LMFDB - Embedded newform 285.4.c.a.229.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,4,Mod(229,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("285.229");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	285.c (of order $2$, degree $1$, 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:	$16.8155443516$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	285.229
Dual form			285.4.c.a.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +(-5.00000 - 10.0000i) q^{5} +3.00000 q^{6} -4.00000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +(-5.00000 - 10.0000i) q^{5} +3.00000 q^{6} -4.00000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +(10.0000 - 5.00000i) q^{10} -68.0000 q^{11} -21.0000i q^{12} -82.0000i q^{13} +4.00000 q^{14} +(-30.0000 + 15.0000i) q^{15} +41.0000 q^{16} +86.0000i q^{17} -9.00000i q^{18} -19.0000 q^{19} +(-35.0000 - 70.0000i) q^{20} -12.0000 q^{21} -68.0000i q^{22} +18.0000i q^{23} +45.0000 q^{24} +(-75.0000 + 100.000i) q^{25} +82.0000 q^{26} +27.0000i q^{27} -28.0000i q^{28} -30.0000 q^{29} +(-15.0000 - 30.0000i) q^{30} -298.000 q^{31} +161.000i q^{32} +204.000i q^{33} -86.0000 q^{34} +(-40.0000 + 20.0000i) q^{35} -63.0000 q^{36} -34.0000i q^{37} -19.0000i q^{38} -246.000 q^{39} +(150.000 - 75.0000i) q^{40} +52.0000 q^{41} -12.0000i q^{42} -482.000i q^{43} -476.000 q^{44} +(45.0000 + 90.0000i) q^{45} -18.0000 q^{46} -114.000i q^{47} -123.000i q^{48} +327.000 q^{49} +(-100.000 - 75.0000i) q^{50} +258.000 q^{51} -574.000i q^{52} -362.000i q^{53} -27.0000 q^{54} +(340.000 + 680.000i) q^{55} +60.0000 q^{56} +57.0000i q^{57} -30.0000i q^{58} +210.000 q^{59} +(-210.000 + 105.000i) q^{60} -718.000 q^{61} -298.000i q^{62} +36.0000i q^{63} +167.000 q^{64} +(-820.000 + 410.000i) q^{65} -204.000 q^{66} -904.000i q^{67} +602.000i q^{68} +54.0000 q^{69} +(-20.0000 - 40.0000i) q^{70} -988.000 q^{71} -135.000i q^{72} +488.000i q^{73} +34.0000 q^{74} +(300.000 + 225.000i) q^{75} -133.000 q^{76} +272.000i q^{77} -246.000i q^{78} +530.000 q^{79} +(-205.000 - 410.000i) q^{80} +81.0000 q^{81} +52.0000i q^{82} -1032.00i q^{83} -84.0000 q^{84} +(860.000 - 430.000i) q^{85} +482.000 q^{86} +90.0000i q^{87} -1020.00i q^{88} +880.000 q^{89} +(-90.0000 + 45.0000i) q^{90} -328.000 q^{91} +126.000i q^{92} +894.000i q^{93} +114.000 q^{94} +(95.0000 + 190.000i) q^{95} +483.000 q^{96} +246.000i q^{97} +327.000i q^{98} +612.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 14 q^{4} - 10 q^{5} + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q + 14 * q^4 - 10 * q^5 + 6 * q^6 - 18 * q^9	$ 2 q + 14 q^{4} - 10 q^{5} + 6 q^{6} - 18 q^{9} + 20 q^{10} - 136 q^{11} + 8 q^{14} - 60 q^{15} + 82 q^{16} - 38 q^{19} - 70 q^{20} - 24 q^{21} + 90 q^{24} - 150 q^{25} + 164 q^{26} - 60 q^{29} - 30 q^{30} - 596 q^{31} - 172 q^{34} - 80 q^{35} - 126 q^{36} - 492 q^{39} + 300 q^{40} + 104 q^{41} - 952 q^{44} + 90 q^{45} - 36 q^{46} + 654 q^{49} - 200 q^{50} + 516 q^{51} - 54 q^{54} + 680 q^{55} + 120 q^{56} + 420 q^{59} - 420 q^{60} - 1436 q^{61} + 334 q^{64} - 1640 q^{65} - 408 q^{66} + 108 q^{69} - 40 q^{70} - 1976 q^{71} + 68 q^{74} + 600 q^{75} - 266 q^{76} + 1060 q^{79} - 410 q^{80} + 162 q^{81} - 168 q^{84} + 1720 q^{85} + 964 q^{86} + 1760 q^{89} - 180 q^{90} - 656 q^{91} + 228 q^{94} + 190 q^{95} + 966 q^{96} + 1224 q^{99}+O(q^{100}) $ 2 * q + 14 * q^4 - 10 * q^5 + 6 * q^6 - 18 * q^9 + 20 * q^10 - 136 * q^11 + 8 * q^14 - 60 * q^15 + 82 * q^16 - 38 * q^19 - 70 * q^20 - 24 * q^21 + 90 * q^24 - 150 * q^25 + 164 * q^26 - 60 * q^29 - 30 * q^30 - 596 * q^31 - 172 * q^34 - 80 * q^35 - 126 * q^36 - 492 * q^39 + 300 * q^40 + 104 * q^41 - 952 * q^44 + 90 * q^45 - 36 * q^46 + 654 * q^49 - 200 * q^50 + 516 * q^51 - 54 * q^54 + 680 * q^55 + 120 * q^56 + 420 * q^59 - 420 * q^60 - 1436 * q^61 + 334 * q^64 - 1640 * q^65 - 408 * q^66 + 108 * q^69 - 40 * q^70 - 1976 * q^71 + 68 * q^74 + 600 * q^75 - 266 * q^76 + 1060 * q^79 - 410 * q^80 + 162 * q^81 - 168 * q^84 + 1720 * q^85 + 964 * q^86 + 1760 * q^89 - 180 * q^90 - 656 * q^91 + 228 * q^94 + 190 * q^95 + 966 * q^96 + 1224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.353553i	0.984251	+	0.176777i	$0.0565670\pi$
$2$			1.00000i			0.353553i	−0.984251	+	0.176777i	$0.943433\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	7.00000			0.875000
$5$	−5.00000	−	10.0000i	−0.447214	−	0.894427i
$5$	−5.00000	−	10.0000i	−0.447214	−	0.894427i
$6$	3.00000			0.204124
$7$		−	4.00000i		−	0.215980i	−0.994152	−	0.107990i	$-0.965559\pi$
$7$		−	4.00000i		−	0.215980i	0.994152	−	0.107990i	$-0.0344414\pi$
$8$			15.0000i			0.662913i
$9$	−9.00000			−0.333333
$10$	10.0000	−	5.00000i	0.316228	−	0.158114i
$11$	−68.0000			−1.86389			−0.931944	−	0.362602i	$-0.881889\pi$
$11$	−68.0000			−1.86389			−0.931944	+	0.362602i	$0.881889\pi$
$12$		−	21.0000i		−	0.505181i
$13$		−	82.0000i		−	1.74944i	−0.484629	−	0.874720i	$-0.661046\pi$
$13$		−	82.0000i		−	1.74944i	0.484629	−	0.874720i	$-0.338954\pi$
$14$	4.00000			0.0763604
$15$	−30.0000	+	15.0000i	−0.516398	+	0.258199i
$16$	41.0000			0.640625
$17$			86.0000i			1.22694i	0.789716	+	0.613472i	$0.210228\pi$
$17$			86.0000i			1.22694i	−0.789716	+	0.613472i	$0.789772\pi$
$18$		−	9.00000i		−	0.117851i
$19$	−19.0000			−0.229416
$19$	−19.0000			−0.229416
$20$	−35.0000	−	70.0000i	−0.391312	−	0.782624i
$21$	−12.0000			−0.124696
$22$		−	68.0000i		−	0.658984i
$23$			18.0000i			0.163185i	0.996666	+	0.0815926i	$0.0260006\pi$
$23$			18.0000i			0.163185i	−0.996666	+	0.0815926i	$0.973999\pi$
$24$	45.0000			0.382733
$25$	−75.0000	+	100.000i	−0.600000	+	0.800000i
$26$	82.0000			0.618520
$27$			27.0000i			0.192450i
$28$		−	28.0000i		−	0.188982i
$29$	−30.0000			−0.192099			−0.0960493	−	0.995377i	$-0.530621\pi$
$29$	−30.0000			−0.192099			−0.0960493	+	0.995377i	$0.530621\pi$
$30$	−15.0000	−	30.0000i	−0.0912871	−	0.182574i
$31$	−298.000			−1.72653			−0.863264	−	0.504752i	$-0.831584\pi$
$31$	−298.000			−1.72653			−0.863264	+	0.504752i	$0.831584\pi$
$32$			161.000i			0.889408i
$33$			204.000i			1.07612i
$34$	−86.0000			−0.433791
$35$	−40.0000	+	20.0000i	−0.193178	+	0.0965891i
$36$	−63.0000			−0.291667
$37$		−	34.0000i		−	0.151069i	−0.997143	−	0.0755347i	$-0.975934\pi$
$37$		−	34.0000i		−	0.151069i	0.997143	−	0.0755347i	$-0.0240664\pi$
$38$		−	19.0000i		−	0.0811107i
$39$	−246.000			−1.01004
$40$	150.000	−	75.0000i	0.592927	−	0.296464i
$41$	52.0000			0.198074			0.0990370	−	0.995084i	$-0.468424\pi$
$41$	52.0000			0.198074			0.0990370	+	0.995084i	$0.468424\pi$
$42$		−	12.0000i		−	0.0440867i
$43$		−	482.000i		−	1.70940i	−0.519120	−	0.854701i	$-0.673740\pi$
$43$		−	482.000i		−	1.70940i	0.519120	−	0.854701i	$-0.326260\pi$
$44$	−476.000			−1.63090
$45$	45.0000	+	90.0000i	0.149071	+	0.298142i
$46$	−18.0000			−0.0576947
$47$		−	114.000i		−	0.353800i	−0.984229	−	0.176900i	$-0.943393\pi$
$47$		−	114.000i		−	0.353800i	0.984229	−	0.176900i	$-0.0566069\pi$
$48$		−	123.000i		−	0.369865i
$49$	327.000			0.953353
$50$	−100.000	−	75.0000i	−0.282843	−	0.212132i
$51$	258.000			0.708377
$52$		−	574.000i		−	1.53076i
$53$		−	362.000i		−	0.938199i	−0.883145	−	0.469099i	$-0.844579\pi$
$53$		−	362.000i		−	0.938199i	0.883145	−	0.469099i	$-0.155421\pi$
$54$	−27.0000			−0.0680414
$55$	340.000	+	680.000i	0.833556	+	1.66711i
$56$	60.0000			0.143176
$57$			57.0000i			0.132453i
$58$		−	30.0000i		−	0.0679171i
$59$	210.000			0.463384			0.231692	−	0.972789i	$-0.425574\pi$
$59$	210.000			0.463384			0.231692	+	0.972789i	$0.425574\pi$
$60$	−210.000	+	105.000i	−0.451848	+	0.225924i
$61$	−718.000			−1.50706			−0.753529	−	0.657415i	$-0.771650\pi$
$61$	−718.000			−1.50706			−0.753529	+	0.657415i	$0.771650\pi$
$62$		−	298.000i		−	0.610420i
$63$			36.0000i			0.0719932i
$64$	167.000			0.326172
$65$	−820.000	+	410.000i	−1.56475	+	0.782373i
$66$	−204.000			−0.380465
$67$		−	904.000i		−	1.64838i	−0.566316	−	0.824188i	$-0.691632\pi$
$67$		−	904.000i		−	1.64838i	0.566316	−	0.824188i	$-0.308368\pi$
$68$			602.000i			1.07358i
$69$	54.0000			0.0942150
$70$	−20.0000	−	40.0000i	−0.0341494	−	0.0682988i
$71$	−988.000			−1.65147			−0.825733	−	0.564062i	$-0.809238\pi$
$71$	−988.000			−1.65147			−0.825733	+	0.564062i	$0.809238\pi$
$72$		−	135.000i		−	0.220971i
$73$			488.000i			0.782412i	0.920303	+	0.391206i	$0.127942\pi$
$73$			488.000i			0.782412i	−0.920303	+	0.391206i	$0.872058\pi$
$74$	34.0000			0.0534111
$75$	300.000	+	225.000i	0.461880	+	0.346410i
$76$	−133.000			−0.200739
$77$			272.000i			0.402562i
$78$		−	246.000i		−	0.357103i
$79$	530.000			0.754806			0.377403	−	0.926049i	$-0.376817\pi$
$79$	530.000			0.754806			0.377403	+	0.926049i	$0.376817\pi$
$80$	−205.000	−	410.000i	−0.286496	−	0.572992i
$81$	81.0000			0.111111
$82$			52.0000i			0.0700297i
$83$		−	1032.00i		−	1.36478i	−0.730988	−	0.682390i	$-0.760941\pi$
$83$		−	1032.00i		−	1.36478i	0.730988	−	0.682390i	$-0.239059\pi$
$84$	−84.0000			−0.109109
$85$	860.000	−	430.000i	1.09741	−	0.548706i
$86$	482.000			0.604365
$87$			90.0000i			0.110908i
$88$		−	1020.00i		−	1.23560i
$89$	880.000			1.04809			0.524044	−	0.851691i	$-0.324423\pi$
$89$	880.000			1.04809			0.524044	+	0.851691i	$0.324423\pi$
$90$	−90.0000	+	45.0000i	−0.105409	+	0.0527046i
$91$	−328.000			−0.377843
$92$			126.000i			0.142787i
$93$			894.000i			0.996812i
$94$	114.000			0.125087
$95$	95.0000	+	190.000i	0.102598	+	0.205196i
$96$	483.000			0.513500
$97$			246.000i			0.257500i	0.991677	+	0.128750i	$0.0410965\pi$
$97$			246.000i			0.257500i	−0.991677	+	0.128750i	$0.958903\pi$
$98$			327.000i			0.337061i
$99$	612.000			0.621296
$100$	−525.000	+	700.000i	−0.525000	+	0.700000i
$101$	−858.000			−0.845289			−0.422645	−	0.906296i	$-0.638898\pi$
$101$	−858.000			−0.845289			−0.422645	+	0.906296i	$0.638898\pi$
$102$			258.000i			0.250449i
$103$			1088.00i			1.04081i	0.853918	+	0.520407i	$0.174220\pi$
$103$			1088.00i			1.04081i	−0.853918	+	0.520407i	$0.825780\pi$
$104$	1230.00			1.15973
$105$	60.0000	+	120.000i	0.0557657	+	0.111531i
$106$	362.000			0.331703
$107$			436.000i			0.393923i	0.980411	+	0.196961i	$0.0631073\pi$
$107$			436.000i			0.393923i	−0.980411	+	0.196961i	$0.936893\pi$
$108$			189.000i			0.168394i
$109$	1680.00			1.47628			0.738141	−	0.674646i	$-0.235704\pi$
$109$	1680.00			1.47628			0.738141	+	0.674646i	$0.235704\pi$
$110$	−680.000	+	340.000i	−0.589413	+	0.294707i
$111$	−102.000			−0.0872199
$112$		−	164.000i		−	0.138362i
$113$		−	762.000i		−	0.634362i	−0.948365	−	0.317181i	$-0.897264\pi$
$113$		−	762.000i		−	0.634362i	0.948365	−	0.317181i	$-0.102736\pi$
$114$	−57.0000			−0.0468293
$115$	180.000	−	90.0000i	0.145957	−	0.0729786i
$116$	−210.000			−0.168086
$117$			738.000i			0.583146i
$118$			210.000i			0.163831i
$119$	344.000			0.264995
$120$	−225.000	−	450.000i	−0.171163	−	0.342327i
$121$	3293.00			2.47408
$122$		−	718.000i		−	0.532825i
$123$		−	156.000i		−	0.114358i
$124$	−2086.00			−1.51071
$125$	1375.00	+	250.000i	0.983870	+	0.178885i
$126$	−36.0000			−0.0254535
$127$		−	624.000i		−	0.435992i	−0.975950	−	0.217996i	$-0.930048\pi$
$127$		−	624.000i		−	0.435992i	0.975950	−	0.217996i	$-0.0699521\pi$
$128$			1455.00i			1.00473i
$129$	−1446.00			−0.986924
$130$	−410.000	−	820.000i	−0.276611	−	0.553221i
$131$	1152.00			0.768326			0.384163	−	0.923265i	$-0.374490\pi$
$131$	1152.00			0.768326			0.384163	+	0.923265i	$0.374490\pi$
$132$			1428.00i			0.941602i
$133$			76.0000i			0.0495491i
$134$	904.000			0.582789
$135$	270.000	−	135.000i	0.172133	−	0.0860663i
$136$	−1290.00			−0.813357
$137$		−	1254.00i		−	0.782018i	−0.920387	−	0.391009i	$-0.872126\pi$
$137$		−	1254.00i		−	0.782018i	0.920387	−	0.391009i	$-0.127874\pi$
$138$			54.0000i			0.0333100i
$139$	1300.00			0.793270			0.396635	−	0.917976i	$-0.370178\pi$
$139$	1300.00			0.793270			0.396635	+	0.917976i	$0.370178\pi$
$140$	−280.000	+	140.000i	−0.169031	+	0.0845154i
$141$	−342.000			−0.204267
$142$		−	988.000i		−	0.583881i
$143$			5576.00i			3.26076i
$144$	−369.000			−0.213542
$145$	150.000	+	300.000i	0.0859091	+	0.171818i
$146$	−488.000			−0.276624
$147$		−	981.000i		−	0.550418i
$148$		−	238.000i		−	0.132186i
$149$	−1810.00			−0.995174			−0.497587	−	0.867414i	$-0.665781\pi$
$149$	−1810.00			−0.995174			−0.497587	+	0.867414i	$0.665781\pi$
$150$	−225.000	+	300.000i	−0.122474	+	0.163299i
$151$	1662.00			0.895706			0.447853	−	0.894107i	$-0.352189\pi$
$151$	1662.00			0.895706			0.447853	+	0.894107i	$0.352189\pi$
$152$		−	285.000i		−	0.152083i
$153$		−	774.000i		−	0.408982i
$154$	−272.000			−0.142327
$155$	1490.00	+	2980.00i	0.772127	+	1.54425i
$156$	−1722.00			−0.883784
$157$			706.000i			0.358885i	0.983768	+	0.179442i	$0.0574294\pi$
$157$			706.000i			0.358885i	−0.983768	+	0.179442i	$0.942571\pi$
$158$			530.000i			0.266864i
$159$	−1086.00			−0.541669
$160$	1610.00	−	805.000i	0.795510	−	0.397755i
$161$	72.0000			0.0352447
$162$			81.0000i			0.0392837i
$163$		−	1462.00i		−	0.702532i	−0.936276	−	0.351266i	$-0.885751\pi$
$163$		−	1462.00i		−	0.702532i	0.936276	−	0.351266i	$-0.114249\pi$
$164$	364.000			0.173315
$165$	2040.00	−	1020.00i	0.962508	−	0.481254i
$166$	1032.00			0.482522
$167$		−	624.000i		−	0.289141i	−0.989494	−	0.144571i	$-0.953820\pi$
$167$		−	624.000i		−	0.289141i	0.989494	−	0.144571i	$-0.0461801\pi$
$168$		−	180.000i		−	0.0826625i
$169$	−4527.00			−2.06054
$170$	430.000	+	860.000i	0.193997	+	0.387994i
$171$	171.000			0.0764719
$172$		−	3374.00i		−	1.49573i
$173$			3198.00i			1.40543i	0.711471	+	0.702715i	$0.248029\pi$
$173$			3198.00i			1.40543i	−0.711471	+	0.702715i	$0.751971\pi$
$174$	−90.0000			−0.0392120
$175$	400.000	+	300.000i	0.172784	+	0.129588i
$176$	−2788.00			−1.19405
$177$		−	630.000i		−	0.267535i
$178$			880.000i			0.370555i
$179$	1710.00			0.714030			0.357015	−	0.934099i	$-0.383794\pi$
$179$	1710.00			0.714030			0.357015	+	0.934099i	$0.383794\pi$
$180$	315.000	+	630.000i	0.130437	+	0.260875i
$181$	312.000			0.128126			0.0640629	−	0.997946i	$-0.479594\pi$
$181$	312.000			0.128126			0.0640629	+	0.997946i	$0.479594\pi$
$182$		−	328.000i		−	0.133588i
$183$			2154.00i			0.870100i
$184$	−270.000			−0.108178
$185$	−340.000	+	170.000i	−0.135121	+	0.0675603i
$186$	−894.000			−0.352426
$187$		−	5848.00i		−	2.28689i
$188$		−	798.000i		−	0.309575i
$189$	108.000			0.0415653
$190$	−190.000	+	95.0000i	−0.0725476	+	0.0362738i
$191$	2472.00			0.936480			0.468240	−	0.883601i	$-0.344888\pi$
$191$	2472.00			0.936480			0.468240	+	0.883601i	$0.344888\pi$
$192$		−	501.000i		−	0.188315i
$193$		−	2422.00i		−	0.903313i	−0.892192	−	0.451656i	$-0.850833\pi$
$193$		−	2422.00i		−	0.903313i	0.892192	−	0.451656i	$-0.149167\pi$
$194$	−246.000			−0.0910401
$195$	1230.00	+	2460.00i	0.451703	+	0.903406i
$196$	2289.00			0.834184
$197$		−	3984.00i		−	1.44085i	−0.693531	−	0.720427i	$-0.743946\pi$
$197$		−	3984.00i		−	1.44085i	0.693531	−	0.720427i	$-0.256054\pi$
$198$			612.000i			0.219661i
$199$	2000.00			0.712443			0.356222	−	0.934401i	$-0.384065\pi$
$199$	2000.00			0.712443			0.356222	+	0.934401i	$0.384065\pi$
$200$	−1500.00	−	1125.00i	−0.530330	−	0.397748i
$201$	−2712.00			−0.951690
$202$		−	858.000i		−	0.298855i
$203$			120.000i			0.0414894i
$204$	1806.00			0.619830
$205$	−260.000	−	520.000i	−0.0885814	−	0.177163i
$206$	−1088.00			−0.367983
$207$		−	162.000i		−	0.0543951i
$208$		−	3362.00i		−	1.12073i
$209$	1292.00			0.427605
$210$	−120.000	+	60.0000i	−0.0394323	+	0.0197162i
$211$	−4768.00			−1.55565			−0.777826	−	0.628479i	$-0.783678\pi$
$211$	−4768.00			−1.55565			−0.777826	+	0.628479i	$0.783678\pi$
$212$		−	2534.00i		−	0.820924i
$213$			2964.00i			0.953474i
$214$	−436.000			−0.139273
$215$	−4820.00	+	2410.00i	−1.52894	+	0.764468i
$216$	−405.000			−0.127578
$217$			1192.00i			0.372895i
$218$			1680.00i			0.521945i
$219$	1464.00			0.451726
$220$	2380.00	+	4760.00i	0.729362	+	1.45872i
$221$	7052.00			2.14647
$222$		−	102.000i		−	0.0308369i
$223$			3248.00i			0.975346i	0.873026	+	0.487673i	$0.162154\pi$
$223$			3248.00i			0.975346i	−0.873026	+	0.487673i	$0.837846\pi$
$224$	644.000			0.192094
$225$	675.000	−	900.000i	0.200000	−	0.266667i
$226$	762.000			0.224281
$227$		−	5444.00i		−	1.59177i	−0.605450	−	0.795883i	$-0.707007\pi$
$227$		−	5444.00i		−	1.59177i	0.605450	−	0.795883i	$-0.292993\pi$
$228$			399.000i			0.115897i
$229$	3490.00			1.00710			0.503550	−	0.863966i	$-0.332027\pi$
$229$	3490.00			1.00710			0.503550	+	0.863966i	$0.332027\pi$
$230$	90.0000	+	180.000i	0.0258018	+	0.0516037i
$231$	816.000			0.232419
$232$		−	450.000i		−	0.127345i
$233$		−	4202.00i		−	1.18147i	−0.806866	−	0.590734i	$-0.798838\pi$
$233$		−	4202.00i		−	1.18147i	0.806866	−	0.590734i	$-0.201162\pi$
$234$	−738.000			−0.206173
$235$	−1140.00	+	570.000i	−0.316449	+	0.158224i
$236$	1470.00			0.405461
$237$		−	1590.00i		−	0.435787i
$238$			344.000i			0.0936899i
$239$	−6400.00			−1.73214			−0.866070	−	0.499922i	$-0.833362\pi$
$239$	−6400.00			−1.73214			−0.866070	+	0.499922i	$0.833362\pi$
$240$	−1230.00	+	615.000i	−0.330817	+	0.165409i
$241$	3142.00			0.839809			0.419905	−	0.907568i	$-0.362064\pi$
$241$	3142.00			0.839809			0.419905	+	0.907568i	$0.362064\pi$
$242$			3293.00i			0.874719i
$243$		−	243.000i		−	0.0641500i
$244$	−5026.00			−1.31867
$245$	−1635.00	−	3270.00i	−0.426352	−	0.852705i
$246$	156.000			0.0404317
$247$			1558.00i			0.401349i
$248$		−	4470.00i		−	1.14454i
$249$	−3096.00			−0.787956
$250$	−250.000	+	1375.00i	−0.0632456	+	0.347851i
$251$	−3988.00			−1.00287			−0.501435	−	0.865195i	$-0.667194\pi$
$251$	−3988.00			−1.00287			−0.501435	+	0.865195i	$0.667194\pi$
$252$			252.000i			0.0629941i
$253$		−	1224.00i		−	0.304159i
$254$	624.000			0.154147
$255$	−1290.00	−	2580.00i	−0.316796	−	0.633592i
$256$	−119.000			−0.0290527
$257$			606.000i			0.147087i	0.997292	+	0.0735433i	$0.0234307\pi$
$257$			606.000i			0.147087i	−0.997292	+	0.0735433i	$0.976569\pi$
$258$		−	1446.00i		−	0.348930i
$259$	−136.000			−0.0326279
$260$	−5740.00	+	2870.00i	−1.36915	+	0.684576i
$261$	270.000			0.0640329
$262$			1152.00i			0.271644i
$263$		−	2262.00i		−	0.530346i	−0.964201	−	0.265173i	$-0.914571\pi$
$263$		−	2262.00i		−	0.530346i	0.964201	−	0.265173i	$-0.0854290\pi$
$264$	−3060.00			−0.713371
$265$	−3620.00	+	1810.00i	−0.839150	+	0.419575i
$266$	−76.0000			−0.0175183
$267$		−	2640.00i		−	0.605114i
$268$		−	6328.00i		−	1.44233i
$269$	−1170.00			−0.265190			−0.132595	−	0.991170i	$-0.542331\pi$
$269$	−1170.00			−0.265190			−0.132595	+	0.991170i	$0.542331\pi$
$270$	135.000	+	270.000i	0.0304290	+	0.0608581i
$271$	−7728.00			−1.73226			−0.866130	−	0.499818i	$-0.833400\pi$
$271$	−7728.00			−1.73226			−0.866130	+	0.499818i	$0.833400\pi$
$272$			3526.00i			0.786012i
$273$			984.000i			0.218148i
$274$	1254.00			0.276485
$275$	5100.00	−	6800.00i	1.11833	−	1.49111i
$276$	378.000			0.0824381
$277$			3386.00i			0.734459i	0.930130	+	0.367229i	$0.119694\pi$
$277$			3386.00i			0.734459i	−0.930130	+	0.367229i	$0.880306\pi$
$278$			1300.00i			0.280463i
$279$	2682.00			0.575509
$280$	−300.000	−	600.000i	−0.0640301	−	0.128060i
$281$	−1708.00			−0.362600			−0.181300	−	0.983428i	$-0.558031\pi$
$281$	−1708.00			−0.362600			−0.181300	+	0.983428i	$0.558031\pi$
$282$		−	342.000i		−	0.0722192i
$283$			7378.00i			1.54974i	0.632120	+	0.774870i	$0.282185\pi$
$283$			7378.00i			1.54974i	−0.632120	+	0.774870i	$0.717815\pi$
$284$	−6916.00			−1.44503
$285$	570.000	−	285.000i	0.118470	−	0.0592349i
$286$	−5576.00			−1.15285
$287$		−	208.000i		−	0.0427800i
$288$		−	1449.00i		−	0.296469i
$289$	−2483.00			−0.505394
$290$	−300.000	+	150.000i	−0.0607469	+	0.0303735i
$291$	738.000			0.148668
$292$			3416.00i			0.684611i
$293$			2038.00i			0.406352i	0.979142	+	0.203176i	$0.0651264\pi$
$293$			2038.00i			0.406352i	−0.979142	+	0.203176i	$0.934874\pi$
$294$	981.000			0.194602
$295$	−1050.00	−	2100.00i	−0.207232	−	0.414463i
$296$	510.000			0.100146
$297$		−	1836.00i		−	0.358705i
$298$		−	1810.00i		−	0.351847i
$299$	1476.00			0.285483
$300$	2100.00	+	1575.00i	0.404145	+	0.303109i
$301$	−1928.00			−0.369196
$302$			1662.00i			0.316680i
$303$			2574.00i			0.488028i
$304$	−779.000			−0.146969
$305$	3590.00	+	7180.00i	0.673976	+	1.34795i
$306$	774.000			0.144597
$307$			1636.00i			0.304142i	0.988370	+	0.152071i	$0.0485942\pi$
$307$			1636.00i			0.304142i	−0.988370	+	0.152071i	$0.951406\pi$
$308$			1904.00i			0.352242i
$309$	3264.00			0.600914
$310$	−2980.00	+	1490.00i	−0.545976	+	0.272988i
$311$	−1848.00			−0.336947			−0.168473	−	0.985706i	$-0.553884\pi$
$311$	−1848.00			−0.336947			−0.168473	+	0.985706i	$0.553884\pi$
$312$		−	3690.00i		−	0.669568i
$313$			4908.00i			0.886315i	0.896444	+	0.443157i	$0.146142\pi$
$313$			4908.00i			0.886315i	−0.896444	+	0.443157i	$0.853858\pi$
$314$	−706.000			−0.126885
$315$	360.000	−	180.000i	0.0643927	−	0.0321964i
$316$	3710.00			0.660455
$317$			4526.00i			0.801910i	0.916098	+	0.400955i	$0.131322\pi$
$317$			4526.00i			0.801910i	−0.916098	+	0.400955i	$0.868678\pi$
$318$		−	1086.00i		−	0.191509i
$319$	2040.00			0.358050
$320$	−835.000	−	1670.00i	−0.145868	−	0.291737i
$321$	1308.00			0.227431
$322$			72.0000i			0.0124609i
$323$		−	1634.00i		−	0.281480i
$324$	567.000			0.0972222
$325$	8200.00	+	6150.00i	1.39955	+	1.04966i
$326$	1462.00			0.248382
$327$		−	5040.00i		−	0.852332i
$328$			780.000i			0.131306i
$329$	−456.000			−0.0764137
$330$	1020.00	+	2040.00i	0.170149	+	0.340298i
$331$	−6388.00			−1.06077			−0.530387	−	0.847756i	$-0.677953\pi$
$331$	−6388.00			−1.06077			−0.530387	+	0.847756i	$0.677953\pi$
$332$		−	7224.00i		−	1.19418i
$333$			306.000i			0.0503564i
$334$	624.000			0.102227
$335$	−9040.00	+	4520.00i	−1.47435	+	0.737176i
$336$	−492.000			−0.0798833
$337$			286.000i			0.0462297i	0.999733	+	0.0231149i	$0.00735834\pi$
$337$			286.000i			0.0462297i	−0.999733	+	0.0231149i	$0.992642\pi$
$338$		−	4527.00i		−	0.728510i
$339$	−2286.00			−0.366249
$340$	6020.00	−	3010.00i	0.960236	−	0.480118i
$341$	20264.0			3.21806
$342$			171.000i			0.0270369i
$343$		−	2680.00i		−	0.421885i
$344$	7230.00			1.13318
$345$	−270.000	−	540.000i	−0.0421342	−	0.0842685i
$346$	−3198.00			−0.496895
$347$		−	8904.00i		−	1.37750i	−0.725000	−	0.688749i	$-0.758160\pi$
$347$		−	8904.00i		−	1.37750i	0.725000	−	0.688749i	$-0.241840\pi$
$348$			630.000i			0.0970447i
$349$	−7670.00			−1.17641			−0.588203	−	0.808713i	$-0.700164\pi$
$349$	−7670.00			−1.17641			−0.588203	+	0.808713i	$0.700164\pi$
$350$	−300.000	+	400.000i	−0.0458162	+	0.0610883i
$351$	2214.00			0.336680
$352$		−	10948.0i		−	1.65776i
$353$		−	2.00000i		−	0.000301556i	−1.00000		0.000150778i	$-0.999952\pi$
$353$		−	2.00000i		−	0.000301556i	1.00000		0.000150778i	$-4.79941e-5\pi$
$354$	630.000			0.0945879
$355$	4940.00	+	9880.00i	0.738558	+	1.47712i
$356$	6160.00			0.917077
$357$		−	1032.00i		−	0.152995i
$358$			1710.00i			0.252448i
$359$	1120.00			0.164656			0.0823278	−	0.996605i	$-0.473765\pi$
$359$	1120.00			0.164656			0.0823278	+	0.996605i	$0.473765\pi$
$360$	−1350.00	+	675.000i	−0.197642	+	0.0988212i
$361$	361.000			0.0526316
$362$			312.000i			0.0452993i
$363$		−	9879.00i		−	1.42841i
$364$	−2296.00			−0.330613
$365$	4880.00	−	2440.00i	0.699811	−	0.349905i
$366$	−2154.00			−0.307627
$367$		−	1984.00i		−	0.282191i	−0.989996	−	0.141095i	$-0.954938\pi$
$367$		−	1984.00i		−	0.282191i	0.989996	−	0.141095i	$-0.0450624\pi$
$368$			738.000i			0.104541i
$369$	−468.000			−0.0660247
$370$	−170.000	−	340.000i	−0.0238862	−	0.0477723i
$371$	−1448.00			−0.202632
$372$			6258.00i			0.872210i
$373$			2058.00i			0.285682i	0.989746	+	0.142841i	$0.0456237\pi$
$373$			2058.00i			0.285682i	−0.989746	+	0.142841i	$0.954376\pi$
$374$	5848.00			0.808537
$375$	750.000	−	4125.00i	0.103280	−	0.568038i
$376$	1710.00			0.234539
$377$			2460.00i			0.336065i
$378$			108.000i			0.0146956i
$379$	10640.0			1.44206			0.721029	−	0.692905i	$-0.243669\pi$
$379$	10640.0			1.44206			0.721029	+	0.692905i	$0.243669\pi$
$380$	665.000	+	1330.00i	0.0897731	+	0.179546i
$381$	−1872.00			−0.251720
$382$			2472.00i			0.331096i
$383$		−	5892.00i		−	0.786076i	−0.919522	−	0.393038i	$-0.871424\pi$
$383$		−	5892.00i		−	0.786076i	0.919522	−	0.393038i	$-0.128576\pi$
$384$	4365.00			0.580079
$385$	2720.00	−	1360.00i	0.360062	−	0.180031i
$386$	2422.00			0.319369
$387$			4338.00i			0.569801i
$388$			1722.00i			0.225313i
$389$	−990.000			−0.129036			−0.0645180	−	0.997917i	$-0.520551\pi$
$389$	−990.000			−0.129036			−0.0645180	+	0.997917i	$0.520551\pi$
$390$	−2460.00	+	1230.00i	−0.319402	+	0.159701i
$391$	−1548.00			−0.200219
$392$			4905.00i			0.631990i
$393$		−	3456.00i		−	0.443593i
$394$	3984.00			0.509419
$395$	−2650.00	−	5300.00i	−0.337559	−	0.675119i
$396$	4284.00			0.543634
$397$			526.000i			0.0664967i	0.999447	+	0.0332483i	$0.0105852\pi$
$397$			526.000i			0.0664967i	−0.999447	+	0.0332483i	$0.989415\pi$
$398$			2000.00i			0.251887i
$399$	228.000			0.0286072
$400$	−3075.00	+	4100.00i	−0.384375	+	0.512500i
$401$	9612.00			1.19701			0.598504	−	0.801120i	$-0.295762\pi$
$401$	9612.00			1.19701			0.598504	+	0.801120i	$0.295762\pi$
$402$		−	2712.00i		−	0.336473i
$403$			24436.0i			3.02046i
$404$	−6006.00			−0.739628
$405$	−405.000	−	810.000i	−0.0496904	−	0.0993808i
$406$	−120.000			−0.0146687
$407$			2312.00i			0.281576i
$408$			3870.00i			0.469592i
$409$	9110.00			1.10137			0.550685	−	0.834713i	$-0.314366\pi$
$409$	9110.00			1.10137			0.550685	+	0.834713i	$0.314366\pi$
$410$	520.000	−	260.000i	0.0626365	−	0.0313183i
$411$	−3762.00			−0.451498
$412$			7616.00i			0.910712i
$413$		−	840.000i		−	0.100082i
$414$	162.000			0.0192316
$415$	−10320.0	+	5160.00i	−1.22070	+	0.610348i
$416$	13202.0			1.55596
$417$		−	3900.00i		−	0.457995i
$418$			1292.00i			0.151181i
$419$	−13920.0			−1.62300			−0.811499	−	0.584353i	$-0.801348\pi$
$419$	−13920.0			−1.62300			−0.811499	+	0.584353i	$0.801348\pi$
$420$	420.000	+	840.000i	0.0487950	+	0.0975900i
$421$	−9588.00			−1.10995			−0.554977	−	0.831866i	$-0.687273\pi$
$421$	−9588.00			−1.10995			−0.554977	+	0.831866i	$0.687273\pi$
$422$		−	4768.00i		−	0.550006i
$423$			1026.00i			0.117933i
$424$	5430.00			0.621944
$425$	−8600.00	−	6450.00i	−0.981556	−	0.736167i
$426$	−2964.00			−0.337104
$427$			2872.00i			0.325494i
$428$			3052.00i			0.344682i
$429$	16728.0			1.88260
$430$	−2410.00	−	4820.00i	−0.270280	−	0.540561i
$431$	−4968.00			−0.555221			−0.277610	−	0.960694i	$-0.589542\pi$
$431$	−4968.00			−0.555221			−0.277610	+	0.960694i	$0.589542\pi$
$432$			1107.00i			0.123288i
$433$		−	11342.0i		−	1.25880i	−0.777080	−	0.629402i	$-0.783300\pi$
$433$		−	11342.0i		−	1.25880i	0.777080	−	0.629402i	$-0.216700\pi$
$434$	−1192.00			−0.131838
$435$	900.000	−	450.000i	0.0991993	−	0.0495997i
$436$	11760.0			1.29175
$437$		−	342.000i		−	0.0374373i
$438$			1464.00i			0.159709i
$439$	−3710.00			−0.403345			−0.201673	−	0.979453i	$-0.564638\pi$
$439$	−3710.00			−0.403345			−0.201673	+	0.979453i	$0.564638\pi$
$440$	−10200.0	+	5100.00i	−1.10515	+	0.552575i
$441$	−2943.00			−0.317784
$442$			7052.00i			0.758890i
$443$		−	10772.0i		−	1.15529i	−0.816288	−	0.577645i	$-0.803972\pi$
$443$		−	10772.0i		−	1.15529i	0.816288	−	0.577645i	$-0.196028\pi$
$444$	−714.000			−0.0763174
$445$	−4400.00	−	8800.00i	−0.468719	−	0.937438i
$446$	−3248.00			−0.344837
$447$			5430.00i			0.574564i
$448$		−	668.000i		−	0.0704465i
$449$	1720.00			0.180784			0.0903918	−	0.995906i	$-0.471188\pi$
$449$	1720.00			0.180784			0.0903918	+	0.995906i	$0.471188\pi$
$450$	900.000	+	675.000i	0.0942809	+	0.0707107i
$451$	−3536.00			−0.369188
$452$		−	5334.00i		−	0.555067i
$453$		−	4986.00i		−	0.517136i
$454$	5444.00			0.562774
$455$	1640.00	+	3280.00i	0.168977	+	0.337953i
$456$	−855.000			−0.0878049
$457$			1456.00i			0.149035i	0.997220	+	0.0745173i	$0.0237416\pi$
$457$			1456.00i			0.149035i	−0.997220	+	0.0745173i	$0.976258\pi$
$458$			3490.00i			0.356063i
$459$	−2322.00			−0.236126
$460$	1260.00	−	630.000i	0.127713	−	0.0638563i
$461$	−6218.00			−0.628202			−0.314101	−	0.949390i	$-0.601703\pi$
$461$	−6218.00			−0.628202			−0.314101	+	0.949390i	$0.601703\pi$
$462$			816.000i			0.0821726i
$463$		−	13892.0i		−	1.39442i	−0.716867	−	0.697209i	$-0.754425\pi$
$463$		−	13892.0i		−	1.39442i	0.716867	−	0.697209i	$-0.245575\pi$
$464$	−1230.00			−0.123063
$465$	8940.00	−	4470.00i	0.891575	−	0.445788i
$466$	4202.00			0.417712
$467$		−	6004.00i		−	0.594929i	−0.954733	−	0.297465i	$-0.903859\pi$
$467$		−	6004.00i		−	0.594929i	0.954733	−	0.297465i	$-0.0961410\pi$
$468$			5166.00i			0.510253i
$469$	−3616.00			−0.356016
$470$	−570.000	−	1140.00i	−0.0559407	−	0.111881i
$471$	2118.00			0.207202
$472$			3150.00i			0.307183i
$473$			32776.0i			3.18614i
$474$	1590.00			0.154074
$475$	1425.00	−	1900.00i	0.137649	−	0.183533i
$476$	2408.00			0.231871
$477$			3258.00i			0.312733i
$478$		−	6400.00i		−	0.612404i
$479$	−4800.00			−0.457866			−0.228933	−	0.973442i	$-0.573524\pi$
$479$	−4800.00			−0.457866			−0.228933	+	0.973442i	$0.573524\pi$
$480$	−2415.00	−	4830.00i	−0.229644	−	0.459288i
$481$	−2788.00			−0.264287
$482$			3142.00i			0.296917i
$483$		−	216.000i		−	0.0203485i
$484$	23051.0			2.16482
$485$	2460.00	−	1230.00i	0.230315	−	0.115158i
$486$	243.000			0.0226805
$487$			12616.0i			1.17389i	0.809626	+	0.586946i	$0.199670\pi$
$487$			12616.0i			1.17389i	−0.809626	+	0.586946i	$0.800330\pi$
$488$		−	10770.0i		−	0.999047i
$489$	−4386.00			−0.405607
$490$	3270.00	−	1635.00i	0.301477	−	0.150738i
$491$	4232.00			0.388977			0.194488	−	0.980905i	$-0.437695\pi$
$491$	4232.00			0.388977			0.194488	+	0.980905i	$0.437695\pi$
$492$		−	1092.00i		−	0.100063i
$493$		−	2580.00i		−	0.235694i
$494$	−1558.00			−0.141898
$495$	−3060.00	−	6120.00i	−0.277852	−	0.555704i
$496$	−12218.0			−1.10606
$497$			3952.00i			0.356683i
$498$		−	3096.00i		−	0.278584i
$499$	−6340.00			−0.568772			−0.284386	−	0.958710i	$-0.591790\pi$
$499$	−6340.00			−0.568772			−0.284386	+	0.958710i	$0.591790\pi$
$500$	9625.00	+	1750.00i	0.860886	+	0.156525i
$501$	−1872.00			−0.166936
$502$		−	3988.00i		−	0.354568i
$503$			14878.0i			1.31884i	0.751774	+	0.659421i	$0.229198\pi$
$503$			14878.0i			1.31884i	−0.751774	+	0.659421i	$0.770802\pi$
$504$	−540.000			−0.0477252
$505$	4290.00	+	8580.00i	0.378025	+	0.756049i
$506$	1224.00			0.107536
$507$			13581.0i			1.18965i
$508$		−	4368.00i		−	0.381493i
$509$	6090.00			0.530323			0.265162	−	0.964204i	$-0.414575\pi$
$509$	6090.00			0.530323			0.265162	+	0.964204i	$0.414575\pi$
$510$	2580.00	−	1290.00i	0.224008	−	0.112004i
$511$	1952.00			0.168985
$512$			11521.0i			0.994455i
$513$		−	513.000i		−	0.0441511i
$514$	−606.000			−0.0520029
$515$	10880.0	−	5440.00i	0.930932	−	0.465466i
$516$	−10122.0			−0.863559
$517$			7752.00i			0.659444i
$518$		−	136.000i		−	0.0115357i
$519$	9594.00			0.811426
$520$	−6150.00	−	12300.0i	−0.518645	−	1.03729i
$521$	12612.0			1.06054			0.530270	−	0.847829i	$-0.322090\pi$
$521$	12612.0			1.06054			0.530270	+	0.847829i	$0.322090\pi$
$522$			270.000i			0.0226390i
$523$			8828.00i			0.738091i	0.929411	+	0.369045i	$0.120315\pi$
$523$			8828.00i			0.738091i	−0.929411	+	0.369045i	$0.879685\pi$
$524$	8064.00			0.672285
$525$	900.000	−	1200.00i	0.0748176	−	0.0997567i
$526$	2262.00			0.187505
$527$		−	25628.0i		−	2.11836i
$528$			8364.00i			0.689387i
$529$	11843.0			0.973371
$530$	−1810.00	−	3620.00i	−0.148342	−	0.296684i
$531$	−1890.00			−0.154461
$532$			532.000i			0.0433555i
$533$		−	4264.00i		−	0.346518i
$534$	2640.00			0.213940
$535$	4360.00	−	2180.00i	0.352335	−	0.176168i
$536$	13560.0			1.09273
$537$		−	5130.00i		−	0.412246i
$538$		−	1170.00i		−	0.0937589i
$539$	−22236.0			−1.77694
$540$	1890.00	−	945.000i	0.150616	−	0.0753080i
$541$	−20938.0			−1.66395			−0.831973	−	0.554816i	$-0.812789\pi$
$541$	−20938.0			−1.66395			−0.831973	+	0.554816i	$0.812789\pi$
$542$		−	7728.00i		−	0.612447i
$543$		−	936.000i		−	0.0739735i
$544$	−13846.0			−1.09125
$545$	−8400.00	−	16800.0i	−0.660214	−	1.32043i
$546$	−984.000			−0.0771269
$547$			6316.00i			0.493698i	0.969054	+	0.246849i	$0.0793951\pi$
$547$			6316.00i			0.493698i	−0.969054	+	0.246849i	$0.920605\pi$
$548$		−	8778.00i		−	0.684266i
$549$	6462.00			0.502352
$550$	6800.00	+	5100.00i	0.527187	+	0.395390i
$551$	570.000			0.0440704
$552$			810.000i			0.0624563i
$553$		−	2120.00i		−	0.163023i
$554$	−3386.00			−0.259670
$555$	510.000	+	1020.00i	0.0390059	+	0.0780119i
$556$	9100.00			0.694111
$557$			14776.0i			1.12402i	0.827130	+	0.562010i	$0.189972\pi$
$557$			14776.0i			1.12402i	−0.827130	+	0.562010i	$0.810028\pi$
$558$			2682.00i			0.203473i
$559$	−39524.0			−2.99050
$560$	−1640.00	+	820.000i	−0.123755	+	0.0618774i
$561$	−17544.0			−1.32034
$562$		−	1708.00i		−	0.128199i
$563$		−	7932.00i		−	0.593773i	−0.954913	−	0.296886i	$-0.904052\pi$
$563$		−	7932.00i		−	0.593773i	0.954913	−	0.296886i	$-0.0959482\pi$
$564$	−2394.00			−0.178733
$565$	−7620.00	+	3810.00i	−0.567391	+	0.283695i
$566$	−7378.00			−0.547916
$567$		−	324.000i		−	0.0239977i
$568$		−	14820.0i		−	1.09478i
$569$	8280.00			0.610045			0.305023	−	0.952345i	$-0.401336\pi$
$569$	8280.00			0.610045			0.305023	+	0.952345i	$0.401336\pi$
$570$	285.000	+	570.000i	0.0209427	+	0.0418854i
$571$	−1868.00			−0.136906			−0.0684530	−	0.997654i	$-0.521806\pi$
$571$	−1868.00			−0.136906			−0.0684530	+	0.997654i	$0.521806\pi$
$572$			39032.0i			2.85316i
$573$		−	7416.00i		−	0.540677i
$574$	208.000			0.0151250
$575$	−1800.00	−	1350.00i	−0.130548	−	0.0979111i
$576$	−1503.00			−0.108724
$577$			1656.00i			0.119480i	0.998214	+	0.0597402i	$0.0190272\pi$
$577$			1656.00i			0.119480i	−0.998214	+	0.0597402i	$0.980973\pi$
$578$		−	2483.00i		−	0.178684i
$579$	−7266.00			−0.521528
$580$	1050.00	+	2100.00i	0.0751705	+	0.150341i
$581$	−4128.00			−0.294765
$582$			738.000i			0.0525620i
$583$			24616.0i			1.74870i
$584$	−7320.00			−0.518671
$585$	7380.00	−	3690.00i	0.521582	−	0.260791i
$586$	−2038.00			−0.143667
$587$		−	20664.0i		−	1.45297i	−0.687181	−	0.726486i	$-0.741152\pi$
$587$		−	20664.0i		−	1.45297i	0.687181	−	0.726486i	$-0.258848\pi$
$588$		−	6867.00i		−	0.481616i
$589$	5662.00			0.396093
$590$	2100.00	−	1050.00i	0.146535	−	0.0732675i
$591$	−11952.0			−0.831877
$592$		−	1394.00i		−	0.0967788i
$593$		−	11702.0i		−	0.810360i	−0.914237	−	0.405180i	$-0.867209\pi$
$593$		−	11702.0i		−	0.810360i	0.914237	−	0.405180i	$-0.132791\pi$
$594$	1836.00			0.126822
$595$	−1720.00	−	3440.00i	−0.118509	−	0.237019i
$596$	−12670.0			−0.870778
$597$		−	6000.00i		−	0.411329i
$598$			1476.00i			0.100933i
$599$	−22680.0			−1.54704			−0.773522	−	0.633769i	$-0.781507\pi$
$599$	−22680.0			−1.54704			−0.773522	+	0.633769i	$0.781507\pi$
$600$	−3375.00	+	4500.00i	−0.229640	+	0.306186i
$601$	13742.0			0.932692			0.466346	−	0.884602i	$-0.345570\pi$
$601$	13742.0			0.932692			0.466346	+	0.884602i	$0.345570\pi$
$602$		−	1928.00i		−	0.130531i
$603$			8136.00i			0.549459i
$604$	11634.0			0.783743
$605$	−16465.0	−	32930.0i	−1.10644	−	2.21288i
$606$	−2574.00			−0.172544
$607$		−	4184.00i		−	0.279775i	−0.990167	−	0.139887i	$-0.955326\pi$
$607$		−	4184.00i		−	0.279775i	0.990167	−	0.139887i	$-0.0446741\pi$
$608$		−	3059.00i		−	0.204044i
$609$	360.000			0.0239539
$610$	−7180.00	+	3590.00i	−0.476573	+	0.238287i
$611$	−9348.00			−0.618952
$612$		−	5418.00i		−	0.357859i
$613$			1098.00i			0.0723455i	0.999346	+	0.0361728i	$0.0115167\pi$
$613$			1098.00i			0.0723455i	−0.999346	+	0.0361728i	$0.988483\pi$
$614$	−1636.00			−0.107530
$615$	−1560.00	+	780.000i	−0.102285	+	0.0511425i
$616$	−4080.00			−0.266863
$617$			21426.0i			1.39802i	0.715112	+	0.699010i	$0.246376\pi$
$617$			21426.0i			1.39802i	−0.715112	+	0.699010i	$0.753624\pi$
$618$			3264.00i			0.212455i
$619$	−8020.00			−0.520761			−0.260380	−	0.965506i	$-0.583848\pi$
$619$	−8020.00			−0.520761			−0.260380	+	0.965506i	$0.583848\pi$
$620$	10430.0	+	20860.0i	0.675611	+	1.35122i
$621$	−486.000			−0.0314050
$622$		−	1848.00i		−	0.119129i
$623$		−	3520.00i		−	0.226366i
$624$	−10086.0			−0.647056
$625$	−4375.00	−	15000.0i	−0.280000	−	0.960000i
$626$	−4908.00			−0.313360
$627$		−	3876.00i		−	0.246878i
$628$			4942.00i			0.314024i
$629$	2924.00			0.185354
$630$	180.000	+	360.000i	0.0113831	+	0.0227663i
$631$	6292.00			0.396958			0.198479	−	0.980105i	$-0.436400\pi$
$631$	6292.00			0.396958			0.198479	+	0.980105i	$0.436400\pi$
$632$			7950.00i			0.500370i
$633$			14304.0i			0.898156i
$634$	−4526.00			−0.283518
$635$	−6240.00	+	3120.00i	−0.389964	+	0.194982i
$636$	−7602.00			−0.473961
$637$		−	26814.0i		−	1.66783i
$638$			2040.00i			0.126590i
$639$	8892.00			0.550488
$640$	14550.0	−	7275.00i	0.898655	−	0.449328i
$641$	19332.0			1.19121			0.595607	−	0.803276i	$-0.296912\pi$
$641$	19332.0			1.19121			0.595607	+	0.803276i	$0.296912\pi$
$642$			1308.00i			0.0804091i
$643$		−	20702.0i		−	1.26968i	−0.772642	−	0.634842i	$-0.781065\pi$
$643$		−	20702.0i		−	1.26968i	0.772642	−	0.634842i	$-0.218935\pi$
$644$	504.000			0.0308391
$645$	7230.00	+	14460.0i	0.441366	+	0.882732i
$646$	1634.00			0.0995184
$647$		−	11754.0i		−	0.714215i	−0.934063	−	0.357108i	$-0.883763\pi$
$647$		−	11754.0i		−	0.714215i	0.934063	−	0.357108i	$-0.116237\pi$
$648$			1215.00i			0.0736570i
$649$	−14280.0			−0.863697
$650$	−6150.00	+	8200.00i	−0.371112	+	0.494816i
$651$	3576.00			0.215291
$652$		−	10234.0i		−	0.614715i
$653$			448.000i			0.0268478i	0.999910	+	0.0134239i	$0.00427308\pi$
$653$			448.000i			0.0268478i	−0.999910	+	0.0134239i	$0.995727\pi$
$654$	5040.00			0.301345
$655$	−5760.00	−	11520.0i	−0.343606	−	0.687212i
$656$	2132.00			0.126891
$657$		−	4392.00i		−	0.260804i
$658$		−	456.000i		−	0.0270163i
$659$	28910.0			1.70891			0.854457	−	0.519523i	$-0.173890\pi$
$659$	28910.0			1.70891			0.854457	+	0.519523i	$0.173890\pi$
$660$	14280.0	−	7140.00i	0.842194	−	0.421097i
$661$	−8748.00			−0.514762			−0.257381	−	0.966310i	$-0.582860\pi$
$661$	−8748.00			−0.514762			−0.257381	+	0.966310i	$0.582860\pi$
$662$		−	6388.00i		−	0.375040i
$663$		−	21156.0i		−	1.23926i
$664$	15480.0			0.904730
$665$	760.000	−	380.000i	0.0443181	−	0.0221590i
$666$	−306.000			−0.0178037
$667$		−	540.000i		−	0.0313477i
$668$		−	4368.00i		−	0.252998i
$669$	9744.00			0.563116
$670$	−4520.00	−	9040.00i	−0.260631	−	0.521262i
$671$	48824.0			2.80899
$672$		−	1932.00i		−	0.110906i
$673$		−	5002.00i		−	0.286498i	−0.989687	−	0.143249i	$-0.954245\pi$
$673$		−	5002.00i		−	0.286498i	0.989687	−	0.143249i	$-0.0457549\pi$
$674$	−286.000			−0.0163447
$675$	−2700.00	−	2025.00i	−0.153960	−	0.115470i
$676$	−31689.0			−1.80297
$677$			26706.0i			1.51609i	0.652201	+	0.758046i	$0.273846\pi$
$677$			26706.0i			1.51609i	−0.652201	+	0.758046i	$0.726154\pi$
$678$		−	2286.00i		−	0.129489i
$679$	984.000			0.0556148
$680$	6450.00	+	12900.0i	0.363744	+	0.727489i
$681$	−16332.0			−0.919007
$682$			20264.0i			1.13775i
$683$			22668.0i			1.26994i	0.772538	+	0.634968i	$0.218987\pi$
$683$			22668.0i			1.26994i	−0.772538	+	0.634968i	$0.781013\pi$
$684$	1197.00			0.0669129
$685$	−12540.0	+	6270.00i	−0.699458	+	0.349729i
$686$	2680.00			0.149159
$687$		−	10470.0i		−	0.581449i
$688$		−	19762.0i		−	1.09509i
$689$	−29684.0			−1.64132
$690$	540.000	−	270.000i	0.0297934	−	0.0148967i
$691$	−21228.0			−1.16867			−0.584335	−	0.811512i	$-0.698645\pi$
$691$	−21228.0			−1.16867			−0.584335	+	0.811512i	$0.698645\pi$
$692$			22386.0i			1.22975i
$693$		−	2448.00i		−	0.134187i
$694$	8904.00			0.487019
$695$	−6500.00	−	13000.0i	−0.354761	−	0.709522i
$696$	−1350.00			−0.0735224
$697$			4472.00i			0.243026i
$698$		−	7670.00i		−	0.415922i
$699$	−12606.0			−0.682121
$700$	2800.00	+	2100.00i	0.151186	+	0.113389i
$701$	−22158.0			−1.19386			−0.596930	−	0.802293i	$-0.703613\pi$
$701$	−22158.0			−1.19386			−0.596930	+	0.802293i	$0.703613\pi$
$702$			2214.00i			0.119034i
$703$			646.000i			0.0346577i
$704$	−11356.0			−0.607948
$705$	1710.00	+	3420.00i	0.0913508	+	0.182702i
$706$	2.00000			0.000106616
$707$			3432.00i			0.182565i
$708$		−	4410.00i		−	0.234093i
$709$	10850.0			0.574725			0.287363	−	0.957822i	$-0.407221\pi$
$709$	10850.0			0.574725			0.287363	+	0.957822i	$0.407221\pi$
$710$	−9880.00	+	4940.00i	−0.522239	+	0.261120i
$711$	−4770.00			−0.251602
$712$			13200.0i			0.694791i
$713$		−	5364.00i		−	0.281744i
$714$	1032.00			0.0540919
$715$	55760.0	−	27880.0i	2.91651	−	1.45826i
$716$	11970.0			0.624776
$717$			19200.0i			1.00005i
$718$			1120.00i			0.0582145i
$719$	−23160.0			−1.20128			−0.600641	−	0.799519i	$-0.705088\pi$
$719$	−23160.0			−1.20128			−0.600641	+	0.799519i	$0.705088\pi$
$720$	1845.00	+	3690.00i	0.0954987	+	0.190997i
$721$	4352.00			0.224795
$722$			361.000i			0.0186081i
$723$		−	9426.00i		−	0.484864i
$724$	2184.00			0.112110
$725$	2250.00	−	3000.00i	0.115259	−	0.153679i
$726$	9879.00			0.505019
$727$		−	7144.00i		−	0.364452i	−0.983257	−	0.182226i	$-0.941670\pi$
$727$		−	7144.00i		−	0.364452i	0.983257	−	0.182226i	$-0.0583302\pi$
$728$		−	4920.00i		−	0.250477i
$729$	−729.000			−0.0370370
$730$	2440.00	+	4880.00i	0.123710	+	0.247420i
$731$	41452.0			2.09734
$732$			15078.0i			0.761337i
$733$		−	7242.00i		−	0.364924i	−0.983213	−	0.182462i	$-0.941593\pi$
$733$		−	7242.00i		−	0.364924i	0.983213	−	0.182462i	$-0.0584067\pi$
$734$	1984.00			0.0997694
$735$	−9810.00	+	4905.00i	−0.492309	+	0.246155i
$736$	−2898.00			−0.145138
$737$			61472.0i			3.07239i
$738$		−	468.000i		−	0.0233432i
$739$	3380.00			0.168248			0.0841240	−	0.996455i	$-0.473191\pi$
$739$	3380.00			0.168248			0.0841240	+	0.996455i	$0.473191\pi$
$740$	−2380.00	+	1190.00i	−0.118230	+	0.0591152i
$741$	4674.00			0.231719
$742$		−	1448.00i		−	0.0716412i
$743$			3848.00i			0.189999i	0.995477	+	0.0949996i	$0.0302850\pi$
$743$			3848.00i			0.189999i	−0.995477	+	0.0949996i	$0.969715\pi$
$744$	−13410.0			−0.660799
$745$	9050.00	+	18100.0i	0.445055	+	0.890111i
$746$	−2058.00			−0.101004
$747$			9288.00i			0.454927i
$748$		−	40936.0i		−	2.00103i
$749$	1744.00			0.0850793
$750$	4125.00	+	750.000i	0.200832	+	0.0365148i
$751$	−22558.0			−1.09608			−0.548038	−	0.836453i	$-0.684625\pi$
$751$	−22558.0			−1.09608			−0.548038	+	0.836453i	$0.684625\pi$
$752$		−	4674.00i		−	0.226653i
$753$			11964.0i			0.579007i
$754$	−2460.00			−0.118817
$755$	−8310.00	−	16620.0i	−0.400572	−	0.801144i
$756$	756.000			0.0363696
$757$			15866.0i			0.761770i	0.924623	+	0.380885i	$0.124381\pi$
$757$			15866.0i			0.761770i	−0.924623	+	0.380885i	$0.875619\pi$
$758$			10640.0i			0.509845i
$759$	−3672.00			−0.175606
$760$	−2850.00	+	1425.00i	−0.136027	+	0.0680134i
$761$	462.000			0.0220072			0.0110036	−	0.999939i	$-0.496497\pi$
$761$	462.000			0.0220072			0.0110036	+	0.999939i	$0.496497\pi$
$762$		−	1872.00i		−	0.0889966i
$763$		−	6720.00i		−	0.318847i
$764$	17304.0			0.819420
$765$	−7740.00	+	3870.00i	−0.365804	+	0.182902i
$766$	5892.00			0.277920
$767$		−	17220.0i		−	0.810663i
$768$			357.000i			0.0167736i
$769$	22210.0			1.04150			0.520750	−	0.853709i	$-0.325652\pi$
$769$	22210.0			1.04150			0.520750	+	0.853709i	$0.325652\pi$
$770$	1360.00	+	2720.00i	0.0636506	+	0.127301i
$771$	1818.00			0.0849205
$772$		−	16954.0i		−	0.790399i
$773$			658.000i			0.0306166i	0.999883	+	0.0153083i	$0.00487297\pi$
$773$			658.000i			0.0306166i	−0.999883	+	0.0153083i	$0.995127\pi$
$774$	−4338.00			−0.201455
$775$	22350.0	−	29800.0i	1.03592	−	1.38122i
$776$	−3690.00			−0.170700
$777$			408.000i			0.0188377i
$778$		−	990.000i		−	0.0456211i
$779$	−988.000			−0.0454413
$780$	8610.00	+	17220.0i	0.395240	+	0.790481i
$781$	67184.0			3.07815
$782$		−	1548.00i		−	0.0707882i
$783$		−	810.000i		−	0.0369694i
$784$	13407.0			0.610742
$785$	7060.00	−	3530.00i	0.320996	−	0.160498i
$786$	3456.00			0.156834
$787$			36016.0i			1.63130i	0.578547	+	0.815649i	$0.303620\pi$
$787$			36016.0i			1.63130i	−0.578547	+	0.815649i	$0.696380\pi$
$788$		−	27888.0i		−	1.26075i
$789$	−6786.00			−0.306195
$790$	5300.00	−	2650.00i	0.238691	−	0.119345i
$791$	−3048.00			−0.137009
$792$			9180.00i			0.411865i
$793$			58876.0i			2.63650i
$794$	−526.000			−0.0235101
$795$	5430.00	+	10860.0i	0.242242	+	0.484484i
$796$	14000.0			0.623388
$797$			5346.00i			0.237597i	0.992918	+	0.118799i	$0.0379043\pi$
$797$			5346.00i			0.237597i	−0.992918	+	0.118799i	$0.962096\pi$
$798$			228.000i			0.0101142i
$799$	9804.00			0.434093
$800$	−16100.0	−	12075.0i	−0.711526	−	0.533645i
$801$	−7920.00			−0.349363
$802$			9612.00i			0.423206i
$803$		−	33184.0i		−	1.45833i
$804$	−18984.0			−0.832729
$805$	−360.000	−	720.000i	−0.0157619	−	0.0315238i
$806$	−24436.0			−1.06789
$807$			3510.00i			0.153108i
$808$		−	12870.0i		−	0.560353i
$809$	24170.0			1.05040			0.525199	−	0.850979i	$-0.323991\pi$
$809$	24170.0			1.05040			0.525199	+	0.850979i	$0.323991\pi$
$810$	810.000	−	405.000i	0.0351364	−	0.0175682i
$811$	13932.0			0.603229			0.301614	−	0.953430i	$-0.402474\pi$
$811$	13932.0			0.603229			0.301614	+	0.953430i	$0.402474\pi$
$812$			840.000i			0.0363032i
$813$			23184.0i			1.00012i
$814$	−2312.00			−0.0995523
$815$	−14620.0	+	7310.00i	−0.628364	+	0.314182i
$816$	10578.0			0.453804
$817$			9158.00i			0.392164i
$818$			9110.00i			0.389393i
$819$	2952.00			0.125948
$820$	−1820.00	−	3640.00i	−0.0775087	−	0.155017i
$821$	14202.0			0.603719			0.301859	−	0.953352i	$-0.402393\pi$
$821$	14202.0			0.603719			0.301859	+	0.953352i	$0.402393\pi$
$822$		−	3762.00i		−	0.159629i
$823$			2688.00i			0.113849i	0.998378	+	0.0569245i	$0.0181294\pi$
$823$			2688.00i			0.113849i	−0.998378	+	0.0569245i	$0.981871\pi$
$824$	−16320.0			−0.689969
$825$	−20400.0	−	15300.0i	−0.860893	−	0.645670i
$826$	840.000			0.0353842
$827$			4236.00i			0.178114i	0.996027	+	0.0890569i	$0.0283853\pi$
$827$			4236.00i			0.178114i	−0.996027	+	0.0890569i	$0.971615\pi$
$828$		−	1134.00i		−	0.0475957i
$829$	20800.0			0.871428			0.435714	−	0.900085i	$-0.356496\pi$
$829$	20800.0			0.871428			0.435714	+	0.900085i	$0.356496\pi$
$830$	−5160.00	−	10320.0i	−0.215791	−	0.431581i
$831$	10158.0			0.424040
$832$		−	13694.0i		−	0.570618i
$833$			28122.0i			1.16971i
$834$	3900.00			0.161926
$835$	−6240.00	+	3120.00i	−0.258616	+	0.129308i
$836$	9044.00			0.374155
$837$		−	8046.00i		−	0.332271i
$838$		−	13920.0i		−	0.573817i
$839$	−1020.00			−0.0419718			−0.0209859	−	0.999780i	$-0.506681\pi$
$839$	−1020.00			−0.0419718			−0.0209859	+	0.999780i	$0.506681\pi$
$840$	−1800.00	+	900.000i	−0.0739356	+	0.0369678i
$841$	−23489.0			−0.963098
$842$		−	9588.00i		−	0.392428i
$843$			5124.00i			0.209347i
$844$	−33376.0			−1.36120
$845$	22635.0	+	45270.0i	0.921500	+	1.84300i
$846$	−1026.00			−0.0416958
$847$		−	13172.0i		−	0.534351i
$848$		−	14842.0i		−	0.601033i
$849$	22134.0			0.894743
$850$	6450.00	−	8600.00i	0.260274	−	0.347032i
$851$	612.000			0.0246523
$852$			20748.0i			0.834290i
$853$		−	32102.0i		−	1.28857i	−0.764785	−	0.644286i	$-0.777155\pi$
$853$		−	32102.0i		−	1.28857i	0.764785	−	0.644286i	$-0.222845\pi$
$854$	−2872.00			−0.115079
$855$	−855.000	−	1710.00i	−0.0341993	−	0.0683986i
$856$	−6540.00			−0.261136
$857$		−	31434.0i		−	1.25293i	−0.779448	−	0.626467i	$-0.784500\pi$
$857$		−	31434.0i		−	1.25293i	0.779448	−	0.626467i	$-0.215500\pi$
$858$			16728.0i			0.665600i
$859$	−25660.0			−1.01922			−0.509609	−	0.860406i	$-0.670210\pi$
$859$	−25660.0			−1.01922			−0.509609	+	0.860406i	$0.670210\pi$
$860$	−33740.0	+	16870.0i	−1.33782	+	0.668910i
$861$	−624.000			−0.0246990
$862$		−	4968.00i		−	0.196300i
$863$		−	14212.0i		−	0.560582i	−0.959915	−	0.280291i	$-0.909569\pi$
$863$		−	14212.0i		−	0.560582i	0.959915	−	0.280291i	$-0.0904309\pi$
$864$	−4347.00			−0.171167
$865$	31980.0	−	15990.0i	1.25706	−	0.628528i
$866$	11342.0			0.445054
$867$			7449.00i			0.291789i
$868$			8344.00i			0.326283i
$869$	−36040.0			−1.40687
$870$	450.000	+	900.000i	0.0175361	+	0.0350723i
$871$	−74128.0			−2.88373
$872$			25200.0i			0.978646i
$873$		−	2214.00i		−	0.0858334i
$874$	342.000			0.0132361
$875$	1000.00	−	5500.00i	0.0386356	−	0.212496i
$876$	10248.0			0.395260
$877$		−	46294.0i		−	1.78248i	−0.453529	−	0.891241i	$-0.649835\pi$
$877$		−	46294.0i		−	1.78248i	0.453529	−	0.891241i	$-0.350165\pi$
$878$		−	3710.00i		−	0.142604i
$879$	6114.00			0.234608
$880$	13940.0	+	27880.0i	0.533997	+	1.06799i
$881$	−7558.00			−0.289030			−0.144515	−	0.989503i	$-0.546162\pi$
$881$	−7558.00			−0.289030			−0.144515	+	0.989503i	$0.546162\pi$
$882$		−	2943.00i		−	0.112354i
$883$		−	27202.0i		−	1.03672i	−0.855164	−	0.518358i	$-0.826543\pi$
$883$		−	27202.0i		−	1.03672i	0.855164	−	0.518358i	$-0.173457\pi$
$884$	49364.0			1.87816
$885$	−6300.00	+	3150.00i	−0.239291	+	0.119645i
$886$	10772.0			0.408456
$887$			36196.0i			1.37017i	0.728462	+	0.685086i	$0.240235\pi$
$887$			36196.0i			1.37017i	−0.728462	+	0.685086i	$0.759765\pi$
$888$		−	1530.00i		−	0.0578192i
$889$	−2496.00			−0.0941655
$890$	8800.00	−	4400.00i	0.331434	−	0.165717i
$891$	−5508.00			−0.207099
$892$			22736.0i			0.853428i
$893$			2166.00i			0.0811673i
$894$	−5430.00			−0.203139
$895$	−8550.00	−	17100.0i	−0.319324	−	0.638648i
$896$	5820.00			0.217001
$897$		−	4428.00i		−	0.164823i
$898$			1720.00i			0.0639166i
$899$	8940.00			0.331664
$900$	4725.00	−	6300.00i	0.175000	−	0.233333i
$901$	31132.0			1.15112
$902$		−	3536.00i		−	0.130528i
$903$			5784.00i			0.213156i
$904$	11430.0			0.420527
$905$	−1560.00	−	3120.00i	−0.0572996	−	0.114599i
$906$	4986.00			0.182835
$907$		−	2424.00i		−	0.0887405i	−0.999015	−	0.0443702i	$-0.985872\pi$
$907$		−	2424.00i		−	0.0887405i	0.999015	−	0.0443702i	$-0.0141281\pi$
$908$		−	38108.0i		−	1.39280i
$909$	7722.00			0.281763
$910$	−3280.00	+	1640.00i	−0.119485	+	0.0597423i
$911$	37252.0			1.35479			0.677395	−	0.735619i	$-0.263109\pi$
$911$	37252.0			1.35479			0.677395	+	0.735619i	$0.263109\pi$
$912$			2337.00i			0.0848529i
$913$			70176.0i			2.54380i
$914$	−1456.00			−0.0526917
$915$	21540.0	−	10770.0i	0.778241	−	0.389120i
$916$	24430.0			0.881212
$917$		−	4608.00i		−	0.165943i
$918$		−	2322.00i		−	0.0834830i
$919$	45980.0			1.65042			0.825212	−	0.564823i	$-0.191055\pi$
$919$	45980.0			1.65042			0.825212	+	0.564823i	$0.191055\pi$
$920$	1350.00	+	2700.00i	0.0483785	+	0.0967569i
$921$	4908.00			0.175596
$922$		−	6218.00i		−	0.222103i
$923$			81016.0i			2.88914i
$924$	5712.00			0.203367
$925$	3400.00	+	2550.00i	0.120855	+	0.0906416i
$926$	13892.0			0.493002
$927$		−	9792.00i		−	0.346938i
$928$		−	4830.00i		−	0.170854i
$929$	34470.0			1.21736			0.608678	−	0.793417i	$-0.291700\pi$
$929$	34470.0			1.21736			0.608678	+	0.793417i	$0.291700\pi$
$930$	4470.00	+	8940.00i	0.157610	+	0.315220i
$931$	−6213.00			−0.218714
$932$		−	29414.0i		−	1.03378i
$933$			5544.00i			0.194536i
$934$	6004.00			0.210339
$935$	−58480.0	+	29240.0i	−2.04546	+	1.02273i
$936$	−11070.0			−0.386575
$937$		−	12764.0i		−	0.445018i	−0.974931	−	0.222509i	$-0.928575\pi$
$937$		−	12764.0i		−	0.445018i	0.974931	−	0.222509i	$-0.0714246\pi$
$938$		−	3616.00i		−	0.125871i
$939$	14724.0			0.511714
$940$	−7980.00	+	3990.00i	−0.276892	+	0.138446i
$941$	−55538.0			−1.92400			−0.962002	−	0.273044i	$-0.911970\pi$
$941$	−55538.0			−1.92400			−0.962002	+	0.273044i	$0.911970\pi$
$942$			2118.00i			0.0732571i
$943$			936.000i			0.0323228i
$944$	8610.00			0.296856
$945$	−540.000	−	1080.00i	−0.0185886	−	0.0371771i
$946$	−32776.0			−1.12647
$947$		−	8604.00i		−	0.295240i	−0.989044	−	0.147620i	$-0.952839\pi$
$947$		−	8604.00i		−	0.295240i	0.989044	−	0.147620i	$-0.0471613\pi$
$948$		−	11130.0i		−	0.381314i
$949$	40016.0			1.36878
$950$	1900.00	+	1425.00i	0.0648886	+	0.0486664i
$951$	13578.0			0.462983
$952$			5160.00i			0.175669i
$953$			18018.0i			0.612445i	0.951960	+	0.306223i	$0.0990652\pi$
$953$			18018.0i			0.612445i	−0.951960	+	0.306223i	$0.900935\pi$
$954$	−3258.00			−0.110568
$955$	−12360.0	−	24720.0i	−0.418806	−	0.837613i
$956$	−44800.0			−1.51562
$957$		−	6120.00i		−	0.206720i
$958$		−	4800.00i		−	0.161880i
$959$	−5016.00			−0.168900
$960$	−5010.00	+	2505.00i	−0.168434	+	0.0842172i
$961$	59013.0			1.98090
$962$		−	2788.00i		−	0.0934394i
$963$		−	3924.00i		−	0.131308i
$964$	21994.0			0.734833
$965$	−24220.0	+	12110.0i	−0.807948	+	0.403974i
$966$	216.000			0.00719429
$967$			45496.0i			1.51298i	0.654005	+	0.756491i	$0.273088\pi$
$967$			45496.0i			1.51298i	−0.654005	+	0.756491i	$0.726912\pi$
$968$			49395.0i			1.64010i
$969$	−4902.00			−0.162513
$970$	1230.00	+	2460.00i	0.0407144	+	0.0814287i
$971$	37722.0			1.24671			0.623356	−	0.781938i	$-0.285769\pi$
$971$	37722.0			1.24671			0.623356	+	0.781938i	$0.285769\pi$
$972$		−	1701.00i		−	0.0561313i
$973$		−	5200.00i		−	0.171330i
$974$	−12616.0			−0.415034
$975$	18450.0	−	24600.0i	0.606023	−	0.808031i
$976$	−29438.0			−0.965458
$977$		−	43474.0i		−	1.42360i	−0.702383	−	0.711800i	$-0.747880\pi$
$977$		−	43474.0i		−	1.42360i	0.702383	−	0.711800i	$-0.252120\pi$
$978$		−	4386.00i		−	0.143404i
$979$	−59840.0			−1.95352
$980$	−11445.0	−	22890.0i	−0.373058	−	0.746117i
$981$	−15120.0			−0.492094
$982$			4232.00i			0.137524i
$983$		−	13032.0i		−	0.422845i	−0.977395	−	0.211422i	$-0.932190\pi$
$983$		−	13032.0i		−	0.422845i	0.977395	−	0.211422i	$-0.0678095\pi$
$984$	2340.00			0.0758094
$985$	−39840.0	+	19920.0i	−1.28874	+	0.644370i
$986$	2580.00			0.0833306
$987$			1368.00i			0.0441174i
$988$			10906.0i			0.351180i
$989$	8676.00			0.278949
$990$	6120.00	−	3060.00i	0.196471	−	0.0982355i
$991$	−52978.0			−1.69819			−0.849093	−	0.528244i	$-0.822851\pi$
$991$	−52978.0			−1.69819			−0.849093	+	0.528244i	$0.822851\pi$
$992$		−	47978.0i		−	1.53559i
$993$			19164.0i			0.612438i
$994$	−3952.00			−0.126106
$995$	−10000.0	−	20000.0i	−0.318614	−	0.637229i
$996$	−21672.0			−0.689461
$997$		−	1774.00i		−	0.0563522i	−0.999603	−	0.0281761i	$-0.991030\pi$
$997$		−	1774.00i		−	0.0563522i	0.999603	−	0.0281761i	$-0.00896992\pi$
$998$		−	6340.00i		−	0.201091i
$999$	918.000			0.0290733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.4.c.a.229.2	yes	2
5.2	odd	4		1425.4.a.b.1.1		1
5.3	odd	4		1425.4.a.d.1.1		1
5.4	even	2	inner	285.4.c.a.229.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.4.c.a.229.1	✓	2	5.4	even	2	inner
285.4.c.a.229.2	yes	2	1.1	even	1	trivial
1425.4.a.b.1.1		1	5.2	odd	4
1425.4.a.d.1.1		1	5.3	odd	4

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	285.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +(-5.00000 - 10.0000i) q^{5} +3.00000 q^{6} -4.00000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.00000i q^{3} +7.00000 q^{4} +(-5.00000 - 10.0000i) q^{5} +3.00000 q^{6} -4.00000i q^{7} +15.0000i q^{8} -9.00000 q^{9} +(10.0000 - 5.00000i) q^{10} -68.0000 q^{11} -21.0000i q^{12} -82.0000i q^{13} +4.00000 q^{14} +(-30.0000 + 15.0000i) q^{15} +41.0000 q^{16} +86.0000i q^{17} -9.00000i q^{18} -19.0000 q^{19} +(-35.0000 - 70.0000i) q^{20} -12.0000 q^{21} -68.0000i q^{22} +18.0000i q^{23} +45.0000 q^{24} +(-75.0000 + 100.000i) q^{25} +82.0000 q^{26} +27.0000i q^{27} -28.0000i q^{28} -30.0000 q^{29} +(-15.0000 - 30.0000i) q^{30} -298.000 q^{31} +161.000i q^{32} +204.000i q^{33} -86.0000 q^{34} +(-40.0000 + 20.0000i) q^{35} -63.0000 q^{36} -34.0000i q^{37} -19.0000i q^{38} -246.000 q^{39} +(150.000 - 75.0000i) q^{40} +52.0000 q^{41} -12.0000i q^{42} -482.000i q^{43} -476.000 q^{44} +(45.0000 + 90.0000i) q^{45} -18.0000 q^{46} -114.000i q^{47} -123.000i q^{48} +327.000 q^{49} +(-100.000 - 75.0000i) q^{50} +258.000 q^{51} -574.000i q^{52} -362.000i q^{53} -27.0000 q^{54} +(340.000 + 680.000i) q^{55} +60.0000 q^{56} +57.0000i q^{57} -30.0000i q^{58} +210.000 q^{59} +(-210.000 + 105.000i) q^{60} -718.000 q^{61} -298.000i q^{62} +36.0000i q^{63} +167.000 q^{64} +(-820.000 + 410.000i) q^{65} -204.000 q^{66} -904.000i q^{67} +602.000i q^{68} +54.0000 q^{69} +(-20.0000 - 40.0000i) q^{70} -988.000 q^{71} -135.000i q^{72} +488.000i q^{73} +34.0000 q^{74} +(300.000 + 225.000i) q^{75} -133.000 q^{76} +272.000i q^{77} -246.000i q^{78} +530.000 q^{79} +(-205.000 - 410.000i) q^{80} +81.0000 q^{81} +52.0000i q^{82} -1032.00i q^{83} -84.0000 q^{84} +(860.000 - 430.000i) q^{85} +482.000 q^{86} +90.0000i q^{87} -1020.00i q^{88} +880.000 q^{89} +(-90.0000 + 45.0000i) q^{90} -328.000 q^{91} +126.000i q^{92} +894.000i q^{93} +114.000 q^{94} +(95.0000 + 190.000i) q^{95} +483.000 q^{96} +246.000i q^{97} +327.000i q^{98} +612.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 14 q^{4} - 10 q^{5} + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q + 14 * q^4 - 10 * q^5 + 6 * q^6 - 18 * q^9	\( 2 q + 14 q^{4} - 10 q^{5} + 6 q^{6} - 18 q^{9} + 20 q^{10} - 136 q^{11} + 8 q^{14} - 60 q^{15} + 82 q^{16} - 38 q^{19} - 70 q^{20} - 24 q^{21} + 90 q^{24} - 150 q^{25} + 164 q^{26} - 60 q^{29} - 30 q^{30} - 596 q^{31} - 172 q^{34} - 80 q^{35} - 126 q^{36} - 492 q^{39} + 300 q^{40} + 104 q^{41} - 952 q^{44} + 90 q^{45} - 36 q^{46} + 654 q^{49} - 200 q^{50} + 516 q^{51} - 54 q^{54} + 680 q^{55} + 120 q^{56} + 420 q^{59} - 420 q^{60} - 1436 q^{61} + 334 q^{64} - 1640 q^{65} - 408 q^{66} + 108 q^{69} - 40 q^{70} - 1976 q^{71} + 68 q^{74} + 600 q^{75} - 266 q^{76} + 1060 q^{79} - 410 q^{80} + 162 q^{81} - 168 q^{84} + 1720 q^{85} + 964 q^{86} + 1760 q^{89} - 180 q^{90} - 656 q^{91} + 228 q^{94} + 190 q^{95} + 966 q^{96} + 1224 q^{99}+O(q^{100}) \) 2 * q + 14 * q^4 - 10 * q^5 + 6 * q^6 - 18 * q^9 + 20 * q^10 - 136 * q^11 + 8 * q^14 - 60 * q^15 + 82 * q^16 - 38 * q^19 - 70 * q^20 - 24 * q^21 + 90 * q^24 - 150 * q^25 + 164 * q^26 - 60 * q^29 - 30 * q^30 - 596 * q^31 - 172 * q^34 - 80 * q^35 - 126 * q^36 - 492 * q^39 + 300 * q^40 + 104 * q^41 - 952 * q^44 + 90 * q^45 - 36 * q^46 + 654 * q^49 - 200 * q^50 + 516 * q^51 - 54 * q^54 + 680 * q^55 + 120 * q^56 + 420 * q^59 - 420 * q^60 - 1436 * q^61 + 334 * q^64 - 1640 * q^65 - 408 * q^66 + 108 * q^69 - 40 * q^70 - 1976 * q^71 + 68 * q^74 + 600 * q^75 - 266 * q^76 + 1060 * q^79 - 410 * q^80 + 162 * q^81 - 168 * q^84 + 1720 * q^85 + 964 * q^86 + 1760 * q^89 - 180 * q^90 - 656 * q^91 + 228 * q^94 + 190 * q^95 + 966 * q^96 + 1224 * q^99

Introduction

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