LMFDB - Embedded newform 950.2.e.o.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 10x^{8} - 12x^{7} + 85x^{6} - 70x^{5} + 186x^{4} - 110x^{3} + 285x^{2} - 150x + 100 $ x^10 + 10x^8 - 12x^7 + 85x^6 - 70x^5 + 186x^4 - 110x^3 + 285x^2 - 150x + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$1.17030 - 2.02701i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.o.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.17030 + 2.02701i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17030 + 2.02701i) q^{6} -1.34059 q^{7} -1.00000 q^{8} +(-1.23919 - 2.14634i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.17030 + 2.02701i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17030 + 2.02701i) q^{6} -1.34059 q^{7} -1.00000 q^{8} +(-1.23919 - 2.14634i) q^{9} +3.25749 q^{11} +2.34059 q^{12} +(-0.745938 - 1.29200i) q^{13} +(-0.670297 + 1.16099i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.29230 + 5.70242i) q^{17} -2.47838 q^{18} +(-1.25821 + 4.17336i) q^{19} +(1.56889 - 2.71740i) q^{21} +(1.62875 - 2.82107i) q^{22} +(-1.07564 - 1.86306i) q^{23} +(1.17030 - 2.02701i) q^{24} -1.49188 q^{26} -1.22089 q^{27} +(0.670297 + 1.16099i) q^{28} +(-2.65543 - 4.59933i) q^{29} -2.76561 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.81223 + 6.60298i) q^{33} +(3.29230 + 5.70242i) q^{34} +(-1.23919 + 2.14634i) q^{36} -5.27098 q^{37} +(2.98513 + 3.17632i) q^{38} +3.49188 q^{39} +(-2.79230 + 4.83640i) q^{41} +(-1.56889 - 2.71740i) q^{42} +(-3.81898 + 6.61466i) q^{43} +(-1.62875 - 2.82107i) q^{44} -2.15128 q^{46} +(0.465912 + 0.806983i) q^{47} +(-1.17030 - 2.02701i) q^{48} -5.20281 q^{49} +(-7.70593 - 13.3471i) q^{51} +(-0.745938 + 1.29200i) q^{52} +(-4.54498 - 7.87214i) q^{53} +(-0.610447 + 1.05732i) q^{54} +1.34059 q^{56} +(-6.98698 - 7.43448i) q^{57} -5.31085 q^{58} +(0.0837650 - 0.145085i) q^{59} +(-5.84474 - 10.1234i) q^{61} +(-1.38281 + 2.39509i) q^{62} +(1.66125 + 2.87738i) q^{63} +1.00000 q^{64} +(3.81223 + 6.60298i) q^{66} +(6.53563 + 11.3201i) q^{67} +6.58459 q^{68} +5.03528 q^{69} +(-3.59466 + 6.22613i) q^{71} +(1.23919 + 2.14634i) q^{72} +(-7.62615 + 13.2089i) q^{73} +(-2.63549 + 4.56480i) q^{74} +(4.24334 - 0.997038i) q^{76} -4.36697 q^{77} +(1.74594 - 3.02405i) q^{78} +(7.75423 - 13.4307i) q^{79} +(5.14638 - 8.91380i) q^{81} +(2.79230 + 4.83640i) q^{82} +0.313611 q^{83} -3.13779 q^{84} +(3.81898 + 6.61466i) q^{86} +12.4306 q^{87} -3.25749 q^{88} +(4.90689 + 8.49898i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.07564 + 1.86306i) q^{92} +(3.23659 - 5.60594i) q^{93} +0.931824 q^{94} -2.34059 q^{96} +(6.01504 - 10.4184i) q^{97} +(-2.60140 + 4.50576i) q^{98} +(-4.03665 - 6.99169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9	$ 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{13} + 5 q^{14} - 5 q^{16} - 4 q^{17} - 10 q^{18} + 11 q^{19} + 20 q^{21} - 3 q^{22} - 13 q^{23} + 4 q^{26} - 36 q^{27} - 5 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} - 2 q^{33} + 4 q^{34} - 5 q^{36} - 10 q^{37} + 13 q^{38} + 16 q^{39} + q^{41} - 20 q^{42} + 3 q^{44} - 26 q^{46} + 10 q^{47} - 20 q^{49} + 4 q^{51} + 2 q^{52} - 5 q^{53} - 18 q^{54} - 10 q^{56} + 10 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{61} - 4 q^{62} - 23 q^{63} + 10 q^{64} + 2 q^{66} - 4 q^{67} + 8 q^{68} - 24 q^{69} - 22 q^{71} + 5 q^{72} - 26 q^{73} - 5 q^{74} + 2 q^{76} - 10 q^{77} + 8 q^{78} + 2 q^{79} - 5 q^{81} - q^{82} - 12 q^{83} - 40 q^{84} + 20 q^{87} + 6 q^{88} - q^{89} + 10 q^{91} - 13 q^{92} - 6 q^{93} + 20 q^{94} - 8 q^{97} - 10 q^{98} + 13 q^{99}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^13 + 5 * q^14 - 5 * q^16 - 4 * q^17 - 10 * q^18 + 11 * q^19 + 20 * q^21 - 3 * q^22 - 13 * q^23 + 4 * q^26 - 36 * q^27 - 5 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 - 2 * q^33 + 4 * q^34 - 5 * q^36 - 10 * q^37 + 13 * q^38 + 16 * q^39 + q^41 - 20 * q^42 + 3 * q^44 - 26 * q^46 + 10 * q^47 - 20 * q^49 + 4 * q^51 + 2 * q^52 - 5 * q^53 - 18 * q^54 - 10 * q^56 + 10 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^61 - 4 * q^62 - 23 * q^63 + 10 * q^64 + 2 * q^66 - 4 * q^67 + 8 * q^68 - 24 * q^69 - 22 * q^71 + 5 * q^72 - 26 * q^73 - 5 * q^74 + 2 * q^76 - 10 * q^77 + 8 * q^78 + 2 * q^79 - 5 * q^81 - q^82 - 12 * q^83 - 40 * q^84 + 20 * q^87 + 6 * q^88 - q^89 + 10 * q^91 - 13 * q^92 - 6 * q^93 + 20 * q^94 - 8 * q^97 - 10 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.17030	+	2.02701i	−0.675671	+	1.17030i	0.300601	+	0.953750i	$0.402813\pi$
$3$	−1.17030	+	2.02701i	−0.675671	+	1.17030i	−0.976272	+	0.216547i	$0.930520\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.17030	+	2.02701i	0.477772	+	0.827525i
$7$	−1.34059			−0.506697			−0.253349	−	0.967375i	$-0.581532\pi$
$7$	−1.34059			−0.506697			−0.253349	+	0.967375i	$0.581532\pi$
$8$	−1.00000			−0.353553
$9$	−1.23919	−	2.14634i	−0.413064	−	0.715448i
$10$		0			0
$11$	3.25749			0.982170			0.491085	−	0.871112i	$-0.336600\pi$
$11$	3.25749			0.982170			0.491085	+	0.871112i	$0.336600\pi$
$12$	2.34059			0.675671
$13$	−0.745938	−	1.29200i	−0.206886	−	0.358337i	0.743846	−	0.668351i	$-0.233000\pi$
$13$	−0.745938	−	1.29200i	−0.206886	−	0.358337i	−0.950732	+	0.310014i	$0.899666\pi$
$14$	−0.670297	+	1.16099i	−0.179144	+	0.310287i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.29230	+	5.70242i	−0.798499	+	1.38304i	0.122094	+	0.992519i	$0.461039\pi$
$17$	−3.29230	+	5.70242i	−0.798499	+	1.38304i	−0.920593	+	0.390523i	$0.872294\pi$
$18$	−2.47838			−0.584161
$19$	−1.25821	+	4.17336i	−0.288653	+	0.957434i
$19$	−1.25821	+	4.17336i	−0.288653	+	0.957434i
$20$		0			0
$21$	1.56889	−	2.71740i	0.342361	−	0.592986i
$22$	1.62875	−	2.82107i	0.347250	−	0.601454i
$23$	−1.07564	−	1.86306i	−0.224287	−	0.388476i	0.731819	−	0.681499i	$-0.238672\pi$
$23$	−1.07564	−	1.86306i	−0.224287	−	0.388476i	−0.956105	+	0.293024i	$0.905338\pi$
$24$	1.17030	−	2.02701i	0.238886	−	0.413763i
$25$		0			0
$26$	−1.49188			−0.292581
$27$	−1.22089			−0.234961
$28$	0.670297	+	1.16099i	0.126674	+	0.219406i
$29$	−2.65543	−	4.59933i	−0.493100	−	0.854075i	0.506868	−	0.862024i	$-0.330803\pi$
$29$	−2.65543	−	4.59933i	−0.493100	−	0.854075i	−0.999968	+	0.00794880i	$0.997470\pi$
$30$		0			0
$31$	−2.76561			−0.496719			−0.248360	−	0.968668i	$-0.579891\pi$
$31$	−2.76561			−0.496719			−0.248360	+	0.968668i	$0.579891\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.81223	+	6.60298i	−0.663624	+	1.14943i
$34$	3.29230	+	5.70242i	0.564624	+	0.977958i
$35$		0			0
$36$	−1.23919	+	2.14634i	−0.206532	+	0.357724i
$37$	−5.27098			−0.866544			−0.433272	−	0.901263i	$-0.642641\pi$
$37$	−5.27098			−0.866544			−0.433272	+	0.901263i	$0.642641\pi$
$38$	2.98513	+	3.17632i	0.484252	+	0.515267i
$39$	3.49188			0.559148
$40$		0			0
$41$	−2.79230	+	4.83640i	−0.436083	+	0.755319i	−0.997383	−	0.0722938i	$-0.976968\pi$
$41$	−2.79230	+	4.83640i	−0.436083	+	0.755319i	0.561300	+	0.827612i	$0.310301\pi$
$42$	−1.56889	−	2.71740i	−0.242086	−	0.419305i
$43$	−3.81898	+	6.61466i	−0.582389	+	1.00873i	0.412807	+	0.910819i	$0.364548\pi$
$43$	−3.81898	+	6.61466i	−0.582389	+	1.00873i	−0.995195	+	0.0979082i	$0.968785\pi$
$44$	−1.62875	−	2.82107i	−0.245543	−	0.425292i
$45$		0			0
$46$	−2.15128			−0.317189
$47$	0.465912	+	0.806983i	0.0679602	+	0.117711i	0.898003	−	0.439989i	$-0.145018\pi$
$47$	0.465912	+	0.806983i	0.0679602	+	0.117711i	−0.830043	+	0.557699i	$0.811684\pi$
$48$	−1.17030	−	2.02701i	−0.168918	−	0.292574i
$49$	−5.20281			−0.743258
$50$		0			0
$51$	−7.70593	−	13.3471i	−1.07905	−	1.86896i
$52$	−0.745938	+	1.29200i	−0.103443	+	0.179168i
$53$	−4.54498	−	7.87214i	−0.624301	−	1.08132i	−0.988676	−	0.150069i	$-0.952051\pi$
$53$	−4.54498	−	7.87214i	−0.624301	−	1.08132i	0.364375	−	0.931252i	$-0.381283\pi$
$54$	−0.610447	+	1.05732i	−0.0830713	+	0.143884i
$55$		0			0
$56$	1.34059			0.179144
$57$	−6.98698	−	7.43448i	−0.925448	−	0.984720i
$58$	−5.31085			−0.697349
$59$	0.0837650	−	0.145085i	0.0109053	−	0.0188885i	−0.860521	−	0.509415i	$-0.829862\pi$
$59$	0.0837650	−	0.145085i	0.0109053	−	0.0188885i	0.871427	+	0.490526i	$0.163195\pi$
$60$		0			0
$61$	−5.84474	−	10.1234i	−0.748342	−	1.29617i	−0.948617	−	0.316427i	$-0.897517\pi$
$61$	−5.84474	−	10.1234i	−0.748342	−	1.29617i	0.200274	−	0.979740i	$-0.435817\pi$
$62$	−1.38281	+	2.39509i	−0.175617	+	0.304177i
$63$	1.66125	+	2.87738i	0.209298	+	0.362515i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.81223	+	6.60298i	0.469253	+	0.812771i
$67$	6.53563	+	11.3201i	0.798455	+	1.38296i	0.920622	+	0.390455i	$0.127682\pi$
$67$	6.53563	+	11.3201i	0.798455	+	1.38296i	−0.122167	+	0.992510i	$0.538984\pi$
$68$	6.58459			0.798499
$69$	5.03528			0.606176
$70$		0			0
$71$	−3.59466	+	6.22613i	−0.426607	+	0.738906i	−0.996569	−	0.0827657i	$-0.973625\pi$
$71$	−3.59466	+	6.22613i	−0.426607	+	0.738906i	0.569962	+	0.821671i	$0.306958\pi$
$72$	1.23919	+	2.14634i	0.146040	+	0.252949i
$73$	−7.62615	+	13.2089i	−0.892573	+	1.54598i	−0.0557926	+	0.998442i	$0.517769\pi$
$73$	−7.62615	+	13.2089i	−0.892573	+	1.54598i	−0.836780	+	0.547539i	$0.815565\pi$
$74$	−2.63549	+	4.56480i	−0.306370	+	0.530648i
$75$		0			0
$76$	4.24334	−	0.997038i	0.486744	−	0.114368i
$77$	−4.36697			−0.497663
$78$	1.74594	−	3.02405i	0.197689	−	0.342407i
$79$	7.75423	−	13.4307i	0.872419	−	1.51107i	0.0129320	−	0.999916i	$-0.495883\pi$
$79$	7.75423	−	13.4307i	0.872419	−	1.51107i	0.859487	−	0.511158i	$-0.170783\pi$
$80$		0			0
$81$	5.14638	−	8.91380i	0.571820	−	0.990422i
$82$	2.79230	+	4.83640i	0.308358	+	0.534091i
$83$	0.313611			0.0344233			0.0172116	−	0.999852i	$-0.494521\pi$
$83$	0.313611			0.0344233			0.0172116	+	0.999852i	$0.494521\pi$
$84$	−3.13779			−0.342361
$85$		0			0
$86$	3.81898	+	6.61466i	0.411811	+	0.713278i
$87$	12.4306			1.33270
$88$	−3.25749			−0.347250
$89$	4.90689	+	8.49898i	0.520129	+	0.900890i	0.999726	+	0.0234013i	$0.00744955\pi$
$89$	4.90689	+	8.49898i	0.520129	+	0.900890i	−0.479597	+	0.877489i	$0.659217\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−1.07564	+	1.86306i	−0.112143	+	0.194238i
$93$	3.23659	−	5.60594i	0.335619	−	0.581309i
$94$	0.931824			0.0961103
$95$		0			0
$96$	−2.34059			−0.238886
$97$	6.01504	−	10.4184i	0.610735	−	1.05782i	−0.380382	−	0.924829i	$-0.624208\pi$
$97$	6.01504	−	10.4184i	0.610735	−	1.05782i	0.991117	−	0.132994i	$-0.0424591\pi$
$98$	−2.60140	+	4.50576i	−0.262781	+	0.455151i
$99$	−4.03665	−	6.99169i	−0.405699	−	0.702691i
$100$		0			0
$101$	6.25008	+	10.8255i	0.621907	+	1.07717i	0.989130	+	0.147041i	$0.0469750\pi$
$101$	6.25008	+	10.8255i	0.621907	+	1.07717i	−0.367224	+	0.930133i	$0.619692\pi$
$102$	−15.4119			−1.52600
$103$	8.78740			0.865848			0.432924	−	0.901430i	$-0.357482\pi$
$103$	8.78740			0.865848			0.432924	+	0.901430i	$0.357482\pi$
$104$	0.745938	+	1.29200i	0.0731452	+	0.126691i
$105$		0			0
$106$	−9.08996			−0.882895
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$	0.610447	+	1.05732i	0.0587403	+	0.101741i
$109$	−8.17306	+	14.1562i	−0.782838	+	1.35591i	0.147445	+	0.989070i	$0.452895\pi$
$109$	−8.17306	+	14.1562i	−0.782838	+	1.35591i	−0.930282	+	0.366844i	$0.880438\pi$
$110$		0			0
$111$	6.16862	−	10.6844i	0.585499	−	1.01411i
$112$	0.670297	−	1.16099i	0.0633371	−	0.109703i
$113$	−6.36514			−0.598782			−0.299391	−	0.954131i	$-0.596783\pi$
$113$	−6.36514			−0.598782			−0.299391	+	0.954131i	$0.596783\pi$
$114$	−9.93193	+	2.33366i	−0.930211	+	0.218568i
$115$		0			0
$116$	−2.65543	+	4.59933i	−0.246550	+	0.427037i
$117$	−1.84872	+	3.20208i	−0.170914	+	0.296032i
$118$	−0.0837650	−	0.145085i	−0.00771120	−	0.0133562i
$119$	4.41364	−	7.64464i	0.404597	−	0.700783i
$120$		0			0
$121$	−0.388758			−0.0353416
$122$	−11.6895			−1.05832
$123$	−6.53563	−	11.3201i	−0.589298	−	1.02069i
$124$	1.38281	+	2.39509i	0.124180	+	0.215086i
$125$		0			0
$126$	3.32251			0.295992
$127$	−0.220635	−	0.382151i	−0.0195782	−	0.0339104i	0.856070	−	0.516859i	$-0.172899\pi$
$127$	−0.220635	−	0.382151i	−0.0195782	−	0.0339104i	−0.875649	+	0.482949i	$0.839566\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−8.93868	−	15.4822i	−0.787007	−	1.36314i
$130$		0			0
$131$	−3.56077	+	6.16743i	−0.311106	+	0.538851i	−0.978602	−	0.205762i	$-0.934033\pi$
$131$	−3.56077	+	6.16743i	−0.311106	+	0.538851i	0.667496	+	0.744613i	$0.267366\pi$
$132$	7.62446			0.663624
$133$	1.68675	−	5.59478i	0.146260	−	0.485129i
$134$	13.0713			1.12919
$135$		0			0
$136$	3.29230	−	5.70242i	0.282312	−	0.488979i
$137$	−1.51487	−	2.62383i	−0.129424	−	0.224169i	0.794029	−	0.607879i	$-0.207980\pi$
$137$	−1.51487	−	2.62383i	−0.129424	−	0.224169i	−0.923454	+	0.383710i	$0.874646\pi$
$138$	2.51764	−	4.36068i	0.214316	−	0.371205i
$139$	6.69534	+	11.5967i	0.567891	+	0.983617i	0.996774	+	0.0802567i	$0.0255740\pi$
$139$	6.69534	+	11.5967i	0.567891	+	0.983617i	−0.428883	+	0.903360i	$0.641093\pi$
$140$		0			0
$141$	−2.18102			−0.183675
$142$	3.59466	+	6.22613i	0.301657	+	0.522485i
$143$	−2.42988	−	4.20868i	−0.203197	−	0.351948i
$144$	2.47838			0.206532
$145$		0			0
$146$	7.62615	+	13.2089i	0.631144	+	1.09317i
$147$	6.08883	−	10.5462i	0.502198	−	0.869833i
$148$	2.63549	+	4.56480i	0.216636	+	0.375225i
$149$	−10.9212	+	18.9161i	−0.894700	+	1.54967i	−0.0605252	+	0.998167i	$0.519278\pi$
$149$	−10.9212	+	18.9161i	−0.894700	+	1.54967i	−0.834175	+	0.551500i	$0.814056\pi$
$150$		0			0
$151$	18.3441			1.49282			0.746410	−	0.665486i	$-0.231776\pi$
$151$	18.3441			1.49282			0.746410	+	0.665486i	$0.231776\pi$
$152$	1.25821	−	4.17336i	0.102054	−	0.338504i
$153$	16.3191			1.31932
$154$	−2.18349	+	3.78191i	−0.175950	+	0.304755i
$155$		0			0
$156$	−1.74594	−	3.02405i	−0.139787	−	0.242118i
$157$	3.72080	−	6.44462i	0.296952	−	0.514337i	−0.678485	−	0.734614i	$-0.737363\pi$
$157$	3.72080	−	6.44462i	0.296952	−	0.514337i	0.975437	+	0.220278i	$0.0706964\pi$
$158$	−7.75423	−	13.4307i	−0.616893	−	1.06849i
$159$	21.2759			1.68729
$160$		0			0
$161$	1.44200	+	2.49761i	0.113645	+	0.196839i
$162$	−5.14638	−	8.91380i	−0.404338	−	0.700334i
$163$	15.5400			1.21719			0.608595	−	0.793481i	$-0.291733\pi$
$163$	15.5400			1.21719			0.608595	+	0.793481i	$0.291733\pi$
$164$	5.58459			0.436083
$165$		0			0
$166$	0.156805	−	0.271595i	0.0121705	−	0.0210799i
$167$	−11.0317	−	19.1074i	−0.853655	−	1.47857i	−0.877887	−	0.478868i	$-0.841047\pi$
$167$	−11.0317	−	19.1074i	−0.853655	−	1.47857i	0.0242320	−	0.999706i	$-0.492286\pi$
$168$	−1.56889	+	2.71740i	−0.121043	+	0.209652i
$169$	5.38715	−	9.33082i	0.414396	−	0.717756i
$170$		0			0
$171$	10.5166	−	2.47104i	0.804226	−	0.188965i
$172$	7.63796			0.582389
$173$	−0.190893	+	0.330637i	−0.0145134	+	0.0251379i	−0.873191	−	0.487378i	$-0.837953\pi$
$173$	−0.190893	+	0.330637i	−0.0145134	+	0.0251379i	0.858678	+	0.512516i	$0.171287\pi$
$174$	6.21528	−	10.7652i	0.471179	−	0.816106i
$175$		0			0
$176$	−1.62875	+	2.82107i	−0.122771	+	0.212646i
$177$	0.196060	+	0.339586i	0.0147368	+	0.0255248i
$178$	9.81378			0.735574
$179$	12.1814			0.910477			0.455239	−	0.890369i	$-0.349554\pi$
$179$	12.1814			0.910477			0.455239	+	0.890369i	$0.349554\pi$
$180$		0			0
$181$	0.996021	+	1.72516i	0.0740337	+	0.128230i	0.900666	−	0.434513i	$-0.143079\pi$
$181$	0.996021	+	1.72516i	0.0740337	+	0.128230i	−0.826632	+	0.562743i	$0.809746\pi$
$182$	2.00000			0.148250
$183$	27.3603			2.02253
$184$	1.07564	+	1.86306i	0.0792973	+	0.137347i
$185$		0			0
$186$	−3.23659	−	5.60594i	−0.237318	−	0.411048i
$187$	−10.7246	+	18.5756i	−0.784262	+	1.35838i
$188$	0.465912	−	0.806983i	0.0339801	−	0.0588553i
$189$	1.63672			0.119054
$190$		0			0
$191$	−10.6217			−0.768560			−0.384280	−	0.923217i	$-0.625550\pi$
$191$	−10.6217			−0.768560			−0.384280	+	0.923217i	$0.625550\pi$
$192$	−1.17030	+	2.02701i	−0.0844589	+	0.146287i
$193$	7.64118	−	13.2349i	0.550024	−	0.952670i	−0.448248	−	0.893909i	$-0.647952\pi$
$193$	7.64118	−	13.2349i	0.550024	−	0.952670i	0.998272	−	0.0587608i	$-0.0187149\pi$
$194$	−6.01504	−	10.4184i	−0.431855	−	0.747994i
$195$		0			0
$196$	2.60140	+	4.50576i	0.185814	+	0.321840i
$197$	4.10865			0.292729			0.146365	−	0.989231i	$-0.453243\pi$
$197$	4.10865			0.292729			0.146365	+	0.989231i	$0.453243\pi$
$198$	−8.07331			−0.573745
$199$	5.20281	+	9.01152i	0.368817	+	0.638810i	0.989381	−	0.145346i	$-0.0464295\pi$
$199$	5.20281	+	9.01152i	0.368817	+	0.638810i	−0.620564	+	0.784156i	$0.713096\pi$
$200$		0			0
$201$	−30.5945			−2.15797
$202$	12.5002			0.879509
$203$	3.55985	+	6.16584i	0.249853	+	0.432757i
$204$	−7.70593	+	13.3471i	−0.539523	+	0.934481i
$205$		0			0
$206$	4.39370	−	7.61011i	0.306124	−	0.530222i
$207$	−2.66585	+	4.61739i	−0.185289	+	0.320931i
$208$	1.49188			0.103443
$209$	−4.09860	+	13.5947i	−0.283506	+	0.940363i
$210$		0			0
$211$	6.98513	−	12.0986i	0.480876	−	0.832902i	−0.518883	−	0.854845i	$-0.673652\pi$
$211$	6.98513	−	12.0986i	0.480876	−	0.832902i	0.999759	+	0.0219433i	$0.00698534\pi$
$212$	−4.54498	+	7.87214i	−0.312151	+	0.540661i
$213$	−8.41364	−	14.5728i	−0.576493	−	0.998515i
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$		0			0
$216$	1.22089			0.0830713
$217$	3.70757			0.251686
$218$	8.17306	+	14.1562i	0.553550	+	0.958776i
$219$	−17.8497	−	30.9166i	−1.20617	−	2.08915i
$220$		0			0
$221$	9.82339			0.660793
$222$	−6.16862	−	10.6844i	−0.414010	−	0.717087i
$223$	2.32970	−	4.03516i	0.156008	−	0.270215i	−0.777417	−	0.628985i	$-0.783471\pi$
$223$	2.32970	−	4.03516i	0.156008	−	0.270215i	0.933426	+	0.358771i	$0.116804\pi$
$224$	−0.670297	−	1.16099i	−0.0447861	−	0.0775718i
$225$		0			0
$226$	−3.18257	+	5.51237i	−0.211701	+	0.366677i
$227$	4.14740			0.275273			0.137636	−	0.990483i	$-0.456049\pi$
$227$	4.14740			0.275273			0.137636	+	0.990483i	$0.456049\pi$
$228$	−2.94496	+	9.76814i	−0.195034	+	0.646911i
$229$	−20.8071			−1.37497			−0.687487	−	0.726196i	$-0.741286\pi$
$229$	−20.8071			−1.37497			−0.687487	+	0.726196i	$0.741286\pi$
$230$		0			0
$231$	5.11066	−	8.85192i	0.336257	−	0.582414i
$232$	2.65543	+	4.59933i	0.174337	+	0.301961i
$233$	0.506444	−	0.877186i	0.0331782	−	0.0574664i	−0.848960	−	0.528458i	$-0.822770\pi$
$233$	0.506444	−	0.877186i	0.0331782	−	0.0574664i	0.882138	+	0.470992i	$0.156104\pi$
$234$	1.84872	+	3.20208i	0.120855	+	0.209326i
$235$		0			0
$236$	−0.167530			−0.0109053
$237$	18.1495	+	31.4359i	1.17894	+	2.04198i
$238$	−4.41364	−	7.64464i	−0.286093	−	0.495528i
$239$	−22.7248			−1.46994			−0.734971	−	0.678098i	$-0.762804\pi$
$239$	−22.7248			−1.46994			−0.734971	+	0.678098i	$0.762804\pi$
$240$		0			0
$241$	7.36702	+	12.7600i	0.474551	+	0.821947i	0.999575	−	0.0291404i	$-0.00927699\pi$
$241$	7.36702	+	12.7600i	0.474551	+	0.821947i	−0.525024	+	0.851087i	$0.675944\pi$
$242$	−0.194379	+	0.336674i	−0.0124952	+	0.0216422i
$243$	10.2143	+	17.6916i	0.655245	+	1.13492i
$244$	−5.84474	+	10.1234i	−0.374171	+	0.648083i
$245$		0			0
$246$	−13.0713			−0.833394
$247$	6.33053	−	1.48746i	0.402802	−	0.0946446i
$248$	2.76561			0.175617
$249$	−0.367018	+	0.635694i	−0.0232588	+	0.0402854i
$250$		0			0
$251$	−9.81668	−	17.0030i	−0.619623	−	1.07322i	−0.989554	−	0.144160i	$-0.953952\pi$
$251$	−9.81668	−	17.0030i	−0.619623	−	1.07322i	0.369931	−	0.929059i	$-0.379381\pi$
$252$	1.66125	−	2.87738i	0.104649	−	0.181258i
$253$	−3.50389	−	6.06891i	−0.220288	−	0.381549i
$254$	−0.441270			−0.0276877
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.29075	−	2.23565i	−0.0805148	−	0.139456i	0.822956	−	0.568105i	$-0.192323\pi$
$257$	−1.29075	−	2.23565i	−0.0805148	−	0.139456i	−0.903471	+	0.428649i	$0.858990\pi$
$258$	−17.8774			−1.11300
$259$	7.06625			0.439075
$260$		0			0
$261$	−6.58117	+	11.3989i	−0.407364	+	0.705575i
$262$	3.56077	+	6.16743i	0.219985	+	0.381025i
$263$	3.93122	−	6.80906i	0.242409	−	0.419865i	−0.718991	−	0.695020i	$-0.755396\pi$
$263$	3.93122	−	6.80906i	0.242409	−	0.419865i	0.961400	+	0.275155i	$0.0887290\pi$
$264$	3.81223	−	6.60298i	0.234627	−	0.406385i
$265$		0			0
$266$	−4.00185	−	4.25816i	−0.245369	−	0.261084i
$267$	−22.9701			−1.40575
$268$	6.53563	−	11.3201i	0.399227	−	0.691482i
$269$	−1.04119	+	1.80340i	−0.0634826	+	0.109955i	−0.896020	−	0.444014i	$-0.853554\pi$
$269$	−1.04119	+	1.80340i	−0.0634826	+	0.109955i	0.832537	+	0.553969i	$0.186887\pi$
$270$		0			0
$271$	−5.38624	+	9.32923i	−0.327190	+	0.566711i	−0.981953	−	0.189124i	$-0.939435\pi$
$271$	−5.38624	+	9.32923i	−0.327190	+	0.566711i	0.654763	+	0.755834i	$0.272769\pi$
$272$	−3.29230	−	5.70242i	−0.199625	−	0.345760i
$273$	−4.68119			−0.283318
$274$	−3.02974			−0.183033
$275$		0			0
$276$	−2.51764	−	4.36068i	−0.151544	−	0.262482i
$277$	8.52030			0.511935			0.255967	−	0.966685i	$-0.417606\pi$
$277$	8.52030			0.511935			0.255967	+	0.966685i	$0.417606\pi$
$278$	13.3907			0.803120
$279$	3.42713	+	5.93596i	0.205177	+	0.355377i
$280$		0			0
$281$	−3.29766	−	5.71172i	−0.196722	−	0.340733i	0.750742	−	0.660596i	$-0.229696\pi$
$281$	−3.29766	−	5.71172i	−0.196722	−	0.340733i	−0.947464	+	0.319863i	$0.896363\pi$
$282$	−1.09051	+	1.88882i	−0.0649390	+	0.112478i
$283$	−3.36481	+	5.82802i	−0.200017	+	0.346440i	−0.948534	−	0.316676i	$-0.897433\pi$
$283$	−3.36481	+	5.82802i	−0.200017	+	0.346440i	0.748516	+	0.663116i	$0.230766\pi$
$284$	7.18931			0.426607
$285$		0			0
$286$	−4.85977			−0.287364
$287$	3.74334	−	6.48365i	0.220962	−	0.382718i
$288$	1.23919	−	2.14634i	0.0730201	−	0.126474i
$289$	−13.1784	−	22.8257i	−0.775202	−	1.34269i
$290$		0			0
$291$	14.0788	+	24.3851i	0.825312	+	1.42948i
$292$	15.2523			0.892573
$293$	1.06829			0.0624103			0.0312051	−	0.999513i	$-0.490065\pi$
$293$	1.06829			0.0624103			0.0312051	+	0.999513i	$0.490065\pi$
$294$	−6.08883	−	10.5462i	−0.355108	−	0.615065i
$295$		0			0
$296$	5.27098			0.306370
$297$	−3.97705			−0.230772
$298$	10.9212	+	18.9161i	0.632649	+	1.09578i
$299$	−1.60472	+	2.77946i	−0.0928034	+	0.160740i
$300$		0			0
$301$	5.11970	−	8.86758i	0.295095	−	0.511119i
$302$	9.17204	−	15.8864i	0.527792	−	0.914162i
$303$	−29.2578			−1.68082
$304$	−2.98513	−	3.17632i	−0.171209	−	0.182174i
$305$		0			0
$306$	8.15957	−	14.1328i	0.466452	−	0.807918i
$307$	−1.67862	+	2.90746i	−0.0958041	+	0.165937i	−0.909944	−	0.414731i	$-0.863876\pi$
$307$	−1.67862	+	2.90746i	−0.0958041	+	0.165937i	0.814140	+	0.580669i	$0.197209\pi$
$308$	2.18349	+	3.78191i	0.124416	+	0.215494i
$309$	−10.2839	+	17.8122i	−0.585029	+	1.01330i
$310$		0			0
$311$	−7.70225			−0.436755			−0.218377	−	0.975864i	$-0.570076\pi$
$311$	−7.70225			−0.436755			−0.218377	+	0.975864i	$0.570076\pi$
$312$	−3.49188			−0.197689
$313$	2.87534	+	4.98024i	0.162524	+	0.281500i	0.935773	−	0.352602i	$-0.114703\pi$
$313$	2.87534	+	4.98024i	0.162524	+	0.281500i	−0.773249	+	0.634102i	$0.781370\pi$
$314$	−3.72080	−	6.44462i	−0.209977	−	0.363691i
$315$		0			0
$316$	−15.5085			−0.872419
$317$	−8.71462	−	15.0942i	−0.489462	−	0.847772i	0.510465	−	0.859899i	$-0.329473\pi$
$317$	−8.71462	−	15.0942i	−0.489462	−	0.847772i	−0.999926	+	0.0121262i	$0.996140\pi$
$318$	10.6380	−	18.4255i	0.596547	−	1.03325i
$319$	−8.65003	−	14.9823i	−0.484308	−	0.838847i
$320$		0			0
$321$	−11.7030	+	20.2701i	−0.653196	+	1.13137i
$322$	2.88400			0.160719
$323$	−19.6559	−	20.9148i	−1.09368	−	1.16373i
$324$	−10.2928			−0.571820
$325$		0			0
$326$	7.77002	−	13.4581i	0.430342	−	0.745373i
$327$	−19.1298	−	33.1338i	−1.05788	−	1.83231i
$328$	2.79230	−	4.83640i	0.154179	−	0.267045i
$329$	−0.624599	−	1.08184i	−0.0344353	−	0.0596436i
$330$		0			0
$331$	−12.1108			−0.665670			−0.332835	−	0.942985i	$-0.608005\pi$
$331$	−12.1108			−0.665670			−0.332835	+	0.942985i	$0.608005\pi$
$332$	−0.156805	−	0.271595i	−0.00860581	−	0.0149057i
$333$	6.53176	+	11.3133i	0.357938	+	0.619967i
$334$	−22.0633			−1.20725
$335$		0			0
$336$	1.56889	+	2.71740i	0.0855902	+	0.148247i
$337$	16.1078	−	27.8995i	0.877445	−	1.51978i	0.0233106	−	0.999728i	$-0.492579\pi$
$337$	16.1078	−	27.8995i	0.877445	−	1.51978i	0.854135	−	0.520052i	$-0.174087\pi$
$338$	−5.38715	−	9.33082i	−0.293023	−	0.507530i
$339$	7.44910	−	12.9022i	0.404580	−	0.700753i
$340$		0			0
$341$	−9.00896			−0.487863
$342$	3.11832	−	10.3432i	0.168620	−	0.559295i
$343$	16.3590			0.883304
$344$	3.81898	−	6.61466i	0.205905	−	0.356639i
$345$		0			0
$346$	0.190893	+	0.330637i	0.0102625	+	0.0177752i
$347$	−15.2549	+	26.4222i	−0.818924	+	1.41842i	0.0875523	+	0.996160i	$0.472095\pi$
$347$	−15.2549	+	26.4222i	−0.818924	+	1.41842i	−0.906476	+	0.422257i	$0.861238\pi$
$348$	−6.21528	−	10.7652i	−0.333174	−	0.577074i
$349$	26.3315			1.40949			0.704747	−	0.709459i	$-0.251061\pi$
$349$	26.3315			1.40949			0.704747	+	0.709459i	$0.251061\pi$
$350$		0			0
$351$	0.910710	+	1.57740i	0.0486101	+	0.0841952i
$352$	1.62875	+	2.82107i	0.0868124	+	0.150363i
$353$	−0.368812			−0.0196299			−0.00981493	−	0.999952i	$-0.503124\pi$
$353$	−0.368812			−0.0196299			−0.00981493	+	0.999952i	$0.503124\pi$
$354$	0.392120			0.0208409
$355$		0			0
$356$	4.90689	−	8.49898i	0.260065	−	0.450445i
$357$	10.3305	+	17.8930i	0.546750	+	0.946998i
$358$	6.09068	−	10.5494i	0.321902	−	0.557551i
$359$	−14.7532	+	25.5533i	−0.778645	+	1.34865i	0.154079	+	0.988059i	$0.450759\pi$
$359$	−14.7532	+	25.5533i	−0.778645	+	1.34865i	−0.932723	+	0.360593i	$0.882574\pi$
$360$		0			0
$361$	−15.8338	−	10.5019i	−0.833359	−	0.552732i
$362$	1.99204			0.104699
$363$	0.454962	−	0.788018i	0.0238793	−	0.0413602i
$364$	1.00000	−	1.73205i	0.0524142	−	0.0907841i
$365$		0			0
$366$	13.6802	−	23.6947i	0.715074	−	1.23854i
$367$	9.16862	+	15.8805i	0.478598	+	0.828956i	0.999699	−	0.0245392i	$-0.00781185\pi$
$367$	9.16862	+	15.8805i	0.478598	+	0.828956i	−0.521101	+	0.853495i	$0.674479\pi$
$368$	2.15128			0.112143
$369$	13.8408			0.720521
$370$		0			0
$371$	6.09298	+	10.5533i	0.316332	+	0.547902i
$372$	−6.47318			−0.335619
$373$	−20.1928			−1.04554			−0.522772	−	0.852473i	$-0.675102\pi$
$373$	−20.1928			−1.04554			−0.522772	+	0.852473i	$0.675102\pi$
$374$	10.7246	+	18.5756i	0.554557	+	0.960521i
$375$		0			0
$376$	−0.465912	−	0.806983i	−0.0240276	−	0.0416170i
$377$	−3.96157	+	6.86163i	−0.204031	+	0.353392i
$378$	0.818361	−	1.41744i	0.0420920	−	0.0729054i
$379$	15.2700			0.784367			0.392183	−	0.919887i	$-0.371720\pi$
$379$	15.2700			0.784367			0.392183	+	0.919887i	$0.371720\pi$
$380$		0			0
$381$	1.03283			0.0529137
$382$	−5.31085	+	9.19867i	−0.271727	+	0.470645i
$383$	−13.4026	+	23.2139i	−0.684838	+	1.18617i	0.288649	+	0.957435i	$0.406794\pi$
$383$	−13.4026	+	23.2139i	−0.684838	+	1.18617i	−0.973488	+	0.228740i	$0.926539\pi$
$384$	1.17030	+	2.02701i	0.0597215	+	0.103441i
$385$		0			0
$386$	−7.64118	−	13.2349i	−0.388926	−	0.673640i
$387$	18.9298			0.962255
$388$	−12.0301			−0.610735
$389$	12.1644	+	21.0694i	0.616761	+	1.06826i	0.990073	+	0.140556i	$0.0448890\pi$
$389$	12.1644	+	21.0694i	0.616761	+	1.06826i	−0.373311	+	0.927706i	$0.621778\pi$
$390$		0			0
$391$	14.1653			0.716370
$392$	5.20281			0.262781
$393$	−8.33432	−	14.4355i	−0.420411	−	0.728173i
$394$	2.05433	−	3.55820i	0.103495	−	0.179259i
$395$		0			0
$396$	−4.03665	+	6.99169i	−0.202850	+	0.351346i
$397$	−9.53415	+	16.5136i	−0.478505	+	0.828795i	−0.999696	−	0.0246449i	$-0.992155\pi$
$397$	−9.53415	+	16.5136i	−0.478505	+	0.828795i	0.521191	+	0.853440i	$0.325488\pi$
$398$	10.4056			0.521586
$399$	9.36670	+	9.96662i	0.468922	+	0.498955i
$400$		0			0
$401$	4.80098	−	8.31554i	0.239750	−	0.415258i	−0.720893	−	0.693047i	$-0.756268\pi$
$401$	4.80098	−	8.31554i	0.239750	−	0.415258i	0.960642	+	0.277788i	$0.0896013\pi$
$402$	−15.2973	+	26.4956i	−0.762958	+	1.32148i
$403$	2.06298	+	3.57318i	0.102764	+	0.177993i
$404$	6.25008	−	10.8255i	0.310953	−	0.538587i
$405$		0			0
$406$	7.11970			0.353345
$407$	−17.1702			−0.851094
$408$	7.70593	+	13.3471i	0.381500	+	0.660778i
$409$	11.3689	+	19.6916i	0.562158	+	0.973685i	0.997308	+	0.0733276i	$0.0233619\pi$
$409$	11.3689	+	19.6916i	0.562158	+	0.973685i	−0.435150	+	0.900358i	$0.643305\pi$
$410$		0			0
$411$	7.09140			0.349793
$412$	−4.39370	−	7.61011i	−0.216462	−	0.374923i
$413$	−0.112295	+	0.194501i	−0.00552567	+	0.00957075i
$414$	2.66585	+	4.61739i	0.131019	+	0.226932i
$415$		0			0
$416$	0.745938	−	1.29200i	0.0365726	−	0.0633456i
$417$	−31.3422			−1.53483
$418$	9.72403	+	10.3468i	0.475618	+	0.506080i
$419$	36.5783			1.78697			0.893483	−	0.449097i	$-0.148254\pi$
$419$	36.5783			1.78697			0.893483	+	0.449097i	$0.148254\pi$
$420$		0			0
$421$	−5.51620	+	9.55434i	−0.268843	+	0.465650i	−0.968563	−	0.248767i	$-0.919975\pi$
$421$	−5.51620	+	9.55434i	−0.268843	+	0.465650i	0.699720	+	0.714417i	$0.253308\pi$
$422$	−6.98513	−	12.0986i	−0.340031	−	0.588951i
$423$	1.15471	−	2.00001i	0.0561438	−	0.0972440i
$424$	4.54498	+	7.87214i	0.220724	+	0.382305i
$425$		0			0
$426$	−16.8273			−0.815284
$427$	7.83543	+	13.5714i	0.379183	+	0.656764i
$428$	−5.00000	−	8.66025i	−0.241684	−	0.418609i
$429$	11.3747			0.549178
$430$		0			0
$431$	10.4489	+	18.0980i	0.503306	+	0.871752i	0.999993	+	0.00382204i	$0.00121659\pi$
$431$	10.4489	+	18.0980i	0.503306	+	0.871752i	−0.496686	+	0.867930i	$0.665450\pi$
$432$	0.610447	−	1.05732i	0.0293701	−	0.0508705i
$433$	7.12477	+	12.3405i	0.342394	+	0.593045i	0.984877	−	0.173256i	$-0.0554288\pi$
$433$	7.12477	+	12.3405i	0.342394	+	0.593045i	−0.642482	+	0.766300i	$0.722095\pi$
$434$	1.85378	−	3.21085i	0.0889845	−	0.154126i
$435$		0			0
$436$	16.3461			0.782838
$437$	9.12861	−	2.14491i	0.436681	−	0.102605i
$438$	−35.6994			−1.70578
$439$	5.25331	−	9.09900i	0.250727	−	0.434272i	−0.712999	−	0.701165i	$-0.752664\pi$
$439$	5.25331	−	9.09900i	0.250727	−	0.434272i	0.963726	+	0.266893i	$0.0859971\pi$
$440$		0			0
$441$	6.44727	+	11.1670i	0.307013	+	0.531762i
$442$	4.91170	−	8.50731i	0.233626	−	0.404651i
$443$	19.2281	+	33.3040i	0.913553	+	1.58232i	0.809006	+	0.587801i	$0.200006\pi$
$443$	19.2281	+	33.3040i	0.913553	+	1.58232i	0.104548	+	0.994520i	$0.466660\pi$
$444$	−12.3372			−0.585499
$445$		0			0
$446$	−2.32970	−	4.03516i	−0.110315	−	0.191071i
$447$	−25.5621	−	44.2749i	−1.20905	−	2.09413i
$448$	−1.34059			−0.0633371
$449$	−26.9402			−1.27139			−0.635694	−	0.771941i	$-0.719286\pi$
$449$	−26.9402			−1.27139			−0.635694	+	0.771941i	$0.719286\pi$
$450$		0			0
$451$	−9.09588	+	15.7545i	−0.428308	+	0.741852i
$452$	3.18257	+	5.51237i	0.149695	+	0.259280i
$453$	−21.4680	+	37.1837i	−1.00866	+	1.74704i
$454$	2.07370	−	3.59176i	0.0973236	−	0.168569i
$455$		0			0
$456$	6.98698	+	7.43448i	0.327195	+	0.348151i
$457$	14.6472			0.685166			0.342583	−	0.939488i	$-0.388698\pi$
$457$	14.6472			0.685166			0.342583	+	0.939488i	$0.388698\pi$
$458$	−10.4036	+	18.0195i	−0.486127	+	0.841997i
$459$	4.01954	−	6.96205i	0.187616	−	0.324961i
$460$		0			0
$461$	0.104103	−	0.180311i	0.00484855	−	0.00839794i	−0.863591	−	0.504193i	$-0.831790\pi$
$461$	0.104103	−	0.180311i	0.00484855	−	0.00839794i	0.868440	+	0.495795i	$0.165123\pi$
$462$	−5.11066	−	8.85192i	−0.237769	−	0.411829i
$463$	−24.6580			−1.14596			−0.572978	−	0.819571i	$-0.694212\pi$
$463$	−24.6580			−1.14596			−0.572978	+	0.819571i	$0.694212\pi$
$464$	5.31085			0.246550
$465$		0			0
$466$	−0.506444	−	0.877186i	−0.0234605	−	0.0406349i
$467$	−22.4281			−1.03785			−0.518925	−	0.854820i	$-0.673668\pi$
$467$	−22.4281			−1.03785			−0.518925	+	0.854820i	$0.673668\pi$
$468$	3.69744			0.170914
$469$	−8.76164	−	15.1756i	−0.404575	−	0.700744i
$470$		0			0
$471$	8.70889	+	15.0842i	0.401284	+	0.695045i
$472$	−0.0837650	+	0.145085i	−0.00385560	+	0.00667809i
$473$	−12.4403	+	21.5472i	−0.572005	+	0.990741i
$474$	36.2990			1.66727
$475$		0			0
$476$	−8.82727			−0.404597
$477$	−11.2642	+	19.5102i	−0.515752	+	0.893309i
$478$	−11.3624	+	19.6802i	−0.519703	+	0.900152i
$479$	−8.17582	−	14.1609i	−0.373563	−	0.647030i	0.616548	−	0.787317i	$-0.288531\pi$
$479$	−8.17582	−	14.1609i	−0.373563	−	0.647030i	−0.990111	+	0.140288i	$0.955197\pi$
$480$		0			0
$481$	3.93182	+	6.81012i	0.179276	+	0.310515i
$482$	14.7340			0.671117
$483$	−6.75026			−0.307148
$484$	0.194379	+	0.336674i	0.00883541	+	0.0153034i
$485$		0			0
$486$	20.4285			0.926656
$487$	40.7859			1.84819			0.924093	−	0.382168i	$-0.124823\pi$
$487$	40.7859			1.84819			0.924093	+	0.382168i	$0.124823\pi$
$488$	5.84474	+	10.1234i	0.264579	+	0.458264i
$489$	−18.1865	+	31.4999i	−0.822420	+	1.42447i
$490$		0			0
$491$	−11.1912	+	19.3838i	−0.505053	+	0.874778i	0.494930	+	0.868933i	$0.335194\pi$
$491$	−11.1912	+	19.3838i	−0.505053	+	0.874778i	−0.999983	+	0.00584462i	$0.998140\pi$
$492$	−6.53563	+	11.3201i	−0.294649	+	0.510347i
$493$	34.9698			1.57496
$494$	1.87709	−	6.22613i	0.0844543	−	0.280127i
$495$		0			0
$496$	1.38281	−	2.39509i	0.0620899	−	0.107543i
$497$	4.81898	−	8.34671i	0.216161	−	0.374401i
$498$	0.367018	+	0.635694i	0.0164465	+	0.0284861i
$499$	4.07719	−	7.06189i	0.182520	−	0.316134i	−0.760218	−	0.649668i	$-0.774908\pi$
$499$	4.07719	−	7.06189i	0.182520	−	0.316134i	0.942738	+	0.333534i	$0.108241\pi$
$500$		0			0
$501$	51.6413			2.30716
$502$	−19.6334			−0.876280
$503$	−12.0711	−	20.9078i	−0.538224	−	0.932232i	−0.999000	−	0.0447150i	$-0.985762\pi$
$503$	−12.0711	−	20.9078i	−0.538224	−	0.932232i	0.460776	−	0.887517i	$-0.347571\pi$
$504$	−1.66125	−	2.87738i	−0.0739981	−	0.128169i
$505$		0			0
$506$	−7.00778			−0.311534
$507$	12.6091	+	21.8397i	0.559992	+	0.969934i
$508$	−0.220635	+	0.382151i	−0.00978909	+	0.0169552i
$509$	7.16576	+	12.4115i	0.317617	+	0.550128i	0.979990	−	0.199046i	$-0.0637842\pi$
$509$	7.16576	+	12.4115i	0.317617	+	0.550128i	−0.662374	+	0.749174i	$0.730451\pi$
$510$		0			0
$511$	10.2236	−	17.7077i	0.452264	−	0.783344i
$512$	−1.00000			−0.0441942
$513$	1.53614	−	5.09522i	0.0678222	−	0.224960i
$514$	−2.58150			−0.113865
$515$		0			0
$516$	−8.93868	+	15.4822i	−0.393503	+	0.681568i
$517$	1.51770	+	2.62874i	0.0667485	+	0.115612i
$518$	3.53313	−	6.11955i	0.155237	−	0.268878i
$519$	−0.446804	−	0.773888i	−0.0196125	−	0.0339699i
$520$		0			0
$521$	3.10621			0.136086			0.0680428	−	0.997682i	$-0.478325\pi$
$521$	3.10621			0.136086			0.0680428	+	0.997682i	$0.478325\pi$
$522$	6.58117	+	11.3989i	0.288050	+	0.498917i
$523$	−11.5122	−	19.9398i	−0.503394	−	0.871905i	−0.999992	−	0.00392391i	$-0.998751\pi$
$523$	−11.5122	−	19.9398i	−0.503394	−	0.871905i	0.496598	−	0.867981i	$-0.334582\pi$
$524$	7.12154			0.311106
$525$		0			0
$526$	−3.93122	−	6.80906i	−0.171409	−	0.296889i
$527$	9.10522	−	15.7707i	0.396630	−	0.686983i
$528$	−3.81223	−	6.60298i	−0.165906	−	0.287358i
$529$	9.18600	−	15.9106i	0.399391	−	0.691766i
$530$		0			0
$531$	−0.415204			−0.0180183
$532$	−5.68860	+	1.33662i	−0.246632	+	0.0579500i
$533$	8.33152			0.360878
$534$	−11.4850	+	19.8927i	−0.497006	+	0.860840i
$535$		0			0
$536$	−6.53563	−	11.3201i	−0.282296	−	0.488952i
$537$	−14.2558	+	24.6918i	−0.615184	+	1.06553i
$538$	1.04119	+	1.80340i	0.0448890	+	0.0777500i
$539$	−16.9481			−0.730006
$540$		0			0
$541$	10.2489	+	17.7516i	0.440633	+	0.763199i	0.997737	−	0.0672443i	$-0.0214207\pi$
$541$	10.2489	+	17.7516i	0.440633	+	0.763199i	−0.557104	+	0.830443i	$0.688087\pi$
$542$	5.38624	+	9.32923i	0.231359	+	0.400725i
$543$	−4.66256			−0.200090
$544$	−6.58459			−0.282312
$545$		0			0
$546$	−2.34059	+	4.05403i	−0.100168	+	0.173496i
$547$	6.62783	+	11.4797i	0.283385	+	0.490838i	0.972216	−	0.234084i	$-0.0752091\pi$
$547$	6.62783	+	11.4797i	0.283385	+	0.490838i	−0.688831	+	0.724922i	$0.741876\pi$
$548$	−1.51487	+	2.62383i	−0.0647121	+	0.112085i
$549$	−14.4855	+	25.0896i	−0.618226	+	1.07080i
$550$		0			0
$551$	22.5357	−	5.29512i	0.960055	−	0.225580i
$552$	−5.03528			−0.214316
$553$	−10.3953	+	18.0052i	−0.442052	+	0.765657i
$554$	4.26015	−	7.37879i	0.180996	−	0.313495i
$555$		0			0
$556$	6.69534	−	11.5967i	0.283946	−	0.491808i
$557$	−12.1148	−	20.9834i	−0.513319	−	0.889094i	−0.999881	−	0.0154482i	$-0.995082\pi$
$557$	−12.1148	−	20.9834i	−0.513319	−	0.889094i	0.486562	−	0.873646i	$-0.338251\pi$
$558$	6.85425			0.290164
$559$	11.3949			0.481952
$560$		0			0
$561$	−25.1020	−	43.4779i	−1.05981	−	1.83564i
$562$	−6.59533			−0.278207
$563$	−27.1643			−1.14484			−0.572420	−	0.819961i	$-0.693995\pi$
$563$	−27.1643			−1.14484			−0.572420	+	0.819961i	$0.693995\pi$
$564$	1.09051	+	1.88882i	0.0459188	+	0.0795337i
$565$		0			0
$566$	3.36481	+	5.82802i	0.141434	+	0.244970i
$567$	−6.89921	+	11.9498i	−0.289740	+	0.501844i
$568$	3.59466	−	6.22613i	0.150828	−	0.261243i
$569$	−43.8600			−1.83871			−0.919353	−	0.393433i	$-0.871287\pi$
$569$	−43.8600			−1.83871			−0.919353	+	0.393433i	$0.871287\pi$
$570$		0			0
$571$	30.5834			1.27988			0.639938	−	0.768427i	$-0.278960\pi$
$571$	30.5834			1.27988			0.639938	+	0.768427i	$0.278960\pi$
$572$	−2.42988	+	4.20868i	−0.101599	+	0.175974i
$573$	12.4306	−	21.5304i	0.519294	−	0.899443i
$574$	−3.74334	−	6.48365i	−0.156244	−	0.270622i
$575$		0			0
$576$	−1.23919	−	2.14634i	−0.0516330	−	0.0894310i
$577$	40.9572			1.70507			0.852536	−	0.522669i	$-0.175064\pi$
$577$	40.9572			1.70507			0.852536	+	0.522669i	$0.175064\pi$
$578$	−26.3569			−1.09630
$579$	17.8849	+	30.9776i	0.743272	+	1.28738i
$580$		0			0
$581$	−0.420425			−0.0174422
$582$	28.1575			1.16717
$583$	−14.8052	−	25.6434i	−0.613170	−	1.06204i
$584$	7.62615	−	13.2089i	0.315572	−	0.546587i
$585$		0			0
$586$	0.534146	−	0.925168i	0.0220654	−	0.0382183i
$587$	−8.82971	+	15.2935i	−0.364441	+	0.631231i	−0.988686	−	0.149998i	$-0.952073\pi$
$587$	−8.82971	+	15.2935i	−0.364441	+	0.631231i	0.624245	+	0.781229i	$0.285407\pi$
$588$	−12.1777			−0.502198
$589$	3.47972	−	11.5419i	0.143379	−	0.475576i
$590$		0			0
$591$	−4.80834	+	8.32830i	−0.197789	+	0.342580i
$592$	2.63549	−	4.56480i	0.108318	−	0.187612i
$593$	−10.4599	−	18.1171i	−0.429538	−	0.743982i	0.567294	−	0.823515i	$-0.307990\pi$
$593$	−10.4599	−	18.1171i	−0.429538	−	0.743982i	−0.996832	+	0.0795335i	$0.974657\pi$
$594$	−1.98852	+	3.44422i	−0.0815901	+	0.141318i
$595$		0			0
$596$	21.8424			0.894700
$597$	−24.3553			−0.996797
$598$	1.60472	+	2.77946i	0.0656219	+	0.113661i
$599$	−6.31990	−	10.9464i	−0.258224	−	0.447257i	0.707542	−	0.706671i	$-0.249804\pi$
$599$	−6.31990	−	10.9464i	−0.258224	−	0.447257i	−0.965766	+	0.259414i	$0.916471\pi$
$600$		0			0
$601$	−43.8933			−1.79045			−0.895223	−	0.445618i	$-0.852984\pi$
$601$	−43.8933			−1.79045			−0.895223	+	0.445618i	$0.852984\pi$
$602$	−5.11970	−	8.86758i	−0.208663	−	0.361416i
$603$	16.1978	−	28.0554i	0.659626	−	1.14251i
$604$	−9.17204	−	15.8864i	−0.373205	−	0.646410i
$605$		0			0
$606$	−14.6289	+	25.3380i	−0.594259	+	1.02929i
$607$	0.939196			0.0381208			0.0190604	−	0.999818i	$-0.493933\pi$
$607$	0.939196			0.0381208			0.0190604	+	0.999818i	$0.493933\pi$
$608$	−4.24334	+	0.997038i	−0.172090	+	0.0404352i
$609$	−16.6643			−0.675273
$610$		0			0
$611$	0.695083	−	1.20392i	0.0281200	−	0.0487053i
$612$	−8.15957	−	14.1328i	−0.329831	−	0.571284i
$613$	−4.05797	+	7.02861i	−0.163900	+	0.283883i	−0.936264	−	0.351297i	$-0.885741\pi$
$613$	−4.05797	+	7.02861i	−0.163900	+	0.283883i	0.772364	+	0.635180i	$0.219074\pi$
$614$	1.67862	+	2.90746i	0.0677437	+	0.117336i
$615$		0			0
$616$	4.36697			0.175950
$617$	−4.63950	−	8.03585i	−0.186779	−	0.323511i	0.757395	−	0.652957i	$-0.226472\pi$
$617$	−4.63950	−	8.03585i	−0.186779	−	0.323511i	−0.944175	+	0.329445i	$0.893138\pi$
$618$	10.2839	+	17.8122i	0.413678	+	0.716511i
$619$	−1.87972			−0.0755521			−0.0377761	−	0.999286i	$-0.512027\pi$
$619$	−1.87972			−0.0755521			−0.0377761	+	0.999286i	$0.512027\pi$
$620$		0			0
$621$	1.31324	+	2.27460i	0.0526986	+	0.0912766i
$622$	−3.85113	+	6.67035i	−0.154416	+	0.267457i
$623$	−6.57815	−	11.3937i	−0.263548	−	0.456478i
$624$	−1.74594	+	3.02405i	−0.0698934	+	0.121059i
$625$		0			0
$626$	5.75069			0.229844
$627$	−22.7600	−	24.2177i	−0.908947	−	0.967163i
$628$	−7.44160			−0.296952
$629$	17.3536	−	30.0574i	0.691935	−	1.19847i
$630$		0			0
$631$	−7.83481	−	13.5703i	−0.311899	−	0.540225i	0.666875	−	0.745170i	$-0.267632\pi$
$631$	−7.83481	−	13.5703i	−0.311899	−	0.540225i	−0.978773	+	0.204945i	$0.934298\pi$
$632$	−7.75423	+	13.4307i	−0.308447	+	0.534245i
$633$	16.3494	+	28.3179i	0.649829	+	1.12554i
$634$	−17.4292			−0.692203
$635$		0			0
$636$	−10.6380	−	18.4255i	−0.421822	−	0.730618i
$637$	3.88097	+	6.72204i	0.153770	+	0.266337i
$638$	−17.3001			−0.684916
$639$	17.8179			0.704864
$640$		0			0
$641$	−14.3585	+	24.8696i	−0.567125	+	0.982289i	0.429724	+	0.902960i	$0.358611\pi$
$641$	−14.3585	+	24.8696i	−0.567125	+	0.982289i	−0.996849	+	0.0793287i	$0.974722\pi$
$642$	11.7030	+	20.2701i	0.461880	+	0.799999i
$643$	−8.41674	+	14.5782i	−0.331924	+	0.574909i	−0.982889	−	0.184199i	$-0.941031\pi$
$643$	−8.41674	+	14.5782i	−0.331924	+	0.574909i	0.650965	+	0.759108i	$0.274364\pi$
$644$	1.44200	−	2.49761i	0.0568227	−	0.0984197i
$645$		0			0
$646$	−27.9407	+	6.56509i	−1.09931	+	0.258300i
$647$	−8.10908			−0.318801			−0.159400	−	0.987214i	$-0.550956\pi$
$647$	−8.10908			−0.318801			−0.159400	+	0.987214i	$0.550956\pi$
$648$	−5.14638	+	8.91380i	−0.202169	+	0.350167i
$649$	0.272864	−	0.472614i	0.0107108	−	0.0185517i
$650$		0			0
$651$	−4.33896	+	7.51529i	−0.170057	+	0.294548i
$652$	−7.77002	−	13.4581i	−0.304297	−	0.527059i
$653$	33.6755			1.31782			0.658912	−	0.752220i	$-0.271017\pi$
$653$	33.6755			1.31782			0.658912	+	0.752220i	$0.271017\pi$
$654$	−38.2597			−1.49607
$655$		0			0
$656$	−2.79230	−	4.83640i	−0.109021	−	0.188830i
$657$	37.8010			1.47476
$658$	−1.24920			−0.0486988
$659$	−10.2712	−	17.7903i	−0.400111	−	0.693012i	0.593628	−	0.804739i	$-0.297695\pi$
$659$	−10.2712	−	17.7903i	−0.400111	−	0.693012i	−0.993739	+	0.111727i	$0.964362\pi$
$660$		0			0
$661$	2.11413	+	3.66179i	0.0822302	+	0.142427i	0.904208	−	0.427093i	$-0.140462\pi$
$661$	2.11413	+	3.66179i	0.0822302	+	0.142427i	−0.821977	+	0.569520i	$0.807129\pi$
$662$	−6.05540	+	10.4883i	−0.235350	+	0.407638i
$663$	−11.4963	+	19.9122i	−0.446479	+	0.773324i
$664$	−0.313611			−0.0121705
$665$		0			0
$666$	13.0635			0.506201
$667$	−5.71257	+	9.89446i	−0.221192	+	0.383115i
$668$	−11.0317	+	19.1074i	−0.426828	+	0.739287i
$669$	5.45289	+	9.44468i	0.210821	+	0.365152i
$670$		0			0
$671$	−19.0392	−	32.9768i	−0.735000	−	1.27306i
$672$	3.13779			0.121043
$673$	21.0671			0.812076			0.406038	−	0.913856i	$-0.366910\pi$
$673$	21.0671			0.812076			0.406038	+	0.913856i	$0.366910\pi$
$674$	−16.1078	−	27.8995i	−0.620448	−	1.07465i
$675$		0			0
$676$	−10.7743			−0.414396
$677$	5.16536			0.198521			0.0992604	−	0.995061i	$-0.468352\pi$
$677$	5.16536			0.198521			0.0992604	+	0.995061i	$0.468352\pi$
$678$	−7.44910	−	12.9022i	−0.286081	−	0.495507i
$679$	−8.06373	+	13.9668i	−0.309457	+	0.535996i
$680$		0			0
$681$	−4.85369	+	8.40684i	−0.185994	+	0.322151i
$682$	−4.50448	+	7.80199i	−0.172486	+	0.298754i
$683$	17.1692			0.656961			0.328480	−	0.944511i	$-0.393464\pi$
$683$	17.1692			0.656961			0.328480	+	0.944511i	$0.393464\pi$
$684$	−7.39829	−	7.87214i	−0.282881	−	0.300999i
$685$		0			0
$686$	8.17951	−	14.1673i	0.312295	−	0.540911i
$687$	24.3505	−	42.1764i	0.929031	−	1.60913i
$688$	−3.81898	−	6.61466i	−0.145597	−	0.252182i
$689$	−6.78054	+	11.7442i	−0.258318	+	0.447420i
$690$		0			0
$691$	−2.98323			−0.113488			−0.0567438	−	0.998389i	$-0.518072\pi$
$691$	−2.98323			−0.113488			−0.0567438	+	0.998389i	$0.518072\pi$
$692$	0.381787			0.0145134
$693$	5.41152	+	9.37302i	0.205567	+	0.356052i
$694$	15.2549	+	26.4222i	0.579066	+	1.00297i
$695$		0			0
$696$	−12.4306			−0.471179
$697$	−18.3861	−	31.8457i	−0.696425	−	1.20624i
$698$	13.1658	−	22.8038i	0.498331	−	0.863135i
$699$	1.18538	+	2.05314i	0.0448352	+	0.0776568i
$700$		0			0
$701$	11.6523	−	20.1824i	0.440103	−	0.762280i	−0.557594	−	0.830114i	$-0.688275\pi$
$701$	11.6523	−	20.1824i	0.440103	−	0.762280i	0.997697	+	0.0678338i	$0.0216087\pi$
$702$	1.82142			0.0687451
$703$	6.63199	−	21.9977i	0.250130	−	0.829659i
$704$	3.25749			0.122771
$705$		0			0
$706$	−0.184406	+	0.319400i	−0.00694020	+	0.0120208i
$707$	−8.37883	−	14.5126i	−0.315118	−	0.545801i
$708$	0.196060	−	0.339586i	0.00736839	−	0.0127624i
$709$	−12.7003	−	21.9976i	−0.476970	−	0.826137i	0.522681	−	0.852528i	$-0.324932\pi$
$709$	−12.7003	−	21.9976i	−0.476970	−	0.826137i	−0.999652	+	0.0263912i	$0.991598\pi$
$710$		0			0
$711$	−38.4359			−1.44146
$712$	−4.90689	−	8.49898i	−0.183893	−	0.318513i
$713$	2.97481	+	5.15252i	0.111407	+	0.192963i
$714$	20.6611			0.773221
$715$		0			0
$716$	−6.09068	−	10.5494i	−0.227619	−	0.394248i
$717$	26.5947	−	46.0634i	0.993198	−	1.72027i
$718$	14.7532	+	25.5533i	0.550585	+	0.953641i
$719$	20.8709	−	36.1495i	0.778353	−	1.34815i	−0.154537	−	0.987987i	$-0.549389\pi$
$719$	20.8709	−	36.1495i	0.778353	−	1.34815i	0.932890	−	0.360161i	$-0.117278\pi$
$720$		0			0
$721$	−11.7803			−0.438723
$722$	−17.0118	+	8.46154i	−0.633115	+	0.314906i
$723$	−34.4864			−1.28256
$724$	0.996021	−	1.72516i	0.0370168	−	0.0641150i
$725$		0			0
$726$	−0.454962	−	0.788018i	−0.0168852	−	0.0292461i
$727$	−9.83583	+	17.0362i	−0.364791	+	0.631836i	−0.988743	−	0.149627i	$-0.952193\pi$
$727$	−9.83583	+	17.0362i	−0.364791	+	0.631836i	0.623952	+	0.781463i	$0.285526\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$	−16.9366			−0.627280
$730$		0			0
$731$	−25.1464	−	43.5549i	−0.930074	−	1.61094i
$732$	−13.6802	−	23.6947i	−0.505634	−	0.875783i
$733$	28.9684			1.06997			0.534987	−	0.844861i	$-0.320317\pi$
$733$	28.9684			1.06997			0.534987	+	0.844861i	$0.320317\pi$
$734$	18.3372			0.676840
$735$		0			0
$736$	1.07564	−	1.86306i	0.0396486	−	0.0686734i
$737$	21.2898	+	36.8750i	0.784219	+	1.35831i
$738$	6.92038	−	11.9865i	0.254743	−	0.441227i
$739$	−3.07219	+	5.32118i	−0.113012	+	0.195743i	−0.916983	−	0.398925i	$-0.869383\pi$
$739$	−3.07219	+	5.32118i	−0.113012	+	0.195743i	0.803971	+	0.594668i	$0.202717\pi$
$740$		0			0
$741$	−4.39351	+	14.5728i	−0.161400	+	0.535347i
$742$	12.1860			0.447360
$743$	−2.64392	+	4.57940i	−0.0969959	+	0.168002i	−0.910440	−	0.413641i	$-0.864257\pi$
$743$	−2.64392	+	4.57940i	−0.0969959	+	0.168002i	0.813444	+	0.581643i	$0.197590\pi$
$744$	−3.23659	+	5.60594i	−0.118659	+	0.205524i
$745$		0			0
$746$	−10.0964	+	17.4875i	−0.369656	+	0.640262i
$747$	−0.388624	−	0.673116i	−0.0142190	−	0.0246280i
$748$	21.4492			0.784262
$749$	−13.4059			−0.489843
$750$		0			0
$751$	−18.1097	−	31.3669i	−0.660832	−	1.14460i	−0.980397	−	0.197031i	$-0.936870\pi$
$751$	−18.1097	−	31.3669i	−0.660832	−	1.14460i	0.319565	−	0.947564i	$-0.396463\pi$
$752$	−0.931824			−0.0339801
$753$	45.9537			1.67465
$754$	3.96157	+	6.86163i	0.144272	+	0.249886i
$755$		0			0
$756$	−0.818361	−	1.41744i	−0.0297635	−	0.0515519i
$757$	−15.2376	+	26.3922i	−0.553818	+	0.959242i	0.444176	+	0.895940i	$0.353496\pi$
$757$	−15.2376	+	26.3922i	−0.553818	+	0.959242i	−0.997994	+	0.0633020i	$0.979837\pi$
$758$	7.63500	−	13.2242i	0.277316	−	0.480325i
$759$	16.4024			0.595368
$760$		0			0
$761$	1.54196			0.0558962			0.0279481	−	0.999609i	$-0.491103\pi$
$761$	1.54196			0.0558962			0.0279481	+	0.999609i	$0.491103\pi$
$762$	0.516417	−	0.894460i	0.0187078	−	0.0324029i
$763$	10.9568	−	18.9777i	0.396662	−	0.687038i
$764$	5.31085	+	9.19867i	0.192140	+	0.332796i
$765$		0			0
$766$	13.4026	+	23.2139i	0.484254	+	0.838752i
$767$	−0.249934			−0.00902459
$768$	2.34059			0.0844589
$769$	3.58197	+	6.20415i	0.129169	+	0.223728i	0.923355	−	0.383948i	$-0.125436\pi$
$769$	3.58197	+	6.20415i	0.129169	+	0.223728i	−0.794186	+	0.607675i	$0.792102\pi$
$770$		0			0
$771$	6.04225			0.217606
$772$	−15.2824			−0.550024
$773$	−12.9561	−	22.4406i	−0.465998	−	0.807131i	0.533248	−	0.845959i	$-0.320971\pi$
$773$	−12.9561	−	22.4406i	−0.465998	−	0.807131i	−0.999246	+	0.0388273i	$0.987638\pi$
$774$	9.46489	−	16.3937i	0.340208	−	0.589258i
$775$		0			0
$776$	−6.01504	+	10.4184i	−0.215927	+	0.373997i
$777$	−8.26961	+	14.3234i	−0.296671	+	0.513849i
$778$	24.3289			0.872232
$779$	−16.6707	−	17.7384i	−0.597291	−	0.635546i
$780$		0			0
$781$	−11.7096	+	20.2816i	−0.419001	+	0.725731i
$782$	7.08265	−	12.2675i	0.253275	−	0.438685i
$783$	3.24199	+	5.61530i	0.115859	+	0.200674i
$784$	2.60140	−	4.50576i	0.0929072	−	0.160920i
$785$		0			0
$786$	−16.6686			−0.594551
$787$	55.7022			1.98557			0.992785	−	0.119912i	$-0.0382612\pi$
$787$	55.7022			1.98557			0.992785	+	0.119912i	$0.0382612\pi$
$788$	−2.05433	−	3.55820i	−0.0731823	−	0.126756i
$789$	9.20138	+	15.9373i	0.327578	+	0.567381i
$790$		0			0
$791$	8.53307			0.303401
$792$	4.03665	+	6.99169i	0.143436	+	0.248439i
$793$	−8.71962	+	15.1028i	−0.309643	+	0.536317i
$794$	9.53415	+	16.5136i	0.338354	+	0.586047i
$795$		0			0
$796$	5.20281	−	9.01152i	0.184409	−	0.319405i
$797$	−35.0111			−1.24016			−0.620078	−	0.784540i	$-0.712899\pi$
$797$	−35.0111			−1.24016			−0.620078	+	0.784540i	$0.712899\pi$
$798$	13.3147	−	3.12850i	0.471335	−	0.110748i
$799$	−6.13568			−0.217065
$800$		0			0
$801$	12.1612	−	21.0637i	0.429693	−	0.744250i
$802$	−4.80098	−	8.31554i	−0.169529	−	0.293632i
$803$	−24.8421	+	43.0278i	−0.876658	+	1.51842i
$804$	15.2973	+	26.4956i	0.539493	+	0.934430i
$805$		0			0
$806$	4.12595			0.145330
$807$	−2.43701	−	4.22102i	−0.0857868	−	0.148587i
$808$	−6.25008	−	10.8255i	−0.219877	−	0.380838i
$809$	−31.0000			−1.08990			−0.544951	−	0.838468i	$-0.683452\pi$
$809$	−31.0000			−1.08990			−0.544951	+	0.838468i	$0.683452\pi$
$810$		0			0
$811$	−1.77251	−	3.07008i	−0.0622412	−	0.107805i	0.833226	−	0.552933i	$-0.186491\pi$
$811$	−1.77251	−	3.07008i	−0.0622412	−	0.107805i	−0.895467	+	0.445128i	$0.853158\pi$
$812$	3.55985	−	6.16584i	0.124926	−	0.216379i
$813$	−12.6070	−	21.8360i	−0.442147	−	0.765820i
$814$	−8.58509	+	14.8698i	−0.300907	+	0.521186i
$815$		0			0
$816$	15.4119			0.539523
$817$	−22.8003	−	24.2606i	−0.797681	−	0.848770i
$818$	22.7379			0.795011
$819$	2.47838	−	4.29269i	0.0866017	−	0.149999i
$820$		0			0
$821$	−2.84352	−	4.92512i	−0.0992395	−	0.171888i	0.812131	−	0.583476i	$-0.198308\pi$
$821$	−2.84352	−	4.92512i	−0.0992395	−	0.171888i	−0.911370	+	0.411588i	$0.864974\pi$
$822$	3.54570	−	6.14133i	0.123670	−	0.214203i
$823$	−15.6478	−	27.1028i	−0.545449	−	0.944745i	−0.998579	−	0.0533007i	$-0.983026\pi$
$823$	−15.6478	−	27.1028i	−0.545449	−	0.944745i	0.453130	−	0.891445i	$-0.350308\pi$
$824$	−8.78740			−0.306124
$825$		0			0
$826$	0.112295	+	0.194501i	0.00390724	+	0.00676754i
$827$	−1.11429	−	1.93001i	−0.0387477	−	0.0671130i	0.846001	−	0.533181i	$-0.179004\pi$
$827$	−1.11429	−	1.93001i	−0.0387477	−	0.0671130i	−0.884749	+	0.466068i	$0.845670\pi$
$828$	5.33170			0.185289
$829$	1.17604			0.0408456			0.0204228	−	0.999791i	$-0.493499\pi$
$829$	1.17604			0.0408456			0.0204228	+	0.999791i	$0.493499\pi$
$830$		0			0
$831$	−9.97128	+	17.2708i	−0.345900	+	0.599116i
$832$	−0.745938	−	1.29200i	−0.0258607	−	0.0447921i
$833$	17.1292	−	29.6686i	0.593491	−	1.02796i
$834$	−15.6711	+	27.1431i	−0.542645	+	0.939889i
$835$		0			0
$836$	13.8226	−	3.24784i	0.478066	−	0.112329i
$837$	3.37652			0.116710
$838$	18.2891	−	31.6777i	0.631788	−	1.09429i
$839$	−14.8851	+	25.7817i	−0.513890	+	0.890084i	0.485980	+	0.873970i	$0.338463\pi$
$839$	−14.8851	+	25.7817i	−0.513890	+	0.890084i	−0.999870	+	0.0161138i	$0.994871\pi$
$840$		0			0
$841$	0.397419	−	0.688350i	0.0137041	−	0.0237362i
$842$	5.51620	+	9.55434i	0.190101	+	0.329264i
$843$	15.4370			0.531678
$844$	−13.9703			−0.480876
$845$		0			0
$846$	−1.15471	−	2.00001i	−0.0396997	−	0.0687619i
$847$	0.521167			0.0179075
$848$	9.08996			0.312151
$849$	−7.87566	−	13.6410i	−0.270292	−	0.468159i
$850$		0			0
$851$	5.66968	+	9.82018i	0.194354	+	0.336631i
$852$	−8.41364	+	14.5728i	−0.288246	+	0.499257i
$853$	−17.7542	+	30.7512i	−0.607893	+	1.05290i	0.383694	+	0.923460i	$0.374652\pi$
$853$	−17.7542	+	30.7512i	−0.607893	+	1.05290i	−0.991587	+	0.129442i	$0.958682\pi$
$854$	15.6709			0.536246
$855$		0			0
$856$	−10.0000			−0.341793
$857$	−3.58488	+	6.20920i	−0.122457	+	0.212102i	−0.920736	−	0.390186i	$-0.872411\pi$
$857$	−3.58488	+	6.20920i	−0.122457	+	0.212102i	0.798279	+	0.602288i	$0.205744\pi$
$858$	5.68737	−	9.85082i	0.194164	−	0.336302i
$859$	11.0661	+	19.1671i	0.377572	+	0.653973i	0.990708	−	0.136003i	$-0.0434258\pi$
$859$	11.0661	+	19.1671i	0.377572	+	0.653973i	−0.613137	+	0.789977i	$0.710093\pi$
$860$		0			0
$861$	8.76164	+	15.1756i	0.298596	+	0.517183i
$862$	20.8978			0.711783
$863$	27.8800			0.949048			0.474524	−	0.880243i	$-0.342620\pi$
$863$	27.8800			0.949048			0.474524	+	0.880243i	$0.342620\pi$
$864$	−0.610447	−	1.05732i	−0.0207678	−	0.0359709i
$865$		0			0
$866$	14.2495			0.484219
$867$	61.6907			2.09513
$868$	−1.85378	−	3.21085i	−0.0629215	−	0.108983i
$869$	25.2593	−	43.7504i	0.856864	−	1.48413i
$870$		0			0
$871$	9.75035	−	16.8881i	0.330378	−	0.572232i
$872$	8.17306	−	14.1562i	0.276775	−	0.479388i
$873$	−29.8151			−1.00909
$874$	2.70676	−	8.97806i	0.0915575	−	0.303688i
$875$		0			0
$876$	−17.8497	+	30.9166i	−0.603086	+	1.04458i
$877$	−11.8945	+	20.6018i	−0.401648	+	0.695675i	−0.993925	−	0.110060i	$-0.964896\pi$
$877$	−11.8945	+	20.6018i	−0.401648	+	0.695675i	0.592277	+	0.805735i	$0.298229\pi$
$878$	−5.25331	−	9.09900i	−0.177291	−	0.307076i
$879$	−1.25022	+	2.16544i	−0.0421688	+	0.0730386i
$880$		0			0
$881$	24.4819			0.824815			0.412408	−	0.910999i	$-0.364688\pi$
$881$	24.4819			0.824815			0.412408	+	0.910999i	$0.364688\pi$
$882$	12.8945			0.434182
$883$	16.2170	+	28.0887i	0.545746	+	0.945260i	0.998560	+	0.0536549i	$0.0170871\pi$
$883$	16.2170	+	28.0887i	0.545746	+	0.945260i	−0.452813	+	0.891605i	$0.649580\pi$
$884$	−4.91170	−	8.50731i	−0.165198	−	0.286132i
$885$		0			0
$886$	38.4561			1.29196
$887$	4.65631	+	8.06497i	0.156344	+	0.270795i	0.933547	−	0.358454i	$-0.116696\pi$
$887$	4.65631	+	8.06497i	0.156344	+	0.270795i	−0.777204	+	0.629249i	$0.783363\pi$
$888$	−6.16862	+	10.6844i	−0.207005	+	0.358544i
$889$	0.295782	+	0.512309i	0.00992021	+	0.0171823i
$890$		0			0
$891$	16.7643	−	29.0366i	0.561625	−	0.972763i
$892$	−4.65941			−0.156008
$893$	−3.95404	+	0.929064i	−0.132317	+	0.0310899i
$894$	−51.1242			−1.70985
$895$		0			0
$896$	−0.670297	+	1.16099i	−0.0223931	+	0.0387859i
$897$	−3.75600	−	6.50559i	−0.125409	−	0.217215i
$898$	−13.4701	+	23.3309i	−0.449504	+	0.778563i
$899$	7.34389	+	12.7200i	0.244932	+	0.424235i
$900$		0			0
$901$	59.8537			1.99402
$902$	9.09588	+	15.7545i	0.302860	+	0.524568i
$903$	11.9831	+	20.7554i	0.398774	+	0.690697i
$904$	6.36514			0.211701
$905$		0			0
$906$	21.4680	+	37.1837i	0.713228	+	1.23535i
$907$	−5.47615	+	9.48497i	−0.181833	+	0.314943i	−0.942505	−	0.334193i	$-0.891536\pi$
$907$	−5.47615	+	9.48497i	−0.181833	+	0.314943i	0.760672	+	0.649136i	$0.224870\pi$
$908$	−2.07370	−	3.59176i	−0.0688182	−	0.119197i
$909$	15.4901	−	26.8296i	0.513774	−	0.889883i
$910$		0			0
$911$	−53.5887			−1.77547			−0.887736	−	0.460353i	$-0.847723\pi$
$911$	−53.5887			−1.77547			−0.887736	+	0.460353i	$0.847723\pi$
$912$	9.93193	−	2.33366i	0.328879	−	0.0772753i
$913$	1.02158			0.0338095
$914$	7.32358	−	12.6848i	0.242243	−	0.419577i
$915$		0			0
$916$	10.4036	+	18.0195i	0.343744	+	0.595381i
$917$	4.77355	−	8.26803i	0.157636	−	0.273034i
$918$	−4.01954	−	6.96205i	−0.132665	−	0.229782i
$919$	−14.8653			−0.490362			−0.245181	−	0.969477i	$-0.578847\pi$
$919$	−14.8653			−0.490362			−0.245181	+	0.969477i	$0.578847\pi$
$920$		0			0
$921$	−3.92898	−	6.80518i	−0.129464	−	0.224238i
$922$	−0.104103	−	0.180311i	−0.00342845	−	0.00593824i
$923$	10.7256			0.353036
$924$	−10.2213			−0.336257
$925$		0			0
$926$	−12.3290	+	21.3545i	−0.405157	+	0.701752i
$927$	−10.8893	−	18.8608i	−0.357651	−	0.619469i
$928$	2.65543	−	4.59933i	0.0871686	−	0.150981i
$929$	15.1444	−	26.2309i	0.496872	−	0.860608i	−0.503122	−	0.864216i	$-0.667815\pi$
$929$	15.1444	−	26.2309i	0.496872	−	0.860608i	0.999993	+	0.00360816i	$0.00114852\pi$
$930$		0			0
$931$	6.54621	−	21.7132i	0.214544	−	0.711620i
$932$	−1.01289			−0.0331782
$933$	9.01393	−	15.6126i	0.295103	−	0.511133i
$934$	−11.2141	+	19.4233i	−0.366935	+	0.635551i
$935$		0			0
$936$	1.84872	−	3.20208i	0.0604273	−	0.104663i
$937$	1.26101	+	2.18413i	0.0411954	+	0.0713525i	0.885888	−	0.463899i	$-0.153550\pi$
$937$	1.26101	+	2.18413i	0.0411954	+	0.0713525i	−0.844693	+	0.535252i	$0.820217\pi$
$938$	−17.5233			−0.572155
$939$	−13.4600			−0.439251
$940$		0			0
$941$	24.8927	+	43.1154i	0.811478	+	1.40552i	0.911829	+	0.410570i	$0.134670\pi$
$941$	24.8927	+	43.1154i	0.811478	+	1.40552i	−0.100351	+	0.994952i	$0.531996\pi$
$942$	17.4178			0.567502
$943$	12.0140			0.391231
$944$	0.0837650	+	0.145085i	0.00272632	+	0.00472212i
$945$		0			0
$946$	12.4403	+	21.5472i	0.404468	+	0.700560i
$947$	−27.0397	+	46.8341i	−0.878672	+	1.52190i	−0.0258727	+	0.999665i	$0.508236\pi$
$947$	−27.0397	+	46.8341i	−0.878672	+	1.52190i	−0.852799	+	0.522239i	$0.825097\pi$
$948$	18.1495	−	31.4359i	0.589469	−	1.02099i
$949$	22.7545			0.738643
$950$		0			0
$951$	40.7948			1.32286
$952$	−4.41364	+	7.64464i	−0.143047	+	0.247764i
$953$	15.1018	−	26.1570i	0.489194	−	0.847309i	−0.510728	−	0.859742i	$-0.670624\pi$
$953$	15.1018	−	26.1570i	0.489194	−	0.847309i	0.999923	+	0.0124327i	$0.00395754\pi$
$954$	11.2642	+	19.5102i	0.364692	+	0.631665i
$955$		0			0
$956$	11.3624	+	19.6802i	0.367486	+	0.636504i
$957$	40.4924			1.30893
$958$	−16.3516			−0.528298
$959$	2.03083	+	3.51750i	0.0655788	+	0.113586i
$960$		0			0
$961$	−23.3514			−0.753270
$962$	7.86365			0.253534
$963$	−12.3919	−	21.4634i	−0.399324	−	0.691649i
$964$	7.36702	−	12.7600i	0.237276	−	0.410974i
$965$		0			0
$966$	−3.37513	+	5.84590i	−0.108593	+	0.188089i
$967$	−12.9400	+	22.4127i	−0.416122	+	0.720745i	−0.995546	−	0.0942818i	$-0.969945\pi$
$967$	−12.9400	+	22.4127i	−0.416122	+	0.720745i	0.579423	+	0.815027i	$0.303278\pi$
$968$	0.388758			0.0124952
$969$	65.3977	−	15.3662i	2.10088	−	0.493634i
$970$		0			0
$971$	13.1440	−	22.7660i	0.421811	−	0.730597i	−0.574306	−	0.818641i	$-0.694728\pi$
$971$	13.1440	−	22.7660i	0.421811	−	0.730597i	0.996117	+	0.0880434i	$0.0280614\pi$
$972$	10.2143	−	17.6916i	0.327622	−	0.567459i
$973$	−8.97574	−	15.5464i	−0.287749	−	0.498396i
$974$	20.3929	−	35.3216i	0.653432	−	1.13178i
$975$		0			0
$976$	11.6895			0.374171
$977$	−49.3857			−1.57999			−0.789995	−	0.613114i	$-0.789917\pi$
$977$	−49.3857			−1.57999			−0.789995	+	0.613114i	$0.789917\pi$
$978$	18.1865	+	31.4999i	0.581539	+	1.00726i
$979$	15.9841	+	27.6853i	0.510855	+	0.884828i
$980$		0			0
$981$	40.5120			1.29345
$982$	11.1912	+	19.3838i	0.357126	+	0.618561i
$983$	10.3400	−	17.9094i	0.329795	−	0.571221i	−0.652676	−	0.757637i	$-0.726354\pi$
$983$	10.3400	−	17.9094i	0.329795	−	0.571221i	0.982471	+	0.186416i	$0.0596871\pi$
$984$	6.53563	+	11.3201i	0.208348	+	0.360870i
$985$		0			0
$986$	17.4849	−	30.2847i	0.556833	−	0.964463i
$987$	2.92387			0.0930677
$988$	−4.45344	−	4.73867i	−0.141683	−	0.150757i
$989$	16.4314			0.522488
$990$		0			0
$991$	−1.94256	+	3.36461i	−0.0617074	+	0.106880i	−0.895229	−	0.445607i	$-0.852988\pi$
$991$	−1.94256	+	3.36461i	−0.0617074	+	0.106880i	0.833521	+	0.552487i	$0.186321\pi$
$992$	−1.38281	−	2.39509i	−0.0439042	−	0.0760443i
$993$	14.1732	−	24.5488i	0.449774	−	0.779032i
$994$	−4.81898	−	8.34671i	−0.152849	−	0.264742i
$995$		0			0
$996$	0.734036			0.0232588
$997$	−23.6968	−	41.0440i	−0.750484	−	1.29988i	−0.947588	−	0.319494i	$-0.896487\pi$
$997$	−23.6968	−	41.0440i	−0.750484	−	1.29988i	0.197104	−	0.980383i	$-0.436846\pi$
$998$	−4.07719	−	7.06189i	−0.129061	−	0.223540i
$999$	6.43531			0.203604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.o.201.1		10
5.2	odd	4		190.2.i.a.49.10	yes	20
5.3	odd	4		190.2.i.a.49.1	✓	20
5.4	even	2		950.2.e.n.201.5		10
15.2	even	4		1710.2.t.d.1189.5		20
15.8	even	4		1710.2.t.d.1189.6		20
19.7	even	3	inner	950.2.e.o.501.1		10
95.7	odd	12		190.2.i.a.159.1	yes	20
95.64	even	6		950.2.e.n.501.5		10
95.83	odd	12		190.2.i.a.159.10	yes	20
285.83	even	12		1710.2.t.d.919.5		20
285.197	even	12		1710.2.t.d.919.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.1	✓	20	5.3	odd	4
190.2.i.a.49.10	yes	20	5.2	odd	4
190.2.i.a.159.1	yes	20	95.7	odd	12
190.2.i.a.159.10	yes	20	95.83	odd	12
950.2.e.n.201.5		10	5.4	even	2
950.2.e.n.501.5		10	95.64	even	6
950.2.e.o.201.1		10	1.1	even	1	trivial
950.2.e.o.501.1		10	19.7	even	3	inner
1710.2.t.d.919.5		20	285.83	even	12
1710.2.t.d.919.6		20	285.197	even	12
1710.2.t.d.1189.5		20	15.2	even	4
1710.2.t.d.1189.6		20	15.8	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.17030 + 2.02701i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17030 + 2.02701i) q^{6} -1.34059 q^{7} -1.00000 q^{8} +(-1.23919 - 2.14634i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.17030 + 2.02701i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17030 + 2.02701i) q^{6} -1.34059 q^{7} -1.00000 q^{8} +(-1.23919 - 2.14634i) q^{9} +3.25749 q^{11} +2.34059 q^{12} +(-0.745938 - 1.29200i) q^{13} +(-0.670297 + 1.16099i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.29230 + 5.70242i) q^{17} -2.47838 q^{18} +(-1.25821 + 4.17336i) q^{19} +(1.56889 - 2.71740i) q^{21} +(1.62875 - 2.82107i) q^{22} +(-1.07564 - 1.86306i) q^{23} +(1.17030 - 2.02701i) q^{24} -1.49188 q^{26} -1.22089 q^{27} +(0.670297 + 1.16099i) q^{28} +(-2.65543 - 4.59933i) q^{29} -2.76561 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.81223 + 6.60298i) q^{33} +(3.29230 + 5.70242i) q^{34} +(-1.23919 + 2.14634i) q^{36} -5.27098 q^{37} +(2.98513 + 3.17632i) q^{38} +3.49188 q^{39} +(-2.79230 + 4.83640i) q^{41} +(-1.56889 - 2.71740i) q^{42} +(-3.81898 + 6.61466i) q^{43} +(-1.62875 - 2.82107i) q^{44} -2.15128 q^{46} +(0.465912 + 0.806983i) q^{47} +(-1.17030 - 2.02701i) q^{48} -5.20281 q^{49} +(-7.70593 - 13.3471i) q^{51} +(-0.745938 + 1.29200i) q^{52} +(-4.54498 - 7.87214i) q^{53} +(-0.610447 + 1.05732i) q^{54} +1.34059 q^{56} +(-6.98698 - 7.43448i) q^{57} -5.31085 q^{58} +(0.0837650 - 0.145085i) q^{59} +(-5.84474 - 10.1234i) q^{61} +(-1.38281 + 2.39509i) q^{62} +(1.66125 + 2.87738i) q^{63} +1.00000 q^{64} +(3.81223 + 6.60298i) q^{66} +(6.53563 + 11.3201i) q^{67} +6.58459 q^{68} +5.03528 q^{69} +(-3.59466 + 6.22613i) q^{71} +(1.23919 + 2.14634i) q^{72} +(-7.62615 + 13.2089i) q^{73} +(-2.63549 + 4.56480i) q^{74} +(4.24334 - 0.997038i) q^{76} -4.36697 q^{77} +(1.74594 - 3.02405i) q^{78} +(7.75423 - 13.4307i) q^{79} +(5.14638 - 8.91380i) q^{81} +(2.79230 + 4.83640i) q^{82} +0.313611 q^{83} -3.13779 q^{84} +(3.81898 + 6.61466i) q^{86} +12.4306 q^{87} -3.25749 q^{88} +(4.90689 + 8.49898i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.07564 + 1.86306i) q^{92} +(3.23659 - 5.60594i) q^{93} +0.931824 q^{94} -2.34059 q^{96} +(6.01504 - 10.4184i) q^{97} +(-2.60140 + 4.50576i) q^{98} +(-4.03665 - 6.99169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{13} + 5 q^{14} - 5 q^{16} - 4 q^{17} - 10 q^{18} + 11 q^{19} + 20 q^{21} - 3 q^{22} - 13 q^{23} + 4 q^{26} - 36 q^{27} - 5 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} - 2 q^{33} + 4 q^{34} - 5 q^{36} - 10 q^{37} + 13 q^{38} + 16 q^{39} + q^{41} - 20 q^{42} + 3 q^{44} - 26 q^{46} + 10 q^{47} - 20 q^{49} + 4 q^{51} + 2 q^{52} - 5 q^{53} - 18 q^{54} - 10 q^{56} + 10 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{61} - 4 q^{62} - 23 q^{63} + 10 q^{64} + 2 q^{66} - 4 q^{67} + 8 q^{68} - 24 q^{69} - 22 q^{71} + 5 q^{72} - 26 q^{73} - 5 q^{74} + 2 q^{76} - 10 q^{77} + 8 q^{78} + 2 q^{79} - 5 q^{81} - q^{82} - 12 q^{83} - 40 q^{84} + 20 q^{87} + 6 q^{88} - q^{89} + 10 q^{91} - 13 q^{92} - 6 q^{93} + 20 q^{94} - 8 q^{97} - 10 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^13 + 5 * q^14 - 5 * q^16 - 4 * q^17 - 10 * q^18 + 11 * q^19 + 20 * q^21 - 3 * q^22 - 13 * q^23 + 4 * q^26 - 36 * q^27 - 5 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 - 2 * q^33 + 4 * q^34 - 5 * q^36 - 10 * q^37 + 13 * q^38 + 16 * q^39 + q^41 - 20 * q^42 + 3 * q^44 - 26 * q^46 + 10 * q^47 - 20 * q^49 + 4 * q^51 + 2 * q^52 - 5 * q^53 - 18 * q^54 - 10 * q^56 + 10 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^61 - 4 * q^62 - 23 * q^63 + 10 * q^64 + 2 * q^66 - 4 * q^67 + 8 * q^68 - 24 * q^69 - 22 * q^71 + 5 * q^72 - 26 * q^73 - 5 * q^74 + 2 * q^76 - 10 * q^77 + 8 * q^78 + 2 * q^79 - 5 * q^81 - q^82 - 12 * q^83 - 40 * q^84 + 20 * q^87 + 6 * q^88 - q^89 + 10 * q^91 - 13 * q^92 - 6 * q^93 + 20 * q^94 - 8 * q^97 - 10 * q^98 + 13 * q^99

Introduction

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