LMFDB - Embedded newform 512.2.o.a.141.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			141.35
Character	$\chi$	$=$	512.141
Dual form			512.2.o.a.69.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.226216 - 1.39600i) q^{2} +(-0.295495 + 0.894475i) q^{3} +(-1.89765 - 0.631596i) q^{4} +(0.910328 - 2.35994i) q^{5} +(1.18185 + 0.614856i) q^{6} +(1.81204 - 3.02321i) q^{7} +(-1.31099 + 2.50625i) q^{8} +(1.69685 + 1.25847i) q^{9} +O(q^{10})$	\(q+(0.226216 - 1.39600i) q^{2} +(-0.295495 + 0.894475i) q^{3} +(-1.89765 - 0.631596i) q^{4} +(0.910328 - 2.35994i) q^{5} +(1.18185 + 0.614856i) q^{6} +(1.81204 - 3.02321i) q^{7} +(-1.31099 + 2.50625i) q^{8} +(1.69685 + 1.25847i) q^{9} +(-3.08855 - 1.80468i) q^{10} +(0.0911253 + 0.738825i) q^{11} +(1.12569 - 1.51077i) q^{12} +(0.0129157 - 0.526128i) q^{13} +(-3.81050 - 3.21351i) q^{14} +(1.84191 + 1.51161i) q^{15} +(3.20217 + 2.39710i) q^{16} +(-1.06725 - 1.30045i) q^{17} +(2.14069 - 2.08413i) q^{18} +(-6.10322 - 4.29837i) q^{19} +(-3.21801 + 3.90338i) q^{20} +(2.16874 + 2.51417i) q^{21} +(1.05202 + 0.0399225i) q^{22} +(2.24626 - 4.74931i) q^{23} +(-1.85439 - 1.91323i) q^{24} +(-1.03584 - 0.938835i) q^{25} +(-0.731554 - 0.137049i) q^{26} +(-3.93763 + 2.77319i) q^{27} +(-5.34807 + 4.59252i) q^{28} +(3.30863 - 0.915621i) q^{29} +(2.52689 - 2.22936i) q^{30} +(-3.39018 + 0.674349i) q^{31} +(4.07074 - 3.92798i) q^{32} +(-0.687788 - 0.136809i) q^{33} +(-2.05687 + 1.19571i) q^{34} +(-5.48503 - 7.02841i) q^{35} +(-2.42519 - 3.45987i) q^{36} +(-0.872037 - 3.88336i) q^{37} +(-7.38118 + 7.54775i) q^{38} +(0.466792 + 0.167021i) q^{39} +(4.72117 + 5.37536i) q^{40} +(2.86506 - 2.59674i) q^{41} +(4.00039 - 2.45882i) q^{42} +(0.0319438 - 0.0634614i) q^{43} +(0.293715 - 1.45959i) q^{44} +(4.51461 - 2.85884i) q^{45} +(-6.12192 - 4.21015i) q^{46} +(0.210283 + 0.112399i) q^{47} +(-3.09037 + 2.15593i) q^{48} +(-2.55652 - 4.78291i) q^{49} +(-1.54494 + 1.23366i) q^{50} +(1.47859 - 0.570356i) q^{51} +(-0.356810 + 0.990250i) q^{52} +(-0.706752 - 0.195585i) q^{53} +(2.98063 + 6.12429i) q^{54} +(1.82653 + 0.457523i) q^{55} +(5.20136 + 8.50483i) q^{56} +(5.64826 - 4.18903i) q^{57} +(-0.529746 - 4.82599i) q^{58} +(-14.6850 + 0.360498i) q^{59} +(-2.54057 - 4.03186i) q^{60} +(10.8083 + 9.32332i) q^{61} +(0.174481 + 4.88525i) q^{62} +(6.87939 - 2.84954i) q^{63} +(-4.56261 - 6.57134i) q^{64} +(-1.22987 - 0.509429i) q^{65} +(-0.346575 + 0.929206i) q^{66} +(12.8262 - 0.946114i) q^{67} +(1.20392 + 3.14188i) q^{68} +(3.58439 + 3.41262i) q^{69} +(-11.0525 + 6.06718i) q^{70} +(-1.08039 + 7.28341i) q^{71} +(-5.37861 + 2.60290i) q^{72} +(5.82837 + 9.72405i) q^{73} +(-5.61845 + 0.338890i) q^{74} +(1.14585 - 0.649117i) q^{75} +(8.86695 + 12.0116i) q^{76} +(2.39874 + 1.06329i) q^{77} +(0.338757 - 0.613860i) q^{78} +(6.61419 + 2.00639i) q^{79} +(8.57203 - 5.37478i) q^{80} +(0.522760 + 1.72331i) q^{81} +(-2.97694 - 4.58706i) q^{82} +(-3.11611 + 13.8766i) q^{83} +(-2.52757 - 6.14078i) q^{84} +(-4.04054 + 1.33481i) q^{85} +(-0.0813662 - 0.0589496i) q^{86} +(-0.158682 + 3.23005i) q^{87} +(-1.97115 - 0.740208i) q^{88} +(1.97538 + 4.17658i) q^{89} +(-2.96968 - 6.94912i) q^{90} +(-1.56719 - 0.992412i) q^{91} +(-7.26226 + 7.59382i) q^{92} +(0.398592 - 3.23170i) q^{93} +(0.204478 - 0.268129i) q^{94} +(-15.6998 + 10.4903i) q^{95} +(2.31060 + 4.80188i) q^{96} +(10.0479 + 6.71378i) q^{97} +(-7.25528 + 2.48694i) q^{98} +(-0.775164 + 1.36836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{79}{128}\right)$	$1$

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 $

$2$	0.226216	−	1.39600i	0.159959	−	0.987124i
$2$	0.226216	−	1.39600i	0.159959	−	0.987124i
$3$	−0.295495	+	0.894475i	−0.170604	+	0.516426i	−0.999047	−	0.0436477i	$-0.986102\pi$
$3$	−0.295495	+	0.894475i	−0.170604	+	0.516426i	0.828443	+	0.560073i	$0.189227\pi$
$4$	−1.89765	−	0.631596i	−0.948826	−	0.315798i
$5$	0.910328	−	2.35994i	0.407111	−	1.05540i	−0.565867	−	0.824497i	$-0.691458\pi$
$5$	0.910328	−	2.35994i	0.407111	−	1.05540i	0.972978	−	0.230899i	$-0.0741666\pi$
$6$	1.18185	+	0.614856i	0.482486	+	0.251014i
$7$	1.81204	−	3.02321i	0.684887	−	1.14267i	−0.297304	−	0.954783i	$-0.596088\pi$
$7$	1.81204	−	3.02321i	0.684887	−	1.14267i	0.982192	−	0.187882i	$-0.0601624\pi$
$8$	−1.31099	+	2.50625i	−0.463505	+	0.886094i
$9$	1.69685	+	1.25847i	0.565618	+	0.419491i
$10$	−3.08855	−	1.80468i	−0.976685	−	0.570688i
$11$	0.0911253	+	0.738825i	0.0274753	+	0.222764i	0.999947	−	0.0102554i	$-0.00326444\pi$
$11$	0.0911253	+	0.738825i	0.0274753	+	0.222764i	−0.972472	+	0.233019i	$0.925139\pi$
$12$	1.12569	−	1.51077i	0.324960	−	0.436122i
$13$	0.0129157	−	0.526128i	0.00358217	−	0.145922i	−0.995242	−	0.0974366i	$-0.968936\pi$
$13$	0.0129157	−	0.526128i	0.00358217	−	0.145922i	0.998824	−	0.0484850i	$-0.0154393\pi$
$14$	−3.81050	−	3.21351i	−1.01840	−	0.858848i
$15$	1.84191	+	1.51161i	0.475578	+	0.390297i
$16$	3.20217	+	2.39710i	0.800543	+	0.599275i
$17$	−1.06725	−	1.30045i	−0.258847	−	0.315406i	0.627329	−	0.778754i	$-0.284148\pi$
$17$	−1.06725	−	1.30045i	−0.258847	−	0.315406i	−0.886176	+	0.463348i	$0.846648\pi$
$18$	2.14069	−	2.08413i	0.504565	−	0.491234i
$19$	−6.10322	−	4.29837i	−1.40017	−	0.986114i	−0.997492	−	0.0707736i	$-0.977453\pi$
$19$	−6.10322	−	4.29837i	−1.40017	−	0.986114i	−0.402682	−	0.915340i	$-0.631922\pi$
$20$	−3.21801	+	3.90338i	−0.719569	+	0.872822i
$21$	2.16874	+	2.51417i	0.473257	+	0.548637i
$22$	1.05202	+	0.0399225i	0.224291	+	0.00851150i
$23$	2.24626	−	4.74931i	0.468377	−	0.990300i	−0.522134	−	0.852864i	$-0.674864\pi$
$23$	2.24626	−	4.74931i	0.468377	−	0.990300i	0.990511	−	0.137436i	$-0.0438862\pi$
$24$	−1.85439	−	1.91323i	−0.378526	−	0.390537i
$25$	−1.03584	−	0.938835i	−0.207169	−	0.187767i
$26$	−0.731554	−	0.137049i	−0.143470	−	0.0268775i
$27$	−3.93763	+	2.77319i	−0.757797	+	0.533701i
$28$	−5.34807	+	4.59252i	−1.01069	+	0.867905i
$29$	3.30863	−	0.915621i	0.614397	−	0.170027i	0.0543973	−	0.998519i	$-0.482676\pi$
$29$	3.30863	−	0.915621i	0.614397	−	0.170027i	0.560000	+	0.828493i	$0.310801\pi$
$30$	2.52689	−	2.22936i	0.461345	−	0.407023i
$31$	−3.39018	+	0.674349i	−0.608894	+	0.121117i	−0.489900	−	0.871778i	$-0.662967\pi$
$31$	−3.39018	+	0.674349i	−0.608894	+	0.121117i	−0.118994	+	0.992895i	$0.537967\pi$
$32$	4.07074	−	3.92798i	0.719612	−	0.694376i
$33$	−0.687788	−	0.136809i	−0.119728	−	0.0238155i
$34$	−2.05687	+	1.19571i	−0.352750	+	0.205062i
$35$	−5.48503	−	7.02841i	−0.927139	−	1.18802i
$36$	−2.42519	−	3.45987i	−0.404199	−	0.576645i
$37$	−0.872037	−	3.88336i	−0.143362	−	0.638420i	−0.993689	−	0.112166i	$-0.964221\pi$
$37$	−0.872037	−	3.88336i	−0.143362	−	0.638420i	0.850327	−	0.526254i	$-0.176404\pi$
$38$	−7.38118	+	7.54775i	−1.19739	+	1.22441i
$39$	0.466792	+	0.167021i	0.0747465	+	0.0267447i
$40$	4.72117	+	5.37536i	0.746482	+	0.849919i
$41$	2.86506	−	2.59674i	0.447447	−	0.405543i	−0.416491	−	0.909140i	$-0.636740\pi$
$41$	2.86506	−	2.59674i	0.447447	−	0.405543i	0.863939	+	0.503597i	$0.167990\pi$
$42$	4.00039	−	2.45882i	0.617274	−	0.379404i
$43$	0.0319438	−	0.0634614i	0.00487138	−	0.00967777i	−0.890776	−	0.454444i	$-0.849838\pi$
$43$	0.0319438	−	0.0634614i	0.00487138	−	0.00967777i	0.895647	+	0.444766i	$0.146713\pi$
$44$	0.293715	−	1.45959i	0.0442791	−	0.220041i
$45$	4.51461	−	2.85884i	0.672998	−	0.426171i
$46$	−6.12192	−	4.21015i	−0.902628	−	0.620753i
$47$	0.210283	+	0.112399i	0.0306729	+	0.0163950i	0.486662	−	0.873590i	$-0.338214\pi$
$47$	0.210283	+	0.112399i	0.0306729	+	0.0163950i	−0.455989	+	0.889985i	$0.650714\pi$
$48$	−3.09037	+	2.15593i	−0.446057	+	0.311182i
$49$	−2.55652	−	4.78291i	−0.365217	−	0.683272i
$50$	−1.54494	+	1.23366i	−0.218488	+	0.174466i
$51$	1.47859	−	0.570356i	0.207044	−	0.0798658i
$52$	−0.356810	+	0.990250i	−0.0494806	+	0.137323i
$53$	−0.706752	−	0.195585i	−0.0970798	−	0.0268656i	0.217834	−	0.975986i	$-0.430101\pi$
$53$	−0.706752	−	0.195585i	−0.0970798	−	0.0268656i	−0.314914	+	0.949120i	$0.601976\pi$
$54$	2.98063	+	6.12429i	0.405613	+	0.833410i
$55$	1.82653	+	0.457523i	0.246290	+	0.0616923i
$56$	5.20136	+	8.50483i	0.695061	+	1.13651i
$57$	5.64826	−	4.18903i	0.748130	−	0.554851i
$58$	−0.529746	−	4.82599i	−0.0695591	−	0.633683i
$59$	−14.6850	+	0.360498i	−1.91183	+	0.0469328i	−0.963098	−	0.269150i	$-0.913257\pi$
$59$	−14.6850	+	0.360498i	−1.91183	+	0.0469328i	−0.948732	+	0.316083i	$0.897632\pi$
$60$	−2.54057	−	4.03186i	−0.327986	−	0.520511i
$61$	10.8083	+	9.32332i	1.38386	+	1.19373i	0.957238	+	0.289300i	$0.0934226\pi$
$61$	10.8083	+	9.32332i	1.38386	+	1.19373i	0.426625	+	0.904429i	$0.359702\pi$
$62$	0.174481	+	4.88525i	0.0221591	+	0.620428i
$63$	6.87939	−	2.84954i	0.866722	−	0.359008i
$64$	−4.56261	−	6.57134i	−0.570327	−	0.821418i
$65$	−1.22987	−	0.509429i	−0.152547	−	0.0631869i
$66$	−0.346575	+	0.929206i	−0.0426604	+	0.114377i
$67$	12.8262	−	0.946114i	1.56696	−	0.115586i	0.737966	−	0.674838i	$-0.235786\pi$
$67$	12.8262	−	0.946114i	1.56696	−	0.115586i	0.828998	+	0.559251i	$0.188911\pi$
$68$	1.20392	+	3.14188i	0.145996	+	0.381009i
$69$	3.58439	+	3.41262i	0.431509	+	0.410831i
$70$	−11.0525	+	6.06718i	−1.32102	+	0.725167i
$71$	−1.08039	+	7.28341i	−0.128219	+	0.864382i	0.825655	+	0.564175i	$0.190806\pi$
$71$	−1.08039	+	7.28341i	−0.128219	+	0.864382i	−0.953874	+	0.300207i	$0.902944\pi$
$72$	−5.37861	+	2.60290i	−0.633875	+	0.306755i
$73$	5.82837	+	9.72405i	0.682159	+	1.13811i	0.982853	+	0.184393i	$0.0590319\pi$
$73$	5.82837	+	9.72405i	0.682159	+	1.13811i	−0.300693	+	0.953721i	$0.597218\pi$
$74$	−5.61845	+	0.338890i	−0.653131	+	0.0393952i
$75$	1.14585	−	0.649117i	0.132312	−	0.0749535i
$76$	8.86695	+	12.0116i	1.01711	+	1.37782i
$77$	2.39874	+	1.06329i	0.273362	+	0.121173i
$78$	0.338757	−	0.613860i	0.0383567	−	0.0695060i
$79$	6.61419	+	2.00639i	0.744154	+	0.225737i	0.639521	−	0.768774i	$-0.279133\pi$
$79$	6.61419	+	2.00639i	0.744154	+	0.225737i	0.104634	+	0.994511i	$0.466633\pi$
$80$	8.57203	−	5.37478i	0.958382	−	0.600918i
$81$	0.522760	+	1.72331i	0.0580845	+	0.191479i
$82$	−2.97694	−	4.58706i	−0.328748	−	0.506556i
$83$	−3.11611	+	13.8766i	−0.342037	+	1.52316i	0.438892	+	0.898540i	$0.355371\pi$
$83$	−3.11611	+	13.8766i	−0.342037	+	1.52316i	−0.780929	+	0.624620i	$0.785254\pi$
$84$	−2.52757	−	6.14078i	−0.275781	−	0.670015i
$85$	−4.04054	+	1.33481i	−0.438258	+	0.144781i
$86$	−0.0813662	−	0.0589496i	−0.00877394	−	0.00635670i
$87$	−0.158682	+	3.23005i	−0.0170125	+	0.346298i
$88$	−1.97115	−	0.740208i	−0.210125	−	0.0789065i
$89$	1.97538	+	4.17658i	0.209389	+	0.442717i	0.981163	−	0.193180i	$-0.0618803\pi$
$89$	1.97538	+	4.17658i	0.209389	+	0.442717i	−0.771774	+	0.635897i	$0.780630\pi$
$90$	−2.96968	−	6.94912i	−0.313032	−	0.732502i
$91$	−1.56719	−	0.992412i	−0.164286	−	0.104033i
$92$	−7.26226	+	7.59382i	−0.757143	+	0.791710i
$93$	0.398592	−	3.23170i	0.0413321	−	0.335112i
$94$	0.204478	−	0.268129i	0.0210903	−	0.0276554i
$95$	−15.6998	+	10.4903i	−1.61077	+	1.07628i
$96$	2.31060	+	4.80188i	0.235825	+	0.490090i
$97$	10.0479	+	6.71378i	1.02021	+	0.681681i	0.948836	−	0.315769i	$-0.102262\pi$
$97$	10.0479	+	6.71378i	1.02021	+	0.681681i	0.0713717	+	0.997450i	$0.477262\pi$
$98$	−7.25528	+	2.48694i	−0.732894	+	0.251219i
$99$	−0.775164	+	1.36836i	−0.0779069	+	0.137525i
$100$	1.37271	+	2.43582i	0.137271	+	0.243582i
$101$	−10.8284	−	1.87891i	−1.07747	−	0.186958i	−0.395592	−	0.918427i	$-0.629460\pi$
$101$	−10.8284	−	1.87891i	−1.07747	−	0.186958i	−0.681875	+	0.731468i	$0.738835\pi$
$102$	−0.461738	−	2.19314i	−0.0457189	−	0.217153i
$103$	6.42349	−	0.315566i	0.632925	−	0.0310936i	0.269923	−	0.962882i	$-0.413002\pi$
$103$	6.42349	−	0.315566i	0.632925	−	0.0310936i	0.363002	+	0.931788i	$0.381752\pi$
$104$	1.30168	+	0.722118i	0.127640	+	0.0708095i
$105$	7.90754	−	2.82936i	0.771697	−	0.276117i
$106$	−0.432915	+	0.942384i	−0.0420484	+	0.0915324i
$107$	11.5573	+	0.852520i	1.11729	+	0.0824163i	0.619585	−	0.784930i	$-0.287301\pi$
$107$	11.5573	+	0.852520i	1.11729	+	0.0824163i	0.497705	+	0.867346i	$0.334176\pi$
$108$	9.22379	−	2.77556i	0.887560	−	0.267079i
$109$	−0.821299	−	4.73326i	−0.0786662	−	0.453364i	−0.998180	−	0.0603065i	$-0.980792\pi$
$109$	−0.821299	−	4.73326i	−0.0786662	−	0.453364i	0.919514	−	0.393058i	$-0.128583\pi$
$110$	1.05189	−	2.44635i	0.100294	−	0.233250i
$111$	3.73125	+	0.367496i	0.354155	+	0.0348812i
$112$	13.0494	−	5.33719i	1.23305	−	0.504317i
$113$	−1.40498	−	14.2650i	−0.132169	−	1.34194i	−0.801064	−	0.598579i	$-0.795732\pi$
$113$	−1.40498	−	14.2650i	−0.132169	−	1.34194i	0.668895	−	0.743357i	$-0.266768\pi$
$114$	−4.57018	−	8.83261i	−0.428037	−	0.827250i
$115$	−9.16324	−	9.62445i	−0.854477	−	0.897485i
$116$	−6.85693	−	0.352186i	−0.636650	−	0.0326997i
$117$	0.684033	−	0.876507i	0.0632389	−	0.0810331i
$118$	−2.81873	+	20.5819i	−0.259485	+	1.89472i
$119$	−5.86545	+	0.870057i	−0.537685	+	0.0797580i
$120$	−6.20321	+	2.63458i	−0.566273	+	0.240503i
$121$	10.1328	−	2.53813i	0.921162	−	0.230739i
$122$	15.4604	−	12.9794i	1.39972	−	1.17510i
$123$	1.47611	+	3.33005i	0.133096	+	0.300261i
$124$	6.85930	+	0.861545i	0.615983	+	0.0773690i
$125$	8.13817	−	4.09641i	0.727900	−	0.366394i
$126$	−2.42174	−	10.2483i	−0.215746	−	0.912988i
$127$	1.60119	−	1.60119i	0.142083	−	0.142083i	−0.632488	−	0.774570i	$-0.717966\pi$
$127$	1.60119	−	1.60119i	0.142083	−	0.142083i	0.774570	+	0.632488i	$0.217966\pi$
$128$	−10.2058	+	4.88288i	−0.902070	+	0.431590i
$129$	0.0473254	+	0.0473254i	0.00416677	+	0.00416677i
$130$	−0.989380	+	1.60166i	−0.0867744	+	0.140475i
$131$	−0.629267	−	1.25014i	−0.0549793	−	0.109225i	0.864064	−	0.503383i	$-0.167911\pi$
$131$	−0.629267	−	1.25014i	−0.0549793	−	0.109225i	−0.919043	+	0.394158i	$0.871036\pi$
$132$	1.21877	+	0.694021i	0.106081	+	0.0604068i
$133$	−24.0541	+	10.6625i	−2.08576	+	0.924553i
$134$	1.58070	−	18.1194i	0.136552	−	1.56528i
$135$	2.96002	+	11.8171i	0.254758	+	1.01705i
$136$	4.65842	−	0.969930i	0.399457	−	0.0831708i
$137$	−2.36265	−	15.9277i	−0.201855	−	1.36080i	−0.818931	−	0.573892i	$-0.805433\pi$
$137$	−2.36265	−	15.9277i	−0.201855	−	1.36080i	0.617076	−	0.786903i	$-0.288317\pi$
$138$	5.57487	−	4.23183i	0.474565	−	0.360237i
$139$	3.98160	+	3.10727i	0.337715	+	0.263556i	0.769811	−	0.638272i	$-0.220351\pi$
$139$	3.98160	+	3.10727i	0.337715	+	0.263556i	−0.432095	+	0.901828i	$0.642226\pi$
$140$	5.96956	+	16.8018i	0.504520	+	1.42001i
$141$	−0.162675	+	0.154880i	−0.0136997	+	0.0130432i
$142$	9.92327	+	3.15585i	0.832742	+	0.264833i
$143$	0.389893	−	0.0384011i	0.0326045	−	0.00321126i
$144$	2.41693	+	8.09737i	0.201411	+	0.674781i
$145$	0.851130	−	8.64167i	0.0706825	−	0.717651i
$146$	14.8933	−	5.93669i	1.23258	−	0.491324i
$147$	5.03363	−	0.873417i	0.415167	−	0.0720383i
$148$	−0.797890	+	7.92004i	−0.0655861	+	0.651023i
$149$	−0.106858	+	1.44864i	−0.00875415	+	0.118677i	−0.999901	−	0.0140957i	$-0.995513\pi$
$149$	−0.106858	+	1.44864i	−0.00875415	+	0.118677i	0.991146	+	0.132773i	$0.0423881\pi$
$150$	−0.646960	−	1.74645i	−0.0528240	−	0.142597i
$151$	1.90239	+	5.31682i	0.154814	+	0.432677i	0.993760	−	0.111538i	$-0.0355777\pi$
$151$	1.90239	+	5.31682i	0.154814	+	0.432677i	−0.838946	+	0.544215i	$0.816828\pi$
$152$	18.7741	−	9.66109i	1.52278	−	0.783618i
$153$	−0.174390	−	3.54979i	−0.0140986	−	0.286983i
$154$	2.02699	−	3.10812i	0.163340	−	0.250460i
$155$	−1.49475	+	8.61448i	−0.120062	+	0.691932i
$156$	−0.780319	−	0.611771i	−0.0624755	−	0.0489809i
$157$	1.91362	+	1.08405i	0.152723	+	0.0865168i	0.567358	−	0.823471i	$-0.307966\pi$
$157$	1.91362	+	1.08405i	0.152723	+	0.0865168i	−0.414635	+	0.909988i	$0.636091\pi$
$158$	4.29717	−	8.77956i	0.341864	−	0.698464i
$159$	0.383787	−	0.574378i	0.0304363	−	0.0455511i
$160$	−5.56408	−	13.1824i	−0.439879	−	1.04216i
$161$	−10.2878	−	15.3969i	−0.810796	−	1.21344i
$162$	2.52400	−	0.339935i	0.198304	−	0.0267078i
$163$	−12.0440	−	1.48549i	−0.943359	−	0.116352i	−0.363977	−	0.931408i	$-0.618581\pi$
$163$	−12.0440	−	1.48549i	−0.943359	−	0.116352i	−0.579383	+	0.815056i	$0.696706\pi$
$164$	−7.07698	+	3.11815i	−0.552620	+	0.243487i
$165$	−0.948974	+	1.49859i	−0.0738775	+	0.116665i
$166$	18.6669	+	7.48921i	1.44884	+	0.581276i
$167$	−11.1434	+	5.27045i	−0.862305	+	0.407840i	−0.806945	−	0.590626i	$-0.798881\pi$
$167$	−11.1434	+	5.27045i	−0.862305	+	0.407840i	−0.0553601	+	0.998466i	$0.517631\pi$
$168$	−9.14433	+	2.13936i	−0.705501	+	0.165055i
$169$	12.7077	+	0.624289i	0.977515	+	0.0480222i
$170$	0.949371	+	5.94256i	0.0728134	+	0.455774i
$171$	−4.94688	−	14.9744i	−0.378298	−	1.14512i
$172$	−0.100700	+	0.100252i	−0.00767832	+	0.00764415i
$173$	−11.3216	−	2.54236i	−0.860769	−	0.193292i	−0.233750	−	0.972297i	$-0.575100\pi$
$173$	−11.3216	−	2.54236i	−0.860769	−	0.193292i	−0.627018	+	0.779005i	$0.715725\pi$
$174$	4.47326	+	0.952209i	0.339117	+	0.0721868i
$175$	−4.71529	+	1.43037i	−0.356442	+	0.108126i
$176$	−1.47924	+	2.58428i	−0.111502	+	0.194797i
$177$	4.01690	−	13.2419i	0.301929	−	0.995325i
$178$	6.27738	−	1.81282i	0.470510	−	0.135877i
$179$	−2.98954	+	6.74430i	−0.223449	+	0.504093i	−0.990503	−	0.137490i	$-0.956097\pi$
$179$	−2.98954	+	6.74430i	−0.223449	+	0.504093i	0.767054	+	0.641582i	$0.221722\pi$
$180$	−10.3728	+	2.57368i	−0.773142	+	0.191831i
$181$	−0.497703	−	0.878569i	−0.0369940	−	0.0653035i	0.850977	−	0.525203i	$-0.176011\pi$
$181$	−0.497703	−	0.878569i	−0.0369940	−	0.0653035i	−0.887971	+	0.459899i	$0.847886\pi$
$182$	−1.73993	+	1.96330i	−0.128972	+	0.145530i
$183$	−11.5333	+	6.91278i	−0.852565	+	0.511008i
$184$	8.95816	+	11.8560i	0.660404	+	0.874035i
$185$	−9.95831	−	1.47718i	−0.732150	−	0.108604i
$186$	−4.42130	−	1.28750i	−0.324185	−	0.0944039i
$187$	0.863553	−	0.907018i	0.0631492	−	0.0663277i
$188$	−0.328053	−	0.346107i	−0.0239257	−	0.0252425i
$189$	1.24879	+	16.9294i	0.0908360	+	1.23143i
$190$	11.0929	+	24.2901i	0.804765	+	1.76219i
$191$	5.71022	−	13.7857i	0.413177	−	0.997498i	−0.571102	−	0.820879i	$-0.693484\pi$
$191$	5.71022	−	13.7857i	0.413177	−	0.997498i	0.984279	−	0.176619i	$-0.0565161\pi$
$192$	7.22613	−	2.13935i	0.521501	−	0.154394i
$193$	5.43597	+	13.1236i	0.391289	+	0.944656i	0.989660	+	0.143436i	$0.0458153\pi$
$193$	5.43597	+	13.1236i	0.391289	+	0.944656i	−0.598370	+	0.801220i	$0.704185\pi$
$194$	11.6455	−	12.5081i	0.836095	−	0.898031i
$195$	0.819092	−	0.949555i	0.0586564	−	0.0679990i
$196$	1.83052	+	10.6910i	0.130751	+	0.763641i
$197$	0.663130	+	27.0129i	0.0472461	+	1.92459i	0.294519	+	0.955646i	$0.404840\pi$
$197$	0.663130	+	27.0129i	0.0472461	+	1.92459i	−0.247273	+	0.968946i	$0.579535\pi$
$198$	1.73488	+	1.39168i	0.123292	+	0.0989021i
$199$	10.1283	+	13.6564i	0.717973	+	0.968074i	0.999963	+	0.00865667i	$0.00275554\pi$
$199$	10.1283	+	13.6564i	0.717973	+	0.968074i	−0.281990	+	0.959417i	$0.590994\pi$
$200$	3.71094	−	1.36529i	0.262403	−	0.0965403i
$201$	−2.94379	+	11.7523i	−0.207639	+	0.828940i
$202$	−5.07252	+	14.6915i	−0.356901	+	1.03369i
$203$	3.22726	−	11.6618i	0.226509	−	0.818499i
$204$	−3.16609	+	0.148465i	−0.221670	+	0.0103946i
$205$	−3.52000	−	9.12525i	−0.245847	−	0.637335i
$206$	1.01256	−	9.03861i	0.0705487	−	0.629749i
$207$	9.78845	−	5.23203i	0.680344	−	0.363651i
$208$	1.30254	−	1.65379i	0.0903148	−	0.114670i
$209$	2.61958	−	4.90090i	0.181200	−	0.339002i
$210$	−2.16099	−	11.6790i	−0.149123	−	0.805927i
$211$	−12.7509	−	20.1359i	−0.877807	−	1.38621i	−0.922001	−	0.387186i	$-0.873447\pi$
$211$	−12.7509	−	20.1359i	−0.877807	−	1.38621i	0.0441941	−	0.999023i	$-0.485928\pi$
$212$	1.21764	+	0.817533i	0.0836278	+	0.0561484i
$213$	−6.19558	−	3.11859i	−0.424514	−	0.213683i
$214$	3.80457	−	15.9412i	0.260075	−	1.08972i
$215$	−0.120686	−	0.133156i	−0.00823068	−	0.00908116i
$216$	−1.78813	−	13.5043i	−0.121667	−	0.918853i
$217$	−4.10445	+	11.4712i	−0.278628	+	0.778713i
$218$	−6.79344	+	0.0757979i	−0.460110	+	0.00513368i
$219$	−10.4202	+	2.33993i	−0.704130	+	0.158118i
$220$	−3.17716	−	2.02185i	−0.214204	−	0.136313i
$221$	−0.697989	+	0.544716i	−0.0469518	+	0.0366415i
$222$	1.35709	−	5.12571i	0.0910821	−	0.344015i
$223$	0.982272	−	4.93821i	0.0657778	−	0.330687i	−0.933859	−	0.357642i	$-0.883581\pi$
$223$	0.982272	−	4.93821i	0.0657778	−	0.330687i	0.999637	+	0.0269545i	$0.00858093\pi$
$224$	−4.49876	−	19.4244i	−0.300586	−	1.29785i
$225$	−0.576179	−	2.89665i	−0.0384119	−	0.193110i
$226$	−20.2318	−	1.26561i	−1.34580	−	0.0841870i
$227$	−3.49777	−	12.6393i	−0.232155	−	0.838902i	−0.983790	−	0.179323i	$-0.942609\pi$
$227$	−3.49777	−	12.6393i	−0.232155	−	0.838902i	0.751635	−	0.659579i	$-0.229266\pi$
$228$	−13.3642	+	4.38191i	−0.885066	+	0.290199i
$229$	3.30733	+	4.69605i	0.218555	+	0.310324i	0.912004	−	0.410182i	$-0.134535\pi$
$229$	3.30733	+	4.69605i	0.218555	+	0.310324i	−0.693449	+	0.720506i	$0.743910\pi$
$230$	−15.5086	+	10.6147i	−1.02261	+	0.699914i
$231$	−1.65990	+	1.83142i	−0.109214	+	0.120499i
$232$	−2.04280	+	9.49263i	−0.134116	+	0.623222i
$233$	7.50601	+	3.55008i	0.491735	+	0.232573i	0.657305	−	0.753625i	$-0.271696\pi$
$233$	7.50601	+	3.55008i	0.491735	+	0.232573i	−0.165570	+	0.986198i	$0.552946\pi$
$234$	−1.06887	−	1.15319i	−0.0698741	−	0.0753865i
$235$	0.456679	−	0.393934i	0.0297905	−	0.0256974i
$236$	28.0948	+	8.59092i	1.82882	+	0.559221i
$237$	−3.74913	+	5.32335i	−0.243532	+	0.345789i
$238$	−0.112254	+	8.38501i	−0.00727634	+	0.543519i
$239$	−7.80867	+	6.40841i	−0.505101	+	0.414526i	−0.852131	−	0.523328i	$-0.824690\pi$
$239$	−7.80867	+	6.40841i	−0.505101	+	0.414526i	0.347030	+	0.937854i	$0.387190\pi$
$240$	2.27461	+	9.25569i	0.146826	+	0.597452i
$241$	−10.7427	+	13.0900i	−0.691998	+	0.843202i	−0.993917	−	0.110132i	$-0.964873\pi$
$241$	−10.7427	+	13.0900i	−0.691998	+	0.843202i	0.301919	+	0.953334i	$0.402373\pi$
$242$	−1.25104	−	14.7196i	−0.0804202	−	0.946210i
$243$	−16.1401	−	0.396217i	−1.03539	−	0.0254173i
$244$	−14.6219	−	24.5189i	−0.936069	−	1.56966i
$245$	−13.6146	+	1.67920i	−0.869806	+	0.107280i
$246$	4.98268	−	1.30734i	0.317684	−	0.0833533i
$247$	−2.34032	+	3.15555i	−0.148911	+	0.200783i
$248$	2.75440	−	9.38071i	0.174905	−	0.595676i
$249$	−11.4915	−	6.88776i	−0.728246	−	0.436494i
$250$	−3.87762	−	12.2876i	−0.245242	−	0.777136i
$251$	−9.50925	−	3.66812i	−0.600218	−	0.231530i	0.0406590	−	0.999173i	$-0.487054\pi$
$251$	−9.50925	−	3.66812i	−0.600218	−	0.231530i	−0.640877	+	0.767643i	$0.721429\pi$
$252$	−14.8545	+	1.06244i	−0.935743	+	0.0669272i
$253$	3.71360	+	1.22681i	0.233472	+	0.0771287i
$254$	−1.87306	−	2.59749i	−0.117526	−	0.162981i
$255$		−	4.00859i		−	0.251028i
$256$	4.50782	+	15.3519i	0.281739	+	0.959491i
$257$			14.4194i			0.899460i	0.893165	+	0.449730i	$0.148480\pi$
$257$			14.4194i			0.899460i	−0.893165	+	0.449730i	$0.851520\pi$
$258$	0.0767723	−	0.0553607i	0.00477963	−	0.00344661i
$259$	−13.3204	−	4.40045i	−0.827687	−	0.273431i
$260$	2.01211	+	1.74350i	0.124786	+	0.108127i
$261$	6.76654	+	2.61014i	0.418838	+	0.161564i
$262$	−1.88755	+	0.595658i	−0.116613	+	0.0367998i
$263$	16.9621	+	10.1667i	1.04593	+	0.626904i	0.930455	−	0.366407i	$-0.119412\pi$
$263$	16.9621	+	10.1667i	1.04593	+	0.626904i	0.115471	+	0.993311i	$0.463162\pi$
$264$	1.24456	−	1.54441i	0.0765975	−	0.0950521i
$265$	−1.10494	+	1.48984i	−0.0678761	+	0.0915203i
$266$	9.44342	+	35.9917i	0.579013	+	2.20679i
$267$	−4.31956	+	0.532767i	−0.264353	+	0.0326048i
$268$	−24.9372	−	6.30555i	−1.52328	−	0.385173i
$269$	1.08134	+	0.0265455i	0.0659307	+	0.00161851i	0.0574932	−	0.998346i	$-0.481689\pi$
$269$	1.08134	+	0.0265455i	0.0659307	+	0.00161851i	0.00843745	+	0.999964i	$0.497314\pi$
$270$	17.1663	−	1.45899i	1.04471	−	0.0887915i
$271$	1.38099	−	1.68274i	0.0838891	−	0.102219i	−0.729374	−	0.684115i	$-0.760189\pi$
$271$	1.38099	−	1.68274i	0.0838891	−	0.102219i	0.813264	+	0.581896i	$0.197689\pi$
$272$	−0.300216	−	6.72259i	−0.0182033	−	0.407617i
$273$	1.35078	−	1.10856i	0.0817532	−	0.0670931i
$274$	−22.7696	−	0.304827i	−1.37556	−	0.0184153i
$275$	0.599243	−	0.850859i	0.0361357	−	0.0513087i
$276$	−4.64652	−	8.73985i	−0.279688	−	0.526077i
$277$	−13.0809	+	11.2837i	−0.785956	+	0.677970i	−0.951300	−	0.308266i	$-0.900251\pi$
$277$	−13.0809	+	11.2837i	−0.785956	+	0.677970i	0.165345	+	0.986236i	$0.447126\pi$
$278$	5.23847	−	4.85542i	0.314182	−	0.291209i
$279$	−6.60129	−	3.12218i	−0.395209	−	0.186920i
$280$	24.8058	−	4.53269i	1.48243	−	0.270880i
$281$	−12.3912	+	13.6716i	−0.739196	+	0.815577i	−0.988239	−	0.152915i	$-0.951134\pi$
$281$	−12.3912	+	13.6716i	−0.739196	+	0.815577i	0.249044	+	0.968492i	$0.419884\pi$
$282$	0.179413	+	0.262131i	0.0106839	+	0.0156097i
$283$	18.0759	+	25.6659i	1.07450	+	1.52568i	0.831398	+	0.555678i	$0.187541\pi$
$283$	18.0759	+	25.6659i	1.07450	+	1.52568i	0.243106	+	0.970000i	$0.421834\pi$
$284$	6.65038	−	13.1390i	0.394628	−	0.779657i
$285$	−4.74408	−	17.1429i	−0.281015	−	1.01546i
$286$	0.0345918	−	0.552979i	0.00204546	−	0.0326983i
$287$	−2.65888	−	13.3671i	−0.156949	−	0.789034i
$288$	11.8507	−	1.54230i	0.698310	−	0.0908806i
$289$	2.76439	−	13.8975i	0.162611	−	0.817501i
$290$	−11.8713	−	3.14306i	−0.697104	−	0.184567i
$291$	−8.97441	+	7.00370i	−0.526089	+	0.410564i
$292$	−4.91855	−	22.1340i	−0.287837	−	1.29530i
$293$	0.301917	−	0.0677978i	0.0176382	−	0.00396079i	−0.210273	−	0.977643i	$-0.567435\pi$
$293$	0.301917	−	0.0677978i	0.0176382	−	0.00396079i	0.227911	+	0.973682i	$0.426810\pi$
$294$	−0.0806079	−	7.22455i	−0.00470115	−	0.421344i
$295$	−12.5175	+	34.9839i	−0.728794	+	2.03684i
$296$	10.8759	+	2.90549i	0.632149	+	0.168878i
$297$	−2.40772	−	2.65651i	−0.139710	−	0.154146i
$298$	1.99813	+	0.476879i	0.115749	+	0.0276249i
$299$	−2.46973	−	1.24316i	−0.142828	−	0.0718937i
$300$	−2.58441	+	0.508083i	−0.149211	+	0.0293342i
$301$	−0.133974	−	0.211567i	−0.00772211	−	0.0121945i
$302$	7.85265	−	1.45299i	0.451869	−	0.0836104i
$303$	4.88038	−	9.13054i	0.280370	−	0.524536i
$304$	−9.23993	−	28.3941i	−0.529946	−	1.62852i
$305$	31.8415	−	17.0197i	1.82324	−	0.974543i
$306$	−4.99497	−	0.559569i	−0.285543	−	0.0319884i
$307$	−5.88500	−	15.2563i	−0.335875	−	0.870722i	−0.993126	−	0.117051i	$-0.962656\pi$
$307$	−5.88500	−	15.2563i	−0.335875	−	0.870722i	0.657251	−	0.753672i	$-0.271719\pi$
$308$	−3.88041	−	3.53279i	−0.221107	−	0.201300i
$309$	−1.61584	+	5.83890i	−0.0919221	+	0.332164i
$310$	11.6877	+	4.03542i	0.663818	+	0.229196i
$311$	2.00671	−	8.01125i	0.113790	−	0.454276i	−0.886168	−	0.463363i	$-0.846643\pi$
$311$	2.00671	−	8.01125i	0.113790	−	0.454276i	0.999959	+	0.00908694i	$0.00289250\pi$
$312$	−1.03056	+	0.950936i	−0.0583437	+	0.0538361i
$313$	−11.8845	−	16.0244i	−0.671754	−	0.905755i	0.327482	−	0.944858i	$-0.393800\pi$
$313$	−11.8845	−	16.0244i	−0.671754	−	0.905755i	−0.999235	+	0.0391028i	$0.987550\pi$
$314$	1.94623	−	2.42619i	0.109832	−	0.136918i
$315$	−0.462224	−	18.8289i	−0.0260434	−	1.06089i
$316$	−11.2842	−	7.98493i	−0.634786	−	0.449188i
$317$	−3.79979	+	4.40502i	−0.213418	+	0.247410i	−0.853745	−	0.520692i	$-0.825674\pi$
$317$	−3.79979	+	4.40502i	−0.213418	+	0.247410i	0.640327	+	0.768103i	$0.278799\pi$
$318$	−0.715015	−	0.665701i	−0.0400961	−	0.0373307i
$319$	0.977983	+	2.36106i	0.0547566	+	0.132194i
$320$	−19.6614	+	4.78540i	−1.09911	+	0.267512i
$321$	−4.17769	+	10.0858i	−0.233176	+	0.562937i
$322$	−23.8213	+	10.8789i	−1.32751	+	0.606255i
$323$	0.923855	+	12.5244i	0.0514047	+	0.696876i
$324$	0.0964181	−	3.60042i	0.00535656	−	0.200023i
$325$	−0.507326	+	0.532861i	−0.0281414	+	0.0295578i
$326$	−4.79829	+	16.4774i	−0.265753	+	0.912601i
$327$	4.47648	+	0.664023i	0.247550	+	0.0367205i
$328$	2.75202	+	10.5849i	0.151955	+	0.584452i
$329$	0.720845	−	0.432058i	0.0397415	−	0.0238201i
$330$	1.87737	+	1.66378i	0.103346	+	0.0915879i
$331$	2.42353	+	4.27813i	0.133209	+	0.235147i	0.928711	−	0.370804i	$-0.120918\pi$
$331$	2.42353	+	4.27813i	0.133209	+	0.235147i	−0.795502	+	0.605951i	$0.792793\pi$
$332$	14.6777	−	24.3649i	0.805545	−	1.33720i
$333$	3.40738	−	7.68692i	0.186723	−	0.421241i
$334$	4.83675	+	16.7485i	0.264655	+	0.916439i
$335$	9.44324	−	31.1302i	0.515939	−	1.70082i
$336$	0.917956	+	13.2495i	0.0500786	+	0.722818i
$337$	2.15244	−	0.652935i	0.117251	−	0.0355676i	−0.231114	−	0.972927i	$-0.574237\pi$
$337$	2.15244	−	0.652935i	0.117251	−	0.0355676i	0.348365	+	0.937359i	$0.386737\pi$
$338$	3.74619	−	17.5988i	0.203766	−	0.957247i
$339$	13.1748	+	2.95851i	0.715559	+	0.160684i
$340$	8.51060	+	0.0189754i	0.461552	+	0.00102908i
$341$	−0.807157	−	2.44330i	−0.0437100	−	0.132312i
$342$	−22.0234	+	3.51842i	−1.19089	+	0.190254i
$343$	5.55072	+	0.272689i	0.299711	+	0.0147238i
$344$	0.117172	+	0.163256i	0.00631751	+	0.00880220i
$345$	11.3165	−	5.35232i	0.609261	−	0.288159i
$346$	−6.11028	+	15.2299i	−0.328491	+	0.818766i
$347$	−6.94919	+	10.9740i	−0.373052	+	0.589114i	−0.978368	−	0.206872i	$-0.933672\pi$
$347$	−6.94919	+	10.9740i	−0.373052	+	0.589114i	0.605316	+	0.795985i	$0.293047\pi$
$348$	2.34121	−	6.02929i	0.125502	−	0.323204i
$349$	−30.7197	−	3.78891i	−1.64439	−	0.202816i	−0.753631	−	0.657298i	$-0.771699\pi$
$349$	−30.7197	−	3.78891i	−1.64439	−	0.202816i	−0.890756	+	0.454482i	$0.849824\pi$
$350$	0.930125	+	6.90613i	0.0497173	+	0.369148i
$351$	1.40820	+	2.10751i	0.0751639	+	0.112491i
$352$	3.27304	+	2.64963i	0.174454	+	0.141226i
$353$	12.9487	−	19.3792i	0.689192	−	1.03145i	−0.307608	−	0.951513i	$-0.599528\pi$
$353$	12.9487	−	19.3792i	0.689192	−	1.03145i	0.996800	−	0.0799358i	$-0.0254715\pi$
$354$	−17.5771	−	8.60314i	−0.934213	−	0.457252i
$355$	16.2049	+	9.17994i	0.860065	+	0.487221i
$356$	−1.11067	−	9.17334i	−0.0588651	−	0.486186i
$357$	0.954965	−	5.50360i	0.0505421	−	0.291281i
$358$	8.73878	+	5.69908i	0.461859	+	0.301206i
$359$	−1.61867	−	32.9487i	−0.0854300	−	1.73897i	−0.534233	−	0.845337i	$-0.679399\pi$
$359$	−1.61867	−	32.9487i	−0.0854300	−	1.73897i	0.448803	−	0.893631i	$-0.351851\pi$
$360$	1.24638	+	15.0627i	0.0656902	+	0.793872i
$361$	12.3724	+	34.5784i	0.651177	+	1.81992i
$362$	−1.33907	+	0.496049i	−0.0703801	+	0.0260718i
$363$	−0.723890	+	9.81353i	−0.0379944	+	0.515077i
$364$	2.34718	+	2.87308i	0.123026	+	0.150590i
$365$	28.2539	−	4.90251i	1.47887	−	0.256609i
$366$	7.04126	+	17.6643i	0.368053	+	0.923327i
$367$	1.38471	−	14.0592i	0.0722814	−	0.733885i	−0.888925	−	0.458054i	$-0.848547\pi$
$367$	1.38471	−	14.0592i	0.0722814	−	0.733885i	0.961206	−	0.275832i	$-0.0889532\pi$
$368$	18.5775	−	9.82361i	0.968418	−	0.512091i
$369$	8.12951	−	0.800687i	0.423206	−	0.0416821i
$370$	−4.31487	+	13.5677i	−0.224319	+	0.705350i
$371$	−1.87196	+	1.78225i	−0.0971871	+	0.0925298i
$372$	−2.79752	+	5.88089i	−0.145045	+	0.304910i
$373$	15.3255	+	11.9602i	0.793526	+	0.619274i	0.928397	−	0.371589i	$-0.121187\pi$
$373$	15.3255	+	11.9602i	0.793526	+	0.619274i	−0.134871	+	0.990863i	$0.543062\pi$
$374$	−1.07085	−	1.41070i	−0.0553724	−	0.0729458i
$375$	1.25935	+	8.48987i	0.0650327	+	0.438415i
$376$	−0.557378	+	0.379669i	−0.0287446	+	0.0195799i
$377$	−0.439000	−	1.75259i	−0.0226097	−	0.0902628i
$378$	23.9160	+	2.08639i	1.23011	+	0.107312i
$379$	25.7400	−	11.4098i	1.32217	−	0.586080i	0.381180	−	0.924501i	$-0.375518\pi$
$379$	25.7400	−	11.4098i	1.32217	−	0.586080i	0.940995	+	0.338421i	$0.109893\pi$
$380$	36.4184	−	9.99096i	1.86822	−	0.512526i
$381$	0.959084	+	1.90537i	0.0491353	+	0.0976152i
$382$	−17.9531	−	11.0900i	−0.918563	−	0.567416i
$383$	26.1189	+	26.1189i	1.33461	+	1.33461i	0.901191	+	0.433422i	$0.142694\pi$
$383$	26.1189	+	26.1189i	1.33461	+	1.33461i	0.433422	+	0.901191i	$0.357306\pi$
$384$	−1.35187	−	10.5717i	−0.0689874	−	0.539483i
$385$	4.69294	−	4.69294i	0.239174	−	0.239174i
$386$	19.5503	−	4.61987i	0.995083	−	0.235145i
$387$	0.134068	−	0.0674843i	0.00681508	−	0.00343042i
$388$	−14.8270	−	19.0866i	−0.752727	−	0.968977i
$389$	−10.6156	−	23.9485i	−0.538234	−	1.21424i	−0.952628	−	0.304138i	$-0.901632\pi$
$389$	−10.6156	−	23.9485i	−0.538234	−	1.21424i	0.414394	−	0.910097i	$-0.363993\pi$
$390$	−1.14029	−	1.35826i	−0.0577409	−	0.0687781i
$391$	−8.57359	+	2.14757i	−0.433585	+	0.108607i
$392$	15.3387	−	0.136939i	0.774723	−	0.00691647i
$393$	1.30416	−	0.193454i	0.0657863	−	0.00975848i
$394$	37.8602	+	5.18502i	1.90737	+	0.261217i
$395$	10.7560	−	13.7826i	0.541195	−	0.693477i
$396$	2.33524	−	2.10707i	0.117350	−	0.105884i
$397$	10.2771	+	10.7943i	0.515791	+	0.541752i	0.929580	−	0.368621i	$-0.120170\pi$
$397$	10.2771	+	10.7943i	0.515791	+	0.541752i	−0.413789	+	0.910373i	$0.635795\pi$
$398$	21.3555	−	11.0498i	1.07045	−	0.553876i
$399$	−2.42944	−	24.6665i	−0.121624	−	1.23487i
$400$	−1.06647	−	5.48933i	−0.0533236	−	0.274467i
$401$	−37.4361	−	3.68714i	−1.86947	−	0.184127i	−0.901095	−	0.433623i	$-0.857235\pi$
$401$	−37.4361	−	3.68714i	−1.86947	−	0.184127i	−0.968376	+	0.249496i	$0.919735\pi$
$402$	15.7403	+	6.76808i	0.785053	+	0.337561i
$403$	0.311007	+	1.79238i	0.0154924	+	0.0892846i
$404$	19.3619	+	10.4047i	0.963288	+	0.517653i
$405$	4.54278	+	0.335096i	0.225733	+	0.0166510i
$406$	−15.5499	−	7.14335i	−0.771728	−	0.354519i
$407$	2.78965	−	0.998155i	0.138278	−	0.0494767i
$408$	−0.508962	+	4.45346i	−0.0251974	+	0.220479i
$409$	−30.0173	+	1.47466i	−1.48426	+	0.0729171i	−0.774970	−	0.631998i	$-0.782235\pi$
$409$	−30.0173	+	1.47466i	−1.48426	+	0.0729171i	−0.709292	+	0.704915i	$0.750985\pi$
$410$	−13.5352	+	2.84965i	−0.668454	+	0.140734i
$411$	14.9451	+	2.59322i	0.737187	+	0.127914i
$412$	−12.3889	−	3.45822i	−0.610356	−	0.170374i
$413$	−25.5200	+	45.0492i	−1.25576	+	2.21673i
$414$	−5.08964	−	14.8483i	−0.250142	−	0.729753i
$415$	29.9113	+	19.9861i	1.46829	+	0.981079i
$416$	−2.01404	−	2.19246i	−0.0987466	−	0.107494i
$417$	−3.95592	+	2.64326i	−0.193722	+	0.129441i
$418$	−6.24908	−	4.76561i	−0.305652	−	0.233094i
$419$	−3.40441	+	27.6022i	−0.166316	+	1.34846i	0.645149	+	0.764057i	$0.276795\pi$
$419$	−3.40441	+	27.6022i	−0.166316	+	1.34846i	−0.811466	+	0.584400i	$0.801330\pi$
$420$	−16.7928	+	0.374778i	−0.819403	+	0.0182873i
$421$	−0.265789	−	0.168309i	−0.0129538	−	0.00820289i	0.528505	−	0.848930i	$-0.322753\pi$
$421$	−0.265789	−	0.168309i	−0.0129538	−	0.00820289i	−0.541459	+	0.840727i	$0.682128\pi$
$422$	−30.9942	+	13.2452i	−1.50877	+	0.644768i
$423$	0.215369	+	0.455359i	0.0104716	+	0.0221403i
$424$	1.41673	−	1.51489i	0.0688024	−	0.0735695i
$425$	−0.115401	+	2.34904i	−0.00559777	+	0.113945i
$426$	−5.75511	+	7.94358i	−0.278836	+	0.384868i
$427$	47.7715	−	15.7816i	2.31182	−	0.763723i
$428$	−21.3934	−	8.91736i	−1.03409	−	0.431037i
$429$	−0.0808625	+	0.360097i	−0.00390408	+	0.0173856i
$430$	−0.213187	+	0.138355i	−0.0102808	+	0.00667209i
$431$	−8.74558	−	28.8303i	−0.421260	−	1.38871i	−0.869119	−	0.494603i	$-0.835313\pi$
$431$	−8.74558	−	28.8303i	−0.421260	−	1.38871i	0.447859	−	0.894104i	$-0.352187\pi$
$432$	−19.2566	−	0.558654i	−0.926483	−	0.0268782i
$433$	−38.2965	−	11.6171i	−1.84041	−	0.558283i	−0.999863	−	0.0165453i	$-0.994733\pi$
$433$	−38.2965	−	11.6171i	−1.84041	−	0.558283i	−0.840548	−	0.541737i	$-0.817767\pi$
$434$	15.0853	+	8.32478i	0.724118	+	0.399602i
$435$	7.47826	+	3.31488i	0.358555	+	0.158936i
$436$	−1.43097	+	9.50082i	−0.0685310	+	0.455007i
$437$	−34.1237	+	19.3308i	−1.63236	+	0.924719i
$438$	0.909341	+	15.0759i	0.0434500	+	0.720356i
$439$	14.7085	+	24.5397i	0.701999	+	1.17122i	0.977707	+	0.209974i	$0.0673378\pi$
$439$	14.7085	+	24.5397i	0.701999	+	1.17122i	−0.275708	+	0.961242i	$0.588912\pi$
$440$	−3.54123	+	3.97795i	−0.168822	+	0.189641i
$441$	1.68112	−	11.3332i	0.0800534	−	0.539676i
$442$	0.602529	+	1.09762i	0.0286594	+	0.0522084i
$443$	−6.14059	−	5.84633i	−0.291748	−	0.277767i	0.529535	−	0.848288i	$-0.322366\pi$
$443$	−6.14059	−	5.84633i	−0.291748	−	0.277767i	−0.821283	+	0.570521i	$0.806741\pi$
$444$	−6.84851	−	3.05402i	−0.325016	−	0.144937i
$445$	11.6547	−	0.859702i	0.552486	−	0.0407538i
$446$	−6.67156	−	2.48836i	−0.315907	−	0.117827i
$447$	−1.26420	−	0.523647i	−0.0597944	−	0.0247677i
$448$	−28.1342	+	1.88618i	−1.32922	+	0.0891138i
$449$	−30.3030	+	12.5519i	−1.43009	+	0.592361i	−0.957373	−	0.288856i	$-0.906725\pi$
$449$	−30.3030	+	12.5519i	−1.43009	+	0.592361i	−0.472713	+	0.881217i	$0.656725\pi$
$450$	−4.17407	+	0.149081i	−0.196768	+	0.00702773i
$451$	2.17962	+	1.88015i	0.102634	+	0.0885328i
$452$	−6.34355	+	27.9574i	−0.298375	+	1.31500i
$453$	−5.31791	+	0.130547i	−0.249857	+	0.00613365i
$454$	−18.4358	+	2.02369i	−0.865235	+	0.0949765i
$455$	−3.76868	+	2.79505i	−0.176679	+	0.131034i
$456$	3.09397	+	19.6477i	0.144889	+	0.920090i
$457$	5.96100	+	1.49315i	0.278844	+	0.0698467i	0.379879	−	0.925036i	$-0.375966\pi$
$457$	5.96100	+	1.49315i	0.278844	+	0.0698467i	−0.101035	+	0.994883i	$0.532216\pi$
$458$	7.30387	−	3.55473i	0.341288	−	0.166101i
$459$	7.80886	+	2.16100i	0.364486	+	0.100867i
$460$	11.3099	+	24.0513i	0.527326	+	1.12140i
$461$	35.0831	−	13.5331i	1.63398	−	0.630298i	0.643195	−	0.765703i	$-0.277609\pi$
$461$	35.0831	−	13.5331i	1.63398	−	0.630298i	0.990790	+	0.135405i	$0.0432336\pi$
$462$	2.18117	+	2.73153i	0.101477	+	0.127082i
$463$	2.14808	+	4.01877i	0.0998296	+	0.186768i	0.926878	−	0.375363i	$-0.122482\pi$
$463$	2.14808	+	4.01877i	0.0998296	+	0.186768i	−0.827048	+	0.562131i	$0.809982\pi$
$464$	12.7896	+	4.99914i	0.593744	+	0.232079i
$465$	−7.26375	−	3.88256i	−0.336848	−	0.180049i
$466$	6.65390	−	9.67533i	0.308236	−	0.448201i
$467$	−21.3266	+	13.5049i	−0.986877	+	0.624933i	−0.927705	−	0.373315i	$-0.878221\pi$
$467$	−21.3266	+	13.5049i	−0.986877	+	0.624933i	−0.0591726	+	0.998248i	$0.518846\pi$
$468$	−1.85166	+	1.23127i	−0.0855928	+	0.0569157i
$469$	20.3812	−	40.4905i	0.941118	−	1.86968i
$470$	−0.446626	−	0.726640i	−0.0206013	−	0.0335174i
$471$	−1.53512	+	1.39135i	−0.0707347	+	0.0641102i
$472$	18.3484	−	37.2771i	0.844555	−	1.71582i
$473$	0.0497977	+	0.0178179i	0.00228970	+	0.000819269i
$474$	6.58331	+	6.43802i	0.302381	+	0.295708i
$475$	2.28652	+	10.1824i	0.104913	+	0.467198i
$476$	11.6801	+	2.05353i	0.535357	+	0.0941233i
$477$	−0.953116	−	1.22131i	−0.0436402	−	0.0559197i
$478$	7.17972	+	12.3506i	0.328393	+	0.564904i
$479$	−24.8063	−	4.93428i	−1.13343	−	0.225453i	−0.407489	−	0.913210i	$-0.633595\pi$
$479$	−24.8063	−	4.93428i	−1.13343	−	0.225453i	−0.725941	+	0.687757i	$0.758595\pi$
$480$	13.4355	−	1.08159i	0.613245	−	0.0493675i
$481$	−2.05440	+	0.408646i	−0.0936728	+	0.0186327i
$482$	15.8435	+	17.9580i	0.721653	+	0.817965i
$483$	16.8121	−	4.65254i	0.764978	−	0.211698i
$484$	−20.8316	−	1.58334i	−0.946890	−	0.0719699i
$485$	24.9910	−	17.6006i	1.13478	−	0.799203i
$486$	−4.20427	+	22.4420i	−0.190709	+	1.01799i
$487$	17.8070	+	16.1393i	0.806912	+	0.731343i	0.966729	−	0.255804i	$-0.0823403\pi$
$487$	17.8070	+	16.1393i	0.806912	+	0.731343i	−0.159816	+	0.987147i	$0.551090\pi$
$488$	−37.5362	+	14.8656i	−1.69918	+	0.672935i
$489$	4.88767	−	10.3341i	0.221028	−	0.467325i
$490$	−0.735667	+	19.3859i	−0.0332341	+	0.875767i
$491$	1.97038	+	2.28421i	0.0889218	+	0.103085i	0.799913	−	0.600115i	$-0.204879\pi$
$491$	1.97038	+	2.28421i	0.0889218	+	0.103085i	−0.710992	+	0.703200i	$0.751754\pi$
$492$	−0.697897	−	7.25158i	−0.0314636	−	0.326927i
$493$	−4.72187	−	3.32552i	−0.212662	−	0.149774i
$494$	3.87575	+	3.98093i	0.174378	+	0.179110i
$495$	2.52358	+	3.07499i	0.113426	+	0.138210i
$496$	−12.4724	−	5.96722i	−0.560028	−	0.267936i
$497$	20.0615	+	16.4641i	0.899883	+	0.738515i
$498$	−12.2149	+	14.4841i	−0.547363	+	0.649048i
$499$	0.777195	−	31.6594i	0.0347920	−	1.41727i	−0.687752	−	0.725946i	$-0.741402\pi$
$499$	0.777195	−	31.6594i	0.0347920	−	1.41727i	0.722544	−	0.691325i	$-0.242973\pi$
$500$	−18.0307	+	2.63353i	−0.806358	+	0.117775i
$501$	−1.42146	−	11.5249i	−0.0635063	−	0.514896i
$502$	−7.27185	+	12.4452i	−0.324559	+	0.555455i
$503$	−24.3795	−	18.0811i	−1.08703	−	0.806195i	−0.104914	−	0.994481i	$-0.533457\pi$
$503$	−24.3795	−	18.0811i	−1.08703	−	0.806195i	−0.982114	+	0.188286i	$0.939707\pi$
$504$	−1.87715	+	20.9772i	−0.0836148	+	0.934399i
$505$	−14.2915	+	23.8439i	−0.635963	+	1.06104i
$506$	2.55270	−	4.90668i	0.113481	−	0.218128i
$507$	−4.31347	+	11.1822i	−0.191568	+	0.496621i
$508$	−4.04982	+	2.02720i	−0.179681	+	0.0899425i
$509$	−2.18012	+	6.59933i	−0.0966322	+	0.292510i	−0.986513	−	0.163683i	$-0.947662\pi$
$509$	−2.18012	+	6.59933i	−0.0966322	+	0.292510i	0.889881	+	0.456193i	$0.150787\pi$
$510$	−5.59601	−	0.906807i	−0.247795	−	0.0401541i
$511$	39.9591			1.76769
$512$	22.4510	−	2.82010i	0.992203	−	0.124632i
$513$	35.9524			1.58734
$514$	20.1296	+	3.26190i	0.887878	+	0.143876i
$515$	5.10277	−	15.4463i	0.224855	−	0.680645i
$516$	−0.0599167	−	0.119698i	−0.00263769	−	0.00526940i
$517$	−0.0638807	+	0.165604i	−0.00280947	+	0.00728328i
$518$	−9.15632	+	17.5998i	−0.402306	+	0.773292i
$519$	5.61957	−	9.37568i	0.246672	−	0.411547i
$520$	2.88910	−	2.41451i	0.126696	−	0.105883i
$521$	9.92515	+	7.36099i	0.434829	+	0.322491i	0.790875	−	0.611977i	$-0.209626\pi$
$521$	9.92515	+	7.36099i	0.434829	+	0.322491i	−0.356047	+	0.934468i	$0.615876\pi$
$522$	5.17447	−	8.85566i	0.226480	−	0.387602i
$523$	3.77280	+	30.5891i	0.164973	+	1.33757i	0.815797	+	0.578339i	$0.196299\pi$
$523$	3.77280	+	30.5891i	0.164973	+	1.33757i	−0.650824	+	0.759229i	$0.725576\pi$
$524$	0.404547	+	2.76977i	0.0176727	+	0.120998i
$525$	0.113915	−	4.64037i	0.00497165	−	0.202522i
$526$	18.0298	−	21.3792i	0.786136	−	0.932179i
$527$	4.49514	+	3.68907i	0.195811	+	0.160698i
$528$	−1.87447	−	2.08678i	−0.0815758	−	0.0908156i
$529$	−2.91925	−	3.55711i	−0.126924	−	0.154657i
$530$	1.82987	+	1.87953i	0.0794845	+	0.0816416i
$531$	−25.3720	−	17.8690i	−1.10105	−	0.775449i
$532$	52.3808	−	5.04116i	2.27100	−	0.218562i
$533$	−1.32921	−	1.54093i	−0.0575746	−	0.0667449i
$534$	−0.233408	+	6.15065i	−0.0101006	+	0.266164i
$535$	12.5329	−	26.4985i	0.541843	−	1.14563i
$536$	−14.4438	+	33.3859i	−0.623875	+	1.44205i
$537$	−5.14922	−	4.66698i	−0.222205	−	0.201395i
$538$	0.281675	−	1.50355i	0.0121439	−	0.0648228i
$539$	3.30077	−	2.32466i	0.142174	−	0.100130i
$540$	1.84652	−	24.2942i	0.0794616	−	1.04546i
$541$	−37.7355	+	10.4428i	−1.62238	+	0.448972i	−0.955208	−	0.295935i	$-0.904369\pi$
$541$	−37.7355	+	10.4428i	−1.62238	+	0.448972i	−0.667168	+	0.744907i	$0.732494\pi$
$542$	−2.03671	−	2.30853i	−0.0874842	−	0.0991598i
$543$	0.932927	−	0.185571i	0.0400357	−	0.00796360i
$544$	−9.45268	−	1.10165i	−0.405280	−	0.0472330i
$545$	−11.9178	−	2.37061i	−0.510504	−	0.101546i
$546$	−1.24199	−	2.13647i	−0.0531521	−	0.0914326i
$547$	−5.26981	−	6.75264i	−0.225321	−	0.288722i	0.662356	−	0.749190i	$-0.269557\pi$
$547$	−5.26981	−	6.75264i	−0.225321	−	0.288722i	−0.887677	+	0.460467i	$0.847682\pi$
$548$	−5.57638	+	31.7175i	−0.238211	+	1.35490i
$549$	6.60699	+	29.4223i	0.281980	+	1.25571i
$550$	−1.05224	−	1.02902i	−0.0448678	−	0.0438777i
$551$	−24.1290	−	8.63348i	−1.02793	−	0.367799i
$552$	−13.2520	+	4.50947i	−0.564042	+	0.191936i
$553$	18.0509	−	16.3604i	0.767603	−	0.695715i
$554$	12.7929	+	20.8135i	0.543520	+	0.884283i
$555$	4.26393	−	8.47097i	0.180994	−	0.359573i
$556$	−5.59316	−	8.41129i	−0.237203	−	0.356718i
$557$	9.26844	−	5.86918i	0.392717	−	0.248685i	−0.323989	−	0.946061i	$-0.605024\pi$
$557$	9.26844	−	5.86918i	0.392717	−	0.248685i	0.716706	+	0.697376i	$0.245649\pi$
$558$	−5.85188	+	8.50914i	−0.247730	+	0.360220i
$559$	−0.0329762	−	0.0176262i	−0.00139475	−	0.000745507i
$560$	−0.716195	−	35.6543i	−0.0302648	−	1.50667i
$561$	0.556130	+	1.04045i	0.0234798	+	0.0439277i
$562$	16.2825	+	20.3909i	0.686834	+	0.860136i
$563$	7.46735	−	2.88048i	0.314711	−	0.121398i	−0.197384	−	0.980326i	$-0.563245\pi$
$563$	7.46735	−	2.88048i	0.314711	−	0.121398i	0.512095	+	0.858929i	$0.328870\pi$
$564$	0.406522	−	0.191163i	0.0171177	−	0.00804941i
$565$	−34.9434	−	9.67015i	−1.47008	−	0.406826i
$566$	39.9187	−	19.4281i	1.67791	−	0.816622i
$567$	6.15718	+	1.54229i	0.258577	+	0.0647703i
$568$	−16.8377	−	12.2562i	−0.706494	−	0.514259i
$569$	−7.29965	+	5.41379i	−0.306017	+	0.226958i	−0.737799	−	0.675020i	$-0.764135\pi$
$569$	−7.29965	+	5.41379i	−0.306017	+	0.226958i	0.431782	+	0.901978i	$0.357885\pi$
$570$	−25.0048	+	2.74476i	−1.04733	+	0.114965i
$571$	−4.37286	+	0.107348i	−0.182998	+	0.00449236i	−0.115937	−	0.993257i	$-0.536987\pi$
$571$	−4.37286	+	0.107348i	−0.182998	+	0.00449236i	−0.0670610	+	0.997749i	$0.521362\pi$
$572$	−0.764136	−	0.173383i	−0.0319501	−	0.00724950i
$573$	10.6436	+	9.18126i	0.444644	+	0.383553i
$574$	−19.2620	+	0.687959i	−0.803979	+	0.0287148i
$575$	−6.78559	+	2.81068i	−0.282979	+	0.117214i
$576$	0.527768	−	16.8925i	0.0219903	−	0.703855i
$577$	−26.6687	−	11.0465i	−1.11023	−	0.459873i	−0.249214	−	0.968448i	$-0.580172\pi$
$577$	−26.6687	−	11.0465i	−1.11023	−	0.459873i	−0.861017	+	0.508575i	$0.830172\pi$
$578$	−18.7756	−	7.00294i	−0.780964	−	0.291284i
$579$	−13.3450	+	0.984388i	−0.554600	+	0.0409098i
$580$	−7.07319	+	15.8613i	−0.293698	+	0.658605i
$581$	36.3055	+	34.5657i	1.50621	+	1.43403i
$582$	7.74704	+	14.1127i	0.321125	+	0.584988i
$583$	0.0800997	−	0.539988i	0.00331739	−	0.0223640i
$584$	−32.0119	+	1.85925i	−1.32466	+	0.0769363i
$585$	−1.44581	−	2.41218i	−0.0597768	−	0.0997315i
$586$	−0.0263475	−	0.436814i	−0.00108841	−	0.0180446i
$587$	13.5483	−	7.67503i	0.559199	−	0.316782i	−0.187156	−	0.982330i	$-0.559927\pi$
$587$	13.5483	−	7.67503i	0.559199	−	0.316782i	0.746355	+	0.665548i	$0.231802\pi$
$588$	−10.1037	−	1.52178i	−0.416671	−	0.0627570i
$589$	23.5896	+	10.4566i	0.971993	+	0.430855i
$590$	46.0061	+	25.3883i	1.89404	+	1.04522i
$591$	−24.3584	−	7.38903i	−1.00197	−	0.303944i
$592$	6.51638	−	14.5255i	0.267822	−	0.596996i
$593$	4.56273	+	15.0413i	0.187369	+	0.617673i	0.999419	+	0.0340848i	$0.0108516\pi$
$593$	4.56273	+	15.0413i	0.187369	+	0.617673i	−0.812050	+	0.583588i	$0.801648\pi$
$594$	−4.25316	+	2.76024i	−0.174509	+	0.113254i
$595$	−3.28620	+	14.6341i	−0.134721	+	0.599940i
$596$	1.11773	−	2.68152i	0.0457842	−	0.109839i
$597$	−15.2081	+	5.02409i	−0.622427	+	0.205622i
$598$	−2.29415	+	3.16653i	−0.0938146	+	0.129489i
$599$	0.172511	−	3.51154i	0.00704860	−	0.143478i	−0.992691	−	0.120680i	$-0.961493\pi$
$599$	0.172511	−	3.51154i	0.00704860	−	0.143478i	0.999740	−	0.0227979i	$-0.00725741\pi$
$600$	0.124652	+	3.72278i	0.00508890	+	0.151982i
$601$	10.4802	+	22.1586i	0.427497	+	0.903867i	0.996662	+	0.0816432i	$0.0260168\pi$
$601$	10.4802	+	22.1586i	0.427497	+	0.903867i	−0.569164	+	0.822224i	$0.692733\pi$
$602$	−0.325656	+	0.139168i	−0.0132727	+	0.00567205i
$603$	22.9548	+	14.5359i	0.934790	+	0.591949i
$604$	−0.251991	−	11.2910i	−0.0102534	−	0.459425i
$605$	3.23433	−	26.2233i	0.131494	−	1.06613i
$606$	−11.6422	−	8.87849i	−0.472934	−	0.360664i
$607$	−18.9998	+	12.6952i	−0.771177	+	0.515284i	−0.877807	−	0.479015i	$-0.840994\pi$
$607$	−18.9998	+	12.6952i	−0.771177	+	0.515284i	0.106630	+	0.994299i	$0.465994\pi$
$608$	−41.7286	+	6.47577i	−1.69232	+	0.262627i
$609$	9.47757	+	6.33271i	0.384051	+	0.256614i
$610$	−16.5565	−	48.3010i	−0.670351	−	1.95565i
$611$	0.0618519	−	0.109184i	0.00250226	−	0.00441711i
$612$	−1.91110	+	6.84641i	−0.0772517	+	0.276750i
$613$	15.2458	+	2.64540i	0.615774	+	0.106847i	0.470287	−	0.882513i	$-0.344150\pi$
$613$	15.2458	+	2.64540i	0.615774	+	0.106847i	0.145486	+	0.989360i	$0.453525\pi$
$614$	−22.6291	+	4.76427i	−0.913237	+	0.192270i
$615$	9.20245	−	0.452087i	0.371079	−	0.0182299i
$616$	−5.80960	+	4.61790i	−0.234076	+	0.186060i
$617$	−2.83124	+	1.01303i	−0.113981	+	0.0407832i	−0.393263	−	0.919426i	$-0.628654\pi$
$617$	−2.83124	+	1.01303i	−0.113981	+	0.0407832i	0.279281	+	0.960209i	$0.409904\pi$
$618$	7.78560	+	3.57657i	0.313183	+	0.143871i
$619$	37.5230	+	2.76786i	1.50818	+	0.111250i	0.802230	−	0.597015i	$-0.203647\pi$
$619$	37.5230	+	2.76786i	1.50818	+	0.111250i	0.705946	+	0.708265i	$0.250522\pi$
$620$	8.27740	−	15.4032i	0.332428	−	0.618608i
$621$	4.32582	+	24.9303i	0.173589	+	1.00042i
$622$	−10.7298	−	4.61365i	−0.430225	−	0.184991i
$623$	16.2061	+	1.59616i	0.649285	+	0.0639490i
$624$	1.09438	+	1.65378i	0.0438104	+	0.0662040i
$625$	−2.94400	−	29.8910i	−0.117760	−	1.19564i
$626$	−25.0586	+	12.9659i	−1.00154	+	0.518220i
$627$	3.60966	+	3.79134i	0.144156	+	0.151412i
$628$	−2.94670	−	3.26579i	−0.117586	−	0.130319i
$629$	−4.11944	+	5.27857i	−0.164253	+	0.210470i
$630$	−26.3898	−	3.61413i	−1.05140	−	0.143991i
$631$	−35.6470	+	5.28773i	−1.41908	+	0.210501i	−0.811777	−	0.583967i	$-0.801500\pi$
$631$	−35.6470	+	5.28773i	−1.41908	+	0.210501i	−0.607306	+	0.794468i	$0.707750\pi$
$632$	−13.6997	+	13.9465i	−0.544943	+	0.554761i
$633$	21.7788	−	5.45532i	0.865631	−	0.216829i
$634$	5.28985	+	6.30101i	0.210087	+	0.250245i
$635$	−2.32110	−	5.23632i	−0.0921101	−	0.207797i
$636$	−1.09107	+	0.847571i	−0.0432637	+	0.0336084i
$637$	−2.54944	+	1.28328i	−0.101012	+	0.0508454i
$638$	3.51728	−	0.831159i	0.139251	−	0.0329059i
$639$	−10.9992	+	10.9992i	−0.435123	+	0.435123i
$640$	2.23271	+	28.5300i	0.0882556	+	1.12775i
$641$	−23.8147	−	23.8147i	−0.940625	−	0.940625i	0.0577081	−	0.998333i	$-0.481621\pi$
$641$	−23.8147	−	23.8147i	−0.940625	−	0.940625i	−0.998333	+	0.0577081i	$0.981621\pi$
$642$	13.1348	+	8.11365i	0.518390	+	0.320220i
$643$	2.81315	+	5.58876i	0.110940	+	0.220399i	0.941870	−	0.335977i	$-0.109066\pi$
$643$	2.81315	+	5.58876i	0.110940	+	0.220399i	−0.830931	+	0.556376i	$0.812191\pi$
$644$	9.79817	+	35.7156i	0.386102	+	1.40739i
$645$	0.154767	−	0.0686033i	0.00609393	−	0.00270125i
$646$	17.6931	+	1.54351i	0.696126	+	0.0607286i
$647$	−6.13494	−	24.4921i	−0.241189	−	0.962882i	−0.962720	−	0.270500i	$-0.912811\pi$
$647$	−6.13494	−	24.4921i	−0.241189	−	0.962882i	0.721531	−	0.692383i	$-0.243439\pi$
$648$	−5.00438	−	0.949071i	−0.196591	−	0.0372830i
$649$	−1.60452	−	10.8168i	−0.0629831	−	0.424597i
$650$	0.629110	+	0.828770i	0.0246757	+	0.0325070i
$651$	−9.04783	−	7.06100i	−0.354613	−	0.276742i
$652$	21.9171	+	10.4259i	0.858340	+	0.408309i
$653$	23.3203	−	22.2027i	0.912592	−	0.868860i	−0.0791818	−	0.996860i	$-0.525231\pi$
$653$	23.3203	−	22.2027i	0.912592	−	0.868860i	0.991774	+	0.128000i	$0.0408558\pi$
$654$	1.93963	−	6.09897i	0.0758454	−	0.238488i
$655$	−3.52308	+	0.346993i	−0.137658	+	0.0135582i
$656$	15.3991	−	1.44737i	0.601233	−	0.0565104i
$657$	−2.34756	+	23.8351i	−0.0915869	+	0.929897i
$658$	−0.440088	−	1.10404i	−0.0171564	−	0.0430400i
$659$	18.5705	−	3.22229i	0.723405	−	0.125523i	0.202677	−	0.979246i	$-0.435036\pi$
$659$	18.5705	−	3.22229i	0.723405	−	0.125523i	0.520728	+	0.853723i	$0.325661\pi$
$660$	2.74733	−	2.24444i	0.106940	−	0.0873648i
$661$	2.20093	−	29.8373i	0.0856062	−	1.16053i	−0.768294	−	0.640098i	$-0.778894\pi$
$661$	2.20093	−	29.8373i	0.0856062	−	1.16053i	0.853900	−	0.520437i	$-0.174231\pi$
$662$	6.52053	−	2.41548i	0.253428	−	0.0938802i
$663$	−0.280983	−	0.785294i	−0.0109125	−	0.0304983i
$664$	−30.6932	−	26.0019i	−1.19113	−	1.00907i
$665$	3.26559	+	66.4726i	0.126634	+	2.57770i
$666$	−9.96017	−	6.49561i	−0.385949	−	0.251700i
$667$	3.08346	−	17.7704i	0.119392	−	0.688074i
$668$	24.4752	−	2.96334i	0.946973	−	0.114655i
$669$	4.12685	+	2.33783i	0.159553	+	0.0903859i
$670$	−41.3216	−	20.2249i	−1.59639	−	0.781357i
$671$	−5.90339	+	8.83504i	−0.227898	+	0.341073i
$672$	18.7040	+	1.71577i	0.721522	+	0.0661873i
$673$	19.3266	+	28.9244i	0.744987	+	1.11495i	0.989391	+	0.145279i	$0.0464079\pi$
$673$	19.3266	+	28.9244i	0.744987	+	1.11495i	−0.244403	+	0.969674i	$0.578592\pi$
$674$	−0.424584	−	3.15252i	−0.0163544	−	0.121430i
$675$	6.68234	+	0.824188i	0.257203	+	0.0317230i
$676$	−23.7205	−	9.21082i	−0.912327	−	0.354262i
$677$	−17.6695	+	27.9032i	−0.679094	+	1.07241i	0.313342	+	0.949640i	$0.398552\pi$
$677$	−17.6695	+	27.9032i	−0.679094	+	1.07241i	−0.992436	+	0.122766i	$0.960823\pi$
$678$	7.11045	−	17.7229i	0.273075	−	0.680642i
$679$	38.5043	−	18.2112i	1.47766	−	0.698881i
$680$	1.95172	−	11.8765i	0.0748451	−	0.455444i
$681$	12.3391	+	0.606183i	0.472837	+	0.0232290i
$682$	−3.59344	+	0.574081i	−0.137600	+	0.0219827i
$683$	3.93283	+	11.9048i	0.150485	+	0.455526i	0.997050	−	0.0767610i	$-0.0244578\pi$
$683$	3.93283	+	11.9048i	0.150485	+	0.455526i	−0.846564	+	0.532287i	$0.821333\pi$
$684$	−0.0703236	+	31.5407i	−0.00268889	+	1.20599i
$685$	−39.7391	−	8.92372i	−1.51835	−	0.340958i
$686$	1.63634	−	7.68714i	0.0624756	−	0.293496i
$687$	−5.17780	+	1.57067i	−0.197545	+	0.0599247i
$688$	0.254413	−	0.126642i	0.00969940	−	0.00482818i
$689$	−0.112031	+	0.369315i	−0.00426803	+	0.0140698i
$690$	−4.91188	−	17.0087i	−0.186992	−	0.647510i
$691$	13.4877	−	30.4278i	0.513096	−	1.15753i	−0.451133	−	0.892457i	$-0.648980\pi$
$691$	13.4877	−	30.4278i	0.513096	−	1.15753i	0.964229	−	0.265070i	$-0.0853950\pi$
$692$	19.8788	+	11.9752i	0.755679	+	0.455230i
$693$	2.73220	+	4.82300i	0.103788	+	0.183211i
$694$	13.7477	+	12.1836i	0.521855	+	0.462482i
$695$	10.9575	−	6.56769i	0.415643	−	0.249127i
$696$	−7.88729	−	4.63226i	−0.298967	−	0.175585i
$697$	−6.43469	−	0.954496i	−0.243731	−	0.0361541i
$698$	−12.2386	+	42.0277i	−0.463238	+	1.59077i
$699$	−5.39344	+	5.66491i	−0.203999	+	0.214267i
$700$	9.85139	+	0.263817i	0.372347	+	0.00997136i
$701$	−1.51473	−	20.5347i	−0.0572106	−	0.775585i	−0.947412	−	0.320017i	$-0.896311\pi$
$701$	−1.51473	−	20.5347i	−0.0572106	−	0.775585i	0.890201	−	0.455568i	$-0.150564\pi$
$702$	3.26065	−	1.48909i	0.123065	−	0.0562022i
$703$	−11.3699	+	27.4493i	−0.428823	+	1.03527i
$704$	4.43930	−	3.96979i	0.167312	−	0.149617i
$705$	0.217418	+	0.524894i	0.00818845	+	0.0197687i
$706$	−24.1242	−	22.4604i	−0.907925	−	0.845307i
$707$	−25.3019	+	29.3319i	−0.951574	+	1.10314i
$708$	−15.9862	+	22.5915i	−0.600799	+	0.849042i
$709$	−1.11874	−	45.5723i	−0.0420150	−	1.71150i	−0.537812	−	0.843065i	$-0.680749\pi$
$709$	−1.11874	−	45.5723i	−0.0420150	−	1.71150i	0.495797	−	0.868438i	$-0.334876\pi$
$710$	16.4810	−	20.5454i	0.618522	−	0.771055i
$711$	8.69832	+	11.7283i	0.326213	+	0.439847i
$712$	−13.0573	−	0.524661i	−0.489342	−	0.0196625i
$713$	−4.41252	+	17.6158i	−0.165250	+	0.659716i
$714$	−7.46701	−	2.57813i	−0.279446	−	0.0964843i
$715$	0.264306	−	0.955080i	0.00988449	−	0.0357180i
$716$	9.93279	−	10.9102i	0.371206	−	0.407732i
$717$	−3.42474	−	8.87832i	−0.127899	−	0.331567i
$718$	−46.3627	−	5.19386i	−1.73024	−	0.193833i
$719$	25.4597	−	13.6085i	0.949485	−	0.507510i	0.0774730	−	0.996994i	$-0.475315\pi$
$719$	25.4597	−	13.6085i	0.949485	−	0.507510i	0.872012	+	0.489484i	$0.162815\pi$
$720$	21.3095	+	1.66745i	0.794157	+	0.0621424i
$721$	10.6856	−	19.9914i	0.397953	−	0.744518i
$722$	51.0704	−	9.44968i	1.90065	−	0.351681i
$723$	−8.53428	−	13.4771i	−0.317393	−	0.501219i
$724$	0.389567	+	1.98157i	0.0144781	+	0.0736443i
$725$	−4.28684	−	2.15782i	−0.159209	−	0.0801392i
$726$	13.5360	+	3.23053i	0.502367	+	0.119896i
$727$	−12.3013	−	13.5724i	−0.456232	−	0.503374i	0.468779	−	0.883316i	$-0.344694\pi$
$727$	−12.3013	−	13.5724i	−0.456232	−	0.503374i	−0.925011	+	0.379941i	$0.875944\pi$
$728$	4.54180	−	2.62673i	0.168330	−	0.0973532i
$729$	3.30365	−	9.23309i	0.122358	−	0.341966i
$730$	−0.452454	−	40.5515i	−0.0167461	−	1.50088i
$731$	−0.116621	+	0.0261881i	−0.00431337	+	0.000968600i
$732$	26.2523	−	5.83369i	0.970311	−	0.215619i
$733$	26.1849	−	20.4349i	0.967163	−	0.754781i	−0.00230579	−	0.999997i	$-0.500734\pi$
$733$	26.1849	−	20.4349i	0.967163	−	0.754781i	0.969468	+	0.245216i	$0.0788590\pi$
$734$	−19.3135	−	5.11348i	−0.712873	−	0.188742i
$735$	2.52104	−	12.6741i	0.0929901	−	0.467493i
$736$	−9.51128	−	28.1565i	−0.350591	−	1.03786i
$737$	1.86780	+	9.39007i	0.0688013	+	0.345888i
$738$	0.721262	−	11.5300i	0.0265500	−	0.424424i
$739$	−2.31403	−	8.36183i	−0.0851230	−	0.307595i	0.908864	−	0.417092i	$-0.136951\pi$
$739$	−2.31403	−	8.36183i	−0.0851230	−	0.307595i	−0.993987	+	0.109497i	$0.965076\pi$
$740$	17.9644	+	9.09280i	0.660386	+	0.334258i
$741$	−2.13101	−	3.02581i	−0.0782848	−	0.111156i
$742$	2.06456	+	3.01643i	0.0757925	+	0.110737i
$743$	7.14992	−	7.88872i	0.262305	−	0.289409i	−0.595531	−	0.803332i	$-0.703058\pi$
$743$	7.14992	−	7.88872i	0.262305	−	0.289409i	0.857836	+	0.513923i	$0.171808\pi$
$744$	7.57691	+	5.23570i	0.277783	+	0.191950i
$745$	3.32142	+	1.57091i	0.121687	+	0.0575538i
$746$	20.1633	−	18.6889i	0.738231	−	0.684250i
$747$	−22.7510	+	19.6251i	−0.832414	+	0.718045i
$748$	−2.21159	+	1.17579i	−0.0808638	+	0.0429911i
$749$	23.5197	−	33.3954i	0.859392	−	1.22024i
$750$	12.1368	+	0.162480i	0.443172	+	0.00593295i
$751$	−3.72965	+	3.06085i	−0.136097	+	0.111692i	−0.699979	−	0.714164i	$-0.746807\pi$
$751$	−3.72965	+	3.06085i	−0.136097	+	0.111692i	0.563882	+	0.825855i	$0.309307\pi$
$752$	0.403931	+	0.863988i	0.0147299	+	0.0315064i
$753$	6.09098	−	7.42188i	0.221968	−	0.270468i
$754$	−2.54593	+	0.216383i	−0.0927172	+	0.00788021i
$755$	14.2792	+	0.350534i	0.519672	+	0.0127572i
$756$	8.32278	−	32.9149i	0.302697	−	1.19710i
$757$	11.0263	−	1.35997i	0.400759	−	0.0494289i	0.0804898	−	0.996755i	$-0.474352\pi$
$757$	11.0263	−	1.35997i	0.400759	−	0.0494289i	0.320269	+	0.947327i	$0.396227\pi$
$758$	−10.1053	−	38.5142i	−0.367040	−	1.39890i
$759$	−2.19470	+	2.95921i	−0.0796625	+	0.107412i
$760$	−5.70901	−	53.1003i	−0.207087	−	1.92615i
$761$	−9.64087	−	5.77851i	−0.349481	−	0.209471i	0.328581	−	0.944476i	$-0.393430\pi$
$761$	−9.64087	−	5.77851i	−0.349481	−	0.209471i	−0.678062	+	0.735005i	$0.737180\pi$
$762$	2.87687	−	0.907859i	0.104218	−	0.0328883i
$763$	−15.7979	−	6.09391i	−0.571921	−	0.220614i
$764$	−19.5430	+	22.5539i	−0.707042	+	0.815972i
$765$	−8.53602	−	2.81992i	−0.308621	−	0.101954i
$766$	42.3706	−	30.5536i	1.53091	−	1.10395i
$767$			7.73086i			0.279145i
$768$	−15.0639	−	0.504258i	−0.543572	−	0.0181959i
$769$		−	48.6227i		−	1.75338i	−0.481056	−	0.876690i	$-0.659746\pi$
$769$		−	48.6227i		−	1.75338i	0.481056	−	0.876690i	$-0.340254\pi$
$770$	−5.48974	−	7.61298i	−0.197837	−	0.274353i
$771$	−12.8978	−	4.26087i	−0.464504	−	0.153451i
$772$	−2.02677	−	28.3373i	−0.0729452	−	1.01988i
$773$	24.0417	+	9.27392i	0.864721	+	0.333560i	0.751279	−	0.659985i	$-0.229437\pi$
$773$	24.0417	+	9.27392i	0.864721	+	0.333560i	0.113442	+	0.993545i	$0.463812\pi$
$774$	−0.0638800	−	0.202426i	−0.00229612	−	0.00727605i
$775$	4.14480	+	2.48430i	0.148886	+	0.0892386i
$776$	−29.9991	+	16.3808i	−1.07691	+	0.588038i
$777$	7.87219	−	10.6144i	0.282413	−	0.380790i
$778$	−35.8336	+	9.40193i	−1.28470	+	0.337076i
$779$	−28.6478	+	3.53337i	−1.02642	+	0.126596i
$780$	−2.15409	+	1.28459i	−0.0771287	+	0.0459957i
$781$	−5.47961	−	0.134517i	−0.196076	−	0.00481340i
$782$	1.05854	+	12.4546i	0.0378532	+	0.445375i
$783$	−10.4890	+	12.7808i	−0.374845	+	0.456750i
$784$	3.27870	−	21.4439i	0.117096	−	0.765854i
$785$	4.30031	−	3.52918i	0.153485	−	0.125962i
$786$	0.0249593	−	1.86438i	0.000890268	−	0.0665002i
$787$	8.23280	−	11.6897i	0.293468	−	0.416692i	−0.643859	−	0.765144i	$-0.722668\pi$
$787$	8.23280	−	11.6897i	0.293468	−	0.416692i	0.937327	+	0.348452i	$0.113293\pi$
$788$	15.8029	−	51.6800i	0.562954	−	1.84102i
$789$	−14.1060	+	12.1680i	−0.502188	+	0.433191i
$790$	−16.8074	−	18.1333i	−0.597979	−	0.645154i
$791$	−45.6719	−	21.6012i	−1.62391	−	0.768050i
$792$	−2.41321	−	3.73666i	−0.0857499	−	0.132776i
$793$	5.04485	−	5.56614i	0.179148	−	0.197659i
$794$	17.3938	−	11.9050i	0.617282	−	0.422491i
$795$	−1.00612	−	1.42858i	−0.0356835	−	0.0506667i
$796$	−10.5946	−	32.3120i	−0.375516	−	1.14527i
$797$	−2.06374	−	7.45741i	−0.0731015	−	0.264155i	0.918132	−	0.396274i	$-0.129697\pi$
$797$	−2.06374	−	7.45741i	−0.0731015	−	0.264155i	−0.991234	+	0.132119i	$0.957822\pi$
$798$	−34.9842	−	2.18845i	−1.23843	−	0.0774703i
$799$	−0.0782562	−	0.393421i	−0.00276851	−	0.0139182i
$800$	−7.90438	+	0.247025i	−0.279462	+	0.00873366i
$801$	−1.90419	+	9.57300i	−0.0672812	+	0.338245i
$802$	−13.6159	+	51.4269i	−0.480794	+	1.81595i
$803$	−6.65326	+	5.19225i	−0.234788	+	0.183231i
$804$	13.0090	−	20.4424i	0.458791	−	0.720948i
$805$	−45.7009	+	10.2625i	−1.61074	+	0.361705i
$806$	2.57252	−	0.0287029i	0.0906131	−	0.00101102i
$807$	−0.343276	+	0.959391i	−0.0120839	+	0.0337722i
$808$	18.9049	−	24.6755i	0.665074	−	0.868081i
$809$	5.90455	+	6.51467i	0.207593	+	0.229044i	0.835844	−	0.548967i	$-0.184979\pi$
$809$	5.90455	+	6.51467i	0.207593	+	0.229044i	−0.628251	+	0.778011i	$0.716229\pi$
$810$	1.49544	−	6.26594i	0.0525445	−	0.220163i
$811$	23.3213	+	11.7389i	0.818920	+	0.412210i	0.809049	−	0.587742i	$-0.199983\pi$
$811$	23.3213	+	11.7389i	0.818920	+	0.412210i	0.00987124	+	0.999951i	$0.496858\pi$
$812$	−13.4898	+	20.0918i	−0.473398	+	0.705082i
$813$	1.09709	+	1.73250i	0.0384768	+	0.0607615i
$814$	−0.762364	−	4.12017i	−0.0267208	−	0.144412i
$815$	−14.4696	+	27.0708i	−0.506850	+	0.948249i
$816$	6.10191	+	1.71795i	0.213609	+	0.0601404i
$817$	−0.467740	+	0.250012i	−0.0163642	+	0.00874683i
$818$	−4.73177	+	42.2379i	−0.165442	+	1.47681i
$819$	−1.41037	−	3.65624i	−0.0492822	−	0.127759i
$820$	0.916260	+	19.5398i	0.0319972	+	0.682358i
$821$	11.7653	−	42.5145i	0.410613	−	1.48377i	−0.409895	−	0.912133i	$-0.634435\pi$
$821$	11.7653	−	42.5145i	0.410613	−	1.48377i	0.820509	−	0.571634i	$-0.193690\pi$
$822$	7.00096	−	20.2768i	0.244186	−	0.707234i
$823$	−11.9589	+	47.7428i	−0.416863	+	1.66421i	0.290129	+	0.956987i	$0.406302\pi$
$823$	−11.9589	+	47.7428i	−0.416863	+	1.66421i	−0.706992	+	0.707222i	$0.749948\pi$
$824$	−7.63024	+	16.5126i	−0.265812	+	0.575244i
$825$	0.584000	+	0.787432i	0.0203323	+	0.0274149i
$826$	57.1158	+	45.8169i	1.98731	+	1.59417i
$827$	−0.389553	−	15.8686i	−0.0135461	−	0.551807i	−0.967645	−	0.252315i	$-0.918808\pi$
$827$	−0.389553	−	15.8686i	−0.0135461	−	0.551807i	0.954099	−	0.299492i	$-0.0968170\pi$
$828$	−21.8796	+	3.74624i	−0.760369	+	0.130191i
$829$	−9.22152	+	10.6903i	−0.320277	+	0.371290i	−0.894237	−	0.447593i	$-0.852281\pi$
$829$	−9.22152	+	10.6903i	−0.320277	+	0.371290i	0.573961	+	0.818883i	$0.305406\pi$
$830$	34.6671	−	37.2351i	1.20331	−	1.29245i
$831$	−6.22763	−	15.0348i	−0.216034	−	0.521552i
$832$	−3.51629	+	2.31564i	−0.121906	+	0.0802805i
$833$	−3.49149	+	8.42921i	−0.120973	+	0.292055i
$834$	2.79511	+	6.12043i	0.0967869	+	0.211933i
$835$	2.29375	+	31.0956i	0.0793786	+	1.07611i
$836$	−8.06645	+	7.64568i	−0.278984	+	0.264431i
$837$	11.4792	−	12.0570i	0.396778	−	0.416749i
$838$	37.7627	+	10.9966i	1.30449	+	0.379872i
$839$	46.1823	+	6.85050i	1.59439	+	0.236505i	0.884063	−	0.467367i	$-0.154797\pi$
$839$	46.1823	+	6.85050i	1.59439	+	0.236505i	0.710327	+	0.703872i	$0.248547\pi$
$840$	−3.27560	+	23.5276i	−0.113019	+	0.811778i
$841$	−14.7655	+	8.85008i	−0.509154	+	0.305175i
$842$	−0.295086	+	0.332969i	−0.0101693	+	0.0114749i
$843$	−8.56735	−	15.1235i	−0.295075	−	0.520880i
$844$	11.4790	+	46.2643i	0.395125	+	1.59248i
$845$	13.0415	−	29.4210i	0.448640	−	1.01211i
$846$	0.684402	−	0.197646i	0.0235302	−	0.00679522i
$847$	10.6877	−	35.2327i	0.367235	−	1.21061i
$848$	−1.79431	−	2.32045i	−0.0616167	−	0.0796846i
$849$	−28.2988	+	8.58436i	−0.971214	+	0.294614i
$850$	3.25317	+	0.692491i	0.111583	+	0.0237522i
$851$	−20.4021	−	4.58144i	−0.699375	−	0.157050i
$852$	9.78737	+	9.83111i	0.335310	+	0.336808i
$853$	−11.5227	−	34.8796i	−0.394529	−	1.19425i	−0.935534	−	0.353236i	$-0.885081\pi$
$853$	−11.5227	−	34.8796i	−0.394529	−	1.19425i	0.541006	−	0.841019i	$-0.318044\pi$
$854$	−11.2245	−	70.2592i	−0.384093	−	2.40422i
$855$	−39.8420	−	1.95731i	−1.36257	−	0.0669386i
$856$	−17.2882	+	27.8480i	−0.590898	+	0.951824i
$857$	−38.8010	+	18.3515i	−1.32542	+	0.626876i	−0.953501	−	0.301390i	$-0.902549\pi$
$857$	−38.8010	+	18.3515i	−1.32542	+	0.626876i	−0.371917	+	0.928266i	$0.621299\pi$
$858$	0.484404	+	0.194344i	0.0165373	+	0.00663479i
$859$	−6.55449	+	10.3507i	−0.223636	+	0.353160i	−0.938012	−	0.346602i	$-0.887336\pi$
$859$	−6.55449	+	10.3507i	−0.223636	+	0.353160i	0.714376	+	0.699762i	$0.246711\pi$
$860$	0.144918	+	0.328908i	0.00494168	+	0.0112157i
$861$	12.7422	+	1.57160i	0.434253	+	0.0535600i
$862$	−42.2256	+	5.68699i	−1.43821	+	0.193700i
$863$	2.13709	+	3.19838i	0.0727473	+	0.108874i	0.866059	−	0.499941i	$-0.166645\pi$
$863$	2.13709	+	3.19838i	0.0727473	+	0.108874i	−0.793312	+	0.608815i	$0.791645\pi$
$864$	−5.13603	+	26.7559i	−0.174731	+	0.910254i
$865$	−16.3062	+	24.4040i	−0.554428	+	0.829760i
$866$	−24.8808	+	50.8340i	−0.845484	+	1.72741i
$867$	11.6141	+	6.57932i	0.394437	+	0.223446i
$868$	15.0340	−	19.1759i	0.510286	−	0.650874i
$869$	−0.879652	+	5.06956i	−0.0298402	+	0.171973i
$870$	6.31929	−	9.68979i	0.214244	−	0.328515i
$871$	−0.332118	−	6.76042i	−0.0112534	−	0.229068i
$872$	12.9395	+	4.14687i	0.438186	+	0.140431i
$873$	8.60068	+	24.0373i	0.291089	+	0.813539i
$874$	19.2666	+	52.0097i	0.651702	+	1.75926i
$875$	2.36240	−	32.0263i	0.0798637	−	1.08269i
$876$	21.2518	+	2.14097i	0.718031	+	0.0723367i
$877$	−22.2792	+	3.86581i	−0.752315	+	0.130539i	−0.534170	−	0.845377i	$-0.679376\pi$
$877$	−22.2792	+	3.86581i	−0.752315	+	0.130539i	−0.218146	+	0.975916i	$0.570001\pi$
$878$	37.5848	−	14.9819i	1.26843	−	0.505614i
$879$	−0.0285715	+	0.290091i	−0.000963693	+	0.00978454i
$880$	4.75215	+	5.84345i	0.160195	+	0.196983i
$881$	−40.8957	+	4.02788i	−1.37781	+	0.135703i	−0.759642	−	0.650342i	$-0.774626\pi$
$881$	−40.8957	+	4.02788i	−1.37781	+	0.135703i	−0.618170	+	0.786044i	$0.712126\pi$
$882$	−15.4409	−	4.91060i	−0.519922	−	0.165348i
$883$	16.6988	−	15.8986i	0.561959	−	0.535029i	−0.354553	−	0.935036i	$-0.615367\pi$
$883$	16.6988	−	15.8986i	0.561959	−	0.535029i	0.916512	+	0.400006i	$0.130992\pi$
$884$	1.66858	−	0.592834i	0.0561204	−	0.0199392i
$885$	−27.5934	−	21.5341i	−0.927543	−	0.723862i
$886$	−9.55059	+	7.24975i	−0.320858	+	0.243560i
$887$	4.44711	+	29.9800i	0.149319	+	1.00663i	0.926214	+	0.376999i	$0.123044\pi$
$887$	4.44711	+	29.9800i	0.149319	+	1.00663i	−0.776894	+	0.629631i	$0.783206\pi$
$888$	−5.81267	+	8.86967i	−0.195060	+	0.297647i
$889$	−1.93931	−	7.74217i	−0.0650424	−	0.259664i
$890$	1.43633	−	16.4645i	0.0481459	−	0.551891i
$891$	−1.22559	+	0.543265i	−0.0410587	+	0.0182001i
$892$	−4.98297	+	8.75061i	−0.166842	+	0.292992i
$893$	−0.800271	−	1.58987i	−0.0267801	−	0.0532028i
$894$	−1.01699	+	1.64637i	−0.0340134	+	0.0550627i
$895$	13.1946	+	13.1946i	0.441048	+	0.441048i
$896$	−3.73128	+	39.7021i	−0.124653	+	1.32635i
$897$	1.84177	−	1.84177i	0.0614948	−	0.0614948i
$898$	10.6675	+	45.1425i	0.355979	+	1.50642i
$899$	−10.5994	+	5.33529i	−0.353510	+	0.177942i
$900$	−0.736123	+	5.86074i	−0.0245374	+	0.195358i
$901$	0.499935	+	1.12784i	0.0166553	+	0.0375737i
$902$	3.11776	−	2.61743i	0.103810	−	0.0871509i
$903$	0.228830	−	0.0573190i	0.00761500	−	0.00190746i
$904$	37.5936	+	15.1800i	1.25034	+	0.504880i
$905$	−2.52644	+	0.374762i	−0.0839817	+	0.0124575i
$906$	−1.02075	+	7.45336i	−0.0339122	+	0.247621i
$907$	−27.7252	+	35.5265i	−0.920599	+	1.17964i	0.0627713	+	0.998028i	$0.480006\pi$
$907$	−27.7252	+	35.5265i	−0.920599	+	1.17964i	−0.983370	+	0.181611i	$0.941869\pi$
$908$	−1.34539	+	26.1942i	−0.0446484	+	0.869287i
$909$	−16.0097	−	16.8155i	−0.531007	−	0.557734i
$910$	3.04936	+	5.89338i	0.101085	+	0.195364i
$911$	−0.438070	−	4.44780i	−0.0145139	−	0.147362i	0.985196	−	0.171429i	$-0.0548385\pi$
$911$	−0.438070	−	4.44780i	−0.0145139	−	0.147362i	−0.999710	+	0.0240670i	$0.992338\pi$
$912$	28.1282	+	0.125431i	0.931418	+	0.00415343i
$913$	−10.5364	−	1.03774i	−0.348703	−	0.0343442i
$914$	3.43292	−	7.98380i	0.113551	−	0.264081i
$915$	5.81466	+	33.5107i	0.192227	+	1.10783i
$916$	−3.31016	−	11.0004i	−0.109371	−	0.363462i
$917$	−4.91968	−	0.362898i	−0.162462	−	0.0119839i
$918$	4.78325	−	10.4123i	0.157871	−	0.343659i
$919$	−35.4921	+	12.6993i	−1.17077	+	0.418910i	−0.849250	−	0.527991i	$-0.822945\pi$
$919$	−35.4921	+	12.6993i	−1.17077	+	0.418910i	−0.321525	+	0.946901i	$0.604195\pi$
$920$	36.1342	−	10.3478i	1.19131	−	0.341158i
$921$	15.3854	−	0.755834i	0.506965	−	0.0249056i
$922$	−10.9558	−	52.0376i	−0.360812	−	1.71377i
$923$	3.81805	+	0.662494i	0.125673	+	0.0218063i
$924$	4.30664	−	2.42701i	0.141678	−	0.0798428i
$925$	−2.74254	+	4.84125i	−0.0901740	+	0.159179i
$926$	6.09615	−	2.08962i	0.200332	−	0.0686690i
$927$	11.2969	+	7.54832i	0.371037	+	0.247919i
$928$	9.87203	−	16.7235i	0.324065	−	0.548976i
$929$	−21.8940	+	14.6291i	−0.718319	+	0.479965i	−0.860225	−	0.509915i	$-0.829677\pi$
$929$	−21.8940	+	14.6291i	−0.718319	+	0.479965i	0.141906	+	0.989880i	$0.454677\pi$
$930$	−7.06324	+	9.26193i	−0.231613	+	0.303711i
$931$	−4.95573	+	40.1800i	−0.162417	+	1.31685i
$932$	−12.0016	−	11.4776i	−0.393125	−	0.375961i
$933$	6.57289	+	4.16224i	0.215187	+	0.136266i
$934$	14.0285	+	32.8270i	0.459027	+	1.07413i
$935$	−1.35439	−	2.86361i	−0.0442932	−	0.0936502i
$936$	1.29999	+	2.86345i	0.0424915	+	0.0935949i
$937$	−0.457851	+	9.31977i	−0.0149573	+	0.304464i	0.979647	+	0.200726i	$0.0643302\pi$
$937$	−0.457851	+	9.31977i	−0.0149573	+	0.304464i	−0.994605	+	0.103737i	$0.966920\pi$
$938$	−51.9144	−	37.6119i	−1.69506	−	1.22807i
$939$	17.8453	−	5.89529i	0.582359	−	0.192385i
$940$	−1.11543	+	0.459114i	−0.0363812	+	0.0149746i
$941$	−2.06960	+	9.21633i	−0.0674669	+	0.300444i	−0.997802	−	0.0662670i	$-0.978891\pi$
$941$	−2.06960	+	9.21633i	−0.0674669	+	0.300444i	0.930335	+	0.366711i	$0.119516\pi$
$942$	1.59507	+	2.45778i	0.0519701	+	0.0800789i
$943$	−5.89706	−	19.4400i	−0.192035	−	0.633054i
$944$	−47.8882	−	34.0471i	−1.55863	−	1.10814i
$945$	41.0891	+	12.4643i	1.33663	+	0.405462i
$946$	0.0361389	−	0.0654871i	0.00117498	−	0.00212917i
$947$	20.1661	+	8.93904i	0.655312	+	0.290480i	0.705976	−	0.708236i	$-0.250509\pi$
$947$	20.1661	+	8.93904i	0.655312	+	0.290480i	−0.0506640	+	0.998716i	$0.516134\pi$
$948$	10.4768	−	7.73394i	0.340269	−	0.251187i
$949$	5.19137	−	2.94087i	0.168519	−	0.0954648i
$950$	14.7319	−	0.888587i	0.477964	−	0.0288296i
$951$	−2.81736	−	4.70048i	−0.0913592	−	0.152424i
$952$	5.50896	−	15.8409i	0.178546	−	0.513408i
$953$	−8.73073	+	58.8578i	−0.282816	+	1.90659i	0.122594	+	0.992457i	$0.460879\pi$
$953$	−8.73073	+	58.8578i	−0.282816	+	1.90659i	−0.405410	+	0.914135i	$0.632871\pi$
$954$	−1.92056	+	1.05428i	−0.0621803	+	0.0341334i
$955$	−27.3352	−	26.0253i	−0.884546	−	0.842158i
$956$	18.8657	−	7.22901i	0.610160	−	0.233803i
$957$	−2.40090	+	0.177101i	−0.0776101	+	0.00572486i
$958$	−12.4999	+	33.5135i	−0.403852	+	1.08277i
$959$	−52.4340	−	21.7189i	−1.69318	−	0.701339i
$960$	1.52943	−	19.0007i	0.0493620	−	0.613246i
$961$	−17.6017	+	7.29086i	−0.567797	+	0.235189i
$962$	0.105733	+	2.96040i	0.00340898	+	0.0954471i
$963$	18.5382	+	15.9912i	0.597386	+	0.515309i
$964$	28.6535	−	18.0553i	0.922867	−	0.581521i
$965$	35.9193	−	0.881770i	1.15628	−	0.0283852i
$966$	−2.69180	−	24.5222i	−0.0866071	−	0.788990i
$967$	−26.1952	+	19.4277i	−0.842380	+	0.624752i	−0.928417	−	0.371540i	$-0.878830\pi$
$967$	−26.1952	+	19.4277i	−0.842380	+	0.624752i	0.0860367	+	0.996292i	$0.472580\pi$
$968$	−6.92278	+	28.7228i	−0.222506	+	0.923186i
$969$	−11.4758	−	2.87453i	−0.368655	−	0.0923432i
$970$	−18.9172	−	38.8690i	−0.607394	−	1.24801i
$971$	−29.6188	−	8.19662i	−0.950512	−	0.263042i	−0.243226	−	0.969970i	$-0.578206\pi$
$971$	−29.6188	−	8.19662i	−0.950512	−	0.263042i	−0.707286	+	0.706928i	$0.750081\pi$
$972$	30.3781	+	10.9459i	0.974377	+	0.351090i
$973$	16.6088	−	6.40671i	0.532453	−	0.205390i
$974$	26.5588	−	21.2077i	0.850998	−	0.679537i
$975$	−0.326719	−	0.611248i	−0.0104634	−	0.0195756i
$976$	12.2612	+	55.7635i	0.392471	+	1.78495i
$977$	11.1056	+	5.93606i	0.355299	+	0.189911i	0.639384	−	0.768888i	$-0.279190\pi$
$977$	11.1056	+	5.93606i	0.355299	+	0.189911i	−0.284084	+	0.958799i	$0.591690\pi$
$978$	−13.3208	−	9.16095i	−0.425952	−	0.292935i
$979$	−2.90575	+	1.84005i	−0.0928683	+	0.0588082i
$980$	26.8964	+	5.41239i	0.859174	+	0.172893i
$981$	4.56306	−	9.06523i	0.145687	−	0.289431i
$982$	3.63450	−	2.23393i	0.115982	−	0.0712875i
$983$	12.3930	−	11.2323i	0.395275	−	0.358256i	−0.449591	−	0.893235i	$-0.648430\pi$
$983$	12.3930	−	11.2323i	0.395275	−	0.358256i	0.844866	+	0.534978i	$0.179680\pi$
$984$	−10.2811	−	0.666156i	−0.327750	−	0.0212363i
$985$	64.3524	+	23.0257i	2.05044	+	0.733659i
$986$	−5.71060	+	5.83947i	−0.181862	+	0.185966i
$987$	0.173459	+	0.772449i	0.00552127	+	0.0245873i
$988$	6.43415	−	4.51001i	0.204698	−	0.143483i
$989$	−0.229644	−	0.294262i	−0.00730226	−	0.00935698i
$990$	4.86357	−	2.82731i	0.154574	−	0.0898579i
$991$	3.45883	+	0.688005i	0.109873	+	0.0218552i	0.249721	−	0.968318i	$-0.419661\pi$
$991$	3.45883	+	0.688005i	0.109873	+	0.0218552i	−0.139847	+	0.990173i	$0.544661\pi$
$992$	−11.1517	+	16.0617i	−0.354067	+	0.509959i
$993$	−4.54283	+	0.903624i	−0.144162	+	0.0286756i
$994$	27.5222	−	24.2816i	0.872950	−	0.770164i
$995$	41.4482	−	11.4703i	1.31400	−	0.363631i
$996$	17.4567	+	20.3286i	0.553135	+	0.644136i
$997$	−7.60840	+	5.35844i	−0.240960	+	0.169703i	−0.690002	−	0.723807i	$-0.742390\pi$
$997$	−7.60840	+	5.35844i	−0.240960	+	0.169703i	0.449042	+	0.893511i	$0.351765\pi$
$998$	−44.0209	−	8.24683i	−1.39346	−	0.261049i
$999$	14.2031	+	12.8729i	0.449365	+	0.407280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.141.35	yes	4032
512.69	even	128	inner	512.2.o.a.69.35	✓	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.69.35	✓	4032	512.69	even	128	inner
512.2.o.a.141.35	yes	4032	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.226216 - 1.39600i) q^{2} +(-0.295495 + 0.894475i) q^{3} +(-1.89765 - 0.631596i) q^{4} +(0.910328 - 2.35994i) q^{5} +(1.18185 + 0.614856i) q^{6} +(1.81204 - 3.02321i) q^{7} +(-1.31099 + 2.50625i) q^{8} +(1.69685 + 1.25847i) q^{9} +O(q^{10})\)	\(q+(0.226216 - 1.39600i) q^{2} +(-0.295495 + 0.894475i) q^{3} +(-1.89765 - 0.631596i) q^{4} +(0.910328 - 2.35994i) q^{5} +(1.18185 + 0.614856i) q^{6} +(1.81204 - 3.02321i) q^{7} +(-1.31099 + 2.50625i) q^{8} +(1.69685 + 1.25847i) q^{9} +(-3.08855 - 1.80468i) q^{10} +(0.0911253 + 0.738825i) q^{11} +(1.12569 - 1.51077i) q^{12} +(0.0129157 - 0.526128i) q^{13} +(-3.81050 - 3.21351i) q^{14} +(1.84191 + 1.51161i) q^{15} +(3.20217 + 2.39710i) q^{16} +(-1.06725 - 1.30045i) q^{17} +(2.14069 - 2.08413i) q^{18} +(-6.10322 - 4.29837i) q^{19} +(-3.21801 + 3.90338i) q^{20} +(2.16874 + 2.51417i) q^{21} +(1.05202 + 0.0399225i) q^{22} +(2.24626 - 4.74931i) q^{23} +(-1.85439 - 1.91323i) q^{24} +(-1.03584 - 0.938835i) q^{25} +(-0.731554 - 0.137049i) q^{26} +(-3.93763 + 2.77319i) q^{27} +(-5.34807 + 4.59252i) q^{28} +(3.30863 - 0.915621i) q^{29} +(2.52689 - 2.22936i) q^{30} +(-3.39018 + 0.674349i) q^{31} +(4.07074 - 3.92798i) q^{32} +(-0.687788 - 0.136809i) q^{33} +(-2.05687 + 1.19571i) q^{34} +(-5.48503 - 7.02841i) q^{35} +(-2.42519 - 3.45987i) q^{36} +(-0.872037 - 3.88336i) q^{37} +(-7.38118 + 7.54775i) q^{38} +(0.466792 + 0.167021i) q^{39} +(4.72117 + 5.37536i) q^{40} +(2.86506 - 2.59674i) q^{41} +(4.00039 - 2.45882i) q^{42} +(0.0319438 - 0.0634614i) q^{43} +(0.293715 - 1.45959i) q^{44} +(4.51461 - 2.85884i) q^{45} +(-6.12192 - 4.21015i) q^{46} +(0.210283 + 0.112399i) q^{47} +(-3.09037 + 2.15593i) q^{48} +(-2.55652 - 4.78291i) q^{49} +(-1.54494 + 1.23366i) q^{50} +(1.47859 - 0.570356i) q^{51} +(-0.356810 + 0.990250i) q^{52} +(-0.706752 - 0.195585i) q^{53} +(2.98063 + 6.12429i) q^{54} +(1.82653 + 0.457523i) q^{55} +(5.20136 + 8.50483i) q^{56} +(5.64826 - 4.18903i) q^{57} +(-0.529746 - 4.82599i) q^{58} +(-14.6850 + 0.360498i) q^{59} +(-2.54057 - 4.03186i) q^{60} +(10.8083 + 9.32332i) q^{61} +(0.174481 + 4.88525i) q^{62} +(6.87939 - 2.84954i) q^{63} +(-4.56261 - 6.57134i) q^{64} +(-1.22987 - 0.509429i) q^{65} +(-0.346575 + 0.929206i) q^{66} +(12.8262 - 0.946114i) q^{67} +(1.20392 + 3.14188i) q^{68} +(3.58439 + 3.41262i) q^{69} +(-11.0525 + 6.06718i) q^{70} +(-1.08039 + 7.28341i) q^{71} +(-5.37861 + 2.60290i) q^{72} +(5.82837 + 9.72405i) q^{73} +(-5.61845 + 0.338890i) q^{74} +(1.14585 - 0.649117i) q^{75} +(8.86695 + 12.0116i) q^{76} +(2.39874 + 1.06329i) q^{77} +(0.338757 - 0.613860i) q^{78} +(6.61419 + 2.00639i) q^{79} +(8.57203 - 5.37478i) q^{80} +(0.522760 + 1.72331i) q^{81} +(-2.97694 - 4.58706i) q^{82} +(-3.11611 + 13.8766i) q^{83} +(-2.52757 - 6.14078i) q^{84} +(-4.04054 + 1.33481i) q^{85} +(-0.0813662 - 0.0589496i) q^{86} +(-0.158682 + 3.23005i) q^{87} +(-1.97115 - 0.740208i) q^{88} +(1.97538 + 4.17658i) q^{89} +(-2.96968 - 6.94912i) q^{90} +(-1.56719 - 0.992412i) q^{91} +(-7.26226 + 7.59382i) q^{92} +(0.398592 - 3.23170i) q^{93} +(0.204478 - 0.268129i) q^{94} +(-15.6998 + 10.4903i) q^{95} +(2.31060 + 4.80188i) q^{96} +(10.0479 + 6.71378i) q^{97} +(-7.25528 + 2.48694i) q^{98} +(-0.775164 + 1.36836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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