LMFDB - Embedded newform 252.4.w.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.15302 + 0.668133i) q^{3} +(9.18977 + 15.9171i) q^{5} +(18.3240 - 2.68897i) q^{7} +(26.1072 - 6.88581i) q^{9} +O(q^{10})$	\(q+(-5.15302 + 0.668133i) q^{3} +(9.18977 + 15.9171i) q^{5} +(18.3240 - 2.68897i) q^{7} +(26.1072 - 6.88581i) q^{9} +(-47.9540 - 27.6862i) q^{11} +(68.0763 + 39.3039i) q^{13} +(-57.9898 - 75.8813i) q^{15} +(9.99021 + 17.3036i) q^{17} +(-16.7611 - 9.67700i) q^{19} +(-92.6274 + 26.0992i) q^{21} +(107.511 - 62.0716i) q^{23} +(-106.404 + 184.296i) q^{25} +(-129.930 + 52.9258i) q^{27} +(-48.2851 + 27.8774i) q^{29} +317.989i q^{31} +(265.606 + 110.628i) q^{33} +(211.194 + 266.955i) q^{35} +(20.5303 - 35.5595i) q^{37} +(-377.059 - 157.050i) q^{39} +(-53.1315 + 92.0264i) q^{41} +(279.238 + 483.655i) q^{43} +(349.521 + 352.273i) q^{45} +147.916 q^{47} +(328.539 - 98.5453i) q^{49} +(-63.0408 - 82.4907i) q^{51} +(-570.090 + 329.141i) q^{53} -1017.72i q^{55} +(92.8356 + 38.6672i) q^{57} -568.509 q^{59} -140.951i q^{61} +(459.873 - 196.377i) q^{63} +1444.77i q^{65} -294.283 q^{67} +(-512.535 + 391.688i) q^{69} -602.374i q^{71} +(541.701 - 312.751i) q^{73} +(425.165 - 1020.77i) q^{75} +(-953.157 - 378.377i) q^{77} -534.044 q^{79} +(634.171 - 359.538i) q^{81} +(-352.414 - 610.399i) q^{83} +(-183.615 + 318.031i) q^{85} +(230.188 - 175.914i) q^{87} +(-38.6630 + 66.9663i) q^{89} +(1353.12 + 537.150i) q^{91} +(-212.459 - 1638.60i) q^{93} -355.718i q^{95} +(382.120 - 220.617i) q^{97} +(-1442.59 - 392.608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	−5.15302	+	0.668133i	−0.991699	+	0.128582i
$3$	−5.15302	+	0.668133i	−0.991699	+	0.128582i
$4$		0			0
$5$	9.18977	+	15.9171i	0.821958	+	1.42367i	0.904222	+	0.427062i	$0.140451\pi$
$5$	9.18977	+	15.9171i	0.821958	+	1.42367i	−0.0822649	+	0.996611i	$0.526215\pi$
$6$		0			0
$7$	18.3240	−	2.68897i	0.989404	−	0.145191i
$7$	18.3240	−	2.68897i	0.989404	−	0.145191i
$8$		0			0
$9$	26.1072	−	6.88581i	0.966933	−	0.255030i
$10$		0			0
$11$	−47.9540	−	27.6862i	−1.31442	−	0.758883i	−0.331599	−	0.943420i	$-0.607588\pi$
$11$	−47.9540	−	27.6862i	−1.31442	−	0.758883i	−0.982826	+	0.184537i	$0.940921\pi$
$12$		0			0
$13$	68.0763	+	39.3039i	1.45238	+	0.838534i	0.998616	−	0.0525871i	$-0.0167467\pi$
$13$	68.0763	+	39.3039i	1.45238	+	0.838534i	0.453766	+	0.891121i	$0.350080\pi$
$14$		0			0
$15$	−57.9898	−	75.8813i	−0.998193	−	1.30616i
$16$		0			0
$17$	9.99021	+	17.3036i	0.142528	+	0.246866i	0.928448	−	0.371462i	$-0.121143\pi$
$17$	9.99021	+	17.3036i	0.142528	+	0.246866i	−0.785920	+	0.618329i	$0.787810\pi$
$18$		0			0
$19$	−16.7611	−	9.67700i	−0.202382	−	0.116845i	0.395384	−	0.918516i	$-0.370611\pi$
$19$	−16.7611	−	9.67700i	−0.202382	−	0.116845i	−0.597766	+	0.801671i	$0.703945\pi$
$20$		0			0
$21$	−92.6274	+	26.0992i	−0.962522	+	0.271205i
$22$		0			0
$23$	107.511	−	62.0716i	0.974679	−	0.562731i	0.0740195	−	0.997257i	$-0.476417\pi$
$23$	107.511	−	62.0716i	0.974679	−	0.562731i	0.900659	+	0.434526i	$0.143084\pi$
$24$		0			0
$25$	−106.404	+	184.296i	−0.851229	+	1.47437i
$26$		0			0
$27$	−129.930	+	52.9258i	−0.926114	+	0.377243i
$28$		0			0
$29$	−48.2851	+	27.8774i	−0.309183	+	0.178507i	−0.646561	−	0.762862i	$-0.723793\pi$
$29$	−48.2851	+	27.8774i	−0.309183	+	0.178507i	0.337378	+	0.941369i	$0.390460\pi$
$30$		0			0
$31$			317.989i			1.84234i	0.389160	+	0.921170i	$0.372765\pi$
$31$			317.989i			1.84234i	−0.389160	+	0.921170i	$0.627235\pi$
$32$		0			0
$33$	265.606	+	110.628i	1.40109	+	0.583572i
$34$		0			0
$35$	211.194	+	266.955i	1.01995	+	1.28925i
$36$		0			0
$37$	20.5303	−	35.5595i	0.0912205	−	0.157999i	−0.816804	−	0.576915i	$-0.804257\pi$
$37$	20.5303	−	35.5595i	0.0912205	−	0.157999i	0.908025	+	0.418916i	$0.137590\pi$
$38$		0			0
$39$	−377.059	−	157.050i	−1.54815	−	0.644822i
$40$		0			0
$41$	−53.1315	+	92.0264i	−0.202384	+	0.350539i	−0.949296	−	0.314383i	$-0.898202\pi$
$41$	−53.1315	+	92.0264i	−0.202384	+	0.350539i	0.746912	+	0.664923i	$0.231536\pi$
$42$		0			0
$43$	279.238	+	483.655i	0.990312	+	1.71527i	0.615414	+	0.788204i	$0.288989\pi$
$43$	279.238	+	483.655i	0.990312	+	1.71527i	0.374898	+	0.927066i	$0.377678\pi$
$44$		0			0
$45$	349.521	+	352.273i	1.15786	+	1.16697i
$46$		0			0
$47$	147.916			0.459059			0.229529	−	0.973302i	$-0.426281\pi$
$47$	147.916			0.459059			0.229529	+	0.973302i	$0.426281\pi$
$48$		0			0
$49$	328.539	−	98.5453i	0.957839	−	0.287304i
$50$		0			0
$51$	−63.0408	−	82.4907i	−0.173088	−	0.226490i
$52$		0			0
$53$	−570.090	+	329.141i	−1.47751	+	0.853038i	−0.999677	−	0.0254144i	$-0.991909\pi$
$53$	−570.090	+	329.141i	−1.47751	+	0.853038i	−0.477829	+	0.878453i	$0.658576\pi$
$54$		0			0
$55$		−	1017.72i		−	2.49508i
$56$		0			0
$57$	92.8356	+	38.6672i	0.215726	+	0.0898525i
$58$		0			0
$59$	−568.509			−1.25447			−0.627234	−	0.778831i	$-0.715813\pi$
$59$	−568.509			−1.25447			−0.627234	+	0.778831i	$0.715813\pi$
$60$		0			0
$61$		−	140.951i		−	0.295852i	−0.988998	−	0.147926i	$-0.952740\pi$
$61$		−	140.951i		−	0.295852i	0.988998	−	0.147926i	$-0.0472598\pi$
$62$		0			0
$63$	459.873	−	196.377i	0.919659	−	0.392717i
$64$		0			0
$65$			1444.77i			2.75696i
$66$		0			0
$67$	−294.283			−0.536603			−0.268302	−	0.963335i	$-0.586462\pi$
$67$	−294.283			−0.536603			−0.268302	+	0.963335i	$0.586462\pi$
$68$		0			0
$69$	−512.535	+	391.688i	−0.894231	+	0.683386i
$70$		0			0
$71$		−	602.374i		−	1.00688i	−0.864030	−	0.503441i	$-0.832067\pi$
$71$		−	602.374i		−	1.00688i	0.864030	−	0.503441i	$-0.167933\pi$
$72$		0			0
$73$	541.701	−	312.751i	0.868510	−	0.501435i	0.00165750	−	0.999999i	$-0.499472\pi$
$73$	541.701	−	312.751i	0.868510	−	0.501435i	0.866853	+	0.498564i	$0.166139\pi$
$74$		0			0
$75$	425.165	−	1020.77i	0.654584	−	1.57159i
$76$		0			0
$77$	−953.157	−	378.377i	−1.41068	−	0.560000i
$78$		0			0
$79$	−534.044			−0.760565			−0.380282	−	0.924870i	$-0.624173\pi$
$79$	−534.044			−0.760565			−0.380282	+	0.924870i	$0.624173\pi$
$80$		0			0
$81$	634.171	−	359.538i	0.869920	−	0.493194i
$82$		0			0
$83$	−352.414	−	610.399i	−0.466054	−	0.807229i	0.533195	−	0.845993i	$-0.320991\pi$
$83$	−352.414	−	610.399i	−0.466054	−	0.807229i	−0.999248	+	0.0387640i	$0.987658\pi$
$84$		0			0
$85$	−183.615	+	318.031i	−0.234305	+	0.405827i
$86$		0			0
$87$	230.188	−	175.914i	0.283664	−	0.216781i
$88$		0			0
$89$	−38.6630	+	66.9663i	−0.0460480	+	0.0797574i	−0.888131	−	0.459591i	$-0.847996\pi$
$89$	−38.6630	+	66.9663i	−0.0460480	+	0.0797574i	0.842083	+	0.539348i	$0.181329\pi$
$90$		0			0
$91$	1353.12	+	537.150i	1.55874	+	0.618776i
$92$		0			0
$93$	−212.459	−	1638.60i	−0.236892	−	1.82705i
$94$		0			0
$95$		−	355.718i		−	0.384167i
$96$		0			0
$97$	382.120	−	220.617i	0.399984	−	0.230931i	−0.286493	−	0.958082i	$-0.592490\pi$
$97$	382.120	−	220.617i	0.399984	−	0.230931i	0.686477	+	0.727151i	$0.259156\pi$
$98$		0			0
$99$	−1442.59	−	392.608i	−1.46450	−	0.398572i
$100$		0			0
$101$	−559.177	+	968.522i	−0.550893	+	0.954174i	0.447318	+	0.894375i	$0.352379\pi$
$101$	−559.177	+	968.522i	−0.550893	+	0.954174i	−0.998210	+	0.0597989i	$0.980954\pi$
$102$		0			0
$103$	705.623	−	407.392i	0.675020	−	0.389723i	−0.122956	−	0.992412i	$-0.539237\pi$
$103$	705.623	−	407.392i	0.675020	−	0.389723i	0.797976	+	0.602689i	$0.205904\pi$
$104$		0			0
$105$	−1266.65	−	1234.52i	−1.17726	−	1.14740i
$106$		0			0
$107$	1320.94	+	762.645i	1.19346	+	0.689044i	0.959089	−	0.283103i	$-0.0913639\pi$
$107$	1320.94	+	762.645i	1.19346	+	0.689044i	0.234370	+	0.972147i	$0.424697\pi$
$108$		0			0
$109$	101.432	+	175.685i	0.0891319	+	0.154381i	0.907144	−	0.420819i	$-0.138257\pi$
$109$	101.432	+	175.685i	0.0891319	+	0.154381i	−0.818013	+	0.575200i	$0.804924\pi$
$110$		0			0
$111$	−82.0345	+	196.956i	−0.0701475	+	0.168416i
$112$		0			0
$113$	−75.2101	−	43.4226i	−0.0626121	−	0.0361491i	0.468367	−	0.883534i	$-0.344842\pi$
$113$	−75.2101	−	43.4226i	−0.0626121	−	0.0361491i	−0.530979	+	0.847385i	$0.678176\pi$
$114$		0			0
$115$	1976.00	+	1140.85i	1.60229	+	0.925082i
$116$		0			0
$117$	2047.92	+	557.354i	1.61821	+	0.440405i
$118$		0			0
$119$	229.589	+	290.207i	0.176861	+	0.223557i
$120$		0			0
$121$	867.557	+	1502.65i	0.651808	+	1.12896i
$122$		0			0
$123$	212.302	−	509.713i	0.155631	−	0.373653i
$124$		0			0
$125$	−1613.85			−1.15478
$126$		0			0
$127$	−486.709			−0.340066			−0.170033	−	0.985438i	$-0.554388\pi$
$127$	−486.709			−0.340066			−0.170033	+	0.985438i	$0.554388\pi$
$128$		0			0
$129$	−1762.06	−	2305.71i	−1.20264	−	1.57369i
$130$		0			0
$131$	400.978	+	694.514i	0.267432	+	0.463206i	0.968198	−	0.250186i	$-0.0804916\pi$
$131$	400.978	+	694.514i	0.267432	+	0.463206i	−0.700766	+	0.713391i	$0.747158\pi$
$132$		0			0
$133$	−333.151	−	132.252i	−0.217202	−	0.0862231i
$134$		0			0
$135$	−2036.46	−	1581.74i	−1.29830	−	1.00841i
$136$		0			0
$137$	795.730	+	459.415i	0.496232	+	0.286500i	0.727156	−	0.686472i	$-0.240842\pi$
$137$	795.730	+	459.415i	0.496232	+	0.286500i	−0.230924	+	0.972972i	$0.574175\pi$
$138$		0			0
$139$	−159.738	−	92.2248i	−0.0974734	−	0.0562763i	0.450471	−	0.892791i	$-0.351256\pi$
$139$	−159.738	−	92.2248i	−0.0974734	−	0.0562763i	−0.547944	+	0.836515i	$0.684589\pi$
$140$		0			0
$141$	−762.213	+	98.8276i	−0.455248	+	0.0590268i
$142$		0			0
$143$	−2176.35	−	3769.56i	−1.27270	−	2.20438i
$144$		0			0
$145$	−887.457	−	512.374i	−0.508271	−	0.293450i
$146$		0			0
$147$	−1627.13	+	727.314i	−0.912946	+	0.408080i
$148$		0			0
$149$	1940.53	−	1120.36i	1.06694	−	0.615998i	0.139596	−	0.990209i	$-0.455420\pi$
$149$	1940.53	−	1120.36i	1.06694	−	0.615998i	0.927344	+	0.374211i	$0.122086\pi$
$150$		0			0
$151$	1064.55	−	1843.85i	0.573721	−	0.993714i	−0.422458	−	0.906382i	$-0.638833\pi$
$151$	1064.55	−	1843.85i	0.573721	−	0.993714i	0.996179	−	0.0873314i	$-0.0278339\pi$
$152$		0			0
$153$	379.965	+	382.957i	0.200774	+	0.202354i
$154$		0			0
$155$	−5061.48	+	2922.25i	−2.62289	+	1.51433i
$156$		0			0
$157$		−	2774.77i		−	1.41051i	−0.708952	−	0.705256i	$-0.750832\pi$
$157$		−	2774.77i		−	1.41051i	0.708952	−	0.705256i	$-0.249168\pi$
$158$		0			0
$159$	2717.77	−	2076.97i	1.35556	−	1.03594i
$160$		0			0
$161$	1803.13	−	1426.49i	0.882648	−	0.698282i
$162$		0			0
$163$	−536.860	+	929.870i	−0.257976	+	0.446828i	−0.965700	−	0.259661i	$-0.916389\pi$
$163$	−536.860	+	929.870i	−0.257976	+	0.446828i	0.707723	+	0.706490i	$0.249722\pi$
$164$		0			0
$165$	679.973	+	5244.33i	0.320823	+	2.47437i
$166$		0			0
$167$	−22.8325	+	39.5471i	−0.0105798	+	0.0183248i	−0.871267	−	0.490810i	$-0.836701\pi$
$167$	−22.8325	+	39.5471i	−0.0105798	+	0.0183248i	0.860687	+	0.509134i	$0.170034\pi$
$168$		0			0
$169$	1991.09	+	3448.67i	0.906277	+	1.56972i
$170$		0			0
$171$	−504.218	−	137.226i	−0.225489	−	0.0613680i
$172$		0			0
$173$	909.083			0.399516			0.199758	−	0.979845i	$-0.435984\pi$
$173$	909.083			0.399516			0.199758	+	0.979845i	$0.435984\pi$
$174$		0			0
$175$	−1454.17	+	3663.16i	−0.628144	+	1.58234i
$176$		0			0
$177$	2929.54	−	379.840i	1.24405	−	0.161302i
$178$		0			0
$179$	3140.15	−	1812.96i	1.31120	−	0.757024i	0.328909	−	0.944362i	$-0.393319\pi$
$179$	3140.15	−	1812.96i	1.31120	−	0.757024i	0.982296	+	0.187338i	$0.0599858\pi$
$180$		0			0
$181$		−	1659.16i		−	0.681351i	−0.940181	−	0.340676i	$-0.889344\pi$
$181$		−	1659.16i		−	0.681351i	0.940181	−	0.340676i	$-0.110656\pi$
$182$		0			0
$183$	94.1743	+	726.325i	0.0380414	+	0.293396i
$184$		0			0
$185$	754.674			0.299918
$186$		0			0
$187$		−	1106.37i		−	0.432650i
$188$		0			0
$189$	−2238.53	+	1319.19i	−0.861529	+	0.507709i
$190$		0			0
$191$			1540.32i			0.583527i	0.956491	+	0.291763i	$0.0942420\pi$
$191$			1540.32i			0.583527i	−0.956491	+	0.291763i	$0.905758\pi$
$192$		0			0
$193$	−2900.09			−1.08162			−0.540811	−	0.841144i	$-0.681883\pi$
$193$	−2900.09			−1.08162			−0.540811	+	0.841144i	$0.681883\pi$
$194$		0			0
$195$	−965.302	−	7444.95i	−0.354496	−	2.73407i
$196$		0			0
$197$			2096.85i			0.758347i	0.925326	+	0.379173i	$0.123792\pi$
$197$			2096.85i			0.758347i	−0.925326	+	0.379173i	$0.876208\pi$
$198$		0			0
$199$	3937.78	−	2273.48i	1.40272	−	0.809862i	0.408051	−	0.912959i	$-0.366209\pi$
$199$	3937.78	−	2273.48i	1.40272	−	0.809862i	0.994671	+	0.103097i	$0.0328752\pi$
$200$		0			0
$201$	1516.45	−	196.620i	0.532149	−	0.0689977i
$202$		0			0
$203$	−809.815	+	640.663i	−0.279990	+	0.221506i
$204$		0			0
$205$	−1953.06			−0.665404
$206$		0			0
$207$	2379.40	−	2360.82i	0.798936	−	0.792696i
$208$		0			0
$209$	535.840	+	928.102i	0.177344	+	0.307168i
$210$		0			0
$211$	1506.32	−	2609.03i	0.491467	−	0.851245i	−0.508485	−	0.861071i	$-0.669794\pi$
$211$	1506.32	−	2609.03i	0.491467	−	0.851245i	0.999952	+	0.00982544i	$0.00312758\pi$
$212$		0			0
$213$	402.466	+	3104.04i	0.129467	+	0.998523i
$214$		0			0
$215$	−5132.26	+	8889.34i	−1.62799	+	2.81976i
$216$		0			0
$217$	855.062	+	5826.84i	0.267490	+	1.82282i
$218$		0			0
$219$	−2582.43	+	1973.54i	−0.796825	+	0.608947i
$220$		0			0
$221$			1570.62i			0.478059i
$222$		0			0
$223$	230.173	−	132.890i	0.0691188	−	0.0399058i	−0.465042	−	0.885288i	$-0.653961\pi$
$223$	230.173	−	132.890i	0.0691188	−	0.0399058i	0.534161	+	0.845383i	$0.320628\pi$
$224$		0			0
$225$	−1508.87	+	5544.14i	−0.447072	+	1.64271i
$226$		0			0
$227$	−579.422	+	1003.59i	−0.169417	+	0.293439i	−0.938215	−	0.346053i	$-0.887522\pi$
$227$	−579.422	+	1003.59i	−0.169417	+	0.293439i	0.768798	+	0.639492i	$0.220855\pi$
$228$		0			0
$229$	989.740	−	571.427i	0.285606	−	0.164895i	−0.350352	−	0.936618i	$-0.613938\pi$
$229$	989.740	−	571.427i	0.285606	−	0.164895i	0.635959	+	0.771723i	$0.280605\pi$
$230$		0			0
$231$	5164.44	+	1312.95i	1.47098	+	0.373963i
$232$		0			0
$233$	−4943.19	−	2853.95i	−1.38987	−	0.802440i	−0.396567	−	0.918006i	$-0.629799\pi$
$233$	−4943.19	−	2853.95i	−1.38987	−	0.802440i	−0.993300	+	0.115565i	$0.963132\pi$
$234$		0			0
$235$	1359.31	+	2354.40i	0.377327	+	0.653549i
$236$		0			0
$237$	2751.94	−	356.812i	0.754251	−	0.0977952i
$238$		0			0
$239$	310.843	+	179.466i	0.0841288	+	0.0485718i	0.541474	−	0.840717i	$-0.317866\pi$
$239$	310.843	+	179.466i	0.0841288	+	0.0485718i	−0.457345	+	0.889289i	$0.651200\pi$
$240$		0			0
$241$	3845.00	+	2219.91i	1.02771	+	0.593349i	0.916328	−	0.400429i	$-0.131139\pi$
$241$	3845.00	+	2219.91i	1.02771	+	0.593349i	0.111382	+	0.993778i	$0.464472\pi$
$242$		0			0
$243$	−3027.68	+	2276.42i	−0.799282	+	0.600956i
$244$		0			0
$245$	4587.75	+	4323.79i	1.19633	+	1.12750i
$246$		0			0
$247$	−760.688	−	1317.55i	−0.195957	−	0.339408i
$248$		0			0
$249$	2223.82	+	2909.94i	0.565980	+	0.740601i
$250$		0			0
$251$	−3438.88			−0.864782			−0.432391	−	0.901686i	$-0.642330\pi$
$251$	−3438.88			−0.864782			−0.432391	+	0.901686i	$0.642330\pi$
$252$		0			0
$253$	−6874.12			−1.70819
$254$		0			0
$255$	733.686	−	1761.50i	0.180177	−	0.432586i
$256$		0			0
$257$	−910.835	−	1577.61i	−0.221075	−	0.382913i	0.734060	−	0.679085i	$-0.237623\pi$
$257$	−910.835	−	1577.61i	−0.221075	−	0.382913i	−0.955135	+	0.296172i	$0.904290\pi$
$258$		0			0
$259$	280.579	−	706.798i	0.0673140	−	0.169569i
$260$		0			0
$261$	−1068.63	+	1060.28i	−0.253435	+	0.251455i
$262$		0			0
$263$	−3674.68	−	2121.58i	−0.861561	−	0.497422i	0.00297373	−	0.999996i	$-0.499053\pi$
$263$	−3674.68	−	2121.58i	−0.861561	−	0.497422i	−0.864535	+	0.502573i	$0.832387\pi$
$264$		0			0
$265$	−10478.0	−	6049.46i	−2.42889	−	1.40232i
$266$		0			0
$267$	154.489	−	370.910i	0.0354103	−	0.0850163i
$268$		0			0
$269$	−1538.72	−	2665.14i	−0.348763	−	0.604075i	0.637267	−	0.770643i	$-0.280065\pi$
$269$	−1538.72	−	2665.14i	−0.348763	−	0.604075i	−0.986030	+	0.166568i	$0.946731\pi$
$270$		0			0
$271$	−623.012	−	359.696i	−0.139651	−	0.0806273i	0.428547	−	0.903520i	$-0.359026\pi$
$271$	−623.012	−	359.696i	−0.139651	−	0.0806273i	−0.568197	+	0.822892i	$0.692359\pi$
$272$		0			0
$273$	−7331.53	−	1863.88i	−1.62536	−	0.413213i
$274$		0			0
$275$	10205.0	−	5891.83i	2.23775	−	1.29197i
$276$		0			0
$277$	455.590	−	789.105i	0.0988221	−	0.171165i	−0.812375	−	0.583135i	$-0.801826\pi$
$277$	455.590	−	789.105i	0.0988221	−	0.171165i	0.911197	+	0.411970i	$0.135159\pi$
$278$		0			0
$279$	2189.61	+	8301.81i	0.469852	+	1.78142i
$280$		0			0
$281$	4142.21	−	2391.50i	0.879372	−	0.507705i	0.00892043	−	0.999960i	$-0.497161\pi$
$281$	4142.21	−	2391.50i	0.879372	−	0.507705i	0.870451	+	0.492255i	$0.163827\pi$
$282$		0			0
$283$			4008.65i			0.842013i	0.907058	+	0.421006i	$0.138323\pi$
$283$			4008.65i			0.842013i	−0.907058	+	0.421006i	$0.861677\pi$
$284$		0			0
$285$	237.667	+	1833.02i	0.0493971	+	0.380978i
$286$		0			0
$287$	−726.126	+	1829.16i	−0.149344	+	0.376209i
$288$		0			0
$289$	2256.89	−	3909.05i	0.459371	−	0.795654i
$290$		0			0
$291$	−1821.67	+	1392.15i	−0.366970	+	0.280445i
$292$		0			0
$293$	3758.85	−	6510.51i	0.749468	−	1.29812i	−0.198610	−	0.980079i	$-0.563643\pi$
$293$	3758.85	−	6510.51i	0.749468	−	1.29812i	0.948078	−	0.318038i	$-0.103024\pi$
$294$		0			0
$295$	−5224.47	−	9049.04i	−1.03112	−	1.78595i
$296$		0			0
$297$	7695.99	+	1059.28i	1.50359	+	0.206955i
$298$		0			0
$299$	9758.62			1.88748
$300$		0			0
$301$	6417.29	+	8111.63i	1.22886	+	1.55331i
$302$		0			0
$303$	2234.35	−	5364.42i	0.423630	−	1.01709i
$304$		0			0
$305$	2243.54	−	1295.31i	0.421196	−	0.243178i
$306$		0			0
$307$			6149.80i			1.14328i	0.820504	+	0.571641i	$0.193693\pi$
$307$			6149.80i			1.14328i	−0.820504	+	0.571641i	$0.806307\pi$
$308$		0			0
$309$	−3363.90	+	2570.75i	−0.619305	+	0.473284i
$310$		0			0
$311$	2119.34			0.386421			0.193211	−	0.981157i	$-0.438110\pi$
$311$	2119.34			0.386421			0.193211	+	0.981157i	$0.438110\pi$
$312$		0			0
$313$		−	145.759i		−	0.0263220i	−0.999913	−	0.0131610i	$-0.995811\pi$
$313$		−	145.759i		−	0.0263220i	0.999913	−	0.0131610i	$-0.00418939\pi$
$314$		0			0
$315$	7351.88	+	5515.20i	1.31502	+	0.986497i
$316$		0			0
$317$		−	2607.15i		−	0.461931i	−0.972962	−	0.230966i	$-0.925811\pi$
$317$		−	2607.15i		−	0.461931i	0.972962	−	0.230966i	$-0.0741885\pi$
$318$		0			0
$319$	3087.28			0.541864
$320$		0			0
$321$	−7316.38	−	3047.36i	−1.27215	−	0.529866i
$322$		0			0
$323$		−	386.701i		−	0.0666150i
$324$		0			0
$325$	−14487.1	+	8364.15i	−2.47262	+	1.42757i
$326$		0			0
$327$	−640.059	−	837.536i	−0.108243	−	0.141639i
$328$		0			0
$329$	2710.41	−	397.741i	0.454194	−	0.0666510i
$330$		0			0
$331$	−10890.0			−1.80837			−0.904185	−	0.427142i	$-0.859521\pi$
$331$	−10890.0			−1.80837			−0.904185	+	0.427142i	$0.859521\pi$
$332$		0			0
$333$	291.132	−	1069.73i	0.0479098	−	0.176038i
$334$		0			0
$335$	−2704.39	−	4684.15i	−0.441065	−	0.763947i
$336$		0			0
$337$	1171.50	−	2029.09i	0.189364	−	0.327987i	−0.755675	−	0.654947i	$-0.772691\pi$
$337$	1171.50	−	2029.09i	0.189364	−	0.327987i	0.945038	+	0.326960i	$0.106024\pi$
$338$		0			0
$339$	416.571	+	173.507i	0.0667405	+	0.0277982i
$340$		0			0
$341$	8803.93	−	15248.8i	1.39812	−	2.42162i
$342$		0			0
$343$	5755.17	−	2689.18i	0.905976	−	0.423329i
$344$		0			0
$345$	−10944.6	−	4558.57i	−1.70794	−	0.711377i
$346$		0			0
$347$		−	3903.65i		−	0.603916i	−0.953321	−	0.301958i	$-0.902360\pi$
$347$		−	3903.65i		−	0.603916i	0.953321	−	0.301958i	$-0.0976403\pi$
$348$		0			0
$349$	1985.23	−	1146.17i	0.304490	−	0.175797i	−0.339968	−	0.940437i	$-0.610416\pi$
$349$	1985.23	−	1146.17i	0.304490	−	0.175797i	0.644458	+	0.764640i	$0.277083\pi$
$350$		0			0
$351$	−10925.4	−	1503.77i	−1.66140	−	0.228676i
$352$		0			0
$353$	3872.95	−	6708.15i	0.583956	−	1.01144i	−0.411049	−	0.911613i	$-0.634837\pi$
$353$	3872.95	−	6708.15i	0.583956	−	1.01144i	0.995005	−	0.0998278i	$-0.0318292\pi$
$354$		0			0
$355$	9588.07	−	5535.67i	1.43347	−	0.827614i
$356$		0			0
$357$	−1376.98	−	1342.05i	−0.204138	−	0.198960i
$358$		0			0
$359$	−5235.74	−	3022.86i	−0.769727	−	0.444402i	0.0630502	−	0.998010i	$-0.479917\pi$
$359$	−5235.74	−	3022.86i	−0.769727	−	0.444402i	−0.832777	+	0.553608i	$0.813251\pi$
$360$		0			0
$361$	−3242.21	−	5615.67i	−0.472694	−	0.818731i
$362$		0			0
$363$	−5474.51	−	7163.55i	−0.791562	−	1.03578i
$364$		0			0
$365$	9956.20	+	5748.22i	1.42776	+	0.824316i
$366$		0			0
$367$	−9468.66	−	5466.74i	−1.34676	−	0.777551i	−0.358969	−	0.933349i	$-0.616872\pi$
$367$	−9468.66	−	5466.74i	−1.34676	−	0.777551i	−0.987789	+	0.155798i	$0.950205\pi$
$368$		0			0
$369$	−753.438	+	2768.41i	−0.106294	+	0.390562i
$370$		0			0
$371$	−9561.28	+	7564.14i	−1.33800	+	1.05852i
$372$		0			0
$373$	−1432.56	−	2481.26i	−0.198861	−	0.344437i	0.749298	−	0.662232i	$-0.230391\pi$
$373$	−1432.56	−	2481.26i	−0.198861	−	0.344437i	−0.948159	+	0.317795i	$0.897058\pi$
$374$		0			0
$375$	8316.22	−	1078.27i	1.14519	−	0.148484i
$376$		0			0
$377$	−4382.76			−0.598737
$378$		0			0
$379$	−2071.78			−0.280792			−0.140396	−	0.990095i	$-0.544838\pi$
$379$	−2071.78			−0.280792			−0.140396	+	0.990095i	$0.544838\pi$
$380$		0			0
$381$	2508.02	−	325.187i	0.337244	−	0.0437265i
$382$		0			0
$383$	3714.00	+	6432.84i	0.495500	+	0.858232i	0.999987	−	0.00518791i	$-0.00165137\pi$
$383$	3714.00	+	6432.84i	0.495500	+	0.858232i	−0.504486	+	0.863420i	$0.668318\pi$
$384$		0			0
$385$	−2736.62	−	18648.7i	−0.362262	−	2.46864i
$386$		0			0
$387$	10620.5	+	10704.1i	1.39501	+	1.40599i
$388$		0			0
$389$	6567.95	+	3792.01i	0.856062	+	0.494248i	0.862692	−	0.505730i	$-0.168777\pi$
$389$	6567.95	+	3792.01i	0.856062	+	0.494248i	−0.00662941	+	0.999978i	$0.502110\pi$
$390$		0			0
$391$	2148.12	+	1240.22i	0.277839	+	0.160410i
$392$		0			0
$393$	−2530.27	−	3310.94i	−0.324772	−	0.424973i
$394$		0			0
$395$	−4907.74	−	8500.45i	−0.625152	−	1.08279i
$396$		0			0
$397$	1031.73	+	595.671i	0.130431	+	0.0753044i	0.563796	−	0.825914i	$-0.309340\pi$
$397$	1031.73	+	595.671i	0.130431	+	0.0753044i	−0.433365	+	0.901219i	$0.642674\pi$
$398$		0			0
$399$	1805.10	+	458.906i	0.226486	+	0.0575790i
$400$		0			0
$401$	−5591.97	+	3228.52i	−0.696383	+	0.402057i	−0.805999	−	0.591917i	$-0.798371\pi$
$401$	−5591.97	+	3228.52i	−0.696383	+	0.402057i	0.109616	+	0.993974i	$0.465038\pi$
$402$		0			0
$403$	−12498.2	+	21647.5i	−1.54486	+	2.67578i
$404$		0			0
$405$	11550.7	+	6790.12i	1.41718	+	0.833096i
$406$		0			0
$407$	−1969.02	+	1136.81i	−0.239805	+	0.138451i
$408$		0			0
$409$			1896.49i			0.229280i	0.993407	+	0.114640i	$0.0365715\pi$
$409$			1896.49i			0.229280i	−0.993407	+	0.114640i	$0.963429\pi$
$410$		0			0
$411$	−4407.36	−	1835.72i	−0.528951	−	0.220315i
$412$		0			0
$413$	−10417.4	+	1528.70i	−1.24117	+	0.182137i
$414$		0			0
$415$	6477.20	−	11218.8i	0.766153	−	1.32702i
$416$		0			0
$417$	884.752	+	368.510i	0.103900	+	0.0432758i
$418$		0			0
$419$	7002.37	−	12128.5i	0.816440	−	1.41412i	−0.0918495	−	0.995773i	$-0.529278\pi$
$419$	7002.37	−	12128.5i	0.816440	−	1.41412i	0.908289	−	0.418342i	$-0.137389\pi$
$420$		0			0
$421$	4485.43	+	7769.00i	0.519256	+	0.899377i	0.999750	+	0.0223789i	$0.00712403\pi$
$421$	4485.43	+	7769.00i	0.519256	+	0.899377i	−0.480494	+	0.876998i	$0.659543\pi$
$422$		0			0
$423$	3861.67	−	1018.52i	0.443879	−	0.117074i
$424$		0			0
$425$	−4251.98			−0.485297
$426$		0			0
$427$	−379.014	−	2582.80i	−0.0429549	−	0.292717i
$428$		0			0
$429$	13733.4	+	17970.5i	1.54558	+	2.02243i
$430$		0			0
$431$	−8722.70	+	5036.05i	−0.974844	+	0.562826i	−0.900709	−	0.434422i	$-0.856953\pi$
$431$	−8722.70	+	5036.05i	−0.974844	+	0.562826i	−0.0741343	+	0.997248i	$0.523619\pi$
$432$		0			0
$433$		−	10574.2i		−	1.17358i	−0.809738	−	0.586791i	$-0.800391\pi$
$433$		−	10574.2i		−	1.17358i	0.809738	−	0.586791i	$-0.199609\pi$
$434$		0			0
$435$	4915.42	+	2047.33i	0.541784	+	0.225660i
$436$		0			0
$437$	−2402.67			−0.263010
$438$		0			0
$439$			9055.68i			0.984520i	0.870448	+	0.492260i	$0.163829\pi$
$439$			9055.68i			0.984520i	−0.870448	+	0.492260i	$0.836171\pi$
$440$		0			0
$441$	7898.67	−	4835.00i	0.852896	−	0.522082i
$442$		0			0
$443$			3546.64i			0.380374i	0.981748	+	0.190187i	$0.0609095\pi$
$443$			3546.64i			0.380374i	−0.981748	+	0.190187i	$0.939091\pi$
$444$		0			0
$445$	−1421.22			−0.151398
$446$		0			0
$447$	−9251.01	+	7069.78i	−0.978876	+	0.748074i
$448$		0			0
$449$			200.727i			0.0210977i	0.999944	+	0.0105489i	$0.00335787\pi$
$449$			200.727i			0.0210977i	−0.999944	+	0.0105489i	$0.996642\pi$
$450$		0			0
$451$	5095.73	−	2942.02i	0.532037	−	0.307172i
$452$		0			0
$453$	−4253.70	+	10212.7i	−0.441184	+	1.05924i
$454$		0			0
$455$	3884.95	+	26474.1i	0.400284	+	2.72774i
$456$		0			0
$457$	−8584.04			−0.878654			−0.439327	−	0.898327i	$-0.644783\pi$
$457$	−8584.04			−0.878654			−0.439327	+	0.898327i	$0.644783\pi$
$458$		0			0
$459$	−2213.83	−	1719.52i	−0.225126	−	0.174859i
$460$		0			0
$461$	5807.63	+	10059.1i	0.586742	+	1.01627i	0.994656	+	0.103247i	$0.0329232\pi$
$461$	5807.63	+	10059.1i	0.586742	+	1.01627i	−0.407913	+	0.913021i	$0.633743\pi$
$462$		0			0
$463$	5426.15	−	9398.36i	0.544653	−	0.943367i	−0.453976	−	0.891014i	$-0.649995\pi$
$463$	5426.15	−	9398.36i	0.544653	−	0.943367i	0.998629	−	0.0523527i	$-0.0166720\pi$
$464$		0			0
$465$	24129.4	−	18440.1i	2.40640	−	1.83901i
$466$		0			0
$467$	3071.32	−	5319.68i	0.304333	−	0.527120i	−0.672780	−	0.739843i	$-0.734900\pi$
$467$	3071.32	−	5319.68i	0.304333	−	0.527120i	0.977113	+	0.212723i	$0.0682331\pi$
$468$		0			0
$469$	−5392.45	+	791.317i	−0.530917	+	0.0779097i
$470$		0			0
$471$	1853.91	+	14298.4i	0.181367	+	1.39880i
$472$		0			0
$473$		−	30924.2i		−	3.00612i
$474$		0			0
$475$	3566.87	−	2059.34i	0.344546	−	0.198924i
$476$		0			0
$477$	−12617.0	+	12518.5i	−1.21110	+	1.20164i
$478$		0			0
$479$	−7606.81	+	13175.4i	−0.725603	+	1.25678i	0.233122	+	0.972448i	$0.425106\pi$
$479$	−7606.81	+	13175.4i	−0.725603	+	1.25678i	−0.958725	+	0.284334i	$0.908227\pi$
$480$		0			0
$481$	2795.25	−	1613.84i	0.264974	−	0.152983i
$482$		0			0
$483$	−8338.46	+	8555.48i	−0.785534	+	0.805979i
$484$		0			0
$485$	7023.19	+	4054.84i	0.657540	+	0.379631i
$486$		0			0
$487$	−780.525	−	1351.91i	−0.0726262	−	0.125792i	0.827425	−	0.561576i	$-0.189805\pi$
$487$	−780.525	−	1351.91i	−0.0726262	−	0.125792i	−0.900052	+	0.435783i	$0.856471\pi$
$488$		0			0
$489$	2145.17	−	5150.33i	0.198381	−	0.476290i
$490$		0			0
$491$	5107.22	+	2948.66i	0.469421	+	0.271020i	0.715997	−	0.698103i	$-0.245972\pi$
$491$	5107.22	+	2948.66i	0.469421	+	0.271020i	−0.246576	+	0.969123i	$0.579306\pi$
$492$		0			0
$493$	−964.757	−	557.002i	−0.0881348	−	0.0508846i
$494$		0			0
$495$	−7007.83	−	26569.8i	−0.636320	−	2.41258i
$496$		0			0
$497$	−1619.76	−	11037.9i	−0.146190	−	0.996213i
$498$		0			0
$499$	5845.81	+	10125.2i	0.524438	+	0.908353i	0.999595	+	0.0284519i	$0.00905774\pi$
$499$	5845.81	+	10125.2i	0.524438	+	0.908353i	−0.475158	+	0.879901i	$0.657609\pi$
$500$		0			0
$501$	91.2336	−	219.042i	0.00813576	−	0.0195331i
$502$		0			0
$503$	2180.14			0.193255			0.0966277	−	0.995321i	$-0.469194\pi$
$503$	2180.14			0.193255			0.0966277	+	0.995321i	$0.469194\pi$
$504$		0			0
$505$	−20554.8			−1.81124
$506$		0			0
$507$	−12564.3	−	16440.7i	−1.10059	−	1.44016i
$508$		0			0
$509$	−797.527	−	1381.36i	−0.0694494	−	0.120290i	0.829210	−	0.558938i	$-0.188791\pi$
$509$	−797.527	−	1381.36i	−0.0694494	−	0.120290i	−0.898659	+	0.438648i	$0.855458\pi$
$510$		0			0
$511$	9085.15	−	7187.47i	0.786504	−	0.622221i
$512$		0			0
$513$	2689.93	+	370.243i	0.231508	+	0.0318648i
$514$		0			0
$515$	12969.0	+	7487.67i	1.10968	+	0.640672i
$516$		0			0
$517$	−7093.16	−	4095.24i	−0.603398	−	0.348372i
$518$		0			0
$519$	−4684.52	+	607.389i	−0.396200	+	0.0513707i
$520$		0			0
$521$	2974.63	+	5152.20i	0.250136	+	0.433248i	0.963563	−	0.267481i	$-0.0861914\pi$
$521$	2974.63	+	5152.20i	0.250136	+	0.433248i	−0.713427	+	0.700729i	$0.752858\pi$
$522$		0			0
$523$	12106.0	+	6989.39i	1.01216	+	0.584369i	0.911822	−	0.410585i	$-0.134675\pi$
$523$	12106.0	+	6989.39i	1.01216	+	0.584369i	0.100334	+	0.994954i	$0.468009\pi$
$524$		0			0
$525$	5045.90	−	19847.9i	0.419469	−	1.64997i
$526$		0			0
$527$	−5502.34	+	3176.78i	−0.454812	+	0.262586i
$528$		0			0
$529$	1622.26	−	2809.84i	0.133333	−	0.230939i
$530$		0			0
$531$	−14842.2	+	3914.64i	−1.21299	+	0.319927i
$532$		0			0
$533$	−7233.99	+	4176.55i	−0.587878	+	0.339412i
$534$		0			0
$535$			28034.1i			2.26546i
$536$		0			0
$537$	−14969.9	+	11440.3i	−1.20298	+	0.919338i
$538$		0			0
$539$	−18483.1	−	4370.37i	−1.47704	−	0.349249i
$540$		0			0
$541$	6174.78	−	10695.0i	0.490710	−	0.849935i	−0.509232	−	0.860629i	$-0.670071\pi$
$541$	6174.78	−	10695.0i	0.490710	−	0.849935i	0.999943	+	0.0106936i	$0.00340395\pi$
$542$		0			0
$543$	1108.54	+	8549.69i	0.0876097	+	0.675695i
$544$		0			0
$545$	−1864.26	+	3229.00i	−0.146525	+	0.253789i
$546$		0			0
$547$	8771.44	+	15192.6i	0.685630	+	1.18755i	0.973238	+	0.229798i	$0.0738064\pi$
$547$	8771.44	+	15192.6i	0.685630	+	1.18755i	−0.287609	+	0.957748i	$0.592860\pi$
$548$		0			0
$549$	−970.564	−	3679.85i	−0.0754511	−	0.286069i
$550$		0			0
$551$	1079.08			0.0834307
$552$		0			0
$553$	−9785.82	+	1436.03i	−0.752506	+	0.110427i
$554$		0			0
$555$	−3888.85	+	504.223i	−0.297428	+	0.0385641i
$556$		0			0
$557$	19166.8	−	11065.9i	1.45803	−	0.841794i	0.459116	−	0.888376i	$-0.348166\pi$
$557$	19166.8	−	11065.9i	1.45803	−	0.841794i	0.998914	+	0.0465824i	$0.0148330\pi$
$558$		0			0
$559$			43900.6i			3.32164i
$560$		0			0
$561$	739.200	+	5701.12i	0.0556311	+	0.429058i
$562$		0			0
$563$	9616.20			0.719848			0.359924	−	0.932982i	$-0.382803\pi$
$563$	9616.20			0.719848			0.359924	+	0.932982i	$0.382803\pi$
$564$		0			0
$565$		−	1596.17i		−	0.118852i
$566$		0			0
$567$	10653.8	−	8293.45i	0.789095	−	0.614272i
$568$		0			0
$569$		−	11413.1i		−	0.840881i	−0.907320	−	0.420441i	$-0.861875\pi$
$569$		−	11413.1i		−	0.840881i	0.907320	−	0.420441i	$-0.138125\pi$
$570$		0			0
$571$	−19183.8			−1.40599			−0.702993	−	0.711197i	$-0.748153\pi$
$571$	−19183.8			−1.40599			−0.702993	+	0.711197i	$0.748153\pi$
$572$		0			0
$573$	−1029.14	−	7937.30i	−0.0750312	−	0.578683i
$574$		0			0
$575$			26418.5i			1.91605i
$576$		0			0
$577$	9697.32	−	5598.75i	0.699661	−	0.403950i	−0.107560	−	0.994199i	$-0.534304\pi$
$577$	9697.32	−	5598.75i	0.699661	−	0.403950i	0.807221	+	0.590249i	$0.200970\pi$
$578$		0			0
$579$	14944.2	−	1937.65i	1.07264	−	0.139078i
$580$		0			0
$581$	−8098.98	−	10237.3i	−0.578317	−	0.731008i
$582$		0			0
$583$	36450.8			2.58943
$584$		0			0
$585$	9948.43	+	37719.0i	0.703106	+	2.66579i
$586$		0			0
$587$	−5285.80	−	9155.27i	−0.371666	−	0.643745i	0.618156	−	0.786056i	$-0.287880\pi$
$587$	−5285.80	−	9155.27i	−0.371666	−	0.643745i	−0.989822	+	0.142311i	$0.954547\pi$
$588$		0			0
$589$	3077.18	−	5329.84i	0.215268	−	0.372856i
$590$		0			0
$591$	−1400.97	−	10805.1i	−0.0975100	−	0.752052i
$592$		0			0
$593$	−7667.36	+	13280.3i	−0.530963	+	0.919655i	0.468384	+	0.883525i	$0.344836\pi$
$593$	−7667.36	+	13280.3i	−0.530963	+	0.919655i	−0.999347	+	0.0361297i	$0.988497\pi$
$594$		0			0
$595$	−2509.40	+	6321.34i	−0.172900	+	0.435546i
$596$		0			0
$597$	−18772.5	+	14346.2i	−1.28694	+	0.983505i
$598$		0			0
$599$		−	8922.83i		−	0.608643i	−0.952569	−	0.304321i	$-0.901570\pi$
$599$		−	8922.83i		−	0.608643i	0.952569	−	0.304321i	$-0.0984297\pi$
$600$		0			0
$601$	6221.25	−	3591.84i	0.422246	−	0.243784i	−0.273792	−	0.961789i	$-0.588278\pi$
$601$	6221.25	−	3591.84i	0.422246	−	0.243784i	0.696038	+	0.718005i	$0.254945\pi$
$602$		0			0
$603$	−7682.91	+	2026.38i	−0.518859	+	0.136850i
$604$		0			0
$605$	−15945.3	+	27618.0i	−1.07152	+	1.85592i
$606$		0			0
$607$	−4773.64	+	2756.06i	−0.319203	+	0.184292i	−0.651037	−	0.759046i	$-0.725666\pi$
$607$	−4773.64	+	2756.06i	−0.319203	+	0.184292i	0.331834	+	0.943338i	$0.392332\pi$
$608$		0			0
$609$	3744.94	−	3842.41i	0.249184	−	0.255669i
$610$		0			0
$611$	10069.6	+	5813.67i	0.666729	+	0.384936i
$612$		0			0
$613$	−12611.1	−	21843.0i	−0.830925	−	1.43920i	−0.897306	−	0.441410i	$-0.854478\pi$
$613$	−12611.1	−	21843.0i	−0.830925	−	1.43920i	0.0663806	−	0.997794i	$-0.478855\pi$
$614$		0			0
$615$	10064.2	−	1304.91i	0.659881	−	0.0855592i
$616$		0			0
$617$	22013.2	+	12709.3i	1.43633	+	0.829268i	0.997593	−	0.0693457i	$-0.0220912\pi$
$617$	22013.2	+	12709.3i	1.43633	+	0.829268i	0.438741	+	0.898613i	$0.355424\pi$
$618$		0			0
$619$	9378.16	+	5414.48i	0.608950	+	0.351577i	0.772554	−	0.634949i	$-0.218979\pi$
$619$	9378.16	+	5414.48i	0.608950	+	0.351577i	−0.163604	+	0.986526i	$0.552312\pi$
$620$		0			0
$621$	−10683.8	+	13755.1i	−0.690377	+	0.888844i
$622$		0			0
$623$	−528.391	+	1331.05i	−0.0339800	+	0.0855980i
$624$		0			0
$625$	−1530.49	−	2650.89i	−0.0979515	−	0.169657i
$626$		0			0
$627$	−3381.29	−	4424.51i	−0.215368	−	0.281815i
$628$		0			0
$629$	820.408			0.0520061
$630$		0			0
$631$	25750.8			1.62460			0.812301	−	0.583239i	$-0.198215\pi$
$631$	25750.8			1.62460			0.812301	+	0.583239i	$0.198215\pi$
$632$		0			0
$633$	−6018.93	+	14450.8i	−0.377932	+	0.907373i
$634$		0			0
$635$	−4472.74	−	7747.02i	−0.279520	−	0.484143i
$636$		0			0
$637$	26238.9	+	6204.25i	1.63206	+	0.385905i
$638$		0			0
$639$	−4147.83	−	15726.3i	−0.256785	−	0.973587i
$640$		0			0
$641$	−6561.40	−	3788.22i	−0.404305	−	0.233426i	0.284035	−	0.958814i	$-0.408327\pi$
$641$	−6561.40	−	3788.22i	−0.404305	−	0.233426i	−0.688340	+	0.725388i	$0.741660\pi$
$642$		0			0
$643$	−15581.8	−	8996.16i	−0.955655	−	0.551748i	−0.0608220	−	0.998149i	$-0.519372\pi$
$643$	−15581.8	−	8996.16i	−0.955655	−	0.551748i	−0.894833	+	0.446401i	$0.852706\pi$
$644$		0			0
$645$	20507.4	−	49236.0i	1.25190	−	3.00568i
$646$		0			0
$647$	−8457.22	−	14648.3i	−0.513891	−	0.890086i	−0.999870	−	0.0161153i	$-0.994870\pi$
$647$	−8457.22	−	14648.3i	−0.513891	−	0.890086i	0.485979	−	0.873971i	$-0.338463\pi$
$648$		0			0
$649$	27262.3	+	15739.9i	1.64890	+	0.951995i
$650$		0			0
$651$	−8299.25	−	29454.5i	−0.499652	−	1.77329i
$652$		0			0
$653$	−15111.6	+	8724.69i	−0.905609	+	0.522854i	−0.879016	−	0.476792i	$-0.841799\pi$
$653$	−15111.6	+	8724.69i	−0.905609	+	0.522854i	−0.0265935	+	0.999646i	$0.508466\pi$
$654$		0			0
$655$	−7369.78	+	12764.8i	−0.439635	+	0.761471i
$656$		0			0
$657$	11988.7	−	11895.1i	0.711911	−	0.706350i
$658$		0			0
$659$	−1730.83	+	999.298i	−0.102312	+	0.0590700i	−0.550283	−	0.834978i	$-0.685480\pi$
$659$	−1730.83	+	999.298i	−0.102312	+	0.0590700i	0.447971	+	0.894048i	$0.352147\pi$
$660$		0			0
$661$			33493.6i			1.97088i	0.170023	+	0.985440i	$0.445616\pi$
$661$			33493.6i			1.97088i	−0.170023	+	0.985440i	$0.554384\pi$
$662$		0			0
$663$	−1049.38	−	8093.42i	−0.0614700	−	0.474091i
$664$		0			0
$665$	−956.513	−	6518.17i	−0.0557774	−	0.380096i
$666$		0			0
$667$	−3460.79	+	5994.26i	−0.200903	+	0.347974i
$668$		0			0
$669$	−1097.29	+	838.571i	−0.0634139	+	0.0484620i
$670$		0			0
$671$	−3902.42	+	6759.18i	−0.224517	+	0.388875i
$672$		0			0
$673$	−16342.6	−	28306.3i	−0.936051	−	1.62129i	−0.772749	−	0.634712i	$-0.781119\pi$
$673$	−16342.6	−	28306.3i	−0.936051	−	1.62129i	−0.163303	−	0.986576i	$-0.552215\pi$
$674$		0			0
$675$	4071.01	−	29577.2i	0.232138	−	1.68656i
$676$		0			0
$677$	−7327.73			−0.415993			−0.207997	−	0.978130i	$-0.566694\pi$
$677$	−7327.73			−0.415993			−0.207997	+	0.978130i	$0.566694\pi$
$678$		0			0
$679$	6408.75	−	5070.10i	0.362217	−	0.286558i
$680$		0			0
$681$	2315.24	−	5558.64i	0.130279	−	0.312787i
$682$		0			0
$683$	−12311.2	+	7107.88i	−0.689715	+	0.398207i	−0.803505	−	0.595298i	$-0.797034\pi$
$683$	−12311.2	+	7107.88i	−0.689715	+	0.398207i	0.113790	+	0.993505i	$0.463701\pi$
$684$		0			0
$685$			16887.7i			0.941962i
$686$		0			0
$687$	−4718.36	+	3605.85i	−0.262033	+	0.200250i
$688$		0			0
$689$	−51746.1			−2.86121
$690$		0			0
$691$		−	14322.3i		−	0.788492i	−0.919005	−	0.394246i	$-0.871006\pi$
$691$		−	14322.3i		−	0.788492i	0.919005	−	0.394246i	$-0.128994\pi$
$692$		0			0
$693$	−27489.7	−	3315.10i	−1.50685	−	0.181717i
$694$		0			0
$695$		−	3390.10i		−	0.185027i
$696$		0			0
$697$	−2123.18			−0.115382
$698$		0			0
$699$	27379.2	+	11403.8i	1.48151	+	0.617067i
$700$		0			0
$701$		−	3371.89i		−	0.181675i	−0.995866	−	0.0908377i	$-0.971046\pi$
$701$		−	3371.89i		−	0.181675i	0.995866	−	0.0908377i	$-0.0289544\pi$
$702$		0			0
$703$	−688.219	+	397.344i	−0.0369227	+	0.0213173i
$704$		0			0
$705$	−8577.61	−	11224.1i	−0.458229	−	0.599606i
$706$		0			0
$707$	−7642.04	+	19250.8i	−0.406518	+	1.02405i
$708$		0			0
$709$	−30716.8			−1.62707			−0.813537	−	0.581514i	$-0.802461\pi$
$709$	−30716.8			−1.62707			−0.813537	+	0.581514i	$0.802461\pi$
$710$		0			0
$711$	−13942.4	+	3677.32i	−0.735415	+	0.193967i
$712$		0			0
$713$	19738.1	+	34187.4i	1.03674	+	1.79569i
$714$		0			0
$715$	40000.4	−	69282.7i	2.09221	−	3.62381i
$716$		0			0
$717$	−1721.69	−	717.104i	−0.0896759	−	0.0373511i
$718$		0			0
$719$	5218.17	−	9038.14i	0.270661	−	0.468798i	−0.698371	−	0.715736i	$-0.746091\pi$
$719$	5218.17	−	9038.14i	0.270661	−	0.468798i	0.969031	+	0.246939i	$0.0794246\pi$
$720$		0			0
$721$	11834.4	−	9362.45i	0.611284	−	0.483600i
$722$		0			0
$723$	−21296.5	−	8870.27i	−1.09547	−	0.456278i
$724$		0			0
$725$		−	11865.0i		−	0.607801i
$726$		0			0
$727$	22053.0	−	12732.3i	1.12503	−	0.649538i	0.182352	−	0.983233i	$-0.441629\pi$
$727$	22053.0	−	12732.3i	1.12503	−	0.649538i	0.942681	+	0.333696i	$0.108296\pi$
$728$		0			0
$729$	14080.7	−	13753.3i	0.715375	−	0.698741i
$730$		0			0
$731$	−5579.30	+	9663.62i	−0.282295	+	0.488949i
$732$		0			0
$733$	−8899.02	+	5137.85i	−0.448421	+	0.258896i	−0.707163	−	0.707050i	$-0.750025\pi$
$733$	−8899.02	+	5137.85i	−0.448421	+	0.258896i	0.258742	+	0.965947i	$0.416692\pi$
$734$		0			0
$735$	−26529.7	−	19215.3i	−1.33138	−	0.964311i
$736$		0			0
$737$	14112.1	+	8147.60i	0.705324	+	0.407219i
$738$		0			0
$739$	−8232.96	−	14259.9i	−0.409816	−	0.709823i	0.585053	−	0.810995i	$-0.301074\pi$
$739$	−8232.96	−	14259.9i	−0.409816	−	0.709823i	−0.994869	+	0.101173i	$0.967741\pi$
$740$		0			0
$741$	4800.14	+	6281.12i	0.237972	+	0.311394i
$742$		0			0
$743$	−34426.3	−	19876.0i	−1.69984	−	0.981400i	−0.945904	−	0.324448i	$-0.894822\pi$
$743$	−34426.3	−	19876.0i	−1.69984	−	0.981400i	−0.753932	−	0.656953i	$-0.771845\pi$
$744$		0			0
$745$	35665.9	+	20591.7i	1.75396	+	1.01265i
$746$		0			0
$747$	−13403.6	−	13509.1i	−0.656510	−	0.661678i
$748$		0			0
$749$	26255.7	+	10422.8i	1.28086	+	0.508464i
$750$		0			0
$751$	−9238.85	−	16002.2i	−0.448909	−	0.777533i	0.549406	−	0.835555i	$-0.314854\pi$
$751$	−9238.85	−	16002.2i	−0.448909	−	0.777533i	−0.998315	+	0.0580222i	$0.981521\pi$
$752$		0			0
$753$	17720.6	−	2297.63i	0.857604	−	0.111196i
$754$		0			0
$755$	39131.9			1.88630
$756$		0			0
$757$	14830.5			0.712053			0.356026	−	0.934476i	$-0.384131\pi$
$757$	14830.5			0.712053			0.356026	+	0.934476i	$0.384131\pi$
$758$		0			0
$759$	35422.4	−	4592.83i	1.69401	−	0.219643i
$760$		0			0
$761$	−2987.19	−	5173.96i	−0.142294	−	0.246460i	0.786066	−	0.618142i	$-0.212114\pi$
$761$	−2987.19	−	5173.96i	−0.142294	−	0.246460i	−0.928360	+	0.371682i	$0.878781\pi$
$762$		0			0
$763$	2331.04	+	2946.50i	0.110602	+	0.139804i
$764$		0			0
$765$	−2603.78	+	9567.24i	−0.123059	+	0.452163i
$766$		0			0
$767$	−38702.0	−	22344.6i	−1.82197	−	1.05191i
$768$		0			0
$769$	−16782.8	−	9689.54i	−0.786999	−	0.454374i	0.0519057	−	0.998652i	$-0.483470\pi$
$769$	−16782.8	−	9689.54i	−0.786999	−	0.454374i	−0.838905	+	0.544278i	$0.816804\pi$
$770$		0			0
$771$	5747.60	+	7520.91i	0.268476	+	0.351308i
$772$		0			0
$773$	−8932.67	−	15471.8i	−0.415635	−	0.719900i	0.579860	−	0.814716i	$-0.303107\pi$
$773$	−8932.67	−	15471.8i	−0.415635	−	0.719900i	−0.995495	+	0.0948156i	$0.969774\pi$
$774$		0			0
$775$	−58604.3	−	33835.2i	−2.71629	−	1.56825i
$776$		0			0
$777$	−973.594	+	3829.61i	−0.0449517	+	0.176817i
$778$		0			0
$779$	1781.08	−	1028.31i	0.0819176	−	0.0472952i
$780$		0			0
$781$	−16677.5	+	28886.2i	−0.764106	+	1.32347i
$782$		0			0
$783$	4798.26	−	6177.64i	0.218998	−	0.281955i
$784$		0			0
$785$	44166.3	−	25499.5i	2.00811	−	1.15938i
$786$		0			0
$787$			12028.3i			0.544806i	0.962183	+	0.272403i	$0.0878184\pi$
$787$			12028.3i			0.544806i	−0.962183	+	0.272403i	$0.912182\pi$
$788$		0			0
$789$	20353.2	+	8477.35i	0.918369	+	0.382512i
$790$		0			0
$791$	−1494.91	−	593.438i	−0.0671972	−	0.0266754i
$792$		0			0
$793$	5539.94	−	9595.45i	0.248082	−	0.429691i
$794$		0			0
$795$	58035.1	+	24172.3i	2.58905	+	1.07837i
$796$		0			0
$797$	−13117.1	+	22719.5i	−0.582976	+	1.00974i	0.412149	+	0.911117i	$0.364778\pi$
$797$	−13117.1	+	22719.5i	−0.582976	+	1.00974i	−0.995124	+	0.0986270i	$0.968555\pi$
$798$		0			0
$799$	1477.71	+	2559.47i	0.0654289	+	0.113326i
$800$		0			0
$801$	−548.265	+	2014.53i	−0.0241848	+	0.0888637i
$802$		0			0
$803$	−34635.6			−1.52212
$804$		0			0
$805$	39276.0	+	15591.5i	1.71962	+	0.682643i
$806$		0			0
$807$	9709.70	+	12705.4i	0.423541	+	0.554216i
$808$		0			0
$809$	24743.3	−	14285.5i	1.07531	−	0.620832i	0.145684	−	0.989331i	$-0.453462\pi$
$809$	24743.3	−	14285.5i	1.07531	−	0.620832i	0.929628	+	0.368499i	$0.120128\pi$
$810$		0			0
$811$		−	36790.7i		−	1.59297i	−0.604661	−	0.796483i	$-0.706692\pi$
$811$		−	36790.7i		−	1.59297i	0.604661	−	0.796483i	$-0.293308\pi$
$812$		0			0
$813$	3450.72	+	1437.27i	0.148859	+	0.0620014i
$814$		0			0
$815$	−19734.5			−0.848183
$816$		0			0
$817$		−	10808.8i		−	0.462852i
$818$		0			0
$819$	39024.8	+	4706.17i	1.66500	+	0.200790i
$820$		0			0
$821$		−	27440.8i		−	1.16649i	−0.812295	−	0.583246i	$-0.801782\pi$
$821$		−	27440.8i		−	1.16649i	0.812295	−	0.583246i	$-0.198218\pi$
$822$		0			0
$823$	−29435.0			−1.24671			−0.623354	−	0.781940i	$-0.714230\pi$
$823$	−29435.0			−1.24671			−0.623354	+	0.781940i	$0.714230\pi$
$824$		0			0
$825$	−48649.8	+	37179.0i	−2.05305	+	1.56898i
$826$		0			0
$827$		−	9108.48i		−	0.382990i	−0.981494	−	0.191495i	$-0.938666\pi$
$827$		−	9108.48i		−	0.382990i	0.981494	−	0.191495i	$-0.0613336\pi$
$828$		0			0
$829$	745.006	−	430.129i	0.0312124	−	0.0180205i	−0.484313	−	0.874895i	$-0.660930\pi$
$829$	745.006	−	430.129i	0.0312124	−	0.0180205i	0.515525	+	0.856875i	$0.327597\pi$
$830$		0			0
$831$	−1820.44	+	4370.66i	−0.0759930	+	0.182451i
$832$		0			0
$833$	4987.36	+	4700.40i	0.207445	+	0.195509i
$834$		0			0
$835$	−839.301			−0.0347847
$836$		0			0
$837$	−16829.8	−	41316.4i	−0.695011	−	1.70622i
$838$		0			0
$839$	13869.3	+	24022.3i	0.570704	+	0.988488i	0.996494	+	0.0836658i	$0.0266628\pi$
$839$	13869.3	+	24022.3i	0.570704	+	0.988488i	−0.425790	+	0.904822i	$0.640004\pi$
$840$		0			0
$841$	−10640.2	+	18429.4i	−0.436270	+	0.755643i
$842$		0			0
$843$	−19747.0	+	15091.0i	−0.806790	+	0.616563i
$844$		0			0
$845$	−36595.3	+	63384.9i	−1.48984	+	2.58048i
$846$		0			0
$847$	19937.7	+	25201.8i	0.808816	+	1.02237i
$848$		0			0
$849$	−2678.31	−	20656.7i	−0.108268	−	0.835023i
$850$		0			0
$851$		−	5097.39i		−	0.205331i
$852$		0			0
$853$	−13605.1	+	7854.94i	−0.546109	+	0.315296i	−0.747551	−	0.664204i	$-0.768771\pi$
$853$	−13605.1	+	7854.94i	−0.546109	+	0.315296i	0.201442	+	0.979500i	$0.435437\pi$
$854$		0			0
$855$	−2449.40	−	9286.79i	−0.0979740	−	0.371464i
$856$		0			0
$857$	20532.6	−	35563.5i	0.818414	−	1.41754i	−0.0884360	−	0.996082i	$-0.528187\pi$
$857$	20532.6	−	35563.5i	0.818414	−	1.41754i	0.906850	−	0.421453i	$-0.138480\pi$
$858$		0			0
$859$	−3324.84	+	1919.60i	−0.132063	+	0.0762466i	−0.564576	−	0.825381i	$-0.690960\pi$
$859$	−3324.84	+	1919.60i	−0.132063	+	0.0762466i	0.432513	+	0.901628i	$0.357627\pi$
$860$		0			0
$861$	2519.62	−	9910.86i	0.0997309	−	0.392289i
$862$		0			0
$863$	24681.4	+	14249.8i	0.973540	+	0.562074i	0.900314	−	0.435242i	$-0.143337\pi$
$863$	24681.4	+	14249.8i	0.973540	+	0.562074i	0.0732263	+	0.997315i	$0.476670\pi$
$864$		0			0
$865$	8354.26	+	14470.0i	0.328385	+	0.568780i
$866$		0			0
$867$	−9018.04	+	21651.3i	−0.353251	+	0.848117i
$868$		0			0
$869$	25609.5	+	14785.7i	0.999705	+	0.577180i
$870$		0			0
$871$	−20033.7	−	11566.5i	−0.779353	−	0.449960i
$872$		0			0
$873$	8456.96	−	8390.91i	0.327864	−	0.325303i
$874$		0			0
$875$	−29572.3	+	4339.60i	−1.14254	+	0.167663i
$876$		0			0
$877$	2004.33	+	3471.60i	0.0771737	+	0.133669i	0.902029	−	0.431674i	$-0.142077\pi$
$877$	2004.33	+	3471.60i	0.0771737	+	0.133669i	−0.824856	+	0.565343i	$0.808744\pi$
$878$		0			0
$879$	−15019.5	+	36060.2i	−0.576332	+	1.38371i
$880$		0			0
$881$	−20416.0			−0.780742			−0.390371	−	0.920658i	$-0.627653\pi$
$881$	−20416.0			−0.780742			−0.390371	+	0.920658i	$0.627653\pi$
$882$		0			0
$883$	16822.4			0.641133			0.320566	−	0.947226i	$-0.396127\pi$
$883$	16822.4			0.641133			0.320566	+	0.947226i	$0.396127\pi$
$884$		0			0
$885$	32967.7	+	43139.2i	1.25220	+	1.63854i
$886$		0			0
$887$	15727.6	+	27241.1i	0.595358	+	1.03119i	0.993496	+	0.113865i	$0.0363231\pi$
$887$	15727.6	+	27241.1i	0.595358	+	1.03119i	−0.398138	+	0.917325i	$0.630344\pi$
$888$		0			0
$889$	−8918.46	+	1308.74i	−0.336463	+	0.0493744i
$890$		0			0
$891$	−40365.3	−	316.533i	−1.51772	−	0.0119015i
$892$		0			0
$893$	−2479.23	−	1431.38i	−0.0929051	−	0.0536388i
$894$		0			0
$895$	57714.4	+	33321.4i	2.15551	+	1.24448i
$896$		0			0
$897$	−50286.3	+	6520.06i	−1.87181	+	0.242696i
$898$		0			0
$899$	−8864.71	−	15354.1i	−0.328871	−	0.569621i
$900$		0			0
$901$	−11390.6	−	6576.38i	−0.421173	−	0.243164i
$902$		0			0
$903$	−38488.1	−	37511.8i	−1.41839	−	1.38241i
$904$		0			0
$905$	26409.1	−	15247.3i	0.970021	−	0.560042i
$906$		0			0
$907$	108.041	−	187.133i	0.00395529	−	0.00685076i	−0.864041	−	0.503421i	$-0.832074\pi$
$907$	108.041	−	187.133i	0.00395529	−	0.00685076i	0.867996	+	0.496571i	$0.165408\pi$
$908$		0			0
$909$	−7929.48	+	29135.8i	−0.289333	+	1.06312i
$910$		0			0
$911$	9169.28	−	5293.88i	0.333471	−	0.192529i	−0.323910	−	0.946088i	$-0.604998\pi$
$911$	9169.28	−	5293.88i	0.333471	−	0.192529i	0.657381	+	0.753558i	$0.271664\pi$
$912$		0			0
$913$			39028.1i			1.41472i
$914$		0			0
$915$	−10695.6	+	8173.74i	−0.386432	+	0.295318i
$916$		0			0
$917$	9215.04	+	11648.1i	0.331851	+	0.419469i
$918$		0			0
$919$	−14001.8	+	24251.8i	−0.502586	+	0.870504i	0.497410	+	0.867516i	$0.334285\pi$
$919$	−14001.8	+	24251.8i	−0.502586	+	0.870504i	−0.999996	+	0.00298831i	$0.999049\pi$
$920$		0			0
$921$	−4108.89	−	31690.0i	−0.147006	−	1.13379i
$922$		0			0
$923$	23675.6	−	41007.4i	0.844304	−	1.46238i
$924$		0			0
$925$	4368.99	+	7567.32i	0.155299	+	0.268986i
$926$		0			0
$927$	15616.6	−	15494.6i	0.553309	−	0.548987i
$928$		0			0
$929$	27296.5			0.964013			0.482007	−	0.876168i	$-0.339908\pi$
$929$	27296.5			0.964013			0.482007	+	0.876168i	$0.339908\pi$
$930$		0			0
$931$	−6460.29	−	1527.55i	−0.227419	−	0.0537738i
$932$		0			0
$933$	−10921.0	+	1416.00i	−0.383213	+	0.0496869i
$934$		0			0
$935$	17610.2	−	10167.2i	0.615951	−	0.355620i
$936$		0			0
$937$			6443.03i			0.224637i	0.993672	+	0.112318i	$0.0358277\pi$
$937$			6443.03i			0.224637i	−0.993672	+	0.112318i	$0.964172\pi$
$938$		0			0
$939$	97.3864	+	751.098i	0.00338454	+	0.0261035i
$940$		0			0
$941$	−35678.2			−1.23600			−0.617999	−	0.786179i	$-0.712057\pi$
$941$	−35678.2			−1.23600			−0.617999	+	0.786179i	$0.712057\pi$
$942$		0			0
$943$			13191.8i			0.455551i
$944$		0			0
$945$	−41569.3	−	23507.9i	−1.43095	−	0.809219i
$946$		0			0
$947$			5139.71i			0.176366i	0.996104	+	0.0881828i	$0.0281060\pi$
$947$			5139.71i			0.176366i	−0.996104	+	0.0881828i	$0.971894\pi$
$948$		0			0
$949$	49169.3			1.68188
$950$		0			0
$951$	1741.93	+	13434.7i	0.0593962	+	0.458097i
$952$		0			0
$953$			12018.0i			0.408502i	0.978919	+	0.204251i	$0.0654758\pi$
$953$			12018.0i			0.408502i	−0.978919	+	0.204251i	$0.934524\pi$
$954$		0			0
$955$	−24517.5	+	14155.2i	−0.830751	+	0.479634i
$956$		0			0
$957$	−15908.8	+	2062.72i	−0.537366	+	0.0696742i
$958$		0			0
$959$	15816.3	+	6278.63i	0.532571	+	0.211416i
$960$		0			0
$961$	−71326.1			−2.39422
$962$		0			0
$963$	39737.5	+	10814.8i	1.32972	+	0.361892i
$964$		0			0
$965$	−26651.2	−	46161.2i	−0.889048	−	1.53988i
$966$		0			0
$967$	7474.18	−	12945.7i	0.248556	−	0.430511i	−0.714570	−	0.699564i	$-0.753377\pi$
$967$	7474.18	−	12945.7i	0.248556	−	0.430511i	0.963125	+	0.269053i	$0.0867108\pi$
$968$		0			0
$969$	258.368	+	1992.68i	0.00856551	+	0.0660620i
$970$		0			0
$971$	−21188.3	+	36699.3i	−0.700274	+	1.21291i	0.268096	+	0.963392i	$0.413605\pi$
$971$	−21188.3	+	36699.3i	−0.700274	+	1.21291i	−0.968370	+	0.249518i	$0.919728\pi$
$972$		0			0
$973$	−3175.03	−	1260.40i	−0.104611	−	0.0415278i
$974$		0			0
$975$	69064.1	−	52779.9i	2.26853	−	1.73365i
$976$		0			0
$977$			15836.9i			0.518594i	0.965798	+	0.259297i	$0.0834909\pi$
$977$			15836.9i			0.518594i	−0.965798	+	0.259297i	$0.916509\pi$
$978$		0			0
$979$	3708.09	−	2140.87i	0.121053	−	0.0698901i
$980$		0			0
$981$	3857.82	+	3888.19i	0.125556	+	0.126545i
$982$		0			0
$983$	7127.39	−	12345.0i	0.231260	−	0.400554i	−0.726919	−	0.686723i	$-0.759049\pi$
$983$	7127.39	−	12345.0i	0.231260	−	0.400554i	0.958179	+	0.286169i	$0.0923820\pi$
$984$		0			0
$985$	−33375.8	+	19269.6i	−1.07964	+	0.623329i
$986$		0			0
$987$	−13701.1	+	3860.48i	−0.441854	+	0.124499i
$988$		0			0
$989$	60042.4	+	34665.5i	1.93047	+	1.11456i
$990$		0			0
$991$	1262.03	+	2185.91i	0.0404539	+	0.0700682i	0.885543	−	0.464557i	$-0.153786\pi$
$991$	1262.03	+	2185.91i	0.0404539	+	0.0700682i	−0.845090	+	0.534625i	$0.820453\pi$
$992$		0			0
$993$	56116.5	−	7275.99i	1.79336	−	0.232524i
$994$		0			0
$995$	72374.5	+	41785.5i	2.30596	+	1.33134i
$996$		0			0
$997$	43322.6	+	25012.3i	1.37617	+	0.794531i	0.991696	−	0.128606i	$-0.0410503\pi$
$997$	43322.6	+	25012.3i	1.37617	+	0.794531i	0.384472	+	0.923137i	$0.374384\pi$
$998$		0			0
$999$	−785.491	+	5706.84i	−0.0248767	+	0.180737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.2	✓	48
3.2	odd	2		756.4.w.a.341.2		48
7.3	odd	6		252.4.bm.a.185.7	yes	48
9.2	odd	6		252.4.bm.a.173.7	yes	48
9.7	even	3		756.4.bm.a.89.2		48
21.17	even	6		756.4.bm.a.17.2		48
63.38	even	6	inner	252.4.w.a.101.2	yes	48
63.52	odd	6		756.4.w.a.521.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.2	✓	48	1.1	even	1	trivial
252.4.w.a.101.2	yes	48	63.38	even	6	inner
252.4.bm.a.173.7	yes	48	9.2	odd	6
252.4.bm.a.185.7	yes	48	7.3	odd	6
756.4.w.a.341.2		48	3.2	odd	2
756.4.w.a.521.2		48	63.52	odd	6
756.4.bm.a.17.2		48	21.17	even	6
756.4.bm.a.89.2		48	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.15302 + 0.668133i) q^{3} +(9.18977 + 15.9171i) q^{5} +(18.3240 - 2.68897i) q^{7} +(26.1072 - 6.88581i) q^{9} +O(q^{10})\)	\(q+(-5.15302 + 0.668133i) q^{3} +(9.18977 + 15.9171i) q^{5} +(18.3240 - 2.68897i) q^{7} +(26.1072 - 6.88581i) q^{9} +(-47.9540 - 27.6862i) q^{11} +(68.0763 + 39.3039i) q^{13} +(-57.9898 - 75.8813i) q^{15} +(9.99021 + 17.3036i) q^{17} +(-16.7611 - 9.67700i) q^{19} +(-92.6274 + 26.0992i) q^{21} +(107.511 - 62.0716i) q^{23} +(-106.404 + 184.296i) q^{25} +(-129.930 + 52.9258i) q^{27} +(-48.2851 + 27.8774i) q^{29} +317.989i q^{31} +(265.606 + 110.628i) q^{33} +(211.194 + 266.955i) q^{35} +(20.5303 - 35.5595i) q^{37} +(-377.059 - 157.050i) q^{39} +(-53.1315 + 92.0264i) q^{41} +(279.238 + 483.655i) q^{43} +(349.521 + 352.273i) q^{45} +147.916 q^{47} +(328.539 - 98.5453i) q^{49} +(-63.0408 - 82.4907i) q^{51} +(-570.090 + 329.141i) q^{53} -1017.72i q^{55} +(92.8356 + 38.6672i) q^{57} -568.509 q^{59} -140.951i q^{61} +(459.873 - 196.377i) q^{63} +1444.77i q^{65} -294.283 q^{67} +(-512.535 + 391.688i) q^{69} -602.374i q^{71} +(541.701 - 312.751i) q^{73} +(425.165 - 1020.77i) q^{75} +(-953.157 - 378.377i) q^{77} -534.044 q^{79} +(634.171 - 359.538i) q^{81} +(-352.414 - 610.399i) q^{83} +(-183.615 + 318.031i) q^{85} +(230.188 - 175.914i) q^{87} +(-38.6630 + 66.9663i) q^{89} +(1353.12 + 537.150i) q^{91} +(-212.459 - 1638.60i) q^{93} -355.718i q^{95} +(382.120 - 220.617i) q^{97} +(-1442.59 - 392.608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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