LMFDB - Embedded newform 378.3.i.a.179.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(179,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.179"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.8
Character	$\chi$	$=$	378.179
Dual form			378.3.i.a.359.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +8.56422i q^{5} +(4.01479 - 5.73423i) q^{7} -2.82843i q^{8} +(6.05582 - 10.4890i) q^{10} -7.05296i q^{11} +(7.43588 - 12.8793i) q^{13} +(-8.97181 + 4.18408i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(12.4500 + 7.18802i) q^{17} +(9.66453 + 16.7395i) q^{19} +(-14.8337 + 8.56422i) q^{20} +(-4.98720 + 8.63808i) q^{22} +39.3708i q^{23} -48.3459 q^{25} +(-18.2141 + 10.5159i) q^{26} +(13.9468 + 1.21960i) q^{28} +(11.7844 - 6.80374i) q^{29} +(12.0515 + 20.8737i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-10.1654 - 17.6070i) q^{34} +(49.1092 + 34.3836i) q^{35} +(17.6184 + 30.5159i) q^{37} -27.3354i q^{38} +24.2233 q^{40} +(-7.79426 - 4.50002i) q^{41} +(32.4531 + 56.2103i) q^{43} +(12.2161 - 7.05296i) q^{44} +(27.8394 - 48.2192i) q^{46} +(-28.9083 - 16.6902i) q^{47} +(-16.7628 - 46.0435i) q^{49} +(59.2113 + 34.1857i) q^{50} +29.7435 q^{52} +(-52.4399 - 30.2762i) q^{53} +60.4031 q^{55} +(-16.2189 - 11.3556i) q^{56} -19.2439 q^{58} +(62.6286 - 36.1586i) q^{59} +(3.99141 - 6.91332i) q^{61} -34.0867i q^{62} -8.00000 q^{64} +(110.301 + 63.6825i) q^{65} +(41.8073 + 72.4124i) q^{67} +28.7521i q^{68} +(-35.8334 - 76.8366i) q^{70} +61.0012i q^{71} +(-9.83762 + 17.0393i) q^{73} -49.8323i q^{74} +(-19.3291 + 33.4789i) q^{76} +(-40.4433 - 28.3162i) q^{77} +(5.09411 - 8.82326i) q^{79} +(-29.6673 - 17.1284i) q^{80} +(6.36399 + 11.0228i) q^{82} +(-15.8646 + 9.15941i) q^{83} +(-61.5598 + 106.625i) q^{85} -91.7911i q^{86} -19.9488 q^{88} +(40.0208 - 23.1060i) q^{89} +(-43.9995 - 94.3469i) q^{91} +(-68.1923 + 39.3708i) q^{92} +(23.6036 + 40.8826i) q^{94} +(-143.360 + 82.7691i) q^{95} +(-49.1454 - 85.1224i) q^{97} +(-12.0275 + 68.2447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44}+ \cdots + 288 q^{98}+O(q^{100}) $ 32 * q + 32 * q^4 + 2 * q^7 + 10 * q^13 - 36 * q^14 - 64 * q^16 - 54 * q^17 + 28 * q^19 - 160 * q^25 - 72 * q^26 - 4 * q^28 - 36 * q^29 - 8 * q^31 - 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 + 72 * q^44 - 12 * q^46 + 108 * q^47 + 74 * q^49 + 288 * q^50 + 40 * q^52 - 72 * q^53 - 24 * q^55 + 48 * q^58 + 90 * q^59 - 62 * q^61 - 256 * q^64 - 378 * q^65 + 70 * q^67 - 108 * q^70 + 196 * q^73 - 56 * q^76 - 630 * q^77 - 38 * q^79 + 60 * q^85 - 486 * q^89 - 122 * q^91 - 252 * q^92 + 168 * q^94 + 72 * q^95 - 38 * q^97 + 288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$			8.56422i			1.71284i	0.516277	+	0.856422i	$0.327318\pi$
$5$			8.56422i			1.71284i	−0.516277	+	0.856422i	$0.672682\pi$
$6$		0			0
$7$	4.01479	−	5.73423i	0.573542	−	0.819176i
$7$	4.01479	−	5.73423i	0.573542	−	0.819176i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	6.05582	−	10.4890i	0.605582	−	1.04890i
$11$		−	7.05296i		−	0.641178i	−0.947218	−	0.320589i	$-0.896119\pi$
$11$		−	7.05296i		−	0.641178i	0.947218	−	0.320589i	$-0.103881\pi$
$12$		0			0
$13$	7.43588	−	12.8793i	0.571991	−	0.990717i	−0.424371	−	0.905489i	$-0.639505\pi$
$13$	7.43588	−	12.8793i	0.571991	−	0.990717i	0.996361	−	0.0852287i	$-0.0271621\pi$
$14$	−8.97181	+	4.18408i	−0.640844	+	0.298863i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	12.4500	+	7.18802i	0.732354	+	0.422825i	0.819283	−	0.573390i	$-0.194372\pi$
$17$	12.4500	+	7.18802i	0.732354	+	0.422825i	−0.0869287	+	0.996215i	$0.527705\pi$
$18$		0			0
$19$	9.66453	+	16.7395i	0.508659	+	0.881024i	0.999950	+	0.0100280i	$0.00319207\pi$
$19$	9.66453	+	16.7395i	0.508659	+	0.881024i	−0.491290	+	0.870996i	$0.663475\pi$
$20$	−14.8337	+	8.56422i	−0.741683	+	0.428211i
$21$		0			0
$22$	−4.98720	+	8.63808i	−0.226691	+	0.392640i
$23$			39.3708i			1.71178i	0.517161	+	0.855888i	$0.326989\pi$
$23$			39.3708i			1.71178i	−0.517161	+	0.855888i	$0.673011\pi$
$24$		0			0
$25$	−48.3459			−1.93383
$26$	−18.2141	+	10.5159i	−0.700543	+	0.404459i
$27$		0			0
$28$	13.9468	+	1.21960i	0.498099	+	0.0435570i
$29$	11.7844	−	6.80374i	0.406360	−	0.234612i	−0.282865	−	0.959160i	$-0.591285\pi$
$29$	11.7844	−	6.80374i	0.406360	−	0.234612i	0.689224	+	0.724548i	$0.257951\pi$
$30$		0			0
$31$	12.0515	+	20.8737i	0.388757	+	0.673346i	0.992283	−	0.123997i	$-0.0395714\pi$
$31$	12.0515	+	20.8737i	0.388757	+	0.673346i	−0.603526	+	0.797343i	$0.706238\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		0			0
$34$	−10.1654	−	17.6070i	−0.298982	−	0.517853i
$35$	49.1092	+	34.3836i	1.40312	+	0.982388i
$36$		0			0
$37$	17.6184	+	30.5159i	0.476172	+	0.824755i	0.999627	−	0.0272985i	$-0.00869046\pi$
$37$	17.6184	+	30.5159i	0.476172	+	0.824755i	−0.523455	+	0.852053i	$0.675357\pi$
$38$		−	27.3354i		−	0.719353i
$39$		0			0
$40$	24.2233			0.605582
$41$	−7.79426	−	4.50002i	−0.190104	−	0.109757i	0.401927	−	0.915672i	$-0.368340\pi$
$41$	−7.79426	−	4.50002i	−0.190104	−	0.109757i	−0.592031	+	0.805915i	$0.701674\pi$
$42$		0			0
$43$	32.4531	+	56.2103i	0.754722	+	1.30722i	0.945512	+	0.325586i	$0.105562\pi$
$43$	32.4531	+	56.2103i	0.754722	+	1.30722i	−0.190790	+	0.981631i	$0.561105\pi$
$44$	12.2161	−	7.05296i	0.277638	−	0.160295i
$45$		0			0
$46$	27.8394	−	48.2192i	0.605204	−	1.04824i
$47$	−28.9083	−	16.6902i	−0.615071	−	0.355111i	0.159876	−	0.987137i	$-0.448890\pi$
$47$	−28.9083	−	16.6902i	−0.615071	−	0.355111i	−0.774947	+	0.632026i	$0.782224\pi$
$48$		0			0
$49$	−16.7628	−	46.0435i	−0.342099	−	0.939664i
$50$	59.2113	+	34.1857i	1.18423	+	0.683714i
$51$		0			0
$52$	29.7435			0.571991
$53$	−52.4399	−	30.2762i	−0.989433	−	0.571249i	−0.0843280	−	0.996438i	$-0.526874\pi$
$53$	−52.4399	−	30.2762i	−0.989433	−	0.571249i	−0.905105	+	0.425189i	$0.860208\pi$
$54$		0			0
$55$	60.4031			1.09824
$56$	−16.2189	−	11.3556i	−0.289622	−	0.202778i
$57$		0			0
$58$	−19.2439			−0.331791
$59$	62.6286	−	36.1586i	1.06150	−	0.612858i	0.135654	−	0.990756i	$-0.456686\pi$
$59$	62.6286	−	36.1586i	1.06150	−	0.612858i	0.925847	+	0.377898i	$0.123353\pi$
$60$		0			0
$61$	3.99141	−	6.91332i	0.0654329	−	0.113333i	−0.831453	−	0.555595i	$-0.812490\pi$
$61$	3.99141	−	6.91332i	0.0654329	−	0.113333i	0.896886	+	0.442262i	$0.145824\pi$
$62$		−	34.0867i		−	0.549785i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	110.301	+	63.6825i	1.69694	+	0.979731i
$66$		0			0
$67$	41.8073	+	72.4124i	0.623990	+	1.08078i	0.988735	+	0.149675i	$0.0478228\pi$
$67$	41.8073	+	72.4124i	0.623990	+	1.08078i	−0.364745	+	0.931107i	$0.618844\pi$
$68$			28.7521i			0.422825i
$69$		0			0
$70$	−35.8334	−	76.8366i	−0.511906	−	1.09767i
$71$			61.0012i			0.859172i	0.903026	+	0.429586i	$0.141340\pi$
$71$			61.0012i			0.859172i	−0.903026	+	0.429586i	$0.858660\pi$
$72$		0			0
$73$	−9.83762	+	17.0393i	−0.134762	+	0.233415i	−0.925506	−	0.378732i	$-0.876360\pi$
$73$	−9.83762	+	17.0393i	−0.134762	+	0.233415i	0.790745	+	0.612146i	$0.209694\pi$
$74$		−	49.8323i		−	0.673410i
$75$		0			0
$76$	−19.3291	+	33.4789i	−0.254330	+	0.440512i
$77$	−40.4433	−	28.3162i	−0.525238	−	0.367743i
$78$		0			0
$79$	5.09411	−	8.82326i	0.0644824	−	0.111687i	−0.831982	−	0.554803i	$-0.812794\pi$
$79$	5.09411	−	8.82326i	0.0644824	−	0.111687i	0.896464	+	0.443116i	$0.146127\pi$
$80$	−29.6673	−	17.1284i	−0.370842	−	0.214105i
$81$		0			0
$82$	6.36399	+	11.0228i	0.0776096	+	0.134424i
$83$	−15.8646	+	9.15941i	−0.191139	+	0.110354i	−0.592516	−	0.805559i	$-0.701865\pi$
$83$	−15.8646	+	9.15941i	−0.191139	+	0.110354i	0.401376	+	0.915913i	$0.368532\pi$
$84$		0			0
$85$	−61.5598	+	106.625i	−0.724233	+	1.25441i
$86$		−	91.7911i		−	1.06734i
$87$		0			0
$88$	−19.9488			−0.226691
$89$	40.0208	−	23.1060i	0.449672	−	0.259618i	−0.258020	−	0.966140i	$-0.583070\pi$
$89$	40.0208	−	23.1060i	0.449672	−	0.259618i	0.707692	+	0.706522i	$0.249737\pi$
$90$		0			0
$91$	−43.9995	−	94.3469i	−0.483511	−	1.03678i
$92$	−68.1923	+	39.3708i	−0.741221	+	0.427944i
$93$		0			0
$94$	23.6036	+	40.8826i	0.251102	+	0.434921i
$95$	−143.360	+	82.7691i	−1.50906	+	0.871254i
$96$		0			0
$97$	−49.1454	−	85.1224i	−0.506654	−	0.877550i	−0.999970	−	0.00770043i	$-0.997549\pi$
$97$	−49.1454	−	85.1224i	−0.506654	−	0.877550i	0.493316	−	0.869850i	$-0.335784\pi$
$98$	−12.0275	+	68.2447i	−0.122729	+	0.696375i
$99$		0			0
$100$	−48.3459	−	83.7375i	−0.483459	−	0.837375i
$101$			110.793i			1.09696i	0.836164	+	0.548480i	$0.184793\pi$
$101$			110.793i			1.09696i	−0.836164	+	0.548480i	$0.815207\pi$
$102$		0			0
$103$	87.6160			0.850640			0.425320	−	0.905043i	$-0.360161\pi$
$103$	87.6160			0.850640			0.425320	+	0.905043i	$0.360161\pi$
$104$	−36.4282	−	21.0318i	−0.350271	−	0.202229i
$105$		0			0
$106$	42.8170	+	74.1613i	0.403934	+	0.699635i
$107$	−22.3256	+	12.8897i	−0.208651	+	0.120465i	−0.600684	−	0.799486i	$-0.705105\pi$
$107$	−22.3256	+	12.8897i	−0.208651	+	0.120465i	0.392033	+	0.919951i	$0.371772\pi$
$108$		0			0
$109$	52.7615	−	91.3856i	0.484050	−	0.838400i	−0.515782	−	0.856720i	$-0.672498\pi$
$109$	52.7615	−	91.3856i	0.484050	−	0.838400i	0.999832	+	0.0183201i	$0.00583180\pi$
$110$	−73.9784	−	42.7114i	−0.672531	−	0.388286i
$111$		0			0
$112$	11.8344	+	25.3761i	0.105664	+	0.226573i
$113$	−12.7398	−	7.35535i	−0.112742	−	0.0650916i	0.442569	−	0.896735i	$-0.354067\pi$
$113$	−12.7398	−	7.35535i	−0.112742	−	0.0650916i	−0.555311	+	0.831643i	$0.687401\pi$
$114$		0			0
$115$	−337.181			−2.93200
$116$	23.5689	+	13.6075i	0.203180	+	0.117306i
$117$		0			0
$118$	−102.272			−0.866712
$119$	91.2021	−	42.5329i	0.766404	−	0.357419i
$120$		0			0
$121$	71.2557			0.588890
$122$	−9.77691	+	5.64470i	−0.0801386	+	0.0462681i
$123$		0			0
$124$	−24.1029	+	41.7475i	−0.194378	+	0.336673i
$125$		−	199.939i		−	1.59951i
$126$		0			0
$127$	−14.2742			−0.112395			−0.0561976	−	0.998420i	$-0.517898\pi$
$127$	−14.2742			−0.112395			−0.0561976	+	0.998420i	$0.517898\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−90.0607	−	155.990i	−0.692775	−	1.19992i
$131$		−	172.745i		−	1.31867i	−0.751851	−	0.659333i	$-0.770839\pi$
$131$		−	172.745i		−	1.31867i	0.751851	−	0.659333i	$-0.229161\pi$
$132$		0			0
$133$	134.789	+	11.7868i	1.01345	+	0.0886227i
$134$		−	118.249i		−	0.882455i
$135$		0			0
$136$	20.3308	−	35.2140i	0.149491	−	0.258926i
$137$		−	162.089i		−	1.18313i	−0.806256	−	0.591567i	$-0.798510\pi$
$137$		−	162.089i		−	1.18313i	0.806256	−	0.591567i	$-0.201490\pi$
$138$		0			0
$139$	−78.4637	+	135.903i	−0.564487	+	0.977720i	0.432610	+	0.901581i	$0.357593\pi$
$139$	−78.4637	+	135.903i	−0.564487	+	0.977720i	−0.997097	+	0.0761389i	$0.975741\pi$
$140$	−10.4449	+	119.443i	−0.0746063	+	0.853166i
$141$		0			0
$142$	43.1344	−	74.7109i	0.303763	−	0.526133i
$143$	−90.8374	−	52.4450i	−0.635226	−	0.366748i
$144$		0			0
$145$	58.2687	+	100.924i	0.401853	+	0.696030i
$146$	24.0972	−	13.9125i	0.165049	−	0.0952911i
$147$		0			0
$148$	−35.2368	+	61.0319i	−0.238086	+	0.412377i
$149$		−	248.161i		−	1.66551i	−0.553641	−	0.832755i	$-0.686762\pi$
$149$		−	248.161i		−	1.66551i	0.553641	−	0.832755i	$-0.313238\pi$
$150$		0			0
$151$	−94.4026			−0.625183			−0.312592	−	0.949888i	$-0.601197\pi$
$151$	−94.4026			−0.625183			−0.312592	+	0.949888i	$0.601197\pi$
$152$	47.3463	−	27.3354i	0.311489	−	0.179838i
$153$		0			0
$154$	29.5102	+	63.2779i	0.191625	+	0.410895i
$155$	−178.767	+	103.211i	−1.15334	+	0.665879i
$156$		0			0
$157$	−102.528	−	177.583i	−0.653042	−	1.13110i	−0.982381	−	0.186890i	$-0.940159\pi$
$157$	−102.528	−	177.583i	−0.653042	−	1.13110i	0.329339	−	0.944212i	$-0.393174\pi$
$158$	−12.4780	+	7.20416i	−0.0789745	+	0.0455960i
$159$		0			0
$160$	24.2233	+	41.9559i	0.151395	+	0.262225i
$161$	225.762	+	158.066i	1.40225	+	0.981775i
$162$		0			0
$163$	−130.276	−	225.645i	−0.799241	−	1.38433i	−0.920111	−	0.391657i	$-0.871902\pi$
$163$	−130.276	−	225.645i	−0.799241	−	1.38433i	0.120870	−	0.992668i	$-0.461431\pi$
$164$		−	18.0001i		−	0.109757i
$165$		0			0
$166$	25.9067			0.156065
$167$	110.267	+	63.6624i	0.660279	+	0.381212i	0.792383	−	0.610024i	$-0.208840\pi$
$167$	110.267	+	63.6624i	0.660279	+	0.381212i	−0.132105	+	0.991236i	$0.542173\pi$
$168$		0			0
$169$	−26.0847	−	45.1800i	−0.154347	−	0.267337i
$170$	150.790	−	87.0587i	0.887001	−	0.512110i
$171$		0			0
$172$	−64.9061	+	112.421i	−0.377361	+	0.653609i
$173$	−5.66762	−	3.27220i	−0.0327608	−	0.0189145i	0.483530	−	0.875328i	$-0.339354\pi$
$173$	−5.66762	−	3.27220i	−0.0327608	−	0.0189145i	−0.516291	+	0.856413i	$0.672688\pi$
$174$		0			0
$175$	−194.099	+	277.226i	−1.10914	+	1.58415i
$176$	24.4322	+	14.1059i	0.138819	+	0.0801473i
$177$		0			0
$178$	−65.3537			−0.367155
$179$	3.77964	+	2.18217i	0.0211153	+	0.0121909i	0.510520	−	0.859866i	$-0.329453\pi$
$179$	3.77964	+	2.18217i	0.0211153	+	0.0121909i	−0.489405	+	0.872057i	$0.662786\pi$
$180$		0			0
$181$	71.3386			0.394136			0.197068	−	0.980390i	$-0.436858\pi$
$181$	71.3386			0.394136			0.197068	+	0.980390i	$0.436858\pi$
$182$	−12.8252	+	146.663i	−0.0704680	+	0.805842i
$183$		0			0
$184$	111.358			0.605204
$185$	−261.345	+	150.888i	−1.41268	+	0.815609i
$186$		0			0
$187$	50.6968	−	87.8095i	0.271106	−	0.469570i
$188$		−	66.7609i		−	0.355111i
$189$		0			0
$190$	234.106			1.23214
$191$	102.594	+	59.2326i	0.537140	+	0.310118i	0.743919	−	0.668270i	$-0.232965\pi$
$191$	102.594	+	59.2326i	0.537140	+	0.310118i	−0.206779	+	0.978388i	$0.566298\pi$
$192$		0			0
$193$	96.1455	+	166.529i	0.498163	+	0.862844i	0.999998	−	0.00211988i	$-0.000674780\pi$
$193$	96.1455	+	166.529i	0.498163	+	0.862844i	−0.501835	+	0.864964i	$0.667341\pi$
$194$			139.004i			0.716517i
$195$		0			0
$196$	62.9869	−	75.0776i	0.321362	−	0.383049i
$197$			278.566i			1.41404i	0.707193	+	0.707021i	$0.249961\pi$
$197$			278.566i			1.41404i	−0.707193	+	0.707021i	$0.750039\pi$
$198$		0			0
$199$	−121.675	+	210.747i	−0.611431	+	1.05903i	0.379568	+	0.925164i	$0.376073\pi$
$199$	−121.675	+	210.747i	−0.611431	+	1.05903i	−0.990999	+	0.133866i	$0.957261\pi$
$200$			136.743i			0.683714i
$201$		0			0
$202$	78.3424	−	135.693i	0.387834	−	0.671748i
$203$	8.29781	−	94.8903i	0.0408759	−	0.467440i
$204$		0			0
$205$	38.5392	−	66.7518i	0.187996	−	0.325618i
$206$	−107.307	−	61.9538i	−0.520909	−	0.300747i
$207$		0			0
$208$	29.7435	+	51.5173i	0.142998	+	0.247679i
$209$	118.063	−	68.1635i	0.564893	−	0.326141i
$210$		0			0
$211$	65.3669	−	113.219i	0.309796	−	0.536582i	−0.668522	−	0.743693i	$-0.733073\pi$
$211$	65.3669	−	113.219i	0.309796	−	0.536582i	0.978318	+	0.207110i	$0.0664060\pi$
$212$		−	121.105i		−	0.571249i
$213$		0			0
$214$	36.4576			0.170363
$215$	−481.398	+	277.935i	−2.23906	+	1.29272i
$216$		0			0
$217$	168.079	+	14.6979i	0.774557	+	0.0677322i
$218$	−129.239	+	74.6160i	−0.592838	+	0.342275i
$219$		0			0
$220$	60.4031	+	104.621i	0.274560	+	0.475551i
$221$	185.154	−	106.899i	0.837800	−	0.483704i
$222$		0			0
$223$	−25.5565	−	44.2652i	−0.114603	−	0.198498i	0.803018	−	0.595955i	$-0.203226\pi$
$223$	−25.5565	−	44.2652i	−0.114603	−	0.198498i	−0.917621	+	0.397456i	$0.869893\pi$
$224$	3.44954	−	39.4474i	0.0153997	−	0.176105i
$225$		0			0
$226$	10.4020	+	18.0169i	0.0460267	+	0.0797206i
$227$		−	346.919i		−	1.52828i	−0.645052	−	0.764139i	$-0.723164\pi$
$227$		−	346.919i		−	1.52828i	0.645052	−	0.764139i	$-0.276836\pi$
$228$		0			0
$229$	−167.226			−0.730246			−0.365123	−	0.930959i	$-0.618973\pi$
$229$	−167.226			−0.730246			−0.365123	+	0.930959i	$0.618973\pi$
$230$	412.960	+	238.423i	1.79548	+	1.03662i
$231$		0			0
$232$	−19.2439	−	33.3314i	−0.0829478	−	0.143670i
$233$	−171.970	+	99.2867i	−0.738067	+	0.426123i	−0.821366	−	0.570401i	$-0.806788\pi$
$233$	−171.970	+	99.2867i	−0.738067	+	0.426123i	0.0832991	+	0.996525i	$0.473454\pi$
$234$		0			0
$235$	142.939	−	247.577i	0.608250	−	1.05352i
$236$	125.257	+	72.3172i	0.530751	+	0.306429i
$237$		0			0
$238$	−141.775	−	12.3977i	−0.595691	−	0.0520911i
$239$	248.637	+	143.551i	1.04032	+	0.600631i	0.919925	−	0.392095i	$-0.128249\pi$
$239$	248.637	+	143.551i	1.04032	+	0.600631i	0.120398	+	0.992726i	$0.461583\pi$
$240$		0			0
$241$	378.594			1.57093			0.785464	−	0.618907i	$-0.212424\pi$
$241$	378.594			1.57093			0.785464	+	0.618907i	$0.212424\pi$
$242$	−87.2701	−	50.3854i	−0.360620	−	0.208204i
$243$		0			0
$244$	15.9656			0.0654329
$245$	394.327	−	143.561i	1.60950	−	0.585962i
$246$		0			0
$247$	287.457			1.16379
$248$	59.0398	−	34.0867i	0.238064	−	0.137446i
$249$		0			0
$250$	−141.378	+	244.874i	−0.565513	+	0.979497i
$251$		−	98.4672i		−	0.392300i	−0.980574	−	0.196150i	$-0.937156\pi$
$251$		−	98.4672i		−	0.392300i	0.980574	−	0.196150i	$-0.0628439\pi$
$252$		0			0
$253$	277.681			1.09755
$254$	17.4823	+	10.0934i	0.0688278	+	0.0397377i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$		−	215.281i		−	0.837670i	−0.908062	−	0.418835i	$-0.862439\pi$
$257$		−	215.281i		−	0.837670i	0.908062	−	0.418835i	$-0.137561\pi$
$258$		0			0
$259$	245.720	+	21.4873i	0.948724	+	0.0829625i
$260$			254.730i			0.979731i
$261$		0			0
$262$	−122.149	+	211.569i	−0.466219	+	0.807515i
$263$			12.5158i			0.0475886i	0.999717	+	0.0237943i	$0.00757468\pi$
$263$			12.5158i			0.0475886i	−0.999717	+	0.0237943i	$0.992425\pi$
$264$		0			0
$265$	259.292	−	449.107i	0.978461	−	1.69474i
$266$	−156.748	−	109.746i	−0.589277	−	0.412579i
$267$		0			0
$268$	−83.6147	+	144.825i	−0.311995	+	0.540391i
$269$	−150.771	−	87.0476i	−0.560487	−	0.323597i	0.192854	−	0.981227i	$-0.438226\pi$
$269$	−150.771	−	87.0476i	−0.560487	−	0.323597i	−0.753341	+	0.657630i	$0.771559\pi$
$270$		0			0
$271$	−17.5923	−	30.4707i	−0.0649161	−	0.112438i	0.831741	−	0.555164i	$-0.187345\pi$
$271$	−17.5923	−	30.4707i	−0.0649161	−	0.112438i	−0.896657	+	0.442726i	$0.854011\pi$
$272$	−49.8001	+	28.7521i	−0.183089	+	0.105706i
$273$		0			0
$274$	−114.614	+	198.518i	−0.418301	+	0.724519i
$275$			340.981i			1.23993i
$276$		0			0
$277$	−52.5103			−0.189568			−0.0947839	−	0.995498i	$-0.530216\pi$
$277$	−52.5103			−0.189568			−0.0947839	+	0.995498i	$0.530216\pi$
$278$	192.196	−	110.964i	0.691352	−	0.399152i
$279$		0			0
$280$	97.2515	−	138.902i	0.347327	−	0.496078i
$281$	−327.425	+	189.039i	−1.16521	+	0.672737i	−0.952548	−	0.304388i	$-0.901548\pi$
$281$	−327.425	+	189.039i	−1.16521	+	0.672737i	−0.212666	+	0.977125i	$0.568215\pi$
$282$		0			0
$283$	−275.881	−	477.840i	−0.974844	−	1.68848i	−0.680448	−	0.732796i	$-0.738215\pi$
$283$	−275.881	−	477.840i	−0.974844	−	1.68848i	−0.294396	−	0.955684i	$-0.595118\pi$
$284$	−105.657	+	61.0012i	−0.372032	+	0.214793i
$285$		0			0
$286$	74.1684	+	128.463i	0.259330	+	0.449173i
$287$	−57.0965	+	26.6275i	−0.198943	+	0.0927786i
$288$		0			0
$289$	−41.1647	−	71.2993i	−0.142438	−	0.246710i
$290$		−	164.809i		−	0.568306i
$291$		0			0
$292$	−39.3505			−0.134762
$293$	−344.440	−	198.863i	−1.17556	−	0.678712i	−0.220579	−	0.975369i	$-0.570795\pi$
$293$	−344.440	−	198.863i	−1.17556	−	0.678712i	−0.954984	+	0.296657i	$0.904128\pi$
$294$		0			0
$295$	309.670	+	536.365i	1.04973	+	1.81819i
$296$	86.3121	−	49.8323i	0.291595	−	0.168352i
$297$		0			0
$298$	−175.476	+	303.934i	−0.588847	+	1.01991i
$299$	507.070	+	292.757i	1.69589	+	0.979120i
$300$		0			0
$301$	452.616	+	39.5796i	1.50371	+	0.131494i
$302$	115.619	+	66.7528i	0.382845	+	0.221036i
$303$		0			0
$304$	−77.3162			−0.254330
$305$	59.2072	+	34.1833i	0.194122	+	0.112076i
$306$		0			0
$307$	−295.323			−0.961964			−0.480982	−	0.876731i	$-0.659720\pi$
$307$	−295.323			−0.961964			−0.480982	+	0.876731i	$0.659720\pi$
$308$	8.60176	−	98.3661i	0.0279278	−	0.319370i
$309$		0			0
$310$	291.926			0.941695
$311$	241.377	−	139.359i	0.776132	−	0.448100i	−0.0589258	−	0.998262i	$-0.518768\pi$
$311$	241.377	−	139.359i	0.776132	−	0.448100i	0.835058	+	0.550162i	$0.185434\pi$
$312$		0			0
$313$	−99.7337	+	172.744i	−0.318638	+	0.551897i	−0.980204	−	0.197990i	$-0.936559\pi$
$313$	−99.7337	+	172.744i	−0.318638	+	0.551897i	0.661566	+	0.749887i	$0.269892\pi$
$314$			289.992i			0.923541i
$315$		0			0
$316$	20.3764			0.0644824
$317$	−16.1995	−	9.35277i	−0.0511025	−	0.0295040i	0.474231	−	0.880400i	$-0.342726\pi$
$317$	−16.1995	−	9.35277i	−0.0511025	−	0.0295040i	−0.525334	+	0.850896i	$0.676059\pi$
$318$		0			0
$319$	−47.9865	−	83.1151i	−0.150428	−	0.260549i
$320$		−	68.5138i		−	0.214105i
$321$		0			0
$322$	−164.731	−	353.228i	−0.511587	−	1.09698i
$323$			277.875i			0.860295i
$324$		0			0
$325$	−359.494	+	622.662i	−1.10614	+	1.91588i
$326$			368.477i			1.13030i
$327$		0			0
$328$	−12.7280	+	22.0455i	−0.0388048	+	0.0672119i
$329$	−211.767	+	98.7593i	−0.643668	+	0.300180i
$330$		0			0
$331$	−105.691	+	183.062i	−0.319308	+	0.553058i	−0.980344	−	0.197297i	$-0.936784\pi$
$331$	−105.691	+	183.062i	−0.319308	+	0.553058i	0.661036	+	0.750354i	$0.270117\pi$
$332$	−31.7291	−	18.3188i	−0.0955697	−	0.0551772i
$333$		0			0
$334$	−90.0322	−	155.940i	−0.269558	−	0.466887i
$335$	−620.156	+	358.047i	−1.85121	+	1.06880i
$336$		0			0
$337$	271.681	−	470.566i	0.806175	−	1.39634i	−0.109319	−	0.994007i	$-0.534867\pi$
$337$	271.681	−	470.566i	0.806175	−	1.39634i	0.915495	−	0.402330i	$-0.131800\pi$
$338$			73.7786i			0.218280i
$339$		0			0
$340$	−246.239			−0.724233
$341$	147.222	−	84.9984i	0.431735	−	0.249262i
$342$		0			0
$343$	−331.324	−	88.7332i	−0.965958	−	0.258698i
$344$	158.987	−	91.7911i	0.462171	−	0.266835i
$345$		0			0
$346$	4.62759	+	8.01523i	0.0133745	+	0.0231654i
$347$	128.969	−	74.4605i	0.371670	−	0.214584i	−0.302518	−	0.953144i	$-0.597827\pi$
$347$	128.969	−	74.4605i	0.371670	−	0.214584i	0.674188	+	0.738560i	$0.264494\pi$
$348$		0			0
$349$	−229.407	−	397.344i	−0.657325	−	1.13852i	−0.981305	−	0.192457i	$-0.938354\pi$
$349$	−229.407	−	397.344i	−0.657325	−	1.13852i	0.323980	−	0.946064i	$-0.394979\pi$
$350$	433.750	−	202.283i	1.23929	−	0.577952i
$351$		0			0
$352$	−19.9488	−	34.5523i	−0.0566727	−	0.0981600i
$353$		−	484.311i		−	1.37199i	−0.727608	−	0.685993i	$-0.759368\pi$
$353$		−	484.311i		−	1.37199i	0.727608	−	0.685993i	$-0.240632\pi$
$354$		0			0
$355$	−522.428			−1.47163
$356$	80.0415	+	46.2120i	0.224836	+	0.129809i
$357$		0			0
$358$	−3.08606	−	5.34521i	−0.00862028	−	0.0149308i
$359$	321.625	−	185.690i	0.895892	−	0.517244i	0.0200269	−	0.999799i	$-0.493625\pi$
$359$	321.625	−	185.690i	0.895892	−	0.517244i	0.875865	+	0.482556i	$0.160291\pi$
$360$		0			0
$361$	−6.30620	+	10.9227i	−0.0174687	+	0.0302567i
$362$	−87.3716	−	50.4440i	−0.241358	−	0.139348i
$363$		0			0
$364$	119.414	−	170.556i	0.328061	−	0.468561i
$365$	−145.928	−	84.2516i	−0.399803	−	0.230826i
$366$		0			0
$367$	244.691			0.666733			0.333366	−	0.942797i	$-0.391815\pi$
$367$	244.691			0.666733			0.333366	+	0.942797i	$0.391815\pi$
$368$	−136.385	−	78.7417i	−0.370610	−	0.213972i
$369$		0			0
$370$	426.775			1.15345
$371$	−384.146	+	179.150i	−1.03544	+	0.482884i
$372$		0			0
$373$	−649.307			−1.74077			−0.870385	−	0.492373i	$-0.836130\pi$
$373$	−649.307			−1.74077			−0.870385	+	0.492373i	$0.836130\pi$
$374$	−124.181	+	71.6962i	−0.332036	+	0.191701i
$375$		0			0
$376$	−47.2071	+	81.7651i	−0.125551	+	0.217460i
$377$		−	202.367i		−	0.536783i
$378$		0			0
$379$	−118.934			−0.313809			−0.156905	−	0.987614i	$-0.550152\pi$
$379$	−118.934			−0.313809			−0.156905	+	0.987614i	$0.550152\pi$
$380$	−286.721	−	165.538i	−0.754528	−	0.435627i
$381$		0			0
$382$	−83.7675	−	145.090i	−0.219287	−	0.379816i
$383$			357.562i			0.933582i	0.884368	+	0.466791i	$0.154590\pi$
$383$			357.562i			0.933582i	−0.884368	+	0.466791i	$0.845410\pi$
$384$		0			0
$385$	242.506	−	346.365i	0.629886	−	0.899651i
$386$		−	271.940i		−	0.704509i
$387$		0			0
$388$	98.2909	−	170.245i	0.253327	−	0.438775i
$389$		−	350.758i		−	0.901691i	−0.892602	−	0.450845i	$-0.851123\pi$
$389$		−	350.758i		−	0.901691i	0.892602	−	0.450845i	$-0.148877\pi$
$390$		0			0
$391$	−282.999	+	490.168i	−0.723781	+	1.25363i
$392$	−130.231	+	47.4125i	−0.332221	+	0.120950i
$393$		0			0
$394$	196.976	−	341.172i	0.499939	−	0.865920i
$395$	75.5643	+	43.6271i	0.191302	+	0.110448i
$396$		0			0
$397$	126.600	+	219.278i	0.318893	+	0.552338i	0.980257	−	0.197726i	$-0.0633557\pi$
$397$	126.600	+	219.278i	0.318893	+	0.552338i	−0.661365	+	0.750065i	$0.730022\pi$
$398$	298.041	−	172.074i	0.748847	−	0.432347i
$399$		0			0
$400$	96.6917	−	167.475i	0.241729	−	0.418687i
$401$			479.464i			1.19567i	0.801619	+	0.597835i	$0.203972\pi$
$401$			479.464i			1.19567i	−0.801619	+	0.597835i	$0.796028\pi$
$402$		0			0
$403$	358.453			0.889461
$404$	−191.899	+	110.793i	−0.474998	+	0.274240i
$405$		0			0
$406$	−77.2603	+	110.349i	−0.190296	+	0.271795i
$407$	215.228	−	124.262i	0.528815	−	0.305311i
$408$		0			0
$409$	−5.29891	−	9.17798i	−0.0129558	−	0.0224400i	0.859475	−	0.511178i	$-0.170791\pi$
$409$	−5.29891	−	9.17798i	−0.0129558	−	0.0224400i	−0.872431	+	0.488738i	$0.837457\pi$
$410$	−94.4013	+	54.5026i	−0.230247	+	0.132933i
$411$		0			0
$412$	87.6160	+	151.755i	0.212660	+	0.368338i
$413$	44.0989	−	504.296i	0.106777	−	1.22106i
$414$		0			0
$415$	−78.4432	−	135.868i	−0.189020	−	0.327392i
$416$		−	84.1274i		−	0.202229i
$417$		0			0
$418$	−192.796			−0.461233
$419$	−611.154	−	352.850i	−1.45860	−	0.842124i	−0.459659	−	0.888095i	$-0.652028\pi$
$419$	−611.154	−	352.850i	−1.45860	−	0.842124i	−0.998943	+	0.0459710i	$0.985362\pi$
$420$		0			0
$421$	212.170	+	367.490i	0.503968	+	0.872897i	0.999989	+	0.00458746i	$0.00146024\pi$
$421$	212.170	+	367.490i	0.503968	+	0.872897i	−0.496022	+	0.868310i	$0.665206\pi$
$422$	−160.116	+	92.4428i	−0.379421	+	0.219059i
$423$		0			0
$424$	−85.6341	+	148.323i	−0.201967	+	0.349817i
$425$	−601.907	−	347.511i	−1.41625	−	0.817673i
$426$		0			0
$427$	−23.6179	−	50.6432i	−0.0553113	−	0.118602i
$428$	−44.6513	−	25.7794i	−0.104325	−	0.0602323i
$429$		0			0
$430$	786.119			1.82818
$431$	360.974	+	208.408i	0.837526	+	0.483546i	0.856423	−	0.516276i	$-0.172682\pi$
$431$	360.974	+	208.408i	0.837526	+	0.483546i	−0.0188965	+	0.999821i	$0.506015\pi$
$432$		0			0
$433$	−457.197			−1.05588			−0.527941	−	0.849281i	$-0.677036\pi$
$433$	−457.197			−1.05588			−0.527941	+	0.849281i	$0.677036\pi$
$434$	−195.461	−	136.851i	−0.450371	−	0.315325i
$435$		0			0
$436$	211.046			0.484050
$437$	−659.046	+	380.501i	−1.50812	+	0.870711i
$438$		0			0
$439$	61.3814	−	106.316i	0.139821	−	0.242177i	−0.787608	−	0.616177i	$-0.788681\pi$
$439$	61.3814	−	106.316i	0.139821	−	0.242177i	0.927429	+	0.374000i	$0.122014\pi$
$440$		−	170.846i		−	0.388286i
$441$		0			0
$442$	−302.355			−0.684061
$443$	271.478	+	156.738i	0.612818	+	0.353811i	0.774068	−	0.633103i	$-0.218219\pi$
$443$	271.478	+	156.738i	0.612818	+	0.353811i	−0.161249	+	0.986914i	$0.551552\pi$
$444$		0			0
$445$	197.885	+	342.747i	0.444685	+	0.770217i
$446$			72.2847i			0.162073i
$447$		0			0
$448$	−32.1184	+	45.8739i	−0.0716928	+	0.102397i
$449$		−	216.459i		−	0.482092i	−0.970514	−	0.241046i	$-0.922510\pi$
$449$		−	216.459i		−	0.482092i	0.970514	−	0.241046i	$-0.0774904\pi$
$450$		0			0
$451$	−31.7385	+	54.9726i	−0.0703735	+	0.121891i
$452$		−	29.4214i		−	0.0650916i
$453$		0			0
$454$	−245.309	+	424.887i	−0.540328	+	0.935875i
$455$	808.008	−	376.821i	1.77584	−	0.828179i
$456$		0			0
$457$	−282.487	+	489.281i	−0.618133	+	1.07064i	0.371693	+	0.928356i	$0.378777\pi$
$457$	−282.487	+	489.281i	−0.618133	+	1.07064i	−0.989826	+	0.142282i	$0.954556\pi$
$458$	204.810	+	118.247i	0.447182	+	0.258181i
$459$		0			0
$460$	−337.181	−	584.014i	−0.733001	−	1.26960i
$461$	504.476	−	291.259i	1.09431	−	0.631799i	0.159588	−	0.987184i	$-0.448983\pi$
$461$	504.476	−	291.259i	1.09431	−	0.631799i	0.934720	+	0.355385i	$0.115650\pi$
$462$		0			0
$463$	128.093	−	221.863i	0.276658	−	0.479186i	−0.693894	−	0.720077i	$-0.744106\pi$
$463$	128.093	−	221.863i	0.276658	−	0.479186i	0.970552	+	0.240891i	$0.0774397\pi$
$464$			54.4299i			0.117306i
$465$		0			0
$466$	280.825			0.602629
$467$	−300.844	+	173.693i	−0.644206	+	0.371933i	−0.786233	−	0.617930i	$-0.787971\pi$
$467$	−300.844	+	173.693i	−0.644206	+	0.371933i	0.142027	+	0.989863i	$0.454638\pi$
$468$		0			0
$469$	583.078	+	50.9880i	1.24324	+	0.108716i
$470$	−350.127	+	202.146i	−0.744952	+	0.430098i
$471$		0			0
$472$	−102.272	−	177.140i	−0.216678	−	0.375297i
$473$	396.449	−	228.890i	0.838159	−	0.483911i
$474$		0			0
$475$	−467.240	−	809.283i	−0.983663	−	1.70375i
$476$	164.871	+	115.434i	0.346368	+	0.242508i
$477$		0			0
$478$	−203.011	−	351.626i	−0.424710	−	0.735620i
$479$			67.8475i			0.141644i	0.997489	+	0.0708220i	$0.0225622\pi$
$479$			67.8475i			0.141644i	−0.997489	+	0.0708220i	$0.977438\pi$
$480$		0			0
$481$	524.033			1.08947
$482$	−463.681	−	267.706i	−0.961993	−	0.555407i
$483$		0			0
$484$	71.2557	+	123.419i	0.147223	+	0.254997i
$485$	729.007	−	420.892i	1.50311	−	0.867819i
$486$		0			0
$487$	−231.777	+	401.449i	−0.475927	+	0.824330i	−0.999620	−	0.0275774i	$-0.991221\pi$
$487$	−231.777	+	401.449i	−0.475927	+	0.824330i	0.523693	+	0.851907i	$0.324554\pi$
$488$	−19.5538	−	11.2894i	−0.0400693	−	0.0231340i
$489$		0			0
$490$	−584.463	−	103.006i	−1.19278	−	0.210216i
$491$	−93.7518	−	54.1276i	−0.190941	−	0.110240i	0.401482	−	0.915867i	$-0.368495\pi$
$491$	−93.7518	−	54.1276i	−0.190941	−	0.110240i	−0.592423	+	0.805627i	$0.701828\pi$
$492$		0			0
$493$	195.622			0.396799
$494$	−352.062	−	203.263i	−0.712675	−	0.411463i
$495$		0			0
$496$	−96.4116			−0.194378
$497$	349.795	+	244.907i	0.703813	+	0.492771i
$498$		0			0
$499$	−7.53911			−0.0151084			−0.00755422	−	0.999971i	$-0.502405\pi$
$499$	−7.53911			−0.0151084			−0.00755422	+	0.999971i	$0.502405\pi$
$500$	346.305	−	199.939i	0.692609	−	0.399878i
$501$		0			0
$502$	−69.6268	+	120.597i	−0.138699	+	0.240233i
$503$			402.034i			0.799272i	0.916674	+	0.399636i	$0.130863\pi$
$503$			402.034i			0.799272i	−0.916674	+	0.399636i	$0.869137\pi$
$504$		0			0
$505$	−948.855			−1.87892
$506$	−340.088	−	196.350i	−0.672111	−	0.388044i
$507$		0			0
$508$	−14.2742	−	24.7236i	−0.0280988	−	0.0486686i
$509$		−	736.522i		−	1.44700i	−0.690325	−	0.723499i	$-0.742533\pi$
$509$		−	736.522i		−	1.44700i	0.690325	−	0.723499i	$-0.257467\pi$
$510$		0			0
$511$	58.2111	+	124.820i	0.113916	+	0.244267i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−152.227	+	263.664i	−0.296161	+	0.512966i
$515$			750.362i			1.45701i
$516$		0			0
$517$	−117.716	+	203.889i	−0.227690	+	0.394370i
$518$	−285.750	−	200.066i	−0.551641	−	0.386229i
$519$		0			0
$520$	180.121	−	311.979i	0.346387	−	0.599960i
$521$	455.192	+	262.805i	0.873690	+	0.504425i	0.868573	−	0.495562i	$-0.165038\pi$
$521$	455.192	+	262.805i	0.873690	+	0.504425i	0.00511719	+	0.999987i	$0.498371\pi$
$522$		0			0
$523$	46.2741	+	80.1490i	0.0884781	+	0.153249i	0.906868	−	0.421415i	$-0.138466\pi$
$523$	46.2741	+	80.1490i	0.0884781	+	0.153249i	−0.818390	+	0.574663i	$0.805133\pi$
$524$	299.203	−	172.745i	0.570999	−	0.329666i
$525$		0			0
$526$	8.85001	−	15.3287i	0.0168251	−	0.0291420i
$527$			346.504i			0.657504i
$528$		0			0
$529$	−1021.06			−1.93018
$530$	−635.133	+	366.694i	−1.19836	+	0.691876i
$531$		0			0
$532$	114.374	+	245.248i	0.214988	+	0.460993i
$533$	−115.914	+	66.9232i	−0.217475	+	0.125560i
$534$		0			0
$535$	−110.390	−	191.202i	−0.206337	−	0.357386i
$536$	204.813	−	118.249i	0.382114	−	0.220614i
$537$		0			0
$538$	123.104	+	213.222i	0.228818	+	0.396324i
$539$	−324.743	+	118.228i	−0.602492	+	0.219346i
$540$		0			0
$541$	−66.8426	−	115.775i	−0.123554	−	0.214001i	0.797613	−	0.603170i	$-0.206096\pi$
$541$	−66.8426	−	115.775i	−0.123554	−	0.214001i	−0.921167	+	0.389168i	$0.872762\pi$
$542$			49.7584i			0.0918052i
$543$		0			0
$544$	81.3232			0.149491
$545$	782.646	+	451.861i	1.43605	+	0.829103i
$546$		0			0
$547$	28.0279	+	48.5457i	0.0512393	+	0.0887490i	0.890507	−	0.454969i	$-0.150350\pi$
$547$	28.0279	+	48.5457i	0.0512393	+	0.0887490i	−0.839268	+	0.543718i	$0.817016\pi$
$548$	280.747	−	162.089i	0.512312	−	0.295783i
$549$		0			0
$550$	241.110	−	417.615i	0.438382	−	0.759300i
$551$	227.782	+	131.510i	0.413397	+	0.238675i
$552$		0			0
$553$	−30.1428	−	64.6344i	−0.0545078	−	0.116880i
$554$	64.3117	+	37.1304i	0.116086	+	0.0670223i
$555$		0			0
$556$	−313.855			−0.564487
$557$	173.289	+	100.048i	0.311111	+	0.179620i	0.647423	−	0.762130i	$-0.275847\pi$
$557$	173.289	+	100.048i	0.311111	+	0.179620i	−0.336313	+	0.941750i	$0.609180\pi$
$558$		0			0
$559$	965.268			1.72678
$560$	−217.327	+	101.352i	−0.388083	+	0.180986i
$561$		0			0
$562$	534.683			0.951393
$563$	−522.623	+	301.737i	−0.928283	+	0.535945i	−0.886268	−	0.463172i	$-0.846711\pi$
$563$	−522.623	+	301.737i	−0.928283	+	0.535945i	−0.0420150	+	0.999117i	$0.513378\pi$
$564$		0			0
$565$	62.9929	−	109.107i	0.111492	−	0.193109i
$566$			780.309i			1.37864i
$567$		0			0
$568$	172.537			0.303763
$569$	−3.47634	−	2.00707i	−0.00610956	−	0.00352736i	0.496942	−	0.867784i	$-0.334456\pi$
$569$	−3.47634	−	2.00707i	−0.00610956	−	0.00352736i	−0.503052	+	0.864256i	$0.667789\pi$
$570$		0			0
$571$	303.356	+	525.428i	0.531271	+	0.920189i	0.999334	+	0.0364935i	$0.0116188\pi$
$571$	303.356	+	525.428i	0.531271	+	0.920189i	−0.468063	+	0.883695i	$0.655048\pi$
$572$		−	209.780i		−	0.366748i
$573$		0			0
$574$	88.7571	+	7.76149i	0.154629	+	0.0135218i
$575$		−	1903.42i		−	3.31029i
$576$		0			0
$577$	290.727	−	503.553i	0.503859	−	0.872709i	−0.496131	−	0.868248i	$-0.665247\pi$
$577$	290.727	−	503.553i	0.503859	−	0.872709i	0.999990	−	0.00446157i	$-0.00142017\pi$
$578$			116.431i			0.201438i
$579$		0			0
$580$	−116.537	+	201.849i	−0.200927	+	0.348015i
$581$	−11.1708	+	127.744i	−0.0192268	+	0.219870i
$582$		0			0
$583$	−213.537	+	369.857i	−0.366273	+	0.634403i
$584$	48.1943	+	27.8250i	0.0825245	+	0.0476455i
$585$		0			0
$586$	281.234	+	487.112i	0.479922	+	0.831249i
$587$	−119.284	+	68.8684i	−0.203209	+	0.117323i	−0.598151	−	0.801383i	$-0.704098\pi$
$587$	−119.284	+	68.8684i	−0.203209	+	0.117323i	0.394943	+	0.918706i	$0.370764\pi$
$588$		0			0
$589$	−232.943	+	403.469i	−0.395489	+	0.685008i
$590$		−	875.880i		−	1.48454i
$591$		0			0
$592$	−140.947			−0.238086
$593$	−491.375	+	283.696i	−0.828626	+	0.478407i	−0.853382	−	0.521286i	$-0.825452\pi$
$593$	−491.375	+	283.696i	−0.828626	+	0.478407i	0.0247561	+	0.999694i	$0.492119\pi$
$594$		0			0
$595$	364.261	+	781.075i	0.612203	+	1.31273i
$596$	429.828	−	248.161i	0.721187	−	0.416378i
$597$		0			0
$598$	−414.021	−	717.105i	−0.692343	−	1.19917i
$599$	703.550	−	406.195i	1.17454	−	0.678121i	0.219795	−	0.975546i	$-0.429461\pi$
$599$	703.550	−	406.195i	1.17454	−	0.678121i	0.954745	+	0.297425i	$0.0961277\pi$
$600$		0			0
$601$	370.313	+	641.402i	0.616162	+	1.06722i	0.990179	+	0.139802i	$0.0446467\pi$
$601$	370.313	+	641.402i	0.616162	+	1.06722i	−0.374017	+	0.927422i	$0.622020\pi$
$602$	−526.352	−	368.522i	−0.874338	−	0.612163i
$603$		0			0
$604$	−94.4026	−	163.510i	−0.156296	−	0.270712i
$605$			610.250i			1.00868i
$606$		0			0
$607$	186.920			0.307941			0.153971	−	0.988075i	$-0.450794\pi$
$607$	186.920			0.307941			0.153971	+	0.988075i	$0.450794\pi$
$608$	94.6926	+	54.6708i	0.155744	+	0.0899191i
$609$		0			0
$610$	−48.3425	−	83.7316i	−0.0792500	−	0.137265i
$611$	−429.918	+	248.213i	−0.703630	+	0.406241i
$612$		0			0
$613$	435.744	−	754.731i	0.710839	−	1.23121i	−0.253704	−	0.967282i	$-0.581649\pi$
$613$	435.744	−	754.731i	0.710839	−	1.23121i	0.964543	−	0.263927i	$-0.0850178\pi$
$614$	361.695	+	208.825i	0.589080	+	0.340105i
$615$		0			0
$616$	−80.0903	+	114.391i	−0.130017	+	0.185700i
$617$	−441.505	−	254.903i	−0.715567	−	0.413133i	0.0975522	−	0.995230i	$-0.468899\pi$
$617$	−441.505	−	254.903i	−0.715567	−	0.413133i	−0.813119	+	0.582098i	$0.802232\pi$
$618$		0			0
$619$	−1064.80			−1.72019			−0.860097	−	0.510131i	$-0.829597\pi$
$619$	−1064.80			−1.72019			−0.860097	+	0.510131i	$0.829597\pi$
$620$	−357.534	−	206.423i	−0.576668	−	0.332940i
$621$		0			0
$622$	−394.167			−0.633709
$623$	28.1800	−	322.254i	0.0452327	−	0.517262i
$624$		0			0
$625$	503.675			0.805880
$626$	244.297	−	141.045i	0.390250	−	0.225311i
$627$		0			0
$628$	205.055	−	355.166i	0.326521	−	0.565551i
$629$			506.565i			0.805350i
$630$		0			0
$631$	479.402			0.759750			0.379875	−	0.925038i	$-0.375967\pi$
$631$	479.402			0.759750			0.379875	+	0.925038i	$0.375967\pi$
$632$	−24.9560	−	14.4083i	−0.0394873	−	0.0227980i
$633$		0			0
$634$	13.2268	+	22.9095i	0.0208625	+	0.0361349i
$635$		−	122.247i		−	0.192516i
$636$		0			0
$637$	−717.656	−	126.480i	−1.12662	−	0.198556i
$638$			135.726i			0.212737i
$639$		0			0
$640$	−48.4465	+	83.9119i	−0.0756977	+	0.131112i
$641$			209.386i			0.326655i	0.986572	+	0.163327i	$0.0522227\pi$
$641$			209.386i			0.326655i	−0.986572	+	0.163327i	$0.947777\pi$
$642$		0			0
$643$	−184.919	+	320.289i	−0.287588	+	0.498117i	−0.973234	−	0.229818i	$-0.926187\pi$
$643$	−184.919	+	320.289i	−0.287588	+	0.498117i	0.685645	+	0.727936i	$0.259520\pi$
$644$	−48.0165	+	549.096i	−0.0745598	+	0.852634i
$645$		0			0
$646$	196.488	−	340.326i	0.304160	−	0.526821i
$647$	−227.896	−	131.576i	−0.352235	−	0.203363i	0.313434	−	0.949610i	$-0.398521\pi$
$647$	−227.896	−	131.576i	−0.352235	−	0.203363i	−0.665669	+	0.746247i	$0.731854\pi$
$648$		0			0
$649$	−255.025	−	441.717i	−0.392951	−	0.680611i
$650$	880.577	−	508.401i	1.35473	−	0.782156i
$651$		0			0
$652$	260.553	−	451.290i	0.399620	−	0.692163i
$653$			811.255i			1.24235i	0.783672	+	0.621175i	$0.213345\pi$
$653$			811.255i			1.24235i	−0.783672	+	0.621175i	$0.786655\pi$
$654$		0			0
$655$	1479.43			2.25867
$656$	31.1771	−	18.0001i	0.0475260	−	0.0274391i
$657$		0			0
$658$	329.194	+	28.7868i	0.500294	+	0.0437489i
$659$	−31.0199	+	17.9093i	−0.0470711	+	0.0271765i	−0.523351	−	0.852117i	$-0.675318\pi$
$659$	−31.0199	+	17.9093i	−0.0470711	+	0.0271765i	0.476280	+	0.879294i	$0.341985\pi$
$660$		0			0
$661$	−194.584	−	337.029i	−0.294378	−	0.509877i	0.680462	−	0.732783i	$-0.261779\pi$
$661$	−194.584	−	337.029i	−0.294378	−	0.509877i	−0.974840	+	0.222906i	$0.928446\pi$
$662$	258.889	−	149.470i	0.391071	−	0.225785i
$663$		0			0
$664$	25.9067	+	44.8718i	0.0390162	+	0.0675780i
$665$	−100.945	+	1154.36i	−0.151797	+	1.73588i
$666$		0			0
$667$	267.869	+	463.963i	0.401603	+	0.695596i
$668$			254.650i			0.381212i
$669$		0			0
$670$	1012.71			1.51151
$671$	−48.7594	−	28.1512i	−0.0726668	−	0.0419542i
$672$		0			0
$673$	−399.256	−	691.532i	−0.593248	−	1.02754i	−0.993792	−	0.111258i	$-0.964512\pi$
$673$	−399.256	−	691.532i	−0.593248	−	1.02754i	0.400543	−	0.916278i	$-0.368821\pi$
$674$	−665.480	+	384.215i	−0.987359	+	0.570052i
$675$		0			0
$676$	52.1693	−	90.3600i	0.0771736	−	0.133669i
$677$	443.787	+	256.221i	0.655521	+	0.378465i	0.790568	−	0.612374i	$-0.209785\pi$
$677$	443.787	+	256.221i	0.655521	+	0.378465i	−0.135048	+	0.990839i	$0.543119\pi$
$678$		0			0
$679$	−685.420	−	59.9375i	−1.00946	−	0.0882733i
$680$	301.580	+	174.117i	0.443500	+	0.256055i
$681$		0			0
$682$	−240.412			−0.352510
$683$	−1041.76	−	601.463i	−1.52528	−	0.880619i	−0.999551	−	0.0299649i	$-0.990460\pi$
$683$	−1041.76	−	601.463i	−1.52528	−	0.880619i	−0.525726	−	0.850654i	$-0.676206\pi$
$684$		0			0
$685$	1388.17			2.02652
$686$	343.043	+	342.957i	0.500063	+	0.499937i
$687$		0			0
$688$	−259.624			−0.377361
$689$	−779.874	+	450.261i	−1.13189	+	0.653499i
$690$		0			0
$691$	270.992	−	469.372i	0.392174	−	0.679265i	−0.600562	−	0.799578i	$-0.705057\pi$
$691$	270.992	−	469.372i	0.392174	−	0.679265i	0.992736	+	0.120313i	$0.0383899\pi$
$692$		−	13.0888i		−	0.0189145i
$693$		0			0
$694$	−210.606			−0.303467
$695$	−1163.90	−	671.980i	−1.67468	−	0.966878i
$696$		0			0
$697$	−64.6925	−	112.051i	−0.0928156	−	0.160761i
$698$			648.860i			0.929599i
$699$		0			0
$700$	−674.269	−	58.9624i	−0.963241	−	0.0842320i
$701$			1106.17i			1.57800i	0.614396	+	0.788998i	$0.289400\pi$
$701$			1106.17i			1.57800i	−0.614396	+	0.788998i	$0.710600\pi$
$702$		0			0
$703$	−340.547	+	589.844i	−0.484419	+	0.839039i
$704$			56.4237i			0.0801473i
$705$		0			0
$706$	−342.460	+	593.158i	−0.485070	+	0.840167i
$707$	635.313	+	444.811i	0.898603	+	0.629153i
$708$		0			0
$709$	−679.865	+	1177.56i	−0.958907	+	1.66088i	−0.233744	+	0.972298i	$0.575098\pi$
$709$	−679.865	+	1177.56i	−0.958907	+	1.66088i	−0.725163	+	0.688577i	$0.758236\pi$
$710$	639.840	+	369.412i	0.901184	+	0.520299i
$711$		0			0
$712$	−65.3537	−	113.196i	−0.0917888	−	0.158983i
$713$	−821.816	+	474.476i	−1.15262	+	0.665464i
$714$		0			0
$715$	449.150	−	777.951i	0.628182	−	1.08804i
$716$			8.72869i			0.0121909i
$717$		0			0
$718$	−525.212			−0.731493
$719$	669.276	−	386.407i	0.930843	−	0.537422i	0.0437647	−	0.999042i	$-0.486065\pi$
$719$	669.276	−	386.407i	0.930843	−	0.537422i	0.887078	+	0.461620i	$0.152731\pi$
$720$		0			0
$721$	351.760	−	502.410i	0.487878	−	0.696824i
$722$	15.4470	−	8.91832i	0.0213947	−	0.0123522i
$723$		0			0
$724$	71.3386	+	123.562i	0.0985340	+	0.170666i
$725$	−569.728	+	328.933i	−0.785832	+	0.453700i
$726$		0			0
$727$	−332.257	−	575.485i	−0.457024	−	0.791589i	0.541778	−	0.840522i	$-0.317751\pi$
$727$	−332.257	−	575.485i	−0.457024	−	0.791589i	−0.998802	+	0.0489326i	$0.984418\pi$
$728$	−266.853	+	124.449i	−0.366557	+	0.170947i
$729$		0			0
$730$	119.150	+	206.373i	0.163219	+	0.282703i
$731$			933.093i			1.27646i
$732$		0			0
$733$	982.898			1.34092			0.670462	−	0.741944i	$-0.266096\pi$
$733$	982.898			1.34092			0.670462	+	0.741944i	$0.266096\pi$
$734$	−299.684	−	173.023i	−0.408289	−	0.235726i
$735$		0			0
$736$	111.358	+	192.877i	0.151301	+	0.262061i
$737$	510.722	−	294.865i	0.692974	−	0.400089i
$738$		0			0
$739$	−451.664	+	782.306i	−0.611183	+	1.05860i	0.379858	+	0.925045i	$0.375973\pi$
$739$	−451.664	+	782.306i	−0.611183	+	1.05860i	−0.991041	+	0.133556i	$0.957360\pi$
$740$	−522.690	−	301.775i	−0.706338	−	0.407805i
$741$		0			0
$742$	597.160	+	52.2195i	0.804797	+	0.0703766i
$743$	662.703	+	382.612i	0.891928	+	0.514955i	0.874573	−	0.484894i	$-0.161142\pi$
$743$	662.703	+	382.612i	0.891928	+	0.514955i	0.0173557	+	0.999849i	$0.494475\pi$
$744$		0			0
$745$	2125.31			2.85276
$746$	795.235	+	459.129i	1.06600	+	0.615455i
$747$		0			0
$748$	202.787			0.271106
$749$	−15.7202	+	179.770i	−0.0209883	+	0.240013i
$750$		0			0
$751$	448.075			0.596638			0.298319	−	0.954466i	$-0.403574\pi$
$751$	448.075			0.596638			0.298319	+	0.954466i	$0.403574\pi$
$752$	115.633	−	66.7609i	0.153768	−	0.0887779i
$753$		0			0
$754$	−143.095	+	247.848i	−0.189782	+	0.328711i
$755$		−	808.485i		−	1.07084i
$756$		0			0
$757$	−1350.52			−1.78404			−0.892020	−	0.451995i	$-0.850712\pi$
$757$	−1350.52			−1.78404			−0.892020	+	0.451995i	$0.850712\pi$
$758$	145.663	+	84.0988i	0.192168	+	0.110948i
$759$		0			0
$760$	234.106	+	405.484i	0.308035	+	0.533532i
$761$		−	212.791i		−	0.279620i	−0.990178	−	0.139810i	$-0.955351\pi$
$761$		−	212.791i		−	0.279620i	0.990178	−	0.139810i	$-0.0446492\pi$
$762$		0			0
$763$	−312.200	−	669.441i	−0.409174	−	0.877380i
$764$			236.930i			0.310118i
$765$		0			0
$766$	252.834	−	437.922i	0.330071	−	0.571700i
$767$		−	1075.48i		−	1.40220i
$768$		0			0
$769$	349.195	−	604.823i	0.454090	−	0.786506i	−0.544546	−	0.838731i	$-0.683298\pi$
$769$	349.195	−	604.823i	0.454090	−	0.786506i	0.998635	+	0.0522249i	$0.0166313\pi$
$770$	−541.925	+	252.732i	−0.703799	+	0.328223i
$771$		0			0
$772$	−192.291	+	333.058i	−0.249082	+	0.431422i
$773$	156.237	+	90.2037i	0.202118	+	0.116693i	0.597643	−	0.801762i	$-0.296104\pi$
$773$	156.237	+	90.2037i	0.202118	+	0.116693i	−0.395525	+	0.918455i	$0.629437\pi$
$774$		0			0
$775$	−582.638	−	1009.16i	−0.751791	−	1.30214i
$776$	−240.762	+	139.004i	−0.310261	+	0.179129i
$777$		0			0
$778$	−248.023	+	429.589i	−0.318796	+	0.552170i
$779$		−	173.962i		−	0.223315i
$780$		0			0
$781$	430.239			0.550882
$782$	693.202	−	400.220i	0.886448	−	0.511791i
$783$		0			0
$784$	193.025	+	34.0189i	0.246206	+	0.0433914i
$785$	1520.86	−	878.069i	1.93740	−	1.11856i
$786$		0			0
$787$	−80.2269	−	138.957i	−0.101940	−	0.176566i	0.810544	−	0.585678i	$-0.199172\pi$
$787$	−80.2269	−	138.957i	−0.101940	−	0.176566i	−0.912484	+	0.409113i	$0.865838\pi$
$788$	−482.491	+	278.566i	−0.612298	+	0.353510i
$789$		0			0
$790$	−61.6980	−	106.864i	−0.0780988	−	0.135271i
$791$	−93.3252	+	43.5230i	−0.117984	+	0.0550228i
$792$		0			0
$793$	−59.3593	−	102.813i	−0.0748541	−	0.129651i
$794$		−	358.080i		−	0.450982i
$795$		0			0
$796$	−486.699			−0.611431
$797$	969.679	+	559.844i	1.21666	+	0.702439i	0.964202	−	0.265168i	$-0.0854275\pi$
$797$	969.679	+	559.844i	1.21666	+	0.702439i	0.252459	+	0.967608i	$0.418761\pi$
$798$		0			0
$799$	−239.940	−	415.588i	−0.300300	−	0.520135i
$800$	−236.845	+	136.743i	−0.296057	+	0.170928i
$801$		0			0
$802$	339.032	−	587.221i	0.422733	−	0.732196i
$803$	120.177	+	69.3844i	0.149660	+	0.0864064i
$804$		0			0
$805$	−1353.71	+	1933.47i	−1.68163	+	2.40183i
$806$	−439.013	−	253.464i	−0.544681	−	0.314472i
$807$		0			0
$808$	313.370			0.387834
$809$	262.167	+	151.362i	0.324063	+	0.187098i	0.653202	−	0.757183i	$-0.273425\pi$
$809$	262.167	+	151.362i	0.324063	+	0.187098i	−0.329139	+	0.944282i	$0.606758\pi$
$810$		0			0
$811$	1037.56			1.27936			0.639680	−	0.768641i	$-0.279067\pi$
$811$	1037.56			1.27936			0.639680	+	0.768641i	$0.279067\pi$
$812$	172.653	−	80.5180i	0.212626	−	0.0991601i
$813$		0			0
$814$	−351.465			−0.431776
$815$	1932.47	−	1115.71i	2.37113	−	1.36897i
$816$		0			0
$817$	−627.287	+	1086.49i	−0.767793	+	1.32986i
$818$			14.9876i			0.0183222i
$819$		0			0
$820$	154.157			0.187996
$821$	−523.028	−	301.971i	−0.637063	−	0.367808i	0.146419	−	0.989223i	$-0.453225\pi$
$821$	−523.028	−	301.971i	−0.637063	−	0.367808i	−0.783482	+	0.621414i	$0.786558\pi$
$822$		0			0
$823$	14.2238	+	24.6363i	0.0172828	+	0.0299347i	0.874537	−	0.484958i	$-0.161165\pi$
$823$	14.2238	+	24.6363i	0.0172828	+	0.0299347i	−0.857255	+	0.514893i	$0.827832\pi$
$824$		−	247.815i		−	0.300747i
$825$		0			0
$826$	−410.601	+	586.452i	−0.497096	+	0.709990i
$827$		−	798.699i		−	0.965778i	−0.875681	−	0.482889i	$-0.839587\pi$
$827$		−	798.699i		−	0.965778i	0.875681	−	0.482889i	$-0.160413\pi$
$828$		0			0
$829$	216.869	−	375.628i	0.261603	−	0.453110i	−0.705065	−	0.709143i	$-0.749082\pi$
$829$	216.869	−	375.628i	0.261603	−	0.453110i	0.966668	+	0.256033i	$0.0824154\pi$
$830$			221.871i			0.267314i
$831$		0			0
$832$	−59.4871	+	103.035i	−0.0714989	+	0.123840i
$833$	122.264	−	693.735i	0.146776	−	0.832815i
$834$		0			0
$835$	−545.219	+	944.347i	−0.652957	+	1.13095i
$836$	236.125	+	136.327i	0.282447	+	0.163071i
$837$		0			0
$838$	499.005	+	864.303i	0.595472	+	1.03139i
$839$	−338.993	+	195.718i	−0.404044	+	0.233275i	−0.688227	−	0.725495i	$-0.741611\pi$
$839$	−338.993	+	195.718i	−0.404044	+	0.233275i	0.284183	+	0.958770i	$0.408278\pi$
$840$		0			0
$841$	−327.918	+	567.971i	−0.389915	+	0.675352i
$842$		−	600.108i		−	0.712718i
$843$		0			0
$844$	261.468			0.309796
$845$	386.931	−	223.395i	0.457907	−	0.264373i
$846$		0			0
$847$	286.077	−	408.597i	0.337753	−	0.482405i
$848$	209.760	−	121.105i	0.247358	−	0.142812i
$849$		0			0
$850$	491.455	+	851.225i	0.578182	+	1.00144i
$851$	−1201.44	+	693.651i	−1.41180	+	0.815101i
$852$		0			0
$853$	−517.801	−	896.857i	−0.607035	−	1.05141i	−0.991726	−	0.128370i	$-0.959026\pi$
$853$	−517.801	−	896.857i	−0.607035	−	1.05141i	0.384692	−	0.923045i	$-0.374308\pi$
$854$	−6.88426	+	78.7254i	−0.00806119	+	0.0921843i
$855$		0			0
$856$	36.4576	+	63.1464i	0.0425907	+	0.0737692i
$857$		−	849.651i		−	0.991424i	−0.868487	−	0.495712i	$-0.834907\pi$
$857$		−	849.651i		−	0.991424i	0.868487	−	0.495712i	$-0.165093\pi$
$858$		0			0
$859$	1221.58			1.42210			0.711050	−	0.703142i	$-0.248220\pi$
$859$	1221.58			1.42210			0.711050	+	0.703142i	$0.248220\pi$
$860$	−962.795	−	555.870i	−1.11953	−	0.646361i
$861$		0			0
$862$	−294.734	−	510.494i	−0.341919	−	0.592220i
$863$	−232.708	+	134.354i	−0.269650	+	0.155682i	−0.628728	−	0.777625i	$-0.716424\pi$
$863$	−232.708	+	134.354i	−0.269650	+	0.155682i	0.359079	+	0.933307i	$0.383091\pi$
$864$		0			0
$865$	28.0239	−	48.5387i	0.0323975	−	0.0561142i
$866$	559.949	+	323.287i	0.646593	+	0.373310i
$867$		0			0
$868$	142.621	+	305.819i	0.164310	+	0.352326i
$869$	−62.2301	−	35.9286i	−0.0716112	−	0.0413447i
$870$		0			0
$871$	1243.50			1.42767
$872$	−258.477	−	149.232i	−0.296419	−	0.171138i
$873$		0			0
$874$	1076.22			1.23137
$875$	−1146.50	−	802.714i	−1.31028	−	0.917388i
$876$		0			0
$877$	−1004.06			−1.14488			−0.572438	−	0.819948i	$-0.694002\pi$
$877$	−1004.06			−1.14488			−0.572438	+	0.819948i	$0.694002\pi$
$878$	−150.353	+	86.8064i	−0.171245	+	0.0988684i
$879$		0			0
$880$	−120.806	+	209.242i	−0.137280	+	0.237776i
$881$		−	370.961i		−	0.421068i	−0.977587	−	0.210534i	$-0.932480\pi$
$881$		−	370.961i		−	0.421068i	0.977587	−	0.210534i	$-0.0675203\pi$
$882$		0			0
$883$	694.091			0.786060			0.393030	−	0.919526i	$-0.371427\pi$
$883$	694.091			0.786060			0.393030	+	0.919526i	$0.371427\pi$
$884$	370.308	+	213.797i	0.418900	+	0.241852i
$885$		0			0
$886$	−221.661	−	383.929i	−0.250182	−	0.433328i
$887$		−	291.012i		−	0.328086i	−0.986453	−	0.164043i	$-0.947546\pi$
$887$		−	291.012i		−	0.328086i	0.986453	−	0.164043i	$-0.0524536\pi$
$888$		0			0
$889$	−57.3080	+	81.8516i	−0.0644634	+	0.0920715i
$890$		−	559.703i		−	0.628880i
$891$		0			0
$892$	51.1130	−	88.5303i	0.0573016	−	0.0992492i
$893$		−	645.213i		−	0.722523i
$894$		0			0
$895$	−18.6886	+	32.3696i	−0.0208811	+	0.0361672i
$896$	71.7745	−	33.4727i	0.0801055	−	0.0373579i
$897$		0			0
$898$	−153.060	+	265.107i	−0.170445	+	0.295220i
$899$	284.039	+	163.990i	0.315950	+	0.182414i
$900$		0			0
$901$	−435.252	−	753.879i	−0.483077	−	0.836713i
$902$	77.7430	−	44.8850i	0.0861896	−	0.0497616i
$903$		0			0
$904$	−20.8041	+	36.0337i	−0.0230134	+	0.0398603i
$905$			610.960i			0.675094i
$906$		0			0
$907$	−1455.65			−1.60490			−0.802451	−	0.596719i	$-0.796471\pi$
$907$	−1455.65			−1.60490			−0.802451	+	0.596719i	$0.796471\pi$
$908$	600.881	−	346.919i	0.661763	−	0.382069i
$909$		0			0
$910$	−1256.06	−	109.838i	−1.38028	−	0.120701i
$911$	−310.858	+	179.474i	−0.341228	+	0.197008i	−0.660815	−	0.750549i	$-0.729789\pi$
$911$	−310.858	+	179.474i	−0.341228	+	0.197008i	0.319587	+	0.947557i	$0.396456\pi$
$912$		0			0
$913$	64.6010	+	111.892i	0.0707568	+	0.122554i
$914$	691.948	−	399.496i	0.757055	−	0.437086i
$915$		0			0
$916$	−167.226	−	289.644i	−0.182561	−	0.316206i
$917$	−990.561	−	693.537i	−1.08022	−	0.756310i
$918$		0			0
$919$	−739.927	−	1281.59i	−0.805144	−	1.39455i	−0.916194	−	0.400735i	$-0.868755\pi$
$919$	−739.927	−	1281.59i	−0.805144	−	1.39455i	0.111050	−	0.993815i	$-0.464579\pi$
$920$			953.691i			1.03662i
$921$		0			0
$922$	−823.806			−0.893499
$923$	785.654	+	453.598i	0.851196	+	0.491438i
$924$		0			0
$925$	−851.776	−	1475.32i	−0.920839	−	1.59494i
$926$	−313.762	+	181.150i	−0.338835	+	0.195627i
$927$		0			0
$928$	38.4878	−	66.6628i	0.0414739	−	0.0718349i
$929$	−428.161	−	247.199i	−0.460884	−	0.266092i	0.251532	−	0.967849i	$-0.419066\pi$
$929$	−428.161	−	247.199i	−0.460884	−	0.266092i	−0.712416	+	0.701757i	$0.752399\pi$
$930$		0			0
$931$	608.739	−	725.590i	0.653855	−	0.779366i
$932$	−343.939	−	198.573i	−0.369033	−	0.213062i
$933$		0			0
$934$	491.277			0.525992
$935$	752.020	+	434.179i	0.804299	+	0.464362i
$936$		0			0
$937$	−1460.33			−1.55852			−0.779258	−	0.626704i	$-0.784404\pi$
$937$	−1460.33			−1.55852			−0.779258	+	0.626704i	$0.784404\pi$
$938$	−678.067	−	474.745i	−0.722886	−	0.506125i
$939$		0			0
$940$	571.755			0.608250
$941$	1143.15	−	660.000i	1.21483	−	0.701381i	0.251021	−	0.967982i	$-0.419234\pi$
$941$	1143.15	−	660.000i	1.21483	−	0.701381i	0.963807	+	0.266600i	$0.0859003\pi$
$942$		0			0
$943$	177.170	−	306.867i	0.187879	−	0.325415i
$944$			289.269i			0.306429i
$945$		0			0
$946$	−647.399			−0.684354
$947$	458.361	+	264.635i	0.484013	+	0.279445i	0.722087	−	0.691802i	$-0.243183\pi$
$947$	458.361	+	264.635i	0.484013	+	0.279445i	−0.238074	+	0.971247i	$0.576516\pi$
$948$		0			0
$949$	146.303	+	253.404i	0.154165	+	0.267022i
$950$			1321.55i			1.39111i
$951$		0			0
$952$	−120.301	−	257.958i	−0.126367	−	0.270965i
$953$		−	193.203i		−	0.202731i	−0.994849	−	0.101366i	$-0.967679\pi$
$953$		−	193.203i		−	0.202731i	0.994849	−	0.101366i	$-0.0323212\pi$
$954$		0			0
$955$	−507.281	+	878.636i	−0.531184	+	0.920038i
$956$			574.203i			0.600631i
$957$		0			0
$958$	47.9754	−	83.0959i	0.0500787	−	0.0867389i
$959$	−929.458	−	650.755i	−0.969195	−	0.678577i
$960$		0			0
$961$	190.025	−	329.133i	0.197737	−	0.342490i
$962$	−641.806	−	370.547i	−0.667159	−	0.385184i
$963$		0			0
$964$	378.594	+	655.743i	0.392732	+	0.680232i
$965$	−1426.19	+	823.411i	−1.47792	+	0.853275i
$966$		0			0
$967$	−802.035	+	1389.17i	−0.829405	+	1.43657i	0.0691002	+	0.997610i	$0.477987\pi$
$967$	−802.035	+	1389.17i	−0.829405	+	1.43657i	−0.898505	+	0.438962i	$0.855346\pi$
$968$		−	201.542i		−	0.208204i
$969$		0			0
$970$	−1190.46			−1.22728
$971$	1197.47	−	691.361i	1.23324	−	0.712010i	0.265534	−	0.964102i	$-0.414452\pi$
$971$	1197.47	−	691.361i	1.23324	−	0.712010i	0.967703	+	0.252092i	$0.0811185\pi$
$972$		0			0
$973$	464.284	+	995.552i	0.477168	+	1.02318i
$974$	567.734	−	327.781i	0.582889	−	0.336531i
$975$		0			0
$976$	15.9656	+	27.6533i	0.0163582	+	0.0283333i
$977$	−1120.07	+	646.671i	−1.14643	+	0.661894i	−0.948016	−	0.318223i	$-0.896914\pi$
$977$	−1120.07	+	646.671i	−1.14643	+	0.661894i	−0.198419	+	0.980117i	$0.563581\pi$
$978$		0			0
$979$	−162.966	−	282.265i	−0.166461	−	0.288320i
$980$	642.981	+	539.434i	0.656103	+	0.550442i
$981$		0			0
$982$	76.5481	+	132.585i	0.0779512	+	0.135015i
$983$			1406.31i			1.43063i	0.698800	+	0.715317i	$0.253718\pi$
$983$			1406.31i			1.43063i	−0.698800	+	0.715317i	$0.746282\pi$
$984$		0			0
$985$	−2385.70			−2.42203
$986$	−239.587	−	138.325i	−0.242989	−	0.140290i
$987$		0			0
$988$	287.457	+	497.890i	0.290949	+	0.503938i
$989$	−2213.05	+	1277.70i	−2.23766	+	1.29192i
$990$		0			0
$991$	929.154	−	1609.34i	0.937593	−	1.62396i	0.167649	−	0.985847i	$-0.446383\pi$
$991$	929.154	−	1609.34i	0.937593	−	1.62396i	0.769944	−	0.638111i	$-0.220284\pi$
$992$	118.080	+	68.1733i	0.119032	+	0.0687231i
$993$		0			0
$994$	−255.234	−	547.291i	−0.256775	−	0.550595i
$995$	−1804.88	−	1042.05i	−1.81395	−	1.04729i
$996$		0			0
$997$	642.749			0.644683			0.322341	−	0.946623i	$-0.395530\pi$
$997$	642.749			0.644683			0.322341	+	0.946623i	$0.395530\pi$
$998$	9.23349	+	5.33096i	0.00925200	+	0.00534164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.i.a.179.8		32
3.2	odd	2		126.3.i.a.95.9	yes	32
7.2	even	3		378.3.r.a.233.16		32
9.2	odd	6		378.3.r.a.305.8		32
9.7	even	3		126.3.r.a.11.13	yes	32
21.2	odd	6		126.3.r.a.23.5	yes	32
63.2	odd	6	inner	378.3.i.a.359.1		32
63.16	even	3		126.3.i.a.65.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.9	✓	32	63.16	even	3
126.3.i.a.95.9	yes	32	3.2	odd	2
126.3.r.a.11.13	yes	32	9.7	even	3
126.3.r.a.23.5	yes	32	21.2	odd	6
378.3.i.a.179.8		32	1.1	even	1	trivial
378.3.i.a.359.1		32	63.2	odd	6	inner
378.3.r.a.233.16		32	7.2	even	3
378.3.r.a.305.8		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +8.56422i q^{5} +(4.01479 - 5.73423i) q^{7} -2.82843i q^{8} +(6.05582 - 10.4890i) q^{10} -7.05296i q^{11} +(7.43588 - 12.8793i) q^{13} +(-8.97181 + 4.18408i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(12.4500 + 7.18802i) q^{17} +(9.66453 + 16.7395i) q^{19} +(-14.8337 + 8.56422i) q^{20} +(-4.98720 + 8.63808i) q^{22} +39.3708i q^{23} -48.3459 q^{25} +(-18.2141 + 10.5159i) q^{26} +(13.9468 + 1.21960i) q^{28} +(11.7844 - 6.80374i) q^{29} +(12.0515 + 20.8737i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-10.1654 - 17.6070i) q^{34} +(49.1092 + 34.3836i) q^{35} +(17.6184 + 30.5159i) q^{37} -27.3354i q^{38} +24.2233 q^{40} +(-7.79426 - 4.50002i) q^{41} +(32.4531 + 56.2103i) q^{43} +(12.2161 - 7.05296i) q^{44} +(27.8394 - 48.2192i) q^{46} +(-28.9083 - 16.6902i) q^{47} +(-16.7628 - 46.0435i) q^{49} +(59.2113 + 34.1857i) q^{50} +29.7435 q^{52} +(-52.4399 - 30.2762i) q^{53} +60.4031 q^{55} +(-16.2189 - 11.3556i) q^{56} -19.2439 q^{58} +(62.6286 - 36.1586i) q^{59} +(3.99141 - 6.91332i) q^{61} -34.0867i q^{62} -8.00000 q^{64} +(110.301 + 63.6825i) q^{65} +(41.8073 + 72.4124i) q^{67} +28.7521i q^{68} +(-35.8334 - 76.8366i) q^{70} +61.0012i q^{71} +(-9.83762 + 17.0393i) q^{73} -49.8323i q^{74} +(-19.3291 + 33.4789i) q^{76} +(-40.4433 - 28.3162i) q^{77} +(5.09411 - 8.82326i) q^{79} +(-29.6673 - 17.1284i) q^{80} +(6.36399 + 11.0228i) q^{82} +(-15.8646 + 9.15941i) q^{83} +(-61.5598 + 106.625i) q^{85} -91.7911i q^{86} -19.9488 q^{88} +(40.0208 - 23.1060i) q^{89} +(-43.9995 - 94.3469i) q^{91} +(-68.1923 + 39.3708i) q^{92} +(23.6036 + 40.8826i) q^{94} +(-143.360 + 82.7691i) q^{95} +(-49.1454 - 85.1224i) q^{97} +(-12.0275 + 68.2447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44}+ \cdots + 288 q^{98}+O(q^{100}) \) 32 * q + 32 * q^4 + 2 * q^7 + 10 * q^13 - 36 * q^14 - 64 * q^16 - 54 * q^17 + 28 * q^19 - 160 * q^25 - 72 * q^26 - 4 * q^28 - 36 * q^29 - 8 * q^31 - 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 + 72 * q^44 - 12 * q^46 + 108 * q^47 + 74 * q^49 + 288 * q^50 + 40 * q^52 - 72 * q^53 - 24 * q^55 + 48 * q^58 + 90 * q^59 - 62 * q^61 - 256 * q^64 - 378 * q^65 + 70 * q^67 - 108 * q^70 + 196 * q^73 - 56 * q^76 - 630 * q^77 - 38 * q^79 + 60 * q^85 - 486 * q^89 - 122 * q^91 - 252 * q^92 + 168 * q^94 + 72 * q^95 - 38 * q^97 + 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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