LMFDB - Embedded newform 1248.2.ca.b.49.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1248,2,Mod(49,1248)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1248, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1248.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.15
Character	$\chi$	$=$	1248.49
Dual form			1248.2.ca.b.433.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +1.88587 q^{5} +(-3.80954 - 2.19944i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.0662772 + 0.114795i) q^{11} +(-3.59512 + 0.274112i) q^{13} +(1.63321 - 0.942933i) q^{15} +(1.14806 - 1.98850i) q^{17} +(2.18964 - 3.79257i) q^{19} -4.39888 q^{21} +(-1.97584 - 3.42225i) q^{23} -1.44351 q^{25} -1.00000i q^{27} +(2.20762 - 1.27457i) q^{29} +1.06736i q^{31} +(0.114795 + 0.0662772i) q^{33} +(-7.18429 - 4.14785i) q^{35} +(-5.28540 - 9.15458i) q^{37} +(-2.97641 + 2.03495i) q^{39} +(7.14559 - 4.12551i) q^{41} +(-8.32354 - 4.80560i) q^{43} +(0.942933 - 1.63321i) q^{45} +10.1114i q^{47} +(6.17508 + 10.6956i) q^{49} -2.29612i q^{51} -8.28514i q^{53} +(0.124990 + 0.216489i) q^{55} -4.37928i q^{57} +(-1.65394 + 2.86472i) q^{59} +(6.40470 + 3.69775i) q^{61} +(-3.80954 + 2.19944i) q^{63} +(-6.77991 + 0.516938i) q^{65} +(-0.540655 - 0.936442i) q^{67} +(-3.42225 - 1.97584i) q^{69} +(-6.45016 - 3.72400i) q^{71} +6.14363i q^{73} +(-1.25011 + 0.721753i) q^{75} -0.583091i q^{77} +15.9309 q^{79} +(-0.500000 - 0.866025i) q^{81} -0.144468 q^{83} +(2.16509 - 3.75004i) q^{85} +(1.27457 - 2.20762i) q^{87} +(-14.2114 + 8.20498i) q^{89} +(14.2986 + 6.86301i) q^{91} +(0.533679 + 0.924359i) q^{93} +(4.12937 - 7.15228i) q^{95} +(6.11866 + 3.53261i) q^{97} +0.132554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) $ 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	1.88587			0.843385			0.421693	−	0.906739i	$-0.361436\pi$
$5$	1.88587			0.843385			0.421693	+	0.906739i	$0.361436\pi$
$6$		0			0
$7$	−3.80954	−	2.19944i	−1.43987	−	0.831311i	−0.442032	−	0.896999i	$-0.645742\pi$
$7$	−3.80954	−	2.19944i	−1.43987	−	0.831311i	−0.997840	+	0.0656885i	$0.979076\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.0662772	+	0.114795i	0.0199833	+	0.0346121i	0.875844	−	0.482594i	$-0.160305\pi$
$11$	0.0662772	+	0.114795i	0.0199833	+	0.0346121i	−0.855861	+	0.517206i	$0.826972\pi$
$12$		0			0
$13$	−3.59512	+	0.274112i	−0.997106	+	0.0760249i
$13$	−3.59512	+	0.274112i	−0.997106	+	0.0760249i
$14$		0			0
$15$	1.63321	−	0.942933i	0.421693	−	0.243464i
$16$		0			0
$17$	1.14806	−	1.98850i	0.278446	−	0.482282i	−0.692553	−	0.721367i	$-0.743514\pi$
$17$	1.14806	−	1.98850i	0.278446	−	0.482282i	0.970999	+	0.239085i	$0.0768475\pi$
$18$		0			0
$19$	2.18964	−	3.79257i	0.502338	−	0.870075i	−0.497658	−	0.867373i	$-0.665807\pi$
$19$	2.18964	−	3.79257i	0.502338	−	0.870075i	0.999996	−	0.00270169i	$-0.000859974\pi$
$20$		0			0
$21$	−4.39888			−0.959915
$22$		0			0
$23$	−1.97584	−	3.42225i	−0.411991	−	0.713589i	0.583117	−	0.812388i	$-0.301833\pi$
$23$	−1.97584	−	3.42225i	−0.411991	−	0.713589i	−0.995107	+	0.0987997i	$0.968500\pi$
$24$		0			0
$25$	−1.44351			−0.288701
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	2.20762	−	1.27457i	0.409944	−	0.236682i	−0.280821	−	0.959760i	$-0.590607\pi$
$29$	2.20762	−	1.27457i	0.409944	−	0.236682i	0.690766	+	0.723078i	$0.257274\pi$
$30$		0			0
$31$			1.06736i			0.191703i	0.995396	+	0.0958516i	$0.0305574\pi$
$31$			1.06736i			0.191703i	−0.995396	+	0.0958516i	$0.969443\pi$
$32$		0			0
$33$	0.114795	+	0.0662772i	0.0199833	+	0.0115374i
$34$		0			0
$35$	−7.18429	−	4.14785i	−1.21437	−	0.701115i
$36$		0			0
$37$	−5.28540	−	9.15458i	−0.868914	−	1.50500i	−0.863108	−	0.505020i	$-0.831485\pi$
$37$	−5.28540	−	9.15458i	−0.868914	−	1.50500i	−0.00580626	−	0.999983i	$-0.501848\pi$
$38$		0			0
$39$	−2.97641	+	2.03495i	−0.476606	+	0.325852i
$40$		0			0
$41$	7.14559	−	4.12551i	1.11595	−	0.644296i	0.175589	−	0.984464i	$-0.443817\pi$
$41$	7.14559	−	4.12551i	1.11595	−	0.644296i	0.940365	+	0.340168i	$0.110484\pi$
$42$		0			0
$43$	−8.32354	−	4.80560i	−1.26933	−	0.732847i	−0.294467	−	0.955662i	$-0.595142\pi$
$43$	−8.32354	−	4.80560i	−1.26933	−	0.732847i	−0.974861	+	0.222815i	$0.928475\pi$
$44$		0			0
$45$	0.942933	−	1.63321i	0.140564	−	0.243464i
$46$		0			0
$47$			10.1114i			1.47491i	0.675399	+	0.737453i	$0.263972\pi$
$47$			10.1114i			1.47491i	−0.675399	+	0.737453i	$0.736028\pi$
$48$		0			0
$49$	6.17508	+	10.6956i	0.882155	+	1.52794i
$50$		0			0
$51$		−	2.29612i		−	0.321521i
$52$		0			0
$53$		−	8.28514i		−	1.13805i	−0.822320	−	0.569026i	$-0.807320\pi$
$53$		−	8.28514i		−	1.13805i	0.822320	−	0.569026i	$-0.192680\pi$
$54$		0			0
$55$	0.124990	+	0.216489i	0.0168536	+	0.0291914i
$56$		0			0
$57$		−	4.37928i		−	0.580050i
$58$		0			0
$59$	−1.65394	+	2.86472i	−0.215325	+	0.372954i	−0.953373	−	0.301794i	$-0.902415\pi$
$59$	−1.65394	+	2.86472i	−0.215325	+	0.372954i	0.738048	+	0.674748i	$0.235748\pi$
$60$		0			0
$61$	6.40470	+	3.69775i	0.820038	+	0.473449i	0.850429	−	0.526089i	$-0.176342\pi$
$61$	6.40470	+	3.69775i	0.820038	+	0.473449i	−0.0303918	+	0.999538i	$0.509675\pi$
$62$		0			0
$63$	−3.80954	+	2.19944i	−0.479957	+	0.277104i
$64$		0			0
$65$	−6.77991	+	0.516938i	−0.840944	+	0.0641183i
$66$		0			0
$67$	−0.540655	−	0.936442i	−0.0660515	−	0.114405i	0.831108	−	0.556110i	$-0.187707\pi$
$67$	−0.540655	−	0.936442i	−0.0660515	−	0.114405i	−0.897160	+	0.441706i	$0.854373\pi$
$68$		0			0
$69$	−3.42225	−	1.97584i	−0.411991	−	0.237863i
$70$		0			0
$71$	−6.45016	−	3.72400i	−0.765493	−	0.441958i	0.0657714	−	0.997835i	$-0.479049\pi$
$71$	−6.45016	−	3.72400i	−0.765493	−	0.441958i	−0.831265	+	0.555877i	$0.812383\pi$
$72$		0			0
$73$			6.14363i			0.719057i	0.933134	+	0.359529i	$0.117062\pi$
$73$			6.14363i			0.719057i	−0.933134	+	0.359529i	$0.882938\pi$
$74$		0			0
$75$	−1.25011	+	0.721753i	−0.144351	+	0.0833409i
$76$		0			0
$77$		−	0.583091i		−	0.0664494i
$78$		0			0
$79$	15.9309			1.79236			0.896182	−	0.443688i	$-0.146330\pi$
$79$	15.9309			1.79236			0.896182	+	0.443688i	$0.146330\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.144468			−0.0158574			−0.00792871	−	0.999969i	$-0.502524\pi$
$83$	−0.144468			−0.0158574			−0.00792871	+	0.999969i	$0.502524\pi$
$84$		0			0
$85$	2.16509	−	3.75004i	0.234837	−	0.406749i
$86$		0			0
$87$	1.27457	−	2.20762i	0.136648	−	0.236682i
$88$		0			0
$89$	−14.2114	+	8.20498i	−1.50641	+	0.869726i	−0.506437	+	0.862277i	$0.669038\pi$
$89$	−14.2114	+	8.20498i	−1.50641	+	0.869726i	−0.999972	+	0.00744871i	$0.997629\pi$
$90$		0			0
$91$	14.2986	+	6.86301i	1.49891	+	0.719439i
$92$		0			0
$93$	0.533679	+	0.924359i	0.0553399	+	0.0958516i
$94$		0			0
$95$	4.12937	−	7.15228i	0.423664	−	0.733808i
$96$		0			0
$97$	6.11866	+	3.53261i	0.621256	+	0.358682i	0.777358	−	0.629059i	$-0.216560\pi$
$97$	6.11866	+	3.53261i	0.621256	+	0.358682i	−0.156102	+	0.987741i	$0.549893\pi$
$98$		0			0
$99$	0.132554			0.0133222
$100$		0			0
$101$	9.34844	−	5.39732i	0.930204	−	0.537054i	0.0433280	−	0.999061i	$-0.486204\pi$
$101$	9.34844	−	5.39732i	0.930204	−	0.537054i	0.886876	+	0.462007i	$0.152871\pi$
$102$		0			0
$103$	10.9719			1.08110			0.540548	−	0.841313i	$-0.318217\pi$
$103$	10.9719			1.08110			0.540548	+	0.841313i	$0.318217\pi$
$104$		0			0
$105$	−8.29571			−0.809578
$106$		0			0
$107$	−3.34576	+	1.93168i	−0.323447	+	0.186742i	−0.652928	−	0.757420i	$-0.726460\pi$
$107$	−3.34576	+	1.93168i	−0.323447	+	0.186742i	0.329481	+	0.944162i	$0.393126\pi$
$108$		0			0
$109$	−1.14546			−0.109716			−0.0548578	−	0.998494i	$-0.517471\pi$
$109$	−1.14546			−0.109716			−0.0548578	+	0.998494i	$0.517471\pi$
$110$		0			0
$111$	−9.15458	−	5.28540i	−0.868914	−	0.501668i
$112$		0			0
$113$	4.88900	−	8.46799i	0.459918	−	0.796601i	−0.539038	−	0.842281i	$-0.681212\pi$
$113$	4.88900	−	8.46799i	0.459918	−	0.796601i	0.998956	+	0.0456800i	$0.0145454\pi$
$114$		0			0
$115$	−3.72617	−	6.45391i	−0.347467	−	0.601830i
$116$		0			0
$117$	−1.56017	+	3.25052i	−0.144238	+	0.300511i
$118$		0			0
$119$	−8.74717	+	5.05018i	−0.801852	+	0.462949i
$120$		0			0
$121$	5.49121	−	9.51106i	0.499201	−	0.864642i
$122$		0			0
$123$	4.12551	−	7.14559i	0.371984	−	0.644296i
$124$		0			0
$125$	−12.1516			−1.08687
$126$		0			0
$127$	7.37989	+	12.7824i	0.654860	+	1.13425i	0.981929	+	0.189250i	$0.0606056\pi$
$127$	7.37989	+	12.7824i	0.654860	+	1.13425i	−0.327069	+	0.945000i	$0.606061\pi$
$128$		0			0
$129$	−9.61119			−0.846218
$130$		0			0
$131$		−	1.23181i		−	0.107624i	−0.998551	−	0.0538118i	$-0.982863\pi$
$131$		−	1.23181i		−	0.107624i	0.998551	−	0.0538118i	$-0.0171371\pi$
$132$		0			0
$133$	−16.6831	+	9.63197i	−1.44660	+	0.835198i
$134$		0			0
$135$		−	1.88587i		−	0.162310i
$136$		0			0
$137$	−15.7493	−	9.09286i	−1.34555	−	0.776856i	−0.357938	−	0.933745i	$-0.616520\pi$
$137$	−15.7493	−	9.09286i	−1.34555	−	0.776856i	−0.987616	+	0.156890i	$0.949853\pi$
$138$		0			0
$139$	−4.13153	−	2.38534i	−0.350432	−	0.202322i	0.314444	−	0.949276i	$-0.398182\pi$
$139$	−4.13153	−	2.38534i	−0.350432	−	0.202322i	−0.664875	+	0.746954i	$0.731515\pi$
$140$		0			0
$141$	5.05572	+	8.75677i	0.425768	+	0.737453i
$142$		0			0
$143$	−0.269741	−	0.394536i	−0.0225569	−	0.0329927i
$144$		0			0
$145$	4.16327	−	2.40367i	0.345741	−	0.199614i
$146$		0			0
$147$	10.6956	+	6.17508i	0.882155	+	0.509312i
$148$		0			0
$149$	3.97531	−	6.88544i	0.325670	−	0.564077i	−0.655978	−	0.754780i	$-0.727743\pi$
$149$	3.97531	−	6.88544i	0.325670	−	0.564077i	0.981648	+	0.190703i	$0.0610768\pi$
$150$		0			0
$151$			13.5552i			1.10311i	0.834139	+	0.551554i	$0.185965\pi$
$151$			13.5552i			1.10311i	−0.834139	+	0.551554i	$0.814035\pi$
$152$		0			0
$153$	−1.14806	−	1.98850i	−0.0928152	−	0.160761i
$154$		0			0
$155$			2.01290i			0.161680i
$156$		0			0
$157$			0.0648041i			0.00517193i	0.999997	+	0.00258597i	$0.000823140\pi$
$157$			0.0648041i			0.00517193i	−0.999997	+	0.00258597i	$0.999177\pi$
$158$		0			0
$159$	−4.14257	−	7.17514i	−0.328527	−	0.569026i
$160$		0			0
$161$			17.3830i			1.36997i
$162$		0			0
$163$	5.26292	−	9.11565i	0.412224	−	0.713993i	−0.582909	−	0.812538i	$-0.698085\pi$
$163$	5.26292	−	9.11565i	0.412224	−	0.713993i	0.995133	+	0.0985448i	$0.0314188\pi$
$164$		0			0
$165$	0.216489	+	0.124990i	0.0168536	+	0.00973045i
$166$		0			0
$167$	12.4804	−	7.20556i	0.965762	−	0.557583i	0.0678204	−	0.997698i	$-0.478396\pi$
$167$	12.4804	−	7.20556i	0.965762	−	0.557583i	0.897942	+	0.440115i	$0.145062\pi$
$168$		0			0
$169$	12.8497	−	1.97093i	0.988440	−	0.151610i
$170$		0			0
$171$	−2.18964	−	3.79257i	−0.167446	−	0.290025i
$172$		0			0
$173$	−7.41252	−	4.27962i	−0.563564	−	0.325374i	0.191011	−	0.981588i	$-0.438823\pi$
$173$	−7.41252	−	4.27962i	−0.563564	−	0.325374i	−0.754575	+	0.656214i	$0.772157\pi$
$174$		0			0
$175$	5.49910	+	3.17491i	0.415693	+	0.240000i
$176$		0			0
$177$			3.30789i			0.248636i
$178$		0			0
$179$	−14.8169	+	8.55453i	−1.10747	+	0.639396i	−0.938172	−	0.346170i	$-0.887482\pi$
$179$	−14.8169	+	8.55453i	−1.10747	+	0.639396i	−0.169294	+	0.985566i	$0.554149\pi$
$180$		0			0
$181$			11.8391i			0.879992i	0.898000	+	0.439996i	$0.145020\pi$
$181$			11.8391i			0.879992i	−0.898000	+	0.439996i	$0.854980\pi$
$182$		0			0
$183$	7.39551			0.546692
$184$		0			0
$185$	−9.96755	−	17.2643i	−0.732829	−	1.26930i
$186$		0			0
$187$	0.304361			0.0222571
$188$		0			0
$189$	−2.19944	+	3.80954i	−0.159986	+	0.277104i
$190$		0			0
$191$	3.55694	−	6.16081i	0.257371	−	0.445780i	−0.708166	−	0.706046i	$-0.750477\pi$
$191$	3.55694	−	6.16081i	0.257371	−	0.445780i	0.965537	+	0.260266i	$0.0838103\pi$
$192$		0			0
$193$	−12.1721	+	7.02758i	−0.876169	+	0.505857i	−0.869393	−	0.494120i	$-0.835490\pi$
$193$	−12.1721	+	7.02758i	−0.876169	+	0.505857i	−0.00677591	+	0.999977i	$0.502157\pi$
$194$		0			0
$195$	−5.61311	+	3.83764i	−0.401963	+	0.274819i
$196$		0			0
$197$	11.2731	+	19.5256i	0.803178	+	1.39114i	0.917514	+	0.397702i	$0.130192\pi$
$197$	11.2731	+	19.5256i	0.803178	+	1.39114i	−0.114337	+	0.993442i	$0.536474\pi$
$198$		0			0
$199$	6.49779	−	11.2545i	0.460616	−	0.797811i	−0.538375	−	0.842705i	$-0.680962\pi$
$199$	6.49779	−	11.2545i	0.460616	−	0.797811i	0.998992	+	0.0448942i	$0.0142951\pi$
$200$		0			0
$201$	−0.936442	−	0.540655i	−0.0660515	−	0.0381348i
$202$		0			0
$203$	−11.2134			−0.787024
$204$		0			0
$205$	13.4756	−	7.78016i	0.941179	−	0.543390i
$206$		0			0
$207$	−3.95167			−0.274660
$208$		0			0
$209$	0.580493			0.0401535
$210$		0			0
$211$	8.91704	−	5.14826i	0.613875	−	0.354421i	−0.160606	−	0.987019i	$-0.551345\pi$
$211$	8.91704	−	5.14826i	0.613875	−	0.354421i	0.774480	+	0.632598i	$0.218011\pi$
$212$		0			0
$213$	−7.44800			−0.510329
$214$		0			0
$215$	−15.6971	−	9.06271i	−1.07053	−	0.618072i
$216$		0			0
$217$	2.34759	−	4.06615i	0.159365	−	0.276028i
$218$		0			0
$219$	3.07181	+	5.32054i	0.207574	+	0.359529i
$220$		0			0
$221$	−3.58234	+	7.46358i	−0.240974	+	0.502055i
$222$		0			0
$223$	−2.03847	+	1.17691i	−0.136506	+	0.0788117i	−0.566698	−	0.823926i	$-0.691779\pi$
$223$	−2.03847	+	1.17691i	−0.136506	+	0.0788117i	0.430192	+	0.902737i	$0.358446\pi$
$224$		0			0
$225$	−0.721753	+	1.25011i	−0.0481169	+	0.0833409i
$226$		0			0
$227$	13.6449	−	23.6336i	0.905643	−	1.56862i	0.0855919	−	0.996330i	$-0.472722\pi$
$227$	13.6449	−	23.6336i	0.905643	−	1.56862i	0.820051	−	0.572290i	$-0.193945\pi$
$228$		0			0
$229$	14.1611			0.935794			0.467897	−	0.883783i	$-0.345012\pi$
$229$	14.1611			0.935794			0.467897	+	0.883783i	$0.345012\pi$
$230$		0			0
$231$	−0.291545	−	0.504972i	−0.0191823	−	0.0332247i
$232$		0			0
$233$	12.3422			0.808562			0.404281	−	0.914635i	$-0.367522\pi$
$233$	12.3422			0.808562			0.404281	+	0.914635i	$0.367522\pi$
$234$		0			0
$235$			19.0688i			1.24391i
$236$		0			0
$237$	13.7965	−	7.96544i	0.896182	−	0.517411i
$238$		0			0
$239$		−	17.4020i		−	1.12564i	−0.826578	−	0.562822i	$-0.809715\pi$
$239$		−	17.4020i		−	1.12564i	0.826578	−	0.562822i	$-0.190285\pi$
$240$		0			0
$241$	12.5141	+	7.22501i	0.806103	+	0.465404i	0.845601	−	0.533816i	$-0.179242\pi$
$241$	12.5141	+	7.22501i	0.806103	+	0.465404i	−0.0394975	+	0.999220i	$0.512576\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	11.6454	+	20.1704i	0.743996	+	1.28864i
$246$		0			0
$247$	−6.83242	+	14.2349i	−0.434737	+	0.905747i
$248$		0			0
$249$	−0.125113	+	0.0722340i	−0.00792871	+	0.00457765i
$250$		0			0
$251$	26.7083	+	15.4201i	1.68581	+	0.973305i	0.957664	+	0.287887i	$0.0929528\pi$
$251$	26.7083	+	15.4201i	1.68581	+	0.973305i	0.728150	+	0.685418i	$0.240381\pi$
$252$		0			0
$253$	0.261906	−	0.453634i	0.0164659	−	0.0285197i
$254$		0			0
$255$		−	4.33018i		−	0.271166i
$256$		0			0
$257$	9.77864	+	16.9371i	0.609975	+	1.05651i	0.991244	+	0.132044i	$0.0421539\pi$
$257$	9.77864	+	16.9371i	0.609975	+	1.05651i	−0.381269	+	0.924464i	$0.624513\pi$
$258$		0			0
$259$			46.4997i			2.88935i
$260$		0			0
$261$		−	2.54914i		−	0.157788i
$262$		0			0
$263$	15.8081	+	27.3804i	0.974769	+	1.68835i	0.680695	+	0.732567i	$0.261678\pi$
$263$	15.8081	+	27.3804i	0.974769	+	1.68835i	0.294074	+	0.955783i	$0.404989\pi$
$264$		0			0
$265$		−	15.6247i		−	0.959816i
$266$		0			0
$267$	−8.20498	+	14.2114i	−0.502136	+	0.869726i
$268$		0			0
$269$	0.118107	+	0.0681891i	0.00720111	+	0.00415756i	0.503596	−	0.863939i	$-0.332010\pi$
$269$	0.118107	+	0.0681891i	0.00720111	+	0.00415756i	−0.496395	+	0.868097i	$0.665343\pi$
$270$		0			0
$271$	−13.1075	+	7.56763i	−0.796226	+	0.459701i	−0.842150	−	0.539244i	$-0.818710\pi$
$271$	−13.1075	+	7.56763i	−0.796226	+	0.459701i	0.0459241	+	0.998945i	$0.485377\pi$
$272$		0			0
$273$	15.8145	−	1.20579i	0.957137	−	0.0729774i
$274$		0			0
$275$	−0.0956715	−	0.165708i	−0.00576921	−	0.00999256i
$276$		0			0
$277$	−10.7192	−	6.18871i	−0.644051	−	0.371843i	0.142122	−	0.989849i	$-0.454607\pi$
$277$	−10.7192	−	6.18871i	−0.644051	−	0.371843i	−0.786174	+	0.618006i	$0.787941\pi$
$278$		0			0
$279$	0.924359	+	0.533679i	0.0553399	+	0.0319505i
$280$		0			0
$281$			1.09096i			0.0650813i	0.999470	+	0.0325406i	$0.0103598\pi$
$281$			1.09096i			0.0650813i	−0.999470	+	0.0325406i	$0.989640\pi$
$282$		0			0
$283$	4.12015	−	2.37877i	0.244917	−	0.141403i	−0.372517	−	0.928025i	$-0.621505\pi$
$283$	4.12015	−	2.37877i	0.244917	−	0.141403i	0.617435	+	0.786622i	$0.288172\pi$
$284$		0			0
$285$		−	8.25874i		−	0.489205i
$286$		0			0
$287$	−36.2952			−2.14244
$288$		0			0
$289$	5.86392	+	10.1566i	0.344936	+	0.597447i
$290$		0			0
$291$	7.06522			0.414170
$292$		0			0
$293$	−0.923728	+	1.59994i	−0.0539647	+	0.0934697i	−0.891746	−	0.452537i	$-0.850519\pi$
$293$	−0.923728	+	1.59994i	−0.0539647	+	0.0934697i	0.837781	+	0.546006i	$0.183853\pi$
$294$		0			0
$295$	−3.11912	+	5.40247i	−0.181602	+	0.314544i
$296$		0			0
$297$	0.114795	−	0.0662772i	0.00666111	−	0.00384579i
$298$		0			0
$299$	8.04144	+	11.7618i	0.465049	+	0.680202i
$300$		0			0
$301$	21.1393	+	36.6143i	1.21845	+	2.11041i
$302$		0			0
$303$	5.39732	−	9.34844i	0.310068	−	0.537054i
$304$		0			0
$305$	12.0784	+	6.97347i	0.691608	+	0.399300i
$306$		0			0
$307$	14.5220			0.828815			0.414408	−	0.910091i	$-0.363989\pi$
$307$	14.5220			0.828815			0.414408	+	0.910091i	$0.363989\pi$
$308$		0			0
$309$	9.50197	−	5.48597i	0.540548	−	0.312086i
$310$		0			0
$311$	15.6062			0.884944			0.442472	−	0.896782i	$-0.354102\pi$
$311$	15.6062			0.884944			0.442472	+	0.896782i	$0.354102\pi$
$312$		0			0
$313$	−29.5504			−1.67029			−0.835143	−	0.550032i	$-0.814615\pi$
$313$	−29.5504			−1.67029			−0.835143	+	0.550032i	$0.814615\pi$
$314$		0			0
$315$	−7.18429	+	4.14785i	−0.404789	+	0.233705i
$316$		0			0
$317$	−14.3523			−0.806105			−0.403052	−	0.915177i	$-0.632051\pi$
$317$	−14.3523			−0.806105			−0.403052	+	0.915177i	$0.632051\pi$
$318$		0			0
$319$	0.292629	+	0.168950i	0.0163841	+	0.00945936i
$320$		0			0
$321$	−1.93168	+	3.34576i	−0.107816	+	0.186742i
$322$		0			0
$323$	−5.02768	−	8.70819i	−0.279747	−	0.484537i
$324$		0			0
$325$	5.18957	−	0.395682i	0.287866	−	0.0219485i
$326$		0			0
$327$	−0.992001	+	0.572732i	−0.0548578	+	0.0316722i
$328$		0			0
$329$	22.2395	−	38.5200i	1.22610	−	2.12368i
$330$		0			0
$331$	−11.0998	+	19.2255i	−0.610102	+	1.05673i	0.381120	+	0.924525i	$0.375538\pi$
$331$	−11.0998	+	19.2255i	−0.610102	+	1.05673i	−0.991223	+	0.132203i	$0.957795\pi$
$332$		0			0
$333$	−10.5708			−0.579276
$334$		0			0
$335$	−1.01960	−	1.76600i	−0.0557069	−	0.0964871i
$336$		0			0
$337$	16.9924			0.925633			0.462817	−	0.886454i	$-0.346839\pi$
$337$	16.9924			0.925633			0.462817	+	0.886454i	$0.346839\pi$
$338$		0			0
$339$		−	9.77799i		−	0.531068i
$340$		0			0
$341$	−0.122528	+	0.0707415i	−0.00663525	+	0.00383086i
$342$		0			0
$343$		−	23.5348i		−	1.27076i
$344$		0			0
$345$	−6.45391	−	3.72617i	−0.347467	−	0.200610i
$346$		0			0
$347$	10.8759	+	6.27918i	0.583846	+	0.337084i	0.762660	−	0.646799i	$-0.223893\pi$
$347$	10.8759	+	6.27918i	0.583846	+	0.337084i	−0.178814	+	0.983883i	$0.557226\pi$
$348$		0			0
$349$	−14.8271	−	25.6812i	−0.793674	−	1.37468i	−0.923678	−	0.383170i	$-0.874832\pi$
$349$	−14.8271	−	25.6812i	−0.793674	−	1.37468i	0.130004	−	0.991513i	$-0.458501\pi$
$350$		0			0
$351$	0.274112	+	3.59512i	0.0146310	+	0.191893i
$352$		0			0
$353$	−28.0507	+	16.1951i	−1.49299	+	0.861977i	−0.999968	−	0.00804129i	$-0.997440\pi$
$353$	−28.0507	+	16.1951i	−1.49299	+	0.861977i	−0.493020	+	0.870018i	$0.664107\pi$
$354$		0			0
$355$	−12.1641	−	7.02297i	−0.645606	−	0.372741i
$356$		0			0
$357$	−5.05018	+	8.74717i	−0.267284	+	0.462949i
$358$		0			0
$359$		−	2.96930i		−	0.156714i	−0.996925	−	0.0783568i	$-0.975033\pi$
$359$		−	2.96930i		−	0.156714i	0.996925	−	0.0783568i	$-0.0249673\pi$
$360$		0			0
$361$	−0.0890480	−	0.154236i	−0.00468674	−	0.00811767i
$362$		0			0
$363$		−	10.9824i		−	0.576428i
$364$		0			0
$365$			11.5861i			0.606442i
$366$		0			0
$367$	2.58053	+	4.46960i	0.134702	+	0.233311i	0.925484	−	0.378787i	$-0.123659\pi$
$367$	2.58053	+	4.46960i	0.134702	+	0.233311i	−0.790781	+	0.612099i	$0.790326\pi$
$368$		0			0
$369$		−	8.25101i		−	0.429531i
$370$		0			0
$371$	−18.2227	+	31.5626i	−0.946074	+	1.63865i
$372$		0			0
$373$	4.57477	+	2.64124i	0.236873	+	0.136758i	0.613738	−	0.789509i	$-0.289665\pi$
$373$	4.57477	+	2.64124i	0.236873	+	0.136758i	−0.376866	+	0.926268i	$0.622998\pi$
$374$		0			0
$375$	−10.5236	+	6.07580i	−0.543436	+	0.313753i
$376$		0			0
$377$	−7.58727	+	5.18736i	−0.390764	+	0.267163i
$378$		0			0
$379$	−18.1432	−	31.4249i	−0.931951	−	1.61419i	−0.779982	−	0.625802i	$-0.784772\pi$
$379$	−18.1432	−	31.4249i	−0.931951	−	1.61419i	−0.151970	−	0.988385i	$-0.548562\pi$
$380$		0			0
$381$	12.7824	+	7.37989i	0.654860	+	0.378083i
$382$		0			0
$383$	−8.44275	−	4.87443i	−0.431405	−	0.249072i	0.268540	−	0.963268i	$-0.413459\pi$
$383$	−8.44275	−	4.87443i	−0.431405	−	0.249072i	−0.699945	+	0.714197i	$0.746792\pi$
$384$		0			0
$385$		−	1.09963i		−	0.0560424i
$386$		0			0
$387$	−8.32354	+	4.80560i	−0.423109	+	0.244282i
$388$		0			0
$389$		−	14.8911i		−	0.755010i	−0.926008	−	0.377505i	$-0.876782\pi$
$389$		−	14.8911i		−	0.755010i	0.926008	−	0.377505i	$-0.123218\pi$
$390$		0			0
$391$	−9.07352			−0.458868
$392$		0			0
$393$	−0.615904	−	1.06678i	−0.0310683	−	0.0538118i
$394$		0			0
$395$	30.0435			1.51165
$396$		0			0
$397$	10.5034	−	18.1925i	0.527152	−	0.913055i	−0.472347	−	0.881413i	$-0.656593\pi$
$397$	10.5034	−	18.1925i	0.527152	−	0.913055i	0.999499	−	0.0316419i	$-0.0100736\pi$
$398$		0			0
$399$	−9.63197	+	16.6831i	−0.482202	+	0.835198i
$400$		0			0
$401$	13.7620	−	7.94551i	0.687243	−	0.396780i	−0.115335	−	0.993327i	$-0.536794\pi$
$401$	13.7620	−	7.94551i	0.687243	−	0.396780i	0.802578	+	0.596547i	$0.203461\pi$
$402$		0			0
$403$	−0.292575	−	3.83728i	−0.0145742	−	0.191148i
$404$		0			0
$405$	−0.942933	−	1.63321i	−0.0468547	−	0.0811548i
$406$		0			0
$407$	0.700602	−	1.21348i	0.0347276	−	0.0601499i
$408$		0			0
$409$	13.7176	+	7.91987i	0.678292	+	0.391612i	0.799211	−	0.601050i	$-0.205251\pi$
$409$	13.7176	+	7.91987i	0.678292	+	0.391612i	−0.120919	+	0.992662i	$0.538584\pi$
$410$		0			0
$411$	−18.1857			−0.897036
$412$		0			0
$413$	12.6016	−	7.27551i	0.620082	−	0.358004i
$414$		0			0
$415$	−0.272448			−0.0133739
$416$		0			0
$417$	−4.77068			−0.233621
$418$		0			0
$419$	19.4162	−	11.2100i	0.948544	−	0.547642i	0.0559155	−	0.998436i	$-0.482192\pi$
$419$	19.4162	−	11.2100i	0.948544	−	0.547642i	0.892628	+	0.450793i	$0.148859\pi$
$420$		0			0
$421$	−1.50715			−0.0734541			−0.0367270	−	0.999325i	$-0.511693\pi$
$421$	−1.50715			−0.0734541			−0.0367270	+	0.999325i	$0.511693\pi$
$422$		0			0
$423$	8.75677	+	5.05572i	0.425768	+	0.245818i
$424$		0			0
$425$	−1.65723	+	2.87041i	−0.0803876	+	0.139235i
$426$		0			0
$427$	−16.2660	−	28.1735i	−0.787166	−	1.36341i
$428$		0			0
$429$	−0.430870	−	0.206807i	−0.0208026	−	0.00998475i
$430$		0			0
$431$	−20.0881	+	11.5979i	−0.967609	+	0.558649i	−0.898507	−	0.438960i	$-0.855347\pi$
$431$	−20.0881	+	11.5979i	−0.967609	+	0.558649i	−0.0691026	+	0.997610i	$0.522014\pi$
$432$		0			0
$433$	−7.02656	+	12.1704i	−0.337675	+	0.584870i	−0.983995	−	0.178197i	$-0.942974\pi$
$433$	−7.02656	+	12.1704i	−0.337675	+	0.584870i	0.646320	+	0.763066i	$0.276307\pi$
$434$		0			0
$435$	2.40367	−	4.16327i	0.115247	−	0.199614i
$436$		0			0
$437$	−17.3055			−0.827834
$438$		0			0
$439$	−6.40295	−	11.0902i	−0.305596	−	0.529308i	0.671798	−	0.740735i	$-0.265522\pi$
$439$	−6.40295	−	11.0902i	−0.305596	−	0.529308i	−0.977394	+	0.211426i	$0.932189\pi$
$440$		0			0
$441$	12.3502			0.588103
$442$		0			0
$443$		−	6.06204i		−	0.288016i	−0.989577	−	0.144008i	$-0.954001\pi$
$443$		−	6.06204i		−	0.288016i	0.989577	−	0.144008i	$-0.0459992\pi$
$444$		0			0
$445$	−26.8009	+	15.4735i	−1.27048	+	0.733514i
$446$		0			0
$447$		−	7.95062i		−	0.376051i
$448$		0			0
$449$	−6.72376	−	3.88197i	−0.317314	−	0.183201i	0.332881	−	0.942969i	$-0.391979\pi$
$449$	−6.72376	−	3.88197i	−0.317314	−	0.183201i	−0.650195	+	0.759768i	$0.725313\pi$
$450$		0			0
$451$	0.947179	+	0.546854i	0.0446009	+	0.0257503i
$452$		0			0
$453$	6.77761	+	11.7392i	0.318440	+	0.551554i
$454$		0			0
$455$	26.9653	+	12.9427i	1.26415	+	0.606764i
$456$		0			0
$457$	−11.5888	+	6.69082i	−0.542103	+	0.312983i	−0.745931	−	0.666023i	$-0.767995\pi$
$457$	−11.5888	+	6.69082i	−0.542103	+	0.312983i	0.203828	+	0.979007i	$0.434662\pi$
$458$		0			0
$459$	−1.98850	−	1.14806i	−0.0928152	−	0.0535869i
$460$		0			0
$461$	−17.4992	+	30.3095i	−0.815019	+	1.41165i	0.0942954	+	0.995544i	$0.469940\pi$
$461$	−17.4992	+	30.3095i	−0.815019	+	1.41165i	−0.909314	+	0.416110i	$0.863393\pi$
$462$		0			0
$463$		−	18.2272i		−	0.847092i	−0.905875	−	0.423546i	$-0.860785\pi$
$463$		−	18.2272i		−	0.847092i	0.905875	−	0.423546i	$-0.139215\pi$
$464$		0			0
$465$	1.00645	+	1.74322i	0.0466729	+	0.0808398i
$466$		0			0
$467$		−	11.4947i		−	0.531910i	−0.963985	−	0.265955i	$-0.914313\pi$
$467$		−	11.4947i		−	0.531910i	0.963985	−	0.265955i	$-0.0856873\pi$
$468$		0			0
$469$			4.75655i			0.219637i
$470$		0			0
$471$	0.0324021	+	0.0561220i	0.00149301	+	0.00258597i
$472$		0			0
$473$		−	1.27401i		−	0.0585788i
$474$		0			0
$475$	−3.16076	+	5.47460i	−0.145026	+	0.251192i
$476$		0			0
$477$	−7.17514	−	4.14257i	−0.328527	−	0.189675i
$478$		0			0
$479$	−3.75092	+	2.16560i	−0.171384	+	0.0989487i	−0.583238	−	0.812301i	$-0.698215\pi$
$479$	−3.75092	+	2.16560i	−0.171384	+	0.0989487i	0.411854	+	0.911250i	$0.364881\pi$
$480$		0			0
$481$	21.5110	+	31.4630i	0.980817	+	1.43459i
$482$		0			0
$483$	8.69148	+	15.0541i	0.395476	+	0.684984i
$484$		0			0
$485$	11.5390	+	6.66203i	0.523958	+	0.302507i
$486$		0			0
$487$	25.1811	+	14.5383i	1.14107	+	0.658795i	0.946694	−	0.322133i	$-0.104400\pi$
$487$	25.1811	+	14.5383i	1.14107	+	0.658795i	0.194372	+	0.980928i	$0.437733\pi$
$488$		0			0
$489$		−	10.5258i		−	0.475995i
$490$		0			0
$491$	15.9306	−	9.19753i	0.718938	−	0.415079i	−0.0954238	−	0.995437i	$-0.530421\pi$
$491$	15.9306	−	9.19753i	0.718938	−	0.415079i	0.814362	+	0.580358i	$0.197087\pi$
$492$		0			0
$493$		−	5.85313i		−	0.263612i
$494$		0			0
$495$	0.249980			0.0112358
$496$		0			0
$497$	16.3814	+	28.3735i	0.734808	+	1.27273i
$498$		0			0
$499$	−3.03922			−0.136054			−0.0680270	−	0.997683i	$-0.521670\pi$
$499$	−3.03922			−0.136054			−0.0680270	+	0.997683i	$0.521670\pi$
$500$		0			0
$501$	7.20556	−	12.4804i	0.321921	−	0.557583i
$502$		0			0
$503$	0.148336	−	0.256925i	0.00661396	−	0.0114557i	−0.862699	−	0.505717i	$-0.831228\pi$
$503$	0.148336	−	0.256925i	0.00661396	−	0.0114557i	0.869313	+	0.494261i	$0.164561\pi$
$504$		0			0
$505$	17.6299	−	10.1786i	0.784520	−	0.452943i
$506$		0			0
$507$	10.1427	−	8.13174i	0.450454	−	0.361143i
$508$		0			0
$509$	−12.2950	−	21.2955i	−0.544965	−	0.943906i	−0.998609	−	0.0527236i	$-0.983210\pi$
$509$	−12.2950	−	21.2955i	−0.544965	−	0.943906i	0.453645	−	0.891183i	$-0.350124\pi$
$510$		0			0
$511$	13.5125	−	23.4044i	0.597760	−	1.03535i
$512$		0			0
$513$	−3.79257	−	2.18964i	−0.167446	−	0.0966750i
$514$		0			0
$515$	20.6916			0.911781
$516$		0			0
$517$	−1.16075	+	0.670158i	−0.0510496	+	0.0294735i
$518$		0			0
$519$	−8.55924			−0.375709
$520$		0			0
$521$	−27.3639			−1.19883			−0.599417	−	0.800437i	$-0.704601\pi$
$521$	−27.3639			−1.19883			−0.599417	+	0.800437i	$0.704601\pi$
$522$		0			0
$523$	18.8023	−	10.8555i	0.822167	−	0.474678i	−0.0289964	−	0.999580i	$-0.509231\pi$
$523$	18.8023	−	10.8555i	0.822167	−	0.474678i	0.851163	+	0.524901i	$0.175898\pi$
$524$		0			0
$525$	6.34982			0.277129
$526$		0			0
$527$	2.12244	+	1.22539i	0.0924549	+	0.0533789i
$528$		0			0
$529$	3.69213	−	6.39496i	0.160527	−	0.278042i
$530$		0			0
$531$	1.65394	+	2.86472i	0.0717751	+	0.124318i
$532$		0			0
$533$	−24.5584	+	16.7904i	−1.06374	+	0.727272i
$534$		0			0
$535$	−6.30966	+	3.64288i	−0.272790	+	0.157496i
$536$		0			0
$537$	−8.55453	+	14.8169i	−0.369155	+	0.639396i
$538$		0			0
$539$	−0.818534	+	1.41774i	−0.0352568	+	0.0610665i
$540$		0			0
$541$	33.0198			1.41963			0.709816	−	0.704387i	$-0.248778\pi$
$541$	33.0198			1.41963			0.709816	+	0.704387i	$0.248778\pi$
$542$		0			0
$543$	5.91954	+	10.2529i	0.254032	+	0.439996i
$544$		0			0
$545$	−2.16019			−0.0925325
$546$		0			0
$547$			29.1932i			1.24821i	0.781340	+	0.624105i	$0.214536\pi$
$547$			29.1932i			1.24821i	−0.781340	+	0.624105i	$0.785464\pi$
$548$		0			0
$549$	6.40470	−	3.69775i	0.273346	−	0.157816i
$550$		0			0
$551$		−	11.1634i		−	0.475576i
$552$		0			0
$553$	−60.6894	−	35.0390i	−2.58077	−	1.49001i
$554$		0			0
$555$	−17.2643	−	9.96755i	−0.732829	−	0.423099i
$556$		0			0
$557$	−5.03804	−	8.72614i	−0.213469	−	0.369739i	0.739329	−	0.673344i	$-0.235143\pi$
$557$	−5.03804	−	8.72614i	−0.213469	−	0.369739i	−0.952798	+	0.303606i	$0.901809\pi$
$558$		0			0
$559$	31.2414	+	14.9951i	1.32137	+	0.634225i
$560$		0			0
$561$	0.263584	−	0.152180i	0.0111285	−	0.00642506i
$562$		0			0
$563$	−20.2190	−	11.6734i	−0.852128	−	0.491977i	0.00923997	−	0.999957i	$-0.497059\pi$
$563$	−20.2190	−	11.6734i	−0.852128	−	0.491977i	−0.861368	+	0.507981i	$0.830392\pi$
$564$		0			0
$565$	9.22000	−	15.9695i	0.387888	−	0.671842i
$566$		0			0
$567$			4.39888i			0.184736i
$568$		0			0
$569$	−21.2506	−	36.8071i	−0.890870	−	1.54303i	−0.838834	−	0.544388i	$-0.816762\pi$
$569$	−21.2506	−	36.8071i	−0.890870	−	1.54303i	−0.0520365	−	0.998645i	$-0.516571\pi$
$570$		0			0
$571$		−	5.43630i		−	0.227502i	−0.993509	−	0.113751i	$-0.963713\pi$
$571$		−	5.43630i		−	0.227502i	0.993509	−	0.113751i	$-0.0362866\pi$
$572$		0			0
$573$		−	7.11389i		−	0.297187i
$574$		0			0
$575$	2.85213	+	4.94004i	0.118942	+	0.206014i
$576$		0			0
$577$		−	4.39252i		−	0.182863i	−0.995811	−	0.0914316i	$-0.970856\pi$
$577$		−	4.39252i		−	0.182863i	0.995811	−	0.0914316i	$-0.0291443\pi$
$578$		0			0
$579$	−7.02758	+	12.1721i	−0.292056	+	0.505857i
$580$		0			0
$581$	0.550357	+	0.317749i	0.0228327	+	0.0131825i
$582$		0			0
$583$	0.951096	−	0.549116i	0.0393904	−	0.0227420i
$584$		0			0
$585$	−2.94227	+	6.13004i	−0.121648	+	0.253446i
$586$		0			0
$587$	−15.7922	−	27.3529i	−0.651813	−	1.12897i	−0.982683	−	0.185297i	$-0.940675\pi$
$587$	−15.7922	−	27.3529i	−0.651813	−	1.12897i	0.330869	−	0.943677i	$-0.392658\pi$
$588$		0			0
$589$	4.04803	+	2.33713i	0.166796	+	0.0962998i
$590$		0			0
$591$	19.5256	+	11.2731i	0.803178	+	0.463715i
$592$		0			0
$593$			8.50710i			0.349345i	0.984627	+	0.174672i	$0.0558866\pi$
$593$			8.50710i			0.349345i	−0.984627	+	0.174672i	$0.944113\pi$
$594$		0			0
$595$	−16.4960	+	9.52397i	−0.676270	+	0.390445i
$596$		0			0
$597$		−	12.9956i		−	0.531874i
$598$		0			0
$599$	−26.3372			−1.07611			−0.538055	−	0.842910i	$-0.680841\pi$
$599$	−26.3372			−1.07611			−0.538055	+	0.842910i	$0.680841\pi$
$600$		0			0
$601$	3.29321	+	5.70401i	0.134333	+	0.232672i	0.925342	−	0.379132i	$-0.123777\pi$
$601$	3.29321	+	5.70401i	0.134333	+	0.232672i	−0.791009	+	0.611804i	$0.790444\pi$
$602$		0			0
$603$	−1.08131			−0.0440343
$604$		0			0
$605$	10.3557	−	17.9366i	0.421019	−	0.729226i
$606$		0			0
$607$	2.47666	−	4.28970i	0.100524	−	0.174113i	−0.811376	−	0.584524i	$-0.801281\pi$
$607$	2.47666	−	4.28970i	0.100524	−	0.174113i	0.911901	+	0.410411i	$0.134615\pi$
$608$		0			0
$609$	−9.71106	+	5.60668i	−0.393512	+	0.227194i
$610$		0			0
$611$	−2.77166	−	36.3518i	−0.112130	−	1.47064i
$612$		0			0
$613$	6.25855	+	10.8401i	0.252780	+	0.437828i	0.964290	−	0.264848i	$-0.0853217\pi$
$613$	6.25855	+	10.8401i	0.252780	+	0.437828i	−0.711510	+	0.702676i	$0.751988\pi$
$614$		0			0
$615$	7.78016	−	13.4756i	0.313726	−	0.543390i
$616$		0			0
$617$	22.7830	+	13.1538i	0.917210	+	0.529551i	0.882744	−	0.469855i	$-0.155694\pi$
$617$	22.7830	+	13.1538i	0.917210	+	0.529551i	0.0344658	+	0.999406i	$0.489027\pi$
$618$		0			0
$619$	−2.56782			−0.103209			−0.0516047	−	0.998668i	$-0.516434\pi$
$619$	−2.56782			−0.103209			−0.0516047	+	0.998668i	$0.516434\pi$
$620$		0			0
$621$	−3.42225	+	1.97584i	−0.137330	+	0.0792876i
$622$		0			0
$623$	72.1855			2.89205
$624$		0			0
$625$	−15.6988			−0.627950
$626$		0			0
$627$	0.502721	−	0.290246i	0.0200768	−	0.0115913i
$628$		0			0
$629$	−24.2718			−0.967781
$630$		0			0
$631$	−32.2263	−	18.6058i	−1.28291	−	0.740687i	−0.305528	−	0.952183i	$-0.598833\pi$
$631$	−32.2263	−	18.6058i	−1.28291	−	0.740687i	−0.977379	+	0.211496i	$0.932166\pi$
$632$		0			0
$633$	5.14826	−	8.91704i	0.204625	−	0.354421i
$634$		0			0
$635$	13.9175	+	24.1058i	0.552299	+	0.956610i
$636$		0			0
$637$	−25.1319	−	36.7591i	−0.995763	−	1.45645i
$638$		0			0
$639$	−6.45016	+	3.72400i	−0.255164	+	0.147319i
$640$		0			0
$641$	23.2163	−	40.2117i	0.916987	−	1.58827i	0.113021	−	0.993593i	$-0.463947\pi$
$641$	23.2163	−	40.2117i	0.916987	−	1.58827i	0.803966	−	0.594675i	$-0.202719\pi$
$642$		0			0
$643$	8.31198	−	14.3968i	0.327792	−	0.567753i	−0.654281	−	0.756251i	$-0.727029\pi$
$643$	8.31198	−	14.3968i	0.327792	−	0.567753i	0.982073	+	0.188498i	$0.0603620\pi$
$644$		0			0
$645$	−18.1254			−0.713688
$646$		0			0
$647$	14.5656	+	25.2283i	0.572632	+	0.991828i	0.996294	+	0.0860076i	$0.0274109\pi$
$647$	14.5656	+	25.2283i	0.572632	+	0.991828i	−0.423662	+	0.905820i	$0.639256\pi$
$648$		0			0
$649$	−0.438475			−0.0172117
$650$		0			0
$651$		−	4.69518i		−	0.184019i
$652$		0			0
$653$	13.0481	−	7.53330i	0.510610	−	0.294801i	−0.222475	−	0.974938i	$-0.571413\pi$
$653$	13.0481	−	7.53330i	0.510610	−	0.294801i	0.733084	+	0.680138i	$0.238080\pi$
$654$		0			0
$655$		−	2.32303i		−	0.0907682i
$656$		0			0
$657$	5.32054	+	3.07181i	0.207574	+	0.119843i
$658$		0			0
$659$	−42.5147	−	24.5459i	−1.65614	−	0.956171i	−0.974473	−	0.224506i	$-0.927923\pi$
$659$	−42.5147	−	24.5459i	−1.65614	−	0.956171i	−0.681664	−	0.731665i	$-0.738744\pi$
$660$		0			0
$661$	−3.87600	−	6.71343i	−0.150759	−	0.261122i	0.780748	−	0.624846i	$-0.214838\pi$
$661$	−3.87600	−	6.71343i	−0.150759	−	0.261122i	−0.931507	+	0.363724i	$0.881505\pi$
$662$		0			0
$663$	0.629393	+	8.25482i	0.0244436	+	0.320591i
$664$		0			0
$665$	−31.4620	+	18.1646i	−1.22005	+	0.704393i
$666$		0			0
$667$	−8.72379	−	5.03668i	−0.337787	−	0.195021i
$668$		0			0
$669$	−1.17691	+	2.03847i	−0.0455019	+	0.0788117i
$670$		0			0
$671$			0.980307i			0.0378443i
$672$		0			0
$673$	−4.40466	−	7.62909i	−0.169787	−	0.294080i	0.768558	−	0.639780i	$-0.220975\pi$
$673$	−4.40466	−	7.62909i	−0.169787	−	0.294080i	−0.938345	+	0.345700i	$0.887641\pi$
$674$		0			0
$675$			1.44351i			0.0555606i
$676$		0			0
$677$		−	33.6470i		−	1.29316i	−0.762846	−	0.646580i	$-0.776198\pi$
$677$		−	33.6470i		−	1.29316i	0.762846	−	0.646580i	$-0.223802\pi$
$678$		0			0
$679$	−15.5395	−	26.9153i	−0.596353	−	1.03291i
$680$		0			0
$681$		−	27.2898i		−	1.04575i
$682$		0			0
$683$	−1.34924	+	2.33695i	−0.0516273	+	0.0894211i	−0.890684	−	0.454623i	$-0.849774\pi$
$683$	−1.34924	+	2.33695i	−0.0516273	+	0.0894211i	0.839057	+	0.544044i	$0.183107\pi$
$684$		0			0
$685$	−29.7011	−	17.1479i	−1.13482	−	0.655189i
$686$		0			0
$687$	12.2639	−	7.08056i	0.467897	−	0.270140i
$688$		0			0
$689$	2.27105	+	29.7860i	0.0865202	+	1.13476i
$690$		0			0
$691$	2.01331	+	3.48715i	0.0765898	+	0.132657i	0.901777	−	0.432203i	$-0.142263\pi$
$691$	2.01331	+	3.48715i	0.0765898	+	0.132657i	−0.825187	+	0.564860i	$0.808930\pi$
$692$		0			0
$693$	−0.504972	−	0.291545i	−0.0191823	−	0.0110749i
$694$		0			0
$695$	−7.79151	−	4.49843i	−0.295549	−	0.170635i
$696$		0			0
$697$		−	18.9453i		−	0.717605i
$698$		0			0
$699$	10.6886	−	6.17108i	0.404281	−	0.233412i
$700$		0			0
$701$		−	26.9620i		−	1.01834i	−0.860666	−	0.509171i	$-0.829952\pi$
$701$		−	26.9620i		−	1.01834i	0.860666	−	0.509171i	$-0.170048\pi$
$702$		0			0
$703$	−46.2925			−1.74595
$704$		0			0
$705$	9.53442	+	16.5141i	0.359087	+	0.621957i
$706$		0			0
$707$	−47.4844			−1.78583
$708$		0			0
$709$	1.66790	−	2.88889i	0.0626393	−	0.108494i	−0.833005	−	0.553265i	$-0.813382\pi$
$709$	1.66790	−	2.88889i	0.0626393	−	0.108494i	0.895644	+	0.444771i	$0.146715\pi$
$710$		0			0
$711$	7.96544	−	13.7965i	0.298727	−	0.517411i
$712$		0			0
$713$	3.65277	−	2.10893i	0.136797	−	0.0789799i
$714$		0			0
$715$	−0.508695	−	0.744041i	−0.0190241	−	0.0278256i
$716$		0			0
$717$	−8.70102	−	15.0706i	−0.324946	−	0.562822i
$718$		0			0
$719$	−3.27398	+	5.67070i	−0.122099	+	0.211481i	−0.920595	−	0.390518i	$-0.872296\pi$
$719$	−3.27398	+	5.67070i	−0.122099	+	0.211481i	0.798496	+	0.602000i	$0.205629\pi$
$720$		0			0
$721$	−41.7981	−	24.1321i	−1.55664	−	0.898727i
$722$		0			0
$723$	14.4500			0.537402
$724$		0			0
$725$	−3.18671	+	1.83985i	−0.118351	+	0.0683303i
$726$		0			0
$727$	−39.4666			−1.46374			−0.731868	−	0.681447i	$-0.761351\pi$
$727$	−39.4666			−1.46374			−0.731868	+	0.681447i	$0.761351\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−19.1118	+	11.0342i	−0.706877	+	0.408116i
$732$		0			0
$733$	−23.7942			−0.878860			−0.439430	−	0.898277i	$-0.644820\pi$
$733$	−23.7942			−0.878860			−0.439430	+	0.898277i	$0.644820\pi$
$734$		0			0
$735$	20.1704	+	11.6454i	0.743996	+	0.429547i
$736$		0			0
$737$	0.0716661	−	0.124129i	0.00263986	−	0.00457236i
$738$		0			0
$739$	1.53475	+	2.65827i	0.0564568	+	0.0977861i	0.892873	−	0.450309i	$-0.148686\pi$
$739$	1.53475	+	2.65827i	0.0564568	+	0.0977861i	−0.836416	+	0.548096i	$0.815353\pi$
$740$		0			0
$741$	1.20041	+	15.7440i	0.0440982	+	0.578371i
$742$		0			0
$743$	32.7810	−	18.9261i	1.20262	−	0.694332i	0.241482	−	0.970405i	$-0.422366\pi$
$743$	32.7810	−	18.9261i	1.20262	−	0.694332i	0.961137	+	0.276073i	$0.0890331\pi$
$744$		0			0
$745$	7.49691	−	12.9850i	0.274665	−	0.475734i
$746$		0			0
$747$	−0.0722340	+	0.125113i	−0.00264290	+	0.00457765i
$748$		0			0
$749$	16.9944			0.620963
$750$		0			0
$751$	−2.75896	−	4.77866i	−0.100676	−	0.174376i	0.811287	−	0.584647i	$-0.198767\pi$
$751$	−2.75896	−	4.77866i	−0.100676	−	0.174376i	−0.911963	+	0.410272i	$0.865434\pi$
$752$		0			0
$753$	30.8401			1.12388
$754$		0			0
$755$			25.5633i			0.930345i
$756$		0			0
$757$	18.7724	−	10.8383i	0.682296	−	0.393924i	−0.118424	−	0.992963i	$-0.537784\pi$
$757$	18.7724	−	10.8383i	0.682296	−	0.393924i	0.800720	+	0.599039i	$0.204451\pi$
$758$		0			0
$759$		−	0.523812i		−	0.0190132i
$760$		0			0
$761$	16.0378	+	9.25942i	0.581369	+	0.335654i	0.761677	−	0.647957i	$-0.224376\pi$
$761$	16.0378	+	9.25942i	0.581369	+	0.335654i	−0.180308	+	0.983610i	$0.557709\pi$
$762$		0			0
$763$	4.36370	+	2.51938i	0.157976	+	0.0912078i
$764$		0			0
$765$	−2.16509	−	3.75004i	−0.0782789	−	0.135583i
$766$		0			0
$767$	5.16087	−	10.7524i	0.186348	−	0.388245i
$768$		0			0
$769$	1.51439	−	0.874333i	0.0546103	−	0.0315293i	−0.472446	−	0.881359i	$-0.656629\pi$
$769$	1.51439	−	0.874333i	0.0546103	−	0.0315293i	0.527057	+	0.849830i	$0.323296\pi$
$770$		0			0
$771$	16.9371	+	9.77864i	0.609975	+	0.352169i
$772$		0			0
$773$	3.35588	−	5.81256i	0.120703	−	0.209063i	−0.799342	−	0.600876i	$-0.794819\pi$
$773$	3.35588	−	5.81256i	0.120703	−	0.209063i	0.920045	+	0.391813i	$0.128152\pi$
$774$		0			0
$775$		−	1.54074i		−	0.0553449i
$776$		0			0
$777$	23.2498	+	40.2699i	0.834083	+	1.44467i
$778$		0			0
$779$		−	36.1335i		−	1.29462i
$780$		0			0
$781$		−	0.987265i		−	0.0353271i
$782$		0			0
$783$	−1.27457	−	2.20762i	−0.0455494	−	0.0788939i
$784$		0			0
$785$			0.122212i			0.00436193i
$786$		0			0
$787$	25.3707	−	43.9434i	0.904369	−	1.56641i	0.0826068	−	0.996582i	$-0.473675\pi$
$787$	25.3707	−	43.9434i	0.904369	−	1.56641i	0.821762	−	0.569831i	$-0.192991\pi$
$788$		0			0
$789$	27.3804	+	15.8081i	0.974769	+	0.562783i
$790$		0			0
$791$	−37.2497	+	21.5061i	−1.32445	+	0.764670i
$792$		0			0
$793$	−24.0392	−	11.5383i	−0.853658	−	0.409735i
$794$		0			0
$795$	−7.81234	−	13.5314i	−0.277075	−	0.479908i
$796$		0			0
$797$	8.65924	+	4.99942i	0.306726	+	0.177088i	0.645461	−	0.763794i	$-0.276665\pi$
$797$	8.65924	+	4.99942i	0.306726	+	0.177088i	−0.338734	+	0.940882i	$0.609999\pi$
$798$		0			0
$799$	20.1066	+	11.6085i	0.711320	+	0.410681i
$800$		0			0
$801$			16.4100i			0.579817i
$802$		0			0
$803$	−0.705260	+	0.407182i	−0.0248881	+	0.0143691i
$804$		0			0
$805$			32.7819i			1.15541i
$806$		0			0
$807$	0.136378			0.00480074
$808$		0			0
$809$	1.54330	+	2.67308i	0.0542596	+	0.0939804i	0.891879	−	0.452273i	$-0.149387\pi$
$809$	1.54330	+	2.67308i	0.0542596	+	0.0939804i	−0.837620	+	0.546254i	$0.816053\pi$
$810$		0			0
$811$	−28.0084			−0.983508			−0.491754	−	0.870734i	$-0.663644\pi$
$811$	−28.0084			−0.983508			−0.491754	+	0.870734i	$0.663644\pi$
$812$		0			0
$813$	−7.56763	+	13.1075i	−0.265409	+	0.459701i
$814$		0			0
$815$	9.92517	−	17.1909i	0.347664	−	0.602171i
$816$		0			0
$817$	−36.4511	+	21.0451i	−1.27526	+	0.736273i
$818$		0			0
$819$	13.0929	−	8.95149i	0.457502	−	0.312790i
$820$		0			0
$821$	−11.8321	−	20.4937i	−0.412942	−	0.715236i	0.582268	−	0.812997i	$-0.302165\pi$
$821$	−11.8321	−	20.4937i	−0.412942	−	0.715236i	−0.995210	+	0.0977607i	$0.968832\pi$
$822$		0			0
$823$	7.69409	−	13.3266i	0.268199	−	0.464535i	−0.700198	−	0.713949i	$-0.746905\pi$
$823$	7.69409	−	13.3266i	0.268199	−	0.464535i	0.968397	+	0.249414i	$0.0802381\pi$
$824$		0			0
$825$	−0.165708	−	0.0956715i	−0.00576921	−	0.00333085i
$826$		0			0
$827$	−32.9357			−1.14529			−0.572643	−	0.819805i	$-0.694082\pi$
$827$	−32.9357			−1.14529			−0.572643	+	0.819805i	$0.694082\pi$
$828$		0			0
$829$	−7.25966	+	4.19137i	−0.252138	+	0.145572i	−0.620743	−	0.784014i	$-0.713169\pi$
$829$	−7.25966	+	4.19137i	−0.252138	+	0.145572i	0.368605	+	0.929586i	$0.379836\pi$
$830$		0			0
$831$	−12.3774			−0.429368
$832$		0			0
$833$	28.3575			0.982528
$834$		0			0
$835$	23.5364	−	13.5887i	0.814509	−	0.470257i
$836$		0			0
$837$	1.06736			0.0368933
$838$		0			0
$839$	−24.9098	−	14.3817i	−0.859983	−	0.496512i	0.00402335	−	0.999992i	$-0.498719\pi$
$839$	−24.9098	−	14.3817i	−0.859983	−	0.496512i	−0.864007	+	0.503480i	$0.832053\pi$
$840$		0			0
$841$	−11.2509	+	19.4872i	−0.387964	+	0.671973i
$842$		0			0
$843$	0.545480	+	0.944800i	0.0187873	+	0.0325406i
$844$		0			0
$845$	24.2329	−	3.71691i	0.833636	−	0.127865i
$846$		0			0
$847$	−41.8381	+	24.1552i	−1.43757	+	0.829983i
$848$		0			0
$849$	2.37877	−	4.12015i	0.0816391	−	0.141403i
$850$		0			0
$851$	−20.8862	+	36.1759i	−0.715969	+	1.24009i
$852$		0			0
$853$	23.9537			0.820160			0.410080	−	0.912049i	$-0.365501\pi$
$853$	23.9537			0.820160			0.410080	+	0.912049i	$0.365501\pi$
$854$		0			0
$855$	−4.12937	−	7.15228i	−0.141221	−	0.244603i
$856$		0			0
$857$	35.6876			1.21907			0.609533	−	0.792761i	$-0.291357\pi$
$857$	35.6876			1.21907			0.609533	+	0.792761i	$0.291357\pi$
$858$		0			0
$859$		−	34.6818i		−	1.18333i	−0.806185	−	0.591664i	$-0.798471\pi$
$859$		−	34.6818i		−	1.18333i	0.806185	−	0.591664i	$-0.201529\pi$
$860$		0			0
$861$	−31.4326	+	18.1476i	−1.07122	+	0.618469i
$862$		0			0
$863$			23.4077i			0.796807i	0.917210	+	0.398404i	$0.130436\pi$
$863$			23.4077i			0.796807i	−0.917210	+	0.398404i	$0.869564\pi$
$864$		0			0
$865$	−13.9790	−	8.07080i	−0.475301	−	0.274415i
$866$		0			0
$867$	10.1566	+	5.86392i	0.344936	+	0.199149i
$868$		0			0
$869$	1.05585	+	1.82879i	0.0358174	+	0.0620375i
$870$		0			0
$871$	2.20041	+	3.21842i	0.0745579	+	0.109052i
$872$		0			0
$873$	6.11866	−	3.53261i	0.207085	−	0.119561i
$874$		0			0
$875$	46.2920	+	26.7267i	1.56496	+	0.903528i
$876$		0			0
$877$	−22.9591	+	39.7663i	−0.775274	+	1.34281i	0.159367	+	0.987219i	$0.449055\pi$
$877$	−22.9591	+	39.7663i	−0.775274	+	1.34281i	−0.934641	+	0.355594i	$0.884279\pi$
$878$		0			0
$879$			1.84746i			0.0623131i
$880$		0			0
$881$	3.74833	+	6.49229i	0.126284	+	0.218731i	0.922234	−	0.386632i	$-0.126362\pi$
$881$	3.74833	+	6.49229i	0.126284	+	0.218731i	−0.795950	+	0.605362i	$0.793028\pi$
$882$		0			0
$883$			50.0570i			1.68455i	0.539046	+	0.842276i	$0.318785\pi$
$883$			50.0570i			1.68455i	−0.539046	+	0.842276i	$0.681215\pi$
$884$		0			0
$885$			6.23824i			0.209696i
$886$		0			0
$887$	−11.5973	−	20.0872i	−0.389400	−	0.674461i	0.602969	−	0.797765i	$-0.293984\pi$
$887$	−11.5973	−	20.0872i	−0.389400	−	0.674461i	−0.992369	+	0.123304i	$0.960651\pi$
$888$		0			0
$889$		−	64.9266i		−	2.17757i
$890$		0			0
$891$	0.0662772	−	0.114795i	0.00222037	−	0.00384579i
$892$		0			0
$893$	38.3483	+	22.1404i	1.28328	+	0.740901i
$894$		0			0
$895$	−27.9427	+	16.1327i	−0.934021	+	0.539257i
$896$		0			0
$897$	12.8450	+	6.16529i	0.428882	+	0.205853i
$898$		0			0
$899$	1.36042	+	2.35632i	0.0453726	+	0.0785877i
$900$		0			0
$901$	−16.4750	−	9.51184i	−0.548861	−	0.316885i
$902$		0			0
$903$	36.6143	+	21.1393i	1.21845	+	0.703470i
$904$		0			0
$905$			22.3269i			0.742172i
$906$		0			0
$907$	−19.4736	+	11.2431i	−0.646610	+	0.373321i	−0.787156	−	0.616754i	$-0.788447\pi$
$907$	−19.4736	+	11.2431i	−0.646610	+	0.373321i	0.140546	+	0.990074i	$0.455114\pi$
$908$		0			0
$909$		−	10.7946i		−	0.358036i
$910$		0			0
$911$	3.74738			0.124156			0.0620781	−	0.998071i	$-0.480227\pi$
$911$	3.74738			0.124156			0.0620781	+	0.998071i	$0.480227\pi$
$912$		0			0
$913$	−0.00957493	−	0.0165843i	−0.000316884	−	0.000548859i
$914$		0			0
$915$	13.9469			0.461072
$916$		0			0
$917$	−2.70929	+	4.69263i	−0.0894687	+	0.154964i
$918$		0			0
$919$	6.20682	−	10.7505i	0.204744	−	0.354627i	−0.745307	−	0.666721i	$-0.767697\pi$
$919$	6.20682	−	10.7505i	0.204744	−	0.354627i	0.950051	+	0.312094i	$0.101030\pi$
$920$		0			0
$921$	12.5764	−	7.26101i	0.414408	−	0.239258i
$922$		0			0
$923$	24.2099	+	11.6202i	0.796877	+	0.382482i
$924$		0			0
$925$	7.62950	+	13.2147i	0.250857	+	0.434496i
$926$		0			0
$927$	5.48597	−	9.50197i	0.180183	−	0.312086i
$928$		0			0
$929$	35.0237	+	20.2210i	1.14909	+	0.663428i	0.948666	−	0.316280i	$-0.102434\pi$
$929$	35.0237	+	20.2210i	1.14909	+	0.663428i	0.200426	+	0.979709i	$0.435767\pi$
$930$		0			0
$931$	54.0849			1.77256
$932$		0			0
$933$	13.5153	−	7.80308i	0.442472	−	0.255461i
$934$		0			0
$935$	0.573984			0.0187713
$936$		0			0
$937$	2.03951			0.0666277			0.0333139	−	0.999445i	$-0.489394\pi$
$937$	2.03951			0.0666277			0.0333139	+	0.999445i	$0.489394\pi$
$938$		0			0
$939$	−25.5914	+	14.7752i	−0.835143	+	0.482170i
$940$		0			0
$941$	35.2677			1.14969			0.574847	−	0.818261i	$-0.305062\pi$
$941$	35.2677			1.14969			0.574847	+	0.818261i	$0.305062\pi$
$942$		0			0
$943$	−28.2370	−	16.3027i	−0.919525	−	0.530888i
$944$		0			0
$945$	−4.14785	+	7.18429i	−0.134930	+	0.233705i
$946$		0			0
$947$	−12.6695	−	21.9442i	−0.411702	−	0.713089i	0.583374	−	0.812204i	$-0.301732\pi$
$947$	−12.6695	−	21.9442i	−0.411702	−	0.713089i	−0.995076	+	0.0991144i	$0.968399\pi$
$948$		0			0
$949$	−1.68404	−	22.0871i	−0.0546662	−	0.716976i
$950$		0			0
$951$	−12.4294	+	7.17614i	−0.403052	+	0.232702i
$952$		0			0
$953$	16.5824	−	28.7215i	0.537155	−	0.930380i	−0.461901	−	0.886932i	$-0.652832\pi$
$953$	16.5824	−	28.7215i	0.537155	−	0.930380i	0.999056	−	0.0434482i	$-0.0138343\pi$
$954$		0			0
$955$	6.70792	−	11.6185i	0.217063	−	0.375965i
$956$		0			0
$957$	0.337899			0.0109227
$958$		0			0
$959$	39.9984	+	69.2793i	1.29162	+	2.23715i
$960$		0			0
$961$	29.8607			0.963250
$962$		0			0
$963$			3.86335i			0.124495i
$964$		0			0
$965$	−22.9550	+	13.2531i	−0.738948	+	0.426632i
$966$		0			0
$967$			24.5985i			0.791035i	0.918459	+	0.395517i	$0.129435\pi$
$967$			24.5985i			0.791035i	−0.918459	+	0.395517i	$0.870565\pi$
$968$		0			0
$969$	−8.70819	−	5.02768i	−0.279747	−	0.161512i
$970$		0			0
$971$	16.8251	+	9.71399i	0.539944	+	0.311737i	0.745056	−	0.667002i	$-0.232423\pi$
$971$	16.8251	+	9.71399i	0.539944	+	0.311737i	−0.205112	+	0.978738i	$0.565756\pi$
$972$		0			0
$973$	10.4928	+	18.1741i	0.336384	+	0.582635i
$974$		0			0
$975$	4.29646	−	2.93746i	0.137597	−	0.0940739i
$976$		0			0
$977$	−10.4801	+	6.05071i	−0.335290	+	0.193580i	−0.658187	−	0.752854i	$-0.728676\pi$
$977$	−10.4801	+	6.05071i	−0.335290	+	0.193580i	0.322898	+	0.946434i	$0.395343\pi$
$978$		0			0
$979$	−1.88379	−	1.08761i	−0.0602061	−	0.0347600i
$980$		0			0
$981$	−0.572732	+	0.992001i	−0.0182859	+	0.0316722i
$982$		0			0
$983$			26.8688i			0.856983i	0.903546	+	0.428492i	$0.140955\pi$
$983$			26.8688i			0.856983i	−0.903546	+	0.428492i	$0.859045\pi$
$984$		0			0
$985$	21.2596	+	36.8228i	0.677388	+	1.17327i
$986$		0			0
$987$		−	44.4790i		−	1.41578i
$988$		0			0
$989$			37.9803i			1.20770i
$990$		0			0
$991$	−3.63276	−	6.29212i	−0.115398	−	0.199876i	0.802541	−	0.596598i	$-0.203481\pi$
$991$	−3.63276	−	6.29212i	−0.115398	−	0.199876i	−0.917939	+	0.396722i	$0.870148\pi$
$992$		0			0
$993$			22.1997i			0.704485i
$994$		0			0
$995$	12.2540	−	21.2245i	0.388477	−	0.672862i
$996$		0			0
$997$	−17.0286	−	9.83147i	−0.539301	−	0.311366i	0.205494	−	0.978658i	$-0.434120\pi$
$997$	−17.0286	−	9.83147i	−0.539301	−	0.311366i	−0.744796	+	0.667293i	$0.767453\pi$
$998$		0			0
$999$	−9.15458	+	5.28540i	−0.289638	+	0.167223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.ca.b.49.15		48
4.3	odd	2		312.2.bk.b.205.16	yes	48
8.3	odd	2		312.2.bk.b.205.8	✓	48
8.5	even	2	inner	1248.2.ca.b.49.10		48
12.11	even	2		936.2.dg.e.829.9		48
13.4	even	6	inner	1248.2.ca.b.433.10		48
24.11	even	2		936.2.dg.e.829.17		48
52.43	odd	6		312.2.bk.b.277.8	yes	48
104.43	odd	6		312.2.bk.b.277.16	yes	48
104.69	even	6	inner	1248.2.ca.b.433.15		48
156.95	even	6		936.2.dg.e.901.17		48
312.251	even	6		936.2.dg.e.901.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.8	✓	48	8.3	odd	2
312.2.bk.b.205.16	yes	48	4.3	odd	2
312.2.bk.b.277.8	yes	48	52.43	odd	6
312.2.bk.b.277.16	yes	48	104.43	odd	6
936.2.dg.e.829.9		48	12.11	even	2
936.2.dg.e.829.17		48	24.11	even	2
936.2.dg.e.901.9		48	312.251	even	6
936.2.dg.e.901.17		48	156.95	even	6
1248.2.ca.b.49.10		48	8.5	even	2	inner
1248.2.ca.b.49.15		48	1.1	even	1	trivial
1248.2.ca.b.433.10		48	13.4	even	6	inner
1248.2.ca.b.433.15		48	104.69	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +1.88587 q^{5} +(-3.80954 - 2.19944i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.0662772 + 0.114795i) q^{11} +(-3.59512 + 0.274112i) q^{13} +(1.63321 - 0.942933i) q^{15} +(1.14806 - 1.98850i) q^{17} +(2.18964 - 3.79257i) q^{19} -4.39888 q^{21} +(-1.97584 - 3.42225i) q^{23} -1.44351 q^{25} -1.00000i q^{27} +(2.20762 - 1.27457i) q^{29} +1.06736i q^{31} +(0.114795 + 0.0662772i) q^{33} +(-7.18429 - 4.14785i) q^{35} +(-5.28540 - 9.15458i) q^{37} +(-2.97641 + 2.03495i) q^{39} +(7.14559 - 4.12551i) q^{41} +(-8.32354 - 4.80560i) q^{43} +(0.942933 - 1.63321i) q^{45} +10.1114i q^{47} +(6.17508 + 10.6956i) q^{49} -2.29612i q^{51} -8.28514i q^{53} +(0.124990 + 0.216489i) q^{55} -4.37928i q^{57} +(-1.65394 + 2.86472i) q^{59} +(6.40470 + 3.69775i) q^{61} +(-3.80954 + 2.19944i) q^{63} +(-6.77991 + 0.516938i) q^{65} +(-0.540655 - 0.936442i) q^{67} +(-3.42225 - 1.97584i) q^{69} +(-6.45016 - 3.72400i) q^{71} +6.14363i q^{73} +(-1.25011 + 0.721753i) q^{75} -0.583091i q^{77} +15.9309 q^{79} +(-0.500000 - 0.866025i) q^{81} -0.144468 q^{83} +(2.16509 - 3.75004i) q^{85} +(1.27457 - 2.20762i) q^{87} +(-14.2114 + 8.20498i) q^{89} +(14.2986 + 6.86301i) q^{91} +(0.533679 + 0.924359i) q^{93} +(4.12937 - 7.15228i) q^{95} +(6.11866 + 3.53261i) q^{97} +0.132554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) \) 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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