LMFDB - Embedded newform 325.2.e.b.126.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(126,325)]

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, 4]))

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

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

chi := DirichletCharacter("325.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			126.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	325.126
Dual form			325.2.e.b.276.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.535233i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.690983 + 1.19682i) q^{6} +(2.11803 + 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.535233i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.690983 + 1.19682i) q^{6} +(2.11803 + 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.118034 - 0.204441i) q^{11} +3.61803 q^{12} +(1.00000 + 3.46410i) q^{13} -2.61803 q^{14} +(-0.927051 + 1.60570i) q^{16} +(-1.73607 - 3.00696i) q^{17} +1.23607 q^{18} +(-2.11803 - 3.66854i) q^{19} +9.47214 q^{21} +(0.0729490 + 0.126351i) q^{22} +(1.88197 - 3.25966i) q^{23} +(-2.50000 + 4.33013i) q^{24} +(-2.16312 - 0.535233i) q^{26} +2.23607 q^{27} +(-3.42705 + 5.93583i) q^{28} +(3.73607 - 6.47106i) q^{29} +(-2.80902 - 4.86536i) q^{32} +(-0.263932 - 0.457144i) q^{33} +2.14590 q^{34} +(1.61803 - 2.80252i) q^{36} +(1.50000 - 2.59808i) q^{37} +2.61803 q^{38} +(7.82624 + 1.93649i) q^{39} +(-5.97214 + 10.3440i) q^{41} +(-2.92705 + 5.06980i) q^{42} +(-3.11803 - 5.40059i) q^{43} +0.381966 q^{44} +(1.16312 + 2.01458i) q^{46} +4.94427 q^{47} +(2.07295 + 3.59045i) q^{48} +(-5.47214 + 9.47802i) q^{49} -7.76393 q^{51} +(-4.04508 + 4.20378i) q^{52} -6.00000 q^{53} +(-0.690983 + 1.19682i) q^{54} +(-4.73607 - 8.20311i) q^{56} -9.47214 q^{57} +(2.30902 + 3.99933i) q^{58} +(0.354102 + 0.613323i) q^{59} +(-7.20820 - 12.4850i) q^{61} +(4.23607 - 7.33708i) q^{63} -0.236068 q^{64} +0.326238 q^{66} +(-1.35410 + 2.34537i) q^{67} +(2.80902 - 4.86536i) q^{68} +(-4.20820 - 7.28882i) q^{69} +(3.11803 + 5.40059i) q^{71} +(2.23607 + 3.87298i) q^{72} +6.00000 q^{73} +(0.927051 + 1.60570i) q^{74} +(3.42705 - 5.93583i) q^{76} +1.00000 q^{77} +(-3.45492 + 3.59045i) q^{78} +(5.50000 - 9.52628i) q^{81} +(-3.69098 - 6.39297i) q^{82} -8.94427 q^{83} +(7.66312 + 13.2729i) q^{84} +3.85410 q^{86} +(-8.35410 - 14.4697i) q^{87} +(-0.263932 + 0.457144i) q^{88} +(4.50000 - 7.79423i) q^{89} +(-10.5902 + 11.0056i) q^{91} +6.09017 q^{92} +(-1.52786 + 2.64634i) q^{94} -12.5623 q^{96} +(-1.73607 - 3.00696i) q^{97} +(-3.38197 - 5.85774i) q^{98} -0.472136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + q^2 + q^4 + 5 * q^6 + 4 * q^7 - 4 * q^9	$ 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 10 q^{12} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{21} + 7 q^{22} + 12 q^{23} - 10 q^{24} + 7 q^{26} - 7 q^{28} + 6 q^{29} - 9 q^{32} - 10 q^{33} + 22 q^{34} + 2 q^{36} + 6 q^{37} + 6 q^{38} - 6 q^{41} - 5 q^{42} - 8 q^{43} + 6 q^{44} - 11 q^{46} - 16 q^{47} + 15 q^{48} - 4 q^{49} - 40 q^{51} - 5 q^{52} - 24 q^{53} - 5 q^{54} - 10 q^{56} - 20 q^{57} + 7 q^{58} - 12 q^{59} - 2 q^{61} + 8 q^{63} + 8 q^{64} - 30 q^{66} + 8 q^{67} + 9 q^{68} + 10 q^{69} + 8 q^{71} + 24 q^{73} - 3 q^{74} + 7 q^{76} + 4 q^{77} - 25 q^{78} + 22 q^{81} - 17 q^{82} + 15 q^{84} + 2 q^{86} - 20 q^{87} - 10 q^{88} + 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} - 10 q^{96} + 2 q^{97} - 18 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^4 + 5 * q^6 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 10 * q^12 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^21 + 7 * q^22 + 12 * q^23 - 10 * q^24 + 7 * q^26 - 7 * q^28 + 6 * q^29 - 9 * q^32 - 10 * q^33 + 22 * q^34 + 2 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^41 - 5 * q^42 - 8 * q^43 + 6 * q^44 - 11 * q^46 - 16 * q^47 + 15 * q^48 - 4 * q^49 - 40 * q^51 - 5 * q^52 - 24 * q^53 - 5 * q^54 - 10 * q^56 - 20 * q^57 + 7 * q^58 - 12 * q^59 - 2 * q^61 + 8 * q^63 + 8 * q^64 - 30 * q^66 + 8 * q^67 + 9 * q^68 + 10 * q^69 + 8 * q^71 + 24 * q^73 - 3 * q^74 + 7 * q^76 + 4 * q^77 - 25 * q^78 + 22 * q^81 - 17 * q^82 + 15 * q^84 + 2 * q^86 - 20 * q^87 - 10 * q^88 + 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 - 10 * q^96 + 2 * q^97 - 18 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.535233i	−0.218508	+	0.378467i	−0.954352	−	0.298684i	$-0.903452\pi$
$2$	−0.309017	+	0.535233i	−0.218508	+	0.378467i	0.735844	+	0.677151i	$0.236786\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	−0.338689	−	0.940898i	$-0.609984\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	0.984186	−	0.177136i	$-0.0566831\pi$
$4$	0.809017	+	1.40126i	0.404508	+	0.700629i
$5$		0			0
$5$		0			0
$6$	0.690983	+	1.19682i	0.282093	+	0.488599i
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	0.919260	+	0.393651i	$0.128788\pi$
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	−0.118718	+	0.992928i	$0.537879\pi$
$8$	−2.23607			−0.790569
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	0.118034	−	0.204441i	0.0355886	−	0.0616412i	−0.847683	−	0.530504i	$-0.822003\pi$
$11$	0.118034	−	0.204441i	0.0355886	−	0.0616412i	0.883271	+	0.468863i	$0.155336\pi$
$12$	3.61803			1.04444
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	−2.61803			−0.699699
$15$		0			0
$16$	−0.927051	+	1.60570i	−0.231763	+	0.401425i
$17$	−1.73607	−	3.00696i	−0.421058	−	0.729294i	0.574985	−	0.818164i	$-0.305008\pi$
$17$	−1.73607	−	3.00696i	−0.421058	−	0.729294i	−0.996043	+	0.0888696i	$0.971675\pi$
$18$	1.23607			0.291344
$19$	−2.11803	−	3.66854i	−0.485910	−	0.841621i	0.513959	−	0.857815i	$-0.328179\pi$
$19$	−2.11803	−	3.66854i	−0.485910	−	0.841621i	−0.999869	+	0.0161937i	$0.994845\pi$
$20$		0			0
$21$	9.47214			2.06699
$22$	0.0729490	+	0.126351i	0.0155528	+	0.0269382i
$23$	1.88197	−	3.25966i	0.392417	−	0.679686i	−0.600351	−	0.799737i	$-0.704972\pi$
$23$	1.88197	−	3.25966i	0.392417	−	0.679686i	0.992768	+	0.120051i	$0.0383057\pi$
$24$	−2.50000	+	4.33013i	−0.510310	+	0.883883i
$25$		0			0
$26$	−2.16312	−	0.535233i	−0.424223	−	0.104968i
$27$	2.23607			0.430331
$28$	−3.42705	+	5.93583i	−0.647652	+	1.12177i
$29$	3.73607	−	6.47106i	0.693770	−	1.20165i	−0.276823	−	0.960921i	$-0.589282\pi$
$29$	3.73607	−	6.47106i	0.693770	−	1.20165i	0.970593	−	0.240725i	$-0.0773851\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−2.80902	−	4.86536i	−0.496569	−	0.860082i
$33$	−0.263932	−	0.457144i	−0.0459447	−	0.0795785i
$34$	2.14590			0.368018
$35$		0			0
$36$	1.61803	−	2.80252i	0.269672	−	0.467086i
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$	2.61803			0.424701
$39$	7.82624	+	1.93649i	1.25320	+	0.310087i
$40$		0			0
$41$	−5.97214	+	10.3440i	−0.932691	+	1.61547i	−0.153990	+	0.988072i	$0.549212\pi$
$41$	−5.97214	+	10.3440i	−0.932691	+	1.61547i	−0.778701	+	0.627396i	$0.784121\pi$
$42$	−2.92705	+	5.06980i	−0.451654	+	0.782287i
$43$	−3.11803	−	5.40059i	−0.475496	−	0.823583i	0.524110	−	0.851650i	$-0.324398\pi$
$43$	−3.11803	−	5.40059i	−0.475496	−	0.823583i	−0.999606	+	0.0280676i	$0.991065\pi$
$44$	0.381966			0.0575835
$45$		0			0
$46$	1.16312	+	2.01458i	0.171493	+	0.297034i
$47$	4.94427			0.721196			0.360598	−	0.932721i	$-0.382573\pi$
$47$	4.94427			0.721196			0.360598	+	0.932721i	$0.382573\pi$
$48$	2.07295	+	3.59045i	0.299204	+	0.518237i
$49$	−5.47214	+	9.47802i	−0.781734	+	1.35400i
$50$		0			0
$51$	−7.76393			−1.08717
$52$	−4.04508	+	4.20378i	−0.560952	+	0.582959i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−0.690983	+	1.19682i	−0.0940309	+	0.162866i
$55$		0			0
$56$	−4.73607	−	8.20311i	−0.632884	−	1.09619i
$57$	−9.47214			−1.25462
$58$	2.30902	+	3.99933i	0.303189	+	0.525138i
$59$	0.354102	+	0.613323i	0.0461001	+	0.0798478i	0.888155	−	0.459545i	$-0.151987\pi$
$59$	0.354102	+	0.613323i	0.0461001	+	0.0798478i	−0.842055	+	0.539392i	$0.818654\pi$
$60$		0			0
$61$	−7.20820	−	12.4850i	−0.922916	−	1.59854i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	−7.20820	−	12.4850i	−0.922916	−	1.59854i	−0.128037	−	0.991769i	$-0.540868\pi$
$62$		0			0
$63$	4.23607	−	7.33708i	0.533694	−	0.924386i
$64$	−0.236068			−0.0295085
$65$		0			0
$66$	0.326238			0.0401571
$67$	−1.35410	+	2.34537i	−0.165430	+	0.286533i	−0.936808	−	0.349844i	$-0.886234\pi$
$67$	−1.35410	+	2.34537i	−0.165430	+	0.286533i	0.771378	+	0.636377i	$0.219568\pi$
$68$	2.80902	−	4.86536i	0.340643	−	0.590012i
$69$	−4.20820	−	7.28882i	−0.506608	−	0.877471i
$70$		0			0
$71$	3.11803	+	5.40059i	0.370043	+	0.640933i	0.989572	−	0.144041i	$-0.0460098\pi$
$71$	3.11803	+	5.40059i	0.370043	+	0.640933i	−0.619529	+	0.784974i	$0.712676\pi$
$72$	2.23607	+	3.87298i	0.263523	+	0.456435i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	0.927051	+	1.60570i	0.107767	+	0.186659i
$75$		0			0
$76$	3.42705	−	5.93583i	0.393110	−	0.680886i
$77$	1.00000			0.113961
$78$	−3.45492	+	3.59045i	−0.391192	+	0.406539i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.69098	−	6.39297i	−0.407601	−	0.705985i
$83$	−8.94427			−0.981761			−0.490881	−	0.871227i	$-0.663325\pi$
$83$	−8.94427			−0.981761			−0.490881	+	0.871227i	$0.663325\pi$
$84$	7.66312	+	13.2729i	0.836115	+	1.44819i
$85$		0			0
$86$	3.85410			0.415599
$87$	−8.35410	−	14.4697i	−0.895654	−	1.55132i
$88$	−0.263932	+	0.457144i	−0.0281352	+	0.0487317i
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$		0			0
$91$	−10.5902	+	11.0056i	−1.11015	+	1.15370i
$92$	6.09017			0.634944
$93$		0			0
$94$	−1.52786	+	2.64634i	−0.157587	+	0.272949i
$95$		0			0
$96$	−12.5623			−1.28213
$97$	−1.73607	−	3.00696i	−0.176271	−	0.305310i	0.764329	−	0.644826i	$-0.223070\pi$
$97$	−1.73607	−	3.00696i	−0.176271	−	0.305310i	−0.940600	+	0.339516i	$0.889737\pi$
$98$	−3.38197	−	5.85774i	−0.341630	−	0.591721i
$99$	−0.472136			−0.0474514
$100$		0			0
$101$	−0.263932	+	0.457144i	−0.0262622	+	0.0454875i	−0.878858	−	0.477084i	$-0.841694\pi$
$101$	−0.263932	+	0.457144i	−0.0262622	+	0.0454875i	0.852596	+	0.522571i	$0.175027\pi$
$102$	2.39919	−	4.15551i	0.237555	−	0.411457i
$103$	−12.9443			−1.27544			−0.637719	−	0.770270i	$-0.720122\pi$
$103$	−12.9443			−1.27544			−0.637719	+	0.770270i	$0.720122\pi$
$104$	−2.23607	−	7.74597i	−0.219265	−	0.759555i
$105$		0			0
$106$	1.85410	−	3.21140i	0.180086	−	0.311919i
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	−0.971040	−	0.238919i	$-0.923207\pi$
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	0.692429	+	0.721486i	$0.256540\pi$
$108$	1.80902	+	3.13331i	0.174073	+	0.301503i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−3.35410	−	5.80948i	−0.318357	−	0.551411i
$112$	−7.85410			−0.742143
$113$	0.736068	+	1.27491i	0.0692435	+	0.119933i	0.898568	−	0.438833i	$-0.144608\pi$
$113$	0.736068	+	1.27491i	0.0692435	+	0.119933i	−0.829325	+	0.558766i	$0.811275\pi$
$114$	2.92705	−	5.06980i	0.274143	−	0.474830i
$115$		0			0
$116$	12.0902			1.12254
$117$	5.00000	−	5.19615i	0.462250	−	0.480384i
$118$	−0.437694			−0.0402930
$119$	7.35410	−	12.7377i	0.674149	−	1.16766i
$120$		0			0
$121$	5.47214	+	9.47802i	0.497467	+	0.861638i
$122$	8.90983			0.806658
$123$	13.3541	+	23.1300i	1.20410	+	2.08556i
$124$		0			0
$125$		0			0
$126$	2.61803	+	4.53457i	0.233233	+	0.403971i
$127$	−2.11803	+	3.66854i	−0.187945	+	0.325531i	−0.944565	−	0.328325i	$-0.893516\pi$
$127$	−2.11803	+	3.66854i	−0.187945	+	0.325531i	0.756620	+	0.653855i	$0.226849\pi$
$128$	5.69098	−	9.85707i	0.503017	−	0.871250i
$129$	−13.9443			−1.22772
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	0.427051	−	0.739674i	0.0371700	−	0.0643804i
$133$	8.97214	−	15.5402i	0.777983	−	1.34751i
$134$	−0.836881	−	1.44952i	−0.0722955	−	0.125219i
$135$		0			0
$136$	3.88197	+	6.72376i	0.332876	+	0.576558i
$137$	0.736068	+	1.27491i	0.0628865	+	0.108923i	0.895755	−	0.444549i	$-0.146636\pi$
$137$	0.736068	+	1.27491i	0.0628865	+	0.108923i	−0.832868	+	0.553472i	$0.813303\pi$
$138$	5.20163			0.442792
$139$	8.35410	+	14.4697i	0.708586	+	1.22731i	0.965382	+	0.260841i	$0.0839998\pi$
$139$	8.35410	+	14.4697i	0.708586	+	1.22731i	−0.256796	+	0.966466i	$0.582667\pi$
$140$		0			0
$141$	5.52786	−	9.57454i	0.465530	−	0.806322i
$142$	−3.85410			−0.323429
$143$	0.826238	+	0.204441i	0.0690935	+	0.0170962i
$144$	3.70820			0.309017
$145$		0			0
$146$	−1.85410	+	3.21140i	−0.153447	+	0.265777i
$147$	12.2361	+	21.1935i	1.00921	+	1.74801i
$148$	4.85410			0.399005
$149$	−2.26393	−	3.92125i	−0.185469	−	0.321241i	0.758266	−	0.651946i	$-0.226047\pi$
$149$	−2.26393	−	3.92125i	−0.185469	−	0.321241i	−0.943734	+	0.330705i	$0.892714\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	4.73607	+	8.20311i	0.384146	+	0.665360i
$153$	−3.47214	+	6.01392i	−0.280706	+	0.486196i
$154$	−0.309017	+	0.535233i	−0.0249013	+	0.0431303i
$155$		0			0
$156$	3.61803	+	12.5332i	0.289675	+	1.00346i
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$		0			0
$159$	−6.70820	+	11.6190i	−0.531995	+	0.921443i
$160$		0			0
$161$	15.9443			1.25658
$162$	3.39919	+	5.88756i	0.267065	+	0.462571i
$163$	7.35410	+	12.7377i	0.576018	+	0.997692i	0.995930	+	0.0901274i	$0.0287274\pi$
$163$	7.35410	+	12.7377i	0.576018	+	0.997692i	−0.419913	+	0.907565i	$0.637939\pi$
$164$	−19.3262			−1.50913
$165$		0			0
$166$	2.76393	−	4.78727i	0.214523	−	0.371564i
$167$	−8.59017	+	14.8786i	−0.664727	+	1.15134i	0.314632	+	0.949214i	$0.398119\pi$
$167$	−8.59017	+	14.8786i	−0.664727	+	1.15134i	−0.979359	+	0.202128i	$0.935214\pi$
$168$	−21.1803			−1.63410
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	−4.23607	+	7.33708i	−0.323940	+	0.561081i
$172$	5.04508	−	8.73834i	0.384684	−	0.666292i
$173$	−9.44427	−	16.3580i	−0.718035	−	1.24367i	−0.961777	−	0.273833i	$-0.911709\pi$
$173$	−9.44427	−	16.3580i	−0.718035	−	1.24367i	0.243743	−	0.969840i	$-0.421625\pi$
$174$	10.3262			0.782830
$175$		0			0
$176$	0.218847	+	0.379054i	0.0164962	+	0.0285723i
$177$	1.58359			0.119030
$178$	2.78115	+	4.81710i	0.208456	+	0.361057i
$179$	4.11803	−	7.13264i	0.307796	−	0.533119i	−0.670084	−	0.742286i	$-0.733742\pi$
$179$	4.11803	−	7.13264i	0.307796	−	0.533119i	0.977880	+	0.209167i	$0.0670751\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−2.61803	−	9.06914i	−0.194062	−	0.672249i
$183$	−32.2361			−2.38296
$184$	−4.20820	+	7.28882i	−0.310233	+	0.537339i
$185$		0			0
$186$		0			0
$187$	−0.819660			−0.0599395
$188$	4.00000	+	6.92820i	0.291730	+	0.505291i
$189$	4.73607	+	8.20311i	0.344498	+	0.596688i
$190$		0			0
$191$	13.5902	+	23.5389i	0.983350	+	1.70321i	0.649050	+	0.760746i	$0.275167\pi$
$191$	13.5902	+	23.5389i	0.983350	+	1.70321i	0.334300	+	0.942467i	$0.391500\pi$
$192$	−0.263932	+	0.457144i	−0.0190477	+	0.0329915i
$193$	−1.73607	+	3.00696i	−0.124965	+	0.216446i	−0.921719	−	0.387858i	$-0.873215\pi$
$193$	−1.73607	+	3.00696i	−0.124965	+	0.216446i	0.796754	+	0.604303i	$0.206548\pi$
$194$	2.14590			0.154067
$195$		0			0
$196$	−17.7082			−1.26487
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	−0.807630	−	0.589689i	$-0.799250\pi$
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	0.914501	+	0.404584i	$0.132584\pi$
$198$	0.145898	−	0.252703i	0.0103685	−	0.0179588i
$199$	0.645898	+	1.11873i	0.0457865	+	0.0793045i	0.888010	−	0.459823i	$-0.152087\pi$
$199$	0.645898	+	1.11873i	0.0457865	+	0.0793045i	−0.842224	+	0.539128i	$0.818754\pi$
$200$		0			0
$201$	3.02786	+	5.24441i	0.213569	+	0.369912i
$202$	−0.163119	−	0.282530i	−0.0114770	−	0.0198788i
$203$	31.6525			2.22157
$204$	−6.28115	−	10.8793i	−0.439769	−	0.761702i
$205$		0			0
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	−7.52786			−0.523223
$208$	−6.48936	−	1.60570i	−0.449956	−	0.111335i
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	6.59017	−	11.4145i	0.453686	−	0.785807i	−0.544926	−	0.838484i	$-0.683442\pi$
$211$	6.59017	−	11.4145i	0.453686	−	0.785807i	0.998612	+	0.0526772i	$0.0167754\pi$
$212$	−4.85410	−	8.40755i	−0.333381	−	0.577433i
$213$	13.9443			0.955446
$214$	−1.78115	−	3.08505i	−0.121757	−	0.210889i
$215$		0			0
$216$	−5.00000			−0.340207
$217$		0			0
$218$	0.618034	−	1.07047i	0.0418585	−	0.0725011i
$219$	6.70820	−	11.6190i	0.453298	−	0.785136i
$220$		0			0
$221$	8.68034	−	9.02087i	0.583903	−	0.606810i
$222$	4.14590			0.278254
$223$	0.354102	−	0.613323i	0.0237124	−	0.0410711i	−0.853926	−	0.520395i	$-0.825785\pi$
$223$	0.354102	−	0.613323i	0.0237124	−	0.0410711i	0.877638	+	0.479324i	$0.159118\pi$
$224$	11.8992	−	20.6100i	0.795048	−	1.37706i
$225$		0			0
$226$	−0.909830			−0.0605210
$227$	−3.11803	−	5.40059i	−0.206951	−	0.358450i	0.743801	−	0.668401i	$-0.233021\pi$
$227$	−3.11803	−	5.40059i	−0.206951	−	0.358450i	−0.950753	+	0.309951i	$0.899687\pi$
$228$	−7.66312	−	13.2729i	−0.507502	−	0.879020i
$229$	15.8885			1.04994			0.524972	−	0.851119i	$-0.324076\pi$
$229$	15.8885			1.04994			0.524972	+	0.851119i	$0.324076\pi$
$230$		0			0
$231$	1.11803	−	1.93649i	0.0735612	−	0.127412i
$232$	−8.35410	+	14.4697i	−0.548474	+	0.949984i
$233$	15.8885			1.04089			0.520447	−	0.853894i	$-0.325765\pi$
$233$	15.8885			1.04089			0.520447	+	0.853894i	$0.325765\pi$
$234$	1.23607	+	4.28187i	0.0808043	+	0.279914i
$235$		0			0
$236$	−0.572949	+	0.992377i	−0.0372958	+	0.0645982i
$237$		0			0
$238$	4.54508	+	7.87232i	0.294614	+	0.510287i
$239$	−25.8885			−1.67459			−0.837295	−	0.546751i	$-0.815864\pi$
$239$	−25.8885			−1.67459			−0.837295	+	0.546751i	$0.815864\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$	−6.76393			−0.434802
$243$	−8.94427	−	15.4919i	−0.573775	−	0.993808i
$244$	11.6631	−	20.2011i	0.746655	−	1.29324i
$245$		0			0
$246$	−16.5066			−1.05242
$247$	10.5902	−	11.0056i	0.673836	−	0.700271i
$248$		0			0
$249$	−10.0000	+	17.3205i	−0.633724	+	1.09764i
$250$		0			0
$251$	−10.1180	−	17.5249i	−0.638645	−	1.10616i	−0.985730	−	0.168332i	$-0.946162\pi$
$251$	−10.1180	−	17.5249i	−0.638645	−	1.10616i	0.347086	−	0.937833i	$-0.387171\pi$
$252$	13.7082			0.863536
$253$	−0.444272	−	0.769502i	−0.0279311	−	0.0483781i
$254$	−1.30902	−	2.26728i	−0.0821350	−	0.142262i
$255$		0			0
$256$	3.28115	+	5.68312i	0.205072	+	0.355195i
$257$	8.73607	−	15.1313i	0.544941	−	0.943865i	−0.453670	−	0.891170i	$-0.649885\pi$
$257$	8.73607	−	15.1313i	0.544941	−	0.943865i	0.998611	−	0.0526955i	$-0.0167813\pi$
$258$	4.30902	−	7.46344i	0.268268	−	0.464653i
$259$	12.7082			0.789649
$260$		0			0
$261$	−14.9443			−0.925027
$262$	3.70820	−	6.42280i	0.229094	−	0.396802i
$263$	1.88197	−	3.25966i	0.116047	−	0.200999i	−0.802151	−	0.597122i	$-0.796311\pi$
$263$	1.88197	−	3.25966i	0.116047	−	0.200999i	0.918198	+	0.396122i	$0.129644\pi$
$264$	0.590170	+	1.02220i	0.0363224	+	0.0629123i
$265$		0			0
$266$	5.54508	+	9.60437i	0.339991	+	0.588882i
$267$	−10.0623	−	17.4284i	−0.615803	−	1.06660i
$268$	−4.38197			−0.267671
$269$	3.26393	+	5.65330i	0.199005	+	0.344688i	0.948206	−	0.317655i	$-0.102896\pi$
$269$	3.26393	+	5.65330i	0.199005	+	0.344688i	−0.749201	+	0.662343i	$0.769562\pi$
$270$		0			0
$271$	−0.645898	+	1.11873i	−0.0392355	+	0.0679579i	−0.884976	−	0.465636i	$-0.845826\pi$
$271$	−0.645898	+	1.11873i	−0.0392355	+	0.0679579i	0.845741	+	0.533594i	$0.179159\pi$
$272$	6.43769			0.390343
$273$	9.47214	+	32.8124i	0.573280	+	1.98590i
$274$	−0.909830			−0.0549648
$275$		0			0
$276$	6.80902	−	11.7936i	0.409855	−	0.709889i
$277$	8.44427	+	14.6259i	0.507367	+	0.878786i	0.999964	+	0.00852782i	$0.00271452\pi$
$277$	8.44427	+	14.6259i	0.507367	+	0.878786i	−0.492597	+	0.870258i	$0.663952\pi$
$278$	−10.3262			−0.619327
$279$		0			0
$280$		0			0
$281$	−15.8885			−0.947831			−0.473916	−	0.880570i	$-0.657160\pi$
$281$	−15.8885			−0.947831			−0.473916	+	0.880570i	$0.657160\pi$
$282$	3.41641	+	5.91739i	0.203444	+	0.352376i
$283$	−5.35410	+	9.27358i	−0.318268	+	0.551257i	−0.980127	−	0.198372i	$-0.936435\pi$
$283$	−5.35410	+	9.27358i	−0.318268	+	0.551257i	0.661859	+	0.749629i	$0.269768\pi$
$284$	−5.04508	+	8.73834i	−0.299371	+	0.518525i
$285$		0			0
$286$	−0.364745	+	0.379054i	−0.0215678	+	0.0224139i
$287$	−50.5967			−2.98663
$288$	−5.61803	+	9.73072i	−0.331046	+	0.573388i
$289$	2.47214	−	4.28187i	0.145420	−	0.251874i
$290$		0			0
$291$	−7.76393			−0.455130
$292$	4.85410	+	8.40755i	0.284065	+	0.492015i
$293$	−14.9721	−	25.9325i	−0.874682	−	1.51499i	−0.857102	−	0.515147i	$-0.827737\pi$
$293$	−14.9721	−	25.9325i	−0.874682	−	1.51499i	−0.0175799	−	0.999845i	$-0.505596\pi$
$294$	−15.1246			−0.882085
$295$		0			0
$296$	−3.35410	+	5.80948i	−0.194953	+	0.337669i
$297$	0.263932	−	0.457144i	0.0153149	−	0.0265262i
$298$	2.79837			0.162105
$299$	13.1738	+	3.25966i	0.761858	+	0.188511i
$300$		0			0
$301$	13.2082	−	22.8773i	0.761308	−	1.31862i
$302$	−2.47214	+	4.28187i	−0.142255	+	0.246394i
$303$	0.590170	+	1.02220i	0.0339044	+	0.0587241i
$304$	7.85410			0.450464
$305$		0			0
$306$	−2.14590	−	3.71680i	−0.122673	−	0.212476i
$307$	−24.9443			−1.42364			−0.711822	−	0.702360i	$-0.752130\pi$
$307$	−24.9443			−1.42364			−0.711822	+	0.702360i	$0.752130\pi$
$308$	0.809017	+	1.40126i	0.0460980	+	0.0798441i
$309$	−14.4721	+	25.0665i	−0.823291	+	1.42598i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	−17.5000	−	4.33013i	−0.990742	−	0.245145i
$313$	−3.88854			−0.219793			−0.109897	−	0.993943i	$-0.535052\pi$
$313$	−3.88854			−0.219793			−0.109897	+	0.993943i	$0.535052\pi$
$314$	−5.56231	+	9.63420i	−0.313899	+	0.543689i
$315$		0			0
$316$		0			0
$317$	11.8885			0.667727			0.333864	−	0.942621i	$-0.391648\pi$
$317$	11.8885			0.667727			0.333864	+	0.942621i	$0.391648\pi$
$318$	−4.14590	−	7.18091i	−0.232490	−	0.402685i
$319$	−0.881966	−	1.52761i	−0.0493806	−	0.0855297i
$320$		0			0
$321$	6.44427	+	11.1618i	0.359684	+	0.622991i
$322$	−4.92705	+	8.53390i	−0.274574	+	0.475576i
$323$	−7.35410	+	12.7377i	−0.409193	+	0.708743i
$324$	17.7984			0.988799
$325$		0			0
$326$	−9.09017			−0.503458
$327$	−2.23607	+	3.87298i	−0.123655	+	0.214176i
$328$	13.3541	−	23.1300i	0.737357	−	1.27714i
$329$	10.4721	+	18.1383i	0.577348	+	0.999995i
$330$		0			0
$331$	2.82624	+	4.89519i	0.155344	+	0.269064i	0.933184	−	0.359398i	$-0.117018\pi$
$331$	2.82624	+	4.89519i	0.155344	+	0.269064i	−0.777840	+	0.628462i	$0.783685\pi$
$332$	−7.23607	−	12.5332i	−0.397131	−	0.687851i
$333$	−6.00000			−0.328798
$334$	−5.30902	−	9.19549i	−0.290496	−	0.503155i
$335$		0			0
$336$	−8.78115	+	15.2094i	−0.479051	+	0.829741i
$337$	7.88854			0.429716			0.214858	−	0.976645i	$-0.431071\pi$
$337$	7.88854			0.429716			0.214858	+	0.976645i	$0.431071\pi$
$338$	−0.309017	−	8.02850i	−0.0168083	−	0.436693i
$339$	3.29180			0.178786
$340$		0			0
$341$		0			0
$342$	−2.61803	−	4.53457i	−0.141567	−	0.245201i
$343$	−16.7082			−0.902158
$344$	6.97214	+	12.0761i	0.375912	+	0.651099i
$345$		0			0
$346$	11.6738			0.627585
$347$	15.3541	+	26.5941i	0.824251	+	1.42765i	0.902490	+	0.430711i	$0.141737\pi$
$347$	15.3541	+	26.5941i	0.824251	+	1.42765i	−0.0782387	+	0.996935i	$0.524930\pi$
$348$	13.5172	−	23.4125i	0.724599	−	1.25504i
$349$	−1.20820	+	2.09267i	−0.0646737	+	0.112018i	−0.896549	−	0.442944i	$-0.853934\pi$
$349$	−1.20820	+	2.09267i	−0.0646737	+	0.112018i	0.831876	+	0.554962i	$0.187267\pi$
$350$		0			0
$351$	2.23607	+	7.74597i	0.119352	+	0.413449i
$352$	−1.32624			−0.0706887
$353$	−9.73607	+	16.8634i	−0.518199	+	0.897546i	0.481578	+	0.876403i	$0.340064\pi$
$353$	−9.73607	+	16.8634i	−0.518199	+	0.897546i	−0.999776	+	0.0211430i	$0.993269\pi$
$354$	−0.489357	+	0.847591i	−0.0260090	+	0.0450490i
$355$		0			0
$356$	14.5623			0.771801
$357$	−16.4443	−	28.4823i	−0.870323	−	1.50744i
$358$	2.54508	+	4.40822i	0.134512	+	0.232981i
$359$	17.8885			0.944121			0.472061	−	0.881566i	$-0.343510\pi$
$359$	17.8885			0.944121			0.472061	+	0.881566i	$0.343510\pi$
$360$		0			0
$361$	0.527864	−	0.914287i	0.0277823	−	0.0481204i
$362$	−1.85410	+	3.21140i	−0.0974494	+	0.168787i
$363$	24.4721			1.28445
$364$	−23.9894	−	5.93583i	−1.25738	−	0.311122i
$365$		0			0
$366$	9.96149	−	17.2538i	0.520696	−	0.901871i
$367$	2.82624	−	4.89519i	0.147528	−	0.255527i	−0.782785	−	0.622292i	$-0.786202\pi$
$367$	2.82624	−	4.89519i	0.147528	−	0.255527i	0.930313	+	0.366766i	$0.119535\pi$
$368$	3.48936	+	6.04374i	0.181895	+	0.315052i
$369$	23.8885			1.24359
$370$		0			0
$371$	−12.7082	−	22.0113i	−0.659777	−	1.14277i
$372$		0			0
$373$	13.9721	+	24.2004i	0.723450	+	1.25305i	0.959609	+	0.281337i	$0.0907780\pi$
$373$	13.9721	+	24.2004i	0.723450	+	1.25305i	−0.236159	+	0.971714i	$0.575889\pi$
$374$	0.253289	−	0.438709i	0.0130973	−	0.0226851i
$375$		0			0
$376$	−11.0557			−0.570156
$377$	26.1525	+	6.47106i	1.34692	+	0.333277i
$378$	−5.85410			−0.301103
$379$	−5.40983	+	9.37010i	−0.277884	+	0.481310i	−0.970859	−	0.239652i	$-0.922967\pi$
$379$	−5.40983	+	9.37010i	−0.277884	+	0.481310i	0.692974	+	0.720962i	$0.256300\pi$
$380$		0			0
$381$	4.73607	+	8.20311i	0.242636	+	0.420258i
$382$	−16.7984			−0.859480
$383$	2.11803	+	3.66854i	0.108226	+	0.187454i	0.915052	−	0.403336i	$-0.132149\pi$
$383$	2.11803	+	3.66854i	0.108226	+	0.187454i	−0.806825	+	0.590790i	$0.798816\pi$
$384$	−12.7254	−	22.0411i	−0.649392	−	1.12478i
$385$		0			0
$386$	−1.07295	−	1.85840i	−0.0546117	−	0.0945902i
$387$	−6.23607	+	10.8012i	−0.316997	+	0.549055i
$388$	2.80902	−	4.86536i	0.142606	−	0.247001i
$389$	−0.111456			−0.00565105			−0.00282553	−	0.999996i	$-0.500899\pi$
$389$	−0.111456			−0.00565105			−0.00282553	+	0.999996i	$0.500899\pi$
$390$		0			0
$391$	−13.0689			−0.660922
$392$	12.2361	−	21.1935i	0.618015	−	1.07043i
$393$	−13.4164	+	23.2379i	−0.676768	+	1.17220i
$394$	0.927051	+	1.60570i	0.0467042	+	0.0808940i
$395$		0			0
$396$	−0.381966	−	0.661585i	−0.0191945	−	0.0332459i
$397$	13.9721	+	24.2004i	0.701241	+	1.21459i	0.968031	+	0.250831i	$0.0807038\pi$
$397$	13.9721	+	24.2004i	0.701241	+	1.21459i	−0.266790	+	0.963755i	$0.585963\pi$
$398$	−0.798374			−0.0400189
$399$	−20.0623	−	34.7489i	−1.00437	−	1.73962i
$400$		0			0
$401$	−4.44427	+	7.69770i	−0.221936	+	0.384405i	−0.955396	−	0.295328i	$-0.904571\pi$
$401$	−4.44427	+	7.69770i	−0.221936	+	0.384405i	0.733460	+	0.679733i	$0.237904\pi$
$402$	−3.74265			−0.186666
$403$		0			0
$404$	−0.854102			−0.0424932
$405$		0			0
$406$	−9.78115	+	16.9415i	−0.485430	+	0.840790i
$407$	−0.354102	−	0.613323i	−0.0175522	−	0.0304013i
$408$	17.3607			0.859482
$409$	−12.4443	−	21.5541i	−0.615330	−	1.06578i	−0.990327	−	0.138756i	$-0.955690\pi$
$409$	−12.4443	−	21.5541i	−0.615330	−	1.06578i	0.374997	−	0.927026i	$-0.377644\pi$
$410$		0			0
$411$	3.29180			0.162372
$412$	−10.4721	−	18.1383i	−0.515925	−	0.893609i
$413$	−1.50000	+	2.59808i	−0.0738102	+	0.127843i
$414$	2.32624	−	4.02916i	0.114328	−	0.198023i
$415$		0			0
$416$	14.0451	−	14.5961i	0.688617	−	0.715632i
$417$	37.3607			1.82956
$418$	0.309017	−	0.535233i	0.0151145	−	0.0261791i
$419$	−8.82624	+	15.2875i	−0.431190	+	0.746843i	−0.996976	−	0.0777091i	$-0.975239\pi$
$419$	−8.82624	+	15.2875i	−0.431190	+	0.746843i	0.565786	+	0.824552i	$0.308573\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	4.07295	+	7.05455i	0.198268	+	0.343410i
$423$	−4.94427	−	8.56373i	−0.240399	−	0.416383i
$424$	13.4164			0.651558
$425$		0			0
$426$	−4.30902	+	7.46344i	−0.208773	+	0.361605i
$427$	30.5344	−	52.8872i	1.47767	−	2.55939i
$428$	−9.32624			−0.450801
$429$	1.31966	−	1.37143i	0.0637138	−	0.0662133i
$430$		0			0
$431$	−13.5902	+	23.5389i	−0.654615	+	1.13383i	0.327375	+	0.944895i	$0.393836\pi$
$431$	−13.5902	+	23.5389i	−0.654615	+	1.13383i	−0.981990	+	0.188933i	$0.939497\pi$
$432$	−2.07295	+	3.59045i	−0.0997348	+	0.172746i
$433$	−7.26393	−	12.5815i	−0.349082	−	0.604628i	0.637004	−	0.770860i	$-0.280173\pi$
$433$	−7.26393	−	12.5815i	−0.349082	−	0.604628i	−0.986087	+	0.166232i	$0.946840\pi$
$434$		0			0
$435$		0			0
$436$	−1.61803	−	2.80252i	−0.0774898	−	0.134216i
$437$	−15.9443			−0.762718
$438$	4.14590	+	7.18091i	0.198099	+	0.343117i
$439$	11.3541	−	19.6659i	0.541902	−	0.938601i	−0.456893	−	0.889522i	$-0.651038\pi$
$439$	11.3541	−	19.6659i	0.541902	−	0.938601i	0.998795	−	0.0490797i	$-0.0156288\pi$
$440$		0			0
$441$	21.8885			1.04231
$442$	2.14590	+	7.43361i	0.102070	+	0.353581i
$443$	−0.944272			−0.0448637			−0.0224319	−	0.999748i	$-0.507141\pi$
$443$	−0.944272			−0.0448637			−0.0224319	+	0.999748i	$0.507141\pi$
$444$	5.42705	−	9.39993i	0.257556	−	0.446101i
$445$		0			0
$446$	0.218847	+	0.379054i	0.0103627	+	0.0179487i
$447$	−10.1246			−0.478878
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−1.97214	−	3.41584i	−0.0930709	−	0.161203i	0.815731	−	0.578431i	$-0.196335\pi$
$449$	−1.97214	−	3.41584i	−0.0930709	−	0.161203i	−0.908802	+	0.417228i	$0.863002\pi$
$450$		0			0
$451$	1.40983	+	2.44190i	0.0663863	+	0.114984i
$452$	−1.19098	+	2.06284i	−0.0560191	+	0.0970280i
$453$	8.94427	−	15.4919i	0.420239	−	0.727875i
$454$	3.85410			0.180882
$455$		0			0
$456$	21.1803			0.991860
$457$	−0.791796	+	1.37143i	−0.0370387	+	0.0641528i	−0.883950	−	0.467580i	$-0.845126\pi$
$457$	−0.791796	+	1.37143i	−0.0370387	+	0.0641528i	0.846912	+	0.531733i	$0.178459\pi$
$458$	−4.90983	+	8.50408i	−0.229421	+	0.397369i
$459$	−3.88197	−	6.72376i	−0.181195	−	0.313838i
$460$		0			0
$461$	0.791796	+	1.37143i	0.0368776	+	0.0638739i	0.883875	−	0.467723i	$-0.154925\pi$
$461$	0.791796	+	1.37143i	0.0368776	+	0.0638739i	−0.846998	+	0.531597i	$0.821592\pi$
$462$	0.690983	+	1.19682i	0.0321474	+	0.0556810i
$463$	−11.0557			−0.513803			−0.256902	−	0.966438i	$-0.582702\pi$
$463$	−11.0557			−0.513803			−0.256902	+	0.966438i	$0.582702\pi$
$464$	6.92705	+	11.9980i	0.321580	+	0.556993i
$465$		0			0
$466$	−4.90983	+	8.50408i	−0.227443	+	0.393944i
$467$	−8.94427			−0.413892			−0.206946	−	0.978352i	$-0.566352\pi$
$467$	−8.94427			−0.413892			−0.206946	+	0.978352i	$0.566352\pi$
$468$	11.3262	+	2.80252i	0.523556	+	0.129546i
$469$	−11.4721			−0.529734
$470$		0			0
$471$	20.1246	−	34.8569i	0.927293	−	1.60612i
$472$	−0.791796	−	1.37143i	−0.0364454	−	0.0631252i
$473$	−1.47214			−0.0676889
$474$		0			0
$475$		0			0
$476$	23.7984			1.09080
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	8.00000	−	13.8564i	0.365911	−	0.633777i
$479$	−16.0623	+	27.8207i	−0.733905	+	1.27116i	0.221296	+	0.975207i	$0.428971\pi$
$479$	−16.0623	+	27.8207i	−0.733905	+	1.27116i	−0.955202	+	0.295955i	$0.904362\pi$
$480$		0			0
$481$	10.5000	+	2.59808i	0.478759	+	0.118462i
$482$	9.27051			0.422260
$483$	17.8262	−	30.8759i	0.811122	−	1.40490i
$484$	−8.85410	+	15.3358i	−0.402459	+	0.697080i
$485$		0			0
$486$	11.0557			0.501498
$487$	7.06231	+	12.2323i	0.320024	+	0.554297i	0.980493	−	0.196556i	$-0.0629758\pi$
$487$	7.06231	+	12.2323i	0.320024	+	0.554297i	−0.660469	+	0.750853i	$0.729642\pi$
$488$	16.1180	+	27.9173i	0.729629	+	1.26375i
$489$	32.8885			1.48727
$490$		0			0
$491$	0.118034	−	0.204441i	0.00532680	−	0.00922629i	−0.863350	−	0.504606i	$-0.831638\pi$
$491$	0.118034	−	0.204441i	0.00532680	−	0.00922629i	0.868677	+	0.495380i	$0.164971\pi$
$492$	−21.6074	+	37.4251i	−0.974136	+	1.68725i
$493$	−25.9443			−1.16847
$494$	2.61803	+	9.06914i	0.117791	+	0.408040i
$495$		0			0
$496$		0			0
$497$	−13.2082	+	22.8773i	−0.592469	+	1.02619i
$498$	−6.18034	−	10.7047i	−0.276948	−	0.479687i
$499$	−21.8885			−0.979866			−0.489933	−	0.871760i	$-0.662979\pi$
$499$	−21.8885			−0.979866			−0.489933	+	0.871760i	$0.662979\pi$
$500$		0			0
$501$	19.2082	+	33.2696i	0.858159	+	1.48638i
$502$	12.5066			0.558196
$503$	4.59017	+	7.95041i	0.204666	+	0.354491i	0.950026	−	0.312170i	$-0.101056\pi$
$503$	4.59017	+	7.95041i	0.204666	+	0.354491i	−0.745361	+	0.666662i	$0.767723\pi$
$504$	−9.47214	+	16.4062i	−0.421922	+	0.730791i
$505$		0			0
$506$	0.549150			0.0244127
$507$	1.11803	+	29.0474i	0.0496536	+	1.29004i
$508$	−6.85410			−0.304102
$509$	16.6803	−	28.8912i	0.739343	−	1.28058i	−0.213448	−	0.976954i	$-0.568470\pi$
$509$	16.6803	−	28.8912i	0.739343	−	1.28058i	0.952791	−	0.303625i	$-0.0981971\pi$
$510$		0			0
$511$	12.7082	+	22.0113i	0.562178	+	0.973721i
$512$	18.7082			0.826794
$513$	−4.73607	−	8.20311i	−0.209103	−	0.362176i
$514$	5.39919	+	9.35167i	0.238148	+	0.412484i
$515$		0			0
$516$	−11.2812	−	19.5395i	−0.496625	−	0.860180i
$517$	0.583592	−	1.01081i	0.0256664	−	0.0444554i
$518$	−3.92705	+	6.80185i	−0.172545	+	0.298856i
$519$	−42.2361			−1.85396
$520$		0			0
$521$	29.7771			1.30456			0.652279	−	0.757979i	$-0.273813\pi$
$521$	29.7771			1.30456			0.652279	+	0.757979i	$0.273813\pi$
$522$	4.61803	−	7.99867i	0.202126	−	0.350092i
$523$	2.64590	−	4.58283i	0.115697	−	0.200393i	−0.802361	−	0.596839i	$-0.796423\pi$
$523$	2.64590	−	4.58283i	0.115697	−	0.200393i	0.918058	+	0.396446i	$0.129756\pi$
$524$	−9.70820	−	16.8151i	−0.424105	−	0.734571i
$525$		0			0
$526$	1.16312	+	2.01458i	0.0507144	+	0.0878399i
$527$		0			0
$528$	0.978714			0.0425930
$529$	4.41641	+	7.64944i	0.192018	+	0.332584i
$530$		0			0
$531$	0.708204	−	1.22665i	0.0307334	−	0.0532319i
$532$	29.0344			1.25880
$533$	−41.8050	−	10.3440i	−1.81077	−	0.448050i
$534$	12.4377			0.538232
$535$		0			0
$536$	3.02786	−	5.24441i	0.130784	−	0.226524i
$537$	−9.20820	−	15.9491i	−0.397363	−	0.688253i
$538$	−4.03444			−0.173937
$539$	1.29180	+	2.23746i	0.0556416	+	0.0963741i
$540$		0			0
$541$	−27.8885			−1.19902			−0.599511	−	0.800366i	$-0.704638\pi$
$541$	−27.8885			−1.19902			−0.599511	+	0.800366i	$0.704638\pi$
$542$	−0.399187	−	0.691412i	−0.0171465	−	0.0296987i
$543$	6.70820	−	11.6190i	0.287877	−	0.498617i
$544$	−9.75329	+	16.8932i	−0.418169	+	0.724290i
$545$		0			0
$546$	−20.4894	−	5.06980i	−0.876864	−	0.216967i
$547$	−18.8328			−0.805233			−0.402617	−	0.915369i	$-0.631899\pi$
$547$	−18.8328			−0.805233			−0.402617	+	0.915369i	$0.631899\pi$
$548$	−1.19098	+	2.06284i	−0.0508763	+	0.0881203i
$549$	−14.4164	+	24.9700i	−0.615277	+	1.06569i
$550$		0			0
$551$	−31.6525			−1.34844
$552$	9.40983	+	16.2983i	0.400509	+	0.693702i
$553$		0			0
$554$	−10.4377			−0.443455
$555$		0			0
$556$	−13.5172	+	23.4125i	−0.573258	+	0.992912i
$557$	−4.97214	+	8.61199i	−0.210676	+	0.364902i	−0.951926	−	0.306327i	$-0.900900\pi$
$557$	−4.97214	+	8.61199i	−0.210676	+	0.364902i	0.741250	+	0.671229i	$0.234233\pi$
$558$		0			0
$559$	15.5902	−	16.2018i	0.659394	−	0.685262i
$560$		0			0
$561$	−0.916408	+	1.58726i	−0.0386908	+	0.0670144i
$562$	4.90983	−	8.50408i	0.207109	−	0.358723i
$563$	15.3541	+	26.5941i	0.647098	+	1.12081i	0.983813	+	0.179200i	$0.0573510\pi$
$563$	15.3541	+	26.5941i	0.647098	+	1.12081i	−0.336714	+	0.941607i	$0.609316\pi$
$564$	17.8885			0.753244
$565$		0			0
$566$	−3.30902	−	5.73139i	−0.139088	−	0.240908i
$567$	46.5967			1.95688
$568$	−6.97214	−	12.0761i	−0.292544	−	0.506702i
$569$	−8.44427	+	14.6259i	−0.354002	+	0.613150i	−0.986947	−	0.161047i	$-0.948513\pi$
$569$	−8.44427	+	14.6259i	−0.354002	+	0.613150i	0.632944	+	0.774197i	$0.281846\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	0.381966	+	1.32317i	0.0159708	+	0.0553245i
$573$	60.7771			2.53900
$574$	15.6353	−	27.0811i	0.652603	−	1.13034i
$575$		0			0
$576$	0.236068	+	0.408882i	0.00983617	+	0.0170367i
$577$	−27.8885			−1.16102			−0.580508	−	0.814255i	$-0.697146\pi$
$577$	−27.8885			−1.16102			−0.580508	+	0.814255i	$0.697146\pi$
$578$	1.52786	+	2.64634i	0.0635508	+	0.110073i
$579$	3.88197	+	6.72376i	0.161329	+	0.279430i
$580$		0			0
$581$	−18.9443	−	32.8124i	−0.785941	−	1.36129i
$582$	2.39919	−	4.15551i	0.0994495	−	0.172252i
$583$	−0.708204	+	1.22665i	−0.0293308	+	0.0508025i
$584$	−13.4164			−0.555175
$585$		0			0
$586$	18.5066			0.764500
$587$	5.11803	−	8.86469i	0.211244	−	0.365885i	−0.740860	−	0.671659i	$-0.765582\pi$
$587$	5.11803	−	8.86469i	0.211244	−	0.365885i	0.952104	+	0.305774i	$0.0989152\pi$
$588$	−19.7984	+	34.2918i	−0.816471	+	1.41417i
$589$		0			0
$590$		0			0
$591$	−3.35410	−	5.80948i	−0.137969	−	0.238970i
$592$	2.78115	+	4.81710i	0.114305	+	0.197982i
$593$	7.88854			0.323944			0.161972	−	0.986795i	$-0.448215\pi$
$593$	7.88854			0.323944			0.161972	+	0.986795i	$0.448215\pi$
$594$	0.163119	+	0.282530i	0.00669285	+	0.0115924i
$595$		0			0
$596$	3.66312	−	6.34471i	0.150047	−	0.259889i
$597$	2.88854			0.118220
$598$	−5.81559	+	6.04374i	−0.237817	+	0.247147i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−21.9721	+	38.0569i	−0.896262	+	1.55237i	−0.0640274	+	0.997948i	$0.520394\pi$
$601$	−21.9721	+	38.0569i	−0.896262	+	1.55237i	−0.832235	+	0.554423i	$0.812939\pi$
$602$	8.16312	+	14.1389i	0.332704	+	0.576260i
$603$	5.41641			0.220573
$604$	6.47214	+	11.2101i	0.263347	+	0.456131i
$605$		0			0
$606$	−0.729490			−0.0296335
$607$	−0.354102	−	0.613323i	−0.0143726	−	0.0248940i	0.858750	−	0.512395i	$-0.171242\pi$
$607$	−0.354102	−	0.613323i	−0.0143726	−	0.0248940i	−0.873122	+	0.487501i	$0.837908\pi$
$608$	−11.8992	+	20.6100i	−0.482576	+	0.835846i
$609$	35.3885	−	61.2948i	1.43402	−	2.48379i
$610$		0			0
$611$	4.94427	+	17.1275i	0.200024	+	0.692903i
$612$	−11.2361			−0.454191
$613$	19.9721	−	34.5928i	0.806667	−	1.39719i	−0.108493	−	0.994097i	$-0.534602\pi$
$613$	19.9721	−	34.5928i	0.806667	−	1.39719i	0.915160	−	0.403091i	$-0.132064\pi$
$614$	7.70820	−	13.3510i	0.311078	−	0.538803i
$615$		0			0
$616$	−2.23607			−0.0900937
$617$	−20.2082	−	35.0016i	−0.813552	−	1.40911i	−0.910363	−	0.413810i	$-0.864198\pi$
$617$	−20.2082	−	35.0016i	−0.813552	−	1.40911i	0.0968116	−	0.995303i	$-0.469136\pi$
$618$	−8.94427	−	15.4919i	−0.359791	−	0.623177i
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$		0			0
$621$	4.20820	−	7.28882i	0.168869	−	0.292490i
$622$	7.41641	−	12.8456i	0.297371	−	0.515061i
$623$	38.1246			1.52743
$624$	−10.3647	+	10.7714i	−0.414922	+	0.431199i
$625$		0			0
$626$	1.20163	−	2.08128i	0.0480266	−	0.0831846i
$627$	−1.11803	+	1.93649i	−0.0446500	+	0.0773360i
$628$	14.5623	+	25.2227i	0.581099	+	1.00649i
$629$	−10.4164			−0.415329
$630$		0			0
$631$	8.06231	+	13.9643i	0.320955	+	0.555911i	0.980685	−	0.195592i	$-0.0626627\pi$
$631$	8.06231	+	13.9643i	0.320955	+	0.555911i	−0.659730	+	0.751503i	$0.729329\pi$
$632$		0			0
$633$	−14.7361	−	25.5236i	−0.585706	−	1.01447i
$634$	−3.67376	+	6.36314i	−0.145904	+	0.252713i
$635$		0			0
$636$	−21.7082			−0.860786
$637$	−38.3050	−	9.47802i	−1.51770	−	0.375533i
$638$	1.09017			0.0431602
$639$	6.23607	−	10.8012i	0.246695	−	0.427288i
$640$		0			0
$641$	−4.44427	−	7.69770i	−0.175538	−	0.304041i	0.764809	−	0.644257i	$-0.222833\pi$
$641$	−4.44427	−	7.69770i	−0.175538	−	0.304041i	−0.940347	+	0.340216i	$0.889500\pi$
$642$	−7.96556			−0.314376
$643$	−8.64590	−	14.9751i	−0.340961	−	0.590562i	0.643650	−	0.765320i	$-0.277419\pi$
$643$	−8.64590	−	14.9751i	−0.340961	−	0.590562i	−0.984611	+	0.174758i	$0.944086\pi$
$644$	12.8992	+	22.3420i	0.508299	+	0.880400i
$645$		0			0
$646$	−4.54508	−	7.87232i	−0.178824	−	0.309732i
$647$	1.29837	−	2.24885i	0.0510443	−	0.0884114i	−0.839374	−	0.543554i	$-0.817078\pi$
$647$	1.29837	−	2.24885i	0.0510443	−	0.0884114i	0.890419	+	0.455142i	$0.150412\pi$
$648$	−12.2984	+	21.3014i	−0.483126	+	0.836798i
$649$	0.167184			0.00656256
$650$		0			0
$651$		0			0
$652$	−11.8992	+	20.6100i	−0.466008	+	0.807150i
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	−0.994988	−	0.0999939i	$-0.968118\pi$
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	0.584091	+	0.811688i	$0.301451\pi$
$654$	−1.38197	−	2.39364i	−0.0540391	−	0.0935985i
$655$		0			0
$656$	−11.0729	−	19.1789i	−0.432326	−	0.748811i
$657$	−6.00000	−	10.3923i	−0.234082	−	0.405442i
$658$	−12.9443			−0.504620
$659$	21.8820	+	37.9007i	0.852400	+	1.47640i	0.879036	+	0.476756i	$0.158187\pi$
$659$	21.8820	+	37.9007i	0.852400	+	1.47640i	−0.0266355	+	0.999645i	$0.508479\pi$
$660$		0			0
$661$	20.6803	−	35.8194i	0.804372	−	1.39321i	−0.112342	−	0.993670i	$-0.535835\pi$
$661$	20.6803	−	35.8194i	0.804372	−	1.39321i	0.916714	−	0.399544i	$-0.130831\pi$
$662$	−3.49342			−0.135776
$663$	−7.76393	−	26.8950i	−0.301526	−	1.04452i
$664$	20.0000			0.776151
$665$		0			0
$666$	1.85410	−	3.21140i	0.0718450	−	0.124439i
$667$	−14.0623	−	24.3566i	−0.544495	−	0.943092i
$668$	−27.7984			−1.07555
$669$	−0.791796	−	1.37143i	−0.0306126	−	0.0530226i
$670$		0			0
$671$	−3.40325			−0.131381
$672$	−26.6074	−	46.0854i	−1.02640	−	1.77778i
$673$	−4.79180	+	8.29963i	−0.184710	+	0.319927i	−0.943479	−	0.331433i	$-0.892468\pi$
$673$	−4.79180	+	8.29963i	−0.184710	+	0.319927i	0.758769	+	0.651360i	$0.225801\pi$
$674$	−2.43769	+	4.22221i	−0.0938965	+	0.162633i
$675$		0			0
$676$	−18.6074	−	9.80881i	−0.715669	−	0.377262i
$677$	−12.1115			−0.465481			−0.232741	−	0.972539i	$-0.574769\pi$
$677$	−12.1115			−0.465481			−0.232741	+	0.972539i	$0.574769\pi$
$678$	−1.01722	+	1.76188i	−0.0390661	+	0.0676645i
$679$	7.35410	−	12.7377i	0.282225	−	0.488827i
$680$		0			0
$681$	−13.9443			−0.534346
$682$		0			0
$683$	12.8820	+	22.3122i	0.492915	+	0.853753i	0.999967	−	0.00816213i	$-0.00259812\pi$
$683$	12.8820	+	22.3122i	0.492915	+	0.853753i	−0.507052	+	0.861915i	$0.669265\pi$
$684$	−13.7082			−0.524146
$685$		0			0
$686$	5.16312	−	8.94278i	0.197129	−	0.341437i
$687$	17.7639	−	30.7680i	0.677736	−	1.17387i
$688$	11.5623			0.440809
$689$	−6.00000	−	20.7846i	−0.228582	−	0.791831i
$690$		0			0
$691$	−19.2984	+	33.4258i	−0.734145	+	1.27158i	0.220953	+	0.975284i	$0.429083\pi$
$691$	−19.2984	+	33.4258i	−0.734145	+	1.27158i	−0.955098	+	0.296291i	$0.904250\pi$
$692$	15.2812	−	26.4677i	0.580902	−	1.00615i
$693$	−1.00000	−	1.73205i	−0.0379869	−	0.0657952i
$694$	−18.9787			−0.720422
$695$		0			0
$696$	18.6803	+	32.3553i	0.708076	+	1.22642i
$697$	41.4721			1.57087
$698$	−0.746711	−	1.29334i	−0.0282634	−	0.0489537i
$699$	17.7639	−	30.7680i	0.671894	−	1.16375i
$700$		0			0
$701$	7.88854			0.297946			0.148973	−	0.988841i	$-0.452403\pi$
$701$	7.88854			0.297946			0.148973	+	0.988841i	$0.452403\pi$
$702$	−4.83688	−	1.19682i	−0.182556	−	0.0451710i
$703$	−12.7082			−0.479299
$704$	−0.0278640	+	0.0482619i	−0.00105017	+	0.00181894i
$705$		0			0
$706$	−6.01722	−	10.4221i	−0.226461	−	0.392242i
$707$	−2.23607			−0.0840960
$708$	1.28115	+	2.21902i	0.0481487	+	0.0833960i
$709$	−12.1525	−	21.0487i	−0.456396	−	0.790501i	0.542371	−	0.840139i	$-0.317527\pi$
$709$	−12.1525	−	21.0487i	−0.456396	−	0.790501i	−0.998767	+	0.0496381i	$0.984193\pi$
$710$		0			0
$711$		0			0
$712$	−10.0623	+	17.4284i	−0.377101	+	0.653158i
$713$		0			0
$714$	20.3262			0.760690
$715$		0			0
$716$	13.3262			0.498025
$717$	−28.9443	+	50.1329i	−1.08094	+	1.87225i
$718$	−5.52786	+	9.57454i	−0.206298	+	0.357319i
$719$	16.0623	+	27.8207i	0.599023	+	1.03754i	0.992966	+	0.118403i	$0.0377775\pi$
$719$	16.0623	+	27.8207i	0.599023	+	1.03754i	−0.393943	+	0.919135i	$0.628889\pi$
$720$		0			0
$721$	−27.4164	−	47.4866i	−1.02104	−	1.76849i
$722$	0.326238	+	0.565061i	0.0121413	+	0.0210294i
$723$	−33.5410			−1.24740
$724$	4.85410	+	8.40755i	0.180401	+	0.312464i
$725$		0			0
$726$	−7.56231	+	13.0983i	−0.280663	+	0.486123i
$727$	−28.9443			−1.07348			−0.536742	−	0.843747i	$-0.680345\pi$
$727$	−28.9443			−1.07348			−0.536742	+	0.843747i	$0.680345\pi$
$728$	23.6803	−	24.6093i	0.877652	−	0.912082i
$729$	−7.00000			−0.259259
$730$		0			0
$731$	−10.8262	+	18.7516i	−0.400423	+	0.693553i
$732$	−26.0795	−	45.1711i	−0.963927	−	1.66957i
$733$	43.8885			1.62106			0.810530	−	0.585697i	$-0.199179\pi$
$733$	43.8885			1.62106			0.810530	+	0.585697i	$0.199179\pi$
$734$	1.74671	+	3.02539i	0.0644723	+	0.111669i
$735$		0			0
$736$	−21.1459			−0.779448
$737$	0.319660	+	0.553668i	0.0117748	+	0.0203946i
$738$	−7.38197	+	12.7859i	−0.271734	+	0.470657i
$739$	−13.7705	+	23.8512i	−0.506556	+	0.877381i	0.493415	+	0.869794i	$0.335748\pi$
$739$	−13.7705	+	23.8512i	−0.506556	+	0.877381i	−0.999971	+	0.00758729i	$0.997585\pi$
$740$		0			0
$741$	−9.47214	−	32.8124i	−0.347968	−	1.20540i
$742$	15.7082			0.576666
$743$	−19.0623	+	33.0169i	−0.699328	+	1.21127i	0.269372	+	0.963036i	$0.413184\pi$
$743$	−19.0623	+	33.0169i	−0.699328	+	1.21127i	−0.968700	+	0.248236i	$0.920149\pi$
$744$		0			0
$745$		0			0
$746$	−17.2705			−0.632318
$747$	8.94427	+	15.4919i	0.327254	+	0.566820i
$748$	−0.663119	−	1.14856i	−0.0242460	−	0.0419954i
$749$	−24.4164			−0.892156
$750$		0			0
$751$	15.3541	−	26.5941i	0.560279	−	0.970432i	−0.437193	−	0.899368i	$-0.644027\pi$
$751$	15.3541	−	26.5941i	0.560279	−	0.970432i	0.997472	−	0.0710640i	$-0.0226395\pi$
$752$	−4.58359	+	7.93901i	−0.167146	+	0.289506i
$753$	−45.2492			−1.64897
$754$	−11.5451	+	11.9980i	−0.420447	+	0.436942i
$755$		0			0
$756$	−7.66312	+	13.2729i	−0.278705	+	0.482731i
$757$	−3.44427	+	5.96565i	−0.125184	+	0.216825i	−0.921805	−	0.387654i	$-0.873286\pi$
$757$	−3.44427	+	5.96565i	−0.125184	+	0.216825i	0.796621	+	0.604479i	$0.206619\pi$
$758$	−3.34346	−	5.79104i	−0.121440	−	0.210340i
$759$	−1.98684			−0.0721179
$760$		0			0
$761$	18.9721	+	32.8607i	0.687739	+	1.19120i	0.972567	+	0.232621i	$0.0747302\pi$
$761$	18.9721	+	32.8607i	0.687739	+	1.19120i	−0.284828	+	0.958579i	$0.591937\pi$
$762$	−5.85410			−0.212072
$763$	−4.23607	−	7.33708i	−0.153356	−	0.265620i
$764$	−21.9894	+	38.0867i	−0.795547	+	1.37793i
$765$		0			0
$766$	−2.61803			−0.0945934
$767$	−1.77051	+	1.83997i	−0.0639294	+	0.0664374i
$768$	14.6738			0.529494
$769$	−14.9164	+	25.8360i	−0.537899	+	0.931669i	0.461118	+	0.887339i	$0.347449\pi$
$769$	−14.9164	+	25.8360i	−0.537899	+	0.931669i	−0.999017	+	0.0443301i	$0.985885\pi$
$770$		0			0
$771$	−19.5344	−	33.8346i	−0.703516	−	1.21853i
$772$	−5.61803			−0.202197
$773$	−10.0279	−	17.3688i	−0.360677	−	0.624711i	0.627395	−	0.778701i	$-0.284121\pi$
$773$	−10.0279	−	17.3688i	−0.360677	−	0.624711i	−0.988072	+	0.153990i	$0.950788\pi$
$774$	−3.85410	−	6.67550i	−0.138533	−	0.239946i
$775$		0			0
$776$	3.88197	+	6.72376i	0.139354	+	0.241369i
$777$	14.2082	−	24.6093i	0.509716	−	0.882855i
$778$	0.0344419	−	0.0596550i	0.00123480	−	0.00213874i
$779$	50.5967			1.81282
$780$		0			0
$781$	1.47214			0.0526772
$782$	4.03851	−	6.99490i	0.144417	−	0.250137i
$783$	8.35410	−	14.4697i	0.298551	−	0.517106i
$784$	−10.1459	−	17.5732i	−0.362354	−	0.627615i
$785$		0			0
$786$	−8.29180	−	14.3618i	−0.295759	−	0.512269i
$787$	14.7705	+	25.5833i	0.526512	+	0.911945i	0.999523	+	0.0308887i	$0.00983374\pi$
$787$	14.7705	+	25.5833i	0.526512	+	0.911945i	−0.473011	+	0.881057i	$0.656833\pi$
$788$	4.85410			0.172920
$789$	−4.20820	−	7.28882i	−0.149816	−	0.259489i
$790$		0			0
$791$	−3.11803	+	5.40059i	−0.110865	+	0.192023i
$792$	1.05573			0.0375137
$793$	36.0410	−	37.4549i	1.27985	−	1.33006i
$794$	−17.2705			−0.612907
$795$		0			0
$796$	−1.04508	+	1.81014i	−0.0370421	+	0.0641587i
$797$	26.9164	+	46.6206i	0.953428	+	1.65139i	0.737925	+	0.674883i	$0.235806\pi$
$797$	26.9164	+	46.6206i	0.953428	+	1.65139i	0.215503	+	0.976503i	$0.430861\pi$
$798$	24.7984			0.877853
$799$	−8.58359	−	14.8672i	−0.303666	−	0.525964i
$800$		0			0
$801$	−18.0000			−0.635999
$802$	−2.74671	−	4.75744i	−0.0969897	−	0.167991i
$803$	0.708204	−	1.22665i	0.0249920	−	0.0432874i
$804$	−4.89919	+	8.48564i	−0.172781	+	0.299265i
$805$		0			0
$806$		0			0
$807$	14.5967			0.513830
$808$	0.590170	−	1.02220i	0.0207621	−	0.0359610i
$809$	1.44427	−	2.50155i	0.0507779	−	0.0879499i	−0.839519	−	0.543330i	$-0.817163\pi$
$809$	1.44427	−	2.50155i	0.0507779	−	0.0879499i	0.890297	+	0.455380i	$0.150497\pi$
$810$		0			0
$811$	31.7771			1.11584			0.557922	−	0.829893i	$-0.311599\pi$
$811$	31.7771			1.11584			0.557922	+	0.829893i	$0.311599\pi$
$812$	25.6074	+	44.3533i	0.898643	+	1.55650i
$813$	1.44427	+	2.50155i	0.0506528	+	0.0877333i
$814$	0.437694			0.0153412
$815$		0			0
$816$	7.19756	−	12.4665i	0.251965	−	0.436416i
$817$	−13.2082	+	22.8773i	−0.462097	+	0.800375i
$818$	15.3820			0.537818
$819$	29.6525	+	7.33708i	1.03614	+	0.256378i
$820$		0			0
$821$	12.6803	−	21.9630i	0.442547	−	0.766514i	−0.555331	−	0.831630i	$-0.687408\pi$
$821$	12.6803	−	21.9630i	0.442547	−	0.766514i	0.997878	+	0.0651158i	$0.0207417\pi$
$822$	−1.01722	+	1.76188i	−0.0354797	+	0.0614526i
$823$	−13.2984	−	23.0335i	−0.463552	−	0.802896i	0.535583	−	0.844483i	$-0.320092\pi$
$823$	−13.2984	−	23.0335i	−0.463552	−	0.802896i	−0.999135	+	0.0415869i	$0.986759\pi$
$824$	28.9443			1.00832
$825$		0			0
$826$	−0.927051	−	1.60570i	−0.0322562	−	0.0558694i
$827$	8.94427			0.311023			0.155511	−	0.987834i	$-0.450297\pi$
$827$	8.94427			0.311023			0.155511	+	0.987834i	$0.450297\pi$
$828$	−6.09017	−	10.5485i	−0.211648	−	0.366585i
$829$	21.6246	−	37.4549i	0.751054	−	1.30086i	−0.196259	−	0.980552i	$-0.562879\pi$
$829$	21.6246	−	37.4549i	0.751054	−	1.30086i	0.947312	−	0.320311i	$-0.103787\pi$
$830$		0			0
$831$	37.7639			1.31002
$832$	−0.236068	−	0.817763i	−0.00818418	−	0.0283508i
$833$	38.0000			1.31662
$834$	−11.5451	+	19.9967i	−0.399774	+	0.692428i
$835$		0			0
$836$	−0.809017	−	1.40126i	−0.0279804	−	0.0484635i
$837$		0			0
$838$	−5.45492	−	9.44819i	−0.188437	−	0.326382i
$839$	−15.3541	−	26.5941i	−0.530082	−	0.918130i	−0.999384	−	0.0350918i	$-0.988828\pi$
$839$	−15.3541	−	26.5941i	−0.530082	−	0.918130i	0.469302	−	0.883038i	$-0.344506\pi$
$840$		0			0
$841$	−13.4164	−	23.2379i	−0.462635	−	0.801307i
$842$	−1.85410	+	3.21140i	−0.0638966	+	0.110672i
$843$	−17.7639	+	30.7680i	−0.611822	+	1.05971i
$844$	21.3262			0.734079
$845$		0			0
$846$	6.11146			0.210116
$847$	−23.1803	+	40.1495i	−0.796486	+	1.37955i
$848$	5.56231	−	9.63420i	0.191010	−	0.330840i
$849$	11.9721	+	20.7363i	0.410883	+	0.711670i
$850$		0			0
$851$	−5.64590	−	9.77898i	−0.193539	−	0.335219i
$852$	11.2812	+	19.5395i	0.386486	+	0.669413i
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$	18.8713	+	32.6861i	0.645763	+	1.11849i
$855$		0			0
$856$	6.44427	−	11.1618i	0.220261	−	0.381503i
$857$	−35.8885			−1.22593			−0.612965	−	0.790110i	$-0.710023\pi$
$857$	−35.8885			−1.22593			−0.612965	+	0.790110i	$0.710023\pi$
$858$	0.326238	+	1.13012i	0.0111376	+	0.0385817i
$859$	21.8885			0.746827			0.373414	−	0.927665i	$-0.378187\pi$
$859$	21.8885			0.746827			0.373414	+	0.927665i	$0.378187\pi$
$860$		0			0
$861$	−56.5689	+	97.9802i	−1.92786	+	3.33916i
$862$	−8.39919	−	14.5478i	−0.286077	−	0.495501i
$863$	−14.8328			−0.504915			−0.252457	−	0.967608i	$-0.581239\pi$
$863$	−14.8328			−0.504915			−0.252457	+	0.967608i	$0.581239\pi$
$864$	−6.28115	−	10.8793i	−0.213689	−	0.370120i
$865$		0			0
$866$	8.97871			0.305109
$867$	−5.52786	−	9.57454i	−0.187736	−	0.325168i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−9.47871	−	2.34537i	−0.321174	−	0.0794699i
$872$	4.47214			0.151446
$873$	−3.47214	+	6.01392i	−0.117514	+	0.203540i
$874$	4.92705	−	8.53390i	0.166660	−	0.288664i
$875$		0			0
$876$	21.7082			0.733452
$877$	−16.8607	−	29.2036i	−0.569345	−	0.986134i	−0.996631	−	0.0820175i	$-0.973864\pi$
$877$	−16.8607	−	29.2036i	−0.569345	−	0.986134i	0.427286	−	0.904116i	$-0.359470\pi$
$878$	7.01722	+	12.1542i	0.236820	+	0.410184i
$879$	−66.9574			−2.25842
$880$		0			0
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	−0.964263	−	0.264946i	$-0.914646\pi$
$881$	−7.50000	+	12.9904i	−0.252681	+	0.437657i	0.711582	+	0.702603i	$0.247979\pi$
$882$	−6.76393	+	11.7155i	−0.227753	+	0.394481i
$883$	42.8328			1.44144			0.720720	−	0.693227i	$-0.243812\pi$
$883$	42.8328			1.44144			0.720720	+	0.693227i	$0.243812\pi$
$884$	19.6631	+	4.86536i	0.661342	+	0.163640i
$885$		0			0
$886$	0.291796	−	0.505406i	0.00980308	−	0.0169794i
$887$	22.2426	−	38.5254i	0.746835	−	1.29356i	−0.202498	−	0.979283i	$-0.564906\pi$
$887$	22.2426	−	38.5254i	0.746835	−	1.29356i	0.949333	−	0.314273i	$-0.101761\pi$
$888$	7.50000	+	12.9904i	0.251684	+	0.435929i
$889$	−17.9443			−0.601832
$890$		0			0
$891$	−1.29837	−	2.24885i	−0.0434972	−	0.0753393i
$892$	1.14590			0.0383675
$893$	−10.4721	−	18.1383i	−0.350437	−	0.606974i
$894$	3.12868	−	5.41903i	0.104639	−	0.181239i
$895$		0			0
$896$	48.2148			1.61074
$897$	21.0410	−	21.8665i	0.702539	−	0.730100i
$898$	2.43769			0.0813469
$899$		0			0
$900$		0			0
$901$	10.4164	+	18.0417i	0.347021	+	0.601058i
$902$	−1.74265			−0.0580238
$903$	−29.5344	−	51.1552i	−0.982845	−	1.70234i
$904$	−1.64590	−	2.85078i	−0.0547418	−	0.0948155i
$905$		0			0
$906$	5.52786	+	9.57454i	0.183651	+	0.318093i
$907$	10.0623	−	17.4284i	0.334113	−	0.578701i	−0.649201	−	0.760617i	$-0.724896\pi$
$907$	10.0623	−	17.4284i	0.334113	−	0.578701i	0.983314	+	0.181916i	$0.0582298\pi$
$908$	5.04508	−	8.73834i	0.167427	−	0.289992i
$909$	1.05573			0.0350163
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	8.78115	−	15.2094i	0.290773	−	0.503634i
$913$	−1.05573	+	1.82857i	−0.0349395	+	0.0605170i
$914$	−0.489357	−	0.847591i	−0.0161865	−	0.0280358i
$915$		0			0
$916$	12.8541	+	22.2640i	0.424711	+	0.735622i
$917$	−25.4164	−	44.0225i	−0.839324	−	1.45375i
$918$	4.79837			0.158370
$919$	−23.3541	−	40.4505i	−0.770381	−	1.33434i	−0.937354	−	0.348377i	$-0.886733\pi$
$919$	−23.3541	−	40.4505i	−0.770381	−	1.33434i	0.166974	−	0.985961i	$-0.446601\pi$
$920$		0			0
$921$	−27.8885	+	48.3044i	−0.918959	+	1.59168i
$922$	−0.978714			−0.0322322
$923$	−15.5902	+	16.2018i	−0.513157	+	0.533288i
$924$	3.61803			0.119025
$925$		0			0
$926$	3.41641	−	5.91739i	0.112270	−	0.194458i
$927$	12.9443	+	22.4201i	0.425146	+	0.736374i
$928$	−41.9787			−1.37802
$929$	−9.97214	−	17.2722i	−0.327175	−	0.566684i	0.654775	−	0.755824i	$-0.272763\pi$
$929$	−9.97214	−	17.2722i	−0.327175	−	0.566684i	−0.981950	+	0.189140i	$0.939430\pi$
$930$		0			0
$931$	46.3607			1.51941
$932$	12.8541	+	22.2640i	0.421050	+	0.729280i
$933$	−26.8328	+	46.4758i	−0.878467	+	1.52155i
$934$	2.76393	−	4.78727i	0.0904386	−	0.156644i
$935$		0			0
$936$	−11.1803	+	11.6190i	−0.365441	+	0.379777i
$937$	6.00000			0.196011			0.0980057	−	0.995186i	$-0.468754\pi$
$937$	6.00000			0.196011			0.0980057	+	0.995186i	$0.468754\pi$
$938$	3.54508	−	6.14027i	0.115751	−	0.200487i
$939$	−4.34752	+	7.53013i	−0.141876	+	0.245737i
$940$		0			0
$941$	−11.8885			−0.387555			−0.193778	−	0.981045i	$-0.562074\pi$
$941$	−11.8885			−0.387555			−0.193778	+	0.981045i	$0.562074\pi$
$942$	12.4377	+	21.5427i	0.405242	+	0.701900i
$943$	22.4787	+	38.9343i	0.732008	+	1.26787i
$944$	−1.31308			−0.0427372
$945$		0			0
$946$	0.454915	−	0.787936i	0.0147906	−	0.0256180i
$947$	19.5902	−	33.9312i	0.636595	−	1.10261i	−0.349580	−	0.936907i	$-0.613676\pi$
$947$	19.5902	−	33.9312i	0.636595	−	1.10261i	0.986175	−	0.165708i	$-0.0529910\pi$
$948$		0			0
$949$	6.00000	+	20.7846i	0.194768	+	0.674697i
$950$		0			0
$951$	13.2918	−	23.0221i	0.431016	−	0.746542i
$952$	−16.4443	+	28.4823i	−0.532962	+	0.923117i
$953$	21.0967	+	36.5406i	0.683391	+	1.18367i	0.973940	+	0.226807i	$0.0728288\pi$
$953$	21.0967	+	36.5406i	0.683391	+	1.18367i	−0.290549	+	0.956860i	$0.593838\pi$
$954$	−7.41641			−0.240115
$955$		0			0
$956$	−20.9443	−	36.2765i	−0.677386	−	1.17327i
$957$	−3.94427			−0.127500
$958$	−9.92705	−	17.1942i	−0.320728	−	0.555518i
$959$	−3.11803	+	5.40059i	−0.100687	+	0.174394i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−4.63525	+	4.81710i	−0.149447	+	0.155309i
$963$	11.5279			0.371480
$964$	12.1353	−	21.0189i	0.390850	−	0.676972i
$965$		0			0
$966$	11.0172	+	19.0824i	0.354473	+	0.613966i
$967$	54.8328			1.76330			0.881652	−	0.471900i	$-0.156432\pi$
$967$	54.8328			1.76330			0.881652	+	0.471900i	$0.156432\pi$
$968$	−12.2361	−	21.1935i	−0.393282	−	0.681185i
$969$	16.4443	+	28.4823i	0.528266	+	0.914984i
$970$		0			0
$971$	5.88197	+	10.1879i	0.188761	+	0.326944i	0.944838	−	0.327539i	$-0.106219\pi$
$971$	5.88197	+	10.1879i	0.188761	+	0.326944i	−0.756076	+	0.654484i	$0.772886\pi$
$972$	14.4721	−	25.0665i	0.464194	−	0.804008i
$973$	−35.3885	+	61.2948i	−1.13450	+	1.96502i
$974$	−8.72949			−0.279711
$975$		0			0
$976$	26.7295			0.855590
$977$	3.79180	−	6.56758i	0.121310	−	0.210116i	−0.798974	−	0.601365i	$-0.794624\pi$
$977$	3.79180	−	6.56758i	0.121310	−	0.210116i	0.920285	+	0.391250i	$0.127957\pi$
$978$	−10.1631	+	17.6030i	−0.324981	+	0.562883i
$979$	−1.06231	−	1.83997i	−0.0339514	−	0.0588056i
$980$		0			0
$981$	2.00000	+	3.46410i	0.0638551	+	0.110600i
$982$	0.0729490	+	0.126351i	0.00232790	+	0.00403204i
$983$	−38.8328			−1.23857			−0.619287	−	0.785165i	$-0.712578\pi$
$983$	−38.8328			−1.23857			−0.619287	+	0.785165i	$0.712578\pi$
$984$	−29.8607	−	51.7202i	−0.951924	−	1.64878i
$985$		0			0
$986$	8.01722	−	13.8862i	0.255320	−	0.442228i
$987$	46.8328			1.49070
$988$	23.9894	+	5.93583i	0.763203	+	0.188844i
$989$	−23.4721			−0.746371
$990$		0			0
$991$	23.3541	−	40.4505i	0.741867	−	1.28495i	−0.209777	−	0.977749i	$-0.567274\pi$
$991$	23.3541	−	40.4505i	0.741867	−	1.28495i	0.951644	−	0.307203i	$-0.0993930\pi$
$992$		0			0
$993$	12.6393			0.401097
$994$	−8.16312	−	14.1389i	−0.258918	−	0.448460i
$995$		0			0
$996$	−32.3607			−1.02539
$997$	−9.44427	−	16.3580i	−0.299103	−	0.518062i	0.676828	−	0.736141i	$-0.263354\pi$
$997$	−9.44427	−	16.3580i	−0.299103	−	0.518062i	−0.975931	+	0.218080i	$0.930021\pi$
$998$	6.76393	−	11.7155i	0.214109	−	0.370847i
$999$	3.35410	−	5.80948i	0.106119	−	0.183804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.b.126.1		4
5.2	odd	4		325.2.o.a.74.2		8
5.3	odd	4		325.2.o.a.74.3		8
5.4	even	2		65.2.e.a.61.2	yes	4
13.3	even	3	inner	325.2.e.b.276.1		4
13.4	even	6		4225.2.a.y.1.1		2
13.9	even	3		4225.2.a.u.1.2		2
15.14	odd	2		585.2.j.e.451.1		4
20.19	odd	2		1040.2.q.n.321.2		4
65.3	odd	12		325.2.o.a.224.2		8
65.4	even	6		845.2.a.b.1.2		2
65.9	even	6		845.2.a.e.1.1		2
65.19	odd	12		845.2.c.c.506.3		4
65.24	odd	12		845.2.m.e.361.2		8
65.29	even	6		65.2.e.a.16.2	✓	4
65.34	odd	4		845.2.m.e.316.3		8
65.42	odd	12		325.2.o.a.224.3		8
65.44	odd	4		845.2.m.e.316.2		8
65.49	even	6		845.2.e.g.146.1		4
65.54	odd	12		845.2.m.e.361.3		8
65.59	odd	12		845.2.c.c.506.2		4
65.64	even	2		845.2.e.g.191.1		4
195.29	odd	6		585.2.j.e.406.1		4
195.74	odd	6		7605.2.a.ba.1.2		2
195.134	odd	6		7605.2.a.bf.1.1		2
260.159	odd	6		1040.2.q.n.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.a.16.2	✓	4	65.29	even	6
65.2.e.a.61.2	yes	4	5.4	even	2
325.2.e.b.126.1		4	1.1	even	1	trivial
325.2.e.b.276.1		4	13.3	even	3	inner
325.2.o.a.74.2		8	5.2	odd	4
325.2.o.a.74.3		8	5.3	odd	4
325.2.o.a.224.2		8	65.3	odd	12
325.2.o.a.224.3		8	65.42	odd	12
585.2.j.e.406.1		4	195.29	odd	6
585.2.j.e.451.1		4	15.14	odd	2
845.2.a.b.1.2		2	65.4	even	6
845.2.a.e.1.1		2	65.9	even	6
845.2.c.c.506.2		4	65.59	odd	12
845.2.c.c.506.3		4	65.19	odd	12
845.2.e.g.146.1		4	65.49	even	6
845.2.e.g.191.1		4	65.64	even	2
845.2.m.e.316.2		8	65.44	odd	4
845.2.m.e.316.3		8	65.34	odd	4
845.2.m.e.361.2		8	65.24	odd	12
845.2.m.e.361.3		8	65.54	odd	12
1040.2.q.n.81.2		4	260.159	odd	6
1040.2.q.n.321.2		4	20.19	odd	2
4225.2.a.u.1.2		2	13.9	even	3
4225.2.a.y.1.1		2	13.4	even	6
7605.2.a.ba.1.2		2	195.74	odd	6
7605.2.a.bf.1.1		2	195.134	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.535233i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.690983 + 1.19682i) q^{6} +(2.11803 + 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.535233i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.690983 + 1.19682i) q^{6} +(2.11803 + 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.118034 - 0.204441i) q^{11} +3.61803 q^{12} +(1.00000 + 3.46410i) q^{13} -2.61803 q^{14} +(-0.927051 + 1.60570i) q^{16} +(-1.73607 - 3.00696i) q^{17} +1.23607 q^{18} +(-2.11803 - 3.66854i) q^{19} +9.47214 q^{21} +(0.0729490 + 0.126351i) q^{22} +(1.88197 - 3.25966i) q^{23} +(-2.50000 + 4.33013i) q^{24} +(-2.16312 - 0.535233i) q^{26} +2.23607 q^{27} +(-3.42705 + 5.93583i) q^{28} +(3.73607 - 6.47106i) q^{29} +(-2.80902 - 4.86536i) q^{32} +(-0.263932 - 0.457144i) q^{33} +2.14590 q^{34} +(1.61803 - 2.80252i) q^{36} +(1.50000 - 2.59808i) q^{37} +2.61803 q^{38} +(7.82624 + 1.93649i) q^{39} +(-5.97214 + 10.3440i) q^{41} +(-2.92705 + 5.06980i) q^{42} +(-3.11803 - 5.40059i) q^{43} +0.381966 q^{44} +(1.16312 + 2.01458i) q^{46} +4.94427 q^{47} +(2.07295 + 3.59045i) q^{48} +(-5.47214 + 9.47802i) q^{49} -7.76393 q^{51} +(-4.04508 + 4.20378i) q^{52} -6.00000 q^{53} +(-0.690983 + 1.19682i) q^{54} +(-4.73607 - 8.20311i) q^{56} -9.47214 q^{57} +(2.30902 + 3.99933i) q^{58} +(0.354102 + 0.613323i) q^{59} +(-7.20820 - 12.4850i) q^{61} +(4.23607 - 7.33708i) q^{63} -0.236068 q^{64} +0.326238 q^{66} +(-1.35410 + 2.34537i) q^{67} +(2.80902 - 4.86536i) q^{68} +(-4.20820 - 7.28882i) q^{69} +(3.11803 + 5.40059i) q^{71} +(2.23607 + 3.87298i) q^{72} +6.00000 q^{73} +(0.927051 + 1.60570i) q^{74} +(3.42705 - 5.93583i) q^{76} +1.00000 q^{77} +(-3.45492 + 3.59045i) q^{78} +(5.50000 - 9.52628i) q^{81} +(-3.69098 - 6.39297i) q^{82} -8.94427 q^{83} +(7.66312 + 13.2729i) q^{84} +3.85410 q^{86} +(-8.35410 - 14.4697i) q^{87} +(-0.263932 + 0.457144i) q^{88} +(4.50000 - 7.79423i) q^{89} +(-10.5902 + 11.0056i) q^{91} +6.09017 q^{92} +(-1.52786 + 2.64634i) q^{94} -12.5623 q^{96} +(-1.73607 - 3.00696i) q^{97} +(-3.38197 - 5.85774i) q^{98} -0.472136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + q^2 + q^4 + 5 * q^6 + 4 * q^7 - 4 * q^9	\( 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 10 q^{12} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{21} + 7 q^{22} + 12 q^{23} - 10 q^{24} + 7 q^{26} - 7 q^{28} + 6 q^{29} - 9 q^{32} - 10 q^{33} + 22 q^{34} + 2 q^{36} + 6 q^{37} + 6 q^{38} - 6 q^{41} - 5 q^{42} - 8 q^{43} + 6 q^{44} - 11 q^{46} - 16 q^{47} + 15 q^{48} - 4 q^{49} - 40 q^{51} - 5 q^{52} - 24 q^{53} - 5 q^{54} - 10 q^{56} - 20 q^{57} + 7 q^{58} - 12 q^{59} - 2 q^{61} + 8 q^{63} + 8 q^{64} - 30 q^{66} + 8 q^{67} + 9 q^{68} + 10 q^{69} + 8 q^{71} + 24 q^{73} - 3 q^{74} + 7 q^{76} + 4 q^{77} - 25 q^{78} + 22 q^{81} - 17 q^{82} + 15 q^{84} + 2 q^{86} - 20 q^{87} - 10 q^{88} + 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} - 10 q^{96} + 2 q^{97} - 18 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^4 + 5 * q^6 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 10 * q^12 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^21 + 7 * q^22 + 12 * q^23 - 10 * q^24 + 7 * q^26 - 7 * q^28 + 6 * q^29 - 9 * q^32 - 10 * q^33 + 22 * q^34 + 2 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^41 - 5 * q^42 - 8 * q^43 + 6 * q^44 - 11 * q^46 - 16 * q^47 + 15 * q^48 - 4 * q^49 - 40 * q^51 - 5 * q^52 - 24 * q^53 - 5 * q^54 - 10 * q^56 - 20 * q^57 + 7 * q^58 - 12 * q^59 - 2 * q^61 + 8 * q^63 + 8 * q^64 - 30 * q^66 + 8 * q^67 + 9 * q^68 + 10 * q^69 + 8 * q^71 + 24 * q^73 - 3 * q^74 + 7 * q^76 + 4 * q^77 - 25 * q^78 + 22 * q^81 - 17 * q^82 + 15 * q^84 + 2 * q^86 - 20 * q^87 - 10 * q^88 + 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 - 10 * q^96 + 2 * q^97 - 18 * q^98 + 16 * q^99

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