LMFDB - Embedded newform 189.2.ba.a.101.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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			101.18
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06515 - 1.26940i) q^{2} +(-0.257071 + 1.71287i) q^{3} +(-0.129525 - 0.734574i) q^{4} +(-2.93903 + 2.46614i) q^{5} +(1.90049 + 2.15078i) q^{6} +(2.02233 + 1.70592i) q^{7} +(1.79971 + 1.03907i) q^{8} +(-2.86783 - 0.880657i) q^{9} +O(q^{10})$	\(q+(1.06515 - 1.26940i) q^{2} +(-0.257071 + 1.71287i) q^{3} +(-0.129525 - 0.734574i) q^{4} +(-2.93903 + 2.46614i) q^{5} +(1.90049 + 2.15078i) q^{6} +(2.02233 + 1.70592i) q^{7} +(1.79971 + 1.03907i) q^{8} +(-2.86783 - 0.880657i) q^{9} +6.35759i q^{10} +(1.84743 - 2.20168i) q^{11} +(1.29153 - 0.0330219i) q^{12} +(1.44158 - 3.96072i) q^{13} +(4.31958 - 0.750072i) q^{14} +(-3.46863 - 5.66814i) q^{15} +(4.63779 - 1.68802i) q^{16} -3.18833 q^{17} +(-4.17257 + 2.70238i) q^{18} +2.26672i q^{19} +(2.19224 + 1.83951i) q^{20} +(-3.44191 + 3.02544i) q^{21} +(-0.827014 - 4.69023i) q^{22} +(-0.782500 + 2.14990i) q^{23} +(-2.24244 + 2.81556i) q^{24} +(1.68781 - 9.57204i) q^{25} +(-3.49221 - 6.04869i) q^{26} +(2.24568 - 4.68582i) q^{27} +(0.991186 - 1.70651i) q^{28} +(0.356349 + 0.979061i) q^{29} +(-10.8897 - 1.63435i) q^{30} +(8.54472 - 1.50666i) q^{31} +(1.37565 - 3.77958i) q^{32} +(3.29626 + 3.73038i) q^{33} +(-3.39605 + 4.04725i) q^{34} +(-10.1507 - 0.0264162i) q^{35} +(-0.275452 + 2.22070i) q^{36} +(-0.0122349 + 0.0211914i) q^{37} +(2.87736 + 2.41439i) q^{38} +(6.41360 + 3.48743i) q^{39} +(-7.85188 + 1.38450i) q^{40} +(2.99981 + 1.09184i) q^{41} +(0.174337 + 7.59168i) q^{42} +(-0.110557 + 0.627001i) q^{43} +(-1.85658 - 1.07190i) q^{44} +(10.6004 - 4.48418i) q^{45} +(1.89560 + 3.28327i) q^{46} +(1.86595 - 10.5823i) q^{47} +(1.69911 + 8.37787i) q^{48} +(1.17964 + 6.89989i) q^{49} +(-10.3529 - 12.3382i) q^{50} +(0.819627 - 5.46119i) q^{51} +(-3.09616 - 0.545937i) q^{52} +(-1.91685 - 1.10670i) q^{53} +(-3.55617 - 7.84176i) q^{54} +11.0268i q^{55} +(1.86705 + 5.17151i) q^{56} +(-3.88258 - 0.582707i) q^{57} +(1.62238 + 0.590498i) q^{58} +(-10.2914 - 3.74577i) q^{59} +(-3.71439 + 3.28213i) q^{60} +(-7.50570 - 1.32346i) q^{61} +(7.18884 - 12.4514i) q^{62} +(-4.29736 - 6.67328i) q^{63} +(1.60294 + 2.77637i) q^{64} +(5.53082 + 15.1958i) q^{65} +(8.24634 - 0.210843i) q^{66} +(-8.32749 + 6.98759i) q^{67} +(0.412969 + 2.34207i) q^{68} +(-3.48134 - 1.89300i) q^{69} +(-10.8456 + 12.8571i) q^{70} +(3.88604 - 2.24361i) q^{71} +(-4.24621 - 4.56479i) q^{72} +(1.92730 - 1.11273i) q^{73} +(0.0138683 + 0.0381028i) q^{74} +(15.9618 + 5.35169i) q^{75} +(1.66507 - 0.293597i) q^{76} +(7.49200 - 1.30095i) q^{77} +(11.2584 - 4.42676i) q^{78} +(-9.68949 - 8.13045i) q^{79} +(-9.46771 + 16.3986i) q^{80} +(7.44889 + 5.05115i) q^{81} +(4.58122 - 2.64497i) q^{82} +(-4.16888 + 1.51735i) q^{83} +(2.66822 + 2.13646i) q^{84} +(9.37059 - 7.86286i) q^{85} +(0.678152 + 0.808190i) q^{86} +(-1.76861 + 0.358690i) q^{87} +(5.61252 - 2.04279i) q^{88} +4.73160 q^{89} +(5.59885 - 18.2325i) q^{90} +(9.67205 - 5.55065i) q^{91} +(1.68062 + 0.296338i) q^{92} +(0.384117 + 15.0233i) q^{93} +(-11.4457 - 13.6404i) q^{94} +(-5.59003 - 6.66194i) q^{95} +(6.12027 + 3.32793i) q^{96} +(13.0174 + 2.29533i) q^{97} +(10.0152 + 5.85198i) q^{98} +(-7.23702 + 4.68708i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.06515	−	1.26940i	0.753174	−	0.897598i	−0.244222	−	0.969719i	$-0.578532\pi$
$2$	1.06515	−	1.26940i	0.753174	−	0.897598i	0.997396	+	0.0721215i	$0.0229769\pi$
$3$	−0.257071	+	1.71287i	−0.148420	+	0.988924i
$3$	−0.257071	+	1.71287i	−0.148420	+	0.988924i
$4$	−0.129525	−	0.734574i	−0.0647626	−	0.367287i
$5$	−2.93903	+	2.46614i	−1.31437	+	1.10289i	−0.326907	+	0.945057i	$0.606006\pi$
$5$	−2.93903	+	2.46614i	−1.31437	+	1.10289i	−0.987466	+	0.157833i	$0.949549\pi$
$6$	1.90049	+	2.15078i	0.775870	+	0.878054i
$7$	2.02233	+	1.70592i	0.764369	+	0.644779i
$7$	2.02233	+	1.70592i	0.764369	+	0.644779i
$8$	1.79971	+	1.03907i	0.636295	+	0.367365i
$9$	−2.86783	−	0.880657i	−0.955943	−	0.293552i
$10$			6.35759i			2.01045i
$11$	1.84743	−	2.20168i	0.557020	−	0.663830i	−0.411893	−	0.911232i	$-0.635132\pi$
$11$	1.84743	−	2.20168i	0.557020	−	0.663830i	0.968913	+	0.247402i	$0.0795767\pi$
$12$	1.29153	−	0.0330219i	0.372831	−	0.00953260i
$13$	1.44158	−	3.96072i	0.399823	−	1.09851i	−0.562547	−	0.826765i	$-0.690179\pi$
$13$	1.44158	−	3.96072i	0.399823	−	1.09851i	0.962371	−	0.271740i	$-0.0875992\pi$
$14$	4.31958	−	0.750072i	1.15446	−	0.200465i
$15$	−3.46863	−	5.66814i	−0.895595	−	1.46351i
$16$	4.63779	−	1.68802i	1.15945	−	0.422005i
$17$	−3.18833			−0.773284			−0.386642	−	0.922230i	$-0.626365\pi$
$17$	−3.18833			−0.773284			−0.386642	+	0.922230i	$0.626365\pi$
$18$	−4.17257	+	2.70238i	−0.983483	+	0.636956i
$19$			2.26672i			0.520020i	0.965606	+	0.260010i	$0.0837259\pi$
$19$			2.26672i			0.520020i	−0.965606	+	0.260010i	$0.916274\pi$
$20$	2.19224	+	1.83951i	0.490200	+	0.411326i
$21$	−3.44191	+	3.02544i	−0.751085	+	0.660205i
$22$	−0.827014	−	4.69023i	−0.176320	−	0.999960i
$23$	−0.782500	+	2.14990i	−0.163163	+	0.448285i	−0.994150	−	0.108005i	$-0.965554\pi$
$23$	−0.782500	+	2.14990i	−0.163163	+	0.448285i	0.830988	+	0.556291i	$0.187776\pi$
$24$	−2.24244	+	2.81556i	−0.457735	+	0.574723i
$25$	1.68781	−	9.57204i	0.337562	−	1.91441i
$26$	−3.49221	−	6.04869i	−0.684880	−	1.18625i
$27$	2.24568	−	4.68582i	0.432182	−	0.901786i
$28$	0.991186	−	1.70651i	0.187317	−	0.322501i
$29$	0.356349	+	0.979061i	0.0661723	+	0.181807i	0.968372	−	0.249513i	$-0.0802704\pi$
$29$	0.356349	+	0.979061i	0.0661723	+	0.181807i	−0.902199	+	0.431320i	$0.858048\pi$
$30$	−10.8897	−	1.63435i	−1.98818	−	0.298390i
$31$	8.54472	−	1.50666i	1.53468	−	0.270605i	0.658495	−	0.752585i	$-0.271194\pi$
$31$	8.54472	−	1.50666i	1.53468	−	0.270605i	0.876182	+	0.481981i	$0.160082\pi$
$32$	1.37565	−	3.77958i	0.243183	−	0.668141i
$33$	3.29626	+	3.73038i	0.573805	+	0.649376i
$34$	−3.39605	+	4.04725i	−0.582417	+	0.694098i
$35$	−10.1507	−	0.0264162i	−1.71579	−	0.00446515i
$36$	−0.275452	+	2.22070i	−0.0459086	+	0.370117i
$37$	−0.0122349	+	0.0211914i	−0.00201140	+	0.00348384i	−0.867029	−	0.498257i	$-0.833974\pi$
$37$	−0.0122349	+	0.0211914i	−0.00201140	+	0.00348384i	0.865018	+	0.501741i	$0.167307\pi$
$38$	2.87736	+	2.41439i	0.466769	+	0.391666i
$39$	6.41360	+	3.48743i	1.02700	+	0.558435i
$40$	−7.85188	+	1.38450i	−1.24149	+	0.218909i
$41$	2.99981	+	1.09184i	0.468492	+	0.170517i	0.565469	−	0.824770i	$-0.308695\pi$
$41$	2.99981	+	1.09184i	0.468492	+	0.170517i	−0.0969772	+	0.995287i	$0.530917\pi$
$42$	0.174337	+	7.59168i	0.0269008	+	1.17142i
$43$	−0.110557	+	0.627001i	−0.0168598	+	0.0956167i	−0.992077	−	0.125635i	$-0.959903\pi$
$43$	−0.110557	+	0.627001i	−0.0168598	+	0.0956167i	0.975217	+	0.221252i	$0.0710143\pi$
$44$	−1.85658	−	1.07190i	−0.279890	−	0.161595i
$45$	10.6004	−	4.48418i	1.58022	−	0.668463i
$46$	1.89560	+	3.28327i	0.279490	+	0.484091i
$47$	1.86595	−	10.5823i	0.272177	−	1.54359i	−0.475611	−	0.879656i	$-0.657773\pi$
$47$	1.86595	−	10.5823i	0.272177	−	1.54359i	0.747788	−	0.663937i	$-0.231116\pi$
$48$	1.69911	+	8.37787i	0.245245	+	1.20924i
$49$	1.17964	+	6.89989i	0.168520	+	0.985698i
$50$	−10.3529	−	12.3382i	−1.46413	−	1.74488i
$51$	0.819627	−	5.46119i	0.114771	−	0.764719i
$52$	−3.09616	−	0.545937i	−0.429361	−	0.0757079i
$53$	−1.91685	−	1.10670i	−0.263300	−	0.152016i	0.362539	−	0.931969i	$-0.381910\pi$
$53$	−1.91685	−	1.10670i	−0.263300	−	0.152016i	−0.625839	+	0.779952i	$0.715243\pi$
$54$	−3.55617	−	7.84176i	−0.483933	−	1.06713i
$55$			11.0268i			1.48685i
$56$	1.86705	+	5.17151i	0.249495	+	0.691072i
$57$	−3.88258	−	0.582707i	−0.514261	−	0.0771814i
$58$	1.62238	+	0.590498i	0.213029	+	0.0775362i
$59$	−10.2914	−	3.74577i	−1.33983	−	0.487658i	−0.430070	−	0.902795i	$-0.641511\pi$
$59$	−10.2914	−	3.74577i	−1.33983	−	0.487658i	−0.909759	+	0.415138i	$0.863733\pi$
$60$	−3.71439	+	3.28213i	−0.479526	+	0.423721i
$61$	−7.50570	−	1.32346i	−0.961006	−	0.169451i	−0.328927	−	0.944355i	$-0.606687\pi$
$61$	−7.50570	−	1.32346i	−0.961006	−	0.169451i	−0.632079	+	0.774904i	$0.717798\pi$
$62$	7.18884	−	12.4514i	0.912984	−	1.58133i
$63$	−4.29736	−	6.67328i	−0.541417	−	0.840754i
$64$	1.60294	+	2.77637i	0.200367	+	0.347046i
$65$	5.53082	+	15.1958i	0.686014	+	1.88481i
$66$	8.24634	−	0.210843i	1.01505	−	0.0259530i
$67$	−8.32749	+	6.98759i	−1.01736	+	0.853670i	−0.989294	−	0.145936i	$-0.953381\pi$
$67$	−8.32749	+	6.98759i	−1.01736	+	0.853670i	−0.0280702	+	0.999606i	$0.508936\pi$
$68$	0.412969	+	2.34207i	0.0500799	+	0.284017i
$69$	−3.48134	−	1.89300i	−0.419104	−	0.227890i
$70$	−10.8456	+	12.8571i	−1.29629	+	1.53672i
$71$	3.88604	−	2.24361i	0.461188	−	0.266267i	−0.251356	−	0.967895i	$-0.580876\pi$
$71$	3.88604	−	2.24361i	0.461188	−	0.266267i	0.712544	+	0.701628i	$0.247543\pi$
$72$	−4.24621	−	4.56479i	−0.500421	−	0.537966i
$73$	1.92730	−	1.11273i	0.225574	−	0.130235i	−0.382955	−	0.923767i	$-0.625093\pi$
$73$	1.92730	−	1.11273i	0.225574	−	0.130235i	0.608528	+	0.793532i	$0.291760\pi$
$74$	0.0138683	+	0.0381028i	0.00161216	+	0.00442937i
$75$	15.9618	+	5.35169i	1.84310	+	0.617960i
$76$	1.66507	−	0.293597i	0.190997	−	0.0336779i
$77$	7.49200	−	1.30095i	0.853793	−	0.148257i
$78$	11.2584	−	4.42676i	1.27476	−	0.501232i
$79$	−9.68949	−	8.13045i	−1.09015	−	0.914747i	−0.0934288	−	0.995626i	$-0.529783\pi$
$79$	−9.68949	−	8.13045i	−1.09015	−	0.914747i	−0.996724	+	0.0808793i	$0.974227\pi$
$80$	−9.46771	+	16.3986i	−1.05852	+	1.83342i
$81$	7.44889	+	5.05115i	0.827654	+	0.561239i
$82$	4.58122	−	2.64497i	0.505912	−	0.292088i
$83$	−4.16888	+	1.51735i	−0.457594	+	0.166550i	−0.560524	−	0.828138i	$-0.689400\pi$
$83$	−4.16888	+	1.51735i	−0.457594	+	0.166550i	0.102931	+	0.994689i	$0.467178\pi$
$84$	2.66822	+	2.13646i	0.291127	+	0.233107i
$85$	9.37059	−	7.86286i	1.01638	−	0.852846i
$86$	0.678152	+	0.808190i	0.0731270	+	0.0871494i
$87$	−1.76861	+	0.358690i	−0.189615	+	0.0384557i
$88$	5.61252	−	2.04279i	0.598297	−	0.217762i
$89$	4.73160			0.501549			0.250774	−	0.968046i	$-0.419315\pi$
$89$	4.73160			0.501549			0.250774	+	0.968046i	$0.419315\pi$
$90$	5.59885	−	18.2325i	0.590171	−	1.92187i
$91$	9.67205	−	5.55065i	1.01391	−	0.581866i
$92$	1.68062	+	0.296338i	0.175216	+	0.0308954i
$93$	0.384117	+	15.0233i	0.0398311	+	1.55784i
$94$	−11.4457	−	13.6404i	−1.18053	−	1.40690i
$95$	−5.59003	−	6.66194i	−0.573525	−	0.683500i
$96$	6.12027	+	3.32793i	0.624648	+	0.339655i
$97$	13.0174	+	2.29533i	1.32172	+	0.233055i	0.789605	−	0.613616i	$-0.210286\pi$
$97$	13.0174	+	2.29533i	1.32172	+	0.233055i	0.532117	+	0.846671i	$0.321397\pi$
$98$	10.0152	+	5.85198i	1.01169	+	0.591139i
$99$	−7.23702	+	4.68708i	−0.727348	+	0.471070i
$100$	−7.24999			−0.724999
$101$	2.55038	−	0.928261i	0.253772	−	0.0923654i	−0.212002	−	0.977269i	$-0.567998\pi$
$101$	2.55038	−	0.928261i	0.253772	−	0.0923654i	0.465774	+	0.884904i	$0.345776\pi$
$102$	−6.05938	−	6.85741i	−0.599968	−	0.678984i
$103$	−6.27600	−	7.47944i	−0.618393	−	0.736972i	0.362401	−	0.932022i	$-0.381957\pi$
$103$	−6.27600	−	7.47944i	−0.618393	−	0.736972i	−0.980793	+	0.195051i	$0.937513\pi$
$104$	6.70988	−	5.63026i	0.657958	−	0.552092i
$105$	2.65470	−	17.3801i	0.259073	−	1.69612i
$106$	−3.44657	+	1.25445i	−0.334761	+	0.121843i
$107$	−12.2288	+	7.06029i	−1.18220	+	0.682544i	−0.956523	−	0.291658i	$-0.905793\pi$
$107$	−12.2288	+	7.06029i	−1.18220	+	0.682544i	−0.225678	+	0.974202i	$0.572460\pi$
$108$	−3.73296	−	1.04269i	−0.359204	−	0.100333i
$109$	2.48897	−	4.31103i	0.238400	−	0.412922i	−0.721855	−	0.692044i	$-0.756710\pi$
$109$	2.48897	−	4.31103i	0.238400	−	0.412922i	0.960255	+	0.279123i	$0.0900436\pi$
$110$	13.9974	+	11.7452i	1.33460	+	1.11986i
$111$	−0.0331528	−	0.0264044i	−0.00314672	−	0.00250619i
$112$	12.2588	+	4.49799i	1.15835	+	0.425021i
$113$	7.89136	−	1.39146i	0.742357	−	0.130898i	0.210336	−	0.977629i	$-0.432544\pi$
$113$	7.89136	−	1.39146i	0.742357	−	0.130898i	0.532020	+	0.846732i	$0.321433\pi$
$114$	−4.87521	+	4.30786i	−0.456606	+	0.403468i
$115$	−3.00216	−	8.24837i	−0.279953	−	0.769164i
$116$	0.673037	−	0.388578i	0.0624899	−	0.0360786i
$117$	−7.62225	+	10.0891i	−0.704677	+	0.932740i
$118$	−15.7168	+	9.07408i	−1.44684	+	0.835336i
$119$	−6.44786	−	5.43905i	−0.591074	−	0.498597i
$120$	−0.352972	−	13.8052i	−0.0322218	−	1.26023i
$121$	0.475733	+	2.69802i	0.0432485	+	0.245274i
$122$	−9.67468	+	8.11802i	−0.875904	+	0.734971i
$123$	−2.64134	+	4.85760i	−0.238162	+	0.437995i
$124$	−2.21351	−	6.08158i	−0.198779	−	0.546142i
$125$	9.05388	+	15.6818i	0.809804	+	1.40262i
$126$	−13.0484	−	1.65298i	−1.16244	−	0.147260i
$127$	−3.39217	+	5.87541i	−0.301006	+	0.521358i	−0.976364	−	0.216132i	$-0.930656\pi$
$127$	−3.39217	+	5.87541i	−0.301006	+	0.521358i	0.675358	+	0.737490i	$0.263989\pi$
$128$	13.1537	+	2.31936i	1.16264	+	0.205004i
$129$	−1.04555	−	0.350553i	−0.0920554	−	0.0308645i
$130$	25.1806	+	9.16500i	2.20849	+	0.803823i
$131$	18.8911	+	6.87581i	1.65053	+	0.600742i	0.988832	−	0.149033i	$-0.0476160\pi$
$131$	18.8911	+	6.87581i	1.65053	+	0.600742i	0.661693	+	0.749775i	$0.269838\pi$
$132$	2.31329	−	2.90453i	0.201346	−	0.252807i
$133$	−3.86685	+	4.58405i	−0.335298	+	0.397487i
$134$			18.0137i			1.55615i
$135$	4.95574	+	19.3099i	0.426523	+	1.66193i
$136$	−5.73808	−	3.31288i	−0.492036	−	0.284077i
$137$	−18.4568	−	3.25444i	−1.57687	−	0.278045i	−0.684387	−	0.729119i	$-0.739930\pi$
$137$	−18.4568	−	3.25444i	−1.57687	−	0.278045i	−0.892487	+	0.451073i	$0.851041\pi$
$138$	−6.11110	+	2.40287i	−0.520212	+	0.204546i
$139$	−8.49230	−	10.1207i	−0.720308	−	0.858429i	0.274353	−	0.961629i	$-0.411536\pi$
$139$	−8.49230	−	10.1207i	−0.720308	−	0.858429i	−0.994661	+	0.103200i	$0.967092\pi$
$140$	1.29537	+	7.45989i	0.109479	+	0.630475i
$141$	17.6465	+	5.91654i	1.48610	+	0.498263i
$142$	1.29119	−	7.32269i	0.108354	−	0.614507i
$143$	−6.05700	−	10.4910i	−0.506512	−	0.877304i
$144$	−14.7870	+	0.756645i	−1.23225	+	0.0630537i
$145$	−3.46182	−	1.99868i	−0.287488	−	0.165981i
$146$	0.640372	−	3.63173i	0.0529976	−	0.300564i
$147$	−12.1218	+	0.246808i	−0.999793	+	0.0203564i
$148$	0.0171514	+	0.00624259i	0.00140983	+	0.000513138i
$149$	13.0187	−	2.29555i	1.06654	−	0.188059i	0.387282	−	0.921962i	$-0.373414\pi$
$149$	13.0187	−	2.29555i	1.06654	−	0.188059i	0.679255	+	0.733902i	$0.262303\pi$
$150$	23.7951	−	14.5614i	1.94286	−	1.18894i
$151$	−9.62231	−	8.07407i	−0.783052	−	0.657059i	0.160963	−	0.986960i	$-0.448540\pi$
$151$	−9.62231	−	8.07407i	−0.783052	−	0.657059i	−0.944015	+	0.329902i	$0.892984\pi$
$152$	−2.35527	+	4.07944i	−0.191037	+	0.330886i
$153$	9.14358	+	2.80782i	0.739215	+	0.226999i
$154$	6.32868	−	10.8960i	0.509980	−	0.878026i
$155$	−21.3975	+	25.5006i	−1.71869	+	2.04825i
$156$	1.73105	−	5.16297i	0.138595	−	0.413369i
$157$	−6.20286	+	17.0422i	−0.495042	+	1.36012i	0.400971	+	0.916091i	$0.368673\pi$
$157$	−6.20286	+	17.0422i	−0.495042	+	1.36012i	−0.896013	+	0.444027i	$0.853549\pi$
$158$	−20.6415	+	3.63965i	−1.64215	+	0.289555i
$159$	2.38839	−	2.99882i	0.189412	−	0.237822i
$160$	5.27787	+	14.5008i	0.417252	+	1.14639i
$161$	−5.25004	+	3.01292i	−0.413761	+	0.237452i
$162$	14.3461	−	4.07536i	1.12713	−	0.320190i
$163$	2.93944	+	5.09126i	0.230235	+	0.398779i	0.957877	−	0.287178i	$-0.0927172\pi$
$163$	2.93944	+	5.09126i	0.230235	+	0.398779i	−0.727642	+	0.685957i	$0.759384\pi$
$164$	0.413488	−	2.34501i	0.0322880	−	0.183114i
$165$	−18.8874	−	2.83467i	−1.47038	−	0.220679i
$166$	−2.51436	+	6.90815i	−0.195152	+	0.536177i
$167$	1.43991	+	8.16616i	0.111424	+	0.631916i	0.988459	+	0.151490i	$0.0484070\pi$
$167$	1.43991	+	8.16616i	0.111424	+	0.631916i	−0.877035	+	0.480427i	$0.840482\pi$
$168$	−9.33807	+	1.86856i	−0.720448	+	0.144163i
$169$	−3.65055	−	3.06317i	−0.280811	−	0.235629i
$170$		−	20.2701i		−	1.55464i
$171$	1.99620	−	6.50055i	0.152653	−	0.497110i
$172$	0.474899			0.0362107
$173$	−18.3478	+	6.67804i	−1.39495	+	0.507722i	−0.926677	−	0.375860i	$-0.877347\pi$
$173$	−18.3478	+	6.67804i	−1.39495	+	0.507722i	−0.468277	+	0.883582i	$0.655125\pi$
$174$	−1.42851	+	2.62712i	−0.108295	+	0.199162i
$175$	19.7425	−	16.4786i	1.49239	−	1.24566i
$176$	4.85151	−	13.3294i	0.365696	−	1.00474i
$177$	9.06163	−	16.6649i	0.681114	−	1.25261i
$178$	5.03986	−	6.00627i	0.377754	−	0.450189i
$179$		−	2.96390i		−	0.221532i	−0.993846	−	0.110766i	$-0.964670\pi$
$179$		−	2.96390i		−	0.221532i	0.993846	−	0.110766i	$-0.0353305\pi$
$180$	−4.66699	−	7.20600i	−0.347857	−	0.537104i
$181$	−22.0624	−	12.7377i	−1.63988	−	0.946787i	−0.980872	−	0.194653i	$-0.937642\pi$
$181$	−22.0624	−	12.7377i	−1.63988	−	0.946787i	−0.659011	−	0.752134i	$-0.729025\pi$
$182$	3.25620	−	18.1899i	0.241366	−	1.34833i
$183$	4.19640	−	12.5160i	0.310207	−	0.925213i
$184$	−3.64216	+	3.05614i	−0.268504	+	0.225302i
$185$	−0.0163023	−	0.0924549i	−0.00119857	−	0.00679742i
$186$	19.4796	+	15.5144i	1.42832	+	1.13757i
$187$	−5.89020	+	7.01967i	−0.430734	+	0.513329i
$188$	−8.01521			−0.584569
$189$	12.5352	−	5.64531i	0.911799	−	0.410636i
$190$	−14.4108			−1.04547
$191$	14.5728	−	17.3672i	1.05445	−	1.25665i	0.0890120	−	0.996031i	$-0.471629\pi$
$191$	14.5728	−	17.3672i	1.05445	−	1.25665i	0.965442	−	0.260619i	$-0.0839265\pi$
$192$	−5.16762	+	2.03189i	−0.372941	+	0.146639i
$193$	−2.59185	−	14.6991i	−0.186566	−	1.05807i	−0.923927	−	0.382568i	$-0.875040\pi$
$193$	−2.59185	−	14.6991i	−0.186566	−	1.05807i	0.737361	−	0.675498i	$-0.236071\pi$
$194$	16.7792	−	14.0794i	1.20468	−	1.01084i
$195$	−27.4502	+	5.56716i	−1.96575	+	0.398673i
$196$	4.91569	−	1.76024i	0.351121	−	0.125732i
$197$	16.5142	+	9.53447i	1.17659	+	0.679303i	0.955222	−	0.295889i	$-0.0956158\pi$
$197$	16.5142	+	9.53447i	1.17659	+	0.679303i	0.221364	+	0.975191i	$0.428949\pi$
$198$	−1.75875	+	14.1791i	−0.124989	+	1.00766i
$199$		−	5.80784i		−	0.411707i	−0.978583	−	0.205854i	$-0.934003\pi$
$199$		−	5.80784i		−	0.411707i	0.978583	−	0.205854i	$-0.0659971\pi$
$200$	12.9836	−	15.4732i	0.918076	−	1.09412i
$201$	−9.82806	−	16.0602i	−0.693218	−	1.13280i
$202$	1.53820	−	4.22617i	0.108227	−	0.297352i
$203$	−0.949549	+	2.58789i	−0.0666453	+	0.181634i
$204$	−4.11781	+	0.105285i	−0.288304	+	0.00737140i
$205$	−11.5092	+	4.18899i	−0.803834	+	0.292572i
$206$	−16.1792			−1.12726
$207$	4.13740	−	5.47644i	0.287569	−	0.380639i
$208$		−	20.8024i		−	1.44239i
$209$	4.99057	+	4.18759i	0.345205	+	0.289662i
$210$	−19.2345	−	21.8822i	−1.32731	−	1.51002i
$211$	0.180568	+	1.02405i	0.0124308	+	0.0704985i	0.990392	−	0.138288i	$-0.0441599\pi$
$211$	0.180568	+	1.02405i	0.0124308	+	0.0704985i	−0.977961	+	0.208786i	$0.933049\pi$
$212$	−0.564670	+	1.55142i	−0.0387817	+	0.106552i
$213$	2.84401	+	7.23303i	0.194868	+	0.495599i
$214$	−4.06317	+	23.0434i	−0.277753	+	1.57521i
$215$	−1.22134	−	2.11542i	−0.0832946	−	0.144271i
$216$	8.91046	−	6.09972i	0.606280	−	0.415034i
$217$	19.8505	+	11.5297i	1.34754	+	0.782685i
$218$	−2.82127	−	7.75138i	−0.191081	−	0.524990i
$219$	1.41050	+	3.58726i	0.0953130	+	0.242405i
$220$	8.10000	−	1.42825i	0.546102	−	0.0962925i
$221$	−4.59624	+	12.6281i	−0.309177	+	0.849456i
$222$	−0.0688302	+	0.0139594i	−0.00461958	+	0.000936895i
$223$	−4.95104	+	5.90042i	−0.331546	+	0.395122i	−0.905904	−	0.423483i	$-0.860807\pi$
$223$	−4.95104	+	5.90042i	−0.331546	+	0.395122i	0.574358	+	0.818604i	$0.305252\pi$
$224$	9.22970	−	5.29679i	0.616685	−	0.353907i
$225$	−13.2700	+	25.9646i	−0.884669	+	1.73097i
$226$	6.63916	−	11.4994i	0.441630	−	0.764926i
$227$	2.48407	+	2.08438i	0.164873	+	0.138345i	0.721491	−	0.692423i	$-0.243457\pi$
$227$	2.48407	+	2.08438i	0.164873	+	0.138345i	−0.556618	+	0.830768i	$0.687901\pi$
$228$	0.0748513	+	2.92752i	0.00495715	+	0.193880i
$229$	−21.5273	+	3.79585i	−1.42257	+	0.250837i	−0.831382	−	0.555701i	$-0.812450\pi$
$229$	−21.5273	+	3.79585i	−1.42257	+	0.250837i	−0.591183	+	0.806537i	$0.701339\pi$
$230$	−13.6682	−	4.97481i	−0.901254	−	0.328030i
$231$	0.302375	+	13.1672i	0.0198948	+	0.866341i
$232$	−0.375982	+	2.13230i	−0.0246844	+	0.139992i
$233$	8.06698	+	4.65747i	0.528486	+	0.305121i	0.740400	−	0.672167i	$-0.234636\pi$
$233$	8.06698	+	4.65747i	0.528486	+	0.305121i	−0.211914	+	0.977288i	$0.567970\pi$
$234$	4.68825	+	20.4221i	0.306481	+	1.33503i
$235$	20.6134	+	35.7035i	1.34467	+	2.32904i
$236$	−1.41855	+	8.04499i	−0.0923396	+	0.523684i
$237$	16.4173	−	14.5067i	1.06642	−	0.942312i
$238$	−13.7722	+	2.39148i	−0.892721	+	0.155016i
$239$	−3.92573	−	4.67850i	−0.253934	−	0.302627i	0.623984	−	0.781437i	$-0.285513\pi$
$239$	−3.92573	−	4.67850i	−0.253934	−	0.302627i	−0.877919	+	0.478810i	$0.841068\pi$
$240$	−25.6547	−	20.4325i	−1.65600	−	1.31891i
$241$	0.327723	+	0.0577863i	0.0211105	+	0.00372235i	0.184193	−	0.982890i	$-0.441033\pi$
$241$	0.327723	+	0.0577863i	0.0211105	+	0.00372235i	−0.163083	+	0.986612i	$0.552144\pi$
$242$	3.93158	+	2.26990i	0.252731	+	0.145915i
$243$	−10.5668	+	11.4605i	−0.677863	+	0.735188i
$244$			5.68492i			0.363939i
$245$	−20.4831	−	17.3698i	−1.30861	−	1.10972i
$246$	3.35279	+	8.52698i	0.213766	+	0.543660i
$247$	8.97782	+	3.26766i	0.571245	+	0.207916i
$248$	16.9436	+	6.16695i	1.07592	+	0.391602i
$249$	−1.52732	−	7.53080i	−0.0967898	−	0.477245i
$250$	29.5501	+	5.21048i	1.86891	+	0.329540i
$251$	−6.85299	+	11.8697i	−0.432557	+	0.749210i	−0.997093	−	0.0761982i	$-0.975722\pi$
$251$	−6.85299	+	11.8697i	−0.432557	+	0.749210i	0.564536	+	0.825409i	$0.309055\pi$
$252$	−4.34540	+	4.02109i	−0.273735	+	0.253305i
$253$	3.28778	+	5.69460i	0.206701	+	0.358016i
$254$	3.84505	+	10.5642i	0.241260	+	0.662856i
$255$	11.0591	+	18.0719i	0.692549	+	1.13171i
$256$	12.0432	−	10.1054i	0.752700	−	0.631590i
$257$	−0.00716061	−	0.0406099i	−0.000446667	−	0.00253317i	0.984584	−	0.174915i	$-0.0559649\pi$
$257$	−0.00716061	−	0.0406099i	−0.000446667	−	0.00253317i	−0.985030	+	0.172381i	$0.944854\pi$
$258$	−1.55866	+	0.953822i	−0.0970376	+	0.0593824i
$259$	−0.0608938	+	0.0219842i	−0.00378376	+	0.00136603i
$260$	10.4461	−	6.03104i	0.647837	−	0.374029i
$261$	−0.159731	−	3.12160i	−0.00988712	−	0.193222i
$262$	28.8500	−	16.6565i	1.78236	−	1.02904i
$263$	−4.77109	−	13.1085i	−0.294198	−	0.808302i	−0.995441	−	0.0953797i	$-0.969593\pi$
$263$	−4.77109	−	13.1085i	−0.294198	−	0.808302i	0.701243	−	0.712922i	$-0.252629\pi$
$264$	2.05621	+	10.1387i	0.126551	+	0.623991i
$265$	8.36295	−	1.47461i	0.513732	−	0.0905848i
$266$	1.70020	+	9.79125i	0.104246	+	0.600340i
$267$	−1.21636	+	8.10461i	−0.0744399	+	0.495994i
$268$	6.21152	+	5.21209i	0.379429	+	0.318379i
$269$	11.2526	−	19.4900i	0.686081	−	1.18833i	−0.287015	−	0.957926i	$-0.592663\pi$
$269$	11.2526	−	19.4900i	0.686081	−	1.18833i	0.973096	−	0.230401i	$-0.0740038\pi$
$270$	29.7905	+	14.2771i	1.81299	+	0.868879i
$271$	5.53035	−	3.19295i	0.335945	−	0.193958i	−0.322533	−	0.946558i	$-0.604534\pi$
$271$	5.53035	−	3.19295i	0.335945	−	0.193958i	0.658477	+	0.752601i	$0.271201\pi$
$272$	−14.7868	+	5.38196i	−0.896582	+	0.326329i
$273$	7.02112	+	17.9938i	0.424938	+	1.08904i
$274$	−23.7905	+	19.9626i	−1.43723	+	1.20598i
$275$	−17.9564	−	21.3997i	−1.08281	−	1.29045i
$276$	−0.939625	+	2.80249i	−0.0565588	+	0.168690i
$277$	−5.89401	+	2.14524i	−0.354137	+	0.128895i	−0.512962	−	0.858412i	$-0.671452\pi$
$277$	−5.89401	+	2.14524i	−0.354137	+	0.128895i	0.158825	+	0.987307i	$0.449229\pi$
$278$	−21.8928			−1.31304
$279$	−25.8316	−	3.20411i	−1.54650	−	0.191825i
$280$	−18.2410	−	10.5948i	−1.09011	−	0.633161i
$281$	−6.25888	−	1.10361i	−0.373373	−	0.0658358i	−0.0161870	−	0.999869i	$-0.505153\pi$
$281$	−6.25888	−	1.10361i	−0.373373	−	0.0658358i	−0.357186	+	0.934033i	$0.616264\pi$
$282$	26.3065	−	16.0983i	1.56653	−	0.958642i
$283$	−0.373940	−	0.445644i	−0.0222284	−	0.0264908i	0.754816	−	0.655937i	$-0.227726\pi$
$283$	−0.373940	−	0.445644i	−0.0222284	−	0.0264908i	−0.777044	+	0.629446i	$0.783282\pi$
$284$	−2.15144	−	2.56398i	−0.127664	−	0.152144i
$285$	12.8481	−	7.86239i	0.761053	−	0.465728i
$286$	−19.7689	−	3.48579i	−1.16896	−	0.206119i
$287$	4.20401	+	7.32552i	0.248155	+	0.432412i
$288$	−7.27365	+	9.62770i	−0.428604	+	0.567318i
$289$	−6.83455			−0.402033
$290$	−6.22447	+	2.26552i	−0.365513	+	0.133036i
$291$	−7.27800	+	21.7071i	−0.426644	+	1.27249i
$292$	−1.06702	−	1.27162i	−0.0624424	−	0.0744160i
$293$	7.63328	−	6.40508i	0.445941	−	0.374189i	−0.391986	−	0.919971i	$-0.628212\pi$
$293$	7.63328	−	6.40508i	0.445941	−	0.374189i	0.837927	+	0.545782i	$0.183767\pi$
$294$	−12.5983	+	15.6503i	−0.734746	+	0.912744i
$295$	39.4843	−	14.3711i	2.29887	−	0.836719i
$296$	−0.0440385	+	0.0254256i	−0.00255968	+	0.00147783i
$297$	−6.16792	−	13.6010i	−0.357899	−	0.789209i
$298$	10.9529	−	18.9710i	0.634486	−	1.09896i
$299$	7.38711	+	6.19852i	0.427208	+	0.358470i
$300$	1.86376	−	12.4183i	0.107604	−	0.716969i
$301$	−1.29320	+	1.07940i	−0.0745388	+	0.0622156i
$302$	−20.4984	+	3.61442i	−1.17955	+	0.207986i
$303$	0.934361	+	4.60709i	0.0536776	+	0.264670i
$304$	3.82626	+	10.5126i	0.219451	+	0.602937i
$305$	25.3233	−	14.6204i	1.45001	−	0.837162i
$306$	13.3035	−	8.61607i	0.760512	−	0.492548i
$307$	−1.93850	+	1.11920i	−0.110636	+	0.0638759i	−0.554297	−	0.832319i	$-0.687013\pi$
$307$	−1.93850	+	1.11920i	−0.110636	+	0.0638759i	0.443661	+	0.896195i	$0.353680\pi$
$308$	−1.92605	−	5.33493i	−0.109747	−	0.303986i
$309$	14.4247	−	8.82721i	0.820591	−	0.502162i
$310$	9.57875	+	54.3238i	0.544037	+	3.08538i
$311$	−2.85296	+	2.39391i	−0.161776	+	0.135746i	−0.720082	−	0.693889i	$-0.755896\pi$
$311$	−2.85296	+	2.39391i	−0.161776	+	0.135746i	0.558306	+	0.829635i	$0.311452\pi$
$312$	7.91897	+	12.9405i	0.448324	+	0.732612i
$313$	4.97702	+	13.6743i	0.281318	+	0.772915i	0.997206	+	0.0746997i	$0.0237998\pi$
$313$	4.97702	+	13.6743i	0.281318	+	0.772915i	−0.715888	+	0.698215i	$0.753978\pi$
$314$	15.0263	+	26.0264i	0.847986	+	1.46875i
$315$	29.0873	+	9.01506i	1.63888	+	0.507941i
$316$	−4.71738	+	8.17075i	−0.265374	+	0.459641i
$317$	1.20663	+	0.212762i	0.0677713	+	0.0119499i	0.207431	−	0.978250i	$-0.433490\pi$
$317$	1.20663	+	0.212762i	0.0677713	+	0.0119499i	−0.139660	+	0.990200i	$0.544601\pi$
$318$	−1.26269	−	6.22600i	−0.0708082	−	0.349137i
$319$	2.81390	+	1.02418i	0.157548	+	0.0573429i
$320$	−11.5580	−	4.20676i	−0.646111	−	0.235165i
$321$	−8.94967	−	22.7613i	−0.499522	−	1.27041i
$322$	−1.76749	+	9.87359i	−0.0984982	+	0.550234i
$323$		−	7.22704i		−	0.402123i
$324$	2.74562	−	6.12601i	0.152535	−	0.340334i
$325$	−35.4790	−	20.4838i	−1.96802	−	1.13624i
$326$	9.59377	+	1.69164i	0.531350	+	0.0936913i
$327$	6.74438	+	5.37152i	0.372965	+	0.297046i
$328$	4.26431	+	5.08200i	0.235457	+	0.280607i
$329$	21.8263	−	18.2178i	1.20332	−	1.00438i
$330$	−23.7162	+	20.9563i	−1.30554	+	1.15360i
$331$	3.55819	−	20.1795i	0.195576	−	1.10917i	−0.716020	−	0.698080i	$-0.754038\pi$
$331$	3.55819	−	20.1795i	0.195576	−	1.10917i	0.911596	−	0.411087i	$-0.134851\pi$
$332$	1.65458	+	2.86582i	0.0908068	+	0.157282i
$333$	0.0537498	−	0.0499986i	0.00294547	−	0.00273990i
$334$	11.8998	+	6.87035i	0.651128	+	0.375929i
$335$	7.24235	−	41.0734i	0.395692	−	2.24408i
$336$	−10.8558	+	19.8414i	−0.592235	+	1.08244i
$337$	18.8694	+	6.86790i	1.02788	+	0.374119i	0.800274	−	0.599634i	$-0.204687\pi$
$337$	18.8694	+	6.86790i	1.02788	+	0.374119i	0.227608	+	0.973753i	$0.426909\pi$
$338$	−7.77675	+	1.37125i	−0.422999	+	0.0745862i
$339$	0.354746	+	13.8746i	0.0192672	+	0.753562i
$340$	−6.98958	−	5.86495i	−0.379063	−	0.318072i
$341$	12.4685	−	21.5962i	0.675209	−	1.16950i
$342$	−6.12552	−	9.45802i	−0.331230	−	0.511431i
$343$	−9.38507	+	15.9662i	−0.506746	+	0.862095i
$344$	−0.850466	+	1.01355i	−0.0458540	+	0.0546467i
$345$	14.9001	−	3.02189i	0.802196	−	0.162693i
$346$	−11.0660	+	30.4037i	−0.594913	+	1.63451i
$347$	0.621132	−	0.109522i	0.0333441	−	0.00587947i	−0.156951	−	0.987606i	$-0.550167\pi$
$347$	0.621132	−	0.109522i	0.0333441	−	0.00587947i	0.190295	+	0.981727i	$0.439055\pi$
$348$	0.492564	+	1.25271i	0.0264042	+	0.0671526i
$349$	0.582328	+	1.59993i	0.0311713	+	0.0856425i	0.954302	−	0.298844i	$-0.0966009\pi$
$349$	0.582328	+	1.59993i	0.0311713	+	0.0856425i	−0.923131	+	0.384486i	$0.874379\pi$
$350$	0.110896	−	42.6132i	0.00592765	−	2.27777i
$351$	−15.3219	−	15.6495i	−0.817821	−	0.835310i
$352$	−5.77999	−	10.0112i	−0.308074	−	0.533600i
$353$	−4.15166	+	23.5452i	−0.220971	+	1.25319i	0.649269	+	0.760559i	$0.275075\pi$
$353$	−4.15166	+	23.5452i	−0.220971	+	1.25319i	−0.870240	+	0.492628i	$0.836036\pi$
$354$	−11.5024	−	29.2534i	−0.611344	−	1.55480i
$355$	−5.88813	+	16.1775i	−0.312510	+	0.858613i
$356$	−0.612862	−	3.47571i	−0.0324816	−	0.184212i
$357$	10.9739	−	9.64610i	0.580802	−	0.510526i
$358$	−3.76236	−	3.15700i	−0.198847	−	0.166852i
$359$		−	12.5117i		−	0.660342i	−0.943921	−	0.330171i	$-0.892894\pi$
$359$		−	12.5117i		−	0.660342i	0.943921	−	0.330171i	$-0.107106\pi$
$360$	23.7371	+	2.94431i	1.25106	+	0.155179i
$361$	13.8620			0.729579
$362$	−39.6689	+	14.4383i	−2.08495	+	0.758860i
$363$	−4.74364	+	0.121286i	−0.248977	+	0.00636587i
$364$	−5.33014	−	6.38589i	−0.279375	−	0.334711i
$365$	−2.92025	+	8.02333i	−0.152853	+	0.419960i
$366$	−11.4180	−	18.6583i	−0.596829	−	0.975288i
$367$	8.47365	−	10.0985i	0.442321	−	0.527138i	−0.498114	−	0.867112i	$-0.665974\pi$
$367$	8.47365	−	10.0985i	0.442321	−	0.527138i	0.940435	+	0.339974i	$0.110418\pi$
$368$			11.2917i			0.588619i
$369$	−7.64141	−	5.77302i	−0.397796	−	0.300531i
$370$	−0.134726	−	0.0777842i	−0.00700408	−	0.00404381i
$371$	−1.98857	−	5.50812i	−0.103242	−	0.285967i
$372$	10.9860	−	2.22806i	0.569596	−	0.115519i
$373$	−8.57998	+	7.19946i	−0.444255	+	0.372774i	−0.837299	−	0.546746i	$-0.815866\pi$
$373$	−8.57998	+	7.19946i	−0.444255	+	0.372774i	0.393044	+	0.919520i	$0.371422\pi$
$374$	2.63679	+	14.9540i	0.136345	+	0.773252i
$375$	−29.1883	+	11.4768i	−1.50728	+	0.592658i
$376$	14.3539	−	17.1063i	0.740247	−	0.882192i
$377$	4.39149			0.226173
$378$	6.18570	−	21.9252i	0.318158	−	1.12771i
$379$	−6.24758			−0.320917			−0.160458	−	0.987043i	$-0.551297\pi$
$379$	−6.24758			−0.320917			−0.160458	+	0.987043i	$0.551297\pi$
$380$	−4.16964	+	4.96918i	−0.213898	+	0.254914i
$381$	−9.19176	−	7.32073i	−0.470908	−	0.375052i
$382$	−6.52364	−	36.9974i	−0.333778	−	1.89295i
$383$	−10.9842	+	9.21682i	−0.561266	+	0.470958i	−0.878734	−	0.477311i	$-0.841612\pi$
$383$	−10.9842	+	9.21682i	−0.561266	+	0.470958i	0.317469	+	0.948269i	$0.397167\pi$
$384$	−7.35420	+	21.9344i	−0.375293	+	1.11933i
$385$	−18.8109	+	22.2998i	−0.958691	+	1.13650i
$386$	−21.4197	−	12.3667i	−1.09023	−	0.629447i
$387$	0.869232	−	1.70077i	0.0441855	−	0.0864549i
$388$		−	9.85959i		−	0.500545i
$389$	−5.55007	+	6.61432i	−0.281400	+	0.335359i	−0.888167	−	0.459520i	$-0.848021\pi$
$389$	−5.55007	+	6.61432i	−0.281400	+	0.335359i	0.606768	+	0.794879i	$0.292466\pi$
$390$	−22.1716	+	40.7750i	−1.12270	+	2.06472i
$391$	2.49487	−	6.85459i	0.126171	−	0.346652i
$392$	−5.04642	+	13.6435i	−0.254883	+	0.689103i
$393$	−16.6337	+	30.5904i	−0.839059	+	1.54308i
$394$	29.6931	−	10.8074i	1.49591	−	0.544469i
$395$	48.5285			2.44173
$396$	4.38039	+	4.70904i	0.220123	+	0.236638i
$397$		−	0.00726859i		−	0.000364800i	−1.00000		0.000182400i	$-0.999942\pi$
$397$		−	0.00726859i		−	0.000364800i	1.00000		0.000182400i	$-5.80597e-5\pi$
$398$	−7.37245	−	6.18622i	−0.369548	−	0.310087i
$399$	−6.85781	−	7.80182i	−0.343320	−	0.390580i
$400$	−8.33008	−	47.2422i	−0.416504	−	2.36211i
$401$	−5.18167	+	14.2365i	−0.258760	+	0.710939i	0.740484	+	0.672074i	$0.234596\pi$
$401$	−5.18167	+	14.2365i	−0.258760	+	0.710939i	−0.999244	+	0.0388646i	$0.987626\pi$
$402$	−30.8551	−	4.63080i	−1.53891	−	0.230963i
$403$	6.35045	−	36.0152i	0.316338	−	1.79404i
$404$	−1.01222	−	1.75321i	−0.0503596	−	0.0872254i
$405$	−34.3493	+	3.52452i	−1.70683	+	0.175135i
$406$	2.27364	+	3.96184i	0.112839	+	0.196623i
$407$	0.0240536	+	0.0660867i	0.00119229	+	0.00327580i
$408$	7.14962	−	8.97693i	0.353959	−	0.444424i
$409$	10.0811	−	1.77758i	0.498480	−	0.0878955i	0.0812453	−	0.996694i	$-0.474110\pi$
$409$	10.0811	−	1.77758i	0.498480	−	0.0878955i	0.417235	+	0.908799i	$0.362999\pi$
$410$	−6.94148	+	19.0716i	−0.342815	+	0.941878i
$411$	10.3191	−	30.7775i	0.509006	−	1.51814i
$412$	−4.68131	+	5.57897i	−0.230631	+	0.274856i
$413$	−14.4227	−	25.1316i	−0.709692	−	1.23664i
$414$	−2.54481	−	11.0852i	−0.125071	−	0.544809i
$415$	8.51046	−	14.7405i	0.417762	−	0.723585i
$416$	−12.9867	−	10.8971i	−0.636726	−	0.534277i
$417$	19.5186	−	11.9444i	0.955830	−	0.584922i
$418$	10.6314	−	1.87460i	0.519999	−	0.0916899i
$419$	37.4662	+	13.6366i	1.83034	+	0.666190i	0.992795	+	0.119827i	$0.0382340\pi$
$419$	37.4662	+	13.6366i	1.83034	+	0.666190i	0.837548	+	0.546363i	$0.183988\pi$
$420$	−13.1108	+	0.301079i	−0.639741	+	0.0146912i
$421$	3.81518	−	21.6370i	0.185940	−	1.05452i	−0.738801	−	0.673924i	$-0.764608\pi$
$421$	3.81518	−	21.6370i	0.185940	−	1.05452i	0.924741	−	0.380597i	$-0.124281\pi$
$422$	1.49225	+	0.861554i	0.0726418	+	0.0419398i
$423$	−14.6706	+	28.7051i	−0.713311	+	1.39569i
$424$	−2.29986	−	3.98347i	−0.111691	−	0.193455i
$425$	−5.38129	+	30.5188i	−0.261031	+	1.48038i
$426$	12.2109	+	4.09409i	0.591619	+	0.198359i
$427$	−12.9213	−	15.4806i	−0.625305	−	0.749160i
$428$	6.77024	+	8.06846i	0.327252	+	0.390004i
$429$	19.5268	−	7.67790i	0.942764	−	0.370692i
$430$	−3.98621	−	0.702877i	−0.192232	−	0.0338957i
$431$	−5.61933	−	3.24432i	−0.270673	−	0.156273i	0.358520	−	0.933522i	$-0.383281\pi$
$431$	−5.61933	−	3.24432i	−0.270673	−	0.156273i	−0.629194	+	0.777249i	$0.716615\pi$
$432$	2.50527	−	25.5226i	0.120535	−	1.22796i
$433$			1.48559i			0.0713927i	0.999363	+	0.0356963i	$0.0113649\pi$
$433$			1.48559i			0.0713927i	−0.999363	+	0.0356963i	$0.988635\pi$
$434$	35.7794	−	12.9173i	1.71747	−	0.620051i
$435$	4.31341	−	5.41583i	0.206812	−	0.259669i
$436$	−3.48916	−	1.26995i	−0.167100	−	0.0608195i
$437$	−4.87321	−	1.77371i	−0.233117	−	0.0848478i
$438$	6.05605	+	2.03048i	0.289369	+	0.0970203i
$439$	12.4170	+	2.18946i	0.592632	+	0.104497i	0.461917	−	0.886923i	$-0.347162\pi$
$439$	12.4170	+	2.18946i	0.592632	+	0.104497i	0.130715	+	0.991420i	$0.458273\pi$
$440$	−11.4576	+	19.8451i	−0.546217	+	0.946076i
$441$	2.69342	−	20.8266i	0.128258	−	0.991741i
$442$	11.1343	+	19.2852i	0.529606	+	0.917305i
$443$	−0.531961	−	1.46155i	−0.0252742	−	0.0694403i	0.926414	−	0.376507i	$-0.122875\pi$
$443$	−0.531961	−	1.46155i	−0.0252742	−	0.0694403i	−0.951688	+	0.307066i	$0.900653\pi$
$444$	−0.0151018	+	0.0277732i	−0.000716702	+	0.00131806i
$445$	−13.9063	+	11.6688i	−0.659222	+	0.553153i
$446$	2.21637	+	12.5697i	0.104948	+	0.595191i
$447$	0.585241	+	22.8895i	0.0276810	+	1.08264i
$448$	−1.49461	+	8.34922i	−0.0706136	+	0.394464i
$449$	−3.71332	+	2.14388i	−0.175242	+	0.101176i	−0.585055	−	0.810993i	$-0.698927\pi$
$449$	−3.71332	+	2.14388i	−0.175242	+	0.101176i	0.409813	+	0.912169i	$0.365594\pi$
$450$	18.8248	+	44.5011i	0.887409	+	2.09780i
$451$	7.94581	−	4.58752i	0.374154	−	0.216018i
$452$	−2.04426	−	5.61656i	−0.0961540	−	0.264181i
$453$	16.3034	−	14.4061i	0.766002	−	0.676859i
$454$	5.29180	−	0.933088i	0.248357	−	0.0437920i
$455$	−14.7377	+	40.1661i	−0.690916	+	1.88302i
$456$	−6.38207	−	5.08296i	−0.298868	−	0.238032i
$457$	11.5949	+	9.72925i	0.542385	+	0.455115i	0.872353	−	0.488877i	$-0.162593\pi$
$457$	11.5949	+	9.72925i	0.542385	+	0.455115i	−0.329968	+	0.943992i	$0.607038\pi$
$458$	−18.1114	+	31.3698i	−0.846289	+	1.46582i
$459$	−7.15998	+	14.9399i	−0.334199	+	0.697337i
$460$	−5.67019	+	3.27368i	−0.264374	+	0.152636i
$461$	6.54769	−	2.38316i	0.304956	−	0.110995i	−0.185009	−	0.982737i	$-0.559232\pi$
$461$	6.54769	−	2.38316i	0.304956	−	0.110995i	0.489966	+	0.871742i	$0.337009\pi$
$462$	17.0365	+	13.6412i	0.792610	+	0.634648i
$463$	−30.9400	+	25.9617i	−1.43790	+	1.20654i	−0.497051	+	0.867721i	$0.665584\pi$
$463$	−30.9400	+	25.9617i	−1.43790	+	1.20654i	−0.940851	+	0.338822i	$0.889972\pi$
$464$	3.30535	+	3.93916i	0.153447	+	0.182871i
$465$	−38.1784	−	43.2066i	−1.77048	−	2.00366i
$466$	14.5047	−	5.27928i	0.671918	−	0.244558i
$467$	8.42978			0.390084			0.195042	−	0.980795i	$-0.437516\pi$
$467$	8.42978			0.390084			0.195042	+	0.980795i	$0.437516\pi$
$468$	8.39848	+	4.29231i	0.388220	+	0.198412i
$469$	−28.7612	−	0.0748481i	−1.32807	−	0.00345616i
$470$	67.2782	+	11.8630i	3.10331	+	0.547197i
$471$	−27.5965	−	15.0057i	−1.27158	−	0.691428i
$472$	−14.6295	−	17.4348i	−0.673378	−	0.802500i
$473$	1.17621	+	1.40175i	0.0540820	+	0.0644525i
$474$	−0.927913	−	36.2918i	−0.0426205	−	1.66694i
$475$	21.6971	+	3.82578i	0.995531	+	0.175539i
$476$	−3.16023	+	5.44092i	−0.144849	+	0.249384i
$477$	4.52259	+	4.86191i	0.207075	+	0.222611i
$478$	−10.1204			−0.462894
$479$	21.6306	−	7.87291i	0.988329	−	0.359722i	0.203256	−	0.979126i	$-0.434848\pi$
$479$	21.6306	−	7.87291i	0.988329	−	0.359722i	0.785073	+	0.619403i	$0.212625\pi$
$480$	−26.1948	+	5.31255i	−1.19562	+	0.242484i
$481$	0.0662955	+	0.0790079i	0.00302282	+	0.00360245i
$482$	0.422427	−	0.354458i	0.0192410	−	0.0161451i
$483$	−3.81111	−	9.76716i	−0.173411	−	0.444421i
$484$	1.92028	−	0.698923i	0.0872852	−	0.0317692i
$485$	−43.9192	+	25.3568i	−1.99427	+	1.15139i
$486$	3.29259	+	25.6206i	0.149355	+	1.16217i
$487$	−13.2168	+	22.8922i	−0.598912	+	1.03735i	0.394070	+	0.919080i	$0.371067\pi$
$487$	−13.2168	+	22.8922i	−0.598912	+	1.03735i	−0.992982	+	0.118265i	$0.962267\pi$
$488$	−12.1330	−	10.1808i	−0.549233	−	0.460861i
$489$	−9.47631	+	3.72606i	−0.428533	+	0.168498i
$490$	−43.8667	+	7.49967i	−1.98169	+	0.338801i
$491$	−12.8648	+	2.26841i	−0.580580	+	0.102372i	−0.456223	−	0.889866i	$-0.650798\pi$
$491$	−12.8648	+	2.26841i	−0.580580	+	0.102372i	−0.124357	+	0.992238i	$0.539687\pi$
$492$	3.91039	+	1.31108i	0.176294	+	0.0591082i
$493$	−1.13616	−	3.12157i	−0.0511700	−	0.140588i
$494$	13.7107	−	7.91586i	0.616872	−	0.356151i
$495$	9.71082	−	31.6229i	0.436469	−	1.42135i
$496$	37.0854	−	21.4112i	1.66518	−	0.961393i
$497$	11.6863	+	2.09198i	0.524201	+	0.0938380i
$498$	−11.1864	−	6.08265i	−0.501274	−	0.272570i
$499$	4.49105	+	25.4700i	0.201047	+	1.14019i	0.903540	+	0.428503i	$0.140959\pi$
$499$	4.49105	+	25.4700i	0.201047	+	1.14019i	−0.702494	+	0.711690i	$0.747930\pi$
$500$	10.3467	−	8.68194i	0.462720	−	0.388268i
$501$	−14.3577	+	0.367100i	−0.641455	+	0.0164008i
$502$	7.76792	+	21.3422i	0.346699	+	0.952548i
$503$	−11.7401	−	20.3345i	−0.523467	−	0.906672i	−0.999627	−	0.0273131i	$-0.991305\pi$
$503$	−11.7401	−	20.3345i	−0.523467	−	0.906672i	0.476160	−	0.879359i	$-0.342028\pi$
$504$	−0.800051	−	16.4752i	−0.0356371	−	0.733865i
$505$	−5.20641	+	9.01776i	−0.231682	+	0.401285i
$506$	10.7307	+	1.89211i	0.477036	+	0.0841143i
$507$	6.18526	−	5.46545i	0.274697	−	0.242729i
$508$	4.75530	+	1.73079i	0.210982	+	0.0767912i
$509$	26.6729	+	9.70814i	1.18226	+	0.430306i	0.856998	−	0.515320i	$-0.172327\pi$
$509$	26.6729	+	9.70814i	1.18226	+	0.430306i	0.325257	+	0.945626i	$0.394549\pi$
$510$	34.7200	+	5.21085i	1.53743	+	0.230740i
$511$	5.79587	+	1.03753i	0.256394	+	0.0458975i
$512$			0.661943i			0.0292540i
$513$	10.6214	+	5.09033i	0.468947	+	0.224743i
$514$	−0.0591771	−	0.0341659i	−0.00261019	−	0.00150699i
$515$	36.8907	+	6.50482i	1.62560	+	0.286637i
$516$	−0.122083	+	0.813438i	−0.00537439	+	0.0358096i
$517$	−19.8517	−	23.6583i	−0.873076	−	1.04049i
$518$	−0.0369543	+	0.100715i	−0.00162368	+	0.00442515i
$519$	−6.72192	−	33.1440i	−0.295059	−	1.45486i
$520$	−5.83554	+	33.0950i	−0.255905	+	1.45131i
$521$	−7.53866	−	13.0573i	−0.330275	−	0.572053i	0.652291	−	0.757969i	$-0.273808\pi$
$521$	−7.53866	−	13.0573i	−0.330275	−	0.572053i	−0.982566	+	0.185916i	$0.940475\pi$
$522$	−4.13268	−	3.12221i	−0.180883	−	0.136655i
$523$	−4.13584	−	2.38783i	−0.180848	−	0.104412i	0.406843	−	0.913498i	$-0.366630\pi$
$523$	−4.13584	−	2.38783i	−0.180848	−	0.104412i	−0.587691	+	0.809086i	$0.699963\pi$
$524$	2.60391	−	14.7675i	0.113752	−	0.645122i
$525$	23.1504	+	38.0524i	1.01036	+	1.66074i
$526$	−21.7217	−	7.90606i	−0.947112	−	0.344721i
$527$	−27.2434	+	4.80374i	−1.18674	+	0.209254i
$528$	21.5843	+	11.7366i	0.939337	+	0.510770i
$529$	13.6093	+	11.4195i	0.591707	+	0.496501i
$530$	7.03592	−	12.1866i	0.305621	−	0.529351i
$531$	26.2153	+	19.8054i	1.13765	+	0.859483i
$532$	3.86818	+	2.24674i	0.167707	+	0.0974084i
$533$	8.64896	−	10.3074i	0.374628	−	0.446464i
$534$	8.99235	+	10.1767i	0.389137	+	0.440387i
$535$	18.5291	−	50.9082i	0.801082	−	2.20095i
$536$	−22.2477	+	3.92286i	−0.960952	+	0.169442i
$537$	5.07677	+	0.761933i	0.219079	+	0.0328798i
$538$	−12.7549	−	35.0437i	−0.549902	−	1.51084i
$539$	17.3706	+	10.1498i	0.748206	+	0.437185i
$540$	13.5427	−	6.14149i	0.582784	−	0.264287i
$541$	−10.3759	−	17.9716i	−0.446094	−	0.772657i	0.552034	−	0.833822i	$-0.313852\pi$
$541$	−10.3759	−	17.9716i	−0.446094	−	0.772657i	−0.998128	+	0.0611643i	$0.980519\pi$
$542$	1.83753	−	10.4212i	0.0789287	−	0.447627i
$543$	27.4896	−	34.5154i	1.17969	−	1.48120i
$544$	−4.38604	+	12.0505i	−0.188050	+	0.516662i
$545$	3.31642	+	18.8084i	0.142060	+	0.805662i
$546$	30.3198	+	10.2535i	1.29757	+	0.438811i
$547$	−9.38962	−	7.87883i	−0.401471	−	0.336874i	0.419591	−	0.907713i	$-0.362174\pi$
$547$	−9.38962	−	7.87883i	−0.401471	−	0.336874i	−0.821062	+	0.570839i	$0.806618\pi$
$548$			13.9795i			0.597173i
$549$	20.3596	+	10.4054i	0.868925	+	0.444091i
$550$	−46.2909			−1.97385
$551$	−2.21925	+	0.807742i	−0.0945433	+	0.0344110i
$552$	−4.29847	−	7.02419i	−0.182955	−	0.298969i
$553$	−5.72542	−	32.9720i	−0.243470	−	1.40211i
$554$	−3.55484	+	9.76683i	−0.151031	+	0.414953i
$555$	0.162554	−	0.00415620i	0.00690002	−	0.000176421i
$556$	−6.33446	+	7.54912i	−0.268641	+	0.320154i
$557$			21.4809i			0.910173i	0.890447	+	0.455086i	$0.150392\pi$
$557$			21.4809i			0.910173i	−0.890447	+	0.455086i	$0.849608\pi$
$558$	−31.5818	+	29.3777i	−1.33697	+	1.24366i
$559$	2.32400	+	1.34176i	0.0982945	+	0.0567504i
$560$	−47.1216	+	17.0121i	−1.99125	+	0.718893i
$561$	−10.5096	−	11.8937i	−0.443714	−	0.502152i
$562$	−8.06755	+	6.76948i	−0.340309	+	0.285553i
$563$	−2.80189	−	15.8903i	−0.118085	−	0.669696i	−0.985176	−	0.171546i	$-0.945124\pi$
$563$	−2.80189	−	15.8903i	−0.118085	−	0.669696i	0.867091	−	0.498150i	$-0.165987\pi$
$564$	2.06048	−	13.7290i	0.0867617	−	0.578094i
$565$	−19.7614	+	23.5507i	−0.831368	+	0.990786i
$566$	−0.964001			−0.0405200
$567$	6.44723	+	22.9223i	0.270758	+	0.962647i
$568$	9.32501			0.391269
$569$	−17.0772	+	20.3518i	−0.715912	+	0.853191i	−0.994227	−	0.107299i	$-0.965780\pi$
$569$	−17.0772	+	20.3518i	−0.715912	+	0.853191i	0.278314	+	0.960490i	$0.410224\pi$
$570$	3.70461	−	24.6839i	0.155169	−	1.03389i
$571$	5.14784	+	29.1948i	0.215430	+	1.22177i	0.880158	+	0.474680i	$0.157436\pi$
$571$	5.14784	+	29.1948i	0.215430	+	1.22177i	−0.664728	+	0.747085i	$0.731453\pi$
$572$	−6.92191	+	5.80817i	−0.289420	+	0.242852i
$573$	26.0015	+	29.4260i	1.08623	+	1.22929i
$574$	13.7769	+	2.46622i	0.575036	+	0.102938i
$575$	19.2582	+	11.1187i	0.803124	+	0.463684i
$576$	−2.15192	−	9.37379i	−0.0896634	−	0.390574i
$577$			36.2985i			1.51113i	0.655075	+	0.755564i	$0.272637\pi$
$577$			36.2985i			1.51113i	−0.655075	+	0.755564i	$0.727363\pi$
$578$	−7.27982	+	8.67575i	−0.302801	+	0.360864i
$579$	25.8440	−	0.660782i	1.07404	−	0.0274611i
$580$	−1.01979	+	2.80184i	−0.0423443	+	0.116340i
$581$	−11.0193	−	4.04321i	−0.457159	−	0.167741i
$582$	19.8027	+	32.3600i	0.820850	+	1.34136i
$583$	−5.97783	+	2.17575i	−0.247577	+	0.0901105i
$584$	4.62479			0.191375
$585$	−2.47916	−	48.4497i	−0.102501	−	2.00315i
$586$		−	16.5120i		−	0.682105i
$587$	−27.4601	−	23.0418i	−1.13340	−	0.951035i	−0.134196	−	0.990955i	$-0.542845\pi$
$587$	−27.4601	−	23.0418i	−1.13340	−	0.951035i	−0.999203	+	0.0399198i	$0.987290\pi$
$588$	1.75138	+	8.87243i	0.0722259	+	0.365893i
$589$	3.41518	+	19.3684i	0.140720	+	0.798063i
$590$	23.8141	−	65.4286i	0.980410	−	2.69365i
$591$	−20.5766	+	25.8356i	−0.846408	+	1.06273i
$592$	−0.0209713	+	0.118934i	−0.000861913	+	0.00488815i
$593$	−9.90996	−	17.1646i	−0.406953	−	0.704864i	0.587593	−	0.809156i	$-0.300076\pi$
$593$	−9.90996	−	17.1646i	−0.406953	−	0.704864i	−0.994547	+	0.104293i	$0.966742\pi$
$594$	−23.8348	−	6.65753i	−0.977952	−	0.273162i
$595$	32.3639	+	0.0842236i	1.32679	+	0.00345283i
$596$	−3.37251	−	9.26590i	−0.138143	−	0.379546i
$597$	9.94807	+	1.49303i	0.407147	+	0.0611056i
$598$	15.7368	−	2.77481i	0.643524	−	0.113471i
$599$	6.33165	−	17.3961i	0.258704	−	0.710783i	−0.740544	−	0.672008i	$-0.765432\pi$
$599$	6.33165	−	17.3961i	0.258704	−	0.710783i	0.999248	−	0.0387755i	$-0.0123457\pi$
$600$	23.1658	+	26.2168i	0.945741	+	1.07030i
$601$	−27.1016	+	32.2984i	−1.10550	+	1.31748i	−0.161741	+	0.986833i	$0.551711\pi$
$601$	−27.1016	+	32.2984i	−1.10550	+	1.31748i	−0.943755	+	0.330646i	$0.892734\pi$
$602$	−0.00726407	+	2.79130i	−0.000296062	+	0.113765i
$603$	30.0355	−	12.7056i	1.22314	−	0.517410i
$604$	−4.68468	+	8.11410i	−0.190617	+	0.330158i
$605$	−8.05187	−	6.75632i	−0.327355	−	0.274684i
$606$	6.84345	+	3.72116i	0.277996	+	0.151162i
$607$	40.5770	−	7.15482i	1.64697	−	0.290405i	0.728249	−	0.685313i	$-0.240335\pi$
$607$	40.5770	−	7.15482i	1.64697	−	0.290405i	0.918721	+	0.394908i	$0.129223\pi$
$608$	8.56722	+	3.11821i	0.347447	+	0.126460i
$609$	−4.18861	−	2.29172i	−0.169731	−	0.0928653i
$610$	8.41400	−	47.7182i	0.340673	−	1.93205i
$611$	−39.2237	−	22.6458i	−1.58682	−	0.916153i
$612$	0.878230	−	7.08033i	0.0355004	−	0.286205i
$613$	16.8946	+	29.2623i	0.682366	+	1.18189i	0.974257	+	0.225441i	$0.0723823\pi$
$613$	16.8946	+	29.2623i	0.682366	+	1.18189i	−0.291891	+	0.956452i	$0.594284\pi$
$614$	−0.644094	+	3.65284i	−0.0259935	+	0.147417i
$615$	−4.21652	−	20.7905i	−0.170026	−	0.838355i
$616$	14.8352	+	5.44334i	0.597728	+	0.219319i
$617$	12.0622	+	14.3752i	0.485607	+	0.578724i	0.952095	−	0.305803i	$-0.0989251\pi$
$617$	12.0622	+	14.3752i	0.485607	+	0.578724i	−0.466487	+	0.884528i	$0.654481\pi$
$618$	4.15921	−	27.7129i	0.167308	−	1.11478i
$619$	−14.2587	−	2.51420i	−0.573107	−	0.101054i	−0.120419	−	0.992723i	$-0.538424\pi$
$619$	−14.2587	−	2.51420i	−0.573107	−	0.101054i	−0.452688	+	0.891669i	$0.649535\pi$
$620$	21.5036	+	12.4151i	0.863605	+	0.498602i
$621$	8.31680	+	8.49465i	0.333742	+	0.340879i
$622$			6.17140i			0.247451i
$623$	9.56886	+	8.07176i	0.383368	+	0.323388i
$624$	35.6318	+	5.34770i	1.42641	+	0.214079i
$625$	−19.6153	−	7.13939i	−0.784613	−	0.285576i
$626$	22.6593	+	8.24731i	0.905648	+	0.329629i
$627$	−8.45572	+	7.47168i	−0.337689	+	0.298390i
$628$	13.3222	+	2.34907i	0.531614	+	0.0937379i
$629$	0.0390087	−	0.0675651i	0.00155538	−	0.00269400i
$630$	42.4260	−	27.3209i	1.69029	−	1.08849i
$631$	3.09835	+	5.36650i	0.123343	+	0.213637i	0.921084	−	0.389363i	$-0.127305\pi$
$631$	3.09835	+	5.36650i	0.123343	+	0.213637i	−0.797741	+	0.603001i	$0.793972\pi$
$632$	−8.99024	−	24.7005i	−0.357613	−	0.982533i
$633$	−1.80048	+	0.0460349i	−0.0715626	+	0.00182972i
$634$	1.55532	−	1.30507i	0.0617698	−	0.0518310i
$635$	−4.51988	−	25.6335i	−0.179366	−	1.01724i
$636$	−2.51221	−	1.36603i	−0.0996157	−	0.0541666i
$637$	29.0291	+	5.27454i	1.15017	+	0.208985i
$638$	4.29731	−	2.48105i	0.170132	−	0.0982259i
$639$	−13.1203	+	3.01201i	−0.519033	+	0.119153i
$640$	−44.3791	+	25.6223i	−1.75424	+	1.01281i
$641$	2.87706	+	7.90466i	0.113637	+	0.312215i	0.983454	−	0.181160i	$-0.0579852\pi$
$641$	2.87706	+	7.90466i	0.113637	+	0.312215i	−0.869817	+	0.493375i	$0.835763\pi$
$642$	−38.4258	−	12.8835i	−1.51654	−	0.508470i
$643$	12.6614	−	2.23255i	0.499317	−	0.0880430i	0.0816827	−	0.996658i	$-0.473971\pi$
$643$	12.6614	−	2.23255i	0.499317	−	0.0880430i	0.417634	+	0.908615i	$0.362859\pi$
$644$	2.89323	+	3.46630i	0.114009	+	0.136591i
$645$	3.93741	−	1.54818i	0.155035	−	0.0609595i
$646$	−9.17397	−	7.69787i	−0.360945	−	0.302869i
$647$	3.45841	−	5.99014i	0.135964	−	0.235497i	−0.790001	−	0.613105i	$-0.789920\pi$
$647$	3.45841	−	5.99014i	0.135964	−	0.235497i	0.925965	+	0.377609i	$0.123253\pi$
$648$	8.15739	+	16.8305i	0.320453	+	0.661164i
$649$	−27.2596	+	15.7383i	−1.07003	+	0.617784i
$650$	−63.7926	+	23.2186i	−2.50215	+	0.910708i
$651$	−24.8518	+	31.0373i	−0.974018	+	1.21645i
$652$	3.35918	−	2.81869i	0.131556	−	0.110388i
$653$	4.91550	+	5.85806i	0.192358	+	0.229244i	0.853600	−	0.520930i	$-0.174415\pi$
$653$	4.91550	+	5.85806i	0.192358	+	0.229244i	−0.661241	+	0.750173i	$0.729970\pi$
$654$	14.0024	−	2.83981i	0.547535	−	0.111045i
$655$	−72.4782	+	26.3799i	−2.83196	+	1.03075i
$656$	15.7556			0.615151
$657$	−6.50711	+	1.49382i	−0.253866	+	0.0582796i
$658$	0.122601	−	47.1108i	0.00477948	−	1.83657i
$659$	−5.58789	−	0.985295i	−0.217673	−	0.0383817i	0.0637479	−	0.997966i	$-0.479695\pi$
$659$	−5.58789	−	0.985295i	−0.217673	−	0.0383817i	−0.281421	+	0.959584i	$0.590806\pi$
$660$	0.364126	+	14.2414i	0.0141736	+	0.554345i
$661$	30.7788	+	36.6808i	1.19716	+	1.42672i	0.877763	+	0.479094i	$0.159035\pi$
$661$	30.7788	+	36.6808i	1.19716	+	1.42672i	0.319394	+	0.947622i	$0.396521\pi$
$662$	−21.8258	−	26.0110i	−0.848283	−	1.01094i
$663$	−20.4487	−	11.1191i	−0.794160	−	0.431829i
$664$	−9.07941	−	1.60094i	−0.352349	−	0.0621287i
$665$	0.0598780	−	23.0088i	0.00232197	−	0.892243i
$666$	−0.00621639	−	0.121486i	−0.000240880	−	0.00470747i
$667$	−2.38373			−0.0922983
$668$	5.81214	−	2.11545i	0.224879	−	0.0818491i
$669$	−8.83387	−	9.99731i	−0.341537	−	0.386518i
$670$	−44.4242	−	52.9427i	−1.71626	−	2.04536i
$671$	−16.7800	+	14.0801i	−0.647787	+	0.543557i
$672$	6.70001	+	17.1709i	0.258459	+	0.662382i
$673$	−17.7107	+	6.44618i	−0.682699	+	0.248482i	−0.660006	−	0.751260i	$-0.729446\pi$
$673$	−17.7107	+	6.44618i	−0.682699	+	0.248482i	−0.0226931	+	0.999742i	$0.507224\pi$
$674$	28.8168	−	16.6374i	1.10998	−	0.640849i
$675$	−41.0626	−	29.4046i	−1.58050	−	1.13178i
$676$	−1.77729	+	3.07836i	−0.0683573	+	0.118398i
$677$	9.98143	+	8.37542i	0.383618	+	0.321893i	0.814121	−	0.580696i	$-0.197219\pi$
$677$	9.98143	+	8.37542i	0.383618	+	0.321893i	−0.430503	+	0.902589i	$0.641664\pi$
$678$	17.9902	+	14.3282i	0.690908	+	0.550270i
$679$	22.4099	+	26.8487i	0.860014	+	1.03036i
$680$	25.0344	−	4.41424i	0.960025	−	0.169278i
$681$	−4.20885	+	3.71904i	−0.161283	+	0.142514i
$682$	−14.1332	−	38.8306i	−0.541188	−	1.48690i
$683$	−35.9360	+	20.7476i	−1.37505	+	0.793886i	−0.991559	−	0.129658i	$-0.958612\pi$
$683$	−35.9360	+	20.7476i	−1.37505	+	0.793886i	−0.383493	+	0.923544i	$0.625279\pi$
$684$	−5.03370	−	0.624370i	−0.192468	−	0.0238734i
$685$	62.2710	−	35.9522i	2.37925	−	1.37366i
$686$	10.2710	+	28.9198i	0.392147	+	1.10416i
$687$	−0.967735	−	37.8493i	−0.0369214	−	1.44404i
$688$	0.545648	+	3.09452i	0.0208026	+	0.117978i
$689$	−7.14662	+	5.99672i	−0.272264	+	0.228457i
$690$	12.0349	−	22.1329i	0.458160	−	0.842586i
$691$	2.20345	+	6.05394i	0.0838234	+	0.230303i	0.974522	−	0.224291i	$-0.0720066\pi$
$691$	2.20345	+	6.05394i	0.0838234	+	0.230303i	−0.890699	+	0.454594i	$0.849784\pi$
$692$	7.28201	+	12.6128i	0.276821	+	0.479467i
$693$	−22.6315	−	2.86699i	−0.859698	−	0.108908i
$694$	0.522571	−	0.905120i	0.0198365	−	0.0343579i
$695$	49.9182	+	8.80193i	1.89351	+	0.333876i
$696$	−3.55569	−	1.19216i	−0.134778	−	0.0451887i
$697$	−9.56439	−	3.48115i	−0.362277	−	0.131858i
$698$	2.65121	+	0.964963i	0.100350	+	0.0365244i
$699$	−10.0514	+	12.6204i	−0.380180	+	0.477346i
$700$	−14.6619	−	12.3679i	−0.554167	−	0.467464i
$701$		−	10.7905i		−	0.407550i	−0.979018	−	0.203775i	$-0.934679\pi$
$701$		−	10.7905i		−	0.407550i	0.979018	−	0.203775i	$-0.0653211\pi$
$702$	−36.1855	+	2.78043i	−1.36573	+	0.104941i
$703$	−0.0480348	−	0.0277329i	−0.00181167	−	0.00104597i
$704$	9.07397	+	1.59999i	0.341988	+	0.0603017i
$705$	−66.4544	+	26.1297i	−2.50282	+	0.984102i
$706$	25.4661	+	30.3493i	0.958428	+	1.14221i
$707$	6.74125	+	2.47350i	0.253531	+	0.0930255i
$708$	−13.4153	−	4.49792i	−0.504179	−	0.169042i
$709$	8.07759	−	45.8103i	0.303360	−	1.72044i	−0.327765	−	0.944759i	$-0.606295\pi$
$709$	8.07759	−	45.8103i	0.303360	−	1.72044i	0.631125	−	0.775681i	$-0.282594\pi$
$710$	14.2639	+	24.7058i	0.535315	+	0.927194i
$711$	20.6277	+	31.8498i	0.773598	+	1.19446i
$712$	8.51553	+	4.91644i	0.319133	+	0.184252i
$713$	−3.44706	+	19.5493i	−0.129093	+	0.732126i
$714$	−0.555844	−	24.2048i	−0.0208019	−	0.905841i
$715$	43.6740	+	15.8960i	1.63332	+	0.594478i
$716$	−2.17721	+	0.383900i	−0.0813660	+	0.0143470i
$717$	9.02284	−	5.52155i	0.336964	−	0.206206i
$718$	−15.8823	−	13.3268i	−0.592722	−	0.497353i
$719$	−7.91160	+	13.7033i	−0.295053	+	0.511047i	−0.974997	−	0.222217i	$-0.928671\pi$
$719$	−7.91160	+	13.7033i	−0.295053	+	0.511047i	0.679944	+	0.733264i	$0.262004\pi$
$720$	41.5933	−	38.6905i	1.55009	−	1.44191i
$721$	0.0672258	−	25.8323i	0.00250362	−	0.962045i
$722$	14.7651	−	17.5964i	0.549500	−	0.654869i
$723$	−0.183228	+	0.546490i	−0.00681433	+	0.0203242i
$724$	−6.49916	+	17.8563i	−0.241540	+	0.663624i
$725$	9.97306	−	1.75852i	0.370390	−	0.0653098i
$726$	−4.89873	+	6.15075i	−0.181809	+	0.228276i
$727$	11.4600	+	31.4861i	0.425028	+	1.16775i	0.948795	+	0.315893i	$0.102304\pi$
$727$	11.4600	+	31.4861i	0.425028	+	1.16775i	−0.523767	+	0.851862i	$0.675474\pi$
$728$	23.1744	+	0.0603089i	0.858900	+	0.00223520i
$729$	−16.9138	−	21.0457i	−0.626437	−	0.779472i
$730$	7.07427	+	12.2530i	0.261831	+	0.453504i
$731$	0.352493	−	1.99909i	0.0130374	−	0.0739388i
$732$	−9.73751	−	1.46143i	−0.359909	−	0.0540159i
$733$	1.99386	−	5.47809i	0.0736449	−	0.202338i	−0.897408	−	0.441201i	$-0.854553\pi$
$733$	1.99386	−	5.47809i	0.0736449	−	0.202338i	0.971053	+	0.238863i	$0.0767748\pi$
$734$	−3.79329	−	21.5128i	−0.140013	−	0.794053i
$735$	35.0178	−	30.6195i	1.29165	−	1.12942i
$736$	7.04927	+	5.91504i	0.259839	+	0.218031i
$737$			31.2435i			1.15087i
$738$	−15.4675	+	3.55084i	−0.569366	+	0.130708i
$739$	−45.4032			−1.67019			−0.835093	−	0.550109i	$-0.814586\pi$
$739$	−45.4032			−1.67019			−0.835093	+	0.550109i	$0.814586\pi$
$740$	−0.0658034	+	0.0239505i	−0.00241898	+	0.000880437i
$741$	−7.90500	+	14.5378i	−0.290398	+	0.534059i
$742$	−9.11010	−	3.34268i	−0.334442	−	0.122714i
$743$	8.03623	−	22.0794i	0.294821	−	0.810013i	−0.700524	−	0.713629i	$-0.747050\pi$
$743$	8.03623	−	22.0794i	0.294821	−	0.810013i	0.995344	−	0.0963839i	$-0.0307276\pi$
$744$	−14.9189	+	27.4367i	−0.546952	+	1.00588i
$745$	−32.6013	+	38.8527i	−1.19442	+	1.42345i
$746$			18.5599i			0.679526i
$747$	13.2919	−	0.680142i	0.486325	−	0.0248851i
$748$	5.91940	+	3.41757i	0.216435	+	0.124959i
$749$	−36.7749	−	6.58314i	−1.34373	−	0.240543i
$750$	−16.5213	+	49.2760i	−0.603274	+	1.79930i
$751$	17.6288	−	14.7923i	0.643283	−	0.539779i	−0.261741	−	0.965138i	$-0.584297\pi$
$751$	17.6288	−	14.7923i	0.643283	−	0.539779i	0.905024	+	0.425359i	$0.139852\pi$
$752$	−9.20929	−	52.2285i	−0.335828	−	1.90458i
$753$	−18.5696	−	14.7896i	−0.676712	−	0.538964i
$754$	4.67759	−	5.57454i	0.170348	−	0.203013i
$755$	48.1920			1.75389
$756$	−5.77052	−	8.47681i	−0.209872	−	0.308298i
$757$	−0.0748603			−0.00272084			−0.00136042	−	0.999999i	$-0.500433\pi$
$757$	−0.0748603			−0.00272084			−0.00136042	+	0.999999i	$0.500433\pi$
$758$	−6.65460	+	7.93065i	−0.241706	+	0.288054i
$759$	−10.5993	+	4.16761i	−0.384729	+	0.151275i
$760$	−3.13827	−	17.7980i	−0.113837	−	0.645601i
$761$	2.28947	−	1.92109i	0.0829931	−	0.0696395i	−0.600347	−	0.799739i	$-0.704971\pi$
$761$	2.28947	−	1.92109i	0.0829931	−	0.0696395i	0.683340	+	0.730100i	$0.260527\pi$
$762$	−19.0835	+	3.87031i	−0.691322	+	0.140207i
$763$	12.3878	−	4.47232i	0.448469	−	0.161909i
$764$	−14.6451	−	8.45534i	−0.529840	−	0.305903i
$765$	−33.7977	+	14.2971i	−1.22196	+	0.516911i
$766$			23.7606i			0.858504i
$767$	−29.6719	+	35.3616i	−1.07139	+	1.27683i
$768$	14.2133	+	23.2262i	0.512879	+	0.838104i
$769$	−5.62460	+	15.4535i	−0.202828	+	0.557266i	−0.998847	−	0.0480060i	$-0.984713\pi$
$769$	−5.62460	+	15.4535i	−0.202828	+	0.557266i	0.796019	+	0.605272i	$0.206936\pi$
$770$	8.27089	+	47.6311i	0.298062	+	1.71650i
$771$	0.0714001	−	0.00182557i	0.00257141	−	6.57462e-5i
$772$	−10.4619	+	3.80782i	−0.376532	+	0.137046i
$773$	−39.0394			−1.40415			−0.702074	−	0.712104i	$-0.747743\pi$
$773$	−39.0394			−1.40415			−0.702074	+	0.712104i	$0.747743\pi$
$774$	−1.23309	−	2.91497i	−0.0443223	−	0.104776i
$775$		−	84.3334i		−	3.02934i
$776$	21.0427	+	17.6569i	0.755388	+	0.633846i
$777$	−0.0220021	−	0.109955i	−0.000789320	−	0.00394460i
$778$	2.48453	+	14.0905i	0.0890747	+	0.505168i
$779$	−2.47490	+	6.79972i	−0.0886723	+	0.243625i
$780$	7.64499	+	19.4431i	0.273734	+	0.696176i
$781$	2.23947	−	12.7007i	0.0801347	−	0.454467i
$782$	−6.04378	−	10.4681i	−0.216125	−	0.374340i
$783$	5.38795	+	0.528874i	0.192550	+	0.0189004i
$784$	17.1181	+	30.0090i	0.611360	+	1.07175i
$785$	−23.7981	−	65.3847i	−0.849390	−	2.33368i
$786$	21.1140	+	53.6981i	0.753110	+	1.91535i
$787$	4.74409	−	0.836511i	0.169108	−	0.0298184i	−0.0884527	−	0.996080i	$-0.528192\pi$
$787$	4.74409	−	0.836511i	0.169108	−	0.0298184i	0.257561	+	0.966262i	$0.417081\pi$
$788$	4.86477	−	13.3658i	0.173300	−	0.476139i
$789$	23.6796	−	4.80244i	0.843014	−	0.170971i
$790$	51.6900	−	61.6018i	1.83905	−	2.19169i
$791$	18.3327	+	10.6481i	0.651834	+	0.378602i
$792$	−17.8948	+	0.915670i	−0.635862	+	0.0325369i
$793$	−16.0619	+	27.8201i	−0.570376	+	0.987920i
$794$	−0.00922671	−	0.00774213i	−0.000327444	−	0.000274758i
$795$	0.375946	+	14.7037i	0.0133334	+	0.521487i
$796$	−4.26629	+	0.752263i	−0.151215	+	0.0266632i
$797$	−16.1079	−	5.86280i	−0.570572	−	0.207671i	0.0405913	−	0.999176i	$-0.487076\pi$
$797$	−16.1079	−	5.86280i	−0.570572	−	0.207671i	−0.611163	+	0.791505i	$0.709298\pi$
$798$	−17.2082	+	0.395172i	−0.609163	+	0.0139889i
$799$	−5.94927	+	33.7400i	−0.210470	+	1.19364i
$800$	−33.8564	−	19.5470i	−1.19701	−	0.691091i
$801$	−13.5694	−	4.16692i	−0.479452	−	0.147231i
$802$	12.5525	+	21.7416i	0.443245	+	0.767723i
$803$	1.11068	−	6.29898i	0.0391950	−	0.222286i
$804$	−10.5244	+	9.29964i	−0.371168	+	0.327973i
$805$	7.99974	−	21.8024i	0.281954	−	0.768433i
$806$	−38.9533	−	46.4228i	−1.37207	−	1.63517i
$807$	30.4911	+	24.2845i	1.07334	+	0.854854i
$808$	5.55447	+	0.979403i	0.195406	+	0.0344553i
$809$	1.45376	+	0.839326i	0.0511113	+	0.0295091i	0.525338	−	0.850894i	$-0.323939\pi$
$809$	1.45376	+	0.839326i	0.0511113	+	0.0295091i	−0.474227	+	0.880403i	$0.657272\pi$
$810$	−32.1131	+	47.3570i	−1.12834	+	1.66395i
$811$			24.2899i			0.852933i	0.904503	+	0.426467i	$0.140242\pi$
$811$			24.2899i			0.852933i	−0.904503	+	0.426467i	$0.859758\pi$
$812$	2.02399	+	0.362317i	0.0710280	+	0.0127148i
$813$	4.04740	+	10.2936i	0.141949	+	0.361011i
$814$	0.109511	+	0.0398587i	0.00383835	+	0.00139705i
$815$	−21.1949	−	7.71430i	−0.742423	−	0.270220i
$816$	−5.41732	−	26.7114i	−0.189644	−	0.935086i
$817$	−1.42123	−	0.250602i	−0.0497226	−	0.00876744i
$818$	8.48147	−	14.6903i	0.296548	−	0.513636i
$819$	−32.6260	+	7.40056i	−1.14004	+	0.258596i
$820$	4.56785	+	7.91175i	0.159516	+	0.276290i
$821$	0.666808	+	1.83204i	0.0232718	+	0.0639386i	0.950785	−	0.309853i	$-0.100280\pi$
$821$	0.666808	+	1.83204i	0.0232718	+	0.0639386i	−0.927513	+	0.373791i	$0.878058\pi$
$822$	−28.0774	−	45.8817i	−0.979311	−	1.60031i
$823$	21.0262	−	17.6431i	0.732928	−	0.615000i	−0.198000	−	0.980202i	$-0.563445\pi$
$823$	21.0262	−	17.6431i	0.732928	−	0.615000i	0.930928	+	0.365202i	$0.119000\pi$
$824$	−3.52337	−	19.9820i	−0.122742	−	0.696107i
$825$	41.2708	−	25.2558i	1.43687	−	0.879293i
$826$	−47.2642	−	8.46083i	−1.64453	−	0.294390i
$827$	−39.0581	+	22.5502i	−1.35818	+	0.784147i	−0.989379	−	0.145360i	$-0.953566\pi$
$827$	−39.0581	+	22.5502i	−1.35818	+	0.784147i	−0.368804	+	0.929507i	$0.620233\pi$
$828$	−4.55875	−	2.32989i	−0.158427	−	0.0809694i
$829$	31.0293	−	17.9148i	1.07769	−	0.622207i	0.147420	−	0.989074i	$-0.452903\pi$
$829$	31.0293	−	17.9148i	1.07769	−	0.622207i	0.930273	+	0.366867i	$0.119570\pi$
$830$	−9.64667	−	26.5040i	−0.334841	−	0.919967i
$831$	−2.15934	−	10.6471i	−0.0749067	−	0.369345i
$832$	13.3072	−	2.34641i	0.461343	−	0.0813473i
$833$	−3.76108	−	21.9991i	−0.130314	−	0.762224i
$834$	5.62800	−	37.4994i	0.194882	−	1.29850i
$835$	−24.3708	−	20.4495i	−0.843386	−	0.707685i
$836$	2.42969	−	4.20835i	0.0840326	−	0.145549i
$837$	12.1288	−	43.4225i	0.419232	−	1.50090i
$838$	57.2173	−	33.0344i	1.97654	−	1.14115i
$839$	30.2589	−	11.0133i	1.04465	−	0.380222i	0.238010	−	0.971263i	$-0.423505\pi$
$839$	30.2589	−	11.0133i	1.04465	−	0.380222i	0.806642	+	0.591040i	$0.201283\pi$
$840$	22.8367	−	28.5207i	0.787942	−	0.984058i
$841$	21.3837	−	17.9431i	0.737369	−	0.618726i
$842$	−23.4021	−	27.8895i	−0.806490	−	0.961137i
$843$	3.49931	−	10.4369i	0.120523	−	0.359467i
$844$	0.728852	−	0.265281i	0.0250881	−	0.00913133i
$845$	18.2833			0.628963
$846$	20.8117	+	49.1980i	0.715520	+	1.69146i
$847$	−3.64053	+	6.26785i	−0.125090	+	0.215366i
$848$	−10.7581	−	1.89694i	−0.369435	−	0.0651413i
$849$	0.859459	−	0.525947i	0.0294965	−	0.0180505i
$850$	33.0086	+	39.3381i	1.13218	+	1.34929i
$851$	−0.0359856	−	0.0428860i	−0.00123357	−	0.00147011i
$852$	4.94483	−	3.02600i	0.169407	−	0.103669i
$853$	−29.8196	−	5.25801i	−1.02100	−	0.180031i	−0.362007	−	0.932175i	$-0.617908\pi$
$853$	−29.8196	−	5.25801i	−1.02100	−	0.180031i	−0.658998	+	0.752145i	$0.729019\pi$
$854$	−33.4141	−	0.0869568i	−1.14341	−	0.00297560i
$855$	10.1644	+	24.0282i	0.347614	+	0.821747i
$856$	−29.3444			−1.00297
$857$	43.6527	−	15.8883i	1.49115	−	0.542734i	0.537397	−	0.843329i	$-0.319408\pi$
$857$	43.6527	−	15.8883i	1.49115	−	0.542734i	0.953752	+	0.300596i	$0.0971855\pi$
$858$	11.0527	−	32.9654i	0.377333	−	1.12542i
$859$	29.6335	+	35.3158i	1.01108	+	1.20496i	0.978660	+	0.205487i	$0.0658778\pi$
$859$	29.6335	+	35.3158i	1.01108	+	1.20496i	0.0324227	+	0.999474i	$0.489678\pi$
$860$	−1.39574	+	1.17116i	−0.0475943	+	0.0399364i
$861$	−13.6284	+	5.31773i	−0.464454	+	0.181228i
$862$	−10.1037	+	3.67746i	−0.344135	+	0.125255i
$863$	−2.45633	+	1.41816i	−0.0836143	+	0.0482748i	−0.541224	−	0.840878i	$-0.682039\pi$
$863$	−2.45633	+	1.41816i	−0.0836143	+	0.0482748i	0.457610	+	0.889153i	$0.348706\pi$
$864$	−14.6211	−	14.9338i	−0.497421	−	0.508058i
$865$	37.4556	−	64.8750i	1.27353	−	2.20582i
$866$	1.88580	+	1.58237i	0.0640819	+	0.0537711i
$867$	1.75697	−	11.7067i	0.0596697	−	0.397580i
$868$	5.89826	−	16.0751i	0.200200	−	0.545623i
$869$	−35.8012	+	6.31272i	−1.21447	+	0.214144i
$870$	−2.28041	−	11.2441i	−0.0773130	−	0.381210i
$871$	15.6711	+	43.0560i	0.530995	+	1.45890i
$872$	8.95888	−	5.17241i	0.303386	−	0.175160i
$873$	−35.3104	−	18.0465i	−1.19508	−	0.610782i
$874$	−7.44223	+	4.29678i	−0.251737	+	0.145341i
$875$	−8.44200	+	47.1590i	−0.285392	+	1.59426i
$876$	2.45242	−	1.50076i	0.0828595	−	0.0507060i
$877$	−8.55341	−	48.5088i	−0.288828	−	1.63803i	−0.691282	−	0.722585i	$-0.742954\pi$
$877$	−8.55341	−	48.5088i	−0.288828	−	1.63803i	0.402454	−	0.915440i	$-0.368157\pi$
$878$	16.0053	−	13.4300i	0.540151	−	0.453241i
$879$	9.00876	+	14.7214i	0.303858	+	0.496539i
$880$	18.6134	+	51.1400i	0.627459	+	1.72393i
$881$	−13.9157	−	24.1027i	−0.468833	−	0.812042i	0.530533	−	0.847664i	$-0.321992\pi$
$881$	−13.9157	−	24.1027i	−0.468833	−	0.812042i	−0.999365	+	0.0356225i	$0.988659\pi$
$882$	−23.5682	−	25.6024i	−0.793584	−	0.862078i
$883$	20.7815	−	35.9946i	0.699354	−	1.21132i	−0.269337	−	0.963046i	$-0.586805\pi$
$883$	20.7815	−	35.9946i	0.699354	−	1.21132i	0.968691	−	0.248270i	$-0.0798621\pi$
$884$	9.87159	+	1.74063i	0.332017	+	0.0585436i
$885$	14.4656	+	71.3258i	0.486254	+	2.39759i
$886$	−2.42190	−	0.881500i	−0.0813654	−	0.0296146i
$887$	24.9185	+	9.06959i	0.836681	+	0.304527i	0.724598	−	0.689172i	$-0.242026\pi$
$887$	24.9185	+	9.06959i	0.836681	+	0.304527i	0.112083	+	0.993699i	$0.464248\pi$
$888$	−0.0322297	−	0.0819682i	−0.00108156	−	0.00275067i
$889$	−16.8831	+	6.09523i	−0.566241	+	0.204427i
$890$			30.0816i			1.00834i
$891$	24.8823	−	7.06842i	0.833587	−	0.236801i
$892$	4.97559	+	2.87266i	0.166595	+	0.0961836i
$893$	23.9872	+	4.22958i	0.802700	+	0.141538i
$894$	29.6792	+	23.6378i	0.992620	+	0.790567i
$895$	7.30939	+	8.71099i	0.244326	+	0.291176i
$896$	22.6446	+	27.1298i	0.756502	+	0.906343i
$897$	−12.5163	+	11.0597i	−0.417906	+	0.369272i
$898$	−1.23380	+	6.99722i	−0.0411724	+	0.233500i
$899$	4.52002	+	7.82890i	0.150751	+	0.261108i
$900$	20.7917	+	6.38476i	0.693058	+	0.212825i
$901$	6.11156	+	3.52851i	0.203606	+	0.117552i
$902$	2.64010	−	14.9728i	0.0879058	−	0.498538i
$903$	−1.51643	−	2.49256i	−0.0504635	−	0.0829472i
$904$	15.6480	+	5.69541i	0.520445	+	0.189426i
$905$	96.2548	−	16.9723i	3.19962	−	0.564179i
$906$	−0.921480	−	36.0402i	−0.0306141	−	1.19735i
$907$	−9.86503	−	8.27774i	−0.327563	−	0.274858i	0.464143	−	0.885760i	$-0.346362\pi$
$907$	−9.86503	−	8.27774i	−0.327563	−	0.274858i	−0.791706	+	0.610902i	$0.790807\pi$
$908$	1.20938	−	2.09471i	0.0401348	−	0.0695155i
$909$	−8.13152	+	0.416088i	−0.269706	+	0.0138008i
$910$	35.2887	+	61.4909i	1.16981	+	2.03840i
$911$	−1.43534	+	1.71057i	−0.0475550	+	0.0566738i	−0.789298	−	0.614011i	$-0.789555\pi$
$911$	−1.43534	+	1.71057i	−0.0475550	+	0.0566738i	0.741743	+	0.670685i	$0.234000\pi$
$912$	−18.9902	+	3.85140i	−0.628830	+	0.127533i
$913$	−4.36098	+	11.9817i	−0.144327	+	0.396536i
$914$	24.7005	−	4.35537i	0.817020	−	0.144063i
$915$	18.5329	+	47.1339i	0.612680	+	1.55820i
$916$	5.57667	+	15.3218i	0.184258	+	0.506245i
$917$	26.4745	+	46.1320i	0.874265	+	1.52341i
$918$	11.3382	+	25.0021i	0.374218	+	0.825192i
$919$	−9.06589	−	15.7026i	−0.299056	−	0.517980i	0.676864	−	0.736108i	$-0.263338\pi$
$919$	−9.06589	−	15.7026i	−0.299056	−	0.517980i	−0.975920	+	0.218128i	$0.930005\pi$
$920$	3.16756	−	17.9641i	0.104431	−	0.592260i
$921$	−1.41870	−	3.60811i	−0.0467478	−	0.118891i
$922$	3.94909	−	10.8500i	0.130056	−	0.357327i
$923$	−3.28424	−	18.6258i	−0.108102	−	0.613077i
$924$	9.63315	−	1.92761i	0.316907	−	0.0634136i
$925$	0.182195	+	0.152880i	0.00599053	+	0.00502665i
$926$			66.9281i			2.19939i
$927$	11.4117	+	26.9768i	0.374808	+	0.886033i
$928$	4.19065			0.137565
$929$	18.1050	−	6.58967i	0.594005	−	0.216200i	−0.0274852	−	0.999622i	$-0.508750\pi$
$929$	18.1050	−	6.58967i	0.594005	−	0.216200i	0.621490	+	0.783422i	$0.286528\pi$
$930$	−95.5119	+	2.44206i	−3.13196	+	0.0800783i
$931$	−15.6401	+	2.67391i	−0.512583	+	0.0876339i
$932$	2.37638	−	6.52906i	0.0778410	−	0.213866i
$933$	−3.36704	−	5.50214i	−0.110232	−	0.180132i
$934$	8.97897	−	10.7007i	0.293801	−	0.350138i
$935$		−	35.1570i		−	1.14976i
$936$	−24.2011	+	10.2375i	−0.791038	+	0.334624i
$937$	−26.1439	−	15.0942i	−0.854085	−	0.493106i	0.00794190	−	0.999968i	$-0.497472\pi$
$937$	−26.1439	−	15.0942i	−0.854085	−	0.493106i	−0.862027	+	0.506862i	$0.830805\pi$
$938$	−30.7300	+	36.4296i	−1.00337	+	1.18947i
$939$	−24.7016	+	5.00973i	−0.806107	+	0.163486i
$940$	23.5569	−	19.7666i	0.768341	−	0.644715i
$941$	0.539980	+	3.06238i	0.0176028	+	0.0998306i	0.992343	−	0.123510i	$-0.0394150\pi$
$941$	0.539980	+	3.06238i	0.0176028	+	0.0998306i	−0.974741	+	0.223340i	$0.928304\pi$
$942$	−48.4426	+	19.0475i	−1.57835	+	0.620601i
$943$	−4.69470	+	5.59493i	−0.152881	+	0.182196i
$944$	−54.0524			−1.75926
$945$	−22.9191	+	47.5052i	−0.745559	+	1.54534i
$946$	3.03221			0.0985856
$947$	−32.0105	+	38.1487i	−1.04020	+	1.23967i	−0.0699551	+	0.997550i	$0.522286\pi$
$947$	−32.0105	+	38.1487i	−1.04020	+	1.23967i	−0.970248	+	0.242115i	$0.922159\pi$
$948$	−12.7827	−	10.1807i	−0.415163	−	0.330654i
$949$	−1.62884	−	9.23759i	−0.0528743	−	0.299865i
$950$	27.9671	−	23.4672i	0.907372	−	0.761375i
$951$	−0.674623	+	2.01211i	−0.0218762	+	0.0652471i
$952$	−5.95277	−	16.4885i	−0.192930	−	0.534395i
$953$	−24.6725	−	14.2447i	−0.799222	−	0.461431i	0.0439773	−	0.999033i	$-0.485997\pi$
$953$	−24.6725	−	14.2447i	−0.799222	−	0.461431i	−0.843199	+	0.537602i	$0.819330\pi$
$954$	10.9889	−	0.562300i	0.355779	−	0.0182051i
$955$			86.9814i			2.81465i
$956$	−2.92823	+	3.48972i	−0.0947056	+	0.112866i
$957$	−2.47765	+	4.55656i	−0.0800911	+	0.147293i
$958$	13.0460	−	35.8436i	0.421498	−	1.15806i
$959$	−31.7740	−	38.0675i	−1.02604	−	1.22926i
$960$	10.1768	−	18.7158i	0.328456	−	0.604051i
$961$	41.6117	−	15.1454i	1.34231	−	0.488562i
$962$	0.170907			0.00551026
$963$	41.2877	−	9.47834i	1.33048	−	0.305435i
$964$		−	0.248221i		−	0.00799467i
$965$	43.8676	+	36.8093i	1.41215	+	1.18493i
$966$	−16.4578	−	5.56568i	−0.529521	−	0.179073i
$967$	0.546444	+	3.09904i	0.0175725	+	0.0996584i	0.992333	−	0.123597i	$-0.0394429\pi$
$967$	0.546444	+	3.09904i	0.0175725	+	0.0996584i	−0.974760	+	0.223255i	$0.928332\pi$
$968$	−1.94723	+	5.34998i	−0.0625864	+	0.171955i
$969$	12.3790	+	1.85786i	0.397669	+	0.0596831i
$970$	−14.5927	+	82.7596i	−0.468545	+	2.65725i
$971$	−11.2478	−	19.4817i	−0.360958	−	0.625197i	0.627161	−	0.778890i	$-0.284217\pi$
$971$	−11.2478	−	19.4817i	−0.360958	−	0.625197i	−0.988119	+	0.153693i	$0.950883\pi$
$972$	9.78723	+	6.27771i	0.313925	+	0.201358i
$973$	0.0909659	−	34.9547i	0.00291623	−	1.12060i
$974$	14.9814	+	41.1610i	0.480034	+	1.31888i
$975$	44.2067	−	55.5051i	1.41575	−	1.77759i
$976$	−37.0439	+	6.53184i	−1.18575	+	0.209079i
$977$	−15.2909	+	42.0113i	−0.489198	+	1.34406i	0.412209	+	0.911089i	$0.364757\pi$
$977$	−15.2909	+	42.0113i	−0.489198	+	1.34406i	−0.901407	+	0.432972i	$0.857465\pi$
$978$	−5.36384	+	15.9980i	−0.171517	+	0.511559i
$979$	8.74128	−	10.4175i	0.279373	−	0.332943i
$980$	−10.1063	+	17.2962i	−0.322835	+	0.552506i
$981$	−10.9345	+	10.1714i	−0.349111	+	0.324747i
$982$	−10.8234	+	18.7467i	−0.345389	+	0.598231i
$983$	−0.625742	−	0.525060i	−0.0199581	−	0.0167468i	0.632754	−	0.774353i	$-0.281924\pi$
$983$	−0.625742	−	0.525060i	−0.0199581	−	0.0167468i	−0.652712	+	0.757606i	$0.726369\pi$
$984$	−9.80103	+	5.99776i	−0.312445	+	0.191201i
$985$	−72.0489	+	12.7042i	−2.29567	+	0.404788i
$986$	−5.17268	−	1.88270i	−0.164732	−	0.0599574i
$987$	25.5938	+	42.0687i	0.814660	+	1.33906i
$988$	1.23748	−	7.01812i	0.0393696	−	0.223276i
$989$	−1.26148	−	0.728315i	−0.0401127	−	0.0231591i
$990$	−29.7986	−	46.0100i	−0.947060	−	1.46229i
$991$	5.41879	+	9.38562i	0.172134	+	0.298144i	0.939166	−	0.343465i	$-0.111601\pi$
$991$	5.41879	+	9.38562i	0.172134	+	0.298144i	−0.767032	+	0.641609i	$0.778267\pi$
$992$	6.06001	−	34.3681i	0.192406	−	1.09119i
$993$	33.6501	+	11.2823i	1.06785	+	0.358032i
$994$	15.1032	−	12.6062i	0.479044	−	0.399845i
$995$	14.3229	+	17.0694i	0.454068	+	0.541137i
$996$	−5.33411	+	2.09736i	−0.169018	+	0.0664573i
$997$	50.1411	+	8.84122i	1.58798	+	0.280004i	0.896720	−	0.442598i	$-0.145943\pi$
$997$	50.1411	+	8.84122i	1.58798	+	0.280004i	0.691264	+	0.722603i	$0.257054\pi$
$998$	37.1151	+	21.4284i	1.17486	+	0.678305i
$999$	0.0718234	+	0.104919i	0.00227239	+	0.00331950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.18	✓	132
3.2	odd	2		567.2.ba.a.143.5		132
7.5	odd	6		189.2.bd.a.47.5	yes	132
21.5	even	6		567.2.bd.a.467.18		132
27.4	even	9		567.2.bd.a.17.18		132
27.23	odd	18		189.2.bd.a.185.5	yes	132
189.131	even	18	inner	189.2.ba.a.131.18	yes	132
189.166	odd	18		567.2.ba.a.341.5		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.18	✓	132	1.1	even	1	trivial
189.2.ba.a.131.18	yes	132	189.131	even	18	inner
189.2.bd.a.47.5	yes	132	7.5	odd	6
189.2.bd.a.185.5	yes	132	27.23	odd	18
567.2.ba.a.143.5		132	3.2	odd	2
567.2.ba.a.341.5		132	189.166	odd	18
567.2.bd.a.17.18		132	27.4	even	9
567.2.bd.a.467.18		132	21.5	even	6

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.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06515 - 1.26940i) q^{2} +(-0.257071 + 1.71287i) q^{3} +(-0.129525 - 0.734574i) q^{4} +(-2.93903 + 2.46614i) q^{5} +(1.90049 + 2.15078i) q^{6} +(2.02233 + 1.70592i) q^{7} +(1.79971 + 1.03907i) q^{8} +(-2.86783 - 0.880657i) q^{9} +O(q^{10})\)	\(q+(1.06515 - 1.26940i) q^{2} +(-0.257071 + 1.71287i) q^{3} +(-0.129525 - 0.734574i) q^{4} +(-2.93903 + 2.46614i) q^{5} +(1.90049 + 2.15078i) q^{6} +(2.02233 + 1.70592i) q^{7} +(1.79971 + 1.03907i) q^{8} +(-2.86783 - 0.880657i) q^{9} +6.35759i q^{10} +(1.84743 - 2.20168i) q^{11} +(1.29153 - 0.0330219i) q^{12} +(1.44158 - 3.96072i) q^{13} +(4.31958 - 0.750072i) q^{14} +(-3.46863 - 5.66814i) q^{15} +(4.63779 - 1.68802i) q^{16} -3.18833 q^{17} +(-4.17257 + 2.70238i) q^{18} +2.26672i q^{19} +(2.19224 + 1.83951i) q^{20} +(-3.44191 + 3.02544i) q^{21} +(-0.827014 - 4.69023i) q^{22} +(-0.782500 + 2.14990i) q^{23} +(-2.24244 + 2.81556i) q^{24} +(1.68781 - 9.57204i) q^{25} +(-3.49221 - 6.04869i) q^{26} +(2.24568 - 4.68582i) q^{27} +(0.991186 - 1.70651i) q^{28} +(0.356349 + 0.979061i) q^{29} +(-10.8897 - 1.63435i) q^{30} +(8.54472 - 1.50666i) q^{31} +(1.37565 - 3.77958i) q^{32} +(3.29626 + 3.73038i) q^{33} +(-3.39605 + 4.04725i) q^{34} +(-10.1507 - 0.0264162i) q^{35} +(-0.275452 + 2.22070i) q^{36} +(-0.0122349 + 0.0211914i) q^{37} +(2.87736 + 2.41439i) q^{38} +(6.41360 + 3.48743i) q^{39} +(-7.85188 + 1.38450i) q^{40} +(2.99981 + 1.09184i) q^{41} +(0.174337 + 7.59168i) q^{42} +(-0.110557 + 0.627001i) q^{43} +(-1.85658 - 1.07190i) q^{44} +(10.6004 - 4.48418i) q^{45} +(1.89560 + 3.28327i) q^{46} +(1.86595 - 10.5823i) q^{47} +(1.69911 + 8.37787i) q^{48} +(1.17964 + 6.89989i) q^{49} +(-10.3529 - 12.3382i) q^{50} +(0.819627 - 5.46119i) q^{51} +(-3.09616 - 0.545937i) q^{52} +(-1.91685 - 1.10670i) q^{53} +(-3.55617 - 7.84176i) q^{54} +11.0268i q^{55} +(1.86705 + 5.17151i) q^{56} +(-3.88258 - 0.582707i) q^{57} +(1.62238 + 0.590498i) q^{58} +(-10.2914 - 3.74577i) q^{59} +(-3.71439 + 3.28213i) q^{60} +(-7.50570 - 1.32346i) q^{61} +(7.18884 - 12.4514i) q^{62} +(-4.29736 - 6.67328i) q^{63} +(1.60294 + 2.77637i) q^{64} +(5.53082 + 15.1958i) q^{65} +(8.24634 - 0.210843i) q^{66} +(-8.32749 + 6.98759i) q^{67} +(0.412969 + 2.34207i) q^{68} +(-3.48134 - 1.89300i) q^{69} +(-10.8456 + 12.8571i) q^{70} +(3.88604 - 2.24361i) q^{71} +(-4.24621 - 4.56479i) q^{72} +(1.92730 - 1.11273i) q^{73} +(0.0138683 + 0.0381028i) q^{74} +(15.9618 + 5.35169i) q^{75} +(1.66507 - 0.293597i) q^{76} +(7.49200 - 1.30095i) q^{77} +(11.2584 - 4.42676i) q^{78} +(-9.68949 - 8.13045i) q^{79} +(-9.46771 + 16.3986i) q^{80} +(7.44889 + 5.05115i) q^{81} +(4.58122 - 2.64497i) q^{82} +(-4.16888 + 1.51735i) q^{83} +(2.66822 + 2.13646i) q^{84} +(9.37059 - 7.86286i) q^{85} +(0.678152 + 0.808190i) q^{86} +(-1.76861 + 0.358690i) q^{87} +(5.61252 - 2.04279i) q^{88} +4.73160 q^{89} +(5.59885 - 18.2325i) q^{90} +(9.67205 - 5.55065i) q^{91} +(1.68062 + 0.296338i) q^{92} +(0.384117 + 15.0233i) q^{93} +(-11.4457 - 13.6404i) q^{94} +(-5.59003 - 6.66194i) q^{95} +(6.12027 + 3.32793i) q^{96} +(13.0174 + 2.29533i) q^{97} +(10.0152 + 5.85198i) q^{98} +(-7.23702 + 4.68708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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