LMFDB - Embedded newform 325.2.e.b.276.2

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			276.2
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	325.276
Dual form			325.2.e.b.126.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 1.40126i) q^{2} +(-1.11803 - 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(1.80902 - 3.13331i) q^{6} +(-0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.809017 + 1.40126i) q^{2} +(-1.11803 - 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(1.80902 - 3.13331i) q^{6} +(-0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-2.11803 - 3.66854i) q^{11} +1.38197 q^{12} +(1.00000 - 3.46410i) q^{13} -0.381966 q^{14} +(2.42705 + 4.20378i) q^{16} +(2.73607 - 4.73901i) q^{17} -3.23607 q^{18} +(0.118034 - 0.204441i) q^{19} +0.527864 q^{21} +(3.42705 - 5.93583i) q^{22} +(4.11803 + 7.13264i) q^{23} +(-2.50000 - 4.33013i) q^{24} +(5.66312 - 1.40126i) q^{26} -2.23607 q^{27} +(-0.0729490 - 0.126351i) q^{28} +(-0.736068 - 1.27491i) q^{29} +(-1.69098 + 2.92887i) q^{32} +(-4.73607 + 8.20311i) q^{33} +8.85410 q^{34} +(-0.618034 - 1.07047i) q^{36} +(1.50000 + 2.59808i) q^{37} +0.381966 q^{38} +(-7.82624 + 1.93649i) q^{39} +(2.97214 + 5.14789i) q^{41} +(0.427051 + 0.739674i) q^{42} +(-0.881966 + 1.52761i) q^{43} +2.61803 q^{44} +(-6.66312 + 11.5409i) q^{46} -12.9443 q^{47} +(5.42705 - 9.39993i) q^{48} +(3.47214 + 6.01392i) q^{49} -12.2361 q^{51} +(1.54508 + 1.60570i) q^{52} -6.00000 q^{53} +(-1.80902 - 3.13331i) q^{54} +(-0.263932 + 0.457144i) q^{56} -0.527864 q^{57} +(1.19098 - 2.06284i) q^{58} +(-6.35410 + 11.0056i) q^{59} +(6.20820 - 10.7529i) q^{61} +(-0.236068 - 0.408882i) q^{63} +4.23607 q^{64} -15.3262 q^{66} +(5.35410 + 9.27358i) q^{67} +(1.69098 + 2.92887i) q^{68} +(9.20820 - 15.9491i) q^{69} +(0.881966 - 1.52761i) q^{71} +(-2.23607 + 3.87298i) q^{72} +6.00000 q^{73} +(-2.42705 + 4.20378i) q^{74} +(0.0729490 + 0.126351i) q^{76} +1.00000 q^{77} +(-9.04508 - 9.39993i) q^{78} +(5.50000 + 9.52628i) q^{81} +(-4.80902 + 8.32946i) q^{82} +8.94427 q^{83} +(-0.163119 + 0.282530i) q^{84} -2.85410 q^{86} +(-1.64590 + 2.85078i) q^{87} +(-4.73607 - 8.20311i) q^{88} +(4.50000 + 7.79423i) q^{89} +(0.590170 + 0.613323i) q^{91} -5.09017 q^{92} +(-10.4721 - 18.1383i) q^{94} +7.56231 q^{96} +(2.73607 - 4.73901i) q^{97} +(-5.61803 + 9.73072i) q^{98} +8.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.809017	+	1.40126i	0.572061	+	0.990839i	0.996354	+	0.0853143i	$0.0271894\pi$
$2$	0.809017	+	1.40126i	0.572061	+	0.990839i	−0.424293	+	0.905525i	$0.639477\pi$
$3$	−1.11803	−	1.93649i	−0.645497	−	1.11803i	−0.984186	−	0.177136i	$-0.943317\pi$
$3$	−1.11803	−	1.93649i	−0.645497	−	1.11803i	0.338689	−	0.940898i	$-0.390016\pi$
$4$	−0.309017	+	0.535233i	−0.154508	+	0.267617i
$5$		0			0
$5$		0			0
$6$	1.80902	−	3.13331i	0.738528	−	1.27917i
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	−0.887469	−	0.460866i	$-0.847539\pi$
$7$	−0.118034	+	0.204441i	−0.0446127	+	0.0772714i	0.842857	+	0.538138i	$0.180872\pi$
$8$	2.23607			0.790569
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	−2.11803	−	3.66854i	−0.638611	−	1.10611i	−0.985738	−	0.168289i	$-0.946176\pi$
$11$	−2.11803	−	3.66854i	−0.638611	−	1.10611i	0.347126	−	0.937818i	$-0.387157\pi$
$12$	1.38197			0.398939
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$	−0.381966			−0.102085
$15$		0			0
$16$	2.42705	+	4.20378i	0.606763	+	1.05094i
$17$	2.73607	−	4.73901i	0.663594	−	1.14938i	−0.316071	−	0.948736i	$-0.602364\pi$
$17$	2.73607	−	4.73901i	0.663594	−	1.14938i	0.979664	−	0.200643i	$-0.0643030\pi$
$18$	−3.23607			−0.762749
$19$	0.118034	−	0.204441i	0.0270789	−	0.0469020i	−0.852168	−	0.523268i	$-0.824713\pi$
$19$	0.118034	−	0.204441i	0.0270789	−	0.0469020i	0.879247	+	0.476366i	$0.158046\pi$
$20$		0			0
$21$	0.527864			0.115189
$22$	3.42705	−	5.93583i	0.730650	−	1.26552i
$23$	4.11803	+	7.13264i	0.858669	+	1.48726i	0.873199	+	0.487365i	$0.162042\pi$
$23$	4.11803	+	7.13264i	0.858669	+	1.48726i	−0.0145291	+	0.999894i	$0.504625\pi$
$24$	−2.50000	−	4.33013i	−0.510310	−	0.883883i
$25$		0			0
$26$	5.66312	−	1.40126i	1.11063	−	0.274809i
$27$	−2.23607			−0.430331
$28$	−0.0729490	−	0.126351i	−0.0137861	−	0.0238782i
$29$	−0.736068	−	1.27491i	−0.136684	−	0.236744i	0.789555	−	0.613679i	$-0.210311\pi$
$29$	−0.736068	−	1.27491i	−0.136684	−	0.236744i	−0.926240	+	0.376935i	$0.876978\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.69098	+	2.92887i	−0.298926	+	0.517756i
$33$	−4.73607	+	8.20311i	−0.824444	+	1.42798i
$34$	8.85410			1.51847
$35$		0			0
$36$	−0.618034	−	1.07047i	−0.103006	−	0.178411i
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$	0.381966			0.0619631
$39$	−7.82624	+	1.93649i	−1.25320	+	0.310087i
$40$		0			0
$41$	2.97214	+	5.14789i	0.464170	+	0.803965i	0.999164	−	0.0408904i	$-0.0130195\pi$
$41$	2.97214	+	5.14789i	0.464170	+	0.803965i	−0.534994	+	0.844856i	$0.679686\pi$
$42$	0.427051	+	0.739674i	0.0658954	+	0.114134i
$43$	−0.881966	+	1.52761i	−0.134499	+	0.232958i	−0.925406	−	0.378978i	$-0.876276\pi$
$43$	−0.881966	+	1.52761i	−0.134499	+	0.232958i	0.790907	+	0.611936i	$0.209609\pi$
$44$	2.61803			0.394683
$45$		0			0
$46$	−6.66312	+	11.5409i	−0.982423	+	1.70161i
$47$	−12.9443			−1.88812			−0.944058	−	0.329779i	$-0.893026\pi$
$47$	−12.9443			−1.88812			−0.944058	+	0.329779i	$0.893026\pi$
$48$	5.42705	−	9.39993i	0.783327	−	1.35676i
$49$	3.47214	+	6.01392i	0.496019	+	0.859131i
$50$		0			0
$51$	−12.2361			−1.71339
$52$	1.54508	+	1.60570i	0.214265	+	0.222670i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.80902	−	3.13331i	−0.246176	−	0.426389i
$55$		0			0
$56$	−0.263932	+	0.457144i	−0.0352694	+	0.0610884i
$57$	−0.527864			−0.0699173
$58$	1.19098	−	2.06284i	0.156384	−	0.270865i
$59$	−6.35410	+	11.0056i	−0.827234	+	1.43281i	0.0729666	+	0.997334i	$0.476753\pi$
$59$	−6.35410	+	11.0056i	−0.827234	+	1.43281i	−0.900200	+	0.435476i	$0.856580\pi$
$60$		0			0
$61$	6.20820	−	10.7529i	0.794879	−	1.37677i	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	6.20820	−	10.7529i	0.794879	−	1.37677i	0.922916	−	0.385002i	$-0.125799\pi$
$62$		0			0
$63$	−0.236068	−	0.408882i	−0.0297418	−	0.0515143i
$64$	4.23607			0.529508
$65$		0			0
$66$	−15.3262			−1.88653
$67$	5.35410	+	9.27358i	0.654108	+	1.13295i	0.982117	+	0.188273i	$0.0602890\pi$
$67$	5.35410	+	9.27358i	0.654108	+	1.13295i	−0.328009	+	0.944675i	$0.606378\pi$
$68$	1.69098	+	2.92887i	0.205062	+	0.355177i
$69$	9.20820	−	15.9491i	1.10854	−	1.92004i
$70$		0			0
$71$	0.881966	−	1.52761i	0.104670	−	0.181294i	−0.808933	−	0.587900i	$-0.799955\pi$
$71$	0.881966	−	1.52761i	0.104670	−	0.181294i	0.913603	+	0.406607i	$0.133288\pi$
$72$	−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	$0.385800\pi$
$74$	−2.42705	+	4.20378i	−0.282139	+	0.488679i
$75$		0			0
$76$	0.0729490	+	0.126351i	0.00836783	+	0.0144935i
$77$	1.00000			0.113961
$78$	−9.04508	−	9.39993i	−1.02415	−	1.06433i
$79$		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
$82$	−4.80902	+	8.32946i	−0.531067	+	0.919835i
$83$	8.94427			0.981761			0.490881	−	0.871227i	$-0.336675\pi$
$83$	8.94427			0.981761			0.490881	+	0.871227i	$0.336675\pi$
$84$	−0.163119	+	0.282530i	−0.0177977	+	0.0308266i
$85$		0			0
$86$	−2.85410			−0.307766
$87$	−1.64590	+	2.85078i	−0.176459	+	0.305636i
$88$	−4.73607	−	8.20311i	−0.504867	−	0.874455i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	0.590170	+	0.613323i	0.0618666	+	0.0642937i
$92$	−5.09017			−0.530687
$93$		0			0
$94$	−10.4721	−	18.1383i	−1.08012	−	1.87082i
$95$		0			0
$96$	7.56231			0.771825
$97$	2.73607	−	4.73901i	0.277806	−	0.481173i	−0.693034	−	0.720905i	$-0.743726\pi$
$97$	2.73607	−	4.73901i	0.277806	−	0.481173i	0.970839	+	0.239732i	$0.0770596\pi$
$98$	−5.61803	+	9.73072i	−0.567507	+	0.982951i
$99$	8.47214			0.851482
$100$		0			0
$101$	−4.73607	−	8.20311i	−0.471256	−	0.816240i	0.528203	−	0.849118i	$-0.322866\pi$
$101$	−4.73607	−	8.20311i	−0.471256	−	0.816240i	−0.999459	+	0.0328781i	$0.989533\pi$
$102$	−9.89919	−	17.1459i	−0.980166	−	1.69770i
$103$	4.94427			0.487174			0.243587	−	0.969879i	$-0.421676\pi$
$103$	4.94427			0.487174			0.243587	+	0.969879i	$0.421676\pi$
$104$	2.23607	−	7.74597i	0.219265	−	0.759555i
$105$		0			0
$106$	−4.85410	−	8.40755i	−0.471472	−	0.816614i
$107$	−5.11803	−	8.86469i	−0.494779	−	0.856982i	0.505203	−	0.863001i	$-0.331418\pi$
$107$	−5.11803	−	8.86469i	−0.494779	−	0.856982i	−0.999982	+	0.00601821i	$0.998084\pi$
$108$	0.690983	−	1.19682i	0.0664899	−	0.115164i
$109$	−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
$112$	−1.14590			−0.108277
$113$	−3.73607	+	6.47106i	−0.351460	+	0.608746i	−0.986505	−	0.163728i	$-0.947648\pi$
$113$	−3.73607	+	6.47106i	−0.351460	+	0.608746i	0.635046	+	0.772475i	$0.280981\pi$
$114$	−0.427051	−	0.739674i	−0.0399970	−	0.0692768i
$115$		0			0
$116$	0.909830			0.0844756
$117$	5.00000	+	5.19615i	0.462250	+	0.480384i
$118$	−20.5623			−1.89291
$119$	0.645898	+	1.11873i	0.0592094	+	0.102554i
$120$		0			0
$121$	−3.47214	+	6.01392i	−0.315649	+	0.546720i
$122$	20.0902			1.81888
$123$	6.64590	−	11.5110i	0.599240	−	1.03791i
$124$		0			0
$125$		0			0
$126$	0.381966	−	0.661585i	0.0340282	−	0.0589386i
$127$	0.118034	+	0.204441i	0.0104738	+	0.0181412i	0.871215	−	0.490902i	$-0.163333\pi$
$127$	0.118034	+	0.204441i	0.0104738	+	0.0181412i	−0.860741	+	0.509043i	$0.829999\pi$
$128$	6.80902	+	11.7936i	0.601838	+	1.04241i
$129$	3.94427			0.347274
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−2.92705	−	5.06980i	−0.254767	−	0.441270i
$133$	0.0278640	+	0.0482619i	0.00241612	+	0.00418484i
$134$	−8.66312	+	15.0050i	−0.748379	+	1.29623i
$135$		0			0
$136$	6.11803	−	10.5967i	0.524617	−	0.908663i
$137$	−3.73607	+	6.47106i	−0.319194	+	0.552860i	−0.980320	−	0.197415i	$-0.936745\pi$
$137$	−3.73607	+	6.47106i	−0.319194	+	0.552860i	0.661126	+	0.750275i	$0.270079\pi$
$138$	29.7984			2.53661
$139$	1.64590	−	2.85078i	0.139603	−	0.241800i	−0.787743	−	0.616004i	$-0.788751\pi$
$139$	1.64590	−	2.85078i	0.139603	−	0.241800i	0.927346	+	0.374204i	$0.122084\pi$
$140$		0			0
$141$	14.4721	+	25.0665i	1.21877	+	2.11098i
$142$	2.85410			0.239511
$143$	−14.8262	+	3.66854i	−1.23983	+	0.306779i
$144$	−9.70820			−0.809017
$145$		0			0
$146$	4.85410	+	8.40755i	0.401728	+	0.695814i
$147$	7.76393	−	13.4475i	0.640358	−	1.10913i
$148$	−1.85410			−0.152406
$149$	−6.73607	+	11.6672i	−0.551840	+	0.955815i	0.446302	+	0.894883i	$0.352741\pi$
$149$	−6.73607	+	11.6672i	−0.551840	+	0.955815i	−0.998142	+	0.0609327i	$0.980593\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	0.263932	−	0.457144i	0.0214077	−	0.0370792i
$153$	5.47214	+	9.47802i	0.442396	+	0.766252i
$154$	0.809017	+	1.40126i	0.0651924	+	0.112917i
$155$		0			0
$156$	1.38197	−	4.78727i	0.110646	−	0.383288i
$157$	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
$161$	−1.94427			−0.153230
$162$	−8.89919	+	15.4138i	−0.699186	+	1.21103i
$163$	0.645898	−	1.11873i	0.0505906	−	0.0876256i	−0.839621	−	0.543173i	$-0.817223\pi$
$163$	0.645898	−	1.11873i	0.0505906	−	0.0876256i	0.890212	+	0.455547i	$0.150556\pi$
$164$	−3.67376			−0.286873
$165$		0			0
$166$	7.23607	+	12.5332i	0.561628	+	0.972768i
$167$	2.59017	+	4.48631i	0.200433	+	0.347161i	0.948668	−	0.316273i	$-0.102432\pi$
$167$	2.59017	+	4.48631i	0.200433	+	0.347161i	−0.748235	+	0.663434i	$0.769098\pi$
$168$	1.18034			0.0910652
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	0.236068	+	0.408882i	0.0180526	+	0.0312680i
$172$	−0.545085	−	0.944115i	−0.0415623	−	0.0719881i
$173$	8.44427	−	14.6259i	0.642006	−	1.11199i	−0.342978	−	0.939343i	$-0.611436\pi$
$173$	8.44427	−	14.6259i	0.642006	−	1.11199i	0.984984	−	0.172644i	$-0.0552310\pi$
$174$	−5.32624			−0.403781
$175$		0			0
$176$	10.2812	−	17.8075i	0.774971	−	1.34229i
$177$	28.4164			2.13591
$178$	−7.28115	+	12.6113i	−0.545745	+	0.945259i
$179$	1.88197	+	3.25966i	0.140665	+	0.243638i	0.927747	−	0.373209i	$-0.121743\pi$
$179$	1.88197	+	3.25966i	0.140665	+	0.243638i	−0.787082	+	0.616848i	$0.788409\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−0.381966	+	1.32317i	−0.0283132	+	0.0980798i
$183$	−27.7639			−2.05237
$184$	9.20820	+	15.9491i	0.678838	+	1.17578i
$185$		0			0
$186$		0			0
$187$	−23.1803			−1.69511
$188$	4.00000	−	6.92820i	0.291730	−	0.505291i
$189$	0.263932	−	0.457144i	0.0191982	−	0.0332523i
$190$		0			0
$191$	2.40983	−	4.17395i	0.174369	−	0.302016i	−0.765574	−	0.643348i	$-0.777545\pi$
$191$	2.40983	−	4.17395i	0.174369	−	0.302016i	0.939943	+	0.341332i	$0.110878\pi$
$192$	−4.73607	−	8.20311i	−0.341796	−	0.592008i
$193$	2.73607	+	4.73901i	0.196946	+	0.341121i	0.947537	−	0.319646i	$-0.103564\pi$
$193$	2.73607	+	4.73901i	0.196946	+	0.341121i	−0.750590	+	0.660768i	$0.770231\pi$
$194$	8.85410			0.635687
$195$		0			0
$196$	−4.29180			−0.306557
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$	6.85410	+	11.8717i	0.487100	+	0.843682i
$199$	7.35410	−	12.7377i	0.521318	−	0.902950i	−0.478374	−	0.878156i	$-0.658774\pi$
$199$	7.35410	−	12.7377i	0.521318	−	0.902950i	0.999693	−	0.0247939i	$-0.00789296\pi$
$200$		0			0
$201$	11.9721	−	20.7363i	0.844449	−	1.46263i
$202$	7.66312	−	13.2729i	0.539175	−	0.933879i
$203$	0.347524			0.0243914
$204$	3.78115	−	6.54915i	0.264734	−	0.458532i
$205$		0			0
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	−16.4721			−1.14489
$208$	16.9894	−	4.20378i	1.17800	−	0.291479i
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	−4.59017	−	7.95041i	−0.316000	−	0.547329i	0.663649	−	0.748044i	$-0.269007\pi$
$211$	−4.59017	−	7.95041i	−0.316000	−	0.547329i	−0.979650	+	0.200715i	$0.935673\pi$
$212$	1.85410	−	3.21140i	0.127340	−	0.220560i
$213$	−3.94427			−0.270257
$214$	8.28115	−	14.3434i	0.566088	−	0.980493i
$215$		0			0
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−1.61803	−	2.80252i	−0.109587	−	0.189810i
$219$	−6.70820	−	11.6190i	−0.453298	−	0.785136i
$220$		0			0
$221$	−13.6803	−	14.2170i	−0.920239	−	0.956341i
$222$	10.8541			0.728480
$223$	−6.35410	−	11.0056i	−0.425502	−	0.736991i	0.570965	−	0.820974i	$-0.306569\pi$
$223$	−6.35410	−	11.0056i	−0.425502	−	0.736991i	−0.996467	+	0.0839830i	$0.973236\pi$
$224$	−0.399187	−	0.691412i	−0.0266718	−	0.0461969i
$225$		0			0
$226$	−12.0902			−0.804226
$227$	−0.881966	+	1.52761i	−0.0585381	+	0.101391i	−0.893809	−	0.448447i	$-0.851977\pi$
$227$	−0.881966	+	1.52761i	−0.0585381	+	0.101391i	0.835271	+	0.549838i	$0.185311\pi$
$228$	0.163119	−	0.282530i	0.0108028	−	0.0187110i
$229$	−19.8885			−1.31427			−0.657136	−	0.753772i	$-0.728232\pi$
$229$	−19.8885			−1.31427			−0.657136	+	0.753772i	$0.728232\pi$
$230$		0			0
$231$	−1.11803	−	1.93649i	−0.0735612	−	0.127412i
$232$	−1.64590	−	2.85078i	−0.108058	−	0.187163i
$233$	−19.8885			−1.30294			−0.651471	−	0.758674i	$-0.725848\pi$
$233$	−19.8885			−1.30294			−0.651471	+	0.758674i	$0.725848\pi$
$234$	−3.23607	+	11.2101i	−0.211548	+	0.732825i
$235$		0			0
$236$	−3.92705	−	6.80185i	−0.255629	−	0.442763i
$237$		0			0
$238$	−1.04508	+	1.81014i	−0.0677428	+	0.117334i
$239$	9.88854			0.639637			0.319818	−	0.947479i	$-0.396378\pi$
$239$	9.88854			0.639637			0.319818	+	0.947479i	$0.396378\pi$
$240$		0			0
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$	−11.2361			−0.722282
$243$	8.94427	−	15.4919i	0.573775	−	0.993808i
$244$	3.83688	+	6.64567i	0.245631	+	0.425446i
$245$		0			0
$246$	21.5066			1.37121
$247$	−0.590170	−	0.613323i	−0.0375516	−	0.0390248i
$248$		0			0
$249$	−10.0000	−	17.3205i	−0.633724	−	1.09764i
$250$		0			0
$251$	−7.88197	+	13.6520i	−0.497505	+	0.861704i	−0.999996	−	0.00287826i	$-0.999084\pi$
$251$	−7.88197	+	13.6520i	−0.497505	+	0.861704i	0.502491	+	0.864583i	$0.332417\pi$
$252$	0.291796			0.0183814
$253$	17.4443	−	30.2144i	1.09671	−	1.89956i
$254$	−0.190983	+	0.330792i	−0.0119833	+	0.0207558i
$255$		0			0
$256$	−6.78115	+	11.7453i	−0.423822	+	0.734081i
$257$	4.26393	+	7.38535i	0.265977	+	0.460685i	0.967819	−	0.251647i	$-0.0809722\pi$
$257$	4.26393	+	7.38535i	0.265977	+	0.460685i	−0.701842	+	0.712332i	$0.747639\pi$
$258$	3.19098	+	5.52694i	0.198662	+	0.344093i
$259$	−0.708204			−0.0440057
$260$		0			0
$261$	2.94427			0.182246
$262$	−9.70820	−	16.8151i	−0.599775	−	1.03884i
$263$	4.11803	+	7.13264i	0.253929	+	0.439818i	0.964604	−	0.263703i	$-0.0849438\pi$
$263$	4.11803	+	7.13264i	0.253929	+	0.439818i	−0.710675	+	0.703520i	$0.751610\pi$
$264$	−10.5902	+	18.3427i	−0.651780	+	1.12892i
$265$		0			0
$266$	−0.0450850	+	0.0780895i	−0.00276434	+	0.00478797i
$267$	10.0623	−	17.4284i	0.615803	−	1.06660i
$268$	−6.61803			−0.404261
$269$	7.73607	−	13.3993i	0.471676	−	0.816967i	−0.527799	−	0.849370i	$-0.676982\pi$
$269$	7.73607	−	13.3993i	0.471676	−	0.816967i	0.999475	+	0.0324021i	$0.0103157\pi$
$270$		0			0
$271$	−7.35410	−	12.7377i	−0.446730	−	0.773759i	0.551441	−	0.834214i	$-0.314078\pi$
$271$	−7.35410	−	12.7377i	−0.446730	−	0.773759i	−0.998171	+	0.0604550i	$0.980745\pi$
$272$	26.5623			1.61058
$273$	0.527864	−	1.82857i	0.0319478	−	0.110670i
$274$	−12.0902			−0.730394
$275$		0			0
$276$	5.69098	+	9.85707i	0.342557	+	0.593326i
$277$	−9.44427	+	16.3580i	−0.567451	+	0.982854i	0.429366	+	0.903131i	$0.358737\pi$
$277$	−9.44427	+	16.3580i	−0.567451	+	0.982854i	−0.996817	+	0.0797238i	$0.974596\pi$
$278$	5.32624			0.319447
$279$		0			0
$280$		0			0
$281$	19.8885			1.18645			0.593226	−	0.805036i	$-0.297854\pi$
$281$	19.8885			1.18645			0.593226	+	0.805036i	$0.297854\pi$
$282$	−23.4164	+	40.5584i	−1.39443	+	2.41522i
$283$	1.35410	+	2.34537i	0.0804930	+	0.139418i	0.903462	−	0.428669i	$-0.141017\pi$
$283$	1.35410	+	2.34537i	0.0804930	+	0.139418i	−0.822969	+	0.568087i	$0.807684\pi$
$284$	0.545085	+	0.944115i	0.0323448	+	0.0560229i
$285$		0			0
$286$	−17.1353	−	17.8075i	−1.01323	−	1.05298i
$287$	−1.40325			−0.0828314
$288$	−3.38197	−	5.85774i	−0.199284	−	0.345170i
$289$	−6.47214	−	11.2101i	−0.380714	−	0.659416i
$290$		0			0
$291$	−12.2361			−0.717291
$292$	−1.85410	+	3.21140i	−0.108503	+	0.187933i
$293$	−6.02786	+	10.4406i	−0.352152	+	0.609944i	−0.986626	−	0.162999i	$-0.947883\pi$
$293$	−6.02786	+	10.4406i	−0.352152	+	0.609944i	0.634475	+	0.772944i	$0.281217\pi$
$294$	25.1246			1.46530
$295$		0			0
$296$	3.35410	+	5.80948i	0.194953	+	0.337669i
$297$	4.73607	+	8.20311i	0.274815	+	0.475993i
$298$	−21.7984			−1.26275
$299$	28.8262	−	7.13264i	1.66706	−	0.412491i
$300$		0			0
$301$	−0.208204	−	0.360620i	−0.0120007	−	0.0207858i
$302$	6.47214	+	11.2101i	0.372430	+	0.645067i
$303$	−10.5902	+	18.3427i	−0.608389	+	1.05376i
$304$	1.14590			0.0657218
$305$		0			0
$306$	−8.85410	+	15.3358i	−0.506155	+	0.876687i
$307$	−7.05573			−0.402692			−0.201346	−	0.979520i	$-0.564532\pi$
$307$	−7.05573			−0.402692			−0.201346	+	0.979520i	$0.564532\pi$
$308$	−0.309017	+	0.535233i	−0.0176079	+	0.0304977i
$309$	−5.52786	−	9.57454i	−0.314469	−	0.544677i
$310$		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
$313$	31.8885			1.80245			0.901224	−	0.433355i	$-0.142670\pi$
$313$	31.8885			1.80245			0.901224	+	0.433355i	$0.142670\pi$
$314$	14.5623	+	25.2227i	0.821798	+	1.42340i
$315$		0			0
$316$		0			0
$317$	−23.8885			−1.34171			−0.670857	−	0.741587i	$-0.734074\pi$
$317$	−23.8885			−1.34171			−0.670857	+	0.741587i	$0.734074\pi$
$318$	−10.8541	+	18.7999i	−0.608668	+	1.05424i
$319$	−3.11803	+	5.40059i	−0.174576	+	0.302375i
$320$		0			0
$321$	−11.4443	+	19.8221i	−0.638757	+	1.10636i
$322$	−1.57295	−	2.72443i	−0.0876570	−	0.151826i
$323$	−0.645898	−	1.11873i	−0.0359387	−	0.0622477i
$324$	−6.79837			−0.377687
$325$		0			0
$326$	2.09017			0.115764
$327$	2.23607	+	3.87298i	0.123655	+	0.214176i
$328$	6.64590	+	11.5110i	0.366958	+	0.635590i
$329$	1.52786	−	2.64634i	0.0842339	−	0.145897i
$330$		0			0
$331$	−12.8262	+	22.2157i	−0.704994	+	1.22109i	0.261700	+	0.965149i	$0.415717\pi$
$331$	−12.8262	+	22.2157i	−0.704994	+	1.22109i	−0.966694	+	0.255936i	$0.917616\pi$
$332$	−2.76393	+	4.78727i	−0.151690	+	0.262736i
$333$	−6.00000			−0.328798
$334$	−4.19098	+	7.25900i	−0.229320	+	0.397195i
$335$		0			0
$336$	1.28115	+	2.21902i	0.0698926	+	0.121058i
$337$	−27.8885			−1.51919			−0.759593	−	0.650399i	$-0.774602\pi$
$337$	−27.8885			−1.51919			−0.759593	+	0.650399i	$0.774602\pi$
$338$	0.809017	−	21.0189i	0.0440047	−	1.14328i
$339$	16.7082			0.907465
$340$		0			0
$341$		0			0
$342$	−0.381966	+	0.661585i	−0.0206544	+	0.0357744i
$343$	−3.29180			−0.177740
$344$	−1.97214	+	3.41584i	−0.106330	+	0.184170i
$345$		0			0
$346$	27.3262			1.46907
$347$	8.64590	−	14.9751i	0.464136	−	0.803907i	−0.535026	−	0.844836i	$-0.679698\pi$
$347$	8.64590	−	14.9751i	0.464136	−	0.803907i	0.999162	+	0.0409283i	$0.0130315\pi$
$348$	−1.01722	−	1.76188i	−0.0545288	−	0.0944466i
$349$	12.2082	+	21.1452i	0.653490	+	1.13188i	0.982270	+	0.187472i	$0.0600293\pi$
$349$	12.2082	+	21.1452i	0.653490	+	1.13188i	−0.328780	+	0.944407i	$0.606637\pi$
$350$		0			0
$351$	−2.23607	+	7.74597i	−0.119352	+	0.413449i
$352$	14.3262			0.763591
$353$	−5.26393	−	9.11740i	−0.280171	−	0.485270i	0.691256	−	0.722610i	$-0.257058\pi$
$353$	−5.26393	−	9.11740i	−0.280171	−	0.485270i	−0.971427	+	0.237340i	$0.923724\pi$
$354$	22.9894	+	39.8187i	1.22187	+	2.11634i
$355$		0			0
$356$	−5.56231			−0.294802
$357$	1.44427	−	2.50155i	0.0764390	−	0.132396i
$358$	−3.04508	+	5.27424i	−0.160938	+	0.278752i
$359$	−17.8885			−0.944121			−0.472061	−	0.881566i	$-0.656490\pi$
$359$	−17.8885			−0.944121			−0.472061	+	0.881566i	$0.656490\pi$
$360$		0			0
$361$	9.47214	+	16.4062i	0.498533	+	0.863485i
$362$	4.85410	+	8.40755i	0.255126	+	0.441891i
$363$	15.5279			0.815001
$364$	−0.510643	+	0.126351i	−0.0267650	+	0.00662261i
$365$		0			0
$366$	−22.4615	−	38.9044i	−1.17408	−	2.03357i
$367$	−12.8262	−	22.2157i	−0.669524	−	1.15965i	−0.978037	−	0.208430i	$-0.933165\pi$
$367$	−12.8262	−	22.2157i	−0.669524	−	1.15965i	0.308513	−	0.951220i	$-0.400169\pi$
$368$	−19.9894	+	34.6226i	−1.04202	+	1.80483i
$369$	−11.8885			−0.618893
$370$		0			0
$371$	0.708204	−	1.22665i	0.0367681	−	0.0636842i
$372$		0			0
$373$	5.02786	−	8.70852i	0.260333	−	0.450910i	−0.705997	−	0.708214i	$-0.749501\pi$
$373$	5.02786	−	8.70852i	0.260333	−	0.450910i	0.966330	+	0.257305i	$0.0828343\pi$
$374$	−18.7533	−	32.4816i	−0.969709	−	1.67959i
$375$		0			0
$376$	−28.9443			−1.49269
$377$	−5.15248	+	1.27491i	−0.265366	+	0.0656611i
$378$	0.854102			0.0439303
$379$	−16.5902	−	28.7350i	−0.852180	−	1.47602i	−0.879237	−	0.476385i	$-0.841947\pi$
$379$	−16.5902	−	28.7350i	−0.852180	−	1.47602i	0.0270571	−	0.999634i	$-0.491386\pi$
$380$		0			0
$381$	0.263932	−	0.457144i	0.0135216	−	0.0234202i
$382$	7.79837			0.399000
$383$	−0.118034	+	0.204441i	−0.00603126	+	0.0104464i	−0.869025	−	0.494768i	$-0.835253\pi$
$383$	−0.118034	+	0.204441i	−0.00603126	+	0.0104464i	0.862994	+	0.505214i	$0.168586\pi$
$384$	15.2254	−	26.3712i	0.776969	−	1.34575i
$385$		0			0
$386$	−4.42705	+	7.66788i	−0.225331	+	0.390285i
$387$	−1.76393	−	3.05522i	−0.0896657	−	0.155306i
$388$	1.69098	+	2.92887i	0.0858467	+	0.148691i
$389$	−35.8885			−1.81962			−0.909811	−	0.415023i	$-0.863773\pi$
$389$	−35.8885			−1.81962			−0.909811	+	0.415023i	$0.863773\pi$
$390$		0			0
$391$	45.0689			2.27923
$392$	7.76393	+	13.4475i	0.392138	+	0.679203i
$393$	13.4164	+	23.2379i	0.676768	+	1.17220i
$394$	−2.42705	+	4.20378i	−0.122273	+	0.211783i
$395$		0			0
$396$	−2.61803	+	4.53457i	−0.131561	+	0.227871i
$397$	5.02786	−	8.70852i	0.252341	−	0.437068i	−0.711829	−	0.702353i	$-0.752133\pi$
$397$	5.02786	−	8.70852i	0.252341	−	0.437068i	0.964170	+	0.265285i	$0.0854661\pi$
$398$	23.7984			1.19290
$399$	0.0623059	−	0.107917i	0.00311920	−	0.00540261i
$400$		0			0
$401$	13.4443	+	23.2862i	0.671375	+	1.16286i	0.977514	+	0.210869i	$0.0676293\pi$
$401$	13.4443	+	23.2862i	0.671375	+	1.16286i	−0.306139	+	0.951987i	$0.599037\pi$
$402$	38.7426			1.93231
$403$		0			0
$404$	5.85410			0.291252
$405$		0			0
$406$	0.281153	+	0.486971i	0.0139534	+	0.0241680i
$407$	6.35410	−	11.0056i	0.314961	−	0.545529i
$408$	−27.3607			−1.35456
$409$	5.44427	−	9.42976i	0.269202	−	0.466271i	−0.699454	−	0.714678i	$-0.746573\pi$
$409$	5.44427	−	9.42976i	0.269202	−	0.466271i	0.968656	+	0.248406i	$0.0799068\pi$
$410$		0			0
$411$	16.7082			0.824155
$412$	−1.52786	+	2.64634i	−0.0752725	+	0.130376i
$413$	−1.50000	−	2.59808i	−0.0738102	−	0.127843i
$414$	−13.3262	−	23.0817i	−0.654949	−	1.13440i
$415$		0			0
$416$	8.45492	+	8.78661i	0.414536	+	0.430799i
$417$	−7.36068			−0.360454
$418$	−0.809017	−	1.40126i	−0.0395703	−	0.0685378i
$419$	6.82624	+	11.8234i	0.333484	+	0.577610i	0.983192	−	0.182573i	$-0.0584425\pi$
$419$	6.82624	+	11.8234i	0.333484	+	0.577610i	−0.649709	+	0.760183i	$0.725109\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	7.42705	−	12.8640i	0.361543	−	0.626211i
$423$	12.9443	−	22.4201i	0.629372	−	1.09010i
$424$	−13.4164			−0.651558
$425$		0			0
$426$	−3.19098	−	5.52694i	−0.154604	−	0.267781i
$427$	1.46556	+	2.53842i	0.0709233	+	0.122843i
$428$	6.32624			0.305790
$429$	23.6803	+	24.6093i	1.14330	+	1.18815i
$430$		0			0
$431$	−2.40983	−	4.17395i	−0.116077	−	0.201052i	0.802133	−	0.597146i	$-0.203699\pi$
$431$	−2.40983	−	4.17395i	−0.116077	−	0.201052i	−0.918210	+	0.396094i	$0.870365\pi$
$432$	−5.42705	−	9.39993i	−0.261109	−	0.452254i
$433$	−11.7361	+	20.3275i	−0.563999	+	0.976876i	0.433143	+	0.901325i	$0.357405\pi$
$433$	−11.7361	+	20.3275i	−0.563999	+	0.976876i	−0.997142	+	0.0755503i	$0.975929\pi$
$434$		0			0
$435$		0			0
$436$	0.618034	−	1.07047i	0.0295985	−	0.0512660i
$437$	1.94427			0.0930071
$438$	10.8541	−	18.7999i	0.518629	−	0.898292i
$439$	4.64590	+	8.04693i	0.221737	+	0.384059i	0.955335	−	0.295524i	$-0.0954941\pi$
$439$	4.64590	+	8.04693i	0.221737	+	0.384059i	−0.733599	+	0.679583i	$0.762161\pi$
$440$		0			0
$441$	−13.8885			−0.661359
$442$	8.85410	−	30.6715i	0.421147	−	1.45889i
$443$	16.9443			0.805047			0.402523	−	0.915410i	$-0.368133\pi$
$443$	16.9443			0.805047			0.402523	+	0.915410i	$0.368133\pi$
$444$	2.07295	+	3.59045i	0.0983778	+	0.170395i
$445$		0			0
$446$	10.2812	−	17.8075i	0.486827	−	0.843209i
$447$	30.1246			1.42485
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	6.97214	−	12.0761i	0.329035	−	0.569906i	−0.653285	−	0.757112i	$-0.726610\pi$
$449$	6.97214	−	12.0761i	0.329035	−	0.569906i	0.982321	+	0.187206i	$0.0599431\pi$
$450$		0			0
$451$	12.5902	−	21.8068i	0.592848	−	1.02684i
$452$	−2.30902	−	3.99933i	−0.108607	−	0.188113i
$453$	−8.94427	−	15.4919i	−0.420239	−	0.727875i
$454$	−2.85410			−0.133950
$455$		0			0
$456$	−1.18034			−0.0552745
$457$	−14.2082	−	24.6093i	−0.664632	−	1.15118i	−0.979385	−	0.202002i	$-0.935255\pi$
$457$	−14.2082	−	24.6093i	−0.664632	−	1.15118i	0.314753	−	0.949174i	$-0.398078\pi$
$458$	−16.0902	−	27.8690i	−0.751844	−	1.30223i
$459$	−6.11803	+	10.5967i	−0.285565	+	0.494614i
$460$		0			0
$461$	14.2082	−	24.6093i	0.661742	−	1.14617i	−0.318416	−	0.947951i	$-0.603151\pi$
$461$	14.2082	−	24.6093i	0.661742	−	1.14617i	0.980158	−	0.198220i	$-0.0635159\pi$
$462$	1.80902	−	3.13331i	0.0841631	−	0.145775i
$463$	−28.9443			−1.34515			−0.672577	−	0.740027i	$-0.734813\pi$
$463$	−28.9443			−1.34515			−0.672577	+	0.740027i	$0.734813\pi$
$464$	3.57295	−	6.18853i	0.165870	−	0.287295i
$465$		0			0
$466$	−16.0902	−	27.8690i	−0.745363	−	1.29101i
$467$	8.94427			0.413892			0.206946	−	0.978352i	$-0.433648\pi$
$467$	8.94427			0.413892			0.206946	+	0.978352i	$0.433648\pi$
$468$	−4.32624	+	1.07047i	−0.199980	+	0.0494823i
$469$	−2.52786			−0.116726
$470$		0			0
$471$	−20.1246	−	34.8569i	−0.927293	−	1.60612i
$472$	−14.2082	+	24.6093i	−0.653986	+	1.13274i
$473$	7.47214			0.343569
$474$		0			0
$475$		0			0
$476$	−0.798374			−0.0365934
$477$	6.00000	−	10.3923i	0.274721	−	0.475831i
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	4.06231	+	7.03612i	0.185611	+	0.321489i	0.943782	−	0.330567i	$-0.107240\pi$
$479$	4.06231	+	7.03612i	0.185611	+	0.321489i	−0.758171	+	0.652056i	$0.773907\pi$
$480$		0			0
$481$	10.5000	−	2.59808i	0.478759	−	0.118462i
$482$	−24.2705			−1.10549
$483$	2.17376	+	3.76507i	0.0989096	+	0.171316i
$484$	−2.14590	−	3.71680i	−0.0975408	−	0.168946i
$485$		0			0
$486$	28.9443			1.31294
$487$	−13.0623	+	22.6246i	−0.591910	+	1.02522i	0.402065	+	0.915611i	$0.368292\pi$
$487$	−13.0623	+	22.6246i	−0.591910	+	1.02522i	−0.993975	+	0.109607i	$0.965041\pi$
$488$	13.8820	−	24.0443i	0.628407	−	1.08843i
$489$	−2.88854			−0.130624
$490$		0			0
$491$	−2.11803	−	3.66854i	−0.0955855	−	0.165559i	0.814267	−	0.580490i	$-0.197139\pi$
$491$	−2.11803	−	3.66854i	−0.0955855	−	0.165559i	−0.909853	+	0.414931i	$0.863806\pi$
$492$	4.10739	+	7.11421i	0.185175	+	0.320733i
$493$	−8.05573			−0.362812
$494$	0.381966	−	1.32317i	0.0171855	−	0.0595322i
$495$		0			0
$496$		0			0
$497$	0.208204	+	0.360620i	0.00933922	+	0.0161760i
$498$	16.1803	−	28.0252i	0.725058	−	1.25584i
$499$	13.8885			0.621737			0.310868	−	0.950453i	$-0.399380\pi$
$499$	13.8885			0.621737			0.310868	+	0.950453i	$0.399380\pi$
$500$		0			0
$501$	5.79180	−	10.0317i	0.258758	−	0.448183i
$502$	−25.5066			−1.13841
$503$	−6.59017	+	11.4145i	−0.293841	+	0.508948i	−0.974715	−	0.223453i	$-0.928267\pi$
$503$	−6.59017	+	11.4145i	−0.293841	+	0.508948i	0.680873	+	0.732401i	$0.261600\pi$
$504$	−0.527864	−	0.914287i	−0.0235129	−	0.0407256i
$505$		0			0
$506$	56.4508			2.50955
$507$	−1.11803	+	29.0474i	−0.0496536	+	1.29004i
$508$	−0.145898			−0.00647318
$509$	−5.68034	−	9.83864i	−0.251777	−	0.436090i	0.712238	−	0.701938i	$-0.247681\pi$
$509$	−5.68034	−	9.83864i	−0.251777	−	0.436090i	−0.964015	+	0.265848i	$0.914348\pi$
$510$		0			0
$511$	−0.708204	+	1.22665i	−0.0313291	+	0.0542636i
$512$	5.29180			0.233867
$513$	−0.263932	+	0.457144i	−0.0116529	+	0.0201834i
$514$	−6.89919	+	11.9497i	−0.304310	+	0.527081i
$515$		0			0
$516$	−1.21885	+	2.11111i	−0.0536567	+	0.0929362i
$517$	27.4164	+	47.4866i	1.20577	+	2.08846i
$518$	−0.572949	−	0.992377i	−0.0251739	−	0.0436025i
$519$	−37.7639			−1.65765
$520$		0			0
$521$	−41.7771			−1.83029			−0.915144	−	0.403128i	$-0.867923\pi$
$521$	−41.7771			−1.83029			−0.915144	+	0.403128i	$0.867923\pi$
$522$	2.38197	+	4.12569i	0.104256	+	0.180576i
$523$	9.35410	+	16.2018i	0.409026	+	0.708454i	0.994781	−	0.102034i	$-0.0325351\pi$
$523$	9.35410	+	16.2018i	0.409026	+	0.708454i	−0.585755	+	0.810488i	$0.699202\pi$
$524$	3.70820	−	6.42280i	0.161994	−	0.280581i
$525$		0			0
$526$	−6.66312	+	11.5409i	−0.290526	+	0.503205i
$527$		0			0
$528$	−45.9787			−2.00097
$529$	−22.4164	+	38.8264i	−0.974626	+	1.68810i
$530$		0			0
$531$	−12.7082	−	22.0113i	−0.551489	−	0.955207i
$532$	−0.0344419			−0.00149324
$533$	20.8050	−	5.14789i	0.901162	−	0.222980i
$534$	32.5623			1.40911
$535$		0			0
$536$	11.9721	+	20.7363i	0.517118	+	0.895674i
$537$	4.20820	−	7.28882i	0.181597	−	0.314536i
$538$	25.0344			1.07931
$539$	14.7082	−	25.4754i	0.633527	−	1.09730i
$540$		0			0
$541$	7.88854			0.339155			0.169577	−	0.985517i	$-0.445760\pi$
$541$	7.88854			0.339155			0.169577	+	0.985517i	$0.445760\pi$
$542$	11.8992	−	20.6100i	0.511114	−	0.885275i
$543$	−6.70820	−	11.6190i	−0.287877	−	0.498617i
$544$	9.25329	+	16.0272i	0.396731	+	0.687159i
$545$		0			0
$546$	2.98936	−	0.739674i	0.127933	−	0.0316551i
$547$	34.8328			1.48934			0.744672	−	0.667431i	$-0.232606\pi$
$547$	34.8328			1.48934			0.744672	+	0.667431i	$0.232606\pi$
$548$	−2.30902	−	3.99933i	−0.0986363	−	0.170843i
$549$	12.4164	+	21.5058i	0.529919	+	0.917847i
$550$		0			0
$551$	−0.347524			−0.0148050
$552$	20.5902	−	35.6632i	0.876376	−	1.51793i
$553$		0			0
$554$	−30.5623			−1.29847
$555$		0			0
$556$	1.01722	+	1.76188i	0.0431398	+	0.0747203i
$557$	3.97214	+	6.87994i	0.168305	+	0.291512i	0.937824	−	0.347111i	$-0.112837\pi$
$557$	3.97214	+	6.87994i	0.168305	+	0.291512i	−0.769519	+	0.638624i	$0.779504\pi$
$558$		0			0
$559$	4.40983	+	4.58283i	0.186516	+	0.193833i
$560$		0			0
$561$	25.9164	+	44.8885i	1.09419	+	1.89520i
$562$	16.0902	+	27.8690i	0.678723	+	1.17558i
$563$	8.64590	−	14.9751i	0.364381	−	0.631127i	−0.624295	−	0.781188i	$-0.714614\pi$
$563$	8.64590	−	14.9751i	0.364381	−	0.631127i	0.988677	+	0.150062i	$0.0479472\pi$
$564$	−17.8885			−0.753244
$565$		0			0
$566$	−2.19098	+	3.79489i	−0.0920939	+	0.159511i
$567$	−2.59675			−0.109053
$568$	1.97214	−	3.41584i	0.0827490	−	0.143325i
$569$	9.44427	+	16.3580i	0.395924	+	0.685761i	0.993219	−	0.116261i	$-0.0370909\pi$
$569$	9.44427	+	16.3580i	0.395924	+	0.685761i	−0.597294	+	0.802022i	$0.703758\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	2.61803	−	9.06914i	0.109466	−	0.379200i
$573$	−10.7771			−0.450219
$574$	−1.13525	−	1.96632i	−0.0473846	−	0.0820726i
$575$		0			0
$576$	−4.23607	+	7.33708i	−0.176503	+	0.305712i
$577$	7.88854			0.328404			0.164202	−	0.986427i	$-0.447495\pi$
$577$	7.88854			0.328404			0.164202	+	0.986427i	$0.447495\pi$
$578$	10.4721	−	18.1383i	0.435583	−	0.754453i
$579$	6.11803	−	10.5967i	0.254257	−	0.440386i
$580$		0			0
$581$	−1.05573	+	1.82857i	−0.0437990	+	0.0758621i
$582$	−9.89919	−	17.1459i	−0.410335	−	0.710720i
$583$	12.7082	+	22.0113i	0.526320	+	0.911613i
$584$	13.4164			0.555175
$585$		0			0
$586$	−19.5066			−0.805809
$587$	2.88197	+	4.99171i	0.118951	+	0.206030i	0.919352	−	0.393435i	$-0.128713\pi$
$587$	2.88197	+	4.99171i	0.118951	+	0.206030i	−0.800401	+	0.599465i	$0.795380\pi$
$588$	4.79837	+	8.31103i	0.197882	+	0.342741i
$589$		0			0
$590$		0			0
$591$	3.35410	−	5.80948i	0.137969	−	0.238970i
$592$	−7.28115	+	12.6113i	−0.299254	+	0.518322i
$593$	−27.8885			−1.14525			−0.572623	−	0.819819i	$-0.694074\pi$
$593$	−27.8885			−1.14525			−0.572623	+	0.819819i	$0.694074\pi$
$594$	−7.66312	+	13.2729i	−0.314422	+	0.544594i
$595$		0			0
$596$	−4.16312	−	7.21073i	−0.170528	−	0.295363i
$597$	−32.8885			−1.34604
$598$	33.3156	+	34.6226i	1.36238	+	1.41582i
$599$	−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
$601$	−13.0279	−	22.5649i	−0.531418	−	0.920442i	−0.999328	−	0.0366662i	$-0.988326\pi$
$601$	−13.0279	−	22.5649i	−0.531418	−	0.920442i	0.467910	−	0.883776i	$-0.345007\pi$
$602$	0.336881	−	0.583495i	0.0137302	−	0.0237815i
$603$	−21.4164			−0.872144
$604$	−2.47214	+	4.28187i	−0.100590	+	0.174227i
$605$		0			0
$606$	−34.2705			−1.39214
$607$	6.35410	−	11.0056i	0.257905	−	0.446705i	−0.707775	−	0.706437i	$-0.750301\pi$
$607$	6.35410	−	11.0056i	0.257905	−	0.446705i	0.965681	+	0.259733i	$0.0836345\pi$
$608$	0.399187	+	0.691412i	0.0161892	+	0.0280405i
$609$	−0.388544	−	0.672978i	−0.0157446	−	0.0272704i
$610$		0			0
$611$	−12.9443	+	44.8403i	−0.523669	+	1.81404i
$612$	−6.76393			−0.273416
$613$	11.0279	+	19.1008i	0.445411	+	0.771475i	0.998081	−	0.0619256i	$-0.0197242\pi$
$613$	11.0279	+	19.1008i	0.445411	+	0.771475i	−0.552670	+	0.833400i	$0.686391\pi$
$614$	−5.70820	−	9.88690i	−0.230364	−	0.399003i
$615$		0			0
$616$	2.23607			0.0900937
$617$	−6.79180	+	11.7637i	−0.273427	+	0.473590i	−0.969737	−	0.244151i	$-0.921491\pi$
$617$	−6.79180	+	11.7637i	−0.273427	+	0.473590i	0.696310	+	0.717741i	$0.254824\pi$
$618$	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
$621$	−9.20820	−	15.9491i	−0.369512	−	0.640014i
$622$	−19.4164	−	33.6302i	−0.778527	−	1.34845i
$623$	−2.12461			−0.0851208
$624$	−27.1353	−	28.1998i	−1.08628	−	1.12889i
$625$		0			0
$626$	25.7984	+	44.6841i	1.03111	+	1.78594i
$627$	1.11803	+	1.93649i	0.0446500	+	0.0773360i
$628$	−5.56231	+	9.63420i	−0.221960	+	0.384446i
$629$	16.4164			0.654565
$630$		0			0
$631$	−12.0623	+	20.8925i	−0.480193	+	0.831718i	−0.999742	−	0.0227223i	$-0.992767\pi$
$631$	−12.0623	+	20.8925i	−0.480193	+	0.831718i	0.519549	+	0.854441i	$0.326100\pi$
$632$		0			0
$633$	−10.2639	+	17.7777i	−0.407955	+	0.706598i
$634$	−19.3262	−	33.4740i	−0.767543	−	1.32942i
$635$		0			0
$636$	−8.29180			−0.328791
$637$	24.3050	−	6.01392i	0.962997	−	0.238280i
$638$	−10.0902			−0.399474
$639$	1.76393	+	3.05522i	0.0697801	+	0.120863i
$640$		0			0
$641$	13.4443	−	23.2862i	0.531017	−	0.919748i	−0.468328	−	0.883555i	$-0.655143\pi$
$641$	13.4443	−	23.2862i	0.531017	−	0.919748i	0.999345	−	0.0361934i	$-0.0115232\pi$
$642$	−37.0344			−1.46163
$643$	−15.3541	+	26.5941i	−0.605507	+	1.04877i	0.386465	+	0.922304i	$0.373696\pi$
$643$	−15.3541	+	26.5941i	−0.605507	+	1.04877i	−0.991971	+	0.126464i	$0.959637\pi$
$644$	0.600813	−	1.04064i	0.0236754	−	0.0410069i
$645$		0			0
$646$	1.04508	−	1.81014i	0.0411183	−	0.0712190i
$647$	−23.2984	−	40.3540i	−0.915954	−	1.58648i	−0.805499	−	0.592597i	$-0.798103\pi$
$647$	−23.2984	−	40.3540i	−0.915954	−	1.58648i	−0.110454	−	0.993881i	$-0.535231\pi$
$648$	12.2984	+	21.3014i	0.483126	+	0.836798i
$649$	53.8328			2.11312
$650$		0			0
$651$		0			0
$652$	0.399187	+	0.691412i	0.0156334	+	0.0270778i
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	0.584091	−	0.811688i	$-0.301451\pi$
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	−0.994988	+	0.0999939i	$0.968118\pi$
$654$	−3.61803	+	6.26662i	−0.141476	+	0.245044i
$655$		0			0
$656$	−14.4271	+	24.9884i	−0.563282	+	0.975633i
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$	4.94427			0.192748
$659$	24.1180	−	41.7737i	0.939505	−	1.62727i	0.173109	−	0.984903i	$-0.444619\pi$
$659$	24.1180	−	41.7737i	0.939505	−	1.62727i	0.766396	−	0.642368i	$-0.222048\pi$
$660$		0			0
$661$	−1.68034	−	2.91043i	−0.0653576	−	0.113203i	0.831495	−	0.555532i	$-0.187485\pi$
$661$	−1.68034	−	2.91043i	−0.0653576	−	0.113203i	−0.896853	+	0.442330i	$0.854152\pi$
$662$	−41.5066			−1.61320
$663$	−12.2361	+	42.3870i	−0.475210	+	1.64617i
$664$	20.0000			0.776151
$665$		0			0
$666$	−4.85410	−	8.40755i	−0.188093	−	0.325786i
$667$	6.06231	−	10.5002i	0.234733	−	0.406570i
$668$	−3.20163			−0.123875
$669$	−14.2082	+	24.6093i	−0.549321	+	0.951452i
$670$		0			0
$671$	−52.5967			−2.03047
$672$	−0.892609	+	1.54604i	−0.0344331	+	0.0596400i
$673$	−18.2082	−	31.5375i	−0.701875	−	1.21568i	−0.967808	−	0.251691i	$-0.919013\pi$
$673$	−18.2082	−	31.5375i	−0.701875	−	1.21568i	0.265933	−	0.963992i	$-0.414320\pi$
$674$	−22.5623	−	39.0791i	−0.869068	−	1.50527i
$675$		0			0
$676$	7.10739	−	3.74663i	0.273361	−	0.144101i
$677$	−47.8885			−1.84051			−0.920253	−	0.391324i	$-0.872017\pi$
$677$	−47.8885			−1.84051			−0.920253	+	0.391324i	$0.872017\pi$
$678$	13.5172	+	23.4125i	0.519126	+	0.899152i
$679$	0.645898	+	1.11873i	0.0247873	+	0.0429328i
$680$		0			0
$681$	3.94427			0.151145
$682$		0			0
$683$	15.1180	−	26.1852i	0.578475	−	1.00195i	−0.417179	−	0.908824i	$-0.636981\pi$
$683$	15.1180	−	26.1852i	0.578475	−	1.00195i	0.995654	−	0.0931246i	$-0.0296855\pi$
$684$	−0.291796			−0.0111571
$685$		0			0
$686$	−2.66312	−	4.61266i	−0.101678	−	0.176112i
$687$	22.2361	+	38.5140i	0.848359	+	1.46940i
$688$	−8.56231			−0.326435
$689$	−6.00000	+	20.7846i	−0.228582	+	0.791831i
$690$		0			0
$691$	5.29837	+	9.17705i	0.201560	+	0.349112i	0.949031	−	0.315182i	$-0.102066\pi$
$691$	5.29837	+	9.17705i	0.201560	+	0.349112i	−0.747471	+	0.664294i	$0.768732\pi$
$692$	5.21885	+	9.03931i	0.198391	+	0.343623i
$693$	−1.00000	+	1.73205i	−0.0379869	+	0.0657952i
$694$	27.9787			1.06206
$695$		0			0
$696$	−3.68034	+	6.37454i	−0.139503	+	0.241626i
$697$	32.5279			1.23208
$698$	−19.7533	+	34.2137i	−0.747673	+	1.29501i
$699$	22.2361	+	38.5140i	0.841045	+	1.45673i
$700$		0			0
$701$	−27.8885			−1.05334			−0.526668	−	0.850071i	$-0.676559\pi$
$701$	−27.8885			−1.05334			−0.526668	+	0.850071i	$0.676559\pi$
$702$	−12.6631	+	3.13331i	−0.477939	+	0.118259i
$703$	0.708204			0.0267104
$704$	−8.97214	−	15.5402i	−0.338150	−	0.585693i
$705$		0			0
$706$	8.51722	−	14.7523i	0.320550	−	0.555209i
$707$	2.23607			0.0840960
$708$	−8.78115	+	15.2094i	−0.330016	+	0.571604i
$709$	19.1525	−	33.1731i	0.719286	−	1.24584i	−0.241997	−	0.970277i	$-0.577802\pi$
$709$	19.1525	−	33.1731i	0.719286	−	1.24584i	0.961283	−	0.275563i	$-0.0888644\pi$
$710$		0			0
$711$		0			0
$712$	10.0623	+	17.4284i	0.377101	+	0.653158i
$713$		0			0
$714$	4.67376			0.174911
$715$		0			0
$716$	−2.32624			−0.0869356
$717$	−11.0557	−	19.1491i	−0.412884	−	0.715136i
$718$	−14.4721	−	25.0665i	−0.540095	−	0.935473i
$719$	−4.06231	+	7.03612i	−0.151498	+	0.262403i	−0.931779	−	0.363027i	$-0.881743\pi$
$719$	−4.06231	+	7.03612i	−0.151498	+	0.262403i	0.780280	+	0.625430i	$0.215077\pi$
$720$		0			0
$721$	−0.583592	+	1.01081i	−0.0217341	+	0.0376446i
$722$	−15.3262	+	26.5458i	−0.570384	+	0.987933i
$723$	33.5410			1.24740
$724$	−1.85410	+	3.21140i	−0.0689072	+	0.119351i
$725$		0			0
$726$	12.5623	+	21.7586i	0.466231	+	0.807536i
$727$	−11.0557			−0.410034			−0.205017	−	0.978758i	$-0.565725\pi$
$727$	−11.0557			−0.410034			−0.205017	+	0.978758i	$0.565725\pi$
$728$	1.31966	+	1.37143i	0.0489099	+	0.0508286i
$729$	−7.00000			−0.259259
$730$		0			0
$731$	4.82624	+	8.35929i	0.178505	+	0.309179i
$732$	8.57953	−	14.8602i	0.317108	−	0.549248i
$733$	8.11146			0.299603			0.149802	−	0.988716i	$-0.452136\pi$
$733$	8.11146			0.299603			0.149802	+	0.988716i	$0.452136\pi$
$734$	20.7533	−	35.9458i	0.766018	−	1.32678i
$735$		0			0
$736$	−27.8541			−1.02672
$737$	22.6803	−	39.2835i	0.835441	−	1.44703i
$738$	−9.61803	−	16.6589i	−0.354045	−	0.613223i
$739$	19.7705	+	34.2435i	0.727270	+	1.25967i	0.958033	+	0.286659i	$0.0925445\pi$
$739$	19.7705	+	34.2435i	0.727270	+	1.25967i	−0.230763	+	0.973010i	$0.574122\pi$
$740$		0			0
$741$	−0.527864	+	1.82857i	−0.0193916	+	0.0671744i
$742$	2.29180			0.0841345
$743$	1.06231	+	1.83997i	0.0389722	+	0.0675019i	0.884854	−	0.465869i	$-0.154258\pi$
$743$	1.06231	+	1.83997i	0.0389722	+	0.0675019i	−0.845881	+	0.533371i	$0.820925\pi$
$744$		0			0
$745$		0			0
$746$	16.2705			0.595706
$747$	−8.94427	+	15.4919i	−0.327254	+	0.566820i
$748$	7.16312	−	12.4069i	0.261910	−	0.453641i
$749$	2.41641			0.0882936
$750$		0			0
$751$	8.64590	+	14.9751i	0.315493	+	0.546450i	0.979542	−	0.201239i	$-0.0644967\pi$
$751$	8.64590	+	14.9751i	0.315493	+	0.546450i	−0.664049	+	0.747689i	$0.731163\pi$
$752$	−31.4164	−	54.4148i	−1.14564	−	1.98430i
$753$	35.2492			1.28455
$754$	−5.95492	−	6.18853i	−0.216865	−	0.225373i
$755$		0			0
$756$	0.163119	+	0.282530i	0.00593258	+	0.0102755i
$757$	14.4443	+	25.0182i	0.524986	+	0.909302i	0.999577	+	0.0290958i	$0.00926278\pi$
$757$	14.4443	+	25.0182i	0.524986	+	0.909302i	−0.474591	+	0.880207i	$0.657404\pi$
$758$	26.8435	−	46.4942i	0.974998	−	1.68875i
$759$	−78.0132			−2.83170
$760$		0			0
$761$	10.0279	−	17.3688i	0.363510	−	0.629617i	−0.625026	−	0.780604i	$-0.714912\pi$
$761$	10.0279	−	17.3688i	0.363510	−	0.629617i	0.988536	+	0.150986i	$0.0482450\pi$
$762$	0.854102			0.0309408
$763$	0.236068	−	0.408882i	0.00854623	−	0.0148025i
$764$	1.48936	+	2.57964i	0.0538830	+	0.0933282i
$765$		0			0
$766$	−0.381966			−0.0138010
$767$	31.7705	+	33.0169i	1.14717	+	1.19217i
$768$	30.3262			1.09430
$769$	11.9164	+	20.6398i	0.429717	+	0.744291i	0.996848	−	0.0793363i	$-0.0252801\pi$
$769$	11.9164	+	20.6398i	0.429717	+	0.744291i	−0.567131	+	0.823627i	$0.691947\pi$
$770$		0			0
$771$	9.53444	−	16.5141i	0.343375	−	0.594742i
$772$	−3.38197			−0.121720
$773$	−18.9721	+	32.8607i	−0.682380	+	1.18192i	0.291872	+	0.956457i	$0.405722\pi$
$773$	−18.9721	+	32.8607i	−0.682380	+	1.18192i	−0.974252	+	0.225460i	$0.927612\pi$
$774$	2.85410	−	4.94345i	0.102589	−	0.177689i
$775$		0			0
$776$	6.11803	−	10.5967i	0.219625	−	0.380401i
$777$	0.791796	+	1.37143i	0.0284055	+	0.0491998i
$778$	−29.0344	−	50.2891i	−1.04094	−	1.80295i
$779$	1.40325			0.0502767
$780$		0			0
$781$	−7.47214			−0.267374
$782$	36.4615	+	63.1532i	1.30386	+	2.25835i
$783$	1.64590	+	2.85078i	0.0588196	+	0.101879i
$784$	−16.8541	+	29.1922i	−0.601932	+	1.04258i
$785$		0			0
$786$	−21.7082	+	37.5997i	−0.774306	+	1.34114i
$787$	−18.7705	+	32.5115i	−0.669096	+	1.15891i	0.309061	+	0.951042i	$0.399985\pi$
$787$	−18.7705	+	32.5115i	−0.669096	+	1.15891i	−0.978157	+	0.207867i	$0.933348\pi$
$788$	−1.85410			−0.0660496
$789$	9.20820	−	15.9491i	0.327821	−	0.567802i
$790$		0			0
$791$	−0.881966	−	1.52761i	−0.0313591	−	0.0543156i
$792$	18.9443			0.673155
$793$	−31.0410	−	32.2588i	−1.10230	−	1.14554i
$794$	16.2705			0.577419
$795$		0			0
$796$	4.54508	+	7.87232i	0.161096	+	0.279027i
$797$	0.0835921	−	0.144786i	0.00296099	−	0.00512858i	−0.864541	−	0.502562i	$-0.832391\pi$
$797$	0.0835921	−	0.144786i	0.00296099	−	0.00512858i	0.867502	+	0.497434i	$0.165724\pi$
$798$	0.201626			0.00713749
$799$	−35.4164	+	61.3430i	−1.25294	+	2.17016i
$800$		0			0
$801$	−18.0000			−0.635999
$802$	−21.7533	+	37.6778i	−0.768135	+	1.33045i
$803$	−12.7082	−	22.0113i	−0.448463	−	0.776760i
$804$	7.39919	+	12.8158i	0.260949	+	0.451977i
$805$		0			0
$806$		0			0
$807$	−34.5967			−1.21786
$808$	−10.5902	−	18.3427i	−0.372561	−	0.645294i
$809$	−16.4443	−	28.4823i	−0.578150	−	1.00138i	−0.995692	−	0.0927271i	$-0.970442\pi$
$809$	−16.4443	−	28.4823i	−0.578150	−	1.00138i	0.417542	−	0.908658i	$-0.362892\pi$
$810$		0			0
$811$	−39.7771			−1.39676			−0.698381	−	0.715726i	$-0.746096\pi$
$811$	−39.7771			−1.39676			−0.698381	+	0.715726i	$0.746096\pi$
$812$	−0.107391	+	0.186006i	−0.00376868	+	0.00652755i
$813$	−16.4443	+	28.4823i	−0.576726	+	0.998918i
$814$	20.5623			0.720708
$815$		0			0
$816$	−29.6976	−	51.4377i	−1.03962	−	1.80068i
$817$	0.208204	+	0.360620i	0.00728413	+	0.0126165i
$818$	17.6180			0.616000
$819$	−1.65248	+	0.408882i	−0.0577422	+	0.0142875i
$820$		0			0
$821$	−9.68034	−	16.7668i	−0.337846	−	0.585167i	0.646181	−	0.763184i	$-0.276365\pi$
$821$	−9.68034	−	16.7668i	−0.337846	−	0.585167i	−0.984027	+	0.178017i	$0.943032\pi$
$822$	13.5172	+	23.4125i	0.471467	+	0.816605i
$823$	11.2984	−	19.5694i	0.393837	−	0.682145i	−0.599115	−	0.800663i	$-0.704481\pi$
$823$	11.2984	−	19.5694i	0.393837	−	0.682145i	0.992952	+	0.118518i	$0.0378143\pi$
$824$	11.0557			0.385145
$825$		0			0
$826$	2.42705	−	4.20378i	0.0844479	−	0.146268i
$827$	−8.94427			−0.311023			−0.155511	−	0.987834i	$-0.549703\pi$
$827$	−8.94427			−0.311023			−0.155511	+	0.987834i	$0.549703\pi$
$828$	5.09017	−	8.81643i	0.176896	−	0.306392i
$829$	−18.6246	−	32.2588i	−0.646860	−	1.12039i	−0.983869	−	0.178892i	$-0.942749\pi$
$829$	−18.6246	−	32.2588i	−0.646860	−	1.12039i	0.337009	−	0.941501i	$-0.390585\pi$
$830$		0			0
$831$	42.2361			1.46515
$832$	4.23607	−	14.6742i	0.146859	−	0.508735i
$833$	38.0000			1.31662
$834$	−5.95492	−	10.3142i	−0.206202	−	0.357152i
$835$		0			0
$836$	0.309017	−	0.535233i	0.0106876	−	0.0185114i
$837$		0			0
$838$	−11.0451	+	19.1306i	−0.381546	+	0.660857i
$839$	−8.64590	+	14.9751i	−0.298490	+	0.516999i	−0.975791	−	0.218707i	$-0.929816\pi$
$839$	−8.64590	+	14.9751i	−0.298490	+	0.516999i	0.677301	+	0.735706i	$0.263149\pi$
$840$		0			0
$841$	13.4164	−	23.2379i	0.462635	−	0.801307i
$842$	4.85410	+	8.40755i	0.167283	+	0.289743i
$843$	−22.2361	−	38.5140i	−0.765851	−	1.32649i
$844$	5.67376			0.195299
$845$		0			0
$846$	41.8885			1.44016
$847$	−0.819660	−	1.41969i	−0.0281639	−	0.0487812i
$848$	−14.5623	−	25.2227i	−0.500072	−	0.866149i
$849$	3.02786	−	5.24441i	0.103916	−	0.179988i
$850$		0			0
$851$	−12.3541	+	21.3979i	−0.423493	+	0.733512i
$852$	1.21885	−	2.11111i	0.0417570	−	0.0723253i
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$	−2.37132	+	4.10725i	−0.0811450	+	0.140547i
$855$		0			0
$856$	−11.4443	−	19.8221i	−0.391157	−	0.677504i
$857$	−0.111456			−0.00380727			−0.00190364	−	0.999998i	$-0.500606\pi$
$857$	−0.111456			−0.00380727			−0.00190364	+	0.999998i	$0.500606\pi$
$858$	−15.3262	+	53.0916i	−0.523229	+	1.81252i
$859$	−13.8885			−0.473871			−0.236935	−	0.971525i	$-0.576143\pi$
$859$	−13.8885			−0.473871			−0.236935	+	0.971525i	$0.576143\pi$
$860$		0			0
$861$	1.56888	+	2.71739i	0.0534674	+	0.0926083i
$862$	3.89919	−	6.75359i	0.132807	−	0.230028i
$863$	38.8328			1.32188			0.660942	−	0.750437i	$-0.270157\pi$
$863$	38.8328			1.32188			0.660942	+	0.750437i	$0.270157\pi$
$864$	3.78115	−	6.54915i	0.128637	−	0.222807i
$865$		0			0
$866$	−37.9787			−1.29057
$867$	−14.4721	+	25.0665i	−0.491500	+	0.851302i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	37.4787	−	9.27358i	1.26992	−	0.314223i
$872$	−4.47214			−0.151446
$873$	5.47214	+	9.47802i	0.185204	+	0.320782i
$874$	1.57295	+	2.72443i	0.0532058	+	0.0921551i
$875$		0			0
$876$	8.29180			0.280154
$877$	27.8607	−	48.2561i	0.940788	−	1.62949i	0.176816	−	0.984244i	$-0.443420\pi$
$877$	27.8607	−	48.2561i	0.940788	−	1.62949i	0.763972	−	0.645249i	$-0.223246\pi$
$878$	−7.51722	+	13.0202i	−0.253694	+	0.439411i
$879$	26.9574			0.909251
$880$		0			0
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	0.711582	−	0.702603i	$-0.247979\pi$
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	−0.964263	+	0.264946i	$0.914646\pi$
$882$	−11.2361	−	19.4614i	−0.378338	−	0.655301i
$883$	−10.8328			−0.364553			−0.182277	−	0.983247i	$-0.558347\pi$
$883$	−10.8328			−0.364553			−0.182277	+	0.983247i	$0.558347\pi$
$884$	11.8369	−	2.92887i	0.398117	−	0.0985085i
$885$		0			0
$886$	13.7082	+	23.7433i	0.460536	+	0.797672i
$887$	−20.2426	−	35.0613i	−0.679682	−	1.17724i	−0.975077	−	0.221868i	$-0.928785\pi$
$887$	−20.2426	−	35.0613i	−0.679682	−	1.17724i	0.295395	−	0.955375i	$-0.404549\pi$
$888$	7.50000	−	12.9904i	0.251684	−	0.435929i
$889$	−0.0557281			−0.00186906
$890$		0			0
$891$	23.2984	−	40.3540i	0.780525	−	1.35191i
$892$	7.85410			0.262975
$893$	−1.52786	+	2.64634i	−0.0511280	+	0.0885563i
$894$	24.3713	+	42.2124i	0.815099	+	1.41179i
$895$		0			0
$896$	−3.21478			−0.107398
$897$	−46.0410	−	47.8472i	−1.53726	−	1.59757i
$898$	22.5623			0.752914
$899$		0			0
$900$		0			0
$901$	−16.4164	+	28.4341i	−0.546910	+	0.947276i
$902$	40.7426			1.35658
$903$	−0.465558	+	0.806370i	−0.0154928	+	0.0268343i
$904$	−8.35410	+	14.4697i	−0.277853	+	0.481256i
$905$		0			0
$906$	14.4721	−	25.0665i	0.480805	−	0.832778i
$907$	−10.0623	−	17.4284i	−0.334113	−	0.578701i	0.649201	−	0.760617i	$-0.275104\pi$
$907$	−10.0623	−	17.4284i	−0.334113	−	0.578701i	−0.983314	+	0.181916i	$0.941770\pi$
$908$	−0.545085	−	0.944115i	−0.0180893	−	0.0313316i
$909$	18.9443			0.628342
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−1.28115	−	2.21902i	−0.0424232	−	0.0734792i
$913$	−18.9443	−	32.8124i	−0.626964	−	1.08593i
$914$	22.9894	−	39.8187i	0.760420	−	1.31709i
$915$		0			0
$916$	6.14590	−	10.6450i	0.203066	−	0.351721i
$917$	1.41641	−	2.45329i	0.0467739	−	0.0810148i
$918$	−19.7984			−0.653444
$919$	−16.6459	+	28.8315i	−0.549098	+	0.951065i	0.449239	+	0.893412i	$0.351695\pi$
$919$	−16.6459	+	28.8315i	−0.549098	+	0.951065i	−0.998337	+	0.0576532i	$0.981638\pi$
$920$		0			0
$921$	7.88854	+	13.6634i	0.259936	+	0.450223i
$922$	45.9787			1.51423
$923$	−4.40983	−	4.58283i	−0.145151	−	0.150846i
$924$	1.38197			0.0454633
$925$		0			0
$926$	−23.4164	−	40.5584i	−0.769511	−	1.33283i
$927$	−4.94427	+	8.56373i	−0.162391	+	0.281270i
$928$	4.97871			0.163434
$929$	−1.02786	+	1.78031i	−0.0337231	+	0.0584102i	−0.882394	−	0.470511i	$-0.844070\pi$
$929$	−1.02786	+	1.78031i	−0.0337231	+	0.0584102i	0.848671	+	0.528921i	$0.177403\pi$
$930$		0			0
$931$	1.63932			0.0537266
$932$	6.14590	−	10.6450i	0.201316	−	0.348689i
$933$	26.8328	+	46.4758i	0.878467	+	1.52155i
$934$	7.23607	+	12.5332i	0.236771	+	0.410100i
$935$		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	$0.468754\pi$
$938$	−2.04508	−	3.54219i	−0.0667744	−	0.115657i
$939$	−35.6525	−	61.7519i	−1.16347	−	2.01520i
$940$		0			0
$941$	23.8885			0.778744			0.389372	−	0.921081i	$-0.372692\pi$
$941$	23.8885			0.778744			0.389372	+	0.921081i	$0.372692\pi$
$942$	32.5623	−	56.3996i	1.06094	−	1.83760i
$943$	−24.4787	+	42.3984i	−0.797137	+	1.38068i
$944$	−61.6869			−2.00774
$945$		0			0
$946$	6.04508	+	10.4704i	0.196543	+	0.340422i
$947$	8.40983	+	14.5663i	0.273283	+	0.473340i	0.969700	−	0.244297i	$-0.0785572\pi$
$947$	8.40983	+	14.5663i	0.273283	+	0.473340i	−0.696418	+	0.717637i	$0.745224\pi$
$948$		0			0
$949$	6.00000	−	20.7846i	0.194768	−	0.674697i
$950$		0			0
$951$	26.7082	+	46.2600i	0.866073	+	1.50008i
$952$	1.44427	+	2.50155i	0.0468091	+	0.0810758i
$953$	−28.0967	+	48.6650i	−0.910143	+	1.57641i	−0.0962820	+	0.995354i	$0.530695\pi$
$953$	−28.0967	+	48.6650i	−0.910143	+	1.57641i	−0.813861	+	0.581060i	$0.802638\pi$
$954$	19.4164			0.628629
$955$		0			0
$956$	−3.05573	+	5.29268i	−0.0988293	+	0.171177i
$957$	13.9443			0.450754
$958$	−6.57295	+	11.3847i	−0.212362	+	0.367822i
$959$	−0.881966	−	1.52761i	−0.0284802	−	0.0493291i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	12.1353	+	12.6113i	0.391256	+	0.406605i
$963$	20.4721			0.659705
$964$	−4.63525	−	8.02850i	−0.149292	−	0.258580i
$965$		0			0
$966$	−3.51722	+	6.09201i	−0.113165	+	0.196007i
$967$	1.16718			0.0375341			0.0187671	−	0.999824i	$-0.494026\pi$
$967$	1.16718			0.0375341			0.0187671	+	0.999824i	$0.494026\pi$
$968$	−7.76393	+	13.4475i	−0.249542	+	0.432220i
$969$	−1.44427	+	2.50155i	−0.0463967	+	0.0803614i
$970$		0			0
$971$	8.11803	−	14.0608i	0.260520	−	0.451234i	−0.705860	−	0.708351i	$-0.749439\pi$
$971$	8.11803	−	14.0608i	0.260520	−	0.451234i	0.966380	+	0.257117i	$0.0827726\pi$
$972$	5.52786	+	9.57454i	0.177306	+	0.307104i
$973$	0.388544	+	0.672978i	0.0124561	+	0.0215747i
$974$	−42.2705			−1.35443
$975$		0			0
$976$	60.2705			1.92921
$977$	17.2082	+	29.8055i	0.550539	+	0.953562i	0.998236	+	0.0593763i	$0.0189112\pi$
$977$	17.2082	+	29.8055i	0.550539	+	0.953562i	−0.447696	+	0.894186i	$0.647755\pi$
$978$	−2.33688	−	4.04760i	−0.0747252	−	0.129428i
$979$	19.0623	−	33.0169i	0.609234	−	1.05522i
$980$		0			0
$981$	2.00000	−	3.46410i	0.0638551	−	0.110600i
$982$	3.42705	−	5.93583i	0.109362	−	0.189420i
$983$	14.8328			0.473093			0.236547	−	0.971620i	$-0.423984\pi$
$983$	14.8328			0.473093			0.236547	+	0.971620i	$0.423984\pi$
$984$	14.8607	−	25.7395i	0.473741	−	0.820544i
$985$		0			0
$986$	−6.51722	−	11.2882i	−0.207551	−	0.359488i
$987$	−6.83282			−0.217491
$988$	0.510643	−	0.126351i	0.0162457	−	0.00401977i
$989$	−14.5279			−0.461959
$990$		0			0
$991$	16.6459	+	28.8315i	0.528774	+	0.915864i	0.999437	+	0.0335508i	$0.0106816\pi$
$991$	16.6459	+	28.8315i	0.528774	+	0.915864i	−0.470663	+	0.882313i	$0.655985\pi$
$992$		0			0
$993$	57.3607			1.82029
$994$	−0.336881	+	0.583495i	−0.0106852	+	0.0185073i
$995$		0			0
$996$	12.3607			0.391663
$997$	8.44427	−	14.6259i	0.267433	−	0.463207i	−0.700765	−	0.713392i	$-0.747158\pi$
$997$	8.44427	−	14.6259i	0.267433	−	0.463207i	0.968198	+	0.250185i	$0.0804913\pi$
$998$	11.2361	+	19.4614i	0.355672	+	0.616041i
$999$	−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.276.2		4
5.2	odd	4		325.2.o.a.224.1		8
5.3	odd	4		325.2.o.a.224.4		8
5.4	even	2		65.2.e.a.16.1	✓	4
13.3	even	3		4225.2.a.u.1.1		2
13.9	even	3	inner	325.2.e.b.126.2		4
13.10	even	6		4225.2.a.y.1.2		2
15.14	odd	2		585.2.j.e.406.2		4
20.19	odd	2		1040.2.q.n.81.1		4
65.4	even	6		845.2.e.g.191.2		4
65.9	even	6		65.2.e.a.61.1	yes	4
65.19	odd	12		845.2.m.e.316.4		8
65.22	odd	12		325.2.o.a.74.4		8
65.24	odd	12		845.2.c.c.506.4		4
65.29	even	6		845.2.a.e.1.2		2
65.34	odd	4		845.2.m.e.361.4		8
65.44	odd	4		845.2.m.e.361.1		8
65.48	odd	12		325.2.o.a.74.1		8
65.49	even	6		845.2.a.b.1.1		2
65.54	odd	12		845.2.c.c.506.1		4
65.59	odd	12		845.2.m.e.316.1		8
65.64	even	2		845.2.e.g.146.2		4
195.29	odd	6		7605.2.a.ba.1.1		2
195.74	odd	6		585.2.j.e.451.2		4
195.179	odd	6		7605.2.a.bf.1.2		2
260.139	odd	6		1040.2.q.n.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.a.16.1	✓	4	5.4	even	2
65.2.e.a.61.1	yes	4	65.9	even	6
325.2.e.b.126.2		4	13.9	even	3	inner
325.2.e.b.276.2		4	1.1	even	1	trivial
325.2.o.a.74.1		8	65.48	odd	12
325.2.o.a.74.4		8	65.22	odd	12
325.2.o.a.224.1		8	5.2	odd	4
325.2.o.a.224.4		8	5.3	odd	4
585.2.j.e.406.2		4	15.14	odd	2
585.2.j.e.451.2		4	195.74	odd	6
845.2.a.b.1.1		2	65.49	even	6
845.2.a.e.1.2		2	65.29	even	6
845.2.c.c.506.1		4	65.54	odd	12
845.2.c.c.506.4		4	65.24	odd	12
845.2.e.g.146.2		4	65.64	even	2
845.2.e.g.191.2		4	65.4	even	6
845.2.m.e.316.1		8	65.59	odd	12
845.2.m.e.316.4		8	65.19	odd	12
845.2.m.e.361.1		8	65.44	odd	4
845.2.m.e.361.4		8	65.34	odd	4
1040.2.q.n.81.1		4	20.19	odd	2
1040.2.q.n.321.1		4	260.139	odd	6
4225.2.a.u.1.1		2	13.3	even	3
4225.2.a.y.1.2		2	13.10	even	6
7605.2.a.ba.1.1		2	195.29	odd	6
7605.2.a.bf.1.2		2	195.179	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 1.40126i) q^{2} +(-1.11803 - 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(1.80902 - 3.13331i) q^{6} +(-0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 1.40126i) q^{2} +(-1.11803 - 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(1.80902 - 3.13331i) q^{6} +(-0.118034 + 0.204441i) q^{7} +2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-2.11803 - 3.66854i) q^{11} +1.38197 q^{12} +(1.00000 - 3.46410i) q^{13} -0.381966 q^{14} +(2.42705 + 4.20378i) q^{16} +(2.73607 - 4.73901i) q^{17} -3.23607 q^{18} +(0.118034 - 0.204441i) q^{19} +0.527864 q^{21} +(3.42705 - 5.93583i) q^{22} +(4.11803 + 7.13264i) q^{23} +(-2.50000 - 4.33013i) q^{24} +(5.66312 - 1.40126i) q^{26} -2.23607 q^{27} +(-0.0729490 - 0.126351i) q^{28} +(-0.736068 - 1.27491i) q^{29} +(-1.69098 + 2.92887i) q^{32} +(-4.73607 + 8.20311i) q^{33} +8.85410 q^{34} +(-0.618034 - 1.07047i) q^{36} +(1.50000 + 2.59808i) q^{37} +0.381966 q^{38} +(-7.82624 + 1.93649i) q^{39} +(2.97214 + 5.14789i) q^{41} +(0.427051 + 0.739674i) q^{42} +(-0.881966 + 1.52761i) q^{43} +2.61803 q^{44} +(-6.66312 + 11.5409i) q^{46} -12.9443 q^{47} +(5.42705 - 9.39993i) q^{48} +(3.47214 + 6.01392i) q^{49} -12.2361 q^{51} +(1.54508 + 1.60570i) q^{52} -6.00000 q^{53} +(-1.80902 - 3.13331i) q^{54} +(-0.263932 + 0.457144i) q^{56} -0.527864 q^{57} +(1.19098 - 2.06284i) q^{58} +(-6.35410 + 11.0056i) q^{59} +(6.20820 - 10.7529i) q^{61} +(-0.236068 - 0.408882i) q^{63} +4.23607 q^{64} -15.3262 q^{66} +(5.35410 + 9.27358i) q^{67} +(1.69098 + 2.92887i) q^{68} +(9.20820 - 15.9491i) q^{69} +(0.881966 - 1.52761i) q^{71} +(-2.23607 + 3.87298i) q^{72} +6.00000 q^{73} +(-2.42705 + 4.20378i) q^{74} +(0.0729490 + 0.126351i) q^{76} +1.00000 q^{77} +(-9.04508 - 9.39993i) q^{78} +(5.50000 + 9.52628i) q^{81} +(-4.80902 + 8.32946i) q^{82} +8.94427 q^{83} +(-0.163119 + 0.282530i) q^{84} -2.85410 q^{86} +(-1.64590 + 2.85078i) q^{87} +(-4.73607 - 8.20311i) q^{88} +(4.50000 + 7.79423i) q^{89} +(0.590170 + 0.613323i) q^{91} -5.09017 q^{92} +(-10.4721 - 18.1383i) q^{94} +7.56231 q^{96} +(2.73607 - 4.73901i) q^{97} +(-5.61803 + 9.73072i) q^{98} +8.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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