LMFDB - Embedded newform 161.4.c.b.160.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(160,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("161.160");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} - 2516x^{5} + 43236x^{4} + 20128x^{3} - 55968x^{2} - 6463604x + 23372755 $ x^8 - 16x^6 - 2516x^5 + 43236x^4 + 20128x^3 - 55968x^2 - 6463604x + 23372755
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.1
Root			$-10.4466 + 12.7456i$ of defining polynomial
Character	$\chi$	$=$	161.160
Dual form			161.4.c.b.160.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -5.83095i q^{3} -7.00000 q^{4} -20.8933 q^{5} +5.83095i q^{6} +(-5.36058 - 17.7275i) q^{7} +15.0000 q^{8} -7.00000 q^{9} +20.8933 q^{10} -15.7947i q^{11} +40.8167i q^{12} +35.4193i q^{13} +(5.36058 + 17.7275i) q^{14} +121.828i q^{15} +41.0000 q^{16} +20.8933 q^{17} +7.00000 q^{18} -92.0980 q^{19} +146.253 q^{20} +(-103.368 + 31.2573i) q^{21} +15.7947i q^{22} +(79.2642 + 76.7085i) q^{23} -87.4643i q^{24} +311.528 q^{25} -35.4193i q^{26} -116.619i q^{27} +(37.5241 + 124.092i) q^{28} -150.528 q^{29} -121.828i q^{30} -172.133i q^{31} -161.000 q^{32} -92.0980 q^{33} -20.8933 q^{34} +(112.000 + 370.385i) q^{35} +49.0000 q^{36} +69.9138i q^{37} +92.0980 q^{38} +206.528 q^{39} -313.399 q^{40} +446.621i q^{41} +(103.368 - 31.2573i) q^{42} -83.5031i q^{43} +110.563i q^{44} +146.253 q^{45} +(-79.2642 - 76.7085i) q^{46} -8.86623i q^{47} -239.069i q^{48} +(-285.528 + 190.059i) q^{49} -311.528 q^{50} -121.828i q^{51} -247.935i q^{52} +588.814i q^{53} +116.619i q^{54} +330.002i q^{55} +(-80.4087 - 265.912i) q^{56} +537.019i q^{57} +150.528 q^{58} -522.424i q^{59} -852.793i q^{60} -170.990 q^{61} +172.133i q^{62} +(37.5241 + 124.092i) q^{63} -167.000 q^{64} -740.025i q^{65} +92.0980 q^{66} -895.647i q^{67} -146.253 q^{68} +(447.283 - 462.186i) q^{69} +(-112.000 - 370.385i) q^{70} +241.472 q^{71} -105.000 q^{72} +775.756i q^{73} -69.9138i q^{74} -1816.51i q^{75} +644.686 q^{76} +(-280.000 + 84.6686i) q^{77} -206.528 q^{78} +514.489i q^{79} -856.624 q^{80} -869.000 q^{81} -446.621i q^{82} -209.771 q^{83} +(723.577 - 218.801i) q^{84} -436.528 q^{85} +83.5031i q^{86} +877.724i q^{87} -236.920i q^{88} +1216.49 q^{89} -146.253 q^{90} +(627.896 - 189.868i) q^{91} +(-554.849 - 536.959i) q^{92} -1003.70 q^{93} +8.86623i q^{94} +1924.23 q^{95} +938.783i q^{96} -379.084 q^{97} +(285.528 - 190.059i) q^{98} +110.563i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 56 q^{4} + 120 q^{8} - 56 q^{9} + 328 q^{16} + 56 q^{18} - 124 q^{23} + 976 q^{25} + 312 q^{29} - 1288 q^{32} + 896 q^{35} + 392 q^{36} + 136 q^{39} + 124 q^{46} - 768 q^{49} - 976 q^{50}+ \cdots + 768 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 56 * q^4 + 120 * q^8 - 56 * q^9 + 328 * q^16 + 56 * q^18 - 124 * q^23 + 976 * q^25 + 312 * q^29 - 1288 * q^32 + 896 * q^35 + 392 * q^36 + 136 * q^39 + 124 * q^46 - 768 * q^49 - 976 * q^50 - 312 * q^58 - 1336 * q^64 - 896 * q^70 + 3448 * q^71 - 840 * q^72 - 2240 * q^77 - 136 * q^78 - 6952 * q^81 - 1976 * q^85 + 868 * q^92 + 2584 * q^93 + 3264 * q^95 + 768 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.353553			−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000			−0.353553			−0.176777	+	0.984251i	$0.556567\pi$
$3$		−	5.83095i		−	1.12217i	−0.827759	−	0.561084i	$-0.810385\pi$
$3$		−	5.83095i		−	1.12217i	0.827759	−	0.561084i	$-0.189615\pi$
$4$	−7.00000			−0.875000
$5$	−20.8933			−1.86875			−0.934375	−	0.356291i	$-0.884041\pi$
$5$	−20.8933			−1.86875			−0.934375	+	0.356291i	$0.884041\pi$
$6$			5.83095i			0.396746i
$7$	−5.36058	−	17.7275i	−0.289444	−	0.957195i
$7$	−5.36058	−	17.7275i	−0.289444	−	0.957195i
$8$	15.0000			0.662913
$9$	−7.00000			−0.259259
$10$	20.8933			0.660703
$11$		−	15.7947i		−	0.432934i	−0.976290	−	0.216467i	$-0.930547\pi$
$11$		−	15.7947i		−	0.432934i	0.976290	−	0.216467i	$-0.0694534\pi$
$12$			40.8167i			0.981896i
$13$			35.4193i			0.755658i	0.925875	+	0.377829i	$0.123329\pi$
$13$			35.4193i			0.755658i	−0.925875	+	0.377829i	$0.876671\pi$
$14$	5.36058	+	17.7275i	0.102334	+	0.338420i
$15$			121.828i			2.09705i
$16$	41.0000			0.640625
$17$	20.8933			0.298080			0.149040	−	0.988831i	$-0.452382\pi$
$17$	20.8933			0.298080			0.149040	+	0.988831i	$0.452382\pi$
$18$	7.00000			0.0916620
$19$	−92.0980			−1.11204			−0.556019	−	0.831170i	$-0.687672\pi$
$19$	−92.0980			−1.11204			−0.556019	+	0.831170i	$0.687672\pi$
$20$	146.253			1.63516
$21$	−103.368	+	31.2573i	−1.07413	+	0.324805i
$22$			15.7947i			0.153065i
$23$	79.2642	+	76.7085i	0.718597	+	0.695427i
$23$	79.2642	+	76.7085i	0.718597	+	0.695427i
$24$		−	87.4643i		−	0.743899i
$25$	311.528			2.49223
$26$		−	35.4193i		−	0.267165i
$27$		−	116.619i		−	0.831235i
$28$	37.5241	+	124.092i	0.253264	+	0.837546i
$29$	−150.528			−0.963876			−0.481938	−	0.876205i	$-0.660067\pi$
$29$	−150.528			−0.963876			−0.481938	+	0.876205i	$0.660067\pi$
$30$		−	121.828i		−	0.741419i
$31$		−	172.133i		−	0.997290i	−0.866806	−	0.498645i	$-0.833831\pi$
$31$		−	172.133i		−	0.997290i	0.866806	−	0.498645i	$-0.166169\pi$
$32$	−161.000			−0.889408
$33$	−92.0980			−0.485824
$34$	−20.8933			−0.105387
$35$	112.000	+	370.385i	0.540899	+	1.78876i
$36$	49.0000			0.226852
$37$			69.9138i			0.310642i	0.987864	+	0.155321i	$0.0496412\pi$
$37$			69.9138i			0.310642i	−0.987864	+	0.155321i	$0.950359\pi$
$38$	92.0980			0.393165
$39$	206.528			0.847974
$40$	−313.399			−1.23882
$41$			446.621i			1.70123i	0.525787	+	0.850616i	$0.323771\pi$
$41$			446.621i			1.70123i	−0.525787	+	0.850616i	$0.676229\pi$
$42$	103.368	−	31.2573i	0.379763	−	0.114836i
$43$		−	83.5031i		−	0.296142i	−0.988977	−	0.148071i	$-0.952694\pi$
$43$		−	83.5031i		−	0.296142i	0.988977	−	0.148071i	$-0.0473064\pi$
$44$			110.563i			0.378817i
$45$	146.253			0.484491
$46$	−79.2642	−	76.7085i	−0.254062	−	0.245871i
$47$		−	8.86623i		−	0.0275164i	−0.999905	−	0.0137582i	$-0.995620\pi$
$47$		−	8.86623i		−	0.0275164i	0.999905	−	0.0137582i	$-0.00437951\pi$
$48$		−	239.069i		−	0.718888i
$49$	−285.528	+	190.059i	−0.832444	+	0.554109i
$50$	−311.528			−0.881135
$51$		−	121.828i		−	0.334496i
$52$		−	247.935i		−	0.661201i
$53$			588.814i			1.52603i	0.646379	+	0.763017i	$0.276283\pi$
$53$			588.814i			1.52603i	−0.646379	+	0.763017i	$0.723717\pi$
$54$			116.619i			0.293886i
$55$			330.002i			0.809045i
$56$	−80.4087	−	265.912i	−0.191876	−	0.634537i
$57$			537.019i			1.24789i
$58$	150.528			0.340782
$59$		−	522.424i		−	1.15278i	−0.817176	−	0.576388i	$-0.804462\pi$
$59$		−	522.424i		−	1.15278i	0.817176	−	0.576388i	$-0.195538\pi$
$60$		−	852.793i		−	1.83492i
$61$	−170.990			−0.358901			−0.179451	−	0.983767i	$-0.557432\pi$
$61$	−170.990			−0.358901			−0.179451	+	0.983767i	$0.557432\pi$
$62$			172.133i			0.352595i
$63$	37.5241	+	124.092i	0.0750411	+	0.248162i
$64$	−167.000			−0.326172
$65$		−	740.025i		−	1.41214i
$66$	92.0980			0.171765
$67$		−	895.647i		−	1.63315i	−0.577243	−	0.816573i	$-0.695871\pi$
$67$		−	895.647i		−	1.63315i	0.577243	−	0.816573i	$-0.304129\pi$
$68$	−146.253			−0.260820
$69$	447.283	−	462.186i	0.780385	−	0.806386i
$70$	−112.000	−	370.385i	−0.191237	−	0.632421i
$71$	241.472			0.403626			0.201813	−	0.979424i	$-0.435317\pi$
$71$	241.472			0.403626			0.201813	+	0.979424i	$0.435317\pi$
$72$	−105.000			−0.171866
$73$			775.756i			1.24377i	0.783108	+	0.621886i	$0.213633\pi$
$73$			775.756i			1.24377i	−0.783108	+	0.621886i	$0.786367\pi$
$74$		−	69.9138i		−	0.109829i
$75$		−	1816.51i		−	2.79670i
$76$	644.686			0.973033
$77$	−280.000	+	84.6686i	−0.414402	+	0.125310i
$78$	−206.528			−0.299804
$79$			514.489i			0.732716i	0.930474	+	0.366358i	$0.119395\pi$
$79$			514.489i			0.732716i	−0.930474	+	0.366358i	$0.880605\pi$
$80$	−856.624			−1.19717
$81$	−869.000			−1.19204
$82$		−	446.621i		−	0.601476i
$83$	−209.771			−0.277414			−0.138707	−	0.990333i	$-0.544295\pi$
$83$	−209.771			−0.277414			−0.138707	+	0.990333i	$0.544295\pi$
$84$	723.577	−	218.801i	0.939866	−	0.284204i
$85$	−436.528			−0.557037
$86$			83.5031i			0.104702i
$87$			877.724i			1.08163i
$88$		−	236.920i		−	0.286997i
$89$	1216.49			1.44885			0.724426	−	0.689353i	$-0.242105\pi$
$89$	1216.49			1.44885			0.724426	+	0.689353i	$0.242105\pi$
$90$	−146.253			−0.171293
$91$	627.896	−	189.868i	0.723312	−	0.218721i
$92$	−554.849	−	536.959i	−0.628772	−	0.608499i
$93$	−1003.70			−1.11913
$94$			8.86623i			0.00972852i
$95$	1924.23			2.07812
$96$			938.783i			0.998064i
$97$	−379.084			−0.396806			−0.198403	−	0.980121i	$-0.563575\pi$
$97$	−379.084			−0.396806			−0.198403	+	0.980121i	$0.563575\pi$
$98$	285.528	−	190.059i	0.294313	−	0.195907i
$99$			110.563i			0.112242i
$100$	−2180.70			−2.18070
$101$			1154.09i			1.13700i	0.822684	+	0.568499i	$0.192476\pi$
$101$			1154.09i			1.13700i	−0.822684	+	0.568499i	$0.807524\pi$
$102$			121.828i			0.118262i
$103$	−677.109			−0.647743			−0.323872	−	0.946101i	$-0.604985\pi$
$103$	−677.109			−0.647743			−0.323872	+	0.946101i	$0.604985\pi$
$104$			531.290i			0.500935i
$105$	2159.70	−	653.067i	2.00729	−	0.606979i
$106$		−	588.814i		−	0.539534i
$107$			1802.56i			1.62860i	0.580445	+	0.814299i	$0.302878\pi$
$107$			1802.56i			1.62860i	−0.580445	+	0.814299i	$0.697122\pi$
$108$			816.333i			0.727331i
$109$		−	291.039i		−	0.255748i	−0.991790	−	0.127874i	$-0.959185\pi$
$109$		−	291.039i		−	0.255748i	0.991790	−	0.127874i	$-0.0408153\pi$
$110$		−	330.002i		−	0.286041i
$111$	407.664			0.348592
$112$	−219.784	−	726.827i	−0.185425	−	0.613203i
$113$			1096.33i			0.912690i	0.889803	+	0.456345i	$0.150842\pi$
$113$			1096.33i			0.912690i	−0.889803	+	0.456345i	$0.849158\pi$
$114$		−	537.019i		−	0.441197i
$115$	−1656.09	−	1602.69i	−1.34288	−	1.29958i
$116$	1053.70			0.843392
$117$		−	247.935i		−	0.195911i
$118$			522.424i			0.407568i
$119$	−112.000	−	370.385i	−0.0862775	−	0.285321i
$120$			1827.41i			1.39016i
$121$	1081.53			0.812568
$122$	170.990			0.126891
$123$	2604.23			1.90907
$124$			1204.93i			0.872628i
$125$	−3897.19			−2.78860
$126$	−37.5241	−	124.092i	−0.0265310	−	0.0877384i
$127$	−1820.23			−1.27180			−0.635902	−	0.771770i	$-0.719372\pi$
$127$	−1820.23			−1.27180			−0.635902	+	0.771770i	$0.719372\pi$
$128$	1455.00			1.00473
$129$	−486.903			−0.332321
$130$			740.025i			0.499265i
$131$			420.547i			0.280484i	0.990117	+	0.140242i	$0.0447880\pi$
$131$			420.547i			0.280484i	−0.990117	+	0.140242i	$0.955212\pi$
$132$	644.686			0.425096
$133$	493.699	+	1632.67i	0.321873	+	1.06444i
$134$			895.647i			0.577404i
$135$			2436.55i			1.55337i
$136$	313.399			0.197601
$137$		−	2332.96i		−	1.45488i	−0.686172	−	0.727440i	$-0.740710\pi$
$137$		−	2332.96i		−	1.45488i	0.686172	−	0.727440i	$-0.259290\pi$
$138$	−447.283	+	462.186i	−0.275908	+	0.285100i
$139$		−	1822.58i		−	1.11215i	−0.831132	−	0.556076i	$-0.812307\pi$
$139$		−	1822.58i		−	1.11215i	0.831132	−	0.556076i	$-0.187693\pi$
$140$	−784.000	−	2592.70i	−0.473286	−	1.56516i
$141$	−51.6985			−0.0308780
$142$	−241.472			−0.142703
$143$	559.437			0.327150
$144$	−287.000			−0.166088
$145$	3145.03			1.80124
$146$		−	775.756i		−	0.439740i
$147$	1108.23	+	1664.90i	0.621803	+	0.934142i
$148$		−	489.397i		−	0.271812i
$149$			625.052i			0.343666i	0.985126	+	0.171833i	$0.0549689\pi$
$149$			625.052i			0.343666i	−0.985126	+	0.171833i	$0.945031\pi$
$150$			1816.51i			0.988781i
$151$	−2461.70			−1.32669			−0.663345	−	0.748314i	$-0.730864\pi$
$151$	−2461.70			−1.32669			−0.663345	+	0.748314i	$0.730864\pi$
$152$	−1381.47			−0.737184
$153$	−146.253			−0.0772800
$154$	280.000	−	84.6686i	0.146513	−	0.0443038i
$155$			3596.42i			1.86369i
$156$	−1445.70			−0.741978
$157$	1444.99			0.734539			0.367269	−	0.930115i	$-0.380293\pi$
$157$	1444.99			0.734539			0.367269	+	0.930115i	$0.380293\pi$
$158$		−	514.489i		−	0.259054i
$159$	3433.34			1.71246
$160$	3363.82			1.66208
$161$	934.947	−	1816.36i	0.457666	−	0.889124i
$162$	869.000			0.421451
$163$	468.000			0.224887			0.112444	−	0.993658i	$-0.464132\pi$
$163$	468.000			0.224887			0.112444	+	0.993658i	$0.464132\pi$
$164$		−	3126.35i		−	1.48858i
$165$	1924.23			0.907884
$166$	209.771			0.0980805
$167$			1273.94i			0.590303i	0.955450	+	0.295152i	$0.0953702\pi$
$167$			1273.94i			0.590303i	−0.955450	+	0.295152i	$0.904630\pi$
$168$	−1550.52	+	468.859i	−0.712056	+	0.215317i
$169$	942.472			0.428981
$170$	436.528			0.196942
$171$	644.686			0.288306
$172$			584.522i			0.259124i
$173$			3137.58i			1.37888i	0.724345	+	0.689438i	$0.242142\pi$
$173$			3137.58i			1.37888i	−0.724345	+	0.689438i	$0.757858\pi$
$174$		−	877.724i		−	0.382414i
$175$	−1669.97	−	5522.62i	−0.721360	−	2.38555i
$176$		−	647.582i		−	0.277348i
$177$	−3046.23			−1.29361
$178$	−1216.49			−0.512246
$179$	860.000			0.359103			0.179551	−	0.983749i	$-0.442535\pi$
$179$	860.000			0.359103			0.179551	+	0.983749i	$0.442535\pi$
$180$	−1023.77			−0.423929
$181$	257.915			0.105915			0.0529576	−	0.998597i	$-0.483135\pi$
$181$	257.915			0.105915			0.0529576	+	0.998597i	$0.483135\pi$
$182$	−627.896	+	189.868i	−0.255729	+	0.0773295i
$183$			997.032i			0.402747i
$184$	1188.96	+	1150.63i	0.476367	+	0.461007i
$185$		−	1460.73i		−	0.580513i
$186$	1003.70			0.395671
$187$		−	330.002i		−	0.129049i
$188$			62.0636i			0.0240769i
$189$	−2067.36	+	625.146i	−0.795654	+	0.240596i
$190$	−1924.23			−0.734727
$191$			3948.07i			1.49567i	0.663886	+	0.747834i	$0.268906\pi$
$191$			3948.07i			1.49567i	−0.663886	+	0.747834i	$0.731094\pi$
$192$			973.769i			0.366019i
$193$	−4015.70			−1.49770			−0.748851	−	0.662739i	$-0.769394\pi$
$193$	−4015.70			−1.49770			−0.748851	+	0.662739i	$0.769394\pi$
$194$	379.084			0.140292
$195$	−4315.05			−1.58465
$196$	1998.70	−	1330.42i	0.728389	−	0.484845i
$197$	−2870.23			−1.03805			−0.519023	−	0.854760i	$-0.673704\pi$
$197$	−2870.23			−1.03805			−0.519023	+	0.854760i	$0.673704\pi$
$198$		−	110.563i		−	0.0396836i
$199$	4066.01			1.44840			0.724200	−	0.689590i	$-0.242209\pi$
$199$	4066.01			1.44840			0.724200	+	0.689590i	$0.242209\pi$
$200$	4672.93			1.65213
$201$	−5222.48			−1.83266
$202$		−	1154.09i		−	0.401989i
$203$	806.919	+	2668.49i	0.278988	+	0.922618i
$204$			852.793i			0.292684i
$205$		−	9331.37i		−	3.17918i
$206$	677.109			0.229012
$207$	−554.849	−	536.959i	−0.186303	−	0.180296i
$208$			1452.19i			0.484093i
$209$			1454.66i			0.481439i
$210$	−2159.70	+	653.067i	−0.709683	+	0.214599i
$211$	−4695.40			−1.53196			−0.765982	−	0.642862i	$-0.777747\pi$
$211$	−4695.40			−1.53196			−0.765982	+	0.642862i	$0.777747\pi$
$212$		−	4121.69i		−	1.33528i
$213$		−	1408.01i		−	0.452935i
$214$		−	1802.56i		−	0.575797i
$215$			1744.65i			0.553415i
$216$		−	1749.29i		−	0.551036i
$217$	−3051.49	+	922.732i	−0.954601	+	0.288660i
$218$			291.039i			0.0904205i
$219$	4523.40			1.39572
$220$		−	2310.02i		−	0.707915i
$221$			740.025i			0.225247i
$222$	−407.664			−0.123246
$223$		−	301.372i		−	0.0904994i	−0.998976	−	0.0452497i	$-0.985592\pi$
$223$		−	301.372i		−	0.0904994i	0.998976	−	0.0452497i	$-0.0144084\pi$
$224$	863.053	+	2854.13i	0.257434	+	0.851337i
$225$	−2180.70			−0.646133
$226$		−	1096.33i		−	0.322685i
$227$	5207.10			1.52250			0.761250	−	0.648458i	$-0.224586\pi$
$227$	5207.10			1.52250			0.761250	+	0.648458i	$0.224586\pi$
$228$		−	3759.13i		−	1.09191i
$229$	−448.122			−0.129313			−0.0646566	−	0.997908i	$-0.520595\pi$
$229$	−448.122			−0.129313			−0.0646566	+	0.997908i	$0.520595\pi$
$230$	1656.09	+	1602.69i	0.474779	+	0.459471i
$231$	493.699	+	1632.67i	0.140619	+	0.465028i
$232$	−2257.93			−0.638966
$233$	−4785.70			−1.34559			−0.672793	−	0.739831i	$-0.734906\pi$
$233$	−4785.70			−1.34559			−0.672793	+	0.739831i	$0.734906\pi$
$234$			247.935i			0.0692651i
$235$			185.244i			0.0514213i
$236$			3656.97i			1.00868i
$237$	2999.96			0.822229
$238$	112.000	+	370.385i	0.0305037	+	0.100876i
$239$	822.075			0.222492			0.111246	−	0.993793i	$-0.464516\pi$
$239$	822.075			0.222492			0.111246	+	0.993793i	$0.464516\pi$
$240$			4994.93i			1.34342i
$241$	80.5677			0.0215345			0.0107673	−	0.999942i	$-0.496573\pi$
$241$	80.5677			0.0215345			0.0107673	+	0.999942i	$0.496573\pi$
$242$	−1081.53			−0.287286
$243$			1918.38i			0.506438i
$244$	1196.93			0.314038
$245$	5965.62	−	3970.96i	1.55563	−	1.03549i
$246$	−2604.23			−0.674957
$247$		−	3262.05i		−	0.840320i
$248$		−	2581.99i		−	0.661116i
$249$			1223.16i			0.311304i
$250$	3897.19			0.985919
$251$	−2638.42			−0.663488			−0.331744	−	0.943369i	$-0.607637\pi$
$251$	−2638.42			−0.663488			−0.331744	+	0.943369i	$0.607637\pi$
$252$	−262.668	−	868.647i	−0.0656609	−	0.217141i
$253$	1211.59	−	1251.95i	0.301074	−	0.311105i
$254$	1820.23			0.449650
$255$			2545.38i			0.625089i
$256$	−119.000			−0.0290527
$257$		−	5325.82i		−	1.29267i	−0.763055	−	0.646333i	$-0.776302\pi$
$257$		−	5325.82i		−	1.29267i	0.763055	−	0.646333i	$-0.223698\pi$
$258$	486.903			0.117493
$259$	1239.40	−	374.779i	0.297345	−	0.0899136i
$260$			5180.18i			1.23562i
$261$	1053.70			0.249894
$262$		−	420.547i		−	0.0991660i
$263$		−	284.066i		−	0.0666017i	−0.999445	−	0.0333009i	$-0.989398\pi$
$263$		−	284.066i		−	0.0666017i	0.999445	−	0.0333009i	$-0.0106020\pi$
$264$	−1381.47			−0.322059
$265$		−	12302.2i		−	2.85177i
$266$	−493.699	−	1632.67i	−0.113799	−	0.376335i
$267$		−	7093.30i		−	1.62585i
$268$			6269.53i			1.42900i
$269$			1840.02i			0.417057i	0.978016	+	0.208528i	$0.0668674\pi$
$269$			1840.02i			0.417057i	−0.978016	+	0.208528i	$0.933133\pi$
$270$		−	2436.55i		−	0.549199i
$271$		−	1737.82i		−	0.389538i	−0.980849	−	0.194769i	$-0.937604\pi$
$271$		−	1737.82i		−	0.389538i	0.980849	−	0.194769i	$-0.0623958\pi$
$272$	856.624			0.190958
$273$	−1107.11	−	3661.23i	−0.245441	−	0.811677i
$274$			2332.96i			0.514377i
$275$		−	4920.49i		−	1.07897i
$276$	−3130.98	+	3235.30i	−0.682837	+	0.705587i
$277$	−949.699			−0.205999			−0.103000	−	0.994681i	$-0.532844\pi$
$277$	−949.699			−0.205999			−0.103000	+	0.994681i	$0.532844\pi$
$278$			1822.58i			0.393205i
$279$			1204.93i			0.258557i
$280$	1680.00	+	5555.78i	0.358569	+	1.18579i
$281$			4521.45i			0.959883i	0.877301	+	0.479941i	$0.159342\pi$
$281$			4521.45i			0.959883i	−0.877301	+	0.479941i	$0.840658\pi$
$282$	51.6985			0.0109170
$283$	−7228.23			−1.51828			−0.759141	−	0.650926i	$-0.774381\pi$
$283$	−7228.23			−1.51828			−0.759141	+	0.650926i	$0.774381\pi$
$284$	−1690.30			−0.353172
$285$		−	11220.1i		−	2.33200i
$286$	−559.437			−0.115665
$287$	7917.48	−	2394.15i	1.62841	−	0.492412i
$288$	1127.00			0.230587
$289$	−4476.47			−0.911148
$290$	−3145.03			−0.636836
$291$			2210.42i			0.445282i
$292$		−	5430.29i		−	1.08830i
$293$	−4549.21			−0.907057			−0.453529	−	0.891242i	$-0.649835\pi$
$293$	−4549.21			−0.907057			−0.453529	+	0.891242i	$0.649835\pi$
$294$	−1108.23	−	1664.90i	−0.219840	−	0.330269i
$295$			10915.1i			2.15425i
$296$			1048.71i			0.205929i
$297$	−1841.96			−0.359870
$298$		−	625.052i		−	0.121504i
$299$	−2716.96	+	2807.48i	−0.525505	+	0.543013i
$300$			12715.5i			2.44711i
$301$	−1480.30	+	447.625i	−0.283466	+	0.0857166i
$302$	2461.70			0.469056
$303$	6729.47			1.27590
$304$	−3776.02			−0.712399
$305$	3572.53			0.670696
$306$	146.253			0.0273226
$307$		−	612.729i		−	0.113910i	−0.998377	−	0.0569549i	$-0.981861\pi$
$307$		−	612.729i		−	0.113910i	0.998377	−	0.0569549i	$-0.0181391\pi$
$308$	1960.00	−	592.680i	0.362602	−	0.109646i
$309$			3948.19i			0.726876i
$310$		−	3596.42i		−	0.658912i
$311$			375.018i			0.0683773i	0.999415	+	0.0341886i	$0.0108847\pi$
$311$			375.018i			0.0683773i	−0.999415	+	0.0341886i	$0.989115\pi$
$312$	3097.93			0.562133
$313$	3421.81			0.617931			0.308965	−	0.951073i	$-0.400017\pi$
$313$	3421.81			0.617931			0.308965	+	0.951073i	$0.400017\pi$
$314$	−1444.99			−0.259699
$315$	−784.000	−	2592.70i	−0.140233	−	0.463752i
$316$		−	3601.42i		−	0.641126i
$317$	5681.93			1.00672			0.503358	−	0.864078i	$-0.332098\pi$
$317$	5681.93			1.00672			0.503358	+	0.864078i	$0.332098\pi$
$318$	−3433.34			−0.605448
$319$			2377.55i			0.417295i
$320$	3489.17			0.609534
$321$	10510.6			1.82756
$322$	−934.947	+	1816.36i	−0.161809	+	0.314353i
$323$	−1924.23			−0.331476
$324$	6083.00			1.04304
$325$			11034.1i			1.88327i
$326$	−468.000			−0.0795096
$327$	−1697.04			−0.286992
$328$			6699.32i			1.12777i
$329$	−157.176	+	47.5281i	−0.0263386	+	0.00796447i
$330$	−1924.23			−0.320985
$331$	1399.40			0.232380			0.116190	−	0.993227i	$-0.462932\pi$
$331$	1399.40			0.232380			0.116190	+	0.993227i	$0.462932\pi$
$332$	1468.39			0.242737
$333$		−	489.397i		−	0.0805369i
$334$		−	1273.94i		−	0.208704i
$335$			18713.0i			3.05194i
$336$	−4238.10	+	1281.55i	−0.688116	+	0.208078i
$337$		−	6483.68i		−	1.04804i	−0.851707	−	0.524019i	$-0.824432\pi$
$337$		−	6483.68i		−	1.04804i	0.851707	−	0.524019i	$-0.175568\pi$
$338$	−942.472			−0.151668
$339$	6392.64			1.02419
$340$	3055.70			0.487407
$341$	−2718.78			−0.431760
$342$	−644.686			−0.101932
$343$	4899.87	+	4042.88i	0.771336	+	0.636428i
$344$		−	1252.55i		−	0.196316i
$345$	−9345.21	+	9656.56i	−1.45835	+	1.50693i
$346$		−	3137.58i		−	0.487506i
$347$	−12474.0			−1.92979			−0.964896	−	0.262634i	$-0.915409\pi$
$347$	−12474.0			−1.92979			−0.964896	+	0.262634i	$0.915409\pi$
$348$		−	6144.07i		−	0.946427i
$349$		−	3405.32i		−	0.522300i	−0.965298	−	0.261150i	$-0.915898\pi$
$349$		−	3405.32i		−	0.522300i	0.965298	−	0.261150i	$-0.0841017\pi$
$350$	1669.97	+	5522.62i	0.255039	+	0.843418i
$351$	4130.57			0.628129
$352$			2542.94i			0.385055i
$353$		−	4908.22i		−	0.740052i	−0.929021	−	0.370026i	$-0.879349\pi$
$353$		−	4908.22i		−	0.740052i	0.929021	−	0.370026i	$-0.120651\pi$
$354$	3046.23			0.457359
$355$	−5045.13			−0.754275
$356$	−8515.43			−1.26774
$357$	−2159.70	+	653.067i	−0.320178	+	0.0968178i
$358$	−860.000			−0.126962
$359$			369.060i			0.0542570i	0.999632	+	0.0271285i	$0.00863633\pi$
$359$			369.060i			0.0542570i	−0.999632	+	0.0271285i	$0.991364\pi$
$360$	2193.79			0.321175
$361$	1623.04			0.236629
$362$	−257.915			−0.0374467
$363$		−	6306.34i		−	0.911837i
$364$	−4395.27	+	1329.08i	−0.632898	+	0.191381i
$365$		−	16208.1i		−	2.32430i
$366$		−	997.032i		−	0.142393i
$367$	−10842.3			−1.54213			−0.771065	−	0.636756i	$-0.780276\pi$
$367$	−10842.3			−1.54213			−0.771065	+	0.636756i	$0.780276\pi$
$368$	3249.83	+	3145.05i	0.460351	+	0.445508i
$369$		−	3126.35i		−	0.441060i
$370$			1460.73i			0.205242i
$371$	10438.2	−	3156.38i	1.46071	−	0.441701i
$372$	7025.89			0.979235
$373$		−	5670.05i		−	0.787088i	−0.919306	−	0.393544i	$-0.871249\pi$
$373$		−	5670.05i		−	0.787088i	0.919306	−	0.393544i	$-0.128751\pi$
$374$			330.002i			0.0456257i
$375$			22724.3i			3.12927i
$376$		−	132.993i		−	0.0182410i
$377$		−	5331.61i		−	0.728361i
$378$	2067.36	−	625.146i	0.281306	−	0.0850636i
$379$			1089.36i			0.147642i	0.997271	+	0.0738212i	$0.0235194\pi$
$379$			1089.36i			0.147642i	−0.997271	+	0.0738212i	$0.976481\pi$
$380$	−13469.6			−1.81836
$381$			10613.7i			1.42718i
$382$		−	3948.07i		−	0.528798i
$383$	−1620.17			−0.216153			−0.108077	−	0.994143i	$-0.534469\pi$
$383$	−1620.17			−0.216153			−0.108077	+	0.994143i	$0.534469\pi$
$384$		−	8484.04i		−	1.12747i
$385$	5850.11	−	1769.00i	0.774414	−	0.234173i
$386$	4015.70			0.529517
$387$			584.522i			0.0767776i
$388$	2653.59			0.347205
$389$		−	9875.13i		−	1.28712i	−0.765397	−	0.643559i	$-0.777457\pi$
$389$		−	9875.13i		−	1.28712i	0.765397	−	0.643559i	$-0.222543\pi$
$390$	4315.05			0.560259
$391$	1656.09	+	1602.69i	0.214199	+	0.207293i
$392$	−4282.93	+	2850.89i	−0.551838	+	0.367326i
$393$	2452.19			0.314750
$394$	2870.23			0.367005
$395$		−	10749.4i		−	1.36926i
$396$		−	773.939i		−	0.0982118i
$397$			6695.53i			0.846446i	0.906026	+	0.423223i	$0.139101\pi$
$397$			6695.53i			0.846446i	−0.906026	+	0.423223i	$0.860899\pi$
$398$	−4066.01			−0.512087
$399$	9520.00	−	2878.73i	1.19448	−	0.361195i
$400$	12772.7			1.59658
$401$			10839.3i			1.34985i	0.737887	+	0.674925i	$0.235824\pi$
$401$			10839.3i			1.34985i	−0.737887	+	0.674925i	$0.764176\pi$
$402$	5222.48			0.647944
$403$	6096.83			0.753610
$404$		−	8078.66i		−	0.994873i
$405$	18156.2			2.22763
$406$	−806.919	−	2668.49i	−0.0986373	−	0.326195i
$407$	1104.27			0.134488
$408$		−	1827.41i		−	0.221741i
$409$			5976.01i			0.722480i	0.932473	+	0.361240i	$0.117647\pi$
$409$			5976.01i			0.722480i	−0.932473	+	0.361240i	$0.882353\pi$
$410$			9331.37i			1.12401i
$411$	−13603.4			−1.63262
$412$	4739.76			0.566775
$413$	−9261.26	+	2800.49i	−1.10343	+	0.333664i
$414$	554.849	+	536.959i	0.0658680	+	0.0637442i
$415$	4382.79			0.518417
$416$		−	5702.51i		−	0.672088i
$417$	−10627.4			−1.24802
$418$		−	1454.66i		−	0.170214i
$419$	−7995.76			−0.932264			−0.466132	−	0.884715i	$-0.654353\pi$
$419$	−7995.76			−0.932264			−0.466132	+	0.884715i	$0.654353\pi$
$420$	−15117.9	+	4571.47i	−1.75637	+	0.531106i
$421$			7113.86i			0.823535i	0.911289	+	0.411768i	$0.135088\pi$
$421$			7113.86i			0.823535i	−0.911289	+	0.411768i	$0.864912\pi$
$422$	4695.40			0.541631
$423$			62.0636i			0.00713389i
$424$			8832.20i			1.01163i
$425$	6508.84			0.742883
$426$			1408.01i			0.160137i
$427$	916.603	+	3031.22i	0.103882	+	0.343538i
$428$		−	12617.9i		−	1.42502i
$429$		−	3262.05i		−	0.367117i
$430$		−	1744.65i		−	0.195662i
$431$		−	4192.44i		−	0.468545i	−0.972171	−	0.234272i	$-0.924729\pi$
$431$		−	4192.44i		−	0.468545i	0.972171	−	0.234272i	$-0.0752708\pi$
$432$		−	4781.38i		−	0.532510i
$433$	14887.2			1.65228			0.826138	−	0.563468i	$-0.190533\pi$
$433$	14887.2			1.65228			0.826138	+	0.563468i	$0.190533\pi$
$434$	3051.49	−	922.732i	0.337502	−	0.102057i
$435$		−	18338.5i		−	2.02130i
$436$			2037.27i			0.223779i
$437$	−7300.07	−	7064.69i	−0.799107	−	0.773341i
$438$	−4523.40			−0.493462
$439$			14132.5i			1.53647i	0.640169	+	0.768234i	$0.278864\pi$
$439$			14132.5i			1.53647i	−0.640169	+	0.768234i	$0.721136\pi$
$440$			4950.03i			0.536326i
$441$	1998.70	−	1330.42i	0.215819	−	0.143658i
$442$		−	740.025i		−	0.0796367i
$443$	−8654.19			−0.928156			−0.464078	−	0.885794i	$-0.653614\pi$
$443$	−8654.19			−0.928156			−0.464078	+	0.885794i	$0.653614\pi$
$444$	−2853.65			−0.305018
$445$	−25416.5			−2.70754
$446$			301.372i			0.0319964i
$447$	3644.65			0.385651
$448$	895.217	+	2960.49i	0.0944085	+	0.312210i
$449$	8249.59			0.867087			0.433544	−	0.901133i	$-0.357263\pi$
$449$	8249.59			0.867087			0.433544	+	0.901133i	$0.357263\pi$
$450$	2180.70			0.228442
$451$	7054.24			0.736521
$452$		−	7674.31i		−	0.798604i
$453$			14354.0i			1.48877i
$454$	−5207.10			−0.538285
$455$	−13118.8	+	3966.96i	−1.35169	+	0.408734i
$456$			8055.28i			0.827244i
$457$		−	10215.4i		−	1.04564i	−0.852444	−	0.522819i	$-0.824880\pi$
$457$		−	10215.4i		−	1.04564i	0.852444	−	0.522819i	$-0.175120\pi$
$458$	448.122			0.0457191
$459$		−	2436.55i		−	0.247775i
$460$	11592.6	+	11218.8i	1.17502	+	1.13713i
$461$		−	14852.8i		−	1.50058i	−0.661111	−	0.750288i	$-0.729915\pi$
$461$		−	14852.8i		−	1.50058i	0.661111	−	0.750288i	$-0.270085\pi$
$462$	−493.699	−	1632.67i	−0.0497163	−	0.164412i
$463$	4969.10			0.498776			0.249388	−	0.968404i	$-0.419770\pi$
$463$	4969.10			0.498776			0.249388	+	0.968404i	$0.419770\pi$
$464$	−6171.66			−0.617483
$465$	20970.5			2.09137
$466$	4785.70			0.475736
$467$	−6965.78			−0.690231			−0.345115	−	0.938560i	$-0.612160\pi$
$467$	−6965.78			−0.690231			−0.345115	+	0.938560i	$0.612160\pi$
$468$			1735.55i			0.171422i
$469$	−15877.6	+	4801.19i	−1.56324	+	0.472704i
$470$		−	185.244i		−	0.0181802i
$471$		−	8425.65i		−	0.824275i
$472$		−	7836.35i		−	0.764189i
$473$	−1318.90			−0.128210
$474$	−2999.96			−0.290702
$475$	−28691.1			−2.77145
$476$	784.000	+	2592.70i	0.0754928	+	0.249656i
$477$		−	4121.69i		−	0.395638i
$478$	−822.075			−0.0786628
$479$	−9568.28			−0.912705			−0.456352	−	0.889799i	$-0.650844\pi$
$479$	−9568.28			−0.912705			−0.456352	+	0.889799i	$0.650844\pi$
$480$		−	19614.2i		−	1.86513i
$481$	−2476.30			−0.234739
$482$	−80.5677			−0.00761361
$483$	−10591.1	−	5451.63i	−0.997746	−	0.513577i
$484$	−7570.70			−0.710997
$485$	7920.30			0.741531
$486$		−	1918.38i		−	0.179053i
$487$	−19805.6			−1.84287			−0.921434	−	0.388535i	$-0.872981\pi$
$487$	−19805.6			−1.84287			−0.921434	+	0.388535i	$0.872981\pi$
$488$	−2564.84			−0.237920
$489$		−	2728.89i		−	0.252361i
$490$	−5965.62	+	3970.96i	−0.549998	+	0.366101i
$491$	7182.57			0.660173			0.330086	−	0.943951i	$-0.392922\pi$
$491$	7182.57			0.660173			0.330086	+	0.943951i	$0.392922\pi$
$492$	−18229.6			−1.67043
$493$	−3145.03			−0.287312
$494$			3262.05i			0.297098i
$495$		−	2310.02i		−	0.209752i
$496$		−	7057.45i		−	0.638889i
$497$	−1294.43	−	4280.69i	−0.116827	−	0.386348i
$498$		−	1223.16i		−	0.110063i
$499$	9716.99			0.871727			0.435864	−	0.900013i	$-0.356443\pi$
$499$	9716.99			0.871727			0.435864	+	0.900013i	$0.356443\pi$
$500$	27280.3			2.44002
$501$	7428.30			0.662419
$502$	2638.42			0.234578
$503$	−5290.39			−0.468960			−0.234480	−	0.972121i	$-0.575339\pi$
$503$	−5290.39			−0.468960			−0.234480	+	0.972121i	$0.575339\pi$
$504$	562.861	+	1861.39i	0.0497457	+	0.164509i
$505$		−	24112.8i		−	2.12476i
$506$	−1211.59	+	1251.95i	−0.106446	+	0.109992i
$507$		−	5495.51i		−	0.481389i
$508$	12741.6			1.11283
$509$			10463.4i			0.911167i	0.890193	+	0.455583i	$0.150569\pi$
$509$			10463.4i			0.911167i	−0.890193	+	0.455583i	$0.849431\pi$
$510$		−	2545.38i		−	0.221002i
$511$	13752.2	−	4158.50i	1.19053	−	0.360003i
$512$	−11521.0			−0.994455
$513$			10740.4i			0.924365i
$514$			5325.82i			0.457027i
$515$	14147.0			1.21047
$516$	3408.32			0.290781
$517$	−140.039			−0.0119128
$518$	−1239.40	+	374.779i	−0.105127	+	0.0317892i
$519$	18295.1			1.54733
$520$		−	11100.4i		−	0.936123i
$521$	1129.02			0.0949387			0.0474693	−	0.998873i	$-0.484884\pi$
$521$	1129.02			0.0949387			0.0474693	+	0.998873i	$0.484884\pi$
$522$	−1053.70			−0.0883508
$523$	8771.67			0.733381			0.366691	−	0.930343i	$-0.380491\pi$
$523$	8771.67			0.733381			0.366691	+	0.930343i	$0.380491\pi$
$524$		−	2943.83i		−	0.245423i
$525$	−32202.1	+	9737.53i	−2.67698	+	0.809487i
$526$			284.066i			0.0235473i
$527$		−	3596.42i		−	0.297272i
$528$	−3776.02			−0.311231
$529$	398.621	+	12160.5i	0.0327625	+	0.999463i
$530$			12302.2i			1.00825i
$531$			3656.97i			0.298868i
$532$	−3455.89	−	11428.7i	−0.281639	−	0.931383i
$533$	−15819.0			−1.28555
$534$			7093.30i			0.574826i
$535$		−	37661.4i		−	3.04344i
$536$		−	13434.7i		−	1.08263i
$537$		−	5014.62i		−	0.402973i
$538$		−	1840.02i		−	0.147452i
$539$	3001.92	+	4509.83i	0.239892	+	0.360393i
$540$		−	17055.9i		−	1.35920i
$541$	10860.5			0.863085			0.431543	−	0.902093i	$-0.357969\pi$
$541$	10860.5			0.863085			0.431543	+	0.902093i	$0.357969\pi$
$542$			1737.82i			0.137723i
$543$		−	1503.89i		−	0.118855i
$544$	−3363.82			−0.265115
$545$			6080.76i			0.477929i
$546$	1107.11	+	3661.23i	0.0867766	+	0.286971i
$547$	−3492.83			−0.273021			−0.136511	−	0.990639i	$-0.543589\pi$
$547$	−3492.83			−0.273021			−0.136511	+	0.990639i	$0.543589\pi$
$548$			16330.7i			1.27302i
$549$	1196.93			0.0930484
$550$			4920.49i			0.381473i
$551$	13863.4			1.07187
$552$	6709.25	−	6932.78i	0.517327	−	0.534563i
$553$	9120.60	−	2757.96i	0.701352	−	0.212080i
$554$	949.699			0.0728318
$555$	−8517.43			−0.651432
$556$			12758.0i			0.973132i
$557$			18223.1i			1.38624i	0.720822	+	0.693120i	$0.243764\pi$
$557$			18223.1i			1.38624i	−0.720822	+	0.693120i	$0.756236\pi$
$558$		−	1204.93i		−	0.0914135i
$559$	2957.62			0.223782
$560$	4592.00	+	15185.8i	0.346513	+	1.14592i
$561$	−1924.23			−0.144814
$562$		−	4521.45i		−	0.339370i
$563$	12708.3			0.951314			0.475657	−	0.879631i	$-0.342210\pi$
$563$	12708.3			0.951314			0.475657	+	0.879631i	$0.342210\pi$
$564$	361.890			0.0270183
$565$		−	22905.9i		−	1.70559i
$566$	7228.23			0.536794
$567$	4658.34	+	15405.2i	0.345030	+	1.14102i
$568$	3622.07			0.267568
$569$			3834.35i			0.282503i	0.989974	+	0.141252i	$0.0451127\pi$
$569$			3834.35i			0.282503i	−0.989974	+	0.141252i	$0.954887\pi$
$570$			11220.1i			0.824486i
$571$			21202.1i			1.55391i	0.629558	+	0.776953i	$0.283236\pi$
$571$			21202.1i			1.55391i	−0.629558	+	0.776953i	$0.716764\pi$
$572$	−3916.06			−0.286256
$573$	23021.0			1.67839
$574$	−7917.48	+	2394.15i	−0.575730	+	0.174094i
$575$	24693.0	+	23896.9i	1.79091	+	1.73316i
$576$	1169.00			0.0845631
$577$			21934.3i			1.58256i	0.611455	+	0.791279i	$0.290585\pi$
$577$			21934.3i			1.58256i	−0.611455	+	0.791279i	$0.709415\pi$
$578$	4476.47			0.322140
$579$			23415.3i			1.68067i
$580$	−22015.2			−1.57609
$581$	1124.49	+	3718.71i	0.0802957	+	0.265539i
$582$		−	2210.42i		−	0.157431i
$583$	9300.12			0.660671
$584$			11636.3i			0.824512i
$585$			5180.18i			0.366109i
$586$	4549.21			0.320693
$587$			9268.05i			0.651675i	0.945426	+	0.325838i	$0.105646\pi$
$587$			9268.05i			0.651675i	−0.945426	+	0.325838i	$0.894354\pi$
$588$	−7757.59	−	11654.3i	−0.544077	−	0.817374i
$589$			15853.1i			1.10902i
$590$		−	10915.1i		−	0.761642i
$591$			16736.2i			1.16486i
$592$			2866.47i			0.199005i
$593$		−	9700.10i		−	0.671729i	−0.941910	−	0.335865i	$-0.890972\pi$
$593$		−	9700.10i		−	0.671729i	0.941910	−	0.335865i	$-0.109028\pi$
$594$	1841.96			0.127233
$595$	2340.05	+	7738.56i	0.161231	+	0.533193i
$596$		−	4375.36i		−	0.300708i
$597$		−	23708.7i		−	1.62535i
$598$	2716.96	−	2807.48i	0.185794	−	0.191984i
$599$	−3745.36			−0.255478			−0.127739	−	0.991808i	$-0.540772\pi$
$599$	−3745.36			−0.255478			−0.127739	+	0.991808i	$0.540772\pi$
$600$		−	27247.6i		−	1.85396i
$601$		−	10117.8i		−	0.686711i	−0.939206	−	0.343355i	$-0.888437\pi$
$601$		−	10117.8i		−	0.686711i	0.939206	−	0.343355i	$-0.111563\pi$
$602$	1480.30	−	447.625i	0.100220	−	0.0303054i
$603$			6269.53i			0.423408i
$604$	17231.9			1.16085
$605$	−22596.7			−1.51849
$606$	−6729.47			−0.451099
$607$			24691.1i			1.65104i	0.564374	+	0.825519i	$0.309118\pi$
$607$			24691.1i			1.65104i	−0.564374	+	0.825519i	$0.690882\pi$
$608$	14827.8			0.989055
$609$	15559.8	−	4705.11i	1.03533	−	0.313072i
$610$	−3572.53			−0.237127
$611$	314.036			0.0207930
$612$	1023.77			0.0676200
$613$			12506.3i			0.824023i	0.911179	+	0.412012i	$0.135174\pi$
$613$			12506.3i			0.824023i	−0.911179	+	0.412012i	$0.864826\pi$
$614$			612.729i			0.0402732i
$615$	−54410.8			−3.56757
$616$	−4200.00	+	1270.03i	−0.274712	+	0.0830697i
$617$		−	16067.8i		−	1.04840i	−0.851594	−	0.524201i	$-0.824364\pi$
$617$		−	16067.8i		−	1.04840i	0.851594	−	0.524201i	$-0.175636\pi$
$618$		−	3948.19i		−	0.256990i
$619$	−26407.0			−1.71468			−0.857339	−	0.514752i	$-0.827884\pi$
$619$	−26407.0			−1.71468			−0.857339	+	0.514752i	$0.827884\pi$
$620$		−	25174.9i		−	1.63072i
$621$	8945.67	−	9243.71i	0.578063	−	0.597323i
$622$		−	375.018i		−	0.0241750i
$623$	−6521.10	−	21565.3i	−0.419361	−	1.38683i
$624$	8467.66			0.543234
$625$	42483.9			2.71897
$626$	−3421.81			−0.218472
$627$	8482.04			0.540255
$628$	−10114.9			−0.642721
$629$			1460.73i			0.0925962i
$630$	784.000	+	2592.70i	0.0495799	+	0.163961i
$631$			13957.1i			0.880546i	0.897864	+	0.440273i	$0.145118\pi$
$631$			13957.1i			0.880546i	−0.897864	+	0.440273i	$0.854882\pi$
$632$			7717.34i			0.485726i
$633$			27378.6i			1.71912i
$634$	−5681.93			−0.355928
$635$	38030.5			2.37668
$636$	−24033.4			−1.49841
$637$	−6731.77	−	10113.2i	−0.418717	−	0.629043i
$638$		−	2377.55i		−	0.147536i
$639$	−1690.30			−0.104644
$640$	−30399.7			−1.87758
$641$			11767.9i			0.725125i	0.931959	+	0.362563i	$0.118098\pi$
$641$			11767.9i			0.725125i	−0.931959	+	0.362563i	$0.881902\pi$
$642$	−10510.6			−0.646140
$643$	18456.4			1.13196			0.565979	−	0.824420i	$-0.308498\pi$
$643$	18456.4			1.13196			0.565979	+	0.824420i	$0.308498\pi$
$644$	−6544.63	+	12714.5i	−0.400457	+	0.777984i
$645$	10173.0			0.621025
$646$	1924.23			0.117195
$647$			12931.1i			0.785738i	0.919595	+	0.392869i	$0.128517\pi$
$647$			12931.1i			0.785738i	−0.919595	+	0.392869i	$0.871483\pi$
$648$	−13035.0			−0.790221
$649$	−8251.51			−0.499076
$650$		−	11034.1i		−	0.665837i
$651$	5380.41	+	17793.1i	0.323924	+	1.07122i
$652$	−3276.00			−0.196776
$653$	840.191			0.0503510			0.0251755	−	0.999683i	$-0.491986\pi$
$653$	840.191			0.0503510			0.0251755	+	0.999683i	$0.491986\pi$
$654$	1697.04			0.101467
$655$		−	8786.61i		−	0.524154i
$656$			18311.5i			1.08985i
$657$		−	5430.29i		−	0.322460i
$658$	157.176	−	47.5281i	0.00931209	−	0.00281586i
$659$			2845.25i			0.168187i	0.996458	+	0.0840934i	$0.0267994\pi$
$659$			2845.25i			0.168187i	−0.996458	+	0.0840934i	$0.973201\pi$
$660$	−13469.6			−0.794399
$661$	22797.9			1.34151			0.670753	−	0.741681i	$-0.265971\pi$
$661$	22797.9			1.34151			0.670753	+	0.741681i	$0.265971\pi$
$662$	−1399.40			−0.0821588
$663$	4315.05			0.252764
$664$	−3146.56			−0.183901
$665$	−10315.0	−	34111.7i	−0.601500	−	1.98917i
$666$			489.397i			0.0284741i
$667$	−11931.5	−	11546.8i	−0.692638	−	0.670306i
$668$		−	8917.60i		−	0.516516i
$669$	−1757.29			−0.101556
$670$		−	18713.0i		−	1.07902i
$671$			2700.72i			0.155380i
$672$	16642.3	−	5032.42i	0.955342	−	0.288884i
$673$	18718.6			1.07214			0.536068	−	0.844175i	$-0.319909\pi$
$673$	18718.6			1.07214			0.536068	+	0.844175i	$0.319909\pi$
$674$			6483.68i			0.370537i
$675$		−	36330.1i		−	2.07163i
$676$	−6597.30			−0.375359
$677$	−16328.0			−0.926935			−0.463468	−	0.886114i	$-0.653395\pi$
$677$	−16328.0			−0.926935			−0.463468	+	0.886114i	$0.653395\pi$
$678$	−6392.64			−0.362106
$679$	2032.11	+	6720.21i	0.114853	+	0.379820i
$680$	−6547.93			−0.369267
$681$		−	30362.4i		−	1.70850i
$682$	2718.78			0.152650
$683$	−1241.59			−0.0695579			−0.0347790	−	0.999395i	$-0.511073\pi$
$683$	−1241.59			−0.0695579			−0.0347790	+	0.999395i	$0.511073\pi$
$684$	−4512.80			−0.252268
$685$			48743.2i			2.71881i
$686$	−4899.87	−	4042.88i	−0.272709	−	0.225011i
$687$			2612.97i			0.145111i
$688$		−	3423.63i		−	0.189716i
$689$	−20855.4			−1.15316
$690$	9345.21	−	9656.56i	0.515603	−	0.532781i
$691$		−	12873.3i		−	0.708719i	−0.935109	−	0.354360i	$-0.884699\pi$
$691$		−	12873.3i		−	0.708719i	0.935109	−	0.354360i	$-0.115301\pi$
$692$		−	21963.0i		−	1.20652i
$693$	1960.00	−	592.680i	0.107438	−	0.0324878i
$694$	12474.0			0.682284
$695$			38079.6i			2.07833i
$696$			13165.9i			0.717026i
$697$			9331.37i			0.507103i
$698$			3405.32i			0.184661i
$699$			27905.2i			1.50997i
$700$	11689.8	+	38658.3i	0.631190	+	2.08735i
$701$			3110.36i			0.167584i	0.996483	+	0.0837922i	$0.0267032\pi$
$701$			3110.36i			0.167584i	−0.996483	+	0.0837922i	$0.973297\pi$
$702$	−4130.57			−0.222077
$703$		−	6438.92i		−	0.345446i
$704$			2637.71i			0.141211i
$705$	1080.15			0.0577033
$706$			4908.22i			0.261648i
$707$	20459.2	−	6186.62i	1.08833	−	0.329097i
$708$	21323.6			1.13191
$709$			27905.1i			1.47814i	0.673630	+	0.739069i	$0.264734\pi$
$709$			27905.1i			1.47814i	−0.673630	+	0.739069i	$0.735266\pi$
$710$	5045.13			0.266677
$711$		−	3601.42i		−	0.189963i
$712$	18247.4			0.960462
$713$	13204.1	−	13644.0i	0.693542	−	0.716649i
$714$	2159.70	−	653.067i	0.113200	−	0.0342303i
$715$	−11688.5			−0.611361
$716$	−6020.00			−0.314215
$717$		−	4793.48i		−	0.249673i
$718$		−	369.060i		−	0.0191827i
$719$			5116.03i			0.265362i	0.991159	+	0.132681i	$0.0423587\pi$
$719$			5116.03i			0.265362i	−0.991159	+	0.132681i	$0.957641\pi$
$720$	5996.37			0.310377
$721$	3629.70	+	12003.5i	0.187485	+	0.620017i
$722$	−1623.04			−0.0836609
$723$		−	469.787i		−	0.0241654i
$724$	−1805.40			−0.0926759
$725$	−46893.9			−2.40220
$726$			6306.34i			0.322383i
$727$	35674.0			1.81991			0.909954	−	0.414708i	$-0.136116\pi$
$727$	35674.0			1.81991			0.909954	+	0.414708i	$0.136116\pi$
$728$	9418.44	−	2848.02i	0.479493	−	0.144993i
$729$	−12277.0			−0.623736
$730$			16208.1i			0.821764i
$731$		−	1744.65i		−	0.0882740i
$732$		−	6979.22i		−	0.352404i
$733$	−19488.1			−0.982004			−0.491002	−	0.871158i	$-0.663369\pi$
$733$	−19488.1			−0.982004			−0.491002	+	0.871158i	$0.663369\pi$
$734$	10842.3			0.545226
$735$	−23154.5	−	34785.2i	−1.16199	−	1.74568i
$736$	−12761.5	−	12350.1i	−0.639125	−	0.618518i
$737$	−14146.5			−0.707044
$738$			3126.35i			0.155938i
$739$	24822.2			1.23559			0.617794	−	0.786340i	$-0.288027\pi$
$739$	24822.2			1.23559			0.617794	+	0.786340i	$0.288027\pi$
$740$			10225.1i			0.507949i
$741$	−19020.8			−0.942980
$742$	−10438.2	+	3156.38i	−0.516439	+	0.156165i
$743$		−	3748.17i		−	0.185070i	−0.995709	−	0.0925349i	$-0.970503\pi$
$743$		−	3748.17i		−	0.185070i	0.995709	−	0.0925349i	$-0.0294970\pi$
$744$	−15055.5			−0.741883
$745$		−	13059.4i		−	0.642226i
$746$			5670.05i			0.278278i
$747$	1468.39			0.0719220
$748$			2310.02i			0.112918i
$749$	31954.9	−	9662.77i	1.55889	−	0.471388i
$750$		−	22724.3i		−	1.10637i
$751$		−	15506.8i		−	0.753463i	−0.926322	−	0.376732i	$-0.877048\pi$
$751$		−	15506.8i		−	0.753463i	0.926322	−	0.376732i	$-0.122952\pi$
$752$		−	363.515i		−	0.0176277i
$753$			15384.5i			0.744544i
$754$			5331.61i			0.257514i
$755$	51432.9			2.47925
$756$	14471.5	−	4376.02i	0.696197	−	0.210522i
$757$		−	15098.9i		−	0.724941i	−0.931995	−	0.362470i	$-0.881933\pi$
$757$		−	15098.9i		−	0.724941i	0.931995	−	0.362470i	$-0.118067\pi$
$758$		−	1089.36i		−	0.0521995i
$759$	−7300.07	−	7064.69i	−0.349112	−	0.337855i
$760$	28863.4			1.37761
$761$		−	39800.6i		−	1.89589i	−0.318435	−	0.947945i	$-0.603157\pi$
$761$		−	39800.6i		−	1.89589i	0.318435	−	0.947945i	$-0.396843\pi$
$762$		−	10613.7i		−	0.504583i
$763$	−5159.40	+	1560.14i	−0.244800	+	0.0740247i
$764$		−	27636.5i		−	1.30871i
$765$	3055.70			0.144417
$766$	1620.17			0.0764217
$767$	18503.9			0.871104
$768$			693.883i			0.0326020i
$769$	4772.54			0.223800			0.111900	−	0.993719i	$-0.464306\pi$
$769$	4772.54			0.223800			0.111900	+	0.993719i	$0.464306\pi$
$770$	−5850.11	+	1769.00i	−0.273797	+	0.0827928i
$771$	−31054.6			−1.45059
$772$	28109.9			1.31049
$773$	−31119.4			−1.44798			−0.723990	−	0.689811i	$-0.757694\pi$
$773$	−31119.4			−1.44798			−0.723990	+	0.689811i	$0.757694\pi$
$774$		−	584.522i		−	0.0271450i
$775$		−	53624.3i		−	2.48547i
$776$	−5686.26			−0.263047
$777$	−2185.32	−	7226.86i	−0.100898	−	0.333671i
$778$			9875.13i			0.455065i
$779$		−	41132.9i		−	1.89183i
$780$	30205.4			1.38657
$781$		−	3813.97i		−	0.174743i
$782$	−1656.09	−	1602.69i	−0.0757309	−	0.0732891i
$783$			17554.5i			0.801208i
$784$	−11706.7	+	7792.43i	−0.533285	+	0.354976i
$785$	−30190.5			−1.37267
$786$	−2452.19			−0.111281
$787$	19852.2			0.899180			0.449590	−	0.893235i	$-0.351570\pi$
$787$	19852.2			0.899180			0.449590	+	0.893235i	$0.351570\pi$
$788$	20091.6			0.908291
$789$	−1656.38			−0.0747383
$790$			10749.4i			0.484107i
$791$	19435.2	−	5876.96i	0.873622	−	0.264173i
$792$			1658.44i			0.0744067i
$793$		−	6056.33i		−	0.271206i
$794$		−	6695.53i		−	0.299264i
$795$	−71733.7			−3.20017
$796$	−28462.1			−1.26735
$797$	−21633.5			−0.961477			−0.480739	−	0.876864i	$-0.659631\pi$
$797$	−21633.5			−0.961477			−0.480739	+	0.876864i	$0.659631\pi$
$798$	−9520.00	+	2878.73i	−0.422311	+	0.127702i
$799$		−	185.244i		−	0.00820210i
$800$	−50156.1			−2.21661
$801$	−8515.43			−0.375628
$802$		−	10839.3i		−	0.477244i
$803$	12252.8			0.538471
$804$	36557.3			1.60358
$805$	−19534.1	+	37949.6i	−0.855263	+	1.66155i
$806$	−6096.83			−0.266441
$807$	10729.1			0.468008
$808$			17311.4i			0.753730i
$809$	10759.7			0.467603			0.233802	−	0.972284i	$-0.424883\pi$
$809$	10759.7			0.467603			0.233802	+	0.972284i	$0.424883\pi$
$810$	−18156.2			−0.787587
$811$		−	27495.2i		−	1.19049i	−0.803544	−	0.595245i	$-0.797055\pi$
$811$		−	27495.2i		−	1.19049i	0.803544	−	0.595245i	$-0.202945\pi$
$812$	−5648.44	−	18679.4i	−0.244115	−	0.807290i
$813$	−10133.1			−0.437127
$814$	−1104.27			−0.0475485
$815$	−9778.05			−0.420258
$816$		−	4994.93i		−	0.214286i
$817$			7690.47i			0.329321i
$818$		−	5976.01i		−	0.255435i
$819$	−4395.27	+	1329.08i	−0.187525	+	0.0567054i
$820$			65319.6i			2.78178i
$821$	−20234.5			−0.860155			−0.430078	−	0.902792i	$-0.641514\pi$
$821$	−20234.5			−0.860155			−0.430078	+	0.902792i	$0.641514\pi$
$822$	13603.4			0.577218
$823$	3378.41			0.143091			0.0715456	−	0.997437i	$-0.477207\pi$
$823$	3378.41			0.143091			0.0715456	+	0.997437i	$0.477207\pi$
$824$	−10156.6			−0.429397
$825$	−28691.1			−1.21078
$826$	9261.26	−	2800.49i	0.390122	−	0.117968i
$827$		−	27515.3i		−	1.15696i	−0.815698	−	0.578478i	$-0.803647\pi$
$827$		−	27515.3i		−	1.15696i	0.815698	−	0.578478i	$-0.196353\pi$
$828$	3883.94	+	3758.72i	0.163015	+	0.157759i
$829$		−	36959.9i		−	1.54846i	−0.632907	−	0.774228i	$-0.718138\pi$
$829$		−	36959.9i		−	1.54846i	0.632907	−	0.774228i	$-0.281862\pi$
$830$	−4382.79			−0.183288
$831$			5537.65i			0.231166i
$832$		−	5915.03i		−	0.246474i
$833$	−5965.62	+	3970.96i	−0.248135	+	0.165169i
$834$	10627.4			0.441242
$835$		−	26616.8i		−	1.10313i
$836$		−	10182.6i		−	0.421259i
$837$	−20074.0			−0.828982
$838$	7995.76			0.329605
$839$	−26912.3			−1.10741			−0.553705	−	0.832713i	$-0.686787\pi$
$839$	−26912.3			−1.10741			−0.553705	+	0.832713i	$0.686787\pi$
$840$	32395.5	−	9796.00i	1.33065	−	0.402374i
$841$	−1730.21			−0.0709423
$842$		−	7113.86i		−	0.291164i
$843$	26364.3			1.07715
$844$	32867.8			1.34047
$845$	−19691.3			−0.801659
$846$		−	62.0636i		−	0.00252221i
$847$	−5797.62	−	19172.8i	−0.235193	−	0.777786i
$848$			24141.4i			0.977615i
$849$			42147.5i			1.70377i
$850$	−6508.84			−0.262649
$851$	−5362.98	+	5541.66i	−0.216029	+	0.223226i
$852$			9856.07i			0.396318i
$853$			31079.1i			1.24751i	0.781618	+	0.623757i	$0.214394\pi$
$853$			31079.1i			1.24751i	−0.781618	+	0.623757i	$0.785606\pi$
$854$	−916.603	−	3031.22i	−0.0367278	−	0.121459i
$855$	−13469.6			−0.538772
$856$			27038.4i			1.07962i
$857$			1986.04i			0.0791619i	0.999216	+	0.0395809i	$0.0126023\pi$
$857$			1986.04i			0.0791619i	−0.999216	+	0.0395809i	$0.987398\pi$
$858$			3262.05i			0.129795i
$859$			40956.5i			1.62680i	0.581707	+	0.813398i	$0.302385\pi$
$859$			40956.5i			1.62680i	−0.581707	+	0.813398i	$0.697615\pi$
$860$		−	12212.6i		−	0.484239i
$861$	−13960.2	−	46166.4i	−0.552568	−	1.82735i
$862$			4192.44i			0.165656i
$863$	44096.8			1.73936			0.869682	−	0.493612i	$-0.164324\pi$
$863$	44096.8			1.73936			0.869682	+	0.493612i	$0.164324\pi$
$864$			18775.7i			0.739307i
$865$		−	65554.2i		−	2.57677i
$866$	−14887.2			−0.584168
$867$			26102.1i			1.02246i
$868$	21360.4	−	6459.12i	0.835275	−	0.252577i
$869$	8126.18			0.317217
$870$			18338.5i			0.714636i
$871$	31723.2			1.23410
$872$		−	4365.59i		−	0.169538i
$873$	2653.59			0.102876
$874$	7300.07	+	7064.69i	0.282527	+	0.273417i
$875$	20891.2	+	69087.4i	0.807144	+	2.66923i
$876$	−31663.8			−1.22126
$877$	−39412.9			−1.51753			−0.758767	−	0.651362i	$-0.774198\pi$
$877$	−39412.9			−1.51753			−0.758767	+	0.651362i	$0.774198\pi$
$878$		−	14132.5i		−	0.543224i
$879$			26526.2i			1.01787i
$880$			13530.1i			0.518295i
$881$	29181.2			1.11594			0.557968	−	0.829863i	$-0.311581\pi$
$881$	29181.2			1.11594			0.557968	+	0.829863i	$0.311581\pi$
$882$	−1998.70	+	1330.42i	−0.0763035	+	0.0507907i
$883$	−15043.8			−0.573345			−0.286672	−	0.958029i	$-0.592549\pi$
$883$	−15043.8			−0.573345			−0.286672	+	0.958029i	$0.592549\pi$
$884$		−	5180.18i		−	0.197091i
$885$	63645.6			2.41743
$886$	8654.19			0.328153
$887$		−	22905.3i		−	0.867064i	−0.901138	−	0.433532i	$-0.857267\pi$
$887$		−	22905.3i		−	0.867064i	0.901138	−	0.433532i	$-0.142733\pi$
$888$	6114.96			0.231086
$889$	9757.47	+	32268.1i	0.368116	+	1.21736i
$890$	25416.5			0.957260
$891$			13725.6i			0.516076i
$892$			2109.61i			0.0791870i
$893$			816.561i			0.0305993i
$894$	−3644.65			−0.136348
$895$	−17968.2			−0.671074
$896$	−7799.64	−	25793.5i	−0.290812	−	0.961719i
$897$	16370.3	+	15842.5i	0.609352	+	0.589704i
$898$	−8249.59			−0.306562
$899$			25910.9i			0.961264i
$900$	15264.9			0.565366
$901$			12302.2i			0.454880i
$902$	−7054.24			−0.260399
$903$	2610.08	+	8631.57i	0.0961883	+	0.318096i
$904$			16444.9i			0.605034i
$905$	−5388.68			−0.197929
$906$		−	14354.0i		−	0.526359i
$907$		−	20693.8i		−	0.757582i	−0.925482	−	0.378791i	$-0.876340\pi$
$907$		−	20693.8i		−	0.757582i	0.925482	−	0.378791i	$-0.123660\pi$
$908$	−36449.7			−1.33219
$909$		−	8078.66i		−	0.294777i
$910$	13118.8	−	3966.96i	0.477894	−	0.144509i
$911$			49907.6i			1.81505i	0.419996	+	0.907526i	$0.362031\pi$
$911$			49907.6i			1.81505i	−0.419996	+	0.907526i	$0.637969\pi$
$912$			22017.8i			0.799431i
$913$			3313.26i			0.120102i
$914$			10215.4i			0.369689i
$915$		−	20831.2i		−	0.752633i
$916$	3136.85			0.113149
$917$	7455.25	−	2254.38i	0.268478	−	0.0811844i
$918$			2436.55i			0.0876015i
$919$		−	9215.03i		−	0.330768i	−0.986229	−	0.165384i	$-0.947114\pi$
$919$		−	9215.03i		−	0.330768i	0.986229	−	0.165384i	$-0.0528863\pi$
$920$	−24841.3	−	24040.4i	−0.890211	−	0.861508i
$921$	−3572.79			−0.127826
$922$			14852.8i			0.530534i
$923$			8552.76i			0.305003i
$924$	−3455.89	−	11428.7i	−0.123042	−	0.406900i
$925$			21780.1i			0.774191i
$926$	−4969.10			−0.176344
$927$	4739.76			0.167933
$928$	24235.1			0.857279
$929$		−	38118.8i		−	1.34622i	−0.739543	−	0.673109i	$-0.764959\pi$
$929$		−	38118.8i		−	1.34622i	0.739543	−	0.673109i	$-0.235041\pi$
$930$	−20970.5			−0.739410
$931$	26296.6	−	17504.1i	0.925710	−	0.616190i
$932$	33499.9			1.17739
$933$	2186.71			0.0767307
$934$	6965.78			0.244033
$935$			6894.82i			0.241160i
$936$		−	3719.03i		−	0.129872i
$937$	−45024.8			−1.56979			−0.784897	−	0.619626i	$-0.787284\pi$
$937$	−45024.8			−1.56979			−0.784897	+	0.619626i	$0.787284\pi$
$938$	15877.6	−	4801.19i	0.552688	−	0.167126i
$939$		−	19952.4i		−	0.693422i
$940$		−	1296.71i		−	0.0449937i
$941$	−2642.81			−0.0915549			−0.0457775	−	0.998952i	$-0.514577\pi$
$941$	−2642.81			−0.0915549			−0.0457775	+	0.998952i	$0.514577\pi$
$942$			8425.65i			0.291425i
$943$	−34259.6	+	35401.1i	−1.18308	+	1.22250i
$944$		−	21419.4i		−	0.738497i
$945$	43194.0	−	13061.3i	1.48688	−	0.449614i
$946$	1318.90			0.0453290
$947$	−12827.8			−0.440176			−0.220088	−	0.975480i	$-0.570634\pi$
$947$	−12827.8			−0.440176			−0.220088	+	0.975480i	$0.570634\pi$
$948$	−20999.7			−0.719451
$949$	−27476.8			−0.939867
$950$	28691.1			0.979856
$951$		−	33131.0i		−	1.12970i
$952$	−1680.00	−	5555.78i	−0.0571944	−	0.189143i
$953$			28178.5i			0.957809i	0.877867	+	0.478905i	$0.158966\pi$
$953$			28178.5i			0.957809i	−0.877867	+	0.478905i	$0.841034\pi$
$954$			4121.69i			0.139879i
$955$		−	82488.1i		−	2.79503i
$956$	−5754.52			−0.194680
$957$	13863.4			0.468274
$958$	9568.28			0.322690
$959$	−41357.6	+	12506.0i	−1.39260	+	0.421106i
$960$		−	20345.2i		−	0.683999i
$961$	161.272			0.00541345
$962$	2476.30			0.0829928
$963$		−	12617.9i		−	0.422229i
$964$	−563.974			−0.0188427
$965$	83901.0			2.79883
$966$	10591.1	+	5451.63i	0.352757	+	0.181577i
$967$	−16918.3			−0.562623			−0.281311	−	0.959617i	$-0.590769\pi$
$967$	−16918.3			−0.562623			−0.281311	+	0.959617i	$0.590769\pi$
$968$	16222.9			0.538662
$969$			11220.1i			0.371972i
$970$	−7920.30			−0.262171
$971$	3245.22			0.107254			0.0536272	−	0.998561i	$-0.482922\pi$
$971$	3245.22			0.107254			0.0536272	+	0.998561i	$0.482922\pi$
$972$		−	13428.7i		−	0.443133i
$973$	−32309.7	+	9770.07i	−1.06455	+	0.321906i
$974$	19805.6			0.651552
$975$	64339.4			2.11334
$976$	−7010.57			−0.229921
$977$		−	6365.67i		−	0.208450i	−0.994554	−	0.104225i	$-0.966764\pi$
$977$		−	6365.67i		−	0.208450i	0.994554	−	0.104225i	$-0.0332362\pi$
$978$			2728.89i			0.0892230i
$979$		−	19214.1i		−	0.627257i
$980$	−41759.3	+	27796.7i	−1.36118	+	0.906055i
$981$			2037.27i			0.0663050i
$982$	−7182.57			−0.233406
$983$	−28349.1			−0.919834			−0.459917	−	0.887962i	$-0.652121\pi$
$983$	−28349.1			−0.919834			−0.459917	+	0.887962i	$0.652121\pi$
$984$	39063.4			1.26554
$985$	59968.4			1.93985
$986$	3145.03			0.101580
$987$	277.134	+	916.486i	0.00893746	+	0.0295563i
$988$			22834.3i			0.735280i
$989$	6405.40	−	6618.81i	0.205945	−	0.212807i
$990$			2310.02i			0.0741587i
$991$	7404.99			0.237364			0.118682	−	0.992932i	$-0.462133\pi$
$991$	7404.99			0.237364			0.118682	+	0.992932i	$0.462133\pi$
$992$			27713.4i			0.886997i
$993$		−	8159.82i		−	0.260769i
$994$	1294.43	+	4280.69i	0.0413046	+	0.136595i
$995$	−84952.2			−2.70670
$996$		−	8562.14i		−	0.272391i
$997$			18086.5i			0.574530i	0.957851	+	0.287265i	$0.0927460\pi$
$997$			18086.5i			0.574530i	−0.957851	+	0.287265i	$0.907254\pi$
$998$	−9716.99			−0.308202
$999$	8153.28			0.258217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.c.b.160.1	✓	8
7.6	odd	2	inner	161.4.c.b.160.8	yes	8
23.22	odd	2	inner	161.4.c.b.160.4	yes	8
161.160	even	2	inner	161.4.c.b.160.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.c.b.160.1	✓	8	1.1	even	1	trivial
161.4.c.b.160.4	yes	8	23.22	odd	2	inner
161.4.c.b.160.5	yes	8	161.160	even	2	inner
161.4.c.b.160.8	yes	8	7.6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -5.83095i q^{3} -7.00000 q^{4} -20.8933 q^{5} +5.83095i q^{6} +(-5.36058 - 17.7275i) q^{7} +15.0000 q^{8} -7.00000 q^{9} +20.8933 q^{10} -15.7947i q^{11} +40.8167i q^{12} +35.4193i q^{13} +(5.36058 + 17.7275i) q^{14} +121.828i q^{15} +41.0000 q^{16} +20.8933 q^{17} +7.00000 q^{18} -92.0980 q^{19} +146.253 q^{20} +(-103.368 + 31.2573i) q^{21} +15.7947i q^{22} +(79.2642 + 76.7085i) q^{23} -87.4643i q^{24} +311.528 q^{25} -35.4193i q^{26} -116.619i q^{27} +(37.5241 + 124.092i) q^{28} -150.528 q^{29} -121.828i q^{30} -172.133i q^{31} -161.000 q^{32} -92.0980 q^{33} -20.8933 q^{34} +(112.000 + 370.385i) q^{35} +49.0000 q^{36} +69.9138i q^{37} +92.0980 q^{38} +206.528 q^{39} -313.399 q^{40} +446.621i q^{41} +(103.368 - 31.2573i) q^{42} -83.5031i q^{43} +110.563i q^{44} +146.253 q^{45} +(-79.2642 - 76.7085i) q^{46} -8.86623i q^{47} -239.069i q^{48} +(-285.528 + 190.059i) q^{49} -311.528 q^{50} -121.828i q^{51} -247.935i q^{52} +588.814i q^{53} +116.619i q^{54} +330.002i q^{55} +(-80.4087 - 265.912i) q^{56} +537.019i q^{57} +150.528 q^{58} -522.424i q^{59} -852.793i q^{60} -170.990 q^{61} +172.133i q^{62} +(37.5241 + 124.092i) q^{63} -167.000 q^{64} -740.025i q^{65} +92.0980 q^{66} -895.647i q^{67} -146.253 q^{68} +(447.283 - 462.186i) q^{69} +(-112.000 - 370.385i) q^{70} +241.472 q^{71} -105.000 q^{72} +775.756i q^{73} -69.9138i q^{74} -1816.51i q^{75} +644.686 q^{76} +(-280.000 + 84.6686i) q^{77} -206.528 q^{78} +514.489i q^{79} -856.624 q^{80} -869.000 q^{81} -446.621i q^{82} -209.771 q^{83} +(723.577 - 218.801i) q^{84} -436.528 q^{85} +83.5031i q^{86} +877.724i q^{87} -236.920i q^{88} +1216.49 q^{89} -146.253 q^{90} +(627.896 - 189.868i) q^{91} +(-554.849 - 536.959i) q^{92} -1003.70 q^{93} +8.86623i q^{94} +1924.23 q^{95} +938.783i q^{96} -379.084 q^{97} +(285.528 - 190.059i) q^{98} +110.563i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 56 q^{4} + 120 q^{8} - 56 q^{9} + 328 q^{16} + 56 q^{18} - 124 q^{23} + 976 q^{25} + 312 q^{29} - 1288 q^{32} + 896 q^{35} + 392 q^{36} + 136 q^{39} + 124 q^{46} - 768 q^{49} - 976 q^{50}+ \cdots + 768 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 56 * q^4 + 120 * q^8 - 56 * q^9 + 328 * q^16 + 56 * q^18 - 124 * q^23 + 976 * q^25 + 312 * q^29 - 1288 * q^32 + 896 * q^35 + 392 * q^36 + 136 * q^39 + 124 * q^46 - 768 * q^49 - 976 * q^50 - 312 * q^58 - 1336 * q^64 - 896 * q^70 + 3448 * q^71 - 840 * q^72 - 2240 * q^77 - 136 * q^78 - 6952 * q^81 - 1976 * q^85 + 868 * q^92 + 2584 * q^93 + 3264 * q^95 + 768 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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