LMFDB - Embedded newform 684.3.s.a.445.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.19
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.283015 - 2.98662i) q^{3} +(1.65331 + 2.86362i) q^{5} +(0.469266 + 0.812792i) q^{7} +(-8.83980 + 1.69052i) q^{9} +O(q^{10})$	\(q+(-0.283015 - 2.98662i) q^{3} +(1.65331 + 2.86362i) q^{5} +(0.469266 + 0.812792i) q^{7} +(-8.83980 + 1.69052i) q^{9} +(-3.23717 - 5.60694i) q^{11} +9.70848i q^{13} +(8.08462 - 5.74825i) q^{15} +(-1.26353 + 2.18849i) q^{17} +(-15.4195 + 11.1013i) q^{19} +(2.29469 - 1.63155i) q^{21} -43.4437 q^{23} +(7.03314 - 12.1817i) q^{25} +(7.55073 + 25.9227i) q^{27} +(17.3006 + 9.98850i) q^{29} +(-40.8887 - 23.6071i) q^{31} +(-15.8296 + 11.2550i) q^{33} +(-1.55168 + 2.68759i) q^{35} +47.4213i q^{37} +(28.9956 - 2.74765i) q^{39} +(-6.34554 + 3.66360i) q^{41} -62.8168 q^{43} +(-19.4559 - 22.5189i) q^{45} +(-20.9612 + 36.3058i) q^{47} +(24.0596 - 41.6724i) q^{49} +(6.89379 + 3.15430i) q^{51} +(26.2764 - 15.1707i) q^{53} +(10.7041 - 18.5400i) q^{55} +(37.5193 + 42.9104i) q^{57} +(66.5860 - 38.4435i) q^{59} +(-50.0409 + 86.6734i) q^{61} +(-5.52226 - 6.39162i) q^{63} +(-27.8014 + 16.0511i) q^{65} -22.8794i q^{67} +(12.2952 + 129.750i) q^{69} +(4.42365 + 2.55400i) q^{71} +(-42.4021 + 73.4425i) q^{73} +(-38.3727 - 17.5577i) q^{75} +(3.03818 - 5.26228i) q^{77} +111.844i q^{79} +(75.2843 - 29.8877i) q^{81} +(46.4633 + 80.4768i) q^{83} -8.35599 q^{85} +(24.9355 - 54.4972i) q^{87} +(-88.1242 + 50.8785i) q^{89} +(-7.89098 + 4.55586i) q^{91} +(-58.9334 + 128.800i) q^{93} +(-57.2831 - 25.8017i) q^{95} +83.1892i q^{97} +(38.0945 + 44.0917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.283015	−	2.98662i	−0.0943384	−	0.995540i
$3$	−0.283015	−	2.98662i	−0.0943384	−	0.995540i
$4$		0			0
$5$	1.65331	+	2.86362i	0.330662	+	0.572723i	0.982642	−	0.185513i	$-0.0593947\pi$
$5$	1.65331	+	2.86362i	0.330662	+	0.572723i	−0.651980	+	0.758236i	$0.726061\pi$
$6$		0			0
$7$	0.469266	+	0.812792i	0.0670379	+	0.116113i	0.897596	−	0.440819i	$-0.145312\pi$
$7$	0.469266	+	0.812792i	0.0670379	+	0.116113i	−0.830558	+	0.556932i	$0.811978\pi$
$8$		0			0
$9$	−8.83980	+	1.69052i	−0.982201	+	0.187835i
$10$		0			0
$11$	−3.23717	−	5.60694i	−0.294288	−	0.509721i	0.680531	−	0.732719i	$-0.261749\pi$
$11$	−3.23717	−	5.60694i	−0.294288	−	0.509721i	−0.974819	+	0.222998i	$0.928416\pi$
$12$		0			0
$13$			9.70848i			0.746806i	0.927669	+	0.373403i	$0.121809\pi$
$13$			9.70848i			0.746806i	−0.927669	+	0.373403i	$0.878191\pi$
$14$		0			0
$15$	8.08462	−	5.74825i	0.538975	−	0.383217i
$16$		0			0
$17$	−1.26353	+	2.18849i	−0.0743250	+	0.128735i	−0.900793	−	0.434250i	$-0.857014\pi$
$17$	−1.26353	+	2.18849i	−0.0743250	+	0.128735i	0.826468	+	0.562984i	$0.190347\pi$
$18$		0			0
$19$	−15.4195	+	11.1013i	−0.811553	+	0.584279i
$19$	−15.4195	+	11.1013i	−0.811553	+	0.584279i
$20$		0			0
$21$	2.29469	−	1.63155i	0.109271	−	0.0776929i
$22$		0			0
$23$	−43.4437			−1.88886			−0.944428	−	0.328718i	$-0.893383\pi$
$23$	−43.4437			−1.88886			−0.944428	+	0.328718i	$0.893383\pi$
$24$		0			0
$25$	7.03314	−	12.1817i	0.281325	−	0.487270i
$26$		0			0
$27$	7.55073	+	25.9227i	0.279657	+	0.960100i
$28$		0			0
$29$	17.3006	+	9.98850i	0.596572	+	0.344431i	0.767692	−	0.640819i	$-0.221405\pi$
$29$	17.3006	+	9.98850i	0.596572	+	0.344431i	−0.171120	+	0.985250i	$0.554739\pi$
$30$		0			0
$31$	−40.8887	−	23.6071i	−1.31899	−	0.761520i	−0.335425	−	0.942067i	$-0.608880\pi$
$31$	−40.8887	−	23.6071i	−1.31899	−	0.761520i	−0.983566	+	0.180547i	$0.942213\pi$
$32$		0			0
$33$	−15.8296	+	11.2550i	−0.479686	+	0.341062i
$34$		0			0
$35$	−1.55168	+	2.68759i	−0.0443338	+	0.0767884i
$36$		0			0
$37$			47.4213i			1.28166i	0.767684	+	0.640828i	$0.221409\pi$
$37$			47.4213i			1.28166i	−0.767684	+	0.640828i	$0.778591\pi$
$38$		0			0
$39$	28.9956	−	2.74765i	0.743476	−	0.0704525i
$40$		0			0
$41$	−6.34554	+	3.66360i	−0.154769	+	0.0893561i	−0.575385	−	0.817883i	$-0.695148\pi$
$41$	−6.34554	+	3.66360i	−0.154769	+	0.0893561i	0.420615	+	0.907239i	$0.361814\pi$
$42$		0			0
$43$	−62.8168			−1.46086			−0.730428	−	0.682989i	$-0.760680\pi$
$43$	−62.8168			−1.46086			−0.730428	+	0.682989i	$0.760680\pi$
$44$		0			0
$45$	−19.4559	−	22.5189i	−0.432354	−	0.500419i
$46$		0			0
$47$	−20.9612	+	36.3058i	−0.445983	+	0.772465i	−0.998120	−	0.0612883i	$-0.980479\pi$
$47$	−20.9612	+	36.3058i	−0.445983	+	0.772465i	0.552137	+	0.833753i	$0.313812\pi$
$48$		0			0
$49$	24.0596	−	41.6724i	0.491012	−	0.850457i
$50$		0			0
$51$	6.89379	+	3.15430i	0.135172	+	0.0618489i
$52$		0			0
$53$	26.2764	−	15.1707i	0.495780	−	0.286239i	−0.231189	−	0.972909i	$-0.574262\pi$
$53$	26.2764	−	15.1707i	0.495780	−	0.286239i	0.726969	+	0.686670i	$0.240928\pi$
$54$		0			0
$55$	10.7041	−	18.5400i	0.194620	−	0.337091i
$56$		0			0
$57$	37.5193	+	42.9104i	0.658234	+	0.752814i
$58$		0			0
$59$	66.5860	−	38.4435i	1.12858	−	0.651584i	0.185000	−	0.982738i	$-0.440771\pi$
$59$	66.5860	−	38.4435i	1.12858	−	0.651584i	0.943577	+	0.331154i	$0.107438\pi$
$60$		0			0
$61$	−50.0409	+	86.6734i	−0.820343	+	1.42088i	0.0850836	+	0.996374i	$0.472884\pi$
$61$	−50.0409	+	86.6734i	−0.820343	+	1.42088i	−0.905427	+	0.424502i	$0.860449\pi$
$62$		0			0
$63$	−5.52226	−	6.39162i	−0.0876549	−	0.101454i
$64$		0			0
$65$	−27.8014	+	16.0511i	−0.427713	+	0.246940i
$66$		0			0
$67$		−	22.8794i		−	0.341483i	−0.985316	−	0.170742i	$-0.945384\pi$
$67$		−	22.8794i		−	0.341483i	0.985316	−	0.170742i	$-0.0546163\pi$
$68$		0			0
$69$	12.2952	+	129.750i	0.178192	+	1.88043i
$70$		0			0
$71$	4.42365	+	2.55400i	0.0623050	+	0.0359718i	0.530829	−	0.847479i	$-0.321881\pi$
$71$	4.42365	+	2.55400i	0.0623050	+	0.0359718i	−0.468524	+	0.883451i	$0.655214\pi$
$72$		0			0
$73$	−42.4021	+	73.4425i	−0.580850	+	1.00606i	0.414529	+	0.910036i	$0.363946\pi$
$73$	−42.4021	+	73.4425i	−0.580850	+	1.00606i	−0.995379	+	0.0960259i	$0.969387\pi$
$74$		0			0
$75$	−38.3727	−	17.5577i	−0.511637	−	0.234103i
$76$		0			0
$77$	3.03818	−	5.26228i	0.0394569	−	0.0683414i
$78$		0			0
$79$			111.844i			1.41575i	0.706338	+	0.707874i	$0.250346\pi$
$79$			111.844i			1.41575i	−0.706338	+	0.707874i	$0.749654\pi$
$80$		0			0
$81$	75.2843	−	29.8877i	0.929436	−	0.368984i
$82$		0			0
$83$	46.4633	+	80.4768i	0.559798	+	0.969599i	0.997513	+	0.0704853i	$0.0224548\pi$
$83$	46.4633	+	80.4768i	0.559798	+	0.969599i	−0.437714	+	0.899114i	$0.644212\pi$
$84$		0			0
$85$	−8.35599			−0.0983058
$86$		0			0
$87$	24.9355	−	54.4972i	0.286615	−	0.626404i
$88$		0			0
$89$	−88.1242	+	50.8785i	−0.990160	+	0.571669i	−0.905322	−	0.424726i	$-0.860371\pi$
$89$	−88.1242	+	50.8785i	−0.990160	+	0.571669i	−0.0848378	+	0.996395i	$0.527037\pi$
$90$		0			0
$91$	−7.89098	+	4.55586i	−0.0867140	+	0.0500644i
$92$		0			0
$93$	−58.9334	+	128.800i	−0.633692	+	1.38495i
$94$		0			0
$95$	−57.2831	−	25.8017i	−0.602980	−	0.271597i
$96$		0			0
$97$			83.1892i			0.857621i	0.903395	+	0.428810i	$0.141067\pi$
$97$			83.1892i			0.857621i	−0.903395	+	0.428810i	$0.858933\pi$
$98$		0			0
$99$	38.0945	+	44.0917i	0.384793	+	0.445371i
$100$		0			0
$101$	−4.92072	+	8.52294i	−0.0487200	+	0.0843856i	−0.889357	−	0.457213i	$-0.848848\pi$
$101$	−4.92072	+	8.52294i	−0.0487200	+	0.0843856i	0.840637	+	0.541599i	$0.182181\pi$
$102$		0			0
$103$	111.897	+	64.6035i	1.08637	+	0.627218i	0.932609	−	0.360889i	$-0.117527\pi$
$103$	111.897	+	64.6035i	1.08637	+	0.627218i	0.153765	+	0.988107i	$0.450860\pi$
$104$		0			0
$105$	8.46597	+	3.87366i	0.0806283	+	0.0368920i
$106$		0			0
$107$		−	149.653i		−	1.39863i	−0.714814	−	0.699314i	$-0.753489\pi$
$107$		−	149.653i		−	1.39863i	0.714814	−	0.699314i	$-0.246511\pi$
$108$		0			0
$109$	−16.9036	−	9.75927i	−0.155078	−	0.0895346i	0.420453	−	0.907315i	$-0.361871\pi$
$109$	−16.9036	−	9.75927i	−0.155078	−	0.0895346i	−0.575531	+	0.817780i	$0.695205\pi$
$110$		0			0
$111$	141.629	−	13.4209i	1.27594	−	0.120909i
$112$		0			0
$113$	−126.156	−	72.8365i	−1.11643	−	0.644570i	−0.175942	−	0.984401i	$-0.556297\pi$
$113$	−126.156	−	72.8365i	−1.11643	−	0.644570i	−0.940487	+	0.339830i	$0.889630\pi$
$114$		0			0
$115$	−71.8259	−	124.406i	−0.624573	−	1.08179i
$116$		0			0
$117$	−16.4124	−	85.8211i	−0.140277	−	0.733514i
$118$		0			0
$119$	−2.37172			−0.0199304
$120$		0			0
$121$	39.5415	−	68.4879i	0.326789	−	0.566016i
$122$		0			0
$123$	12.7377	+	17.9149i	0.103558	+	0.145649i
$124$		0			0
$125$	129.177			1.03342
$126$		0			0
$127$	−36.0768	+	20.8289i	−0.284069	+	0.164007i	−0.635264	−	0.772295i	$-0.719109\pi$
$127$	−36.0768	+	20.8289i	−0.284069	+	0.164007i	0.351195	+	0.936302i	$0.385775\pi$
$128$		0			0
$129$	17.7781	+	187.610i	0.137815	+	1.45434i
$130$		0			0
$131$	−99.5045	−	172.347i	−0.759576	−	1.31562i	−0.943067	−	0.332603i	$-0.892073\pi$
$131$	−99.5045	−	172.347i	−0.759576	−	1.31562i	0.183491	−	0.983021i	$-0.441260\pi$
$132$		0			0
$133$	−16.2589	−	7.32339i	−0.122247	−	0.0550631i
$134$		0			0
$135$	−61.7490	+	64.4807i	−0.457400	+	0.477634i
$136$		0			0
$137$	112.883	−	195.518i	0.823960	−	1.42714i	−0.0787510	−	0.996894i	$-0.525093\pi$
$137$	112.883	−	195.518i	0.823960	−	1.42714i	0.902711	−	0.430247i	$-0.141573\pi$
$138$		0			0
$139$	−226.405			−1.62882			−0.814408	−	0.580293i	$-0.802938\pi$
$139$	−226.405			−1.62882			−0.814408	+	0.580293i	$0.802938\pi$
$140$		0			0
$141$	114.364	+	52.3280i	0.811093	+	0.371121i
$142$		0			0
$143$	54.4348	−	31.4280i	0.380663	−	0.219776i
$144$		0			0
$145$			66.0563i			0.455561i
$146$		0			0
$147$	−131.269	−	60.0629i	−0.892986	−	0.408591i
$148$		0			0
$149$	30.4398	+	52.7233i	0.204294	+	0.353847i	0.949908	−	0.312531i	$-0.101177\pi$
$149$	30.4398	+	52.7233i	0.204294	+	0.353847i	−0.745614	+	0.666379i	$0.767844\pi$
$150$		0			0
$151$	−150.252	+	86.7480i	−0.995046	+	0.574490i	−0.906779	−	0.421607i	$-0.861466\pi$
$151$	−150.252	+	86.7480i	−0.995046	+	0.574490i	−0.0882673	+	0.996097i	$0.528133\pi$
$152$		0			0
$153$	7.46964	−	21.4818i	0.0488212	−	0.140404i
$154$		0			0
$155$		−	156.119i		−	1.00722i
$156$		0			0
$157$	2.13088	+	3.69079i	0.0135725	+	0.0235082i	0.872732	−	0.488200i	$-0.162346\pi$
$157$	2.13088	+	3.69079i	0.0135725	+	0.0235082i	−0.859159	+	0.511708i	$0.829013\pi$
$158$		0			0
$159$	−52.7456	−	74.1840i	−0.331734	−	0.466566i
$160$		0			0
$161$	−20.3866	−	35.3107i	−0.126625	−	0.219321i
$162$		0			0
$163$	160.906			0.987155			0.493577	−	0.869702i	$-0.335689\pi$
$163$	160.906			0.987155			0.493577	+	0.869702i	$0.335689\pi$
$164$		0			0
$165$	−58.4014	−	26.7219i	−0.353948	−	0.161951i
$166$		0			0
$167$		−	138.295i		−	0.828114i	−0.910251	−	0.414057i	$-0.864111\pi$
$167$		−	138.295i		−	0.828114i	0.910251	−	0.414057i	$-0.135889\pi$
$168$		0			0
$169$	74.7453			0.442280
$170$		0			0
$171$	117.538	−	124.200i	0.687360	−	0.726317i
$172$		0			0
$173$		−	222.132i		−	1.28400i	−0.766705	−	0.642000i	$-0.778105\pi$
$173$		−	222.132i		−	1.28400i	0.766705	−	0.642000i	$-0.221895\pi$
$174$		0			0
$175$	13.2016			0.0754379
$176$		0			0
$177$	−133.661	−	187.987i	−0.755146	−	1.06207i
$178$		0			0
$179$		−	266.245i		−	1.48740i	−0.668513	−	0.743701i	$-0.733069\pi$
$179$		−	266.245i		−	1.48740i	0.668513	−	0.743701i	$-0.266931\pi$
$180$		0			0
$181$	−156.234	+	90.2018i	−0.863172	+	0.498352i	−0.865073	−	0.501646i	$-0.832728\pi$
$181$	−156.234	+	90.2018i	−0.863172	+	0.498352i	0.00190136	+	0.999998i	$0.499395\pi$
$182$		0			0
$183$	273.023	+	124.923i	1.49193	+	0.682641i
$184$		0			0
$185$	−135.796	+	78.4021i	−0.734035	+	0.423795i
$186$		0			0
$187$	16.3610			0.0874918
$188$		0			0
$189$	−17.5265	+	18.3018i	−0.0927326	+	0.0968350i
$190$		0			0
$191$	182.479	+	316.064i	0.955389	+	1.65478i	0.733474	+	0.679717i	$0.237897\pi$
$191$	182.479	+	316.064i	0.955389	+	1.65478i	0.221915	+	0.975066i	$0.428769\pi$
$192$		0			0
$193$	−47.1980	+	27.2498i	−0.244549	+	0.141191i	−0.617266	−	0.786755i	$-0.711760\pi$
$193$	−47.1980	+	27.2498i	−0.244549	+	0.141191i	0.372717	+	0.927945i	$0.378426\pi$
$194$		0			0
$195$	55.8068	+	78.4894i	0.286189	+	0.402510i
$196$		0			0
$197$	−196.844			−0.999210			−0.499605	−	0.866253i	$-0.666522\pi$
$197$	−196.844			−0.999210			−0.499605	+	0.866253i	$0.666522\pi$
$198$		0			0
$199$	−43.1118	−	74.6719i	−0.216642	−	0.375236i	0.737137	−	0.675743i	$-0.236177\pi$
$199$	−43.1118	−	74.6719i	−0.216642	−	0.375236i	−0.953779	+	0.300508i	$0.902844\pi$
$200$		0			0
$201$	−68.3320	+	6.47521i	−0.339960	+	0.0322150i
$202$		0			0
$203$			18.7490i			0.0923598i
$204$		0			0
$205$	−20.9823	−	12.1141i	−0.102353	−	0.0590933i
$206$		0			0
$207$	384.034	−	73.4423i	1.85524	−	0.354794i
$208$		0			0
$209$	112.160	+	50.5194i	0.536650	+	0.241720i
$210$		0			0
$211$	63.7790	−	36.8228i	0.302270	−	0.174516i	−0.341192	−	0.939994i	$-0.610831\pi$
$211$	63.7790	−	36.8228i	0.302270	−	0.174516i	0.643462	+	0.765478i	$0.277497\pi$
$212$		0			0
$213$	6.37586	−	13.9346i	0.0299336	−	0.0654206i
$214$		0			0
$215$	−103.856	−	179.883i	−0.483050	−	0.836667i
$216$		0			0
$217$		−	44.3120i		−	0.204203i
$218$		0			0
$219$	231.345	+	105.854i	1.05637	+	0.483349i
$220$		0			0
$221$	−21.2469	−	12.2669i	−0.0961399	−	0.0555064i
$222$		0			0
$223$		−	157.391i		−	0.705790i	−0.935663	−	0.352895i	$-0.885197\pi$
$223$		−	157.391i		−	0.705790i	0.935663	−	0.352895i	$-0.114803\pi$
$224$		0			0
$225$	−41.5781	+	119.574i	−0.184791	+	0.531440i
$226$		0			0
$227$	−55.7254	+	32.1731i	−0.245486	+	0.141732i	−0.617696	−	0.786417i	$-0.711934\pi$
$227$	−55.7254	+	32.1731i	−0.245486	+	0.141732i	0.372209	+	0.928149i	$0.378600\pi$
$228$		0			0
$229$	55.4226	−	95.9948i	0.242020	−	0.419191i	−0.719269	−	0.694731i	$-0.755523\pi$
$229$	55.4226	−	95.9948i	0.242020	−	0.419191i	0.961290	+	0.275540i	$0.0888567\pi$
$230$		0			0
$231$	−16.5763	−	7.58459i	−0.0717589	−	0.0328337i
$232$		0			0
$233$	69.3501	−	120.118i	0.297640	−	0.515528i	−0.677956	−	0.735103i	$-0.737134\pi$
$233$	69.3501	−	120.118i	0.297640	−	0.515528i	0.975596	+	0.219575i	$0.0704671\pi$
$234$		0			0
$235$	−138.621			−0.589878
$236$		0			0
$237$	334.036	−	31.6536i	1.40944	−	0.133559i
$238$		0			0
$239$	159.842	−	276.855i	0.668796	−	1.15839i	−0.309446	−	0.950917i	$-0.600143\pi$
$239$	159.842	−	276.855i	0.668796	−	1.15839i	0.978241	−	0.207471i	$-0.0665232\pi$
$240$		0			0
$241$	−374.229	−	216.061i	−1.55282	−	0.896518i	−0.997911	−	0.0646044i	$-0.979421\pi$
$241$	−374.229	−	216.061i	−1.55282	−	0.896518i	−0.554905	−	0.831914i	$-0.687245\pi$
$242$		0			0
$243$	−110.570	−	216.387i	−0.455020	−	0.890481i
$244$		0			0
$245$	159.112			0.649436
$246$		0			0
$247$	−107.777	−	149.700i	−0.436343	−	0.606073i
$248$		0			0
$249$	227.204	−	161.544i	0.912465	−	0.648772i
$250$		0			0
$251$	192.373	+	333.199i	0.766425	+	1.32749i	0.939490	+	0.342576i	$0.111300\pi$
$251$	192.373	+	333.199i	0.766425	+	1.32749i	−0.173065	+	0.984910i	$0.555367\pi$
$252$		0			0
$253$	140.634	+	243.586i	0.555867	+	0.962790i
$254$		0			0
$255$	2.36487	+	24.9562i	0.00927401	+	0.0978674i
$256$		0			0
$257$			101.060i			0.393229i	0.980481	+	0.196615i	$0.0629948\pi$
$257$			101.060i			0.393229i	−0.980481	+	0.196615i	$0.937005\pi$
$258$		0			0
$259$	−38.5436	+	22.2532i	−0.148817	+	0.0859196i
$260$		0			0
$261$	−169.820	−	59.0494i	−0.650650	−	0.226243i
$262$		0			0
$263$	242.225			0.921007			0.460504	−	0.887658i	$-0.347669\pi$
$263$	242.225			0.921007			0.460504	+	0.887658i	$0.347669\pi$
$264$		0			0
$265$	86.8859	+	50.1636i	0.327871	+	0.189297i
$266$		0			0
$267$	176.895	+	248.794i	0.662530	+	0.931814i
$268$		0			0
$269$	−113.354	−	65.4450i	−0.421391	−	0.243290i	0.274281	−	0.961649i	$-0.411560\pi$
$269$	−113.354	−	65.4450i	−0.421391	−	0.243290i	−0.695672	+	0.718359i	$0.744893\pi$
$270$		0			0
$271$	−7.21325	+	12.4937i	−0.0266172	+	0.0461023i	−0.879027	−	0.476772i	$-0.841807\pi$
$271$	−7.21325	+	12.4937i	−0.0266172	+	0.0461023i	0.852410	+	0.522874i	$0.175140\pi$
$272$		0			0
$273$	15.8399	+	22.2780i	0.0580216	+	0.0816043i
$274$		0			0
$275$	−91.0697			−0.331163
$276$		0			0
$277$	66.5611	+	115.287i	0.240293	+	0.416199i	0.960798	−	0.277251i	$-0.0894232\pi$
$277$	66.5611	+	115.287i	0.240293	+	0.416199i	−0.720505	+	0.693450i	$0.756090\pi$
$278$		0			0
$279$	401.357	+	139.559i	1.43855	+	0.500212i
$280$		0			0
$281$	52.2796	+	30.1836i	0.186048	+	0.107415i	0.590131	−	0.807307i	$-0.299076\pi$
$281$	52.2796	+	30.1836i	0.186048	+	0.107415i	−0.404083	+	0.914722i	$0.632409\pi$
$282$		0			0
$283$	208.370	+	360.908i	0.736291	+	1.27529i	0.954155	+	0.299314i	$0.0967576\pi$
$283$	208.370	+	360.908i	0.736291	+	1.27529i	−0.217864	+	0.975979i	$0.569909\pi$
$284$		0			0
$285$	−60.8478	+	178.385i	−0.213501	+	0.625912i
$286$		0			0
$287$	−5.95549	−	3.43840i	−0.0207508	−	0.0119805i
$288$		0			0
$289$	141.307	+	244.751i	0.488952	+	0.846889i
$290$		0			0
$291$	248.455	−	23.5438i	0.853796	−	0.0809065i
$292$		0			0
$293$	−217.396	−	125.514i	−0.741968	−	0.428375i	0.0808167	−	0.996729i	$-0.474247\pi$
$293$	−217.396	−	125.514i	−0.741968	−	0.428375i	−0.822784	+	0.568354i	$0.807580\pi$
$294$		0			0
$295$	220.175	+	127.118i	0.746355	+	0.430908i
$296$		0			0
$297$	120.904	−	126.253i	0.407084	−	0.425093i
$298$		0			0
$299$		−	421.772i		−	1.41061i
$300$		0			0
$301$	−29.4778	−	51.0570i	−0.0979328	−	0.169625i
$302$		0			0
$303$	26.8474	+	12.2842i	0.0886054	+	0.0405419i
$304$		0			0
$305$	−330.933			−1.08502
$306$		0			0
$307$	−417.994	−	241.329i	−1.36155	−	0.786089i	−0.371716	−	0.928347i	$-0.621230\pi$
$307$	−417.994	−	241.329i	−1.36155	−	0.786089i	−0.989830	+	0.142258i	$0.954564\pi$
$308$		0			0
$309$	161.278	−	352.476i	0.521934	−	1.14070i
$310$		0			0
$311$	249.109	−	431.470i	0.800995	−	1.38736i	−0.117967	−	0.993017i	$-0.537638\pi$
$311$	249.109	−	431.470i	0.800995	−	1.38736i	0.918962	−	0.394346i	$-0.129029\pi$
$312$		0			0
$313$	−124.958	+	216.434i	−0.399227	+	0.691482i	−0.993631	−	0.112685i	$-0.964055\pi$
$313$	−124.958	+	216.434i	−0.399227	+	0.691482i	0.594403	+	0.804167i	$0.297388\pi$
$314$		0			0
$315$	9.17315	−	26.3809i	0.0291211	−	0.0837490i
$316$		0			0
$317$	271.158	+	156.553i	0.855389	+	0.493859i	0.862466	−	0.506116i	$-0.168919\pi$
$317$	271.158	+	156.553i	0.855389	+	0.493859i	−0.00707617	+	0.999975i	$0.502252\pi$
$318$		0			0
$319$		−	129.338i		−	0.405447i
$320$		0			0
$321$	−446.958	+	42.3541i	−1.39239	+	0.131944i
$322$		0			0
$323$	−4.81214	−	47.7722i	−0.0148983	−	0.147902i
$324$		0			0
$325$	118.266	+	68.2811i	0.363896	+	0.210096i
$326$		0			0
$327$	−24.3633	+	53.2465i	−0.0745054	+	0.162833i
$328$		0			0
$329$	−39.3455			−0.119591
$330$		0			0
$331$	−197.344	+	113.937i	−0.596205	+	0.344219i	−0.767547	−	0.640992i	$-0.778523\pi$
$331$	−197.344	+	113.937i	−0.596205	+	0.344219i	0.171342	+	0.985212i	$0.445190\pi$
$332$		0			0
$333$	−80.1666	−	419.195i	−0.240740	−	1.25884i
$334$		0			0
$335$	65.5177	−	37.8267i	0.195575	−	0.112915i
$336$		0			0
$337$	−111.371	+	64.3001i	−0.330478	+	0.190801i	−0.656053	−	0.754715i	$-0.727775\pi$
$337$	−111.371	+	64.3001i	−0.330478	+	0.190801i	0.325575	+	0.945516i	$0.394442\pi$
$338$		0			0
$339$	−181.831	+	397.395i	−0.536374	+	1.17226i
$340$		0			0
$341$			305.681i			0.896424i
$342$		0			0
$343$	91.1494			0.265742
$344$		0			0
$345$	−351.226	+	249.725i	−1.01805	+	0.723842i
$346$		0			0
$347$	−123.034	−	213.102i	−0.354566	−	0.614127i	0.632477	−	0.774579i	$-0.282038\pi$
$347$	−123.034	−	213.102i	−0.354566	−	0.614127i	−0.987044	+	0.160452i	$0.948705\pi$
$348$		0			0
$349$	−232.101	−	402.011i	−0.665047	−	1.15189i	−0.979273	−	0.202547i	$-0.935078\pi$
$349$	−232.101	−	402.011i	−0.665047	−	1.15189i	0.314226	−	0.949348i	$-0.398255\pi$
$350$		0			0
$351$	−251.670	+	73.3062i	−0.717009	+	0.208850i
$352$		0			0
$353$	247.665	+	428.968i	0.701600	+	1.21521i	0.967904	+	0.251318i	$0.0808641\pi$
$353$	247.665	+	428.968i	0.701600	+	1.21521i	−0.266304	+	0.963889i	$0.585803\pi$
$354$		0			0
$355$			16.8902i			0.0475780i
$356$		0			0
$357$	0.671232	+	7.08342i	0.00188020	+	0.0198415i
$358$		0			0
$359$	26.1525	−	45.2974i	0.0728482	−	0.126177i	−0.827300	−	0.561760i	$-0.810124\pi$
$359$	26.1525	−	45.2974i	0.0728482	−	0.126177i	0.900148	+	0.435583i	$0.143458\pi$
$360$		0			0
$361$	114.522	−	342.353i	0.317237	−	0.948346i
$362$		0			0
$363$	−215.738	−	98.7124i	−0.594320	−	0.271935i
$364$		0			0
$365$	−280.415			−0.768260
$366$		0			0
$367$	31.7890	−	55.0601i	0.0866184	−	0.150028i	−0.819461	−	0.573135i	$-0.805727\pi$
$367$	31.7890	−	55.0601i	0.0866184	−	0.150028i	0.906080	+	0.423107i	$0.139061\pi$
$368$		0			0
$369$	49.9000	−	43.1128i	0.135230	−	0.116837i
$370$		0			0
$371$	24.6612	+	14.2381i	0.0664722	+	0.0383777i
$372$		0			0
$373$	−157.808	−	91.1106i	−0.423078	−	0.244264i	0.273315	−	0.961924i	$-0.411880\pi$
$373$	−157.808	−	91.1106i	−0.423078	−	0.244264i	−0.696393	+	0.717660i	$0.745213\pi$
$374$		0			0
$375$	−36.5591	−	385.803i	−0.0974910	−	1.02881i
$376$		0			0
$377$	−96.9732	+	167.962i	−0.257223	+	0.445524i
$378$		0			0
$379$			348.320i			0.919051i	0.888165	+	0.459526i	$0.151981\pi$
$379$			348.320i			0.919051i	−0.888165	+	0.459526i	$0.848019\pi$
$380$		0			0
$381$	72.4184	+	101.853i	0.190074	+	0.267330i
$382$		0			0
$383$	−525.677	+	303.499i	−1.37252	+	0.792427i	−0.991245	−	0.132033i	$-0.957849\pi$
$383$	−525.677	+	303.499i	−1.37252	+	0.792427i	−0.381278	+	0.924460i	$0.624516\pi$
$384$		0			0
$385$	20.0922			0.0521876
$386$		0			0
$387$	555.289	−	106.193i	1.43485	−	0.274401i
$388$		0			0
$389$	−256.650	+	444.530i	−0.659768	+	1.14275i	0.320908	+	0.947110i	$0.396012\pi$
$389$	−256.650	+	444.530i	−0.659768	+	1.14275i	−0.980676	+	0.195641i	$0.937321\pi$
$390$		0			0
$391$	54.8922	−	95.0761i	0.140389	−	0.243161i
$392$		0			0
$393$	−486.573	+	345.959i	−1.23810	+	0.880302i
$394$		0			0
$395$	−320.279	+	184.913i	−0.810832	+	0.468134i
$396$		0			0
$397$	270.903	−	469.219i	0.682376	−	1.18191i	−0.291877	−	0.956456i	$-0.594280\pi$
$397$	270.903	−	469.219i	0.682376	−	1.18191i	0.974254	−	0.225455i	$-0.0723868\pi$
$398$		0			0
$399$	−17.2707	+	50.6318i	−0.0432849	+	0.126897i
$400$		0			0
$401$	−88.0777	+	50.8517i	−0.219645	+	0.126812i	−0.605786	−	0.795628i	$-0.707141\pi$
$401$	−88.0777	+	50.8517i	−0.219645	+	0.126812i	0.386141	+	0.922440i	$0.373808\pi$
$402$		0			0
$403$	229.189	−	396.968i	0.568708	−	0.985031i
$404$		0			0
$405$	210.055	+	166.172i	0.518655	+	0.410301i
$406$		0			0
$407$	265.888	−	153.511i	0.653288	−	0.377176i
$408$		0			0
$409$			105.270i			0.257384i	0.991685	+	0.128692i	$0.0410779\pi$
$409$			105.270i			0.257384i	−0.991685	+	0.128692i	$0.958922\pi$
$410$		0			0
$411$	−615.887	−	281.803i	−1.49851	−	0.685651i
$412$		0			0
$413$	62.4931	+	36.0804i	0.151315	+	0.0873617i
$414$		0			0
$415$	−153.636	+	266.106i	−0.370208	+	0.641219i
$416$		0			0
$417$	64.0762	+	676.187i	0.153660	+	1.62155i
$418$		0			0
$419$	241.360	−	418.048i	0.576038	−	0.997728i	−0.419890	−	0.907575i	$-0.637931\pi$
$419$	241.360	−	418.048i	0.576038	−	0.997728i	0.995928	−	0.0901524i	$-0.0287354\pi$
$420$		0			0
$421$		−	138.743i		−	0.329556i	−0.986331	−	0.164778i	$-0.947309\pi$
$421$		−	138.743i		−	0.329556i	0.986331	−	0.164778i	$-0.0526908\pi$
$422$		0			0
$423$	123.917	−	356.372i	0.292948	−	0.842487i
$424$		0			0
$425$	17.7731	+	30.7839i	0.0418190	+	0.0724327i
$426$		0			0
$427$	−93.9300			−0.219977
$428$		0			0
$429$	−109.269	−	153.682i	−0.254707	−	0.358232i
$430$		0			0
$431$	−390.007	+	225.170i	−0.904888	+	0.522437i	−0.878783	−	0.477222i	$-0.841644\pi$
$431$	−390.007	+	225.170i	−0.904888	+	0.522437i	−0.0261049	+	0.999659i	$0.508310\pi$
$432$		0			0
$433$	−53.5521	+	30.9183i	−0.123677	+	0.0714049i	−0.560562	−	0.828112i	$-0.689415\pi$
$433$	−53.5521	+	30.9183i	−0.123677	+	0.0714049i	0.436885	+	0.899517i	$0.356082\pi$
$434$		0			0
$435$	197.285	−	18.6949i	0.453529	−	0.0429769i
$436$		0			0
$437$	669.880	−	482.281i	1.53291	−	1.10362i
$438$		0			0
$439$			380.623i			0.867023i	0.901148	+	0.433512i	$0.142726\pi$
$439$			380.623i			0.867023i	−0.901148	+	0.433512i	$0.857274\pi$
$440$		0			0
$441$	−142.234	+	409.049i	−0.322526	+	0.927549i
$442$		0			0
$443$	274.799	−	475.966i	0.620314	−	1.07441i	−0.369114	−	0.929384i	$-0.620339\pi$
$443$	274.799	−	475.966i	0.620314	−	1.07441i	0.989427	−	0.145030i	$-0.0463280\pi$
$444$		0			0
$445$	−291.393	−	168.236i	−0.654816	−	0.378058i
$446$		0			0
$447$	148.849	−	105.834i	0.332997	−	0.236764i
$448$		0			0
$449$			279.754i			0.623060i	0.950236	+	0.311530i	$0.100841\pi$
$449$			279.754i			0.623060i	−0.950236	+	0.311530i	$0.899159\pi$
$450$		0			0
$451$	41.0831	+	23.7194i	0.0910934	+	0.0525928i
$452$		0			0
$453$	301.607	+	424.195i	0.665799	+	0.936412i
$454$		0			0
$455$	−26.0925	−	15.0645i	−0.0573461	−	0.0331088i
$456$		0			0
$457$	232.179	+	402.145i	0.508049	+	0.879967i	0.999957	+	0.00931954i	$0.00296654\pi$
$457$	232.179	+	402.145i	0.508049	+	0.879967i	−0.491907	+	0.870648i	$0.663700\pi$
$458$		0			0
$459$	−66.2721	−	16.2293i	−0.144384	−	0.0353579i
$460$		0			0
$461$	−194.100			−0.421042			−0.210521	−	0.977589i	$-0.567516\pi$
$461$	−194.100			−0.421042			−0.210521	+	0.977589i	$0.567516\pi$
$462$		0			0
$463$	−282.866	+	489.938i	−0.610941	+	1.05818i	0.380141	+	0.924929i	$0.375876\pi$
$463$	−282.866	+	489.938i	−0.610941	+	1.05818i	−0.991082	+	0.133253i	$0.957458\pi$
$464$		0			0
$465$	−466.270	+	44.1842i	−1.00273	+	0.0950197i
$466$		0			0
$467$	100.230			0.214625			0.107312	−	0.994225i	$-0.465776\pi$
$467$	100.230			0.214625			0.107312	+	0.994225i	$0.465776\pi$
$468$		0			0
$469$	18.5962	−	10.7365i	0.0396507	−	0.0228923i
$470$		0			0
$471$	10.4199	−	7.40868i	0.0221230	−	0.0157297i
$472$		0			0
$473$	203.349	+	352.210i	0.429912	+	0.744630i
$474$		0			0
$475$	26.7857	+	265.913i	0.0563910	+	0.559818i
$476$		0			0
$477$	−206.632	+	178.526i	−0.433190	+	0.374269i
$478$		0			0
$479$	−326.218	+	565.026i	−0.681040	+	1.17960i	0.293624	+	0.955921i	$0.405139\pi$
$479$	−326.218	+	565.026i	−0.681040	+	1.17960i	−0.974664	+	0.223675i	$0.928195\pi$
$480$		0			0
$481$	−460.389			−0.957150
$482$		0			0
$483$	−99.6899	+	70.8806i	−0.206397	+	0.146751i
$484$		0			0
$485$	−238.222	+	137.537i	−0.491179	+	0.283582i
$486$		0			0
$487$			730.195i			1.49937i	0.661793	+	0.749687i	$0.269796\pi$
$487$			730.195i			1.49937i	−0.661793	+	0.749687i	$0.730204\pi$
$488$		0			0
$489$	−45.5389	−	480.566i	−0.0931266	−	0.982752i
$490$		0			0
$491$	−488.048	−	845.324i	−0.993987	−	1.72164i	−0.591818	−	0.806071i	$-0.701590\pi$
$491$	−488.048	−	845.324i	−0.993987	−	1.72164i	−0.402169	−	0.915565i	$-0.631744\pi$
$492$		0			0
$493$	−43.7195	+	25.2414i	−0.0886804	+	0.0511997i
$494$		0			0
$495$	−63.2797	+	181.985i	−0.127838	+	0.367647i
$496$		0			0
$497$			4.79401i			0.00964590i
$498$		0			0
$499$	−50.1197	−	86.8098i	−0.100440	−	0.173968i	0.811426	−	0.584455i	$-0.198692\pi$
$499$	−50.1197	−	86.8098i	−0.100440	−	0.173968i	−0.911866	+	0.410488i	$0.865358\pi$
$500$		0			0
$501$	−413.035	+	39.1396i	−0.824421	+	0.0781229i
$502$		0			0
$503$	363.502	+	629.603i	0.722667	+	1.25170i	0.959927	+	0.280250i	$0.0904175\pi$
$503$	363.502	+	629.603i	0.722667	+	1.25170i	−0.237260	+	0.971446i	$0.576249\pi$
$504$		0			0
$505$	−32.5419			−0.0644394
$506$		0			0
$507$	−21.1541	−	223.236i	−0.0417240	−	0.440308i
$508$		0			0
$509$			427.606i			0.840090i	0.907503	+	0.420045i	$0.137986\pi$
$509$			427.606i			0.840090i	−0.907503	+	0.420045i	$0.862014\pi$
$510$		0			0
$511$	−79.5913			−0.155756
$512$		0			0
$513$	−404.204	−	315.892i	−0.787922	−	0.615775i
$514$		0			0
$515$			427.238i			0.829589i
$516$		0			0
$517$	271.419			0.524989
$518$		0			0
$519$	−663.424	+	62.8667i	−1.27827	+	0.121130i
$520$		0			0
$521$			239.575i			0.459837i	0.973210	+	0.229918i	$0.0738459\pi$
$521$			239.575i			0.459837i	−0.973210	+	0.229918i	$0.926154\pi$
$522$		0			0
$523$	626.617	−	361.778i	1.19812	−	0.691735i	0.237985	−	0.971269i	$-0.423513\pi$
$523$	626.617	−	361.778i	1.19812	−	0.691735i	0.960136	+	0.279534i	$0.0901798\pi$
$524$		0			0
$525$	−3.73626	−	39.4283i	−0.00711669	−	0.0751015i
$526$		0			0
$527$	103.328	−	59.6564i	0.196068	−	0.113200i
$528$		0			0
$529$	1358.35			2.56778
$530$		0			0
$531$	−523.618	+	452.398i	−0.986098	+	0.851973i
$532$		0			0
$533$	−35.5680	−	61.6056i	−0.0667317	−	0.115583i
$534$		0			0
$535$	428.549	−	247.423i	0.801027	−	0.462473i
$536$		0			0
$537$	−795.172	+	75.3513i	−1.48077	+	0.140319i
$538$		0			0
$539$	−311.539			−0.577995
$540$		0			0
$541$	219.332	+	379.894i	0.405420	+	0.702207i	0.994370	−	0.105962i	$-0.0337921\pi$
$541$	219.332	+	379.894i	0.405420	+	0.702207i	−0.588951	+	0.808169i	$0.700459\pi$
$542$		0			0
$543$	313.615	+	441.083i	0.577560	+	0.812308i
$544$		0			0
$545$		−	64.5404i		−	0.118423i
$546$		0			0
$547$	−507.581	−	293.052i	−0.927937	−	0.535744i	−0.0417783	−	0.999127i	$-0.513302\pi$
$547$	−507.581	−	293.052i	−0.927937	−	0.535744i	−0.886158	+	0.463382i	$0.846636\pi$
$548$		0			0
$549$	295.829	−	850.771i	0.538851	−	1.54967i
$550$		0			0
$551$	−377.652	+	38.0412i	−0.685393	+	0.0690403i
$552$		0			0
$553$	−90.9060	+	52.4846i	−0.164387	+	0.0949089i
$554$		0			0
$555$	272.590	+	383.383i	0.491153	+	0.690781i
$556$		0			0
$557$	317.743	+	550.346i	0.570454	+	0.988055i	0.996519	+	0.0833624i	$0.0265659\pi$
$557$	317.743	+	550.346i	0.570454	+	0.988055i	−0.426066	+	0.904692i	$0.640101\pi$
$558$		0			0
$559$		−	609.856i		−	1.09098i
$560$		0			0
$561$	−4.63040	−	48.8640i	−0.00825383	−	0.0871016i
$562$		0			0
$563$	532.494	+	307.435i	0.945814	+	0.546066i	0.891778	−	0.452473i	$-0.149458\pi$
$563$	532.494	+	307.435i	0.945814	+	0.546066i	0.0540362	+	0.998539i	$0.482791\pi$
$564$		0			0
$565$		−	481.685i		−	0.852540i
$566$		0			0
$567$	59.6208	+	47.1652i	0.105151	+	0.0831838i
$568$		0			0
$569$	−88.0952	+	50.8618i	−0.154825	+	0.0893880i	−0.575411	−	0.817865i	$-0.695158\pi$
$569$	−88.0952	+	50.8618i	−0.154825	+	0.0893880i	0.420586	+	0.907253i	$0.361824\pi$
$570$		0			0
$571$	−257.573	+	446.130i	−0.451092	+	0.781314i	−0.998454	−	0.0555819i	$-0.982299\pi$
$571$	−257.573	+	446.130i	−0.451092	+	0.781314i	0.547362	+	0.836896i	$0.315632\pi$
$572$		0			0
$573$	892.318	−	634.447i	1.55727	−	1.10724i
$574$		0			0
$575$	−305.545	+	529.220i	−0.531383	+	0.920383i
$576$		0			0
$577$	380.264			0.659037			0.329519	−	0.944149i	$-0.393114\pi$
$577$	380.264			0.659037			0.329519	+	0.944149i	$0.393114\pi$
$578$		0			0
$579$	94.7425	+	133.250i	0.163631	+	0.230139i
$580$		0			0
$581$	−43.6072	+	75.5299i	−0.0750555	+	0.130000i
$582$		0			0
$583$	−170.122	−	98.2199i	−0.291804	−	0.168473i
$584$		0			0
$585$	218.624	−	188.888i	0.373716	−	0.322885i
$586$		0			0
$587$	−31.2866			−0.0532991			−0.0266496	−	0.999645i	$-0.508484\pi$
$587$	−31.2866			−0.0532991			−0.0266496	+	0.999645i	$0.508484\pi$
$588$		0			0
$589$	892.554	−	89.9078i	1.51537	−	0.152645i
$590$		0			0
$591$	55.7100	+	587.900i	0.0942639	+	0.994754i
$592$		0			0
$593$	354.819	+	614.564i	0.598345	+	1.03636i	0.993065	+	0.117563i	$0.0375081\pi$
$593$	354.819	+	614.564i	0.598345	+	1.03636i	−0.394721	+	0.918801i	$0.629159\pi$
$594$		0			0
$595$	−3.92118	−	6.79168i	−0.00659022	−	0.0114146i
$596$		0			0
$597$	−210.815	+	149.892i	−0.353124	+	0.251075i
$598$		0			0
$599$		−	163.425i		−	0.272830i	−0.990652	−	0.136415i	$-0.956442\pi$
$599$		−	163.425i		−	0.272830i	0.990652	−	0.136415i	$-0.0435580\pi$
$600$		0			0
$601$	−20.4263	+	11.7931i	−0.0339872	+	0.0196225i	−0.516897	−	0.856047i	$-0.672913\pi$
$601$	−20.4263	+	11.7931i	−0.0339872	+	0.0196225i	0.482910	+	0.875670i	$0.339580\pi$
$602$		0			0
$603$	38.6780	+	202.249i	0.0641426	+	0.335405i
$604$		0			0
$605$	261.497			0.432227
$606$		0			0
$607$	169.180	+	97.6760i	0.278715	+	0.160916i	0.632841	−	0.774281i	$-0.281888\pi$
$607$	169.180	+	97.6760i	0.278715	+	0.160916i	−0.354127	+	0.935197i	$0.615222\pi$
$608$		0			0
$609$	55.9963	−	5.30626i	0.0919479	−	0.00871307i
$610$		0			0
$611$	−352.475	−	203.501i	−0.576882	−	0.333063i
$612$		0			0
$613$	213.026	−	368.971i	0.347513	−	0.601911i	−0.638294	−	0.769793i	$-0.720360\pi$
$613$	213.026	−	368.971i	0.347513	−	0.601911i	0.985807	+	0.167882i	$0.0536928\pi$
$614$		0			0
$615$	−30.2420	+	66.0946i	−0.0491740	+	0.107471i
$616$		0			0
$617$	−509.263			−0.825385			−0.412693	−	0.910870i	$-0.635412\pi$
$617$	−509.263			−0.825385			−0.412693	+	0.910870i	$0.635412\pi$
$618$		0			0
$619$	407.902	+	706.508i	0.658970	+	1.14137i	0.980883	+	0.194600i	$0.0623409\pi$
$619$	407.902	+	706.508i	0.658970	+	1.14137i	−0.321913	+	0.946769i	$0.604326\pi$
$620$		0			0
$621$	−328.032	−	1126.18i	−0.528232	−	1.81349i
$622$		0			0
$623$	−82.7073	−	47.7511i	−0.132757	−	0.0766470i
$624$		0			0
$625$	37.7416	+	65.3704i	0.0603866	+	0.104593i
$626$		0			0
$627$	119.139	−	349.276i	0.190015	−	0.557060i
$628$		0			0
$629$	−103.781	−	59.9180i	−0.164994	−	0.0952592i
$630$		0			0
$631$	−292.777	−	507.104i	−0.463989	−	0.803652i	0.535167	−	0.844746i	$-0.320249\pi$
$631$	−292.777	−	507.104i	−0.463989	−	0.803652i	−0.999155	+	0.0410947i	$0.986915\pi$
$632$		0			0
$633$	−128.026	−	180.062i	−0.202253	−	0.284459i
$634$		0			0
$635$	−119.292	−	68.8733i	−0.187862	−	0.108462i
$636$		0			0
$637$	404.576	+	233.582i	0.635127	+	0.366691i
$638$		0			0
$639$	−43.4218	−	15.0986i	−0.0679528	−	0.0236284i
$640$		0			0
$641$		−	463.764i		−	0.723500i	−0.932275	−	0.361750i	$-0.882179\pi$
$641$		−	463.764i		−	0.723500i	0.932275	−	0.361750i	$-0.117821\pi$
$642$		0			0
$643$	269.350	+	466.528i	0.418895	+	0.725548i	0.995829	−	0.0912431i	$-0.0290840\pi$
$643$	269.350	+	466.528i	0.418895	+	0.725548i	−0.576933	+	0.816791i	$0.695751\pi$
$644$		0			0
$645$	−507.850	+	361.087i	−0.787365	+	0.559825i
$646$		0			0
$647$	331.854			0.512912			0.256456	−	0.966556i	$-0.417445\pi$
$647$	331.854			0.512912			0.256456	+	0.966556i	$0.417445\pi$
$648$		0			0
$649$	−431.100	−	248.896i	−0.664253	−	0.383506i
$650$		0			0
$651$	−132.343	+	12.5410i	−0.203292	+	0.0192642i
$652$		0			0
$653$	−368.959	+	639.055i	−0.565021	+	0.978645i	0.432027	+	0.901861i	$0.357799\pi$
$653$	−368.959	+	639.055i	−0.565021	+	0.978645i	−0.997048	+	0.0767845i	$0.975535\pi$
$654$		0			0
$655$	329.023	−	569.885i	0.502326	−	0.870054i
$656$		0			0
$657$	250.670	−	720.899i	0.381537	−	1.09726i
$658$		0			0
$659$	−79.3434	−	45.8089i	−0.120400	−	0.0695128i	0.438591	−	0.898687i	$-0.355478\pi$
$659$	−79.3434	−	45.8089i	−0.120400	−	0.0695128i	−0.558990	+	0.829174i	$0.688811\pi$
$660$		0			0
$661$		−	436.659i		−	0.660603i	−0.943875	−	0.330302i	$-0.892850\pi$
$661$		−	436.659i		−	0.660603i	0.943875	−	0.330302i	$-0.107150\pi$
$662$		0			0
$663$	−30.6234	+	66.9282i	−0.0461892	+	0.100948i
$664$		0			0
$665$	−5.90959	−	58.6671i	−0.00888660	−	0.0882211i
$666$		0			0
$667$	−751.601	−	433.937i	−1.12684	−	0.650581i
$668$		0			0
$669$	−470.068	+	44.5441i	−0.702642	+	0.0665831i
$670$		0			0
$671$	647.963			0.965668
$672$		0			0
$673$	−286.025	+	165.136i	−0.425000	+	0.245374i	−0.697214	−	0.716863i	$-0.745577\pi$
$673$	−286.025	+	165.136i	−0.425000	+	0.245374i	0.272214	+	0.962237i	$0.412244\pi$
$674$		0			0
$675$	368.889	+	90.3367i	0.546502	+	0.133832i
$676$		0			0
$677$	617.914	−	356.753i	0.912724	−	0.526961i	0.0314171	−	0.999506i	$-0.489998\pi$
$677$	617.914	−	356.753i	0.912724	−	0.526961i	0.881306	+	0.472545i	$0.156665\pi$
$678$		0			0
$679$	−67.6155	+	39.0378i	−0.0995810	+	0.0574931i
$680$		0			0
$681$	111.860	+	157.325i	0.164258	+	0.231021i
$682$		0			0
$683$			726.833i			1.06418i	0.846689	+	0.532088i	$0.178593\pi$
$683$			726.833i			1.06418i	−0.846689	+	0.532088i	$0.821407\pi$
$684$		0			0
$685$	746.519			1.08981
$686$		0			0
$687$	−302.385	−	138.358i	−0.440153	−	0.201395i
$688$		0			0
$689$	147.284	+	255.104i	0.213765	+	0.370252i
$690$		0			0
$691$	−282.530	−	489.357i	−0.408872	−	0.708187i	0.585892	−	0.810389i	$-0.300744\pi$
$691$	−282.530	−	489.357i	−0.408872	−	0.708187i	−0.994764	+	0.102202i	$0.967411\pi$
$692$		0			0
$693$	−17.9609	+	51.6537i	−0.0259177	+	0.0745363i
$694$		0			0
$695$	−374.318	−	648.338i	−0.538587	−	0.932861i
$696$		0			0
$697$		−	18.5162i		−	0.0265656i
$698$		0			0
$699$	−378.374	−	173.127i	−0.541307	−	0.247679i
$700$		0			0
$701$	131.719	−	228.144i	0.187901	−	0.325455i	−0.756649	−	0.653821i	$-0.773165\pi$
$701$	131.719	−	228.144i	0.187901	−	0.325455i	0.944550	+	0.328367i	$0.106498\pi$
$702$		0			0
$703$	−526.438	−	731.213i	−0.748845	−	1.04013i
$704$		0			0
$705$	39.2319	+	414.009i	0.0556481	+	0.587247i
$706$		0			0
$707$	−9.23650			−0.0130644
$708$		0			0
$709$	374.213	−	648.156i	0.527804	−	0.914183i	−0.471671	−	0.881775i	$-0.656349\pi$
$709$	374.213	−	648.156i	0.527804	−	0.914183i	0.999475	−	0.0324085i	$-0.0103178\pi$
$710$		0			0
$711$	−189.075	−	988.681i	−0.265928	−	1.39055i
$712$		0			0
$713$	1776.36	+	1025.58i	2.49138	+	1.43840i
$714$		0			0
$715$	179.995	+	103.920i	0.251742	+	0.145343i
$716$		0			0
$717$	−872.098	−	399.034i	−1.21631	−	0.556532i
$718$		0			0
$719$	−88.3525	+	153.031i	−0.122882	+	0.212839i	−0.920903	−	0.389791i	$-0.872547\pi$
$719$	−88.3525	+	153.031i	−0.122882	+	0.212839i	0.798021	+	0.602630i	$0.205880\pi$
$720$		0			0
$721$			121.265i			0.168190i
$722$		0			0
$723$	−539.380	+	1178.83i	−0.746030	+	1.63047i
$724$		0			0
$725$	243.355	−	140.501i	0.335662	−	0.193794i
$726$		0			0
$727$	124.579			0.171361			0.0856805	−	0.996323i	$-0.472694\pi$
$727$	124.579			0.171361			0.0856805	+	0.996323i	$0.472694\pi$
$728$		0			0
$729$	−614.973	+	391.471i	−0.843584	+	0.536997i
$730$		0			0
$731$	79.3707	−	137.474i	0.108578	−	0.188063i
$732$		0			0
$733$	210.303	−	364.256i	0.286907	−	0.496938i	−0.686163	−	0.727448i	$-0.740706\pi$
$733$	210.303	−	364.256i	0.286907	−	0.496938i	0.973070	+	0.230510i	$0.0740395\pi$
$734$		0			0
$735$	−45.0310	−	475.206i	−0.0612667	−	0.646539i
$736$		0			0
$737$	−128.283	+	74.0643i	−0.174061	+	0.100494i
$738$		0			0
$739$	−156.056	+	270.296i	−0.211171	+	0.365759i	−0.952081	−	0.305845i	$-0.901061\pi$
$739$	−156.056	+	270.296i	−0.211171	+	0.365759i	0.740910	+	0.671604i	$0.234394\pi$
$740$		0			0
$741$	−416.595	+	364.256i	−0.562206	+	0.491573i
$742$		0			0
$743$	854.420	−	493.300i	1.14996	−	0.663930i	0.201083	−	0.979574i	$-0.435554\pi$
$743$	854.420	−	493.300i	1.14996	−	0.663930i	0.948877	+	0.315645i	$0.102221\pi$
$744$		0			0
$745$	−100.653	+	174.336i	−0.135104	+	0.234008i
$746$		0			0
$747$	−546.774	−	632.852i	−0.731959	−	0.847191i
$748$		0			0
$749$	121.637	−	70.2271i	0.162399	−	0.0937612i
$750$		0			0
$751$			105.285i			0.140193i	0.997540	+	0.0700967i	$0.0223308\pi$
$751$			105.285i			0.140193i	−0.997540	+	0.0700967i	$0.977669\pi$
$752$		0			0
$753$	940.695	−	668.844i	1.24926	−	0.888240i
$754$		0			0
$755$	−496.826	−	286.843i	−0.658048	−	0.379924i
$756$		0			0
$757$	695.420	−	1204.50i	0.918653	−	1.59115i	0.117189	−	0.993110i	$-0.462612\pi$
$757$	695.420	−	1204.50i	0.918653	−	1.59115i	0.801463	−	0.598044i	$-0.204055\pi$
$758$		0			0
$759$	687.697	−	488.960i	0.906057	−	0.644216i
$760$		0			0
$761$	−338.936	+	587.054i	−0.445382	+	0.771424i	−0.998079	−	0.0619582i	$-0.980265\pi$
$761$	−338.936	+	587.054i	−0.445382	+	0.771424i	0.552697	+	0.833382i	$0.313599\pi$
$762$		0			0
$763$		−	18.3188i		−	0.0240089i
$764$		0			0
$765$	73.8654	−	14.1260i	0.0965560	−	0.0184653i
$766$		0			0
$767$	373.228	+	646.449i	0.486607	+	0.842828i
$768$		0			0
$769$	−410.039			−0.533210			−0.266605	−	0.963806i	$-0.585902\pi$
$769$	−410.039			−0.533210			−0.266605	+	0.963806i	$0.585902\pi$
$770$		0			0
$771$	301.828	−	28.6015i	0.391476	−	0.0370966i
$772$		0			0
$773$	−1261.22	+	728.168i	−1.63160	+	0.942003i	−0.647997	+	0.761643i	$0.724393\pi$
$773$	−1261.22	+	728.168i	−1.63160	+	0.942003i	−0.983601	+	0.180360i	$0.942274\pi$
$774$		0			0
$775$	−575.152	+	332.064i	−0.742131	+	0.428470i
$776$		0			0
$777$	77.3703	+	108.817i	0.0995756	+	0.140048i
$778$		0			0
$779$	57.1744	−	126.935i	0.0733946	−	0.162946i
$780$		0			0
$781$		−	33.0709i		−	0.0423442i
$782$		0			0
$783$	−128.297	+	523.898i	−0.163853	+	0.669091i
$784$		0			0
$785$	−7.04601	+	12.2040i	−0.00897581	+	0.0155466i
$786$		0			0
$787$	1224.10	+	706.736i	1.55540	+	0.898013i	0.997687	+	0.0679824i	$0.0216562\pi$
$787$	1224.10	+	706.736i	1.55540	+	0.898013i	0.557718	+	0.830031i	$0.311677\pi$
$788$		0			0
$789$	−68.5533	−	723.434i	−0.0868863	−	0.916900i
$790$		0			0
$791$		−	136.719i		−	0.172843i
$792$		0			0
$793$	−841.468	−	485.822i	−1.06112	−	0.612638i
$794$		0			0
$795$	125.230	−	273.692i	0.157522	−	0.344267i
$796$		0			0
$797$	−12.2359	−	7.06438i	−0.0153524	−	0.00886372i	0.492304	−	0.870423i	$-0.336155\pi$
$797$	−12.2359	−	7.06438i	−0.0153524	−	0.00886372i	−0.507657	+	0.861560i	$0.669488\pi$
$798$		0			0
$799$	−52.9700	−	91.7467i	−0.0662954	−	0.114827i
$800$		0			0
$801$	692.990	−	598.732i	0.865156	−	0.747481i
$802$		0			0
$803$	549.050			0.683749
$804$		0			0
$805$	67.4108	−	116.759i	0.0837402	−	0.145042i
$806$		0			0
$807$	−163.379	+	357.068i	−0.202452	+	0.442463i
$808$		0			0
$809$	−1260.84			−1.55852			−0.779260	−	0.626701i	$-0.784405\pi$
$809$	−1260.84			−1.55852			−0.779260	+	0.626701i	$0.784405\pi$
$810$		0			0
$811$	−128.106	+	73.9620i	−0.157961	+	0.0911985i	−0.576897	−	0.816817i	$-0.695736\pi$
$811$	−128.106	+	73.9620i	−0.157961	+	0.0911985i	0.418936	+	0.908016i	$0.362403\pi$
$812$		0			0
$813$	39.3554	+	18.0073i	0.0484077	+	0.0221492i
$814$		0			0
$815$	266.028	+	460.774i	0.326414	+	0.565366i
$816$		0			0
$817$	968.605	−	697.348i	1.18556	−	0.853548i
$818$		0			0
$819$	62.0529	−	53.6127i	0.0757667	−	0.0654612i
$820$		0			0
$821$	61.5192	−	106.554i	0.0749320	−	0.129786i	−0.826125	−	0.563487i	$-0.809459\pi$
$821$	61.5192	−	106.554i	0.0749320	−	0.129786i	0.901057	+	0.433701i	$0.142793\pi$
$822$		0			0
$823$	−239.361			−0.290840			−0.145420	−	0.989370i	$-0.546453\pi$
$823$	−239.361			−0.290840			−0.145420	+	0.989370i	$0.546453\pi$
$824$		0			0
$825$	25.7741	+	271.991i	0.0312413	+	0.329686i
$826$		0			0
$827$	−1038.77	+	599.733i	−1.25607	+	0.725191i	−0.972308	−	0.233704i	$-0.924915\pi$
$827$	−1038.77	+	599.733i	−1.25607	+	0.725191i	−0.283760	+	0.958895i	$0.591582\pi$
$828$		0			0
$829$		−	411.137i		−	0.495943i	−0.968767	−	0.247972i	$-0.920236\pi$
$829$		−	411.137i		−	0.495943i	0.968767	−	0.247972i	$-0.0797640\pi$
$830$		0			0
$831$	325.481	−	231.421i	0.391674	−	0.278485i
$832$		0			0
$833$	60.7998	+	105.308i	0.0729889	+	0.126421i
$834$		0			0
$835$	396.024	−	228.645i	0.474280	−	0.273826i
$836$		0			0
$837$	303.220	−	1238.20i	0.362270	−	1.47933i
$838$		0			0
$839$		−	215.012i		−	0.256272i	−0.991757	−	0.128136i	$-0.959101\pi$
$839$		−	215.012i		−	0.256272i	0.991757	−	0.128136i	$-0.0408994\pi$
$840$		0			0
$841$	−220.960	−	382.714i	−0.262735	−	0.455070i
$842$		0			0
$843$	75.3511	−	164.682i	0.0893845	−	0.195352i
$844$		0			0
$845$	123.577	+	214.042i	0.146245	+	0.253304i
$846$		0			0
$847$	74.2219			0.0876292
$848$		0			0
$849$	1018.92	−	724.465i	1.20014	−	0.853316i
$850$		0			0
$851$		−	2060.16i		−	2.42087i
$852$		0			0
$853$	853.786			1.00092			0.500461	−	0.865759i	$-0.333164\pi$
$853$	853.786			1.00092			0.500461	+	0.865759i	$0.333164\pi$
$854$		0			0
$855$	549.989	+	131.244i	0.643262	+	0.153501i
$856$		0			0
$857$			608.821i			0.710410i	0.934788	+	0.355205i	$0.115589\pi$
$857$			608.821i			0.710410i	−0.934788	+	0.355205i	$0.884411\pi$
$858$		0			0
$859$	−892.344			−1.03882			−0.519409	−	0.854526i	$-0.673848\pi$
$859$	−892.344			−1.03882			−0.519409	+	0.854526i	$0.673848\pi$
$860$		0			0
$861$	−8.58371	+	18.7599i	−0.00996947	+	0.0217885i
$862$		0			0
$863$			674.510i			0.781587i	0.920478	+	0.390794i	$0.127799\pi$
$863$			674.510i			0.781587i	−0.920478	+	0.390794i	$0.872201\pi$
$864$		0			0
$865$	636.101	−	367.253i	0.735376	−	0.424570i
$866$		0			0
$867$	690.986	−	491.299i	0.796985	−	0.566665i
$868$		0			0
$869$	627.103	−	362.058i	0.721638	−	0.416638i
$870$		0			0
$871$	222.124			0.255022
$872$		0			0
$873$	−140.633	−	735.376i	−0.161091	−	0.842355i
$874$		0			0
$875$	60.6185	+	104.994i	0.0692782	+	0.119993i
$876$		0			0
$877$	17.6672	−	10.2001i	0.0201450	−	0.0116307i	−0.489894	−	0.871782i	$-0.662964\pi$
$877$	17.6672	−	10.2001i	0.0201450	−	0.0116307i	0.510039	+	0.860151i	$0.329631\pi$
$878$		0			0
$879$	−313.336	+	684.803i	−0.356469	+	0.779071i
$880$		0			0
$881$	348.299			0.395346			0.197673	−	0.980268i	$-0.436662\pi$
$881$	348.299			0.395346			0.197673	+	0.980268i	$0.436662\pi$
$882$		0			0
$883$	−62.6238	−	108.468i	−0.0709216	−	0.122840i	0.828384	−	0.560161i	$-0.189261\pi$
$883$	−62.6238	−	108.468i	−0.0709216	−	0.122840i	−0.899305	+	0.437321i	$0.855927\pi$
$884$		0			0
$885$	317.340	−	693.554i	0.358576	−	0.783677i
$886$		0			0
$887$			370.031i			0.417171i	0.978004	+	0.208586i	$0.0668860\pi$
$887$			370.031i			0.417171i	−0.978004	+	0.208586i	$0.933114\pi$
$888$		0			0
$889$	−33.8592	−	19.5486i	−0.0380868	−	0.0219894i
$890$		0			0
$891$	−411.286	−	325.363i	−0.461601	−	0.365166i
$892$		0			0
$893$	−79.8308	−	792.515i	−0.0893962	−	0.887474i
$894$		0			0
$895$	762.423	−	440.185i	0.851869	−	0.491827i
$896$		0			0
$897$	−1259.67	+	119.368i	−1.40432	+	0.133075i
$898$		0			0
$899$	−471.599	−	816.834i	−0.524582	−	0.908603i
$900$		0			0
$901$			76.6741i			0.0850989i
$902$		0			0
$903$	−144.145	+	102.489i	−0.159629	+	0.113498i
$904$		0			0
$905$	−516.607	−	298.263i	−0.570836	−	0.329572i
$906$		0			0
$907$		−	687.835i		−	0.758363i	−0.925322	−	0.379181i	$-0.876206\pi$
$907$		−	687.835i		−	0.758363i	0.925322	−	0.379181i	$-0.123794\pi$
$908$		0			0
$909$	29.0900	−	83.6597i	0.0320022	−	0.0920349i
$910$		0			0
$911$	−715.229	+	412.937i	−0.785103	+	0.453279i	−0.838236	−	0.545308i	$-0.816413\pi$
$911$	−715.229	+	412.937i	−0.785103	+	0.453279i	0.0531329	+	0.998587i	$0.483079\pi$
$912$		0			0
$913$	300.819	−	521.033i	0.329484	−	0.570683i
$914$		0			0
$915$	93.6590	+	988.370i	0.102360	+	1.08019i
$916$		0			0
$917$	93.3881	−	161.753i	0.101841	−	0.176394i
$918$		0			0
$919$	−1036.64			−1.12800			−0.564002	−	0.825773i	$-0.690739\pi$
$919$	−1036.64			−1.12800			−0.564002	+	0.825773i	$0.690739\pi$
$920$		0			0
$921$	−602.460	+	1316.69i	−0.654137	+	1.42963i
$922$		0			0
$923$	−24.7954	+	42.9470i	−0.0268640	+	0.0465298i
$924$		0			0
$925$	577.674	+	333.520i	0.624513	+	0.360563i
$926$		0			0
$927$	−1098.36	−	381.919i	−1.18485	−	0.411995i
$928$		0			0
$929$	−13.8032			−0.0148581			−0.00742905	−	0.999972i	$-0.502365\pi$
$929$	−13.8032			−0.0148581			−0.00742905	+	0.999972i	$0.502365\pi$
$930$		0			0
$931$	91.6310	+	909.661i	0.0984221	+	0.977079i
$932$		0			0
$933$	−1359.14	−	621.883i	−1.45674	−	0.666541i
$934$		0			0
$935$	27.0497	+	46.8515i	0.0289302	+	0.0501086i
$936$		0			0
$937$	415.505	+	719.675i	0.443441	+	0.768063i	0.997942	−	0.0641202i	$-0.0204241\pi$
$937$	415.505	+	719.675i	0.443441	+	0.768063i	−0.554501	+	0.832183i	$0.687091\pi$
$938$		0			0
$939$	681.771	+	311.949i	0.726061	+	0.332214i
$940$		0			0
$941$			791.872i			0.841522i	0.907172	+	0.420761i	$0.138237\pi$
$941$			791.872i			0.841522i	−0.907172	+	0.420761i	$0.861763\pi$
$942$		0			0
$943$	275.674	−	159.160i	0.292337	−	0.168781i
$944$		0			0
$945$	−81.3860	−	19.9305i	−0.0861228	−	0.0210905i
$946$		0			0
$947$	858.938			0.907009			0.453505	−	0.891254i	$-0.350174\pi$
$947$	858.938			0.907009			0.453505	+	0.891254i	$0.350174\pi$
$948$		0			0
$949$	−713.016	−	411.660i	−0.751334	−	0.433783i
$950$		0			0
$951$	390.824	−	854.154i	0.410961	−	0.898164i
$952$		0			0
$953$	201.788	+	116.502i	0.211739	+	0.122248i	0.602119	−	0.798406i	$-0.294323\pi$
$953$	201.788	+	116.502i	0.211739	+	0.122248i	−0.390380	+	0.920654i	$0.627656\pi$
$954$		0			0
$955$	−603.390	+	1045.10i	−0.631822	+	1.09435i
$956$		0			0
$957$	−386.283	+	36.6045i	−0.403639	+	0.0382492i
$958$		0			0
$959$	211.888			0.220946
$960$		0			0
$961$	634.092	+	1098.28i	0.659825	+	1.14285i
$962$		0			0
$963$	252.992	+	1322.91i	0.262712	+	1.37373i
$964$		0			0
$965$	−156.066	−	90.1046i	−0.161726	−	0.0933726i
$966$		0			0
$967$	−422.446	−	731.698i	−0.436863	−	0.756668i	0.560583	−	0.828098i	$-0.310577\pi$
$967$	−422.446	−	731.698i	−0.436863	−	0.756668i	−0.997446	+	0.0714301i	$0.977244\pi$
$968$		0			0
$969$	−141.316	+	27.8923i	−0.145836	+	0.0287846i
$970$		0			0
$971$	624.591	+	360.608i	0.643245	+	0.371378i	0.785864	−	0.618400i	$-0.212219\pi$
$971$	624.591	+	360.608i	0.643245	+	0.371378i	−0.142618	+	0.989778i	$0.545552\pi$
$972$		0			0
$973$	−106.244	−	184.020i	−0.109192	−	0.189127i
$974$		0			0
$975$	170.459	−	372.541i	0.174829	−	0.382094i
$976$		0			0
$977$	−705.428	−	407.279i	−0.722035	−	0.416867i	0.0934662	−	0.995622i	$-0.470205\pi$
$977$	−705.428	−	407.279i	−0.722035	−	0.416867i	−0.815501	+	0.578755i	$0.803539\pi$
$978$		0			0
$979$	570.545	+	329.405i	0.582784	+	0.336470i
$980$		0			0
$981$	165.922	+	57.6943i	0.169136	+	0.0588117i
$982$		0			0
$983$		−	1247.52i		−	1.26909i	−0.772886	−	0.634545i	$-0.781187\pi$
$983$		−	1247.52i		−	1.26909i	0.772886	−	0.634545i	$-0.218813\pi$
$984$		0			0
$985$	−325.445	−	563.687i	−0.330401	−	0.572271i
$986$		0			0
$987$	11.1354	+	117.510i	0.0112820	+	0.119058i
$988$		0			0
$989$	2729.00			2.75935
$990$		0			0
$991$	829.981	+	479.190i	0.837519	+	0.483542i	0.856420	−	0.516279i	$-0.172683\pi$
$991$	829.981	+	479.190i	0.837519	+	0.483542i	−0.0189011	+	0.999821i	$0.506017\pi$
$992$		0			0
$993$	396.137	+	557.146i	0.398929	+	0.561073i
$994$		0			0
$995$	142.554	−	246.911i	0.143271	−	0.248152i
$996$		0			0
$997$	−251.966	+	436.418i	−0.252724	+	0.437731i	−0.964275	−	0.264904i	$-0.914660\pi$
$997$	−251.966	+	436.418i	−0.252724	+	0.437731i	0.711551	+	0.702635i	$0.247993\pi$
$998$		0			0
$999$	−1229.29	+	358.066i	−1.23052	+	0.358424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.19	✓	80
3.2	odd	2		2052.3.s.a.901.13		80
9.2	odd	6		2052.3.bl.a.1585.28		80
9.7	even	3		684.3.bl.a.673.6	yes	80
19.12	odd	6		684.3.bl.a.373.6	yes	80
57.50	even	6		2052.3.bl.a.145.28		80
171.88	odd	6	inner	684.3.s.a.601.19	yes	80
171.164	even	6		2052.3.s.a.829.13		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.19	✓	80	1.1	even	1	trivial
684.3.s.a.601.19	yes	80	171.88	odd	6	inner
684.3.bl.a.373.6	yes	80	19.12	odd	6
684.3.bl.a.673.6	yes	80	9.7	even	3
2052.3.s.a.829.13		80	171.164	even	6
2052.3.s.a.901.13		80	3.2	odd	2
2052.3.bl.a.145.28		80	57.50	even	6
2052.3.bl.a.1585.28		80	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.283015 - 2.98662i) q^{3} +(1.65331 + 2.86362i) q^{5} +(0.469266 + 0.812792i) q^{7} +(-8.83980 + 1.69052i) q^{9} +O(q^{10})\)	\(q+(-0.283015 - 2.98662i) q^{3} +(1.65331 + 2.86362i) q^{5} +(0.469266 + 0.812792i) q^{7} +(-8.83980 + 1.69052i) q^{9} +(-3.23717 - 5.60694i) q^{11} +9.70848i q^{13} +(8.08462 - 5.74825i) q^{15} +(-1.26353 + 2.18849i) q^{17} +(-15.4195 + 11.1013i) q^{19} +(2.29469 - 1.63155i) q^{21} -43.4437 q^{23} +(7.03314 - 12.1817i) q^{25} +(7.55073 + 25.9227i) q^{27} +(17.3006 + 9.98850i) q^{29} +(-40.8887 - 23.6071i) q^{31} +(-15.8296 + 11.2550i) q^{33} +(-1.55168 + 2.68759i) q^{35} +47.4213i q^{37} +(28.9956 - 2.74765i) q^{39} +(-6.34554 + 3.66360i) q^{41} -62.8168 q^{43} +(-19.4559 - 22.5189i) q^{45} +(-20.9612 + 36.3058i) q^{47} +(24.0596 - 41.6724i) q^{49} +(6.89379 + 3.15430i) q^{51} +(26.2764 - 15.1707i) q^{53} +(10.7041 - 18.5400i) q^{55} +(37.5193 + 42.9104i) q^{57} +(66.5860 - 38.4435i) q^{59} +(-50.0409 + 86.6734i) q^{61} +(-5.52226 - 6.39162i) q^{63} +(-27.8014 + 16.0511i) q^{65} -22.8794i q^{67} +(12.2952 + 129.750i) q^{69} +(4.42365 + 2.55400i) q^{71} +(-42.4021 + 73.4425i) q^{73} +(-38.3727 - 17.5577i) q^{75} +(3.03818 - 5.26228i) q^{77} +111.844i q^{79} +(75.2843 - 29.8877i) q^{81} +(46.4633 + 80.4768i) q^{83} -8.35599 q^{85} +(24.9355 - 54.4972i) q^{87} +(-88.1242 + 50.8785i) q^{89} +(-7.89098 + 4.55586i) q^{91} +(-58.9334 + 128.800i) q^{93} +(-57.2831 - 25.8017i) q^{95} +83.1892i q^{97} +(38.0945 + 44.0917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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