LMFDB - Embedded newform 169.2.g.a.14.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			14.5
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707334 + 1.02475i) q^{2} +(2.32028 - 1.21778i) q^{3} +(0.159418 + 0.420350i) q^{4} +(1.61135 + 1.42753i) q^{5} +(-0.393297 + 3.23909i) q^{6} +(-1.03213 - 0.254398i) q^{7} +(-2.96148 - 0.729939i) q^{8} +(2.19654 - 3.18224i) q^{9} +O(q^{10})$	\(q+(-0.707334 + 1.02475i) q^{2} +(2.32028 - 1.21778i) q^{3} +(0.159418 + 0.420350i) q^{4} +(1.61135 + 1.42753i) q^{5} +(-0.393297 + 3.23909i) q^{6} +(-1.03213 - 0.254398i) q^{7} +(-2.96148 - 0.729939i) q^{8} +(2.19654 - 3.18224i) q^{9} +(-2.60263 + 0.641490i) q^{10} +(-0.173539 - 0.251415i) q^{11} +(0.881788 + 0.781196i) q^{12} +(-2.66602 - 2.42741i) q^{13} +(0.990757 - 0.877734i) q^{14} +(5.47721 + 1.35001i) q^{15} +(2.16976 - 1.92224i) q^{16} +(3.99680 + 0.985122i) q^{17} +(1.70731 + 4.50181i) q^{18} -4.43794 q^{19} +(-0.343185 + 0.904905i) q^{20} +(-2.70464 + 0.666634i) q^{21} +0.380387 q^{22} +0.658914 q^{23} +(-7.76038 + 1.91276i) q^{24} +(-0.0440806 - 0.363036i) q^{25} +(4.37326 - 1.01502i) q^{26} +(0.273757 - 2.25459i) q^{27} +(-0.0576041 - 0.474412i) q^{28} +(-0.846759 + 1.22674i) q^{29} +(-5.25764 + 4.65787i) q^{30} +(-0.816771 + 6.72671i) q^{31} +(-0.300231 - 2.47262i) q^{32} +(-0.708827 - 0.372021i) q^{33} +(-3.83658 + 3.39891i) q^{34} +(-1.29997 - 1.88333i) q^{35} +(1.68782 + 0.416010i) q^{36} +(1.23739 - 10.1908i) q^{37} +(3.13911 - 4.54778i) q^{38} +(-9.14198 - 2.38565i) q^{39} +(-3.72997 - 5.40380i) q^{40} +(6.43378 - 3.37671i) q^{41} +(1.22995 - 3.24312i) q^{42} +(-0.964779 - 7.94567i) q^{43} +(0.0780169 - 0.113027i) q^{44} +(8.08214 - 1.99207i) q^{45} +(-0.466073 + 0.675223i) q^{46} +(-3.81052 + 10.0475i) q^{47} +(2.69359 - 7.10242i) q^{48} +(-5.19761 - 2.72792i) q^{49} +(0.403201 + 0.211616i) q^{50} +(10.4734 - 2.58145i) q^{51} +(0.595349 - 1.50764i) q^{52} +(-0.0863969 - 0.0212949i) q^{53} +(2.11676 + 1.87528i) q^{54} +(0.0792703 - 0.652849i) q^{55} +(2.87094 + 1.50679i) q^{56} +(-10.2973 + 5.40443i) q^{57} +(-0.658163 - 1.73543i) q^{58} +(-0.0867438 - 0.0768483i) q^{59} +(0.305687 + 2.51756i) q^{60} +(-9.22781 + 2.27445i) q^{61} +(-6.31547 - 5.59502i) q^{62} +(-3.07667 + 2.72569i) q^{63} +(7.87964 + 4.13555i) q^{64} +(-0.830697 - 7.71724i) q^{65} +(0.882607 - 0.463228i) q^{66} +(-4.21608 + 11.1169i) q^{67} +(0.223064 + 1.83710i) q^{68} +(1.52887 - 0.802412i) q^{69} +2.84945 q^{70} +(7.87842 - 4.13492i) q^{71} +(-8.82785 + 7.82079i) q^{72} +(-1.33823 - 1.93876i) q^{73} +(9.56780 + 8.47633i) q^{74} +(-0.544377 - 0.788666i) q^{75} +(-0.707486 - 1.86549i) q^{76} +(0.115156 + 0.303641i) q^{77} +(8.91113 - 7.68080i) q^{78} +(-4.47220 + 11.7922i) q^{79} +6.24029 q^{80} +(2.00306 + 5.28163i) q^{81} +(-1.09055 + 8.98148i) q^{82} +(5.08576 + 2.66921i) q^{83} +(-0.711387 - 1.03062i) q^{84} +(5.03395 + 7.29294i) q^{85} +(8.82475 + 4.63159i) q^{86} +(-0.470821 + 3.87756i) q^{87} +(0.330415 + 0.871233i) q^{88} -3.23720 q^{89} +(-3.67540 + 9.69124i) q^{90} +(2.13416 + 3.18364i) q^{91} +(0.105043 + 0.276975i) q^{92} +(6.29651 + 16.6025i) q^{93} +(-7.60089 - 11.0118i) q^{94} +(-7.15108 - 6.33530i) q^{95} +(-3.70773 - 5.37158i) q^{96} +(10.6058 - 9.39595i) q^{97} +(6.47189 - 3.39671i) q^{98} -1.18125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	−0.707334	+	1.02475i	−0.500161	+	0.724608i	−0.989024	−	0.147752i	$-0.952796\pi$
$2$	−0.707334	+	1.02475i	−0.500161	+	0.724608i	0.488864	+	0.872360i	$0.337412\pi$
$3$	2.32028	−	1.21778i	1.33962	−	0.703085i	0.365859	−	0.930670i	$-0.380775\pi$
$3$	2.32028	−	1.21778i	1.33962	−	0.703085i	0.973758	+	0.227585i	$0.0730830\pi$
$4$	0.159418	+	0.420350i	0.0797088	+	0.210175i
$5$	1.61135	+	1.42753i	0.720618	+	0.638412i	0.941548	−	0.336878i	$-0.109371\pi$
$5$	1.61135	+	1.42753i	0.720618	+	0.638412i	−0.220931	+	0.975290i	$0.570909\pi$
$6$	−0.393297	+	3.23909i	−0.160563	+	1.32235i
$7$	−1.03213	−	0.254398i	−0.390109	−	0.0961533i	0.0393822	−	0.999224i	$-0.487461\pi$
$7$	−1.03213	−	0.254398i	−0.390109	−	0.0961533i	−0.429491	+	0.903071i	$0.641307\pi$
$8$	−2.96148	−	0.729939i	−1.04704	−	0.258073i
$9$	2.19654	−	3.18224i	0.732180	−	1.06075i
$10$	−2.60263	+	0.641490i	−0.823023	+	0.202857i
$11$	−0.173539	−	0.251415i	−0.0523240	−	0.0758044i	0.795949	−	0.605364i	$-0.206973\pi$
$11$	−0.173539	−	0.251415i	−0.0523240	−	0.0758044i	−0.848273	+	0.529560i	$0.822357\pi$
$12$	0.881788	+	0.781196i	0.254550	+	0.225512i
$13$	−2.66602	−	2.42741i	−0.739422	−	0.673242i
$13$	−2.66602	−	2.42741i	−0.739422	−	0.673242i
$14$	0.990757	−	0.877734i	0.264791	−	0.234584i
$15$	5.47721	+	1.35001i	1.41421	+	0.348571i
$16$	2.16976	−	1.92224i	0.542439	−	0.480559i
$17$	3.99680	+	0.985122i	0.969366	+	0.238927i	0.692049	−	0.721851i	$-0.256708\pi$
$17$	3.99680	+	0.985122i	0.969366	+	0.238927i	0.277318	+	0.960778i	$0.410555\pi$
$18$	1.70731	+	4.50181i	0.402417	+	1.06109i
$19$	−4.43794			−1.01813			−0.509067	−	0.860727i	$-0.670009\pi$
$19$	−4.43794			−1.01813			−0.509067	+	0.860727i	$0.670009\pi$
$20$	−0.343185	+	0.904905i	−0.0767385	+	0.202343i
$21$	−2.70464	+	0.666634i	−0.590201	+	0.145471i
$22$	0.380387			0.0810989
$23$	0.658914			0.137393			0.0686966	−	0.997638i	$-0.478116\pi$
$23$	0.658914			0.137393			0.0686966	+	0.997638i	$0.478116\pi$
$24$	−7.76038	+	1.91276i	−1.58408	+	0.390441i
$25$	−0.0440806	−	0.363036i	−0.00881611	−	0.0726072i
$26$	4.37326	−	1.01502i	0.857667	−	0.199062i
$27$	0.273757	−	2.25459i	0.0526846	−	0.433896i
$28$	−0.0576041	−	0.474412i	−0.0108861	−	0.0896555i
$29$	−0.846759	+	1.22674i	−0.157239	+	0.227800i	−0.893684	−	0.448698i	$-0.851888\pi$
$29$	−0.846759	+	1.22674i	−0.157239	+	0.227800i	0.736444	+	0.676498i	$0.236503\pi$
$30$	−5.25764	+	4.65787i	−0.959910	+	0.850406i
$31$	−0.816771	+	6.72671i	−0.146696	+	1.20815i	0.714410	+	0.699728i	$0.246695\pi$
$31$	−0.816771	+	6.72671i	−0.146696	+	1.20815i	−0.861106	+	0.508425i	$0.830228\pi$
$32$	−0.300231	−	2.47262i	−0.0530738	−	0.437102i
$33$	−0.708827	−	0.372021i	−0.123391	−	0.0647606i
$34$	−3.83658	+	3.39891i	−0.657968	+	0.582908i
$35$	−1.29997	−	1.88333i	−0.219734	−	0.318340i
$36$	1.68782	+	0.416010i	0.281303	+	0.0693350i
$37$	1.23739	−	10.1908i	0.203426	−	1.67536i	−0.430981	−	0.902361i	$-0.641832\pi$
$37$	1.23739	−	10.1908i	0.203426	−	1.67536i	0.634406	−	0.773000i	$-0.281245\pi$
$38$	3.13911	−	4.54778i	0.509231	−	0.737748i
$39$	−9.14198	−	2.38565i	−1.46389	−	0.382010i
$40$	−3.72997	−	5.40380i	−0.589760	−	0.854415i
$41$	6.43378	−	3.37671i	1.00479	−	0.527353i	0.119716	−	0.992808i	$-0.461802\pi$
$41$	6.43378	−	3.37671i	1.00479	−	0.527353i	0.885072	+	0.465455i	$0.154109\pi$
$42$	1.22995	−	3.24312i	0.189786	−	0.500424i
$43$	−0.964779	−	7.94567i	−0.147127	−	1.21170i	−0.859957	−	0.510366i	$-0.829510\pi$
$43$	−0.964779	−	7.94567i	−0.147127	−	1.21170i	0.712830	−	0.701337i	$-0.247413\pi$
$44$	0.0780169	−	0.113027i	0.0117615	−	0.0170395i
$45$	8.08214	−	1.99207i	1.20481	−	0.296960i
$46$	−0.466073	+	0.675223i	−0.0687187	+	0.0995562i
$47$	−3.81052	+	10.0475i	−0.555822	+	1.46558i	0.302842	+	0.953041i	$0.402065\pi$
$47$	−3.81052	+	10.0475i	−0.555822	+	1.46558i	−0.858663	+	0.512540i	$0.828705\pi$
$48$	2.69359	−	7.10242i	0.388786	−	1.02515i
$49$	−5.19761	−	2.72792i	−0.742516	−	0.389703i
$50$	0.403201	+	0.211616i	0.0570212	+	0.0299271i
$51$	10.4734	−	2.58145i	1.46657	−	0.361476i
$52$	0.595349	−	1.50764i	0.0825601	−	0.209071i
$53$	−0.0863969	−	0.0212949i	−0.0118675	−	0.00292508i	0.233377	−	0.972386i	$-0.425022\pi$
$53$	−0.0863969	−	0.0212949i	−0.0118675	−	0.00292508i	−0.245245	+	0.969461i	$0.578868\pi$
$54$	2.11676	+	1.87528i	0.288054	+	0.255194i
$55$	0.0792703	−	0.652849i	0.0106888	−	0.0880302i
$56$	2.87094	+	1.50679i	0.383646	+	0.201353i
$57$	−10.2973	+	5.40443i	−1.36391	+	0.715835i
$58$	−0.658163	−	1.73543i	−0.0864211	−	0.227874i
$59$	−0.0867438	−	0.0768483i	−0.0112931	−	0.0100048i	0.657457	−	0.753492i	$-0.271632\pi$
$59$	−0.0867438	−	0.0768483i	−0.0112931	−	0.0100048i	−0.668750	+	0.743487i	$0.733170\pi$
$60$	0.305687	+	2.51756i	0.0394640	+	0.325016i
$61$	−9.22781	+	2.27445i	−1.18150	+	0.291213i	−0.780673	−	0.624940i	$-0.785123\pi$
$61$	−9.22781	+	2.27445i	−1.18150	+	0.291213i	−0.400827	+	0.916154i	$0.631277\pi$
$62$	−6.31547	−	5.59502i	−0.802066	−	0.710568i
$63$	−3.07667	+	2.72569i	−0.387624	+	0.343405i
$64$	7.87964	+	4.13555i	0.984955	+	0.516944i
$65$	−0.830697	−	7.71724i	−0.103035	−	0.957206i
$66$	0.882607	−	0.463228i	0.108641	−	0.0570194i
$67$	−4.21608	+	11.1169i	−0.515076	+	1.35814i	0.385203	+	0.922832i	$0.374131\pi$
$67$	−4.21608	+	11.1169i	−0.515076	+	1.35814i	−0.900280	+	0.435312i	$0.856638\pi$
$68$	0.223064	+	1.83710i	0.0270505	+	0.222781i
$69$	1.52887	−	0.802412i	0.184054	−	0.0965991i
$70$	2.84945			0.340574
$71$	7.87842	−	4.13492i	0.934997	−	0.490724i	0.0728277	−	0.997345i	$-0.476798\pi$
$71$	7.87842	−	4.13492i	0.934997	−	0.490724i	0.862169	+	0.506620i	$0.169105\pi$
$72$	−8.82785	+	7.82079i	−1.04037	+	0.921689i
$73$	−1.33823	−	1.93876i	−0.156628	−	0.226915i	0.736812	−	0.676098i	$-0.236330\pi$
$73$	−1.33823	−	1.93876i	−0.156628	−	0.226915i	−0.893440	+	0.449183i	$0.851715\pi$
$74$	9.56780	+	8.47633i	1.11223	+	0.985354i
$75$	−0.544377	−	0.788666i	−0.0628593	−	0.0910674i
$76$	−0.707486	−	1.86549i	−0.0811542	−	0.213986i
$77$	0.115156	+	0.303641i	0.0131232	+	0.0346031i
$78$	8.91113	−	7.68080i	1.00899	−	0.869680i
$79$	−4.47220	+	11.7922i	−0.503161	+	1.32673i	0.407361	+	0.913267i	$0.366449\pi$
$79$	−4.47220	+	11.7922i	−0.503161	+	1.32673i	−0.910522	+	0.413460i	$0.864320\pi$
$80$	6.24029			0.697686
$81$	2.00306	+	5.28163i	0.222562	+	0.586848i
$82$	−1.09055	+	8.98148i	−0.120431	+	0.991839i
$83$	5.08576	+	2.66921i	0.558235	+	0.292984i	0.720148	−	0.693821i	$-0.244074\pi$
$83$	5.08576	+	2.66921i	0.558235	+	0.292984i	−0.161913	+	0.986805i	$0.551766\pi$
$84$	−0.711387	−	1.03062i	−0.0776187	−	0.112450i
$85$	5.03395	+	7.29294i	0.546009	+	0.791030i
$86$	8.82475	+	4.63159i	0.951598	+	0.499437i
$87$	−0.470821	+	3.87756i	−0.0504773	+	0.415718i
$88$	0.330415	+	0.871233i	0.0352223	+	0.0928737i
$89$	−3.23720			−0.343143			−0.171571	−	0.985172i	$-0.554884\pi$
$89$	−3.23720			−0.343143			−0.171571	+	0.985172i	$0.554884\pi$
$90$	−3.67540	+	9.69124i	−0.387421	+	1.02155i
$91$	2.13416	+	3.18364i	0.223721	+	0.333736i
$92$	0.105043	+	0.276975i	0.0109514	+	0.0288766i
$93$	6.29651	+	16.6025i	0.652918	+	1.72160i
$94$	−7.60089	−	11.0118i	−0.783972	−	1.13578i
$95$	−7.15108	−	6.33530i	−0.733685	−	0.649988i
$96$	−3.70773	−	5.37158i	−0.378419	−	0.548234i
$97$	10.6058	−	9.39595i	1.07686	−	0.954014i	0.0777826	−	0.996970i	$-0.475216\pi$
$97$	10.6058	−	9.39595i	1.07686	−	0.954014i	0.999077	+	0.0429560i	$0.0136775\pi$
$98$	6.47189	−	3.39671i	0.653759	−	0.343119i
$99$	−1.18125			−0.118720
$100$	0.145575	−	0.0764036i	0.0145575	−	0.00764036i
$101$	0.463832	+	3.82000i	0.0461530	+	0.380104i	0.997423	+	0.0717448i	$0.0228567\pi$
$101$	0.463832	+	3.82000i	0.0461530	+	0.380104i	−0.951270	+	0.308359i	$0.900220\pi$
$102$	−4.76283	+	12.5585i	−0.471590	+	1.24348i
$103$	6.88908	−	3.61567i	0.678801	−	0.356262i	−0.0898278	−	0.995957i	$-0.528632\pi$
$103$	6.88908	−	3.61567i	0.678801	−	0.356262i	0.768629	+	0.639695i	$0.220939\pi$
$104$	6.12352	+	9.13476i	0.600461	+	0.895737i
$105$	−5.30977	−	2.78678i	−0.518180	−	0.271962i
$106$	0.0829334	−	0.0734726i	0.00805521	−	0.00713629i
$107$	−3.70944	−	3.28628i	−0.358605	−	0.317697i	0.464513	−	0.885566i	$-0.346229\pi$
$107$	−3.70944	−	3.28628i	−0.358605	−	0.317697i	−0.823119	+	0.567870i	$0.807768\pi$
$108$	0.991359	−	0.244348i	0.0953936	−	0.0235124i
$109$	1.67156	+	13.7666i	0.160107	+	1.31860i	0.822210	+	0.569185i	$0.192741\pi$
$109$	1.67156	+	13.7666i	0.160107	+	1.31860i	−0.662103	+	0.749413i	$0.730336\pi$
$110$	0.612937	+	0.543015i	0.0584413	+	0.0517745i
$111$	−9.53907	−	25.1525i	−0.905409	−	2.38737i
$112$	−2.72849	+	1.43202i	−0.257818	+	0.135313i
$113$	15.4717	+	8.12019i	1.45546	+	0.763883i	0.992471	−	0.122482i	$-0.0390854\pi$
$113$	15.4717	+	8.12019i	1.45546	+	0.763883i	0.462987	+	0.886365i	$0.346778\pi$
$114$	1.74543	−	14.3749i	0.163474	−	1.34633i
$115$	1.06174	+	0.940621i	0.0990079	+	0.0877134i
$116$	−0.650649	−	0.160371i	−0.0604113	−	0.0148900i
$117$	−13.5806	+	3.15202i	−1.25553	+	0.291405i
$118$	0.140107	−	0.0345333i	0.0128979	−	0.00317905i
$119$	−3.87461	−	2.03355i	−0.355185	−	0.186416i
$120$	−15.2352	−	7.99606i	−1.39078	−	0.729937i
$121$	3.86756	−	10.1979i	0.351596	−	0.927083i
$122$	4.19640	−	11.0650i	0.379924	−	1.00178i
$123$	10.8161	−	15.6698i	0.975256	−	1.41290i
$124$	−2.95778	+	0.729027i	−0.265617	+	0.0654686i
$125$	6.56170	−	9.50626i	0.586896	−	0.850266i
$126$	−0.616921	−	5.08080i	−0.0549597	−	0.452634i
$127$	−3.15395	+	8.31628i	−0.279868	+	0.737950i	0.719201	+	0.694802i	$0.244508\pi$
$127$	−3.15395	+	8.31628i	−0.279868	+	0.737950i	−0.999069	+	0.0431482i	$0.986261\pi$
$128$	−5.40049	+	2.83440i	−0.477341	+	0.250528i
$129$	−11.9146	−	17.2613i	−1.04903	−	1.51978i
$130$	8.49583	+	4.60741i	0.745133	+	0.404097i
$131$	−7.63564	+	11.0621i	−0.667129	+	0.966503i	0.332597	+	0.943069i	$0.392075\pi$
$131$	−7.63564	+	11.0621i	−0.667129	+	0.966503i	−0.999725	+	0.0234336i	$0.992540\pi$
$132$	0.0433795	−	0.357262i	0.00377570	−	0.0310957i
$133$	4.58054	+	1.12900i	0.397183	+	0.0978969i
$134$	−8.40986	−	12.1838i	−0.726501	−	1.05252i
$135$	3.65962	−	3.24214i	0.314970	−	0.279039i
$136$	−11.1174	−	5.83484i	−0.953306	−	0.500334i
$137$	−0.747822	−	6.15887i	−0.0638907	−	0.526188i	−0.989156	−	0.146867i	$-0.953081\pi$
$137$	−0.747822	−	6.15887i	−0.0638907	−	0.526188i	0.925265	−	0.379320i	$-0.123842\pi$
$138$	−0.259149	+	2.13428i	−0.0220602	+	0.181682i
$139$	16.0613	−	14.2290i	1.36230	−	1.20689i	0.406224	−	0.913774i	$-0.366845\pi$
$139$	16.0613	−	14.2290i	1.36230	−	1.20689i	0.956076	−	0.293118i	$-0.0946930\pi$
$140$	0.584418	−	0.846676i	0.0493924	−	0.0715572i
$141$	3.39417	+	27.9535i	0.285840	+	2.35411i
$142$	−1.33542	+	10.9982i	−0.112066	+	0.922948i
$143$	−0.147627	+	1.09153i	−0.0123452	+	0.0912781i
$144$	−1.35106	−	11.1269i	−0.112588	−	0.927245i
$145$	−3.11564	+	0.767936i	−0.258740	+	0.0637736i
$146$	2.93333			0.242764
$147$	−15.3819			−1.26868
$148$	4.48097	−	1.10446i	0.368334	−	0.0907861i
$149$	−5.89123	+	15.5339i	−0.482628	+	1.27259i	0.443804	+	0.896124i	$0.353629\pi$
$149$	−5.89123	+	15.5339i	−0.482628	+	1.27259i	−0.926432	+	0.376462i	$0.877141\pi$
$150$	1.19324			0.0974279
$151$	−0.803587	−	2.11889i	−0.0653950	−	0.172433i	0.898335	−	0.439310i	$-0.144777\pi$
$151$	−0.803587	−	2.11889i	−0.0653950	−	0.172433i	−0.963730	+	0.266878i	$0.914008\pi$
$152$	13.1429	+	3.23943i	1.06603	+	0.262752i
$153$	11.9140	−	10.5549i	0.963191	−	0.853313i
$154$	−0.392610	−	0.0967697i	−0.0316374	−	0.00779792i
$155$	−10.9187	+	9.67312i	−0.877011	+	0.776964i
$156$	−0.454587	−	4.22315i	−0.0363961	−	0.338122i
$157$	−0.126137	−	0.111748i	−0.0100669	−	0.00891845i	0.658074	−	0.752953i	$-0.271371\pi$
$157$	−0.126137	−	0.111748i	−0.0100669	−	0.00891845i	−0.668141	+	0.744035i	$0.732910\pi$
$158$	−8.92074	−	12.9239i	−0.709696	−	1.02817i
$159$	−0.226398	+	0.0558020i	−0.0179545	+	0.00442539i
$160$	3.04597	−	4.41285i	0.240805	−	0.348867i
$161$	−0.680087	−	0.167626i	−0.0535983	−	0.0132108i
$162$	−6.82918	−	1.68324i	−0.536551	−	0.132248i
$163$	−0.177932	+	1.46540i	−0.0139367	+	0.114779i	−0.998017	−	0.0629457i	$-0.979951\pi$
$163$	−0.177932	+	1.46540i	−0.0139367	+	0.114779i	0.984080	+	0.177725i	$0.0568736\pi$
$164$	2.44506	+	2.16613i	0.190927	+	0.169146i
$165$	−0.611097	−	1.61133i	−0.0475738	−	0.125442i
$166$	−6.33261	+	3.32361i	−0.491506	+	0.257962i
$167$	3.06091	−	4.43450i	0.236861	−	0.343152i	−0.686470	−	0.727158i	$-0.740841\pi$
$167$	3.06091	−	4.43450i	0.236861	−	0.343152i	0.923330	+	0.384007i	$0.125456\pi$
$168$	8.49634			0.655507
$169$	1.21538	+	12.9431i	0.0934904	+	0.995620i
$170$	−11.0341			−0.846279
$171$	−9.74811	+	14.1226i	−0.745457	+	1.07998i
$172$	3.18616	−	1.67223i	0.242942	−	0.127506i
$173$	8.34501	+	22.0040i	0.634460	+	1.67293i	0.735057	+	0.678006i	$0.237155\pi$
$173$	8.34501	+	22.0040i	0.634460	+	1.67293i	−0.100597	+	0.994927i	$0.532075\pi$
$174$	−3.64050	−	3.22520i	−0.275986	−	0.244502i
$175$	−0.0468586	+	0.385915i	−0.00354218	+	0.0291724i
$176$	−0.859815	−	0.211925i	−0.0648110	−	0.0159745i
$177$	−0.294855	−	0.0726751i	−0.0221626	−	0.00546260i
$178$	2.28978	−	3.31732i	0.171627	−	0.248644i
$179$	−8.44609	+	2.08177i	−0.631290	+	0.155599i	−0.541962	−	0.840403i	$-0.682318\pi$
$179$	−8.44609	+	2.08177i	−0.631290	+	0.155599i	−0.0893285	+	0.996002i	$0.528472\pi$
$180$	2.12580	+	3.07976i	0.158448	+	0.229551i
$181$	11.5344	+	10.2186i	0.857344	+	0.759541i	0.972277	−	0.233833i	$-0.0751267\pi$
$181$	11.5344	+	10.2186i	0.857344	+	0.759541i	−0.114933	+	0.993373i	$0.536665\pi$
$182$	−4.77200	−	0.0649112i	−0.353724	−	0.00481154i
$183$	−18.6414	+	16.5148i	−1.37801	+	1.22081i
$184$	−1.95136	−	0.480967i	−0.143856	−	0.0354574i
$185$	16.5416	−	14.6546i	1.21616	−	1.07743i
$186$	−21.4672	−	5.29119i	−1.57405	−	0.387969i
$187$	−0.445926	−	1.17581i	−0.0326094	−	0.0859838i
$188$	−4.83094			−0.352332
$189$	−0.856116	+	2.25739i	−0.0622733	+	0.164201i
$190$	11.5503	−	2.84690i	0.837947	−	0.206536i
$191$	−20.9705			−1.51737			−0.758685	−	0.651458i	$-0.774158\pi$
$191$	−20.9705			−1.51737			−0.758685	+	0.651458i	$0.774158\pi$
$192$	23.3192			1.68292
$193$	18.3760	−	4.52928i	1.32273	−	0.326024i	0.486155	−	0.873872i	$-0.338399\pi$
$193$	18.3760	−	4.52928i	1.32273	−	0.326024i	0.836578	+	0.547848i	$0.184553\pi$
$194$	2.12664	+	17.5144i	0.152684	+	1.25746i
$195$	−11.3253	−	16.8946i	−0.811025	−	1.20985i
$196$	0.318089	−	2.61969i	0.0227206	−	0.187121i
$197$	−2.45725	−	20.2373i	−0.175072	−	1.44185i	−0.769988	−	0.638059i	$-0.779738\pi$
$197$	−2.45725	−	20.2373i	−0.175072	−	1.44185i	0.594916	−	0.803788i	$-0.297185\pi$
$198$	0.835536	−	1.21048i	0.0593789	−	0.0860253i
$199$	−11.9935	+	10.6254i	−0.850200	+	0.753211i	−0.970902	−	0.239478i	$-0.923024\pi$
$199$	−11.9935	+	10.6254i	−0.850200	+	0.753211i	0.120702	+	0.992689i	$0.461485\pi$
$200$	−0.134451	+	1.10730i	−0.00950709	+	0.0782980i
$201$	3.75541	+	30.9286i	0.264886	+	2.18153i
$202$	−4.24263	−	2.22670i	−0.298510	−	0.156670i
$203$	1.18605	−	1.05075i	0.0832442	−	0.0737480i
$204$	2.75475	+	3.99095i	0.192871	+	0.279422i
$205$	15.1874	+	3.74337i	1.06074	+	0.261448i
$206$	−1.16772	+	9.61707i	−0.0813592	+	0.670053i
$207$	1.44733	−	2.09682i	0.100596	−	0.145739i
$208$	−10.4507	−	0.142155i	−0.724624	−	0.00985670i
$209$	0.770156	+	1.11576i	0.0532728	+	0.0771790i
$210$	6.61153	−	3.47000i	0.456239	−	0.239453i
$211$	6.43656	−	16.9718i	0.443111	−	1.16839i	−0.508495	−	0.861065i	$-0.669798\pi$
$211$	6.43656	−	16.9718i	0.443111	−	1.16839i	0.951606	−	0.307322i	$-0.0994329\pi$
$212$	−0.00482187	−	0.0397117i	−0.000331168	−	0.00272741i
$213$	13.2448	−	19.1884i	0.907517	−	1.31477i
$214$	5.99143	−	1.47676i	0.409566	−	0.100949i
$215$	9.78810	−	14.1805i	0.667543	−	0.967103i
$216$	−2.45644	+	6.47710i	−0.167140	+	0.440711i
$217$	2.55428	−	6.73507i	0.173396	−	0.457207i
$218$	−15.2897	−	8.02463i	−1.03555	−	0.543496i
$219$	−5.46606	−	2.86881i	−0.369362	−	0.193856i
$220$	0.287062	−	0.0707545i	0.0193537	−	0.00477027i
$221$	−8.26427	−	12.3282i	−0.555915	−	0.829286i
$222$	32.5223	+	8.01603i	2.18276	+	0.538001i
$223$	−9.82530	−	8.70445i	−0.657950	−	0.582893i	0.266668	−	0.963789i	$-0.414077\pi$
$223$	−9.82530	−	8.70445i	−0.657950	−	0.582893i	−0.924618	+	0.380895i	$0.875616\pi$
$224$	−0.319152	+	2.62845i	−0.0213242	+	0.175621i
$225$	−1.25209	−	0.657148i	−0.0834727	−	0.0438099i
$226$	−19.2649	+	10.1110i	−1.28148	+	0.672572i
$227$	−5.55674	−	14.6519i	−0.368814	−	0.972481i	−0.983046	−	0.183357i	$-0.941304\pi$
$227$	−5.55674	−	14.6519i	−0.368814	−	0.972481i	0.614233	−	0.789125i	$-0.289466\pi$
$228$	−3.91332	−	3.46690i	−0.259166	−	0.229601i
$229$	−1.70496	−	14.0416i	−0.112667	−	0.927896i	−0.933957	−	0.357385i	$-0.883668\pi$
$229$	−1.70496	−	14.0416i	−0.112667	−	0.927896i	0.821290	−	0.570511i	$-0.193255\pi$
$230$	−1.71491	+	0.422687i	−0.113078	+	0.0278712i
$231$	0.636962	+	0.564299i	0.0419090	+	0.0371282i
$232$	3.40311	−	3.01489i	0.223425	−	0.197937i
$233$	−17.3955	−	9.12988i	−1.13962	−	0.598118i	−0.214097	−	0.976812i	$-0.568681\pi$
$233$	−17.3955	−	9.12988i	−1.13962	−	0.598118i	−0.925522	+	0.378694i	$0.876373\pi$
$234$	6.37600	−	16.1463i	0.416812	−	1.05552i
$235$	−20.4832	+	10.7504i	−1.33618	+	0.701281i
$236$	0.0184747	−	0.0487137i	0.00120260	−	0.00317099i
$237$	3.98354	+	32.8074i	0.258759	+	2.13107i
$238$	4.82453	−	2.53211i	0.312728	−	0.164132i
$239$	−7.12576			−0.460927			−0.230464	−	0.973081i	$-0.574024\pi$
$239$	−7.12576			−0.460927			−0.230464	+	0.973081i	$0.574024\pi$
$240$	14.4792	−	7.59929i	0.934631	−	0.490532i
$241$	−2.90404	+	2.57276i	−0.187066	+	0.165726i	−0.751458	−	0.659781i	$-0.770649\pi$
$241$	−2.90404	+	2.57276i	−0.187066	+	0.165726i	0.564392	+	0.825507i	$0.309111\pi$
$242$	7.71467	+	11.1766i	0.495917	+	0.718460i
$243$	16.1795	+	14.3338i	1.03791	+	0.919511i
$244$	−2.42714	−	3.51632i	−0.155382	−	0.225109i
$245$	−4.48099	−	11.8154i	−0.286280	−	0.754858i
$246$	8.40708	+	22.1676i	0.536016	+	1.41336i
$247$	11.8317	+	10.7727i	0.752831	+	0.685450i
$248$	7.32894	−	19.3248i	0.465388	−	1.22713i
$249$	15.0509			0.953813
$250$	5.10023	+	13.4482i	0.322567	+	0.850540i
$251$	−0.681858	+	5.61560i	−0.0430385	+	0.354454i	0.955242	+	0.295827i	$0.0955952\pi$
$251$	−0.681858	+	5.61560i	−0.0430385	+	0.354454i	−0.998280	+	0.0586266i	$0.981328\pi$
$252$	−1.63622	−	0.858755i	−0.103072	−	0.0540965i
$253$	−0.114347	−	0.165661i	−0.00718895	−	0.0104150i
$254$	−6.29121	−	9.11440i	−0.394746	−	0.571888i
$255$	20.5614	+	10.7914i	1.28760	+	0.675787i
$256$	−1.22990	+	10.1291i	−0.0768687	+	0.633071i
$257$	2.64879	+	6.98428i	0.165227	+	0.435667i	0.991901	−	0.127014i	$-0.0405392\pi$
$257$	2.64879	+	6.98428i	0.165227	+	0.435667i	−0.826674	+	0.562681i	$0.809770\pi$
$258$	26.1162			1.62592
$259$	−3.86967	+	10.2035i	−0.240450	+	0.634014i
$260$	3.11151	−	1.57945i	0.192968	−	0.0979532i
$261$	2.04384	+	5.38918i	0.126511	+	0.333582i
$262$	−5.93498	−	15.6492i	−0.366664	−	0.966814i
$263$	7.28078	+	10.5480i	0.448952	+	0.650420i	0.980479	−	0.196621i	$-0.0629970\pi$
$263$	7.28078	+	10.5480i	0.448952	+	0.650420i	−0.531527	+	0.847041i	$0.678382\pi$
$264$	1.82763	+	1.61913i	0.112483	+	0.0996509i
$265$	−0.108816	−	0.157648i	−0.00668454	−	0.00968423i
$266$	−4.39692	+	3.89533i	−0.269592	+	0.238838i
$267$	−7.51123	+	3.94220i	−0.459680	+	0.241258i
$268$	−5.34510			−0.326504
$269$	−17.1834	+	9.01856i	−1.04769	+	0.549871i	−0.898517	−	0.438940i	$-0.855354\pi$
$269$	−17.1834	+	9.01856i	−1.04769	+	0.549871i	−0.149175	+	0.988811i	$0.547662\pi$
$270$	0.733811	+	6.04347i	0.0446583	+	0.367794i
$271$	−1.74606	+	4.60398i	−0.106066	+	0.279672i	−0.977533	−	0.210781i	$-0.932399\pi$
$271$	−1.74606	+	4.60398i	−0.106066	+	0.279672i	0.871468	+	0.490453i	$0.163169\pi$
$272$	10.5657	−	5.54531i	0.640641	−	0.336234i
$273$	8.82883	+	4.78801i	0.534345	+	0.289783i
$274$	6.84026	+	3.59005i	0.413235	+	0.216883i
$275$	−0.0836229	+	0.0740834i	−0.00504265	+	0.00446740i
$276$	0.581022	+	0.514741i	0.0349734	+	0.0309838i
$277$	9.50971	−	2.34393i	0.571383	−	0.140833i	0.0569702	−	0.998376i	$-0.481856\pi$
$277$	9.50971	−	2.34393i	0.571383	−	0.140833i	0.514413	+	0.857543i	$0.328010\pi$
$278$	3.22054	+	26.5235i	0.193155	+	1.59077i
$279$	19.6119	+	17.3746i	1.17414	+	1.04019i
$280$	2.47511	+	6.52633i	0.147916	+	0.390023i
$281$	−9.29229	+	4.87697i	−0.554331	+	0.290936i	−0.718535	−	0.695491i	$-0.755187\pi$
$281$	−9.29229	+	4.87697i	−0.554331	+	0.290936i	0.164203	+	0.986426i	$0.447495\pi$
$282$	−31.0462	−	16.2943i	−1.84877	−	0.970310i
$283$	2.48551	−	20.4700i	0.147748	−	1.21682i	−0.710543	−	0.703654i	$-0.751550\pi$
$283$	2.48551	−	20.4700i	0.147748	−	1.21682i	0.858291	−	0.513163i	$-0.171526\pi$
$284$	2.99407	+	2.65252i	0.177665	+	0.157398i
$285$	−24.3075	−	5.99127i	−1.43985	−	0.354892i
$286$	−1.01412	−	0.923356i	−0.0599663	−	0.0545992i
$287$	−7.49954	+	1.84847i	−0.442684	+	0.109112i
$288$	−8.52794	−	4.47581i	−0.502514	−	0.263740i
$289$	−0.0488170	−	0.0256211i	−0.00287159	−	0.00150713i
$290$	1.41686	−	3.73594i	0.0832006	−	0.219382i
$291$	13.1664	−	34.7168i	0.771826	−	2.03514i
$292$	0.601621	−	0.871599i	0.0352072	−	0.0510065i
$293$	10.6902	−	2.63489i	0.624525	−	0.153932i	0.0856611	−	0.996324i	$-0.472700\pi$
$293$	10.6902	−	2.63489i	0.624525	−	0.153932i	0.538864	+	0.842393i	$0.318854\pi$
$294$	10.8802	−	15.7627i	0.634545	−	0.919297i
$295$	−0.0300713	−	0.247659i	−0.00175082	−	0.0144193i
$296$	−11.1032	+	29.2767i	−0.645360	+	1.70167i
$297$	−0.614345	+	0.322433i	−0.0356479	+	0.0187095i
$298$	−11.7513	−	17.0247i	−0.680734	−	0.986214i
$299$	−1.75668	−	1.59945i	−0.101592	−	0.0924988i
$300$	0.244733	−	0.354556i	0.0141296	−	0.0204703i
$301$	−1.02558	+	8.44642i	−0.0591135	+	0.486844i
$302$	2.73973	+	0.675284i	0.157654	+	0.0388582i
$303$	5.72813	+	8.29863i	0.329073	+	0.476744i
$304$	−9.62925	+	8.53077i	−0.552275	+	0.489273i
$305$	−18.1161	−	9.50805i	−1.03732	−	0.544429i
$306$	2.38895	+	19.6747i	0.136567	+	1.12473i
$307$	−1.02049	+	8.40452i	−0.0582426	+	0.479671i	0.934180	+	0.356801i	$0.116133\pi$
$307$	−1.02049	+	8.40452i	−0.0582426	+	0.479671i	−0.992423	+	0.122870i	$0.960790\pi$
$308$	−0.109278	+	0.0968115i	−0.00622667	+	0.00551635i
$309$	11.5815	−	16.7787i	0.658850	−	0.954510i
$310$	−2.18937	−	18.0311i	−0.124348	−	1.02410i
$311$	3.68467	−	30.3460i	0.208938	−	1.72076i	−0.390724	−	0.920508i	$-0.627775\pi$
$311$	3.68467	−	30.3460i	0.208938	−	1.72076i	0.599662	−	0.800253i	$-0.295302\pi$
$312$	25.3324	+	13.7381i	1.43417	+	0.777769i
$313$	1.24764	+	10.2752i	0.0705206	+	0.580789i	0.984545	+	0.175131i	$0.0560348\pi$
$313$	1.24764	+	10.2752i	0.0705206	+	0.580789i	−0.914025	+	0.405659i	$0.867042\pi$
$314$	0.203735	−	0.0502162i	0.0114974	−	0.00283386i
$315$	−8.84861			−0.498563
$316$	−5.66980			−0.318951
$317$	24.5967	−	6.06255i	1.38149	−	0.340507i	0.522561	−	0.852602i	$-0.324977\pi$
$317$	24.5967	−	6.06255i	1.38149	−	0.340507i	0.858929	+	0.512095i	$0.171131\pi$
$318$	0.102956	−	0.271472i	0.00577347	−	0.0152234i
$319$	0.455367			0.0254956
$320$	6.79323	+	17.9123i	0.379753	+	1.00133i
$321$	−12.6089	−	3.10782i	−0.703761	−	0.173462i
$322$	0.652824	−	0.578351i	0.0363804	−	0.0322303i
$323$	−17.7376	−	4.37192i	−0.986944	−	0.243260i
$324$	−1.90081	+	1.68397i	−0.105601	+	0.0935539i
$325$	−0.763717	+	1.07486i	−0.0423634	+	0.0596228i
$326$	−1.37581	−	1.21886i	−0.0761991	−	0.0675065i
$327$	20.6431	+	29.9068i	1.14157	+	1.65385i
$328$	−21.5183	+	5.30379i	−1.18815	+	0.292853i
$329$	6.48903	−	9.40098i	0.357752	−	0.518293i
$330$	2.08346	+	0.513527i	0.114691	+	0.0282687i
$331$	−16.7556	−	4.12989i	−0.920973	−	0.226999i	−0.249798	−	0.968298i	$-0.580364\pi$
$331$	−16.7556	−	4.12989i	−0.920973	−	0.226999i	−0.671175	+	0.741299i	$0.734210\pi$
$332$	−0.311243	+	2.56332i	−0.0170817	+	0.140680i
$333$	−29.7116	−	26.3222i	−1.62819	−	1.44245i
$334$	2.37917	+	6.27334i	0.130182	+	0.343262i
$335$	−22.6633	+	11.8946i	−1.23823	+	0.649872i
$336$	−4.58698	+	6.64539i	−0.250240	+	0.362536i
$337$	11.2869			0.614835			0.307418	−	0.951575i	$-0.400535\pi$
$337$	11.2869			0.614835			0.307418	+	0.951575i	$0.400535\pi$
$338$	−14.1231	−	7.90962i	−0.768195	−	0.430226i
$339$	45.7874			2.48683
$340$	−2.26308	+	3.27864i	−0.122733	+	0.177809i
$341$	1.83294	−	0.961999i	0.0992590	−	0.0520952i
$342$	−7.57695	−	19.9788i	−0.409714	−	1.08033i
$343$	10.2404	+	9.07223i	0.552931	+	0.489854i
$344$	−2.94268	+	24.2352i	−0.158659	+	1.30667i
$345$	3.60901	+	0.889541i	0.194303	+	0.0478913i
$346$	−28.4513	−	7.01262i	−1.52955	−	0.377001i
$347$	−7.81461	+	11.3214i	−0.419510	+	0.607765i	−0.974580	−	0.224038i	$-0.928076\pi$
$347$	−7.81461	+	11.3214i	−0.419510	+	0.607765i	0.555070	+	0.831803i	$0.312691\pi$
$348$	−1.70499	+	0.420242i	−0.0913969	+	0.0225273i
$349$	−8.67793	−	12.5722i	−0.464519	−	0.672972i	0.518793	−	0.854900i	$-0.326382\pi$
$349$	−8.67793	−	12.5722i	−0.464519	−	0.672972i	−0.983312	+	0.181928i	$0.941766\pi$
$350$	−0.362322	−	0.320989i	−0.0193669	−	0.0171576i
$351$	−6.20266	+	5.34628i	−0.331073	+	0.285363i
$352$	−0.569552	+	0.504579i	−0.0303572	+	0.0268942i
$353$	−13.3447	−	3.28916i	−0.710265	−	0.175065i	−0.132399	−	0.991196i	$-0.542268\pi$
$353$	−13.3447	−	3.28916i	−0.710265	−	0.175065i	−0.577866	+	0.816132i	$0.696114\pi$
$354$	0.283035	−	0.250747i	0.0150431	−	0.0133270i
$355$	18.5976	+	4.58390i	0.987060	+	0.243288i
$356$	−0.516067	−	1.36076i	−0.0273515	−	0.0721200i
$357$	−11.4666			−0.606878
$358$	3.84091	−	10.1276i	0.202998	−	0.535263i
$359$	23.4633	−	5.78319i	1.23835	−	0.305225i	0.434833	−	0.900511i	$-0.356807\pi$
$359$	23.4633	−	5.78319i	1.23835	−	0.305225i	0.803514	+	0.595286i	$0.202961\pi$
$360$	−25.3892			−1.33813
$361$	0.695322			0.0365959
$362$	−18.6302	+	4.59192i	−0.979179	+	0.241346i
$363$	−3.44497	−	28.3719i	−0.180814	−	1.48914i
$364$	−0.998018	+	1.40462i	−0.0523104	+	0.0736223i
$365$	0.611286	−	5.03440i	0.0319962	−	0.263512i
$366$	−3.73788	−	30.7842i	−0.195382	−	1.60912i
$367$	9.64833	−	13.9780i	0.503639	−	0.729646i	−0.485884	−	0.874023i	$-0.661502\pi$
$367$	9.64833	−	13.9780i	0.503639	−	0.729646i	0.989523	+	0.144377i	$0.0461177\pi$
$368$	1.42968	−	1.26659i	0.0745274	−	0.0660255i
$369$	3.38657	−	27.8909i	0.176298	−	1.45194i
$370$	3.31685	+	27.3167i	0.172435	+	1.42013i
$371$	0.0837556	+	0.0439583i	0.00434837	+	0.00228220i
$372$	−5.97510	+	5.29347i	−0.309794	+	0.274454i
$373$	−14.5950	−	21.1445i	−0.755700	−	1.09482i	−0.992378	−	0.123232i	$-0.960674\pi$
$373$	−14.5950	−	21.1445i	−0.755700	−	1.09482i	0.236678	−	0.971588i	$-0.423941\pi$
$374$	1.52033	+	0.374728i	0.0786145	+	0.0193767i
$375$	3.64848	−	30.0479i	0.188407	−	1.55167i
$376$	18.6189	−	26.9741i	0.960195	−	1.39108i
$377$	5.23529	−	1.21510i	0.269631	−	0.0625806i
$378$	−1.70770	−	2.47404i	−0.0878349	−	0.127251i
$379$	6.69618	−	3.51443i	0.343960	−	0.180524i	−0.283893	−	0.958856i	$-0.591626\pi$
$379$	6.69618	−	3.51443i	0.343960	−	0.180524i	0.627853	+	0.778332i	$0.283934\pi$
$380$	1.52304	−	4.01591i	0.0781301	−	0.206012i
$381$	2.80933	+	23.1369i	0.143926	+	1.18534i
$382$	14.8331	−	21.4895i	0.758929	−	1.09950i
$383$	15.4682	−	3.81256i	0.790386	−	0.194813i	0.176597	−	0.984283i	$-0.443491\pi$
$383$	15.4682	−	3.81256i	0.790386	−	0.194813i	0.613788	+	0.789471i	$0.289645\pi$
$384$	−9.07901	+	13.1532i	−0.463311	+	0.671222i
$385$	−0.247901	+	0.653661i	−0.0126342	+	0.0333136i
$386$	−8.35659	+	22.0345i	−0.425339	+	1.12153i
$387$	−27.4042	−	14.3828i	−1.39303	−	0.731120i
$388$	5.64034	+	2.96028i	0.286345	+	0.150286i
$389$	−19.8565	+	4.89419i	−1.00677	+	0.248145i	−0.708024	−	0.706189i	$-0.750413\pi$
$389$	−19.8565	+	4.89419i	−1.00677	+	0.248145i	−0.298742	+	0.954334i	$0.596567\pi$
$390$	25.3235	+	0.344464i	1.28231	+	0.0174426i
$391$	2.63355	+	0.649111i	0.133184	+	0.0328270i
$392$	13.4014	+	11.8726i	0.676874	+	0.599658i
$393$	−4.24562	+	34.9658i	−0.214163	+	1.76379i
$394$	22.4763	+	11.7965i	1.13234	+	0.594297i
$395$	−24.0400	+	12.6172i	−1.20959	+	0.634839i
$396$	−0.188311	−	0.496537i	−0.00946301	−	0.0249519i
$397$	0.0984081	+	0.0871820i	0.00493896	+	0.00437554i	0.665589	−	0.746319i	$-0.268181\pi$
$397$	0.0984081	+	0.0871820i	0.00493896	+	0.00437554i	−0.660650	+	0.750694i	$0.729719\pi$
$398$	−2.40489	−	19.8061i	−0.120546	−	0.992788i
$399$	12.0030	−	2.95848i	0.600903	−	0.148109i
$400$	−0.793485	−	0.702966i	−0.0396742	−	0.0351483i
$401$	13.4930	−	11.9537i	0.673807	−	0.596941i	−0.255251	−	0.966875i	$-0.582158\pi$
$401$	13.4930	−	11.9537i	0.673807	−	0.596941i	0.929058	+	0.369934i	$0.120620\pi$
$402$	−34.3504	−	18.0285i	−1.71324	−	0.899180i
$403$	18.5060	−	15.9509i	0.921850	−	0.794573i
$404$	−1.53179	+	0.803947i	−0.0762095	+	0.0399978i
$405$	−4.31207	+	11.3700i	−0.214268	+	0.564979i
$406$	0.237821	+	1.95863i	0.0118029	+	0.0972053i
$407$	−2.77686	+	1.45741i	−0.137644	+	0.0722410i
$408$	−32.9010			−1.62884
$409$	−13.2405	+	6.94915i	−0.654701	+	0.343614i	−0.759149	−	0.650917i	$-0.774385\pi$
$409$	−13.2405	+	6.94915i	−0.654701	+	0.343614i	0.104448	+	0.994530i	$0.466692\pi$
$410$	−14.5786	+	12.9155i	−0.719986	+	0.637852i
$411$	−9.23530	−	13.3796i	−0.455544	−	0.659969i
$412$	2.61809	+	2.31942i	0.128984	+	0.114270i
$413$	0.0699810	+	0.101385i	0.00344354	+	0.00498883i
$414$	1.12497	+	2.96631i	0.0552893	+	0.145786i
$415$	4.38455	+	11.5611i	0.215229	+	0.567513i
$416$	−5.20165	+	7.32086i	−0.255032	+	0.358935i
$417$	19.9389	−	52.5745i	0.976412	−	2.57459i
$418$	−1.68814			−0.0825695
$419$	−2.43664	−	6.42490i	−0.119038	−	0.313877i	0.862233	−	0.506513i	$-0.169066\pi$
$419$	−2.43664	−	6.42490i	−0.119038	−	0.313877i	−0.981270	+	0.192636i	$0.938296\pi$
$420$	0.324952	−	2.67622i	0.0158560	−	0.130586i
$421$	−14.8896	−	7.81469i	−0.725677	−	0.380864i	0.0610758	−	0.998133i	$-0.480547\pi$
$421$	−14.8896	−	7.81469i	−0.725677	−	0.380864i	−0.786752	+	0.617269i	$0.788239\pi$
$422$	12.8391	+	18.6006i	0.624996	+	0.905463i
$423$	23.6036	+	34.1957i	1.14765	+	1.66265i
$424$	0.240319	+	0.126129i	0.0116709	+	0.00612536i
$425$	0.181454	−	1.49441i	0.00880180	−	0.0724894i
$426$	10.2948	+	27.1452i	0.498785	+	1.31519i
$427$	10.1029			0.488915
$428$	0.790036	−	2.08315i	0.0381878	−	0.100693i
$429$	0.986703	+	2.71243i	0.0476385	+	0.130957i
$430$	7.60803	+	20.0607i	0.366892	+	0.967414i
$431$	8.93024	+	23.5471i	0.430155	+	1.13422i	0.958474	+	0.285179i	$0.0920530\pi$
$431$	8.93024	+	23.5471i	0.430155	+	1.13422i	−0.528320	+	0.849045i	$0.677178\pi$
$432$	−3.73987	−	5.41814i	−0.179935	−	0.260680i
$433$	13.3190	+	11.7996i	0.640072	+	0.567054i	0.919489	−	0.393115i	$-0.128603\pi$
$433$	13.3190	+	11.7996i	0.640072	+	0.567054i	−0.279417	+	0.960170i	$0.590141\pi$
$434$	5.09504	+	7.38144i	0.244570	+	0.354321i
$435$	−6.29399	+	5.57599i	−0.301774	+	0.267348i
$436$	−5.52030	+	2.89728i	−0.264374	+	0.138754i
$437$	−2.92422			−0.139885
$438$	6.80615	−	3.57214i	0.325210	−	0.170684i
$439$	−4.69844	−	38.6952i	−0.224244	−	1.84682i	−0.476520	−	0.879164i	$-0.658102\pi$
$439$	−4.69844	−	38.6952i	−0.224244	−	1.84682i	0.252275	−	0.967656i	$-0.418821\pi$
$440$	−0.711298	+	1.87554i	−0.0339098	+	0.0894128i
$441$	−20.0976	+	10.5481i	−0.957031	+	0.502288i
$442$	18.4790	+	0.251360i	0.878954	+	0.0119560i
$443$	−30.5225	−	16.0194i	−1.45017	−	0.761107i	−0.458351	−	0.888771i	$-0.651560\pi$
$443$	−30.5225	−	16.0194i	−1.45017	−	0.761107i	−0.991817	+	0.127664i	$0.959252\pi$
$444$	9.05214	−	8.01950i	0.429596	−	0.380589i
$445$	−5.21627	−	4.62121i	−0.247275	−	0.219066i
$446$	15.8697	−	3.91152i	0.751450	−	0.185216i
$447$	5.24752	+	43.2172i	0.248199	+	2.04411i
$448$	−7.08076	−	6.27300i	−0.334534	−	0.296372i
$449$	6.95091	+	18.3281i	0.328034	+	0.864954i	0.993004	+	0.118084i	$0.0376752\pi$
$449$	6.95091	+	18.3281i	0.328034	+	0.864954i	−0.664970	+	0.746870i	$0.731556\pi$
$450$	1.55906	−	0.818258i	0.0734948	−	0.0385730i
$451$	−1.96547	−	1.03156i	−0.0925502	−	0.0485741i
$452$	−0.946854	+	7.79804i	−0.0445362	+	0.366789i
$453$	−4.44489	−	3.93783i	−0.208839	−	0.185015i
$454$	18.9450	+	4.66953i	0.889134	+	0.219152i
$455$	−1.10586	+	8.17654i	−0.0518435	+	0.383322i
$456$	34.4401	−	8.48873i	1.61281	−	0.397521i
$457$	−24.9511	−	13.0953i	−1.16716	−	0.612574i	−0.234073	−	0.972219i	$-0.575205\pi$
$457$	−24.9511	−	13.0953i	−1.16716	−	0.612574i	−0.933089	+	0.359645i	$0.882898\pi$
$458$	15.5951	+	8.18496i	0.728713	+	0.382458i
$459$	3.31520	−	8.74146i	0.154740	−	0.408017i
$460$	−0.226130	+	0.596255i	−0.0105433	+	0.0278005i
$461$	8.81714	−	12.7738i	0.410655	−	0.594937i	−0.562015	−	0.827127i	$-0.689974\pi$
$461$	8.81714	−	12.7738i	0.410655	−	0.594937i	0.972670	+	0.232190i	$0.0745892\pi$
$462$	−1.02881	+	0.253579i	−0.0478646	+	0.0117976i
$463$	3.96727	−	5.74758i	0.184375	−	0.267113i	−0.719887	−	0.694091i	$-0.755807\pi$
$463$	3.96727	−	5.74758i	0.184375	−	0.267113i	0.904262	+	0.426978i	$0.140422\pi$
$464$	0.520828	+	4.28940i	0.0241788	+	0.199130i
$465$	−13.5548	+	35.7410i	−0.628587	+	1.65745i
$466$	21.6603	−	11.3682i	1.00339	−	0.526622i
$467$	−17.6471	−	25.5662i	−0.816609	−	1.18306i	−0.980487	−	0.196581i	$-0.937016\pi$
$467$	−17.6471	−	25.5662i	−0.816609	−	1.18306i	0.163879	−	0.986480i	$-0.447599\pi$
$468$	−3.48994	−	5.20612i	−0.161323	−	0.240653i
$469$	7.17966	−	10.4015i	0.331526	−	0.480298i
$470$	3.47198	−	28.5944i	0.160151	−	1.31896i
$471$	−0.428759	−	0.105680i	−0.0197562	−	0.00486946i
$472$	0.200795	+	0.290902i	0.00924236	+	0.0133899i
$473$	−1.83023	+	1.62144i	−0.0841541	+	0.0745540i
$474$	−36.4371	−	19.1237i	−1.67361	−	0.878380i
$475$	0.195627	+	1.61113i	0.00897598	+	0.0739238i
$476$	0.237122	−	1.95288i	0.0108685	−	0.0895100i
$477$	−0.257540	+	0.228160i	−0.0117919	+	0.0104467i
$478$	5.04030	−	7.30213i	0.230538	−	0.333992i
$479$	2.00982	+	16.5524i	0.0918311	+	0.756297i	0.963780	+	0.266700i	$0.0859332\pi$
$479$	2.00982	+	16.5524i	0.0918311	+	0.756297i	−0.871949	+	0.489597i	$0.837144\pi$
$480$	1.69364	−	13.9484i	0.0773038	−	0.636654i
$481$	−28.0362	+	24.1653i	−1.27834	+	1.10184i
$482$	−0.582306	−	4.79572i	−0.0265233	−	0.218439i
$483$	−1.78213	+	0.439255i	−0.0810896	+	0.0199868i
$484$	4.90325			0.222875
$485$	30.5027			1.38506
$486$	−26.1328	+	6.44116i	−1.18541	+	0.292177i
$487$	4.56331	−	12.0325i	0.206783	−	0.545243i	−0.790998	−	0.611819i	$-0.790438\pi$
$487$	4.56331	−	12.0325i	0.206783	−	0.545243i	0.997781	+	0.0665760i	$0.0212075\pi$
$488$	28.9882			1.31223
$489$	1.37168	+	3.61682i	0.0620295	+	0.163558i
$490$	15.2774	+	3.76554i	0.690162	+	0.170110i
$491$	9.71271	−	8.60471i	0.438329	−	0.388325i	−0.414896	−	0.909869i	$-0.636182\pi$
$491$	9.71271	−	8.60471i	0.438329	−	0.388325i	0.853225	+	0.521544i	$0.174644\pi$
$492$	8.31110	+	2.04850i	0.374693	+	0.0923536i
$493$	−4.59282	+	4.06888i	−0.206850	+	0.183253i
$494$	−19.4083	+	4.50460i	−0.873219	+	0.202672i
$495$	−1.90340	−	1.68627i	−0.0855515	−	0.0757920i
$496$	11.1581	+	16.1653i	0.501015	+	0.725846i
$497$	−9.18349	+	2.26353i	−0.411936	+	0.101533i
$498$	−10.6460	+	15.4234i	−0.477060	+	0.691141i
$499$	33.0985	+	8.15804i	1.48169	+	0.365204i	0.895534	−	0.444993i	$-0.146794\pi$
$499$	33.0985	+	8.15804i	1.48169	+	0.365204i	0.586157	+	0.810197i	$0.300640\pi$
$500$	5.04201	+	1.24274i	0.225485	+	0.0555772i
$501$	1.70195	−	14.0168i	0.0760375	−	0.626225i
$502$	−5.27229	−	4.67084i	−0.235314	−	0.208470i
$503$	10.4759	+	27.6228i	0.467099	+	1.23164i	0.937128	+	0.348987i	$0.113474\pi$
$503$	10.4759	+	27.6228i	0.467099	+	1.23164i	−0.470029	+	0.882651i	$0.655756\pi$
$504$	11.1011	−	5.82631i	0.494482	−	0.259524i
$505$	−4.70577	+	6.81749i	−0.209404	+	0.303374i
$506$	0.250643			0.0111424
$507$	18.5818	+	28.5515i	0.825247	+	1.26802i
$508$	−3.99854			−0.177407
$509$	15.9839	−	23.1567i	0.708473	−	1.02640i	−0.289136	−	0.957288i	$-0.593368\pi$
$509$	15.9839	−	23.1567i	0.708473	−	1.02640i	0.997609	−	0.0691125i	$-0.0220167\pi$
$510$	−25.6023	+	13.4371i	−1.13369	+	0.595006i
$511$	0.888015	+	2.34150i	0.0392835	+	0.103582i
$512$	−18.6404	−	16.5139i	−0.823796	−	0.729820i
$513$	−1.21492	+	10.0057i	−0.0536399	+	0.441764i
$514$	−9.03072	−	2.22587i	−0.398328	−	0.0981791i
$515$	16.2622	+	4.00827i	0.716598	+	0.176626i
$516$	5.35639	−	7.76008i	0.235802	−	0.341618i
$517$	3.18737	−	0.785615i	0.140180	−	0.0345513i
$518$	−7.71888	−	11.1827i	−0.339148	−	0.491341i
$519$	46.1588	+	40.8931i	2.02615	+	1.79501i
$520$	−3.17303	+	23.4608i	−0.139146	+	1.02883i
$521$	22.8319	−	20.2273i	1.00029	−	0.886175i	0.00678175	−	0.999977i	$-0.497841\pi$
$521$	22.8319	−	20.2273i	1.00029	−	0.886175i	0.993503	+	0.113802i	$0.0363028\pi$
$522$	−6.96824	−	1.71752i	−0.304992	−	0.0751737i
$523$	−22.5419	+	19.9704i	−0.985689	+	0.873244i	−0.991936	−	0.126736i	$-0.959550\pi$
$523$	−22.5419	+	19.9704i	−0.985689	+	0.873244i	0.00624731	+	0.999980i	$0.498011\pi$
$524$	−5.86722	−	1.44614i	−0.256311	−	0.0631749i
$525$	0.361234	+	0.952496i	0.0157656	+	0.0415704i
$526$	−15.9591			−0.695848
$527$	−9.89110	+	26.0807i	−0.430863	+	1.13609i
$528$	−2.25309	+	0.555338i	−0.0980534	+	0.0241680i
$529$	−22.5658			−0.981123
$530$	0.238519			0.0103606
$531$	−0.435086	+	0.107239i	−0.0188811	+	0.00465377i
$532$	0.255643	+	2.10541i	0.0110836	+	0.0912812i
$533$	−25.3493	−	6.61503i	−1.09800	−	0.286529i
$534$	1.27318	−	10.4856i	0.0550959	−	0.453756i
$535$	−1.28594	−	10.5907i	−0.0555962	−	0.457876i
$536$	20.6005	−	29.8450i	0.889806	−	1.28911i
$537$	−17.0622	+	15.1158i	−0.736288	+	0.652294i
$538$	2.91265	−	23.9879i	0.125573	−	1.03419i
$539$	0.216150	+	1.78016i	0.00931024	+	0.0766768i
$540$	1.94624	+	1.02147i	0.0837529	+	0.0439569i
$541$	−7.03431	+	6.23186i	−0.302429	+	0.267929i	−0.800664	−	0.599113i	$-0.795520\pi$
$541$	−7.03431	+	6.23186i	−0.302429	+	0.267929i	0.498236	+	0.867042i	$0.333981\pi$
$542$	−3.48289	−	5.04583i	−0.149603	−	0.216737i
$543$	39.2070	+	9.66366i	1.68253	+	0.414708i
$544$	1.23587	−	10.1783i	0.0529877	−	0.436393i
$545$	−16.9587	+	24.5690i	−0.726433	+	1.05242i
$546$	−11.1514	+	5.66063i	−0.477238	+	0.242253i
$547$	−5.85070	−	8.47620i	−0.250158	−	0.362416i	0.677708	−	0.735332i	$-0.262974\pi$
$547$	−5.85070	−	8.47620i	−0.250158	−	0.362416i	−0.927865	+	0.372915i	$0.878358\pi$
$548$	2.46966	−	1.29618i	0.105499	−	0.0553700i
$549$	−13.0314	+	34.3610i	−0.556167	+	1.46649i
$550$	−0.0167677	−	0.138094i	−0.000714977	−	0.00588836i
$551$	3.75787	−	5.44421i	0.160091	−	0.231931i
$552$	−5.11343	+	1.26035i	−0.217642	+	0.0536439i
$553$	7.61581	−	11.0334i	0.323857	−	0.469188i
$554$	−4.32460	+	11.4030i	−0.183735	+	0.484468i
$555$	20.5352	−	54.1468i	0.871669	−	2.29840i
$556$	8.54163	+	4.48299i	0.362246	+	0.190121i
$557$	−13.6446	−	7.16122i	−0.578139	−	0.303431i	0.150191	−	0.988657i	$-0.452011\pi$
$557$	−13.6446	−	7.16122i	−0.578139	−	0.303431i	−0.728330	+	0.685226i	$0.759703\pi$
$558$	−31.6769	+	7.80765i	−1.34099	+	0.330524i
$559$	−16.7153	+	23.5253i	−0.706980	+	0.995013i
$560$	−6.44080	−	1.58752i	−0.272174	−	0.0670848i
$561$	−2.46655	−	2.18518i	−0.104138	−	0.0922582i
$562$	1.57508	−	12.9719i	0.0664406	−	0.547188i
$563$	26.2076	+	13.7548i	1.10452	+	0.579696i	0.915516	−	0.402280i	$-0.131782\pi$
$563$	26.2076	+	13.7548i	1.10452	+	0.579696i	0.189002	+	0.981977i	$0.439475\pi$
$564$	−11.2091	+	5.88302i	−0.471990	+	0.247720i
$565$	13.3385	+	35.1709i	0.561157	+	1.47965i
$566$	19.2186	+	17.0262i	0.807818	+	0.715664i
$567$	−0.723786	−	5.96091i	−0.0303962	−	0.250335i
$568$	−26.3500	+	6.49470i	−1.10562	+	0.272512i
$569$	25.1866	+	22.3134i	1.05588	+	0.935425i	0.998020	−	0.0628996i	$-0.0200348\pi$
$569$	25.1866	+	22.3134i	1.05588	+	0.935425i	0.0578570	+	0.998325i	$0.481573\pi$
$570$	23.3331	−	20.6713i	0.977316	−	0.865827i
$571$	28.6275	+	15.0249i	1.19802	+	0.628772i	0.941254	−	0.337700i	$-0.109649\pi$
$571$	28.6275	+	15.0249i	1.19802	+	0.628772i	0.256771	+	0.966472i	$0.417341\pi$
$572$	−0.482358	+	0.111954i	−0.0201684	+	0.00468103i
$573$	−48.6575	+	25.5374i	−2.03269	+	1.06684i
$574$	3.41046	−	8.99265i	0.142350	−	0.375346i
$575$	−0.0290453	−	0.239210i	−0.00121127	−	0.00997573i
$576$	30.4683	−	15.9910i	1.26951	−	0.666291i
$577$	−14.6886			−0.611495			−0.305747	−	0.952113i	$-0.598906\pi$
$577$	−14.6886			−0.611495			−0.305747	+	0.952113i	$0.598906\pi$
$578$	0.0607852	−	0.0319026i	0.00252833	−	0.00132697i
$579$	37.1219	−	32.8871i	1.54273	−	1.36674i
$580$	−0.819490	−	1.18724i	−0.0340275	−	0.0492973i
$581$	−4.57013	−	4.04879i	−0.189601	−	0.167972i
$582$	26.2631	+	38.0487i	1.08864	+	1.57717i
$583$	0.00963937	+	0.0254169i	0.000399222	+	0.00105266i
$584$	2.54797	+	6.71844i	0.105436	+	0.278011i
$585$	−26.3827	−	14.3077i	−1.09079	−	0.591553i
$586$	−4.86141	+	12.8185i	−0.200823	+	0.529527i
$587$	−22.1554			−0.914451			−0.457225	−	0.889351i	$-0.651157\pi$
$587$	−22.1554			−0.914451			−0.457225	+	0.889351i	$0.651157\pi$
$588$	−2.45215	−	6.46580i	−0.101125	−	0.266645i
$589$	3.62478	−	29.8528i	0.149356	−	1.23006i
$590$	0.275059	+	0.144362i	0.0113240	+	0.00594330i
$591$	−30.3461	−	43.9639i	−1.24827	−	1.80843i
$592$	−16.9043	−	24.4901i	−0.694764	−	1.00654i
$593$	7.66895	+	4.02498i	0.314926	+	0.165286i	0.614779	−	0.788700i	$-0.289245\pi$
$593$	7.66895	+	4.02498i	0.314926	+	0.165286i	−0.299853	+	0.953985i	$0.596938\pi$
$594$	0.104134	−	0.857618i	0.00427266	−	0.0351885i
$595$	−3.34040	−	8.80790i	−0.136943	−	0.361089i
$596$	−7.46883			−0.305935
$597$	−14.8891	+	39.2593i	−0.609370	+	1.60678i
$598$	2.88160	−	0.668812i	0.117837	−	0.0273498i
$599$	5.34658	+	14.0978i	0.218455	+	0.576019i	0.998781	−	0.0493537i	$-0.0157161\pi$
$599$	5.34658	+	14.0978i	0.218455	+	0.576019i	−0.780326	+	0.625373i	$0.784947\pi$
$600$	1.03648	+	2.73298i	0.0423143	+	0.111574i
$601$	3.31468	+	4.80214i	0.135209	+	0.195884i	0.884739	−	0.466086i	$-0.154336\pi$
$601$	3.31468	+	4.80214i	0.135209	+	0.195884i	−0.749531	+	0.661969i	$0.769721\pi$
$602$	−7.93005	−	7.02541i	−0.323205	−	0.286334i
$603$	26.1158	+	37.8352i	1.06352	+	1.54077i
$604$	0.762567	−	0.675576i	0.0310284	−	0.0274888i
$605$	20.7898	−	10.9114i	0.845228	−	0.443610i
$606$	−12.5557			−0.510042
$607$	−5.49944	+	2.88633i	−0.223215	+	0.117152i	−0.572624	−	0.819818i	$-0.694075\pi$
$607$	−5.49944	+	2.88633i	−0.223215	+	0.117152i	0.349409	+	0.936970i	$0.386382\pi$
$608$	1.33241	+	10.9734i	0.0540362	+	0.445028i
$609$	1.47239	−	3.88238i	0.0596643	−	0.157322i
$610$	22.5575	−	11.8391i	0.913327	−	0.479351i
$611$	34.5484	−	17.5372i	1.39768	−	0.709481i
$612$	6.33606	+	3.32542i	0.256120	+	0.134422i
$613$	−19.3968	+	17.1841i	−0.783429	+	0.694058i	−0.956783	−	0.290802i	$-0.906078\pi$
$613$	−19.3968	+	17.1841i	−0.783429	+	0.694058i	0.173354	+	0.984860i	$0.444539\pi$
$614$	−7.89070	−	6.99055i	−0.318443	−	0.282116i
$615$	39.7978	−	9.80927i	1.60480	−	0.395548i
$616$	−0.119392	−	0.983284i	−0.00481045	−	0.0396176i
$617$	−24.5929	−	21.7874i	−0.990071	−	0.877126i	0.00235163	−	0.999997i	$-0.499251\pi$
$617$	−24.5929	−	21.7874i	−0.990071	−	0.877126i	−0.992423	+	0.122871i	$0.960790\pi$
$618$	9.00202	+	23.7364i	0.362114	+	0.954817i
$619$	−8.01952	+	4.20897i	−0.322332	+	0.169173i	−0.618126	−	0.786079i	$-0.712108\pi$
$619$	−8.01952	+	4.20897i	−0.322332	+	0.169173i	0.295794	+	0.955252i	$0.404416\pi$
$620$	−5.80673	−	3.04761i	−0.233204	−	0.122395i
$621$	0.180382	−	1.48558i	0.00723849	−	0.0596144i
$622$	28.4908	+	25.2406i	1.14238	+	1.01206i
$623$	3.34122	+	0.823537i	0.133863	+	0.0329943i
$624$	−24.4216	+	12.3968i	−0.977648	+	0.496268i
$625$	22.3683	−	5.51329i	0.894733	−	0.220532i
$626$	−11.4120	−	5.98949i	−0.456116	−	0.239388i
$627$	3.14573	+	1.65101i	0.125629	+	0.0659349i
$628$	0.0268647	−	0.0708364i	0.00107202	−	0.00282668i
$629$	14.9848	−	39.5117i	0.597483	−	1.57543i
$630$	6.25893	−	9.06762i	0.249362	−	0.361263i
$631$	−14.8776	+	3.66700i	−0.592268	+	0.145981i	−0.524047	−	0.851689i	$-0.675578\pi$
$631$	−14.8776	+	3.66700i	−0.592268	+	0.145981i	−0.0682210	+	0.997670i	$0.521732\pi$
$632$	21.8519	−	31.6580i	0.869223	−	1.25929i
$633$	−5.73327	−	47.2177i	−0.227877	−	1.87674i
$634$	−11.1855	+	29.4938i	−0.444233	+	1.17135i
$635$	−16.9539	+	8.89807i	−0.672794	+	0.353109i
$636$	−0.0595482	−	0.0862705i	−0.00236124	−	0.00342085i
$637$	7.23519	+	19.8894i	0.286669	+	0.788048i
$638$	−0.322096	+	0.466637i	−0.0127519	+	0.0184743i
$639$	4.14699	−	34.1535i	0.164052	−	1.35109i
$640$	−12.7483	−	3.14217i	−0.503920	−	0.124205i
$641$	−15.5817	−	22.5740i	−0.615441	−	0.891621i	0.384056	−	0.923310i	$-0.374527\pi$
$641$	−15.5817	−	22.5740i	−0.615441	−	0.891621i	−0.999498	+	0.0316888i	$0.989911\pi$
$642$	12.1035	−	10.7227i	0.477686	−	0.423193i
$643$	8.82585	+	4.63216i	0.348057	+	0.182675i	0.629688	−	0.776848i	$-0.283183\pi$
$643$	8.82585	+	4.63216i	0.348057	+	0.182675i	−0.281630	+	0.959523i	$0.590875\pi$
$644$	−0.0379561	−	0.312597i	−0.00149568	−	0.0123180i
$645$	5.44245	−	44.8226i	0.214296	−	1.76489i
$646$	17.0265	−	15.0842i	0.669899	−	0.593479i
$647$	−12.9059	+	18.6975i	−0.507384	+	0.735073i	−0.990048	−	0.140733i	$-0.955054\pi$
$647$	−12.9059	+	18.6975i	−0.507384	+	0.735073i	0.482663	+	0.875806i	$0.339669\pi$
$648$	−2.07675	−	17.1036i	−0.0815824	−	0.671891i
$649$	−0.00426736	+	0.0351448i	−0.000167508	+	0.00137956i
$650$	−0.561265	−	1.54291i	−0.0220146	−	0.0605178i
$651$	−2.27518	−	18.7378i	−0.0891715	−	0.734393i
$652$	−0.644345	+	0.158817i	−0.0252345	+	0.00621975i
$653$	−8.57144			−0.335426			−0.167713	−	0.985836i	$-0.553638\pi$
$653$	−8.57144			−0.335426			−0.167713	+	0.985836i	$0.553638\pi$
$654$	−45.2486			−1.76936
$655$	−28.0952	+	6.92485i	−1.09777	+	0.270576i
$656$	7.46890	−	19.6939i	0.291612	−	0.768917i
$657$	−9.10908			−0.355379
$658$	5.04375	+	13.2993i	0.196626	+	0.518460i
$659$	1.65773	+	0.408593i	0.0645759	+	0.0159165i	0.271471	−	0.962447i	$-0.412490\pi$
$659$	1.65773	+	0.408593i	0.0645759	+	0.0159165i	−0.206895	+	0.978363i	$0.566336\pi$
$660$	0.579903	−	0.513749i	0.0225727	−	0.0199977i
$661$	−24.3057	−	5.99083i	−0.945384	−	0.233016i	−0.263652	−	0.964618i	$-0.584927\pi$
$661$	−24.3057	−	5.99083i	−0.945384	−	0.233016i	−0.681732	+	0.731602i	$0.738773\pi$
$662$	16.0839	−	14.2491i	0.625120	−	0.553808i
$663$	−34.1885	−	18.5409i	−1.32777	−	0.720070i
$664$	−13.1130	−	11.6171i	−0.508884	−	0.450832i
$665$	5.76917	+	8.35809i	0.223719	+	0.324113i
$666$	47.9898	−	11.8284i	1.85957	−	0.458342i
$667$	−0.557942	+	0.808318i	−0.0216036	+	0.0312982i
$668$	2.35200	+	0.579717i	0.0910018	+	0.0224299i
$669$	−33.3976	−	8.23176i	−1.29123	−	0.318258i
$670$	3.84151	−	31.6377i	0.148411	−	1.22227i
$671$	2.17321	+	1.92530i	0.0838960	+	0.0743254i
$672$	2.46035	+	6.48742i	0.0949101	+	0.250257i
$673$	11.2409	−	5.89968i	0.433305	−	0.227416i	−0.233945	−	0.972250i	$-0.575164\pi$
$673$	11.2409	−	5.89968i	0.433305	−	0.227416i	0.667250	+	0.744834i	$0.267471\pi$
$674$	−7.98360	+	11.5662i	−0.307517	+	0.445515i
$675$	−0.830565			−0.0319685
$676$	−5.24686	+	2.57424i	−0.201802	+	0.0990091i
$677$	14.3483			0.551452			0.275726	−	0.961236i	$-0.411082\pi$
$677$	14.3483			0.551452			0.275726	+	0.961236i	$0.411082\pi$
$678$	−32.3870	+	46.9207i	−1.24382	+	1.80198i
$679$	−13.3369	+	6.99976i	−0.511825	+	0.268626i
$680$	−9.58454	−	25.2724i	−0.367551	−	0.969151i
$681$	−30.7360	−	27.2297i	−1.17781	−	1.04345i
$682$	−0.310689	+	2.55876i	−0.0118969	+	0.0979798i
$683$	−30.9554	−	7.62983i	−1.18448	−	0.291947i	−0.402597	−	0.915377i	$-0.631893\pi$
$683$	−30.9554	−	7.62983i	−1.18448	−	0.291947i	−0.781879	+	0.623430i	$0.785739\pi$
$684$	−7.49045	−	1.84623i	−0.286404	−	0.0705923i
$685$	7.58698	−	10.9916i	0.289884	−	0.419969i
$686$	−16.5402	+	4.07679i	−0.631507	+	0.155653i
$687$	−21.0556	−	30.5043i	−0.803321	−	1.16381i
$688$	−17.3668	−	15.3856i	−0.662103	−	0.586572i
$689$	0.178645	+	0.266493i	0.00680582	+	0.0101526i
$690$	−3.46434	+	3.06913i	−0.131885	+	0.116840i
$691$	−19.8906	−	4.90259i	−0.756674	−	0.186503i	−0.157937	−	0.987449i	$-0.550484\pi$
$691$	−19.8906	−	4.90259i	−0.756674	−	0.186503i	−0.598737	+	0.800946i	$0.704331\pi$
$692$	−7.91903	+	7.01565i	−0.301037	+	0.266695i
$693$	1.21920	+	0.300506i	0.0463137	+	0.0114153i
$694$	−6.07409	−	16.0161i	−0.230569	−	0.607961i
$695$	46.1928			1.75219
$696$	4.22471	−	11.1396i	0.160137	−	0.422247i
$697$	29.0410	−	7.15796i	1.10001	−	0.271127i
$698$	19.0215			0.719975
$699$	−51.4808			−1.94718
$700$	−0.169689	+	0.0418247i	−0.00641366	+	0.00158083i
$701$	−1.55117	−	12.7750i	−0.0585868	−	0.482506i	−0.992241	−	0.124330i	$-0.960322\pi$
$701$	−1.55117	−	12.7750i	−0.0585868	−	0.482506i	0.933654	−	0.358176i	$-0.116601\pi$
$702$	−1.09125	−	10.1378i	−0.0411865	−	0.382626i
$703$	−5.49146	+	45.2263i	−0.207114	+	1.70574i
$704$	−0.327686	−	2.69874i	−0.0123501	−	0.101712i
$705$	−34.4353	+	49.8881i	−1.29691	+	1.87890i
$706$	12.8097	−	11.3484i	0.482100	−	0.427103i
$707$	0.493063	−	4.06074i	0.0185435	−	0.152720i
$708$	−0.0164560	−	0.135528i	−0.000618456	−	0.00509345i
$709$	33.8821	+	17.7827i	1.27247	+	0.667844i	0.959444	−	0.281901i	$-0.0909648\pi$
$709$	33.8821	+	17.7827i	1.27247	+	0.667844i	0.313026	+	0.949744i	$0.398657\pi$
$710$	−17.8521	+	15.8156i	−0.669977	+	0.593548i
$711$	27.7023	+	40.1336i	1.03892	+	1.50513i
$712$	9.58691	+	2.36296i	0.359285	+	0.0885557i
$713$	−0.538182	+	4.43233i	−0.0201551	+	0.165992i
$714$	8.11073	−	11.7504i	0.303537	−	0.439749i
$715$	−1.79607	+	1.54809i	−0.0671692	+	0.0578953i
$716$	−2.22153	−	3.21844i	−0.0830224	−	0.120279i
$717$	−16.5338	+	8.67760i	−0.617466	+	0.324071i
$718$	−10.6701	+	28.1347i	−0.398204	+	1.04998i
$719$	3.31595	+	27.3093i	0.123664	+	1.01846i	0.913978	+	0.405763i	$0.132994\pi$
$719$	3.31595	+	27.3093i	0.123664	+	1.01846i	−0.790314	+	0.612702i	$0.790083\pi$
$720$	13.7070	−	19.8581i	0.510831	−	0.740067i
$721$	−8.03026	+	1.97928i	−0.299062	+	0.0737123i
$722$	−0.491825	+	0.712532i	−0.0183038	+	0.0265177i
$723$	−3.60516	+	9.50602i	−0.134077	+	0.353533i
$724$	−2.45659	+	6.47750i	−0.0912985	+	0.240734i
$725$	0.482677	+	0.253329i	0.0179262	+	0.00940839i
$726$	31.5109	+	16.5382i	1.16948	+	0.613790i
$727$	−14.7141	+	3.62669i	−0.545714	+	0.134506i	−0.502528	−	0.864561i	$-0.667597\pi$
$727$	−14.7141	+	3.62669i	−0.545714	+	0.134506i	−0.0431855	+	0.999067i	$0.513751\pi$
$728$	−3.99642	−	10.9861i	−0.148117	−	0.407172i
$729$	38.5426	+	9.49990i	1.42750	+	0.351848i
$730$	4.72662	+	4.18742i	0.174940	+	0.154983i
$731$	3.97143	−	32.7077i	0.146889	−	1.20974i
$732$	−9.91376	−	5.20314i	−0.366423	−	0.192314i
$733$	−11.5994	+	6.08785i	−0.428434	+	0.224860i	−0.665135	−	0.746723i	$-0.731626\pi$
$733$	−11.5994	+	6.08785i	−0.428434	+	0.224860i	0.236701	+	0.971583i	$0.423934\pi$
$734$	7.49939	+	19.7743i	0.276807	+	0.729881i
$735$	−24.7857	−	21.9582i	−0.914234	−	0.809941i
$736$	−0.197826	−	1.62925i	−0.00729198	−	0.0600548i
$737$	3.52660	−	0.869229i	0.129904	−	0.0320185i
$738$	26.1858	+	23.1986i	0.963911	+	0.853951i
$739$	−7.97113	+	7.06180i	−0.293223	+	0.259773i	−0.796889	−	0.604126i	$-0.793523\pi$
$739$	−7.97113	+	7.06180i	−0.293223	+	0.259773i	0.503666	+	0.863898i	$0.331984\pi$
$740$	8.79707	+	4.61706i	0.323387	+	0.169726i
$741$	40.5716	+	10.5874i	1.49043	+	0.388937i
$742$	−0.104290	+	0.0547354i	−0.00382859	+	0.00200940i
$743$	−4.66283	+	12.2949i	−0.171063	+	0.451055i	−0.992941	−	0.118607i	$-0.962157\pi$
$743$	−4.66283	+	12.2949i	−0.171063	+	0.451055i	0.821878	+	0.569663i	$0.192926\pi$
$744$	−6.52815	−	53.7642i	−0.239334	−	1.97109i
$745$	−31.6679	+	16.6206i	−1.16022	+	0.608932i
$746$	31.9914			1.17129
$747$	19.6651	−	10.3211i	0.719510	−	0.377628i
$748$	0.423163	−	0.374890i	0.0154724	−	0.0137073i
$749$	2.99261	+	4.33555i	0.109348	+	0.158417i
$750$	28.2109	+	24.9927i	1.03012	+	0.912605i
$751$	−2.17047	−	3.14447i	−0.0792015	−	0.114743i	0.781381	−	0.624054i	$-0.214516\pi$
$751$	−2.17047	−	3.14447i	−0.0792015	−	0.114743i	−0.860582	+	0.509311i	$0.829900\pi$
$752$	11.0458	+	29.1254i	0.402799	+	1.06209i
$753$	5.25646	+	13.8601i	0.191556	+	0.505092i
$754$	−2.45793	+	6.22434i	−0.0895124	+	0.226677i
$755$	1.72992	−	4.56141i	0.0629581	−	0.166007i
$756$	−1.08538			−0.0394747
$757$	−10.4558	−	27.5696i	−0.380021	−	1.00203i	−0.979465	−	0.201616i	$-0.935381\pi$
$757$	−10.4558	−	27.5696i	−0.380021	−	1.00203i	0.599444	−	0.800417i	$-0.295389\pi$
$758$	−1.13503	+	9.34779i	−0.0412260	+	0.339527i
$759$	−0.467056	−	0.245130i	−0.0169531	−	0.00889766i
$760$	16.5534	+	23.9817i	0.600455	+	0.869909i
$761$	15.2971	+	22.1617i	0.554520	+	0.803362i	0.995560	−	0.0941260i	$-0.0300056\pi$
$761$	15.2971	+	22.1617i	0.554520	+	0.803362i	−0.441040	+	0.897488i	$0.645390\pi$
$762$	−25.6967	−	13.4867i	−0.930894	−	0.488571i
$763$	1.77691	−	14.6342i	0.0643284	−	0.529792i
$764$	−3.34306	−	8.81494i	−0.120948	−	0.318913i
$765$	34.2651			1.23886
$766$	−7.03424	+	18.5478i	−0.254157	+	0.670158i
$767$	0.0447189	+	0.415442i	0.00161471	+

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707334 + 1.02475i) q^{2} +(2.32028 - 1.21778i) q^{3} +(0.159418 + 0.420350i) q^{4} +(1.61135 + 1.42753i) q^{5} +(-0.393297 + 3.23909i) q^{6} +(-1.03213 - 0.254398i) q^{7} +(-2.96148 - 0.729939i) q^{8} +(2.19654 - 3.18224i) q^{9} +O(q^{10})\)	\(q+(-0.707334 + 1.02475i) q^{2} +(2.32028 - 1.21778i) q^{3} +(0.159418 + 0.420350i) q^{4} +(1.61135 + 1.42753i) q^{5} +(-0.393297 + 3.23909i) q^{6} +(-1.03213 - 0.254398i) q^{7} +(-2.96148 - 0.729939i) q^{8} +(2.19654 - 3.18224i) q^{9} +(-2.60263 + 0.641490i) q^{10} +(-0.173539 - 0.251415i) q^{11} +(0.881788 + 0.781196i) q^{12} +(-2.66602 - 2.42741i) q^{13} +(0.990757 - 0.877734i) q^{14} +(5.47721 + 1.35001i) q^{15} +(2.16976 - 1.92224i) q^{16} +(3.99680 + 0.985122i) q^{17} +(1.70731 + 4.50181i) q^{18} -4.43794 q^{19} +(-0.343185 + 0.904905i) q^{20} +(-2.70464 + 0.666634i) q^{21} +0.380387 q^{22} +0.658914 q^{23} +(-7.76038 + 1.91276i) q^{24} +(-0.0440806 - 0.363036i) q^{25} +(4.37326 - 1.01502i) q^{26} +(0.273757 - 2.25459i) q^{27} +(-0.0576041 - 0.474412i) q^{28} +(-0.846759 + 1.22674i) q^{29} +(-5.25764 + 4.65787i) q^{30} +(-0.816771 + 6.72671i) q^{31} +(-0.300231 - 2.47262i) q^{32} +(-0.708827 - 0.372021i) q^{33} +(-3.83658 + 3.39891i) q^{34} +(-1.29997 - 1.88333i) q^{35} +(1.68782 + 0.416010i) q^{36} +(1.23739 - 10.1908i) q^{37} +(3.13911 - 4.54778i) q^{38} +(-9.14198 - 2.38565i) q^{39} +(-3.72997 - 5.40380i) q^{40} +(6.43378 - 3.37671i) q^{41} +(1.22995 - 3.24312i) q^{42} +(-0.964779 - 7.94567i) q^{43} +(0.0780169 - 0.113027i) q^{44} +(8.08214 - 1.99207i) q^{45} +(-0.466073 + 0.675223i) q^{46} +(-3.81052 + 10.0475i) q^{47} +(2.69359 - 7.10242i) q^{48} +(-5.19761 - 2.72792i) q^{49} +(0.403201 + 0.211616i) q^{50} +(10.4734 - 2.58145i) q^{51} +(0.595349 - 1.50764i) q^{52} +(-0.0863969 - 0.0212949i) q^{53} +(2.11676 + 1.87528i) q^{54} +(0.0792703 - 0.652849i) q^{55} +(2.87094 + 1.50679i) q^{56} +(-10.2973 + 5.40443i) q^{57} +(-0.658163 - 1.73543i) q^{58} +(-0.0867438 - 0.0768483i) q^{59} +(0.305687 + 2.51756i) q^{60} +(-9.22781 + 2.27445i) q^{61} +(-6.31547 - 5.59502i) q^{62} +(-3.07667 + 2.72569i) q^{63} +(7.87964 + 4.13555i) q^{64} +(-0.830697 - 7.71724i) q^{65} +(0.882607 - 0.463228i) q^{66} +(-4.21608 + 11.1169i) q^{67} +(0.223064 + 1.83710i) q^{68} +(1.52887 - 0.802412i) q^{69} +2.84945 q^{70} +(7.87842 - 4.13492i) q^{71} +(-8.82785 + 7.82079i) q^{72} +(-1.33823 - 1.93876i) q^{73} +(9.56780 + 8.47633i) q^{74} +(-0.544377 - 0.788666i) q^{75} +(-0.707486 - 1.86549i) q^{76} +(0.115156 + 0.303641i) q^{77} +(8.91113 - 7.68080i) q^{78} +(-4.47220 + 11.7922i) q^{79} +6.24029 q^{80} +(2.00306 + 5.28163i) q^{81} +(-1.09055 + 8.98148i) q^{82} +(5.08576 + 2.66921i) q^{83} +(-0.711387 - 1.03062i) q^{84} +(5.03395 + 7.29294i) q^{85} +(8.82475 + 4.63159i) q^{86} +(-0.470821 + 3.87756i) q^{87} +(0.330415 + 0.871233i) q^{88} -3.23720 q^{89} +(-3.67540 + 9.69124i) q^{90} +(2.13416 + 3.18364i) q^{91} +(0.105043 + 0.276975i) q^{92} +(6.29651 + 16.6025i) q^{93} +(-7.60089 - 11.0118i) q^{94} +(-7.15108 - 6.33530i) q^{95} +(-3.70773 - 5.37158i) q^{96} +(10.6058 - 9.39595i) q^{97} +(6.47189 - 3.39671i) q^{98} -1.18125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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