LMFDB - Embedded newform 475.2.e.h.26.2

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			26.2
Root			$-0.928369 + 1.60798i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.h.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.740597 - 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	$-0.991225\pi$
$2$	−0.740597	−	1.28275i	−0.523681	−	0.907043i	0.475939	−	0.879478i	$-0.342108\pi$
$3$	1.42837	+	2.47401i	0.824669	+	1.42837i	0.902172	+	0.431377i	$0.141972\pi$
$3$	1.42837	+	2.47401i	0.824669	+	1.42837i	−0.0775023	+	0.996992i	$0.524695\pi$
$4$	−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	$-0.753744\pi$
$7$	−3.78541			−1.43075			−0.715375	+	0.698740i	$0.753744\pi$
$8$	−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	$0.404866\pi$
$13$	−2.45326	+	4.24917i	−0.680411	+	1.17851i	−0.974855	+	0.222838i	$0.928468\pi$
$14$	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	0.952416	−	0.304802i	$-0.0985902\pi$
$17$	0.875095	+	1.51571i	0.212242	+	0.367614i	−0.740174	+	0.672415i	$0.765257\pi$
$18$	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	−0.894747	−	0.446574i	$-0.852644\pi$
$23$	−0.290768	+	0.503625i	−0.0606294	+	0.105013i	0.834118	+	0.551587i	$0.185977\pi$
$24$	−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	$-0.437771\pi$
$37$	2.36322			0.388510			0.194255	+	0.980951i	$0.437771\pi$
$38$	−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	0.903975	−	0.427585i	$-0.140636\pi$
$43$	0.535664	+	0.927797i	0.0816880	+	0.141488i	−0.822287	+	0.569073i	$0.807302\pi$
$44$	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	−0.971895	−	0.235416i	$-0.924355\pi$
$47$	−1.93378	+	3.34941i	−0.282071	+	0.488561i	0.689824	+	0.723977i	$0.257688\pi$
$48$	−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	−0.532472	−	0.846448i	$-0.678737\pi$
$53$	3.39842	−	5.88624i	0.466809	−	0.808537i	0.999281	+	0.0379106i	$0.0120702\pi$
$54$	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	−0.888904	−	0.458093i	$-0.848533\pi$
$67$	−0.390703	+	0.676717i	−0.0477319	+	0.0826742i	0.841172	+	0.540767i	$0.181866\pi$
$68$	−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	0.769020	−	0.639225i	$-0.220745\pi$
$73$	−1.44458	−	2.50208i	−0.169075	−	0.292846i	−0.938095	+	0.346378i	$0.887411\pi$
$74$	−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	$-0.693150\pi$
$83$	−10.3903			−1.14048			−0.570240	+	0.821478i	$0.693150\pi$
$84$	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	$-0.978069\pi$
$97$	−5.49995	−	9.52619i	−0.558435	−	0.967238i	0.439192	−	0.898393i	$-0.355265\pi$
$98$	−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	$-0.624845\pi$
$103$	−7.75851			−0.764469			−0.382235	+	0.924065i	$0.624845\pi$
$104$	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	$-0.709459\pi$
$107$	−12.6521			−1.22313			−0.611564	+	0.791195i	$0.709459\pi$
$108$	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	$-0.701086\pi$
$113$	−12.5551			−1.18108			−0.590541	+	0.807007i	$0.701086\pi$
$114$	−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	−0.626287	−	0.779592i	$-0.715426\pi$
$127$	4.07957	−	7.06602i	0.362003	−	0.627007i	0.988290	+	0.152585i	$0.0487597\pi$
$128$	−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	−0.830496	−	0.557024i	$-0.811943\pi$
$137$	0.785955	−	1.36131i	0.0671487	−	0.116305i	0.897645	+	0.440719i	$0.145276\pi$
$138$	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	$0.182228\pi$
$157$	11.1445	+	19.3028i	0.889425	+	1.54053i	0.0488688	+	0.998805i	$0.484438\pi$
$158$	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	$-0.299639\pi$
$163$	15.0321			1.17741			0.588703	+	0.808350i	$0.299639\pi$
$164$	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	−0.618398	−	0.785865i	$-0.712218\pi$
$167$	4.79928	−	8.31260i	0.371380	−	0.643249i	0.989778	+	0.142616i	$0.0455515\pi$
$168$	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	0.647878	−	0.761744i	$-0.275657\pi$
$173$	−4.41611	−	7.64894i	−0.335751	−	0.581538i	−0.983629	+	0.180207i	$0.942323\pi$
$174$	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	$0.0550981\pi$
$193$	8.91459	+	15.4405i	0.641686	+	1.11143i	−0.343370	+	0.939200i	$0.611569\pi$
$194$	−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	$-0.293041\pi$
$197$	16.9925			1.21066			0.605332	+	0.795973i	$0.293041\pi$
$198$	−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	0.966607	−	0.256263i	$-0.0824915\pi$
$223$	3.90313	+	6.76042i	0.261373	+	0.452711i	−0.705234	+	0.708974i	$0.749158\pi$
$224$	−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	$-0.688900\pi$
$227$	−16.8511			−1.11845			−0.559223	+	0.829017i	$0.688900\pi$
$228$	−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	$0.108152\pi$
$233$	11.6014	+	20.0943i	0.760035	+	1.31642i	−0.182797	+	0.983151i	$0.558515\pi$
$234$	−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	−0.855021	−	0.518594i	$-0.826456\pi$
$257$	0.346352	−	0.599899i	0.0216048	−	0.0374207i	0.876626	+	0.481173i	$0.159789\pi$
$258$	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	0.987705	−	0.156328i	$-0.0499658\pi$
$263$	5.81338	+	10.0691i	0.358468	+	0.620885i	−0.629237	+	0.777214i	$0.716632\pi$
$264$	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	$-0.310648\pi$
$277$	18.6537			1.12079			0.560397	+	0.828224i	$0.310648\pi$
$278$	−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	$-0.904719\pi$
$283$	−12.3334	−	21.3620i	−0.733143	−	1.26984i	0.222390	−	0.974958i	$-0.428614\pi$
$284$	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	$-0.599993\pi$
$293$	−10.5784			−0.617994			−0.308997	+	0.951063i	$0.599993\pi$
$294$	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	0.622966	−	0.782249i	$-0.285928\pi$
$307$	−6.41222	−	11.1063i	−0.365965	−	0.633870i	−0.988931	+	0.148379i	$0.952594\pi$
$308$	−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	−0.823028	−	0.568001i	$-0.807717\pi$
$313$	1.42224	−	2.46339i	0.0803896	−	0.139239i	0.903417	+	0.428762i	$0.141050\pi$
$314$	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	−0.793120	−	0.609066i	$-0.791545\pi$
$317$	2.33072	−	4.03693i	0.130907	−	0.226737i	0.924026	+	0.382329i	$0.124878\pi$
$318$	−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	0.989366	−	0.145449i	$-0.0464626\pi$
$337$	6.76881	+	11.7239i	0.368721	+	0.638643i	−0.620645	+	0.784092i	$0.713129\pi$
$338$	−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	$-0.965981\pi$
$347$	−10.9817	−	19.0208i	−0.589527	−	1.02109i	0.404768	−	0.914420i	$-0.367352\pi$
$348$	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	$-0.505752\pi$
$353$	−0.679013			−0.0361402			−0.0180701	+	0.999837i	$0.505752\pi$
$354$	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	−0.977128	−	0.212650i	$-0.931790\pi$
$367$	−5.83153	+	10.1005i	−0.304404	+	0.527243i	0.672725	+	0.739893i	$0.265124\pi$
$368$	−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	$-0.610062\pi$
$373$	−13.0913			−0.677843			−0.338921	+	0.940815i	$0.610062\pi$
$374$	−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	$0.0607537\pi$
$383$	12.8227	+	22.2096i	0.655211	+	1.13486i	−0.326630	+	0.945152i	$0.605913\pi$
$384$	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	0.605601	−	0.795768i	$-0.292933\pi$
$397$	−7.69806	−	13.3334i	−0.386355	−	0.669186i	−0.991956	+	0.126582i	$0.959599\pi$
$398$	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	−0.988146	−	0.153520i	$-0.950939\pi$
$433$	−7.51443	+	13.0154i	−0.361120	+	0.625479i	0.627025	+	0.778999i	$0.284272\pi$
$434$	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	−0.667154	−	0.744920i	$-0.732488\pi$
$443$	6.55722	−	11.3574i	0.311543	−	0.539608i	0.978697	+	0.205312i	$0.0658209\pi$
$444$	−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	$-0.332891\pi$
$457$	21.4290			1.00240			0.501202	+	0.865330i	$0.332891\pi$
$458$	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	$-0.509246\pi$
$463$	−1.24981			−0.0580838			−0.0290419	+	0.999578i	$0.509246\pi$
$464$	−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	$-0.241703\pi$
$467$	31.3476			1.45059			0.725296	+	0.688437i	$0.241703\pi$
$468$	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	$-0.626242\pi$
$487$	−17.0491			−0.772569			−0.386285	+	0.922380i	$0.626242\pi$
$488$	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	$0.348679\pi$
$503$	−12.1368	+	21.0215i	−0.541153	+	0.937304i	−0.998838	+	0.0481900i	$0.984655\pi$
$504$	−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	−0.962095	−	0.272714i	$-0.912079\pi$
$523$	−5.59998	+	9.69944i	−0.244870	+	0.424127i	0.717225	+	0.696842i	$0.245412\pi$
$524$	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	−0.709056	−	0.705152i	$-0.750879\pi$
$547$	5.99088	−	10.3765i	0.256151	−	0.443667i	0.965208	+	0.261485i	$0.0842121\pi$
$548$	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	$0.428135\pi$
$557$	−17.2786	+	29.9275i	−0.732119	+	1.26807i	−0.955976	+	0.293446i	$0.905198\pi$
$558$	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	$-0.675680\pi$
$563$	−24.8817			−1.04864			−0.524318	+	0.851522i	$0.675680\pi$
$564$	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	$-0.651049\pi$
$577$	−21.9514			−0.913847			−0.456923	+	0.889506i	$0.651049\pi$
$578$	−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	$0.154977\pi$
$587$	20.5232	+	35.5472i	0.847084	+	1.46719i	−0.0367158	+	0.999326i	$0.511690\pi$
$588$	−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	−0.748820	−	0.662774i	$-0.769379\pi$
$593$	4.85982	−	8.41745i	0.199569	−	0.345663i	0.948389	+	0.317110i	$0.102713\pi$
$594$	−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	$-0.209139\pi$
$607$	39.0162			1.58362			0.791810	+	0.610767i	$0.209139\pi$
$608$	−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	0.811419	−	0.584465i	$-0.198696\pi$
$613$	−2.48708	−	4.30775i	−0.100452	−	0.173988i	−0.911871	+	0.410477i	$0.865362\pi$
$614$	−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	$-0.549652\pi$
$617$	19.3210	−	33.4649i	0.777834	−	1.34725i	0.933188	−	0.359389i	$-0.117015\pi$
$618$	−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	0.999762	−	0.0218020i	$-0.00694033\pi$
$643$	12.1969	+	21.1257i	0.481000	+	0.833117i	−0.518762	+	0.854919i	$0.673607\pi$
$644$	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	$-0.449401\pi$
$647$	8.05266			0.316583			0.158291	+	0.987392i	$0.449401\pi$
$648$	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	$-0.627910\pi$
$653$	−19.9890			−0.782228			−0.391114	+	0.920342i	$0.627910\pi$
$654$	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	$-0.321486\pi$
$673$	27.5963			1.06376			0.531880	+	0.846820i	$0.321486\pi$
$674$	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	$-0.366362\pi$
$677$	21.2114			0.815221			0.407610	+	0.913156i	$0.366362\pi$
$678$	−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	$-0.379205\pi$
$683$	19.3626			0.740891			0.370446	+	0.928854i	$0.379205\pi$
$684$	−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	0.770771	−	0.637112i	$-0.219871\pi$
$727$	−4.48581	−	7.76966i	−0.166370	−	0.288161i	−0.937141	+	0.348951i	$0.886538\pi$
$728$	−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	$-0.349010\pi$
$733$	24.7325			0.913516			0.456758	+	0.889591i	$0.349010\pi$
$734$	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	0.998094	−	0.0617109i	$-0.0196557\pi$
$743$	12.1463	+	21.0380i	0.445604	+	0.771808i	−0.552490	+	0.833519i	$0.686322\pi$
$744$	−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	0.893807	−	0.448452i	$-0.148025\pi$
$757$	1.61043	+	2.78935i	0.0585321	+	0.101381i	−0.835275	+	0.549833i	$0.814691\pi$
$758$	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	−0.989867	−	0.141994i	$-0.954649\pi$
$773$	−10.3416	+	17.9122i	−0.371963	+	0.644259i	0.617904	+	0.786253i	$0.287982\pi$
$774$	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	$-0.806175\pi$
$787$	−46.0227			−1.64053			−0.820266	+	0.571982i	$0.806175\pi$
$788$	−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	$-0.646538\pi$
$797$	−25.0847			−0.888546			−0.444273	+	0.895891i	$0.646538\pi$
$798$	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	−0.822436	−	0.568857i	$-0.807386\pi$
$823$	2.33597	−	4.04602i	0.0814269	−	0.141035i	0.903863	+	0.427822i	$0.140719\pi$
$824$	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	−0.522821	−	0.852443i	$-0.675120\pi$
$827$	13.7124	−	23.7506i	0.476827	−	0.825888i	0.999647	+	0.0265546i	$0.00845358\pi$
$828$	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	$-0.880097\pi$
$853$	−22.8832	−	39.6348i	−0.783505	−	1.35707i	0.146384	−	0.989228i	$-0.453237\pi$
$854$	−78.2745			−2.67850
$855$		0			0
$856$	33.8461			1.15684
$857$	7.45807	+	12.9177i	0.254763	+	0.441262i	0.964831	−	0.262871i	$-0.0846693\pi$
$857$	7.45807	+	12.9177i	0.254763	+	0.441262i	−0.710068	+	0.704133i	$0.751336\pi$
$858$	−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	$-0.616099\pi$
$863$	−20.9577			−0.713407			−0.356704	+	0.934218i	$0.616099\pi$
$864$	−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	0.555481	−	0.831529i	$-0.312534\pi$
$877$	−13.1009	−	22.6914i	−0.442385	−	0.766233i	−0.997866	+	0.0652963i	$0.979201\pi$
$878$	−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	$0.426619\pi$
$883$	−21.6585	+	37.5136i	−0.728867	+	1.26243i	−0.957362	+	0.288890i	$0.906714\pi$
$884$	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	$-0.606005\pi$
$887$	19.5073	−	33.7877i	0.654992	−	1.13448i	0.981896	−	0.189422i	$-0.0606614\pi$
$888$	−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	$-0.853414\pi$
$907$	−25.0804	−	43.4405i	−0.832780	−	1.44242i	0.0630443	−	0.998011i	$-0.479919\pi$
$908$	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	−0.995659	−	0.0930789i	$-0.970329\pi$
$937$	−12.7713	+	22.1206i	−0.417221	+	0.722647i	0.578438	+	0.815726i	$0.303662\pi$
$938$	−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	$0.0479753\pi$
$947$	19.2138	+	33.2793i	0.624364	+	1.08143i	−0.364299	+	0.931282i	$0.618691\pi$
$948$	−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	0.785003	−	0.619492i	$-0.212661\pi$
$953$	−4.44520	−	7.69932i	−0.143994	−	0.249405i	−0.928997	+	0.370087i	$0.879328\pi$
$954$	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	$0.290450\pi$
$967$	30.8149	+	53.3729i	0.990939	+	1.71636i	0.379150	+	0.925335i	$0.376216\pi$
$968$	−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	$-0.487772\pi$
$977$	2.40082			0.0768089			0.0384044	+	0.999262i	$0.487772\pi$
$978$	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	0.974502	−	0.224380i	$-0.0720357\pi$
$983$	9.18425	+	15.9076i	0.292932	+	0.507373i	−0.681570	+	0.731753i	$0.738702\pi$
$984$	−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	−0.847221	−	0.531241i	$-0.821726\pi$
$997$	1.15115	−	1.99385i	0.0364573	−	0.0631459i	0.883678	+	0.468095i	$0.155059\pi$
$998$	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.h.26.2	yes	12
5.2	odd	4		475.2.j.d.349.10		24
5.3	odd	4		475.2.j.d.349.3		24
5.4	even	2		475.2.e.f.26.5	✓	12
19.7	even	3		9025.2.a.br.1.5		6
19.11	even	3	inner	475.2.e.h.201.2	yes	12
19.12	odd	6		9025.2.a.by.1.2		6
95.49	even	6		475.2.e.f.201.5	yes	12
95.64	even	6		9025.2.a.bz.1.2		6
95.68	odd	12		475.2.j.d.49.10		24
95.69	odd	6		9025.2.a.bs.1.5		6
95.87	odd	12		475.2.j.d.49.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.5	✓	12	5.4	even	2
475.2.e.f.201.5	yes	12	95.49	even	6
475.2.e.h.26.2	yes	12	1.1	even	1	trivial
475.2.e.h.201.2	yes	12	19.11	even	3	inner
475.2.j.d.49.3		24	95.87	odd	12
475.2.j.d.49.10		24	95.68	odd	12
475.2.j.d.349.3		24	5.3	odd	4
475.2.j.d.349.10		24	5.2	odd	4
9025.2.a.br.1.5		6	19.7	even	3
9025.2.a.bs.1.5		6	95.69	odd	6
9025.2.a.by.1.2		6	19.12	odd	6
9025.2.a.bz.1.2		6	95.64	even	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
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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