LMFDB - Embedded newform 252.8.e.a.71.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,8,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	252.e (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:	$78.7210264220$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.8
Character	$\chi$	$=$	252.71
Dual form			252.8.e.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.8566 + 3.18337i) q^{2} +(107.732 - 69.1213i) q^{4} -512.680i q^{5} -343.000i q^{7} +(-949.569 + 1093.38i) q^{8} +(1632.05 + 5565.97i) q^{10} +6950.61 q^{11} -968.015 q^{13} +(1091.90 + 3723.82i) q^{14} +(6828.49 - 14893.2i) q^{16} +6796.54i q^{17} +37771.6i q^{19} +(-35437.1 - 55232.2i) q^{20} +(-75460.1 + 22126.4i) q^{22} +2978.61 q^{23} -184716. q^{25} +(10509.4 - 3081.55i) q^{26} +(-23708.6 - 36952.2i) q^{28} +179257. i q^{29} +200289. i q^{31} +(-26723.7 + 183427. i) q^{32} +(-21635.9 - 73787.5i) q^{34} -175849. q^{35} -425727. q^{37} +(-120241. - 410072. i) q^{38} +(560552. + 486826. i) q^{40} +244050. i q^{41} -88312.9i q^{43} +(748805. - 480435. i) q^{44} +(-32337.6 + 9482.02i) q^{46} +453536. q^{47} -117649. q^{49} +(2.00539e6 - 588020. i) q^{50} +(-104287. + 66910.5i) q^{52} +1.57314e6i q^{53} -3.56344e6i q^{55} +(375028. + 325702. i) q^{56} +(-570643. - 1.94613e6i) q^{58} +77228.5 q^{59} -1.19278e6 q^{61} +(-637593. - 2.17446e6i) q^{62} +(-293788. - 2.07647e6i) q^{64} +496282. i q^{65} -1.71428e6i q^{67} +(469786. + 732207. i) q^{68} +(1.90913e6 - 559794. i) q^{70} +1.52612e6 q^{71} -5.69727e6 q^{73} +(4.62196e6 - 1.35525e6i) q^{74} +(2.61082e6 + 4.06922e6i) q^{76} -2.38406e6i q^{77} +8.63828e6i q^{79} +(-7.63545e6 - 3.50083e6i) q^{80} +(-776900. - 2.64955e6i) q^{82} +866901. q^{83} +3.48445e6 q^{85} +(281133. + 958779. i) q^{86} +(-6.60009e6 + 7.59963e6i) q^{88} +6.05763e6i q^{89} +332029. i q^{91} +(320892. - 205885. i) q^{92} +(-4.92387e6 + 1.44377e6i) q^{94} +1.93648e7 q^{95} +1.19866e7 q^{97} +(1.27727e6 - 374521. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 104 q^{4} - 5816 q^{10} + 16684 q^{16} - 201700 q^{22} - 1312500 q^{25} + 39788 q^{28} - 400048 q^{34} - 165544 q^{37} - 1477624 q^{40} + 1616724 q^{46} - 9882516 q^{49} - 3744592 q^{52} + 12053212 q^{58}+ \cdots + 73638456 q^{94}+O(q^{100}) $ 84 * q + 104 * q^4 - 5816 * q^10 + 16684 * q^16 - 201700 * q^22 - 1312500 * q^25 + 39788 * q^28 - 400048 * q^34 - 165544 * q^37 - 1477624 * q^40 + 1616724 * q^46 - 9882516 * q^49 - 3744592 * q^52 + 12053212 * q^58 - 8764504 * q^61 - 5645200 * q^64 + 8997576 * q^70 - 38069208 * q^76 + 24696392 * q^82 - 29977064 * q^85 - 48692036 * q^88 + 73638456 * q^94

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−10.8566	+	3.18337i	−0.959598	+	0.281373i
$2$	−10.8566	+	3.18337i	−0.959598	+	0.281373i
$3$		0			0
$3$		0			0
$4$	107.732	−	69.1213i	0.841658	−	0.540010i
$5$		−	512.680i		−	1.83422i	−0.398633	−	0.917110i	$-0.630515\pi$
$5$		−	512.680i		−	1.83422i	0.398633	−	0.917110i	$-0.369485\pi$
$6$		0			0
$7$		−	343.000i		−	0.377964i
$7$		−	343.000i		−	0.377964i
$8$	−949.569	+	1093.38i	−0.655710	+	0.755013i
$9$		0			0
$10$	1632.05	+	5565.97i	0.516100	+	1.76012i
$11$	6950.61			1.57452			0.787260	−	0.616621i	$-0.211499\pi$
$11$	6950.61			1.57452			0.787260	+	0.616621i	$0.211499\pi$
$12$		0			0
$13$	−968.015			−0.122203			−0.0611013	−	0.998132i	$-0.519461\pi$
$13$	−968.015			−0.122203			−0.0611013	+	0.998132i	$0.519461\pi$
$14$	1091.90	+	3723.82i	0.106349	+	0.362694i
$15$		0			0
$16$	6828.49	−	14893.2i	0.416778	−	0.909008i
$17$			6796.54i			0.335519i	0.985828	+	0.167759i	$0.0536532\pi$
$17$			6796.54i			0.335519i	−0.985828	+	0.167759i	$0.946347\pi$
$18$		0			0
$19$			37771.6i			1.26336i	0.775228	+	0.631681i	$0.217635\pi$
$19$			37771.6i			1.26336i	−0.775228	+	0.631681i	$0.782365\pi$
$20$	−35437.1	−	55232.2i	−0.990498	−	1.54379i
$21$		0			0
$22$	−75460.1	+	22126.4i	−1.51091	+	0.443028i
$23$	2978.61			0.0510465			0.0255233	−	0.999674i	$-0.491875\pi$
$23$	2978.61			0.0510465			0.0255233	+	0.999674i	$0.491875\pi$
$24$		0			0
$25$	−184716.			−2.36437
$26$	10509.4	−	3081.55i	0.117265	−	0.0343845i
$27$		0			0
$28$	−23708.6	−	36952.2i	−0.204105	−	0.318117i
$29$			179257.i			1.36485i	0.730957	+	0.682423i	$0.239074\pi$
$29$			179257.i			1.36485i	−0.730957	+	0.682423i	$0.760926\pi$
$30$		0			0
$31$			200289.i			1.20751i	0.797170	+	0.603755i	$0.206329\pi$
$31$			200289.i			1.20751i	−0.797170	+	0.603755i	$0.793671\pi$
$32$	−26723.7	+	183427.i	−0.144169	+	0.989553i
$33$		0			0
$34$	−21635.9	−	73787.5i	−0.0944060	−	0.321963i
$35$	−175849.			−0.693270
$36$		0			0
$37$	−425727.			−1.38174			−0.690869	−	0.722980i	$-0.742772\pi$
$37$	−425727.			−1.38174			−0.690869	+	0.722980i	$0.742772\pi$
$38$	−120241.	−	410072.i	−0.355476	−	1.21232i
$39$		0			0
$40$	560552.	+	486826.i	1.38486	+	1.20272i
$41$			244050.i			0.553012i	0.961012	+	0.276506i	$0.0891766\pi$
$41$			244050.i			0.553012i	−0.961012	+	0.276506i	$0.910823\pi$
$42$		0			0
$43$		−	88312.9i		−	0.169389i	−0.996407	−	0.0846943i	$-0.973009\pi$
$43$		−	88312.9i		−	0.169389i	0.996407	−	0.0846943i	$-0.0269914\pi$
$44$	748805.	−	480435.i	1.32521	−	0.850257i
$45$		0			0
$46$	−32337.6	+	9482.02i	−0.0489842	+	0.0143631i
$47$	453536.			0.637191			0.318595	−	0.947891i	$-0.396789\pi$
$47$	453536.			0.637191			0.318595	+	0.947891i	$0.396789\pi$
$48$		0			0
$49$	−117649.			−0.142857
$50$	2.00539e6	−	588020.i	2.26884	−	0.665269i
$51$		0			0
$52$	−104287.	+	66910.5i	−0.102853	+	0.0659907i
$53$			1.57314e6i			1.45145i	0.687984	+	0.725726i	$0.258496\pi$
$53$			1.57314e6i			1.45145i	−0.687984	+	0.725726i	$0.741504\pi$
$54$		0			0
$55$		−	3.56344e6i		−	2.88802i
$56$	375028.	+	325702.i	0.285368	+	0.247835i
$57$		0			0
$58$	−570643.	−	1.94613e6i	−0.384031	−	1.30970i
$59$	77228.5			0.0489548			0.0244774	−	0.999700i	$-0.492208\pi$
$59$	77228.5			0.0489548			0.0244774	+	0.999700i	$0.492208\pi$
$60$		0			0
$61$	−1.19278e6			−0.672828			−0.336414	−	0.941714i	$-0.609214\pi$
$61$	−1.19278e6			−0.672828			−0.336414	+	0.941714i	$0.609214\pi$
$62$	−637593.	−	2.17446e6i	−0.339760	−	1.15872i
$63$		0			0
$64$	−293788.	−	2.07647e6i	−0.140089	−	0.990139i
$65$			496282.i			0.224147i
$66$		0			0
$67$		−	1.71428e6i		−	0.696338i	−0.937432	−	0.348169i	$-0.886804\pi$
$67$		−	1.71428e6i		−	0.696338i	0.937432	−	0.348169i	$-0.113196\pi$
$68$	469786.	+	732207.i	0.181184	+	0.282392i
$69$		0			0
$70$	1.90913e6	−	559794.i	0.665261	−	0.195068i
$71$	1.52612e6			0.506039			0.253020	−	0.967461i	$-0.418576\pi$
$71$	1.52612e6			0.506039			0.253020	+	0.967461i	$0.418576\pi$
$72$		0			0
$73$	−5.69727e6			−1.71410			−0.857051	−	0.515232i	$-0.827706\pi$
$73$	−5.69727e6			−1.71410			−0.857051	+	0.515232i	$0.827706\pi$
$74$	4.62196e6	−	1.35525e6i	1.32591	−	0.388784i
$75$		0			0
$76$	2.61082e6	+	4.06922e6i	0.682228	+	1.06332i
$77$		−	2.38406e6i		−	0.595113i
$78$		0			0
$79$			8.63828e6i			1.97121i	0.169068	+	0.985604i	$0.445924\pi$
$79$			8.63828e6i			1.97121i	−0.169068	+	0.985604i	$0.554076\pi$
$80$	−7.63545e6	−	3.50083e6i	−1.66732	−	0.764463i
$81$		0			0
$82$	−776900.	−	2.64955e6i	−0.155603	−	0.530669i
$83$	866901.			0.166416			0.0832082	−	0.996532i	$-0.473483\pi$
$83$	866901.			0.166416			0.0832082	+	0.996532i	$0.473483\pi$
$84$		0			0
$85$	3.48445e6			0.615416
$86$	281133.	+	958779.i	0.0476614	+	0.162545i
$87$		0			0
$88$	−6.60009e6	+	7.59963e6i	−1.03243	+	1.18878i
$89$			6.05763e6i			0.910831i	0.890279	+	0.455416i	$0.150509\pi$
$89$			6.05763e6i			0.910831i	−0.890279	+	0.455416i	$0.849491\pi$
$90$		0			0
$91$			332029.i			0.0461883i
$92$	320892.	−	205885.i	0.0429637	−	0.0275656i
$93$		0			0
$94$	−4.92387e6	+	1.44377e6i	−0.611447	+	0.179288i
$95$	1.93648e7			2.31729
$96$		0			0
$97$	1.19866e7			1.33351			0.666756	−	0.745276i	$-0.267683\pi$
$97$	1.19866e7			1.33351			0.666756	+	0.745276i	$0.267683\pi$
$98$	1.27727e6	−	374521.i	0.137085	−	0.0401961i
$99$		0			0
$100$	−1.98999e7	+	1.27678e7i	−1.98999	+	1.27678i
$101$		−	9.58096e6i		−	0.925303i	−0.886540	−	0.462652i	$-0.846898\pi$
$101$		−	9.58096e6i		−	0.925303i	0.886540	−	0.462652i	$-0.153102\pi$
$102$		0			0
$103$			1.28909e7i			1.16240i	0.813762	+	0.581198i	$0.197416\pi$
$103$			1.28909e7i			1.16240i	−0.813762	+	0.581198i	$0.802584\pi$
$104$	919198.	−	1.05840e6i	0.0801295	−	0.0922646i
$105$		0			0
$106$	−5.00790e6	−	1.70790e7i	−0.408399	−	1.39281i
$107$	−6.50775e6			−0.513556			−0.256778	−	0.966470i	$-0.582661\pi$
$107$	−6.50775e6			−0.513556			−0.256778	+	0.966470i	$0.582661\pi$
$108$		0			0
$109$	−2.28730e7			−1.69173			−0.845865	−	0.533397i	$-0.820915\pi$
$109$	−2.28730e7			−1.69173			−0.845865	+	0.533397i	$0.820915\pi$
$110$	1.13438e7	+	3.86869e7i	0.812611	+	2.77134i
$111$		0			0
$112$	−5.10836e6	−	2.34217e6i	−0.343573	−	0.157527i
$113$		−	1.68905e7i		−	1.10121i	−0.834767	−	0.550603i	$-0.814398\pi$
$113$		−	1.68905e7i		−	1.10121i	0.834767	−	0.550603i	$-0.185602\pi$
$114$		0			0
$115$		−	1.52707e6i		−	0.0936306i
$116$	1.23905e7	+	1.93118e7i	0.737031	+	1.14873i
$117$		0			0
$118$	−838440.	+	245847.i	−0.0469770	+	0.0137746i
$119$	2.33121e6			0.126814
$120$		0			0
$121$	2.88238e7			1.47912
$122$	1.29495e7	−	3.79705e6i	0.645645	−	0.189316i
$123$		0			0
$124$	1.38442e7	+	2.15776e7i	0.652067	+	1.01631i
$125$			5.46472e7i			2.50255i
$126$		0			0
$127$		−	341188.i		−	0.0147802i	−0.999973	−	0.00739010i	$-0.997648\pi$
$127$		−	341188.i		−	0.0147802i	0.999973	−	0.00739010i	$-0.00235236\pi$
$128$	9.79973e6	+	2.16082e7i	0.413028	+	0.910719i
$129$		0			0
$130$	−1.57985e6	−	5.38795e6i	−0.0630688	−	0.215091i
$131$	9.47174e6			0.368112			0.184056	−	0.982916i	$-0.441077\pi$
$131$	9.47174e6			0.368112			0.184056	+	0.982916i	$0.441077\pi$
$132$		0			0
$133$	1.29557e7			0.477506
$134$	5.45719e6	+	1.86113e7i	0.195931	+	0.668205i
$135$		0			0
$136$	−7.43118e6	−	6.45379e6i	−0.253321	−	0.220003i
$137$			2.45922e7i			0.817099i	0.912736	+	0.408550i	$0.133965\pi$
$137$			2.45922e7i			0.817099i	−0.912736	+	0.408550i	$0.866035\pi$
$138$		0			0
$139$			5.44958e7i			1.72112i	0.509348	+	0.860561i	$0.329887\pi$
$139$			5.44958e7i			1.72112i	−0.509348	+	0.860561i	$0.670113\pi$
$140$	−1.89447e7	+	1.21549e7i	−0.583497	+	0.374373i
$141$		0			0
$142$	−1.65685e7	+	4.85821e6i	−0.485595	+	0.142386i
$143$	−6.72830e6			−0.192411
$144$		0			0
$145$	9.19017e7			2.50343
$146$	6.18530e7	−	1.81365e7i	1.64485	−	0.482302i
$147$		0			0
$148$	−4.58646e7	+	2.94268e7i	−1.16295	+	0.746152i
$149$			4.71462e6i			0.116760i	0.998294	+	0.0583801i	$0.0185935\pi$
$149$			4.71462e6i			0.116760i	−0.998294	+	0.0583801i	$0.981406\pi$
$150$		0			0
$151$			6.10409e7i			1.44279i	0.692526	+	0.721393i	$0.256498\pi$
$151$			6.10409e7i			1.44279i	−0.692526	+	0.721393i	$0.743502\pi$
$152$	−4.12986e7	−	3.58668e7i	−0.953855	−	0.828399i
$153$		0			0
$154$	7.58935e6	+	2.58828e7i	0.167449	+	0.571070i
$155$	1.02684e8			2.21484
$156$		0			0
$157$	−4.67384e7			−0.963884			−0.481942	−	0.876203i	$-0.660068\pi$
$157$	−4.67384e7			−0.963884			−0.481942	+	0.876203i	$0.660068\pi$
$158$	−2.74989e7	−	9.37825e7i	−0.554645	−	1.89157i
$159$		0			0
$160$	9.40396e7	+	1.37007e7i	1.81506	+	0.264438i
$161$		−	1.02166e6i		−	0.0192938i
$162$		0			0
$163$		−	4.74541e7i		−	0.858257i	−0.903243	−	0.429128i	$-0.858821\pi$
$163$		−	4.74541e7i		−	0.858257i	0.903243	−	0.429128i	$-0.141179\pi$
$164$	1.68690e7	+	2.62920e7i	0.298632	+	0.465447i
$165$		0			0
$166$	−9.41161e6	+	2.75967e6i	−0.159693	+	0.0468251i
$167$	−7.81920e7			−1.29914			−0.649568	−	0.760304i	$-0.725050\pi$
$167$	−7.81920e7			−1.29914			−0.649568	+	0.760304i	$0.725050\pi$
$168$		0			0
$169$	−6.18115e7			−0.985067
$170$	−3.78294e7	+	1.10923e7i	−0.590552	+	0.173161i
$171$		0			0
$172$	−6.10430e6	−	9.51415e6i	−0.0914716	−	0.142567i
$173$			9.24523e7i			1.35755i	0.734346	+	0.678776i	$0.237489\pi$
$173$			9.24523e7i			1.35755i	−0.734346	+	0.678776i	$0.762511\pi$
$174$		0			0
$175$			6.33576e7i			0.893646i
$176$	4.74622e7	−	1.03517e8i	0.656226	−	1.43125i
$177$		0			0
$178$	−1.92837e7	−	6.57654e7i	−0.256283	−	0.874032i
$179$	−3.31204e7			−0.431628			−0.215814	−	0.976434i	$-0.569241\pi$
$179$	−3.31204e7			−0.431628			−0.215814	+	0.976434i	$0.569241\pi$
$180$		0			0
$181$	−3.97750e7			−0.498581			−0.249290	−	0.968429i	$-0.580197\pi$
$181$	−3.97750e7			−0.498581			−0.249290	+	0.968429i	$0.580197\pi$
$182$	−1.05697e6	−	3.60472e6i	−0.0129961	−	0.0443222i
$183$		0			0
$184$	−2.82840e6	+	3.25674e6i	−0.0334717	+	0.0385408i
$185$			2.18262e8i			2.53441i
$186$		0			0
$187$			4.72401e7i			0.528281i
$188$	4.88605e7	−	3.13490e7i	0.536297	−	0.344090i
$189$		0			0
$190$	−2.10236e8	+	6.16452e7i	−2.22366	+	0.652022i
$191$	−9.10602e7			−0.945610			−0.472805	−	0.881167i	$-0.656758\pi$
$191$	−9.10602e7			−0.945610			−0.472805	+	0.881167i	$0.656758\pi$
$192$		0			0
$193$	7.26301e7			0.727221			0.363610	−	0.931551i	$-0.381544\pi$
$193$	7.26301e7			0.727221			0.363610	+	0.931551i	$0.381544\pi$
$194$	−1.30134e8	+	3.81580e7i	−1.27964	+	0.375214i
$195$		0			0
$196$	−1.26746e7	+	8.13205e6i	−0.120237	+	0.0771443i
$197$		−	1.49839e8i		−	1.39635i	−0.715927	−	0.698175i	$-0.753996\pi$
$197$		−	1.49839e8i		−	1.39635i	0.715927	−	0.698175i	$-0.246004\pi$
$198$		0			0
$199$		−	7.77032e7i		−	0.698961i	−0.936944	−	0.349481i	$-0.886358\pi$
$199$		−	7.77032e7i		−	0.698961i	0.936944	−	0.349481i	$-0.113642\pi$
$200$	1.75401e8	−	2.01964e8i	1.55034	−	1.78513i
$201$		0			0
$202$	3.04998e7	+	1.04017e8i	0.260355	+	0.887920i
$203$	6.14853e7			0.515864
$204$		0			0
$205$	1.25119e8			1.01435
$206$	−4.10366e7	−	1.39952e8i	−0.327067	−	1.11543i
$207$		0			0
$208$	−6.61008e6	+	1.44168e7i	−0.0509314	+	0.111083i
$209$			2.62536e8i			1.98919i
$210$		0			0
$211$		−	1.31549e7i		−	0.0964050i	−0.998838	−	0.0482025i	$-0.984651\pi$
$211$		−	1.31549e7i		−	0.0964050i	0.998838	−	0.0482025i	$-0.0153493\pi$
$212$	1.08738e8	+	1.69478e8i	0.783799	+	1.22163i
$213$		0			0
$214$	7.06522e7	−	2.07166e7i	0.492808	−	0.144501i
$215$	−4.52763e7			−0.310696
$216$		0			0
$217$	6.86990e7			0.456396
$218$	2.48324e8	−	7.28134e7i	1.62338	−	0.476007i
$219$		0			0
$220$	−2.46310e8	−	3.83898e8i	−1.55956	−	2.43073i
$221$		−	6.57916e6i		−	0.0410013i
$222$		0			0
$223$		−	1.23865e8i		−	0.747968i	−0.927435	−	0.373984i	$-0.877991\pi$
$223$		−	1.23865e8i		−	0.747968i	0.927435	−	0.373984i	$-0.122009\pi$
$224$	6.29156e7	+	9.16624e6i	0.374016	+	0.0544908i
$225$		0			0
$226$	5.37688e7	+	1.83374e8i	0.309849	+	1.05671i
$227$	1.65072e8			0.936661			0.468330	−	0.883553i	$-0.344856\pi$
$227$	1.65072e8			0.936661			0.468330	+	0.883553i	$0.344856\pi$
$228$		0			0
$229$	4.70535e7			0.258922			0.129461	−	0.991585i	$-0.458675\pi$
$229$	4.70535e7			0.258922			0.129461	+	0.991585i	$0.458675\pi$
$230$	4.86125e6	+	1.65789e7i	0.0263451	+	0.0898478i
$231$		0			0
$232$	−1.95996e8	−	1.70217e8i	−1.03048	−	0.894944i
$233$		−	1.57640e8i		−	0.816436i	−0.912885	−	0.408218i	$-0.866150\pi$
$233$		−	1.57640e8i		−	0.816436i	0.912885	−	0.408218i	$-0.133850\pi$
$234$		0			0
$235$		−	2.32519e8i		−	1.16875i
$236$	8.32000e6	−	5.33813e6i	0.0412032	−	0.0264361i
$237$		0			0
$238$	−2.53091e7	+	7.42112e6i	−0.121691	+	0.0356821i
$239$	−2.25713e8			−1.06946			−0.534730	−	0.845023i	$-0.679587\pi$
$239$	−2.25713e8			−1.06946			−0.534730	+	0.845023i	$0.679587\pi$
$240$		0			0
$241$	1.45737e8			0.670673			0.335336	−	0.942098i	$-0.391150\pi$
$241$	1.45737e8			0.670673			0.335336	+	0.942098i	$0.391150\pi$
$242$	−3.12929e8	+	9.17569e7i	−1.41936	+	0.416183i
$243$		0			0
$244$	−1.28500e8	+	8.24462e7i	−0.566292	+	0.363334i
$245$			6.03163e7i			0.262032i
$246$		0			0
$247$		−	3.65635e7i		−	0.154386i
$248$	−2.18991e8	−	1.90188e8i	−0.911685	−	0.791776i
$249$		0			0
$250$	−1.73962e8	−	5.93283e8i	−0.704150	−	2.40144i
$251$	1.30634e8			0.521432			0.260716	−	0.965416i	$-0.416041\pi$
$251$	1.30634e8			0.521432			0.260716	+	0.965416i	$0.416041\pi$
$252$		0			0
$253$	2.07031e7			0.0803738
$254$	1.08613e6	+	3.70415e6i	0.00415875	+	0.0141831i
$255$		0			0
$256$	−1.75179e8	−	2.03396e8i	−0.652592	−	0.757709i
$257$		−	1.00167e8i		−	0.368095i	−0.982917	−	0.184048i	$-0.941080\pi$
$257$		−	1.00167e8i		−	0.368095i	0.982917	−	0.184048i	$-0.0589200\pi$
$258$		0			0
$259$			1.46024e8i			0.522248i
$260$	3.43037e7	+	5.34656e7i	0.121041	+	0.188655i
$261$		0			0
$262$	−1.02831e8	+	3.01521e7i	−0.353240	+	0.103577i
$263$	4.92409e8			1.66909			0.834547	−	0.550937i	$-0.185730\pi$
$263$	4.92409e8			1.66909			0.834547	+	0.550937i	$0.185730\pi$
$264$		0			0
$265$	8.06519e8			2.66228
$266$	−1.40655e8	+	4.12427e7i	−0.458214	+	0.134357i
$267$		0			0
$268$	−1.18493e8	−	1.84683e8i	−0.376030	−	0.586079i
$269$		−	1.03348e8i		−	0.323719i	−0.986814	−	0.161859i	$-0.948251\pi$
$269$		−	1.03348e8i		−	0.323719i	0.986814	−	0.161859i	$-0.0517491\pi$
$270$		0			0
$271$			6.11019e8i			1.86493i	0.361264	+	0.932464i	$0.382345\pi$
$271$			6.11019e8i			1.86493i	−0.361264	+	0.932464i	$0.617655\pi$
$272$	1.01222e8	+	4.64101e7i	0.304989	+	0.139837i
$273$		0			0
$274$	−7.82860e7	−	2.66988e8i	−0.229910	−	0.784087i
$275$	−1.28389e9			−3.72274
$276$		0			0
$277$	6.69007e8			1.89126			0.945630	−	0.325245i	$-0.105447\pi$
$277$	6.69007e8			1.89126			0.945630	+	0.325245i	$0.105447\pi$
$278$	−1.73481e8	−	5.91640e8i	−0.484277	−	1.65159i
$279$		0			0
$280$	1.66981e8	−	1.92269e8i	0.454584	−	0.523428i
$281$		−	3.40848e8i		−	0.916408i	−0.888847	−	0.458204i	$-0.848493\pi$
$281$		−	3.40848e8i		−	0.916408i	0.888847	−	0.458204i	$-0.151507\pi$
$282$		0			0
$283$			1.30260e8i			0.341633i	0.985303	+	0.170816i	$0.0546405\pi$
$283$			1.30260e8i			0.341633i	−0.985303	+	0.170816i	$0.945359\pi$
$284$	1.64412e8	−	1.05487e8i	0.425912	−	0.273266i
$285$		0			0
$286$	7.30465e7	−	2.14187e7i	0.184637	−	0.0541391i
$287$	8.37090e7			0.209019
$288$		0			0
$289$	3.64146e8			0.887427
$290$	−9.97742e8	+	2.92557e8i	−2.40229	+	0.704398i
$291$		0			0
$292$	−6.13779e8	+	3.93802e8i	−1.44269	+	0.925632i
$293$		−	4.55641e8i		−	1.05825i	−0.848545	−	0.529123i	$-0.822521\pi$
$293$		−	4.55641e8i		−	1.05825i	0.848545	−	0.529123i	$-0.177479\pi$
$294$		0			0
$295$		−	3.95935e7i		−	0.0897939i
$296$	4.04258e8	−	4.65480e8i	0.906019	−	1.04323i
$297$		0			0
$298$	−1.50084e7	−	5.11848e7i	−0.0328532	−	0.112043i
$299$	−2.88334e6			−0.00623802
$300$		0			0
$301$	−3.02913e7			−0.0640229
$302$	−1.94316e8	−	6.62698e8i	−0.405961	−	1.38450i
$303$		0			0
$304$	5.62540e8	+	2.57923e8i	1.14841	+	0.526541i
$305$			6.11513e8i			1.23412i
$306$		0			0
$307$		−	9.01188e8i		−	1.77759i	−0.458307	−	0.888794i	$-0.651544\pi$
$307$		−	9.01188e8i		−	1.77759i	0.458307	−	0.888794i	$-0.348456\pi$
$308$	−1.64789e8	−	2.56840e8i	−0.321367	−	0.500882i
$309$		0			0
$310$	−1.11480e9	+	3.26882e8i	−2.12536	+	0.623196i
$311$	−8.22596e8			−1.55069			−0.775345	−	0.631538i	$-0.782424\pi$
$311$	−8.22596e8			−1.55069			−0.775345	+	0.631538i	$0.782424\pi$
$312$		0			0
$313$	−3.31209e8			−0.610515			−0.305258	−	0.952270i	$-0.598743\pi$
$313$	−3.31209e8			−0.610515			−0.305258	+	0.952270i	$0.598743\pi$
$314$	5.07420e8	−	1.48786e8i	0.924941	−	0.271211i
$315$		0			0
$316$	5.97089e8	+	9.30622e8i	1.06447	+	1.65908i
$317$			3.47756e8i			0.613150i	0.951847	+	0.306575i	$0.0991830\pi$
$317$			3.47756e8i			0.613150i	−0.951847	+	0.306575i	$0.900817\pi$
$318$		0			0
$319$			1.24595e9i			2.14898i
$320$	−1.06457e9	+	1.50619e8i	−1.81613	+	0.256954i
$321$		0			0
$322$	3.25233e6	+	1.10918e7i	0.00542875	+	0.0185143i
$323$	−2.56716e8			−0.423882
$324$		0			0
$325$	1.78808e8			0.288932
$326$	1.51064e8	+	5.15191e8i	0.241490	+	0.823582i
$327$		0			0
$328$	−2.66838e8	−	2.31742e8i	−0.417531	−	0.362615i
$329$		−	1.55563e8i		−	0.240835i
$330$		0			0
$331$		−	1.14708e9i		−	1.73858i	−0.494298	−	0.869292i	$-0.664575\pi$
$331$		−	1.14708e9i		−	1.73858i	0.494298	−	0.869292i	$-0.335425\pi$
$332$	9.33932e7	−	5.99213e7i	0.140066	−	0.0898665i
$333$		0			0
$334$	8.48900e8	−	2.48914e8i	1.24665	−	0.365542i
$335$	−8.78878e8			−1.27724
$336$		0			0
$337$	8.31129e8			1.18294			0.591471	−	0.806326i	$-0.298547\pi$
$337$	8.31129e8			1.18294			0.591471	+	0.806326i	$0.298547\pi$
$338$	6.71063e8	−	1.96769e8i	0.945268	−	0.277171i
$339$		0			0
$340$	3.75388e8	−	2.40850e8i	0.517970	−	0.332331i
$341$			1.39213e9i			1.90125i
$342$		0			0
$343$			4.03536e7i			0.0539949i
$344$	9.65591e7	+	8.38592e7i	0.127891	+	0.111070i
$345$		0			0
$346$	−2.94310e8	−	1.00372e9i	−0.381978	−	1.30270i
$347$	9.66197e8			1.24140			0.620701	−	0.784047i	$-0.286848\pi$
$347$	9.66197e8			1.24140			0.620701	+	0.784047i	$0.286848\pi$
$348$		0			0
$349$	1.56923e9			1.97605			0.988027	−	0.154280i	$-0.0493058\pi$
$349$	1.56923e9			1.97605			0.988027	+	0.154280i	$0.0493058\pi$
$350$	−2.01691e8	−	6.87850e8i	−0.251448	−	0.857542i
$351$		0			0
$352$	−1.85746e8	+	1.27493e9i	−0.226997	+	1.55807i
$353$			7.01860e8i			0.849257i	0.905368	+	0.424629i	$0.139595\pi$
$353$			7.01860e8i			0.849257i	−0.905368	+	0.424629i	$0.860405\pi$
$354$		0			0
$355$		−	7.82411e8i		−	0.928188i
$356$	4.18712e8	+	6.52603e8i	0.491858	+	0.766609i
$357$		0			0
$358$	3.59576e8	−	1.05435e8i	0.414190	−	0.121449i
$359$	−1.49448e9			−1.70474			−0.852370	−	0.522939i	$-0.824836\pi$
$359$	−1.49448e9			−1.70474			−0.852370	+	0.522939i	$0.824836\pi$
$360$		0			0
$361$	−5.32823e8			−0.596084
$362$	4.31822e8	−	1.26619e8i	0.478437	−	0.140287i
$363$		0			0
$364$	2.29503e7	+	3.57703e7i	0.0249421	+	0.0388747i
$365$			2.92088e9i			3.14404i
$366$		0			0
$367$			1.38437e9i			1.46191i	0.682425	+	0.730955i	$0.260925\pi$
$367$			1.38437e9i			1.46191i	−0.682425	+	0.730955i	$0.739075\pi$
$368$	2.03394e7	−	4.43610e7i	0.0212751	−	0.0464017i
$369$		0			0
$370$	−6.94809e8	−	2.36959e9i	−0.713115	−	2.43202i
$371$	5.39588e8			0.548597
$372$		0			0
$373$	−7.73503e8			−0.771758			−0.385879	−	0.922549i	$-0.626102\pi$
$373$	−7.73503e8			−0.771758			−0.385879	+	0.922549i	$0.626102\pi$
$374$	−1.50383e8	−	5.12868e8i	−0.148644	−	0.506938i
$375$		0			0
$376$	−4.30664e8	+	4.95885e8i	−0.417812	+	0.481087i
$377$		−	1.73524e8i		−	0.166788i
$378$		0			0
$379$			6.35484e8i			0.599608i	0.954001	+	0.299804i	$0.0969213\pi$
$379$			6.35484e8i			0.599608i	−0.954001	+	0.299804i	$0.903079\pi$
$380$	2.08621e9	−	1.33852e9i	1.95036	−	1.25136i
$381$		0			0
$382$	9.88606e8	−	2.89879e8i	0.907406	−	0.266069i
$383$	1.60965e9			1.46399			0.731993	−	0.681312i	$-0.238590\pi$
$383$	1.60965e9			1.46399			0.731993	+	0.681312i	$0.238590\pi$
$384$		0			0
$385$	−1.22226e9			−1.09157
$386$	−7.88518e8	+	2.31209e8i	−0.697840	+	0.204620i
$387$		0			0
$388$	1.29135e9	−	8.28533e8i	1.12236	−	0.720110i
$389$		−	6.09066e8i		−	0.524615i	−0.964984	−	0.262308i	$-0.915516\pi$
$389$		−	6.09066e8i		−	0.524615i	0.964984	−	0.262308i	$-0.0844835\pi$
$390$		0			0
$391$			2.02442e7i			0.0171271i
$392$	1.11716e8	−	1.28635e8i	0.0936728	−	0.107859i
$393$		0			0
$394$	4.76995e8	+	1.62675e9i	0.392895	+	1.33994i
$395$	4.42868e9			3.61563
$396$		0			0
$397$	−2.25970e9			−1.81252			−0.906262	−	0.422717i	$-0.861076\pi$
$397$	−2.25970e9			−1.81252			−0.906262	+	0.422717i	$0.861076\pi$
$398$	2.47358e8	+	8.43594e8i	0.196669	+	0.670722i
$399$		0			0
$400$	−1.26133e9	+	2.75101e9i	−0.985416	+	2.14923i
$401$		−	1.34647e9i		−	1.04278i	−0.853319	−	0.521389i	$-0.825414\pi$
$401$		−	1.34647e9i		−	1.04278i	0.853319	−	0.521389i	$-0.174586\pi$
$402$		0			0
$403$		−	1.93883e8i		−	0.147561i
$404$	−6.62248e8	−	1.03218e9i	−0.499673	−	0.778789i
$405$		0			0
$406$	−6.67522e8	+	1.95730e8i	−0.495022	+	0.145150i
$407$	−2.95906e9			−2.17557
$408$		0			0
$409$	1.51324e9			1.09364			0.546821	−	0.837250i	$-0.315838\pi$
$409$	1.51324e9			1.09364			0.546821	+	0.837250i	$0.315838\pi$
$410$	−1.35837e9	+	3.98302e8i	−0.973365	+	0.285410i
$411$		0			0
$412$	8.91038e8	+	1.38877e9i	0.627706	+	0.978340i
$413$		−	2.64894e7i		−	0.0185032i
$414$		0			0
$415$		−	4.44443e8i		−	0.305244i
$416$	2.58690e7	−	1.77560e8i	0.0176178	−	0.120926i
$417$		0			0
$418$	−8.35749e8	−	2.85025e9i	−0.559704	−	1.90882i
$419$	7.19570e7			0.0477886			0.0238943	−	0.999714i	$-0.492393\pi$
$419$	7.19570e7			0.0477886			0.0238943	+	0.999714i	$0.492393\pi$
$420$		0			0
$421$	−1.76118e8			−0.115031			−0.0575156	−	0.998345i	$-0.518318\pi$
$421$	−1.76118e8			−0.115031			−0.0575156	+	0.998345i	$0.518318\pi$
$422$	4.18770e7	+	1.42818e8i	0.0271258	+	0.0925101i
$423$		0			0
$424$	−1.72004e9	−	1.49381e9i	−1.09586	−	0.951731i
$425$		−	1.25543e9i		−	0.793290i
$426$		0			0
$427$			4.09122e8i			0.254305i
$428$	−7.01095e8	+	4.49824e8i	−0.432239	+	0.277326i
$429$		0			0
$430$	4.91547e8	−	1.44131e8i	0.298144	−	0.0874215i
$431$	−1.07945e9			−0.649430			−0.324715	−	0.945812i	$-0.605268\pi$
$431$	−1.07945e9			−0.649430			−0.324715	+	0.945812i	$0.605268\pi$
$432$		0			0
$433$	−2.09096e9			−1.23777			−0.618884	−	0.785483i	$-0.712415\pi$
$433$	−2.09096e9			−1.23777			−0.618884	+	0.785483i	$0.712415\pi$
$434$	−7.45839e8	+	2.18695e8i	−0.437957	+	0.128417i
$435$		0			0
$436$	−2.46416e9	+	1.58101e9i	−1.42386	+	0.913551i
$437$			1.12507e8i			0.0644902i
$438$		0			0
$439$			2.09571e9i			1.18224i	0.806585	+	0.591118i	$0.201313\pi$
$439$			2.09571e9i			1.18224i	−0.806585	+	0.591118i	$0.798687\pi$
$440$	3.89618e9	+	3.38373e9i	2.18049	+	1.89370i
$441$		0			0
$442$	2.09439e7	+	7.14274e7i	0.0115367	+	0.0393448i
$443$	−4.95891e8			−0.271002			−0.135501	−	0.990777i	$-0.543264\pi$
$443$	−4.95891e8			−0.271002			−0.135501	+	0.990777i	$0.543264\pi$
$444$		0			0
$445$	3.10563e9			1.67067
$446$	3.94310e8	+	1.34476e9i	0.210458	+	0.717749i
$447$		0			0
$448$	−7.12230e8	+	1.00769e8i	−0.374237	+	0.0529487i
$449$		−	2.38831e9i		−	1.24517i	−0.782551	−	0.622586i	$-0.786082\pi$
$449$		−	2.38831e9i		−	1.24517i	0.782551	−	0.622586i	$-0.213918\pi$
$450$		0			0
$451$			1.69629e9i			0.870729i
$452$	−1.16749e9	−	1.81965e9i	−0.594662	−	0.926839i
$453$		0			0
$454$	−1.79212e9	+	5.25485e8i	−0.898818	+	0.263551i
$455$	1.70225e8			0.0847195
$456$		0			0
$457$	−1.91773e9			−0.939899			−0.469949	−	0.882693i	$-0.655728\pi$
$457$	−1.91773e9			−0.939899			−0.469949	+	0.882693i	$0.655728\pi$
$458$	−5.10842e8	+	1.49789e8i	−0.248461	+	0.0728535i
$459$		0			0
$460$	−1.05553e8	−	1.64515e8i	−0.0505615	−	0.0788050i
$461$		−	6.71193e8i		−	0.319076i	−0.987192	−	0.159538i	$-0.949000\pi$
$461$		−	6.71193e8i		−	0.319076i	0.987192	−	0.159538i	$-0.0510005\pi$
$462$		0			0
$463$			1.48992e9i			0.697635i	0.937191	+	0.348817i	$0.113417\pi$
$463$			1.48992e9i			0.697635i	−0.937191	+	0.348817i	$0.886583\pi$
$464$	2.66971e9	+	1.22406e9i	1.24066	+	0.568838i
$465$		0			0
$466$	5.01828e8	+	1.71144e9i	0.229723	+	0.783451i
$467$	1.72985e9			0.785956			0.392978	−	0.919548i	$-0.371445\pi$
$467$	1.72985e9			0.785956			0.392978	+	0.919548i	$0.371445\pi$
$468$		0			0
$469$	−5.87998e8			−0.263191
$470$	7.40195e8	+	2.52437e9i	0.328854	+	1.12153i
$471$		0			0
$472$	−7.33338e7	+	8.44397e7i	−0.0321002	+	0.0369615i
$473$		−	6.13828e8i		−	0.266706i
$474$		0			0
$475$		−	6.97702e9i		−	2.98705i
$476$	2.51147e8	−	1.61137e8i	0.106734	−	0.0684810i
$477$		0			0
$478$	2.45048e9	−	7.18529e8i	1.02625	−	0.300917i
$479$	3.39296e9			1.41060			0.705301	−	0.708908i	$-0.250812\pi$
$479$	3.39296e9			1.41060			0.705301	+	0.708908i	$0.250812\pi$
$480$		0			0
$481$	4.12111e8			0.168852
$482$	−1.58221e9	+	4.63936e8i	−0.643577	+	0.188709i
$483$		0			0
$484$	3.10525e9	−	1.99234e9i	1.24491	−	0.798738i
$485$		−	6.14532e9i		−	2.44595i
$486$		0			0
$487$		−	2.58539e9i		−	1.01432i	−0.861852	−	0.507159i	$-0.830696\pi$
$487$		−	2.58539e9i		−	1.01432i	0.861852	−	0.507159i	$-0.169304\pi$
$488$	1.13262e9	−	1.30415e9i	0.441180	−	0.507994i
$489$		0			0
$490$	−1.92009e8	−	6.54831e8i	−0.0737286	−	0.251445i
$491$	1.16509e7			0.00444194			0.00222097	−	0.999998i	$-0.499293\pi$
$491$	1.16509e7			0.00444194			0.00222097	+	0.999998i	$0.499293\pi$
$492$		0			0
$493$	−1.21833e9			−0.457932
$494$	1.16395e8	+	3.96956e8i	0.0434401	+	0.148149i
$495$		0			0
$496$	2.98294e9	+	1.36767e9i	1.09764	+	0.503263i
$497$		−	5.23459e8i		−	0.191265i
$498$		0			0
$499$		−	6.10284e8i		−	0.219877i	−0.993938	−	0.109939i	$-0.964935\pi$
$499$		−	6.10284e8i		−	0.219877i	0.993938	−	0.109939i	$-0.0350654\pi$
$500$	3.77728e9	+	5.88726e9i	1.35140	+	2.10629i
$501$		0			0
$502$	−1.41824e9	+	4.15856e8i	−0.500365	+	0.146717i
$503$	5.36664e9			1.88025			0.940123	−	0.340835i	$-0.110710\pi$
$503$	5.36664e9			1.88025			0.940123	+	0.340835i	$0.110710\pi$
$504$		0			0
$505$	−4.91197e9			−1.69721
$506$	−2.24766e8	+	6.59058e7i	−0.0771266	+	0.0226150i
$507$		0			0
$508$	−2.35834e7	−	3.67570e7i	−0.00798146	−	0.0124399i
$509$			1.27945e9i			0.430043i	0.976609	+	0.215022i	$0.0689822\pi$
$509$			1.27945e9i			0.430043i	−0.976609	+	0.215022i	$0.931018\pi$
$510$		0			0
$511$			1.95416e9i			0.647869i
$512$	2.54934e9	+	1.65053e9i	0.839425	+	0.543475i
$513$		0			0
$514$	3.18870e8	+	1.08748e9i	0.103572	+	0.353224i
$515$	6.60893e9			2.13209
$516$		0			0
$517$	3.15235e9			1.00327
$518$	−4.64850e8	−	1.58533e9i	−0.146946	−	0.501148i
$519$		0			0
$520$	−5.42623e8	−	4.71255e8i	−0.169234	−	0.146975i
$521$			1.78970e9i			0.554431i	0.960808	+	0.277216i	$0.0894116\pi$
$521$			1.78970e9i			0.554431i	−0.960808	+	0.277216i	$0.910588\pi$
$522$		0			0
$523$			1.61533e9i			0.493748i	0.969048	+	0.246874i	$0.0794035\pi$
$523$			1.61533e9i			0.493748i	−0.969048	+	0.246874i	$0.920597\pi$
$524$	1.02041e9	−	6.54699e8i	0.309825	−	0.198784i
$525$		0			0
$526$	−5.34589e9	+	1.56752e9i	−1.60166	+	0.469638i
$527$	−1.36127e9			−0.405142
$528$		0			0
$529$	−3.39595e9			−0.997394
$530$	−8.75607e9	+	2.56745e9i	−2.55472	+	0.749094i
$531$		0			0
$532$	1.39574e9	−	8.95512e8i	0.401897	−	0.257858i
$533$		−	2.36244e8i		−	0.0675795i
$534$		0			0
$535$			3.33640e9i			0.941975i
$536$	1.87435e9	+	1.62783e9i	0.525744	+	0.456596i
$537$		0			0
$538$	3.28994e8	+	1.12201e9i	0.0910857	+	0.310640i
$539$	−8.17732e8			−0.224932
$540$		0			0
$541$	−2.11635e9			−0.574642			−0.287321	−	0.957834i	$-0.592765\pi$
$541$	−2.11635e9			−0.574642			−0.287321	+	0.957834i	$0.592765\pi$
$542$	−1.94510e9	−	6.63360e9i	−0.524740	−	1.78958i
$543$		0			0
$544$	−1.24667e9	−	1.81629e8i	−0.332014	−	0.0483715i
$545$			1.17266e10i			3.10301i
$546$		0			0
$547$		−	3.87336e9i		−	1.01189i	−0.862566	−	0.505944i	$-0.831144\pi$
$547$		−	3.87336e9i		−	1.01189i	0.862566	−	0.505944i	$-0.168856\pi$
$548$	1.69984e9	+	2.64937e9i	0.441242	+	0.687719i
$549$		0			0
$550$	1.39387e10	−	4.08710e9i	3.57234	−	1.04748i
$551$	−6.77084e9			−1.72430
$552$		0			0
$553$	2.96293e9			0.745047
$554$	−7.26315e9	+	2.12970e9i	−1.81485	+	0.532149i
$555$		0			0
$556$	3.76682e9	+	5.87096e9i	0.929423	+	1.44860i
$557$			3.18813e9i			0.781705i	0.920453	+	0.390853i	$0.127820\pi$
$557$			3.18813e9i			0.781705i	−0.920453	+	0.390853i	$0.872180\pi$
$558$		0			0
$559$			8.54882e7i			0.0206997i
$560$	−1.20079e9	+	2.61896e9i	−0.288940	+	0.630189i
$561$		0			0
$562$	1.08505e9	+	3.70046e9i	0.257853	+	0.879384i
$563$	−1.86008e9			−0.439292			−0.219646	−	0.975580i	$-0.570490\pi$
$563$	−1.86008e9			−0.439292			−0.219646	+	0.975580i	$0.570490\pi$
$564$		0			0
$565$	−8.65943e9			−2.01985
$566$	−4.14667e8	−	1.41419e9i	−0.0961263	−	0.327830i
$567$		0			0
$568$	−1.44916e9	+	1.66862e9i	−0.331815	+	0.382066i
$569$		−	4.37966e9i		−	0.996661i	−0.866987	−	0.498331i	$-0.833947\pi$
$569$		−	4.37966e9i		−	0.996661i	0.866987	−	0.498331i	$-0.166053\pi$
$570$		0			0
$571$		−	1.50649e8i		−	0.0338642i	−0.999857	−	0.0169321i	$-0.994610\pi$
$571$		−	1.50649e8i		−	0.0338642i	0.999857	−	0.0169321i	$-0.00538991\pi$
$572$	−7.24855e8	+	4.65069e8i	−0.161944	+	0.103904i
$573$		0			0
$574$	−9.08796e8	+	2.66477e8i	−0.200574	+	0.0588123i
$575$	−5.50197e8			−0.120693
$576$		0			0
$577$	−2.10867e9			−0.456975			−0.228488	−	0.973547i	$-0.573378\pi$
$577$	−2.10867e9			−0.456975			−0.228488	+	0.973547i	$0.573378\pi$
$578$	−3.95339e9	+	1.15921e9i	−0.851574	+	0.249698i
$579$		0			0
$580$	9.90078e9	−	6.35237e9i	2.10703	−	1.35188i
$581$		−	2.97347e8i		−	0.0628995i
$582$		0			0
$583$			1.09343e10i			2.28534i
$584$	5.40995e9	−	6.22925e9i	1.12395	−	1.29417i
$585$		0			0
$586$	1.45048e9	+	4.94672e9i	0.297762	+	1.01549i
$587$	−8.38246e9			−1.71056			−0.855280	−	0.518167i	$-0.826615\pi$
$587$	−8.38246e9			−1.71056			−0.855280	+	0.518167i	$0.826615\pi$
$588$		0			0
$589$	−7.56522e9			−1.52552
$590$	1.26041e8	+	4.29852e8i	0.0252656	+	0.0861661i
$591$		0			0
$592$	−2.90708e9	+	6.34044e9i	−0.575878	+	1.25601i
$593$			6.67307e8i			0.131412i	0.997839	+	0.0657059i	$0.0209299\pi$
$593$			6.67307e8i			0.131412i	−0.997839	+	0.0657059i	$0.979070\pi$
$594$		0			0
$595$		−	1.19517e9i		−	0.232605i
$596$	3.25881e8	+	5.07917e8i	0.0630517	+	0.0982722i
$597$		0			0
$598$	3.13033e7	−	9.17874e6i	0.00598599	−	0.00175521i
$599$	−4.39677e9			−0.835872			−0.417936	−	0.908476i	$-0.637246\pi$
$599$	−4.39677e9			−0.835872			−0.417936	+	0.908476i	$0.637246\pi$
$600$		0			0
$601$	−7.73210e9			−1.45290			−0.726452	−	0.687217i	$-0.758832\pi$
$601$	−7.73210e9			−1.45290			−0.726452	+	0.687217i	$0.758832\pi$
$602$	3.28861e8	−	9.64285e7i	0.0614363	−	0.0180143i
$603$		0			0
$604$	4.21923e9	+	6.57608e9i	0.779119	+	1.21433i
$605$		−	1.47774e10i		−	2.71303i
$606$		0			0
$607$		−	4.36451e9i		−	0.792091i	−0.918231	−	0.396045i	$-0.870382\pi$
$607$		−	4.36451e9i		−	0.792091i	0.918231	−	0.396045i	$-0.129618\pi$
$608$	−6.92834e9	−	1.00940e9i	−1.25016	−	0.182138i
$609$		0			0
$610$	−1.94667e9	−	6.63896e9i	−0.347247	−	1.18426i
$611$	−4.39030e8			−0.0778664
$612$		0			0
$613$	1.20038e9			0.210478			0.105239	−	0.994447i	$-0.466439\pi$
$613$	1.20038e9			0.210478			0.105239	+	0.994447i	$0.466439\pi$
$614$	2.86882e9	+	9.78385e9i	0.500165	+	1.70577i
$615$		0			0
$616$	2.60667e9	+	2.26383e9i	0.449318	+	0.390221i
$617$		−	8.52396e9i		−	1.46098i	−0.682925	−	0.730488i	$-0.739293\pi$
$617$		−	8.52396e9i		−	1.46098i	0.682925	−	0.730488i	$-0.260707\pi$
$618$		0			0
$619$		−	4.84688e9i		−	0.821381i	−0.911775	−	0.410691i	$-0.865288\pi$
$619$		−	4.84688e9i		−	0.821381i	0.911775	−	0.410691i	$-0.134712\pi$
$620$	1.10624e10	−	7.09766e9i	1.86414	−	1.19604i
$621$		0			0
$622$	8.93061e9	−	2.61863e9i	1.48804	−	0.436322i
$623$	2.07777e9			0.344262
$624$		0			0
$625$	1.35856e10			2.22586
$626$	3.59581e9	−	1.05436e9i	0.585850	−	0.171783i
$627$		0			0
$628$	−5.03523e9	+	3.23062e9i	−0.811261	+	0.520507i
$629$		−	2.89348e9i		−	0.463599i
$630$		0			0
$631$		−	9.50221e9i		−	1.50564i	−0.658225	−	0.752821i	$-0.728692\pi$
$631$		−	9.50221e9i		−	1.50564i	0.658225	−	0.752821i	$-0.271308\pi$
$632$	−9.44489e9	−	8.20265e9i	−1.48829	−	1.29254i
$633$		0			0
$634$	−1.10704e9	−	3.77545e9i	−0.172524	−	0.588378i
$635$	−1.74920e8			−0.0271102
$636$		0			0
$637$	1.13886e8			0.0174575
$638$	−3.96631e9	−	1.35268e10i	−0.604665	−	2.06216i
$639$		0			0
$640$	1.10781e10	−	5.02413e9i	1.67046	−	0.757584i
$641$			8.25267e8i			0.123763i	0.998083	+	0.0618816i	$0.0197101\pi$
$641$			8.25267e8i			0.123763i	−0.998083	+	0.0618816i	$0.980290\pi$
$642$		0			0
$643$		−	1.46353e9i		−	0.217102i	−0.994091	−	0.108551i	$-0.965379\pi$
$643$		−	1.46353e9i		−	0.217102i	0.994091	−	0.108551i	$-0.0346211\pi$
$644$	−7.06187e7	−	1.10066e8i	−0.0104188	−	0.0162388i
$645$		0			0
$646$	2.78707e9	−	8.17224e8i	0.406756	−	0.119269i
$647$	−8.14995e9			−1.18301			−0.591507	−	0.806300i	$-0.701467\pi$
$647$	−8.14995e9			−1.18301			−0.591507	+	0.806300i	$0.701467\pi$
$648$		0			0
$649$	5.36785e8			0.0770804
$650$	−1.94125e9	+	5.69213e8i	−0.277259	+	0.0812976i
$651$		0			0
$652$	−3.28009e9	−	5.11234e9i	−0.463468	−	0.722359i
$653$			7.90957e9i			1.11162i	0.831309	+	0.555811i	$0.187592\pi$
$653$			7.90957e9i			1.11162i	−0.831309	+	0.555811i	$0.812408\pi$
$654$		0			0
$655$		−	4.85598e9i		−	0.675199i
$656$	3.63468e9	+	1.66649e9i	0.502692	+	0.230483i
$657$		0			0
$658$	4.95215e8	+	1.68889e9i	0.0677646	+	0.231105i
$659$	1.79941e9			0.244924			0.122462	−	0.992473i	$-0.460921\pi$
$659$	1.79941e9			0.244924			0.122462	+	0.992473i	$0.460921\pi$
$660$		0			0
$661$	−2.56731e9			−0.345759			−0.172879	−	0.984943i	$-0.555307\pi$
$661$	−2.56731e9			−0.345759			−0.172879	+	0.984943i	$0.555307\pi$
$662$	3.65158e9	+	1.24534e10i	0.489191	+	1.66834i
$663$		0			0
$664$	−8.23182e8	+	9.47848e8i	−0.109121	+	0.125646i
$665$		−	6.64211e9i		−	0.875852i
$666$		0			0
$667$			5.33937e8i			0.0696707i
$668$	−8.42380e9	+	5.40473e9i	−1.09343	+	0.701546i
$669$		0			0
$670$	9.54164e9	−	2.79780e9i	1.22564	−	0.359380i
$671$	−8.29052e9			−1.05938
$672$		0			0
$673$	1.58520e9			0.200462			0.100231	−	0.994964i	$-0.468042\pi$
$673$	1.58520e9			0.200462			0.100231	+	0.994964i	$0.468042\pi$
$674$	−9.02325e9	+	2.64579e9i	−1.13515	+	0.332848i
$675$		0			0
$676$	−6.65909e9	+	4.27249e9i	−0.829090	+	0.531946i
$677$			1.07207e9i			0.132789i	0.997793	+	0.0663947i	$0.0211497\pi$
$677$			1.07207e9i			0.132789i	−0.997793	+	0.0663947i	$0.978850\pi$
$678$		0			0
$679$		−	4.11142e9i		−	0.504020i
$680$	−3.30873e9	+	3.80982e9i	−0.403534	+	0.464647i
$681$		0			0
$682$	−4.43166e9	−	1.51138e10i	−0.534960	−	1.82444i
$683$	4.50598e9			0.541149			0.270575	−	0.962699i	$-0.412786\pi$
$683$	4.50598e9			0.541149			0.270575	+	0.962699i	$0.412786\pi$
$684$		0			0
$685$	1.26079e10			1.49874
$686$	−1.28461e8	−	4.38104e8i	−0.0151927	−	0.0518134i
$687$		0			0
$688$	−1.31526e9	−	6.03043e8i	−0.153976	−	0.0705975i
$689$		−	1.52283e9i		−	0.177371i
$690$		0			0
$691$			2.55258e9i			0.294311i	0.989113	+	0.147155i	$0.0470117\pi$
$691$			2.55258e9i			0.294311i	−0.989113	+	0.147155i	$0.952988\pi$
$692$	6.39042e9	+	9.96009e9i	0.733092	+	1.14259i
$693$		0			0
$694$	−1.04896e10	+	3.07577e9i	−1.19125	+	0.349297i
$695$	2.79389e10			3.15692
$696$		0			0
$697$	−1.65869e9			−0.185546
$698$	−1.70366e10	+	4.99546e9i	−1.89622	+	0.556008i
$699$		0			0
$700$	4.37936e9	+	6.82566e9i	0.482578	+	0.752145i
$701$		−	3.27800e9i		−	0.359414i	−0.983720	−	0.179707i	$-0.942485\pi$
$701$		−	3.27800e9i		−	0.359414i	0.983720	−	0.179707i	$-0.0575150\pi$
$702$		0			0
$703$		−	1.60804e10i		−	1.74563i
$704$	−2.04201e9	−	1.44327e10i	−0.220573	−	1.55899i
$705$		0			0
$706$	−2.23428e9	−	7.61983e9i	−0.238958	−	0.814946i
$707$	−3.28627e9			−0.349732
$708$		0			0
$709$	−1.00606e10			−1.06014			−0.530069	−	0.847954i	$-0.677834\pi$
$709$	−1.00606e10			−1.06014			−0.530069	+	0.847954i	$0.677834\pi$
$710$	2.49071e9	+	8.49434e9i	0.261167	+	0.890688i
$711$		0			0
$712$	−6.62327e9	−	5.75214e9i	−0.687689	−	0.597241i
$713$			5.96582e8i			0.0616391i
$714$		0			0
$715$			3.44947e9i			0.352924i
$716$	−3.56814e9	+	2.28933e9i	−0.363284	+	0.233084i
$717$		0			0
$718$	1.62249e10	−	4.75747e9i	1.63587	−	0.479668i
$719$	−1.81069e10			−1.81675			−0.908373	−	0.418161i	$-0.862675\pi$
$719$	−1.81069e10			−1.81675			−0.908373	+	0.418161i	$0.862675\pi$
$720$		0			0
$721$	4.42159e9			0.439344
$722$	5.78465e9	−	1.69617e9i	0.572001	−	0.167722i
$723$		0			0
$724$	−4.28505e9	+	2.74930e9i	−0.419635	+	0.269239i
$725$		−	3.31117e10i		−	3.22700i
$726$		0			0
$727$			1.39140e10i			1.34301i	0.740998	+	0.671507i	$0.234353\pi$
$727$			1.39140e10i			1.34301i	−0.740998	+	0.671507i	$0.765647\pi$
$728$	−3.63033e8	−	3.15285e8i	−0.0348727	−	0.0302861i
$729$		0			0
$730$	−9.29823e9	−	3.17108e10i	−0.884648	−	3.01702i
$731$	6.00222e8			0.0568331
$732$		0			0
$733$	−5.67481e8			−0.0532215			−0.0266107	−	0.999646i	$-0.508471\pi$
$733$	−5.67481e8			−0.0532215			−0.0266107	+	0.999646i	$0.508471\pi$
$734$	−4.40696e9	−	1.50296e10i	−0.411342	−	1.40285i
$735$		0			0
$736$	−7.95995e7	+	5.46358e8i	−0.00735933	+	0.0505132i
$737$		−	1.19153e10i		−	1.09640i
$738$		0			0
$739$			2.66240e9i			0.242671i	0.992612	+	0.121335i	$0.0387177\pi$
$739$			2.66240e9i			0.242671i	−0.992612	+	0.121335i	$0.961282\pi$
$740$	1.50866e10	+	2.35139e10i	1.36861	+	2.13311i
$741$		0			0
$742$	−5.85810e9	+	1.71771e9i	−0.526433	+	0.154360i
$743$	1.17550e10			1.05139			0.525693	−	0.850674i	$-0.323806\pi$
$743$	1.17550e10			1.05139			0.525693	+	0.850674i	$0.323806\pi$
$744$		0			0
$745$	2.41709e9			0.214164
$746$	8.39763e9	−	2.46235e9i	0.740578	−	0.217152i
$747$		0			0
$748$	3.26530e9	+	5.08929e9i	0.285277	+	0.444633i
$749$			2.23216e9i			0.194106i
$750$		0			0
$751$			3.68001e9i			0.317037i	0.987356	+	0.158518i	$0.0506717\pi$
$751$			3.68001e9i			0.317037i	−0.987356	+	0.158518i	$0.949328\pi$
$752$	3.09697e9	−	6.75460e9i	0.265567	−	0.579212i
$753$		0			0
$754$	5.52391e8	+	1.88388e9i	0.0469296	+	0.160049i
$755$	3.12945e10			2.64639
$756$		0			0
$757$	−6.00364e9			−0.503013			−0.251507	−	0.967856i	$-0.580926\pi$
$757$	−6.00364e9			−0.503013			−0.251507	+	0.967856i	$0.580926\pi$
$758$	−2.02298e9	−	6.89921e9i	−0.168714	−	0.575383i
$759$		0			0
$760$	−1.83882e10	+	2.11730e10i	−1.51947	+	1.74958i
$761$			2.05678e10i			1.69177i	0.533366	+	0.845885i	$0.320927\pi$
$761$			2.05678e10i			1.69177i	−0.533366	+	0.845885i	$0.679073\pi$
$762$		0			0
$763$			7.84545e9i			0.639414i
$764$	−9.81013e9	+	6.29420e9i	−0.795881	+	0.510639i
$765$		0			0
$766$	−1.74754e10	+	5.12413e9i	−1.40484	+	0.411926i
$767$	−7.47584e7			−0.00598241
$768$		0			0
$769$	−3.33896e9			−0.264770			−0.132385	−	0.991198i	$-0.542264\pi$
$769$	−3.33896e9			−0.264770			−0.132385	+	0.991198i	$0.542264\pi$
$770$	1.32696e10	−	3.89091e9i	1.04747	−	0.307138i
$771$		0			0
$772$	7.82461e9	−	5.02029e9i	0.612072	−	0.392707i
$773$			4.49786e9i			0.350250i	0.984546	+	0.175125i	$0.0560329\pi$
$773$			4.49786e9i			0.350250i	−0.984546	+	0.175125i	$0.943967\pi$
$774$		0			0
$775$		−	3.69965e10i		−	2.85499i
$776$	−1.13822e10	+	1.31059e10i	−0.874396	+	1.00682i
$777$		0			0
$778$	1.93888e9	+	6.61240e9i	0.147613	+	0.503420i
$779$	−9.21814e9			−0.698654
$780$		0			0
$781$	1.06075e10			0.796770
$782$	−6.44450e7	−	2.19784e8i	−0.00481909	−	0.0164351i
$783$		0			0
$784$	−8.03365e8	+	1.75217e9i	−0.0595397	+	0.129858i
$785$			2.39618e10i			1.76798i
$786$		0			0
$787$			1.52635e10i			1.11620i	0.829773	+	0.558101i	$0.188470\pi$
$787$			1.52635e10i			1.11620i	−0.829773	+	0.558101i	$0.811530\pi$
$788$	−1.03571e10	−	1.61425e10i	−0.754043	−	1.17525i
$789$		0			0
$790$	−4.80805e10	+	1.40981e10i	−3.46956	+	1.01734i
$791$	−5.79345e9			−0.416216
$792$		0			0
$793$	1.15463e9			0.0822214
$794$	2.45327e10	−	7.19346e9i	1.73929	−	0.509995i
$795$		0			0
$796$	−5.37095e9	−	8.37115e9i	−0.377446	−	0.588287i
$797$		−	2.04580e8i		−	0.0143139i	−0.999974	−	0.00715696i	$-0.997722\pi$
$797$		−	2.04580e8i		−	0.0143139i	0.999974	−	0.00715696i	$-0.00227815\pi$
$798$		0			0
$799$			3.08248e9i			0.213790i
$800$	4.93630e9	−	3.38820e10i	0.340869	−	2.33967i
$801$		0			0
$802$	4.28632e9	+	1.46181e10i	0.293410	+	1.00065i
$803$	−3.95995e10			−2.69889
$804$		0			0
$805$	−5.23786e8			−0.0353890
$806$	6.17200e8	+	2.10491e9i	0.0415196	+	0.141599i
$807$		0			0
$808$	1.04756e10	+	9.09779e9i	0.698616	+	0.606731i
$809$		−	8.93941e9i		−	0.593594i	−0.954941	−	0.296797i	$-0.904082\pi$
$809$		−	8.93941e9i		−	0.593594i	0.954941	−	0.296797i	$-0.0959184\pi$
$810$		0			0
$811$		−	5.70590e9i		−	0.375622i	−0.982205	−	0.187811i	$-0.939861\pi$
$811$		−	5.70590e9i		−	0.375622i	0.982205	−	0.187811i	$-0.0601393\pi$
$812$	6.62395e9	−	4.24994e9i	0.434181	−	0.278572i
$813$		0			0
$814$	3.21254e10	−	9.41980e9i	2.08768	−	0.612148i
$815$	−2.43288e10			−1.57423
$816$		0			0
$817$	3.33572e9			0.213999
$818$	−1.64286e10	+	4.81719e9i	−1.04946	+	0.307721i
$819$		0			0
$820$	1.34794e10	−	8.64842e9i	0.853733	−	0.547757i
$821$			1.17803e10i			0.742942i	0.928445	+	0.371471i	$0.121146\pi$
$821$			1.17803e10i			0.742942i	−0.928445	+	0.371471i	$0.878854\pi$
$822$		0			0
$823$			7.47614e9i			0.467496i	0.972297	+	0.233748i	$0.0750991\pi$
$823$			7.47614e9i			0.467496i	−0.972297	+	0.233748i	$0.924901\pi$
$824$	−1.40946e10	−	1.22408e10i	−0.877624	−	0.762194i
$825$		0			0
$826$	8.43255e7	+	2.87585e8i	0.00520630	+	0.0177556i
$827$	−5.68386e9			−0.349441			−0.174721	−	0.984618i	$-0.555902\pi$
$827$	−5.68386e9			−0.349441			−0.174721	+	0.984618i	$0.555902\pi$
$828$		0			0
$829$	1.59689e10			0.973498			0.486749	−	0.873542i	$-0.338183\pi$
$829$	1.59689e10			0.973498			0.486749	+	0.873542i	$0.338183\pi$
$830$	1.41483e9	+	4.82515e9i	0.0858875	+	0.292912i
$831$		0			0
$832$	2.84391e8	+	2.01006e9i	0.0171193	+	0.120998i
$833$		−	7.99607e8i		−	0.0479313i
$834$		0			0
$835$			4.00875e10i			2.38290i
$836$	1.81468e10	+	2.82836e10i	1.07418	+	1.67422i
$837$		0			0
$838$	−7.81210e8	+	2.29066e8i	−0.0458578	+	0.0134464i
$839$	1.98205e10			1.15864			0.579318	−	0.815101i	$-0.303319\pi$
$839$	1.98205e10			1.15864			0.579318	+	0.815101i	$0.303319\pi$
$840$		0			0
$841$	−1.48833e10			−0.862807
$842$	1.91204e9	−	5.60648e8i	0.110384	−	0.0323666i
$843$		0			0
$844$	−9.09285e8	−	1.41721e9i	−0.0520597	−	0.0811401i
$845$			3.16895e10i			1.80683i
$846$		0			0
$847$		−	9.88656e9i		−	0.559053i
$848$	2.34291e10	+	1.07422e10i	1.31938	+	0.604933i
$849$		0			0
$850$	3.99651e9	+	1.36297e10i	0.223210	+	0.761239i
$851$	−1.26808e9			−0.0705329
$852$		0			0
$853$	−1.55847e10			−0.859762			−0.429881	−	0.902886i	$-0.641444\pi$
$853$	−1.55847e10			−0.859762			−0.429881	+	0.902886i	$0.641444\pi$
$854$	−1.30239e9	−	4.44168e9i	−0.0715546	−	0.244031i
$855$		0			0
$856$	6.17956e9	−	7.11542e9i	0.336744	−	0.387742i
$857$		−	1.07475e10i		−	0.583277i	−0.956529	−	0.291638i	$-0.905800\pi$
$857$		−	1.07475e10i		−	0.583277i	0.956529	−	0.291638i	$-0.0942004\pi$
$858$		0			0
$859$		−	1.22437e9i		−	0.0659077i	−0.999457	−	0.0329538i	$-0.989509\pi$
$859$		−	1.22437e9i		−	0.0659077i	0.999457	−	0.0329538i	$-0.0104914\pi$
$860$	−4.87772e9	+	3.12955e9i	−0.261500	+	0.167779i
$861$		0			0
$862$	1.17192e10	−	3.43629e9i	0.623192	−	0.182732i
$863$	2.77391e10			1.46911			0.734555	−	0.678549i	$-0.237391\pi$
$863$	2.77391e10			1.46911			0.734555	+	0.678549i	$0.237391\pi$
$864$		0			0
$865$	4.73985e10			2.49005
$866$	2.27008e10	−	6.65632e9i	1.18776	−	0.348274i
$867$		0			0
$868$	7.40110e9	−	4.74857e9i	0.384129	−	0.246458i
$869$			6.00413e10i			3.10371i
$870$		0			0
$871$			1.65945e9i			0.0850943i
$872$	2.17195e10	−	2.50088e10i	1.10928	−	1.27728i
$873$		0			0
$874$	−3.58151e8	−	1.22144e9i	−0.0181458	−	0.0618847i
$875$	1.87440e10			0.945875
$876$		0			0
$877$	−4.17436e9			−0.208974			−0.104487	−	0.994526i	$-0.533320\pi$
$877$	−4.17436e9			−0.208974			−0.104487	+	0.994526i	$0.533320\pi$
$878$	−6.67141e9	−	2.27523e10i	−0.332649	−	1.13447i
$879$		0			0
$880$	−5.30710e10	−	2.43329e10i	−2.62523	−	1.20366i
$881$			4.37768e9i			0.215689i	0.994168	+	0.107845i	$0.0343949\pi$
$881$			4.37768e9i			0.215689i	−0.994168	+	0.107845i	$0.965605\pi$
$882$		0			0
$883$			2.27246e10i			1.11080i	0.831585	+	0.555398i	$0.187434\pi$
$883$			2.27246e10i			1.11080i	−0.831585	+	0.555398i	$0.812566\pi$
$884$	−4.54760e8	−	7.08788e8i	−0.0221411	−	0.0345091i
$885$		0			0
$886$	5.38370e9	−	1.57861e9i	0.260054	−	0.0762528i
$887$	2.78475e9			0.133984			0.0669921	−	0.997754i	$-0.478660\pi$
$887$	2.78475e9			0.133984			0.0669921	+	0.997754i	$0.478660\pi$
$888$		0			0
$889$	−1.17027e8			−0.00558639
$890$	−3.37166e10	+	9.88637e9i	−1.60317	+	0.470080i
$891$		0			0
$892$	−8.56174e9	−	1.33443e10i	−0.403910	−	0.629534i
$893$			1.71308e10i			0.805003i
$894$		0			0
$895$			1.69802e10i			0.791702i
$896$	7.41162e9	−	3.36131e9i	0.344219	−	0.156110i
$897$		0			0
$898$	7.60289e9	+	2.59290e10i	0.350358	+	1.19487i
$899$	−3.59032e10			−1.64807
$900$		0			0
$901$	−1.06919e10			−0.486989
$902$	−5.39993e9	−	1.84160e10i	−0.245000	−	0.835550i
$903$		0			0
$904$	1.84677e10	+	1.60387e10i	0.831424	+	0.722071i
$905$			2.03919e10i			0.914507i
$906$		0			0
$907$		−	2.37580e9i		−	0.105726i	−0.998602	−	0.0528632i	$-0.983165\pi$
$907$		−	2.37580e9i		−	0.105726i	0.998602	−	0.0528632i	$-0.0168347\pi$
$908$	1.77836e10	−	1.14100e10i	0.788348	−	0.505806i
$909$		0			0
$910$	−1.84807e9	+	5.41889e8i	−0.0812967	+	0.0238378i
$911$	2.73821e10			1.19992			0.599961	−	0.800030i	$-0.295183\pi$
$911$	2.73821e10			1.19992			0.599961	+	0.800030i	$0.295183\pi$
$912$		0			0
$913$	6.02549e9			0.262026
$914$	2.08201e10	−	6.10485e9i	0.901926	−	0.264462i
$915$		0			0
$916$	5.06919e9	−	3.25240e9i	0.217923	−	0.139820i
$917$		−	3.24881e9i		−	0.139133i
$918$		0			0
$919$		−	1.23130e9i		−	0.0523311i	−0.999658	−	0.0261656i	$-0.991670\pi$
$919$		−	1.23130e9i		−	0.0523311i	0.999658	−	0.0261656i	$-0.00832970\pi$
$920$	1.66967e9	+	1.45006e9i	0.0706923	+	0.0613945i
$921$		0			0
$922$	2.13666e9	+	7.28689e9i	0.0897794	+	0.306185i
$923$	−1.47731e9			−0.0618393
$924$		0			0
$925$	7.86387e10			3.26693
$926$	−4.74295e9	−	1.61754e10i	−0.196296	−	0.669449i
$927$		0			0
$928$	−3.28807e10	−	4.79042e9i	−1.35059	−	0.196769i
$929$			2.93114e10i			1.19945i	0.800207	+	0.599723i	$0.204723\pi$
$929$			2.93114e10i			1.19945i	−0.800207	+	0.599723i	$0.795277\pi$
$930$		0			0
$931$		−	4.44379e9i		−	0.180480i
$932$	−1.08963e10	−	1.69830e10i	−0.440884	−	0.687160i
$933$		0			0
$934$	−1.87803e10	+	5.50674e9i	−0.754202	+	0.221147i
$935$	2.42191e10			0.968985
$936$		0			0
$937$	−2.39661e9			−0.0951720			−0.0475860	−	0.998867i	$-0.515153\pi$
$937$	−2.39661e9			−0.0951720			−0.0475860	+	0.998867i	$0.515153\pi$
$938$	6.38367e9	−	1.87182e9i	0.252558	−	0.0740549i
$939$		0			0
$940$	−1.60720e10	−	2.50498e10i	−0.631136	−	0.983687i
$941$			1.91604e10i			0.749620i	0.927102	+	0.374810i	$0.122292\pi$
$941$			1.91604e10i			0.749620i	−0.927102	+	0.374810i	$0.877708\pi$
$942$		0			0
$943$			7.26928e8i			0.0282293i
$944$	5.27354e8	−	1.15018e9i	0.0204033	−	0.0445003i
$945$		0			0
$946$	1.95404e9	+	6.66410e9i	0.0750439	+	0.255931i
$947$	3.09806e10			1.18540			0.592700	−	0.805423i	$-0.298062\pi$
$947$	3.09806e10			1.18540			0.592700	+	0.805423i	$0.298062\pi$
$948$		0			0
$949$	5.51504e9			0.209468
$950$	2.22105e10	+	7.57469e10i	0.840475	+	2.86637i
$951$		0			0
$952$	−2.21365e9	+	2.54889e9i	−0.0831533	+	0.0957464i
$953$			2.24750e10i			0.841152i	0.907257	+	0.420576i	$0.138172\pi$
$953$			2.24750e10i			0.841152i	−0.907257	+	0.420576i	$0.861828\pi$
$954$		0			0
$955$			4.66848e10i			1.73446i
$956$	−2.43166e10	+	1.56016e10i	−0.900120	+	0.577519i
$957$		0			0
$958$	−3.68361e10	+	1.08011e10i	−1.35361	+	0.396906i
$959$	8.43511e9			0.308835
$960$		0			0
$961$	−1.26029e10			−0.458079
$962$	−4.47413e9	+	1.31190e9i	−0.162030	+	0.0475104i
$963$		0			0
$964$	1.57006e10	−	1.00735e10i	0.564477	−	0.362170i
$965$		−	3.72360e10i		−	1.33388i
$966$		0			0
$967$		−	4.14573e10i		−	1.47437i	−0.675688	−	0.737187i	$-0.736153\pi$
$967$		−	4.14573e10i		−	1.47437i	0.675688	−	0.737187i	$-0.263847\pi$
$968$	−2.73702e10	+	3.15152e10i	−0.969871	+	1.11675i
$969$		0			0
$970$	1.95628e10	+	6.67174e10i	0.688225	+	2.34713i
$971$	3.03308e9			0.106320			0.0531602	−	0.998586i	$-0.483071\pi$
$971$	3.03308e9			0.106320			0.0531602	+	0.998586i	$0.483071\pi$
$972$		0			0
$973$	1.86921e10			0.650523
$974$	8.23025e9	+	2.80686e10i	0.285402	+	0.973339i
$975$		0			0
$976$	−8.14486e9	+	1.77642e10i	−0.280420	+	0.611607i
$977$		−	2.89511e10i		−	0.993194i	−0.867981	−	0.496597i	$-0.834583\pi$
$977$		−	2.89511e10i		−	0.993194i	0.867981	−	0.496597i	$-0.165417\pi$
$978$		0			0
$979$			4.21042e10i			1.43412i
$980$	4.16914e9	+	6.49802e9i	0.141500	+	0.220541i
$981$		0			0
$982$	−1.26489e8	+	3.70890e7i	−0.00426248	+	0.00124984i
$983$	−3.71869e10			−1.24868			−0.624341	−	0.781152i	$-0.714633\pi$
$983$	−3.71869e10			−1.24868			−0.624341	+	0.781152i	$0.714633\pi$
$984$		0			0
$985$	−7.68197e10			−2.56121
$986$	1.32269e10	−	3.87840e9i	0.439431	−	0.128850i
$987$		0			0
$988$	−2.52732e9	−	3.93907e9i	−0.0833701	−	0.129940i
$989$		−	2.63049e8i		−	0.00864670i
$990$		0			0
$991$			2.03370e10i			0.663788i	0.943317	+	0.331894i	$0.107688\pi$
$991$			2.03370e10i			0.663788i	−0.943317	+	0.331894i	$0.892312\pi$
$992$	−3.67384e10	−	5.35246e9i	−1.19489	−	0.174086i
$993$		0			0
$994$	1.66636e9	+	5.68299e9i	0.0538168	+	0.183538i
$995$	−3.98369e10			−1.28205
$996$		0			0
$997$	2.69713e10			0.861923			0.430961	−	0.902370i	$-0.358175\pi$
$997$	2.69713e10			0.861923			0.430961	+	0.902370i	$0.358175\pi$
$998$	1.94276e9	+	6.62562e9i	0.0618675	+	0.210994i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.8.e.a.71.8	yes	84
3.2	odd	2	inner	252.8.e.a.71.77	yes	84
4.3	odd	2	inner	252.8.e.a.71.78	yes	84
12.11	even	2	inner	252.8.e.a.71.7	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.8.e.a.71.7	✓	84	12.11	even	2	inner
252.8.e.a.71.8	yes	84	1.1	even	1	trivial
252.8.e.a.71.77	yes	84	3.2	odd	2	inner
252.8.e.a.71.78	yes	84	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.8566 + 3.18337i) q^{2} +(107.732 - 69.1213i) q^{4} -512.680i q^{5} -343.000i q^{7} +(-949.569 + 1093.38i) q^{8} +(1632.05 + 5565.97i) q^{10} +6950.61 q^{11} -968.015 q^{13} +(1091.90 + 3723.82i) q^{14} +(6828.49 - 14893.2i) q^{16} +6796.54i q^{17} +37771.6i q^{19} +(-35437.1 - 55232.2i) q^{20} +(-75460.1 + 22126.4i) q^{22} +2978.61 q^{23} -184716. q^{25} +(10509.4 - 3081.55i) q^{26} +(-23708.6 - 36952.2i) q^{28} +179257. i q^{29} +200289. i q^{31} +(-26723.7 + 183427. i) q^{32} +(-21635.9 - 73787.5i) q^{34} -175849. q^{35} -425727. q^{37} +(-120241. - 410072. i) q^{38} +(560552. + 486826. i) q^{40} +244050. i q^{41} -88312.9i q^{43} +(748805. - 480435. i) q^{44} +(-32337.6 + 9482.02i) q^{46} +453536. q^{47} -117649. q^{49} +(2.00539e6 - 588020. i) q^{50} +(-104287. + 66910.5i) q^{52} +1.57314e6i q^{53} -3.56344e6i q^{55} +(375028. + 325702. i) q^{56} +(-570643. - 1.94613e6i) q^{58} +77228.5 q^{59} -1.19278e6 q^{61} +(-637593. - 2.17446e6i) q^{62} +(-293788. - 2.07647e6i) q^{64} +496282. i q^{65} -1.71428e6i q^{67} +(469786. + 732207. i) q^{68} +(1.90913e6 - 559794. i) q^{70} +1.52612e6 q^{71} -5.69727e6 q^{73} +(4.62196e6 - 1.35525e6i) q^{74} +(2.61082e6 + 4.06922e6i) q^{76} -2.38406e6i q^{77} +8.63828e6i q^{79} +(-7.63545e6 - 3.50083e6i) q^{80} +(-776900. - 2.64955e6i) q^{82} +866901. q^{83} +3.48445e6 q^{85} +(281133. + 958779. i) q^{86} +(-6.60009e6 + 7.59963e6i) q^{88} +6.05763e6i q^{89} +332029. i q^{91} +(320892. - 205885. i) q^{92} +(-4.92387e6 + 1.44377e6i) q^{94} +1.93648e7 q^{95} +1.19866e7 q^{97} +(1.27727e6 - 374521. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 104 q^{4} - 5816 q^{10} + 16684 q^{16} - 201700 q^{22} - 1312500 q^{25} + 39788 q^{28} - 400048 q^{34} - 165544 q^{37} - 1477624 q^{40} + 1616724 q^{46} - 9882516 q^{49} - 3744592 q^{52} + 12053212 q^{58}+ \cdots + 73638456 q^{94}+O(q^{100}) \) 84 * q + 104 * q^4 - 5816 * q^10 + 16684 * q^16 - 201700 * q^22 - 1312500 * q^25 + 39788 * q^28 - 400048 * q^34 - 165544 * q^37 - 1477624 * q^40 + 1616724 * q^46 - 9882516 * q^49 - 3744592 * q^52 + 12053212 * q^58 - 8764504 * q^61 - 5645200 * q^64 + 8997576 * q^70 - 38069208 * q^76 + 24696392 * q^82 - 29977064 * q^85 - 48692036 * q^88 + 73638456 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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