LMFDB - Embedded newform 475.2.e.h.201.6

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			201.6
Root			$-0.975939 - 1.69038i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.h.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08504 - 1.87935i) q^{2} +(1.47594 - 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} -0.591620 q^{7} -1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +O(q^{10})$	\(q+(1.08504 - 1.87935i) q^{2} +(1.47594 - 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} -0.591620 q^{7} -1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +2.58045 q^{11} -7.99745 q^{12} +(3.43332 + 5.94669i) q^{13} +(-0.641933 + 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(-2.61787 + 4.53429i) q^{17} -12.3990 q^{18} +(-2.26423 + 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(2.79990 - 4.84957i) q^{22} +(1.45072 + 2.51271i) q^{23} +(-2.27175 + 3.93478i) q^{24} +14.9012 q^{26} -8.01017 q^{27} +(0.801431 + 1.38812i) q^{28} +(-3.52494 - 6.10538i) q^{29} -6.81421 q^{31} +(-3.79432 - 6.57195i) q^{32} +(3.80859 - 6.59667i) q^{33} +(5.68101 + 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} +4.82538 q^{37} +(4.54320 + 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(1.89491 + 3.28208i) q^{42} +(2.18013 - 3.77609i) q^{43} +(-3.49558 - 6.05452i) q^{44} +6.29636 q^{46} +(1.27941 + 2.21600i) q^{47} +(-3.06756 - 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(9.30181 - 16.1112i) q^{52} +(-4.79573 - 8.30645i) q^{53} +(-8.69138 + 15.0539i) q^{54} +0.910615 q^{56} +(6.17993 + 11.2857i) q^{57} -15.2989 q^{58} +(1.46221 - 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(-7.39371 + 12.8063i) q^{62} +(1.69013 + 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(2.15122 + 3.72603i) q^{67} +14.1851 q^{68} +8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(4.39714 + 7.61607i) q^{72} +(-4.21337 + 7.29777i) q^{73} +(5.23574 - 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} -1.52665 q^{77} +(21.9933 - 38.0935i) q^{78} +(-2.93630 + 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(6.75806 + 11.7053i) q^{82} +4.02036 q^{83} +4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} -20.8104 q^{87} -3.97180 q^{88} +(-1.85823 - 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(3.93039 - 6.80764i) q^{92} +(-10.0574 + 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(1.26285 - 2.18732i) q^{97} +(-7.21552 + 12.4977i) q^{98} +(-7.37182 - 12.7684i) 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	$-0.554962\pi$
$2$	1.08504	−	1.87935i	0.767241	−	1.32890i	0.939053	−	0.343771i	$-0.111705\pi$
$3$	1.47594	−	2.55640i	0.852134	−	1.47594i	−0.0271449	−	0.999632i	$-0.508642\pi$
$3$	1.47594	−	2.55640i	0.852134	−	1.47594i	0.879279	−	0.476308i	$-0.158025\pi$
$4$	−1.35464	−	2.34630i	−0.677319	−	1.17315i
$5$		0			0
$5$		0			0
$6$	−3.20292	−	5.54761i	−1.30758	−	2.26480i
$7$	−0.591620			−0.223611			−0.111806	−	0.993730i	$-0.535663\pi$
$7$	−0.591620			−0.223611			−0.111806	+	0.993730i	$0.535663\pi$
$8$	−1.53919			−0.544185
$9$	−2.85679	−	4.94811i	−0.952264	−	1.64937i
$10$		0			0
$11$	2.58045			0.778036			0.389018	−	0.921230i	$-0.372814\pi$
$11$	2.58045			0.778036			0.389018	+	0.921230i	$0.372814\pi$
$12$	−7.99745			−2.30867
$13$	3.43332	+	5.94669i	0.952232	+	1.64931i	0.740579	+	0.671969i	$0.234551\pi$
$13$	3.43332	+	5.94669i	0.952232	+	1.64931i	0.211653	+	0.977345i	$0.432115\pi$
$14$	−0.641933	+	1.11186i	−0.171564	+	0.297157i
$15$		0			0
$16$	1.03919	−	1.79993i	0.259797	−	0.449982i
$17$	−2.61787	+	4.53429i	−0.634927	+	1.09973i	0.351603	+	0.936149i	$0.385637\pi$
$17$	−2.61787	+	4.53429i	−0.634927	+	1.09973i	−0.986531	+	0.163577i	$0.947697\pi$
$18$	−12.3990			−2.92247
$19$	−2.26423	+	3.72468i	−0.519449	+	0.854501i
$19$	−2.26423	+	3.72468i	−0.519449	+	0.854501i
$20$		0			0
$21$	−0.873195	+	1.51242i	−0.190547	+	0.330037i
$22$	2.79990	−	4.84957i	0.596941	−	1.03393i
$23$	1.45072	+	2.51271i	0.302495	+	0.523937i	0.976701	−	0.214607i	$-0.0688470\pi$
$23$	1.45072	+	2.51271i	0.302495	+	0.523937i	−0.674205	+	0.738544i	$0.735514\pi$
$24$	−2.27175	+	3.93478i	−0.463719	+	0.803185i
$25$		0			0
$26$	14.9012			2.92237
$27$	−8.01017			−1.54156
$28$	0.801431	+	1.38812i	0.151456	+	0.262330i
$29$	−3.52494	−	6.10538i	−0.654565	−	1.13374i	−0.982003	−	0.188867i	$-0.939518\pi$
$29$	−3.52494	−	6.10538i	−0.654565	−	1.13374i	0.327438	−	0.944873i	$-0.393815\pi$
$30$		0			0
$31$	−6.81421			−1.22387			−0.611934	−	0.790909i	$-0.709608\pi$
$31$	−6.81421			−1.22387			−0.611934	+	0.790909i	$0.709608\pi$
$32$	−3.79432	−	6.57195i	−0.670747	−	1.16177i
$33$	3.80859	−	6.59667i	0.662990	−	1.14833i
$34$	5.68101	+	9.83980i	0.974285	+	1.68751i
$35$		0			0
$36$	−7.73984	+	13.4058i	−1.28997	+	2.23430i
$37$	4.82538			0.793287			0.396644	−	0.917973i	$-0.370175\pi$
$37$	4.82538			0.793287			0.396644	+	0.917973i	$0.370175\pi$
$38$	4.54320	+	8.29672i	0.737005	+	1.34591i
$39$	20.2695			3.24572
$40$		0			0
$41$	−3.11419	+	5.39393i	−0.486355	+	0.842391i	−0.999877	−	0.0156852i	$-0.995007\pi$
$41$	−3.11419	+	5.39393i	−0.486355	+	0.842391i	0.513522	+	0.858076i	$0.328340\pi$
$42$	1.89491	+	3.28208i	0.292391	+	0.506436i
$43$	2.18013	−	3.77609i	0.332467	−	0.575849i	−0.650528	−	0.759482i	$-0.725452\pi$
$43$	2.18013	−	3.77609i	0.332467	−	0.575849i	0.982995	+	0.183633i	$0.0587858\pi$
$44$	−3.49558	−	6.05452i	−0.526978	−	0.912753i
$45$		0			0
$46$	6.29636			0.928348
$47$	1.27941	+	2.21600i	0.186621	+	0.323237i	0.944121	−	0.329598i	$-0.106913\pi$
$47$	1.27941	+	2.21600i	0.186621	+	0.323237i	−0.757501	+	0.652834i	$0.773580\pi$
$48$	−3.06756	−	5.31317i	−0.442764	−	0.766890i
$49$	−6.64999			−0.949998
$50$		0			0
$51$	7.72764	+	13.3847i	1.08209	+	1.87423i
$52$	9.30181	−	16.1112i	1.28993	−	2.23422i
$53$	−4.79573	−	8.30645i	−0.658745	−	1.14098i	−0.980941	−	0.194306i	$-0.937754\pi$
$53$	−4.79573	−	8.30645i	−0.658745	−	1.14098i	0.322196	−	0.946673i	$-0.395579\pi$
$54$	−8.69138	+	15.0539i	−1.18275	+	2.04858i
$55$		0			0
$56$	0.910615			0.121686
$57$	6.17993	+	11.2857i	0.818551	+	1.49483i
$58$	−15.2989			−2.00884
$59$	1.46221	−	2.53263i	0.190364	−	0.329720i	−0.755007	−	0.655717i	$-0.772367\pi$
$59$	1.46221	−	2.53263i	0.190364	−	0.329720i	0.945371	+	0.325997i	$0.105700\pi$
$60$		0			0
$61$	−1.16586	−	2.01932i	−0.149273	−	0.258548i	0.781686	−	0.623672i	$-0.214360\pi$
$61$	−1.16586	−	2.01932i	−0.149273	−	0.258548i	−0.930959	+	0.365124i	$0.881027\pi$
$62$	−7.39371	+	12.8063i	−0.939003	+	1.62640i
$63$	1.69013	+	2.92740i	0.212937	+	0.368818i
$64$	−12.3112			−1.53891
$65$		0			0
$66$	−8.26497	−	14.3153i	−1.01735	−	1.76210i
$67$	2.15122	+	3.72603i	0.262814	+	0.455207i	0.966989	−	0.254820i	$-0.0820162\pi$
$67$	2.15122	+	3.72603i	0.262814	+	0.455207i	−0.704175	+	0.710027i	$0.748683\pi$
$68$	14.1851			1.72019
$69$	8.56468			1.03107
$70$		0			0
$71$	6.74645	−	11.6852i	0.800656	−	1.38678i	−0.118528	−	0.992951i	$-0.537818\pi$
$71$	6.74645	−	11.6852i	0.800656	−	1.38678i	0.919185	−	0.393827i	$-0.128849\pi$
$72$	4.39714	+	7.61607i	0.518208	+	0.897563i
$73$	−4.21337	+	7.29777i	−0.493137	+	0.854139i	−0.999969	−	0.00790620i	$-0.997483\pi$
$73$	−4.21337	+	7.29777i	−0.493137	+	0.854139i	0.506831	+	0.862045i	$0.330817\pi$
$74$	5.23574	−	9.06858i	0.608643	−	1.05420i
$75$		0			0
$76$	11.8064	+	0.266962i	1.35429	+	0.0306226i
$77$	−1.52665			−0.173978
$78$	21.9933	−	38.0935i	2.49025	−	4.31324i
$79$	−2.93630	+	5.08583i	−0.330360	+	0.572200i	−0.982582	−	0.185827i	$-0.940503\pi$
$79$	−2.93630	+	5.08583i	−0.330360	+	0.572200i	0.652222	+	0.758028i	$0.273837\pi$
$80$		0			0
$81$	−3.25215	+	5.63288i	−0.361350	+	0.625876i
$82$	6.75806	+	11.7053i	0.746303	+	1.29263i
$83$	4.02036			0.441292			0.220646	−	0.975354i	$-0.429184\pi$
$83$	4.02036			0.441292			0.220646	+	0.975354i	$0.429184\pi$
$84$	4.73145			0.516244
$85$		0			0
$86$	−4.73107	−	8.19445i	−0.510164	−	0.883630i
$87$	−20.8104			−2.23111
$88$	−3.97180			−0.423396
$89$	−1.85823	−	3.21855i	−0.196972	−	0.341166i	0.750573	−	0.660787i	$-0.229778\pi$
$89$	−1.85823	−	3.21855i	−0.196972	−	0.341166i	−0.947545	+	0.319622i	$0.896444\pi$
$90$		0			0
$91$	−2.03122	−	3.51818i	−0.212930	−	0.368805i
$92$	3.93039	−	6.80764i	0.409772	−	0.709745i
$93$	−10.0574	+	17.4199i	−1.04290	+	1.80636i
$94$	5.55285			0.572733
$95$		0			0
$96$	−22.4007			−2.28627
$97$	1.26285	−	2.18732i	0.128223	−	0.222089i	−0.794765	−	0.606917i	$-0.792406\pi$
$97$	1.26285	−	2.18732i	0.128223	−	0.222089i	0.922988	+	0.384828i	$0.125739\pi$
$98$	−7.21552	+	12.4977i	−0.728878	+	1.26245i
$99$	−7.37182	−	12.7684i	−0.740895	−	1.28327i
$100$		0			0
$101$	−0.692736	−	1.19985i	−0.0689298	−	0.119390i	0.829501	−	0.558506i	$-0.188625\pi$
$101$	−0.692736	−	1.19985i	−0.0689298	−	0.119390i	−0.898430	+	0.439116i	$0.855292\pi$
$102$	33.5393			3.32088
$103$	−0.166774			−0.0164328			−0.00821638	−	0.999966i	$-0.502615\pi$
$103$	−0.166774			−0.0164328			−0.00821638	+	0.999966i	$0.502615\pi$
$104$	−5.28453	−	9.15307i	−0.518191	−	0.897533i
$105$		0			0
$106$	−20.8143			−2.02166
$107$	4.51729			0.436703			0.218351	−	0.975870i	$-0.429932\pi$
$107$	4.51729			0.436703			0.218351	+	0.975870i	$0.429932\pi$
$108$	10.8509	+	18.7943i	1.04413	+	1.80848i
$109$	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
$111$	7.12196	−	12.3356i	0.675987	−	1.17084i
$112$	−0.614805	+	1.06487i	−0.0580936	+	0.100621i
$113$	−13.2065			−1.24237			−0.621183	−	0.783665i	$-0.713348\pi$
$113$	−13.2065			−1.24237			−0.621183	+	0.783665i	$0.713348\pi$
$114$	27.9152	+	0.631206i	2.61450	+	0.0591178i
$115$		0			0
$116$	−9.55004	+	16.5411i	−0.886699	+	1.53581i
$117$	19.6166	−	33.9769i	1.81355	−	3.14117i
$118$	−3.17313	−	5.49602i	−0.292110	−	0.505950i
$119$	1.54879	−	2.68257i	0.141977	−	0.245911i
$120$		0			0
$121$	−4.34127			−0.394661
$122$	−5.06002			−0.458113
$123$	9.19271	+	15.9222i	0.828879	+	1.43566i
$124$	9.23079	+	15.9882i	0.828949	+	1.43578i
$125$		0			0
$126$	7.33548			0.653496
$127$	0.860805	+	1.49096i	0.0763841	+	0.132301i	0.901687	−	0.432389i	$-0.142329\pi$
$127$	0.860805	+	1.49096i	0.0763841	+	0.132301i	−0.825303	+	0.564690i	$0.808996\pi$
$128$	−5.76959	+	9.99323i	−0.509965	+	0.883285i
$129$	−6.43548	−	11.1466i	−0.566612	−	0.981401i
$130$		0			0
$131$	−1.64201	+	2.84405i	−0.143463	+	0.248486i	−0.928799	−	0.370585i	$-0.879157\pi$
$131$	−1.64201	+	2.84405i	−0.143463	+	0.248486i	0.785335	+	0.619071i	$0.212491\pi$
$132$	−20.6370			−1.79622
$133$	1.33956	−	2.20360i	0.116155	−	0.191076i
$134$	9.33668			0.806567
$135$		0			0
$136$	4.02940	−	6.97913i	0.345518	−	0.598455i
$137$	4.07541	+	7.05882i	0.348186	+	0.603075i	0.985927	−	0.167175i	$-0.0534645\pi$
$137$	4.07541	+	7.05882i	0.348186	+	0.603075i	−0.637741	+	0.770251i	$0.720131\pi$
$138$	9.29304	−	16.0960i	0.791076	−	1.37018i
$139$	7.81401	+	13.5343i	0.662776	+	1.14796i	0.979883	+	0.199571i	$0.0639550\pi$
$139$	7.81401	+	13.5343i	0.662776	+	1.14796i	−0.317108	+	0.948390i	$0.602712\pi$
$140$		0			0
$141$	7.55331			0.636103
$142$	−14.6404	−	25.3579i	−1.22859	−	2.12799i
$143$	8.85952	+	15.3451i	0.740870	+	1.28323i
$144$	−11.8750			−0.989582
$145$		0			0
$146$	9.14337	+	15.8368i	0.756711	+	1.31066i
$147$	−9.81497	+	17.0000i	−0.809525	+	1.40214i
$148$	−6.53664	−	11.3218i	−0.537308	−	0.930646i
$149$	−1.61005	+	2.78869i	−0.131900	+	0.228458i	−0.924409	−	0.381402i	$-0.875441\pi$
$149$	−1.61005	+	2.78869i	−0.131900	+	0.228458i	0.792509	+	0.609861i	$0.208775\pi$
$150$		0			0
$151$	−11.1226			−0.905142			−0.452571	−	0.891728i	$-0.649493\pi$
$151$	−11.1226			−0.905142			−0.452571	+	0.891728i	$0.649493\pi$
$152$	3.48507	−	5.73299i	0.282677	−	0.465007i
$153$	29.9149			2.41847
$154$	−1.65648	+	2.86910i	−0.133483	+	0.231199i
$155$		0			0
$156$	−27.4578	−	47.5583i	−2.19838	−	3.80771i
$157$	10.7157	−	18.5602i	0.855209	−	1.48127i	−0.0212418	−	0.999774i	$-0.506762\pi$
$157$	10.7157	−	18.5602i	0.855209	−	1.48127i	0.876451	−	0.481491i	$-0.159905\pi$
$158$	6.37203	+	11.0367i	0.506932	+	0.878032i
$159$	−28.3128			−2.24535
$160$		0			0
$161$	−0.858273	−	1.48657i	−0.0676414	−	0.117158i
$162$	7.05744	+	12.2238i	0.554485	+	0.960396i
$163$	−10.3129			−0.807768			−0.403884	−	0.914810i	$-0.632340\pi$
$163$	−10.3129			−0.807768			−0.403884	+	0.914810i	$0.632340\pi$
$164$	16.8744			1.31767
$165$		0			0
$166$	4.36226	−	7.55566i	0.338577	−	0.586433i
$167$	3.25342	+	5.63509i	0.251757	+	0.436056i	0.964010	−	0.265867i	$-0.0856582\pi$
$167$	3.25342	+	5.63509i	0.251757	+	0.436056i	−0.712252	+	0.701923i	$0.752325\pi$
$168$	1.34401	−	2.32790i	0.103693	−	0.179601i
$169$	−17.0754	+	29.5754i	−1.31349	+	2.27503i
$170$		0			0
$171$	24.8986	+	0.562995i	1.90404	+	0.0430533i
$172$	−11.8131			−0.900744
$173$	3.13027	−	5.42179i	0.237990	−	0.412211i	−0.722147	−	0.691739i	$-0.756845\pi$
$173$	3.13027	−	5.42179i	0.237990	−	0.412211i	0.960137	+	0.279528i	$0.0901781\pi$
$174$	−22.5802	+	39.1100i	−1.71180	+	2.96492i
$175$		0			0
$176$	2.68158	−	4.64463i	0.202131	−	0.350102i
$177$	−4.31628	−	7.47601i	−0.324431	−	0.561931i
$178$	−8.06505			−0.604501
$179$	23.1893			1.73325			0.866624	−	0.498961i	$-0.166285\pi$
$179$	23.1893			1.73325			0.866624	+	0.498961i	$0.166285\pi$
$180$		0			0
$181$	1.59948	+	2.77039i	0.118889	+	0.205921i	0.919328	−	0.393493i	$-0.128733\pi$
$181$	1.59948	+	2.77039i	0.118889	+	0.205921i	−0.800439	+	0.599414i	$0.795400\pi$
$182$	−8.81585			−0.653474
$183$	−6.88294			−0.508801
$184$	−2.23293	−	3.86754i	−0.164614	−	0.285119i
$185$		0			0
$186$	21.8253	+	37.8026i	1.60031	+	2.77182i
$187$	−6.75529	+	11.7005i	−0.493996	+	0.855626i
$188$	3.46627	−	6.00375i	0.252803	−	0.437868i
$189$	4.73898			0.344710
$190$		0			0
$191$	18.9443			1.37076			0.685382	−	0.728184i	$-0.259635\pi$
$191$	18.9443			1.37076			0.685382	+	0.728184i	$0.259635\pi$
$192$	−18.1706	+	31.4725i	−1.31135	+	2.27133i
$193$	−0.515269	+	0.892472i	−0.0370899	+	0.0642415i	−0.883974	−	0.467535i	$-0.845142\pi$
$193$	−0.515269	+	0.892472i	−0.0370899	+	0.0642415i	0.846885	+	0.531777i	$0.178475\pi$
$194$	−2.74049	−	4.74667i	−0.196756	−	0.340791i
$195$		0			0
$196$	9.00832	+	15.6029i	0.643452	+	1.11449i
$197$	18.5515			1.32174			0.660868	−	0.750502i	$-0.270188\pi$
$197$	18.5515			1.32174			0.660868	+	0.750502i	$0.270188\pi$
$198$	−31.9950			−2.27378
$199$	−11.3166	−	19.6010i	−0.802215	−	1.38948i	−0.918155	−	0.396221i	$-0.870321\pi$
$199$	−11.3166	−	19.6010i	−0.802215	−	1.38948i	0.115940	−	0.993256i	$-0.463012\pi$
$200$		0			0
$201$	12.7003			0.895810
$202$	−3.00659			−0.211543
$203$	2.08542	+	3.61206i	0.146368	+	0.253517i
$204$	20.9363	−	36.2627i	1.46583	−	2.53890i
$205$		0			0
$206$	−0.180957	+	0.313427i	−0.0126079	+	0.0218375i
$207$	8.28879	−	14.3566i	0.576111	−	0.997853i
$208$	14.2715			0.989549
$209$	−5.84273	+	9.61137i	−0.404150	+	0.664832i
$210$		0			0
$211$	−6.21978	+	10.7730i	−0.428187	+	0.741642i	−0.996712	−	0.0810240i	$-0.974181\pi$
$211$	−6.21978	+	10.7730i	−0.428187	+	0.741642i	0.568525	+	0.822666i	$0.307514\pi$
$212$	−12.9930	+	22.5045i	−0.892360	+	1.54561i
$213$	−19.9147	−	34.4933i	−1.36453	−	2.36344i
$214$	4.90145	−	8.48956i	0.335056	−	0.580335i
$215$		0			0
$216$	12.3292			0.838893
$217$	4.03142			0.273671
$218$	−11.6200	−	20.1265i	−0.787008	−	1.36314i
$219$	12.4373	+	21.5421i	0.840438	+	1.45568i
$220$		0			0
$221$	−35.9520			−2.41839
$222$	−15.4553	−	26.7693i	−1.03729	−	1.79664i
$223$	−9.58654	+	16.6044i	−0.641962	+	1.11191i	0.343032	+	0.939324i	$0.388546\pi$
$223$	−9.58654	+	16.6044i	−0.641962	+	1.11191i	−0.984994	+	0.172588i	$0.944787\pi$
$224$	2.24479	+	3.88810i	0.149987	+	0.259784i
$225$		0			0
$226$	−14.3297	+	24.8197i	−0.953195	+	1.65098i
$227$	26.5208			1.76025			0.880123	−	0.474745i	$-0.157460\pi$
$227$	26.5208			1.76025			0.880123	+	0.474745i	$0.157460\pi$
$228$	18.1080	−	29.7880i	1.19923	−	1.97276i
$229$	−8.81023			−0.582196			−0.291098	−	0.956693i	$-0.594021\pi$
$229$	−8.81023			−0.582196			−0.291098	+	0.956693i	$0.594021\pi$
$230$		0			0
$231$	−2.25324	+	3.90272i	−0.148252	+	0.256780i
$232$	5.42555	+	9.39733i	0.356205	+	0.616965i
$233$	−2.25616	+	3.90778i	−0.147806	+	0.256007i	−0.930416	−	0.366505i	$-0.880554\pi$
$233$	−2.25616	+	3.90778i	−0.147806	+	0.256007i	0.782610	+	0.622512i	$0.213888\pi$
$234$	−42.5697	−	73.7328i	−2.78287	−	4.82006i
$235$		0			0
$236$	−7.92308			−0.515749
$237$	8.66761	+	15.0127i	0.563022	+	0.975182i
$238$	−3.36100	−	5.82142i	−0.217861	−	0.377347i
$239$	−7.82431			−0.506112			−0.253056	−	0.967452i	$-0.581436\pi$
$239$	−7.82431			−0.506112			−0.253056	+	0.967452i	$0.581436\pi$
$240$		0			0
$241$	−13.6697	−	23.6766i	−0.880541	−	1.52514i	−0.850740	−	0.525586i	$-0.823846\pi$
$241$	−13.6697	−	23.6766i	−0.880541	−	1.52514i	−0.0298010	−	0.999556i	$-0.509487\pi$
$242$	−4.71046	+	8.15876i	−0.302800	+	0.524465i
$243$	−2.41531	−	4.18345i	−0.154942	−	0.268368i
$244$	−3.15863	+	5.47091i	−0.202210	+	0.350239i
$245$		0			0
$246$	39.8979			2.54380
$247$	−29.9233	−	0.676612i	−1.90398	−	0.0430518i
$248$	10.4884			0.666011
$249$	5.93380	−	10.2777i	0.376040	−	0.651320i
$250$		0			0
$251$	8.11886	+	14.0623i	0.512458	+	0.887603i	0.999896	+	0.0144451i	$0.00459818\pi$
$251$	8.11886	+	14.0623i	0.512458	+	0.887603i	−0.487438	+	0.873158i	$0.662068\pi$
$252$	4.57904	−	7.93113i	0.288452	−	0.499614i
$253$	3.74350	+	6.48394i	0.235352	+	0.407642i
$254$	3.73604			0.234420
$255$		0			0
$256$	0.209275	+	0.362476i	0.0130797	+	0.0226547i
$257$	−4.57174	−	7.91848i	−0.285177	−	0.493941i	0.687475	−	0.726208i	$-0.258719\pi$
$257$	−4.57174	−	7.91848i	−0.285177	−	0.493941i	−0.972652	+	0.232267i	$0.925386\pi$
$258$	−27.9311			−1.73891
$259$	−2.85479			−0.177388
$260$		0			0
$261$	−20.1400	+	34.8836i	−1.24664	+	2.15924i
$262$	3.56331	+	6.17183i	0.220142	+	0.381297i
$263$	−7.64861	+	13.2478i	−0.471634	+	0.816894i	−0.999473	−	0.0324505i	$-0.989669\pi$
$263$	−7.64861	+	13.2478i	−0.471634	+	0.816894i	0.527840	+	0.849344i	$0.323002\pi$
$264$	−5.86214	+	10.1535i	−0.360790	+	0.624906i
$265$		0			0
$266$	−2.68785	−	4.90850i	−0.164803	−	0.300960i
$267$	−10.9705			−0.671386
$268$	5.82826	−	10.0948i	0.356017	−	0.616640i
$269$	7.07334	−	12.2514i	0.431269	−	0.746981i	−0.565714	−	0.824602i	$-0.691399\pi$
$269$	7.07334	−	12.2514i	0.431269	−	0.746981i	0.996983	+	0.0776213i	$0.0247325\pi$
$270$		0			0
$271$	5.68158	−	9.84078i	0.345131	−	0.597785i	−0.640246	−	0.768170i	$-0.721168\pi$
$271$	5.68158	−	9.84078i	0.345131	−	0.597785i	0.985378	+	0.170385i	$0.0545010\pi$
$272$	5.44093	+	9.42396i	0.329905	+	0.571412i
$273$	−11.9918			−0.725779
$274$	17.6880			1.06857
$275$		0			0
$276$	−11.6020	−	20.0953i	−0.698360	−	1.20960i
$277$	−18.9102			−1.13620			−0.568101	−	0.822959i	$-0.692322\pi$
$277$	−18.9102			−1.13620			−0.568101	+	0.822959i	$0.692322\pi$
$278$	33.9142			2.03404
$279$	19.4668	+	33.7175i	1.16545	+	2.01861i
$280$		0			0
$281$	13.9438	+	24.1513i	0.831816	+	1.44075i	0.896596	+	0.442849i	$0.146032\pi$
$281$	13.9438	+	24.1513i	0.831816	+	1.44075i	−0.0647802	+	0.997900i	$0.520635\pi$
$282$	8.19567	−	14.1953i	0.488045	−	0.845318i
$283$	7.19798	−	12.4673i	0.427876	−	0.741102i	−0.568809	−	0.822470i	$-0.692595\pi$
$283$	7.19798	−	12.4673i	0.427876	−	0.741102i	0.996684	+	0.0813677i	$0.0259288\pi$
$284$	−36.5560			−2.16920
$285$		0			0
$286$	38.4519			2.27371
$287$	1.84242	−	3.19116i	0.108754	−	0.188368i
$288$	−21.6792	+	37.5494i	−1.27746	+	2.21262i
$289$	−5.20651	−	9.01794i	−0.306265	−	0.530467i
$290$		0			0
$291$	−3.72778	−	6.45670i	−0.218526	−	0.378498i
$292$	22.8303			1.33605
$293$	−2.63178			−0.153750			−0.0768752	−	0.997041i	$-0.524494\pi$
$293$	−2.63178			−0.153750			−0.0768752	+	0.997041i	$0.524494\pi$
$294$	21.2993	+	36.8915i	1.24220	+	2.15156i
$295$		0			0
$296$	−7.42717			−0.431695
$297$	−20.6699			−1.19939
$298$	3.49395	+	6.05169i	0.202399	+	0.350565i
$299$	−9.96155	+	17.2539i	−0.576091	+	0.997819i
$300$		0			0
$301$	−1.28981	+	2.23401i	−0.0743433	+	0.128766i
$302$	−12.0685	+	20.9032i	−0.694463	+	1.20284i
$303$	−4.08974			−0.234950
$304$	4.35120	+	7.94610i	0.249559	+	0.455740i
$305$		0			0
$306$	32.4589	−	56.2205i	1.85555	−	3.21391i
$307$	−8.41257	+	14.5710i	−0.480131	+	0.831611i	−0.999740	−	0.0227929i	$-0.992744\pi$
$307$	−8.41257	+	14.5710i	−0.480131	+	0.831611i	0.519609	+	0.854404i	$0.326077\pi$
$308$	2.06805	+	3.58197i	0.117838	+	0.204102i
$309$	−0.246149	+	0.426342i	−0.0140029	+	0.0242538i
$310$		0			0
$311$	−18.3273			−1.03924			−0.519622	−	0.854396i	$-0.673927\pi$
$311$	−18.3273			−1.03924			−0.519622	+	0.854396i	$0.673927\pi$
$312$	−31.1986			−1.76627
$313$	−11.7527	−	20.3562i	−0.664299	−	1.15060i	−0.979475	−	0.201567i	$-0.935397\pi$
$313$	−11.7527	−	20.3562i	−0.664299	−	1.15060i	0.315176	−	0.949033i	$-0.397937\pi$
$314$	−23.2541	−	40.2772i	−1.31230	−	2.27298i
$315$		0			0
$316$	15.9105			0.895036
$317$	−1.94177	−	3.36324i	−0.109061	−	0.188899i	0.806329	−	0.591467i	$-0.201451\pi$
$317$	−1.94177	−	3.36324i	−0.109061	−	0.188899i	−0.915390	+	0.402568i	$0.868118\pi$
$318$	−30.7207	+	53.2097i	−1.72273	+	2.98385i
$319$	−9.09594	−	15.7546i	−0.509275	−	0.882090i
$320$		0			0
$321$	6.66724	−	11.5480i	0.372129	−	0.644546i
$322$	−3.72505			−0.207589
$323$	−10.9613	−	20.0174i	−0.609905	−	1.11380i
$324$	17.6219			0.978996
$325$		0			0
$326$	−11.1899	+	19.3815i	−0.619753	+	1.07344i
$327$	−15.8062	−	27.3772i	−0.874087	−	1.51396i
$328$	4.79333	−	8.30228i	0.264667	−	0.458417i
$329$	−0.756923	−	1.31103i	−0.0417305	−	0.0722793i
$330$		0			0
$331$	3.25821			0.179087			0.0895437	−	0.995983i	$-0.471459\pi$
$331$	3.25821			0.179087			0.0895437	+	0.995983i	$0.471459\pi$
$332$	−5.44613	−	9.43297i	−0.298895	−	0.517702i
$333$	−13.7851	−	23.8765i	−0.755419	−	1.30842i
$334$	14.1204			0.772635
$335$		0			0
$336$	1.81483	+	3.14338i	0.0990070	+	0.171485i
$337$	−11.0987	+	19.2234i	−0.604582	+	1.04717i	0.387535	+	0.921855i	$0.373327\pi$
$337$	−11.0987	+	19.2234i	−0.604582	+	1.04717i	−0.992117	+	0.125312i	$0.960007\pi$
$338$	37.0551	+	64.1813i	2.01553	+	3.49100i
$339$	−19.4921	+	33.7612i	−1.05866	+	1.83366i
$340$		0			0
$341$	−17.5837			−0.952213
$342$	28.0741	−	46.1823i	1.51807	−	2.49725i
$343$	8.07560			0.436042
$344$	−3.35563	+	5.81212i	−0.180923	+	0.313369i
$345$		0			0
$346$	−6.79296	−	11.7658i	−0.365192	−	0.632531i
$347$	−1.49728	+	2.59336i	−0.0803780	+	0.139219i	−0.903412	−	0.428773i	$-0.858946\pi$
$347$	−1.49728	+	2.59336i	−0.0803780	+	0.139219i	0.823034	+	0.567992i	$0.192279\pi$
$348$	28.1905	+	48.8274i	1.51117	+	2.61743i
$349$	15.1407			0.810461			0.405230	−	0.914215i	$-0.367191\pi$
$349$	15.1407			0.810461			0.405230	+	0.914215i	$0.367191\pi$
$350$		0			0
$351$	−27.5015	−	47.6340i	−1.46792	−	2.54251i
$352$	−9.79106	−	16.9586i	−0.521865	−	0.903897i
$353$	34.4369			1.83289			0.916446	−	0.400159i	$-0.131045\pi$
$353$	34.4369			1.83289			0.916446	+	0.400159i	$0.131045\pi$
$354$	−18.7334			−0.995668
$355$		0			0
$356$	−5.03446	+	8.71994i	−0.266826	+	0.462156i
$357$	−4.57182	−	7.91863i	−0.241967	−	0.419098i
$358$	25.1614	−	43.5808i	1.32982	−	2.30332i
$359$	−1.58165	+	2.73950i	−0.0834763	+	0.144585i	−0.904741	−	0.425962i	$-0.859936\pi$
$359$	−1.58165	+	2.73950i	−0.0834763	+	0.144585i	0.821265	+	0.570548i	$0.193269\pi$
$360$		0			0
$361$	−8.74655	−	16.8671i	−0.460345	−	0.887740i
$362$	6.94204			0.364865
$363$	−6.40744	+	11.0980i	−0.336304	+	0.582495i
$364$	−5.50314	+	9.53171i	−0.288443	+	0.499597i
$365$		0			0
$366$	−7.46829	+	12.9354i	−0.390374	+	0.676147i
$367$	10.7270	+	18.5797i	0.559945	+	0.969853i	0.997500	+	0.0706615i	$0.0225110\pi$
$367$	10.7270	+	18.5797i	0.559945	+	0.969853i	−0.437556	+	0.899191i	$0.644156\pi$
$368$	6.03027			0.314350
$369$	35.5864			1.85255
$370$		0			0
$371$	2.83725	+	4.91426i	0.147303	+	0.255136i
$372$	54.4963			2.82550
$373$	33.1587			1.71689			0.858446	−	0.512904i	$-0.171430\pi$
$373$	33.1587			1.71689			0.858446	+	0.512904i	$0.171430\pi$
$374$	14.6596	+	25.3911i	0.758028	+	1.31294i
$375$		0			0
$376$	−1.96925	−	3.41084i	−0.101556	−	0.175901i
$377$	24.2045	−	41.9234i	1.24660	−	2.15917i
$378$	5.14199	−	8.90619i	0.264476	−	0.458085i
$379$	−14.1646			−0.727589			−0.363795	−	0.931479i	$-0.618519\pi$
$379$	−14.1646			−0.727589			−0.363795	+	0.931479i	$0.618519\pi$
$380$		0			0
$381$	5.08198			0.260358
$382$	20.5554	−	35.6030i	1.05171	−	1.82161i
$383$	5.41036	−	9.37102i	0.276457	−	0.478837i	−0.694045	−	0.719932i	$-0.744173\pi$
$383$	5.41036	−	9.37102i	0.276457	−	0.478837i	0.970502	+	0.241095i	$0.0775065\pi$
$384$	17.0311	+	29.4988i	0.869117	+	1.50535i
$385$		0			0
$386$	1.11818	+	1.93674i	0.0569138	+	0.0985775i
$387$	−24.9127			−1.26638
$388$	−6.84281			−0.347391
$389$	−5.38703	−	9.33061i	−0.273133	−	0.473081i	0.696529	−	0.717529i	$-0.254727\pi$
$389$	−5.38703	−	9.33061i	−0.273133	−	0.473081i	−0.969662	+	0.244448i	$0.921393\pi$
$390$		0			0
$391$	−15.1912			−0.768250
$392$	10.2356			0.516975
$393$	4.84702	+	8.39529i	0.244500	+	0.423486i
$394$	20.1291	−	34.8647i	1.01409	−	1.75646i
$395$		0			0
$396$	−19.9723	+	34.5930i	−1.00364	+	1.73836i
$397$	−1.55107	+	2.68653i	−0.0778461	+	0.134833i	−0.902320	−	0.431066i	$-0.858138\pi$
$397$	−1.55107	+	2.68653i	−0.0778461	+	0.134833i	0.824474	+	0.565899i	$0.191471\pi$
$398$	−49.1162			−2.46197
$399$	−3.65617	−	6.67683i	−0.183037	−	0.334260i
$400$		0			0
$401$	5.65671	−	9.79771i	0.282483	−	0.489274i	−0.689513	−	0.724273i	$-0.742175\pi$
$401$	5.65671	−	9.79771i	0.282483	−	0.489274i	0.971996	+	0.234999i	$0.0755088\pi$
$402$	13.7804	−	23.8683i	0.687303	−	1.19044i
$403$	−23.3954	−	40.5220i	−1.16541	−	2.01854i
$404$	−1.87681	+	3.25074i	−0.0933749	+	0.161730i
$405$		0			0
$406$	9.05110			0.449199
$407$	12.4517			0.617206
$408$	−11.8943	−	20.6015i	−0.588855	−	1.01993i
$409$	−7.11186	−	12.3181i	−0.351659	−	0.609091i	0.634882	−	0.772609i	$-0.281049\pi$
$409$	−7.11186	−	12.3181i	−0.351659	−	0.609091i	−0.986540	+	0.163519i	$0.947716\pi$
$410$		0			0
$411$	24.0602			1.18680
$412$	0.225919	+	0.391303i	0.0111302	+	0.0192781i
$413$	−0.865075	+	1.49835i	−0.0425675	+	0.0737291i
$414$	−17.9874	−	31.1551i	−0.884032	−	1.53119i
$415$		0			0
$416$	26.0542	−	45.1272i	1.27741	−	2.21255i
$417$	46.1320			2.25909
$418$	11.7235	+	21.4093i	0.573416	+	1.04716i
$419$	−11.0053			−0.537643			−0.268821	−	0.963190i	$-0.586634\pi$
$419$	−11.0053			−0.537643			−0.268821	+	0.963190i	$0.586634\pi$
$420$		0			0
$421$	11.4625	−	19.8536i	0.558646	−	0.967604i	−0.438963	−	0.898505i	$-0.644654\pi$
$421$	11.4625	−	19.8536i	0.558646	−	0.967604i	0.997610	−	0.0690991i	$-0.0220125\pi$
$422$	13.4975	+	23.3783i	0.657046	+	1.13804i
$423$	7.31000	−	12.6613i	0.355424	−	0.615613i
$424$	7.38154	+	12.7852i	0.358479	+	0.620904i
$425$		0			0
$426$	−86.4332			−4.18770
$427$	0.689744	+	1.19467i	0.0333791	+	0.0578142i
$428$	−6.11929	−	10.5989i	−0.295787	−	0.512318i
$429$	52.3045			2.52528
$430$		0			0
$431$	8.49811	+	14.7192i	0.409340	+	0.708997i	0.994816	−	0.101693i	$-0.0324258\pi$
$431$	8.49811	+	14.7192i	0.409340	+	0.708997i	−0.585476	+	0.810690i	$0.699092\pi$
$432$	−8.32408	+	14.4177i	−0.400492	+	0.693673i
$433$	15.7493	+	27.2786i	0.756863	+	1.31093i	0.944443	+	0.328676i	$0.106602\pi$
$433$	15.7493	+	27.2786i	0.756863	+	1.31093i	−0.187580	+	0.982249i	$0.560064\pi$
$434$	4.37427	−	7.57645i	0.209972	−	0.363681i
$435$		0			0
$436$	−29.0144			−1.38954
$437$	−12.6438	−	0.285896i	−0.604836	−	0.0136763i
$438$	53.9802			2.57928
$439$	−1.57963	+	2.73600i	−0.0753916	+	0.130582i	−0.901256	−	0.433286i	$-0.857354\pi$
$439$	−1.57963	+	2.73600i	−0.0753916	+	0.130582i	0.825865	+	0.563868i	$0.190687\pi$
$440$		0			0
$441$	18.9976	+	32.9049i	0.904649	+	1.56690i
$442$	−39.0095	+	67.5664i	−1.85549	+	3.21380i
$443$	−5.94720	−	10.3008i	−0.282560	−	0.489408i	0.689455	−	0.724329i	$-0.257850\pi$
$443$	−5.94720	−	10.3008i	−0.282560	−	0.489408i	−0.972015	+	0.234921i	$0.924517\pi$
$444$	−38.5907			−1.83143
$445$		0			0
$446$	20.8036	+	36.0329i	0.985080	+	1.70621i
$447$	4.75267	+	8.23186i	0.224794	+	0.389354i
$448$	7.28358			0.344117
$449$	21.2175			1.00132			0.500659	−	0.865645i	$-0.333091\pi$
$449$	21.2175			1.00132			0.500659	+	0.865645i	$0.333091\pi$
$450$		0			0
$451$	−8.03602	+	13.9188i	−0.378401	+	0.655410i
$452$	17.8901	+	30.9865i	0.841479	+	1.45748i
$453$	−16.4162	+	28.4338i	−0.771302	+	1.33593i
$454$	28.7762	−	49.8418i	1.35053	−	2.33919i
$455$		0			0
$456$	−9.51208	−	17.3708i	−0.445444	−	0.813462i
$457$	9.41670			0.440495			0.220247	−	0.975444i	$-0.429314\pi$
$457$	9.41670			0.440495			0.220247	+	0.975444i	$0.429314\pi$
$458$	−9.55948	+	16.5575i	−0.446685	+	0.773682i
$459$	20.9696	−	36.3204i	0.978777	−	1.69529i
$460$		0			0
$461$	−1.16004	+	2.00924i	−0.0540282	+	0.0935797i	−0.891775	−	0.452480i	$-0.850539\pi$
$461$	−1.16004	+	2.00924i	−0.0540282	+	0.0935797i	0.837746	+	0.546060i	$0.183873\pi$
$462$	4.88972	+	8.46924i	0.227490	+	0.394025i
$463$	14.7160			0.683909			0.341955	−	0.939716i	$-0.388911\pi$
$463$	14.7160			0.683909			0.341955	+	0.939716i	$0.388911\pi$
$464$	−14.6523			−0.680217
$465$		0			0
$466$	4.89606	+	8.48023i	0.226806	+	0.392839i
$467$	−11.7747			−0.544867			−0.272434	−	0.962175i	$-0.587828\pi$
$467$	−11.7747			−0.544867			−0.272434	+	0.962175i	$0.587828\pi$
$468$	−106.293			−4.91341
$469$	−1.27271	−	2.20439i	−0.0587681	−	0.101789i
$470$		0			0
$471$	−31.6316	−	54.7875i	−1.45751	−	2.52447i
$472$	−2.25062	+	3.89819i	−0.103593	+	0.179429i
$473$	5.62572	−	9.74403i	0.258671	−	0.448031i
$474$	37.6189			1.72789
$475$		0			0
$476$	−8.39217			−0.384655
$477$	−27.4008	+	47.4596i	−1.25460	+	2.17303i
$478$	−8.48971	+	14.7046i	−0.388310	+	0.672573i
$479$	−5.69219	−	9.85915i	−0.260083	−	0.450476i	0.706181	−	0.708031i	$-0.250416\pi$
$479$	−5.69219	−	9.85915i	−0.260083	−	0.450476i	−0.966264	+	0.257555i	$0.917083\pi$
$480$		0			0
$481$	16.5671	+	28.6950i	0.755394	+	1.30838i
$482$	−59.3288			−2.70235
$483$	−5.06703			−0.230558
$484$	5.88084	+	10.1859i	0.267311	+	0.462996i
$485$		0			0
$486$	−10.4829			−0.475513
$487$	−4.77063			−0.216178			−0.108089	−	0.994141i	$-0.534473\pi$
$487$	−4.77063			−0.216178			−0.108089	+	0.994141i	$0.534473\pi$
$488$	1.79447	+	3.10812i	0.0812321	+	0.140698i
$489$	−15.2212	+	26.3639i	−0.688326	+	1.19222i
$490$		0			0
$491$	2.50665	−	4.34165i	0.113124	−	0.195936i	−0.803904	−	0.594758i	$-0.797248\pi$
$491$	2.50665	−	4.34165i	0.113124	−	0.195936i	0.917028	+	0.398822i	$0.130581\pi$
$492$	24.9056	−	43.1377i	1.12283	−	1.94480i
$493$	36.9114			1.66240
$494$	−33.7397	+	55.5023i	−1.51802	+	2.49717i
$495$		0			0
$496$	−7.08125	+	12.2651i	−0.317958	+	0.550719i
$497$	−3.99133	+	6.91319i	−0.179036	+	0.310099i
$498$	−12.8769	−	22.3034i	−0.577026	−	0.999439i
$499$	−10.9112	+	18.8987i	−0.488450	+	0.846021i	−0.999912	−	0.0132853i	$-0.995771\pi$
$499$	−10.9112	+	18.8987i	−0.488450	+	0.846021i	0.511461	+	0.859306i	$0.329104\pi$
$500$		0			0
$501$	19.2074			0.858124
$502$	35.2372			1.57272
$503$	−7.58583	−	13.1391i	−0.338236	−	0.585841i	0.645865	−	0.763451i	$-0.276497\pi$
$503$	−7.58583	−	13.1391i	−0.338236	−	0.585841i	−0.984101	+	0.177610i	$0.943163\pi$
$504$	−2.60144	−	4.50582i	−0.115877	−	0.200705i
$505$		0			0
$506$	16.2475			0.722288
$507$	50.4045	+	87.3031i	2.23854	+	3.87727i
$508$	2.33216	−	4.03941i	0.103473	−	0.179220i
$509$	−2.59122	−	4.48812i	−0.114854	−	0.198933i	0.802868	−	0.596157i	$-0.203307\pi$
$509$	−2.59122	−	4.48812i	−0.114854	−	0.198933i	−0.917721	+	0.397225i	$0.869973\pi$
$510$		0			0
$511$	2.49271	−	4.31750i	0.110271	−	0.190995i
$512$	−22.1701			−0.979789
$513$	18.1368	−	29.8354i	0.800761	−	1.31726i
$514$	−19.8421			−0.875199
$515$		0			0
$516$	−17.4355	+	30.1991i	−0.767554	+	1.32944i
$517$	3.30145	+	5.71828i	0.145198	+	0.251490i
$518$	−3.09757	+	5.36515i	−0.136099	+	0.235731i
$519$	−9.24018	−	16.0045i	−0.405599	−	0.702518i
$520$		0			0
$521$	11.2091			0.491079			0.245540	−	0.969387i	$-0.421035\pi$
$521$	11.2091			0.491079			0.245540	+	0.969387i	$0.421035\pi$
$522$	43.7056	+	75.7004i	1.91294	+	3.31332i
$523$	2.71940	+	4.71014i	0.118911	+	0.205960i	0.919336	−	0.393472i	$-0.128726\pi$
$523$	2.71940	+	4.71014i	0.118911	+	0.205960i	−0.800425	+	0.599433i	$0.795393\pi$
$524$	8.89733			0.388682
$525$		0			0
$526$	16.5982	+	28.7488i	0.723714	+	1.25351i
$527$	17.8387	−	30.8976i	0.777067	−	1.34592i
$528$	−7.91569	−	13.7104i	−0.344486	−	0.596668i
$529$	7.29084	−	12.6281i	0.316993	−	0.549048i
$530$		0			0
$531$	−16.7090			−0.725107
$532$	−6.98492	−	0.157940i	−0.302835	−	0.00684756i
$533$	−42.7680			−1.85249
$534$	−11.9035	+	20.6175i	−0.515116	+	0.892206i
$535$		0			0
$536$	−3.31114	−	5.73506i	−0.143019	−	0.247717i
$537$	34.2260	−	59.2811i	1.47696	−	2.55817i
$538$	−15.3498	−	26.5866i	−0.661776	−	1.14623i
$539$	−17.1600			−0.739132
$540$		0			0
$541$	−7.14111	−	12.3688i	−0.307020	−	0.531775i	0.670689	−	0.741739i	$-0.265999\pi$
$541$	−7.14111	−	12.3688i	−0.307020	−	0.531775i	−0.977709	+	0.209964i	$0.932665\pi$
$542$	−12.3295	−	21.3554i	−0.529598	−	0.917291i
$543$	9.44296			0.405236
$544$	39.7322			1.70350
$545$		0			0
$546$	−13.0117	+	22.5369i	−0.556848	+	0.964488i
$547$	−12.5122	−	21.6717i	−0.534982	−	0.926616i	−0.999164	−	0.0408766i	$-0.986985\pi$
$547$	−12.5122	−	21.6717i	−0.534982	−	0.926616i	0.464182	−	0.885740i	$-0.346348\pi$
$548$	11.0414	−	19.1243i	0.471666	−	0.816949i
$549$	−6.66122	+	11.5376i	−0.284294	+	0.492412i
$550$		0			0
$551$	30.7219	+	0.694668i	1.30880	+	0.0295939i
$552$	−13.1827			−0.561091
$553$	1.73718	−	3.00888i	0.0738722	−	0.127950i
$554$	−20.5184	+	35.5388i	−0.871741	+	1.50990i
$555$		0			0
$556$	21.1703	−	36.6680i	0.897821	−	1.55507i
$557$	−3.57846	−	6.19807i	−0.151624	−	0.262621i	0.780201	−	0.625529i	$-0.215117\pi$
$557$	−3.57846	−	6.19807i	−0.151624	−	0.262621i	−0.931825	+	0.362909i	$0.881784\pi$
$558$	84.4892			3.57671
$559$	29.9403			1.26634
$560$		0			0
$561$	19.9408	+	34.5385i	0.841901	+	1.45822i
$562$	60.5184			2.55282
$563$	−28.9386			−1.21962			−0.609809	−	0.792548i	$-0.708754\pi$
$563$	−28.9386			−1.21962			−0.609809	+	0.792548i	$0.708754\pi$
$564$	−10.2320	−	17.7223i	−0.430845	−	0.746245i
$565$		0			0
$566$	−15.6202	−	27.0551i	−0.656568	−	1.13721i
$567$	1.92403	−	3.33253i	0.0808019	−	0.139953i
$568$	−10.3841	+	17.9857i	−0.435706	+	0.754664i
$569$	38.8864			1.63020			0.815100	−	0.579320i	$-0.196682\pi$
$569$	38.8864			1.63020			0.815100	+	0.579320i	$0.196682\pi$
$570$		0			0
$571$	15.1613			0.634480			0.317240	−	0.948345i	$-0.397244\pi$
$571$	15.1613			0.634480			0.317240	+	0.948345i	$0.397244\pi$
$572$	24.0029	−	41.5742i	1.00361	−	1.73831i
$573$	27.9607	−	48.4293i	1.16807	−	2.02316i
$574$	−3.99820	−	6.92509i	−0.166882	−	0.289048i
$575$		0			0
$576$	35.1707	+	60.9174i	1.46544	+	2.53822i
$577$	−20.6412			−0.859303			−0.429651	−	0.902995i	$-0.641364\pi$
$577$	−20.6412			−0.859303			−0.429651	+	0.902995i	$0.641364\pi$
$578$	−22.5972			−0.939918
$579$	1.52101	+	2.63447i	0.0632111	+	0.109485i
$580$		0			0
$581$	−2.37852			−0.0986778
$582$	−16.1792			−0.670649
$583$	−12.3752	−	21.4344i	−0.512527	−	0.887723i
$584$	6.48517	−	11.2326i	0.268358	−	0.464810i
$585$		0			0
$586$	−2.85560	+	4.94604i	−0.117964	+	0.204319i
$587$	3.58942	−	6.21706i	0.148151	−	0.256606i	−0.782393	−	0.622785i	$-0.786001\pi$
$587$	3.58942	−	6.21706i	0.148151	−	0.256606i	0.930544	+	0.366180i	$0.119334\pi$
$588$	53.1829			2.19323
$589$	15.4289	−	25.3808i	0.635738	−	1.04580i
$590$		0			0
$591$	27.3808	−	47.4250i	1.12630	−	1.95080i
$592$	5.01448	−	8.68533i	0.206094	−	0.356965i
$593$	18.3743	+	31.8253i	0.754543	+	1.30691i	0.945601	+	0.325328i	$0.105475\pi$
$593$	18.3743	+	31.8253i	0.754543	+	1.30691i	−0.191058	+	0.981579i	$0.561192\pi$
$594$	−22.4277	+	38.8459i	−0.920219	+	1.59387i
$595$		0			0
$596$	8.72413			0.357354
$597$	−66.8107			−2.73438
$598$	21.6174	+	37.4425i	0.884002	+	1.53114i
$599$	0.926876	+	1.60540i	0.0378711	+	0.0655947i	0.884340	−	0.466844i	$-0.154609\pi$
$599$	0.926876	+	1.60540i	0.0378711	+	0.0655947i	−0.846469	+	0.532439i	$0.821276\pi$
$600$		0			0
$601$	−38.1633			−1.55671			−0.778356	−	0.627823i	$-0.783946\pi$
$601$	−38.1633			−1.55671			−0.778356	+	0.627823i	$0.783946\pi$
$602$	2.79899	+	4.84800i	0.114078	+	0.197590i
$603$	12.2912	−	21.2890i	0.500536	−	0.866954i
$604$	15.0671	+	26.0969i	0.613070	+	1.06187i
$605$		0			0
$606$	−4.43755	+	7.68606i	−0.180263	+	0.312225i
$607$	−7.44914			−0.302351			−0.151176	−	0.988507i	$-0.548306\pi$
$607$	−7.44914			−0.302351			−0.151176	+	0.988507i	$0.548306\pi$
$608$	33.0696	+	0.747755i	1.34115	+	0.0303255i
$609$	12.3118			0.498901
$610$		0			0
$611$	−8.78523	+	15.2165i	−0.355412	+	0.615592i
$612$	−40.5238	−	70.1893i	−1.63808	−	2.83723i
$613$	−10.6049	+	18.3682i	−0.428326	+	0.741883i	−0.996725	−	0.0808706i	$-0.974230\pi$
$613$	−10.6049	+	18.3682i	−0.428326	+	0.741883i	0.568398	+	0.822754i	$0.307563\pi$
$614$	18.2560	+	31.6203i	0.736753	+	1.27609i
$615$		0			0
$616$	2.34980			0.0946760
$617$	−15.4076	−	26.6868i	−0.620287	−	1.07437i	−0.989432	−	0.144997i	$-0.953683\pi$
$617$	−15.4076	−	26.6868i	−0.620287	−	1.07437i	0.369145	−	0.929372i	$-0.379651\pi$
$618$	0.534164	+	0.925199i	0.0214872	+	0.0372170i
$619$	7.32036			0.294230			0.147115	−	0.989119i	$-0.453001\pi$
$619$	7.32036			0.294230			0.147115	+	0.989119i	$0.453001\pi$
$620$		0			0
$621$	−11.6205	−	20.1273i	−0.466314	−	0.807680i
$622$	−19.8859	+	34.4434i	−0.797352	+	1.38105i
$623$	1.09937	+	1.90416i	0.0440452	+	0.0762885i
$624$	21.0638	−	36.4836i	0.843228	−	1.46051i
$625$		0			0
$626$	−51.0086			−2.03871
$627$	15.9470	+	29.1222i	0.636862	+	1.16303i
$628$	−58.0638			−2.31700
$629$	−12.6322	+	21.8797i	−0.503680	+	0.872399i
$630$		0			0
$631$	−2.25414	−	3.90429i	−0.0897360	−	0.155427i	0.817664	−	0.575696i	$-0.195269\pi$
$631$	−2.25414	−	3.90429i	−0.0897360	−	0.155427i	−0.907399	+	0.420269i	$0.861936\pi$
$632$	4.51953	−	7.82805i	0.179777	−	0.311383i
$633$	18.3600	+	31.8005i	0.729746	+	1.26396i
$634$	−8.42762			−0.334704
$635$		0			0
$636$	38.3536	+	66.4305i	1.52082	+	2.63414i
$637$	−22.8315	−	39.5454i	−0.904618	−	1.56685i
$638$	−39.4780			−1.56295
$639$	−77.0928			−3.04975
$640$		0			0
$641$	8.48158	−	14.6905i	0.335002	−	0.580241i	−0.648483	−	0.761229i	$-0.724596\pi$
$641$	8.48158	−	14.6905i	0.335002	−	0.580241i	0.983485	+	0.180988i	$0.0579296\pi$
$642$	−14.4685	−	25.0602i	−0.571026	−	0.989046i
$643$	4.64306	−	8.04202i	0.183104	−	0.317146i	−0.759832	−	0.650120i	$-0.774719\pi$
$643$	4.64306	−	8.04202i	0.183104	−	0.317146i	0.942936	+	0.332974i	$0.108052\pi$
$644$	−2.32530	+	4.02753i	−0.0916295	+	0.158707i
$645$		0			0
$646$	−49.5132	−	1.11957i	−1.94807	−	0.0440489i
$647$	−39.2779			−1.54418			−0.772088	−	0.635516i	$-0.780787\pi$
$647$	−39.2779			−1.54418			−0.772088	+	0.635516i	$0.780787\pi$
$648$	5.00567	−	8.67007i	0.196641	−	0.340593i
$649$	3.77317	−	6.53533i	0.148110	−	0.256534i
$650$		0			0
$651$	5.95013	−	10.3059i	0.233204	−	0.403921i
$652$	13.9702	+	24.1972i	0.547116	+	0.947634i
$653$	−26.5513			−1.03903			−0.519517	−	0.854460i	$-0.673888\pi$
$653$	−26.5513			−1.03903			−0.519517	+	0.854460i	$0.673888\pi$
$654$	−68.6018			−2.68254
$655$		0			0
$656$	6.47246	+	11.2106i	0.252707	+	0.437702i
$657$	48.1469			1.87839
$658$	−3.28518			−0.128069
$659$	−16.3143	−	28.2573i	−0.635517	−	1.10075i	−0.986405	−	0.164330i	$-0.947454\pi$
$659$	−16.3143	−	28.2573i	−0.635517	−	1.10075i	0.350889	−	0.936417i	$-0.385880\pi$
$660$		0			0
$661$	−3.13332	−	5.42707i	−0.121872	−	0.211088i	0.798634	−	0.601817i	$-0.205556\pi$
$661$	−3.13332	−	5.42707i	−0.121872	−	0.211088i	−0.920506	+	0.390729i	$0.872223\pi$
$662$	3.53530	−	6.12332i	0.137403	−	0.237989i
$663$	−53.0629	+	91.9077i	−2.06079	+	3.56940i
$664$	−6.18809			−0.240145
$665$		0			0
$666$	−59.8297			−2.31836
$667$	10.2274	−	17.7143i	0.396006	−	0.685902i
$668$	8.81442	−	15.2670i	0.341040	−	0.590699i
$669$	28.2983	+	49.0141i	1.09408	+	1.89499i
$670$		0			0
$671$	−3.00844	−	5.21077i	−0.116140	−	0.201160i
$672$	13.2527			0.511235
$673$	7.39044			0.284881			0.142440	−	0.989803i	$-0.454505\pi$
$673$	7.39044			0.284881			0.142440	+	0.989803i	$0.454505\pi$
$674$	24.0850	+	41.7165i	0.927721	+	1.60686i
$675$		0			0
$676$	92.5238			3.55861
$677$	20.2751			0.779234			0.389617	−	0.920977i	$-0.372607\pi$
$677$	20.2751			0.779234			0.389617	+	0.920977i	$0.372607\pi$
$678$	42.2994	+	73.2648i	1.62450	+	2.81372i
$679$	−0.747127	+	1.29406i	−0.0286721	+	0.0496615i
$680$		0			0
$681$	39.1431	−	67.7978i	1.49997	−	2.59802i
$682$	−19.0791	+	33.0460i	−0.730577	+	1.26540i
$683$	−24.6563			−0.943448			−0.471724	−	0.881746i	$-0.656368\pi$
$683$	−24.6563			−0.943448			−0.471724	+	0.881746i	$0.656368\pi$
$684$	−32.4076	−	59.1822i	−1.23914	−	2.26289i
$685$		0			0
$686$	8.76238	−	15.1769i	0.334549	−	0.579456i
$687$	−13.0034	+	22.5225i	−0.496109	+	0.859286i
$688$	−4.53113	−	7.84815i	−0.172748	−	0.299208i
$689$	32.9306	−	57.0374i	1.25456	−	2.17295i
$690$		0			0
$691$	−41.7299			−1.58748			−0.793739	−	0.608258i	$-0.791869\pi$
$691$	−41.7299			−1.58748			−0.793739	+	0.608258i	$0.791869\pi$
$692$	−16.9615			−0.644781
$693$	4.36131	+	7.55402i	0.165673	+	0.286953i
$694$	3.24922	+	5.62782i	0.123339	+	0.213629i
$695$		0			0
$696$	32.0311			1.21414
$697$	−16.3051	−	28.2413i	−0.617600	−	1.06971i
$698$	16.4283	−	28.4546i	0.621819	−	1.07702i
$699$	6.65991	+	11.5353i	0.251901	+	0.436305i
$700$		0			0
$701$	3.60840	−	6.24993i	0.136287	−	0.236057i	−0.789801	−	0.613363i	$-0.789816\pi$
$701$	3.60840	−	6.24993i	0.136287	−	0.236057i	0.926089	+	0.377306i	$0.123150\pi$
$702$	−119.361			−4.50500
$703$	−10.9258	+	17.9730i	−0.412073	+	0.677865i
$704$	−31.7686			−1.19732
$705$		0			0
$706$	37.3655	−	64.7190i	1.40627	−	2.43573i
$707$	0.409836	+	0.709857i	0.0154135	+	0.0266969i
$708$	−11.6940	+	20.2546i	−0.439487	+	0.761213i
$709$	10.3172	+	17.8700i	0.387472	+	0.671122i	0.992109	−	0.125380i	$-0.0400149\pi$
$709$	10.3172	+	17.8700i	0.387472	+	0.671122i	−0.604636	+	0.796502i	$0.706682\pi$
$710$		0			0
$711$	33.5536			1.25836
$712$	2.86017	+	4.95396i	0.107189	+	0.185657i
$713$	−9.88549	−	17.1222i	−0.370214	−	0.641230i
$714$	−19.8425			−0.742587
$715$		0			0
$716$	−31.4131	−	54.4091i	−1.17396	−	2.03336i
$717$	−11.5482	+	20.0021i	−0.431275	+	0.746991i
$718$	3.43232	+	5.94495i	0.128093	+	0.221864i
$719$	−0.748958	+	1.29723i	−0.0279314	+	0.0483787i	−0.879653	−	0.475616i	$-0.842225\pi$
$719$	−0.748958	+	1.29723i	−0.0279314	+	0.0483787i	0.851722	+	0.523994i	$0.175559\pi$
$720$		0			0
$721$	0.0986670			0.00367455
$722$	−41.1895	−	1.86367i	−1.53291	−	0.0693585i
$723$	−80.7024			−3.00136
$724$	4.33344	−	7.50574i	0.161051	−	0.278949i
$725$		0			0
$726$	13.9047	+	24.0837i	0.516052	+	0.893828i
$727$	−5.68222	+	9.84190i	−0.210742	+	0.365016i	−0.951947	−	0.306263i	$-0.900921\pi$
$727$	−5.68222	+	9.84190i	−0.210742	+	0.365016i	0.741205	+	0.671279i	$0.234255\pi$
$728$	3.12643	+	5.41514i	0.115873	+	0.200698i
$729$	−33.7723			−1.25083
$730$		0			0
$731$	11.4146	+	19.7707i	0.422184	+	0.731244i
$732$	9.32389	+	16.1494i	0.344621	+	0.596901i
$733$	−45.6910			−1.68764			−0.843818	−	0.536630i	$-0.819697\pi$
$733$	−45.6910			−1.68764			−0.843818	+	0.536630i	$0.819697\pi$
$734$	46.5570			1.71845
$735$		0			0
$736$	11.0090	−	19.0681i	0.405796	−	0.702859i
$737$	5.55113	+	9.61484i	0.204479	+	0.354167i
$738$	38.6127	−	66.8792i	1.42135	−	2.46186i
$739$	1.78276	−	3.08783i	0.0655799	−	0.113588i	−0.831371	−	0.555718i	$-0.812444\pi$
$739$	1.78276	−	3.08783i	0.0655799	−	0.113588i	0.896951	+	0.442130i	$0.145777\pi$
$740$		0			0
$741$	−45.8947	+	75.4975i	−1.68599	+	2.77347i
$742$	12.3142			0.452067
$743$	21.2482	−	36.8030i	0.779522	−	1.35017i	−0.152696	−	0.988273i	$-0.548795\pi$
$743$	21.2482	−	36.8030i	0.779522	−	1.35017i	0.932218	−	0.361898i	$-0.117871\pi$
$744$	15.4802	−	26.8125i	0.567531	−	0.982992i
$745$		0			0
$746$	35.9786	−	62.3168i	1.31727	−	2.28158i
$747$	−11.4853	−	19.8932i	−0.420226	−	0.727853i
$748$	36.6039			1.33837
$749$	−2.67252			−0.0976516
$750$		0			0
$751$	6.38588	+	11.0607i	0.233024	+	0.403610i	0.958697	−	0.284431i	$-0.0918045\pi$
$751$	6.38588	+	11.0607i	0.233024	+	0.403610i	−0.725672	+	0.688040i	$0.758471\pi$
$752$	5.31818			0.193934
$753$	47.9317			1.74673
$754$	−52.5259	−	90.9775i	−1.91288	−	3.31320i
$755$		0			0
$756$	−6.41960	−	11.1191i	−0.233478	−	0.404396i
$757$	−5.67306	+	9.82603i	−0.206191	+	0.357133i	−0.950512	−	0.310689i	$-0.899440\pi$
$757$	−5.67306	+	9.82603i	−0.206191	+	0.357133i	0.744321	+	0.667822i	$0.232773\pi$
$758$	−15.3693	+	26.6203i	−0.558237	+	0.966894i
$759$	22.1007			0.802206
$760$		0			0
$761$	−36.9214			−1.33840			−0.669199	−	0.743083i	$-0.733363\pi$
$761$	−36.9214			−1.33840			−0.669199	+	0.743083i	$0.733363\pi$
$762$	5.51417	−	9.55082i	0.199757	−	0.345990i
$763$	−3.16791	+	5.48698i	−0.114686	+	0.198642i
$764$	−25.6627	−	44.4491i	−0.928444	−	1.60811i
$765$		0			0
$766$	−11.7410	−	20.3359i	−0.424218	−	0.734767i
$767$	20.0810			0.725083
$768$	1.23551			0.0445827
$769$	−14.2528	−	24.6866i	−0.513971	−	0.890223i	−0.999869	−	0.0162076i	$-0.994841\pi$
$769$	−14.2528	−	24.6866i	−0.513971	−	0.890223i	0.485898	−	0.874015i	$-0.338493\pi$
$770$		0			0
$771$	−26.9904			−0.972036
$772$	2.79201			0.100487
$773$	−7.60956	−	13.1801i	−0.273697	−	0.474057i	0.696109	−	0.717936i	$-0.254913\pi$
$773$	−7.60956	−	13.1801i	−0.273697	−	0.474057i	−0.969805	+	0.243880i	$0.921580\pi$
$774$	−27.0314	+	46.8197i	−0.971622	+	1.68290i
$775$		0			0
$776$	−1.94376	+	3.36670i	−0.0697770	+	0.120857i
$777$	−4.21350	+	7.29799i	−0.151158	+	0.261814i
$778$	−23.3807			−0.838237
$779$	−13.0395	−	23.8125i	−0.467188	−	0.853170i
$780$		0			0
$781$	17.4089	−	30.1531i	0.622939	−	1.07896i
$782$	−16.4831	+	28.5495i	−0.589433	+	1.02093i
$783$	28.2354	+	48.9051i	1.00905	+	1.74773i
$784$	−6.91059	+	11.9695i	−0.246807	+	0.427482i
$785$		0			0
$786$	21.0369			0.750362
$787$	46.5712			1.66008			0.830042	−	0.557700i	$-0.188316\pi$
$787$	46.5712			1.66008			0.830042	+	0.557700i	$0.188316\pi$
$788$	−25.1305	−	43.5273i	−0.895237	−	1.55060i
$789$	22.5778	+	39.1059i	0.803790	+	1.39221i
$790$		0			0
$791$	7.81325			0.277807
$792$	11.3466	+	19.6529i	0.403184	+	0.698336i
$793$	8.00553	−	13.8660i	0.284285	−	0.492395i
$794$	3.36596	+	5.83001i	0.119453	+	0.206899i
$795$		0			0
$796$	−30.6599	+	53.1045i	−1.08671	+	1.88224i
$797$	8.32080			0.294738			0.147369	−	0.989082i	$-0.452920\pi$
$797$	8.32080			0.294738			0.147369	+	0.989082i	$0.452920\pi$
$798$	−16.5152	−	0.373434i	−0.584632	−	0.0132194i
$799$	−13.3973			−0.473962
$800$		0			0
$801$	−10.6172	+	18.3895i	−0.375139	+	0.649760i
$802$	−12.2755	−	21.2619i	−0.433465	−	0.750783i
$803$	−10.8724	+	18.8315i	−0.383678	+	0.664551i
$804$	−17.2043	−	29.7987i	−0.606749	−	1.05092i
$805$		0			0
$806$	−101.540			−3.57659
$807$	−20.8796	−	36.1646i	−0.734998	−	1.27305i
$808$	1.06625	+	1.84680i	0.0375106	+	0.0649703i
$809$	−14.2469			−0.500893			−0.250447	−	0.968130i	$-0.580577\pi$
$809$	−14.2469			−0.500893			−0.250447	+	0.968130i	$0.580577\pi$
$810$		0			0
$811$	16.4331	+	28.4630i	0.577045	+	0.999471i	0.995816	+	0.0913794i	$0.0291276\pi$
$811$	16.4331	+	28.4630i	0.577045	+	0.999471i	−0.418771	+	0.908092i	$0.637539\pi$
$812$	5.64999	−	9.78607i	0.198276	−	0.343424i
$813$	−16.7713	−	29.0488i	−0.588196	−	1.01879i
$814$	13.5106	−	23.4010i	0.473546	−	0.820206i
$815$		0			0
$816$	32.1219			1.12449
$817$	9.12845	+	16.6702i	0.319364	+	0.583218i
$818$	−30.8667			−1.07923
$819$	−11.6056	+	20.1014i	−0.405531	+	0.702400i
$820$		0			0
$821$	−6.58734	−	11.4096i	−0.229900	−	0.398198i	0.727878	−	0.685706i	$-0.240507\pi$
$821$	−6.58734	−	11.4096i	−0.229900	−	0.398198i	−0.957778	+	0.287508i	$0.907173\pi$
$822$	26.1064	−	45.2176i	0.910565	−	1.57714i
$823$	15.5045	+	26.8545i	0.540452	+	0.936090i	0.998878	+	0.0473572i	$0.0150799\pi$
$823$	15.5045	+	26.8545i	0.540452	+	0.936090i	−0.458426	+	0.888732i	$0.651587\pi$
$824$	0.256697			0.00894247
$825$		0			0
$826$	1.87729	+	3.25156i	0.0653192	+	0.113136i
$827$	9.79469	+	16.9649i	0.340595	+	0.589927i	0.984543	−	0.175141i	$-0.0560382\pi$
$827$	9.79469	+	16.9649i	0.340595	+	0.589927i	−0.643949	+	0.765069i	$0.722705\pi$
$828$	−44.9132			−1.56084
$829$	−14.9634			−0.519699			−0.259850	−	0.965649i	$-0.583673\pi$
$829$	−14.9634			−0.519699			−0.259850	+	0.965649i	$0.583673\pi$
$830$		0			0
$831$	−27.9103	+	48.3420i	−0.968196	+	1.67697i
$832$	−42.2685	−	73.2111i	−1.46539	−	2.53814i
$833$	17.4088	−	30.1529i	0.603180	−	1.04474i
$834$	50.0552	−	86.6982i	1.73327	−	3.00211i
$835$		0			0
$836$	30.4660	+	0.688881i	1.05369	+	0.0238255i
$837$	54.5830			1.88666
$838$	−11.9412	+	20.6828i	−0.412502	+	0.714474i
$839$	13.2661	−	22.9776i	0.457997	−	0.793274i	−0.540858	−	0.841114i	$-0.681900\pi$
$839$	13.2661	−	22.9776i	0.457997	−	0.793274i	0.998855	+	0.0478399i	$0.0152337\pi$
$840$		0			0
$841$	−10.3504	+	17.9274i	−0.356911	+	0.618188i
$842$	−24.8745	−	43.0840i	−0.857233	−	1.48477i
$843$	82.3207			2.83528
$844$	33.7022			1.16008
$845$		0			0
$846$	−15.8633	−	27.4761i	−0.545393	−	0.944648i
$847$	2.56838			0.0882505
$848$	−19.9347			−0.684560
$849$	−21.2476	−	36.8019i	−0.729215	−	1.26304i
$850$		0			0
$851$	7.00026	+	12.1248i	0.239966	+	0.415633i
$852$	−53.9544	+	93.4518i	−1.84845	+	3.20160i
$853$	−3.10745	+	5.38226i	−0.106397	+	0.184285i	−0.914308	−	0.405019i	$-0.867265\pi$
$853$	−3.10745	+	5.38226i	−0.106397	+	0.184285i	0.807911	+	0.589304i	$0.200598\pi$
$854$	2.99361			0.102439
$855$		0			0
$856$	−6.95296			−0.237647
$857$	18.6965	−	32.3832i	0.638659	−	1.10619i	−0.347068	−	0.937840i	$-0.612823\pi$
$857$	18.6965	−	32.3832i	0.638659	−	1.10619i	0.985727	−	0.168350i	$-0.0538439\pi$
$858$	56.7526	−	98.2984i	1.93750	−	3.35585i
$859$	21.4745	+	37.1950i	0.732701	+	1.26908i	0.955725	+	0.294263i	$0.0950741\pi$
$859$	21.4745	+	37.1950i	0.732701	+	1.26908i	−0.223023	+	0.974813i	$0.571593\pi$
$860$		0			0
$861$	−5.43859	−	9.41991i	−0.185347	−	0.321030i
$862$	36.8833			1.25625
$863$	37.3005			1.26972			0.634862	−	0.772625i	$-0.281057\pi$
$863$	37.3005			1.26972			0.634862	+	0.772625i	$0.281057\pi$
$864$	30.3931	+	52.6425i	1.03400	+	1.79093i
$865$		0			0
$866$	68.3547			2.32279
$867$	−30.7380			−1.04392
$868$	−5.46112	−	9.45893i	−0.185362	−	0.321057i
$869$	−7.57699	+	13.1237i	−0.257032	+	0.445192i
$870$		0			0
$871$	−14.7717	+	25.5853i	−0.500519	+	0.866925i
$872$	−8.24180	+	14.2752i	−0.279103	+	0.483420i
$873$	−14.4308			−0.488408
$874$	−14.2564	+	23.4520i	−0.482230	+	0.793274i
$875$		0			0
$876$	33.6962	−	58.3635i	1.13849	−	1.97192i
$877$	−18.7681	+	32.5073i	−0.633754	+	1.09769i	0.353024	+	0.935614i	$0.385153\pi$
$877$	−18.7681	+	32.5073i	−0.633754	+	1.09769i	−0.986778	+	0.162079i	$0.948180\pi$
$878$	3.42793	+	5.93735i	0.115687	+	0.200376i
$879$	−3.88435	+	6.72789i	−0.131016	+	0.226926i
$880$		0			0
$881$	24.1432			0.813404			0.406702	−	0.913561i	$-0.366679\pi$
$881$	24.1432			0.813404			0.406702	+	0.913561i	$0.366679\pi$
$882$	82.4530			2.77634
$883$	15.5062	+	26.8575i	0.521825	+	0.903827i	0.999678	+	0.0253873i	$0.00808189\pi$
$883$	15.5062	+	26.8575i	0.521825	+	0.903827i	−0.477853	+	0.878440i	$0.658585\pi$
$884$	48.7019	+	84.3542i	1.63802	+	2.83714i
$885$		0			0
$886$	−25.8119			−0.867167
$887$	18.6066	+	32.2276i	0.624750	+	1.08210i	0.988589	+	0.150637i	$0.0481324\pi$
$887$	18.6066	+	32.2276i	0.624750	+	1.08210i	−0.363839	+	0.931462i	$0.618534\pi$
$888$	−10.9620	+	18.9868i	−0.367862	+	0.637156i
$889$	−0.509269	−	0.882080i	−0.0170803	−	0.0295840i
$890$		0			0
$891$	−8.39201	+	14.5354i	−0.281143	+	0.486954i
$892$	51.9452			1.73925
$893$	−11.1508	−	0.252136i	−0.373146	−	0.00843740i
$894$	20.6274			0.689884
$895$		0			0
$896$	3.41341	−	5.91219i	0.114034	−	0.197513i
$897$	29.4053	+	50.9314i	0.981814	+	1.70055i
$898$	23.0219	−	39.8752i	0.768252	−	1.33065i
$899$	24.0197	+	41.6033i	0.801102	+	1.38755i
$900$		0			0
$901$	50.2185			1.67302
$902$	17.4389	+	30.2050i	0.580650	+	1.00572i
$903$	3.80735	+	6.59453i	0.126701	+	0.219452i
$904$	20.3274			0.676078
$905$		0			0
$906$	35.6247	+	61.7037i	1.18355	+	2.04997i
$907$	4.44080	−	7.69168i	0.147454	−	0.255398i	−0.782832	−	0.622234i	$-0.786225\pi$
$907$	4.44080	−	7.69168i	0.147454	−	0.255398i	0.930286	+	0.366835i	$0.119559\pi$
$908$	−35.9261	−	62.2258i	−1.19225	−	2.06503i
$909$	−3.95801	+	6.85547i	−0.131279	+	0.227382i
$910$		0			0
$911$	−7.31703			−0.242424			−0.121212	−	0.992627i	$-0.538678\pi$
$911$	−7.31703			−0.242424			−0.121212	+	0.992627i	$0.538678\pi$
$912$	26.7355	+	0.604531i	0.885302	+	0.0200180i
$913$	10.3743			0.343341
$914$	10.2175	−	17.6973i	0.337966	−	0.585374i
$915$		0			0
$916$	11.9347	+	20.6715i	0.394333	+	0.683004i
$917$	0.971448	−	1.68260i	0.0320800	−	0.0555642i
$918$	−45.5059	−	78.8184i	−1.50192	−	2.60140i
$919$	−18.1725			−0.599454			−0.299727	−	0.954025i	$-0.596896\pi$
$919$	−18.1725			−0.599454			−0.299727	+	0.954025i	$0.596896\pi$
$920$		0			0
$921$	24.8329	+	43.0118i	0.818271	+	1.41729i
$922$	2.51738	+	4.36023i	0.0829054	+	0.143596i
$923$	92.6509			3.04964
$924$	12.2093			0.401656
$925$		0			0
$926$	15.9675	−	27.6565i	0.524724	−	0.908848i
$927$	0.476440	+	0.825218i	0.0156483	+	0.0271037i
$928$	−26.7495	+	46.3315i	−0.878095	+	1.52091i
$929$	−3.62348	+	6.27605i	−0.118882	+	0.205910i	−0.919325	−	0.393499i	$-0.871265\pi$
$929$	−3.62348	+	6.27605i	−0.118882	+	0.205910i	0.800443	+	0.599409i	$0.204598\pi$
$930$		0			0
$931$	15.0571	−	24.7691i	0.493476	−	0.811774i
$932$	12.2251			0.400447
$933$	−27.0500	+	46.8519i	−0.885576	+	1.53386i
$934$	−12.7760	+	22.1287i	−0.418045	+	0.724074i
$935$		0			0
$936$	−30.1936	+	52.2969i	−0.986909	+	1.70938i
$937$	−0.874288	−	1.51431i	−0.0285618	−	0.0494704i	0.851391	−	0.524531i	$-0.175759\pi$
$937$	−0.874288	−	1.51431i	−0.0285618	−	0.0494704i	−0.879953	+	0.475061i	$0.842426\pi$
$938$	−5.52377			−0.180357
$939$	−69.3848			−2.26429
$940$		0			0
$941$	−14.2280	−	24.6436i	−0.463819	−	0.803359i	0.535328	−	0.844644i	$-0.320188\pi$
$941$	−14.2280	−	24.6436i	−0.463819	−	0.803359i	−0.999147	+	0.0412856i	$0.986855\pi$
$942$	−137.286			−4.47303
$943$	−18.0712			−0.588480
$944$	−3.03903	−	5.26376i	−0.0989121	−	0.171321i
$945$		0			0
$946$	−12.2083	−	21.1454i	−0.396926	−	0.687496i
$947$	5.53560	−	9.58793i	0.179883	−	0.311566i	−0.761957	−	0.647627i	$-0.775762\pi$
$947$	5.53560	−	9.58793i	0.179883	−	0.311566i	0.941840	+	0.336061i	$0.109095\pi$
$948$	23.4829	−	40.6737i	0.762691	−	1.32102i
$949$	−57.8634			−1.87832
$950$		0			0
$951$	−11.4637			−0.371737
$952$	−2.38387	+	4.12899i	−0.0772618	+	0.133821i
$953$	−26.2385	+	45.4464i	−0.849949	+	1.47215i	0.0313045	+	0.999510i	$0.490034\pi$
$953$	−26.2385	+	45.4464i	−0.849949	+	1.47215i	−0.881253	+	0.472644i	$0.843299\pi$
$954$	59.4622	+	102.992i	1.92516	+	3.33447i
$955$		0			0
$956$	10.5991	+	18.3582i	0.342799	+	0.593746i
$957$	−53.7002			−1.73588
$958$	−24.7051			−0.798185
$959$	−2.41109	−	4.17614i	−0.0778583	−	0.134854i
$960$		0			0
$961$	15.4335			0.497854
$962$	71.9040			2.31828
$963$	−12.9050	−	22.3520i	−0.415856	−	0.720284i
$964$	−37.0349	+	64.1464i	−1.19281	+	2.06602i
$965$		0			0
$966$	−5.49795	+	9.52273i	−0.176894	+	0.306389i
$967$	7.63706	−	13.2278i	0.245591	−	0.425376i	−0.716707	−	0.697375i	$-0.754351\pi$
$967$	7.63706	−	13.2278i	0.245591	−	0.425376i	0.962298	+	0.271999i	$0.0876846\pi$
$968$	6.68203			0.214769
$969$	−67.3508	−	1.52290i	−2.16362	−	0.0489227i
$970$		0			0
$971$	−26.3376	+	45.6181i	−0.845215	+	1.46396i	0.0402194	+	0.999191i	$0.487194\pi$
$971$	−26.3376	+	45.6181i	−0.845215	+	1.46396i	−0.885434	+	0.464764i	$0.846139\pi$
$972$	−6.54375	+	11.3341i	−0.209891	+	0.363542i
$973$	−4.62292	−	8.00714i	−0.148204	−	0.256697i
$974$	−5.17634	+	8.96568i	−0.165861	+	0.287279i
$975$		0			0
$976$	−4.84618			−0.155123
$977$	−56.5695			−1.80982			−0.904909	−	0.425605i	$-0.860061\pi$
$977$	−56.5695			−1.80982			−0.904909	+	0.425605i	$0.860061\pi$
$978$	33.0313	+	57.2119i	1.05623	+	1.82944i
$979$	−4.79508	−	8.30532i	−0.153251	−	0.265439i
$980$		0			0
$981$	−61.1883			−1.95359
$982$	−5.43965	−	9.42176i	−0.173586	−	0.300660i
$983$	30.8770	−	53.4806i	0.984825	−	1.70577i	0.342111	−	0.939659i	$-0.388858\pi$
$983$	30.8770	−	53.4806i	0.984825	−	1.70577i	0.642713	−	0.766107i	$-0.277809\pi$
$984$	−14.1493	−	24.5073i	−0.451064	−	0.781265i
$985$		0			0
$986$	40.0504	−	69.3694i	1.27547	−	2.20917i
$987$	−4.46869			−0.142240
$988$	38.9478	+	71.1258i	1.23909	+	2.26281i
$989$	12.6510			0.402278
$990$		0			0
$991$	28.5967	−	49.5310i	0.908404	−	1.57340i	0.0921233	−	0.995748i	$-0.470635\pi$
$991$	28.5967	−	49.5310i	0.908404	−	1.57340i	0.816281	−	0.577655i	$-0.196032\pi$
$992$	25.8553	+	44.7827i	0.820906	+	1.42185i
$993$	4.80892	−	8.32929i	0.152606	−	0.264322i
$994$	8.66154	+	15.0022i	0.274727	+	0.475842i
$995$		0			0
$996$	−32.1526			−1.01879
$997$	−15.4592	−	26.7761i	−0.489597	−	0.848007i	0.510332	−	0.859978i	$-0.329523\pi$
$997$	−15.4592	−	26.7761i	−0.489597	−	0.848007i	−0.999928	+	0.0119712i	$0.996189\pi$
$998$	23.6782	+	41.0118i	0.749519	+	1.29820i
$999$	−38.6521			−1.22290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.h.201.6	yes	12
5.2	odd	4		475.2.j.d.49.11		24
5.3	odd	4		475.2.j.d.49.2		24
5.4	even	2		475.2.e.f.201.1	yes	12
19.7	even	3	inner	475.2.e.h.26.6	yes	12
19.8	odd	6		9025.2.a.by.1.6		6
19.11	even	3		9025.2.a.br.1.1		6
95.7	odd	12		475.2.j.d.349.2		24
95.49	even	6		9025.2.a.bz.1.6		6
95.64	even	6		475.2.e.f.26.1	✓	12
95.83	odd	12		475.2.j.d.349.11		24
95.84	odd	6		9025.2.a.bs.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.1	✓	12	95.64	even	6
475.2.e.f.201.1	yes	12	5.4	even	2
475.2.e.h.26.6	yes	12	19.7	even	3	inner
475.2.e.h.201.6	yes	12	1.1	even	1	trivial
475.2.j.d.49.2		24	5.3	odd	4
475.2.j.d.49.11		24	5.2	odd	4
475.2.j.d.349.2		24	95.7	odd	12
475.2.j.d.349.11		24	95.83	odd	12
9025.2.a.br.1.1		6	19.11	even	3
9025.2.a.bs.1.1		6	95.84	odd	6
9025.2.a.by.1.6		6	19.8	odd	6
9025.2.a.bz.1.6		6	95.49	even	6

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)

\(f(q)\)	\(=\)	\(q+(1.08504 - 1.87935i) q^{2} +(1.47594 - 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} -0.591620 q^{7} -1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +O(q^{10})\)	\(q+(1.08504 - 1.87935i) q^{2} +(1.47594 - 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} -0.591620 q^{7} -1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +2.58045 q^{11} -7.99745 q^{12} +(3.43332 + 5.94669i) q^{13} +(-0.641933 + 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(-2.61787 + 4.53429i) q^{17} -12.3990 q^{18} +(-2.26423 + 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(2.79990 - 4.84957i) q^{22} +(1.45072 + 2.51271i) q^{23} +(-2.27175 + 3.93478i) q^{24} +14.9012 q^{26} -8.01017 q^{27} +(0.801431 + 1.38812i) q^{28} +(-3.52494 - 6.10538i) q^{29} -6.81421 q^{31} +(-3.79432 - 6.57195i) q^{32} +(3.80859 - 6.59667i) q^{33} +(5.68101 + 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} +4.82538 q^{37} +(4.54320 + 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(1.89491 + 3.28208i) q^{42} +(2.18013 - 3.77609i) q^{43} +(-3.49558 - 6.05452i) q^{44} +6.29636 q^{46} +(1.27941 + 2.21600i) q^{47} +(-3.06756 - 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(9.30181 - 16.1112i) q^{52} +(-4.79573 - 8.30645i) q^{53} +(-8.69138 + 15.0539i) q^{54} +0.910615 q^{56} +(6.17993 + 11.2857i) q^{57} -15.2989 q^{58} +(1.46221 - 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(-7.39371 + 12.8063i) q^{62} +(1.69013 + 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(2.15122 + 3.72603i) q^{67} +14.1851 q^{68} +8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(4.39714 + 7.61607i) q^{72} +(-4.21337 + 7.29777i) q^{73} +(5.23574 - 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} -1.52665 q^{77} +(21.9933 - 38.0935i) q^{78} +(-2.93630 + 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(6.75806 + 11.7053i) q^{82} +4.02036 q^{83} +4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} -20.8104 q^{87} -3.97180 q^{88} +(-1.85823 - 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(3.93039 - 6.80764i) q^{92} +(-10.0574 + 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(1.26285 - 2.18732i) q^{97} +(-7.21552 + 12.4977i) q^{98} +(-7.37182 - 12.7684i) 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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