i
$523$	431.531	+	431.531i	0.825107	+	0.825107i	0.986835	−	0.161728i	$-0.0517068\pi$
$523$	431.531	+	431.531i	0.825107	+	0.825107i	−0.161728	+	0.986835i	$0.551707\pi$
$524$		−	5.99279i		−	0.0114366i
$525$		0			0
$526$	885.986			1.68438
$527$	−223.631	+	223.631i	−0.424347	+	0.424347i
$528$	321.442	+	321.442i	0.608791	+	0.608791i
$529$			864.452i			1.63413i
$530$		0			0
$531$	49.4020			0.0930358
$532$	8.83734	−	8.83734i	0.0166115	−	0.0166115i
$533$	23.0157	+	23.0157i	0.0431814	+	0.0431814i
$534$		−	98.2854i		−	0.184055i
$535$		0			0
$536$	316.870			0.591175
$537$	198.868	−	198.868i	0.370332	−	0.370332i
$538$	−162.844	−	162.844i	−0.302684	−	0.302684i
$539$		−	123.291i		−	0.228740i
$540$		0			0
$541$	−571.616			−1.05659			−0.528295	−	0.849061i	$-0.677169\pi$
$541$	−571.616			−1.05659			−0.528295	+	0.849061i	$0.677169\pi$
$542$	520.017	−	520.017i	0.959441	−	0.959441i
$543$	315.034	+	315.034i	0.580173	+	0.580173i
$544$		−	80.8946i		−	0.148703i
$545$		0			0
$546$	151.998			0.278384
$547$	−259.835	+	259.835i	−0.475017	+	0.475017i	−0.903534	−	0.428516i	$-0.859036\pi$
$547$	−259.835	+	259.835i	−0.475017	+	0.475017i	0.428516	+	0.903534i	$0.359036\pi$
$548$	4.45334	+	4.45334i	0.00812653	+	0.00812653i
$549$		−	22.1108i		−	0.0402746i
$550$		0			0
$551$	−52.6898			−0.0956258
$552$	−376.574	+	376.574i	−0.682200	+	0.682200i
$553$	4.65245	+	4.65245i	0.00841311	+	0.00841311i
$554$		−	1024.39i		−	1.84907i
$555$		0			0
$556$	−7.60677			−0.0136812
$557$	−503.660	+	503.660i	−0.904237	+	0.904237i	−0.995799	−	0.0915625i	$-0.970814\pi$
$557$	−503.660	+	503.660i	−0.904237	+	0.904237i	0.0915625	+	0.995799i	$0.470814\pi$
$558$	66.1278	+	66.1278i	0.118509	+	0.118509i
$559$		−	1032.94i		−	1.84784i
$560$		0			0
$561$	−598.703			−1.06721
$562$	−411.506	+	411.506i	−0.732216	+	0.732216i
$563$	405.076	+	405.076i	0.719495	+	0.719495i	0.968502	−	0.249007i	$-0.0801042\pi$
$563$	405.076	+	405.076i	0.719495	+	0.719495i	−0.249007	+	0.968502i	$0.580104\pi$
$564$			36.4981i			0.0647129i
$565$		0			0
$566$	375.242			0.662972
$567$	16.8375	−	16.8375i	0.0296957	−	0.0296957i
$568$	−463.605	−	463.605i	−0.816207	−	0.816207i
$569$		−	674.447i		−	1.18532i	−0.805453	−	0.592660i	$-0.798078\pi$
$569$		−	674.447i		−	1.18532i	0.805453	−	0.592660i	$-0.201922\pi$
$570$		0			0
$571$	825.137			1.44507			0.722537	−	0.691333i	$-0.242976\pi$
$571$	825.137			1.44507			0.722537	+	0.691333i	$0.242976\pi$
$572$	55.1023	−	55.1023i	0.0963328	−	0.0963328i
$573$	−409.189	−	409.189i	−0.714116	−	0.714116i
$574$		−	9.71539i		−	0.0169258i
$575$		0			0
$576$	−202.736			−0.351972
$577$	−532.596	+	532.596i	−0.923043	+	0.923043i	−0.997243	−	0.0742001i	$-0.976360\pi$
$577$	−532.596	+	532.596i	−0.923043	+	0.923043i	0.0742001	+	0.997243i	$0.476360\pi$
$578$	−131.526	−	131.526i	−0.227554	−	0.227554i
$579$		−	48.8873i		−	0.0844340i
$580$		0			0
$581$	−108.666			−0.187032
$582$	298.605	−	298.605i	0.513067	−	0.513067i
$583$	−1172.26	−	1172.26i	−2.01074	−	2.01074i
$584$		−	737.416i		−	1.26270i
$585$		0			0
$586$	−529.349			−0.903325
$587$	−800.352	+	800.352i	−1.36346	+	1.36346i	−0.493999	+	0.869463i	$0.664465\pi$
$587$	−800.352	+	800.352i	−1.36346	+	1.36346i	−0.869463	+	0.493999i	$0.835535\pi$
$588$	2.21217	+	2.21217i	0.00376219	+	0.00376219i
$589$			295.013i			0.500871i
$590$		0			0
$591$	−89.4682			−0.151384
$592$	−37.6168	+	37.6168i	−0.0635419	+	0.0635419i
$593$	−254.908	−	254.908i	−0.429862	−	0.429862i	0.458719	−	0.888581i	$-0.348308\pi$
$593$	−254.908	−	254.908i	−0.429862	−	0.429862i	−0.888581	+	0.458719i	$0.848308\pi$
$594$			177.037i			0.298042i
$595$		0			0
$596$	−3.71174			−0.00622775
$597$	−229.786	+	229.786i	−0.384900	+	0.384900i
$598$	−875.505	−	875.505i	−1.46406	−	1.46406i
$599$			661.029i			1.10355i	0.833991	+	0.551777i	$0.186050\pi$
$599$			661.029i			1.10355i	−0.833991	+	0.551777i	$0.813950\pi$
$600$		0			0
$601$	−410.580			−0.683162			−0.341581	−	0.939852i	$-0.610962\pi$
$601$	−410.580			−0.683162			−0.341581	+	0.939852i	$0.610962\pi$
$602$	−218.013	+	218.013i	−0.362148	+	0.362148i
$603$	81.6072	+	81.6072i	0.135335	+	0.135335i
$604$			3.96258i			0.00656056i
$605$		0			0
$606$	−292.602			−0.482842
$607$	604.297	−	604.297i	0.995548	−	0.995548i	−0.00444263	−	0.999990i	$-0.501414\pi$
$607$	604.297	−	604.297i	0.995548	−	0.995548i	0.999990	+	0.00444263i	$0.00141414\pi$
$608$	−53.3579	−	53.3579i	−0.0877598	−	0.0877598i
$609$		−	13.1894i		−	0.0216574i
$610$		0			0
$611$	−1400.27			−2.29177
$612$	10.7424	−	10.7424i	0.0175529	−	0.0175529i
$613$	61.4626	+	61.4626i	0.100265	+	0.100265i	0.755460	−	0.655195i	$-0.227413\pi$
$613$	61.4626	+	61.4626i	0.100265	+	0.100265i	−0.655195	+	0.755460i	$0.727413\pi$
$614$			335.198i			0.545926i
$615$		0			0
$616$	−383.831			−0.623103
$617$	509.151	−	509.151i	0.825204	−	0.825204i	−0.161645	−	0.986849i	$-0.551680\pi$
$617$	509.151	−	509.151i	0.825204	−	0.825204i	0.986849	+	0.161645i	$0.0516800\pi$
$618$	−123.103	−	123.103i	−0.199196	−	0.199196i
$619$		−	735.555i		−	1.18830i	−0.804356	−	0.594148i	$-0.797489\pi$
$619$		−	735.555i		−	1.18830i	0.804356	−	0.594148i	$-0.202511\pi$
$620$		0			0
$621$	−193.967			−0.312346
$622$	161.473	−	161.473i	0.259603	−	0.259603i
$623$	54.8798	+	54.8798i	0.0880895	+	0.0880895i
$624$		−	442.550i		−	0.709214i
$625$		0			0
$626$	791.928			1.26506
$627$	−394.903	+	394.903i	−0.629830	+	0.629830i
$628$	−16.3275	−	16.3275i	−0.0259992	−	0.0259992i
$629$		−	70.0634i		−	0.111389i
$630$		0			0
$631$	649.002			1.02853			0.514265	−	0.857631i	$-0.328065\pi$
$631$	649.002			1.02853			0.514265	+	0.857631i	$0.328065\pi$
$632$	14.4841	−	14.4841i	0.0229179	−	0.0229179i
$633$	−90.1914	−	90.1914i	−0.142482	−	0.142482i
$634$		−	799.517i		−	1.26107i
$635$		0			0
$636$	42.0671			0.0661432
$637$	−84.8713	+	84.8713i	−0.133236	+	0.133236i
$638$	69.3396	+	69.3396i	0.108683	+	0.108683i
$639$		−	238.795i		−	0.373702i
$640$		0			0
$641$	−103.576			−0.161585			−0.0807925	−	0.996731i	$-0.525745\pi$
$641$	−103.576			−0.161585			−0.0807925	+	0.996731i	$0.525745\pi$
$642$	308.198	−	308.198i	0.480059	−	0.480059i
$643$	−504.926	−	504.926i	−0.785266	−	0.785266i	0.195448	−	0.980714i	$-0.437384\pi$
$643$	−504.926	−	504.926i	−0.785266	−	0.785266i	−0.980714	+	0.195448i	$0.937384\pi$
$644$		−	25.4841i		−	0.0395716i
$645$		0			0
$646$	−694.994			−1.07584
$647$	−134.888	+	134.888i	−0.208482	+	0.208482i	−0.803622	−	0.595140i	$-0.797097\pi$
$647$	−134.888	+	134.888i	−0.208482	+	0.208482i	0.595140	+	0.803622i	$0.297097\pi$
$648$	−52.4187	−	52.4187i	−0.0808931	−	0.0808931i
$649$		−	290.039i		−	0.446901i
$650$		0			0
$651$	−73.8478			−0.113438
$652$	−31.2875	+	31.2875i	−0.0479870	+	0.0479870i
$653$	123.054	+	123.054i	0.188444	+	0.188444i	0.795023	−	0.606579i	$-0.207459\pi$
$653$	123.054	+	123.054i	0.188444	+	0.188444i	−0.606579	+	0.795023i	$0.707459\pi$
$654$		−	484.578i		−	0.740944i
$655$		0			0
$656$	−28.2869			−0.0431202
$657$	189.915	−	189.915i	0.289064	−	0.289064i
$658$	295.542	+	295.542i	0.449151	+	0.449151i
$659$		−	811.814i		−	1.23189i	−0.787790	−	0.615944i	$-0.788775\pi$
$659$		−	811.814i		−	1.23189i	0.787790	−	0.615944i	$-0.211225\pi$
$660$		0			0
$661$	979.510			1.48186			0.740930	−	0.671582i	$-0.234385\pi$
$661$	979.510			1.48186			0.740930	+	0.671582i	$0.234385\pi$
$662$	794.329	−	794.329i	1.19989	−	1.19989i
$663$	412.137	+	412.137i	0.621625	+	0.621625i
$664$			338.300i			0.509488i
$665$		0			0
$666$	−20.7178			−0.0311078
$667$	−75.9705	+	75.9705i	−0.113899	+	0.113899i
$668$	13.2170	+	13.2170i	0.0197860	+	0.0197860i
$669$		−	632.510i		−	0.945456i
$670$		0			0
$671$	−129.812			−0.193461
$672$	13.3566	−	13.3566i	0.0198759	−	0.0198759i
$673$	327.449	+	327.449i	0.486552	+	0.486552i	0.907216	−	0.420664i	$-0.138203\pi$
$673$	327.449	+	327.449i	0.486552	+	0.486552i	−0.420664	+	0.907216i	$0.638203\pi$
$674$			693.868i			1.02948i
$675$		0			0
$676$	−32.2555			−0.0477152
$677$	−463.677	+	463.677i	−0.684900	+	0.684900i	−0.961100	−	0.276200i	$-0.910925\pi$
$677$	−463.677	+	463.677i	−0.684900	+	0.684900i	0.276200	+	0.961100i	$0.410925\pi$
$678$	−96.0929	−	96.0929i	−0.141730	−	0.141730i
$679$			333.465i			0.491112i
$680$		0			0
$681$	23.8317			0.0349951
$682$	388.236	−	388.236i	0.569261	−	0.569261i
$683$	−667.534	−	667.534i	−0.977356	−	0.977356i	0.0223933	−	0.999749i	$-0.492871\pi$
$683$	−667.534	−	667.534i	−0.977356	−	0.977356i	−0.999749	+	0.0223933i	$0.992871\pi$
$684$		−	14.1713i		−	0.0207182i
$685$		0			0
$686$	35.8259			0.0522243
$687$	−132.330	+	132.330i	−0.192621	+	0.192621i
$688$	634.756	+	634.756i	0.922610	+	0.922610i
$689$			1613.93i			2.34242i
$690$		0			0
$691$	−622.518			−0.900895			−0.450447	−	0.892803i	$-0.648736\pi$
$691$	−622.518			−0.900895			−0.450447	+	0.892803i	$0.648736\pi$
$692$	20.2663	−	20.2663i	0.0292866	−	0.0292866i
$693$	−98.8525	−	98.8525i	−0.142644	−	0.142644i
$694$			164.846i			0.237531i
$695$		0			0
$696$	−41.0614			−0.0589963
$697$	26.3430	−	26.3430i	0.0377948	−	0.0377948i
$698$	−476.269	−	476.269i	−0.682334	−	0.682334i
$699$			6.05816i			0.00866689i
$700$		0			0
$701$	−821.585			−1.17202			−0.586009	−	0.810304i	$-0.699302\pi$
$701$	−821.585			−1.17202			−0.586009	+	0.810304i	$0.699302\pi$
$702$	121.869	−	121.869i	0.173603	−	0.173603i
$703$	−46.2137	−	46.2137i	−0.0657378	−	0.0657378i
$704$			1190.26i			1.69071i
$705$		0			0
$706$	−309.482			−0.438359
$707$	163.381	−	163.381i	0.231090	−	0.231090i
$708$	5.20408	+	5.20408i	0.00735039	+	0.00735039i
$709$		−	1124.01i		−	1.58535i	−0.609647	−	0.792673i	$-0.708689\pi$
$709$		−	1124.01i		−	1.58535i	0.609647	−	0.792673i	$-0.291311\pi$
$710$		0			0
$711$	7.46052			0.0104930
$712$	170.853	−	170.853i	0.239962	−	0.239962i
$713$	425.363	+	425.363i	0.596581	+	0.596581i
$714$		−	173.971i		−	0.243658i
$715$		0			0
$716$	41.8982			0.0585170
$717$	282.884	−	282.884i	0.394538	−	0.394538i
$718$	−144.514	−	144.514i	−0.201273	−	0.201273i
$719$		−	826.757i		−	1.14987i	−0.818199	−	0.574936i	$-0.805027\pi$
$719$		−	826.757i		−	1.14987i	0.818199	−	0.574936i	$-0.194973\pi$
$720$		0			0
$721$	137.475			0.190672
$722$	35.3734	−	35.3734i	0.0489936	−	0.0489936i
$723$	−343.424	−	343.424i	−0.474998	−	0.474998i
$724$			66.3722i			0.0916744i
$725$		0			0
$726$	633.972			0.873239
$727$	−829.278	+	829.278i	−1.14069	+	1.14069i	−0.152360	+	0.988325i	$0.548687\pi$
$727$	−829.278	+	829.278i	−1.14069	+	1.14069i	−0.988325	+	0.152360i	$0.951313\pi$
$728$	264.223	+	264.223i	0.362944	+	0.362944i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−1182.27			−1.61733
$732$	2.32918	−	2.32918i	0.00318194	−	0.00318194i
$733$	306.100	+	306.100i	0.417599	+	0.417599i	0.884375	−	0.466776i	$-0.154585\pi$
$733$	306.100	+	306.100i	0.417599	+	0.417599i	−0.466776	+	0.884375i	$0.654585\pi$
$734$		−	629.666i		−	0.857856i
$735$		0			0
$736$	−153.868			−0.209059
$737$	479.115	−	479.115i	0.650088	−	0.650088i
$738$	−7.78964	−	7.78964i	−0.0105551	−	0.0105551i
$739$		−	1152.24i		−	1.55919i	−0.626283	−	0.779596i	$-0.715425\pi$
$739$		−	1152.24i		−	1.55919i	0.626283	−	0.779596i	$-0.284575\pi$
$740$		0			0
$741$	543.689			0.733724
$742$	340.636	−	340.636i	0.459078	−	0.459078i
$743$	87.8428	+	87.8428i	0.118227	+	0.118227i	0.763745	−	0.645518i	$-0.223358\pi$
$743$	87.8428	+	87.8428i	0.118227	+	0.118227i	−0.645518	+	0.763745i	$0.723358\pi$
$744$			229.905i			0.309012i
$745$		0			0
$746$	578.475			0.775436
$747$	−87.1263	+	87.1263i	−0.116635	+	0.116635i
$748$	−63.0682	−	63.0682i	−0.0843158	−	0.0843158i
$749$			344.178i			0.459517i
$750$		0			0
$751$	−601.083			−0.800377			−0.400189	−	0.916433i	$-0.631055\pi$
$751$	−601.083			−0.800377			−0.400189	+	0.916433i	$0.631055\pi$
$752$	860.485	−	860.485i	1.14426	−	1.14426i
$753$	65.4916	+	65.4916i	0.0869743	+	0.0869743i
$754$		−	95.4645i		−	0.126611i
$755$		0			0
$756$	3.54736			0.00469228
$757$	−650.454	+	650.454i	−0.859252	+	0.859252i	−0.991250	−	0.131998i	$-0.957861\pi$
$757$	−650.454	+	650.454i	−0.859252	+	0.859252i	0.131998	+	0.991250i	$0.457861\pi$
$758$	180.938	+	180.938i	0.238704	+	0.238704i
$759$			1138.78i			1.50037i
$760$		0			0
$761$	344.833			0.453131			0.226566	−	0.973996i	$-0.427250\pi$
$761$	344.833			0.453131			0.226566	+	0.973996i	$0.427250\pi$
$762$	−40.8969	+	40.8969i	−0.0536704	+	0.0536704i
$763$	270.574	+	270.574i	0.354619	+	0.354619i
$764$		−	86.2090i		−	0.112839i
$765$		0			0
$766$	−409.087			−0.534056
$767$	−199.658	+	199.658i	−0.260310	+	0.260310i
$768$	−60.4187	−	60.4187i	−0.0786702	−	0.0786702i
$769$		−	953.105i		−	1.23941i	−0.784836	−	0.619704i	$-0.787253\pi$
$769$		−	953.105i		−	1.23941i	0.784836	−	0.619704i	$-0.212747\pi$
$770$		0			0
$771$	−193.355			−0.250785
$772$	5.14986	−	5.14986i	0.00667080	−	0.00667080i
$773$	716.434	+	716.434i	0.926823	+	0.926823i	0.997499	−	0.0706765i	$-0.0225158\pi$
$773$	716.434	+	716.434i	0.926823	+	0.926823i	−0.0706765	+	0.997499i	$0.522516\pi$
$774$			349.598i			0.451677i
$775$		0			0
$776$	1038.15			1.33782
$777$	11.5682	−	11.5682i	0.0148883	−	0.0148883i
$778$	395.417	+	395.417i	0.508248	+	0.508248i
$779$		−	34.7515i		−	0.0446104i
$780$		0			0
$781$	−1401.96			−1.79509
$782$	−1002.07	+	1002.07i	−1.28142	+	1.28142i
$783$	−10.5750	−	10.5750i	−0.0135058	−	0.0135058i
$784$		−	104.309i		−	0.133047i
$785$		0			0
$786$	−77.8153			−0.0990017
$787$	−475.797	+	475.797i	−0.604570	+	0.604570i	−0.941522	−	0.336952i	$-0.890604\pi$
$787$	−475.797	+	475.797i	−0.604570	+	0.604570i	0.336952	+	0.941522i	$0.390604\pi$
$788$	−9.42471	−	9.42471i	−0.0119603	−	0.0119603i
$789$			793.300i			1.00545i
$790$		0			0
$791$	107.311			0.135665
$792$	−307.750	+	307.750i	−0.388573	+	0.388573i
$793$	89.3604	+	89.3604i	0.112687	+	0.112687i
$794$		−	1375.75i		−	1.73268i
$795$		0			0
$796$	−48.4119			−0.0608189
$797$	523.540	−	523.540i	0.656889	−	0.656889i	−0.297754	−	0.954643i	$-0.596238\pi$
$797$	523.540	−	523.540i	0.656889	−	0.656889i	0.954643	+	0.297754i	$0.0962375\pi$
$798$	−114.751	−	114.751i	−0.143799	−	0.143799i
$799$			1602.70i			2.00589i
$800$		0			0
$801$	88.0034			0.109867
$802$	555.222	−	555.222i	0.692297	−	0.692297i
$803$	−1114.99	−	1114.99i	−1.38853	−	1.38853i
$804$			17.1932i			0.0213846i
$805$		0			0
$806$	−534.510			−0.663164
$807$	145.808	−	145.808i	0.180680	−	0.180680i
$808$	−508.640	−	508.640i	−0.629505	−	0.629505i
$809$			801.958i			0.991295i	0.868524	+	0.495648i	$0.165069\pi$
$809$			801.958i			0.991295i	−0.868524	+	0.495648i	$0.834931\pi$
$810$		0			0
$811$	56.4562			0.0696130			0.0348065	−	0.999394i	$-0.488919\pi$
$811$	56.4562			0.0696130			0.0348065	+	0.999394i	$0.488919\pi$
$812$	1.38939	−	1.38939i	0.00171107	−	0.00171107i
$813$	465.616	+	465.616i	0.572714	+	0.572714i
$814$			121.634i			0.149428i
$815$		0			0
$816$	−506.527			−0.620744
$817$	−779.822	+	779.822i	−0.954495	+	0.954495i
$818$	−691.306	−	691.306i	−0.845118	−	0.845118i
$819$			136.097i			0.166174i
$820$		0			0
$821$	983.386			1.19779			0.598896	−	0.800827i	$-0.295606\pi$
$821$	983.386			1.19779			0.598896	+	0.800827i	$0.295606\pi$
$822$	57.8258	−	57.8258i	0.0703477	−	0.0703477i
$823$	−8.06828	−	8.06828i	−0.00980350	−	0.00980350i	0.702188	−	0.711992i	$-0.252207\pi$
$823$	−8.06828	−	8.06828i	−0.00980350	−	0.00980350i	−0.711992	+	0.702188i	$0.752207\pi$
$824$		−	427.989i		−	0.519405i
$825$		0			0
$826$	84.2796			0.102033
$827$	−917.498	+	917.498i	−1.10943	+	1.10943i	−0.116204	+	0.993225i	$0.537073\pi$
$827$	−917.498	+	917.498i	−1.10943	+	1.10943i	−0.993225	+	0.116204i	$0.962927\pi$
$828$	−20.4328	−	20.4328i	−0.0246773	−	0.0246773i
$829$			589.450i			0.711037i	0.934669	+	0.355518i	$0.115696\pi$
$829$			589.450i			0.711037i	−0.934669	+	0.355518i	$0.884304\pi$
$830$		0			0
$831$	917.223			1.10376
$832$	819.356	−	819.356i	0.984803	−	0.984803i
$833$	97.1407	+	97.1407i	0.116616	+	0.116616i
$834$			98.7725i			0.118432i
$835$		0			0
$836$	−83.1994			−0.0995208
$837$	−59.2100	+	59.2100i	−0.0707407	+	0.0707407i
$838$	757.224	+	757.224i	0.903609	+	0.903609i
$839$		−	230.274i		−	0.274463i	−0.990539	−	0.137231i	$-0.956180\pi$
$839$		−	230.274i		−	0.274463i	0.990539	−	0.137231i	$-0.0438204\pi$
$840$		0			0
$841$	832.716			0.990150
$842$	−438.316	+	438.316i	−0.520566	+	0.520566i
$843$	−368.457	−	368.457i	−0.437078	−	0.437078i
$844$		−	19.0018i		−	0.0225140i
$845$		0			0
$846$	473.921			0.560190
$847$	−353.992	+	353.992i	−0.417936	+	0.417936i
$848$	−991.780	−	991.780i	−1.16955	−	1.16955i
$849$			335.987i			0.395744i
$850$		0			0
$851$	−133.266			−0.156599
$852$	25.1550	−	25.1550i	0.0295247	−	0.0295247i
$853$	843.744	+	843.744i	0.989148	+	0.989148i	0.999942	−	0.0107933i	$-0.00343569\pi$
$853$	843.744	+	843.744i	0.989148	+	0.989148i	−0.0107933	+	0.999942i	$0.503436\pi$
$854$		−	37.7209i		−	0.0441696i
$855$		0			0
$856$	1071.50			1.25176
$857$	−437.772	+	437.772i	−0.510819	+	0.510819i	−0.914777	−	0.403959i	$-0.867634\pi$
$857$	−437.772	+	437.772i	−0.510819	+	0.510819i	0.403959	+	0.914777i	$0.367634\pi$
$858$	−715.494	−	715.494i	−0.833909	−	0.833909i
$859$			1402.95i			1.63324i	0.577175	+	0.816621i	$0.304155\pi$
$859$			1402.95i			1.63324i	−0.577175	+	0.816621i	$0.695845\pi$
$860$		0			0
$861$	8.69903			0.0101034
$862$	303.482	−	303.482i	0.352068	−	0.352068i
$863$	−1049.60	−	1049.60i	−1.21622	−	1.21622i	−0.968944	−	0.247281i	$-0.920463\pi$
$863$	−1049.60	−	1049.60i	−1.21622	−	1.21622i	−0.247281	−	0.968944i	$-0.579537\pi$
$864$		−	21.4182i		−	0.0247896i
$865$		0			0
$866$	443.543			0.512174
$867$	117.767	−	117.767i	0.135832	−	0.135832i
$868$	−7.77924	−	7.77924i	−0.00896225	−	0.00896225i
$869$		−	43.8006i		−	0.0504035i
$870$		0			0
$871$	−659.629			−0.757324
$872$	842.358	−	842.358i	0.966007	−	0.966007i
$873$	267.367	+	267.367i	0.306262	+	0.306262i
$874$			1321.93i			1.51251i
$875$		0			0
$876$	40.0119			0.0456757
$877$	236.787	−	236.787i	0.269996	−	0.269996i	−0.559102	−	0.829099i	$-0.688854\pi$
$877$	236.787	−	236.787i	0.269996	−	0.269996i	0.829099	+	0.559102i	$0.188854\pi$
$878$	829.599	+	829.599i	0.944874	+	0.944874i
$879$		−	473.972i		−	0.539217i
$880$		0			0
$881$	311.627			0.353720			0.176860	−	0.984236i	$-0.443406\pi$
$881$	311.627			0.353720			0.176860	+	0.984236i	$0.443406\pi$
$882$	28.7246	−	28.7246i	0.0325676	−	0.0325676i
$883$	54.4472	+	54.4472i	0.0616616	+	0.0616616i	0.737265	−	0.675604i	$-0.236117\pi$
$883$	54.4472	+	54.4472i	0.0616616	+	0.0616616i	−0.675604	+	0.737265i	$0.736117\pi$
$884$			86.8302i			0.0982242i
$885$		0			0
$886$	26.6834			0.0301167
$887$	485.748	−	485.748i	0.547631	−	0.547631i	−0.378124	−	0.925755i	$-0.623431\pi$
$887$	485.748	−	485.748i	0.547631	−	0.547631i	0.925755	+	0.378124i	$0.123431\pi$
$888$	−36.0145	−	36.0145i	−0.0405569	−	0.0405569i
$889$		−	45.6713i		−	0.0513738i
$890$		0			0
$891$	−158.517			−0.177909
$892$	66.6295	−	66.6295i	0.0746968	−	0.0746968i
$893$	1057.14	+	1057.14i	1.18381	+	1.18381i
$894$			48.1963i			0.0539108i
$895$		0			0
$896$	−302.244			−0.337326
$897$	783.916	−	783.916i	0.873931	−	0.873931i
$898$	614.103	+	614.103i	0.683856	+	0.683856i
$899$			46.3812i			0.0515920i
$900$		0			0
$901$	1847.25			2.05022
$902$	−45.7329	+	45.7329i	−0.0507017	+	0.0507017i
$903$	−195.206	−	195.206i	−0.216175	−	0.216175i
$904$		−	334.083i		−	0.369561i
$905$		0			0
$906$	51.4533			0.0567918
$907$	−355.846	+	355.846i	−0.392334	+	0.392334i	−0.875518	−	0.483185i	$-0.839480\pi$
$907$	−355.846	+	355.846i	−0.392334	+	0.392334i	0.483185	+	0.875518i	$0.339480\pi$
$908$	2.51046	+	2.51046i	0.00276482	+	0.00276482i
$909$		−	261.992i		−	0.288220i
$910$		0			0
$911$	440.542			0.483581			0.241790	−	0.970329i	$-0.422265\pi$
$911$	440.542			0.483581			0.241790	+	0.970329i	$0.422265\pi$
$912$	−334.104	+	334.104i	−0.366342	+	0.366342i
$913$	511.517	+	511.517i	0.560260	+	0.560260i
$914$			1009.08i			1.10403i
$915$		0			0
$916$	−27.8797			−0.0304364
$917$	43.4499	−	43.4499i	0.0473826	−	0.0473826i
$918$	−139.487	−	139.487i	−0.151947	−	0.151947i
$919$			576.067i			0.626841i	0.949614	+	0.313420i	$0.101475\pi$
$919$			576.067i			0.626841i	−0.949614	+	0.313420i	$0.898525\pi$
$920$		0			0
$921$	−300.132			−0.325876
$922$	−694.801	+	694.801i	−0.753580	+	0.753580i
$923$	965.089	+	965.089i	1.04560	+	1.04560i
$924$		−	20.8265i		−	0.0225395i
$925$		0			0
$926$	−698.769			−0.754611
$927$	110.225	−	110.225i	0.118905	−	0.118905i
$928$	−8.38881	−	8.38881i	−0.00903967	−	0.00903967i
$929$		−	513.292i		−	0.552521i	−0.961083	−	0.276260i	$-0.910905\pi$
$929$		−	513.292i		−	0.552521i	0.961083	−	0.276260i	$-0.0890952\pi$
$930$		0			0
$931$	128.148			0.137645
$932$	−0.638175	+	0.638175i	−0.000684737	+	0.000684737i
$933$	144.581	+	144.581i	0.154964	+	0.154964i
$934$			1117.11i			1.19605i
$935$		0			0
$936$	423.699			0.452670
$937$	224.557	−	224.557i	0.239655	−	0.239655i	−0.577052	−	0.816707i	$-0.695797\pi$
$937$	224.557	−	224.557i	0.239655	−	0.239655i	0.816707	+	0.577052i	$0.195797\pi$
$938$	139.221	+	139.221i	0.148424	+	0.148424i
$939$			709.082i			0.755146i
$940$		0			0
$941$	595.500			0.632838			0.316419	−	0.948620i	$-0.397519\pi$
$941$	595.500			0.632838			0.316419	+	0.948620i	$0.397519\pi$
$942$	−212.010	+	212.010i	−0.225063	+	0.225063i
$943$	−50.1063	−	50.1063i	−0.0531350	−	0.0531350i
$944$		−	245.385i		−	0.259941i
$945$		0			0
$946$	2052.49			2.16965
$947$	890.942	−	890.942i	0.940805	−	0.940805i	−0.0575384	−	0.998343i	$-0.518325\pi$
$947$	890.942	−	890.942i	0.940805	−	0.940805i	0.998343	+	0.0575384i	$0.0183252\pi$
$948$	0.785902	+	0.785902i	0.000829010	+	0.000829010i
$949$			1535.08i			1.61758i
$950$		0			0
$951$	715.877			0.752762
$952$	302.421	−	302.421i	0.317669	−	0.317669i
$953$	−270.103	−	270.103i	−0.283424	−	0.283424i	0.551049	−	0.834473i	$-0.314228\pi$
$953$	−270.103	−	270.103i	−0.283424	−	0.283424i	−0.834473	+	0.551049i	$0.814228\pi$
$954$		−	546.233i		−	0.572571i
$955$		0			0
$956$	59.5988			0.0623418
$957$	−62.0858	+	62.0858i	−0.0648754	+	0.0648754i
$958$	909.258	+	909.258i	0.949121	+	0.949121i
$959$			64.5766i			0.0673374i
$960$		0			0
$961$	−701.309			−0.729770
$962$	83.7308	−	83.7308i	0.0870383	−	0.0870383i
$963$	275.956	+	275.956i	0.286559	+	0.286559i
$964$		−	72.3535i		−	0.0750555i
$965$		0			0
$966$	−330.907			−0.342554
$967$	−1139.02	+	1139.02i	−1.17789	+	1.17789i	−0.197611	+	0.980281i	$0.563318\pi$
$967$	−1139.02	+	1139.02i	−1.17789	+	1.17789i	−0.980281	+	0.197611i	$0.936682\pi$
$968$	1102.06	+	1102.06i	1.13849	+	1.13849i
$969$		−	622.288i		−	0.642196i
$970$		0			0
$971$	−736.722			−0.758725			−0.379363	−	0.925248i	$-0.623857\pi$
$971$	−736.722			−0.758725			−0.379363	+	0.925248i	$0.623857\pi$
$972$	2.84422	−	2.84422i	0.00292615	−	0.00292615i
$973$	−55.1518	−	55.1518i	−0.0566822	−	0.0566822i
$974$		−	915.673i		−	0.940116i
$975$		0			0
$976$	−109.826			−0.112527
$977$	993.980	−	993.980i	1.01738	−	1.01738i	0.0175332	−	0.999846i	$-0.494419\pi$
$977$	993.980	−	993.980i	1.01738	−	1.01738i	0.999846	−	0.0175332i	$-0.00558127\pi$
$978$	406.263	+	406.263i	0.415401	+	0.415401i
$979$		−	516.667i		−	0.527750i
$980$		0			0
$981$	433.884			0.442288
$982$	−427.115	+	427.115i	−0.434944	+	0.434944i
$983$	546.928	+	546.928i	0.556387	+	0.556387i	0.928277	−	0.371890i	$-0.121290\pi$
$983$	546.928	+	546.928i	0.556387	+	0.556387i	−0.371890	+	0.928277i	$0.621290\pi$
$984$		−	27.0820i		−	0.0275224i
$985$		0			0
$986$	−109.265			−0.110817
$987$	−264.624	+	264.624i	−0.268109	+	0.268109i
$988$	57.2730	+	57.2730i	0.0579686	+	0.0579686i
$989$			2248.77i			2.27378i
$990$		0			0
$991$	−1132.40			−1.14269			−0.571343	−	0.820711i	$-0.693577\pi$
$991$	−1132.40			−1.14269			−0.571343	+	0.820711i	$0.693577\pi$
$992$	−46.9694	+	46.9694i	−0.0473481	+	0.0473481i
$993$	711.231	+	711.231i	0.716245	+	0.716245i
$994$		−	407.384i		−	0.409843i
$995$		0			0
$996$	−18.3560			−0.0184297
$997$	44.1992	−	44.1992i	0.0443322	−	0.0443322i	−0.684593	−	0.728925i	$-0.740020\pi$
$997$	44.1992	−	44.1992i	0.0443322	−	0.0443322i	0.728925	+	0.684593i	$0.240020\pi$
$998$	−122.239	−	122.239i	−0.122484	−	0.122484i
$999$		−	18.5505i		−	0.0185690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.l.e.43.10		24
5.2	odd	4	inner	525.3.l.e.232.10		24
5.3	odd	4		105.3.l.a.22.3	✓	24
5.4	even	2		105.3.l.a.43.3	yes	24
15.8	even	4		315.3.o.b.127.10		24
15.14	odd	2		315.3.o.b.253.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.3	✓	24	5.3	odd	4
105.3.l.a.43.3	yes	24	5.4	even	2
315.3.o.b.127.10		24	15.8	even	4
315.3.o.b.253.10		24	15.14	odd	2
525.3.l.e.43.10		24	1.1	even	1	trivial
525.3.l.e.232.10		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)

\(f(q)\)	\(=\)	\(q+(1.36784 - 1.36784i) q^{2} +(1.22474 + 1.22474i) q^{3} +0.258033i q^{4} +3.35051 q^{6} +(-1.87083 + 1.87083i) q^{7} +(5.82430 + 5.82430i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.36784 - 1.36784i) q^{2} +(1.22474 + 1.22474i) q^{3} +0.258033i q^{4} +3.35051 q^{6} +(-1.87083 + 1.87083i) q^{7} +(5.82430 + 5.82430i) q^{8} +3.00000i q^{9} +17.6130 q^{11} +(-0.316024 + 0.316024i) q^{12} +(-12.1245 - 12.1245i) q^{13} +5.11799i q^{14} +14.9013 q^{16} +(-13.8772 + 13.8772i) q^{17} +(4.10352 + 4.10352i) q^{18} +18.3068i q^{19} -4.58258 q^{21} +(24.0917 - 24.0917i) q^{22} +(26.3956 + 26.3956i) q^{23} +14.2666i q^{24} -33.1686 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.482735 - 0.482735i) q^{28} +2.87815i q^{29} +16.1149 q^{31} +(-2.91465 + 2.91465i) q^{32} +(21.5714 + 21.5714i) q^{33} +37.9637i q^{34} -0.774098 q^{36} +(-2.52440 + 2.52440i) q^{37} +(25.0408 + 25.0408i) q^{38} -29.6988i q^{39} -1.89828 q^{41} +(-6.26823 + 6.26823i) q^{42} +(42.5974 + 42.5974i) q^{43} +4.54472i q^{44} +72.2098 q^{46} +(57.7457 - 57.7457i) q^{47} +(18.2503 + 18.2503i) q^{48} -7.00000i q^{49} -33.9922 q^{51} +(3.12851 - 3.12851i) q^{52} +(-66.5567 - 66.5567i) q^{53} +10.0515i q^{54} -21.7925 q^{56} +(-22.4212 + 22.4212i) q^{57} +(3.93685 + 3.93685i) q^{58} -16.4673i q^{59} -7.37026 q^{61} +(22.0426 - 22.0426i) q^{62} +(-5.61249 - 5.61249i) q^{63} +67.5787i q^{64} +59.0124 q^{66} +(27.2024 - 27.2024i) q^{67} +(-3.58078 - 3.58078i) q^{68} +64.6557i q^{69} -79.5984 q^{71} +(-17.4729 + 17.4729i) q^{72} +(-63.3051 - 63.3051i) q^{73} +6.90594i q^{74} -4.72376 q^{76} +(-32.9508 + 32.9508i) q^{77} +(-40.6231 - 40.6231i) q^{78} -2.48684i q^{79} -9.00000 q^{81} +(-2.59655 + 2.59655i) q^{82} +(29.0421 + 29.0421i) q^{83} -1.18245i q^{84} +116.533 q^{86} +(-3.52500 + 3.52500i) q^{87} +(102.583 + 102.583i) q^{88} -29.3345i q^{89} +45.3656 q^{91} +(-6.81092 + 6.81092i) q^{92} +(19.7367 + 19.7367i) q^{93} -157.974i q^{94} -7.13941 q^{96} +(89.1223 - 89.1223i) q^{97} +(-9.57487 - 9.57487i) q^{98} +52.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more