LMFDB - Embedded newform 1380.3.v.a.277.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,3,Mod(277,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1380.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1380.v (of order $4$, 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:	$37.6022764817$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.10
Character	$\chi$	$=$	1380.277
Dual form			1380.3.v.a.553.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(-2.12370 + 4.52657i) q^{5} +(-4.15416 - 4.15416i) q^{7} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 + 1.22474i) q^{3} +(-2.12370 + 4.52657i) q^{5} +(-4.15416 - 4.15416i) q^{7} -3.00000i q^{9} -0.562567 q^{11} +(11.2449 - 11.2449i) q^{13} +(-2.94290 - 8.14490i) q^{15} +(-0.756625 - 0.756625i) q^{17} +14.8949i q^{19} +10.1756 q^{21} +(3.39116 - 3.39116i) q^{23} +(-15.9798 - 19.2262i) q^{25} +(3.67423 + 3.67423i) q^{27} +17.9006i q^{29} +45.3724 q^{31} +(0.689001 - 0.689001i) q^{33} +(27.6263 - 9.98191i) q^{35} +(6.41281 + 6.41281i) q^{37} +27.5443i q^{39} -5.86507 q^{41} +(38.1017 - 38.1017i) q^{43} +(13.5797 + 6.37111i) q^{45} +(2.79002 + 2.79002i) q^{47} -14.4859i q^{49} +1.85334 q^{51} +(-34.9974 + 34.9974i) q^{53} +(1.19473 - 2.54650i) q^{55} +(-18.2424 - 18.2424i) q^{57} +69.5687i q^{59} -38.3580 q^{61} +(-12.4625 + 12.4625i) q^{63} +(27.0201 + 74.7819i) q^{65} +(76.4370 + 76.4370i) q^{67} +8.30662i q^{69} -56.9363 q^{71} +(-62.0316 + 62.0316i) q^{73} +(43.1183 + 3.97607i) q^{75} +(2.33699 + 2.33699i) q^{77} -33.2153i q^{79} -9.00000 q^{81} +(-43.8882 + 43.8882i) q^{83} +(5.03177 - 1.81807i) q^{85} +(-21.9237 - 21.9237i) q^{87} +103.496i q^{89} -93.4265 q^{91} +(-55.5696 + 55.5696i) q^{93} +(-67.4229 - 31.6324i) q^{95} +(-13.4157 - 13.4157i) q^{97} +1.68770i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 16 q^{5} - 16 q^{7}+O(q^{10}) $ 88 * q - 16 * q^5 - 16 * q^7	$ 88 q - 16 q^{5} - 16 q^{7} - 8 q^{13} + 48 q^{15} + 24 q^{17} + 48 q^{21} + 24 q^{25} - 88 q^{31} - 48 q^{33} - 24 q^{35} - 128 q^{37} - 376 q^{41} + 24 q^{45} + 136 q^{47} + 224 q^{53} + 184 q^{55} - 48 q^{57} + 688 q^{61} - 48 q^{63} - 288 q^{65} + 16 q^{67} + 168 q^{71} - 128 q^{73} + 144 q^{75} - 88 q^{77} - 792 q^{81} + 288 q^{83} + 40 q^{85} + 144 q^{87} - 528 q^{91} - 576 q^{95} - 120 q^{97}+O(q^{100}) $ 88 * q - 16 * q^5 - 16 * q^7 - 8 * q^13 + 48 * q^15 + 24 * q^17 + 48 * q^21 + 24 * q^25 - 88 * q^31 - 48 * q^33 - 24 * q^35 - 128 * q^37 - 376 * q^41 + 24 * q^45 + 136 * q^47 + 224 * q^53 + 184 * q^55 - 48 * q^57 + 688 * q^61 - 48 * q^63 - 288 * q^65 + 16 * q^67 + 168 * q^71 - 128 * q^73 + 144 * q^75 - 88 * q^77 - 792 * q^81 + 288 * q^83 + 40 * q^85 + 144 * q^87 - 528 * q^91 - 576 * q^95 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$	−2.12370	+	4.52657i	−0.424741	+	0.905315i
$5$	−2.12370	+	4.52657i	−0.424741	+	0.905315i
$6$		0			0
$7$	−4.15416	−	4.15416i	−0.593452	−	0.593452i	0.345111	−	0.938562i	$-0.387841\pi$
$7$	−4.15416	−	4.15416i	−0.593452	−	0.593452i	−0.938562	+	0.345111i	$0.887841\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−0.562567			−0.0511424			−0.0255712	−	0.999673i	$-0.508140\pi$
$11$	−0.562567			−0.0511424			−0.0255712	+	0.999673i	$0.508140\pi$
$12$		0			0
$13$	11.2449	−	11.2449i	0.864995	−	0.864995i	−0.126919	−	0.991913i	$-0.540509\pi$
$13$	11.2449	−	11.2449i	0.864995	−	0.864995i	0.991913	+	0.126919i	$0.0405087\pi$
$14$		0			0
$15$	−2.94290	−	8.14490i	−0.196194	−	0.542993i
$16$		0			0
$17$	−0.756625	−	0.756625i	−0.0445073	−	0.0445073i	0.684503	−	0.729010i	$-0.260019\pi$
$17$	−0.756625	−	0.756625i	−0.0445073	−	0.0445073i	−0.729010	+	0.684503i	$0.760019\pi$
$18$		0			0
$19$			14.8949i			0.783942i	0.919978	+	0.391971i	$0.128207\pi$
$19$			14.8949i			0.783942i	−0.919978	+	0.391971i	$0.871793\pi$
$20$		0			0
$21$	10.1756			0.484551
$22$		0			0
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		0			0
$25$	−15.9798	−	19.2262i	−0.639190	−	0.769048i
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$			17.9006i			0.617263i	0.951182	+	0.308632i	$0.0998710\pi$
$29$			17.9006i			0.617263i	−0.951182	+	0.308632i	$0.900129\pi$
$30$		0			0
$31$	45.3724			1.46362			0.731812	−	0.681506i	$-0.238675\pi$
$31$	45.3724			1.46362			0.731812	+	0.681506i	$0.238675\pi$
$32$		0			0
$33$	0.689001	−	0.689001i	0.0208788	−	0.0208788i
$34$		0			0
$35$	27.6263	−	9.98191i	0.789324	−	0.285197i
$36$		0			0
$37$	6.41281	+	6.41281i	0.173319	+	0.173319i	0.788436	−	0.615117i	$-0.210891\pi$
$37$	6.41281	+	6.41281i	0.173319	+	0.173319i	−0.615117	+	0.788436i	$0.710891\pi$
$38$		0			0
$39$			27.5443i			0.706265i
$40$		0			0
$41$	−5.86507			−0.143051			−0.0715253	−	0.997439i	$-0.522787\pi$
$41$	−5.86507			−0.143051			−0.0715253	+	0.997439i	$0.522787\pi$
$42$		0			0
$43$	38.1017	−	38.1017i	0.886086	−	0.886086i	−0.108058	−	0.994145i	$-0.534463\pi$
$43$	38.1017	−	38.1017i	0.886086	−	0.886086i	0.994145	+	0.108058i	$0.0344633\pi$
$44$		0			0
$45$	13.5797	+	6.37111i	0.301772	+	0.141580i
$46$		0			0
$47$	2.79002	+	2.79002i	0.0593622	+	0.0593622i	0.736165	−	0.676802i	$-0.236635\pi$
$47$	2.79002	+	2.79002i	0.0593622	+	0.0593622i	−0.676802	+	0.736165i	$0.736635\pi$
$48$		0			0
$49$		−	14.4859i		−	0.295631i
$50$		0			0
$51$	1.85334			0.0363401
$52$		0			0
$53$	−34.9974	+	34.9974i	−0.660328	+	0.660328i	−0.955457	−	0.295129i	$-0.904637\pi$
$53$	−34.9974	+	34.9974i	−0.660328	+	0.660328i	0.295129	+	0.955457i	$0.404637\pi$
$54$		0			0
$55$	1.19473	−	2.54650i	0.0217223	−	0.0463000i
$56$		0			0
$57$	−18.2424	−	18.2424i	−0.320043	−	0.320043i
$58$		0			0
$59$			69.5687i			1.17913i	0.807721	+	0.589565i	$0.200701\pi$
$59$			69.5687i			1.17913i	−0.807721	+	0.589565i	$0.799299\pi$
$60$		0			0
$61$	−38.3580			−0.628820			−0.314410	−	0.949287i	$-0.601807\pi$
$61$	−38.3580			−0.628820			−0.314410	+	0.949287i	$0.601807\pi$
$62$		0			0
$63$	−12.4625	+	12.4625i	−0.197817	+	0.197817i
$64$		0			0
$65$	27.0201	+	74.7819i	0.415694	+	1.15049i
$66$		0			0
$67$	76.4370	+	76.4370i	1.14085	+	1.14085i	0.988295	+	0.152555i	$0.0487502\pi$
$67$	76.4370	+	76.4370i	1.14085	+	1.14085i	0.152555	+	0.988295i	$0.451250\pi$
$68$		0			0
$69$			8.30662i			0.120386i
$70$		0			0
$71$	−56.9363			−0.801920			−0.400960	−	0.916095i	$-0.631323\pi$
$71$	−56.9363			−0.801920			−0.400960	+	0.916095i	$0.631323\pi$
$72$		0			0
$73$	−62.0316	+	62.0316i	−0.849747	+	0.849747i	−0.990101	−	0.140354i	$-0.955176\pi$
$73$	−62.0316	+	62.0316i	−0.849747	+	0.849747i	0.140354	+	0.990101i	$0.455176\pi$
$74$		0			0
$75$	43.1183	+	3.97607i	0.574911	+	0.0530143i
$76$		0			0
$77$	2.33699	+	2.33699i	0.0303506	+	0.0303506i
$78$		0			0
$79$		−	33.2153i		−	0.420447i	−0.977653	−	0.210223i	$-0.932581\pi$
$79$		−	33.2153i		−	0.420447i	0.977653	−	0.210223i	$-0.0674191\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−43.8882	+	43.8882i	−0.528774	+	0.528774i	−0.920207	−	0.391433i	$-0.871979\pi$
$83$	−43.8882	+	43.8882i	−0.528774	+	0.528774i	0.391433	+	0.920207i	$0.371979\pi$
$84$		0			0
$85$	5.03177	−	1.81807i	0.0591973	−	0.0213891i
$86$		0			0
$87$	−21.9237	−	21.9237i	−0.251997	−	0.251997i
$88$		0			0
$89$			103.496i			1.16288i	0.813590	+	0.581439i	$0.197510\pi$
$89$			103.496i			1.16288i	−0.813590	+	0.581439i	$0.802490\pi$
$90$		0			0
$91$	−93.4265			−1.02666
$92$		0			0
$93$	−55.5696	+	55.5696i	−0.597522	+	0.597522i
$94$		0			0
$95$	−67.4229	−	31.6324i	−0.709714	−	0.332972i
$96$		0			0
$97$	−13.4157	−	13.4157i	−0.138306	−	0.138306i	0.634564	−	0.772870i	$-0.281180\pi$
$97$	−13.4157	−	13.4157i	−0.138306	−	0.138306i	−0.772870	+	0.634564i	$0.781180\pi$
$98$		0			0
$99$			1.68770i			0.0170475i
$100$		0			0
$101$	2.72695			0.0269995			0.0134998	−	0.999909i	$-0.495703\pi$
$101$	2.72695			0.0269995			0.0134998	+	0.999909i	$0.495703\pi$
$102$		0			0
$103$	43.4751	−	43.4751i	0.422089	−	0.422089i	−0.463834	−	0.885922i	$-0.653526\pi$
$103$	43.4751	−	43.4751i	0.422089	−	0.422089i	0.885922	+	0.463834i	$0.153526\pi$
$104$		0			0
$105$	−21.6099	+	46.0605i	−0.205809	+	0.438671i
$106$		0			0
$107$	21.4285	+	21.4285i	0.200266	+	0.200266i	0.800114	−	0.599848i	$-0.204772\pi$
$107$	21.4285	+	21.4285i	0.200266	+	0.200266i	−0.599848	+	0.800114i	$0.704772\pi$
$108$		0			0
$109$			138.355i			1.26932i	0.772793	+	0.634658i	$0.218859\pi$
$109$			138.355i			1.26932i	−0.772793	+	0.634658i	$0.781141\pi$
$110$		0			0
$111$	−15.7081			−0.141514
$112$		0			0
$113$	−11.3789	+	11.3789i	−0.100698	+	0.100698i	−0.755661	−	0.654963i	$-0.772684\pi$
$113$	−11.3789	+	11.3789i	−0.100698	+	0.100698i	0.654963	+	0.755661i	$0.272684\pi$
$114$		0			0
$115$	8.14853	+	22.5522i	0.0708568	+	0.196106i
$116$		0			0
$117$	−33.7348	−	33.7348i	−0.288332	−	0.288332i
$118$		0			0
$119$			6.28628i			0.0528259i
$120$		0			0
$121$	−120.684			−0.997384
$122$		0			0
$123$	7.18322	−	7.18322i	0.0584001	−	0.0584001i
$124$		0			0
$125$	120.965	−	31.5028i	0.967721	−	0.252022i
$126$		0			0
$127$	85.6073	+	85.6073i	0.674074	+	0.674074i	0.958653	−	0.284579i	$-0.0918538\pi$
$127$	85.6073	+	85.6073i	0.674074	+	0.674074i	−0.284579	+	0.958653i	$0.591854\pi$
$128$		0			0
$129$			93.3298i			0.723486i
$130$		0			0
$131$	−16.9266			−0.129211			−0.0646054	−	0.997911i	$-0.520579\pi$
$131$	−16.9266			−0.129211			−0.0646054	+	0.997911i	$0.520579\pi$
$132$		0			0
$133$	61.8758	−	61.8758i	0.465232	−	0.465232i
$134$		0			0
$135$	−24.4347	+	8.82871i	−0.180998	+	0.0653979i
$136$		0			0
$137$	32.6251	+	32.6251i	0.238139	+	0.238139i	0.816079	−	0.577940i	$-0.196143\pi$
$137$	32.6251	+	32.6251i	0.238139	+	0.238139i	−0.577940	+	0.816079i	$0.696143\pi$
$138$		0			0
$139$		−	46.9658i		−	0.337883i	−0.985626	−	0.168942i	$-0.945965\pi$
$139$		−	46.9658i		−	0.337883i	0.985626	−	0.168942i	$-0.0540350\pi$
$140$		0			0
$141$	−6.83414			−0.0484691
$142$		0			0
$143$	−6.32603	+	6.32603i	−0.0442379	+	0.0442379i
$144$		0			0
$145$	−81.0286	−	38.0156i	−0.558818	−	0.262177i
$146$		0			0
$147$	17.7415	+	17.7415i	0.120691	+	0.120691i
$148$		0			0
$149$			139.524i			0.936405i	0.883621	+	0.468203i	$0.155098\pi$
$149$			139.524i			0.936405i	−0.883621	+	0.468203i	$0.844902\pi$
$150$		0			0
$151$	−175.888			−1.16482			−0.582409	−	0.812896i	$-0.697890\pi$
$151$	−175.888			−1.16482			−0.582409	+	0.812896i	$0.697890\pi$
$152$		0			0
$153$	−2.26987	+	2.26987i	−0.0148358	+	0.0148358i
$154$		0			0
$155$	−96.3575	+	205.381i	−0.621661	+	1.32504i
$156$		0			0
$157$	115.114	+	115.114i	0.733210	+	0.733210i	0.971254	−	0.238044i	$-0.0765063\pi$
$157$	115.114	+	115.114i	0.733210	+	0.733210i	−0.238044	+	0.971254i	$0.576506\pi$
$158$		0			0
$159$		−	85.7258i		−	0.539156i
$160$		0			0
$161$	−28.1749			−0.174999
$162$		0			0
$163$	8.07514	−	8.07514i	0.0495407	−	0.0495407i	−0.681902	−	0.731443i	$-0.738847\pi$
$163$	8.07514	−	8.07514i	0.0495407	−	0.0495407i	0.731443	+	0.681902i	$0.238847\pi$
$164$		0			0
$165$	1.65558	+	4.58205i	0.0100338	+	0.0277700i
$166$		0			0
$167$	94.6537	+	94.6537i	0.566789	+	0.566789i	0.931227	−	0.364439i	$-0.118739\pi$
$167$	94.6537	+	94.6537i	0.566789	+	0.566789i	−0.364439	+	0.931227i	$0.618739\pi$
$168$		0			0
$169$		−	83.8969i		−	0.496431i
$170$		0			0
$171$	44.6847			0.261314
$172$		0			0
$173$	181.132	−	181.132i	1.04700	−	1.04700i	0.0481635	−	0.998839i	$-0.484663\pi$
$173$	181.132	−	181.132i	1.04700	−	1.04700i	0.998839	−	0.0481635i	$-0.0153369\pi$
$174$		0			0
$175$	−13.4863	+	146.251i	−0.0770645	+	0.835722i
$176$		0			0
$177$	−85.2039	−	85.2039i	−0.481378	−	0.481378i
$178$		0			0
$179$			91.8338i			0.513038i	0.966539	+	0.256519i	$0.0825756\pi$
$179$			91.8338i			0.513038i	−0.966539	+	0.256519i	$0.917424\pi$
$180$		0			0
$181$	−327.678			−1.81037			−0.905187	−	0.425014i	$-0.860269\pi$
$181$	−327.678			−1.81037			−0.905187	+	0.425014i	$0.860269\pi$
$182$		0			0
$183$	46.9788	−	46.9788i	0.256715	−	0.256715i
$184$		0			0
$185$	−42.6470	+	15.4091i	−0.230524	+	0.0832927i
$186$		0			0
$187$	0.425652	+	0.425652i	0.00227621	+	0.00227621i
$188$		0			0
$189$		−	30.5267i		−	0.161517i
$190$		0			0
$191$	214.733			1.12426			0.562128	−	0.827050i	$-0.309983\pi$
$191$	214.733			1.12426			0.562128	+	0.827050i	$0.309983\pi$
$192$		0			0
$193$	−141.787	+	141.787i	−0.734648	+	0.734648i	−0.971537	−	0.236888i	$-0.923872\pi$
$193$	−141.787	+	141.787i	−0.734648	+	0.734648i	0.236888	+	0.971537i	$0.423872\pi$
$194$		0			0
$195$	−124.682	−	58.4960i	−0.639392	−	0.299980i
$196$		0			0
$197$	207.578	+	207.578i	1.05370	+	1.05370i	0.998474	+	0.0552232i	$0.0175870\pi$
$197$	207.578	+	207.578i	1.05370	+	1.05370i	0.0552232	+	0.998474i	$0.482413\pi$
$198$		0			0
$199$			83.0757i			0.417466i	0.977973	+	0.208733i	$0.0669340\pi$
$199$			83.0757i			0.417466i	−0.977973	+	0.208733i	$0.933066\pi$
$200$		0			0
$201$	−187.232			−0.931500
$202$		0			0
$203$	74.3621	−	74.3621i	0.366316	−	0.366316i
$204$		0			0
$205$	12.4557	−	26.5487i	0.0607594	−	0.129506i
$206$		0			0
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$		0			0
$209$		−	8.37938i		−	0.0400927i
$210$		0			0
$211$	135.812			0.643659			0.321829	−	0.946798i	$-0.395702\pi$
$211$	135.812			0.643659			0.321829	+	0.946798i	$0.395702\pi$
$212$		0			0
$213$	69.7325	−	69.7325i	0.327383	−	0.327383i
$214$		0			0
$215$	91.5535	+	253.387i	0.425830	+	1.17854i
$216$		0			0
$217$	−188.484	−	188.484i	−0.868590	−	0.868590i
$218$		0			0
$219$		−	151.946i		−	0.693816i
$220$		0			0
$221$	−17.0164			−0.0769972
$222$		0			0
$223$	199.219	−	199.219i	0.893359	−	0.893359i	−0.101479	−	0.994838i	$-0.532357\pi$
$223$	199.219	−	199.219i	0.893359	−	0.893359i	0.994838	+	0.101479i	$0.0323574\pi$
$224$		0			0
$225$	−57.6786	+	47.9393i	−0.256349	+	0.213063i
$226$		0			0
$227$	267.964	+	267.964i	1.18046	+	1.18046i	0.979625	+	0.200834i	$0.0643651\pi$
$227$	267.964	+	267.964i	1.18046	+	1.18046i	0.200834	+	0.979625i	$0.435635\pi$
$228$		0			0
$229$			298.270i			1.30249i	0.758868	+	0.651244i	$0.225753\pi$
$229$			298.270i			1.30249i	−0.758868	+	0.651244i	$0.774247\pi$
$230$		0			0
$231$	−5.72444			−0.0247811
$232$		0			0
$233$	25.1811	−	25.1811i	0.108073	−	0.108073i	−0.651002	−	0.759076i	$-0.725651\pi$
$233$	25.1811	−	25.1811i	0.108073	−	0.108073i	0.759076	+	0.651002i	$0.225651\pi$
$234$		0			0
$235$	−18.5544	+	6.70407i	−0.0789551	+	0.0285280i
$236$		0			0
$237$	40.6803	+	40.6803i	0.171647	+	0.171647i
$238$		0			0
$239$			360.324i			1.50763i	0.657086	+	0.753816i	$0.271789\pi$
$239$			360.324i			1.50763i	−0.657086	+	0.753816i	$0.728211\pi$
$240$		0			0
$241$	153.993			0.638975			0.319488	−	0.947590i	$-0.396489\pi$
$241$	153.993			0.638975			0.319488	+	0.947590i	$0.396489\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$	65.5715	+	30.7638i	0.267639	+	0.125566i
$246$		0			0
$247$	167.492	+	167.492i	0.678106	+	0.678106i
$248$		0			0
$249$		−	107.504i		−	0.431742i
$250$		0			0
$251$	97.5472			0.388634			0.194317	−	0.980939i	$-0.437751\pi$
$251$	97.5472			0.388634			0.194317	+	0.980939i	$0.437751\pi$
$252$		0			0
$253$	−1.90776	+	1.90776i	−0.00754054	+	0.00754054i
$254$		0			0
$255$	−3.93596	+	8.38930i	−0.0154351	+	0.0328992i
$256$		0			0
$257$	−68.5959	−	68.5959i	−0.266910	−	0.266910i	0.560944	−	0.827854i	$-0.310438\pi$
$257$	−68.5959	−	68.5959i	−0.266910	−	0.266910i	−0.827854	+	0.560944i	$0.810438\pi$
$258$		0			0
$259$		−	53.2797i		−	0.205713i
$260$		0			0
$261$	53.7019			0.205754
$262$		0			0
$263$	−50.8944	+	50.8944i	−0.193515	+	0.193515i	−0.797213	−	0.603698i	$-0.793693\pi$
$263$	−50.8944	+	50.8944i	−0.193515	+	0.193515i	0.603698	+	0.797213i	$0.293693\pi$
$264$		0			0
$265$	−84.0942	−	232.742i	−0.317337	−	0.878273i
$266$		0			0
$267$	−126.756	−	126.756i	−0.474743	−	0.474743i
$268$		0			0
$269$		−	176.485i		−	0.656078i	−0.944664	−	0.328039i	$-0.893612\pi$
$269$		−	176.485i		−	0.656078i	0.944664	−	0.328039i	$-0.106388\pi$
$270$		0			0
$271$	−56.5326			−0.208607			−0.104304	−	0.994545i	$-0.533261\pi$
$271$	−56.5326			−0.208607			−0.104304	+	0.994545i	$0.533261\pi$
$272$		0			0
$273$	114.424	−	114.424i	0.419134	−	0.419134i
$274$		0			0
$275$	8.98968	+	10.8160i	0.0326898	+	0.0393310i
$276$		0			0
$277$	−65.1282	−	65.1282i	−0.235120	−	0.235120i	0.579706	−	0.814826i	$-0.303167\pi$
$277$	−65.1282	−	65.1282i	−0.235120	−	0.235120i	−0.814826	+	0.579706i	$0.803167\pi$
$278$		0			0
$279$		−	136.117i		−	0.487875i
$280$		0			0
$281$	−51.3193			−0.182631			−0.0913155	−	0.995822i	$-0.529107\pi$
$281$	−51.3193			−0.182631			−0.0913155	+	0.995822i	$0.529107\pi$
$282$		0			0
$283$	300.842	−	300.842i	1.06305	−	1.06305i	0.0651720	−	0.997874i	$-0.479240\pi$
$283$	300.842	−	300.842i	1.06305	−	1.06305i	0.997874	−	0.0651720i	$-0.0207596\pi$
$284$		0			0
$285$	121.317	−	43.8342i	0.425675	−	0.153804i
$286$		0			0
$287$	24.3644	+	24.3644i	0.0848935	+	0.0848935i
$288$		0			0
$289$		−	287.855i		−	0.996038i
$290$		0			0
$291$	32.8616			0.112927
$292$		0			0
$293$	−21.3529	+	21.3529i	−0.0728768	+	0.0728768i	−0.742606	−	0.669729i	$-0.766410\pi$
$293$	−21.3529	+	21.3529i	−0.0728768	+	0.0728768i	0.669729	+	0.742606i	$0.266410\pi$
$294$		0			0
$295$	−314.908	−	147.743i	−1.06748	−	0.500825i
$296$		0			0
$297$	−2.06700	−	2.06700i	−0.00695961	−	0.00695961i
$298$		0			0
$299$		−	76.2668i		−	0.255073i
$300$		0			0
$301$	−316.561			−1.05170
$302$		0			0
$303$	−3.33982	+	3.33982i	−0.0110225	+	0.0110225i
$304$		0			0
$305$	81.4610	−	173.630i	0.267085	−	0.569280i
$306$		0			0
$307$	229.182	+	229.182i	0.746520	+	0.746520i	0.973824	−	0.227304i	$-0.0729910\pi$
$307$	229.182	+	229.182i	0.746520	+	0.746520i	−0.227304	+	0.973824i	$0.572991\pi$
$308$		0			0
$309$			106.492i			0.344634i
$310$		0			0
$311$	294.457			0.946807			0.473403	−	0.880846i	$-0.343025\pi$
$311$	294.457			0.946807			0.473403	+	0.880846i	$0.343025\pi$
$312$		0			0
$313$	−178.401	+	178.401i	−0.569972	+	0.569972i	−0.932121	−	0.362148i	$-0.882043\pi$
$313$	−178.401	+	178.401i	−0.569972	+	0.569972i	0.362148	+	0.932121i	$0.382043\pi$
$314$		0			0
$315$	−29.9457	−	82.8790i	−0.0950658	−	0.263108i
$316$		0			0
$317$	−366.990	−	366.990i	−1.15770	−	1.15770i	−0.984970	−	0.172727i	$-0.944742\pi$
$317$	−366.990	−	366.990i	−1.15770	−	1.15770i	−0.172727	−	0.984970i	$-0.555258\pi$
$318$		0			0
$319$		−	10.0703i		−	0.0315683i
$320$		0			0
$321$	−52.4889			−0.163517
$322$		0			0
$323$	11.2698	−	11.2698i	0.0348912	−	0.0348912i
$324$		0			0
$325$	−395.889	−	36.5061i	−1.21812	−	0.112327i
$326$		0			0
$327$	−169.450	−	169.450i	−0.518196	−	0.518196i
$328$		0			0
$329$		−	23.1804i		−	0.0704572i
$330$		0			0
$331$	−216.737			−0.654795			−0.327398	−	0.944887i	$-0.606172\pi$
$331$	−216.737			−0.654795			−0.327398	+	0.944887i	$0.606172\pi$
$332$		0			0
$333$	19.2384	−	19.2384i	0.0577730	−	0.0577730i
$334$		0			0
$335$	−508.327	+	183.668i	−1.51739	+	0.548263i
$336$		0			0
$337$	−37.5217	−	37.5217i	−0.111340	−	0.111340i	0.649242	−	0.760582i	$-0.275086\pi$
$337$	−37.5217	−	37.5217i	−0.111340	−	0.111340i	−0.760582	+	0.649242i	$0.775086\pi$
$338$		0			0
$339$		−	27.8725i		−	0.0822197i
$340$		0			0
$341$	−25.5250			−0.0748533
$342$		0			0
$343$	−263.731	+	263.731i	−0.768894	+	0.768894i
$344$		0			0
$345$	−37.6006	−	17.6408i	−0.108987	−	0.0511328i
$346$		0			0
$347$	62.4146	+	62.4146i	0.179869	+	0.179869i	0.791299	−	0.611430i	$-0.209405\pi$
$347$	62.4146	+	62.4146i	0.179869	+	0.179869i	−0.611430	+	0.791299i	$0.709405\pi$
$348$		0			0
$349$		−	276.357i		−	0.791854i	−0.918282	−	0.395927i	$-0.870423\pi$
$349$		−	276.357i		−	0.791854i	0.918282	−	0.395927i	$-0.129577\pi$
$350$		0			0
$351$	82.6330			0.235422
$352$		0			0
$353$	127.854	−	127.854i	0.362193	−	0.362193i	−0.502427	−	0.864620i	$-0.667559\pi$
$353$	127.854	−	127.854i	0.362193	−	0.362193i	0.864620	+	0.502427i	$0.167559\pi$
$354$		0			0
$355$	120.916	−	257.727i	0.340608	−	0.725991i
$356$		0			0
$357$	−7.69909	−	7.69909i	−0.0215661	−	0.0215661i
$358$		0			0
$359$			70.7688i			0.197128i	0.995131	+	0.0985638i	$0.0314248\pi$
$359$			70.7688i			0.197128i	−0.995131	+	0.0985638i	$0.968575\pi$
$360$		0			0
$361$	139.142			0.385435
$362$		0			0
$363$	147.807	−	147.807i	0.407180	−	0.407180i
$364$		0			0
$365$	−149.054	−	412.527i	−0.408367	−	1.13021i
$366$		0			0
$367$	285.475	+	285.475i	0.777860	+	0.777860i	0.979467	−	0.201606i	$-0.0646161\pi$
$367$	285.475	+	285.475i	0.777860	+	0.777860i	−0.201606	+	0.979467i	$0.564616\pi$
$368$		0			0
$369$			17.5952i			0.0476835i
$370$		0			0
$371$	290.770			0.783746
$372$		0			0
$373$	−64.6009	+	64.6009i	−0.173193	+	0.173193i	−0.788381	−	0.615188i	$-0.789080\pi$
$373$	−64.6009	+	64.6009i	−0.173193	+	0.173193i	0.615188	+	0.788381i	$0.289080\pi$
$374$		0			0
$375$	−109.569	+	186.734i	−0.292183	+	0.497958i
$376$		0			0
$377$	201.291	+	201.291i	0.533929	+	0.533929i
$378$		0			0
$379$			263.850i			0.696173i	0.937462	+	0.348086i	$0.113168\pi$
$379$			263.850i			0.696173i	−0.937462	+	0.348086i	$0.886832\pi$
$380$		0			0
$381$	−209.694			−0.550379
$382$		0			0
$383$	367.856	−	367.856i	0.960459	−	0.960459i	−0.0387880	−	0.999247i	$-0.512350\pi$
$383$	367.856	−	367.856i	0.960459	−	0.960459i	0.999247	+	0.0387880i	$0.0123497\pi$
$384$		0			0
$385$	−15.5417	+	5.61549i	−0.0403679	+	0.0145857i
$386$		0			0
$387$	−114.305	−	114.305i	−0.295362	−	0.295362i
$388$		0			0
$389$			84.4819i			0.217177i	0.994087	+	0.108589i	$0.0346331\pi$
$389$			84.4819i			0.217177i	−0.994087	+	0.108589i	$0.965367\pi$
$390$		0			0
$391$	−5.13168			−0.0131245
$392$		0			0
$393$	20.7308	−	20.7308i	0.0527501	−	0.0527501i
$394$		0			0
$395$	150.351	+	70.5394i	0.380637	+	0.178581i
$396$		0			0
$397$	−79.7214	−	79.7214i	−0.200810	−	0.200810i	0.599537	−	0.800347i	$-0.295351\pi$
$397$	−79.7214	−	79.7214i	−0.200810	−	0.200810i	−0.800347	+	0.599537i	$0.795351\pi$
$398$		0			0
$399$			151.564i			0.379860i
$400$		0			0
$401$	−138.568			−0.345555			−0.172777	−	0.984961i	$-0.555274\pi$
$401$	−138.568			−0.345555			−0.172777	+	0.984961i	$0.555274\pi$
$402$		0			0
$403$	510.209	−	510.209i	1.26603	−	1.26603i
$404$		0			0
$405$	19.1133	−	40.7392i	0.0471934	−	0.100591i
$406$		0			0
$407$	−3.60763	−	3.60763i	−0.00886396	−	0.00886396i
$408$		0			0
$409$		−	442.963i		−	1.08304i	−0.840688	−	0.541519i	$-0.817849\pi$
$409$		−	442.963i		−	1.08304i	0.840688	−	0.541519i	$-0.182151\pi$
$410$		0			0
$411$	−79.9148			−0.194440
$412$		0			0
$413$	289.000	−	289.000i	0.699757	−	0.699757i
$414$		0			0
$415$	−105.458	−	291.869i	−0.254115	−	0.703298i
$416$		0			0
$417$	57.5211	+	57.5211i	0.137940	+	0.137940i
$418$		0			0
$419$		−	409.699i		−	0.977802i	−0.872339	−	0.488901i	$-0.837398\pi$
$419$		−	409.699i		−	0.977802i	0.872339	−	0.488901i	$-0.162602\pi$
$420$		0			0
$421$	384.771			0.913945			0.456973	−	0.889481i	$-0.348934\pi$
$421$	384.771			0.913945			0.456973	+	0.889481i	$0.348934\pi$
$422$		0			0
$423$	8.37007	−	8.37007i	0.0197874	−	0.0197874i
$424$		0			0
$425$	−2.45635	+	26.6377i	−0.00577964	+	0.0626770i
$426$		0			0
$427$	159.345	+	159.345i	0.373174	+	0.373174i
$428$		0			0
$429$		−	15.4955i		−	0.0361201i
$430$		0			0
$431$	73.1230			0.169659			0.0848295	−	0.996395i	$-0.472965\pi$
$431$	73.1230			0.169659			0.0848295	+	0.996395i	$0.472965\pi$
$432$		0			0
$433$	105.267	−	105.267i	0.243112	−	0.243112i	−0.575024	−	0.818136i	$-0.695007\pi$
$433$	105.267	−	105.267i	0.243112	−	0.243112i	0.818136	+	0.575024i	$0.195007\pi$
$434$		0			0
$435$	145.799	−	52.6798i	0.335170	−	0.121103i
$436$		0			0
$437$	50.5111	+	50.5111i	0.115586	+	0.115586i
$438$		0			0
$439$		−	150.445i		−	0.342699i	−0.985210	−	0.171350i	$-0.945187\pi$
$439$		−	150.445i		−	0.342699i	0.985210	−	0.171350i	$-0.0548128\pi$
$440$		0			0
$441$	−43.4577			−0.0985435
$442$		0			0
$443$	426.982	−	426.982i	0.963841	−	0.963841i	−0.0355276	−	0.999369i	$-0.511311\pi$
$443$	426.982	−	426.982i	0.963841	−	0.963841i	0.999369	+	0.0355276i	$0.0113112\pi$
$444$		0			0
$445$	−468.483	−	219.795i	−1.05277	−	0.493922i
$446$		0			0
$447$	−170.882	−	170.882i	−0.382286	−	0.382286i
$448$		0			0
$449$			738.746i			1.64531i	0.568538	+	0.822657i	$0.307509\pi$
$449$			738.746i			1.64531i	−0.568538	+	0.822657i	$0.692491\pi$
$450$		0			0
$451$	3.29949			0.00731595
$452$		0			0
$453$	215.417	−	215.417i	0.475535	−	0.475535i
$454$		0			0
$455$	198.410	−	422.902i	0.436066	−	0.929455i
$456$		0			0
$457$	−500.507	−	500.507i	−1.09520	−	1.09520i	−0.994964	−	0.100237i	$-0.968040\pi$
$457$	−500.507	−	500.507i	−1.09520	−	1.09520i	−0.100237	−	0.994964i	$-0.531960\pi$
$458$		0			0
$459$		−	5.56003i		−	0.0121134i
$460$		0			0
$461$	−418.214			−0.907189			−0.453595	−	0.891208i	$-0.649859\pi$
$461$	−418.214			−0.907189			−0.453595	+	0.891208i	$0.649859\pi$
$462$		0			0
$463$	−475.560	+	475.560i	−1.02713	+	1.02713i	−0.0275048	+	0.999622i	$0.508756\pi$
$463$	−475.560	+	475.560i	−1.02713	+	1.02713i	−0.999622	+	0.0275048i	$0.991244\pi$
$464$		0			0
$465$	−133.526	−	369.553i	−0.287154	−	0.794738i
$466$		0			0
$467$	498.661	+	498.661i	1.06780	+	1.06780i	0.997528	+	0.0702680i	$0.0223854\pi$
$467$	498.661	+	498.661i	1.06780	+	1.06780i	0.0702680	+	0.997528i	$0.477615\pi$
$468$		0			0
$469$		−	635.063i		−	1.35408i
$470$		0			0
$471$	−281.971			−0.598664
$472$		0			0
$473$	−21.4348	+	21.4348i	−0.0453166	+	0.0453166i
$474$		0			0
$475$	286.372	−	238.017i	0.602889	−	0.501088i
$476$		0			0
$477$	104.992	+	104.992i	0.220109	+	0.220109i
$478$		0			0
$479$			485.159i			1.01286i	0.862282	+	0.506429i	$0.169035\pi$
$479$			485.159i			1.01286i	−0.862282	+	0.506429i	$0.830965\pi$
$480$		0			0
$481$	144.223			0.299840
$482$		0			0
$483$	34.5070	−	34.5070i	0.0714432	−	0.0714432i
$484$		0			0
$485$	89.2182	−	32.2362i	0.183955	−	0.0664664i
$486$		0			0
$487$	262.728	+	262.728i	0.539483	+	0.539483i	0.923377	−	0.383894i	$-0.125417\pi$
$487$	262.728	+	262.728i	0.539483	+	0.539483i	−0.383894	+	0.923377i	$0.625417\pi$
$488$		0			0
$489$			19.7800i			0.0404498i
$490$		0			0
$491$	−555.556			−1.13148			−0.565739	−	0.824584i	$-0.691409\pi$
$491$	−555.556			−1.13148			−0.565739	+	0.824584i	$0.691409\pi$
$492$		0			0
$493$	13.5441	−	13.5441i	0.0274727	−	0.0274727i
$494$		0			0
$495$	−7.63950	−	3.58418i	−0.0154333	−	0.00724076i
$496$		0			0
$497$	236.523	+	236.523i	0.475901	+	0.475901i
$498$		0			0
$499$		−	735.639i		−	1.47423i	−0.675770	−	0.737113i	$-0.736189\pi$
$499$		−	735.639i		−	1.47423i	0.675770	−	0.737113i	$-0.263811\pi$
$500$		0			0
$501$	−231.853			−0.462781
$502$		0			0
$503$	188.322	−	188.322i	0.374398	−	0.374398i	−0.494678	−	0.869076i	$-0.664714\pi$
$503$	188.322	−	188.322i	0.374398	−	0.374398i	0.869076	+	0.494678i	$0.164714\pi$
$504$		0			0
$505$	−5.79124	+	12.3438i	−0.0114678	+	0.0244431i
$506$		0			0
$507$	102.752	+	102.752i	0.202667	+	0.202667i
$508$		0			0
$509$			405.239i			0.796148i	0.917353	+	0.398074i	$0.130321\pi$
$509$			405.239i			0.796148i	−0.917353	+	0.398074i	$0.869679\pi$
$510$		0			0
$511$	515.378			1.00857
$512$		0			0
$513$	−54.7273	+	54.7273i	−0.106681	+	0.106681i
$514$		0			0
$515$	104.465	+	289.122i	0.202845	+	0.561401i
$516$		0			0
$517$	−1.56958	−	1.56958i	−0.00303593	−	0.00303593i
$518$		0			0
$519$			443.680i			0.854874i
$520$		0			0
$521$	10.6892			0.0205168			0.0102584	−	0.999947i	$-0.496735\pi$
$521$	10.6892			0.0205168			0.0102584	+	0.999947i	$0.496735\pi$
$522$		0			0
$523$	539.475	−	539.475i	1.03150	−	1.03150i	0.0320134	−	0.999487i	$-0.489808\pi$
$523$	539.475	−	539.475i	1.03150	−	1.03150i	0.999487	−	0.0320134i	$-0.0101919\pi$
$524$		0			0
$525$	−162.603	−	195.638i	−0.309720	−	0.372643i
$526$		0			0
$527$	−34.3299	−	34.3299i	−0.0651420	−	0.0651420i
$528$		0			0
$529$		−	23.0000i		−	0.0434783i
$530$		0			0
$531$	208.706			0.393044
$532$		0			0
$533$	−65.9523	+	65.9523i	−0.123738	+	0.123738i
$534$		0			0
$535$	−142.505	+	51.4899i	−0.266365	+	0.0962428i
$536$		0			0
$537$	−112.473	−	112.473i	−0.209447	−	0.209447i
$538$		0			0
$539$			8.14929i			0.0151193i
$540$		0			0
$541$	414.830			0.766784			0.383392	−	0.923586i	$-0.374756\pi$
$541$	414.830			0.766784			0.383392	+	0.923586i	$0.374756\pi$
$542$		0			0
$543$	401.321	−	401.321i	0.739082	−	0.739082i
$544$		0			0
$545$	−626.276	−	293.826i	−1.14913	−	0.539130i
$546$		0			0
$547$	−52.4887	−	52.4887i	−0.0959574	−	0.0959574i	0.657498	−	0.753456i	$-0.271615\pi$
$547$	−52.4887	−	52.4887i	−0.0959574	−	0.0959574i	−0.753456	+	0.657498i	$0.771615\pi$
$548$		0			0
$549$			115.074i			0.209607i
$550$		0			0
$551$	−266.628			−0.483898
$552$		0			0
$553$	−137.982	+	137.982i	−0.249515	+	0.249515i
$554$		0			0
$555$	33.3594	−	71.1039i	0.0601070	−	0.128115i
$556$		0			0
$557$	394.203	+	394.203i	0.707725	+	0.707725i	0.966056	−	0.258331i	$-0.0831726\pi$
$557$	394.203	+	394.203i	0.707725	+	0.707725i	−0.258331	+	0.966056i	$0.583173\pi$
$558$		0			0
$559$		−	856.902i		−	1.53292i
$560$		0			0
$561$	−1.04263			−0.00185852
$562$		0			0
$563$	−618.141	+	618.141i	−1.09794	+	1.09794i	−0.103290	+	0.994651i	$0.532937\pi$
$563$	−618.141	+	618.141i	−1.09794	+	1.09794i	−0.994651	+	0.103290i	$0.967063\pi$
$564$		0			0
$565$	−27.3420	−	75.6728i	−0.0483929	−	0.133934i
$566$		0			0
$567$	37.3874	+	37.3874i	0.0659391	+	0.0659391i
$568$		0			0
$569$			663.026i			1.16525i	0.812742	+	0.582623i	$0.197974\pi$
$569$			663.026i			1.16525i	−0.812742	+	0.582623i	$0.802026\pi$
$570$		0			0
$571$	312.297			0.546929			0.273465	−	0.961882i	$-0.411830\pi$
$571$	312.297			0.546929			0.273465	+	0.961882i	$0.411830\pi$
$572$		0			0
$573$	−262.993	+	262.993i	−0.458975	+	0.458975i
$574$		0			0
$575$	−119.389	−	11.0093i	−0.207634	−	0.0191465i
$576$		0			0
$577$	−3.94929	−	3.94929i	−0.00684452	−	0.00684452i	0.703676	−	0.710521i	$-0.251541\pi$
$577$	−3.94929	−	3.94929i	−0.00684452	−	0.00684452i	−0.710521	+	0.703676i	$0.751541\pi$
$578$		0			0
$579$		−	347.306i		−	0.599838i
$580$		0			0
$581$	364.637			0.627603
$582$		0			0
$583$	19.6884	−	19.6884i	0.0337708	−	0.0337708i
$584$		0			0
$585$	224.346	−	81.0603i	0.383497	−	0.138565i
$586$		0			0
$587$	−395.119	−	395.119i	−0.673115	−	0.673115i	0.285318	−	0.958433i	$-0.407901\pi$
$587$	−395.119	−	395.119i	−0.673115	−	0.673115i	−0.958433	+	0.285318i	$0.907901\pi$
$588$		0			0
$589$			675.817i			1.14740i
$590$		0			0
$591$	−508.461			−0.860340
$592$		0			0
$593$	64.1567	−	64.1567i	0.108190	−	0.108190i	−0.650940	−	0.759130i	$-0.725625\pi$
$593$	64.1567	−	64.1567i	0.108190	−	0.108190i	0.759130	+	0.650940i	$0.225625\pi$
$594$		0			0
$595$	−28.4553	−	13.3502i	−0.0478241	−	0.0224373i
$596$		0			0
$597$	−101.747	−	101.747i	−0.170430	−	0.170430i
$598$		0			0
$599$			1024.59i			1.71049i	0.518222	+	0.855246i	$0.326594\pi$
$599$			1024.59i			1.71049i	−0.518222	+	0.855246i	$0.673406\pi$
$600$		0			0
$601$	−757.613			−1.26059			−0.630294	−	0.776357i	$-0.717066\pi$
$601$	−757.613			−1.26059			−0.630294	+	0.776357i	$0.717066\pi$
$602$		0			0
$603$	229.311	−	229.311i	0.380283	−	0.380283i
$604$		0			0
$605$	256.296	−	546.283i	0.423630	−	0.902947i
$606$		0			0
$607$	−629.378	−	629.378i	−1.03687	−	1.03687i	−0.999294	−	0.0375730i	$-0.988037\pi$
$607$	−629.378	−	629.378i	−1.03687	−	1.03687i	−0.0375730	−	0.999294i	$-0.511963\pi$
$608$		0			0
$609$			182.149i			0.299096i
$610$		0			0
$611$	62.7473			0.102696
$612$		0			0
$613$	−12.6301	+	12.6301i	−0.0206037	+	0.0206037i	−0.717334	−	0.696730i	$-0.754638\pi$
$613$	−12.6301	+	12.6301i	−0.0206037	+	0.0206037i	0.696730	+	0.717334i	$0.254638\pi$
$614$		0			0
$615$	17.2603	+	47.7704i	0.0280656	+	0.0776754i
$616$		0			0
$617$	14.0248	+	14.0248i	0.0227306	+	0.0227306i	0.718381	−	0.695650i	$-0.244884\pi$
$617$	14.0248	+	14.0248i	0.0227306	+	0.0227306i	−0.695650	+	0.718381i	$0.744884\pi$
$618$		0			0
$619$		−	114.339i		−	0.184715i	−0.995726	−	0.0923577i	$-0.970560\pi$
$619$		−	114.339i		−	0.184715i	0.995726	−	0.0923577i	$-0.0294403\pi$
$620$		0			0
$621$	24.9199			0.0401286
$622$		0			0
$623$	429.940	−	429.940i	0.690112	−	0.690112i
$624$		0			0
$625$	−114.294	+	614.461i	−0.182871	+	0.983137i
$626$		0			0
$627$	10.2626	+	10.2626i	0.0163678	+	0.0163678i
$628$		0			0
$629$		−	9.70418i		−	0.0154279i
$630$		0			0
$631$	141.230			0.223819			0.111910	−	0.993718i	$-0.464303\pi$
$631$	141.230			0.223819			0.111910	+	0.993718i	$0.464303\pi$
$632$		0			0
$633$	−166.335	+	166.335i	−0.262773	+	0.262773i
$634$		0			0
$635$	−569.313	+	205.703i	−0.896556	+	0.323942i
$636$		0			0
$637$	−162.893	−	162.893i	−0.255719	−	0.255719i
$638$		0			0
$639$			170.809i			0.267307i
$640$		0			0
$641$	−890.692			−1.38953			−0.694767	−	0.719234i	$-0.744493\pi$
$641$	−890.692			−1.38953			−0.694767	+	0.719234i	$0.744493\pi$
$642$		0			0
$643$	234.637	−	234.637i	0.364910	−	0.364910i	−0.500707	−	0.865617i	$-0.666927\pi$
$643$	234.637	−	234.637i	0.364910	−	0.364910i	0.865617	+	0.500707i	$0.166927\pi$
$644$		0			0
$645$	−422.464	−	198.205i	−0.654983	−	0.307294i
$646$		0			0
$647$	−50.3531	−	50.3531i	−0.0778254	−	0.0778254i	0.667123	−	0.744948i	$-0.267526\pi$
$647$	−50.3531	−	50.3531i	−0.0778254	−	0.0778254i	−0.744948	+	0.667123i	$0.767526\pi$
$648$		0			0
$649$		−	39.1371i		−	0.0603036i
$650$		0			0
$651$	461.690			0.709201
$652$		0			0
$653$	601.036	−	601.036i	0.920423	−	0.920423i	−0.0766359	−	0.997059i	$-0.524418\pi$
$653$	601.036	−	601.036i	0.920423	−	0.920423i	0.997059	+	0.0766359i	$0.0244179\pi$
$654$		0			0
$655$	35.9471	−	76.6195i	0.0548811	−	0.116976i
$656$		0			0
$657$	186.095	+	186.095i	0.283249	+	0.283249i
$658$		0			0
$659$		−	1219.89i		−	1.85112i	−0.378597	−	0.925562i	$-0.623593\pi$
$659$		−	1219.89i		−	1.85112i	0.378597	−	0.925562i	$-0.376407\pi$
$660$		0			0
$661$	−1129.09			−1.70815			−0.854076	−	0.520148i	$-0.825877\pi$
$661$	−1129.09			−1.70815			−0.854076	+	0.520148i	$0.825877\pi$
$662$		0			0
$663$	20.8407	−	20.8407i	0.0314340	−	0.0314340i
$664$		0			0
$665$	148.680	+	411.491i	0.223578	+	0.618784i
$666$		0			0
$667$	60.7040	+	60.7040i	0.0910105	+	0.0910105i
$668$		0			0
$669$			487.985i			0.729425i
$670$		0			0
$671$	21.5789			0.0321594
$672$		0			0
$673$	309.114	−	309.114i	0.459308	−	0.459308i	−0.439120	−	0.898428i	$-0.644710\pi$
$673$	309.114	−	309.114i	0.459308	−	0.459308i	0.898428	+	0.439120i	$0.144710\pi$
$674$		0			0
$675$	11.9282	−	129.355i	0.0176714	−	0.191637i
$676$		0			0
$677$	526.675	+	526.675i	0.777954	+	0.777954i	0.979483	−	0.201528i	$-0.0645908\pi$
$677$	526.675	+	526.675i	0.777954	+	0.777954i	−0.201528	+	0.979483i	$0.564591\pi$
$678$		0			0
$679$			111.462i			0.164156i
$680$		0			0
$681$	−656.376			−0.963841
$682$		0			0
$683$	567.989	−	567.989i	0.831609	−	0.831609i	−0.156128	−	0.987737i	$-0.549901\pi$
$683$	567.989	−	567.989i	0.831609	−	0.831609i	0.987737	+	0.156128i	$0.0499013\pi$
$684$		0			0
$685$	−216.966	+	78.3939i	−0.316739	+	0.114444i
$686$		0			0
$687$	−365.304	−	365.304i	−0.531739	−	0.531739i
$688$		0			0
$689$			787.087i			1.14236i
$690$		0			0
$691$	88.9962			0.128793			0.0643966	−	0.997924i	$-0.479488\pi$
$691$	88.9962			0.128793			0.0643966	+	0.997924i	$0.479488\pi$
$692$		0			0
$693$	7.01098	−	7.01098i	0.0101169	−	0.0101169i
$694$		0			0
$695$	212.594	+	99.7415i	0.305891	+	0.143513i
$696$		0			0
$697$	4.43766	+	4.43766i	0.00636680	+	0.00636680i
$698$		0			0
$699$			61.6808i			0.0882415i
$700$		0			0
$701$	541.473			0.772430			0.386215	−	0.922409i	$-0.373782\pi$
$701$	541.473			0.772430			0.386215	+	0.922409i	$0.373782\pi$
$702$		0			0
$703$	−95.5181	+	95.5181i	−0.135872	+	0.135872i
$704$		0			0
$705$	14.5137	−	30.9352i	0.0205868	−	0.0438798i
$706$		0			0
$707$	−11.3282	−	11.3282i	−0.0160229	−	0.0160229i
$708$		0			0
$709$			671.434i			0.947015i	0.880790	+	0.473508i	$0.157012\pi$
$709$			671.434i			0.947015i	−0.880790	+	0.473508i	$0.842988\pi$
$710$		0			0
$711$	−99.6459			−0.140149
$712$		0			0
$713$	153.865	−	153.865i	0.215800	−	0.215800i
$714$		0			0
$715$	−15.2006	−	42.0698i	−0.0212596	−	0.0588389i
$716$		0			0
$717$	−441.305	−	441.305i	−0.615488	−	0.615488i
$718$		0			0
$719$			1299.95i			1.80799i	0.427539	+	0.903997i	$0.359381\pi$
$719$			1299.95i			1.80799i	−0.427539	+	0.903997i	$0.640619\pi$
$720$		0			0
$721$	−361.205			−0.500978
$722$		0			0
$723$	−188.602	+	188.602i	−0.260861	+	0.260861i
$724$		0			0
$725$	344.161	−	286.048i	0.474705	−	0.394549i
$726$		0			0
$727$	−5.53524	−	5.53524i	−0.00761381	−	0.00761381i	0.703290	−	0.710903i	$-0.251714\pi$
$727$	−5.53524	−	5.53524i	−0.00761381	−	0.00761381i	−0.710903	+	0.703290i	$0.751714\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−57.6574			−0.0788747
$732$		0			0
$733$	737.211	−	737.211i	1.00575	−	1.00575i	0.00576185	−	0.999983i	$-0.498166\pi$
$733$	737.211	−	737.211i	1.00575	−	1.00575i	0.999983	−	0.00576185i	$-0.00183406\pi$
$734$		0			0
$735$	−117.986	+	42.6306i	−0.160525	+	0.0580008i
$736$		0			0
$737$	−43.0009	−	43.0009i	−0.0583459	−	0.0583459i
$738$		0			0
$739$			752.054i			1.01766i	0.860866	+	0.508832i	$0.169923\pi$
$739$			752.054i			1.01766i	−0.860866	+	0.508832i	$0.830077\pi$
$740$		0			0
$741$	−410.270			−0.553671
$742$		0			0
$743$	−284.266	+	284.266i	−0.382592	+	0.382592i	−0.872035	−	0.489443i	$-0.837200\pi$
$743$	−284.266	+	284.266i	−0.382592	+	0.382592i	0.489443	+	0.872035i	$0.337200\pi$
$744$		0			0
$745$	−631.568	−	296.309i	−0.847742	−	0.397730i
$746$		0			0
$747$	131.665	+	131.665i	0.176258	+	0.176258i
$748$		0			0
$749$		−	178.035i		−	0.237697i
$750$		0			0
$751$	−830.598			−1.10599			−0.552995	−	0.833185i	$-0.686515\pi$
$751$	−830.598			−1.10599			−0.552995	+	0.833185i	$0.686515\pi$
$752$		0			0
$753$	−119.470	+	119.470i	−0.158659	+	0.158659i
$754$		0			0
$755$	373.533	−	796.169i	0.494746	−	1.05453i
$756$		0			0
$757$	837.915	+	837.915i	1.10689	+	1.10689i	0.993557	+	0.113331i	$0.0361521\pi$
$757$	837.915	+	837.915i	1.10689	+	1.10689i	0.113331	+	0.993557i	$0.463848\pi$
$758$		0			0
$759$		−	4.67303i		−	0.00615683i
$760$		0			0
$761$	−238.847			−0.313859			−0.156930	−	0.987610i	$-0.550160\pi$
$761$	−238.847			−0.313859			−0.156930	+	0.987610i	$0.550160\pi$
$762$		0			0
$763$	574.751	−	574.751i	0.753278	−	0.753278i
$764$		0			0
$765$	−5.45422	−	15.0953i	−0.00712969	−	0.0197324i
$766$		0			0
$767$	782.295	+	782.295i	1.01994	+	1.01994i
$768$		0			0
$769$		−	132.550i		−	0.172366i	−0.996279	−	0.0861831i	$-0.972533\pi$
$769$		−	132.550i		−	0.172366i	0.996279	−	0.0861831i	$-0.0274670\pi$
$770$		0			0
$771$	168.025			0.217931
$772$		0			0
$773$	−231.200	+	231.200i	−0.299095	+	0.299095i	−0.840659	−	0.541565i	$-0.817832\pi$
$773$	−231.200	+	231.200i	−0.299095	+	0.299095i	0.541565	+	0.840659i	$0.317832\pi$
$774$		0			0
$775$	−725.039	−	872.339i	−0.935535	−	1.12560i
$776$		0			0
$777$	65.2540	+	65.2540i	0.0839820	+	0.0839820i
$778$		0			0
$779$		−	87.3596i		−	0.112143i
$780$		0			0
$781$	32.0305			0.0410122
$782$		0			0
$783$	−65.7711	+	65.7711i	−0.0839989	+	0.0839989i
$784$		0			0
$785$	−765.540	+	276.604i	−0.975210	+	0.352362i
$786$		0			0
$787$	274.965	+	274.965i	0.349384	+	0.349384i	0.859880	−	0.510496i	$-0.170538\pi$
$787$	274.965	+	274.965i	0.349384	+	0.349384i	−0.510496	+	0.859880i	$0.670538\pi$
$788$		0			0
$789$		−	124.665i		−	0.158004i
$790$		0			0
$791$	94.5395			0.119519
$792$		0			0
$793$	−431.333	+	431.333i	−0.543926	+	0.543926i
$794$		0			0
$795$	388.044	+	182.056i	0.488106	+	0.229001i
$796$		0			0
$797$	−750.746	−	750.746i	−0.941964	−	0.941964i	0.0564415	−	0.998406i	$-0.482025\pi$
$797$	−750.746	−	750.746i	−0.941964	−	0.941964i	−0.998406	+	0.0564415i	$0.982025\pi$
$798$		0			0
$799$		−	4.22200i		−	0.00528411i
$800$		0			0
$801$	310.489			0.387626
$802$		0			0
$803$	34.8969	−	34.8969i	0.0434582	−	0.0434582i
$804$		0			0
$805$	59.8351	−	127.536i	0.0743294	−	0.158429i
$806$		0			0
$807$	216.149	+	216.149i	0.267843	+	0.267843i
$808$		0			0
$809$		−	786.749i		−	0.972495i	−0.873821	−	0.486248i	$-0.838365\pi$
$809$		−	786.749i		−	0.972495i	0.873821	−	0.486248i	$-0.161635\pi$
$810$		0			0
$811$	107.704			0.132804			0.0664019	−	0.997793i	$-0.478848\pi$
$811$	107.704			0.132804			0.0664019	+	0.997793i	$0.478848\pi$
$812$		0			0
$813$	69.2380	−	69.2380i	0.0851636	−	0.0851636i
$814$		0			0
$815$	19.4035	+	53.7019i	0.0238080	+	0.0658919i
$816$		0			0
$817$	567.521	+	567.521i	0.694640	+	0.694640i
$818$		0			0
$819$			280.279i			0.342222i
$820$		0			0
$821$	1002.17			1.22067			0.610337	−	0.792142i	$-0.291034\pi$
$821$	1002.17			1.22067			0.610337	+	0.792142i	$0.291034\pi$
$822$		0			0
$823$	−364.982	+	364.982i	−0.443478	+	0.443478i	−0.893179	−	0.449701i	$-0.851530\pi$
$823$	−364.982	+	364.982i	−0.443478	+	0.443478i	0.449701	+	0.893179i	$0.351530\pi$
$824$		0			0
$825$	−24.2569	−	2.23681i	−0.0294024	−	0.00271128i
$826$		0			0
$827$	−427.327	−	427.327i	−0.516719	−	0.516719i	0.399858	−	0.916577i	$-0.369059\pi$
$827$	−427.327	−	427.327i	−0.516719	−	0.516719i	−0.916577	+	0.399858i	$0.869059\pi$
$828$		0			0
$829$			860.051i			1.03746i	0.854939	+	0.518728i	$0.173594\pi$
$829$			860.051i			1.03746i	−0.854939	+	0.518728i	$0.826406\pi$
$830$		0			0
$831$	159.531			0.191974
$832$		0			0
$833$	−10.9604	+	10.9604i	−0.0131577	+	0.0131577i
$834$		0			0
$835$	−629.473	+	227.441i	−0.753860	+	0.272384i
$836$		0			0
$837$	166.709	+	166.709i	0.199174	+	0.199174i
$838$		0			0
$839$			533.019i			0.635303i	0.948208	+	0.317651i	$0.102894\pi$
$839$			533.019i			0.635303i	−0.948208	+	0.317651i	$0.897106\pi$
$840$		0			0
$841$	520.567			0.618986
$842$		0			0
$843$	62.8531	−	62.8531i	0.0745588	−	0.0745588i
$844$		0			0
$845$	379.766	+	178.172i	0.449427	+	0.210855i
$846$		0			0
$847$	501.339	+	501.339i	0.591899	+	0.591899i
$848$		0			0
$849$			736.909i			0.867973i
$850$		0			0
$851$	43.4938			0.0511090
$852$		0			0
$853$	−679.244	+	679.244i	−0.796300	+	0.796300i	−0.982510	−	0.186210i	$-0.940380\pi$
$853$	−679.244	+	679.244i	−0.796300	+	0.796300i	0.186210	+	0.982510i	$0.440380\pi$
$854$		0			0
$855$	−94.8971	+	202.269i	−0.110991	+	0.236571i
$856$		0			0
$857$	430.849	+	430.849i	0.502741	+	0.502741i	0.912289	−	0.409548i	$-0.134313\pi$
$857$	430.849	+	430.849i	0.502741	+	0.502741i	−0.409548	+	0.912289i	$0.634313\pi$
$858$		0			0
$859$			947.210i			1.10269i	0.834278	+	0.551345i	$0.185885\pi$
$859$			947.210i			1.10269i	−0.834278	+	0.551345i	$0.814115\pi$
$860$		0			0
$861$	−59.6805			−0.0693153
$862$		0			0
$863$	−279.203	+	279.203i	−0.323527	+	0.323527i	−0.850118	−	0.526592i	$-0.823470\pi$
$863$	−279.203	+	279.203i	−0.323527	+	0.323527i	0.526592	+	0.850118i	$0.323470\pi$
$864$		0			0
$865$	435.236	+	1204.58i	0.503163	+	1.39257i
$866$		0			0
$867$	352.549	+	352.549i	0.406631	+	0.406631i
$868$		0			0
$869$			18.6858i			0.0215027i
$870$		0			0
$871$	1719.06			1.97366
$872$		0			0
$873$	−40.2471	+	40.2471i	−0.0461021	+	0.0461021i
$874$		0			0
$875$	−633.376	−	371.641i	−0.723859	−	0.424733i
$876$		0			0
$877$	−688.936	−	688.936i	−0.785560	−	0.785560i	0.195203	−	0.980763i	$-0.437463\pi$
$877$	−688.936	−	688.936i	−0.785560	−	0.785560i	−0.980763	+	0.195203i	$0.937463\pi$
$878$		0			0
$879$		−	52.3037i		−	0.0595036i
$880$		0			0
$881$	−20.6747			−0.0234673			−0.0117337	−	0.999931i	$-0.503735\pi$
$881$	−20.6747			−0.0234673			−0.0117337	+	0.999931i	$0.503735\pi$
$882$		0			0
$883$	112.709	−	112.709i	0.127643	−	0.127643i	−0.640399	−	0.768042i	$-0.721231\pi$
$883$	112.709	−	112.709i	0.127643	−	0.127643i	0.768042	+	0.640399i	$0.221231\pi$
$884$		0			0
$885$	566.630	−	204.734i	0.640260	−	0.231338i
$886$		0			0
$887$	−527.324	−	527.324i	−0.594503	−	0.594503i	0.344341	−	0.938845i	$-0.388102\pi$
$887$	−527.324	−	527.324i	−0.594503	−	0.594503i	−0.938845	+	0.344341i	$0.888102\pi$
$888$		0			0
$889$		−	711.253i		−	0.800060i
$890$		0			0
$891$	5.06310			0.00568249
$892$		0			0
$893$	−41.5571	+	41.5571i	−0.0465365	+	0.0465365i
$894$		0			0
$895$	−415.693	−	195.028i	−0.464461	−	0.217908i
$896$		0			0
$897$	93.4074	+	93.4074i	0.104133	+	0.104133i
$898$		0			0
$899$			812.194i			0.903441i
$900$		0			0
$901$	52.9598			0.0587789
$902$		0			0
$903$	387.707	−	387.707i	0.429354	−	0.429354i
$904$		0			0
$905$	695.890	−	1483.26i	0.768939	−	1.63896i
$906$		0			0
$907$	−207.311	−	207.311i	−0.228568	−	0.228568i	0.583526	−	0.812094i	$-0.301673\pi$
$907$	−207.311	−	207.311i	−0.228568	−	0.228568i	−0.812094	+	0.583526i	$0.801673\pi$
$908$		0			0
$909$		−	8.18086i		−	0.00899984i
$910$		0			0
$911$	1336.00			1.46652			0.733259	−	0.679950i	$-0.237998\pi$
$911$	1336.00			1.46652			0.733259	+	0.679950i	$0.237998\pi$
$912$		0			0
$913$	24.6901	−	24.6901i	0.0270428	−	0.0270428i
$914$		0			0
$915$	112.884	+	312.422i	0.123370	+	0.341445i
$916$		0			0
$917$	70.3158	+	70.3158i	0.0766803	+	0.0766803i
$918$		0			0
$919$			1614.36i			1.75665i	0.478067	+	0.878323i	$0.341338\pi$
$919$			1614.36i			1.75665i	−0.478067	+	0.878323i	$0.658662\pi$
$920$		0			0
$921$	−561.378			−0.609531
$922$		0			0
$923$	−640.245	+	640.245i	−0.693657	+	0.693657i
$924$		0			0
$925$	20.8189	−	225.769i	0.0225069	−	0.244075i
$926$		0			0
$927$	−130.425	−	130.425i	−0.140696	−	0.140696i
$928$		0			0
$929$			865.769i			0.931937i	0.884801	+	0.465968i	$0.154294\pi$
$929$			865.769i			0.931937i	−0.884801	+	0.465968i	$0.845706\pi$
$930$		0			0
$931$	215.766			0.231757
$932$		0			0
$933$	−360.635	+	360.635i	−0.386532	+	0.386532i
$934$		0			0
$935$	−2.83071	+	1.02279i	−0.00302749	+	0.00109389i
$936$		0			0
$937$	646.125	+	646.125i	0.689568	+	0.689568i	0.962136	−	0.272569i	$-0.0878732\pi$
$937$	646.125	+	646.125i	0.689568	+	0.689568i	−0.272569	+	0.962136i	$0.587873\pi$
$938$		0			0
$939$		−	436.992i		−	0.465381i
$940$		0			0
$941$	−939.037			−0.997914			−0.498957	−	0.866627i	$-0.666283\pi$
$941$	−939.037			−0.997914			−0.498957	+	0.866627i	$0.666283\pi$
$942$		0			0
$943$	−19.8894	+	19.8894i	−0.0210916	+	0.0210916i
$944$		0			0
$945$	138.181	+	64.8297i	0.146224	+	0.0686029i
$946$		0			0
$947$	−1008.58	−	1008.58i	−1.06502	−	1.06502i	−0.997733	−	0.0672898i	$-0.978565\pi$
$947$	−1008.58	−	1008.58i	−1.06502	−	1.06502i	−0.0672898	−	0.997733i	$-0.521435\pi$
$948$		0			0
$949$			1395.08i			1.47005i
$950$		0			0
$951$	898.938			0.945255
$952$		0			0
$953$	−6.76412	+	6.76412i	−0.00709772	+	0.00709772i	−0.710647	−	0.703549i	$-0.751598\pi$
$953$	−6.76412	+	6.76412i	−0.00709772	+	0.00709772i	0.703549	+	0.710647i	$0.251598\pi$
$954$		0			0
$955$	−456.029	+	972.004i	−0.477517	+	1.01781i
$956$		0			0
$957$	12.3336	+	12.3336i	0.0128877	+	0.0128877i
$958$		0			0
$959$		−	271.060i		−	0.282648i
$960$		0			0
$961$	1097.65			1.14220
$962$		0			0
$963$	64.2855	−	64.2855i	0.0667554	−	0.0667554i
$964$		0			0
$965$	−340.696	−	942.924i	−0.353053	−	0.977123i
$966$		0			0
$967$	586.557	+	586.557i	0.606574	+	0.606574i	0.942049	−	0.335475i	$-0.108897\pi$
$967$	586.557	+	586.557i	0.606574	+	0.606574i	−0.335475	+	0.942049i	$0.608897\pi$
$968$		0			0
$969$			27.6054i			0.0284885i
$970$		0			0
$971$	−1040.46			−1.07154			−0.535769	−	0.844365i	$-0.679978\pi$
$971$	−1040.46			−1.07154			−0.535769	+	0.844365i	$0.679978\pi$
$972$		0			0
$973$	−195.103	+	195.103i	−0.200517	+	0.200517i
$974$		0			0
$975$	529.573	−	440.152i	0.543152	−	0.451438i
$976$		0			0
$977$	940.678	+	940.678i	0.962823	+	0.962823i	0.999333	−	0.0365103i	$-0.0116242\pi$
$977$	940.678	+	940.678i	0.962823	+	0.962823i	−0.0365103	+	0.999333i	$0.511624\pi$
$978$		0			0
$979$		−	58.2235i		−	0.0594725i
$980$		0			0
$981$	415.066			0.423105
$982$		0			0
$983$	−113.902	+	113.902i	−0.115871	+	0.115871i	−0.762665	−	0.646794i	$-0.776110\pi$
$983$	−113.902	+	113.902i	−0.115871	+	0.115871i	0.646794	+	0.762665i	$0.276110\pi$
$984$		0			0
$985$	−1380.45	+	498.784i	−1.40148	+	0.506380i
$986$		0			0
$987$	28.3901	+	28.3901i	0.0287640	+	0.0287640i
$988$		0			0
$989$		−	258.418i		−	0.261293i
$990$		0			0
$991$	1594.43			1.60891			0.804457	−	0.594011i	$-0.202456\pi$
$991$	1594.43			1.60891			0.804457	+	0.594011i	$0.202456\pi$
$992$		0			0
$993$	265.448	−	265.448i	0.267319	−	0.267319i
$994$		0			0
$995$	−376.049	−	176.428i	−0.377938	−	0.177315i
$996$		0			0
$997$	711.571	+	711.571i	0.713712	+	0.713712i	0.967310	−	0.253598i	$-0.0816139\pi$
$997$	711.571	+	711.571i	0.713712	+	0.713712i	−0.253598	+	0.967310i	$0.581614\pi$
$998$		0			0
$999$			47.1243i			0.0471715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.3.v.a.277.10	✓	88
5.3	odd	4	inner	1380.3.v.a.553.10	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.3.v.a.277.10	✓	88	1.1	even	1	trivial
1380.3.v.a.553.10	yes	88	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1380.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(-2.12370 + 4.52657i) q^{5} +(-4.15416 - 4.15416i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{3} +(-2.12370 + 4.52657i) q^{5} +(-4.15416 - 4.15416i) q^{7} -3.00000i q^{9} -0.562567 q^{11} +(11.2449 - 11.2449i) q^{13} +(-2.94290 - 8.14490i) q^{15} +(-0.756625 - 0.756625i) q^{17} +14.8949i q^{19} +10.1756 q^{21} +(3.39116 - 3.39116i) q^{23} +(-15.9798 - 19.2262i) q^{25} +(3.67423 + 3.67423i) q^{27} +17.9006i q^{29} +45.3724 q^{31} +(0.689001 - 0.689001i) q^{33} +(27.6263 - 9.98191i) q^{35} +(6.41281 + 6.41281i) q^{37} +27.5443i q^{39} -5.86507 q^{41} +(38.1017 - 38.1017i) q^{43} +(13.5797 + 6.37111i) q^{45} +(2.79002 + 2.79002i) q^{47} -14.4859i q^{49} +1.85334 q^{51} +(-34.9974 + 34.9974i) q^{53} +(1.19473 - 2.54650i) q^{55} +(-18.2424 - 18.2424i) q^{57} +69.5687i q^{59} -38.3580 q^{61} +(-12.4625 + 12.4625i) q^{63} +(27.0201 + 74.7819i) q^{65} +(76.4370 + 76.4370i) q^{67} +8.30662i q^{69} -56.9363 q^{71} +(-62.0316 + 62.0316i) q^{73} +(43.1183 + 3.97607i) q^{75} +(2.33699 + 2.33699i) q^{77} -33.2153i q^{79} -9.00000 q^{81} +(-43.8882 + 43.8882i) q^{83} +(5.03177 - 1.81807i) q^{85} +(-21.9237 - 21.9237i) q^{87} +103.496i q^{89} -93.4265 q^{91} +(-55.5696 + 55.5696i) q^{93} +(-67.4229 - 31.6324i) q^{95} +(-13.4157 - 13.4157i) q^{97} +1.68770i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 16 q^{5} - 16 q^{7}+O(q^{10}) \) 88 * q - 16 * q^5 - 16 * q^7	\( 88 q - 16 q^{5} - 16 q^{7} - 8 q^{13} + 48 q^{15} + 24 q^{17} + 48 q^{21} + 24 q^{25} - 88 q^{31} - 48 q^{33} - 24 q^{35} - 128 q^{37} - 376 q^{41} + 24 q^{45} + 136 q^{47} + 224 q^{53} + 184 q^{55} - 48 q^{57} + 688 q^{61} - 48 q^{63} - 288 q^{65} + 16 q^{67} + 168 q^{71} - 128 q^{73} + 144 q^{75} - 88 q^{77} - 792 q^{81} + 288 q^{83} + 40 q^{85} + 144 q^{87} - 528 q^{91} - 576 q^{95} - 120 q^{97}+O(q^{100}) \) 88 * q - 16 * q^5 - 16 * q^7 - 8 * q^13 + 48 * q^15 + 24 * q^17 + 48 * q^21 + 24 * q^25 - 88 * q^31 - 48 * q^33 - 24 * q^35 - 128 * q^37 - 376 * q^41 + 24 * q^45 + 136 * q^47 + 224 * q^53 + 184 * q^55 - 48 * q^57 + 688 * q^61 - 48 * q^63 - 288 * q^65 + 16 * q^67 + 168 * q^71 - 128 * q^73 + 144 * q^75 - 88 * q^77 - 792 * q^81 + 288 * q^83 + 40 * q^85 + 144 * q^87 - 528 * q^91 - 576 * q^95 - 120 * q^97

Introduction

L-functions

Modular forms

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