LMFDB - Embedded newform 196.2.j.a.111.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(27,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("196.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.8
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.865405 + 1.11851i) q^{2} +(0.0500641 + 0.0627784i) q^{3} +(-0.502147 - 1.93594i) q^{4} +(-2.66268 + 2.12341i) q^{5} +(-0.113544 + 0.00166863i) q^{6} +(-2.36082 - 1.19436i) q^{7} +(2.59993 + 1.11371i) q^{8} +(0.666128 - 2.91850i) q^{9} +O(q^{10})$	\(q+(-0.865405 + 1.11851i) q^{2} +(0.0500641 + 0.0627784i) q^{3} +(-0.502147 - 1.93594i) q^{4} +(-2.66268 + 2.12341i) q^{5} +(-0.113544 + 0.00166863i) q^{6} +(-2.36082 - 1.19436i) q^{7} +(2.59993 + 1.11371i) q^{8} +(0.666128 - 2.91850i) q^{9} +(-0.0707731 - 4.81585i) q^{10} +(-1.87399 + 0.427725i) q^{11} +(0.0963954 - 0.128445i) q^{12} +(-4.45886 + 1.01770i) q^{13} +(3.37898 - 1.60701i) q^{14} +(-0.266609 - 0.0608517i) q^{15} +(-3.49570 + 1.94425i) q^{16} +(2.04254 - 4.24138i) q^{17} +(2.68791 + 3.27076i) q^{18} -6.13285 q^{19} +(5.44785 + 4.08851i) q^{20} +(-0.0432122 - 0.208003i) q^{21} +(1.14334 - 2.46623i) q^{22} +(3.21229 + 6.67039i) q^{23} +(0.0602462 + 0.218976i) q^{24} +(1.46836 - 6.43329i) q^{25} +(2.72040 - 5.86802i) q^{26} +(0.433602 - 0.208812i) q^{27} +(-1.12673 + 5.17015i) q^{28} +(-2.47012 - 1.18955i) q^{29} +(0.298788 - 0.245544i) q^{30} -0.671221 q^{31} +(0.850526 - 5.59255i) q^{32} +(-0.120671 - 0.0962321i) q^{33} +(2.97642 + 5.95513i) q^{34} +(8.82224 - 1.83280i) q^{35} +(-5.98452 + 0.175933i) q^{36} +(3.19581 + 1.53902i) q^{37} +(5.30740 - 6.85968i) q^{38} +(-0.287118 - 0.228969i) q^{39} +(-9.28765 + 2.55528i) q^{40} +(-6.69401 + 5.33830i) q^{41} +(0.270051 + 0.131674i) q^{42} +(-0.476065 - 0.379649i) q^{43} +(1.76906 + 3.41314i) q^{44} +(4.42349 + 9.18548i) q^{45} +(-10.2409 - 2.17960i) q^{46} +(2.47240 + 10.8323i) q^{47} +(-0.297066 - 0.122117i) q^{48} +(4.14699 + 5.63937i) q^{49} +(5.92500 + 7.20978i) q^{50} +(0.368525 - 0.0841134i) q^{51} +(4.20921 + 8.12102i) q^{52} +(-4.09626 + 1.97266i) q^{53} +(-0.141683 + 0.665696i) q^{54} +(4.08158 - 5.11814i) q^{55} +(-4.80781 - 5.73454i) q^{56} +(-0.307035 - 0.385010i) q^{57} +(3.46818 - 1.73342i) q^{58} +(-1.77788 + 2.22940i) q^{59} +(0.0160718 + 0.546694i) q^{60} +(1.90411 - 3.95392i) q^{61} +(0.580878 - 0.750770i) q^{62} +(-5.05836 + 6.09446i) q^{63} +(5.51929 + 5.79115i) q^{64} +(9.71148 - 12.1778i) q^{65} +(0.212066 - 0.0516927i) q^{66} -1.25096i q^{67} +(-9.23670 - 1.82443i) q^{68} +(-0.257936 + 0.535609i) q^{69} +(-5.58480 + 11.4539i) q^{70} +(-6.71573 - 13.9454i) q^{71} +(4.98225 - 6.84602i) q^{72} +(-1.18301 - 0.270013i) q^{73} +(-4.48709 + 2.24268i) q^{74} +(0.477383 - 0.229896i) q^{75} +(3.07959 + 11.8728i) q^{76} +(4.93501 + 1.22844i) q^{77} +(0.504579 - 0.122995i) q^{78} -13.4536i q^{79} +(5.17947 - 12.5997i) q^{80} +(-8.05648 - 3.87979i) q^{81} +(-0.177925 - 12.1071i) q^{82} +(0.443031 - 1.94105i) q^{83} +(-0.380983 + 0.188104i) q^{84} +(3.56758 + 15.6306i) q^{85} +(0.836632 - 0.203935i) q^{86} +(-0.0489865 - 0.214624i) q^{87} +(-5.34860 - 0.975023i) q^{88} +(2.31111 + 0.527495i) q^{89} +(-14.1022 - 3.00142i) q^{90} +(11.7421 + 2.92288i) q^{91} +(11.3004 - 9.56830i) q^{92} +(-0.0336040 - 0.0421381i) q^{93} +(-14.2557 - 6.60891i) q^{94} +(16.3298 - 13.0226i) q^{95} +(0.393672 - 0.226591i) q^{96} -6.93563i q^{97} +(-9.89654 - 0.241882i) q^{98} +5.75414i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$	−0.865405	+	1.11851i	−0.611934	+	0.790909i
$2$	−0.865405	+	1.11851i	−0.611934	+	0.790909i
$3$	0.0500641	+	0.0627784i	0.0289045	+	0.0362451i	0.796074	−	0.605200i	$-0.206907\pi$
$3$	0.0500641	+	0.0627784i	0.0289045	+	0.0362451i	−0.767169	+	0.641445i	$0.778335\pi$
$4$	−0.502147	−	1.93594i	−0.251073	−	0.967968i
$5$	−2.66268	+	2.12341i	−1.19079	+	0.949619i	−0.999491	−	0.0319134i	$-0.989840\pi$
$5$	−2.66268	+	2.12341i	−1.19079	+	0.949619i	−0.191294	+	0.981533i	$0.561269\pi$
$6$	−0.113544	+	0.00166863i	−0.0463542	+	0.000681215i
$7$	−2.36082	−	1.19436i	−0.892308	−	0.451427i
$7$	−2.36082	−	1.19436i	−0.892308	−	0.451427i
$8$	2.59993	+	1.11371i	0.919215	+	0.393756i
$9$	0.666128	−	2.91850i	0.222043	−	0.972833i
$10$	−0.0707731	−	4.81585i	−0.0223804	−	1.52291i
$11$	−1.87399	+	0.427725i	−0.565028	+	0.128964i	−0.495487	−	0.868615i	$-0.665010\pi$
$11$	−1.87399	+	0.427725i	−0.565028	+	0.128964i	−0.0695406	+	0.997579i	$0.522153\pi$
$12$	0.0963954	−	0.128445i	0.0278269	−	0.0370788i
$13$	−4.45886	+	1.01770i	−1.23666	+	0.282260i	−0.790372	−	0.612627i	$-0.790113\pi$
$13$	−4.45886	+	1.01770i	−1.23666	+	0.282260i	−0.446292	+	0.894887i	$0.647256\pi$
$14$	3.37898	−	1.60701i	0.903071	−	0.429490i
$15$	−0.266609	−	0.0608517i	−0.0688381	−	0.0157118i
$16$	−3.49570	+	1.94425i	−0.873924	+	0.486062i
$17$	2.04254	−	4.24138i	0.495389	−	1.02869i	−0.492032	−	0.870577i	$-0.663746\pi$
$17$	2.04254	−	4.24138i	0.495389	−	1.02869i	0.987422	−	0.158110i	$-0.0505399\pi$
$18$	2.68791	+	3.27076i	0.633546	+	0.770925i
$19$	−6.13285			−1.40697			−0.703486	−	0.710709i	$-0.748374\pi$
$19$	−6.13285			−1.40697			−0.703486	+	0.710709i	$0.748374\pi$
$20$	5.44785	+	4.08851i	1.21818	+	0.914218i
$21$	−0.0432122	−	0.208003i	−0.00942968	−	0.0453901i
$22$	1.14334	−	2.46623i	0.243761	−	0.525803i
$23$	3.21229	+	6.67039i	0.669809	+	1.39087i	0.907716	+	0.419584i	$0.137824\pi$
$23$	3.21229	+	6.67039i	0.669809	+	1.39087i	−0.237908	+	0.971288i	$0.576462\pi$
$24$	0.0602462	+	0.218976i	0.0122977	+	0.0446984i
$25$	1.46836	−	6.43329i	0.293671	−	1.28666i
$26$	2.72040	−	5.86802i	0.533515	−	1.15081i
$27$	0.433602	−	0.208812i	0.0834467	−	0.0401858i
$28$	−1.12673	+	5.17015i	−0.212933	+	0.977067i
$29$	−2.47012	−	1.18955i	−0.458690	−	0.220893i	0.190246	−	0.981736i	$-0.439071\pi$
$29$	−2.47012	−	1.18955i	−0.458690	−	0.220893i	−0.648936	+	0.760843i	$0.724786\pi$
$30$	0.298788	−	0.245544i	0.0545510	−	0.0448300i
$31$	−0.671221			−0.120555			−0.0602774	−	0.998182i	$-0.519199\pi$
$31$	−0.671221			−0.120555			−0.0602774	+	0.998182i	$0.519199\pi$
$32$	0.850526	−	5.59255i	0.150353	−	0.988632i
$33$	−0.120671	−	0.0962321i	−0.0210062	−	0.0167519i
$34$	2.97642	+	5.95513i	0.510452	+	1.02130i
$35$	8.82224	−	1.83280i	1.49123	−	0.309800i
$36$	−5.98452	+	0.175933i	−0.997420	+	0.0293222i
$37$	3.19581	+	1.53902i	0.525388	+	0.253014i	0.677726	−	0.735315i	$-0.262966\pi$
$37$	3.19581	+	1.53902i	0.525388	+	0.253014i	−0.152337	+	0.988329i	$0.548680\pi$
$38$	5.30740	−	6.85968i	0.860974	−	1.11279i
$39$	−0.287118	−	0.228969i	−0.0459757	−	0.0366644i
$40$	−9.28765	+	2.55528i	−1.46851	+	0.404025i
$41$	−6.69401	+	5.33830i	−1.04543	+	0.833702i	−0.986368	−	0.164553i	$-0.947382\pi$
$41$	−6.69401	+	5.33830i	−1.04543	+	0.833702i	−0.0590605	+	0.998254i	$0.518811\pi$
$42$	0.270051	+	0.131674i	0.0416698	+	0.0203177i
$43$	−0.476065	−	0.379649i	−0.0725992	−	0.0578960i	0.586518	−	0.809936i	$-0.300498\pi$
$43$	−0.476065	−	0.379649i	−0.0725992	−	0.0578960i	−0.659117	+	0.752040i	$0.729070\pi$
$44$	1.76906	+	3.41314i	0.266696	+	0.514549i
$45$	4.42349	+	9.18548i	0.659416	+	1.36929i
$46$	−10.2409	−	2.17960i	−1.50993	−	0.321364i
$47$	2.47240	+	10.8323i	0.360636	+	1.58005i	0.751583	+	0.659638i	$0.229291\pi$
$47$	2.47240	+	10.8323i	0.360636	+	1.58005i	−0.390947	+	0.920413i	$0.627852\pi$
$48$	−0.297066	−	0.122117i	−0.0428777	−	0.0176261i
$49$	4.14699	+	5.63937i	0.592426	+	0.805625i
$50$	5.92500	+	7.20978i	0.837921	+	1.01962i
$51$	0.368525	−	0.0841134i	0.0516038	−	0.0117782i
$52$	4.20921	+	8.12102i	0.583713	+	1.12618i
$53$	−4.09626	+	1.97266i	−0.562665	+	0.270965i	−0.693521	−	0.720436i	$-0.743942\pi$
$53$	−4.09626	+	1.97266i	−0.562665	+	0.270965i	0.130856	+	0.991401i	$0.458227\pi$
$54$	−0.141683	+	0.665696i	−0.0192806	+	0.0905898i
$55$	4.08158	−	5.11814i	0.550360	−	0.690130i
$56$	−4.80781	−	5.73454i	−0.642470	−	0.766311i
$57$	−0.307035	−	0.385010i	−0.0406678	−	0.0509958i
$58$	3.46818	−	1.73342i	0.455394	−	0.227610i
$59$	−1.77788	+	2.22940i	−0.231461	+	0.290243i	−0.883975	−	0.467534i	$-0.845143\pi$
$59$	−1.77788	+	2.22940i	−0.231461	+	0.290243i	0.652515	+	0.757776i	$0.273714\pi$
$60$	0.0160718	+	0.546694i	0.00207486	+	0.0705779i
$61$	1.90411	−	3.95392i	0.243796	−	0.506248i	−0.742783	−	0.669532i	$-0.766495\pi$
$61$	1.90411	−	3.95392i	0.243796	−	0.506248i	0.986579	+	0.163284i	$0.0522088\pi$
$62$	0.580878	−	0.750770i	0.0737716	−	0.0953478i
$63$	−5.05836	+	6.09446i	−0.637294	+	0.767830i
$64$	5.51929	+	5.79115i	0.689912	+	0.723893i
$65$	9.71148	−	12.1778i	1.20456	−	1.51047i
$66$	0.212066	−	0.0516927i	0.0261036	−	0.00636293i
$67$		−	1.25096i		−	0.152829i	−0.997076	−	0.0764144i	$-0.975653\pi$
$67$		−	1.25096i		−	0.152829i	0.997076	−	0.0764144i	$-0.0243472\pi$
$68$	−9.23670	−	1.82443i	−1.12011	−	0.221245i
$69$	−0.257936	+	0.535609i	−0.0310518	+	0.0644797i
$70$	−5.58480	+	11.4539i	−0.667512	+	1.36900i
$71$	−6.71573	−	13.9454i	−0.797010	−	1.65501i	−0.754850	−	0.655898i	$-0.772290\pi$
$71$	−6.71573	−	13.9454i	−0.797010	−	1.65501i	−0.0421607	−	0.999111i	$-0.513424\pi$
$72$	4.98225	−	6.84602i	0.587164	−	0.806811i
$73$	−1.18301	−	0.270013i	−0.138460	−	0.0316027i	0.152729	−	0.988268i	$-0.451194\pi$
$73$	−1.18301	−	0.270013i	−0.138460	−	0.0316027i	−0.291189	+	0.956665i	$0.594051\pi$
$74$	−4.48709	+	2.24268i	−0.521614	+	0.260707i
$75$	0.477383	−	0.229896i	0.0551234	−	0.0265460i
$76$	3.07959	+	11.8728i	0.353253	+	1.36190i
$77$	4.93501	+	1.22844i	0.562397	+	0.139994i
$78$	0.504579	−	0.122995i	0.0571323	−	0.0139264i
$79$		−	13.4536i		−	1.51365i	−0.653616	−	0.756826i	$-0.726749\pi$
$79$		−	13.4536i		−	1.51365i	0.653616	−	0.756826i	$-0.273251\pi$
$80$	5.17947	−	12.5997i	0.579082	−	1.40869i
$81$	−8.05648	−	3.87979i	−0.895164	−	0.431088i
$82$	−0.177925	−	12.1071i	−0.0196485	−	1.33701i
$83$	0.443031	−	1.94105i	0.0486290	−	0.213058i	−0.944776	−	0.327717i	$-0.893721\pi$
$83$	0.443031	−	1.94105i	0.0486290	−	0.213058i	0.993405	+	0.114660i	$0.0365778\pi$
$84$	−0.380983	+	0.188104i	−0.0415686	+	0.0205239i
$85$	3.56758	+	15.6306i	0.386958	+	1.69538i
$86$	0.836632	−	0.203935i	0.0902164	−	0.0219909i
$87$	−0.0489865	−	0.214624i	−0.00525190	−	0.0230101i
$88$	−5.34860	−	0.975023i	−0.570162	−	0.103938i
$89$	2.31111	+	0.527495i	0.244977	+	0.0559144i	0.343246	−	0.939245i	$-0.388473\pi$
$89$	2.31111	+	0.527495i	0.244977	+	0.0559144i	−0.0982693	+	0.995160i	$0.531331\pi$
$90$	−14.1022	−	3.00142i	−1.48650	−	0.316378i
$91$	11.7421	+	2.92288i	1.23091	+	0.306401i
$92$	11.3004	−	9.56830i	1.17815	−	0.997564i
$93$	−0.0336040	−	0.0421381i	−0.00348458	−	0.00436952i
$94$	−14.2557	−	6.60891i	−1.47036	−	0.681657i
$95$	16.3298	−	13.0226i	1.67540	−	1.33609i
$96$	0.393672	−	0.226591i	0.0401790	−	0.0231264i
$97$		−	6.93563i		−	0.704207i	−0.935961	−	0.352103i	$-0.885467\pi$
$97$		−	6.93563i		−	0.704207i	0.935961	−	0.352103i	$-0.114533\pi$
$98$	−9.89654	−	0.241882i	−0.999701	−	0.0244337i
$99$			5.75414i			0.578313i
$100$	−13.1918	+	0.387812i	−1.31918	+	0.0387812i
$101$	−1.97297	+	1.57339i	−0.196318	+	0.156559i	−0.716715	−	0.697366i	$-0.754355\pi$
$101$	−1.97297	+	1.57339i	−0.196318	+	0.156559i	0.520397	+	0.853924i	$0.325784\pi$
$102$	−0.224842	+	0.484993i	−0.0222626	+	0.0480214i
$103$	−1.04936	−	1.31586i	−0.103397	−	0.129656i	0.727441	−	0.686171i	$-0.240710\pi$
$103$	−1.04936	−	1.31586i	−0.103397	−	0.129656i	−0.830838	+	0.556515i	$0.812138\pi$
$104$	−12.7262	−	2.31991i	−1.24790	−	0.227486i
$105$	0.556738	+	0.462088i	0.0543320	+	0.0450952i
$106$	1.33848	−	6.28888i	0.130005	−	0.610830i
$107$	10.8900	+	2.48556i	1.05277	+	0.240289i	0.713686	−	0.700466i	$-0.247025\pi$
$107$	10.8900	+	2.48556i	1.05277	+	0.240289i	0.339088	+	0.940755i	$0.389882\pi$
$108$	−0.621978	−	0.734571i	−0.0598498	−	0.0706841i
$109$	−3.94276	−	17.2744i	−0.377648	−	1.65459i	−0.704645	−	0.709560i	$-0.748894\pi$
$109$	−3.94276	−	17.2744i	−0.377648	−	1.65459i	0.326997	−	0.945025i	$-0.393963\pi$
$110$	2.19249	+	8.99457i	0.209046	+	0.857598i
$111$	0.0633781	+	0.277678i	0.00601558	+	0.0263560i
$112$	10.5749	−	0.414893i	0.999231	−	0.0392037i
$113$	−2.77270	+	12.1480i	−0.260834	+	1.14279i	0.659515	+	0.751691i	$0.270762\pi$
$113$	−2.77270	+	12.1480i	−0.260834	+	1.14279i	−0.920349	+	0.391097i	$0.872096\pi$
$114$	0.696349	−	0.0102335i	0.0652191	−	0.000958451i
$115$	−22.7173	−	10.9401i	−2.11840	−	1.02017i
$116$	−1.06252	+	5.37932i	−0.0986529	+	0.499458i
$117$			13.6911i			1.26574i
$118$	−0.955020	−	3.91792i	−0.0879168	−	0.360674i
$119$	−9.88784	+	7.57362i	−0.906417	+	0.694273i
$120$	−0.625394	−	0.455136i	−0.0570904	−	0.0415480i
$121$	−6.58178	+	3.16962i	−0.598344	+	0.288147i
$122$	2.77469	+	5.55152i	0.251209	+	0.502611i
$123$	−0.670259	−	0.152982i	−0.0604352	−	0.0137939i
$124$	0.337051	+	1.29944i	0.0302681	+	0.116693i
$125$	2.36240	+	4.90558i	0.211300	+	0.438768i
$126$	−2.43921	−	10.9320i	−0.217302	−	0.973903i
$127$	−1.20411	+	2.50035i	−0.106847	+	0.221870i	−0.947537	−	0.319647i	$-0.896436\pi$
$127$	−1.20411	+	2.50035i	−0.106847	+	0.221870i	0.840690	+	0.541517i	$0.182150\pi$
$128$	−11.2539	+	1.16172i	−0.994714	+	0.102682i
$129$		−	0.0488934i		−	0.00430482i
$130$	5.21668	+	21.4012i	0.457533	+	1.87701i
$131$	4.82357	−	6.04857i	0.421438	−	0.528466i	−0.525108	−	0.851036i	$-0.675975\pi$
$131$	4.82357	−	6.04857i	0.421438	−	0.528466i	0.946546	+	0.322569i	$0.104547\pi$
$132$	−0.125704	+	0.281934i	−0.0109412	+	0.0245392i
$133$	14.4786	+	7.32486i	1.25545	+	0.635146i
$134$	1.39921	+	1.08259i	0.120874	+	0.0935211i
$135$	−0.711148	+	1.47671i	−0.0612058	+	0.127095i
$136$	10.0341	−	8.75251i	0.860421	−	0.750521i
$137$	1.84829	−	2.31769i	0.157910	−	0.198013i	−0.696582	−	0.717477i	$-0.745297\pi$
$137$	1.84829	−	2.31769i	0.157910	−	0.198013i	0.854493	+	0.519464i	$0.173868\pi$
$138$	−0.375867	−	0.752024i	−0.0319959	−	0.0640165i
$139$	−2.88773	−	3.62110i	−0.244934	−	0.307137i	0.644134	−	0.764913i	$-0.277218\pi$
$139$	−2.88773	−	3.62110i	−0.244934	−	0.307137i	−0.889068	+	0.457775i	$0.848646\pi$
$140$	−7.97825	−	16.1590i	−0.674285	−	1.36568i
$141$	−0.556255	+	0.697522i	−0.0468451	+	0.0587419i
$142$	21.4099	+	4.55675i	1.79668	+	0.382394i
$143$	7.92053	−	3.81433i	0.662348	−	0.318970i
$144$	3.34570	+	11.4973i	0.278809	+	0.958109i
$145$	9.10303	−	2.07771i	0.755966	−	0.172544i
$146$	1.32579	−	1.08954i	0.109723	−	0.0901708i
$147$	−0.146416	+	0.542671i	−0.0120761	+	0.0447587i
$148$	1.37468	−	6.95970i	0.112998	−	0.572084i
$149$	2.02505	+	8.87233i	0.165899	+	0.726850i	0.987608	+	0.156943i	$0.0501637\pi$
$149$	2.02505	+	8.87233i	0.165899	+	0.726850i	−0.821709	+	0.569907i	$0.806979\pi$
$150$	−0.155988	+	0.732912i	−0.0127364	+	0.0598420i
$151$	5.91167	+	12.2757i	0.481085	+	0.998983i	0.990378	+	0.138390i	$0.0441926\pi$
$151$	5.91167	+	12.2757i	0.481085	+	0.998983i	−0.509293	+	0.860593i	$0.670093\pi$
$152$	−15.9450	−	6.83022i	−1.29331	−	0.554004i
$153$	−11.0179	−	8.78646i	−0.890742	−	0.710343i
$154$	−5.64481	+	4.45678i	−0.454872	+	0.359138i
$155$	1.78724	−	1.42528i	0.143555	−	0.114481i
$156$	−0.299094	+	0.670819i	−0.0239467	+	0.0537085i
$157$	−6.53001	−	5.20751i	−0.521152	−	0.415604i	0.327266	−	0.944932i	$-0.393873\pi$
$157$	−6.53001	−	5.20751i	−0.521152	−	0.415604i	−0.848417	+	0.529328i	$0.822444\pi$
$158$	15.0481	+	11.6429i	1.19716	+	0.926256i
$159$	−0.328916	−	0.158398i	−0.0260847	−	0.0125617i
$160$	9.61062	+	16.6972i	0.759786	+	1.32003i
$161$	0.383225	−	19.5843i	0.0302023	−	1.54346i
$162$	11.3117	−	5.65369i	0.888733	−	0.444196i
$163$	−2.98169	−	2.37782i	−0.233544	−	0.186245i	0.499724	−	0.866184i	$-0.333435\pi$
$163$	−2.98169	−	2.37782i	−0.233544	−	0.186245i	−0.733268	+	0.679939i	$0.762006\pi$
$164$	13.6960	+	10.2786i	1.06948	+	0.802621i
$165$	0.525649			0.0409217
$166$	1.78769	+	2.17533i	0.138751	+	0.168838i
$167$	−3.24440	−	1.56242i	−0.251059	−	0.120904i	0.304122	−	0.952633i	$-0.401637\pi$
$167$	−3.24440	−	1.56242i	−0.251059	−	0.120904i	−0.555181	+	0.831729i	$0.687351\pi$
$168$	0.119307	−	0.588921i	0.00920473	−	0.0454362i
$169$	7.13308	−	3.43511i	0.548698	−	0.264239i
$170$	−20.5704	−	9.53641i	−1.57768	−	0.731409i
$171$	−4.08526	+	17.8987i	−0.312408	+	1.36875i
$172$	−0.495922	+	1.11227i	−0.0378137	+	0.0848099i
$173$	−2.43106	−	5.04815i	−0.184830	−	0.383804i	0.787879	−	0.615830i	$-0.211179\pi$
$173$	−2.43106	−	5.04815i	−0.184830	−	0.383804i	−0.972710	+	0.232026i	$0.925465\pi$
$174$	0.282453	+	0.130944i	0.0214127	+	0.00992687i
$175$	−11.1502	+	13.4341i	−0.842877	+	1.01552i
$176$	5.71928	−	5.13869i	0.431107	−	0.387343i
$177$	−0.228966			−0.0172101
$178$	−2.59006	+	2.12851i	−0.194133	+	0.159538i
$179$	−5.35781	+	11.1256i	−0.400462	+	0.831567i	0.599062	+	0.800703i	$0.295540\pi$
$179$	−5.35781	+	11.1256i	−0.400462	+	0.831567i	−0.999524	+	0.0308646i	$0.990174\pi$
$180$	15.5613	−	13.1761i	1.15987	−	0.982086i
$181$	−9.88740	−	2.25673i	−0.734924	−	0.167742i	−0.161352	−	0.986897i	$-0.551586\pi$
$181$	−9.88740	−	2.25673i	−0.734924	−	0.167742i	−0.573572	+	0.819155i	$0.694443\pi$
$182$	−13.4309	+	10.6042i	−0.995568	+	0.786037i
$183$	0.343548	−	0.0784126i	0.0253958	−	0.00579643i
$184$	0.922849	+	20.9201i	0.0680333	+	1.54225i
$185$	−11.7774	+	2.68811i	−0.865891	+	0.197634i
$186$	0.0762132	−	0.00112002i	0.00558822	−	8.21238e-5i
$187$	−2.01355	+	8.82194i	−0.147245	+	0.645124i
$188$	19.7291	−	10.2258i	1.43889	−	0.745794i
$189$	−1.27305	−	0.0249111i	−0.0926011	−	0.00181202i
$190$	0.434041	+	29.5349i	0.0314886	+	2.14269i
$191$	−16.8887	+	13.4683i	−1.22203	+	0.974534i	−1.00000		0.000507130i	$-0.999839\pi$
$191$	−16.8887	+	13.4683i	−1.22203	+	0.974534i	−0.222026	+	0.975041i	$0.571267\pi$
$192$	−0.0872404	+	0.636421i	−0.00629603	+	0.0459297i
$193$	−0.911495	−	1.14298i	−0.0656108	−	0.0822734i	0.747943	−	0.663763i	$-0.231042\pi$
$193$	−0.911495	−	1.14298i	−0.0656108	−	0.0822734i	−0.813554	+	0.581489i	$0.802470\pi$
$194$	7.75760	+	6.00213i	0.556963	+	0.430928i
$195$	1.25070			0.0895644
$196$	8.83507	−	10.8601i	0.631076	−	0.775721i
$197$	−11.4842			−0.818215			−0.409108	−	0.912486i	$-0.634160\pi$
$197$	−11.4842			−0.818215			−0.409108	+	0.912486i	$0.634160\pi$
$198$	−6.43609	−	4.97967i	−0.457393	−	0.353889i
$199$	−1.95880	−	2.45626i	−0.138856	−	0.174119i	0.707541	−	0.706672i	$-0.249804\pi$
$199$	−1.95880	−	2.45626i	−0.138856	−	0.174119i	−0.846397	+	0.532553i	$0.821233\pi$
$200$	10.9824	−	15.0908i	0.776576	−	1.06708i
$201$	0.0785331	−	0.0626280i	0.00553930	−	0.00441744i
$202$	−0.0524410	−	3.56842i	−0.00368974	−	0.251073i
$203$	4.41077	+	5.75854i	0.309575	+	0.404170i
$204$	−0.347892	−	0.671204i	−0.0243573	−	0.0469937i
$205$	6.48858	−	28.4283i	0.453182	−	1.98552i
$206$	2.37993	−	0.0349752i	0.165818	−	0.00243684i
$207$	21.6073	−	4.93173i	1.50181	−	0.342779i
$208$	13.6081	−	12.2267i	0.943555	−	0.847770i
$209$	11.4929	−	2.62317i	0.794978	−	0.181449i
$210$	−0.998656	+	0.222825i	−0.0689138	+	0.0153764i
$211$	13.5594	+	3.09485i	0.933469	+	0.213058i	0.662098	−	0.749417i	$-0.269666\pi$
$211$	13.5594	+	3.09485i	0.933469	+	0.213058i	0.271370	+	0.962475i	$0.412523\pi$
$212$	5.87586	+	6.93954i	0.403556	+	0.476610i
$213$	0.539250	−	1.11976i	0.0369488	−	0.0767249i
$214$	−12.2044	+	10.0296i	−0.834274	+	0.685607i
$215$	2.07376			0.141429
$216$	1.35989	−	0.0599889i	0.0925288	−	0.00408172i
$217$	1.58463	+	0.801682i	0.107572	+	0.0544217i
$218$	22.7337	+	10.5393i	1.53972	+	0.713812i
$219$	−0.0422751	−	0.0877852i	−0.00285669	−	0.00593197i
$220$	−11.9579	−	5.33162i	−0.806204	−	0.359458i
$221$	−4.79093	+	20.9904i	−0.322273	+	1.41197i
$222$	−0.365434	−	0.169414i	−0.0245263	−	0.0113703i
$223$	−8.23205	+	3.96435i	−0.551259	+	0.265472i	−0.688711	−	0.725036i	$-0.741823\pi$
$223$	−8.23205	+	3.96435i	−0.551259	+	0.265472i	0.137452	+	0.990508i	$0.456109\pi$
$224$	−8.68749	+	12.1872i	−0.580457	+	0.814291i
$225$	−17.7974	−	8.57078i	−1.18649	−	0.571386i
$226$	−11.1882	−	13.6143i	−0.744228	−	0.905607i
$227$	12.9650			0.860515			0.430258	−	0.902706i	$-0.358423\pi$
$227$	12.9650			0.860515			0.430258	+	0.902706i	$0.358423\pi$
$228$	−0.591178	+	0.787732i	−0.0391517	+	0.0521689i
$229$	14.8237	+	11.8215i	0.979579	+	0.781188i	0.975769	−	0.218805i	$-0.0702157\pi$
$229$	14.8237	+	11.8215i	0.979579	+	0.781188i	0.00381023	+	0.999993i	$0.498787\pi$
$230$	31.8963	−	15.9420i	2.10318	−	1.05118i
$231$	0.169947	+	0.371313i	0.0111817	+	0.0244306i
$232$	−5.09733	−	5.84374i	−0.334656	−	0.383661i
$233$	−0.102552	−	0.0493866i	−0.00671842	−	0.00323542i	0.430522	−	0.902580i	$-0.358330\pi$
$233$	−0.102552	−	0.0493866i	−0.00671842	−	0.00323542i	−0.437240	+	0.899345i	$0.644044\pi$
$234$	−15.3137	−	11.8483i	−1.00109	−	0.774550i
$235$	−29.5846	−	23.5929i	−1.92989	−	1.53903i
$236$	5.20873	+	2.32239i	0.339059	+	0.151174i
$237$	0.844598	−	0.673544i	0.0548625	−	0.0437514i
$238$	0.0857926	−	17.6139i	0.00556111	−	1.14174i
$239$	−16.3374	−	13.0286i	−1.05678	−	0.842753i	−0.0688445	−	0.997627i	$-0.521931\pi$
$239$	−16.3374	−	13.0286i	−1.05678	−	0.842753i	−0.987934	+	0.154875i	$0.950503\pi$
$240$	1.05029	−	0.305635i	0.0677962	−	0.0197286i
$241$	11.1824	+	23.2206i	0.720324	+	1.49577i	0.862570	+	0.505937i	$0.168853\pi$
$241$	11.1824	+	23.2206i	0.720324	+	1.49577i	−0.142246	+	0.989831i	$0.545433\pi$
$242$	2.15065	−	10.1048i	0.138249	−	0.649563i
$243$	−0.481045	−	2.10760i	−0.0308591	−	0.135202i
$244$	−8.61068	−	1.70078i	−0.551243	−	0.108881i
$245$	−23.0168	−	6.21006i	−1.47049	−	0.396746i
$246$	0.751158	−	0.617302i	0.0478921	−	0.0393578i
$247$	27.3455	−	6.24143i	1.73995	−	0.397133i
$248$	−1.74513	−	0.747546i	−0.110816	−	0.0474692i
$249$	0.144036	−	0.0693639i	0.00912789	−	0.00439576i
$250$	−7.53139	−	1.60293i	−0.476327	−	0.101378i
$251$	6.16865	−	7.73525i	0.389362	−	0.488245i	−0.548060	−	0.836439i	$-0.684634\pi$
$251$	6.16865	−	7.73525i	0.389362	−	0.488245i	0.937422	+	0.348194i	$0.113205\pi$
$252$	14.3385	+	6.73235i	0.903242	+	0.424098i
$253$	−8.87287	−	11.1262i	−0.557833	−	0.699500i
$254$	−1.75464	−	3.51063i	−0.110096	−	0.220276i
$255$	−0.802655	+	1.00650i	−0.0502642	+	0.0630293i
$256$	8.43979	−	13.5930i	0.527487	−	0.849563i
$257$	3.46199	−	7.18889i	0.215953	−	0.448431i	−0.764647	−	0.644449i	$-0.777087\pi$
$257$	3.46199	−	7.18889i	0.215953	−	0.448431i	0.980600	+	0.196018i	$0.0628011\pi$
$258$	0.0546879	+	0.0423126i	0.00340472	+	0.00263427i
$259$	−5.70660	−	7.45033i	−0.354591	−	0.462941i
$260$	−28.4521	−	12.6858i	−1.76452	−	0.786737i
$261$	−5.11711	+	6.41665i	−0.316741	+	0.397181i
$262$	2.59106	+	10.6297i	0.160076	+	0.656705i
$263$			23.1861i			1.42972i	0.699269	+	0.714859i	$0.253509\pi$
$263$			23.1861i			1.42972i	−0.699269	+	0.714859i	$0.746491\pi$
$264$	−0.206562	−	0.384590i	−0.0127130	−	0.0236699i
$265$	6.71826	−	13.9506i	0.412699	−	0.856979i
$266$	−20.7228	+	9.85552i	−1.27060	+	0.604281i
$267$	0.0825882	+	0.171496i	0.00505431	+	0.0104954i
$268$	−2.42177	+	0.628165i	−0.147933	+	0.0383713i
$269$	11.8256	+	2.69912i	0.721021	+	0.164568i	0.567259	−	0.823540i	$-0.308004\pi$
$269$	11.8256	+	2.69912i	0.721021	+	0.164568i	0.153762	+	0.988108i	$0.450861\pi$
$270$	−1.03629	−	2.07338i	−0.0630668	−	0.126182i
$271$	−21.8199	+	10.5079i	−1.32547	+	0.638311i	−0.956663	−	0.291196i	$-0.905947\pi$
$271$	−21.8199	+	10.5079i	−1.32547	+	0.638311i	−0.368804	+	0.929507i	$0.620233\pi$
$272$	1.10619	+	18.7978i	0.0670729	+	1.13978i
$273$	0.404363	+	0.883480i	0.0244732	+	0.0534706i
$274$	0.992842	+	4.07308i	0.0599798	+	0.246064i
$275$			12.6839i			0.764870i
$276$	1.16643	+	0.230393i	0.0702106	+	0.0138680i
$277$	11.2457	+	5.41565i	0.675689	+	0.325395i	0.740069	−	0.672531i	$-0.234793\pi$
$277$	11.2457	+	5.41565i	0.675689	+	0.325395i	−0.0643800	+	0.997925i	$0.520507\pi$
$278$	6.54930	−	0.0962477i	0.392801	−	0.00577255i
$279$	−0.447119	+	1.95896i	−0.0267683	+	0.117280i
$280$	24.9784	+	5.06027i	1.49275	+	0.302409i
$281$	−3.22099	−	14.1121i	−0.192148	−	0.841856i	−0.975451	−	0.220216i	$-0.929324\pi$
$281$	−3.22099	−	14.1121i	−0.192148	−	0.841856i	0.783303	−	0.621640i	$-0.213533\pi$
$282$	−0.298802	−	1.22582i	−0.0177934	−	0.0729964i
$283$	3.89076	+	17.0465i	0.231282	+	1.01331i	0.948578	+	0.316543i	$0.102522\pi$
$283$	3.89076	+	17.0465i	0.231282	+	1.01331i	−0.717296	+	0.696768i	$0.754621\pi$
$284$	−23.6250	+	20.0038i	−1.40189	+	1.18701i
$285$	1.63507	+	0.373194i	0.0968533	+	0.0221061i
$286$	−2.58809	+	12.1602i	−0.153037	+	0.719046i
$287$	22.1793	−	4.60769i	1.30920	−	0.271983i
$288$	−15.7553	−	6.20761i	−0.928389	−	0.365787i
$289$	−3.21803	−	4.03528i	−0.189296	−	0.237369i
$290$	−5.55387	+	11.9799i	−0.326134	+	0.703486i
$291$	0.435407	−	0.347226i	0.0255240	−	0.0203547i
$292$	0.0713142	+	2.42581i	0.00417335	+	0.141960i
$293$			21.1702i			1.23677i	0.785874	+	0.618387i	$0.212213\pi$
$293$			21.1702i			1.23677i	−0.785874	+	0.618387i	$0.787787\pi$
$294$	−0.480276	−	0.633398i	−0.0280103	−	0.0369405i
$295$		−	9.71135i		−	0.565416i
$296$	6.59487	+	7.56056i	0.383319	+	0.439449i
$297$	−0.723249	+	0.576772i	−0.0419672	+	0.0334677i
$298$	−11.6763	−	5.41312i	−0.676391	−	0.313573i
$299$	−21.1116	−	26.4731i	−1.22092	−	1.53098i
$300$	−0.684779	−	0.808742i	−0.0395358	−	0.0466927i
$301$	0.670466	+	1.46488i	0.0386450	+	0.0844343i
$302$	−18.8465	−	4.01118i	−1.08450	−	0.230817i
$303$	−0.197550	−	0.0450895i	−0.0113490	−	0.00259033i
$304$	21.4386	−	11.9238i	1.22959	−	0.683876i
$305$	3.32579	+	14.5712i	0.190434	+	0.834346i
$306$	19.3627	−	4.71979i	1.10689	−	0.269813i
$307$	−3.86847	−	16.9489i	−0.220785	−	0.967324i	−0.956889	−	0.290455i	$-0.906193\pi$
$307$	−3.86847	−	16.9489i	−0.220785	−	0.967324i	0.736103	−	0.676869i	$-0.236664\pi$
$308$	−0.0999216	−	10.1707i	−0.00569356	−	0.579531i
$309$	0.0300721	−	0.131755i	0.00171074	−	0.00749526i
$310$	0.0475044	+	3.23250i	0.00269807	+	0.183594i
$311$	−22.0330	−	10.6105i	−1.24938	−	0.601669i	−0.312033	−	0.950071i	$-0.601010\pi$
$311$	−22.0330	−	10.6105i	−1.24938	−	0.601669i	−0.937345	+	0.348402i	$0.886724\pi$
$312$	−0.491483	−	0.915071i	−0.0278247	−	0.0518057i
$313$			1.11284i			0.0629013i	0.999505	+	0.0314507i	$0.0100127\pi$
$313$			1.11284i			0.0629013i	−0.999505	+	0.0314507i	$0.989987\pi$
$314$	11.4758	−	2.79730i	0.647616	−	0.157861i
$315$	0.527721	−	26.9686i	0.0297337	−	1.51951i
$316$	−26.0454	+	6.75570i	−1.46517	+	0.380038i
$317$	−19.7244	+	9.49875i	−1.10783	+	0.533503i	−0.896112	−	0.443828i	$-0.853620\pi$
$317$	−19.7244	+	9.49875i	−1.10783	+	0.533503i	−0.211718	+	0.977331i	$0.567906\pi$
$318$	0.461815	−	0.230819i	0.0258973	−	0.0129437i
$319$	5.13777	+	1.17266i	0.287660	+	0.0656565i
$320$	−26.9931	−	3.70021i	−1.50896	−	0.206848i
$321$	0.389157	+	0.808092i	0.0217206	+	0.0451033i
$322$	21.5736	+	17.3770i	1.20225	+	0.968380i
$323$	−12.5266	+	26.0118i	−0.696999	+	1.44733i
$324$	−3.46550	+	17.5450i	−0.192528	+	0.974725i
$325$			30.1794i			1.67405i
$326$	5.23999	−	1.27728i	0.290216	−	0.0707422i
$327$	0.887066	−	1.11235i	0.0490549	−	0.0615129i
$328$	−23.3493	+	6.42401i	−1.28925	+	0.354707i
$329$	7.10080	−	28.5261i	0.391480	−	1.57269i
$330$	−0.454899	+	0.587946i	−0.0250414	+	0.0323653i
$331$	3.79475	−	7.87988i	0.208578	−	0.433117i	−0.770266	−	0.637722i	$-0.779877\pi$
$331$	3.79475	−	7.87988i	0.208578	−	0.433117i	0.978845	+	0.204605i	$0.0655910\pi$
$332$	−3.98021	+	0.117011i	−0.218442	+	0.00642179i
$333$	6.62045	−	8.30178i	0.362799	−	0.454935i
$334$	4.55531	−	2.27678i	0.249255	−	0.124580i
$335$	2.65630	+	3.33090i	0.145129	+	0.181986i
$336$	0.555467	+	0.643102i	0.0303032	+	0.0350841i
$337$	6.28089	−	7.87599i	0.342142	−	0.429032i	−0.580756	−	0.814078i	$-0.697243\pi$
$337$	6.28089	−	7.87599i	0.342142	−	0.429032i	0.922898	+	0.385046i	$0.125814\pi$
$338$	−2.33079	+	10.9512i	−0.126778	+	0.595667i
$339$	−0.901445	+	0.434113i	−0.0489598	+	0.0235778i
$340$	28.4684	−	14.7555i	1.54391	−	0.800227i
$341$	1.25786	−	0.287098i	0.0681168	−	0.0155472i
$342$	−16.4845	−	20.0591i	−0.891382	−	1.08467i
$343$	−3.05484	−	18.2666i	−0.164946	−	0.986303i
$344$	−0.814917	−	1.51726i	−0.0439374	−	0.0818052i
$345$	−0.450520	−	1.97386i	−0.0242552	−	0.106269i
$346$	7.75029	+	1.64952i	0.416658	+	0.0886789i
$347$	−10.2389	−	21.2613i	−0.549654	−	1.14137i	−0.972010	−	0.234938i	$-0.924511\pi$
$347$	−10.2389	−	21.2613i	−0.549654	−	1.14137i	0.422356	−	0.906430i	$-0.361203\pi$
$348$	−0.390899	+	0.202607i	−0.0209544	+	0.0108609i
$349$	−5.73626	−	4.57451i	−0.307055	−	0.244868i	0.457823	−	0.889043i	$-0.348629\pi$
$349$	−5.73626	−	4.57451i	−0.307055	−	0.244868i	−0.764878	+	0.644175i	$0.777201\pi$
$350$	−5.37678	−	24.0976i	−0.287401	−	1.28807i
$351$	−1.72086	+	1.37234i	−0.0918526	+	0.0732500i
$352$	0.798200	+	10.8441i	0.0425442	+	0.577995i
$353$	−0.622464	−	0.496399i	−0.0331304	−	0.0264206i	0.606785	−	0.794866i	$-0.292459\pi$
$353$	−0.622464	−	0.496399i	−0.0331304	−	0.0264206i	−0.639915	+	0.768446i	$0.721030\pi$
$354$	0.198148	−	0.256102i	0.0105315	−	0.0136117i
$355$	47.4936	+	22.8717i	2.52070	+	1.21390i
$356$	−0.139319	−	4.73904i	−0.00738387	−	0.251168i
$357$	−0.970485	−	0.241576i	−0.0513635	−	0.0127856i
$358$	−7.80747	−	15.6210i	−0.412638	−	0.825593i
$359$	2.40304	+	1.91636i	0.126828	+	0.101142i	0.684849	−	0.728685i	$-0.259868\pi$
$359$	2.40304	+	1.91636i	0.126828	+	0.101142i	−0.558022	+	0.829826i	$0.688439\pi$
$360$	1.27081	+	28.8081i	0.0669777	+	1.51832i
$361$	18.6118			0.979569
$362$	11.0808	−	9.10620i	0.582394	−	0.478611i
$363$	−0.528495	−	0.254510i	−0.0277388	−	0.0133583i
$364$	−0.237748	−	24.1996i	−0.0124614	−	1.26841i
$365$	3.72331	−	1.79305i	0.194887	−	0.0938527i
$366$	−0.209603	+	0.452122i	−0.0109561	+	0.0236328i
$367$	6.25274	−	27.3950i	0.326390	−	1.43001i	−0.499566	−	0.866276i	$-0.666507\pi$
$367$	6.25274	−	27.3950i	0.326390	−	1.43001i	0.825957	−	0.563734i	$-0.190636\pi$
$368$	−24.1981	−	17.0722i	−1.26141	−	0.889948i
$369$	11.1207	+	23.0924i	0.578922	+	1.20214i
$370$	7.18553	−	15.4995i	0.373558	−	0.805780i
$371$	12.0266	+	0.235337i	0.624392	+	0.0122181i
$372$	−0.0647026	+	0.0862148i	−0.00335467	+	0.00447003i
$373$	−9.43158			−0.488349			−0.244174	−	0.969731i	$-0.578517\pi$
$373$	−9.43158			−0.488349			−0.244174	+	0.969731i	$0.578517\pi$
$374$	−8.12492	−	9.88673i	−0.420130	−	0.511231i
$375$	−0.189693	+	0.393901i	−0.00979568	+	0.0203409i
$376$	−5.63597	+	30.9168i	−0.290653	+	1.59441i
$377$	12.2245	+	2.79017i	0.629595	+	0.143701i
$378$	1.12957	−	1.40237i	0.0580989	−	0.0721302i
$379$	23.4834	−	5.35993i	1.20626	−	0.275321i	0.428302	−	0.903636i	$-0.359112\pi$
$379$	23.4834	−	5.35993i	1.20626	−	0.275321i	0.777960	+	0.628314i	$0.216255\pi$
$380$	−33.4108	−	25.0742i	−1.71394	−	1.28628i
$381$	−0.217251	+	0.0495860i	−0.0111301	+	0.00254037i
$382$	−0.448898	−	30.5458i	−0.0229676	−	1.56286i
$383$	−3.03704	+	13.3061i	−0.155185	+	0.679911i	0.836144	+	0.548510i	$0.184805\pi$
$383$	−3.03704	+	13.3061i	−0.155185	+	0.679911i	−0.991329	+	0.131401i	$0.958052\pi$
$384$	−0.636347	−	0.648341i	−0.0324735	−	0.0330855i
$385$	−15.7488	+	7.20813i	−0.802634	+	0.367360i
$386$	2.06725	−	0.0303800i	0.105220	−	0.00154630i
$387$	−1.42513	+	1.13650i	−0.0724432	+	0.0577715i
$388$	−13.4269	+	3.48271i	−0.681649	+	0.176808i
$389$	9.65354	+	12.1052i	0.489454	+	0.613756i	0.963814	−	0.266575i	$-0.0858920\pi$
$389$	9.65354	+	12.1052i	0.489454	+	0.613756i	−0.474360	+	0.880331i	$0.657321\pi$
$390$	−1.08236	+	1.39892i	−0.0548075	+	0.0708373i
$391$	34.8529			1.76259
$392$	4.50125	+	19.2805i	0.227347	+	0.973814i
$393$	0.621207			0.0313358
$394$	9.93849	−	12.8452i	0.500694	−	0.647134i
$395$	28.5676	+	35.8227i	1.43739	+	1.80244i
$396$	11.1397	−	2.88942i	0.559789	−	0.145199i
$397$	−0.788216	+	0.628581i	−0.0395594	+	0.0315476i	−0.643070	−	0.765807i	$-0.722340\pi$
$397$	−0.788216	+	0.628581i	−0.0395594	+	0.0315476i	0.603511	+	0.797355i	$0.293768\pi$
$398$	4.44251	−	0.0652866i	0.222683	−	0.00327252i
$399$	0.265014	+	1.27565i	0.0132673	+	0.0638626i
$400$	7.37498	+	25.3437i	0.368749	+	1.26718i
$401$	−8.21845	+	36.0074i	−0.410410	+	1.79812i	0.171854	+	0.985122i	$0.445024\pi$
$401$	−8.21845	+	36.0074i	−0.410410	+	1.79812i	−0.582264	+	0.813000i	$0.697833\pi$
$402$	0.00208739	+	0.142039i	0.000104109	+	0.00708426i
$403$	2.99288	−	0.683104i	0.149086	−	0.0340279i
$404$	4.03671	+	3.02948i	0.200834	+	0.150722i
$405$	29.6902	−	6.77659i	1.47532	−	0.336732i
$406$	−10.2581	−	0.0499644i	−0.509101	−	0.00247969i
$407$	−6.64718	−	1.51718i	−0.329489	−	0.0752036i
$408$	1.05182	+	0.191741i	0.0520728	+	0.00949261i
$409$	10.4663	−	21.7335i	0.517525	−	1.07465i	−0.464442	−	0.885603i	$-0.653745\pi$
$409$	10.4663	−	21.7335i	0.517525	−	1.07465i	0.981968	−	0.189049i	$-0.0605405\pi$
$410$	26.1822	+	31.8596i	1.29305	+	1.57343i
$411$	0.238034			0.0117413
$412$	−2.02049	+	2.69226i	−0.0995422	+	0.132638i
$413$	6.85999	−	3.13977i	0.337558	−	0.154498i
$414$	−13.1829	+	28.4360i	−0.647903	+	1.39755i
$415$	2.94200	+	6.10912i	0.144417	+	0.299885i
$416$	1.89919	+	25.8020i	0.0931156	+	1.26504i
$417$	0.0827551	−	0.362574i	0.00405253	−	0.0177553i
$418$	−7.01193	+	15.1250i	−0.342965	+	0.739790i
$419$	−20.8748	+	10.0528i	−1.01980	+	0.491110i	−0.867612	−	0.497242i	$-0.834346\pi$
$419$	−20.8748	+	10.0528i	−1.01980	+	0.491110i	−0.152188	+	0.988352i	$0.548632\pi$
$420$	0.615010	−	1.30984i	0.0300094	−	0.0639139i
$421$	1.48184	+	0.713617i	0.0722205	+	0.0347796i	0.469645	−	0.882855i	$-0.344382\pi$
$421$	1.48184	+	0.713617i	0.0722205	+	0.0347796i	−0.397425	+	0.917635i	$0.630096\pi$
$422$	−15.1960	+	12.4881i	−0.739731	+	0.607911i
$423$	33.2609			1.61720
$424$	−12.8470	+	0.566719i	−0.623904	+	0.0275223i
$425$	−24.2869	−	19.3681i	−1.17809	−	0.939492i
$426$	0.785802	+	1.57221i	0.0380722	+	0.0761737i
$427$	−9.21769	+	7.06032i	−0.446075	+	0.341673i
$428$	−0.656471	−	22.3304i	−0.0317317	−	1.07938i
$429$	0.635991	+	0.306277i	0.0307060	+	0.0147872i
$430$	−1.79464	+	2.31953i	−0.0865453	+	0.111858i
$431$	−2.21158	−	1.76368i	−0.106528	−	0.0849533i	0.568777	−	0.822492i	$-0.307417\pi$
$431$	−2.21158	−	1.76368i	−0.106528	−	0.0849533i	−0.675305	+	0.737538i	$0.735988\pi$
$432$	−1.10976	+	1.57297i	−0.0533933	+	0.0756796i
$433$	−27.5735	+	21.9891i	−1.32510	+	1.05673i	−0.331533	+	0.943444i	$0.607566\pi$
$433$	−27.5735	+	21.9891i	−1.32510	+	1.05673i	−0.993563	+	0.113285i	$0.963863\pi$
$434$	−2.26804	+	1.07866i	−0.108870	+	0.0517771i
$435$	0.586170	+	0.467455i	0.0281047	+	0.0224127i
$436$	−31.4622	+	16.3072i	−1.50677	+	0.780974i
$437$	−19.7005	−	40.9085i	−0.942402	−	1.95692i
$438$	0.134774	+	0.0286845i	0.00643975	+	0.00137060i
$439$	−4.16005	−	18.2264i	−0.198548	−	0.869898i	−0.971802	−	0.235800i	$-0.924229\pi$
$439$	−4.16005	−	18.2264i	−0.198548	−	0.869898i	0.773253	−	0.634097i	$-0.218628\pi$
$440$	16.3120	−	8.76111i	0.777642	−	0.417670i
$441$	19.2209	−	8.34642i	0.915282	−	0.397449i
$442$	−19.3320	−	23.5239i	−0.919529	−	1.11892i
$443$	−14.7602	+	3.36892i	−0.701278	+	0.160062i	−0.558270	−	0.829659i	$-0.688535\pi$
$443$	−14.7602	+	3.36892i	−0.701278	+	0.160062i	−0.143008	+	0.989722i	$0.545678\pi$
$444$	0.505741	−	0.262131i	0.0240014	−	0.0124402i
$445$	−7.27382	+	3.50289i	−0.344812	+	0.166053i
$446$	2.68989	−	12.6384i	0.127370	−	0.598447i
$447$	−0.455608	+	0.571315i	−0.0215495	+	0.0270223i
$448$	−6.11334	−	20.2639i	−0.288828	−	0.957381i
$449$	16.6885	+	20.9268i	0.787581	+	0.987595i	0.999946	+	0.0104045i	$0.00331190\pi$
$449$	16.6885	+	20.9268i	0.787581	+	0.987595i	−0.212365	+	0.977190i	$0.568117\pi$
$450$	24.9885	−	12.4895i	1.17797	−	0.588759i
$451$	10.2612	−	12.8671i	0.483179	−	0.605887i
$452$	24.9101	−	0.732308i	1.17167	−	0.0344449i
$453$	−0.474687	+	0.985697i	−0.0223027	+	0.0463121i
$454$	−11.2200	+	14.5015i	−0.526579	+	0.680589i
$455$	−37.4719	+	17.1506i	−1.75671	+	0.804034i
$456$	−0.369481	−	1.34295i	−0.0173025	−	0.0628893i
$457$	4.00223	−	5.01864i	0.187217	−	0.234762i	−0.679361	−	0.733804i	$-0.737743\pi$
$457$	4.00223	−	5.01864i	0.187217	−	0.234762i	0.866578	+	0.499042i	$0.166315\pi$
$458$	−26.0511	+	6.35013i	−1.21729	+	0.296722i
$459$		−	2.26558i		−	0.105748i
$460$	−9.77185	+	49.4727i	−0.455615	+	2.30668i
$461$	12.1909	−	25.3147i	0.567788	−	1.17902i	−0.397443	−	0.917627i	$-0.630102\pi$
$461$	12.1909	−	25.3147i	0.567788	−	1.17902i	0.965231	−	0.261397i	$-0.0841833\pi$
$462$	−0.562392	−	0.131247i	−0.0261648	−	0.00610618i
$463$	3.97996	+	8.26447i	0.184964	+	0.384083i	0.972746	−	0.231872i	$-0.0744849\pi$
$463$	3.97996	+	8.26447i	0.184964	+	0.384083i	−0.787782	+	0.615954i	$0.788771\pi$
$464$	10.9476	−	0.644232i	0.508228	−	0.0299077i
$465$	0.178953	+	0.0408449i	0.00829876	+	0.00189414i
$466$	0.143989	−	0.0719667i	0.00667015	−	0.00333379i
$467$	4.22022	−	2.03235i	0.195288	−	0.0940460i	−0.333684	−	0.942685i	$-0.608292\pi$
$467$	4.22022	−	2.03235i	0.195288	−	0.0940460i	0.528972	+	0.848639i	$0.322578\pi$
$468$	26.5051	−	6.87494i	1.22520	−	0.317794i
$469$	−1.49410	+	2.95329i	−0.0689911	+	0.136370i
$470$	51.9917	−	12.6733i	2.39820	−	0.584578i
$471$		−	0.670652i		−	0.0309020i
$472$	−7.10528	+	3.81623i	−0.327047	+	0.175656i
$473$	1.05452	+	0.507832i	0.0484871	+	0.0233501i
$474$	0.0224492	+	1.52758i	0.00103112	+	0.0701642i
$475$	−9.00520	+	39.4544i	−0.413187	+	1.81029i
$476$	19.6272	+	15.3392i	0.899611	+	0.703069i
$477$	3.02856	+	13.2690i	0.138668	+	0.607545i
$478$	28.7112	−	6.99855i	1.31322	−	0.320106i
$479$	−8.25074	−	36.1488i	−0.376986	−	1.65168i	−0.706634	−	0.707579i	$-0.749787\pi$
$479$	−8.25074	−	36.1488i	−0.376986	−	1.65168i	0.329649	−	0.944104i	$-0.393070\pi$
$480$	−0.567074	+	1.43927i	−0.0258833	+	0.0656933i
$481$	−15.8159	−	3.60988i	−0.721144	−	0.164597i
$482$	−35.6499	−	7.58749i	−1.62381	−	0.345601i
$483$	1.24865	−	0.956410i	0.0568157	−	0.0435181i
$484$	9.44121	+	11.1503i	0.429146	+	0.506832i
$485$	14.7272	+	18.4673i	0.668728	+	0.838559i
$486$	2.77368	+	1.28587i	0.125816	+	0.0583282i
$487$	−8.86107	+	7.06646i	−0.401533	+	0.320212i	−0.803349	−	0.595508i	$-0.796951\pi$
$487$	−8.86107	+	7.06646i	−0.401533	+	0.320212i	0.401816	+	0.915721i	$0.368379\pi$
$488$	9.35408	−	8.15930i	0.423439	−	0.369354i
$489$		−	0.306229i		−	0.0138481i
$490$	26.8649	−	20.3704i	1.21363	−	0.920241i
$491$			9.93164i			0.448209i	0.974565	+	0.224104i	$0.0719457\pi$
$491$			9.93164i			0.448209i	−0.974565	+	0.224104i	$0.928054\pi$
$492$	0.0404047	+	1.37440i	0.00182158	+	0.0619626i
$493$	−10.0907	+	8.04703i	−0.454460	+	0.362420i
$494$	−16.6838	+	35.9877i	−0.750640	+	1.61916i
$495$	−12.2184	−	15.3214i	−0.549177	−	0.688646i
$496$	2.34638	−	1.30502i	0.105356	−	0.0585971i
$497$	−0.801183	+	40.9436i	−0.0359380	+	1.83657i
$498$	−0.0470647	+	0.221134i	−0.00210902	+	0.00990925i
$499$	−37.0653	−	8.45992i	−1.65927	−	0.378718i	−0.712765	−	0.701403i	$-0.752558\pi$
$499$	−37.0653	−	8.45992i	−1.65927	−	0.378718i	−0.946507	+	0.322685i	$0.895415\pi$
$500$	8.31061	−	7.03678i	0.371662	−	0.314694i
$501$	−0.0643416	−	0.281899i	−0.00287457	−	0.0125943i
$502$	3.31360	+	13.5939i	0.147893	+	0.606723i
$503$	1.69977	+	7.44716i	0.0757888	+	0.332053i	0.998582	−	0.0532442i	$-0.0169562\pi$
$503$	1.69977	+	7.44716i	0.0757888	+	0.332053i	−0.922793	+	0.385297i	$0.874099\pi$
$504$	−19.9389	+	10.2116i	−0.888148	+	0.454862i
$505$	1.91242	−	8.37888i	0.0851017	−	0.372855i
$506$	20.1235	−	0.295732i	0.894598	−	0.0131469i
$507$	0.572761	+	0.275827i	0.0254372	+	0.0122499i
$508$	5.44516	+	1.07553i	0.241590	+	0.0477189i
$509$		−	32.7615i		−	1.45213i	−0.687627	−	0.726064i	$-0.741347\pi$
$509$		−	32.7615i		−	1.45213i	0.687627	−	0.726064i	$-0.258653\pi$
$510$	−0.431160	−	1.76881i	−0.0190921	−	0.0783242i
$511$	2.47038	+	2.05040i	0.109283	+	0.0907041i
$512$	7.90013	+	21.2035i	0.349140	+	0.937071i
$513$	−2.65921	+	1.28061i	−0.117407	+	0.0565403i
$514$	5.04485	+	10.0936i	0.222519	+	0.445209i
$515$	5.58823	+	1.27548i	0.246247	+	0.0562042i
$516$	−0.0946544	+	0.0245517i	−0.00416693	+	0.00108083i
$517$	−9.26648	−	19.2420i	−0.407539	−	0.846264i
$518$	13.2718	+	0.0646433i	0.583130	+	0.00284026i
$519$	0.195206	−	0.405349i	0.00856859	−	0.0177929i
$520$	38.8118	−	20.8457i	1.70201	−	0.914144i
$521$		−	18.0543i		−	0.790975i	−0.918471	−	0.395487i	$-0.870576\pi$
$521$		−	18.0543i		−	0.790975i	0.918471	−	0.395487i	$-0.129424\pi$
$522$	−2.74874	−	11.2766i	−0.120309	−	0.493562i
$523$	24.5794	−	30.8215i	1.07478	−	1.34773i	0.140949	−	0.990017i	$-0.454985\pi$
$523$	24.5794	−	30.8215i	1.07478	−	1.34773i	0.933831	−	0.357715i	$-0.116444\pi$
$524$	−14.1318	−	6.30086i	−0.617350	−	0.275254i
$525$	−1.40160	−	0.0274264i	−0.0611707	−	0.00119699i
$526$	−25.9340	−	20.0654i	−1.13078	−	0.874893i
$527$	−1.37100	+	2.84690i	−0.0597216	+	0.124013i
$528$	0.608929	+	0.101783i	0.0265002	+	0.00442955i
$529$	−19.8350	+	24.8723i	−0.862391	+	1.08140i
$530$	9.78993	+	19.5874i	0.425247	+	0.850822i
$531$	5.32219	+	6.67382i	0.230963	+	0.289619i
$532$	6.91008	−	31.7078i	0.299590	−	1.37471i
$533$	24.4148	−	30.6152i	1.05752	−	1.32609i
$534$	−0.263293	−	0.0560376i	−0.0113938	−	0.00242499i
$535$	−34.2743	+	16.5057i	−1.48181	+	0.713602i
$536$	1.39321	−	3.25240i	0.0601773	−	0.140482i
$537$	−0.966682	+	0.220639i	−0.0417154	+	0.00952127i
$538$	−13.2530	+	10.8913i	−0.571375	+	0.469557i
$539$	−10.1835	−	8.79433i	−0.438634	−	0.378799i
$540$	3.21592	+	0.635209i	0.138391	+	0.0273351i
$541$	−1.82460	−	7.99408i	−0.0784456	−	0.343692i	0.920440	−	0.390883i	$-0.127830\pi$
$541$	−1.82460	−	7.99408i	−0.0784456	−	0.343692i	−0.998886	+	0.0471906i	$0.984973\pi$
$542$	7.12983	−	33.4995i	0.306252	−	1.43893i
$543$	−0.353329	−	0.733696i	−0.0151628	−	0.0314859i
$544$	−21.9829	−	15.0304i	−0.942509	−	0.644424i
$545$	47.1789	+	37.6240i	2.02092	+	1.61163i
$546$	−1.33812	−	0.312283i	−0.0572664	−	0.0133645i
$547$	−27.4432	+	21.8852i	−1.17339	+	0.935744i	−0.998804	−	0.0488980i	$-0.984429\pi$
$547$	−27.4432	+	21.8852i	−1.17339	+	0.935744i	−0.174583	+	0.984643i	$0.555858\pi$
$548$	−5.41501	−	2.41436i	−0.231318	−	0.103136i
$549$	−10.2711	−	8.19096i	−0.438361	−	0.349581i
$550$	−14.1872	−	10.9767i	−0.604942	−	0.468050i
$551$	15.1489	+	7.29531i	0.645364	+	0.310791i
$552$	−1.26713	+	1.10528i	−0.0539326	+	0.0470439i
$553$	−16.0686	+	31.7617i	−0.683304	+	1.35064i
$554$	−15.7896	+	7.89175i	−0.670835	+	0.335288i
$555$	−0.758379	−	0.604787i	−0.0321914	−	0.0256718i
$556$	−5.56015	+	7.40878i	−0.235803	+	0.314202i
$557$	−8.06998			−0.341936			−0.170968	−	0.985277i	$-0.554689\pi$
$557$	−8.06998			−0.341936			−0.170968	+	0.985277i	$0.554689\pi$
$558$	−1.80418	−	2.19540i	−0.0763770	−	0.0929387i
$559$	2.50908	+	1.20831i	0.106123	+	0.0511059i
$560$	−27.2765	+	23.5595i	−1.15264	+	0.995572i
$561$	−0.654633	+	0.315255i	−0.0276386	+	0.0133101i
$562$	18.5720	+	8.60995i	0.783414	+	0.363189i
$563$	1.89250	−	8.29157i	0.0797592	−	0.349448i	−0.919264	−	0.393642i	$-0.871215\pi$
$563$	1.89250	−	8.29157i	0.0797592	−	0.349448i	0.999023	+	0.0441942i	$0.0140720\pi$
$564$	1.62968	+	0.726616i	0.0686219	+	0.0305960i
$565$	−18.4124	−	38.2338i	−0.774617	−	1.60851i
$566$	−22.4339	−	10.4003i	−0.942966	−	0.437157i
$567$	14.3860	+	18.7819i	0.604157	+	0.788765i
$568$	−1.92934	−	43.7364i	−0.0809534	−	1.83514i
$569$	−12.9987			−0.544933			−0.272467	−	0.962165i	$-0.587839\pi$
$569$	−12.9987			−0.544933			−0.272467	+	0.962165i	$0.587839\pi$
$570$	−1.83242	+	1.50589i	−0.0767517	+	0.0630746i
$571$	−15.3795	+	31.9358i	−0.643612	+	1.33647i	0.282516	+	0.959263i	$0.408831\pi$
$571$	−15.3795	+	31.9358i	−0.643612	+	1.33647i	−0.926127	+	0.377211i	$0.876883\pi$
$572$	−11.3616	−	13.4183i	−0.475051	−	0.561047i
$573$	−1.69104	−	0.385968i	−0.0706441	−	0.0161241i
$574$	−14.0403	+	28.7953i	−0.586030	+	1.20189i
$575$	47.6293	−	10.8711i	1.98628	−	0.453355i
$576$	20.5780	−	12.2504i	0.857417	−	0.510434i
$577$	−24.8156	+	5.66400i	−1.03309	+	0.235795i	−0.705265	−	0.708944i	$-0.749172\pi$
$577$	−24.8156	+	5.66400i	−1.03309	+	0.235795i	−0.327822	+	0.944739i	$0.606315\pi$
$578$	7.29841	−	0.107256i	0.303574	−	0.00446128i
$579$	0.0261212	−	0.114444i	0.00108556	−	0.00475614i
$580$	−8.59337	−	16.5796i	−0.356820	−	0.688429i
$581$	−3.36424	+	4.05333i	−0.139572	+	0.168160i
$582$	0.0115730	+	0.787501i	0.000479716	+	0.0326429i
$583$	6.83258	−	5.44880i	0.282977	−	0.225666i
$584$	−2.77502	−	2.01954i	−0.114831	−	0.0835693i
$585$	−29.0718	−	36.4549i	−1.20197	−	1.50723i
$586$	−23.6791	−	18.3208i	−0.978175	−	0.756824i
$587$	−19.9884			−0.825010			−0.412505	−	0.910955i	$-0.635346\pi$
$587$	−19.9884			−0.825010			−0.412505	+	0.910955i	$0.635346\pi$
$588$	1.12410	+	0.0109506i	0.0463570	+	0.000451595i
$589$	4.11649			0.169617
$590$	10.8623	+	8.40425i	0.447193	+	0.345998i
$591$	−0.574946	−	0.720959i	−0.0236501	−	0.0296563i
$592$	−14.1638	+	0.833499i	−0.582130	+	0.0342566i
$593$	−17.3176	+	13.8103i	−0.711147	+	0.567120i	−0.910851	−	0.412736i	$-0.864573\pi$
$593$	−17.3176	+	13.8103i	−0.711147	+	0.567120i	0.199704	+	0.979856i	$0.436002\pi$
$594$	−0.0192237	−	1.30811i	−0.000788760	−	0.0536722i
$595$	10.2462	−	41.1621i	0.420053	−	1.68748i
$596$	16.1594	−	8.37559i	0.661915	−	0.343077i
$597$	0.0561343	−	0.245940i	0.00229742	−	0.0100657i
$598$	47.8807	−	0.703648i	1.95799	−	0.0287743i
$599$	3.15451	−	0.719996i	0.128890	−	0.0294182i	−0.157589	−	0.987505i	$-0.550372\pi$
$599$	3.15451	−	0.719996i	0.128890	−	0.0294182i	0.286479	+	0.958086i	$0.407515\pi$
$600$	1.49720	−	0.0660460i	0.0611230	−	0.00269632i
$601$	2.00055	−	0.456614i	0.0816043	−	0.0186257i	−0.181524	−	0.983387i	$-0.558103\pi$
$601$	2.00055	−	0.456614i	0.0816043	−	0.0186257i	0.263128	+	0.964761i	$0.415246\pi$
$602$	−2.21871	−	0.517789i	−0.0904280	−	0.0211035i
$603$	−3.65092	−	0.833298i	−0.148677	−	0.0339345i
$604$	20.7965	−	17.6088i	0.846196	−	0.716493i
$605$	10.7947	−	22.4155i	0.438869	−	0.911321i
$606$	0.221394	−	0.181942i	0.00899353	−	0.00739088i
$607$	−20.3591			−0.826349			−0.413175	−	0.910652i	$-0.635580\pi$
$607$	−20.3591			−0.826349			−0.413175	+	0.910652i	$0.635580\pi$
$608$	−5.21614	+	34.2983i	−0.211543	+	1.39098i
$609$	−0.140691	+	0.565197i	−0.00570107	+	0.0229029i
$610$	−19.1763	−	8.89008i	−0.776425	−	0.359949i
$611$	−22.0481	−	45.7834i	−0.891972	−	1.85220i
$612$	−11.4774	+	25.7420i	−0.463948	+	1.04056i
$613$	4.37367	−	19.1623i	0.176651	−	0.773959i	−0.806510	−	0.591220i	$-0.798647\pi$
$613$	4.37367	−	19.1623i	0.176651	−	0.773959i	0.983161	−	0.182739i	$-0.0584963\pi$
$614$	22.3054	+	10.3407i	0.900171	+	0.417317i
$615$	2.10953	−	1.01589i	0.0850643	−	0.0409648i
$616$	11.4626	+	8.69003i	0.461840	+	0.350131i
$617$	−1.46739	−	0.706657i	−0.0590748	−	0.0284489i	0.404113	−	0.914709i	$-0.367580\pi$
$617$	−1.46739	−	0.706657i	−0.0590748	−	0.0284489i	−0.463188	+	0.886260i	$0.653294\pi$
$618$	0.121345	+	0.147657i	0.00488121	+	0.00593965i
$619$	31.2009			1.25407			0.627036	−	0.778990i	$-0.284268\pi$
$619$	31.2009			1.25407			0.627036	+	0.778990i	$0.284268\pi$
$620$	−3.65671	−	2.74429i	−0.146857	−	0.110213i
$621$	2.78571	+	2.22153i	0.111787	+	0.0891468i
$622$	30.9355	−	15.4618i	1.24040	−	0.619963i
$623$	−4.82610	−	4.00563i	−0.193354	−	0.160482i
$624$	1.44885	+	0.242178i	0.0580005	+	0.00969486i
$625$	13.0194	+	6.26980i	0.520775	+	0.250792i
$626$	−1.24472	−	0.963056i	−0.0497492	−	0.0384914i
$627$	0.740058	+	0.590177i	0.0295551	+	0.0235694i
$628$	−6.80238	+	15.2566i	−0.271445	+	0.608805i
$629$	13.0552	−	10.4111i	0.520543	−	0.415120i
$630$	29.7080	+	23.9290i	1.18360	+	0.953355i
$631$	2.03967	+	1.62659i	0.0811981	+	0.0647533i	0.663248	−	0.748400i	$-0.269178\pi$
$631$	2.03967	+	1.62659i	0.0811981	+	0.0647533i	−0.582050	+	0.813153i	$0.697749\pi$
$632$	14.9835	−	34.9786i	0.596010	−	1.39137i
$633$	0.484550	+	1.00618i	0.0192591	+	0.0399920i
$634$	6.44508	−	30.2822i	0.255967	−	1.20266i
$635$	−2.10314	−	9.21445i	−0.0834604	−	0.365664i
$636$	−0.141483	+	0.716299i	−0.00561018	+	0.0284031i
$637$	−24.2300	−	20.9247i	−0.960028	−	0.829068i
$638$	−5.75789	+	4.73184i	−0.227957	+	0.187335i
$639$	−45.1730	+	10.3104i	−1.78702	+	0.407875i
$640$	27.4987	−	26.9900i	1.08698	−	1.06687i
$641$	27.1415	−	13.0706i	1.07202	−	0.516259i	0.187265	−	0.982309i	$-0.440038\pi$
$641$	27.1415	−	13.0706i	1.07202	−	0.516259i	0.884758	+	0.466050i	$0.154323\pi$
$642$	−1.24064	−	0.264050i	−0.0489642	−	0.0104212i
$643$	1.53208	−	1.92117i	0.0604195	−	0.0757636i	−0.750703	−	0.660639i	$-0.770285\pi$
$643$	1.53208	−	1.92117i	0.0604195	−	0.0757636i	0.811123	+	0.584876i	$0.198857\pi$
$644$	−38.1063	+	9.09228i	−1.50160	+	0.358286i
$645$	0.103821	+	0.130187i	0.00408794	+	0.00512612i
$646$	−18.2539	−	36.5219i	−0.718191	−	1.43693i
$647$	−24.7984	+	31.0962i	−0.974924	+	1.22252i	4.63982e−6		1.00000i	$0.499999\pi$
$647$	−24.7984	+	31.0962i	−0.974924	+	1.22252i	−0.974929	+	0.222516i	$0.928573\pi$
$648$	−16.6253	−	19.0598i	−0.653104	−	0.748739i
$649$	2.37816	−	4.93830i	0.0933510	−	0.193845i
$650$	−33.7561	−	26.1175i	−1.32402	−	1.02441i
$651$	0.0290049	+	0.139616i	0.00113679	+	0.00547199i
$652$	−3.10606	+	6.96637i	−0.121643	+	0.272824i
$653$	−15.4874	+	19.4206i	−0.606070	+	0.759988i	−0.986310	−	0.164900i	$-0.947270\pi$
$653$	−15.4874	+	19.4206i	−0.606070	+	0.759988i	0.380240	+	0.924888i	$0.375841\pi$
$654$	0.476502	+	1.95483i	0.0186327	+	0.0764397i
$655$			26.3478i			1.02949i
$656$	13.0213	−	31.6759i	0.508395	−	1.23674i
$657$	−1.57607	+	3.27274i	−0.0614882	+	0.127682i
$658$	25.7617	+	32.6290i	1.00430	+	1.27201i
$659$	0.0294533	+	0.0611603i	0.00114734	+	0.00238247i	0.901542	−	0.432692i	$-0.142436\pi$
$659$	0.0294533	+	0.0611603i	0.00114734	+	0.00238247i	−0.900394	+	0.435075i	$0.856722\pi$
$660$	−0.263953	−	1.01762i	−0.0102744	−	0.0396109i
$661$	28.1377	+	6.42225i	1.09443	+	0.249796i	0.731378	−	0.681973i	$-0.238878\pi$
$661$	28.1377	+	6.42225i	1.09443	+	0.249796i	0.363052	+	0.931769i	$0.381735\pi$
$662$	5.52976	+	11.0638i	0.214920	+	0.430006i
$663$	−1.55760	+	0.750099i	−0.0604921	+	0.0291314i
$664$	3.31362	−	4.55318i	0.128593	−	0.176698i
$665$	−54.1055	+	11.2403i	−2.09812	+	0.435879i
$666$	3.55629	+	14.5895i	0.137803	+	0.565331i
$667$		−	20.2978i		−	0.785935i
$668$	−1.39558	+	7.06551i	−0.0539966	+	0.273373i
$669$	−0.661005	−	0.318323i	−0.0255559	−	0.0123071i
$670$	−6.02443	+	0.0885342i	−0.232744	+	0.00342037i
$671$	−1.87708	+	8.22403i	−0.0724639	+	0.317485i
$672$	−1.20002	+	0.0647542i	−0.0462919	+	0.00249795i
$673$	4.75394	+	20.8284i	0.183251	+	0.802875i	0.980069	+	0.198656i	$0.0636576\pi$
$673$	4.75394	+	20.8284i	0.183251	+	0.802875i	−0.796818	+	0.604219i	$0.793485\pi$
$674$	3.37388	+	13.8412i	0.129957	+	0.533142i
$675$	−0.706663	−	3.09609i	−0.0271995	−	0.119169i
$676$	−10.2320	−	12.0842i	−0.393539	−	0.464779i
$677$	−0.503420	−	0.114902i	−0.0193480	−	0.00441605i	0.212836	−	0.977088i	$-0.431730\pi$
$677$	−0.503420	−	0.114902i	−0.0193480	−	0.00441605i	−0.232184	+	0.972672i	$0.574587\pi$
$678$	0.294554	−	1.38396i	0.0113123	−	0.0531508i
$679$	−8.28367	+	16.3738i	−0.317898	+	0.628369i
$680$	−8.13250	+	44.6117i	−0.311867	+	1.71078i
$681$	0.649079	+	0.813920i	0.0248728	+	0.0311895i
$682$	−0.767434	+	1.65539i	−0.0293866	+	0.0633881i
$683$	7.54053	−	6.01337i	0.288530	−	0.230095i	−0.468518	−	0.883454i	$-0.655212\pi$
$683$	7.54053	−	6.01337i	0.288530	−	0.230095i	0.757049	+	0.653359i	$0.226641\pi$
$684$	36.7021	−	1.07897i	1.40334	−	0.0412555i
$685$			10.0959i			0.385746i
$686$	23.0751	+	12.3911i	0.881011	+	0.473095i
$687$			1.52244i			0.0580848i
$688$	2.40231	+	0.401550i	0.0915873	+	0.0153089i
$689$	16.2571	−	12.9646i	0.619345	−	0.493911i
$690$	2.59767	+	1.20427i	0.0988916	+	0.0458459i
$691$	25.8177	+	32.3744i	0.982151	+	1.23158i	0.972806	+	0.231622i	$0.0744033\pi$
$691$	25.8177	+	32.3744i	0.982151	+	1.23158i	0.00934519	+	0.999956i	$0.497025\pi$
$692$	−8.55215	+	7.24130i	−0.325104	+	0.275273i
$693$	6.87254	−	13.5845i	0.261066	−	0.516033i
$694$	32.6419	+	6.94730i	1.23907	+	0.263716i
$695$	15.3782	+	3.50997i	0.583327	+	0.133141i
$696$	0.111667	−	0.612564i	0.00423274	−	0.0232192i
$697$	8.96896	+	39.2956i	0.339723	+	1.48843i
$698$	10.0808	−	2.45728i	0.381566	−	0.0930093i
$699$	−0.00203378	−	0.00891055i	−7.69245e−5	−	0.000337028i
$700$	31.6066	+	14.8402i	1.19462	+	0.560907i
$701$	0.230882	−	1.01156i	0.00872030	−	0.0382061i	−0.970381	−	0.241581i	$-0.922334\pi$
$701$	0.230882	−	1.01156i	0.00872030	−	0.0382061i	0.979101	+	0.203375i	$0.0651911\pi$
$702$	−0.0457399	−	3.11243i	−0.00172634	−	0.117471i
$703$	−19.5994	−	9.43859i	−0.739206	−	0.355983i
$704$	−12.8201	−	8.49179i	−0.483176	−	0.320046i
$705$		−	3.03843i		−	0.114434i
$706$	1.09391	−	0.266649i	0.0411700	−	0.0100355i
$707$	6.53705	−	1.35806i	0.245851	−	0.0510750i
$708$	0.114975	+	0.443264i	0.00432101	+	0.0166589i
$709$	45.4077	−	21.8672i	1.70532	−	0.821240i	0.712495	−	0.701677i	$-0.247565\pi$
$709$	45.4077	−	21.8672i	1.70532	−	0.821240i	0.992827	−	0.119563i	$-0.0381493\pi$
$710$	−66.6835	+	33.3289i	−2.50259	+	1.25081i
$711$	−39.2644	−	8.96185i	−1.47253	−	0.336096i
$712$	5.42125	+	3.94536i	0.203170	+	0.147859i
$713$	−2.15615	−	4.47730i	−0.0807486	−	0.167676i
$714$	1.11007	−	0.876440i	0.0415433	−	0.0327999i
$715$	−12.9904	+	26.9749i	−0.485814	+	1.00880i
$716$	24.2289	+	4.78569i	0.905476	+	0.178850i
$717$		−	1.67790i		−	0.0626624i
$718$	−4.22308	+	1.02941i	−0.157604	+	0.0384171i
$719$	7.97413	−	9.99925i	0.297385	−	0.372909i	−0.610580	−	0.791954i	$-0.709064\pi$
$719$	7.97413	−	9.99925i	0.297385	−	0.372909i	0.907965	+	0.419045i	$0.137635\pi$
$720$	−33.3221	−	23.5093i	−1.24184	−	0.876139i
$721$	0.905746	+	4.35984i	0.0337318	+	0.162369i
$722$	−16.1068	+	20.8176i	−0.599432	+	0.774750i
$723$	−0.897911	+	1.86453i	−0.0333937	+	0.0693427i
$724$	0.596034	+	20.2746i	0.0221514	+	0.753499i
$725$	−11.2797	+	14.1443i	−0.418918	+	0.525307i
$726$	0.742035	−	0.370875i	0.0275395	−	0.0137644i
$727$	13.5677	+	17.0134i	0.503199	+	0.630992i	0.966948	−	0.254975i	$-0.0820673\pi$
$727$	13.5677	+	17.0134i	0.503199	+	0.630992i	−0.463749	+	0.885967i	$0.653496\pi$
$728$	27.2734	+	20.6766i	1.01082	+	0.766325i
$729$	−16.6175	+	20.8377i	−0.615464	+	0.771768i
$730$	−1.21662	+	5.71629i	−0.0450291	+	0.211570i
$731$	−2.58262	+	1.24372i	−0.0955217	+	0.0460008i
$732$	−0.324314	−	0.625713i	−0.0119870	−	0.0231270i
$733$	−33.1480	+	7.56581i	−1.22435	+	0.279449i	−0.785358	−	0.619042i	$-0.787521\pi$
$733$	−33.1480	+	7.56581i	−1.22435	+	0.279449i	−0.438991	+	0.898492i	$0.644664\pi$
$734$	25.2306	+	30.7016i	0.931278	+	1.13322i
$735$	−0.762457	−	1.75586i	−0.0281237	−	0.0647658i
$736$	40.0366	−	12.2915i	1.47577	−	0.453073i
$737$	0.535066	+	2.34428i	0.0197094	+	0.0863525i
$738$	−35.4532	−	7.54563i	−1.30505	−	0.277758i
$739$	3.76001	+	7.80774i	0.138314	+	0.287213i	0.958608	−	0.284731i	$-0.0919041\pi$
$739$	3.76001	+	7.80774i	0.138314	+	0.287213i	−0.820293	+	0.571943i	$0.806190\pi$
$740$	11.1180	+	21.4504i	0.408706	+	0.788534i
$741$	1.76085	+	1.40423i	0.0646865	+	0.0515858i
$742$	−10.6711	+	13.2483i	−0.391750	+	0.486360i
$743$	37.3504	−	29.7859i	1.37025	−	1.09274i	0.384760	−	0.923017i	$-0.374284\pi$
$743$	37.3504	−	29.7859i	1.37025	−	1.09274i	0.985492	−	0.169723i	$-0.0542873\pi$
$744$	−0.0404385	−	0.146981i	−0.00148255	−	0.00538860i
$745$	−24.2317	−	19.3241i	−0.887780	−	0.707981i
$746$	8.16214	−	10.5494i	0.298837	−	0.386239i
$747$	−5.36983	−	2.58597i	−0.196472	−	0.0946158i
$748$	18.0898	−	0.531805i	0.661429	−	0.0194447i
$749$	−22.7406	−	18.8746i	−0.830925	−	0.689662i
$750$	−0.276422	−	0.553058i	−0.0100935	−	0.0201948i
$751$	22.8316	+	18.2076i	0.833137	+	0.664405i	0.944187	−	0.329410i	$-0.106850\pi$
$751$	22.8316	+	18.2076i	0.833137	+	0.664405i	−0.111050	+	0.993815i	$0.535421\pi$
$752$	−29.7034	−	33.0594i	−1.08317	−	1.20555i
$753$	0.794434			0.0289508
$754$	−13.7000	+	11.2587i	−0.498925	+	0.410017i
$755$	−41.8073	−	20.1333i	−1.52152	−	0.732726i
$756$	0.591034	+	2.47706i	0.0214957	+	0.0900898i
$757$	42.1420	−	20.2945i	1.53168	−	0.737617i	0.537288	−	0.843399i	$-0.319449\pi$
$757$	42.1420	−	20.2945i	1.53168	−	0.737617i	0.994389	+	0.105782i	$0.0337345\pi$
$758$	−14.3275	+	30.9050i	−0.520398	+	1.12252i
$759$	0.254274	−	1.11405i	0.00922958	−	0.0404374i
$760$	56.9597	−	15.6711i	2.06615	−	0.568452i
$761$	9.62914	+	19.9951i	0.349056	+	0.724823i	0.999393	−	0.0348229i	$-0.0110867\pi$
$761$	9.62914	+	19.9951i	0.349056	+	0.724823i	−0.650337	+	0.759646i	$0.725372\pi$
$762$	0.132547	−	0.285910i	0.00480168	−	0.0103574i
$763$	−11.3237	+	45.4909i	−0.409947	+	1.64688i
$764$	34.5544	+	25.9324i	1.25014	+	0.938203i
$765$	47.9943			1.73524
$766$	−12.2548	−	14.9122i	−0.442785	−	0.538798i
$767$	5.65846	−

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.865405 + 1.11851i) q^{2} +(0.0500641 + 0.0627784i) q^{3} +(-0.502147 - 1.93594i) q^{4} +(-2.66268 + 2.12341i) q^{5} +(-0.113544 + 0.00166863i) q^{6} +(-2.36082 - 1.19436i) q^{7} +(2.59993 + 1.11371i) q^{8} +(0.666128 - 2.91850i) q^{9} +O(q^{10})\)	\(q+(-0.865405 + 1.11851i) q^{2} +(0.0500641 + 0.0627784i) q^{3} +(-0.502147 - 1.93594i) q^{4} +(-2.66268 + 2.12341i) q^{5} +(-0.113544 + 0.00166863i) q^{6} +(-2.36082 - 1.19436i) q^{7} +(2.59993 + 1.11371i) q^{8} +(0.666128 - 2.91850i) q^{9} +(-0.0707731 - 4.81585i) q^{10} +(-1.87399 + 0.427725i) q^{11} +(0.0963954 - 0.128445i) q^{12} +(-4.45886 + 1.01770i) q^{13} +(3.37898 - 1.60701i) q^{14} +(-0.266609 - 0.0608517i) q^{15} +(-3.49570 + 1.94425i) q^{16} +(2.04254 - 4.24138i) q^{17} +(2.68791 + 3.27076i) q^{18} -6.13285 q^{19} +(5.44785 + 4.08851i) q^{20} +(-0.0432122 - 0.208003i) q^{21} +(1.14334 - 2.46623i) q^{22} +(3.21229 + 6.67039i) q^{23} +(0.0602462 + 0.218976i) q^{24} +(1.46836 - 6.43329i) q^{25} +(2.72040 - 5.86802i) q^{26} +(0.433602 - 0.208812i) q^{27} +(-1.12673 + 5.17015i) q^{28} +(-2.47012 - 1.18955i) q^{29} +(0.298788 - 0.245544i) q^{30} -0.671221 q^{31} +(0.850526 - 5.59255i) q^{32} +(-0.120671 - 0.0962321i) q^{33} +(2.97642 + 5.95513i) q^{34} +(8.82224 - 1.83280i) q^{35} +(-5.98452 + 0.175933i) q^{36} +(3.19581 + 1.53902i) q^{37} +(5.30740 - 6.85968i) q^{38} +(-0.287118 - 0.228969i) q^{39} +(-9.28765 + 2.55528i) q^{40} +(-6.69401 + 5.33830i) q^{41} +(0.270051 + 0.131674i) q^{42} +(-0.476065 - 0.379649i) q^{43} +(1.76906 + 3.41314i) q^{44} +(4.42349 + 9.18548i) q^{45} +(-10.2409 - 2.17960i) q^{46} +(2.47240 + 10.8323i) q^{47} +(-0.297066 - 0.122117i) q^{48} +(4.14699 + 5.63937i) q^{49} +(5.92500 + 7.20978i) q^{50} +(0.368525 - 0.0841134i) q^{51} +(4.20921 + 8.12102i) q^{52} +(-4.09626 + 1.97266i) q^{53} +(-0.141683 + 0.665696i) q^{54} +(4.08158 - 5.11814i) q^{55} +(-4.80781 - 5.73454i) q^{56} +(-0.307035 - 0.385010i) q^{57} +(3.46818 - 1.73342i) q^{58} +(-1.77788 + 2.22940i) q^{59} +(0.0160718 + 0.546694i) q^{60} +(1.90411 - 3.95392i) q^{61} +(0.580878 - 0.750770i) q^{62} +(-5.05836 + 6.09446i) q^{63} +(5.51929 + 5.79115i) q^{64} +(9.71148 - 12.1778i) q^{65} +(0.212066 - 0.0516927i) q^{66} -1.25096i q^{67} +(-9.23670 - 1.82443i) q^{68} +(-0.257936 + 0.535609i) q^{69} +(-5.58480 + 11.4539i) q^{70} +(-6.71573 - 13.9454i) q^{71} +(4.98225 - 6.84602i) q^{72} +(-1.18301 - 0.270013i) q^{73} +(-4.48709 + 2.24268i) q^{74} +(0.477383 - 0.229896i) q^{75} +(3.07959 + 11.8728i) q^{76} +(4.93501 + 1.22844i) q^{77} +(0.504579 - 0.122995i) q^{78} -13.4536i q^{79} +(5.17947 - 12.5997i) q^{80} +(-8.05648 - 3.87979i) q^{81} +(-0.177925 - 12.1071i) q^{82} +(0.443031 - 1.94105i) q^{83} +(-0.380983 + 0.188104i) q^{84} +(3.56758 + 15.6306i) q^{85} +(0.836632 - 0.203935i) q^{86} +(-0.0489865 - 0.214624i) q^{87} +(-5.34860 - 0.975023i) q^{88} +(2.31111 + 0.527495i) q^{89} +(-14.1022 - 3.00142i) q^{90} +(11.7421 + 2.92288i) q^{91} +(11.3004 - 9.56830i) q^{92} +(-0.0336040 - 0.0421381i) q^{93} +(-14.2557 - 6.60891i) q^{94} +(16.3298 - 13.0226i) q^{95} +(0.393672 - 0.226591i) q^{96} -6.93563i q^{97} +(-9.89654 - 0.241882i) q^{98} +5.75414i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

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