LMFDB - Embedded newform 475.2.e.f.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, 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("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
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			201.2
Root			$1.20634 + 2.08945i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.f.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08504 + 1.87935i) q^{2} +(0.706345 - 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} -1.76171 q^{7} +1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +O(q^{10})$	\(q+(-1.08504 + 1.87935i) q^{2} +(0.706345 - 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} -1.76171 q^{7} +1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +1.83810 q^{11} -3.82736 q^{12} +(1.30242 + 2.25586i) q^{13} +(1.91153 - 3.31086i) q^{14} +(1.03919 - 1.79993i) q^{16} +(-2.11787 + 3.66826i) q^{17} -2.17944 q^{18} +(4.01936 + 1.68664i) q^{19} +(-1.24437 + 2.15532i) q^{21} +(-1.99442 + 3.45443i) q^{22} +(1.10274 + 1.91001i) q^{23} +(1.08720 - 1.88308i) q^{24} -5.65274 q^{26} +5.65684 q^{27} +(2.38647 + 4.13349i) q^{28} +(3.56413 + 6.17325i) q^{29} +0.303952 q^{31} +(3.79432 + 6.57195i) q^{32} +(1.29833 - 2.24878i) q^{33} +(-4.59597 - 7.96045i) q^{34} +(1.36047 - 2.35641i) q^{36} +3.90376 q^{37} +(-7.53097 + 5.72370i) q^{38} +3.67984 q^{39} +(-4.11981 + 7.13572i) q^{41} +(-2.70039 - 4.67722i) q^{42} +(-1.17451 + 2.03431i) q^{43} +(-2.48996 - 4.31273i) q^{44} -4.78610 q^{46} +(3.62738 + 6.28281i) q^{47} +(-1.46805 - 2.54274i) q^{48} -3.89639 q^{49} +(2.99190 + 5.18211i) q^{51} +(3.52862 - 6.11176i) q^{52} +(-5.31020 - 9.19753i) q^{53} +(-6.13792 + 10.6312i) q^{54} -2.71160 q^{56} +(4.90253 - 3.72603i) q^{57} -15.4689 q^{58} +(6.02692 - 10.4389i) q^{59} +(-5.26716 - 9.12299i) q^{61} +(-0.329801 + 0.571231i) q^{62} +(-0.884649 - 1.53226i) q^{63} -12.3112 q^{64} +(2.81749 + 4.88004i) q^{66} +(-6.51579 - 11.2857i) q^{67} +11.4758 q^{68} +3.11567 q^{69} +(-5.91294 + 10.2415i) q^{71} +(0.772911 + 1.33872i) q^{72} +(4.58454 - 7.94066i) q^{73} +(-4.23574 + 7.33652i) q^{74} +(-1.48740 - 11.7154i) q^{76} -3.23819 q^{77} +(-3.99278 + 6.91571i) q^{78} +(-3.94192 + 6.82761i) q^{79} +(2.48922 - 4.31145i) q^{81} +(-8.94034 - 15.4851i) q^{82} +6.93584 q^{83} +6.74269 q^{84} +(-2.54879 - 4.41463i) q^{86} +10.0700 q^{87} +2.82918 q^{88} +(6.23646 + 10.8019i) q^{89} +(-2.29449 - 3.97417i) q^{91} +(2.98764 - 5.17474i) q^{92} +(0.214695 - 0.371862i) q^{93} -15.7435 q^{94} +10.7204 q^{96} +(-3.87944 + 6.71939i) q^{97} +(4.22775 - 7.32268i) q^{98} +(0.923009 + 1.59870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.08504	+	1.87935i	−0.767241	+	1.32890i	0.171812	+	0.985130i	$0.445038\pi$
$2$	−1.08504	+	1.87935i	−0.767241	+	1.32890i	−0.939053	+	0.343771i	$0.888295\pi$
$3$	0.706345	−	1.22342i	0.407808	−	0.706345i	−0.586836	−	0.809706i	$-0.699627\pi$
$3$	0.706345	−	1.22342i	0.407808	−	0.706345i	0.994644	+	0.103361i	$0.0329598\pi$
$4$	−1.35464	−	2.34630i	−0.677319	−	1.17315i
$5$		0			0
$5$		0			0
$6$	1.53283	+	2.65494i	0.625775	+	1.08387i
$7$	−1.76171			−0.665862			−0.332931	−	0.942951i	$-0.608038\pi$
$7$	−1.76171			−0.665862			−0.332931	+	0.942951i	$0.608038\pi$
$8$	1.53919			0.544185
$9$	0.502155	+	0.869757i	0.167385	+	0.289919i
$10$		0			0
$11$	1.83810			0.554208			0.277104	−	0.960840i	$-0.410625\pi$
$11$	1.83810			0.554208			0.277104	+	0.960840i	$0.410625\pi$
$12$	−3.82736			−1.10486
$13$	1.30242	+	2.25586i	0.361227	+	0.625664i	0.988163	−	0.153407i	$-0.0490245\pi$
$13$	1.30242	+	2.25586i	0.361227	+	0.625664i	−0.626936	+	0.779071i	$0.715691\pi$
$14$	1.91153	−	3.31086i	0.510877	−	0.884865i
$15$		0			0
$16$	1.03919	−	1.79993i	0.259797	−	0.449982i
$17$	−2.11787	+	3.66826i	−0.513659	+	0.889684i	0.486215	+	0.873839i	$0.338377\pi$
$17$	−2.11787	+	3.66826i	−0.513659	+	0.889684i	−0.999874	+	0.0158451i	$0.994956\pi$
$18$	−2.17944			−0.513698
$19$	4.01936	+	1.68664i	0.922104	+	0.386943i
$19$	4.01936	+	1.68664i	0.922104	+	0.386943i
$20$		0			0
$21$	−1.24437	+	2.15532i	−0.271544	+	0.470328i
$22$	−1.99442	+	3.45443i	−0.425211	+	0.736487i
$23$	1.10274	+	1.91001i	0.229938	+	0.398264i	0.957790	−	0.287470i	$-0.0928143\pi$
$23$	1.10274	+	1.91001i	0.229938	+	0.398264i	−0.727851	+	0.685735i	$0.759481\pi$
$24$	1.08720	−	1.88308i	0.221923	−	0.384382i
$25$		0			0
$26$	−5.65274			−1.10859
$27$	5.65684			1.08866
$28$	2.38647	+	4.13349i	0.451001	+	0.781157i
$29$	3.56413	+	6.17325i	0.661842	+	1.14634i	0.980131	+	0.198351i	$0.0635585\pi$
$29$	3.56413	+	6.17325i	0.661842	+	1.14634i	−0.318289	+	0.947994i	$0.603108\pi$
$30$		0			0
$31$	0.303952			0.0545913			0.0272957	−	0.999627i	$-0.491310\pi$
$31$	0.303952			0.0545913			0.0272957	+	0.999627i	$0.491310\pi$
$32$	3.79432	+	6.57195i	0.670747	+	1.16177i
$33$	1.29833	−	2.24878i	0.226010	−	0.391462i
$34$	−4.59597	−	7.96045i	−0.788202	−	1.36521i
$35$		0			0
$36$	1.36047	−	2.35641i	0.226746	−	0.392735i
$37$	3.90376			0.641774			0.320887	−	0.947118i	$-0.396019\pi$
$37$	3.90376			0.641774			0.320887	+	0.947118i	$0.396019\pi$
$38$	−7.53097	+	5.72370i	−1.22168	+	0.928506i
$39$	3.67984			0.589246
$40$		0			0
$41$	−4.11981	+	7.13572i	−0.643406	+	1.11441i	0.341261	+	0.939969i	$0.389146\pi$
$41$	−4.11981	+	7.13572i	−0.643406	+	1.11441i	−0.984667	+	0.174444i	$0.944187\pi$
$42$	−2.70039	−	4.67722i	−0.416680	−	0.721711i
$43$	−1.17451	+	2.03431i	−0.179111	+	0.310229i	−0.941576	−	0.336800i	$-0.890655\pi$
$43$	−1.17451	+	2.03431i	−0.179111	+	0.310229i	0.762465	+	0.647029i	$0.223989\pi$
$44$	−2.48996	−	4.31273i	−0.375375	−	0.650169i
$45$		0			0
$46$	−4.78610			−0.705672
$47$	3.62738	+	6.28281i	0.529108	+	0.916441i	0.999424	+	0.0339433i	$0.0108066\pi$
$47$	3.62738	+	6.28281i	0.529108	+	0.916441i	−0.470316	+	0.882498i	$0.655860\pi$
$48$	−1.46805	−	2.54274i	−0.211895	−	0.367013i
$49$	−3.89639			−0.556627
$50$		0			0
$51$	2.99190	+	5.18211i	0.418949	+	0.725641i
$52$	3.52862	−	6.11176i	0.489332	−	0.847548i
$53$	−5.31020	−	9.19753i	−0.729412	−	1.26338i	−0.957132	−	0.289652i	$-0.906460\pi$
$53$	−5.31020	−	9.19753i	−0.729412	−	1.26338i	0.227720	−	0.973727i	$-0.426873\pi$
$54$	−6.13792	+	10.6312i	−0.835265	+	1.44672i
$55$		0			0
$56$	−2.71160			−0.362353
$57$	4.90253	−	3.72603i	0.649356	−	0.493525i
$58$	−15.4689			−2.03117
$59$	6.02692	−	10.4389i	0.784638	−	1.35903i	−0.144578	−	0.989493i	$-0.546182\pi$
$59$	6.02692	−	10.4389i	0.784638	−	1.35903i	0.929215	−	0.369539i	$-0.120484\pi$
$60$		0			0
$61$	−5.26716	−	9.12299i	−0.674390	−	1.16808i	−0.976647	−	0.214852i	$-0.931073\pi$
$61$	−5.26716	−	9.12299i	−0.674390	−	1.16808i	0.302256	−	0.953227i	$-0.402260\pi$
$62$	−0.329801	+	0.571231i	−0.0418847	+	0.0725464i
$63$	−0.884649	−	1.53226i	−0.111455	−	0.193046i
$64$	−12.3112			−1.53891
$65$		0			0
$66$	2.81749	+	4.88004i	0.346809	+	0.600691i
$67$	−6.51579	−	11.2857i	−0.796031	−	1.37877i	−0.922183	−	0.386755i	$-0.873596\pi$
$67$	−6.51579	−	11.2857i	−0.796031	−	1.37877i	0.126152	−	0.992011i	$-0.459737\pi$
$68$	11.4758			1.39164
$69$	3.11567			0.375083
$70$		0			0
$71$	−5.91294	+	10.2415i	−0.701737	+	1.21544i	0.266119	+	0.963940i	$0.414259\pi$
$71$	−5.91294	+	10.2415i	−0.701737	+	1.21544i	−0.967856	+	0.251504i	$0.919075\pi$
$72$	0.772911	+	1.33872i	0.0910884	+	0.157770i
$73$	4.58454	−	7.94066i	0.536580	−	0.929384i	−0.462505	−	0.886617i	$-0.653049\pi$
$73$	4.58454	−	7.94066i	0.536580	−	0.929384i	0.999085	−	0.0427676i	$-0.0136175\pi$
$74$	−4.23574	+	7.33652i	−0.492395	+	0.852854i
$75$		0			0
$76$	−1.48740	−	11.7154i	−0.170616	−	1.34385i
$77$	−3.23819			−0.369026
$78$	−3.99278	+	6.91571i	−0.452094	+	0.783049i
$79$	−3.94192	+	6.82761i	−0.443501	+	0.768167i	−0.997946	−	0.0640536i	$-0.979597\pi$
$79$	−3.94192	+	6.82761i	−0.443501	+	0.768167i	0.554445	+	0.832220i	$0.312930\pi$
$80$		0			0
$81$	2.48922	−	4.31145i	0.276580	−	0.479050i
$82$	−8.94034	−	15.4851i	−0.987296	−	1.71005i
$83$	6.93584			0.761307			0.380654	−	0.924718i	$-0.375699\pi$
$83$	6.93584			0.761307			0.380654	+	0.924718i	$0.375699\pi$
$84$	6.74269			0.735688
$85$		0			0
$86$	−2.54879	−	4.41463i	−0.274843	−	0.476041i
$87$	10.0700			1.07962
$88$	2.82918			0.301592
$89$	6.23646	+	10.8019i	0.661063	+	1.14500i	0.980337	+	0.197333i	$0.0632279\pi$
$89$	6.23646	+	10.8019i	0.661063	+	1.14500i	−0.319273	+	0.947663i	$0.603439\pi$
$90$		0			0
$91$	−2.29449	−	3.97417i	−0.240528	−	0.416606i
$92$	2.98764	−	5.17474i	0.311483	−	0.539504i
$93$	0.214695	−	0.371862i	0.0222628	−	0.0385603i
$94$	−15.7435			−1.62381
$95$		0			0
$96$	10.7204			1.09414
$97$	−3.87944	+	6.71939i	−0.393898	+	0.682251i	−0.992960	−	0.118452i	$-0.962207\pi$
$97$	−3.87944	+	6.71939i	−0.393898	+	0.682251i	0.599062	+	0.800703i	$0.295540\pi$
$98$	4.22775	−	7.32268i	0.427067	−	0.739703i
$99$	0.923009	+	1.59870i	0.0927659	+	0.160675i
$100$		0			0
$101$	−1.43509	−	2.48565i	−0.142797	−	0.247331i	0.785752	−	0.618542i	$-0.212276\pi$
$101$	−1.43509	−	2.48565i	−0.142797	−	0.247331i	−0.928549	+	0.371210i	$0.878943\pi$
$102$	−12.9853			−1.28574
$103$	7.62702			0.751513			0.375756	−	0.926718i	$-0.377383\pi$
$103$	7.62702			0.751513			0.375756	+	0.926718i	$0.377383\pi$
$104$	2.00468	+	3.47220i	0.196575	+	0.340477i
$105$		0			0
$106$	23.0472			2.23854
$107$	6.43891			0.622473			0.311236	−	0.950333i	$-0.399257\pi$
$107$	6.43891			0.622473			0.311236	+	0.950333i	$0.399257\pi$
$108$	−7.66297	−	13.2727i	−0.737370	−	1.27716i
$109$	5.35464	−	9.27450i	0.512881	−	0.888336i	−0.487007	−	0.873398i	$-0.661911\pi$
$109$	5.35464	−	9.27450i	0.512881	−	0.888336i	0.999888	−	0.0149384i	$-0.00475523\pi$
$110$		0			0
$111$	2.75740	−	4.77595i	0.261721	−	0.453313i
$112$	−1.83075	+	3.17094i	−0.172989	+	0.299626i
$113$	12.6800			1.19283			0.596417	−	0.802674i	$-0.296590\pi$
$113$	12.6800			1.19283			0.596417	+	0.802674i	$0.296590\pi$
$114$	1.68305	+	13.2565i	0.157632	+	1.24158i
$115$		0			0
$116$	9.65621	−	16.7250i	0.896556	−	1.55288i
$117$	−1.30804	+	2.26558i	−0.120928	+	0.209453i
$118$	13.0789	+	22.6534i	1.20401	+	2.08541i
$119$	3.73107	−	6.46240i	0.342027	−	0.592407i
$120$		0			0
$121$	−7.62139			−0.692854
$122$	22.8604			2.06968
$123$	5.82001	+	10.0806i	0.524773	+	0.908933i
$124$	−0.411744	−	0.713162i	−0.0369757	−	0.0640438i
$125$		0			0
$126$	3.83953			0.342052
$127$	7.60506	+	13.1724i	0.674840	+	1.16886i	0.976516	+	0.215447i	$0.0691208\pi$
$127$	7.60506	+	13.1724i	0.674840	+	1.16886i	−0.301675	+	0.953411i	$0.597546\pi$
$128$	5.76959	−	9.99323i	0.509965	−	0.883285i
$129$	1.65922	+	2.87385i	0.146086	+	0.253028i
$130$		0			0
$131$	3.52804	−	6.11075i	0.308246	−	0.533898i	−0.669733	−	0.742602i	$-0.733591\pi$
$131$	3.52804	−	6.11075i	0.308246	−	0.533898i	0.977979	+	0.208704i	$0.0669246\pi$
$132$	−7.03507			−0.612324
$133$	−7.08093	−	2.97137i	−0.613994	−	0.257651i
$134$	28.2797			2.44299
$135$		0			0
$136$	−3.25981	+	5.64615i	−0.279526	+	0.484153i
$137$	−11.1936	−	19.3878i	−0.956331	−	1.65641i	−0.731291	−	0.682065i	$-0.761082\pi$
$137$	−11.1936	−	19.3878i	−0.956331	−	1.65641i	−0.225040	−	0.974350i	$-0.572251\pi$
$138$	−3.38064	+	5.85543i	−0.287779	+	0.498448i
$139$	−9.38099	−	16.2484i	−0.795685	−	1.37817i	−0.922403	−	0.386229i	$-0.873777\pi$
$139$	−9.38099	−	16.2484i	−0.795685	−	1.37817i	0.126717	−	0.991939i	$-0.459556\pi$
$140$		0			0
$141$	10.2487			0.863098
$142$	−12.8316	−	22.2250i	−1.07680	−	1.86508i
$143$	2.39398	+	4.14650i	0.200195	+	0.346748i
$144$	2.08733			0.173944
$145$		0			0
$146$	9.94886	+	17.2319i	0.823373	+	1.42612i
$147$	−2.75219	+	4.76694i	−0.226997	+	0.393171i
$148$	−5.28818	−	9.15939i	−0.434685	−	0.752897i
$149$	−9.07030	+	15.7102i	−0.743068	+	1.28703i	0.208024	+	0.978124i	$0.433297\pi$
$149$	−9.07030	+	15.7102i	−0.743068	+	1.28703i	−0.951092	+	0.308907i	$0.900037\pi$
$150$		0			0
$151$	2.71348			0.220820			0.110410	−	0.993886i	$-0.464784\pi$
$151$	2.71348			0.220820			0.110410	+	0.993886i	$0.464784\pi$
$152$	6.18655	+	2.59606i	0.501795	+	0.210569i
$153$	−4.25400			−0.343915
$154$	3.51358	−	6.08569i	0.283132	−	0.490399i
$155$		0			0
$156$	−4.98485	−	8.63401i	−0.399107	−	0.691274i
$157$	−0.638899	+	1.10660i	−0.0509897	+	0.0883167i	−0.890394	−	0.455191i	$-0.849571\pi$
$157$	−0.638899	+	1.10660i	−0.0509897	+	0.0883167i	0.839404	+	0.543508i	$0.182904\pi$
$158$	−8.55432	−	14.8165i	−0.680545	−	1.17874i
$159$	−15.0033			−1.18984
$160$		0			0
$161$	−1.94271	−	3.36488i	−0.153107	−	0.265189i
$162$	5.40182	+	9.35622i	0.424407	+	0.735094i
$163$	7.74374			0.606537			0.303268	−	0.952905i	$-0.401922\pi$
$163$	7.74374			0.606537			0.303268	+	0.952905i	$0.401922\pi$
$164$	22.3234			1.74316
$165$		0			0
$166$	−7.52568	+	13.0349i	−0.584106	+	1.01170i
$167$	−3.42446	−	5.93135i	−0.264993	−	0.458981i	0.702569	−	0.711616i	$-0.252036\pi$
$167$	−3.42446	−	5.93135i	−0.264993	−	0.458981i	−0.967562	+	0.252635i	$0.918703\pi$
$168$	−1.91532	+	3.31744i	−0.147770	+	0.255946i
$169$	3.10739	−	5.38215i	0.239030	−	0.414012i
$170$		0			0
$171$	0.551367	+	4.34282i	0.0421641	+	0.332104i
$172$	6.36413			0.485261
$173$	−4.10680	+	7.11319i	−0.312234	+	0.540806i	−0.978846	−	0.204600i	$-0.934411\pi$
$173$	−4.10680	+	7.11319i	−0.312234	+	0.540806i	0.666611	+	0.745405i	$0.267744\pi$
$174$	−10.9264	+	18.9251i	−0.828328	+	1.43471i
$175$		0			0
$176$	1.91013	−	3.30844i	0.143982	−	0.249383i
$177$	−8.51416	−	14.7470i	−0.639963	−	1.10845i
$178$	−27.0673			−2.02878
$179$	4.46213			0.333515			0.166758	−	0.985998i	$-0.446670\pi$
$179$	4.46213			0.333515			0.166758	+	0.985998i	$0.446670\pi$
$180$		0			0
$181$	−3.77070	−	6.53105i	−0.280274	−	0.485449i	0.691178	−	0.722685i	$-0.257092\pi$
$181$	−3.77070	−	6.53105i	−0.280274	−	0.485449i	−0.971452	+	0.237235i	$0.923759\pi$
$182$	9.95847			0.738171
$183$	−14.8817			−1.10009
$184$	1.69733	+	2.93986i	0.125129	+	0.216730i
$185$		0			0
$186$	0.465906	+	0.806972i	0.0341619	+	0.0591701i
$187$	−3.89286	+	6.74263i	−0.284674	+	0.493070i
$188$	9.82757	−	17.0219i	0.716749	−	1.24145i
$189$	−9.96570			−0.724898
$190$		0			0
$191$	−13.7765			−0.996834			−0.498417	−	0.866938i	$-0.666085\pi$
$191$	−13.7765			−0.996834			−0.498417	+	0.866938i	$0.666085\pi$
$192$	−8.69598	+	15.0619i	−0.627578	+	1.08700i
$193$	4.24539	−	7.35324i	0.305590	−	0.529297i	−0.671802	−	0.740730i	$-0.734480\pi$
$193$	4.24539	−	7.35324i	0.305590	−	0.529297i	0.977393	+	0.211433i	$0.0678130\pi$
$194$	−8.41872	−	14.5817i	−0.604429	−	1.04690i
$195$		0			0
$196$	5.27820	+	9.14211i	0.377014	+	0.653008i
$197$	2.87111			0.204558			0.102279	−	0.994756i	$-0.467387\pi$
$197$	2.87111			0.204558			0.102279	+	0.994756i	$0.467387\pi$
$198$	−4.00602			−0.284695
$199$	−11.4245	−	19.7879i	−0.809865	−	1.40273i	−0.912957	−	0.408055i	$-0.866207\pi$
$199$	−11.4245	−	19.7879i	−0.809865	−	1.40273i	0.103092	−	0.994672i	$-0.467126\pi$
$200$		0			0
$201$	−18.4096			−1.29851
$202$	6.22854			0.438238
$203$	−6.27895	−	10.8755i	−0.440696	−	0.763308i
$204$	8.10587	−	14.0398i	0.567524	−	0.982981i
$205$		0			0
$206$	−8.27565	+	14.3338i	−0.576592	+	0.998686i
$207$	−1.10750	+	1.91824i	−0.0769763	+	0.133327i
$208$	5.41386			0.375383
$209$	7.38797	+	3.10022i	0.511037	+	0.214447i
$210$		0			0
$211$	7.04497	−	12.2022i	0.484995	−	0.840037i	−0.514856	−	0.857277i	$-0.672155\pi$
$211$	7.04497	−	12.2022i	0.484995	−	0.840037i	0.999851	+	0.0172400i	$0.00548794\pi$
$212$	−14.3868	+	24.9187i	−0.988089	+	1.71142i
$213$	8.35315	+	14.4681i	0.572348	+	0.991337i
$214$	−6.98650	+	12.1010i	−0.477587	+	0.827205i
$215$		0			0
$216$	8.70695			0.592433
$217$	−0.535473			−0.0363503
$218$	11.6200	+	20.1265i	0.787008	+	1.36314i
$219$	−6.47654	−	11.2177i	−0.437644	−	0.758021i
$220$		0			0
$221$	−11.0335			−0.742191
$222$	5.98379	+	10.3642i	0.401606	+	0.695602i
$223$	−8.55095	+	14.8107i	−0.572614	+	0.991796i	0.423683	+	0.905811i	$0.360737\pi$
$223$	−8.55095	+	14.8107i	−0.572614	+	0.991796i	−0.996296	+	0.0859855i	$0.972596\pi$
$224$	−6.68448	−	11.5779i	−0.446625	−	0.773578i
$225$		0			0
$226$	−13.7584	+	23.8302i	−0.915192	+	1.58516i
$227$	10.2807			0.682356			0.341178	−	0.939999i	$-0.389174\pi$
$227$	10.2807			0.682356			0.341178	+	0.939999i	$0.389174\pi$
$228$	−15.3835	−	6.45540i	−1.01880	−	0.427519i
$229$	12.8863			0.851553			0.425777	−	0.904828i	$-0.360001\pi$
$229$	12.8863			0.851553			0.425777	+	0.904828i	$0.360001\pi$
$230$		0			0
$231$	−2.28728	+	3.96168i	−0.150492	+	0.260659i
$232$	5.48587	+	9.50180i	0.360165	+	0.623824i
$233$	−0.497436	+	0.861584i	−0.0325881	+	0.0564442i	−0.881859	−	0.471512i	$-0.843708\pi$
$233$	−0.497436	+	0.861584i	−0.0325881	+	0.0564442i	0.849271	+	0.527957i	$0.177042\pi$
$234$	−2.83855	−	4.91651i	−0.185562	−	0.321403i
$235$		0			0
$236$	−32.6571			−2.12580
$237$	5.56871	+	9.64530i	0.361727	+	0.626529i
$238$	8.09674	+	14.0240i	0.524834	+	0.909039i
$239$	−0.764329			−0.0494404			−0.0247202	−	0.999694i	$-0.507869\pi$
$239$	−0.764329			−0.0494404			−0.0247202	+	0.999694i	$0.507869\pi$
$240$		0			0
$241$	6.27892	+	10.8754i	0.404461	+	0.700547i	0.994259	−	0.107004i	$-0.0341258\pi$
$241$	6.27892	+	10.8754i	0.404461	+	0.700547i	−0.589798	+	0.807551i	$0.700793\pi$
$242$	8.26954	−	14.3233i	0.531586	−	0.920735i
$243$	4.96878	+	8.60617i	0.318747	+	0.552086i
$244$	−14.2702	+	24.7167i	−0.913555	+	1.58232i
$245$		0			0
$246$	−25.2599			−1.61051
$247$	1.43007	+	11.2638i	0.0909929	+	0.716701i
$248$	0.467839			0.0297078
$249$	4.89909	−	8.48548i	0.310467	−	0.537745i
$250$		0			0
$251$	4.96004	+	8.59105i	0.313075	+	0.542262i	0.979026	−	0.203733i	$-0.0653075\pi$
$251$	4.96004	+	8.59105i	0.313075	+	0.542262i	−0.665951	+	0.745995i	$0.731974\pi$
$252$	−2.39676	+	4.15131i	−0.150982	+	0.261508i
$253$	2.02695	+	3.51078i	0.127433	+	0.220721i
$254$	−33.0073			−2.07106
$255$		0			0
$256$	0.209275	+	0.362476i	0.0130797	+	0.0226547i
$257$	−7.62426	−	13.2056i	−0.475588	−	0.823743i	0.524021	−	0.851705i	$-0.324431\pi$
$257$	−7.62426	−	13.2056i	−0.475588	−	0.823743i	−0.999609	+	0.0279628i	$0.991098\pi$
$258$	−7.20128			−0.448332
$259$	−6.87727			−0.427333
$260$		0			0
$261$	−3.57949	+	6.19985i	−0.221565	+	0.383761i
$262$	7.65615	+	13.2608i	0.472999	+	0.819258i
$263$	−3.97607	+	6.88675i	−0.245175	+	0.424655i	−0.962181	−	0.272412i	$-0.912179\pi$
$263$	−3.97607	+	6.88675i	−0.245175	+	0.424655i	0.717006	+	0.697067i	$0.245512\pi$
$264$	1.99838	−	3.46129i	0.122992	−	0.213028i
$265$		0			0
$266$	13.2674	−	10.0835i	0.813474	−	0.618257i
$267$	17.6204			1.07835
$268$	−17.6531	+	30.5760i	−1.07833	+	1.86773i
$269$	−10.1217	+	17.5312i	−0.617128	+	1.06890i	0.372879	+	0.927880i	$0.378371\pi$
$269$	−10.1217	+	17.5312i	−0.617128	+	1.06890i	−0.990007	+	0.141018i	$0.954963\pi$
$270$		0			0
$271$	2.41486	−	4.18265i	0.146692	−	0.254078i	−0.783311	−	0.621630i	$-0.786471\pi$
$271$	2.41486	−	4.18265i	0.146692	−	0.254078i	0.930003	+	0.367552i	$0.119804\pi$
$272$	4.40174	+	7.62403i	0.266895	+	0.462275i
$273$	−6.48280			−0.392357
$274$	48.5820			2.93495
$275$		0			0
$276$	−4.22060	−	7.31030i	−0.254050	−	0.440028i
$277$	−26.4360			−1.58839			−0.794194	−	0.607665i	$-0.792106\pi$
$277$	−26.4360			−1.58839			−0.794194	+	0.607665i	$0.792106\pi$
$278$	40.7151			2.44193
$279$	0.152631	+	0.264364i	0.00913776	+	0.0158271i
$280$		0			0
$281$	−2.64587	−	4.58278i	−0.157839	−	0.273386i	0.776250	−	0.630425i	$-0.217119\pi$
$281$	−2.64587	−	4.58278i	−0.157839	−	0.273386i	−0.934089	+	0.357040i	$0.883786\pi$
$282$	−11.1203	+	19.2609i	−0.662204	+	1.14697i
$283$	9.90480	−	17.1556i	0.588779	−	1.01980i	−0.405614	−	0.914045i	$-0.632942\pi$
$283$	9.90480	−	17.1556i	0.588779	−	1.01980i	0.994393	−	0.105751i	$-0.0337245\pi$
$284$	32.0396			1.90120
$285$		0			0
$286$	−10.3903			−0.614391
$287$	7.25790	−	12.5710i	0.428420	−	0.742045i
$288$	−3.81067	+	6.60027i	−0.224546	+	0.388925i
$289$	−0.470765	−	0.815389i	−0.0276921	−	0.0479641i
$290$		0			0
$291$	5.48045	+	9.49241i	0.321269	+	0.556455i
$292$	−24.8416			−1.45374
$293$	19.3477			1.13030			0.565152	−	0.824987i	$-0.308817\pi$
$293$	19.3477			1.13030			0.565152	+	0.824987i	$0.308817\pi$
$294$	−5.97250	−	10.3447i	−0.348323	−	0.603314i
$295$		0			0
$296$	6.00862			0.349244
$297$	10.3978			0.603344
$298$	−19.6833	−	34.0925i	−1.14022	−	1.97493i
$299$	−2.87248	+	4.97528i	−0.166120	+	0.287728i
$300$		0			0
$301$	2.06914	−	3.58385i	0.119263	−	0.206570i
$302$	−2.94424	+	5.09958i	−0.169422	+	0.293448i
$303$	−4.05467			−0.232935
$304$	7.21271	−	5.48181i	0.413677	−	0.314403i
$305$		0			0
$306$	4.61577	−	7.99475i	0.263866	−	0.457029i
$307$	−14.0604	+	24.3533i	−0.802469	+	1.38992i	0.115517	+	0.993305i	$0.463147\pi$
$307$	−14.0604	+	24.3533i	−0.802469	+	1.38992i	−0.917986	+	0.396612i	$0.870186\pi$
$308$	4.38657	+	7.59777i	0.249948	+	0.432923i
$309$	5.38731	−	9.33109i	0.306473	−	0.530827i
$310$		0			0
$311$	2.75320			0.156120			0.0780598	−	0.996949i	$-0.475127\pi$
$311$	2.75320			0.156120			0.0780598	+	0.996949i	$0.475127\pi$
$312$	5.66397			0.320659
$313$	−10.5784	−	18.3223i	−0.597924	−	1.03564i	−0.993127	−	0.117041i	$-0.962659\pi$
$313$	−10.5784	−	18.3223i	−0.597924	−	1.03564i	0.395203	−	0.918594i	$-0.370674\pi$
$314$	−1.38647	−	2.40143i	−0.0782428	−	0.135520i
$315$		0			0
$316$	21.3595			1.20157
$317$	−15.9665	−	27.6548i	−0.896768	−	1.55325i	−0.831602	−	0.555373i	$-0.812576\pi$
$317$	−15.9665	−	27.6548i	−0.896768	−	1.55325i	−0.0651661	−	0.997874i	$-0.520758\pi$
$318$	16.2793	−	28.1965i	0.912895	−	1.58118i
$319$	6.55122	+	11.3470i	0.366798	+	0.635313i
$320$		0			0
$321$	4.54809	−	7.87752i	0.253850	−	0.439680i
$322$	8.43170			0.469880
$323$	−14.6995	+	11.1720i	−0.817904	+	0.621624i
$324$	−13.4880			−0.749331
$325$		0			0
$326$	−8.40230	+	14.5532i	−0.465360	+	0.806028i
$327$	−7.56444	−	13.1020i	−0.418314	−	0.724542i
$328$	−6.34117	+	10.9832i	−0.350132	+	0.606447i
$329$	−6.39038	−	11.0685i	−0.352313	−	0.610224i
$330$		0			0
$331$	35.8528			1.97065			0.985324	−	0.170695i	$-0.0546013\pi$
$331$	35.8528			1.97065			0.985324	+	0.170695i	$0.0546013\pi$
$332$	−9.39555	−	16.2736i	−0.515648	−	0.893128i
$333$	1.96029	+	3.39532i	0.107423	+	0.186062i
$334$	14.8628			0.813254
$335$		0			0
$336$	2.58627	+	4.47956i	0.141093	+	0.244380i
$337$	4.72285	−	8.18021i	0.257270	−	0.445605i	−0.708240	−	0.705972i	$-0.750510\pi$
$337$	4.72285	−	8.18021i	0.257270	−	0.445605i	0.965510	+	0.260368i	$0.0838437\pi$
$338$	6.74330	+	11.6797i	0.366787	+	0.635294i
$339$	8.95646	−	15.5130i	0.486448	−	0.842552i
$340$		0			0
$341$	0.558693			0.0302549
$342$	−8.75994	−	3.67594i	−0.473683	−	0.198772i
$343$	19.1962			1.03650
$344$	−1.80779	+	3.13118i	−0.0974695	+	0.168822i
$345$		0			0
$346$	−8.91211	−	15.4362i	−0.479118	−	0.829857i
$347$	−4.64930	+	8.05283i	−0.249588	+	0.432299i	−0.963411	−	0.268027i	$-0.913628\pi$
$347$	−4.64930	+	8.05283i	−0.249588	+	0.432299i	0.713824	+	0.700325i	$0.246962\pi$
$348$	−13.6412	−	23.6273i	−0.731246	−	1.26656i
$349$	−22.9611			−1.22908			−0.614540	−	0.788886i	$-0.710658\pi$
$349$	−22.9611			−1.22908			−0.614540	+	0.788886i	$0.710658\pi$
$350$		0			0
$351$	7.36761	+	12.7611i	0.393254	+	0.681135i
$352$	6.97433	+	12.0799i	0.371733	+	0.643861i
$353$	−28.2455			−1.50336			−0.751679	−	0.659529i	$-0.770756\pi$
$353$	−28.2455			−1.50336			−0.751679	+	0.659529i	$0.770756\pi$
$354$	36.9529			1.96403
$355$		0			0
$356$	16.8963	−	29.2652i	0.895501	−	1.55105i
$357$	−5.27084	−	9.12936i	−0.278962	−	0.483177i
$358$	−4.84160	+	8.38590i	−0.255887	+	0.443209i
$359$	2.17756	−	3.77165i	0.114927	−	0.199060i	−0.802823	−	0.596217i	$-0.796670\pi$
$359$	2.17756	−	3.77165i	0.114927	−	0.199060i	0.917751	+	0.397157i	$0.130003\pi$
$360$		0			0
$361$	13.3105	+	13.5585i	0.700551	+	0.713603i
$362$	16.3655			0.860152
$363$	−5.38333	+	9.32420i	−0.282552	+	0.489394i
$364$	−6.21640	+	10.7671i	−0.325828	+	0.564350i
$365$		0			0
$366$	16.1473	−	27.9680i	0.844033	−	1.46191i
$367$	4.02245	+	6.96709i	0.209970	+	0.363679i	0.951705	−	0.307014i	$-0.0993299\pi$
$367$	4.02245	+	6.96709i	0.209970	+	0.363679i	−0.741735	+	0.670694i	$0.765997\pi$
$368$	4.58384			0.238949
$369$	−8.27513			−0.430786
$370$		0			0
$371$	9.35501	+	16.2034i	0.485688	+	0.841236i
$372$	−1.16333			−0.0603160
$373$	−12.4203			−0.643099			−0.321549	−	0.946893i	$-0.604204\pi$
$373$	−12.4203			−0.643099			−0.321549	+	0.946893i	$0.604204\pi$
$374$	−8.44784	−	14.6321i	−0.436827	−	0.756607i
$375$		0			0
$376$	5.58322	+	9.67042i	0.287933	+	0.498714i
$377$	−9.28401	+	16.0804i	−0.478151	+	0.828182i
$378$	10.8132	−	18.7290i	0.556172	−	0.963318i
$379$	21.2202			1.09001			0.545005	−	0.838433i	$-0.316528\pi$
$379$	21.2202			1.09001			0.545005	+	0.838433i	$0.316528\pi$
$380$		0			0
$381$	21.4872			1.10082
$382$	14.9481	−	25.8909i	0.764812	−	1.32469i
$383$	15.5779	−	26.9817i	0.795993	−	1.37870i	−0.126213	−	0.992003i	$-0.540282\pi$
$383$	15.5779	−	26.9817i	0.795993	−	1.37870i	0.922206	−	0.386698i	$-0.126384\pi$
$384$	−8.15064	−	14.1173i	−0.415936	−	0.720422i
$385$		0			0
$386$	9.21287	+	15.9572i	0.468923	+	0.812198i
$387$	−2.35914			−0.119922
$388$	21.0210			1.06718
$389$	10.8314	+	18.7606i	0.549176	+	0.951201i	0.998331	+	0.0577469i	$0.0183916\pi$
$389$	10.8314	+	18.7606i	0.549176	+	0.951201i	−0.449155	+	0.893454i	$0.648275\pi$
$390$		0			0
$391$	−9.34189			−0.472439
$392$	−5.99728			−0.302908
$393$	−4.98402	−	8.63258i	−0.251411	−	0.435456i
$394$	−3.11528	+	5.39582i	−0.156946	+	0.271838i
$395$		0			0
$396$	2.50069	−	4.33132i	0.125664	−	0.217657i
$397$	1.31690	−	2.28093i	0.0660932	−	0.114477i	−0.831085	−	0.556145i	$-0.812280\pi$
$397$	1.31690	−	2.28093i	0.0660932	−	0.114477i	0.897178	+	0.441668i	$0.145613\pi$
$398$	49.5845			2.48545
$399$	−8.63682	+	6.56417i	−0.432382	+	0.328619i
$400$		0			0
$401$	12.4825	−	21.6203i	0.623347	−	1.07967i	−0.365511	−	0.930807i	$-0.619106\pi$
$401$	12.4825	−	21.6203i	0.623347	−	1.07967i	0.988858	−	0.148862i	$-0.0475609\pi$
$402$	19.9752	−	34.5980i	0.996272	−	1.72559i
$403$	0.395874	+	0.685673i	0.0197199	+	0.0341558i
$404$	−3.88805	+	6.73431i	−0.193438	+	0.335044i
$405$		0			0
$406$	27.2517			1.35248
$407$	7.17549			0.355676
$408$	4.60509	+	7.97625i	0.227986	+	0.394883i
$409$	10.7964	+	18.6999i	0.533848	+	0.924652i	0.999218	+	0.0395357i	$0.0125879\pi$
$409$	10.7964	+	18.6999i	0.533848	+	0.924652i	−0.465370	+	0.885116i	$0.654079\pi$
$410$		0			0
$411$	−31.6261			−1.56000
$412$	−10.3319	−	17.8953i	−0.509014	−	0.881638i
$413$	−10.6177	+	18.3903i	−0.522461	+	0.904928i
$414$	−2.40336	−	4.16275i	−0.118119	−	0.204588i
$415$		0			0
$416$	−9.88362	+	17.1189i	−0.484584	+	0.839325i
$417$	−26.5049			−1.29795
$418$	−13.8427	+	10.5207i	−0.677067	+	0.514585i
$419$	−11.6894			−0.571067			−0.285533	−	0.958369i	$-0.592171\pi$
$419$	−11.6894			−0.571067			−0.285533	+	0.958369i	$0.592171\pi$
$420$		0			0
$421$	15.8270	−	27.4132i	0.771362	−	1.33604i	−0.165454	−	0.986218i	$-0.552909\pi$
$421$	15.8270	−	27.4132i	0.771362	−	1.33604i	0.936816	−	0.349821i	$-0.113758\pi$
$422$	15.2882	+	26.4799i	0.744217	+	1.28902i
$423$	−3.64301	+	6.30988i	−0.177129	+	0.306797i
$424$	−8.17340	−	14.1567i	−0.396935	−	0.687512i
$425$		0			0
$426$	−36.2541			−1.75652
$427$	9.27919	+	16.0720i	0.449051	+	0.777780i
$428$	−8.72239	−	15.1076i	−0.421613	−	0.730254i
$429$	6.76391			0.326564
$430$		0			0
$431$	−3.01371	−	5.21990i	−0.145165	−	0.251434i	0.784269	−	0.620421i	$-0.213038\pi$
$431$	−3.01371	−	5.21990i	−0.145165	−	0.251434i	−0.929435	+	0.368987i	$0.879705\pi$
$432$	5.87853	−	10.1819i	0.282831	−	0.489877i
$433$	−7.88878	−	13.6638i	−0.379111	−	0.656639i	0.611822	−	0.790995i	$-0.290437\pi$
$433$	−7.88878	−	13.6638i	−0.379111	−	0.656639i	−0.990933	+	0.134356i	$0.957103\pi$
$434$	0.581012	−	1.00634i	0.0278895	−	0.0483060i
$435$		0			0
$436$	−29.0144			−1.38954
$437$	1.21082	+	9.53695i	0.0579212	+	0.456214i
$438$	28.1093			1.34311
$439$	−19.6880	+	34.1007i	−0.939658	+	1.62754i	−0.173549	+	0.984825i	$0.555524\pi$
$439$	−19.6880	+	34.1007i	−0.939658	+	1.62754i	−0.766109	+	0.642711i	$0.777810\pi$
$440$		0			0
$441$	−1.95659	−	3.38891i	−0.0931710	−	0.161377i
$442$	11.9718	−	20.7357i	0.569440	−	0.986299i
$443$	6.58164	+	11.3997i	0.312703	+	0.541618i	0.978947	−	0.204116i	$-0.0654321\pi$
$443$	6.58164	+	11.3997i	0.312703	+	0.541618i	−0.666243	+	0.745734i	$0.732099\pi$
$444$	−14.9411			−0.709073
$445$		0			0
$446$	−18.5563	−	32.1404i	−0.878666	−	1.52189i
$447$	12.8135	+	22.1937i	0.606058	+	1.04972i
$448$	21.6888			1.02470
$449$	3.54345			0.167226			0.0836129	−	0.996498i	$-0.473354\pi$
$449$	3.54345			0.167226			0.0836129	+	0.996498i	$0.473354\pi$
$450$		0			0
$451$	−7.57262	+	13.1162i	−0.356581	+	0.617616i
$452$	−17.1768	−	29.7511i	−0.807930	−	1.39937i
$453$	1.91665	−	3.31974i	0.0900522	−	0.155975i
$454$	−11.1550	+	19.3211i	−0.523532	+	0.906784i
$455$		0			0
$456$	7.54593	−	5.73506i	0.353370	−	0.268569i
$457$	14.7013			0.687697			0.343848	−	0.939025i	$-0.388269\pi$
$457$	14.7013			0.687697			0.343848	+	0.939025i	$0.388269\pi$
$458$	−13.9822	+	24.2179i	−0.653347	+	1.13163i
$459$	−11.9805	+	20.7508i	−0.559201	+	0.968564i
$460$		0			0
$461$	−3.32663	+	5.76190i	−0.154937	+	0.268358i	−0.933036	−	0.359783i	$-0.882851\pi$
$461$	−3.32663	+	5.76190i	−0.154937	+	0.268358i	0.778099	+	0.628141i	$0.216184\pi$
$462$	−4.96359	−	8.59719i	−0.230927	−	0.399978i
$463$	−25.0561			−1.16445			−0.582227	−	0.813026i	$-0.697819\pi$
$463$	−25.0561			−1.16445			−0.582227	+	0.813026i	$0.697819\pi$
$464$	14.8152			0.687779
$465$		0			0
$466$	−1.07948	−	1.86971i	−0.0500059	−	0.0866127i
$467$	−30.1338			−1.39442			−0.697212	−	0.716865i	$-0.745576\pi$
$467$	−30.1338			−1.39442			−0.697212	+	0.716865i	$0.745576\pi$
$468$	7.08766			0.327627
$469$	11.4789	+	19.8821i	0.530047	+	0.918068i
$470$		0			0
$471$	0.902565	+	1.56329i	0.0415880	+	0.0720326i
$472$	9.27656	−	16.0675i	0.426988	−	0.739566i
$473$	−2.15886	+	3.73926i	−0.0992646	+	0.171931i
$474$	−24.1692			−1.11013
$475$		0			0
$476$	−20.2170			−0.926644
$477$	5.33308	−	9.23717i	0.244185	−	0.422941i
$478$	0.829330	−	1.43644i	0.0379327	−	0.0657013i
$479$	−2.50428	−	4.33754i	−0.114424	−	0.198187i	0.803126	−	0.595810i	$-0.203169\pi$
$479$	−2.50428	−	4.33754i	−0.114424	−	0.198187i	−0.917549	+	0.397622i	$0.869835\pi$
$480$		0			0
$481$	5.08434	+	8.80634i	0.231826	+	0.401535i
$482$	−27.2516			−1.24128
$483$	−5.48890			−0.249753
$484$	10.3242	+	17.8821i	0.469283	+	0.812822i
$485$		0			0
$486$	−21.5653			−0.978224
$487$	40.8880			1.85281			0.926406	−	0.376527i	$-0.122882\pi$
$487$	40.8880			1.85281			0.926406	+	0.376527i	$0.122882\pi$
$488$	−8.10715	−	14.0420i	−0.366993	−	0.635651i
$489$	5.46975	−	9.47389i	0.247351	−	0.428424i
$490$		0			0
$491$	17.1773	−	29.7519i	0.775200	−	1.34269i	−0.159482	−	0.987201i	$-0.550982\pi$
$491$	17.1773	−	29.7519i	0.775200	−	1.34269i	0.934682	−	0.355485i	$-0.115684\pi$
$492$	15.7680	−	27.3110i	0.710877	−	1.23127i
$493$	−30.1935			−1.35985
$494$	−22.7204	−	9.53417i	−1.02224	−	0.428962i
$495$		0			0
$496$	0.315863	−	0.547091i	0.0141827	−	0.0245651i
$497$	10.4169	−	18.0425i	0.467260	−	0.809319i
$498$	10.6315	+	18.4142i	0.476407	+	0.825161i
$499$	−6.63881	+	11.4988i	−0.297194	+	0.514755i	−0.975493	−	0.220031i	$-0.929384\pi$
$499$	−6.63881	+	11.4988i	−0.297194	+	0.514755i	0.678299	+	0.734786i	$0.262718\pi$
$500$		0			0
$501$	−9.67541			−0.432265
$502$	−21.5274			−0.960817
$503$	−4.03885	−	6.99549i	−0.180083	−	0.311913i	0.761825	−	0.647782i	$-0.224303\pi$
$503$	−4.03885	−	6.99549i	−0.180083	−	0.311913i	−0.941909	+	0.335869i	$0.890970\pi$
$504$	−1.36164	−	2.35843i	−0.0606523	−	0.105053i
$505$		0			0
$506$	−8.79732			−0.391089
$507$	−4.38977	−	7.60331i	−0.194957	−	0.337675i
$508$	20.6042	−	35.6875i	0.914164	−	1.58338i
$509$	−2.82539	−	4.89373i	−0.125233	−	0.216911i	0.796591	−	0.604519i	$-0.206635\pi$
$509$	−2.82539	−	4.89373i	−0.125233	−	0.216911i	−0.921824	+	0.387608i	$0.873301\pi$
$510$		0			0
$511$	−8.07662	+	13.9891i	−0.357289	+	0.618842i
$512$	22.1701			0.979789
$513$	22.7369	+	9.54108i	1.00386	+	0.421249i
$514$	33.0906			1.45956
$515$		0			0
$516$	4.49527	−	7.78604i	0.197893	−	0.342761i
$517$	6.66748	+	11.5484i	0.293235	+	0.507899i
$518$	7.46214	−	12.9248i	0.327868	−	0.567883i
$519$	5.80163	+	10.0487i	0.254663	+	0.441090i
$520$		0			0
$521$	−33.8049			−1.48102			−0.740510	−	0.672045i	$-0.765416\pi$
$521$	−33.8049			−1.48102			−0.740510	+	0.672045i	$0.765416\pi$
$522$	−7.76780	−	13.4542i	−0.339987	−	0.588875i
$523$	6.31778	+	10.9427i	0.276257	+	0.478491i	0.970452	−	0.241296i	$-0.0775725\pi$
$523$	6.31778	+	10.9427i	0.276257	+	0.478491i	−0.694194	+	0.719788i	$0.744239\pi$
$524$	−19.1169			−0.835124
$525$		0			0
$526$	−8.62841	−	14.9448i	−0.376217	−	0.651626i
$527$	−0.643730	+	1.11497i	−0.0280413	+	0.0485690i
$528$	−2.69842	−	4.67380i	−0.117434	−	0.203401i
$529$	9.06791	−	15.7061i	0.394257	−	0.682873i
$530$		0			0
$531$	12.1058			0.525346
$532$	2.62036	+	20.6391i	0.113607	+	0.894819i
$533$	−21.4629			−0.929663
$534$	−19.1189	+	33.1148i	−0.827354	+	1.43302i
$535$		0			0
$536$	−10.0290	−	17.3708i	−0.433188	−	0.750304i
$537$	3.15180	−	5.45908i	0.136010	−	0.235577i
$538$	−21.9649	−	38.0443i	−0.946973	−	1.64021i
$539$	−7.16195			−0.308487
$540$		0			0
$541$	−23.0175	−	39.8675i	−0.989599	−	1.71404i	−0.619378	−	0.785093i	$-0.712615\pi$
$541$	−23.0175	−	39.8675i	−0.989599	−	1.71404i	−0.370222	−	0.928943i	$-0.620718\pi$
$542$	5.24045	+	9.07672i	0.225097	+	0.389879i
$543$	−10.6537			−0.457193
$544$	−32.1435			−1.37814
$545$		0			0
$546$	7.03411	−	12.1834i	0.301032	−	0.521403i
$547$	11.4775	+	19.8796i	0.490741	+	0.849989i	0.999943	−	0.0106584i	$-0.00339274\pi$
$547$	11.4775	+	19.8796i	0.490741	+	0.849989i	−0.509202	+	0.860647i	$0.670059\pi$
$548$	−30.3265	+	52.5270i	−1.29548	+	2.24384i
$549$	5.28985	−	9.16230i	0.225765	−	0.391037i
$550$		0			0
$551$	3.91343	+	30.8239i	0.166718	+	1.31314i
$552$	4.79560			0.204114
$553$	6.94451	−	12.0282i	0.295311	−	0.511493i
$554$	28.6842	−	49.6826i	1.21868	−	2.11081i
$555$		0			0
$556$	−25.4157	+	44.0213i	−1.07787	+	1.86692i
$557$	0.961865	+	1.66600i	0.0407555	+	0.0705906i	0.885684	−	0.464289i	$-0.153690\pi$
$557$	0.961865	+	1.66600i	0.0407555	+	0.0705906i	−0.844928	+	0.534880i	$0.820357\pi$
$558$	−0.662443			−0.0280435
$559$	−6.11883			−0.258799
$560$		0			0
$561$	5.49940	+	9.52524i	0.232185	+	0.402156i
$562$	11.4835			0.484403
$563$	−0.929173			−0.0391600			−0.0195800	−	0.999808i	$-0.506233\pi$
$563$	−0.929173			−0.0391600			−0.0195800	+	0.999808i	$0.506233\pi$
$564$	−13.8833	−	24.0466i	−0.584592	−	1.01254i
$565$		0			0
$566$	21.4943	+	37.2292i	0.903471	+	1.56486i
$567$	−4.38527	+	7.59551i	−0.184164	+	0.318982i
$568$	−9.10114	+	15.7636i	−0.381875	+	0.661427i
$569$	17.5587			0.736098			0.368049	−	0.929806i	$-0.380026\pi$
$569$	17.5587			0.736098			0.368049	+	0.929806i	$0.380026\pi$
$570$		0			0
$571$	40.0798			1.67729			0.838644	−	0.544680i	$-0.183349\pi$
$571$	40.0798			1.67729			0.838644	+	0.544680i	$0.183349\pi$
$572$	6.48596	−	11.2340i	0.271191	−	0.469717i
$573$	−9.73097	+	16.8545i	−0.406517	+	0.704108i
$574$	15.7503	+	27.2803i	0.657403	+	1.13866i
$575$		0			0
$576$	−6.18215	−	10.7078i	−0.257589	−	0.446158i
$577$	31.6555			1.31784			0.658919	−	0.752214i	$-0.271014\pi$
$577$	31.6555			1.31784			0.658919	+	0.752214i	$0.271014\pi$
$578$	2.04320			0.0849860
$579$	−5.99742	−	10.3878i	−0.249244	−	0.431704i
$580$		0			0
$581$	−12.2189			−0.506926
$582$	−23.7861			−0.985965
$583$	−9.76067	−	16.9060i	−0.404246	−	0.700174i
$584$	7.05648	−	12.2222i	0.291999	−	0.505758i
$585$		0			0
$586$	−20.9931	+	36.3611i	−0.867217	+	1.50206i
$587$	2.62029	−	4.53848i	0.108151	−	0.187323i	−0.806870	−	0.590729i	$-0.798840\pi$
$587$	2.62029	−	4.53848i	0.108151	−	0.187323i	0.915021	+	0.403406i	$0.132174\pi$
$588$	14.9129			0.614998
$589$	1.22169	+	0.512658i	0.0503388	+	0.0211237i
$590$		0			0
$591$	2.02799	−	3.51259i	0.0834205	−	0.144489i
$592$	4.05674	−	7.02648i	0.166731	−	0.288787i
$593$	−12.3988	−	21.4753i	−0.509157	−	0.881886i	−0.999944	−	0.0106059i	$-0.996624\pi$
$593$	−12.3988	−	21.4753i	−0.509157	−	0.881886i	0.490787	−	0.871280i	$-0.336709\pi$
$594$	−11.2821	+	19.5412i	−0.462910	+	0.801784i
$595$		0			0
$596$	49.1479			2.01317
$597$	−32.2787			−1.32108
$598$	−6.23353	−	10.7968i	−0.254908	−	0.441514i
$599$	−8.60774	−	14.9091i	−0.351703	−	0.609167i	0.634845	−	0.772639i	$-0.281064\pi$
$599$	−8.60774	−	14.9091i	−0.351703	−	0.609167i	−0.986548	+	0.163472i	$0.947731\pi$
$600$		0			0
$601$	−1.76204			−0.0718750			−0.0359375	−	0.999354i	$-0.511442\pi$
$601$	−1.76204			−0.0718750			−0.0359375	+	0.999354i	$0.511442\pi$
$602$	4.49021	+	7.77727i	0.183007	+	0.316978i
$603$	6.54387	−	11.3343i	0.266487	−	0.461569i
$604$	−3.67578	−	6.36664i	−0.149565	−	0.259055i
$605$		0			0
$606$	4.39949	−	7.62015i	0.178717	−	0.309547i
$607$	−9.48260			−0.384887			−0.192443	−	0.981308i	$-0.561641\pi$
$607$	−9.48260			−0.384887			−0.192443	+	0.981308i	$0.561641\pi$
$608$	4.16618	+	32.8147i	0.168961	+	1.33081i
$609$	−17.7404			−0.718878
$610$		0			0
$611$	−9.44877	+	16.3657i	−0.382256	+	0.662087i
$612$	5.76262	+	9.98116i	0.232940	+	0.403464i
$613$	−7.93785	+	13.7488i	−0.320607	+	0.555307i	−0.980613	−	0.195953i	$-0.937220\pi$
$613$	−7.93785	+	13.7488i	−0.320607	+	0.555307i	0.660007	+	0.751260i	$0.270553\pi$
$614$	−30.5123	−	52.8488i	−1.23138	−	2.13280i
$615$		0			0
$616$	−4.98419			−0.200819
$617$	14.8994	+	25.8066i	0.599828	+	1.03893i	0.992846	+	0.119402i	$0.0380978\pi$
$617$	14.8994	+	25.8066i	0.599828	+	1.03893i	−0.393018	+	0.919531i	$0.628569\pi$
$618$	11.6909	+	20.2493i	0.470278	+	0.814545i
$619$	12.8374			0.515980			0.257990	−	0.966148i	$-0.416940\pi$
$619$	12.8374			0.515980			0.257990	+	0.966148i	$0.416940\pi$
$620$		0			0
$621$	6.23805	+	10.8046i	0.250324	+	0.433575i
$622$	−2.98734	+	5.17423i	−0.119781	+	0.207468i
$623$	−10.9868	−	19.0297i	−0.440177	−	0.762409i
$624$	3.82405	−	6.62344i	0.153084	−	0.265150i
$625$		0			0
$626$	45.9119			1.83501
$627$	9.01134	−	6.84881i	0.359878	−	0.273515i
$628$	3.46190			0.138145
$629$	−8.26766	+	14.3200i	−0.329653	+	0.570976i
$630$		0			0
$631$	9.70768	+	16.8142i	0.386456	+	0.669362i	0.991970	−	0.126473i	$-0.0403656\pi$
$631$	9.70768	+	16.8142i	0.386456	+	0.669362i	−0.605514	+	0.795835i	$0.707032\pi$
$632$	−6.06737	+	10.5090i	−0.241347	+	0.418025i
$633$	−9.95235	−	17.2380i	−0.395570	−	0.685148i
$634$	69.2973			2.75215
$635$		0			0
$636$	20.3241	+	35.2023i	0.805902	+	1.39586i
$637$	−5.07475	−	8.78973i	−0.201069	−	0.348262i
$638$	−28.4334			−1.12569
$639$	−11.8768			−0.469841
$640$		0			0
$641$	−10.1981	+	17.6637i	−0.402802	+	0.697673i	−0.994063	−	0.108807i	$-0.965297\pi$
$641$	−10.1981	+	17.6637i	−0.402802	+	0.697673i	0.591261	+	0.806480i	$0.298630\pi$
$642$	9.86975	+	17.0949i	0.389528	+	0.674682i
$643$	10.0616	−	17.4272i	0.396791	−	0.687263i	−0.596537	−	0.802586i	$-0.703457\pi$
$643$	10.0616	−	17.4272i	0.396791	−	0.687263i	0.993328	+	0.115323i	$0.0367903\pi$
$644$	−5.26334	+	9.11637i	−0.207405	+	0.359235i
$645$		0			0
$646$	−5.04639	−	39.7476i	−0.198547	−	1.56385i
$647$	−29.3758			−1.15488			−0.577441	−	0.816432i	$-0.695949\pi$
$647$	−29.3758			−1.15488			−0.577441	+	0.816432i	$0.695949\pi$
$648$	3.83138	−	6.63614i	0.150511	−	0.260692i
$649$	11.0781	−	19.1878i	0.434852	−	0.753186i
$650$		0			0
$651$	−0.378229	+	0.655111i	−0.0148240	+	0.0256758i
$652$	−10.4900	−	18.1692i	−0.410819	−	0.711559i
$653$	−21.6479			−0.847149			−0.423575	−	0.905861i	$-0.639225\pi$
$653$	−21.6479			−0.847149			−0.423575	+	0.905861i	$0.639225\pi$
$654$	32.8310			1.28379
$655$		0			0
$656$	8.56252	+	14.8307i	0.334310	+	0.579042i
$657$	9.20860			0.359262
$658$	27.7353			1.08124
$659$	15.3377	+	26.5658i	0.597474	+	1.03485i	0.993193	+	0.116483i	$0.0371621\pi$
$659$	15.3377	+	26.5658i	0.597474	+	1.03485i	−0.395719	+	0.918372i	$0.629505\pi$
$660$		0			0
$661$	−10.5645	−	18.2982i	−0.410910	−	0.711718i	0.584079	−	0.811697i	$-0.301456\pi$
$661$	−10.5645	−	18.2982i	−0.410910	−	0.711718i	−0.994990	+	0.0999790i	$0.968122\pi$
$662$	−38.9018	+	67.3800i	−1.51196	+	2.61880i
$663$	−7.79343	+	13.4986i	−0.302672	+	0.524243i
$664$	10.6756			0.414292
$665$		0			0
$666$	−8.50799			−0.329678
$667$	−7.86065	+	13.6150i	−0.304365	+	0.527176i
$668$	−9.27782	+	16.0696i	−0.358969	+	0.621753i
$669$	12.0798	+	20.9229i	0.467033	+	0.808925i
$670$		0			0
$671$	−9.68155	−	16.7689i	−0.373752	−	0.647358i
$672$	−18.8862			−0.728550
$673$	40.4354			1.55867			0.779334	−	0.626609i	$-0.215557\pi$
$673$	40.4354			1.55867			0.779334	+	0.626609i	$0.215557\pi$
$674$	10.2490	+	17.7518i	0.394776	+	0.683772i
$675$		0			0
$676$	−16.8375			−0.647597
$677$	0.405154			0.0155713			0.00778566	−	0.999970i	$-0.497522\pi$
$677$	0.405154			0.0155713			0.00778566	+	0.999970i	$0.497522\pi$
$678$	19.4363	+	33.6646i	0.746446	+	1.29288i
$679$	6.83444	−	11.8376i	0.262282	−	0.454285i
$680$		0			0
$681$	7.26174	−	12.5777i	0.278270	−	0.481979i
$682$	−0.606206	+	1.04998i	−0.0232128	+	0.0402058i
$683$	20.9178			0.800396			0.400198	−	0.916429i	$-0.368941\pi$
$683$	20.9178			0.800396			0.400198	+	0.916429i	$0.368941\pi$
$684$	9.44266	−	7.17662i	0.361049	−	0.274405i
$685$		0			0
$686$	−20.8288	+	36.0765i	−0.795245	+	1.37741i
$687$	9.10220	−	15.7655i	0.347271	−	0.601490i
$688$	2.44107	+	4.22806i	0.0930650	+	0.161193i
$689$	13.8323	−	23.9582i	0.526967	−	0.912733i
$690$		0			0
$691$	28.8456			1.09734			0.548669	−	0.836040i	$-0.315135\pi$
$691$	28.8456			1.09734			0.548669	+	0.836040i	$0.315135\pi$
$692$	22.2529			0.845928
$693$	−1.62607	−	2.81644i	−0.0617694	−	0.106988i
$694$	−10.0894	−	17.4753i	−0.382988	−	0.663355i
$695$		0			0
$696$	15.4997			0.587513
$697$	−17.4505	−	30.2251i	−0.660983	−	1.14486i
$698$	24.9138	−	43.1520i	0.943001	−	1.63333i
$699$	0.702722	+	1.21715i	0.0265794	+	0.0460369i
$700$		0			0
$701$	22.6884	−	39.2974i	0.856928	−	1.48424i	−0.0179163	−	0.999839i	$-0.505703\pi$
$701$	22.6884	−	39.2974i	0.856928	−	1.48424i	0.874845	−	0.484404i	$-0.160963\pi$
$702$	−31.9767			−1.20688
$703$	15.6906	+	6.58425i	0.591782	+	0.248330i
$704$	−22.6293			−0.852873
$705$		0			0
$706$	30.6476	−	53.0833i	1.15344	−	1.99781i
$707$	2.52821	+	4.37898i	0.0950830	+	0.164689i
$708$	−23.0672	+	39.9536i	−0.866918	+	1.50155i
$709$	0.953671	+	1.65181i	0.0358159	+	0.0620349i	0.883378	−	0.468662i	$-0.155264\pi$
$709$	0.953671	+	1.65181i	0.0358159	+	0.0620349i	−0.847562	+	0.530697i	$0.821930\pi$
$710$		0			0
$711$	−7.91782			−0.296941
$712$	9.59909	+	16.6261i	0.359741	+	0.623090i
$713$	0.335181	+	0.580550i	0.0125526	+	0.0217418i
$714$	22.8764			0.856126
$715$		0			0
$716$	−6.04457	−	10.4695i	−0.225896	−	0.391264i
$717$	−0.539880	+	0.935099i	−0.0201622	+	0.0349219i
$718$	4.72550	+	8.18481i	0.176354	+	0.305455i
$719$	9.26475	−	16.0470i	0.345517	−	0.598453i	−0.639931	−	0.768433i	$-0.721037\pi$
$719$	9.26475	−	16.0470i	0.345517	−	0.598453i	0.985448	+	0.169980i	$0.0543703\pi$
$720$		0			0
$721$	−13.4366			−0.500404
$722$	−39.9235	+	10.3035i	−1.48580	+	0.383457i
$723$	17.7403			0.659770
$724$	−10.2159	+	17.6944i	−0.379670	+	0.657608i
$725$		0			0
$726$	−11.6823	−	20.2343i	−0.433571	−	0.750966i
$727$	−24.7775	+	42.9159i	−0.918948	+	1.59166i	−0.117931	+	0.993022i	$0.537626\pi$
$727$	−24.7775	+	42.9159i	−0.918948	+	1.59166i	−0.801017	+	0.598642i	$0.795707\pi$
$728$	−3.53165	−	6.11700i	−0.130892	−	0.226711i
$729$	28.9740			1.07311
$730$		0			0
$731$	−4.97492	−	8.61681i	−0.184004	−	0.318704i
$732$	20.1593	+	34.9170i	0.745110	+	1.29057i
$733$	33.4077			1.23394			0.616971	−	0.786986i	$-0.288359\pi$
$733$	33.4077			1.23394			0.616971	+	0.786986i	$0.288359\pi$
$734$	−17.4581			−0.644392
$735$		0			0
$736$	−8.36833	+	14.4944i	−0.308461	+	0.534269i
$737$	−11.9767	−	20.7442i	−0.441166	−	0.764122i
$738$	8.97887	−	15.5519i	0.330517	−	0.572472i
$739$	16.1610	−	27.9917i	0.594493	−	1.02969i	−0.399125	−	0.916897i	$-0.630686\pi$
$739$	16.1610	−	27.9917i	0.594493	−	1.02969i	0.993618	−	0.112796i	$-0.0359807\pi$
$740$		0			0
$741$	14.7906	+	6.20658i	0.543346	+	0.228004i
$742$	−40.6024			−1.49056
$743$	5.18904	−	8.98768i	0.190367	−	0.329726i	−0.755005	−	0.655719i	$-0.772365\pi$
$743$	5.18904	−	8.98768i	0.190367	−	0.329726i	0.945372	+	0.325993i	$0.105699\pi$
$744$	0.330455	−	0.572366i	0.0121151	−	0.0209839i
$745$		0			0
$746$	13.4766	−	23.3421i	0.493412	−	0.854615i
$747$	3.48286	+	6.03249i	0.127431	+	0.220717i
$748$	21.0936			0.771260
$749$	−11.3435			−0.414481
$750$		0			0
$751$	−5.54684	−	9.60741i	−0.202407	−	0.350580i	0.746896	−	0.664940i	$-0.231543\pi$
$751$	−5.54684	−	9.60741i	−0.202407	−	0.350580i	−0.949304	+	0.314361i	$0.898210\pi$
$752$	15.0781			0.549843
$753$	14.0140			0.510699
$754$	−20.1471	−	34.8958i	−0.733714	−	1.27083i
$755$		0			0
$756$	13.4999	+	23.3825i	0.490987	+	0.850414i
$757$	12.5754	−	21.7812i	0.457061	−	0.791653i	−0.541743	−	0.840544i	$-0.682236\pi$
$757$	12.5754	−	21.7812i	0.457061	−	0.791653i	0.998804	+	0.0488915i	$0.0155688\pi$
$758$	−23.0249	+	39.8803i	−0.836301	+	1.44852i
$759$	5.72691			0.207874
$760$		0			0
$761$	7.40847			0.268557			0.134278	−	0.990944i	$-0.457128\pi$
$761$	7.40847			0.268557			0.134278	+	0.990944i	$0.457128\pi$
$762$	−23.3145	+	40.3819i	−0.844596	+	1.46288i
$763$	−9.43330	+	16.3390i	−0.341508	+	0.591510i
$764$	18.6622	+	32.3239i	0.675174	+	1.16944i
$765$		0			0
$766$	33.8054	+	58.5526i	1.22144	+	2.11559i
$767$	31.3984			1.13373
$768$	0.591282			0.0213361
$769$	−14.3791	−	24.9053i	−0.518524	−	0.898109i	−0.999768	−	0.0215231i	$-0.993148\pi$
$769$	−14.3791	−	24.9053i	−0.518524	−	0.898109i	0.481245	−	0.876586i	$-0.340185\pi$
$770$		0			0
$771$	−21.5414			−0.775795
$772$	−23.0039			−0.827928
$773$	22.5882	+	39.1240i	0.812442	+	1.40719i	0.911150	+	0.412075i	$0.135196\pi$
$773$	22.5882	+	39.1240i	0.812442	+	1.40719i	−0.0987075	+	0.995116i	$0.531471\pi$
$774$	2.55977	−	4.43365i	0.0920090	−	0.159364i
$775$		0			0
$776$	−5.97119	+	10.3424i	−0.214353	+	0.371271i
$777$	−4.85772	+	8.41383i	−0.174270	+	0.301844i
$778$	−47.0103			−1.68540
$779$	−28.5944	+	21.7324i	−1.02450	+	0.778642i
$780$		0			0
$781$	−10.8686	+	18.8249i	−0.388908	+	0.673608i
$782$	10.1363	−	17.5567i	0.362475	−	0.627825i
$783$	20.1617	+	34.9211i	0.720521	+	1.24798i
$784$	−4.04909	+	7.01322i	−0.144610	+	0.250472i
$785$		0			0
$786$	21.6315			0.771571
$787$	−9.67026			−0.344707			−0.172354	−	0.985035i	$-0.555137\pi$
$787$	−9.67026			−0.344707			−0.172354	+	0.985035i	$0.555137\pi$
$788$	−3.88932	−	6.73649i	−0.138551	−	0.239978i
$789$	5.61695	+	9.72884i	0.199969	+	0.346356i
$790$		0			0
$791$	−22.3385			−0.794264
$792$	1.42069	+	2.46070i	0.0504819	+	0.0874372i
$793$	13.7201	−	23.7640i	0.487216	−	0.843884i
$794$	2.85778	+	4.94982i	0.101419	+	0.175663i
$795$		0			0
$796$	−30.9522	+	53.6109i	−1.09707	+	1.90019i
$797$	−20.4295			−0.723651			−0.361825	−	0.932246i	$-0.617846\pi$
$797$	−20.4295			−0.723651			−0.361825	+	0.932246i	$0.617846\pi$
$798$	−2.96504	−	23.3540i	−0.104961	−	0.826723i
$799$	−30.7293			−1.08712
$800$		0			0
$801$	−6.26333	+	10.8484i	−0.221304	+	0.383310i
$802$	27.0881	+	46.9180i	0.956515	+	1.65673i
$803$	8.42684	−	14.5957i	0.297377	−	0.515072i
$804$	24.9383	+	43.1944i	0.879506	+	1.52335i
$805$		0			0
$806$	−1.71816			−0.0605196
$807$	14.2988	+	24.7662i	0.503340	+	0.871811i
$808$	−2.20887	−	3.82588i	−0.0777079	−	0.134594i
$809$	−32.9158			−1.15726			−0.578630	−	0.815590i	$-0.696412\pi$
$809$	−32.9158			−1.15726			−0.578630	+	0.815590i	$0.696412\pi$
$810$		0			0
$811$	−9.92532	−	17.1912i	−0.348525	−	0.603663i	0.637462	−	0.770481i	$-0.279984\pi$
$811$	−9.92532	−	17.1912i	−0.348525	−	0.603663i	−0.985988	+	0.166818i	$0.946651\pi$
$812$	−17.0114	+	29.4646i	−0.596983	+	1.03401i
$813$	−3.41144	−	5.90879i	−0.119645	−	0.207230i
$814$	−7.78571	+	13.4853i	−0.272889	+	0.472658i
$815$		0			0
$816$	12.4366			0.435367
$817$	−8.15192	+	6.19563i	−0.285200	+	0.216758i
$818$	−46.8583			−1.63836
$819$	2.30437	−	3.99129i	0.0805214	−	0.139467i
$820$		0			0
$821$	23.3799	+	40.4952i	0.815965	+	1.41329i	0.908633	+	0.417595i	$0.137127\pi$
$821$	23.3799	+	40.4952i	0.815965	+	1.41329i	−0.0926686	+	0.995697i	$0.529540\pi$
$822$	34.3157	−	59.4365i	1.19690	−	2.07309i
$823$	4.75713	+	8.23959i	0.165823	+	0.287214i	0.936947	−	0.349471i	$-0.113639\pi$
$823$	4.75713	+	8.23959i	0.165823	+	0.287214i	−0.771124	+	0.636685i	$0.780305\pi$
$824$	11.7394			0.408962
$825$		0			0
$826$	−23.0412	−	39.9086i	−0.801707	−	1.38860i
$827$	−17.1130	−	29.6406i	−0.595077	−	1.03070i	−0.993536	−	0.113517i	$-0.963788\pi$
$827$	−17.1130	−	29.6406i	−0.595077	−	1.03070i	0.398459	−	0.917186i	$-0.369545\pi$
$828$	6.00102			0.208550
$829$	−26.9726			−0.936798			−0.468399	−	0.883517i	$-0.655169\pi$
$829$	−26.9726			−0.936798			−0.468399	+	0.883517i	$0.655169\pi$
$830$		0			0
$831$	−18.6729	+	32.3425i	−0.647757	+	1.12195i
$832$	−16.0345	−	27.7725i	−0.555895	−	0.962838i
$833$	8.25206	−	14.2930i	0.285917	−	0.495223i
$834$	28.7589	−	49.8119i	0.995840	−	1.72485i
$835$		0			0
$836$	−2.73398	−	21.5341i	−0.0945567	−	0.744772i
$837$	1.71941			0.0594314
$838$	12.6836	−	21.9686i	0.438146	−	0.758891i
$839$	20.6632	−	35.7898i	0.713374	−	1.23560i	−0.250210	−	0.968192i	$-0.580500\pi$
$839$	20.6632	−	35.7898i	0.713374	−	1.23560i	0.963583	−	0.267408i	$-0.0861671\pi$
$840$		0			0
$841$	−10.9060	+	18.8898i	−0.376070	+	0.651373i
$842$	34.3460	+	59.4891i	1.18364	+	2.05013i
$843$	−7.47558			−0.257473
$844$	−38.1735			−1.31399
$845$		0			0
$846$	−7.90565	−	13.6930i	−0.271802	−	0.470774i
$847$	13.4267			0.461345
$848$	−22.0732			−0.757997
$849$	−13.9924	−	24.2355i	−0.480218	−	0.831762i
$850$		0			0
$851$	4.30484	+	7.45621i	0.147568	+	0.255596i
$852$	22.6310	−	39.1980i	0.775325	−	1.34290i
$853$	−15.4062	+	26.6843i	−0.527497	+	0.913652i	0.471989	+	0.881604i	$0.343536\pi$
$853$	−15.4062	+	26.6843i	−0.527497	+	0.913652i	−0.999486	+	0.0320475i	$0.989797\pi$
$854$	−40.2733			−1.37812
$855$		0			0
$856$	9.91070			0.338741
$857$	6.96440	−	12.0627i	0.237900	−	0.412054i	−0.722212	−	0.691672i	$-0.756874\pi$
$857$	6.96440	−	12.0627i	0.237900	−	0.412054i	0.960111	+	0.279618i	$0.0902078\pi$
$858$	−7.33913	+	12.7117i	−0.250554	+	0.433972i
$859$	6.09063	+	10.5493i	0.207810	+	0.359937i	0.951024	−	0.309116i	$-0.100033\pi$
$859$	6.09063	+	10.5493i	0.207810	+	0.359937i	−0.743215	+	0.669053i	$0.766700\pi$
$860$		0			0
$861$	−10.2532	−	17.7590i	−0.349426	−	0.605224i
$862$	13.0800			0.445507
$863$	32.2800			1.09882			0.549412	−	0.835551i	$-0.314852\pi$
$863$	32.2800			1.09882			0.549412	+	0.835551i	$0.314852\pi$
$864$	21.4639	+	37.1765i	0.730216	+	1.26477i
$865$		0			0
$866$	34.2387			1.16348
$867$	−1.33009			−0.0451722
$868$	0.725372	+	1.25638i	0.0246207	+	0.0426444i
$869$	−7.24564	+	12.5498i	−0.245792	+	0.425724i
$870$		0			0
$871$	16.9726	−	29.3975i	0.575096	−	0.996095i
$872$	8.24180	−	14.2752i	0.279103	−	0.483420i
$873$	−7.79232			−0.263730
$874$	−19.2370	−	8.07245i	−0.650703	−	0.273055i
$875$		0			0
$876$	−17.5467	+	30.3918i	−0.592849	+	1.02684i
$877$	−14.1372	+	24.4863i	−0.477379	+	0.826845i	−0.999664	−	0.0259260i	$-0.991747\pi$
$877$	−14.1372	+	24.4863i	−0.477379	+	0.826845i	0.522285	+	0.852771i	$0.325080\pi$
$878$	−42.7247	−	74.0014i	−1.44189	−	2.49743i
$879$	13.6661	−	23.6705i	0.460948	−	0.798385i
$880$		0			0
$881$	−43.4261			−1.46306			−0.731532	−	0.681807i	$-0.761194\pi$
$881$	−43.4261			−1.46306			−0.731532	+	0.681807i	$0.761194\pi$
$882$	8.49194			0.285939
$883$	−11.0337	−	19.1110i	−0.371314	−	0.643135i	0.618454	−	0.785821i	$-0.287759\pi$
$883$	−11.0337	−	19.1110i	−0.371314	−	0.643135i	−0.989768	+	0.142686i	$0.954426\pi$
$884$	14.9463	+	25.8878i	0.502700	+	0.870702i
$885$		0			0
$886$	−28.5655			−0.959676
$887$	−16.7324	−	28.9814i	−0.561819	−	0.973099i	−0.997338	−	0.0729195i	$-0.976768\pi$
$887$	−16.7324	−	28.9814i	−0.561819	−	0.973099i	0.435519	−	0.900180i	$-0.356565\pi$
$888$	4.24416	−	7.35109i	0.142425	−	0.246687i
$889$	−13.3979	−	23.2058i	−0.449351	−	0.778298i
$890$		0			0
$891$	4.57543	−	7.92487i	0.153283	−	0.265493i
$892$	46.3337			1.55137
$893$	3.98288	+	31.3709i	0.133282	+	1.04979i
$894$	−55.6129			−1.85997
$895$		0			0
$896$	−10.1643	+	17.6051i	−0.339566	+	0.588146i
$897$	4.05792	+	7.02853i	0.135490	+	0.234676i
$898$	−3.84480	+	6.65938i	−0.128303	+	0.222227i
$899$	1.08332	+	1.87637i	0.0361308	+	0.0625804i
$900$		0			0
$901$	44.9853			1.49868
$902$	−16.4332	−	28.4632i	−0.547167	−	0.947721i
$903$	−2.92305	−	5.06287i	−0.0972730	−	0.168482i
$904$	19.5169			0.649123
$905$		0			0
$906$	4.15930	+	7.20412i	0.138184	+	0.239341i
$907$	10.0745	−	17.4495i	0.334518	−	0.579402i	−0.648874	−	0.760896i	$-0.724760\pi$
$907$	10.0745	−	17.4495i	0.334518	−	0.579402i	0.983392	+	0.181494i	$0.0580933\pi$
$908$	−13.9267	−	24.1217i	−0.462173	−	0.800506i
$909$	1.44127	−	2.49636i	0.0478040	−	0.0827990i
$910$		0			0
$911$	−5.36397			−0.177716			−0.0888582	−	0.996044i	$-0.528322\pi$
$911$	−5.36397			−0.177716			−0.0888582	+	0.996044i	$0.528322\pi$
$912$	−1.61193	−	12.6963i	−0.0533762	−	0.420415i
$913$	12.7488			0.421922
$914$	−15.9515	+	27.6289i	−0.527630	+	0.913881i
$915$		0			0
$916$	−17.4563	−	30.2352i	−0.576773	−	0.999000i
$917$	−6.21537	+	10.7653i	−0.205250	+	0.355503i
$918$	−25.9987	−	45.0310i	−0.858084	−	1.48624i
$919$	8.22087			0.271181			0.135591	−	0.990765i	$-0.456707\pi$
$919$	8.22087			0.271181			0.135591	+	0.990765i	$0.456707\pi$
$920$		0			0
$921$	19.8630	+	34.4037i	0.654507	+	1.13364i
$922$	−7.21908	−	12.5038i	−0.237748	−	0.411791i
$923$	−30.8046			−1.01395
$924$	12.3937			0.407724
$925$		0			0
$926$	27.1869	−	47.0891i	0.893418	−	1.54745i
$927$	3.82994	+	6.63366i	0.125792	+	0.217878i
$928$	−27.0469	+	46.8466i	−0.887858	+	1.53781i
$929$	−5.94771	+	10.3017i	−0.195138	+	0.337989i	−0.946946	−	0.321393i	$-0.895849\pi$
$929$	−5.94771	+	10.3017i	−0.195138	+	0.337989i	0.751808	+	0.659382i	$0.229182\pi$
$930$		0			0
$931$	−15.6610	−	6.57183i	−0.513268	−	0.215383i
$932$	2.69538			0.0882901
$933$	1.94471	−	3.36833i	0.0636669	−	0.110274i
$934$	32.6964	−	56.6319i	1.06986	−	1.85305i
$935$		0			0
$936$	−2.01331	+	3.48716i	−0.0658072	+	0.113981i
$937$	−18.7506	−	32.4770i	−0.612555	−	1.06098i	−0.990808	−	0.135274i	$-0.956809\pi$
$937$	−18.7506	−	32.4770i	−0.612555	−	1.06098i	0.378254	−	0.925702i	$-0.376525\pi$
$938$	−49.8205			−1.62670
$939$	−29.8879			−0.975354
$940$		0			0
$941$	−23.5916	−	40.8618i	−0.769063	−	1.33206i	−0.938071	−	0.346442i	$-0.887390\pi$
$941$	−23.5916	−	40.8618i	−0.769063	−	1.33206i	0.169008	−	0.985615i	$-0.445944\pi$
$942$	−3.91729			−0.127632
$943$	−18.1724			−0.591774
$944$	−12.5262	−	21.6960i	−0.407693	−	0.706146i
$945$		0			0
$946$	−4.68492	−	8.11452i	−0.152320	−	0.263826i
$947$	22.6206	−	39.1799i	0.735069	−	1.27318i	−0.219624	−	0.975585i	$-0.570483\pi$
$947$	22.6206	−	39.1799i	0.735069	−	1.27318i	0.954693	−	0.297592i	$-0.0961837\pi$
$948$	15.0872	−	26.1318i	0.490009	−	0.848720i
$949$	23.8841			0.775310
$950$		0			0
$951$	−45.1114			−1.46284
$952$	5.74282	−	9.94686i	0.186126	−	0.322379i
$953$	−6.16935	+	10.6856i	−0.199845	+	0.346141i	−0.948478	−	0.316843i	$-0.897377\pi$
$953$	−6.16935	+	10.6856i	−0.199845	+	0.346141i	0.748633	+	0.662984i	$0.230710\pi$
$954$	11.5732	+	20.0455i	0.374698	+	0.648995i
$955$		0			0
$956$	1.03539	+	1.79335i	0.0334869	+	0.0580010i
$957$	18.5097			0.598333
$958$	10.8690			0.351162
$959$	19.7198	+	34.1557i	0.636785	+	1.10294i
$960$		0			0
$961$	−30.9076			−0.997020
$962$	−22.0669			−0.711466
$963$	3.23333	+	5.60029i	0.104193	+	0.180467i
$964$	17.0113	−	29.4645i	0.547898	−	0.948987i
$965$		0			0
$966$	5.95569	−	10.3156i	0.191621	−	0.331898i
$967$	27.7295	−	48.0289i	0.891720	−	1.54450i	0.0539076	−	0.998546i	$-0.482832\pi$
$967$	27.7295	−	48.0289i	0.891720	−	1.54450i	0.837812	−	0.545958i	$-0.183834\pi$
$968$	−11.7308			−0.377041
$969$	3.28511	+	25.8750i	0.105533	+	0.831226i
$970$		0			0
$971$	−11.6670	+	20.2078i	−0.374412	+	0.648500i	−0.990239	−	0.139381i	$-0.955489\pi$
$971$	−11.6670	+	20.2078i	−0.374412	+	0.648500i	0.615827	+	0.787881i	$0.288822\pi$
$972$	13.4618	−	23.3165i	0.431787	−	0.747877i
$973$	16.5266	+	28.6248i	0.529817	+	0.917670i
$974$	−44.3652	+	76.8428i	−1.42155	+	2.46220i
$975$		0			0
$976$	−21.8943			−0.700819
$977$	11.3809			0.364107			0.182054	−	0.983289i	$-0.441726\pi$
$977$	11.3809			0.364107			0.182054	+	0.983289i	$0.441726\pi$
$978$	11.8698	+	20.5592i	0.379556	+	0.657409i
$979$	11.4632	+	19.8549i	0.366366	+	0.634565i
$980$		0			0
$981$	10.7554			0.343394
$982$	37.2762	+	64.5643i	1.18953	+	2.06033i
$983$	−20.6632	+	35.7897i	−0.659054	+	1.14151i	0.321807	+	0.946805i	$0.395710\pi$
$983$	−20.6632	+	35.7897i	−0.659054	+	1.14151i	−0.980861	+	0.194709i	$0.937624\pi$
$984$	8.95810	+	15.5159i	0.285574	+	0.494628i
$985$		0			0
$986$	32.7612	−	56.7441i	1.04333	−	1.80710i
$987$	−18.0552			−0.574704
$988$	24.4912	−	18.6138i	0.779167	−	0.592184i
$989$	−5.18073			−0.164738
$990$		0			0
$991$	4.04937	−	7.01371i	0.128632	−	0.222798i	−0.794515	−	0.607245i	$-0.792275\pi$
$991$	4.04937	−	7.01371i	0.128632	−	0.222798i	0.923147	+	0.384447i	$0.125608\pi$
$992$	1.15329	+	1.99756i	0.0366170	+	0.0634224i
$993$	25.3244	−	43.8632i	0.803646	−	1.39196i
$994$	22.6055	+	39.1539i	0.717003	+	1.24189i
$995$		0			0
$996$	−26.5460			−0.841141
$997$	18.2128	+	31.5454i	0.576804	+	0.999054i	0.995843	+	0.0910857i	$0.0290337\pi$
$997$	18.2128	+	31.5454i	0.576804	+	0.999054i	−0.419039	+	0.907968i	$0.637633\pi$
$998$	−14.4068	−	24.9533i	−0.456039	−	0.789883i
$999$	22.0829			0.698673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.f.201.2	yes	12
5.2	odd	4		475.2.j.d.49.1		24
5.3	odd	4		475.2.j.d.49.12		24
5.4	even	2		475.2.e.h.201.5	yes	12
19.7	even	3	inner	475.2.e.f.26.2	✓	12
19.8	odd	6		9025.2.a.bs.1.2		6
19.11	even	3		9025.2.a.bz.1.5		6
95.7	odd	12		475.2.j.d.349.12		24
95.49	even	6		9025.2.a.br.1.2		6
95.64	even	6		475.2.e.h.26.5	yes	12
95.83	odd	12		475.2.j.d.349.1		24
95.84	odd	6		9025.2.a.by.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.2	✓	12	19.7	even	3	inner
475.2.e.f.201.2	yes	12	1.1	even	1	trivial
475.2.e.h.26.5	yes	12	95.64	even	6
475.2.e.h.201.5	yes	12	5.4	even	2
475.2.j.d.49.1		24	5.2	odd	4
475.2.j.d.49.12		24	5.3	odd	4
475.2.j.d.349.1		24	95.83	odd	12
475.2.j.d.349.12		24	95.7	odd	12
9025.2.a.br.1.2		6	95.49	even	6
9025.2.a.bs.1.2		6	19.8	odd	6
9025.2.a.by.1.5		6	95.84	odd	6
9025.2.a.bz.1.5		6	19.11	even	3

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08504 + 1.87935i) q^{2} +(0.706345 - 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} -1.76171 q^{7} +1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +O(q^{10})\)	\(q+(-1.08504 + 1.87935i) q^{2} +(0.706345 - 1.22342i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(1.53283 + 2.65494i) q^{6} -1.76171 q^{7} +1.53919 q^{8} +(0.502155 + 0.869757i) q^{9} +1.83810 q^{11} -3.82736 q^{12} +(1.30242 + 2.25586i) q^{13} +(1.91153 - 3.31086i) q^{14} +(1.03919 - 1.79993i) q^{16} +(-2.11787 + 3.66826i) q^{17} -2.17944 q^{18} +(4.01936 + 1.68664i) q^{19} +(-1.24437 + 2.15532i) q^{21} +(-1.99442 + 3.45443i) q^{22} +(1.10274 + 1.91001i) q^{23} +(1.08720 - 1.88308i) q^{24} -5.65274 q^{26} +5.65684 q^{27} +(2.38647 + 4.13349i) q^{28} +(3.56413 + 6.17325i) q^{29} +0.303952 q^{31} +(3.79432 + 6.57195i) q^{32} +(1.29833 - 2.24878i) q^{33} +(-4.59597 - 7.96045i) q^{34} +(1.36047 - 2.35641i) q^{36} +3.90376 q^{37} +(-7.53097 + 5.72370i) q^{38} +3.67984 q^{39} +(-4.11981 + 7.13572i) q^{41} +(-2.70039 - 4.67722i) q^{42} +(-1.17451 + 2.03431i) q^{43} +(-2.48996 - 4.31273i) q^{44} -4.78610 q^{46} +(3.62738 + 6.28281i) q^{47} +(-1.46805 - 2.54274i) q^{48} -3.89639 q^{49} +(2.99190 + 5.18211i) q^{51} +(3.52862 - 6.11176i) q^{52} +(-5.31020 - 9.19753i) q^{53} +(-6.13792 + 10.6312i) q^{54} -2.71160 q^{56} +(4.90253 - 3.72603i) q^{57} -15.4689 q^{58} +(6.02692 - 10.4389i) q^{59} +(-5.26716 - 9.12299i) q^{61} +(-0.329801 + 0.571231i) q^{62} +(-0.884649 - 1.53226i) q^{63} -12.3112 q^{64} +(2.81749 + 4.88004i) q^{66} +(-6.51579 - 11.2857i) q^{67} +11.4758 q^{68} +3.11567 q^{69} +(-5.91294 + 10.2415i) q^{71} +(0.772911 + 1.33872i) q^{72} +(4.58454 - 7.94066i) q^{73} +(-4.23574 + 7.33652i) q^{74} +(-1.48740 - 11.7154i) q^{76} -3.23819 q^{77} +(-3.99278 + 6.91571i) q^{78} +(-3.94192 + 6.82761i) q^{79} +(2.48922 - 4.31145i) q^{81} +(-8.94034 - 15.4851i) q^{82} +6.93584 q^{83} +6.74269 q^{84} +(-2.54879 - 4.41463i) q^{86} +10.0700 q^{87} +2.82918 q^{88} +(6.23646 + 10.8019i) q^{89} +(-2.29449 - 3.97417i) q^{91} +(2.98764 - 5.17474i) q^{92} +(0.214695 - 0.371862i) q^{93} -15.7435 q^{94} +10.7204 q^{96} +(-3.87944 + 6.71939i) q^{97} +(4.22775 - 7.32268i) q^{98} +(0.923009 + 1.59870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

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