LMFDB - Embedded newform 175.2.e.e.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(51,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("175.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.e (of order $3$, degree $2$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.3
Root			$1.09935 + 1.90412i$ of defining polynomial
Character	$\chi$	$=$	175.151
Dual form			175.2.e.e.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09935 + 1.90412i) q^{2} +(-1.41712 + 2.45453i) q^{3} +(-1.41712 + 2.45453i) q^{4} -6.23163 q^{6} +(2.43359 - 1.03810i) q^{7} -1.83424 q^{8} +(-2.51647 - 4.35865i) q^{9} +O(q^{10})$	\(q+(1.09935 + 1.90412i) q^{2} +(-1.41712 + 2.45453i) q^{3} +(-1.41712 + 2.45453i) q^{4} -6.23163 q^{6} +(2.43359 - 1.03810i) q^{7} -1.83424 q^{8} +(-2.51647 - 4.35865i) q^{9} +(1.28157 - 2.21974i) q^{11} +(-4.01647 - 6.95673i) q^{12} -0.563139 q^{13} +(4.65202 + 3.49262i) q^{14} +(0.817776 + 1.41643i) q^{16} +(-2.59935 + 4.50220i) q^{17} +(5.53293 - 9.58332i) q^{18} +(-0.234898 - 0.406855i) q^{19} +(-0.900654 + 7.44442i) q^{21} +5.63555 q^{22} +(-2.01647 - 3.49262i) q^{23} +(2.59935 - 4.50220i) q^{24} +(-0.619085 - 1.07229i) q^{26} +5.76183 q^{27} +(-0.900654 + 7.44442i) q^{28} +2.86718 q^{29} +(1.93359 - 3.34907i) q^{31} +(-3.63228 + 6.29129i) q^{32} +(3.63228 + 6.29129i) q^{33} -11.4303 q^{34} +14.2646 q^{36} +(-1.11581 - 1.93264i) q^{37} +(0.516467 - 0.894547i) q^{38} +(0.798037 - 1.38224i) q^{39} +3.30404 q^{41} +(-15.1652 + 6.46903i) q^{42} +10.4303 q^{43} +(3.63228 + 6.29129i) q^{44} +(4.43359 - 7.67920i) q^{46} +(-4.68222 - 8.10985i) q^{47} -4.63555 q^{48} +(4.84471 - 5.05260i) q^{49} +(-7.36718 - 12.7603i) q^{51} +(0.798037 - 1.38224i) q^{52} +(-5.35071 + 9.26770i) q^{53} +(6.33424 + 10.9712i) q^{54} +(-4.46379 + 1.90412i) q^{56} +1.33151 q^{57} +(3.15202 + 5.45946i) q^{58} +(-1.98026 + 3.42991i) q^{59} +(1.93359 + 3.34907i) q^{61} +8.50273 q^{62} +(-10.6487 - 7.99482i) q^{63} -12.7014 q^{64} +(-7.98626 + 13.8326i) q^{66} +(3.83424 - 6.64110i) q^{67} +(-7.36718 - 12.7603i) q^{68} +11.4303 q^{69} -8.73436 q^{71} +(4.61581 + 7.99482i) q^{72} +(5.66849 - 9.81811i) q^{73} +(2.45333 - 4.24929i) q^{74} +1.33151 q^{76} +(0.814504 - 6.73234i) q^{77} +3.50927 q^{78} +(-2.57961 - 4.46801i) q^{79} +(-0.615813 + 1.06662i) q^{81} +(3.63228 + 6.29129i) q^{82} +3.13282 q^{83} +(-16.9962 - 12.7603i) q^{84} +(11.4665 + 19.8606i) q^{86} +(-4.06314 + 7.03756i) q^{87} +(-2.35071 + 4.07155i) q^{88} +(2.78757 + 4.82821i) q^{89} +(-1.37045 + 0.584593i) q^{91} +11.4303 q^{92} +(5.48026 + 9.49209i) q^{93} +(10.2948 - 17.8311i) q^{94} +(-10.2948 - 17.8311i) q^{96} -15.2975 q^{97} +(14.9468 + 3.67036i) q^{98} -12.9001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 3 q^{3} - 3 q^{4} - 4 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q + q^2 - 3 * q^3 - 3 * q^4 - 4 * q^6 - 2 * q^7 - 4 * q^9	$ 6 q + q^{2} - 3 q^{3} - 3 q^{4} - 4 q^{6} - 2 q^{7} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 8 q^{13} + 17 q^{14} + 5 q^{16} - 10 q^{17} + 11 q^{18} + 4 q^{19} - 11 q^{21} + 34 q^{22} - q^{23} + 10 q^{24} - 15 q^{26} + 12 q^{27} - 11 q^{28} - 16 q^{29} - 5 q^{31} + 6 q^{32} - 6 q^{33} - 24 q^{34} + 30 q^{36} + 10 q^{37} - 8 q^{38} - 12 q^{39} - 2 q^{41} - 41 q^{42} + 18 q^{43} - 6 q^{44} + 10 q^{46} - 28 q^{47} - 28 q^{48} + 12 q^{49} - 11 q^{51} - 12 q^{52} - 10 q^{53} + 27 q^{54} - 21 q^{56} + 30 q^{57} + 8 q^{58} + 5 q^{59} - 5 q^{61} + 18 q^{62} - 25 q^{63} - 32 q^{64} - 26 q^{66} + 12 q^{67} - 11 q^{68} + 24 q^{69} + 14 q^{71} + 11 q^{72} + 12 q^{73} + 15 q^{74} + 30 q^{76} - 23 q^{77} + 44 q^{78} + 7 q^{79} + 13 q^{81} - 6 q^{82} + 52 q^{83} - 13 q^{84} + 30 q^{86} - 13 q^{87} + 8 q^{88} + 6 q^{89} - 3 q^{91} + 24 q^{92} + 16 q^{93} + 17 q^{94} - 17 q^{96} - 14 q^{97} + 34 q^{98} - 22 q^{99}+O(q^{100}) $ 6 * q + q^2 - 3 * q^3 - 3 * q^4 - 4 * q^6 - 2 * q^7 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 8 * q^13 + 17 * q^14 + 5 * q^16 - 10 * q^17 + 11 * q^18 + 4 * q^19 - 11 * q^21 + 34 * q^22 - q^23 + 10 * q^24 - 15 * q^26 + 12 * q^27 - 11 * q^28 - 16 * q^29 - 5 * q^31 + 6 * q^32 - 6 * q^33 - 24 * q^34 + 30 * q^36 + 10 * q^37 - 8 * q^38 - 12 * q^39 - 2 * q^41 - 41 * q^42 + 18 * q^43 - 6 * q^44 + 10 * q^46 - 28 * q^47 - 28 * q^48 + 12 * q^49 - 11 * q^51 - 12 * q^52 - 10 * q^53 + 27 * q^54 - 21 * q^56 + 30 * q^57 + 8 * q^58 + 5 * q^59 - 5 * q^61 + 18 * q^62 - 25 * q^63 - 32 * q^64 - 26 * q^66 + 12 * q^67 - 11 * q^68 + 24 * q^69 + 14 * q^71 + 11 * q^72 + 12 * q^73 + 15 * q^74 + 30 * q^76 - 23 * q^77 + 44 * q^78 + 7 * q^79 + 13 * q^81 - 6 * q^82 + 52 * q^83 - 13 * q^84 + 30 * q^86 - 13 * q^87 + 8 * q^88 + 6 * q^89 - 3 * q^91 + 24 * q^92 + 16 * q^93 + 17 * q^94 - 17 * q^96 - 14 * q^97 + 34 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.09935	+	1.90412i	0.777355	+	1.34642i	0.933461	+	0.358678i	$0.116772\pi$
$2$	1.09935	+	1.90412i	0.777355	+	1.34642i	−0.156107	+	0.987740i	$0.549894\pi$
$3$	−1.41712	+	2.45453i	−0.818176	+	1.41712i	0.0888496	+	0.996045i	$0.471681\pi$
$3$	−1.41712	+	2.45453i	−0.818176	+	1.41712i	−0.907025	+	0.421077i	$0.861652\pi$
$4$	−1.41712	+	2.45453i	−0.708561	+	1.22726i
$5$		0			0
$5$		0			0
$6$	−6.23163			−2.54405
$7$	2.43359	−	1.03810i	0.919810	−	0.392364i
$7$	2.43359	−	1.03810i	0.919810	−	0.392364i
$8$	−1.83424			−0.648503
$9$	−2.51647	−	4.35865i	−0.838822	−	1.45288i
$10$		0			0
$11$	1.28157	−	2.21974i	0.386408	−	0.669278i	−0.605556	−	0.795803i	$-0.707049\pi$
$11$	1.28157	−	2.21974i	0.386408	−	0.669278i	0.991963	+	0.126525i	$0.0403824\pi$
$12$	−4.01647	−	6.95673i	−1.15945	−	2.00823i
$13$	−0.563139			−0.156187			−0.0780934	−	0.996946i	$-0.524883\pi$
$13$	−0.563139			−0.156187			−0.0780934	+	0.996946i	$0.524883\pi$
$14$	4.65202	+	3.49262i	1.24330	+	0.933443i
$15$		0			0
$16$	0.817776	+	1.41643i	0.204444	+	0.354107i
$17$	−2.59935	+	4.50220i	−0.630434	+	1.09194i	0.357029	+	0.934093i	$0.383790\pi$
$17$	−2.59935	+	4.50220i	−0.630434	+	1.09194i	−0.987463	+	0.157850i	$0.949544\pi$
$18$	5.53293	−	9.58332i	1.30413	−	2.25881i
$19$	−0.234898	−	0.406855i	−0.0538892	−	0.0933388i	0.837822	−	0.545943i	$-0.183828\pi$
$19$	−0.234898	−	0.406855i	−0.0538892	−	0.0933388i	−0.891712	+	0.452604i	$0.850495\pi$
$20$		0			0
$21$	−0.900654	+	7.44442i	−0.196539	+	1.62451i
$22$	5.63555			1.20150
$23$	−2.01647	−	3.49262i	−0.420462	−	0.728262i	0.575522	−	0.817786i	$-0.304799\pi$
$23$	−2.01647	−	3.49262i	−0.420462	−	0.728262i	−0.995985	+	0.0895238i	$0.971465\pi$
$24$	2.59935	−	4.50220i	0.530589	−	0.919007i
$25$		0			0
$26$	−0.619085	−	1.07229i	−0.121413	−	0.210293i
$27$	5.76183			1.10886
$28$	−0.900654	+	7.44442i	−0.170208	+	1.40686i
$29$	2.86718			0.532422			0.266211	−	0.963915i	$-0.414228\pi$
$29$	2.86718			0.532422			0.266211	+	0.963915i	$0.414228\pi$
$30$		0			0
$31$	1.93359	−	3.34907i	0.347283	−	0.601511i	−0.638483	−	0.769636i	$-0.720438\pi$
$31$	1.93359	−	3.34907i	0.347283	−	0.601511i	0.985766	+	0.168124i	$0.0537711\pi$
$32$	−3.63228	+	6.29129i	−0.642102	+	1.11215i
$33$	3.63228	+	6.29129i	0.632299	+	1.09517i
$34$	−11.4303			−1.96028
$35$		0			0
$36$	14.2646			2.37743
$37$	−1.11581	−	1.93264i	−0.183439	−	0.317725i	0.759611	−	0.650378i	$-0.225389\pi$
$37$	−1.11581	−	1.93264i	−0.183439	−	0.317725i	−0.943049	+	0.332653i	$0.892056\pi$
$38$	0.516467	−	0.894547i	0.0837820	−	0.145115i
$39$	0.798037	−	1.38224i	0.127788	−	0.221336i
$40$		0			0
$41$	3.30404			0.516004			0.258002	−	0.966144i	$-0.416936\pi$
$41$	3.30404			0.516004			0.258002	+	0.966144i	$0.416936\pi$
$42$	−15.1652	+	6.46903i	−2.34004	+	0.998193i
$43$	10.4303			1.59061			0.795304	−	0.606211i	$-0.207311\pi$
$43$	10.4303			1.59061			0.795304	+	0.606211i	$0.207311\pi$
$44$	3.63228	+	6.29129i	0.547587	+	0.948448i
$45$		0			0
$46$	4.43359	−	7.67920i	0.653697	−	1.13224i
$47$	−4.68222	−	8.10985i	−0.682973	−	1.18294i	−0.974069	−	0.226250i	$-0.927354\pi$
$47$	−4.68222	−	8.10985i	−0.682973	−	1.18294i	0.291097	−	0.956694i	$-0.405980\pi$
$48$	−4.63555			−0.669084
$49$	4.84471	−	5.05260i	0.692101	−	0.721800i
$50$		0			0
$51$	−7.36718	−	12.7603i	−1.03161	−	1.78680i
$52$	0.798037	−	1.38224i	0.110668	−	0.191682i
$53$	−5.35071	+	9.26770i	−0.734977	+	1.27302i	0.219757	+	0.975555i	$0.429474\pi$
$53$	−5.35071	+	9.26770i	−0.734977	+	1.27302i	−0.954734	+	0.297462i	$0.903860\pi$
$54$	6.33424	+	10.9712i	0.861981	+	1.49300i
$55$		0			0
$56$	−4.46379	+	1.90412i	−0.596500	+	0.254449i
$57$	1.33151			0.176363
$58$	3.15202	+	5.45946i	0.413880	+	0.716862i
$59$	−1.98026	+	3.42991i	−0.257808	+	0.446537i	−0.965654	−	0.259830i	$-0.916334\pi$
$59$	−1.98026	+	3.42991i	−0.257808	+	0.446537i	0.707846	+	0.706366i	$0.249667\pi$
$60$		0			0
$61$	1.93359	+	3.34907i	0.247571	+	0.428805i	0.962851	−	0.270032i	$-0.0870344\pi$
$61$	1.93359	+	3.34907i	0.247571	+	0.428805i	−0.715281	+	0.698837i	$0.753701\pi$
$62$	8.50273			1.07985
$63$	−10.6487	−	7.99482i	−1.34162	−	1.00725i
$64$	−12.7014			−1.58768
$65$		0			0
$66$	−7.98626	+	13.8326i	−0.983041	+	1.70268i
$67$	3.83424	−	6.64110i	0.468427	−	0.811340i	−0.530922	−	0.847421i	$-0.678154\pi$
$67$	3.83424	−	6.64110i	0.468427	−	0.811340i	0.999349	+	0.0360810i	$0.0114874\pi$
$68$	−7.36718	−	12.7603i	−0.893402	−	1.54742i
$69$	11.4303			1.37605
$70$		0			0
$71$	−8.73436			−1.03658			−0.518289	−	0.855206i	$-0.673431\pi$
$71$	−8.73436			−1.03658			−0.518289	+	0.855206i	$0.673431\pi$
$72$	4.61581	+	7.99482i	0.543979	+	0.942199i
$73$	5.66849	−	9.81811i	0.663446	−	1.14912i	−0.316258	−	0.948673i	$-0.602427\pi$
$73$	5.66849	−	9.81811i	0.663446	−	1.14912i	0.979704	−	0.200449i	$-0.0642402\pi$
$74$	2.45333	−	4.24929i	0.285194	−	0.493970i
$75$		0			0
$76$	1.33151			0.152735
$77$	0.814504	−	6.73234i	0.0928214	−	0.767221i
$78$	3.50927			0.397347
$79$	−2.57961	−	4.46801i	−0.290228	−	0.502690i	0.683635	−	0.729824i	$-0.260398\pi$
$79$	−2.57961	−	4.46801i	−0.290228	−	0.502690i	−0.973864	+	0.227134i	$0.927065\pi$
$80$		0			0
$81$	−0.615813	+	1.06662i	−0.0684236	+	0.118513i
$82$	3.63228	+	6.29129i	0.401118	+	0.694757i
$83$	3.13282			0.343872			0.171936	−	0.985108i	$-0.444998\pi$
$83$	3.13282			0.343872			0.171936	+	0.985108i	$0.444998\pi$
$84$	−16.9962	−	12.7603i	−1.85444	−	1.39227i
$85$		0			0
$86$	11.4665	+	19.8606i	1.23647	+	2.14162i
$87$	−4.06314	+	7.03756i	−0.435614	+	0.754506i
$88$	−2.35071	+	4.07155i	−0.250587	+	0.434029i
$89$	2.78757	+	4.82821i	0.295482	+	0.511790i	0.975097	−	0.221779i	$-0.0711864\pi$
$89$	2.78757	+	4.82821i	0.295482	+	0.511790i	−0.679615	+	0.733569i	$0.737853\pi$
$90$		0			0
$91$	−1.37045	+	0.584593i	−0.143662	+	0.0612820i
$92$	11.4303			1.19169
$93$	5.48026	+	9.49209i	0.568277	+	0.984284i
$94$	10.2948	−	17.8311i	1.06182	−	1.83913i
$95$		0			0
$96$	−10.2948	−	17.8311i	−1.05071	−	1.81987i
$97$	−15.2975			−1.55323			−0.776613	−	0.629978i	$-0.783064\pi$
$97$	−15.2975			−1.55323			−0.776613	+	0.629978i	$0.783064\pi$
$98$	14.9468	+	3.67036i	1.50985	+	0.370763i
$99$	−12.9001			−1.29651
$100$		0			0
$101$	−2.49673	+	4.32446i	−0.248434	+	0.430300i	−0.963091	−	0.269175i	$-0.913249\pi$
$101$	−2.49673	+	4.32446i	−0.248434	+	0.430300i	0.714658	+	0.699474i	$0.246582\pi$
$102$	16.1981	−	28.0560i	1.60386	−	2.77796i
$103$	−10.0132	−	17.3434i	−0.986629	−	1.70889i	−0.634459	−	0.772956i	$-0.718777\pi$
$103$	−10.0132	−	17.3434i	−0.986629	−	1.70889i	−0.352170	−	0.935936i	$-0.614556\pi$
$104$	1.03293			0.101288
$105$		0			0
$106$	−23.5291			−2.28535
$107$	5.68495	+	9.84663i	0.549585	+	0.951910i	0.998303	+	0.0582359i	$0.0185476\pi$
$107$	5.68495	+	9.84663i	0.549585	+	0.951910i	−0.448718	+	0.893674i	$0.648119\pi$
$108$	−8.16521	+	14.1426i	−0.785698	+	1.36087i
$109$	−4.48026	+	7.76004i	−0.429131	+	0.743277i	−0.996796	−	0.0799826i	$-0.974514\pi$
$109$	−4.48026	+	7.76004i	−0.429131	+	0.743277i	0.567665	+	0.823260i	$0.307847\pi$
$110$		0			0
$111$	6.32497			0.600340
$112$	3.46052	+	2.59808i	0.326989	+	0.245495i
$113$	−11.8672			−1.11637			−0.558185	−	0.829716i	$-0.688502\pi$
$113$	−11.8672			−1.11637			−0.558185	+	0.829716i	$0.688502\pi$
$114$	1.46379	+	2.53537i	0.137097	+	0.237459i
$115$		0			0
$116$	−4.06314	+	7.03756i	−0.377253	+	0.653421i
$117$	1.41712	+	2.45453i	0.131013	+	0.226921i
$118$	−8.70796			−0.801633
$119$	−1.65202	+	13.6549i	−0.151440	+	1.25174i
$120$		0			0
$121$	2.21516	+	3.83677i	0.201378	+	0.348797i
$122$	−4.25136	+	7.36358i	−0.384900	+	0.666667i
$123$	−4.68222	+	8.10985i	−0.422182	+	0.731241i
$124$	5.48026	+	9.49209i	0.492142	+	0.852415i
$125$		0			0
$126$	3.51647	−	29.0656i	0.313272	−	2.58937i
$127$	−12.4303			−1.10301			−0.551506	−	0.834171i	$-0.685947\pi$
$127$	−12.4303			−1.10301			−0.551506	+	0.834171i	$0.685947\pi$
$128$	−6.69869	−	11.6025i	−0.592086	−	1.02552i
$129$	−14.7810	+	25.6015i	−1.30140	+	2.25409i
$130$		0			0
$131$	−2.49673	−	4.32446i	−0.218140	−	0.377830i	0.736099	−	0.676874i	$-0.236666\pi$
$131$	−2.49673	−	4.32446i	−0.218140	−	0.377830i	−0.954239	+	0.299044i	$0.903332\pi$
$132$	−20.5895			−1.79209
$133$	−0.993999	−	0.746270i	−0.0861906	−	0.0647098i
$134$	16.8606			1.45654
$135$		0			0
$136$	4.76783	−	8.25813i	0.408838	−	0.708129i
$137$	−0.254637	+	0.441044i	−0.0217551	+	0.0376809i	−0.876698	−	0.481041i	$-0.840259\pi$
$137$	−0.254637	+	0.441044i	−0.0217551	+	0.0376809i	0.854943	+	0.518722i	$0.173592\pi$
$138$	12.5659	+	21.7647i	1.06968	+	1.85274i
$139$	22.2975			1.89125			0.945624	−	0.325261i	$-0.105452\pi$
$139$	22.2975			1.89125			0.945624	+	0.325261i	$0.105452\pi$
$140$		0			0
$141$	26.5411			2.23517
$142$	−9.60208	−	16.6313i	−0.805788	−	1.39567i
$143$	−0.721702	+	1.25002i	−0.0603518	+	0.104532i
$144$	4.11581	−	7.12880i	0.342984	−	0.594066i
$145$		0			0
$146$	24.9265			2.06293
$147$	5.53621	+	19.0516i	0.456619	+	1.57135i
$148$	6.32497			0.519909
$149$	−5.23490	−	9.06711i	−0.428860	−	0.742806i	0.567913	−	0.823089i	$-0.307751\pi$
$149$	−5.23490	−	9.06711i	−0.428860	−	0.742806i	−0.996772	+	0.0802824i	$0.974418\pi$
$150$		0			0
$151$	−4.99673	+	8.65459i	−0.406628	+	0.704300i	−0.994509	−	0.104647i	$-0.966629\pi$
$151$	−4.99673	+	8.65459i	−0.406628	+	0.704300i	0.587881	+	0.808947i	$0.299962\pi$
$152$	0.430859	+	0.746270i	0.0349473	+	0.0605305i
$153$	26.1647			2.11529
$154$	13.7146	−	5.85025i	1.10516	−	0.471427i
$155$		0			0
$156$	2.26183	+	3.91761i	0.181091	+	0.313659i
$157$	3.31177	−	5.73616i	0.264308	−	0.457796i	−0.703074	−	0.711117i	$-0.748190\pi$
$157$	3.31177	−	5.73616i	0.264308	−	0.457796i	0.967382	+	0.253321i	$0.0815230\pi$
$158$	5.67176	−	9.82377i	0.451221	−	0.781537i
$159$	−15.1652	−	26.2669i	−1.20268	−	2.08310i
$160$		0			0
$161$	−8.53293	−	6.40632i	−0.672489	−	0.504889i
$162$	−2.70796			−0.212758
$163$	3.60981	+	6.25238i	0.282742	+	0.489724i	0.972059	−	0.234736i	$-0.0754226\pi$
$163$	3.60981	+	6.25238i	0.282742	+	0.489724i	−0.689317	+	0.724460i	$0.742089\pi$
$164$	−4.68222	+	8.10985i	−0.365620	+	0.633273i
$165$		0			0
$166$	3.44405	+	5.96528i	0.267310	+	0.462995i
$167$	21.1712			1.63828			0.819139	−	0.573595i	$-0.194452\pi$
$167$	21.1712			1.63828			0.819139	+	0.573595i	$0.194452\pi$
$168$	1.65202	−	13.6549i	0.127456	−	1.05350i
$169$	−12.6829			−0.975606
$170$		0			0
$171$	−1.18222	+	2.04767i	−0.0904069	+	0.156589i
$172$	−14.7810	+	25.6015i	−1.12704	+	1.95210i
$173$	−3.73490	−	6.46903i	−0.283959	−	0.491831i	0.688397	−	0.725334i	$-0.258315\pi$
$173$	−3.73490	−	6.46903i	−0.283959	−	0.491831i	−0.972356	+	0.233503i	$0.924981\pi$
$174$	−17.8672			−1.35451
$175$		0			0
$176$	4.19215			0.315995
$177$	−5.61254	−	9.72121i	−0.421864	−	0.730691i
$178$	−6.12901	+	10.6158i	−0.459389	+	0.795684i
$179$	0.364448	−	0.631243i	0.0272401	−	0.0471813i	−0.852084	−	0.523405i	$-0.824661\pi$
$179$	0.364448	−	0.631243i	0.0272401	−	0.0471813i	0.879324	+	0.476224i	$0.157995\pi$
$180$		0			0
$181$	−2.00654			−0.149145			−0.0745726	−	0.997216i	$-0.523759\pi$
$181$	−2.00654			−0.149145			−0.0745726	+	0.997216i	$0.523759\pi$
$182$	−2.61973	−	1.96683i	−0.194188	−	0.145791i
$183$	−10.9605			−0.810225
$184$	3.69869	+	6.40632i	0.272671	+	0.472280i
$185$		0			0
$186$	−12.0494	+	20.8702i	−0.883505	+	1.53028i
$187$	6.66248	+	11.5398i	0.487209	+	0.843871i
$188$	26.5411			1.93571
$189$	14.0219	−	5.98134i	1.01995	−	0.435078i
$190$		0			0
$191$	−1.06314	−	1.84141i	−0.0769261	−	0.133240i	0.824996	−	0.565138i	$-0.191177\pi$
$191$	−1.06314	−	1.84141i	−0.0769261	−	0.133240i	−0.901922	+	0.431898i	$0.857844\pi$
$192$	17.9995	−	31.1760i	1.29900	−	2.24993i
$193$	1.32051	−	2.28718i	0.0950521	−	0.164635i	−0.814578	−	0.580054i	$-0.803032\pi$
$193$	1.32051	−	2.28718i	0.0950521	−	0.164635i	0.909630	+	0.415419i	$0.136365\pi$
$194$	−16.8172	−	29.1283i	−1.20741	−	2.09129i
$195$		0			0
$196$	5.53621	+	19.0516i	0.395443	+	1.36083i
$197$	6.17122			0.439681			0.219840	−	0.975536i	$-0.429446\pi$
$197$	6.17122			0.439681			0.219840	+	0.975536i	$0.429446\pi$
$198$	−14.1817	−	24.5634i	−1.00785	−	1.74564i
$199$	11.3836	−	19.7171i	0.806965	−	1.39770i	−0.107991	−	0.994152i	$-0.534442\pi$
$199$	11.3836	−	19.7171i	0.806965	−	1.39770i	0.914956	−	0.403553i	$-0.132225\pi$
$200$		0			0
$201$	10.8672	+	18.8225i	0.766512	+	1.32764i
$202$	−10.9791			−0.772485
$203$	6.97753	−	2.97641i	0.489727	−	0.208903i
$204$	41.7607			2.92384
$205$		0			0
$206$	22.0159	−	38.1327i	1.53392	−	2.65683i
$207$	−10.1487	+	17.5781i	−0.705387	+	1.22177i
$208$	−0.460522	−	0.797647i	−0.0319314	−	0.0553069i
$209$	−1.20415			−0.0832928
$210$		0			0
$211$	−15.8672			−1.09234			−0.546171	−	0.837674i	$-0.683915\pi$
$211$	−15.8672			−1.09234			−0.546171	+	0.837674i	$0.683915\pi$
$212$	−15.1652	−	26.2669i	−1.04155	−	1.80402i
$213$	12.3776	−	21.4387i	0.848102	−	1.46896i
$214$	−12.4995	+	21.6497i	−0.854445	+	1.47994i
$215$		0			0
$216$	−10.5686			−0.719102
$217$	1.22890	−	10.1575i	0.0834229	−	0.689538i
$218$	−19.7014			−1.33435
$219$	16.0659	+	27.8269i	1.08563	+	1.88037i
$220$		0			0
$221$	1.46379	−	2.53537i	0.0984654	−	0.170547i
$222$	6.95333	+	12.0435i	0.466677	+	0.808308i
$223$	7.56314			0.506465			0.253233	−	0.967405i	$-0.418506\pi$
$223$	7.56314			0.506465			0.253233	+	0.967405i	$0.418506\pi$
$224$	−2.30850	+	19.0811i	−0.154243	+	1.27491i
$225$		0			0
$226$	−13.0461	−	22.5966i	−0.867816	−	1.50310i
$227$	−6.66248	+	11.5398i	−0.442205	+	0.765921i	−0.997853	−	0.0654966i	$-0.979137\pi$
$227$	−6.66248	+	11.5398i	−0.442205	+	0.765921i	0.555648	+	0.831418i	$0.312470\pi$
$228$	−1.88692	+	3.26824i	−0.124964	+	0.216444i
$229$	6.41058	+	11.1034i	0.423623	+	0.733736i	0.996291	−	0.0860511i	$-0.0274248\pi$
$229$	6.41058	+	11.1034i	0.423623	+	0.733736i	−0.572668	+	0.819788i	$0.694092\pi$
$230$		0			0
$231$	15.3704	+	11.5398i	1.01130	+	0.759261i
$232$	−5.25910			−0.345277
$233$	10.3068	+	17.8518i	0.675219	+	1.16951i	0.976405	+	0.215948i	$0.0692841\pi$
$233$	10.3068	+	17.8518i	0.675219	+	1.16951i	−0.301186	+	0.953565i	$0.597383\pi$
$234$	−3.11581	+	5.39675i	−0.203687	+	0.352796i
$235$		0			0
$236$	−5.61254	−	9.72121i	−0.365345	−	0.632797i
$237$	14.6225			0.949831
$238$	−27.8167	+	11.8658i	−1.80309	+	0.769144i
$239$	−15.4753			−1.00101			−0.500505	−	0.865733i	$-0.666852\pi$
$239$	−15.4753			−1.00101			−0.500505	+	0.865733i	$0.666852\pi$
$240$		0			0
$241$	−5.51920	+	9.55953i	−0.355523	+	0.615783i	−0.987207	−	0.159442i	$-0.949030\pi$
$241$	−5.51920	+	9.55953i	−0.355523	+	0.615783i	0.631685	+	0.775226i	$0.282364\pi$
$242$	−4.87045	+	8.43587i	−0.313084	+	0.542278i
$243$	6.89738	+	11.9466i	0.442467	+	0.766376i
$244$	−10.9605			−0.701676
$245$		0			0
$246$	−20.5895			−1.31274
$247$	0.132280	+	0.229116i	0.00841678	+	0.0145783i
$248$	−3.54667	+	6.14302i	−0.225214	+	0.390082i
$249$	−4.43959	+	7.68960i	−0.281348	+	0.487308i
$250$		0			0
$251$	−27.8541			−1.75813			−0.879067	−	0.476698i	$-0.841834\pi$
$251$	−27.8541			−1.75813			−0.879067	+	0.476698i	$0.841834\pi$
$252$	34.7141	−	14.8080i	2.18678	−	0.932816i
$253$	−10.3370			−0.649880
$254$	−13.6652	−	23.6688i	−0.857432	−	1.48512i
$255$		0			0
$256$	2.02693	−	3.51075i	0.126683	−	0.219422i
$257$	−7.26456	−	12.5826i	−0.453151	−	0.784880i	0.545429	−	0.838157i	$-0.316367\pi$
$257$	−7.26456	−	12.5826i	−0.453151	−	0.784880i	−0.998580	+	0.0532768i	$0.983033\pi$
$258$	−64.9978			−4.04659
$259$	−4.72170	−	3.54494i	−0.293392	−	0.220272i
$260$		0			0
$261$	−7.21516	−	12.4970i	−0.446607	−	0.773546i
$262$	5.48953	−	9.50815i	0.339145	−	0.587416i
$263$	0.146018	−	0.252910i	0.00900384	−	0.0155951i	−0.861488	−	0.507777i	$-0.830467\pi$
$263$	0.146018	−	0.252910i	0.00900384	−	0.0155951i	0.870492	+	0.492182i	$0.163801\pi$
$264$	−6.66248	−	11.5398i	−0.410048	−	0.710223i
$265$		0			0
$266$	0.328242	−	2.71310i	0.0201258	−	0.166351i
$267$	−15.8013			−0.967024
$268$	10.8672	+	18.8225i	0.663819	+	1.14977i
$269$	−4.26837	+	7.39304i	−0.260247	+	0.450762i	−0.966308	−	0.257390i	$-0.917137\pi$
$269$	−4.26837	+	7.39304i	−0.260247	+	0.450762i	0.706060	+	0.708152i	$0.250471\pi$
$270$		0			0
$271$	−1.45606	−	2.52197i	−0.0884492	−	0.153198i	0.818407	−	0.574640i	$-0.194858\pi$
$271$	−1.45606	−	2.52197i	−0.0884492	−	0.153198i	−0.906856	+	0.421441i	$0.861524\pi$
$272$	−8.50273			−0.515554
$273$	0.507194	−	4.19224i	0.0306968	−	0.253726i
$274$	−1.11973			−0.0676457
$275$		0			0
$276$	−16.1981	+	28.0560i	−0.975014	+	1.68877i
$277$	0.919851	−	1.59323i	0.0552685	−	0.0957278i	−0.837067	−	0.547100i	$-0.815732\pi$
$277$	0.919851	−	1.59323i	0.0552685	−	0.0957278i	0.892336	+	0.451372i	$0.149065\pi$
$278$	24.5127	+	42.4572i	1.47017	+	2.54641i
$279$	−19.4633			−1.16523
$280$		0			0
$281$	−0.608077			−0.0362748			−0.0181374	−	0.999836i	$-0.505774\pi$
$281$	−0.608077			−0.0362748			−0.0181374	+	0.999836i	$0.505774\pi$
$282$	29.1779	+	50.5375i	1.73752	+	3.00947i
$283$	−5.84744	+	10.1281i	−0.347594	+	0.602051i	−0.985822	−	0.167797i	$-0.946335\pi$
$283$	−5.84744	+	10.1281i	−0.347594	+	0.602051i	0.638227	+	0.769848i	$0.279668\pi$
$284$	12.3776	−	21.4387i	0.734478	−	1.27215i
$285$		0			0
$286$	−3.17360			−0.187659
$287$	8.04067	−	3.42991i	0.474626	−	0.202461i
$288$	36.5621			2.15444
$289$	−5.01320	−	8.68311i	−0.294894	−	0.510771i
$290$		0			0
$291$	21.6784	−	37.5481i	1.27081	−	2.20111i
$292$	16.0659	+	27.8269i	0.940184	+	1.62845i
$293$	−28.0253			−1.63726			−0.818628	−	0.574324i	$-0.805265\pi$
$293$	−28.0253			−1.63726			−0.818628	+	0.574324i	$0.805265\pi$
$294$	−30.1904	+	31.4859i	−1.76074	+	1.83630i
$295$		0			0
$296$	2.04667	+	3.54494i	0.118960	+	0.206045i
$297$	7.38419	−	12.7898i	0.428474	−	0.742139i
$298$	11.5099	−	19.9358i	0.666752	−	1.15485i
$299$	1.13555	+	1.96683i	0.0656707	+	0.113745i
$300$		0			0
$301$	25.3831	−	10.8277i	1.46306	−	0.624097i
$302$	−21.9725			−1.26438
$303$	−7.07633	−	12.2566i	−0.406525	−	0.704122i
$304$	0.384187	−	0.665432i	0.0220346	−	0.0381651i
$305$		0			0
$306$	28.7640	+	49.8207i	1.64433	+	2.84806i
$307$	−5.55660			−0.317132			−0.158566	−	0.987348i	$-0.550687\pi$
$307$	−5.55660			−0.317132			−0.158566	+	0.987348i	$0.550687\pi$
$308$	15.3704	+	11.5398i	0.875813	+	0.657539i
$309$	56.7597			3.22894
$310$		0			0
$311$	−3.30404	+	5.72276i	−0.187355	+	0.324508i	−0.944368	−	0.328892i	$-0.893325\pi$
$311$	−3.30404	+	5.72276i	−0.187355	+	0.324508i	0.757013	+	0.653400i	$0.226658\pi$
$312$	−1.46379	+	2.53537i	−0.0828710	+	0.143537i
$313$	−5.95006	−	10.3058i	−0.336317	−	0.582518i	0.647420	−	0.762134i	$-0.275848\pi$
$313$	−5.95006	−	10.3058i	−0.336317	−	0.582518i	−0.983737	+	0.179615i	$0.942515\pi$
$314$	14.5631			0.821845
$315$		0			0
$316$	14.6225			0.822578
$317$	4.35517	+	7.54338i	0.244611	+	0.423679i	0.962022	−	0.272971i	$-0.0880064\pi$
$317$	4.35517	+	7.54338i	0.244611	+	0.423679i	−0.717411	+	0.696650i	$0.754673\pi$
$318$	33.3436	−	57.7529i	1.86982	−	3.23862i
$319$	3.67449	−	6.36440i	0.205732	−	0.356338i
$320$		0			0
$321$	−32.2251			−1.79863
$322$	2.81778	−	23.2905i	0.157029	−	1.29793i
$323$	2.44232			0.135894
$324$	−1.74536	−	3.02306i	−0.0969646	−	0.167948i
$325$		0			0
$326$	−7.93686	+	13.7470i	−0.439582	+	0.761378i
$327$	−12.6981	−	21.9938i	−0.702209	−	1.21626i
$328$	−6.06041			−0.334630
$329$	−19.8134	−	14.8754i	−1.09235	−	0.820109i
$330$		0			0
$331$	6.23436	+	10.7982i	0.342671	+	0.593524i	0.984928	−	0.172966i	$-0.0553350\pi$
$331$	6.23436	+	10.7982i	0.342671	+	0.593524i	−0.642257	+	0.766490i	$0.722002\pi$
$332$	−4.43959	+	7.68960i	−0.243654	+	0.422021i
$333$	−5.61581	+	9.72687i	−0.307745	+	0.533029i
$334$	23.2745	+	40.3126i	1.27352	+	2.20581i
$335$		0			0
$336$	−11.2810	+	4.81215i	−0.615430	+	0.262524i
$337$	3.61462			0.196901			0.0984505	−	0.995142i	$-0.468611\pi$
$337$	3.61462			0.196901			0.0984505	+	0.995142i	$0.468611\pi$
$338$	−13.9429	−	24.1497i	−0.758392	−	1.31357i
$339$	16.8172	−	29.1283i	0.913387	−	1.58203i
$340$		0			0
$341$	−4.95606	−	8.58414i	−0.268386	−	0.464857i
$342$	−5.19869			−0.281113
$343$	6.54494	−	17.3252i	0.353393	−	0.935475i
$344$	−19.1317			−1.03151
$345$		0			0
$346$	8.21189	−	14.2234i	0.441474	−	0.764655i
$347$	10.9199	−	18.9137i	0.586208	−	1.01534i	−0.408515	−	0.912751i	$-0.633953\pi$
$347$	10.9199	−	18.9137i	0.586208	−	1.01534i	0.994724	−	0.102591i	$-0.0327133\pi$
$348$	−11.5159	−	19.9462i	−0.617318	−	1.06923i
$349$	−3.69596			−0.197840			−0.0989201	−	0.995095i	$-0.531539\pi$
$349$	−3.69596			−0.197840			−0.0989201	+	0.995095i	$0.531539\pi$
$350$		0			0
$351$	−3.24471			−0.173190
$352$	9.31004	+	16.1255i	0.496227	+	0.859490i
$353$	−15.8217	+	27.4040i	−0.842104	+	1.45857i	0.0460086	+	0.998941i	$0.485350\pi$
$353$	−15.8217	+	27.4040i	−0.842104	+	1.45857i	−0.888113	+	0.459626i	$0.847984\pi$
$354$	12.3402	−	21.3739i	0.655877	−	1.13601i
$355$		0			0
$356$	−15.8013			−0.837468
$357$	−31.1751	−	23.4055i	−1.64996	−	1.23875i
$358$	1.60262			0.0847010
$359$	8.56914	+	14.8422i	0.452262	+	0.783341i	0.998526	−	0.0542722i	$-0.0172839\pi$
$359$	8.56914	+	14.8422i	0.452262	+	0.783341i	−0.546264	+	0.837613i	$0.683951\pi$
$360$		0			0
$361$	9.38965	−	16.2633i	0.494192	−	0.855965i
$362$	−2.20589	−	3.82071i	−0.115939	−	0.200812i
$363$	−12.5566			−0.659050
$364$	0.507194	−	4.19224i	0.0265842	−	0.219733i
$365$		0			0
$366$	−12.0494	−	20.8702i	−0.629832	−	1.09090i
$367$	5.89411	−	10.2089i	0.307670	−	0.532900i	−0.670182	−	0.742197i	$-0.733784\pi$
$367$	5.89411	−	10.2089i	0.307670	−	0.532900i	0.977852	+	0.209296i	$0.0671174\pi$
$368$	3.29804	−	5.71237i	0.171922	−	0.297778i
$369$	−8.31450	−	14.4011i	−0.432836	−	0.749694i
$370$		0			0
$371$	−3.40065	+	28.1083i	−0.176553	+	1.45931i
$372$	−31.0648			−1.61063
$373$	4.70196	+	8.14404i	0.243458	+	0.421682i	0.961697	−	0.274114i	$-0.0883847\pi$
$373$	4.70196	+	8.14404i	0.243458	+	0.421682i	−0.718239	+	0.695797i	$0.755051\pi$
$374$	−14.6487	+	25.3724i	−0.757469	+	1.31197i
$375$		0			0
$376$	8.58834	+	14.8754i	0.442910	+	0.767142i
$377$	−1.61462			−0.0831572
$378$	26.8041	+	20.1239i	1.37866	+	1.03506i
$379$	−17.3490			−0.891157			−0.445579	−	0.895243i	$-0.647002\pi$
$379$	−17.3490			−0.891157			−0.445579	+	0.895243i	$0.647002\pi$
$380$		0			0
$381$	17.6153	−	30.5105i	0.902458	−	1.56310i
$382$	2.33752	−	4.04869i	0.119598	−	0.207149i
$383$	2.91058	+	5.04127i	0.148724	+	0.257597i	0.930756	−	0.365641i	$-0.119150\pi$
$383$	2.91058	+	5.04127i	0.148724	+	0.257597i	−0.782032	+	0.623238i	$0.785817\pi$
$384$	37.9714			1.93772
$385$		0			0
$386$	5.80677			0.295557
$387$	−26.2476	−	45.4621i	−1.33424	−	2.31097i
$388$	21.6784	−	37.5481i	1.10055	−	1.90622i
$389$	13.3140	−	23.0605i	0.675045	−	1.16921i	−0.301411	−	0.953494i	$-0.597458\pi$
$389$	13.3140	−	23.0605i	0.675045	−	1.16921i	0.976456	−	0.215717i	$-0.0692090\pi$
$390$		0			0
$391$	20.9660			1.06030
$392$	−8.88637	+	9.26770i	−0.448830	+	0.468090i
$393$	14.1527			0.713908
$394$	6.78430	+	11.7508i	0.341788	+	0.591994i
$395$		0			0
$396$	18.2810	−	31.6637i	0.918656	−	1.59116i
$397$	17.6153	+	30.5105i	0.884085	+	1.53128i	0.846759	+	0.531977i	$0.178551\pi$
$397$	17.6153	+	30.5105i	0.884085	+	1.53128i	0.0373264	+	0.999303i	$0.488116\pi$
$398$	50.0582			2.50919
$399$	3.24036	−	1.38224i	0.162221	−	0.0691986i
$400$		0			0
$401$	12.2184	+	21.1629i	0.610159	+	1.05683i	0.991213	+	0.132274i	$0.0422279\pi$
$401$	12.2184	+	21.1629i	0.610159	+	1.05683i	−0.381054	+	0.924553i	$0.624439\pi$
$402$	−23.8936	+	41.3849i	−1.19170	+	2.06409i
$403$	−1.08888	+	1.88600i	−0.0542410	+	0.0939481i
$404$	−7.07633	−	12.2566i	−0.352061	−	0.609787i
$405$		0			0
$406$	13.3382	+	10.0140i	0.661962	+	0.496985i
$407$	−5.71997			−0.283528
$408$	13.5132	+	23.4055i	0.669003	+	1.15875i
$409$	−14.7436	+	25.5367i	−0.729026	+	1.26271i	0.228270	+	0.973598i	$0.426693\pi$
$409$	−14.7436	+	25.5367i	−0.729026	+	1.26271i	−0.957295	+	0.289111i	$0.906640\pi$
$410$		0			0
$411$	−0.721702	−	1.25002i	−0.0355989	−	0.0616592i
$412$	56.7597			2.79635
$413$	−1.25856	+	10.4027i	−0.0619296	+	0.511883i
$414$	−44.6279			−2.19334
$415$		0			0
$416$	2.04548	−	3.54287i	0.100288	−	0.173704i
$417$	−31.5983	+	54.7298i	−1.54737	+	2.68013i
$418$	−1.32378	−	2.29285i	−0.0647481	−	0.112147i
$419$	9.74090			0.475874			0.237937	−	0.971281i	$-0.423529\pi$
$419$	9.74090			0.475874			0.237937	+	0.971281i	$0.423529\pi$
$420$		0			0
$421$	−2.68942			−0.131074			−0.0655371	−	0.997850i	$-0.520876\pi$
$421$	−2.68942			−0.131074			−0.0655371	+	0.997850i	$0.520876\pi$
$422$	−17.4435	−	30.2130i	−0.849137	−	1.47075i
$423$	−23.5653	+	40.8163i	−1.14579	+	1.98456i
$424$	9.81450	−	16.9992i	0.476634	−	0.825555i
$425$		0			0
$426$	54.4292			2.63710
$427$	8.18222	+	6.14302i	0.395966	+	0.297281i
$428$	−32.2251			−1.55766
$429$	−2.04548	−	3.54287i	−0.0987567	−	0.171052i
$430$		0			0
$431$	4.71843	−	8.17256i	0.227279	−	0.393658i	−0.729722	−	0.683744i	$-0.760350\pi$
$431$	4.71843	−	8.17256i	0.227279	−	0.393658i	0.957001	+	0.290086i	$0.0936838\pi$
$432$	4.71189	+	8.16123i	0.226701	+	0.392657i
$433$	20.8541			1.00218			0.501092	−	0.865394i	$-0.332932\pi$
$433$	20.8541			1.00218			0.501092	+	0.865394i	$0.332932\pi$
$434$	20.6921	−	8.82666i	0.993255	−	0.423693i
$435$		0			0
$436$	−12.6981	−	21.9938i	−0.608131	−	1.05331i
$437$	−0.947326	+	1.64082i	−0.0453168	+	0.0784909i
$438$	−35.3239	+	61.1828i	−1.68784	+	2.92343i
$439$	11.2810	+	19.5393i	0.538414	+	0.932561i	0.998990	+	0.0449400i	$0.0143097\pi$
$439$	11.2810	+	19.5393i	0.538414	+	0.932561i	−0.460576	+	0.887620i	$0.652357\pi$
$440$		0			0
$441$	−34.2141	−	8.40168i	−1.62924	−	0.400080i
$442$	6.43686			0.306170
$443$	−15.2980	−	26.4970i	−0.726832	−	1.25891i	−0.958216	−	0.286047i	$-0.907659\pi$
$443$	−15.2980	−	26.4970i	−0.726832	−	1.25891i	0.231384	−	0.972863i	$-0.425675\pi$
$444$	−8.96325	+	15.5248i	−0.425377	+	0.736775i
$445$		0			0
$446$	8.31450	+	14.4011i	0.393703	+	0.681914i
$447$	29.6739			1.40353
$448$	−30.9100	+	13.1853i	−1.46036	+	0.622947i
$449$	1.25256			0.0591118			0.0295559	−	0.999563i	$-0.490591\pi$
$449$	1.25256			0.0591118			0.0295559	+	0.999563i	$0.490591\pi$
$450$		0			0
$451$	4.23436	−	7.33412i	0.199388	−	0.345350i
$452$	16.8172	−	29.1283i	0.791016	−	1.37008i
$453$	−14.1619	−	24.5292i	−0.665386	−	1.15248i
$454$	−29.2975			−1.37500
$455$		0			0
$456$	−2.44232			−0.114372
$457$	11.8809	+	20.5783i	0.555766	+	0.962615i	0.997844	+	0.0656378i	$0.0209082\pi$
$457$	11.8809	+	20.5783i	0.555766	+	0.962615i	−0.442078	+	0.896977i	$0.645758\pi$
$458$	−14.0949	+	24.4131i	−0.658611	+	1.14075i
$459$	−14.9770	+	25.9409i	−0.699066	+	1.21082i
$460$		0			0
$461$	−31.0833			−1.44770			−0.723848	−	0.689960i	$-0.757628\pi$
$461$	−31.0833			−1.44770			−0.723848	+	0.689960i	$0.757628\pi$
$462$	−5.07568	+	41.9534i	−0.236142	+	1.95185i
$463$	24.8606			1.15537			0.577686	−	0.816259i	$-0.303956\pi$
$463$	24.8606			1.15537			0.577686	+	0.816259i	$0.303956\pi$
$464$	2.34471	+	4.06116i	0.108850	+	0.188534i
$465$		0			0
$466$	−22.6614	+	39.2507i	−1.04977	+	1.81825i
$467$	6.83370	+	11.8363i	0.316226	+	0.547719i	0.979697	−	0.200482i	$-0.0642509\pi$
$467$	6.83370	+	11.8363i	0.316226	+	0.547719i	−0.663471	+	0.748202i	$0.730918\pi$
$468$	−8.03293			−0.371323
$469$	2.43686	−	20.1420i	0.112524	−	0.930073i
$470$		0			0
$471$	9.38637	+	16.2577i	0.432501	+	0.749114i
$472$	3.63228	−	6.29129i	0.167189	−	0.289580i
$473$	13.3672	−	23.1526i	0.614623	−	1.06456i
$474$	16.0751	+	27.8430i	0.738356	+	1.27887i
$475$		0			0
$476$	−31.1751	−	23.4055i	−1.42891	−	1.07279i
$477$	53.8595			2.46606
$478$	−17.0127	−	29.4668i	−0.778141	−	1.34778i
$479$	2.08288	−	3.60765i	0.0951691	−	0.164838i	−0.814510	−	0.580149i	$-0.802994\pi$
$479$	2.08288	−	3.60765i	0.0951691	−	0.164838i	0.909679	+	0.415312i	$0.136327\pi$
$480$		0			0
$481$	0.628358	+	1.08835i	0.0286507	+	0.0496244i
$482$	−24.2700			−1.10547
$483$	27.8167	−	11.8658i	1.26570	−	0.539912i
$484$	−12.5566			−0.570754
$485$		0			0
$486$	−15.1652	+	26.2669i	−0.687908	+	1.19149i
$487$	7.09007	−	12.2804i	0.321282	−	0.556476i	−0.659471	−	0.751730i	$-0.729220\pi$
$487$	7.09007	−	12.2804i	0.321282	−	0.556476i	0.980753	+	0.195254i	$0.0625530\pi$
$488$	−3.54667	−	6.14302i	−0.160550	−	0.278081i
$489$	−20.4622			−0.925331
$490$		0			0
$491$	18.8737			0.851759			0.425880	−	0.904780i	$-0.359965\pi$
$491$	18.8737			0.851759			0.425880	+	0.904780i	$0.359965\pi$
$492$	−13.2706	−	22.9853i	−0.598283	−	1.03626i
$493$	−7.45279	+	12.9086i	−0.335657	+	0.581374i
$494$	−0.290843	+	0.503755i	−0.0130856	+	0.0226650i
$495$		0			0
$496$	6.32497			0.284000
$497$	−21.2558	+	9.06711i	−0.953454	+	0.406715i
$498$	−19.5226			−0.874828
$499$	5.26183	+	9.11376i	0.235552	+	0.407988i	0.959433	−	0.281937i	$-0.0909769\pi$
$499$	5.26183	+	9.11376i	0.235552	+	0.407988i	−0.723881	+	0.689925i	$0.757644\pi$
$500$		0			0
$501$	−30.0022	+	51.9653i	−1.34040	+	2.32164i
$502$	−30.6213	−	53.0376i	−1.36669	−	2.36718i
$503$	19.3854			0.864351			0.432176	−	0.901789i	$-0.357746\pi$
$503$	19.3854			0.864351			0.432176	+	0.901789i	$0.357746\pi$
$504$	19.5324	+	14.6644i	0.870042	+	0.653206i
$505$		0			0
$506$	−11.3639	−	19.6829i	−0.505187	−	0.875010i
$507$	17.9732	−	31.1305i	0.798217	−	1.38255i
$508$	17.6153	−	30.5105i	0.781551	−	1.35369i
$509$	−9.53566	−	16.5163i	−0.422661	−	0.732070i	0.573538	−	0.819179i	$-0.305571\pi$
$509$	−9.53566	−	16.5163i	−0.422661	−	0.732070i	−0.996199	+	0.0871089i	$0.972237\pi$
$510$		0			0
$511$	3.60262	−	29.7777i	0.159370	−	1.31729i
$512$	−17.8816			−0.790261
$513$	−1.35344	−	2.34423i	−0.0597558	−	0.103500i
$514$	15.9725	−	27.6652i	0.704518	−	1.22026i
$515$		0			0
$516$	−41.8930	−	72.5608i	−1.84424	−	3.19431i
$517$	−24.0024			−1.05562
$518$	1.55922	−	12.8878i	0.0685081	−	0.566258i
$519$	21.1712			0.929313
$520$		0			0
$521$	4.82224	−	8.35237i	0.211266	−	0.365924i	−0.740845	−	0.671676i	$-0.765575\pi$
$521$	4.82224	−	8.35237i	0.211266	−	0.365924i	0.952111	+	0.305752i	$0.0989080\pi$
$522$	15.8639	−	27.4771i	0.694344	−	1.20264i
$523$	15.3068	+	26.5121i	0.669318	+	1.15929i	0.978095	+	0.208159i	$0.0667470\pi$
$523$	15.3068	+	26.5121i	0.669318	+	1.15929i	−0.308777	+	0.951135i	$0.599920\pi$
$524$	14.1527			0.618262
$525$		0			0
$526$	0.642096			0.0279967
$527$	10.0521	+	17.4108i	0.437878	+	0.758426i
$528$	−5.94078	+	10.2897i	−0.258539	+	0.447803i
$529$	3.36772	−	5.83306i	0.146423	−	0.253611i
$530$		0			0
$531$	19.9330			0.865021
$532$	3.24036	−	1.38224i	0.140487	−	0.0599277i
$533$	−1.86063			−0.0805930
$534$	−17.3711	−	30.0876i	−0.751721	−	1.30202i
$535$		0			0
$536$	−7.03293	+	12.1814i	−0.303776	+	0.526156i
$537$	1.03293	+	1.78909i	0.0445744	+	0.0772051i
$538$	−18.7697			−0.809218
$539$	−5.00665	−	17.2293i	−0.215652	−	0.742117i
$540$		0			0
$541$	15.8414	+	27.4382i	0.681077	+	1.17966i	0.974653	+	0.223724i	$0.0718213\pi$
$541$	15.8414	+	27.4382i	0.681077	+	1.17966i	−0.293576	+	0.955936i	$0.594845\pi$
$542$	3.20142	−	5.54502i	0.137513	−	0.238179i
$543$	2.84352	−	4.92512i	0.122027	−	0.211357i
$544$	−18.8831	−	32.7065i	−0.809606	−	1.40228i
$545$		0			0
$546$	8.54013	−	3.64297i	0.365484	−	0.155905i
$547$	−5.91866			−0.253064			−0.126532	−	0.991963i	$-0.540385\pi$
$547$	−5.91866			−0.253064			−0.126532	+	0.991963i	$0.540385\pi$
$548$	−0.721702	−	1.25002i	−0.0308296	−	0.0533984i
$549$	9.73163	−	16.8557i	0.415336	−	0.719382i
$550$		0			0
$551$	−0.673493	−	1.16652i	−0.0286918	−	0.0496956i
$552$	−20.9660			−0.892371
$553$	−10.9159	−	8.19542i	−0.464193	−	0.348505i
$554$	4.04494			0.171853
$555$		0			0
$556$	−31.5983	+	54.7298i	−1.34006	+	2.32106i
$557$	15.7903	−	27.3496i	0.669057	−	1.15884i	−0.309112	−	0.951026i	$-0.600032\pi$
$557$	15.7903	−	27.3496i	0.669057	−	1.15884i	0.978168	−	0.207814i	$-0.0666349\pi$
$558$	−21.3968	−	37.0604i	−0.905800	−	1.56889i
$559$	−5.87372			−0.248432
$560$		0			0
$561$	−37.7662			−1.59449
$562$	−0.668486	−	1.15785i	−0.0281984	−	0.0488411i
$563$	10.4660	−	18.1276i	0.441089	−	0.763988i	−0.556682	−	0.830726i	$-0.687926\pi$
$563$	10.4660	−	18.1276i	0.441089	−	0.763988i	0.997771	+	0.0667380i	$0.0212592\pi$
$564$	−37.6120	+	65.1459i	−1.58375	+	2.74314i
$565$		0			0
$566$	−25.7134			−1.08082
$567$	−0.391381	+	3.23499i	−0.0164365	+	0.135857i
$568$	16.0209			0.672223
$569$	−13.3612	−	23.1422i	−0.560130	−	0.970173i	−0.997485	−	0.0708840i	$-0.977418\pi$
$569$	−13.3612	−	23.1422i	−0.560130	−	0.970173i	0.437355	−	0.899289i	$-0.355915\pi$
$570$		0			0
$571$	−11.6422	+	20.1649i	−0.487211	+	0.843874i	−0.999892	−	0.0147050i	$-0.995319\pi$
$571$	−11.6422	+	20.1649i	−0.487211	+	0.843874i	0.512681	+	0.858579i	$0.328652\pi$
$572$	−2.04548	−	3.54287i	−0.0855258	−	0.148135i
$573$	6.02639			0.251756
$574$	15.3704	+	11.5398i	0.641550	+	0.481660i
$575$		0			0
$576$	31.9627	+	55.3610i	1.33178	+	2.30671i
$577$	−7.39684	+	12.8117i	−0.307934	+	0.533358i	−0.977910	−	0.209025i	$-0.932971\pi$
$577$	−7.39684	+	12.8117i	−0.307934	+	0.533358i	0.669976	+	0.742383i	$0.266304\pi$
$578$	11.0225	−	19.0915i	0.458474	−	0.794101i
$579$	3.74263	+	6.48243i	0.155539	+	0.269401i
$580$		0			0
$581$	7.62400	−	3.25217i	0.316297	−	0.134923i
$582$	95.3283			3.95148
$583$	13.7146	+	23.7544i	0.568001	+	0.983807i
$584$	−10.3974	+	18.0088i	−0.430247	+	0.745209i
$585$		0			0
$586$	−30.8095	−	53.3636i	−1.27273	−	2.20443i
$587$	−34.6334			−1.42947			−0.714736	−	0.699394i	$-0.753453\pi$
$587$	−34.6334			−1.42947			−0.714736	+	0.699394i	$0.753453\pi$
$588$	−54.6082	−	13.4097i	−2.25200	−	0.553007i
$589$	−1.81678			−0.0748592
$590$		0			0
$591$	−8.74536	+	15.1474i	−0.359736	+	0.623081i
$592$	1.82497	−	3.16094i	0.0750058	−	0.129914i
$593$	−2.92759	−	5.07073i	−0.120222	−	0.208230i	0.799633	−	0.600489i	$-0.205027\pi$
$593$	−2.92759	−	5.07073i	−0.120222	−	0.208230i	−0.919855	+	0.392259i	$0.871694\pi$
$594$	32.4711			1.33231
$595$		0			0
$596$	29.6739			1.21549
$597$	32.2640	+	55.8829i	1.32048	+	2.28714i
$598$	−2.49673	+	4.32446i	−0.102099	+	0.176840i
$599$	−16.3634	+	28.3422i	−0.668589	+	1.15803i	0.309710	+	0.950831i	$0.399768\pi$
$599$	−16.3634	+	28.3422i	−0.668589	+	1.15803i	−0.978299	+	0.207199i	$0.933565\pi$
$600$		0			0
$601$	26.9485			1.09925			0.549627	−	0.835410i	$-0.314770\pi$
$601$	26.9485			1.09925			0.549627	+	0.835410i	$0.314770\pi$
$602$	48.5220	+	36.4292i	1.97761	+	1.48474i
$603$	−38.5950			−1.57171
$604$	−14.1619	−	24.5292i	−0.576241	−	0.998079i
$605$		0			0
$606$	15.5587	−	26.9484i	0.632028	−	1.09470i
$607$	−7.70469	−	13.3449i	−0.312724	−	0.541654i	0.666227	−	0.745749i	$-0.267908\pi$
$607$	−7.70469	−	13.3449i	−0.312724	−	0.541654i	−0.978951	+	0.204095i	$0.934575\pi$
$608$	3.41285			0.138410
$609$	−2.58234	+	21.3445i	−0.104642	+	0.864922i
$610$		0			0
$611$	2.63674	+	4.56698i	0.106671	+	0.184760i
$612$	−37.0785	+	64.2219i	−1.49881	+	2.59602i
$613$	−19.9363	+	34.5307i	−0.805220	+	1.39468i	0.110922	+	0.993829i	$0.464620\pi$
$613$	−19.9363	+	34.5307i	−0.805220	+	1.39468i	−0.916142	+	0.400853i	$0.868714\pi$
$614$	−6.10862	−	10.5804i	−0.246524	−	0.426992i
$615$		0			0
$616$	−1.49400	+	12.3487i	−0.0601949	+	0.497545i
$617$	36.7409			1.47913			0.739566	−	0.673084i	$-0.235031\pi$
$617$	36.7409			1.47913			0.739566	+	0.673084i	$0.235031\pi$
$618$	62.3985	+	108.077i	2.51004	+	4.34751i
$619$	12.8644	−	22.2819i	0.517066	−	0.895584i	−0.482738	−	0.875765i	$-0.660358\pi$
$619$	12.8644	−	22.2819i	0.517066	−	0.895584i	0.999804	−	0.0198193i	$-0.00630910\pi$
$620$		0			0
$621$	−11.6185	−	20.1239i	−0.466236	−	0.807545i
$622$	−14.5291			−0.582565
$623$	11.7960	+	8.85612i	0.472595	+	0.354813i
$624$	2.61046			0.104502
$625$		0			0
$626$	13.0823	−	22.6593i	0.522875	−	0.905647i
$627$	1.70643	−	2.95562i	0.0681481	−	0.118036i
$628$	9.38637	+	16.2577i	0.374557	+	0.648752i
$629$	11.6015			0.462583
$630$		0			0
$631$	2.47525			0.0985383			0.0492692	−	0.998786i	$-0.484311\pi$
$631$	2.47525			0.0985383			0.0492692	+	0.998786i	$0.484311\pi$
$632$	4.73163	+	8.19542i	0.188214	+	0.325996i
$633$	22.4857	−	38.9464i	0.893727	−	1.54798i
$634$	−9.57568	+	16.5856i	−0.380299	+	0.658697i
$635$		0			0
$636$	85.9638			3.40869
$637$	−2.72825	+	2.84532i	−0.108097	+	0.112736i
$638$	16.1581			0.639706
$639$	21.9797	+	38.0700i	0.869504	+	1.50603i
$640$		0			0
$641$	17.6679	−	30.6018i	0.697842	−	1.20870i	−0.271371	−	0.962475i	$-0.587477\pi$
$641$	17.6679	−	30.6018i	0.697842	−	1.20870i	0.969213	−	0.246223i	$-0.0791895\pi$
$642$	−35.4265	−	61.3605i	−1.39817	−	2.42171i
$643$	2.98691			0.117792			0.0588962	−	0.998264i	$-0.481242\pi$
$643$	2.98691			0.117792			0.0588962	+	0.998264i	$0.481242\pi$
$644$	27.8167	−	11.8658i	1.09613	−	0.467577i
$645$		0			0
$646$	2.68495	+	4.65048i	0.105638	+	0.182971i
$647$	−13.0137	+	22.5405i	−0.511623	+	0.886157i	0.488286	+	0.872683i	$0.337622\pi$
$647$	−13.0137	+	22.5405i	−0.511623	+	0.886157i	−0.999909	+	0.0134733i	$0.995711\pi$
$648$	1.12955	−	1.95644i	0.0443729	−	0.0768562i
$649$	5.07568	+	8.79134i	0.199238	+	0.345090i
$650$		0			0
$651$	23.1904	+	17.4108i	0.908904	+	0.682383i
$652$	−20.4622			−0.801360
$653$	−8.94678	−	15.4963i	−0.350115	−	0.606416i	0.636155	−	0.771562i	$-0.280524\pi$
$653$	−8.94678	−	15.4963i	−0.350115	−	0.606416i	−0.986269	+	0.165145i	$0.947191\pi$
$654$	27.9193	−	48.3577i	1.09173	−	1.89093i
$655$		0			0
$656$	2.70196	+	4.67994i	0.105494	+	0.182721i
$657$	−57.0582			−2.22605
$658$	6.54286	−	54.0804i	0.255067	−	2.10827i
$659$	−15.2076			−0.592405			−0.296202	−	0.955125i	$-0.595720\pi$
$659$	−15.2076			−0.592405			−0.296202	+	0.955125i	$0.595720\pi$
$660$		0			0
$661$	2.74090	−	4.74738i	0.106609	−	0.184652i	−0.807786	−	0.589476i	$-0.799334\pi$
$661$	2.74090	−	4.74738i	0.106609	−	0.184652i	0.914394	+	0.404825i	$0.132667\pi$
$662$	−13.7074	+	23.7420i	−0.532754	+	0.922757i
$663$	4.14875	+	7.18584i	0.161124	+	0.279075i
$664$	−5.74636			−0.223002
$665$		0			0
$666$	−24.6949			−0.956907
$667$	−5.78157	−	10.0140i	−0.223863	−	0.387743i
$668$	−30.0022	+	51.9653i	−1.16082	+	2.01060i
$669$	−10.7179	+	18.5639i	−0.414377	+	0.717723i
$670$		0			0
$671$	9.91211			0.382653
$672$	−43.5636	−	32.7065i	−1.68050	−	1.26168i
$673$	−30.6763			−1.18249			−0.591243	−	0.806494i	$-0.701363\pi$
$673$	−30.6763			−1.18249			−0.591243	+	0.806494i	$0.701363\pi$
$674$	3.97372	+	6.88268i	0.153062	+	0.265111i
$675$		0			0
$676$	17.9732	−	31.1305i	0.691276	−	1.19733i
$677$	2.77056	+	4.79875i	0.106481	+	0.184431i	0.914342	−	0.404942i	$-0.132708\pi$
$677$	2.77056	+	4.79875i	0.106481	+	0.184431i	−0.807861	+	0.589373i	$0.799375\pi$
$678$	73.9518			2.84010
$679$	−37.2278	+	15.8803i	−1.42867	+	0.609429i
$680$		0			0
$681$	−18.8831	−	32.7065i	−0.723602	−	1.25332i
$682$	10.8968	−	18.8739i	0.417262	−	0.722718i
$683$	0.953328	−	1.65121i	0.0364781	−	0.0631819i	−0.847210	−	0.531258i	$-0.821719\pi$
$683$	0.953328	−	1.65121i	0.0364781	−	0.0631819i	0.883688	+	0.468076i	$0.155053\pi$
$684$	−3.35071	−	5.80360i	−0.128118	−	0.221906i
$685$		0			0
$686$	40.1845	−	6.58406i	1.53425	−	0.251381i
$687$	−36.3383			−1.38639
$688$	8.52966	+	14.7738i	0.325190	+	0.563246i
$689$	3.01320	−	5.21901i	0.114794	−	0.198828i
$690$		0			0
$691$	0.452786	+	0.784248i	0.0172248	+	0.0298342i	0.874509	−	0.485009i	$-0.161184\pi$
$691$	0.452786	+	0.784248i	0.0172248	+	0.0298342i	−0.857285	+	0.514843i	$0.827850\pi$
$692$	21.1712			0.804809
$693$	−31.3936	+	13.3916i	−1.19254	+	0.508704i
$694$	48.0188			1.82277
$695$		0			0
$696$	7.45279	−	12.9086i	0.282497	−	0.489299i
$697$	−8.58834	+	14.8754i	−0.325306	+	0.563447i
$698$	−4.06314	−	7.03756i	−0.153792	−	0.266376i
$699$	−58.4238			−2.20979
$700$		0			0
$701$	36.8541			1.39196			0.695980	−	0.718061i	$-0.254970\pi$
$701$	36.8541			1.39196			0.695980	+	0.718061i	$0.254970\pi$
$702$	−3.56706	−	6.17833i	−0.134630	−	0.233186i
$703$	−0.524203	+	0.907947i	−0.0197707	+	0.0342439i
$704$	−16.2778	+	28.1939i	−0.613491	+	1.06260i
$705$		0			0
$706$	−69.5741			−2.61845
$707$	−1.58680	+	13.1158i	−0.0596778	+	0.493271i
$708$	31.8146			1.19567
$709$	20.8409	+	36.0975i	0.782696	+	1.35567i	0.930366	+	0.366633i	$0.119489\pi$
$709$	20.8409	+	36.0975i	0.782696	+	1.35567i	−0.147669	+	0.989037i	$0.547177\pi$
$710$		0			0
$711$	−12.9830	+	22.4872i	−0.486900	+	0.843336i
$712$	−5.11308	−	8.85612i	−0.191621	−	0.331897i
$713$	−15.5961			−0.584078
$714$	10.2948	−	85.0921i	0.385272	−	3.18449i
$715$		0			0
$716$	1.03293	+	1.78909i	0.0386026	+	0.0668616i
$717$	21.9303	−	37.9844i	0.819003	−	1.41855i
$718$	−18.8409	+	32.6334i	−0.703136	+	1.21787i
$719$	22.4298	+	38.8495i	0.836489	+	1.44884i	0.892812	+	0.450430i	$0.148729\pi$
$719$	22.4298	+	38.8495i	0.836489	+	1.44884i	−0.0563225	+	0.998413i	$0.517938\pi$
$720$		0			0
$721$	−42.3721	−	31.8119i	−1.57802	−	1.18474i
$722$	41.2899			1.53665
$723$	−15.6427	−	27.0940i	−0.581760	−	1.00764i
$724$	2.84352	−	4.92512i	0.105678	−	0.183040i
$725$		0			0
$726$	−13.8040	−	23.9093i	−0.512316	−	0.887357i
$727$	9.08134			0.336808			0.168404	−	0.985718i	$-0.446139\pi$
$727$	9.08134			0.336808			0.168404	+	0.985718i	$0.446139\pi$
$728$	2.51374	−	1.07229i	0.0931653	−	0.0397416i
$729$	−42.7926			−1.58491
$730$		0			0
$731$	−27.1120	+	46.9594i	−1.00277	+	1.73685i
$732$	15.5324	−	26.9029i	0.574094	−	0.994360i
$733$	−14.2102	−	24.6127i	−0.524864	−	0.909091i	−0.999581	−	0.0289524i	$-0.990783\pi$
$733$	−14.2102	−	24.6127i	−0.524864	−	0.909091i	0.474717	−	0.880139i	$-0.342550\pi$
$734$	25.9187			0.956675
$735$		0			0
$736$	29.2975			1.07992
$737$	−9.82770	−	17.0221i	−0.362008	−	0.627016i
$738$	18.2810	−	31.6637i	0.672934	−	1.16556i
$739$	−2.70524	+	4.68560i	−0.0995137	+	0.172363i	−0.911483	−	0.411337i	$-0.865062\pi$
$739$	−2.70524	+	4.68560i	−0.0995137	+	0.172363i	0.811970	+	0.583699i	$0.198395\pi$
$740$		0			0
$741$	−0.749828			−0.0275456
$742$	−57.2602	+	24.4255i	−2.10209	+	0.896689i
$743$	30.1712			1.10687			0.553437	−	0.832891i	$-0.313316\pi$
$743$	30.1712			1.10687			0.553437	+	0.832891i	$0.313316\pi$
$744$	−10.0521	−	17.4108i	−0.368529	−	0.638311i
$745$		0			0
$746$	−10.3382	+	17.9062i	−0.378507	+	0.655594i
$747$	−7.88364	−	13.6549i	−0.288447	−	0.499606i
$748$	−37.7662			−1.38087
$749$	24.0566	+	18.0611i	0.879009	+	0.659939i
$750$		0			0
$751$	−21.9528	−	38.0233i	−0.801069	−	1.38749i	−0.918913	−	0.394459i	$-0.870932\pi$
$751$	−21.9528	−	38.0233i	−0.801069	−	1.38749i	0.117845	−	0.993032i	$-0.462401\pi$
$752$	7.65802	−	13.2641i	0.279259	−	0.483691i
$753$	39.4726	−	68.3686i	1.43846	−	2.49149i
$754$	−1.77503	−	3.07443i	−0.0646426	−	0.111964i
$755$		0			0
$756$	−5.18942	+	42.8935i	−0.188737	+	1.56002i
$757$	−38.6914			−1.40626			−0.703132	−	0.711060i	$-0.748216\pi$
$757$	−38.6914			−1.40626			−0.703132	+	0.711060i	$0.748216\pi$
$758$	−19.0725	−	33.0346i	−0.692745	−	1.19987i
$759$	14.6487	−	25.3724i	0.531716	−	0.920959i
$760$		0			0
$761$	15.6647	+	27.1320i	0.567844	+	0.983535i	0.996779	+	0.0801991i	$0.0255556\pi$
$761$	15.6647	+	27.1320i	0.567844	+	0.983535i	−0.428935	+	0.903335i	$0.641111\pi$
$762$	77.4611			2.80612
$763$	−2.84744	+	23.5357i	−0.103084	+	0.852049i
$764$	6.02639			0.218027
$765$		0			0
$766$	−6.39946	+	11.0842i	−0.231222	+	0.400488i
$767$	1.11516	−	1.93152i	0.0402662	−	0.0697431i
$768$	5.74482	+	9.95032i	0.207298	+	0.359051i
$769$	9.00654			0.324784			0.162392	−	0.986726i	$-0.448079\pi$
$769$	9.00654			0.324784			0.162392	+	0.986726i	$0.448079\pi$
$770$		0			0
$771$	41.1791			1.48303
$772$	3.74263	+	6.48243i	0.134700	+	0.233308i
$773$	7.88364	−	13.6549i	0.283555	−	0.491132i	−0.688703	−	0.725044i	$-0.741819\pi$
$773$	7.88364	−	13.6549i	0.283555	−	0.491132i	0.972258	+	0.233912i	$0.0751528\pi$
$774$	57.7103	−	99.9571i	2.07435	−	3.59288i
$775$		0			0
$776$	28.0593			1.00727
$777$	15.3924	−	6.56593i	0.552198	−	0.235552i
$778$	58.5466			2.09900
$779$	−0.776111	−	1.34426i	−0.0278070	−	0.0481632i
$780$		0			0
$781$	−11.1937	+	19.3880i	−0.400542	+	0.693758i
$782$	23.0489	+	39.9218i	0.824226	+	1.42760i
$783$	16.5202			0.590383
$784$	11.1185	+	2.73029i	0.397091	+	0.0975104i
$785$		0			0
$786$	15.5587	+	26.9484i	0.554960	+	0.961218i
$787$	−17.8112	+	30.8500i	−0.634902	+	1.09968i	0.351634	+	0.936138i	$0.385626\pi$
$787$	−17.8112	+	30.8500i	−0.634902	+	1.09968i	−0.986536	+	0.163545i	$0.947707\pi$
$788$	−8.74536	+	15.1474i	−0.311541	+	0.539604i
$789$	0.413850	+	0.716809i	0.0147334	+	0.0255191i
$790$		0			0
$791$	−28.8798	+	12.3193i	−1.02685	+	0.438023i
$792$	23.6619			0.840791
$793$	−1.08888	−	1.88600i	−0.0386673	−	0.0669737i
$794$	−38.7305	+	67.0833i	−1.37450	+	2.38070i
$795$		0			0
$796$	32.2640	+	55.8829i	1.14357	+	1.98072i
$797$	39.6268			1.40365			0.701827	−	0.712347i	$-0.252368\pi$
$797$	39.6268			1.40365			0.701827	+	0.712347i	$0.252368\pi$
$798$	6.19423	+	4.65048i	0.219273	+	0.164625i
$799$	48.6829			1.72228
$800$		0			0
$801$	14.0297	−	24.3001i	0.495714	−	0.858601i
$802$	−26.8646	+	46.5308i	−0.948620	+	1.64306i
$803$	−14.5291	−	25.1652i	−0.512722	−	0.888060i
$804$	−61.6004			−2.17248
$805$		0			0
$806$	−4.78822			−0.168658
$807$	−12.0976	−	20.9537i	−0.425856	−	0.737604i
$808$	4.57961	−	7.93211i	0.161110	−	0.279051i
$809$	3.41266	−	5.91090i	0.119983	−	0.207816i	−0.799778	−	0.600296i	$-0.795049\pi$
$809$	3.41266	−	5.91090i	0.119983	−	0.207816i	0.919761	+	0.392480i	$0.128383\pi$
$810$		0			0
$811$	46.4303			1.63039			0.815194	−	0.579187i	$-0.196630\pi$
$811$	46.4303			1.63039			0.815194	+	0.579187i	$0.196630\pi$
$812$	−2.58234	+	21.3445i	−0.0906222	+	0.749044i
$813$	8.25364			0.289468
$814$	−6.28822	−	10.8915i	−0.220402	−	0.381748i
$815$		0			0
$816$	12.0494	−	20.8702i	0.421813	−	0.730602i
$817$	−2.45006	−	4.24362i	−0.0857166	−	0.148466i
$818$	−64.8334			−2.26685
$819$	5.99673	+	4.50220i	0.209543	+	0.157320i
$820$		0			0
$821$	−19.2245	−	33.2979i	−0.670941	−	1.16210i	−0.977638	−	0.210297i	$-0.932557\pi$
$821$	−19.2245	−	33.2979i	−0.670941	−	1.16210i	0.306697	−	0.951807i	$-0.400776\pi$
$822$	1.58680	−	2.74842i	0.0553460	−	0.0958621i
$823$	−11.2970	+	19.5669i	−0.393787	+	0.682059i	−0.992946	−	0.118571i	$-0.962169\pi$
$823$	−11.2970	+	19.5669i	−0.393787	+	0.682059i	0.599159	+	0.800630i	$0.295502\pi$
$824$	18.3666	+	31.8119i	0.639832	+	1.10822i
$825$		0			0
$826$	−21.1916	+	9.03971i	−0.737350	+	0.314532i
$827$	−15.2460			−0.530156			−0.265078	−	0.964227i	$-0.585398\pi$
$827$	−15.2460			−0.530156			−0.265078	+	0.964227i	$0.585398\pi$
$828$	−28.7640	−	49.8207i	−0.999619	−	1.73139i
$829$	−6.48353	+	11.2298i	−0.225182	+	0.390027i	−0.956374	−	0.292145i	$-0.905631\pi$
$829$	−6.48353	+	11.2298i	−0.225182	+	0.390027i	0.731192	+	0.682172i	$0.238964\pi$
$830$		0			0
$831$	2.60708	+	4.51560i	0.0904387	+	0.156644i
$832$	7.15267			0.247974
$833$	10.1547	+	34.9453i	0.351841	+	1.21078i
$834$	−138.950			−4.81143
$835$		0			0
$836$	1.70643	−	2.95562i	0.0590180	−	0.102222i
$837$	11.1410	−	19.2968i	0.385090	−	0.666995i
$838$	10.7086	+	18.5479i	0.369923	+	0.640725i
$839$	19.4818			0.672586			0.336293	−	0.941757i	$-0.390827\pi$
$839$	19.4818			0.672586			0.336293	+	0.941757i	$0.390827\pi$
$840$		0			0
$841$	−20.7793			−0.716527
$842$	−2.95660	−	5.12098i	−0.101891	−	0.176481i
$843$	0.861719	−	1.49254i	0.0296792	−	0.0514058i
$844$	22.4857	−	38.9464i	0.773990	−	1.34059i
$845$		0			0
$846$	−103.626			−3.56273
$847$	9.37372	+	7.03756i	0.322085	+	0.241814i
$848$	−17.5027			−0.601046
$849$	−16.5731	−	28.7054i	−0.568786	−	0.985166i
$850$		0			0
$851$	−4.50000	+	7.79423i	−0.154258	+	0.267183i
$852$	35.0813	+	60.7625i	1.20186	+	2.08169i
$853$	−20.0449			−0.686326			−0.343163	−	0.939276i	$-0.611498\pi$
$853$	−20.0449			−0.686326			−0.343163	+	0.939276i	$0.611498\pi$
$854$	−2.70196	+	22.3333i	−0.0924593	+	0.764228i
$855$		0			0
$856$	−10.4276	−	18.0611i	−0.356408	−	0.617316i
$857$	25.1691	−	43.5942i	0.859761	−	1.48915i	−0.0123951	−	0.999923i	$-0.503946\pi$
$857$	25.1691	−	43.5942i	0.859761	−	1.48915i	0.872156	−	0.489227i	$-0.162721\pi$
$858$	4.49738	−	7.78969i	0.153538	−	0.265936i
$859$	−19.0698	−	33.0298i	−0.650653	−	1.12696i	−0.982965	−	0.183794i	$-0.941162\pi$
$859$	−19.0698	−	33.0298i	−0.650653	−	1.12696i	0.332312	−	0.943170i	$-0.392171\pi$
$860$		0			0
$861$	−2.97580	+	24.5966i	−0.101415	+	0.838251i
$862$	20.7487			0.706705
$863$	0.432052	+	0.748335i	0.0147072	+	0.0254736i	0.873285	−	0.487209i	$-0.161985\pi$
$863$	0.432052	+	0.748335i	0.0147072	+	0.0254736i	−0.858578	+	0.512683i	$0.828652\pi$
$864$	−20.9286	+	36.2494i	−0.712005	+	1.23323i
$865$		0			0
$866$	22.9259	+	39.7087i	0.779052	+	1.34936i
$867$	28.4172			0.965100
$868$	23.1904	+	17.4108i	0.787134	+	0.590961i
$869$	−13.2238			−0.448586
$870$		0			0
$871$	−2.15921	+	3.73987i	−0.0731621	+	0.126721i
$872$	8.21789	−	14.2338i	0.278293	−	0.482017i
$873$	38.4956	+	66.6764i	1.30288	+	2.25665i
$874$	−4.16576			−0.140909
$875$		0			0
$876$	−91.0692			−3.07694
$877$	−4.65648	−	8.06527i	−0.157238	−	0.272345i	0.776634	−	0.629953i	$-0.216926\pi$
$877$	−4.65648	−	8.06527i	−0.157238	−	0.272345i	−0.933872	+	0.357608i	$0.883592\pi$
$878$	−24.8035	+	42.9609i	−0.837077	+	1.44986i
$879$	39.7153	−	68.7889i	1.33956	−	2.32019i
$880$		0			0
$881$	−19.4602			−0.655630			−0.327815	−	0.944742i	$-0.606312\pi$
$881$	−19.4602			−0.655630			−0.327815	+	0.944742i	$0.606312\pi$
$882$	−21.6153	−	74.3841i	−0.727824	−	2.50464i
$883$	−43.1712			−1.45283			−0.726414	−	0.687258i	$-0.758814\pi$
$883$	−43.1712			−1.45283			−0.726414	+	0.687258i	$0.758814\pi$
$884$	4.14875	+	7.18584i	0.139537	+	0.241686i
$885$		0			0
$886$	33.6357	−	58.2587i	1.13001	−	1.95724i
$887$	−8.74536	−	15.1474i	−0.293641	−	0.508600i	0.681027	−	0.732258i	$-0.261534\pi$
$887$	−8.74536	−	15.1474i	−0.293641	−	0.508600i	−0.974668	+	0.223658i	$0.928200\pi$
$888$	−11.6015			−0.389322
$889$	−30.2503	+	12.9039i	−1.01456	+	0.432782i
$890$		0			0
$891$	1.57841	+	2.73389i	0.0528789	+	0.0915889i
$892$	−10.7179	+	18.5639i	−0.358861	+	0.621566i
$893$	−2.19969	+	3.80997i	−0.0736097	+	0.127496i
$894$	32.6219	+	56.5028i	1.09104	+	1.88974i
$895$		0			0
$896$	−28.3464	−	21.2818i	−0.946985	−	0.710974i
$897$	−6.43686			−0.214921
$898$	1.37699	+	2.38502i	0.0459509	+	0.0795892i
$899$	5.54394	−	9.60239i	0.184901	−	0.320258i
$900$		0			0
$901$	−27.8167	−	48.1799i	−0.926708	−	1.60511i
$902$	18.6201			0.619981
$903$	−9.39411	+	77.6476i	−0.312616	+	2.58395i
$904$	21.7673			0.723969
$905$		0			0
$906$	31.1377	−	53.9321i	1.03448	−	1.79178i
$907$	8.37264	−	14.5018i	0.278009	−	0.481525i	−0.692881	−	0.721052i	$-0.743659\pi$
$907$	8.37264	−	14.5018i	0.278009	−	0.481525i	0.970890	+	0.239527i	$0.0769922\pi$
$908$	−18.8831	−	32.7065i	−0.626658	−	1.08540i
$909$	25.1317			0.833567
$910$		0			0
$911$	−27.9485			−0.925976			−0.462988	−	0.886365i	$-0.653223\pi$
$911$	−27.9485			−0.925976			−0.462988	+	0.886365i	$0.653223\pi$
$912$	1.08888	+	1.88600i	0.0360564	+	0.0624515i
$913$	4.01493	−	6.95406i	0.132875	−	0.230146i
$914$	−26.1225	+	45.2454i	−0.864054	+	1.49659i
$915$		0			0
$916$	−36.3383			−1.20065
$917$	−10.5652	−	7.93211i	−0.348894	−	0.261941i
$918$	−65.8595			−2.17369
$919$	−11.6470	−	20.1732i	−0.384199	−	0.665453i	0.607458	−	0.794352i	$-0.292189\pi$
$919$	−11.6470	−	20.1732i	−0.384199	−	0.665453i	−0.991658	+	0.128899i	$0.958856\pi$
$920$		0			0
$921$	7.87437	−	13.6388i	0.259469	−	0.449414i
$922$	−34.1713	−	59.1865i	−1.12537	−	1.94920i
$923$	4.91866			0.161900
$924$	−50.1064	+	21.3739i	−1.64838	+	0.703151i
$925$		0			0
$926$	27.3304	+	47.3377i	0.898134	+	1.55561i
$927$	−50.3958	+	87.2880i	−1.65521	+	2.86691i
$928$	−10.4144	+	18.0383i	−0.341869	+	0.592135i
$929$	19.8474	+	34.3768i	0.651173	+	1.12787i	0.982838	+	0.184468i	$0.0590562\pi$
$929$	19.8474	+	34.3768i	0.651173	+	1.12787i	−0.331665	+	0.943397i	$0.607610\pi$
$930$		0			0
$931$	−3.19368	−	0.784248i	−0.104669	−	0.0257027i
$932$	−58.4238			−1.91373
$933$	−9.36445	−	16.2197i	−0.306578	−	0.531009i
$934$	−15.0252	+	26.0244i	−0.491640	+	0.851545i
$935$		0			0
$936$	−2.59935	−	4.50220i	−0.0849623	−	0.147159i
$937$	−2.00654			−0.0655509			−0.0327755	−	0.999463i	$-0.510435\pi$
$937$	−2.00654			−0.0655509			−0.0327755	+	0.999463i	$0.510435\pi$
$938$	41.0318	−	17.5030i	1.33974	−	0.571492i
$939$	33.7278			1.10067
$940$		0			0
$941$	22.0159	−	38.1327i	0.717699	−	1.24309i	−0.244211	−	0.969722i	$-0.578529\pi$
$941$	22.0159	−	38.1327i	0.717699	−	1.24309i	0.961909	−	0.273368i	$-0.0881378\pi$
$942$	−20.6377	+	35.7456i	−0.672414	+	1.16465i
$943$	−6.66248	−	11.5398i	−0.216960	−	0.375786i
$944$	−6.47764			−0.210829
$945$		0			0
$946$	58.7806			1.91112
$947$	12.3304	+	21.3569i	0.400685	+	0.694007i	0.993809	−	0.111104i	$-0.0354388\pi$
$947$	12.3304	+	21.3569i	0.400685	+	0.694007i	−0.593124	+	0.805111i	$0.702105\pi$
$948$	−20.7218	+	35.8912i	−0.673013	+	1.16569i
$949$	−3.19215	+	5.52896i	−0.103621	+	0.179478i
$950$		0			0
$951$	−24.6872			−0.800539
$952$	3.03020	−	25.0464i	0.0982095	−	0.811757i
$953$	35.5435			1.15137			0.575684	−	0.817673i	$-0.304736\pi$
$953$	35.5435			1.15137			0.575684	+	0.817673i	$0.304736\pi$
$954$	59.2103	+	102.555i	1.91700	+	3.32035i
$955$		0			0
$956$	21.9303	−	37.9844i	0.709277	−	1.22850i
$957$	10.4144	+	18.0383i	0.336649	+	0.583094i
$958$	9.15921			0.295921
$959$	−0.161835	+	1.33766i	−0.00522592	+	0.0431952i
$960$		0			0
$961$	8.02247	+	13.8953i	0.258789	+	0.448236i
$962$	−1.38157	+	2.39294i	−0.0445435	+	0.0771515i
$963$	28.6120	−	49.5574i	0.922009	−	1.59697i
$964$	−15.6427	−	27.0940i	−0.503819	−	0.872640i
$965$		0			0
$966$	53.1741	+	39.9218i	1.71085	+	1.28446i
$967$	38.3228			1.23238			0.616189	−	0.787598i	$-0.288676\pi$
$967$	38.3228			1.23238			0.616189	+	0.787598i	$0.288676\pi$
$968$	−4.06314	−	7.03756i	−0.130594	−	0.226196i
$969$	−3.46106	+	5.99474i	−0.111185	+	0.192579i
$970$		0			0
$971$	23.7910	+	41.2071i	0.763488	+	1.32240i	0.941042	+	0.338289i	$0.109848\pi$
$971$	23.7910	+	41.2071i	0.763488	+	1.32240i	−0.177554	+	0.984111i	$0.556819\pi$
$972$	−39.0977			−1.25406
$973$	54.2629	−	23.1470i	1.73959	−	0.742058i
$974$	31.1778			0.999000
$975$		0			0
$976$	−3.16248	+	5.47758i	−0.101229	+	0.175333i
$977$	5.24209	−	9.07957i	0.167709	−	0.290481i	−0.769905	−	0.638159i	$-0.779696\pi$
$977$	5.24209	−	9.07957i	0.167709	−	0.290481i	0.937614	+	0.347678i	$0.113030\pi$
$978$	−22.4950	−	38.9625i	−0.719311	−	1.24588i
$979$	14.2899			0.456706
$980$		0			0
$981$	45.0977			1.43986
$982$	20.7487	+	35.9379i	0.662119	+	1.14682i
$983$	−5.11308	+	8.85612i	−0.163082	+	0.282466i	−0.935973	−	0.352073i	$-0.885477\pi$
$983$	−5.11308	+	8.85612i	−0.163082	+	0.282466i	0.772890	+	0.634539i	$0.218810\pi$
$984$	8.58834	−	14.8754i	0.273786	−	0.474212i
$985$		0			0
$986$	−32.7727			−1.04370
$987$	64.5902	−	27.5523i	2.05593	−	0.876998i
$988$	−0.749828			−0.0238552
$989$	−21.0324	−	36.4292i	−0.668791	−	1.15838i
$990$		0			0
$991$	−0.639366	+	1.10741i	−0.0203101	+	0.0351782i	−0.876002	−	0.482308i	$-0.839799\pi$
$991$	−0.639366	+	1.10741i	−0.0203101	+	0.0351782i	0.855692	+	0.517486i	$0.173132\pi$
$992$	14.0467	+	24.3295i	0.445982	+	0.772464i
$993$	−35.3394			−1.12146
$994$	−40.6324	−	30.5058i	−1.28878	−	0.967586i
$995$		0			0
$996$	−12.5829	−	21.7942i	−0.398704	−	0.690575i
$997$	13.8600	−	24.0062i	0.438950	−	0.760284i	−0.558659	−	0.829398i	$-0.688684\pi$
$997$	13.8600	−	24.0062i	0.438950	−	0.760284i	0.997609	+	0.0691138i	$0.0220172\pi$
$998$	−11.5691	+	20.0383i	−0.366215	+	0.634303i
$999$	−6.42912	−	11.1356i	−0.203408	−	0.352314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.e.e.151.3	yes	6
5.2	odd	4		175.2.k.b.74.1		12
5.3	odd	4		175.2.k.b.74.6		12
5.4	even	2		175.2.e.d.151.1	yes	6
7.2	even	3	inner	175.2.e.e.51.3	yes	6
7.3	odd	6		1225.2.a.w.1.1		3
7.4	even	3		1225.2.a.x.1.1		3
35.2	odd	12		175.2.k.b.149.6		12
35.3	even	12		1225.2.b.m.99.6		6
35.4	even	6		1225.2.a.y.1.3		3
35.9	even	6		175.2.e.d.51.1	✓	6
35.17	even	12		1225.2.b.m.99.1		6
35.18	odd	12		1225.2.b.l.99.6		6
35.23	odd	12		175.2.k.b.149.1		12
35.24	odd	6		1225.2.a.z.1.3		3
35.32	odd	12		1225.2.b.l.99.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.e.d.51.1	✓	6	35.9	even	6
175.2.e.d.151.1	yes	6	5.4	even	2
175.2.e.e.51.3	yes	6	7.2	even	3	inner
175.2.e.e.151.3	yes	6	1.1	even	1	trivial
175.2.k.b.74.1		12	5.2	odd	4
175.2.k.b.74.6		12	5.3	odd	4
175.2.k.b.149.1		12	35.23	odd	12
175.2.k.b.149.6		12	35.2	odd	12
1225.2.a.w.1.1		3	7.3	odd	6
1225.2.a.x.1.1		3	7.4	even	3
1225.2.a.y.1.3		3	35.4	even	6
1225.2.a.z.1.3		3	35.24	odd	6
1225.2.b.l.99.1		6	35.32	odd	12
1225.2.b.l.99.6		6	35.18	odd	12
1225.2.b.m.99.1		6	35.17	even	12
1225.2.b.m.99.6		6	35.3	even	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09935 + 1.90412i) q^{2} +(-1.41712 + 2.45453i) q^{3} +(-1.41712 + 2.45453i) q^{4} -6.23163 q^{6} +(2.43359 - 1.03810i) q^{7} -1.83424 q^{8} +(-2.51647 - 4.35865i) q^{9} +O(q^{10})\)	\(q+(1.09935 + 1.90412i) q^{2} +(-1.41712 + 2.45453i) q^{3} +(-1.41712 + 2.45453i) q^{4} -6.23163 q^{6} +(2.43359 - 1.03810i) q^{7} -1.83424 q^{8} +(-2.51647 - 4.35865i) q^{9} +(1.28157 - 2.21974i) q^{11} +(-4.01647 - 6.95673i) q^{12} -0.563139 q^{13} +(4.65202 + 3.49262i) q^{14} +(0.817776 + 1.41643i) q^{16} +(-2.59935 + 4.50220i) q^{17} +(5.53293 - 9.58332i) q^{18} +(-0.234898 - 0.406855i) q^{19} +(-0.900654 + 7.44442i) q^{21} +5.63555 q^{22} +(-2.01647 - 3.49262i) q^{23} +(2.59935 - 4.50220i) q^{24} +(-0.619085 - 1.07229i) q^{26} +5.76183 q^{27} +(-0.900654 + 7.44442i) q^{28} +2.86718 q^{29} +(1.93359 - 3.34907i) q^{31} +(-3.63228 + 6.29129i) q^{32} +(3.63228 + 6.29129i) q^{33} -11.4303 q^{34} +14.2646 q^{36} +(-1.11581 - 1.93264i) q^{37} +(0.516467 - 0.894547i) q^{38} +(0.798037 - 1.38224i) q^{39} +3.30404 q^{41} +(-15.1652 + 6.46903i) q^{42} +10.4303 q^{43} +(3.63228 + 6.29129i) q^{44} +(4.43359 - 7.67920i) q^{46} +(-4.68222 - 8.10985i) q^{47} -4.63555 q^{48} +(4.84471 - 5.05260i) q^{49} +(-7.36718 - 12.7603i) q^{51} +(0.798037 - 1.38224i) q^{52} +(-5.35071 + 9.26770i) q^{53} +(6.33424 + 10.9712i) q^{54} +(-4.46379 + 1.90412i) q^{56} +1.33151 q^{57} +(3.15202 + 5.45946i) q^{58} +(-1.98026 + 3.42991i) q^{59} +(1.93359 + 3.34907i) q^{61} +8.50273 q^{62} +(-10.6487 - 7.99482i) q^{63} -12.7014 q^{64} +(-7.98626 + 13.8326i) q^{66} +(3.83424 - 6.64110i) q^{67} +(-7.36718 - 12.7603i) q^{68} +11.4303 q^{69} -8.73436 q^{71} +(4.61581 + 7.99482i) q^{72} +(5.66849 - 9.81811i) q^{73} +(2.45333 - 4.24929i) q^{74} +1.33151 q^{76} +(0.814504 - 6.73234i) q^{77} +3.50927 q^{78} +(-2.57961 - 4.46801i) q^{79} +(-0.615813 + 1.06662i) q^{81} +(3.63228 + 6.29129i) q^{82} +3.13282 q^{83} +(-16.9962 - 12.7603i) q^{84} +(11.4665 + 19.8606i) q^{86} +(-4.06314 + 7.03756i) q^{87} +(-2.35071 + 4.07155i) q^{88} +(2.78757 + 4.82821i) q^{89} +(-1.37045 + 0.584593i) q^{91} +11.4303 q^{92} +(5.48026 + 9.49209i) q^{93} +(10.2948 - 17.8311i) q^{94} +(-10.2948 - 17.8311i) q^{96} -15.2975 q^{97} +(14.9468 + 3.67036i) q^{98} -12.9001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 3 q^{3} - 3 q^{4} - 4 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q + q^2 - 3 * q^3 - 3 * q^4 - 4 * q^6 - 2 * q^7 - 4 * q^9	\( 6 q + q^{2} - 3 q^{3} - 3 q^{4} - 4 q^{6} - 2 q^{7} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 8 q^{13} + 17 q^{14} + 5 q^{16} - 10 q^{17} + 11 q^{18} + 4 q^{19} - 11 q^{21} + 34 q^{22} - q^{23} + 10 q^{24} - 15 q^{26} + 12 q^{27} - 11 q^{28} - 16 q^{29} - 5 q^{31} + 6 q^{32} - 6 q^{33} - 24 q^{34} + 30 q^{36} + 10 q^{37} - 8 q^{38} - 12 q^{39} - 2 q^{41} - 41 q^{42} + 18 q^{43} - 6 q^{44} + 10 q^{46} - 28 q^{47} - 28 q^{48} + 12 q^{49} - 11 q^{51} - 12 q^{52} - 10 q^{53} + 27 q^{54} - 21 q^{56} + 30 q^{57} + 8 q^{58} + 5 q^{59} - 5 q^{61} + 18 q^{62} - 25 q^{63} - 32 q^{64} - 26 q^{66} + 12 q^{67} - 11 q^{68} + 24 q^{69} + 14 q^{71} + 11 q^{72} + 12 q^{73} + 15 q^{74} + 30 q^{76} - 23 q^{77} + 44 q^{78} + 7 q^{79} + 13 q^{81} - 6 q^{82} + 52 q^{83} - 13 q^{84} + 30 q^{86} - 13 q^{87} + 8 q^{88} + 6 q^{89} - 3 q^{91} + 24 q^{92} + 16 q^{93} + 17 q^{94} - 17 q^{96} - 14 q^{97} + 34 q^{98} - 22 q^{99}+O(q^{100}) \) 6 * q + q^2 - 3 * q^3 - 3 * q^4 - 4 * q^6 - 2 * q^7 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 8 * q^13 + 17 * q^14 + 5 * q^16 - 10 * q^17 + 11 * q^18 + 4 * q^19 - 11 * q^21 + 34 * q^22 - q^23 + 10 * q^24 - 15 * q^26 + 12 * q^27 - 11 * q^28 - 16 * q^29 - 5 * q^31 + 6 * q^32 - 6 * q^33 - 24 * q^34 + 30 * q^36 + 10 * q^37 - 8 * q^38 - 12 * q^39 - 2 * q^41 - 41 * q^42 + 18 * q^43 - 6 * q^44 + 10 * q^46 - 28 * q^47 - 28 * q^48 + 12 * q^49 - 11 * q^51 - 12 * q^52 - 10 * q^53 + 27 * q^54 - 21 * q^56 + 30 * q^57 + 8 * q^58 + 5 * q^59 - 5 * q^61 + 18 * q^62 - 25 * q^63 - 32 * q^64 - 26 * q^66 + 12 * q^67 - 11 * q^68 + 24 * q^69 + 14 * q^71 + 11 * q^72 + 12 * q^73 + 15 * q^74 + 30 * q^76 - 23 * q^77 + 44 * q^78 + 7 * q^79 + 13 * q^81 - 6 * q^82 + 52 * q^83 - 13 * q^84 + 30 * q^86 - 13 * q^87 + 8 * q^88 + 6 * q^89 - 3 * q^91 + 24 * q^92 + 16 * q^93 + 17 * q^94 - 17 * q^96 - 14 * q^97 + 34 * q^98 - 22 * q^99

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