LMFDB - Embedded newform 975.2.i.l.601.2

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			601.2
Root			$0.500000 + 1.75780i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.l.451.2

$q$-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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

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

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	0.799668	−	0.600443i	$-0.205009\pi$
$2$	−0.169938	−	0.294342i	−0.120165	−	0.208131i	−0.919832	+	0.392311i	$0.871676\pi$
$3$	−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	−0.796884	−	0.604132i	$-0.793520\pi$
$7$	0.330062	−	0.571683i	0.124752	−	0.216076i	0.921636	+	0.388056i	$0.126853\pi$
$8$	−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	0.810228	−	0.586115i	$-0.199343\pi$
$11$	−0.339877	−	0.588684i	−0.102477	−	0.177495i	−0.912704	+	0.408620i	$0.866010\pi$
$12$	−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	0.0745938	−	0.997214i	$-0.476234\pi$
$17$	3.71455	−	6.43378i	0.900910	−	1.56042i	0.826316	−	0.563207i	$-0.190433\pi$
$18$	0.339877			0.0801098
$19$	−0.0577581	+	0.100040i	−0.0132506	+	0.0229508i	−0.872575	−	0.488481i	$-0.837551\pi$
$19$	−0.0577581	+	0.100040i	−0.0132506	+	0.0229508i	0.859324	+	0.511431i	$0.170885\pi$
$20$		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	−0.912883	−	0.408220i	$-0.866150\pi$
$23$	−3.88448	−	6.72812i	−0.809971	−	1.40291i	0.102913	−	0.994690i	$-0.467184\pi$
$24$	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	−0.999852	−	0.0171792i	$-0.994531\pi$
$29$	−2.77230	−	4.80177i	−0.514804	−	0.891666i	0.485049	−	0.874487i	$-0.338802\pi$
$30$		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	0.917630	+	0.397435i	$0.130100\pi$
$37$	4.88448	+	8.46017i	0.803004	+	1.39084i	−0.114626	+	0.993409i	$0.536567\pi$
$38$	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	0.652618	−	0.757687i	$-0.273671\pi$
$41$	−2.11218	−	3.65840i	−0.329867	−	0.571347i	−0.982485	+	0.186340i	$0.940337\pi$
$42$	0.112180	+	0.194302i	0.0173098	+	0.0299814i
$43$	−0.272303	+	0.471643i	−0.0415259	+	0.0719249i	−0.886041	−	0.463606i	$-0.846555\pi$
$43$	−0.272303	+	0.471643i	−0.0415259	+	0.0719249i	0.844515	+	0.535531i	$0.179889\pi$
$44$	−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	−0.929296	−	0.369336i	$-0.879585\pi$
$59$	−1.11218	+	1.92635i	−0.144794	+	0.250790i	0.784502	+	0.620126i	$0.212918\pi$
$60$		0			0
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	−0.699470	−	0.714662i	$-0.746581\pi$
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	0.968650	+	0.248428i	$0.0799139\pi$
$62$	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	0.532950	−	0.846147i	$-0.321083\pi$
$67$	−3.81691	−	6.61108i	−0.466310	−	0.807672i	−0.999260	+	0.0384746i	$0.987750\pi$
$68$	−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	−0.997212	−	0.0746227i	$-0.976225\pi$
$71$	−3.65679	+	6.33374i	−0.433981	+	0.751677i	0.563231	+	0.826299i	$0.309558\pi$
$72$	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	−0.961845	−	0.273595i	$-0.911787\pi$
$89$	−6.77230	−	11.7300i	−0.717863	−	1.24337i	0.243982	−	0.969780i	$-0.421546\pi$
$90$		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	−0.497190	−	0.867642i	$-0.665635\pi$
$97$	4.95206	−	8.57721i	0.502805	−	0.870884i	0.999995	−	0.00324223i	$-0.00103204\pi$
$98$	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	0.999231	−	0.0392165i	$-0.0124862\pi$
$101$	4.67975	+	8.10557i	0.465653	+	0.806534i	−0.533578	+	0.845751i	$0.679153\pi$
$102$	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	0.879494	−	0.475911i	$-0.157881\pi$
$107$	0.285455	+	0.494422i	0.0275960	+	0.0477976i	−0.851898	+	0.523708i	$0.824548\pi$
$108$	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	−0.963593	−	0.267374i	$-0.913844\pi$
$113$	−2.66012	+	4.60747i	−0.250243	+	0.433434i	0.713349	+	0.700809i	$0.247177\pi$
$114$	−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	−0.999244	−	0.0388704i	$-0.987624\pi$
$127$	−6.00982	−	10.4093i	−0.533285	−	0.923676i	0.465959	−	0.884806i	$-0.345709\pi$
$128$	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	−0.784494	−	0.620136i	$-0.787077\pi$
$137$	1.69491	−	2.93568i	0.144806	−	0.250812i	0.929301	+	0.369324i	$0.120411\pi$
$138$	2.64049			0.224774
$139$	−7.40411	+	12.8243i	−0.628009	+	1.08774i	0.359942	+	0.932975i	$0.382796\pi$
$139$	−7.40411	+	12.8243i	−0.628009	+	1.08774i	−0.987951	+	0.154768i	$0.950537\pi$
$140$		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	−0.268464	−	0.963290i	$-0.586516\pi$
$149$	8.54461	−	14.7997i	0.700001	−	1.21244i	0.968465	−	0.249148i	$-0.0801507\pi$
$150$		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	−0.521961	−	0.852969i	$-0.674799\pi$
$163$	6.09903	−	10.5638i	0.477713	−	0.827423i	0.999674	+	0.0255466i	$0.00813262\pi$
$164$	−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	0.833614	−	0.552347i	$-0.186268\pi$
$167$	−0.795270	−	1.37745i	−0.0615398	−	0.106590i	−0.895154	+	0.445757i	$0.852934\pi$
$168$	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	−0.515188	−	0.857077i	$-0.672278\pi$
$173$	6.37467	−	11.0412i	0.484657	−	0.839451i	0.999845	+	0.0176268i	$0.00561108\pi$
$174$	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	−0.979607	−	0.200923i	$-0.935606\pi$
$179$	−8.88115	−	15.3826i	−0.663808	−	1.14975i	0.315799	−	0.948826i	$-0.397728\pi$
$180$		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	−0.495144	−	0.868811i	$-0.664885\pi$
$191$	6.97703	−	12.0846i	0.504840	−	0.874409i	0.999984	−	0.00559828i	$-0.00178200\pi$
$192$	2.67975	+	4.64147i	0.193395	+	0.334969i
$193$	11.8747	+	20.5675i	0.854757	+	1.48048i	0.876870	+	0.480728i	$0.159627\pi$
$193$	11.8747	+	20.5675i	0.854757	+	1.48048i	−0.0221126	+	0.999755i	$0.507039\pi$
$194$	−3.36618			−0.241678
$195$		0			0
$196$	12.3702			0.883586
$197$	7.90411	+	13.6903i	0.563145	+	0.975395i	0.997220	+	0.0745186i	$0.0237420\pi$
$197$	7.90411	+	13.6903i	0.563145	+	0.975395i	−0.434075	+	0.900877i	$0.642925\pi$
$198$	−0.115516	−	0.200080i	−0.00820939	−	0.0142191i
$199$	−4.38448	+	7.59415i	−0.310808	+	0.538335i	−0.978537	−	0.206069i	$-0.933933\pi$
$199$	−4.38448	+	7.59415i	−0.310808	+	0.538335i	0.667730	+	0.744404i	$0.267266\pi$
$200$		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	0.673665	−	0.739037i	$-0.264719\pi$
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	−0.976857	+	0.213893i	$0.931386\pi$
$212$	−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	0.983703	−	0.179801i	$-0.0575454\pi$
$223$	5.01963	+	8.69426i	0.336139	+	0.582210i	−0.647564	+	0.762011i	$0.724212\pi$
$224$	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	−0.845224	−	0.534412i	$-0.820533\pi$
$227$	0.605701	−	1.04910i	0.0402018	−	0.0696315i	0.885426	+	0.464780i	$0.153867\pi$
$228$	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	−0.947544	−	0.319626i	$-0.896443\pi$
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	0.750576	+	0.660784i	$0.229776\pi$
$242$	−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	−0.914157	−	0.405361i	$-0.867146\pi$
$251$	−1.67975	+	2.90942i	−0.106025	+	0.183641i	0.808131	+	0.589002i	$0.200479\pi$
$252$	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	0.664212	−	0.747544i	$-0.268767\pi$
$257$	−5.05442	−	8.75452i	−0.315286	−	0.546092i	−0.979498	+	0.201452i	$0.935434\pi$
$258$	−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	−0.970426	−	0.241397i	$-0.922394\pi$
$263$	−11.2592	−	19.5014i	−0.694269	−	1.20251i	0.276157	−	0.961112i	$-0.410939\pi$
$264$	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	−0.965965	−	0.258674i	$-0.916714\pi$
$269$	−4.24733	+	7.35659i	−0.258964	+	0.448539i	0.707001	+	0.707213i	$0.250048\pi$
$270$		0			0
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	0.687912	−	0.725794i	$-0.258527\pi$
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	−0.972512	+	0.232853i	$0.925194\pi$
$272$	−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	−0.855023	−	0.518590i	$-0.826457\pi$
$277$	0.359508	−	0.622685i	0.0216007	−	0.0374135i	0.876624	+	0.481177i	$0.159790\pi$
$278$	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	−0.998983	−	0.0450980i	$-0.985640\pi$
$283$	−9.05977	−	15.6920i	−0.538547	−	0.932791i	0.460435	−	0.887693i	$-0.347693\pi$
$284$	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	−0.0524523	+	0.998623i	$0.516704\pi$
$293$	−15.2525	+	26.4181i	−0.891059	+	1.54336i	−0.838607	+	0.544737i	$0.816630\pi$
$294$	−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	−0.930335	−	0.366711i	$-0.880484\pi$
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	0.782749	+	0.622338i	$0.213817\pi$
$332$	−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	−0.391505	−	0.920176i	$-0.628045\pi$
$347$	11.1981	−	19.3956i	0.601143	−	1.04121i	0.992648	−	0.121035i	$-0.0386212\pi$
$348$	5.22436	+	9.04886i	0.280055	+	0.485070i
$349$	5.98685	+	10.3695i	0.320469	+	0.555068i	0.980585	−	0.196096i	$-0.0628263\pi$
$349$	5.98685	+	10.3695i	0.320469	+	0.555068i	−0.660116	+	0.751164i	$0.729493\pi$
$350$		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	0.545210	−	0.838299i	$-0.316450\pi$
$353$	−8.51830	−	14.7541i	−0.453384	−	0.785283i	−0.998594	+	0.0530161i	$0.983117\pi$
$354$	−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	0.999605	+	0.0281143i	$0.00895024\pi$
$367$	10.0413	+	17.3920i	0.524150	+	0.907855i	−0.475455	+	0.879740i	$0.657716\pi$
$368$	−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	0.383745	+	0.923439i	$0.374634\pi$
$373$	−11.7395	+	20.3334i	−0.607849	+	1.05283i	−0.991594	+	0.129387i	$0.958699\pi$
$374$	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	−0.998731	−	0.0503631i	$-0.983962\pi$
$379$	−10.5707	−	18.3090i	−0.542981	−	0.940471i	0.455750	−	0.890108i	$-0.349371\pi$
$380$		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	−0.842960	−	0.537976i	$-0.819189\pi$
$383$	0.869323	−	1.50571i	0.0444203	−	0.0769383i	0.887381	+	0.461037i	$0.152523\pi$
$384$	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	−0.623788	−	0.781594i	$-0.714407\pi$
$397$	7.27230	−	12.5960i	0.364986	−	0.632175i	0.988774	+	0.149419i	$0.0477403\pi$
$398$	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	0.951398	−	0.307964i	$-0.0996478\pi$
$401$	4.18510	+	7.24880i	0.208994	+	0.361988i	−0.742404	+	0.669952i	$0.766314\pi$
$402$	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	−0.996568	−	0.0827798i	$-0.973620\pi$
$409$	−8.62734	+	14.9430i	−0.426595	+	0.738883i	0.569973	+	0.821663i	$0.306954\pi$
$410$		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	0.665032	−	0.746815i	$-0.268418\pi$
$419$	−6.43243	−	11.1413i	−0.314245	−	0.544288i	−0.979277	+	0.202527i	$0.935085\pi$
$420$		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	−0.993291	−	0.115645i	$-0.963106\pi$
$431$	−12.3898	−	21.4598i	−0.596797	−	1.03368i	0.396493	−	0.918038i	$-0.370227\pi$
$432$	−1.66012	−	2.87542i	−0.0798727	−	0.138344i
$433$	−7.02945	+	12.1754i	−0.337814	+	0.585110i	−0.984021	−	0.178051i	$-0.943021\pi$
$433$	−7.02945	+	12.1754i	−0.337814	+	0.585110i	0.646208	+	0.763162i	$0.276354\pi$
$434$	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	0.502552	−	0.864547i	$-0.332395\pi$
$439$	−10.4226	−	18.0525i	−0.497444	−	0.861598i	−0.999996	+	0.00294880i	$0.999061\pi$
$440$		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	0.379675	+	0.925120i	$0.376036\pi$
$449$	−12.9541	+	22.4371i	−0.611340	+	1.05887i	−0.991015	+	0.133752i	$0.957297\pi$
$450$		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	0.926774	−	0.375619i	$-0.122570\pi$
$457$	2.95206	+	5.11311i	0.138091	+	0.239181i	−0.788683	+	0.614800i	$0.789237\pi$
$458$	−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	−0.627320	−	0.778762i	$-0.715848\pi$
$461$	7.74600	−	13.4165i	0.360767	−	0.624867i	0.988087	+	0.153894i	$0.0491815\pi$
$462$	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	0.772017	+	0.635602i	$0.219248\pi$
$479$	20.4953	+	35.4990i	0.936456	+	1.62199i	0.164439	+	0.986387i	$0.447419\pi$
$480$		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	−0.453397	−	0.891309i	$-0.649788\pi$
$487$	12.0315	−	20.8391i	0.545197	−	0.944309i	0.998594	−	0.0530008i	$-0.0168786\pi$
$488$	−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	−0.898218	−	0.439550i	$-0.855138\pi$
$491$	−18.3865	−	31.8463i	−0.829771	−	1.43721i	0.0684471	−	0.997655i	$-0.478196\pi$
$492$	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	0.249368	+	0.968409i	$0.419777\pi$
$503$	−16.0130	+	27.7353i	−0.713983	+	1.23665i	−0.963351	+	0.268245i	$0.913556\pi$
$504$	−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	0.804960	+	0.593329i	$0.202187\pi$
$509$	20.6731	+	35.8068i	0.916318	+	1.58711i	0.111359	+	0.993780i	$0.464480\pi$
$510$		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	−0.965064	−	0.262013i	$-0.915614\pi$
$523$	−16.2244	−	28.1014i	−0.709442	−	1.22879i	0.255623	−	0.966777i	$-0.417720\pi$
$524$	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	−0.858701	−	0.512477i	$-0.828728\pi$
$557$	−20.6075	−	35.6933i	−0.873169	−	1.51237i	−0.0144676	−	0.999895i	$-0.504605\pi$
$558$	−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	−0.965337	−	0.261007i	$-0.915945\pi$
$563$	−6.08921	+	10.5468i	−0.256630	+	0.444496i	0.708707	+	0.705503i	$0.249279\pi$
$564$	−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	0.784034	−	0.620718i	$-0.213159\pi$
$569$	−3.47169	−	6.01314i	−0.145541	−	0.252084i	−0.929575	+	0.368634i	$0.879826\pi$
$570$		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	0.929741	+	0.368215i	$0.120031\pi$
$587$	18.9889	+	32.8897i	0.783754	+	1.35750i	−0.145987	+	0.989287i	$0.546636\pi$
$588$	−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	0.976472	−	0.215643i	$-0.0691848\pi$
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	−0.674989	+	0.737828i	$0.735851\pi$
$602$	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	−0.991667	−	0.128831i	$-0.958878\pi$
$607$	−9.46722	+	16.3977i	−0.384263	+	0.665562i	0.607404	+	0.794393i	$0.292211\pi$
$608$	−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	0.838755	−	0.544509i	$-0.183284\pi$
$613$	−1.29193	−	2.23770i	−0.0521807	−	0.0903797i	−0.890936	+	0.454129i	$0.849951\pi$
$614$	−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	−0.689425	−	0.724357i	$-0.742137\pi$
$617$	7.01963	−	12.1584i	0.282600	−	0.489477i	0.972024	+	0.234880i	$0.0754699\pi$
$618$	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	−0.503113	−	0.864221i	$-0.667812\pi$
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	0.999994	+	0.00359801i	$0.00114528\pi$
$632$	−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	−0.998975	−	0.0452686i	$-0.985586\pi$
$641$	−11.6535	+	20.1844i	−0.460284	+	0.797235i	0.538691	+	0.842503i	$0.318919\pi$
$642$	−0.194039			−0.00765811
$643$	22.7395	−	39.3860i	0.896759	−	1.55323i	0.0651470	−	0.997876i	$-0.479248\pi$
$643$	22.7395	−	39.3860i	0.896759	−	1.55323i	0.831612	−	0.555357i	$-0.187418\pi$
$644$	−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	0.922120	−	0.386904i	$-0.126456\pi$
$647$	3.20473	+	5.55076i	0.125991	+	0.218223i	−0.796129	+	0.605127i	$0.793122\pi$
$648$	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	0.880157	−	0.474682i	$-0.157437\pi$
$653$	0.740848	+	1.28319i	0.0289916	+	0.0502150i	−0.851166	+	0.524897i	$0.824104\pi$
$654$	−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	−0.788691	−	0.614790i	$-0.789241\pi$
$659$	3.54461	−	6.13944i	0.138078	−	0.239159i	0.926769	+	0.375631i	$0.122574\pi$
$660$		0			0
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	0.854339	−	0.519716i	$-0.173962\pi$
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	−0.877257	+	0.480021i	$0.840629\pi$
$662$	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	0.966588	−	0.256334i	$-0.0825145\pi$
$673$	6.77878	+	11.7412i	0.261303	+	0.452590i	−0.705286	+	0.708923i	$0.749181\pi$
$674$	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	0.0279296	+	0.999610i	$0.491109\pi$
$683$	−22.2592	+	38.5540i	−0.851723	+	1.47523i	−0.879652	+	0.475617i	$0.842225\pi$
$684$	−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	0.911867	−	0.410486i	$-0.134641\pi$
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	−0.811425	+	0.584457i	$0.801308\pi$
$692$	−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	−0.880127	−	0.474737i	$-0.842543\pi$
$709$	−0.770294	+	1.33419i	−0.0289290	+	0.0501065i	0.851198	+	0.524844i	$0.175876\pi$
$710$		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	0.281826	+	0.959466i	$0.409060\pi$
$719$	−18.5020	+	32.0464i	−0.690009	+	1.19513i	−0.971835	+	0.235664i	$0.924273\pi$
$720$		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	0.805127	−	0.593103i	$-0.202097\pi$
$739$	−3.01963	−	5.23015i	−0.111079	−	0.192394i	−0.916206	+	0.400709i	$0.868764\pi$
$740$		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	0.721041	−	0.692893i	$-0.243664\pi$
$743$	−6.52945	−	11.3093i	−0.239542	−	0.414899i	−0.960583	+	0.277993i	$0.910331\pi$
$744$	−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	−0.855475	−	0.517845i	$-0.826735\pi$
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.0207292	−	0.999785i	$-0.506599\pi$
$752$	−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	0.821569	−	0.570110i	$-0.193099\pi$
$757$	−2.28212	−	3.95275i	−0.0829450	−	0.143665i	−0.904514	+	0.426445i	$0.859766\pi$
$758$	−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	−0.991382	−	0.131000i	$-0.958181\pi$
$761$	−10.5446	+	18.2638i	−0.382242	+	0.662062i	0.609141	+	0.793062i	$0.291514\pi$
$762$	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	−0.941147	−	0.337996i	$-0.890251\pi$
$769$	−21.1666	−	36.6616i	−0.763287	−	1.32205i	0.177860	−	0.984056i	$-0.443083\pi$
$770$		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	0.0807410	−	0.996735i	$-0.474271\pi$
$773$	25.1218	−	43.5122i	0.903568	−	1.56503i	0.822827	−	0.568291i	$-0.192395\pi$
$774$	−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	−0.944783	−	0.327698i	$-0.893727\pi$
$787$	−5.29080	+	9.16393i	−0.188597	+	0.326659i	0.756186	+	0.654357i	$0.227061\pi$
$788$	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	−0.987431	−	0.158049i	$-0.949480\pi$
$797$	−10.0741	+	17.4488i	−0.356841	+	0.618067i	0.630590	+	0.776116i	$0.282813\pi$
$798$	−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	0.729946	−	0.683505i	$-0.239545\pi$
$809$	−6.45539	−	11.1811i	−0.226960	−	0.393105i	−0.956906	+	0.290399i	$0.906212\pi$
$810$		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	0.983209	+	0.182483i	$0.0584136\pi$
$821$	18.6142	+	32.2407i	0.649640	+	1.12521i	−0.333569	+	0.942726i	$0.608253\pi$
$822$	0.576062	+	0.997769i	0.0200925	+	0.0348012i
$823$	−2.44872	+	4.24131i	−0.0853571	+	0.147843i	−0.905543	−	0.424254i	$-0.860536\pi$
$823$	−2.44872	+	4.24131i	−0.0853571	+	0.147843i	0.820186	+	0.572097i	$0.193870\pi$
$824$	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	0.881777	+	0.471667i	$0.156348\pi$
$829$	24.4552	+	42.3576i	0.849364	+	1.47114i	−0.0324123	+	0.999475i	$0.510319\pi$
$830$		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	0.0619688	+	0.998078i	$0.480262\pi$
$839$	−24.1392	+	41.8103i	−0.833377	+	1.44345i	−0.895345	+	0.445372i	$0.853071\pi$
$840$		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	−0.904119	−	0.427280i	$-0.859472\pi$
$877$	−2.42909	+	4.20731i	−0.0820246	+	0.142071i	0.822095	+	0.569351i	$0.192805\pi$
$878$	−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	0.992823	−	0.119595i	$-0.0381595\pi$
$881$	11.6601	+	20.1959i	0.392840	+	0.680418i	−0.599983	+	0.800013i	$0.704826\pi$
$882$	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	0.999750	+	0.0223448i	$0.00711317\pi$
$887$	15.4639	+	26.7842i	0.519226	+	0.899326i	−0.480524	+	0.876982i	$0.659553\pi$
$888$	−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	0.690194	−	0.723624i	$-0.257525\pi$
$907$	−8.48018	−	14.6881i	−0.281580	−	0.487710i	−0.971774	+	0.235914i	$0.924192\pi$
$908$	−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	0.317552	+	0.948241i	$0.397139\pi$
$919$	−20.0814	+	34.7820i	−0.662425	+	1.14735i	−0.979977	+	0.199112i	$0.936194\pi$
$920$		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	−0.992438	−	0.122747i	$-0.960830\pi$
$929$	−11.8845	+	20.5845i	−0.389917	+	0.675357i	0.602521	+	0.798103i	$0.294163\pi$
$930$		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	0.956655	−	0.291222i	$-0.0940618\pi$
$947$	6.95854	+	12.0525i	0.226122	+	0.391655i	−0.730533	+	0.682877i	$0.760729\pi$
$948$	−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	−0.939162	−	0.343474i	$-0.888396\pi$
$953$	−5.31357	+	9.20338i	−0.172124	+	0.298127i	0.767039	+	0.641601i	$0.221729\pi$
$954$	−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	−0.284058	−	0.958807i	$-0.591681\pi$
$971$	21.4487	−	37.1503i	0.688322	−	1.19221i	0.972380	−	0.233402i	$-0.0749858\pi$
$972$	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	0.973946	−	0.226780i	$-0.0728197\pi$
$977$	9.08254	+	15.7314i	0.290576	+	0.503293i	−0.683370	+	0.730072i	$0.739486\pi$
$978$	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	0.987177	−	0.159633i	$-0.0510309\pi$
$991$	11.1862	+	19.3751i	0.355342	+	0.615471i	−0.631834	+	0.775104i	$0.717698\pi$
$992$	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	−0.991602	−	0.129326i	$-0.958719\pi$
$997$	−12.1187	+	20.9901i	−0.383802	+	0.664764i	0.607800	+	0.794090i	$0.292052\pi$
$998$	−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.601.2		6
5.2	odd	4		975.2.bb.k.874.4		12
5.3	odd	4		975.2.bb.k.874.3		12
5.4	even	2		195.2.i.d.16.2	✓	6
13.9	even	3	inner	975.2.i.l.451.2		6
15.14	odd	2		585.2.j.f.406.2		6
65.9	even	6		195.2.i.d.61.2	yes	6
65.22	odd	12		975.2.bb.k.724.3		12
65.29	even	6		2535.2.a.bb.1.2		3
65.48	odd	12		975.2.bb.k.724.4		12
65.49	even	6		2535.2.a.ba.1.2		3
195.29	odd	6		7605.2.a.bv.1.2		3
195.74	odd	6		585.2.j.f.451.2		6
195.179	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	5.4	even	2
195.2.i.d.61.2	yes	6	65.9	even	6
585.2.j.f.406.2		6	15.14	odd	2
585.2.j.f.451.2		6	195.74	odd	6
975.2.i.l.451.2		6	13.9	even	3	inner
975.2.i.l.601.2		6	1.1	even	1	trivial
975.2.bb.k.724.3		12	65.22	odd	12
975.2.bb.k.724.4		12	65.48	odd	12
975.2.bb.k.874.3		12	5.3	odd	4
975.2.bb.k.874.4		12	5.2	odd	4
2535.2.a.ba.1.2		3	65.49	even	6
2535.2.a.bb.1.2		3	65.29	even	6
7605.2.a.bv.1.2		3	195.29	odd	6
7605.2.a.bw.1.2		3	195.179	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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