LMFDB - Embedded newform 975.2.bc.l.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 150x^{8} + 520x^{6} + 825x^{4} + 512x^{2} + 100 $ x^12 + 20x^10 + 150x^8 + 520x^6 + 825x^4 + 512*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.1
Root			$2.58535i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.l.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23898 + 1.29268i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.34202 - 4.05650i) q^{4} +(-2.23898 - 1.29268i) q^{6} +(-3.35046 - 1.93439i) q^{7} +6.93919i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.23898 + 1.29268i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.34202 - 4.05650i) q^{4} +(-2.23898 - 1.29268i) q^{6} +(-3.35046 - 1.93439i) q^{7} +6.93919i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.25929 - 0.727051i) q^{11} +4.68404 q^{12} +(-2.77764 + 2.29885i) q^{13} +10.0022 q^{14} +(-4.28608 - 7.42371i) q^{16} +(1.85757 - 3.21740i) q^{17} -2.58535i q^{18} +(-4.01125 - 2.31589i) q^{19} -3.86878i q^{21} +(-1.87968 + 3.25571i) q^{22} +(2.79319 + 4.83794i) q^{23} +(-6.00952 + 3.46960i) q^{24} +(3.24742 - 8.73767i) q^{26} -1.00000 q^{27} +(-15.6937 + 9.06076i) q^{28} +(0.944061 + 1.63516i) q^{29} +8.50057i q^{31} +(7.17387 + 4.14184i) q^{32} +(1.25929 + 0.727051i) q^{33} +9.60493i q^{34} +(2.34202 + 4.05650i) q^{36} +(8.21667 - 4.74390i) q^{37} +11.9748 q^{38} +(-3.37968 - 1.25608i) q^{39} +(5.90180 - 3.40740i) q^{41} +(5.00108 + 8.66212i) q^{42} +(4.81154 - 8.33383i) q^{43} -6.81107i q^{44} +(-12.5078 - 7.22137i) q^{46} +5.84469i q^{47} +(4.28608 - 7.42371i) q^{48} +(3.98372 + 6.90001i) q^{49} +3.71513 q^{51} +(2.81998 + 16.6515i) q^{52} +12.9092 q^{53} +(2.23898 - 1.29268i) q^{54} +(13.4231 - 23.2495i) q^{56} -4.63179i q^{57} +(-4.22747 - 2.44073i) q^{58} +(8.34670 + 4.81897i) q^{59} +(0.669226 - 1.15913i) q^{61} +(-10.9885 - 19.0326i) q^{62} +(3.35046 - 1.93439i) q^{63} -4.27188 q^{64} -3.75936 q^{66} +(3.16059 - 1.82477i) q^{67} +(-8.70092 - 15.0704i) q^{68} +(-2.79319 + 4.83794i) q^{69} +(-6.09191 - 3.51717i) q^{71} +(-6.00952 - 3.46960i) q^{72} +3.43865i q^{73} +(-12.2646 + 21.2430i) q^{74} +(-18.7888 + 10.8477i) q^{76} -5.62560 q^{77} +(9.19075 - 1.55649i) q^{78} +15.4528 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.80934 + 15.2582i) q^{82} +0.637239i q^{83} +(-15.6937 - 9.06076i) q^{84} +24.8790i q^{86} +(-0.944061 + 1.63516i) q^{87} +(5.04515 + 8.73845i) q^{88} +(2.83218 - 1.63516i) q^{89} +(13.7532 - 2.32916i) q^{91} +26.1668 q^{92} +(-7.36171 + 4.25028i) q^{93} +(-7.55528 - 13.0861i) q^{94} +8.28367i q^{96} +(-12.8109 - 7.39637i) q^{97} +(-17.8390 - 10.2993i) q^{98} +1.45410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9} + 9 q^{11} + 16 q^{12} - 3 q^{13} + 10 q^{14} - 4 q^{16} - 9 q^{19} + 15 q^{22} + q^{23} - 5 q^{26} - 12 q^{27} - 39 q^{28} - 16 q^{29} + 30 q^{32} + 9 q^{33} + 8 q^{36} - 15 q^{37} + 30 q^{38} - 3 q^{39} + 18 q^{41} + 5 q^{42} + q^{43} - 45 q^{46} + 4 q^{48} + 31 q^{49} - 40 q^{52} - 16 q^{53} + 25 q^{56} - 30 q^{58} + 54 q^{59} - 11 q^{61} - 20 q^{62} + 3 q^{63} + 16 q^{64} + 30 q^{66} + 45 q^{67} - 30 q^{68} - q^{69} - 33 q^{71} + 5 q^{74} - 27 q^{76} - 28 q^{77} + 20 q^{78} + 18 q^{79} - 6 q^{81} - 20 q^{82} - 39 q^{84} + 16 q^{87} - 5 q^{88} - 48 q^{89} - 29 q^{91} + 46 q^{92} - 12 q^{93} - 30 q^{94} - 9 q^{97} + 105 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9 + 9 * q^11 + 16 * q^12 - 3 * q^13 + 10 * q^14 - 4 * q^16 - 9 * q^19 + 15 * q^22 + q^23 - 5 * q^26 - 12 * q^27 - 39 * q^28 - 16 * q^29 + 30 * q^32 + 9 * q^33 + 8 * q^36 - 15 * q^37 + 30 * q^38 - 3 * q^39 + 18 * q^41 + 5 * q^42 + q^43 - 45 * q^46 + 4 * q^48 + 31 * q^49 - 40 * q^52 - 16 * q^53 + 25 * q^56 - 30 * q^58 + 54 * q^59 - 11 * q^61 - 20 * q^62 + 3 * q^63 + 16 * q^64 + 30 * q^66 + 45 * q^67 - 30 * q^68 - q^69 - 33 * q^71 + 5 * q^74 - 27 * q^76 - 28 * q^77 + 20 * q^78 + 18 * q^79 - 6 * q^81 - 20 * q^82 - 39 * q^84 + 16 * q^87 - 5 * q^88 - 48 * q^89 - 29 * q^91 + 46 * q^92 - 12 * q^93 - 30 * q^94 - 9 * q^97 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.23898	+	1.29268i	−1.58320	+	0.914060i	−0.588809	+	0.808272i	$0.700403\pi$
$2$	−2.23898	+	1.29268i	−1.58320	+	0.914060i	−0.994389	+	0.105788i	$0.966264\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.34202	−	4.05650i	1.17101	−	2.02825i
$5$		0			0
$5$		0			0
$6$	−2.23898	−	1.29268i	−0.914060	−	0.527733i
$7$	−3.35046	−	1.93439i	−1.26636	−	0.731130i	−0.292059	−	0.956400i	$-0.594340\pi$
$7$	−3.35046	−	1.93439i	−1.26636	−	0.731130i	−0.974296	+	0.225270i	$0.927674\pi$
$8$			6.93919i			2.45337i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.25929	−	0.727051i	0.379690	−	0.219214i	−0.297993	−	0.954568i	$-0.596317\pi$
$11$	1.25929	−	0.727051i	0.379690	−	0.219214i	0.677683	+	0.735354i	$0.262984\pi$
$12$	4.68404			1.35217
$13$	−2.77764	+	2.29885i	−0.770379	+	0.637586i
$13$	−2.77764	+	2.29885i	−0.770379	+	0.637586i
$14$	10.0022			2.67319
$15$		0			0
$16$	−4.28608	−	7.42371i	−1.07152	−	1.85593i
$17$	1.85757	−	3.21740i	0.450526	−	0.780334i	−0.547893	−	0.836549i	$-0.684570\pi$
$17$	1.85757	−	3.21740i	0.450526	−	0.780334i	0.998419	+	0.0562145i	$0.0179031\pi$
$18$		−	2.58535i		−	0.609373i
$19$	−4.01125	−	2.31589i	−0.920243	−	0.531303i	−0.0365305	−	0.999333i	$-0.511631\pi$
$19$	−4.01125	−	2.31589i	−0.920243	−	0.531303i	−0.883713	+	0.468030i	$0.844964\pi$
$20$		0			0
$21$		−	3.86878i		−	0.844237i
$22$	−1.87968	+	3.25571i	−0.400750	+	0.694119i
$23$	2.79319	+	4.83794i	0.582420	+	1.00878i	0.995192	+	0.0979465i	$0.0312274\pi$
$23$	2.79319	+	4.83794i	0.582420	+	1.00878i	−0.412772	+	0.910835i	$0.635439\pi$
$24$	−6.00952	+	3.46960i	−1.22669	+	0.708228i
$25$		0			0
$26$	3.24742	−	8.73767i	0.636871	−	1.71360i
$27$	−1.00000			−0.192450
$28$	−15.6937	+	9.06076i	−2.96583	+	1.71232i
$29$	0.944061	+	1.63516i	0.175308	+	0.303642i	0.940268	−	0.340436i	$-0.110575\pi$
$29$	0.944061	+	1.63516i	0.175308	+	0.303642i	−0.764960	+	0.644078i	$0.777241\pi$
$30$		0			0
$31$			8.50057i			1.52675i	0.645957	+	0.763373i	$0.276458\pi$
$31$			8.50057i			1.52675i	−0.645957	+	0.763373i	$0.723542\pi$
$32$	7.17387	+	4.14184i	1.26817	+	0.732180i
$33$	1.25929	+	0.727051i	0.219214	+	0.126563i
$34$			9.60493i			1.64723i
$35$		0			0
$36$	2.34202	+	4.05650i	0.390337	+	0.676083i
$37$	8.21667	−	4.74390i	1.35081	−	0.779892i	0.362449	−	0.932003i	$-0.381941\pi$
$37$	8.21667	−	4.74390i	1.35081	−	0.779892i	0.988363	+	0.152111i	$0.0486072\pi$
$38$	11.9748			1.94257
$39$	−3.37968	−	1.25608i	−0.541182	−	0.201134i
$40$		0			0
$41$	5.90180	−	3.40740i	0.921706	−	0.532147i	0.0375270	−	0.999296i	$-0.488052\pi$
$41$	5.90180	−	3.40740i	0.921706	−	0.532147i	0.884179	+	0.467148i	$0.154719\pi$
$42$	5.00108	+	8.66212i	0.771683	+	1.33659i
$43$	4.81154	−	8.33383i	0.733753	−	1.27090i	−0.221515	−	0.975157i	$-0.571100\pi$
$43$	4.81154	−	8.33383i	0.733753	−	1.27090i	0.955268	−	0.295741i	$-0.0955665\pi$
$44$		−	6.81107i		−	1.02681i
$45$		0			0
$46$	−12.5078	−	7.22137i	−1.84417	−	1.06473i
$47$			5.84469i			0.852535i	0.904597	+	0.426268i	$0.140172\pi$
$47$			5.84469i			0.852535i	−0.904597	+	0.426268i	$0.859828\pi$
$48$	4.28608	−	7.42371i	0.618643	−	1.07152i
$49$	3.98372	+	6.90001i	0.569103	+	0.985716i
$50$		0			0
$51$	3.71513			0.520223
$52$	2.81998	+	16.6515i	0.391061	+	2.30914i
$53$	12.9092			1.77321			0.886604	−	0.462529i	$-0.153058\pi$
$53$	12.9092			1.77321			0.886604	+	0.462529i	$0.153058\pi$
$54$	2.23898	−	1.29268i	0.304687	−	0.175911i
$55$		0			0
$56$	13.4231	−	23.2495i	1.79374	−	3.10684i
$57$		−	4.63179i		−	0.613495i
$58$	−4.22747	−	2.44073i	−0.555094	−	0.320483i
$59$	8.34670	+	4.81897i	1.08665	+	0.627376i	0.932682	−	0.360700i	$-0.117462\pi$
$59$	8.34670	+	4.81897i	1.08665	+	0.627376i	0.153966	+	0.988076i	$0.450795\pi$
$60$		0			0
$61$	0.669226	−	1.15913i	0.0856856	−	0.148412i	−0.819998	−	0.572367i	$-0.806025\pi$
$61$	0.669226	−	1.15913i	0.0856856	−	0.148412i	0.905683	+	0.423955i	$0.139359\pi$
$62$	−10.9885	−	19.0326i	−1.39554	−	2.41714i
$63$	3.35046	−	1.93439i	0.422118	−	0.243710i
$64$	−4.27188			−0.533985
$65$		0			0
$66$	−3.75936			−0.462746
$67$	3.16059	−	1.82477i	0.386128	−	0.222931i	−0.294353	−	0.955697i	$-0.595104\pi$
$67$	3.16059	−	1.82477i	0.386128	−	0.222931i	0.680481	+	0.732766i	$0.261771\pi$
$68$	−8.70092	−	15.0704i	−1.05514	−	1.82756i
$69$	−2.79319	+	4.83794i	−0.336260	+	0.582420i
$70$		0			0
$71$	−6.09191	−	3.51717i	−0.722977	−	0.417411i	0.0928702	−	0.995678i	$-0.470396\pi$
$71$	−6.09191	−	3.51717i	−0.722977	−	0.417411i	−0.815848	+	0.578267i	$0.803729\pi$
$72$	−6.00952	−	3.46960i	−0.708228	−	0.408896i
$73$			3.43865i			0.402464i	0.979544	+	0.201232i	$0.0644945\pi$
$73$			3.43865i			0.402464i	−0.979544	+	0.201232i	$0.935506\pi$
$74$	−12.2646	+	21.2430i	−1.42574	+	2.46945i
$75$		0			0
$76$	−18.7888	+	10.8477i	−2.15523	+	1.24432i
$77$	−5.62560			−0.641096
$78$	9.19075	−	1.55649i	1.04065	−	0.176237i
$79$	15.4528			1.73857			0.869286	−	0.494310i	$-0.164579\pi$
$79$	15.4528			1.73857			0.869286	+	0.494310i	$0.164579\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.80934	+	15.2582i	−0.972829	+	1.68499i
$83$			0.637239i			0.0699461i	0.999388	+	0.0349730i	$0.0111345\pi$
$83$			0.637239i			0.0699461i	−0.999388	+	0.0349730i	$0.988865\pi$
$84$	−15.6937	−	9.06076i	−1.71232	−	0.988610i
$85$		0			0
$86$			24.8790i			2.68278i
$87$	−0.944061	+	1.63516i	−0.101214	+	0.175308i
$88$	5.04515	+	8.73845i	0.537814	+	0.931522i
$89$	2.83218	−	1.63516i	0.300211	−	0.173327i	−0.342327	−	0.939581i	$-0.611215\pi$
$89$	2.83218	−	1.63516i	0.300211	−	0.173327i	0.642538	+	0.766254i	$0.277882\pi$
$90$		0			0
$91$	13.7532	−	2.32916i	1.44173	−	0.244162i
$92$	26.1668			2.72808
$93$	−7.36171	+	4.25028i	−0.763373	+	0.440734i
$94$	−7.55528	−	13.0861i	−0.779268	−	1.34973i
$95$		0			0
$96$			8.28367i			0.845449i
$97$	−12.8109	−	7.39637i	−1.30075	−	0.750987i	−0.320216	−	0.947345i	$-0.603755\pi$
$97$	−12.8109	−	7.39637i	−1.30075	−	0.750987i	−0.980532	+	0.196357i	$0.937089\pi$
$98$	−17.8390	−	10.2993i	−1.80201	−	1.04039i
$99$			1.45410i			0.146143i
$100$		0			0
$101$	7.77054	+	13.4590i	0.773197	+	1.33922i	0.935802	+	0.352526i	$0.114677\pi$
$101$	7.77054	+	13.4590i	0.773197	+	1.33922i	−0.162605	+	0.986691i	$0.551990\pi$
$102$	−8.31811	+	4.80246i	−0.823616	+	0.475515i
$103$	4.87124			0.479978			0.239989	−	0.970776i	$-0.422856\pi$
$103$	4.87124			0.479978			0.239989	+	0.970776i	$0.422856\pi$
$104$	−15.9521	−	19.2746i	−1.56424	−	1.89003i
$105$		0			0
$106$	−28.9033	+	16.6874i	−2.80734	+	1.62082i
$107$	6.24850	+	10.8227i	0.604065	+	1.04627i	0.992199	+	0.124668i	$0.0397866\pi$
$107$	6.24850	+	10.8227i	0.604065	+	1.04627i	−0.388134	+	0.921603i	$0.626880\pi$
$108$	−2.34202	+	4.05650i	−0.225361	+	0.390337i
$109$		−	12.7448i		−	1.22073i	−0.792121	−	0.610365i	$-0.791023\pi$
$109$		−	12.7448i		−	1.22073i	0.792121	−	0.610365i	$-0.208977\pi$
$110$		0			0
$111$	8.21667	+	4.74390i	0.779892	+	0.450271i
$112$			33.1638i			3.13368i
$113$	−2.82647	+	4.89560i	−0.265892	+	0.460539i	−0.967797	−	0.251732i	$-0.919000\pi$
$113$	−2.82647	+	4.89560i	−0.265892	+	0.460539i	0.701905	+	0.712271i	$0.252333\pi$
$114$	5.98740	+	10.3705i	0.560771	+	0.971285i
$115$		0			0
$116$	8.84404			0.821149
$117$	−0.602040	−	3.55493i	−0.0556586	−	0.328654i
$118$	−24.9175			−2.29384
$119$	−12.4474	+	7.18652i	−1.14105	+	0.658787i
$120$		0			0
$121$	−4.44279	+	7.69514i	−0.403890	+	0.699559i
$122$			3.46037i			0.313287i
$123$	5.90180	+	3.40740i	0.532147	+	0.307235i
$124$	34.4825	+	19.9085i	3.09662	+	1.78784i
$125$		0			0
$126$	−5.00108	+	8.66212i	−0.445531	+	0.771683i
$127$	−3.65858	−	6.33685i	−0.324647	−	0.562305i	0.656794	−	0.754070i	$-0.271912\pi$
$127$	−3.65858	−	6.33685i	−0.324647	−	0.562305i	−0.981441	+	0.191765i	$0.938579\pi$
$128$	−4.78309	+	2.76152i	−0.422770	+	0.244086i
$129$	9.62308			0.847265
$130$		0			0
$131$	−8.08883			−0.706724			−0.353362	−	0.935487i	$-0.614962\pi$
$131$	−8.08883			−0.706724			−0.353362	+	0.935487i	$0.614962\pi$
$132$	5.89856	−	3.40554i	0.513404	−	0.296414i
$133$	8.95968	+	15.5186i	0.776903	+	1.34564i
$134$	−4.71767	+	8.17124i	−0.407545	+	0.705888i
$135$		0			0
$136$	22.3262	+	12.8900i	1.91445	+	1.10531i
$137$	2.41933	+	1.39680i	0.206697	+	0.119337i	0.599776	−	0.800168i	$-0.295256\pi$
$137$	2.41933	+	1.39680i	0.206697	+	0.119337i	−0.393078	+	0.919505i	$0.628590\pi$
$138$		−	14.4427i		−	1.22945i
$139$	−3.70950	+	6.42504i	−0.314636	+	0.544965i	−0.979360	−	0.202124i	$-0.935216\pi$
$139$	−3.70950	+	6.42504i	−0.314636	+	0.544965i	0.664724	+	0.747089i	$0.268549\pi$
$140$		0			0
$141$	−5.06165	+	2.92234i	−0.426268	+	0.246106i
$142$	18.1862			1.52615
$143$	−1.82647	+	4.91440i	−0.152737	+	0.410963i
$144$	8.57216			0.714347
$145$		0			0
$146$	−4.44506	−	7.69907i	−0.367876	−	0.637180i
$147$	−3.98372	+	6.90001i	−0.328572	+	0.569103i
$148$		−	44.4412i		−	3.65305i
$149$	−1.89731	−	1.09541i	−0.155434	−	0.0897399i	0.420266	−	0.907401i	$-0.361937\pi$
$149$	−1.89731	−	1.09541i	−0.155434	−	0.0897399i	−0.575700	+	0.817661i	$0.695270\pi$
$150$		0			0
$151$			13.7543i			1.11931i	0.828726	+	0.559655i	$0.189066\pi$
$151$			13.7543i			1.11931i	−0.828726	+	0.559655i	$0.810934\pi$
$152$	16.0704	−	27.8348i	1.30348	−	2.25770i
$153$	1.85757	+	3.21740i	0.150175	+	0.260111i
$154$	12.5956	−	7.27207i	1.01498	−	0.586000i
$155$		0			0
$156$	−13.0106	+	10.7679i	−1.04168	+	0.862122i
$157$	−15.1199			−1.20670			−0.603351	−	0.797476i	$-0.706168\pi$
$157$	−15.1199			−1.20670			−0.603351	+	0.797476i	$0.706168\pi$
$158$	−34.5984	+	19.9754i	−2.75250	+	1.58916i
$159$	6.45458	+	11.1797i	0.511881	+	0.886604i
$160$		0			0
$161$		−	21.6125i		−	1.70330i
$162$	2.23898	+	1.29268i	0.175911	+	0.101562i
$163$	2.24594	+	1.29669i	0.175915	+	0.101565i	0.585372	−	0.810765i	$-0.300948\pi$
$163$	2.24594	+	1.29669i	0.175915	+	0.101565i	−0.409457	+	0.912330i	$0.634282\pi$
$164$		−	31.9208i		−	2.49260i
$165$		0			0
$166$	−0.823743	−	1.42677i	−0.0639349	−	0.110738i
$167$	−19.4021	+	11.2018i	−1.50138	+	0.866820i	−0.501378	+	0.865229i	$0.667173\pi$
$167$	−19.4021	+	11.2018i	−1.50138	+	0.866820i	−0.999999	+	0.00159141i	$0.999493\pi$
$168$	26.8462			2.07123
$169$	2.43059	−	12.7708i	0.186969	−	0.982366i
$170$		0			0
$171$	4.01125	−	2.31589i	0.306748	−	0.177101i
$172$	−22.5375	−	39.0360i	−1.71847	−	2.97647i
$173$	9.86943	−	17.0943i	0.750359	−	1.29966i	−0.197290	−	0.980345i	$-0.563214\pi$
$173$	9.86943	−	17.0943i	0.750359	−	1.29966i	0.947649	−	0.319314i	$-0.103452\pi$
$174$		−	4.88146i		−	0.370062i
$175$		0			0
$176$	−10.7948	−	6.23240i	−0.813691	−	0.469785i
$177$			9.63794i			0.724432i
$178$	−4.22747	+	7.32219i	−0.316862	+	0.548821i
$179$	−5.50008	−	9.52641i	−0.411095	−	0.712037i	0.583915	−	0.811815i	$-0.301520\pi$
$179$	−5.50008	−	9.52641i	−0.411095	−	0.712037i	−0.995010	+	0.0997776i	$0.968187\pi$
$180$		0			0
$181$	7.26182			0.539767			0.269883	−	0.962893i	$-0.413015\pi$
$181$	7.26182			0.539767			0.269883	+	0.962893i	$0.413015\pi$
$182$	−27.7824	+	22.9934i	−2.05937	+	1.70439i
$183$	1.33845			0.0989412
$184$	−33.5714	+	19.3825i	−2.47492	+	1.42889i
$185$		0			0
$186$	10.9885	−	19.0326i	0.805714	−	1.39554i
$187$		−	5.40218i		−	0.395047i
$188$	23.7090	+	13.6884i	1.72915	+	0.998328i
$189$	3.35046	+	1.93439i	0.243710	+	0.140706i
$190$		0			0
$191$	5.98810	−	10.3717i	0.433284	−	0.750469i	−0.563870	−	0.825863i	$-0.690688\pi$
$191$	5.98810	−	10.3717i	0.433284	−	0.750469i	0.997154	+	0.0753942i	$0.0240215\pi$
$192$	−2.13594	−	3.69955i	−0.154148	−	0.266992i
$193$	9.51605	−	5.49410i	0.684980	−	0.395474i	−0.116748	−	0.993162i	$-0.537247\pi$
$193$	9.51605	−	5.49410i	0.684980	−	0.395474i	0.801729	+	0.597688i	$0.203914\pi$
$194$	38.2444			2.74579
$195$		0			0
$196$	37.3199			2.66570
$197$	21.6979	−	12.5273i	1.54591	−	0.892531i	0.547462	−	0.836831i	$-0.315594\pi$
$197$	21.6979	−	12.5273i	1.54591	−	0.892531i	0.998448	−	0.0557002i	$-0.0177391\pi$
$198$	−1.87968	−	3.25571i	−0.133583	−	0.231373i
$199$	0.903593	−	1.56507i	0.0640540	−	0.110945i	−0.832220	−	0.554446i	$-0.812930\pi$
$199$	0.903593	−	1.56507i	0.0640540	−	0.110945i	0.896274	+	0.443501i	$0.146264\pi$
$200$		0			0
$201$	3.16059	+	1.82477i	0.222931	+	0.128709i
$202$	−34.7961	−	20.0896i	−2.44825	−	1.41350i
$203$		−	7.30473i		−	0.512691i
$204$	8.70092	−	15.0704i	0.609186	−	1.05514i
$205$		0			0
$206$	−10.9066	+	6.29694i	−0.759900	+	0.438728i
$207$	−5.58638			−0.388280
$208$	28.9712	+	10.7674i	2.00879	+	0.746582i
$209$	−6.73509			−0.465876
$210$		0			0
$211$	−4.49046	−	7.77771i	−0.309136	−	0.535440i	0.669037	−	0.743229i	$-0.266707\pi$
$211$	−4.49046	−	7.77771i	−0.309136	−	0.535440i	−0.978174	+	0.207789i	$0.933373\pi$
$212$	30.2335	−	52.3660i	2.07645	−	3.59651i
$213$		−	7.03434i		−	0.481985i
$214$	−27.9805	−	16.1546i	−1.91271	−	1.10430i
$215$		0			0
$216$		−	6.93919i		−	0.472152i
$217$	16.4434	−	28.4808i	1.11625	−	1.93340i
$218$	16.4749	+	28.5353i	1.11582	+	1.93266i
$219$	−2.97796	+	1.71933i	−0.201232	+	0.116181i
$220$		0			0
$221$	2.23666	+	13.2071i	0.150454	+	0.888402i
$222$	−24.5293			−1.64630
$223$	−0.247214	+	0.142729i	−0.0165547	+	0.00955784i	−0.508254	−	0.861207i	$-0.669709\pi$
$223$	−0.247214	+	0.142729i	−0.0165547	+	0.00955784i	0.491700	+	0.870765i	$0.336376\pi$
$224$	−16.0238	−	27.7541i	−1.07064	−	1.85440i
$225$		0			0
$226$		−	14.6149i		−	0.972166i
$227$	24.5524	+	14.1753i	1.62960	+	0.940849i	0.984212	+	0.176994i	$0.0566372\pi$
$227$	24.5524	+	14.1753i	1.62960	+	0.940849i	0.645387	+	0.763856i	$0.276696\pi$
$228$	−18.7888	−	10.8477i	−1.24432	−	0.718409i
$229$			6.48853i			0.428774i	0.976749	+	0.214387i	$0.0687754\pi$
$229$			6.48853i			0.428774i	−0.976749	+	0.214387i	$0.931225\pi$
$230$		0			0
$231$	−2.81280	−	4.87191i	−0.185069	−	0.320548i
$232$	−11.3467	+	6.55102i	−0.744947	+	0.430095i
$233$	−4.71245			−0.308723			−0.154361	−	0.988014i	$-0.549332\pi$
$233$	−4.71245			−0.308723			−0.154361	+	0.988014i	$0.549332\pi$
$234$	5.94333	+	7.18118i	0.388528	+	0.469448i
$235$		0			0
$236$	39.0963	−	22.5722i	2.54495	−	1.46933i
$237$	7.72638	+	13.3825i	0.501882	+	0.869286i
$238$	18.5797	−	32.1809i	1.20434	−	2.08598i
$239$		−	1.12495i		−	0.0727672i	−0.999338	−	0.0363836i	$-0.988416\pi$
$239$		−	1.12495i		−	0.0727672i	0.999338	−	0.0363836i	$-0.0115838\pi$
$240$		0			0
$241$	−3.04976	−	1.76078i	−0.196453	−	0.113422i	0.398547	−	0.917148i	$-0.369515\pi$
$241$	−3.04976	−	1.76078i	−0.196453	−	0.113422i	−0.595000	+	0.803726i	$0.702848\pi$
$242$		−	22.9724i		−	1.47672i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.13468	−	5.42943i	−0.200677	−	0.347583i
$245$		0			0
$246$	−17.6187			−1.12333
$247$	16.4657	−	2.78852i	1.04769	−	0.177429i
$248$	−58.9871			−3.74568
$249$	−0.551865	+	0.318619i	−0.0349730	+	0.0201917i
$250$		0			0
$251$	−8.11650	+	14.0582i	−0.512309	+	0.887346i	0.487589	+	0.873073i	$0.337876\pi$
$251$	−8.11650	+	14.0582i	−0.512309	+	0.887346i	−0.999898	+	0.0142722i	$0.995457\pi$
$252$		−	18.1215i		−	1.14155i
$253$	7.03486	+	4.06158i	0.442278	+	0.255349i
$254$	16.3830	+	9.45872i	1.02796	+	0.593493i
$255$		0			0
$256$	11.4114	−	19.7651i	0.713211	−	1.23532i
$257$	5.57362	+	9.65380i	0.347673	+	0.602187i	0.985836	−	0.167714i	$-0.0536386\pi$
$257$	5.57362	+	9.65380i	0.347673	+	0.602187i	−0.638163	+	0.769902i	$0.720305\pi$
$258$	−21.5459	+	12.4395i	−1.34139	+	0.774451i
$259$	−36.7062			−2.28081
$260$		0			0
$261$	−1.88812			−0.116872
$262$	18.1107	−	10.4562i	1.11888	−	0.645988i
$263$	−5.95701	−	10.3178i	−0.367325	−	0.636225i	0.621822	−	0.783159i	$-0.286393\pi$
$263$	−5.95701	−	10.3178i	−0.367325	−	0.636225i	−0.989146	+	0.146934i	$0.953060\pi$
$264$	−5.04515	+	8.73845i	−0.310507	+	0.537814i
$265$		0			0
$266$	−40.1211	−	23.1639i	−2.45998	−	1.42027i
$267$	2.83218	+	1.63516i	0.173327	+	0.100070i
$268$		−	17.0946i		−	1.04422i
$269$	−5.83583	+	10.1080i	−0.355817	+	0.616293i	−0.987257	−	0.159131i	$-0.949131\pi$
$269$	−5.83583	+	10.1080i	−0.355817	+	0.616293i	0.631441	+	0.775424i	$0.282464\pi$
$270$		0			0
$271$	11.8335	−	6.83207i	0.718833	−	0.415019i	−0.0954899	−	0.995430i	$-0.530442\pi$
$271$	11.8335	−	6.83207i	0.718833	−	0.415019i	0.814323	+	0.580412i	$0.197108\pi$
$272$	−31.8467			−1.93099
$273$	8.89374	+	10.7461i	0.538273	+	0.650383i
$274$	−7.22245			−0.436324
$275$		0			0
$276$	13.0834	+	22.6611i	0.787529	+	1.36404i
$277$	10.4158	−	18.0406i	0.625822	−	1.08396i	−0.362559	−	0.931961i	$-0.618097\pi$
$277$	10.4158	−	18.0406i	0.625822	−	1.08396i	0.988381	−	0.151995i	$-0.0485697\pi$
$278$		−	19.1807i		−	1.15038i
$279$	−7.36171	−	4.25028i	−0.440734	−	0.254458i
$280$		0			0
$281$		−	12.9350i		−	0.771635i	−0.922575	−	0.385818i	$-0.873919\pi$
$281$		−	12.9350i		−	0.771635i	0.922575	−	0.385818i	$-0.126081\pi$
$282$	7.55528	−	13.0861i	0.449911	−	0.779268i
$283$	−2.97674	−	5.15587i	−0.176949	−	0.306485i	0.763885	−	0.645352i	$-0.223289\pi$
$283$	−2.97674	−	5.15587i	−0.176949	−	0.306485i	−0.940834	+	0.338868i	$0.889956\pi$
$284$	−28.5348	+	16.4746i	−1.69323	+	0.977586i
$285$		0			0
$286$	−2.26329	−	13.3643i	−0.133831	−	0.790247i
$287$	−26.3650			−1.55628
$288$	−7.17387	+	4.14184i	−0.422724	+	0.244060i
$289$	1.59889	+	2.76936i	0.0940524	+	0.162903i
$290$		0			0
$291$		−	14.7927i		−	0.867166i
$292$	13.9489	+	8.05339i	0.816297	+	0.471289i
$293$	10.4173	+	6.01445i	0.608587	+	0.351368i	0.772412	−	0.635121i	$-0.219050\pi$
$293$	10.4173	+	6.01445i	0.608587	+	0.351368i	−0.163825	+	0.986489i	$0.552383\pi$
$294$		−	20.5987i		−	1.20134i
$295$		0			0
$296$	32.9188	+	57.0171i	1.91337	+	3.31405i
$297$	−1.25929	+	0.727051i	−0.0730714	+	0.0421878i
$298$	5.66406			0.328110
$299$	−18.8802	−	7.01696i	−1.09187	−	0.405801i
$300$		0			0
$301$	−32.2418	+	18.6148i	−1.85838	+	1.07294i
$302$	−17.7799	−	30.7956i	−1.02312	−	1.77209i
$303$	−7.77054	+	13.4590i	−0.446406	+	0.773197i
$304$			39.7044i			2.27721i
$305$		0			0
$306$	−8.31811	−	4.80246i	−0.475515	−	0.274539i
$307$			6.28897i			0.358930i	0.983764	+	0.179465i	$0.0574367\pi$
$307$			6.28897i			0.358930i	−0.983764	+	0.179465i	$0.942563\pi$
$308$	−13.1753	+	22.8202i	−0.750731	+	1.30030i
$309$	2.43562	+	4.21862i	0.138558	+	0.239989i
$310$		0			0
$311$	28.4919			1.61563			0.807814	−	0.589438i	$-0.200651\pi$
$311$	28.4919			1.61563			0.807814	+	0.589438i	$0.200651\pi$
$312$	8.71621	−	23.4523i	0.493458	−	1.32772i
$313$	−1.75476			−0.0991849			−0.0495924	−	0.998770i	$-0.515792\pi$
$313$	−1.75476			−0.0991849			−0.0495924	+	0.998770i	$0.515792\pi$
$314$	33.8532	−	19.5452i	1.91045	−	1.10300i
$315$		0			0
$316$	36.1907	−	62.6841i	2.03589	−	3.52626i
$317$			12.0631i			0.677532i	0.940871	+	0.338766i	$0.110010\pi$
$317$			12.0631i			0.677532i	−0.940871	+	0.338766i	$0.889990\pi$
$318$	−28.9033	−	16.6874i	−1.62082	−	0.935780i
$319$	2.37769	+	1.37276i	0.133125	+	0.0768599i
$320$		0			0
$321$	−6.24850	+	10.8227i	−0.348757	+	0.604065i
$322$	27.9379	+	48.3899i	1.55692	+	2.69666i
$323$	−14.9023	+	8.60386i	−0.829187	+	0.478731i
$324$	−4.68404			−0.260225
$325$		0			0
$326$	−6.70481			−0.371345
$327$	11.0373	−	6.37239i	0.610365	−	0.352394i
$328$	23.6446	+	40.9537i	1.30556	+	2.26129i
$329$	11.3059	−	19.5824i	0.623314	−	1.07961i
$330$		0			0
$331$	−1.52636	−	0.881246i	−0.0838965	−	0.0484377i	0.457465	−	0.889228i	$-0.348758\pi$
$331$	−1.52636	−	0.881246i	−0.0838965	−	0.0484377i	−0.541361	+	0.840790i	$0.682091\pi$
$332$	2.58496	+	1.49243i	0.141868	+	0.0819076i
$333$			9.48780i			0.519928i
$334$	28.9605	−	50.1611i	1.58465	−	2.74470i
$335$		0			0
$336$	−28.7207	+	16.5819i	−1.56684	+	0.904617i
$337$	4.32619			0.235663			0.117831	−	0.993034i	$-0.462406\pi$
$337$	4.32619			0.235663			0.117831	+	0.993034i	$0.462406\pi$
$338$	11.0664	+	31.7354i	0.601933	+	1.72618i
$339$	−5.65295			−0.307026
$340$		0			0
$341$	6.18035	+	10.7047i	0.334684	+	0.579691i
$342$	−5.98740	+	10.3705i	−0.323762	+	0.560771i
$343$		−	3.74284i		−	0.202094i
$344$	57.8301	+	33.3882i	3.11799	+	1.80017i
$345$		0			0
$346$			51.0319i			2.74349i
$347$	−14.2274	+	24.6426i	−0.763768	+	1.32289i	0.177127	+	0.984188i	$0.443320\pi$
$347$	−14.2274	+	24.6426i	−0.763768	+	1.32289i	−0.940895	+	0.338697i	$0.890014\pi$
$348$	4.42202	+	7.65916i	0.237045	+	0.410574i
$349$	6.58229	−	3.80029i	0.352342	−	0.203425i	−0.313374	−	0.949630i	$-0.601459\pi$
$349$	6.58229	−	3.80029i	0.352342	−	0.203425i	0.665716	+	0.746205i	$0.268126\pi$
$350$		0			0
$351$	2.77764	−	2.29885i	0.148260	−	0.122703i
$352$	12.0453			0.642017
$353$	6.22033	−	3.59131i	0.331075	−	0.191146i	−0.325243	−	0.945630i	$-0.605446\pi$
$353$	6.22033	−	3.59131i	0.331075	−	0.191146i	0.656318	+	0.754484i	$0.272113\pi$
$354$	−12.4587	−	21.5791i	−0.662174	−	1.14692i
$355$		0			0
$356$		−	15.3183i		−	0.811870i
$357$	−12.4474	−	7.18652i	−0.658787	−	0.380351i
$358$	24.6291	+	14.2196i	1.30169	+	0.751531i
$359$		−	16.3412i		−	0.862456i	−0.902243	−	0.431228i	$-0.858080\pi$
$359$		−	16.3412i		−	0.862456i	0.902243	−	0.431228i	$-0.141920\pi$
$360$		0			0
$361$	1.22673	+	2.12476i	0.0645649	+	0.111830i
$362$	−16.2591	+	9.38718i	−0.854558	+	0.493379i
$363$	−8.88559			−0.466372
$364$	22.7622	−	61.2450i	1.19306	−	3.21011i
$365$		0			0
$366$	−2.99677	+	1.73018i	−0.156643	+	0.0904381i
$367$	8.01762	+	13.8869i	0.418517	+	0.724892i	0.995790	−	0.0916587i	$-0.0292169\pi$
$367$	8.01762	+	13.8869i	0.418517	+	0.724892i	−0.577274	+	0.816551i	$0.695884\pi$
$368$	23.9437	−	41.4716i	1.24815	−	2.16186i
$369$			6.81481i			0.354765i
$370$		0			0
$371$	−43.2516	−	24.9713i	−2.24551	−	1.29645i
$372$			39.8170i			2.06442i
$373$	9.17621	−	15.8937i	0.475126	−	0.822942i	−0.524468	−	0.851430i	$-0.675736\pi$
$373$	9.17621	−	15.8937i	0.475126	−	0.822942i	0.999594	+	0.0284878i	$0.00906918\pi$
$374$	6.98327	+	12.0954i	0.361096	+	0.625437i
$375$		0			0
$376$	−40.5574			−2.09159
$377$	−6.38125	−	2.37164i	−0.328651	−	0.122146i
$378$	−10.0022			−0.514455
$379$	−1.64459	+	0.949505i	−0.0844769	+	0.0487728i	−0.541643	−	0.840608i	$-0.682198\pi$
$379$	−1.64459	+	0.949505i	−0.0844769	+	0.0487728i	0.457166	+	0.889381i	$0.348864\pi$
$380$		0			0
$381$	3.65858	−	6.33685i	0.187435	−	0.324647i
$382$			30.9627i			1.58419i
$383$	16.4396	+	9.49143i	0.840026	+	0.484989i	0.857273	−	0.514862i	$-0.172157\pi$
$383$	16.4396	+	9.49143i	0.840026	+	0.484989i	−0.0172470	+	0.999851i	$0.505490\pi$
$384$	−4.78309	−	2.76152i	−0.244086	−	0.140923i
$385$		0			0
$386$	−14.2042	+	24.6023i	−0.722973	+	1.25223i
$387$	4.81154	+	8.33383i	0.244584	+	0.423633i
$388$	−60.0067	+	34.6449i	−3.04638	+	1.75883i
$389$	−15.9971			−0.811084			−0.405542	−	0.914076i	$-0.632917\pi$
$389$	−15.9971			−0.811084			−0.405542	+	0.914076i	$0.632917\pi$
$390$		0			0
$391$	20.7541			1.04958
$392$	−47.8805	+	27.6438i	−2.41833	+	1.39622i
$393$	−4.04442	−	7.00513i	−0.204014	−	0.353362i
$394$	−32.3874	+	56.0966i	−1.63165	+	2.82611i
$395$		0			0
$396$	5.89856	+	3.40554i	0.296414	+	0.171135i
$397$	25.4136	+	14.6726i	1.27547	+	0.736396i	0.976013	−	0.217713i	$-0.0698596\pi$
$397$	25.4136	+	14.6726i	1.27547	+	0.736396i	0.299462	+	0.954108i	$0.403193\pi$
$398$			4.67221i			0.234197i
$399$	−8.95968	+	15.5186i	−0.448545	+	0.776903i
$400$		0			0
$401$	8.31056	−	4.79811i	0.415010	−	0.239606i	−0.277930	−	0.960601i	$-0.589648\pi$
$401$	8.31056	−	4.79811i	0.415010	−	0.239606i	0.692940	+	0.720995i	$0.256315\pi$
$402$	−9.43534			−0.470592
$403$	−19.5415	−	23.6115i	−0.973432	−	1.17617i
$404$	72.7950			3.62169
$405$		0			0
$406$	9.44264	+	16.3551i	0.468630	+	0.811692i
$407$	6.89811	−	11.9479i	0.341927	−	0.592234i
$408$			25.7800i			1.27630i
$409$	3.21284	+	1.85494i	0.158865	+	0.0917207i	0.577325	−	0.816515i	$-0.304097\pi$
$409$	3.21284	+	1.85494i	0.158865	+	0.0917207i	−0.418460	+	0.908235i	$0.637430\pi$
$410$		0			0
$411$			2.79360i			0.137798i
$412$	11.4086	−	19.7602i	0.562059	−	0.973515i
$413$	−18.6435	−	32.2915i	−0.917388	−	1.58896i
$414$	12.5078	−	7.22137i	0.614724	−	0.354911i
$415$		0			0
$416$	−29.4479	+	4.98710i	−1.44380	+	0.244513i
$417$	−7.41900			−0.363310
$418$	15.0797	−	8.70629i	0.737574	−	0.425839i
$419$	−11.3343	−	19.6315i	−0.553715	−	0.959062i	−0.998002	−	0.0631779i	$-0.979876\pi$
$419$	−11.3343	−	19.6315i	−0.553715	−	0.959062i	0.444287	−	0.895884i	$-0.353457\pi$
$420$		0			0
$421$			29.9153i			1.45798i	0.684524	+	0.728991i	$0.260010\pi$
$421$			29.9153i			1.45798i	−0.684524	+	0.728991i	$0.739990\pi$
$422$	20.1081	+	11.6094i	0.978848	+	0.565138i
$423$	−5.06165	−	2.92234i	−0.246106	−	0.142089i
$424$			89.5791i			4.35035i
$425$		0			0
$426$	9.09312	+	15.7497i	0.440563	+	0.763077i
$427$	−4.48443	+	2.58909i	−0.217017	+	0.125295i
$428$	58.5364			2.82947
$429$	−5.16923	+	0.875428i	−0.249573	+	0.0422660i
$430$		0			0
$431$	−1.95227	+	1.12714i	−0.0940373	+	0.0542925i	−0.546281	−	0.837602i	$-0.683957\pi$
$431$	−1.95227	+	1.12714i	−0.0940373	+	0.0542925i	0.452244	+	0.891894i	$0.350624\pi$
$432$	4.28608	+	7.42371i	0.206214	+	0.357173i
$433$	17.0243	−	29.4870i	0.818137	−	1.41705i	−0.0889169	−	0.996039i	$-0.528341\pi$
$433$	17.0243	−	29.4870i	0.818137	−	1.41705i	0.907054	−	0.421015i	$-0.138326\pi$
$434$			85.0240i			4.08128i
$435$		0			0
$436$	−51.6992	−	29.8486i	−2.47594	−	1.42949i
$437$		−	25.8749i		−	1.23777i
$438$	4.44506	−	7.69907i	0.212393	−	0.367876i
$439$	−10.3598	−	17.9437i	−0.494447	−	0.856407i	0.505533	−	0.862808i	$-0.331296\pi$
$439$	−10.3598	−	17.9437i	−0.494447	−	0.856407i	−0.999980	+	0.00640022i	$0.997963\pi$
$440$		0			0
$441$	−7.96745			−0.379402
$442$	−22.0803	−	26.6790i	−1.05025	−	1.26899i
$443$	−25.5489			−1.21387			−0.606933	−	0.794753i	$-0.707601\pi$
$443$	−25.5489			−1.21387			−0.606933	+	0.794753i	$0.707601\pi$
$444$	38.4872	−	22.2206i	1.82652	−	1.05454i
$445$		0			0
$446$	0.369005	−	0.639135i	0.0174729	−	0.0302639i
$447$		−	2.19083i		−	0.103623i
$448$	14.3128	+	8.26348i	0.676214	+	0.390413i
$449$	−16.0195	−	9.24883i	−0.756005	−	0.436479i	0.0718548	−	0.997415i	$-0.477108\pi$
$449$	−16.0195	−	9.24883i	−0.756005	−	0.436479i	−0.827859	+	0.560936i	$0.810442\pi$
$450$		0			0
$451$	4.95471	−	8.58182i	0.233308	−	0.404102i
$452$	13.2393	+	22.9312i	0.622726	+	1.07859i
$453$	−11.9116	+	6.87715i	−0.559655	+	0.323117i
$454$	−73.2964			−3.43997
$455$		0			0
$456$	32.1409			1.50513
$457$	5.53055	−	3.19306i	0.258708	−	0.149365i	−0.365037	−	0.930993i	$-0.618944\pi$
$457$	5.53055	−	3.19306i	0.258708	−	0.149365i	0.623745	+	0.781628i	$0.285610\pi$
$458$	−8.38756	−	14.5277i	−0.391925	−	0.678834i
$459$	−1.85757	+	3.21740i	−0.0867038	+	0.150175i
$460$		0			0
$461$	16.7150	+	9.65044i	0.778497	+	0.449466i	0.835898	−	0.548886i	$-0.184948\pi$
$461$	16.7150	+	9.65044i	0.778497	+	0.449466i	−0.0574001	+	0.998351i	$0.518281\pi$
$462$	12.5956	+	7.27207i	0.586000	+	0.338328i
$463$			25.7074i			1.19473i	0.801971	+	0.597363i	$0.203785\pi$
$463$			25.7074i			1.19473i	−0.801971	+	0.597363i	$0.796215\pi$
$464$	8.09264	−	14.0169i	0.375692	−	0.650717i
$465$		0			0
$466$	10.5511	−	6.09167i	0.488769	−	0.282191i
$467$	−34.8997			−1.61496			−0.807482	−	0.589892i	$-0.799170\pi$
$467$	−34.8997			−1.61496			−0.807482	+	0.589892i	$0.799170\pi$
$468$	−15.8306	−	5.88355i	−0.731768	−	0.271967i
$469$	−14.1193			−0.651967
$470$		0			0
$471$	−7.55996	−	13.0942i	−0.348345	−	0.603351i
$472$	−33.4397	+	57.9193i	−1.53919	+	2.66595i
$473$		−	13.9929i		−	0.643396i
$474$	−34.5984	−	19.9754i	−1.58916	−	0.917501i
$475$		0			0
$476$			67.3239i			3.08578i
$477$	−6.45458	+	11.1797i	−0.295535	+	0.511881i
$478$	1.45420	+	2.51875i	0.0665135	+	0.115205i
$479$	−4.17388	+	2.40979i	−0.190709	+	0.110106i	−0.592315	−	0.805707i	$-0.701786\pi$
$479$	−4.17388	+	2.40979i	−0.190709	+	0.110106i	0.401605	+	0.915813i	$0.368452\pi$
$480$		0			0
$481$	−11.9175	+	32.0657i	−0.543390	+	1.46207i
$482$	9.10448			0.414698
$483$	18.7169	−	10.8062i	0.851650	−	0.491700i
$484$	20.8102	+	36.0444i	0.945920	+	1.63838i
$485$		0			0
$486$			2.58535i			0.117274i
$487$	−17.6415	−	10.1853i	−0.799414	−	0.461542i	0.0438521	−	0.999038i	$-0.486037\pi$
$487$	−17.6415	−	10.1853i	−0.799414	−	0.461542i	−0.843266	+	0.537496i	$0.819370\pi$
$488$	8.04344	+	4.64388i	0.364110	+	0.210219i
$489$			2.59339i			0.117277i
$490$		0			0
$491$	−11.3693	−	19.6922i	−0.513090	−	0.888698i	−0.999885	−	0.0151819i	$-0.995167\pi$
$491$	−11.3693	−	19.6922i	−0.513090	−	0.888698i	0.486794	−	0.873517i	$-0.338166\pi$
$492$	27.6443	−	15.9604i	1.24630	−	0.719551i
$493$	7.01463			0.315923
$494$	−33.2617	+	27.5283i	−1.49652	+	1.23855i
$495$		0			0
$496$	63.1058	−	36.4341i	2.83353	−	1.63594i
$497$	13.6071	+	23.5683i	0.610364	+	1.05718i
$498$	0.823743	−	1.42677i	0.0369128	−	0.0639349i
$499$		−	25.6902i		−	1.15005i	−0.818136	−	0.575025i	$-0.804992\pi$
$499$		−	25.6902i		−	1.15005i	0.818136	−	0.575025i	$-0.195008\pi$
$500$		0			0
$501$	−19.4021	−	11.2018i	−0.866820	−	0.500459i
$502$		−	41.9680i		−	1.87312i
$503$	−6.59323	+	11.4198i	−0.293978	+	0.509184i	−0.974747	−	0.223314i	$-0.928313\pi$
$503$	−6.59323	+	11.4198i	−0.293978	+	0.509184i	0.680769	+	0.732498i	$0.261646\pi$
$504$	13.4231	+	23.2495i	0.597912	+	1.03561i
$505$		0			0
$506$	−21.0012			−0.933618
$507$	12.2751	−	4.28042i	0.545156	−	0.190100i
$508$	−34.2739			−1.52066
$509$	17.5993	−	10.1609i	0.780074	−	0.450376i	−0.0563823	−	0.998409i	$-0.517957\pi$
$509$	17.5993	−	10.1609i	0.780074	−	0.450376i	0.836457	+	0.548033i	$0.184623\pi$
$510$		0			0
$511$	6.65169	−	11.5211i	0.294254	−	0.509662i
$512$			47.9588i			2.11950i
$513$	4.01125	+	2.31589i	0.177101	+	0.102249i
$514$	−24.9585	−	14.4098i	−1.10087	−	0.635588i
$515$		0			0
$516$	22.5375	−	39.0360i	0.992156	−	1.71847i
$517$	4.24939	+	7.36015i	0.186888	+	0.323699i
$518$	82.1844	−	47.4492i	3.61098	−	2.08480i
$519$	19.7389			0.866439
$520$		0			0
$521$	5.27143			0.230945			0.115473	−	0.993311i	$-0.463162\pi$
$521$	5.27143			0.230945			0.115473	+	0.993311i	$0.463162\pi$
$522$	4.22747	−	2.44073i	0.185031	−	0.106828i
$523$	15.0898	+	26.1363i	0.659831	+	1.14286i	0.980659	+	0.195723i	$0.0627053\pi$
$523$	15.0898	+	26.1363i	0.659831	+	1.14286i	−0.320829	+	0.947137i	$0.603961\pi$
$524$	−18.9442	+	32.8123i	−0.827582	+	1.43341i
$525$		0			0
$526$	26.6752	+	15.4010i	1.16310	+	0.671514i
$527$	27.3497	+	15.7904i	1.19137	+	0.687839i
$528$		−	12.4648i		−	0.542461i
$529$	−4.10380	+	7.10799i	−0.178426	+	0.309043i
$530$		0			0
$531$	−8.34670	+	4.81897i	−0.362216	+	0.209125i
$532$	83.9351			3.63905
$533$	−8.55998	+	23.0319i	−0.370774	+	0.997622i
$534$	−8.45493			−0.365881
$535$		0			0
$536$	12.6624	+	21.9320i	0.546933	+	0.947316i
$537$	5.50008	−	9.52641i	0.237346	−	0.411095i
$538$		−	30.1753i		−	1.30095i
$539$	10.0333	+	5.79274i	0.432166	+	0.249511i
$540$		0			0
$541$		−	2.65684i		−	0.114226i	−0.998368	−	0.0571132i	$-0.981810\pi$
$541$		−	2.65684i		−	0.114226i	0.998368	−	0.0571132i	$-0.0181896\pi$
$542$	−17.6633	+	30.5937i	−0.758703	+	1.31411i
$543$	3.63091	+	6.28892i	0.155817	+	0.269883i
$544$	26.6519	−	15.3875i	1.14269	−	0.659733i
$545$		0			0
$546$	−33.8041	−	12.5635i	−1.44668	−	0.537670i
$547$	−16.5521			−0.707717			−0.353858	−	0.935299i	$-0.615131\pi$
$547$	−16.5521			−0.707717			−0.353858	+	0.935299i	$0.615131\pi$
$548$	11.3323	−	6.54268i	0.484090	−	0.279489i
$549$	0.669226	+	1.15913i	0.0285619	+	0.0494706i
$550$		0			0
$551$		−	8.74538i		−	0.372566i
$552$	−33.5714	−	19.3825i	−1.42889	−	0.824973i
$553$	−51.7739	−	29.8917i	−2.20165	−	1.27112i
$554$			53.8568i			2.28815i
$555$		0			0
$556$	17.3755	+	30.0952i	0.736884	+	1.27632i
$557$	20.4650	−	11.8155i	0.867129	−	0.500637i	0.000735809	−	1.00000i	$-0.499766\pi$
$557$	20.4650	−	11.8155i	0.867129	−	0.500637i	0.866393	+	0.499363i	$0.166432\pi$
$558$	21.9770			0.930359
$559$	5.79348	+	34.2094i	0.245038	+	1.44690i
$560$		0			0
$561$	4.67843	−	2.70109i	0.197523	−	0.114040i
$562$	16.7207	+	28.9611i	0.705321	+	1.22165i
$563$	−0.655261	+	1.13495i	−0.0276160	+	0.0478322i	−0.879503	−	0.475893i	$-0.842125\pi$
$563$	−0.655261	+	1.13495i	−0.0276160	+	0.0478322i	0.851887	+	0.523725i	$0.175458\pi$
$564$			27.3768i			1.15277i
$565$		0			0
$566$	13.3297	+	7.69593i	0.560291	+	0.323484i
$567$			3.86878i			0.162473i
$568$	24.4063	−	42.2730i	1.02407	−	1.77373i
$569$	−1.89517	−	3.28252i	−0.0794495	−	0.137611i	0.823563	−	0.567225i	$-0.191983\pi$
$569$	−1.89517	−	3.28252i	−0.0794495	−	0.137611i	−0.903013	+	0.429614i	$0.858650\pi$
$570$		0			0
$571$	0.483465			0.0202324			0.0101162	−	0.999949i	$-0.496780\pi$
$571$	0.483465			0.0202324			0.0101162	+	0.999949i	$0.496780\pi$
$572$	15.6576	+	18.9187i	0.654678	+	0.791032i
$573$	11.9762			0.500313
$574$	59.0307	−	34.0814i	2.46389	−	1.42253i
$575$		0			0
$576$	2.13594	−	3.69955i	0.0889975	−	0.154148i
$577$		−	29.5959i		−	1.23209i	−0.787710	−	0.616047i	$-0.788733\pi$
$577$		−	29.5959i		−	1.23209i	0.787710	−	0.616047i	$-0.211267\pi$
$578$	−7.15977	−	4.13369i	−0.297807	−	0.171939i
$579$	9.51605	+	5.49410i	0.395474	+	0.228327i
$580$		0			0
$581$	1.23267	−	2.13504i	0.0511397	−	0.0885765i
$582$	19.1222	+	33.1206i	0.792641	+	1.37289i
$583$	16.2564	−	9.38561i	0.673270	−	0.388712i
$584$	−23.8615			−0.987394
$585$		0			0
$586$	−31.0989			−1.28469
$587$	−32.4898	+	18.7580i	−1.34100	+	0.774224i	−0.986954	−	0.161005i	$-0.948526\pi$
$587$	−32.4898	+	18.7580i	−1.34100	+	0.774224i	−0.354042	+	0.935229i	$0.615193\pi$
$588$	18.6599	+	32.3199i	0.769523	+	1.33285i
$589$	19.6864	−	34.0979i	0.811165	−	1.40498i
$590$		0			0
$591$	21.6979	+	12.5273i	0.892531	+	0.515303i
$592$	−70.4347	−	40.6655i	−2.89485	−	1.67134i
$593$		−	35.7276i		−	1.46716i	−0.679604	−	0.733579i	$-0.737849\pi$
$593$		−	35.7276i		−	1.46716i	0.679604	−	0.733579i	$-0.262151\pi$
$594$	1.87968	−	3.25571i	0.0771243	−	0.133583i
$595$		0			0
$596$	−8.88710	+	5.13097i	−0.364030	+	0.210173i
$597$	1.80719			0.0739632
$598$	51.3430	−	8.69511i	2.09957	−	0.355570i
$599$	20.5481			0.839574			0.419787	−	0.907623i	$-0.362105\pi$
$599$	20.5481			0.839574			0.419787	+	0.907623i	$0.362105\pi$
$600$		0			0
$601$	−10.0067	−	17.3321i	−0.408181	−	0.706990i	0.586505	−	0.809946i	$-0.300503\pi$
$601$	−10.0067	−	17.3321i	−0.408181	−	0.706990i	−0.994686	+	0.102956i	$0.967170\pi$
$602$	48.1258	−	83.3563i	1.96146	−	3.39735i
$603$			3.64954i			0.148621i
$604$	55.7943	+	32.2129i	2.27024	+	1.31072i
$605$		0			0
$606$		−	40.1791i		−	1.63217i
$607$	−11.4603	+	19.8498i	−0.465159	+	0.805678i	−0.999209	−	0.0397745i	$-0.987336\pi$
$607$	−11.4603	+	19.8498i	−0.465159	+	0.805678i	0.534050	+	0.845453i	$0.320669\pi$
$608$	−19.1841	−	33.2279i	−0.778018	−	1.34757i
$609$	6.32608	−	3.65236i	0.256346	−	0.148001i
$610$		0			0
$611$	−13.4360	−	16.2344i	−0.543564	−	0.656775i
$612$	17.4018			0.703428
$613$	−14.7117	+	8.49382i	−0.594201	+	0.343062i	−0.766757	−	0.641938i	$-0.778131\pi$
$613$	−14.7117	+	8.49382i	−0.594201	+	0.343062i	0.172556	+	0.985000i	$0.444797\pi$
$614$	−8.12960	−	14.0809i	−0.328084	−	0.568258i
$615$		0			0
$616$		−	39.0371i		−	1.57285i
$617$	32.7396	+	18.9022i	1.31805	+	0.760976i	0.983414	−	0.181373i	$-0.0580540\pi$
$617$	32.7396	+	18.9022i	1.31805	+	0.760976i	0.334634	+	0.942348i	$0.391387\pi$
$618$	−10.9066	−	6.29694i	−0.438728	−	0.253300i
$619$		−	16.1816i		−	0.650394i	−0.945646	−	0.325197i	$-0.894569\pi$
$619$		−	16.1816i		−	0.650394i	0.945646	−	0.325197i	$-0.105431\pi$
$620$		0			0
$621$	−2.79319	−	4.83794i	−0.112087	−	0.194140i
$622$	−63.7928	+	36.8308i	−2.55786	+	1.47678i
$623$	−12.6522			−0.506898
$624$	5.16079	+	30.4735i	0.206597	+	1.21991i
$625$		0			0
$626$	3.92887	−	2.26834i	0.157029	−	0.0906609i
$627$	−3.36755	−	5.83276i	−0.134487	−	0.232938i
$628$	−35.4112	+	61.3340i	−1.41306	+	2.44749i
$629$		−	35.2484i		−	1.40545i
$630$		0			0
$631$	3.63548	+	2.09894i	0.144726	+	0.0835576i	0.570615	−	0.821218i	$-0.306705\pi$
$631$	3.63548	+	2.09894i	0.144726	+	0.0835576i	−0.425888	+	0.904776i	$0.640038\pi$
$632$			107.230i			4.26537i
$633$	4.49046	−	7.77771i	0.178480	−	0.309136i
$634$	−15.5937	−	27.0091i	−0.619305	−	1.07267i
$635$		0			0
$636$	60.4670			2.39767
$637$	−26.9274	−	10.0078i	−1.06690	−	0.396523i
$638$	−7.09814			−0.281018
$639$	6.09191	−	3.51717i	0.240992	−	0.139137i
$640$		0			0
$641$	−9.06398	+	15.6993i	−0.358006	+	0.620084i	−0.987628	−	0.156818i	$-0.949877\pi$
$641$	−9.06398	+	15.6993i	−0.358006	+	0.620084i	0.629622	+	0.776902i	$0.283210\pi$
$642$		−	32.3091i		−	1.27514i
$643$	2.01630	+	1.16411i	0.0795150	+	0.0459080i	0.539230	−	0.842158i	$-0.318715\pi$
$643$	2.01630	+	1.16411i	0.0795150	+	0.0459080i	−0.459715	+	0.888066i	$0.652049\pi$
$644$	−87.6709	−	50.6168i	−3.45472	−	1.99458i
$645$		0			0
$646$	22.2440	−	38.5277i	0.875178	−	1.51585i
$647$	6.60278	+	11.4364i	0.259582	+	0.449610i	0.966130	−	0.258056i	$-0.0830818\pi$
$647$	6.60278	+	11.4364i	0.259582	+	0.449610i	−0.706548	+	0.707665i	$0.749748\pi$
$648$	6.00952	−	3.46960i	0.236076	−	0.136299i
$649$	14.0145			0.550119
$650$		0			0
$651$	32.8868			1.28894
$652$	10.5201	−	6.07376i	0.411998	−	0.237867i
$653$	14.5932	+	25.2762i	0.571076	+	0.989133i	0.996456	+	0.0841176i	$0.0268072\pi$
$653$	14.5932	+	25.2762i	0.571076	+	0.989133i	−0.425380	+	0.905015i	$0.639860\pi$
$654$	−16.4749	+	28.5353i	−0.644219	+	1.11582i
$655$		0			0
$656$	−50.5912	−	29.2088i	−1.97525	−	1.14041i
$657$	−2.97796	−	1.71933i	−0.116181	−	0.0670773i
$658$			58.4594i			2.27899i
$659$	4.55618	−	7.89153i	0.177483	−	0.307410i	−0.763534	−	0.645767i	$-0.776538\pi$
$659$	4.55618	−	7.89153i	0.177483	−	0.307410i	0.941018	+	0.338357i	$0.109871\pi$
$660$		0			0
$661$	−3.17818	+	1.83492i	−0.123617	+	0.0713702i	−0.560533	−	0.828132i	$-0.689404\pi$
$661$	−3.17818	+	1.83492i	−0.123617	+	0.0713702i	0.436917	+	0.899502i	$0.356071\pi$
$662$	4.55666			0.177100
$663$	−10.3193	+	8.54053i	−0.400769	+	0.331687i
$664$	−4.42192			−0.171604
$665$		0			0
$666$	−12.2646	−	21.2430i	−0.475245	−	0.823149i
$667$	−5.27388	+	9.13463i	−0.204205	+	0.353694i
$668$			104.939i			4.06022i
$669$	−0.247214	−	0.142729i	−0.00955784	−	0.00551822i
$670$		0			0
$671$		−	1.94624i		−	0.0751339i
$672$	16.0238	−	27.7541i	0.618133	−	1.07064i
$673$	−4.33922	−	7.51575i	−0.167265	−	0.289711i	0.770192	−	0.637812i	$-0.220160\pi$
$673$	−4.33922	−	7.51575i	−0.167265	−	0.289711i	−0.937457	+	0.348100i	$0.886827\pi$
$674$	−9.68626	+	5.59237i	−0.373101	+	0.215410i
$675$		0			0
$676$	−46.1121	−	39.7691i	−1.77354	−	1.52958i
$677$	27.2042			1.04554			0.522771	−	0.852473i	$-0.324898\pi$
$677$	27.2042			1.04554			0.522771	+	0.852473i	$0.324898\pi$
$678$	12.6568	−	7.30743i	0.486083	−	0.280640i
$679$	28.6149	+	49.5625i	1.09814	+	1.90203i
$680$		0			0
$681$			28.3507i			1.08640i
$682$	−27.6753	−	15.9784i	−1.05974	−	0.611843i
$683$	−18.0269	−	10.4078i	−0.689780	−	0.398244i	0.113750	−	0.993509i	$-0.463714\pi$
$683$	−18.0269	−	10.4078i	−0.689780	−	0.398244i	−0.803529	+	0.595265i	$0.797047\pi$
$684$		−	21.6955i		−	0.829548i
$685$		0			0
$686$	4.83828	+	8.38015i	0.184726	+	0.319956i
$687$	−5.61923	+	3.24426i	−0.214387	+	0.123776i
$688$	−82.4906			−3.14493
$689$	−35.8570	+	29.6762i	−1.36604	+	1.13057i
$690$		0			0
$691$	2.19328	−	1.26629i	0.0834365	−	0.0481721i	−0.457701	−	0.889106i	$-0.651327\pi$
$691$	2.19328	−	1.26629i	0.0834365	−	0.0481721i	0.541138	+	0.840934i	$0.317994\pi$
$692$	−46.2288	−	80.0706i	−1.75736	−	3.04383i
$693$	2.81280	−	4.87191i	0.106849	−	0.185069i
$694$		−	73.5658i		−	2.79252i
$695$		0			0
$696$	−11.3467	−	6.55102i	−0.430095	−	0.248316i
$697$		−	25.3179i		−	0.958985i
$698$	−9.82508	+	17.0175i	−0.371885	+	0.644123i
$699$	−2.35622	−	4.08110i	−0.0891206	−	0.154361i
$700$		0			0
$701$	−45.3126			−1.71143			−0.855717	−	0.517444i	$-0.826883\pi$
$701$	−45.3126			−1.71143			−0.855717	+	0.517444i	$0.826883\pi$
$702$	−3.24742	+	8.73767i	−0.122566	+	0.329782i
$703$	−43.9455			−1.65743
$704$	−5.37953	+	3.10587i	−0.202749	+	0.117057i
$705$		0			0
$706$	−9.28479	+	16.0817i	−0.349438	+	0.605244i
$707$		−	60.1250i		−	2.26123i
$708$	39.0963	+	22.5722i	1.46933	+	0.848317i
$709$	32.6704	+	18.8623i	1.22696	+	0.708388i	0.966393	−	0.257067i	$-0.0827562\pi$
$709$	32.6704	+	18.8623i	1.22696	+	0.708388i	0.260570	+	0.965455i	$0.416090\pi$
$710$		0			0
$711$	−7.72638	+	13.3825i	−0.289762	+	0.501882i
$712$	11.3467	+	19.6531i	0.425235	+	0.736529i
$713$	−41.1253	+	23.7437i	−1.54015	+	0.889208i
$714$	37.1593			1.39065
$715$		0			0
$716$	−51.5252			−1.92559
$717$	0.974238	−	0.562477i	0.0363836	−	0.0210061i
$718$	21.1239	+	36.5876i	0.788336	+	1.36544i
$719$	−1.06999	+	1.85328i	−0.0399040	+	0.0691157i	−0.885288	−	0.465044i	$-0.846039\pi$
$719$	−1.06999	+	1.85328i	−0.0399040	+	0.0691157i	0.845384	+	0.534160i	$0.179372\pi$
$720$		0			0
$721$	−16.3209	−	9.42288i	−0.607822	−	0.350926i
$722$	−5.49326	−	3.17153i	−0.204438	−	0.118032i
$723$		−	3.52156i		−	0.130968i
$724$	17.0073	−	29.4576i	0.632073	−	1.09478i
$725$		0			0
$726$	19.8947	−	11.4862i	0.738360	−	0.426292i
$727$	25.9144			0.961110			0.480555	−	0.876965i	$-0.340435\pi$
$727$	25.9144			0.961110			0.480555	+	0.876965i	$0.340435\pi$
$728$	16.1625	+	95.4364i	0.599022	+	3.53711i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−17.8755	−	30.9613i	−0.661150	−	1.14515i
$732$	3.13468	−	5.42943i	0.115861	−	0.200677i
$733$			49.2982i			1.82087i	0.413650	+	0.910436i	$0.364254\pi$
$733$			49.2982i			1.82087i	−0.413650	+	0.910436i	$0.635746\pi$
$734$	−35.9026	−	20.7284i	−1.32519	−	0.765098i
$735$		0			0
$736$			46.2757i			1.70575i
$737$	2.65340	−	4.59582i	0.0977393	−	0.169289i
$738$	−8.80934	−	15.2582i	−0.324276	−	0.561663i
$739$	−19.7165	+	11.3833i	−0.725283	+	0.418742i	−0.816694	−	0.577071i	$-0.804196\pi$
$739$	−19.7165	+	11.3833i	−0.725283	+	0.418742i	0.0914111	+	0.995813i	$0.470862\pi$
$740$		0			0
$741$	10.6478	+	12.8655i	0.391156	+	0.472624i
$742$	129.119			4.74012
$743$	30.3228	−	17.5069i	1.11244	−	0.642265i	0.172977	−	0.984926i	$-0.444661\pi$
$743$	30.3228	−	17.5069i	1.11244	−	0.642265i	0.939459	+	0.342660i	$0.111328\pi$
$744$	−29.4935	−	51.0843i	−1.08129	−	1.87284i
$745$		0			0
$746$			47.4474i			1.73717i
$747$	−0.551865	−	0.318619i	−0.0201917	−	0.0116577i
$748$	−21.9140	−	12.6520i	−0.801253	−	0.462604i
$749$		−	48.3481i		−	1.76660i
$750$		0			0
$751$	−26.0854	−	45.1812i	−0.951869	−	1.64868i	−0.741377	−	0.671089i	$-0.765827\pi$
$751$	−26.0854	−	45.1812i	−0.951869	−	1.64868i	−0.210492	−	0.977596i	$-0.567507\pi$
$752$	43.3893	−	25.0508i	1.58224	−	0.913509i
$753$	−16.2330			−0.591564
$754$	17.3533	−	2.93883i	0.631968	−	0.107026i
$755$		0			0
$756$	15.6937	−	9.06076i	0.570774	−	0.329537i
$757$	10.6633	+	18.4694i	0.387564	+	0.671281i	0.992121	−	0.125281i	$-0.0399832\pi$
$757$	10.6633	+	18.4694i	0.387564	+	0.671281i	−0.604557	+	0.796562i	$0.706650\pi$
$758$	2.45480	−	4.25184i	0.0891625	−	0.154434i
$759$			8.12316i			0.294852i
$760$		0			0
$761$	19.9344	+	11.5091i	0.722620	+	0.417205i	0.815716	−	0.578452i	$-0.196343\pi$
$761$	19.9344	+	11.5091i	0.722620	+	0.417205i	−0.0930963	+	0.995657i	$0.529676\pi$
$762$			18.9174i			0.685307i
$763$	−24.6534	+	42.7009i	−0.892512	+	1.54588i
$764$	−28.0485	−	48.5814i	−1.01476	−	1.75761i
$765$		0			0
$766$	−49.0774			−1.77324
$767$	−34.2622	+	5.80242i	−1.23714	+	0.209513i
$768$	22.8228			0.823545
$769$	2.24475	−	1.29601i	0.0809478	−	0.0467352i	−0.458980	−	0.888447i	$-0.651785\pi$
$769$	2.24475	−	1.29601i	0.0809478	−	0.0467352i	0.539928	+	0.841711i	$0.318452\pi$
$770$		0			0
$771$	−5.57362	+	9.65380i	−0.200729	+	0.347673i
$772$		−	51.4691i		−	1.85242i
$773$	−36.3147	−	20.9663i	−1.30615	−	0.754105i	−0.324697	−	0.945818i	$-0.605262\pi$
$773$	−36.3147	−	20.9663i	−1.30615	−	0.754105i	−0.981451	+	0.191713i	$0.938596\pi$
$774$	−21.5459	−	12.4395i	−0.774451	−	0.447129i
$775$		0			0
$776$	51.3248	−	88.8972i	1.84245	−	3.19122i
$777$	−18.3531	−	31.7885i	−0.658414	−	1.14041i
$778$	35.8171	−	20.6790i	1.28411	−	0.741379i
$779$	−31.5648			−1.13092
$780$		0			0
$781$	−10.2286			−0.366010
$782$	−46.4681	+	26.8284i	−1.66170	+	0.959380i
$783$	−0.944061	−	1.63516i	−0.0337380	−	0.0584359i
$784$	34.1491	−	59.1480i	1.21961	−	2.11243i
$785$		0			0
$786$	18.1107	+	10.4562i	0.645988	+	0.372962i
$787$	−27.2465	−	15.7308i	−0.971234	−	0.560742i	−0.0716219	−	0.997432i	$-0.522818\pi$
$787$	−27.2465	−	15.7308i	−0.971234	−	0.560742i	−0.899612	+	0.436690i	$0.856151\pi$
$788$		−	117.357i		−	4.18065i
$789$	5.95701	−	10.3178i	0.212075	−	0.367325i
$790$		0			0
$791$	18.9400	−	10.9350i	0.673428	−	0.388804i
$792$	−10.0903			−0.358543
$793$	0.805801	+	4.75810i	0.0286148	+	0.168965i
$794$	−75.8675			−2.69244
$795$		0			0
$796$	−4.23247	−	7.33085i	−0.150016	−	0.259835i
$797$	−2.47023	+	4.27857i	−0.0875001	+	0.151555i	−0.906454	−	0.422305i	$-0.861221\pi$
$797$	−2.47023	+	4.27857i	−0.0875001	+	0.151555i	0.818954	+	0.573860i	$0.194554\pi$
$798$		−	46.3279i		−	1.63999i
$799$	18.8047	+	10.8569i	0.665262	+	0.384089i
$800$		0			0
$801$			3.27032i			0.115551i
$802$	−12.4048	+	21.4857i	−0.438028	+	0.758687i
$803$	2.50008	+	4.33026i	0.0882257	+	0.152811i
$804$	14.8044	−	8.54730i	0.522109	−	0.301440i
$805$		0			0
$806$	74.2751	+	27.6049i	2.61623	+	0.972341i
$807$	−11.6717			−0.410862
$808$	−93.3943	+	53.9212i	−3.28560	+	1.89694i
$809$	21.2844	+	36.8657i	0.748320	+	1.29613i	0.948628	+	0.316395i	$0.102472\pi$
$809$	21.2844	+	36.8657i	0.748320	+	1.29613i	−0.200308	+	0.979733i	$0.564194\pi$
$810$		0			0
$811$			31.0724i			1.09110i	0.838078	+	0.545550i	$0.183679\pi$
$811$			31.0724i			1.09110i	−0.838078	+	0.545550i	$0.816321\pi$
$812$	−29.6316	−	17.1078i	−1.03987	−	0.600367i
$813$	11.8335	+	6.83207i	0.415019	+	0.239611i
$814$			35.6681i			1.25017i
$815$		0			0
$816$	−15.9234	−	27.5801i	−0.557429	−	0.965496i
$817$	−38.6006	+	22.2860i	−1.35046	+	0.779690i
$818$	−9.59132			−0.335353
$819$	−4.85951	+	13.0752i	−0.169805	+	0.456886i
$820$		0			0
$821$	−0.737419	+	0.425749i	−0.0257361	+	0.0148587i	−0.512813	−	0.858500i	$-0.671397\pi$
$821$	−0.737419	+	0.425749i	−0.0257361	+	0.0148587i	0.487077	+	0.873359i	$0.338063\pi$
$822$	−3.61122	−	6.25482i	−0.125956	−	0.218162i
$823$	−19.8356	+	34.3562i	−0.691424	+	1.19758i	0.279948	+	0.960015i	$0.409683\pi$
$823$	−19.8356	+	34.3562i	−0.691424	+	1.19758i	−0.971371	+	0.237566i	$0.923650\pi$
$824$			33.8025i			1.17757i
$825$		0			0
$826$	83.4849	+	48.2001i	2.90481	+	1.67709i
$827$		−	2.94968i		−	0.102570i	−0.998684	−	0.0512852i	$-0.983668\pi$
$827$		−	2.94968i		−	0.102570i	0.998684	−	0.0512852i	$-0.0163318\pi$
$828$	−13.0834	+	22.6611i	−0.454680	+	0.787529i
$829$	−16.5769	−	28.7121i	−0.575741	−	0.997212i	−0.995961	−	0.0897897i	$-0.971380\pi$
$829$	−16.5769	−	28.7121i	−0.575741	−	0.997212i	0.420220	−	0.907422i	$-0.361953\pi$
$830$		0			0
$831$	20.8315			0.722637
$832$	11.8657	−	9.82040i	0.411371	−	0.340461i
$833$	29.6001			1.02558
$834$	16.6110	−	9.59036i	0.575192	−	0.332087i
$835$		0			0
$836$	−15.7737	+	27.3209i	−0.545546	+	0.944913i
$837$		−	8.50057i		−	0.293823i
$838$	50.7544	+	29.3030i	1.75328	+	1.01226i
$839$	22.6820	+	13.0955i	0.783071	+	0.452106i	0.837518	−	0.546410i	$-0.184006\pi$
$839$	22.6820	+	13.0955i	0.783071	+	0.452106i	−0.0544464	+	0.998517i	$0.517339\pi$
$840$		0			0
$841$	12.7175	−	22.0274i	0.438534	−	0.759564i
$842$	−38.6708	−	66.9797i	−1.33268	−	2.30827i
$843$	11.2020	−	6.46748i	0.385818	−	0.222752i
$844$	−42.0670			−1.44801
$845$		0			0
$846$	15.1106			0.519512
$847$	29.7708	−	17.1882i	1.02294	−	0.590593i
$848$	−55.3297	−	95.8338i	−1.90003	−	3.29095i
$849$	2.97674	−	5.15587i	0.102162	−	0.176949i
$850$		0			0
$851$	45.9014	+	26.5012i	1.57348	+	0.908450i
$852$	−28.5348	−	16.4746i	−0.977586	−	0.564409i
$853$		−	2.15719i		−	0.0738606i	−0.999318	−	0.0369303i	$-0.988242\pi$
$853$		−	2.15719i		−	0.0738606i	0.999318	−	0.0369303i	$-0.0117580\pi$
$854$	6.69370	−	11.5938i	0.229054	−	0.396732i
$855$		0			0
$856$	−75.1009	+	43.3595i	−2.56689	+	1.48200i
$857$	−22.0284			−0.752477			−0.376238	−	0.926523i	$-0.622783\pi$
$857$	−22.0284			−0.752477			−0.376238	+	0.926523i	$0.622783\pi$
$858$	10.4422	−	8.64221i	0.356490	−	0.295040i
$859$	11.8687			0.404956			0.202478	−	0.979287i	$-0.435100\pi$
$859$	11.8687			0.404956			0.202478	+	0.979287i	$0.435100\pi$
$860$		0			0
$861$	−13.1825	−	22.8327i	−0.449258	−	0.778138i
$862$	2.91406	−	5.04729i	0.0992531	−	0.171911i
$863$		−	43.6086i		−	1.48446i	−0.670148	−	0.742228i	$-0.733769\pi$
$863$		−	43.6086i		−	1.48446i	0.670148	−	0.742228i	$-0.266231\pi$
$864$	−7.17387	−	4.14184i	−0.244060	−	0.140908i
$865$		0			0
$866$			88.0277i			2.99130i
$867$	−1.59889	+	2.76936i	−0.0543012	+	0.0940524i
$868$	−77.0216	−	133.405i	−2.61428	−	4.52807i
$869$	19.4595	−	11.2349i	0.660118	−	0.381119i
$870$		0			0
$871$	−4.58413	+	12.3343i	−0.155327	+	0.417931i
$872$	88.4385			2.99491
$873$	12.8109	−	7.39637i	0.433583	−	0.250329i
$874$	33.4479	+	57.9334i	1.13139	+	1.95963i
$875$		0			0
$876$			16.1068i			0.544198i
$877$	−42.7430	−	24.6777i	−1.44333	−	0.833307i	−0.445260	−	0.895401i	$-0.646889\pi$
$877$	−42.7430	−	24.6777i	−1.44333	−	0.833307i	−0.998070	+	0.0620944i	$0.980222\pi$
$878$	46.3908	+	26.7838i	1.56561	+	0.903908i
$879$			12.0289i			0.405725i
$880$		0			0
$881$	−13.1182	−	22.7214i	−0.441963	−	0.765502i	0.555872	−	0.831268i	$-0.312384\pi$
$881$	−13.1182	−	22.7214i	−0.441963	−	0.765502i	−0.997835	+	0.0657658i	$0.979051\pi$
$882$	17.8390	−	10.2993i	0.600669	−	0.346796i
$883$	1.41937			0.0477656			0.0238828	−	0.999715i	$-0.492397\pi$
$883$	1.41937			0.0477656			0.0238828	+	0.999715i	$0.492397\pi$
$884$	58.8127	+	21.8582i	1.97809	+	0.735170i
$885$		0			0
$886$	57.2036	−	33.0265i	1.92179	−	1.10955i
$887$	16.4649	+	28.5180i	0.552836	+	0.957541i	0.998068	+	0.0621256i	$0.0197879\pi$
$887$	16.4649	+	28.5180i	0.552836	+	0.957541i	−0.445232	+	0.895415i	$0.646879\pi$
$888$	−32.9188	+	57.0171i	−1.10468	+	1.91337i
$889$			28.3085i			0.949436i
$890$		0			0
$891$	−1.25929	−	0.727051i	−0.0421878	−	0.0243571i
$892$			1.33710i			0.0447693i
$893$	13.5357	−	23.4445i	0.452954	−	0.784540i
$894$	2.83203	+	4.90522i	0.0947173	+	0.164055i
$895$		0			0
$896$	21.3674			0.713835
$897$	−3.36322	−	19.8592i	−0.112295	−	0.663079i
$898$	47.8230			1.59587
$899$	−13.8998	+	8.02505i	−0.463584	+	0.267651i
$900$		0			0
$901$	23.9796	−	41.5339i	0.798877	−	1.38370i
$902$			25.6193i			0.853031i
$903$	−32.2418	−	18.6148i	−1.07294	−	0.619461i
$904$	−33.9715	−	19.6134i	−1.12987	−	0.652334i
$905$		0			0
$906$	17.7799	−	30.7956i	0.590696	−	1.02312i
$907$	5.21544	+	9.03340i	0.173176	+	0.299949i	0.939528	−	0.342471i	$-0.111264\pi$
$907$	5.21544	+	9.03340i	0.173176	+	0.299949i	−0.766353	+	0.642420i	$0.777930\pi$
$908$	115.004	−	66.3978i	3.81656	−	2.20349i
$909$	−15.5411			−0.515465
$910$		0			0
$911$	−6.49344			−0.215137			−0.107569	−	0.994198i	$-0.534307\pi$
$911$	−6.49344			−0.215137			−0.107569	+	0.994198i	$0.534307\pi$
$912$	−34.3851	+	19.8522i	−1.13860	+	0.657373i
$913$	0.463305	+	0.802468i	0.0153332	+	0.0265578i
$914$	−8.25519	+	14.2984i	−0.273058	+	0.472950i
$915$		0			0
$916$	26.3207	+	15.1963i	0.869661	+	0.502099i
$917$	27.1013	+	15.6469i	0.894964	+	0.516708i
$918$		−	9.60493i		−	0.317010i
$919$	−11.1055	+	19.2352i	−0.366335	+	0.634511i	−0.988989	−	0.147986i	$-0.952721\pi$
$919$	−11.1055	+	19.2352i	−0.366335	+	0.634511i	0.622654	+	0.782497i	$0.286054\pi$
$920$		0			0
$921$	−5.44641	+	3.14448i	−0.179465	+	0.103614i
$922$	−49.8995			−1.64335
$923$	25.0066	−	4.23495i	0.823102	−	0.139395i
$924$	−26.3505			−0.866869
$925$		0			0
$926$	−33.2314	−	57.5585i	−1.09205	−	1.89149i
$927$	−2.43562	+	4.21862i	−0.0799963	+	0.138558i
$928$			15.6406i			0.513427i
$929$	41.0441	+	23.6968i	1.34661	+	0.777468i	0.987768	−	0.155928i	$-0.0498369\pi$
$929$	41.0441	+	23.6968i	1.34661	+	0.777468i	0.358846	+	0.933397i	$0.383170\pi$
$930$		0			0
$931$		−	36.9035i		−	1.20946i
$932$	−11.0367	+	19.1160i	−0.361518	+	0.626167i
$933$	14.2459	+	24.6747i	0.466391	+	0.807814i
$934$	78.1397	−	45.1140i	2.55681	−	1.47617i
$935$		0			0
$936$	24.6684	−	4.17767i	0.806311	−	0.136551i
$937$	−1.49770			−0.0489279			−0.0244639	−	0.999701i	$-0.507788\pi$
$937$	−1.49770			−0.0489279			−0.0244639	+	0.999701i	$0.507788\pi$
$938$	31.6127	−	18.2516i	1.03219	−	0.595937i
$939$	−0.877380	−	1.51967i	−0.0286322	−	0.0495924i
$940$		0			0
$941$			45.4563i			1.48183i	0.671597	+	0.740917i	$0.265609\pi$
$941$			45.4563i			1.48183i	−0.671597	+	0.740917i	$0.734391\pi$
$942$	33.8532	+	19.5452i	1.10300	+	0.636816i
$943$	32.9697	+	19.0350i	1.07364	+	0.619866i
$944$		−	82.6180i		−	2.68899i
$945$		0			0
$946$	18.0883	+	31.3299i	0.588103	+	1.01862i
$947$	25.3214	−	14.6193i	0.822835	−	0.475064i	−0.0285579	−	0.999592i	$-0.509092\pi$
$947$	25.3214	−	14.6193i	0.822835	−	0.475064i	0.851393	+	0.524528i	$0.175758\pi$
$948$	72.3814			2.35084
$949$	−7.90494	−	9.55134i	−0.256605	−	0.310050i
$950$		0			0
$951$	−10.4470	+	6.03156i	−0.338766	+	0.195587i
$952$	−49.8686	−	86.3750i	−1.61625	−	2.79943i
$953$	−2.01551	+	3.49096i	−0.0652886	+	0.113083i	−0.896822	−	0.442392i	$-0.854130\pi$
$953$	−2.01551	+	3.49096i	−0.0652886	+	0.113083i	0.831533	+	0.555475i	$0.187463\pi$
$954$		−	33.3747i		−	1.08055i
$955$		0			0
$956$	−4.56337	−	2.63466i	−0.147590	−	0.0852111i
$957$			2.74552i			0.0887501i
$958$	6.23015	−	10.7909i	0.201287	−	0.348639i
$959$	−5.40392	−	9.35986i	−0.174502	−	0.302246i
$960$		0			0
$961$	−41.2596			−1.33096
$962$	−14.7676	−	87.2000i	−0.476127	−	2.81144i
$963$	−12.4970			−0.402710
$964$	−14.2852	+	8.24758i	−0.460096	+	0.265637i
$965$		0			0
$966$	−27.9379	+	48.3899i	−0.898887	+	1.55692i
$967$			40.8236i			1.31280i	0.754413	+	0.656400i	$0.227921\pi$
$967$			40.8236i			1.31280i	−0.754413	+	0.656400i	$0.772079\pi$
$968$	−53.3981	−	30.8294i	−1.71628	−	0.990894i
$969$	−14.9023	−	8.60386i	−0.478731	−	0.276396i
$970$		0			0
$971$	−2.69783	+	4.67279i	−0.0865776	+	0.149957i	−0.906062	−	0.423144i	$-0.860926\pi$
$971$	−2.69783	+	4.67279i	−0.0865776	+	0.149957i	0.819485	+	0.573101i	$0.194260\pi$
$972$	−2.34202	−	4.05650i	−0.0751204	−	0.130112i
$973$	24.8571	−	14.3512i	0.796881	−	0.460080i
$974$	52.6654			1.68751
$975$		0			0
$976$	−11.4734			−0.367255
$977$	41.8577	−	24.1666i	1.33915	−	0.773157i	0.352466	−	0.935825i	$-0.385343\pi$
$977$	41.8577	−	24.1666i	1.33915	−	0.773157i	0.986681	+	0.162668i	$0.0520098\pi$
$978$	−3.35241	−	5.80654i	−0.107198	−	0.185673i
$979$	2.37769	−	4.11828i	0.0759914	−	0.131621i
$980$		0			0
$981$	11.0373	+	6.37239i	0.352394	+	0.203455i
$982$	50.9114	+	29.3937i	1.62465	+	0.937990i
$983$			42.5874i			1.35833i	0.733987	+	0.679164i	$0.237657\pi$
$983$			42.5874i			1.35833i	−0.733987	+	0.679164i	$0.762343\pi$
$984$	−23.6446	+	40.9537i	−0.753763	+	1.30556i
$985$		0			0
$986$	−15.7056	+	9.06764i	−0.500168	+	0.288772i
$987$	22.6118			0.719741
$988$	27.2514	−	73.3239i	0.866982	−	2.33274i
$989$	53.7582			1.70941
$990$		0			0
$991$	23.9448	+	41.4736i	0.760632	+	1.31745i	0.942525	+	0.334135i	$0.108444\pi$
$991$	23.9448	+	41.4736i	0.760632	+	1.31745i	−0.181894	+	0.983318i	$0.558223\pi$
$992$	−35.2080	+	60.9820i	−1.11785	+	1.93618i
$993$		−	1.76249i		−	0.0559310i
$994$	−60.9323	−	35.1793i	−1.93265	−	1.11582i
$995$		0			0
$996$			2.98485i			0.0945787i
$997$	−17.0894	+	29.5998i	−0.541228	+	0.937435i	0.457606	+	0.889155i	$0.348707\pi$
$997$	−17.0894	+	29.5998i	−0.541228	+	0.937435i	−0.998834	+	0.0482794i	$0.984626\pi$
$998$	33.2091	+	57.5198i	1.05121	+	1.82076i
$999$	−8.21667	+	4.74390i	−0.259964	+	0.150090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.l.751.1	yes	12
5.2	odd	4		975.2.w.k.49.1		24
5.3	odd	4		975.2.w.k.49.12		24
5.4	even	2		975.2.bc.k.751.6	✓	12
13.4	even	6	inner	975.2.bc.l.901.1	yes	12
65.4	even	6		975.2.bc.k.901.6	yes	12
65.17	odd	12		975.2.w.k.199.12		24
65.43	odd	12		975.2.w.k.199.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.k.49.1		24	5.2	odd	4
975.2.w.k.49.12		24	5.3	odd	4
975.2.w.k.199.1		24	65.43	odd	12
975.2.w.k.199.12		24	65.17	odd	12
975.2.bc.k.751.6	✓	12	5.4	even	2
975.2.bc.k.901.6	yes	12	65.4	even	6
975.2.bc.l.751.1	yes	12	1.1	even	1	trivial
975.2.bc.l.901.1	yes	12	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23898 + 1.29268i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.34202 - 4.05650i) q^{4} +(-2.23898 - 1.29268i) q^{6} +(-3.35046 - 1.93439i) q^{7} +6.93919i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.23898 + 1.29268i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.34202 - 4.05650i) q^{4} +(-2.23898 - 1.29268i) q^{6} +(-3.35046 - 1.93439i) q^{7} +6.93919i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.25929 - 0.727051i) q^{11} +4.68404 q^{12} +(-2.77764 + 2.29885i) q^{13} +10.0022 q^{14} +(-4.28608 - 7.42371i) q^{16} +(1.85757 - 3.21740i) q^{17} -2.58535i q^{18} +(-4.01125 - 2.31589i) q^{19} -3.86878i q^{21} +(-1.87968 + 3.25571i) q^{22} +(2.79319 + 4.83794i) q^{23} +(-6.00952 + 3.46960i) q^{24} +(3.24742 - 8.73767i) q^{26} -1.00000 q^{27} +(-15.6937 + 9.06076i) q^{28} +(0.944061 + 1.63516i) q^{29} +8.50057i q^{31} +(7.17387 + 4.14184i) q^{32} +(1.25929 + 0.727051i) q^{33} +9.60493i q^{34} +(2.34202 + 4.05650i) q^{36} +(8.21667 - 4.74390i) q^{37} +11.9748 q^{38} +(-3.37968 - 1.25608i) q^{39} +(5.90180 - 3.40740i) q^{41} +(5.00108 + 8.66212i) q^{42} +(4.81154 - 8.33383i) q^{43} -6.81107i q^{44} +(-12.5078 - 7.22137i) q^{46} +5.84469i q^{47} +(4.28608 - 7.42371i) q^{48} +(3.98372 + 6.90001i) q^{49} +3.71513 q^{51} +(2.81998 + 16.6515i) q^{52} +12.9092 q^{53} +(2.23898 - 1.29268i) q^{54} +(13.4231 - 23.2495i) q^{56} -4.63179i q^{57} +(-4.22747 - 2.44073i) q^{58} +(8.34670 + 4.81897i) q^{59} +(0.669226 - 1.15913i) q^{61} +(-10.9885 - 19.0326i) q^{62} +(3.35046 - 1.93439i) q^{63} -4.27188 q^{64} -3.75936 q^{66} +(3.16059 - 1.82477i) q^{67} +(-8.70092 - 15.0704i) q^{68} +(-2.79319 + 4.83794i) q^{69} +(-6.09191 - 3.51717i) q^{71} +(-6.00952 - 3.46960i) q^{72} +3.43865i q^{73} +(-12.2646 + 21.2430i) q^{74} +(-18.7888 + 10.8477i) q^{76} -5.62560 q^{77} +(9.19075 - 1.55649i) q^{78} +15.4528 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.80934 + 15.2582i) q^{82} +0.637239i q^{83} +(-15.6937 - 9.06076i) q^{84} +24.8790i q^{86} +(-0.944061 + 1.63516i) q^{87} +(5.04515 + 8.73845i) q^{88} +(2.83218 - 1.63516i) q^{89} +(13.7532 - 2.32916i) q^{91} +26.1668 q^{92} +(-7.36171 + 4.25028i) q^{93} +(-7.55528 - 13.0861i) q^{94} +8.28367i q^{96} +(-12.8109 - 7.39637i) q^{97} +(-17.8390 - 10.2993i) q^{98} +1.45410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9} + 9 q^{11} + 16 q^{12} - 3 q^{13} + 10 q^{14} - 4 q^{16} - 9 q^{19} + 15 q^{22} + q^{23} - 5 q^{26} - 12 q^{27} - 39 q^{28} - 16 q^{29} + 30 q^{32} + 9 q^{33} + 8 q^{36} - 15 q^{37} + 30 q^{38} - 3 q^{39} + 18 q^{41} + 5 q^{42} + q^{43} - 45 q^{46} + 4 q^{48} + 31 q^{49} - 40 q^{52} - 16 q^{53} + 25 q^{56} - 30 q^{58} + 54 q^{59} - 11 q^{61} - 20 q^{62} + 3 q^{63} + 16 q^{64} + 30 q^{66} + 45 q^{67} - 30 q^{68} - q^{69} - 33 q^{71} + 5 q^{74} - 27 q^{76} - 28 q^{77} + 20 q^{78} + 18 q^{79} - 6 q^{81} - 20 q^{82} - 39 q^{84} + 16 q^{87} - 5 q^{88} - 48 q^{89} - 29 q^{91} + 46 q^{92} - 12 q^{93} - 30 q^{94} - 9 q^{97} + 105 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9 + 9 * q^11 + 16 * q^12 - 3 * q^13 + 10 * q^14 - 4 * q^16 - 9 * q^19 + 15 * q^22 + q^23 - 5 * q^26 - 12 * q^27 - 39 * q^28 - 16 * q^29 + 30 * q^32 + 9 * q^33 + 8 * q^36 - 15 * q^37 + 30 * q^38 - 3 * q^39 + 18 * q^41 + 5 * q^42 + q^43 - 45 * q^46 + 4 * q^48 + 31 * q^49 - 40 * q^52 - 16 * q^53 + 25 * q^56 - 30 * q^58 + 54 * q^59 - 11 * q^61 - 20 * q^62 + 3 * q^63 + 16 * q^64 + 30 * q^66 + 45 * q^67 - 30 * q^68 - q^69 - 33 * q^71 + 5 * q^74 - 27 * q^76 - 28 * q^77 + 20 * q^78 + 18 * q^79 - 6 * q^81 - 20 * q^82 - 39 * q^84 + 16 * q^87 - 5 * q^88 - 48 * q^89 - 29 * q^91 + 46 * q^92 - 12 * q^93 - 30 * q^94 - 9 * q^97 + 105 * q^98

Introduction

L-functions

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Database

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