LMFDB - Embedded newform 1148.2.k.b.337.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.12
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.805830 + 0.805830i) q^{3} -0.251332i q^{5} +(0.707107 + 0.707107i) q^{7} -1.70128i q^{9} +O(q^{10})$	\(q+(0.805830 + 0.805830i) q^{3} -0.251332i q^{5} +(0.707107 + 0.707107i) q^{7} -1.70128i q^{9} +(-2.93936 - 2.93936i) q^{11} +(1.89283 + 1.89283i) q^{13} +(0.202531 - 0.202531i) q^{15} +(2.33562 - 2.33562i) q^{17} +(1.33917 - 1.33917i) q^{19} +1.13962i q^{21} +6.67279 q^{23} +4.93683 q^{25} +(3.78843 - 3.78843i) q^{27} +(-0.0155144 - 0.0155144i) q^{29} -3.61614 q^{31} -4.73725i q^{33} +(0.177719 - 0.177719i) q^{35} +9.22196 q^{37} +3.05060i q^{39} +(-6.16529 + 1.72894i) q^{41} -1.97318i q^{43} -0.427585 q^{45} +(-2.41064 + 2.41064i) q^{47} +1.00000i q^{49} +3.76423 q^{51} +(3.16272 + 3.16272i) q^{53} +(-0.738756 + 0.738756i) q^{55} +2.15829 q^{57} -4.91005 q^{59} +9.53072i q^{61} +(1.20298 - 1.20298i) q^{63} +(0.475729 - 0.475729i) q^{65} +(8.59321 - 8.59321i) q^{67} +(5.37714 + 5.37714i) q^{69} +(-9.30998 - 9.30998i) q^{71} +5.52711i q^{73} +(3.97825 + 3.97825i) q^{75} -4.15689i q^{77} +(4.22270 + 4.22270i) q^{79} +1.00184 q^{81} +6.78231 q^{83} +(-0.587017 - 0.587017i) q^{85} -0.0250039i q^{87} +(-1.72662 - 1.72662i) q^{89} +2.67687i q^{91} +(-2.91399 - 2.91399i) q^{93} +(-0.336577 - 0.336577i) q^{95} +(-2.76074 + 2.76074i) q^{97} +(-5.00066 + 5.00066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.805830	+	0.805830i	0.465246	+	0.465246i	0.900370	−	0.435124i	$-0.143296\pi$
$3$	0.805830	+	0.805830i	0.465246	+	0.465246i	−0.435124	+	0.900370i	$0.643296\pi$
$4$		0			0
$5$		−	0.251332i		−	0.112399i	−0.998420	−	0.0561996i	$-0.982102\pi$
$5$		−	0.251332i		−	0.112399i	0.998420	−	0.0561996i	$-0.0178983\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$		−	1.70128i		−	0.567092i
$10$		0			0
$11$	−2.93936	−	2.93936i	−0.886251	−	0.886251i	0.107910	−	0.994161i	$-0.465584\pi$
$11$	−2.93936	−	2.93936i	−0.886251	−	0.886251i	−0.994161	+	0.107910i	$0.965584\pi$
$12$		0			0
$13$	1.89283	+	1.89283i	0.524977	+	0.524977i	0.919070	−	0.394094i	$-0.128941\pi$
$13$	1.89283	+	1.89283i	0.524977	+	0.524977i	−0.394094	+	0.919070i	$0.628941\pi$
$14$		0			0
$15$	0.202531	−	0.202531i	0.0522933	−	0.0522933i
$16$		0			0
$17$	2.33562	−	2.33562i	0.566472	−	0.566472i	−0.364667	−	0.931138i	$-0.618817\pi$
$17$	2.33562	−	2.33562i	0.566472	−	0.566472i	0.931138	+	0.364667i	$0.118817\pi$
$18$		0			0
$19$	1.33917	−	1.33917i	0.307227	−	0.307227i	−0.536606	−	0.843833i	$-0.680294\pi$
$19$	1.33917	−	1.33917i	0.307227	−	0.307227i	0.843833	+	0.536606i	$0.180294\pi$
$20$		0			0
$21$			1.13962i			0.248685i
$22$		0			0
$23$	6.67279			1.39137			0.695687	−	0.718345i	$-0.255100\pi$
$23$	6.67279			1.39137			0.695687	+	0.718345i	$0.255100\pi$
$24$		0			0
$25$	4.93683			0.987366
$26$		0			0
$27$	3.78843	−	3.78843i	0.729084	−	0.729084i
$28$		0			0
$29$	−0.0155144	−	0.0155144i	−0.00288095	−	0.00288095i	0.705665	−	0.708546i	$-0.250648\pi$
$29$	−0.0155144	−	0.0155144i	−0.00288095	−	0.00288095i	−0.708546	+	0.705665i	$0.750648\pi$
$30$		0			0
$31$	−3.61614			−0.649478			−0.324739	−	0.945804i	$-0.605276\pi$
$31$	−3.61614			−0.649478			−0.324739	+	0.945804i	$0.605276\pi$
$32$		0			0
$33$		−	4.73725i		−	0.824650i
$34$		0			0
$35$	0.177719	−	0.177719i	0.0300399	−	0.0300399i
$36$		0			0
$37$	9.22196			1.51608			0.758040	−	0.652208i	$-0.226157\pi$
$37$	9.22196			1.51608			0.758040	+	0.652208i	$0.226157\pi$
$38$		0			0
$39$			3.05060i			0.488487i
$40$		0			0
$41$	−6.16529	+	1.72894i	−0.962856	+	0.270015i
$41$	−6.16529	+	1.72894i	−0.962856	+	0.270015i
$42$		0			0
$43$		−	1.97318i		−	0.300908i	−0.988617	−	0.150454i	$-0.951927\pi$
$43$		−	1.97318i		−	0.300908i	0.988617	−	0.150454i	$-0.0480735\pi$
$44$		0			0
$45$	−0.427585			−0.0637407
$46$		0			0
$47$	−2.41064	+	2.41064i	−0.351628	+	0.351628i	−0.860715	−	0.509087i	$-0.829983\pi$
$47$	−2.41064	+	2.41064i	−0.351628	+	0.351628i	0.509087	+	0.860715i	$0.329983\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	3.76423			0.527098
$52$		0			0
$53$	3.16272	+	3.16272i	0.434434	+	0.434434i	0.890133	−	0.455700i	$-0.150611\pi$
$53$	3.16272	+	3.16272i	0.434434	+	0.434434i	−0.455700	+	0.890133i	$0.650611\pi$
$54$		0			0
$55$	−0.738756	+	0.738756i	−0.0996139	+	0.0996139i
$56$		0			0
$57$	2.15829			0.285873
$58$		0			0
$59$	−4.91005			−0.639234			−0.319617	−	0.947547i	$-0.603554\pi$
$59$	−4.91005			−0.639234			−0.319617	+	0.947547i	$0.603554\pi$
$60$		0			0
$61$			9.53072i			1.22028i	0.792292	+	0.610142i	$0.208888\pi$
$61$			9.53072i			1.22028i	−0.792292	+	0.610142i	$0.791112\pi$
$62$		0			0
$63$	1.20298	−	1.20298i	0.151562	−	0.151562i
$64$		0			0
$65$	0.475729	−	0.475729i	0.0590070	−	0.0590070i
$66$		0			0
$67$	8.59321	−	8.59321i	1.04983	−	1.04983i	0.0511362	−	0.998692i	$-0.483716\pi$
$67$	8.59321	−	8.59321i	1.04983	−	1.04983i	0.998692	−	0.0511362i	$-0.0162843\pi$
$68$		0			0
$69$	5.37714	+	5.37714i	0.647332	+	0.647332i
$70$		0			0
$71$	−9.30998	−	9.30998i	−1.10489	−	1.10489i	−0.993811	−	0.111080i	$-0.964569\pi$
$71$	−9.30998	−	9.30998i	−1.10489	−	1.10489i	−0.111080	−	0.993811i	$-0.535431\pi$
$72$		0			0
$73$			5.52711i			0.646899i	0.946245	+	0.323449i	$0.104843\pi$
$73$			5.52711i			0.646899i	−0.946245	+	0.323449i	$0.895157\pi$
$74$		0			0
$75$	3.97825	+	3.97825i	0.459369	+	0.459369i
$76$		0			0
$77$		−	4.15689i		−	0.473721i
$78$		0			0
$79$	4.22270	+	4.22270i	0.475091	+	0.475091i	0.903557	−	0.428467i	$-0.140946\pi$
$79$	4.22270	+	4.22270i	0.475091	+	0.475091i	−0.428467	+	0.903557i	$0.640946\pi$
$80$		0			0
$81$	1.00184			0.111315
$82$		0			0
$83$	6.78231			0.744455			0.372227	−	0.928142i	$-0.378594\pi$
$83$	6.78231			0.744455			0.372227	+	0.928142i	$0.378594\pi$
$84$		0			0
$85$	−0.587017	−	0.587017i	−0.0636709	−	0.0636709i
$86$		0			0
$87$		−	0.0250039i		−	0.00268070i
$88$		0			0
$89$	−1.72662	−	1.72662i	−0.183022	−	0.183022i	0.609649	−	0.792671i	$-0.291310\pi$
$89$	−1.72662	−	1.72662i	−0.183022	−	0.183022i	−0.792671	+	0.609649i	$0.791310\pi$
$90$		0			0
$91$			2.67687i			0.280612i
$92$		0			0
$93$	−2.91399	−	2.91399i	−0.302167	−	0.302167i
$94$		0			0
$95$	−0.336577	−	0.336577i	−0.0345321	−	0.0345321i
$96$		0			0
$97$	−2.76074	+	2.76074i	−0.280311	+	0.280311i	−0.833233	−	0.552922i	$-0.813513\pi$
$97$	−2.76074	+	2.76074i	−0.280311	+	0.280311i	0.552922	+	0.833233i	$0.313513\pi$
$98$		0			0
$99$	−5.00066	+	5.00066i	−0.502586	+	0.502586i
$100$		0			0
$101$	11.9870	−	11.9870i	1.19275	−	1.19275i	0.216454	−	0.976293i	$-0.430551\pi$
$101$	11.9870	−	11.9870i	1.19275	−	1.19275i	0.976293	−	0.216454i	$-0.0694491\pi$
$102$		0			0
$103$		−	2.76891i		−	0.272829i	−0.990652	−	0.136414i	$-0.956442\pi$
$103$		−	2.76891i		−	0.272829i	0.990652	−	0.136414i	$-0.0435579\pi$
$104$		0			0
$105$	0.286422			0.0279520
$106$		0			0
$107$	−3.25137			−0.314322			−0.157161	−	0.987573i	$-0.550234\pi$
$107$	−3.25137			−0.314322			−0.157161	+	0.987573i	$0.550234\pi$
$108$		0			0
$109$	−3.32806	+	3.32806i	−0.318770	+	0.318770i	−0.848295	−	0.529524i	$-0.822370\pi$
$109$	−3.32806	+	3.32806i	−0.318770	+	0.318770i	0.529524	+	0.848295i	$0.322370\pi$
$110$		0			0
$111$	7.43133	+	7.43133i	0.705351	+	0.705351i
$112$		0			0
$113$	−6.47898			−0.609491			−0.304745	−	0.952434i	$-0.598571\pi$
$113$	−6.47898			−0.609491			−0.304745	+	0.952434i	$0.598571\pi$
$114$		0			0
$115$		−	1.67709i		−	0.156389i
$116$		0			0
$117$	3.22023	−	3.22023i	0.297710	−	0.297710i
$118$		0			0
$119$	3.30307			0.302792
$120$		0			0
$121$			6.27970i			0.570881i
$122$		0			0
$123$	−6.36141	−	3.57494i	−0.573589	−	0.322342i
$124$		0			0
$125$		−	2.49745i		−	0.223378i
$126$		0			0
$127$	−14.7703			−1.31065			−0.655327	−	0.755345i	$-0.727469\pi$
$127$	−14.7703			−1.31065			−0.655327	+	0.755345i	$0.727469\pi$
$128$		0			0
$129$	1.59005	−	1.59005i	0.139996	−	0.139996i
$130$		0			0
$131$			9.39527i			0.820869i	0.911890	+	0.410434i	$0.134623\pi$
$131$			9.39527i			0.820869i	−0.911890	+	0.410434i	$0.865377\pi$
$132$		0			0
$133$	1.89388			0.164220
$134$		0			0
$135$	−0.952155	−	0.952155i	−0.0819484	−	0.0819484i
$136$		0			0
$137$	8.34033	−	8.34033i	0.712562	−	0.712562i	−0.254508	−	0.967071i	$-0.581914\pi$
$137$	8.34033	−	8.34033i	0.712562	−	0.712562i	0.967071	+	0.254508i	$0.0819137\pi$
$138$		0			0
$139$	3.27568			0.277839			0.138920	−	0.990304i	$-0.455637\pi$
$139$	3.27568			0.277839			0.138920	+	0.990304i	$0.455637\pi$
$140$		0			0
$141$	−3.88514			−0.327188
$142$		0			0
$143$		−	11.1274i		−	0.930522i
$144$		0			0
$145$	−0.00389927	+	0.00389927i	−0.000323817	+	0.000323817i
$146$		0			0
$147$	−0.805830	+	0.805830i	−0.0664638	+	0.0664638i
$148$		0			0
$149$	−0.0335973	+	0.0335973i	−0.00275239	+	0.00275239i	−0.708482	−	0.705729i	$-0.750620\pi$
$149$	−0.0335973	+	0.0335973i	−0.00275239	+	0.00275239i	0.705729	+	0.708482i	$0.250620\pi$
$150$		0			0
$151$	−1.45616	−	1.45616i	−0.118501	−	0.118501i	0.645370	−	0.763870i	$-0.276703\pi$
$151$	−1.45616	−	1.45616i	−0.118501	−	0.118501i	−0.763870	+	0.645370i	$0.776703\pi$
$152$		0			0
$153$	−3.97354	−	3.97354i	−0.321241	−	0.321241i
$154$		0			0
$155$			0.908852i			0.0730008i
$156$		0			0
$157$	6.76143	+	6.76143i	0.539621	+	0.539621i	0.923418	−	0.383797i	$-0.125384\pi$
$157$	6.76143	+	6.76143i	0.539621	+	0.539621i	−0.383797	+	0.923418i	$0.625384\pi$
$158$		0			0
$159$			5.09724i			0.404237i
$160$		0			0
$161$	4.71838	+	4.71838i	0.371860	+	0.371860i
$162$		0			0
$163$	−16.6072			−1.30078			−0.650388	−	0.759602i	$-0.725394\pi$
$163$	−16.6072			−1.30078			−0.650388	+	0.759602i	$0.725394\pi$
$164$		0			0
$165$	−1.19062			−0.0926900
$166$		0			0
$167$	−5.56993	−	5.56993i	−0.431014	−	0.431014i	0.457959	−	0.888973i	$-0.348581\pi$
$167$	−5.56993	−	5.56993i	−0.431014	−	0.431014i	−0.888973	+	0.457959i	$0.848581\pi$
$168$		0			0
$169$		−	5.83438i		−	0.448799i
$170$		0			0
$171$	−2.27830	−	2.27830i	−0.174226	−	0.174226i
$172$		0			0
$173$			20.6379i			1.56907i	0.620082	+	0.784537i	$0.287099\pi$
$173$			20.6379i			1.56907i	−0.620082	+	0.784537i	$0.712901\pi$
$174$		0			0
$175$	3.49087	+	3.49087i	0.263885	+	0.263885i
$176$		0			0
$177$	−3.95667	−	3.95667i	−0.297401	−	0.297401i
$178$		0			0
$179$	−13.8890	+	13.8890i	−1.03811	+	1.03811i	−0.0388691	+	0.999244i	$0.512376\pi$
$179$	−13.8890	+	13.8890i	−1.03811	+	1.03811i	−0.999244	+	0.0388691i	$0.987624\pi$
$180$		0			0
$181$	0.658651	−	0.658651i	0.0489572	−	0.0489572i	−0.682204	−	0.731162i	$-0.738979\pi$
$181$	0.658651	−	0.658651i	0.0489572	−	0.0489572i	0.731162	+	0.682204i	$0.238979\pi$
$182$		0			0
$183$	−7.68015	+	7.68015i	−0.567733	+	0.567733i
$184$		0			0
$185$		−	2.31778i		−	0.170406i
$186$		0			0
$187$	−13.7305			−1.00407
$188$		0			0
$189$	5.35765			0.389712
$190$		0			0
$191$	0.280520	−	0.280520i	0.0202977	−	0.0202977i	−0.696885	−	0.717183i	$-0.745431\pi$
$191$	0.280520	−	0.280520i	0.0202977	−	0.0202977i	0.717183	+	0.696885i	$0.245431\pi$
$192$		0			0
$193$	0.497202	+	0.497202i	0.0357894	+	0.0357894i	0.724775	−	0.688986i	$-0.241944\pi$
$193$	0.497202	+	0.497202i	0.0357894	+	0.0357894i	−0.688986	+	0.724775i	$0.741944\pi$
$194$		0			0
$195$	0.766714			0.0549056
$196$		0			0
$197$		−	20.6787i		−	1.47329i	−0.676277	−	0.736647i	$-0.736408\pi$
$197$		−	20.6787i		−	1.47329i	0.676277	−	0.736647i	$-0.263592\pi$
$198$		0			0
$199$	−18.3611	+	18.3611i	−1.30159	+	1.30159i	−0.374262	+	0.927323i	$0.622104\pi$
$199$	−18.3611	+	18.3611i	−1.30159	+	1.30159i	−0.927323	+	0.374262i	$0.877896\pi$
$200$		0			0
$201$	13.8493			0.976857
$202$		0			0
$203$		−	0.0219407i		−	0.00153993i
$204$		0			0
$205$	0.434539	+	1.54954i	0.0303495	+	0.108224i
$206$		0			0
$207$		−	11.3523i		−	0.789037i
$208$		0			0
$209$	−7.87263			−0.544561
$210$		0			0
$211$	−9.29562	+	9.29562i	−0.639937	+	0.639937i	−0.950540	−	0.310603i	$-0.899469\pi$
$211$	−9.29562	+	9.29562i	−0.639937	+	0.639937i	0.310603	+	0.950540i	$0.399469\pi$
$212$		0			0
$213$		−	15.0045i		−	1.02809i
$214$		0			0
$215$	−0.495925			−0.0338218
$216$		0			0
$217$	−2.55700	−	2.55700i	−0.173580	−	0.173580i
$218$		0			0
$219$	−4.45391	+	4.45391i	−0.300967	+	0.300967i
$220$		0			0
$221$	8.84188			0.594769
$222$		0			0
$223$	16.8455			1.12805			0.564027	−	0.825756i	$-0.309251\pi$
$223$	16.8455			1.12805			0.564027	+	0.825756i	$0.309251\pi$
$224$		0			0
$225$		−	8.39891i		−	0.559927i
$226$		0			0
$227$	3.51778	−	3.51778i	0.233483	−	0.233483i	−0.580662	−	0.814145i	$-0.697206\pi$
$227$	3.51778	−	3.51778i	0.233483	−	0.233483i	0.814145	+	0.580662i	$0.197206\pi$
$228$		0			0
$229$	18.4731	−	18.4731i	1.22074	−	1.22074i	0.253365	−	0.967371i	$-0.418463\pi$
$229$	18.4731	−	18.4731i	1.22074	−	1.22074i	0.967371	−	0.253365i	$-0.0815374\pi$
$230$		0			0
$231$	3.34974	−	3.34974i	0.220397	−	0.220397i
$232$		0			0
$233$	18.7275	+	18.7275i	1.22688	+	1.22688i	0.965138	+	0.261740i	$0.0842962\pi$
$233$	18.7275	+	18.7275i	1.22688	+	1.22688i	0.261740	+	0.965138i	$0.415704\pi$
$234$		0			0
$235$	0.605872	+	0.605872i	0.0395228	+	0.0395228i
$236$		0			0
$237$			6.80555i			0.442068i
$238$		0			0
$239$	−18.4946	−	18.4946i	−1.19631	−	1.19631i	−0.975262	−	0.221051i	$-0.929051\pi$
$239$	−18.4946	−	18.4946i	−1.19631	−	1.19631i	−0.221051	−	0.975262i	$-0.570949\pi$
$240$		0			0
$241$		−	4.82354i		−	0.310711i	−0.987859	−	0.155356i	$-0.950348\pi$
$241$		−	4.82354i		−	0.310711i	0.987859	−	0.155356i	$-0.0496524\pi$
$242$		0			0
$243$	−10.5580	−	10.5580i	−0.677295	−	0.677295i
$244$		0			0
$245$	0.251332			0.0160570
$246$		0			0
$247$	5.06966			0.322575
$248$		0			0
$249$	5.46539	+	5.46539i	0.346355	+	0.346355i
$250$		0			0
$251$			3.48952i			0.220256i	0.993917	+	0.110128i	$0.0351261\pi$
$251$			3.48952i			0.220256i	−0.993917	+	0.110128i	$0.964874\pi$
$252$		0			0
$253$	−19.6138	−	19.6138i	−1.23311	−	1.23311i
$254$		0			0
$255$		−	0.946072i		−	0.0592453i
$256$		0			0
$257$	−1.97950	−	1.97950i	−0.123478	−	0.123478i	0.642668	−	0.766145i	$-0.277828\pi$
$257$	−1.97950	−	1.97950i	−0.123478	−	0.123478i	−0.766145	+	0.642668i	$0.777828\pi$
$258$		0			0
$259$	6.52091	+	6.52091i	0.405190	+	0.405190i
$260$		0			0
$261$	−0.0263943	+	0.0263943i	−0.00163376	+	0.00163376i
$262$		0			0
$263$	−8.28189	+	8.28189i	−0.510683	+	0.510683i	−0.914736	−	0.404053i	$-0.867601\pi$
$263$	−8.28189	+	8.28189i	−0.510683	+	0.510683i	0.404053	+	0.914736i	$0.367601\pi$
$264$		0			0
$265$	0.794895	−	0.794895i	0.0488300	−	0.0488300i
$266$		0			0
$267$		−	2.78273i		−	0.170300i
$268$		0			0
$269$	−10.6204			−0.647536			−0.323768	−	0.946136i	$-0.604950\pi$
$269$	−10.6204			−0.647536			−0.323768	+	0.946136i	$0.604950\pi$
$270$		0			0
$271$	−12.9253			−0.785157			−0.392578	−	0.919719i	$-0.628417\pi$
$271$	−12.9253			−0.785157			−0.392578	+	0.919719i	$0.628417\pi$
$272$		0			0
$273$	−2.15710	+	2.15710i	−0.130554	+	0.130554i
$274$		0			0
$275$	−14.5111	−	14.5111i	−0.875054	−	0.875054i
$276$		0			0
$277$	−26.9179			−1.61734			−0.808671	−	0.588261i	$-0.799813\pi$
$277$	−26.9179			−1.61734			−0.808671	+	0.588261i	$0.799813\pi$
$278$		0			0
$279$			6.15205i			0.368313i
$280$		0			0
$281$	−8.65940	+	8.65940i	−0.516576	+	0.516576i	−0.916534	−	0.399957i	$-0.869025\pi$
$281$	−8.65940	+	8.65940i	−0.516576	+	0.516576i	0.399957	+	0.916534i	$0.369025\pi$
$282$		0			0
$283$	−15.0160			−0.892610			−0.446305	−	0.894881i	$-0.647260\pi$
$283$	−15.0160			−0.892610			−0.446305	+	0.894881i	$0.647260\pi$
$284$		0			0
$285$		−	0.542449i		−	0.0321319i
$286$		0			0
$287$	−5.58206	−	3.13697i	−0.329499	−	0.185169i
$288$		0			0
$289$			6.08974i			0.358220i
$290$		0			0
$291$	−4.44938			−0.260827
$292$		0			0
$293$	1.60587	−	1.60587i	0.0938161	−	0.0938161i	−0.658641	−	0.752457i	$-0.728868\pi$
$293$	1.60587	−	1.60587i	0.0938161	−	0.0938161i	0.752457	+	0.658641i	$0.228868\pi$
$294$		0			0
$295$			1.23405i			0.0718494i
$296$		0			0
$297$	−22.2711			−1.29230
$298$		0			0
$299$	12.6305	+	12.6305i	0.730439	+	0.730439i
$300$		0			0
$301$	1.39525	−	1.39525i	0.0804210	−	0.0804210i
$302$		0			0
$303$	19.3189			1.10984
$304$		0			0
$305$	2.39538			0.137159
$306$		0			0
$307$			32.4083i			1.84964i	0.380406	+	0.924820i	$0.375784\pi$
$307$			32.4083i			1.84964i	−0.380406	+	0.924820i	$0.624216\pi$
$308$		0			0
$309$	2.23127	−	2.23127i	0.126933	−	0.126933i
$310$		0			0
$311$	5.87863	−	5.87863i	0.333346	−	0.333346i	−0.520509	−	0.853856i	$-0.674258\pi$
$311$	5.87863	−	5.87863i	0.333346	−	0.333346i	0.853856	+	0.520509i	$0.174258\pi$
$312$		0			0
$313$	−14.7559	+	14.7559i	−0.834051	+	0.834051i	−0.988068	−	0.154017i	$-0.950779\pi$
$313$	−14.7559	+	14.7559i	−0.834051	+	0.834051i	0.154017	+	0.988068i	$0.450779\pi$
$314$		0			0
$315$	−0.302348	−	0.302348i	−0.0170354	−	0.0170354i
$316$		0			0
$317$	15.4241	+	15.4241i	0.866306	+	0.866306i	0.992061	−	0.125755i	$-0.0401353\pi$
$317$	15.4241	+	15.4241i	0.866306	+	0.866306i	−0.125755	+	0.992061i	$0.540135\pi$
$318$		0			0
$319$			0.0912049i			0.00510649i
$320$		0			0
$321$	−2.62005	−	2.62005i	−0.146237	−	0.146237i
$322$		0			0
$323$		−	6.25561i		−	0.348071i
$324$		0			0
$325$	9.34459	+	9.34459i	0.518344	+	0.518344i
$326$		0			0
$327$	−5.36370			−0.296613
$328$		0			0
$329$	−3.40916			−0.187953
$330$		0			0
$331$	2.74721	+	2.74721i	0.151001	+	0.151001i	0.778565	−	0.627564i	$-0.215948\pi$
$331$	2.74721	+	2.74721i	0.151001	+	0.151001i	−0.627564	+	0.778565i	$0.715948\pi$
$332$		0			0
$333$		−	15.6891i		−	0.859757i
$334$		0			0
$335$	−2.15975	−	2.15975i	−0.118000	−	0.118000i
$336$		0			0
$337$			1.03529i			0.0563957i	0.999602	+	0.0281978i	$0.00897684\pi$
$337$			1.03529i			0.0563957i	−0.999602	+	0.0281978i	$0.991023\pi$
$338$		0			0
$339$	−5.22096	−	5.22096i	−0.283563	−	0.283563i
$340$		0			0
$341$	10.6291	+	10.6291i	0.575600	+	0.575600i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	1.35145	−	1.35145i	0.0727596	−	0.0727596i
$346$		0			0
$347$	−19.4454	+	19.4454i	−1.04389	+	1.04389i	−0.0448940	+	0.998992i	$0.514295\pi$
$347$	−19.4454	+	19.4454i	−1.04389	+	1.04389i	−0.998992	+	0.0448940i	$0.985705\pi$
$348$		0			0
$349$			10.7361i			0.574692i	0.957827	+	0.287346i	$0.0927729\pi$
$349$			10.7361i			0.574692i	−0.957827	+	0.287346i	$0.907227\pi$
$350$		0			0
$351$	14.3417			0.765504
$352$		0			0
$353$	−28.7630			−1.53090			−0.765450	−	0.643495i	$-0.777484\pi$
$353$	−28.7630			−1.53090			−0.765450	+	0.643495i	$0.777484\pi$
$354$		0			0
$355$	−2.33990	+	2.33990i	−0.124189	+	0.124189i
$356$		0			0
$357$	2.66171	+	2.66171i	0.140873	+	0.140873i
$358$		0			0
$359$	−16.6893			−0.880830			−0.440415	−	0.897794i	$-0.645169\pi$
$359$	−16.6893			−0.880830			−0.440415	+	0.897794i	$0.645169\pi$
$360$		0			0
$361$			15.4132i			0.811223i
$362$		0			0
$363$	−5.06037	+	5.06037i	−0.265600	+	0.265600i
$364$		0			0
$365$	1.38914			0.0727109
$366$		0			0
$367$			14.5495i			0.759478i	0.925094	+	0.379739i	$0.123986\pi$
$367$			14.5495i			0.759478i	−0.925094	+	0.379739i	$0.876014\pi$
$368$		0			0
$369$	2.94141	+	10.4888i	0.153123	+	0.546028i
$370$		0			0
$371$			4.47277i			0.232215i
$372$		0			0
$373$	36.4059			1.88502			0.942512	−	0.334172i	$-0.108457\pi$
$373$	36.4059			1.88502			0.942512	+	0.334172i	$0.108457\pi$
$374$		0			0
$375$	2.01252	−	2.01252i	0.103926	−	0.103926i
$376$		0			0
$377$		−	0.0587323i		−	0.00302487i
$378$		0			0
$379$	−20.6143			−1.05889			−0.529443	−	0.848346i	$-0.677599\pi$
$379$	−20.6143			−1.05889			−0.529443	+	0.848346i	$0.677599\pi$
$380$		0			0
$381$	−11.9024	−	11.9024i	−0.609777	−	0.609777i
$382$		0			0
$383$	15.1886	−	15.1886i	0.776101	−	0.776101i	−0.203065	−	0.979165i	$-0.565090\pi$
$383$	15.1886	−	15.1886i	0.776101	−	0.776101i	0.979165	+	0.203065i	$0.0650902\pi$
$384$		0			0
$385$	−1.04476			−0.0532459
$386$		0			0
$387$	−3.35693			−0.170642
$388$		0			0
$389$		−	15.8359i		−	0.802911i	−0.915879	−	0.401456i	$-0.868504\pi$
$389$		−	15.8359i		−	0.802911i	0.915879	−	0.401456i	$-0.131496\pi$
$390$		0			0
$391$	15.5851	−	15.5851i	0.788174	−	0.788174i
$392$		0			0
$393$	−7.57099	+	7.57099i	−0.381906	+	0.381906i
$394$		0			0
$395$	1.06130	−	1.06130i	0.0533998	−	0.0533998i
$396$		0			0
$397$	21.2558	+	21.2558i	1.06680	+	1.06680i	0.997603	+	0.0691953i	$0.0220432\pi$
$397$	21.2558	+	21.2558i	1.06680	+	1.06680i	0.0691953	+	0.997603i	$0.477957\pi$
$398$		0			0
$399$	1.52614	+	1.52614i	0.0764027	+	0.0764027i
$400$		0			0
$401$		−	9.85414i		−	0.492092i	−0.969258	−	0.246046i	$-0.920869\pi$
$401$		−	9.85414i		−	0.492092i	0.969258	−	0.246046i	$-0.0791315\pi$
$402$		0			0
$403$	−6.84474	−	6.84474i	−0.340961	−	0.340961i
$404$		0			0
$405$		−	0.251794i		−	0.0125117i
$406$		0			0
$407$	−27.1067	−	27.1067i	−1.34363	−	1.34363i
$408$		0			0
$409$	−35.0043			−1.73085			−0.865426	−	0.501037i	$-0.832952\pi$
$409$	−35.0043			−1.73085			−0.865426	+	0.501037i	$0.832952\pi$
$410$		0			0
$411$	13.4418			0.663034
$412$		0			0
$413$	−3.47193	−	3.47193i	−0.170843	−	0.170843i
$414$		0			0
$415$		−	1.70461i		−	0.0836761i
$416$		0			0
$417$	2.63964	+	2.63964i	0.129264	+	0.129264i
$418$		0			0
$419$		−	10.1050i		−	0.493660i	−0.969059	−	0.246830i	$-0.920611\pi$
$419$		−	10.1050i		−	0.493660i	0.969059	−	0.246830i	$-0.0793889\pi$
$420$		0			0
$421$	12.4472	+	12.4472i	0.606642	+	0.606642i	0.942067	−	0.335425i	$-0.108880\pi$
$421$	12.4472	+	12.4472i	0.606642	+	0.606642i	−0.335425	+	0.942067i	$0.608880\pi$
$422$		0			0
$423$	4.10117	+	4.10117i	0.199406	+	0.199406i
$424$		0			0
$425$	11.5306	−	11.5306i	0.559315	−	0.559315i
$426$		0			0
$427$	−6.73924	+	6.73924i	−0.326135	+	0.326135i
$428$		0			0
$429$	8.96682	−	8.96682i	0.432922	−	0.432922i
$430$		0			0
$431$		−	28.9838i		−	1.39610i	−0.716048	−	0.698051i	$-0.754051\pi$
$431$		−	28.9838i		−	1.39610i	0.716048	−	0.698051i	$-0.245949\pi$
$432$		0			0
$433$	9.54664			0.458782			0.229391	−	0.973334i	$-0.426327\pi$
$433$	9.54664			0.458782			0.229391	+	0.973334i	$0.426327\pi$
$434$		0			0
$435$	−0.00628430			−0.000301309
$436$		0			0
$437$	8.93603	−	8.93603i	0.427468	−	0.427468i
$438$		0			0
$439$	18.1559	+	18.1559i	0.866534	+	0.866534i	0.992087	−	0.125553i	$-0.0400704\pi$
$439$	18.1559	+	18.1559i	0.866534	+	0.866534i	−0.125553	+	0.992087i	$0.540070\pi$
$440$		0			0
$441$	1.70128			0.0810131
$442$		0			0
$443$			9.77375i			0.464365i	0.972672	+	0.232182i	$0.0745866\pi$
$443$			9.77375i			0.464365i	−0.972672	+	0.232182i	$0.925413\pi$
$444$		0			0
$445$	−0.433956	+	0.433956i	−0.0205715	+	0.0205715i
$446$		0			0
$447$	−0.0541474			−0.00256108
$448$		0			0
$449$		−	5.24705i		−	0.247624i	−0.992306	−	0.123812i	$-0.960488\pi$
$449$		−	5.24705i		−	0.247624i	0.992306	−	0.123812i	$-0.0395119\pi$
$450$		0			0
$451$	23.2040	+	13.0400i	1.09263	+	0.614031i
$452$		0			0
$453$		−	2.34684i		−	0.110264i
$454$		0			0
$455$	0.672783			0.0315406
$456$		0			0
$457$	−5.36459	+	5.36459i	−0.250945	+	0.250945i	−0.821358	−	0.570413i	$-0.806783\pi$
$457$	−5.36459	+	5.36459i	−0.250945	+	0.250945i	0.570413	+	0.821358i	$0.306783\pi$
$458$		0			0
$459$		−	17.6967i		−	0.826010i
$460$		0			0
$461$	25.2557			1.17627			0.588137	−	0.808762i	$-0.299862\pi$
$461$	25.2557			1.17627			0.588137	+	0.808762i	$0.299862\pi$
$462$		0			0
$463$	2.71331	+	2.71331i	0.126098	+	0.126098i	0.767339	−	0.641241i	$-0.221580\pi$
$463$	2.71331	+	2.71331i	0.126098	+	0.126098i	−0.641241	+	0.767339i	$0.721580\pi$
$464$		0			0
$465$	−0.732381	+	0.732381i	−0.0339633	+	0.0339633i
$466$		0			0
$467$	−9.12402			−0.422209			−0.211105	−	0.977463i	$-0.567706\pi$
$467$	−9.12402			−0.422209			−0.211105	+	0.977463i	$0.567706\pi$
$468$		0			0
$469$	12.1526			0.561157
$470$		0			0
$471$			10.8971i			0.502113i
$472$		0			0
$473$	−5.79990	+	5.79990i	−0.266680	+	0.266680i
$474$		0			0
$475$	6.61127	−	6.61127i	0.303346	−	0.303346i
$476$		0			0
$477$	5.38066	−	5.38066i	0.246364	−	0.246364i
$478$		0			0
$479$	−3.86377	−	3.86377i	−0.176540	−	0.176540i	0.613306	−	0.789846i	$-0.289839\pi$
$479$	−3.86377	−	3.86377i	−0.176540	−	0.176540i	−0.789846	+	0.613306i	$0.789839\pi$
$480$		0			0
$481$	17.4556	+	17.4556i	0.795907	+	0.795907i
$482$		0			0
$483$			7.60442i			0.346013i
$484$		0			0
$485$	0.693863	+	0.693863i	0.0315067	+	0.0315067i
$486$		0			0
$487$		−	4.69099i		−	0.212569i	−0.994336	−	0.106285i	$-0.966105\pi$
$487$		−	4.69099i		−	0.212569i	0.994336	−	0.106285i	$-0.0338955\pi$
$488$		0			0
$489$	−13.3826	−	13.3826i	−0.605182	−	0.605182i
$490$		0			0
$491$	10.5610			0.476609			0.238305	−	0.971190i	$-0.423408\pi$
$491$	10.5610			0.476609			0.238305	+	0.971190i	$0.423408\pi$
$492$		0			0
$493$	−0.0724715			−0.00326395
$494$		0			0
$495$	1.25683	+	1.25683i	0.0564902	+	0.0564902i
$496$		0			0
$497$		−	13.1663i		−	0.590589i
$498$		0			0
$499$	0.375630	+	0.375630i	0.0168155	+	0.0168155i	0.715465	−	0.698649i	$-0.246215\pi$
$499$	0.375630	+	0.375630i	0.0168155	+	0.0168155i	−0.698649	+	0.715465i	$0.746215\pi$
$500$		0			0
$501$		−	8.97684i		−	0.401055i
$502$		0			0
$503$	16.0124	+	16.0124i	0.713959	+	0.713959i	0.967361	−	0.253402i	$-0.0815495\pi$
$503$	16.0124	+	16.0124i	0.713959	+	0.713959i	−0.253402	+	0.967361i	$0.581550\pi$
$504$		0			0
$505$	−3.01271	−	3.01271i	−0.134064	−	0.134064i
$506$		0			0
$507$	4.70152	−	4.70152i	0.208802	−	0.208802i
$508$		0			0
$509$	12.8161	−	12.8161i	0.568065	−	0.568065i	−0.363521	−	0.931586i	$-0.618425\pi$
$509$	12.8161	−	12.8161i	0.568065	−	0.568065i	0.931586	+	0.363521i	$0.118425\pi$
$510$		0			0
$511$	−3.90825	+	3.90825i	−0.172891	+	0.172891i
$512$		0			0
$513$		−	10.1467i		−	0.447989i
$514$		0			0
$515$	−0.695916			−0.0306657
$516$		0			0
$517$	14.1715			0.623262
$518$		0			0
$519$	−16.6307	+	16.6307i	−0.730006	+	0.730006i
$520$		0			0
$521$	−25.9848	−	25.9848i	−1.13841	−	1.13841i	−0.988735	−	0.149678i	$-0.952176\pi$
$521$	−25.9848	−	25.9848i	−1.13841	−	1.13841i	−0.149678	−	0.988735i	$-0.547824\pi$
$522$		0			0
$523$	14.4566			0.632142			0.316071	−	0.948736i	$-0.397636\pi$
$523$	14.4566			0.632142			0.316071	+	0.948736i	$0.397636\pi$
$524$		0			0
$525$			5.62609i			0.245543i
$526$		0			0
$527$	−8.44593	+	8.44593i	−0.367911	+	0.367911i
$528$		0			0
$529$	21.5262			0.935921
$530$		0			0
$531$			8.35335i			0.362504i
$532$		0			0
$533$	−14.9424	−	8.39725i	−0.647229	−	0.363725i
$534$		0			0
$535$			0.817174i			0.0353295i
$536$		0			0
$537$	−22.3844			−0.965957
$538$		0			0
$539$	2.93936	−	2.93936i	0.126607	−	0.126607i
$540$		0			0
$541$		−	15.2484i		−	0.655578i	−0.944751	−	0.327789i	$-0.893696\pi$
$541$		−	15.2484i		−	0.655578i	0.944751	−	0.327789i	$-0.106304\pi$
$542$		0			0
$543$	1.06152			0.0455543
$544$		0			0
$545$	0.836449	+	0.836449i	0.0358295	+	0.0358295i
$546$		0			0
$547$	27.9756	−	27.9756i	1.19615	−	1.19615i	0.220839	−	0.975310i	$-0.429120\pi$
$547$	27.9756	−	27.9756i	1.19615	−	1.19615i	0.975310	−	0.220839i	$-0.0708795\pi$
$548$		0			0
$549$	16.2144			0.692013
$550$		0			0
$551$	−0.0415529			−0.00177021
$552$		0			0
$553$			5.97180i			0.253947i
$554$		0			0
$555$	1.86773	−	1.86773i	0.0792809	−	0.0792809i
$556$		0			0
$557$	3.14092	−	3.14092i	0.133085	−	0.133085i	−0.637426	−	0.770511i	$-0.720001\pi$
$557$	3.14092	−	3.14092i	0.133085	−	0.133085i	0.770511	+	0.637426i	$0.220001\pi$
$558$		0			0
$559$	3.73490	−	3.73490i	0.157970	−	0.157970i
$560$		0			0
$561$	−11.0644	−	11.0644i	−0.467141	−	0.467141i
$562$		0			0
$563$	26.3968	+	26.3968i	1.11249	+	1.11249i	0.992812	+	0.119681i	$0.0381871\pi$
$563$	26.3968	+	26.3968i	1.11249	+	1.11249i	0.119681	+	0.992812i	$0.461813\pi$
$564$		0			0
$565$			1.62838i			0.0685063i
$566$		0			0
$567$	0.708406	+	0.708406i	0.0297502	+	0.0297502i
$568$		0			0
$569$			4.73462i			0.198486i	0.995063	+	0.0992429i	$0.0316421\pi$
$569$			4.73462i			0.198486i	−0.995063	+	0.0992429i	$0.968358\pi$
$570$		0			0
$571$	0.339810	+	0.339810i	0.0142206	+	0.0142206i	0.714181	−	0.699961i	$-0.246799\pi$
$571$	0.339810	+	0.339810i	0.0142206	+	0.0142206i	−0.699961	+	0.714181i	$0.746799\pi$
$572$		0			0
$573$	0.452103			0.0188869
$574$		0			0
$575$	32.9425			1.37380
$576$		0			0
$577$	17.2352	+	17.2352i	0.717511	+	0.717511i	0.968095	−	0.250584i	$-0.0806225\pi$
$577$	17.2352	+	17.2352i	0.717511	+	0.717511i	−0.250584	+	0.968095i	$0.580623\pi$
$578$		0			0
$579$			0.801321i			0.0333018i
$580$		0			0
$581$	4.79581	+	4.79581i	0.198964	+	0.198964i
$582$		0			0
$583$		−	18.5928i		−	0.770034i
$584$		0			0
$585$	−0.809347	−	0.809347i	−0.0334624	−	0.0334624i
$586$		0			0
$587$	29.5688	+	29.5688i	1.22043	+	1.22043i	0.967478	+	0.252955i	$0.0814025\pi$
$587$	29.5688	+	29.5688i	1.22043	+	1.22043i	0.252955	+	0.967478i	$0.418598\pi$
$588$		0			0
$589$	−4.84264	+	4.84264i	−0.199537	+	0.199537i
$590$		0			0
$591$	16.6635	−	16.6635i	0.685445	−	0.685445i
$592$		0			0
$593$	20.7699	−	20.7699i	0.852918	−	0.852918i	−0.137573	−	0.990492i	$-0.543930\pi$
$593$	20.7699	−	20.7699i	0.852918	−	0.852918i	0.990492	+	0.137573i	$0.0439303\pi$
$594$		0			0
$595$		−	0.830168i		−	0.0340336i
$596$		0			0
$597$	−29.5919			−1.21112
$598$		0			0
$599$	−6.18039			−0.252524			−0.126262	−	0.991997i	$-0.540298\pi$
$599$	−6.18039			−0.252524			−0.126262	+	0.991997i	$0.540298\pi$
$600$		0			0
$601$	−15.2543	+	15.2543i	−0.622236	+	0.622236i	−0.946103	−	0.323867i	$-0.895017\pi$
$601$	−15.2543	+	15.2543i	−0.622236	+	0.622236i	0.323867	+	0.946103i	$0.395017\pi$
$602$		0			0
$603$	−14.6194	−	14.6194i	−0.595349	−	0.595349i
$604$		0			0
$605$	1.57829			0.0641666
$606$		0			0
$607$		−	24.5297i		−	0.995631i	−0.867283	−	0.497815i	$-0.834136\pi$
$607$		−	24.5297i		−	0.995631i	0.867283	−	0.497815i	$-0.165864\pi$
$608$		0			0
$609$	0.0176805	−	0.0176805i	0.000716448	−	0.000716448i
$610$		0			0
$611$	−9.12588			−0.369194
$612$		0			0
$613$			30.7130i			1.24049i	0.784409	+	0.620244i	$0.212966\pi$
$613$			30.7130i			1.24049i	−0.784409	+	0.620244i	$0.787034\pi$
$614$		0			0
$615$	−0.898498	+	1.59883i	−0.0362309	+	0.0644709i
$616$		0			0
$617$			0.0231327i			0.000931289i	1.00000		0.000465645i	$0.000148219\pi$
$617$			0.0231327i			0.000931289i	−1.00000		0.000465645i	$0.999852\pi$
$618$		0			0
$619$	−19.6769			−0.790882			−0.395441	−	0.918491i	$-0.629408\pi$
$619$	−19.6769			−0.790882			−0.395441	+	0.918491i	$0.629408\pi$
$620$		0			0
$621$	25.2794	−	25.2794i	1.01443	−	1.01443i
$622$		0			0
$623$		−	2.44181i		−	0.0978293i
$624$		0			0
$625$	24.0565			0.962259
$626$		0			0
$627$	−6.34400	−	6.34400i	−0.253355	−	0.253355i
$628$		0			0
$629$	21.5390	−	21.5390i	0.858816	−	0.858816i
$630$		0			0
$631$	1.80666			0.0719221			0.0359610	−	0.999353i	$-0.488551\pi$
$631$	1.80666			0.0719221			0.0359610	+	0.999353i	$0.488551\pi$
$632$		0			0
$633$	−14.9814			−0.595456
$634$		0			0
$635$			3.71226i			0.147316i
$636$		0			0
$637$	−1.89283	+	1.89283i	−0.0749967	+	0.0749967i
$638$		0			0
$639$	−15.8388	+	15.8388i	−0.626575	+	0.626575i
$640$		0			0
$641$	24.2949	−	24.2949i	0.959592	−	0.959592i	−0.0396225	−	0.999215i	$-0.512616\pi$
$641$	24.2949	−	24.2949i	0.959592	−	0.959592i	0.999215	+	0.0396225i	$0.0126155\pi$
$642$		0			0
$643$	12.3547	+	12.3547i	0.487223	+	0.487223i	0.907429	−	0.420206i	$-0.138042\pi$
$643$	12.3547	+	12.3547i	0.487223	+	0.487223i	−0.420206	+	0.907429i	$0.638042\pi$
$644$		0			0
$645$	−0.399631	−	0.399631i	−0.0157355	−	0.0157355i
$646$		0			0
$647$			13.8408i			0.544136i	0.962278	+	0.272068i	$0.0877076\pi$
$647$			13.8408i			0.544136i	−0.962278	+	0.272068i	$0.912292\pi$
$648$		0			0
$649$	14.4324	+	14.4324i	0.566522	+	0.566522i
$650$		0			0
$651$		−	4.12101i		−	0.161515i
$652$		0			0
$653$	7.41607	+	7.41607i	0.290213	+	0.290213i	0.837164	−	0.546951i	$-0.184212\pi$
$653$	7.41607	+	7.41607i	0.290213	+	0.290213i	−0.546951	+	0.837164i	$0.684212\pi$
$654$		0			0
$655$	2.36133			0.0922650
$656$		0			0
$657$	9.40313			0.366851
$658$		0			0
$659$	−12.5341	−	12.5341i	−0.488258	−	0.488258i	0.419498	−	0.907756i	$-0.362206\pi$
$659$	−12.5341	−	12.5341i	−0.488258	−	0.488258i	−0.907756	+	0.419498i	$0.862206\pi$
$660$		0			0
$661$		−	17.7094i		−	0.688815i	−0.938820	−	0.344408i	$-0.888080\pi$
$661$		−	17.7094i		−	0.688815i	0.938820	−	0.344408i	$-0.111920\pi$
$662$		0			0
$663$	7.12505	+	7.12505i	0.276714	+	0.276714i
$664$		0			0
$665$		−	0.475992i		−	0.0184582i
$666$		0			0
$667$	−0.103524	−	0.103524i	−0.00400848	−	0.00400848i
$668$		0			0
$669$	13.5746	+	13.5746i	0.524823	+	0.524823i
$670$		0			0
$671$	28.0142	−	28.0142i	1.08148	−	1.08148i
$672$		0			0
$673$	−11.3633	+	11.3633i	−0.438024	+	0.438024i	−0.891347	−	0.453322i	$-0.850239\pi$
$673$	−11.3633	+	11.3633i	−0.438024	+	0.438024i	0.453322	+	0.891347i	$0.350239\pi$
$674$		0			0
$675$	18.7028	−	18.7028i	0.719873	−	0.719873i
$676$		0			0
$677$		−	2.90980i		−	0.111833i	−0.998435	−	0.0559164i	$-0.982192\pi$
$677$		−	2.90980i		−	0.111833i	0.998435	−	0.0559164i	$-0.0178080\pi$
$678$		0			0
$679$	−3.90428			−0.149832
$680$		0			0
$681$	5.66947			0.217254
$682$		0			0
$683$	−1.92137	+	1.92137i	−0.0735191	+	0.0735191i	−0.742910	−	0.669391i	$-0.766555\pi$
$683$	−1.92137	+	1.92137i	−0.0735191	+	0.0735191i	0.669391	+	0.742910i	$0.266555\pi$
$684$		0			0
$685$	−2.09619	−	2.09619i	−0.0800914	−	0.0800914i
$686$		0			0
$687$	29.7723			1.13589
$688$		0			0
$689$			11.9730i			0.456135i
$690$		0			0
$691$	27.1912	−	27.1912i	1.03440	−	1.03440i	0.0350170	−	0.999387i	$-0.488851\pi$
$691$	27.1912	−	27.1912i	1.03440	−	1.03440i	0.999387	−	0.0350170i	$-0.0111485\pi$
$692$		0			0
$693$	−7.07201			−0.268643
$694$		0			0
$695$		−	0.823283i		−	0.0312289i
$696$		0			0
$697$	−10.3616	+	18.4379i	−0.392475	+	0.698387i
$698$		0			0
$699$			30.1823i			1.14160i
$700$		0			0
$701$	−15.7290			−0.594076			−0.297038	−	0.954866i	$-0.595999\pi$
$701$	−15.7290			−0.594076			−0.297038	+	0.954866i	$0.595999\pi$
$702$		0			0
$703$	12.3498	−	12.3498i	0.465781	−	0.465781i
$704$		0			0
$705$			0.976461i			0.0367756i
$706$		0			0
$707$	16.9521			0.637550
$708$		0			0
$709$	1.87844	+	1.87844i	0.0705463	+	0.0705463i	0.741500	−	0.670953i	$-0.234115\pi$
$709$	1.87844	+	1.87844i	0.0705463	+	0.0705463i	−0.670953	+	0.741500i	$0.734115\pi$
$710$		0			0
$711$	7.18397	−	7.18397i	0.269420	−	0.269420i
$712$		0			0
$713$	−24.1298			−0.903666
$714$		0			0
$715$	−2.79668			−0.104590
$716$		0			0
$717$		−	29.8069i		−	1.11316i
$718$		0			0
$719$	−3.04723	+	3.04723i	−0.113642	+	0.113642i	−0.761641	−	0.647999i	$-0.775606\pi$
$719$	−3.04723	+	3.04723i	−0.113642	+	0.113642i	0.647999	+	0.761641i	$0.275606\pi$
$720$		0			0
$721$	1.95792	−	1.95792i	0.0729166	−	0.0729166i
$722$		0			0
$723$	3.88695	−	3.88695i	0.144557	−	0.144557i
$724$		0			0
$725$	−0.0765920	−	0.0765920i	−0.00284455	−	0.00284455i
$726$		0			0
$727$	8.14245	+	8.14245i	0.301987	+	0.301987i	0.841791	−	0.539804i	$-0.181502\pi$
$727$	8.14245	+	8.14245i	0.301987	+	0.301987i	−0.539804	+	0.841791i	$0.681502\pi$
$728$		0			0
$729$		−	20.0214i		−	0.741533i
$730$		0			0
$731$	−4.60861	−	4.60861i	−0.170456	−	0.170456i
$732$		0			0
$733$			48.1604i			1.77884i	0.457087	+	0.889422i	$0.348893\pi$
$733$			48.1604i			1.77884i	−0.457087	+	0.889422i	$0.651107\pi$
$734$		0			0
$735$	0.202531	+	0.202531i	0.00747047	+	0.00747047i
$736$		0			0
$737$	−50.5171			−1.86082
$738$		0			0
$739$	−39.0976			−1.43823			−0.719114	−	0.694892i	$-0.755452\pi$
$739$	−39.0976			−1.43823			−0.719114	+	0.694892i	$0.755452\pi$
$740$		0			0
$741$	4.08528	+	4.08528i	0.150077	+	0.150077i
$742$		0			0
$743$			41.5962i			1.52602i	0.646389	+	0.763008i	$0.276278\pi$
$743$			41.5962i			1.52602i	−0.646389	+	0.763008i	$0.723722\pi$
$744$		0			0
$745$	0.00844407	+	0.00844407i	0.000309367	+	0.000309367i
$746$		0			0
$747$		−	11.5386i		−	0.422174i
$748$		0			0
$749$	−2.29907	−	2.29907i	−0.0840061	−	0.0840061i
$750$		0			0
$751$	37.4849	+	37.4849i	1.36784	+	1.36784i	0.863507	+	0.504337i	$0.168263\pi$
$751$	37.4849	+	37.4849i	1.36784	+	1.36784i	0.504337	+	0.863507i	$0.331737\pi$
$752$		0			0
$753$	−2.81196	+	2.81196i	−0.102473	+	0.102473i
$754$		0			0
$755$	−0.365981	+	0.365981i	−0.0133194	+	0.0133194i
$756$		0			0
$757$	−7.22630	+	7.22630i	−0.262644	+	0.262644i	−0.826128	−	0.563483i	$-0.809461\pi$
$757$	−7.22630	+	7.22630i	−0.262644	+	0.262644i	0.563483	+	0.826128i	$0.309461\pi$
$758$		0			0
$759$		−	31.6107i		−	1.14740i
$760$		0			0
$761$	41.1038			1.49001			0.745005	−	0.667059i	$-0.232447\pi$
$761$	41.1038			1.49001			0.745005	+	0.667059i	$0.232447\pi$
$762$		0			0
$763$	−4.70659			−0.170390
$764$		0			0
$765$	−0.998678	+	0.998678i	−0.0361073	+	0.0361073i
$766$		0			0
$767$	−9.29390	−	9.29390i	−0.335583	−	0.335583i
$768$		0			0
$769$	−34.5557			−1.24611			−0.623055	−	0.782178i	$-0.714109\pi$
$769$	−34.5557			−1.24611			−0.623055	+	0.782178i	$0.714109\pi$
$770$		0			0
$771$		−	3.19028i		−	0.114895i
$772$		0			0
$773$	−15.8386	+	15.8386i	−0.569673	+	0.569673i	−0.932037	−	0.362364i	$-0.881970\pi$
$773$	−15.8386	+	15.8386i	−0.569673	+	0.569673i	0.362364	+	0.932037i	$0.381970\pi$
$774$		0			0
$775$	−17.8523			−0.641273
$776$		0			0
$777$			10.5095i			0.377026i
$778$		0			0
$779$	−5.94103	+	10.5717i	−0.212860	+	0.378772i
$780$		0			0
$781$			54.7308i			1.95842i
$782$		0			0
$783$	−0.117550			−0.00420091
$784$		0			0
$785$	1.69936	−	1.69936i	0.0606529	−	0.0606529i
$786$		0			0
$787$		−	13.9193i		−	0.496171i	−0.968738	−	0.248085i	$-0.920199\pi$
$787$		−	13.9193i		−	0.496171i	0.968738	−	0.248085i	$-0.0798014\pi$
$788$		0			0
$789$	−13.3476			−0.475187
$790$		0			0
$791$	−4.58133	−	4.58133i	−0.162893	−	0.162893i
$792$		0			0
$793$	−18.0400	+	18.0400i	−0.640621	+	0.640621i
$794$		0			0
$795$	1.28110			0.0454359
$796$		0			0
$797$	−54.7723			−1.94014			−0.970068	−	0.242834i	$-0.921923\pi$
$797$	−54.7723			−1.94014			−0.970068	+	0.242834i	$0.921923\pi$
$798$		0			0
$799$			11.2607i			0.398375i
$800$		0			0
$801$	−2.93746	+	2.93746i	−0.103790	+	0.103790i
$802$		0			0
$803$	16.2462	−	16.2462i	0.573315	−	0.573315i
$804$		0			0
$805$	1.18588	−	1.18588i	0.0417968	−	0.0417968i
$806$		0			0
$807$	−8.55823	−	8.55823i	−0.301264	−	0.301264i
$808$		0			0
$809$	13.5463	+	13.5463i	0.476263	+	0.476263i	0.903934	−	0.427671i	$-0.140666\pi$
$809$	13.5463	+	13.5463i	0.476263	+	0.476263i	−0.427671	+	0.903934i	$0.640666\pi$
$810$		0			0
$811$		−	52.7075i		−	1.85081i	−0.378979	−	0.925405i	$-0.623725\pi$
$811$		−	52.7075i		−	1.85081i	0.378979	−	0.925405i	$-0.376275\pi$
$812$		0			0
$813$	−10.4156	−	10.4156i	−0.365291	−	0.365291i
$814$		0			0
$815$			4.17393i			0.146206i
$816$		0			0
$817$	−2.64244	−	2.64244i	−0.0924471	−	0.0924471i
$818$		0			0
$819$	4.55409			0.159133
$820$		0			0
$821$	40.1616			1.40165			0.700825	−	0.713333i	$-0.252815\pi$
$821$	40.1616			1.40165			0.700825	+	0.713333i	$0.252815\pi$
$822$		0			0
$823$	−16.8151	−	16.8151i	−0.586138	−	0.586138i	0.350445	−	0.936583i	$-0.386030\pi$
$823$	−16.8151	−	16.8151i	−0.586138	−	0.586138i	−0.936583	+	0.350445i	$0.886030\pi$
$824$		0			0
$825$		−	23.3870i		−	0.814232i
$826$		0			0
$827$	11.7356	+	11.7356i	0.408087	+	0.408087i	0.881071	−	0.472984i	$-0.156823\pi$
$827$	11.7356	+	11.7356i	0.408087	+	0.408087i	−0.472984	+	0.881071i	$0.656823\pi$
$828$		0			0
$829$			51.1586i			1.77681i	0.459057	+	0.888407i	$0.348187\pi$
$829$			51.1586i			1.77681i	−0.459057	+	0.888407i	$0.651813\pi$
$830$		0			0
$831$	−21.6913	−	21.6913i	−0.752463	−	0.752463i
$832$		0			0
$833$	2.33562	+	2.33562i	0.0809245	+	0.0809245i
$834$		0			0
$835$	−1.39990	+	1.39990i	−0.0484456	+	0.0484456i
$836$		0			0
$837$	−13.6995	+	13.6995i	−0.473524	+	0.473524i
$838$		0			0
$839$	−5.71879	+	5.71879i	−0.197434	+	0.197434i	−0.798899	−	0.601465i	$-0.794584\pi$
$839$	−5.71879	+	5.71879i	−0.197434	+	0.197434i	0.601465	+	0.798899i	$0.294584\pi$
$840$		0			0
$841$		−	28.9995i		−	0.999983i
$842$		0			0
$843$	−13.9560			−0.480671
$844$		0			0
$845$	−1.46637			−0.0504446
$846$		0			0
$847$	−4.44042	+	4.44042i	−0.152574	+	0.152574i
$848$		0			0
$849$	−12.1004	−	12.1004i	−0.415283	−	0.415283i
$850$		0			0
$851$	61.5362			2.10943
$852$		0			0
$853$		−	11.5830i		−	0.396593i	−0.980142	−	0.198297i	$-0.936459\pi$
$853$		−	11.5830i		−	0.396593i	0.980142	−	0.198297i	$-0.0635409\pi$
$854$		0			0
$855$	−0.572611	+	0.572611i	−0.0195829	+	0.0195829i
$856$		0			0
$857$	−10.9897			−0.375402			−0.187701	−	0.982226i	$-0.560104\pi$
$857$	−10.9897			−0.375402			−0.187701	+	0.982226i	$0.560104\pi$
$858$		0			0
$859$			56.4252i			1.92520i	0.270920	+	0.962602i	$0.412672\pi$
$859$			56.4252i			1.92520i	−0.270920	+	0.962602i	$0.587328\pi$
$860$		0			0
$861$	−1.97033	−	7.02606i	−0.0671486	−	0.239447i
$862$		0			0
$863$		−	16.0485i		−	0.546296i	−0.961972	−	0.273148i	$-0.911935\pi$
$863$		−	16.0485i		−	0.546296i	0.961972	−	0.273148i	$-0.0880648\pi$
$864$		0			0
$865$	5.18698			0.176363
$866$		0			0
$867$	−4.90730	+	4.90730i	−0.166661	+	0.166661i
$868$		0			0
$869$		−	24.8241i		−	0.842099i
$870$		0			0
$871$	32.5310			1.10227
$872$		0			0
$873$	4.69678	+	4.69678i	0.158962	+	0.158962i
$874$		0			0
$875$	1.76596	−	1.76596i	0.0597004	−	0.0597004i
$876$		0			0
$877$	−25.1322			−0.848655			−0.424327	−	0.905509i	$-0.639489\pi$
$877$	−25.1322			−0.848655			−0.424327	+	0.905509i	$0.639489\pi$
$878$		0			0
$879$	2.58812			0.0872952
$880$		0			0
$881$			25.9285i			0.873555i	0.899570	+	0.436777i	$0.143880\pi$
$881$			25.9285i			0.873555i	−0.899570	+	0.436777i	$0.856120\pi$
$882$		0			0
$883$	26.3964	−	26.3964i	0.888309	−	0.888309i	−0.106052	−	0.994361i	$-0.533821\pi$
$883$	26.3964	−	26.3964i	0.888309	−	0.888309i	0.994361	+	0.106052i	$0.0338209\pi$
$884$		0			0
$885$	−0.994438	+	0.994438i	−0.0334277	+	0.0334277i
$886$		0			0
$887$	−15.8761	+	15.8761i	−0.533066	+	0.533066i	−0.921484	−	0.388417i	$-0.873022\pi$
$887$	−15.8761	+	15.8761i	−0.533066	+	0.533066i	0.388417	+	0.921484i	$0.373022\pi$
$888$		0			0
$889$	−10.4442	−	10.4442i	−0.350287	−	0.350287i
$890$		0			0
$891$	−2.94476	−	2.94476i	−0.0986532	−	0.0986532i
$892$		0			0
$893$			6.45654i			0.216060i
$894$		0			0
$895$	3.49076	+	3.49076i	0.116683	+	0.116683i
$896$		0			0
$897$			20.3560i			0.679668i
$898$		0			0
$899$	0.0561022	+	0.0561022i	0.00187111	+	0.00187111i
$900$		0			0
$901$	14.7739			0.492189
$902$		0			0
$903$	2.24867			0.0748311
$904$		0			0
$905$	−0.165540	−	0.165540i	−0.00550275	−	0.00550275i
$906$		0			0
$907$		−	38.8133i		−	1.28877i	−0.764700	−	0.644387i	$-0.777113\pi$
$907$		−	38.8133i		−	1.28877i	0.764700	−	0.644387i	$-0.222887\pi$
$908$		0			0
$909$	−20.3931	−	20.3931i	−0.676397	−	0.676397i
$910$		0			0
$911$			38.4491i			1.27388i	0.770915	+	0.636938i	$0.219799\pi$
$911$			38.4491i			1.27388i	−0.770915	+	0.636938i	$0.780201\pi$
$912$		0			0
$913$	−19.9356	−	19.9356i	−0.659774	−	0.659774i
$914$		0			0
$915$	1.93027	+	1.93027i	0.0638127	+	0.0638127i
$916$		0			0
$917$	−6.64346	+	6.64346i	−0.219386	+	0.219386i
$918$		0			0
$919$	23.3680	−	23.3680i	0.770838	−	0.770838i	−0.207415	−	0.978253i	$-0.566505\pi$
$919$	23.3680	−	23.3680i	0.770838	−	0.770838i	0.978253	+	0.207415i	$0.0665050\pi$
$920$		0			0
$921$	−26.1156	+	26.1156i	−0.860538	+	0.860538i
$922$		0			0
$923$		−	35.2444i		−	1.16008i
$924$		0			0
$925$	45.5273			1.49693
$926$		0			0
$927$	−4.71068			−0.154719
$928$		0			0
$929$	−19.0547	+	19.0547i	−0.625165	+	0.625165i	−0.946848	−	0.321682i	$-0.895752\pi$
$929$	−19.0547	+	19.0547i	−0.625165	+	0.625165i	0.321682	+	0.946848i	$0.395752\pi$
$930$		0			0
$931$	1.33917	+	1.33917i	0.0438896	+	0.0438896i
$932$		0			0
$933$	9.47436			0.310176
$934$		0			0
$935$			3.45091i			0.112857i
$936$		0			0
$937$	0.000932308	0	0.000932308i	3.04572e−5	0	3.04572e-5i	−0.707092	−	0.707122i	$-0.749993\pi$
$937$	0.000932308	0	0.000932308i	3.04572e−5	0	3.04572e-5i	0.707122	+	0.707092i	$0.249993\pi$
$938$		0			0
$939$	−23.7814			−0.776078
$940$		0			0
$941$			35.6335i			1.16162i	0.814039	+	0.580810i	$0.197264\pi$
$941$			35.6335i			1.16162i	−0.814039	+	0.580810i	$0.802736\pi$
$942$		0			0
$943$	−41.1397	+	11.5369i	−1.33969	+	0.375692i
$944$		0			0
$945$		−	1.34655i		−	0.0438033i
$946$		0			0
$947$	20.2183			0.657006			0.328503	−	0.944503i	$-0.393456\pi$
$947$	20.2183			0.657006			0.328503	+	0.944503i	$0.393456\pi$
$948$		0			0
$949$	−10.4619	+	10.4619i	−0.339607	+	0.339607i
$950$		0			0
$951$			24.8585i			0.806092i
$952$		0			0
$953$	−48.9387			−1.58528			−0.792641	−	0.609689i	$-0.791294\pi$
$953$	−48.9387			−1.58528			−0.792641	+	0.609689i	$0.791294\pi$
$954$		0			0
$955$	−0.0705038	−	0.0705038i	−0.00228145	−	0.00228145i
$956$		0			0
$957$	−0.0734956	+	0.0734956i	−0.00237578	+	0.00237578i
$958$		0			0
$959$	11.7950			0.380880
$960$		0			0
$961$	−17.9235			−0.578179
$962$		0			0
$963$			5.53148i			0.178249i
$964$		0			0
$965$	0.124963	−	0.124963i	0.00402270	−	0.00402270i
$966$		0			0
$967$	12.8816	−	12.8816i	0.414245	−	0.414245i	−0.468969	−	0.883214i	$-0.655375\pi$
$967$	12.8816	−	12.8816i	0.414245	−	0.414245i	0.883214	+	0.468969i	$0.155375\pi$
$968$		0			0
$969$	5.04096	−	5.04096i	0.161939	−	0.161939i
$970$		0			0
$971$	−9.40187	−	9.40187i	−0.301720	−	0.301720i	0.539966	−	0.841687i	$-0.318437\pi$
$971$	−9.40187	−	9.40187i	−0.301720	−	0.301720i	−0.841687	+	0.539966i	$0.818437\pi$
$972$		0			0
$973$	2.31625	+	2.31625i	0.0742557	+	0.0742557i
$974$		0			0
$975$			15.0603i			0.482316i
$976$		0			0
$977$	−33.7732	−	33.7732i	−1.08050	−	1.08050i	−0.996463	−	0.0840367i	$-0.973219\pi$
$977$	−33.7732	−	33.7732i	−1.08050	−	1.08050i	−0.0840367	−	0.996463i	$-0.526781\pi$
$978$		0			0
$979$			10.1503i			0.324406i
$980$		0			0
$981$	5.66194	+	5.66194i	0.180772	+	0.180772i
$982$		0			0
$983$	12.3461			0.393779			0.196890	−	0.980426i	$-0.436916\pi$
$983$	12.3461			0.393779			0.196890	+	0.980426i	$0.436916\pi$
$984$		0			0
$985$	−5.19722			−0.165597
$986$		0			0
$987$	−2.74721	−	2.74721i	−0.0874446	−	0.0874446i
$988$		0			0
$989$		−	13.1667i		−	0.418675i
$990$		0			0
$991$	−32.2467	−	32.2467i	−1.02435	−	1.02435i	−0.999696	−	0.0246531i	$-0.992152\pi$
$991$	−32.2467	−	32.2467i	−1.02435	−	1.02435i	−0.0246531	−	0.999696i	$-0.507848\pi$
$992$		0			0
$993$			4.42758i			0.140505i
$994$		0			0
$995$	4.61474	+	4.61474i	0.146297	+	0.146297i
$996$		0			0
$997$	7.32451	+	7.32451i	0.231970	+	0.231970i	0.813514	−	0.581545i	$-0.197552\pi$
$997$	7.32451	+	7.32451i	0.231970	+	0.231970i	−0.581545	+	0.813514i	$0.697552\pi$
$998$		0			0
$999$	34.9367	−	34.9367i	1.10535	−	1.10535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.12	✓	36
41.32	even	4	inner	1148.2.k.b.729.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.12	✓	36	1.1	even	1	trivial
1148.2.k.b.729.12	yes	36	41.32	even	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.805830 + 0.805830i) q^{3} -0.251332i q^{5} +(0.707107 + 0.707107i) q^{7} -1.70128i q^{9} +O(q^{10})\)	\(q+(0.805830 + 0.805830i) q^{3} -0.251332i q^{5} +(0.707107 + 0.707107i) q^{7} -1.70128i q^{9} +(-2.93936 - 2.93936i) q^{11} +(1.89283 + 1.89283i) q^{13} +(0.202531 - 0.202531i) q^{15} +(2.33562 - 2.33562i) q^{17} +(1.33917 - 1.33917i) q^{19} +1.13962i q^{21} +6.67279 q^{23} +4.93683 q^{25} +(3.78843 - 3.78843i) q^{27} +(-0.0155144 - 0.0155144i) q^{29} -3.61614 q^{31} -4.73725i q^{33} +(0.177719 - 0.177719i) q^{35} +9.22196 q^{37} +3.05060i q^{39} +(-6.16529 + 1.72894i) q^{41} -1.97318i q^{43} -0.427585 q^{45} +(-2.41064 + 2.41064i) q^{47} +1.00000i q^{49} +3.76423 q^{51} +(3.16272 + 3.16272i) q^{53} +(-0.738756 + 0.738756i) q^{55} +2.15829 q^{57} -4.91005 q^{59} +9.53072i q^{61} +(1.20298 - 1.20298i) q^{63} +(0.475729 - 0.475729i) q^{65} +(8.59321 - 8.59321i) q^{67} +(5.37714 + 5.37714i) q^{69} +(-9.30998 - 9.30998i) q^{71} +5.52711i q^{73} +(3.97825 + 3.97825i) q^{75} -4.15689i q^{77} +(4.22270 + 4.22270i) q^{79} +1.00184 q^{81} +6.78231 q^{83} +(-0.587017 - 0.587017i) q^{85} -0.0250039i q^{87} +(-1.72662 - 1.72662i) q^{89} +2.67687i q^{91} +(-2.91399 - 2.91399i) q^{93} +(-0.336577 - 0.336577i) q^{95} +(-2.76074 + 2.76074i) q^{97} +(-5.00066 + 5.00066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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