LMFDB - Embedded newform 1148.2.ba.a.113.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.13
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06924i q^{3} +(0.727989 + 2.24052i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.85672 q^{9} +O(q^{10})$	\(q+1.06924i q^{3} +(0.727989 + 2.24052i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.85672 q^{9} +(-5.06104 - 1.64443i) q^{11} +(-3.77521 + 5.19613i) q^{13} +(-2.39565 + 0.778395i) q^{15} +(-6.88228 - 2.23619i) q^{17} +(-2.95505 - 4.06728i) q^{19} +(0.865034 - 0.628484i) q^{21} +(-0.323552 - 0.235074i) q^{23} +(-0.444870 + 0.323217i) q^{25} +5.19301i q^{27} +(1.59102 - 0.516955i) q^{29} +(0.969786 - 2.98469i) q^{31} +(1.75829 - 5.41147i) q^{33} +(1.38472 - 1.90590i) q^{35} +(1.22037 + 3.75592i) q^{37} +(-5.55591 - 4.03661i) q^{39} +(1.37748 + 6.25320i) q^{41} +(2.21734 + 1.61099i) q^{43} +(1.35167 + 4.16002i) q^{45} +(-4.48048 + 6.16686i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.39102 - 7.35882i) q^{51} +(7.71403 - 2.50644i) q^{53} -12.5365i q^{55} +(4.34890 - 3.15966i) q^{57} +(-8.99273 - 6.53360i) q^{59} +(-10.7395 + 7.80272i) q^{61} +(-1.09135 - 1.50212i) q^{63} +(-14.3903 - 4.67570i) q^{65} +(12.1237 - 3.93924i) q^{67} +(0.251351 - 0.345955i) q^{69} +(-10.8704 - 3.53199i) q^{71} -13.1398 q^{73} +(-0.345597 - 0.475674i) q^{75} +(1.64443 + 5.06104i) q^{77} +11.9532i q^{79} +0.0175922 q^{81} +14.5368 q^{83} -17.0478i q^{85} +(0.552750 + 1.70119i) q^{87} +(-8.48226 - 11.6748i) q^{89} +6.42276 q^{91} +(3.19136 + 1.03693i) q^{93} +(6.96156 - 9.58177i) q^{95} +(-5.79801 + 1.88389i) q^{97} +(-9.39695 - 3.05325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$			1.06924i			0.617327i	0.951171	+	0.308663i	$0.0998816\pi$
$3$			1.06924i			0.617327i	−0.951171	+	0.308663i	$0.900118\pi$
$4$		0			0
$5$	0.727989	+	2.24052i	0.325566	+	1.00199i	0.971184	+	0.238330i	$0.0765999\pi$
$5$	0.727989	+	2.24052i	0.325566	+	1.00199i	−0.645618	+	0.763661i	$0.723400\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	1.85672			0.618908
$10$		0			0
$11$	−5.06104	−	1.64443i	−1.52596	−	0.495815i	−0.578498	−	0.815684i	$-0.696361\pi$
$11$	−5.06104	−	1.64443i	−1.52596	−	0.495815i	−0.947462	+	0.319869i	$0.896361\pi$
$12$		0			0
$13$	−3.77521	+	5.19613i	−1.04705	+	1.44115i	−0.155718	+	0.987802i	$0.549769\pi$
$13$	−3.77521	+	5.19613i	−1.04705	+	1.44115i	−0.891336	+	0.453344i	$0.850231\pi$
$14$		0			0
$15$	−2.39565	+	0.778395i	−0.618555	+	0.200981i
$16$		0			0
$17$	−6.88228	−	2.23619i	−1.66920	−	0.542355i	−0.686430	−	0.727196i	$-0.740823\pi$
$17$	−6.88228	−	2.23619i	−1.66920	−	0.542355i	−0.982768	+	0.184841i	$0.940823\pi$
$18$		0			0
$19$	−2.95505	−	4.06728i	−0.677935	−	0.933097i	0.321972	−	0.946749i	$-0.395654\pi$
$19$	−2.95505	−	4.06728i	−0.677935	−	0.933097i	−0.999907	+	0.0136521i	$0.995654\pi$
$20$		0			0
$21$	0.865034	−	0.628484i	0.188766	−	0.137146i
$22$		0			0
$23$	−0.323552	−	0.235074i	−0.0674653	−	0.0490164i	0.553541	−	0.832822i	$-0.313276\pi$
$23$	−0.323552	−	0.235074i	−0.0674653	−	0.0490164i	−0.621007	+	0.783805i	$0.713276\pi$
$24$		0			0
$25$	−0.444870	+	0.323217i	−0.0889741	+	0.0646434i
$26$		0			0
$27$			5.19301i			0.999395i
$28$		0			0
$29$	1.59102	−	0.516955i	0.295446	−	0.0959962i	−0.157544	−	0.987512i	$-0.550357\pi$
$29$	1.59102	−	0.516955i	0.295446	−	0.0959962i	0.452990	+	0.891516i	$0.350357\pi$
$30$		0			0
$31$	0.969786	−	2.98469i	0.174179	−	0.536067i	−0.825416	−	0.564524i	$-0.809060\pi$
$31$	0.969786	−	2.98469i	0.174179	−	0.536067i	0.999595	+	0.0284577i	$0.00905958\pi$
$32$		0			0
$33$	1.75829	−	5.41147i	0.306080	−	0.942016i
$34$		0			0
$35$	1.38472	−	1.90590i	0.234060	−	0.322156i
$36$		0			0
$37$	1.22037	+	3.75592i	0.200628	+	0.617470i	0.999865	+	0.0164533i	$0.00523748\pi$
$37$	1.22037	+	3.75592i	0.200628	+	0.617470i	−0.799236	+	0.601017i	$0.794763\pi$
$38$		0			0
$39$	−5.55591	−	4.03661i	−0.889658	−	0.646374i
$40$		0			0
$41$	1.37748	+	6.25320i	0.215126	+	0.976586i
$41$	1.37748	+	6.25320i	0.215126	+	0.976586i
$42$		0			0
$43$	2.21734	+	1.61099i	0.338141	+	0.245674i	0.743877	−	0.668316i	$-0.232985\pi$
$43$	2.21734	+	1.61099i	0.338141	+	0.245674i	−0.405736	+	0.913990i	$0.632985\pi$
$44$		0			0
$45$	1.35167	+	4.16002i	0.201496	+	0.620140i
$46$		0			0
$47$	−4.48048	+	6.16686i	−0.653546	+	0.899529i	−0.999246	−	0.0388163i	$-0.987641\pi$
$47$	−4.48048	+	6.16686i	−0.653546	+	0.899529i	0.345701	+	0.938345i	$0.387641\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	2.39102	−	7.35882i	0.334810	−	1.03044i
$52$		0			0
$53$	7.71403	−	2.50644i	1.05960	−	0.344286i	0.273173	−	0.961965i	$-0.411927\pi$
$53$	7.71403	−	2.50644i	1.05960	−	0.344286i	0.786431	+	0.617679i	$0.211927\pi$
$54$		0			0
$55$		−	12.5365i		−	1.69042i
$56$		0			0
$57$	4.34890	−	3.15966i	0.576026	−	0.418507i
$58$		0			0
$59$	−8.99273	−	6.53360i	−1.17075	−	0.850602i	−0.179655	−	0.983730i	$-0.557498\pi$
$59$	−8.99273	−	6.53360i	−1.17075	−	0.850602i	−0.991099	+	0.133127i	$0.957498\pi$
$60$		0			0
$61$	−10.7395	+	7.80272i	−1.37505	+	0.999035i	−0.377731	+	0.925915i	$0.623296\pi$
$61$	−10.7395	+	7.80272i	−1.37505	+	0.999035i	−0.997323	+	0.0731200i	$0.976704\pi$
$62$		0			0
$63$	−1.09135	−	1.50212i	−0.137498	−	0.189249i
$64$		0			0
$65$	−14.3903	−	4.67570i	−1.78490	−	0.579949i
$66$		0			0
$67$	12.1237	−	3.93924i	1.48115	−	0.481255i	0.546693	−	0.837333i	$-0.315886\pi$
$67$	12.1237	−	3.93924i	1.48115	−	0.481255i	0.934456	+	0.356078i	$0.115886\pi$
$68$		0			0
$69$	0.251351	−	0.345955i	0.0302591	−	0.0416481i
$70$		0			0
$71$	−10.8704	−	3.53199i	−1.29007	−	0.419170i	−0.417956	−	0.908467i	$-0.637254\pi$
$71$	−10.8704	−	3.53199i	−1.29007	−	0.419170i	−0.872117	+	0.489297i	$0.837254\pi$
$72$		0			0
$73$	−13.1398			−1.53790			−0.768949	−	0.639310i	$-0.779220\pi$
$73$	−13.1398			−1.53790			−0.768949	+	0.639310i	$0.779220\pi$
$74$		0			0
$75$	−0.345597	−	0.475674i	−0.0399061	−	0.0549261i
$76$		0			0
$77$	1.64443	+	5.06104i	0.187400	+	0.576759i
$78$		0			0
$79$			11.9532i			1.34484i	0.740168	+	0.672422i	$0.234746\pi$
$79$			11.9532i			1.34484i	−0.740168	+	0.672422i	$0.765254\pi$
$80$		0			0
$81$	0.0175922			0.00195469
$82$		0			0
$83$	14.5368			1.59562			0.797810	−	0.602909i	$-0.205992\pi$
$83$	14.5368			1.59562			0.797810	+	0.602909i	$0.205992\pi$
$84$		0			0
$85$		−	17.0478i		−	1.84909i
$86$		0			0
$87$	0.552750	+	1.70119i	0.0592610	+	0.182387i
$88$		0			0
$89$	−8.48226	−	11.6748i	−0.899118	−	1.23753i	−0.970749	−	0.240099i	$-0.922820\pi$
$89$	−8.48226	−	11.6748i	−0.899118	−	1.23753i	0.0716305	−	0.997431i	$-0.477180\pi$
$90$		0			0
$91$	6.42276			0.673289
$92$		0			0
$93$	3.19136	+	1.03693i	0.330928	+	0.107525i
$94$		0			0
$95$	6.96156	−	9.58177i	0.714241	−	0.983069i
$96$		0			0
$97$	−5.79801	+	1.88389i	−0.588698	+	0.191280i	−0.588194	−	0.808720i	$-0.700161\pi$
$97$	−5.79801	+	1.88389i	−0.588698	+	0.191280i	−0.000504716		1.00000i	$0.500161\pi$
$98$		0			0
$99$	−9.39695	−	3.05325i	−0.944429	−	0.306863i
$100$		0			0
$101$	−3.71789	−	5.11724i	−0.369944	−	0.509184i	0.582942	−	0.812514i	$-0.301902\pi$
$101$	−3.71789	−	5.11724i	−0.369944	−	0.509184i	−0.952886	+	0.303330i	$0.901902\pi$
$102$		0			0
$103$	1.34492	−	0.977139i	0.132519	−	0.0962803i	−0.519551	−	0.854439i	$-0.673901\pi$
$103$	1.34492	−	0.977139i	0.132519	−	0.0962803i	0.652070	+	0.758159i	$0.273901\pi$
$104$		0			0
$105$	2.03787	+	1.48060i	0.198875	+	0.144491i
$106$		0			0
$107$	0.620276	−	0.450657i	0.0599643	−	0.0435666i	−0.557399	−	0.830245i	$-0.688201\pi$
$107$	0.620276	−	0.450657i	0.0599643	−	0.0435666i	0.617364	+	0.786678i	$0.288201\pi$
$108$		0			0
$109$			6.85277i			0.656376i	0.944612	+	0.328188i	$0.106438\pi$
$109$			6.85277i			0.656376i	−0.944612	+	0.328188i	$0.893562\pi$
$110$		0			0
$111$	−4.01599	+	1.30487i	−0.381181	+	0.123853i
$112$		0			0
$113$	0.983477	−	3.02683i	0.0925178	−	0.284740i	−0.894081	−	0.447905i	$-0.852170\pi$
$113$	0.983477	−	3.02683i	0.0925178	−	0.284740i	0.986599	+	0.163165i	$0.0521702\pi$
$114$		0			0
$115$	0.291146	−	0.896056i	0.0271495	−	0.0835576i
$116$		0			0
$117$	−7.00951	+	9.64777i	−0.648030	+	0.891936i
$118$		0			0
$119$	2.23619	+	6.88228i	0.204991	+	0.630898i
$120$		0			0
$121$	14.0108	+	10.1794i	1.27371	+	0.925401i
$122$		0			0
$123$	−6.68618	+	1.47285i	−0.602873	+	0.132803i
$124$		0			0
$125$	8.48146	+	6.16214i	0.758605	+	0.551159i
$126$		0			0
$127$	5.15073	+	15.8523i	0.457054	+	1.40667i	0.868707	+	0.495326i	$0.164951\pi$
$127$	5.15073	+	15.8523i	0.457054	+	1.40667i	−0.411654	+	0.911340i	$0.635049\pi$
$128$		0			0
$129$	−1.72254	+	2.37087i	−0.151661	+	0.208744i
$130$		0			0
$131$	−3.93063	+	12.0972i	−0.343421	+	1.05694i	0.619003	+	0.785388i	$0.287537\pi$
$131$	−3.93063	+	12.0972i	−0.343421	+	1.05694i	−0.962424	+	0.271552i	$0.912463\pi$
$132$		0			0
$133$	−1.55356	+	4.78137i	−0.134711	+	0.414597i
$134$		0			0
$135$	−11.6350	+	3.78045i	−1.00138	+	0.325369i
$136$		0			0
$137$			12.4445i			1.06321i	0.846993	+	0.531604i	$0.178411\pi$
$137$			12.4445i			1.06321i	−0.846993	+	0.531604i	$0.821589\pi$
$138$		0			0
$139$	−5.64370	+	4.10039i	−0.478692	+	0.347790i	−0.800819	−	0.598906i	$-0.795602\pi$
$139$	−5.64370	+	4.10039i	−0.478692	+	0.347790i	0.322127	+	0.946696i	$0.395602\pi$
$140$		0			0
$141$	−6.59386	−	4.79072i	−0.555303	−	0.403451i
$142$		0			0
$143$	27.6511	−	20.0897i	2.31230	−	1.67999i
$144$		0			0
$145$	2.31650	+	3.18838i	0.192375	+	0.264781i
$146$		0			0
$147$	−1.01691	−	0.330414i	−0.0838732	−	0.0272521i
$148$		0			0
$149$	−0.139122	+	0.0452035i	−0.0113973	+	0.00370322i	−0.314710	−	0.949188i	$-0.601907\pi$
$149$	−0.139122	+	0.0452035i	−0.0113973	+	0.00370322i	0.303313	+	0.952891i	$0.401907\pi$
$150$		0			0
$151$	−0.697695	+	0.960295i	−0.0567776	+	0.0781477i	−0.836462	−	0.548025i	$-0.815380\pi$
$151$	−0.697695	+	0.960295i	−0.0567776	+	0.0781477i	0.779684	+	0.626173i	$0.215380\pi$
$152$		0			0
$153$	−12.7785	−	4.15198i	−1.03308	−	0.335668i
$154$		0			0
$155$	7.39325			0.593840
$156$		0			0
$157$	7.82229	+	10.7665i	0.624287	+	0.859257i	0.997656	−	0.0684258i	$-0.0217977\pi$
$157$	7.82229	+	10.7665i	0.624287	+	0.859257i	−0.373370	+	0.927683i	$0.621798\pi$
$158$		0			0
$159$	2.67999	+	8.24816i	0.212537	+	0.654122i
$160$		0			0
$161$			0.399932i			0.0315191i
$162$		0			0
$163$	−5.36696			−0.420373			−0.210186	−	0.977661i	$-0.567407\pi$
$163$	−5.36696			−0.420373			−0.210186	+	0.977661i	$0.567407\pi$
$164$		0			0
$165$	13.4045			1.04354
$166$		0			0
$167$		−	19.9599i		−	1.54454i	−0.635291	−	0.772272i	$-0.719120\pi$
$167$		−	19.9599i		−	1.54454i	0.635291	−	0.772272i	$-0.280880\pi$
$168$		0			0
$169$	−8.73032	−	26.8691i	−0.671563	−	2.06686i
$170$		0			0
$171$	−5.48671	−	7.55181i	−0.419579	−	0.577501i
$172$		0			0
$173$	2.84802			0.216531			0.108265	−	0.994122i	$-0.465470\pi$
$173$	2.84802			0.216531			0.108265	+	0.994122i	$0.465470\pi$
$174$		0			0
$175$	0.522976	+	0.169925i	0.0395333	+	0.0128451i
$176$		0			0
$177$	6.98599	−	9.61540i	0.525099	−	0.722737i
$178$		0			0
$179$	−2.71707	+	0.882831i	−0.203084	+	0.0659859i	−0.408792	−	0.912627i	$-0.634050\pi$
$179$	−2.71707	+	0.882831i	−0.203084	+	0.0659859i	0.205709	+	0.978613i	$0.434050\pi$
$180$		0			0
$181$	14.2444	+	4.62830i	1.05878	+	0.344018i	0.786108	−	0.618089i	$-0.212093\pi$
$181$	14.2444	+	4.62830i	1.05878	+	0.344018i	0.272672	+	0.962107i	$0.412093\pi$
$182$		0			0
$183$	−8.34298	−	11.4831i	−0.616731	−	0.848858i
$184$		0			0
$185$	−7.52680	+	5.46854i	−0.553381	+	0.402055i
$186$		0			0
$187$	31.1542	+	22.6349i	2.27822	+	1.65523i
$188$		0			0
$189$	4.20123	−	3.05237i	0.305595	−	0.222028i
$190$		0			0
$191$		−	5.05513i		−	0.365777i	−0.983134	−	0.182888i	$-0.941455\pi$
$191$		−	5.05513i		−	0.365777i	0.983134	−	0.182888i	$-0.0585447\pi$
$192$		0			0
$193$	0.121457	−	0.0394638i	0.00874268	−	0.00284067i	−0.304642	−	0.952467i	$-0.598537\pi$
$193$	0.121457	−	0.0394638i	0.00874268	−	0.00284067i	0.313385	+	0.949626i	$0.398537\pi$
$194$		0			0
$195$	4.99945	−	15.3867i	0.358018	−	1.10187i
$196$		0			0
$197$	−4.48175	+	13.7934i	−0.319312	+	0.982740i	0.654631	+	0.755948i	$0.272824\pi$
$197$	−4.48175	+	13.7934i	−0.319312	+	0.982740i	−0.973943	+	0.226792i	$0.927176\pi$
$198$		0			0
$199$	−1.96010	+	2.69784i	−0.138948	+	0.191245i	−0.872820	−	0.488043i	$-0.837711\pi$
$199$	−1.96010	+	2.69784i	−0.138948	+	0.191245i	0.733872	+	0.679288i	$0.237711\pi$
$200$		0			0
$201$	4.21200	+	12.9632i	0.297091	+	0.914353i
$202$		0			0
$203$	−1.35341	−	0.983307i	−0.0949905	−	0.0690147i
$204$		0			0
$205$	−13.0076	+	7.63852i	−0.908492	+	0.533497i
$206$		0			0
$207$	−0.600747	−	0.436468i	−0.0417548	−	0.0303366i
$208$		0			0
$209$	8.26726	+	25.4440i	0.571858	+	1.76000i
$210$		0			0
$211$	1.68113	−	2.31388i	0.115734	−	0.159294i	−0.747220	−	0.664577i	$-0.768612\pi$
$211$	1.68113	−	2.31388i	0.115734	−	0.159294i	0.862954	+	0.505283i	$0.168612\pi$
$212$		0			0
$213$	3.77655	−	11.6230i	0.258765	−	0.796397i
$214$		0			0
$215$	−1.99526	+	6.14078i	−0.136076	+	0.418797i
$216$		0			0
$217$	−2.98469	+	0.969786i	−0.202614	+	0.0658333i
$218$		0			0
$219$		−	14.0496i		−	0.949386i
$220$		0			0
$221$	37.6015	−	27.3191i	2.52935	−	1.83768i
$222$		0			0
$223$	−4.40673	−	3.20168i	−0.295097	−	0.214400i	0.430379	−	0.902648i	$-0.358380\pi$
$223$	−4.40673	−	3.20168i	−0.295097	−	0.214400i	−0.725475	+	0.688248i	$0.758380\pi$
$224$		0			0
$225$	−0.826001	+	0.600125i	−0.0550667	+	0.0400083i
$226$		0			0
$227$	6.61776	+	9.10857i	0.439236	+	0.604557i	0.970042	−	0.242936i	$-0.0781106\pi$
$227$	6.61776	+	9.10857i	0.439236	+	0.604557i	−0.530806	+	0.847494i	$0.678111\pi$
$228$		0			0
$229$	14.9488	+	4.85716i	0.987844	+	0.320970i	0.757998	−	0.652257i	$-0.226178\pi$
$229$	14.9488	+	4.85716i	0.987844	+	0.320970i	0.229846	+	0.973227i	$0.426178\pi$
$230$		0			0
$231$	−5.41147	+	1.75829i	−0.356049	+	0.115687i
$232$		0			0
$233$	−5.07160	+	6.98046i	−0.332252	+	0.457305i	−0.942158	−	0.335168i	$-0.891207\pi$
$233$	−5.07160	+	6.98046i	−0.332252	+	0.457305i	0.609907	+	0.792473i	$0.291207\pi$
$234$		0			0
$235$	−17.0787	−	5.54921i	−1.11409	−	0.361990i
$236$		0			0
$237$	−12.7809			−0.830208
$238$		0			0
$239$	−15.3779	−	21.1659i	−0.994713	−	1.36911i	−0.928513	−	0.371299i	$-0.878912\pi$
$239$	−15.3779	−	21.1659i	−0.994713	−	1.36911i	−0.0662000	−	0.997806i	$-0.521088\pi$
$240$		0			0
$241$	4.37637	+	13.4691i	0.281907	+	0.867620i	0.987309	+	0.158812i	$0.0507665\pi$
$241$	4.37637	+	13.4691i	0.281907	+	0.867620i	−0.705402	+	0.708808i	$0.749233\pi$
$242$		0			0
$243$			15.5978i			1.00060i
$244$		0			0
$245$	−2.35582			−0.150508
$246$		0			0
$247$	32.2900			2.05456
$248$		0			0
$249$			15.5433i			0.985018i
$250$		0			0
$251$	7.15199	+	22.0116i	0.451430	+	1.38936i	0.875276	+	0.483624i	$0.160680\pi$
$251$	7.15199	+	22.0116i	0.451430	+	1.38936i	−0.423846	+	0.905734i	$0.639320\pi$
$252$		0			0
$253$	1.25095	+	1.72178i	0.0786463	+	0.108247i
$254$		0			0
$255$	18.2282			1.14149
$256$		0			0
$257$	−27.6362	−	8.97954i	−1.72390	−	0.560129i	−0.731352	−	0.682000i	$-0.761110\pi$
$257$	−27.6362	−	8.97954i	−1.72390	−	0.560129i	−0.992546	+	0.121871i	$0.961110\pi$
$258$		0			0
$259$	2.32129	−	3.19498i	0.144238	−	0.198526i
$260$		0			0
$261$	2.95409	−	0.959843i	0.182854	−	0.0594128i
$262$		0			0
$263$	−11.3121	−	3.67554i	−0.697537	−	0.226643i	−0.0612798	−	0.998121i	$-0.519518\pi$
$263$	−11.3121	−	3.67554i	−0.697537	−	0.226643i	−0.636257	+	0.771477i	$0.719518\pi$
$264$		0			0
$265$	11.2315	+	15.4588i	0.689943	+	0.949625i
$266$		0			0
$267$	12.4832	−	9.06958i	0.763960	−	0.555050i
$268$		0			0
$269$	2.05046	+	1.48975i	0.125019	+	0.0908314i	0.648537	−	0.761183i	$-0.275381\pi$
$269$	2.05046	+	1.48975i	0.125019	+	0.0908314i	−0.523519	+	0.852014i	$0.675381\pi$
$270$		0			0
$271$	18.7397	−	13.6152i	1.13836	−	0.827064i	0.151466	−	0.988462i	$-0.451600\pi$
$271$	18.7397	−	13.6152i	1.13836	−	0.827064i	0.986889	+	0.161399i	$0.0516005\pi$
$272$		0			0
$273$			6.86748i			0.415639i
$274$		0			0
$275$	2.78301	−	0.904256i	0.167822	−	0.0545287i
$276$		0			0
$277$	−6.21766	+	19.1360i	−0.373583	+	1.14977i	0.570846	+	0.821057i	$0.306615\pi$
$277$	−6.21766	+	19.1360i	−0.373583	+	1.14977i	−0.944429	+	0.328714i	$0.893385\pi$
$278$		0			0
$279$	1.80062	−	5.54175i	0.107801	−	0.331776i
$280$		0			0
$281$	−9.99171	+	13.7524i	−0.596055	+	0.820400i	−0.995340	−	0.0964271i	$-0.969259\pi$
$281$	−9.99171	+	13.7524i	−0.596055	+	0.820400i	0.399285	+	0.916827i	$0.369259\pi$
$282$		0			0
$283$	−4.45478	−	13.7104i	−0.264809	−	0.814999i	−0.991737	−	0.128286i	$-0.959053\pi$
$283$	−4.45478	−	13.7104i	−0.264809	−	0.814999i	0.726928	−	0.686714i	$-0.240947\pi$
$284$		0			0
$285$	10.2452	+	7.44359i	0.606875	+	0.440920i
$286$		0			0
$287$	4.24929	−	4.78994i	0.250828	−	0.282741i
$288$		0			0
$289$	28.6120	+	20.7878i	1.68306	+	1.22281i
$290$		0			0
$291$	−2.01433	−	6.19947i	−0.118082	−	0.363419i
$292$		0			0
$293$	−1.37079	+	1.88673i	−0.0800825	+	0.110224i	−0.847179	−	0.531308i	$-0.821701\pi$
$293$	−1.37079	+	1.88673i	−0.0800825	+	0.110224i	0.767096	+	0.641532i	$0.221701\pi$
$294$		0			0
$295$	8.09205	−	24.9048i	0.471137	−	1.45001i
$296$		0			0
$297$	8.53954	−	26.2820i	0.495515	−	1.52504i
$298$		0			0
$299$	2.44295	−	0.793763i	0.141279	−	0.0459045i
$300$		0			0
$301$		−	2.74078i		−	0.157976i
$302$		0			0
$303$	5.47156	−	3.97532i	0.314333	−	0.228376i
$304$		0			0
$305$	−25.3004	−	18.3818i	−1.44870	−	1.05254i
$306$		0			0
$307$	−17.2615	+	12.5412i	−0.985168	+	0.715766i	−0.958858	−	0.283888i	$-0.908376\pi$
$307$	−17.2615	+	12.5412i	−0.985168	+	0.715766i	−0.0263101	+	0.999654i	$0.508376\pi$
$308$		0			0
$309$	1.04480	+	1.43804i	0.0594364	+	0.0818072i
$310$		0			0
$311$	−2.83654	−	0.921649i	−0.160846	−	0.0522619i	0.227487	−	0.973781i	$-0.426949\pi$
$311$	−2.83654	−	0.921649i	−0.160846	−	0.0522619i	−0.388333	+	0.921519i	$0.626949\pi$
$312$		0			0
$313$	19.6248	−	6.37648i	1.10926	−	0.360420i	0.303599	−	0.952800i	$-0.401812\pi$
$313$	19.6248	−	6.37648i	1.10926	−	0.360420i	0.805659	+	0.592380i	$0.201812\pi$
$314$		0			0
$315$	2.57104	−	3.53873i	0.144861	−	0.199385i
$316$		0			0
$317$	17.2415	+	5.60210i	0.968379	+	0.314646i	0.750162	−	0.661255i	$-0.229976\pi$
$317$	17.2415	+	5.60210i	0.968379	+	0.314646i	0.218218	+	0.975900i	$0.429976\pi$
$318$		0			0
$319$	−8.90233			−0.498435
$320$		0			0
$321$	0.481861	+	0.663224i	0.0268948	+	0.0370176i
$322$		0			0
$323$	11.2423	+	34.6002i	0.625537	+	1.92521i
$324$		0			0
$325$		−	3.53181i		−	0.195910i
$326$		0			0
$327$	−7.32726			−0.405198
$328$		0			0
$329$	7.62265			0.420251
$330$		0			0
$331$			21.8420i			1.20054i	0.799796	+	0.600272i	$0.204941\pi$
$331$			21.8420i			1.20054i	−0.799796	+	0.600272i	$0.795059\pi$
$332$		0			0
$333$	2.26590	+	6.97371i	0.124170	+	0.382157i
$334$		0			0
$335$	17.6519	+	24.2957i	0.964425	+	1.32742i
$336$		0			0
$337$	24.1267			1.31427			0.657133	−	0.753775i	$-0.271769\pi$
$337$	24.1267			1.31427			0.657133	+	0.753775i	$0.271769\pi$
$338$		0			0
$339$	3.23641	+	1.05157i	0.175778	+	0.0571137i
$340$		0			0
$341$	−9.81624	+	13.5109i	−0.531579	+	0.731656i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	0.958099	+	0.311305i	0.0515823	+	0.0167601i
$346$		0			0
$347$	−6.69024	−	9.20832i	−0.359151	−	0.494328i	0.590761	−	0.806846i	$-0.298828\pi$
$347$	−6.69024	−	9.20832i	−0.359151	−	0.494328i	−0.949912	+	0.312518i	$0.898828\pi$
$348$		0			0
$349$	4.02434	−	2.92385i	0.215418	−	0.156510i	−0.474844	−	0.880070i	$-0.657495\pi$
$349$	4.02434	−	2.92385i	0.215418	−	0.156510i	0.690262	+	0.723560i	$0.257495\pi$
$350$		0			0
$351$	−26.9835	−	19.6047i	−1.44027	−	1.04642i
$352$		0			0
$353$	14.9641	−	10.8721i	0.796459	−	0.578661i	−0.113414	−	0.993548i	$-0.536179\pi$
$353$	14.9641	−	10.8721i	0.796459	−	0.578661i	0.909873	+	0.414887i	$0.136179\pi$
$354$		0			0
$355$		−	26.9265i		−	1.42911i
$356$		0			0
$357$	−7.35882	+	2.39102i	−0.389470	+	0.126546i
$358$		0			0
$359$	4.74933	−	14.6169i	0.250660	−	0.771452i	−0.743994	−	0.668187i	$-0.767071\pi$
$359$	4.74933	−	14.6169i	0.250660	−	0.771452i	0.994654	−	0.103266i	$-0.0329292\pi$
$360$		0			0
$361$	−1.93910	+	5.96793i	−0.102058	+	0.314101i
$362$		0			0
$363$	−10.8842	+	14.9809i	−0.571275	+	0.786292i
$364$		0			0
$365$	−9.56563	−	29.4400i	−0.500688	−	1.54096i
$366$		0			0
$367$	−20.1325	−	14.6272i	−1.05091	−	0.763531i	−0.0785250	−	0.996912i	$-0.525021\pi$
$367$	−20.1325	−	14.6272i	−1.05091	−	0.763531i	−0.972385	+	0.233381i	$0.925021\pi$
$368$		0			0
$369$	2.55759	+	11.6105i	0.133143	+	0.604417i
$370$		0			0
$371$	−6.56195	−	4.76754i	−0.340679	−	0.247518i
$372$		0			0
$373$	−7.67868	−	23.6326i	−0.397587	−	1.22365i	−0.926928	−	0.375238i	$-0.877561\pi$
$373$	−7.67868	−	23.6326i	−0.397587	−	1.22365i	0.529341	−	0.848409i	$-0.322439\pi$
$374$		0			0
$375$	−6.58881	+	9.06872i	−0.340245	+	0.468307i
$376$		0			0
$377$	−3.32028	+	10.2188i	−0.171003	+	0.526294i
$378$		0			0
$379$	3.39876	−	10.4603i	0.174583	−	0.537310i	−0.825032	−	0.565087i	$-0.808843\pi$
$379$	3.39876	−	10.4603i	0.174583	−	0.537310i	0.999614	+	0.0277768i	$0.00884276\pi$
$380$		0			0
$381$	−16.9500	+	5.50737i	−0.868373	+	0.282151i
$382$		0			0
$383$			3.65639i			0.186833i	0.995627	+	0.0934164i	$0.0297788\pi$
$383$			3.65639i			0.186833i	−0.995627	+	0.0934164i	$0.970221\pi$
$384$		0			0
$385$	−10.1422	+	7.36875i	−0.516895	+	0.375547i
$386$		0			0
$387$	4.11699	+	2.99117i	0.209278	+	0.152050i
$388$		0			0
$389$	−12.1519	+	8.82884i	−0.616123	+	0.447640i	−0.851565	−	0.524249i	$-0.824346\pi$
$389$	−12.1519	+	8.82884i	−0.616123	+	0.447640i	0.235442	+	0.971888i	$0.424346\pi$
$390$		0			0
$391$	1.70111	+	2.34137i	0.0860286	+	0.118408i
$392$		0			0
$393$	−12.9349	−	4.20279i	−0.652477	−	0.212003i
$394$		0			0
$395$	−26.7814	+	8.70181i	−1.34752	+	0.437836i
$396$		0			0
$397$	19.1158	−	26.3107i	0.959397	−	1.32050i	0.0121718	−	0.999926i	$-0.496125\pi$
$397$	19.1158	−	26.3107i	0.959397	−	1.32050i	0.947225	−	0.320570i	$-0.103875\pi$
$398$		0			0
$399$	−5.11244	−	1.66113i	−0.255942	−	0.0831606i
$400$		0			0
$401$	−35.0510			−1.75036			−0.875181	−	0.483795i	$-0.839258\pi$
$401$	−35.0510			−1.75036			−0.875181	+	0.483795i	$0.839258\pi$
$402$		0			0
$403$	11.8477	+	16.3070i	0.590176	+	0.812308i
$404$		0			0
$405$	0.0128069	+	0.0394157i	0.000636381	+	0.00195858i
$406$		0			0
$407$		−	21.0157i		−	1.04171i
$408$		0			0
$409$	29.9150			1.47920			0.739600	−	0.673047i	$-0.235015\pi$
$409$	29.9150			1.47920			0.739600	+	0.673047i	$0.235015\pi$
$410$		0			0
$411$	−13.3062			−0.656347
$412$		0			0
$413$			11.1156i			0.546964i
$414$		0			0
$415$	10.5826	+	32.5699i	0.519480	+	1.59880i
$416$		0			0
$417$	−4.38430	−	6.03447i	−0.214700	−	0.295509i
$418$		0			0
$419$	−10.8450			−0.529811			−0.264905	−	0.964274i	$-0.585341\pi$
$419$	−10.8450			−0.529811			−0.264905	+	0.964274i	$0.585341\pi$
$420$		0			0
$421$	−15.2006	−	4.93899i	−0.740834	−	0.240711i	−0.0858012	−	0.996312i	$-0.527345\pi$
$421$	−15.2006	−	4.93899i	−0.740834	−	0.240711i	−0.655032	+	0.755601i	$0.727345\pi$
$422$		0			0
$423$	−8.31902	+	11.4501i	−0.404485	+	0.556725i
$424$		0			0
$425$	3.78450	−	1.22966i	0.183575	−	0.0596472i
$426$		0			0
$427$	12.6251	+	4.10213i	0.610969	+	0.198516i
$428$		0			0
$429$	21.4808	+	29.5657i	1.03710	+	1.42745i
$430$		0			0
$431$	−21.6374	+	15.7205i	−1.04224	+	0.757231i	−0.970721	−	0.240208i	$-0.922784\pi$
$431$	−21.6374	+	15.7205i	−1.04224	+	0.757231i	−0.0715179	+	0.997439i	$0.522784\pi$
$432$		0			0
$433$	11.6473	+	8.46224i	0.559732	+	0.406669i	0.831361	−	0.555733i	$-0.187562\pi$
$433$	11.6473	+	8.46224i	0.559732	+	0.406669i	−0.271629	+	0.962402i	$0.587562\pi$
$434$		0			0
$435$	−3.40915	+	2.47689i	−0.163456	+	0.118758i
$436$		0			0
$437$			2.01063i			0.0961815i
$438$		0			0
$439$	19.3755	−	6.29548i	0.924742	−	0.300467i	0.192331	−	0.981330i	$-0.438395\pi$
$439$	19.3755	−	6.29548i	0.924742	−	0.300467i	0.732411	+	0.680863i	$0.238395\pi$
$440$		0			0
$441$	−0.573759	+	1.76585i	−0.0273219	+	0.0840880i
$442$		0			0
$443$	−1.65971	+	5.10806i	−0.0788552	+	0.242691i	−0.982711	−	0.185146i	$-0.940724\pi$
$443$	−1.65971	+	5.10806i	−0.0788552	+	0.242691i	0.903856	+	0.427837i	$0.140724\pi$
$444$		0			0
$445$	19.9827	−	27.5038i	0.947270	−	1.30381i
$446$		0			0
$447$	−0.0483335	−	0.148755i	−0.00228609	−	0.00703588i
$448$		0			0
$449$	−18.4335	−	13.3927i	−0.869931	−	0.632042i	0.0606371	−	0.998160i	$-0.480687\pi$
$449$	−18.4335	−	13.3927i	−0.869931	−	0.632042i	−0.930569	+	0.366118i	$0.880687\pi$
$450$		0			0
$451$	3.31151	−	33.9129i	0.155933	−	1.59689i
$452$		0			0
$453$	−1.02679	−	0.746005i	−0.0482427	−	0.0350504i
$454$		0			0
$455$	4.67570	+	14.3903i	0.219200	+	0.674629i
$456$		0			0
$457$	−0.176619	+	0.243096i	−0.00826190	+	0.0113715i	−0.813128	−	0.582085i	$-0.802237\pi$
$457$	−0.176619	+	0.243096i	−0.00826190	+	0.0113715i	0.804866	+	0.593457i	$0.202237\pi$
$458$		0			0
$459$	11.6125	−	35.7397i	0.542027	−	1.66819i
$460$		0			0
$461$	−1.40869	+	4.33551i	−0.0656094	+	0.201925i	−0.978487	−	0.206308i	$-0.933855\pi$
$461$	−1.40869	+	4.33551i	−0.0656094	+	0.201925i	0.912878	+	0.408233i	$0.133855\pi$
$462$		0			0
$463$	11.8962	−	3.86530i	0.552862	−	0.179636i	−0.0192448	−	0.999815i	$-0.506126\pi$
$463$	11.8962	−	3.86530i	0.552862	−	0.179636i	0.572107	+	0.820179i	$0.306126\pi$
$464$		0			0
$465$			7.90517i			0.366594i
$466$		0			0
$467$	−26.1594	+	19.0059i	−1.21051	+	0.879490i	−0.995277	−	0.0970720i	$-0.969052\pi$
$467$	−26.1594	+	19.0059i	−1.21051	+	0.879490i	−0.215237	+	0.976562i	$0.569052\pi$
$468$		0			0
$469$	−10.3131	−	7.49288i	−0.476213	−	0.345989i
$470$		0			0
$471$	−11.5119	+	8.36391i	−0.530442	+	0.385389i
$472$		0			0
$473$	−8.57288	−	11.7996i	−0.394181	−	0.542544i
$474$		0			0
$475$	2.62923	+	0.854288i	0.120637	+	0.0391974i
$476$		0			0
$477$	14.3228	−	4.65377i	0.655797	−	0.213081i
$478$		0			0
$479$	−2.21588	+	3.04990i	−0.101246	+	0.139354i	−0.856634	−	0.515924i	$-0.827449\pi$
$479$	−2.21588	+	3.04990i	−0.101246	+	0.139354i	0.755388	+	0.655278i	$0.227449\pi$
$480$		0			0
$481$	−24.1234	−	7.83817i	−1.09993	−	0.357390i
$482$		0			0
$483$	−0.427624			−0.0194576
$484$		0			0
$485$	−8.44176	−	11.6191i	−0.383321	−	0.527596i
$486$		0			0
$487$	−5.99724	−	18.4576i	−0.271761	−	0.836395i	−0.990058	−	0.140658i	$-0.955078\pi$
$487$	−5.99724	−	18.4576i	−0.271761	−	0.836395i	0.718297	−	0.695736i	$-0.244922\pi$
$488$		0			0
$489$		−	5.73857i		−	0.259507i
$490$		0			0
$491$	11.8973			0.536918			0.268459	−	0.963291i	$-0.413486\pi$
$491$	11.8973			0.536918			0.268459	+	0.963291i	$0.413486\pi$
$492$		0			0
$493$	−12.1059			−0.545222
$494$		0			0
$495$		−	23.2768i		−	1.04621i
$496$		0			0
$497$	3.53199	+	10.8704i	0.158432	+	0.487602i
$498$		0			0
$499$	8.68246	+	11.9504i	0.388681	+	0.534973i	0.957858	−	0.287242i	$-0.0927383\pi$
$499$	8.68246	+	11.9504i	0.388681	+	0.534973i	−0.569178	+	0.822215i	$0.692738\pi$
$500$		0			0
$501$	21.3420			0.953489
$502$		0			0
$503$	11.7726	+	3.82514i	0.524912	+	0.170554i	0.559474	−	0.828848i	$-0.311003\pi$
$503$	11.7726	+	3.82514i	0.524912	+	0.170554i	−0.0345612	+	0.999403i	$0.511003\pi$
$504$		0			0
$505$	8.75868	−	12.0553i	0.389756	−	0.536454i
$506$		0			0
$507$	28.7296	−	9.33481i	1.27593	−	0.414574i
$508$		0			0
$509$	36.8310	+	11.9671i	1.63250	+	0.530433i	0.974845	−	0.222884i	$-0.0715470\pi$
$509$	36.8310	+	11.9671i	1.63250	+	0.530433i	0.657659	+	0.753316i	$0.271547\pi$
$510$		0			0
$511$	7.72339	+	10.6303i	0.341662	+	0.470258i
$512$		0			0
$513$	21.1214	−	15.3456i	0.932533	−	0.677525i
$514$		0			0
$515$	3.16838	+	2.30196i	0.139616	+	0.101437i
$516$		0			0
$517$	32.8169	−	23.8428i	1.44328	−	1.04861i
$518$		0			0
$519$			3.04522i			0.133670i
$520$		0			0
$521$	16.5051	−	5.36282i	0.723100	−	0.234950i	0.0757335	−	0.997128i	$-0.475870\pi$
$521$	16.5051	−	5.36282i	0.723100	−	0.234950i	0.647367	+	0.762179i	$0.275870\pi$
$522$		0			0
$523$	−8.85198	+	27.2436i	−0.387070	+	1.19128i	0.547897	+	0.836546i	$0.315428\pi$
$523$	−8.85198	+	27.2436i	−0.387070	+	1.19128i	−0.934967	+	0.354734i	$0.884572\pi$
$524$		0			0
$525$	−0.181691	+	0.559188i	−0.00792965	+	0.0244050i
$526$		0			0
$527$	−13.3487	+	18.3729i	−0.581477	+	0.800335i
$528$		0			0
$529$	−7.05796	−	21.7222i	−0.306868	−	0.944443i
$530$		0			0
$531$	−16.6970	−	12.1311i	−0.724589	−	0.526444i
$532$		0			0
$533$	−37.6927	−	16.4496i	−1.63265	−	0.712511i
$534$		0			0
$535$	1.46126	+	1.06167i	0.0631757	+	0.0458998i
$536$		0			0
$537$	−0.943959	−	2.90521i	−0.0407348	−	0.125369i
$538$		0			0
$539$	3.12789	−	4.30518i	0.134728	−	0.185437i
$540$		0			0
$541$	−1.36494	+	4.20086i	−0.0586834	+	0.180609i	−0.976101	−	0.217316i	$-0.930270\pi$
$541$	−1.36494	+	4.20086i	−0.0586834	+	0.180609i	0.917418	+	0.397925i	$0.130270\pi$
$542$		0			0
$543$	−4.94876	+	15.2307i	−0.212372	+	0.653613i
$544$		0			0
$545$	−15.3538	+	4.98874i	−0.657683	+	0.213694i
$546$		0			0
$547$		−	27.7416i		−	1.18614i	−0.805150	−	0.593072i	$-0.797915\pi$
$547$		−	27.7416i		−	1.18614i	0.805150	−	0.593072i	$-0.202085\pi$
$548$		0			0
$549$	−19.9403	+	14.4875i	−0.851032	+	0.618311i
$550$		0			0
$551$	−6.80416	−	4.94351i	−0.289867	−	0.210601i
$552$		0			0
$553$	9.67037	−	7.02593i	0.411226	−	0.298773i
$554$		0			0
$555$	−5.84719	−	8.04796i	−0.248199	−	0.341617i
$556$		0			0
$557$	−13.3970	−	4.35296i	−0.567651	−	0.184441i	0.0111099	−	0.999938i	$-0.496464\pi$
$557$	−13.3970	−	4.35296i	−0.567651	−	0.184441i	−0.578761	+	0.815497i	$0.696464\pi$
$558$		0			0
$559$	−16.7418	+	5.43975i	−0.708104	+	0.230077i
$560$		0			0
$561$	−24.2021	+	33.3114i	−1.02181	+	1.40641i
$562$		0			0
$563$	−37.7423	−	12.2632i	−1.59065	−	0.516833i	−0.625876	−	0.779922i	$-0.715258\pi$
$563$	−37.7423	−	12.2632i	−1.59065	−	0.516833i	−0.964771	+	0.263090i	$0.915258\pi$
$564$		0			0
$565$	7.49763			0.315428
$566$		0			0
$567$	−0.0103404	−	0.0142324i	−0.000434258	−	0.000597704i
$568$		0			0
$569$	4.14492	+	12.7568i	0.173764	+	0.534791i	0.999575	−	0.0291562i	$-0.00928201\pi$
$569$	4.14492	+	12.7568i	0.173764	+	0.534791i	−0.825811	+	0.563948i	$0.809282\pi$
$570$		0			0
$571$			36.6178i			1.53241i	0.642597	+	0.766205i	$0.277857\pi$
$571$			36.6178i			1.53241i	−0.642597	+	0.766205i	$0.722143\pi$
$572$		0			0
$573$	5.40516			0.225804
$574$		0			0
$575$	0.219919			0.00917125
$576$		0			0
$577$		−	8.07091i		−	0.335996i	−0.985787	−	0.167998i	$-0.946270\pi$
$577$		−	8.07091i		−	0.335996i	0.985787	−	0.167998i	$-0.0537303\pi$
$578$		0			0
$579$	0.0421964	+	0.129867i	0.00175362	+	0.00539709i
$580$		0			0
$581$	−8.54451	−	11.7605i	−0.354486	−	0.487908i
$582$		0			0
$583$	−43.1627			−1.78762
$584$		0			0
$585$	−26.7188	−	8.68148i	−1.10469	−	0.358935i
$586$		0			0
$587$	2.00612	−	2.76119i	0.0828016	−	0.113967i	−0.765607	−	0.643309i	$-0.777561\pi$
$587$	2.00612	−	2.76119i	0.0828016	−	0.113967i	0.848408	+	0.529342i	$0.177561\pi$
$588$		0			0
$589$	−15.0053	+	4.87553i	−0.618284	+	0.200893i
$590$		0			0
$591$	−14.7485	−	4.79208i	−0.606672	−	0.197120i
$592$		0			0
$593$	−2.11067	−	2.90508i	−0.0866747	−	0.119297i	0.763478	−	0.645834i	$-0.223490\pi$
$593$	−2.11067	−	2.90508i	−0.0866747	−	0.119297i	−0.850152	+	0.526537i	$0.823490\pi$
$594$		0			0
$595$	−13.7920	+	10.0204i	−0.565415	+	0.410798i
$596$		0			0
$597$	−2.88464	−	2.09582i	−0.118061	−	0.0857761i
$598$		0			0
$599$	16.0782	−	11.6815i	0.656937	−	0.477293i	−0.208690	−	0.977982i	$-0.566920\pi$
$599$	16.0782	−	11.6815i	0.656937	−	0.477293i	0.865627	+	0.500689i	$0.166920\pi$
$600$		0			0
$601$			15.7216i			0.641299i	0.947198	+	0.320650i	$0.103901\pi$
$601$			15.7216i			0.641299i	−0.947198	+	0.320650i	$0.896099\pi$
$602$		0			0
$603$	22.5104	−	7.31408i	0.916695	−	0.297852i
$604$		0			0
$605$	−12.6075	+	38.8019i	−0.512567	+	1.57752i
$606$		0			0
$607$	−1.65147	+	5.08270i	−0.0670311	+	0.206300i	−0.978962	−	0.204044i	$-0.934591\pi$
$607$	−1.65147	+	5.08270i	−0.0670311	+	0.206300i	0.911931	+	0.410344i	$0.134591\pi$
$608$		0			0
$609$	1.05139	−	1.44712i	0.0426046	−	0.0586402i
$610$		0			0
$611$	−15.1290	−	46.5623i	−0.612054	−	1.88371i
$612$		0			0
$613$	18.2599	+	13.2666i	0.737509	+	0.535832i	0.891930	−	0.452173i	$-0.149351\pi$
$613$	18.2599	+	13.2666i	0.737509	+	0.535832i	−0.154421	+	0.988005i	$0.549351\pi$
$614$		0			0
$615$	−8.16742	−	13.9083i	−0.329342	−	0.560837i
$616$		0			0
$617$	19.6016	+	14.2414i	0.789129	+	0.573336i	0.907705	−	0.419609i	$-0.137833\pi$
$617$	19.6016	+	14.2414i	0.789129	+	0.573336i	−0.118576	+	0.992945i	$0.537833\pi$
$618$		0			0
$619$	−5.30776	−	16.3356i	−0.213337	−	0.656584i	−0.999267	−	0.0382688i	$-0.987816\pi$
$619$	−5.30776	−	16.3356i	−0.213337	−	0.656584i	0.785931	−	0.618315i	$-0.212184\pi$
$620$		0			0
$621$	1.22074	−	1.68021i	0.0489867	−	0.0674244i
$622$		0			0
$623$	−4.45939	+	13.7246i	−0.178662	+	0.549864i
$624$		0			0
$625$	−8.48161	+	26.1037i	−0.339264	+	1.04415i
$626$		0			0
$627$	−27.2058	+	8.83969i	−1.08649	+	0.353023i
$628$		0			0
$629$		−	28.5783i		−	1.13949i
$630$		0			0
$631$	−30.0162	+	21.8081i	−1.19493	+	0.868165i	−0.993776	−	0.111395i	$-0.964468\pi$
$631$	−30.0162	+	21.8081i	−1.19493	+	0.868165i	−0.201151	+	0.979560i	$0.564468\pi$
$632$		0			0
$633$	2.47409	+	1.79753i	0.0983363	+	0.0714455i
$634$		0			0
$635$	−31.7677	+	23.0806i	−1.26066	+	0.915926i
$636$		0			0
$637$	−3.77521	−	5.19613i	−0.149579	−	0.205878i
$638$		0			0
$639$	−20.1832	−	6.55793i	−0.798437	−	0.259428i
$640$		0			0
$641$	−22.1531	+	7.19799i	−0.874997	+	0.284304i	−0.711878	−	0.702303i	$-0.752155\pi$
$641$	−22.1531	+	7.19799i	−0.874997	+	0.284304i	−0.163118	+	0.986607i	$0.552155\pi$
$642$		0			0
$643$	3.61173	−	4.97112i	0.142433	−	0.196042i	−0.731841	−	0.681476i	$-0.761338\pi$
$643$	3.61173	−	4.97112i	0.142433	−	0.196042i	0.874273	+	0.485434i	$0.161338\pi$
$644$		0			0
$645$	−6.56597	−	2.13341i	−0.258535	−	0.0840030i
$646$		0			0
$647$	21.6649			0.851735			0.425867	−	0.904786i	$-0.359969\pi$
$647$	21.6649			0.851735			0.425867	+	0.904786i	$0.359969\pi$
$648$		0			0
$649$	34.7685	+	47.8547i	1.36478	+	1.87846i
$650$		0			0
$651$	−1.03693	−	3.19136i	−0.0406407	−	0.125079i
$652$		0			0
$653$			14.7647i			0.577787i	0.957361	+	0.288893i	$0.0932873\pi$
$653$			14.7647i			0.577787i	−0.957361	+	0.288893i	$0.906713\pi$
$654$		0			0
$655$	−29.9655			−1.17085
$656$		0			0
$657$	−24.3970			−0.951817
$658$		0			0
$659$		−	33.7317i		−	1.31400i	−0.753890	−	0.657001i	$-0.771825\pi$
$659$		−	33.7317i		−	1.31400i	0.753890	−	0.657001i	$-0.228175\pi$
$660$		0			0
$661$	−3.31046	−	10.1885i	−0.128762	−	0.396288i	0.865806	−	0.500380i	$-0.166806\pi$
$661$	−3.31046	−	10.1885i	−0.128762	−	0.396288i	−0.994568	+	0.104092i	$0.966806\pi$
$662$		0			0
$663$	29.2107	+	40.2051i	1.13445	+	1.56144i
$664$		0			0
$665$	−11.8437			−0.459280
$666$		0			0
$667$	−0.636302	−	0.206747i	−0.0246377	−	0.00800528i
$668$		0			0
$669$	3.42337	−	4.71186i	0.132355	−	0.182171i
$670$		0			0
$671$	67.1841	−	21.8294i	2.59361	−	0.842716i
$672$		0			0
$673$	−34.9491	−	11.3556i	−1.34719	−	0.437728i	−0.455442	−	0.890266i	$-0.650519\pi$
$673$	−34.9491	−	11.3556i	−1.34719	−	0.437728i	−0.891745	+	0.452538i	$0.850519\pi$
$674$		0			0
$675$	−1.67847	−	2.31022i	−0.0646043	−	0.0889202i
$676$		0			0
$677$	19.8485	−	14.4208i	0.762839	−	0.554235i	−0.136941	−	0.990579i	$-0.543727\pi$
$677$	19.8485	−	14.4208i	0.762839	−	0.554235i	0.899780	+	0.436344i	$0.143727\pi$
$678$		0			0
$679$	4.93208	+	3.58336i	0.189276	+	0.137517i
$680$		0			0
$681$	−9.73926	+	7.07599i	−0.373209	+	0.271152i
$682$		0			0
$683$		−	15.1599i		−	0.580078i	−0.957015	−	0.290039i	$-0.906332\pi$
$683$		−	15.1599i		−	0.580078i	0.957015	−	0.290039i	$-0.0936683\pi$
$684$		0			0
$685$	−27.8822	+	9.05948i	−1.06532	+	0.346145i
$686$		0			0
$687$	−5.19347	+	15.9839i	−0.198143	+	0.609822i
$688$		0			0
$689$	−16.0983	+	49.5454i	−0.613296	+	1.88753i
$690$		0			0
$691$	−30.3945	+	41.8344i	−1.15626	+	1.59145i	−0.432093	+	0.901829i	$0.642225\pi$
$691$	−30.3945	+	41.8344i	−1.15626	+	1.59145i	−0.724166	+	0.689626i	$0.757775\pi$
$692$		0			0
$693$	3.05325	+	9.39695i	0.115983	+	0.356960i
$694$		0			0
$695$	−13.2955	−	9.65978i	−0.504329	−	0.366416i
$696$		0			0
$697$	4.50317	−	46.1166i	0.170570	−	1.74679i
$698$		0			0
$699$	−7.46379	−	5.42276i	−0.282307	−	0.205108i
$700$		0			0
$701$	−11.7561	−	36.1816i	−0.444023	−	1.36656i	−0.883552	−	0.468333i	$-0.844855\pi$
$701$	−11.7561	−	36.1816i	−0.444023	−	1.36656i	0.439529	−	0.898228i	$-0.355145\pi$
$702$		0			0
$703$	11.6701	−	16.0625i	0.440147	−	0.605810i
$704$		0			0
$705$	5.93344	−	18.2612i	0.223466	−	0.687758i
$706$		0			0
$707$	−1.95461	+	6.01567i	−0.0735107	+	0.226243i
$708$		0			0
$709$	18.1328	−	5.89169i	0.680990	−	0.221267i	0.0519611	−	0.998649i	$-0.483453\pi$
$709$	18.1328	−	5.89169i	0.680990	−	0.221267i	0.629029	+	0.777382i	$0.283453\pi$
$710$		0			0
$711$			22.1938i			0.832334i
$712$		0			0
$713$	−1.01540	+	0.737732i	−0.0380271	+	0.0276283i
$714$		0			0
$715$	65.1411	+	47.3278i	2.43614	+	1.76996i
$716$		0			0
$717$	22.6314	−	16.4427i	0.845185	−	0.614063i
$718$		0			0
$719$	9.31758	+	12.8245i	0.347487	+	0.478275i	0.946609	−	0.322382i	$-0.104484\pi$
$719$	9.31758	+	12.8245i	0.347487	+	0.478275i	−0.599122	+	0.800657i	$0.704484\pi$
$720$		0			0
$721$	−1.58104	−	0.513712i	−0.0588811	−	0.0191316i
$722$		0			0
$723$	−14.4017	+	4.67940i	−0.535605	+	0.174029i
$724$		0			0
$725$	−0.540711	+	0.744225i	−0.0200815	+	0.0276398i
$726$		0			0
$727$	42.5975	+	13.8408i	1.57985	+	0.513326i	0.962019	−	0.272982i	$-0.0880099\pi$
$727$	42.5975	+	13.8408i	1.57985	+	0.513326i	0.617835	+	0.786308i	$0.288010\pi$
$728$		0			0
$729$	−16.6251			−0.615743
$730$		0			0
$731$	−11.6579	−	16.0457i	−0.431182	−	0.593471i
$732$		0			0
$733$	−12.2090	−	37.5753i	−0.450948	−	1.38788i	−0.875827	−	0.482626i	$-0.839683\pi$
$733$	−12.2090	−	37.5753i	−0.450948	−	1.38788i	0.424878	−	0.905250i	$-0.360317\pi$
$734$		0			0
$735$		−	2.51894i		−	0.0929125i
$736$		0			0
$737$	−67.8365			−2.49879
$738$		0			0
$739$	−21.5720			−0.793541			−0.396770	−	0.917918i	$-0.629869\pi$
$739$	−21.5720			−0.793541			−0.396770	+	0.917918i	$0.629869\pi$
$740$		0			0
$741$			34.5258i			1.26834i
$742$		0			0
$743$	−4.91530	−	15.1277i	−0.180325	−	0.554983i	0.819512	−	0.573062i	$-0.194245\pi$
$743$	−4.91530	−	15.1277i	−0.180325	−	0.554983i	−0.999837	+	0.0180796i	$0.994245\pi$
$744$		0			0
$745$	−0.202559	−	0.278798i	−0.00742117	−	0.0102144i
$746$		0			0
$747$	26.9908			0.987541
$748$		0			0
$749$	−0.729178	−	0.236924i	−0.0266436	−	0.00865703i
$750$		0			0
$751$	−27.8026	+	38.2670i	−1.01453	+	1.39638i	−0.0985617	+	0.995131i	$0.531424\pi$
$751$	−27.8026	+	38.2670i	−1.01453	+	1.39638i	−0.915969	+	0.401250i	$0.868576\pi$
$752$		0			0
$753$	−23.5357	+	7.64720i	−0.857688	+	0.278680i
$754$		0			0
$755$	−2.65947	−	0.864115i	−0.0967881	−	0.0314484i
$756$		0			0
$757$	22.5860	+	31.0870i	0.820903	+	1.12988i	0.989549	+	0.144199i	$0.0460605\pi$
$757$	22.5860	+	31.0870i	0.820903	+	1.12988i	−0.168646	+	0.985677i	$0.553939\pi$
$758$		0			0
$759$	−1.84100	+	1.33756i	−0.0668239	+	0.0485504i
$760$		0			0
$761$	−23.9830	−	17.4246i	−0.869382	−	0.631643i	0.0610390	−	0.998135i	$-0.480559\pi$
$761$	−23.9830	−	17.4246i	−0.869382	−	0.631643i	−0.930421	+	0.366492i	$0.880559\pi$
$762$		0			0
$763$	5.54401	−	4.02796i	0.200706	−	0.145822i
$764$		0			0
$765$		−	31.6530i		−	1.14442i
$766$		0			0
$767$	67.8988	−	22.0617i	2.45168	−	0.796600i
$768$		0			0
$769$	13.4537	−	41.4061i	0.485152	−	1.49314i	−0.346610	−	0.938009i	$-0.612667\pi$
$769$	13.4537	−	41.4061i	0.485152	−	1.49314i	0.831761	−	0.555133i	$-0.187333\pi$
$770$		0			0
$771$	9.60130	−	29.5498i	0.345782	−	1.06421i
$772$		0			0
$773$	1.69578	−	2.33404i	0.0609929	−	0.0839495i	−0.777431	−	0.628968i	$-0.783478\pi$
$773$	1.69578	−	2.33404i	0.0609929	−	0.0839495i	0.838424	+	0.545019i	$0.183478\pi$
$774$		0			0
$775$	0.533275	+	1.64125i	0.0191558	+	0.0589556i
$776$		0			0
$777$	3.41620	+	2.48202i	0.122556	+	0.0890419i
$778$		0			0
$779$	21.3630	−	24.0811i	0.765409	−	0.862795i
$780$		0			0
$781$	49.2072	+	35.7511i	1.76077	+	1.27927i
$782$		0			0
$783$	2.68455	+	8.26221i	0.0959381	+	0.295267i
$784$		0			0
$785$	−18.4279	+	25.3638i	−0.657720	+	0.905274i
$786$		0			0
$787$	−3.96071	+	12.1898i	−0.141184	+	0.434520i	−0.996501	−	0.0835859i	$-0.973363\pi$
$787$	−3.96071	+	12.1898i	−0.141184	+	0.434520i	0.855316	+	0.518106i	$0.173363\pi$
$788$		0			0
$789$	3.93004	−	12.0954i	0.139913	−	0.430608i
$790$		0			0
$791$	−3.02683	+	0.983477i	−0.107622	+	0.0349684i
$792$		0			0
$793$		−	85.2607i		−	3.02770i
$794$		0			0
$795$	−16.5292	+	12.0091i	−0.586229	+	0.425920i
$796$		0			0
$797$	−16.5539	−	12.0271i	−0.586370	−	0.426023i	0.254645	−	0.967035i	$-0.418041\pi$
$797$	−16.5539	−	12.0271i	−0.586370	−	0.426023i	−0.841015	+	0.541012i	$0.818041\pi$
$798$		0			0
$799$	44.6262	−	32.4228i	1.57876	−	1.14704i
$800$		0			0
$801$	−15.7492	−	21.6769i	−0.556471	−	0.765917i
$802$		0			0
$803$	66.5011	+	21.6075i	2.34677	+	0.762512i
$804$		0			0
$805$	−0.896056	+	0.291146i	−0.0315818	+	0.0102616i
$806$		0			0
$807$	−1.59290	+	2.19244i	−0.0560727	+	0.0771774i
$808$		0			0
$809$	8.11804	+	2.63771i	0.285415	+	0.0927370i	0.448226	−	0.893920i	$-0.352056\pi$
$809$	8.11804	+	2.63771i	0.285415	+	0.0927370i	−0.162811	+	0.986657i	$0.552056\pi$
$810$		0			0
$811$	0.528531			0.0185592			0.00927962	−	0.999957i	$-0.497046\pi$
$811$	0.528531			0.0185592			0.00927962	+	0.999957i	$0.497046\pi$
$812$		0			0
$813$	14.5579	+	20.0373i	0.510569	+	0.702737i
$814$		0			0
$815$	−3.90708	−	12.0248i	−0.136859	−	0.421209i
$816$		0			0
$817$		−	13.7791i		−	0.482070i
$818$		0			0
$819$	11.9253			0.416704
$820$		0			0
$821$	−30.9778			−1.08113			−0.540567	−	0.841301i	$-0.681790\pi$
$821$	−30.9778			−1.08113			−0.540567	+	0.841301i	$0.681790\pi$
$822$		0			0
$823$			17.9045i			0.624111i	0.950064	+	0.312056i	$0.101018\pi$
$823$			17.9045i			0.624111i	−0.950064	+	0.312056i	$0.898982\pi$
$824$		0			0
$825$	0.966868	+	2.97571i	0.0336620	+	0.103601i
$826$		0			0
$827$	11.5207	+	15.8569i	0.400615	+	0.551400i	0.960898	−	0.276901i	$-0.0893076\pi$
$827$	11.5207	+	15.8569i	0.400615	+	0.551400i	−0.560283	+	0.828301i	$0.689308\pi$
$828$		0			0
$829$	−33.2201			−1.15378			−0.576891	−	0.816821i	$-0.695734\pi$
$829$	−33.2201			−1.15378			−0.576891	+	0.816821i	$0.695734\pi$
$830$		0			0
$831$	−20.4610	−	6.64818i	−0.709784	−	0.230623i
$832$		0			0
$833$	4.25348	−	5.85442i	0.147374	−	0.202844i
$834$		0			0
$835$	44.7206	−	14.5306i	1.54762	−	0.502852i
$836$		0			0
$837$	15.4995	+	5.03611i	0.535742	+	0.174073i
$838$		0			0
$839$	−28.9590	−	39.8587i	−0.999776	−	1.37607i	−0.925463	−	0.378839i	$-0.876323\pi$
$839$	−28.9590	−	39.8587i	−0.999776	−	1.37607i	−0.0743138	−	0.997235i	$-0.523677\pi$
$840$		0			0
$841$	−21.1974	+	15.4008i	−0.730944	+	0.531062i
$842$		0			0
$843$	−14.7046	−	10.6835i	−0.506455	−	0.367961i
$844$		0			0
$845$	53.8453	−	39.1209i	1.85233	−	1.34580i
$846$		0			0
$847$		−	17.3183i		−	0.595062i
$848$		0			0
$849$	14.6597	−	4.76324i	0.503121	−	0.163474i
$850$		0			0
$851$	0.488067	−	1.50211i	0.0167307	−	0.0514918i
$852$		0			0
$853$	−10.2000	+	31.3923i	−0.349241	+	1.07485i	0.610033	+	0.792376i	$0.291156\pi$
$853$	−10.2000	+	31.3923i	−0.349241	+	1.07485i	−0.959274	+	0.282477i	$0.908844\pi$
$854$		0			0
$855$	12.9257	−	17.7907i	0.442050	−	0.608429i
$856$		0			0
$857$	5.30801	+	16.3364i	0.181318	+	0.558040i	0.999866	−	0.0163989i	$-0.00522016\pi$
$857$	5.30801	+	16.3364i	0.181318	+	0.558040i	−0.818547	+	0.574439i	$0.805220\pi$
$858$		0			0
$859$	7.13688	+	5.18524i	0.243507	+	0.176918i	0.702844	−	0.711344i	$-0.251913\pi$
$859$	7.13688	+	5.18524i	0.243507	+	0.176918i	−0.459337	+	0.888262i	$0.651913\pi$
$860$		0			0
$861$	5.12160	+	4.54351i	0.174544	+	0.154843i
$862$		0			0
$863$	−1.31627	−	0.956326i	−0.0448064	−	0.0325537i	0.565157	−	0.824984i	$-0.308816\pi$
$863$	−1.31627	−	0.956326i	−0.0448064	−	0.0325537i	−0.609963	+	0.792430i	$0.708816\pi$
$864$		0			0
$865$	2.07333	+	6.38104i	0.0704952	+	0.216962i
$866$		0			0
$867$	−22.2272	+	30.5931i	−0.754874	+	1.03900i
$868$		0			0
$869$	19.6563	−	60.4957i	0.666793	−	2.05218i
$870$		0			0
$871$	−25.3008	+	77.8679i	−0.857285	+	2.63845i
$872$		0			0
$873$	−10.7653	+	3.49786i	−0.364350	+	0.118384i
$874$		0			0
$875$		−	10.4837i		−	0.354412i
$876$		0			0
$877$	41.6442	−	30.2562i	1.40622	−	1.02168i	0.412365	−	0.911019i	$-0.364703\pi$
$877$	41.6442	−	30.2562i	1.40622	−	1.02168i	0.993858	−	0.110662i	$-0.0352972\pi$
$878$		0			0
$879$	−2.01737	−	1.46571i	−0.0680443	−	0.0494371i
$880$		0			0
$881$	−4.81537	+	3.49857i	−0.162234	+	0.117870i	−0.665940	−	0.746005i	$-0.731969\pi$
$881$	−4.81537	+	3.49857i	−0.162234	+	0.117870i	0.503706	+	0.863875i	$0.331969\pi$
$882$		0			0
$883$	1.83766	+	2.52932i	0.0618422	+	0.0851185i	0.838818	−	0.544412i	$-0.183247\pi$
$883$	1.83766	+	2.52932i	0.0618422	+	0.0851185i	−0.776976	+	0.629531i	$0.783247\pi$
$884$		0			0
$885$	26.6292	+	8.65235i	0.895131	+	0.290846i
$886$		0			0
$887$	−43.2800	+	14.0625i	−1.45320	+	0.472174i	−0.925986	−	0.377558i	$-0.876764\pi$
$887$	−43.2800	+	14.0625i	−1.45320	+	0.472174i	−0.527215	+	0.849732i	$0.676764\pi$
$888$		0			0
$889$	9.79727	−	13.4848i	0.328590	−	0.452265i
$890$		0			0
$891$	−0.0890348	−	0.0289292i	−0.00298278	−	0.000969163i
$892$		0			0
$893$	38.3224			1.28241
$894$		0			0
$895$	−3.95600	−	5.44496i	−0.132234	−	0.182005i
$896$		0			0
$897$	0.848724	+	2.61210i	0.0283381	+	0.0872156i
$898$		0			0
$899$		−	5.25006i		−	0.175099i
$900$		0			0
$901$	−58.6950			−1.95541
$902$		0			0
$903$	2.93056			0.0975229
$904$		0			0
$905$			35.2843i			1.17289i
$906$		0			0
$907$	6.04124	+	18.5930i	0.200596	+	0.617371i	0.999866	+	0.0163986i	$0.00522006\pi$
$907$	6.04124	+	18.5930i	0.200596	+	0.617371i	−0.799269	+	0.600973i	$0.794780\pi$
$908$		0			0
$909$	−6.90310	−	9.50130i	−0.228961	−	0.315138i
$910$		0			0
$911$	22.9521			0.760438			0.380219	−	0.924897i	$-0.375849\pi$
$911$	22.9521			0.760438			0.380219	+	0.924897i	$0.375849\pi$
$912$		0			0
$913$	−73.5712	−	23.9047i	−2.43485	−	0.791131i
$914$		0			0
$915$	19.6546	−	27.0522i	0.649760	−	0.894318i
$916$		0			0
$917$	12.0972	−	3.93063i	0.399486	−	0.129801i
$918$		0			0
$919$	23.5943	+	7.66626i	0.778305	+	0.252886i	0.671116	−	0.741352i	$-0.265815\pi$
$919$	23.5943	+	7.66626i	0.778305	+	0.252886i	0.107188	+	0.994239i	$0.465815\pi$
$920$		0			0
$921$	−13.4096	−	18.4567i	−0.441862	−	0.608170i
$922$		0			0
$923$	59.3905	−	43.1497i	1.95486	−	1.42029i
$924$		0			0
$925$	−1.75689	−	1.27645i	−0.0577661	−	0.0419695i
$926$		0			0
$927$	2.49714	−	1.81428i	0.0820168	−	0.0595887i
$928$		0			0
$929$		−	3.17280i		−	0.104096i	−0.998645	−	0.0520480i	$-0.983425\pi$
$929$		−	3.17280i		−	0.104096i	0.998645	−	0.0520480i	$-0.0165749\pi$
$930$		0			0
$931$	4.78137	−	1.55356i	0.156703	−	0.0509159i
$932$		0			0
$933$	0.985465	−	3.03295i	0.0322627	−	0.0992943i
$934$		0			0
$935$	−28.0339	+	86.2795i	−0.916807	+	2.82164i
$936$		0			0
$937$	−29.3398	+	40.3827i	−0.958488	+	1.31925i	−0.0108363	+	0.999941i	$0.503449\pi$
$937$	−29.3398	+	40.3827i	−0.958488	+	1.31925i	−0.947652	+	0.319305i	$0.896551\pi$
$938$		0			0
$939$	6.81799	+	20.9836i	0.222497	+	0.684774i
$940$		0			0
$941$	−22.1704	−	16.1077i	−0.722734	−	0.525097i	0.164523	−	0.986373i	$-0.447392\pi$
$941$	−22.1704	−	16.1077i	−0.722734	−	0.525097i	−0.887256	+	0.461276i	$0.847392\pi$
$942$		0			0
$943$	1.02428	−	2.34705i	0.0333552	−	0.0764303i
$944$		0			0
$945$	9.89735	+	7.19084i	0.321961	+	0.233918i
$946$		0			0
$947$	12.1457	+	37.3805i	0.394681	+	1.21470i	0.929210	+	0.369553i	$0.120489\pi$
$947$	12.1457	+	37.3805i	0.394681	+	1.21470i	−0.534529	+	0.845150i	$0.679511\pi$
$948$		0			0
$949$	49.6055	−	68.2761i	1.61026	−	2.21634i
$950$		0			0
$951$	−5.99000	+	18.4353i	−0.194239	+	0.597806i
$952$		0			0
$953$	9.47316	−	29.1554i	0.306866	−	0.944436i	−0.672109	−	0.740453i	$-0.734611\pi$
$953$	9.47316	−	29.1554i	0.306866	−	0.944436i	0.978974	−	0.203983i	$-0.0653888\pi$
$954$		0			0
$955$	11.3261	−	3.68008i	0.366505	−	0.119085i
$956$		0			0
$957$		−	9.51874i		−	0.307697i
$958$		0			0
$959$	10.0678	−	7.31472i	0.325108	−	0.236204i
$960$		0			0
$961$	17.1116	+	12.4323i	0.551988	+	0.401042i
$962$		0			0
$963$	1.15168	−	0.836745i	0.0371124	−	0.0269637i
$964$		0			0
$965$	0.176839	+	0.243398i	0.00569265	+	0.00783526i
$966$		0			0
$967$	15.1692	+	4.92876i	0.487807	+	0.158498i	0.542586	−	0.840000i	$-0.317445\pi$
$967$	15.1692	+	4.92876i	0.487807	+	0.158498i	−0.0547786	+	0.998499i	$0.517445\pi$
$968$		0			0
$969$	−36.9959	+	12.0207i	−1.18848	+	0.386161i
$970$		0			0
$971$	7.00000	−	9.63467i	0.224641	−	0.309191i	−0.681788	−	0.731549i	$-0.738798\pi$
$971$	7.00000	−	9.63467i	0.224641	−	0.309191i	0.906429	+	0.422358i	$0.138798\pi$
$972$		0			0
$973$	6.63457	+	2.15570i	0.212694	+	0.0691086i
$974$		0			0
$975$	3.77636			0.120940
$976$		0			0
$977$	32.2151	+	44.3403i	1.03065	+	1.41857i	0.904456	+	0.426566i	$0.140277\pi$
$977$	32.2151	+	44.3403i	1.03065	+	1.41857i	0.126196	+	0.992005i	$0.459723\pi$
$978$		0			0
$979$	23.7306	+	73.0353i	0.758433	+	2.33422i
$980$		0			0
$981$			12.7237i			0.406236i
$982$		0			0
$983$	34.7901			1.10963			0.554816	−	0.831973i	$-0.312789\pi$
$983$	34.7901			1.10963			0.554816	+	0.831973i	$0.312789\pi$
$984$		0			0
$985$	−34.1671			−1.08865
$986$		0			0
$987$			8.15046i			0.259432i
$988$		0			0
$989$	−0.338722	−	1.04248i	−0.0107707	−	0.0331489i
$990$		0			0
$991$	−23.8062	−	32.7664i	−0.756228	−	1.04086i	−0.997518	−	0.0704057i	$-0.977571\pi$
$991$	−23.8062	−	32.7664i	−0.756228	−	1.04086i	0.241290	−	0.970453i	$-0.422429\pi$
$992$		0			0
$993$	−23.3543			−0.741128
$994$		0			0
$995$	−7.47150	−	2.42764i	−0.236862	−	0.0769612i
$996$		0			0
$997$	16.1572	−	22.2385i	0.511705	−	0.704302i	−0.472501	−	0.881330i	$-0.656649\pi$
$997$	16.1572	−	22.2385i	0.511705	−	0.704302i	0.984206	+	0.177029i	$0.0566485\pi$
$998$		0			0
$999$	−19.5045	+	6.33741i	−0.617096	+	0.200507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.13	✓	80
41.4	even	10	inner	1148.2.ba.a.701.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.13	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.8	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.06924i q^{3} +(0.727989 + 2.24052i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.85672 q^{9} +O(q^{10})\)	\(q+1.06924i q^{3} +(0.727989 + 2.24052i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.85672 q^{9} +(-5.06104 - 1.64443i) q^{11} +(-3.77521 + 5.19613i) q^{13} +(-2.39565 + 0.778395i) q^{15} +(-6.88228 - 2.23619i) q^{17} +(-2.95505 - 4.06728i) q^{19} +(0.865034 - 0.628484i) q^{21} +(-0.323552 - 0.235074i) q^{23} +(-0.444870 + 0.323217i) q^{25} +5.19301i q^{27} +(1.59102 - 0.516955i) q^{29} +(0.969786 - 2.98469i) q^{31} +(1.75829 - 5.41147i) q^{33} +(1.38472 - 1.90590i) q^{35} +(1.22037 + 3.75592i) q^{37} +(-5.55591 - 4.03661i) q^{39} +(1.37748 + 6.25320i) q^{41} +(2.21734 + 1.61099i) q^{43} +(1.35167 + 4.16002i) q^{45} +(-4.48048 + 6.16686i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.39102 - 7.35882i) q^{51} +(7.71403 - 2.50644i) q^{53} -12.5365i q^{55} +(4.34890 - 3.15966i) q^{57} +(-8.99273 - 6.53360i) q^{59} +(-10.7395 + 7.80272i) q^{61} +(-1.09135 - 1.50212i) q^{63} +(-14.3903 - 4.67570i) q^{65} +(12.1237 - 3.93924i) q^{67} +(0.251351 - 0.345955i) q^{69} +(-10.8704 - 3.53199i) q^{71} -13.1398 q^{73} +(-0.345597 - 0.475674i) q^{75} +(1.64443 + 5.06104i) q^{77} +11.9532i q^{79} +0.0175922 q^{81} +14.5368 q^{83} -17.0478i q^{85} +(0.552750 + 1.70119i) q^{87} +(-8.48226 - 11.6748i) q^{89} +6.42276 q^{91} +(3.19136 + 1.03693i) q^{93} +(6.96156 - 9.58177i) q^{95} +(-5.79801 + 1.88389i) q^{97} +(-9.39695 - 3.05325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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