LMFDB - Embedded newform 189.2.bd.a.185.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.2
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47573 + 0.436538i) q^{2} +(-1.50729 - 0.853281i) q^{3} +(4.05929 - 1.47746i) q^{4} +(-2.58032 + 0.939158i) q^{5} +(4.10412 + 1.45451i) q^{6} +(-2.62404 - 0.338290i) q^{7} +(-5.05050 + 2.91591i) q^{8} +(1.54382 + 2.57228i) q^{9} +O(q^{10})$	\(q+(-2.47573 + 0.436538i) q^{2} +(-1.50729 - 0.853281i) q^{3} +(4.05929 - 1.47746i) q^{4} +(-2.58032 + 0.939158i) q^{5} +(4.10412 + 1.45451i) q^{6} +(-2.62404 - 0.338290i) q^{7} +(-5.05050 + 2.91591i) q^{8} +(1.54382 + 2.57228i) q^{9} +(5.97819 - 3.45151i) q^{10} +(1.43170 - 3.93357i) q^{11} +(-7.37920 - 1.23676i) q^{12} +(0.0398496 + 0.109486i) q^{13} +(6.64408 - 0.307977i) q^{14} +(4.69064 + 0.786155i) q^{15} +(4.61245 - 3.87030i) q^{16} +(2.57344 + 4.45733i) q^{17} +(-4.94499 - 5.69433i) q^{18} +(4.51931 + 2.60922i) q^{19} +(-9.08669 + 7.62463i) q^{20} +(3.66652 + 2.74894i) q^{21} +(-1.82736 + 10.3635i) q^{22} +(7.39321 + 1.30362i) q^{23} +(10.1006 - 0.0856107i) q^{24} +(1.94579 - 1.63271i) q^{25} +(-0.146452 - 0.253662i) q^{26} +(-0.132107 - 5.19447i) q^{27} +(-11.1515 + 2.50369i) q^{28} +(1.21597 - 3.34086i) q^{29} +(-11.9559 + 0.101336i) q^{30} +(-0.106042 - 0.291348i) q^{31} +(-2.23240 + 2.66047i) q^{32} +(-5.51443 + 4.70737i) q^{33} +(-8.31695 - 9.91175i) q^{34} +(7.08855 - 1.59149i) q^{35} +(10.0673 + 8.16068i) q^{36} +1.91994 q^{37} +(-12.3276 - 4.48688i) q^{38} +(0.0333575 - 0.199030i) q^{39} +(10.2934 - 12.2672i) q^{40} +(-6.29347 + 2.29063i) q^{41} +(-10.2773 - 5.20506i) q^{42} +(0.411100 + 2.33146i) q^{43} -18.0828i q^{44} +(-6.39933 - 5.18740i) q^{45} -18.8727 q^{46} +(-4.74491 - 1.72700i) q^{47} +(-10.2547 + 1.89794i) q^{48} +(6.77112 + 1.77537i) q^{49} +(-4.10452 + 4.89157i) q^{50} +(-0.0755560 - 8.91435i) q^{51} +(0.323522 + 0.385559i) q^{52} +(3.76047 + 2.17111i) q^{53} +(2.59465 + 12.8024i) q^{54} +11.4945i q^{55} +(14.2391 - 5.94291i) q^{56} +(-4.58549 - 7.78908i) q^{57} +(-1.55201 + 8.80190i) q^{58} +(8.02306 + 6.73214i) q^{59} +(20.2022 - 3.73901i) q^{60} +(-0.395365 + 1.08626i) q^{61} +(0.389715 + 0.675007i) q^{62} +(-3.18087 - 7.27201i) q^{63} +(-1.65570 + 2.86775i) q^{64} +(-0.205649 - 0.245083i) q^{65} +(11.5973 - 14.0614i) q^{66} +(1.92499 - 10.9172i) q^{67} +(17.0319 + 14.2915i) q^{68} +(-10.0313 - 8.27342i) q^{69} +(-16.8546 + 7.03452i) q^{70} +(-5.47124 - 3.15882i) q^{71} +(-15.2976 - 8.48964i) q^{72} -2.58177i q^{73} +(-4.75325 + 0.838127i) q^{74} +(-4.32603 + 0.800659i) q^{75} +(22.2002 + 3.91449i) q^{76} +(-5.08753 + 9.83750i) q^{77} +(0.00429980 + 0.507305i) q^{78} +(2.74201 + 15.5507i) q^{79} +(-8.26674 + 14.3184i) q^{80} +(-4.23322 + 7.94228i) q^{81} +(14.5810 - 8.41833i) q^{82} +(10.6778 + 3.88640i) q^{83} +(18.9449 + 5.74161i) q^{84} +(-10.8264 - 9.08446i) q^{85} +(-2.03554 - 5.59261i) q^{86} +(-4.68352 + 3.99807i) q^{87} +(4.23912 + 24.0412i) q^{88} +(-0.456832 + 0.791256i) q^{89} +(18.1075 + 10.0490i) q^{90} +(-0.0675288 - 0.300776i) q^{91} +(31.9372 - 5.63140i) q^{92} +(-0.0887660 + 0.529628i) q^{93} +(12.5010 + 2.20427i) q^{94} +(-14.1117 - 2.48828i) q^{95} +(5.63499 - 2.10523i) q^{96} +(5.88114 - 1.03700i) q^{97} +(-17.5385 - 1.43948i) q^{98} +(12.3285 - 2.39000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.47573	+	0.436538i	−1.75061	+	0.308679i	−0.954883	−	0.296982i	$-0.904020\pi$
$2$	−2.47573	+	0.436538i	−1.75061	+	0.308679i	−0.795723	+	0.605661i	$0.792909\pi$
$3$	−1.50729	−	0.853281i	−0.870232	−	0.492642i
$3$	−1.50729	−	0.853281i	−0.870232	−	0.492642i
$4$	4.05929	−	1.47746i	2.02965	−	0.738731i
$5$	−2.58032	+	0.939158i	−1.15395	+	0.420004i	−0.846933	−	0.531699i	$-0.821554\pi$
$5$	−2.58032	+	0.939158i	−1.15395	+	0.420004i	−0.307019	+	0.951703i	$0.599332\pi$
$6$	4.10412	+	1.45451i	1.67550	+	0.593800i
$7$	−2.62404	−	0.338290i	−0.991792	−	0.127862i
$7$	−2.62404	−	0.338290i	−0.991792	−	0.127862i
$8$	−5.05050	+	2.91591i	−1.78562	+	1.03093i
$9$	1.54382	+	2.57228i	0.514608	+	0.857426i
$10$	5.97819	−	3.45151i	1.89047	−	1.09146i
$11$	1.43170	−	3.93357i	0.431675	−	1.18602i	−0.513109	−	0.858323i	$-0.671506\pi$
$11$	1.43170	−	3.93357i	0.431675	−	1.18602i	0.944784	−	0.327694i	$-0.106271\pi$
$12$	−7.37920	−	1.23676i	−2.13019	−	0.357022i
$13$	0.0398496	+	0.109486i	0.0110523	+	0.0303659i	0.945096	−	0.326793i	$-0.105968\pi$
$13$	0.0398496	+	0.109486i	0.0110523	+	0.0303659i	−0.934044	+	0.357158i	$0.883746\pi$
$14$	6.64408	−	0.307977i	1.77571	−	0.0823103i
$15$	4.69064	+	0.786155i	1.21112	+	0.202984i
$16$	4.61245	−	3.87030i	1.15311	−	0.967575i
$17$	2.57344	+	4.45733i	0.624152	+	1.08106i	0.988704	+	0.149879i	$0.0478886\pi$
$17$	2.57344	+	4.45733i	0.624152	+	1.08106i	−0.364553	+	0.931183i	$0.618778\pi$
$18$	−4.94499	−	5.69433i	−1.16554	−	1.34217i
$19$	4.51931	+	2.60922i	1.03680	+	0.598597i	0.918925	−	0.394432i	$-0.129059\pi$
$19$	4.51931	+	2.60922i	1.03680	+	0.598597i	0.117875	+	0.993028i	$0.462392\pi$
$20$	−9.08669	+	7.62463i	−2.03184	+	1.70492i
$21$	3.66652	+	2.74894i	0.800099	+	0.599868i
$22$	−1.82736	+	10.3635i	−0.389594	+	2.20950i
$23$	7.39321	+	1.30362i	1.54159	+	0.271824i	0.878877	−	0.477049i	$-0.158294\pi$
$23$	7.39321	+	1.30362i	1.54159	+	0.271824i	0.662714	+	0.748873i	$0.269405\pi$
$24$	10.1006	−	0.0856107i	2.06178	−	0.0174752i
$25$	1.94579	−	1.63271i	0.389158	−	0.326543i
$26$	−0.146452	−	0.253662i	−0.0287215	−	0.0497472i
$27$	−0.132107	−	5.19447i	−0.0254240	−	0.999677i
$28$	−11.1515	+	2.50369i	−2.10744	+	0.473153i
$29$	1.21597	−	3.34086i	0.225801	−	0.620383i	−0.774119	−	0.633040i	$-0.781807\pi$
$29$	1.21597	−	3.34086i	0.225801	−	0.620383i	0.999920	+	0.0126573i	$0.00402906\pi$
$30$	−11.9559	+	0.101336i	−2.18285	+	0.0185013i
$31$	−0.106042	−	0.291348i	−0.0190457	−	0.0523276i	0.929805	−	0.368051i	$-0.119975\pi$
$31$	−0.106042	−	0.291348i	−0.0190457	−	0.0523276i	−0.948851	+	0.315724i	$0.897753\pi$
$32$	−2.23240	+	2.66047i	−0.394636	+	0.470309i
$33$	−5.51443	+	4.70737i	−0.959939	+	0.819449i
$34$	−8.31695	−	9.91175i	−1.42634	−	1.69985i
$35$	7.08855	−	1.59149i	1.19818	−	0.269011i
$36$	10.0673	+	8.16068i	1.67788	+	1.36011i
$37$	1.91994			0.315636			0.157818	−	0.987468i	$-0.449554\pi$
$37$	1.91994			0.315636			0.157818	+	0.987468i	$0.449554\pi$
$38$	−12.3276	−	4.48688i	−1.99980	−	0.727868i
$39$	0.0333575	−	0.199030i	0.00534147	−	0.0318702i
$40$	10.2934	−	12.2672i	1.62753	−	1.93961i
$41$	−6.29347	+	2.29063i	−0.982874	+	0.357737i	−0.782957	−	0.622076i	$-0.786290\pi$
$41$	−6.29347	+	2.29063i	−0.982874	+	0.357737i	−0.199917	+	0.979813i	$0.564067\pi$
$42$	−10.2773	−	5.20506i	−1.58582	−	0.803158i
$43$	0.411100	+	2.33146i	0.0626921	+	0.355545i	0.999976	+	0.00697673i	$0.00222078\pi$
$43$	0.411100	+	2.33146i	0.0626921	+	0.355545i	−0.937284	+	0.348568i	$0.886668\pi$
$44$		−	18.0828i		−	2.72609i
$45$	−6.39933	−	5.18740i	−0.953955	−	0.773291i
$46$	−18.8727			−2.78262
$47$	−4.74491	−	1.72700i	−0.692116	−	0.251910i	−0.0280749	−	0.999606i	$-0.508938\pi$
$47$	−4.74491	−	1.72700i	−0.692116	−	0.251910i	−0.664041	+	0.747696i	$0.731160\pi$
$48$	−10.2547	+	1.89794i	−1.48014	+	0.273944i
$49$	6.77112	+	1.77537i	0.967303	+	0.253624i
$50$	−4.10452	+	4.89157i	−0.580466	+	0.691773i
$51$	−0.0755560	−	8.91435i	−0.0105800	−	1.24826i
$52$	0.323522	+	0.385559i	0.0448645	+	0.0534674i
$53$	3.76047	+	2.17111i	0.516541	+	0.298225i	0.735518	−	0.677505i	$-0.236939\pi$
$53$	3.76047	+	2.17111i	0.516541	+	0.298225i	−0.218977	+	0.975730i	$0.570272\pi$
$54$	2.59465	+	12.8024i	0.353087	+	1.74219i
$55$			11.4945i			1.54991i
$56$	14.2391	−	5.94291i	1.90278	−	0.794155i
$57$	−4.58549	−	7.78908i	−0.607362	−	1.03169i
$58$	−1.55201	+	8.80190i	−0.203789	+	1.15575i
$59$	8.02306	+	6.73214i	1.04451	+	0.876450i	0.992506	−	0.122196i	$-0.0389937\pi$
$59$	8.02306	+	6.73214i	1.04451	+	0.876450i	0.0520070	+	0.998647i	$0.483438\pi$
$60$	20.2022	−	3.73901i	2.60809	−	0.482704i
$61$	−0.395365	+	1.08626i	−0.0506214	+	0.139081i	−0.962427	−	0.271542i	$-0.912466\pi$
$61$	−0.395365	+	1.08626i	−0.0506214	+	0.139081i	0.911805	+	0.410623i	$0.134689\pi$
$62$	0.389715	+	0.675007i	0.0494939	+	0.0857260i
$63$	−3.18087	−	7.27201i	−0.400752	−	0.916187i
$64$	−1.65570	+	2.86775i	−0.206962	+	0.358469i
$65$	−0.205649	−	0.245083i	−0.0255077	−	0.0303988i
$66$	11.5973	−	14.0614i	1.42753	−	1.73084i
$67$	1.92499	−	10.9172i	0.235175	−	1.33374i	−0.607070	−	0.794648i	$-0.707655\pi$
$67$	1.92499	−	10.9172i	0.235175	−	1.33374i	0.842245	−	0.539095i	$-0.181234\pi$
$68$	17.0319	+	14.2915i	2.06542	+	1.73309i
$69$	−10.0313	−	8.27342i	−1.20763	−	0.996002i
$70$	−16.8546	+	7.03452i	−2.01451	+	0.840786i
$71$	−5.47124	−	3.15882i	−0.649317	−	0.374883i	0.138878	−	0.990310i	$-0.455650\pi$
$71$	−5.47124	−	3.15882i	−0.649317	−	0.374883i	−0.788194	+	0.615426i	$0.788984\pi$
$72$	−15.2976	−	8.48964i	−1.80284	−	1.00051i
$73$		−	2.58177i		−	0.302173i	−0.988521	−	0.151087i	$-0.951723\pi$
$73$		−	2.58177i		−	0.302173i	0.988521	−	0.151087i	$-0.0482773\pi$
$74$	−4.75325	+	0.838127i	−0.552555	+	0.0974303i
$75$	−4.32603	+	0.800659i	−0.499527	+	0.0924521i
$76$	22.2002	+	3.91449i	2.54654	+	0.449023i
$77$	−5.08753	+	9.83750i	−0.579778	+	1.12109i
$78$	0.00429980	+	0.507305i	0.000486857	+	0.0574410i
$79$	2.74201	+	15.5507i	0.308501	+	1.74959i	0.606552	+	0.795044i	$0.292552\pi$
$79$	2.74201	+	15.5507i	0.308501	+	1.74959i	−0.298052	+	0.954550i	$0.596337\pi$
$80$	−8.26674	+	14.3184i	−0.924250	+	1.60085i
$81$	−4.23322	+	7.94228i	−0.470358	+	0.882476i
$82$	14.5810	−	8.41833i	1.61020	−	0.929649i
$83$	10.6778	+	3.88640i	1.17204	+	0.426588i	0.853384	−	0.521282i	$-0.174546\pi$
$83$	10.6778	+	3.88640i	1.17204	+	0.426588i	0.318657	+	0.947870i	$0.396768\pi$
$84$	18.9449	+	5.74161i	2.06706	+	0.626461i
$85$	−10.8264	−	9.08446i	−1.17429	−	0.985348i
$86$	−2.03554	−	5.59261i	−0.219498	−	0.603067i
$87$	−4.68352	+	3.99807i	−0.502126	+	0.428638i
$88$	4.23912	+	24.0412i	0.451891	+	2.56280i
$89$	−0.456832	+	0.791256i	−0.0484241	+	0.0838730i	−0.889221	−	0.457477i	$-0.848753\pi$
$89$	−0.456832	+	0.791256i	−0.0484241	+	0.0838730i	0.840797	+	0.541350i	$0.182087\pi$
$90$	18.1075	+	10.0490i	1.90870	+	1.05926i
$91$	−0.0675288	−	0.300776i	−0.00707894	−	0.0315299i
$92$	31.9372	−	5.63140i	3.32969	−	0.587114i
$93$	−0.0887660	+	0.529628i	−0.00920460	+	0.0549198i
$94$	12.5010	+	2.20427i	1.28938	+	0.227353i
$95$	−14.1117	−	2.48828i	−1.44783	−	0.255292i
$96$	5.63499	−	2.10523i	0.575119	−	0.214864i
$97$	5.88114	−	1.03700i	0.597140	−	0.105292i	0.133094	−	0.991103i	$-0.457509\pi$
$97$	5.88114	−	1.03700i	0.597140	−	0.105292i	0.464045	+	0.885812i	$0.346398\pi$
$98$	−17.5385	−	1.43948i	−1.77165	−	0.145410i
$99$	12.3285	−	2.39000i	1.23906	−	0.240204i
$100$	5.48627	−	9.50249i	0.548627	−	0.950249i
$101$	1.43057	+	8.11319i	0.142347	+	0.807292i	0.969459	+	0.245254i	$0.0788714\pi$
$101$	1.43057	+	8.11319i	0.142347	+	0.807292i	−0.827111	+	0.562038i	$0.810017\pi$
$102$	4.07851	+	22.0365i	0.403833	+	2.18194i
$103$	−0.337183	−	0.926404i	−0.0332237	−	0.0912813i	0.921972	−	0.387257i	$-0.126577\pi$
$103$	−0.337183	−	0.926404i	−0.0332237	−	0.0912813i	−0.955195	+	0.295976i	$0.904355\pi$
$104$	−0.520511	−	0.436761i	−0.0510403	−	0.0428279i
$105$	−12.0425	−	3.64969i	−1.17522	−	0.356174i
$106$	−10.2577	−	3.73349i	−0.996315	−	0.362629i
$107$	11.2050	−	6.46919i	1.08322	−	0.625400i	0.151460	−	0.988463i	$-0.451603\pi$
$107$	11.2050	−	6.46919i	1.08322	−	0.625400i	0.931764	+	0.363064i	$0.118269\pi$
$108$	−8.21089	−	20.8907i	−0.790093	−	2.01021i
$109$	1.89554	−	3.28318i	0.181560	−	0.314471i	−0.760852	−	0.648926i	$-0.775219\pi$
$109$	1.89554	−	3.28318i	0.181560	−	0.314471i	0.942412	+	0.334454i	$0.108552\pi$
$110$	−5.01777	−	28.4572i	−0.478426	−	2.71329i
$111$	−2.89390	−	1.63825i	−0.274677	−	0.155496i
$112$	−13.4125	+	8.59546i	−1.26736	+	0.812195i
$113$	2.66007	+	0.469041i	0.250238	+	0.0441237i	0.297360	−	0.954765i	$-0.403894\pi$
$113$	2.66007	+	0.469041i	0.250238	+	0.0441237i	−0.0471221	+	0.998889i	$0.515005\pi$
$114$	14.7527	+	17.2819i	1.38171	+	1.61860i
$115$	−20.3011	+	3.57964i	−1.89309	+	0.333803i
$116$		−	15.3581i		−	1.42596i
$117$	−0.220107	+	0.271531i	−0.0203489	+	0.0251031i
$118$	−22.8018	−	13.1646i	−2.09907	−	1.21190i
$119$	−5.24493	−	12.5668i	−0.480802	−	1.15199i
$120$	−25.9824	+	9.70700i	−2.37186	+	0.886124i
$121$	−4.99673	−	4.19276i	−0.454249	−	0.381160i
$122$	0.504625	−	2.86187i	0.0456866	−	0.259102i
$123$	11.4406	+	1.91745i	1.03156	+	0.172891i
$124$	−0.860909	−	1.02599i	−0.0773120	−	0.0921368i
$125$	3.37741	−	5.84984i	0.302084	−	0.523225i
$126$	11.0495	+	16.6150i	0.984366	+	1.48018i
$127$	0.619432	+	1.07289i	0.0549657	+	0.0952034i	0.892199	−	0.451642i	$-0.149162\pi$
$127$	0.619432	+	1.07289i	0.0549657	+	0.0952034i	−0.837233	+	0.546846i	$0.815828\pi$
$128$	5.22285	−	14.3496i	0.461639	−	1.26834i
$129$	1.36975	−	3.86496i	0.120600	−	0.340291i
$130$	0.616120	+	0.516986i	0.0540373	+	0.0453427i
$131$	1.30100	−	7.37831i	0.113669	−	0.644646i	−0.873732	−	0.486407i	$-0.838307\pi$
$131$	1.30100	−	7.37831i	0.113669	−	0.644646i	0.987401	−	0.158239i	$-0.0505817\pi$
$132$	−15.4297	+	27.2560i	−1.34298	+	2.37233i
$133$	−10.9761	−	8.37553i	−0.951752	−	0.726250i
$134$			27.8683i			2.40745i
$135$	5.21931	+	13.2793i	0.449207	+	1.14290i
$136$	−25.9943	−	15.0078i	−2.22900	−	1.28691i
$137$	10.4685	+	12.4759i	0.894383	+	1.06588i	0.997461	+	0.0712111i	$0.0226864\pi$
$137$	10.4685	+	12.4759i	0.894383	+	1.06588i	−0.103078	+	0.994673i	$0.532869\pi$
$138$	28.4465	+	16.1037i	2.42153	+	1.37084i
$139$	6.25623	−	7.45589i	0.530647	−	0.632400i	−0.432417	−	0.901674i	$-0.642339\pi$
$139$	6.25623	−	7.45589i	0.530647	−	0.632400i	0.963064	+	0.269274i	$0.0867836\pi$
$140$	26.4231	−	16.9334i	2.23316	−	1.43113i
$141$	5.67831	+	6.65183i	0.478200	+	0.560185i
$142$	14.9243	+	5.43199i	1.25242	+	0.455842i
$143$	0.487724			0.0407855
$144$	17.0763	+	5.88943i	1.42302	+	0.490786i
$145$			9.76248i			0.810730i
$146$	1.12704	+	6.39177i	0.0932746	+	0.528987i
$147$	−8.69113	−	8.45366i	−0.716832	−	0.697246i
$148$	7.79359	−	2.83664i	0.640630	−	0.233170i
$149$	−10.7706	+	12.8359i	−0.882365	+	1.05156i	0.115934	+	0.993257i	$0.463014\pi$
$149$	−10.7706	+	12.8359i	−0.882365	+	1.05156i	−0.998299	+	0.0583043i	$0.981431\pi$
$150$	10.3606	−	3.87069i	0.845936	−	0.316041i
$151$	14.0649	+	5.11922i	1.14459	+	0.416596i	0.843568	−	0.537022i	$-0.180451\pi$
$151$	14.0649	+	5.11922i	1.14459	+	0.416596i	0.301020	+	0.953618i	$0.402673\pi$
$152$	−30.4330			−2.46844
$153$	−7.49256	+	13.5009i	−0.605738	+	1.09149i
$154$	8.30090	−	26.5759i	0.668906	−	2.14155i
$155$	0.547243	+	0.652179i	0.0439556	+	0.0523843i
$156$	−0.158651	−	0.857203i	−0.0127022	−	0.0686312i
$157$	−2.07640	+	2.47456i	−0.165715	+	0.197492i	−0.842511	−	0.538679i	$-0.818924\pi$
$157$	−2.07640	+	2.47456i	−0.165715	+	0.197492i	0.676796	+	0.736171i	$0.263368\pi$
$158$	−13.5770	−	37.3024i	−1.08013	−	2.96762i
$159$	−3.81554	−	6.48123i	−0.302592	−	0.513995i
$160$	3.26169	−	8.96143i	0.257860	−	0.708464i
$161$	−18.9590	−	5.92180i	−1.49418	−	0.466703i
$162$	7.01321	−	21.5109i	0.551010	−	1.69006i
$163$	3.85622	+	6.67918i	0.302043	+	0.523153i	0.976599	−	0.215070i	$-0.0689981\pi$
$163$	3.85622	+	6.67918i	0.302043	+	0.523153i	−0.674556	+	0.738224i	$0.735665\pi$
$164$	−22.1627	+	18.5967i	−1.73062	+	1.45216i
$165$	9.80801	−	17.3254i	0.763552	−	1.34878i
$166$	−28.1319	−	4.96042i	−2.18346	−	0.385003i
$167$	0.286318	−	1.62379i	0.0221559	−	0.125652i	−0.971724	−	0.236121i	$-0.924124\pi$
$167$	0.286318	−	1.62379i	0.0221559	−	0.125652i	0.993880	+	0.110468i	$0.0352350\pi$
$168$	−26.5334	−	3.19230i	−2.04710	−	0.246291i
$169$	9.94818	−	8.34751i	0.765245	−	0.642116i
$170$	30.7691	+	17.7645i	2.35988	+	1.36248i
$171$	0.265363	+	15.6531i	0.0202928	+	1.19702i
$172$	5.11342	+	8.85670i	0.389894	+	0.675317i
$173$	−14.0046	+	11.7513i	−1.06475	+	0.893434i	−0.994567	−	0.104100i	$-0.966804\pi$
$173$	−14.0046	+	11.7513i	−1.06475	+	0.893434i	−0.0701858	+	0.997534i	$0.522359\pi$
$174$	9.84982	−	11.9427i	0.746713	−	0.905372i
$175$	−5.65816	+	3.62606i	−0.427716	+	0.274104i
$176$	−8.62046	−	23.6845i	−0.649792	−	1.78529i
$177$	−6.34863	−	16.9932i	−0.477192	−	1.27729i
$178$	0.785580	−	2.15836i	0.0588817	−	0.161776i
$179$	3.65498	−	2.11020i	0.273186	−	0.157724i	−0.357149	−	0.934048i	$-0.616251\pi$
$179$	3.65498	−	2.11020i	0.273186	−	0.157724i	0.630335	+	0.776324i	$0.282918\pi$
$180$	−33.6409	−	11.6024i	−2.50745	−	0.864791i
$181$	−9.51249	+	5.49204i	−0.707058	+	0.408220i	−0.809971	−	0.586470i	$-0.800517\pi$
$181$	−9.51249	+	5.49204i	−0.707058	+	0.408220i	0.102913	+	0.994690i	$0.467184\pi$
$182$	0.298483	+	0.715161i	0.0221250	+	0.0530112i
$183$	1.52281	−	1.29994i	0.112569	−	0.0960946i
$184$	−41.1406	+	14.9740i	−3.03293	+	1.10390i
$185$	−4.95405	+	1.80313i	−0.364229	+	0.132569i
$186$	−0.0114420	−	1.34997i	−0.000838968	−	0.0989843i
$187$	21.2177	−	3.74125i	1.55159	−	0.273587i
$188$	−21.8125			−1.59084
$189$	−1.41058	+	13.6752i	−0.102605	+	0.994722i
$190$	36.0230			2.61338
$191$	−10.0041	+	1.76400i	−0.723872	+	0.127638i	−0.523432	−	0.852068i	$-0.675348\pi$
$191$	−10.0041	+	1.76400i	−0.723872	+	0.127638i	−0.200441	+	0.979706i	$0.564237\pi$
$192$	4.94260	−	2.90974i	0.356702	−	0.209993i
$193$	−8.12064	+	2.95567i	−0.584536	+	0.212754i	−0.617325	−	0.786708i	$-0.711784\pi$
$193$	−8.12064	+	2.95567i	−0.584536	+	0.212754i	0.0327883	+	0.999462i	$0.489561\pi$
$194$	−14.1074	+	5.13469i	−1.01285	+	0.368649i
$195$	0.100847	+	0.544887i	0.00722183	+	0.0390202i
$196$	30.1090	−	2.79733i	2.15064	−	0.199809i
$197$	0.625155	−	0.360933i	0.0445405	−	0.0257154i	−0.477564	−	0.878597i	$-0.658480\pi$
$197$	0.625155	−	0.360933i	0.0445405	−	0.0257154i	0.522105	+	0.852881i	$0.325147\pi$
$198$	−29.4788	+	11.2989i	−2.09497	+	0.802976i
$199$	18.8603	−	10.8890i	1.33697	−	0.771899i	0.350612	−	0.936521i	$-0.385974\pi$
$199$	18.8603	−	10.8890i	1.33697	−	0.771899i	0.986357	+	0.164622i	$0.0526403\pi$
$200$	−5.06638	+	13.9198i	−0.358247	+	0.984276i
$201$	−12.2169	+	14.8127i	−0.861715	+	1.04481i
$202$	−7.08343	−	19.4616i	−0.498388	−	1.36931i
$203$	−4.32094	+	8.35519i	−0.303271	+	0.586419i
$204$	−13.4773	−	36.0743i	−0.943600	−	2.52571i
$205$	14.0879	−	11.8211i	0.983939	−	0.825623i
$206$	1.23919	+	2.14633i	0.0863382	+	0.149542i
$207$	8.06052	+	21.0299i	0.560245	+	1.46168i
$208$	0.607548	+	0.350768i	0.0421259	+	0.0243214i
$209$	16.7339	−	14.0414i	1.15751	−	0.971263i
$210$	31.4071	+	3.77867i	2.16730	+	0.260753i
$211$	1.68157	−	9.53668i	0.115764	−	0.656532i	−0.870605	−	0.491983i	$-0.836272\pi$
$211$	1.68157	−	9.53668i	0.115764	−	0.656532i	0.986369	−	0.164549i	$-0.0526168\pi$
$212$	18.4726	+	3.25722i	1.26870	+	0.223706i
$213$	5.55136	+	9.42975i	0.380373	+	0.646116i
$214$	−24.9164	+	20.9074i	−1.70325	+	1.42920i
$215$	−3.25038	−	5.62982i	−0.221674	−	0.383951i
$216$	15.8138	+	25.8495i	1.07599	+	1.75883i
$217$	0.179698	+	0.800379i	0.0121987	+	0.0543333i
$218$	−3.25962	+	8.95574i	−0.220769	+	0.606559i
$219$	−2.20298	+	3.89147i	−0.148863	+	0.262961i
$220$	16.9826	+	46.6594i	1.14497	+	3.14577i
$221$	−0.385465	+	0.459379i	−0.0259292	+	0.0309012i
$222$	7.87967	+	2.79256i	0.528849	+	0.187425i
$223$	−18.0896	−	21.5583i	−1.21137	−	1.44365i	−0.862184	−	0.506596i	$-0.830904\pi$
$223$	−18.0896	−	21.5583i	−1.21137	−	1.44365i	−0.349183	−	0.937055i	$-0.613541\pi$
$224$	6.75791	−	6.22597i	0.451532	−	0.415990i
$225$	7.20375	+	2.48450i	0.480250	+	0.165633i
$226$	−6.79036			−0.451688
$227$	−7.19954	−	2.62042i	−0.477850	−	0.173923i	0.0918550	−	0.995772i	$-0.470720\pi$
$227$	−7.19954	−	2.62042i	−0.477850	−	0.173923i	−0.569705	+	0.821849i	$0.692943\pi$
$228$	−30.1219	−	24.8433i	−1.99487	−	1.64529i
$229$	9.13922	−	10.8917i	0.603937	−	0.719744i	−0.374283	−	0.927314i	$-0.622111\pi$
$229$	9.13922	−	10.8917i	0.603937	−	0.719744i	0.978220	+	0.207571i	$0.0665557\pi$
$230$	48.6975	−	17.7244i	3.21102	−	1.16871i
$231$	16.0625	−	10.4868i	1.05684	−	0.689983i
$232$	3.60037	+	20.4187i	0.236376	+	1.34055i
$233$			22.4909i			1.47343i	0.676204	+	0.736714i	$0.263624\pi$
$233$			22.4909i			1.47343i	−0.676204	+	0.736714i	$0.736376\pi$
$234$	0.426393	−	0.768323i	0.0278742	−	0.0502269i
$235$	13.8653			0.904472
$236$	42.5144	+	15.4740i	2.76745	+	1.00727i
$237$	9.13614	−	25.7791i	0.593456	−	1.67453i
$238$	18.4709	+	28.8223i	1.19729	+	1.86827i
$239$	−15.3178	+	18.2550i	−0.990825	+	1.18082i	−0.00731345	+	0.999973i	$0.502328\pi$
$239$	−15.3178	+	18.2550i	−0.990825	+	1.18082i	−0.983511	+	0.180846i	$0.942116\pi$
$240$	24.6780	−	14.5281i	1.59296	−	0.937785i
$241$	8.71797	+	10.3897i	0.561574	+	0.669257i	0.969879	−	0.243588i	$-0.0783245\pi$
$241$	8.71797	+	10.3897i	0.561574	+	0.669257i	−0.408305	+	0.912846i	$0.633880\pi$
$242$	14.2009	+	8.19887i	0.912866	+	0.527044i
$243$	13.1577	−	8.35916i	0.844065	−	0.536240i
$244$			4.99357i			0.319681i
$245$	−19.1390	+	1.77814i	−1.22274	+	0.113601i
$246$	−29.1609	+	0.247161i	−1.85923	+	0.0157584i
$247$	−0.105581	+	0.598777i	−0.00671793	+	0.0380993i
$248$	1.38511	+	1.16224i	0.0879544	+	0.0738025i
$249$	−12.7783	−	14.9691i	−0.809792	−	0.948627i
$250$	−5.80787	+	15.9570i	−0.367322	+	1.00921i
$251$	4.77251	+	8.26623i	0.301238	+	0.521760i	0.976417	−	0.215895i	$-0.0692668\pi$
$251$	4.77251	+	8.26623i	0.301238	+	0.521760i	−0.675179	+	0.737654i	$0.735933\pi$
$252$	−23.6562	−	24.8196i	−1.49020	−	1.56349i
$253$	15.7128	−	27.2153i	0.987854	−	1.71101i
$254$	−2.00190	−	2.38578i	−0.125611	−	0.149697i
$255$	8.56694	+	22.9309i	0.536483	+	1.43599i
$256$	−5.51615	+	31.2837i	−0.344760	+	1.95523i
$257$	−4.23694	−	3.55522i	−0.264293	−	0.221768i	0.501005	−	0.865445i	$-0.332964\pi$
$257$	−4.23694	−	3.55522i	−0.264293	−	0.221768i	−0.765298	+	0.643676i	$0.777408\pi$
$258$	−1.70392	+	10.1666i	−0.106082	+	0.632942i
$259$	−5.03799	−	0.649496i	−0.313045	−	0.0403577i
$260$	−1.19689	−	0.691025i	−0.0742280	−	0.0428556i
$261$	10.4709	−	2.02988i	0.648131	−	0.125646i
$262$			18.8347i			1.16361i
$263$	−8.23979	+	1.45290i	−0.508087	+	0.0895895i	−0.421815	−	0.906682i	$-0.638607\pi$
$263$	−8.23979	+	1.45290i	−0.508087	+	0.0895895i	−0.0862727	+	0.996272i	$0.527496\pi$
$264$	14.1244	−	39.8542i	0.869295	−	2.45285i
$265$	−11.7422	−	2.07047i	−0.721319	−	0.127188i
$266$	30.8302	+	15.9440i	1.89032	+	0.977592i
$267$	1.36374	−	0.802844i	0.0834596	−	0.0491332i
$268$	−8.31559	−	47.1600i	−0.507955	−	2.88076i
$269$	9.52435	−	16.4967i	0.580710	−	1.00582i	−0.414685	−	0.909965i	$-0.636108\pi$
$269$	9.52435	−	16.4967i	0.580710	−	1.00582i	0.995395	−	0.0958542i	$-0.0305583\pi$
$270$	−18.7185	−	30.5976i	−1.13917	−	1.86211i
$271$	−21.6453	+	12.4969i	−1.31486	+	0.759134i	−0.982896	−	0.184159i	$-0.941044\pi$
$271$	−21.6453	+	12.4969i	−1.31486	+	0.759134i	−0.331962	+	0.943293i	$0.607710\pi$
$272$	29.1211	+	10.5992i	1.76573	+	0.642671i
$273$	−0.154861	+	0.510976i	−0.00937261	+	0.0309257i
$274$	−31.3633	−	26.3170i	−1.89473	−	1.58987i
$275$	−3.63660	−	9.99148i	−0.219295	−	0.602509i
$276$	−52.9437	−	18.7633i	−3.18684	−	1.12942i
$277$	3.87669	+	21.9858i	0.232928	+	1.32100i	0.846934	+	0.531698i	$0.178446\pi$
$277$	3.87669	+	21.9858i	0.232928	+	1.32100i	−0.614006	+	0.789301i	$0.710443\pi$
$278$	−12.2340	+	21.1899i	−0.733745	+	1.27088i
$279$	0.585717	−	0.722558i	0.0350660	−	0.0432584i
$280$	−31.1601	+	28.7074i	−1.86217	+	1.71559i
$281$	11.7375	−	2.06964i	0.700200	−	0.123464i	0.187795	−	0.982208i	$-0.439866\pi$
$281$	11.7375	−	2.06964i	0.700200	−	0.123464i	0.512405	+	0.858744i	$0.328755\pi$
$282$	−16.9617	−	13.9893i	−1.01006	−	0.833053i
$283$	−3.98101	−	0.701959i	−0.236646	−	0.0417271i	0.0540671	−	0.998537i	$-0.482782\pi$
$283$	−3.98101	−	0.701959i	−0.236646	−	0.0417271i	−0.290713	+	0.956810i	$0.593893\pi$
$284$	−26.8764	−	4.73903i	−1.59482	−	0.281210i
$285$	19.1472	+	15.7918i	1.13418	+	0.935425i
$286$	−1.20747	+	0.212910i	−0.0713994	+	0.0125896i
$287$	17.2892	−	3.88169i	1.02055	−	0.229129i
$288$	−10.2899	−	1.63506i	−0.606338	−	0.0963467i
$289$	−4.74522	+	8.21896i	−0.279130	+	0.483468i
$290$	−4.26169	−	24.1693i	−0.250255	−	1.41927i
$291$	−9.74942	−	3.45521i	−0.571521	−	0.202548i
$292$	−3.81447	−	10.4802i	−0.223225	−	0.613305i
$293$	−1.36115	−	1.14214i	−0.0795192	−	0.0667245i	0.602162	−	0.798374i	$-0.294306\pi$
$293$	−1.36115	−	1.14214i	−0.0795192	−	0.0667245i	−0.681681	+	0.731650i	$0.738751\pi$
$294$	25.2072	+	17.1350i	1.47012	+	0.999332i
$295$	−27.0246	−	9.83614i	−1.57343	−	0.572682i
$296$	−9.69666	+	5.59837i	−0.563607	+	0.325399i
$297$	−20.6220	−	6.91729i	−1.19661	−	0.401382i
$298$	21.0618	−	36.4801i	1.22008	−	2.11324i
$299$	0.151888	+	0.861401i	0.00878392	+	0.0498161i
$300$	−16.3777	+	9.64165i	−0.945565	+	0.556661i
$301$	−0.290030	−	6.25691i	−0.0167170	−	0.360642i
$302$	−37.0557	−	6.53392i	−2.13232	−	0.375985i
$303$	4.76654	−	13.4496i	0.273831	−	0.772658i
$304$	30.9435	−	5.45618i	1.77473	−	0.312933i
$305$		−	3.17420i		−	0.181754i
$306$	12.6559	−	36.6955i	0.723489	−	2.09774i
$307$	17.0250	+	9.82941i	0.971670	+	0.560994i	0.899745	−	0.436416i	$-0.143752\pi$
$307$	17.0250	+	9.82941i	0.971670	+	0.560994i	0.0719253	+	0.997410i	$0.477086\pi$
$308$	−6.11723	+	47.4499i	−0.348561	+	2.70371i
$309$	−0.282251	+	1.68407i	−0.0160567	+	0.0958033i
$310$	−1.63953	−	1.37573i	−0.0931189	−	0.0781360i
$311$	4.59744	−	26.0734i	0.260697	−	1.47849i	−0.520317	−	0.853973i	$-0.674186\pi$
$311$	4.59744	−	26.0734i	0.260697	−	1.47849i	0.781014	−	0.624514i	$-0.214703\pi$
$312$	0.411880	+	1.10247i	0.0233181	+	0.0624149i
$313$	3.24044	+	3.86181i	0.183161	+	0.218282i	0.849810	−	0.527089i	$-0.176717\pi$
$313$	3.24044	+	3.86181i	0.183161	+	0.218282i	−0.666649	+	0.745371i	$0.732272\pi$
$314$	4.06038	−	7.03278i	0.229140	−	0.396883i
$315$	15.0372	+	15.7767i	0.847251	+	0.888918i
$316$	34.1062	+	59.0737i	1.91862	+	3.32316i
$317$	10.5704	−	29.0420i	0.593694	−	1.63116i	−0.169897	−	0.985462i	$-0.554344\pi$
$317$	10.5704	−	29.0420i	0.593694	−	1.63116i	0.763592	−	0.645699i	$-0.223434\pi$
$318$	12.2756	+	14.3801i	0.688379	+	0.806398i
$319$	−11.4006	−	9.56625i	−0.638312	−	0.535607i
$320$	1.57895	−	8.95466i	0.0882659	−	0.500581i
$321$	−22.4091	+	0.189934i	−1.25075	+	0.0106011i
$322$	49.5225	+	6.38443i	2.75978	+	0.355790i
$323$			26.8587i			1.49446i
$324$	−5.44947	+	38.4945i	−0.302748	+	2.13858i
$325$	0.256298	+	0.147974i	0.0142169	+	0.00820811i
$326$	−12.4627	−	14.8525i	−0.690244	−	0.822601i
$327$	−5.65860	+	3.33125i	−0.312921	+	0.184219i
$328$	25.1059	−	29.9200i	1.38624	−	1.65206i
$329$	11.8666	+	6.13688i	0.654225	+	0.338337i
$330$	−16.7188	+	47.1747i	−0.920338	+	2.59688i
$331$	−15.4130	−	5.60987i	−0.847174	−	0.308346i	−0.118286	−	0.992980i	$-0.537740\pi$
$331$	−15.4130	−	5.60987i	−0.847174	−	0.308346i	−0.728888	+	0.684633i	$0.759962\pi$
$332$	49.0863			2.69396
$333$	2.96405	+	4.93862i	0.162429	+	0.270635i
$334$			4.14505i			0.226807i
$335$	5.28586	+	29.9776i	0.288797	+	1.63785i
$336$	27.5508	−	1.51119i	1.50302	−	0.0824420i
$337$	−1.34897	+	0.490985i	−0.0734831	+	0.0267457i	−0.378500	−	0.925601i	$-0.623560\pi$
$337$	−1.34897	+	0.490985i	−0.0734831	+	0.0267457i	0.305017	+	0.952347i	$0.401338\pi$
$338$	−20.9850	+	25.0090i	−1.14143	+	1.36031i
$339$	−3.60926	−	2.97676i	−0.196028	−	0.161676i
$340$	−57.3696	−	20.8808i	−3.11130	−	1.13242i
$341$	−1.29786			−0.0702829
$342$	−7.49013	−	38.6370i	−0.405020	−	2.08925i
$343$	−17.1671	−	6.94923i	−0.926934	−	0.375223i
$344$	−8.87459	−	10.5763i	−0.478486	−	0.570237i
$345$	33.6540	+	11.9270i	1.81187	+	0.642130i
$346$	29.5418	−	35.2066i	1.58818	−	1.89272i
$347$	2.17743	+	5.98243i	0.116890	+	0.321154i	0.984316	−	0.176413i	$-0.0564493\pi$
$347$	2.17743	+	5.98243i	0.116890	+	0.321154i	−0.867426	+	0.497566i	$0.834227\pi$
$348$	−13.1048	+	23.1490i	−0.702489	+	1.24092i
$349$	−2.99689	+	8.23388i	−0.160420	+	0.440749i	−0.993696	−	0.112107i	$-0.964240\pi$
$349$	−2.99689	+	8.23388i	−0.160420	+	0.440749i	0.833276	+	0.552856i	$0.186462\pi$
$350$	12.4252	−	11.4471i	0.664153	−	0.611875i
$351$	0.563457	−	0.221462i	0.0300751	−	0.0118207i
$352$	7.26902	+	12.5903i	0.387440	+	0.671066i
$353$	−1.68284	+	1.41207i	−0.0895683	+	0.0751568i	−0.686472	−	0.727156i	$-0.740842\pi$
$353$	−1.68284	+	1.41207i	−0.0895683	+	0.0751568i	0.596904	+	0.802313i	$0.296397\pi$
$354$	23.1357	+	39.2991i	1.22965	+	2.08873i
$355$	17.0842	+	3.01240i	0.906733	+	0.159881i
$356$	−0.685364	+	3.88689i	−0.0363242	+	0.206005i
$357$	−2.81737	+	23.4171i	−0.149111	+	1.23937i
$358$	−8.12756	+	6.81983i	−0.429555	+	0.360439i
$359$	−11.5360	−	6.66031i	−0.608847	−	0.351518i	0.163667	−	0.986516i	$-0.447668\pi$
$359$	−11.5360	−	6.66031i	−0.608847	−	0.351518i	−0.772514	+	0.634998i	$0.781001\pi$
$360$	47.4458	+	7.53910i	2.50061	+	0.397345i
$361$	4.11608	+	7.12926i	0.216636	+	0.375224i
$362$	21.1529	−	17.7494i	1.11177	−	0.932887i
$363$	3.95391	+	10.5833i	0.207526	+	0.555479i
$364$	−0.718503	−	1.12116i	−0.0376598	−	0.0587650i
$365$	2.42469	+	6.66179i	0.126914	+	0.348694i
$366$	−3.20260	+	3.88307i	−0.167402	+	0.202972i
$367$	−3.64673	+	10.0193i	−0.190358	+	0.523003i	−0.997752	−	0.0670083i	$-0.978655\pi$
$367$	−3.64673	+	10.0193i	−0.190358	+	0.523003i	0.807395	+	0.590012i	$0.200877\pi$
$368$	39.1462	−	22.6011i	2.04064	−	1.17816i
$369$	−15.6081	−	12.6522i	−0.812527	−	0.658648i
$370$	11.4778	−	6.62669i	0.596701	−	0.344505i
$371$	−9.13315	−	6.96920i	−0.474169	−	0.361823i
$372$	0.422177	+	2.28106i	0.0218889	+	0.118268i
$373$	13.1561	−	4.78843i	0.681197	−	0.247935i	0.0218355	−	0.999762i	$-0.493049\pi$
$373$	13.1561	−	4.78843i	0.681197	−	0.247935i	0.659361	+	0.751826i	$0.270827\pi$
$374$	−50.8960	+	18.5246i	−2.63177	+	0.957886i
$375$	−10.0823	+	5.93550i	−0.520646	+	0.306508i
$376$	28.9999	−	5.11347i	1.49556	−	0.263707i
$377$	0.414234			0.0213341
$378$	−2.47751	−	34.4718i	−0.127429	−	1.77304i
$379$	−34.6102			−1.77781			−0.888903	−	0.458095i	$-0.848532\pi$
$379$	−34.6102			−1.77781			−0.888903	+	0.458095i	$0.848532\pi$
$380$	−60.9599	+	10.7489i	−3.12718	+	0.551405i
$381$	−0.0181865	−	2.14570i	−0.000931720	−	0.109928i
$382$	23.9974	−	8.73436i	1.22782	−	0.446888i
$383$	−15.9030	+	5.78823i	−0.812607	+	0.295765i	−0.714700	−	0.699431i	$-0.753437\pi$
$383$	−15.9030	+	5.78823i	−0.812607	+	0.295765i	−0.0979068	+	0.995196i	$0.531215\pi$
$384$	−20.1166	+	17.1725i	−1.02657	+	0.876329i
$385$	3.88846	−	30.1619i	0.198174	−	1.53719i
$386$	18.8143	−	10.8624i	0.957620	−	0.552882i
$387$	−5.36250	+	4.65683i	−0.272591	+	0.236720i
$388$	22.3411	−	12.8987i	1.13420	−	0.654830i
$389$	1.49572	−	4.10945i	0.0758359	−	0.208357i	−0.895982	−	0.444090i	$-0.853527\pi$
$389$	1.49572	−	4.10945i	0.0758359	−	0.208357i	0.971818	+	0.235733i	$0.0757491\pi$
$390$	−0.487535	−	1.30497i	−0.0246873	−	0.0660797i
$391$	13.2153	+	36.3088i	0.668327	+	1.83621i
$392$	−39.3744	+	10.7775i	−1.98871	+	0.544344i
$393$	−8.25675	+	10.0111i	−0.416498	+	0.504994i
$394$	−1.39015	+	1.16648i	−0.0700350	+	0.0587663i
$395$	−21.6799	−	37.5506i	−1.09083	−	1.88938i
$396$	46.5140	−	27.9166i	2.33742	−	1.40286i
$397$	9.37906	+	5.41500i	0.470721	+	0.271771i	0.716542	−	0.697544i	$-0.245724\pi$
$397$	9.37906	+	5.41500i	0.470721	+	0.271771i	−0.245820	+	0.969315i	$0.579057\pi$
$398$	−41.9395	+	35.1914i	−2.10224	+	1.76399i
$399$	9.39751	+	21.9900i	0.470464	+	1.10088i
$400$	2.65577	−	15.0616i	0.132788	−	0.753080i
$401$	6.39743	+	1.12804i	0.319472	+	0.0563316i	0.331085	−	0.943601i	$-0.392585\pi$
$401$	6.39743	+	1.12804i	0.319472	+	0.0563316i	−0.0116126	+	0.999933i	$0.503696\pi$
$402$	23.7795	−	42.0055i	1.18601	−	2.09504i
$403$	0.0276727	−	0.0232202i	0.00137848	−	0.00115668i
$404$	17.7940	+	30.8202i	0.885286	+	1.53336i
$405$	3.46399	−	24.4693i	0.172127	−	1.21589i
$406$	7.05013	−	22.5715i	0.349892	−	1.12020i
$407$	2.74878	−	7.55222i	0.136252	−	0.374350i
$408$	26.3750	+	44.8016i	1.30576	+	2.21801i
$409$	−5.29809	−	14.5564i	−0.261974	−	0.719766i	−0.999034	−	0.0439398i	$-0.986009\pi$
$409$	−5.29809	−	14.5564i	−0.261974	−	0.719766i	0.737061	−	0.675827i	$-0.236213\pi$
$410$	−29.7174	+	35.4158i	−1.46764	+	1.74906i
$411$	−5.13359	−	27.7372i	−0.253221	−	1.36818i
$412$	−2.73745	−	3.26237i	−0.134865	−	0.160725i
$413$	−18.7754	−	20.3795i	−0.923875	−	1.00281i
$414$	−29.1361	−	48.5457i	−1.43196	−	2.38589i
$415$	−31.2021			−1.53165
$416$	−0.380244	−	0.138398i	−0.0186430	−	0.00678550i
$417$	−15.7919	+	5.89983i	−0.773333	+	0.288916i
$418$	−35.2990	+	42.0677i	−1.72653	+	2.05760i
$419$	14.7586	−	5.37170i	0.721006	−	0.262425i	0.0446532	−	0.999003i	$-0.485782\pi$
$419$	14.7586	−	5.37170i	0.721006	−	0.262425i	0.676353	+	0.736578i	$0.263559\pi$
$420$	−54.2761	+	2.97709i	−2.64840	+	0.145267i
$421$	−2.01941	−	11.4527i	−0.0984202	−	0.558168i	−0.993646	−	0.112555i	$-0.964097\pi$
$421$	−2.01941	−	11.4527i	−0.0984202	−	0.558168i	0.895225	−	0.445614i	$-0.147014\pi$
$422$			24.3443i			1.18506i
$423$	−2.88296	−	14.8714i	−0.140174	−	0.723073i
$424$	−25.3230			−1.22980
$425$	12.2849	+	4.47135i	0.595907	+	0.216892i
$426$	−17.8601	−	20.9221i	−0.865325	−	1.01368i
$427$	1.40492	−	2.71663i	0.0679890	−	0.131467i
$428$	35.9262	−	42.8152i	1.73656	−	2.06955i
$429$	−0.735139	−	0.416165i	−0.0354929	−	0.0200927i
$430$	10.5047	+	12.5190i	0.506581	+	0.603720i
$431$	−12.5999	−	7.27456i	−0.606916	−	0.350403i	0.164841	−	0.986320i	$-0.447289\pi$
$431$	−12.5999	−	7.27456i	−0.606916	−	0.350403i	−0.771758	+	0.635917i	$0.780622\pi$
$432$	−20.7135	−	23.4479i	−0.996579	−	1.12814i
$433$			12.8056i			0.615396i	0.951484	+	0.307698i	$0.0995587\pi$
$433$			12.8056i			0.615396i	−0.951484	+	0.307698i	$0.900441\pi$
$434$	−0.794279	−	1.90308i	−0.0381266	−	0.0913507i
$435$	8.33014	−	14.7148i	0.399400	−	0.705523i
$436$	2.84379	−	16.1280i	0.136193	−	0.772389i
$437$	30.0107	+	25.1820i	1.43561	+	1.20462i
$438$	3.75520	−	10.5959i	0.179430	−	0.506292i
$439$	10.3334	−	28.3908i	0.493187	−	1.35502i	−0.404561	−	0.914511i	$-0.632576\pi$
$439$	10.3334	−	28.3908i	0.493187	−	1.35502i	0.897748	−	0.440509i	$-0.145202\pi$
$440$	−33.5168	−	58.0528i	−1.59785	−	2.76756i
$441$	5.88667	+	20.1581i	0.280318	+	0.959907i
$442$	0.753770	−	1.30557i	0.0358532	−	0.0620995i
$443$	−16.6774	−	19.8753i	−0.792367	−	0.944306i	0.207054	−	0.978329i	$-0.433612\pi$
$443$	−16.6774	−	19.8753i	−0.792367	−	0.944306i	−0.999421	+	0.0340234i	$0.989168\pi$
$444$	−14.1676	−	2.37450i	−0.672366	−	0.112689i
$445$	0.435656	−	2.47073i	0.0206521	−	0.117124i
$446$	54.1959	+	45.4758i	2.56625	+	2.15334i
$447$	27.1871	−	10.1571i	1.28591	−	0.480412i
$448$	5.31473	−	6.96497i	0.251098	−	0.329064i
$449$	4.52779	+	2.61412i	0.213680	+	0.123368i	0.603020	−	0.797726i	$-0.293964\pi$
$449$	4.52779	+	2.61412i	0.213680	+	0.123368i	−0.389341	+	0.921094i	$0.627297\pi$
$450$	−18.9191	−	3.00623i	−0.891856	−	0.141715i
$451$			28.0353i			1.32013i
$452$	11.4910	−	2.02617i	0.540490	−	0.0953029i
$453$	−16.8317	−	19.7175i	−0.790824	−	0.926407i
$454$	18.9680	+	3.34458i	0.890214	+	0.156969i
$455$	0.456722	+	0.712676i	0.0214114	+	0.0334108i
$456$	45.8712	+	25.9679i	2.14812	+	1.21606i
$457$	6.70647	+	38.0343i	0.313715	+	1.77917i	0.579335	+	0.815090i	$0.303312\pi$
$457$	6.70647	+	38.0343i	0.313715	+	1.77917i	−0.265620	+	0.964078i	$0.585576\pi$
$458$	−17.8716	+	30.9545i	−0.835085	+	1.44641i
$459$	22.8135	−	13.9565i	1.06484	−	0.651435i
$460$	−77.1194	+	44.5249i	−3.59571	+	2.07598i
$461$	15.4949	+	5.63970i	0.721671	+	0.262667i	0.676635	−	0.736318i	$-0.263437\pi$
$461$	15.4949	+	5.63970i	0.721671	+	0.262667i	0.0450362	+	0.998985i	$0.485660\pi$
$462$	−35.1886	+	32.9745i	−1.63712	+	1.53411i
$463$	31.2960	+	26.2605i	1.45445	+	1.22043i	0.929251	+	0.369448i	$0.120453\pi$
$463$	31.2960	+	26.2605i	1.45445	+	1.22043i	0.525198	+	0.850980i	$0.323991\pi$
$464$	−7.32153	−	20.1157i	−0.339893	−	0.933850i
$465$	−0.268360	−	1.44997i	−0.0124449	−	0.0672409i
$466$	−9.81814	−	55.6814i	−0.454816	−	2.57939i
$467$	19.3503	−	33.5157i	0.895424	−	1.55092i	0.0621443	−	0.998067i	$-0.480206\pi$
$467$	19.3503	−	33.5157i	0.895424	−	1.55092i	0.833279	−	0.552852i	$-0.186461\pi$
$468$	−0.492303	+	1.42742i	−0.0227567	+	0.0659827i
$469$	−8.74441	+	27.9958i	−0.403779	+	1.29273i
$470$	−34.3267	+	6.05273i	−1.58337	+	0.279192i
$471$	5.24123	−	1.95812i	0.241503	−	0.0902253i
$472$	−60.1508	−	10.6062i	−2.76866	−	0.488190i
$473$	9.75955	+	1.72087i	0.448744	+	0.0791258i
$474$	−11.3651	+	67.8104i	−0.522015	+	3.11463i
$475$	13.0537	−	2.30173i	0.598947	−	0.105610i
$476$	−39.8576	−	43.2630i	−1.82687	−	1.98296i
$477$	0.220806	+	13.0248i	0.0101100	+	0.596364i
$478$	29.9537	−	51.8813i	1.37005	−	2.37300i
$479$	5.01429	+	28.4374i	0.229109	+	1.29934i	0.854673	+	0.519167i	$0.173758\pi$
$479$	5.01429	+	28.4374i	0.229109	+	1.29934i	−0.625564	+	0.780172i	$0.715131\pi$
$480$	−12.5629	+	10.7243i	−0.573417	+	0.489495i
$481$	0.0765089	+	0.210206i	0.00348850	+	0.00958459i
$482$	−26.1188	−	21.9163i	−1.18968	−	0.998260i
$483$	23.5237	+	25.1032i	1.07037	+	1.14224i
$484$	−26.4778	−	9.63714i	−1.20354	−	0.438052i
$485$	−14.2013	+	8.19912i	−0.644848	+	0.372303i
$486$	−28.9258	+	26.4389i	−1.31210	+	1.19929i
$487$	10.6879	−	18.5119i	0.484313	−	0.838854i	−0.515525	−	0.856875i	$-0.672403\pi$
$487$	10.6879	−	18.5119i	0.484313	−	0.838854i	0.999838	+	0.0180204i	$0.00573637\pi$
$488$	−1.17063	−	6.63899i	−0.0529921	−	0.300533i
$489$	−0.113218	−	13.3579i	−0.00511991	−	0.604064i
$490$	46.6067	−	12.7571i	2.10548	−	0.576307i
$491$	−17.7129	−	3.12326i	−0.799372	−	0.140951i	−0.240982	−	0.970530i	$-0.577469\pi$
$491$	−17.7129	−	3.12326i	−0.799372	−	0.140951i	−0.558390	+	0.829579i	$0.688581\pi$
$492$	49.2737	−	9.11955i	2.22143	−	0.411141i
$493$	18.0206	−	3.17752i	0.811606	−	0.143108i
$494$		−	1.52850i		−	0.0687705i
$495$	−29.5669	+	17.7454i	−1.32894	+	0.797597i
$496$	−1.61672	−	0.933411i	−0.0725927	−	0.0419114i
$497$	13.2881	+	10.1397i	0.596054	+	0.454829i
$498$	38.1702	+	31.4812i	1.71045	+	1.41071i
$499$	−8.16488	−	6.85115i	−0.365510	−	0.306700i	0.441472	−	0.897275i	$-0.354456\pi$
$499$	−8.16488	−	6.85115i	−0.365510	−	0.306700i	−0.806983	+	0.590575i	$0.798901\pi$
$500$	5.06696	−	28.7362i	0.226602	−	1.28512i
$501$	−1.81711	+	2.20320i	−0.0811825	+	0.0984318i
$502$	−15.4240	−	18.3816i	−0.688405	−	0.820410i
$503$	1.68293	−	2.91493i	0.0750383	−	0.129970i	−0.826065	−	0.563575i	$-0.809425\pi$
$503$	1.68293	−	2.91493i	0.0750383	−	0.129970i	0.901103	+	0.433605i	$0.142759\pi$
$504$	37.2695	+	27.4521i	1.66011	+	1.22282i
$505$	−11.3109	−	19.5911i	−0.503328	−	0.871790i
$506$	−27.0201	+	74.2370i	−1.20119	+	3.30024i
$507$	−22.1175	+	4.09350i	−0.982274	+	0.181799i
$508$	4.09961	+	3.43998i	0.181891	+	0.152624i
$509$	1.45437	−	8.24815i	0.0644639	−	0.365593i	−0.935462	−	0.353427i	$-0.885016\pi$
$509$	1.45437	−	8.24815i	0.0644639	−	0.365593i	0.999926	−	0.0121658i	$-0.00387258\pi$
$510$	−31.2196	−	53.0309i	−1.38243	−	2.34825i
$511$	−0.873387	+	6.77466i	−0.0386364	+	0.299693i
$512$		−	49.3168i		−	2.17951i
$513$	12.9565	−	23.8201i	0.572044	−	1.05168i
$514$	12.0415	+	6.95217i	0.531128	+	0.306647i
$515$	1.74008	+	2.07375i	0.0766771	+	0.0913802i
$516$	−0.150129	−	17.7128i	−0.00660907	−	0.779761i
$517$	−13.5866	+	16.1919i	−0.597538	+	0.712118i
$518$	12.7562	−	0.591297i	0.560477	−	0.0259801i
$519$	31.1361	−	5.76266i	1.36672	−	0.252953i
$520$	1.75327	+	0.638139i	0.0768861	+	0.0279842i
$521$	−16.2480			−0.711838			−0.355919	−	0.934517i	$-0.615832\pi$
$521$	−16.2480			−0.711838			−0.355919	+	0.934517i	$0.615832\pi$
$522$	−25.0370	+	9.59636i	−1.09584	+	0.420021i
$523$		−	28.2596i		−	1.23571i	−0.786294	−	0.617853i	$-0.788003\pi$
$523$		−	28.2596i		−	1.23571i	0.786294	−	0.617853i	$-0.211997\pi$
$524$	−5.62005	−	31.8729i	−0.245513	−	1.39237i
$525$	11.6225	−	0.637505i	0.507248	−	0.0278230i
$526$	19.7653	−	7.19397i	0.861806	−	0.313672i
$527$	1.02574	−	1.22243i	0.0446820	−	0.0532499i
$528$	−7.21605	+	43.0550i	−0.314038	+	1.87373i
$529$	31.3472	+	11.4094i	1.36292	+	0.496062i
$530$	29.9744			1.30201
$531$	−4.93076	+	31.0308i	−0.213977	+	1.34662i
$532$	−56.9299	−	17.7819i	−2.46822	−	0.770942i
$533$	−0.501584	−	0.597765i	−0.0217260	−	0.0258921i
$534$	−3.02578	+	2.58295i	−0.130938	+	0.111775i
$535$	−22.8367	+	27.2158i	−0.987319	+	1.17664i
$536$	22.1113	+	60.7502i	0.955062	+	2.62401i
$537$	−7.30969	+	0.0619553i	−0.315437	+	0.00267357i
$538$	−16.3783	+	44.9990i	−0.706119	+	1.94005i
$539$	16.6778	−	24.0929i	0.718363	−	1.03775i
$540$	40.8064	+	46.1933i	1.75603	+	1.98784i
$541$	3.36773	+	5.83309i	0.144790	+	0.250784i	0.929295	−	0.369339i	$-0.120416\pi$
$541$	3.36773	+	5.83309i	0.144790	+	0.250784i	−0.784504	+	0.620123i	$0.787083\pi$
$542$	48.1325	−	40.3880i	2.06747	−	1.73481i
$543$	19.0243	−	0.161246i	0.816411	−	0.00691971i
$544$	−17.6036	−	3.10398i	−0.754746	−	0.133082i
$545$	−1.80768	+	10.2518i	−0.0774324	+	0.439141i
$546$	0.160333	−	1.33264i	0.00686164	−	0.0570318i
$547$	−31.5987	+	26.5144i	−1.35106	+	1.13368i	−0.372429	+	0.928061i	$0.621475\pi$
$547$	−31.5987	+	26.5144i	−1.35106	+	1.13368i	−0.978633	+	0.205615i	$0.934080\pi$
$548$	60.9272	+	35.1764i	2.60268	+	1.50266i
$549$	−3.40453	+	0.660000i	−0.145302	+	0.0281681i
$550$	13.3649	+	23.1487i	0.569881	+	0.987063i
$551$	14.2124	−	11.9256i	0.605469	−	0.508049i
$552$	74.7877	+	12.5345i	3.18318	+	0.533503i
$553$	−1.93448	−	41.7332i	−0.0822627	−	1.77468i
$554$	−19.1953	−	52.7386i	−0.815530	−	2.24065i
$555$	9.00575	+	1.50937i	0.382273	+	0.0640692i
$556$	14.3801	−	39.5090i	0.609852	−	1.67555i
$557$	−5.64369	+	3.25839i	−0.239131	+	0.138062i	−0.614777	−	0.788701i	$-0.710754\pi$
$557$	−5.64369	+	3.25839i	−0.239131	+	0.138062i	0.375646	+	0.926763i	$0.377421\pi$
$558$	−1.13465	+	2.04455i	−0.0480337	+	0.0865526i
$559$	−0.238880	+	0.137917i	−0.0101036	+	0.00583329i
$560$	26.5360	−	34.7755i	1.12135	−	1.46953i
$561$	−35.1734	−	12.4655i	−1.48502	−	0.526294i
$562$	−28.1554	+	10.2477i	−1.18766	+	0.432274i
$563$	25.6976	−	9.35315i	1.08302	−	0.394188i	0.261991	−	0.965070i	$-0.415621\pi$
$563$	25.6976	−	9.35315i	1.08302	−	0.394188i	0.821032	+	0.570882i	$0.193399\pi$
$564$	32.8777	+	18.6122i	1.38440	+	0.783716i
$565$	−7.30431	+	1.28795i	−0.307295	+	0.0541844i
$566$	10.1623			0.427155
$567$	13.7949	−	19.4088i	0.579332	−	0.815092i
$568$	36.8433			1.54591
$569$	28.6452	−	5.05093i	1.20087	−	0.211746i	0.462796	−	0.886465i	$-0.346846\pi$
$569$	28.6452	−	5.05093i	1.20087	−	0.211746i	0.738075	+	0.674719i	$0.235735\pi$
$570$	−54.2970	−	30.7378i	−2.27425	−	1.28746i
$571$	−16.3768	+	5.96065i	−0.685346	+	0.249446i	−0.661141	−	0.750262i	$-0.729928\pi$
$571$	−16.3768	+	5.96065i	−0.685346	+	0.249446i	−0.0242047	+	0.999707i	$0.507705\pi$
$572$	1.97981	−	0.720593i	0.0827801	−	0.0301295i
$573$	16.5842	+	5.87748i	0.692817	+	0.245535i
$574$	−41.1088	+	17.1574i	−1.71585	+	0.716136i
$575$	16.5141	−	9.53441i	0.688685	−	0.397612i
$576$	−9.93275	+	0.168387i	−0.413864	+	0.00701614i
$577$	−19.6718	+	11.3575i	−0.818949	+	0.472821i	−0.850054	−	0.526696i	$-0.823431\pi$
$577$	−19.6718	+	11.3575i	−0.818949	+	0.472821i	0.0311048	+	0.999516i	$0.490097\pi$
$578$	8.15999	−	22.4194i	0.339411	−	0.932524i
$579$	14.7621	+	2.47415i	0.613494	+	0.102822i
$580$	14.4237	+	39.6287i	0.598911	+	1.64549i
$581$	−26.7042	−	13.8102i	−1.10788	−	0.572946i
$582$	25.6453	+	4.29817i	1.06303	+	0.178165i
$583$	13.9241	−	11.6837i	0.576677	−	0.483890i
$584$	7.52821	+	13.0392i	0.311519	+	0.539567i
$585$	0.312936	−	0.907352i	0.0129383	−	0.0375144i
$586$	3.86842	+	2.23344i	0.159803	+	0.0922624i
$587$	1.35014	−	1.13291i	0.0557264	−	0.0467600i	−0.614499	−	0.788918i	$-0.710642\pi$
$587$	1.35014	−	1.13291i	0.0557264	−	0.0467600i	0.670225	+	0.742158i	$0.266197\pi$
$588$	−47.7698	−	21.4751i	−1.96999	−	0.885616i
$589$	0.280955	−	1.59338i	0.0115766	−	0.0656539i
$590$	71.1994	+	12.5544i	2.93123	+	0.516856i
$591$	−1.25027	+	0.0105970i	−0.0514290	+	0.000435901i
$592$	8.85562	−	7.43075i	0.363964	−	0.305402i
$593$	20.7313	+	35.9077i	0.851334	+	1.47455i	0.880005	+	0.474965i	$0.157539\pi$
$593$	20.7313	+	35.9077i	0.851334	+	1.47455i	−0.0286712	+	0.999589i	$0.509128\pi$
$594$	54.0741	+	8.12308i	2.21869	+	0.333294i
$595$	25.3358	+	27.5004i	1.03867	+	1.12741i
$596$	−24.7565	+	68.0180i	−1.01407	+	2.78613i
$597$	−37.7192	+	0.319699i	−1.54374	+	0.0130844i
$598$	−0.752069	−	2.06629i	−0.0307544	−	0.0844970i
$599$	13.6209	−	16.2328i	0.556535	−	0.663253i	−0.412274	−	0.911060i	$-0.635265\pi$
$599$	13.6209	−	16.2328i	0.556535	−	0.663253i	0.968809	+	0.247807i	$0.0797098\pi$
$600$	19.5140	−	16.6580i	0.796654	−	0.680061i
$601$	−5.31277	−	6.33151i	−0.216712	−	0.258268i	0.646726	−	0.762723i	$-0.276138\pi$
$601$	−5.31277	−	6.33151i	−0.216712	−	0.258268i	−0.863438	+	0.504455i	$0.831693\pi$
$602$	3.44941	+	15.3638i	0.140588	+	0.626182i
$603$	31.0538	−	11.9026i	1.26461	−	0.484709i
$604$	64.6571			2.63086
$605$	16.8308	+	6.12592i	0.684270	+	0.249054i
$606$	−5.92943	+	35.3783i	−0.240867	+	1.43715i
$607$	−10.1572	+	12.1049i	−0.412267	+	0.491321i	−0.931720	−	0.363179i	$-0.881691\pi$
$607$	−10.1572	+	12.1049i	−0.412267	+	0.491321i	0.519452	+	0.854499i	$0.326136\pi$
$608$	−17.0307	+	6.19865i	−0.690684	+	0.251389i
$609$	13.6422	−	8.90669i	0.552811	−	0.360917i
$610$	1.38566	+	7.85846i	0.0561037	+	0.318180i
$611$		−	0.588321i		−	0.0238009i
$612$	−10.4674	+	65.8742i	−0.423118	+	2.66281i
$613$	−18.8108			−0.759762			−0.379881	−	0.925035i	$-0.624035\pi$
$613$	−18.8108			−0.759762			−0.379881	+	0.925035i	$0.624035\pi$
$614$	−46.4403	−	16.9029i	−1.87418	−	0.682145i
$615$	−31.3212	+	5.79690i	−1.26299	+	0.233754i
$616$	−2.99069	−	64.5191i	−0.120498	−	2.59955i
$617$	−1.65294	+	1.96989i	−0.0665447	+	0.0793049i	−0.798290	−	0.602273i	$-0.794262\pi$
$617$	−1.65294	+	1.96989i	−0.0665447	+	0.0793049i	0.731745	+	0.681578i	$0.238706\pi$
$618$	−0.0363823	−	4.29251i	−0.00146351	−	0.172670i
$619$	−10.1248	−	12.0663i	−0.406951	−	0.484985i	0.523175	−	0.852225i	$-0.324747\pi$
$619$	−10.1248	−	12.0663i	−0.406951	−	0.484985i	−0.930126	+	0.367240i	$0.880303\pi$
$620$	3.18499	+	1.83885i	0.127912	+	0.0738501i
$621$	5.79494	−	38.5760i	0.232543	−	1.54800i
$622$			66.5577i			2.66872i
$623$	1.46642	−	1.92174i	0.0587508	−	0.0769930i
$624$	−0.616445	−	1.04712i	−0.0246775	−	0.0419182i
$625$	−5.42623	+	30.7737i	−0.217049	+	1.23095i
$626$	−9.70829	−	8.14622i	−0.388021	−	0.325588i
$627$	−37.2040	+	6.88569i	−1.48578	+	0.274988i
$628$	−4.77266	+	13.1128i	−0.190450	+	0.523257i
$629$	4.94086	+	8.55781i	0.197005	+	0.341222i
$630$	−44.1152	−	32.4946i	−1.75759	−	1.29462i
$631$	−21.8676	+	37.8758i	−0.870536	+	1.50781i	−0.00909374	+	0.999959i	$0.502895\pi$
$631$	−21.8676	+	37.8758i	−0.870536	+	1.50781i	−0.861443	+	0.507855i	$0.830439\pi$
$632$	−59.1930	−	70.5435i	−2.35457	−	2.80607i
$633$	−10.6721	+	12.9396i	−0.424177	+	0.514305i
$634$	−13.4916	+	76.5146i	−0.535819	+	3.03878i
$635$	−2.60594	−	2.18665i	−0.103414	−	0.0867744i
$636$	−25.0642	−	20.6719i	−0.993858	−	0.819693i
$637$	0.0754487	+	0.812090i	0.00298938	+	0.0321762i
$638$	32.4009	+	18.7067i	1.28276	+	0.740604i
$639$	−0.321258	−	18.9502i	−0.0127088	−	0.749658i
$640$			41.9317i			1.65750i
$641$	24.5241	−	4.32427i	0.968645	−	0.170798i	0.333125	−	0.942883i	$-0.391897\pi$
$641$	24.5241	−	4.32427i	0.968645	−	0.170798i	0.635520	+	0.772084i	$0.280786\pi$
$642$	55.3960	−	10.2527i	2.18631	−	0.404640i
$643$	−22.2139	−	3.91690i	−0.876029	−	0.154468i	−0.282488	−	0.959271i	$-0.591160\pi$
$643$	−22.2139	−	3.91690i	−0.876029	−	0.154468i	−0.593542	+	0.804803i	$0.702271\pi$
$644$	−85.7095	+	3.97294i	−3.37743	+	0.156556i
$645$	0.0954307	+	11.2592i	0.00375758	+	0.443332i
$646$	−11.7249	−	66.4950i	−0.461308	−	2.61621i
$647$	1.19357	−	2.06732i	0.0469239	−	0.0812747i	−0.841609	−	0.540087i	$-0.818391\pi$
$647$	1.19357	−	2.06732i	0.0469239	−	0.0812747i	0.888533	+	0.458812i	$0.151725\pi$
$648$	−1.77907	−	52.4562i	−0.0698883	−	2.06067i
$649$	37.9680	−	21.9208i	1.49038	−	0.860468i
$650$	−0.699122	−	0.254459i	−0.0274218	−	0.00998072i
$651$	0.412093	−	1.35973i	0.0161512	−	0.0532921i
$652$	25.5218	+	21.4153i	0.999509	+	0.838688i
$653$	−12.6049	−	34.6318i	−0.493269	−	1.35525i	−0.897672	−	0.440665i	$-0.854743\pi$
$653$	−12.6049	−	34.6318i	−0.493269	−	1.35525i	0.404403	−	0.914581i	$-0.367479\pi$
$654$	12.5549	−	10.7175i	0.490937	−	0.419087i
$655$	3.57242	+	20.2602i	0.139586	+	0.791633i
$656$	−20.1628	+	34.9230i	−0.787226	+	1.36352i
$657$	6.64103	−	3.98580i	0.259091	−	0.155501i
$658$	−32.0574	−	10.0130i	−1.24973	−	0.390349i
$659$	−7.39431	+	1.30382i	−0.288041	+	0.0507895i	−0.315802	−	0.948825i	$-0.602274\pi$
$659$	−7.39431	+	1.30382i	−0.288041	+	0.0507895i	0.0277605	+	0.999615i	$0.491162\pi$
$660$	14.2159	−	84.8199i	0.553353	−	3.30161i
$661$	−8.19948	−	1.44579i	−0.318923	−	0.0562347i	0.0118952	−	0.999929i	$-0.496214\pi$
$661$	−8.19948	−	1.44579i	−0.318923	−	0.0562347i	−0.330818	+	0.943695i	$0.607325\pi$
$662$	40.6073	+	7.16016i	1.57825	+	0.278288i
$663$	0.972985	−	0.363506i	0.0377876	−	0.0141174i
$664$	−65.2606	+	11.5072i	−2.53260	+	0.446566i
$665$	36.1879	+	11.3032i	1.40331	+	0.438318i
$666$	−9.49408	−	10.9328i	−0.367888	−	0.423636i
$667$	13.3452	−	23.1145i	0.516727	−	0.894998i
$668$	−1.23684	−	7.01445i	−0.0478546	−	0.271397i
$669$	8.87085	+	47.9300i	0.342967	+	1.85308i
$670$	−26.1727	−	71.9090i	−1.01114	−	2.77809i
$671$	3.70683	+	3.11040i	0.143100	+	0.120076i
$672$	−15.4986	+	3.61792i	−0.597871	+	0.139564i
$673$	36.7067	+	13.3601i	1.41494	+	0.514995i	0.932575	−	0.360976i	$-0.117556\pi$
$673$	36.7067	+	13.3601i	1.41494	+	0.514995i	0.482363	+	0.875971i	$0.339779\pi$
$674$	3.12535	−	1.80442i	0.120384	−	0.0695038i
$675$	−8.73814	−	9.89167i	−0.336331	−	0.380731i
$676$	28.0494	−	48.5830i	1.07882	−	1.86858i
$677$	−3.32662	−	18.8662i	−0.127852	−	0.725087i	−0.979573	−	0.201090i	$-0.935552\pi$
$677$	−3.32662	−	18.8662i	−0.127852	−	0.725087i	0.851720	−	0.523997i	$-0.175560\pi$
$678$	10.2350	+	5.79408i	0.393073	+	0.222520i
$679$	−15.7831	+	0.731604i	−0.605701	+	0.0280764i
$680$	81.1684	+	14.3122i	3.11267	+	0.548847i
$681$	8.61581	+	10.0929i	0.330159	+	0.386763i
$682$	3.21315	−	0.566564i	0.123038	−	0.0216949i
$683$			41.1007i			1.57268i	0.617796	+	0.786338i	$0.288026\pi$
$683$			41.1007i			1.57268i	−0.617796	+	0.786338i	$0.711974\pi$
$684$	24.2040	+	63.1484i	0.925463	+	2.41454i
$685$	−38.7288	−	22.3601i	−1.47975	−	0.854335i
$686$	45.5346	+	9.71034i	1.73852	+	0.370743i
$687$	−23.0691	+	8.61858i	−0.880141	+	0.328819i
$688$	10.9196	+	9.16266i	0.416307	+	0.349323i
$689$	−0.0878526	+	0.498237i	−0.00334692	+	0.0189813i
$690$	−88.5249	−	14.8368i	−3.37009	−	0.564829i
$691$	27.2928	+	32.5263i	1.03827	+	1.23736i	0.970863	+	0.239634i	$0.0770274\pi$
$691$	27.2928	+	32.5263i	1.03827	+	1.23736i	0.0674047	+	0.997726i	$0.478528\pi$
$692$	−39.4868	+	68.3932i	−1.50106	+	2.59992i
$693$	−33.1590	+	2.10083i	−1.25961	+	0.0798038i
$694$	−8.00228	−	13.8604i	−0.303763	−	0.526132i
$695$	−9.14080	+	25.1141i	−0.346730	+	0.952634i
$696$	11.9961	−	33.8490i	0.454711	−	1.28304i
$697$	−26.4060	−	22.1573i	−1.00020	−	0.839266i
$698$	3.82508	−	21.6931i	0.144781	−	0.821097i
$699$	19.1911	−	33.9002i	0.725873	−	1.28222i
$700$	−17.6107	+	23.0789i	−0.665624	+	0.872301i
$701$			18.1159i			0.684229i	0.939658	+	0.342114i	$0.111143\pi$
$701$			18.1159i			0.684229i	−0.939658	+	0.342114i	$0.888857\pi$
$702$	−1.29829	+	0.794250i	−0.0490009	+	0.0299770i
$703$	8.67679	+	5.00955i	0.327252	+	0.188939i
$704$	8.91004	+	10.6186i	0.335810	+	0.400202i
$705$	−20.8990	−	11.8310i	−0.787100	−	0.445581i
$706$	3.54983	−	4.23052i	0.133600	−	0.159218i
$707$	−1.00927	−	21.7732i	−0.0379574	−	0.818867i
$708$	−50.8777	−	59.6004i	−1.91210	−	2.23992i
$709$	8.87470	+	3.23013i	0.333296	+	0.121310i	0.503247	−	0.864143i	$-0.332139\pi$
$709$	8.87470	+	3.23013i	0.333296	+	0.121310i	−0.169951	+	0.985453i	$0.554361\pi$
$710$	−43.6108			−1.63668
$711$	−35.7676	+	31.0608i	−1.34139	+	1.16487i
$712$		−	5.32832i		−	0.199687i
$713$	−0.404182	−	2.29223i	−0.0151367	−	0.0858448i
$714$	−3.24741	−	59.2044i	−0.121531	−	2.21567i
$715$	−1.25848	+	0.458050i	−0.0470645	+	0.0171301i
$716$	11.7189	−	13.9660i	0.437955	−	0.521934i
$717$	38.6649	−	14.4452i	1.44397	−	0.539465i
$718$	31.4675	+	11.4532i	1.17436	+	0.427431i
$719$	−14.5552			−0.542817			−0.271408	−	0.962464i	$-0.587489\pi$
$719$	−14.5552			−0.542817			−0.271408	+	0.962464i	$0.587489\pi$
$720$	−49.5933	+	0.840744i	−1.84823	+	0.0313327i
$721$	0.571388	+	2.54498i	0.0212796	+	0.0947801i
$722$	−13.3025	−	15.8533i	−0.495068	−	0.589999i
$723$	−4.27516	−	23.0991i	−0.158995	−	0.859064i
$724$	−30.4997	+	36.3481i	−1.13351	+	1.35087i
$725$	−3.08864	−	8.48596i	−0.114709	−	0.315161i
$726$	−14.4088	−	24.4754i	−0.534762	−	0.908366i
$727$	5.63920	−	15.4936i	0.209146	−	0.574625i	−0.790119	−	0.612954i	$-0.789981\pi$
$727$	5.63920	−	15.4936i	0.209146	−	0.574625i	0.999265	+	0.0383287i	$0.0122034\pi$
$728$	1.21809	+	1.32216i	0.0451454	+	0.0490025i
$729$	−26.9651	+	1.37245i	−0.998707	+	0.0508315i
$730$	−8.91101	−	15.4343i	−0.329811	−	0.571250i
$731$	−9.33416	+	7.83229i	−0.345236	+	0.289688i
$732$	4.26092	−	7.52674i	0.157488	−	0.278196i
$733$	30.6823	+	5.41012i	1.13328	+	0.199827i	0.708663	−	0.705547i	$-0.249299\pi$
$733$	30.6823	+	5.41012i	1.13328	+	0.199827i	0.424614	+	0.905374i	$0.360410\pi$
$734$	4.65451	−	26.3970i	0.171801	−	0.974332i
$735$	30.3652	+	13.6508i	1.12004	+	0.503516i
$736$	−19.9728	+	16.7592i	−0.736209	+	0.617753i
$737$	−40.1874	−	23.2022i	−1.48032	−	0.854665i
$738$	44.1647	+	24.5099i	1.62573	+	0.902222i
$739$	2.09919	+	3.63590i	0.0772198	+	0.133749i	0.902049	−	0.431633i	$-0.142062\pi$
$739$	2.09919	+	3.63590i	0.0772198	+	0.133749i	−0.824830	+	0.565381i	$0.808729\pi$
$740$	−17.4459	+	14.6388i	−0.641324	+	0.538134i
$741$	0.670065	−	0.812438i	0.0246155	−	0.0298457i
$742$	25.6535	+	13.2669i	0.941771	+	0.487043i
$743$	−15.8926	−	43.6646i	−0.583044	−	1.60190i	−0.782950	−	0.622085i	$-0.786286\pi$
$743$	−15.8926	−	43.6646i	−0.583044	−	1.60190i	0.199906	−	0.979815i	$-0.435936\pi$
$744$	−1.09603	−	2.93372i	−0.0401825	−	0.107555i
$745$	15.7367	−	43.2361i	0.576547	−	1.58405i
$746$	−30.4806	+	17.5980i	−1.11597	+	0.644308i
$747$	6.48773	+	33.4662i	0.237374	+	1.22446i
$748$	80.6011	−	46.5351i	2.94707	−	1.70149i
$749$	−31.5907	+	13.1848i	−1.15430	+	0.481764i
$750$	22.3699	−	19.0960i	0.816834	−	0.697287i
$751$	−48.5632	+	17.6756i	−1.77210	+	0.644990i	−0.772142	+	0.635450i	$0.780815\pi$
$751$	−48.5632	+	17.6756i	−1.77210	+	0.644990i	−0.999954	+	0.00954055i	$0.996963\pi$
$752$	−28.5697	+	10.3985i	−1.04183	+	0.379194i
$753$	−0.140120	−	16.5319i	−0.00510627	−	0.602455i
$754$	−1.02553	+	0.180829i	−0.0373476	+	0.00658540i
$755$	−41.0997			−1.49577
$756$	14.4786	+	57.5956i	0.526580	+	2.09473i
$757$	−34.5687			−1.25642			−0.628210	−	0.778044i	$-0.716212\pi$
$757$	−34.5687			−1.25642			−0.628210	+	0.778044i	$0.716212\pi$
$758$	85.6855	−	15.1087i	3.11224	−	0.548772i
$759$	−46.9060	+	27.6139i	−1.70258	+	1.00232i
$760$	78.5268	−	28.5814i	2.84847	−	1.03676i
$761$	−8.42366	+	3.06596i	−0.305357	+	0.111141i	−0.490154	−	0.871636i	$-0.663060\pi$
$761$	−8.42366	+	3.06596i	−0.305357	+	0.111141i	0.184797	+	0.982777i	$0.440837\pi$
$762$	0.981704	+	5.30423i	0.0355634	+	0.192152i
$763$	−6.08463	+	7.97393i	−0.220279	+	0.288675i
$764$	−38.0034	+	21.9413i	−1.37491	+	0.793807i
$765$	6.65365	−	41.8734i	0.240563	−	1.51394i
$766$	36.8448	−	21.2724i	1.33126	−	0.768602i
$767$	−0.417359	+	1.14669i	−0.0150700	+	0.0414044i
$768$	35.0082	−	42.4466i	1.26325	−	1.53166i
$769$	−2.93294	−	8.05819i	−0.105765	−	0.290586i	0.875510	−	0.483200i	$-0.160526\pi$
$769$	−2.93294	−	8.05819i	−0.105765	−	0.290586i	−0.981275	+	0.192614i	$0.938303\pi$
$770$	3.54003	+	76.3701i	0.127574	+	2.75219i
$771$	3.35268	+	8.97403i	0.120744	+	0.323192i
$772$	−28.5971	+	23.9959i	−1.02923	+	0.863630i
$773$	−0.449480	−	0.778522i	−0.0161667	−	0.0280015i	0.857829	−	0.513935i	$-0.171813\pi$
$773$	−0.449480	−	0.778522i	−0.0161667	−	0.0280015i	−0.873996	+	0.485934i	$0.838480\pi$
$774$	11.2432	−	13.8700i	0.404129	−	0.498546i
$775$	−0.682022	−	0.393766i	−0.0244990	−	0.0141445i
$776$	−26.6789	+	22.3863i	−0.957717	+	0.803620i
$777$	7.03949	+	5.27780i	0.252540	+	0.189340i
$778$	−1.90906	+	10.8268i	−0.0684432	+	0.388161i
$779$	−34.4189	−	6.06897i	−1.23318	−	0.217444i
$780$	1.21442	+	2.06286i	0.0434832	+	0.0738621i
$781$	−20.2586	+	16.9990i	−0.724911	+	0.608273i
$782$	−48.5677	−	84.1218i	−1.73678	−	3.00819i
$783$	−17.5147	−	5.87500i	−0.625923	−	0.209955i
$784$	38.1026	−	18.0175i	1.36081	−	0.643482i
$785$	3.03377	−	8.33523i	0.108280	−	0.297497i
$786$	16.0713	−	28.3892i	0.573243	−	1.01261i
$787$	−13.7718	−	37.8376i	−0.490911	−	1.34877i	−0.899848	−	0.436203i	$-0.856323\pi$
$787$	−13.7718	−	37.8376i	−0.490911	−	1.34877i	0.408938	−	0.912562i	$-0.365899\pi$
$788$	2.00442	−	2.38878i	0.0714046	−	0.0850966i
$789$	13.6595	+	4.84093i	0.486290	+	0.172342i
$790$	70.0658	+	83.5011i	2.49283	+	2.97084i
$791$	−6.82143	−	2.13065i	−0.242542	−	0.0757573i
$792$	−55.2963	+	48.0196i	−1.96487	+	1.70630i
$793$	−0.134685			−0.00478281
$794$	−25.5839	−	9.31177i	−0.907938	−	0.330462i
$795$	15.9322	+	13.1402i	0.565057	+	0.466035i
$796$	60.4713	−	72.0668i	2.14335	−	2.55434i
$797$	−32.3110	+	11.7602i	−1.14451	+	0.416569i	−0.843542	−	0.537064i	$-0.819533\pi$
$797$	−32.3110	+	11.7602i	−1.14451	+	0.416569i	−0.300972	+	0.953633i	$0.597311\pi$
$798$	−32.8652	−	50.3391i	−1.16342	−	1.78198i
$799$	−4.51291	−	25.5940i	−0.159655	−	0.905450i
$800$			8.82159i			0.311890i
$801$	−2.74060	+	0.0464607i	−0.0968343	+	0.00164161i
$802$	−16.3307			−0.576658
$803$	−10.1556	−	3.69633i	−0.358383	−	0.130441i
$804$	−27.7068	+	78.1792i	−0.977143	+	2.75717i
$805$	54.4818	−	2.52543i	1.92023	−	0.0890096i
$806$	−0.0583737	+	0.0695671i	−0.00205613	+	0.00245040i
$807$	−28.4322	+	16.7382i	−1.00086	+	0.589214i
$808$	−30.8824	−	36.8042i	−1.08644	−	1.29477i
$809$	−26.8173	−	15.4830i	−0.942848	−	0.544353i	−0.0519959	−	0.998647i	$-0.516558\pi$
$809$	−26.8173	−	15.4830i	−0.942848	−	0.544353i	−0.890852	+	0.454294i	$0.849892\pi$
$810$	2.10585	+	62.0915i	0.0739920	+	2.18167i
$811$		−	44.9726i		−	1.57920i	−0.613622	−	0.789600i	$-0.710288\pi$
$811$		−	44.9726i		−	1.57920i	0.613622	−	0.789600i	$-0.289712\pi$
$812$	−5.19549	+	40.3002i	−0.182326	+	1.41426i
$813$	43.2890	−	0.366908i	1.51821	−	0.0128680i
$814$	−3.50842	+	19.8972i	−0.122970	+	0.697397i
$815$	−16.2231	−	13.6128i	−0.568270	−	0.476835i
$816$	−34.8497	−	40.8245i	−1.21998	−	1.42914i
$817$	−4.22542	+	11.6092i	−0.147829	+	0.406156i
$818$	19.4710	+	33.7248i	0.680789	+	1.17916i
$819$	0.669426	−	0.638047i	0.0233916	−	0.0222952i
$820$	39.7215	−	68.7996i	1.38713	−	2.40259i
$821$	10.7469	+	12.8077i	0.375071	+	0.446992i	0.920252	−	0.391326i	$-0.127984\pi$
$821$	10.7469	+	12.8077i	0.375071	+	0.446992i	−0.545181	+	0.838318i	$0.683539\pi$
$822$	24.8178	+	66.4289i	0.865619	+	2.31698i
$823$	−4.81216	+	27.2911i	−0.167741	+	0.951308i	0.778452	+	0.627705i	$0.216005\pi$
$823$	−4.81216	+	27.2911i	−0.167741	+	0.951308i	−0.946193	+	0.323603i	$0.895106\pi$
$824$	4.40425	+	3.69561i	0.153429	+	0.128743i
$825$	−3.04414	+	18.1631i	−0.105983	+	0.632356i
$826$	55.3792	+	42.2580i	1.92689	+	1.47034i
$827$	12.2895	+	7.09535i	0.427348	+	0.246730i	0.698216	−	0.715887i	$-0.253977\pi$
$827$	12.2895	+	7.09535i	0.427348	+	0.246730i	−0.270868	+	0.962616i	$0.587311\pi$
$828$	63.7909	+	73.4575i	2.21689	+	2.55283i
$829$			4.62117i			0.160500i	0.996775	+	0.0802500i	$0.0255719\pi$
$829$			4.62117i			0.160500i	−0.996775	+	0.0802500i	$0.974428\pi$
$830$	77.2479	−	13.6209i	2.68131	−	0.472788i
$831$	12.9168	−	36.4468i	0.448079	−	1.26433i
$832$	−0.379957	−	0.0669967i	−0.0131726	−	0.00232269i
$833$	9.51168	+	34.7500i	0.329560	+	1.20401i
$834$	36.5210	−	21.5002i	1.26462	−	0.744490i
$835$	0.786204	+	4.45878i	0.0272077	+	0.154303i
$836$	47.1821	−	81.7217i	1.63183	−	2.82640i
$837$	−1.49939	+	0.589321i	−0.0518264	+	0.0203699i
$838$	−34.1934	+	19.7416i	−1.18119	+	0.681962i
$839$	26.3117	+	9.57669i	0.908382	+	0.330624i	0.753607	−	0.657325i	$-0.228312\pi$
$839$	26.3117	+	9.57669i	0.908382	+	0.330624i	0.154776	+	0.987950i	$0.450535\pi$
$840$	71.4626	−	16.6819i	2.46569	−	0.575581i
$841$	12.5325	+	10.5160i	0.432156	+	0.362622i
$842$	9.99904	+	27.4721i	0.344590	+	0.946753i
$843$	−19.4577	−	6.89584i	−0.670160	−	0.237505i
$844$	−7.26407	−	41.1966i	−0.250040	−	1.41805i
$845$	−17.8298	+	30.8821i	−0.613364	+	1.06238i
$846$	13.6294	+	35.5591i	0.468587	+	1.22255i
$847$	11.6932	+	12.6923i	0.401784	+	0.436112i
$848$	25.7478	−	4.54004i	0.884184	−	0.155906i
$849$	5.40155	+	4.45497i	0.185381	+	0.152894i
$850$	−32.3661	−	5.70702i	−1.11015	−	0.195749i
$851$	14.1945	+	2.50288i	0.486582	+	0.0857975i
$852$	36.4667	+	30.0762i	1.24933	+	1.03039i
$853$	−26.0162	+	4.58736i	−0.890779	+	0.157068i	−0.600264	−	0.799802i	$-0.704938\pi$
$853$	−26.0162	+	4.58736i	−0.890779	+	0.157068i	−0.290515	+	0.956870i	$0.593827\pi$
$854$	−2.29230	+	7.33895i	−0.0784408	+	0.251134i
$855$	−15.3854	−	40.1407i	−0.526171	−	1.37278i
$856$	−37.7271	+	65.3453i	−1.28949	+	2.23345i
$857$	1.78248	+	10.1089i	0.0608882	+	0.345314i	0.999999	+	0.00169852i	$0.000540657\pi$
$857$	1.78248	+	10.1089i	0.0608882	+	0.345314i	−0.939110	+	0.343616i	$0.888348\pi$
$858$	2.00168	+	0.709397i	0.0683362	+	0.0242184i
$859$	0.383066	+	1.05247i	0.0130700	+	0.0359097i	0.946056	−	0.324003i	$-0.105029\pi$
$859$	0.383066	+	1.05247i	0.0130700	+	0.0359097i	−0.932986	+	0.359913i	$0.882807\pi$
$860$	−21.5121	−	18.0508i	−0.733556	−	0.615526i
$861$	−29.3719	−	8.90171i	−1.00099	−	0.303369i
$862$	34.3696	+	12.5095i	1.17063	+	0.426076i
$863$	22.3865	−	12.9249i	0.762046	−	0.439968i	−0.0679836	−	0.997686i	$-0.521657\pi$
$863$	22.3865	−	12.9249i	0.762046	−	0.439968i	0.830030	+	0.557719i	$0.188323\pi$
$864$	14.1147	+	11.2447i	0.480190	+	0.382552i
$865$	25.1001	−	43.4746i	0.853428	−	1.47818i
$866$	−5.59012	−	31.7031i	−0.189960	−	1.07732i
$867$	14.1655	−	8.33931i	0.481085	−	0.283218i
$868$	1.91197	+	2.98348i	0.0648966	+	0.101266i
$869$	65.0957	+	11.4781i	2.20822	+	0.389369i
$870$	−14.1996	+	40.0664i	−0.481411	+	1.35838i
$871$	1.27199	−	0.224285i	0.0430996	−	0.00759962i
$872$			22.1089i			0.748702i
$873$	11.7469	+	13.5270i	0.397572	+	0.457819i
$874$	−85.2914	−	49.2430i	−2.88502	−	1.66567i
$875$	−10.8414	+	14.2076i	−0.366505	+	0.480306i
$876$	−3.19303	+	19.0514i	−0.107882	+	0.643687i
$877$	14.6459	+	12.2894i	0.494557	+	0.414982i	0.855656	−	0.517545i	$-0.173154\pi$
$877$	14.6459	+	12.2894i	0.494557	+	0.414982i	−0.361099	+	0.932527i	$0.617598\pi$
$878$	−13.1891	+	74.7989i	−0.445110	+	2.52434i
$879$	1.07707	+	2.88297i	0.0363288	+	0.0972403i
$880$	44.4870	+	53.0176i	1.49966	+	1.78722i
$881$	17.8333	−	30.8881i	0.600818	−	1.04065i	−0.391879	−	0.920017i	$-0.628175\pi$
$881$	17.8333	−	30.8881i	0.600818	−	1.04065i	0.992697	−	0.120631i	$-0.0384918\pi$
$882$	−23.3736	−	47.3362i	−0.787029	−	1.59389i
$883$	−22.8393	−	39.5588i	−0.768602	−	1.33126i	−0.938321	−	0.345766i	$-0.887619\pi$
$883$	−22.8393	−	39.5588i	−0.768602	−	1.33126i	0.169718	−	0.985493i	$-0.445714\pi$
$884$	−0.885999	+	2.43426i	−0.0297994	+	0.0818731i
$885$	32.3408	+	37.8854i	1.08712	+	1.27350i
$886$	49.9651	+	41.9257i	1.67861	+	1.40852i
$887$	−7.00402	+	39.7218i	−0.235172	+	1.33373i	0.607080	+	0.794641i	$0.292341\pi$
$887$	−7.00402	+	39.7218i	−0.235172	+	1.33373i	−0.842251	+	0.539085i	$0.818770\pi$
$888$	19.3926	−	0.164367i	0.650774	−	0.00551581i
$889$	−1.26246	−	3.02484i	−0.0423417	−	0.101450i
$890$			6.30704i			0.211413i
$891$	25.1808	+	28.0227i	0.843589	+	0.938795i
$892$	−105.282	−	60.7848i	−3.52511	−	2.03523i
$893$	−16.9375	−	20.1854i	−0.566793	−	0.675478i
$894$	−62.8740	+	37.0143i	−2.10282	+	1.23794i
$895$	−7.44919	+	8.87759i	−0.248999	+	0.296745i
$896$	−18.5593	+	35.8871i	−0.620022	+	1.19891i
$897$	0.506078	−	1.42798i	0.0168975	−	0.0476789i
$898$	−12.3508	−	4.49531i	−0.412150	−	0.150010i
$899$	−1.10230			−0.0367637
$900$	32.9129	−	0.557964i	1.09710	−	0.0185988i
$901$			22.3489i			0.744550i
$902$	−12.2385	−	69.4079i	−0.407497	−	2.31103i
$903$	−4.90174	+	9.67843i	−0.163120	+	0.322078i
$904$	−14.8023	+	5.38761i	−0.492319	+	0.179189i
$905$	19.3873	−	23.1049i	0.644457	−	0.768034i
$906$	50.2783	+	41.4674i	1.67038	+	1.37766i
$907$	−32.3007	−	11.7565i	−1.07253	−	0.390367i	−0.255405	−	0.966834i	$-0.582209\pi$
$907$	−32.3007	−	11.7565i	−1.07253	−	0.390367i	−0.817121	+	0.576467i	$0.804431\pi$
$908$	−33.0966			−1.09835
$909$	−18.6608	+	16.2052i	−0.618940	+	0.537491i
$910$	−1.44183	−	1.56502i	−0.0477962	−	0.0518798i
$911$	2.82347	+	3.36488i	0.0935458	+	0.111484i	0.810787	−	0.585342i	$-0.199040\pi$
$911$	2.82347	+	3.36488i	0.0935458	+	0.111484i	−0.717241	+	0.696825i	$0.754595\pi$
$912$	−51.2964	−	18.1795i	−1.69859	−	0.601983i
$913$	30.5749	−	36.4377i	1.01188	−	1.20591i
$914$	−33.2068	−	91.2350i	−1.09838	−	3.01778i
$915$	−2.70848	+	4.78443i	−0.0895397	+	0.158168i
$916$	21.0067	−	57.7154i	0.694081	−	1.90697i
$917$	−5.90987	+	18.9208i	−0.195161	+	0.624821i
$918$	−50.3876	+	44.5116i	−1.66304	+	1.46910i
$919$	−11.3040	−	19.5792i	−0.372886	−	0.645857i	0.617122	−	0.786867i	$-0.288298\pi$
$919$	−11.3040	−	19.5792i	−0.372886	−	0.645857i	−0.990008	+	0.141010i	$0.954965\pi$
$920$	92.0929	−	77.2752i	3.03621	−	2.54769i
$921$	−17.2744	−	29.3429i	−0.569209	−	0.966881i
$922$	−40.8232	−	7.19824i	−1.34444	−	0.237061i
$923$	0.127820	−	0.724901i	0.00420724	−	0.0238604i
$924$	49.7085	−	66.3009i	1.63529	−	2.18114i
$925$	3.73580	−	3.13471i	0.122832	−	0.103069i
$926$	−88.9442	−	51.3520i	−2.92289	−	1.68753i
$927$	1.86242	−	2.29753i	0.0611698	−	0.0754609i
$928$	6.17373	+	10.6932i	0.202663	+	0.351022i
$929$	12.2360	−	10.2672i	0.401449	−	0.336856i	−0.419605	−	0.907707i	$-0.637831\pi$
$929$	12.2360	−	10.2672i	0.401449	−	0.336856i	0.821053	+	0.570851i	$0.193387\pi$
$930$	1.29736	+	3.47259i	0.0425419	+	0.113871i
$931$	25.9684	+	25.6908i	0.851081	+	0.841982i
$932$	33.2294	+	91.2971i	1.08847	+	2.99054i
$933$	−29.1776	+	35.3772i	−0.955232	+	1.15820i
$934$	−33.2752	+	91.4228i	−1.08880	+	2.99145i
$935$	−51.2346	+	29.5803i	−1.67555	+	0.967380i
$936$	0.319893	−	2.01318i	0.0104560	−	0.0658029i
$937$	51.5494	−	29.7620i	1.68404	−	0.972283i	0.725119	−	0.688623i	$-0.241785\pi$
$937$	51.5494	−	29.7620i	1.68404	−	0.972283i	0.958925	−	0.283660i	$-0.0915487\pi$
$938$	9.42756	−	73.1273i	0.307821	−	2.38769i
$939$	−1.58907	−	8.58586i	−0.0518572	−	0.280189i
$940$	56.2833	−	20.4854i	1.83576	−	0.668161i
$941$	38.2145	−	13.9089i	1.24576	−	0.453418i	0.366790	−	0.930304i	$-0.380457\pi$
$941$	38.2145	−	13.9089i	1.24576	−	0.453418i	0.878965	+	0.476886i	$0.158234\pi$
$942$	−12.1211	+	7.13577i	−0.394926	+	0.232496i
$943$	−49.5150	+	8.73083i	−1.61243	+	0.284315i
$944$	63.0613			2.05247
$945$	−9.20340	−	36.6110i	−0.299386	−	1.19096i
$946$	−24.9132			−0.809999
$947$	−38.9630	+	6.87023i	−1.26613	+	0.223253i	−0.766080	−	0.642745i	$-0.777796\pi$
$947$	−38.9630	+	6.87023i	−1.26613	+	0.223253i	−0.500048	+	0.865998i	$0.666684\pi$
$948$	−1.00135	−	118.143i	−0.0325225	−	3.83711i
$949$	0.282668	−	0.102883i	0.00917578	−	0.00333971i
$950$	−31.3128	+	11.3969i	−1.01592	+	0.369765i
$951$	−40.7136	+	34.7551i	−1.32023	+	1.12701i
$952$	63.1331	+	48.1747i	2.04616	+	1.56135i
$953$	−10.2234	+	5.90251i	−0.331170	+	0.191201i	−0.656360	−	0.754447i	$-0.727905\pi$
$953$	−10.2234	+	5.90251i	−0.331170	+	0.191201i	0.325190	+	0.945649i	$0.394572\pi$
$954$	−6.23247	−	32.1495i	−0.201784	−	1.04088i
$955$	24.1571	−	13.9471i	0.781706	−	0.451318i
$956$	−35.2082	+	96.7339i	−1.13872	+	3.12860i
$957$	9.02129	+	24.1470i	0.291617	+	0.780562i
$958$	−24.8280	−	68.2145i	−0.802158	−	2.20391i
$959$	−23.2492	−	36.2785i	−0.750757	−	1.17149i
$960$	−10.0208	+	12.1499i	−0.323419	+	0.392138i
$961$	23.6737	−	19.8646i	0.763669	−	0.640794i
$962$	−0.281178	−	0.487015i	−0.00906556	−	0.0157020i
$963$	33.9390	+	18.8350i	1.09367	+	0.606949i
$964$	50.7391	+	29.2942i	1.63420	+	0.943504i
$965$	18.1780	−	15.2531i	0.585170	−	0.491016i
$966$	−69.1969	−	51.8798i	−2.22637	−	1.66921i
$967$	−3.86189	+	21.9019i	−0.124190	+	0.704317i	0.857596	+	0.514325i	$0.171957\pi$
$967$	−3.86189	+	21.9019i	−0.124190	+	0.704317i	−0.981786	+	0.189992i	$0.939154\pi$
$968$	37.4617	+	6.60551i	1.20406	+	0.212309i
$969$	22.9181	−	40.4838i	0.736234	−	1.30053i
$970$	31.5794	−	26.4982i	1.01395	−	0.850807i
$971$	−1.25978	−	2.18201i	−0.0404284	−	0.0700240i	0.845103	−	0.534603i	$-0.179539\pi$
$971$	−1.25978	−	2.18201i	−0.0404284	−	0.0700240i	−0.885532	+	0.464579i	$0.846206\pi$
$972$	41.0605	−	53.3722i	1.31702	−	1.71191i
$973$	−18.9388	+	17.4481i	−0.607151	+	0.559360i
$974$	−18.3791	+	50.4961i	−0.588904	+	1.61800i
$975$	−0.260051	−	0.441733i	−0.00832831	−	0.0141468i
$976$	2.38054	+	6.54049i	0.0761993	+	0.209356i
$977$	11.6467	−	13.8800i	0.372611	−	0.444060i	−0.546857	−	0.837226i	$-0.684176\pi$
$977$	11.6467	−	13.8800i	0.372611	−	0.444060i	0.919468	+	0.393166i	$0.128620\pi$
$978$	6.11152	+	33.0211i	0.195425	+	1.05590i
$979$	2.45842	+	2.92983i	0.0785713	+	0.0936377i
$980$	−75.0636	+	35.4951i	−2.39782	+	1.13385i
$981$	11.3716	−	0.192780i	0.363068	−	0.00615500i
$982$	45.2158			1.44289
$983$	37.9664	+	13.8186i	1.21094	+	0.440746i	0.867030	−	0.498256i	$-0.166026\pi$
$983$	37.9664	+	13.8186i	1.21094	+	0.440746i	0.343910	+	0.939002i	$0.388248\pi$
$984$	−63.3719	+	23.6757i	−2.02022	+	0.754752i
$985$	−1.27412	+	1.51844i	−0.0405970	+	0.0483816i
$986$	−43.2270	+	15.7333i	−1.37663	+	0.501052i
$987$	−12.6498	−	19.3755i	−0.402649	−	0.616731i
$988$	0.456087	+	2.58660i	0.0145101	+	0.0822907i
$989$			17.7729i			0.565145i
$990$	65.4532	−	56.8399i	2.08024	−	1.80649i
$991$	26.2787			0.834772			0.417386	−	0.908729i	$-0.362946\pi$
$991$	26.2787			0.834772			0.417386	+	0.908729i	$0.362946\pi$
$992$	1.01185	+	0.368283i	0.0321263	+	0.0116930i
$993$	18.4450	+	21.6073i	0.585334	+	0.685686i
$994$	−37.3242	−	19.3024i	−1.18385	−	0.612236i
$995$	−38.4390	+	45.8098i	−1.21860	+	1.45227i
$996$	−73.9871	−	41.8844i	−2.34437	−	1.32716i
$997$	8.82324	+	10.5151i	0.279435	+	0.333017i	0.887447	−	0.460911i	$-0.152477\pi$
$997$	8.82324	+	10.5151i	0.279435	+	0.333017i	−0.608012	+	0.793928i	$0.708033\pi$
$998$	23.2048	+	13.3973i	0.734536	+	0.424085i
$999$	−0.253637	−	9.97308i	−0.00802472	−	0.315534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.2	yes	132
3.2	odd	2		567.2.bd.a.17.21		132
7.5	odd	6		189.2.ba.a.131.21	yes	132
21.5	even	6		567.2.ba.a.341.2		132
27.7	even	9		567.2.ba.a.143.2		132
27.20	odd	18		189.2.ba.a.101.21	✓	132
189.47	even	18	inner	189.2.bd.a.47.2	yes	132
189.61	odd	18		567.2.bd.a.467.21		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.21	✓	132	27.20	odd	18
189.2.ba.a.131.21	yes	132	7.5	odd	6
189.2.bd.a.47.2	yes	132	189.47	even	18	inner
189.2.bd.a.185.2	yes	132	1.1	even	1	trivial
567.2.ba.a.143.2		132	27.7	even	9
567.2.ba.a.341.2		132	21.5	even	6
567.2.bd.a.17.21		132	3.2	odd	2
567.2.bd.a.467.21		132	189.61	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47573 + 0.436538i) q^{2} +(-1.50729 - 0.853281i) q^{3} +(4.05929 - 1.47746i) q^{4} +(-2.58032 + 0.939158i) q^{5} +(4.10412 + 1.45451i) q^{6} +(-2.62404 - 0.338290i) q^{7} +(-5.05050 + 2.91591i) q^{8} +(1.54382 + 2.57228i) q^{9} +O(q^{10})\)	\(q+(-2.47573 + 0.436538i) q^{2} +(-1.50729 - 0.853281i) q^{3} +(4.05929 - 1.47746i) q^{4} +(-2.58032 + 0.939158i) q^{5} +(4.10412 + 1.45451i) q^{6} +(-2.62404 - 0.338290i) q^{7} +(-5.05050 + 2.91591i) q^{8} +(1.54382 + 2.57228i) q^{9} +(5.97819 - 3.45151i) q^{10} +(1.43170 - 3.93357i) q^{11} +(-7.37920 - 1.23676i) q^{12} +(0.0398496 + 0.109486i) q^{13} +(6.64408 - 0.307977i) q^{14} +(4.69064 + 0.786155i) q^{15} +(4.61245 - 3.87030i) q^{16} +(2.57344 + 4.45733i) q^{17} +(-4.94499 - 5.69433i) q^{18} +(4.51931 + 2.60922i) q^{19} +(-9.08669 + 7.62463i) q^{20} +(3.66652 + 2.74894i) q^{21} +(-1.82736 + 10.3635i) q^{22} +(7.39321 + 1.30362i) q^{23} +(10.1006 - 0.0856107i) q^{24} +(1.94579 - 1.63271i) q^{25} +(-0.146452 - 0.253662i) q^{26} +(-0.132107 - 5.19447i) q^{27} +(-11.1515 + 2.50369i) q^{28} +(1.21597 - 3.34086i) q^{29} +(-11.9559 + 0.101336i) q^{30} +(-0.106042 - 0.291348i) q^{31} +(-2.23240 + 2.66047i) q^{32} +(-5.51443 + 4.70737i) q^{33} +(-8.31695 - 9.91175i) q^{34} +(7.08855 - 1.59149i) q^{35} +(10.0673 + 8.16068i) q^{36} +1.91994 q^{37} +(-12.3276 - 4.48688i) q^{38} +(0.0333575 - 0.199030i) q^{39} +(10.2934 - 12.2672i) q^{40} +(-6.29347 + 2.29063i) q^{41} +(-10.2773 - 5.20506i) q^{42} +(0.411100 + 2.33146i) q^{43} -18.0828i q^{44} +(-6.39933 - 5.18740i) q^{45} -18.8727 q^{46} +(-4.74491 - 1.72700i) q^{47} +(-10.2547 + 1.89794i) q^{48} +(6.77112 + 1.77537i) q^{49} +(-4.10452 + 4.89157i) q^{50} +(-0.0755560 - 8.91435i) q^{51} +(0.323522 + 0.385559i) q^{52} +(3.76047 + 2.17111i) q^{53} +(2.59465 + 12.8024i) q^{54} +11.4945i q^{55} +(14.2391 - 5.94291i) q^{56} +(-4.58549 - 7.78908i) q^{57} +(-1.55201 + 8.80190i) q^{58} +(8.02306 + 6.73214i) q^{59} +(20.2022 - 3.73901i) q^{60} +(-0.395365 + 1.08626i) q^{61} +(0.389715 + 0.675007i) q^{62} +(-3.18087 - 7.27201i) q^{63} +(-1.65570 + 2.86775i) q^{64} +(-0.205649 - 0.245083i) q^{65} +(11.5973 - 14.0614i) q^{66} +(1.92499 - 10.9172i) q^{67} +(17.0319 + 14.2915i) q^{68} +(-10.0313 - 8.27342i) q^{69} +(-16.8546 + 7.03452i) q^{70} +(-5.47124 - 3.15882i) q^{71} +(-15.2976 - 8.48964i) q^{72} -2.58177i q^{73} +(-4.75325 + 0.838127i) q^{74} +(-4.32603 + 0.800659i) q^{75} +(22.2002 + 3.91449i) q^{76} +(-5.08753 + 9.83750i) q^{77} +(0.00429980 + 0.507305i) q^{78} +(2.74201 + 15.5507i) q^{79} +(-8.26674 + 14.3184i) q^{80} +(-4.23322 + 7.94228i) q^{81} +(14.5810 - 8.41833i) q^{82} +(10.6778 + 3.88640i) q^{83} +(18.9449 + 5.74161i) q^{84} +(-10.8264 - 9.08446i) q^{85} +(-2.03554 - 5.59261i) q^{86} +(-4.68352 + 3.99807i) q^{87} +(4.23912 + 24.0412i) q^{88} +(-0.456832 + 0.791256i) q^{89} +(18.1075 + 10.0490i) q^{90} +(-0.0675288 - 0.300776i) q^{91} +(31.9372 - 5.63140i) q^{92} +(-0.0887660 + 0.529628i) q^{93} +(12.5010 + 2.20427i) q^{94} +(-14.1117 - 2.48828i) q^{95} +(5.63499 - 2.10523i) q^{96} +(5.88114 - 1.03700i) q^{97} +(-17.5385 - 1.43948i) q^{98} +(12.3285 - 2.39000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more