LMFDB - Embedded newform 512.2.o.a.117.1

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			117.1
Character	$\chi$	$=$	512.117
Dual form			512.2.o.a.477.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41419 - 0.00887673i) q^{2} +(0.0605891 + 2.46813i) q^{3} +(1.99984 + 0.0251067i) q^{4} +(0.349161 + 1.26170i) q^{5} +(-0.0637753 - 3.49093i) q^{6} +(0.896663 - 1.89584i) q^{7} +(-2.82793 - 0.0532576i) q^{8} +(-3.09158 + 0.151880i) q^{9} +O(q^{10})$	\(q+(-1.41419 - 0.00887673i) q^{2} +(0.0605891 + 2.46813i) q^{3} +(1.99984 + 0.0251067i) q^{4} +(0.349161 + 1.26170i) q^{5} +(-0.0637753 - 3.49093i) q^{6} +(0.896663 - 1.89584i) q^{7} +(-2.82793 - 0.0532576i) q^{8} +(-3.09158 + 0.151880i) q^{9} +(-0.482578 - 1.78738i) q^{10} +(4.25960 + 2.99995i) q^{11} +(0.0592021 + 4.93738i) q^{12} +(4.83089 - 0.595834i) q^{13} +(-1.28488 + 2.67310i) q^{14} +(-3.09289 + 0.938218i) q^{15} +(3.99874 + 0.100419i) q^{16} +(0.174230 - 0.574360i) q^{17} +(4.37342 - 0.187343i) q^{18} +(-0.452585 + 6.13554i) q^{19} +(0.666589 + 2.53198i) q^{20} +(4.73349 + 2.09821i) q^{21} +(-5.99724 - 4.28030i) q^{22} +(1.31407 - 0.974580i) q^{23} +(-0.0398950 - 6.98290i) q^{24} +(2.81866 - 1.68944i) q^{25} +(-6.83707 + 0.799737i) q^{26} +(-0.0173108 - 0.234677i) q^{27} +(1.84078 - 3.76886i) q^{28} +(-6.47217 + 1.45337i) q^{29} +(4.38225 - 1.29936i) q^{30} +(-4.94811 - 7.40537i) q^{31} +(-5.65407 - 0.177507i) q^{32} +(-7.14617 + 10.6950i) q^{33} +(-0.251492 + 0.810705i) q^{34} +(2.70506 + 0.469373i) q^{35} +(-6.18649 + 0.226116i) q^{36} +(-0.410392 - 0.815310i) q^{37} +(0.694502 - 8.67277i) q^{38} +(1.76329 + 11.8872i) q^{39} +(-0.920205 - 3.58660i) q^{40} +(-8.55449 - 5.12737i) q^{41} +(-6.67540 - 3.00928i) q^{42} +(-1.32611 - 1.39286i) q^{43} +(8.44322 + 6.10637i) q^{44} +(-1.27109 - 3.84764i) q^{45} +(-1.86699 + 1.36657i) q^{46} +(5.16060 + 4.23520i) q^{47} +(-0.00556638 + 9.87547i) q^{48} +(1.65057 + 2.01122i) q^{49} +(-4.00110 + 2.36416i) q^{50} +(1.42815 + 0.395222i) q^{51} +(9.67599 - 1.07029i) q^{52} +(-4.29546 - 0.964579i) q^{53} +(0.0223975 + 0.332030i) q^{54} +(-2.29777 + 6.42182i) q^{55} +(-2.63666 + 5.31353i) q^{56} +(-15.1707 - 0.745289i) q^{57} +(9.16575 - 1.99789i) q^{58} +(-1.31412 + 10.6546i) q^{59} +(-6.20885 + 1.79864i) q^{60} +(-4.74179 - 10.6973i) q^{61} +(6.93181 + 10.5165i) q^{62} +(-2.48417 + 5.99732i) q^{63} +(7.99433 + 0.301217i) q^{64} +(2.43852 + 5.88712i) q^{65} +(10.2009 - 15.0613i) q^{66} +(0.339650 - 0.880511i) q^{67} +(0.362853 - 1.14425i) q^{68} +(2.48500 + 3.18424i) q^{69} +(-3.82130 - 0.687793i) q^{70} +(9.42388 + 10.3976i) q^{71} +(8.75086 - 0.264854i) q^{72} +(-1.30912 - 2.76789i) q^{73} +(0.573134 + 1.15664i) q^{74} +(4.34053 + 6.85444i) q^{75} +(-1.05914 + 12.2587i) q^{76} +(9.50684 - 5.38556i) q^{77} +(-2.38810 - 16.8263i) q^{78} +(-0.106193 + 1.07819i) q^{79} +(1.26950 + 5.08029i) q^{80} +(-8.66306 + 0.853237i) q^{81} +(12.0521 + 7.32698i) q^{82} +(5.18551 - 10.3018i) q^{83} +(9.41355 + 4.31493i) q^{84} +(0.785506 + 0.0192831i) q^{85} +(1.86300 + 1.98153i) q^{86} +(-3.97925 - 15.8861i) q^{87} +(-11.8861 - 8.71049i) q^{88} +(-0.269754 - 0.200063i) q^{89} +(1.76340 + 5.45255i) q^{90} +(3.20208 - 9.69284i) q^{91} +(2.65240 - 1.91602i) q^{92} +(17.9776 - 12.6612i) q^{93} +(-7.26045 - 6.03516i) q^{94} +(-7.89926 + 1.57126i) q^{95} +(0.0955338 - 13.9657i) q^{96} +(-12.4396 - 2.47439i) q^{97} +(-2.31635 - 2.85889i) q^{98} +(-13.6246 - 8.62765i) 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 $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{53}{128}\right)$	$1$

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 $

$2$	−1.41419	−	0.00887673i	−0.999980	−	0.00627680i
$2$	−1.41419	−	0.00887673i	−0.999980	−	0.00627680i
$3$	0.0605891	+	2.46813i	0.0349811	+	1.42497i	0.718747	+	0.695271i	$0.244716\pi$
$3$	0.0605891	+	2.46813i	0.0349811	+	1.42497i	−0.683766	+	0.729701i	$0.739659\pi$
$4$	1.99984	+	0.0251067i	0.999921	+	0.0125533i
$5$	0.349161	+	1.26170i	0.156149	+	0.564251i	0.999633	+	0.0270962i	$0.00862605\pi$
$5$	0.349161	+	1.26170i	0.156149	+	0.564251i	−0.843483	+	0.537155i	$0.819499\pi$
$6$	−0.0637753	−	3.49093i	−0.0260362	−	1.42516i
$7$	0.896663	−	1.89584i	0.338907	−	0.716558i	−0.660506	−	0.750821i	$-0.729658\pi$
$7$	0.896663	−	1.89584i	0.338907	−	0.716558i	0.999413	+	0.0342624i	$0.0109082\pi$
$8$	−2.82793	−	0.0532576i	−0.999823	−	0.0188294i
$9$	−3.09158	+	0.151880i	−1.03053	+	0.0506266i
$10$	−0.482578	−	1.78738i	−0.152605	−	0.565220i
$11$	4.25960	+	2.99995i	1.28432	+	0.904519i	0.998553	−	0.0537803i	$-0.0171271\pi$
$11$	4.25960	+	2.99995i	1.28432	+	0.904519i	0.285766	+	0.958299i	$0.407752\pi$
$12$	0.0592021	+	4.93738i	0.0170902	+	1.42530i
$13$	4.83089	−	0.595834i	1.33985	−	0.165255i	0.579608	−	0.814896i	$-0.303206\pi$
$13$	4.83089	−	0.595834i	1.33985	−	0.165255i	0.760241	+	0.649641i	$0.225081\pi$
$14$	−1.28488	+	2.67310i	−0.343398	+	0.714417i
$15$	−3.09289	+	0.938218i	−0.798581	+	0.242247i
$16$	3.99874	+	0.100419i	0.999685	+	0.0251047i
$17$	0.174230	−	0.574360i	0.0422570	−	0.139303i	−0.933274	−	0.359166i	$-0.883061\pi$
$17$	0.174230	−	0.574360i	0.0422570	−	0.139303i	0.975531	+	0.219863i	$0.0705612\pi$
$18$	4.37342	−	0.187343i	1.03083	−	0.0441572i
$19$	−0.452585	+	6.13554i	−0.103830	+	1.40759i	0.654669	+	0.755915i	$0.272808\pi$
$19$	−0.452585	+	6.13554i	−0.103830	+	1.40759i	−0.758499	+	0.651674i	$0.774067\pi$
$20$	0.666589	+	2.53198i	0.149054	+	0.566167i
$21$	4.73349	+	2.09821i	1.03293	+	0.457867i
$22$	−5.99724	−	4.28030i	−1.27862	−	0.912563i
$23$	1.31407	−	0.974580i	0.274002	−	0.203214i	−0.449969	−	0.893044i	$-0.648565\pi$
$23$	1.31407	−	0.974580i	0.274002	−	0.203214i	0.723971	+	0.689830i	$0.242315\pi$
$24$	−0.0398950	−	6.98290i	−0.00814353	−	1.42538i
$25$	2.81866	−	1.68944i	0.563732	−	0.337888i
$26$	−6.83707	+	0.799737i	−1.34086	+	0.156841i
$27$	−0.0173108	−	0.234677i	−0.00333147	−	0.0451636i
$28$	1.84078	−	3.76886i	0.347875	−	0.712248i
$29$	−6.47217	+	1.45337i	−1.20185	+	0.269885i	−0.773541	−	0.633747i	$-0.781516\pi$
$29$	−6.47217	+	1.45337i	−1.20185	+	0.269885i	−0.428311	+	0.903631i	$0.640891\pi$
$30$	4.38225	−	1.29936i	0.800085	−	0.237229i
$31$	−4.94811	−	7.40537i	−0.888706	−	1.33004i	−0.943440	−	0.331542i	$-0.892431\pi$
$31$	−4.94811	−	7.40537i	−0.888706	−	1.33004i	0.0547342	−	0.998501i	$-0.482569\pi$
$32$	−5.65407	−	0.177507i	−0.999508	−	0.0313790i
$33$	−7.14617	+	10.6950i	−1.24399	+	1.86176i
$34$	−0.251492	+	0.810705i	−0.0431305	+	0.139035i
$35$	2.70506	+	0.469373i	0.457239	+	0.0793385i
$36$	−6.18649	+	0.226116i	−1.03108	+	0.0376860i
$37$	−0.410392	−	0.815310i	−0.0674681	−	0.134036i	0.856973	−	0.515362i	$-0.172343\pi$
$37$	−0.410392	−	0.815310i	−0.0674681	−	0.134036i	−0.924441	+	0.381326i	$0.875468\pi$
$38$	0.694502	−	8.67277i	0.112663	−	1.40691i
$39$	1.76329	+	11.8872i	0.282353	+	1.90347i
$40$	−0.920205	−	3.58660i	−0.145497	−	0.567092i
$41$	−8.55449	−	5.12737i	−1.33599	−	0.800760i	−0.345507	−	0.938416i	$-0.612293\pi$
$41$	−8.55449	−	5.12737i	−1.33599	−	0.800760i	−0.990480	+	0.137656i	$0.956043\pi$
$42$	−6.67540	−	3.00928i	−1.03004	−	0.464342i
$43$	−1.32611	−	1.39286i	−0.202230	−	0.212409i	0.615303	−	0.788291i	$-0.289034\pi$
$43$	−1.32611	−	1.39286i	−0.202230	−	0.212409i	−0.817533	+	0.575882i	$0.804659\pi$
$44$	8.44322	+	6.10637i	1.27286	+	0.920570i
$45$	−1.27109	−	3.84764i	−0.189482	−	0.573572i
$46$	−1.86699	+	1.36657i	−0.275273	+	0.201490i
$47$	5.16060	+	4.23520i	0.752751	+	0.617767i	0.930493	−	0.366310i	$-0.119379\pi$
$47$	5.16060	+	4.23520i	0.752751	+	0.617767i	−0.177742	+	0.984077i	$0.556879\pi$
$48$	−0.00556638	+	9.87547i	−0.000803438	+	1.42540i
$49$	1.65057	+	2.01122i	0.235795	+	0.287317i
$50$	−4.00110	+	2.36416i	−0.565841	+	0.334343i
$51$	1.42815	+	0.395222i	0.199981	+	0.0553421i
$52$	9.67599	−	1.07029i	1.34182	−	0.148422i
$53$	−4.29546	−	0.964579i	−0.590027	−	0.132495i	−0.0861678	−	0.996281i	$-0.527462\pi$
$53$	−4.29546	−	0.964579i	−0.590027	−	0.132495i	−0.503860	+	0.863786i	$0.668087\pi$
$54$	0.0223975	+	0.332030i	0.00304792	+	0.0451836i
$55$	−2.29777	+	6.42182i	−0.309831	+	0.865919i
$56$	−2.63666	+	5.31353i	−0.352339	+	0.710050i
$57$	−15.1707	−	0.745289i	−2.00941	−	0.0987159i
$58$	9.16575	−	1.99789i	1.20352	−	0.262336i
$59$	−1.31412	+	10.6546i	−0.171084	+	1.38712i	0.624383	+	0.781119i	$0.285351\pi$
$59$	−1.31412	+	10.6546i	−0.171084	+	1.38712i	−0.795467	+	0.605997i	$0.792774\pi$
$60$	−6.20885	+	1.79864i	−0.801559	+	0.232203i
$61$	−4.74179	−	10.6973i	−0.607124	−	1.36965i	−0.909197	−	0.416365i	$-0.863304\pi$
$61$	−4.74179	−	10.6973i	−0.607124	−	1.36965i	0.302073	−	0.953285i	$-0.402321\pi$
$62$	6.93181	+	10.5165i	0.880340	+	1.33559i
$63$	−2.48417	+	5.99732i	−0.312976	+	0.755591i
$64$	7.99433	+	0.301217i	0.999291	+	0.0376521i
$65$	2.43852	+	5.88712i	0.302462	+	0.730207i
$66$	10.2009	−	15.0613i	1.25565	−	1.85392i
$67$	0.339650	−	0.880511i	0.0414949	−	0.107572i	−0.910694	−	0.413082i	$-0.864452\pi$
$67$	0.339650	−	0.880511i	0.0414949	−	0.107572i	0.952189	+	0.305511i	$0.0988272\pi$
$68$	0.362853	−	1.14425i	0.0440024	−	0.138761i
$69$	2.48500	+	3.18424i	0.299159	+	0.383337i
$70$	−3.82130	−	0.687793i	−0.456732	−	0.0822070i
$71$	9.42388	+	10.3976i	1.11841	+	1.23397i	0.969492	+	0.245124i	$0.0788287\pi$
$71$	9.42388	+	10.3976i	1.11841	+	1.23397i	0.148917	+	0.988850i	$0.452421\pi$
$72$	8.75086	−	0.264854i	1.03130	−	0.0312134i
$73$	−1.30912	−	2.76789i	−0.153220	−	0.323957i	0.812749	−	0.582614i	$-0.197970\pi$
$73$	−1.30912	−	2.76789i	−0.153220	−	0.323957i	−0.965969	+	0.258657i	$0.916720\pi$
$74$	0.573134	+	1.15664i	0.0666255	+	0.134457i
$75$	4.34053	+	6.85444i	0.501201	+	0.791482i
$76$	−1.05914	+	12.2587i	−0.121492	+	1.40617i
$77$	9.50684	−	5.38556i	1.08341	−	0.613741i
$78$	−2.38810	−	16.8263i	−0.270400	−	1.90520i
$79$	−0.106193	+	1.07819i	−0.0119476	+	0.121306i	−0.999309	−	0.0371819i	$-0.988162\pi$
$79$	−0.106193	+	1.07819i	−0.0119476	+	0.121306i	0.987361	+	0.158488i	$0.0506619\pi$
$80$	1.26950	+	5.08029i	0.141935	+	0.567994i
$81$	−8.66306	+	0.853237i	−0.962562	+	0.0948041i
$82$	12.0521	+	7.32698i	1.33093	+	0.809130i
$83$	5.18551	−	10.3018i	0.569184	−	1.13077i	−0.406919	−	0.913464i	$-0.633397\pi$
$83$	5.18551	−	10.3018i	0.569184	−	1.13077i	0.976103	−	0.217309i	$-0.0697281\pi$
$84$	9.41355	+	4.31493i	1.02710	+	0.470798i
$85$	0.785506	+	0.0192831i	0.0852001	+	0.00209155i
$86$	1.86300	+	1.98153i	0.200893	+	0.213674i
$87$	−3.97925	−	15.8861i	−0.426621	−	1.70316i
$88$	−11.8861	−	8.71049i	−1.26706	−	0.928542i
$89$	−0.269754	−	0.200063i	−0.0285939	−	0.0212066i	0.581308	−	0.813684i	$-0.302541\pi$
$89$	−0.269754	−	0.200063i	−0.0285939	−	0.0212066i	−0.609902	+	0.792477i	$0.708791\pi$
$90$	1.76340	+	5.45255i	0.185879	+	0.574750i
$91$	3.20208	−	9.69284i	0.335669	−	1.01609i
$92$	2.65240	−	1.91602i	0.276532	−	0.199758i
$93$	17.9776	−	12.6612i	1.86419	−	1.31291i
$94$	−7.26045	−	6.03516i	−0.748859	−	0.622479i
$95$	−7.89926	+	1.57126i	−0.810447	+	0.161208i
$96$	0.0955338	−	13.9657i	0.00975038	−	1.42537i
$97$	−12.4396	−	2.47439i	−1.26305	−	0.251236i	−0.482259	−	0.876029i	$-0.660184\pi$
$97$	−12.4396	−	2.47439i	−1.26305	−	0.251236i	−0.780791	+	0.624792i	$0.785184\pi$
$98$	−2.31635	−	2.85889i	−0.233987	−	0.288792i
$99$	−13.6246	−	8.62765i	−1.36932	−	0.867112i
$100$	5.67929	−	3.30784i	0.567929	−	0.330784i
$101$	4.25295	+	3.66862i	0.423184	+	0.365041i	0.838745	−	0.544524i	$-0.183290\pi$
$101$	4.25295	+	3.66862i	0.423184	+	0.365041i	−0.415561	+	0.909565i	$0.636415\pi$
$102$	−2.01616	−	0.571594i	−0.199629	−	0.0565963i
$103$	13.0213	+	3.26167i	1.28303	+	0.321382i	0.823772	−	0.566921i	$-0.191866\pi$
$103$	13.0213	+	3.26167i	1.28303	+	0.321382i	0.459257	+	0.888303i	$0.348116\pi$
$104$	−13.6931	+	1.42769i	−1.34272	+	0.139997i
$105$	−0.994574	+	6.70487i	−0.0970605	+	0.654329i
$106$	6.06602	+	1.40222i	0.589184	+	0.136196i
$107$	−2.71516	−	7.03879i	−0.262485	−	0.680466i	−0.999987	−	0.00512109i	$-0.998370\pi$
$107$	−2.71516	−	7.03879i	−0.262485	−	0.680466i	0.737502	−	0.675345i	$-0.236005\pi$
$108$	−0.0287269	−	0.469751i	−0.00276425	−	0.0452019i
$109$	−6.61467	−	7.66824i	−0.633570	−	0.734484i	0.345407	−	0.938453i	$-0.387741\pi$
$109$	−6.61467	−	7.66824i	−0.633570	−	0.734484i	−0.978977	+	0.203969i	$0.934616\pi$
$110$	3.30647	−	9.06126i	0.315260	−	0.863957i
$111$	1.98742	−	1.06230i	0.188638	−	0.100829i
$112$	3.77590	−	7.49091i	0.356789	−	0.707824i
$113$	−1.46681	+	2.74421i	−0.137986	+	0.258153i	−0.941417	−	0.337244i	$-0.890505\pi$
$113$	−1.46681	+	2.74421i	−0.137986	+	0.258153i	0.803432	+	0.595397i	$0.203005\pi$
$114$	21.4476	+	1.18864i	2.00875	+	0.111327i
$115$	1.68845	+	1.31768i	0.157449	+	0.122875i
$116$	−12.9798	+	2.74402i	−1.20514	+	0.254776i
$117$	−14.8446	+	2.57579i	−1.37239	+	0.238132i
$118$	1.95299	−	15.0560i	0.179788	−	1.38601i
$119$	−0.932666	−	0.845319i	−0.0854973	−	0.0774902i
$120$	8.79643	−	2.48849i	0.803000	−	0.227167i
$121$	5.43872	+	15.2002i	0.494429	+	1.38184i
$122$	6.61082	+	15.1701i	0.598515	+	1.37343i
$123$	12.1367	−	21.4242i	1.09433	−	1.93176i
$124$	−9.70951	−	14.9338i	−0.871940	−	1.34109i
$125$	7.85639	+	7.47991i	0.702697	+	0.669023i
$126$	3.56632	−	8.45927i	0.317713	−	0.753612i
$127$	−8.34676	−	8.34676i	−0.740655	−	0.740655i	0.232049	−	0.972704i	$-0.425457\pi$
$127$	−8.34676	−	8.34676i	−0.740655	−	0.740655i	−0.972704	+	0.232049i	$0.925457\pi$
$128$	−11.3028	−	0.496940i	−0.999035	−	0.0439237i
$129$	3.35739	−	3.35739i	0.295602	−	0.295602i
$130$	−3.39627	−	8.34713i	−0.297872	−	0.732091i
$131$	−7.74121	+	8.13085i	−0.676353	+	0.710396i	−0.969341	−	0.245720i	$-0.920975\pi$
$131$	−7.74121	+	8.13085i	−0.676353	+	0.710396i	0.292988	+	0.956116i	$0.405350\pi$
$132$	−14.5597	+	21.2089i	−1.26726	+	1.84600i
$133$	11.2262	+	6.35954i	0.973431	+	0.551442i
$134$	−0.488145	+	1.24219i	−0.0421693	+	0.107309i
$135$	0.290049	−	0.103781i	0.0249634	−	0.00893205i
$136$	−0.523299	+	1.61497i	−0.0448725	+	0.138482i
$137$	10.8311	−	11.9503i	0.925363	−	1.02098i	−0.0743550	−	0.997232i	$-0.523690\pi$
$137$	10.8311	−	11.9503i	0.925363	−	1.02098i	0.999718	−	0.0237488i	$-0.00756020\pi$
$138$	−3.48599	−	4.52516i	−0.296747	−	0.385208i
$139$	2.22169	+	12.8039i	0.188441	+	1.08601i	0.916362	+	0.400351i	$0.131112\pi$
$139$	2.22169	+	12.8039i	0.188441	+	1.08601i	−0.727921	+	0.685661i	$0.759513\pi$
$140$	5.39792	+	1.00659i	0.456207	+	0.0850721i
$141$	−10.1403	+	12.9936i	−0.853969	+	1.09426i
$142$	−13.2348	−	14.7879i	−1.11064	−	1.24097i
$143$	22.3652	+	11.9544i	1.87027	+	0.999680i
$144$	−12.3777	+	0.296874i	−1.03147	+	0.0247395i
$145$	−4.09356	−	7.65850i	−0.339951	−	0.636004i
$146$	1.82676	+	3.92593i	0.151184	+	0.324913i
$147$	−4.86394	+	4.19566i	−0.401171	+	0.346052i
$148$	−0.800250	−	1.64079i	−0.0657802	−	0.134872i
$149$	2.77255	−	1.06949i	0.227136	−	0.0876160i	−0.243651	−	0.969863i	$-0.578345\pi$
$149$	2.77255	−	1.06949i	0.227136	−	0.0876160i	0.470787	+	0.882247i	$0.343970\pi$
$150$	−6.07746	−	9.73198i	−0.496223	−	0.794613i
$151$	4.13192	+	0.612913i	0.336251	+	0.0498781i	0.312721	−	0.949845i	$-0.398759\pi$
$151$	4.13192	+	0.612913i	0.336251	+	0.0498781i	0.0235300	+	0.999723i	$0.492509\pi$
$152$	1.60664	−	17.3267i	0.130316	−	1.40538i
$153$	−0.451413	+	1.80214i	−0.0364946	+	0.145695i
$154$	−13.4922	+	7.53179i	−1.08724	+	0.606929i
$155$	7.61570	−	8.82871i	0.611708	−	0.709139i
$156$	3.22786	+	23.8167i	0.258436	+	1.90686i
$157$	8.59661	−	13.5755i	0.686084	−	1.08344i	−0.305275	−	0.952264i	$-0.598748\pi$
$157$	8.59661	−	13.5755i	0.686084	−	1.08344i	0.991358	−	0.131181i	$-0.0418767\pi$
$158$	0.159747	−	1.52382i	0.0127088	−	0.121229i
$159$	2.12044	−	10.6602i	0.168162	−	0.845408i
$160$	−1.75022	−	7.19574i	−0.138367	−	0.568873i
$161$	−0.669366	−	3.36513i	−0.0527534	−	0.265209i
$162$	12.2588	−	1.12974i	0.963138	−	0.0887604i
$163$	−4.30690	−	6.11533i	−0.337343	−	0.478990i	0.613049	−	0.790045i	$-0.289943\pi$
$163$	−4.30690	−	6.11533i	−0.337343	−	0.478990i	−0.950392	+	0.311055i	$0.899318\pi$
$164$	−16.9789	−	10.4687i	−1.32583	−	0.817468i
$165$	−15.9891	−	5.28208i	−1.24475	−	0.411209i
$166$	−7.42472	+	14.5227i	−0.576270	+	1.12718i
$167$	9.80814	−	13.2248i	0.758977	−	1.02336i	−0.239644	−	0.970861i	$-0.577031\pi$
$167$	9.80814	−	13.2248i	0.758977	−	1.02336i	0.998621	−	0.0525011i	$-0.0167193\pi$
$168$	−13.2742	−	6.18568i	−1.02413	−	0.477235i
$169$	10.3721	−	2.59808i	0.797855	−	0.199852i
$170$	−1.11068	−	0.0342426i	−0.0851853	−	0.00262629i
$171$	0.467339	−	19.0373i	0.0357383	−	1.45582i
$172$	−2.61704	−	2.81879i	−0.199547	−	0.214930i
$173$	5.02381	+	2.52877i	0.381953	+	0.192259i	0.630191	−	0.776440i	$-0.282976\pi$
$173$	5.02381	+	2.52877i	0.381953	+	0.192259i	−0.248238	+	0.968699i	$0.579851\pi$
$174$	5.48638	+	22.5012i	0.415922	+	1.70581i
$175$	−0.675510	−	6.85857i	−0.0510638	−	0.518459i
$176$	16.7318	+	12.4238i	1.26121	+	0.936477i
$177$	−26.3766	−	2.59787i	−1.98259	−	0.195268i
$178$	0.379706	+	0.285321i	0.0284602	+	0.0213857i
$179$	−8.89862	−	15.7083i	−0.665114	−	1.17409i	−0.974763	−	0.223240i	$-0.928337\pi$
$179$	−8.89862	−	15.7083i	−0.665114	−	1.17409i	0.309649	−	0.950851i	$-0.399788\pi$
$180$	−2.44537	−	7.72658i	−0.182267	−	0.575905i
$181$	−5.21859	+	3.30464i	−0.387895	+	0.245632i	−0.714657	−	0.699475i	$-0.753417\pi$
$181$	−5.21859	+	3.30464i	−0.387895	+	0.245632i	0.326762	+	0.945107i	$0.394042\pi$
$182$	−4.61438	+	13.6791i	−0.342041	+	1.01396i
$183$	26.1150	−	12.3515i	1.93048	−	0.913047i
$184$	−3.76800	+	2.68606i	−0.277780	+	0.198019i
$185$	0.885387	−	0.802468i	0.0650950	−	0.0589986i
$186$	−25.5360	+	17.7458i	−1.87239	+	1.30118i
$187$	2.46520	−	1.92386i	0.180273	−	0.140687i
$188$	10.2141	+	8.59929i	0.744937	+	0.627168i
$189$	−0.460431	−	0.177608i	−0.0334914	−	0.0129191i
$190$	11.1850	−	2.15193i	0.811443	−	0.156118i
$191$	11.6931	−	4.84342i	0.846080	−	0.350458i	0.0828321	−	0.996564i	$-0.473603\pi$
$191$	11.6931	−	4.84342i	0.846080	−	0.350458i	0.763248	+	0.646106i	$0.223603\pi$
$192$	−0.259072	+	19.7493i	−0.0186969	+	1.42528i
$193$	25.3418	+	10.4969i	1.82414	+	0.755584i	0.973061	+	0.230547i	$0.0740517\pi$
$193$	25.3418	+	10.4969i	1.82414	+	0.755584i	0.851080	+	0.525037i	$0.175948\pi$
$194$	17.5699	+	3.60967i	1.26145	+	0.259159i
$195$	−14.3824	+	6.37528i	−1.02995	+	0.456543i
$196$	3.25038	+	4.06357i	0.232170	+	0.290255i
$197$	7.09267	+	0.874797i	0.505332	+	0.0623267i	0.371043	−	0.928616i	$-0.379000\pi$
$197$	7.09267	+	0.874797i	0.505332	+	0.0623267i	0.134288	+	0.990942i	$0.457125\pi$
$198$	19.1911	+	12.3220i	1.36385	+	0.875690i
$199$	−0.492300	+	10.0210i	−0.0348982	+	0.710369i	0.916058	+	0.401045i	$0.131353\pi$
$199$	−0.492300	+	10.0210i	−0.0348982	+	0.710369i	−0.950957	+	0.309324i	$0.899897\pi$
$200$	−8.06093	+	4.62749i	−0.569994	+	0.327213i
$201$	2.19379	+	0.784950i	0.154738	+	0.0553661i
$202$	−5.98189	−	5.22586i	−0.420884	−	0.367690i
$203$	−3.04800	+	13.5734i	−0.213928	+	0.952663i
$204$	2.84615	+	0.826237i	0.199270	+	0.0578482i
$205$	3.48233	−	12.5835i	0.243216	−	0.878871i
$206$	−18.3856	−	4.72820i	−1.28099	−	0.329429i
$207$	−3.91454	+	3.21258i	−0.272079	+	0.223290i
$208$	19.3773	−	1.89747i	1.34358	−	0.131566i
$209$	−20.3341	+	24.7772i	−1.40654	+	1.71388i
$210$	1.46603	−	9.47311i	0.101166	−	0.653707i
$211$	10.3514	−	3.41966i	0.712623	−	0.235419i	0.0655527	−	0.997849i	$-0.479119\pi$
$211$	10.3514	−	3.41966i	0.712623	−	0.235419i	0.647070	+	0.762430i	$0.275994\pi$
$212$	−8.56604	−	2.03685i	−0.588318	−	0.139891i
$213$	−25.0917	+	23.8893i	−1.71926	+	1.63687i
$214$	3.77726	+	9.97826i	0.258208	+	0.682100i
$215$	1.29435	−	2.15949i	0.0882738	−	0.147276i
$216$	0.0364554	+	0.664571i	0.00248047	+	0.0452183i
$217$	−18.4761	+	2.74068i	−1.25424	+	0.186049i
$218$	9.28630	+	10.9030i	0.628947	+	0.738446i
$219$	6.75219	−	3.39876i	0.456270	−	0.229667i
$220$	−4.75640	+	12.7849i	−0.320676	+	0.861961i
$221$	0.499464	−	2.87848i	0.0335976	−	0.193628i
$222$	−2.82001	+	1.48465i	−0.189267	+	0.0996429i
$223$	−1.05389	−	0.704184i	−0.0705734	−	0.0471557i	0.519783	−	0.854298i	$-0.326013\pi$
$223$	−1.05389	−	0.704184i	−0.0705734	−	0.0471557i	−0.590356	+	0.807143i	$0.701013\pi$
$224$	−5.40632	+	10.5600i	−0.361225	+	0.705571i
$225$	−8.45753	+	5.65114i	−0.563835	+	0.376743i
$226$	2.09870	−	3.86780i	0.139603	−	0.257282i
$227$	3.55976	+	15.8523i	0.236270	+	1.05216i	0.939862	+	0.341553i	$0.110953\pi$
$227$	3.55976	+	15.8523i	0.236270	+	1.05216i	−0.703593	+	0.710604i	$0.748422\pi$
$228$	−30.3203	−	1.87135i	−2.00801	−	0.123933i
$229$	8.86258	−	0.653743i	0.585656	−	0.0432006i	0.222506	−	0.974931i	$-0.428576\pi$
$229$	8.86258	−	0.653743i	0.585656	−	0.0432006i	0.363150	+	0.931731i	$0.381701\pi$
$230$	−2.37609	−	1.87844i	−0.156675	−	0.123860i
$231$	13.8682	+	23.1378i	0.912464	+	1.52235i
$232$	18.3802	−	3.76534i	1.20672	−	0.247207i
$233$	−15.5064	−	20.9079i	−1.01586	−	1.36972i	−0.927579	−	0.373627i	$-0.878114\pi$
$233$	−15.5064	−	20.9079i	−1.01586	−	1.36972i	−0.0882772	−	0.996096i	$-0.528136\pi$
$234$	21.0159	−	3.51087i	1.37385	−	0.229513i
$235$	−3.54169	+	7.98992i	−0.231034	+	0.521205i
$236$	−2.89554	+	21.2746i	−0.188484	+	1.38486i
$237$	−2.66754	−	0.196770i	−0.173276	−	0.0127816i
$238$	1.31146	+	1.20372i	0.0850092	+	0.0780254i
$239$	−19.6369	−	5.95678i	−1.27020	−	0.385312i	−0.417964	−	0.908463i	$-0.637256\pi$
$239$	−19.6369	−	5.95678i	−1.27020	−	0.385312i	−0.852240	+	0.523151i	$0.824756\pi$
$240$	−12.4619	+	3.44110i	−0.804410	+	0.222122i
$241$	−2.59517	−	8.55512i	−0.167169	−	0.551084i	0.832828	−	0.553533i	$-0.186721\pi$
$241$	−2.59517	−	8.55512i	−0.167169	−	0.551084i	−0.999997	+	0.00244865i	$0.999221\pi$
$242$	−7.55644	−	21.5442i	−0.485746	−	1.38491i
$243$	−2.71720	−	22.0305i	−0.174308	−	1.41325i
$244$	−9.21426	−	21.5120i	−0.589883	−	1.37716i
$245$	−1.96125	+	2.78477i	−0.125300	+	0.177912i
$246$	−17.3537	+	30.1901i	−1.10643	+	1.92485i
$247$	1.46937	+	29.9098i	0.0934941	+	1.90312i
$248$	13.5985	+	21.2053i	0.863505	+	1.34654i
$249$	25.7404	+	12.1743i	1.63123	+	0.771515i
$250$	−11.0440	−	10.6477i	−0.698484	−	0.673421i
$251$	−21.3002	+	5.89455i	−1.34445	+	0.372061i	−0.863351	−	0.504604i	$-0.831639\pi$
$251$	−21.3002	+	5.89455i	−1.34445	+	0.372061i	−0.481103	+	0.876664i	$0.659764\pi$
$252$	−5.11852	+	11.9313i	−0.322437	+	0.751603i
$253$	8.52111	−	0.209181i	0.535717	−	0.0131511i
$254$	11.7298	+	11.8780i	0.735991	+	0.745289i
$255$			1.93990i			0.121481i
$256$	15.9798	+	0.803098i	0.998740	+	0.0501936i
$257$		−	11.1736i		−	0.696990i	−0.937311	−	0.348495i	$-0.886693\pi$
$257$		−	11.1736i		−	0.696990i	0.937311	−	0.348495i	$-0.113307\pi$
$258$	−4.77778	+	4.71818i	−0.297452	+	0.293741i
$259$	−1.91368	+	0.0469781i	−0.118910	+	0.00291908i
$260$	4.72886	+	11.8345i	0.293271	+	0.733947i
$261$	19.7885	−	5.47622i	1.22488	−	0.338970i
$262$	11.0197	−	11.4298i	0.680799	−	0.706136i
$263$	−19.1959	−	9.07900i	−1.18367	−	0.559835i	−0.268649	−	0.963238i	$-0.586577\pi$
$263$	−19.1959	−	9.07900i	−1.18367	−	0.559835i	−0.915022	+	0.403403i	$0.867827\pi$
$264$	20.7784	−	29.8641i	1.27882	−	1.83801i
$265$	−0.282794	−	5.75640i	−0.0173719	−	0.353613i
$266$	−15.8194	−	9.09322i	−0.969951	−	0.557541i
$267$	0.477437	−	0.677908i	0.0292186	−	0.0414873i
$268$	0.701354	−	1.75236i	0.0428420	−	0.107042i
$269$	−2.04624	−	16.5905i	−0.124761	−	1.01154i	−0.916320	−	0.400446i	$-0.868855\pi$
$269$	−2.04624	−	16.5905i	−0.124761	−	1.01154i	0.791559	−	0.611093i	$-0.209270\pi$
$270$	−0.411104	+	0.144191i	−0.0250190	+	0.00877519i
$271$	6.73660	+	22.2076i	0.409219	+	1.34902i	0.883413	+	0.468595i	$0.155240\pi$
$271$	6.73660	+	22.2076i	0.409219	+	1.34902i	−0.474194	+	0.880421i	$0.657260\pi$
$272$	0.754377	−	2.27922i	0.0457408	−	0.138198i
$273$	24.1172	+	7.31586i	1.45964	+	0.442776i
$274$	−15.4233	+	16.8038i	−0.931753	+	1.01515i
$275$	17.0746	+	1.25950i	1.02964	+	0.0759506i
$276$	4.88967	+	6.43037i	0.294324	+	0.387063i
$277$	0.807766	−	1.82229i	0.0485340	−	0.109491i	−0.888302	−	0.459259i	$-0.848115\pi$
$277$	0.807766	−	1.82229i	0.0485340	−	0.109491i	0.936836	+	0.349769i	$0.113740\pi$
$278$	−3.02822	−	18.1268i	−0.181621	−	1.08717i
$279$	16.4222	+	22.1428i	0.983172	+	1.32565i
$280$	−7.62472	−	1.47142i	−0.455664	−	0.0879340i
$281$	−1.07441	−	1.79255i	−0.0640942	−	0.106935i	0.824013	−	0.566570i	$-0.191730\pi$
$281$	−1.07441	−	1.79255i	−0.0640942	−	0.106935i	−0.888108	+	0.459636i	$0.847980\pi$
$282$	14.4556	−	18.2854i	0.860820	−	1.08888i
$283$	0.254632	−	0.0187828i	0.0151363	−	0.00111652i	−0.0659943	−	0.997820i	$-0.521022\pi$
$283$	0.254632	−	0.0187828i	0.0151363	−	0.00111652i	0.0811306	+	0.996703i	$0.474147\pi$
$284$	18.5852	+	21.0303i	1.10283	+	1.24792i
$285$	−4.35668	−	19.4012i	−0.258067	−	1.14923i
$286$	−31.5224	−	17.1043i	−1.86396	−	1.01140i
$287$	−17.3911	+	11.6204i	−1.02657	+	0.685930i
$288$	17.5070	−	0.309962i	1.03161	−	0.0182647i
$289$	13.8355	+	9.24455i	0.813850	+	0.543797i
$290$	5.72106	+	10.8669i	0.335952	+	0.638125i
$291$	5.35340	−	30.8524i	0.313822	−	1.80860i
$292$	−2.54853	−	5.56822i	−0.149142	−	0.325855i
$293$	−0.305432	+	0.153742i	−0.0178435	+	0.00898168i	−0.458511	−	0.888689i	$-0.651617\pi$
$293$	−0.305432	+	0.153742i	−0.0178435	+	0.00898168i	0.440667	+	0.897671i	$0.354742\pi$
$294$	6.91576	−	5.89027i	0.403335	−	0.343528i
$295$	−13.9018	+	2.06214i	−0.809397	+	0.120063i
$296$	1.11714	+	2.32749i	0.0649323	+	0.135283i
$297$	0.630282	−	1.05156i	0.0365727	−	0.0610178i
$298$	−3.93039	+	1.48785i	−0.227681	+	0.0861886i
$299$	5.76744	−	5.49106i	0.333540	−	0.317556i
$300$	8.50828	+	13.8168i	0.491226	+	0.797712i
$301$	−3.82970	+	1.26516i	−0.220740	+	0.0729227i
$302$	−5.83786	−	0.903450i	−0.335931	−	0.0519877i
$303$	−8.79693	+	10.7191i	−0.505370	+	0.615795i
$304$	−2.42589	+	24.4890i	−0.139134	+	1.40454i
$305$	11.8412	−	9.71782i	0.678025	−	0.556441i
$306$	0.654380	−	2.54456i	0.0374084	−	0.145463i
$307$	3.54130	−	12.7966i	0.202113	−	0.730341i	−0.790860	−	0.611997i	$-0.790366\pi$
$307$	3.54130	−	12.7966i	0.202113	−	0.730341i	0.992973	−	0.118344i	$-0.0377585\pi$
$308$	19.1474	−	10.5316i	1.09102	−	0.600093i
$309$	−7.26127	+	32.3359i	−0.413079	+	1.83952i
$310$	−10.8484	+	12.4178i	−0.616147	+	0.705286i
$311$	−15.4897	−	5.54232i	−0.878342	−	0.314276i	−0.141174	−	0.989985i	$-0.545088\pi$
$311$	−15.4897	−	5.54232i	−0.878342	−	0.314276i	−0.737169	+	0.675709i	$0.763838\pi$
$312$	−4.35338	−	33.7099i	−0.246462	−	1.90845i
$313$	−0.906777	+	18.4579i	−0.0512541	+	1.04330i	0.826120	+	0.563494i	$0.190543\pi$
$313$	−0.906777	+	18.4579i	−0.0512541	+	1.04330i	−0.877374	+	0.479807i	$0.840707\pi$
$314$	−12.2777	+	19.1220i	−0.692871	+	1.07912i
$315$	−8.43422	−	1.04026i	−0.475214	−	0.0586121i
$316$	−0.239438	+	2.15355i	−0.0134694	+	0.121146i
$317$	−5.34689	+	2.37011i	−0.300311	+	0.133119i	−0.549894	−	0.835235i	$-0.685332\pi$
$317$	−5.34689	+	2.37011i	−0.300311	+	0.133119i	0.249582	+	0.968354i	$0.419707\pi$
$318$	−3.09333	+	15.0567i	−0.173465	+	0.844336i
$319$	−31.9289	−	13.2254i	−1.78768	−	0.740480i
$320$	2.41126	+	10.1917i	0.134793	+	0.569731i
$321$	17.2081	−	7.12783i	0.960463	−	0.397837i
$322$	0.916736	+	4.76486i	0.0510877	+	0.265535i
$323$	3.44515	+	1.32894i	0.191693	+	0.0739443i
$324$	−17.3462	+	1.48884i	−0.963677	+	0.0827133i
$325$	12.6100	−	9.84095i	0.699478	−	0.545878i
$326$	6.03648	+	8.68644i	0.334329	+	0.481098i
$327$	18.5254	−	16.7904i	1.02446	−	0.928513i
$328$	23.9184	+	14.9554i	1.32067	+	0.825774i
$329$	12.6566	−	5.98610i	0.697778	−	0.330025i
$330$	22.5646	+	7.61177i	1.24214	+	0.419014i
$331$	−13.4013	+	8.48631i	−0.736605	+	0.466450i	−0.849788	−	0.527124i	$-0.823270\pi$
$331$	−13.4013	+	8.48631i	−0.736605	+	0.466450i	0.113184	+	0.993574i	$0.463895\pi$
$332$	10.6288	−	20.4719i	0.583334	−	1.12354i
$333$	1.39259	+	2.45827i	0.0763136	+	0.134712i
$334$	−13.9879	+	18.6152i	−0.765385	+	1.01858i
$335$	1.22954	+	0.121099i	0.0671768	+	0.00661633i
$336$	18.7173	+	8.86553i	1.02111	+	0.483654i
$337$	−2.57167	−	26.1106i	−0.140088	−	1.42233i	−0.766200	−	0.642602i	$-0.777855\pi$
$337$	−2.57167	−	26.1106i	−0.140088	−	1.42233i	0.626113	−	0.779733i	$-0.284645\pi$
$338$	−14.6912	+	3.58210i	−0.799094	+	0.194840i
$339$	−6.86191	−	3.45400i	−0.372688	−	0.187595i
$340$	1.57040	+	0.0582846i	0.0851672	+	0.00316093i
$341$	1.13876	−	46.3880i	0.0616674	−	2.51205i
$342$	−0.829893	+	26.9181i	−0.0448755	+	1.45556i
$343$	19.5333	−	4.89284i	1.05470	−	0.264189i
$344$	3.67596	+	4.00952i	0.198194	+	0.216179i
$345$	−3.14990	+	4.24715i	−0.169585	+	0.228659i
$346$	−7.08216	−	3.62075i	−0.380739	−	0.194653i
$347$	−15.4125	−	5.09161i	−0.827387	−	0.273332i	−0.131349	−	0.991336i	$-0.541931\pi$
$347$	−15.4125	−	5.09161i	−0.827387	−	0.273332i	−0.696038	+	0.718005i	$0.745056\pi$
$348$	−7.55903	−	31.8695i	−0.405207	−	1.70839i
$349$	16.3566	+	23.2246i	0.875548	+	1.24318i	0.968876	+	0.247547i	$0.0796245\pi$
$349$	16.3566	+	23.2246i	0.875548	+	1.24318i	−0.0933281	+	0.995635i	$0.529751\pi$
$350$	0.894415	+	9.70529i	0.0478085	+	0.518769i
$351$	−0.223455	−	1.12339i	−0.0119272	−	0.0599619i
$352$	−23.5516	−	17.7180i	−1.25530	−	0.944374i
$353$	3.94891	−	19.8525i	0.210179	−	1.05664i	−0.721237	−	0.692688i	$-0.756426\pi$
$353$	3.94891	−	19.8525i	0.210179	−	1.05664i	0.931417	−	0.363955i	$-0.118574\pi$
$354$	37.2783	+	3.90801i	1.98132	+	0.207708i
$355$	−9.82831	+	15.5206i	−0.521633	+	0.823748i
$356$	−0.534442	−	0.406867i	−0.0283254	−	0.0215639i
$357$	2.02984	−	2.35315i	0.107431	−	0.124542i
$358$	12.4449	+	22.2934i	0.657732	+	1.17824i
$359$	3.66428	−	14.6286i	0.193393	−	0.772070i	−0.793212	−	0.608945i	$-0.791593\pi$
$359$	3.66428	−	14.6286i	0.193393	−	0.772070i	0.986606	−	0.163124i	$-0.0521572\pi$
$360$	3.38962	+	10.9485i	0.178649	+	0.577038i
$361$	−18.6456	−	2.76582i	−0.981350	−	0.145570i
$362$	7.40939	−	4.62705i	0.389429	−	0.243192i
$363$	−37.1865	+	14.3444i	−1.95179	+	0.752887i
$364$	6.64702	−	19.3038i	0.348398	−	1.01179i
$365$	3.03517	−	2.61816i	0.158868	−	0.137041i
$366$	−37.0411	+	17.2355i	−1.93617	+	0.900912i
$367$	0.810984	+	1.51725i	0.0423330	+	0.0791996i	0.902198	−	0.431322i	$-0.141953\pi$
$367$	0.810984	+	1.51725i	0.0423330	+	0.0791996i	−0.859865	+	0.510521i	$0.829453\pi$
$368$	5.35249	−	3.76514i	0.279018	−	0.196271i
$369$	27.2257	+	14.5524i	1.41731	+	0.757569i
$370$	−1.25923	+	1.12698i	−0.0654640	+	0.0585889i
$371$	−5.68027	+	7.27859i	−0.294905	+	0.377886i
$372$	36.2702	−	24.8691i	1.88052	−	1.28940i
$373$	−0.249655	−	1.43880i	−0.0129266	−	0.0744980i	0.978110	−	0.208089i	$-0.0667243\pi$
$373$	−0.249655	−	1.43880i	−0.0129266	−	0.0744980i	−0.991037	+	0.133591i	$0.957349\pi$
$374$	−3.50333	+	2.69882i	−0.181153	+	0.139552i
$375$	−17.9853	+	19.8438i	−0.928759	+	1.02473i
$376$	−14.3682	−	12.2517i	−0.740985	−	0.631831i
$377$	−30.4004	+	10.8774i	−1.56570	+	0.560216i
$378$	0.649558	+	0.255257i	0.0334097	+	0.0131290i
$379$	−7.88207	−	4.46514i	−0.404875	−	0.229359i	0.276934	−	0.960889i	$-0.410682\pi$
$379$	−7.88207	−	4.46514i	−0.404875	−	0.229359i	−0.681809	+	0.731530i	$0.738807\pi$
$380$	−15.8367	+	2.94395i	−0.812407	+	0.151021i
$381$	20.0951	−	21.1066i	1.02950	−	1.08132i
$382$	−16.5792	+	6.74570i	−0.848263	+	0.345140i
$383$	−25.3010	+	25.3010i	−1.29282	+	1.29282i	−0.359790	+	0.933033i	$0.617152\pi$
$383$	−25.3010	+	25.3010i	−1.29282	+	1.29282i	−0.933033	+	0.359790i	$0.882848\pi$
$384$	0.541685	−	27.9268i	0.0276428	−	1.42513i
$385$	10.1144	+	10.1144i	0.515478	+	0.515478i
$386$	−35.7448	−	15.0695i	−1.81936	−	0.767019i
$387$	4.31132	+	4.10472i	0.219157	+	0.208655i
$388$	−24.8151	−	5.26071i	−1.25980	−	0.267072i
$389$	−7.77955	+	13.7328i	−0.394439	+	0.696282i	−0.994621	−	0.103581i	$-0.966970\pi$
$389$	−7.77955	+	13.7328i	−0.394439	+	0.696282i	0.600182	+	0.799864i	$0.295095\pi$
$390$	20.3960	−	8.88816i	1.03279	−	0.450069i
$391$	−0.330809	−	0.924550i	−0.0167297	−	0.0467565i
$392$	−4.56057	−	5.77549i	−0.230343	−	0.291706i
$393$	−20.5370	−	18.6136i	−1.03595	−	0.938934i
$394$	−10.0226	−	1.30009i	−0.504930	−	0.0654974i
$395$	−1.39744	+	0.242478i	−0.0703127	+	0.0122004i
$396$	−27.0303	−	17.5960i	−1.35833	−	0.884233i
$397$	−26.2156	−	20.4588i	−1.31572	−	1.02680i	−0.996875	−	0.0789921i	$-0.974830\pi$
$397$	−26.2156	−	20.4588i	−1.31572	−	1.02680i	−0.318846	−	0.947807i	$-0.603295\pi$
$398$	0.785157	−	14.1672i	0.0393564	−	0.710136i
$399$	−15.0160	+	28.0929i	−0.751738	+	1.40640i
$400$	11.4407	−	6.47258i	0.572037	−	0.323629i
$401$	25.4330	−	13.5942i	1.27007	−	0.678864i	0.307923	−	0.951411i	$-0.400366\pi$
$401$	25.4330	−	13.5942i	1.27007	−	0.678864i	0.962142	+	0.272547i	$0.0878660\pi$
$402$	−3.09546	−	1.12954i	−0.154387	−	0.0563363i
$403$	−28.3162	−	32.8263i	−1.41053	−	1.63519i
$404$	8.41312	+	7.44344i	0.418568	+	0.370325i
$405$	−4.10133	−	10.6323i	−0.203797	−	0.528323i
$406$	4.43092	−	19.1682i	0.219903	−	0.951301i
$407$	0.697780	−	4.70405i	0.0345877	−	0.233171i
$408$	−4.01765	−	1.19372i	−0.198903	−	0.0590978i
$409$	−0.941014	−	0.235712i	−0.0465301	−	0.0116552i	0.219645	−	0.975580i	$-0.429510\pi$
$409$	−0.941014	−	0.235712i	−0.0465301	−	0.0116552i	−0.266175	+	0.963925i	$0.585760\pi$
$410$	−5.03636	+	17.7645i	−0.248728	+	0.877327i
$411$	30.1510	+	26.0084i	1.48724	+	1.28290i
$412$	25.9587	+	6.84975i	1.27889	+	0.337463i
$413$	19.0211	+	12.0450i	0.935968	+	0.592695i
$414$	5.56440	−	4.50843i	0.273475	−	0.221577i
$415$	14.8085	+	2.94558i	0.726918	+	0.144593i
$416$	−27.4200	+	2.51137i	−1.34437	+	0.123130i
$417$	−31.4670	+	6.25918i	−1.54095	+	0.306513i
$418$	28.9762	−	34.8591i	1.41727	−	1.70501i
$419$	30.1340	−	21.2228i	1.47214	−	1.03680i	0.485439	−	0.874270i	$-0.338660\pi$
$419$	30.1340	−	21.2228i	1.47214	−	1.03680i	0.986704	−	0.162530i	$-0.0519654\pi$
$420$	−2.15733	+	13.3837i	−0.105267	+	0.653059i
$421$	3.91856	−	11.8616i	0.190979	−	0.578101i	−0.808974	−	0.587845i	$-0.799977\pi$
$421$	3.91856	−	11.8616i	0.190979	−	0.578101i	0.999953	+	0.00974371i	$0.00310157\pi$
$422$	−14.6692	+	4.74414i	−0.714087	+	0.230941i
$423$	−16.5977	−	12.3097i	−0.807006	−	0.598517i
$424$	12.0959	+	2.95652i	0.587428	+	0.143581i
$425$	−0.479250	−	1.91327i	−0.0232471	−	0.0928074i
$426$	35.6964	−	33.5612i	1.72950	−	1.62604i
$427$	−24.5321	−	0.602230i	−1.18719	−	0.0291439i
$428$	−5.25317	−	14.1446i	−0.253922	−	0.683707i
$429$	−28.1499	+	55.9243i	−1.35909	+	2.70005i
$430$	−1.84962	+	3.04243i	−0.0891964	+	0.146719i
$431$	24.5505	−	2.41801i	1.18256	−	0.116472i	0.512437	−	0.858725i	$-0.328743\pi$
$431$	24.5505	−	2.41801i	1.18256	−	0.116472i	0.670120	+	0.742253i	$0.266243\pi$
$432$	−0.0456554	−	0.940150i	−0.00219660	−	0.0452330i
$433$	−3.32081	+	33.7168i	−0.159588	+	1.62032i	0.498160	+	0.867085i	$0.334009\pi$
$433$	−3.32081	+	33.7168i	−0.159588	+	1.62032i	−0.657748	+	0.753238i	$0.728491\pi$
$434$	26.1530	−	3.71182i	1.25539	−	0.178173i
$435$	18.6541	−	10.5674i	0.894397	−	0.506669i
$436$	−13.0358	−	15.5013i	−0.624300	−	0.742379i
$437$	5.38485	+	8.50361i	0.257592	+	0.406783i
$438$	−9.57901	+	4.74655i	−0.457703	+	0.226799i
$439$	−7.57164	−	16.0089i	−0.361374	−	0.764062i	0.638611	−	0.769530i	$-0.279509\pi$
$439$	−7.57164	−	16.0089i	−0.361374	−	0.764062i	−0.999985	+	0.00546794i	$0.998259\pi$
$440$	6.83992	−	18.0381i	0.326080	−	0.859931i
$441$	−5.40833	−	5.96717i	−0.257540	−	0.284151i
$442$	−0.731887	+	4.06628i	−0.0348123	+	0.193413i
$443$	1.19075	+	1.52580i	0.0565740	+	0.0724929i	0.815800	−	0.578335i	$-0.196297\pi$
$443$	1.19075	+	1.52580i	0.0565740	+	0.0724929i	−0.759226	+	0.650827i	$0.774422\pi$
$444$	4.00120	−	2.07453i	0.189889	−	0.0984530i
$445$	0.158233	−	0.410204i	0.00750097	−	0.0194455i
$446$	1.48414	+	1.00520i	0.0702761	+	0.0475977i
$447$	2.80762	+	6.77819i	0.132796	+	0.320598i
$448$	7.73928	−	14.8858i	0.365647	−	0.703290i
$449$	3.06711	−	7.40465i	0.144746	−	0.349447i	−0.834834	−	0.550501i	$-0.814437\pi$
$449$	3.06711	−	7.40465i	0.144746	−	0.349447i	0.979580	+	0.201054i	$0.0644367\pi$
$450$	12.0107	−	7.91668i	0.566189	−	0.373196i
$451$	−21.0569	−	47.5036i	−0.991531	−	2.23686i
$452$	−3.00228	+	5.45115i	−0.141216	+	0.256401i
$453$	−1.26240	+	10.2352i	−0.0593125	+	0.480893i
$454$	−4.89345	−	22.4498i	−0.229661	−	1.05362i
$455$	13.3475	+	0.655723i	0.625743	+	0.0307408i
$456$	42.8619	+	2.91558i	2.00719	+	0.136534i
$457$	3.54831	−	9.91688i	0.165983	−	0.463892i	−0.829536	−	0.558453i	$-0.811395\pi$
$457$	3.54831	−	9.91688i	0.165983	−	0.463892i	0.995519	+	0.0945616i	$0.0301449\pi$
$458$	−12.5391	+	0.845844i	−0.585916	+	0.0395237i
$459$	−0.137805	−	0.0309451i	−0.00643219	−	0.00144440i
$460$	3.34356	+	2.67755i	0.155894	+	0.124841i
$461$	2.32120	+	0.642362i	0.108109	+	0.0299178i	0.320347	−	0.947300i	$-0.396200\pi$
$461$	2.32120	+	0.642362i	0.108109	+	0.0299178i	−0.212238	+	0.977218i	$0.568075\pi$
$462$	−19.4069	−	32.8442i	−0.902890	−	1.52805i
$463$	6.96957	+	8.49244i	0.323903	+	0.394677i	0.909349	−	0.416034i	$-0.136580\pi$
$463$	6.96957	+	8.49244i	0.323903	+	0.394677i	−0.585446	+	0.810712i	$0.699080\pi$
$464$	−26.0265	+	5.16174i	−1.20825	+	0.239628i
$465$	22.2518	+	18.2616i	1.03190	+	0.846860i
$466$	21.7433	+	29.7053i	1.00724	+	1.37607i
$467$	4.19330	+	12.6933i	0.194043	+	0.587376i	0.999989	−	0.00461222i	$-0.00146812\pi$
$467$	4.19330	+	12.6933i	0.194043	+	0.587376i	−0.805946	+	0.591988i	$0.798343\pi$
$468$	−29.7516	+	4.77847i	−1.37527	+	0.220885i
$469$	−1.36475	−	1.43344i	−0.0630184	−	0.0661902i
$470$	5.07953	−	11.2678i	0.234301	−	0.519744i
$471$	34.0270	+	20.3950i	1.56788	+	0.939751i
$472$	4.28369	−	30.0605i	0.197173	−	1.38365i
$473$	−1.47020	−	9.91127i	−0.0675998	−	0.455721i
$474$	3.77066	+	0.301948i	0.173192	+	0.0138689i
$475$	9.08994	+	18.0586i	0.417075	+	0.828585i
$476$	−1.84396	−	1.71392i	−0.0845178	−	0.0785574i
$477$	13.4263	+	2.32968i	0.614748	+	0.106669i
$478$	27.7173	+	8.59831i	1.26776	+	0.393277i
$479$	0.456915	−	0.683821i	0.0208770	−	0.0312446i	−0.820884	−	0.571094i	$-0.806519\pi$
$479$	0.456915	−	0.683821i	0.0208770	−	0.0312446i	0.841761	+	0.539850i	$0.181519\pi$
$480$	17.6539	−	4.75574i	0.805789	−	0.217069i
$481$	−2.46835	−	3.69415i	−0.112547	−	0.168439i
$482$	3.59411	+	12.1216i	0.163707	+	0.552122i
$483$	8.26501	−	1.85597i	0.376071	−	0.0844495i
$484$	10.4950	+	30.5346i	0.477044	+	1.38794i
$485$	−1.22147	−	16.5591i	−0.0554641	−	0.751908i
$486$	3.64706	+	31.1793i	0.165434	+	1.41432i
$487$	10.6714	−	6.39621i	0.483569	−	0.289840i	−0.251470	−	0.967865i	$-0.580914\pi$
$487$	10.6714	−	6.39621i	0.483569	−	0.289840i	0.735039	+	0.678025i	$0.237164\pi$
$488$	12.8397	+	30.5037i	0.581227	+	1.38084i
$489$	14.8325	−	11.0005i	0.670747	−	0.497460i
$490$	2.79830	−	3.92077i	0.126414	−	0.177122i
$491$	−14.2367	−	6.31070i	−0.642493	−	0.284798i	0.0581516	−	0.998308i	$-0.481479\pi$
$491$	−14.2367	−	6.31070i	−0.642493	−	0.284798i	−0.700645	+	0.713510i	$0.747104\pi$
$492$	24.8093	−	42.5404i	1.11849	−	1.91787i
$493$	−0.292887	+	3.97057i	−0.0131910	+	0.178826i
$494$	−1.81247	−	42.3111i	−0.0815468	−	1.90366i
$495$	6.12839	−	20.2026i	0.275451	−	0.908039i
$496$	−19.0426	−	30.1090i	−0.855036	−	1.35193i
$497$	28.1623	−	8.54293i	1.26325	−	0.383203i
$498$	−36.2937	−	17.4452i	−1.62636	−	0.781739i
$499$	16.2787	−	2.00778i	0.728734	−	0.0898807i	0.250504	−	0.968116i	$-0.419404\pi$
$499$	16.2787	−	2.00778i	0.728734	−	0.0898807i	0.478230	+	0.878235i	$0.341279\pi$
$500$	15.5237	+	15.1559i	0.694243	+	0.677792i
$501$	33.2346	+	23.4065i	1.48481	+	1.04572i
$502$	30.1747	−	8.14691i	1.34676	−	0.363614i
$503$	−36.1409	+	1.77549i	−1.61144	+	0.0791651i	−0.834719	−	0.550676i	$-0.814370\pi$
$503$	−36.1409	+	1.77549i	−1.61144	+	0.0791651i	−0.776724	+	0.629841i	$0.783120\pi$
$504$	7.34445	−	16.8277i	0.327148	−	0.749564i
$505$	−3.14375	+	6.64690i	−0.139895	+	0.295783i
$506$	−12.0523	+	0.220182i	−0.535789	+	0.00978828i
$507$	7.04083	+	25.4423i	0.312694	+	1.12993i
$508$	−16.4826	−	16.9018i	−0.731299	−	0.749894i
$509$	0.107590	+	4.38274i	0.00476886	+	0.194262i	0.997353	+	0.0727057i	$0.0231634\pi$
$509$	0.107590	+	4.38274i	0.00476886	+	0.194262i	−0.992585	+	0.121556i	$0.961212\pi$
$510$	0.0172199	−	2.74337i	0.000762512	−	0.121479i
$511$	−6.42130			−0.284062
$512$	−22.5913	−	1.27758i	−0.998405	−	0.0564615i
$513$	1.44770			0.0639177
$514$	−0.0991850	+	15.8015i	−0.00437486	+	0.696976i
$515$	0.431268	+	17.5679i	0.0190039	+	0.774135i
$516$	6.79855	−	6.62997i	0.299290	−	0.291868i
$517$	9.27673	+	33.5218i	0.407990	+	1.47429i
$518$	2.70671	−	0.0494486i	0.118926	−	0.00217265i
$519$	−5.93694	+	12.5526i	−0.260603	+	0.550999i
$520$	−6.58243	−	16.7782i	−0.288659	−	0.735773i
$521$	−4.40285	+	0.216298i	−0.192892	+	0.00947619i	−0.145285	−	0.989390i	$-0.546410\pi$
$521$	−4.40285	+	0.216298i	−0.192892	+	0.00947619i	−0.0476078	+	0.998866i	$0.515160\pi$
$522$	−28.0332	+	7.56873i	−1.22698	+	0.331275i
$523$	21.9218	+	15.4391i	0.958575	+	0.675105i	0.945778	−	0.324813i	$-0.105301\pi$
$523$	21.9218	+	15.4391i	0.958575	+	0.675105i	0.0127972	+	0.999918i	$0.495926\pi$
$524$	−15.6853	+	16.0661i	−0.685218	+	0.701849i
$525$	16.8869	−	2.08280i	0.737004	−	0.0909007i
$526$	27.0660	+	13.0098i	1.18013	+	0.567254i
$527$	−5.11545	+	1.55176i	−0.222833	+	0.0675955i
$528$	−29.6496	+	42.0489i	−1.29034	+	1.82994i
$529$	−5.89958	+	19.4483i	−0.256503	+	0.845578i
$530$	0.348825	+	8.14313i	0.0151520	+	0.353715i
$531$	2.44450	−	33.1393i	0.106082	−	1.43812i
$532$	22.2909	+	12.9999i	0.966432	+	0.563618i
$533$	−44.3809	−	19.6727i	−1.92235	−	0.852120i
$534$	−0.681202	+	0.954450i	−0.0294785	+	0.0413031i
$535$	7.93285	−	5.88340i	0.342967	−	0.254362i
$536$	−1.00740	+	2.47193i	−0.0435131	+	0.106771i
$537$	38.2308	−	22.9147i	1.64978	−	0.988841i
$538$	2.74649	+	23.4802i	0.118410	+	1.01230i
$539$	0.997194	+	13.5186i	0.0429522	+	0.582288i
$540$	0.582657	−	0.200264i	0.0250736	−	0.00861797i
$541$	0.603227	−	0.135459i	0.0259347	−	0.00582384i	−0.206115	−	0.978528i	$-0.566082\pi$
$541$	0.603227	−	0.135459i	0.0259347	−	0.00582384i	0.232049	+	0.972704i	$0.425457\pi$
$542$	−9.32968	−	31.4655i	−0.400744	−	1.35156i
$543$	−8.47245	−	12.6799i	−0.363587	−	0.544147i
$544$	−1.08706	+	3.21654i	−0.0466074	+	0.137908i
$545$	7.36547	−	11.0232i	0.315502	−	0.472182i
$546$	−34.0412	−	10.5601i	−1.45683	−	0.451929i
$547$	−11.5504	−	2.00418i	−0.493859	−	0.0856927i	−0.0814238	−	0.996680i	$-0.525947\pi$
$547$	−11.5504	−	2.00418i	−0.493859	−	0.0856927i	−0.412435	+	0.910987i	$0.635322\pi$
$548$	21.9605	−	23.6267i	0.938107	−	1.00928i
$549$	16.2844	+	32.3515i	0.694999	+	1.38073i
$550$	−24.1355	−	1.93273i	−1.02914	−	0.0824119i
$551$	−5.98803	−	40.3680i	−0.255099	−	1.71974i
$552$	−6.85782	−	9.13714i	−0.291888	−	0.388902i
$553$	1.94885	+	1.16810i	0.0828737	+	0.0496726i
$554$	−1.15851	+	2.56989i	−0.0492203	+	0.109184i
$555$	2.03424	+	2.13663i	0.0863485	+	0.0906947i
$556$	4.12156	+	25.6616i	0.174793	+	1.08829i
$557$	0.833437	+	2.52285i	0.0353138	+	0.106897i	0.965680	−	0.259736i	$-0.0836356\pi$
$557$	0.833437	+	2.52285i	0.0353138	+	0.106897i	−0.930366	+	0.366633i	$0.880511\pi$
$558$	−23.0275	−	31.4598i	−0.974832	−	1.33180i
$559$	−7.23620	−	5.93860i	−0.306059	−	0.251176i
$560$	10.7697	+	2.14854i	0.455103	+	0.0907924i
$561$	4.89770	+	5.96786i	0.206781	+	0.251963i
$562$	1.50351	+	2.54454i	0.0634217	+	0.107335i
$563$	11.4091	+	3.15732i	0.480835	+	0.133065i	0.498699	−	0.866775i	$-0.333811\pi$
$563$	11.4091	+	3.15732i	0.480835	+	0.133065i	−0.0178634	+	0.999840i	$0.505686\pi$
$564$	−20.6053	+	25.7306i	−0.867638	+	1.08345i
$565$	−3.97453	−	0.892510i	−0.167210	−	0.0375482i
$566$	−0.360264	+	0.0243021i	−0.0151430	+	0.00102149i
$567$	−6.15025	+	17.1888i	−0.258286	+	0.721862i
$568$	−26.0963	−	29.9057i	−1.09498	−	1.25481i
$569$	−4.75214	−	0.233458i	−0.199220	−	0.00978706i	−0.0507870	−	0.998710i	$-0.516173\pi$
$569$	−4.75214	−	0.233458i	−0.199220	−	0.00978706i	−0.148433	+	0.988922i	$0.547423\pi$
$570$	5.98893	+	27.4755i	0.250849	+	1.15082i
$571$	−2.19059	+	17.7609i	−0.0916734	+	0.743269i	0.874437	+	0.485139i	$0.161231\pi$
$571$	−2.19059	+	17.7609i	−0.0916734	+	0.743269i	−0.966110	+	0.258129i	$0.916894\pi$
$572$	44.4267	+	24.4685i	1.85757	+	1.02308i
$573$	12.6626	+	28.5665i	0.528990	+	1.19338i
$574$	24.6975	−	16.2790i	1.03085	−	0.679473i
$575$	2.05742	−	4.96705i	0.0858003	−	0.207140i
$576$	−24.7609	+	0.282939i	−1.03170	+	0.0117891i
$577$	17.4012	+	42.0102i	0.724421	+	1.74891i	0.660345	+	0.750963i	$0.270410\pi$
$577$	17.4012	+	42.0102i	0.724421	+	1.74891i	0.0640764	+	0.997945i	$0.479590\pi$
$578$	−19.4838	−	13.1963i	−0.810421	−	0.548895i
$579$	−24.3722	+	63.1827i	−1.01288	+	2.62578i
$580$	−7.99419	−	15.4186i	−0.331940	−	0.640221i
$581$	−14.8809	−	19.0682i	−0.617365	−	0.791080i
$582$	−7.84457	+	43.5835i	−0.325168	+	1.80660i
$583$	−15.4033	−	16.9949i	−0.637939	−	0.703857i
$584$	3.55467	+	7.89711i	0.147093	+	0.326785i
$585$	−8.43304	−	17.8302i	−0.348663	−	0.737187i
$586$	0.433302	−	0.214708i	0.0178996	−	0.00886950i
$587$	11.9754	+	18.9112i	0.494276	+	0.780547i	0.996447	−	0.0842214i	$-0.0268403\pi$
$587$	11.9754	+	18.9112i	0.494276	+	0.780547i	−0.502171	+	0.864768i	$0.667465\pi$
$588$	−9.83245	+	8.26855i	−0.405483	+	0.340989i
$589$	47.6753	−	27.0077i	1.96443	−	1.11283i
$590$	19.6781	−	2.79285i	0.810134	−	0.114980i
$591$	−1.72937	+	17.5586i	−0.0711368	+	0.722264i
$592$	−1.55918	−	3.30142i	−0.0640819	−	0.135688i
$593$	37.5013	−	3.69356i	1.53999	−	0.151676i	0.707901	−	0.706312i	$-0.249642\pi$
$593$	37.5013	−	3.69356i	1.53999	−	0.151676i	0.832093	+	0.554636i	$0.187142\pi$
$594$	−0.900670	+	1.48151i	−0.0369549	+	0.0607871i
$595$	0.740892	−	1.47190i	0.0303736	−	0.0603420i
$596$	5.57151	−	2.06920i	0.228218	−	0.0847578i
$597$	−24.7629	−	0.607895i	−1.01348	−	0.0248795i
$598$	−8.20498	+	7.71419i	−0.335527	+	0.315457i
$599$	−9.81522	−	39.1845i	−0.401039	−	1.60104i	−0.748362	−	0.663291i	$-0.769159\pi$
$599$	−9.81522	−	39.1845i	−0.401039	−	1.60104i	0.347323	−	0.937746i	$-0.387091\pi$
$600$	−11.9096	−	19.6150i	−0.486209	−	0.800779i
$601$	−15.8852	−	11.7813i	−0.647970	−	0.480568i	0.221103	−	0.975250i	$-0.429034\pi$
$601$	−15.8852	−	11.7813i	−0.647970	−	0.480568i	−0.869074	+	0.494683i	$0.835284\pi$
$602$	5.42714	−	1.75518i	0.221194	−	0.0715357i
$603$	−0.916326	+	2.77376i	−0.0373157	+	0.112956i
$604$	8.24780	+	1.32947i	0.335598	+	0.0540953i
$605$	−17.2792	+	12.1694i	−0.702499	+	0.494756i
$606$	12.5356	−	15.0807i	0.509225	−	0.612611i
$607$	3.11048	−	0.618712i	0.126250	−	0.0251128i	−0.131561	−	0.991308i	$-0.541999\pi$
$607$	3.11048	−	0.618712i	0.126250	−	0.0251128i	0.257811	+	0.966195i	$0.416999\pi$
$608$	3.64804	−	34.6104i	0.147948	−	1.40364i
$609$	−33.6854	−	6.70044i	−1.36500	−	0.271516i
$610$	−16.8319	+	13.6377i	−0.681504	+	0.552174i
$611$	27.4538	+	17.3849i	1.11066	+	0.703319i
$612$	−0.948001	+	3.59267i	−0.0383207	+	0.145225i
$613$	1.17156	+	1.01060i	0.0473190	+	0.0408176i	0.676513	−	0.736430i	$-0.263490\pi$
$613$	1.17156	+	1.01060i	0.0473190	+	0.0408176i	−0.629194	+	0.777248i	$0.716615\pi$
$614$	−5.12165	+	18.0653i	−0.206693	+	0.729058i
$615$	31.2687	+	7.83240i	1.26088	+	0.315833i
$616$	−27.1715	+	14.7237i	−1.09477	+	0.593233i
$617$	0.263009	−	1.77306i	0.0105883	−	0.0713808i	−0.983238	−	0.182325i	$-0.941638\pi$
$617$	0.263009	−	1.77306i	0.0105883	−	0.0713808i	0.993827	+	0.110945i	$0.0353876\pi$
$618$	10.5558	−	45.6645i	0.424617	−	1.83690i
$619$	11.1935	+	29.0182i	0.449907	+	1.16634i	0.953231	+	0.302242i	$0.0977350\pi$
$619$	11.1935	+	29.0182i	0.449907	+	1.16634i	−0.503325	+	0.864097i	$0.667890\pi$
$620$	15.4519	−	17.4648i	0.620561	−	0.701404i
$621$	−0.251459	−	0.291511i	−0.0100907	−	0.0116979i
$622$	21.8562	+	7.97536i	0.876352	+	0.319783i
$623$	−0.621165	+	0.332020i	−0.0248865	+	0.0133021i
$624$	5.85725	+	47.7107i	0.234478	+	1.90996i
$625$	1.05121	−	1.96667i	0.0420482	−	0.0786667i
$626$	1.44620	−	26.0948i	0.0578016	−	1.04296i
$627$	−62.3853	−	48.6860i	−2.49143	−	1.94433i
$628$	17.5327	−	26.9331i	0.699631	−	1.07475i
$629$	−0.539784	+	0.0936614i	−0.0215226	+	0.00373452i
$630$	11.9183	+	1.54599i	0.474837	+	0.0615938i
$631$	−34.0924	−	30.8996i	−1.35720	−	1.23009i	−0.948246	−	0.317537i	$-0.897144\pi$
$631$	−34.0924	−	30.8996i	−1.35720	−	1.23009i	−0.408953	−	0.912556i	$-0.634106\pi$
$632$	0.357726	−	3.04339i	0.0142296	−	0.121059i
$633$	9.06732	+	25.3415i	0.360394	+	1.00723i
$634$	7.58254	−	3.30432i	0.301141	−	0.131231i
$635$	7.61678	−	13.4455i	0.302263	−	0.533568i
$636$	4.50819	−	21.2655i	0.178762	−	0.843230i
$637$	9.17207	+	8.73253i	0.363411	+	0.345996i
$638$	45.0360	+	18.9866i	1.78299	+	0.751686i
$639$	−30.7139	−	30.7139i	−1.21502	−	1.21502i
$640$	−3.31950	−	14.4343i	−0.131215	−	0.570565i
$641$	−33.2451	+	33.2451i	−1.31310	+	1.31310i	−0.393986	+	0.919117i	$0.628904\pi$
$641$	−33.2451	+	33.2451i	−1.31310	+	1.31310i	−0.919117	+	0.393986i	$0.871096\pi$
$642$	−24.3987	+	9.92733i	−0.962941	+	0.391800i
$643$	−27.2233	+	28.5935i	−1.07358	+	1.12762i	−0.0821996	+	0.996616i	$0.526194\pi$
$643$	−27.2233	+	28.5935i	−1.07358	+	1.12762i	−0.991382	+	0.131002i	$0.958181\pi$
$644$	−1.25414	−	6.74654i	−0.0494200	−	0.265851i
$645$	5.40831	+	3.06377i	0.212952	+	0.120636i
$646$	−4.86029	−	1.90995i	−0.191225	−	0.0751461i
$647$	17.5112	−	6.26561i	0.688437	−	0.246327i	0.0306492	−	0.999530i	$-0.490243\pi$
$647$	17.5112	−	6.26561i	0.688437	−	0.246327i	0.657787	+	0.753204i	$0.271493\pi$
$648$	24.5439	−	1.95152i	0.964177	−	0.0766628i
$649$	−37.5610	+	41.4422i	−1.47440	+	1.62675i
$650$	−17.9203	+	13.8050i	−0.702890	+	0.541477i
$651$	−7.88378	−	45.4354i	−0.308990	−	1.78075i
$652$	−8.45959	−	12.3378i	−0.331303	−	0.483187i
$653$	−9.52794	+	12.2089i	−0.372857	+	0.477772i	−0.937710	−	0.347420i	$-0.887058\pi$
$653$	−9.52794	+	12.2089i	−0.372857	+	0.477772i	0.564853	+	0.825192i	$0.308933\pi$
$654$	−26.3474	+	23.5803i	−1.03026	+	0.922065i
$655$	−12.9617	−	6.92815i	−0.506454	−	0.270705i
$656$	−33.6923	−	21.3620i	−1.31546	−	0.834047i
$657$	4.46763	+	8.35834i	0.174299	+	0.326090i
$658$	−17.9519	+	8.35311i	−0.699836	+	0.325638i
$659$	5.50370	−	4.74753i	0.214394	−	0.184937i	−0.539397	−	0.842051i	$-0.681348\pi$
$659$	5.50370	−	4.74753i	0.214394	−	0.184937i	0.753791	+	0.657114i	$0.228223\pi$
$660$	−31.8430	−	10.9648i	−1.23949	−	0.426803i
$661$	5.22031	−	2.01369i	0.203046	−	0.0783236i	−0.256235	−	0.966615i	$-0.582482\pi$
$661$	5.22031	−	2.01369i	0.203046	−	0.0783236i	0.459281	+	0.888291i	$0.348107\pi$
$662$	19.0273	−	11.8823i	0.739518	−	0.461817i
$663$	7.13472	+	1.05834i	0.277090	+	0.0411023i
$664$	−15.2129	+	28.8567i	−0.590374	+	1.11986i
$665$	−4.10413	+	16.3846i	−0.159151	+	0.635367i
$666$	−1.94756	−	3.48881i	−0.0754665	−	0.135189i
$667$	−7.08845	+	8.21748i	−0.274466	+	0.318182i
$668$	19.9468	−	26.2012i	0.771764	−	1.01375i
$669$	1.67416	−	2.64379i	0.0647268	−	0.102215i
$670$	−1.73772	−	0.182170i	−0.0671339	−	0.00703786i
$671$	11.8933	−	59.7914i	0.459134	−	2.30822i
$672$	−26.3910	−	12.7037i	−1.01806	−	0.490054i
$673$	7.66779	+	38.5486i	0.295571	+	1.48594i	0.788049	+	0.615613i	$0.211091\pi$
$673$	7.66779	+	38.5486i	0.295571	+	1.48594i	−0.492477	+	0.870325i	$0.663909\pi$
$674$	3.40504	+	36.9481i	0.131157	+	1.42319i
$675$	−0.445265	−	0.632228i	−0.0171383	−	0.0243345i
$676$	20.8078	−	4.93534i	0.800301	−	0.189821i
$677$	25.4493	+	8.40732i	0.978097	+	0.323120i	0.757925	−	0.652341i	$-0.226213\pi$
$677$	25.4493	+	8.40732i	0.978097	+	0.323120i	0.220172	+	0.975461i	$0.429338\pi$
$678$	9.67336	+	4.94551i	0.371503	+	0.189931i
$679$	−15.8452	+	21.3647i	−0.608082	+	0.819904i
$680$	−2.22033	−	0.0963653i	−0.0851456	−	0.00369544i
$681$	−38.9099	+	9.74642i	−1.49103	+	0.373484i
$682$	−2.02219	+	65.5911i	−0.0774338	+	2.51161i
$683$	−0.907597	+	36.9714i	−0.0347282	+	1.41467i	0.689088	+	0.724678i	$0.258011\pi$
$683$	−0.907597	+	36.9714i	−0.0347282	+	1.41467i	−0.723816	+	0.689993i	$0.757614\pi$
$684$	1.41257	−	38.0598i	0.0540108	−	1.45525i
$685$	18.8595	+	9.49308i	0.720585	+	0.362712i
$686$	−27.6672	+	6.74599i	−1.05634	+	0.257563i
$687$	2.15050	+	21.8344i	0.0820466	+	0.833033i
$688$	−5.16290	−	5.70283i	−0.196834	−	0.217419i
$689$	−21.3257	−	2.10039i	−0.812443	−	0.0800187i
$690$	4.49225	−	5.97830i	0.171017	−	0.227590i
$691$	23.2817	+	41.0979i	0.885676	+	1.56344i	0.824895	+	0.565285i	$0.191234\pi$
$691$	23.2817	+	41.0979i	0.885676	+	1.56344i	0.0607805	+	0.998151i	$0.480641\pi$
$692$	9.98334	+	5.18328i	0.379510	+	0.197039i
$693$	−28.5732	+	18.0938i	−1.08541	+	0.687327i
$694$	21.7510	+	7.33729i	0.825655	+	0.278520i
$695$	−15.3790	+	7.27373i	−0.583359	+	0.275908i
$696$	10.4070	+	45.1365i	0.394475	+	1.71090i
$697$	−4.43540	+	4.02001i	−0.168003	+	0.152269i
$698$	−22.9251	−	32.9890i	−0.867727	−	1.24865i
$699$	50.6638	−	39.5385i	1.91628	−	1.49548i
$700$	−1.17872	−	13.7330i	−0.0445513	−	0.519059i
$701$	−45.4931	−	17.5486i	−1.71825	−	0.662802i	−0.718777	−	0.695241i	$-0.755298\pi$
$701$	−45.4931	−	17.5486i	−1.71825	−	0.662802i	−0.999474	+	0.0324382i	$0.989673\pi$
$702$	0.306035	+	1.59066i	0.0115506	+	0.0600355i
$703$	5.18810	−	2.14898i	0.195673	−	0.0810504i
$704$	33.1490	+	25.2657i	1.24935	+	0.952235i
$705$	−19.9347	−	8.25722i	−0.750784	−	0.310985i
$706$	−5.76072	+	28.0401i	−0.216807	+	1.05530i
$707$	10.7686	−	4.77337i	0.404993	−	0.179521i
$708$	−52.6838	−	5.85756i	−1.97998	−	0.220140i
$709$	3.81293	+	0.470280i	0.143198	+	0.0176617i	0.193691	−	0.981063i	$-0.437954\pi$
$709$	3.81293	+	0.470280i	0.143198	+	0.0176617i	−0.0504929	+	0.998724i	$0.516079\pi$
$710$	14.0368	−	21.8618i	0.526793	−	0.820457i
$711$	0.164548	−	3.34945i	0.00617102	−	0.125614i
$712$	0.752189	+	0.580130i	0.0281895	+	0.0217413i
$713$	−13.7193	−	4.90884i	−0.513791	−	0.183837i
$714$	−2.89146	+	3.30978i	−0.108210	+	0.123865i
$715$	−7.27392	+	32.3922i	−0.272029	+	1.21140i
$716$	−17.4015	−	31.6375i	−0.650323	−	1.18235i
$717$	13.5123	−	48.8272i	0.504626	−	1.82348i
$718$	−5.31183	+	20.6551i	−0.198236	+	0.770841i
$719$	35.6082	−	29.2229i	1.32796	−	1.08983i	0.339140	−	0.940736i	$-0.389864\pi$
$719$	35.6082	−	29.2229i	1.32796	−	1.08983i	0.988823	−	0.149095i	$-0.0476359\pi$
$720$	−4.69637	−	15.5133i	−0.175023	−	0.578148i
$721$	17.8593	−	21.7617i	0.665117	−	0.810447i
$722$	26.3439	+	4.07690i	0.980417	+	0.151726i
$723$	20.9579	−	6.92355i	0.779432	−	0.257489i
$724$	−10.5193	+	6.47773i	−0.390948	+	0.240743i
$725$	−15.7874	+	15.0309i	−0.586331	+	0.558233i
$726$	52.7159	−	19.9556i	1.95647	−	0.740621i
$727$	−2.36476	+	3.94536i	−0.0877040	+	0.146325i	−0.898455	−	0.439066i	$-0.855309\pi$
$727$	−2.36476	+	3.94536i	−0.0877040	+	0.146325i	0.810751	+	0.585392i	$0.199059\pi$
$728$	−9.57147	+	27.2401i	−0.354742	+	1.00959i
$729$	28.3770	−	4.20933i	1.05100	−	0.155901i
$730$	−4.31553	+	3.67562i	−0.159725	+	0.136041i
$731$	−1.03105	+	0.518986i	−0.0381347	+	0.0191954i
$732$	52.5360	−	24.0453i	1.94179	−	0.888741i
$733$	−4.29202	+	24.7355i	−0.158529	+	0.913627i	0.793715	+	0.608290i	$0.208144\pi$
$733$	−4.29202	+	24.7355i	−0.158529	+	0.913627i	−0.952244	+	0.305337i	$0.901231\pi$
$734$	−1.13341	−	2.15287i	−0.0418351	−	0.0794637i
$735$	−6.99198	−	4.67189i	−0.257903	−	0.172325i
$736$	−7.60283	+	5.27709i	−0.280244	+	0.194516i
$737$	4.08826	−	2.73169i	0.150593	−	0.100623i
$738$	−38.3730	−	20.8215i	−1.41253	−	0.766451i
$739$	−7.28248	−	32.4303i	−0.267890	−	1.19297i	−0.906085	−	0.423095i	$-0.860944\pi$
$739$	−7.28248	−	32.4303i	−0.267890	−	1.19297i	0.638195	−	0.769875i	$-0.279681\pi$
$740$	1.79078	−	1.58258i	0.0658305	−	0.0581768i
$741$	−73.7321	+	5.43881i	−2.70862	+	0.199800i
$742$	8.09756	−	10.2429i	0.297271	−	0.376027i
$743$	−12.3008	−	20.5227i	−0.451273	−	0.752904i	0.545066	−	0.838393i	$-0.316505\pi$
$743$	−12.3008	−	20.5227i	−0.451273	−	0.752904i	−0.996339	+	0.0854893i	$0.972755\pi$
$744$	−51.5135	+	34.8476i	−1.88858	+	1.27757i
$745$	2.31744	+	3.12471i	0.0849046	+	0.114481i
$746$	0.340286	+	2.03694i	0.0124588	+	0.0745777i
$747$	−14.4668	+	32.6366i	−0.529312	+	1.19411i
$748$	4.97832	−	3.78553i	0.182025	−	0.138413i
$749$	−15.7790	−	1.16393i	−0.576551	−	0.0425290i
$750$	25.6107	−	27.9031i	0.935172	−	1.01888i
$751$	−17.7529	−	5.38528i	−0.647812	−	0.196512i	−0.0507557	−	0.998711i	$-0.516163\pi$
$751$	−17.7529	−	5.38528i	−0.647812	−	0.196512i	−0.597056	+	0.802200i	$0.703663\pi$
$752$	20.2106	+	17.4537i	0.737005	+	0.636470i
$753$	−15.8390	−	52.2143i	−0.577207	−	1.90280i
$754$	43.0884	−	15.1129i	1.56919	−	0.550378i
$755$	0.669390	+	5.42727i	0.0243616	+	0.197519i
$756$	−0.916330	−	0.366747i	−0.0333266	−	0.0133385i
$757$	27.9315	−	39.6596i	1.01519	−	1.44145i	0.121590	−	0.992580i	$-0.461201\pi$
$757$	27.9315	−	39.6596i	1.01519	−	1.44145i	0.893596	−	0.448873i	$-0.148174\pi$
$758$	11.1071	+	6.38450i	0.403427	+	0.231895i
$759$	1.03257	+	21.0185i	0.0374800	+	0.762923i
$760$	22.4222	−	4.02271i	0.813339	−	0.145919i
$761$	30.5076	+	14.4290i	1.10590	+	0.523051i	0.891191	−	0.453627i	$-0.149870\pi$
$761$	30.5076	+	14.4290i	1.10590	+	0.523051i	0.214707	+	0.976678i	$0.431120\pi$
$762$	−28.6056	+	29.6702i	−1.03627	+	1.07484i
$763$	−20.4688	+	5.66449i	−0.741022	+	0.205068i
$764$	23.5059	−	9.39251i	0.850413	−	0.339809i
$765$	−2.43139	+	0.0596872i	−0.0879070	+	0.00215800i
$766$	36.0050	−	35.5558i	1.30091	−	1.28468i
$767$			52.2544i			1.88680i
$768$	−1.01394	+	39.4889i	−0.0365875	+	1.42493i
$769$		−	22.8322i		−	0.823349i	−0.911331	−	0.411674i	$-0.864944\pi$
$769$		−	22.8322i		−	0.823349i	0.911331	−	0.411674i	$-0.135056\pi$
$770$	−14.2139	−	14.3934i	−0.512232	−	0.518703i
$771$	27.5778	−	0.676998i	0.993191	−	0.0243815i
$772$	50.4160	+	21.6284i	1.81451	+	0.778423i
$773$	−7.58525	+	2.09912i	−0.272823	+	0.0755002i	−0.400439	−	0.916323i	$-0.631142\pi$
$773$	−7.58525	+	2.09912i	−0.272823	+	0.0755002i	0.127616	+	0.991824i	$0.459267\pi$
$774$	−6.06058	−	5.84311i	−0.217843	−	0.210026i
$775$	−26.4579	−	12.5137i	−0.950397	−	0.449504i
$776$	35.0465	+	7.65990i	1.25810	+	0.274974i
$777$	−0.231896	−	4.72035i	−0.00831922	−	0.169342i
$778$	11.1236	−	19.3517i	0.398802	−	0.693793i
$779$	35.3308	−	50.1659i	1.26586	−	1.79738i
$780$	−28.9226	+	12.3885i	−1.03560	+	0.443578i
$781$	8.94955	+	72.5610i	0.320240	+	2.59644i
$782$	0.459619	+	1.31042i	0.0164359	+	0.0468606i
$783$	0.453112	+	1.49371i	0.0161929	+	0.0533808i
$784$	6.39822	+	8.20810i	0.228508	+	0.293146i
$785$	20.1299	+	6.10634i	0.718467	+	0.217945i
$786$	28.8779	+	26.5055i	1.03004	+	0.945418i
$787$	−24.0270	−	1.77234i	−0.856471	−	0.0631771i	−0.361798	−	0.932256i	$-0.617837\pi$
$787$	−24.0270	−	1.77234i	−0.856471	−	0.0631771i	−0.494673	+	0.869079i	$0.664712\pi$
$788$	14.1623	+	1.92753i	0.504509	+	0.0686654i
$789$	21.2450	−	47.9280i	0.756343	−	1.70628i
$790$	1.97839	−	0.330505i	0.0703879	−	0.0117588i
$791$	3.88733	+	5.24145i	0.138217	+	0.186365i
$792$	38.0697	+	25.1240i	1.35275	+	0.892741i
$793$	−29.2809	−	48.8523i	−1.03980	−	1.73479i
$794$	36.8921	+	29.1653i	1.30925	+	1.03504i
$795$	14.1904	−	1.04675i	0.503281	−	0.0371242i
$796$	−1.23612	+	20.0280i	−0.0438130	+	0.709875i
$797$	−7.88145	−	35.0977i	−0.279175	−	1.24322i	−0.891647	−	0.452731i	$-0.850450\pi$
$797$	−7.88145	−	35.0977i	−0.279175	−	1.24322i	0.612472	−	0.790493i	$-0.290175\pi$
$798$	21.4847	−	39.5952i	0.760551	−	1.40166i
$799$	3.33166	−	2.22614i	0.117866	−	0.0787553i
$800$	−16.2368	+	9.05187i	−0.574057	+	0.320032i
$801$	0.864352	+	0.577542i	0.0305404	+	0.0204064i
$802$	−36.0877	+	18.9990i	−1.27430	+	0.670879i
$803$	2.72723	−	15.7174i	0.0962418	−	0.554655i
$804$	4.36753	+	1.62486i	0.154031	+	0.0573043i
$805$	4.01208	−	2.01951i	0.141407	−	0.0711785i
$806$	39.7529	+	46.6738i	1.40024	+	1.64402i
$807$	40.8234	−	6.05557i	1.43705	−	0.213166i
$808$	−11.8316	−	10.6011i	−0.416236	−	0.372945i
$809$	−5.93418	+	9.90059i	−0.208635	+	0.348086i	−0.944203	−	0.329365i	$-0.893165\pi$
$809$	−5.93418	+	9.90059i	−0.208635	+	0.348086i	0.735568	+	0.677451i	$0.236915\pi$
$810$	5.70567	+	15.0725i	0.200477	+	0.529592i
$811$	15.7663	−	15.0108i	0.553630	−	0.527100i	−0.360372	−	0.932809i	$-0.617350\pi$
$811$	15.7663	−	15.0108i	0.553630	−	0.527100i	0.914002	+	0.405709i	$0.132975\pi$
$812$	−6.43630	+	27.0680i	−0.225870	+	0.949902i
$813$	−54.4030	+	17.9723i	−1.90800	+	0.630317i
$814$	−1.02855	+	6.64621i	−0.0360506	+	0.232950i
$815$	6.21194	−	7.56927i	0.217595	−	0.265140i
$816$	5.67110	+	1.72380i	0.198528	+	0.0603451i
$817$	9.14610	−	7.50601i	0.319981	−	0.262602i
$818$	1.32868	+	0.341693i	0.0464561	+	0.0119470i
$819$	−8.42736	+	30.4526i	−0.294476	+	1.06410i
$820$	7.28004	−	25.0776i	0.254230	−	0.875749i
$821$	1.70126	−	7.57606i	0.0593744	−	0.264406i	−0.937017	−	0.349284i	$-0.886425\pi$
$821$	1.70126	−	7.57606i	0.0593744	−	0.264406i	0.996391	+	0.0848776i	$0.0270499\pi$
$822$	−42.4083	−	37.0484i	−1.47916	−	1.29221i
$823$	−29.6644	−	10.6141i	−1.03403	−	0.369984i	−0.235463	−	0.971883i	$-0.575661\pi$
$823$	−29.6644	−	10.6141i	−1.03403	−	0.369984i	−0.798572	+	0.601900i	$0.794411\pi$
$824$	−36.6496	−	9.91725i	−1.27675	−	0.345484i
$825$	−2.07406	+	42.2186i	−0.0722097	+	1.46986i
$826$	−26.7925	−	17.2027i	−0.932229	−	0.598558i
$827$	−14.6337	−	1.80490i	−0.508864	−	0.0627624i	−0.136112	−	0.990693i	$-0.543461\pi$
$827$	−14.6337	−	1.80490i	−0.508864	−	0.0627624i	−0.372752	+	0.927931i	$0.621586\pi$
$828$	−7.90912	+	6.32637i	−0.274861	+	0.219857i
$829$	47.9205	−	21.2417i	1.66435	−	0.737754i	0.664393	−	0.747383i	$-0.268690\pi$
$829$	47.9205	−	21.2417i	1.66435	−	0.737754i	0.999954	+	0.00962867i	$0.00306495\pi$
$830$	−20.9158	−	4.29705i	−0.725996	−	0.149153i
$831$	4.54658	+	1.88326i	0.157719	+	0.0653294i
$832$	38.7992	−	3.30814i	1.34512	−	0.114689i
$833$	1.44274	−	0.597604i	0.0499881	−	0.0207057i
$834$	44.5558	−	8.57232i	1.54284	−	0.296835i
$835$	20.1103	+	7.75742i	0.695947	+	0.268456i
$836$	−41.2872	+	49.0400i	−1.42795	+	1.69608i
$837$	−1.65221	+	1.28940i	−0.0571088	+	0.0445682i
$838$	−42.8035	+	29.7454i	−1.47862	+	1.02754i
$839$	−33.3942	+	30.2668i	−1.15290	+	1.04493i	−0.154520	+	0.987990i	$0.549383\pi$
$839$	−33.3942	+	30.2668i	−1.15290	+	1.04493i	−0.998378	+	0.0569356i	$0.981867\pi$
$840$	3.16967	−	18.9079i	0.109364	−	0.652385i
$841$	13.5610	−	6.41387i	0.467620	−	0.221168i
$842$	−5.64686	+	16.7398i	−0.194604	+	0.576891i
$843$	4.35915	−	2.76040i	0.150137	−	0.0950732i
$844$	20.7871	−	6.57888i	0.715522	−	0.226455i
$845$	6.89955	+	12.1794i	0.237352	+	0.418984i
$846$	23.3629	+	17.5555i	0.803234	+	0.603570i
$847$	33.6938	+	3.31855i	1.15773	+	0.114027i
$848$	−17.0796	−	4.28845i	−0.586515	−	0.147266i
$849$	0.0617863	+	0.627326i	0.00212050	+	0.0215298i
$850$	0.660765	+	2.70998i	0.0226641	+	0.0929515i
$851$	−1.33387	−	0.671413i	−0.0457244	−	0.0230158i
$852$	−50.7792	+	47.1449i	−1.73967	+	1.61516i
$853$	0.124566	−	5.07427i	0.00426507	−	0.173740i	−0.993785	−	0.111318i	$-0.964493\pi$
$853$	0.124566	−	5.07427i	0.00426507	−	0.173740i	0.998050	−	0.0624214i	$-0.0198823\pi$
$854$	34.6876	+	1.06943i	1.18699	+	0.0365951i
$855$	24.1826	−	6.05742i	0.827027	−	0.207159i
$856$	7.30341	+	20.0498i	0.249625	+	0.685287i
$857$	5.11736	−	6.89997i	0.174806	−	0.235698i	−0.707112	−	0.707102i	$-0.750002\pi$
$857$	5.11736	−	6.89997i	0.174806	−	0.235698i	0.881918	+	0.471403i	$0.156252\pi$
$858$	40.3057	−	78.8375i	1.37601	−	2.69147i
$859$	−10.0495	−	3.31992i	−0.342886	−	0.113274i	0.137083	−	0.990560i	$-0.456227\pi$
$859$	−10.0495	−	3.31992i	−0.342886	−	0.113274i	−0.479969	+	0.877285i	$0.659352\pi$
$860$	2.64271	−	4.28614i	0.0901156	−	0.146156i
$861$	−29.7343	−	42.2194i	−1.01334	−	1.43883i
$862$	−34.7404	+	3.20159i	−1.18326	+	0.109047i
$863$	−3.85599	−	19.3854i	−0.131259	−	0.659886i	−0.989252	−	0.146223i	$-0.953288\pi$
$863$	−3.85599	−	19.3854i	−0.131259	−	0.659886i	0.857992	−	0.513663i	$-0.171712\pi$
$864$	0.0562198	+	1.32995i	0.00191264	+	0.0452459i
$865$	−1.43645	+	7.22151i	−0.0488407	+	0.245539i
$866$	4.99554	−	47.6523i	0.169755	−	1.61929i
$867$	−21.9784	+	34.7077i	−0.746427	+	1.17874i
$868$	−37.0182	+	5.01705i	−1.25648	+	0.170290i
$869$	−3.68686	+	4.27409i	−0.125068	+	0.144989i
$870$	−26.4742	+	14.7787i	−0.897559	+	0.501045i
$871$	1.11618	−	4.45603i	0.0378202	−	0.150987i
$872$	18.2974	+	22.0375i	0.619628	+	0.746283i
$873$	38.8339	+	5.76046i	1.31433	+	0.194962i
$874$	−7.53969	−	12.0735i	−0.255034	−	0.408391i
$875$	21.2252	−	8.18747i	0.717543	−	0.276787i
$876$	13.5886	−	6.62747i	0.459118	−	0.223921i
$877$	−17.0882	+	14.7404i	−0.577028	+	0.497747i	−0.892415	−	0.451216i	$-0.850991\pi$
$877$	−17.0882	+	14.7404i	−0.577028	+	0.497747i	0.315387	+	0.948963i	$0.397866\pi$
$878$	10.5656	+	22.7067i	0.356571	+	0.766315i
$879$	−0.397959	−	0.744529i	−0.0134228	−	0.0251124i
$880$	−9.83304	+	25.4485i	−0.331472	+	0.857868i
$881$	−20.2290	−	10.8126i	−0.681533	−	0.364287i	0.0940194	−	0.995570i	$-0.470028\pi$
$881$	−20.2290	−	10.8126i	−0.681533	−	0.364287i	−0.775552	+	0.631284i	$0.782528\pi$
$882$	7.59541	+	8.48670i	0.255751	+	0.285762i
$883$	14.3517	−	18.3900i	0.482974	−	0.618874i	−0.483592	−	0.875294i	$-0.660668\pi$
$883$	14.3517	−	18.3900i	0.482974	−	0.618874i	0.966565	+	0.256420i	$0.0825430\pi$
$884$	1.07112	−	5.74397i	0.0360256	−	0.193191i
$885$	−5.93193	−	34.1865i	−0.199400	−	1.14917i
$886$	−1.67039	−	2.16833i	−0.0561179	−	0.0728466i
$887$	−6.15378	+	6.78965i	−0.206624	+	0.227974i	−0.835443	−	0.549578i	$-0.814789\pi$
$887$	−6.15378	+	6.78965i	−0.206624	+	0.227974i	0.628819	+	0.777552i	$0.283539\pi$
$888$	−5.67685	+	2.89826i	−0.190503	+	0.0972591i
$889$	−23.3083	+	8.33985i	−0.781736	+	0.279709i
$890$	−0.227412	+	0.578700i	−0.00762288	+	0.0193981i
$891$	−39.4609	−	22.3543i	−1.32199	−	0.748897i
$892$	−2.08993	−	1.43472i	−0.0699759	−	0.0480379i
$893$	−28.3208	+	29.7463i	−0.947720	+	0.995421i
$894$	−3.91033	−	9.61055i	−0.130781	−	0.321425i
$895$	16.7121	−	16.7121i	0.558625	−	0.558625i
$896$	−11.0769	+	20.9826i	−0.370054	+	0.700981i
$897$	13.9021	+	13.9021i	0.464177	+	0.464177i
$898$	−4.40319	+	10.4443i	−0.146936	+	0.348531i
$899$	42.7878	+	40.7373i	1.42705	+	1.35867i
$900$	−17.0556	+	11.0890i	−0.568520	+	0.369635i
$901$	−1.30241	+	2.29908i	−0.0433897	+	0.0765936i
$902$	29.3567	+	67.3658i	0.977471	+	2.24304i
$903$	−3.35461	−	9.37552i	−0.111635	−	0.311998i
$904$	4.29417	−	7.68229i	0.142822	−	0.255509i
$905$	−5.99160	−	5.43047i	−0.199168	−	0.180515i
$906$	1.87612	−	14.4633i	0.0623298	−	0.480512i
$907$	−47.0549	+	8.16480i	−1.56243	+	0.271108i	−0.885395	−	0.464840i	$-0.846112\pi$
$907$	−47.0549	+	8.16480i	−1.56243	+	0.271108i	−0.677038	+	0.735948i	$0.736737\pi$
$908$	6.72096	+	31.7916i	0.223043	+	1.05504i
$909$	−13.7055	−	10.6959i	−0.454584	−	0.354761i
$910$	−18.8701	−	1.04580i	−0.625537	−	0.0346678i
$911$	15.9340	−	29.8104i	0.527917	−	0.987663i	−0.466737	−	0.884396i	$-0.654570\pi$
$911$	15.9340	−	29.8104i	0.527917	−	0.987663i	0.994654	−	0.103267i	$-0.0329296\pi$
$912$	−60.5888	−	4.50364i	−2.00630	−	0.149130i
$913$	52.9932	−	28.3255i	1.75382	−	0.937436i
$914$	−5.10601	+	13.9928i	−0.168892	+	0.462841i
$915$	24.7022	+	28.6368i	0.816631	+	0.946702i
$916$	17.7402	−	1.08487i	0.586152	−	0.0358452i
$917$	8.47349	+	21.9667i	0.279819	+	0.725404i
$918$	0.194607	+	0.0449854i	0.00642299	+	0.00148474i
$919$	1.81129	−	12.2107i	0.0597488	−	0.402794i	−0.938583	−	0.345054i	$-0.887861\pi$
$919$	1.81129	−	12.2107i	0.0597488	−	0.402794i	0.998332	−	0.0577399i	$-0.0183894\pi$
$920$	−4.70465	−	3.81623i	−0.155108	−	0.125817i
$921$	31.7982	+	7.96503i	1.04779	+	0.262457i
$922$	−3.27690	−	0.929023i	−0.107919	−	0.0305957i
$923$	51.7210	+	44.6149i	1.70242	+	1.46852i
$924$	27.1534	+	46.6201i	0.893281	+	1.53369i
$925$	−2.53417	−	1.60475i	−0.0833231	−	0.0527637i
$926$	−9.78088	−	12.0718i	−0.321419	−	0.396702i
$927$	−40.7519	−	8.10606i	−1.33847	−	0.266238i
$928$	36.8521	−	7.06862i	1.20973	−	0.232039i
$929$	35.6318	−	7.08760i	1.16904	−	0.232537i	0.427862	−	0.903844i	$-0.359267\pi$
$929$	35.6318	−	7.08760i	1.16904	−	0.232537i	0.741179	+	0.671307i	$0.234267\pi$
$930$	−31.3061	−	26.0228i	−1.02657	−	0.853321i
$931$	−13.0869	+	9.21687i	−0.428907	+	0.302071i
$932$	−30.4854	−	42.2019i	−0.998581	−	1.38237i
$933$	12.7406	−	38.5664i	0.417109	−	1.26261i
$934$	−5.81743	−	17.9879i	−0.190352	−	0.588583i
$935$	3.28810	+	2.43862i	0.107532	+	0.0797514i
$936$	42.1167	−	6.49354i	1.37663	−	0.212248i
$937$	−10.6626	−	42.5676i	−0.348333	−	1.39062i	−0.850556	−	0.525885i	$-0.823734\pi$
$937$	−10.6626	−	42.5676i	−0.348333	−	1.39062i	0.502223	−	0.864738i	$-0.332516\pi$
$938$	1.91729	+	2.03927i	0.0626016	+	0.0665845i
$939$	−45.6113	−	1.11969i	−1.48847	−	0.0365398i
$940$	−7.28341	+	15.8897i	−0.237559	+	0.518263i
$941$	4.94025	−	9.81460i	0.161048	−	0.319947i	−0.798258	−	0.602315i	$-0.794245\pi$
$941$	4.94025	−	9.81460i	0.161048	−	0.319947i	0.959306	+	0.282368i	$0.0911201\pi$
$942$	−47.9394	−	29.1443i	−1.56195	−	0.949573i
$943$	−16.2382	+	1.59933i	−0.528790	+	0.0520812i
$944$	−6.32477	+	42.4731i	−0.205854	+	1.38238i
$945$	0.0633242	−	0.642941i	0.00205994	−	0.0209149i
$946$	1.99115	+	14.0294i	0.0647380	+	0.456136i
$947$	6.20588	−	3.51559i	0.201664	−	0.114241i	−0.388745	−	0.921345i	$-0.627091\pi$
$947$	6.20588	−	3.51559i	0.201664	−	0.114241i	0.590409	+	0.807104i	$0.298966\pi$
$948$	−5.32973	−	0.460482i	−0.173102	−	0.0149558i
$949$	−7.97340	−	12.5914i	−0.258828	−	0.408733i
$950$	−12.6946	−	25.6189i	−0.411866	−	0.831187i
$951$	−6.17370	−	13.0532i	−0.200196	−	0.423279i
$952$	2.59249	+	2.44017i	0.0840231	+	0.0790864i
$953$	−16.1233	−	17.7893i	−0.522285	−	0.576253i	0.421494	−	0.906831i	$-0.361506\pi$
$953$	−16.1233	−	17.7893i	−0.522285	−	0.576253i	−0.943778	+	0.330579i	$0.892756\pi$
$954$	−18.9666	−	3.41379i	−0.614066	−	0.110525i
$955$	10.1937	+	13.0621i	0.329861	+	0.422678i
$956$	−39.1211	−	12.4056i	−1.26527	−	0.401227i
$957$	30.7074	−	79.6059i	0.992629	−	2.57329i
$958$	−0.652233	+	0.962994i	−0.0210727	+	0.0311129i
$959$	−12.9439	−	31.2493i	−0.417980	−	1.00909i
$960$	−25.0082	+	6.56879i	−0.807135	+	0.212007i
$961$	−18.4925	+	44.6448i	−0.596532	+	1.44016i
$962$	3.45792	+	5.24612i	0.111488	+	0.169142i
$963$	9.46320	+	21.3486i	0.304947	+	0.687950i
$964$	−4.97514	−	17.1741i	−0.160238	−	0.553139i
$965$	−4.39564	+	35.6389i	−0.141501	+	1.14726i
$966$	−11.7047	+	2.55132i	−0.376593	+	0.0820873i
$967$	31.7920	+	1.56184i	1.02236	+	0.0502254i	0.553335	−	0.832959i	$-0.313355\pi$
$967$	31.7920	+	1.56184i	1.02236	+	0.0502254i	0.469027	+	0.883184i	$0.344605\pi$
$968$	−14.5708	−	43.2747i	−0.468323	−	1.39090i
$969$	−3.07126	+	8.58359i	−0.0986630	+	0.275744i
$970$	1.58039	+	23.4284i	0.0507434	+	0.752242i
$971$	48.1606	+	10.8148i	1.54555	+	0.347065i	0.906535	−	0.422131i	$-0.138718\pi$
$971$	48.1606	+	10.8148i	1.54555	+	0.347065i	0.639014	+	0.769195i	$0.279343\pi$
$972$	−4.88085	−	44.1257i	−0.156553	−	1.41533i
$973$	26.2662	+	7.26883i	0.842055	+	0.233028i
$974$	−15.1482	+	8.95071i	−0.485379	+	0.286799i
$975$	25.0527	+	30.5268i	0.802330	+	0.977641i
$976$	−17.8870	−	43.2519i	−0.572548	−	1.38446i
$977$	22.1531	+	18.1806i	0.708740	+	0.581648i	0.918175	−	0.396175i	$-0.129662\pi$
$977$	22.1531	+	18.1806i	0.708740	+	0.581648i	−0.209435	+	0.977823i	$0.567162\pi$
$978$	−21.0735	+	15.4251i	−0.673856	+	0.493240i
$979$	−0.548865	−	1.66144i	−0.0175418	−	0.0530998i
$980$	−3.99212	+	5.51985i	−0.127523	+	0.176325i
$981$	21.6144	+	22.7024i	0.690096	+	0.724831i
$982$	20.0773	+	9.05087i	0.640693	+	0.288825i
$983$	−36.1028	−	21.6392i	−1.15150	−	0.690183i	−0.194681	−	0.980867i	$-0.562367\pi$
$983$	−36.1028	−	21.6392i	−1.15150	−	0.690183i	−0.956819	+	0.290684i	$0.906117\pi$
$984$	−35.4626	+	59.9397i	−1.13051	+	1.91081i
$985$	1.37274	+	9.25430i	0.0437393	+	0.294866i
$986$	0.449443	−	5.61253i	0.0143132	−	0.178739i
$987$	15.5413	+	30.8753i	0.494685	+	0.982771i
$988$	2.18758	+	59.8518i	0.0695962	+	1.90414i
$989$	−3.10005	−	0.537910i	−0.0985758	−	0.0171045i
$990$	−8.84602	+	28.5158i	−0.281145	+	0.906292i
$991$	−8.23580	+	12.3257i	−0.261619	+	0.391540i	−0.938903	−	0.344181i	$-0.888157\pi$
$991$	−8.23580	+	12.3257i	−0.261619	+	0.391540i	0.677285	+	0.735721i	$0.263157\pi$
$992$	26.6624	+	42.7488i	0.846533	+	1.35727i
$993$	−21.7572	−	32.5620i	−0.690445	−	1.03332i
$994$	−39.9025	+	11.8313i	−1.26563	+	0.375266i
$995$	−12.8154	+	2.87780i	−0.406276	+	0.0912324i
$996$	51.1711	+	24.9930i	1.62142	+	0.791932i
$997$	−0.948632	−	12.8603i	−0.0300435	−	0.407289i	−0.991299	−	0.131630i	$-0.957979\pi$
$997$	−0.948632	−	12.8603i	−0.0300435	−	0.407289i	0.961255	−	0.275659i	$-0.0888961\pi$
$998$	−23.0389	+	2.69488i	−0.729284	+	0.0853049i
$999$	−0.184230	+	0.110423i	−0.00582878	+	0.00349364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.117.1	✓	4032
512.477	even	128	inner	512.2.o.a.477.1	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.117.1	✓	4032	1.1	even	1	trivial
512.2.o.a.477.1	yes	4032	512.477	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41419 - 0.00887673i) q^{2} +(0.0605891 + 2.46813i) q^{3} +(1.99984 + 0.0251067i) q^{4} +(0.349161 + 1.26170i) q^{5} +(-0.0637753 - 3.49093i) q^{6} +(0.896663 - 1.89584i) q^{7} +(-2.82793 - 0.0532576i) q^{8} +(-3.09158 + 0.151880i) q^{9} +O(q^{10})\)	\(q+(-1.41419 - 0.00887673i) q^{2} +(0.0605891 + 2.46813i) q^{3} +(1.99984 + 0.0251067i) q^{4} +(0.349161 + 1.26170i) q^{5} +(-0.0637753 - 3.49093i) q^{6} +(0.896663 - 1.89584i) q^{7} +(-2.82793 - 0.0532576i) q^{8} +(-3.09158 + 0.151880i) q^{9} +(-0.482578 - 1.78738i) q^{10} +(4.25960 + 2.99995i) q^{11} +(0.0592021 + 4.93738i) q^{12} +(4.83089 - 0.595834i) q^{13} +(-1.28488 + 2.67310i) q^{14} +(-3.09289 + 0.938218i) q^{15} +(3.99874 + 0.100419i) q^{16} +(0.174230 - 0.574360i) q^{17} +(4.37342 - 0.187343i) q^{18} +(-0.452585 + 6.13554i) q^{19} +(0.666589 + 2.53198i) q^{20} +(4.73349 + 2.09821i) q^{21} +(-5.99724 - 4.28030i) q^{22} +(1.31407 - 0.974580i) q^{23} +(-0.0398950 - 6.98290i) q^{24} +(2.81866 - 1.68944i) q^{25} +(-6.83707 + 0.799737i) q^{26} +(-0.0173108 - 0.234677i) q^{27} +(1.84078 - 3.76886i) q^{28} +(-6.47217 + 1.45337i) q^{29} +(4.38225 - 1.29936i) q^{30} +(-4.94811 - 7.40537i) q^{31} +(-5.65407 - 0.177507i) q^{32} +(-7.14617 + 10.6950i) q^{33} +(-0.251492 + 0.810705i) q^{34} +(2.70506 + 0.469373i) q^{35} +(-6.18649 + 0.226116i) q^{36} +(-0.410392 - 0.815310i) q^{37} +(0.694502 - 8.67277i) q^{38} +(1.76329 + 11.8872i) q^{39} +(-0.920205 - 3.58660i) q^{40} +(-8.55449 - 5.12737i) q^{41} +(-6.67540 - 3.00928i) q^{42} +(-1.32611 - 1.39286i) q^{43} +(8.44322 + 6.10637i) q^{44} +(-1.27109 - 3.84764i) q^{45} +(-1.86699 + 1.36657i) q^{46} +(5.16060 + 4.23520i) q^{47} +(-0.00556638 + 9.87547i) q^{48} +(1.65057 + 2.01122i) q^{49} +(-4.00110 + 2.36416i) q^{50} +(1.42815 + 0.395222i) q^{51} +(9.67599 - 1.07029i) q^{52} +(-4.29546 - 0.964579i) q^{53} +(0.0223975 + 0.332030i) q^{54} +(-2.29777 + 6.42182i) q^{55} +(-2.63666 + 5.31353i) q^{56} +(-15.1707 - 0.745289i) q^{57} +(9.16575 - 1.99789i) q^{58} +(-1.31412 + 10.6546i) q^{59} +(-6.20885 + 1.79864i) q^{60} +(-4.74179 - 10.6973i) q^{61} +(6.93181 + 10.5165i) q^{62} +(-2.48417 + 5.99732i) q^{63} +(7.99433 + 0.301217i) q^{64} +(2.43852 + 5.88712i) q^{65} +(10.2009 - 15.0613i) q^{66} +(0.339650 - 0.880511i) q^{67} +(0.362853 - 1.14425i) q^{68} +(2.48500 + 3.18424i) q^{69} +(-3.82130 - 0.687793i) q^{70} +(9.42388 + 10.3976i) q^{71} +(8.75086 - 0.264854i) q^{72} +(-1.30912 - 2.76789i) q^{73} +(0.573134 + 1.15664i) q^{74} +(4.34053 + 6.85444i) q^{75} +(-1.05914 + 12.2587i) q^{76} +(9.50684 - 5.38556i) q^{77} +(-2.38810 - 16.8263i) q^{78} +(-0.106193 + 1.07819i) q^{79} +(1.26950 + 5.08029i) q^{80} +(-8.66306 + 0.853237i) q^{81} +(12.0521 + 7.32698i) q^{82} +(5.18551 - 10.3018i) q^{83} +(9.41355 + 4.31493i) q^{84} +(0.785506 + 0.0192831i) q^{85} +(1.86300 + 1.98153i) q^{86} +(-3.97925 - 15.8861i) q^{87} +(-11.8861 - 8.71049i) q^{88} +(-0.269754 - 0.200063i) q^{89} +(1.76340 + 5.45255i) q^{90} +(3.20208 - 9.69284i) q^{91} +(2.65240 - 1.91602i) q^{92} +(17.9776 - 12.6612i) q^{93} +(-7.26045 - 6.03516i) q^{94} +(-7.89926 + 1.57126i) q^{95} +(0.0955338 - 13.9657i) q^{96} +(-12.4396 - 2.47439i) q^{97} +(-2.31635 - 2.85889i) q^{98} +(-13.6246 - 8.62765i) 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

Modular forms

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