LMFDB - Embedded newform 403.2.bi.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(14,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("403.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bi (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$15$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	403.14
Dual form			403.2.bi.a.144.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269588 + 0.829708i) q^{2} +(-1.42637 + 1.58415i) q^{3} +(1.00230 + 0.728211i) q^{4} +(-1.58260 + 2.74115i) q^{5} +(-0.929847 - 1.61054i) q^{6} +(-0.112042 + 1.06601i) q^{7} +(-2.28599 + 1.66087i) q^{8} +(-0.161400 - 1.53561i) q^{9} +O(q^{10})$	\(q+(-0.269588 + 0.829708i) q^{2} +(-1.42637 + 1.58415i) q^{3} +(1.00230 + 0.728211i) q^{4} +(-1.58260 + 2.74115i) q^{5} +(-0.929847 - 1.61054i) q^{6} +(-0.112042 + 1.06601i) q^{7} +(-2.28599 + 1.66087i) q^{8} +(-0.161400 - 1.53561i) q^{9} +(-1.84770 - 2.05208i) q^{10} +(1.69493 - 0.754634i) q^{11} +(-2.58325 + 0.549086i) q^{12} +(0.978148 + 0.207912i) q^{13} +(-0.854269 - 0.380345i) q^{14} +(-2.08500 - 6.41698i) q^{15} +(0.00392645 + 0.0120844i) q^{16} +(-0.811527 - 0.361315i) q^{17} +(1.31762 + 0.280069i) q^{18} +(6.31064 - 1.34137i) q^{19} +(-3.58237 + 1.59498i) q^{20} +(-1.52890 - 1.69802i) q^{21} +(0.169191 + 1.60974i) q^{22} +(0.589241 - 0.428109i) q^{23} +(0.629614 - 5.99038i) q^{24} +(-2.50926 - 4.34617i) q^{25} +(-0.436203 + 0.755526i) q^{26} +(-2.51085 - 1.82424i) q^{27} +(-0.888578 + 0.986866i) q^{28} +(0.514119 - 1.58229i) q^{29} +5.88631 q^{30} +(4.68437 + 3.00943i) q^{31} -5.66237 q^{32} +(-1.22216 + 3.76142i) q^{33} +(0.518564 - 0.575924i) q^{34} +(-2.74477 - 1.99419i) q^{35} +(0.956482 - 1.65667i) q^{36} +(-1.45797 - 2.52528i) q^{37} +(-0.588332 + 5.59761i) q^{38} +(-1.72457 + 1.25297i) q^{39} +(-0.934875 - 8.89474i) q^{40} +(-1.67005 - 1.85478i) q^{41} +(1.82103 - 0.810775i) q^{42} +(-6.58097 + 1.39883i) q^{43} +(2.24836 + 0.477904i) q^{44} +(4.46478 + 1.98785i) q^{45} +(0.196353 + 0.604311i) q^{46} +(1.47087 + 4.52686i) q^{47} +(-0.0247440 - 0.0110167i) q^{48} +(5.72322 + 1.21651i) q^{49} +(4.28252 - 0.910277i) q^{50} +(1.72992 - 0.770209i) q^{51} +(0.828991 + 0.920688i) q^{52} +(-1.07760 - 10.2527i) q^{53} +(2.19048 - 1.59147i) q^{54} +(-0.613846 + 5.84035i) q^{55} +(-1.51437 - 2.62297i) q^{56} +(-6.87641 + 11.9103i) q^{57} +(1.17424 + 0.853136i) q^{58} +(-10.1677 + 11.2924i) q^{59} +(2.58313 - 7.95005i) q^{60} +5.40875 q^{61} +(-3.75980 + 3.07535i) q^{62} +1.65506 q^{63} +(1.51866 - 4.67394i) q^{64} +(-2.11794 + 2.35221i) q^{65} +(-2.79140 - 2.02807i) q^{66} +(-0.807775 + 1.39911i) q^{67} +(-0.550277 - 0.953108i) q^{68} +(-0.162290 + 1.54409i) q^{69} +(2.39455 - 1.73974i) q^{70} +(1.09555 + 10.4235i) q^{71} +(2.91942 + 3.24234i) q^{72} +(6.92631 - 3.08379i) q^{73} +(2.48829 - 0.528903i) q^{74} +(10.4641 + 2.22422i) q^{75} +(7.30194 + 3.25103i) q^{76} +(0.614541 + 1.89136i) q^{77} +(-0.574677 - 1.76867i) q^{78} +(-9.71336 - 4.32467i) q^{79} +(-0.0393390 - 0.00836177i) q^{80} +(11.0023 - 2.33860i) q^{81} +(1.98915 - 0.885625i) q^{82} +(5.75391 + 6.39036i) q^{83} +(-0.295898 - 2.81528i) q^{84} +(2.27474 - 1.65270i) q^{85} +(0.613535 - 5.83739i) q^{86} +(1.77326 + 3.07138i) q^{87} +(-2.62126 + 4.54016i) q^{88} +(12.1735 + 8.84456i) q^{89} +(-2.85298 + 3.16856i) q^{90} +(-0.331229 + 1.01942i) q^{91} +0.902348 q^{92} +(-11.4491 + 3.12816i) q^{93} -4.15250 q^{94} +(-6.31035 + 19.4213i) q^{95} +(8.07666 - 8.97004i) q^{96} +(3.42130 + 2.48572i) q^{97} +(-2.55226 + 4.42064i) q^{98} +(-1.43239 - 2.48097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 13 q^{5} - 10 q^{6} - 16 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) $ 120 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 13 * q^5 - 10 * q^6 - 16 * q^7 - 6 * q^8 + 13 * q^9	\( 120 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 13 q^{5} - 10 q^{6} - 16 q^{7} - 6 q^{8} + 13 q^{9} + 3 q^{10} + 3 q^{11} - 12 q^{12} - 15 q^{13} - 3 q^{14} - 39 q^{15} - 2 q^{16} + 6 q^{17} - 34 q^{18} - 25 q^{19} - 10 q^{20} + 40 q^{21} + 18 q^{22} + q^{23} + 46 q^{24} - 45 q^{25} - 12 q^{26} + 26 q^{27} - 13 q^{28} + 14 q^{29} - 28 q^{30} - 14 q^{31} - 76 q^{32} + 63 q^{33} + 36 q^{34} + 50 q^{35} - 42 q^{36} + 14 q^{37} + 44 q^{38} - 6 q^{39} + 27 q^{40} - 17 q^{41} - 159 q^{42} - 15 q^{43} + 70 q^{44} + 40 q^{45} - 62 q^{46} + 9 q^{47} + 19 q^{48} - 151 q^{49} - 22 q^{50} - 25 q^{51} - q^{52} - 69 q^{53} + 51 q^{54} + 27 q^{55} + 51 q^{56} - 28 q^{57} + 156 q^{58} - 27 q^{59} + 87 q^{60} - 28 q^{61} - 25 q^{62} - 88 q^{63} + 10 q^{64} + 7 q^{65} + 30 q^{66} + 61 q^{67} + 124 q^{68} + 3 q^{69} - 263 q^{70} + 31 q^{71} + 31 q^{72} - 50 q^{73} - 90 q^{74} + 78 q^{75} + 66 q^{76} - 38 q^{77} + 31 q^{79} - 145 q^{80} + 36 q^{81} + 3 q^{82} + 23 q^{83} - 228 q^{84} - 58 q^{85} - 12 q^{86} + 68 q^{87} + 28 q^{88} + 39 q^{89} - 7 q^{90} - 12 q^{91} - 32 q^{92} - 17 q^{93} + 14 q^{94} + 123 q^{95} + 165 q^{96} - 51 q^{97} + 45 q^{98} - 45 q^{99}+O(q^{100}) \) 120 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 13 * q^5 - 10 * q^6 - 16 * q^7 - 6 * q^8 + 13 * q^9 + 3 * q^10 + 3 * q^11 - 12 * q^12 - 15 * q^13 - 3 * q^14 - 39 * q^15 - 2 * q^16 + 6 * q^17 - 34 * q^18 - 25 * q^19 - 10 * q^20 + 40 * q^21 + 18 * q^22 + q^23 + 46 * q^24 - 45 * q^25 - 12 * q^26 + 26 * q^27 - 13 * q^28 + 14 * q^29 - 28 * q^30 - 14 * q^31 - 76 * q^32 + 63 * q^33 + 36 * q^34 + 50 * q^35 - 42 * q^36 + 14 * q^37 + 44 * q^38 - 6 * q^39 + 27 * q^40 - 17 * q^41 - 159 * q^42 - 15 * q^43 + 70 * q^44 + 40 * q^45 - 62 * q^46 + 9 * q^47 + 19 * q^48 - 151 * q^49 - 22 * q^50 - 25 * q^51 - q^52 - 69 * q^53 + 51 * q^54 + 27 * q^55 + 51 * q^56 - 28 * q^57 + 156 * q^58 - 27 * q^59 + 87 * q^60 - 28 * q^61 - 25 * q^62 - 88 * q^63 + 10 * q^64 + 7 * q^65 + 30 * q^66 + 61 * q^67 + 124 * q^68 + 3 * q^69 - 263 * q^70 + 31 * q^71 + 31 * q^72 - 50 * q^73 - 90 * q^74 + 78 * q^75 + 66 * q^76 - 38 * q^77 + 31 * q^79 - 145 * q^80 + 36 * q^81 + 3 * q^82 + 23 * q^83 - 228 * q^84 - 58 * q^85 - 12 * q^86 + 68 * q^87 + 28 * q^88 + 39 * q^89 - 7 * q^90 - 12 * q^91 - 32 * q^92 - 17 * q^93 + 14 * q^94 + 123 * q^95 + 165 * q^96 - 51 * q^97 + 45 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.269588	+	0.829708i	−0.190628	+	0.586692i	−1.00000		0.000604337i	$-0.999808\pi$
$2$	−0.269588	+	0.829708i	−0.190628	+	0.586692i	0.809372	+	0.587296i	$0.199808\pi$
$3$	−1.42637	+	1.58415i	−0.823518	+	0.914609i	−0.997538	−	0.0701331i	$-0.977658\pi$
$3$	−1.42637	+	1.58415i	−0.823518	+	0.914609i	0.174020	+	0.984742i	$0.444324\pi$
$4$	1.00230	+	0.728211i	0.501149	+	0.364106i
$5$	−1.58260	+	2.74115i	−0.707761	+	1.22588i	0.257924	+	0.966165i	$0.416961\pi$
$5$	−1.58260	+	2.74115i	−0.707761	+	1.22588i	−0.965686	+	0.259713i	$0.916372\pi$
$6$	−0.929847	−	1.61054i	−0.379608	−	0.657501i
$7$	−0.112042	+	1.06601i	−0.0423478	+	0.402913i	0.952730	+	0.303818i	$0.0982614\pi$
$7$	−0.112042	+	1.06601i	−0.0423478	+	0.402913i	−0.995078	+	0.0990950i	$0.968405\pi$
$8$	−2.28599	+	1.66087i	−0.808221	+	0.587207i
$9$	−0.161400	−	1.53561i	−0.0537999	−	0.511871i
$10$	−1.84770	−	2.05208i	−0.584294	−	0.648924i
$11$	1.69493	−	0.754634i	0.511042	−	0.227531i	−0.134981	−	0.990848i	$-0.543097\pi$
$11$	1.69493	−	0.754634i	0.511042	−	0.227531i	0.646023	+	0.763318i	$0.276431\pi$
$12$	−2.58325	+	0.549086i	−0.745719	+	0.158507i
$13$	0.978148	+	0.207912i	0.271289	+	0.0576643i
$13$	0.978148	+	0.207912i	0.271289	+	0.0576643i
$14$	−0.854269	−	0.380345i	−0.228313	−	0.101652i
$15$	−2.08500	−	6.41698i	−0.538346	−	1.65686i
$16$	0.00392645	+	0.0120844i	0.000981612	+	0.00302109i
$17$	−0.811527	−	0.361315i	−0.196824	−	0.0876318i	0.305958	−	0.952045i	$-0.401023\pi$
$17$	−0.811527	−	0.361315i	−0.196824	−	0.0876318i	−0.502782	+	0.864413i	$0.667690\pi$
$18$	1.31762	+	0.280069i	0.310567	+	0.0660130i
$19$	6.31064	−	1.34137i	1.44776	−	0.307731i	0.584050	−	0.811718i	$-0.301467\pi$
$19$	6.31064	−	1.34137i	1.44776	−	0.307731i	0.863711	+	0.503987i	$0.168134\pi$
$20$	−3.58237	+	1.59498i	−0.801043	+	0.356647i
$21$	−1.52890	−	1.69802i	−0.333634	−	0.370538i
$22$	0.169191	+	1.60974i	0.0360716	+	0.343198i
$23$	0.589241	−	0.428109i	0.122865	−	0.0892668i	−0.524656	−	0.851315i	$-0.675806\pi$
$23$	0.589241	−	0.428109i	0.122865	−	0.0892668i	0.647521	+	0.762048i	$0.275806\pi$
$24$	0.629614	−	5.99038i	0.128519	−	1.22278i
$25$	−2.50926	−	4.34617i	−0.501852	−	0.869234i
$26$	−0.436203	+	0.755526i	−0.0855465	+	0.148171i
$27$	−2.51085	−	1.82424i	−0.483212	−	0.351074i
$28$	−0.888578	+	0.986866i	−0.167925	+	0.186500i
$29$	0.514119	−	1.58229i	0.0954694	−	0.293825i	−0.891906	−	0.452220i	$-0.850632\pi$
$29$	0.514119	−	1.58229i	0.0954694	−	0.293825i	0.987376	+	0.158396i	$0.0506321\pi$
$30$	5.88631			1.07469
$31$	4.68437	+	3.00943i	0.841338	+	0.540510i
$31$	4.68437	+	3.00943i	0.841338	+	0.540510i
$32$	−5.66237			−1.00098
$33$	−1.22216	+	3.76142i	−0.212751	+	0.654779i
$34$	0.518564	−	0.575924i	0.0889330	−	0.0987701i
$35$	−2.74477	−	1.99419i	−0.463950	−	0.337079i
$36$	0.956482	−	1.65667i	0.159414	−	0.276112i
$37$	−1.45797	−	2.52528i	−0.239689	−	0.415153i	0.720936	−	0.693001i	$-0.243712\pi$
$37$	−1.45797	−	2.52528i	−0.239689	−	0.415153i	−0.960625	+	0.277849i	$0.910379\pi$
$38$	−0.588332	+	5.59761i	−0.0954401	+	0.908052i
$39$	−1.72457	+	1.25297i	−0.276152	+	0.200636i
$40$	−0.934875	−	8.89474i	−0.147817	−	1.40638i
$41$	−1.67005	−	1.85478i	−0.260818	−	0.289667i	0.598486	−	0.801133i	$-0.295769\pi$
$41$	−1.67005	−	1.85478i	−0.260818	−	0.289667i	−0.859303	+	0.511466i	$0.829103\pi$
$42$	1.82103	−	0.810775i	0.280991	−	0.125105i
$43$	−6.58097	+	1.39883i	−1.00359	+	0.213319i	−0.680263	−	0.732968i	$-0.738134\pi$
$43$	−6.58097	+	1.39883i	−1.00359	+	0.213319i	−0.323326	+	0.946288i	$0.604801\pi$
$44$	2.24836	+	0.477904i	0.338953	+	0.0720467i
$45$	4.46478	+	1.98785i	0.665570	+	0.296331i
$46$	0.196353	+	0.604311i	0.0289506	+	0.0891008i
$47$	1.47087	+	4.52686i	0.214548	+	0.660311i	0.999185	+	0.0403558i	$0.0128491\pi$
$47$	1.47087	+	4.52686i	0.214548	+	0.660311i	−0.784637	+	0.619955i	$0.787151\pi$
$48$	−0.0247440	−	0.0110167i	−0.00357149	−	0.00159013i
$49$	5.72322	+	1.21651i	0.817602	+	0.173787i
$50$	4.28252	−	0.910277i	0.605639	−	0.128733i
$51$	1.72992	−	0.770209i	0.242237	−	0.107851i
$52$	0.828991	+	0.920688i	0.114960	+	0.127676i
$53$	−1.07760	−	10.2527i	−0.148020	−	1.40831i	−0.776319	−	0.630340i	$-0.782915\pi$
$53$	−1.07760	−	10.2527i	−0.148020	−	1.40831i	0.628300	−	0.777972i	$-0.283751\pi$
$54$	2.19048	−	1.59147i	0.298086	−	0.216572i
$55$	−0.613846	+	5.84035i	−0.0827709	+	0.787513i
$56$	−1.51437	−	2.62297i	−0.202367	−	0.350509i
$57$	−6.87641	+	11.9103i	−0.910803	+	1.57756i
$58$	1.17424	+	0.853136i	0.154185	+	0.112022i
$59$	−10.1677	+	11.2924i	−1.32373	+	1.47015i	−0.552634	+	0.833424i	$0.686377\pi$
$59$	−10.1677	+	11.2924i	−1.32373	+	1.47015i	−0.771092	+	0.636724i	$0.780289\pi$
$60$	2.58313	−	7.95005i	0.333480	−	1.02635i
$61$	5.40875			0.692519			0.346260	−	0.938139i	$-0.387452\pi$
$61$	5.40875			0.692519			0.346260	+	0.938139i	$0.387452\pi$
$62$	−3.75980	+	3.07535i	−0.477495	+	0.390570i
$63$	1.65506			0.208518
$64$	1.51866	−	4.67394i	0.189832	−	0.584243i
$65$	−2.11794	+	2.35221i	−0.262698	+	0.291755i
$66$	−2.79140	−	2.02807i	−0.343597	−	0.249638i
$67$	−0.807775	+	1.39911i	−0.0986854	+	0.170928i	−0.911141	−	0.412095i	$-0.864797\pi$
$67$	−0.807775	+	1.39911i	−0.0986854	+	0.170928i	0.812455	+	0.583023i	$0.198130\pi$
$68$	−0.550277	−	0.953108i	−0.0667309	−	0.115581i
$69$	−0.162290	+	1.54409i	−0.0195375	+	0.185887i
$70$	2.39455	−	1.73974i	0.286204	−	0.207939i
$71$	1.09555	+	10.4235i	0.130018	+	1.23704i	0.843794	+	0.536667i	$0.180317\pi$
$71$	1.09555	+	10.4235i	0.130018	+	1.23704i	−0.713776	+	0.700374i	$0.753017\pi$
$72$	2.91942	+	3.24234i	0.344056	+	0.382113i
$73$	6.92631	−	3.08379i	0.810663	−	0.360931i	0.0408223	−	0.999166i	$-0.487002\pi$
$73$	6.92631	−	3.08379i	0.810663	−	0.360931i	0.769841	+	0.638236i	$0.220336\pi$
$74$	2.48829	−	0.528903i	0.289258	−	0.0614837i
$75$	10.4641	+	2.22422i	1.20829	+	0.256831i
$76$	7.30194	+	3.25103i	0.837590	+	0.372919i
$77$	0.614541	+	1.89136i	0.0700335	+	0.215541i
$78$	−0.574677	−	1.76867i	−0.0650693	−	0.200263i
$79$	−9.71336	−	4.32467i	−1.09284	−	0.486563i	−0.220461	−	0.975396i	$-0.570756\pi$
$79$	−9.71336	−	4.32467i	−1.09284	−	0.486563i	−0.872377	+	0.488833i	$0.837423\pi$
$80$	−0.0393390	−	0.00836177i	−0.00439824	−	0.000934874i
$81$	11.0023	−	2.33860i	1.22247	−	0.259845i
$82$	1.98915	−	0.885625i	0.219665	−	0.0978009i
$83$	5.75391	+	6.39036i	0.631574	+	0.701433i	0.970968	−	0.239211i	$-0.0768887\pi$
$83$	5.75391	+	6.39036i	0.631574	+	0.701433i	−0.339394	+	0.940644i	$0.610222\pi$
$84$	−0.295898	−	2.81528i	−0.0322851	−	0.307172i
$85$	2.27474	−	1.65270i	0.246730	−	0.179260i
$86$	0.613535	−	5.83739i	0.0661591	−	0.629462i
$87$	1.77326	+	3.07138i	0.190114	+	0.329287i
$88$	−2.62126	+	4.54016i	−0.279427	+	0.483982i
$89$	12.1735	+	8.84456i	1.29039	+	0.937522i	0.999813	−	0.0193304i	$-0.00615343\pi$
$89$	12.1735	+	8.84456i	1.29039	+	0.937522i	0.290575	+	0.956852i	$0.406153\pi$
$90$	−2.85298	+	3.16856i	−0.300731	+	0.333995i
$91$	−0.331229	+	1.01942i	−0.0347222	+	0.106864i
$92$	0.902348			0.0940763
$93$	−11.4491	+	3.12816i	−1.18721	+	0.324375i
$94$	−4.15250			−0.428298
$95$	−6.31035	+	19.4213i	−0.647428	+	1.99258i
$96$	8.07666	−	8.97004i	0.824321	−	0.915501i
$97$	3.42130	+	2.48572i	0.347380	+	0.252386i	0.747769	−	0.663959i	$-0.231125\pi$
$97$	3.42130	+	2.48572i	0.347380	+	0.252386i	−0.400389	+	0.916345i	$0.631125\pi$
$98$	−2.55226	+	4.42064i	−0.257817	+	0.446552i
$99$	−1.43239	−	2.48097i	−0.143960	−	0.249347i
$100$	0.649904	−	6.18342i	0.0649904	−	0.618342i
$101$	−5.79532	+	4.21055i	−0.576656	+	0.418965i	−0.837517	−	0.546411i	$-0.815994\pi$
$101$	−5.79532	+	4.21055i	−0.576656	+	0.418965i	0.260861	+	0.965376i	$0.415994\pi$
$102$	0.172683	+	1.64297i	0.0170981	+	0.162678i
$103$	1.42867	+	1.58670i	0.140771	+	0.156342i	0.809407	−	0.587247i	$-0.199788\pi$
$103$	1.42867	+	1.58670i	0.140771	+	0.156342i	−0.668637	+	0.743589i	$0.733122\pi$
$104$	−2.58135	+	1.14929i	−0.253123	+	0.112697i
$105$	7.07416	−	1.50366i	0.690367	−	0.146742i
$106$	8.79722	+	1.86991i	0.854462	+	0.181621i
$107$	−5.04002	−	2.24396i	−0.487237	−	0.216932i	0.148389	−	0.988929i	$-0.452591\pi$
$107$	−5.04002	−	2.24396i	−0.487237	−	0.216932i	−0.635626	+	0.771997i	$0.719258\pi$
$108$	−1.18818	−	3.65685i	−0.114333	−	0.351881i
$109$	−1.32501	−	4.07797i	−0.126913	−	0.390599i	0.867331	−	0.497731i	$-0.165833\pi$
$109$	−1.32501	−	4.07797i	−0.126913	−	0.390599i	−0.994245	+	0.107132i	$0.965833\pi$
$110$	−4.68030	−	2.08380i	−0.446249	−	0.198683i
$111$	6.08002	+	1.29235i	0.577090	+	0.122664i
$112$	−0.0133219	+	0.00283167i	−0.00125881	+	0.000267567i
$113$	10.6620	−	4.74705i	1.00300	−	0.446565i	0.161530	−	0.986868i	$-0.448357\pi$
$113$	10.6620	−	4.74705i	1.00300	−	0.446565i	0.841470	+	0.540303i	$0.181690\pi$
$114$	−8.02826	−	8.91629i	−0.751916	−	0.835087i
$115$	0.240975	+	2.29272i	0.0224710	+	0.213798i
$116$	1.66754	−	1.21154i	0.154828	−	0.112489i
$117$	0.161400	−	1.53561i	0.0149214	−	0.141968i
$118$	−6.62830	−	11.4806i	−0.610184	−	1.05687i
$119$	0.476089	−	0.824611i	0.0436430	−	0.0755920i
$120$	15.4241	+	11.2063i	1.40802	+	1.02299i
$121$	−5.05710	+	5.61648i	−0.459737	+	0.510589i
$122$	−1.45814	+	4.48768i	−0.132013	+	0.406295i
$123$	5.32035			0.479720
$124$	2.50363	+	6.42756i	0.224832	+	0.577212i
$125$	0.0586269			0.00524375
$126$	−0.446185	+	1.37322i	−0.0397493	+	0.122336i
$127$	−8.73343	+	9.69946i	−0.774967	+	0.860687i	−0.993345	−	0.115177i	$-0.963257\pi$
$127$	−8.73343	+	9.69946i	−0.774967	+	0.860687i	0.218379	+	0.975864i	$0.429923\pi$
$128$	−5.69331	−	4.13643i	−0.503223	−	0.365613i
$129$	7.17098	−	12.4205i	0.631369	−	1.09356i
$130$	−1.38067	−	2.39139i	−0.121093	−	0.209739i
$131$	1.63793	−	15.5839i	0.143107	−	1.36157i	−0.653433	−	0.756985i	$-0.726672\pi$
$131$	1.63793	−	15.5839i	0.143107	−	1.36157i	0.796539	−	0.604587i	$-0.206662\pi$
$132$	−3.96408	+	2.88007i	−0.345029	+	0.250678i
$133$	0.722852	+	6.87748i	0.0626793	+	0.596353i
$134$	−0.943084	−	1.04740i	−0.0814700	−	0.0904816i
$135$	8.97417	−	3.99556i	0.772374	−	0.343883i
$136$	2.45524	−	0.521878i	0.210535	−	0.0447507i
$137$	11.4381	+	2.43125i	0.977226	+	0.207716i	0.668726	−	0.743509i	$-0.266840\pi$
$137$	11.4381	+	2.43125i	0.977226	+	0.207716i	0.308500	+	0.951224i	$0.400173\pi$
$138$	−1.23739	−	0.550922i	−0.105334	−	0.0468976i
$139$	−0.132820	−	0.408776i	−0.0112656	−	0.0346720i	0.945266	−	0.326302i	$-0.105803\pi$
$139$	−0.132820	−	0.408776i	−0.0112656	−	0.0346720i	−0.956531	+	0.291630i	$0.905803\pi$
$140$	−1.29888	−	3.99754i	−0.109775	−	0.337854i
$141$	−9.26923	−	4.12693i	−0.780610	−	0.347550i
$142$	−8.94380	−	1.90106i	−0.750547	−	0.159534i
$143$	1.81479	−	0.385746i	0.151761	−	0.0322577i
$144$	0.0179232	−	0.00797992i	0.00149360	−	0.000664993i
$145$	3.52366	+	3.91342i	0.292624	+	0.324992i
$146$	0.691393	+	6.57817i	0.0572201	+	0.544413i
$147$	−10.0906	+	7.33123i	−0.832257	+	0.604670i
$148$	0.377617	−	3.59279i	0.0310399	−	0.295325i
$149$	−7.59654	−	13.1576i	−0.622333	−	1.07791i	−0.989050	−	0.147580i	$-0.952852\pi$
$149$	−7.59654	−	13.1576i	−0.622333	−	1.07791i	0.366717	−	0.930333i	$-0.380482\pi$
$150$	−4.66646	+	8.08254i	−0.381015	+	0.659937i
$151$	−15.2260	−	11.0623i	−1.23907	−	0.900240i	−0.241538	−	0.970391i	$-0.577652\pi$
$151$	−15.2260	−	11.0623i	−1.23907	−	0.900240i	−0.997536	+	0.0701514i	$0.977652\pi$
$152$	−12.1982	+	13.5475i	−0.989409	+	1.09885i
$153$	−0.423860	+	1.30451i	−0.0342671	+	0.105463i
$154$	−1.73495			−0.139806
$155$	−15.6628	+	8.07781i	−1.25807	+	0.648826i
$156$	−2.64096			−0.211446
$157$	−3.57010	+	10.9877i	−0.284925	+	0.876910i	0.701496	+	0.712674i	$0.252516\pi$
$157$	−3.57010	+	10.9877i	−0.284925	+	0.876910i	−0.986421	+	0.164236i	$0.947484\pi$
$158$	6.20682	−	6.89337i	0.493788	−	0.548407i
$159$	17.7788	+	12.9171i	1.40995	+	1.02439i
$160$	8.96128	−	15.5214i	0.708452	−	1.22707i
$161$	0.390347	+	0.676101i	0.0307637	+	0.0532843i
$162$	−1.02572	+	9.75912i	−0.0805886	+	0.766749i
$163$	15.3818	−	11.1755i	1.20479	−	0.875334i	0.210046	−	0.977692i	$-0.432639\pi$
$163$	15.3818	−	11.1755i	1.20479	−	0.875334i	0.994748	+	0.102358i	$0.0326387\pi$
$164$	−0.323215	−	3.07518i	−0.0252388	−	0.240132i
$165$	−8.37642	−	9.30295i	−0.652103	−	0.724234i
$166$	−6.85332	+	3.05129i	−0.531921	+	0.236826i
$167$	−11.5972	+	2.46507i	−0.897420	+	0.190753i	−0.633455	−	0.773780i	$-0.718364\pi$
$167$	−11.5972	+	2.46507i	−0.897420	+	0.190753i	−0.263965	+	0.964532i	$0.585030\pi$
$168$	6.31524	+	1.34235i	0.487232	+	0.103564i
$169$	0.913545	+	0.406737i	0.0702727	+	0.0312874i
$170$	0.758011	+	2.33292i	0.0581368	+	0.178927i
$171$	−3.07836	−	9.47422i	−0.235408	−	0.724512i
$172$	−7.61473	−	3.39030i	−0.580618	−	0.258508i
$173$	−5.67574	−	1.20642i	−0.431519	−	0.0917221i	−0.0129686	−	0.999916i	$-0.504128\pi$
$173$	−5.67574	−	1.20642i	−0.431519	−	0.0917221i	−0.418550	+	0.908194i	$0.637461\pi$
$174$	−3.02640	+	0.643282i	−0.229431	+	0.0487671i
$175$	4.91419	−	2.18794i	0.371478	−	0.165393i
$176$	0.0157743	+	0.0175192i	0.00118904	+	0.00132056i
$177$	−3.38587	−	32.2144i	−0.254498	−	2.42138i
$178$	−10.6202	+	7.71605i	−0.796020	+	0.578343i
$179$	0.981170	−	9.33521i	0.0733361	−	0.697747i	−0.894654	−	0.446759i	$-0.852578\pi$
$179$	0.981170	−	9.33521i	0.0733361	−	0.697747i	0.967990	−	0.250987i	$-0.0807553\pi$
$180$	3.02746	+	5.24372i	0.225654	+	0.390843i
$181$	6.84344	−	11.8532i	0.508669	−	0.881041i	−0.491280	−	0.871001i	$-0.663471\pi$
$181$	6.84344	−	11.8532i	0.508669	−	0.881041i	0.999950	−	0.0100395i	$-0.00319572\pi$
$182$	−0.756523	−	0.549646i	−0.0560772	−	0.0407425i
$183$	−7.71490	+	8.56826i	−0.570302	+	0.633384i
$184$	−0.635968	+	1.95731i	−0.0468842	+	0.144295i
$185$	9.22954			0.678569
$186$	0.491071	−	10.3427i	0.0360071	−	0.758362i
$187$	−1.64815			−0.120524
$188$	−1.82227	+	5.60836i	−0.132903	+	0.409032i
$189$	2.22597	−	2.47219i	0.161915	−	0.179825i
$190$	−14.4128	−	10.4715i	−1.04561	−	0.759682i
$191$	−0.685603	+	1.18750i	−0.0496085	+	0.0859244i	−0.889763	−	0.456422i	$-0.849131\pi$
$191$	−0.685603	+	1.18750i	−0.0496085	+	0.0859244i	0.840155	+	0.542347i	$0.182464\pi$
$192$	5.23805	+	9.07257i	0.378024	+	0.654756i
$193$	−0.637621	+	6.06656i	−0.0458970	+	0.436681i	0.947310	+	0.320319i	$0.103790\pi$
$193$	−0.637621	+	6.06656i	−0.0458970	+	0.436681i	−0.993207	+	0.116362i	$0.962877\pi$
$194$	−2.98476	+	2.16856i	−0.214293	+	0.155693i
$195$	−0.705276	−	6.71025i	−0.0505059	−	0.480531i
$196$	4.85049	+	5.38701i	0.346463	+	0.384787i
$197$	12.9102	−	5.74797i	0.919810	−	0.409526i	0.108470	−	0.994100i	$-0.465405\pi$
$197$	12.9102	−	5.74797i	0.919810	−	0.409526i	0.811341	+	0.584574i	$0.198738\pi$
$198$	2.44463	−	0.519623i	0.173733	−	0.0369280i
$199$	4.30767	+	0.915623i	0.305362	+	0.0649068i	0.358044	−	0.933705i	$-0.383444\pi$
$199$	4.30767	+	0.915623i	0.305362	+	0.0649068i	−0.0526820	+	0.998611i	$0.516777\pi$
$200$	12.9546	+	5.76775i	0.916027	+	0.407842i
$201$	−1.06421	−	3.27529i	−0.0750633	−	0.231021i
$202$	−1.93117	−	5.94354i	−0.135877	−	0.418186i
$203$	1.62913	+	0.725337i	0.114343	+	0.0509087i
$204$	2.29477	+	0.487768i	0.160666	+	0.0341506i
$205$	7.72724	−	1.64247i	0.539694	−	0.114715i
$206$	−1.70165	+	0.757622i	−0.118559	+	0.0527861i
$207$	−0.752513	−	0.835751i	−0.0523033	−	0.0580887i
$208$	0.00132816	+	0.0126366i	9.20916e−5	+	0.000876193i
$209$	9.68389	−	7.03576i	0.669849	−	0.486673i
$210$	−0.659513	+	6.27485i	−0.0455107	+	0.433006i
$211$	−3.66536	−	6.34858i	−0.252334	−	0.437055i	0.711834	−	0.702347i	$-0.247865\pi$
$211$	−3.66536	−	6.34858i	−0.252334	−	0.437055i	−0.964168	+	0.265293i	$0.914531\pi$
$212$	6.38603	−	11.0609i	0.438595	−	0.759668i
$213$	−18.0750	−	13.1323i	−1.23848	−	0.899809i
$214$	3.22056	−	3.57679i	0.220153	−	0.244505i
$215$	6.58067	−	20.2532i	0.448798	−	1.38126i
$216$	8.76960			0.596695
$217$	−3.73292	+	4.65639i	−0.253407	+	0.316096i
$218$	3.74073			0.253355
$219$	−4.99432	+	15.3709i	−0.337485	+	1.03867i
$220$	−4.86827	+	5.40676i	−0.328219	+	0.364524i
$221$	−0.718671	−	0.522145i	−0.0483431	−	0.0351233i
$222$	−2.71137	+	4.69624i	−0.181976	+	0.315191i
$223$	5.81814	+	10.0773i	0.389611	+	0.674826i	0.992397	−	0.123077i	$-0.0392761\pi$
$223$	5.81814	+	10.0773i	0.389611	+	0.674826i	−0.602786	+	0.797903i	$0.705943\pi$
$224$	0.634423	−	6.03613i	0.0423891	−	0.403306i
$225$	−6.26904	+	4.55473i	−0.417936	+	0.303648i
$226$	1.06430	+	10.1261i	0.0707961	+	0.673580i
$227$	19.5158	+	21.6745i	1.29531	+	1.43859i	0.834419	+	0.551131i	$0.185804\pi$
$227$	19.5158	+	21.6745i	1.29531	+	1.43859i	0.460892	+	0.887456i	$0.347530\pi$
$228$	−15.5654	+	6.93017i	−1.03085	+	0.458962i
$229$	−14.2400	+	3.02681i	−0.941006	+	0.200017i	−0.652782	−	0.757546i	$-0.726398\pi$
$229$	−14.2400	+	3.02681i	−0.941006	+	0.200017i	−0.288224	+	0.957563i	$0.593065\pi$
$230$	−1.96725	−	0.418153i	−0.129717	−	0.0275722i
$231$	−3.87277	−	1.72427i	−0.254809	−	0.113448i
$232$	1.45272	+	4.47100i	0.0953754	+	0.293535i
$233$	−6.54643	−	20.1478i	−0.428871	−	1.31993i	−0.899239	−	0.437458i	$-0.855879\pi$
$233$	−6.54643	−	20.1478i	−0.428871	−	1.31993i	0.470368	−	0.882470i	$-0.344121\pi$
$234$	1.23060	+	0.547898i	0.0804468	+	0.0358172i
$235$	−14.7366	−	3.13236i	−0.961310	−	0.204333i
$236$	−18.4144	+	3.91409i	−1.19867	+	0.254786i
$237$	20.7058	−	9.21882i	1.34499	−	0.598826i
$238$	0.555838	+	0.617321i	0.0360296	+	0.0400149i
$239$	1.68529	+	16.0344i	0.109012	+	1.03718i	0.903115	+	0.429399i	$0.141274\pi$
$239$	1.68529	+	16.0344i	0.109012	+	1.03718i	−0.794103	+	0.607783i	$0.792059\pi$
$240$	0.0693585	−	0.0503919i	0.00447707	−	0.00325278i
$241$	1.08367	−	10.3104i	0.0698051	−	0.664151i	−0.902541	−	0.430605i	$-0.858300\pi$
$241$	1.08367	−	10.3104i	0.0698051	−	0.664151i	0.972346	−	0.233546i	$-0.0750331\pi$
$242$	−3.29670	−	5.71006i	−0.211920	−	0.367056i
$243$	−7.33328	+	12.7016i	−0.470430	+	0.814809i
$244$	5.42117	+	3.93871i	0.347055	+	0.252150i
$245$	−12.3922	+	13.7629i	−0.791709	+	0.879282i
$246$	−1.43431	+	4.41434i	−0.0914480	+	0.281448i
$247$	6.45163			0.410507
$248$	−15.7067	+	0.900592i	−0.997377	+	0.0571876i
$249$	−18.3305			−1.16165
$250$	−0.0158051	+	0.0486432i	−0.000999605	+	0.00307647i
$251$	−7.48475	+	8.31266i	−0.472433	+	0.524690i	−0.931515	−	0.363704i	$-0.881512\pi$
$251$	−7.48475	+	8.31266i	−0.472433	+	0.524690i	0.459081	+	0.888394i	$0.348179\pi$
$252$	1.65886	+	1.20523i	0.104498	+	0.0759226i
$253$	0.675660	−	1.17028i	0.0424784	−	0.0735747i
$254$	−5.69328	−	9.86105i	−0.357228	−	0.618737i
$255$	−0.626515	+	5.96090i	−0.0392339	+	0.373286i
$256$	12.9187	−	9.38596i	0.807417	−	0.586623i
$257$	−1.07774	−	10.2540i	−0.0672275	−	0.639627i	−0.975311	−	0.220837i	$-0.929121\pi$
$257$	−1.07774	−	10.2540i	−0.0672275	−	0.639627i	0.908083	−	0.418790i	$-0.137546\pi$
$258$	8.37217	+	9.29824i	0.521228	+	0.578883i
$259$	2.85532	−	1.27127i	0.177421	−	0.0789928i
$260$	−3.83570	+	0.815304i	−0.237880	+	0.0505630i
$261$	−2.51277	−	0.534106i	−0.155537	−	0.0330603i
$262$	12.4885	+	5.56024i	0.771543	+	0.343513i
$263$	5.70832	+	17.5684i	0.351990	+	1.08331i	0.957734	+	0.287655i	$0.0928757\pi$
$263$	5.70832	+	17.5684i	0.351990	+	1.08331i	−0.605744	+	0.795660i	$0.707124\pi$
$264$	−3.45339	−	10.6284i	−0.212541	−	0.654135i
$265$	29.8095	+	13.2720i	1.83118	+	0.815295i
$266$	−5.90117	−	1.25433i	−0.361824	−	0.0769081i
$267$	−31.3751	+	6.66898i	−1.92012	+	0.408135i
$268$	−1.82848	+	0.814090i	−0.111692	+	0.0497285i
$269$	12.0554	+	13.3889i	0.735033	+	0.816337i	0.988534	−	0.150998i	$-0.0482487\pi$
$269$	12.0554	+	13.3889i	0.735033	+	0.816337i	−0.253501	+	0.967335i	$0.581582\pi$
$270$	0.895813	+	8.52309i	0.0545175	+	0.518699i
$271$	18.5648	−	13.4881i	1.12773	−	0.819346i	0.142370	−	0.989814i	$-0.454528\pi$
$271$	18.5648	−	13.4881i	1.12773	−	0.819346i	0.985363	+	0.170467i	$0.0545277\pi$
$272$	0.00117984	−	0.0112255i	7.15386e−5	−	0.000680644i
$273$	−1.14245	−	1.97879i	−0.0691444	−	0.119762i
$274$	−5.10081	+	8.83487i	−0.308151	+	0.533734i
$275$	−7.53280	−	5.47290i	−0.454245	−	0.330028i
$276$	−1.28709	+	1.42945i	−0.0774735	+	0.0860431i
$277$	−2.64103	+	8.12827i	−0.158684	+	0.488380i	−0.998516	−	0.0544674i	$-0.982654\pi$
$277$	−2.64103	+	8.12827i	−0.158684	+	0.488380i	0.839831	+	0.542848i	$0.182654\pi$
$278$	0.374972			0.0224893
$279$	3.86527	−	7.67911i	0.231408	−	0.459736i
$280$	9.58661			0.572909
$281$	3.04776	−	9.38003i	0.181814	−	0.559565i	−0.818065	−	0.575126i	$-0.804953\pi$
$281$	3.04776	−	9.38003i	0.181814	−	0.559565i	0.999879	+	0.0155602i	$0.00495316\pi$
$282$	5.92302	−	6.57818i	0.352711	−	0.391725i
$283$	−5.93499	−	4.31202i	−0.352799	−	0.256323i	0.397244	−	0.917713i	$-0.369967\pi$
$283$	−5.93499	−	4.31202i	−0.352799	−	0.256323i	−0.750042	+	0.661390i	$0.769967\pi$
$284$	−6.49243	+	11.2452i	−0.385255	+	0.667281i
$285$	−21.7653	−	37.6985i	−1.28926	−	2.23307i
$286$	−0.169191	+	1.60974i	−0.0100044	+	0.0951860i
$287$	2.16432	−	1.57247i	0.127756	−	0.0928200i
$288$	0.913904	+	8.69522i	0.0538523	+	0.512371i
$289$	−10.8472	−	12.0470i	−0.638070	−	0.708649i
$290$	−4.19693	+	1.86859i	−0.246452	+	0.109728i
$291$	−8.81780	+	1.87428i	−0.516909	+	0.109872i
$292$	9.18787	+	1.95294i	0.537680	+	0.114287i
$293$	−5.02593	−	2.23769i	−0.293618	−	0.130727i	0.254641	−	0.967036i	$-0.418043\pi$
$293$	−5.02593	−	2.23769i	−0.293618	−	0.130727i	−0.548259	+	0.836308i	$0.684709\pi$
$294$	−3.36248	−	10.3486i	−0.196104	−	0.603545i
$295$	−14.8627	−	45.7427i	−0.865340	−	2.66324i
$296$	7.52706	+	3.35126i	0.437502	+	0.194788i
$297$	−5.63235	−	1.19719i	−0.326822	−	0.0694682i
$298$	12.9649	−	2.75577i	0.751037	−	0.159638i
$299$	0.665374	−	0.296243i	0.0384796	−	0.0171322i
$300$	8.86846	+	9.84942i	0.512021	+	0.568657i
$301$	−0.753817	−	7.17209i	−0.0434493	−	0.413392i
$302$	13.2833	−	9.65085i	0.764365	−	0.555344i
$303$	1.59616	−	15.1865i	0.0916971	−	0.872440i
$304$	0.0409880	+	0.0709933i	0.00235082	+	0.00407174i
$305$	−8.55990	+	14.8262i	−0.490138	+	0.848945i
$306$	−0.968093	−	0.703361i	−0.0553422	−	0.0402084i
$307$	−9.46445	+	10.5113i	−0.540165	+	0.599914i	−0.950002	−	0.312245i	$-0.898919\pi$
$307$	−9.46445	+	10.5113i	−0.540165	+	0.599914i	0.409837	+	0.912159i	$0.365586\pi$
$308$	−0.761360	+	2.34322i	−0.0433825	+	0.133518i
$309$	−4.55138			−0.258919
$310$	−2.47972	−	15.1732i	−0.140838	−	0.861781i
$311$	1.85224			0.105031			0.0525153	−	0.998620i	$-0.483276\pi$
$311$	1.85224			0.105031			0.0525153	+	0.998620i	$0.483276\pi$
$312$	1.86133	−	5.72857i	0.105377	−	0.324316i
$313$	12.4727	−	13.8524i	0.705000	−	0.782982i	−0.279164	−	0.960244i	$-0.590057\pi$
$313$	12.4727	−	13.8524i	0.705000	−	0.782982i	0.984164	+	0.177262i	$0.0567239\pi$
$314$	−8.15408	−	5.92429i	−0.460161	−	0.334327i
$315$	−2.61930	+	4.53676i	−0.147581	+	0.255618i
$316$	−6.58640	−	11.4080i	−0.370514	−	0.641749i
$317$	−0.172114	+	1.63756i	−0.00966689	+	0.0919743i	−0.998292	−	0.0584295i	$-0.981391\pi$
$317$	−0.172114	+	1.63756i	−0.00966689	+	0.0919743i	0.988625	+	0.150404i	$0.0480574\pi$
$318$	−15.5103	+	11.2689i	−0.869777	+	0.631930i
$319$	−0.322655	−	3.06986i	−0.0180652	−	0.171879i
$320$	10.4085	+	11.5599i	0.581855	+	0.646216i
$321$	10.7437	−	4.78341i	0.599656	−	0.266984i
$322$	−0.666200	+	0.141605i	−0.0371259	+	0.00789134i
$323$	−5.60591	−	1.19157i	−0.311921	−	0.0663009i
$324$	12.7305	+	5.66800i	0.707252	+	0.314889i
$325$	−1.55081	−	4.77290i	−0.0860234	−	0.264753i
$326$	5.12566	+	15.7752i	0.283884	+	0.873705i
$327$	8.35009	+	3.71770i	0.461761	+	0.205589i
$328$	6.89826	+	1.46627i	0.380893	+	0.0809612i
$329$	−4.99047	+	1.06076i	−0.275133	+	0.0584814i
$330$	9.97691	−	4.44201i	0.549211	−	0.244525i
$331$	13.6992	+	15.2145i	0.752978	+	0.836267i	0.990841	−	0.135032i	$-0.0431137\pi$
$331$	13.6992	+	15.2145i	0.752978	+	0.836267i	−0.237863	+	0.971299i	$0.576447\pi$
$332$	1.11359	+	10.5951i	0.0611162	+	0.581482i
$333$	−3.64253	+	2.64646i	−0.199610	+	0.145025i
$334$	1.08119	−	10.2869i	0.0591602	−	0.562872i
$335$	−2.55677	−	4.42846i	−0.139691	−	0.241953i
$336$	0.0145163	−	0.0251430i	0.000791929	−	0.00137166i
$337$	9.48811	+	6.89352i	0.516851	+	0.375514i	0.815416	−	0.578875i	$-0.196508\pi$
$337$	9.48811	+	6.89352i	0.516851	+	0.375514i	−0.298566	+	0.954389i	$0.596508\pi$
$338$	−0.583754	+	0.648324i	−0.0317520	+	0.0352642i
$339$	−7.68803	+	23.6613i	−0.417557	+	1.28511i
$340$	3.48348			0.188918
$341$	10.2107	+	1.56581i	0.552941	+	0.0847933i
$342$	8.69072			0.469940
$343$	−4.25665	+	13.1006i	−0.229837	+	0.707367i
$344$	12.7208	−	14.1279i	0.685859	−	0.761723i
$345$	−3.97574	−	2.88854i	−0.214046	−	0.155514i
$346$	2.53109	−	4.38397i	0.136072	−	0.235684i
$347$	7.67169	+	13.2878i	0.411838	+	0.713324i	0.995091	−	0.0989666i	$-0.0315537\pi$
$347$	7.67169	+	13.2878i	0.411838	+	0.713324i	−0.583253	+	0.812291i	$0.698220\pi$
$348$	−0.459279	+	4.36975i	−0.0246200	+	0.234243i
$349$	−10.1014	+	7.33913i	−0.540718	+	0.392855i	−0.824352	−	0.566078i	$-0.808460\pi$
$349$	−10.1014	+	7.33913i	−0.540718	+	0.392855i	0.283634	+	0.958933i	$0.408460\pi$
$350$	0.490541	+	4.66718i	0.0262205	+	0.249471i
$351$	−2.07670	−	2.30641i	−0.110846	−	0.123107i
$352$	−9.59735	+	4.27302i	−0.511540	+	0.227752i
$353$	23.0469	−	4.89876i	1.22666	−	0.260735i	0.451368	−	0.892338i	$-0.350936\pi$
$353$	23.0469	−	4.89876i	1.22666	−	0.260735i	0.775292	+	0.631603i	$0.217603\pi$
$354$	27.6413	+	5.87535i	1.46912	+	0.312271i
$355$	−30.3061	−	13.4932i	−1.60848	−	0.716143i
$356$	5.76075	+	17.7298i	0.305319	+	0.939675i
$357$	0.627225	+	1.93040i	0.0331963	+	0.102168i
$358$	7.48099	+	3.33075i	0.395382	+	0.176036i
$359$	25.3915	+	5.39713i	1.34011	+	0.284850i	0.821524	−	0.570174i	$-0.193124\pi$
$359$	25.3915	+	5.39713i	1.34011	+	0.284850i	0.518589	+	0.855024i	$0.326458\pi$
$360$	−13.5080	+	2.87122i	−0.711935	+	0.151326i
$361$	20.6676	−	9.20181i	1.08777	−	0.484306i
$362$	7.98977	+	8.87354i	0.419933	+	0.466383i
$363$	−1.68402	−	16.0224i	−0.0883883	−	0.840959i
$364$	−1.07434	+	0.780555i	−0.0563108	+	0.0409122i
$365$	−2.50847	+	23.8665i	−0.131299	+	1.24923i
$366$	−5.02931	−	8.71102i	−0.262886	−	0.455332i
$367$	0.698137	−	1.20921i	0.0364424	−	0.0631201i	−0.847229	−	0.531228i	$-0.821731\pi$
$367$	0.698137	−	1.20921i	0.0364424	−	0.0631201i	0.883671	+	0.468108i	$0.155064\pi$
$368$	0.00748704	+	0.00543966i	0.000390289	+	0.000283562i
$369$	−2.57867	+	2.86391i	−0.134240	+	0.149089i
$370$	−2.48818	+	7.65782i	−0.129354	+	0.398111i
$371$	11.0501			0.573695
$372$	−13.7533	−	5.20198i	−0.713076	−	0.269710i
$373$	29.3341			1.51886			0.759431	−	0.650588i	$-0.225478\pi$
$373$	29.3341			1.51886			0.759431	+	0.650588i	$0.225478\pi$
$374$	0.444321	−	1.36748i	0.0229753	−	0.0707107i
$375$	−0.0836240	+	0.0928738i	−0.00431832	+	0.00479598i
$376$	−10.8809	−	7.90546i	−0.561141	−	0.407693i
$377$	0.831861	−	1.44083i	0.0428430	−	0.0742063i
$378$	1.45110	+	2.51338i	0.0746364	+	0.129274i
$379$	−1.88077	+	17.8944i	−0.0966089	+	0.919172i	0.833656	+	0.552284i	$0.186244\pi$
$379$	−1.88077	+	17.8944i	−0.0966089	+	0.919172i	−0.930265	+	0.366888i	$0.880423\pi$
$380$	−20.4676	+	14.8706i	−1.04997	+	0.762846i
$381$	−2.90825	−	27.6701i	−0.148994	−	1.41758i
$382$	−0.800447	−	0.888986i	−0.0409544	−	0.0454845i
$383$	2.18832	−	0.974304i	0.111818	−	0.0497846i	−0.350065	−	0.936725i	$-0.613841\pi$
$383$	2.18832	−	0.974304i	0.111818	−	0.0497846i	0.461883	+	0.886941i	$0.347174\pi$
$384$	14.6735	−	3.11895i	0.748805	−	0.159163i
$385$	−6.15708	−	1.30873i	−0.313794	−	0.0666990i
$386$	−4.86158	−	2.16451i	−0.247448	−	0.110171i
$387$	3.21023	+	9.88007i	0.163185	+	0.502232i
$388$	1.61903	+	4.98286i	0.0821937	+	0.252966i
$389$	10.4096	+	4.63467i	0.527789	+	0.234987i	0.653292	−	0.757106i	$-0.273388\pi$
$389$	10.4096	+	4.63467i	0.527789	+	0.234987i	−0.125502	+	0.992093i	$0.540054\pi$
$390$	5.75768	+	1.22383i	0.291552	+	0.0619712i
$391$	−0.632867	+	0.134520i	−0.0320055	+	0.00680297i
$392$	−15.1037	+	6.72460i	−0.762852	+	0.339643i
$393$	22.3509	+	24.8232i	1.12745	+	1.25216i
$394$	1.28871	+	12.2612i	0.0649242	+	0.617712i
$395$	27.2269	−	19.7815i	1.36994	−	0.995316i
$396$	0.370992	−	3.52975i	0.0186430	−	0.177377i
$397$	14.8724	+	25.7598i	0.746425	+	1.29285i	0.949526	+	0.313688i	$0.101565\pi$
$397$	14.8724	+	25.7598i	0.746425	+	1.29285i	−0.203101	+	0.979158i	$0.565102\pi$
$398$	−1.92100	+	3.32726i	−0.0962908	+	0.166781i
$399$	−11.9260	−	8.66476i	−0.597048	−	0.433780i
$400$	0.0426682	−	0.0473878i	0.00213341	−	0.00236939i
$401$	6.18170	−	19.0253i	0.308699	−	0.950079i	−0.669571	−	0.742748i	$-0.733522\pi$
$401$	6.18170	−	19.0253i	0.308699	−	0.950079i	0.978271	−	0.207331i	$-0.0664778\pi$
$402$	3.00443			0.149847
$403$	3.95631	+	3.91760i	0.197078	+	0.195150i
$404$	−8.87480			−0.441538
$405$	−11.0017	+	33.8599i	−0.546681	+	1.68251i
$406$	−1.04101	+	1.15616i	−0.0516646	+	0.0573794i
$407$	−4.37682	−	3.17995i	−0.216951	−	0.157624i
$408$	−2.67536	+	4.63386i	−0.132450	+	0.229410i
$409$	17.4005	+	30.1385i	0.860399	+	1.49026i	0.871544	+	0.490317i	$0.163119\pi$
$409$	17.4005	+	30.1385i	0.860399	+	1.49026i	−0.0111447	+	0.999938i	$0.503548\pi$
$410$	−0.720399	+	6.85414i	−0.0355780	+	0.338502i
$411$	−20.1665	+	14.6518i	−0.994741	+	0.722722i
$412$	0.276499	+	2.63072i	0.0136221	+	0.129606i
$413$	−10.8986	−	12.1041i	−0.536284	−	0.595604i
$414$	0.896297	−	0.399057i	0.0440506	−	0.0196126i
$415$	−26.6231	+	5.65891i	−1.30688	+	0.277785i
$416$	−5.53863	−	1.17727i	−0.271554	−	0.0577206i
$417$	0.837013	+	0.372662i	0.0409887	+	0.0182494i
$418$	3.22696	+	9.93155i	0.157836	+	0.485768i
$419$	11.7295	+	36.0996i	0.573022	+	1.76358i	0.642817	+	0.766020i	$0.277766\pi$
$419$	11.7295	+	36.0996i	0.573022	+	1.76358i	−0.0697947	+	0.997561i	$0.522234\pi$
$420$	8.18539	+	3.64437i	0.399406	+	0.177827i
$421$	−29.0551	−	6.17586i	−1.41606	−	0.300993i	−0.564580	−	0.825379i	$-0.690962\pi$
$421$	−29.0551	−	6.17586i	−1.41606	−	0.300993i	−0.851481	+	0.524386i	$0.824295\pi$
$422$	6.25561	−	1.32967i	0.304518	−	0.0647273i
$423$	6.71412	−	2.98932i	0.326452	−	0.145346i
$424$	19.4917	+	21.6478i	0.946602	+	1.05131i
$425$	0.465997	+	4.43367i	0.0226042	+	0.215064i
$426$	15.7688	−	11.4567i	0.763999	−	0.555078i
$427$	−0.606006	+	5.76576i	−0.0293267	+	0.279025i
$428$	−3.41752	−	5.91931i	−0.165192	−	0.286121i
$429$	−1.97750	+	3.42512i	−0.0954744	+	0.165366i
$430$	15.0302	+	10.9201i	0.724819	+	0.526612i
$431$	16.3861	−	18.1986i	0.789290	−	0.876595i	−0.205488	−	0.978660i	$-0.565878\pi$
$431$	16.3861	−	18.1986i	0.789290	−	0.876595i	0.994778	+	0.102064i	$0.0325448\pi$
$432$	0.0121860	−	0.0375047i	0.000586300	−	0.00180445i
$433$	10.3636			0.498041			0.249020	−	0.968498i	$-0.419891\pi$
$433$	10.3636			0.498041			0.249020	+	0.968498i	$0.419891\pi$
$434$	−2.85709	−	4.35254i	−0.137145	−	0.208929i
$435$	−11.2255			−0.538221
$436$	1.64157	−	5.05223i	0.0786169	−	0.241958i
$437$	3.14424	−	3.49203i	0.150409	−	0.167047i
$438$	−11.4070	−	8.28766i	−0.545047	−	0.396000i
$439$	9.29118	−	16.0928i	0.443444	−	0.768067i	−0.554499	−	0.832185i	$-0.687090\pi$
$439$	9.29118	−	16.0928i	0.443444	−	0.768067i	0.997942	+	0.0641176i	$0.0204233\pi$
$440$	−8.29683	−	14.3705i	−0.395536	−	0.685088i
$441$	0.944361	−	8.98500i	0.0449696	−	0.427857i
$442$	0.626973	−	0.455523i	0.0298221	−	0.0216670i
$443$	−2.24234	−	21.3344i	−0.106537	−	1.01363i	−0.908963	−	0.416877i	$-0.863125\pi$
$443$	−2.24234	−	21.3344i	−0.106537	−	1.01363i	0.802426	−	0.596751i	$-0.203542\pi$
$444$	5.15289	+	5.72286i	0.244545	+	0.271595i
$445$	−43.5101	+	19.3719i	−2.06257	+	0.918317i
$446$	−9.92972	+	2.11063i	−0.470186	+	0.0999411i
$447$	31.6791	+	6.73361i	1.49837	+	0.318489i
$448$	4.81230	+	2.14258i	0.227360	+	0.101227i
$449$	−5.31968	−	16.3723i	−0.251051	−	0.772657i	−0.994582	−	0.103955i	$-0.966850\pi$
$449$	−5.31968	−	16.3723i	−0.251051	−	0.772657i	0.743531	−	0.668702i	$-0.233150\pi$
$450$	−2.08903	−	6.42937i	−0.0984778	−	0.303084i
$451$	−4.23030	−	1.88345i	−0.199197	−	0.0886882i
$452$	14.1434	+	3.00627i	0.665249	+	0.141403i
$453$	39.2424	−	8.34122i	1.84377	−	0.391905i
$454$	−23.2447	+	10.3492i	−1.09093	+	0.485713i
$455$	−2.27017	−	2.52128i	−0.106427	−	0.118199i
$456$	−4.06204	−	38.6477i	−0.190222	−	1.80984i
$457$	25.0446	−	18.1960i	1.17154	−	0.851171i	0.180345	−	0.983604i	$-0.442279\pi$
$457$	25.0446	−	18.1960i	1.17154	−	0.851171i	0.991192	+	0.132432i	$0.0422787\pi$
$458$	1.32758	−	12.6310i	0.0620335	−	0.590209i
$459$	1.37849	+	2.38762i	0.0643426	+	0.111445i
$460$	−1.42806	+	2.47347i	−0.0665836	+	0.115326i
$461$	−2.61491	−	1.89984i	−0.121788	−	0.0884845i	0.525224	−	0.850964i	$-0.323982\pi$
$461$	−2.61491	−	1.89984i	−0.121788	−	0.0884845i	−0.647012	+	0.762480i	$0.723982\pi$
$462$	2.47469	−	2.74842i	0.115133	−	0.127868i
$463$	−12.9728	+	39.9262i	−0.602898	+	1.85553i	−0.0922543	+	0.995735i	$0.529407\pi$
$463$	−12.9728	+	39.9262i	−0.602898	+	1.85553i	−0.510643	+	0.859793i	$0.670593\pi$
$464$	0.0211397			0.000981385
$465$	9.54455	−	36.3342i	0.442618	−	1.68496i
$466$	18.4817			0.856146
$467$	−1.47949	+	4.55341i	−0.0684628	+	0.210707i	−0.979435	−	0.201762i	$-0.935333\pi$
$467$	−1.47949	+	4.55341i	−0.0684628	+	0.210707i	0.910972	+	0.412469i	$0.135333\pi$
$468$	1.28002	−	1.42161i	0.0591691	−	0.0657139i
$469$	−1.40095	−	1.01785i	−0.0646901	−	0.0470001i
$470$	6.57176	−	11.3826i	0.303133	−	0.525041i
$471$	−12.3138	−	21.3281i	−0.567389	−	0.982746i
$472$	4.48813	−	42.7017i	0.206583	−	1.96550i
$473$	−10.0987	+	7.33715i	−0.464339	+	0.337362i
$474$	2.06688	+	19.6650i	0.0949349	+	0.903245i
$475$	−21.6649	−	24.0613i	−0.994052	−	1.10401i
$476$	1.07767	−	0.479811i	0.0493951	−	0.0219921i
$477$	−15.5702	+	3.30955i	−0.712911	+	0.151534i
$478$	−13.7582	−	2.92440i	−0.629287	−	0.133759i
$479$	−0.00860095	−	0.00382939i	−0.000392988	−	0.000174969i	0.406540	−	0.913633i	$-0.366735\pi$
$479$	−0.00860095	−	0.00382939i	−0.000392988	−	0.000174969i	−0.406933	+	0.913458i	$0.633402\pi$
$480$	11.8061	+	36.3353i	0.538871	+	1.65847i
$481$	−0.901074	−	2.77322i	−0.0410854	−	0.126448i
$482$	8.26247	+	3.67869i	0.376345	+	0.167560i
$483$	−1.62783	−	0.346005i	−0.0740687	−	0.0157438i
$484$	−9.15871	+	1.94674i	−0.416305	+	0.0884883i
$485$	−12.2283	+	5.44438i	−0.555257	+	0.247217i
$486$	−8.56166	−	9.50869i	−0.388365	−	0.431323i
$487$	−1.19639	−	11.3828i	−0.0542134	−	0.515806i	−0.987606	−	0.156950i	$-0.949834\pi$
$487$	−1.19639	−	11.3828i	−0.0542134	−	0.515806i	0.933393	−	0.358856i	$-0.116833\pi$
$488$	−12.3644	+	8.98323i	−0.559708	+	0.406652i
$489$	−4.23649	+	40.3075i	−0.191581	+	1.82277i
$490$	−8.07842	−	13.9922i	−0.364946	−	0.632104i
$491$	16.1234	−	27.9266i	0.727639	−	1.26031i	−0.230239	−	0.973134i	$-0.573951\pi$
$491$	16.1234	−	27.9266i	0.727639	−	1.26031i	0.957878	−	0.287174i	$-0.0927159\pi$
$492$	5.33258	+	3.87434i	0.240411	+	0.174669i
$493$	−0.988928	+	1.09832i	−0.0445391	+	0.0494656i
$494$	−1.73928	+	5.35296i	−0.0782541	+	0.240841i
$495$	9.06760			0.407558
$496$	−0.0179741	+	0.0684240i	−0.000807063	+	0.00307233i
$497$	−11.2343			−0.503925
$498$	4.94169	−	15.2090i	0.221443	−	0.681530i
$499$	24.5384	−	27.2527i	1.09849	−	1.22000i	0.124787	−	0.992184i	$-0.460175\pi$
$499$	24.5384	−	27.2527i	1.09849	−	1.22000i	0.973704	−	0.227815i	$-0.0731581\pi$
$500$	0.0587616	+	0.0426928i	0.00262790	+	0.00190928i
$501$	12.6370	−	21.8878i	0.564577	−	0.977877i
$502$	−4.87928	−	8.45115i	−0.217773	−	0.377193i
$503$	2.01352	−	19.1573i	0.0897783	−	0.854183i	−0.853257	−	0.521490i	$-0.825376\pi$
$503$	2.01352	−	19.1573i	0.0897783	−	0.854183i	0.943035	−	0.332693i	$-0.107957\pi$
$504$	−3.78345	+	2.74884i	−0.168528	+	0.122443i
$505$	−2.37004	−	22.5495i	−0.105466	−	1.00344i
$506$	0.788838	+	0.876094i	0.0350681	+	0.0389471i
$507$	−1.94739	+	0.867034i	−0.0864866	+	0.0385063i
$508$	−15.8167	+	3.36195i	−0.701755	+	0.149163i
$509$	−30.2740	−	6.43495i	−1.34187	−	0.285224i	−0.519645	−	0.854382i	$-0.673936\pi$
$509$	−30.2740	−	6.43495i	−1.34187	−	0.285224i	−0.822228	+	0.569158i	$0.807269\pi$
$510$	−4.77690	−	2.12681i	−0.211525	−	0.0941769i
$511$	2.51131	+	7.72901i	0.111094	+	0.341911i
$512$	−0.0444225	−	0.136718i	−0.00196321	−	0.00604215i
$513$	−18.2920	−	8.14413i	−0.807612	−	0.359572i
$514$	8.79837	+	1.87015i	0.388080	+	0.0824889i
$515$	−6.61039	+	1.40508i	−0.291289	+	0.0619153i
$516$	16.2322	−	7.22704i	0.714583	−	0.318153i
$517$	5.90915	+	6.56277i	0.259884	+	0.288630i
$518$	0.285021	+	2.71180i	0.0125231	+	0.119149i
$519$	10.0069	−	7.27042i	0.439253	−	0.319136i
$520$	0.934875	−	8.89474i	0.0409970	−	0.390060i
$521$	−11.2944	−	19.5625i	−0.494817	−	0.857048i	0.505165	−	0.863023i	$-0.331432\pi$
$521$	−11.2944	−	19.5625i	−0.494817	−	0.857048i	−0.999982	+	0.00597467i	$0.998098\pi$
$522$	1.12057	−	1.94088i	0.0490458	−	0.0849499i
$523$	−19.6745	−	14.2943i	−0.860304	−	0.625048i	0.0676634	−	0.997708i	$-0.478446\pi$
$523$	−19.6745	−	14.2943i	−0.860304	−	0.625048i	−0.927968	+	0.372661i	$0.878446\pi$
$524$	12.9901	−	14.4269i	0.567474	−	0.630243i
$525$	−3.54345	+	10.9056i	−0.154649	+	0.475961i
$526$	−16.1155			−0.702671
$527$	−2.71414	−	4.13477i	−0.118230	−	0.180113i
$528$	−0.0502531			−0.00218699
$529$	−6.94346	+	21.3698i	−0.301890	+	0.929121i
$530$	−19.0482	+	21.1552i	−0.827401	+	0.918922i
$531$	18.9819	+	13.7911i	0.823743	+	0.598484i
$532$	−4.28375	+	7.41967i	−0.185724	+	0.321683i
$533$	−1.24792	−	2.16147i	−0.0540536	−	0.0936235i
$534$	2.92505	−	27.8300i	0.126579	−	1.20432i
$535$	14.1274	−	10.2641i	0.610779	−	0.443757i
$536$	−0.477169	−	4.53996i	−0.0206106	−	0.196096i
$537$	13.3889	+	14.8698i	0.577772	+	0.641681i
$538$	−14.3589	+	6.39300i	−0.619056	+	0.275622i
$539$	10.6185	−	2.25703i	0.457371	−	0.0972172i
$540$	11.9044	+	2.53036i	0.512284	+	0.108889i
$541$	−31.9027	−	14.2040i	−1.37160	−	0.610678i	−0.417096	−	0.908862i	$-0.636952\pi$
$541$	−31.9027	−	14.2040i	−1.37160	−	0.610678i	−0.954508	+	0.298185i	$0.903619\pi$
$542$	6.18635	+	19.0396i	0.265727	+	0.817822i
$543$	9.01591	+	27.7481i	0.386910	+	1.19079i
$544$	4.59517	+	2.04590i	0.197016	+	0.0877172i
$545$	13.2753	+	2.82175i	0.568651	+	0.120871i
$546$	1.94981	−	0.414444i	0.0834440	−	0.0177366i
$547$	−39.3091	+	17.5015i	−1.68073	+	0.748311i	−0.680861	+	0.732413i	$0.738394\pi$
$547$	−39.3091	+	17.5015i	−1.68073	+	0.748311i	−0.999874	+	0.0158979i	$0.994939\pi$
$548$	9.69394	+	10.7662i	0.414105	+	0.459910i
$549$	−0.872970	−	8.30575i	−0.0372574	−	0.354481i
$550$	6.57166	−	4.77459i	0.280217	−	0.203589i
$551$	1.12198	−	10.6749i	0.0477979	−	0.454767i
$552$	−2.19354	−	3.79932i	−0.0933632	−	0.161710i
$553$	5.69843	−	9.86996i	0.242322	−	0.419714i
$554$	−6.03209	−	4.38257i	−0.256279	−	0.186198i
$555$	−13.1648	+	14.6210i	−0.558814	+	0.620626i
$556$	0.164551	−	0.506436i	0.00697852	−	0.0214777i
$557$	−36.7304			−1.55632			−0.778158	−	0.628069i	$-0.783846\pi$
$557$	−36.7304			−1.55632			−0.778158	+	0.628069i	$0.783846\pi$
$558$	5.32938	+	5.27724i	0.225611	+	0.223404i
$559$	−6.72800			−0.284564
$560$	0.0133213	−	0.0409988i	0.000562929	−	0.00173252i
$561$	2.35087	−	2.61091i	0.0992539	−	0.110233i
$562$	6.96104	+	5.05749i	0.293634	+	0.213337i
$563$	5.66926	−	9.81944i	0.238931	−	0.413840i	−0.721477	−	0.692438i	$-0.756536\pi$
$563$	5.66926	−	9.81944i	0.238931	−	0.413840i	0.960408	+	0.278598i	$0.0898698\pi$
$564$	−6.28525	−	10.8864i	−0.264657	−	0.458399i
$565$	−3.86142	+	36.7389i	−0.162451	+	1.54562i
$566$	5.17772	−	3.76184i	0.217636	−	0.158122i
$567$	1.26025	+	11.9905i	0.0529257	+	0.503554i
$568$	−19.8165	−	22.0084i	−0.831482	−	0.923454i
$569$	−43.5536	+	19.3913i	−1.82586	+	0.812926i	−0.898010	+	0.439975i	$0.854987\pi$
$569$	−43.5536	+	19.3913i	−1.82586	+	0.812926i	−0.927851	+	0.372950i	$0.878346\pi$
$570$	37.1464	−	7.89571i	1.55589	−	0.330715i
$571$	20.0907	+	4.27041i	0.840769	+	0.178711i	0.608115	−	0.793849i	$-0.291926\pi$
$571$	20.0907	+	4.27041i	0.840769	+	0.178711i	0.232654	+	0.972560i	$0.425259\pi$
$572$	2.09987	+	0.934921i	0.0877999	+	0.0390910i
$573$	−0.903250	−	2.77992i	−0.0377338	−	0.116133i
$574$	0.721215	+	2.21967i	0.0301029	+	0.0926473i
$575$	−3.33919	−	1.48670i	−0.139254	−	0.0619999i
$576$	−7.42249	−	1.57770i	−0.309270	−	0.0657374i
$577$	−33.4492	+	7.10985i	−1.39251	+	0.295987i	−0.842286	−	0.539030i	$-0.818791\pi$
$577$	−33.4492	+	7.10985i	−1.39251	+	0.295987i	−0.550224	+	0.835017i	$0.685458\pi$
$578$	12.9198	−	5.75226i	0.537392	−	0.239262i
$579$	−8.70085	−	9.66327i	−0.361595	−	0.401592i
$580$	0.681956	+	6.48838i	0.0283167	+	0.269415i
$581$	−7.45685	+	5.41772i	−0.309362	+	0.224765i
$582$	0.822071	−	7.82148i	0.0340759	−	0.324211i
$583$	−9.56346	−	16.5644i	−0.396078	−	0.686028i
$584$	−10.7117	+	18.5532i	−0.443254	+	0.767738i
$585$	3.95391	+	2.87269i	0.163474	+	0.118771i
$586$	3.21156	−	3.56680i	0.132668	−	0.147343i
$587$	3.52290	−	10.8424i	0.145406	−	0.447512i	−0.851657	−	0.524099i	$-0.824402\pi$
$587$	3.52290	−	10.8424i	0.145406	−	0.447512i	0.997063	+	0.0765867i	$0.0244022\pi$
$588$	−15.4524			−0.637248
$589$	33.5981	+	12.7080i	1.38439	+	0.523624i
$590$	41.9599			1.72746
$591$	−9.30907	+	28.6504i	−0.382924	+	1.17852i
$592$	0.0247917	−	0.0275340i	0.00101893	−	0.00113164i
$593$	−16.1057	−	11.7015i	−0.661382	−	0.480522i	0.205747	−	0.978605i	$-0.434038\pi$
$593$	−16.1057	−	11.7015i	−0.661382	−	0.480522i	−0.867129	+	0.498083i	$0.834038\pi$
$594$	2.51174	−	4.35045i	0.103058	−	0.178501i
$595$	1.50692	+	2.61006i	0.0617777	+	0.107002i
$596$	1.96752	−	18.7197i	0.0805928	−	0.766789i
$597$	−7.59483	+	5.51797i	−0.310836	+	0.225835i
$598$	0.0664185	+	0.631929i	0.00271605	+	0.0258415i
$599$	31.1792	+	34.6280i	1.27395	+	1.41486i	0.864583	+	0.502489i	$0.167582\pi$
$599$	31.1792	+	34.6280i	1.27395	+	1.41486i	0.409363	+	0.912372i	$0.365751\pi$
$600$	−27.6151	+	12.2950i	−1.12738	+	0.501942i
$601$	−32.4679	+	6.90126i	−1.32439	+	0.281508i	−0.815218	−	0.579155i	$-0.803383\pi$
$601$	−32.4679	+	6.90126i	−1.32439	+	0.281508i	−0.509175	+	0.860663i	$0.670049\pi$
$602$	6.15396	+	1.30806i	0.250817	+	0.0533127i
$603$	2.27886	+	1.01462i	0.0928025	+	0.0413183i
$604$	−7.20525	−	22.1755i	−0.293178	−	0.902308i
$605$	−7.39223	−	22.7509i	−0.300537	−	0.924957i
$606$	12.1700	+	5.41844i	0.494374	+	0.220109i
$607$	34.0059	+	7.22818i	1.38026	+	0.293383i	0.837468	−	0.546486i	$-0.184035\pi$
$607$	34.0059	+	7.22818i	1.38026	+	0.293383i	0.542790	+	0.839869i	$0.317368\pi$
$608$	−35.7332	+	7.59533i	−1.44917	+	0.308031i
$609$	−3.47280	+	1.54619i	−0.140725	+	0.0626548i
$610$	−9.99374	−	11.0992i	−0.404635	−	0.449393i
$611$	0.497537	+	4.73375i	0.0201282	+	0.191507i
$612$	−1.37479	+	0.998845i	−0.0555727	+	0.0403759i
$613$	−0.534162	+	5.08221i	−0.0215746	+	0.205269i	−0.999999	−	0.00133602i	$-0.999575\pi$
$613$	−0.534162	+	5.08221i	−0.0215746	+	0.205269i	0.978425	+	0.206605i	$0.0662414\pi$
$614$	−6.16983	−	10.6865i	−0.248994	−	0.431270i
$615$	−8.42001	+	14.5839i	−0.339527	+	0.588079i
$616$	−4.54615	−	3.30297i	−0.183170	−	0.133080i
$617$	13.4962	−	14.9891i	0.543338	−	0.603438i	−0.407470	−	0.913219i	$-0.633589\pi$
$617$	13.4962	−	14.9891i	0.543338	−	0.603438i	0.950808	+	0.309780i	$0.100256\pi$
$618$	1.22700	−	3.77632i	0.0493572	−	0.151906i
$619$	−28.7089			−1.15391			−0.576955	−	0.816776i	$-0.695759\pi$
$619$	−28.7089			−1.15391			−0.576955	+	0.816776i	$0.695759\pi$
$620$	−21.5811	−	3.30946i	−0.866719	−	0.132911i
$621$	−2.26046			−0.0907093
$622$	−0.499341	+	1.53681i	−0.0200218	+	0.0616206i
$623$	−10.7923	+	11.9861i	−0.432385	+	0.480212i
$624$	−0.0219128	−	0.0159206i	−0.000877214	−	0.000637333i
$625$	12.4535	−	21.5701i	0.498141	−	0.862805i
$626$	8.13091	+	14.0832i	0.324977	+	0.562876i
$627$	−2.66716	+	25.3763i	−0.106516	+	1.01343i
$628$	−11.5796	+	8.41310i	−0.462078	+	0.335719i
$629$	0.270761	+	2.57612i	0.0107959	+	0.102716i
$630$	−3.05805	−	3.39631i	−0.121836	−	0.135312i
$631$	−22.8660	+	10.1806i	−0.910281	+	0.405283i	−0.807803	−	0.589452i	$-0.799344\pi$
$631$	−22.8660	+	10.1806i	−0.910281	+	0.405283i	−0.102478	+	0.994735i	$0.532677\pi$
$632$	29.3874	−	6.24648i	1.16897	−	0.248472i
$633$	15.2853	+	3.24899i	0.607535	+	0.129136i
$634$	−1.31229	−	0.584271i	−0.0521178	−	0.0232044i
$635$	−12.7661	−	39.2900i	−0.506607	−	1.55918i
$636$	8.41330	+	25.8935i	0.333609	+	1.02674i
$637$	5.34522	+	2.37985i	0.211785	+	0.0942930i
$638$	2.63407	+	0.559888i	0.104284	+	0.0221662i
$639$	15.8296	−	3.36469i	0.626211	−	0.133105i
$640$	20.3488	−	9.05988i	0.804358	−	0.358123i
$641$	5.20698	+	5.78294i	0.205663	+	0.228412i	0.837149	−	0.546976i	$-0.184221\pi$
$641$	5.20698	+	5.78294i	0.205663	+	0.228412i	−0.631485	+	0.775388i	$0.717554\pi$
$642$	1.07245	+	10.2037i	0.0423263	+	0.402708i
$643$	10.4524	−	7.59410i	0.412202	−	0.299482i	−0.362291	−	0.932065i	$-0.618005\pi$
$643$	10.4524	−	7.59410i	0.412202	−	0.299482i	0.774493	+	0.632583i	$0.218005\pi$
$644$	−0.101101	+	0.961910i	−0.00398393	+	0.0379046i
$645$	22.6976	+	39.3134i	0.893718	+	1.54796i
$646$	2.49995	−	4.33003i	0.0983591	−	0.170363i
$647$	6.91708	+	5.02555i	0.271938	+	0.197575i	0.715393	−	0.698722i	$-0.246247\pi$
$647$	6.91708	+	5.02555i	0.271938	+	0.197575i	−0.443455	+	0.896297i	$0.646247\pi$
$648$	−21.2670	+	23.6194i	−0.835446	+	0.927856i
$649$	−8.71202	+	26.8128i	−0.341977	+	1.05250i
$650$	4.37819			0.171727
$651$	−2.05187	−	12.5553i	−0.0804191	−	0.492079i
$652$	23.5552			0.922495
$653$	−6.64881	+	20.4629i	−0.260188	+	0.800776i	0.732575	+	0.680686i	$0.238318\pi$
$653$	−6.64881	+	20.4629i	−0.260188	+	0.800776i	−0.992763	+	0.120090i	$0.961682\pi$
$654$	−5.33569	+	5.92588i	−0.208642	+	0.231720i
$655$	40.1256	+	29.1529i	1.56784	+	1.13910i
$656$	0.0158564	−	0.0274641i	0.000619089	−	0.00107229i
$657$	−5.85342	−	10.1384i	−0.228364	−	0.395537i
$658$	0.465254	−	4.42660i	0.0181375	−	0.172567i
$659$	28.8884	−	20.9886i	1.12533	−	0.817600i	0.140322	−	0.990106i	$-0.455186\pi$
$659$	28.8884	−	20.9886i	1.12533	−	0.817600i	0.985009	+	0.172505i	$0.0551863\pi$
$660$	−1.62114	−	15.4241i	−0.0631028	−	0.600383i
$661$	−7.06240	−	7.84359i	−0.274696	−	0.305080i	0.589973	−	0.807423i	$-0.299138\pi$
$661$	−7.06240	−	7.84359i	−0.274696	−	0.305080i	−0.864669	+	0.502342i	$0.832472\pi$
$662$	−16.3168	+	7.26469i	−0.634169	+	0.282350i
$663$	1.85225	−	0.393708i	0.0719355	−	0.0152904i
$664$	−23.7670	−	5.05182i	−0.922337	−	0.196049i
$665$	−19.9962	−	8.90287i	−0.775419	−	0.345239i
$666$	−1.21380	−	3.73569i	−0.0470338	−	0.144755i
$667$	−0.374454	−	1.15245i	−0.0144989	−	0.0446231i
$668$	−13.4190	−	5.97450i	−0.519195	−	0.231161i
$669$	−24.2628	−	5.15722i	−0.938054	−	0.199390i
$670$	4.36361	−	0.927513i	0.168581	−	0.0358330i
$671$	9.16748	−	4.08162i	0.353906	−	0.157569i
$672$	8.65720	+	9.61480i	0.333959	+	0.370899i
$673$	−1.45458	−	13.8394i	−0.0560701	−	0.533471i	−0.986120	−	0.166037i	$-0.946903\pi$
$673$	−1.45458	−	13.8394i	−0.0560701	−	0.533471i	0.930049	−	0.367434i	$-0.119764\pi$
$674$	−8.27749	+	6.01395i	−0.318837	+	0.231649i
$675$	−1.62807	+	15.4900i	−0.0626644	+	0.596212i
$676$	0.619454	+	1.07293i	0.0238251	+	0.0412664i
$677$	18.6191	−	32.2493i	0.715592	−	1.23944i	−0.247139	−	0.968980i	$-0.579491\pi$
$677$	18.6191	−	32.2493i	0.715592	−	1.23944i	0.962731	−	0.270461i	$-0.0871761\pi$
$678$	−17.5594	−	12.7576i	−0.674364	−	0.489954i
$679$	−3.03312	+	3.36862i	−0.116401	+	0.129276i
$680$	−2.45513	+	7.55611i	−0.0941499	+	0.289764i
$681$	−62.1725			−2.38246
$682$	−4.05186	+	8.04979i	−0.155154	+	0.308242i
$683$	−10.2209			−0.391093			−0.195547	−	0.980694i	$-0.562648\pi$
$683$	−10.2209			−0.391093			−0.195547	+	0.980694i	$0.562648\pi$
$684$	3.81380	−	11.7377i	0.145824	−	0.448801i
$685$	−24.7664	+	27.5059i	−0.946277	+	1.05095i
$686$	−9.72213	−	7.06354i	−0.371193	−	0.269687i
$687$	15.5167	−	26.8757i	0.591998	−	1.02537i
$688$	−0.0427438	−	0.0740344i	−0.00162959	−	0.00282254i
$689$	1.07760	−	10.2527i	0.0410532	−	0.390595i
$690$	3.46846	−	2.51998i	0.132042	−	0.0959341i
$691$	2.02507	+	19.2672i	0.0770373	+	0.732961i	0.963054	+	0.269308i	$0.0867949\pi$
$691$	2.02507	+	19.2672i	0.0770373	+	0.732961i	−0.886017	+	0.463653i	$0.846538\pi$
$692$	−4.81025	−	5.34233i	−0.182858	−	0.203085i
$693$	2.80522	−	1.24896i	0.106561	−	0.0474442i
$694$	−13.0931	+	2.78303i	−0.497009	+	0.105643i
$695$	1.33072	+	0.282853i	0.0504770	+	0.0107292i
$696$	−9.15485	−	4.07600i	−0.347014	−	0.154500i
$697$	0.685130	+	2.10861i	0.0259511	+	0.0798694i
$698$	−3.36610	−	10.3598i	−0.127409	−	0.392124i
$699$	41.2548	+	18.3678i	1.56040	+	0.694735i
$700$	6.51876	+	1.38560i	0.246386	+	0.0523709i
$701$	37.0092	−	7.86655i	1.39782	−	0.297116i	0.553452	−	0.832881i	$-0.313310\pi$
$701$	37.0092	−	7.86655i	1.39782	−	0.297116i	0.844367	+	0.535765i	$0.179977\pi$
$702$	2.47350	−	1.10127i	0.0933561	−	0.0415648i
$703$	−12.5880	−	13.9804i	−0.474767	−	0.527282i
$704$	−0.953091	−	9.06806i	−0.0359210	−	0.341765i
$705$	25.9820	−	18.8770i	0.978540	−	0.710951i
$706$	−2.14862	+	20.4428i	−0.0808646	+	0.769375i
$707$	−3.83916	−	6.64961i	−0.144386	−	0.250084i
$708$	20.0653	−	34.7541i	0.754099	−	1.30614i
$709$	27.3375	+	19.8619i	1.02668	+	0.745928i	0.967642	−	0.252328i	$-0.0811961\pi$
$709$	27.3375	+	19.8619i	1.02668	+	0.745928i	0.0590398	+	0.998256i	$0.481196\pi$
$710$	19.3656	−	21.5076i	0.726777	−	0.807167i
$711$	−5.07329	+	15.6140i	−0.190263	+	0.585570i
$712$	−42.5182			−1.59344
$713$	4.04859	−	0.232138i	0.151621	−	0.00869364i
$714$	−1.77076			−0.0662691
$715$	−1.81471	+	5.58510i	−0.0678663	+	0.208871i
$716$	7.78143	−	8.64216i	0.290806	−	0.322973i
$717$	−27.8048	−	20.2014i	−1.03839	−	0.754434i
$718$	−11.3233	+	19.6125i	−0.422582	+	0.731933i
$719$	−0.778159	−	1.34781i	−0.0290205	−	0.0502649i	0.851150	−	0.524922i	$-0.175905\pi$
$719$	−0.778159	−	1.34781i	−0.0290205	−	0.0502649i	−0.880171	+	0.474657i	$0.842572\pi$
$720$	−0.00649115	+	0.0617591i	−0.000241911	+	0.00230163i
$721$	−1.85150	+	1.34520i	−0.0689535	+	0.0500977i
$722$	2.06307	+	19.6288i	0.0767794	+	0.730507i
$723$	14.7875	+	16.4232i	0.549953	+	0.610785i
$724$	15.4908	−	6.89695i	0.575711	−	0.256323i
$725$	−8.16697	+	1.73594i	−0.303314	+	0.0644713i
$726$	13.7479	+	2.92221i	0.510233	+	0.108453i
$727$	−3.60339	−	1.60433i	−0.133642	−	0.0595013i	0.338826	−	0.940849i	$-0.389970\pi$
$727$	−3.60339	−	1.60433i	−0.133642	−	0.0595013i	−0.472468	+	0.881348i	$0.656637\pi$
$728$	−0.935934	−	2.88051i	−0.0346880	−	0.106759i
$729$	0.766268	+	2.35833i	0.0283803	+	0.0873456i
$730$	−19.1259	−	8.51541i	−0.707882	−	0.315169i
$731$	5.84605	+	1.24262i	0.216224	+	0.0459599i
$732$	−13.9721	+	2.96987i	−0.516425	+	0.109769i
$733$	24.8479	−	11.0630i	0.917777	−	0.408621i	0.107190	−	0.994239i	$-0.465815\pi$
$733$	24.8479	−	11.0630i	0.917777	−	0.408621i	0.810587	+	0.585618i	$0.199148\pi$
$734$	0.815080	+	0.905238i	0.0300851	+	0.0334129i
$735$	−4.12662	−	39.2622i	−0.152213	−	1.44821i
$736$	−3.33650	+	2.42411i	−0.122985	+	0.0893539i
$737$	−0.313313	+	2.98097i	−0.0115410	+	0.109805i
$738$	−1.68103	−	2.91162i	−0.0618794	−	0.107178i
$739$	−12.3295	+	21.3553i	−0.453548	+	0.785568i	−0.998603	−	0.0528317i	$-0.983175\pi$
$739$	−12.3295	+	21.3553i	−0.453548	+	0.785568i	0.545055	+	0.838400i	$0.316509\pi$
$740$	9.25074	+	6.72106i	0.340064	+	0.247071i
$741$	−9.20244	+	10.2203i	−0.338060	+	0.375454i
$742$	−2.97899	+	9.16839i	−0.109362	+	0.336582i
$743$	33.6381			1.23406			0.617031	−	0.786939i	$-0.288335\pi$
$743$	33.6381			1.23406			0.617031	+	0.786939i	$0.288335\pi$
$744$	20.9770	−	26.1664i	0.769054	−	0.959305i
$745$	48.0892			1.76185
$746$	−7.90813	+	24.3387i	−0.289537	+	0.891104i
$747$	8.88445	−	9.86719i	0.325065	−	0.361021i
$748$	−1.65193	−	1.20020i	−0.0604006	−	0.0438836i
$749$	2.95677	−	5.12128i	0.108038	−	0.187127i
$750$	−0.0545141	−	0.0944211i	−0.00199057	−	0.00344777i
$751$	−0.601137	+	5.71944i	−0.0219358	+	0.208705i	0.978064	+	0.208304i	$0.0667944\pi$
$751$	−0.601137	+	5.71944i	−0.0219358	+	0.208705i	−1.00000		0.000401134i	$0.999872\pi$
$752$	−0.0489290	+	0.0355490i	−0.00178426	+	0.00129634i
$753$	−2.49243	−	23.7139i	−0.0908294	−	0.864184i
$754$	0.971204	+	1.07863i	0.0353692	+	0.0392814i
$755$	54.4202	−	24.2294i	1.98055	−	0.881799i
$756$	4.03136	−	0.856891i	0.146619	−	0.0311648i
$757$	15.4042	+	3.27426i	0.559874	+	0.119005i	0.479152	−	0.877732i	$-0.340944\pi$
$757$	15.4042	+	3.27426i	0.559874	+	0.119005i	0.0807218	+	0.996737i	$0.474277\pi$
$758$	−14.3401	−	6.38461i	−0.520855	−	0.231899i
$759$	0.890150	+	2.73960i	0.0323104	+	0.0994412i
$760$	−17.8308	−	54.8776i	−0.646791	−	1.99062i
$761$	24.2188	+	10.7829i	0.877929	+	0.390879i	0.795669	−	0.605732i	$-0.207119\pi$
$761$	24.2188	+	10.7829i	0.877929	+	0.390879i	0.0822602	+	0.996611i	$0.473786\pi$
$762$	23.7421	+	5.04655i	0.860087	+	0.182817i
$763$	4.49561	−	0.955571i	0.162752	−	0.0345940i
$764$	−1.55193	+	0.690963i	−0.0561468	+	0.0249982i
$765$	−2.90505	−	3.22638i	−0.105032	−	0.116650i
$766$	0.218441	+	2.07833i	0.00789260	+	0.0750931i
$767$	−12.2934	+	8.93166i	−0.443888	+	0.322503i
$768$	−3.55809	+	33.8530i	−0.128392	+	1.22156i
$769$	−8.03418	−	13.9156i	−0.289720	−	0.501810i	0.684023	−	0.729461i	$-0.260229\pi$
$769$	−8.03418	−	13.9156i	−0.289720	−	0.501810i	−0.973743	+	0.227651i	$0.926896\pi$
$770$	2.74574	−	4.75576i	0.0989496	−	0.171386i
$771$	17.7811	+	12.9188i	0.640372	+	0.465257i
$772$	−5.05683	+	5.61617i	−0.181999	+	0.202130i
$773$	12.5287	−	38.5595i	0.450627	−	1.38689i	−0.425566	−	0.904928i	$-0.639925\pi$
$773$	12.5287	−	38.5595i	0.450627	−	1.38689i	0.876193	−	0.481960i	$-0.160075\pi$
$774$	−9.06301			−0.325763
$775$	1.32519	−	27.9105i	0.0476023	−	1.00258i
$776$	−11.9495			−0.428963
$777$	−2.05887	+	6.33655i	−0.0738616	+	0.227322i
$778$	−6.65173	+	7.38750i	−0.238476	+	0.264855i
$779$	−13.0270	−	9.46468i	−0.466741	−	0.339107i
$780$	4.17959	−	7.23926i	0.149653	−	0.259207i
$781$	9.72280	+	16.8404i	0.347909	+	0.602597i
$782$	0.0590013	−	0.561360i	0.00210988	−	0.0200742i
$783$	−4.17735	+	3.03502i	−0.149286	+	0.108463i
$784$	0.00777119	+	0.0739379i	0.000277543	+	0.00264064i
$785$	−24.4687	−	27.1753i	−0.873326	−	0.969927i
$786$	−26.6215	+	11.8527i	−0.949559	+	0.422771i
$787$	−39.0665	+	8.30385i	−1.39257	+	0.296000i	−0.842311	−	0.538992i	$-0.818805\pi$
$787$	−39.0665	+	8.30385i	−1.39257	+	0.296000i	−0.550261	+	0.834993i	$0.685472\pi$
$788$	17.1255	+	3.64015i	0.610072	+	0.129675i
$789$	−35.9732	−	16.0163i	−1.28068	−	0.570195i
$790$	9.07282	+	27.9233i	0.322796	+	0.993465i
$791$	3.86579	+	11.8977i	0.137452	+	0.423033i
$792$	7.39500	+	3.29247i	0.262770	+	0.116993i
$793$	5.29055	+	1.12454i	0.187873	+	0.0399337i
$794$	−25.3825	+	5.39522i	−0.900791	+	0.191469i
$795$	−63.5444	+	28.2918i	−2.25369	+	1.00341i
$796$	3.65080	+	4.05462i	0.129399	+	0.143712i
$797$	1.91120	+	18.1839i	0.0676984	+	0.644107i	0.974782	+	0.223157i	$0.0716364\pi$
$797$	1.91120	+	18.1839i	0.0676984	+	0.644107i	−0.907084	+	0.420949i	$0.861697\pi$
$798$	10.4043	−	7.55919i	0.368309	−	0.267592i
$799$	0.441976	−	4.20512i	0.0156360	−	0.148766i
$800$	14.2084	+	24.6096i	0.502342	+	0.870081i
$801$	11.6170	−	20.1213i	0.410468	−	0.710951i
$802$	14.1189	+	10.2580i	0.498557	+	0.362223i
$803$	9.41251	−	10.4537i	0.332160	−	0.368901i
$804$	1.31845	−	4.05778i	0.0464982	−	0.143107i
$805$	−2.47106			−0.0870934
$806$	−4.31704	+	2.22644i	−0.152061	+	0.0784230i
$807$	−38.4056			−1.35194
$808$	6.25489	−	19.2506i	0.220046	−	0.677233i
$809$	14.1939	−	15.7639i	0.499029	−	0.554228i	−0.440030	−	0.897983i	$-0.645032\pi$
$809$	14.1939	−	15.7639i	0.499029	−	0.554228i	0.939059	+	0.343755i	$0.111699\pi$
$810$	−25.1279	−	18.2565i	−0.882904	−	0.641467i
$811$	23.7666	−	41.1649i	0.834556	−	1.44549i	−0.0598345	−	0.998208i	$-0.519057\pi$
$811$	23.7666	−	41.1649i	0.834556	−	1.44549i	0.894391	−	0.447286i	$-0.147609\pi$
$812$	1.10468	+	1.91336i	0.0387666	+	0.0671457i
$813$	−5.11317	+	48.6486i	−0.179327	+	1.70618i
$814$	3.81836	−	2.77420i	0.133834	−	0.0972358i
$815$	6.29050	+	59.8501i	0.220347	+	2.09646i
$816$	0.0160999	+	0.0178808i	0.000563610	+	0.000625952i
$817$	−39.6538	+	17.6550i	−1.38731	+	0.617671i
$818$	−29.6972	+	6.31233i	−1.03834	+	0.220705i
$819$	1.61889	+	0.344106i	0.0565687	+	0.0120240i
$820$	8.94105	+	3.98081i	0.312235	+	0.139016i
$821$	−2.51815	−	7.75007i	−0.0878841	−	0.270479i	0.897450	−	0.441116i	$-0.145417\pi$
$821$	−2.51815	−	7.75007i	−0.0878841	−	0.270479i	−0.985334	+	0.170637i	$0.945417\pi$
$822$	−6.72008	−	20.6823i	−0.234390	−	0.721378i
$823$	47.1380	+	20.9872i	1.64313	+	0.731567i	0.999432	−	0.0337142i	$-0.0107336\pi$
$823$	47.1380	+	20.9872i	1.64313	+	0.731567i	0.643696	+	0.765282i	$0.277400\pi$
$824$	−5.90123	−	1.25434i	−0.205579	−	0.0436972i
$825$	19.4145	−	4.12667i	0.675925	−	0.143672i
$826$	12.9810	−	5.77951i	0.451667	−	0.201095i
$827$	−27.4882	−	30.5287i	−0.955857	−	1.06159i	−0.998046	−	0.0624769i	$-0.980100\pi$
$827$	−27.4882	−	30.5287i	−0.955857	−	1.06159i	0.0421896	−	0.999110i	$-0.486567\pi$
$828$	−0.145639	−	1.38566i	−0.00506129	−	0.0481550i
$829$	−26.7036	+	19.4013i	−0.927455	+	0.673836i	−0.945368	−	0.326004i	$-0.894298\pi$
$829$	−26.7036	+	19.4013i	−0.927455	+	0.673836i	0.0179133	+	0.999840i	$0.494298\pi$
$830$	2.48203	−	23.6149i	0.0861526	−	0.819687i
$831$	−9.10929	−	15.7777i	−0.315998	−	0.547324i
$832$	2.45724	−	4.25606i	0.0851894	−	0.147552i
$833$	−4.20500	−	3.05511i	−0.145695	−	0.105853i
$834$	−0.534850	+	0.594011i	−0.0185203	+	0.0205689i
$835$	11.5967	−	35.6909i	0.401320	−	1.23514i
$836$	14.8297			0.512894
$837$	−6.27181	−	16.1016i	−0.216786	−	0.556553i
$838$	−33.1142			−1.14391
$839$	−9.43235	+	29.0298i	−0.325641	+	1.00222i	0.645510	+	0.763752i	$0.276645\pi$
$839$	−9.43235	+	29.0298i	−0.325641	+	1.00222i	−0.971150	+	0.238468i	$0.923355\pi$
$840$	−13.6741	+	15.1866i	−0.471801	+	0.523988i
$841$	21.2222	+	15.4188i	0.731798	+	0.531683i
$842$	12.9571	−	22.4423i	0.446531	−	0.773414i
$843$	10.5121	+	18.2075i	0.362057	+	0.627101i
$844$	0.949335	−	9.03232i	0.0326775	−	0.310905i
$845$	−2.56070	+	1.86046i	−0.0880909	+	0.0640018i
$846$	0.670212	+	6.37664i	0.0230424	+	0.219233i
$847$	−5.42060	−	6.02019i	−0.186254	−	0.206856i
$848$	0.119666	−	0.0532786i	0.00410934	−	0.00182960i
$849$	15.2964	−	3.25135i	0.524971	−	0.111586i
$850$	−3.80427	−	0.808623i	−0.130486	−	0.0277356i
$851$	−1.94019	−	0.863827i	−0.0665088	−	0.0296116i
$852$	−8.55347	−	26.3249i	−0.293037	−	0.901876i
$853$	12.0633	+	37.1270i	0.413040	+	1.27120i	0.913993	+	0.405731i	$0.132983\pi$
$853$	12.0633	+	37.1270i	0.413040	+	1.27120i	−0.500953	+	0.865474i	$0.667017\pi$
$854$	−4.62053	−	2.05719i	−0.158111	−	0.0703956i
$855$	30.8421	+	6.55568i	1.05478	+	0.224200i
$856$	15.2484	−	3.24114i	0.521179	−	0.110780i
$857$	26.3667	−	11.7392i	0.900671	−	0.401005i	0.0964519	−	0.995338i	$-0.469251\pi$
$857$	26.3667	−	11.7392i	0.900671	−	0.401005i	0.804219	+	0.594333i	$0.202584\pi$
$858$	−2.30874	−	2.56412i	−0.0788191	−	0.0875375i
$859$	−1.50754	−	14.3432i	−0.0514364	−	0.489385i	−0.989668	−	0.143377i	$-0.954204\pi$
$859$	−1.50754	−	14.3432i	−0.0514364	−	0.489385i	0.938232	−	0.346008i	$-0.112463\pi$
$860$	21.3444	−	15.5076i	0.727838	−	0.528805i
$861$	−0.596102	+	5.67154i	−0.0203151	+	0.193285i
$862$	10.6820	+	18.5018i	0.363831	+	0.630173i
$863$	−1.21350	+	2.10184i	−0.0413080	+	0.0715476i	−0.885940	−	0.463799i	$-0.846486\pi$
$863$	−1.21350	+	2.10184i	−0.0413080	+	0.0715476i	0.844632	+	0.535347i	$0.179819\pi$
$864$	14.2173	+	10.3295i	0.483684	+	0.351417i
$865$	12.2894	−	13.6488i	0.417852	−	0.464072i
$866$	−2.79389	+	8.59872i	−0.0949404	+	0.292196i
$867$	34.5565			1.17360
$868$	−7.13233	+	1.94873i	−0.242087	+	0.0661441i
$869$	−19.7270			−0.669194
$870$	3.02626	−	9.31388i	0.102600	−	0.315770i
$871$	−1.08101	+	1.20059i	−0.0366288	+	0.0406804i
$872$	9.80196	+	7.12154i	0.331936	+	0.241166i
$873$	3.26491	−	5.65499i	0.110500	−	0.191392i
$874$	2.04972	+	3.55021i	0.0693326	+	0.120088i
$875$	−0.00656867	+	0.0624967i	−0.000222062	+	0.00211278i
$876$	−16.1991	+	11.7693i	−0.547317	+	0.397649i
$877$	2.29153	+	21.8025i	0.0773795	+	0.736217i	0.962578	+	0.271004i	$0.0873556\pi$
$877$	2.29153	+	21.8025i	0.0773795	+	0.736217i	−0.885199	+	0.465213i	$0.845978\pi$
$878$	10.8475	+	12.0474i	0.366086	+	0.406580i
$879$	10.7137	−	4.77004i	0.361364	−	0.160889i
$880$	−0.0729871	+	0.0155139i	−0.00246040	+	0.000522973i
$881$	10.3220	+	2.19401i	0.347758	+	0.0739182i	0.378479	−	0.925610i	$-0.376447\pi$
$881$	10.3220	+	2.19401i	0.347758	+	0.0739182i	−0.0307214	+	0.999528i	$0.509780\pi$
$882$	7.20033	+	3.20579i	0.242448	+	0.107945i
$883$	−16.4173	−	50.5272i	−0.552486	−	1.70038i	−0.702492	−	0.711691i	$-0.747930\pi$
$883$	−16.4173	−	50.5272i	−0.552486	−	1.70038i	0.150007	−	0.988685i	$-0.452070\pi$
$884$	−0.340090	−	1.04669i	−0.0114385	−	0.0352040i
$885$	93.6630	+	41.7015i	3.14845	+	1.40178i
$886$	18.3058	+	3.89102i	0.614996	+	0.130722i
$887$	26.4813	−	5.62878i	0.889156	−	0.188996i	0.259382	−	0.965775i	$-0.416481\pi$
$887$	26.4813	−	5.62878i	0.889156	−	0.188996i	0.629773	+	0.776779i	$0.283148\pi$
$888$	−16.0453	+	7.14383i	−0.538446	+	0.239731i
$889$	−9.36118	−	10.3966i	−0.313964	−	0.348692i
$890$	−4.34323	−	41.3231i	−0.145585	−	1.38515i
$891$	16.8833	−	12.2665i	0.565613	−	0.410942i
$892$	−1.50691	+	14.3373i	−0.0504551	+	0.480048i
$893$	15.3543	+	26.5944i	0.513812	+	0.889949i
$894$	−14.1272	+	24.4691i	−0.472486	+	0.818369i
$895$	24.0364	+	17.4635i	0.803448	+	0.583739i
$896$	5.04736	−	5.60566i	0.168620	−	0.187272i
$897$	−0.479778	+	1.47661i	−0.0160193	+	0.0493024i
$898$	15.0183			0.501169
$899$	7.17013	−	5.86485i	0.239137	−	0.195604i
$900$	−9.60025			−0.320008
$901$	−2.82994	+	8.70966i	−0.0942790	+	0.290161i
$902$	2.70315	−	3.00215i	0.0900051	−	0.0999608i
$903$	12.4369	+	9.03593i	0.413874	+	0.300697i
$904$	−16.4891	+	28.5600i	−0.548420	+	0.949892i
$905$	21.6609	+	37.5178i	0.720033	+	1.24713i
$906$	−3.65851	+	34.8084i	−0.121546	+	1.15643i
$907$	30.7878	−	22.3687i	1.02229	−	0.742740i	0.0555417	−	0.998456i	$-0.482311\pi$
$907$	30.7878	−	22.3687i	1.02229	−	0.742740i	0.966752	+	0.255717i	$0.0823114\pi$
$908$	3.77702	+	35.9359i	0.125345	+	1.19258i
$909$	7.40114	+	8.21980i	0.245480	+	0.272634i
$910$	2.70394	−	1.20387i	0.0896346	−	0.0399079i
$911$	−15.1909	+	3.22892i	−0.503296	+	0.106979i	−0.452561	−	0.891733i	$-0.649490\pi$
$911$	−15.1909	+	3.22892i	−0.503296	+	0.106979i	−0.0507345	+	0.998712i	$0.516156\pi$
$912$	−0.170928	−	0.0363319i	−0.00566000	−	0.00120307i
$913$	14.5749	+	6.48916i	0.482358	+	0.214760i
$914$	8.34560	+	25.6851i	0.276048	+	0.849588i
$915$	−11.2773	−	34.7078i	−0.372815	−	1.14741i
$916$	−16.4769	−	7.33598i	−0.544411	−	0.242387i
$917$	16.4290	+	3.49210i	0.542534	+	0.115319i
$918$	−2.35265	+	0.500072i	−0.0776492	+	0.0165048i
$919$	−53.1540	+	23.6657i	−1.75339	+	0.780659i	−0.762338	+	0.647180i	$0.775948\pi$
$919$	−53.1540	+	23.6657i	−1.75339	+	0.780659i	−0.991052	+	0.133479i	$0.957385\pi$
$920$	−4.35879	−	4.84092i	−0.143705	−	0.159600i
$921$	−3.15168	−	29.9862i	−0.103851	−	0.988079i
$922$	2.28126	−	1.65743i	0.0751294	−	0.0545847i
$923$	−1.09555	+	10.4235i	−0.0360606	+	0.343093i
$924$	−2.62603	−	4.54842i	−0.0863901	−	0.149632i
$925$	−7.31685	+	12.6732i	−0.240576	+	0.416691i
$926$	−29.6298	−	21.5273i	−0.973694	−	0.707430i
$927$	2.20597	−	2.44998i	0.0724535	−	0.0804678i
$928$	−2.91113	+	8.95954i	−0.0955625	+	0.294111i
$929$	−5.85843			−0.192209			−0.0961044	−	0.995371i	$-0.530638\pi$
$929$	−5.85843			−0.192209			−0.0961044	+	0.995371i	$0.530638\pi$
$930$	27.5737	+	17.7145i	0.904176	+	0.580880i
$931$	37.7490			1.23717
$932$	8.11042	−	24.9613i	0.265666	−	0.817635i
$933$	−2.64198	+	2.93422i	−0.0864946	+	0.0960620i
$934$	−3.37915	−	2.45509i	−0.110569	−	0.0803331i
$935$	2.60836	−	4.51781i	0.0853025	−	0.147748i
$936$	2.18150	+	3.77847i	0.0713045	+	0.123503i
$937$	−0.484411	+	4.60886i	−0.0158250	+	0.150565i	−0.999581	−	0.0289461i	$-0.990785\pi$
$937$	−0.484411	+	4.60886i	−0.0158250	+	0.150565i	0.983756	+	0.179511i	$0.0574516\pi$
$938$	1.22220	−	0.887981i	0.0399063	−	0.0289936i
$939$	4.15344	+	39.5173i	0.135542	+	1.28960i
$940$	−12.4894	−	13.8709i	−0.407360	−	0.452419i
$941$	3.55329	−	1.58203i	0.115834	−	0.0515726i	−0.348001	−	0.937494i	$-0.613140\pi$
$941$	3.55329	−	1.58203i	0.115834	−	0.0515726i	0.463835	+	0.885921i	$0.346473\pi$
$942$	21.0157	−	4.46703i	0.684729	−	0.145544i
$943$	−1.77811	−	0.377948i	−0.0579031	−	0.0123077i
$944$	−0.176385	−	0.0785315i	−0.00574083	−	0.00255598i
$945$	3.25381	+	10.0142i	0.105846	+	0.325762i
$946$	−3.36519	−	10.3570i	−0.109412	−	0.336735i
$947$	−27.1553	−	12.0903i	−0.882428	−	0.392882i	−0.0850601	−	0.996376i	$-0.527108\pi$
$947$	−27.1553	−	12.0903i	−0.882428	−	0.392882i	−0.797368	+	0.603494i	$0.793775\pi$
$948$	27.4666	+	5.83821i	0.892074	+	0.189616i
$949$	7.41611	−	1.57634i	0.240737	−	0.0511702i
$950$	25.8044	−	11.4889i	0.837206	−	0.372748i
$951$	−2.34864	−	2.60842i	−0.0761597	−	0.0845839i
$952$	0.281236	+	2.67578i	0.00911490	+	0.0867225i
$953$	27.2819	−	19.8215i	0.883748	−	0.642081i	−0.0504920	−	0.998724i	$-0.516079\pi$
$953$	27.2819	−	19.8215i	0.883748	−	0.642081i	0.934241	+	0.356644i	$0.116079\pi$
$954$	1.45159	−	13.8109i	0.0469969	−	0.447146i
$955$	−2.17007	−	3.75868i	−0.0702219	−	0.121628i
$956$	−9.98731	+	17.2985i	−0.323013	+	0.559474i
$957$	5.32334	+	3.86763i	0.172079	+	0.125023i
$958$	0.00549599	−	0.00610392i	0.000177567	−	0.000197209i
$959$	−3.87328	+	11.9207i	−0.125075	+	0.384940i
$960$	−33.1590			−1.07020
$961$	12.8866	+	28.1946i	0.415698	+	0.909503i
$962$	2.54388			0.0820180
$963$	−2.63240	+	8.10170i	−0.0848279	+	0.261073i
$964$	8.59431	−	9.54495i	0.276804	−	0.307422i
$965$	−15.6202	−	11.3488i	−0.502833	−	0.365330i
$966$	0.725926	−	1.25734i	0.0233563	−	0.0404543i
$967$	4.54283	+	7.86842i	0.146088	+	0.253031i	0.929778	−	0.368120i	$-0.119999\pi$
$967$	4.54283	+	7.86842i	0.146088	+	0.253031i	−0.783691	+	0.621151i	$0.786665\pi$
$968$	2.23225	−	21.2384i	0.0717472	−	0.682629i
$969$	9.88376	−	7.18097i	0.317512	−	0.230686i
$970$	−1.22064	−	11.6136i	−0.0391925	−	0.372891i
$971$	−13.5028	−	14.9963i	−0.433325	−	0.481256i	0.486447	−	0.873710i	$-0.338293\pi$
$971$	−13.5028	−	14.9963i	−0.433325	−	0.481256i	−0.919771	+	0.392454i	$0.871626\pi$
$972$	−16.5996	+	7.39062i	−0.532432	+	0.237054i
$973$	0.450640	−	0.0957865i	0.0144469	−	0.00307077i
$974$	9.76697	+	2.07603i	0.312954	+	0.0665204i
$975$	9.77302	+	4.35123i	0.312987	+	0.139351i
$976$	0.0212372	+	0.0653613i	0.000679785	+	0.00209216i
$977$	10.9124	+	33.5849i	0.349118	+	1.07448i	0.959342	+	0.282246i	$0.0910795\pi$
$977$	10.9124	+	33.5849i	0.349118	+	1.07448i	−0.610224	+	0.792229i	$0.708920\pi$
$978$	−32.3013	−	14.3815i	−1.03288	−	0.459869i
$979$	27.3077	+	5.80443i	0.872758	+	0.185510i
$980$	−22.4430	+	4.77041i	−0.716915	+	0.152385i
$981$	−6.04834	+	2.69289i	−0.193109	+	0.0859775i
$982$	18.8242	+	20.9064i	0.600705	+	0.667150i
$983$	−6.02337	−	57.3085i	−0.192116	−	1.82786i	−0.488240	−	0.872709i	$-0.662361\pi$
$983$	−6.02337	−	57.3085i	−0.192116	−	1.82786i	0.296124	−	0.955149i	$-0.404306\pi$
$984$	−12.1623	+	8.83642i	−0.387720	+	0.281695i
$985$	−4.67560	+	44.4854i	−0.148977	+	1.41742i
$986$	−0.644677	−	1.11661i	−0.0205307	−	0.0355602i
$987$	5.43788	−	9.41868i	0.173090	−	0.299800i
$988$	6.46645	+	4.69815i	0.205725	+	0.149468i
$989$	−3.27893	+	3.64162i	−0.104264	+	0.115797i
$990$	−2.44452	+	7.52346i	−0.0776919	+	0.239111i
$991$	−59.7844			−1.89911			−0.949556	−	0.313596i	$-0.898466\pi$
$991$	−59.7844			−1.89911			−0.949556	+	0.313596i	$0.898466\pi$
$992$	−26.5246	−	17.0405i	−0.842158	−	0.541037i
$993$	−43.6423			−1.38495
$994$	3.02863	−	9.32115i	0.0960622	−	0.295649i
$995$	−9.32718	+	10.3589i	−0.295692	+	0.328399i
$996$	−18.3726	−	13.3485i	−0.582159	−	0.422963i
$997$	−13.2635	+	22.9731i	−0.420060	+	0.727566i	−0.995945	−	0.0899650i	$-0.971324\pi$
$997$	−13.2635	+	22.9731i	−0.420060	+	0.727566i	0.575884	+	0.817531i	$0.304658\pi$
$998$	15.9965	+	27.7067i	0.506360	+	0.877042i
$999$	−0.945965	+	9.00025i	−0.0299290	+	0.284755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bi.a.14.6	✓	120
31.20	even	15	inner	403.2.bi.a.144.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bi.a.14.6	✓	120	1.1	even	1	trivial
403.2.bi.a.144.6	yes	120	31.20	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bi (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.269588 + 0.829708i) q^{2} +(-1.42637 + 1.58415i) q^{3} +(1.00230 + 0.728211i) q^{4} +(-1.58260 + 2.74115i) q^{5} +(-0.929847 - 1.61054i) q^{6} +(-0.112042 + 1.06601i) q^{7} +(-2.28599 + 1.66087i) q^{8} +(-0.161400 - 1.53561i) q^{9} +O(q^{10})\)	\(q+(-0.269588 + 0.829708i) q^{2} +(-1.42637 + 1.58415i) q^{3} +(1.00230 + 0.728211i) q^{4} +(-1.58260 + 2.74115i) q^{5} +(-0.929847 - 1.61054i) q^{6} +(-0.112042 + 1.06601i) q^{7} +(-2.28599 + 1.66087i) q^{8} +(-0.161400 - 1.53561i) q^{9} +(-1.84770 - 2.05208i) q^{10} +(1.69493 - 0.754634i) q^{11} +(-2.58325 + 0.549086i) q^{12} +(0.978148 + 0.207912i) q^{13} +(-0.854269 - 0.380345i) q^{14} +(-2.08500 - 6.41698i) q^{15} +(0.00392645 + 0.0120844i) q^{16} +(-0.811527 - 0.361315i) q^{17} +(1.31762 + 0.280069i) q^{18} +(6.31064 - 1.34137i) q^{19} +(-3.58237 + 1.59498i) q^{20} +(-1.52890 - 1.69802i) q^{21} +(0.169191 + 1.60974i) q^{22} +(0.589241 - 0.428109i) q^{23} +(0.629614 - 5.99038i) q^{24} +(-2.50926 - 4.34617i) q^{25} +(-0.436203 + 0.755526i) q^{26} +(-2.51085 - 1.82424i) q^{27} +(-0.888578 + 0.986866i) q^{28} +(0.514119 - 1.58229i) q^{29} +5.88631 q^{30} +(4.68437 + 3.00943i) q^{31} -5.66237 q^{32} +(-1.22216 + 3.76142i) q^{33} +(0.518564 - 0.575924i) q^{34} +(-2.74477 - 1.99419i) q^{35} +(0.956482 - 1.65667i) q^{36} +(-1.45797 - 2.52528i) q^{37} +(-0.588332 + 5.59761i) q^{38} +(-1.72457 + 1.25297i) q^{39} +(-0.934875 - 8.89474i) q^{40} +(-1.67005 - 1.85478i) q^{41} +(1.82103 - 0.810775i) q^{42} +(-6.58097 + 1.39883i) q^{43} +(2.24836 + 0.477904i) q^{44} +(4.46478 + 1.98785i) q^{45} +(0.196353 + 0.604311i) q^{46} +(1.47087 + 4.52686i) q^{47} +(-0.0247440 - 0.0110167i) q^{48} +(5.72322 + 1.21651i) q^{49} +(4.28252 - 0.910277i) q^{50} +(1.72992 - 0.770209i) q^{51} +(0.828991 + 0.920688i) q^{52} +(-1.07760 - 10.2527i) q^{53} +(2.19048 - 1.59147i) q^{54} +(-0.613846 + 5.84035i) q^{55} +(-1.51437 - 2.62297i) q^{56} +(-6.87641 + 11.9103i) q^{57} +(1.17424 + 0.853136i) q^{58} +(-10.1677 + 11.2924i) q^{59} +(2.58313 - 7.95005i) q^{60} +5.40875 q^{61} +(-3.75980 + 3.07535i) q^{62} +1.65506 q^{63} +(1.51866 - 4.67394i) q^{64} +(-2.11794 + 2.35221i) q^{65} +(-2.79140 - 2.02807i) q^{66} +(-0.807775 + 1.39911i) q^{67} +(-0.550277 - 0.953108i) q^{68} +(-0.162290 + 1.54409i) q^{69} +(2.39455 - 1.73974i) q^{70} +(1.09555 + 10.4235i) q^{71} +(2.91942 + 3.24234i) q^{72} +(6.92631 - 3.08379i) q^{73} +(2.48829 - 0.528903i) q^{74} +(10.4641 + 2.22422i) q^{75} +(7.30194 + 3.25103i) q^{76} +(0.614541 + 1.89136i) q^{77} +(-0.574677 - 1.76867i) q^{78} +(-9.71336 - 4.32467i) q^{79} +(-0.0393390 - 0.00836177i) q^{80} +(11.0023 - 2.33860i) q^{81} +(1.98915 - 0.885625i) q^{82} +(5.75391 + 6.39036i) q^{83} +(-0.295898 - 2.81528i) q^{84} +(2.27474 - 1.65270i) q^{85} +(0.613535 - 5.83739i) q^{86} +(1.77326 + 3.07138i) q^{87} +(-2.62126 + 4.54016i) q^{88} +(12.1735 + 8.84456i) q^{89} +(-2.85298 + 3.16856i) q^{90} +(-0.331229 + 1.01942i) q^{91} +0.902348 q^{92} +(-11.4491 + 3.12816i) q^{93} -4.15250 q^{94} +(-6.31035 + 19.4213i) q^{95} +(8.07666 - 8.97004i) q^{96} +(3.42130 + 2.48572i) q^{97} +(-2.55226 + 4.42064i) q^{98} +(-1.43239 - 2.48097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 13 q^{5} - 10 q^{6} - 16 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) \) 120 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 13 * q^5 - 10 * q^6 - 16 * q^7 - 6 * q^8 + 13 * q^9	\( 120 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 13 q^{5} - 10 q^{6} - 16 q^{7} - 6 q^{8} + 13 q^{9} + 3 q^{10} + 3 q^{11} - 12 q^{12} - 15 q^{13} - 3 q^{14} - 39 q^{15} - 2 q^{16} + 6 q^{17} - 34 q^{18} - 25 q^{19} - 10 q^{20} + 40 q^{21} + 18 q^{22} + q^{23} + 46 q^{24} - 45 q^{25} - 12 q^{26} + 26 q^{27} - 13 q^{28} + 14 q^{29} - 28 q^{30} - 14 q^{31} - 76 q^{32} + 63 q^{33} + 36 q^{34} + 50 q^{35} - 42 q^{36} + 14 q^{37} + 44 q^{38} - 6 q^{39} + 27 q^{40} - 17 q^{41} - 159 q^{42} - 15 q^{43} + 70 q^{44} + 40 q^{45} - 62 q^{46} + 9 q^{47} + 19 q^{48} - 151 q^{49} - 22 q^{50} - 25 q^{51} - q^{52} - 69 q^{53} + 51 q^{54} + 27 q^{55} + 51 q^{56} - 28 q^{57} + 156 q^{58} - 27 q^{59} + 87 q^{60} - 28 q^{61} - 25 q^{62} - 88 q^{63} + 10 q^{64} + 7 q^{65} + 30 q^{66} + 61 q^{67} + 124 q^{68} + 3 q^{69} - 263 q^{70} + 31 q^{71} + 31 q^{72} - 50 q^{73} - 90 q^{74} + 78 q^{75} + 66 q^{76} - 38 q^{77} + 31 q^{79} - 145 q^{80} + 36 q^{81} + 3 q^{82} + 23 q^{83} - 228 q^{84} - 58 q^{85} - 12 q^{86} + 68 q^{87} + 28 q^{88} + 39 q^{89} - 7 q^{90} - 12 q^{91} - 32 q^{92} - 17 q^{93} + 14 q^{94} + 123 q^{95} + 165 q^{96} - 51 q^{97} + 45 q^{98} - 45 q^{99}+O(q^{100}) \) 120 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 13 * q^5 - 10 * q^6 - 16 * q^7 - 6 * q^8 + 13 * q^9 + 3 * q^10 + 3 * q^11 - 12 * q^12 - 15 * q^13 - 3 * q^14 - 39 * q^15 - 2 * q^16 + 6 * q^17 - 34 * q^18 - 25 * q^19 - 10 * q^20 + 40 * q^21 + 18 * q^22 + q^23 + 46 * q^24 - 45 * q^25 - 12 * q^26 + 26 * q^27 - 13 * q^28 + 14 * q^29 - 28 * q^30 - 14 * q^31 - 76 * q^32 + 63 * q^33 + 36 * q^34 + 50 * q^35 - 42 * q^36 + 14 * q^37 + 44 * q^38 - 6 * q^39 + 27 * q^40 - 17 * q^41 - 159 * q^42 - 15 * q^43 + 70 * q^44 + 40 * q^45 - 62 * q^46 + 9 * q^47 + 19 * q^48 - 151 * q^49 - 22 * q^50 - 25 * q^51 - q^52 - 69 * q^53 + 51 * q^54 + 27 * q^55 + 51 * q^56 - 28 * q^57 + 156 * q^58 - 27 * q^59 + 87 * q^60 - 28 * q^61 - 25 * q^62 - 88 * q^63 + 10 * q^64 + 7 * q^65 + 30 * q^66 + 61 * q^67 + 124 * q^68 + 3 * q^69 - 263 * q^70 + 31 * q^71 + 31 * q^72 - 50 * q^73 - 90 * q^74 + 78 * q^75 + 66 * q^76 - 38 * q^77 + 31 * q^79 - 145 * q^80 + 36 * q^81 + 3 * q^82 + 23 * q^83 - 228 * q^84 - 58 * q^85 - 12 * q^86 + 68 * q^87 + 28 * q^88 + 39 * q^89 - 7 * q^90 - 12 * q^91 - 32 * q^92 - 17 * q^93 + 14 * q^94 + 123 * q^95 + 165 * q^96 - 51 * q^97 + 45 * q^98 - 45 * q^99

Introduction

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