LMFDB - Embedded newform 475.2.e.f.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.5
Root			$-0.928369 + 1.60798i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.f.201.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.740597 + 1.28275i) q^{2} +(-1.42837 - 2.47401i) q^{3} +(-0.0969683 + 0.167954i) q^{4} +(2.11569 - 3.66449i) q^{6} +3.78541 q^{7} +2.67513 q^{8} +(-2.58048 + 4.46952i) q^{9} -5.59460 q^{11} +0.554026 q^{12} +(2.45326 - 4.24917i) q^{13} +(2.80346 + 4.85574i) q^{14} +(2.17513 + 3.76744i) q^{16} +(-0.875095 - 1.51571i) q^{17} -7.64438 q^{18} +(0.636061 - 4.31224i) q^{19} +(-5.40696 - 9.36514i) q^{21} +(-4.14335 - 7.17648i) q^{22} +(0.290768 - 0.503625i) q^{23} +(-3.82107 - 6.61830i) q^{24} +7.26750 q^{26} +6.17328 q^{27} +(-0.367065 + 0.635775i) q^{28} +(-0.832153 + 1.44133i) q^{29} +7.01680 q^{31} +(-0.546661 + 0.946844i) q^{32} +(7.99116 + 13.8411i) q^{33} +(1.29619 - 2.24506i) q^{34} +(-0.500449 - 0.866803i) q^{36} -2.36322 q^{37} +(6.00260 - 2.37773i) q^{38} -14.0166 q^{39} +(-0.417676 - 0.723435i) q^{41} +(8.00877 - 13.8716i) q^{42} +(-0.535664 - 0.927797i) q^{43} +(0.542499 - 0.939635i) q^{44} +0.861369 q^{46} +(1.93378 - 3.34941i) q^{47} +(6.21378 - 10.7626i) q^{48} +7.32934 q^{49} +(-2.49992 + 4.32999i) q^{51} +(0.475776 + 0.824069i) q^{52} +(-3.39842 + 5.88624i) q^{53} +(4.57192 + 7.91879i) q^{54} +10.1265 q^{56} +(-11.5771 + 4.58585i) q^{57} -2.46516 q^{58} +(0.204282 + 0.353827i) q^{59} +(-6.98016 + 12.0900i) q^{61} +(5.19662 + 9.00081i) q^{62} +(-9.76817 + 16.9190i) q^{63} +7.08110 q^{64} +(-11.8365 + 20.5013i) q^{66} +(0.390703 - 0.676717i) q^{67} +0.339426 q^{68} -1.66130 q^{69} +(-3.18919 - 5.52384i) q^{71} +(-6.90312 + 11.9565i) q^{72} +(1.44458 + 2.50208i) q^{73} +(-1.75019 - 3.03142i) q^{74} +(0.662580 + 0.524980i) q^{76} -21.1779 q^{77} +(-10.3807 - 17.9799i) q^{78} +(6.25135 + 10.8276i) q^{79} +(-1.07630 - 1.86420i) q^{81} +(0.618659 - 1.07155i) q^{82} +10.3903 q^{83} +2.09722 q^{84} +(0.793422 - 1.37425i) q^{86} +4.75449 q^{87} -14.9663 q^{88} +(-8.92106 + 15.4517i) q^{89} +(9.28659 - 16.0848i) q^{91} +(0.0563906 + 0.0976714i) q^{92} +(-10.0226 - 17.3596i) q^{93} +5.72861 q^{94} +3.12333 q^{96} +(5.49995 + 9.52619i) q^{97} +(5.42809 + 9.40172i) q^{98} +(14.4367 - 25.0052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.740597	+	1.28275i	0.523681	+	0.907043i	0.999620	+	0.0275641i	$0.00877505\pi$
$2$	0.740597	+	1.28275i	0.523681	+	0.907043i	−0.475939	+	0.879478i	$0.657892\pi$
$3$	−1.42837	−	2.47401i	−0.824669	−	1.42837i	−0.902172	−	0.431377i	$-0.858028\pi$
$3$	−1.42837	−	2.47401i	−0.824669	−	1.42837i	0.0775023	−	0.996992i	$-0.475305\pi$
$4$	−0.0969683	+	0.167954i	−0.0484841	+	0.0839770i
$5$		0			0
$5$		0			0
$6$	2.11569	−	3.66449i	0.863728	−	1.49602i
$7$	3.78541			1.43075			0.715375	−	0.698740i	$-0.246256\pi$
$7$	3.78541			1.43075			0.715375	+	0.698740i	$0.246256\pi$
$8$	2.67513			0.945802
$9$	−2.58048	+	4.46952i	−0.860159	+	1.48984i
$10$		0			0
$11$	−5.59460			−1.68684			−0.843418	−	0.537258i	$-0.819460\pi$
$11$	−5.59460			−1.68684			−0.843418	+	0.537258i	$0.819460\pi$
$12$	0.554026			0.159934
$13$	2.45326	−	4.24917i	0.680411	−	1.17851i	−0.294444	−	0.955669i	$-0.595134\pi$
$13$	2.45326	−	4.24917i	0.680411	−	1.17851i	0.974855	−	0.222838i	$-0.0715322\pi$
$14$	2.80346	+	4.85574i	0.749257	+	1.29775i
$15$		0			0
$16$	2.17513	+	3.76744i	0.543783	+	0.941859i
$17$	−0.875095	−	1.51571i	−0.212242	−	0.367614i	0.740174	−	0.672415i	$-0.234743\pi$
$17$	−0.875095	−	1.51571i	−0.212242	−	0.367614i	−0.952416	+	0.304802i	$0.901410\pi$
$18$	−7.64438			−1.80180
$19$	0.636061	−	4.31224i	0.145922	−	0.989296i
$19$	0.636061	−	4.31224i	0.145922	−	0.989296i
$20$		0			0
$21$	−5.40696	−	9.36514i	−1.17990	−	2.04364i
$22$	−4.14335	−	7.17648i	−0.883364	−	1.53003i
$23$	0.290768	−	0.503625i	0.0606294	−	0.105013i	−0.834118	−	0.551587i	$-0.814023\pi$
$23$	0.290768	−	0.503625i	0.0606294	−	0.105013i	0.894747	+	0.446574i	$0.147356\pi$
$24$	−3.82107	−	6.61830i	−0.779974	−	1.35095i
$25$		0			0
$26$	7.26750			1.42527
$27$	6.17328			1.18805
$28$	−0.367065	+	0.635775i	−0.0693687	+	0.120150i
$29$	−0.832153	+	1.44133i	−0.154527	+	0.267649i	−0.932887	−	0.360170i	$-0.882719\pi$
$29$	−0.832153	+	1.44133i	−0.154527	+	0.267649i	0.778360	+	0.627819i	$0.216052\pi$
$30$		0			0
$31$	7.01680			1.26025			0.630127	−	0.776492i	$-0.283003\pi$
$31$	7.01680			1.26025			0.630127	+	0.776492i	$0.283003\pi$
$32$	−0.546661	+	0.946844i	−0.0966369	+	0.167380i
$33$	7.99116	+	13.8411i	1.39108	+	2.40942i
$34$	1.29619	−	2.24506i	0.222294	−	0.385025i
$35$		0			0
$36$	−0.500449	−	0.866803i	−0.0834082	−	0.144467i
$37$	−2.36322			−0.388510			−0.194255	−	0.980951i	$-0.562229\pi$
$37$	−2.36322			−0.388510			−0.194255	+	0.980951i	$0.562229\pi$
$38$	6.00260	−	2.37773i	0.973750	−	0.385718i
$39$	−14.0166			−2.24446
$40$		0			0
$41$	−0.417676	−	0.723435i	−0.0652300	−	0.112982i	0.831566	−	0.555426i	$-0.187445\pi$
$41$	−0.417676	−	0.723435i	−0.0652300	−	0.112982i	−0.896796	+	0.442444i	$0.854111\pi$
$42$	8.00877	−	13.8716i	1.23578	−	2.14043i
$43$	−0.535664	−	0.927797i	−0.0816880	−	0.141488i	0.822287	−	0.569073i	$-0.192698\pi$
$43$	−0.535664	−	0.927797i	−0.0816880	−	0.141488i	−0.903975	+	0.427585i	$0.859364\pi$
$44$	0.542499	−	0.939635i	0.0817848	−	0.141655i
$45$		0			0
$46$	0.861369			0.127002
$47$	1.93378	−	3.34941i	0.282071	−	0.488561i	−0.689824	−	0.723977i	$-0.742312\pi$
$47$	1.93378	−	3.34941i	0.282071	−	0.488561i	0.971895	+	0.235416i	$0.0756453\pi$
$48$	6.21378	−	10.7626i	0.896882	−	1.55345i
$49$	7.32934			1.04705
$50$		0			0
$51$	−2.49992	+	4.32999i	−0.350059	+	0.606319i
$52$	0.475776	+	0.824069i	0.0659783	+	0.114278i
$53$	−3.39842	+	5.88624i	−0.466809	+	0.808537i	−0.999281	−	0.0379106i	$-0.987930\pi$
$53$	−3.39842	+	5.88624i	−0.466809	+	0.808537i	0.532472	+	0.846448i	$0.321263\pi$
$54$	4.57192	+	7.91879i	0.622159	+	1.07761i
$55$		0			0
$56$	10.1265			1.35321
$57$	−11.5771	+	4.58585i	−1.53342	+	0.607411i
$58$	−2.46516			−0.323691
$59$	0.204282	+	0.353827i	0.0265953	+	0.0460643i	0.879017	−	0.476791i	$-0.158200\pi$
$59$	0.204282	+	0.353827i	0.0265953	+	0.0460643i	−0.852421	+	0.522855i	$0.824867\pi$
$60$		0			0
$61$	−6.98016	+	12.0900i	−0.893718	+	1.54796i	−0.0583341	+	0.998297i	$0.518579\pi$
$61$	−6.98016	+	12.0900i	−0.893718	+	1.54796i	−0.835384	+	0.549667i	$0.814754\pi$
$62$	5.19662	+	9.00081i	0.659971	+	1.14310i
$63$	−9.76817	+	16.9190i	−1.23067	+	2.13159i
$64$	7.08110			0.885138
$65$		0			0
$66$	−11.8365	+	20.5013i	−1.45697	+	2.52354i
$67$	0.390703	−	0.676717i	0.0477319	−	0.0826742i	−0.841172	−	0.540767i	$-0.818134\pi$
$67$	0.390703	−	0.676717i	0.0477319	−	0.0826742i	0.888904	+	0.458093i	$0.151467\pi$
$68$	0.339426			0.0411614
$69$	−1.66130			−0.199997
$70$		0			0
$71$	−3.18919	−	5.52384i	−0.378487	−	0.655559i	0.612355	−	0.790583i	$-0.290222\pi$
$71$	−3.18919	−	5.52384i	−0.378487	−	0.655559i	−0.990842	+	0.135024i	$0.956889\pi$
$72$	−6.90312	+	11.9565i	−0.813540	+	1.40909i
$73$	1.44458	+	2.50208i	0.169075	+	0.292846i	0.938095	−	0.346378i	$-0.112589\pi$
$73$	1.44458	+	2.50208i	0.169075	+	0.292846i	−0.769020	+	0.639225i	$0.779255\pi$
$74$	−1.75019	−	3.03142i	−0.203456	−	0.352395i
$75$		0			0
$76$	0.662580	+	0.524980i	0.0760032	+	0.0602193i
$77$	−21.1779			−2.41344
$78$	−10.3807	−	17.9799i	−1.17538	−	2.03582i
$79$	6.25135	+	10.8276i	0.703331	+	1.21821i	0.967290	+	0.253672i	$0.0816383\pi$
$79$	6.25135	+	10.8276i	0.703331	+	1.21821i	−0.263959	+	0.964534i	$0.585028\pi$
$80$		0			0
$81$	−1.07630	−	1.86420i	−0.119589	−	0.207133i
$82$	0.618659	−	1.07155i	0.0683194	−	0.118333i
$83$	10.3903			1.14048			0.570240	−	0.821478i	$-0.306850\pi$
$83$	10.3903			1.14048			0.570240	+	0.821478i	$0.306850\pi$
$84$	2.09722			0.228825
$85$		0			0
$86$	0.793422	−	1.37425i	0.0855569	−	0.148189i
$87$	4.75449			0.509735
$88$	−14.9663			−1.59541
$89$	−8.92106	+	15.4517i	−0.945631	+	1.63788i	−0.191148	+	0.981561i	$0.561221\pi$
$89$	−8.92106	+	15.4517i	−0.945631	+	1.63788i	−0.754483	+	0.656320i	$0.772112\pi$
$90$		0			0
$91$	9.28659	−	16.0848i	0.973499	−	1.68615i
$92$	0.0563906	+	0.0976714i	0.00587913	+	0.0101829i
$93$	−10.0226	−	17.3596i	−1.03929	−	1.80011i
$94$	5.72861			0.590861
$95$		0			0
$96$	3.12333			0.318774
$97$	5.49995	+	9.52619i	0.558435	+	0.967238i	0.997627	+	0.0688448i	$0.0219313\pi$
$97$	5.49995	+	9.52619i	0.558435	+	0.967238i	−0.439192	+	0.898393i	$0.644735\pi$
$98$	5.42809	+	9.40172i	0.548319	+	0.949717i
$99$	14.4367	−	25.0052i	1.45095	−	2.51311i
$100$		0			0
$101$	−2.57944	+	4.46772i	−0.256664	+	0.444555i	−0.965346	−	0.260973i	$-0.915957\pi$
$101$	−2.57944	+	4.46772i	−0.256664	+	0.444555i	0.708682	+	0.705528i	$0.249290\pi$
$102$	−7.40573			−0.733277
$103$	7.75851			0.764469			0.382235	−	0.924065i	$-0.375155\pi$
$103$	7.75851			0.764469			0.382235	+	0.924065i	$0.375155\pi$
$104$	6.56279	−	11.3671i	0.643534	−	1.11463i
$105$		0			0
$106$	−10.0674			−0.977837
$107$	12.6521			1.22313			0.611564	−	0.791195i	$-0.290541\pi$
$107$	12.6521			1.22313			0.611564	+	0.791195i	$0.290541\pi$
$108$	−0.598613	+	1.03683i	−0.0576015	+	0.0997688i
$109$	4.09697	+	7.09616i	0.392418	+	0.679689i	0.992768	−	0.120049i	$-0.0383052\pi$
$109$	4.09697	+	7.09616i	0.392418	+	0.679689i	−0.600350	+	0.799738i	$0.704972\pi$
$110$		0			0
$111$	3.37554	+	5.84661i	0.320392	+	0.554936i
$112$	8.23376	+	14.2613i	0.778018	+	1.34757i
$113$	12.5551			1.18108			0.590541	−	0.807007i	$-0.298914\pi$
$113$	12.5551			1.18108			0.590541	+	0.807007i	$0.298914\pi$
$114$	−14.4564	−	11.4542i	−1.35397	−	1.07279i
$115$		0			0
$116$	−0.161385	−	0.279527i	−0.0149842	−	0.0259534i
$117$	12.6612	+	21.9298i	1.17052	+	2.02741i
$118$	−0.302581	+	0.524086i	−0.0278549	+	0.0482461i
$119$	−3.31260	−	5.73758i	−0.303665	−	0.525963i
$120$		0			0
$121$	20.2996			1.84541
$122$	−20.6779			−1.87209
$123$	−1.19319	+	2.06667i	−0.107586	+	0.186345i
$124$	−0.680407	+	1.17850i	−0.0611023	+	0.105832i
$125$		0			0
$126$	−28.9371			−2.57792
$127$	−4.07957	+	7.06602i	−0.362003	+	0.627007i	−0.988290	−	0.152585i	$-0.951240\pi$
$127$	−4.07957	+	7.06602i	−0.362003	+	0.627007i	0.626287	+	0.779592i	$0.284574\pi$
$128$	6.33757	+	10.9770i	0.560167	+	0.970238i
$129$	−1.53025	+	2.65047i	−0.134731	+	0.233361i
$130$		0			0
$131$	−9.62491	−	16.6708i	−0.840932	−	1.45654i	−0.889108	−	0.457698i	$-0.848674\pi$
$131$	−9.62491	−	16.6708i	−0.840932	−	1.45654i	0.0481757	−	0.998839i	$-0.484659\pi$
$132$	−3.09955			−0.269782
$133$	2.40775	−	16.3236i	0.208779	−	1.41544i
$134$	1.15741			0.0999853
$135$		0			0
$136$	−2.34099	−	4.05472i	−0.200739	−	0.347689i
$137$	−0.785955	+	1.36131i	−0.0671487	+	0.116305i	−0.897645	−	0.440719i	$-0.854724\pi$
$137$	−0.785955	+	1.36131i	−0.0671487	+	0.116305i	0.830496	+	0.557024i	$0.188057\pi$
$138$	−1.23035	−	2.13103i	−0.104735	−	0.181406i
$139$	1.02459	−	1.77464i	0.0869047	−	0.150523i	−0.819297	−	0.573370i	$-0.805636\pi$
$139$	1.02459	−	1.77464i	0.0869047	−	0.150523i	0.906201	+	0.422847i	$0.138969\pi$
$140$		0			0
$141$	−11.0486			−0.930461
$142$	4.72381	−	8.18188i	0.396413	−	0.686608i
$143$	−13.7250	+	23.7724i	−1.14774	+	1.98795i
$144$	−22.4515			−1.87096
$145$		0			0
$146$	−2.13970	+	3.70607i	−0.177083	+	0.306716i
$147$	−10.4690	−	18.1328i	−0.863468	−	1.49557i
$148$	0.229157	−	0.396911i	0.0188366	−	0.0326259i
$149$	0.737839	+	1.27797i	0.0604461	+	0.104696i	0.894665	−	0.446738i	$-0.147414\pi$
$149$	0.737839	+	1.27797i	0.0604461	+	0.104696i	−0.834219	+	0.551434i	$0.814081\pi$
$150$		0			0
$151$	6.42543			0.522894			0.261447	−	0.965218i	$-0.415800\pi$
$151$	6.42543			0.522894			0.261447	+	0.965218i	$0.415800\pi$
$152$	1.70155	−	11.5358i	0.138014	−	0.935678i
$153$	9.03266			0.730247
$154$	−15.6843	−	27.1659i	−1.26387	−	2.18909i
$155$		0			0
$156$	1.35917	−	2.35415i	0.108821	−	0.188483i
$157$	−11.1445	−	19.3028i	−0.889425	−	1.54053i	−0.840556	−	0.541724i	$-0.817772\pi$
$157$	−11.1445	−	19.3028i	−0.889425	−	1.54053i	−0.0488688	−	0.998805i	$-0.515562\pi$
$158$	−9.25946	+	16.0379i	−0.736643	+	1.27590i
$159$	19.4168			1.53985
$160$		0			0
$161$	1.10068	−	1.90643i	0.0867455	−	0.150248i
$162$	1.59420	−	2.76124i	0.125253	−	0.216944i
$163$	−15.0321			−1.17741			−0.588703	−	0.808350i	$-0.700361\pi$
$163$	−15.0321			−1.17741			−0.588703	+	0.808350i	$0.700361\pi$
$164$	0.162005			0.0126505
$165$		0			0
$166$	7.69500	+	13.3281i	0.597248	+	1.03446i
$167$	−4.79928	+	8.31260i	−0.371380	+	0.643249i	−0.989778	−	0.142616i	$-0.954449\pi$
$167$	−4.79928	+	8.31260i	−0.371380	+	0.643249i	0.618398	+	0.785865i	$0.287782\pi$
$168$	−14.4643	−	25.0530i	−1.11595	−	1.93288i
$169$	−5.53695	−	9.59028i	−0.425919	−	0.737714i
$170$		0			0
$171$	17.6323	+	13.9705i	1.34838	+	1.06835i
$172$	0.207770			0.0158423
$173$	4.41611	+	7.64894i	0.335751	+	0.581538i	0.983629	−	0.180207i	$-0.0576766\pi$
$173$	4.41611	+	7.64894i	0.335751	+	0.581538i	−0.647878	+	0.761744i	$0.724343\pi$
$174$	3.52116	+	6.09883i	0.266938	+	0.462351i
$175$		0			0
$176$	−12.1690	−	21.0773i	−0.917272	−	1.58876i
$177$	0.583580	−	1.01079i	0.0438646	−	0.0759757i
$178$	−26.4277			−1.98084
$179$	10.8178			0.808564			0.404282	−	0.914634i	$-0.367522\pi$
$179$	10.8178			0.808564			0.404282	+	0.914634i	$0.367522\pi$
$180$		0			0
$181$	−5.37359	+	9.30733i	−0.399416	+	0.691808i	−0.993654	−	0.112481i	$-0.964120\pi$
$181$	−5.37359	+	9.30733i	−0.399416	+	0.691808i	0.594238	+	0.804289i	$0.297454\pi$
$182$	27.5105			2.03921
$183$	39.8810			2.94809
$184$	0.777843	−	1.34726i	0.0573434	−	0.0993216i
$185$		0			0
$186$	14.8454	−	25.7130i	1.08852	−	1.88537i
$187$	4.89581	+	8.47979i	0.358017	+	0.620104i
$188$	0.375031	+	0.649573i	0.0273519	+	0.0473750i
$189$	23.3684			1.69980
$190$		0			0
$191$	−6.28362			−0.454667			−0.227334	−	0.973817i	$-0.573001\pi$
$191$	−6.28362			−0.454667			−0.227334	+	0.973817i	$0.573001\pi$
$192$	−10.1144	−	17.5187i	−0.729946	−	1.26430i
$193$	−8.91459	−	15.4405i	−0.641686	−	1.11143i	−0.985056	−	0.172233i	$-0.944902\pi$
$193$	−8.91459	−	15.4405i	−0.641686	−	1.11143i	0.343370	−	0.939200i	$-0.388431\pi$
$194$	−8.14649	+	14.1101i	−0.584884	+	1.01305i
$195$		0			0
$196$	−0.710713	+	1.23099i	−0.0507652	+	0.0879279i
$197$	−16.9925			−1.21066			−0.605332	−	0.795973i	$-0.706959\pi$
$197$	−16.9925			−1.21066			−0.605332	+	0.795973i	$0.706959\pi$
$198$	42.7672			3.03934
$199$	−8.22212	+	14.2411i	−0.582850	+	1.00953i	0.412289	+	0.911053i	$0.364729\pi$
$199$	−8.22212	+	14.2411i	−0.582850	+	1.00953i	−0.995140	+	0.0984735i	$0.968604\pi$
$200$		0			0
$201$	−2.23227			−0.157452
$202$	−7.64131			−0.537641
$203$	−3.15004	+	5.45603i	−0.221090	+	0.382938i
$204$	−0.484826	−	0.839743i	−0.0339446	−	0.0587937i
$205$		0			0
$206$	5.74593	+	9.95225i	0.400338	+	0.693406i
$207$	1.50064	+	2.59919i	0.104302	+	0.180656i
$208$	21.3446			1.47998
$209$	−3.55851	+	24.1253i	−0.246147	+	1.66878i
$210$		0			0
$211$	−7.79632	−	13.5036i	−0.536721	−	0.929628i	−0.999078	−	0.0429343i	$-0.986329\pi$
$211$	−7.79632	−	13.5036i	−0.536721	−	0.929628i	0.462357	−	0.886694i	$-0.347004\pi$
$212$	−0.659078	−	1.14156i	−0.0452657	−	0.0784024i
$213$	−9.11068	+	15.7802i	−0.624253	+	1.08124i
$214$	9.37013	+	16.2295i	0.640529	+	1.10943i
$215$		0			0
$216$	16.5143			1.12366
$217$	26.5615			1.80311
$218$	−6.06841	+	10.5108i	−0.411004	+	0.711880i
$219$	4.12678	−	7.14779i	0.278862	−	0.483003i
$220$		0			0
$221$	−8.58734			−0.577647
$222$	−4.99984	+	8.65997i	−0.335567	+	0.581219i
$223$	−3.90313	−	6.76042i	−0.261373	−	0.452711i	0.705234	−	0.708974i	$-0.250842\pi$
$223$	−3.90313	−	6.76042i	−0.261373	−	0.452711i	−0.966607	+	0.256263i	$0.917509\pi$
$224$	−2.06933	+	3.58419i	−0.138263	+	0.239479i
$225$		0			0
$226$	9.29826	+	16.1051i	0.618511	+	1.07129i
$227$	16.8511			1.11845			0.559223	−	0.829017i	$-0.311100\pi$
$227$	16.8511			1.11845			0.559223	+	0.829017i	$0.311100\pi$
$228$	0.352394	−	2.38909i	0.0233379	−	0.158222i
$229$	−0.251385			−0.0166120			−0.00830600	−	0.999966i	$-0.502644\pi$
$229$	−0.251385			−0.0166120			−0.00830600	+	0.999966i	$0.502644\pi$
$230$		0			0
$231$	30.2498	+	52.3942i	1.99029	+	3.44729i
$232$	−2.22612	+	3.85575i	−0.146152	+	0.253142i
$233$	−11.6014	−	20.0943i	−0.760035	−	1.31642i	−0.942832	−	0.333269i	$-0.891848\pi$
$233$	−11.6014	−	20.0943i	−0.760035	−	1.31642i	0.182797	−	0.983151i	$-0.441485\pi$
$234$	−18.7536	+	32.4822i	−1.22596	+	2.12343i
$235$		0			0
$236$	−0.0792355			−0.00515779
$237$	17.8585	−	30.9318i	1.16003	−	2.00923i
$238$	4.90660	−	8.49848i	0.318047	−	0.550874i
$239$	−7.58778			−0.490813			−0.245406	−	0.969420i	$-0.578921\pi$
$239$	−7.58778			−0.490813			−0.245406	+	0.969420i	$0.578921\pi$
$240$		0			0
$241$	2.75808	−	4.77714i	0.177664	−	0.307723i	−0.763416	−	0.645907i	$-0.776479\pi$
$241$	2.75808	−	4.77714i	0.177664	−	0.307723i	0.941080	+	0.338184i	$0.109813\pi$
$242$	15.0338	+	26.0393i	0.966409	+	1.67387i
$243$	6.18523	−	10.7131i	0.396783	−	0.687248i
$244$	−1.35371	−	2.34469i	−0.0866623	−	0.150103i
$245$		0			0
$246$	−3.53469			−0.225364
$247$	−16.7630	−	13.2818i	−1.06661	−	0.845099i
$248$	18.7708			1.19195
$249$	−14.8411	−	25.7056i	−0.940519	−	1.62903i
$250$		0			0
$251$	9.32933	−	16.1589i	0.588862	−	1.01994i	−0.405520	−	0.914086i	$-0.632910\pi$
$251$	9.32933	−	16.1589i	0.588862	−	1.01994i	0.994382	−	0.105852i	$-0.0337571\pi$
$252$	−1.89441	−	3.28121i	−0.119336	−	0.206697i
$253$	−1.62673	+	2.81758i	−0.102272	+	0.177140i
$254$	−12.0853			−0.758297
$255$		0			0
$256$	−2.30606	+	3.99422i	−0.144129	+	0.249639i
$257$	−0.346352	+	0.599899i	−0.0216048	+	0.0374207i	−0.876626	−	0.481173i	$-0.840211\pi$
$257$	−0.346352	+	0.599899i	−0.0216048	+	0.0374207i	0.855021	+	0.518594i	$0.173544\pi$
$258$	−4.53320			−0.282225
$259$	−8.94574			−0.555861
$260$		0			0
$261$	−4.29470	−	7.43865i	−0.265836	−	0.460441i
$262$	14.2564	−	24.6927i	0.880761	−	1.52552i
$263$	−5.81338	−	10.0691i	−0.358468	−	0.620885i	0.629237	−	0.777214i	$-0.283368\pi$
$263$	−5.81338	−	10.0691i	−0.358468	−	0.620885i	−0.987705	+	0.156328i	$0.950034\pi$
$264$	21.3774	+	37.0267i	1.31569	+	2.27884i
$265$		0			0
$266$	22.7223	−	9.00067i	1.39319	−	0.551866i
$267$	50.9703			3.11933
$268$	0.0757716	+	0.131240i	0.00462849	+	0.00801677i
$269$	11.8057	+	20.4481i	0.719809	+	1.24675i	0.961075	+	0.276286i	$0.0891038\pi$
$269$	11.8057	+	20.4481i	0.719809	+	1.24675i	−0.241267	+	0.970459i	$0.577563\pi$
$270$		0			0
$271$	3.81995	+	6.61635i	0.232046	+	0.401915i	0.958410	−	0.285395i	$-0.0921248\pi$
$271$	3.81995	+	6.61635i	0.232046	+	0.401915i	−0.726364	+	0.687310i	$0.758791\pi$
$272$	3.80689	−	6.59373i	0.230827	−	0.399804i
$273$	−53.0587			−3.21126
$274$	−2.32830			−0.140658
$275$		0			0
$276$	0.161093	−	0.279022i	0.00969667	−	0.0167951i
$277$	−18.6537			−1.12079			−0.560397	−	0.828224i	$-0.689352\pi$
$277$	−18.6537			−1.12079			−0.560397	+	0.828224i	$0.689352\pi$
$278$	3.03524			0.182041
$279$	−18.1067	+	31.3617i	−1.08402	+	1.87758i
$280$		0			0
$281$	−6.99489	+	12.1155i	−0.417280	+	0.722750i	−0.995665	−	0.0930139i	$-0.970350\pi$
$281$	−6.99489	+	12.1155i	−0.417280	+	0.722750i	0.578385	+	0.815764i	$0.303683\pi$
$282$	−8.18257	−	14.1726i	−0.487265	−	0.843968i
$283$	12.3334	+	21.3620i	0.733143	+	1.26984i	0.955533	+	0.294884i	$0.0952809\pi$
$283$	12.3334	+	21.3620i	0.733143	+	1.26984i	−0.222390	+	0.974958i	$0.571386\pi$
$284$	1.23700			0.0734025
$285$		0			0
$286$	−40.6588			−2.40420
$287$	−1.58107	−	2.73850i	−0.0933278	−	0.161649i
$288$	−2.82129	−	4.88662i	−0.166246	−	0.287947i
$289$	6.96842	−	12.0697i	0.409907	−	0.709979i
$290$		0			0
$291$	15.7119	−	27.2138i	0.921049	−	1.59530i
$292$	−0.560312			−0.0327898
$293$	10.5784			0.617994			0.308997	−	0.951063i	$-0.400007\pi$
$293$	10.5784			0.617994			0.308997	+	0.951063i	$0.400007\pi$
$294$	15.5066	−	26.8583i	0.904365	−	1.56641i
$295$		0			0
$296$	−6.32191			−0.367454
$297$	−34.5371			−2.00404
$298$	−1.09288	+	1.89293i	−0.0633090	+	0.109654i
$299$	−1.42666	−	2.47105i	−0.0825058	−	0.142904i
$300$		0			0
$301$	−2.02771	−	3.51209i	−0.116875	−	0.202434i
$302$	4.75866	+	8.24223i	0.273830	+	0.474287i
$303$	14.7376			0.846652
$304$	17.6296	−	6.98337i	1.01113	−	0.400524i
$305$		0			0
$306$	6.68956	+	11.5867i	0.382417	+	0.662365i
$307$	6.41222	+	11.1063i	0.365965	+	0.633870i	0.988931	−	0.148379i	$-0.0474057\pi$
$307$	6.41222	+	11.1063i	0.365965	+	0.633870i	−0.622966	+	0.782249i	$0.714072\pi$
$308$	2.05358	−	3.55691i	0.117014	−	0.202674i
$309$	−11.0820	−	19.1946i	−0.630434	−	1.09194i
$310$		0			0
$311$	3.42706			0.194331			0.0971655	−	0.995268i	$-0.469022\pi$
$311$	3.42706			0.194331			0.0971655	+	0.995268i	$0.469022\pi$
$312$	−37.4963			−2.12281
$313$	−1.42224	+	2.46339i	−0.0803896	+	0.139239i	−0.903417	−	0.428762i	$-0.858950\pi$
$313$	−1.42224	+	2.46339i	−0.0803896	+	0.139239i	0.823028	+	0.568001i	$0.192283\pi$
$314$	16.5071	−	28.5912i	0.931551	−	1.61349i
$315$		0			0
$316$	−2.42473			−0.136402
$317$	−2.33072	+	4.03693i	−0.130907	+	0.226737i	−0.924026	−	0.382329i	$-0.875122\pi$
$317$	−2.33072	+	4.03693i	−0.130907	+	0.226737i	0.793120	+	0.609066i	$0.208455\pi$
$318$	14.3800	+	24.9069i	0.806392	+	1.39671i
$319$	4.65556	−	8.06367i	0.260662	−	0.451479i
$320$		0			0
$321$	−18.0719	−	31.3015i	−1.00868	−	1.74708i
$322$	3.26063			0.181708
$323$	−7.09272	+	2.80954i	−0.394649	+	0.156327i
$324$	0.417467			0.0231926
$325$		0			0
$326$	−11.1327	−	19.2825i	−0.616585	−	1.06796i
$327$	11.7040	−	20.2719i	0.647231	−	1.12104i
$328$	−1.11734	−	1.93528i	−0.0616946	−	0.106858i
$329$	7.32016	−	12.6789i	0.403573	−	0.699010i
$330$		0			0
$331$	−7.00260			−0.384898			−0.192449	−	0.981307i	$-0.561643\pi$
$331$	−7.00260			−0.384898			−0.192449	+	0.981307i	$0.561643\pi$
$332$	−1.00753	+	1.74509i	−0.0552952	+	0.0957741i
$333$	6.09822	−	10.5624i	0.334181	−	0.578818i
$334$	−14.2173			−0.777938
$335$		0			0
$336$	23.5217	−	40.7408i	1.28321	−	2.22259i
$337$	−6.76881	−	11.7239i	−0.368721	−	0.638643i	0.620645	−	0.784092i	$-0.286871\pi$
$337$	−6.76881	−	11.7239i	−0.368721	−	0.638643i	−0.989366	+	0.145449i	$0.953537\pi$
$338$	8.20130	−	14.2051i	0.446092	−	0.772654i
$339$	−17.9333	−	31.0614i	−0.974003	−	1.68702i
$340$		0			0
$341$	−39.2562			−2.12584
$342$	−4.86229	+	32.9644i	−0.262923	+	1.78251i
$343$	1.24667			0.0673140
$344$	−1.43297	−	2.48198i	−0.0772606	−	0.133819i
$345$		0			0
$346$	−6.54112	+	11.3296i	−0.351653	+	0.609081i
$347$	10.9817	+	19.0208i	0.589527	+	1.02109i	0.994294	+	0.106671i	$0.0340190\pi$
$347$	10.9817	+	19.0208i	0.589527	+	1.02109i	−0.404768	+	0.914420i	$0.632648\pi$
$348$	−0.461034	+	0.798535i	−0.0247140	+	0.0428060i
$349$	−22.1930			−1.18796			−0.593981	−	0.804479i	$-0.702445\pi$
$349$	−22.1930			−1.18796			−0.593981	+	0.804479i	$0.702445\pi$
$350$		0			0
$351$	15.1447	−	26.2313i	0.808362	−	1.40012i
$352$	3.05835	−	5.29721i	0.163010	−	0.282342i
$353$	0.679013			0.0361402			0.0180701	−	0.999837i	$-0.494248\pi$
$353$	0.679013			0.0361402			0.0180701	+	0.999837i	$0.494248\pi$
$354$	1.72879			0.0918843
$355$		0			0
$356$	−1.73012	−	2.99666i	−0.0916962	−	0.158822i
$357$	−9.46322	+	16.3908i	−0.500847	+	0.867492i
$358$	8.01166	+	13.8766i	0.423430	+	0.733402i
$359$	12.6627	+	21.9325i	0.668314	+	1.15755i	0.978375	+	0.206837i	$0.0663170\pi$
$359$	12.6627	+	21.9325i	0.668314	+	1.15755i	−0.310062	+	0.950716i	$0.600350\pi$
$360$		0			0
$361$	−18.1909	−	5.48570i	−0.957413	−	0.288721i
$362$	−15.9187			−0.836666
$363$	−28.9953	−	50.2213i	−1.52186	−	2.63593i
$364$	1.80101	+	3.11944i	0.0943985	+	0.163503i
$365$		0			0
$366$	29.5357	+	51.1574i	1.54386	+	2.67404i
$367$	5.83153	−	10.1005i	0.304404	−	0.527243i	−0.672725	−	0.739893i	$-0.734876\pi$
$367$	5.83153	−	10.1005i	0.304404	−	0.527243i	0.977128	+	0.212650i	$0.0682095\pi$
$368$	2.52984			0.131877
$369$	4.31121			0.224433
$370$		0			0
$371$	−12.8644	+	22.2818i	−0.667887	+	1.15681i
$372$	3.88749			0.201557
$373$	13.0913			0.677843			0.338921	−	0.940815i	$-0.389938\pi$
$373$	13.0913			0.677843			0.338921	+	0.940815i	$0.389938\pi$
$374$	−7.25164	+	12.5602i	−0.374974	+	0.649473i
$375$		0			0
$376$	5.17312	−	8.96010i	0.266783	−	0.462082i
$377$	4.08297	+	7.07192i	0.210284	+	0.364222i
$378$	17.3066	+	29.9759i	0.890155	+	1.54179i
$379$	−32.7566			−1.68259			−0.841297	−	0.540573i	$-0.818208\pi$
$379$	−32.7566			−1.68259			−0.841297	+	0.540573i	$0.818208\pi$
$380$		0			0
$381$	23.3085			1.19413
$382$	−4.65363	−	8.06033i	−0.238101	−	0.412402i
$383$	−12.8227	−	22.2096i	−0.655211	−	1.13486i	−0.981841	−	0.189707i	$-0.939246\pi$
$383$	−12.8227	−	22.2096i	−0.655211	−	1.13486i	0.326630	−	0.945152i	$-0.394087\pi$
$384$	18.1048	−	31.3584i	0.923905	−	1.60025i
$385$		0			0
$386$	13.2042	−	22.8704i	0.672078	−	1.16407i
$387$	5.52907			0.281059
$388$	−2.13328			−0.108301
$389$	9.27329	−	16.0618i	0.470174	−	0.814366i	−0.529244	−	0.848470i	$-0.677524\pi$
$389$	9.27329	−	16.0618i	0.470174	−	0.814366i	0.999418	+	0.0341039i	$0.0108577\pi$
$390$		0			0
$391$	−1.01780			−0.0514723
$392$	19.6069			0.990300
$393$	−27.4958	+	47.6242i	−1.38698	+	2.40232i
$394$	−12.5846	−	21.7971i	−0.634002	−	1.09812i
$395$		0			0
$396$	2.79981	+	4.84942i	0.140696	+	0.243692i
$397$	7.69806	+	13.3334i	0.386355	+	0.669186i	0.991956	−	0.126582i	$-0.0404007\pi$
$397$	7.69806	+	13.3334i	0.386355	+	0.669186i	−0.605601	+	0.795768i	$0.707067\pi$
$398$	−24.3571			−1.22091
$399$	−43.8239	+	17.3593i	−2.19394	+	0.869054i
$400$		0			0
$401$	10.2956	+	17.8326i	0.514140	+	0.890517i	0.999865	+	0.0164054i	$0.00522222\pi$
$401$	10.2956	+	17.8326i	0.514140	+	0.890517i	−0.485725	+	0.874112i	$0.661444\pi$
$402$	−1.65321	−	2.86345i	−0.0824548	−	0.142816i
$403$	17.2140	−	29.8155i	0.857491	−	1.48522i
$404$	−0.500248	−	0.866455i	−0.0248883	−	0.0431078i
$405$		0			0
$406$	−9.33165			−0.463122
$407$	13.2212			0.655353
$408$	−6.68761	+	11.5833i	−0.331086	+	0.573458i
$409$	0.811919	−	1.40629i	0.0401468	−	0.0695363i	−0.845254	−	0.534365i	$-0.820551\pi$
$409$	0.811919	−	1.40629i	0.0401468	−	0.0695363i	0.885401	+	0.464829i	$0.153884\pi$
$410$		0			0
$411$	4.49054			0.221502
$412$	−0.752330	+	1.30307i	−0.0370646	+	0.0641978i
$413$	0.773292	+	1.33938i	0.0380512	+	0.0659066i
$414$	−2.22274	+	3.84990i	−0.109242	+	0.189212i
$415$		0			0
$416$	2.68220	+	4.64570i	0.131506	+	0.227774i
$417$	−5.85398			−0.286671
$418$	−33.5822	+	13.3024i	−1.64256	+	0.650643i
$419$	16.8087			0.821161			0.410580	−	0.911824i	$-0.365326\pi$
$419$	16.8087			0.821161			0.410580	+	0.911824i	$0.365326\pi$
$420$		0			0
$421$	−10.4718	−	18.1377i	−0.510365	−	0.883977i	−0.999928	−	0.0120096i	$-0.996177\pi$
$421$	−10.4718	−	18.1377i	−0.510365	−	0.883977i	0.489563	−	0.871968i	$-0.337156\pi$
$422$	11.5479	−	20.0015i	0.562142	−	0.973658i
$423$	9.98016	+	17.2861i	0.485252	+	0.840481i
$424$	−9.09122	+	15.7465i	−0.441509	+	0.764716i
$425$		0			0
$426$	−26.9894			−1.30764
$427$	−26.4228	+	45.7656i	−1.27869	+	2.21475i
$428$	−1.22686	+	2.12498i	−0.0593023	+	0.102715i
$429$	78.4175			3.78603
$430$		0			0
$431$	−16.8908	+	29.2557i	−0.813600	+	1.40920i	0.0967292	+	0.995311i	$0.469162\pi$
$431$	−16.8908	+	29.2557i	−0.813600	+	1.40920i	−0.910329	+	0.413885i	$0.864171\pi$
$432$	13.4277	+	23.2575i	0.646041	+	1.11898i
$433$	7.51443	−	13.0154i	0.361120	−	0.625479i	−0.627025	−	0.778999i	$-0.715728\pi$
$433$	7.51443	−	13.0154i	0.361120	−	0.625479i	0.988146	+	0.153520i	$0.0490610\pi$
$434$	19.6713	+	34.0718i	0.944254	+	1.63550i
$435$		0			0
$436$	−1.58910			−0.0761043
$437$	−1.98681	−	1.57420i	−0.0950419	−	0.0753042i
$438$	12.2251			0.584139
$439$	−18.8607	−	32.6677i	−0.900173	−	1.55915i	−0.827269	−	0.561807i	$-0.810106\pi$
$439$	−18.8607	−	32.6677i	−0.900173	−	1.55915i	−0.0729045	−	0.997339i	$-0.523227\pi$
$440$		0			0
$441$	−18.9132	+	32.7586i	−0.900628	+	1.55993i
$442$	−6.35976	−	11.0154i	−0.302503	−	0.523950i
$443$	−6.55722	+	11.3574i	−0.311543	+	0.539608i	−0.978697	−	0.205312i	$-0.934179\pi$
$443$	−6.55722	+	11.3574i	−0.311543	+	0.539608i	0.667154	+	0.744920i	$0.267512\pi$
$444$	−1.30928			−0.0621358
$445$		0			0
$446$	5.78129	−	10.0135i	0.273752	−	0.474153i
$447$	2.10781	−	3.65084i	0.0996961	−	0.172679i
$448$	26.8049			1.26641
$449$	11.6905			0.551711			0.275855	−	0.961199i	$-0.411039\pi$
$449$	11.6905			0.551711			0.275855	+	0.961199i	$0.411039\pi$
$450$		0			0
$451$	2.33673	+	4.04733i	0.110032	+	0.190581i
$452$	−1.21744	+	2.10868i	−0.0572638	+	0.0991838i
$453$	−9.17789	−	15.8966i	−0.431215	−	0.746886i
$454$	12.4799	+	21.6158i	0.585709	+	1.01448i
$455$		0			0
$456$	−30.9701	+	12.2678i	−1.45031	+	0.574490i
$457$	−21.4290			−1.00240			−0.501202	−	0.865330i	$-0.667109\pi$
$457$	−21.4290			−1.00240			−0.501202	+	0.865330i	$0.667109\pi$
$458$	−0.186175	−	0.322465i	−0.00869939	−	0.0150678i
$459$	−5.40221	−	9.35691i	−0.252154	−	0.436743i
$460$		0			0
$461$	4.82920	+	8.36442i	0.224918	+	0.389570i	0.956295	−	0.292404i	$-0.0944551\pi$
$461$	4.82920	+	8.36442i	0.224918	+	0.389570i	−0.731377	+	0.681974i	$0.761122\pi$
$462$	−44.8058	+	77.6060i	−2.08456	+	3.61056i
$463$	1.24981			0.0580838			0.0290419	−	0.999578i	$-0.490754\pi$
$463$	1.24981			0.0580838			0.0290419	+	0.999578i	$0.490754\pi$
$464$	−7.24017			−0.336116
$465$		0			0
$466$	17.1840	−	29.7635i	0.796032	−	1.37877i
$467$	−31.3476			−1.45059			−0.725296	−	0.688437i	$-0.758297\pi$
$467$	−31.3476			−1.45059			−0.725296	+	0.688437i	$0.758297\pi$
$468$	−4.91092			−0.227007
$469$	1.47897	−	2.56165i	0.0682925	−	0.118286i
$470$		0			0
$471$	−31.8368	+	55.1430i	−1.46696	+	2.54085i
$472$	0.546481	+	0.946533i	0.0251538	+	0.0435677i
$473$	2.99682	+	5.19065i	0.137794	+	0.238666i
$474$	52.9037			2.42995
$475$		0			0
$476$	1.28487			0.0588918
$477$	−17.5391	−	30.3786i	−0.803060	−	1.39094i
$478$	−5.61949	−	9.73324i	−0.257029	−	0.445188i
$479$	−2.37730	+	4.11760i	−0.108622	+	0.188138i	−0.915212	−	0.402973i	$-0.867977\pi$
$479$	−2.37730	+	4.11760i	−0.108622	+	0.188138i	0.806591	+	0.591111i	$0.201310\pi$
$480$		0			0
$481$	−5.79758	+	10.0417i	−0.264347	+	0.457862i
$482$	8.17052			0.372157
$483$	−6.28870			−0.286146
$484$	−1.96841	+	3.40939i	−0.0894733	+	0.154972i
$485$		0			0
$486$	18.3230			0.831150
$487$	17.0491			0.772569			0.386285	−	0.922380i	$-0.373758\pi$
$487$	17.0491			0.772569			0.386285	+	0.922380i	$0.373758\pi$
$488$	−18.6728	+	32.3423i	−0.845280	+	1.46407i
$489$	21.4714	+	37.1896i	0.970970	+	1.68177i
$490$		0			0
$491$	2.14031	+	3.70713i	0.0965910	+	0.167301i	0.910272	−	0.414012i	$-0.135873\pi$
$491$	2.14031	+	3.70713i	0.0965910	+	0.167301i	−0.813680	+	0.581312i	$0.802539\pi$
$492$	−0.231403	−	0.400802i	−0.0104325	−	0.0180696i
$493$	2.91285			0.131188
$494$	4.62258	−	31.3392i	0.207980	−	1.41002i
$495$		0			0
$496$	15.2624	+	26.4353i	0.685304	+	1.18698i
$497$	−12.0724	−	20.9100i	−0.541521	−	0.937942i
$498$	21.9826	−	38.0750i	0.985064	−	1.70618i
$499$	2.41284	+	4.17916i	0.108013	+	0.187085i	0.914965	−	0.403532i	$-0.132218\pi$
$499$	2.41284	+	4.17916i	0.108013	+	0.187085i	−0.806952	+	0.590617i	$0.798884\pi$
$500$		0			0
$501$	27.4206			1.22506
$502$	27.6371			1.23350
$503$	12.1368	−	21.0215i	0.541153	−	0.937304i	−0.457685	−	0.889114i	$-0.651321\pi$
$503$	12.1368	−	21.0215i	0.541153	−	0.937304i	0.998838	−	0.0481900i	$-0.0153453\pi$
$504$	−26.1311	+	45.2604i	−1.16397	+	2.01606i
$505$		0			0
$506$	−4.81901			−0.214231
$507$	−15.8176	+	27.3969i	−0.702485	+	1.21674i
$508$	−0.791177	−	1.37036i	−0.0351028	−	0.0607998i
$509$	5.05690	−	8.75880i	0.224143	−	0.388227i	−0.731919	−	0.681392i	$-0.761375\pi$
$509$	5.05690	−	8.75880i	0.224143	−	0.388227i	0.956062	+	0.293165i	$0.0947084\pi$
$510$		0			0
$511$	5.46831	+	9.47140i	0.241904	+	0.418990i
$512$	18.5188			0.818423
$513$	3.92659	−	26.6207i	0.173363	−	1.17533i
$514$	−1.02603			−0.0452562
$515$		0			0
$516$	−0.296772	−	0.514024i	−0.0130646	−	0.0226286i
$517$	−10.8187	+	18.7386i	−0.475807	+	0.824123i
$518$	−6.62519	−	11.4752i	−0.291094	−	0.504190i
$519$	12.6157	−	21.8510i	0.553767	−	0.959153i
$520$		0			0
$521$	29.3729			1.28685			0.643426	−	0.765508i	$-0.277513\pi$
$521$	29.3729			1.28685			0.643426	+	0.765508i	$0.277513\pi$
$522$	6.36129	−	11.0181i	0.278426	−	0.482248i
$523$	5.59998	−	9.69944i	0.244870	−	0.424127i	−0.717225	−	0.696842i	$-0.754588\pi$
$523$	5.59998	−	9.69944i	0.244870	−	0.424127i	0.962095	+	0.272714i	$0.0879214\pi$
$524$	3.73324			0.163087
$525$		0			0
$526$	8.61074	−	14.9142i	0.375446	−	0.650292i
$527$	−6.14037	−	10.6354i	−0.267479	−	0.463286i
$528$	−34.7636	+	60.2124i	−1.51289	+	2.62041i
$529$	11.3309	+	19.6257i	0.492648	+	0.853292i
$530$		0			0
$531$	−2.10858			−0.0915046
$532$	2.50814	+	1.98726i	0.108742	+	0.0861588i
$533$	−4.09866			−0.177533
$534$	37.7485	+	65.3822i	1.63354	+	2.82937i
$535$		0			0
$536$	1.04518	−	1.81031i	0.0451450	−	0.0781934i
$537$	−15.4519	−	26.7634i	−0.666798	−	1.15493i
$538$	−17.4866	+	30.2877i	−0.753901	+	1.30579i
$539$	−41.0047			−1.76620
$540$		0			0
$541$	−2.84691	+	4.93100i	−0.122398	+	0.212000i	−0.920713	−	0.390241i	$-0.872392\pi$
$541$	−2.84691	+	4.93100i	−0.122398	+	0.212000i	0.798315	+	0.602241i	$0.205725\pi$
$542$	−5.65809	+	9.80010i	−0.243036	+	0.420950i
$543$	30.7019			1.31754
$544$	1.91352			0.0820415
$545$		0			0
$546$	−39.2951	−	68.0612i	−1.68168	−	2.91275i
$547$	−5.99088	+	10.3765i	−0.256151	+	0.443667i	−0.965208	−	0.261485i	$-0.915788\pi$
$547$	−5.99088	+	10.3765i	−0.256151	+	0.443667i	0.709056	+	0.705152i	$0.249121\pi$
$548$	−0.152425	−	0.264009i	−0.00651129	−	0.0112779i
$549$	−36.0243	−	62.3959i	−1.53748	−	2.66299i
$550$		0			0
$551$	5.68607	+	4.50522i	0.242235	+	0.191929i
$552$	−4.44419			−0.189157
$553$	23.6639	+	40.9871i	1.00629	+	1.74295i
$554$	−13.8149	−	23.9281i	−0.586939	−	1.01661i
$555$		0			0
$556$	0.198706	+	0.344168i	0.00842700	+	0.0145960i
$557$	17.2786	−	29.9275i	0.732119	−	1.26807i	−0.223857	−	0.974622i	$-0.571865\pi$
$557$	17.2786	−	29.9275i	0.732119	−	1.26807i	0.955976	−	0.293446i	$-0.0948019\pi$
$558$	−53.6390			−2.27072
$559$	−5.25649			−0.222326
$560$		0			0
$561$	13.9860	−	24.2245i	0.590491	−	1.02276i
$562$	−20.7216			−0.874087
$563$	24.8817			1.04864			0.524318	−	0.851522i	$-0.324320\pi$
$563$	24.8817			1.04864			0.524318	+	0.851522i	$0.324320\pi$
$564$	1.07137	−	1.85566i	0.0451126	−	0.0781374i
$565$		0			0
$566$	−18.2681	+	31.6413i	−0.767867	+	1.32998i
$567$	−4.07422	−	7.05676i	−0.171101	−	0.296356i
$568$	−8.53150	−	14.7770i	−0.357974	−	0.620029i
$569$	−38.7345			−1.62384			−0.811918	−	0.583771i	$-0.801577\pi$
$569$	−38.7345			−1.62384			−0.811918	+	0.583771i	$0.801577\pi$
$570$		0			0
$571$	−4.53514			−0.189790			−0.0948948	−	0.995487i	$-0.530251\pi$
$571$	−4.53514			−0.189790			−0.0948948	+	0.995487i	$0.530251\pi$
$572$	−2.66178	−	4.61034i	−0.111295	−	0.192768i
$573$	8.97534	+	15.5457i	0.374950	+	0.649433i
$574$	2.34188	−	4.05625i	0.0977481	−	0.169305i
$575$		0			0
$576$	−18.2726	+	31.6491i	−0.761359	+	1.31871i
$577$	21.9514			0.913847			0.456923	−	0.889506i	$-0.348951\pi$
$577$	21.9514			0.913847			0.456923	+	0.889506i	$0.348951\pi$
$578$	20.6432			0.858642
$579$	−25.4666	+	44.1095i	−1.05836	+	1.83313i
$580$		0			0
$581$	39.3314			1.63174
$582$	46.5448			1.92934
$583$	19.0128	−	32.9311i	0.787430	−	1.36387i
$584$	3.86443	+	6.69339i	0.159911	+	0.276974i
$585$		0			0
$586$	7.83430	+	13.5694i	0.323632	+	0.560547i
$587$	−20.5232	−	35.5472i	−0.847084	−	1.46719i	−0.883799	−	0.467866i	$-0.845023\pi$
$587$	−20.5232	−	35.5472i	−0.847084	−	1.46719i	0.0367158	−	0.999326i	$-0.488310\pi$
$588$	4.06064			0.167458
$589$	4.46311	−	30.2581i	0.183899	−	1.24676i
$590$		0			0
$591$	24.2715	+	42.0395i	0.998397	+	1.72927i
$592$	−5.14030	−	8.90327i	−0.211265	−	0.365922i
$593$	−4.85982	+	8.41745i	−0.199569	+	0.345663i	−0.948389	−	0.317110i	$-0.897287\pi$
$593$	−4.85982	+	8.41745i	−0.199569	+	0.345663i	0.748820	+	0.662774i	$0.230621\pi$
$594$	−25.5780	−	44.3025i	−1.04948	−	1.81775i
$595$		0			0
$596$	−0.286188			−0.0117227
$597$	46.9769			1.92264
$598$	2.11316	−	3.66010i	0.0864135	−	0.149673i
$599$	15.2247	−	26.3700i	0.622065	−	1.07745i	−0.367036	−	0.930207i	$-0.619627\pi$
$599$	15.2247	−	26.3700i	0.622065	−	1.07745i	0.989101	−	0.147241i	$-0.0470392\pi$
$600$		0			0
$601$	24.5483			1.00135			0.500673	−	0.865637i	$-0.333086\pi$
$601$	24.5483			1.00135			0.500673	+	0.865637i	$0.333086\pi$
$602$	3.00343	−	5.20209i	0.122411	−	0.212021i
$603$	2.01640	+	3.49251i	0.0821142	+	0.142226i
$604$	−0.623063	+	1.07918i	−0.0253521	+	0.0439111i
$605$		0			0
$606$	10.9146	+	18.9047i	0.443376	+	0.767949i
$607$	−39.0162			−1.58362			−0.791810	−	0.610767i	$-0.790861\pi$
$607$	−39.0162			−1.58362			−0.791810	+	0.610767i	$0.790861\pi$
$608$	3.73531	+	2.95958i	0.151487	+	0.120027i
$609$	17.9977			0.729303
$610$		0			0
$611$	−9.48813	−	16.4339i	−0.383849	−	0.664845i
$612$	−0.875881	+	1.51707i	−0.0354054	+	0.0613239i
$613$	2.48708	+	4.30775i	0.100452	+	0.173988i	0.911871	−	0.410477i	$-0.134638\pi$
$613$	2.48708	+	4.30775i	0.100452	+	0.173988i	−0.811419	+	0.584465i	$0.801304\pi$
$614$	−9.49775	+	16.4506i	−0.383298	+	0.663891i
$615$		0			0
$616$	−56.6536			−2.28264
$617$	−19.3210	+	33.4649i	−0.777834	+	1.34725i	0.155354	+	0.987859i	$0.450348\pi$
$617$	−19.3210	+	33.4649i	−0.777834	+	1.34725i	−0.933188	+	0.359389i	$0.882985\pi$
$618$	16.4146	−	28.4310i	0.660293	−	1.14366i
$619$	−27.9053			−1.12161			−0.560804	−	0.827949i	$-0.689508\pi$
$619$	−27.9053			−1.12161			−0.560804	+	0.827949i	$0.689508\pi$
$620$		0			0
$621$	1.79500	−	3.10902i	0.0720307	−	0.124761i
$622$	2.53807	+	4.39607i	0.101767	+	0.176266i
$623$	−33.7699	+	58.4912i	−1.35296	+	2.34340i
$624$	−30.4880	−	52.8068i	−1.22050	−	2.11396i
$625$		0			0
$626$	−4.21322			−0.168394
$627$	64.7690	−	25.6560i	2.58662	−	1.02460i
$628$	4.32264			0.172492
$629$	2.06804	+	3.58195i	0.0824581	+	0.142822i
$630$		0			0
$631$	6.62012	−	11.4664i	0.263543	−	0.456469i	−0.703638	−	0.710559i	$-0.748442\pi$
$631$	6.62012	−	11.4664i	0.263543	−	0.456469i	0.967181	+	0.254089i	$0.0817757\pi$
$632$	16.7232	+	28.9654i	0.665212	+	1.15218i
$633$	−22.2721	+	38.5763i	−0.885235	+	1.53327i
$634$	−6.90451			−0.274213
$635$		0			0
$636$	−1.88281	+	3.26113i	−0.0746584	+	0.129312i
$637$	17.9808	−	31.1436i	0.712423	−	1.23395i
$638$	13.7916			0.546014
$639$	32.9185			1.30224
$640$		0			0
$641$	−18.7555	−	32.4854i	−0.740796	−	1.28310i	−0.952133	−	0.305684i	$-0.901115\pi$
$641$	−18.7555	−	32.4854i	−0.740796	−	1.28310i	0.211337	−	0.977413i	$-0.432218\pi$
$642$	26.7680	−	46.3636i	1.05645	−	1.82982i
$643$	−12.1969	−	21.1257i	−0.481000	−	0.833117i	0.518762	−	0.854919i	$-0.326393\pi$
$643$	−12.1969	−	21.1257i	−0.481000	−	0.833117i	−0.999762	+	0.0218020i	$0.993060\pi$
$644$	0.213462	+	0.369726i	0.00841157	+	0.0145693i
$645$		0			0
$646$	−8.85679	−	7.01746i	−0.348466	−	0.276098i
$647$	−8.05266			−0.316583			−0.158291	−	0.987392i	$-0.550599\pi$
$647$	−8.05266			−0.316583			−0.158291	+	0.987392i	$0.550599\pi$
$648$	−2.87923	−	4.98698i	−0.113107	−	0.195907i
$649$	−1.14288	−	1.97952i	−0.0448618	−	0.0777030i
$650$		0			0
$651$	−37.9396	−	65.7133i	−1.48697	−	2.57551i
$652$	1.45764	−	2.52470i	0.0570855	−	0.0988750i
$653$	19.9890			0.782228			0.391114	−	0.920342i	$-0.372090\pi$
$653$	19.9890			0.782228			0.391114	+	0.920342i	$0.372090\pi$
$654$	34.6717			1.35577
$655$		0			0
$656$	1.81700	−	3.14713i	0.0709419	−	0.122875i
$657$	−14.9108			−0.581725
$658$	21.6852			0.845375
$659$	16.2197	−	28.0933i	0.631829	−	1.09436i	−0.355349	−	0.934734i	$-0.615638\pi$
$659$	16.2197	−	28.0933i	0.631829	−	1.09436i	0.987178	−	0.159626i	$-0.0510287\pi$
$660$		0			0
$661$	17.7771	−	30.7908i	0.691448	−	1.19762i	−0.279915	−	0.960025i	$-0.590306\pi$
$661$	17.7771	−	30.7908i	0.691448	−	1.19762i	0.971363	−	0.237599i	$-0.0763603\pi$
$662$	−5.18610	−	8.98260i	−0.201564	−	0.349118i
$663$	12.2659	+	21.2451i	0.476368	+	0.825093i
$664$	27.7953			1.07867
$665$		0			0
$666$	18.0653			0.700017
$667$	0.483927	+	0.838187i	0.0187377	+	0.0324547i
$668$	−0.930757	−	1.61212i	−0.0360121	−	0.0623747i
$669$	−11.1502	+	19.3127i	−0.431092	+	0.746674i
$670$		0			0
$671$	39.0512	−	67.6387i	1.50755	−	2.61116i
$672$	11.8231			0.456086
$673$	−27.5963			−1.06376			−0.531880	−	0.846820i	$-0.678514\pi$
$673$	−27.5963			−1.06376			−0.531880	+	0.846820i	$0.678514\pi$
$674$	10.0259	−	17.3654i	0.386184	−	0.668891i
$675$		0			0
$676$	2.14763			0.0826013
$677$	−21.2114			−0.815221			−0.407610	−	0.913156i	$-0.633638\pi$
$677$	−21.2114			−0.815221			−0.407610	+	0.913156i	$0.633638\pi$
$678$	26.5627	−	46.0079i	1.02013	−	1.76692i
$679$	20.8196	+	36.0605i	0.798981	+	1.38388i
$680$		0			0
$681$	−24.0696	−	41.6897i	−0.922348	−	1.59755i
$682$	−29.0730	−	50.3559i	−1.11326	−	1.92823i
$683$	−19.3626			−0.740891			−0.370446	−	0.928854i	$-0.620795\pi$
$683$	−19.3626			−0.740891			−0.370446	+	0.928854i	$0.620795\pi$
$684$	−4.05618	+	1.60672i	−0.155092	+	0.0614344i
$685$		0			0
$686$	0.923282	+	1.59917i	0.0352511	+	0.0610567i
$687$	0.359071	+	0.621929i	0.0136994	+	0.0237281i
$688$	2.33028	−	4.03616i	0.0888410	−	0.153877i
$689$	16.6744	+	28.8809i	0.635244	+	1.10028i
$690$		0			0
$691$	−1.28081			−0.0487241			−0.0243621	−	0.999703i	$-0.507755\pi$
$691$	−1.28081			−0.0487241			−0.0243621	+	0.999703i	$0.507755\pi$
$692$	−1.71289			−0.0651144
$693$	54.6490	−	94.6548i	2.07594	−	3.59564i
$694$	−16.2660	+	28.1735i	−0.617448	+	1.06945i
$695$		0			0
$696$	12.7189			0.482108
$697$	−0.731012	+	1.26615i	−0.0276891	+	0.0479588i
$698$	−16.4361	−	28.4681i	−0.622114	−	1.07753i
$699$	−33.1423	+	57.4041i	−1.25356	+	2.17122i
$700$		0			0
$701$	18.5649	+	32.1553i	0.701185	+	1.21449i	0.968051	+	0.250754i	$0.0806787\pi$
$701$	18.5649	+	32.1553i	0.701185	+	1.21449i	−0.266866	+	0.963734i	$0.585988\pi$
$702$	44.8644			1.69330
$703$	−1.50315	+	10.1908i	−0.0566924	+	0.384352i
$704$	−39.6159			−1.49308
$705$		0			0
$706$	0.502875	+	0.871005i	0.0189260	+	0.0327807i
$707$	−9.76425	+	16.9122i	−0.367222	+	0.636048i
$708$	0.113178	+	0.196029i	0.00425347	+	0.00736723i
$709$	−6.57886	+	11.3949i	−0.247074	+	0.427945i	−0.962713	−	0.270526i	$-0.912802\pi$
$709$	−6.57886	+	11.3949i	−0.247074	+	0.427945i	0.715638	+	0.698471i	$0.246136\pi$
$710$		0			0
$711$	−64.5258			−2.41991
$712$	−23.8650	+	41.3354i	−0.894379	+	1.54911i
$713$	2.04026	−	3.53384i	0.0764084	−	0.132343i
$714$	−28.0337			−1.04914
$715$		0			0
$716$	−1.04899	+	1.81690i	−0.0392025	+	0.0679007i
$717$	10.8382	+	18.7722i	0.404758	+	0.701062i
$718$	−18.7560	+	32.4863i	−0.699967	+	1.21238i
$719$	−7.27853	−	12.6068i	−0.271443	−	0.470153i	0.697788	−	0.716304i	$-0.254168\pi$
$719$	−7.27853	−	12.6068i	−0.271443	−	0.470153i	−0.969232	+	0.246150i	$0.920834\pi$
$720$		0			0
$721$	29.3692			1.09376
$722$	−6.43530	−	27.3970i	−0.239497	−	1.01961i
$723$	−15.7583			−0.586056
$724$	−1.04214	−	1.80503i	−0.0387306	−	0.0670834i
$725$		0			0
$726$	42.9476	−	74.3874i	1.59394	−	2.76078i
$727$	4.48581	+	7.76966i	0.166370	+	0.288161i	0.937141	−	0.348951i	$-0.113462\pi$
$727$	4.48581	+	7.76966i	0.166370	+	0.288161i	−0.770771	+	0.637112i	$0.780129\pi$
$728$	24.8428	−	43.0291i	0.920737	−	1.59476i
$729$	−41.7969			−1.54803
$730$		0			0
$731$	−0.937514	+	1.62382i	−0.0346752	+	0.0600592i
$732$	−3.86719	+	6.69817i	−0.142935	+	0.247571i
$733$	−24.7325			−0.913516			−0.456758	−	0.889591i	$-0.650990\pi$
$733$	−24.7325			−0.913516			−0.456758	+	0.889591i	$0.650990\pi$
$734$	17.2753			0.637642
$735$		0			0
$736$	0.317903	+	0.550624i	0.0117181	+	0.0202963i
$737$	−2.18583	+	3.78596i	−0.0805159	+	0.139458i
$738$	3.19287	+	5.53021i	0.117531	+	0.203570i
$739$	0.784588	+	1.35895i	0.0288615	+	0.0499896i	0.880095	−	0.474797i	$-0.157478\pi$
$739$	0.784588	+	1.35895i	0.0288615	+	0.0499896i	−0.851234	+	0.524787i	$0.824145\pi$
$740$		0			0
$741$	−8.91543	+	60.4431i	−0.327517	+	2.22043i
$742$	−38.1094			−1.39904
$743$	−12.1463	−	21.0380i	−0.445604	−	0.771808i	0.552490	−	0.833519i	$-0.313678\pi$
$743$	−12.1463	−	21.0380i	−0.445604	−	0.771808i	−0.998094	+	0.0617109i	$0.980344\pi$
$744$	−26.8117	−	46.4392i	−0.982965	−	1.70254i
$745$		0			0
$746$	9.69539	+	16.7929i	0.354974	+	0.614832i
$747$	−26.8119	+	46.4395i	−0.980994	+	1.69913i
$748$	−1.89895			−0.0694326
$749$	47.8935			1.74999
$750$		0			0
$751$	−17.4771	+	30.2712i	−0.637748	+	1.10461i	0.348178	+	0.937429i	$0.386801\pi$
$751$	−17.4771	+	30.2712i	−0.637748	+	1.10461i	−0.985926	+	0.167184i	$0.946533\pi$
$752$	16.8249			0.613541
$753$	−53.3029			−1.94247
$754$	−6.04768	+	10.4749i	−0.220243	+	0.381473i
$755$		0			0
$756$	−2.26600	+	3.92482i	−0.0824135	+	0.142744i
$757$	−1.61043	−	2.78935i	−0.0585321	−	0.101381i	0.835275	−	0.549833i	$-0.185309\pi$
$757$	−1.61043	−	2.78935i	−0.0585321	−	0.101381i	−0.893807	+	0.448452i	$0.851975\pi$
$758$	−24.2595	−	42.0186i	−0.881143	−	1.52619i
$759$	9.29430			0.337362
$760$		0			0
$761$	3.72402			0.134996			0.0674979	−	0.997719i	$-0.478498\pi$
$761$	3.72402			0.134996			0.0674979	+	0.997719i	$0.478498\pi$
$762$	17.2622	+	29.8990i	0.625344	+	1.08313i
$763$	15.5087	+	26.8619i	0.561453	+	0.972465i
$764$	0.609312	−	1.05536i	0.0220441	−	0.0381816i
$765$		0			0
$766$	18.9930	−	32.8968i	0.686244	−	1.18861i
$767$	2.00463			0.0723829
$768$	13.1756			0.475435
$769$	16.1032	−	27.8915i	0.580695	−	1.00579i	−0.414702	−	0.909957i	$-0.636114\pi$
$769$	16.1032	−	27.8915i	0.580695	−	1.00579i	0.995397	−	0.0958365i	$-0.0305526\pi$
$770$		0			0
$771$	1.97887			0.0712674
$772$	3.45773			0.124446
$773$	10.3416	−	17.9122i	0.371963	−	0.644259i	−0.617904	−	0.786253i	$-0.712018\pi$
$773$	10.3416	−	17.9122i	0.371963	−	0.644259i	0.989867	+	0.141994i	$0.0453515\pi$
$774$	4.09482	+	7.09243i	0.147185	+	0.254932i
$775$		0			0
$776$	14.7131	+	25.4838i	0.528169	+	0.914815i
$777$	12.7778	+	22.1318i	0.458402	+	0.793975i
$778$	27.4711			0.984886
$779$	−3.38530	+	1.34097i	−0.121291	+	0.0480452i
$780$		0			0
$781$	17.8422	+	30.9037i	0.638446	+	1.10582i
$782$	−0.753780	−	1.30558i	−0.0269551	−	0.0466876i
$783$	−5.13712	+	8.89775i	−0.183586	+	0.317980i
$784$	15.9423	+	27.6128i	0.569367	+	0.986172i
$785$		0			0
$786$	−81.4534			−2.90535
$787$	46.0227			1.64053			0.820266	−	0.571982i	$-0.193825\pi$
$787$	46.0227			1.64053			0.820266	+	0.571982i	$0.193825\pi$
$788$	1.64773	−	2.85395i	0.0586980	−	0.101668i
$789$	−16.6073	+	28.7647i	−0.591236	+	1.02405i
$790$		0			0
$791$	47.5261			1.68983
$792$	38.6202	−	66.8921i	1.37231	−	2.37691i
$793$	34.2483	+	59.3197i	1.21619	+	2.10651i
$794$	−11.4023	+	19.7494i	−0.404654	+	0.700880i
$795$		0			0
$796$	−1.59457	−	2.76187i	−0.0565180	−	0.0978920i
$797$	25.0847			0.888546			0.444273	−	0.895891i	$-0.353462\pi$
$797$	25.0847			0.888546			0.444273	+	0.895891i	$0.353462\pi$
$798$	−54.7236	−	43.3589i	−1.93719	−	1.53489i
$799$	−6.76897			−0.239469
$800$		0			0
$801$	−46.0412	−	79.7457i	−1.62679	−	2.81768i
$802$	−15.2499	+	26.4135i	−0.538491	+	0.932694i
$803$	−8.08183	−	13.9981i	−0.285201	−	0.493983i
$804$	0.216460	−	0.374919i	0.00763394	−	0.0132224i
$805$		0			0
$806$	50.9946			1.79621
$807$	33.7259	−	58.4150i	1.18721	−	2.05631i
$808$	−6.90034	+	11.9517i	−0.242753	+	0.420461i
$809$	27.6272			0.971319			0.485660	−	0.874148i	$-0.338579\pi$
$809$	27.6272			0.971319			0.485660	+	0.874148i	$0.338579\pi$
$810$		0			0
$811$	19.2254	−	33.2993i	0.675094	−	1.16930i	−0.301347	−	0.953514i	$-0.597436\pi$
$811$	19.2254	−	33.2993i	0.675094	−	1.16930i	0.976441	−	0.215783i	$-0.0692304\pi$
$812$	−0.610908	−	1.05812i	−0.0214387	−	0.0371329i
$813$	10.9126	−	18.9012i	0.382722	−	0.662893i
$814$	9.79162	+	16.9596i	0.343196	+	0.594433i
$815$		0			0
$816$	−21.7506			−0.761423
$817$	−4.34160	+	1.71978i	−0.151893	+	0.0601674i
$818$	2.40522			0.0840966
$819$	47.9277	+	83.0132i	1.67473	+	2.90071i
$820$		0			0
$821$	−26.3339	+	45.6117i	−0.919060	+	1.59186i	−0.118215	+	0.992988i	$0.537717\pi$
$821$	−26.3339	+	45.6117i	−0.919060	+	1.59186i	−0.800845	+	0.598871i	$0.795616\pi$
$822$	3.32568	+	5.76024i	0.115996	+	0.200912i
$823$	−2.33597	+	4.04602i	−0.0814269	+	0.141035i	−0.903863	−	0.427822i	$-0.859281\pi$
$823$	−2.33597	+	4.04602i	−0.0814269	+	0.141035i	0.822436	+	0.568857i	$0.192614\pi$
$824$	20.7550			0.723036
$825$		0			0
$826$	−1.14540	+	1.98388i	−0.0398534	+	0.0690281i
$827$	−13.7124	+	23.7506i	−0.476827	+	0.825888i	−0.999647	−	0.0265546i	$-0.991546\pi$
$827$	−13.7124	+	23.7506i	−0.476827	+	0.825888i	0.522821	+	0.852443i	$0.324880\pi$
$828$	−0.582059			−0.0202279
$829$	0.156181			0.00542438			0.00271219	−	0.999996i	$-0.499137\pi$
$829$	0.156181			0.00542438			0.00271219	+	0.999996i	$0.499137\pi$
$830$		0			0
$831$	26.6444	+	46.1495i	0.924285	+	1.60091i
$832$	17.3718	−	30.0888i	0.602258	−	1.04314i
$833$	−6.41387	−	11.1091i	−0.222227	−	0.384909i
$834$	−4.33544	−	7.50920i	−0.150124	−	0.260022i
$835$		0			0
$836$	−3.70687	−	2.93705i	−0.128205	−	0.101580i
$837$	43.3167			1.49724
$838$	12.4485	+	21.5615i	0.430027	+	0.744828i
$839$	14.5946	+	25.2786i	0.503862	+	0.872715i	0.999990	+	0.00446519i	$0.00142132\pi$
$839$	14.5946	+	25.2786i	0.503862	+	0.872715i	−0.496128	+	0.868249i	$0.665245\pi$
$840$		0			0
$841$	13.1150	+	22.7159i	0.452243	+	0.783308i
$842$	15.5108	−	26.8655i	0.534537	−	0.925845i
$843$	39.9651			1.37647
$844$	3.02398			0.104090
$845$		0			0
$846$	−14.7826	+	25.6041i	−0.508235	+	0.880288i
$847$	76.8421			2.64033
$848$	−29.5680			−1.01537
$849$	35.2332	−	61.0258i	1.20920	−	2.09440i
$850$		0			0
$851$	−0.687148	+	1.19018i	−0.0235551	+	0.0407987i
$852$	−1.76689	−	3.06035i	−0.0605328	−	0.104846i
$853$	22.8832	+	39.6348i	0.783505	+	1.35707i	0.929888	+	0.367842i	$0.119903\pi$
$853$	22.8832	+	39.6348i	0.783505	+	1.35707i	−0.146384	+	0.989228i	$0.546763\pi$
$854$	−78.2745			−2.67850
$855$		0			0
$856$	33.8461			1.15684
$857$	−7.45807	−	12.9177i	−0.254763	−	0.441262i	0.710068	−	0.704133i	$-0.248664\pi$
$857$	−7.45807	−	12.9177i	−0.254763	−	0.441262i	−0.964831	+	0.262871i	$0.915331\pi$
$858$	58.0757	+	100.590i	1.98267	+	3.43409i
$859$	−24.6100	+	42.6258i	−0.839682	+	1.45437i	0.0504787	+	0.998725i	$0.483925\pi$
$859$	−24.6100	+	42.6258i	−0.839682	+	1.45437i	−0.890161	+	0.455647i	$0.849408\pi$
$860$		0			0
$861$	−4.51671	+	7.82318i	−0.153929	+	0.266613i
$862$	−50.0370			−1.70427
$863$	20.9577			0.713407			0.356704	−	0.934218i	$-0.383901\pi$
$863$	20.9577			0.713407			0.356704	+	0.934218i	$0.383901\pi$
$864$	−3.37469	+	5.84514i	−0.114809	+	0.198856i
$865$		0			0
$866$	22.2607			0.756448
$867$	−39.8139			−1.35215
$868$	−2.57562	+	4.46110i	−0.0874222	+	0.151420i
$869$	−34.9738	−	60.5764i	−1.18640	−	2.05491i
$870$		0			0
$871$	−1.91699	−	3.32032i	−0.0649547	−	0.112505i
$872$	10.9599	+	18.9831i	0.371150	+	0.642851i
$873$	−56.7700			−1.92137
$874$	0.547883	−	3.71443i	0.0185324	−	0.125642i
$875$		0			0
$876$	0.800333	+	1.38622i	0.0270407	+	0.0468359i
$877$	13.1009	+	22.6914i	0.442385	+	0.766233i	0.997866	−	0.0652963i	$-0.0207993\pi$
$877$	13.1009	+	22.6914i	0.442385	+	0.766233i	−0.555481	+	0.831529i	$0.687466\pi$
$878$	27.9364	−	48.3873i	0.942808	−	1.63299i
$879$	−15.1098	−	26.1709i	−0.509641	−	0.882724i
$880$		0			0
$881$	−45.3499			−1.52788			−0.763938	−	0.645289i	$-0.776737\pi$
$881$	−45.3499			−1.52788			−0.763938	+	0.645289i	$0.776737\pi$
$882$	−56.0282			−1.88657
$883$	21.6585	−	37.5136i	0.728867	−	1.26243i	−0.228495	−	0.973545i	$-0.573381\pi$
$883$	21.6585	−	37.5136i	0.728867	−	1.26243i	0.957362	−	0.288890i	$-0.0932861\pi$
$884$	0.832699	−	1.44228i	0.0280067	−	0.0485090i
$885$		0			0
$886$	−19.4250			−0.652597
$887$	−19.5073	+	33.7877i	−0.654992	+	1.13448i	0.326904	+	0.945058i	$0.393995\pi$
$887$	−19.5073	+	33.7877i	−0.654992	+	1.13448i	−0.981896	+	0.189422i	$0.939339\pi$
$888$	9.03002	+	15.6405i	0.303028	+	0.524859i
$889$	−15.4428	+	26.7478i	−0.517936	+	0.897091i
$890$		0			0
$891$	6.02145	+	10.4295i	0.201726	+	0.349400i
$892$	1.51392			0.0506898
$893$	−13.2135	−	10.4694i	−0.442171	−	0.350344i
$894$	6.24416			0.208836
$895$		0			0
$896$	23.9903	+	41.5524i	0.801459	+	1.38817i
$897$	−4.07559	+	7.05913i	−0.136080	+	0.235698i
$898$	8.65798	+	14.9961i	0.288921	+	0.500425i
$899$	−5.83905	+	10.1135i	−0.194743	+	0.337305i
$900$		0			0
$901$	11.8958			0.396306
$902$	−3.46115	+	5.99488i	−0.115244	+	0.199608i
$903$	−5.79263	+	10.0331i	−0.192767	+	0.333882i
$904$	33.5865			1.11707
$905$		0			0
$906$	13.5942	−	23.5459i	0.451638	−	0.782260i
$907$	25.0804	+	43.4405i	0.832780	+	1.44242i	0.895825	+	0.444407i	$0.146586\pi$
$907$	25.0804	+	43.4405i	0.832780	+	1.44242i	−0.0630443	+	0.998011i	$0.520081\pi$
$908$	−1.63402	+	2.83021i	−0.0542269	+	0.0939237i
$909$	−13.3124	−	23.0577i	−0.441544	−	0.764776i
$910$		0			0
$911$	−50.4028			−1.66992			−0.834959	−	0.550312i	$-0.814509\pi$
$911$	−50.4028			−1.66992			−0.834959	+	0.550312i	$0.814509\pi$
$912$	−42.4585	−	33.6410i	−1.40594	−	1.11396i
$913$	−58.1294			−1.92380
$914$	−15.8702	−	27.4880i	−0.524940	−	0.909223i
$915$		0			0
$916$	0.0243764	−	0.0422211i	0.000805418	−	0.00139503i
$917$	−36.4342	−	63.1059i	−1.20316	−	2.08394i
$918$	8.00173	−	13.8594i	0.264096	−	0.457428i
$919$	48.7246			1.60728			0.803638	−	0.595118i	$-0.202895\pi$
$919$	48.7246			1.60728			0.803638	+	0.595118i	$0.202895\pi$
$920$		0			0
$921$	18.3180	−	31.7278i	0.603600	−	1.04547i
$922$	−7.15299	+	12.3893i	−0.235571	+	0.408021i
$923$	−31.2956			−1.03011
$924$	−11.7331			−0.385990
$925$		0			0
$926$	0.925608	+	1.60320i	0.0304174	+	0.0526844i
$927$	−20.0207	+	34.6768i	−0.657565	+	1.13894i
$928$	−0.909811	−	1.57584i	−0.0298660	−	0.0517294i
$929$	−4.01832	−	6.95993i	−0.131837	−	0.228348i	0.792548	−	0.609810i	$-0.208754\pi$
$929$	−4.01832	−	6.95993i	−0.131837	−	0.228348i	−0.924385	+	0.381462i	$0.875421\pi$
$930$		0			0
$931$	4.66191	−	31.6059i	0.152788	−	1.03584i
$932$	4.49989			0.147399
$933$	−4.89511	−	8.47858i	−0.160259	−	0.277576i
$934$	−23.2159	−	40.2111i	−0.759648	−	1.31575i
$935$		0			0
$936$	33.8702	+	58.6650i	1.10708	+	1.91752i
$937$	12.7713	−	22.1206i	0.417221	−	0.722647i	−0.578438	−	0.815726i	$-0.696338\pi$
$937$	12.7713	−	22.1206i	0.417221	−	0.722647i	0.995659	+	0.0930789i	$0.0296709\pi$
$938$	4.38129			0.143054
$939$	8.12592			0.265179
$940$		0			0
$941$	−4.30747	+	7.46075i	−0.140419	+	0.243214i	−0.927655	−	0.373439i	$-0.878178\pi$
$941$	−4.30747	+	7.46075i	−0.140419	+	0.243214i	0.787235	+	0.616653i	$0.211512\pi$
$942$	−94.3130			−3.07288
$943$	−0.485787			−0.0158194
$944$	−0.888680	+	1.53924i	−0.0289241	+	0.0500980i
$945$		0			0
$946$	−4.43888	+	7.68837i	−0.144320	+	0.249970i
$947$	−19.2138	−	33.2793i	−0.624364	−	1.08143i	−0.988663	−	0.150149i	$-0.952025\pi$
$947$	−19.2138	−	33.2793i	−0.624364	−	1.08143i	0.364299	−	0.931282i	$-0.381309\pi$
$948$	3.46341	+	5.99880i	0.112486	+	0.194832i
$949$	14.1757			0.460162
$950$		0			0
$951$	13.3165			0.431819
$952$	−8.86163	−	15.3488i	−0.287207	−	0.497457i
$953$	4.44520	+	7.69932i	0.143994	+	0.249405i	0.928997	−	0.370087i	$-0.120672\pi$
$953$	4.44520	+	7.69932i	0.143994	+	0.249405i	−0.785003	+	0.619492i	$0.787339\pi$
$954$	25.9788	−	44.9966i	0.841095	−	1.45682i
$955$		0			0
$956$	0.735774	−	1.27440i	0.0237966	−	0.0412170i
$957$	−26.5995			−0.859838
$958$	−7.04248			−0.227532
$959$	−2.97516	+	5.15313i	−0.0960730	+	0.166403i
$960$		0			0
$961$	18.2354			0.588239
$962$	−17.1747			−0.553734
$963$	−32.6485	+	56.5489i	−1.05208	+	1.82226i
$964$	0.534893	+	0.926463i	0.0172278	+	0.0298394i
$965$		0			0
$966$	−4.65739	−	8.06684i	−0.149849	−	0.259546i
$967$	−30.8149	−	53.3729i	−0.990939	−	1.71636i	−0.611789	−	0.791021i	$-0.709550\pi$
$967$	−30.8149	−	53.3729i	−0.990939	−	1.71636i	−0.379150	−	0.925335i	$-0.623784\pi$
$968$	54.3040			1.74540
$969$	17.0818	+	13.5344i	0.548748	+	0.434787i
$970$		0			0
$971$	−2.92998	−	5.07488i	−0.0940277	−	0.162861i	0.815175	−	0.579215i	$-0.196641\pi$
$971$	−2.92998	−	5.07488i	−0.0940277	−	0.162861i	−0.909202	+	0.416354i	$0.863308\pi$
$972$	1.19954	+	2.07767i	0.0384753	+	0.0666412i
$973$	3.87850	−	6.71776i	0.124339	−	0.215361i
$974$	12.6265	+	21.8698i	0.404580	+	0.700753i
$975$		0			0
$976$	−60.7310			−1.94395
$977$	−2.40082			−0.0768089			−0.0384044	−	0.999262i	$-0.512228\pi$
$977$	−2.40082			−0.0768089			−0.0384044	+	0.999262i	$0.512228\pi$
$978$	−31.8033	+	55.0850i	−1.01696	+	1.76142i
$979$	49.9098	−	86.4463i	1.59512	−	2.76284i
$980$		0			0
$981$	−42.2885			−1.35017
$982$	−3.17022	+	5.49098i	−0.101166	+	0.175224i
$983$	−9.18425	−	15.9076i	−0.292932	−	0.507373i	0.681570	−	0.731753i	$-0.261298\pi$
$983$	−9.18425	−	15.9076i	−0.292932	−	0.507373i	−0.974502	+	0.224380i	$0.927964\pi$
$984$	−3.19194	+	5.52860i	−0.101755	+	0.176245i
$985$		0			0
$986$	2.15725	+	3.73647i	0.0687009	+	0.118993i
$987$	−41.8236			−1.33126
$988$	3.85621	−	1.52750i	0.122682	−	0.0485964i
$989$	−0.623016			−0.0198108
$990$		0			0
$991$	−5.14734	−	8.91546i	−0.163511	−	0.283209i	0.772615	−	0.634875i	$-0.218948\pi$
$991$	−5.14734	−	8.91546i	−0.163511	−	0.283209i	−0.936125	+	0.351666i	$0.885615\pi$
$992$	−3.83581	+	6.64381i	−0.121787	+	0.210941i
$993$	10.0023	+	17.3245i	0.317413	+	0.549776i
$994$	17.8816	−	30.9718i	0.567169	−	0.982365i
$995$		0			0
$996$	5.75648			0.182401
$997$	−1.15115	+	1.99385i	−0.0364573	+	0.0631459i	−0.883678	−	0.468095i	$-0.844941\pi$
$997$	−1.15115	+	1.99385i	−0.0364573	+	0.0631459i	0.847221	+	0.531241i	$0.178274\pi$
$998$	−3.57388	+	6.19014i	−0.113129	+	0.195946i
$999$	−14.5888			−0.461569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.f.26.5	✓	12
5.2	odd	4		475.2.j.d.349.3		24
5.3	odd	4		475.2.j.d.349.10		24
5.4	even	2		475.2.e.h.26.2	yes	12
19.7	even	3		9025.2.a.bz.1.2		6
19.11	even	3	inner	475.2.e.f.201.5	yes	12
19.12	odd	6		9025.2.a.bs.1.5		6
95.49	even	6		475.2.e.h.201.2	yes	12
95.64	even	6		9025.2.a.br.1.5		6
95.68	odd	12		475.2.j.d.49.3		24
95.69	odd	6		9025.2.a.by.1.2		6
95.87	odd	12		475.2.j.d.49.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.5	✓	12	1.1	even	1	trivial
475.2.e.f.201.5	yes	12	19.11	even	3	inner
475.2.e.h.26.2	yes	12	5.4	even	2
475.2.e.h.201.2	yes	12	95.49	even	6
475.2.j.d.49.3		24	95.68	odd	12
475.2.j.d.49.10		24	95.87	odd	12
475.2.j.d.349.3		24	5.2	odd	4
475.2.j.d.349.10		24	5.3	odd	4
9025.2.a.br.1.5		6	95.64	even	6
9025.2.a.bs.1.5		6	19.12	odd	6
9025.2.a.by.1.2		6	95.69	odd	6
9025.2.a.bz.1.2		6	19.7	even	3

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.740597 + 1.28275i) q^{2} +(-1.42837 - 2.47401i) q^{3} +(-0.0969683 + 0.167954i) q^{4} +(2.11569 - 3.66449i) q^{6} +3.78541 q^{7} +2.67513 q^{8} +(-2.58048 + 4.46952i) q^{9} -5.59460 q^{11} +0.554026 q^{12} +(2.45326 - 4.24917i) q^{13} +(2.80346 + 4.85574i) q^{14} +(2.17513 + 3.76744i) q^{16} +(-0.875095 - 1.51571i) q^{17} -7.64438 q^{18} +(0.636061 - 4.31224i) q^{19} +(-5.40696 - 9.36514i) q^{21} +(-4.14335 - 7.17648i) q^{22} +(0.290768 - 0.503625i) q^{23} +(-3.82107 - 6.61830i) q^{24} +7.26750 q^{26} +6.17328 q^{27} +(-0.367065 + 0.635775i) q^{28} +(-0.832153 + 1.44133i) q^{29} +7.01680 q^{31} +(-0.546661 + 0.946844i) q^{32} +(7.99116 + 13.8411i) q^{33} +(1.29619 - 2.24506i) q^{34} +(-0.500449 - 0.866803i) q^{36} -2.36322 q^{37} +(6.00260 - 2.37773i) q^{38} -14.0166 q^{39} +(-0.417676 - 0.723435i) q^{41} +(8.00877 - 13.8716i) q^{42} +(-0.535664 - 0.927797i) q^{43} +(0.542499 - 0.939635i) q^{44} +0.861369 q^{46} +(1.93378 - 3.34941i) q^{47} +(6.21378 - 10.7626i) q^{48} +7.32934 q^{49} +(-2.49992 + 4.32999i) q^{51} +(0.475776 + 0.824069i) q^{52} +(-3.39842 + 5.88624i) q^{53} +(4.57192 + 7.91879i) q^{54} +10.1265 q^{56} +(-11.5771 + 4.58585i) q^{57} -2.46516 q^{58} +(0.204282 + 0.353827i) q^{59} +(-6.98016 + 12.0900i) q^{61} +(5.19662 + 9.00081i) q^{62} +(-9.76817 + 16.9190i) q^{63} +7.08110 q^{64} +(-11.8365 + 20.5013i) q^{66} +(0.390703 - 0.676717i) q^{67} +0.339426 q^{68} -1.66130 q^{69} +(-3.18919 - 5.52384i) q^{71} +(-6.90312 + 11.9565i) q^{72} +(1.44458 + 2.50208i) q^{73} +(-1.75019 - 3.03142i) q^{74} +(0.662580 + 0.524980i) q^{76} -21.1779 q^{77} +(-10.3807 - 17.9799i) q^{78} +(6.25135 + 10.8276i) q^{79} +(-1.07630 - 1.86420i) q^{81} +(0.618659 - 1.07155i) q^{82} +10.3903 q^{83} +2.09722 q^{84} +(0.793422 - 1.37425i) q^{86} +4.75449 q^{87} -14.9663 q^{88} +(-8.92106 + 15.4517i) q^{89} +(9.28659 - 16.0848i) q^{91} +(0.0563906 + 0.0976714i) q^{92} +(-10.0226 - 17.3596i) q^{93} +5.72861 q^{94} +3.12333 q^{96} +(5.49995 + 9.52619i) q^{97} +(5.42809 + 9.40172i) q^{98} +(14.4367 - 25.0052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

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