LMFDB - Embedded newform 460.2.w.a.167.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.17
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02423 - 0.975163i) q^{2} +(-0.578886 - 1.06015i) q^{3} +(0.0981127 + 1.99759i) q^{4} +(-1.97258 + 1.05306i) q^{5} +(-0.440905 + 1.65035i) q^{6} +(0.795441 + 1.06258i) q^{7} +(1.84749 - 2.14168i) q^{8} +(0.833113 - 1.29635i) q^{9} +O(q^{10})$	\(q+(-1.02423 - 0.975163i) q^{2} +(-0.578886 - 1.06015i) q^{3} +(0.0981127 + 1.99759i) q^{4} +(-1.97258 + 1.05306i) q^{5} +(-0.440905 + 1.65035i) q^{6} +(0.795441 + 1.06258i) q^{7} +(1.84749 - 2.14168i) q^{8} +(0.833113 - 1.29635i) q^{9} +(3.04729 + 0.845009i) q^{10} +(3.89848 - 1.78038i) q^{11} +(2.06095 - 1.26039i) q^{12} +(-2.86500 - 2.14471i) q^{13} +(0.221476 - 1.86402i) q^{14} +(2.25830 + 1.48163i) q^{15} +(-3.98075 + 0.391978i) q^{16} +(-6.12390 + 0.437990i) q^{17} +(-2.11745 + 0.515344i) q^{18} +(-0.0836509 - 0.0965383i) q^{19} +(-2.29711 - 3.83709i) q^{20} +(0.666030 - 1.45840i) q^{21} +(-5.72912 - 1.97813i) q^{22} +(-2.67750 - 3.97881i) q^{23} +(-3.33999 - 0.718828i) q^{24} +(2.78214 - 4.15448i) q^{25} +(0.842986 + 4.99053i) q^{26} +(-5.47107 - 0.391299i) q^{27} +(-2.04457 + 1.69322i) q^{28} +(-5.36995 - 4.65309i) q^{29} +(-0.868195 - 3.71975i) q^{30} +(1.01984 + 3.47325i) q^{31} +(4.45946 + 3.48040i) q^{32} +(-4.14424 - 3.10234i) q^{33} +(6.69942 + 5.52320i) q^{34} +(-2.68803 - 1.25839i) q^{35} +(2.67131 + 1.53703i) q^{36} +(1.76251 + 8.10211i) q^{37} +(-0.00846247 + 0.180451i) q^{38} +(-0.615209 + 4.27887i) q^{39} +(-1.38901 + 6.17014i) q^{40} +(-0.209821 + 0.134844i) q^{41} +(-2.10435 + 0.844258i) q^{42} +(-1.81444 - 3.32290i) q^{43} +(3.93896 + 7.61290i) q^{44} +(-0.278251 + 3.43447i) q^{45} +(-1.13760 + 6.68624i) q^{46} +(7.00832 - 7.00832i) q^{47} +(2.71995 + 3.99328i) q^{48} +(1.47577 - 5.02600i) q^{49} +(-6.90086 + 1.54212i) q^{50} +(4.00937 + 6.23871i) q^{51} +(4.00316 - 5.93352i) q^{52} +(-6.50557 - 8.69042i) q^{53} +(5.22208 + 5.73597i) q^{54} +(-5.81523 + 7.61726i) q^{55} +(3.74528 + 0.259534i) q^{56} +(-0.0539208 + 0.144567i) q^{57} +(0.962568 + 10.0024i) q^{58} +(-1.78727 - 12.4307i) q^{59} +(-2.73813 + 4.65652i) q^{60} +(-12.7815 + 3.75299i) q^{61} +(2.34243 - 4.55192i) q^{62} +(2.04017 - 0.145916i) q^{63} +(-1.17357 - 7.91345i) q^{64} +(7.90994 + 1.21360i) q^{65} +(1.21939 + 7.21884i) q^{66} +(-3.71992 - 9.97348i) q^{67} +(-1.47576 - 12.1901i) q^{68} +(-2.66817 + 5.14184i) q^{69} +(1.52604 + 3.91016i) q^{70} +(0.857791 + 0.391740i) q^{71} +(-1.23720 - 4.17925i) q^{72} +(-7.18499 - 0.513881i) q^{73} +(6.09566 - 10.0172i) q^{74} +(-6.01491 - 0.544516i) q^{75} +(0.184637 - 0.176572i) q^{76} +(4.99281 + 2.72628i) q^{77} +(4.80271 - 3.78264i) q^{78} +(2.30868 + 16.0572i) q^{79} +(7.43957 - 4.96517i) q^{80} +(0.831863 + 1.82153i) q^{81} +(0.346401 + 0.0664982i) q^{82} +(1.59262 + 7.32114i) q^{83} +(2.97864 + 1.18737i) q^{84} +(11.6186 - 7.31279i) q^{85} +(-1.38196 + 5.17280i) q^{86} +(-1.82439 + 8.38657i) q^{87} +(3.38940 - 11.6385i) q^{88} +(0.0839786 - 0.286005i) q^{89} +(3.63416 - 3.24636i) q^{90} -4.75029i q^{91} +(7.68535 - 5.73893i) q^{92} +(3.09179 - 3.09179i) q^{93} +(-14.0124 + 0.343906i) q^{94} +(0.266669 + 0.102340i) q^{95} +(1.10823 - 6.74246i) q^{96} +(10.5280 + 2.29022i) q^{97} +(-6.41271 + 3.70869i) q^{98} +(0.939885 - 6.53705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	−1.02423	−	0.975163i	−0.724243	−	0.689545i
$2$	−1.02423	−	0.975163i	−0.724243	−	0.689545i
$3$	−0.578886	−	1.06015i	−0.334220	−	0.612078i	0.655484	−	0.755209i	$-0.272465\pi$
$3$	−0.578886	−	1.06015i	−0.334220	−	0.612078i	−0.989704	+	0.143131i	$0.954283\pi$
$4$	0.0981127	+	1.99759i	0.0490564	+	0.998796i
$5$	−1.97258	+	1.05306i	−0.882164	+	0.470942i
$5$	−1.97258	+	1.05306i	−0.882164	+	0.470942i
$6$	−0.440905	+	1.65035i	−0.179999	+	0.673753i
$7$	0.795441	+	1.06258i	0.300648	+	0.401619i	0.925270	−	0.379308i	$-0.123838\pi$
$7$	0.795441	+	1.06258i	0.300648	+	0.401619i	−0.624622	+	0.780927i	$0.714747\pi$
$8$	1.84749	−	2.14168i	0.653186	−	0.757198i
$9$	0.833113	−	1.29635i	0.277704	−	0.432116i
$10$	3.04729	+	0.845009i	0.963637	+	0.267215i
$11$	3.89848	−	1.78038i	1.17544	−	0.536804i	0.270654	−	0.962677i	$-0.412760\pi$
$11$	3.89848	−	1.78038i	1.17544	−	0.536804i	0.904783	+	0.425873i	$0.140033\pi$
$12$	2.06095	−	1.26039i	0.594946	−	0.363844i
$13$	−2.86500	−	2.14471i	−0.794607	−	0.594835i	0.122962	−	0.992411i	$-0.460761\pi$
$13$	−2.86500	−	2.14471i	−0.794607	−	0.594835i	−0.917569	+	0.397576i	$0.869852\pi$
$14$	0.221476	−	1.86402i	0.0591918	−	0.498180i
$15$	2.25830	+	1.48163i	0.583090	+	0.382555i
$16$	−3.98075	+	0.391978i	−0.995187	+	0.0979946i
$17$	−6.12390	+	0.437990i	−1.48526	+	0.106228i	−0.790257	−	0.612776i	$-0.790053\pi$
$17$	−6.12390	+	0.437990i	−1.48526	+	0.106228i	−0.695006	+	0.719004i	$0.744598\pi$
$18$	−2.11745	+	0.515344i	−0.499089	+	0.121468i
$19$	−0.0836509	−	0.0965383i	−0.0191908	−	0.0221474i	0.746073	−	0.665864i	$-0.231937\pi$
$19$	−0.0836509	−	0.0965383i	−0.0191908	−	0.0221474i	−0.765264	+	0.643717i	$0.777392\pi$
$20$	−2.29711	−	3.83709i	−0.513650	−	0.858000i
$21$	0.666030	−	1.45840i	0.145340	−	0.318249i
$22$	−5.72912	−	1.97813i	−1.22145	−	0.421739i
$23$	−2.67750	−	3.97881i	−0.558298	−	0.829640i
$23$	−2.67750	−	3.97881i	−0.558298	−	0.829640i
$24$	−3.33999	−	0.718828i	−0.681772	−	0.146730i
$25$	2.78214	−	4.15448i	0.556428	−	0.830896i
$26$	0.842986	+	4.99053i	0.165323	+	0.978723i
$27$	−5.47107	−	0.391299i	−1.05291	−	0.0753055i
$28$	−2.04457	+	1.69322i	−0.386387	+	0.319988i
$29$	−5.36995	−	4.65309i	−0.997175	−	0.864057i	−0.00645573	−	0.999979i	$-0.502055\pi$
$29$	−5.36995	−	4.65309i	−0.997175	−	0.864057i	−0.990720	+	0.135922i	$0.956600\pi$
$30$	−0.868195	−	3.71975i	−0.158510	−	0.679130i
$31$	1.01984	+	3.47325i	0.183168	+	0.623813i	0.998965	+	0.0454754i	$0.0144803\pi$
$31$	1.01984	+	3.47325i	0.183168	+	0.623813i	−0.815797	+	0.578338i	$0.803702\pi$
$32$	4.45946	+	3.48040i	0.788329	+	0.615254i
$33$	−4.14424	−	3.10234i	−0.721420	−	0.540048i
$34$	6.69942	+	5.52320i	1.14894	+	0.947220i
$35$	−2.68803	−	1.25839i	−0.454361	−	0.212706i
$36$	2.67131	+	1.53703i	0.445219	+	0.256172i
$37$	1.76251	+	8.10211i	0.289754	+	1.33198i	0.859912	+	0.510443i	$0.170519\pi$
$37$	1.76251	+	8.10211i	0.289754	+	1.33198i	−0.570158	+	0.821535i	$0.693118\pi$
$38$	−0.00846247	+	0.180451i	−0.00137279	+	0.0292731i
$39$	−0.615209	+	4.27887i	−0.0985122	+	0.685167i
$40$	−1.38901	+	6.17014i	−0.219621	+	0.975585i
$41$	−0.209821	+	0.134844i	−0.0327686	+	0.0210591i	−0.556923	−	0.830564i	$-0.688018\pi$
$41$	−0.209821	+	0.134844i	−0.0327686	+	0.0210591i	0.524154	+	0.851624i	$0.324382\pi$
$42$	−2.10435	+	0.844258i	−0.324708	+	0.130272i
$43$	−1.81444	−	3.32290i	−0.276700	−	0.506737i	0.701963	−	0.712214i	$-0.252307\pi$
$43$	−1.81444	−	3.32290i	−0.276700	−	0.506737i	−0.978662	+	0.205477i	$0.934126\pi$
$44$	3.93896	+	7.61290i	0.593820	+	1.14769i
$45$	−0.278251	+	3.43447i	−0.0414792	+	0.511980i
$46$	−1.13760	+	6.68624i	−0.167730	+	0.985833i
$47$	7.00832	−	7.00832i	1.02227	−	1.02227i	0.0225229	−	0.999746i	$-0.492830\pi$
$47$	7.00832	−	7.00832i	1.02227	−	1.02227i	0.999746	−	0.0225229i	$-0.00716987\pi$
$48$	2.71995	+	3.99328i	0.392592	+	0.576380i
$49$	1.47577	−	5.02600i	0.210824	−	0.718001i
$50$	−6.90086	+	1.54212i	−0.975929	+	0.218089i
$51$	4.00937	+	6.23871i	0.561424	+	0.873593i
$52$	4.00316	−	5.93352i	0.555139	−	0.822831i
$53$	−6.50557	−	8.69042i	−0.893609	−	1.19372i	−0.980306	−	0.197487i	$-0.936722\pi$
$53$	−6.50557	−	8.69042i	−0.893609	−	1.19372i	0.0866967	−	0.996235i	$-0.472369\pi$
$54$	5.22208	+	5.73597i	0.710636	+	0.780567i
$55$	−5.81523	+	7.61726i	−0.784125	+	1.02711i
$56$	3.74528	+	0.259534i	0.500484	+	0.0346817i
$57$	−0.0539208	+	0.144567i	−0.00714198	+	0.0191484i
$58$	0.962568	+	10.0024i	0.126391	+	1.31338i
$59$	−1.78727	−	12.4307i	−0.232682	−	1.61834i	−0.686420	−	0.727206i	$-0.740819\pi$
$59$	−1.78727	−	12.4307i	−0.232682	−	1.61834i	0.453737	−	0.891136i	$-0.350090\pi$
$60$	−2.73813	+	4.65652i	−0.353490	+	0.601155i
$61$	−12.7815	+	3.75299i	−1.63651	+	0.480521i	−0.965385	−	0.260828i	$-0.916005\pi$
$61$	−12.7815	+	3.75299i	−1.63651	+	0.480521i	−0.671120	+	0.741349i	$0.734186\pi$
$62$	2.34243	−	4.55192i	0.297489	−	0.578095i
$63$	2.04017	−	0.145916i	0.257037	−	0.0183837i
$64$	−1.17357	−	7.91345i	−0.146697	−	0.989181i
$65$	7.90994	+	1.21360i	0.981107	+	0.150529i
$66$	1.21939	+	7.21884i	0.150096	+	0.888578i
$67$	−3.71992	−	9.97348i	−0.454460	−	1.21845i	−0.939071	−	0.343724i	$-0.888311\pi$
$67$	−3.71992	−	9.97348i	−0.454460	−	1.21845i	0.484611	−	0.874730i	$-0.338961\pi$
$68$	−1.47576	−	12.1901i	−0.178962	−	1.47826i
$69$	−2.66817	+	5.14184i	−0.321210	+	0.619004i
$70$	1.52604	+	3.91016i	0.182397	+	0.467353i
$71$	0.857791	+	0.391740i	0.101801	+	0.0464910i	0.465665	−	0.884961i	$-0.345815\pi$
$71$	0.857791	+	0.391740i	0.101801	+	0.0464910i	−0.363864	+	0.931452i	$0.618543\pi$
$72$	−1.23720	−	4.17925i	−0.145805	−	0.492529i
$73$	−7.18499	−	0.513881i	−0.840940	−	0.0601452i	−0.355779	−	0.934570i	$-0.615784\pi$
$73$	−7.18499	−	0.513881i	−0.840940	−	0.0601452i	−0.485161	+	0.874425i	$0.661239\pi$
$74$	6.09566	−	10.0172i	0.708606	−	1.16447i
$75$	−6.01491	−	0.544516i	−0.694542	−	0.0628753i
$76$	0.184637	−	0.176572i	0.0211793	−	0.0202542i
$77$	4.99281	+	2.72628i	0.568984	+	0.310689i
$78$	4.80271	−	3.78264i	0.543800	−	0.428299i
$79$	2.30868	+	16.0572i	0.259746	+	1.80658i	0.534617	+	0.845094i	$0.320456\pi$
$79$	2.30868	+	16.0572i	0.259746	+	1.80658i	−0.274871	+	0.961481i	$0.588635\pi$
$80$	7.43957	−	4.96517i	0.831769	−	0.555122i
$81$	0.831863	+	1.82153i	0.0924292	+	0.202392i
$82$	0.346401	+	0.0664982i	0.0382536	+	0.00734350i
$83$	1.59262	+	7.32114i	0.174812	+	0.803600i	0.978121	+	0.208037i	$0.0667073\pi$
$83$	1.59262	+	7.32114i	0.174812	+	0.803600i	−0.803309	+	0.595563i	$0.796929\pi$
$84$	2.97864	+	1.18737i	0.324996	+	0.129552i
$85$	11.6186	−	7.31279i	1.26022	−	0.793183i
$86$	−1.38196	+	5.17280i	−0.149020	+	0.557798i
$87$	−1.82439	+	8.38657i	−0.195595	+	0.899134i
$88$	3.38940	−	11.6385i	0.361312	−	1.24067i
$89$	0.0839786	−	0.286005i	0.00890171	−	0.0303165i	−0.954922	−	0.296856i	$-0.904062\pi$
$89$	0.0839786	−	0.286005i	0.00890171	−	0.0303165i	0.963824	+	0.266539i	$0.0858802\pi$
$90$	3.63416	−	3.24636i	0.383074	−	0.342196i
$91$		−	4.75029i		−	0.497966i
$92$	7.68535	−	5.73893i	0.801253	−	0.598325i
$93$	3.09179	−	3.09179i	0.320604	−	0.320604i
$94$	−14.0124	+	0.343906i	−1.44527	+	0.0354712i
$95$	0.266669	+	0.102340i	0.0273596	+	0.0104999i
$96$	1.10823	−	6.74246i	0.113108	−	0.688149i
$97$	10.5280	+	2.29022i	1.06896	+	0.232537i	0.712426	−	0.701747i	$-0.247596\pi$
$97$	10.5280	+	2.29022i	1.06896	+	0.232537i	0.356529	+	0.934284i	$0.383960\pi$
$98$	−6.41271	+	3.70869i	−0.647781	+	0.374634i
$99$	0.939885	−	6.53705i	0.0944620	−	0.656998i
$100$	8.57192	+	5.14997i	0.857192	+	0.514997i
$101$	−1.84993	−	1.18888i	−0.184075	−	0.118298i	0.445358	−	0.895353i	$-0.353076\pi$
$101$	−1.84993	−	1.18888i	−0.184075	−	0.118298i	−0.629433	+	0.777055i	$0.716713\pi$
$102$	1.97722	−	10.2997i	0.195774	−	1.01982i
$103$	0.817541	−	2.19191i	0.0805547	−	0.215975i	−0.890429	−	0.455123i	$-0.849595\pi$
$103$	0.817541	−	2.19191i	0.0805547	−	0.215975i	0.970983	+	0.239148i	$0.0768680\pi$
$104$	−9.88633	+	2.17358i	−0.969434	+	0.213137i
$105$	0.221985	+	3.57818i	0.0216635	+	0.349195i
$106$	−1.81135	+	15.2450i	−0.175934	+	1.48073i
$107$	7.93956	−	14.5402i	0.767546	−	1.40566i	−0.141920	−	0.989878i	$-0.545327\pi$
$107$	7.93956	−	14.5402i	0.767546	−	1.40566i	0.909466	−	0.415778i	$-0.136491\pi$
$108$	0.244874	−	10.9674i	0.0235630	−	1.05534i
$109$	1.84231	+	1.59637i	0.176461	+	0.152904i	0.738613	−	0.674129i	$-0.235481\pi$
$109$	1.84231	+	1.59637i	0.176461	+	0.152904i	−0.562152	+	0.827034i	$0.690026\pi$
$110$	13.3842	−	2.13107i	1.27614	−	0.203189i
$111$	7.56916	−	6.55872i	0.718433	−	0.622526i
$112$	−3.58296	−	3.91809i	−0.338558	−	0.370224i
$113$	3.71391	+	9.95738i	0.349375	+	0.936712i	0.986179	+	0.165685i	$0.0529836\pi$
$113$	3.71391	+	9.95738i	0.349375	+	0.936712i	−0.636803	+	0.771026i	$0.719744\pi$
$114$	0.196204	−	0.0954892i	0.0183762	−	0.00894338i
$115$	9.47151	+	5.02896i	0.883223	+	0.468953i
$116$	8.76812	−	11.1835i	0.814099	−	1.03836i
$117$	−5.16716	+	1.92725i	−0.477704	+	0.178174i
$118$	−10.2914	+	14.4748i	−0.947400	+	1.33252i
$119$	−5.33660	−	6.15876i	−0.489205	−	0.564573i
$120$	7.34535	−	2.09925i	0.670536	−	0.191635i
$121$	4.82495	−	5.56829i	0.438632	−	0.506209i
$122$	16.7510	+	8.62012i	1.51657	+	0.780429i
$123$	0.264418	+	0.144383i	0.0238417	+	0.0130186i
$124$	−6.83807	+	2.37799i	−0.614077	+	0.213550i
$125$	−1.11308	+	11.1248i	−0.0995571	+	0.995032i
$126$	−2.23191	−	1.84005i	−0.198834	−	0.163925i
$127$	8.77275	+	3.27207i	0.778455	+	0.290349i	0.707111	−	0.707103i	$-0.249998\pi$
$127$	8.77275	+	3.27207i	0.778455	+	0.290349i	0.0713447	+	0.997452i	$0.477271\pi$
$128$	−6.51489	+	9.24966i	−0.575841	+	0.817562i
$129$	−2.47242	+	3.84716i	−0.217684	+	0.338723i
$130$	−6.91817	−	8.95650i	−0.606764	−	0.785537i
$131$	0.0670590	+	0.00964163i	0.00585897	+	0.000842393i	0.145244	−	0.989396i	$-0.453603\pi$
$131$	0.0670590	+	0.00964163i	0.00585897	+	0.000842393i	−0.139385	+	0.990238i	$0.544512\pi$
$132$	5.79061	−	8.58289i	0.504008	−	0.747044i
$133$	0.0360408	−	0.165677i	0.00312513	−	0.0143660i
$134$	−5.91571	+	13.8427i	−0.511039	+	1.19583i
$135$	11.2042	−	4.98949i	0.964303	−	0.429427i
$136$	−10.3758	+	13.9246i	−0.889717	+	1.19402i
$137$	7.25777	+	7.25777i	0.620074	+	0.620074i	0.945550	−	0.325477i	$-0.105525\pi$
$137$	7.25777	+	7.25777i	0.620074	+	0.620074i	−0.325477	+	0.945550i	$0.605525\pi$
$138$	7.74697	−	2.66454i	0.659465	−	0.226821i
$139$	4.69795			0.398475			0.199238	−	0.979951i	$-0.436153\pi$
$139$	4.69795			0.398475			0.199238	+	0.979951i	$0.436153\pi$
$140$	2.25001	−	5.49306i	0.190161	−	0.464248i
$141$	−11.4869	−	3.37286i	−0.967371	−	0.284046i
$142$	−0.496569	−	1.23772i	−0.0416711	−	0.103867i
$143$	−14.9875	−	3.26034i	−1.25332	−	0.272643i
$144$	−2.80827	+	5.48700i	−0.234023	+	0.457250i
$145$	15.4926	+	3.52372i	1.28659	+	0.292629i
$146$	6.85800	+	7.53288i	0.567572	+	0.623425i
$147$	−6.18262	+	1.34495i	−0.509934	+	0.110929i
$148$	−16.0118	+	4.31569i	−1.31616	+	0.354747i
$149$	14.7463	−	6.73441i	1.20806	−	0.551705i	0.293428	−	0.955981i	$-0.405204\pi$
$149$	14.7463	−	6.73441i	1.20806	−	0.551705i	0.914637	+	0.404276i	$0.132477\pi$
$150$	5.62969	+	6.42324i	0.459662	+	0.524455i
$151$	10.4511	−	1.50264i	0.850498	−	0.122283i	0.296737	−	0.954959i	$-0.404101\pi$
$151$	10.4511	−	1.50264i	0.850498	−	0.122283i	0.553760	+	0.832676i	$0.313192\pi$
$152$	−0.361298		0.000800008i	−0.0293052		6.48892e-5i
$153$	−4.53411	+	8.30360i	−0.366561	+	0.671306i
$154$	−2.45524	−	7.66116i	−0.197849	−	0.617354i
$155$	−5.66924	−	5.77730i	−0.455364	−	0.464044i
$156$	−8.60780	−	0.809124i	−0.689175	−	0.0647818i
$157$	0.230682	−	3.22536i	0.0184105	−	0.257412i	−0.979908	−	0.199449i	$-0.936085\pi$
$157$	0.230682	−	3.22536i	0.0184105	−	0.257412i	0.998319	−	0.0579631i	$-0.0184606\pi$
$158$	13.2938	−	18.6977i	1.05760	−	1.48751i
$159$	−5.44717	+	11.9276i	−0.431989	+	0.945924i
$160$	−12.4617	−	2.16930i	−0.985184	−	0.171498i
$161$	2.09803	−	6.00999i	0.165348	−	0.473653i
$162$	0.924262	−	2.67687i	0.0726169	−	0.210315i
$163$	−0.555441	+	0.207169i	−0.0435055	+	0.0162267i	−0.371123	−	0.928584i	$-0.621027\pi$
$163$	−0.555441	+	0.207169i	−0.0435055	+	0.0162267i	0.327617	+	0.944811i	$0.393754\pi$
$164$	−0.289949	−	0.405908i	−0.0226413	−	0.0316961i
$165$	11.4418	+	1.75549i	0.890743	+	0.136665i
$166$	5.50810	−	9.05163i	0.427511	−	0.702543i
$167$	0.971842	+	13.5881i	0.0752034	+	1.05148i	0.885250	+	0.465116i	$0.153987\pi$
$167$	0.971842	+	13.5881i	0.0752034	+	1.05148i	−0.810047	+	0.586366i	$0.800558\pi$
$168$	−1.89295	−	4.12080i	−0.146044	−	0.317927i
$169$	−0.0540963	−	0.184235i	−0.00416126	−	0.0141719i
$170$	−19.0314	−	3.84007i	−1.45964	−	0.294520i
$171$	−0.194838	+	0.0280135i	−0.0148996	+	0.00214224i
$172$	6.45978	−	3.95053i	0.492553	−	0.301225i
$173$	0.343779	+	0.128223i	0.0261370	+	0.00974861i	0.362499	−	0.931984i	$-0.381924\pi$
$173$	0.343779	+	0.128223i	0.0261370	+	0.00974861i	−0.336362	+	0.941733i	$0.609196\pi$
$174$	10.0469	−	6.81074i	0.761651	−	0.516321i
$175$	6.62751	−	0.348385i	0.500993	−	0.0263354i
$176$	−14.8210	+	8.61535i	−1.11718	+	0.649407i
$177$	−12.1438	+	9.09074i	−0.912784	+	0.683302i
$178$	−0.364915	+	0.211043i	−0.0273516	+	0.0158184i
$179$	−4.14851	+	2.66609i	−0.310074	+	0.199273i	−0.686417	−	0.727208i	$-0.740818\pi$
$179$	−4.14851	+	2.66609i	−0.310074	+	0.199273i	0.376343	+	0.926480i	$0.377181\pi$
$180$	−6.88796	−	0.218867i	−0.513398	−	0.0163134i
$181$	−0.521341	−	0.153079i	−0.0387509	−	0.0113783i	0.262300	−	0.964986i	$-0.415519\pi$
$181$	−0.521341	−	0.153079i	−0.0387509	−	0.0113783i	−0.301051	+	0.953608i	$0.597337\pi$
$182$	−4.63231	+	4.86541i	−0.343370	+	0.360648i
$183$	11.3778	+	11.3778i	0.841069	+	0.841069i
$184$	−13.4680	−	1.61646i	−0.992874	−	0.119167i
$185$	−12.0087	−	14.1260i	−0.882895	−	1.03857i
$186$	−6.18172	+	0.151718i	−0.453266	+	0.0111245i
$187$	−23.0941	+	12.6103i	−1.68881	+	0.922160i
$188$	14.6874	+	13.3122i	1.07119	+	0.970890i
$189$	−3.93613	−	6.12474i	−0.286311	−	0.445509i
$190$	−0.173333	−	0.364866i	−0.0125749	−	0.0264702i
$191$	−15.6874	−	2.25551i	−1.13510	−	0.163203i	−0.450955	−	0.892547i	$-0.648916\pi$
$191$	−15.6874	−	2.25551i	−1.13510	−	0.163203i	−0.684147	+	0.729344i	$0.739826\pi$
$192$	−7.71008	+	5.82515i	−0.556427	+	0.420394i
$193$	22.9572	−	4.99402i	1.65249	−	0.359478i	0.712765	−	0.701403i	$-0.247442\pi$
$193$	22.9572	−	4.99402i	1.65249	−	0.359478i	0.939727	+	0.341925i	$0.111079\pi$
$194$	−8.54979	−	12.6122i	−0.613839	−	0.905506i
$195$	−3.29235	−	9.08826i	−0.235770	−	0.650824i
$196$	10.1847	+	2.45487i	0.727478	+	0.175348i
$197$	−3.52559	+	4.70963i	−0.251188	+	0.335548i	−0.908357	−	0.418195i	$-0.862663\pi$
$197$	−3.52559	+	4.70963i	−0.251188	+	0.335548i	0.657169	+	0.753743i	$0.271754\pi$
$198$	−7.33735	+	5.77893i	−0.521443	+	0.410690i
$199$	11.1229	−	3.26598i	0.788481	−	0.231519i	0.137389	−	0.990517i	$-0.456129\pi$
$199$	11.1229	−	3.26598i	0.788481	−	0.231519i	0.651093	+	0.758998i	$0.274311\pi$
$200$	−3.75759	−	13.6338i	−0.265702	−	0.964055i
$201$	−8.41998	+	9.71718i	−0.593900	+	0.685397i
$202$	0.735412	+	3.02167i	0.0517434	+	0.212604i
$203$	0.672823	−	9.40729i	0.0472229	−	0.660262i
$204$	−12.0690	+	8.62119i	−0.845000	+	0.603604i
$205$	0.271891	−	0.486945i	0.0189897	−	0.0340097i
$206$	−2.97483	+	1.44780i	−0.207266	+	0.100873i
$207$	−7.38859	+	0.156178i	−0.513543	+	0.0108551i
$208$	12.2455	+	7.41453i	0.849073	+	0.514105i
$209$	−0.497986	−	0.227423i	−0.0344464	−	0.0157312i
$210$	3.26195	−	3.88137i	0.225096	−	0.267840i
$211$	−2.67022	+	2.31376i	−0.183825	+	0.159286i	−0.741912	−	0.670497i	$-0.766081\pi$
$211$	−2.67022	+	2.31376i	−0.183825	+	0.159286i	0.558087	+	0.829782i	$0.311536\pi$
$212$	16.7216	−	13.8481i	1.14845	−	0.951093i
$213$	−0.0812598	−	1.13616i	−0.00556783	−	0.0778484i
$214$	−22.3111	+	7.15023i	−1.52515	+	0.488779i
$215$	7.07833	+	4.64397i	0.482738	+	0.316716i
$216$	−10.9458	+	10.9944i	−0.744766	+	0.748072i
$217$	−2.87940	+	3.84642i	−0.195466	+	0.261112i
$218$	−0.330235	−	3.43160i	−0.0223663	−	0.232418i
$219$	3.61450	+	7.91465i	0.244245	+	0.534823i
$220$	−15.7867	−	10.8691i	−1.06434	−	0.732795i
$221$	18.4843	+	11.8791i	1.24339	+	0.799078i
$222$	−14.1484	−	0.663506i	−0.949580	−	0.0445316i
$223$	−8.68776	+	6.50358i	−0.581776	+	0.435512i	−0.849203	−	0.528066i	$-0.822917\pi$
$223$	−8.68776	+	6.50358i	−0.581776	+	0.435512i	0.267428	+	0.963578i	$0.413826\pi$
$224$	−0.150983	+	7.50701i	−0.0100880	+	0.501583i
$225$	−3.06782	−	7.06777i	−0.204521	−	0.471185i
$226$	5.90616	−	13.8204i	0.392872	−	0.919317i
$227$	−15.6800	+	8.56191i	−1.04072	+	0.568274i	−0.906293	−	0.422650i	$-0.861100\pi$
$227$	−15.6800	+	8.56191i	−1.04072	+	0.568274i	−0.134423	+	0.990924i	$0.542918\pi$
$228$	−0.294077	−	0.0935279i	−0.0194757	−	0.00619403i
$229$		−	6.19869i		−	0.409621i	−0.978802	−	0.204810i	$-0.934342\pi$
$229$		−	6.19869i		−	0.409621i	0.978802	−	0.204810i	$-0.0656578\pi$
$230$	−4.79699	−	14.3871i	−0.316304	−	0.948658i
$231$		−	6.87134i		−	0.452101i
$232$	−19.8864	+	2.90418i	−1.30560	+	0.190669i
$233$	−6.72778	+	3.67365i	−0.440752	+	0.240669i	−0.684272	−	0.729227i	$-0.739880\pi$
$233$	−6.72778	+	3.67365i	−0.440752	+	0.240669i	0.243520	+	0.969896i	$0.421698\pi$
$234$	7.17176	+	3.06487i	0.468833	+	0.200357i
$235$	−6.44431	+	21.2046i	−0.420380	+	1.38324i
$236$	24.6561	−	4.78984i	1.60498	−	0.311792i
$237$	15.6866	−	11.7428i	1.01895	−	0.762779i
$238$	−0.539872	+	11.5121i	−0.0349947	+	0.746217i
$239$	−2.84597	−	1.82899i	−0.184090	−	0.118308i	0.445350	−	0.895357i	$-0.353079\pi$
$239$	−2.84597	−	1.82899i	−0.184090	−	0.118308i	−0.629440	+	0.777049i	$0.716716\pi$
$240$	−9.57048	−	5.01279i	−0.617772	−	0.323574i
$241$	−4.89279	−	10.7137i	−0.315173	−	0.690132i	0.684055	−	0.729431i	$-0.260215\pi$
$241$	−4.89279	−	10.7137i	−0.315173	−	0.690132i	−0.999228	+	0.0392988i	$0.987488\pi$
$242$	−10.3719	+	0.998120i	−0.666730	+	0.0641616i
$243$	−8.41167	+	11.2367i	−0.539609	+	0.720833i
$244$	−8.75097	−	25.1640i	−0.560224	−	1.61096i
$245$	2.38160	+	11.4683i	0.152155	+	0.732680i
$246$	−0.130029	−	0.405732i	−0.00829033	−	0.0258685i
$247$	0.0326130	+	0.455989i	0.00207511	+	0.0290139i
$248$	9.32271	+	4.23262i	0.591993	+	0.268771i
$249$	6.83957	−	5.92652i	0.433440	−	0.375578i
$250$	11.9885	−	10.3090i	0.758222	−	0.651996i
$251$	14.5505	+	6.64499i	0.918420	+	0.419428i	0.817804	−	0.575497i	$-0.195191\pi$
$251$	14.5505	+	6.64499i	0.918420	+	0.419428i	0.100616	+	0.994925i	$0.467919\pi$
$252$	0.491647	+	4.06111i	0.0309709	+	0.255826i
$253$	−17.5220	−	10.7444i	−1.10160	−	0.675493i
$254$	−5.79455	−	11.9062i	−0.363583	−	0.747063i
$255$	−14.4785	−	8.08424i	−0.906680	−	0.506255i
$256$	15.6927	−	3.12073i	0.980794	−	0.195046i
$257$	0.263900	−	3.68980i	0.0164616	−	0.230164i	−0.982560	−	0.185945i	$-0.940466\pi$
$257$	0.263900	−	3.68980i	0.0164616	−	0.230164i	0.999022	−	0.0442190i	$-0.0140799\pi$
$258$	6.28394	−	1.52938i	0.391221	−	0.0952151i
$259$	−7.20721	+	8.31756i	−0.447834	+	0.516828i
$260$	−1.64822	+	15.9199i	−0.102218	+	0.987310i
$261$	−10.5058	+	3.08478i	−0.650293	+	0.190943i
$262$	−0.0592820	−	0.0752688i	−0.00366245	−	0.00465012i
$263$	2.16814	−	2.89630i	0.133693	−	0.178593i	−0.728699	−	0.684834i	$-0.759875\pi$
$263$	2.16814	−	2.89630i	0.133693	−	0.178593i	0.862392	+	0.506241i	$0.168965\pi$
$264$	−14.3007	+	3.14410i	−0.880145	+	0.193506i
$265$	21.9843	+	10.2918i	1.35048	+	0.632221i
$266$	−0.198476	+	0.134546i	−0.0121693	+	0.00824956i
$267$	−0.351822	+	0.0765342i	−0.0215312	+	0.00468382i
$268$	19.5580	−	8.40940i	1.19469	−	0.513686i
$269$	9.59479	+	1.37952i	0.585005	+	0.0841110i	0.428461	−	0.903560i	$-0.359056\pi$
$269$	9.59479	+	1.37952i	0.585005	+	0.0841110i	0.156543	+	0.987671i	$0.449965\pi$
$270$	−16.3413	−	5.81551i	−0.994499	−	0.353921i
$271$	−5.21957	−	8.12181i	−0.317066	−	0.493365i	0.645740	−	0.763557i	$-0.276549\pi$
$271$	−5.21957	−	8.12181i	−0.317066	−	0.493365i	−0.962806	+	0.270193i	$0.912913\pi$
$272$	24.2060	−	4.14396i	1.46770	−	0.251265i
$273$	−5.03602	+	2.74988i	−0.304794	+	0.166430i
$274$	−0.356147	−	14.5112i	−0.0215156	−	0.876652i
$275$	3.44958	−	21.1494i	0.208017	−	1.27536i
$276$	−10.5331	−	4.82544i	−0.634017	−	0.290457i
$277$	8.00773	+	8.00773i	0.481138	+	0.481138i	0.905495	−	0.424357i	$-0.139500\pi$
$277$	8.00773	+	8.00773i	0.481138	+	0.481138i	−0.424357	+	0.905495i	$0.639500\pi$
$278$	−4.81180	−	4.58127i	−0.288593	−	0.274766i
$279$	5.35218	+	1.57154i	0.320426	+	0.0940857i
$280$	−7.66117	+	3.43205i	−0.457843	+	0.205104i
$281$	−4.46222	+	2.86769i	−0.266194	+	0.171072i	−0.666928	−	0.745122i	$-0.732391\pi$
$281$	−4.46222	+	2.86769i	−0.266194	+	0.171072i	0.400735	+	0.916194i	$0.368755\pi$
$282$	8.47619	+	14.6562i	0.504750	+	0.872764i
$283$	15.5398	−	11.6329i	0.923742	−	0.691505i	−0.0276071	−	0.999619i	$-0.508789\pi$
$283$	15.5398	−	11.6329i	0.923742	−	0.691505i	0.951349	+	0.308114i	$0.0996978\pi$
$284$	−0.698376	+	1.75195i	−0.0414410	+	0.103959i
$285$	−0.0458746	−	0.341952i	−0.00271738	−	0.0202555i
$286$	12.1714	+	17.9546i	0.719709	+	1.06168i
$287$	−0.310184	−	0.115693i	−0.0183096	−	0.00682911i
$288$	8.22705	−	2.88145i	0.484783	−	0.169791i
$289$	20.4833	−	2.94506i	1.20490	−	0.173239i
$290$	−12.4319	−	18.7170i	−0.730025	−	1.09910i
$291$	−3.66652	−	12.4870i	−0.214935	−	0.732003i
$292$	0.321585	−	14.4031i	0.0188193	−	0.842878i
$293$	−0.111636	−	1.56088i	−0.00652185	−	0.0911874i	0.993149	−	0.116858i	$-0.0372823\pi$
$293$	−0.111636	−	1.56088i	−0.00652185	−	0.0911874i	−0.999670	+	0.0256709i	$0.991828\pi$
$294$	7.64400	+	4.65152i	0.445807	+	0.271282i
$295$	16.6158	+	22.6385i	0.967408	+	1.31806i
$296$	20.6083	+	11.1938i	1.19783	+	0.650628i
$297$	−22.0255	+	8.21511i	−1.27805	+	0.476689i
$298$	−21.6708	−	7.48244i	−1.25536	−	0.433446i
$299$	−0.862361	+	17.1418i	−0.0498716	+	0.991334i
$300$	0.497581	−	12.0688i	0.0287278	−	0.696791i
$301$	2.08758	−	4.57117i	0.120326	−	0.263478i
$302$	−12.1697	−	8.65246i	−0.700287	−	0.497893i
$303$	−0.189491	+	2.64943i	−0.0108860	+	0.152206i
$304$	0.370834	+	0.351505i	0.0212688	+	0.0201602i
$305$	21.2604	−	20.8627i	1.21737	−	1.19460i
$306$	12.7414	−	4.08334i	0.728375	−	0.233429i
$307$	−1.82666	+	3.34528i	−0.104253	+	0.190925i	−0.924598	−	0.380943i	$-0.875599\pi$
$307$	−1.82666	+	3.34528i	−0.104253	+	0.190925i	0.820345	+	0.571868i	$0.193781\pi$
$308$	−4.95614	+	10.2411i	−0.282402	+	0.583540i
$309$	−2.79702	+	0.402151i	−0.159117	+	0.0228775i
$310$	0.172812	+	11.4457i	0.00981505	+	0.650075i
$311$	−17.9657	+	8.20464i	−1.01874	+	0.465243i	−0.853545	−	0.521019i	$-0.825552\pi$
$311$	−17.9657	+	8.20464i	−1.01874	+	0.465243i	−0.165194	+	0.986261i	$0.552825\pi$
$312$	8.02737	+	9.22274i	0.454460	+	0.522135i
$313$	−19.1075	+	4.15657i	−1.08002	+	0.234944i	−0.717165	−	0.696903i	$-0.754561\pi$
$313$	−19.1075	+	4.15657i	−1.08002	+	0.234944i	−0.362853	+	0.931847i	$0.618197\pi$
$314$	−3.38153	+	3.07857i	−0.190831	+	0.173734i
$315$	−3.87074	+	2.43625i	−0.218092	+	0.137267i
$316$	−31.8492	+	6.18721i	−1.79166	+	0.348058i
$317$	−24.6213	−	5.35603i	−1.38287	−	0.300824i	−0.541233	−	0.840872i	$-0.682042\pi$
$317$	−24.6213	−	5.35603i	−1.38287	−	0.300824i	−0.841634	+	0.540048i	$0.818406\pi$
$318$	17.2106	−	6.90482i	0.965122	−	0.387203i
$319$	−29.2189	−	8.57945i	−1.63595	−	0.480357i
$320$	10.6483	+	14.3741i	0.595258	+	0.803535i
$321$	−20.0109			−1.11690
$322$	−8.00960	+	4.10971i	−0.446357	+	0.229025i
$323$	0.554553	+	0.554553i	0.0308561	+	0.0308561i
$324$	−3.55705	+	1.84044i	−0.197614	+	0.102247i
$325$	−16.8810	+	5.93569i	−0.936388	+	0.329253i
$326$	0.770925	+	0.329456i	0.0426976	+	0.0182469i
$327$	0.625904	−	2.87724i	0.0346126	−	0.159112i
$328$	−0.0988500	+	0.698493i	−0.00545808	+	0.0385678i
$329$	13.0216	+	1.87223i	0.717907	+	0.103219i
$330$	−10.0072	−	12.9557i	−0.550878	−	0.713185i
$331$	−7.05706	+	10.9810i	−0.387891	+	0.603570i	−0.979205	−	0.202871i	$-0.934973\pi$
$331$	−7.05706	+	10.9810i	−0.387891	+	0.603570i	0.591315	+	0.806441i	$0.298609\pi$
$332$	−14.4684	+	3.89970i	−0.794056	+	0.214024i
$333$	11.9715	+	4.46515i	0.656035	+	0.244689i
$334$	12.2553	−	14.8651i	0.670578	−	0.813384i
$335$	17.8405	+	15.7562i	0.974729	+	0.860853i
$336$	−2.07963	+	6.06660i	−0.113453	+	0.330960i
$337$	5.73680	+	3.13253i	0.312503	+	0.170640i	0.627845	−	0.778339i	$-0.283937\pi$
$337$	5.73680	+	3.13253i	0.312503	+	0.170640i	−0.315342	+	0.948978i	$0.602119\pi$
$338$	−0.124252	+	0.241453i	−0.00675842	+	0.0131333i
$339$	8.40639	−	9.70149i	0.456572	−	0.526913i
$340$	15.7479	+	22.4918i	0.854050	+	1.21979i
$341$	10.1595	+	11.7247i	0.550168	+	0.634928i
$342$	0.226878	+	0.161307i	0.0122681	+	0.00872246i
$343$	15.2199	−	5.67675i	0.821800	−	0.306516i
$344$	−10.4687	−	2.25307i	−0.564437	−	0.121477i
$345$	−0.151470	−	12.9524i	−0.00815485	−	0.697335i
$346$	−0.227072	−	0.466571i	−0.0122075	−	0.0250830i
$347$	−12.8534	−	34.4612i	−0.690004	−	1.84997i	−0.494249	−	0.869321i	$-0.664557\pi$
$347$	−12.8534	−	34.4612i	−0.690004	−	1.84997i	−0.195756	−	0.980653i	$-0.562716\pi$
$348$	−16.9319	−	2.82155i	−0.907647	−	0.151251i
$349$	−23.3759	+	20.2553i	−1.25128	+	1.08424i	−0.258289	+	0.966068i	$0.583159\pi$
$349$	−23.3759	+	20.2553i	−1.25128	+	1.08424i	−0.992993	+	0.118175i	$0.962296\pi$
$350$	−7.12786	−	6.10608i	−0.381000	−	0.326384i
$351$	14.8354	+	12.8549i	0.791855	+	0.686146i
$352$	23.5816	+	5.62876i	1.25690	+	0.300014i
$353$	4.23035	−	7.74731i	0.225159	−	0.412348i	−0.740540	−	0.672012i	$-0.765430\pi$
$353$	4.23035	−	7.74731i	0.225159	−	0.412348i	0.965699	+	0.259665i	$0.0836120\pi$
$354$	21.3031	+	2.53115i	1.13224	+	0.134529i
$355$	−2.10459	+	0.130565i	−0.111700	+	0.00692968i
$356$	0.579560	+	0.139694i	0.0307166	+	0.00740378i
$357$	−3.43993	+	9.22282i	−0.182061	+	0.488123i
$358$	6.84892	+	1.31478i	0.361976	+	0.0694882i
$359$	20.4227	+	13.1249i	1.07787	+	0.692704i	0.954064	−	0.299603i	$-0.0968542\pi$
$359$	20.4227	+	13.1249i	1.07787	+	0.692704i	0.123804	+	0.992307i	$0.460491\pi$
$360$	6.84146	+	6.94106i	0.360576	+	0.365826i
$361$	2.70166	−	18.7905i	0.142193	−	0.988971i
$362$	0.384698	+	0.665181i	0.0202193	+	0.0349612i
$363$	−8.69633	−	1.89177i	−0.456439	−	0.0992922i
$364$	9.48914	−	0.466064i	0.497366	−	0.0244284i
$365$	14.7141	−	6.55254i	0.770172	−	0.342976i
$366$	−0.558320	−	22.7487i	−0.0291839	−	1.18909i
$367$	19.3179	−	19.3179i	1.00838	−	1.00838i	0.00841933	−	0.999965i	$-0.497320\pi$
$367$	19.3179	−	19.3179i	1.00838	−	1.00838i	0.999965	−	0.00841933i	$-0.00267999\pi$
$368$	12.2181	+	14.7891i	0.636911	+	0.770937i
$369$			0.384342i			0.0200080i
$370$	−1.47549	+	26.1788i	−0.0767073	+	1.36097i
$371$	4.05951	−	13.8254i	0.210760	−	0.717781i
$372$	6.47948	+	5.87280i	0.335946	+	0.304490i
$373$	−1.87135	+	8.60248i	−0.0968951	+	0.445419i	0.902981	+	0.429680i	$0.141374\pi$
$373$	−1.87135	+	8.60248i	−0.0968951	+	0.445419i	−0.999876	+	0.0157391i	$0.994990\pi$
$374$	35.9509	+	9.60459i	1.85898	+	0.496642i
$375$	12.4383	−	5.25995i	0.642311	−	0.271623i
$376$	−2.06178	−	27.9574i	−0.106328	−	1.44179i
$377$	5.40537	+	24.8481i	0.278391	+	1.27974i
$378$	−1.94110	+	10.1115i	−0.0998394	+	0.520081i
$379$	1.62920	+	3.56745i	0.0836864	+	0.183248i	0.946849	−	0.321678i	$-0.104247\pi$
$379$	1.62920	+	3.56745i	0.0836864	+	0.183248i	−0.863163	+	0.504926i	$0.831520\pi$
$380$	−0.178271	+	0.542736i	−0.00914508	+	0.0278418i
$381$	−1.60954	−	11.1946i	−0.0824591	−	0.573516i
$382$	13.8681	+	17.6080i	0.709554	+	0.900902i
$383$	−1.86823	−	1.02013i	−0.0954622	−	0.0521263i	0.430809	−	0.902443i	$-0.358228\pi$
$383$	−1.86823	−	1.02013i	−0.0954622	−	0.0521263i	−0.526271	+	0.850317i	$0.676410\pi$
$384$	13.5774	+	1.55227i	0.692869	+	0.0792139i
$385$	−12.7197	−	0.120088i	−0.648254	−	0.00612024i
$386$	−28.3835	−	17.2719i	−1.44468	−	0.879118i
$387$	−5.81927	−	0.416202i	−0.295810	−	0.0211568i
$388$	−3.54200	+	21.2553i	−0.179818	+	1.07908i
$389$	12.9970	+	5.93555i	0.658976	+	0.300944i	0.716693	−	0.697389i	$-0.245655\pi$
$389$	12.9970	+	5.93555i	0.658976	+	0.300944i	−0.0577172	+	0.998333i	$0.518382\pi$
$390$	−5.49040	+	12.5191i	−0.278017	+	0.633929i
$391$	18.1394	+	23.1931i	0.917351	+	1.17293i
$392$	−8.03762	−	12.4461i	−0.405961	−	0.628623i
$393$	−0.0285979	−	0.0766740i	−0.00144257	−	0.00386769i
$394$	8.20369	−	1.38575i	0.413296	−	0.0698129i
$395$	−21.4632	−	29.2429i	−1.07993	−	1.47137i
$396$	13.1506	+	1.23614i	0.660841	+	0.0621184i
$397$	3.45887	−	0.247383i	0.173596	−	0.0124158i	0.0157293	−	0.999876i	$-0.494993\pi$
$397$	3.45887	−	0.247383i	0.173596	−	0.0124158i	0.157866	+	0.987460i	$0.449538\pi$
$398$	−14.5773	−	7.50152i	−0.730695	−	0.376017i
$399$	−0.196506	+	0.0576993i	−0.00983759	+	0.00288858i
$400$	−9.44653	+	17.6285i	−0.472326	+	0.881424i
$401$	−2.63759	−	18.3448i	−0.131715	−	0.916097i	−0.943319	−	0.331888i	$-0.892314\pi$
$401$	−2.63759	−	18.3448i	−0.131715	−	0.916097i	0.811604	−	0.584208i	$-0.198595\pi$
$402$	18.0999	−	1.74181i	0.902739	−	0.0868736i
$403$	4.52727	−	12.1381i	0.225520	−	0.604641i
$404$	2.19339	−	3.81205i	0.109125	−	0.189657i
$405$	−3.55909	−	2.71710i	−0.176852	−	0.135014i
$406$	−9.86277	+	8.97916i	−0.489481	+	0.445628i
$407$	21.2959	+	28.4480i	1.05560	+	1.41011i
$408$	20.7686	+	2.93915i	1.02820	+	0.145509i
$409$	−13.7129	−	21.3377i	−0.678060	−	1.05508i	−0.994322	−	0.106410i	$-0.966064\pi$
$409$	−13.7129	−	21.3377i	−0.678060	−	1.05508i	0.316263	−	0.948672i	$-0.397572\pi$
$410$	−0.753331	+	0.233607i	−0.0372043	+	0.0115371i
$411$	3.49291	−	11.8958i	0.172292	−	0.586774i
$412$	4.45876	+	1.41806i	0.219667	+	0.0698627i
$413$	11.7870	−	11.7870i	0.580001	−	0.580001i
$414$	7.71995	+	7.04512i	0.379415	+	0.346249i
$415$	−10.8511	−	12.7644i	−0.532662	−	0.626580i
$416$	−5.31189	−	19.5356i	−0.260437	−	0.957811i
$417$	−2.71958	−	4.98053i	−0.133178	−	0.243898i
$418$	0.288281	+	0.718552i	0.0141003	+	0.0351455i
$419$	−11.7260	+	7.53584i	−0.572852	+	0.368150i	−0.794766	−	0.606917i	$-0.792406\pi$
$419$	−11.7260	+	7.53584i	−0.572852	+	0.368150i	0.221913	+	0.975066i	$0.428770\pi$
$420$	−7.12597	+	0.794500i	−0.347712	+	0.0387676i
$421$	4.92700	−	34.2681i	0.240127	−	1.67012i	−0.411367	−	0.911470i	$-0.634949\pi$
$421$	4.92700	−	34.2681i	0.240127	−	1.67012i	0.651494	−	0.758653i	$-0.274142\pi$
$422$	4.99122	+	0.234069i	0.242969	+	0.0113943i
$423$	−3.24651	−	14.9240i	−0.157851	−	0.725628i
$424$	−30.6311	−	2.12262i	−1.48758	−	0.103083i
$425$	−15.2179	+	26.6602i	−0.738177	+	1.29321i
$426$	−1.02471	+	1.24294i	−0.0496475	+	0.0602204i
$427$	−14.1548	−	10.5962i	−0.684999	−	0.512784i
$428$	29.8244	+	14.4334i	1.44162	+	0.697666i
$429$	5.21962	+	17.7764i	0.252006	+	0.858253i
$430$	−2.72124	−	11.6590i	−0.131230	−	0.562249i
$431$	−9.19233	−	7.96520i	−0.442779	−	0.383670i	0.404743	−	0.914430i	$-0.367361\pi$
$431$	−9.19233	−	7.96520i	−0.442779	−	0.383670i	−0.847522	+	0.530760i	$0.821906\pi$
$432$	21.9324	−	0.586881i	1.05522	−	0.0282363i
$433$	−20.7496	−	1.48404i	−0.997164	−	0.0713186i	−0.436795	−	0.899561i	$-0.643886\pi$
$433$	−20.7496	−	1.48404i	−0.997164	−	0.0713186i	−0.560370	+	0.828243i	$0.689341\pi$
$434$	6.70007	−	1.13176i	0.321614	−	0.0543261i
$435$	−5.23279	−	18.4644i	−0.250893	−	0.885298i
$436$	−3.00814	+	3.83680i	−0.144064	+	0.183749i
$437$	−0.160132	+	0.591313i	−0.00766017	+	0.0282864i
$438$	4.01598	−	11.6312i	0.191891	−	0.555760i
$439$	16.8194	−	36.8294i	0.802747	−	1.75777i	0.166872	−	0.985979i	$-0.446633\pi$
$439$	16.8194	−	36.8294i	0.802747	−	1.75777i	0.635875	−	0.771792i	$-0.280639\pi$
$440$	5.57017	+	26.5271i	0.265547	+	1.26463i
$441$	−5.28597	−	6.10034i	−0.251713	−	0.290492i
$442$	−7.34816	−	30.1922i	−0.349516	−	1.43610i
$443$	39.5845	−	2.83114i	1.88072	−	0.134511i	0.916568	−	0.399879i	$-0.130948\pi$
$443$	39.5845	−	2.83114i	1.88072	−	0.134511i	0.964147	+	0.265367i	$0.0854931\pi$
$444$	13.8443	+	14.4766i	0.657020	+	0.687029i
$445$	0.135525	+	0.652602i	0.00642451	+	0.0309363i
$446$	15.2404	+	1.81080i	0.721652	+	0.0857438i
$447$	−15.6759	−	11.7348i	−0.741446	−	0.555039i
$448$	7.47520	−	7.54171i	0.353170	−	0.356312i
$449$	−25.4223	+	11.6100i	−1.19975	+	0.547909i	−0.912156	−	0.409842i	$-0.865584\pi$
$449$	−25.4223	+	11.6100i	−1.19975	+	0.547909i	−0.287597	+	0.957751i	$0.592856\pi$
$450$	−3.75007	+	10.2307i	−0.176780	+	0.482279i
$451$	−0.577912	+	0.899248i	−0.0272128	+	0.0423440i
$452$	−19.5264	+	8.39582i	−0.918445	+	0.394906i
$453$	−7.64301	−	10.2099i	−0.359100	−	0.479701i
$454$	24.4092	+	6.52113i	1.14558	+	0.306052i
$455$	5.00233	+	9.37033i	0.234513	+	0.439288i
$456$	0.209999	+	0.382567i	0.00983408	+	0.0179154i
$457$	14.7419	+	26.9977i	0.689595	+	1.26290i	0.954381	+	0.298592i	$0.0965169\pi$
$457$	14.7419	+	26.9977i	0.689595	+	1.26290i	−0.264786	+	0.964307i	$0.585301\pi$
$458$	−6.04473	+	6.34891i	−0.282452	+	0.296665i
$459$	33.6757			1.57185
$460$	−9.11654	+	19.4136i	−0.425061	+	0.905165i
$461$	10.3560			0.482327			0.241163	−	0.970485i	$-0.422471\pi$
$461$	10.3560			0.482327			0.241163	+	0.970485i	$0.422471\pi$
$462$	−6.70068	+	7.03786i	−0.311744	+	0.327431i
$463$	−1.43992	−	2.63701i	−0.0669187	−	0.122552i	0.842078	−	0.539356i	$-0.181332\pi$
$463$	−1.43992	−	2.63701i	−0.0669187	−	0.122552i	−0.908997	+	0.416803i	$0.863150\pi$
$464$	23.2003	+	16.4179i	1.07705	+	0.762181i
$465$	−2.84297	+	9.35464i	−0.131840	+	0.433811i
$466$	10.4732	+	2.79801i	0.485163	+	0.129615i
$467$	11.8594	+	15.8424i	0.548790	+	0.733097i	0.986089	−	0.166219i	$-0.0531559\pi$
$467$	11.8594	+	15.8424i	0.548790	+	0.733097i	−0.437299	+	0.899316i	$0.644065\pi$
$468$	−4.35682	−	10.1328i	−0.201394	−	0.468388i
$469$	7.63869	−	11.8860i	0.352722	−	0.548846i
$470$	27.2785	−	15.4343i	1.25826	−	0.711930i
$471$	−3.55291	+	1.62256i	−0.163709	+	0.0747635i
$472$	−29.9246	−	19.1378i	−1.37739	−	0.880891i
$473$	−12.9896	−	9.72388i	−0.597261	−	0.447104i
$474$	−27.5179	−	3.26957i	−1.26394	−	0.150176i
$475$	−0.633795	+	0.0789431i	−0.0290805	+	0.00362216i
$476$	11.7791	−	11.2646i	0.539895	−	0.516312i
$477$	−16.6857	+	1.19338i	−0.763985	+	0.0546413i
$478$	1.13137	+	4.64860i	0.0517477	+	0.212622i
$479$	9.78773	+	11.2956i	0.447213	+	0.516111i	0.933934	−	0.357446i	$-0.116353\pi$
$479$	9.78773	+	11.2956i	0.447213	+	0.516111i	−0.486721	+	0.873558i	$0.661807\pi$
$480$	4.91412	+	14.4671i	0.224298	+	0.660328i
$481$	12.3271	−	26.9926i	0.562067	−	1.23076i
$482$	−5.43626	+	15.7446i	−0.247615	+	0.717149i
$483$	−7.58601	+	1.25487i	−0.345175	+	0.0570985i
$484$	11.5966	+	9.09197i	0.527117	+	0.413271i
$485$	−23.1790	+	6.56893i	−1.05251	+	0.298280i
$486$	19.5731	−	3.30624i	0.887854	−	0.149974i
$487$	−9.55964	−	0.683719i	−0.433189	−	0.0309823i	−0.146957	−	0.989143i	$-0.546948\pi$
$487$	−9.55964	−	0.683719i	−0.433189	−	0.0309823i	−0.286231	+	0.958161i	$0.592403\pi$
$488$	−15.5760	+	34.3075i	−0.705092	+	1.55303i
$489$	0.541167	+	0.468924i	0.0244724	+	0.0212055i
$490$	8.74411	−	14.0686i	0.395019	−	0.635556i
$491$	−0.170243	−	0.579794i	−0.00768295	−	0.0261657i	0.955562	−	0.294789i	$-0.0952494\pi$
$491$	−0.170243	−	0.579794i	−0.00768295	−	0.0261657i	−0.963245	+	0.268624i	$0.913431\pi$
$492$	−0.262475	+	0.542364i	−0.0118333	+	0.0244517i
$493$	34.9230	+	26.1431i	1.57285	+	1.17742i
$494$	0.411260	−	0.498843i	0.0185035	−	0.0224440i
$495$	5.02989	+	13.8846i	0.226077	+	0.624066i
$496$	−5.42115	−	13.4264i	−0.243417	−	0.602861i
$497$	0.266065	+	1.22308i	0.0119346	+	0.0548627i
$498$	−12.7846	−	0.599550i	−0.572894	−	0.0268665i
$499$	3.55505	−	24.7259i	0.159146	−	1.10688i	−0.741067	−	0.671431i	$-0.765680\pi$
$499$	3.55505	−	24.7259i	0.159146	−	1.10688i	0.900212	−	0.435451i	$-0.143411\pi$
$500$	−22.3320	−	1.13200i	−0.998718	−	0.0506246i
$501$	13.8429	−	8.89627i	0.618454	−	0.397456i
$502$	−8.42318	−	20.9952i	−0.375945	−	0.937060i
$503$	10.9353	+	20.0264i	0.487579	+	0.892934i	0.999427	+	0.0338581i	$0.0107794\pi$
$503$	10.9353	+	20.0264i	0.487579	+	0.892934i	−0.511848	+	0.859076i	$0.671039\pi$
$504$	3.45669	−	4.63897i	0.153973	−	0.206636i
$505$	4.90109	+	0.397073i	0.218096	+	0.0176695i
$506$	7.46912	+	28.0916i	0.332043	+	1.24882i
$507$	−0.164001	+	0.164001i	−0.00728356	+	0.00728356i
$508$	−5.67553	+	17.8454i	−0.251811	+	0.791762i
$509$	−1.86743	+	6.35988i	−0.0827723	+	0.281897i	−0.990470	−	0.137728i	$-0.956020\pi$
$509$	−1.86743	+	6.35988i	−0.0827723	+	0.281897i	0.907698	+	0.419625i	$0.137838\pi$
$510$	6.94595	+	22.3991i	0.307572	+	0.991848i
$511$	−5.16920	−	8.04343i	−0.228672	−	0.355820i
$512$	−19.1162	−	12.1066i	−0.844826	−	0.535041i
$513$	0.419885	+	0.560901i	0.0185384	+	0.0247644i
$514$	−3.86846	+	3.52188i	−0.170630	+	0.155343i
$515$	0.695545	+	5.18464i	0.0306494	+	0.228462i
$516$	−7.92763	−	4.56143i	−0.348994	−	0.200806i
$517$	14.8444	−	39.7993i	0.652855	−	1.75037i
$518$	15.4928	−	1.49093i	0.680717	−	0.0655076i
$519$	−0.0630732	−	0.438684i	−0.00276861	−	0.0192561i
$520$	17.2127	−	14.6984i	0.754825	−	0.644569i
$521$	−23.9120	+	7.02120i	−1.04760	+	0.307604i	−0.759849	−	0.650100i	$-0.774727\pi$
$521$	−23.9120	+	7.02120i	−1.04760	+	0.307604i	−0.287755	+	0.957704i	$0.592909\pi$
$522$	13.7686	+	7.08533i	0.602634	+	0.310117i
$523$	15.3926	−	1.10090i	0.673071	−	0.0481390i	0.269380	−	0.963034i	$-0.413181\pi$
$523$	15.3926	−	1.10090i	0.673071	−	0.0481390i	0.403692	+	0.914895i	$0.367727\pi$
$524$	−0.0126807	+	0.134902i	−0.000553959	+	0.00589324i
$525$	−4.20591	−	6.82448i	−0.183561	−	0.297845i
$526$	−5.04504	+	0.852195i	−0.219974	+	0.0371575i
$527$	−7.76662	−	20.8231i	−0.338319	−	0.907069i
$528$	17.7132	+	10.7252i	0.770870	+	0.466754i
$529$	−8.66194	+	21.3066i	−0.376606	+	0.926374i
$530$	−12.4809	−	31.9795i	−0.542134	−	1.38910i
$531$	−17.6035	−	8.03926i	−0.763928	−	0.348874i
$532$	0.334491	+	0.0557398i	0.0145020	+	0.00241662i
$533$	0.890339	+	0.0636783i	0.0385649	+	0.00275821i
$534$	0.434982	+	0.264695i	0.0188235	+	0.0114545i
$535$	−0.349723	+	37.0426i	−0.0151198	+	1.60149i
$536$	−28.2325	−	10.4590i	−1.21946	−	0.451761i
$537$	5.22797	+	2.85468i	0.225603	+	0.123189i
$538$	−8.48205	−	10.7694i	−0.365687	−	0.464304i
$539$	−3.19493	−	22.2212i	−0.137615	−	0.957135i
$540$	11.0662	+	21.8919i	0.476215	+	0.942076i
$541$	7.84924	+	17.1874i	0.337465	+	0.738946i	0.999949	−	0.0101307i	$-0.00322475\pi$
$541$	7.84924	+	17.1874i	0.337465	+	0.738946i	−0.662483	+	0.749077i	$0.730497\pi$
$542$	−2.57403	+	13.4086i	−0.110564	+	0.575947i
$543$	0.139509	+	0.641315i	0.00598693	+	0.0275215i
$544$	−28.8337	−	19.3604i	−1.23623	−	0.830071i
$545$	−5.31516	−	1.20891i	−0.227677	−	0.0517839i
$546$	7.83965	+	2.09443i	0.335506	+	0.0896332i
$547$	−7.75440	+	35.6464i	−0.331554	+	1.52413i	0.445838	+	0.895114i	$0.352906\pi$
$547$	−7.75440	+	35.6464i	−0.331554	+	1.52413i	−0.777392	+	0.629016i	$0.783458\pi$
$548$	−13.7860	+	15.2102i	−0.588908	+	0.649746i
$549$	−5.78326	+	19.6960i	−0.246823	+	0.840603i
$550$	−24.1573	+	18.2981i	−1.03007	+	0.780232i
$551$			0.907642i			0.0386668i
$552$	6.08275	+	15.2139i	0.258899	+	0.647544i
$553$	−15.2257	+	15.2257i	−0.647463	+	0.647463i
$554$	−0.392948	−	16.0106i	−0.0166948	−	0.680227i
$555$	−8.02407	+	20.9084i	−0.340603	+	0.887510i
$556$	0.460929	+	9.38459i	0.0195477	+	0.397995i
$557$	−22.8966	−	4.98086i	−0.970161	−	0.211046i	−0.300557	−	0.953764i	$-0.597173\pi$
$557$	−22.8966	−	4.98086i	−0.970161	−	0.211046i	−0.669604	+	0.742718i	$0.733536\pi$
$558$	−3.94937	−	6.82887i	−0.167190	−	0.289089i
$559$	−1.92829	+	13.4115i	−0.0815579	+	0.567248i
$560$	11.1936	+	3.95567i	0.473018	+	0.167158i
$561$	26.7377	+	17.1833i	1.12887	+	0.725479i
$562$	7.36683	+	1.41420i	0.310751	+	0.0596545i
$563$	2.65597	−	7.12092i	0.111936	−	0.300111i	−0.868888	−	0.495009i	$-0.835165\pi$
$563$	2.65597	−	7.12092i	0.111936	−	0.300111i	0.980824	+	0.194898i	$0.0624375\pi$
$564$	5.61058	−	23.2771i	0.236248	−	0.980141i
$565$	−17.8117	−	15.7308i	−0.749343	−	0.661798i
$566$	−27.2603	−	3.23897i	−1.14584	−	0.136144i
$567$	−1.27383	+	2.33284i	−0.0534957	+	0.0979701i
$568$	2.42374	−	1.11338i	0.101698	−	0.0467163i
$569$	5.24558	+	4.54532i	0.219906	+	0.190550i	0.757846	−	0.652434i	$-0.226252\pi$
$569$	5.24558	+	4.54532i	0.219906	+	0.190550i	−0.537940	+	0.842983i	$0.680797\pi$
$570$	−0.286473	+	0.394974i	−0.0119990	+	0.0165437i
$571$	16.2164	−	14.0516i	0.678635	−	0.588041i	−0.245827	−	0.969314i	$-0.579060\pi$
$571$	16.2164	−	14.0516i	0.678635	−	0.588041i	0.924463	+	0.381273i	$0.124514\pi$
$572$	5.04236	−	30.2589i	0.210832	−	1.26519i
$573$	6.69005	+	17.9367i	0.279481	+	0.749317i
$574$	0.204882	+	0.420976i	0.00855160	+	0.0175712i
$575$	−23.9791	+	0.0540235i	−0.999997	+	0.00225294i
$576$	−11.2363	−	5.07143i	−0.468180	−	0.211310i
$577$	12.5985	−	4.69901i	0.524484	−	0.195623i	−0.0732548	−	0.997313i	$-0.523339\pi$
$577$	12.5985	−	4.69901i	0.524484	−	0.195623i	0.597739	+	0.801691i	$0.296066\pi$
$578$	−23.8516	−	16.9582i	−0.992097	−	0.705366i
$579$	−18.5840	−	21.4471i	−0.772324	−	0.891310i
$580$	−5.51893	+	31.2937i	−0.229161	+	1.29940i
$581$	−6.51250	+	7.51582i	−0.270184	+	0.311809i
$582$	−8.42151	+	16.3651i	−0.349083	+	0.678355i
$583$	−40.8341	−	22.2971i	−1.69118	−	0.923452i
$584$	−14.3748	+	14.4386i	−0.594832	+	0.597472i
$585$	8.16312	−	9.24297i	0.337504	−	0.382150i
$586$	−1.40777	+	1.70757i	−0.0581544	+	0.0705390i
$587$	30.1603	+	11.2492i	1.24485	+	0.464304i	0.883634	−	0.468179i	$-0.155090\pi$
$587$	30.1603	+	11.2492i	1.24485	+	0.464304i	0.361214	+	0.932483i	$0.382362\pi$
$588$	−3.29325	−	12.2184i	−0.135811	−	0.503878i
$589$	0.249991	−	0.388994i	0.0103007	−	0.0160282i
$590$	5.05775	−	39.3902i	0.208224	−	1.62167i
$591$	7.03383	+	1.01131i	0.289333	+	0.0415998i
$592$	−10.1919	−	31.5616i	−0.418886	−	1.29717i
$593$	−0.144838	+	0.665808i	−0.00594777	+	0.0273415i	−0.980025	−	0.198874i	$-0.936272\pi$
$593$	−0.144838	+	0.665808i	−0.00594777	+	0.0273415i	0.974077	+	0.226215i	$0.0726353\pi$
$594$	30.5704	+	13.0643i	1.25432	+	0.536035i
$595$	17.0124	+	6.52890i	0.697440	+	0.267659i
$596$	14.8994	+	28.7964i	0.610304	+	1.17955i
$597$	−9.90132	−	9.90132i	−0.405234	−	0.405234i
$598$	17.5993	−	16.7162i	0.719688	−	0.683578i
$599$	−26.8263			−1.09609			−0.548046	−	0.836448i	$-0.684628\pi$
$599$	−26.8263			−1.09609			−0.548046	+	0.836448i	$0.684628\pi$
$600$	−12.2787	+	11.8760i	−0.501274	+	0.484837i
$601$	27.1345	+	7.96741i	1.10684	+	0.324997i	0.783566	−	0.621309i	$-0.213399\pi$
$601$	27.1345	+	7.96741i	1.10684	+	0.324997i	0.323273	+	0.946306i	$0.395217\pi$
$602$	−6.59581	+	2.64621i	−0.268825	+	0.107852i
$603$	−16.0282	−	3.48672i	−0.652719	−	0.141990i
$604$	4.02705	+	20.7296i	0.163858	+	0.843475i
$605$	−3.65387	+	16.0649i	−0.148551	+	0.653129i
$606$	2.77771	−	2.52885i	0.112837	−	0.102728i
$607$	7.37302	−	1.60390i	0.299262	−	0.0651004i	−0.0604274	−	0.998173i	$-0.519246\pi$
$607$	7.37302	−	1.60390i	0.299262	−	0.0651004i	0.359689	+	0.933072i	$0.382883\pi$
$608$	−0.0370460	−	0.721648i	−0.00150242	−	0.0292667i
$609$	−10.3626	+	4.73245i	−0.419915	+	0.191769i
$610$	−42.1203	+	0.635946i	−1.70540	+	0.0257487i
$611$	−35.1097	+	5.04801i	−1.42038	+	0.204220i
$612$	−17.0321	−	8.24261i	−0.688480	−	0.333188i
$613$	1.21223	−	2.22004i	0.0489617	−	0.0896666i	−0.852052	−	0.523457i	$-0.824642\pi$
$613$	1.21223	−	2.22004i	0.0489617	−	0.0896666i	0.901014	+	0.433790i	$0.142824\pi$
$614$	5.13312	−	1.64506i	0.207156	−	0.0663891i
$615$	−0.673628	−	0.00635980i	−0.0271633	−	0.000256452i
$616$	15.0630	−	5.65623i	0.606905	−	0.227896i
$617$	2.23538	−	31.2547i	0.0899932	−	1.25827i	−0.729019	−	0.684493i	$-0.760024\pi$
$617$	2.23538	−	31.2547i	0.0899932	−	1.25827i	0.819013	−	0.573776i	$-0.194522\pi$
$618$	3.25697	+	2.31565i	0.131014	+	0.0931492i
$619$	1.16057	−	2.54130i	0.0466473	−	0.102143i	−0.884873	−	0.465831i	$-0.845755\pi$
$619$	1.16057	−	2.54130i	0.0466473	−	0.102143i	0.931521	+	0.363688i	$0.118483\pi$
$620$	10.9845	−	11.8916i	0.441147	−	0.477580i
$621$	13.0919	+	22.8161i	0.525361	+	0.915579i
$622$	26.4019	+	9.11598i	1.05862	+	0.365517i
$623$	0.370704	−	0.138266i	0.0148520	−	0.00553949i
$624$	0.771766	−	17.2742i	0.0308954	−	0.691523i
$625$	−9.51941	−	23.1167i	−0.380776	−	0.924667i
$626$	23.6239	+	14.3756i	0.944200	+	0.574564i
$627$	0.0471750	+	0.659592i	0.00188399	+	0.0263416i
$628$	6.46559	+	0.144360i	0.258005	+	0.00576060i
$629$	−14.3420	−	48.8445i	−0.571855	−	1.94756i
$630$	6.34029	+	1.27932i	0.252603	+	0.0509692i
$631$	−5.65993	+	0.813775i	−0.225318	+	0.0323959i	−0.254049	−	0.967191i	$-0.581762\pi$
$631$	−5.65993	+	0.813775i	−0.225318	+	0.0323959i	0.0287310	+	0.999587i	$0.490853\pi$
$632$	38.6546	+	24.7210i	1.53760	+	0.983350i
$633$	3.99868	+	1.49143i	0.158933	+	0.0592791i
$634$	19.9949	+	29.4956i	0.794101	+	1.17142i
$635$	−20.7506	+	2.78380i	−0.823463	+	0.110472i
$636$	−24.3610	−	9.71098i	−0.965977	−	0.385065i
$637$	−15.0074	+	11.2344i	−0.594615	+	0.445123i
$638$	21.5607	+	37.2806i	0.853595	+	1.47595i
$639$	1.22247	−	0.785633i	0.0483601	−	0.0310791i
$640$	3.11072	−	25.1062i	0.122962	−	0.992411i
$641$	−35.2924	−	10.3628i	−1.39397	−	0.409305i	−0.503358	−	0.864078i	$-0.667902\pi$
$641$	−35.2924	−	10.3628i	−1.39397	−	0.409305i	−0.890607	+	0.454773i	$0.849720\pi$
$642$	20.4959	+	19.5139i	0.808908	+	0.770153i
$643$	7.81626	+	7.81626i	0.308243	+	0.308243i	0.844228	−	0.535985i	$-0.180060\pi$
$643$	7.81626	+	7.81626i	0.308243	+	0.308243i	−0.535985	+	0.844228i	$0.680060\pi$
$644$	12.2113	+	3.60135i	0.481194	+	0.141913i
$645$	0.825762	−	10.1924i	0.0325143	−	0.401326i
$646$	−0.0272125	−	1.10877i	−0.00107066	−	0.0436240i
$647$	37.9772	−	20.7371i	1.49304	−	0.815260i	0.494492	−	0.869182i	$-0.335354\pi$
$647$	37.9772	−	20.7371i	1.49304	−	0.815260i	0.998545	+	0.0539220i	$0.0171722\pi$
$648$	5.43798	+	1.58366i	0.213624	+	0.0622122i
$649$	−29.0990	−	45.2789i	−1.14224	−	1.77735i
$650$	23.0783	+	10.3822i	0.905207	+	0.407222i
$651$	5.74463	+	0.825953i	0.225150	+	0.0323717i
$652$	−0.468335	−	1.08922i	−0.0183414	−	0.0426571i
$653$	−31.6185	+	6.87818i	−1.23733	+	0.269164i	−0.783198	−	0.621772i	$-0.786413\pi$
$653$	−31.6185	+	6.87818i	−1.23733	+	0.269164i	−0.454128	+	0.890936i	$0.650049\pi$
$654$	−3.44685	+	2.33661i	−0.134782	+	0.0913685i
$655$	−0.142432	+	0.0515981i	−0.00556529	+	0.00201610i
$656$	0.782390	−	0.619026i	0.0305472	−	0.0241689i
$657$	−6.65208	+	8.88614i	−0.259522	+	0.346681i
$658$	−11.5115	−	14.6158i	−0.448765	−	0.569785i
$659$	15.1168	−	4.43870i	0.588868	−	0.172907i	0.0262938	−	0.999654i	$-0.491629\pi$
$659$	15.1168	−	4.43870i	0.588868	−	0.172907i	0.562574	+	0.826747i	$0.309811\pi$
$660$	−2.38416	+	23.0283i	−0.0928034	+	0.896374i
$661$	16.3302	−	18.8460i	0.635169	−	0.733024i	−0.343344	−	0.939210i	$-0.611560\pi$
$661$	16.3302	−	18.8460i	0.635169	−	0.733024i	0.978513	+	0.206185i	$0.0661050\pi$
$662$	17.9363	−	4.36533i	0.697116	−	0.169663i
$663$	1.89337	−	26.4728i	0.0735325	−	1.02812i
$664$	18.6219	+	10.1148i	0.722669	+	0.392532i
$665$	0.103374	+	0.364764i	0.00400867	+	0.0141449i
$666$	−7.90740	−	16.2475i	−0.306405	−	0.629580i
$667$	−4.13571	+	33.8247i	−0.160135	+	1.30970i
$668$	−27.0482	+	3.27451i	−1.04653	+	0.126695i
$669$	11.9240	+	5.44551i	0.461008	+	0.210535i
$670$	−2.90797	−	33.5354i	−0.112345	−	1.29559i
$671$	−43.1468	+	37.3869i	−1.66566	+	1.44330i
$672$	8.04596	−	4.18564i	0.310380	−	0.161464i
$673$	0.177137	+	2.47669i	0.00682811	+	0.0954695i	0.999723	−	0.0235227i	$-0.00748820\pi$
$673$	0.177137	+	2.47669i	0.00682811	+	0.0954695i	−0.992895	+	0.118992i	$0.962034\pi$
$674$	−2.82110	−	8.80276i	−0.108665	−	0.339070i
$675$	−16.8469	+	21.6408i	−0.648439	+	0.832956i
$676$	0.362719	−	0.126138i	0.0139507	−	0.00485147i
$677$	8.59458	−	11.4810i	0.330316	−	0.441251i	−0.604381	−	0.796695i	$-0.706580\pi$
$677$	8.59458	−	11.4810i	0.330316	−	0.441251i	0.934697	+	0.355444i	$0.115670\pi$
$678$	−18.0707	+	1.73900i	−0.693999	+	0.0667858i
$679$	5.94084	+	13.0086i	0.227988	+	0.499225i
$680$	5.80367	−	38.3937i	0.222561	−	1.47233i
$681$	18.1538	+	11.6668i	0.695656	+	0.447071i
$682$	1.02778	−	21.9160i	0.0393556	−	0.839207i
$683$	−27.5864	+	20.6509i	−1.05556	+	0.790184i	−0.978376	−	0.206832i	$-0.933684\pi$
$683$	−27.5864	+	20.6509i	−1.05556	+	0.790184i	−0.0771861	+	0.997017i	$0.524594\pi$
$684$	−0.0750756	−	0.386458i	−0.00287059	−	0.0147766i
$685$	−21.9594	−	6.67368i	−0.839025	−	0.254988i
$686$	−21.1246	−	9.02762i	−0.806539	−	0.344676i
$687$	−6.57154	+	3.58833i	−0.250720	+	0.136903i
$688$	8.52533	+	12.5164i	0.325025	+	0.477183i
$689$			38.8506i			1.48009i
$690$	−12.4756	+	13.4140i	−0.474937	+	0.510663i
$691$		−	48.6509i		−	1.85077i	−0.379029	−	0.925385i	$-0.623742\pi$
$691$		−	48.6509i		−	1.85077i	0.379029	−	0.925385i	$-0.376258\pi$
$692$	−0.222408	+	0.699311i	−0.00845469	+	0.0265838i
$693$	7.69379	−	4.20113i	0.292263	−	0.159588i
$694$	−20.4404	+	47.8305i	−0.775908	+	1.81562i
$695$	−9.26708	+	4.94721i	−0.351520	+	0.187659i
$696$	14.5908	+	19.4013i	0.553063	+	0.735406i
$697$	1.22586	−	0.917671i	0.0464329	−	0.0347593i
$698$	43.6946	+	2.04911i	1.65387	+	0.0775599i
$699$	7.78924	+	5.00584i	0.294616	+	0.189338i
$700$	1.34617	+	13.2049i	0.0508806	+	0.499098i
$701$	−17.2833	−	37.8451i	−0.652780	−	1.42939i	−0.889100	−	0.457713i	$-0.848669\pi$
$701$	−17.2833	−	37.8451i	−0.652780	−	1.42939i	0.236320	−	0.971675i	$-0.424059\pi$
$702$	−2.65925	−	27.6334i	−0.100367	−	1.04296i
$703$	0.634729	−	0.847898i	0.0239392	−	0.0319791i
$704$	−18.6641	−	28.7610i	−0.703429	−	1.08397i
$705$	26.2106	−	5.44314i	0.987149	−	0.205000i
$706$	−11.8878	+	3.80978i	−0.447402	+	0.143383i
$707$	−0.208227	−	2.91139i	−0.00783117	−	0.109494i
$708$	−19.3510	−	23.3664i	−0.727257	−	0.878165i
$709$	4.27106	−	3.70089i	0.160403	−	0.138990i	−0.570961	−	0.820977i	$-0.693429\pi$
$709$	4.27106	−	3.70089i	0.160403	−	0.138990i	0.731364	+	0.681987i	$0.238884\pi$
$710$	2.28291	+	1.91859i	0.0856761	+	0.0720032i
$711$	22.7391	+	10.3846i	0.852783	+	0.389453i
$712$	−0.457381	−	0.708246i	−0.0171411	−	0.0265426i
$713$	11.0888	−	13.3574i	0.415278	−	0.500238i
$714$	12.5171	−	6.09183i	0.468439	−	0.227981i
$715$	32.9974	−	9.35146i	1.23403	−	0.349725i
$716$	−5.73277	−	8.02545i	−0.214244	−	0.299925i
$717$	−0.291516	+	4.07593i	−0.0108869	+	0.152218i
$718$	−8.11873	−	33.3584i	−0.302988	−	1.24492i
$719$	22.9569	−	26.4936i	0.856146	−	0.988045i	−0.143853	−	0.989599i	$-0.545949\pi$
$719$	22.9569	−	26.4936i	0.856146	−	0.988045i	0.999999	+	0.00155372i	$0.000494566\pi$
$720$	−0.238590	−	13.7808i	−0.00889171	−	0.513581i
$721$	2.97940	−	0.874830i	0.110959	−	0.0325804i
$722$	−21.0909	+	16.6113i	−0.784922	+	0.618208i
$723$	−8.52579	+	11.3891i	−0.317078	+	0.423566i
$724$	0.254640	−	1.05644i	0.00946362	−	0.0392625i
$725$	−34.2711	+	9.36382i	−1.27280	+	0.347763i
$726$	7.06229	+	10.4180i	0.262106	+	0.386647i
$727$	49.4220	−	10.7511i	1.83296	−	0.398736i	0.842749	−	0.538306i	$-0.180936\pi$
$727$	49.4220	−	10.7511i	1.83296	−	0.398736i	0.990212	+	0.139570i	$0.0445720\pi$
$728$	−10.1736	−	8.77611i	−0.377059	−	0.325264i
$729$	22.7283	+	3.26783i	0.841788	+	0.121031i
$730$	−21.4605	−	7.63733i	−0.794289	−	0.282670i
$731$	12.5668	+	19.5544i	0.464801	+	0.723245i
$732$	−21.6118	+	23.8445i	−0.798797	+	0.881316i
$733$	33.9751	−	18.5518i	1.25490	−	0.685226i	0.292343	−	0.956314i	$-0.405565\pi$
$733$	33.9751	−	18.5518i	1.25490	−	0.685226i	0.962555	+	0.271088i	$0.0873833\pi$
$734$	−38.6241	+	0.947949i	−1.42564	+	0.0349894i
$735$	10.7794	−	9.16367i	0.397604	−	0.338007i
$736$	1.90764	−	27.0622i	0.0703167	−	0.997525i
$737$	−32.2586	−	32.2586i	−1.18826	−	1.18826i
$738$	0.374796	−	0.393656i	0.0137964	−	0.0144907i
$739$	12.6049	+	3.70112i	0.463678	+	0.136148i	0.505223	−	0.862989i	$-0.331410\pi$
$739$	12.6049	+	3.70112i	0.463678	+	0.136148i	−0.0415458	+	0.999137i	$0.513228\pi$
$740$	27.0398	−	25.3744i	0.994004	−	0.932780i
$741$	0.464538	−	0.298540i	0.0170652	−	0.0109672i
$742$	−17.6400	+	10.2018i	−0.647583	+	0.374520i
$743$	19.1344	−	14.3239i	0.701975	−	0.525492i	−0.187621	−	0.982242i	$-0.560078\pi$
$743$	19.1344	−	14.3239i	0.701975	−	0.525492i	0.889595	+	0.456750i	$0.150987\pi$
$744$	−0.909576	−	12.3337i	−0.0333467	−	0.452175i
$745$	−21.9965	+	28.8129i	−0.805891	+	1.05562i
$746$	10.3055	−	6.98608i	0.377312	−	0.255779i
$747$	10.8176	+	4.03475i	0.395795	+	0.147624i
$748$	−27.4561	−	44.8954i	−1.00390	−	1.64154i
$749$	21.7657	−	3.12943i	0.795300	−	0.114347i
$750$	−17.8690	−	6.74195i	−0.652485	−	0.246181i
$751$	−1.23572	−	4.20847i	−0.0450920	−	0.153569i	0.933870	−	0.357614i	$-0.116409\pi$
$751$	−1.23572	−	4.20847i	−0.0450920	−	0.153569i	−0.978962	+	0.204044i	$0.934591\pi$
$752$	−25.1513	+	30.6455i	−0.917172	+	1.11753i
$753$	−1.37839	−	19.2724i	−0.0502313	−	0.702326i
$754$	18.6946	−	30.7214i	0.680816	−	1.11881i
$755$	−19.0332	+	13.9697i	−0.692690	+	0.508409i
$756$	11.8485	−	8.46369i	0.430927	−	0.307822i
$757$	27.4990	−	10.2566i	0.999468	−	0.372782i	0.204127	−	0.978944i	$-0.434564\pi$
$757$	27.4990	−	10.2566i	0.999468	−	0.372782i	0.795341	+	0.606162i	$0.207292\pi$
$758$	1.81016	−	5.24264i	0.0657481	−	0.190421i
$759$	−1.24741	+	24.7957i	−0.0452782	+	0.900027i
$760$	0.711847	−	0.382046i	0.0258214	−	0.0138583i
$761$	−20.1202	+	44.0570i	−0.729356	+	1.59707i	0.0709536	+	0.997480i	$0.477396\pi$
$761$	−20.1202	+	44.0570i	−0.729356	+	1.59707i	−0.800310	+	0.599587i	$0.795332\pi$
$762$	−9.26800	+	13.0354i	−0.335744	+	0.472224i
$763$	−0.230830	+	3.22742i	−0.00835660	+	0.116841i
$764$	2.96645	−	31.5584i	0.107323	−	1.14174i
$765$	0.199719	−	21.1542i	0.00722086	−	0.764831i
$766$	0.918713	+	2.86669i	0.0331944	+	0.103578i
$767$	−21.5398	+	39.4471i	−0.777756	+	1.42435i
$768$	−12.3927	−	14.8301i	−0.447184	−	0.535134i
$769$	5.65893	−	0.813631i	0.204066	−	0.0293403i	−0.0395236	−	0.999219i	$-0.512584\pi$
$769$	5.65893	−	0.813631i	0.204066	−	0.0293403i	0.243590	+	0.969878i	$0.421675\pi$
$770$	12.9108	+	12.5267i	0.465273	+	0.451432i
$771$	−4.06451	+	1.85620i	−0.146380	+	0.0668495i
$772$	12.2284	+	45.3691i	0.440110	+	1.63287i
$773$	−5.82158	+	1.26641i	−0.209388	+	0.0455495i	−0.316035	−	0.948747i	$-0.602352\pi$
$773$	−5.82158	+	1.26641i	−0.209388	+	0.0455495i	0.106648	+	0.994297i	$0.465988\pi$
$774$	5.55443	+	6.10103i	0.199650	+	0.219297i
$775$	17.2669	+	5.42616i	0.620244	+	0.194913i
$776$	24.3553	−	18.3164i	0.874303	−	0.657521i
$777$	12.9900	+	2.82580i	0.466014	+	0.101375i
$778$	−7.52388	−	18.7536i	−0.269744	−	0.672350i
$779$	0.0305694	+	0.00897598i	0.00109526	+	0.000321598i
$780$	17.8316	−	7.46844i	0.638474	−	0.267413i
$781$	4.04153			0.144617
$782$	4.03805	−	41.4441i	0.144400	−	1.48204i
$783$	27.5587	+	27.5587i	0.984866	+	0.984866i
$784$	−3.90458	+	20.5857i	−0.139449	+	0.735204i
$785$	2.94145	+	6.60520i	0.104985	+	0.235750i
$786$	−0.0454787	+	0.106420i	−0.00162217	+	0.00379587i
$787$	6.78576	−	31.1936i	0.241886	−	1.11193i	−0.682622	−	0.730771i	$-0.739161\pi$
$787$	6.78576	−	31.1936i	0.241886	−	1.11193i	0.924509	−	0.381161i	$-0.124476\pi$
$788$	−9.75383	−	6.58061i	−0.347466	−	0.234425i
$789$	−4.32561	−	0.621929i	−0.153996	−	0.0221413i
$790$	−6.53328	+	50.8817i	−0.232444	+	1.81029i
$791$	−7.62636	+	11.8669i	−0.271162	+	0.421937i
$792$	−12.2638	−	14.0901i	−0.435776	−	0.500668i
$793$	44.6681	+	16.6603i	1.58621	+	0.591626i
$794$	−3.78393	−	3.11959i	−0.134287	−	0.110710i
$795$	−1.81552	−	29.2644i	−0.0643898	−	1.03790i
$796$	7.61539	+	21.8986i	0.269920	+	0.776175i
$797$	−18.6985	−	10.2101i	−0.662334	−	0.361662i	0.112657	−	0.993634i	$-0.464064\pi$
$797$	−18.6985	−	10.2101i	−0.662334	−	0.361662i	−0.774991	+	0.631972i	$0.782246\pi$
$798$	0.257534	+	0.132528i	0.00911661	+	0.00469143i
$799$	−39.8487	+	45.9878i	−1.40975	+	1.62693i
$800$	26.8661	−	8.84379i	0.949860	−	0.312675i
$801$	−0.300798	−	0.347140i	−0.0106282	−	0.0122656i
$802$	−15.1877	+	21.3615i	−0.536296	+	0.754300i
$803$	−28.9255	+	10.7886i	−1.02076	+	0.380723i
$804$	−20.2371	−	15.8663i	−0.713706	−	0.559562i
$805$	2.19033	+	14.0645i	0.0771990	+	0.495709i
$806$	−16.4736	+	8.01742i	−0.580258	+	0.282402i
$807$	−4.09179	−	10.9705i	−0.144038	−	0.386180i
$808$	−5.96392	+	1.76552i	−0.209810	+	0.0621107i
$809$	38.6810	−	33.5173i	1.35995	−	1.17840i	0.394173	−	0.919036i	$-0.371031\pi$
$809$	38.6810	−	33.5173i	1.35995	−	1.17840i	0.965779	−	0.259368i	$-0.0835143\pi$
$810$	0.995719	+	6.25364i	0.0349860	+	0.219731i
$811$	−25.3908	−	22.0013i	−0.891593	−	0.772570i	0.0830009	−	0.996549i	$-0.473550\pi$
$811$	−25.3908	−	22.0013i	−0.891593	−	0.772570i	−0.974594	+	0.223980i	$0.928095\pi$
$812$	18.8579	+	0.421050i	0.661784	+	0.0147760i
$813$	−5.58880	+	10.2351i	−0.196008	+	0.358962i
$814$	5.92945	−	49.9044i	0.207827	−	1.74915i
$815$	0.877491	−	0.993569i	0.0307372	−	0.0348032i
$816$	−18.4057	−	23.2631i	−0.644330	−	0.814372i
$817$	−0.169008	+	0.453127i	−0.00591282	+	0.0158529i
$818$	−6.76251	+	35.2271i	−0.236446	+	1.23169i
$819$	−6.15803	−	3.95753i	−0.215179	−	0.138287i
$820$	0.999393	+	0.495351i	0.0349003	+	0.0172984i
$821$	−3.76953	+	26.2176i	−0.131557	+	0.915002i	0.811968	+	0.583702i	$0.198396\pi$
$821$	−3.76953	+	26.2176i	−0.131557	+	0.915002i	−0.943526	+	0.331300i	$0.892513\pi$
$822$	−15.1779	+	8.77789i	−0.529389	+	0.306164i
$823$	−21.7945	−	4.74110i	−0.759707	−	0.165264i	−0.184007	−	0.982925i	$-0.558907\pi$
$823$	−21.7945	−	4.74110i	−0.759707	−	0.165264i	−0.575700	+	0.817661i	$0.695271\pi$
$824$	−3.18397	−	5.80044i	−0.110919	−	0.202068i
$825$	−24.4185	+	8.58603i	−0.850142	+	0.298927i
$826$	−23.5669	+	0.578402i	−0.819999	+	0.0201252i
$827$	−3.47457	+	3.47457i	−0.120823	+	0.120823i	−0.764933	−	0.644110i	$-0.777228\pi$
$827$	−3.47457	+	3.47457i	−0.120823	+	0.120823i	0.644110	+	0.764933i	$0.277228\pi$
$828$	−1.03690	−	14.7441i	−0.0360346	−	0.512392i
$829$		−	19.7362i		−	0.685467i	−0.939433	−	0.342734i	$-0.888647\pi$
$829$		−	19.7362i		−	0.685467i	0.939433	−	0.342734i	$-0.111353\pi$
$830$	−1.33327	+	23.6554i	−0.0462785	+	0.821091i
$831$	3.85384	−	13.1250i	0.133688	−	0.455300i
$832$	−13.6098	+	25.1890i	−0.471834	+	0.873271i
$833$	−6.83611	+	31.4251i	−0.236857	+	1.08882i
$834$	−2.07135	+	7.75327i	−0.0717250	+	0.268474i
$835$	−16.2261	−	25.7803i	−0.561528	−	0.892163i
$836$	0.405439	−	1.01709i	0.0140224	−	0.0351767i
$837$	−4.22053	−	19.4014i	−0.145883	−	0.670612i
$838$	19.3588	+	3.71629i	0.668740	+	0.128377i
$839$	−12.8219	−	28.0760i	−0.442660	−	0.969290i	−0.991102	−	0.133102i	$-0.957506\pi$
$839$	−12.8219	−	28.0760i	−0.442660	−	0.969290i	0.548443	−	0.836188i	$-0.315221\pi$
$840$	8.07343	+	6.13523i	0.278560	+	0.211685i
$841$	3.05801	+	21.2689i	0.105449	+	0.733412i
$842$	−38.4634	+	30.2939i	−1.32554	+	1.04400i
$843$	5.62330	+	3.07056i	0.193677	+	0.105756i
$844$	−4.88393	−	5.10700i	−0.168112	−	0.175790i
$845$	0.300720	+	0.306452i	0.0103451	+	0.0105423i
$846$	−11.2281	+	18.4515i	−0.386030	+	0.634376i
$847$	9.75475	+	0.697673i	0.335177	+	0.0239723i
$848$	29.3035	+	32.0443i	1.00629	+	1.10041i
$849$	−21.3284	−	9.74034i	−0.731988	−	0.334288i
$850$	41.5847	−	12.4663i	1.42634	−	0.427591i
$851$	27.5177	−	28.7061i	0.943294	−	0.984033i
$852$	2.26161	−	0.273796i	0.0774815	−	0.00938008i
$853$	11.9005	+	31.9065i	0.407466	+	1.09246i	0.964987	+	0.262297i	$0.0844798\pi$
$853$	11.9005	+	31.9065i	0.407466	+	1.09246i	−0.557521	+	0.830163i	$0.688247\pi$
$854$	4.16486	+	24.6562i	0.142519	+	0.843718i
$855$	0.354834	−	0.260434i	0.0121351	−	0.00890667i
$856$	−16.4722	−	43.8669i	−0.563009	−	1.49934i
$857$	24.8625	−	1.77820i	0.849287	−	0.0607422i	0.360092	−	0.932917i	$-0.382745\pi$
$857$	24.8625	−	1.77820i	0.849287	−	0.0607422i	0.489195	+	0.872175i	$0.337291\pi$
$858$	11.9888	−	23.2972i	0.409290	−	0.795353i
$859$	−40.7175	+	11.9557i	−1.38926	+	0.407925i	−0.888984	−	0.457939i	$-0.848588\pi$
$859$	−40.7175	+	11.9557i	−1.38926	+	0.407925i	−0.500280	+	0.865863i	$0.666770\pi$
$860$	−8.58229	+	14.5953i	−0.292654	+	0.497694i
$861$	0.0569095	+	0.395814i	0.00193947	+	0.0134893i
$862$	1.64773	+	17.1223i	0.0561219	+	0.583186i
$863$	−4.75990	+	12.7618i	−0.162029	+	0.434416i	−0.992439	−	0.122736i	$-0.960833\pi$
$863$	−4.75990	+	12.7618i	−0.162029	+	0.434416i	0.830411	+	0.557152i	$0.188106\pi$
$864$	−23.0362	−	20.7865i	−0.783707	−	0.707172i
$865$	−0.813158	+	0.109089i	−0.0276482	+	0.00370915i
$866$	19.8053	+	21.7543i	0.673012	+	0.739241i
$867$	−14.9797	−	20.0105i	−0.508737	−	0.679594i
$868$	−7.96609	−	5.37448i	−0.270387	−	0.182422i
$869$	37.5882	+	58.4884i	1.27509	+	1.98408i
$870$	−12.6462	+	24.0147i	−0.428745	+	0.814173i
$871$	−10.7327	+	36.5521i	−0.363663	+	1.23852i
$872$	6.82255	−	0.996358i	0.231041	−	0.0337409i
$873$	11.7399	−	11.7399i	0.397336	−	0.397336i
$874$	0.740640	−	0.449488i	0.0250525	−	0.0152042i
$875$	−12.7064	+	7.66637i	−0.429556	+	0.259171i
$876$	−15.4556	+	7.99683i	−0.522197	+	0.270188i
$877$	4.35335	+	7.97256i	0.147002	+	0.269214i	0.940796	−	0.338972i	$-0.110079\pi$
$877$	4.35335	+	7.97256i	0.147002	+	0.269214i	−0.793794	+	0.608186i	$0.791897\pi$
$878$	−53.1417	+	21.3202i	−1.79345	+	0.719524i
$879$	−1.59014	+	1.02192i	−0.0536341	+	0.0344685i
$880$	20.1631	−	32.6018i	0.679700	−	1.09901i
$881$	−3.93042	+	27.3367i	−0.132419	+	0.920996i	0.809969	+	0.586473i	$0.199484\pi$
$881$	−3.93042	+	27.3367i	−0.132419	+	0.920996i	−0.942388	+	0.334523i	$0.891425\pi$
$882$	−0.534750	+	11.4029i	−0.0180060	+	0.383954i
$883$	10.2878	+	47.2923i	0.346212	+	1.59151i	0.740193	+	0.672394i	$0.234734\pi$
$883$	10.2878	+	47.2923i	0.346212	+	1.59151i	−0.393981	+	0.919119i	$0.628902\pi$
$884$	−21.9161	+	38.0896i	−0.737119	+	1.28109i
$885$	14.3815	−	30.7203i	0.483430	−	1.03265i
$886$	−43.3046	−	35.7016i	−1.45485	−	1.19942i
$887$	30.4461	+	22.7917i	1.02228	+	0.765270i	0.972361	−	0.233484i	$-0.0750125\pi$
$887$	30.4461	+	22.7917i	1.02228	+	0.765270i	0.0499197	+	0.998753i	$0.484103\pi$
$888$	−0.0627253	−	28.3279i	−0.00210492	−	0.950621i
$889$	3.50136	+	11.9245i	0.117432	+	0.399936i
$890$	0.497584	−	0.800576i	0.0166790	−	0.0268354i
$891$	6.48600	+	5.62016i	0.217289	+	0.188282i
$892$	−13.8439	−	16.7165i	−0.463527	−	0.559711i
$893$	−1.26283	−	0.0903190i	−0.0422588	−	0.00302241i
$894$	4.61243	+	27.3058i	0.154263	+	0.913243i
$895$	5.37572	−	9.62769i	0.179691	−	0.321818i
$896$	−15.0108	+	0.434931i	−0.501474	+	0.0145300i
$897$	18.6721	−	9.00889i	0.623442	−	0.300798i
$898$	37.3601	+	12.8996i	1.24672	+	0.430464i
$899$	10.6848	−	23.3966i	0.356360	−	0.780319i
$900$	13.8175	−	6.82169i	0.460584	−	0.227390i
$901$	43.6458	+	50.3699i	1.45405	+	1.67806i
$902$	1.46883	−	0.357483i	0.0489067	−	0.0119029i
$903$	−6.05459	+	0.433033i	−0.201484	+	0.0144104i
$904$	28.1869	+	10.4421i	0.937483	+	0.347300i
$905$	1.18959	−	0.247040i	0.0395432	−	0.00821190i
$906$	−2.12805	+	17.9105i	−0.0706998	+	0.595036i
$907$	−8.41457	−	6.29907i	−0.279401	−	0.209157i	0.450382	−	0.892836i	$-0.351288\pi$
$907$	−8.41457	−	6.29907i	−0.279401	−	0.209157i	−0.729783	+	0.683679i	$0.760379\pi$
$908$	−18.6416	−	30.4821i	−0.618643	−	1.01159i
$909$	−3.08240	+	1.40768i	−0.102237	+	0.0466900i
$910$	4.01404	−	14.4755i	0.133064	−	0.479858i
$911$	4.73027	−	7.36045i	0.156721	−	0.243862i	−0.754010	−	0.656863i	$-0.771883\pi$
$911$	4.73027	−	7.36045i	0.156721	−	0.243862i	0.910731	+	0.413001i	$0.135519\pi$
$912$	0.157978	−	0.596622i	0.00523117	−	0.0197561i
$913$	19.2432	+	25.7059i	0.636856	+	0.850741i
$914$	11.2280	−	42.0277i	0.371391	−	1.39015i
$915$	−34.4250	−	10.4621i	−1.13806	−	0.345867i
$916$	12.3824	−	0.608170i	0.409127	−	0.0200945i
$917$	0.0430964	+	0.0789252i	0.00142317	+	0.00260634i
$918$	−34.4918	−	32.8393i	−1.13840	−	1.08386i
$919$	−24.1060			−0.795182			−0.397591	−	0.917563i	$-0.630154\pi$
$919$	−24.1060			−0.795182			−0.397591	+	0.917563i	$0.630154\pi$
$920$	28.2689	−	10.9940i	0.931999	−	0.362461i
$921$	4.60392			0.151704
$922$	−10.6070	−	10.0988i	−0.349322	−	0.332586i
$923$	−1.61740	−	2.96205i	−0.0532374	−	0.0974969i
$924$	13.7261	−	0.674166i	0.451557	−	0.0221784i
$925$	38.5636	+	15.2189i	1.26796	+	0.500394i
$926$	−1.09670	+	4.10507i	−0.0360400	+	0.134901i
$927$	−2.16038	−	2.88593i	−0.0709561	−	0.0947863i
$928$	−7.75248	−	39.4399i	−0.254488	−	1.29468i
$929$	1.19498	−	1.85942i	0.0392060	−	0.0610057i	−0.821097	−	0.570788i	$-0.806638\pi$
$929$	1.19498	−	1.85942i	0.0392060	−	0.0610057i	0.860303	+	0.509782i	$0.170274\pi$
$930$	12.0342	−	6.80899i	0.394616	−	0.223275i
$931$	−0.608652	+	0.277962i	−0.0199477	+	0.00910983i
$932$	−7.99853	−	13.0789i	−0.262001	−	0.428415i
$933$	19.0982	+	14.2967i	0.625248	+	0.468055i
$934$	3.30204	−	27.7912i	0.108046	−	0.909355i
$935$	32.2756	−	49.1943i	1.05552	−	1.60883i
$936$	−5.41871	+	14.6270i	−0.177116	+	0.478097i
$937$	−8.58158	+	0.613767i	−0.280348	+	0.0200509i	−0.210805	−	0.977528i	$-0.567609\pi$
$937$	−8.58158	+	0.613767i	−0.280348	+	0.0200509i	−0.0695428	+	0.997579i	$0.522154\pi$
$938$	−19.4146	+	4.72512i	−0.633910	+	0.154281i
$939$	15.4676	+	17.8506i	0.504767	+	0.582532i
$940$	−42.9905	−	10.7926i	−1.40220	−	0.352017i
$941$	−14.3220	+	31.3609i	−0.466885	+	1.02234i	0.518979	+	0.854787i	$0.326312\pi$
$941$	−14.3220	+	31.3609i	−0.466885	+	1.02234i	−0.985864	+	0.167548i	$0.946415\pi$
$942$	5.22127	+	1.80278i	0.170118	+	0.0587379i
$943$	1.09832	+	0.473795i	0.0357661	+	0.0154289i
$944$	11.9872	+	48.7830i	0.390151	+	1.58775i
$945$	14.2140	+	7.93656i	0.462382	+	0.258176i
$946$	3.82201	+	22.6265i	0.124264	+	0.735651i
$947$	2.73194	+	0.195392i	0.0887762	+	0.00634940i	0.115657	−	0.993289i	$-0.463103\pi$
$947$	2.73194	+	0.195392i	0.0887762	+	0.00634940i	−0.0268804	+	0.999639i	$0.508557\pi$
$948$	24.9964	+	30.1833i	0.811846	+	0.980307i
$949$	19.4829	+	16.8820i	0.632440	+	0.548013i
$950$	0.726137	+	0.537198i	0.0235590	+	0.0174290i
$951$	8.57470	+	29.2028i	0.278054	+	0.946964i
$952$	−23.0494	+	0.0510374i	−0.747035	+	0.00165413i
$953$	−12.3054	−	9.21167i	−0.398609	−	0.298395i	0.381104	−	0.924532i	$-0.375544\pi$
$953$	−12.3054	−	9.21167i	−0.398609	−	0.298395i	−0.779713	+	0.626137i	$0.784635\pi$
$954$	18.2538	+	15.0490i	0.590989	+	0.487228i
$955$	33.3199	−	12.0706i	1.07821	−	0.390595i
$956$	3.37435	−	5.86453i	0.109134	−	0.189672i
$957$	7.81892	+	35.9430i	0.252750	+	1.16187i
$958$	0.990166	−	21.1140i	0.0319908	−	0.682163i
$959$	−1.93887	+	13.4851i	−0.0626093	+	0.435458i
$960$	9.07453	−	19.6097i	0.292879	−	0.632901i
$961$	15.0555	−	9.67558i	0.485661	−	0.312115i
$962$	−38.9480	+	15.6258i	−1.25573	+	0.503796i
$963$	−12.2346	−	22.4061i	−0.394256	−	0.722026i
$964$	20.9216	−	10.8250i	0.673840	−	0.348649i
$965$	−40.0258	+	34.0263i	−1.28848	+	1.09535i
$966$	8.99356	+	6.11232i	0.289363	+	0.196661i
$967$	−24.4711	+	24.4711i	−0.786937	+	0.786937i	−0.980991	−	0.194054i	$-0.937836\pi$
$967$	−24.4711	+	24.4711i	−0.786937	+	0.786937i	0.194054	+	0.980991i	$0.437836\pi$
$968$	−3.01145	−	20.6209i	−0.0967917	−	0.662780i
$969$	0.266886	−	0.908932i	0.00857363	−	0.0291991i
$970$	30.1465	+	15.8752i	0.967947	+	0.509722i
$971$	21.2224	+	33.0227i	0.681059	+	1.05975i	0.993937	+	0.109955i	$0.0350708\pi$
$971$	21.2224	+	33.0227i	0.681059	+	1.05975i	−0.312877	+	0.949794i	$0.601293\pi$
$972$	−23.2716	−	15.7006i	−0.746436	−	0.503598i
$973$	3.73694	+	4.99197i	0.119801	+	0.160035i
$974$	9.12458	+	10.0225i	0.292370	+	0.321142i
$975$	16.0649	+	14.4603i	0.514488	+	0.463100i
$976$	49.4089	−	19.9498i	1.58154	−	0.638577i
$977$	7.58539	−	20.3372i	0.242678	−	0.650646i	−0.757319	−	0.653045i	$-0.773491\pi$
$977$	7.58539	−	20.3372i	0.242678	−	0.650646i	0.999997	+	0.00239971i	$0.000763853\pi$
$978$	−0.0970046	−	1.00801i	−0.00310186	−	0.0322327i
$979$	−0.181807	−	1.26450i	−0.00581059	−	0.0404135i
$980$	−22.6752	+	5.88265i	−0.724334	+	0.187914i
$981$	3.60430	−	1.05832i	0.115076	−	0.0337895i
$982$	−0.391025	+	0.759859i	−0.0124781	+	0.0242481i
$983$	−3.30050	+	0.236056i	−0.105270	+	0.00752903i	−0.123875	−	0.992298i	$-0.539532\pi$
$983$	−3.30050	+	0.236056i	−0.105270	+	0.00752903i	0.0186050	+	0.999827i	$0.494078\pi$
$984$	0.797730	−	0.299552i	0.0254307	−	0.00954936i
$985$	1.99499	−	13.0028i	0.0635655	−	0.414303i
$986$	−10.2756	−	60.8323i	−0.327243	−	1.93730i
$987$	−5.55320	−	14.8887i	−0.176760	−	0.473913i
$988$	−0.907680	+	0.109886i	−0.0288772	+	0.00349593i
$989$	−8.36303	+	16.1164i	−0.265929	+	0.512472i
$990$	8.38797	−	19.1260i	0.266587	−	0.607866i
$991$	−27.3690	−	12.4990i	−0.869406	−	0.397044i	−0.0697941	−	0.997561i	$-0.522234\pi$
$991$	−27.3690	−	12.4990i	−0.869406	−	0.397044i	−0.799612	+	0.600517i	$0.794961\pi$
$992$	−7.54036	+	19.0382i	−0.239407	+	0.604465i
$993$	15.7267	+	1.12480i	0.499073	+	0.0356944i
$994$	0.920191	−	1.51218i	0.0291867	−	0.0479634i
$995$	−18.5015	+	18.1555i	−0.586538	+	0.575567i
$996$	12.5098	+	13.0812i	0.396389	+	0.414494i
$997$	5.70268	+	3.11390i	0.180606	+	0.0986182i	0.567008	−	0.823712i	$-0.308101\pi$
$997$	5.70268	+	3.11390i	0.180606	+	0.0986182i	−0.386403	+	0.922330i	$0.626283\pi$
$998$	−27.7530	+	21.8584i	−0.878505	+	0.691914i
$999$	−6.47245	−	45.0169i	−0.204779	−	1.42427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.17	yes	1360
4.3	odd	2	inner	460.2.w.a.167.33	yes	1360
5.3	odd	4	inner	460.2.w.a.443.18	yes	1360
20.3	even	4	inner	460.2.w.a.443.66	yes	1360
23.4	even	11	inner	460.2.w.a.27.66	yes	1360
92.27	odd	22	inner	460.2.w.a.27.18	✓	1360
115.73	odd	44	inner	460.2.w.a.303.33	yes	1360
460.303	even	44	inner	460.2.w.a.303.17	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.18	✓	1360	92.27	odd	22	inner
460.2.w.a.27.66	yes	1360	23.4	even	11	inner
460.2.w.a.167.17	yes	1360	1.1	even	1	trivial
460.2.w.a.167.33	yes	1360	4.3	odd	2	inner
460.2.w.a.303.17	yes	1360	460.303	even	44	inner
460.2.w.a.303.33	yes	1360	115.73	odd	44	inner
460.2.w.a.443.18	yes	1360	5.3	odd	4	inner
460.2.w.a.443.66	yes	1360	20.3	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02423 - 0.975163i) q^{2} +(-0.578886 - 1.06015i) q^{3} +(0.0981127 + 1.99759i) q^{4} +(-1.97258 + 1.05306i) q^{5} +(-0.440905 + 1.65035i) q^{6} +(0.795441 + 1.06258i) q^{7} +(1.84749 - 2.14168i) q^{8} +(0.833113 - 1.29635i) q^{9} +O(q^{10})\)	\(q+(-1.02423 - 0.975163i) q^{2} +(-0.578886 - 1.06015i) q^{3} +(0.0981127 + 1.99759i) q^{4} +(-1.97258 + 1.05306i) q^{5} +(-0.440905 + 1.65035i) q^{6} +(0.795441 + 1.06258i) q^{7} +(1.84749 - 2.14168i) q^{8} +(0.833113 - 1.29635i) q^{9} +(3.04729 + 0.845009i) q^{10} +(3.89848 - 1.78038i) q^{11} +(2.06095 - 1.26039i) q^{12} +(-2.86500 - 2.14471i) q^{13} +(0.221476 - 1.86402i) q^{14} +(2.25830 + 1.48163i) q^{15} +(-3.98075 + 0.391978i) q^{16} +(-6.12390 + 0.437990i) q^{17} +(-2.11745 + 0.515344i) q^{18} +(-0.0836509 - 0.0965383i) q^{19} +(-2.29711 - 3.83709i) q^{20} +(0.666030 - 1.45840i) q^{21} +(-5.72912 - 1.97813i) q^{22} +(-2.67750 - 3.97881i) q^{23} +(-3.33999 - 0.718828i) q^{24} +(2.78214 - 4.15448i) q^{25} +(0.842986 + 4.99053i) q^{26} +(-5.47107 - 0.391299i) q^{27} +(-2.04457 + 1.69322i) q^{28} +(-5.36995 - 4.65309i) q^{29} +(-0.868195 - 3.71975i) q^{30} +(1.01984 + 3.47325i) q^{31} +(4.45946 + 3.48040i) q^{32} +(-4.14424 - 3.10234i) q^{33} +(6.69942 + 5.52320i) q^{34} +(-2.68803 - 1.25839i) q^{35} +(2.67131 + 1.53703i) q^{36} +(1.76251 + 8.10211i) q^{37} +(-0.00846247 + 0.180451i) q^{38} +(-0.615209 + 4.27887i) q^{39} +(-1.38901 + 6.17014i) q^{40} +(-0.209821 + 0.134844i) q^{41} +(-2.10435 + 0.844258i) q^{42} +(-1.81444 - 3.32290i) q^{43} +(3.93896 + 7.61290i) q^{44} +(-0.278251 + 3.43447i) q^{45} +(-1.13760 + 6.68624i) q^{46} +(7.00832 - 7.00832i) q^{47} +(2.71995 + 3.99328i) q^{48} +(1.47577 - 5.02600i) q^{49} +(-6.90086 + 1.54212i) q^{50} +(4.00937 + 6.23871i) q^{51} +(4.00316 - 5.93352i) q^{52} +(-6.50557 - 8.69042i) q^{53} +(5.22208 + 5.73597i) q^{54} +(-5.81523 + 7.61726i) q^{55} +(3.74528 + 0.259534i) q^{56} +(-0.0539208 + 0.144567i) q^{57} +(0.962568 + 10.0024i) q^{58} +(-1.78727 - 12.4307i) q^{59} +(-2.73813 + 4.65652i) q^{60} +(-12.7815 + 3.75299i) q^{61} +(2.34243 - 4.55192i) q^{62} +(2.04017 - 0.145916i) q^{63} +(-1.17357 - 7.91345i) q^{64} +(7.90994 + 1.21360i) q^{65} +(1.21939 + 7.21884i) q^{66} +(-3.71992 - 9.97348i) q^{67} +(-1.47576 - 12.1901i) q^{68} +(-2.66817 + 5.14184i) q^{69} +(1.52604 + 3.91016i) q^{70} +(0.857791 + 0.391740i) q^{71} +(-1.23720 - 4.17925i) q^{72} +(-7.18499 - 0.513881i) q^{73} +(6.09566 - 10.0172i) q^{74} +(-6.01491 - 0.544516i) q^{75} +(0.184637 - 0.176572i) q^{76} +(4.99281 + 2.72628i) q^{77} +(4.80271 - 3.78264i) q^{78} +(2.30868 + 16.0572i) q^{79} +(7.43957 - 4.96517i) q^{80} +(0.831863 + 1.82153i) q^{81} +(0.346401 + 0.0664982i) q^{82} +(1.59262 + 7.32114i) q^{83} +(2.97864 + 1.18737i) q^{84} +(11.6186 - 7.31279i) q^{85} +(-1.38196 + 5.17280i) q^{86} +(-1.82439 + 8.38657i) q^{87} +(3.38940 - 11.6385i) q^{88} +(0.0839786 - 0.286005i) q^{89} +(3.63416 - 3.24636i) q^{90} -4.75029i q^{91} +(7.68535 - 5.73893i) q^{92} +(3.09179 - 3.09179i) q^{93} +(-14.0124 + 0.343906i) q^{94} +(0.266669 + 0.102340i) q^{95} +(1.10823 - 6.74246i) q^{96} +(10.5280 + 2.29022i) q^{97} +(-6.41271 + 3.70869i) q^{98} +(0.939885 - 6.53705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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