LMFDB - Embedded newform 403.2.i.a.216.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(216,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("403.216");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			216.17
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194750 + 0.194750i) q^{2} -2.63371i q^{3} -1.92414i q^{4} +(-1.36075 - 1.36075i) q^{5} +(0.512915 - 0.512915i) q^{6} +(2.99770 - 2.99770i) q^{7} +(0.764228 - 0.764228i) q^{8} -3.93641 q^{9} +O(q^{10})$	\(q+(0.194750 + 0.194750i) q^{2} -2.63371i q^{3} -1.92414i q^{4} +(-1.36075 - 1.36075i) q^{5} +(0.512915 - 0.512915i) q^{6} +(2.99770 - 2.99770i) q^{7} +(0.764228 - 0.764228i) q^{8} -3.93641 q^{9} -0.530014i q^{10} +(3.48429 + 3.48429i) q^{11} -5.06763 q^{12} +(-1.60689 + 3.22768i) q^{13} +1.16760 q^{14} +(-3.58383 + 3.58383i) q^{15} -3.55062 q^{16} -0.413323 q^{17} +(-0.766617 - 0.766617i) q^{18} +(4.50258 + 4.50258i) q^{19} +(-2.61829 + 2.61829i) q^{20} +(-7.89505 - 7.89505i) q^{21} +1.35713i q^{22} +3.06839 q^{23} +(-2.01275 - 2.01275i) q^{24} -1.29670i q^{25} +(-0.941533 + 0.315650i) q^{26} +2.46623i q^{27} +(-5.76800 - 5.76800i) q^{28} +4.58669i q^{29} -1.39590 q^{30} +(5.50231 + 0.851251i) q^{31} +(-2.21994 - 2.21994i) q^{32} +(9.17660 - 9.17660i) q^{33} +(-0.0804947 - 0.0804947i) q^{34} -8.15825 q^{35} +7.57422i q^{36} +(-7.20858 - 7.20858i) q^{37} +1.75376i q^{38} +(8.50076 + 4.23206i) q^{39} -2.07985 q^{40} +(4.32777 + 4.32777i) q^{41} -3.07513i q^{42} -3.02545 q^{43} +(6.70428 - 6.70428i) q^{44} +(5.35649 + 5.35649i) q^{45} +(0.597570 + 0.597570i) q^{46} +(-6.54570 + 6.54570i) q^{47} +9.35130i q^{48} -10.9724i q^{49} +(0.252532 - 0.252532i) q^{50} +1.08857i q^{51} +(6.21052 + 3.09188i) q^{52} +9.85799i q^{53} +(-0.480299 + 0.480299i) q^{54} -9.48252i q^{55} -4.58185i q^{56} +(11.8585 - 11.8585i) q^{57} +(-0.893259 + 0.893259i) q^{58} +(6.57971 - 6.57971i) q^{59} +(6.89580 + 6.89580i) q^{60} +2.16166i q^{61} +(0.905794 + 1.23736i) q^{62} +(-11.8002 + 11.8002i) q^{63} +6.23658i q^{64} +(6.57865 - 2.20550i) q^{65} +3.57429 q^{66} +(-6.35941 - 6.35941i) q^{67} +0.795293i q^{68} -8.08124i q^{69} +(-1.58882 - 1.58882i) q^{70} +(-0.606704 - 0.606704i) q^{71} +(-3.00832 + 3.00832i) q^{72} +(1.11107 + 1.11107i) q^{73} -2.80774i q^{74} -3.41512 q^{75} +(8.66362 - 8.66362i) q^{76} +20.8897 q^{77} +(0.831330 + 2.47972i) q^{78} -10.5572i q^{79} +(4.83152 + 4.83152i) q^{80} -5.31390 q^{81} +1.68567i q^{82} +(-6.04727 + 6.04727i) q^{83} +(-15.1912 + 15.1912i) q^{84} +(0.562431 + 0.562431i) q^{85} +(-0.589208 - 0.589208i) q^{86} +12.0800 q^{87} +5.32559 q^{88} +(-2.14431 - 2.14431i) q^{89} +2.08635i q^{90} +(4.85865 + 14.4926i) q^{91} -5.90402i q^{92} +(2.24195 - 14.4915i) q^{93} -2.54955 q^{94} -12.2538i q^{95} +(-5.84667 + 5.84667i) q^{96} +(-6.88665 - 6.88665i) q^{97} +(2.13687 - 2.13687i) q^{98} +(-13.7156 - 13.7156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.194750	+	0.194750i	0.137709	+	0.137709i	0.772601	−	0.634892i	$-0.218955\pi$
$2$	0.194750	+	0.194750i	0.137709	+	0.137709i	−0.634892	+	0.772601i	$0.718955\pi$
$3$		−	2.63371i		−	1.52057i	−0.649589	−	0.760286i	$-0.725059\pi$
$3$		−	2.63371i		−	1.52057i	0.649589	−	0.760286i	$-0.274941\pi$
$4$		−	1.92414i		−	0.962072i
$5$	−1.36075	−	1.36075i	−0.608548	−	0.608548i	0.334019	−	0.942566i	$-0.391595\pi$
$5$	−1.36075	−	1.36075i	−0.608548	−	0.608548i	−0.942566	+	0.334019i	$0.891595\pi$
$6$	0.512915	−	0.512915i	0.209397	−	0.209397i
$7$	2.99770	−	2.99770i	1.13302	−	1.13302i	0.143351	−	0.989672i	$-0.454212\pi$
$7$	2.99770	−	2.99770i	1.13302	−	1.13302i	0.989672	−	0.143351i	$-0.0457877\pi$
$8$	0.764228	−	0.764228i	0.270195	−	0.270195i
$9$	−3.93641			−1.31214
$10$		−	0.530014i		−	0.167605i
$11$	3.48429	+	3.48429i	1.05055	+	1.05055i	0.998652	+	0.0519007i	$0.0165279\pi$
$11$	3.48429	+	3.48429i	1.05055	+	1.05055i	0.0519007	+	0.998652i	$0.483472\pi$
$12$	−5.06763			−1.46290
$13$	−1.60689	+	3.22768i	−0.445670	+	0.895197i
$13$	−1.60689	+	3.22768i	−0.445670	+	0.895197i
$14$	1.16760			0.312055
$15$	−3.58383	+	3.58383i	−0.925340	+	0.925340i
$16$	−3.55062			−0.887655
$17$	−0.413323			−0.100246			−0.0501228	−	0.998743i	$-0.515961\pi$
$17$	−0.413323			−0.100246			−0.0501228	+	0.998743i	$0.515961\pi$
$18$	−0.766617	−	0.766617i	−0.180693	−	0.180693i
$19$	4.50258	+	4.50258i	1.03296	+	1.03296i	0.999438	+	0.0335252i	$0.0106734\pi$
$19$	4.50258	+	4.50258i	1.03296	+	1.03296i	0.0335252	+	0.999438i	$0.489327\pi$
$20$	−2.61829	+	2.61829i	−0.585467	+	0.585467i
$21$	−7.89505	−	7.89505i	−1.72284	−	1.72284i
$22$			1.35713i			0.289342i
$23$	3.06839			0.639803			0.319902	−	0.947451i	$-0.396350\pi$
$23$	3.06839			0.639803			0.319902	+	0.947451i	$0.396350\pi$
$24$	−2.01275	−	2.01275i	−0.410851	−	0.410851i
$25$		−	1.29670i		−	0.259339i
$26$	−0.941533	+	0.315650i	−0.184650	+	0.0619041i
$27$			2.46623i			0.474626i
$28$	−5.76800	−	5.76800i	−1.09005	−	1.09005i
$29$			4.58669i			0.851727i	0.904787	+	0.425864i	$0.140030\pi$
$29$			4.58669i			0.851727i	−0.904787	+	0.425864i	$0.859970\pi$
$30$	−1.39590			−0.254856
$31$	5.50231	+	0.851251i	0.988243	+	0.152889i
$31$	5.50231	+	0.851251i	0.988243	+	0.152889i
$32$	−2.21994	−	2.21994i	−0.392434	−	0.392434i
$33$	9.17660	−	9.17660i	1.59744	−	1.59744i
$34$	−0.0804947	−	0.0804947i	−0.0138047	−	0.0138047i
$35$	−8.15825			−1.37900
$36$			7.57422i			1.26237i
$37$	−7.20858	−	7.20858i	−1.18508	−	1.18508i	−0.978410	−	0.206672i	$-0.933737\pi$
$37$	−7.20858	−	7.20858i	−1.18508	−	1.18508i	−0.206672	−	0.978410i	$-0.566263\pi$
$38$			1.75376i			0.284497i
$39$	8.50076	+	4.23206i	1.36121	+	0.677673i
$40$	−2.07985			−0.328854
$41$	4.32777	+	4.32777i	0.675885	+	0.675885i	0.959066	−	0.283182i	$-0.0913899\pi$
$41$	4.32777	+	4.32777i	0.675885	+	0.675885i	−0.283182	+	0.959066i	$0.591390\pi$
$42$		−	3.07513i		−	0.474502i
$43$	−3.02545			−0.461377			−0.230689	−	0.973028i	$-0.574098\pi$
$43$	−3.02545			−0.461377			−0.230689	+	0.973028i	$0.574098\pi$
$44$	6.70428	−	6.70428i	1.01071	−	1.01071i
$45$	5.35649	+	5.35649i	0.798498	+	0.798498i
$46$	0.597570	+	0.597570i	0.0881068	+	0.0881068i
$47$	−6.54570	+	6.54570i	−0.954788	+	0.954788i	−0.999021	−	0.0442329i	$-0.985916\pi$
$47$	−6.54570	+	6.54570i	−0.954788	+	0.954788i	0.0442329	+	0.999021i	$0.485916\pi$
$48$			9.35130i			1.34974i
$49$		−	10.9724i		−	1.56748i
$50$	0.252532	−	0.252532i	0.0357134	−	0.0357134i
$51$			1.08857i			0.152430i
$52$	6.21052	+	3.09188i	0.861245	+	0.428767i
$53$			9.85799i			1.35410i	0.735938	+	0.677049i	$0.236742\pi$
$53$			9.85799i			1.35410i	−0.735938	+	0.677049i	$0.763258\pi$
$54$	−0.480299	+	0.480299i	−0.0653604	+	0.0653604i
$55$		−	9.48252i		−	1.27862i
$56$		−	4.58185i		−	0.612275i
$57$	11.8585	−	11.8585i	1.57069	−	1.57069i
$58$	−0.893259	+	0.893259i	−0.117291	+	0.117291i
$59$	6.57971	−	6.57971i	0.856605	−	0.856605i	−0.134331	−	0.990936i	$-0.542889\pi$
$59$	6.57971	−	6.57971i	0.856605	−	0.856605i	0.990936	+	0.134331i	$0.0428886\pi$
$60$	6.89580	+	6.89580i	0.890244	+	0.890244i
$61$			2.16166i			0.276772i	0.990378	+	0.138386i	$0.0441915\pi$
$61$			2.16166i			0.276772i	−0.990378	+	0.138386i	$0.955808\pi$
$62$	0.905794	+	1.23736i	0.115036	+	0.157145i
$63$	−11.8002	+	11.8002i	−1.48668	+	1.48668i
$64$			6.23658i			0.779572i
$65$	6.57865	−	2.20550i	0.815982	−	0.273559i
$66$	3.57429			0.439965
$67$	−6.35941	−	6.35941i	−0.776925	−	0.776925i	0.202382	−	0.979307i	$-0.435132\pi$
$67$	−6.35941	−	6.35941i	−0.776925	−	0.776925i	−0.979307	+	0.202382i	$0.935132\pi$
$68$			0.795293i			0.0964434i
$69$		−	8.08124i		−	0.972866i
$70$	−1.58882	−	1.58882i	−0.189901	−	0.189901i
$71$	−0.606704	−	0.606704i	−0.0720025	−	0.0720025i	0.670188	−	0.742191i	$-0.266213\pi$
$71$	−0.606704	−	0.606704i	−0.0720025	−	0.0720025i	−0.742191	+	0.670188i	$0.766213\pi$
$72$	−3.00832	+	3.00832i	−0.354533	+	0.354533i
$73$	1.11107	+	1.11107i	0.130041	+	0.130041i	0.769131	−	0.639091i	$-0.220689\pi$
$73$	1.11107	+	1.11107i	0.130041	+	0.130041i	−0.639091	+	0.769131i	$0.720689\pi$
$74$		−	2.80774i		−	0.326394i
$75$	−3.41512			−0.394344
$76$	8.66362	−	8.66362i	0.993785	−	0.993785i
$77$	20.8897			2.38060
$78$	0.831330	+	2.47972i	0.0941296	+	0.280773i
$79$		−	10.5572i		−	1.18777i	−0.804549	−	0.593886i	$-0.797593\pi$
$79$		−	10.5572i		−	1.18777i	0.804549	−	0.593886i	$-0.202407\pi$
$80$	4.83152	+	4.83152i	0.540181	+	0.540181i
$81$	−5.31390			−0.590434
$82$			1.68567i			0.186151i
$83$	−6.04727	+	6.04727i	−0.663775	+	0.663775i	−0.956268	−	0.292493i	$-0.905515\pi$
$83$	−6.04727	+	6.04727i	−0.663775	+	0.663775i	0.292493	+	0.956268i	$0.405515\pi$
$84$	−15.1912	+	15.1912i	−1.65750	+	1.65750i
$85$	0.562431	+	0.562431i	0.0610042	+	0.0610042i
$86$	−0.589208	−	0.589208i	−0.0635359	−	0.0635359i
$87$	12.0800			1.29511
$88$	5.32559			0.567709
$89$	−2.14431	−	2.14431i	−0.227296	−	0.227296i	0.584266	−	0.811562i	$-0.301382\pi$
$89$	−2.14431	−	2.14431i	−0.227296	−	0.227296i	−0.811562	+	0.584266i	$0.801382\pi$
$90$			2.08635i			0.219921i
$91$	4.85865	+	14.4926i	0.509325	+	1.51923i
$92$		−	5.90402i		−	0.615537i
$93$	2.24195	−	14.4915i	0.232479	−	1.50269i
$94$	−2.54955			−0.262966
$95$		−	12.2538i		−	1.25721i
$96$	−5.84667	+	5.84667i	−0.596724	+	0.596724i
$97$	−6.88665	−	6.88665i	−0.699233	−	0.699233i	0.265012	−	0.964245i	$-0.414624\pi$
$97$	−6.88665	−	6.88665i	−0.699233	−	0.699233i	−0.964245	+	0.265012i	$0.914624\pi$
$98$	2.13687	−	2.13687i	0.215857	−	0.215857i
$99$	−13.7156	−	13.7156i	−1.37847	−	1.37847i
$100$	−2.49503			−0.249503
$101$			7.73644i			0.769805i	0.922957	+	0.384902i	$0.125765\pi$
$101$			7.73644i			0.769805i	−0.922957	+	0.384902i	$0.874235\pi$
$102$	−0.212000	+	0.212000i	−0.0209911	+	0.0209911i
$103$			11.7404i			1.15681i	0.815748	+	0.578407i	$0.196325\pi$
$103$			11.7404i			1.15681i	−0.815748	+	0.578407i	$0.803675\pi$
$104$	1.23866	+	3.69471i	0.121460	+	0.362296i
$105$			21.4864i			2.09686i
$106$	−1.91985	+	1.91985i	−0.186472	+	0.186472i
$107$	10.2057			0.986619			0.493309	−	0.869854i	$-0.335787\pi$
$107$	10.2057			0.986619			0.493309	+	0.869854i	$0.335787\pi$
$108$	4.74538			0.456625
$109$	6.57935	+	6.57935i	0.630187	+	0.630187i	0.948115	−	0.317928i	$-0.102987\pi$
$109$	6.57935	+	6.57935i	0.630187	+	0.630187i	−0.317928	+	0.948115i	$0.602987\pi$
$110$	1.84672	−	1.84672i	0.176078	−	0.176078i
$111$	−18.9853	+	18.9853i	−1.80200	+	1.80200i
$112$	−10.6437	+	10.6437i	−1.00573	+	1.00573i
$113$	−3.29736			−0.310190			−0.155095	−	0.987900i	$-0.549568\pi$
$113$	−3.29736			−0.310190			−0.155095	+	0.987900i	$0.549568\pi$
$114$	4.61888			0.432598
$115$	−4.17532	−	4.17532i	−0.389351	−	0.389351i
$116$	8.82546			0.819423
$117$	6.32536	−	12.7055i	0.584780	−	1.17462i
$118$	2.56280			0.235925
$119$	−1.23902	+	1.23902i	−0.113580	+	0.113580i
$120$			5.47772i			0.500045i
$121$			13.2806i			1.20732i
$122$	−0.420984	+	0.420984i	−0.0381141	+	0.0381141i
$123$	11.3981	−	11.3981i	1.02773	−	1.02773i
$124$	1.63793	−	10.5872i	0.147090	−	0.950762i
$125$	−8.56826	+	8.56826i	−0.766368	+	0.766368i
$126$	−4.59617			−0.409459
$127$	−2.59345			−0.230132			−0.115066	−	0.993358i	$-0.536708\pi$
$127$	−2.59345			−0.230132			−0.115066	+	0.993358i	$0.536708\pi$
$128$	−5.65446	+	5.65446i	−0.499788	+	0.499788i
$129$			7.96816i			0.701557i
$130$	1.71072	+	0.851672i	0.150040	+	0.0746966i
$131$	20.0120			1.74845			0.874226	−	0.485519i	$-0.161369\pi$
$131$	20.0120			1.74845			0.874226	+	0.485519i	$0.161369\pi$
$132$	−17.6571	−	17.6571i	−1.53685	−	1.53685i
$133$	26.9947			2.34074
$134$		−	2.47699i		−	0.213980i
$135$	3.35593	−	3.35593i	0.288833	−	0.288833i
$136$	−0.315873	+	0.315873i	−0.0270859	+	0.0270859i
$137$	−9.31610	−	9.31610i	−0.795928	−	0.795928i	0.186523	−	0.982451i	$-0.440278\pi$
$137$	−9.31610	−	9.31610i	−0.795928	−	0.795928i	−0.982451	+	0.186523i	$0.940278\pi$
$138$	1.57382	−	1.57382i	0.133973	−	0.133973i
$139$			3.90431i			0.331159i	0.986196	+	0.165579i	$0.0529494\pi$
$139$			3.90431i			0.331159i	−0.986196	+	0.165579i	$0.947051\pi$
$140$			15.6977i			1.32669i
$141$	17.2395	+	17.2395i	1.45182	+	1.45182i
$142$		−	0.236311i		−	0.0198308i
$143$	−16.8450	+	5.64732i	−1.40865	+	0.472253i
$144$	13.9767			1.16473
$145$	6.24136	−	6.24136i	0.518317	−	0.518317i
$146$			0.432761i			0.0358156i
$147$	−28.8980			−2.38347
$148$	−13.8703	+	13.8703i	−1.14014	+	1.14014i
$149$	0.826473	+	0.826473i	0.0677073	+	0.0677073i	0.740150	−	0.672442i	$-0.234755\pi$
$149$	0.826473	+	0.826473i	0.0677073	+	0.0677073i	−0.672442	+	0.740150i	$0.734755\pi$
$150$	−0.665096	−	0.665096i	−0.0543048	−	0.0543048i
$151$	−3.55683	−	3.55683i	−0.289450	−	0.289450i	0.547412	−	0.836863i	$-0.315613\pi$
$151$	−3.55683	−	3.55683i	−0.289450	−	0.289450i	−0.836863	+	0.547412i	$0.815613\pi$
$152$	6.88200			0.558204
$153$	1.62701			0.131536
$154$	4.06827	+	4.06827i	0.327831	+	0.327831i
$155$	−6.32894	−	8.64563i	−0.508353	−	0.694434i
$156$	8.14310	−	16.3567i	0.651970	−	1.30958i
$157$	−3.21565			−0.256637			−0.128318	−	0.991733i	$-0.540958\pi$
$157$	−3.21565			−0.256637			−0.128318	+	0.991733i	$0.540958\pi$
$158$	2.05601	−	2.05601i	0.163567	−	0.163567i
$159$	25.9630			2.05900
$160$			6.04159i			0.477629i
$161$	9.19810	−	9.19810i	0.724912	−	0.724912i
$162$	−1.03488	−	1.03488i	−0.0813082	−	0.0813082i
$163$	5.69502	−	5.69502i	0.446068	−	0.446068i	−0.447977	−	0.894045i	$-0.647855\pi$
$163$	5.69502	−	5.69502i	0.446068	−	0.446068i	0.894045	+	0.447977i	$0.147855\pi$
$164$	8.32726	−	8.32726i	0.650250	−	0.650250i
$165$	−24.9742			−1.94424
$166$	−2.35542			−0.182816
$167$	−16.9780	−	16.9780i	−1.31380	−	1.31380i	−0.918592	−	0.395208i	$-0.870673\pi$
$167$	−16.9780	−	16.9780i	−1.31380	−	1.31380i	−0.395208	−	0.918592i	$-0.629327\pi$
$168$	−12.0672			−0.931008
$169$	−7.83584	−	10.3730i	−0.602757	−	0.797925i
$170$			0.219067i			0.0168017i
$171$	−17.7240	−	17.7240i	−1.35539	−	1.35539i
$172$			5.82141i			0.443878i
$173$		−	2.14152i		−	0.162817i	−0.996681	−	0.0814085i	$-0.974058\pi$
$173$		−	2.14152i		−	0.162817i	0.996681	−	0.0814085i	$-0.0259418\pi$
$174$	2.35258	+	2.35258i	0.178349	+	0.178349i
$175$	−3.88710	−	3.88710i	−0.293837	−	0.293837i
$176$	−12.3714	−	12.3714i	−0.932529	−	0.932529i
$177$	−17.3290	−	17.3290i	−1.30253	−	1.30253i
$178$		−	0.835210i		−	0.0626016i
$179$	−7.60449			−0.568386			−0.284193	−	0.958767i	$-0.591726\pi$
$179$	−7.60449			−0.568386			−0.284193	+	0.958767i	$0.591726\pi$
$180$	10.3067	−	10.3067i	0.768213	−	0.768213i
$181$	1.54735			0.115013			0.0575067	−	0.998345i	$-0.481685\pi$
$181$	1.54735			0.115013			0.0575067	+	0.998345i	$0.481685\pi$
$182$	−1.87621	+	3.76865i	−0.139074	+	0.279351i
$183$	5.69318			0.420852
$184$	2.34495	−	2.34495i	0.172872	−	0.172872i
$185$			19.6182i			1.44236i
$186$	3.25884	−	2.38560i	0.238949	−	0.174920i
$187$	−1.44014	−	1.44014i	−0.105313	−	0.105313i
$188$	12.5949	+	12.5949i	0.918575	+	0.918575i
$189$	7.39301	+	7.39301i	0.537762	+	0.537762i
$190$	2.38643	−	2.38643i	0.173130	−	0.173130i
$191$	−11.9190			−0.862429			−0.431214	−	0.902250i	$-0.641915\pi$
$191$	−11.9190			−0.862429			−0.431214	+	0.902250i	$0.641915\pi$
$192$	16.4253			1.18539
$193$	6.47109	−	6.47109i	0.465799	−	0.465799i	−0.434751	−	0.900551i	$-0.643164\pi$
$193$	6.47109	−	6.47109i	0.465799	−	0.465799i	0.900551	+	0.434751i	$0.143164\pi$
$194$		−	2.68235i		−	0.192582i
$195$	−5.80865	−	17.3262i	−0.415966	−	1.24076i
$196$	−21.1124			−1.50803
$197$	19.0282	−	19.0282i	1.35570	−	1.35570i	0.476556	−	0.879144i	$-0.341885\pi$
$197$	19.0282	−	19.0282i	1.35570	−	1.35570i	0.879144	−	0.476556i	$-0.158115\pi$
$198$		−	5.34223i		−	0.379656i
$199$	9.74460			0.690777			0.345388	−	0.938460i	$-0.387747\pi$
$199$	9.74460			0.690777			0.345388	+	0.938460i	$0.387747\pi$
$200$	−0.990973	−	0.990973i	−0.0700723	−	0.0700723i
$201$	−16.7488	+	16.7488i	−1.18137	+	1.18137i
$202$	−1.50667	+	1.50667i	−0.106009	+	0.106009i
$203$	13.7495	+	13.7495i	0.965026	+	0.965026i
$204$	2.09457			0.146649
$205$		−	11.7781i		−	0.822616i
$206$	−2.28644	+	2.28644i	−0.159304	+	0.159304i
$207$	−12.0784			−0.839509
$208$	5.70544	−	11.4603i	0.395601	−	0.794627i
$209$			31.3766i			2.17036i
$210$	−4.18449	+	4.18449i	−0.288757	+	0.288757i
$211$	−14.2073			−0.978068			−0.489034	−	0.872265i	$-0.662651\pi$
$211$	−14.2073			−0.978068			−0.489034	+	0.872265i	$0.662651\pi$
$212$	18.9682			1.30274
$213$	−1.59788	+	1.59788i	−0.109485	+	0.109485i
$214$	1.98756	+	1.98756i	0.135866	+	0.135866i
$215$	4.11690	+	4.11690i	0.280770	+	0.280770i
$216$	1.88476	+	1.88476i	0.128242	+	0.128242i
$217$	19.0460	−	13.9425i	1.29293	−	0.946475i
$218$			2.56266i			0.173565i
$219$	2.92623	−	2.92623i	0.197736	−	0.197736i
$220$	−18.2457			−1.23013
$221$	0.664162	−	1.33407i	0.0446764	−	0.0897395i
$222$	−7.39477			−0.496305
$223$	−4.60256	+	4.60256i	−0.308210	+	0.308210i	−0.844215	−	0.536005i	$-0.819933\pi$
$223$	−4.60256	+	4.60256i	−0.308210	+	0.308210i	0.536005	+	0.844215i	$0.319933\pi$
$224$	−13.3094			−0.889273
$225$			5.10433i			0.340289i
$226$	−0.642163	−	0.642163i	−0.0427160	−	0.0427160i
$227$	13.7098	+	13.7098i	0.909950	+	0.909950i	0.996268	−	0.0863175i	$-0.0275100\pi$
$227$	13.7098	+	13.7098i	0.909950	+	0.909950i	−0.0863175	+	0.996268i	$0.527510\pi$
$228$	−22.8174	−	22.8174i	−1.51112	−	1.51112i
$229$	8.52034	+	8.52034i	0.563040	+	0.563040i	0.930170	−	0.367130i	$-0.119660\pi$
$229$	8.52034	+	8.52034i	0.563040	+	0.563040i	−0.367130	+	0.930170i	$0.619660\pi$
$230$		−	1.62629i		−	0.107234i
$231$		−	55.0173i		−	3.61987i
$232$	3.50528	+	3.50528i	0.230133	+	0.230133i
$233$			15.9083i			1.04219i	0.853499	+	0.521094i	$0.174476\pi$
$233$			15.9083i			1.04219i	−0.853499	+	0.521094i	$0.825524\pi$
$234$	3.70626	−	1.24253i	0.242286	−	0.0812267i
$235$	17.8142			1.16207
$236$	−12.6603	−	12.6603i	−0.824116	−	0.824116i
$237$	−27.8044			−1.80609
$238$	−0.482598			−0.0312822
$239$	−8.51257	+	8.51257i	−0.550632	+	0.550632i	−0.926623	−	0.375991i	$-0.877302\pi$
$239$	−8.51257	+	8.51257i	−0.550632	+	0.550632i	0.375991	+	0.926623i	$0.377302\pi$
$240$	12.7248	−	12.7248i	0.821383	−	0.821383i
$241$	17.4841	+	17.4841i	1.12625	+	1.12625i	0.990781	+	0.135471i	$0.0432547\pi$
$241$	17.4841	+	17.4841i	1.12625	+	1.12625i	0.135471	+	0.990781i	$0.456745\pi$
$242$	−2.58639	+	2.58639i	−0.166260	+	0.166260i
$243$			21.3940i			1.37242i
$244$	4.15935			0.266275
$245$	−14.9307	+	14.9307i	−0.953887	+	0.953887i
$246$	4.43956			0.283056
$247$	−21.7680	+	7.29776i	−1.38507	+	0.464345i
$248$	4.85557	−	3.55447i	0.308329	−	0.225709i
$249$	15.9267	+	15.9267i	1.00932	+	1.00932i
$250$	−3.33734			−0.211072
$251$	24.7065			1.55946			0.779731	−	0.626115i	$-0.215356\pi$
$251$	24.7065			1.55946			0.779731	+	0.626115i	$0.215356\pi$
$252$	22.7052	+	22.7052i	1.43029	+	1.43029i
$253$	10.6912	+	10.6912i	0.672147	+	0.672147i
$254$	−0.505076	−	0.505076i	−0.0316913	−	0.0316913i
$255$	1.48128	−	1.48128i	0.0927612	−	0.0927612i
$256$	10.2707			0.641921
$257$		−	6.81431i		−	0.425065i	−0.977154	−	0.212533i	$-0.931829\pi$
$257$		−	6.81431i		−	0.425065i	0.977154	−	0.212533i	$-0.0681712\pi$
$258$	−1.55180	+	1.55180i	−0.0966109	+	0.0966109i
$259$	−43.2182			−2.68545
$260$	−4.24371	−	12.6583i	−0.263184	−	0.785033i
$261$		−	18.0551i		−	1.11758i
$262$	3.89733	+	3.89733i	0.240778	+	0.240778i
$263$		−	13.5652i		−	0.836466i	−0.908340	−	0.418233i	$-0.862650\pi$
$263$		−	13.5652i		−	0.836466i	0.908340	−	0.418233i	$-0.137350\pi$
$264$		−	14.0260i		−	0.863243i
$265$	13.4143	−	13.4143i	0.824034	−	0.824034i
$266$	5.25723	+	5.25723i	0.322342	+	0.322342i
$267$	−5.64748	+	5.64748i	−0.345620	+	0.345620i
$268$	−12.2364	+	12.2364i	−0.747458	+	0.747458i
$269$			10.8101i			0.659102i	0.944138	+	0.329551i	$0.106897\pi$
$269$			10.8101i			0.659102i	−0.944138	+	0.329551i	$0.893103\pi$
$270$	1.30714			0.0795499
$271$	−21.7000	−	21.7000i	−1.31818	−	1.31818i	−0.915214	−	0.402969i	$-0.867978\pi$
$271$	−21.7000	−	21.7000i	−1.31818	−	1.31818i	−0.402969	−	0.915214i	$-0.632022\pi$
$272$	1.46755			0.0889835
$273$	38.1691	−	12.7963i	2.31010	−	0.774465i
$274$		−	3.62862i		−	0.219213i
$275$	4.51807	−	4.51807i	0.272450	−	0.272450i
$276$	−15.5495			−0.935968
$277$	−16.7892			−1.00877			−0.504383	−	0.863480i	$-0.668280\pi$
$277$	−16.7892			−1.00877			−0.504383	+	0.863480i	$0.668280\pi$
$278$	−0.760365	+	0.760365i	−0.0456036	+	0.0456036i
$279$	−21.6593	−	3.35087i	−1.29671	−	0.200612i
$280$	−6.23477	+	6.23477i	−0.372599	+	0.372599i
$281$	12.2491	−	12.2491i	0.730717	−	0.730717i	−0.240045	−	0.970762i	$-0.577162\pi$
$281$	12.2491	−	12.2491i	0.730717	−	0.730717i	0.970762	+	0.240045i	$0.0771620\pi$
$282$			6.71478i			0.399859i
$283$		−	12.4088i		−	0.737629i	−0.929503	−	0.368814i	$-0.879764\pi$
$283$		−	12.4088i		−	0.737629i	0.929503	−	0.368814i	$-0.120236\pi$
$284$	−1.16739	+	1.16739i	−0.0692716	+	0.0692716i
$285$	−32.2729			−1.91168
$286$	−4.38039	−	2.18076i	−0.259018	−	0.128951i
$287$	25.9467			1.53159
$288$	8.73860	+	8.73860i	0.514927	+	0.514927i
$289$	−16.8292			−0.989951
$290$	2.43101			0.142754
$291$	−18.1374	+	18.1374i	−1.06323	+	1.06323i
$292$	2.13785	−	2.13785i	0.125108	−	0.125108i
$293$	−22.2107	+	22.2107i	−1.29756	+	1.29756i	−0.367567	+	0.929997i	$0.619809\pi$
$293$	−22.2107	+	22.2107i	−1.29756	+	1.29756i	−0.929997	+	0.367567i	$0.880191\pi$
$294$	−5.62789	−	5.62789i	−0.328225	−	0.328225i
$295$	−17.9067			−1.04257
$296$	−11.0180			−0.640408
$297$	−8.59306	+	8.59306i	−0.498620	+	0.498620i
$298$			0.321912i			0.0186478i
$299$	−4.93055	+	9.90378i	−0.285141	+	0.572750i
$300$			6.57118i			0.379388i
$301$	−9.06939	+	9.06939i	−0.522751	+	0.522751i
$302$		−	1.38539i		−	0.0797200i
$303$	20.3755			1.17054
$304$	−15.9870	−	15.9870i	−0.916915	−	0.916915i
$305$	2.94149	−	2.94149i	0.168429	−	0.168429i
$306$	0.316860	+	0.316860i	0.0181137	+	0.0181137i
$307$	0.754451	−	0.754451i	0.0430588	−	0.0430588i	−0.685250	−	0.728308i	$-0.740307\pi$
$307$	0.754451	−	0.754451i	0.0430588	−	0.0430588i	0.728308	+	0.685250i	$0.240307\pi$
$308$		−	40.1948i		−	2.29031i
$309$	30.9207			1.75902
$310$	0.451175	−	2.91630i	0.0256250	−	0.165635i
$311$			7.21076i			0.408885i	0.978879	+	0.204442i	$0.0655381\pi$
$311$			7.21076i			0.408885i	−0.978879	+	0.204442i	$0.934462\pi$
$312$	9.73079	−	3.26226i	0.550897	−	0.184689i
$313$			5.63432i			0.318471i	0.987241	+	0.159235i	$0.0509029\pi$
$313$			5.63432i			0.318471i	−0.987241	+	0.159235i	$0.949097\pi$
$314$	−0.626249	−	0.626249i	−0.0353413	−	0.0353413i
$315$	32.1142			1.80943
$316$	−20.3135			−1.14272
$317$	0.559178	+	0.559178i	0.0314066	+	0.0314066i	0.722636	−	0.691229i	$-0.242930\pi$
$317$	0.559178	+	0.559178i	0.0314066	+	0.0314066i	−0.691229	+	0.722636i	$0.742930\pi$
$318$	5.05631	+	5.05631i	0.283544	+	0.283544i
$319$	−15.9814	+	15.9814i	−0.894784	+	0.894784i
$320$	8.48645	−	8.48645i	0.474407	−	0.474407i
$321$		−	26.8787i		−	1.50022i
$322$	3.58266			0.199654
$323$	−1.86102	−	1.86102i	−0.103550	−	0.103550i
$324$			10.2247i			0.568040i
$325$	4.18532	+	2.08364i	0.232160	+	0.115580i
$326$	2.21821			0.122855
$327$	17.3281	−	17.3281i	0.958245	−	0.958245i
$328$	6.61481			0.365242
$329$			39.2440i			2.16359i
$330$	−4.86373	−	4.86373i	−0.267739	−	0.267739i
$331$	−10.0027	+	10.0027i	−0.549796	+	0.549796i	−0.926382	−	0.376586i	$-0.877098\pi$
$331$	−10.0027	+	10.0027i	−0.549796	+	0.549796i	0.376586	+	0.926382i	$0.377098\pi$
$332$	11.6358	+	11.6358i	0.638599	+	0.638599i
$333$	28.3759	+	28.3759i	1.55499	+	1.55499i
$334$		−	6.61295i		−	0.361845i
$335$			17.3072i			0.945592i
$336$	28.0323	+	28.0323i	1.52929	+	1.52929i
$337$	21.5814			1.17562			0.587808	−	0.809001i	$-0.299991\pi$
$337$	21.5814			1.17562			0.587808	+	0.809001i	$0.299991\pi$
$338$	0.494118	−	3.54618i	0.0268765	−	0.192887i
$339$			8.68429i			0.471666i
$340$	1.08220	−	1.08220i	0.0586904	−	0.0586904i
$341$	16.2056	+	22.1376i	0.877584	+	1.19882i
$342$		−	6.90351i		−	0.373299i
$343$	−11.9079	−	11.9079i	−0.642969	−	0.642969i
$344$	−2.31214	+	2.31214i	−0.124662	+	0.124662i
$345$	−10.9966	+	10.9966i	−0.592036	+	0.592036i
$346$	0.417062	−	0.417062i	0.0224214	−	0.0224214i
$347$			10.5626i			0.567029i	0.958968	+	0.283515i	$0.0915004\pi$
$347$			10.5626i			0.567029i	−0.958968	+	0.283515i	$0.908500\pi$
$348$		−	23.2437i		−	1.24599i
$349$	12.3154	−	12.3154i	0.659227	−	0.659227i	−0.295971	−	0.955197i	$-0.595643\pi$
$349$	12.3154	−	12.3154i	0.659227	−	0.659227i	0.955197	+	0.295971i	$0.0956430\pi$
$350$		−	1.51403i		−	0.0809283i
$351$	−7.96020	−	3.96295i	−0.424884	−	0.211527i
$352$		−	15.4698i		−	0.824545i
$353$	−1.06701	+	1.06701i	−0.0567911	+	0.0567911i	−0.734932	−	0.678141i	$-0.762786\pi$
$353$	−1.06701	+	1.06701i	−0.0567911	+	0.0567911i	0.678141	+	0.734932i	$0.262786\pi$
$354$		−	6.74966i		−	0.358741i
$355$			1.65115i			0.0876339i
$356$	−4.12596	+	4.12596i	−0.218675	+	0.218675i
$357$	3.26321	+	3.26321i	0.172707	+	0.172707i
$358$	−1.48098	−	1.48098i	−0.0782720	−	0.0782720i
$359$	−1.75015	+	1.75015i	−0.0923694	+	0.0923694i	−0.751782	−	0.659412i	$-0.770805\pi$
$359$	−1.75015	+	1.75015i	−0.0923694	+	0.0923694i	0.659412	+	0.751782i	$0.270805\pi$
$360$	8.18716			0.431501
$361$			21.5465i			1.13403i
$362$	0.301346	+	0.301346i	0.0158384	+	0.0158384i
$363$	34.9771			1.83582
$364$	27.8858	−	9.34875i	1.46161	−	0.490007i
$365$		−	3.02378i		−	0.158272i
$366$	1.10875	+	1.10875i	0.0579552	+	0.0579552i
$367$			28.5767i			1.49169i	0.666119	+	0.745846i	$0.267954\pi$
$367$			28.5767i			1.49169i	−0.666119	+	0.745846i	$0.732046\pi$
$368$	−10.8947			−0.567925
$369$	−17.0359	−	17.0359i	−0.886853	−	0.886853i
$370$	−3.82065	+	3.82065i	−0.198626	+	0.198626i
$371$	29.5513	+	29.5513i	1.53422	+	1.53422i
$372$	−27.8837	−	4.31383i	−1.44570	−	0.223662i
$373$	1.61896			0.0838265			0.0419132	−	0.999121i	$-0.486655\pi$
$373$	1.61896			0.0838265			0.0419132	+	0.999121i	$0.486655\pi$
$374$		−	0.560934i		−	0.0290052i
$375$	22.5663	+	22.5663i	1.16532	+	1.16532i
$376$			10.0048i			0.515959i
$377$	−14.8044	−	7.37029i	−0.762464	−	0.379589i
$378$			2.87958i			0.148110i
$379$	11.3175	+	11.3175i	0.581339	+	0.581339i	0.935271	−	0.353932i	$-0.115156\pi$
$379$	11.3175	+	11.3175i	0.581339	+	0.581339i	−0.353932	+	0.935271i	$0.615156\pi$
$380$	−23.5781			−1.20953
$381$			6.83039i			0.349932i
$382$	−2.32123	−	2.32123i	−0.118764	−	0.118764i
$383$	13.8254	−	13.8254i	0.706447	−	0.706447i	−0.259339	−	0.965786i	$-0.583505\pi$
$383$	13.8254	−	13.8254i	0.706447	−	0.706447i	0.965786	+	0.259339i	$0.0835048\pi$
$384$	14.8922	+	14.8922i	0.759963	+	0.759963i
$385$	−28.4257	−	28.4257i	−1.44871	−	1.44871i
$386$	2.52049			0.128290
$387$	11.9094			0.605390
$388$	−13.2509	+	13.2509i	−0.672713	+	0.672713i
$389$	−23.2207			−1.17733			−0.588667	−	0.808375i	$-0.700347\pi$
$389$	−23.2207			−1.17733			−0.588667	+	0.808375i	$0.700347\pi$
$390$	2.24306	−	4.50553i	0.113582	−	0.228146i
$391$	−1.26824			−0.0641374
$392$	−8.38539	−	8.38539i	−0.423526	−	0.423526i
$393$		−	52.7056i		−	2.65865i
$394$	7.41148			0.373385
$395$	−14.3657	+	14.3657i	−0.722816	+	0.722816i
$396$	−26.3908	+	26.3908i	−1.32619	+	1.32619i
$397$	2.81313	−	2.81313i	0.141187	−	0.141187i	−0.632981	−	0.774168i	$-0.718169\pi$
$397$	2.81313	−	2.81313i	0.141187	−	0.141187i	0.774168	+	0.632981i	$0.218169\pi$
$398$	1.89776	+	1.89776i	0.0951263	+	0.0951263i
$399$		−	71.0962i		−	3.55926i
$400$			4.60408i			0.230204i
$401$	−11.9998	−	11.9998i	−0.599241	−	0.599241i	0.340870	−	0.940110i	$-0.389278\pi$
$401$	−11.9998	−	11.9998i	−0.599241	−	0.599241i	−0.940110	+	0.340870i	$0.889278\pi$
$402$	−6.52367			−0.325371
$403$	−11.5891	+	16.3918i	−0.577296	+	0.816535i
$404$	14.8860			0.740608
$405$	7.23092	+	7.23092i	0.359307	+	0.359307i
$406$			5.35544i			0.265786i
$407$		−	50.2335i		−	2.48998i
$408$	0.831917	+	0.831917i	0.0411860	+	0.0411860i
$409$	13.7145	−	13.7145i	0.678137	−	0.678137i	−0.281441	−	0.959578i	$-0.590812\pi$
$409$	13.7145	−	13.7145i	0.678137	−	0.678137i	0.959578	+	0.281441i	$0.0908124\pi$
$410$	2.29378	−	2.29378i	0.113282	−	0.113282i
$411$	−24.5359	+	24.5359i	−1.21027	+	1.21027i
$412$	22.5902			1.11294
$413$		−	39.4479i		−	1.94111i
$414$	−2.35228	−	2.35228i	−0.115608	−	0.115608i
$415$	16.4577			0.807877
$416$	10.7325	−	3.59807i	0.526202	−	0.176410i
$417$	10.2828			0.503551
$418$	−6.11060	+	6.11060i	−0.298879	+	0.298879i
$419$	−10.0853			−0.492699			−0.246350	−	0.969181i	$-0.579231\pi$
$419$	−10.0853			−0.492699			−0.246350	+	0.969181i	$0.579231\pi$
$420$	41.3430			2.01733
$421$	−4.64169	−	4.64169i	−0.226222	−	0.226222i	0.584890	−	0.811112i	$-0.301138\pi$
$421$	−4.64169	−	4.64169i	−0.226222	−	0.226222i	−0.811112	+	0.584890i	$0.801138\pi$
$422$	−2.76687	−	2.76687i	−0.134689	−	0.134689i
$423$	25.7666	−	25.7666i	1.25281	−	1.25281i
$424$	7.53375	+	7.53375i	0.365871	+	0.365871i
$425$			0.535954i			0.0259976i
$426$	−0.622375			−0.0301542
$427$	6.48000	+	6.48000i	0.313589	+	0.313589i
$428$		−	19.6372i		−	0.949198i
$429$	14.8734	+	44.3649i	0.718094	+	2.14196i
$430$			1.60353i			0.0773293i
$431$	14.1097	+	14.1097i	0.679642	+	0.679642i	0.959919	−	0.280277i	$-0.0904265\pi$
$431$	14.1097	+	14.1097i	0.679642	+	0.679642i	−0.280277	+	0.959919i	$0.590426\pi$
$432$		−	8.75665i		−	0.421305i
$433$	31.2168			1.50018			0.750092	−	0.661333i	$-0.230009\pi$
$433$	31.2168			1.50018			0.750092	+	0.661333i	$0.230009\pi$
$434$	6.42452	+	0.993925i	0.308387	+	0.0477099i
$435$	−16.4379	−	16.4379i	−0.788137	−	0.788137i
$436$	12.6596	−	12.6596i	0.606286	−	0.606286i
$437$	13.8157	+	13.8157i	0.660893	+	0.660893i
$438$	1.13977			0.0544601
$439$		−	11.7574i		−	0.561150i	−0.959832	−	0.280575i	$-0.909475\pi$
$439$		−	11.7574i		−	0.561150i	0.959832	−	0.280575i	$-0.0905251\pi$
$440$	−7.24681	−	7.24681i	−0.345478	−	0.345478i
$441$			43.1917i			2.05675i
$442$	0.389157	−	0.130465i	0.0185103	−	0.00620561i
$443$	−16.6981			−0.793351			−0.396676	−	0.917959i	$-0.629836\pi$
$443$	−16.6981			−0.793351			−0.396676	+	0.917959i	$0.629836\pi$
$444$	36.5304	+	36.5304i	1.73366	+	1.73366i
$445$			5.83575i			0.276641i
$446$	−1.79270			−0.0848868
$447$	2.17669	−	2.17669i	0.102954	−	0.102954i
$448$	18.6954	+	18.6954i	0.883273	+	0.883273i
$449$	−7.33563	−	7.33563i	−0.346190	−	0.346190i	0.512498	−	0.858688i	$-0.328720\pi$
$449$	−7.33563	−	7.33563i	−0.346190	−	0.346190i	−0.858688	+	0.512498i	$0.828720\pi$
$450$	−0.994070	+	0.994070i	−0.0468609	+	0.0468609i
$451$			30.1584i			1.42011i
$452$			6.34461i			0.298425i
$453$	−9.36764	+	9.36764i	−0.440130	+	0.440130i
$454$			5.33997i			0.250617i
$455$	13.1094	−	26.3322i	0.614577	−	1.23447i
$456$		−	18.1252i		−	0.848789i
$457$	3.88650	−	3.88650i	0.181803	−	0.181803i	−0.610338	−	0.792141i	$-0.708966\pi$
$457$	3.88650	−	3.88650i	0.181803	−	0.181803i	0.792141	+	0.610338i	$0.208966\pi$
$458$			3.31868i			0.155072i
$459$		−	1.01935i		−	0.0475792i
$460$	−8.03392	+	8.03392i	−0.374584	+	0.374584i
$461$	−28.6537	+	28.6537i	−1.33454	+	1.33454i	−0.433274	+	0.901262i	$0.642642\pi$
$461$	−28.6537	+	28.6537i	−1.33454	+	1.33454i	−0.901262	+	0.433274i	$0.857358\pi$
$462$	10.7146	−	10.7146i	0.498490	−	0.498490i
$463$	18.0529	+	18.0529i	0.838990	+	0.838990i	0.988726	−	0.149736i	$-0.0478424\pi$
$463$	18.0529	+	18.0529i	0.838990	+	0.838990i	−0.149736	+	0.988726i	$0.547842\pi$
$464$		−	16.2856i		−	0.756040i
$465$	−22.7700	+	16.6686i	−1.05594	+	0.772987i
$466$	−3.09815	+	3.09815i	−0.143519	+	0.143519i
$467$			14.9155i			0.690209i	0.938564	+	0.345105i	$0.112157\pi$
$467$			14.9155i			0.690209i	−0.938564	+	0.345105i	$0.887843\pi$
$468$	−24.4472	−	12.1709i	−1.13007	−	0.562600i
$469$	−38.1271			−1.76055
$470$	3.46932	+	3.46932i	0.160028	+	0.160028i
$471$			8.46908i			0.390235i
$472$		−	10.0568i		−	0.462902i
$473$	−10.5416	−	10.5416i	−0.484701	−	0.484701i
$474$	−5.41492	−	5.41492i	−0.248716	−	0.248716i
$475$	5.83848	−	5.83848i	0.267888	−	0.267888i
$476$	2.38405	+	2.38405i	0.109273	+	0.109273i
$477$		−	38.8051i		−	1.77676i
$478$	−3.31565			−0.151654
$479$	1.63460	−	1.63460i	0.0746866	−	0.0746866i	−0.668777	−	0.743463i	$-0.733182\pi$
$479$	1.63460	−	1.63460i	0.0746866	−	0.0746866i	0.743463	+	0.668777i	$0.233182\pi$
$480$	15.9118			0.726270
$481$	34.8503	−	11.6836i	1.58904	−	0.532727i
$482$			6.81008i			0.310191i
$483$	−24.2251	−	24.2251i	−1.10228	−	1.10228i
$484$	25.5537			1.16153
$485$			18.7421i			0.851034i
$486$	−4.16648	+	4.16648i	−0.188995	+	0.188995i
$487$	20.9261	−	20.9261i	0.948254	−	0.948254i	−0.0504712	−	0.998726i	$-0.516072\pi$
$487$	20.9261	−	20.9261i	0.948254	−	0.948254i	0.998726	+	0.0504712i	$0.0160723\pi$
$488$	1.65200	+	1.65200i	0.0747827	+	0.0747827i
$489$	−14.9990	−	14.9990i	−0.678279	−	0.678279i
$490$	−5.81551			−0.262718
$491$	−4.58589			−0.206958			−0.103479	−	0.994632i	$-0.532997\pi$
$491$	−4.58589			−0.206958			−0.103479	+	0.994632i	$0.532997\pi$
$492$	−21.9316	−	21.9316i	−0.988751	−	0.988751i
$493$		−	1.89578i		−	0.0853818i
$494$	−5.66057	−	2.81809i	−0.254681	−	0.126792i
$495$			37.3271i			1.67773i
$496$	−19.5366	−	3.02247i	−0.877220	−	0.135713i
$497$	−3.63743			−0.163161
$498$			6.20348i			0.277984i
$499$	0.898596	−	0.898596i	0.0402267	−	0.0402267i	−0.686707	−	0.726934i	$-0.740945\pi$
$499$	0.898596	−	0.898596i	0.0402267	−	0.0402267i	0.726934	+	0.686707i	$0.240945\pi$
$500$	16.4866	+	16.4866i	0.737302	+	0.737302i
$501$	−44.7152	+	44.7152i	−1.99773	+	1.99773i
$502$	4.81160	+	4.81160i	0.214752	+	0.214752i
$503$	−30.8780			−1.37678			−0.688392	−	0.725339i	$-0.741683\pi$
$503$	−30.8780			−1.37678			−0.688392	+	0.725339i	$0.741683\pi$
$504$			18.0360i			0.803389i
$505$	10.5274	−	10.5274i	0.468463	−	0.468463i
$506$			4.16421i			0.185122i
$507$	−27.3195	+	20.6373i	−1.21330	+	0.916535i
$508$			4.99018i			0.221403i
$509$	9.55500	−	9.55500i	0.423518	−	0.423518i	−0.462895	−	0.886413i	$-0.653189\pi$
$509$	9.55500	−	9.55500i	0.423518	−	0.423518i	0.886413	+	0.462895i	$0.153189\pi$
$510$	0.576958			0.0255481
$511$	6.66128			0.294678
$512$	13.3091	+	13.3091i	0.588187	+	0.588187i
$513$	−11.1044	+	11.1044i	−0.490271	+	0.490271i
$514$	1.32709	−	1.32709i	0.0585354	−	0.0585354i
$515$	15.9758	−	15.9758i	0.703976	−	0.703976i
$516$	15.3319			0.674949
$517$	−45.6142			−2.00611
$518$	−8.41676	−	8.41676i	−0.369811	−	0.369811i
$519$	−5.64014			−0.247575
$520$	3.34209	−	6.71310i	0.146560	−	0.294389i
$521$	4.08096			0.178790			0.0893951	−	0.995996i	$-0.471507\pi$
$521$	4.08096			0.178790			0.0893951	+	0.995996i	$0.471507\pi$
$522$	3.51624	−	3.51624i	0.153901	−	0.153901i
$523$		−	4.95819i		−	0.216806i	−0.994107	−	0.108403i	$-0.965426\pi$
$523$		−	4.95819i		−	0.216806i	0.994107	−	0.108403i	$-0.0345737\pi$
$524$		−	38.5059i		−	1.68214i
$525$	−10.2375	+	10.2375i	−0.446801	+	0.446801i
$526$	2.64183	−	2.64183i	0.115189	−	0.115189i
$527$	−2.27423	−	0.351842i	−0.0990670	−	0.0153265i
$528$	−32.5826	+	32.5826i	−1.41798	+	1.41798i
$529$	−13.5850			−0.590652
$530$	5.22488			0.226954
$531$	−25.9004	+	25.9004i	−1.12398	+	1.12398i
$532$		−	51.9418i		−	2.25196i
$533$	−20.9229	+	7.01443i	−0.906272	+	0.303829i
$534$	−2.19970			−0.0951902
$535$	−13.8874	−	13.8874i	−0.600404	−	0.600404i
$536$	−9.72007			−0.419843
$537$			20.0280i			0.864272i
$538$	−2.10527	+	2.10527i	−0.0907644	+	0.0907644i
$539$	38.2309	−	38.2309i	1.64672	−	1.64672i
$540$	−6.45730	−	6.45730i	−0.277878	−	0.277878i
$541$	3.84406	−	3.84406i	0.165269	−	0.165269i	−0.619627	−	0.784896i	$-0.712716\pi$
$541$	3.84406	−	3.84406i	0.165269	−	0.165269i	0.784896	+	0.619627i	$0.212716\pi$
$542$		−	8.45217i		−	0.363052i
$543$		−	4.07526i		−	0.174886i
$544$	0.917552	+	0.917552i	0.0393397	+	0.0393397i
$545$		−	17.9058i		−	0.766998i
$546$	9.92553	+	4.94138i	0.424773	+	0.211471i
$547$	21.0159			0.898574			0.449287	−	0.893388i	$-0.351678\pi$
$547$	21.0159			0.898574			0.449287	+	0.893388i	$0.351678\pi$
$548$	−17.9255	+	17.9255i	−0.765740	+	0.765740i
$549$		−	8.50919i		−	0.363163i
$550$	1.75979			0.0750377
$551$	−20.6519	+	20.6519i	−0.879803	+	0.879803i
$552$	−6.17591	−	6.17591i	−0.262864	−	0.262864i
$553$	−31.6471	−	31.6471i	−1.34577	−	1.34577i
$554$	−3.26971	−	3.26971i	−0.138916	−	0.138916i
$555$	51.6686			2.19321
$556$	7.51245			0.318599
$557$	8.89931	+	8.89931i	0.377076	+	0.377076i	0.870046	−	0.492970i	$-0.164089\pi$
$557$	8.89931	+	8.89931i	0.377076	+	0.377076i	−0.492970	+	0.870046i	$0.664089\pi$
$558$	−3.56558	−	4.87075i	−0.150943	−	0.206195i
$559$	4.86156	−	9.76520i	0.205622	−	0.413024i
$560$	28.9669			1.22407
$561$	−3.79290	+	3.79290i	−0.160136	+	0.160136i
$562$	4.77101			0.201253
$563$		−	6.59108i		−	0.277781i	−0.990308	−	0.138890i	$-0.955646\pi$
$563$		−	6.59108i		−	0.277781i	0.990308	−	0.138890i	$-0.0443536\pi$
$564$	33.1712	−	33.1712i	1.39676	−	1.39676i
$565$	4.48690	+	4.48690i	0.188765	+	0.188765i
$566$	2.41662	−	2.41662i	0.101578	−	0.101578i
$567$	−15.9295	+	15.9295i	−0.668975	+	0.668975i
$568$	−0.927320			−0.0389095
$569$	−27.1705			−1.13905			−0.569523	−	0.821975i	$-0.692872\pi$
$569$	−27.1705			−1.13905			−0.569523	+	0.821975i	$0.692872\pi$
$570$	−6.28517	−	6.28517i	−0.263257	−	0.263257i
$571$	−27.6478			−1.15703			−0.578513	−	0.815673i	$-0.696367\pi$
$571$	−27.6478			−1.15703			−0.578513	+	0.815673i	$0.696367\pi$
$572$	10.8663	+	32.4123i	0.454341	+	1.35523i
$573$			31.3912i			1.31138i
$574$	5.05313	+	5.05313i	0.210913	+	0.210913i
$575$		−	3.97877i		−	0.165926i
$576$		−	24.5497i		−	1.02291i
$577$	2.11865	+	2.11865i	0.0882004	+	0.0882004i	0.749830	−	0.661630i	$-0.230135\pi$
$577$	2.11865	+	2.11865i	0.0882004	+	0.0882004i	−0.661630	+	0.749830i	$0.730135\pi$
$578$	−3.27748	−	3.27748i	−0.136325	−	0.136325i
$579$	−17.0430	−	17.0430i	−0.708281	−	0.708281i
$580$	−12.0093	−	12.0093i	−0.498658	−	0.498658i
$581$			36.2558i			1.50414i
$582$	−7.06453			−0.292834
$583$	−34.3481	+	34.3481i	−1.42255	+	1.42255i
$584$	1.69822			0.0702728
$585$	−25.8963	+	8.68177i	−1.07068	+	0.358947i
$586$	−8.65109			−0.357373
$587$	7.96073	−	7.96073i	0.328575	−	0.328575i	−0.523470	−	0.852044i	$-0.675363\pi$
$587$	7.96073	−	7.96073i	0.328575	−	0.328575i	0.852044	+	0.523470i	$0.175363\pi$
$588$			55.6039i			2.29307i
$589$	20.9418	+	28.6074i	0.862890	+	1.17875i
$590$	−3.48734	−	3.48734i	−0.143572	−	0.143572i
$591$	−50.1146	−	50.1146i	−2.06144	−	2.06144i
$592$	25.5949	+	25.5949i	1.05195	+	1.05195i
$593$	15.4050	−	15.4050i	0.632609	−	0.632609i	−0.316112	−	0.948722i	$-0.602378\pi$
$593$	15.4050	−	15.4050i	0.632609	−	0.632609i	0.948722	+	0.316112i	$0.102378\pi$
$594$	−3.34700			−0.137329
$595$	3.37199			0.138238
$596$	1.59025	−	1.59025i	0.0651393	−	0.0651393i
$597$		−	25.6644i		−	1.05037i
$598$	−2.88899	+	0.968538i	−0.118140	+	0.0396065i
$599$	−4.63032			−0.189190			−0.0945948	−	0.995516i	$-0.530156\pi$
$599$	−4.63032			−0.189190			−0.0945948	+	0.995516i	$0.530156\pi$
$600$	−2.60993	+	2.60993i	−0.106550	+	0.106550i
$601$			21.3452i			0.870688i	0.900264	+	0.435344i	$0.143373\pi$
$601$			21.3452i			0.870688i	−0.900264	+	0.435344i	$0.856627\pi$
$602$	−3.53253			−0.143975
$603$	25.0332	+	25.0332i	1.01943	+	1.01943i
$604$	−6.84385	+	6.84385i	−0.278472	+	0.278472i
$605$	18.0716	−	18.0716i	0.734714	−	0.734714i
$606$	3.96814	+	3.96814i	0.161195	+	0.161195i
$607$	0.427442			0.0173493			0.00867466	−	0.999962i	$-0.497239\pi$
$607$	0.427442			0.0173493			0.00867466	+	0.999962i	$0.497239\pi$
$608$		−	19.9909i		−	0.810739i
$609$	36.2122	−	36.2122i	1.46739	−	1.46739i
$610$	1.14571			0.0463885
$611$	−10.6092	−	31.6456i	−0.429204	−	1.28024i
$612$		−	3.13060i		−	0.126547i
$613$	30.9704	−	30.9704i	1.25088	−	1.25088i	0.295557	−	0.955325i	$-0.404495\pi$
$613$	30.9704	−	30.9704i	1.25088	−	1.25088i	0.955325	−	0.295557i	$-0.0955052\pi$
$614$	0.293859			0.0118592
$615$	−31.0200			−1.25085
$616$	15.9645	−	15.9645i	0.643228	−	0.643228i
$617$	−0.406300	−	0.406300i	−0.0163570	−	0.0163570i	0.698881	−	0.715238i	$-0.253682\pi$
$617$	−0.406300	−	0.406300i	−0.0163570	−	0.0163570i	−0.715238	+	0.698881i	$0.753682\pi$
$618$	6.02182	+	6.02182i	0.242233	+	0.242233i
$619$	−24.3597	−	24.3597i	−0.979099	−	0.979099i	0.0206874	−	0.999786i	$-0.493415\pi$
$619$	−24.3597	−	24.3597i	−0.979099	−	0.979099i	−0.999786	+	0.0206874i	$0.993415\pi$
$620$	−16.6354	+	12.1778i	−0.668095	+	0.489072i
$621$			7.56735i			0.303667i
$622$	−1.40430	+	1.40430i	−0.0563072	+	0.0563072i
$623$	−12.8560			−0.515064
$624$	−30.1830	−	15.0265i	−1.20829	−	0.601540i
$625$	16.8351			0.673404
$626$	−1.09729	+	1.09729i	−0.0438564	+	0.0438564i
$627$	82.6368			3.30019
$628$			6.18738i			0.246903i
$629$	2.97947	+	2.97947i	0.118799	+	0.118799i
$630$	6.25426	+	6.25426i	0.249176	+	0.249176i
$631$	5.12699	+	5.12699i	0.204102	+	0.204102i	0.801755	−	0.597653i	$-0.203900\pi$
$631$	5.12699	+	5.12699i	0.204102	+	0.204102i	−0.597653	+	0.801755i	$0.703900\pi$
$632$	−8.06807	−	8.06807i	−0.320931	−	0.320931i
$633$			37.4177i			1.48722i
$634$			0.217800i			0.00864996i
$635$	3.52905	+	3.52905i	0.140046	+	0.140046i
$636$		−	49.9567i		−	1.98091i
$637$	35.4153	+	17.6313i	1.40320	+	0.698579i
$638$	−6.22475			−0.246440
$639$	2.38823	+	2.38823i	0.0944771	+	0.0944771i
$640$	15.3887			0.608290
$641$	28.2517			1.11588			0.557938	−	0.829882i	$-0.311593\pi$
$641$	28.2517			1.11588			0.557938	+	0.829882i	$0.311593\pi$
$642$	5.23464	−	5.23464i	0.206595	−	0.206595i
$643$	11.8106	−	11.8106i	0.465764	−	0.465764i	−0.434775	−	0.900539i	$-0.643172\pi$
$643$	11.8106	−	11.8106i	0.465764	−	0.465764i	0.900539	+	0.434775i	$0.143172\pi$
$644$	−17.6985	−	17.6985i	−0.697417	−	0.697417i
$645$	10.8427	−	10.8427i	0.426931	−	0.426931i
$646$		−	0.724868i		−	0.0285196i
$647$	−38.4470			−1.51151			−0.755754	−	0.654855i	$-0.772730\pi$
$647$	−38.4470			−1.51151			−0.755754	+	0.654855i	$0.772730\pi$
$648$	−4.06104	+	4.06104i	−0.159533	+	0.159533i
$649$	45.8512			1.79982
$650$	0.409303	+	1.22088i	0.0160542	+	0.0478870i
$651$	−36.7203	−	50.1617i	−1.43918	−	1.96599i
$652$	−10.9580	−	10.9580i	−0.429150	−	0.429150i
$653$	−37.0747			−1.45085			−0.725423	−	0.688303i	$-0.758356\pi$
$653$	−37.0747			−1.45085			−0.725423	+	0.688303i	$0.758356\pi$
$654$	6.74930			0.263918
$655$	−27.2313	−	27.2313i	−1.06402	−	1.06402i
$656$	−15.3663	−	15.3663i	−0.599953	−	0.599953i
$657$	−4.37362	−	4.37362i	−0.170631	−	0.170631i
$658$	−7.64279	+	7.64279i	−0.297947	+	0.297947i
$659$	1.98131			0.0771807			0.0385904	−	0.999255i	$-0.487713\pi$
$659$	1.98131			0.0771807			0.0385904	+	0.999255i	$0.487713\pi$
$660$			48.0539i			1.87050i
$661$	12.3563	−	12.3563i	0.480603	−	0.480603i	−0.424721	−	0.905324i	$-0.639628\pi$
$661$	12.3563	−	12.3563i	0.480603	−	0.480603i	0.905324	+	0.424721i	$0.139628\pi$
$662$	−3.89604			−0.151424
$663$	−3.51356	−	1.74921i	−0.136455	−	0.0679336i
$664$			9.24300i			0.358698i
$665$	−36.7332	−	36.7332i	−1.42445	−	1.42445i
$666$			11.0524i			0.428273i
$667$			14.0737i			0.544938i
$668$	−32.6682	+	32.6682i	−1.26397	+	1.26397i
$669$	12.1218	+	12.1218i	0.468655	+	0.468655i
$670$	−3.37058	+	3.37058i	−0.130217	+	0.130217i
$671$	−7.53186	+	7.53186i	−0.290764	+	0.290764i
$672$			35.0531i			1.35220i
$673$	40.4824			1.56048			0.780242	−	0.625478i	$-0.215096\pi$
$673$	40.4824			1.56048			0.780242	+	0.625478i	$0.215096\pi$
$674$	4.20299	+	4.20299i	0.161893	+	0.161893i
$675$	3.19795			0.123089
$676$	−19.9592	+	15.0773i	−0.767661	+	0.579896i
$677$		−	2.36655i		−	0.0909538i	−0.998965	−	0.0454769i	$-0.985519\pi$
$677$		−	2.36655i		−	0.0909538i	0.998965	−	0.0454769i	$-0.0144807\pi$
$678$	−1.69127	+	1.69127i	−0.0649528	+	0.0649528i
$679$	−41.2882			−1.58449
$680$	0.859651			0.0329661
$681$	36.1075	−	36.1075i	1.38364	−	1.38364i
$682$	−1.15526	+	7.46736i	−0.0442372	+	0.285940i
$683$	24.0562	−	24.0562i	0.920484	−	0.920484i	−0.0765792	−	0.997063i	$-0.524400\pi$
$683$	24.0562	−	24.0562i	0.920484	−	0.920484i	0.997063	+	0.0765792i	$0.0243998\pi$
$684$	−34.1036	+	34.1036i	−1.30398	+	1.30398i
$685$			25.3538i			0.968720i
$686$		−	4.63815i		−	0.177086i
$687$	22.4401	−	22.4401i	0.856142	−	0.856142i
$688$	10.7422			0.409544
$689$	−31.8184	−	15.8407i	−1.21219	−	0.603481i
$690$	−4.28317			−0.163058
$691$	−27.2315	−	27.2315i	−1.03593	−	1.03593i	−0.999330	−	0.0366042i	$-0.988346\pi$
$691$	−27.2315	−	27.2315i	−1.03593	−	1.03593i	−0.0366042	−	0.999330i	$-0.511654\pi$
$692$	−4.12060			−0.156642
$693$	−82.2304			−3.12367
$694$	−2.05707	+	2.05707i	−0.0780852	+	0.0780852i
$695$	5.31280	−	5.31280i	0.201526	−	0.201526i
$696$	9.23188	−	9.23188i	0.349933	−	0.349933i
$697$	−1.78877	−	1.78877i	−0.0677544	−	0.0677544i
$698$	4.79684			0.181563
$699$	41.8978			1.58472
$700$	−7.47935	+	7.47935i	−0.282693	+	0.282693i
$701$		−	41.3630i		−	1.56226i	−0.624370	−	0.781129i	$-0.714644\pi$
$701$		−	41.3630i		−	1.56226i	0.624370	−	0.781129i	$-0.285356\pi$
$702$	−0.778466	−	2.32204i	−0.0293813	−	0.0876397i
$703$		−	64.9144i		−	2.44829i
$704$	−21.7300	+	21.7300i	−0.818982	+	0.818982i
$705$		−	46.9173i		−	1.76701i
$706$	−0.415600			−0.0156413
$707$	23.1915	+	23.1915i	0.872206	+	0.872206i
$708$	−33.3435	+	33.3435i	−1.25313	+	1.25313i
$709$	−22.6221	−	22.6221i	−0.849591	−	0.849591i	0.140491	−	0.990082i	$-0.455132\pi$
$709$	−22.6221	−	22.6221i	−0.849591	−	0.849591i	−0.990082	+	0.140491i	$0.955132\pi$
$710$	−0.321562	+	0.321562i	−0.0120680	+	0.0120680i
$711$			41.5573i			1.55852i
$712$	−3.27748			−0.122829
$713$	16.8832	+	2.61197i	0.632281	+	0.0978190i
$714$			1.27102i			0.0475667i
$715$	30.6066	+	15.2373i	1.14462	+	0.569844i
$716$			14.6321i			0.546829i
$717$	22.4196	+	22.4196i	0.837275	+	0.837275i
$718$	−0.681685			−0.0254402
$719$	−51.2134			−1.90994			−0.954970	−	0.296704i	$-0.904113\pi$
$719$	−51.2134			−1.90994			−0.954970	+	0.296704i	$0.904113\pi$
$720$	−19.0189	−	19.0189i	−0.708791	−	0.708791i
$721$	35.1941	+	35.1941i	1.31070	+	1.31070i
$722$	−4.19618	+	4.19618i	−0.156166	+	0.156166i
$723$	46.0481	−	46.0481i	1.71255	−	1.71255i
$724$		−	2.97732i		−	0.110651i
$725$	5.94755			0.220886
$726$	6.81180	+	6.81180i	0.252809	+	0.252809i
$727$			38.2455i			1.41845i	0.704983	+	0.709224i	$0.250955\pi$
$727$			38.2455i			1.41845i	−0.704983	+	0.709224i	$0.749045\pi$
$728$	14.7887	+	7.36251i	0.548107	+	0.272873i
$729$	40.4037			1.49643
$730$	0.588882	−	0.588882i	0.0217955	−	0.0217955i
$731$	1.25049			0.0462510
$732$		−	10.9545i		−	0.404890i
$733$	−3.83160	−	3.83160i	−0.141523	−	0.141523i	0.632796	−	0.774319i	$-0.281907\pi$
$733$	−3.83160	−	3.83160i	−0.141523	−	0.141523i	−0.774319	+	0.632796i	$0.781907\pi$
$734$	−5.56532	+	5.56532i	−0.205420	+	0.205420i
$735$	39.3231	+	39.3231i	1.45045	+	1.45045i
$736$	−6.81164	−	6.81164i	−0.251080	−	0.251080i
$737$		−	44.3160i		−	1.63240i
$738$		−	6.63549i		−	0.244256i
$739$	14.1216	+	14.1216i	0.519470	+	0.519470i	0.917411	−	0.397941i	$-0.130275\pi$
$739$	14.1216	+	14.1216i	0.519470	+	0.519470i	−0.397941	+	0.917411i	$0.630275\pi$
$740$	37.7482			1.38765
$741$	19.2202	+	57.3306i	0.706070	+	2.10609i
$742$			11.5102i			0.422554i
$743$	−14.8027	+	14.8027i	−0.543057	+	0.543057i	−0.924424	−	0.381367i	$-0.875454\pi$
$743$	−14.8027	+	14.8027i	−0.543057	+	0.543057i	0.381367	+	0.924424i	$0.375454\pi$
$744$	−9.36143	−	12.7881i	−0.343206	−	0.468836i
$745$		−	2.24925i		−	0.0824062i
$746$	0.315293	+	0.315293i	0.0115437	+	0.0115437i
$747$	23.8046	−	23.8046i	0.870963	−	0.870963i
$748$	−2.77103	+	2.77103i	−0.101319	+	0.101319i
$749$	30.5935	−	30.5935i	1.11786	−	1.11786i
$750$			8.78958i			0.320950i
$751$		−	30.0177i		−	1.09536i	−0.836687	−	0.547681i	$-0.815511\pi$
$751$		−	30.0177i		−	1.09536i	0.836687	−	0.547681i	$-0.184489\pi$
$752$	23.2413	−	23.2413i	0.847523	−	0.847523i
$753$		−	65.0697i		−	2.37127i
$754$	−1.44779	−	4.31852i	−0.0527254	−	0.157271i
$755$			9.67993i			0.352289i
$756$	14.2252	−	14.2252i	0.517366	−	0.517366i
$757$			11.5458i			0.419638i	0.977740	+	0.209819i	$0.0672875\pi$
$757$			11.5458i			0.419638i	−0.977740	+	0.209819i	$0.932713\pi$
$758$			4.40816i			0.160112i
$759$	28.1574	−	28.1574i	1.02205	−	1.02205i
$760$	−9.36471	−	9.36471i	−0.339694	−	0.339694i
$761$	7.54700	+	7.54700i	0.273579	+	0.273579i	0.830539	−	0.556960i	$-0.188033\pi$
$761$	7.54700	+	7.54700i	0.273579	+	0.273579i	−0.556960	+	0.830539i	$0.688033\pi$
$762$	−1.33022	+	1.33022i	−0.0481888	+	0.0481888i
$763$	39.4458			1.42803
$764$			22.9339i			0.829719i
$765$	−2.21396	−	2.21396i	−0.0800458	−	0.0800458i
$766$	5.38502			0.194569
$767$	10.6644	+	31.8100i	0.385068	+	1.14859i
$768$		−	27.0501i		−	0.976087i
$769$	17.4594	+	17.4594i	0.629602	+	0.629602i	0.947968	−	0.318366i	$-0.103134\pi$
$769$	17.4594	+	17.4594i	0.629602	+	0.629602i	−0.318366	+	0.947968i	$0.603134\pi$
$770$		−	11.0718i		−	0.399001i
$771$	−17.9469			−0.646342
$772$	−12.4513	−	12.4513i	−0.448133	−	0.448133i
$773$	−0.319624	+	0.319624i	−0.0114961	+	0.0114961i	−0.712831	−	0.701335i	$-0.752588\pi$
$773$	−0.319624	+	0.319624i	−0.0114961	+	0.0114961i	0.701335	+	0.712831i	$0.252588\pi$
$774$	2.31936	+	2.31936i	0.0833678	+	0.0833678i
$775$	1.10381	−	7.13482i	0.0396502	−	0.256290i
$776$	−10.5259			−0.377859
$777$			113.824i			4.08342i
$778$	−4.52223	−	4.52223i	−0.162130	−	0.162130i
$779$			38.9723i			1.39633i
$780$	−33.3382	+	11.1767i	−1.19370	+	0.400189i
$781$		−	4.22786i		−	0.151285i
$782$	−0.246989	−	0.246989i	−0.00883231	−	0.00883231i
$783$	−11.3118			−0.404252
$784$			38.9587i			1.39138i
$785$	4.37571	+	4.37571i	0.156176	+	0.156176i
$786$	10.2644	−	10.2644i	0.366120	−	0.366120i
$787$	0.615690	+	0.615690i	0.0219470	+	0.0219470i	0.717995	−	0.696048i	$-0.245060\pi$
$787$	0.615690	+	0.615690i	0.0219470	+	0.0219470i	−0.696048	+	0.717995i	$0.745060\pi$
$788$	−36.6129	−	36.6129i	−1.30428	−	1.30428i
$789$	−35.7267			−1.27191
$790$	−5.59544			−0.199077
$791$	−9.88450	+	9.88450i	−0.351452	+	0.351452i
$792$	−20.9637			−0.744912
$793$	−6.97715	−	3.47354i	−0.247766	−	0.123349i
$794$	1.09572			0.0388855
$795$	−35.3293	−	35.3293i	−1.25300	−	1.25300i
$796$		−	18.7500i		−	0.664577i
$797$	−5.60890			−0.198677			−0.0993387	−	0.995054i	$-0.531673\pi$
$797$	−5.60890			−0.198677			−0.0993387	+	0.995054i	$0.531673\pi$
$798$	13.8460	−	13.8460i	0.490144	−	0.490144i
$799$	2.70549	−	2.70549i	0.0957132	−	0.0957132i
$800$	−2.87859	+	2.87859i	−0.101774	+	0.101774i
$801$	8.44088	+	8.44088i	0.298244	+	0.298244i
$802$		−	4.67392i		−	0.165042i
$803$			7.74256i			0.273229i
$804$	32.2271	+	32.2271i	1.13656	+	1.13656i
$805$	−25.0327			−0.882287
$806$	−5.44930	+	0.935323i	−0.191943	+	0.0329454i
$807$	28.4706			1.00221
$808$	5.91241	+	5.91241i	0.207998	+	0.207998i
$809$			10.8527i			0.381561i	0.981633	+	0.190781i	$0.0611019\pi$
$809$			10.8527i			0.381561i	−0.981633	+	0.190781i	$0.938898\pi$
$810$			2.81645i			0.0989598i
$811$	36.8973	+	36.8973i	1.29564	+	1.29564i	0.931244	+	0.364397i	$0.118725\pi$
$811$	36.8973	+	36.8973i	1.29564	+	1.29564i	0.364397	+	0.931244i	$0.381275\pi$
$812$	26.4560	−	26.4560i	0.928425	−	0.928425i
$813$	−57.1515	+	57.1515i	−2.00439	+	2.00439i
$814$	9.78300	−	9.78300i	0.342894	−	0.342894i
$815$	−15.4990			−0.542908
$816$		−	3.86510i		−	0.135306i
$817$	−13.6224	−	13.6224i	−0.476586	−	0.476586i
$818$	5.34180			0.186772
$819$	−19.1256	−	57.0487i	−0.668304	−	1.99344i
$820$	−22.6627			−0.791416
$821$	3.87914	−	3.87914i	0.135383	−	0.135383i	−0.636168	−	0.771551i	$-0.719481\pi$
$821$	3.87914	−	3.87914i	0.135383	−	0.135383i	0.771551	+	0.636168i	$0.219481\pi$
$822$	−9.55673			−0.333329
$823$	−53.9210			−1.87957			−0.939785	−	0.341767i	$-0.888975\pi$
$823$	−53.9210			−1.87957			−0.939785	+	0.341767i	$0.888975\pi$
$824$	8.97233	+	8.97233i	0.312566	+	0.312566i
$825$	−11.8993	−	11.8993i	−0.414279	−	0.414279i
$826$	7.68250	−	7.68250i	0.267308	−	0.267308i
$827$	−1.85617	−	1.85617i	−0.0645453	−	0.0645453i	0.674097	−	0.738643i	$-0.264533\pi$
$827$	−1.85617	−	1.85617i	−0.0645453	−	0.0645453i	−0.738643	+	0.674097i	$0.764533\pi$
$828$			23.2407i			0.807669i
$829$	50.8702			1.76680			0.883398	−	0.468624i	$-0.155250\pi$
$829$	50.8702			1.76680			0.883398	+	0.468624i	$0.155250\pi$
$830$	3.20514	+	3.20514i	0.111252	+	0.111252i
$831$			44.2179i			1.53390i
$832$	−20.1297	−	10.0215i	−0.697871	−	0.347432i
$833$			4.53513i			0.157133i
$834$	2.00258	+	2.00258i	0.0693436	+	0.0693436i
$835$			46.2059i			1.59902i
$836$	60.3731			2.08805
$837$	−2.09938	+	13.5700i	−0.0725652	+	0.469046i
$838$	−1.96412	−	1.96412i	−0.0678492	−	0.0678492i
$839$	17.3857	−	17.3857i	0.600222	−	0.600222i	−0.340150	−	0.940371i	$-0.610478\pi$
$839$	17.3857	−	17.3857i	0.600222	−	0.600222i	0.940371	+	0.340150i	$0.110478\pi$
$840$	16.4206	+	16.4206i	0.566563	+	0.566563i
$841$	7.96227			0.274561
$842$		−	1.80794i		−	0.0623058i
$843$	−32.2604	−	32.2604i	−1.11111	−	1.11111i
$844$			27.3368i			0.940972i
$845$	−3.45248	+	24.7778i	−0.118769	+	0.852382i
$846$	10.0361			0.345048
$847$	39.8111	+	39.8111i	1.36792	+	1.36792i
$848$		−	35.0020i		−	1.20197i
$849$	−32.6812			−1.12162
$850$	−0.104377	+	0.104377i	−0.00358011	+	0.00358011i
$851$	−22.1187	−	22.1187i	−0.758220	−	0.758220i
$852$	3.07455	+	3.07455i	0.105332	+	0.105332i
$853$	−19.2055	+	19.2055i	−0.657585	+	0.657585i	−0.954808	−	0.297223i	$-0.903939\pi$
$853$	−19.2055	+	19.2055i	−0.657585	+	0.657585i	0.297223	+	0.954808i	$0.403939\pi$
$854$			2.52397i			0.0863683i
$855$			48.2360i			1.64964i
$856$	7.79946	−	7.79946i	0.266580	−	0.266580i
$857$		−	27.1841i		−	0.928591i	−0.885680	−	0.464296i	$-0.846308\pi$
$857$		−	27.1841i		−	0.928591i	0.885680	−	0.464296i	$-0.153692\pi$
$858$	−5.74347	+	11.5367i	−0.196079	+	0.393855i
$859$			38.0255i			1.29741i	0.761039	+	0.648706i	$0.224690\pi$
$859$			38.0255i			1.29741i	−0.761039	+	0.648706i	$0.775310\pi$
$860$	7.92151	−	7.92151i	0.270121	−	0.270121i
$861$		−	68.3360i		−	2.32888i
$862$			5.49575i			0.187186i
$863$	22.9033	−	22.9033i	0.779636	−	0.779636i	−0.200133	−	0.979769i	$-0.564137\pi$
$863$	22.9033	−	22.9033i	0.779636	−	0.779636i	0.979769	+	0.200133i	$0.0641373\pi$
$864$	5.47489	−	5.47489i	0.186259	−	0.186259i
$865$	−2.91409	+	2.91409i	−0.0990819	+	0.0990819i
$866$	6.07948	+	6.07948i	0.206589	+	0.206589i
$867$			44.3231i			1.50529i
$868$	−26.8273	−	36.6473i	−0.910578	−	1.24389i
$869$	36.7842	−	36.7842i	1.24782	−	1.24782i
$870$		−	6.40257i		−	0.217068i
$871$	30.7450	−	10.3073i	1.04175	−	0.349249i
$872$	10.0562			0.340548
$873$	27.1087	+	27.1087i	0.917490	+	0.917490i
$874$			5.38121i			0.182022i
$875$			51.3701i			1.73662i
$876$	−5.63048	−	5.63048i	−0.190236	−	0.190236i
$877$	−28.6132	−	28.6132i	−0.966199	−	0.966199i	0.0332484	−	0.999447i	$-0.489415\pi$
$877$	−28.6132	−	28.6132i	−0.966199	−	0.966199i	−0.999447	+	0.0332484i	$0.989415\pi$
$878$	2.28976	−	2.28976i	0.0772755	−	0.0772755i
$879$	58.4965	+	58.4965i	1.97304	+	1.97304i
$880$			33.6689i			1.13498i
$881$	6.72600			0.226605			0.113302	−	0.993561i	$-0.463857\pi$
$881$	6.72600			0.226605			0.113302	+	0.993561i	$0.463857\pi$
$882$	−8.41160	+	8.41160i	−0.283233	+	0.283233i
$883$	50.8261			1.71043			0.855217	−	0.518271i	$-0.173424\pi$
$883$	50.8261			1.71043			0.855217	+	0.518271i	$0.173424\pi$
$884$	−2.56695	−	1.27794i	−0.0863359	−	0.0429819i
$885$			47.1611i			1.58530i
$886$	−3.25196	−	3.25196i	−0.109252	−	0.109252i
$887$	8.75602			0.293998			0.146999	−	0.989137i	$-0.453039\pi$
$887$	8.75602			0.293998			0.146999	+	0.989137i	$0.453039\pi$
$888$			29.0182i			0.973786i
$889$	−7.77438	+	7.77438i	−0.260744	+	0.260744i
$890$	−1.13651	+	1.13651i	−0.0380961	+	0.0380961i
$891$	−18.5152	−	18.5152i	−0.620282	−	0.620282i
$892$	8.85599	+	8.85599i	0.296520	+	0.296520i
$893$	−58.9451			−1.97252
$894$	0.847821			0.0283554
$895$	10.3478	+	10.3478i	0.345890	+	0.345890i
$896$			33.9007i			1.13254i
$897$	26.0836	+	12.9856i	0.870908	+	0.433577i
$898$		−	2.85723i		−	0.0953471i
$899$	−3.90443	+	25.2374i	−0.130220	+	0.841714i
$900$	9.82147			0.327382
$901$		−	4.07453i		−	0.135742i
$902$	−5.87336	+	5.87336i	−0.195562	+	0.195562i
$903$	23.8861	+	23.8861i	0.794880	+	0.794880i
$904$	−2.51994	+	2.51994i	−0.0838119	+	0.0838119i
$905$	−2.10556	−	2.10556i	−0.0699911	−	0.0699911i
$906$	−3.64870			−0.121220
$907$		−	5.38884i		−	0.178933i	−0.995990	−	0.0894667i	$-0.971484\pi$
$907$		−	5.38884i		−	0.178933i	0.995990	−	0.0894667i	$-0.0285163\pi$
$908$	26.3796	−	26.3796i	0.875438	−	0.875438i
$909$		−	30.4538i		−	1.01009i
$910$	7.68127	−	2.57516i	0.254631	−	0.0853656i
$911$		−	16.2580i		−	0.538650i	−0.963049	−	0.269325i	$-0.913199\pi$
$911$		−	16.2580i		−	0.538650i	0.963049	−	0.269325i	$-0.0868006\pi$
$912$	−42.1050	+	42.1050i	−1.39424	+	1.39424i
$913$	−42.1409			−1.39466
$914$	1.51379			0.0500719
$915$	−7.74702	−	7.74702i	−0.256109	−	0.256109i
$916$	16.3944	−	16.3944i	0.541685	−	0.541685i
$917$	59.9898	−	59.9898i	1.98104	−	1.98104i
$918$	0.198519	−	0.198519i	0.00655209	−	0.00655209i
$919$	4.72695			0.155928			0.0779638	−	0.996956i	$-0.475158\pi$
$919$	4.72695			0.155928			0.0779638	+	0.996956i	$0.475158\pi$
$920$	−6.38180			−0.210402
$921$	−1.98700	−	1.98700i	−0.0654739	−	0.0654739i
$922$	−11.1606			−0.367556
$923$	2.93315	−	0.983342i	0.0965458	−	0.0323671i
$924$	−105.861			−3.48258
$925$	−9.34734	+	9.34734i	−0.307339	+	0.307339i
$926$			7.03162i			0.231073i
$927$		−	46.2150i		−	1.51790i
$928$	10.1822	−	10.1822i	0.334247	−	0.334247i
$929$	3.75276	−	3.75276i	0.123124	−	0.123124i	−0.642860	−	0.765984i	$-0.722252\pi$
$929$	3.75276	−	3.75276i	0.123124	−	0.123124i	0.765984	+	0.642860i	$0.222252\pi$
$930$	−7.68068	−	1.18826i	−0.251860	−	0.0389647i
$931$	49.4040	−	49.4040i	1.61915	−	1.61915i
$932$	30.6099			1.00266
$933$	18.9910			0.621738
$934$	−2.90481	+	2.90481i	−0.0950482	+	0.0950482i
$935$			3.91934i			0.128176i
$936$	−4.87586	−	14.5439i	−0.159373	−	0.475382i
$937$	−42.1095			−1.37566			−0.687828	−	0.725874i	$-0.741436\pi$
$937$	−42.1095			−1.37566			−0.687828	+	0.725874i	$0.741436\pi$
$938$	−7.42527	−	7.42527i	−0.242444	−	0.242444i
$939$	14.8392			0.484258
$940$		−	34.2770i		−	1.11799i
$941$	−29.4985	+	29.4985i	−0.961622	+	0.961622i	−0.999290	−	0.0376679i	$-0.988007\pi$
$941$	−29.4985	+	29.4985i	−0.961622	+	0.961622i	0.0376679	+	0.999290i	$0.488007\pi$
$942$	−1.64936	+	1.64936i	−0.0537389	+	0.0537389i
$943$	13.2793	+	13.2793i	0.432433	+	0.432433i
$944$	−23.3621	+	23.3621i	−0.760370	+	0.760370i
$945$		−	20.1201i		−	0.654508i
$946$		−	4.10594i		−	0.133496i
$947$	1.45989	+	1.45989i	0.0474401	+	0.0474401i	0.730429	−	0.682989i	$-0.239320\pi$
$947$	1.45989	+	1.45989i	0.0474401	+	0.0474401i	−0.682989	+	0.730429i	$0.739320\pi$
$948$			53.4998i			1.73759i
$949$	−5.37153	+	1.80081i	−0.174367	+	0.0584568i
$950$	2.27409			0.0737813
$951$	1.47271	−	1.47271i	0.0477560	−	0.0477560i
$952$			1.89378i			0.0613778i
$953$	1.14001			0.0369285			0.0184643	−	0.999830i	$-0.494122\pi$
$953$	1.14001			0.0369285			0.0184643	+	0.999830i	$0.494122\pi$
$954$	7.55730	−	7.55730i	0.244677	−	0.244677i
$955$	16.2188	+	16.2188i	0.524829	+	0.524829i
$956$	16.3794	+	16.3794i	0.529748	+	0.529748i
$957$	42.0902	+	42.0902i	1.36058	+	1.36058i
$958$	0.636676			0.0205701
$959$	−55.8537			−1.80361
$960$	−22.3508	−	22.3508i	−0.721369	−	0.721369i
$961$	29.5507	+	9.36769i	0.953250	+	0.302183i
$962$	9.06250	+	4.51172i	0.292187	+	0.145464i
$963$	−40.1737			−1.29458
$964$	33.6420	−	33.6420i	1.08354	−	1.08354i
$965$	−17.6111			−0.566922
$966$		−	9.43569i		−	0.303588i
$967$	4.52724	−	4.52724i	0.145586	−	0.145586i	−0.630557	−	0.776143i	$-0.717173\pi$
$967$	4.52724	−	4.52724i	0.145586	−	0.145586i	0.776143	+	0.630557i	$0.217173\pi$
$968$	10.1494	+	10.1494i	0.326213	+	0.326213i
$969$	−4.90138	+	4.90138i	−0.157455	+	0.157455i
$970$	−3.65002	+	3.65002i	−0.117195	+	0.117195i
$971$	−41.9457			−1.34610			−0.673051	−	0.739596i	$-0.735016\pi$
$971$	−41.9457			−1.34610			−0.673051	+	0.739596i	$0.735016\pi$
$972$	41.1651			1.32037
$973$	11.7039	+	11.7039i	0.375211	+	0.375211i
$974$	8.15075			0.261167
$975$	5.48771	−	11.0229i	0.175747	−	0.353016i
$976$		−	7.67524i		−	0.245679i
$977$	−37.1785	−	37.1785i	−1.18945	−	1.18945i	−0.977221	−	0.212226i	$-0.931929\pi$
$977$	−37.1785	−	37.1785i	−1.18945	−	1.18945i	−0.212226	−	0.977221i	$-0.568071\pi$
$978$		−	5.84212i		−	0.186810i
$979$		−	14.9428i		−	0.477574i
$980$	28.7288	+	28.7288i	0.917708	+	0.917708i
$981$	−25.8990	−	25.8990i	−0.826892	−	0.826892i
$982$	−0.893103	−	0.893103i	−0.0285001	−	0.0285001i
$983$	−21.1441	−	21.1441i	−0.674391	−	0.674391i	0.284334	−	0.958725i	$-0.408227\pi$
$983$	−21.1441	−	21.1441i	−0.674391	−	0.674391i	−0.958725	+	0.284334i	$0.908227\pi$
$984$		−	17.4215i		−	0.555376i
$985$	−51.7853			−1.65002
$986$	0.369204	−	0.369204i	0.0117579	−	0.0117579i
$987$	103.357			3.28990
$988$	14.0419	+	41.8848i	0.446734	+	1.33253i
$989$	−9.28327			−0.295191
$990$	−7.26946	+	7.26946i	−0.231039	+	0.231039i
$991$		−	19.4092i		−	0.616552i	−0.951297	−	0.308276i	$-0.900248\pi$
$991$		−	19.4092i		−	0.616552i	0.951297	−	0.308276i	$-0.0997521\pi$
$992$	−10.3251	−	14.1045i	−0.327821	−	0.447819i
$993$	26.3441	+	26.3441i	0.836004	+	0.836004i
$994$	−0.708390	−	0.708390i	−0.0224688	−	0.0224688i
$995$	−13.2600	−	13.2600i	−0.420370	−	0.420370i
$996$	30.6454	−	30.6454i	0.971035	−	0.971035i
$997$	−7.32070			−0.231849			−0.115924	−	0.993258i	$-0.536983\pi$
$997$	−7.32070			−0.231849			−0.115924	+	0.993258i	$0.536983\pi$
$998$	0.350003			0.0110792
$999$	17.7780	−	17.7780i	0.562471	−	0.562471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.17	✓	68
13.5	odd	4	inner	403.2.i.a.278.17	yes	68
31.30	odd	2	inner	403.2.i.a.216.18	yes	68
403.278	even	4	inner	403.2.i.a.278.18	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.17	✓	68	1.1	even	1	trivial
403.2.i.a.216.18	yes	68	31.30	odd	2	inner
403.2.i.a.278.17	yes	68	13.5	odd	4	inner
403.2.i.a.278.18	yes	68	403.278	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.194750 + 0.194750i) q^{2} -2.63371i q^{3} -1.92414i q^{4} +(-1.36075 - 1.36075i) q^{5} +(0.512915 - 0.512915i) q^{6} +(2.99770 - 2.99770i) q^{7} +(0.764228 - 0.764228i) q^{8} -3.93641 q^{9} +O(q^{10})\)	\(q+(0.194750 + 0.194750i) q^{2} -2.63371i q^{3} -1.92414i q^{4} +(-1.36075 - 1.36075i) q^{5} +(0.512915 - 0.512915i) q^{6} +(2.99770 - 2.99770i) q^{7} +(0.764228 - 0.764228i) q^{8} -3.93641 q^{9} -0.530014i q^{10} +(3.48429 + 3.48429i) q^{11} -5.06763 q^{12} +(-1.60689 + 3.22768i) q^{13} +1.16760 q^{14} +(-3.58383 + 3.58383i) q^{15} -3.55062 q^{16} -0.413323 q^{17} +(-0.766617 - 0.766617i) q^{18} +(4.50258 + 4.50258i) q^{19} +(-2.61829 + 2.61829i) q^{20} +(-7.89505 - 7.89505i) q^{21} +1.35713i q^{22} +3.06839 q^{23} +(-2.01275 - 2.01275i) q^{24} -1.29670i q^{25} +(-0.941533 + 0.315650i) q^{26} +2.46623i q^{27} +(-5.76800 - 5.76800i) q^{28} +4.58669i q^{29} -1.39590 q^{30} +(5.50231 + 0.851251i) q^{31} +(-2.21994 - 2.21994i) q^{32} +(9.17660 - 9.17660i) q^{33} +(-0.0804947 - 0.0804947i) q^{34} -8.15825 q^{35} +7.57422i q^{36} +(-7.20858 - 7.20858i) q^{37} +1.75376i q^{38} +(8.50076 + 4.23206i) q^{39} -2.07985 q^{40} +(4.32777 + 4.32777i) q^{41} -3.07513i q^{42} -3.02545 q^{43} +(6.70428 - 6.70428i) q^{44} +(5.35649 + 5.35649i) q^{45} +(0.597570 + 0.597570i) q^{46} +(-6.54570 + 6.54570i) q^{47} +9.35130i q^{48} -10.9724i q^{49} +(0.252532 - 0.252532i) q^{50} +1.08857i q^{51} +(6.21052 + 3.09188i) q^{52} +9.85799i q^{53} +(-0.480299 + 0.480299i) q^{54} -9.48252i q^{55} -4.58185i q^{56} +(11.8585 - 11.8585i) q^{57} +(-0.893259 + 0.893259i) q^{58} +(6.57971 - 6.57971i) q^{59} +(6.89580 + 6.89580i) q^{60} +2.16166i q^{61} +(0.905794 + 1.23736i) q^{62} +(-11.8002 + 11.8002i) q^{63} +6.23658i q^{64} +(6.57865 - 2.20550i) q^{65} +3.57429 q^{66} +(-6.35941 - 6.35941i) q^{67} +0.795293i q^{68} -8.08124i q^{69} +(-1.58882 - 1.58882i) q^{70} +(-0.606704 - 0.606704i) q^{71} +(-3.00832 + 3.00832i) q^{72} +(1.11107 + 1.11107i) q^{73} -2.80774i q^{74} -3.41512 q^{75} +(8.66362 - 8.66362i) q^{76} +20.8897 q^{77} +(0.831330 + 2.47972i) q^{78} -10.5572i q^{79} +(4.83152 + 4.83152i) q^{80} -5.31390 q^{81} +1.68567i q^{82} +(-6.04727 + 6.04727i) q^{83} +(-15.1912 + 15.1912i) q^{84} +(0.562431 + 0.562431i) q^{85} +(-0.589208 - 0.589208i) q^{86} +12.0800 q^{87} +5.32559 q^{88} +(-2.14431 - 2.14431i) q^{89} +2.08635i q^{90} +(4.85865 + 14.4926i) q^{91} -5.90402i q^{92} +(2.24195 - 14.4915i) q^{93} -2.54955 q^{94} -12.2538i q^{95} +(-5.84667 + 5.84667i) q^{96} +(-6.88665 - 6.88665i) q^{97} +(2.13687 - 2.13687i) q^{98} +(-13.7156 - 13.7156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

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Database

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