LMFDB - Embedded newform 816.2.bq.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [816,2,Mod(49,816)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("816.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(816, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bq (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	816.49
Dual form			816.2.bq.a.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 - 0.923880i) q^{3} +(-1.92388 + 0.796897i) q^{5} +(1.14065 + 0.472474i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.572726 - 1.38268i) q^{11} -4.10973i q^{13} +(1.47247 + 1.47247i) q^{15} +(-2.35743 + 3.38268i) q^{17} +(-4.81684 - 4.81684i) q^{19} -1.23463i q^{21} +(-1.26616 + 3.05679i) q^{23} +(-0.469266 + 0.469266i) q^{25} +(0.923880 + 0.382683i) q^{27} +(5.76745 - 2.38896i) q^{29} +(-3.93015 - 9.48822i) q^{31} -1.49661 q^{33} -2.57099 q^{35} +(-1.50660 - 3.63726i) q^{37} +(-3.79690 + 1.57273i) q^{39} +(-11.2132 - 4.64466i) q^{41} +(-2.43675 + 2.43675i) q^{43} +(0.796897 - 1.92388i) q^{45} +1.56940i q^{47} +(-3.87189 - 3.87189i) q^{49} +(4.02734 + 0.883480i) q^{51} +(-2.80109 - 2.80109i) q^{53} +3.11652i q^{55} +(-2.60685 + 6.29350i) q^{57} +(-5.70144 + 5.70144i) q^{59} +(3.02413 + 1.25264i) q^{61} +(-1.14065 + 0.472474i) q^{63} +(3.27503 + 7.90663i) q^{65} +2.11652 q^{67} +3.30864 q^{69} +(-0.0867259 - 0.209375i) q^{71} +(0.340203 - 0.140917i) q^{73} +(0.613126 + 0.253965i) q^{75} +(1.30656 - 1.30656i) q^{77} +(-1.03893 + 2.50819i) q^{79} -1.00000i q^{81} +(-10.1921 - 10.1921i) q^{83} +(1.83975 - 8.38650i) q^{85} +(-4.41421 - 4.41421i) q^{87} +13.6694i q^{89} +(1.94174 - 4.68777i) q^{91} +(-7.26197 + 7.26197i) q^{93} +(13.1055 + 5.42849i) q^{95} +(-2.48022 + 1.02734i) q^{97} +(0.572726 + 1.38268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} - 8 q^{11} - 8 q^{17} + 8 q^{19} - 8 q^{23} - 16 q^{25} - 8 q^{31} + 8 q^{33} - 32 q^{35} - 8 q^{37} - 16 q^{39} - 24 q^{41} + 8 q^{43} - 8 q^{45} - 8 q^{49} - 32 q^{53} - 16 q^{57} - 16 q^{59}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^11 - 8 * q^17 + 8 * q^19 - 8 * q^23 - 16 * q^25 - 8 * q^31 + 8 * q^33 - 32 * q^35 - 8 * q^37 - 16 * q^39 - 24 * q^41 + 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^53 - 16 * q^57 - 16 * q^59 + 16 * q^61 + 24 * q^65 + 16 * q^67 - 24 * q^69 + 16 * q^71 + 48 * q^73 - 16 * q^75 - 32 * q^83 + 40 * q^85 - 24 * q^87 + 16 * q^91 - 32 * q^93 + 40 * q^95 + 8 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		0			0
$5$	−1.92388	+	0.796897i	−0.860385	+	0.356383i	−0.768858	−	0.639419i	$-0.779175\pi$
$5$	−1.92388	+	0.796897i	−0.860385	+	0.356383i	−0.0915270	+	0.995803i	$0.529175\pi$
$6$		0			0
$7$	1.14065	+	0.472474i	0.431126	+	0.178578i	0.587684	−	0.809091i	$-0.300040\pi$
$7$	1.14065	+	0.472474i	0.431126	+	0.178578i	−0.156558	+	0.987669i	$0.550040\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	0.572726	−	1.38268i	0.172683	−	0.416895i	−0.813716	−	0.581263i	$-0.802559\pi$
$11$	0.572726	−	1.38268i	0.172683	−	0.416895i	0.986399	+	0.164369i	$0.0525586\pi$
$12$		0			0
$13$		−	4.10973i		−	1.13983i	−0.821702	−	0.569917i	$-0.806975\pi$
$13$		−	4.10973i		−	1.13983i	0.821702	−	0.569917i	$-0.193025\pi$
$14$		0			0
$15$	1.47247	+	1.47247i	0.380191	+	0.380191i
$16$		0			0
$17$	−2.35743	+	3.38268i	−0.571760	+	0.820421i
$17$	−2.35743	+	3.38268i	−0.571760	+	0.820421i
$18$		0			0
$19$	−4.81684	−	4.81684i	−1.10506	−	1.10506i	−0.993790	−	0.111268i	$-0.964509\pi$
$19$	−4.81684	−	4.81684i	−1.10506	−	1.10506i	−0.111268	−	0.993790i	$-0.535491\pi$
$20$		0			0
$21$		−	1.23463i		−	0.269419i
$22$		0			0
$23$	−1.26616	+	3.05679i	−0.264013	+	0.637384i	−0.999179	−	0.0405025i	$-0.987104\pi$
$23$	−1.26616	+	3.05679i	−0.264013	+	0.637384i	0.735166	+	0.677887i	$0.237104\pi$
$24$		0			0
$25$	−0.469266	+	0.469266i	−0.0938533	+	0.0938533i
$26$		0			0
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$		0			0
$29$	5.76745	−	2.38896i	1.07099	−	0.443618i	0.223649	−	0.974670i	$-0.428203\pi$
$29$	5.76745	−	2.38896i	1.07099	−	0.443618i	0.847339	+	0.531052i	$0.178203\pi$
$30$		0			0
$31$	−3.93015	−	9.48822i	−0.705876	−	1.70414i	−0.710057	−	0.704144i	$-0.751331\pi$
$31$	−3.93015	−	9.48822i	−0.705876	−	1.70414i	0.00418103	−	0.999991i	$-0.498669\pi$
$32$		0			0
$33$	−1.49661			−0.260526
$34$		0			0
$35$	−2.57099			−0.434577
$36$		0			0
$37$	−1.50660	−	3.63726i	−0.247684	−	0.597962i	0.750323	−	0.661072i	$-0.229898\pi$
$37$	−1.50660	−	3.63726i	−0.247684	−	0.597962i	−0.998007	+	0.0631101i	$0.979898\pi$
$38$		0			0
$39$	−3.79690	+	1.57273i	−0.607990	+	0.251838i
$40$		0			0
$41$	−11.2132	−	4.64466i	−1.75121	−	0.725373i	−0.997689	−	0.0679453i	$-0.978356\pi$
$41$	−11.2132	−	4.64466i	−1.75121	−	0.725373i	−0.753517	−	0.657428i	$-0.771644\pi$
$42$		0			0
$43$	−2.43675	+	2.43675i	−0.371601	+	0.371601i	−0.868060	−	0.496459i	$-0.834633\pi$
$43$	−2.43675	+	2.43675i	−0.371601	+	0.371601i	0.496459	+	0.868060i	$0.334633\pi$
$44$		0			0
$45$	0.796897	−	1.92388i	0.118794	−	0.286795i
$46$		0			0
$47$			1.56940i			0.228920i	0.993428	+	0.114460i	$0.0365138\pi$
$47$			1.56940i			0.228920i	−0.993428	+	0.114460i	$0.963486\pi$
$48$		0			0
$49$	−3.87189	−	3.87189i	−0.553127	−	0.553127i
$50$		0			0
$51$	4.02734	+	0.883480i	0.563940	+	0.123712i
$52$		0			0
$53$	−2.80109	−	2.80109i	−0.384759	−	0.384759i	0.488054	−	0.872813i	$-0.337707\pi$
$53$	−2.80109	−	2.80109i	−0.384759	−	0.384759i	−0.872813	+	0.488054i	$0.837707\pi$
$54$		0			0
$55$			3.11652i			0.420231i
$56$		0			0
$57$	−2.60685	+	6.29350i	−0.345286	+	0.833595i
$58$		0			0
$59$	−5.70144	+	5.70144i	−0.742265	+	0.742265i	−0.973013	−	0.230749i	$-0.925883\pi$
$59$	−5.70144	+	5.70144i	−0.742265	+	0.742265i	0.230749	+	0.973013i	$0.425883\pi$
$60$		0			0
$61$	3.02413	+	1.25264i	0.387200	+	0.160384i	0.567787	−	0.823175i	$-0.307800\pi$
$61$	3.02413	+	1.25264i	0.387200	+	0.160384i	−0.180587	+	0.983559i	$0.557800\pi$
$62$		0			0
$63$	−1.14065	+	0.472474i	−0.143709	+	0.0595261i
$64$		0			0
$65$	3.27503	+	7.90663i	0.406218	+	0.980697i
$66$		0			0
$67$	2.11652			0.258574			0.129287	−	0.991607i	$-0.458731\pi$
$67$	2.11652			0.258574			0.129287	+	0.991607i	$0.458731\pi$
$68$		0			0
$69$	3.30864			0.398314
$70$		0			0
$71$	−0.0867259	−	0.209375i	−0.0102925	−	0.0248482i	0.918650	−	0.395073i	$-0.129281\pi$
$71$	−0.0867259	−	0.209375i	−0.0102925	−	0.0248482i	−0.928942	+	0.370225i	$0.879281\pi$
$72$		0			0
$73$	0.340203	−	0.140917i	0.0398177	−	0.0164930i	−0.362686	−	0.931912i	$-0.618140\pi$
$73$	0.340203	−	0.140917i	0.0398177	−	0.0164930i	0.402503	+	0.915418i	$0.368140\pi$
$74$		0			0
$75$	0.613126	+	0.253965i	0.0707977	+	0.0293254i
$76$		0			0
$77$	1.30656	−	1.30656i	0.148897	−	0.148897i
$78$		0			0
$79$	−1.03893	+	2.50819i	−0.116889	+	0.282194i	−0.971486	−	0.237097i	$-0.923804\pi$
$79$	−1.03893	+	2.50819i	−0.116889	+	0.282194i	0.854597	+	0.519291i	$0.173804\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−10.1921	−	10.1921i	−1.11873	−	1.11873i	−0.991928	−	0.126803i	$-0.959528\pi$
$83$	−10.1921	−	10.1921i	−1.11873	−	1.11873i	−0.126803	−	0.991928i	$-0.540472\pi$
$84$		0			0
$85$	1.83975	−	8.38650i	0.199549	−	0.909644i
$86$		0			0
$87$	−4.41421	−	4.41421i	−0.473253	−	0.473253i
$88$		0			0
$89$			13.6694i			1.44895i	0.689299	+	0.724477i	$0.257918\pi$
$89$			13.6694i			1.44895i	−0.689299	+	0.724477i	$0.742082\pi$
$90$		0			0
$91$	1.94174	−	4.68777i	0.203550	−	0.491412i
$92$		0			0
$93$	−7.26197	+	7.26197i	−0.753031	+	0.753031i
$94$		0			0
$95$	13.1055	+	5.42849i	1.34460	+	0.556952i
$96$		0			0
$97$	−2.48022	+	1.02734i	−0.251828	+	0.104311i	−0.505027	−	0.863104i	$-0.668517\pi$
$97$	−2.48022	+	1.02734i	−0.251828	+	0.104311i	0.253199	+	0.967414i	$0.418517\pi$
$98$		0			0
$99$	0.572726	+	1.38268i	0.0575612	+	0.138965i
$100$		0			0
$101$	2.38009			0.236827			0.118414	−	0.992964i	$-0.462219\pi$
$101$	2.38009			0.236827			0.118414	+	0.992964i	$0.462219\pi$
$102$		0			0
$103$	13.2909			1.30959			0.654796	−	0.755806i	$-0.272755\pi$
$103$	13.2909			1.30959			0.654796	+	0.755806i	$0.272755\pi$
$104$		0			0
$105$	0.983875	+	2.37529i	0.0960164	+	0.231804i
$106$		0			0
$107$	12.0773	−	5.00260i	1.16756	−	0.483619i	0.287175	−	0.957878i	$-0.407284\pi$
$107$	12.0773	−	5.00260i	1.16756	−	0.483619i	0.880386	+	0.474259i	$0.157284\pi$
$108$		0			0
$109$	−0.883480	−	0.365949i	−0.0846220	−	0.0350516i	0.339971	−	0.940436i	$-0.389583\pi$
$109$	−0.883480	−	0.365949i	−0.0846220	−	0.0350516i	−0.424593	+	0.905384i	$0.639583\pi$
$110$		0			0
$111$	−2.78384	+	2.78384i	−0.264230	+	0.264230i
$112$		0			0
$113$	3.30237	−	7.97263i	0.310661	−	0.750002i	−0.689020	−	0.724742i	$-0.741959\pi$
$113$	3.30237	−	7.97263i	0.310661	−	0.750002i	0.999681	−	0.0252597i	$-0.00804126\pi$
$114$		0			0
$115$		−	6.88989i		−	0.642486i
$116$		0			0
$117$	2.90602	+	2.90602i	0.268662	+	0.268662i
$118$		0			0
$119$	−4.28723	+	2.74464i	−0.393010	+	0.251601i
$120$		0			0
$121$	6.19438	+	6.19438i	0.563125	+	0.563125i
$122$		0			0
$123$			12.1371i			1.09436i
$124$		0			0
$125$	4.51334	−	10.8962i	0.403685	−	0.974583i
$126$		0			0
$127$	10.0044	−	10.0044i	0.887749	−	0.887749i	−0.106557	−	0.994307i	$-0.533983\pi$
$127$	10.0044	−	10.0044i	0.887749	−	0.887749i	0.994307	+	0.106557i	$0.0339828\pi$
$128$		0			0
$129$	3.18377	+	1.31876i	0.280315	+	0.116110i
$130$		0			0
$131$	2.39363	−	0.991476i	0.209133	−	0.0866256i	−0.275658	−	0.961256i	$-0.588896\pi$
$131$	2.39363	−	0.991476i	0.209133	−	0.0866256i	0.484791	+	0.874630i	$0.338896\pi$
$132$		0			0
$133$	−3.21851	−	7.77017i	−0.279080	−	0.673759i
$134$		0			0
$135$	−2.08239			−0.179224
$136$		0			0
$137$	15.2684			1.30447			0.652233	−	0.758018i	$-0.273832\pi$
$137$	15.2684			1.30447			0.652233	+	0.758018i	$0.273832\pi$
$138$		0			0
$139$	1.54686	+	3.73445i	0.131203	+	0.316752i	0.975805	−	0.218643i	$-0.0701630\pi$
$139$	1.54686	+	3.73445i	0.131203	+	0.316752i	−0.844602	+	0.535394i	$0.820163\pi$
$140$		0			0
$141$	1.44993	−	0.600582i	0.122106	−	0.0505782i
$142$		0			0
$143$	−5.68246	−	2.35375i	−0.475191	−	0.196831i
$144$		0			0
$145$	−9.19212	+	9.19212i	−0.763364	+	0.763364i
$146$		0			0
$147$	−2.09545	+	5.05887i	−0.172830	+	0.417249i
$148$		0			0
$149$			18.1219i			1.48460i	0.670065	+	0.742302i	$0.266266\pi$
$149$			18.1219i			1.48460i	−0.670065	+	0.742302i	$0.733734\pi$
$150$		0			0
$151$	−3.72739	−	3.72739i	−0.303331	−	0.303331i	0.538985	−	0.842316i	$-0.318808\pi$
$151$	−3.72739	−	3.72739i	−0.303331	−	0.303331i	−0.842316	+	0.538985i	$0.818808\pi$
$152$		0			0
$153$	−0.724967	−	4.05887i	−0.0586101	−	0.328140i
$154$		0			0
$155$	15.1223	+	15.1223i	1.21465	+	1.21465i
$156$		0			0
$157$		−	3.80334i		−	0.303540i	−0.988416	−	0.151770i	$-0.951503\pi$
$157$		−	3.80334i		−	0.303540i	0.988416	−	0.151770i	$-0.0484972\pi$
$158$		0			0
$159$	−1.51594	+	3.65980i	−0.120222	+	0.290241i
$160$		0			0
$161$	−2.88850	+	2.88850i	−0.227646	+	0.227646i
$162$		0			0
$163$	−8.37849	−	3.47049i	−0.656254	−	0.271829i	0.0296072	−	0.999562i	$-0.490574\pi$
$163$	−8.37849	−	3.47049i	−0.656254	−	0.271829i	−0.685861	+	0.727732i	$0.740574\pi$
$164$		0			0
$165$	2.87929	−	1.19264i	0.224152	−	0.0928469i
$166$		0			0
$167$	−3.40115	−	8.21111i	−0.263189	−	0.635395i	0.735943	−	0.677043i	$-0.236739\pi$
$167$	−3.40115	−	8.21111i	−0.263189	−	0.635395i	−0.999132	+	0.0416485i	$0.986739\pi$
$168$		0			0
$169$	−3.88989			−0.299223
$170$		0			0
$171$	6.81204			0.520930
$172$		0			0
$173$	−4.68679	−	11.3149i	−0.356330	−	0.860257i	−0.995810	−	0.0914490i	$-0.970850\pi$
$173$	−4.68679	−	11.3149i	−0.356330	−	0.860257i	0.639480	−	0.768808i	$-0.279150\pi$
$174$		0			0
$175$	−0.756986	+	0.313554i	−0.0572227	+	0.0237024i
$176$		0			0
$177$	7.44930	+	3.08560i	0.559923	+	0.231928i
$178$		0			0
$179$	−7.50756	+	7.50756i	−0.561141	+	0.561141i	−0.929632	−	0.368490i	$-0.879875\pi$
$179$	−7.50756	+	7.50756i	−0.561141	+	0.561141i	0.368490	+	0.929632i	$0.379875\pi$
$180$		0			0
$181$	6.32477	−	15.2693i	0.470116	−	1.13496i	−0.493995	−	0.869465i	$-0.664464\pi$
$181$	6.32477	−	15.2693i	0.470116	−	1.13496i	0.964112	−	0.265497i	$-0.0855360\pi$
$182$		0			0
$183$		−	3.27330i		−	0.241969i
$184$		0			0
$185$	5.79704	+	5.79704i	0.426207	+	0.426207i
$186$		0			0
$187$	3.32702	+	5.19692i	0.243296	+	0.380037i
$188$		0			0
$189$	0.873017	+	0.873017i	0.0635027	+	0.0635027i
$190$		0			0
$191$			12.0167i			0.869498i	0.900552	+	0.434749i	$0.143163\pi$
$191$			12.0167i			0.869498i	−0.900552	+	0.434749i	$0.856837\pi$
$192$		0			0
$193$	4.10172	−	9.90244i	0.295249	−	0.712793i	−0.704746	−	0.709460i	$-0.748939\pi$
$193$	4.10172	−	9.90244i	0.295249	−	0.712793i	0.999994	−	0.00333326i	$-0.00106101\pi$
$194$		0			0
$195$	6.05147	−	6.05147i	0.433355	−	0.433355i
$196$		0			0
$197$	−2.92772	−	1.21270i	−0.208592	−	0.0864015i	0.275941	−	0.961174i	$-0.411010\pi$
$197$	−2.92772	−	1.21270i	−0.208592	−	0.0864015i	−0.484533	+	0.874773i	$0.661010\pi$
$198$		0			0
$199$	12.6337	−	5.23304i	0.895578	−	0.370960i	0.113060	−	0.993588i	$-0.463935\pi$
$199$	12.6337	−	5.23304i	0.895578	−	0.370960i	0.782518	+	0.622628i	$0.213935\pi$
$200$		0			0
$201$	−0.809957	−	1.95541i	−0.0571300	−	0.137924i
$202$		0			0
$203$	7.70737			0.540951
$204$		0			0
$205$	25.2741			1.76522
$206$		0			0
$207$	−1.26616	−	3.05679i	−0.0880044	−	0.212461i
$208$		0			0
$209$	−9.41889	+	3.90143i	−0.651518	+	0.269868i
$210$		0			0
$211$	−5.47727	−	2.26876i	−0.377071	−	0.156188i	0.186095	−	0.982532i	$-0.440417\pi$
$211$	−5.47727	−	2.26876i	−0.377071	−	0.156188i	−0.563166	+	0.826344i	$0.690417\pi$
$212$		0			0
$213$	−0.160248	+	0.160248i	−0.0109800	+	0.0109800i
$214$		0			0
$215$	2.74618	−	6.62986i	0.187288	−	0.452153i
$216$		0			0
$217$		−	12.6797i		−	0.860751i
$218$		0			0
$219$	−0.260380	−	0.260380i	−0.0175948	−	0.0175948i
$220$		0			0
$221$	13.9019	+	9.68838i	0.935144	+	0.651711i
$222$		0			0
$223$	18.4892	+	18.4892i	1.23813	+	1.23813i	0.960766	+	0.277361i	$0.0894599\pi$
$223$	18.4892	+	18.4892i	1.23813	+	1.23813i	0.277361	+	0.960766i	$0.410540\pi$
$224$		0			0
$225$		−	0.663643i		−	0.0442428i
$226$		0			0
$227$	−4.19979	+	10.1392i	−0.278750	+	0.672961i	−0.999802	−	0.0199199i	$-0.993659\pi$
$227$	−4.19979	+	10.1392i	−0.278750	+	0.672961i	0.721052	+	0.692881i	$0.243659\pi$
$228$		0			0
$229$	−10.2440	+	10.2440i	−0.676942	+	0.676942i	−0.959307	−	0.282365i	$-0.908881\pi$
$229$	−10.2440	+	10.2440i	−0.676942	+	0.676942i	0.282365	+	0.959307i	$0.408881\pi$
$230$		0			0
$231$	−1.70711	−	0.707107i	−0.112319	−	0.0465242i
$232$		0			0
$233$	−17.6443	+	7.30850i	−1.15592	+	0.478796i	−0.876513	−	0.481378i	$-0.840136\pi$
$233$	−17.6443	+	7.30850i	−1.15592	+	0.478796i	−0.279402	+	0.960174i	$0.590136\pi$
$234$		0			0
$235$	−1.25065	−	3.01933i	−0.0815833	−	0.196959i
$236$		0			0
$237$	2.71485			0.176348
$238$		0			0
$239$	−0.740970			−0.0479294			−0.0239647	−	0.999713i	$-0.507629\pi$
$239$	−0.740970			−0.0479294			−0.0239647	+	0.999713i	$0.507629\pi$
$240$		0			0
$241$	8.17478	+	19.7357i	0.526584	+	1.27129i	0.933748	+	0.357931i	$0.116518\pi$
$241$	8.17478	+	19.7357i	0.526584	+	1.27129i	−0.407164	+	0.913355i	$0.633482\pi$
$242$		0			0
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$		0			0
$245$	10.5346	+	4.36355i	0.673028	+	0.278777i
$246$		0			0
$247$	−19.7959	+	19.7959i	−1.25958	+	1.25958i
$248$		0			0
$249$	−5.51594	+	13.3167i	−0.349558	+	0.843909i
$250$		0			0
$251$		−	0.938819i		−	0.0592577i	−0.999561	−	0.0296289i	$-0.990567\pi$
$251$		−	0.938819i		−	0.0592577i	0.999561	−	0.0296289i	$-0.00943254\pi$
$252$		0			0
$253$	3.50141	+	3.50141i	0.220132	+	0.220132i
$254$		0			0
$255$	−8.45216	+	1.50967i	−0.529295	+	0.0945390i
$256$		0			0
$257$	11.1930	+	11.1930i	0.698199	+	0.698199i	0.964022	−	0.265823i	$-0.0856436\pi$
$257$	11.1930	+	11.1930i	0.698199	+	0.698199i	−0.265823	+	0.964022i	$0.585644\pi$
$258$		0			0
$259$		−	4.86068i		−	0.302028i
$260$		0			0
$261$	−2.38896	+	5.76745i	−0.147873	+	0.356996i
$262$		0			0
$263$	−8.10152	+	8.10152i	−0.499561	+	0.499561i	−0.911301	−	0.411740i	$-0.864921\pi$
$263$	−8.10152	+	8.10152i	−0.499561	+	0.499561i	0.411740	+	0.911301i	$0.364921\pi$
$264$		0			0
$265$	7.62113	+	3.15678i	0.468163	+	0.193919i
$266$		0			0
$267$	12.6289	−	5.23105i	0.772875	−	0.320135i
$268$		0			0
$269$	−7.33564	−	17.7098i	−0.447262	−	1.07979i	−0.973344	−	0.229351i	$-0.926339\pi$
$269$	−7.33564	−	17.7098i	−0.447262	−	1.07979i	0.526082	−	0.850434i	$-0.323661\pi$
$270$		0			0
$271$	6.82805			0.414775			0.207387	−	0.978259i	$-0.433504\pi$
$271$	6.82805			0.414775			0.207387	+	0.978259i	$0.433504\pi$
$272$		0			0
$273$	−5.07401			−0.307093
$274$		0			0
$275$	0.380086	+	0.917608i	0.0229200	+	0.0553338i
$276$		0			0
$277$	−7.50915	+	3.11039i	−0.451181	+	0.186885i	−0.596690	−	0.802472i	$-0.703518\pi$
$277$	−7.50915	+	3.11039i	−0.451181	+	0.186885i	0.145509	+	0.989357i	$0.453518\pi$
$278$		0			0
$279$	9.48822	+	3.93015i	0.568045	+	0.235292i
$280$		0			0
$281$	−8.20741	+	8.20741i	−0.489613	+	0.489613i	−0.908184	−	0.418571i	$-0.862531\pi$
$281$	−8.20741	+	8.20741i	−0.489613	+	0.489613i	0.418571	+	0.908184i	$0.362531\pi$
$282$		0			0
$283$	2.32061	−	5.60244i	0.137946	−	0.333030i	−0.839777	−	0.542932i	$-0.817314\pi$
$283$	2.32061	−	5.60244i	0.137946	−	0.333030i	0.977723	+	0.209901i	$0.0673142\pi$
$284$		0			0
$285$		−	14.1853i		−	0.840267i
$286$		0			0
$287$	−10.5959	−	10.5959i	−0.625455	−	0.625455i
$288$		0			0
$289$	−5.88509	−	15.9488i	−0.346182	−	0.938167i
$290$		0			0
$291$	1.89828	+	1.89828i	0.111279	+	0.111279i
$292$		0			0
$293$			6.87547i			0.401669i	0.979625	+	0.200835i	$0.0643654\pi$
$293$			6.87547i			0.401669i	−0.979625	+	0.200835i	$0.935635\pi$
$294$		0			0
$295$	6.42543	−	15.5124i	0.374103	−	0.903164i
$296$		0			0
$297$	1.05826	−	1.05826i	0.0614065	−	0.0614065i
$298$		0			0
$299$	12.5626	+	5.20359i	0.726513	+	0.300931i
$300$		0			0
$301$	−3.93079	+	1.62819i	−0.226567	+	0.0938471i
$302$		0			0
$303$	−0.910819	−	2.19891i	−0.0523252	−	0.126324i
$304$		0			0
$305$	−6.81629			−0.390300
$306$		0			0
$307$	−22.2451			−1.26959			−0.634797	−	0.772679i	$-0.718916\pi$
$307$	−22.2451			−1.26959			−0.634797	+	0.772679i	$0.718916\pi$
$308$		0			0
$309$	−5.08621	−	12.2792i	−0.289344	−	0.698539i
$310$		0			0
$311$	−5.00208	+	2.07193i	−0.283642	+	0.117488i	−0.519969	−	0.854185i	$-0.674056\pi$
$311$	−5.00208	+	2.07193i	−0.283642	+	0.117488i	0.236327	+	0.971674i	$0.424056\pi$
$312$		0			0
$313$	−10.4348	−	4.32222i	−0.589808	−	0.244306i	0.0677602	−	0.997702i	$-0.478415\pi$
$313$	−10.4348	−	4.32222i	−0.589808	−	0.244306i	−0.657568	+	0.753395i	$0.728415\pi$
$314$		0			0
$315$	1.81796	−	1.81796i	0.102431	−	0.102431i
$316$		0			0
$317$	7.06127	−	17.0474i	0.396600	−	0.957477i	−0.591866	−	0.806036i	$-0.701609\pi$
$317$	7.06127	−	17.0474i	0.396600	−	0.957477i	0.988466	−	0.151441i	$-0.0483914\pi$
$318$		0			0
$319$		−	9.34277i		−	0.523095i
$320$		0			0
$321$	−9.24360	−	9.24360i	−0.515927	−	0.515927i
$322$		0			0
$323$	27.6492	−	4.93850i	1.53844	−	0.274786i
$324$		0			0
$325$	1.92856	+	1.92856i	0.106977	+	0.106977i
$326$		0			0
$327$			0.956272i			0.0528819i
$328$		0			0
$329$	−0.741499	+	1.79014i	−0.0408802	+	0.0986934i
$330$		0			0
$331$	−4.07722	+	4.07722i	−0.224104	+	0.224104i	−0.810224	−	0.586120i	$-0.800655\pi$
$331$	−4.07722	+	4.07722i	−0.224104	+	0.224104i	0.586120	+	0.810224i	$0.300655\pi$
$332$		0			0
$333$	3.63726	+	1.50660i	0.199321	+	0.0825613i
$334$		0			0
$335$	−4.07193	+	1.68665i	−0.222473	+	0.0921515i
$336$		0			0
$337$	6.22652	+	15.0321i	0.339180	+	0.818853i	0.997795	+	0.0663727i	$0.0211426\pi$
$337$	6.22652	+	15.0321i	0.339180	+	0.818853i	−0.658615	+	0.752480i	$0.728857\pi$
$338$		0			0
$339$	−8.62951			−0.468691
$340$		0			0
$341$	−15.3701			−0.832338
$342$		0			0
$343$	−5.89443	−	14.2304i	−0.318269	−	0.768370i
$344$		0			0
$345$	−6.36543	+	2.63665i	−0.342703	+	0.141952i
$346$		0			0
$347$	−3.96379	−	1.64186i	−0.212787	−	0.0881394i	0.273744	−	0.961803i	$-0.411738\pi$
$347$	−3.96379	−	1.64186i	−0.212787	−	0.0881394i	−0.486531	+	0.873663i	$0.661738\pi$
$348$		0			0
$349$	−10.0093	+	10.0093i	−0.535787	+	0.535787i	−0.922289	−	0.386501i	$-0.873683\pi$
$349$	−10.0093	+	10.0093i	−0.535787	+	0.535787i	0.386501	+	0.922289i	$0.373683\pi$
$350$		0			0
$351$	1.57273	−	3.79690i	0.0839459	−	0.202663i
$352$		0			0
$353$		−	23.8142i		−	1.26750i	−0.773536	−	0.633752i	$-0.781514\pi$
$353$		−	23.8142i		−	1.26750i	0.773536	−	0.633752i	$-0.218486\pi$
$354$		0			0
$355$	0.333700	+	0.333700i	0.0177110	+	0.0177110i
$356$		0			0
$357$	4.17637	+	2.91056i	0.221037	+	0.154043i
$358$		0			0
$359$	−24.9380	−	24.9380i	−1.31618	−	1.31618i	−0.916777	−	0.399400i	$-0.869219\pi$
$359$	−24.9380	−	24.9380i	−1.31618	−	1.31618i	−0.399400	−	0.916777i	$-0.630781\pi$
$360$		0			0
$361$			27.4039i			1.44231i
$362$		0			0
$363$	3.35237	−	8.09334i	0.175954	−	0.424790i
$364$		0			0
$365$	−0.542213	+	0.542213i	−0.0283807	+	0.0283807i
$366$		0			0
$367$	15.0788	+	6.24585i	0.787108	+	0.326031i	0.739780	−	0.672849i	$-0.234930\pi$
$367$	15.0788	+	6.24585i	0.787108	+	0.326031i	0.0473275	+	0.998879i	$0.484930\pi$
$368$		0			0
$369$	11.2132	−	4.64466i	0.583735	−	0.241791i
$370$		0			0
$371$	−1.87163	−	4.51851i	−0.0971700	−	0.234589i
$372$		0			0
$373$	25.0156			1.29526			0.647630	−	0.761955i	$-0.275760\pi$
$373$	25.0156			1.29526			0.647630	+	0.761955i	$0.275760\pi$
$374$		0			0
$375$	−11.7939			−0.609036
$376$		0			0
$377$	−9.81796	−	23.7027i	−0.505651	−	1.22075i
$378$		0			0
$379$	−30.1444	+	12.4862i	−1.54842	+	0.641375i	−0.983029	−	0.183451i	$-0.941273\pi$
$379$	−30.1444	+	12.4862i	−1.54842	+	0.641375i	−0.565387	+	0.824826i	$0.691273\pi$
$380$		0			0
$381$	−13.0714	−	5.41436i	−0.669669	−	0.277386i
$382$		0			0
$383$	−0.413840	+	0.413840i	−0.0211462	+	0.0211462i	−0.717601	−	0.696455i	$-0.754760\pi$
$383$	−0.413840	+	0.413840i	−0.0211462	+	0.0211462i	0.696455	+	0.717601i	$0.254760\pi$
$384$		0			0
$385$	−1.47247	+	3.55487i	−0.0750442	+	0.181173i
$386$		0			0
$387$		−	3.44609i		−	0.175175i
$388$		0			0
$389$	−15.6455	−	15.6455i	−0.793258	−	0.793258i	0.188765	−	0.982022i	$-0.439552\pi$
$389$	−15.6455	−	15.6455i	−0.793258	−	0.793258i	−0.982022	+	0.188765i	$0.939552\pi$
$390$		0			0
$391$	−7.35526	−	11.4892i	−0.371972	−	0.581033i
$392$		0			0
$393$	−1.83201	−	1.83201i	−0.0924126	−	0.0924126i
$394$		0			0
$395$		−	5.65338i		−	0.284453i
$396$		0			0
$397$	−2.23116	+	5.38650i	−0.111979	+	0.270341i	−0.969927	−	0.243395i	$-0.921739\pi$
$397$	−2.23116	+	5.38650i	−0.111979	+	0.270341i	0.857948	+	0.513736i	$0.171739\pi$
$398$		0			0
$399$	−5.94703	+	5.94703i	−0.297724	+	0.297724i
$400$		0			0
$401$	4.79513	+	1.98621i	0.239458	+	0.0991865i	0.499185	−	0.866495i	$-0.333633\pi$
$401$	4.79513	+	1.98621i	0.239458	+	0.0991865i	−0.259728	+	0.965682i	$0.583633\pi$
$402$		0			0
$403$	−38.9941	+	16.1519i	−1.94243	+	0.804582i
$404$		0			0
$405$	0.796897	+	1.92388i	0.0395981	+	0.0955983i
$406$		0			0
$407$	−5.89205			−0.292058
$408$		0			0
$409$	−27.2400			−1.34693			−0.673465	−	0.739219i	$-0.735195\pi$
$409$	−27.2400			−1.34693			−0.673465	+	0.739219i	$0.735195\pi$
$410$		0			0
$411$	−5.84296	−	14.1062i	−0.288212	−	0.695805i
$412$		0			0
$413$	−9.19715	+	3.80958i	−0.452562	+	0.187457i
$414$		0			0
$415$	27.7305	+	11.4863i	1.36124	+	0.563843i
$416$		0			0
$417$	2.85822	−	2.85822i	0.139968	−	0.139968i
$418$		0			0
$419$	5.36909	−	12.9621i	0.262297	−	0.633242i	−0.736782	−	0.676130i	$-0.763656\pi$
$419$	5.36909	−	12.9621i	0.262297	−	0.633242i	0.999080	+	0.0428878i	$0.0136558\pi$
$420$		0			0
$421$		−	15.3811i		−	0.749627i	−0.927100	−	0.374814i	$-0.877707\pi$
$421$		−	15.3811i		−	0.749627i	0.927100	−	0.374814i	$-0.122293\pi$
$422$		0			0
$423$	−1.10973	−	1.10973i	−0.0539570	−	0.0539570i
$424$		0			0
$425$	−0.481119	−	2.69364i	−0.0233377	−	0.130661i
$426$		0			0
$427$	2.85765	+	2.85765i	0.138291	+	0.138291i
$428$		0			0
$429$			6.15065i			0.296956i
$430$		0			0
$431$	6.27243	−	15.1430i	0.302133	−	0.729413i	−0.697782	−	0.716311i	$-0.745829\pi$
$431$	6.27243	−	15.1430i	0.302133	−	0.729413i	0.999914	−	0.0131020i	$-0.00417060\pi$
$432$		0			0
$433$	15.3517	−	15.3517i	0.737757	−	0.737757i	−0.234386	−	0.972144i	$-0.575308\pi$
$433$	15.3517	−	15.3517i	0.737757	−	0.737757i	0.972144	+	0.234386i	$0.0753080\pi$
$434$		0			0
$435$	12.0101	+	4.97474i	0.575840	+	0.238521i
$436$		0			0
$437$	20.8230	−	8.62515i	0.996097	−	0.412597i
$438$		0			0
$439$	9.00469	+	21.7392i	0.429770	+	1.03756i	0.979360	+	0.202123i	$0.0647841\pi$
$439$	9.00469	+	21.7392i	0.429770	+	1.03756i	−0.549590	+	0.835435i	$0.685216\pi$
$440$		0			0
$441$	5.47568			0.260747
$442$		0			0
$443$	15.4238			0.732808			0.366404	−	0.930456i	$-0.380589\pi$
$443$	15.4238			0.732808			0.366404	+	0.930456i	$0.380589\pi$
$444$		0			0
$445$	−10.8931	−	26.2983i	−0.516383	−	1.24666i
$446$		0			0
$447$	16.7425	−	6.93495i	0.791891	−	0.328012i
$448$		0			0
$449$	12.5181	+	5.18515i	0.590764	+	0.244702i	0.657979	−	0.753036i	$-0.271411\pi$
$449$	12.5181	+	5.18515i	0.590764	+	0.244702i	−0.0672154	+	0.997738i	$0.521411\pi$
$450$		0			0
$451$	−12.8442	+	12.8442i	−0.604809	+	0.604809i
$452$		0			0
$453$	−2.01725	+	4.87007i	−0.0947787	+	0.228816i
$454$		0			0
$455$			10.5661i			0.495346i
$456$		0			0
$457$	−10.8806	−	10.8806i	−0.508972	−	0.508972i	0.405239	−	0.914211i	$-0.367188\pi$
$457$	−10.8806	−	10.8806i	−0.508972	−	0.508972i	−0.914211	+	0.405239i	$0.867188\pi$
$458$		0			0
$459$	−3.47247	+	2.22304i	−0.162081	+	0.103763i
$460$		0			0
$461$	14.7082	+	14.7082i	0.685031	+	0.685031i	0.961129	−	0.276099i	$-0.0890416\pi$
$461$	14.7082	+	14.7082i	0.685031	+	0.685031i	−0.276099	+	0.961129i	$0.589042\pi$
$462$		0			0
$463$			26.4325i			1.22842i	0.789141	+	0.614212i	$0.210526\pi$
$463$			26.4325i			1.22842i	−0.789141	+	0.614212i	$0.789474\pi$
$464$		0			0
$465$	8.18412	−	19.7582i	0.379529	−	0.916265i
$466$		0			0
$467$	5.07058	−	5.07058i	0.234638	−	0.234638i	−0.579987	−	0.814626i	$-0.696942\pi$
$467$	5.07058	−	5.07058i	0.234638	−	0.234638i	0.814626	+	0.579987i	$0.196942\pi$
$468$		0			0
$469$	2.41421	+	1.00000i	0.111478	+	0.0461757i
$470$		0			0
$471$	−3.51383	+	1.45548i	−0.161909	+	0.0670648i
$472$		0			0
$473$	1.97367	+	4.76485i	0.0907492	+	0.219088i
$474$		0			0
$475$	4.52076			0.207427
$476$		0			0
$477$	3.96134			0.181377
$478$		0			0
$479$	−1.12279	−	2.71066i	−0.0513017	−	0.123853i	0.896151	−	0.443749i	$-0.146352\pi$
$479$	−1.12279	−	2.71066i	−0.0513017	−	0.123853i	−0.947453	+	0.319896i	$0.896352\pi$
$480$		0			0
$481$	−14.9482	+	6.19173i	−0.681577	+	0.282319i
$482$		0			0
$483$	3.77401	+	1.56325i	0.171724	+	0.0711302i
$484$		0			0
$485$	3.95295	−	3.95295i	0.179494	−	0.179494i
$486$		0			0
$487$	8.89432	−	21.4728i	0.403040	−	0.973025i	−0.583884	−	0.811837i	$-0.698468\pi$
$487$	8.89432	−	21.4728i	0.403040	−	0.973025i	0.986924	−	0.161188i	$-0.0515324\pi$
$488$		0			0
$489$			9.06882i			0.410106i
$490$		0			0
$491$	−9.65807	−	9.65807i	−0.435863	−	0.435863i	0.454754	−	0.890617i	$-0.349727\pi$
$491$	−9.65807	−	9.65807i	−0.435863	−	0.435863i	−0.890617	+	0.454754i	$0.849727\pi$
$492$		0			0
$493$	−5.51525	+	25.1412i	−0.248394	+	1.13230i
$494$		0			0
$495$	−2.20371	−	2.20371i	−0.0990495	−	0.0990495i
$496$		0			0
$497$		−	0.279799i		−	0.0125507i
$498$		0			0
$499$	2.88245	−	6.95884i	0.129036	−	0.311521i	−0.846137	−	0.532966i	$-0.821077\pi$
$499$	2.88245	−	6.95884i	0.129036	−	0.311521i	0.975173	+	0.221445i	$0.0710774\pi$
$500$		0			0
$501$	−6.28451	+	6.28451i	−0.280771	+	0.280771i
$502$		0			0
$503$	−23.7585	−	9.84111i	−1.05934	−	0.438794i	−0.216124	−	0.976366i	$-0.569341\pi$
$503$	−23.7585	−	9.84111i	−1.05934	−	0.438794i	−0.843218	+	0.537572i	$0.819341\pi$
$504$		0			0
$505$	−4.57900	+	1.89668i	−0.203763	+	0.0844013i
$506$		0			0
$507$	1.48860	+	3.59379i	0.0661110	+	0.159606i
$508$		0			0
$509$	−34.7796			−1.54158			−0.770789	−	0.637090i	$-0.780138\pi$
$509$	−34.7796			−1.54158			−0.770789	+	0.637090i	$0.780138\pi$
$510$		0			0
$511$	0.454632			0.0201117
$512$		0			0
$513$	−2.60685	−	6.29350i	−0.115095	−	0.277865i
$514$		0			0
$515$	−25.5701	+	10.5915i	−1.12675	+	0.466716i
$516$		0			0
$517$	2.16998	+	0.898835i	0.0954356	+	0.0395307i
$518$		0			0
$519$	−8.66006	+	8.66006i	−0.380135	+	0.380135i
$520$		0			0
$521$	17.0594	−	41.1851i	0.747387	−	1.80435i	0.174617	−	0.984637i	$-0.444131\pi$
$521$	17.0594	−	41.1851i	0.747387	−	1.80435i	0.572771	−	0.819716i	$-0.305869\pi$
$522$		0			0
$523$			19.8918i			0.869808i	0.900477	+	0.434904i	$0.143218\pi$
$523$			19.8918i			0.869808i	−0.900477	+	0.434904i	$0.856782\pi$
$524$		0			0
$525$	0.579372	+	0.579372i	0.0252859	+	0.0252859i
$526$		0			0
$527$	41.3607	+	9.07332i	1.80170	+	0.395240i
$528$		0			0
$529$	8.52267	+	8.52267i	0.370551	+	0.370551i
$530$		0			0
$531$		−	8.06306i		−	0.349907i
$532$		0			0
$533$	−19.0883	+	46.0832i	−0.826806	+	1.99609i
$534$		0			0
$535$	−19.2488	+	19.2488i	−0.832198	+	0.832198i
$536$		0			0
$537$	9.80910	+	4.06306i	0.423294	+	0.175334i
$538$		0			0
$539$	−7.57113	+	3.13607i	−0.326112	+	0.135080i
$540$		0			0
$541$	−0.299022	−	0.721903i	−0.0128560	−	0.0310370i	0.917321	−	0.398148i	$-0.130347\pi$
$541$	−0.299022	−	0.721903i	−0.0128560	−	0.0310370i	−0.930177	+	0.367111i	$0.880347\pi$
$542$		0			0
$543$	−16.5274			−0.709259
$544$		0			0
$545$	1.99133			0.0852993
$546$		0			0
$547$	−14.9463	−	36.0835i	−0.639057	−	1.54282i	−0.827938	−	0.560819i	$-0.810486\pi$
$547$	−14.9463	−	36.0835i	−0.639057	−	1.54282i	0.188882	−	0.982000i	$-0.439514\pi$
$548$		0			0
$549$	−3.02413	+	1.25264i	−0.129067	+	0.0534612i
$550$		0			0
$551$	−39.2881	−	16.2737i	−1.67373	−	0.693281i
$552$		0			0
$553$	−2.37011	+	2.37011i	−0.100787	+	0.100787i
$554$		0			0
$555$	3.13734	−	7.57420i	0.133172	−	0.321507i
$556$		0			0
$557$			13.0371i			0.552398i	0.961100	+	0.276199i	$0.0890750\pi$
$557$			13.0371i			0.552398i	−0.961100	+	0.276199i	$0.910925\pi$
$558$		0			0
$559$	10.0144	+	10.0144i	0.423564	+	0.423564i
$560$		0			0
$561$	3.52814	−	5.06254i	0.148958	−	0.213741i
$562$		0			0
$563$	7.93150	+	7.93150i	0.334273	+	0.334273i	0.854207	−	0.519934i	$-0.174043\pi$
$563$	7.93150	+	7.93150i	0.334273	+	0.334273i	−0.519934	+	0.854207i	$0.674043\pi$
$564$		0			0
$565$			17.9700i			0.756005i
$566$		0			0
$567$	0.472474	−	1.14065i	0.0198420	−	0.0479029i
$568$		0			0
$569$	25.7878	−	25.7878i	1.08108	−	1.08108i	0.0846732	−	0.996409i	$-0.473015\pi$
$569$	25.7878	−	25.7878i	1.08108	−	1.08108i	0.996409	−	0.0846732i	$-0.0269846\pi$
$570$		0			0
$571$	12.5140	+	5.18346i	0.523693	+	0.216921i	0.628838	−	0.777536i	$-0.283531\pi$
$571$	12.5140	+	5.18346i	0.523693	+	0.216921i	−0.105145	+	0.994457i	$0.533531\pi$
$572$		0			0
$573$	11.1020	−	4.59859i	0.463792	−	0.192109i
$574$		0			0
$575$	−0.840280	−	2.02862i	−0.0350421	−	0.0845991i
$576$		0			0
$577$	7.10617			0.295834			0.147917	−	0.989000i	$-0.452743\pi$
$577$	7.10617			0.295834			0.147917	+	0.989000i	$0.452743\pi$
$578$		0			0
$579$	−10.7183			−0.445438
$580$		0			0
$581$	−6.81016	−	16.4412i	−0.282533	−	0.682095i
$582$		0			0
$583$	−5.47727	+	2.26876i	−0.226846	+	0.0939625i
$584$		0			0
$585$	−7.90663	−	3.27503i	−0.326899	−	0.135406i
$586$		0			0
$587$	28.4929	−	28.4929i	1.17603	−	1.17603i	0.195281	−	0.980747i	$-0.437438\pi$
$587$	28.4929	−	28.4929i	1.17603	−	1.17603i	0.980747	−	0.195281i	$-0.0625619\pi$
$588$		0			0
$589$	−26.7723	+	64.6341i	−1.10314	+	2.66320i
$590$		0			0
$591$			3.16895i			0.130353i
$592$		0			0
$593$	−26.7582	−	26.7582i	−1.09883	−	1.09883i	−0.994548	−	0.104280i	$-0.966746\pi$
$593$	−26.7582	−	26.7582i	−1.09883	−	1.09883i	−0.104280	−	0.994548i	$-0.533254\pi$
$594$		0			0
$595$	6.06092	−	8.69685i	0.248473	−	0.356536i
$596$		0			0
$597$	−9.66940	−	9.66940i	−0.395742	−	0.395742i
$598$		0			0
$599$			10.1505i			0.414739i	0.978263	+	0.207369i	$0.0664902\pi$
$599$			10.1505i			0.414739i	−0.978263	+	0.207369i	$0.933510\pi$
$600$		0			0
$601$	13.4910	−	32.5702i	0.550311	−	1.32857i	−0.366935	−	0.930247i	$-0.619593\pi$
$601$	13.4910	−	32.5702i	0.550311	−	1.32857i	0.917246	−	0.398321i	$-0.130407\pi$
$602$		0			0
$603$	−1.49661	+	1.49661i	−0.0609465	+	0.0609465i
$604$		0			0
$605$	−16.8535	−	6.98095i	−0.685193	−	0.283816i
$606$		0			0
$607$	43.9654	−	18.2111i	1.78450	−	0.739164i	0.792974	−	0.609255i	$-0.208532\pi$
$607$	43.9654	−	18.2111i	1.78450	−	0.739164i	0.991526	−	0.129909i	$-0.0414685\pi$
$608$		0			0
$609$	−2.94948	−	7.12068i	−0.119519	−	0.288545i
$610$		0			0
$611$	6.44980			0.260931
$612$		0			0
$613$	−26.9812			−1.08976			−0.544880	−	0.838514i	$-0.683425\pi$
$613$	−26.9812			−1.08976			−0.544880	+	0.838514i	$0.683425\pi$
$614$		0			0
$615$	−9.67200	−	23.3503i	−0.390013	−	0.941573i
$616$		0			0
$617$	13.8507	−	5.73717i	0.557610	−	0.230970i	−0.0860373	−	0.996292i	$-0.527420\pi$
$617$	13.8507	−	5.73717i	0.557610	−	0.230970i	0.643647	+	0.765322i	$0.277420\pi$
$618$		0			0
$619$	2.03477	+	0.842828i	0.0817841	+	0.0338761i	0.423200	−	0.906036i	$-0.360907\pi$
$619$	2.03477	+	0.842828i	0.0817841	+	0.0338761i	−0.341416	+	0.939912i	$0.610907\pi$
$620$		0			0
$621$	−2.33956	+	2.33956i	−0.0938835	+	0.0938835i
$622$		0			0
$623$	−6.45843	+	15.5920i	−0.258752	+	0.624681i
$624$		0			0
$625$			21.2414i			0.849655i
$626$		0			0
$627$	7.20891	+	7.20891i	0.287896	+	0.287896i
$628$		0			0
$629$	15.8554	+	3.47821i	0.632196	+	0.138685i
$630$		0			0
$631$	24.5529	+	24.5529i	0.977435	+	0.977435i	0.999751	−	0.0223155i	$-0.00710383\pi$
$631$	24.5529	+	24.5529i	0.977435	+	0.977435i	−0.0223155	+	0.999751i	$0.507104\pi$
$632$		0			0
$633$			5.92856i			0.235639i
$634$		0			0
$635$	−11.2748	+	27.2198i	−0.447427	+	1.08019i
$636$		0			0
$637$	−15.9124	+	15.9124i	−0.630474	+	0.630474i
$638$		0			0
$639$	0.209375	+	0.0867259i	0.00828274	+	0.00343082i
$640$		0			0
$641$	−23.0324	+	9.54032i	−0.909724	+	0.376820i	−0.787951	−	0.615738i	$-0.788858\pi$
$641$	−23.0324	+	9.54032i	−0.909724	+	0.376820i	−0.121773	+	0.992558i	$0.538858\pi$
$642$		0			0
$643$	−13.4557	−	32.4849i	−0.530641	−	1.28108i	−0.931100	−	0.364765i	$-0.881149\pi$
$643$	−13.4557	−	32.4849i	−0.530641	−	1.28108i	0.400459	−	0.916315i	$-0.368851\pi$
$644$		0			0
$645$	−7.17611			−0.282559
$646$		0			0
$647$	28.0142			1.10135			0.550677	−	0.834719i	$-0.314370\pi$
$647$	28.0142			1.10135			0.550677	+	0.834719i	$0.314370\pi$
$648$		0			0
$649$	4.61793	+	11.1487i	0.181269	+	0.437623i
$650$		0			0
$651$	−11.7145	+	4.85229i	−0.459127	+	0.190176i
$652$		0			0
$653$	34.8057	+	14.4170i	1.36205	+	0.564181i	0.939622	−	0.342213i	$-0.111177\pi$
$653$	34.8057	+	14.4170i	1.36205	+	0.564181i	0.422432	+	0.906395i	$0.361177\pi$
$654$		0			0
$655$	−3.81496	+	3.81496i	−0.149063	+	0.149063i
$656$		0			0
$657$	−0.140917	+	0.340203i	−0.00549768	+	0.0132726i
$658$		0			0
$659$		−	13.5356i		−	0.527272i	−0.964622	−	0.263636i	$-0.915078\pi$
$659$		−	13.5356i		−	0.527272i	0.964622	−	0.263636i	$-0.0849217\pi$
$660$		0			0
$661$	−1.41864	−	1.41864i	−0.0551787	−	0.0551787i	0.678979	−	0.734158i	$-0.262423\pi$
$661$	−1.41864	−	1.41864i	−0.0551787	−	0.0551787i	−0.734158	+	0.678979i	$0.762423\pi$
$662$		0			0
$663$	3.63087	−	16.5513i	0.141011	−	0.642799i
$664$		0			0
$665$	12.3840	+	12.3840i	0.480233	+	0.480233i
$666$		0			0
$667$			20.6547i			0.799752i
$668$		0			0
$669$	10.0063	−	24.1573i	0.386865	−	0.933974i
$670$		0			0
$671$	3.46400	−	3.46400i	0.133726	−	0.133726i
$672$		0			0
$673$	15.4873	+	6.41506i	0.596992	+	0.247282i	0.660656	−	0.750689i	$-0.270278\pi$
$673$	15.4873	+	6.41506i	0.596992	+	0.247282i	−0.0636633	+	0.997971i	$0.520278\pi$
$674$		0			0
$675$	−0.613126	+	0.253965i	−0.0235992	+	0.00977512i
$676$		0			0
$677$	8.82649	+	21.3090i	0.339230	+	0.818973i	0.997790	+	0.0664448i	$0.0211656\pi$
$677$	8.82649	+	21.3090i	0.339230	+	0.818973i	−0.658561	+	0.752528i	$0.728834\pi$
$678$		0			0
$679$	−3.31446			−0.127197
$680$		0			0
$681$	10.9746			0.420546
$682$		0			0
$683$	−10.7220	−	25.8852i	−0.410265	−	0.990468i	−0.985066	−	0.172175i	$-0.944921\pi$
$683$	−10.7220	−	25.8852i	−0.410265	−	0.990468i	0.574801	−	0.818293i	$-0.305079\pi$
$684$		0			0
$685$	−29.3745	+	12.1673i	−1.12234	+	0.464890i
$686$		0			0
$687$	13.3844	+	5.54401i	0.510647	+	0.211517i
$688$		0			0
$689$	−11.5117	+	11.5117i	−0.438562	+	0.438562i
$690$		0			0
$691$	−10.2085	+	24.6455i	−0.388350	+	0.937560i	0.601940	+	0.798542i	$0.294395\pi$
$691$	−10.2085	+	24.6455i	−0.388350	+	0.937560i	−0.990290	+	0.139019i	$0.955605\pi$
$692$		0			0
$693$			1.84776i			0.0701906i
$694$		0			0
$695$	−5.95194	−	5.95194i	−0.225770	−	0.225770i
$696$		0			0
$697$	42.1457	−	26.9812i	1.59638	−	1.02199i
$698$		0			0
$699$	13.5043	+	13.5043i	0.510781	+	0.510781i
$700$		0			0
$701$		−	9.75054i		−	0.368273i	−0.982901	−	0.184136i	$-0.941051\pi$
$701$		−	9.75054i		−	0.368273i	0.982901	−	0.184136i	$-0.0589488\pi$
$702$		0			0
$703$	−10.2630	+	24.7771i	−0.387077	+	0.934488i
$704$		0			0
$705$	−2.31090	+	2.31090i	−0.0870334	+	0.0870334i
$706$		0			0
$707$	2.71485	+	1.12453i	0.102102	+	0.0422922i
$708$		0			0
$709$	26.5647	−	11.0035i	0.997659	−	0.413244i	0.176721	−	0.984261i	$-0.443451\pi$
$709$	26.5647	−	11.0035i	0.997659	−	0.413244i	0.820938	+	0.571017i	$0.193451\pi$
$710$		0			0
$711$	−1.03893	−	2.50819i	−0.0389628	−	0.0940646i
$712$		0			0
$713$	33.9797			1.27255
$714$		0			0
$715$	12.8081			0.478994
$716$		0			0
$717$	0.283557	+	0.684567i	0.0105896	+	0.0255656i
$718$		0			0
$719$	−43.6299	+	18.0721i	−1.62712	+	0.673976i	−0.994905	−	0.100816i	$-0.967855\pi$
$719$	−43.6299	+	18.0721i	−1.62712	+	0.673976i	−0.632216	+	0.774792i	$0.717855\pi$
$720$		0			0
$721$	15.1603	+	6.27960i	0.564599	+	0.233865i
$722$		0			0
$723$	15.1050	−	15.1050i	0.561762	−	0.561762i
$724$		0			0
$725$	−1.58541	+	3.82752i	−0.0588808	+	0.142151i
$726$		0			0
$727$		−	27.7790i		−	1.03027i	−0.857110	−	0.515134i	$-0.827742\pi$
$727$		−	27.7790i		−	1.03027i	0.857110	−	0.515134i	$-0.172258\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	−2.49830	−	13.9872i	−0.0924030	−	0.517336i
$732$		0			0
$733$	3.81122	+	3.81122i	0.140770	+	0.140770i	0.773980	−	0.633210i	$-0.218263\pi$
$733$	3.81122	+	3.81122i	0.140770	+	0.140770i	−0.633210	+	0.773980i	$0.718263\pi$
$734$		0			0
$735$		−	11.4025i		−	0.420588i
$736$		0			0
$737$	1.21219	−	2.92648i	0.0446515	−	0.107798i
$738$		0			0
$739$	2.55818	−	2.55818i	0.0941043	−	0.0941043i	−0.658487	−	0.752592i	$-0.728803\pi$
$739$	2.55818	−	2.55818i	0.0941043	−	0.0941043i	0.752592	+	0.658487i	$0.228803\pi$
$740$		0			0
$741$	25.8646	+	10.7135i	0.950160	+	0.393569i
$742$		0			0
$743$	5.71326	−	2.36651i	0.209599	−	0.0868188i	−0.275414	−	0.961326i	$-0.588815\pi$
$743$	5.71326	−	2.36651i	0.209599	−	0.0868188i	0.485013	+	0.874507i	$0.338815\pi$
$744$		0			0
$745$	−14.4413	−	34.8644i	−0.529088	−	1.27733i
$746$		0			0
$747$	14.4138			0.527375
$748$		0			0
$749$	16.1396			0.589730
$750$		0			0
$751$	19.6438	+	47.4243i	0.716812	+	1.73054i	0.682233	+	0.731135i	$0.261009\pi$
$751$	19.6438	+	47.4243i	0.716812	+	1.73054i	0.0345787	+	0.999402i	$0.488991\pi$
$752$		0			0
$753$	−0.867355	+	0.359270i	−0.0316082	+	0.0130925i
$754$		0			0
$755$	10.1414	+	4.20071i	0.369084	+	0.152879i
$756$		0			0
$757$	−2.71352	+	2.71352i	−0.0986246	+	0.0986246i	−0.754698	−	0.656073i	$-0.772216\pi$
$757$	−2.71352	+	2.71352i	−0.0986246	+	0.0986246i	0.656073	+	0.754698i	$0.272216\pi$
$758$		0			0
$759$	1.89495	−	4.57481i	0.0687822	−	0.166055i
$760$		0			0
$761$			16.5850i			0.601206i	0.953749	+	0.300603i	$0.0971878\pi$
$761$			16.5850i			0.601206i	−0.953749	+	0.300603i	$0.902812\pi$
$762$		0			0
$763$	−0.834842	−	0.834842i	−0.0302233	−	0.0302233i
$764$		0			0
$765$	4.62925	+	7.23105i	0.167371	+	0.261439i
$766$		0			0
$767$	23.4314	+	23.4314i	0.846059	+	0.846059i
$768$		0			0
$769$		−	27.7826i		−	1.00187i	−0.865486	−	0.500933i	$-0.832990\pi$
$769$		−	27.7826i		−	1.00187i	0.865486	−	0.500933i	$-0.167010\pi$
$770$		0			0
$771$	6.05760	−	14.6243i	0.218159	−	0.526683i
$772$		0			0
$773$	−9.86475	+	9.86475i	−0.354810	+	0.354810i	−0.861896	−	0.507085i	$-0.830723\pi$
$773$	−9.86475	+	9.86475i	−0.354810	+	0.354810i	0.507085	+	0.861896i	$0.330723\pi$
$774$		0			0
$775$	6.29679	+	2.60822i	0.226187	+	0.0936899i
$776$		0			0
$777$	−4.49068	+	1.86010i	−0.161102	+	0.0667307i
$778$		0			0
$779$	31.6396	+	76.3847i	1.13361	+	2.73677i
$780$		0			0
$781$	−0.339169			−0.0121364
$782$		0			0
$783$	6.24264			0.223094
$784$		0			0
$785$	3.03087	+	7.31717i	0.108176	+	0.261161i
$786$		0			0
$787$	−3.90992	+	1.61954i	−0.139373	+	0.0577304i	−0.451280	−	0.892382i	$-0.649032\pi$
$787$	−3.90992	+	1.61954i	−0.139373	+	0.0577304i	0.311907	+	0.950113i	$0.399032\pi$
$788$		0			0
$789$	10.5851	+	4.38451i	0.376841	+	0.156093i
$790$		0			0
$791$	7.53372	−	7.53372i	0.267868	−	0.267868i
$792$		0			0
$793$	5.14800	−	12.4284i	0.182811	−	0.441344i
$794$		0			0
$795$		−	8.24906i		−	0.292564i
$796$		0			0
$797$	−19.6224	−	19.6224i	−0.695059	−	0.695059i	0.268281	−	0.963341i	$-0.413544\pi$
$797$	−19.6224	−	19.6224i	−0.695059	−	0.695059i	−0.963341	+	0.268281i	$0.913544\pi$
$798$		0			0
$799$	−5.30878	−	3.69974i	−0.187811	−	0.130887i
$800$		0			0
$801$	−9.66572	−	9.66572i	−0.341522	−	0.341522i
$802$		0			0
$803$		−	0.551099i		−	0.0194479i
$804$		0			0
$805$	3.25529	−	7.85897i	0.114734	−	0.276992i
$806$		0			0
$807$	−13.5545	+	13.5545i	−0.477141	+	0.477141i
$808$		0			0
$809$	−3.76277	−	1.55859i	−0.132292	−	0.0547971i	0.315555	−	0.948907i	$-0.397809\pi$
$809$	−3.76277	−	1.55859i	−0.132292	−	0.0547971i	−0.447847	+	0.894110i	$0.647809\pi$
$810$		0			0
$811$	5.80819	−	2.40583i	0.203953	−	0.0844802i	−0.278368	−	0.960474i	$-0.589794\pi$
$811$	5.80819	−	2.40583i	0.203953	−	0.0844802i	0.482322	+	0.875994i	$0.339794\pi$
$812$		0			0
$813$	−2.61298	−	6.30830i	−0.0916413	−	0.221242i
$814$		0			0
$815$	18.8848			0.661507
$816$		0			0
$817$	23.4749			0.821282
$818$		0			0
$819$	1.94174	+	4.68777i	0.0678499	+	0.163804i
$820$		0			0
$821$	−18.2926	+	7.57706i	−0.638418	+	0.264441i	−0.678325	−	0.734762i	$-0.737294\pi$
$821$	−18.2926	+	7.57706i	−0.638418	+	0.264441i	0.0399072	+	0.999203i	$0.487294\pi$
$822$		0			0
$823$	−10.7853	−	4.46741i	−0.375951	−	0.155724i	0.186703	−	0.982416i	$-0.440220\pi$
$823$	−10.7853	−	4.46741i	−0.375951	−	0.155724i	−0.562654	+	0.826692i	$0.690220\pi$
$824$		0			0
$825$	0.702307	−	0.702307i	0.0244512	−	0.0244512i
$826$		0			0
$827$	−5.31585	+	12.8336i	−0.184850	+	0.446268i	−0.988954	−	0.148221i	$-0.952645\pi$
$827$	−5.31585	+	12.8336i	−0.184850	+	0.446268i	0.804104	+	0.594488i	$0.202645\pi$
$828$		0			0
$829$			34.2670i			1.19014i	0.803673	+	0.595071i	$0.202876\pi$
$829$			34.2670i			1.19014i	−0.803673	+	0.595071i	$0.797124\pi$
$830$		0			0
$831$	5.74725	+	5.74725i	0.199370	+	0.199370i
$832$		0			0
$833$	22.2251	−	3.96969i	0.770053	−	0.137542i
$834$		0			0
$835$	13.0868	+	13.0868i	0.452888	+	0.452888i
$836$		0			0
$837$		−	10.2700i		−	0.354982i
$838$		0			0
$839$	9.27891	−	22.4013i	0.320344	−	0.773378i	−0.678890	−	0.734240i	$-0.737539\pi$
$839$	9.27891	−	22.4013i	0.320344	−	0.773378i	0.999234	−	0.0391379i	$-0.0124612\pi$
$840$		0			0
$841$	7.05025	−	7.05025i	0.243112	−	0.243112i
$842$		0			0
$843$	10.7235	+	4.44182i	0.369337	+	0.152984i
$844$		0			0
$845$	7.48369	−	3.09985i	0.257447	−	0.106638i
$846$		0			0
$847$	4.13895	+	9.99231i	0.142216	+	0.343340i
$848$		0			0
$849$	−6.06404			−0.208117
$850$		0			0
$851$	13.0259			0.446523
$852$		0			0
$853$	−2.82779	−	6.82689i	−0.0968217	−	0.233748i	0.868046	−	0.496483i	$-0.165376\pi$
$853$	−2.82779	−	6.82689i	−0.0968217	−	0.233748i	−0.964868	+	0.262735i	$0.915376\pi$
$854$		0			0
$855$	−13.1055	+	5.42849i	−0.448200	+	0.185651i
$856$		0			0
$857$	7.42181	+	3.07421i	0.253524	+	0.105013i	0.505826	−	0.862635i	$-0.331188\pi$
$857$	7.42181	+	3.07421i	0.253524	+	0.105013i	−0.252302	+	0.967649i	$0.581188\pi$
$858$		0			0
$859$	−5.42119	+	5.42119i	−0.184969	+	0.184969i	−0.793517	−	0.608548i	$-0.791752\pi$
$859$	−5.42119	+	5.42119i	−0.184969	+	0.184969i	0.608548	+	0.793517i	$0.291752\pi$
$860$		0			0
$861$	−5.73445	+	13.8442i	−0.195429	+	0.471808i
$862$		0			0
$863$		−	14.4183i		−	0.490804i	−0.969421	−	0.245402i	$-0.921080\pi$
$863$		−	14.4183i		−	0.490804i	0.969421	−	0.245402i	$-0.0789200\pi$
$864$		0			0
$865$	18.0336	+	18.0336i	0.613162	+	0.613162i
$866$		0			0
$867$	−12.4827	+	11.5405i	−0.423934	+	0.391935i
$868$		0			0
$869$	2.87302	+	2.87302i	0.0974604	+	0.0974604i
$870$		0			0
$871$		−	8.69833i		−	0.294732i
$872$		0			0
$873$	1.02734	−	2.48022i	0.0347702	−	0.0839426i
$874$		0			0
$875$	10.2963	−	10.2963i	0.348079	−	0.348079i
$876$		0			0
$877$	49.7256	+	20.5970i	1.67912	+	0.695512i	0.999283	−	0.0378554i	$-0.0120526\pi$
$877$	49.7256	+	20.5970i	1.67912	+	0.695512i	0.679832	+	0.733368i	$0.262053\pi$
$878$		0			0
$879$	6.35211	−	2.63113i	0.214251	−	0.0887458i
$880$		0			0
$881$	−11.4019	−	27.5265i	−0.384138	−	0.927392i	−0.991156	−	0.132703i	$-0.957634\pi$
$881$	−11.4019	−	27.5265i	−0.384138	−	0.927392i	0.607018	−	0.794688i	$-0.292366\pi$
$882$		0			0
$883$	−28.2666			−0.951247			−0.475624	−	0.879649i	$-0.657778\pi$
$883$	−28.2666			−0.951247			−0.475624	+	0.879649i	$0.657778\pi$
$884$		0			0
$885$	−16.7905			−0.564405
$886$		0			0
$887$	9.61176	+	23.2049i	0.322731	+	0.779143i	0.999093	+	0.0425732i	$0.0135556\pi$
$887$	9.61176	+	23.2049i	0.322731	+	0.779143i	−0.676362	+	0.736569i	$0.736444\pi$
$888$		0			0
$889$	16.1384	−	6.68474i	0.541265	−	0.224199i
$890$		0			0
$891$	−1.38268	−	0.572726i	−0.0463216	−	0.0191871i
$892$		0			0
$893$	7.55953	−	7.55953i	0.252970	−	0.252970i
$894$		0			0
$895$	8.46088	−	20.4264i	0.282816	−	0.682779i
$896$		0			0
$897$		−	13.5976i		−	0.454012i
$898$		0			0
$899$	−45.3339	−	45.3339i	−1.51197	−	1.51197i
$900$		0			0
$901$	16.0785	−	2.87184i	0.535654	−	0.0956748i
$902$		0			0
$903$	3.00850	+	3.00850i	0.100116	+	0.100116i
$904$		0			0
$905$			34.4166i			1.14405i
$906$		0			0
$907$	18.7895	−	45.3619i	0.623895	−	1.50622i	−0.223199	−	0.974773i	$-0.571650\pi$
$907$	18.7895	−	45.3619i	0.623895	−	1.50622i	0.847094	−	0.531443i	$-0.178350\pi$
$908$		0			0
$909$	−1.68297	+	1.68297i	−0.0558207	+	0.0558207i
$910$		0			0
$911$	7.36911	+	3.05238i	0.244149	+	0.101130i	0.501403	−	0.865214i	$-0.332817\pi$
$911$	7.36911	+	3.05238i	0.244149	+	0.101130i	−0.257253	+	0.966344i	$0.582817\pi$
$912$		0			0
$913$	−19.9298	+	8.25518i	−0.659579	+	0.273207i
$914$		0			0
$915$	2.60848	+	6.29743i	0.0862337	+	0.208187i
$916$		0			0
$917$	3.19875			0.105632
$918$		0			0
$919$	−19.8027			−0.653229			−0.326615	−	0.945158i	$-0.605908\pi$
$919$	−19.8027			−0.653229			−0.326615	+	0.945158i	$0.605908\pi$
$920$		0			0
$921$	8.51282	+	20.5518i	0.280507	+	0.677204i
$922$		0			0
$923$	−0.860474	+	0.356420i	−0.0283228	+	0.0117317i
$924$		0			0
$925$	2.41384	+	0.999845i	0.0793666	+	0.0328747i
$926$		0			0
$927$	−9.39809	+	9.39809i	−0.308674	+	0.308674i
$928$		0			0
$929$	2.13327	−	5.15017i	0.0699903	−	0.168972i	−0.885013	−	0.465566i	$-0.845851\pi$
$929$	2.13327	−	5.15017i	0.0699903	−	0.168972i	0.955004	+	0.296594i	$0.0958509\pi$
$930$		0			0
$931$			37.3005i			1.22248i
$932$		0			0
$933$	3.82843	+	3.82843i	0.125337	+	0.125337i
$934$		0			0
$935$	−10.5422	−	7.34696i	−0.344767	−	0.240271i
$936$		0			0
$937$	−0.281833	−	0.281833i	−0.00920709	−	0.00920709i	0.702488	−	0.711695i	$-0.252072\pi$
$937$	−0.281833	−	0.281833i	−0.00920709	−	0.00920709i	−0.711695	+	0.702488i	$0.752072\pi$
$938$		0			0
$939$			11.2945i			0.368582i
$940$		0			0
$941$	1.64878	−	3.98050i	0.0537486	−	0.129760i	−0.894724	−	0.446619i	$-0.852628\pi$
$941$	1.64878	−	3.98050i	0.0537486	−	0.129760i	0.948473	+	0.316858i	$0.102628\pi$
$942$		0			0
$943$	28.3955	−	28.3955i	0.924683	−	0.924683i
$944$		0			0
$945$	−2.37529	−	0.983875i	−0.0772680	−	0.0320055i
$946$		0			0
$947$	−10.5466	+	4.36856i	−0.342720	+	0.141959i	−0.547403	−	0.836869i	$-0.684384\pi$
$947$	−10.5466	+	4.36856i	−0.342720	+	0.141959i	0.204683	+	0.978828i	$0.434384\pi$
$948$		0			0
$949$	−0.579129	−	1.39814i	−0.0187993	−	0.0453856i
$950$		0			0
$951$	−18.4520			−0.598346
$952$		0			0
$953$	−40.8932			−1.32466			−0.662330	−	0.749213i	$-0.730432\pi$
$953$	−40.8932			−1.32466			−0.662330	+	0.749213i	$0.730432\pi$
$954$		0			0
$955$	−9.57608	−	23.1187i	−0.309875	−	0.748103i
$956$		0			0
$957$	−8.63160	+	3.57532i	−0.279020	+	0.115574i
$958$		0			0
$959$	17.4159	+	7.21391i	0.562389	+	0.232949i
$960$		0			0
$961$	−52.6600	+	52.6600i	−1.69871	+	1.69871i
$962$		0			0
$963$	−5.00260	+	12.0773i	−0.161206	+	0.389187i
$964$		0			0
$965$			22.3197i			0.718498i
$966$		0			0
$967$	−16.6407	−	16.6407i	−0.535130	−	0.535130i	0.386965	−	0.922095i	$-0.373524\pi$
$967$	−16.6407	−	16.6407i	−0.535130	−	0.535130i	−0.922095	+	0.386965i	$0.873524\pi$
$968$		0			0
$969$	−15.1435	−	23.6546i	−0.486478	−	0.759896i
$970$		0			0
$971$	4.55476	+	4.55476i	0.146169	+	0.146169i	0.776404	−	0.630235i	$-0.217042\pi$
$971$	4.55476	+	4.55476i	0.146169	+	0.146169i	−0.630235	+	0.776404i	$0.717042\pi$
$972$		0			0
$973$			4.99055i			0.159990i
$974$		0			0
$975$	1.04373	−	2.51978i	0.0334261	−	0.0806976i
$976$		0			0
$977$	12.6200	−	12.6200i	0.403750	−	0.403750i	−0.475802	−	0.879552i	$-0.657842\pi$
$977$	12.6200	−	12.6200i	0.403750	−	0.403750i	0.879552	+	0.475802i	$0.157842\pi$
$978$		0			0
$979$	18.9004	+	7.82882i	0.604061	+	0.250210i
$980$		0			0
$981$	0.883480	−	0.365949i	0.0282073	−	0.0116839i
$982$		0			0
$983$	−9.22941	−	22.2818i	−0.294372	−	0.710678i	−0.999998	−	0.00209283i	$-0.999334\pi$
$983$	−9.22941	−	22.2818i	−0.294372	−	0.710678i	0.705625	−	0.708585i	$-0.250666\pi$
$984$		0			0
$985$	6.59899			0.210261
$986$		0			0
$987$	1.93763			0.0616755
$988$		0			0
$989$	−4.36331	−	10.5340i	−0.138745	−	0.334961i
$990$		0			0
$991$	−22.3633	+	9.26319i	−0.710394	+	0.294255i	−0.708468	−	0.705743i	$-0.750613\pi$
$991$	−22.3633	+	9.26319i	−0.710394	+	0.294255i	−0.00192659	+	0.999998i	$0.500613\pi$
$992$		0			0
$993$	5.32714	+	2.20657i	0.169052	+	0.0700235i
$994$		0			0
$995$	−20.1355	+	20.1355i	−0.638338	+	0.638338i
$996$		0			0
$997$	14.1268	−	34.1051i	0.447400	−	1.08012i	−0.525892	−	0.850551i	$-0.676268\pi$
$997$	14.1268	−	34.1051i	0.447400	−	1.08012i	0.973292	−	0.229569i	$-0.0737315\pi$
$998$		0			0
$999$		−	3.93694i		−	0.124559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bq.a.49.1		8
4.3	odd	2		51.2.h.a.49.2	yes	8
12.11	even	2		153.2.l.e.100.1		8
17.8	even	8	inner	816.2.bq.a.433.1		8
68.3	even	16		867.2.d.e.577.6		8
68.7	even	16		867.2.e.h.616.2		8
68.11	even	16		867.2.e.i.829.3		8
68.15	odd	8		867.2.h.f.757.1		8
68.19	odd	8		867.2.h.b.757.1		8
68.23	even	16		867.2.e.h.829.3		8
68.27	even	16		867.2.e.i.616.2		8
68.31	even	16		867.2.d.e.577.5		8
68.39	even	16		867.2.a.m.1.2		4
68.43	odd	8		867.2.h.g.688.2		8
68.47	odd	4		867.2.h.f.733.1		8
68.55	odd	4		867.2.h.b.733.1		8
68.59	odd	8		51.2.h.a.25.2	✓	8
68.63	even	16		867.2.a.n.1.2		4
68.67	odd	2		867.2.h.g.712.2		8
204.59	even	8		153.2.l.e.127.1		8
204.107	odd	16		2601.2.a.bc.1.3		4
204.131	odd	16		2601.2.a.bd.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.2	✓	8	68.59	odd	8
51.2.h.a.49.2	yes	8	4.3	odd	2
153.2.l.e.100.1		8	12.11	even	2
153.2.l.e.127.1		8	204.59	even	8
816.2.bq.a.49.1		8	1.1	even	1	trivial
816.2.bq.a.433.1		8	17.8	even	8	inner
867.2.a.m.1.2		4	68.39	even	16
867.2.a.n.1.2		4	68.63	even	16
867.2.d.e.577.5		8	68.31	even	16
867.2.d.e.577.6		8	68.3	even	16
867.2.e.h.616.2		8	68.7	even	16
867.2.e.h.829.3		8	68.23	even	16
867.2.e.i.616.2		8	68.27	even	16
867.2.e.i.829.3		8	68.11	even	16
867.2.h.b.733.1		8	68.55	odd	4
867.2.h.b.757.1		8	68.19	odd	8
867.2.h.f.733.1		8	68.47	odd	4
867.2.h.f.757.1		8	68.15	odd	8
867.2.h.g.688.2		8	68.43	odd	8
867.2.h.g.712.2		8	68.67	odd	2
2601.2.a.bc.1.3		4	204.107	odd	16
2601.2.a.bd.1.3		4	204.131	odd	16

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bq (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{3} +(-1.92388 + 0.796897i) q^{5} +(1.14065 + 0.472474i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.572726 - 1.38268i) q^{11} -4.10973i q^{13} +(1.47247 + 1.47247i) q^{15} +(-2.35743 + 3.38268i) q^{17} +(-4.81684 - 4.81684i) q^{19} -1.23463i q^{21} +(-1.26616 + 3.05679i) q^{23} +(-0.469266 + 0.469266i) q^{25} +(0.923880 + 0.382683i) q^{27} +(5.76745 - 2.38896i) q^{29} +(-3.93015 - 9.48822i) q^{31} -1.49661 q^{33} -2.57099 q^{35} +(-1.50660 - 3.63726i) q^{37} +(-3.79690 + 1.57273i) q^{39} +(-11.2132 - 4.64466i) q^{41} +(-2.43675 + 2.43675i) q^{43} +(0.796897 - 1.92388i) q^{45} +1.56940i q^{47} +(-3.87189 - 3.87189i) q^{49} +(4.02734 + 0.883480i) q^{51} +(-2.80109 - 2.80109i) q^{53} +3.11652i q^{55} +(-2.60685 + 6.29350i) q^{57} +(-5.70144 + 5.70144i) q^{59} +(3.02413 + 1.25264i) q^{61} +(-1.14065 + 0.472474i) q^{63} +(3.27503 + 7.90663i) q^{65} +2.11652 q^{67} +3.30864 q^{69} +(-0.0867259 - 0.209375i) q^{71} +(0.340203 - 0.140917i) q^{73} +(0.613126 + 0.253965i) q^{75} +(1.30656 - 1.30656i) q^{77} +(-1.03893 + 2.50819i) q^{79} -1.00000i q^{81} +(-10.1921 - 10.1921i) q^{83} +(1.83975 - 8.38650i) q^{85} +(-4.41421 - 4.41421i) q^{87} +13.6694i q^{89} +(1.94174 - 4.68777i) q^{91} +(-7.26197 + 7.26197i) q^{93} +(13.1055 + 5.42849i) q^{95} +(-2.48022 + 1.02734i) q^{97} +(0.572726 + 1.38268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} - 8 q^{11} - 8 q^{17} + 8 q^{19} - 8 q^{23} - 16 q^{25} - 8 q^{31} + 8 q^{33} - 32 q^{35} - 8 q^{37} - 16 q^{39} - 24 q^{41} + 8 q^{43} - 8 q^{45} - 8 q^{49} - 32 q^{53} - 16 q^{57} - 16 q^{59}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^11 - 8 * q^17 + 8 * q^19 - 8 * q^23 - 16 * q^25 - 8 * q^31 + 8 * q^33 - 32 * q^35 - 8 * q^37 - 16 * q^39 - 24 * q^41 + 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^53 - 16 * q^57 - 16 * q^59 + 16 * q^61 + 24 * q^65 + 16 * q^67 - 24 * q^69 + 16 * q^71 + 48 * q^73 - 16 * q^75 - 32 * q^83 + 40 * q^85 - 24 * q^87 + 16 * q^91 - 32 * q^93 + 40 * q^95 + 8 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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