LMFDB - Embedded newform 196.2.p.a.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(3,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("196.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.p (of order $42$, degree $12$, 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:	$312$
Relative dimension:	$26$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37261 + 0.340497i) q^{2} +(2.65756 + 1.81189i) q^{3} +(1.76812 - 0.934741i) q^{4} +(-3.39552 - 0.254459i) q^{5} +(-4.26474 - 1.58213i) q^{6} +(0.227059 + 2.63599i) q^{7} +(-2.10867 + 1.88508i) q^{8} +(2.68364 + 6.83780i) q^{9} +O(q^{10})$	\(q+(-1.37261 + 0.340497i) q^{2} +(2.65756 + 1.81189i) q^{3} +(1.76812 - 0.934741i) q^{4} +(-3.39552 - 0.254459i) q^{5} +(-4.26474 - 1.58213i) q^{6} +(0.227059 + 2.63599i) q^{7} +(-2.10867 + 1.88508i) q^{8} +(2.68364 + 6.83780i) q^{9} +(4.74738 - 0.806893i) q^{10} +(-0.627861 - 0.246417i) q^{11} +(6.39254 + 0.719520i) q^{12} +(0.189502 - 0.151122i) q^{13} +(-1.20921 - 3.54088i) q^{14} +(-8.56275 - 6.82857i) q^{15} +(2.25252 - 3.30547i) q^{16} +(2.64410 + 2.84966i) q^{17} +(-6.01185 - 8.47187i) q^{18} +(1.77502 - 3.07443i) q^{19} +(-6.24156 + 2.72402i) q^{20} +(-4.17271 + 7.41671i) q^{21} +(0.945714 + 0.124450i) q^{22} +(3.03684 - 3.27294i) q^{23} +(-9.01947 + 1.18902i) q^{24} +(6.52068 + 0.982835i) q^{25} +(-0.208655 + 0.271957i) q^{26} +(-3.11025 + 13.6269i) q^{27} +(2.86544 + 4.44851i) q^{28} +(-0.473043 - 2.07254i) q^{29} +(14.0784 + 6.45737i) q^{30} +(0.307532 + 0.532662i) q^{31} +(-1.96633 + 5.30411i) q^{32} +(-1.22210 - 1.79249i) q^{33} +(-4.59963 - 3.01117i) q^{34} +(-0.100232 - 9.00835i) q^{35} +(11.1366 + 9.58157i) q^{36} +(-1.57405 - 0.485530i) q^{37} +(-1.38958 + 4.82439i) q^{38} +(0.777429 - 0.0582603i) q^{39} +(7.63971 - 5.86426i) q^{40} +(-1.74132 - 3.61590i) q^{41} +(3.20214 - 11.6010i) q^{42} +(2.65014 - 5.50308i) q^{43} +(-1.34047 + 0.151191i) q^{44} +(-7.37242 - 23.9008i) q^{45} +(-3.05398 + 5.52651i) q^{46} +(0.966783 - 0.145719i) q^{47} +(11.9754 - 4.70317i) q^{48} +(-6.89689 + 1.19705i) q^{49} +(-9.28502 + 0.871225i) q^{50} +(1.86357 + 12.3640i) q^{51} +(0.193802 - 0.444338i) q^{52} +(8.02760 - 2.47619i) q^{53} +(-0.370758 - 19.7635i) q^{54} +(2.06922 + 0.996482i) q^{55} +(-5.44784 - 5.13041i) q^{56} +(10.2878 - 4.95433i) q^{57} +(1.35500 + 2.68372i) q^{58} +(-0.668839 - 8.92504i) q^{59} +(-21.5229 - 4.06979i) q^{60} +(-1.03159 + 3.34433i) q^{61} +(-0.603492 - 0.626423i) q^{62} +(-17.4150 + 8.62663i) q^{63} +(0.892967 - 7.95001i) q^{64} +(-0.681912 + 0.464919i) q^{65} +(2.28780 + 2.04427i) q^{66} +(10.4561 - 6.03686i) q^{67} +(7.33879 + 2.56701i) q^{68} +(14.0008 - 3.19559i) q^{69} +(3.20490 + 12.3308i) q^{70} +(9.25271 + 2.11187i) q^{71} +(-18.5487 - 9.35979i) q^{72} +(-2.30687 + 15.3051i) q^{73} +(2.32588 + 0.130484i) q^{74} +(15.5483 + 14.4267i) q^{75} +(0.264663 - 7.09516i) q^{76} +(0.506992 - 1.71099i) q^{77} +(-1.04727 + 0.344681i) q^{78} +(-8.66734 - 5.00409i) q^{79} +(-8.48959 + 10.6506i) q^{80} +(-16.8021 + 15.5901i) q^{81} +(3.62136 + 4.37030i) q^{82} +(-2.81825 + 3.53397i) q^{83} +(-0.445164 + 17.0141i) q^{84} +(-8.25299 - 10.3489i) q^{85} +(-1.76383 + 8.45595i) q^{86} +(2.49808 - 6.36499i) q^{87} +(1.78847 - 0.663955i) q^{88} +(-2.77674 + 1.08979i) q^{89} +(18.2576 + 30.2962i) q^{90} +(0.441385 + 0.465210i) q^{91} +(2.31016 - 8.62562i) q^{92} +(-0.147841 + 1.97280i) q^{93} +(-1.27740 + 0.529203i) q^{94} +(-6.80946 + 9.98764i) q^{95} +(-14.8361 + 10.5332i) q^{96} +0.505774i q^{97} +(9.05915 - 3.99146i) q^{98} -4.95449i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−1.37261	+	0.340497i	−0.970583	+	0.240768i
$2$	−1.37261	+	0.340497i	−0.970583	+	0.240768i
$3$	2.65756	+	1.81189i	1.53434	+	1.04610i	0.976336	+	0.216260i	$0.0693860\pi$
$3$	2.65756	+	1.81189i	1.53434	+	1.04610i	0.558007	+	0.829837i	$0.311566\pi$
$4$	1.76812	−	0.934741i	0.884062	−	0.467371i
$5$	−3.39552	−	0.254459i	−1.51852	−	0.113798i	−0.710815	−	0.703379i	$-0.751674\pi$
$5$	−3.39552	−	0.254459i	−1.51852	−	0.113798i	−0.807709	+	0.589581i	$0.799293\pi$
$6$	−4.26474	−	1.58213i	−1.74107	−	0.645903i
$7$	0.227059	+	2.63599i	0.0858203	+	0.996311i
$7$	0.227059	+	2.63599i	0.0858203	+	0.996311i
$8$	−2.10867	+	1.88508i	−0.745527	+	0.666475i
$9$	2.68364	+	6.83780i	0.894547	+	2.27927i
$10$	4.74738	−	0.806893i	1.50125	−	0.255162i
$11$	−0.627861	−	0.246417i	−0.189307	−	0.0742977i	0.268794	−	0.963198i	$-0.413375\pi$
$11$	−0.627861	−	0.246417i	−0.189307	−	0.0742977i	−0.458101	+	0.888900i	$0.651470\pi$
$12$	6.39254	+	0.719520i	1.84537	+	0.207708i
$13$	0.189502	−	0.151122i	0.0525583	−	0.0419138i	−0.596858	−	0.802347i	$-0.703585\pi$
$13$	0.189502	−	0.151122i	0.0525583	−	0.0419138i	0.649417	+	0.760433i	$0.275013\pi$
$14$	−1.20921	−	3.54088i	−0.323175	−	0.946339i
$15$	−8.56275	−	6.82857i	−2.21089	−	1.76313i
$16$	2.25252	−	3.30547i	0.563130	−	0.826369i
$17$	2.64410	+	2.84966i	0.641289	+	0.691145i	0.967131	−	0.254279i	$-0.0818383\pi$
$17$	2.64410	+	2.84966i	0.641289	+	0.691145i	−0.325842	+	0.945424i	$0.605648\pi$
$18$	−6.01185	−	8.47187i	−1.41701	−	1.99684i
$19$	1.77502	−	3.07443i	0.407218	−	0.705323i	−0.587358	−	0.809327i	$-0.699832\pi$
$19$	1.77502	−	3.07443i	0.407218	−	0.705323i	0.994577	+	0.104004i	$0.0331654\pi$
$20$	−6.24156	+	2.72402i	−1.39566	+	0.609110i
$21$	−4.17271	+	7.41671i	−0.910560	+	1.61846i
$22$	0.945714	+	0.124450i	0.201627	+	0.0265329i
$23$	3.03684	−	3.27294i	0.633225	−	0.682455i	−0.332178	−	0.943217i	$-0.607783\pi$
$23$	3.03684	−	3.27294i	0.633225	−	0.682455i	0.965403	+	0.260762i	$0.0839738\pi$
$24$	−9.01947	+	1.18902i	−1.84109	+	0.242708i
$25$	6.52068	+	0.982835i	1.30414	+	0.196567i
$26$	−0.208655	+	0.271957i	−0.0409206	+	0.0533352i
$27$	−3.11025	+	13.6269i	−0.598568	+	2.62250i
$28$	2.86544	+	4.44851i	0.541517	+	0.840690i
$29$	−0.473043	−	2.07254i	−0.0878419	−	0.384861i	0.911827	−	0.410574i	$-0.134672\pi$
$29$	−0.473043	−	2.07254i	−0.0878419	−	0.384861i	−0.999669	+	0.0257130i	$0.991814\pi$
$30$	14.0784	+	6.45737i	2.57036	+	1.17895i
$31$	0.307532	+	0.532662i	0.0552344	+	0.0956688i	0.892321	−	0.451402i	$-0.149076\pi$
$31$	0.307532	+	0.532662i	0.0552344	+	0.0956688i	−0.837086	+	0.547071i	$0.815743\pi$
$32$	−1.96633	+	5.30411i	−0.347601	+	0.937643i
$33$	−1.22210	−	1.79249i	−0.212740	−	0.312032i
$34$	−4.59963	−	3.01117i	−0.788829	−	0.516411i
$35$	−0.100232	−	9.00835i	−0.0169423	−	1.52269i
$36$	11.1366	+	9.58157i	1.85610	+	1.59693i
$37$	−1.57405	−	0.485530i	−0.258772	−	0.0798207i	0.162655	−	0.986683i	$-0.447994\pi$
$37$	−1.57405	−	0.485530i	−0.258772	−	0.0798207i	−0.421427	+	0.906862i	$0.638471\pi$
$38$	−1.38958	+	4.82439i	−0.225420	+	0.782620i
$39$	0.777429	−	0.0582603i	0.124488	−	0.00932911i
$40$	7.63971	−	5.86426i	1.20794	−	0.927220i
$41$	−1.74132	−	3.61590i	−0.271949	−	0.564708i	0.719608	−	0.694381i	$-0.244322\pi$
$41$	−1.74132	−	3.61590i	−0.271949	−	0.564708i	−0.991557	+	0.129673i	$0.958607\pi$
$42$	3.20214	−	11.6010i	0.494101	−	1.79008i
$43$	2.65014	−	5.50308i	0.404143	−	0.839211i	−0.595222	−	0.803562i	$-0.702936\pi$
$43$	2.65014	−	5.50308i	0.404143	−	0.839211i	0.999364	−	0.0356496i	$-0.0113500\pi$
$44$	−1.34047	+	0.151191i	−0.202084	+	0.0227930i
$45$	−7.37242	−	23.9008i	−1.09902	−	3.56292i
$46$	−3.05398	+	5.52651i	−0.450284	+	0.814839i
$47$	0.966783	−	0.145719i	0.141020	−	0.0212553i	−0.0781529	−	0.996941i	$-0.524902\pi$
$47$	0.966783	−	0.145719i	0.141020	−	0.0212553i	0.219173	+	0.975686i	$0.429664\pi$
$48$	11.9754	−	4.70317i	1.72850	−	0.678844i
$49$	−6.89689	+	1.19705i	−0.985270	+	0.171007i
$50$	−9.28502	+	0.871225i	−1.31310	+	0.123210i
$51$	1.86357	+	12.3640i	0.260952	+	1.73130i
$52$	0.193802	−	0.444338i	0.0268755	−	0.0616186i
$53$	8.02760	−	2.47619i	1.10268	−	0.340130i	0.310592	−	0.950543i	$-0.399473\pi$
$53$	8.02760	−	2.47619i	1.10268	−	0.340130i	0.792083	+	0.610413i	$0.208997\pi$
$54$	−0.370758	−	19.7635i	−0.0504538	−	2.68947i
$55$	2.06922	+	0.996482i	0.279013	+	0.134366i
$56$	−5.44784	−	5.13041i	−0.727998	−	0.685579i
$57$	10.2878	−	4.95433i	1.36265	−	0.656217i
$58$	1.35500	+	2.68372i	0.177920	+	0.352389i
$59$	−0.668839	−	8.92504i	−0.0870754	−	1.16194i	−0.854024	−	0.520233i	$-0.825845\pi$
$59$	−0.668839	−	8.92504i	−0.0870754	−	1.16194i	0.766949	−	0.641708i	$-0.221774\pi$
$60$	−21.5229	−	4.06979i	−2.77860	−	0.525408i
$61$	−1.03159	+	3.34433i	−0.132082	+	0.428198i	−0.997320	−	0.0731626i	$-0.976691\pi$
$61$	−1.03159	+	3.34433i	−0.132082	+	0.428198i	0.865238	+	0.501361i	$0.167167\pi$
$62$	−0.603492	−	0.626423i	−0.0766436	−	0.0795558i
$63$	−17.4150	+	8.62663i	−2.19409	+	1.08685i
$64$	0.892967	−	7.95001i	0.111621	−	0.993751i
$65$	−0.681912	+	0.464919i	−0.0845807	+	0.0576662i
$66$	2.28780	+	2.04427i	0.281609	+	0.251632i
$67$	10.4561	−	6.03686i	1.27742	−	0.737520i	0.301048	−	0.953609i	$-0.402664\pi$
$67$	10.4561	−	6.03686i	1.27742	−	0.737520i	0.976374	+	0.216089i	$0.0693303\pi$
$68$	7.33879	+	2.56701i	0.889959	+	0.311295i
$69$	14.0008	−	3.19559i	1.68550	−	0.384704i
$70$	3.20490	+	12.3308i	0.383059	+	1.47382i
$71$	9.25271	+	2.11187i	1.09809	+	0.250633i	0.732926	−	0.680309i	$-0.238154\pi$
$71$	9.25271	+	2.11187i	1.09809	+	0.250633i	0.365169	+	0.930941i	$0.381011\pi$
$72$	−18.5487	−	9.35979i	−2.18598	−	1.10306i
$73$	−2.30687	+	15.3051i	−0.269999	+	1.79133i	0.284015	+	0.958820i	$0.408333\pi$
$73$	−2.30687	+	15.3051i	−0.269999	+	1.79133i	−0.554014	+	0.832507i	$0.686905\pi$
$74$	2.32588	+	0.130484i	0.270378	+	0.0151685i
$75$	15.5483	+	14.4267i	1.79536	+	1.66585i
$76$	0.264663	−	7.09516i	0.0303590	−	0.813871i
$77$	0.506992	−	1.71099i	0.0577771	−	0.194985i
$78$	−1.04727	+	0.344681i	−0.118580	+	0.0390275i
$79$	−8.66734	−	5.00409i	−0.975152	−	0.563004i	−0.0743489	−	0.997232i	$-0.523688\pi$
$79$	−8.66734	−	5.00409i	−0.975152	−	0.563004i	−0.900803	+	0.434228i	$0.857021\pi$
$80$	−8.48959	+	10.6506i	−0.949165	+	1.19078i
$81$	−16.8021	+	15.5901i	−1.86690	+	1.73223i
$82$	3.62136	+	4.37030i	0.399913	+	0.482619i
$83$	−2.81825	+	3.53397i	−0.309343	+	0.387904i	−0.912064	−	0.410048i	$-0.865512\pi$
$83$	−2.81825	+	3.53397i	−0.309343	+	0.387904i	0.602721	+	0.797952i	$0.294083\pi$
$84$	−0.445164	+	17.0141i	−0.0485714	+	1.85639i
$85$	−8.25299	−	10.3489i	−0.895162	−	1.12250i
$86$	−1.76383	+	8.45595i	−0.190199	+	0.911829i
$87$	2.49808	−	6.36499i	0.267822	−	0.682399i
$88$	1.78847	−	0.663955i	0.190651	−	0.0707778i
$89$	−2.77674	+	1.08979i	−0.294334	+	0.115518i	−0.507914	−	0.861408i	$-0.669583\pi$
$89$	−2.77674	+	1.08979i	−0.294334	+	0.115518i	0.213579	+	0.976926i	$0.431488\pi$
$90$	18.2576	+	30.2962i	1.92452	+	3.19350i
$91$	0.441385	+	0.465210i	0.0462697	+	0.0487673i
$92$	2.31016	−	8.62562i	0.240851	−	0.899283i
$93$	−0.147841	+	1.97280i	−0.0153304	+	0.204569i
$94$	−1.27740	+	0.529203i	−0.131754	+	0.0545831i
$95$	−6.80946	+	9.98764i	−0.698635	+	1.02471i
$96$	−14.8361	+	10.5332i	−1.51420	+	1.07504i
$97$			0.505774i			0.0513536i	0.999670	+	0.0256768i	$0.00817408\pi$
$97$			0.505774i			0.0513536i	−0.999670	+	0.0256768i	$0.991826\pi$
$98$	9.05915	−	3.99146i	0.915113	−	0.403198i
$99$		−	4.95449i		−	0.497945i
$100$	12.4481	−	4.35738i	1.24481	−	0.435738i
$101$	−8.26027	+	12.1156i	−0.821928	+	1.20555i	0.154133	+	0.988050i	$0.450742\pi$
$101$	−8.26027	+	12.1156i	−0.821928	+	1.20555i	−0.976061	+	0.217497i	$0.930211\pi$
$102$	−6.76786	−	16.3364i	−0.670118	−	1.61754i
$103$	0.589038	−	7.86017i	0.0580396	−	0.774485i	−0.889924	−	0.456108i	$-0.849243\pi$
$103$	0.589038	−	7.86017i	0.0580396	−	0.774485i	0.947964	−	0.318377i	$-0.103138\pi$
$104$	−0.114718	+	0.675892i	−0.0112491	+	0.0662767i
$105$	16.0558	−	24.1218i	1.56688	−	2.35405i
$106$	−10.1756	+	6.13221i	−0.988345	+	0.595613i
$107$	11.3299	−	4.44666i	1.09530	−	0.429875i	0.252226	−	0.967668i	$-0.418837\pi$
$107$	11.3299	−	4.44666i	1.09530	−	0.429875i	0.843077	+	0.537794i	$0.180742\pi$
$108$	7.23831	+	27.0013i	0.696507	+	2.59820i
$109$	2.95401	−	7.52669i	0.282943	−	0.720926i	−0.716778	−	0.697301i	$-0.754384\pi$
$109$	2.95401	−	7.52669i	0.282943	−	0.720926i	0.999721	−	0.0236247i	$-0.00752069\pi$
$110$	−3.17953	−	0.663220i	−0.303156	−	0.0632355i
$111$	−3.30340	−	4.14234i	−0.313545	−	0.393173i
$112$	9.22465	+	5.18708i	0.871648	+	0.490133i
$113$	−2.95648	+	3.70731i	−0.278123	+	0.348755i	−0.901198	−	0.433407i	$-0.857311\pi$
$113$	−2.95648	+	3.70731i	−0.278123	+	0.348755i	0.623076	+	0.782161i	$0.285883\pi$
$114$	−12.4342	+	10.3033i	−1.16457	+	0.964995i
$115$	−11.1445	+	10.3406i	−1.03923	+	0.964265i
$116$	−2.77368	−	3.22233i	−0.257530	−	0.299186i
$117$	1.54190	+	0.890216i	0.142549	+	0.0823005i
$118$	3.95701	+	12.0229i	0.364272	+	1.10679i
$119$	−6.91132	+	7.61687i	−0.633559	+	0.698237i
$120$	30.9284	−	1.74226i	2.82336	−	0.159046i
$121$	−7.73008	−	7.17247i	−0.702735	−	0.652043i
$122$	0.277236	−	4.94172i	0.0250997	−	0.447403i
$123$	1.92395	−	12.7645i	0.173476	−	1.15094i
$124$	1.04166	+	0.654348i	0.0935434	+	0.0587622i
$125$	−5.29268	−	1.20802i	−0.473392	−	0.108049i
$126$	20.9667	−	17.7708i	1.86786	−	1.58315i
$127$	−16.9020	+	3.85776i	−1.49981	+	0.342321i	−0.892099	−	0.451840i	$-0.850768\pi$
$127$	−16.9020	+	3.85776i	−1.49981	+	0.342321i	−0.607707	+	0.794161i	$0.707911\pi$
$128$	1.48126	+	11.2163i	0.130926	+	0.991392i
$129$	17.0139	−	9.82297i	1.49799	−	0.864865i
$130$	0.777696	−	0.870343i	0.0682084	−	0.0763341i
$131$	−14.8851	+	10.1485i	−1.30052	+	0.886679i	−0.997793	−	0.0663981i	$-0.978849\pi$
$131$	−14.8851	+	10.1485i	−1.30052	+	0.886679i	−0.302727	+	0.953077i	$0.597897\pi$
$132$	−3.83633	−	2.02699i	−0.333910	−	0.176427i
$133$	8.50721	+	3.98087i	0.737668	+	0.345185i
$134$	−12.2967	+	11.8465i	−1.06227	+	1.02339i
$135$	14.0284	−	45.4790i	1.20737	−	3.91421i
$136$	−10.9474	−	1.02466i	−0.938729	−	0.0878639i
$137$	−0.775646	−	10.3503i	−0.0662679	−	0.884284i	−0.926960	−	0.375159i	$-0.877588\pi$
$137$	−0.775646	−	10.3503i	−0.0662679	−	0.884284i	0.860692	−	0.509125i	$-0.170031\pi$
$138$	−18.1296	+	9.15354i	−1.54329	+	0.779201i
$139$	3.69058	−	1.77729i	0.313031	−	0.150748i	−0.270771	−	0.962644i	$-0.587279\pi$
$139$	3.69058	−	1.77729i	0.313031	−	0.150748i	0.583802	+	0.811896i	$0.301564\pi$
$140$	−8.59769	−	15.8342i	−0.726638	−	1.33823i
$141$	2.83331	+	1.36445i	0.238608	+	0.114907i
$142$	−13.4195	+	0.251746i	−1.12614	+	0.0211261i
$143$	−0.156220	+	0.0481875i	−0.0130638	+	0.00402964i
$144$	28.6471	+	6.53157i	2.38726	+	0.544298i
$145$	1.07885	+	7.15772i	0.0895939	+	0.594417i
$146$	−2.04491	−	21.7934i	−0.169238	−	1.80364i
$147$	−20.4978	−	9.31519i	−1.69063	−	0.768304i
$148$	−3.23696	+	0.612852i	−0.266076	+	0.0503761i
$149$	−1.13436	+	0.170977i	−0.0929304	+	0.0140070i	−0.195343	−	0.980735i	$-0.562582\pi$
$149$	−1.13436	+	0.170977i	−0.0929304	+	0.0140070i	0.102412	+	0.994742i	$0.467344\pi$
$150$	−26.2540	−	14.5081i	−2.14363	−	1.18458i
$151$	4.79256	+	15.5371i	0.390013	+	1.26439i	0.911560	+	0.411167i	$0.134879\pi$
$151$	4.79256	+	15.5371i	0.390013	+	1.26439i	−0.521547	+	0.853222i	$0.674645\pi$
$152$	2.05260	+	9.82902i	0.166488	+	0.797239i
$153$	−12.3896	+	25.7273i	−1.00164	+	2.07993i
$154$	−0.113317	+	2.52115i	−0.00913131	+	0.203160i
$155$	−0.908693	−	1.88692i	−0.0729880	−	0.151561i
$156$	1.32013	−	0.829706i	0.105695	−	0.0664297i
$157$	−10.0765	+	0.755133i	−0.804196	+	0.0602661i	−0.470483	−	0.882409i	$-0.655920\pi$
$157$	−10.0765	+	0.755133i	−0.804196	+	0.0602661i	−0.333712	+	0.942675i	$0.608301\pi$
$158$	13.6008	+	3.91746i	1.08202	+	0.311657i
$159$	25.8204	+	7.96454i	2.04769	+	0.631629i
$160$	8.02639	−	17.5099i	0.634542	−	1.38428i
$161$	9.31697	+	7.26194i	0.734280	+	0.572321i
$162$	17.7544	−	27.1202i	1.39491	−	2.13076i
$163$	−7.35734	−	10.7912i	−0.576271	−	0.845234i	0.421840	−	0.906670i	$-0.361384\pi$
$163$	−7.35734	−	10.7912i	−0.576271	−	0.845234i	−0.998111	+	0.0614359i	$0.980432\pi$
$164$	−6.45880	−	4.76566i	−0.504348	−	0.372136i
$165$	3.69354	+	6.39741i	0.287542	+	0.498037i
$166$	2.66505	−	5.81038i	0.206848	−	0.450973i
$167$	4.07562	+	17.8565i	0.315381	+	1.38177i	0.845556	+	0.533886i	$0.179269\pi$
$167$	4.07562	+	17.8565i	0.315381	+	1.38177i	−0.530175	+	0.847888i	$0.677874\pi$
$168$	−5.18220	−	23.5053i	−0.399816	−	1.81347i
$169$	−2.87970	+	12.6168i	−0.221515	+	0.970522i
$170$	14.8519	+	11.3949i	1.13909	+	0.873950i
$171$	25.7859	+	3.88660i	1.97190	+	0.297215i
$172$	−0.458174	−	12.2073i	−0.0349355	−	0.930799i
$173$	3.27596	−	3.53065i	0.249067	−	0.268430i	−0.596127	−	0.802890i	$-0.703295\pi$
$173$	3.27596	−	3.53065i	0.249067	−	0.268430i	0.845194	+	0.534460i	$0.179485\pi$
$174$	−1.26162	+	9.58725i	−0.0956434	+	0.726808i
$175$	−1.11016	+	17.4116i	−0.0839204	+	1.31619i
$176$	−2.22880	+	1.52032i	−0.168002	+	0.114598i
$177$	14.3937	−	24.9307i	1.08190	−	1.87390i
$178$	3.44032	−	2.44133i	0.257863	−	0.182986i
$179$	−8.23288	−	8.87294i	−0.615355	−	0.663194i	0.346087	−	0.938202i	$-0.387510\pi$
$179$	−8.23288	−	8.87294i	−0.615355	−	0.663194i	−0.961442	+	0.275008i	$0.911320\pi$
$180$	−35.3764	−	35.3683i	−2.63680	−	2.63619i
$181$	−3.23146	−	2.57700i	−0.240192	−	0.191547i	0.495994	−	0.868326i	$-0.334804\pi$
$181$	−3.23146	−	2.57700i	−0.240192	−	0.191547i	−0.736186	+	0.676779i	$0.763375\pi$
$182$	−0.764253	−	0.488263i	−0.0566502	−	0.0361924i
$183$	−8.80109	+	7.01863i	−0.650595	+	0.518832i
$184$	−0.233954	+	12.6262i	−0.0172473	+	0.930818i
$185$	5.22118	+	2.04916i	0.383869	+	0.150657i
$186$	−0.468804	−	2.75822i	−0.0343744	−	0.202243i
$187$	−0.957922	−	2.44075i	−0.0700502	−	0.178485i
$188$	1.57318	−	1.16134i	0.114736	−	0.0846995i
$189$	−36.6266	−	5.10448i	−2.66419	−	0.371296i
$190$	5.94597	−	16.0277i	0.431366	−	1.16277i
$191$	12.5274	+	0.938797i	0.906449	+	0.0679290i	0.519790	−	0.854294i	$-0.326010\pi$
$191$	12.5274	+	0.938797i	0.906449	+	0.0679290i	0.386659	+	0.922223i	$0.373629\pi$
$192$	16.7777	−	19.5096i	1.21082	−	1.40799i
$193$	−13.3522	−	9.10336i	−0.961110	−	0.655274i	−0.0223156	−	0.999751i	$-0.507104\pi$
$193$	−13.3522	−	9.10336i	−0.961110	−	0.655274i	−0.938795	+	0.344477i	$0.888056\pi$
$194$	−0.172215	−	0.694231i	−0.0123643	−	0.0498429i
$195$	−2.65460			−0.190100
$196$	−11.0756	+	8.56334i	−0.791115	+	0.611667i
$197$	−12.3209			−0.877830			−0.438915	−	0.898529i	$-0.644637\pi$
$197$	−12.3209			−0.877830			−0.438915	+	0.898529i	$0.644637\pi$
$198$	1.68699	+	6.80059i	0.119889	+	0.483297i
$199$	19.1900	+	13.0835i	1.36034	+	0.927465i	0.999986	−	0.00534932i	$-0.00170275\pi$
$199$	19.1900	+	13.0835i	1.36034	+	0.927465i	0.360356	+	0.932815i	$0.382655\pi$
$200$	−15.6027	+	10.2195i	−1.10328	+	0.722629i
$201$	38.7260	+	2.90211i	2.73152	+	0.204699i
$202$	7.21282	−	19.4426i	0.507492	−	1.36798i
$203$	5.35578	−	1.71753i	0.375902	−	0.120547i
$204$	14.8521	+	20.1191i	1.03986	+	1.40862i
$205$	4.99261	+	12.7210i	0.348699	+	0.888470i
$206$	1.86785	+	10.9895i	0.130139	+	0.765676i
$207$	30.5295	+	11.9819i	2.12195	+	0.832803i
$208$	−0.0726756	−	0.966798i	−0.00503915	−	0.0670354i
$209$	−1.87206	+	1.49292i	−0.129493	+	0.103267i
$210$	−13.8249	+	38.5768i	−0.954011	+	2.66205i
$211$	−2.11473	−	1.68644i	−0.145584	−	0.116099i	0.547990	−	0.836485i	$-0.315393\pi$
$211$	−2.11473	−	1.68644i	−0.145584	−	0.116099i	−0.693573	+	0.720386i	$0.743965\pi$
$212$	11.8792	−	11.8819i	0.815866	−	0.816054i
$213$	20.7631	+	22.3773i	1.42267	+	1.53327i
$214$	−14.0375	+	9.96134i	−0.959582	+	0.680943i
$215$	−10.3989	+	18.0115i	−0.709201	+	1.22837i
$216$	−19.1293	−	34.5977i	−1.30158	−	2.35407i
$217$	−1.33426	+	0.931598i	−0.0905757	+	0.0632410i
$218$	−1.49189	+	11.3370i	−0.101043	+	0.767842i
$219$	−33.8619	+	36.4944i	−2.28817	+	2.46606i
$220$	4.59008	−	0.172278i	0.309463	−	0.0116150i
$221$	0.931709	+	0.140433i	0.0626735	+	0.00944652i
$222$	5.94474	+	4.56102i	0.398985	+	0.306115i
$223$	5.19736	−	22.7711i	0.348041	−	1.52487i	−0.433580	−	0.901115i	$-0.642750\pi$
$223$	5.19736	−	22.7711i	0.348041	−	1.52487i	0.781622	−	0.623753i	$-0.214393\pi$
$224$	−14.4280	−	3.97887i	−0.964015	−	0.265850i
$225$	10.7787	+	47.2247i	0.718582	+	3.14831i
$226$	2.79577	−	6.09538i	0.185972	−	0.405458i
$227$	−6.29043	−	10.8953i	−0.417510	−	0.723149i	0.578178	−	0.815911i	$-0.303764\pi$
$227$	−6.29043	−	10.8953i	−0.417510	−	0.723149i	−0.995688	+	0.0927617i	$0.970431\pi$
$228$	13.5590	−	18.3763i	0.897969	−	1.21700i
$229$	−10.4862	−	15.3804i	−0.692945	−	1.01636i	−0.997949	−	0.0640123i	$-0.979610\pi$
$229$	−10.4862	−	15.3804i	−0.692945	−	1.01636i	0.305004	−	0.952351i	$-0.401342\pi$
$230$	11.7761	−	17.9883i	0.776495	−	1.18611i
$231$	4.44749	−	3.62844i	0.292623	−	0.238734i
$232$	4.90439	+	3.47857i	0.321989	+	0.228379i
$233$	−9.37817	−	2.89278i	−0.614384	−	0.189512i	−0.0280831	−	0.999606i	$-0.508940\pi$
$233$	−9.37817	−	2.89278i	−0.614384	−	0.189512i	−0.586301	+	0.810093i	$0.699417\pi$
$234$	−2.41954	−	0.696908i	−0.158171	−	0.0455583i
$235$	−3.31982	+	0.248786i	−0.216561	+	0.0162290i
$236$	−9.52519	−	15.1554i	−0.620037	−	0.986531i
$237$	−13.9671	−	29.0030i	−0.907260	−	1.88394i
$238$	6.89303	−	12.8083i	0.446809	−	0.830237i
$239$	9.96381	−	20.6901i	0.644505	−	1.33833i	−0.281042	−	0.959696i	$-0.590680\pi$
$239$	9.96381	−	20.6901i	0.644505	−	1.33833i	0.925547	−	0.378633i	$-0.123606\pi$
$240$	−41.8594	+	12.9225i	−2.70201	+	0.834143i
$241$	4.93235	+	15.9903i	0.317721	+	1.03002i	0.963771	+	0.266730i	$0.0859433\pi$
$241$	4.93235	+	15.9903i	0.317721	+	1.03002i	−0.646051	+	0.763295i	$0.723580\pi$
$242$	13.0526	+	7.21294i	0.839053	+	0.463665i
$243$	−31.4364	+	4.73827i	−2.01665	+	0.303960i
$244$	1.30211	+	6.87746i	0.0833589	+	0.440284i
$245$	23.7232	−	2.30964i	1.51562	−	0.147557i
$246$	1.70546	+	18.1759i	0.108736	+	1.15885i
$247$	−0.128246	−	0.850855i	−0.00816009	−	0.0541386i
$248$	−1.65259	−	0.543485i	−0.104940	−	0.0345113i
$249$	−13.8928	+	4.28538i	−0.880423	+	0.271575i
$250$	7.67612	−	0.144002i	0.485480	−	0.00910750i
$251$	−16.3020	−	7.85061i	−1.02897	−	0.495526i	−0.158299	−	0.987391i	$-0.550601\pi$
$251$	−16.3020	−	7.85061i	−1.02897	−	0.495526i	−0.870671	+	0.491865i	$0.836315\pi$
$252$	−22.7283	+	31.5315i	−1.43175	+	1.98630i
$253$	−2.71323	+	1.30662i	−0.170579	+	0.0821465i
$254$	21.8863	−	11.0503i	1.37327	−	0.693356i
$255$	−3.18167	−	42.4564i	−0.199244	−	2.65872i
$256$	−5.85232	−	14.8913i	−0.365770	−	0.930705i
$257$	3.62939	−	11.7662i	0.226395	−	0.733955i	−0.769099	−	0.639130i	$-0.779295\pi$
$257$	3.62939	−	11.7662i	0.226395	−	0.733955i	0.995494	−	0.0948249i	$-0.0302291\pi$
$258$	−20.0088	+	19.2763i	−1.24569	+	1.20009i
$259$	0.922450	−	4.25942i	0.0573183	−	0.264668i
$260$	−0.771124	+	1.45945i	−0.0478231	+	0.0905110i
$261$	12.9021	−	8.79652i	0.798622	−	0.544491i
$262$	16.9760	−	18.9983i	1.04878	−	1.17372i
$263$	18.2754	−	10.5513i	1.12691	−	0.650621i	0.183753	−	0.982972i	$-0.441175\pi$
$263$	18.2754	−	10.5513i	1.12691	−	0.650621i	0.943156	+	0.332352i	$0.107842\pi$
$264$	5.95597	+	1.47601i	0.366565	+	0.0908424i
$265$	−27.8880	+	6.36525i	−1.71315	+	0.391014i
$266$	−13.0326	−	2.56750i	−0.799078	−	0.157424i
$267$	−9.35394	−	2.13498i	−0.572452	−	0.130658i
$268$	12.8449	−	20.4477i	0.784624	−	1.24904i
$269$	1.10135	−	7.30698i	0.0671505	−	0.445514i	−0.929838	−	0.367968i	$-0.880053\pi$
$269$	1.10135	−	7.30698i	0.0671505	−	0.445514i	0.996989	−	0.0775458i	$-0.0247084\pi$
$270$	−3.77008	+	67.2017i	−0.229440	+	4.08976i
$271$	−6.43200	−	5.96802i	−0.390716	−	0.362532i	0.460216	−	0.887807i	$-0.347772\pi$
$271$	−6.43200	−	5.96802i	−0.390716	−	0.362532i	−0.850932	+	0.525275i	$0.823962\pi$
$272$	15.3754	−	2.32109i	0.932269	−	0.140737i
$273$	0.330096	+	2.03607i	0.0199783	+	0.123228i
$274$	4.58890	+	13.9428i	0.277226	+	0.842316i
$275$	−3.85190	−	2.22389i	−0.232278	−	0.134106i
$276$	21.7681	−	18.7373i	1.31028	−	1.12785i
$277$	−1.60865	+	1.49261i	−0.0966543	+	0.0896821i	−0.727020	−	0.686616i	$-0.759095\pi$
$277$	−1.60865	+	1.49261i	−0.0966543	+	0.0896821i	0.630366	+	0.776298i	$0.282905\pi$
$278$	−4.46057	+	3.69616i	−0.267527	+	0.221681i
$279$	−2.81693	+	3.53232i	−0.168645	+	0.211474i
$280$	17.1928	+	18.8067i	1.02747	+	1.12391i
$281$	4.52931	+	5.67958i	0.270196	+	0.338815i	0.898355	−	0.439270i	$-0.144763\pi$
$281$	4.52931	+	5.67958i	0.270196	+	0.338815i	−0.628159	+	0.778085i	$0.716191\pi$
$282$	−4.35363	−	0.908125i	−0.259255	−	0.0540781i
$283$	2.74748	−	7.00048i	0.163321	−	0.416135i	−0.825662	−	0.564165i	$-0.809198\pi$
$283$	2.74748	−	7.00048i	0.163321	−	0.416135i	0.988983	+	0.148030i	$0.0472933\pi$
$284$	18.3340	−	4.91484i	1.08792	−	0.291642i
$285$	−36.1931	+	14.2047i	−2.14389	+	0.841416i
$286$	0.198021	−	0.119335i	0.0117093	−	0.00705643i
$287$	9.13608	−	5.41113i	0.539286	−	0.319409i
$288$	−41.5454	+	0.788961i	−2.44808	+	0.0464900i
$289$	0.141102	−	1.88287i	0.00830010	−	0.110757i
$290$	−3.91803	−	9.45742i	−0.230075	−	0.555359i
$291$	−0.916409	+	1.34412i	−0.0537208	+	0.0787940i
$292$	10.2275	+	29.2176i	0.598518	+	1.70983i
$293$			2.59792i			0.151772i	0.997116	+	0.0758861i	$0.0241785\pi$
$293$			2.59792i			0.151772i	−0.997116	+	0.0758861i	$0.975821\pi$
$294$	31.3073	+	5.80668i	1.82588	+	0.338653i
$295$			30.4754i			1.77435i
$296$	4.23441	−	1.94338i	0.246120	−	0.112957i
$297$	5.31071	−	7.78938i	0.308159	−	0.451986i
$298$	1.49882	−	0.620932i	0.0868242	−	0.0359696i
$299$	0.0808720	−	1.07916i	0.00467695	−	0.0624095i
$300$	40.9766	+	10.9746i	2.36578	+	0.633618i
$301$	15.1078	+	5.73622i	0.870799	+	0.330630i
$302$	−11.8687	−	19.6945i	−0.682964	−	1.13329i
$303$	−43.9043	+	17.2312i	−2.52224	+	0.989905i
$304$	−6.16418	−	12.7925i	−0.353540	−	0.733701i
$305$	4.35379	−	11.0933i	0.249297	−	0.635199i
$306$	8.24605	−	39.5322i	0.471395	−	2.25991i
$307$	17.9504	+	22.5091i	1.02448	+	1.28466i	0.957968	+	0.286877i	$0.0926170\pi$
$307$	17.9504	+	22.5091i	1.02448	+	1.28466i	0.0665162	+	0.997785i	$0.478812\pi$
$308$	−0.702906	−	3.49914i	−0.0400518	−	0.199382i
$309$	15.8072	−	19.8216i	0.899239	−	1.12761i
$310$	1.88977	+	2.28060i	0.107332	+	0.129529i
$311$	−10.2240	+	9.48651i	−0.579751	+	0.537931i	−0.914610	−	0.404338i	$-0.867502\pi$
$311$	−10.2240	+	9.48651i	−0.579751	+	0.537931i	0.334858	+	0.942268i	$0.391311\pi$
$312$	−1.52952	+	1.58837i	−0.0865917	+	0.0899235i
$313$	−1.22219	−	0.705631i	−0.0690822	−	0.0398846i	0.465061	−	0.885279i	$-0.346032\pi$
$313$	−1.22219	−	0.705631i	−0.0690822	−	0.0398846i	−0.534143	+	0.845394i	$0.679366\pi$
$314$	13.5741	−	4.46754i	0.766028	−	0.252118i
$315$	61.3283	−	24.8605i	3.45546	−	1.40073i
$316$	−20.0025	−	0.746130i	−1.12523	−	0.0419731i
$317$	20.7844	+	19.2851i	1.16737	+	1.08316i	0.995177	+	0.0980937i	$0.0312745\pi$
$317$	20.7844	+	19.2851i	1.16737	+	1.08316i	0.172189	+	0.985064i	$0.444916\pi$
$318$	−38.1533	−	2.14044i	−2.13953	−	0.120030i
$319$	−0.213704	+	1.41783i	−0.0119651	+	0.0793834i
$320$	−5.05505	+	26.7672i	−0.282586	+	1.49633i
$321$	38.1667	+	8.71131i	2.13026	+	0.486218i
$322$	−15.2613	−	6.79541i	−0.850476	−	0.378693i
$323$	13.4544	−	3.07089i	0.748625	−	0.170869i
$324$	−15.1355	+	43.2708i	−0.840861	+	2.40393i
$325$	1.38421	−	0.799173i	0.0767820	−	0.0443301i
$326$	13.7731	+	12.3070i	0.762824	+	0.681622i
$327$	21.4880	−	14.6503i	1.18829	−	0.810162i
$328$	10.4881	+	4.34220i	0.579109	+	0.239758i
$329$	0.603631	+	2.51534i	0.0332793	+	0.138675i
$330$	−7.24810	−	7.52351i	−0.398995	−	0.414156i
$331$	−0.760439	+	2.46528i	−0.0417975	+	0.135504i	−0.974067	−	0.226261i	$-0.927350\pi$
$331$	−0.760439	+	2.46528i	−0.0417975	+	0.135504i	0.932269	+	0.361765i	$0.117826\pi$
$332$	−1.67966	+	8.88283i	−0.0921835	+	0.487509i
$333$	−0.904224	−	12.0660i	−0.0495512	−	0.661214i
$334$	−11.6743	−	23.1222i	−0.638790	−	1.26519i
$335$	−37.0402	+	17.8376i	−2.02372	+	0.974574i
$336$	15.1166	+	30.4990i	0.824680	+	1.66386i
$337$	−13.1567	−	6.33592i	−0.716690	−	0.345140i	0.0397439	−	0.999210i	$-0.487346\pi$
$337$	−13.1567	−	6.33592i	−0.716690	−	0.345140i	−0.756434	+	0.654070i	$0.773060\pi$
$338$	−0.343275	−	18.2985i	−0.0186717	−	0.995306i
$339$	−14.5743	+	4.49557i	−0.791567	+	0.244166i
$340$	−24.2659	−	10.5838i	−1.31600	−	0.573985i
$341$	−0.0618306	−	0.410219i	−0.00334831	−	0.0222146i
$342$	−36.7174	+	3.44524i	−1.98545	+	0.186297i
$343$	−4.72142	−	17.9083i	−0.254932	−	0.966959i
$344$	4.78545	+	16.5999i	0.258014	+	0.895006i
$345$	−48.3532	+	7.28807i	−2.60325	+	0.392377i
$346$	−3.29445	+	5.96166i	−0.177111	+	0.320501i
$347$	4.61601	+	14.9647i	0.247800	+	0.803349i	0.990951	+	0.134225i	$0.0428544\pi$
$347$	4.61601	+	14.9647i	0.247800	+	0.803349i	−0.743151	+	0.669124i	$0.766669\pi$
$348$	−1.53272	−	13.5891i	−0.0821622	−	0.728455i
$349$	−8.96500	+	18.6160i	−0.479886	+	0.996493i	0.510720	+	0.859747i	$0.329379\pi$
$349$	−8.96500	+	18.6160i	−0.479886	+	0.996493i	−0.990606	+	0.136746i	$0.956336\pi$
$350$	−4.40479	−	24.2774i	−0.235446	−	1.29768i
$351$	1.46993	+	3.05235i	0.0784592	+	0.162922i
$352$	2.54161	−	2.84571i	0.135468	−	0.151677i
$353$	21.0334	−	1.57623i	1.11949	−	0.0838945i	0.497901	−	0.867234i	$-0.334104\pi$
$353$	21.0334	−	1.57623i	1.11949	−	0.0838945i	0.621594	+	0.783340i	$0.286485\pi$
$354$	−11.2682	+	39.1212i	−0.598896	+	2.07927i
$355$	−30.8804	−	9.52535i	−1.63896	−	0.505553i
$356$	−3.89095	+	4.52242i	−0.206220	+	0.239688i
$357$	−32.1682	+	7.71970i	−1.70252	+	0.408570i
$358$	14.3218	+	9.37582i	0.756928	+	0.495527i
$359$	8.83558	+	12.9594i	0.466324	+	0.683972i	0.985303	−	0.170815i	$-0.0546401\pi$
$359$	8.83558	+	12.9594i	0.466324	+	0.683972i	−0.518979	+	0.854787i	$0.673688\pi$
$360$	60.6009	+	36.5013i	3.19395	+	1.92379i
$361$	3.19858	+	5.54010i	0.168346	+	0.291584i
$362$	5.31299	+	2.43692i	0.279245	+	0.128081i
$363$	−7.54740	−	33.0673i	−0.396136	−	1.73559i
$364$	1.21527	+	0.409968i	0.0636977	+	0.0214882i
$365$	11.7276	−	51.3819i	0.613849	−	2.68945i
$366$	9.69064	−	12.6306i	0.506538	−	0.660212i
$367$	−8.49467	−	1.28037i	−0.443418	−	0.0668345i	−0.0764614	−	0.997073i	$-0.524362\pi$
$367$	−8.49467	−	1.28037i	−0.443418	−	0.0668345i	−0.366957	+	0.930238i	$0.619600\pi$
$368$	−3.97807	−	17.4106i	−0.207371	−	0.907588i
$369$	20.0517	−	21.6106i	1.04385	−	1.12500i
$370$	−7.86438	−	1.03490i	−0.408850	−	0.0538021i
$371$	8.34994	+	20.5984i	0.433507	+	1.06942i
$372$	1.58265	+	3.62634i	0.0820567	+	0.188017i
$373$	−2.89284	+	5.01055i	−0.149786	+	0.259436i	−0.931148	−	0.364641i	$-0.881192\pi$
$373$	−2.89284	+	5.01055i	−0.149786	+	0.259436i	0.781363	+	0.624077i	$0.214525\pi$
$374$	2.14592	+	3.02403i	0.110963	+	0.156369i
$375$	−11.8768	−	12.8001i	−0.613315	−	0.660997i
$376$	−1.76393	+	2.12973i	−0.0909680	+	0.109833i
$377$	−0.402849	−	0.321262i	−0.0207478	−	0.0165458i
$378$	52.0121	−	5.46479i	2.67521	−	0.281078i
$379$	−11.5739	+	9.22988i	−0.594511	+	0.474107i	−0.873923	−	0.486064i	$-0.838432\pi$
$379$	−11.5739	+	9.22988i	−0.594511	+	0.474107i	0.279412	+	0.960171i	$0.409861\pi$
$380$	−2.70410	+	24.0245i	−0.138717	+	1.23243i
$381$	−51.9078	−	20.3723i	−2.65932	−	1.04370i
$382$	−17.5149	+	2.97694i	−0.896139	+	0.152313i
$383$	5.98495	+	15.2494i	0.305817	+	0.779208i	0.998328	+	0.0578014i	$0.0184090\pi$
$383$	5.98495	+	15.2494i	0.305817	+	0.779208i	−0.692511	+	0.721407i	$0.743496\pi$
$384$	−16.3862	+	32.4919i	−0.836207	+	1.65810i
$385$	−2.15688	+	5.68069i	−0.109925	+	0.289515i
$386$	21.4270	+	7.94899i	1.09061	+	0.404593i
$387$	44.7410	+	3.35287i	2.27431	+	0.170436i
$388$	0.472768	+	0.894271i	0.0240012	+	0.0453997i
$389$	19.7701	+	13.4790i	1.00238	+	0.683414i	0.949038	−	0.315163i	$-0.102059\pi$
$389$	19.7701	+	13.4790i	1.00238	+	0.683414i	0.0533458	+	0.998576i	$0.483011\pi$
$390$	3.64374	−	0.903886i	0.184508	−	0.0457700i
$391$	17.3565			0.877755
$392$	12.2867	−	15.5254i	0.620573	−	0.784149i
$393$	−57.9461			−2.92299
$394$	16.9119	−	4.19525i	0.852007	−	0.211353i
$395$	28.1568	+	19.1970i	1.41672	+	0.965906i
$396$	−4.63116	−	8.76015i	−0.232725	−	0.440214i
$397$	−7.90535	−	0.592424i	−0.396758	−	0.0297329i	−0.125143	−	0.992139i	$-0.539939\pi$
$397$	−7.90535	−	0.592424i	−0.396758	−	0.0297329i	−0.271615	+	0.962406i	$0.587558\pi$
$398$	−30.7953	−	11.4244i	−1.54363	−	0.572655i
$399$	15.3955	+	25.9935i	0.770739	+	1.30130i
$400$	17.9367	−	19.3401i	0.896835	−	0.967005i
$401$	−9.10970	−	23.2111i	−0.454917	−	1.15911i	−0.955911	−	0.293658i	$-0.905127\pi$
$401$	−9.10970	−	23.2111i	−0.454917	−	1.15911i	0.500994	−	0.865451i	$-0.332968\pi$
$402$	−54.1439	+	9.20262i	−2.70045	+	0.458985i
$403$	0.138775	+	0.0544652i	0.00691287	+	0.00271310i
$404$	−3.28024	+	29.1431i	−0.163198	+	1.44992i
$405$	61.0190	−	48.6610i	3.03206	−	2.41798i
$406$	−6.76659	+	4.18112i	−0.335820	+	0.207506i
$407$	0.868642	+	0.692719i	0.0430570	+	0.0343368i
$408$	−27.2367	−	22.5586i	−1.34842	−	1.11681i
$409$	−15.2989	−	16.4883i	−0.756484	−	0.815296i	0.231010	−	0.972951i	$-0.425797\pi$
$409$	−15.2989	−	16.4883i	−0.756484	−	0.815296i	−0.987494	+	0.157656i	$0.949606\pi$
$410$	−11.1844	−	15.7610i	−0.552356	−	0.778378i
$411$	16.6923	−	28.9119i	0.823369	−	1.42612i
$412$	−6.30573	−	14.4483i	−0.310661	−	0.711818i
$413$	23.3744	−	3.78956i	1.15018	−	0.186472i
$414$	−45.9849	−	6.05134i	−2.26004	−	0.297407i
$415$	10.4687	−	11.2826i	0.513888	−	0.553839i
$416$	0.428948	+	1.30229i	0.0210309	+	0.0638501i
$417$	13.0282	+	1.96369i	0.637994	+	0.0961621i
$418$	2.06128	−	2.68663i	0.100820	−	0.131407i
$419$	4.61900	−	20.2371i	0.225653	−	0.988649i	−0.727488	−	0.686121i	$-0.759312\pi$
$419$	4.61900	−	20.2371i	0.225653	−	0.988649i	0.953140	−	0.302528i	$-0.0978307\pi$
$420$	5.84095	−	57.6584i	0.285009	−	2.81344i
$421$	−6.58946	−	28.8703i	−0.321151	−	1.40705i	−0.835509	−	0.549478i	$-0.814827\pi$
$421$	−6.58946	−	28.8703i	−0.321151	−	1.40705i	0.514358	−	0.857576i	$-0.328030\pi$
$422$	3.47692	+	1.59476i	0.169254	+	0.0776319i
$423$	3.59090	+	6.21962i	0.174595	+	0.302408i
$424$	−12.2597	+	20.3541i	−0.595386	+	0.988482i
$425$	14.4406	+	21.1805i	0.700472	+	1.02740i
$426$	−36.1191	−	23.6456i	−1.74998	−	1.14563i
$427$	−9.04986	−	1.95990i	−0.437953	−	0.0948462i
$428$	15.8762	−	18.4528i	0.767404	−	0.891948i
$429$	−0.502474	−	0.154993i	−0.0242597	−	0.00748312i
$430$	8.14083	−	28.2636i	0.392586	−	1.36299i
$431$	−27.1012	+	2.03095i	−1.30542	+	0.0978276i	−0.709207	−	0.705000i	$-0.750947\pi$
$431$	−27.1012	+	2.03095i	−1.30542	+	0.0978276i	−0.596211	+	0.802828i	$0.703328\pi$
$432$	38.0375	+	40.9757i	1.83008	+	1.97144i
$433$	9.84387	+	20.4410i	0.473066	+	0.982332i	0.991848	+	0.127425i	$0.0406713\pi$
$433$	9.84387	+	20.4410i	0.473066	+	0.982332i	−0.518782	+	0.854906i	$0.673614\pi$
$434$	1.51422	−	1.73303i	0.0726848	−	0.0831883i
$435$	−10.1019	+	20.9768i	−0.484350	+	1.00576i
$436$	−1.81246	−	16.0693i	−0.0868009	−	0.769582i
$437$	−4.67196	−	15.1461i	−0.223490	−	0.724537i
$438$	34.0529	−	61.6225i	1.62711	−	2.94444i
$439$	19.7412	−	2.97550i	0.942194	−	0.142013i	0.340056	−	0.940405i	$-0.389554\pi$
$439$	19.7412	−	2.97550i	0.942194	−	0.142013i	0.602138	+	0.798392i	$0.294316\pi$
$440$	−6.24174	+	1.79938i	−0.297563	+	0.0857822i
$441$	−26.6940	−	43.9471i	−1.27114	−	2.09272i
$442$	−1.32669	+	0.124485i	−0.0631043	+	0.00592116i
$443$	−0.259669	−	1.72279i	−0.0123373	−	0.0818524i	0.981815	−	0.189841i	$-0.0607972\pi$
$443$	−0.259669	−	1.72279i	−0.0123373	−	0.0818524i	−0.994152	+	0.107988i	$0.965559\pi$
$444$	−9.71283	−	4.23633i	−0.460951	−	0.201047i
$445$	9.70581	−	2.99385i	0.460099	−	0.141922i
$446$	0.619553	+	33.0256i	0.0293367	+	1.56381i
$447$	−3.32442	−	1.60096i	−0.157240	−	0.0757227i
$448$	21.1589	+	0.548732i	0.999664	+	0.0259251i
$449$	18.4174	−	8.86936i	0.869172	−	0.418571i	0.0545141	−	0.998513i	$-0.482639\pi$
$449$	18.4174	−	8.86936i	0.869172	−	0.418571i	0.814658	+	0.579942i	$0.196925\pi$
$450$	−30.8749	−	61.1510i	−1.45546	−	2.88269i
$451$	0.202290	+	2.69937i	0.00952547	+	0.127109i
$452$	−1.76205	+	9.31854i	−0.0828799	+	0.438307i
$453$	−15.4150	+	49.9743i	−0.724261	+	2.34800i
$454$	12.3441	+	12.8132i	0.579339	+	0.601353i
$455$	−1.38036	−	1.69195i	−0.0647121	−	0.0793197i
$456$	−12.3542	+	29.8403i	−0.578539	+	1.39740i
$457$	5.45707	−	3.72057i	0.255271	−	0.174041i	−0.428923	−	0.903341i	$-0.641107\pi$
$457$	5.45707	−	3.72057i	0.255271	−	0.174041i	0.684194	+	0.729300i	$0.260154\pi$
$458$	19.6304	+	17.5408i	0.917268	+	0.819626i
$459$	−47.0559	+	27.1677i	−2.19638	+	1.26808i
$460$	−10.0391	+	28.7007i	−0.468075	+	1.33817i
$461$	−6.93792	+	1.58353i	−0.323131	+	0.0737525i	−0.381010	−	0.924571i	$-0.624424\pi$
$461$	−6.93792	+	1.58353i	−0.323131	+	0.0737525i	0.0578786	+	0.998324i	$0.481566\pi$
$462$	−4.86920	+	6.49479i	−0.226536	+	0.302165i
$463$	6.15740	+	1.40539i	0.286159	+	0.0653138i	0.363191	−	0.931715i	$-0.381687\pi$
$463$	6.15740	+	1.40539i	0.286159	+	0.0653138i	−0.0770323	+	0.997029i	$0.524544\pi$
$464$	−7.91626	−	3.10480i	−0.367503	−	0.144137i
$465$	1.00399	−	6.66105i	0.0465590	−	0.308899i
$466$	13.8576	+	0.777423i	0.641939	+	0.0360134i
$467$	−16.4013	−	15.2182i	−0.758960	−	0.704212i	0.202462	−	0.979290i	$-0.435106\pi$
$467$	−16.4013	−	15.2182i	−0.758960	−	0.704212i	−0.961422	+	0.275078i	$0.911296\pi$
$468$	3.55839	+	0.132735i	0.164487	+	0.00613567i
$469$	18.2873	+	26.1916i	0.844427	+	1.20941i
$470$	4.47211	−	1.47188i	0.206283	−	0.0678925i
$471$	−28.1472	−	16.2508i	−1.29696	−	0.748798i
$472$	18.2347	+	17.5591i	0.839322	+	0.808225i
$473$	−3.01998	+	2.80213i	−0.138859	+	0.128842i
$474$	29.0468	+	35.0540i	1.33416	+	1.61008i
$475$	14.5960	−	18.3028i	0.669712	−	0.839792i
$476$	−5.10026	+	19.9278i	−0.233770	+	0.913391i
$477$	38.4748	+	48.2459i	1.76164	+	2.20903i
$478$	−6.63152	+	31.7921i	−0.303319	+	1.45414i
$479$	13.6669	−	34.8228i	0.624458	−	1.59109i	−0.171126	−	0.985249i	$-0.554740\pi$
$479$	13.6669	−	34.8228i	0.624458	−	1.59109i	0.795584	−	0.605844i	$-0.207164\pi$
$480$	53.0566	−	31.9906i	2.42169	−	1.46016i
$481$	−0.371659	+	0.145866i	−0.0169462	+	0.00665090i
$482$	−12.2149	−	20.2690i	−0.556371	−	0.923227i
$483$	11.6026	+	36.1804i	0.527935	+	1.64626i
$484$	−20.3721	−	5.45618i	−0.926006	−	0.248008i
$485$	0.128699	−	1.71737i	0.00584392	−	0.0779817i
$486$	41.5366	−	17.2078i	1.88414	−	0.780563i
$487$	3.95563	−	5.80184i	0.179247	−	0.262907i	−0.726091	−	0.687598i	$-0.758665\pi$
$487$	3.95563	−	5.80184i	0.179247	−	0.262907i	0.905338	+	0.424692i	$0.139617\pi$
$488$	−4.12904	−	8.99672i	−0.186913	−	0.407262i
$489$		−	42.0090i		−	1.89971i
$490$	−31.7762	+	11.2479i	−1.43550	+	0.508129i
$491$		−	26.0674i		−	1.17641i	−0.808713	−	0.588204i	$-0.799835\pi$
$491$		−	26.0674i		−	1.17641i	0.808713	−	0.588204i	$-0.200165\pi$
$492$	−8.52977	−	24.3677i	−0.384552	−	1.09858i
$493$	4.65526	−	6.82801i	0.209662	−	0.307518i
$494$	0.465746	+	1.12423i	0.0209549	+	0.0505813i
$495$	−1.26072	+	16.8231i	−0.0566650	+	0.756142i
$496$	2.45342	+	0.183290i	0.110162	+	0.00822996i
$497$	−3.46596	+	24.8696i	−0.155469	+	1.11555i
$498$	17.6103	−	10.6126i	0.789137	−	0.475563i
$499$	27.3332	−	10.7275i	1.22360	−	0.480229i	0.336449	−	0.941702i	$-0.390774\pi$
$499$	27.3332	−	10.7275i	1.22360	−	0.480229i	0.887155	+	0.461472i	$0.152679\pi$
$500$	−10.4873	+	2.81136i	−0.469006	+	0.125728i
$501$	−21.5228	+	54.8392i	−0.961567	+	2.45003i
$502$	25.0494	+	5.22506i	1.11801	+	0.233206i
$503$	−5.83192	−	7.31299i	−0.260032	−	0.326070i	0.634628	−	0.772818i	$-0.281154\pi$
$503$	−5.83192	−	7.31299i	−0.260032	−	0.326070i	−0.894660	+	0.446748i	$0.852582\pi$
$504$	20.4607	−	51.0194i	0.911391	−	2.27258i
$505$	31.1309	−	39.0369i	1.38531	−	1.73712i
$506$	3.27930	−	2.71733i	0.145783	−	0.120800i
$507$	−30.5132	+	28.3121i	−1.35514	+	1.25739i
$508$	−26.2787	+	22.6199i	−1.16593	+	1.00360i
$509$	−38.1814	−	22.0440i	−1.69236	−	0.977084i	−0.952606	−	0.304206i	$-0.901609\pi$
$509$	−38.1814	−	22.0440i	−1.69236	−	0.977084i	−0.739754	−	0.672878i	$-0.765058\pi$
$510$	18.8235	+	57.1928i	0.833518	+	2.53254i
$511$	−40.8679	−	2.60573i	−1.80789	−	0.115271i
$512$	13.1034	+	18.4472i	0.579094	+	0.815261i
$513$	36.3742	+	33.7503i	1.60596	+	1.49011i
$514$	−0.975383	+	17.3862i	−0.0430223	+	0.766872i
$515$	−4.00019	+	26.5395i	−0.176269	+	1.16947i
$516$	20.9007	−	33.2718i	0.920103	−	1.46471i
$517$	−0.642914	−	0.146741i	−0.0282753	−	0.00645366i
$518$	0.184157	+	6.16063i	0.00809140	+	0.270682i
$519$	15.1032	−	3.44721i	0.662958	−	0.151316i
$520$	0.561516	−	2.26582i	0.0246241	−	0.0993626i
$521$	−35.7636	+	20.6481i	−1.56683	+	0.904610i	−0.570295	+	0.821440i	$0.693171\pi$
$521$	−35.7636	+	20.6481i	−1.56683	+	0.904610i	−0.996535	+	0.0831704i	$0.973495\pi$
$522$	−14.7144	+	16.4673i	−0.644032	+	0.720756i
$523$	−7.51544	+	5.12394i	−0.328627	+	0.224054i	−0.716382	−	0.697708i	$-0.754203\pi$
$523$	−7.51544	+	5.12394i	−0.328627	+	0.224054i	0.387755	+	0.921763i	$0.373251\pi$
$524$	−16.8325	+	31.8576i	−0.735332	+	1.39170i
$525$	−34.4983	+	44.2609i	−1.50563	+	1.93170i
$526$	−21.4923	+	20.7056i	−0.937109	+	0.902805i
$527$	−0.704760	+	2.28477i	−0.0306998	+	0.0995263i
$528$	−8.67781	+	0.00200024i	−0.377653	+	8.70493e-5i
$529$	0.229083	+	3.05690i	0.00996012	+	0.132909i
$530$	36.1120	−	18.2328i	1.56861	−	0.791982i
$531$	59.2327	−	28.5250i	2.57048	−	1.23788i
$532$	18.7629	−	0.913371i	0.813474	−	0.0395996i
$533$	−0.876426	−	0.422065i	−0.0379622	−	0.0182816i
$534$	13.5663	−	0.254500i	0.587070	−	0.0110133i
$535$	−39.6025	+	12.2157i	−1.71216	+	0.528132i
$536$	−10.6686	+	32.4404i	−0.460813	+	1.40121i
$537$	−5.80256	−	38.4975i	−0.250399	−	1.66129i
$538$	0.976282	+	10.4046i	0.0420905	+	0.448576i
$539$	4.62526	+	0.947932i	0.199224	+	0.0408303i
$540$	−17.7071	−	93.5255i	−0.761994	−	4.02470i
$541$	−2.85749	+	0.430697i	−0.122853	+	0.0185171i	−0.210181	−	0.977663i	$-0.567405\pi$
$541$	−2.85749	+	0.430697i	−0.122853	+	0.0185171i	0.0873279	+	0.996180i	$0.472167\pi$
$542$	10.8607	+	6.00170i	0.466508	+	0.257795i
$543$	−3.91854	−	12.7036i	−0.168160	−	0.545163i
$544$	−20.3141	+	8.42123i	−0.870959	+	0.361057i
$545$	−11.9456	+	24.8054i	−0.511695	+	1.06255i
$546$	−1.14637	−	2.68233i	−0.0490600	−	0.114793i
$547$	5.81744	+	12.0800i	0.248736	+	0.516505i	0.987531	−	0.157425i	$-0.0503193\pi$
$547$	5.81744	+	12.0800i	0.248736	+	0.516505i	−0.738795	+	0.673930i	$0.764605\pi$
$548$	−11.0463	−	17.5755i	−0.471873	−	0.750790i
$549$	−25.6363	+	1.92118i	−1.09413	+	0.0819938i
$550$	6.04439	+	1.74098i	0.257734	+	0.0742357i
$551$	−7.21154	−	2.22447i	−0.307222	−	0.0947654i
$552$	−23.4991	+	33.1310i	−1.00019	+	1.41015i
$553$	11.2227	−	23.9832i	0.477239	−	1.01987i
$554$	1.69982	−	2.59651i	0.0722184	−	0.110315i
$555$	10.1627	+	14.9060i	0.431384	+	0.632724i
$556$	4.86410	−	6.59221i	0.206284	−	0.279572i
$557$	−2.16595	−	3.75154i	−0.0917743	−	0.158958i	0.816483	−	0.577369i	$-0.195920\pi$
$557$	−2.16595	−	3.75154i	−0.0917743	−	0.158958i	−0.908258	+	0.418411i	$0.862587\pi$
$558$	2.66380	−	5.80765i	0.112768	−	0.245858i
$559$	−0.329432	−	1.44334i	−0.0139335	−	0.0610467i
$560$	−30.0026	−	19.9602i	−1.26784	−	0.843470i
$561$	1.87664	−	8.22208i	0.0792316	−	0.347136i
$562$	−8.15087	−	6.25363i	−0.343824	−	0.263794i
$563$	9.00456	+	1.35722i	0.379497	+	0.0571999i	0.336021	−	0.941855i	$-0.390919\pi$
$563$	9.00456	+	1.35722i	0.379497	+	0.0571999i	0.0434759	+	0.999054i	$0.486157\pi$
$564$	6.28505	−	0.235895i	0.264648	−	0.00993299i
$565$	10.9822	−	11.8360i	0.462024	−	0.497943i
$566$	−1.38758	+	10.5444i	−0.0583245	+	0.443216i
$567$	−44.9103	−	40.7503i	−1.88606	−	1.71135i
$568$	−23.4919	+	12.9888i	−0.985700	+	0.544999i
$569$	−3.77595	+	6.54014i	−0.158296	+	0.274177i	−0.934254	−	0.356607i	$-0.883933\pi$
$569$	−3.77595	+	6.54014i	−0.158296	+	0.274177i	0.775958	+	0.630784i	$0.217267\pi$
$570$	44.8423	−	31.8212i	1.87824	−	1.33284i
$571$	−12.9183	−	13.9226i	−0.540612	−	0.582642i	0.402373	−	0.915476i	$-0.368185\pi$
$571$	−12.9183	−	13.9226i	−0.540612	−	0.582642i	−0.942985	+	0.332834i	$0.891995\pi$
$572$	−0.231173	+	0.231227i	−0.00966584	+	0.00966807i
$573$	31.5912	+	25.1932i	1.31974	+	1.05246i
$574$	−10.6978	+	10.5382i	−0.446518	+	0.439856i
$575$	23.0190	−	18.3571i	0.959961	−	0.765543i
$576$	56.7570	−	15.2290i	2.36487	−	0.634543i
$577$	31.7395	+	12.4568i	1.32133	+	0.518584i	0.918040	−	0.396488i	$-0.129771\pi$
$577$	31.7395	+	12.4568i	1.32133	+	0.518584i	0.403291	+	0.915072i	$0.367866\pi$
$578$	0.447435	+	2.63250i	0.0186108	+	0.109497i
$579$	−18.9899	−	48.3854i	−0.789192	−	2.01083i
$580$	8.59816	+	11.6473i	0.357019	+	0.483627i
$581$	−9.95543	−	6.62646i	−0.413021	−	0.274912i
$582$	0.800202	−	2.15700i	0.0331694	−	0.0894103i
$583$	−5.65039	−	0.423438i	−0.234015	−	0.0175370i
$584$	−23.9869	−	36.6220i	−0.992584	−	1.51543i
$585$	−5.00903	−	3.41510i	−0.207098	−	0.141197i
$586$	−0.884586	−	3.56594i	−0.0365419	−	0.147308i
$587$	−34.7419			−1.43395			−0.716976	−	0.697097i	$-0.754475\pi$
$587$	−34.7419			−1.43395			−0.716976	+	0.697097i	$0.754475\pi$
$588$	−44.9499	+	2.68975i	−1.85370	+	0.110923i
$589$	2.18351			0.0899699
$590$	−10.3768	−	41.8308i	−0.427206	−	1.72215i
$591$	−32.7436	−	22.3242i	−1.34689	−	0.918295i
$592$	−5.15048	+	4.10932i	−0.211684	+	0.168892i
$593$	−40.2243	−	3.01439i	−1.65181	−	0.123786i	−0.784028	−	0.620726i	$-0.786838\pi$
$593$	−40.2243	−	3.01439i	−1.65181	−	0.123786i	−0.867785	+	0.496940i	$0.834457\pi$
$594$	−4.63728	+	12.5001i	−0.190270	+	0.512884i
$595$	25.4057	−	24.1046i	1.04153	−	0.988192i
$596$	−1.84587	+	1.36264i	−0.0756097	+	0.0558160i
$597$	27.2926	+	69.5404i	1.11701	+	2.84610i
$598$	0.256446	+	1.50881i	0.0104869	+	0.0616997i
$599$	−2.74086	−	1.07571i	−0.111989	−	0.0439523i	0.308685	−	0.951164i	$-0.400111\pi$
$599$	−2.74086	−	1.07571i	−0.111989	−	0.0439523i	−0.420674	+	0.907212i	$0.638206\pi$
$600$	−59.9817	−	1.11141i	−2.44874	−	0.0453733i
$601$	33.1516	−	26.4375i	1.35228	−	1.07841i	0.363092	−	0.931753i	$-0.381721\pi$
$601$	33.1516	−	26.4375i	1.35228	−	1.07841i	0.989188	−	0.146654i	$-0.0468505\pi$
$602$	−22.6903	−	2.72944i	−0.924787	−	0.111244i
$603$	69.3394	+	55.2963i	2.82372	+	2.25184i
$604$	22.9970	+	22.9917i	0.935734	+	0.935518i
$605$	24.4226	+	26.3213i	0.992919	+	1.07011i
$606$	54.3964	−	38.6010i	2.20970	−	1.56806i
$607$	−5.09246	+	8.82041i	−0.206697	+	0.358009i	−0.950672	−	0.310198i	$-0.899605\pi$
$607$	−5.09246	+	8.82041i	−0.206697	+	0.358009i	0.743975	+	0.668207i	$0.232938\pi$
$608$	12.8168	+	15.4603i	0.519792	+	0.626996i
$609$	17.3453	+	5.13967i	0.702866	+	0.208270i
$610$	−2.19883	+	16.7092i	−0.0890279	+	0.676536i
$611$	0.161185	−	0.173717i	0.00652087	−	0.00702782i
$612$	2.14200	+	57.0701i	0.0865852	+	2.30692i
$613$	33.8717	+	5.10533i	1.36806	+	0.206202i	0.791659	−	0.610963i	$-0.209217\pi$
$613$	33.8717	+	5.10533i	1.36806	+	0.206202i	0.576404	+	0.817165i	$0.304456\pi$
$614$	−32.3032	−	24.7842i	−1.30365	−	1.00021i
$615$	−9.78086	+	42.8528i	−0.394402	+	1.72799i
$616$	2.15627	+	4.56363i	0.0868784	+	0.183874i
$617$	7.91803	+	34.6911i	0.318768	+	1.39661i	0.839717	+	0.543025i	$0.182721\pi$
$617$	7.91803	+	34.6911i	0.318768	+	1.39661i	−0.520949	+	0.853588i	$0.674422\pi$
$618$	−14.9479	+	32.5896i	−0.601293	+	1.31095i
$619$	−2.02047	−	3.49955i	−0.0812094	−	0.140659i	0.822560	−	0.568678i	$-0.192545\pi$
$619$	−2.02047	−	3.49955i	−0.0812094	−	0.140659i	−0.903770	+	0.428019i	$0.859212\pi$
$620$	−3.37046	−	2.48691i	−0.135361	−	0.0998769i
$621$	35.1546	+	51.5624i	1.41071	+	2.06913i
$622$	10.8035	−	16.5025i	0.433180	−	0.661692i
$623$	−3.50316	−	7.07202i	−0.140351	−	0.283335i
$624$	1.55860	−	2.70100i	0.0623938	−	0.108127i
$625$	−13.8428	−	4.26994i	−0.553713	−	0.170798i
$626$	1.91786	+	0.552405i	0.0766530	+	0.0220786i
$627$	−7.68013	+	0.575546i	−0.306715	+	0.0229851i
$628$	−17.1107	+	10.7541i	−0.682792	+	0.429136i
$629$	−2.77835	−	5.76930i	−0.110780	−	0.230037i
$630$	−75.7150	+	55.0060i	−3.01656	+	2.19149i
$631$	−18.8953	+	39.2365i	−0.752211	+	1.56198i	0.0731142	+	0.997324i	$0.476706\pi$
$631$	−18.8953	+	39.2365i	−0.752211	+	1.56198i	−0.825325	+	0.564658i	$0.809008\pi$
$632$	27.7096	−	5.78664i	1.10223	−	0.230180i
$633$	−2.56436	−	8.31346i	−0.101924	−	0.330430i
$634$	−35.0954	−	19.3939i	−1.39382	−	0.770230i
$635$	58.3726	−	8.79826i	2.31645	−	0.349148i
$636$	53.0984	−	10.0531i	2.10549	−	0.398631i
$637$	−1.12607	+	1.26912i	−0.0446165	+	0.0502843i
$638$	−0.189436	−	2.01890i	−0.00749984	−	0.0799290i
$639$	10.3904	+	68.9357i	0.411037	+	2.72705i
$640$	−2.17556	−	38.4622i	−0.0859964	−	1.52035i
$641$	−11.9146	+	3.67517i	−0.470599	+	0.145161i	−0.520979	−	0.853570i	$-0.674433\pi$
$641$	−11.9146	+	3.67517i	−0.470599	+	0.145161i	0.0503798	+	0.998730i	$0.483957\pi$
$642$	−55.3543	+	1.03843i	−2.18466	+	0.0409837i
$643$	44.4264	+	21.3946i	1.75201	+	0.843722i	0.977435	+	0.211237i	$0.0677492\pi$
$643$	44.4264	+	21.3946i	1.75201	+	0.843722i	0.774572	+	0.632485i	$0.217965\pi$
$644$	23.2616	+	4.13104i	0.916635	+	0.162786i
$645$	−60.2706	+	29.0248i	−2.37315	+	1.14285i
$646$	−17.4221	+	8.79634i	−0.685463	+	0.346087i
$647$	1.34799	+	17.9877i	0.0529950	+	0.707169i	0.958910	+	0.283710i	$0.0915653\pi$
$647$	1.34799	+	17.9877i	0.0529950	+	0.707169i	−0.905915	+	0.423459i	$0.860816\pi$
$648$	6.04157	−	64.5475i	0.237335	−	2.53567i
$649$	−1.77935	+	5.76850i	−0.0698455	+	0.226433i
$650$	−1.62786	+	1.56827i	−0.0638500	+	0.0615127i
$651$	−5.23384	+	0.0582347i	−0.205130	+	0.00228240i
$652$	−23.0957	−	12.2030i	−0.904497	−	0.477907i
$653$	−28.3565	+	19.3331i	−1.10968	+	0.756565i	−0.972249	−	0.233947i	$-0.924836\pi$
$653$	−28.3565	+	19.3331i	−1.10968	+	0.756565i	−0.137427	+	0.990512i	$0.543883\pi$
$654$	−24.5063	+	27.4257i	−0.958272	+	1.07243i
$655$	53.1252	−	30.6719i	2.07577	−	1.19845i
$656$	−15.8746	−	2.38897i	−0.619799	−	0.0932736i
$657$	−110.844	+	25.2994i	−4.32444	+	0.987025i
$658$	−1.68502	−	3.24706i	−0.0656889	−	0.126583i
$659$	16.7694	+	3.82750i	0.653242	+	0.149098i	0.536283	−	0.844038i	$-0.319828\pi$
$659$	16.7694	+	3.82750i	0.653242	+	0.149098i	0.116960	+	0.993137i	$0.462685\pi$
$660$	12.5106	+	7.85889i	0.486973	+	0.305907i
$661$	2.02254	−	13.4187i	0.0786677	−	0.521926i	−0.914440	−	0.404721i	$-0.867369\pi$
$661$	2.02254	−	13.4187i	0.0786677	−	0.521926i	0.993108	−	0.117205i	$-0.0373933\pi$
$662$	0.204365	−	3.64280i	0.00794286	−	0.141581i
$663$	2.22162	+	2.06136i	0.0862807	+	0.0800568i
$664$	−0.719058	−	12.7646i	−0.0279049	−	0.495363i
$665$	−27.8735	−	15.6819i	−1.08089	−	0.608117i
$666$	5.34960	+	16.2541i	0.207293	+	0.629833i
$667$	−8.21984	−	4.74573i	−0.318274	−	0.183755i
$668$	23.8974	+	27.7628i	0.924617	+	1.07417i
$669$	55.0712	−	51.0986i	2.12917	−	1.97558i
$670$	44.7682	−	37.0962i	1.72955	−	1.43315i
$671$	1.47180	−	1.84558i	0.0568181	−	0.0712477i
$672$	−31.1341	−	36.7162i	−1.20102	−	1.41636i
$673$	12.2101	+	15.3110i	0.470664	+	0.590194i	0.959334	−	0.282275i	$-0.0910890\pi$
$673$	12.2101	+	15.3110i	0.470664	+	0.590194i	−0.488669	+	0.872469i	$0.662518\pi$
$674$	20.2164	+	4.21694i	0.778705	+	0.162431i
$675$	−33.6739	+	85.7998i	−1.29611	+	3.30244i
$676$	6.70177	+	24.9998i	0.257760	+	0.961531i
$677$	21.8717	−	8.58402i	0.840599	−	0.329911i	0.0943181	−	0.995542i	$-0.469933\pi$
$677$	21.8717	−	8.58402i	0.840599	−	0.329911i	0.746281	+	0.665631i	$0.231838\pi$
$678$	18.4741	−	11.1332i	0.709494	−	0.427567i
$679$	−1.33322	+	0.114841i	−0.0511641	+	0.00440718i
$680$	36.9113	+	6.26492i	1.41548	+	0.240249i
$681$	3.02401	−	40.3526i	0.115880	−	1.54631i
$682$	0.224548	+	0.542018i	0.00859838	+	0.0207549i
$683$	−17.6069	+	25.8246i	−0.673711	+	0.988152i	0.325383	+	0.945582i	$0.394507\pi$
$683$	−17.6069	+	25.8246i	−0.673711	+	0.988152i	−0.999093	+	0.0425700i	$0.986445\pi$
$684$	49.2256	−	17.2311i	1.88219	−	0.658849i
$685$			35.3420i			1.35035i
$686$	12.5784	+	22.9735i	0.480246	+	0.877134i
$687$		−	59.8740i		−	2.28434i
$688$	−12.2208	−	21.1558i	−0.465913	−	0.806556i
$689$	1.14703	−	1.68239i	0.0436985	−	0.0640940i
$690$	63.8886	−	26.4678i	2.43220	−	1.00761i
$691$	−1.03121	+	13.7605i	−0.0392290	+	0.523475i	0.942627	+	0.333848i	$0.108347\pi$
$691$	−1.03121	+	13.7605i	−0.0392290	+	0.523475i	−0.981856	+	0.189627i	$0.939272\pi$
$692$	2.49206	−	9.30480i	0.0947340	−	0.353715i
$693$	13.0600	−	1.12496i	0.496108	−	0.0427338i
$694$	−11.4314	−	18.9690i	−0.433931	−	0.720054i
$695$	−12.9837	+	5.09573i	−0.492500	+	0.193292i
$696$	6.73089	+	18.1307i	0.255134	+	0.687244i
$697$	5.69985	−	14.5230i	0.215897	−	0.550097i
$698$	5.96676	−	28.6051i	0.225845	−	1.08272i
$699$	−19.6816	−	24.6800i	−0.744427	−	0.933483i
$700$	14.3125	+	31.8236i	0.540960	+	1.20282i
$701$	−13.6001	+	17.0540i	−0.513668	+	0.644119i	−0.969251	−	0.246074i	$-0.920859\pi$
$701$	−13.6001	+	17.0540i	−0.513668	+	0.644119i	0.455583	+	0.890193i	$0.349431\pi$
$702$	−3.05696	−	3.68918i	−0.115378	−	0.139239i
$703$	−4.28671	+	3.97748i	−0.161676	+	0.150014i
$704$	−2.51968	+	4.77146i	−0.0949640	+	0.179831i
$705$	−9.27338	−	5.35399i	−0.349256	−	0.201643i
$706$	−28.3340	+	9.32537i	−1.06636	+	0.350965i
$707$	−33.8122	−	19.0230i	−1.27164	−	0.715435i
$708$	2.14616	−	57.5349i	0.0806578	−	2.16229i
$709$	−16.5330	−	15.3404i	−0.620910	−	0.576121i	0.305707	−	0.952126i	$-0.401107\pi$
$709$	−16.5330	−	15.3404i	−0.620910	−	0.576121i	−0.926618	+	0.376005i	$0.877298\pi$
$710$	45.6302	+	2.55990i	1.71247	+	0.0960712i
$711$	10.9570	−	72.6947i	0.410918	−	2.72627i
$712$	3.80089	−	7.53238i	0.142444	−	0.282288i
$713$	2.67730	+	0.611075i	0.100265	+	0.0228849i
$714$	41.5259	−	21.5493i	1.55407	−	0.806463i
$715$	0.542710	−	0.123870i	0.0202962	−	0.00463248i
$716$	−22.8506	−	7.99283i	−0.853969	−	0.298706i
$717$	63.9676	−	36.9317i	2.38891	−	1.37924i
$718$	−16.5405	−	14.7797i	−0.617285	−	0.551575i
$719$	3.71601	−	2.53354i	0.138584	−	0.0944849i	−0.492044	−	0.870571i	$-0.663750\pi$
$719$	3.71601	−	2.53354i	0.138584	−	0.0944849i	0.630628	+	0.776086i	$0.282798\pi$
$720$	−95.6100	−	29.4676i	−3.56317	−	1.09819i
$721$	20.8531	−	0.232023i	0.776609	−	0.00864100i
$722$	−6.27679	−	6.51530i	−0.233598	−	0.242474i
$723$	−15.8647	+	51.4320i	−0.590014	+	1.91278i
$724$	−8.12244	−	1.53588i	−0.301868	−	0.0570805i
$725$	−1.04760	−	13.9793i	−0.0389070	−	0.519178i
$726$	21.6190	+	42.8187i	0.802356	+	1.58915i
$727$	2.71323	−	1.30662i	0.100628	−	0.0484600i	−0.382893	−	0.923793i	$-0.625072\pi$
$727$	2.71323	−	1.30662i	0.100628	−	0.0484600i	0.483521	+	0.875333i	$0.339358\pi$
$728$	−1.80769	−	0.148929i	−0.0669976	−	0.00551969i
$729$	−30.1767	−	14.5323i	−1.11766	−	0.538235i
$730$	1.39799	+	74.5205i	0.0517419	+	2.75813i
$731$	22.6892	−	6.99868i	0.839189	−	0.258855i
$732$	−9.00080	+	20.6365i	−0.332679	+	0.762748i
$733$	−5.02303	−	33.3256i	−0.185530	−	1.23091i	−0.866717	−	0.498800i	$-0.833774\pi$
$733$	−5.02303	−	33.3256i	−0.185530	−	1.23091i	0.681187	−	0.732109i	$-0.261464\pi$
$734$	12.0958	−	1.13497i	0.446466	−	0.0418925i
$735$	67.2305	+	36.8458i	2.47983	+	1.35908i
$736$	11.3886	+	22.5434i	0.419789	+	0.830961i
$737$	−8.05260	+	1.21373i	−0.296621	+	0.0447085i
$738$	−20.1648	+	36.4905i	−0.742278	+	1.34323i
$739$	−9.41879	−	30.5350i	−0.346476	−	1.12325i	−0.946347	−	0.323151i	$-0.895258\pi$
$739$	−9.41879	−	30.5350i	−0.346476	−	1.12325i	0.599872	−	0.800096i	$-0.295218\pi$
$740$	11.1471	−	1.25728i	0.409776	−	0.0462185i
$741$	1.20084	−	2.49357i	0.0441139	−	0.0916034i
$742$	−18.4749	−	25.4305i	−0.678236	−	0.933583i
$743$	−8.60386	−	17.8661i	−0.315645	−	0.655444i	0.681429	−	0.731884i	$-0.261359\pi$
$743$	−8.60386	−	17.8661i	−0.315645	−	0.655444i	−0.997074	+	0.0764404i	$0.975645\pi$
$744$	−3.40712	−	4.43866i	−0.124911	−	0.162729i
$745$	3.89525	−	0.291909i	0.142711	−	0.0106947i
$746$	2.26467	−	7.86254i	0.0829154	−	0.287868i
$747$	−31.7278	−	9.78672i	−1.16086	−	0.358078i
$748$	−3.97519	−	3.42013i	−0.145347	−	0.125052i
$749$	14.2939	+	28.8559i	0.522288	+	1.05437i
$750$	20.6606	+	13.5256i	0.754420	+	0.493885i
$751$	12.3839	+	18.1638i	0.451893	+	0.662806i	0.982810	−	0.184618i	$-0.0591048\pi$
$751$	12.3839	+	18.1638i	0.451893	+	0.662806i	−0.530917	+	0.847424i	$0.678152\pi$
$752$	1.69603	−	3.52391i	0.0618477	−	0.128504i
$753$	−29.0989	−	50.4008i	−1.06042	−	1.83671i
$754$	0.662344	+	0.303798i	0.0241212	+	0.0110637i
$755$	−12.3197	−	53.9761i	−0.448359	−	1.96439i
$756$	−69.5317	+	25.2110i	−2.52884	+	0.916916i
$757$	−8.85225	+	38.7842i	−0.321741	+	1.40964i	0.512713	+	0.858560i	$0.328640\pi$
$757$	−8.85225	+	38.7842i	−0.321741	+	1.40964i	−0.834454	+	0.551078i	$0.814217\pi$
$758$	12.7437	−	16.6099i	0.462873	−	0.603299i
$759$	−9.57801	−	1.44365i	−0.347660	−	0.0524013i
$760$	−4.46858	−	33.8970i	−0.162093	−	1.22957i
$761$	−8.74329	+	9.42302i	−0.316944	+	0.341584i	−0.871350	−	0.490662i	$-0.836755\pi$
$761$	−8.74329	+	9.42302i	−0.316944	+	0.341584i	0.554406	+	0.832246i	$0.312945\pi$
$762$	78.1859	+	10.2888i	2.83238	+	0.372724i
$763$	20.5110	+	6.07773i	0.742548	+	0.220029i
$764$	23.0275	−	10.0499i	0.833105	−	0.363594i
$765$	48.6158	−	84.2050i	1.75771	−	3.04444i
$766$	−13.4074	−	18.8936i	−0.484429	−	0.682655i
$767$	−1.47552	−

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.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37261 + 0.340497i) q^{2} +(2.65756 + 1.81189i) q^{3} +(1.76812 - 0.934741i) q^{4} +(-3.39552 - 0.254459i) q^{5} +(-4.26474 - 1.58213i) q^{6} +(0.227059 + 2.63599i) q^{7} +(-2.10867 + 1.88508i) q^{8} +(2.68364 + 6.83780i) q^{9} +O(q^{10})\)	\(q+(-1.37261 + 0.340497i) q^{2} +(2.65756 + 1.81189i) q^{3} +(1.76812 - 0.934741i) q^{4} +(-3.39552 - 0.254459i) q^{5} +(-4.26474 - 1.58213i) q^{6} +(0.227059 + 2.63599i) q^{7} +(-2.10867 + 1.88508i) q^{8} +(2.68364 + 6.83780i) q^{9} +(4.74738 - 0.806893i) q^{10} +(-0.627861 - 0.246417i) q^{11} +(6.39254 + 0.719520i) q^{12} +(0.189502 - 0.151122i) q^{13} +(-1.20921 - 3.54088i) q^{14} +(-8.56275 - 6.82857i) q^{15} +(2.25252 - 3.30547i) q^{16} +(2.64410 + 2.84966i) q^{17} +(-6.01185 - 8.47187i) q^{18} +(1.77502 - 3.07443i) q^{19} +(-6.24156 + 2.72402i) q^{20} +(-4.17271 + 7.41671i) q^{21} +(0.945714 + 0.124450i) q^{22} +(3.03684 - 3.27294i) q^{23} +(-9.01947 + 1.18902i) q^{24} +(6.52068 + 0.982835i) q^{25} +(-0.208655 + 0.271957i) q^{26} +(-3.11025 + 13.6269i) q^{27} +(2.86544 + 4.44851i) q^{28} +(-0.473043 - 2.07254i) q^{29} +(14.0784 + 6.45737i) q^{30} +(0.307532 + 0.532662i) q^{31} +(-1.96633 + 5.30411i) q^{32} +(-1.22210 - 1.79249i) q^{33} +(-4.59963 - 3.01117i) q^{34} +(-0.100232 - 9.00835i) q^{35} +(11.1366 + 9.58157i) q^{36} +(-1.57405 - 0.485530i) q^{37} +(-1.38958 + 4.82439i) q^{38} +(0.777429 - 0.0582603i) q^{39} +(7.63971 - 5.86426i) q^{40} +(-1.74132 - 3.61590i) q^{41} +(3.20214 - 11.6010i) q^{42} +(2.65014 - 5.50308i) q^{43} +(-1.34047 + 0.151191i) q^{44} +(-7.37242 - 23.9008i) q^{45} +(-3.05398 + 5.52651i) q^{46} +(0.966783 - 0.145719i) q^{47} +(11.9754 - 4.70317i) q^{48} +(-6.89689 + 1.19705i) q^{49} +(-9.28502 + 0.871225i) q^{50} +(1.86357 + 12.3640i) q^{51} +(0.193802 - 0.444338i) q^{52} +(8.02760 - 2.47619i) q^{53} +(-0.370758 - 19.7635i) q^{54} +(2.06922 + 0.996482i) q^{55} +(-5.44784 - 5.13041i) q^{56} +(10.2878 - 4.95433i) q^{57} +(1.35500 + 2.68372i) q^{58} +(-0.668839 - 8.92504i) q^{59} +(-21.5229 - 4.06979i) q^{60} +(-1.03159 + 3.34433i) q^{61} +(-0.603492 - 0.626423i) q^{62} +(-17.4150 + 8.62663i) q^{63} +(0.892967 - 7.95001i) q^{64} +(-0.681912 + 0.464919i) q^{65} +(2.28780 + 2.04427i) q^{66} +(10.4561 - 6.03686i) q^{67} +(7.33879 + 2.56701i) q^{68} +(14.0008 - 3.19559i) q^{69} +(3.20490 + 12.3308i) q^{70} +(9.25271 + 2.11187i) q^{71} +(-18.5487 - 9.35979i) q^{72} +(-2.30687 + 15.3051i) q^{73} +(2.32588 + 0.130484i) q^{74} +(15.5483 + 14.4267i) q^{75} +(0.264663 - 7.09516i) q^{76} +(0.506992 - 1.71099i) q^{77} +(-1.04727 + 0.344681i) q^{78} +(-8.66734 - 5.00409i) q^{79} +(-8.48959 + 10.6506i) q^{80} +(-16.8021 + 15.5901i) q^{81} +(3.62136 + 4.37030i) q^{82} +(-2.81825 + 3.53397i) q^{83} +(-0.445164 + 17.0141i) q^{84} +(-8.25299 - 10.3489i) q^{85} +(-1.76383 + 8.45595i) q^{86} +(2.49808 - 6.36499i) q^{87} +(1.78847 - 0.663955i) q^{88} +(-2.77674 + 1.08979i) q^{89} +(18.2576 + 30.2962i) q^{90} +(0.441385 + 0.465210i) q^{91} +(2.31016 - 8.62562i) q^{92} +(-0.147841 + 1.97280i) q^{93} +(-1.27740 + 0.529203i) q^{94} +(-6.80946 + 9.98764i) q^{95} +(-14.8361 + 10.5332i) q^{96} +0.505774i q^{97} +(9.05915 - 3.99146i) q^{98} -4.95449i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

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