LMFDB - Embedded newform 975.2.i.l.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$0.500000 - 1.75780i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.l.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169938 + 0.294342i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.942242 + 1.63201i) q^{4} +(-0.169938 - 0.294342i) q^{6} +(0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.169938 + 0.294342i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.942242 + 1.63201i) q^{4} +(-0.169938 - 0.294342i) q^{6} +(0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.339877 + 0.588684i) q^{11} -1.88448 q^{12} +(-1.93243 - 3.04397i) q^{13} -0.224361 q^{14} +(-1.66012 + 2.87542i) q^{16} +(3.71455 + 6.43378i) q^{17} +0.339877 q^{18} +(-0.0577581 - 0.100040i) q^{19} -0.660123 q^{21} +(-0.115516 - 0.200080i) q^{22} +(-3.88448 + 6.72812i) q^{23} +(0.660123 - 1.14337i) q^{24} +(1.22436 - 0.0515075i) q^{26} +1.00000 q^{27} +(-0.621996 + 1.07733i) q^{28} +(-2.77230 + 4.80177i) q^{29} -9.97370 q^{31} +(-1.88448 - 3.26402i) q^{32} +(-0.339877 - 0.588684i) q^{33} -2.52498 q^{34} +(0.942242 - 1.63201i) q^{36} +(4.88448 - 8.46017i) q^{37} +0.0392613 q^{38} +(3.60236 - 0.151548i) q^{39} +(-2.11218 + 3.65840i) q^{41} +(0.112180 - 0.194302i) q^{42} +(-0.272303 - 0.471643i) q^{43} -1.28098 q^{44} +(-1.32025 - 2.28673i) q^{46} +5.01963 q^{47} +(-1.66012 - 2.87542i) q^{48} +(3.28212 - 5.68480i) q^{49} -7.42909 q^{51} +(3.14697 - 6.02189i) q^{52} -0.679754 q^{53} +(-0.169938 + 0.294342i) q^{54} +(-0.435763 - 0.754763i) q^{56} +0.115516 q^{57} +(-0.942242 - 1.63201i) q^{58} +(-1.11218 - 1.92635i) q^{59} +(2.10236 + 3.64140i) q^{61} +(1.69491 - 2.93568i) q^{62} +(0.330062 - 0.571683i) q^{63} -5.35951 q^{64} +0.231033 q^{66} +(-3.81691 + 6.61108i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(-3.88448 - 6.72812i) q^{69} +(-3.65679 - 6.33374i) q^{71} +(0.660123 + 1.14337i) q^{72} -8.01963 q^{73} +(1.66012 + 2.87542i) q^{74} +(0.108844 - 0.188524i) q^{76} -0.448721 q^{77} +(-0.567573 + 1.08608i) q^{78} +9.97370 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.717881 - 1.24341i) q^{82} -1.76897 q^{83} +(-0.621996 - 1.07733i) q^{84} +0.185099 q^{86} +(-2.77230 - 4.80177i) q^{87} +(0.448721 - 0.777208i) q^{88} +(-6.77230 + 11.7300i) q^{89} +(1.10236 - 2.10943i) q^{91} -14.6405 q^{92} +(4.98685 - 8.63748i) q^{93} +(-0.853028 + 1.47749i) q^{94} +3.76897 q^{96} +(4.95206 + 8.57721i) q^{97} +(1.11552 + 1.93213i) q^{98} +0.679754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9} + 12 q^{12} - 3 q^{13} + 24 q^{14} - 12 q^{16} - 12 q^{19} - 6 q^{21} - 24 q^{22} + 6 q^{24} - 18 q^{26} + 6 q^{27} + 12 q^{28} - 6 q^{29} + 6 q^{31} + 12 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{42} + 9 q^{43} - 24 q^{44} - 12 q^{46} + 24 q^{47} - 12 q^{48} + 6 q^{49} - 12 q^{52} - 30 q^{56} + 24 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{61} - 6 q^{62} + 3 q^{63} - 24 q^{64} + 48 q^{66} + 9 q^{67} - 42 q^{68} + 12 q^{71} + 6 q^{72} - 42 q^{73} + 12 q^{74} - 48 q^{76} + 48 q^{77} - 12 q^{78} - 6 q^{79} - 3 q^{81} - 18 q^{82} + 36 q^{83} + 12 q^{84} - 12 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} - 3 q^{91} - 96 q^{92} - 3 q^{93} - 36 q^{94} - 24 q^{96} + 15 q^{97} + 30 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9 + 12 * q^12 - 3 * q^13 + 24 * q^14 - 12 * q^16 - 12 * q^19 - 6 * q^21 - 24 * q^22 + 6 * q^24 - 18 * q^26 + 6 * q^27 + 12 * q^28 - 6 * q^29 + 6 * q^31 + 12 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^42 + 9 * q^43 - 24 * q^44 - 12 * q^46 + 24 * q^47 - 12 * q^48 + 6 * q^49 - 12 * q^52 - 30 * q^56 + 24 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^61 - 6 * q^62 + 3 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 42 * q^68 + 12 * q^71 + 6 * q^72 - 42 * q^73 + 12 * q^74 - 48 * q^76 + 48 * q^77 - 12 * q^78 - 6 * q^79 - 3 * q^81 - 18 * q^82 + 36 * q^83 + 12 * q^84 - 12 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 - 3 * q^91 - 96 * q^92 - 3 * q^93 - 36 * q^94 - 24 * q^96 + 15 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.169938	+	0.294342i	−0.120165	+	0.208131i	−0.919832	−	0.392311i	$-0.871676\pi$
$2$	−0.169938	+	0.294342i	−0.120165	+	0.208131i	0.799668	+	0.600443i	$0.205009\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.942242	+	1.63201i	0.471121	+	0.816005i
$5$		0			0
$5$		0			0
$6$	−0.169938	−	0.294342i	−0.0693771	−	0.120165i
$7$	0.330062	+	0.571683i	0.124752	+	0.216076i	0.921636	−	0.388056i	$-0.126853\pi$
$7$	0.330062	+	0.571683i	0.124752	+	0.216076i	−0.796884	+	0.604132i	$0.793520\pi$
$8$	−1.32025			−0.466778
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.339877	+	0.588684i	−0.102477	+	0.177495i	−0.912704	−	0.408620i	$-0.866010\pi$
$11$	−0.339877	+	0.588684i	−0.102477	+	0.177495i	0.810228	+	0.586115i	$0.199343\pi$
$12$	−1.88448			−0.544004
$13$	−1.93243	−	3.04397i	−0.535959	−	0.844244i
$13$	−1.93243	−	3.04397i	−0.535959	−	0.844244i
$14$	−0.224361			−0.0599629
$15$		0			0
$16$	−1.66012	+	2.87542i	−0.415031	+	0.718854i
$17$	3.71455	+	6.43378i	0.900910	+	1.56042i	0.826316	+	0.563207i	$0.190433\pi$
$17$	3.71455	+	6.43378i	0.900910	+	1.56042i	0.0745938	+	0.997214i	$0.476234\pi$
$18$	0.339877			0.0801098
$19$	−0.0577581	−	0.100040i	−0.0132506	−	0.0229508i	0.859324	−	0.511431i	$-0.170885\pi$
$19$	−0.0577581	−	0.100040i	−0.0132506	−	0.0229508i	−0.872575	+	0.488481i	$0.837551\pi$
$20$		0			0
$21$	−0.660123			−0.144051
$22$	−0.115516	−	0.200080i	−0.0246282	−	0.0426572i
$23$	−3.88448	+	6.72812i	−0.809971	+	1.40291i	0.102913	+	0.994690i	$0.467184\pi$
$23$	−3.88448	+	6.72812i	−0.809971	+	1.40291i	−0.912883	+	0.408220i	$0.866150\pi$
$24$	0.660123	−	1.14337i	0.134747	−	0.233389i
$25$		0			0
$26$	1.22436	−	0.0515075i	0.240117	−	0.0101015i
$27$	1.00000			0.192450
$28$	−0.621996	+	1.07733i	−0.117546	+	0.203596i
$29$	−2.77230	+	4.80177i	−0.514804	+	0.891666i	0.485049	+	0.874487i	$0.338802\pi$
$29$	−2.77230	+	4.80177i	−0.514804	+	0.891666i	−0.999852	+	0.0171792i	$0.994531\pi$
$30$		0			0
$31$	−9.97370			−1.79133			−0.895664	−	0.444730i	$-0.853299\pi$
$31$	−9.97370			−1.79133			−0.895664	+	0.444730i	$0.853299\pi$
$32$	−1.88448	−	3.26402i	−0.333133	−	0.577003i
$33$	−0.339877	−	0.588684i	−0.0591650	−	0.102477i
$34$	−2.52498			−0.433030
$35$		0			0
$36$	0.942242	−	1.63201i	0.157040	−	0.272002i
$37$	4.88448	−	8.46017i	0.803004	−	1.39084i	−0.114626	−	0.993409i	$-0.536567\pi$
$37$	4.88448	−	8.46017i	0.803004	−	1.39084i	0.917630	−	0.397435i	$-0.130100\pi$
$38$	0.0392613			0.00636903
$39$	3.60236	−	0.151548i	0.576840	−	0.0242670i
$40$		0			0
$41$	−2.11218	+	3.65840i	−0.329867	+	0.571347i	−0.982485	−	0.186340i	$-0.940337\pi$
$41$	−2.11218	+	3.65840i	−0.329867	+	0.571347i	0.652618	+	0.757687i	$0.273671\pi$
$42$	0.112180	−	0.194302i	0.0173098	−	0.0299814i
$43$	−0.272303	−	0.471643i	−0.0415259	−	0.0719249i	0.844515	−	0.535531i	$-0.179889\pi$
$43$	−0.272303	−	0.471643i	−0.0415259	−	0.0719249i	−0.886041	+	0.463606i	$0.846555\pi$
$44$	−1.28098			−0.193116
$45$		0			0
$46$	−1.32025	−	2.28673i	−0.194660	−	0.337160i
$47$	5.01963			0.732188			0.366094	−	0.930578i	$-0.380695\pi$
$47$	5.01963			0.732188			0.366094	+	0.930578i	$0.380695\pi$
$48$	−1.66012	−	2.87542i	−0.239618	−	0.415031i
$49$	3.28212	−	5.68480i	0.468874	−	0.812114i
$50$		0			0
$51$	−7.42909			−1.04028
$52$	3.14697	−	6.02189i	0.436406	−	0.835086i
$53$	−0.679754			−0.0933714			−0.0466857	−	0.998910i	$-0.514866\pi$
$53$	−0.679754			−0.0933714			−0.0466857	+	0.998910i	$0.514866\pi$
$54$	−0.169938	+	0.294342i	−0.0231257	+	0.0400549i
$55$		0			0
$56$	−0.435763	−	0.754763i	−0.0582312	−	0.100859i
$57$	0.115516			0.0153005
$58$	−0.942242	−	1.63201i	−0.123722	−	0.214294i
$59$	−1.11218	−	1.92635i	−0.144794	−	0.250790i	0.784502	−	0.620126i	$-0.212918\pi$
$59$	−1.11218	−	1.92635i	−0.144794	−	0.250790i	−0.929296	+	0.369336i	$0.879585\pi$
$60$		0			0
$61$	2.10236	+	3.64140i	0.269180	+	0.466234i	0.968650	−	0.248428i	$-0.0799139\pi$
$61$	2.10236	+	3.64140i	0.269180	+	0.466234i	−0.699470	+	0.714662i	$0.746581\pi$
$62$	1.69491	−	2.93568i	0.215254	−	0.372832i
$63$	0.330062	−	0.571683i	0.0415838	−	0.0720253i
$64$	−5.35951			−0.669938
$65$		0			0
$66$	0.231033			0.0284381
$67$	−3.81691	+	6.61108i	−0.466310	+	0.807672i	−0.999260	−	0.0384746i	$-0.987750\pi$
$67$	−3.81691	+	6.61108i	−0.466310	+	0.807672i	0.532950	+	0.846147i	$0.321083\pi$
$68$	−7.00000	+	12.1244i	−0.848875	+	1.47029i
$69$	−3.88448	−	6.72812i	−0.467637	−	0.809971i
$70$		0			0
$71$	−3.65679	−	6.33374i	−0.433981	−	0.751677i	0.563231	−	0.826299i	$-0.309558\pi$
$71$	−3.65679	−	6.33374i	−0.433981	−	0.751677i	−0.997212	+	0.0746227i	$0.976225\pi$
$72$	0.660123	+	1.14337i	0.0777963	+	0.134747i
$73$	−8.01963			−0.938627			−0.469313	−	0.883032i	$-0.655499\pi$
$73$	−8.01963			−0.938627			−0.469313	+	0.883032i	$0.655499\pi$
$74$	1.66012	+	2.87542i	0.192985	+	0.334261i
$75$		0			0
$76$	0.108844	−	0.188524i	0.0124853	−	0.0216252i
$77$	−0.448721			−0.0511365
$78$	−0.567573	+	1.08608i	−0.0642650	+	0.122974i
$79$	9.97370			1.12213			0.561064	−	0.827772i	$-0.310392\pi$
$79$	9.97370			1.12213			0.561064	+	0.827772i	$0.310392\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.717881	−	1.24341i	−0.0792767	−	0.137311i
$83$	−1.76897			−0.194169			−0.0970847	−	0.995276i	$-0.530952\pi$
$83$	−1.76897			−0.194169			−0.0970847	+	0.995276i	$0.530952\pi$
$84$	−0.621996	−	1.07733i	−0.0678653	−	0.117546i
$85$		0			0
$86$	0.185099			0.0199598
$87$	−2.77230	−	4.80177i	−0.297222	−	0.514804i
$88$	0.448721	−	0.777208i	0.0478338	−	0.0828506i
$89$	−6.77230	+	11.7300i	−0.717863	+	1.24337i	0.243982	+	0.969780i	$0.421546\pi$
$89$	−6.77230	+	11.7300i	−0.717863	+	1.24337i	−0.961845	+	0.273595i	$0.911787\pi$
$90$		0			0
$91$	1.10236	−	2.10943i	0.115559	−	0.221129i
$92$	−14.6405			−1.52638
$93$	4.98685	−	8.63748i	0.517112	−	0.895664i
$94$	−0.853028	+	1.47749i	−0.0879831	+	0.152391i
$95$		0			0
$96$	3.76897			0.384669
$97$	4.95206	+	8.57721i	0.502805	+	0.870884i	0.999995	+	0.00324223i	$0.00103204\pi$
$97$	4.95206	+	8.57721i	0.502805	+	0.870884i	−0.497190	+	0.867642i	$0.665635\pi$
$98$	1.11552	+	1.93213i	0.112684	+	0.195175i
$99$	0.679754			0.0683178
$100$		0			0
$101$	4.67975	−	8.10557i	0.465653	−	0.806534i	−0.533578	−	0.845751i	$-0.679153\pi$
$101$	4.67975	−	8.10557i	0.465653	−	0.806534i	0.999231	+	0.0392165i	$0.0124862\pi$
$102$	1.26249	−	2.18669i	0.125005	−	0.216515i
$103$	−4.50535			−0.443925			−0.221962	−	0.975055i	$-0.571246\pi$
$103$	−4.50535			−0.443925			−0.221962	+	0.975055i	$0.571246\pi$
$104$	2.55128	+	4.01878i	0.250173	+	0.394074i
$105$		0			0
$106$	0.115516	−	0.200080i	0.0112199	−	0.0194335i
$107$	0.285455	−	0.494422i	0.0275960	−	0.0477976i	−0.851898	−	0.523708i	$-0.824548\pi$
$107$	0.285455	−	0.494422i	0.0275960	−	0.0477976i	0.879494	+	0.475911i	$0.157881\pi$
$108$	0.942242	+	1.63201i	0.0906673	+	0.157040i
$109$	15.4095			1.47596			0.737979	−	0.674823i	$-0.235780\pi$
$109$	15.4095			1.47596			0.737979	+	0.674823i	$0.235780\pi$
$110$		0			0
$111$	4.88448	+	8.46017i	0.463615	+	0.803004i
$112$	−2.19177			−0.207103
$113$	−2.66012	−	4.60747i	−0.250243	−	0.433434i	0.713349	−	0.700809i	$-0.247177\pi$
$113$	−2.66012	−	4.60747i	−0.250243	−	0.433434i	−0.963593	+	0.267374i	$0.913844\pi$
$114$	−0.0196307	+	0.0340013i	−0.00183858	+	0.00318451i
$115$		0			0
$116$	−10.4487			−0.970139
$117$	−1.66994	+	3.19551i	−0.154386	+	0.295425i
$118$	0.756009			0.0695962
$119$	−2.45206	+	4.24709i	−0.224780	+	0.389330i
$120$		0			0
$121$	5.26897	+	9.12612i	0.478997	+	0.829647i
$122$	−1.42909			−0.129384
$123$	−2.11218	−	3.65840i	−0.190449	−	0.329867i
$124$	−9.39764	−	16.2772i	−0.843933	−	1.46173i
$125$		0			0
$126$	0.112180	+	0.194302i	0.00999381	+	0.0173098i
$127$	−6.00982	+	10.4093i	−0.533285	+	0.923676i	0.465959	+	0.884806i	$0.345709\pi$
$127$	−6.00982	+	10.4093i	−0.533285	+	0.923676i	−0.999244	+	0.0388704i	$0.987624\pi$
$128$	4.67975	−	8.10557i	0.413636	−	0.716438i
$129$	0.544607			0.0479500
$130$		0			0
$131$	10.9041			0.952697			0.476348	−	0.879257i	$-0.341960\pi$
$131$	10.9041			0.952697			0.476348	+	0.879257i	$0.341960\pi$
$132$	0.640492	−	1.10937i	0.0557477	−	0.0965579i
$133$	0.0381275	−	0.0660387i	0.00330607	−	0.00572629i
$134$	−1.29728	−	2.24695i	−0.112068	−	0.194107i
$135$		0			0
$136$	−4.90411	−	8.49418i	−0.420524	−	0.728370i
$137$	1.69491	+	2.93568i	0.144806	+	0.250812i	0.929301	−	0.369324i	$-0.120411\pi$
$137$	1.69491	+	2.93568i	0.144806	+	0.250812i	−0.784494	+	0.620136i	$0.787077\pi$
$138$	2.64049			0.224774
$139$	−7.40411	−	12.8243i	−0.628009	−	1.08774i	−0.987951	−	0.154768i	$-0.950537\pi$
$139$	−7.40411	−	12.8243i	−0.628009	−	1.08774i	0.359942	−	0.932975i	$-0.382796\pi$
$140$		0			0
$141$	−2.50982	+	4.34713i	−0.211365	+	0.366094i
$142$	2.48571			0.208597
$143$	2.44872	−	0.103015i	0.204772	−	0.00861455i
$144$	3.32025			0.276687
$145$		0			0
$146$	1.36284	−	2.36051i	0.112790	−	0.195358i
$147$	3.28212	+	5.68480i	0.270705	+	0.468874i
$148$	18.4095			1.51325
$149$	8.54461	+	14.7997i	0.700001	+	1.21244i	0.968465	+	0.249148i	$0.0801507\pi$
$149$	8.54461	+	14.7997i	0.700001	+	1.21244i	−0.268464	+	0.963290i	$0.586516\pi$
$150$		0			0
$151$	13.0130			1.05898			0.529490	−	0.848316i	$-0.322383\pi$
$151$	13.0130			1.05898			0.529490	+	0.848316i	$0.322383\pi$
$152$	0.0762550	+	0.132077i	0.00618510	+	0.0107129i
$153$	3.71455	−	6.43378i	0.300303	−	0.520140i
$154$	0.0762550	−	0.132077i	0.00614480	−	0.0106431i
$155$		0			0
$156$	3.64163	+	5.73630i	0.291563	+	0.459272i
$157$	0.775639			0.0619028			0.0309514	−	0.999521i	$-0.490146\pi$
$157$	0.775639			0.0619028			0.0309514	+	0.999521i	$0.490146\pi$
$158$	−1.69491	+	2.93568i	−0.134840	+	0.233550i
$159$	0.339877	−	0.588684i	0.0269540	−	0.0466857i
$160$		0			0
$161$	−5.12847			−0.404180
$162$	−0.169938	−	0.294342i	−0.0133516	−	0.0231257i
$163$	6.09903	+	10.5638i	0.477713	+	0.827423i	0.999674	−	0.0255466i	$-0.00813262\pi$
$163$	6.09903	+	10.5638i	0.477713	+	0.827423i	−0.521961	+	0.852969i	$0.674799\pi$
$164$	−7.96074			−0.621629
$165$		0			0
$166$	0.300616	−	0.520681i	0.0233323	−	0.0404127i
$167$	−0.795270	+	1.37745i	−0.0615398	+	0.106590i	−0.895154	−	0.445757i	$-0.852934\pi$
$167$	−0.795270	+	1.37745i	−0.0615398	+	0.106590i	0.833614	+	0.552347i	$0.186268\pi$
$168$	0.871525			0.0672396
$169$	−5.53146	+	11.7645i	−0.425497	+	0.904960i
$170$		0			0
$171$	−0.0577581	+	0.100040i	−0.00441688	+	0.00765025i
$172$	0.513151	−	0.888804i	0.0391274	−	0.0677707i
$173$	6.37467	+	11.0412i	0.484657	+	0.839451i	0.999845	−	0.0176268i	$-0.00561108\pi$
$173$	6.37467	+	11.0412i	0.484657	+	0.839451i	−0.515188	+	0.857077i	$0.672278\pi$
$174$	1.88448			0.142862
$175$		0			0
$176$	−1.12847	−	1.95458i	−0.0850620	−	0.147332i
$177$	2.22436			0.167193
$178$	−2.30175	−	3.98675i	−0.172523	−	0.298819i
$179$	−8.88115	+	15.3826i	−0.663808	+	1.14975i	0.315799	+	0.948826i	$0.397728\pi$
$179$	−8.88115	+	15.3826i	−0.663808	+	1.14975i	−0.979607	+	0.200923i	$0.935606\pi$
$180$		0			0
$181$	7.02630			0.522261			0.261130	−	0.965304i	$-0.415905\pi$
$181$	7.02630			0.522261			0.261130	+	0.965304i	$0.415905\pi$
$182$	0.433560	+	0.682946i	0.0321376	+	0.0506233i
$183$	−4.20473			−0.310823
$184$	5.12847	−	8.88278i	0.378076	−	0.654847i
$185$		0			0
$186$	1.69491	+	2.93568i	0.124277	+	0.215254i
$187$	−5.04995			−0.369289
$188$	4.72971	+	8.19209i	0.344949	+	0.597470i
$189$	0.330062	+	0.571683i	0.0240084	+	0.0415838i
$190$		0			0
$191$	6.97703	+	12.0846i	0.504840	+	0.874409i	0.999984	+	0.00559828i	$0.00178200\pi$
$191$	6.97703	+	12.0846i	0.504840	+	0.874409i	−0.495144	+	0.868811i	$0.664885\pi$
$192$	2.67975	−	4.64147i	0.193395	−	0.334969i
$193$	11.8747	−	20.5675i	0.854757	−	1.48048i	−0.0221126	−	0.999755i	$-0.507039\pi$
$193$	11.8747	−	20.5675i	0.854757	−	1.48048i	0.876870	−	0.480728i	$-0.159627\pi$
$194$	−3.36618			−0.241678
$195$		0			0
$196$	12.3702			0.883586
$197$	7.90411	−	13.6903i	0.563145	−	0.975395i	−0.434075	−	0.900877i	$-0.642925\pi$
$197$	7.90411	−	13.6903i	0.563145	−	0.975395i	0.997220	−	0.0745186i	$-0.0237420\pi$
$198$	−0.115516	+	0.200080i	−0.00820939	+	0.0142191i
$199$	−4.38448	−	7.59415i	−0.310808	−	0.538335i	0.667730	−	0.744404i	$-0.267266\pi$
$199$	−4.38448	−	7.59415i	−0.310808	−	0.538335i	−0.978537	+	0.206069i	$0.933933\pi$
$200$		0			0
$201$	−3.81691	−	6.61108i	−0.269224	−	0.466310i
$202$	1.59054	+	2.75490i	0.111910	+	0.193834i
$203$	−3.66012			−0.256890
$204$	−7.00000	−	12.1244i	−0.490098	−	0.848875i
$205$		0			0
$206$	0.765631	−	1.32611i	0.0533441	−	0.0923946i
$207$	7.76897			0.539981
$208$	11.9607	−	0.503175i	0.829328	−	0.0348889i
$209$	0.0785226			0.00543152
$210$		0			0
$211$	−4.40411	+	7.62815i	−0.303192	+	0.525143i	−0.976857	−	0.213893i	$-0.931386\pi$
$211$	−4.40411	+	7.62815i	−0.303192	+	0.525143i	0.673665	+	0.739037i	$0.264719\pi$
$212$	−0.640492	−	1.10937i	−0.0439892	−	0.0761915i
$213$	7.31357			0.501118
$214$	0.0970195	+	0.168043i	0.00663211	+	0.0114872i
$215$		0			0
$216$	−1.32025			−0.0898314
$217$	−3.29193	−	5.70180i	−0.223471	−	0.387063i
$218$	−2.61866	+	4.53565i	−0.177358	+	0.307193i
$219$	4.00982	−	6.94520i	0.270958	−	0.469313i
$220$		0			0
$221$	12.4061	−	23.7398i	0.834526	−	1.59691i
$222$	−3.32025			−0.222840
$223$	5.01963	−	8.69426i	0.336139	−	0.582210i	−0.647564	−	0.762011i	$-0.724212\pi$
$223$	5.01963	−	8.69426i	0.336139	−	0.582210i	0.983703	+	0.179801i	$0.0575454\pi$
$224$	1.24399	−	2.15466i	0.0831177	−	0.143964i
$225$		0			0
$226$	1.80823			0.120282
$227$	0.605701	+	1.04910i	0.0402018	+	0.0696315i	0.885426	−	0.464780i	$-0.153867\pi$
$227$	0.605701	+	1.04910i	0.0402018	+	0.0696315i	−0.845224	+	0.534412i	$0.820533\pi$
$228$	0.108844	+	0.188524i	0.00720839	+	0.0124853i
$229$	19.2440			1.27168			0.635839	−	0.771821i	$-0.280654\pi$
$229$	19.2440			1.27168			0.635839	+	0.771821i	$0.280654\pi$
$230$		0			0
$231$	0.224361	−	0.388604i	0.0147618	−	0.0255683i
$232$	3.66012	−	6.33952i	0.240299	−	0.416210i
$233$	23.9081			1.56627			0.783137	−	0.621849i	$-0.213618\pi$
$233$	23.9081			1.56627			0.783137	+	0.621849i	$0.213618\pi$
$234$	−0.656787	−	1.03457i	−0.0429355	−	0.0676322i
$235$		0			0
$236$	2.09589	−	3.63018i	0.136431	−	0.236305i
$237$	−4.98685	+	8.63748i	−0.323931	+	0.561064i
$238$	−0.833398	−	1.44349i	−0.0540211	−	0.0935674i
$239$	18.6798			1.20829			0.604146	−	0.796873i	$-0.293514\pi$
$239$	18.6798			1.20829			0.604146	+	0.796873i	$0.293514\pi$
$240$		0			0
$241$	−3.05776	−	5.29619i	−0.196968	−	0.341158i	0.750576	−	0.660784i	$-0.229776\pi$
$241$	−3.05776	−	5.29619i	−0.196968	−	0.341158i	−0.947544	+	0.319626i	$0.896443\pi$
$242$	−3.58160			−0.230234
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.96187	+	6.86216i	−0.253633	+	0.439305i
$245$		0			0
$246$	1.43576			0.0915409
$247$	−0.192905	+	0.369134i	−0.0122743	+	0.0234874i
$248$	13.1677			0.836152
$249$	0.884484	−	1.53197i	0.0560519	−	0.0970847i
$250$		0			0
$251$	−1.67975	−	2.90942i	−0.106025	−	0.183641i	0.808131	−	0.589002i	$-0.200479\pi$
$251$	−1.67975	−	2.90942i	−0.106025	−	0.183641i	−0.914157	+	0.405361i	$0.867146\pi$
$252$	1.24399			0.0783641
$253$	−2.64049	−	4.57347i	−0.166006	−	0.287531i
$254$	−2.04260	−	3.53788i	−0.128164	−	0.221986i
$255$		0			0
$256$	−3.76897	−	6.52804i	−0.235560	−	0.408003i
$257$	−5.05442	+	8.75452i	−0.315286	+	0.546092i	−0.979498	−	0.201452i	$-0.935434\pi$
$257$	−5.05442	+	8.75452i	−0.315286	+	0.546092i	0.664212	+	0.747544i	$0.268767\pi$
$258$	−0.0925496	+	0.160301i	−0.00576189	+	0.00997988i
$259$	6.44872			0.400704
$260$		0			0
$261$	5.54461			0.343203
$262$	−1.85303	+	3.20954i	−0.114480	+	0.198286i
$263$	−11.2592	+	19.5014i	−0.694269	+	1.20251i	0.276157	+	0.961112i	$0.410939\pi$
$263$	−11.2592	+	19.5014i	−0.694269	+	1.20251i	−0.970426	+	0.241397i	$0.922394\pi$
$264$	0.448721	+	0.777208i	0.0276169	+	0.0478338i
$265$		0			0
$266$	0.0129587	+	0.0224450i	0.000794546	+	0.00137619i
$267$	−6.77230	−	11.7300i	−0.414458	−	0.717863i
$268$	−14.3858			−0.878753
$269$	−4.24733	−	7.35659i	−0.258964	−	0.448539i	0.707001	−	0.707213i	$-0.250048\pi$
$269$	−4.24733	−	7.35659i	−0.258964	−	0.448539i	−0.965965	+	0.258674i	$0.916714\pi$
$270$		0			0
$271$	−4.68510	+	8.11483i	−0.284600	+	0.492941i	−0.972512	−	0.232853i	$-0.925194\pi$
$271$	−4.68510	+	8.11483i	−0.284600	+	0.492941i	0.687912	+	0.725794i	$0.258527\pi$
$272$	−24.6664			−1.49562
$273$	1.27564	+	2.00939i	0.0772052	+	0.121614i
$274$	−1.15212			−0.0696024
$275$		0			0
$276$	7.32025	−	12.6790i	0.440627	−	0.763188i
$277$	0.359508	+	0.622685i	0.0216007	+	0.0374135i	0.876624	−	0.481177i	$-0.159790\pi$
$277$	0.359508	+	0.622685i	0.0216007	+	0.0374135i	−0.855023	+	0.518590i	$0.826457\pi$
$278$	5.03297			0.301858
$279$	4.98685	+	8.63748i	0.298555	+	0.517112i
$280$		0			0
$281$	1.54461			0.0921435			0.0460718	−	0.998938i	$-0.485330\pi$
$281$	1.54461			0.0921435			0.0460718	+	0.998938i	$0.485330\pi$
$282$	−0.853028	−	1.47749i	−0.0507971	−	0.0879831i
$283$	−9.05977	+	15.6920i	−0.538547	+	0.932791i	0.460435	+	0.887693i	$0.347693\pi$
$283$	−9.05977	+	15.6920i	−0.538547	+	0.932791i	−0.998983	+	0.0450980i	$0.985640\pi$
$284$	6.89116	−	11.9358i	0.408915	−	0.708261i
$285$		0			0
$286$	−0.385810	+	0.738268i	−0.0228134	+	0.0436547i
$287$	−2.78860			−0.164606
$288$	−1.88448	+	3.26402i	−0.111044	+	0.192334i
$289$	−19.0957	+	33.0747i	−1.12328	+	1.94557i
$290$		0			0
$291$	−9.90411			−0.580589
$292$	−7.55643	−	13.0881i	−0.442207	−	0.765924i
$293$	−15.2525	−	26.4181i	−0.891059	−	1.54336i	−0.838607	−	0.544737i	$-0.816630\pi$
$293$	−15.2525	−	26.4181i	−0.891059	−	1.54336i	−0.0524523	−	0.998623i	$-0.516704\pi$
$294$	−2.23103			−0.130116
$295$		0			0
$296$	−6.44872	+	11.1695i	−0.374824	+	0.649215i
$297$	−0.339877	+	0.588684i	−0.0197217	+	0.0341589i
$298$	−5.80823			−0.336462
$299$	27.9867	−	1.17737i	1.61851	−	0.0680890i
$300$		0			0
$301$	0.179754	−	0.311343i	0.0103608	−	0.0179455i
$302$	−2.21140	+	3.83026i	−0.127252	+	0.220407i
$303$	4.67975	+	8.10557i	0.268845	+	0.465653i
$304$	0.383543			0.0219977
$305$		0			0
$306$	1.26249	+	2.18669i	0.0721716	+	0.125005i
$307$	4.77564			0.272560			0.136280	−	0.990670i	$-0.456485\pi$
$307$	4.77564			0.272560			0.136280	+	0.990670i	$0.456485\pi$
$308$	−0.422804	−	0.732318i	−0.0240915	−	0.0417277i
$309$	2.25267	−	3.90174i	0.128150	−	0.221962i
$310$		0			0
$311$	30.5812			1.73410			0.867051	−	0.498220i	$-0.166013\pi$
$311$	30.5812			1.73410			0.867051	+	0.498220i	$0.166013\pi$
$312$	−4.75601	+	0.200080i	−0.269256	+	0.0113273i
$313$	26.7230			1.51048			0.755238	−	0.655451i	$-0.227521\pi$
$313$	26.7230			1.51048			0.755238	+	0.655451i	$0.227521\pi$
$314$	−0.131811	+	0.228303i	−0.00743852	+	0.0128839i
$315$		0			0
$316$	9.39764	+	16.2772i	0.528658	+	0.915663i
$317$	20.6271			1.15854			0.579268	−	0.815137i	$-0.303338\pi$
$317$	20.6271			1.15854			0.579268	+	0.815137i	$0.303338\pi$
$318$	0.115516	+	0.200080i	0.00647783	+	0.0112199i
$319$	−1.88448	−	3.26402i	−0.105511	−	0.182750i
$320$		0			0
$321$	0.285455	+	0.494422i	0.0159325	+	0.0275960i
$322$	0.871525	−	1.50953i	0.0485682	−	0.0841226i
$323$	0.429091	−	0.743207i	0.0238752	−	0.0413531i
$324$	−1.88448			−0.104694
$325$		0			0
$326$	−4.14584			−0.229617
$327$	−7.70473	+	13.3450i	−0.426073	+	0.737979i
$328$	2.78860	−	4.82999i	0.153975	−	0.266692i
$329$	1.65679	+	2.86964i	0.0913416	+	0.158208i
$330$		0			0
$331$	−2.68510	−	4.65073i	−0.147586	−	0.255627i	0.782749	−	0.622338i	$-0.213817\pi$
$331$	−2.68510	−	4.65073i	−0.147586	−	0.255627i	−0.930335	+	0.366711i	$0.880484\pi$
$332$	−1.66680	−	2.88697i	−0.0914773	−	0.158443i
$333$	−9.76897			−0.535336
$334$	−0.270294	−	0.468163i	−0.0147898	−	0.0256167i
$335$		0			0
$336$	1.09589	−	1.89813i	0.0597855	−	0.103551i
$337$	−28.7623			−1.56678			−0.783391	−	0.621529i	$-0.786512\pi$
$337$	−28.7623			−1.56678			−0.783391	+	0.621529i	$0.786512\pi$
$338$	−2.52277	−	3.62738i	−0.137221	−	0.197303i
$339$	5.32025			0.288956
$340$		0			0
$341$	3.38983	−	5.87136i	0.183570	−	0.317952i
$342$	−0.0196307	−	0.0340013i	−0.00106150	−	0.00183858i
$343$	8.95407			0.483474
$344$	0.359508	+	0.622685i	0.0193833	+	0.0335729i
$345$		0			0
$346$	−4.33320			−0.232955
$347$	11.1981	+	19.3956i	0.601143	+	1.04121i	0.992648	+	0.121035i	$0.0386212\pi$
$347$	11.1981	+	19.3956i	0.601143	+	1.04121i	−0.391505	+	0.920176i	$0.628045\pi$
$348$	5.22436	−	9.04886i	0.280055	−	0.485070i
$349$	5.98685	−	10.3695i	0.320469	−	0.555068i	−0.660116	−	0.751164i	$-0.729493\pi$
$349$	5.98685	−	10.3695i	0.320469	−	0.555068i	0.980585	+	0.196096i	$0.0628263\pi$
$350$		0			0
$351$	−1.93243	−	3.04397i	−0.103145	−	0.162475i
$352$	2.56197			0.136553
$353$	−8.51830	+	14.7541i	−0.453384	+	0.785283i	−0.998594	−	0.0530161i	$-0.983117\pi$
$353$	−8.51830	+	14.7541i	−0.453384	+	0.785283i	0.545210	+	0.838299i	$0.316450\pi$
$354$	−0.378004	+	0.654723i	−0.0200907	+	0.0347981i
$355$		0			0
$356$	−25.5246			−1.35280
$357$	−2.45206	−	4.24709i	−0.129777	−	0.224780i
$358$	−3.01850	−	5.22819i	−0.159533	−	0.276318i
$359$	−35.0825			−1.85159			−0.925793	−	0.378031i	$-0.876601\pi$
$359$	−35.0825			−1.85159			−0.925793	+	0.378031i	$0.876601\pi$
$360$		0			0
$361$	9.49333	−	16.4429i	0.499649	−	0.865417i
$362$	−1.19404	+	2.06814i	−0.0627573	+	0.108699i
$363$	−10.5379			−0.553098
$364$	4.48131	−	0.188524i	0.234884	−	0.00988133i
$365$		0			0
$366$	0.714545	−	1.23763i	0.0373499	−	0.0646919i
$367$	10.0413	−	17.3920i	0.524150	−	0.907855i	−0.475455	−	0.879740i	$-0.657716\pi$
$367$	10.0413	−	17.3920i	0.524150	−	0.907855i	0.999605	−	0.0281143i	$-0.00895024\pi$
$368$	−12.8974	−	22.3390i	−0.672326	−	1.16450i
$369$	4.22436			0.219911
$370$		0			0
$371$	−0.224361	−	0.388604i	−0.0116482	−	0.0201753i
$372$	18.7953			0.974489
$373$	−11.7395	−	20.3334i	−0.607849	−	1.05283i	−0.991594	−	0.129387i	$-0.958699\pi$
$373$	−11.7395	−	20.3334i	−0.607849	−	1.05283i	0.383745	−	0.923439i	$-0.374634\pi$
$374$	0.858181	−	1.48641i	0.0443755	−	0.0768606i
$375$		0			0
$376$	−6.62715			−0.341769
$377$	19.9737	−	0.840272i	1.02870	−	0.0432762i
$378$	−0.224361			−0.0115399
$379$	−10.5707	+	18.3090i	−0.542981	+	0.940471i	0.455750	+	0.890108i	$0.349371\pi$
$379$	−10.5707	+	18.3090i	−0.542981	+	0.940471i	−0.998731	+	0.0503631i	$0.983962\pi$
$380$		0			0
$381$	−6.00982	−	10.4093i	−0.307892	−	0.533285i
$382$	−4.74266			−0.242656
$383$	0.869323	+	1.50571i	0.0444203	+	0.0769383i	0.887381	−	0.461037i	$-0.152523\pi$
$383$	0.869323	+	1.50571i	0.0444203	+	0.0769383i	−0.842960	+	0.537976i	$0.819189\pi$
$384$	4.67975	+	8.10557i	0.238813	+	0.413636i
$385$		0			0
$386$	4.03593	+	6.99043i	0.205423	+	0.355803i
$387$	−0.272303	+	0.471643i	−0.0138420	+	0.0239750i
$388$	−9.33207	+	16.1636i	−0.473764	+	0.820584i
$389$	−26.6664			−1.35204			−0.676020	−	0.736883i	$-0.736297\pi$
$389$	−26.6664			−1.35204			−0.676020	+	0.736883i	$0.736297\pi$
$390$		0			0
$391$	−57.7164			−2.91884
$392$	−4.33320	+	7.50533i	−0.218860	+	0.379076i
$393$	−5.45206	+	9.44324i	−0.275020	+	0.476348i
$394$	2.68643	+	4.65303i	0.135340	+	0.234416i
$395$		0			0
$396$	0.640492	+	1.10937i	0.0321860	+	0.0557477i
$397$	7.27230	+	12.5960i	0.364986	+	0.632175i	0.988774	−	0.149419i	$-0.0477403\pi$
$397$	7.27230	+	12.5960i	0.364986	+	0.632175i	−0.623788	+	0.781594i	$0.714407\pi$
$398$	2.98037			0.149392
$399$	0.0381275	+	0.0660387i	0.00190876	+	0.00330607i
$400$		0			0
$401$	4.18510	−	7.24880i	0.208994	−	0.361988i	−0.742404	−	0.669952i	$-0.766314\pi$
$401$	4.18510	−	7.24880i	0.208994	−	0.361988i	0.951398	+	0.307964i	$0.0996478\pi$
$402$	2.59456			0.129405
$403$	19.2734	+	30.3596i	0.960078	+	1.51232i
$404$	17.6378			0.877515
$405$		0			0
$406$	0.621996	−	1.07733i	0.0308691	−	0.0534669i
$407$	3.32025	+	5.75084i	0.164578	+	0.285058i
$408$	9.80823			0.485580
$409$	−8.62734	−	14.9430i	−0.426595	−	0.738883i	0.569973	−	0.821663i	$-0.306954\pi$
$409$	−8.62734	−	14.9430i	−0.426595	−	0.738883i	−0.996568	+	0.0827798i	$0.973620\pi$
$410$		0			0
$411$	−3.38983			−0.167208
$412$	−4.24513	−	7.35277i	−0.209142	−	0.362245i
$413$	0.734176	−	1.27163i	0.0361264	−	0.0625728i
$414$	−1.32025	+	2.28673i	−0.0648866	+	0.112387i
$415$		0			0
$416$	−6.29394	+	12.0438i	−0.308586	+	0.590495i
$417$	14.8082			0.725162
$418$	−0.0133440	+	0.0231125i	−0.000652677	+	0.00113047i
$419$	−6.43243	+	11.1413i	−0.314245	+	0.544288i	−0.979277	−	0.202527i	$-0.935085\pi$
$419$	−6.43243	+	11.1413i	−0.314245	+	0.544288i	0.665032	+	0.746815i	$0.268418\pi$
$420$		0			0
$421$	24.5616			1.19706			0.598529	−	0.801101i	$-0.295752\pi$
$421$	24.5616			1.19706			0.598529	+	0.801101i	$0.295752\pi$
$422$	−1.49686	−	2.59263i	−0.0728658	−	0.126207i
$423$	−2.50982	−	4.34713i	−0.122031	−	0.211365i
$424$	0.897442			0.0435837
$425$		0			0
$426$	−1.24286	+	2.15269i	−0.0602166	+	0.104298i
$427$	−1.38782	+	2.40377i	−0.0671613	+	0.116327i
$428$	1.07587			0.0520041
$429$	−1.13515	+	2.17216i	−0.0548054	+	0.104873i
$430$		0			0
$431$	−12.3898	+	21.4598i	−0.596797	+	1.03368i	0.396493	+	0.918038i	$0.370227\pi$
$431$	−12.3898	+	21.4598i	−0.596797	+	1.03368i	−0.993291	+	0.115645i	$0.963106\pi$
$432$	−1.66012	+	2.87542i	−0.0798727	+	0.138344i
$433$	−7.02945	−	12.1754i	−0.337814	−	0.585110i	0.646208	−	0.763162i	$-0.276354\pi$
$433$	−7.02945	−	12.1754i	−0.337814	−	0.585110i	−0.984021	+	0.178051i	$0.943021\pi$
$434$	2.23770			0.107413
$435$		0			0
$436$	14.5194	+	25.1484i	0.695355	+	1.20439i
$437$	0.897442			0.0429305
$438$	1.36284	+	2.36051i	0.0651192	+	0.112790i
$439$	−10.4226	+	18.0525i	−0.497444	+	0.861598i	−0.999996	−	0.00294880i	$-0.999061\pi$
$439$	−10.4226	+	18.0525i	−0.497444	+	0.861598i	0.502552	+	0.864547i	$0.332395\pi$
$440$		0			0
$441$	−6.56424			−0.312583
$442$	4.87933	+	7.68594i	0.232086	+	0.365583i
$443$	11.4291			0.543012			0.271506	−	0.962437i	$-0.412478\pi$
$443$	11.4291			0.543012			0.271506	+	0.962437i	$0.412478\pi$
$444$	−9.20473	+	15.9431i	−0.436837	+	0.756624i
$445$		0			0
$446$	1.70606	+	2.95498i	0.0807841	+	0.139922i
$447$	−17.0892			−0.808292
$448$	−1.76897	−	3.06394i	−0.0835759	−	0.144758i
$449$	−12.9541	−	22.4371i	−0.611340	−	1.05887i	−0.991015	−	0.133752i	$-0.957297\pi$
$449$	−12.9541	−	22.4371i	−0.611340	−	1.05887i	0.379675	−	0.925120i	$-0.376036\pi$
$450$		0			0
$451$	−1.43576	−	2.48681i	−0.0676074	−	0.117099i
$452$	5.01296	−	8.68270i	0.235790	−	0.408400i
$453$	−6.50648	+	11.2696i	−0.305701	+	0.529490i
$454$	−0.411728			−0.0193233
$455$		0			0
$456$	−0.152510			−0.00714193
$457$	2.95206	−	5.11311i	0.138091	−	0.239181i	−0.788683	−	0.614800i	$-0.789237\pi$
$457$	2.95206	−	5.11311i	0.138091	−	0.239181i	0.926774	+	0.375619i	$0.122570\pi$
$458$	−3.27029	+	5.66432i	−0.152811	+	0.264676i
$459$	3.71455	+	6.43378i	0.173380	+	0.300303i
$460$		0			0
$461$	7.74600	+	13.4165i	0.360767	+	0.624867i	0.988087	−	0.153894i	$-0.0491815\pi$
$461$	7.74600	+	13.4165i	0.360767	+	0.624867i	−0.627320	+	0.778762i	$0.715848\pi$
$462$	0.0762550	+	0.132077i	0.00354770	+	0.00614480i
$463$	−17.4420			−0.810601			−0.405300	−	0.914184i	$-0.632833\pi$
$463$	−17.4420			−0.810601			−0.405300	+	0.914184i	$0.632833\pi$
$464$	−9.20473	−	15.9431i	−0.427319	−	0.740138i
$465$		0			0
$466$	−4.06291	+	7.03717i	−0.188211	+	0.325991i
$467$	20.4790			0.947657			0.473829	−	0.880617i	$-0.342872\pi$
$467$	20.4790			0.947657			0.473829	+	0.880617i	$0.342872\pi$
$468$	−6.78860	+	0.285589i	−0.313803	+	0.0132014i
$469$	−5.03926			−0.232691
$470$		0			0
$471$	−0.387820	+	0.671723i	−0.0178698	+	0.0309514i
$472$	1.46835	+	2.54326i	0.0675864	+	0.117063i
$473$	0.370199			0.0170217
$474$	−1.69491	−	2.93568i	−0.0778500	−	0.134840i
$475$		0			0
$476$	−9.24172			−0.423594
$477$	0.339877	+	0.588684i	0.0155619	+	0.0269540i
$478$	−3.17441	+	5.49824i	−0.145194	+	0.251483i
$479$	20.4953	−	35.4990i	0.936456	−	1.62199i	0.164439	−	0.986387i	$-0.447419\pi$
$479$	20.4953	−	35.4990i	0.936456	−	1.62199i	0.772017	−	0.635602i	$-0.219248\pi$
$480$		0			0
$481$	−35.1914	+	1.48046i	−1.60459	+	0.0675033i
$482$	2.07852			0.0946741
$483$	2.56424	−	4.44139i	0.116677	−	0.202090i
$484$	−9.92928	+	17.1980i	−0.451331	+	0.781728i
$485$		0			0
$486$	0.339877			0.0154171
$487$	12.0315	+	20.8391i	0.545197	+	0.944309i	0.998594	+	0.0530008i	$0.0168786\pi$
$487$	12.0315	+	20.8391i	0.545197	+	0.944309i	−0.453397	+	0.891309i	$0.649788\pi$
$488$	−2.77564	−	4.80755i	−0.125647	−	0.217627i
$489$	−12.1981			−0.551615
$490$		0			0
$491$	−18.3865	+	31.8463i	−0.829771	+	1.43721i	0.0684471	+	0.997655i	$0.478196\pi$
$491$	−18.3865	+	31.8463i	−0.829771	+	1.43721i	−0.898218	+	0.439550i	$0.855138\pi$
$492$	3.98037	−	6.89420i	0.179449	−	0.310815i
$493$	−41.1914			−1.85517
$494$	−0.0758696	−	0.119510i	−0.00341354	−	0.00537701i
$495$		0			0
$496$	16.5576	−	28.6785i	0.743457	−	1.28770i
$497$	2.41393	−	4.18105i	0.108280	−	0.187546i
$498$	0.300616	+	0.520681i	0.0134709	+	0.0233323i
$499$	34.8212			1.55881			0.779405	−	0.626520i	$-0.215521\pi$
$499$	34.8212			1.55881			0.779405	+	0.626520i	$0.215521\pi$
$500$		0			0
$501$	−0.795270	−	1.37745i	−0.0355300	−	0.0615398i
$502$	1.14182			0.0509619
$503$	−16.0130	−	27.7353i	−0.713983	−	1.23665i	−0.963351	−	0.268245i	$-0.913556\pi$
$503$	−16.0130	−	27.7353i	−0.713983	−	1.23665i	0.249368	−	0.968409i	$-0.419777\pi$
$504$	−0.435763	+	0.754763i	−0.0194104	+	0.0336198i
$505$		0			0
$506$	1.79488			0.0797924
$507$	−7.42261	−	10.6726i	−0.329650	−	0.473988i
$508$	−22.6508			−1.00497
$509$	20.6731	−	35.8068i	0.916318	−	1.58711i	0.111359	−	0.993780i	$-0.464480\pi$
$509$	20.6731	−	35.8068i	0.916318	−	1.58711i	0.804960	−	0.593329i	$-0.202187\pi$
$510$		0			0
$511$	−2.64697	−	4.58469i	−0.117095	−	0.202815i
$512$	21.2810			0.940496
$513$	−0.0577581	−	0.100040i	−0.00255008	−	0.00441688i
$514$	−1.71788	−	2.97546i	−0.0757725	−	0.131242i
$515$		0			0
$516$	0.513151	+	0.888804i	0.0225902	+	0.0391274i
$517$	−1.70606	+	2.95498i	−0.0750323	+	0.129960i
$518$	−1.09589	+	1.89813i	−0.0481505	+	0.0833990i
$519$	−12.7493			−0.559634
$520$		0			0
$521$	4.40279			0.192890			0.0964448	−	0.995338i	$-0.469253\pi$
$521$	4.40279			0.192890			0.0964448	+	0.995338i	$0.469253\pi$
$522$	−0.942242	+	1.63201i	−0.0412408	+	0.0714312i
$523$	−16.2244	+	28.1014i	−0.709442	+	1.22879i	0.255623	+	0.966777i	$0.417720\pi$
$523$	−16.2244	+	28.1014i	−0.709442	+	1.22879i	−0.965064	+	0.262013i	$0.915614\pi$
$524$	10.2743	+	17.7956i	0.448835	+	0.777406i
$525$		0			0
$526$	−3.82673	−	6.62808i	−0.166853	−	0.288998i
$527$	−37.0478	−	64.1686i	−1.61383	−	2.79523i
$528$	2.25695			0.0982211
$529$	−18.6784	−	32.3520i	−0.812106	−	1.40661i
$530$		0			0
$531$	−1.11218	+	1.92635i	−0.0482645	+	0.0835966i
$532$	0.143701			0.00623024
$533$	15.2177	−	0.640192i	0.659151	−	0.0277298i
$534$	4.60350			0.199213
$535$		0			0
$536$	5.03926	−	8.72826i	0.217663	−	0.377003i
$537$	−8.88115	−	15.3826i	−0.383250	−	0.663808i
$538$	2.88714			0.124473
$539$	2.23103	+	3.86426i	0.0960974	+	0.166446i
$540$		0			0
$541$	−8.57720			−0.368762			−0.184381	−	0.982855i	$-0.559028\pi$
$541$	−8.57720			−0.368762			−0.184381	+	0.982855i	$0.559028\pi$
$542$	−1.59236	−	2.75804i	−0.0683976	−	0.118468i
$543$	−3.51315	+	6.08496i	−0.150764	+	0.261130i
$544$	14.0000	−	24.2487i	0.600245	−	1.03965i
$545$		0			0
$546$	−0.808229	+	0.0340013i	−0.0345890	+	0.00145512i
$547$	32.4920			1.38926			0.694629	−	0.719368i	$-0.255569\pi$
$547$	32.4920			1.38926			0.694629	+	0.719368i	$0.255569\pi$
$548$	−3.19404	+	5.53224i	−0.136443	+	0.236325i
$549$	2.10236	−	3.64140i	0.0897268	−	0.155411i
$550$		0			0
$551$	0.640492			0.0272859
$552$	5.12847	+	8.88278i	0.218282	+	0.378076i
$553$	3.29193	+	5.70180i	0.139987	+	0.242465i
$554$	−0.244377			−0.0103826
$555$		0			0
$556$	13.9529	−	24.1672i	0.591736	−	1.02492i
$557$	−20.6075	+	35.6933i	−0.873169	+	1.51237i	−0.0144676	+	0.999895i	$0.504605\pi$
$557$	−20.6075	+	35.6933i	−0.873169	+	1.51237i	−0.858701	+	0.512477i	$0.828728\pi$
$558$	−3.38983			−0.143503
$559$	−0.909460	+	1.74030i	−0.0384661	+	0.0736068i
$560$		0			0
$561$	2.52498	−	4.37339i	0.106605	−	0.184645i
$562$	−0.262488	+	0.454643i	−0.0110724	+	0.0191779i
$563$	−6.08921	−	10.5468i	−0.256630	−	0.444496i	0.708707	−	0.705503i	$-0.249279\pi$
$563$	−6.08921	−	10.5468i	−0.256630	−	0.444496i	−0.965337	+	0.261007i	$0.915945\pi$
$564$	−9.45941			−0.398313
$565$		0			0
$566$	−3.07921	−	5.33334i	−0.129429	−	0.224177i
$567$	−0.660123			−0.0277226
$568$	4.82786	+	8.36210i	0.202572	+	0.350866i
$569$	−3.47169	+	6.01314i	−0.145541	+	0.252084i	−0.929575	−	0.368634i	$-0.879826\pi$
$569$	−3.47169	+	6.01314i	−0.145541	+	0.252084i	0.784034	+	0.620718i	$0.213159\pi$
$570$		0			0
$571$	3.51429			0.147068			0.0735341	−	0.997293i	$-0.476572\pi$
$571$	3.51429			0.147068			0.0735341	+	0.997293i	$0.476572\pi$
$572$	2.47541	+	3.89927i	0.103502	+	0.163037i
$573$	−13.9541			−0.582939
$574$	0.473890	−	0.820802i	0.0197798	−	0.0342596i
$575$		0			0
$576$	2.67975	+	4.64147i	0.111656	+	0.193395i
$577$	−3.14182			−0.130796			−0.0653978	−	0.997859i	$-0.520832\pi$
$577$	−3.14182			−0.130796			−0.0653978	+	0.997859i	$0.520832\pi$
$578$	−6.49018	−	11.2413i	−0.269956	−	0.467578i
$579$	11.8747	+	20.5675i	0.493494	+	0.854757i
$580$		0			0
$581$	−0.583868	−	1.01129i	−0.0242229	−	0.0419553i
$582$	1.68309	−	2.91520i	0.0697663	−	0.120839i
$583$	0.231033	−	0.400160i	0.00956839	−	0.0165729i
$584$	10.5879			0.438130
$585$		0			0
$586$	10.3679			0.428295
$587$	18.9889	−	32.8897i	0.783754	−	1.35750i	−0.145987	−	0.989287i	$-0.546636\pi$
$587$	18.9889	−	32.8897i	0.783754	−	1.35750i	0.929741	−	0.368215i	$-0.120031\pi$
$588$	−6.18510	+	10.7129i	−0.255069	+	0.441793i
$589$	0.576062	+	0.997769i	0.0237362	+	0.0411124i
$590$		0			0
$591$	7.90411	+	13.6903i	0.325132	+	0.563145i
$592$	16.2177	+	28.0899i	0.666543	+	1.15449i
$593$	−10.4487			−0.429078			−0.214539	−	0.976715i	$-0.568825\pi$
$593$	−10.4487			−0.429078			−0.214539	+	0.976715i	$0.568825\pi$
$594$	−0.115516	−	0.200080i	−0.00473969	−	0.00820939i
$595$		0			0
$596$	−16.1022	+	27.8898i	−0.659571	+	1.14241i
$597$	8.76897			0.358890
$598$	−4.40946	+	8.43773i	−0.180316	+	0.345044i
$599$	−45.5705			−1.86196			−0.930981	−	0.365069i	$-0.881045\pi$
$599$	−45.5705			−1.86196			−0.930981	+	0.365069i	$0.881045\pi$
$600$		0			0
$601$	7.39096	−	12.8015i	0.301484	−	0.522185i	−0.674989	−	0.737828i	$-0.735851\pi$
$601$	7.39096	−	12.8015i	0.301484	−	0.522185i	0.976472	+	0.215643i	$0.0691848\pi$
$602$	0.0610942	+	0.105818i	0.00249001	+	0.00431283i
$603$	7.63382			0.310873
$604$	12.2614	+	21.2373i	0.498907	+	0.864133i
$605$		0			0
$606$	−3.18108			−0.129223
$607$	−9.46722	−	16.3977i	−0.384263	−	0.665562i	0.607404	−	0.794393i	$-0.292211\pi$
$607$	−9.46722	−	16.3977i	−0.384263	−	0.665562i	−0.991667	+	0.128831i	$0.958878\pi$
$608$	−0.217689	+	0.377048i	−0.00882844	+	0.0152913i
$609$	1.83006	−	3.16976i	0.0741578	−	0.128445i
$610$		0			0
$611$	−9.70007	−	15.2796i	−0.392423	−	0.618146i
$612$	14.0000			0.565916
$613$	−1.29193	+	2.23770i	−0.0521807	+	0.0903797i	−0.890936	−	0.454129i	$-0.849951\pi$
$613$	−1.29193	+	2.23770i	−0.0521807	+	0.0903797i	0.838755	+	0.544509i	$0.183284\pi$
$614$	−0.811565	+	1.40567i	−0.0327521	+	0.0567283i
$615$		0			0
$616$	0.592422			0.0238694
$617$	7.01963	+	12.1584i	0.282600	+	0.489477i	0.972024	−	0.234880i	$-0.0754699\pi$
$617$	7.01963	+	12.1584i	0.282600	+	0.489477i	−0.689425	+	0.724357i	$0.742137\pi$
$618$	0.765631	+	1.32611i	0.0307982	+	0.0533441i
$619$	−17.8582			−0.717781			−0.358890	−	0.933380i	$-0.616845\pi$
$619$	−17.8582			−0.717781			−0.358890	+	0.933380i	$0.616845\pi$
$620$		0			0
$621$	−3.88448	+	6.72812i	−0.155879	+	0.269990i
$622$	−5.19692	+	9.00134i	−0.208378	+	0.360921i
$623$	−8.94111			−0.358218
$624$	−5.54461	+	10.6099i	−0.221962	+	0.424736i
$625$		0			0
$626$	−4.54127	+	7.86571i	−0.181506	+	0.314377i
$627$	−0.0392613	+	0.0680026i	−0.00156795	+	0.00271576i
$628$	0.730840	+	1.26585i	0.0291637	+	0.0505130i
$629$	72.5745			2.89374
$630$		0			0
$631$	12.4815	+	21.6186i	0.496881	+	0.860623i	0.999994	−	0.00359801i	$-0.00114528\pi$
$631$	12.4815	+	21.6186i	0.496881	+	0.860623i	−0.503113	+	0.864221i	$0.667812\pi$
$632$	−13.1677			−0.523784
$633$	−4.40411	−	7.62815i	−0.175048	−	0.303192i
$634$	−3.50535	+	6.07144i	−0.139215	+	0.241128i
$635$		0			0
$636$	1.28098			0.0507944
$637$	−23.6468	+	0.994794i	−0.936920	+	0.0394152i
$638$	1.28098			0.0507147
$639$	−3.65679	+	6.33374i	−0.144660	+	0.250559i
$640$		0			0
$641$	−11.6535	−	20.1844i	−0.460284	−	0.797235i	0.538691	−	0.842503i	$-0.318919\pi$
$641$	−11.6535	−	20.1844i	−0.460284	−	0.797235i	−0.998975	+	0.0452686i	$0.985586\pi$
$642$	−0.194039			−0.00765811
$643$	22.7395	+	39.3860i	0.896759	+	1.55323i	0.831612	+	0.555357i	$0.187418\pi$
$643$	22.7395	+	39.3860i	0.896759	+	1.55323i	0.0651470	+	0.997876i	$0.479248\pi$
$644$	−4.83226	−	8.36973i	−0.190418	−	0.329813i
$645$		0			0
$646$	0.145838	+	0.252599i	0.00573792	+	0.00993836i
$647$	3.20473	−	5.55076i	0.125991	−	0.218223i	−0.796129	−	0.605127i	$-0.793122\pi$
$647$	3.20473	−	5.55076i	0.125991	−	0.218223i	0.922120	+	0.386904i	$0.126456\pi$
$648$	0.660123	−	1.14337i	0.0259321	−	0.0449157i
$649$	1.51202			0.0593519
$650$		0			0
$651$	6.58387			0.258042
$652$	−11.4935	+	19.9074i	−0.450121	+	0.779632i
$653$	0.740848	−	1.28319i	0.0289916	−	0.0502150i	−0.851166	−	0.524897i	$-0.824104\pi$
$653$	0.740848	−	1.28319i	0.0289916	−	0.0502150i	0.880157	+	0.474682i	$0.157437\pi$
$654$	−2.61866	−	4.53565i	−0.102398	−	0.177358i
$655$		0			0
$656$	−7.01296	−	12.1468i	−0.273810	−	0.474253i
$657$	4.00982	+	6.94520i	0.156438	+	0.270958i
$658$	−1.12621			−0.0439041
$659$	3.54461	+	6.13944i	0.138078	+	0.239159i	0.926769	−	0.375631i	$-0.122574\pi$
$659$	3.54461	+	6.13944i	0.138078	+	0.239159i	−0.788691	+	0.614790i	$0.789241\pi$
$660$		0			0
$661$	−0.589214	+	1.02055i	−0.0229178	+	0.0396947i	−0.877257	−	0.480021i	$-0.840629\pi$
$661$	−0.589214	+	1.02055i	−0.0229178	+	0.0396947i	0.854339	+	0.519716i	$0.173962\pi$
$662$	1.82521			0.0709387
$663$	14.3562	+	22.6139i	0.557548	+	0.878251i
$664$	2.33547			0.0906339
$665$		0			0
$666$	1.66012	−	2.87542i	0.0643285	−	0.111420i
$667$	−21.5379	−	37.3048i	−0.833952	−	1.44445i
$668$	−2.99735			−0.115971
$669$	5.01963	+	8.69426i	0.194070	+	0.336139i
$670$		0			0
$671$	−2.85818			−0.110339
$672$	1.24399	+	2.15466i	0.0479880	+	0.0831177i
$673$	6.77878	−	11.7412i	0.261303	−	0.452590i	−0.705286	−	0.708923i	$-0.749181\pi$
$673$	6.77878	−	11.7412i	0.261303	−	0.452590i	0.966588	+	0.256334i	$0.0825145\pi$
$674$	4.88782	−	8.46595i	0.188272	−	0.326096i
$675$		0			0
$676$	−24.4117	+	2.05759i	−0.938913	+	0.0791381i
$677$	−9.53793			−0.366573			−0.183286	−	0.983060i	$-0.558674\pi$
$677$	−9.53793			−0.366573			−0.183286	+	0.983060i	$0.558674\pi$
$678$	−0.904114	+	1.56597i	−0.0347223	+	0.0601408i
$679$	−3.26897	+	5.66202i	−0.125451	+	0.217288i
$680$		0			0
$681$	−1.21140			−0.0464210
$682$	1.15212	+	1.99554i	0.0441171	+	0.0764131i
$683$	−22.2592	−	38.5540i	−0.851723	−	1.47523i	−0.879652	−	0.475617i	$-0.842225\pi$
$683$	−22.2592	−	38.5540i	−0.851723	−	1.47523i	0.0279296	−	0.999610i	$-0.491109\pi$
$684$	−0.217689			−0.00832353
$685$		0			0
$686$	−1.52164	+	2.63556i	−0.0580965	+	0.100626i
$687$	−9.62200	+	16.6658i	−0.367102	+	0.635839i
$688$	1.80823			0.0689381
$689$	1.31357	+	2.06915i	0.0500432	+	0.0788282i
$690$		0			0
$691$	2.64030	−	4.57313i	0.100442	−	0.173970i	−0.811425	−	0.584457i	$-0.801308\pi$
$691$	2.64030	−	4.57313i	0.100442	−	0.173970i	0.911867	+	0.410486i	$0.134641\pi$
$692$	−12.0130	+	20.8071i	−0.456664	+	0.790966i
$693$	0.224361	+	0.388604i	0.00852275	+	0.0147618i
$694$	−7.61192			−0.288945
$695$		0			0
$696$	3.66012	+	6.33952i	0.138737	+	0.240299i
$697$	−31.3832			−1.18872
$698$	2.03479	+	3.52436i	0.0770180	+	0.133399i
$699$	−11.9541	+	20.7051i	−0.452144	+	0.783137i
$700$		0			0
$701$	20.1392			0.760646			0.380323	−	0.924854i	$-0.375813\pi$
$701$	20.1392			0.760646			0.380323	+	0.924854i	$0.375813\pi$
$702$	1.22436	−	0.0515075i	0.0462105	−	0.00194403i
$703$	−1.12847			−0.0425612
$704$	1.82157	−	3.15506i	0.0686531	−	0.118911i
$705$		0			0
$706$	−2.89517	−	5.01459i	−0.108961	−	0.188727i
$707$	6.17843			0.232364
$708$	2.09589	+	3.63018i	0.0787682	+	0.136431i
$709$	−0.770294	−	1.33419i	−0.0289290	−	0.0501065i	0.851198	−	0.524844i	$-0.175876\pi$
$709$	−0.770294	−	1.33419i	−0.0289290	−	0.0501065i	−0.880127	+	0.474737i	$0.842543\pi$
$710$		0			0
$711$	−4.98685	−	8.63748i	−0.187021	−	0.323931i
$712$	8.94111	−	15.4865i	0.335082	−	0.580379i
$713$	38.7427	−	67.1043i	1.45092	−	2.51307i
$714$	1.66680			0.0623782
$715$		0			0
$716$	−33.4728			−1.25094
$717$	−9.33988	+	16.1771i	−0.348804	+	0.604146i
$718$	5.96187	−	10.3263i	0.222495	−	0.385373i
$719$	−18.5020	−	32.0464i	−0.690009	−	1.19513i	−0.971835	−	0.235664i	$-0.924273\pi$
$719$	−18.5020	−	32.0464i	−0.690009	−	1.19513i	0.281826	−	0.959466i	$-0.409060\pi$
$720$		0			0
$721$	−1.48704	−	2.57563i	−0.0553803	−	0.0959215i
$722$	3.22656	+	5.58857i	0.120080	+	0.207985i
$723$	6.11552			0.227438
$724$	6.62048	+	11.4670i	0.246048	+	0.426168i
$725$		0			0
$726$	1.79080	−	3.10176i	0.0664628	−	0.115117i
$727$	44.9015			1.66530			0.832652	−	0.553797i	$-0.186822\pi$
$727$	44.9015			1.66530			0.832652	+	0.553797i	$0.186822\pi$
$728$	−1.45539	+	2.78497i	−0.0539405	+	0.103218i
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.02297	−	3.50388i	0.0748221	−	0.129596i
$732$	−3.96187	−	6.86216i	−0.146435	−	0.253633i
$733$	4.94072			0.182490			0.0912449	−	0.995828i	$-0.470915\pi$
$733$	4.94072			0.182490			0.0912449	+	0.995828i	$0.470915\pi$
$734$	3.41280	+	5.91114i	0.125969	+	0.218184i
$735$		0			0
$736$	29.2810			1.07931
$737$	−2.59456	−	4.49391i	−0.0955718	−	0.165535i
$738$	−0.717881	+	1.24341i	−0.0264256	+	0.0457704i
$739$	−3.01963	+	5.23015i	−0.111079	+	0.192394i	−0.916206	−	0.400709i	$-0.868764\pi$
$739$	−3.01963	+	5.23015i	−0.111079	+	0.192394i	0.805127	+	0.593103i	$0.202097\pi$
$740$		0			0
$741$	−0.223227	−	0.351628i	−0.00820044	−	0.0129174i
$742$	0.152510			0.00559882
$743$	−6.52945	+	11.3093i	−0.239542	+	0.414899i	−0.960583	−	0.277993i	$-0.910331\pi$
$743$	−6.52945	+	11.3093i	−0.239542	+	0.414899i	0.721041	+	0.692893i	$0.243664\pi$
$744$	−6.58387	+	11.4036i	−0.241376	+	0.418076i
$745$		0			0
$746$	7.97998			0.292168
$747$	0.884484	+	1.53197i	0.0323616	+	0.0560519i
$748$	−4.75828	−	8.24158i	−0.173980	−	0.301342i
$749$	0.376871			0.0137706
$750$		0			0
$751$	−24.0118	+	41.5897i	−0.876204	+	1.51763i	−0.0207292	+	0.999785i	$0.506599\pi$
$751$	−24.0118	+	41.5897i	−0.876204	+	1.51763i	−0.855475	+	0.517845i	$0.826735\pi$
$752$	−8.33320	+	14.4335i	−0.303881	+	0.526337i
$753$	3.35951			0.122427
$754$	−3.14697	+	6.02189i	−0.114606	+	0.219304i
$755$		0			0
$756$	−0.621996	+	1.07733i	−0.0226218	+	0.0391820i
$757$	−2.28212	+	3.95275i	−0.0829450	+	0.143665i	−0.904514	−	0.426445i	$-0.859766\pi$
$757$	−2.28212	+	3.95275i	−0.0829450	+	0.143665i	0.821569	+	0.570110i	$0.193099\pi$
$758$	−3.59274	−	6.22281i	−0.130494	−	0.226023i
$759$	5.28098			0.191688
$760$		0			0
$761$	−10.5446	−	18.2638i	−0.382242	−	0.662062i	0.609141	−	0.793062i	$-0.291514\pi$
$761$	−10.5446	−	18.2638i	−0.382242	−	0.662062i	−0.991382	+	0.131000i	$0.958181\pi$
$762$	4.08519			0.147991
$763$	5.08607	+	8.80933i	0.184128	+	0.318919i
$764$	−13.1481	+	22.7732i	−0.475682	+	0.823905i
$765$		0			0
$766$	−0.590926			−0.0213510
$767$	−3.71455	+	7.10797i	−0.134124	+	0.256654i
$768$	7.53793			0.272002
$769$	−21.1666	+	36.6616i	−0.763287	+	1.32205i	0.177860	+	0.984056i	$0.443083\pi$
$769$	−21.1666	+	36.6616i	−0.763287	+	1.32205i	−0.941147	+	0.337996i	$0.890251\pi$
$770$		0			0
$771$	−5.05442	−	8.75452i	−0.182031	−	0.315286i
$772$	44.7552			1.61078
$773$	25.1218	+	43.5122i	0.903568	+	1.56503i	0.822827	+	0.568291i	$0.192395\pi$
$773$	25.1218	+	43.5122i	0.903568	+	1.56503i	0.0807410	+	0.996735i	$0.474271\pi$
$774$	−0.0925496	−	0.160301i	−0.00332663	−	0.00576189i
$775$		0			0
$776$	−6.53793	−	11.3240i	−0.234698	−	0.406509i
$777$	−3.22436	+	5.58476i	−0.115673	+	0.200352i
$778$	4.53165	−	7.84904i	0.162467	−	0.281402i
$779$	0.487982			0.0174838
$780$		0			0
$781$	4.97143			0.177892
$782$	9.80823	−	16.9884i	0.350742	−	0.607502i
$783$	−2.77230	+	4.80177i	−0.0990740	+	0.171601i
$784$	10.8974	+	18.8749i	0.389194	+	0.674104i
$785$		0			0
$786$	−1.85303	−	3.20954i	−0.0660953	−	0.114480i
$787$	−5.29080	−	9.16393i	−0.188597	−	0.326659i	0.756186	−	0.654357i	$-0.227061\pi$
$787$	−5.29080	−	9.16393i	−0.188597	−	0.326659i	−0.944783	+	0.327698i	$0.893727\pi$
$788$	29.7903			1.06124
$789$	−11.2592	−	19.5014i	−0.400836	−	0.694269i
$790$		0			0
$791$	1.75601	−	3.04150i	0.0624365	−	0.108143i
$792$	−0.897442			−0.0318892
$793$	7.02164	−	13.4363i	0.249346	−	0.477136i
$794$	−4.94338			−0.175434
$795$		0			0
$796$	8.26249	−	14.3110i	0.292856	−	0.507242i
$797$	−10.0741	−	17.4488i	−0.356841	−	0.618067i	0.630590	−	0.776116i	$-0.282813\pi$
$797$	−10.0741	−	17.4488i	−0.356841	−	0.618067i	−0.987431	+	0.158049i	$0.949480\pi$
$798$	−0.0259173			−0.000917463
$799$	18.6456	+	32.2952i	0.659636	+	1.14252i
$800$		0			0
$801$	13.5446			0.478575
$802$	1.42242	+	2.46370i	0.0502273	+	0.0869963i
$803$	2.72569	−	4.72103i	0.0961874	−	0.166601i
$804$	7.19291	−	12.4585i	0.253674	−	0.439377i
$805$		0			0
$806$	−12.2114	+	0.513720i	−0.430128	+	0.0180950i
$807$	8.49465			0.299026
$808$	−6.17843	+	10.7013i	−0.217356	+	0.376472i
$809$	−6.45539	+	11.1811i	−0.226960	+	0.393105i	−0.956906	−	0.290399i	$-0.906212\pi$
$809$	−6.45539	+	11.1811i	−0.226960	+	0.393105i	0.729946	+	0.683505i	$0.239545\pi$
$810$		0			0
$811$	−15.8974			−0.558235			−0.279117	−	0.960257i	$-0.590042\pi$
$811$	−15.8974			−0.558235			−0.279117	+	0.960257i	$0.590042\pi$
$812$	−3.44872	−	5.97336i	−0.121026	−	0.209624i
$813$	−4.68510	−	8.11483i	−0.164314	−	0.284600i
$814$	−2.25695			−0.0791061
$815$		0			0
$816$	12.3332	−	21.3617i	0.431749	−	0.747810i
$817$	−0.0314555	+	0.0544825i	−0.00110049	+	0.00190610i
$818$	5.86447			0.205046
$819$	−2.37800	+	0.100040i	−0.0830942	+	0.00349568i
$820$		0			0
$821$	18.6142	−	32.2407i	0.649640	−	1.12521i	−0.333569	−	0.942726i	$-0.608253\pi$
$821$	18.6142	−	32.2407i	0.649640	−	1.12521i	0.983209	−	0.182483i	$-0.0584136\pi$
$822$	0.576062	−	0.997769i	0.0200925	−	0.0348012i
$823$	−2.44872	−	4.24131i	−0.0853571	−	0.147843i	0.820186	−	0.572097i	$-0.193870\pi$
$823$	−2.44872	−	4.24131i	−0.0853571	−	0.147843i	−0.905543	+	0.424254i	$0.860536\pi$
$824$	5.94817			0.207214
$825$		0			0
$826$	0.249529	+	0.432198i	0.00868224	+	0.0150381i
$827$	−37.6334			−1.30864			−0.654321	−	0.756217i	$-0.727046\pi$
$827$	−37.6334			−1.30864			−0.654321	+	0.756217i	$0.727046\pi$
$828$	7.32025	+	12.6790i	0.254396	+	0.440627i
$829$	24.4552	−	42.3576i	0.849364	−	1.47114i	−0.0324123	−	0.999475i	$-0.510319\pi$
$829$	24.4552	−	42.3576i	0.849364	−	1.47114i	0.881777	−	0.471667i	$-0.156348\pi$
$830$		0			0
$831$	−0.719015			−0.0249424
$832$	10.3569	+	16.3142i	0.359059	+	0.565592i
$833$	48.7663			1.68965
$834$	−2.51649	+	4.35868i	−0.0871388	+	0.150929i
$835$		0			0
$836$	0.0739873	+	0.128150i	0.00255890	+	0.00443215i
$837$	−9.97370			−0.344741
$838$	−2.18623	−	3.78667i	−0.0755222	−	0.130808i
$839$	−24.1392	−	41.8103i	−0.833377	−	1.44345i	−0.895345	−	0.445372i	$-0.853071\pi$
$839$	−24.1392	−	41.8103i	−0.833377	−	1.44345i	0.0619688	−	0.998078i	$-0.480262\pi$
$840$		0			0
$841$	−0.871332	−	1.50919i	−0.0300459	−	0.0520411i
$842$	−4.17396	+	7.22951i	−0.143844	+	0.249145i
$843$	−0.772303	+	1.33767i	−0.0265995	+	0.0460718i
$844$	−16.5990			−0.571360
$845$		0			0
$846$	1.70606			0.0586554
$847$	−3.47817	+	6.02436i	−0.119511	+	0.207000i
$848$	1.12847	−	1.95458i	0.0387520	−	0.0671204i
$849$	−9.05977	−	15.6920i	−0.310930	−	0.538547i
$850$		0			0
$851$	37.9474	+	65.7268i	1.30082	+	2.25309i
$852$	6.89116	+	11.9358i	0.236087	+	0.408915i
$853$	14.4291			0.494043			0.247021	−	0.969010i	$-0.420548\pi$
$853$	14.4291			0.494043			0.247021	+	0.969010i	$0.420548\pi$
$854$	−0.471688	−	0.816987i	−0.0161408	−	0.0279567i
$855$		0			0
$856$	−0.376871	+	0.652759i	−0.0128812	+	0.0223108i
$857$	−3.64678			−0.124572			−0.0622858	−	0.998058i	$-0.519839\pi$
$857$	−3.64678			−0.124572			−0.0622858	+	0.998058i	$0.519839\pi$
$858$	−0.446454	−	0.703255i	−0.0152417	−	0.0240087i
$859$	21.7427			0.741850			0.370925	−	0.928663i	$-0.379041\pi$
$859$	21.7427			0.741850			0.370925	+	0.928663i	$0.379041\pi$
$860$		0			0
$861$	1.39430	−	2.41500i	0.0475176	−	0.0823029i
$862$	−4.21102	−	7.29369i	−0.143428	−	0.248424i
$863$	17.0892			0.581724			0.290862	−	0.956765i	$-0.406058\pi$
$863$	17.0892			0.581724			0.290862	+	0.956765i	$0.406058\pi$
$864$	−1.88448	−	3.26402i	−0.0641114	−	0.111044i
$865$		0			0
$866$	4.77829			0.162373
$867$	−19.0957	−	33.0747i	−0.648524	−	1.12328i
$868$	6.20360	−	10.7449i	0.210564	−	0.364707i
$869$	−3.38983	+	5.87136i	−0.114992	+	0.199172i
$870$		0			0
$871$	27.4998	−	1.15689i	0.931795	−	0.0391996i
$872$	−20.3443			−0.688944
$873$	4.95206	−	8.57721i	0.167602	−	0.290295i
$874$	−0.152510	+	0.264155i	−0.00515873	+	0.00893518i
$875$		0			0
$876$	15.1129			0.510616
$877$	−2.42909	−	4.20731i	−0.0820246	−	0.142071i	0.822095	−	0.569351i	$-0.192805\pi$
$877$	−2.42909	−	4.20731i	−0.0820246	−	0.142071i	−0.904119	+	0.427280i	$0.859472\pi$
$878$	−3.54240	−	6.13562i	−0.119550	−	0.207067i
$879$	30.5050			1.02891
$880$		0			0
$881$	11.6601	−	20.1959i	0.392840	−	0.680418i	−0.599983	−	0.800013i	$-0.704826\pi$
$881$	11.6601	−	20.1959i	0.392840	−	0.680418i	0.992823	+	0.119595i	$0.0381595\pi$
$882$	1.11552	−	1.93213i	0.0375614	−	0.0650582i
$883$	12.8934			0.433898			0.216949	−	0.976183i	$-0.430389\pi$
$883$	12.8934			0.433898			0.216949	+	0.976183i	$0.430389\pi$
$884$	50.4331	−	2.12167i	1.69625	−	0.0713593i
$885$		0			0
$886$	−1.94224	+	3.36406i	−0.0652509	+	0.113018i
$887$	15.4639	−	26.7842i	0.519226	−	0.899326i	−0.480524	−	0.876982i	$-0.659553\pi$
$887$	15.4639	−	26.7842i	0.519226	−	0.899326i	0.999750	−	0.0223448i	$-0.00711317\pi$
$888$	−6.44872	−	11.1695i	−0.216405	−	0.374824i
$889$	−7.93444			−0.266112
$890$		0			0
$891$	−0.339877	−	0.588684i	−0.0113863	−	0.0197217i
$892$	18.9188			0.633449
$893$	−0.289925	−	0.502164i	−0.00970196	−	0.0168043i
$894$	2.90411	−	5.03007i	0.0971281	−	0.168231i
$895$		0			0
$896$	6.17843			0.206407
$897$	−12.9737	+	24.8258i	−0.433179	+	0.828911i
$898$	8.80558			0.293846
$899$	27.6501	−	47.8914i	0.922183	−	1.59727i
$900$		0			0
$901$	−2.52498	−	4.37339i	−0.0841192	−	0.145699i
$902$	0.975965			0.0324961
$903$	0.179754	+	0.311343i	0.00598183	+	0.0103608i
$904$	3.51202	+	6.08299i	0.116808	+	0.202317i
$905$		0			0
$906$	−2.21140	−	3.83026i	−0.0734689	−	0.127252i
$907$	−8.48018	+	14.6881i	−0.281580	+	0.487710i	−0.971774	−	0.235914i	$-0.924192\pi$
$907$	−8.48018	+	14.6881i	−0.281580	+	0.487710i	0.690194	+	0.723624i	$0.257525\pi$
$908$	−1.14143	+	1.97702i	−0.0378798	+	0.0656097i
$909$	−9.35951			−0.310435
$910$		0			0
$911$	37.7297			1.25004			0.625020	−	0.780608i	$-0.285091\pi$
$911$	37.7297			1.25004			0.625020	+	0.780608i	$0.285091\pi$
$912$	−0.191771	+	0.332158i	−0.00635018	+	0.0109988i
$913$	0.601231	−	1.04136i	0.0198978	−	0.0344641i
$914$	1.00334	+	1.73783i	0.0331874	+	0.0574823i
$915$		0			0
$916$	18.1325	+	31.4064i	0.599114	+	1.03770i
$917$	3.59903	+	6.23370i	0.118850	+	0.205855i
$918$	−2.52498			−0.0833366
$919$	−20.0814	−	34.7820i	−0.662425	−	1.14735i	−0.979977	−	0.199112i	$-0.936194\pi$
$919$	−20.0814	−	34.7820i	−0.662425	−	1.14735i	0.317552	−	0.948241i	$-0.397139\pi$
$920$		0			0
$921$	−2.38782	+	4.13583i	−0.0786813	+	0.136280i
$922$	−5.26537			−0.173406
$923$	−12.2132	+	23.3706i	−0.402003	+	0.769253i
$924$	0.845608			0.0278185
$925$		0			0
$926$	2.96407	−	5.13393i	0.0974055	−	0.168711i
$927$	2.25267	+	3.90174i	0.0739875	+	0.128150i
$928$	20.8974			0.685992
$929$	−11.8845	−	20.5845i	−0.389917	−	0.675357i	0.602521	−	0.798103i	$-0.294163\pi$
$929$	−11.8845	−	20.5845i	−0.389917	−	0.675357i	−0.992438	+	0.122747i	$0.960830\pi$
$930$		0			0
$931$	−0.758276			−0.0248515
$932$	22.5272	+	39.0183i	0.737904	+	1.27809i
$933$	−15.2906	+	26.4841i	−0.500592	+	0.867051i
$934$	−3.48018	+	6.02784i	−0.113875	+	0.197237i
$935$		0			0
$936$	2.20473	−	4.21886i	0.0720639	−	0.137898i
$937$	7.43803			0.242990			0.121495	−	0.992592i	$-0.461231\pi$
$937$	7.43803			0.242990			0.121495	+	0.992592i	$0.461231\pi$
$938$	0.856364	−	1.48327i	0.0279613	−	0.0484304i
$939$	−13.3615	+	23.1428i	−0.436037	+	0.755238i
$940$		0			0
$941$	−19.3528			−0.630884			−0.315442	−	0.948945i	$-0.602153\pi$
$941$	−19.3528			−0.630884			−0.315442	+	0.948945i	$0.602153\pi$
$942$	−0.131811	−	0.228303i	−0.00429463	−	0.00743852i
$943$	−16.4095	−	28.4220i	−0.534366	−	0.925548i
$944$	7.38542			0.240375
$945$		0			0
$946$	−0.0629110	+	0.108965i	−0.00204541	+	0.00354276i
$947$	6.95854	−	12.0525i	0.226122	−	0.391655i	−0.730533	−	0.682877i	$-0.760729\pi$
$947$	6.95854	−	12.0525i	0.226122	−	0.391655i	0.956655	+	0.291222i	$0.0940618\pi$
$948$	−18.7953			−0.610442
$949$	15.4973	+	24.4115i	0.503065	+	0.792430i
$950$		0			0
$951$	−10.3136	+	17.8636i	−0.334441	+	0.579268i
$952$	3.23732	−	5.60720i	0.104922	−	0.181730i
$953$	−5.31357	−	9.20338i	−0.172124	−	0.298127i	0.767039	−	0.641601i	$-0.221729\pi$
$953$	−5.31357	−	9.20338i	−0.172124	−	0.298127i	−0.939162	+	0.343474i	$0.888396\pi$
$954$	−0.231033			−0.00747996
$955$		0			0
$956$	17.6008	+	30.4856i	0.569252	+	0.985973i
$957$	3.76897			0.121833
$958$	6.96589	+	12.0653i	0.225058	+	0.389811i
$959$	−1.11885	+	1.93791i	−0.0361296	+	0.0625783i
$960$		0			0
$961$	68.4746			2.20886
$962$	5.54461	−	10.6099i	0.178765	−	0.342077i
$963$	−0.570909			−0.0183973
$964$	5.76230	−	9.98059i	0.185591	−	0.321453i
$965$		0			0
$966$	0.871525	+	1.50953i	0.0280409	+	0.0485682i
$967$	−51.6771			−1.66182			−0.830912	−	0.556404i	$-0.812181\pi$
$967$	−51.6771			−1.66182			−0.830912	+	0.556404i	$0.812181\pi$
$968$	−6.95633	−	12.0487i	−0.223585	−	0.387261i
$969$	0.429091	+	0.743207i	0.0137844	+	0.0238752i
$970$		0			0
$971$	21.4487	+	37.1503i	0.688322	+	1.19221i	0.972380	+	0.233402i	$0.0749858\pi$
$971$	21.4487	+	37.1503i	0.688322	+	1.19221i	−0.284058	+	0.958807i	$0.591681\pi$
$972$	0.942242	−	1.63201i	0.0302224	−	0.0523468i
$973$	4.88763	−	8.46562i	0.156690	−	0.271395i
$974$	−8.17843			−0.262054
$975$		0			0
$976$	−13.9607			−0.446872
$977$	9.08254	−	15.7314i	0.290576	−	0.503293i	−0.683370	−	0.730072i	$-0.739486\pi$
$977$	9.08254	−	15.7314i	0.290576	−	0.503293i	0.973946	+	0.226780i	$0.0728197\pi$
$978$	2.07292	−	3.59040i	0.0662846	−	0.114808i
$979$	−4.60350	−	7.97349i	−0.147128	−	0.254834i
$980$		0			0
$981$	−7.70473	−	13.3450i	−0.245993	−	0.426073i
$982$	−6.24914	−	10.8238i	−0.199418	−	0.345402i
$983$	10.8582			0.346322			0.173161	−	0.984894i	$-0.444602\pi$
$983$	10.8582			0.346322			0.173161	+	0.984894i	$0.444602\pi$
$984$	2.78860	+	4.82999i	0.0888973	+	0.153975i
$985$		0			0
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$	−3.31357			−0.105472
$988$	−0.784194	+	0.0329902i	−0.0249485	+	0.00104956i
$989$	4.23103			0.134539
$990$		0			0
$991$	11.1862	−	19.3751i	0.355342	−	0.615471i	−0.631834	−	0.775104i	$-0.717698\pi$
$991$	11.1862	−	19.3751i	0.355342	−	0.615471i	0.987177	+	0.159633i	$0.0510309\pi$
$992$	18.7953	+	32.5544i	0.596750	+	1.03360i
$993$	5.37020			0.170418
$994$	0.820439	+	1.42104i	0.0260227	+	0.0450727i
$995$		0			0
$996$	3.33359			0.105629
$997$	−12.1187	−	20.9901i	−0.383802	−	0.664764i	0.607800	−	0.794090i	$-0.292052\pi$
$997$	−12.1187	−	20.9901i	−0.383802	−	0.664764i	−0.991602	+	0.129326i	$0.958719\pi$
$998$	−5.91746	+	10.2493i	−0.187314	+	0.324437i
$999$	4.88448	−	8.46017i	0.154538	−	0.267668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.l.451.2		6
5.2	odd	4		975.2.bb.k.724.3		12
5.3	odd	4		975.2.bb.k.724.4		12
5.4	even	2		195.2.i.d.61.2	yes	6
13.3	even	3	inner	975.2.i.l.601.2		6
15.14	odd	2		585.2.j.f.451.2		6
65.3	odd	12		975.2.bb.k.874.3		12
65.4	even	6		2535.2.a.ba.1.2		3
65.9	even	6		2535.2.a.bb.1.2		3
65.29	even	6		195.2.i.d.16.2	✓	6
65.42	odd	12		975.2.bb.k.874.4		12
195.29	odd	6		585.2.j.f.406.2		6
195.74	odd	6		7605.2.a.bv.1.2		3
195.134	odd	6		7605.2.a.bw.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.2	✓	6	65.29	even	6
195.2.i.d.61.2	yes	6	5.4	even	2
585.2.j.f.406.2		6	195.29	odd	6
585.2.j.f.451.2		6	15.14	odd	2
975.2.i.l.451.2		6	1.1	even	1	trivial
975.2.i.l.601.2		6	13.3	even	3	inner
975.2.bb.k.724.3		12	5.2	odd	4
975.2.bb.k.724.4		12	5.3	odd	4
975.2.bb.k.874.3		12	65.3	odd	12
975.2.bb.k.874.4		12	65.42	odd	12
2535.2.a.ba.1.2		3	65.4	even	6
2535.2.a.bb.1.2		3	65.9	even	6
7605.2.a.bv.1.2		3	195.74	odd	6
7605.2.a.bw.1.2		3	195.134	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.169938 + 0.294342i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.942242 + 1.63201i) q^{4} +(-0.169938 - 0.294342i) q^{6} +(0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.169938 + 0.294342i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.942242 + 1.63201i) q^{4} +(-0.169938 - 0.294342i) q^{6} +(0.330062 + 0.571683i) q^{7} -1.32025 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.339877 + 0.588684i) q^{11} -1.88448 q^{12} +(-1.93243 - 3.04397i) q^{13} -0.224361 q^{14} +(-1.66012 + 2.87542i) q^{16} +(3.71455 + 6.43378i) q^{17} +0.339877 q^{18} +(-0.0577581 - 0.100040i) q^{19} -0.660123 q^{21} +(-0.115516 - 0.200080i) q^{22} +(-3.88448 + 6.72812i) q^{23} +(0.660123 - 1.14337i) q^{24} +(1.22436 - 0.0515075i) q^{26} +1.00000 q^{27} +(-0.621996 + 1.07733i) q^{28} +(-2.77230 + 4.80177i) q^{29} -9.97370 q^{31} +(-1.88448 - 3.26402i) q^{32} +(-0.339877 - 0.588684i) q^{33} -2.52498 q^{34} +(0.942242 - 1.63201i) q^{36} +(4.88448 - 8.46017i) q^{37} +0.0392613 q^{38} +(3.60236 - 0.151548i) q^{39} +(-2.11218 + 3.65840i) q^{41} +(0.112180 - 0.194302i) q^{42} +(-0.272303 - 0.471643i) q^{43} -1.28098 q^{44} +(-1.32025 - 2.28673i) q^{46} +5.01963 q^{47} +(-1.66012 - 2.87542i) q^{48} +(3.28212 - 5.68480i) q^{49} -7.42909 q^{51} +(3.14697 - 6.02189i) q^{52} -0.679754 q^{53} +(-0.169938 + 0.294342i) q^{54} +(-0.435763 - 0.754763i) q^{56} +0.115516 q^{57} +(-0.942242 - 1.63201i) q^{58} +(-1.11218 - 1.92635i) q^{59} +(2.10236 + 3.64140i) q^{61} +(1.69491 - 2.93568i) q^{62} +(0.330062 - 0.571683i) q^{63} -5.35951 q^{64} +0.231033 q^{66} +(-3.81691 + 6.61108i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(-3.88448 - 6.72812i) q^{69} +(-3.65679 - 6.33374i) q^{71} +(0.660123 + 1.14337i) q^{72} -8.01963 q^{73} +(1.66012 + 2.87542i) q^{74} +(0.108844 - 0.188524i) q^{76} -0.448721 q^{77} +(-0.567573 + 1.08608i) q^{78} +9.97370 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.717881 - 1.24341i) q^{82} -1.76897 q^{83} +(-0.621996 - 1.07733i) q^{84} +0.185099 q^{86} +(-2.77230 - 4.80177i) q^{87} +(0.448721 - 0.777208i) q^{88} +(-6.77230 + 11.7300i) q^{89} +(1.10236 - 2.10943i) q^{91} -14.6405 q^{92} +(4.98685 - 8.63748i) q^{93} +(-0.853028 + 1.47749i) q^{94} +3.76897 q^{96} +(4.95206 + 8.57721i) q^{97} +(1.11552 + 1.93213i) q^{98} +0.679754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9} + 12 q^{12} - 3 q^{13} + 24 q^{14} - 12 q^{16} - 12 q^{19} - 6 q^{21} - 24 q^{22} + 6 q^{24} - 18 q^{26} + 6 q^{27} + 12 q^{28} - 6 q^{29} + 6 q^{31} + 12 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{42} + 9 q^{43} - 24 q^{44} - 12 q^{46} + 24 q^{47} - 12 q^{48} + 6 q^{49} - 12 q^{52} - 30 q^{56} + 24 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{61} - 6 q^{62} + 3 q^{63} - 24 q^{64} + 48 q^{66} + 9 q^{67} - 42 q^{68} + 12 q^{71} + 6 q^{72} - 42 q^{73} + 12 q^{74} - 48 q^{76} + 48 q^{77} - 12 q^{78} - 6 q^{79} - 3 q^{81} - 18 q^{82} + 36 q^{83} + 12 q^{84} - 12 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} - 3 q^{91} - 96 q^{92} - 3 q^{93} - 36 q^{94} - 24 q^{96} + 15 q^{97} + 30 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9 + 12 * q^12 - 3 * q^13 + 24 * q^14 - 12 * q^16 - 12 * q^19 - 6 * q^21 - 24 * q^22 + 6 * q^24 - 18 * q^26 + 6 * q^27 + 12 * q^28 - 6 * q^29 + 6 * q^31 + 12 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^42 + 9 * q^43 - 24 * q^44 - 12 * q^46 + 24 * q^47 - 12 * q^48 + 6 * q^49 - 12 * q^52 - 30 * q^56 + 24 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^61 - 6 * q^62 + 3 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 42 * q^68 + 12 * q^71 + 6 * q^72 - 42 * q^73 + 12 * q^74 - 48 * q^76 + 48 * q^77 - 12 * q^78 - 6 * q^79 - 3 * q^81 - 18 * q^82 + 36 * q^83 + 12 * q^84 - 12 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 - 3 * q^91 - 96 * q^92 - 3 * q^93 - 36 * q^94 - 24 * q^96 + 15 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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