LMFDB - Embedded newform 504.3.g.d.379.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(379,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.379"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.24
Character	$\chi$	$=$	504.379
Dual form			504.3.g.d.379.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.98610 + 0.235345i) q^{2} +(3.88923 + 0.934838i) q^{4} +7.47825i q^{5} -2.64575i q^{7} +(7.50440 + 2.77200i) q^{8} +(-1.75997 + 14.8526i) q^{10} +13.5056 q^{11} -3.54193i q^{13} +(0.622663 - 5.25474i) q^{14} +(14.2522 + 7.27159i) q^{16} -7.84106 q^{17} -11.1174 q^{19} +(-6.99095 + 29.0846i) q^{20} +(26.8235 + 3.17846i) q^{22} +22.3804i q^{23} -30.9242 q^{25} +(0.833575 - 7.03465i) q^{26} +(2.47335 - 10.2899i) q^{28} +52.0985i q^{29} +15.6772i q^{31} +(26.5949 + 17.7963i) q^{32} +(-15.5732 - 1.84535i) q^{34} +19.7856 q^{35} -22.1574i q^{37} +(-22.0803 - 2.61642i) q^{38} +(-20.7297 + 56.1198i) q^{40} -36.1220 q^{41} +81.8151 q^{43} +(52.5262 + 12.6255i) q^{44} +(-5.26710 + 44.4498i) q^{46} -66.3024i q^{47} -7.00000 q^{49} +(-61.4187 - 7.27785i) q^{50} +(3.31113 - 13.7754i) q^{52} -83.6865i q^{53} +100.998i q^{55} +(7.33401 - 19.8548i) q^{56} +(-12.2611 + 103.473i) q^{58} -47.7464 q^{59} -102.992i q^{61} +(-3.68954 + 31.1365i) q^{62} +(48.6321 + 41.6043i) q^{64} +26.4874 q^{65} -10.1586 q^{67} +(-30.4957 - 7.33013i) q^{68} +(39.2963 + 4.65643i) q^{70} -71.0621i q^{71} +42.8065 q^{73} +(5.21463 - 44.0069i) q^{74} +(-43.2381 - 10.3930i) q^{76} -35.7324i q^{77} +10.3881i q^{79} +(-54.3788 + 106.581i) q^{80} +(-71.7420 - 8.50111i) q^{82} +103.602 q^{83} -58.6374i q^{85} +(162.493 + 19.2547i) q^{86} +(101.351 + 37.4374i) q^{88} +60.9498 q^{89} -9.37107 q^{91} +(-20.9220 + 87.0424i) q^{92} +(15.6039 - 131.684i) q^{94} -83.1387i q^{95} +52.2712 q^{97} +(-13.9027 - 1.64741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 10 q^{4} - 10 q^{8} + 12 q^{10} - 32 q^{11} + 14 q^{14} + 66 q^{16} - 16 q^{17} - 64 q^{19} - 20 q^{20} + 12 q^{22} - 72 q^{25} - 100 q^{26} - 14 q^{28} - 98 q^{32} - 108 q^{34} + 72 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 + 12 * q^10 - 32 * q^11 + 14 * q^14 + 66 * q^16 - 16 * q^17 - 64 * q^19 - 20 * q^20 + 12 * q^22 - 72 * q^25 - 100 * q^26 - 14 * q^28 - 98 * q^32 - 108 * q^34 + 72 * q^38 - 332 * q^40 + 80 * q^41 + 32 * q^43 + 292 * q^44 - 168 * q^49 - 46 * q^50 - 4 * q^52 - 98 * q^56 - 96 * q^58 + 16 * q^62 - 182 * q^64 + 192 * q^65 - 32 * q^67 - 188 * q^68 - 84 * q^70 - 240 * q^73 - 208 * q^74 + 8 * q^76 - 484 * q^80 - 372 * q^82 + 320 * q^83 + 604 * q^86 + 468 * q^88 - 400 * q^89 - 352 * q^92 - 72 * q^94 + 144 * q^97 - 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	1.98610	+	0.235345i	0.993052	+	0.117672i
$2$	1.98610	+	0.235345i	0.993052	+	0.117672i
$3$		0			0
$3$		0			0
$4$	3.88923	+	0.934838i	0.972306	+	0.233710i
$5$			7.47825i			1.49565i	0.663896	+	0.747825i	$0.268902\pi$
$5$			7.47825i			1.49565i	−0.663896	+	0.747825i	$0.731098\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	7.50440	+	2.77200i	0.938050	+	0.346499i
$9$		0			0
$10$	−1.75997	+	14.8526i	−0.175997	+	1.48526i
$11$	13.5056			1.22778			0.613889	−	0.789392i	$-0.289604\pi$
$11$	13.5056			1.22778			0.613889	+	0.789392i	$0.289604\pi$
$12$		0			0
$13$		−	3.54193i		−	0.272456i	−0.990677	−	0.136228i	$-0.956502\pi$
$13$		−	3.54193i		−	0.272456i	0.990677	−	0.136228i	$-0.0434980\pi$
$14$	0.622663	−	5.25474i	0.0444760	−	0.375339i
$15$		0			0
$16$	14.2522	+	7.27159i	0.890760	+	0.454475i
$17$	−7.84106			−0.461239			−0.230620	−	0.973044i	$-0.574075\pi$
$17$	−7.84106			−0.461239			−0.230620	+	0.973044i	$0.574075\pi$
$18$		0			0
$19$	−11.1174			−0.585127			−0.292563	−	0.956246i	$-0.594508\pi$
$19$	−11.1174			−0.585127			−0.292563	+	0.956246i	$0.594508\pi$
$20$	−6.99095	+	29.0846i	−0.349548	+	1.45423i
$21$		0			0
$22$	26.8235	+	3.17846i	1.21925	+	0.144476i
$23$			22.3804i			0.973060i	0.873664	+	0.486530i	$0.161738\pi$
$23$			22.3804i			0.973060i	−0.873664	+	0.486530i	$0.838262\pi$
$24$		0			0
$25$	−30.9242			−1.23697
$26$	0.833575	−	7.03465i	0.0320606	−	0.270563i
$27$		0			0
$28$	2.47335	−	10.2899i	0.0883339	−	0.367497i
$29$			52.0985i			1.79650i	0.439484	+	0.898250i	$0.355161\pi$
$29$			52.0985i			1.79650i	−0.439484	+	0.898250i	$0.644839\pi$
$30$		0			0
$31$			15.6772i			0.505716i	0.967503	+	0.252858i	$0.0813705\pi$
$31$			15.6772i			0.505716i	−0.967503	+	0.252858i	$0.918630\pi$
$32$	26.5949	+	17.7963i	0.831092	+	0.556135i
$33$		0			0
$34$	−15.5732	−	1.84535i	−0.458035	−	0.0542751i
$35$	19.7856			0.565302
$36$		0			0
$37$		−	22.1574i		−	0.598849i	−0.954120	−	0.299424i	$-0.903205\pi$
$37$		−	22.1574i		−	0.598849i	0.954120	−	0.299424i	$-0.0967946\pi$
$38$	−22.0803	−	2.61642i	−0.581062	−	0.0688532i
$39$		0			0
$40$	−20.7297	+	56.1198i	−0.518242	+	1.40299i
$41$	−36.1220			−0.881023			−0.440512	−	0.897747i	$-0.645203\pi$
$41$	−36.1220			−0.881023			−0.440512	+	0.897747i	$0.645203\pi$
$42$		0			0
$43$	81.8151			1.90268			0.951338	−	0.308149i	$-0.0997095\pi$
$43$	81.8151			1.90268			0.951338	+	0.308149i	$0.0997095\pi$
$44$	52.5262	+	12.6255i	1.19378	+	0.286944i
$45$		0			0
$46$	−5.26710	+	44.4498i	−0.114502	+	0.966300i
$47$		−	66.3024i		−	1.41069i	−0.708864	−	0.705345i	$-0.750792\pi$
$47$		−	66.3024i		−	1.41069i	0.708864	−	0.705345i	$-0.249208\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−61.4187	−	7.27785i	−1.22837	−	0.145557i
$51$		0			0
$52$	3.31113	−	13.7754i	0.0636756	−	0.264911i
$53$		−	83.6865i		−	1.57899i	−0.613756	−	0.789496i	$-0.710342\pi$
$53$		−	83.6865i		−	1.57899i	0.613756	−	0.789496i	$-0.289658\pi$
$54$		0			0
$55$			100.998i			1.83633i
$56$	7.33401	−	19.8548i	0.130964	−	0.354550i
$57$		0			0
$58$	−12.2611	+	103.473i	−0.211398	+	1.78402i
$59$	−47.7464			−0.809261			−0.404630	−	0.914480i	$-0.632600\pi$
$59$	−47.7464			−0.809261			−0.404630	+	0.914480i	$0.632600\pi$
$60$		0			0
$61$		−	102.992i		−	1.68839i	−0.536039	−	0.844193i	$-0.680080\pi$
$61$		−	102.992i		−	1.68839i	0.536039	−	0.844193i	$-0.319920\pi$
$62$	−3.68954	+	31.1365i	−0.0595087	+	0.502202i
$63$		0			0
$64$	48.6321	+	41.6043i	0.759876	+	0.650068i
$65$	26.4874			0.407499
$66$		0			0
$67$	−10.1586			−0.151621			−0.0758107	−	0.997122i	$-0.524154\pi$
$67$	−10.1586			−0.151621			−0.0758107	+	0.997122i	$0.524154\pi$
$68$	−30.4957	−	7.33013i	−0.448466	−	0.107796i
$69$		0			0
$70$	39.2963	+	4.65643i	0.561375	+	0.0665205i
$71$		−	71.0621i		−	1.00087i	−0.865773	−	0.500437i	$-0.833173\pi$
$71$		−	71.0621i		−	1.00087i	0.865773	−	0.500437i	$-0.166827\pi$
$72$		0			0
$73$	42.8065			0.586390			0.293195	−	0.956053i	$-0.405282\pi$
$73$	42.8065			0.586390			0.293195	+	0.956053i	$0.405282\pi$
$74$	5.21463	−	44.0069i	0.0704679	−	0.594688i
$75$		0			0
$76$	−43.2381	−	10.3930i	−0.568922	−	0.136750i
$77$		−	35.7324i		−	0.464057i
$78$		0			0
$79$			10.3881i			0.131494i	0.997836	+	0.0657472i	$0.0209431\pi$
$79$			10.3881i			0.131494i	−0.997836	+	0.0657472i	$0.979057\pi$
$80$	−54.3788	+	106.581i	−0.679735	+	1.33226i
$81$		0			0
$82$	−71.7420	−	8.50111i	−0.874902	−	0.103672i
$83$	103.602			1.24822			0.624111	−	0.781335i	$-0.285461\pi$
$83$	103.602			1.24822			0.624111	+	0.781335i	$0.285461\pi$
$84$		0			0
$85$		−	58.6374i		−	0.689852i
$86$	162.493	+	19.2547i	1.88946	+	0.223892i
$87$		0			0
$88$	101.351	+	37.4374i	1.15172	+	0.425425i
$89$	60.9498			0.684830			0.342415	−	0.939549i	$-0.388755\pi$
$89$	60.9498			0.684830			0.342415	+	0.939549i	$0.388755\pi$
$90$		0			0
$91$	−9.37107			−0.102979
$92$	−20.9220	+	87.0424i	−0.227414	+	0.946113i
$93$		0			0
$94$	15.6039	−	131.684i	0.165999	−	1.40089i
$95$		−	83.1387i		−	0.875145i
$96$		0			0
$97$	52.2712			0.538878			0.269439	−	0.963017i	$-0.413162\pi$
$97$	52.2712			0.538878			0.269439	+	0.963017i	$0.413162\pi$
$98$	−13.9027	−	1.64741i	−0.141865	−	0.0168103i
$99$		0			0
$100$	−120.271	−	28.9091i	−1.20271	−	0.289091i
$101$		−	22.2697i		−	0.220492i	−0.993904	−	0.110246i	$-0.964836\pi$
$101$		−	22.2697i		−	0.220492i	0.993904	−	0.110246i	$-0.0351639\pi$
$102$		0			0
$103$			133.270i			1.29388i	0.762539	+	0.646942i	$0.223952\pi$
$103$			133.270i			1.29388i	−0.762539	+	0.646942i	$0.776048\pi$
$104$	9.81822	−	26.5801i	0.0944059	−	0.255578i
$105$		0			0
$106$	19.6952	−	166.210i	0.185804	−	1.56802i
$107$	−157.452			−1.47151			−0.735755	−	0.677248i	$-0.763173\pi$
$107$	−157.452			−1.47151			−0.735755	+	0.677248i	$0.763173\pi$
$108$		0			0
$109$		−	134.357i		−	1.23264i	−0.787498	−	0.616318i	$-0.788624\pi$
$109$		−	134.357i		−	1.23264i	0.787498	−	0.616318i	$-0.211376\pi$
$110$	−23.7693	+	200.593i	−0.216085	+	1.82357i
$111$		0			0
$112$	19.2388	−	37.7077i	0.171775	−	0.336676i
$113$	−179.708			−1.59034			−0.795169	−	0.606388i	$-0.792618\pi$
$113$	−179.708			−1.59034			−0.795169	+	0.606388i	$0.792618\pi$
$114$		0			0
$115$	−167.366			−1.45536
$116$	−48.7037	+	202.623i	−0.419859	+	1.74675i
$117$		0			0
$118$	−94.8293	−	11.2369i	−0.803638	−	0.0952276i
$119$			20.7455i			0.174332i
$120$		0			0
$121$	61.4003			0.507440
$122$	24.2385	−	204.552i	0.198676	−	1.67666i
$123$		0			0
$124$	−14.6556	+	60.9721i	−0.118191	+	0.491711i
$125$		−	44.3027i		−	0.354422i
$126$		0			0
$127$			34.9032i			0.274828i	0.990514	+	0.137414i	$0.0438791\pi$
$127$			34.9032i			0.274828i	−0.990514	+	0.137414i	$0.956121\pi$
$128$	86.7971	+	94.0759i	0.678102	+	0.734968i
$129$		0			0
$130$	52.6069	+	6.23368i	0.404668	+	0.0479514i
$131$	−127.352			−0.972150			−0.486075	−	0.873917i	$-0.661572\pi$
$131$	−127.352			−0.972150			−0.486075	+	0.873917i	$0.661572\pi$
$132$		0			0
$133$			29.4139i			0.221157i
$134$	−20.1761	−	2.39078i	−0.150568	−	0.0178416i
$135$		0			0
$136$	−58.8425	−	21.7354i	−0.432665	−	0.159819i
$137$	155.552			1.13542			0.567708	−	0.823230i	$-0.307830\pi$
$137$	155.552			1.13542			0.567708	+	0.823230i	$0.307830\pi$
$138$		0			0
$139$	−50.8834			−0.366067			−0.183034	−	0.983107i	$-0.558592\pi$
$139$	−50.8834			−0.366067			−0.183034	+	0.983107i	$0.558592\pi$
$140$	76.9506	+	18.4963i	0.549647	+	0.132117i
$141$		0			0
$142$	16.7241	−	141.137i	0.117775	−	0.993921i
$143$		−	47.8358i		−	0.334516i
$144$		0			0
$145$	−389.606			−2.68694
$146$	85.0181	+	10.0743i	0.582316	+	0.0690018i
$147$		0			0
$148$	20.7136	−	86.1752i	0.139957	−	0.582265i
$149$		−	253.074i		−	1.69848i	−0.528007	−	0.849240i	$-0.677060\pi$
$149$		−	253.074i		−	1.69848i	0.528007	−	0.849240i	$-0.322940\pi$
$150$		0			0
$151$		−	279.766i		−	1.85275i	−0.376598	−	0.926377i	$-0.622906\pi$
$151$		−	279.766i		−	1.85275i	0.376598	−	0.926377i	$-0.377094\pi$
$152$	−83.4295	−	30.8174i	−0.548878	−	0.202746i
$153$		0			0
$154$	8.40942	−	70.9682i	0.0546066	−	0.460833i
$155$	−117.238			−0.756374
$156$		0			0
$157$			73.6080i			0.468841i	0.972135	+	0.234420i	$0.0753192\pi$
$157$			73.6080i			0.468841i	−0.972135	+	0.234420i	$0.924681\pi$
$158$	−2.44477	+	20.6318i	−0.0154732	+	0.130581i
$159$		0			0
$160$	−133.085	+	198.884i	−0.831783	+	1.24302i
$161$	59.2129			0.367782
$162$		0			0
$163$	171.461			1.05191			0.525953	−	0.850513i	$-0.323709\pi$
$163$	171.461			1.05191			0.525953	+	0.850513i	$0.323709\pi$
$164$	−140.486	−	33.7682i	−0.856625	−	0.205904i
$165$		0			0
$166$	205.765	+	24.3823i	1.23955	+	0.146881i
$167$			181.048i			1.08412i	0.840339	+	0.542061i	$0.182356\pi$
$167$			181.048i			1.08412i	−0.840339	+	0.542061i	$0.817644\pi$
$168$		0			0
$169$	156.455			0.925768
$170$	13.8000	−	116.460i	0.0811765	−	0.685059i
$171$		0			0
$172$	318.197	+	76.4839i	1.84998	+	0.444674i
$173$		−	288.442i		−	1.66729i	−0.552298	−	0.833647i	$-0.686249\pi$
$173$		−	288.442i		−	1.66729i	0.552298	−	0.833647i	$-0.313751\pi$
$174$		0			0
$175$			81.8178i			0.467530i
$176$	192.483	+	98.2070i	1.09366	+	0.557994i
$177$		0			0
$178$	121.053	+	14.3442i	0.680072	+	0.0805855i
$179$	33.2048			0.185502			0.0927510	−	0.995689i	$-0.470434\pi$
$179$	33.2048			0.185502			0.0927510	+	0.995689i	$0.470434\pi$
$180$		0			0
$181$		−	196.790i		−	1.08724i	−0.839332	−	0.543619i	$-0.817054\pi$
$181$		−	196.790i		−	1.08724i	0.839332	−	0.543619i	$-0.182946\pi$
$182$	−18.6119	−	2.20543i	−0.102263	−	0.0121178i
$183$		0			0
$184$	−62.0383	+	167.951i	−0.337165	+	0.912779i
$185$	165.699			0.895668
$186$		0			0
$187$	−105.898			−0.566300
$188$	61.9820	−	257.865i	0.329692	−	1.37162i
$189$		0			0
$190$	19.5663	−	165.122i	0.102980	−	0.869065i
$191$			123.996i			0.649191i	0.945853	+	0.324596i	$0.105228\pi$
$191$			123.996i			0.649191i	−0.945853	+	0.324596i	$0.894772\pi$
$192$		0			0
$193$	68.7028			0.355973			0.177986	−	0.984033i	$-0.443042\pi$
$193$	68.7028			0.355973			0.177986	+	0.984033i	$0.443042\pi$
$194$	103.816	+	12.3017i	0.535134	+	0.0634110i
$195$		0			0
$196$	−27.2246	−	6.54387i	−0.138901	−	0.0333871i
$197$			174.809i			0.887357i	0.896186	+	0.443678i	$0.146327\pi$
$197$			174.809i			0.887357i	−0.896186	+	0.443678i	$0.853673\pi$
$198$		0			0
$199$			131.589i			0.661251i	0.943762	+	0.330625i	$0.107260\pi$
$199$			131.589i			0.661251i	−0.943762	+	0.330625i	$0.892740\pi$
$200$	−232.068	−	85.7218i	−1.16034	−	0.428609i
$201$		0			0
$202$	5.24105	−	44.2300i	0.0259458	−	0.218960i
$203$	137.840			0.679014
$204$		0			0
$205$		−	270.129i		−	1.31770i
$206$	−31.3644	+	264.688i	−0.152254	+	1.28489i
$207$		0			0
$208$	25.7555	−	50.4802i	0.123824	−	0.242693i
$209$	−150.147			−0.718406
$210$		0			0
$211$	−21.4133			−0.101485			−0.0507424	−	0.998712i	$-0.516159\pi$
$211$	−21.4133			−0.101485			−0.0507424	+	0.998712i	$0.516159\pi$
$212$	78.2334	−	325.476i	0.369025	−	1.53526i
$213$		0			0
$214$	−312.715	−	37.0554i	−1.46129	−	0.173156i
$215$			611.834i			2.84574i
$216$		0			0
$217$	41.4779			0.191143
$218$	31.6203	−	266.848i	0.145047	−	1.22407i
$219$		0			0
$220$	−94.4168	+	392.804i	−0.429167	+	1.78547i
$221$			27.7725i			0.125667i
$222$		0			0
$223$			16.9401i			0.0759648i	0.999278	+	0.0379824i	$0.0120931\pi$
$223$			16.9401i			0.0759648i	−0.999278	+	0.0379824i	$0.987907\pi$
$224$	47.0846	−	70.3636i	0.210199	−	0.314123i
$225$		0			0
$226$	−356.919	−	42.2933i	−1.57929	−	0.187139i
$227$	413.555			1.82183			0.910914	−	0.412596i	$-0.135378\pi$
$227$	413.555			1.82183			0.910914	+	0.412596i	$0.135378\pi$
$228$		0			0
$229$			36.0491i			0.157420i	0.996898	+	0.0787099i	$0.0250801\pi$
$229$			36.0491i			0.157420i	−0.996898	+	0.0787099i	$0.974920\pi$
$230$	−332.407	−	39.3887i	−1.44525	−	0.171255i
$231$		0			0
$232$	−144.417	+	390.968i	−0.622487	+	1.68521i
$233$	−303.232			−1.30143			−0.650713	−	0.759324i	$-0.725530\pi$
$233$	−303.232			−1.30143			−0.650713	+	0.759324i	$0.725530\pi$
$234$		0			0
$235$	495.826			2.10990
$236$	−185.696	−	44.6351i	−0.786849	−	0.189132i
$237$		0			0
$238$	−4.88234	+	41.2028i	−0.0205140	+	0.173121i
$239$		−	47.4692i		−	0.198616i	−0.995057	−	0.0993078i	$-0.968337\pi$
$239$		−	47.4692i		−	0.198616i	0.995057	−	0.0993078i	$-0.0316629\pi$
$240$		0			0
$241$	−273.047			−1.13298			−0.566488	−	0.824070i	$-0.691698\pi$
$241$	−273.047			−1.13298			−0.566488	+	0.824070i	$0.691698\pi$
$242$	121.947	+	14.4502i	0.503915	+	0.0597117i
$243$		0			0
$244$	96.2805	−	400.558i	0.394592	−	1.64163i
$245$		−	52.3477i		−	0.213664i
$246$		0			0
$247$			39.3771i			0.159421i
$248$	−43.4571	+	117.648i	−0.175230	+	0.474387i
$249$		0			0
$250$	10.4264	−	87.9898i	0.0417056	−	0.351959i
$251$	384.102			1.53029			0.765144	−	0.643859i	$-0.222668\pi$
$251$	384.102			1.53029			0.765144	+	0.643859i	$0.222668\pi$
$252$		0			0
$253$			302.260i			1.19470i
$254$	−8.21427	+	69.3213i	−0.0323397	+	0.272919i
$255$		0			0
$256$	150.248	+	207.272i	0.586906	+	0.809655i
$257$	−308.955			−1.20216			−0.601080	−	0.799189i	$-0.705263\pi$
$257$	−308.955			−1.20216			−0.601080	+	0.799189i	$0.705263\pi$
$258$		0			0
$259$	−58.6230			−0.226344
$260$	103.016	+	24.7615i	0.396214	+	0.0952365i
$261$		0			0
$262$	−252.934	−	29.9715i	−0.965396	−	0.114395i
$263$			18.7484i			0.0712865i	0.999365	+	0.0356433i	$0.0113480\pi$
$263$			18.7484i			0.0712865i	−0.999365	+	0.0356433i	$0.988652\pi$
$264$		0			0
$265$	625.829			2.36162
$266$	−6.92240	+	58.4191i	−0.0260241	+	0.219621i
$267$		0			0
$268$	−39.5092	−	9.49668i	−0.147422	−	0.0354354i
$269$			344.672i			1.28131i	0.767829	+	0.640655i	$0.221337\pi$
$269$			344.672i			1.28131i	−0.767829	+	0.640655i	$0.778663\pi$
$270$		0			0
$271$		−	54.1955i		−	0.199983i	−0.994988	−	0.0999917i	$-0.968118\pi$
$271$		−	54.1955i		−	0.199983i	0.994988	−	0.0999917i	$-0.0318816\pi$
$272$	−111.752	−	57.0170i	−0.410853	−	0.209621i
$273$		0			0
$274$	308.943	+	36.6083i	1.12753	+	0.133607i
$275$	−417.649			−1.51872
$276$		0			0
$277$		−	72.5083i		−	0.261763i	−0.991398	−	0.130881i	$-0.958219\pi$
$277$		−	72.5083i		−	0.261763i	0.991398	−	0.130881i	$-0.0417807\pi$
$278$	−101.060	−	11.9751i	−0.363524	−	0.0430760i
$279$		0			0
$280$	148.479	+	54.8456i	0.530282	+	0.195877i
$281$	5.38105			0.0191497			0.00957483	−	0.999954i	$-0.496952\pi$
$281$	5.38105			0.0191497			0.00957483	+	0.999954i	$0.496952\pi$
$282$		0			0
$283$	−545.863			−1.92885			−0.964423	−	0.264365i	$-0.914838\pi$
$283$	−545.863			−1.92885			−0.964423	+	0.264365i	$0.914838\pi$
$284$	66.4316	−	276.377i	0.233914	−	0.973157i
$285$		0			0
$286$	11.2579	−	95.0069i	0.0393633	−	0.332192i
$287$			95.5697i			0.332995i
$288$		0			0
$289$	−227.518			−0.787258
$290$	−773.798	−	91.6916i	−2.66827	−	0.316178i
$291$		0			0
$292$	166.484	+	40.0171i	0.570151	+	0.137045i
$293$		−	425.941i		−	1.45373i	−0.686783	−	0.726863i	$-0.740978\pi$
$293$		−	425.941i		−	1.45373i	0.686783	−	0.726863i	$-0.259022\pi$
$294$		0			0
$295$		−	357.059i		−	1.21037i
$296$	61.4202	−	166.278i	0.207501	−	0.561750i
$297$		0			0
$298$	59.5595	−	502.631i	0.199864	−	1.68668i
$299$	79.2698			0.265116
$300$		0			0
$301$		−	216.462i		−	0.719144i
$302$	65.8414	−	555.644i	0.218018	−	1.83988i
$303$		0			0
$304$	−158.447	−	80.8413i	−0.521207	−	0.265925i
$305$	770.197			2.52524
$306$		0			0
$307$	444.426			1.44764			0.723822	−	0.689987i	$-0.242384\pi$
$307$	444.426			1.44764			0.723822	+	0.689987i	$0.242384\pi$
$308$	33.4040	−	138.971i	0.108454	−	0.451205i
$309$		0			0
$310$	−232.847	−	27.5913i	−0.751119	−	0.0890042i
$311$		−	17.4956i		−	0.0562559i	−0.999604	−	0.0281279i	$-0.991045\pi$
$311$		−	17.4956i		−	0.0562559i	0.999604	−	0.0281279i	$-0.00895458\pi$
$312$		0			0
$313$	−382.054			−1.22062			−0.610311	−	0.792162i	$-0.708955\pi$
$313$	−382.054			−1.22062			−0.610311	+	0.792162i	$0.708955\pi$
$314$	−17.3232	+	146.193i	−0.0551696	+	0.465583i
$315$		0			0
$316$	−9.71115	+	40.4015i	−0.0307315	+	0.127853i
$317$			390.680i			1.23243i	0.787579	+	0.616214i	$0.211334\pi$
$317$			390.680i			1.23243i	−0.787579	+	0.616214i	$0.788666\pi$
$318$		0			0
$319$			703.620i			2.20571i
$320$	−311.128	+	363.683i	−0.972274	+	1.13651i
$321$		0			0
$322$	117.603	+	13.9354i	0.365227	+	0.0432778i
$323$	87.1723			0.269883
$324$		0			0
$325$			109.531i			0.337020i
$326$	340.539	+	40.3524i	1.04460	+	0.123780i
$327$		0			0
$328$	−271.074	−	100.130i	−0.826444	−	0.305274i
$329$	−175.420			−0.533191
$330$		0			0
$331$	−283.248			−0.855735			−0.427867	−	0.903842i	$-0.640735\pi$
$331$	−283.248			−0.855735			−0.427867	+	0.903842i	$0.640735\pi$
$332$	402.933	+	96.8516i	1.21366	+	0.291722i
$333$		0			0
$334$	−42.6088	+	359.581i	−0.127571	+	1.07659i
$335$		−	75.9688i		−	0.226772i
$336$		0			0
$337$	−119.881			−0.355730			−0.177865	−	0.984055i	$-0.556919\pi$
$337$	−119.881			−0.355730			−0.177865	+	0.984055i	$0.556919\pi$
$338$	310.735	+	36.8208i	0.919336	+	0.108937i
$339$		0			0
$340$	54.8165	−	228.054i	0.161225	−	0.670748i
$341$			211.729i			0.620907i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	613.973	+	226.791i	1.78481	+	0.659276i
$345$		0			0
$346$	67.8832	−	572.876i	0.196194	−	1.65571i
$347$	−95.3186			−0.274693			−0.137347	−	0.990523i	$-0.543857\pi$
$347$	−95.3186			−0.274693			−0.137347	+	0.990523i	$0.543857\pi$
$348$		0			0
$349$			42.8609i			0.122811i	0.998113	+	0.0614053i	$0.0195582\pi$
$349$			42.8609i			0.122811i	−0.998113	+	0.0614053i	$0.980442\pi$
$350$	−19.2554	+	162.499i	−0.0550154	+	0.464282i
$351$		0			0
$352$	359.180	+	240.349i	1.02040	+	0.682811i
$353$	−324.090			−0.918101			−0.459050	−	0.888410i	$-0.651810\pi$
$353$	−324.090			−0.918101			−0.459050	+	0.888410i	$0.651810\pi$
$354$		0			0
$355$	531.420			1.49696
$356$	237.048	+	56.9782i	0.665864	+	0.160051i
$357$		0			0
$358$	65.9483	+	7.81458i	0.184213	+	0.0218284i
$359$			352.212i			0.981092i	0.871415	+	0.490546i	$0.163203\pi$
$359$			352.212i			0.981092i	−0.871415	+	0.490546i	$0.836797\pi$
$360$		0			0
$361$	−237.403			−0.657627
$362$	46.3135	−	390.846i	0.127938	−	1.07968i
$363$		0			0
$364$	−36.4462	−	8.76044i	−0.100127	−	0.0240671i
$365$			320.117i			0.877034i
$366$		0			0
$367$			402.579i			1.09695i	0.836168	+	0.548473i	$0.184791\pi$
$367$			402.579i			1.09695i	−0.836168	+	0.548473i	$0.815209\pi$
$368$	−162.741	+	318.969i	−0.442231	+	0.866763i
$369$		0			0
$370$	329.095	+	38.9963i	0.889445	+	0.105395i
$371$	−221.414			−0.596803
$372$		0			0
$373$			349.786i			0.937765i	0.883261	+	0.468882i	$0.155343\pi$
$373$			349.786i			0.937765i	−0.883261	+	0.468882i	$0.844657\pi$
$374$	−210.325	−	24.9225i	−0.562365	−	0.0666378i
$375$		0			0
$376$	183.790	−	497.560i	0.488803	−	1.32330i
$377$	184.529			0.489468
$378$		0			0
$379$	−97.5057			−0.257271			−0.128635	−	0.991692i	$-0.541060\pi$
$379$	−97.5057			−0.257271			−0.128635	+	0.991692i	$0.541060\pi$
$380$	77.7213	−	323.345i	0.204530	−	0.850909i
$381$		0			0
$382$	−29.1817	+	246.268i	−0.0763918	+	0.644681i
$383$		−	3.49274i		−	0.00911944i	−0.999990	−	0.00455972i	$-0.998549\pi$
$383$		−	3.49274i		−	0.00911944i	0.999990	−	0.00455972i	$-0.00145141\pi$
$384$		0			0
$385$	267.216			0.694066
$386$	136.451	+	16.1688i	0.353500	+	0.0418881i
$387$		0			0
$388$	203.294	+	48.8651i	0.523955	+	0.125941i
$389$		−	1.14711i		−	0.00294887i	−0.999999	−	0.00147444i	$-0.999531\pi$
$389$		−	1.14711i		−	0.00294887i	0.999999	−	0.00147444i	$-0.000469328\pi$
$390$		0			0
$391$		−	175.486i		−	0.448813i
$392$	−52.5308	−	19.4040i	−0.134007	−	0.0494999i
$393$		0			0
$394$	−41.1404	+	347.190i	−0.104417	+	0.881192i
$395$	−77.6844			−0.196669
$396$		0			0
$397$			683.504i			1.72167i	0.508882	+	0.860836i	$0.330059\pi$
$397$			683.504i			1.72167i	−0.508882	+	0.860836i	$0.669941\pi$
$398$	−30.9687	+	261.349i	−0.0778109	+	0.656657i
$399$		0			0
$400$	−440.737	−	224.868i	−1.10184	−	0.562171i
$401$	−308.774			−0.770011			−0.385005	−	0.922914i	$-0.625800\pi$
$401$	−308.774			−0.770011			−0.385005	+	0.922914i	$0.625800\pi$
$402$		0			0
$403$	55.5275			0.137785
$404$	20.8186	−	86.6119i	0.0515311	−	0.214386i
$405$		0			0
$406$	273.764	+	32.4398i	0.674296	+	0.0799011i
$407$		−	299.248i		−	0.735254i
$408$		0			0
$409$	357.161			0.873253			0.436627	−	0.899643i	$-0.356173\pi$
$409$	357.161			0.873253			0.436627	+	0.899643i	$0.356173\pi$
$410$	63.5734	−	536.504i	0.155057	−	1.30855i
$411$		0			0
$412$	−124.586	+	518.317i	−0.302393	+	1.25805i
$413$			126.325i			0.305872i
$414$		0			0
$415$			774.765i			1.86690i
$416$	63.0333	−	94.1975i	0.151522	−	0.226436i
$417$		0			0
$418$	−298.207	−	35.3363i	−0.713415	−	0.0845365i
$419$	309.516			0.738702			0.369351	−	0.929290i	$-0.379580\pi$
$419$	309.516			0.738702			0.369351	+	0.929290i	$0.379580\pi$
$420$		0			0
$421$		−	108.620i		−	0.258005i	−0.991644	−	0.129002i	$-0.958823\pi$
$421$		−	108.620i		−	0.258005i	0.991644	−	0.129002i	$-0.0411775\pi$
$422$	−42.5290	−	5.03950i	−0.100780	−	0.0119419i
$423$		0			0
$424$	231.979	−	628.017i	0.547120	−	1.48117i
$425$	242.479			0.570538
$426$		0			0
$427$	−272.490			−0.638150
$428$	−612.365	−	147.192i	−1.43076	−	0.343906i
$429$		0			0
$430$	−143.992	+	1215.17i	−0.334865	+	2.82597i
$431$		−	116.061i		−	0.269283i	−0.990894	−	0.134641i	$-0.957012\pi$
$431$		−	116.061i		−	0.269283i	0.990894	−	0.134641i	$-0.0429882\pi$
$432$		0			0
$433$	363.996			0.840637			0.420318	−	0.907377i	$-0.361918\pi$
$433$	363.996			0.840637			0.420318	+	0.907377i	$0.361918\pi$
$434$	82.3795	+	9.76161i	0.189815	+	0.0224922i
$435$		0			0
$436$	125.602	−	522.546i	0.288079	−	1.19850i
$437$		−	248.812i		−	0.569364i
$438$		0			0
$439$			264.500i			0.602507i	0.953544	+	0.301253i	$0.0974050\pi$
$439$			264.500i			0.602507i	−0.953544	+	0.301253i	$0.902595\pi$
$440$	−279.966	+	757.929i	−0.636286	+	1.72257i
$441$		0			0
$442$	−6.53611	+	55.1591i	−0.0147876	+	0.124794i
$443$	−361.826			−0.816763			−0.408382	−	0.912811i	$-0.633907\pi$
$443$	−361.826			−0.816763			−0.408382	+	0.912811i	$0.633907\pi$
$444$		0			0
$445$			455.798i			1.02427i
$446$	−3.98677	+	33.6449i	−0.00893895	+	0.0754370i
$447$		0			0
$448$	110.075	−	128.668i	0.245702	−	0.287206i
$449$	−58.1925			−0.129605			−0.0648023	−	0.997898i	$-0.520642\pi$
$449$	−58.1925			−0.129605			−0.0648023	+	0.997898i	$0.520642\pi$
$450$		0			0
$451$	−487.847			−1.08170
$452$	−698.925	−	167.998i	−1.54630	−	0.371677i
$453$		0			0
$454$	821.364	+	97.3280i	1.80917	+	0.214379i
$455$		−	70.0792i		−	0.154020i
$456$		0			0
$457$	282.240			0.617594			0.308797	−	0.951128i	$-0.400074\pi$
$457$	282.240			0.617594			0.308797	+	0.951128i	$0.400074\pi$
$458$	−8.48397	+	71.5973i	−0.0185239	+	0.156326i
$459$		0			0
$460$	−650.925	−	156.460i	−1.41505	−	0.340131i
$461$			263.726i			0.572073i	0.958219	+	0.286036i	$0.0923378\pi$
$461$			263.726i			0.572073i	−0.958219	+	0.286036i	$0.907662\pi$
$462$		0			0
$463$			203.652i			0.439853i	0.975516	+	0.219927i	$0.0705818\pi$
$463$			203.652i			0.439853i	−0.975516	+	0.219927i	$0.929418\pi$
$464$	−378.839	+	742.516i	−0.816464	+	1.60025i
$465$		0			0
$466$	−602.251	−	71.3641i	−1.29238	−	0.153142i
$467$	−100.538			−0.215285			−0.107643	−	0.994190i	$-0.534330\pi$
$467$	−100.538			−0.215285			−0.107643	+	0.994190i	$0.534330\pi$
$468$		0			0
$469$			26.8772i			0.0573075i
$470$	984.762	+	116.690i	2.09524	+	0.248277i
$471$		0			0
$472$	−358.308	−	132.353i	−0.759127	−	0.280408i
$473$	1104.96			2.33607
$474$		0			0
$475$	343.797			0.723783
$476$	−19.3937	+	80.6840i	−0.0407431	+	0.169504i
$477$		0			0
$478$	11.1716	−	94.2787i	0.0233716	−	0.197236i
$479$		−	491.688i		−	1.02649i	−0.858242	−	0.513245i	$-0.828443\pi$
$479$		−	491.688i		−	1.02649i	0.858242	−	0.513245i	$-0.171557\pi$
$480$		0			0
$481$	−78.4800			−0.163160
$482$	−542.300	−	64.2601i	−1.12510	−	0.133320i
$483$		0			0
$484$	238.800	+	57.3993i	0.493388	+	0.118594i
$485$			390.897i			0.805973i
$486$		0			0
$487$		−	242.746i		−	0.498451i	−0.968446	−	0.249225i	$-0.919824\pi$
$487$		−	242.746i		−	0.498451i	0.968446	−	0.249225i	$-0.0801760\pi$
$488$	285.492	−	772.890i	0.585025	−	1.58379i
$489$		0			0
$490$	12.3198	−	103.968i	0.0251424	−	0.212180i
$491$	525.167			1.06959			0.534793	−	0.844983i	$-0.320390\pi$
$491$	525.167			1.06959			0.534793	+	0.844983i	$0.320390\pi$
$492$		0			0
$493$		−	408.508i		−	0.828616i
$494$	−9.26719	+	78.2071i	−0.0187595	+	0.158314i
$495$		0			0
$496$	−113.998	+	223.434i	−0.229835	+	0.450471i
$497$	−188.013			−0.378295
$498$		0			0
$499$	−231.230			−0.463387			−0.231694	−	0.972789i	$-0.574427\pi$
$499$	−231.230			−0.463387			−0.231694	+	0.972789i	$0.574427\pi$
$500$	41.4159	−	172.303i	0.0828318	−	0.344607i
$501$		0			0
$502$	762.867	+	90.3964i	1.51966	+	0.180073i
$503$			180.388i			0.358624i	0.983792	+	0.179312i	$0.0573872\pi$
$503$			180.388i			0.358624i	−0.983792	+	0.179312i	$0.942613\pi$
$504$		0			0
$505$	166.538			0.329779
$506$	−71.1352	+	600.320i	−0.140583	+	1.18640i
$507$		0			0
$508$	−32.6288	+	135.746i	−0.0642299	+	0.267217i
$509$		−	379.548i		−	0.745674i	−0.927897	−	0.372837i	$-0.878385\pi$
$509$		−	379.548i		−	0.745674i	0.927897	−	0.372837i	$-0.121615\pi$
$510$		0			0
$511$		−	113.255i		−	0.221634i
$512$	249.628	+	447.024i	0.487554	+	0.873093i
$513$		0			0
$514$	−613.617	−	72.7109i	−1.19381	−	0.141461i
$515$	−996.626			−1.93520
$516$		0			0
$517$		−	895.452i		−	1.73201i
$518$	−116.431	−	13.7966i	−0.224771	−	0.0266344i
$519$		0			0
$520$	198.772	+	73.4231i	0.382255	+	0.141198i
$521$	−576.665			−1.10684			−0.553421	−	0.832902i	$-0.686678\pi$
$521$	−576.665			−1.10684			−0.553421	+	0.832902i	$0.686678\pi$
$522$		0			0
$523$	738.590			1.41222			0.706109	−	0.708103i	$-0.250449\pi$
$523$	738.590			1.41222			0.706109	+	0.708103i	$0.250449\pi$
$524$	−495.299	−	119.053i	−0.945228	−	0.227201i
$525$		0			0
$526$	−4.41232	+	37.2362i	−0.00838845	+	0.0707913i
$527$		−	122.926i		−	0.233256i
$528$		0			0
$529$	28.1183			0.0531536
$530$	1242.96	+	147.285i	2.34521	+	0.277897i
$531$		0			0
$532$	−27.4972	+	114.397i	−0.0516865	+	0.215032i
$533$			127.941i			0.240040i
$534$		0			0
$535$		−	1177.46i		−	2.20086i
$536$	−76.2344	−	28.1597i	−0.142228	−	0.0525367i
$537$		0			0
$538$	−81.1168	+	684.555i	−0.150775	+	1.27241i
$539$	−94.5390			−0.175397
$540$		0			0
$541$			119.151i			0.220243i	0.993918	+	0.110121i	$0.0351240\pi$
$541$			119.151i			0.220243i	−0.993918	+	0.110121i	$0.964876\pi$
$542$	12.7546	−	107.638i	0.0235325	−	0.198594i
$543$		0			0
$544$	−208.533	−	139.542i	−0.383332	−	0.256511i
$545$	1004.76			1.84359
$546$		0			0
$547$	−316.005			−0.577706			−0.288853	−	0.957374i	$-0.593274\pi$
$547$	−316.005			−0.577706			−0.288853	+	0.957374i	$0.593274\pi$
$548$	604.977	+	145.416i	1.10397	+	0.265358i
$549$		0			0
$550$	−829.495	−	98.2914i	−1.50817	−	0.178712i
$551$		−	579.201i		−	1.05118i
$552$		0			0
$553$	27.4842			0.0497002
$554$	17.0644	−	144.009i	0.0308022	−	0.259944i
$555$		0			0
$556$	−197.897	−	47.5677i	−0.355930	−	0.0855534i
$557$			611.086i			1.09710i	0.836117	+	0.548551i	$0.184820\pi$
$557$			611.086i			1.09710i	−0.836117	+	0.548551i	$0.815180\pi$
$558$		0			0
$559$		−	289.783i		−	0.518396i
$560$	281.987	+	143.873i	0.503549	+	0.256916i
$561$		0			0
$562$	10.6873	+	1.26640i	0.0190166	+	0.00225338i
$563$	263.337			0.467739			0.233869	−	0.972268i	$-0.424861\pi$
$563$	263.337			0.467739			0.233869	+	0.972268i	$0.424861\pi$
$564$		0			0
$565$		−	1343.90i		−	2.37859i
$566$	−1084.14	−	128.466i	−1.91544	−	0.226972i
$567$		0			0
$568$	196.984	−	533.279i	0.346803	−	0.938871i
$569$	263.864			0.463733			0.231867	−	0.972748i	$-0.425517\pi$
$569$	263.864			0.463733			0.231867	+	0.972748i	$0.425517\pi$
$570$		0			0
$571$	198.806			0.348172			0.174086	−	0.984730i	$-0.444303\pi$
$571$	198.806			0.348172			0.174086	+	0.984730i	$0.444303\pi$
$572$	44.7187	−	186.044i	0.0781796	−	0.325252i
$573$		0			0
$574$	−22.4918	+	189.811i	−0.0391843	+	0.330682i
$575$		−	692.096i		−	1.20364i
$576$		0			0
$577$	−419.509			−0.727051			−0.363526	−	0.931584i	$-0.618427\pi$
$577$	−419.509			−0.727051			−0.363526	+	0.931584i	$0.618427\pi$
$578$	−451.874	−	53.5451i	−0.781789	−	0.0926385i
$579$		0			0
$580$	−1515.26	−	364.218i	−2.61253	−	0.627963i
$581$		−	274.106i		−	0.471784i
$582$		0			0
$583$		−	1130.23i		−	1.93865i
$584$	321.237	+	118.659i	0.550063	+	0.203184i
$585$		0			0
$586$	100.243	−	845.964i	0.171063	−	1.44363i
$587$	536.991			0.914806			0.457403	−	0.889260i	$-0.348780\pi$
$587$	536.991			0.914806			0.457403	+	0.889260i	$0.348780\pi$
$588$		0			0
$589$		−	174.290i		−	0.295908i
$590$	84.0320	−	709.157i	0.142427	−	1.20196i
$591$		0			0
$592$	161.120	−	315.791i	0.272162	−	0.533430i
$593$	−201.757			−0.340231			−0.170115	−	0.985424i	$-0.554414\pi$
$593$	−201.757			−0.340231			−0.170115	+	0.985424i	$0.554414\pi$
$594$		0			0
$595$	−155.140			−0.260740
$596$	236.583	−	984.260i	0.396951	−	1.65144i
$597$		0			0
$598$	157.438	+	18.6557i	0.263275	+	0.0311969i
$599$			487.011i			0.813040i	0.913642	+	0.406520i	$0.133258\pi$
$599$			487.011i			0.813040i	−0.913642	+	0.406520i	$0.866742\pi$
$600$		0			0
$601$	−671.112			−1.11666			−0.558330	−	0.829619i	$-0.688558\pi$
$601$	−671.112			−1.11666			−0.558330	+	0.829619i	$0.688558\pi$
$602$	50.9433	−	429.917i	0.0846233	−	0.714148i
$603$		0			0
$604$	261.536	−	1088.07i	0.433006	−	1.80144i
$605$			459.167i			0.758953i
$606$		0			0
$607$		−	463.776i		−	0.764046i	−0.924153	−	0.382023i	$-0.875228\pi$
$607$		−	463.776i		−	0.764046i	0.924153	−	0.382023i	$-0.124772\pi$
$608$	−295.667	−	197.849i	−0.486294	−	0.325409i
$609$		0			0
$610$	1529.69	+	181.262i	2.50769	+	0.297150i
$611$	−234.839			−0.384351
$612$		0			0
$613$			704.945i			1.14999i	0.818156	+	0.574996i	$0.194997\pi$
$613$			704.945i			1.14999i	−0.818156	+	0.574996i	$0.805003\pi$
$614$	882.678	+	104.593i	1.43759	+	0.170348i
$615$		0			0
$616$	99.0500	−	268.150i	0.160795	−	0.435308i
$617$	−662.653			−1.07399			−0.536996	−	0.843585i	$-0.680441\pi$
$617$	−662.653			−1.07399			−0.536996	+	0.843585i	$0.680441\pi$
$618$		0			0
$619$	325.613			0.526031			0.263015	−	0.964792i	$-0.415283\pi$
$619$	325.613			0.526031			0.263015	+	0.964792i	$0.415283\pi$
$620$	−455.965	−	109.598i	−0.735427	−	0.176772i
$621$		0			0
$622$	4.11749	−	34.7480i	0.00661976	−	0.0558650i
$623$		−	161.258i		−	0.258841i
$624$		0			0
$625$	−441.798			−0.706878
$626$	−758.800	−	89.9145i	−1.21214	−	0.143633i
$627$		0			0
$628$	−68.8116	+	286.278i	−0.109573	+	0.455857i
$629$			173.738i			0.276212i
$630$		0			0
$631$		−	368.582i		−	0.584124i	−0.956399	−	0.292062i	$-0.905659\pi$
$631$		−	368.582i		−	0.584124i	0.956399	−	0.292062i	$-0.0943413\pi$
$632$	−28.7956	+	77.9561i	−0.0455627	+	0.123348i
$633$		0			0
$634$	−91.9443	+	775.931i	−0.145023	+	1.22387i
$635$	−261.015			−0.411046
$636$		0			0
$637$			24.7935i			0.0389223i
$638$	−165.593	+	1397.46i	−0.259550	+	2.19038i
$639$		0			0
$640$	−703.523	+	649.090i	−1.09925	+	1.01420i
$641$	−444.594			−0.693595			−0.346797	−	0.937940i	$-0.612731\pi$
$641$	−444.594			−0.693595			−0.346797	+	0.937940i	$0.612731\pi$
$642$		0			0
$643$	−1180.78			−1.83636			−0.918181	−	0.396162i	$-0.870342\pi$
$643$	−1180.78			−1.83636			−0.918181	+	0.396162i	$0.870342\pi$
$644$	230.292	+	55.3545i	0.357597	+	0.0859542i
$645$		0			0
$646$	173.133	+	20.5155i	0.268008	+	0.0317578i
$647$			112.967i			0.174601i	0.996182	+	0.0873005i	$0.0278240\pi$
$647$			112.967i			0.174601i	−0.996182	+	0.0873005i	$0.972176\pi$
$648$		0			0
$649$	−644.842			−0.993593
$650$	−25.7776	+	217.541i	−0.0396579	+	0.334678i
$651$		0			0
$652$	666.850	+	160.288i	1.02278	+	0.245841i
$653$		−	364.690i		−	0.558484i	−0.960221	−	0.279242i	$-0.909917\pi$
$653$		−	364.690i		−	0.558484i	0.960221	−	0.279242i	$-0.0900831\pi$
$654$		0			0
$655$		−	952.368i		−	1.45400i
$656$	−514.816	−	262.664i	−0.784780	−	0.400403i
$657$		0			0
$658$	−348.402	−	41.2841i	−0.529486	−	0.0627418i
$659$	−12.4844			−0.0189444			−0.00947220	−	0.999955i	$-0.503015\pi$
$659$	−12.4844			−0.0189444			−0.00947220	+	0.999955i	$0.503015\pi$
$660$		0			0
$661$			215.021i			0.325296i	0.986684	+	0.162648i	$0.0520036\pi$
$661$			215.021i			0.325296i	−0.986684	+	0.162648i	$0.947996\pi$
$662$	−562.561	−	66.6609i	−0.849789	−	0.100696i
$663$		0			0
$664$	777.475	+	287.186i	1.17090	+	0.432508i
$665$	−219.964			−0.330774
$666$		0			0
$667$	−1165.99			−1.74810
$668$	−169.251	+	704.138i	−0.253370	+	1.05410i
$669$		0			0
$670$	17.8788	−	150.882i	0.0266848	−	0.225197i
$671$		−	1390.96i		−	2.07297i
$672$		0			0
$673$	−107.429			−0.159627			−0.0798135	−	0.996810i	$-0.525432\pi$
$673$	−107.429			−0.159627			−0.0798135	+	0.996810i	$0.525432\pi$
$674$	−238.096	−	28.2133i	−0.353258	−	0.0418595i
$675$		0			0
$676$	608.488	+	146.260i	0.900130	+	0.216361i
$677$			916.328i			1.35351i	0.736207	+	0.676756i	$0.236615\pi$
$677$			916.328i			1.35351i	−0.736207	+	0.676756i	$0.763385\pi$
$678$		0			0
$679$		−	138.296i		−	0.203677i
$680$	162.543	−	440.039i	0.239033	−	0.647116i
$681$		0			0
$682$	−49.8293	+	420.517i	−0.0730636	+	0.616593i
$683$	−497.699			−0.728696			−0.364348	−	0.931263i	$-0.618708\pi$
$683$	−497.699			−0.728696			−0.364348	+	0.931263i	$0.618708\pi$
$684$		0			0
$685$			1163.26i			1.69819i
$686$	−4.35864	+	36.7832i	−0.00635371	+	0.0536198i
$687$		0			0
$688$	1166.04	+	594.926i	1.69483	+	0.864718i
$689$	−296.412			−0.430206
$690$		0			0
$691$	663.410			0.960073			0.480036	−	0.877249i	$-0.340623\pi$
$691$	663.410			0.960073			0.480036	+	0.877249i	$0.340623\pi$
$692$	269.646	−	1121.82i	0.389663	−	1.62112i
$693$		0			0
$694$	−189.313	−	22.4327i	−0.272785	−	0.0323238i
$695$		−	380.518i		−	0.547508i
$696$		0			0
$697$	283.235			0.406362
$698$	−10.0871	+	85.1262i	−0.0144514	+	0.121957i
$699$		0			0
$700$	−76.4864	+	318.208i	−0.109266	+	0.454583i
$701$		−	1295.94i		−	1.84871i	−0.381537	−	0.924354i	$-0.624605\pi$
$701$		−	1295.94i		−	1.84871i	0.381537	−	0.924354i	$-0.375395\pi$
$702$		0			0
$703$			246.333i			0.350402i
$704$	656.804	+	561.890i	0.932960	+	0.798139i
$705$		0			0
$706$	−643.676	−	76.2727i	−0.911722	−	0.108035i
$707$	−58.9201			−0.0833382
$708$		0			0
$709$			871.601i			1.22934i	0.788785	+	0.614669i	$0.210710\pi$
$709$			871.601i			1.22934i	−0.788785	+	0.614669i	$0.789290\pi$
$710$	1055.46	+	125.067i	1.48656	+	0.176151i
$711$		0			0
$712$	457.392	+	168.953i	0.642405	+	0.237293i
$713$	−350.861			−0.492092
$714$		0			0
$715$	357.728			0.500319
$716$	129.141	+	31.0412i	0.180365	+	0.0433536i
$717$		0			0
$718$	−82.8912	+	699.530i	−0.115447	+	0.974276i
$719$		−	1027.81i		−	1.42950i	−0.699378	−	0.714752i	$-0.746540\pi$
$719$		−	1027.81i		−	1.42950i	0.699378	−	0.714752i	$-0.253460\pi$
$720$		0			0
$721$	352.599			0.489042
$722$	−471.508	−	55.8716i	−0.653058	−	0.0773845i
$723$		0			0
$724$	183.967	−	765.361i	0.254098	−	1.05713i
$725$		−	1611.11i		−	2.22221i
$726$		0			0
$727$		−	460.819i		−	0.633864i	−0.948448	−	0.316932i	$-0.897347\pi$
$727$		−	460.819i		−	0.633864i	0.948448	−	0.316932i	$-0.102653\pi$
$728$	−70.3243	−	25.9766i	−0.0965993	−	0.0356821i
$729$		0			0
$730$	−75.3379	+	635.787i	−0.103203	+	0.870941i
$731$	−641.517			−0.877589
$732$		0			0
$733$			1332.20i			1.81747i	0.417376	+	0.908734i	$0.362950\pi$
$733$			1332.20i			1.81747i	−0.417376	+	0.908734i	$0.637050\pi$
$734$	−94.7449	+	799.565i	−0.129080	+	1.08933i
$735$		0			0
$736$	−398.288	+	595.205i	−0.541153	+	0.808703i
$737$	−137.198			−0.186157
$738$		0			0
$739$	−22.2967			−0.0301715			−0.0150857	−	0.999886i	$-0.504802\pi$
$739$	−22.2967			−0.0301715			−0.0150857	+	0.999886i	$0.504802\pi$
$740$	644.439	+	154.901i	0.870864	+	0.209326i
$741$		0			0
$742$	−439.751	−	52.1085i	−0.592656	−	0.0702271i
$743$			1408.39i			1.89555i	0.318941	+	0.947775i	$0.396673\pi$
$743$			1408.39i			1.89555i	−0.318941	+	0.947775i	$0.603327\pi$
$744$		0			0
$745$	1892.55			2.54033
$746$	−82.3203	+	694.712i	−0.110349	+	0.931250i
$747$		0			0
$748$	−411.861	−	98.9975i	−0.550617	−	0.132350i
$749$			416.578i			0.556179i
$750$		0			0
$751$		−	408.216i		−	0.543563i	−0.962359	−	0.271782i	$-0.912387\pi$
$751$		−	408.216i		−	0.543563i	0.962359	−	0.271782i	$-0.0876129\pi$
$752$	482.124	−	944.952i	0.641123	−	1.25659i
$753$		0			0
$754$	366.495	+	43.4280i	0.486067	+	0.0575968i
$755$	2092.16			2.77107
$756$		0			0
$757$		−	364.759i		−	0.481849i	−0.970544	−	0.240924i	$-0.922549\pi$
$757$		−	364.759i		−	0.481849i	0.970544	−	0.240924i	$-0.0774506\pi$
$758$	−193.657	−	22.9474i	−0.255484	−	0.0302737i
$759$		0			0
$760$	230.460	−	623.906i	0.303237	−	0.820930i
$761$	−1245.82			−1.63709			−0.818543	−	0.574446i	$-0.805218\pi$
$761$	−1245.82			−1.63709			−0.818543	+	0.574446i	$0.805218\pi$
$762$		0			0
$763$	−355.476			−0.465892
$764$	−115.916	+	482.247i	−0.151722	+	0.631213i
$765$		0			0
$766$	0.821999	−	6.93696i	0.00107311	−	0.00905608i
$767$			169.114i			0.220488i
$768$		0			0
$769$	32.0583			0.0416883			0.0208442	−	0.999783i	$-0.493365\pi$
$769$	32.0583			0.0416883			0.0208442	+	0.999783i	$0.493365\pi$
$770$	530.718	+	62.8877i	0.689244	+	0.0816724i
$771$		0			0
$772$	267.201	+	64.2260i	0.346115	+	0.0831943i
$773$		−	1257.99i		−	1.62742i	−0.581272	−	0.813709i	$-0.697445\pi$
$773$		−	1257.99i		−	1.62742i	0.581272	−	0.813709i	$-0.302555\pi$
$774$		0			0
$775$		−	484.805i		−	0.625554i
$776$	392.264	+	144.895i	0.505495	+	0.186721i
$777$		0			0
$778$	0.269966	−	2.27828i	0.000347001	−	0.00292838i
$779$	401.582			0.515510
$780$		0			0
$781$		−	959.734i		−	1.22885i
$782$	41.2997	−	348.534i	0.0528129	−	0.445695i
$783$		0			0
$784$	−99.7651	−	50.9012i	−0.127251	−	0.0649249i
$785$	−550.459			−0.701221
$786$		0			0
$787$	633.258			0.804648			0.402324	−	0.915497i	$-0.368203\pi$
$787$	633.258			0.804648			0.402324	+	0.915497i	$0.368203\pi$
$788$	−163.418	+	679.873i	−0.207384	+	0.862783i
$789$		0			0
$790$	−154.289	−	18.2826i	−0.195303	−	0.0231426i
$791$			475.463i			0.601091i
$792$		0			0
$793$	−364.789			−0.460012
$794$	−160.859	+	1357.51i	−0.202593	+	1.70971i
$795$		0			0
$796$	−123.014	+	511.779i	−0.154541	+	0.642938i
$797$		−	552.494i		−	0.693218i	−0.938010	−	0.346609i	$-0.887333\pi$
$797$		−	552.494i		−	0.693218i	0.938010	−	0.346609i	$-0.112667\pi$
$798$		0			0
$799$			519.882i			0.650665i
$800$	−822.428	−	550.337i	−1.02803	−	0.687921i
$801$		0			0
$802$	−613.258	−	72.6684i	−0.764661	−	0.0906089i
$803$	578.125			0.719957
$804$		0			0
$805$			442.809i			0.550073i
$806$	110.283	+	13.0681i	0.136828	+	0.0162135i
$807$		0			0
$808$	61.7315	−	167.121i	0.0764004	−	0.206833i
$809$	184.780			0.228406			0.114203	−	0.993457i	$-0.463569\pi$
$809$	184.780			0.228406			0.114203	+	0.993457i	$0.463569\pi$
$810$		0			0
$811$	781.297			0.963375			0.481688	−	0.876343i	$-0.340024\pi$
$811$	781.297			0.963375			0.481688	+	0.876343i	$0.340024\pi$
$812$	536.090	+	128.858i	0.660209	+	0.158692i
$813$		0			0
$814$	70.4265	−	594.339i	0.0865190	−	0.730146i
$815$			1282.23i			1.57328i
$816$		0			0
$817$	−909.572			−1.11331
$818$	709.358	+	84.0558i	0.867186	+	0.102758i
$819$		0			0
$820$	252.527	−	1050.59i	0.307960	−	1.28121i
$821$		−	1272.12i		−	1.54947i	−0.632283	−	0.774737i	$-0.717882\pi$
$821$		−	1272.12i		−	1.54947i	0.632283	−	0.774737i	$-0.282118\pi$
$822$		0			0
$823$		−	92.4404i		−	0.112321i	−0.998422	−	0.0561606i	$-0.982114\pi$
$823$		−	92.4404i		−	0.112321i	0.998422	−	0.0561606i	$-0.0178859\pi$
$824$	−369.424	+	1000.11i	−0.448330	+	1.21373i
$825$		0			0
$826$	−29.7299	+	250.895i	−0.0359926	+	0.303747i
$827$	−479.059			−0.579273			−0.289637	−	0.957137i	$-0.593534\pi$
$827$	−479.059			−0.579273			−0.289637	+	0.957137i	$0.593534\pi$
$828$		0			0
$829$			1205.72i			1.45443i	0.686409	+	0.727215i	$0.259186\pi$
$829$			1205.72i			1.45443i	−0.686409	+	0.727215i	$0.740814\pi$
$830$	−182.337	+	1538.77i	−0.219683	+	1.85393i
$831$		0			0
$832$	147.360	−	172.252i	0.177115	−	0.207033i
$833$	54.8875			0.0658913
$834$		0			0
$835$	−1353.92			−1.62147
$836$	−583.955	−	140.363i	−0.698511	−	0.167898i
$837$		0			0
$838$	614.732	+	72.8430i	0.733570	+	0.0869248i
$839$		−	1231.72i		−	1.46808i	−0.679107	−	0.734039i	$-0.737633\pi$
$839$		−	1231.72i		−	1.46808i	0.679107	−	0.734039i	$-0.262367\pi$
$840$		0			0
$841$	−1873.26			−2.22742
$842$	25.5631	−	215.731i	0.0303600	−	0.256212i
$843$		0			0
$844$	−83.2811	−	20.0180i	−0.0986743	−	0.0237180i
$845$			1170.01i			1.38462i
$846$		0			0
$847$		−	162.450i		−	0.191794i
$848$	608.534	−	1192.71i	0.717611	−	1.40650i
$849$		0			0
$850$	481.588	+	57.0661i	0.566574	+	0.0671366i
$851$	495.891			0.582716
$852$		0			0
$853$			1181.27i			1.38484i	0.721493	+	0.692421i	$0.243456\pi$
$853$			1181.27i			1.38484i	−0.721493	+	0.692421i	$0.756544\pi$
$854$	−541.194	−	64.1291i	−0.633717	−	0.0750926i
$855$		0			0
$856$	−1181.58	−	436.455i	−1.38035	−	0.509878i
$857$	1499.85			1.75012			0.875060	−	0.484014i	$-0.160822\pi$
$857$	1499.85			1.75012			0.875060	+	0.484014i	$0.160822\pi$
$858$		0			0
$859$	789.796			0.919437			0.459718	−	0.888065i	$-0.347950\pi$
$859$	789.796			0.919437			0.459718	+	0.888065i	$0.347950\pi$
$860$	−571.965	+	2379.56i	−0.665076	+	2.76693i
$861$		0			0
$862$	27.3143	−	230.509i	0.0316871	−	0.267412i
$863$		−	59.4710i		−	0.0689119i	−0.999406	−	0.0344560i	$-0.989030\pi$
$863$		−	59.4710i		−	0.0689119i	0.999406	−	0.0344560i	$-0.0109698\pi$
$864$		0			0
$865$	2157.04			2.49369
$866$	722.934	+	85.6644i	0.834796	+	0.0989197i
$867$		0			0
$868$	161.317	+	38.7752i	0.185849	+	0.0446718i
$869$			140.297i			0.161446i
$870$		0			0
$871$			35.9812i			0.0413102i
$872$	372.438	−	1008.27i	0.427107	−	1.15627i
$873$		0			0
$874$	58.5565	−	494.167i	0.0669983	−	0.565408i
$875$	−117.214			−0.133959
$876$		0			0
$877$		−	514.929i		−	0.587148i	−0.955936	−	0.293574i	$-0.905155\pi$
$877$		−	514.929i		−	0.587148i	0.955936	−	0.293574i	$-0.0948448\pi$
$878$	−62.2488	+	525.326i	−0.0708984	+	0.598321i
$879$		0			0
$880$	−734.416	+	1439.44i	−0.834564	+	1.63573i
$881$	1362.15			1.54614			0.773071	−	0.634319i	$-0.218719\pi$
$881$	1362.15			1.54614			0.773071	+	0.634319i	$0.218719\pi$
$882$		0			0
$883$	1150.48			1.30292			0.651459	−	0.758684i	$-0.274157\pi$
$883$	1150.48			1.30292			0.651459	+	0.758684i	$0.274157\pi$
$884$	−25.9628	+	108.014i	−0.0293697	+	0.122187i
$885$		0			0
$886$	−718.625	−	85.1539i	−0.811089	−	0.0961105i
$887$			321.470i			0.362424i	0.983444	+	0.181212i	$0.0580021\pi$
$887$			321.470i			0.362424i	−0.983444	+	0.181212i	$0.941998\pi$
$888$		0			0
$889$	92.3451			0.103875
$890$	−107.270	+	905.263i	−0.120528	+	1.01715i
$891$		0			0
$892$	−15.8363	+	65.8840i	−0.0177537	+	0.0738610i
$893$			737.111i			0.825432i
$894$		0			0
$895$			248.314i			0.277446i
$896$	248.901	−	229.643i	0.277792	−	0.256298i
$897$		0			0
$898$	−115.576	−	13.6953i	−0.128704	−	0.0152509i
$899$	−816.758			−0.908519
$900$		0			0
$901$			656.191i			0.728292i
$902$	−968.916	−	114.812i	−1.07419	−	0.127286i
$903$		0			0
$904$	−1348.60	−	498.150i	−1.49182	−	0.551051i
$905$	1471.64			1.62613
$906$		0			0
$907$	116.706			0.128673			0.0643365	−	0.997928i	$-0.479507\pi$
$907$	116.706			0.128673			0.0643365	+	0.997928i	$0.479507\pi$
$908$	1608.41	+	386.607i	1.77138	+	0.425779i
$909$		0			0
$910$	16.4928	−	139.185i	0.0181239	−	0.152950i
$911$			1122.30i			1.23195i	0.787767	+	0.615973i	$0.211237\pi$
$911$			1122.30i			1.23195i	−0.787767	+	0.615973i	$0.788763\pi$
$912$		0			0
$913$	1399.21			1.53254
$914$	560.559	+	66.4237i	0.613303	+	0.0726737i
$915$		0			0
$916$	−33.7001	+	140.203i	−0.0367905	+	0.153060i
$917$			336.941i			0.367438i
$918$		0			0
$919$			1476.99i			1.60717i	0.595187	+	0.803587i	$0.297078\pi$
$919$			1476.99i			1.60717i	−0.595187	+	0.803587i	$0.702922\pi$
$920$	−1255.98	−	463.938i	−1.36520	−	0.504281i
$921$		0			0
$922$	−62.0664	+	523.787i	−0.0673171	+	0.568098i
$923$	−251.697			−0.272695
$924$		0			0
$925$			685.200i			0.740757i
$926$	−47.9284	+	404.475i	−0.0517586	+	0.436798i
$927$		0			0
$928$	−927.162	+	1385.56i	−0.999097	+	1.49306i
$929$	413.368			0.444960			0.222480	−	0.974937i	$-0.428585\pi$
$929$	413.368			0.444960			0.222480	+	0.974937i	$0.428585\pi$
$930$		0			0
$931$	77.8219			0.0835895
$932$	−1179.34	−	283.473i	−1.26539	−	0.304156i
$933$		0			0
$934$	−199.679	−	23.6611i	−0.213790	−	0.0253331i
$935$		−	791.932i		−	0.846986i
$936$		0			0
$937$	−51.5540			−0.0550203			−0.0275102	−	0.999622i	$-0.508758\pi$
$937$	−51.5540			−0.0550203			−0.0275102	+	0.999622i	$0.508758\pi$
$938$	−6.32541	+	53.3810i	−0.00674350	+	0.0569093i
$939$		0			0
$940$	1928.38	+	463.517i	2.05147	+	0.493103i
$941$			247.999i			0.263548i	0.991280	+	0.131774i	$0.0420674\pi$
$941$			247.999i			0.263548i	−0.991280	+	0.131774i	$0.957933\pi$
$942$		0			0
$943$		−	808.423i		−	0.857289i
$944$	−680.489	−	347.192i	−0.720857	−	0.367788i
$945$		0			0
$946$	2194.56	+	260.046i	2.31984	+	0.274890i
$947$	−835.213			−0.881957			−0.440978	−	0.897518i	$-0.645368\pi$
$947$	−835.213			−0.881957			−0.440978	+	0.897518i	$0.645368\pi$
$948$		0			0
$949$		−	151.618i		−	0.159766i
$950$	682.817	+	80.9108i	0.718755	+	0.0851692i
$951$		0			0
$952$	−57.5064	+	155.683i	−0.0604059	+	0.163532i
$953$	−1791.85			−1.88022			−0.940112	−	0.340867i	$-0.889279\pi$
$953$	−1791.85			−1.88022			−0.940112	+	0.340867i	$0.889279\pi$
$954$		0			0
$955$	−927.270			−0.970963
$956$	44.3760	−	184.618i	0.0464184	−	0.193115i
$957$		0			0
$958$	115.716	−	976.544i	0.120789	−	1.01936i
$959$		−	411.552i		−	0.429147i
$960$		0			0
$961$	715.226			0.744252
$962$	−155.870	−	18.4699i	−0.162027	−	0.0191994i
$963$		0			0
$964$	−1061.94	−	255.255i	−1.10160	−	0.264787i
$965$			513.776i			0.532411i
$966$		0			0
$967$		−	605.335i		−	0.625993i	−0.949754	−	0.312997i	$-0.898667\pi$
$967$		−	605.335i		−	0.625993i	0.949754	−	0.312997i	$-0.101333\pi$
$968$	460.772	+	170.201i	0.476005	+	0.175828i
$969$		0			0
$970$	−91.9955	+	776.362i	−0.0948407	+	0.800373i
$971$	−113.638			−0.117032			−0.0585158	−	0.998286i	$-0.518637\pi$
$971$	−113.638			−0.117032			−0.0585158	+	0.998286i	$0.518637\pi$
$972$		0			0
$973$			134.625i			0.138360i
$974$	57.1289	−	482.118i	0.0586539	−	0.494988i
$975$		0			0
$976$	748.913	−	1467.85i	0.767329	−	1.50395i
$977$	−551.794			−0.564784			−0.282392	−	0.959299i	$-0.591128\pi$
$977$	−551.794			−0.564784			−0.282392	+	0.959299i	$0.591128\pi$
$978$		0			0
$979$	823.162			0.840819
$980$	48.9367	−	203.592i	0.0499354	−	0.207747i
$981$		0			0
$982$	1043.04	+	123.595i	1.06215	+	0.125861i
$983$			377.431i			0.383958i	0.981399	+	0.191979i	$0.0614906\pi$
$983$			377.431i			0.383958i	−0.981399	+	0.191979i	$0.938509\pi$
$984$		0			0
$985$	−1307.27			−1.32718
$986$	96.1401	−	811.340i	0.0975052	−	0.822860i
$987$		0			0
$988$	−36.8112	+	153.146i	−0.0372583	+	0.155007i
$989$			1831.05i			1.85142i
$990$		0			0
$991$			179.491i			0.181121i	0.995891	+	0.0905607i	$0.0288659\pi$
$991$			179.491i			0.181121i	−0.995891	+	0.0905607i	$0.971134\pi$
$992$	−278.996	+	416.934i	−0.281246	+	0.420296i
$993$		0			0
$994$	−373.413	−	44.2478i	−0.375667	−	0.0445149i
$995$	−984.055			−0.989000
$996$		0			0
$997$		−	1542.02i		−	1.54666i	−0.634005	−	0.773329i	$-0.718590\pi$
$997$		−	1542.02i		−	1.54666i	0.634005	−	0.773329i	$-0.281410\pi$
$998$	−459.248	−	54.4188i	−0.460168	−	0.0545279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.d.379.24		24
3.2	odd	2		168.3.g.a.43.1	✓	24
4.3	odd	2		2016.3.g.d.1135.22		24
8.3	odd	2	inner	504.3.g.d.379.23		24
8.5	even	2		2016.3.g.d.1135.3		24
12.11	even	2		672.3.g.a.463.2		24
24.5	odd	2		672.3.g.a.463.11		24
24.11	even	2		168.3.g.a.43.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.g.a.43.1	✓	24	3.2	odd	2
168.3.g.a.43.2	yes	24	24.11	even	2
504.3.g.d.379.23		24	8.3	odd	2	inner
504.3.g.d.379.24		24	1.1	even	1	trivial
672.3.g.a.463.2		24	12.11	even	2
672.3.g.a.463.11		24	24.5	odd	2
2016.3.g.d.1135.3		24	8.5	even	2
2016.3.g.d.1135.22		24	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.98610 + 0.235345i) q^{2} +(3.88923 + 0.934838i) q^{4} +7.47825i q^{5} -2.64575i q^{7} +(7.50440 + 2.77200i) q^{8} +(-1.75997 + 14.8526i) q^{10} +13.5056 q^{11} -3.54193i q^{13} +(0.622663 - 5.25474i) q^{14} +(14.2522 + 7.27159i) q^{16} -7.84106 q^{17} -11.1174 q^{19} +(-6.99095 + 29.0846i) q^{20} +(26.8235 + 3.17846i) q^{22} +22.3804i q^{23} -30.9242 q^{25} +(0.833575 - 7.03465i) q^{26} +(2.47335 - 10.2899i) q^{28} +52.0985i q^{29} +15.6772i q^{31} +(26.5949 + 17.7963i) q^{32} +(-15.5732 - 1.84535i) q^{34} +19.7856 q^{35} -22.1574i q^{37} +(-22.0803 - 2.61642i) q^{38} +(-20.7297 + 56.1198i) q^{40} -36.1220 q^{41} +81.8151 q^{43} +(52.5262 + 12.6255i) q^{44} +(-5.26710 + 44.4498i) q^{46} -66.3024i q^{47} -7.00000 q^{49} +(-61.4187 - 7.27785i) q^{50} +(3.31113 - 13.7754i) q^{52} -83.6865i q^{53} +100.998i q^{55} +(7.33401 - 19.8548i) q^{56} +(-12.2611 + 103.473i) q^{58} -47.7464 q^{59} -102.992i q^{61} +(-3.68954 + 31.1365i) q^{62} +(48.6321 + 41.6043i) q^{64} +26.4874 q^{65} -10.1586 q^{67} +(-30.4957 - 7.33013i) q^{68} +(39.2963 + 4.65643i) q^{70} -71.0621i q^{71} +42.8065 q^{73} +(5.21463 - 44.0069i) q^{74} +(-43.2381 - 10.3930i) q^{76} -35.7324i q^{77} +10.3881i q^{79} +(-54.3788 + 106.581i) q^{80} +(-71.7420 - 8.50111i) q^{82} +103.602 q^{83} -58.6374i q^{85} +(162.493 + 19.2547i) q^{86} +(101.351 + 37.4374i) q^{88} +60.9498 q^{89} -9.37107 q^{91} +(-20.9220 + 87.0424i) q^{92} +(15.6039 - 131.684i) q^{94} -83.1387i q^{95} +52.2712 q^{97} +(-13.9027 - 1.64741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 10 q^{4} - 10 q^{8} + 12 q^{10} - 32 q^{11} + 14 q^{14} + 66 q^{16} - 16 q^{17} - 64 q^{19} - 20 q^{20} + 12 q^{22} - 72 q^{25} - 100 q^{26} - 14 q^{28} - 98 q^{32} - 108 q^{34} + 72 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 + 12 * q^10 - 32 * q^11 + 14 * q^14 + 66 * q^16 - 16 * q^17 - 64 * q^19 - 20 * q^20 + 12 * q^22 - 72 * q^25 - 100 * q^26 - 14 * q^28 - 98 * q^32 - 108 * q^34 + 72 * q^38 - 332 * q^40 + 80 * q^41 + 32 * q^43 + 292 * q^44 - 168 * q^49 - 46 * q^50 - 4 * q^52 - 98 * q^56 - 96 * q^58 + 16 * q^62 - 182 * q^64 + 192 * q^65 - 32 * q^67 - 188 * q^68 - 84 * q^70 - 240 * q^73 - 208 * q^74 + 8 * q^76 - 484 * q^80 - 372 * q^82 + 320 * q^83 + 604 * q^86 + 468 * q^88 - 400 * q^89 - 352 * q^92 - 72 * q^94 + 144 * q^97 - 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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