LMFDB - Embedded newform 950.2.e.n.501.5

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			501.5
Root			$1.17030 + 2.02701i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.n.201.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.17030 + 2.02701i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.17030 - 2.02701i) q^{6} +1.34059 q^{7} +1.00000 q^{8} +(-1.23919 + 2.14634i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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	0.976272	+	0.216547i	$0.0694795\pi$
$3$	1.17030	+	2.02701i	0.675671	+	1.17030i	−0.300601	+	0.953750i	$0.597187\pi$
$4$	−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	$-0.418468\pi$
$7$	1.34059			0.506697			0.253349	+	0.967375i	$0.418468\pi$
$8$	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	$-0.767000\pi$
$13$	0.745938	−	1.29200i	0.206886	−	0.358337i	0.950732	+	0.310014i	$0.100334\pi$
$14$	−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	0.920593	+	0.390523i	$0.127706\pi$
$17$	3.29230	+	5.70242i	0.798499	+	1.38304i	−0.122094	+	0.992519i	$0.538961\pi$
$18$	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	$-0.761328\pi$
$23$	1.07564	−	1.86306i	0.224287	−	0.388476i	0.956105	+	0.293024i	$0.0946615\pi$
$24$	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	−0.999968	−	0.00794880i	$-0.997470\pi$
$29$	−2.65543	+	4.59933i	−0.493100	+	0.854075i	0.506868	+	0.862024i	$0.330803\pi$
$30$		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	$-0.357359\pi$
$37$	5.27098			0.866544			0.433272	+	0.901263i	$0.357359\pi$
$38$	−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	0.561300	−	0.827612i	$-0.310301\pi$
$41$	−2.79230	−	4.83640i	−0.436083	−	0.755319i	−0.997383	+	0.0722938i	$0.976968\pi$
$42$	1.56889	−	2.71740i	0.242086	−	0.419305i
$43$	3.81898	+	6.61466i	0.582389	+	1.00873i	0.995195	+	0.0979082i	$0.0312151\pi$
$43$	3.81898	+	6.61466i	0.582389	+	1.00873i	−0.412807	+	0.910819i	$0.635452\pi$
$44$	−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	$-0.854982\pi$
$47$	−0.465912	+	0.806983i	−0.0679602	+	0.117711i	0.830043	+	0.557699i	$0.188316\pi$
$48$	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	−0.364375	−	0.931252i	$-0.618717\pi$
$53$	4.54498	−	7.87214i	0.624301	−	1.08132i	0.988676	−	0.150069i	$-0.0479495\pi$
$54$	−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	0.871427	−	0.490526i	$-0.163195\pi$
$59$	0.0837650	+	0.145085i	0.0109053	+	0.0188885i	−0.860521	+	0.509415i	$0.829862\pi$
$60$		0			0
$61$	−5.84474	+	10.1234i	−0.748342	+	1.29617i	0.200274	+	0.979740i	$0.435817\pi$
$61$	−5.84474	+	10.1234i	−0.748342	+	1.29617i	−0.948617	+	0.316427i	$0.897517\pi$
$62$	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	0.122167	+	0.992510i	$0.461016\pi$
$67$	−6.53563	+	11.3201i	−0.798455	+	1.38296i	−0.920622	+	0.390455i	$0.872318\pi$
$68$	−6.58459			−0.798499
$69$	5.03528			0.606176
$70$		0			0
$71$	−3.59466	−	6.22613i	−0.426607	−	0.738906i	0.569962	−	0.821671i	$-0.306958\pi$
$71$	−3.59466	−	6.22613i	−0.426607	−	0.738906i	−0.996569	+	0.0827657i	$0.973625\pi$
$72$	−1.23919	+	2.14634i	−0.146040	+	0.252949i
$73$	7.62615	+	13.2089i	0.892573	+	1.54598i	0.836780	+	0.547539i	$0.184435\pi$
$73$	7.62615	+	13.2089i	0.892573	+	1.54598i	0.0557926	+	0.998442i	$0.482231\pi$
$74$	−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	0.859487	+	0.511158i	$0.170783\pi$
$79$	7.75423	+	13.4307i	0.872419	+	1.51107i	0.0129320	+	0.999916i	$0.495883\pi$
$80$		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	$-0.505479\pi$
$83$	−0.313611			−0.0344233			−0.0172116	+	0.999852i	$0.505479\pi$
$84$	−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	−0.479597	−	0.877489i	$-0.659217\pi$
$89$	4.90689	−	8.49898i	0.520129	−	0.900890i	0.999726	−	0.0234013i	$-0.00744955\pi$
$90$		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	−0.991117	−	0.132994i	$-0.957541\pi$
$97$	−6.01504	−	10.4184i	−0.610735	−	1.05782i	0.380382	−	0.924829i	$-0.375792\pi$
$98$	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	−0.367224	−	0.930133i	$-0.619692\pi$
$101$	6.25008	−	10.8255i	0.621907	−	1.07717i	0.989130	−	0.147041i	$-0.0469750\pi$
$102$	15.4119			1.52600
$103$	−8.78740			−0.865848			−0.432924	−	0.901430i	$-0.642518\pi$
$103$	−8.78740			−0.865848			−0.432924	+	0.901430i	$0.642518\pi$
$104$	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	$-0.660587\pi$
$107$	−10.0000			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$108$	−0.610447	+	1.05732i	−0.0587403	+	0.101741i
$109$	−8.17306	−	14.1562i	−0.782838	−	1.35591i	−0.930282	−	0.366844i	$-0.880438\pi$
$109$	−8.17306	−	14.1562i	−0.782838	−	1.35591i	0.147445	−	0.989070i	$-0.452895\pi$
$110$		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	$-0.403217\pi$
$113$	6.36514			0.598782			0.299391	+	0.954131i	$0.403217\pi$
$114$	−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	$-0.827101\pi$
$127$	0.220635	−	0.382151i	0.0195782	−	0.0339104i	0.875649	+	0.482949i	$0.160434\pi$
$128$	−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	0.667496	−	0.744613i	$-0.267366\pi$
$131$	−3.56077	−	6.16743i	−0.311106	−	0.538851i	−0.978602	+	0.205762i	$0.934033\pi$
$132$	−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	$-0.792020\pi$
$137$	1.51487	−	2.62383i	0.129424	−	0.224169i	0.923454	+	0.383710i	$0.125354\pi$
$138$	−2.51764	−	4.36068i	−0.214316	−	0.371205i
$139$	6.69534	−	11.5967i	0.567891	−	0.983617i	−0.428883	−	0.903360i	$-0.641093\pi$
$139$	6.69534	−	11.5967i	0.567891	−	0.983617i	0.996774	−	0.0802567i	$-0.0255740\pi$
$140$		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	−0.834175	−	0.551500i	$-0.814056\pi$
$149$	−10.9212	−	18.9161i	−0.894700	−	1.54967i	−0.0605252	−	0.998167i	$-0.519278\pi$
$150$		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	$-0.262637\pi$
$157$	−3.72080	−	6.44462i	−0.296952	−	0.514337i	−0.975437	+	0.220278i	$0.929304\pi$
$158$	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	$-0.708267\pi$
$163$	−15.5400			−1.21719			−0.608595	+	0.793481i	$0.708267\pi$
$164$	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	−0.0242320	−	0.999706i	$-0.507714\pi$
$167$	11.0317	−	19.1074i	0.853655	−	1.47857i	0.877887	−	0.478868i	$-0.158953\pi$
$168$	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	$-0.162047\pi$
$173$	0.190893	+	0.330637i	0.0145134	+	0.0251379i	−0.858678	+	0.512516i	$0.828713\pi$
$174$	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	−0.826632	−	0.562743i	$-0.809746\pi$
$181$	0.996021	−	1.72516i	0.0740337	−	0.128230i	0.900666	+	0.434513i	$0.143079\pi$
$182$	−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	−0.998272	−	0.0587608i	$-0.981285\pi$
$193$	−7.64118	−	13.2349i	−0.550024	−	0.952670i	0.448248	−	0.893909i	$-0.352048\pi$
$194$	−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	$-0.546757\pi$
$197$	−4.10865			−0.292729			−0.146365	+	0.989231i	$0.546757\pi$
$198$	8.07331			0.573745
$199$	5.20281	−	9.01152i	0.368817	−	0.638810i	−0.620564	−	0.784156i	$-0.713096\pi$
$199$	5.20281	−	9.01152i	0.368817	−	0.638810i	0.989381	+	0.145346i	$0.0464295\pi$
$200$		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	0.999759	−	0.0219433i	$-0.00698534\pi$
$211$	6.98513	+	12.0986i	0.480876	+	0.832902i	−0.518883	+	0.854845i	$0.673652\pi$
$212$	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	$-0.216529\pi$
$223$	−2.32970	−	4.03516i	−0.156008	−	0.270215i	−0.933426	+	0.358771i	$0.883196\pi$
$224$	−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	$-0.543951\pi$
$227$	−4.14740			−0.275273			−0.137636	+	0.990483i	$0.543951\pi$
$228$	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	$-0.177230\pi$
$233$	−0.506444	−	0.877186i	−0.0331782	−	0.0574664i	−0.882138	+	0.470992i	$0.843896\pi$
$234$	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	−0.525024	−	0.851087i	$-0.675944\pi$
$241$	7.36702	−	12.7600i	0.474551	−	0.821947i	0.999575	+	0.0291404i	$0.00927699\pi$
$242$	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	0.369931	+	0.929059i	$0.379381\pi$
$251$	−9.81668	+	17.0030i	−0.619623	+	1.07322i	−0.989554	+	0.144160i	$0.953952\pi$
$252$	−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	$-0.807677\pi$
$257$	1.29075	−	2.23565i	0.0805148	−	0.139456i	0.903471	+	0.428649i	$0.141010\pi$
$258$	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	$-0.244604\pi$
$263$	−3.93122	−	6.80906i	−0.242409	−	0.419865i	−0.961400	+	0.275155i	$0.911271\pi$
$264$	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	0.832537	−	0.553969i	$-0.186887\pi$
$269$	−1.04119	−	1.80340i	−0.0634826	−	0.109955i	−0.896020	+	0.444014i	$0.853554\pi$
$270$		0			0
$271$	−5.38624	−	9.32923i	−0.327190	−	0.566711i	0.654763	−	0.755834i	$-0.272769\pi$
$271$	−5.38624	−	9.32923i	−0.327190	−	0.566711i	−0.981953	+	0.189124i	$0.939435\pi$
$272$	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	$-0.582394\pi$
$277$	−8.52030			−0.511935			−0.255967	+	0.966685i	$0.582394\pi$
$278$	−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	−0.947464	−	0.319863i	$-0.896363\pi$
$281$	−3.29766	+	5.71172i	−0.196722	+	0.340733i	0.750742	+	0.660596i	$0.229696\pi$
$282$	1.09051	+	1.88882i	0.0649390	+	0.112478i
$283$	3.36481	+	5.82802i	0.200017	+	0.346440i	0.948534	−	0.316676i	$-0.102567\pi$
$283$	3.36481	+	5.82802i	0.200017	+	0.346440i	−0.748516	+	0.663116i	$0.769234\pi$
$284$	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	$-0.509935\pi$
$293$	−1.06829			−0.0624103			−0.0312051	+	0.999513i	$0.509935\pi$
$294$	−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	$-0.136124\pi$
$307$	1.67862	+	2.90746i	0.0958041	+	0.165937i	−0.814140	+	0.580669i	$0.802791\pi$
$308$	−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	$-0.885297\pi$
$313$	−2.87534	+	4.98024i	−0.162524	+	0.281500i	0.773249	+	0.634102i	$0.218630\pi$
$314$	−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	$-0.670527\pi$
$317$	8.71462	−	15.0942i	0.489462	−	0.847772i	0.999926	+	0.0121262i	$0.00385998\pi$
$318$	−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	−0.854135	−	0.520052i	$-0.825913\pi$
$337$	−16.1078	−	27.8995i	−0.877445	−	1.51978i	−0.0233106	−	0.999728i	$-0.507421\pi$
$338$	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	0.906476	+	0.422257i	$0.138762\pi$
$347$	15.2549	+	26.4222i	0.818924	+	1.41842i	−0.0875523	+	0.996160i	$0.527905\pi$
$348$	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	$-0.496876\pi$
$353$	0.368812			0.0196299			0.00981493	+	0.999952i	$0.496876\pi$
$354$	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	−0.932723	−	0.360593i	$-0.882574\pi$
$359$	−14.7532	−	25.5533i	−0.778645	−	1.34865i	0.154079	−	0.988059i	$-0.450759\pi$
$360$		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	$-0.992188\pi$
$367$	−9.16862	+	15.8805i	−0.478598	+	0.828956i	0.521101	+	0.853495i	$0.325521\pi$
$368$	−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	$-0.324898\pi$
$373$	20.1928			1.04554			0.522772	+	0.852473i	$0.324898\pi$
$374$	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	0.973488	+	0.228740i	$0.0734605\pi$
$383$	13.4026	+	23.2139i	0.684838	+	1.18617i	−0.288649	+	0.957435i	$0.593206\pi$
$384$	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	−0.373311	−	0.927706i	$-0.621778\pi$
$389$	12.1644	−	21.0694i	0.616761	−	1.06826i	0.990073	−	0.140556i	$-0.0448890\pi$
$390$		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	$-0.00784550\pi$
$397$	9.53415	+	16.5136i	0.478505	+	0.828795i	−0.521191	+	0.853440i	$0.674512\pi$
$398$	−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	0.960642	−	0.277788i	$-0.0896013\pi$
$401$	4.80098	+	8.31554i	0.239750	+	0.415258i	−0.720893	+	0.693047i	$0.756268\pi$
$402$	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	−0.435150	−	0.900358i	$-0.643305\pi$
$409$	11.3689	−	19.6916i	0.562158	−	0.973685i	0.997308	−	0.0733276i	$-0.0233619\pi$
$410$		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	0.699720	−	0.714417i	$-0.253308\pi$
$421$	−5.51620	−	9.55434i	−0.268843	−	0.465650i	−0.968563	+	0.248767i	$0.919975\pi$
$422$	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	−0.496686	−	0.867930i	$-0.665450\pi$
$431$	10.4489	−	18.0980i	0.503306	−	0.871752i	0.999993	−	0.00382204i	$-0.00121659\pi$
$432$	−0.610447	−	1.05732i	−0.0293701	−	0.0508705i
$433$	−7.12477	+	12.3405i	−0.342394	+	0.593045i	−0.984877	−	0.173256i	$-0.944571\pi$
$433$	−7.12477	+	12.3405i	−0.342394	+	0.593045i	0.642482	+	0.766300i	$0.277905\pi$
$434$	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	0.963726	−	0.266893i	$-0.0859971\pi$
$439$	5.25331	+	9.09900i	0.250727	+	0.434272i	−0.712999	+	0.701165i	$0.752664\pi$
$440$		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	−0.104548	+	0.994520i	$0.533340\pi$
$443$	−19.2281	+	33.3040i	−0.913553	+	1.58232i	−0.809006	+	0.587801i	$0.799994\pi$
$444$	−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	$-0.611302\pi$
$457$	−14.6472			−0.685166			−0.342583	+	0.939488i	$0.611302\pi$
$458$	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	0.868440	−	0.495795i	$-0.165123\pi$
$461$	0.104103	+	0.180311i	0.00484855	+	0.00839794i	−0.863591	+	0.504193i	$0.831790\pi$
$462$	5.11066	−	8.85192i	0.237769	−	0.411829i
$463$	24.6580			1.14596			0.572978	−	0.819571i	$-0.305788\pi$
$463$	24.6580			1.14596			0.572978	+	0.819571i	$0.305788\pi$
$464$	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	$-0.326332\pi$
$467$	22.4281			1.03785			0.518925	+	0.854820i	$0.326332\pi$
$468$	−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	−0.990111	−	0.140288i	$-0.955197\pi$
$479$	−8.17582	+	14.1609i	−0.373563	+	0.647030i	0.616548	+	0.787317i	$0.288531\pi$
$480$		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	$-0.875177\pi$
$487$	−40.7859			−1.84819			−0.924093	+	0.382168i	$0.875177\pi$
$488$	−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	−0.999983	−	0.00584462i	$-0.998140\pi$
$491$	−11.1912	−	19.3838i	−0.505053	−	0.874778i	0.494930	−	0.868933i	$-0.335194\pi$
$492$	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	0.942738	−	0.333534i	$-0.108241\pi$
$499$	4.07719	+	7.06189i	0.182520	+	0.316134i	−0.760218	+	0.649668i	$0.774908\pi$
$500$		0			0
$501$	51.6413			2.30716
$502$	19.6334			0.876280
$503$	12.0711	−	20.9078i	0.538224	−	0.932232i	−0.460776	−	0.887517i	$-0.652429\pi$
$503$	12.0711	−	20.9078i	0.538224	−	0.932232i	0.999000	−	0.0447150i	$-0.0142380\pi$
$504$	−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	−0.662374	−	0.749174i	$-0.730451\pi$
$509$	7.16576	−	12.4115i	0.317617	−	0.550128i	0.979990	+	0.199046i	$0.0637842\pi$
$510$		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	−0.496598	−	0.867981i	$-0.665418\pi$
$523$	11.5122	−	19.9398i	0.503394	−	0.871905i	0.999992	−	0.00392391i	$-0.00124902\pi$
$524$	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	−0.557104	−	0.830443i	$-0.688087\pi$
$541$	10.2489	−	17.7516i	0.440633	−	0.763199i	0.997737	+	0.0672443i	$0.0214207\pi$
$542$	−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	$-0.924791\pi$
$547$	−6.62783	+	11.4797i	−0.283385	+	0.490838i	0.688831	+	0.724922i	$0.258124\pi$
$548$	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	−0.486562	−	0.873646i	$-0.661749\pi$
$557$	12.1148	−	20.9834i	0.513319	−	0.889094i	0.999881	−	0.0154482i	$-0.00491750\pi$
$558$	−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	$-0.306005\pi$
$563$	27.1643			1.14484			0.572420	+	0.819961i	$0.306005\pi$
$564$	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	$-0.824936\pi$
$577$	−40.9572			−1.70507			−0.852536	+	0.522669i	$0.824936\pi$
$578$	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	$-0.0479267\pi$
$587$	8.82971	+	15.2935i	0.364441	+	0.631231i	−0.624245	+	0.781229i	$0.714593\pi$
$588$	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	$-0.692010\pi$
$593$	10.4599	−	18.1171i	0.429538	−	0.743982i	0.996832	+	0.0795335i	$0.0253431\pi$
$594$	−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	−0.965766	−	0.259414i	$-0.916471\pi$
$599$	−6.31990	+	10.9464i	−0.258224	+	0.447257i	0.707542	+	0.706671i	$0.249804\pi$
$600$		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	$-0.506067\pi$
$607$	−0.939196			−0.0381208			−0.0190604	+	0.999818i	$0.506067\pi$
$608$	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	$-0.114259\pi$
$613$	4.05797	+	7.02861i	0.163900	+	0.283883i	−0.772364	+	0.635180i	$0.780926\pi$
$614$	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	$-0.773528\pi$
$617$	4.63950	−	8.03585i	0.186779	−	0.323511i	0.944175	+	0.329445i	$0.106862\pi$
$618$	−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	−0.978773	−	0.204945i	$-0.934298\pi$
$631$	−7.83481	+	13.5703i	−0.311899	+	0.540225i	0.666875	+	0.745170i	$0.267632\pi$
$632$	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	−0.996849	−	0.0793287i	$-0.974722\pi$
$641$	−14.3585	−	24.8696i	−0.567125	−	0.982289i	0.429724	−	0.902960i	$-0.358611\pi$
$642$	−11.7030	+	20.2701i	−0.461880	+	0.799999i
$643$	8.41674	+	14.5782i	0.331924	+	0.574909i	0.982889	−	0.184199i	$-0.0589690\pi$
$643$	8.41674	+	14.5782i	0.331924	+	0.574909i	−0.650965	+	0.759108i	$0.725636\pi$
$644$	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	$-0.449044\pi$
$647$	8.10908			0.318801			0.159400	+	0.987214i	$0.449044\pi$
$648$	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	$-0.728983\pi$
$653$	−33.6755			−1.31782			−0.658912	+	0.752220i	$0.728983\pi$
$654$	−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	−0.993739	−	0.111727i	$-0.964362\pi$
$659$	−10.2712	+	17.7903i	−0.400111	+	0.693012i	0.593628	+	0.804739i	$0.297695\pi$
$660$		0			0
$661$	2.11413	−	3.66179i	0.0822302	−	0.142427i	−0.821977	−	0.569520i	$-0.807129\pi$
$661$	2.11413	−	3.66179i	0.0822302	−	0.142427i	0.904208	+	0.427093i	$0.140462\pi$
$662$	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	$-0.633090\pi$
$673$	−21.0671			−0.812076			−0.406038	+	0.913856i	$0.633090\pi$
$674$	−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	$-0.531648\pi$
$677$	−5.16536			−0.198521			−0.0992604	+	0.995061i	$0.531648\pi$
$678$	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	$-0.606536\pi$
$683$	−17.1692			−0.656961			−0.328480	+	0.944511i	$0.606536\pi$
$684$	−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	0.997697	−	0.0678338i	$-0.0216087\pi$
$701$	11.6523	+	20.1824i	0.440103	+	0.762280i	−0.557594	+	0.830114i	$0.688275\pi$
$702$	−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	−0.999652	−	0.0263912i	$-0.991598\pi$
$709$	−12.7003	+	21.9976i	−0.476970	+	0.826137i	0.522681	+	0.852528i	$0.324932\pi$
$710$		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	0.932890	+	0.360161i	$0.117278\pi$
$719$	20.8709	+	36.1495i	0.778353	+	1.34815i	−0.154537	+	0.987987i	$0.549389\pi$
$720$		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	$-0.0478072\pi$
$727$	9.83583	+	17.0362i	0.364791	+	0.631836i	−0.623952	+	0.781463i	$0.714474\pi$
$728$	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	$-0.679683\pi$
$733$	−28.9684			−1.06997			−0.534987	+	0.844861i	$0.679683\pi$
$734$	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	0.803971	−	0.594668i	$-0.202717\pi$
$739$	−3.07219	−	5.32118i	−0.113012	−	0.195743i	−0.916983	+	0.398925i	$0.869383\pi$
$740$		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	$-0.135743\pi$
$743$	2.64392	+	4.57940i	0.0969959	+	0.168002i	−0.813444	+	0.581643i	$0.802410\pi$
$744$	−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	0.319565	+	0.947564i	$0.396463\pi$
$751$	−18.1097	+	31.3669i	−0.660832	+	1.14460i	−0.980397	+	0.197031i	$0.936870\pi$
$752$	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	0.997994	+	0.0633020i	$0.0201631\pi$
$757$	15.2376	+	26.3922i	0.553818	+	0.959242i	−0.444176	+	0.895940i	$0.646504\pi$
$758$	−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	−0.794186	−	0.607675i	$-0.792102\pi$
$769$	3.58197	−	6.20415i	0.129169	−	0.223728i	0.923355	+	0.383948i	$0.125436\pi$
$770$		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	$-0.679029\pi$
$773$	12.9561	−	22.4406i	0.465998	−	0.807131i	0.999246	+	0.0388273i	$0.0123622\pi$
$774$	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	$-0.961739\pi$
$787$	−55.7022			−1.98557			−0.992785	+	0.119912i	$0.961739\pi$
$788$	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	$-0.287101\pi$
$797$	35.0111			1.24016			0.620078	+	0.784540i	$0.287101\pi$
$798$	−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	−0.895467	−	0.445128i	$-0.853158\pi$
$811$	−1.77251	+	3.07008i	−0.0622412	+	0.107805i	0.833226	+	0.552933i	$0.186491\pi$
$812$	−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	−0.911370	−	0.411588i	$-0.864974\pi$
$821$	−2.84352	+	4.92512i	−0.0992395	+	0.171888i	0.812131	+	0.583476i	$0.198308\pi$
$822$	−3.54570	−	6.14133i	−0.123670	−	0.214203i
$823$	15.6478	−	27.1028i	0.545449	−	0.944745i	−0.453130	−	0.891445i	$-0.649692\pi$
$823$	15.6478	−	27.1028i	0.545449	−	0.944745i	0.998579	−	0.0533007i	$-0.0169742\pi$
$824$	−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	$-0.820996\pi$
$827$	1.11429	−	1.93001i	0.0387477	−	0.0671130i	0.884749	+	0.466068i	$0.154330\pi$
$828$	−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	−0.999870	−	0.0161138i	$-0.994871\pi$
$839$	−14.8851	−	25.7817i	−0.513890	−	0.890084i	0.485980	−	0.873970i	$-0.338463\pi$
$840$		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	0.991587	+	0.129442i	$0.0413185\pi$
$853$	17.7542	+	30.7512i	0.607893	+	1.05290i	−0.383694	+	0.923460i	$0.625348\pi$
$854$	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	$-0.127589\pi$
$857$	3.58488	+	6.20920i	0.122457	+	0.212102i	−0.798279	+	0.602288i	$0.794256\pi$
$858$	−5.68737	−	9.85082i	−0.194164	−	0.336302i
$859$	11.0661	−	19.1671i	0.377572	−	0.653973i	−0.613137	−	0.789977i	$-0.710093\pi$
$859$	11.0661	−	19.1671i	0.377572	−	0.653973i	0.990708	+	0.136003i	$0.0434258\pi$
$860$		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	$-0.657380\pi$
$863$	−27.8800			−0.949048			−0.474524	+	0.880243i	$0.657380\pi$
$864$	−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	$-0.0351041\pi$
$877$	11.8945	+	20.6018i	0.401648	+	0.695675i	−0.592277	+	0.805735i	$0.701771\pi$
$878$	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	0.452813	+	0.891605i	$0.350420\pi$
$883$	−16.2170	+	28.0887i	−0.545746	+	0.945260i	−0.998560	+	0.0536549i	$0.982913\pi$
$884$	−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	$-0.883304\pi$
$887$	−4.65631	+	8.06497i	−0.156344	+	0.270795i	0.777204	+	0.629249i	$0.216637\pi$
$888$	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	$-0.108464\pi$
$907$	5.47615	+	9.48497i	0.181833	+	0.314943i	−0.760672	+	0.649136i	$0.775130\pi$
$908$	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	0.999993	−	0.00360816i	$-0.00114852\pi$
$929$	15.1444	+	26.2309i	0.496872	+	0.860608i	−0.503122	+	0.864216i	$0.667815\pi$
$930$		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	$-0.846450\pi$
$937$	−1.26101	+	2.18413i	−0.0411954	+	0.0713525i	0.844693	+	0.535252i	$0.179783\pi$
$938$	17.5233			0.572155
$939$	−13.4600			−0.439251
$940$		0			0
$941$	24.8927	−	43.1154i	0.811478	−	1.40552i	−0.100351	−	0.994952i	$-0.531996\pi$
$941$	24.8927	−	43.1154i	0.811478	−	1.40552i	0.911829	−	0.410570i	$-0.134670\pi$
$942$	−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	0.852799	+	0.522239i	$0.174903\pi$
$947$	27.0397	+	46.8341i	0.878672	+	1.52190i	0.0258727	+	0.999665i	$0.491764\pi$
$948$	−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	$-0.329376\pi$
$953$	−15.1018	−	26.1570i	−0.489194	−	0.847309i	−0.999923	+	0.0124327i	$0.996042\pi$
$954$	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	$-0.0300555\pi$
$967$	12.9400	+	22.4127i	0.416122	+	0.720745i	−0.579423	+	0.815027i	$0.696722\pi$
$968$	−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	0.996117	−	0.0880434i	$-0.0280614\pi$
$971$	13.1440	+	22.7660i	0.421811	+	0.730597i	−0.574306	+	0.818641i	$0.694728\pi$
$972$	−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	$-0.210083\pi$
$977$	49.3857			1.57999			0.789995	+	0.613114i	$0.210083\pi$
$978$	−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	$-0.273646\pi$
$983$	−10.3400	−	17.9094i	−0.329795	−	0.571221i	−0.982471	+	0.186416i	$0.940313\pi$
$984$	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	0.833521	−	0.552487i	$-0.186321\pi$
$991$	−1.94256	−	3.36461i	−0.0617074	−	0.106880i	−0.895229	+	0.445607i	$0.852988\pi$
$992$	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	−0.197104	−	0.980383i	$-0.563154\pi$
$997$	23.6968	−	41.0440i	0.750484	−	1.29988i	0.947588	−	0.319494i	$-0.103513\pi$
$998$	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.n.501.5		10
5.2	odd	4		190.2.i.a.159.10	yes	20
5.3	odd	4		190.2.i.a.159.1	yes	20
5.4	even	2		950.2.e.o.501.1		10
15.2	even	4		1710.2.t.d.919.5		20
15.8	even	4		1710.2.t.d.919.6		20
19.11	even	3	inner	950.2.e.n.201.5		10
95.49	even	6		950.2.e.o.201.1		10
95.68	odd	12		190.2.i.a.49.10	yes	20
95.87	odd	12		190.2.i.a.49.1	✓	20
285.68	even	12		1710.2.t.d.1189.5		20
285.182	even	12		1710.2.t.d.1189.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.1	✓	20	95.87	odd	12
190.2.i.a.49.10	yes	20	95.68	odd	12
190.2.i.a.159.1	yes	20	5.3	odd	4
190.2.i.a.159.10	yes	20	5.2	odd	4
950.2.e.n.201.5		10	19.11	even	3	inner
950.2.e.n.501.5		10	1.1	even	1	trivial
950.2.e.o.201.1		10	95.49	even	6
950.2.e.o.501.1		10	5.4	even	2
1710.2.t.d.919.5		20	15.2	even	4
1710.2.t.d.919.6		20	15.8	even	4
1710.2.t.d.1189.5		20	285.68	even	12
1710.2.t.d.1189.6		20	285.182	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more