LMFDB - Embedded newform 325.2.n.f.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("325.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 $ x^10 + 16x^8 + 84x^6 + 163x^4 + 118x^2 + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$0.887996i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.f.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.769027 + 0.443998i) q^{2} +(1.53097 + 2.65171i) q^{3} +(-0.605732 + 1.04916i) q^{4} +(-2.35471 - 1.35949i) q^{6} +(3.08568 + 1.78152i) q^{7} -2.85177i q^{8} +(-3.18771 + 5.52128i) q^{9} +O(q^{10})$	\(q+(-0.769027 + 0.443998i) q^{2} +(1.53097 + 2.65171i) q^{3} +(-0.605732 + 1.04916i) q^{4} +(-2.35471 - 1.35949i) q^{6} +(3.08568 + 1.78152i) q^{7} -2.85177i q^{8} +(-3.18771 + 5.52128i) q^{9} +(0.816654 - 0.471496i) q^{11} -3.70942 q^{12} +(3.56247 + 0.555692i) q^{13} -3.16396 q^{14} +(0.0547156 + 0.0947702i) q^{16} +(0.479950 - 0.831298i) q^{17} -5.66135i q^{18} +(-2.89222 - 1.66983i) q^{19} +10.9098i q^{21} +(-0.418686 + 0.725186i) q^{22} +(-3.29999 - 5.71576i) q^{23} +(7.56206 - 4.36596i) q^{24} +(-2.98636 + 1.15439i) q^{26} -10.3353 q^{27} +(-3.73819 + 2.15824i) q^{28} +(-4.19863 - 7.27224i) q^{29} -4.13976i q^{31} +(4.85525 + 2.80318i) q^{32} +(2.50054 + 1.44369i) q^{33} +0.852387i q^{34} +(-3.86180 - 6.68883i) q^{36} +(6.90720 - 3.98787i) q^{37} +2.96560 q^{38} +(3.98049 + 10.2974i) q^{39} +(0.690562 - 0.398696i) q^{41} +(-4.84392 - 8.38992i) q^{42} +(-4.50437 + 7.80179i) q^{43} +1.14240i q^{44} +(5.07557 + 2.93038i) q^{46} +10.5985i q^{47} +(-0.167535 + 0.290180i) q^{48} +(2.84762 + 4.93222i) q^{49} +2.93915 q^{51} +(-2.74091 + 3.40100i) q^{52} +7.44476 q^{53} +(7.94815 - 4.58886i) q^{54} +(5.08048 - 8.79964i) q^{56} -10.2258i q^{57} +(6.45772 + 3.72837i) q^{58} +(0.869141 + 0.501799i) q^{59} +(-2.26328 + 3.92012i) q^{61} +(1.83805 + 3.18359i) q^{62} +(-19.6725 + 11.3579i) q^{63} -5.19729 q^{64} -2.56398 q^{66} +(0.969702 - 0.559858i) q^{67} +(0.581442 + 1.00709i) q^{68} +(10.1044 - 17.5013i) q^{69} +(-1.60542 - 0.926890i) q^{71} +(15.7454 + 9.09061i) q^{72} +4.69721i q^{73} +(-3.54121 + 6.13356i) q^{74} +(3.50382 - 2.02293i) q^{76} +3.35991 q^{77} +(-7.63313 - 6.15164i) q^{78} +5.64117 q^{79} +(-6.25989 - 10.8425i) q^{81} +(-0.354041 + 0.613216i) q^{82} -0.187778i q^{83} +(-11.4461 - 6.60840i) q^{84} -7.99972i q^{86} +(12.8559 - 22.2671i) q^{87} +(-1.34460 - 2.32891i) q^{88} +(8.21609 - 4.74356i) q^{89} +(10.0027 + 8.06130i) q^{91} +7.99564 q^{92} +(10.9775 - 6.33784i) q^{93} +(-4.70572 - 8.15054i) q^{94} +17.1663i q^{96} +(-14.3274 - 8.27193i) q^{97} +(-4.37979 - 2.52868i) q^{98} +6.01197i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} + 6 q^{4} + 9 q^{6} + 6 q^{7} - 8 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 + 6 * q^4 + 9 * q^6 + 6 * q^7 - 8 * q^9	$ 10 q + 3 q^{3} + 6 q^{4} + 9 q^{6} + 6 q^{7} - 8 q^{9} - 9 q^{11} + 28 q^{12} - 8 q^{13} - 8 q^{14} - 12 q^{16} - 8 q^{17} + 12 q^{22} - 13 q^{23} + 42 q^{24} - 17 q^{26} - 30 q^{27} - 33 q^{28} + 7 q^{29} - 3 q^{32} + 6 q^{33} - 3 q^{36} - 3 q^{37} + 62 q^{38} + 8 q^{39} + 12 q^{41} - 32 q^{42} - 4 q^{43} + 39 q^{46} + 26 q^{48} - q^{49} + 16 q^{51} - 61 q^{52} - 24 q^{53} - 9 q^{54} - 21 q^{56} - 18 q^{58} - 48 q^{59} + 13 q^{61} - 17 q^{62} - 34 q^{64} - 42 q^{66} - 6 q^{67} + 13 q^{68} + 20 q^{69} - 27 q^{71} + 141 q^{72} - 26 q^{74} - 12 q^{76} + 48 q^{77} - 56 q^{78} + 4 q^{79} - 17 q^{81} + q^{82} - 90 q^{84} + 49 q^{87} + 6 q^{88} + 24 q^{89} + 13 q^{91} - 34 q^{92} + 63 q^{93} + 5 q^{94} + 15 q^{97} + 45 q^{98}+O(q^{100}) $ 10 * q + 3 * q^3 + 6 * q^4 + 9 * q^6 + 6 * q^7 - 8 * q^9 - 9 * q^11 + 28 * q^12 - 8 * q^13 - 8 * q^14 - 12 * q^16 - 8 * q^17 + 12 * q^22 - 13 * q^23 + 42 * q^24 - 17 * q^26 - 30 * q^27 - 33 * q^28 + 7 * q^29 - 3 * q^32 + 6 * q^33 - 3 * q^36 - 3 * q^37 + 62 * q^38 + 8 * q^39 + 12 * q^41 - 32 * q^42 - 4 * q^43 + 39 * q^46 + 26 * q^48 - q^49 + 16 * q^51 - 61 * q^52 - 24 * q^53 - 9 * q^54 - 21 * q^56 - 18 * q^58 - 48 * q^59 + 13 * q^61 - 17 * q^62 - 34 * q^64 - 42 * q^66 - 6 * q^67 + 13 * q^68 + 20 * q^69 - 27 * q^71 + 141 * q^72 - 26 * q^74 - 12 * q^76 + 48 * q^77 - 56 * q^78 + 4 * q^79 - 17 * q^81 + q^82 - 90 * q^84 + 49 * q^87 + 6 * q^88 + 24 * q^89 + 13 * q^91 - 34 * q^92 + 63 * q^93 + 5 * q^94 + 15 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.769027	+	0.443998i	−0.543784	+	0.313954i	−0.746611	−	0.665261i	$-0.768320\pi$
$2$	−0.769027	+	0.443998i	−0.543784	+	0.313954i	0.202827	+	0.979215i	$0.434987\pi$
$3$	1.53097	+	2.65171i	0.883904	+	1.53097i	0.846965	+	0.531648i	$0.178427\pi$
$3$	1.53097	+	2.65171i	0.883904	+	1.53097i	0.0369384	+	0.999318i	$0.488239\pi$
$4$	−0.605732	+	1.04916i	−0.302866	+	0.524579i
$5$		0			0
$5$		0			0
$6$	−2.35471	−	1.35949i	−0.961306	−	0.555010i
$7$	3.08568	+	1.78152i	1.16628	+	0.673351i	0.952801	−	0.303597i	$-0.0981877\pi$
$7$	3.08568	+	1.78152i	1.16628	+	0.673351i	0.213477	+	0.976948i	$0.431521\pi$
$8$		−	2.85177i		−	1.00825i
$9$	−3.18771	+	5.52128i	−1.06257	+	1.84043i
$10$		0			0
$11$	0.816654	−	0.471496i	0.246231	−	0.142161i	−0.371806	−	0.928310i	$-0.621262\pi$
$11$	0.816654	−	0.471496i	0.246231	−	0.142161i	0.618037	+	0.786149i	$0.287928\pi$
$12$	−3.70942			−1.07082
$13$	3.56247	+	0.555692i	0.988052	+	0.154121i
$13$	3.56247	+	0.555692i	0.988052	+	0.154121i
$14$	−3.16396			−0.845605
$15$		0			0
$16$	0.0547156	+	0.0947702i	0.0136789	+	0.0236925i
$17$	0.479950	−	0.831298i	0.116405	−	0.201619i	−0.801936	−	0.597411i	$-0.796196\pi$
$17$	0.479950	−	0.831298i	0.116405	−	0.201619i	0.918341	+	0.395791i	$0.129530\pi$
$18$		−	5.66135i		−	1.33439i
$19$	−2.89222	−	1.66983i	−0.663521	−	0.383084i	0.130096	−	0.991501i	$-0.458471\pi$
$19$	−2.89222	−	1.66983i	−0.663521	−	0.383084i	−0.793617	+	0.608417i	$0.791805\pi$
$20$		0			0
$21$			10.9098i			2.38071i
$22$	−0.418686	+	0.725186i	−0.0892642	+	0.154610i
$23$	−3.29999	−	5.71576i	−0.688096	−	1.19182i	−0.972453	−	0.233099i	$-0.925113\pi$
$23$	−3.29999	−	5.71576i	−0.688096	−	1.19182i	0.284357	−	0.958718i	$-0.408220\pi$
$24$	7.56206	−	4.36596i	1.54360	−	0.891197i
$25$		0			0
$26$	−2.98636	+	1.15439i	−0.585674	+	0.226394i
$27$	−10.3353			−1.98903
$28$	−3.73819	+	2.15824i	−0.706451	+	0.407870i
$29$	−4.19863	−	7.27224i	−0.779666	−	1.35042i	−0.932134	−	0.362113i	$-0.882056\pi$
$29$	−4.19863	−	7.27224i	−0.779666	−	1.35042i	0.152468	−	0.988308i	$-0.451278\pi$
$30$		0			0
$31$		−	4.13976i		−	0.743524i	−0.928328	−	0.371762i	$-0.878754\pi$
$31$		−	4.13976i		−	0.743524i	0.928328	−	0.371762i	$-0.121246\pi$
$32$	4.85525	+	2.80318i	0.858295	+	0.495537i
$33$	2.50054	+	1.44369i	0.435288	+	0.251314i
$34$			0.852387i			0.146183i
$35$		0			0
$36$	−3.86180	−	6.68883i	−0.643633	−	1.11480i
$37$	6.90720	−	3.98787i	1.13554	−	0.655602i	0.190215	−	0.981743i	$-0.439082\pi$
$37$	6.90720	−	3.98787i	1.13554	−	0.655602i	0.945321	+	0.326141i	$0.105748\pi$
$38$	2.96560			0.481083
$39$	3.98049	+	10.2974i	0.637389	+	1.64890i
$40$		0			0
$41$	0.690562	−	0.398696i	0.107848	−	0.0622659i	−0.445106	−	0.895478i	$-0.646834\pi$
$41$	0.690562	−	0.398696i	0.107848	−	0.0622659i	0.552954	+	0.833212i	$0.313501\pi$
$42$	−4.84392	−	8.38992i	−0.747433	−	1.29459i
$43$	−4.50437	+	7.80179i	−0.686910	+	1.18976i	0.285923	+	0.958253i	$0.407700\pi$
$43$	−4.50437	+	7.80179i	−0.686910	+	1.18976i	−0.972833	+	0.231510i	$0.925633\pi$
$44$			1.14240i			0.172223i
$45$		0			0
$46$	5.07557	+	2.93038i	0.748352	+	0.432061i
$47$			10.5985i			1.54595i	0.634435	+	0.772976i	$0.281233\pi$
$47$			10.5985i			1.54595i	−0.634435	+	0.772976i	$0.718767\pi$
$48$	−0.167535	+	0.290180i	−0.0241817	+	0.0418839i
$49$	2.84762	+	4.93222i	0.406803	+	0.704603i
$50$		0			0
$51$	2.93915			0.411563
$52$	−2.74091	+	3.40100i	−0.380096	+	0.471633i
$53$	7.44476			1.02262			0.511308	−	0.859397i	$-0.329161\pi$
$53$	7.44476			1.02262			0.511308	+	0.859397i	$0.329161\pi$
$54$	7.94815	−	4.58886i	1.08161	−	0.624465i
$55$		0			0
$56$	5.08048	−	8.79964i	0.678907	−	1.17590i
$57$		−	10.2258i		−	1.35444i
$58$	6.45772	+	3.72837i	0.847940	+	0.489558i
$59$	0.869141	+	0.501799i	0.113153	+	0.0653287i	0.555508	−	0.831511i	$-0.312524\pi$
$59$	0.869141	+	0.501799i	0.113153	+	0.0653287i	−0.442356	+	0.896840i	$0.645857\pi$
$60$		0			0
$61$	−2.26328	+	3.92012i	−0.289784	+	0.501920i	−0.973758	−	0.227586i	$-0.926917\pi$
$61$	−2.26328	+	3.92012i	−0.289784	+	0.501920i	0.683974	+	0.729506i	$0.260250\pi$
$62$	1.83805	+	3.18359i	0.233432	+	0.404317i
$63$	−19.6725	+	11.3579i	−2.47851	+	1.43097i
$64$	−5.19729			−0.649661
$65$		0			0
$66$	−2.56398			−0.315604
$67$	0.969702	−	0.559858i	0.118468	−	0.0683975i	−0.439595	−	0.898196i	$-0.644878\pi$
$67$	0.969702	−	0.559858i	0.118468	−	0.0683975i	0.558063	+	0.829799i	$0.311545\pi$
$68$	0.581442	+	1.00709i	0.0705102	+	0.122127i
$69$	10.1044	−	17.5013i	1.21642	−	2.10690i
$70$		0			0
$71$	−1.60542	−	0.926890i	−0.190528	−	0.110002i	0.401702	−	0.915771i	$-0.368419\pi$
$71$	−1.60542	−	0.926890i	−0.190528	−	0.110002i	−0.592230	+	0.805769i	$0.701752\pi$
$72$	15.7454	+	9.09061i	1.85561	+	1.07134i
$73$			4.69721i			0.549767i	0.961478	+	0.274884i	$0.0886393\pi$
$73$			4.69721i			0.549767i	−0.961478	+	0.274884i	$0.911361\pi$
$74$	−3.54121	+	6.13356i	−0.411658	+	0.713012i
$75$		0			0
$76$	3.50382	−	2.02293i	0.401916	−	0.232046i
$77$	3.35991			0.382898
$78$	−7.63313	−	6.15164i	−0.864281	−	0.696536i
$79$	5.64117			0.634681			0.317340	−	0.948312i	$-0.397210\pi$
$79$	5.64117			0.634681			0.317340	+	0.948312i	$0.397210\pi$
$80$		0			0
$81$	−6.25989	−	10.8425i	−0.695544	−	1.20472i
$82$	−0.354041	+	0.613216i	−0.0390972	+	0.0677184i
$83$		−	0.187778i		−	0.0206114i	−0.999947	−	0.0103057i	$-0.996720\pi$
$83$		−	0.187778i		−	0.0206114i	0.999947	−	0.0103057i	$-0.00328046\pi$
$84$	−11.4461	−	6.60840i	−1.24887	−	0.721035i
$85$		0			0
$86$		−	7.99972i		−	0.862632i
$87$	12.8559	−	22.2671i	1.37830	−	2.38728i
$88$	−1.34460	−	2.32891i	−0.143334	−	0.248262i
$89$	8.21609	−	4.74356i	0.870904	−	0.502817i	0.00325556	−	0.999995i	$-0.498964\pi$
$89$	8.21609	−	4.74356i	0.870904	−	0.502817i	0.867649	+	0.497178i	$0.165630\pi$
$90$		0			0
$91$	10.0027	+	8.06130i	1.04857	+	0.845054i
$92$	7.99564			0.833603
$93$	10.9775	−	6.33784i	1.13831	−	0.657203i
$94$	−4.70572	−	8.15054i	−0.485358	−	0.840664i
$95$		0			0
$96$			17.1663i			1.75203i
$97$	−14.3274	−	8.27193i	−1.45473	−	0.839887i	−0.455983	−	0.889988i	$-0.650712\pi$
$97$	−14.3274	−	8.27193i	−1.45473	−	0.839887i	−0.998744	+	0.0501013i	$0.984046\pi$
$98$	−4.37979	−	2.52868i	−0.442426	−	0.255435i
$99$			6.01197i			0.604226i
$100$		0			0
$101$	−2.75291	−	4.76817i	−0.273924	−	0.474451i	0.695939	−	0.718101i	$-0.254988\pi$
$101$	−2.75291	−	4.76817i	−0.273924	−	0.474451i	−0.969863	+	0.243650i	$0.921655\pi$
$102$	−2.26028	+	1.30498i	−0.223802	+	0.129212i
$103$	−3.49795			−0.344664			−0.172332	−	0.985039i	$-0.555130\pi$
$103$	−3.49795			−0.344664			−0.172332	+	0.985039i	$0.555130\pi$
$104$	1.58470	−	10.1593i	0.155393	−	0.996205i
$105$		0			0
$106$	−5.72522	+	3.30546i	−0.556083	+	0.321054i
$107$	−2.87137	−	4.97336i	−0.277586	−	0.480793i	0.693198	−	0.720747i	$-0.256201\pi$
$107$	−2.87137	−	4.97336i	−0.277586	−	0.480793i	−0.970784	+	0.239954i	$0.922868\pi$
$108$	6.26043	−	10.8434i	0.602410	−	1.04341i
$109$			10.9903i			1.05268i	0.850275	+	0.526339i	$0.176436\pi$
$109$			10.9903i			1.05268i	−0.850275	+	0.526339i	$0.823564\pi$
$110$		0			0
$111$	21.1494	+	12.2106i	2.00741	+	1.15898i
$112$			0.389908i			0.0368428i
$113$	6.85841	−	11.8791i	0.645185	−	1.11749i	−0.339074	−	0.940760i	$-0.610114\pi$
$113$	6.85841	−	11.8791i	0.645185	−	1.11749i	0.984259	−	0.176733i	$-0.0565530\pi$
$114$	4.54023	+	7.86391i	0.425231	+	0.736522i
$115$		0			0
$116$	10.1730			0.944536
$117$	−14.4243	+	17.8980i	−1.33352	+	1.65467i
$118$	−0.891191			−0.0820408
$119$	2.96195	−	1.71008i	0.271521	−	0.156763i
$120$		0			0
$121$	−5.05538	+	8.75618i	−0.459580	+	0.796016i
$122$		−	4.01957i		−	0.363915i
$123$	2.11445	+	1.22078i	0.190654	+	0.110074i
$124$	4.34327	+	2.50759i	0.390037	+	0.225188i
$125$		0			0
$126$	10.0858	−	17.4691i	0.898515	−	1.55627i
$127$	1.75673	+	3.04275i	0.155885	+	0.270001i	0.933381	−	0.358887i	$-0.116844\pi$
$127$	1.75673	+	3.04275i	0.155885	+	0.270001i	−0.777496	+	0.628888i	$0.783510\pi$
$128$	−5.71364	+	3.29877i	−0.505019	+	0.291573i
$129$	−27.5841			−2.42865
$130$		0			0
$131$	−18.0781			−1.57949			−0.789744	−	0.613437i	$-0.789787\pi$
$131$	−18.0781			−1.57949			−0.789744	+	0.613437i	$0.789787\pi$
$132$	−3.02931	+	1.74897i	−0.263668	+	0.152229i
$133$	−5.94965	−	10.3051i	−0.515900	−	0.893565i
$134$	−0.497152	+	0.861092i	−0.0429474	+	0.0743870i
$135$		0			0
$136$	−2.37067	−	1.36871i	−0.203283	−	0.117366i
$137$	−0.675682	−	0.390105i	−0.0577274	−	0.0333290i	0.470858	−	0.882209i	$-0.343944\pi$
$137$	−0.675682	−	0.390105i	−0.0577274	−	0.0333290i	−0.528586	+	0.848880i	$0.677278\pi$
$138$			17.9453i			1.52760i
$139$	−0.139418	+	0.241479i	−0.0118253	+	0.0204820i	−0.871877	−	0.489724i	$-0.837098\pi$
$139$	−0.139418	+	0.241479i	−0.0118253	+	0.0204820i	0.860052	+	0.510206i	$0.170431\pi$
$140$		0			0
$141$	−28.1042	+	16.2260i	−2.36680	+	1.36647i
$142$	1.64615			0.138142
$143$	3.17131	−	1.22588i	0.265199	−	0.102513i
$144$	−0.697671			−0.0581392
$145$		0			0
$146$	−2.08555	−	3.61228i	−0.172602	−	0.298955i
$147$	−8.71922	+	15.1021i	−0.719149	+	1.24560i
$148$			9.66232i			0.794238i
$149$	−0.00883675	−	0.00510190i	−0.000723935	−	0.000417964i	0.499638	−	0.866234i	$-0.333466\pi$
$149$	−0.00883675	−	0.00510190i	−0.000723935	−	0.000417964i	−0.500362	+	0.865816i	$0.666800\pi$
$150$		0			0
$151$		−	0.408335i		−	0.0332298i	−0.999862	−	0.0166149i	$-0.994711\pi$
$151$		−	0.408335i		−	0.0332298i	0.999862	−	0.0166149i	$-0.00528893\pi$
$152$	−4.76195	+	8.24794i	−0.386245	+	0.668997i
$153$	3.05989	+	5.29988i	0.247377	+	0.428470i
$154$	−2.58386	+	1.49180i	−0.208214	+	0.120212i
$155$		0			0
$156$	−13.2147	−	2.06129i	−1.05802	−	0.165035i
$157$	−0.950895			−0.0758897			−0.0379448	−	0.999280i	$-0.512081\pi$
$157$	−0.950895			−0.0758897			−0.0379448	+	0.999280i	$0.512081\pi$
$158$	−4.33821	+	2.50467i	−0.345129	+	0.199261i
$159$	11.3977	+	19.7413i	0.903894	+	1.56559i
$160$		0			0
$161$		−	23.5160i		−	1.85332i
$162$	9.62806	+	5.55876i	0.756451	+	0.436737i
$163$	9.09442	+	5.25067i	0.712330	+	0.411264i	0.811923	−	0.583764i	$-0.198421\pi$
$163$	9.09442	+	5.25067i	0.712330	+	0.411264i	−0.0995930	+	0.995028i	$0.531754\pi$
$164$			0.966011i			0.0754328i
$165$		0			0
$166$	0.0833732	+	0.144407i	0.00647102	+	0.0112081i
$167$	−6.90234	+	3.98507i	−0.534119	+	0.308374i	−0.742692	−	0.669633i	$-0.766451\pi$
$167$	−6.90234	+	3.98507i	−0.534119	+	0.308374i	0.208573	+	0.978007i	$0.433118\pi$
$168$	31.1121			2.40035
$169$	12.3824	+	3.95927i	0.952493	+	0.304559i
$170$		0			0
$171$	18.4392	−	10.6459i	1.41008	−	0.814109i
$172$	−5.45688	−	9.45158i	−0.416083	−	0.720677i
$173$	−4.96645	+	8.60214i	−0.377592	+	0.654009i	−0.990711	−	0.135982i	$-0.956581\pi$
$173$	−4.96645	+	8.60214i	−0.377592	+	0.654009i	0.613119	+	0.789990i	$0.289914\pi$
$174$			22.8320i			1.73089i
$175$		0			0
$176$	0.0893675	+	0.0515963i	0.00673633	+	0.00388922i
$177$			3.07295i			0.230977i
$178$	−4.21227	+	7.29586i	−0.315723	+	0.546848i
$179$	−5.31430	−	9.20463i	−0.397209	−	0.687987i	0.596171	−	0.802857i	$-0.296688\pi$
$179$	−5.31430	−	9.20463i	−0.397209	−	0.687987i	−0.993380	+	0.114871i	$0.963355\pi$
$180$		0			0
$181$	8.66166			0.643816			0.321908	−	0.946771i	$-0.395676\pi$
$181$	8.66166			0.643816			0.321908	+	0.946771i	$0.395676\pi$
$182$	−11.2715	−	1.75819i	−0.835502	−	0.130326i
$183$	−13.8600			−1.02456
$184$	−16.3000	+	9.41081i	−1.20165	+	0.693774i
$185$		0			0
$186$	−5.62798	+	9.74794i	−0.412663	+	0.714754i
$187$		−	0.905177i		−	0.0661931i
$188$	−11.1195	−	6.41985i	−0.810974	−	0.468216i
$189$	−31.8915	−	18.4126i	−2.31977	−	1.33932i
$190$		0			0
$191$	−5.30436	+	9.18742i	−0.383810	+	0.664779i	−0.991603	−	0.129317i	$-0.958722\pi$
$191$	−5.30436	+	9.18742i	−0.383810	+	0.664779i	0.607793	+	0.794095i	$0.292055\pi$
$192$	−7.95687	−	13.7817i	−0.574238	−	0.994609i
$193$	17.7047	−	10.2218i	1.27442	−	0.735784i	0.298600	−	0.954378i	$-0.403480\pi$
$193$	17.7047	−	10.2218i	1.27442	−	0.735784i	0.975816	+	0.218594i	$0.0701471\pi$
$194$	14.6909			1.05474
$195$		0			0
$196$	−6.89957			−0.492827
$197$	−9.95644	+	5.74836i	−0.709367	+	0.409553i	−0.810827	−	0.585286i	$-0.800982\pi$
$197$	−9.95644	+	5.74836i	−0.709367	+	0.409553i	0.101459	+	0.994840i	$0.467649\pi$
$198$	−2.66930	−	4.62337i	−0.189699	−	0.328569i
$199$	−4.97772	+	8.62167i	−0.352861	+	0.611174i	−0.986750	−	0.162251i	$-0.948125\pi$
$199$	−4.97772	+	8.62167i	−0.352861	+	0.611174i	0.633888	+	0.773425i	$0.281458\pi$
$200$		0			0
$201$	2.96916	+	1.71425i	0.209429	+	0.120914i
$202$	4.23412	+	2.44457i	0.297912	+	0.171999i
$203$		−	29.9198i		−	2.09995i
$204$	−1.78033	+	3.08363i	−0.124648	+	0.215897i
$205$		0			0
$206$	2.69002	−	1.55308i	0.187423	−	0.108209i
$207$	42.0777			2.92460
$208$	0.142260	+	0.368021i	0.00986394	+	0.0255177i
$209$	−3.14926			−0.217839
$210$		0			0
$211$	−5.72848	−	9.92202i	−0.394365	−	0.683060i	0.598655	−	0.801007i	$-0.295702\pi$
$211$	−5.72848	−	9.92202i	−0.394365	−	0.683060i	−0.993020	+	0.117947i	$0.962369\pi$
$212$	−4.50952	+	7.81073i	−0.309715	+	0.536443i
$213$		−	5.67615i		−	0.388923i
$214$	4.41632	+	2.54977i	0.301894	+	0.174298i
$215$		0			0
$216$			29.4739i			2.00545i
$217$	7.37507	−	12.7740i	0.500652	−	0.867155i
$218$	−4.87967	−	8.45183i	−0.330493	−	0.572430i
$219$	−12.4557	+	7.19127i	−0.841675	+	0.485941i
$220$		0			0
$221$	2.17175	−	2.69477i	0.146088	−	0.181270i
$222$	−21.6859			−1.45546
$223$	4.26839	−	2.46436i	0.285833	−	0.165026i	−0.350228	−	0.936664i	$-0.613896\pi$
$223$	4.26839	−	2.46436i	0.285833	−	0.165026i	0.636061	+	0.771639i	$0.280563\pi$
$224$	9.98783	+	17.2994i	0.667340	+	1.15587i
$225$		0			0
$226$			12.1805i			0.810233i
$227$	21.0243	+	12.1384i	1.39543	+	0.805653i	0.993910	−	0.110197i	$-0.0351481\pi$
$227$	21.0243	+	12.1384i	1.39543	+	0.805653i	0.401522	+	0.915849i	$0.368481\pi$
$228$	10.7285	+	6.19408i	0.710510	+	0.410213i
$229$		−	28.3643i		−	1.87437i	−0.348837	−	0.937183i	$-0.613423\pi$
$229$		−	28.3643i		−	1.87437i	0.348837	−	0.937183i	$-0.386577\pi$
$230$		0			0
$231$	5.14391	+	8.90952i	0.338445	+	0.586203i
$232$	−20.7387	+	11.9735i	−1.36156	+	0.786099i
$233$	−12.6827			−0.830869			−0.415435	−	0.909623i	$-0.636371\pi$
$233$	−12.6827			−0.830869			−0.415435	+	0.909623i	$0.636371\pi$
$234$	3.14597	−	20.1684i	0.205658	−	1.31845i
$235$		0			0
$236$	−1.05293	+	0.607911i	−0.0685401	+	0.0395716i
$237$	8.63643	+	14.9587i	0.560997	+	0.971675i
$238$	−1.51854	+	2.63020i	−0.0984326	+	0.170490i
$239$		−	29.4374i		−	1.90415i	−0.305872	−	0.952073i	$-0.598948\pi$
$239$		−	29.4374i		−	1.90415i	0.305872	−	0.952073i	$-0.401052\pi$
$240$		0			0
$241$	−10.4631	−	6.04088i	−0.673989	−	0.389128i	0.123598	−	0.992332i	$-0.460557\pi$
$241$	−10.4631	−	6.04088i	−0.673989	−	0.389128i	−0.797586	+	0.603205i	$0.793890\pi$
$242$		−	8.97832i		−	0.577148i
$243$	3.66438	−	6.34689i	0.235070	−	0.407153i
$244$	−2.74188	−	4.74908i	−0.175531	−	0.304029i
$245$		0			0
$246$	−2.16810			−0.138233
$247$	−9.37555	−	7.55589i	−0.596552	−	0.480770i
$248$	−11.8056			−0.749659
$249$	0.497934	−	0.287482i	0.0315553	−	0.0182184i
$250$		0			0
$251$	1.96303	−	3.40006i	0.123905	−	0.214610i	−0.797399	−	0.603452i	$-0.793791\pi$
$251$	1.96303	−	3.40006i	0.123905	−	0.214610i	0.921304	+	0.388842i	$0.127125\pi$
$252$		−	27.5195i		−	1.73356i
$253$	−5.38991	−	3.11186i	−0.338861	−	0.195641i
$254$	−2.70195	−	1.55997i	−0.169536	−	0.0978814i
$255$		0			0
$256$	8.12658	−	14.0757i	0.507912	−	0.879729i
$257$	−10.0300	−	17.3725i	−0.625654	−	1.08366i	−0.988414	−	0.151782i	$-0.951499\pi$
$257$	−10.0300	−	17.3725i	−0.625654	−	1.08366i	0.362760	−	0.931883i	$-0.381835\pi$
$258$	21.2129	−	12.2473i	1.32066	−	0.762484i
$259$	28.4179			1.76580
$260$		0			0
$261$	53.5361			3.31380
$262$	13.9025	−	8.02663i	0.858901	−	0.495887i
$263$	7.97260	+	13.8089i	0.491612	+	0.851496i	0.999953	−	0.00965925i	$-0.00307468\pi$
$263$	7.97260	+	13.8089i	0.491612	+	0.851496i	−0.508342	+	0.861155i	$0.669741\pi$
$264$	4.11706	−	7.13096i	0.253388	−	0.438880i
$265$		0			0
$266$	9.15089	+	5.28327i	0.561077	+	0.323938i
$267$	25.1571	+	14.5245i	1.53959	+	0.888883i
$268$			1.35649i			0.0828611i
$269$	−10.4030	+	18.0185i	−0.634282	+	1.09861i	0.352384	+	0.935855i	$0.385371\pi$
$269$	−10.4030	+	18.0185i	−0.634282	+	1.09861i	−0.986667	+	0.162754i	$0.947962\pi$
$270$		0			0
$271$	−7.53510	+	4.35039i	−0.457725	+	0.264268i	−0.711087	−	0.703104i	$-0.751797\pi$
$271$	−7.53510	+	4.35039i	−0.457725	+	0.264268i	0.253362	+	0.967371i	$0.418464\pi$
$272$	0.105043			0.00636917
$273$	−6.06247	+	38.8658i	−0.366917	+	2.35226i
$274$	0.692824			0.0418550
$275$		0			0
$276$	12.2411	+	21.2021i	0.736825	+	1.27622i
$277$	4.32017	−	7.48276i	0.259574	−	0.449595i	−0.706554	−	0.707659i	$-0.749751\pi$
$277$	4.32017	−	7.48276i	0.259574	−	0.449595i	0.966128	+	0.258064i	$0.0830845\pi$
$278$		−	0.247605i		−	0.0148504i
$279$	22.8568	+	13.1964i	1.36840	+	0.790047i
$280$		0			0
$281$		−	12.5197i		−	0.746862i	−0.927658	−	0.373431i	$-0.878181\pi$
$281$		−	12.5197i		−	0.746862i	0.927658	−	0.373431i	$-0.121819\pi$
$282$	14.4086	−	24.9564i	0.858019	−	1.48613i
$283$	−10.1648	−	17.6060i	−0.604236	−	1.04657i	−0.992172	−	0.124880i	$-0.960145\pi$
$283$	−10.1648	−	17.6060i	−0.604236	−	1.04657i	0.387936	−	0.921686i	$-0.373188\pi$
$284$	1.94491	−	1.12289i	0.115409	−	0.0666314i
$285$		0			0
$286$	−1.89454	+	2.35079i	−0.112026	+	0.139005i
$287$	2.84114			0.167707
$288$	−30.9543	+	17.8715i	−1.82400	+	1.05309i
$289$	8.03930	+	13.9245i	0.472900	+	0.819086i
$290$		0			0
$291$		−	50.6562i		−	2.96952i
$292$	−4.92812	−	2.84525i	−0.288396	−	0.166506i
$293$	22.3448	+	12.9008i	1.30540	+	0.753672i	0.981325	−	0.192360i	$-0.0616140\pi$
$293$	22.3448	+	12.9008i	1.30540	+	0.753672i	0.324074	+	0.946032i	$0.394947\pi$
$294$		−	15.4853i		−	0.903119i
$295$		0			0
$296$	−11.3725	−	19.6977i	−0.661012	−	1.14491i
$297$	−8.44039	+	4.87306i	−0.489761	+	0.282764i
$298$	0.00906094			0.000524886
$299$	−8.57994	−	22.1960i	−0.496191	−	1.28363i
$300$		0			0
$301$	−27.7981	+	16.0492i	−1.60226	+	0.925062i
$302$	0.181300	+	0.314021i	0.0104326	+	0.0180699i
$303$	8.42921	−	14.5998i	0.484245	−	0.838738i
$304$		−	0.365462i		−	0.0209607i
$305$		0			0
$306$	−4.70627	−	2.71717i	−0.269040	−	0.155330i
$307$			5.73478i			0.327301i	0.986518	+	0.163650i	$0.0523269\pi$
$307$			5.73478i			0.327301i	−0.986518	+	0.163650i	$0.947673\pi$
$308$	−2.03521	+	3.52508i	−0.115967	+	0.200860i
$309$	−5.35525	−	9.27556i	−0.304649	−	0.527668i
$310$		0			0
$311$	−16.1145			−0.913771			−0.456886	−	0.889525i	$-0.651035\pi$
$311$	−16.1145			−0.913771			−0.456886	+	0.889525i	$0.651035\pi$
$312$	29.3658	−	11.3514i	1.66251	−	0.642648i
$313$	−20.6515			−1.16729			−0.583646	−	0.812008i	$-0.698374\pi$
$313$	−20.6515			−1.16729			−0.583646	+	0.812008i	$0.698374\pi$
$314$	0.731264	−	0.422196i	0.0412676	−	0.0238259i
$315$		0			0
$316$	−3.41703	+	5.91847i	−0.192223	+	0.332940i
$317$			19.2638i			1.08196i	0.841035	+	0.540981i	$0.181947\pi$
$317$			19.2638i			1.08196i	−0.841035	+	0.540981i	$0.818053\pi$
$318$	−17.5302	−	10.1211i	−0.983047	−	0.567562i
$319$	−6.85766	−	3.95927i	−0.383955	−	0.221677i
$320$		0			0
$321$	8.79194	−	15.2281i	0.490718	−	0.849949i
$322$	10.4411	+	18.0844i	0.581857	+	1.00781i
$323$	−2.77624	+	1.60287i	−0.154474	+	0.0891858i
$324$	15.1673			0.842625
$325$		0			0
$326$	−9.32514			−0.516472
$327$	−29.1431	+	16.8258i	−1.61162	+	0.930467i
$328$	−1.13699	−	1.96932i	−0.0627797	−	0.108738i
$329$	−18.8814	+	32.7036i	−1.04097	+	1.80301i
$330$		0			0
$331$	17.2245	+	9.94456i	0.946743	+	0.546602i	0.892068	−	0.451902i	$-0.149254\pi$
$331$	17.2245	+	9.94456i	0.946743	+	0.546602i	0.0546755	+	0.998504i	$0.482588\pi$
$332$	0.197009	+	0.113743i	0.0108123	+	0.00624247i
$333$			50.8488i			2.78649i
$334$	3.53872	−	6.12925i	0.193630	−	0.335377i
$335$		0			0
$336$	−1.03392	+	0.596935i	−0.0564051	+	0.0325655i
$337$	−14.2197			−0.774599			−0.387299	−	0.921954i	$-0.626592\pi$
$337$	−14.2197			−0.774599			−0.387299	+	0.921954i	$0.626592\pi$
$338$	−11.2803	+	2.45298i	−0.613569	+	0.133425i
$339$	42.0000			2.28112
$340$		0			0
$341$	−1.95188	−	3.38076i	−0.105700	−	0.183078i
$342$	−9.45347	+	16.3739i	−0.511185	+	0.885399i
$343$		−	4.64891i		−	0.251017i
$344$	22.2489	+	12.8454i	1.19958	+	0.692578i
$345$		0			0
$346$		−	8.82037i		−	0.474186i
$347$	2.74135	−	4.74816i	0.147163	−	0.254894i	−0.783015	−	0.622003i	$-0.786319\pi$
$347$	2.74135	−	4.74816i	0.147163	−	0.254894i	0.930178	+	0.367109i	$0.119652\pi$
$348$	15.5745	+	26.9758i	0.834879	+	1.44605i
$349$	4.65835	−	2.68950i	0.249356	−	0.143966i	−0.370113	−	0.928987i	$-0.620681\pi$
$349$	4.65835	−	2.68950i	0.249356	−	0.143966i	0.619469	+	0.785021i	$0.287348\pi$
$350$		0			0
$351$	−36.8193	−	5.74325i	−1.96527	−	0.306552i
$352$	5.28675			0.281785
$353$	−0.206468	+	0.119204i	−0.0109892	+	0.00634460i	−0.505485	−	0.862836i	$-0.668686\pi$
$353$	−0.206468	+	0.119204i	−0.0109892	+	0.00634460i	0.494495	+	0.869180i	$0.335353\pi$
$354$	−1.36438	−	2.36318i	−0.0725161	−	0.125602i
$355$		0			0
$356$			11.4933i			0.609144i
$357$	9.06928	+	5.23615i	0.479997	+	0.277126i
$358$	8.17368	+	4.71908i	0.431992	+	0.249411i
$359$			0.536191i			0.0282991i	0.999900	+	0.0141495i	$0.00450409\pi$
$359$			0.536191i			0.0282991i	−0.999900	+	0.0141495i	$0.995496\pi$
$360$		0			0
$361$	−3.92337	−	6.79547i	−0.206493	−	0.357656i
$362$	−6.66105	+	3.84576i	−0.350097	+	0.202129i
$363$	−30.9585			−1.62490
$364$	−14.5165	+	5.61141i	−0.760872	+	0.294118i
$365$		0			0
$366$	10.6587	−	6.15383i	0.557141	−	0.321666i
$367$	5.02206	+	8.69846i	0.262149	+	0.454056i	0.966813	−	0.255486i	$-0.0822353\pi$
$367$	5.02206	+	8.69846i	0.262149	+	0.454056i	−0.704663	+	0.709542i	$0.748902\pi$
$368$	0.361122	−	0.625482i	0.0188248	−	0.0326055i
$369$			5.08372i			0.264648i
$370$		0			0
$371$	22.9722	+	13.2630i	1.19265	+	0.688580i
$372$			15.3561i			0.796177i
$373$	2.23436	−	3.87003i	0.115691	−	0.200382i	−0.802365	−	0.596834i	$-0.796425\pi$
$373$	2.23436	−	3.87003i	0.115691	−	0.200382i	0.918056	+	0.396451i	$0.129758\pi$
$374$	0.401897	+	0.696106i	0.0207816	+	0.0359948i
$375$		0			0
$376$	30.2245			1.55871
$377$	−10.9164	−	28.2403i	−0.562222	−	1.45445i
$378$	32.7006			1.68194
$379$	22.5652	−	13.0280i	1.15910	−	0.669205i	0.208009	−	0.978127i	$-0.433302\pi$
$379$	22.5652	−	13.0280i	1.15910	−	0.669205i	0.951087	+	0.308922i	$0.0999682\pi$
$380$		0			0
$381$	−5.37900	+	9.31670i	−0.275574	+	0.477309i
$382$		−	9.42050i		−	0.481995i
$383$	27.5903	+	15.9293i	1.40980	+	0.813947i	0.995368	−	0.0961340i	$-0.0306477\pi$
$383$	27.5903	+	15.9293i	1.40980	+	0.813947i	0.414430	+	0.910081i	$0.363981\pi$
$384$	−17.4948	−	10.1006i	−0.892777	−	0.515445i
$385$		0			0
$386$	−9.07695	+	15.7217i	−0.462005	+	0.800216i
$387$	−28.7173	−	49.7398i	−1.45978	−	2.52841i
$388$	17.3571	−	10.0211i	0.881174	−	0.508746i
$389$	−11.6351			−0.589923			−0.294962	−	0.955509i	$-0.595307\pi$
$389$	−11.6351			−0.589923			−0.294962	+	0.955509i	$0.595307\pi$
$390$		0			0
$391$	−6.33533			−0.320391
$392$	14.0655	−	8.12075i	0.710417	−	0.410160i
$393$	−27.6769	−	47.9378i	−1.39612	−	2.41814i
$394$	5.10452	−	8.84128i	0.257162	−	0.445417i
$395$		0			0
$396$	−6.30751	−	3.64164i	−0.316964	−	0.182999i
$397$	−6.99421	−	4.03811i	−0.351029	−	0.202667i	0.314109	−	0.949387i	$-0.398294\pi$
$397$	−6.99421	−	4.03811i	−0.351029	−	0.202667i	−0.665138	+	0.746720i	$0.731627\pi$
$398$		−	8.84039i		−	0.443129i
$399$	18.2174	−	31.5535i	0.912012	−	1.57965i
$400$		0			0
$401$	27.0408	−	15.6120i	1.35035	−	0.779625i	0.362052	−	0.932158i	$-0.382076\pi$
$401$	27.0408	−	15.6120i	1.35035	−	0.779625i	0.988298	+	0.152532i	$0.0487428\pi$
$402$	−3.04449			−0.151845
$403$	2.30043	−	14.7478i	0.114593	−	0.734640i
$404$	6.67009			0.331849
$405$		0			0
$406$	13.2843	+	23.0091i	0.659289	+	1.14192i
$407$	3.76053	−	6.51343i	0.186402	−	0.322858i
$408$		−	8.38176i		−	0.414959i
$409$	−27.8828	−	16.0982i	−1.37872	−	0.796003i	−0.386712	−	0.922200i	$-0.626389\pi$
$409$	−27.8828	−	16.0982i	−1.37872	−	0.796003i	−0.992005	+	0.126197i	$0.959723\pi$
$410$		0			0
$411$		−	2.38895i		−	0.117838i
$412$	2.11882	−	3.66991i	0.104387	−	0.180803i
$413$	1.78793	+	3.09678i	0.0879782	+	0.152383i
$414$	−32.3589	+	18.6824i	−1.59035	+	0.918191i
$415$		0			0
$416$	15.7390	+	12.6843i	0.771667	+	0.621897i
$417$	−0.853777			−0.0418096
$418$	2.42187	−	1.39827i	0.118457	−	0.0683914i
$419$	10.9140	+	18.9036i	0.533185	+	0.923503i	0.999249	+	0.0387522i	$0.0123383\pi$
$419$	10.9140	+	18.9036i	0.533185	+	0.923503i	−0.466064	+	0.884751i	$0.654328\pi$
$420$		0			0
$421$		−	4.55712i		−	0.222100i	−0.993815	−	0.111050i	$-0.964579\pi$
$421$		−	4.55712i		−	0.222100i	0.993815	−	0.111050i	$-0.0354214\pi$
$422$	8.81072	+	5.08687i	0.428899	+	0.247625i
$423$	−58.5174	−	33.7850i	−2.84521	−	1.64268i
$424$		−	21.2307i		−	1.03105i
$425$		0			0
$426$	2.52020	+	4.36511i	0.122104	+	0.211490i
$427$	−13.9675	+	8.06416i	−0.675936	+	0.390252i
$428$	6.95712			0.336285
$429$	8.10586	+	6.53263i	0.391355	+	0.315398i
$430$		0			0
$431$	−25.7415	+	14.8619i	−1.23993	+	0.715871i	−0.969079	−	0.246751i	$-0.920637\pi$
$431$	−25.7415	+	14.8619i	−1.23993	+	0.715871i	−0.270847	+	0.962623i	$0.587304\pi$
$432$	−0.565504	−	0.979481i	−0.0272078	−	0.0471253i
$433$	3.89111	−	6.73960i	0.186995	−	0.323884i	−0.757252	−	0.653123i	$-0.773459\pi$
$433$	3.89111	−	6.73960i	0.186995	−	0.323884i	0.944247	+	0.329238i	$0.106792\pi$
$434$			13.0981i			0.628727i
$435$		0			0
$436$	−11.5305	−	6.65716i	−0.552213	−	0.318820i
$437$			22.0417i			1.05440i
$438$	6.38582	−	11.0606i	0.305126	−	0.528494i
$439$	2.09941	+	3.63629i	0.100199	+	0.173551i	0.911767	−	0.410708i	$-0.134719\pi$
$439$	2.09941	+	3.63629i	0.100199	+	0.173551i	−0.811567	+	0.584259i	$0.801385\pi$
$440$		0			0
$441$	−36.3096			−1.72903
$442$	−0.473664	+	3.03661i	−0.0225299	+	0.144437i
$443$	21.5287			1.02286			0.511430	−	0.859325i	$-0.329116\pi$
$443$	21.5287			1.02286			0.511430	+	0.859325i	$0.329116\pi$
$444$	−25.6217	+	14.7927i	−1.21595	+	0.702029i
$445$		0			0
$446$	−2.18834	+	3.79032i	−0.103621	+	0.179477i
$447$		−	0.0312433i		−	0.00147776i
$448$	−16.0372	−	9.25906i	−0.757685	−	0.437450i
$449$	−20.8626	−	12.0450i	−0.984565	−	0.568439i	−0.0809197	−	0.996721i	$-0.525786\pi$
$449$	−20.8626	−	12.0450i	−0.984565	−	0.568439i	−0.903645	+	0.428282i	$0.859119\pi$
$450$		0			0
$451$	0.375967	−	0.651194i	0.0177036	−	0.0306635i
$452$	8.30871	+	14.3911i	0.390809	+	0.676901i
$453$	1.08279	−	0.625147i	0.0508737	−	0.0293720i
$454$	−21.5577			−1.01175
$455$		0			0
$456$	−29.1615			−1.36561
$457$	28.4266	−	16.4121i	1.32974	−	0.767726i	0.344481	−	0.938793i	$-0.388055\pi$
$457$	28.4266	−	16.4121i	1.32974	−	0.767726i	0.985259	+	0.171068i	$0.0547217\pi$
$458$	12.5937	+	21.8129i	0.588465	+	1.01925i
$459$	−4.96044	+	8.59173i	−0.231534	+	0.401028i
$460$		0			0
$461$	20.9815	+	12.1137i	0.977207	+	0.564191i	0.901426	−	0.432934i	$-0.142522\pi$
$461$	20.9815	+	12.1137i	0.977207	+	0.564191i	0.0757814	+	0.997124i	$0.475855\pi$
$462$	−7.91162	−	4.56777i	−0.368082	−	0.212512i
$463$			3.28092i			0.152477i	0.997090	+	0.0762385i	$0.0242911\pi$
$463$			3.28092i			0.152477i	−0.997090	+	0.0762385i	$0.975709\pi$
$464$	0.459461	−	0.795810i	0.0213299	−	0.0369445i
$465$		0			0
$466$	9.75332	−	5.63108i	0.451814	−	0.260855i
$467$	−7.88097			−0.364688			−0.182344	−	0.983235i	$-0.558368\pi$
$467$	−7.88097			−0.364688			−0.182344	+	0.983235i	$0.558368\pi$
$468$	−10.0406	−	25.9747i	−0.464128	−	1.20068i
$469$	3.98959			0.184222
$470$		0			0
$471$	−1.45579	−	2.52150i	−0.0670792	−	0.116185i
$472$	1.43101	−	2.47859i	0.0658677	−	0.114086i
$473$			8.49516i			0.390608i
$474$	−13.2833	−	7.66912i	−0.610122	−	0.352254i
$475$		0			0
$476$			4.14340i			0.189912i
$477$	−23.7318	+	41.1046i	−1.08660	+	1.88205i
$478$	13.0701	+	22.6381i	0.597814	+	1.03544i
$479$	−28.7996	+	16.6274i	−1.31589	+	0.759727i	−0.983064	−	0.183263i	$-0.941334\pi$
$479$	−28.7996	+	16.6274i	−1.31589	+	0.759727i	−0.332821	+	0.942990i	$0.608001\pi$
$480$		0			0
$481$	26.8227	−	10.3684i	1.22301	−	0.472759i
$482$	10.7286			0.488673
$483$	62.3576	−	36.0022i	2.83737	−	1.63816i
$484$	−6.12441	−	10.6078i	−0.278382	−	0.482172i
$485$		0			0
$486$			6.50790i			0.295204i
$487$	2.75596	+	1.59116i	0.124885	+	0.0721022i	0.561141	−	0.827720i	$-0.310363\pi$
$487$	2.75596	+	1.59116i	0.124885	+	0.0721022i	−0.436256	+	0.899822i	$0.643696\pi$
$488$	11.1793	+	6.45435i	0.506061	+	0.292175i
$489$			32.1544i			1.45407i
$490$		0			0
$491$	16.2919	+	28.2185i	0.735245	+	1.27348i	0.954616	+	0.297840i	$0.0962662\pi$
$491$	16.2919	+	28.2185i	0.735245	+	1.27348i	−0.219371	+	0.975642i	$0.570400\pi$
$492$	−2.56158	+	1.47893i	−0.115485	+	0.0666753i
$493$	−8.06053			−0.363028
$494$	10.5649	+	1.64796i	0.475335	+	0.0741451i
$495$		0			0
$496$	0.392326	−	0.226510i	0.0176160	−	0.0101706i
$497$	−3.30254	−	5.72017i	−0.148139	−	0.256585i
$498$	−0.255283	+	0.442163i	−0.0114395	+	0.0198138i
$499$			9.77164i			0.437439i	0.975788	+	0.218719i	$0.0701879\pi$
$499$			9.77164i			0.437439i	−0.975788	+	0.218719i	$0.929812\pi$
$500$		0			0
$501$	−21.1345	−	12.2020i	−0.944219	−	0.545145i
$502$			3.48632i			0.155602i
$503$	−9.28730	+	16.0861i	−0.414100	+	0.717243i	−0.995334	−	0.0964943i	$-0.969237\pi$
$503$	−9.28730	+	16.0861i	−0.414100	+	0.717243i	0.581233	+	0.813737i	$0.302570\pi$
$504$	32.3902	+	56.1015i	1.44277	+	2.49896i
$505$		0			0
$506$	5.52665			0.245689
$507$	8.45821	+	38.8961i	0.375642	+	1.72744i
$508$	−4.25644			−0.188849
$509$	1.70294	−	0.983191i	0.0754814	−	0.0435792i	−0.461784	−	0.886992i	$-0.652791\pi$
$509$	1.70294	−	0.983191i	0.0754814	−	0.0435792i	0.537266	+	0.843413i	$0.319457\pi$
$510$		0			0
$511$	−8.36818	+	14.4941i	−0.370186	+	0.641181i
$512$			1.23765i			0.0546971i
$513$	29.8921	+	17.2582i	1.31977	+	0.761968i
$514$	15.4267	+	8.90660i	0.680442	+	0.392853i
$515$		0			0
$516$	16.7086	−	28.9401i	0.735554	−	1.27402i
$517$	4.99715	+	8.65532i	0.219774	+	0.380661i
$518$	−21.8541	+	12.6175i	−0.960215	+	0.554380i
$519$	−30.4139			−1.33502
$520$		0			0
$521$	−21.0065			−0.920312			−0.460156	−	0.887838i	$-0.652206\pi$
$521$	−21.0065			−0.920312			−0.460156	+	0.887838i	$0.652206\pi$
$522$	−41.1707	+	23.7699i	−1.80199	+	1.04038i
$523$	10.1448	+	17.5714i	0.443603	+	0.768343i	0.997954	−	0.0639401i	$-0.0203667\pi$
$523$	10.1448	+	17.5714i	0.443603	+	0.768343i	−0.554351	+	0.832283i	$0.687033\pi$
$524$	10.9505	−	18.9667i	0.478373	−	0.828566i
$525$		0			0
$526$	−12.2623	−	7.07964i	−0.534661	−	0.308687i
$527$	−3.44138	−	1.98688i	−0.149909	−	0.0865499i
$528$			0.315969i			0.0137508i
$529$	−10.2799	+	17.8053i	−0.446953	+	0.774145i
$530$		0			0
$531$	−5.54115	+	3.19918i	−0.240465	+	0.138833i
$532$	14.4156			0.624994
$533$	2.68166	−	1.03660i	0.116156	−	0.0449003i
$534$	−25.7953			−1.11627
$535$		0			0
$536$	−1.59658	−	2.76536i	−0.0689619	−	0.119446i
$537$	16.2720	−	28.1840i	0.702189	−	1.21623i
$538$		−	18.4757i		−	0.796542i
$539$	4.65104	+	2.68528i	0.200335	+	0.115663i
$540$		0			0
$541$		−	42.0546i		−	1.80807i	−0.427458	−	0.904035i	$-0.640591\pi$
$541$		−	42.0546i		−	1.80807i	0.427458	−	0.904035i	$-0.359409\pi$
$542$	3.86313	−	6.69114i	0.165936	−	0.287409i
$543$	13.2607	+	22.9682i	0.569072	+	0.985661i
$544$	4.66055	−	2.69077i	0.199820	−	0.115366i
$545$		0			0
$546$	−12.5941	−	32.5806i	−0.538979	−	1.39432i
$547$	31.0572			1.32791			0.663956	−	0.747772i	$-0.268876\pi$
$547$	31.0572			1.32791			0.663956	+	0.747772i	$0.268876\pi$
$548$	0.818564	−	0.472598i	0.0349673	−	0.0201884i
$549$	−14.4294	−	24.9924i	−0.615831	−	1.06665i
$550$		0			0
$551$			28.0439i			1.19471i
$552$	−49.9095	−	28.8153i	−2.12429	−	1.22646i
$553$	17.4068	+	10.0498i	0.740214	+	0.427363i
$554$			7.67259i			0.325977i
$555$		0			0
$556$	−0.168900	−	0.292543i	−0.00716294	−	0.0124066i
$557$	2.84783	−	1.64420i	0.120667	−	0.0696669i	−0.438452	−	0.898755i	$-0.644473\pi$
$557$	2.84783	−	1.64420i	0.120667	−	0.0696669i	0.559118	+	0.829088i	$0.311140\pi$
$558$	−23.4367			−0.992153
$559$	−20.3821	+	25.2906i	−0.862070	+	1.06968i
$560$		0			0
$561$	2.40027	−	1.38580i	0.101339	−	0.0585083i
$562$	5.55872	+	9.62798i	0.234480	+	0.406132i
$563$	−18.2500	+	31.6100i	−0.769147	+	1.33220i	0.168879	+	0.985637i	$0.445985\pi$
$563$	−18.2500	+	31.6100i	−0.769147	+	1.33220i	−0.938026	+	0.346565i	$0.887348\pi$
$564$		−	39.3143i		−	1.65543i
$565$		0			0
$566$	15.6340	+	9.02632i	0.657148	+	0.379404i
$567$		−	44.6085i		−	1.87338i
$568$	−2.64327	+	4.57828i	−0.110909	+	0.192101i
$569$	−6.22813	−	10.7874i	−0.261097	−	0.452233i	0.705437	−	0.708773i	$-0.250751\pi$
$569$	−6.22813	−	10.7874i	−0.261097	−	0.452233i	−0.966534	+	0.256540i	$0.917418\pi$
$570$		0			0
$571$	12.8215			0.536565			0.268282	−	0.963340i	$-0.413544\pi$
$571$	12.8215			0.536565			0.268282	+	0.963340i	$0.413544\pi$
$572$	−0.634821	+	4.06976i	−0.0265432	+	0.170165i
$573$	−32.4832			−1.35700
$574$	−2.18491	+	1.26146i	−0.0911965	+	0.0526523i
$575$		0			0
$576$	16.5675	−	28.6957i	0.690311	−	1.19565i
$577$			22.7641i			0.947681i	0.880611	+	0.473841i	$0.157133\pi$
$577$			22.7641i			0.947681i	−0.880611	+	0.473841i	$0.842867\pi$
$578$	−12.3649	−	7.13886i	−0.514311	−	0.296938i
$579$	54.2107	+	31.2986i	2.25292	+	1.30072i
$580$		0			0
$581$	0.334531	−	0.579424i	0.0138787	−	0.0240386i
$582$	22.4912	+	38.9560i	0.932292	+	1.61478i
$583$	6.07979	−	3.51017i	0.251799	−	0.145376i
$584$	13.3954			0.554304
$585$		0			0
$586$	−22.9117			−0.946474
$587$	16.1045	−	9.29792i	0.664703	−	0.383766i	−0.129364	−	0.991597i	$-0.541293\pi$
$587$	16.1045	−	9.29792i	0.664703	−	0.383766i	0.794067	+	0.607831i	$0.207960\pi$
$588$	−10.5630	−	18.2957i	−0.435611	−	0.754501i
$589$	−6.91268	+	11.9731i	−0.284832	+	0.493344i
$590$		0			0
$591$	−30.4860	−	17.6011i	−1.25402	−	0.724011i
$592$	0.755863	+	0.436398i	0.0310658	+	0.0179358i
$593$		−	36.4829i		−	1.49817i	−0.662473	−	0.749086i	$-0.730493\pi$
$593$		−	36.4829i		−	1.49817i	0.662473	−	0.749086i	$-0.269507\pi$
$594$	4.32726	−	7.49503i	0.177550	−	0.307525i
$595$		0			0
$596$	0.0107054	−	0.00618076i	0.000438510	−	0.000253174i
$597$	−30.4829			−1.24758
$598$	16.4532	+	13.2598i	0.672821	+	0.542236i
$599$	−46.6153			−1.90465			−0.952324	−	0.305089i	$-0.901314\pi$
$599$	−46.6153			−1.90465			−0.952324	+	0.305089i	$0.901314\pi$
$600$		0			0
$601$	1.37814	+	2.38701i	0.0562155	+	0.0973682i	0.892764	−	0.450525i	$-0.148763\pi$
$601$	1.37814	+	2.38701i	0.0562155	+	0.0973682i	−0.836548	+	0.547893i	$0.815430\pi$
$602$	14.2517	−	24.6846i	0.580854	−	1.00607i
$603$			7.13867i			0.290709i
$604$	0.428408	+	0.247341i	0.0174317	+	0.0100642i
$605$		0			0
$606$			14.9702i			0.608123i
$607$	−3.98927	+	6.90961i	−0.161919	+	0.280453i	−0.935557	−	0.353176i	$-0.885102\pi$
$607$	−3.98927	+	6.90961i	−0.161919	+	0.280453i	0.773638	+	0.633628i	$0.218435\pi$
$608$	−9.36164	−	16.2148i	−0.379665	−	0.657598i
$609$	79.3385	−	45.8061i	3.21496	−	1.85616i
$610$		0			0
$611$	−5.88950	+	37.7569i	−0.238264	+	1.52748i
$612$	−7.41388			−0.299688
$613$	−24.5639	+	14.1820i	−0.992125	+	0.572804i	−0.905909	−	0.423473i	$-0.860811\pi$
$613$	−24.5639	+	14.1820i	−0.992125	+	0.572804i	−0.0862164	+	0.996276i	$0.527478\pi$
$614$	−2.54623	−	4.41020i	−0.102757	−	0.177981i
$615$		0			0
$616$		−	9.58169i		−	0.386057i
$617$	−24.9567	−	14.4088i	−1.00472	−	0.580075i	−0.0950788	−	0.995470i	$-0.530310\pi$
$617$	−24.9567	−	14.4088i	−1.00472	−	0.580075i	−0.909641	+	0.415394i	$0.863644\pi$
$618$	8.23666	+	4.75544i	0.331327	+	0.191292i
$619$			11.8346i			0.475671i	0.971305	+	0.237836i	$0.0764380\pi$
$619$			11.8346i			0.475671i	−0.971305	+	0.237836i	$0.923562\pi$
$620$		0			0
$621$	34.1065	+	59.0742i	1.36865	+	2.37057i
$622$	12.3925	−	7.15482i	0.496895	−	0.286882i
$623$	33.8030			1.35429
$624$	−0.758091	+	0.940660i	−0.0303479	+	0.0376565i
$625$		0			0
$626$	15.8816	−	9.16923i	0.634755	−	0.366476i
$627$	−4.82141	−	8.35093i	−0.192549	−	0.333504i
$628$	0.575987	−	0.997639i	0.0229844	−	0.0398101i
$629$		−	7.65592i		−	0.305261i
$630$		0			0
$631$	19.0631	+	11.0061i	0.758889	+	0.438145i	0.828897	−	0.559401i	$-0.188969\pi$
$631$	19.0631	+	11.0061i	0.758889	+	0.438145i	−0.0700074	+	0.997546i	$0.522302\pi$
$632$		−	16.0873i		−	0.639918i
$633$	17.5402	−	30.3806i	0.697161	−	1.20752i
$634$	−8.55309	−	14.8144i	−0.339687	−	0.588354i
$635$		0			0
$636$	−27.6157			−1.09503
$637$	7.40377	+	19.1533i	0.293348	+	0.758882i
$638$	7.03163			0.278385
$639$	10.2352	−	5.90932i	0.404900	−	0.233769i
$640$		0			0
$641$	−1.18143	+	2.04629i	−0.0466636	+	0.0808237i	−0.888414	−	0.459043i	$-0.848192\pi$
$641$	−1.18143	+	2.04629i	−0.0466636	+	0.0808237i	0.841750	+	0.539867i	$0.181526\pi$
$642$			15.6144i			0.616252i
$643$	24.7766	+	14.3048i	0.977093	+	0.564125i	0.901391	−	0.433005i	$-0.142547\pi$
$643$	24.7766	+	14.3048i	0.977093	+	0.564125i	0.0757019	+	0.997130i	$0.475880\pi$
$644$	24.6720	+	14.2444i	0.972213	+	0.561307i
$645$		0			0
$646$	1.42334	−	2.46529i	0.0560005	−	0.0969957i
$647$	−15.5023	−	26.8508i	−0.609458	−	1.05561i	−0.991330	−	0.131397i	$-0.958054\pi$
$647$	−15.5023	−	26.8508i	−0.609458	−	1.05561i	0.381872	−	0.924215i	$-0.375280\pi$
$648$	−30.9201	+	17.8518i	−1.21466	+	0.701283i
$649$	0.946384			0.0371488
$650$		0			0
$651$	45.1639			1.77011
$652$	−11.0176	+	6.36099i	−0.431481	+	0.249116i
$653$	9.87093	+	17.0970i	0.386279	+	0.669056i	0.991946	−	0.126663i	$-0.0404267\pi$
$653$	9.87093	+	17.0970i	0.386279	+	0.669056i	−0.605666	+	0.795719i	$0.707093\pi$
$654$	14.9412	−	25.8789i	0.584247	−	1.01195i
$655$		0			0
$656$	0.0755690	+	0.0436298i	0.00295047	+	0.00170346i
$657$	−25.9346	−	14.9734i	−1.01181	−	0.584167i
$658$		−	33.5333i		−	1.30726i
$659$	17.1915	−	29.7766i	0.669687	−	1.15993i	−0.308304	−	0.951288i	$-0.599761\pi$
$659$	17.1915	−	29.7766i	0.669687	−	1.15993i	0.977992	−	0.208645i	$-0.0669052\pi$
$660$		0			0
$661$	2.52798	−	1.45953i	0.0983271	−	0.0567692i	−0.450030	−	0.893013i	$-0.648587\pi$
$661$	2.52798	−	1.45953i	0.0983271	−	0.0567692i	0.548357	+	0.836244i	$0.315253\pi$
$662$	−17.6615			−0.686432
$663$	10.4706	+	1.63326i	0.406646	+	0.0634306i
$664$	−0.535500			−0.0207814
$665$		0			0
$666$	−22.5767	−	39.1041i	−0.874831	−	1.51525i
$667$	−27.7109	+	47.9967i	−1.07297	+	1.85844i
$668$		−	9.65552i		−	0.373583i
$669$	13.0695	+	7.54569i	0.505297	+	0.291733i
$670$		0			0
$671$			4.26851i			0.164784i
$672$	−30.5821	+	52.9697i	−1.17973	+	2.04335i
$673$	−18.0933	−	31.3384i	−0.697444	−	1.20801i	−0.969350	−	0.245684i	$-0.920987\pi$
$673$	−18.0933	−	31.3384i	−0.697444	−	1.20801i	0.271906	−	0.962324i	$-0.412346\pi$
$674$	10.9354	−	6.31354i	0.421215	−	0.243188i
$675$		0			0
$676$	−11.6543	+	10.5929i	−0.448243	+	0.407417i
$677$	17.8383			0.685580			0.342790	−	0.939412i	$-0.388628\pi$
$677$	17.8383			0.685580			0.342790	+	0.939412i	$0.388628\pi$
$678$	−32.2991	+	18.6479i	−1.24044	+	0.716168i
$679$	−29.4732	−	51.0491i	−1.13108	−	1.95908i
$680$		0			0
$681$			74.3338i			2.84848i
$682$	3.00210	+	1.73326i	0.114956	+	0.0663701i
$683$	−41.5607	−	23.9951i	−1.59028	−	0.918147i	−0.993259	−	0.115919i	$-0.963019\pi$
$683$	−41.5607	−	23.9951i	−1.59028	−	0.918147i	−0.597018	−	0.802227i	$-0.703648\pi$
$684$			25.7941i			0.986262i
$685$		0			0
$686$	2.06411	+	3.57514i	0.0788079	+	0.136499i
$687$	75.2140	−	43.4248i	2.86959	−	1.65676i
$688$	−0.985837			−0.0375847
$689$	26.5217	+	4.13699i	1.01040	+	0.157607i
$690$		0			0
$691$	26.6535	−	15.3884i	1.01395	−	0.585403i	0.101603	−	0.994825i	$-0.467603\pi$
$691$	26.6535	−	15.3884i	1.01395	−	0.585403i	0.912345	+	0.409422i	$0.134270\pi$
$692$	−6.01667	−	10.4212i	−0.228719	−	0.396154i
$693$	−10.7104	+	18.5510i	−0.406856	+	0.704695i
$694$			4.86861i			0.184810i
$695$		0			0
$696$	−63.5006	−	36.6621i	−2.40698	−	1.38967i
$697$		−	0.765417i		−	0.0289922i
$698$	−2.38827	+	4.13660i	−0.0903972	+	0.156573i
$699$	−19.4167	−	33.6308i	−0.734408	−	1.27203i
$700$		0			0
$701$	6.69487			0.252862			0.126431	−	0.991975i	$-0.459648\pi$
$701$	6.69487			0.252862			0.126431	+	0.991975i	$0.459648\pi$
$702$	30.8650	−	11.9310i	1.16493	−	0.450306i
$703$	−26.6362			−1.00460
$704$	−4.24439	+	2.45050i	−0.159966	+	0.0923566i
$705$		0			0
$706$	0.105853	−	0.183342i	0.00398382	−	0.00690018i
$707$		−	19.6174i		−	0.737789i
$708$	−3.22401	−	1.86138i	−0.121166	−	0.0699550i
$709$	12.6384	+	7.29676i	0.474644	+	0.274036i	0.718182	−	0.695856i	$-0.244975\pi$
$709$	12.6384	+	7.29676i	0.474644	+	0.274036i	−0.243538	+	0.969891i	$0.578308\pi$
$710$		0			0
$711$	−17.9824	+	31.1465i	−0.674394	+	1.16808i
$712$	−13.5275	−	23.4304i	−0.506966	−	0.878091i
$713$	−23.6619	+	13.6612i	−0.886144	+	0.511616i
$714$	−9.29936			−0.348020
$715$		0			0
$716$	12.8762			0.481204
$717$	78.0594	−	45.0676i	2.91518	−	1.68308i
$718$	−0.238068	−	0.412346i	−0.00888461	−	0.0153886i
$719$	−7.52798	+	13.0388i	−0.280746	+	0.486267i	−0.971569	−	0.236757i	$-0.923915\pi$
$719$	−7.52798	+	13.0388i	−0.280746	+	0.486267i	0.690822	+	0.723024i	$0.257249\pi$
$720$		0			0
$721$	−10.7936	−	6.23167i	−0.401974	−	0.232080i
$722$	6.03435	+	3.48393i	0.224575	+	0.129659i
$723$		−	36.9936i		−	1.37581i
$724$	−5.24664	+	9.08745i	−0.194990	+	0.337732i
$725$		0			0
$726$	23.8079	−	13.7455i	0.883594	−	0.510144i
$727$	38.0451			1.41102			0.705508	−	0.708702i	$-0.250719\pi$
$727$	38.0451			1.41102			0.705508	+	0.708702i	$0.250719\pi$
$728$	22.9889	−	28.5253i	0.852027	−	1.05722i
$729$	−15.1192			−0.559971
$730$		0			0
$731$	4.32374	+	7.48894i	0.159919	+	0.276989i
$732$	8.39546	−	14.5414i	0.310305	−	0.537464i
$733$		−	1.60488i		−	0.0592776i	−0.999561	−	0.0296388i	$-0.990564\pi$
$733$		−	1.60488i		−	0.0592776i	0.999561	−	0.0296388i	$-0.00943570\pi$
$734$	−7.72420	−	4.45957i	−0.285106	−	0.164606i
$735$		0			0
$736$		−	37.0019i		−	1.36391i
$737$	0.527941	−	0.914421i	0.0194470	−	0.0336831i
$738$	−2.25716	−	3.90951i	−0.0830872	−	0.143911i
$739$	32.6221	−	18.8344i	1.20002	−	0.692833i	0.239462	−	0.970906i	$-0.423029\pi$
$739$	32.6221	−	18.8344i	1.20002	−	0.692833i	0.960560	+	0.278073i	$0.0896957\pi$
$740$		0			0
$741$	5.68238	−	36.4291i	0.208747	−	1.33826i
$742$	−23.5549			−0.864729
$743$	−39.5689	+	22.8451i	−1.45164	+	0.838106i	−0.998575	−	0.0533694i	$-0.983004\pi$
$743$	−39.5689	+	22.8451i	−1.45164	+	0.838106i	−0.453068	+	0.891476i	$0.649671\pi$
$744$	−18.0740	−	31.3051i	−0.662626	−	1.14770i
$745$		0			0
$746$			3.96821i			0.145286i
$747$	1.03678	+	0.598584i	0.0379337	+	0.0219010i
$748$	0.949674	+	0.548294i	0.0347235	+	0.0200476i
$749$		−	20.4616i		−	0.747651i
$750$		0			0
$751$	−19.1650	−	33.1948i	−0.699342	−	1.21130i	−0.968695	−	0.248255i	$-0.920143\pi$
$751$	−19.1650	−	33.1948i	−0.699342	−	1.21130i	0.269352	−	0.963042i	$-0.413190\pi$
$752$	−1.00442	+	0.579904i	−0.0366275	+	0.0211469i
$753$	12.0213			0.438081
$754$	20.9336	+	16.8707i	0.762358	+	0.614395i
$755$		0			0
$756$	38.6354	−	22.3062i	1.40516	−	0.811267i
$757$	−18.0528	−	31.2684i	−0.656141	−	1.13647i	−0.981607	−	0.190915i	$-0.938854\pi$
$757$	−18.0528	−	31.2684i	−0.656141	−	1.13647i	0.325466	−	0.945554i	$-0.394479\pi$
$758$	−11.5688	+	20.0378i	−0.420199	+	0.727806i
$759$		−	19.0566i		−	0.691712i
$760$		0			0
$761$	−9.92472	−	5.73004i	−0.359771	−	0.207714i	0.309209	−	0.950994i	$-0.399936\pi$
$761$	−9.92472	−	5.73004i	−0.359771	−	0.207714i	−0.668980	+	0.743280i	$0.733269\pi$
$762$		−	9.55306i		−	0.346071i
$763$	−19.5794	+	33.9125i	−0.708822	+	1.22772i
$764$	−6.42604	−	11.1302i	−0.232486	−	0.402677i
$765$		0			0
$766$	−28.2902			−1.02217
$767$	2.81745	+	2.27062i	0.101732	+	0.0819873i
$768$	49.7661			1.79578
$769$	17.2077	−	9.93487i	0.620525	−	0.358260i	−0.156548	−	0.987670i	$-0.550037\pi$
$769$	17.2077	−	9.93487i	0.620525	−	0.358260i	0.777073	+	0.629410i	$0.216703\pi$
$770$		0			0
$771$	30.7112	−	53.1933i	1.10604	−	1.91571i
$772$			24.7668i			0.891375i
$773$	40.1408	+	23.1753i	1.44376	+	0.833558i	0.998098	−	0.0616411i	$-0.0196334\pi$
$773$	40.1408	+	23.1753i	1.44376	+	0.833558i	0.445666	+	0.895199i	$0.352967\pi$
$774$	44.1687	+	25.5008i	1.58761	+	0.916608i
$775$		0			0
$776$	−23.5896	+	40.8584i	−0.846818	+	1.46673i
$777$	43.5068	+	75.3560i	1.56080	+	2.70338i
$778$	8.94771	−	5.16596i	0.320791	−	0.185209i
$779$	−2.66301			−0.0954123
$780$		0			0
$781$	−1.74810			−0.0625519
$782$	4.87204	−	2.81287i	0.174224	−	0.100588i
$783$	43.3942	+	75.1610i	1.55078	+	2.68603i
$784$	−0.311618	+	0.539739i	−0.0111292	+	0.0192764i
$785$		0			0
$786$	42.5686	+	24.5770i	1.51837	+	0.876632i
$787$	−30.8013	−	17.7832i	−1.09795	−	0.633901i	−0.162267	−	0.986747i	$-0.551881\pi$
$787$	−30.8013	−	17.7832i	−1.09795	−	0.633901i	−0.935681	+	0.352846i	$0.885214\pi$
$788$		−	13.9278i		−	0.496159i
$789$	−24.4116	+	42.2821i	−0.869074	+	1.50528i
$790$		0			0
$791$	42.3257	−	24.4368i	1.50493	−	0.868872i
$792$	17.1447			0.609212
$793$	−10.2413	+	12.7076i	−0.363678	+	0.451261i
$794$	7.17165			0.254512
$795$		0			0
$796$	−6.03033	−	10.4448i	−0.213739	−	0.370207i
$797$	7.85502	−	13.6053i	0.278239	−	0.481924i	−0.692708	−	0.721218i	$-0.743583\pi$
$797$	7.85502	−	13.6053i	0.278239	−	0.481924i	0.970947	+	0.239294i	$0.0769159\pi$
$798$			32.3540i			1.14532i
$799$	8.81052	+	5.08676i	0.311694	+	0.179956i
$800$		0			0
$801$			60.4845i			2.13711i
$802$	−13.8634	+	24.0121i	−0.489533	+	0.847896i
$803$	2.21472	+	3.83600i	0.0781556	+	0.135370i
$804$	−3.59703	+	2.07675i	−0.126857	+	0.0732412i
$805$		0			0
$806$	4.77890	+	12.3628i	0.168329	+	0.435463i
$807$	−63.7066			−2.24258
$808$	−13.5977	+	7.85064i	−0.478366	+	0.276185i
$809$	24.9367	+	43.1916i	0.876728	+	1.51854i	0.854911	+	0.518775i	$0.173612\pi$
$809$	24.9367	+	43.1916i	0.876728	+	1.51854i	0.0218171	+	0.999762i	$0.493055\pi$
$810$		0			0
$811$		−	38.3395i		−	1.34628i	−0.739514	−	0.673141i	$-0.764945\pi$
$811$		−	38.3395i		−	1.34628i	0.739514	−	0.673141i	$-0.235055\pi$
$812$	31.3905	+	18.1233i	1.10159	+	0.636004i
$813$	−23.0720	−	13.3206i	−0.809170	−	0.467174i
$814$			6.67867i			0.234087i
$815$		0			0
$816$	0.160817	+	0.278544i	0.00562973	+	0.00975098i
$817$	26.0553	−	15.0430i	0.911559	−	0.526289i
$818$	28.5902			0.999633
$819$	−76.3944	+	29.5305i	−2.66944	+	1.03188i
$820$		0			0
$821$	−27.8633	+	16.0869i	−0.972436	+	0.561436i	−0.899978	−	0.435936i	$-0.856418\pi$
$821$	−27.8633	+	16.0869i	−0.972436	+	0.561436i	−0.0724577	+	0.997371i	$0.523084\pi$
$822$	1.06069	+	1.83717i	0.0369958	+	0.0640786i
$823$	5.60008	−	9.69962i	0.195207	−	0.338108i	−0.751762	−	0.659435i	$-0.770796\pi$
$823$	5.60008	−	9.69962i	0.195207	−	0.338108i	0.946968	+	0.321327i	$0.104129\pi$
$824$			9.97535i			0.347508i
$825$		0			0
$826$	−2.74993	−	1.58767i	−0.0956823	−	0.0552422i
$827$			8.21374i			0.285620i	0.989750	+	0.142810i	$0.0456138\pi$
$827$			8.21374i			0.285620i	−0.989750	+	0.142810i	$0.954386\pi$
$828$	−25.4878	+	44.1462i	−0.885763	+	1.53419i
$829$	17.5474	+	30.3930i	0.609447	+	1.05559i	0.991332	+	0.131383i	$0.0419419\pi$
$829$	17.5474	+	30.3930i	0.609447	+	1.05559i	−0.381884	+	0.924210i	$0.624725\pi$
$830$		0			0
$831$	26.4561			0.917753
$832$	−18.5152	−	2.88809i	−0.641899	−	0.100126i
$833$	5.46686			0.189416
$834$	0.656577	−	0.379075i	0.0227354	−	0.0131263i
$835$		0			0
$836$	1.90761	−	3.30407i	0.0659760	−	0.114274i
$837$			42.7858i			1.47889i
$838$	−16.7864	−	9.69161i	−0.579875	−	0.334791i
$839$	15.3296	+	8.85053i	0.529235	+	0.305554i	0.740705	−	0.671830i	$-0.234492\pi$
$839$	15.3296	+	8.85053i	0.529235	+	0.305554i	−0.211470	+	0.977385i	$0.567825\pi$
$840$		0			0
$841$	−20.7570	+	35.9521i	−0.715758	+	1.23973i
$842$	2.02335	+	3.50455i	0.0697293	+	0.120775i
$843$	33.1986	−	19.1672i	1.14342	−	0.660154i
$844$	13.8797			0.477759
$845$		0			0
$846$	60.0019			2.06291
$847$	−31.1986	+	18.0125i	−1.07200	+	0.618918i
$848$	0.407344	+	0.705541i	0.0139883	+	0.0242284i
$849$	31.1240	−	53.9083i	1.06817	−	1.85013i
$850$		0			0
$851$	−45.5874	−	26.3199i	−1.56272	−	0.902234i
$852$	5.95517	+	3.43822i	0.204021	+	0.117792i
$853$			20.4558i			0.700394i	0.936676	+	0.350197i	$0.113885\pi$
$853$			20.4558i			0.700394i	−0.936676	+	0.350197i	$0.886115\pi$
$854$	7.16094	−	12.4031i	0.245042	−	0.424426i
$855$		0			0
$856$	−14.1829	+	8.18848i	−0.484760	+	0.279876i
$857$	−36.3625			−1.24212			−0.621060	−	0.783763i	$-0.713298\pi$
$857$	−36.3625			−1.24212			−0.621060	+	0.783763i	$0.713298\pi$
$858$	−9.13410	−	1.42478i	−0.311833	−	0.0486412i
$859$	−51.0474			−1.74172			−0.870858	−	0.491534i	$-0.836436\pi$
$859$	−51.0474			−1.74172			−0.870858	+	0.491534i	$0.836436\pi$
$860$		0			0
$861$	4.34969	+	7.53388i	0.148237	+	0.256754i
$862$	13.1973	−	22.8584i	0.449501	−	0.778559i
$863$			24.9638i			0.849776i	0.905246	+	0.424888i	$0.139687\pi$
$863$			24.9638i			0.849776i	−0.905246	+	0.424888i	$0.860313\pi$
$864$	−50.1806	−	28.9718i	−1.70718	−	0.985640i
$865$		0			0
$866$			6.91058i			0.234831i
$867$	−24.6158	+	42.6358i	−0.835996	+	1.44799i
$868$	8.93462	+	15.4752i	0.303261	+	0.525263i
$869$	4.60688	−	2.65979i	0.156278	−	0.0902270i
$870$		0			0
$871$	3.76565	−	1.45562i	0.127594	−	0.0493219i
$872$	31.3417			1.06137
$873$	91.3433	−	52.7371i	3.09150	−	1.78488i
$874$	−9.78645	−	16.9506i	−0.331032	−	0.573364i
$875$		0			0
$876$		−	17.4239i		−	0.588700i
$877$	−31.1542	−	17.9869i	−1.05200	−	0.607374i	−0.128794	−	0.991671i	$-0.541111\pi$
$877$	−31.1542	−	17.9869i	−1.05200	−	0.607374i	−0.923210	+	0.384297i	$0.874444\pi$
$878$	−3.22901	−	1.86427i	−0.108974	−	0.0629161i
$879$			79.0027i			2.66469i
$880$		0			0
$881$	−3.88848	−	6.73505i	−0.131006	−	0.226910i	0.793058	−	0.609146i	$-0.208487\pi$
$881$	−3.88848	−	6.73505i	−0.131006	−	0.226910i	−0.924065	+	0.382236i	$0.875154\pi$
$882$	27.9231	−	16.1214i	0.940218	−	0.542835i
$883$	−38.0635			−1.28094			−0.640470	−	0.767983i	$-0.721260\pi$
$883$	−38.0635			−1.28094			−0.640470	+	0.767983i	$0.721260\pi$
$884$	1.51174	+	3.91082i	0.0508453	+	0.131535i
$885$		0			0
$886$	−16.5562	+	9.55870i	−0.556215	+	0.321131i
$887$	11.1820	+	19.3678i	0.375455	+	0.650307i	0.990395	−	0.138267i	$-0.0441532\pi$
$887$	11.1820	+	19.3678i	0.375455	+	0.650307i	−0.614940	+	0.788574i	$0.710820\pi$
$888$	34.8218	−	60.3130i	1.16854	−	2.02397i
$889$			12.5186i			0.419861i
$890$		0			0
$891$	−10.2243	−	5.90302i	−0.342528	−	0.197759i
$892$			5.97096i			0.199922i
$893$	17.6977	−	30.6533i	0.592230	−	1.02577i
$894$	0.0138720	+	0.0240270i	0.000463949	+	0.000803582i
$895$		0			0
$896$	−23.5073			−0.785324
$897$	45.7218	−	56.7328i	1.52661	−	1.89425i
$898$	21.3918			0.713855
$899$	−30.1054	+	17.3813i	−1.00407	+	0.579700i
$900$		0			0
$901$	3.57311	−	6.18881i	0.119038	−	0.206179i
$902$			0.667714i			0.0222325i
$903$	−85.1159	−	49.1417i	−2.83248	−	1.63533i
$904$	−33.8765	−	19.5586i	−1.12671	−	0.650509i
$905$		0			0
$906$	−0.555128	+	0.961510i	−0.0184429	+	0.0319440i
$907$	19.7115	+	34.1414i	0.654510	+	1.13365i	0.982016	+	0.188796i	$0.0604585\pi$
$907$	19.7115	+	34.1414i	0.654510	+	1.13365i	−0.327506	+	0.944849i	$0.606208\pi$
$908$	−25.4702	+	14.7052i	−0.845257	+	0.488009i
$909$	35.1019			1.16426
$910$		0			0
$911$	−32.8525			−1.08845			−0.544227	−	0.838938i	$-0.683177\pi$
$911$	−32.8525			−1.08845			−0.544227	+	0.838938i	$0.683177\pi$
$912$	0.969100	−	0.559510i	0.0320901	−	0.0185272i
$913$	−0.0885367	−	0.153350i	−0.00293014	−	0.00507514i
$914$	−14.5739	+	25.2427i	−0.482061	+	0.834954i
$915$		0			0
$916$	29.7586	+	17.1812i	0.983253	+	0.567682i
$917$	−55.7832	−	32.2064i	−1.84212	−	1.06355i
$918$		−	8.80970i		−	0.290764i
$919$	−4.27163	+	7.39867i	−0.140908	+	0.244060i	−0.927839	−	0.372981i	$-0.878335\pi$
$919$	−4.27163	+	7.39867i	−0.140908	+	0.244060i	0.786931	+	0.617041i	$0.211669\pi$
$920$		0			0
$921$	−15.2070	+	8.77975i	−0.501087	+	0.289303i
$922$	−21.5138			−0.708520
$923$	−5.20420	−	4.19414i	−0.171298	−	0.138052i
$924$	−12.4633			−0.410013
$925$		0			0
$926$	−1.45672	−	2.52311i	−0.0478708	−	0.0829146i
$927$	11.1505	−	19.3132i	0.366230	−	0.634328i
$928$		−	47.0780i		−	1.54541i
$929$	−0.316653	−	0.182820i	−0.0103891	−	0.00599812i	0.494796	−	0.869009i	$-0.335243\pi$
$929$	−0.316653	−	0.182820i	−0.0103891	−	0.00599812i	−0.505186	+	0.863011i	$0.668576\pi$
$930$		0			0
$931$		−	19.0201i		−	0.623359i
$932$	7.68229	−	13.3061i	0.251642	−	0.435856i
$933$	−24.6708	−	42.7311i	−0.807686	−	1.39895i
$934$	6.06068	−	3.49913i	0.198311	−	0.114495i
$935$		0			0
$936$	51.0410	+	41.1346i	1.66833	+	1.34453i
$937$	9.19666			0.300442			0.150221	−	0.988652i	$-0.452001\pi$
$937$	9.19666			0.300442			0.150221	+	0.988652i	$0.452001\pi$
$938$	−3.06810	+	1.77137i	−0.100177	+	0.0578373i
$939$	−31.6168	−	54.7618i	−1.03177	−	1.78708i
$940$		0			0
$941$		−	3.66316i		−	0.119416i	−0.998216	−	0.0597078i	$-0.980983\pi$
$941$		−	3.66316i		−	0.119416i	0.998216	−	0.0597078i	$-0.0190169\pi$
$942$	2.23908	+	1.29273i	0.0729532	+	0.0421196i
$943$	−4.55770	−	2.63139i	−0.148419	−	0.0856898i
$944$			0.109825i			0.00357450i
$945$		0			0
$946$	−3.77183	−	6.53301i	−0.122633	−	0.212406i
$947$	−26.5382	+	15.3219i	−0.862377	+	0.497893i	−0.864807	−	0.502104i	$-0.832560\pi$
$947$	−26.5382	+	15.3219i	−0.862377	+	0.497893i	0.00243083	+	0.999997i	$0.499226\pi$
$948$	−20.9254			−0.679627
$949$	−2.61020	+	16.7337i	−0.0847307	+	0.543199i
$950$		0			0
$951$	−51.0820	+	29.4922i	−1.65645	+	0.956351i
$952$	−4.87675	−	8.44678i	−0.158056	−	0.273762i
$953$	−2.97388	+	5.15090i	−0.0963333	+	0.166854i	−0.910164	−	0.414248i	$-0.864045\pi$
$953$	−2.97388	+	5.15090i	−0.0963333	+	0.166854i	0.813831	+	0.581102i	$0.197378\pi$
$954$		−	42.1474i		−	1.36457i
$955$		0			0
$956$	30.8844	+	17.8311i	0.998874	+	0.576700i
$957$		−	24.2460i		−	0.783763i
$958$	14.7651	−	25.5739i	0.477038	−	0.826255i
$959$	−1.38996	−	2.40748i	−0.0448842	−	0.0777417i
$960$		0			0
$961$	13.8623			0.447173
$962$	−16.0238	+	19.8828i	−0.516629	+	0.641048i
$963$	36.6124			1.17982
$964$	12.6757	−	7.31831i	0.408256	−	0.235707i
$965$		0			0
$966$	−31.9698	+	55.3733i	−1.02861	+	1.78161i
$967$		−	1.71181i		−	0.0550482i	−0.999621	−	0.0275241i	$-0.991238\pi$
$967$		−	1.71181i		−	0.0550482i	0.999621	−	0.0275241i	$-0.00876229\pi$
$968$	24.9706	+	14.4168i	0.802585	+	0.463373i
$969$	−8.50067	−	4.90787i	−0.273081	−	0.157663i
$970$		0			0
$971$	7.13340	−	12.3554i	0.228922	−	0.396504i	−0.728567	−	0.684974i	$-0.759813\pi$
$971$	7.13340	−	12.3554i	0.228922	−	0.396504i	0.957489	+	0.288470i	$0.0931467\pi$
$972$	4.43926	+	7.68902i	0.142389	+	0.246625i
$973$	−0.860399	+	0.496752i	−0.0275831	+	0.0159251i
$974$	−2.82588			−0.0905471
$975$		0			0
$976$	−0.495347			−0.0158557
$977$	−41.1517	+	23.7589i	−1.31656	+	0.760115i	−0.983173	−	0.182676i	$-0.941524\pi$
$977$	−41.1517	+	23.7589i	−1.31656	+	0.760115i	−0.333385	+	0.942791i	$0.608191\pi$
$978$	−14.2765	−	24.7276i	−0.456511	−	0.790701i
$979$	4.47314	−	7.74770i	0.142962	−	0.247618i
$980$		0			0
$981$	−60.6805	−	35.0339i	−1.93738	−	1.11855i
$982$	−25.0579	−	14.4672i	−0.799629	−	0.461666i
$983$			35.3161i			1.12641i	0.826318	+	0.563204i	$0.190432\pi$
$983$			35.3161i			1.12641i	−0.826318	+	0.563204i	$0.809568\pi$
$984$	3.48138	−	6.02993i	0.110982	−	0.192227i
$985$		0			0
$986$	6.19877	−	3.57886i	0.197409	−	0.113974i
$987$	−115.627			−3.68046
$988$	13.6064	−	5.25960i	0.432877	−	0.167330i
$989$	59.4575			1.89064
$990$		0			0
$991$	30.6644	+	53.1123i	0.974087	+	1.68717i	0.682915	+	0.730498i	$0.260712\pi$
$991$	30.6644	+	53.1123i	0.974087	+	1.68717i	0.291172	+	0.956671i	$0.405955\pi$
$992$	11.6045	−	20.0996i	0.368443	−	0.638163i
$993$			60.8991i			1.93258i
$994$	5.07949	+	2.93265i	0.161112	+	0.0930179i
$995$		0			0
$996$			0.696548i			0.0220710i
$997$	10.3298	−	17.8917i	0.327148	−	0.566636i	−0.654797	−	0.755805i	$-0.727246\pi$
$997$	10.3298	−	17.8917i	0.327148	−	0.566636i	0.981945	+	0.189169i	$0.0605793\pi$
$998$	−4.33859	−	7.51465i	−0.137336	−	0.237872i
$999$	−71.3881	+	41.2160i	−2.25862	+	1.30401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.f.101.2	yes	10
5.2	odd	4		325.2.m.d.49.4		20
5.3	odd	4		325.2.m.d.49.7		20
5.4	even	2		325.2.n.e.101.4	✓	10
13.2	odd	12		4225.2.a.bu.1.4		10
13.4	even	6	inner	325.2.n.f.251.2	yes	10
13.11	odd	12		4225.2.a.bu.1.7		10
65.4	even	6		325.2.n.e.251.4	yes	10
65.17	odd	12		325.2.m.d.199.7		20
65.24	odd	12		4225.2.a.bv.1.4		10
65.43	odd	12		325.2.m.d.199.4		20
65.54	odd	12		4225.2.a.bv.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.4		20	5.2	odd	4
325.2.m.d.49.7		20	5.3	odd	4
325.2.m.d.199.4		20	65.43	odd	12
325.2.m.d.199.7		20	65.17	odd	12
325.2.n.e.101.4	✓	10	5.4	even	2
325.2.n.e.251.4	yes	10	65.4	even	6
325.2.n.f.101.2	yes	10	1.1	even	1	trivial
325.2.n.f.251.2	yes	10	13.4	even	6	inner
4225.2.a.bu.1.4		10	13.2	odd	12
4225.2.a.bu.1.7		10	13.11	odd	12
4225.2.a.bv.1.4		10	65.24	odd	12
4225.2.a.bv.1.7		10	65.54	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.769027 + 0.443998i) q^{2} +(1.53097 + 2.65171i) q^{3} +(-0.605732 + 1.04916i) q^{4} +(-2.35471 - 1.35949i) q^{6} +(3.08568 + 1.78152i) q^{7} -2.85177i q^{8} +(-3.18771 + 5.52128i) q^{9} +O(q^{10})\)	\(q+(-0.769027 + 0.443998i) q^{2} +(1.53097 + 2.65171i) q^{3} +(-0.605732 + 1.04916i) q^{4} +(-2.35471 - 1.35949i) q^{6} +(3.08568 + 1.78152i) q^{7} -2.85177i q^{8} +(-3.18771 + 5.52128i) q^{9} +(0.816654 - 0.471496i) q^{11} -3.70942 q^{12} +(3.56247 + 0.555692i) q^{13} -3.16396 q^{14} +(0.0547156 + 0.0947702i) q^{16} +(0.479950 - 0.831298i) q^{17} -5.66135i q^{18} +(-2.89222 - 1.66983i) q^{19} +10.9098i q^{21} +(-0.418686 + 0.725186i) q^{22} +(-3.29999 - 5.71576i) q^{23} +(7.56206 - 4.36596i) q^{24} +(-2.98636 + 1.15439i) q^{26} -10.3353 q^{27} +(-3.73819 + 2.15824i) q^{28} +(-4.19863 - 7.27224i) q^{29} -4.13976i q^{31} +(4.85525 + 2.80318i) q^{32} +(2.50054 + 1.44369i) q^{33} +0.852387i q^{34} +(-3.86180 - 6.68883i) q^{36} +(6.90720 - 3.98787i) q^{37} +2.96560 q^{38} +(3.98049 + 10.2974i) q^{39} +(0.690562 - 0.398696i) q^{41} +(-4.84392 - 8.38992i) q^{42} +(-4.50437 + 7.80179i) q^{43} +1.14240i q^{44} +(5.07557 + 2.93038i) q^{46} +10.5985i q^{47} +(-0.167535 + 0.290180i) q^{48} +(2.84762 + 4.93222i) q^{49} +2.93915 q^{51} +(-2.74091 + 3.40100i) q^{52} +7.44476 q^{53} +(7.94815 - 4.58886i) q^{54} +(5.08048 - 8.79964i) q^{56} -10.2258i q^{57} +(6.45772 + 3.72837i) q^{58} +(0.869141 + 0.501799i) q^{59} +(-2.26328 + 3.92012i) q^{61} +(1.83805 + 3.18359i) q^{62} +(-19.6725 + 11.3579i) q^{63} -5.19729 q^{64} -2.56398 q^{66} +(0.969702 - 0.559858i) q^{67} +(0.581442 + 1.00709i) q^{68} +(10.1044 - 17.5013i) q^{69} +(-1.60542 - 0.926890i) q^{71} +(15.7454 + 9.09061i) q^{72} +4.69721i q^{73} +(-3.54121 + 6.13356i) q^{74} +(3.50382 - 2.02293i) q^{76} +3.35991 q^{77} +(-7.63313 - 6.15164i) q^{78} +5.64117 q^{79} +(-6.25989 - 10.8425i) q^{81} +(-0.354041 + 0.613216i) q^{82} -0.187778i q^{83} +(-11.4461 - 6.60840i) q^{84} -7.99972i q^{86} +(12.8559 - 22.2671i) q^{87} +(-1.34460 - 2.32891i) q^{88} +(8.21609 - 4.74356i) q^{89} +(10.0027 + 8.06130i) q^{91} +7.99564 q^{92} +(10.9775 - 6.33784i) q^{93} +(-4.70572 - 8.15054i) q^{94} +17.1663i q^{96} +(-14.3274 - 8.27193i) q^{97} +(-4.37979 - 2.52868i) q^{98} +6.01197i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} + 6 q^{4} + 9 q^{6} + 6 q^{7} - 8 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 + 6 * q^4 + 9 * q^6 + 6 * q^7 - 8 * q^9	\( 10 q + 3 q^{3} + 6 q^{4} + 9 q^{6} + 6 q^{7} - 8 q^{9} - 9 q^{11} + 28 q^{12} - 8 q^{13} - 8 q^{14} - 12 q^{16} - 8 q^{17} + 12 q^{22} - 13 q^{23} + 42 q^{24} - 17 q^{26} - 30 q^{27} - 33 q^{28} + 7 q^{29} - 3 q^{32} + 6 q^{33} - 3 q^{36} - 3 q^{37} + 62 q^{38} + 8 q^{39} + 12 q^{41} - 32 q^{42} - 4 q^{43} + 39 q^{46} + 26 q^{48} - q^{49} + 16 q^{51} - 61 q^{52} - 24 q^{53} - 9 q^{54} - 21 q^{56} - 18 q^{58} - 48 q^{59} + 13 q^{61} - 17 q^{62} - 34 q^{64} - 42 q^{66} - 6 q^{67} + 13 q^{68} + 20 q^{69} - 27 q^{71} + 141 q^{72} - 26 q^{74} - 12 q^{76} + 48 q^{77} - 56 q^{78} + 4 q^{79} - 17 q^{81} + q^{82} - 90 q^{84} + 49 q^{87} + 6 q^{88} + 24 q^{89} + 13 q^{91} - 34 q^{92} + 63 q^{93} + 5 q^{94} + 15 q^{97} + 45 q^{98}+O(q^{100}) \) 10 * q + 3 * q^3 + 6 * q^4 + 9 * q^6 + 6 * q^7 - 8 * q^9 - 9 * q^11 + 28 * q^12 - 8 * q^13 - 8 * q^14 - 12 * q^16 - 8 * q^17 + 12 * q^22 - 13 * q^23 + 42 * q^24 - 17 * q^26 - 30 * q^27 - 33 * q^28 + 7 * q^29 - 3 * q^32 + 6 * q^33 - 3 * q^36 - 3 * q^37 + 62 * q^38 + 8 * q^39 + 12 * q^41 - 32 * q^42 - 4 * q^43 + 39 * q^46 + 26 * q^48 - q^49 + 16 * q^51 - 61 * q^52 - 24 * q^53 - 9 * q^54 - 21 * q^56 - 18 * q^58 - 48 * q^59 + 13 * q^61 - 17 * q^62 - 34 * q^64 - 42 * q^66 - 6 * q^67 + 13 * q^68 + 20 * q^69 - 27 * q^71 + 141 * q^72 - 26 * q^74 - 12 * q^76 + 48 * q^77 - 56 * q^78 + 4 * q^79 - 17 * q^81 + q^82 - 90 * q^84 + 49 * q^87 + 6 * q^88 + 24 * q^89 + 13 * q^91 - 34 * q^92 + 63 * q^93 + 5 * q^94 + 15 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

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Database

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