LMFDB - Embedded newform 105.2.b.c.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(41,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("105.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.b (of order $2$, degree $1$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.2.b.c.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52434i q^{2} +(-1.68614 + 0.396143i) q^{3} -4.37228 q^{4} -1.00000 q^{5} +(1.00000 + 4.25639i) q^{6} +(-2.00000 - 1.73205i) q^{7} +5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q-2.52434i q^{2} +(-1.68614 + 0.396143i) q^{3} -4.37228 q^{4} -1.00000 q^{5} +(1.00000 + 4.25639i) q^{6} +(-2.00000 - 1.73205i) q^{7} +5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} +2.52434i q^{10} -0.792287i q^{11} +(7.37228 - 1.73205i) q^{12} -5.84096i q^{13} +(-4.37228 + 5.04868i) q^{14} +(1.68614 - 0.396143i) q^{15} +6.37228 q^{16} +1.37228 q^{17} +(-3.37228 - 6.78073i) q^{18} +3.46410i q^{19} +4.37228 q^{20} +(4.05842 + 2.12819i) q^{21} -2.00000 q^{22} -1.87953i q^{23} +(-2.37228 - 10.0974i) q^{24} +1.00000 q^{25} -14.7446 q^{26} +(-4.00000 + 3.31662i) q^{27} +(8.74456 + 7.57301i) q^{28} -4.25639i q^{29} +(-1.00000 - 4.25639i) q^{30} -3.46410i q^{31} -4.10891i q^{32} +(0.313859 + 1.33591i) q^{33} -3.46410i q^{34} +(2.00000 + 1.73205i) q^{35} +(-11.7446 + 5.84096i) q^{36} +4.74456 q^{37} +8.74456 q^{38} +(2.31386 + 9.84868i) q^{39} -5.98844i q^{40} +6.00000 q^{41} +(5.37228 - 10.2448i) q^{42} -6.74456 q^{43} +3.46410i q^{44} +(-2.68614 + 1.33591i) q^{45} -4.74456 q^{46} +7.37228 q^{47} +(-10.7446 + 2.52434i) q^{48} +(1.00000 + 6.92820i) q^{49} -2.52434i q^{50} +(-2.31386 + 0.543620i) q^{51} +25.5383i q^{52} +8.51278i q^{53} +(8.37228 + 10.0974i) q^{54} +0.792287i q^{55} +(10.3723 - 11.9769i) q^{56} +(-1.37228 - 5.84096i) q^{57} -10.7446 q^{58} -2.74456 q^{59} +(-7.37228 + 1.73205i) q^{60} -6.92820i q^{61} -8.74456 q^{62} +(-7.68614 - 1.98072i) q^{63} +2.37228 q^{64} +5.84096i q^{65} +(3.37228 - 0.792287i) q^{66} -6.74456 q^{67} -6.00000 q^{68} +(0.744563 + 3.16915i) q^{69} +(4.37228 - 5.04868i) q^{70} -13.5615i q^{71} +(8.00000 + 16.0858i) q^{72} -6.92820i q^{73} -11.9769i q^{74} +(-1.68614 + 0.396143i) q^{75} -15.1460i q^{76} +(-1.37228 + 1.58457i) q^{77} +(24.8614 - 5.84096i) q^{78} +3.37228 q^{79} -6.37228 q^{80} +(5.43070 - 7.17687i) q^{81} -15.1460i q^{82} -5.48913 q^{83} +(-17.7446 - 9.30506i) q^{84} -1.37228 q^{85} +17.0256i q^{86} +(1.68614 + 7.17687i) q^{87} +4.74456 q^{88} -3.25544 q^{89} +(3.37228 + 6.78073i) q^{90} +(-10.1168 + 11.6819i) q^{91} +8.21782i q^{92} +(1.37228 + 5.84096i) q^{93} -18.6101i q^{94} -3.46410i q^{95} +(1.62772 + 6.92820i) q^{96} +1.08724i q^{97} +(17.4891 - 2.52434i) q^{98} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 6 q^{4} - 4 q^{5} + 4 q^{6} - 8 q^{7} + 5 q^{9}+O(q^{10}) $ 4 * q - q^3 - 6 * q^4 - 4 * q^5 + 4 * q^6 - 8 * q^7 + 5 * q^9	$ 4 q - q^{3} - 6 q^{4} - 4 q^{5} + 4 q^{6} - 8 q^{7} + 5 q^{9} + 18 q^{12} - 6 q^{14} + q^{15} + 14 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{20} - q^{21} - 8 q^{22} + 2 q^{24} + 4 q^{25} - 36 q^{26} - 16 q^{27} + 12 q^{28} - 4 q^{30} + 7 q^{33} + 8 q^{35} - 24 q^{36} - 4 q^{37} + 12 q^{38} + 15 q^{39} + 24 q^{41} + 10 q^{42} - 4 q^{43} - 5 q^{45} + 4 q^{46} + 18 q^{47} - 20 q^{48} + 4 q^{49} - 15 q^{51} + 22 q^{54} + 30 q^{56} + 6 q^{57} - 20 q^{58} + 12 q^{59} - 18 q^{60} - 12 q^{62} - 25 q^{63} - 2 q^{64} + 2 q^{66} - 4 q^{67} - 24 q^{68} - 20 q^{69} + 6 q^{70} + 32 q^{72} - q^{75} + 6 q^{77} + 42 q^{78} + 2 q^{79} - 14 q^{80} - 7 q^{81} + 24 q^{83} - 48 q^{84} + 6 q^{85} + q^{87} - 4 q^{88} - 36 q^{89} + 2 q^{90} - 6 q^{91} - 6 q^{93} + 18 q^{96} + 24 q^{98} + 13 q^{99}+O(q^{100}) $ 4 * q - q^3 - 6 * q^4 - 4 * q^5 + 4 * q^6 - 8 * q^7 + 5 * q^9 + 18 * q^12 - 6 * q^14 + q^15 + 14 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^20 - q^21 - 8 * q^22 + 2 * q^24 + 4 * q^25 - 36 * q^26 - 16 * q^27 + 12 * q^28 - 4 * q^30 + 7 * q^33 + 8 * q^35 - 24 * q^36 - 4 * q^37 + 12 * q^38 + 15 * q^39 + 24 * q^41 + 10 * q^42 - 4 * q^43 - 5 * q^45 + 4 * q^46 + 18 * q^47 - 20 * q^48 + 4 * q^49 - 15 * q^51 + 22 * q^54 + 30 * q^56 + 6 * q^57 - 20 * q^58 + 12 * q^59 - 18 * q^60 - 12 * q^62 - 25 * q^63 - 2 * q^64 + 2 * q^66 - 4 * q^67 - 24 * q^68 - 20 * q^69 + 6 * q^70 + 32 * q^72 - q^75 + 6 * q^77 + 42 * q^78 + 2 * q^79 - 14 * q^80 - 7 * q^81 + 24 * q^83 - 48 * q^84 + 6 * q^85 + q^87 - 4 * q^88 - 36 * q^89 + 2 * q^90 - 6 * q^91 - 6 * q^93 + 18 * q^96 + 24 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	2.52434i		−	1.78498i	−0.451071	−	0.892488i	$-0.648958\pi$
$2$		−	2.52434i		−	1.78498i	0.451071	−	0.892488i	$-0.351042\pi$
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$4$	−4.37228			−2.18614
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.00000	+	4.25639i	0.408248	+	1.73766i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$			5.98844i			2.11723i
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$			2.52434i			0.798266i
$11$		−	0.792287i		−	0.238884i	−0.992841	−	0.119442i	$-0.961890\pi$
$11$		−	0.792287i		−	0.238884i	0.992841	−	0.119442i	$-0.0381105\pi$
$12$	7.37228	−	1.73205i	2.12819	−	0.500000i
$13$		−	5.84096i		−	1.61999i	−0.586436	−	0.809996i	$-0.699469\pi$
$13$		−	5.84096i		−	1.61999i	0.586436	−	0.809996i	$-0.300531\pi$
$14$	−4.37228	+	5.04868i	−1.16854	+	1.34932i
$15$	1.68614	−	0.396143i	0.435360	−	0.102284i
$16$	6.37228			1.59307
$17$	1.37228			0.332827			0.166414	−	0.986056i	$-0.446781\pi$
$17$	1.37228			0.332827			0.166414	+	0.986056i	$0.446781\pi$
$18$	−3.37228	−	6.78073i	−0.794854	−	1.59823i
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	4.37228			0.977672
$21$	4.05842	+	2.12819i	0.885620	+	0.464410i
$22$	−2.00000			−0.426401
$23$		−	1.87953i		−	0.391909i	−0.980613	−	0.195954i	$-0.937220\pi$
$23$		−	1.87953i		−	0.391909i	0.980613	−	0.195954i	$-0.0627804\pi$
$24$	−2.37228	−	10.0974i	−0.484240	−	2.06111i
$25$	1.00000			0.200000
$26$	−14.7446			−2.89165
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$	8.74456	+	7.57301i	1.65257	+	1.43117i
$29$		−	4.25639i		−	0.790392i	−0.918597	−	0.395196i	$-0.870677\pi$
$29$		−	4.25639i		−	0.790392i	0.918597	−	0.395196i	$-0.129323\pi$
$30$	−1.00000	−	4.25639i	−0.182574	−	0.777107i
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$		−	4.10891i		−	0.726360i
$33$	0.313859	+	1.33591i	0.0546359	+	0.232552i
$34$		−	3.46410i		−	0.594089i
$35$	2.00000	+	1.73205i	0.338062	+	0.292770i
$36$	−11.7446	+	5.84096i	−1.95743	+	0.973494i
$37$	4.74456			0.780001			0.390001	−	0.920815i	$-0.372475\pi$
$37$	4.74456			0.780001			0.390001	+	0.920815i	$0.372475\pi$
$38$	8.74456			1.41856
$39$	2.31386	+	9.84868i	0.370514	+	1.57705i
$40$		−	5.98844i		−	0.946855i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	5.37228	−	10.2448i	0.828961	−	1.58081i
$43$	−6.74456			−1.02854			−0.514268	−	0.857629i	$-0.671936\pi$
$43$	−6.74456			−1.02854			−0.514268	+	0.857629i	$0.671936\pi$
$44$			3.46410i			0.522233i
$45$	−2.68614	+	1.33591i	−0.400426	+	0.199145i
$46$	−4.74456			−0.699548
$47$	7.37228			1.07536			0.537679	−	0.843150i	$-0.319301\pi$
$47$	7.37228			1.07536			0.537679	+	0.843150i	$0.319301\pi$
$48$	−10.7446	+	2.52434i	−1.55084	+	0.364357i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		−	2.52434i		−	0.356995i
$51$	−2.31386	+	0.543620i	−0.324005	+	0.0761221i
$52$			25.5383i			3.54153i
$53$			8.51278i			1.16932i	0.811278	+	0.584660i	$0.198772\pi$
$53$			8.51278i			1.16932i	−0.811278	+	0.584660i	$0.801228\pi$
$54$	8.37228	+	10.0974i	1.13932	+	1.37408i
$55$			0.792287i			0.106832i
$56$	10.3723	−	11.9769i	1.38605	−	1.60048i
$57$	−1.37228	−	5.84096i	−0.181763	−	0.773654i
$58$	−10.7446			−1.41083
$59$	−2.74456			−0.357312			−0.178656	−	0.983912i	$-0.557175\pi$
$59$	−2.74456			−0.357312			−0.178656	+	0.983912i	$0.557175\pi$
$60$	−7.37228	+	1.73205i	−0.951757	+	0.223607i
$61$		−	6.92820i		−	0.887066i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$		−	6.92820i		−	0.887066i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	−8.74456			−1.11056
$63$	−7.68614	−	1.98072i	−0.968363	−	0.249547i
$64$	2.37228			0.296535
$65$			5.84096i			0.724482i
$66$	3.37228	−	0.792287i	0.415099	−	0.0975238i
$67$	−6.74456			−0.823979			−0.411990	−	0.911188i	$-0.635166\pi$
$67$	−6.74456			−0.823979			−0.411990	+	0.911188i	$0.635166\pi$
$68$	−6.00000			−0.727607
$69$	0.744563	+	3.16915i	0.0896348	+	0.381521i
$70$	4.37228	−	5.04868i	0.522588	−	0.603432i
$71$		−	13.5615i		−	1.60945i	−0.593649	−	0.804724i	$-0.702313\pi$
$71$		−	13.5615i		−	1.60945i	0.593649	−	0.804724i	$-0.297687\pi$
$72$	8.00000	+	16.0858i	0.942809	+	1.89573i
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$		−	11.9769i		−	1.39228i
$75$	−1.68614	+	0.396143i	−0.194699	+	0.0457427i
$76$		−	15.1460i		−	1.73737i
$77$	−1.37228	+	1.58457i	−0.156386	+	0.180579i
$78$	24.8614	−	5.84096i	2.81500	−	0.661359i
$79$	3.37228			0.379411			0.189706	−	0.981841i	$-0.439247\pi$
$79$	3.37228			0.379411			0.189706	+	0.981841i	$0.439247\pi$
$80$	−6.37228			−0.712443
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$		−	15.1460i		−	1.67260i
$83$	−5.48913			−0.602510			−0.301255	−	0.953544i	$-0.597406\pi$
$83$	−5.48913			−0.602510			−0.301255	+	0.953544i	$0.597406\pi$
$84$	−17.7446	−	9.30506i	−1.93609	−	1.01527i
$85$	−1.37228			−0.148845
$86$			17.0256i			1.83591i
$87$	1.68614	+	7.17687i	0.180773	+	0.769441i
$88$	4.74456			0.505772
$89$	−3.25544			−0.345076			−0.172538	−	0.985003i	$-0.555197\pi$
$89$	−3.25544			−0.345076			−0.172538	+	0.985003i	$0.555197\pi$
$90$	3.37228	+	6.78073i	0.355470	+	0.714751i
$91$	−10.1168	+	11.6819i	−1.06053	+	1.22460i
$92$			8.21782i			0.856767i
$93$	1.37228	+	5.84096i	0.142299	+	0.605680i
$94$		−	18.6101i		−	1.91949i
$95$		−	3.46410i		−	0.355409i
$96$	1.62772	+	6.92820i	0.166128	+	0.707107i
$97$			1.08724i			0.110393i	0.998476	+	0.0551963i	$0.0175785\pi$
$97$			1.08724i			0.110393i	−0.998476	+	0.0551963i	$0.982422\pi$
$98$	17.4891	−	2.52434i	1.76667	−	0.254997i
$99$	−1.05842	−	2.12819i	−0.106375	−	0.213892i
$100$	−4.37228			−0.437228
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	1.37228	+	5.84096i	0.135876	+	0.578341i
$103$			16.2333i			1.59951i	0.600326	+	0.799756i	$0.295038\pi$
$103$			16.2333i			1.59951i	−0.600326	+	0.799756i	$0.704962\pi$
$104$	34.9783			3.42990
$105$	−4.05842	−	2.12819i	−0.396061	−	0.207690i
$106$	21.4891			2.08721
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$	17.4891	−	14.5012i	1.68289	−	1.39538i
$109$	0.116844			0.0111916			0.00559581	−	0.999984i	$-0.498219\pi$
$109$	0.116844			0.0111916			0.00559581	+	0.999984i	$0.498219\pi$
$110$	2.00000			0.190693
$111$	−8.00000	+	1.87953i	−0.759326	+	0.178397i
$112$	−12.7446	−	11.0371i	−1.20425	−	1.04291i
$113$		−	10.0974i		−	0.949879i	−0.880018	−	0.474939i	$-0.842470\pi$
$113$		−	10.0974i		−	0.949879i	0.880018	−	0.474939i	$-0.157530\pi$
$114$	−14.7446	+	3.46410i	−1.38095	+	0.324443i
$115$			1.87953i			0.175267i
$116$			18.6101i			1.72791i
$117$	−7.80298	−	15.6896i	−0.721386	−	1.45051i
$118$			6.92820i			0.637793i
$119$	−2.74456	−	2.37686i	−0.251594	−	0.217886i
$120$	2.37228	+	10.0974i	0.216559	+	0.921758i
$121$	10.3723			0.942935
$122$	−17.4891			−1.58339
$123$	−10.1168	+	2.37686i	−0.912205	+	0.214314i
$124$			15.1460i			1.36015i
$125$	−1.00000			−0.0894427
$126$	−5.00000	+	19.4024i	−0.445435	+	1.72850i
$127$	10.7446			0.953426			0.476713	−	0.879059i	$-0.341828\pi$
$127$	10.7446			0.953426			0.476713	+	0.879059i	$0.341828\pi$
$128$		−	14.2063i		−	1.25567i
$129$	11.3723	−	2.67181i	1.00127	−	0.235240i
$130$	14.7446			1.29318
$131$	17.4891			1.52803			0.764016	−	0.645197i	$-0.223225\pi$
$131$	17.4891			1.52803			0.764016	+	0.645197i	$0.223225\pi$
$132$	−1.37228	−	5.84096i	−0.119442	−	0.508391i
$133$	6.00000	−	6.92820i	0.520266	−	0.600751i
$134$			17.0256i			1.47078i
$135$	4.00000	−	3.31662i	0.344265	−	0.285450i
$136$			8.21782i			0.704673i
$137$			13.2665i			1.13343i	0.823913	+	0.566717i	$0.191787\pi$
$137$			13.2665i			1.13343i	−0.823913	+	0.566717i	$0.808213\pi$
$138$	8.00000	−	1.87953i	0.681005	−	0.159996i
$139$			1.28962i			0.109384i	0.998503	+	0.0546921i	$0.0174177\pi$
$139$			1.28962i			0.109384i	−0.998503	+	0.0546921i	$0.982582\pi$
$140$	−8.74456	−	7.57301i	−0.739050	−	0.640036i
$141$	−12.4307	+	2.92048i	−1.04685	+	0.245949i
$142$	−34.2337			−2.87283
$143$	−4.62772			−0.386989
$144$	17.1168	−	8.51278i	1.42640	−	0.709398i
$145$			4.25639i			0.353474i
$146$	−17.4891			−1.44741
$147$	−4.43070	−	11.2858i	−0.365438	−	0.930836i
$148$	−20.7446			−1.70519
$149$		−	10.0974i		−	0.827207i	−0.910457	−	0.413604i	$-0.864270\pi$
$149$		−	10.0974i		−	0.827207i	0.910457	−	0.413604i	$-0.135730\pi$
$150$	1.00000	+	4.25639i	0.0816497	+	0.347533i
$151$	3.37228			0.274432			0.137216	−	0.990541i	$-0.456184\pi$
$151$	3.37228			0.274432			0.137216	+	0.990541i	$0.456184\pi$
$152$	−20.7446			−1.68261
$153$	3.68614	−	1.83324i	0.298007	−	0.148209i
$154$	4.00000	+	3.46410i	0.322329	+	0.279145i
$155$			3.46410i			0.278243i
$156$	−10.1168	−	43.0612i	−0.809996	−	3.44766i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		−	8.51278i		−	0.677240i
$159$	−3.37228	−	14.3537i	−0.267439	−	1.13833i
$160$			4.10891i			0.324838i
$161$	−3.25544	+	3.75906i	−0.256564	+	0.296255i
$162$	−18.1168	−	13.7089i	−1.42339	−	1.07708i
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−26.2337			−2.04851
$165$	−0.313859	−	1.33591i	−0.0244339	−	0.104000i
$166$			13.8564i			1.07547i
$167$	22.1168			1.71145			0.855726	−	0.517429i	$-0.173111\pi$
$167$	22.1168			1.71145			0.855726	+	0.517429i	$0.173111\pi$
$168$	−12.7446	+	24.3036i	−0.983264	+	1.87506i
$169$	−21.1168			−1.62437
$170$			3.46410i			0.265684i
$171$	4.62772	+	9.30506i	0.353890	+	0.711576i
$172$	29.4891			2.24852
$173$	−16.1168			−1.22534			−0.612670	−	0.790338i	$-0.709905\pi$
$173$	−16.1168			−1.22534			−0.612670	+	0.790338i	$0.709905\pi$
$174$	18.1168	−	4.25639i	1.37343	−	0.322676i
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$		−	5.04868i		−	0.380558i
$177$	4.62772	−	1.08724i	0.347841	−	0.0817220i
$178$			8.21782i			0.615952i
$179$		−	6.63325i		−	0.495792i	−0.968787	−	0.247896i	$-0.920261\pi$
$179$		−	6.63325i		−	0.495792i	0.968787	−	0.247896i	$-0.0797392\pi$
$180$	11.7446	−	5.84096i	0.875388	−	0.435360i
$181$			18.6101i			1.38328i	0.722242	+	0.691640i	$0.243111\pi$
$181$			18.6101i			1.38328i	−0.722242	+	0.691640i	$0.756889\pi$
$182$	29.4891	+	25.5383i	2.18588	+	1.89303i
$183$	2.74456	+	11.6819i	0.202884	+	0.863553i
$184$	11.2554			0.829762
$185$	−4.74456			−0.348827
$186$	14.7446	−	3.46410i	1.08112	−	0.254000i
$187$		−	1.08724i		−	0.0795069i
$188$	−32.2337			−2.35088
$189$	13.7446	+	0.294954i	0.999770	+	0.0214547i
$190$	−8.74456			−0.634397
$191$			15.6434i			1.13191i	0.824435	+	0.565957i	$0.191493\pi$
$191$			15.6434i			1.13191i	−0.824435	+	0.565957i	$0.808507\pi$
$192$	−4.00000	+	0.939764i	−0.288675	+	0.0678216i
$193$	22.2337			1.60042			0.800208	−	0.599723i	$-0.204722\pi$
$193$	22.2337			1.60042			0.800208	+	0.599723i	$0.204722\pi$
$194$	2.74456			0.197048
$195$	−2.31386	−	9.84868i	−0.165699	−	0.705279i
$196$	−4.37228	−	30.2921i	−0.312306	−	2.16372i
$197$			22.3692i			1.59374i	0.604152	+	0.796869i	$0.293512\pi$
$197$			22.3692i			1.59374i	−0.604152	+	0.796869i	$0.706488\pi$
$198$	−5.37228	+	2.67181i	−0.381791	+	0.189878i
$199$		−	12.9715i		−	0.919528i	−0.888041	−	0.459764i	$-0.847934\pi$
$199$		−	12.9715i		−	0.919528i	0.888041	−	0.459764i	$-0.152066\pi$
$200$			5.98844i			0.423447i
$201$	11.3723	−	2.67181i	0.802139	−	0.188455i
$202$			15.1460i			1.06567i
$203$	−7.37228	+	8.51278i	−0.517433	+	0.597480i
$204$	10.1168	−	2.37686i	0.708321	−	0.166414i
$205$	−6.00000			−0.419058
$206$	40.9783			2.85509
$207$	−2.51087	−	5.04868i	−0.174518	−	0.350907i
$208$		−	37.2203i		−	2.58076i
$209$	2.74456			0.189845
$210$	−5.37228	+	10.2448i	−0.370723	+	0.706960i
$211$	6.11684			0.421101			0.210550	−	0.977583i	$-0.432474\pi$
$211$	6.11684			0.421101			0.210550	+	0.977583i	$0.432474\pi$
$212$		−	37.2203i		−	2.55630i
$213$	5.37228	+	22.8665i	0.368103	+	1.56679i
$214$	−16.7446			−1.14463
$215$	6.74456			0.459975
$216$	−19.8614	−	23.9538i	−1.35140	−	1.62985i
$217$	−6.00000	+	6.92820i	−0.407307	+	0.470317i
$218$		−	0.294954i		−	0.0199768i
$219$	2.74456	+	11.6819i	0.185460	+	0.789391i
$220$		−	3.46410i		−	0.233550i
$221$		−	8.01544i		−	0.539177i
$222$	4.74456	+	20.1947i	0.318434	+	1.35538i
$223$		−	20.9870i		−	1.40539i	−0.711490	−	0.702696i	$-0.751979\pi$
$223$		−	20.9870i		−	1.40539i	0.711490	−	0.702696i	$-0.248021\pi$
$224$	−7.11684	+	8.21782i	−0.475514	+	0.549076i
$225$	2.68614	−	1.33591i	0.179076	−	0.0890605i
$226$	−25.4891			−1.69551
$227$	15.6060			1.03580			0.517902	−	0.855440i	$-0.326713\pi$
$227$	15.6060			1.03580			0.517902	+	0.855440i	$0.326713\pi$
$228$	6.00000	+	25.5383i	0.397360	+	1.69132i
$229$			4.75372i			0.314135i	0.987588	+	0.157067i	$0.0502040\pi$
$229$			4.75372i			0.314135i	−0.987588	+	0.157067i	$0.949796\pi$
$230$	4.74456			0.312847
$231$	1.68614	−	3.21543i	0.110940	−	0.211560i
$232$	25.4891			1.67344
$233$			3.75906i			0.246264i	0.992390	+	0.123132i	$0.0392938\pi$
$233$			3.75906i			0.246264i	−0.992390	+	0.123132i	$0.960706\pi$
$234$	−39.6060	+	19.6974i	−2.58912	+	1.28766i
$235$	−7.37228			−0.480915
$236$	12.0000			0.781133
$237$	−5.68614	+	1.33591i	−0.369355	+	0.0867765i
$238$	−6.00000	+	6.92820i	−0.388922	+	0.449089i
$239$			15.6434i			1.01188i	0.862567	+	0.505942i	$0.168855\pi$
$239$			15.6434i			1.01188i	−0.862567	+	0.505942i	$0.831145\pi$
$240$	10.7446	−	2.52434i	0.693559	−	0.162945i
$241$		−	23.3639i		−	1.50500i	−0.658593	−	0.752499i	$-0.728848\pi$
$241$		−	23.3639i		−	1.50500i	0.658593	−	0.752499i	$-0.271152\pi$
$242$		−	26.1831i		−	1.68312i
$243$	−6.31386	+	14.2525i	−0.405034	+	0.914302i
$244$			30.2921i			1.93925i
$245$	−1.00000	−	6.92820i	−0.0638877	−	0.442627i
$246$	6.00000	+	25.5383i	0.382546	+	1.62826i
$247$	20.2337			1.28744
$248$	20.7446			1.31728
$249$	9.25544	−	2.17448i	0.586540	−	0.137802i
$250$			2.52434i			0.159653i
$251$	−17.4891			−1.10390			−0.551952	−	0.833876i	$-0.686117\pi$
$251$	−17.4891			−1.10390			−0.551952	+	0.833876i	$0.686117\pi$
$252$	33.6060	+	8.66025i	2.11698	+	0.545545i
$253$	−1.48913			−0.0936205
$254$		−	27.1229i		−	1.70184i
$255$	2.31386	−	0.543620i	0.144899	−	0.0340428i
$256$	−31.1168			−1.94480
$257$	−23.4891			−1.46521			−0.732606	−	0.680653i	$-0.761696\pi$
$257$	−23.4891			−1.46521			−0.732606	+	0.680653i	$0.761696\pi$
$258$	−6.74456	−	28.7075i	−0.419898	−	1.78725i
$259$	−9.48913	−	8.21782i	−0.589626	−	0.510631i
$260$		−	25.5383i		−	1.58382i
$261$	−5.68614	−	11.4333i	−0.351963	−	0.707701i
$262$		−	44.1485i		−	2.72750i
$263$		−	13.5615i		−	0.836235i	−0.908393	−	0.418118i	$-0.862690\pi$
$263$		−	13.5615i		−	0.836235i	0.908393	−	0.418118i	$-0.137310\pi$
$264$	−8.00000	+	1.87953i	−0.492366	+	0.115677i
$265$		−	8.51278i		−	0.522936i
$266$	−17.4891	−	15.1460i	−1.07233	−	0.928662i
$267$	5.48913	−	1.28962i	0.335929	−	0.0789235i
$268$	29.4891			1.80134
$269$	8.74456			0.533165			0.266583	−	0.963812i	$-0.414105\pi$
$269$	8.74456			0.533165			0.266583	+	0.963812i	$0.414105\pi$
$270$	−8.37228	−	10.0974i	−0.509521	−	0.614505i
$271$		−	15.1460i		−	0.920056i	−0.887905	−	0.460028i	$-0.847839\pi$
$271$		−	15.1460i		−	0.920056i	0.887905	−	0.460028i	$-0.152161\pi$
$272$	8.74456			0.530217
$273$	12.4307	−	23.7051i	0.752340	−	1.43470i
$274$	33.4891			2.02315
$275$		−	0.792287i		−	0.0477767i
$276$	−3.25544	−	13.8564i	−0.195954	−	0.834058i
$277$	−6.23369			−0.374546			−0.187273	−	0.982308i	$-0.559965\pi$
$277$	−6.23369			−0.374546			−0.187273	+	0.982308i	$0.559965\pi$
$278$	3.25544			0.195248
$279$	−4.62772	−	9.30506i	−0.277054	−	0.557080i
$280$	−10.3723	+	11.9769i	−0.619862	+	0.715755i
$281$			4.84630i			0.289106i	0.989497	+	0.144553i	$0.0461744\pi$
$281$			4.84630i			0.289106i	−0.989497	+	0.144553i	$0.953826\pi$
$282$	7.37228	+	31.3793i	0.439013	+	1.86861i
$283$			9.30506i			0.553129i	0.960995	+	0.276564i	$0.0891959\pi$
$283$			9.30506i			0.553129i	−0.960995	+	0.276564i	$0.910804\pi$
$284$			59.2945i			3.51848i
$285$	1.37228	+	5.84096i	0.0812869	+	0.345989i
$286$			11.6819i			0.690767i
$287$	−12.0000	−	10.3923i	−0.708338	−	0.613438i
$288$	−5.48913	−	11.0371i	−0.323450	−	0.650368i
$289$	−15.1168			−0.889226
$290$	10.7446			0.630942
$291$	−0.430703	−	1.83324i	−0.0252483	−	0.107466i
$292$			30.2921i			1.77271i
$293$	28.1168			1.64260			0.821302	−	0.570494i	$-0.193248\pi$
$293$	28.1168			1.64260			0.821302	+	0.570494i	$0.193248\pi$
$294$	−28.4891	+	11.1846i	−1.66152	+	0.652299i
$295$	2.74456			0.159795
$296$			28.4125i			1.65144i
$297$	2.62772	+	3.16915i	0.152476	+	0.183893i
$298$	−25.4891			−1.47655
$299$	−10.9783			−0.634889
$300$	7.37228	−	1.73205i	0.425639	−	0.100000i
$301$	13.4891	+	11.6819i	0.777500	+	0.673335i
$302$		−	8.51278i		−	0.489855i
$303$	10.1168	−	2.37686i	0.581198	−	0.136547i
$304$			22.0742i			1.26604i
$305$			6.92820i			0.396708i
$306$	−4.62772	−	9.30506i	−0.264549	−	0.531935i
$307$			7.13058i			0.406964i	0.979079	+	0.203482i	$0.0652258\pi$
$307$			7.13058i			0.406964i	−0.979079	+	0.203482i	$0.934774\pi$
$308$	6.00000	−	6.92820i	0.341882	−	0.394771i
$309$	−6.43070	−	27.3716i	−0.365830	−	1.55711i
$310$	8.74456			0.496658
$311$	−20.2337			−1.14735			−0.573674	−	0.819084i	$-0.694482\pi$
$311$	−20.2337			−1.14735			−0.573674	+	0.819084i	$0.694482\pi$
$312$	−58.9783	+	13.8564i	−3.33899	+	0.784465i
$313$			24.4511i			1.38206i	0.722827	+	0.691029i	$0.242842\pi$
$313$			24.4511i			1.38206i	−0.722827	+	0.691029i	$0.757158\pi$
$314$		0			0
$315$	7.68614	+	1.98072i	0.433065	+	0.111601i
$316$	−14.7446			−0.829446
$317$			8.51278i			0.478125i	0.971004	+	0.239063i	$0.0768401\pi$
$317$			8.51278i			0.478125i	−0.971004	+	0.239063i	$0.923160\pi$
$318$	−36.2337	+	8.51278i	−2.03188	+	0.477373i
$319$	−3.37228			−0.188812
$320$	−2.37228			−0.132615
$321$	2.62772	+	11.1846i	0.146665	+	0.624263i
$322$	9.48913	+	8.21782i	0.528808	+	0.457961i
$323$			4.75372i			0.264504i
$324$	−23.7446	+	31.3793i	−1.31914	+	1.74329i
$325$		−	5.84096i		−	0.323998i
$326$		−	20.1947i		−	1.11848i
$327$	−0.197015	+	0.0462870i	−0.0108950	+	0.00255968i
$328$			35.9306i			1.98394i
$329$	−14.7446	−	12.7692i	−0.812894	−	0.703987i
$330$	−3.37228	+	0.792287i	−0.185638	+	0.0436140i
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	24.0000			1.31717
$333$	12.7446	−	6.33830i	0.698398	−	0.347336i
$334$		−	55.8304i		−	3.05490i
$335$	6.74456			0.368495
$336$	25.8614	+	13.5615i	1.41086	+	0.739838i
$337$	−18.2337			−0.993252			−0.496626	−	0.867965i	$-0.665428\pi$
$337$	−18.2337			−0.993252			−0.496626	+	0.867965i	$0.665428\pi$
$338$			53.3060i			2.89947i
$339$	4.00000	+	17.0256i	0.217250	+	0.924701i
$340$	6.00000			0.325396
$341$	−2.74456			−0.148626
$342$	23.4891	−	11.6819i	1.27015	−	0.631686i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		−	40.3894i		−	2.17765i
$345$	−0.744563	−	3.16915i	−0.0400859	−	0.170621i
$346$			40.6844i			2.18720i
$347$		−	18.3152i		−	0.983210i	−0.870818	−	0.491605i	$-0.836410\pi$
$347$		−	18.3152i		−	0.983210i	0.870818	−	0.491605i	$-0.163590\pi$
$348$	−7.37228	−	31.3793i	−0.395196	−	1.68211i
$349$		−	4.75372i		−	0.254461i	−0.991873	−	0.127230i	$-0.959391\pi$
$349$		−	4.75372i		−	0.254461i	0.991873	−	0.127230i	$-0.0406088\pi$
$350$	−4.37228	+	5.04868i	−0.233708	+	0.269863i
$351$	19.3723	+	23.3639i	1.03402	+	1.24707i
$352$	−3.25544			−0.173515
$353$	−7.88316			−0.419578			−0.209789	−	0.977747i	$-0.567278\pi$
$353$	−7.88316			−0.419578			−0.209789	+	0.977747i	$0.567278\pi$
$354$	−2.74456	−	11.6819i	−0.145872	−	0.620887i
$355$			13.5615i			0.719767i
$356$	14.2337			0.754384
$357$	5.56930	+	2.92048i	0.294758	+	0.154568i
$358$	−16.7446			−0.884978
$359$			9.80240i			0.517351i	0.965964	+	0.258675i	$0.0832860\pi$
$359$			9.80240i			0.517351i	−0.965964	+	0.258675i	$0.916714\pi$
$360$	−8.00000	−	16.0858i	−0.421637	−	0.847796i
$361$	7.00000			0.368421
$362$	46.9783			2.46912
$363$	−17.4891	+	4.10891i	−0.917941	+	0.215662i
$364$	44.2337	−	51.0767i	2.31848	−	2.67714i
$365$			6.92820i			0.362639i
$366$	29.4891	−	6.92820i	1.54142	−	0.362143i
$367$		−	25.3360i		−	1.32253i	−0.750154	−	0.661263i	$-0.770021\pi$
$367$		−	25.3360i		−	1.32253i	0.750154	−	0.661263i	$-0.229979\pi$
$368$		−	11.9769i		−	0.624338i
$369$	16.1168	−	8.01544i	0.839009	−	0.417267i
$370$			11.9769i			0.622648i
$371$	14.7446	−	17.0256i	0.765500	−	0.883923i
$372$	−6.00000	−	25.5383i	−0.311086	−	1.32410i
$373$	−24.7446			−1.28122			−0.640612	−	0.767864i	$-0.721319\pi$
$373$	−24.7446			−1.28122			−0.640612	+	0.767864i	$0.721319\pi$
$374$	−2.74456			−0.141918
$375$	1.68614	−	0.396143i	0.0870719	−	0.0204568i
$376$			44.1485i			2.27678i
$377$	−24.8614			−1.28043
$378$	0.744563	−	34.6959i	0.0382962	−	1.78457i
$379$	1.48913			0.0764912			0.0382456	−	0.999268i	$-0.487823\pi$
$379$	1.48913			0.0764912			0.0382456	+	0.999268i	$0.487823\pi$
$380$			15.1460i			0.776975i
$381$	−18.1168	+	4.25639i	−0.928154	+	0.218061i
$382$	39.4891			2.02044
$383$	17.4891			0.893653			0.446826	−	0.894621i	$-0.352554\pi$
$383$	17.4891			0.893653			0.446826	+	0.894621i	$0.352554\pi$
$384$	5.62772	+	23.9538i	0.287188	+	1.22239i
$385$	1.37228	−	1.58457i	0.0699379	−	0.0807574i
$386$		−	56.1253i		−	2.85670i
$387$	−18.1168	+	9.01011i	−0.920931	+	0.458010i
$388$		−	4.75372i		−	0.241334i
$389$		−	13.7638i		−	0.697854i	−0.937150	−	0.348927i	$-0.886546\pi$
$389$		−	13.7638i		−	0.697854i	0.937150	−	0.348927i	$-0.113454\pi$
$390$	−24.8614	+	5.84096i	−1.25891	+	0.295769i
$391$		−	2.57924i		−	0.130438i
$392$	−41.4891	+	5.98844i	−2.09552	+	0.302462i
$393$	−29.4891	+	6.92820i	−1.48753	+	0.349482i
$394$	56.4674			2.84479
$395$	−3.37228			−0.169678
$396$	4.62772	+	9.30506i	0.232552	+	0.467597i
$397$		−	3.66648i		−	0.184015i	−0.995758	−	0.0920077i	$-0.970672\pi$
$397$		−	3.66648i		−	0.184015i	0.995758	−	0.0920077i	$-0.0293284\pi$
$398$	−32.7446			−1.64134
$399$	−7.37228	+	14.0588i	−0.369076	+	0.703820i
$400$	6.37228			0.318614
$401$			2.67181i			0.133424i	0.997772	+	0.0667120i	$0.0212509\pi$
$401$			2.67181i			0.133424i	−0.997772	+	0.0667120i	$0.978749\pi$
$402$	−6.74456	−	28.7075i	−0.336388	−	1.43180i
$403$	−20.2337			−1.00791
$404$	26.2337			1.30517
$405$	−5.43070	+	7.17687i	−0.269854	+	0.356622i
$406$	21.4891	+	18.6101i	1.06649	+	0.923605i
$407$		−	3.75906i		−	0.186329i
$408$	−3.25544	−	13.8564i	−0.161168	−	0.685994i
$409$			35.0458i			1.73290i	0.499262	+	0.866451i	$0.333604\pi$
$409$			35.0458i			1.73290i	−0.499262	+	0.866451i	$0.666396\pi$
$410$			15.1460i			0.748009i
$411$	−5.25544	−	22.3692i	−0.259232	−	1.10339i
$412$		−	70.9764i		−	3.49676i
$413$	5.48913	+	4.75372i	0.270102	+	0.233915i
$414$	−12.7446	+	6.33830i	−0.626361	+	0.311510i
$415$	5.48913			0.269451
$416$	−24.0000			−1.17670
$417$	−0.510875	−	2.17448i	−0.0250176	−	0.106485i
$418$		−	6.92820i		−	0.338869i
$419$	2.74456			0.134081			0.0670403	−	0.997750i	$-0.478644\pi$
$419$	2.74456			0.134081			0.0670403	+	0.997750i	$0.478644\pi$
$420$	17.7446	+	9.30506i	0.865846	+	0.454041i
$421$	−25.6060			−1.24796			−0.623979	−	0.781441i	$-0.714485\pi$
$421$	−25.6060			−1.24796			−0.623979	+	0.781441i	$0.714485\pi$
$422$		−	15.4410i		−	0.751655i
$423$	19.8030	−	9.84868i	0.962854	−	0.478859i
$424$	−50.9783			−2.47572
$425$	1.37228			0.0665654
$426$	57.7228	−	13.5615i	2.79668	−	0.657055i
$427$	−12.0000	+	13.8564i	−0.580721	+	0.670559i
$428$			29.0024i			1.40189i
$429$	7.80298	−	1.83324i	0.376732	−	0.0885097i
$430$		−	17.0256i		−	0.821045i
$431$			31.6742i			1.52569i	0.646579	+	0.762847i	$0.276199\pi$
$431$			31.6742i			1.52569i	−0.646579	+	0.762847i	$0.723801\pi$
$432$	−25.4891	+	21.1345i	−1.22635	+	1.01683i
$433$			2.57924i			0.123950i	0.998078	+	0.0619752i	$0.0197400\pi$
$433$			2.57924i			0.123950i	−0.998078	+	0.0619752i	$0.980260\pi$
$434$	17.4891	+	15.1460i	0.839505	+	0.727033i
$435$	−1.68614	−	7.17687i	−0.0808443	−	0.344105i
$436$	−0.510875			−0.0244665
$437$	6.51087			0.311457
$438$	29.4891	−	6.92820i	1.40904	−	0.331042i
$439$		−	1.28962i		−	0.0615502i	−0.999526	−	0.0307751i	$-0.990202\pi$
$439$		−	1.28962i		−	0.0615502i	0.999526	−	0.0307751i	$-0.00979757\pi$
$440$	−4.74456			−0.226188
$441$	11.9416	+	17.2742i	0.568647	+	0.822582i
$442$	−20.2337			−0.962418
$443$		−	6.63325i		−	0.315155i	−0.987507	−	0.157578i	$-0.949632\pi$
$443$		−	6.63325i		−	0.315155i	0.987507	−	0.157578i	$-0.0503684\pi$
$444$	34.9783	−	8.21782i	1.65999	−	0.390001i
$445$	3.25544			0.154323
$446$	−52.9783			−2.50859
$447$	4.00000	+	17.0256i	0.189194	+	0.805281i
$448$	−4.74456	−	4.10891i	−0.224160	−	0.194128i
$449$			28.2101i			1.33132i	0.746256	+	0.665660i	$0.231850\pi$
$449$			28.2101i			1.33132i	−0.746256	+	0.665660i	$0.768150\pi$
$450$	−3.37228	−	6.78073i	−0.158971	−	0.319647i
$451$		−	4.75372i		−	0.223844i
$452$			44.1485i			2.07657i
$453$	−5.68614	+	1.33591i	−0.267158	+	0.0627664i
$454$		−	39.3947i		−	1.84889i
$455$	10.1168	−	11.6819i	0.474285	−	0.547657i
$456$	34.9783	−	8.21782i	1.63801	−	0.384835i
$457$	−32.9783			−1.54266			−0.771329	−	0.636437i	$-0.780408\pi$
$457$	−32.9783			−1.54266			−0.771329	+	0.636437i	$0.780408\pi$
$458$	12.0000			0.560723
$459$	−5.48913	+	4.55134i	−0.256210	+	0.212438i
$460$		−	8.21782i		−	0.383158i
$461$	8.74456			0.407275			0.203637	−	0.979046i	$-0.434724\pi$
$461$	8.74456			0.407275			0.203637	+	0.979046i	$0.434724\pi$
$462$	−8.11684	−	4.25639i	−0.377630	−	0.198025i
$463$	36.4674			1.69478			0.847391	−	0.530969i	$-0.178172\pi$
$463$	36.4674			1.69478			0.847391	+	0.530969i	$0.178172\pi$
$464$		−	27.1229i		−	1.25915i
$465$	−1.37228	−	5.84096i	−0.0636380	−	0.270868i
$466$	9.48913			0.439575
$467$	13.8832			0.642436			0.321218	−	0.947005i	$-0.395908\pi$
$467$	13.8832			0.642436			0.321218	+	0.947005i	$0.395908\pi$
$468$	34.1168	+	68.5996i	1.57705	+	3.17102i
$469$	13.4891	+	11.6819i	0.622870	+	0.539421i
$470$			18.6101i			0.858421i
$471$		0			0
$472$		−	16.4356i		−	0.756512i
$473$			5.34363i			0.245700i
$474$	3.37228	+	14.3537i	0.154894	+	0.659289i
$475$			3.46410i			0.158944i
$476$	12.0000	+	10.3923i	0.550019	+	0.476331i
$477$	11.3723	+	22.8665i	0.520701	+	1.04699i
$478$	39.4891			1.80619
$479$	−18.5109			−0.845783			−0.422892	−	0.906180i	$-0.638985\pi$
$479$	−18.5109			−0.845783			−0.422892	+	0.906180i	$0.638985\pi$
$480$	−1.62772	−	6.92820i	−0.0742949	−	0.316228i
$481$		−	27.7128i		−	1.26360i
$482$	−58.9783			−2.68639
$483$	4.00000	−	7.62792i	0.182006	−	0.347082i
$484$	−45.3505			−2.06139
$485$		−	1.08724i		−	0.0493691i
$486$	35.9783	+	15.9383i	1.63201	+	0.722977i
$487$	14.5109			0.657550			0.328775	−	0.944408i	$-0.393364\pi$
$487$	14.5109			0.657550			0.328775	+	0.944408i	$0.393364\pi$
$488$	41.4891			1.87812
$489$	−13.4891	+	3.16915i	−0.609999	+	0.143314i
$490$	−17.4891	+	2.52434i	−0.790078	+	0.114038i
$491$			10.8896i			0.491442i	0.969341	+	0.245721i	$0.0790248\pi$
$491$			10.8896i			0.491442i	−0.969341	+	0.245721i	$0.920975\pi$
$492$	44.2337	−	10.3923i	1.99421	−	0.468521i
$493$		−	5.84096i		−	0.263064i
$494$		−	51.0767i		−	2.29805i
$495$	1.05842	+	2.12819i	0.0475725	+	0.0956552i
$496$		−	22.0742i		−	0.991162i
$497$	−23.4891	+	27.1229i	−1.05363	+	1.21663i
$498$	−5.48913	−	23.3639i	−0.245974	−	1.04696i
$499$	−10.3505			−0.463353			−0.231677	−	0.972793i	$-0.574421\pi$
$499$	−10.3505			−0.463353			−0.231677	+	0.972793i	$0.574421\pi$
$500$	4.37228			0.195534
$501$	−37.2921	+	8.76144i	−1.66609	+	0.391432i
$502$			44.1485i			1.97044i
$503$	27.6060			1.23089			0.615445	−	0.788180i	$-0.288976\pi$
$503$	27.6060			1.23089			0.615445	+	0.788180i	$0.288976\pi$
$504$	11.8614	−	46.0280i	0.528349	−	2.05025i
$505$	6.00000			0.266996
$506$			3.75906i			0.167110i
$507$	35.6060	−	8.36530i	1.58132	−	0.371516i
$508$	−46.9783			−2.08432
$509$	38.2337			1.69468			0.847339	−	0.531052i	$-0.178203\pi$
$509$	38.2337			1.69468			0.847339	+	0.531052i	$0.178203\pi$
$510$	−1.37228	−	5.84096i	−0.0607656	−	0.258642i
$511$	−12.0000	+	13.8564i	−0.530849	+	0.612971i
$512$			50.1369i			2.21576i
$513$	−11.4891	−	13.8564i	−0.507257	−	0.611775i
$514$			59.2945i			2.61537i
$515$		−	16.2333i		−	0.715323i
$516$	−49.7228	+	11.6819i	−2.18892	+	0.514268i
$517$		−	5.84096i		−	0.256885i
$518$	−20.7446	+	23.9538i	−0.911464	+	1.05247i
$519$	27.1753	−	6.38458i	1.19286	−	0.280252i
$520$	−34.9783			−1.53390
$521$	−34.4674			−1.51004			−0.755022	−	0.655700i	$-0.772374\pi$
$521$	−34.4674			−1.51004			−0.755022	+	0.655700i	$0.772374\pi$
$522$	−28.8614	+	14.3537i	−1.26323	+	0.628246i
$523$		−	10.3923i		−	0.454424i	−0.973845	−	0.227212i	$-0.927039\pi$
$523$		−	10.3923i		−	0.454424i	0.973845	−	0.227212i	$-0.0729610\pi$
$524$	−76.4674			−3.34049
$525$	4.05842	+	2.12819i	0.177124	+	0.0928820i
$526$	−34.2337			−1.49266
$527$		−	4.75372i		−	0.207075i
$528$	2.00000	+	8.51278i	0.0870388	+	0.370471i
$529$	19.4674			0.846408
$530$	−21.4891			−0.933428
$531$	−7.37228	+	3.66648i	−0.319930	+	0.159112i
$532$	−26.2337	+	30.2921i	−1.13737	+	1.31333i
$533$		−	35.0458i		−	1.51800i
$534$	−3.25544	−	13.8564i	−0.140877	−	0.599625i
$535$			6.63325i			0.286780i
$536$		−	40.3894i		−	1.74456i
$537$	2.62772	+	11.1846i	0.113394	+	0.482651i
$538$		−	22.0742i		−	0.951688i
$539$	5.48913	−	0.792287i	0.236433	−	0.0341262i
$540$	−17.4891	+	14.5012i	−0.752612	+	0.624033i
$541$	18.6277			0.800868			0.400434	−	0.916326i	$-0.368859\pi$
$541$	18.6277			0.800868			0.400434	+	0.916326i	$0.368859\pi$
$542$	−38.2337			−1.64228
$543$	−7.37228	−	31.3793i	−0.316375	−	1.34661i
$544$		−	5.63858i		−	0.241752i
$545$	−0.116844			−0.00500505
$546$	−59.8397	−	31.3793i	−2.56090	−	1.34291i
$547$	42.9783			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$547$	42.9783			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$548$		−	58.0049i		−	2.47785i
$549$	−9.25544	−	18.6101i	−0.395012	−	0.794261i
$550$	−2.00000			−0.0852803
$551$	14.7446			0.628139
$552$	−18.9783	+	4.45877i	−0.807768	+	0.189778i
$553$	−6.74456	−	5.84096i	−0.286808	−	0.248383i
$554$			15.7359i			0.668556i
$555$	8.00000	−	1.87953i	0.339581	−	0.0797815i
$556$		−	5.63858i		−	0.239129i
$557$		−	30.8820i		−	1.30851i	−0.756274	−	0.654255i	$-0.772982\pi$
$557$		−	30.8820i		−	1.30851i	0.756274	−	0.654255i	$-0.227018\pi$
$558$	−23.4891	+	11.6819i	−0.994374	+	0.494535i
$559$			39.3947i			1.66622i
$560$	12.7446	+	11.0371i	0.538556	+	0.466403i
$561$	0.430703	+	1.83324i	0.0181843	+	0.0773995i
$562$	12.2337			0.516047
$563$	−5.48913			−0.231339			−0.115670	−	0.993288i	$-0.536901\pi$
$563$	−5.48913			−0.231339			−0.115670	+	0.993288i	$0.536901\pi$
$564$	54.3505	−	12.7692i	2.28857	−	0.537679i
$565$			10.0974i			0.424799i
$566$	23.4891			0.987322
$567$	−23.2921	+	4.94749i	−0.978177	+	0.207775i
$568$	81.2119			3.40758
$569$			10.6873i			0.448033i	0.974585	+	0.224017i	$0.0719170\pi$
$569$			10.6873i			0.448033i	−0.974585	+	0.224017i	$0.928083\pi$
$570$	14.7446	−	3.46410i	0.617582	−	0.145095i
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	20.2337			0.846013
$573$	−6.19702	−	26.3769i	−0.258884	−	1.10191i
$574$	−26.2337	+	30.2921i	−1.09497	+	1.26437i
$575$		−	1.87953i		−	0.0783817i
$576$	6.37228	−	3.16915i	0.265512	−	0.132048i
$577$			12.7692i			0.531587i	0.964030	+	0.265794i	$0.0856340\pi$
$577$			12.7692i			0.531587i	−0.964030	+	0.265794i	$0.914366\pi$
$578$			38.1600i			1.58725i
$579$	−37.4891	+	8.80773i	−1.55799	+	0.366037i
$580$		−	18.6101i		−	0.772744i
$581$	10.9783	+	9.50744i	0.455455	+	0.394435i
$582$	−4.62772	+	1.08724i	−0.191825	+	0.0450676i
$583$	6.74456			0.279331
$584$	41.4891			1.71683
$585$	7.80298	+	15.6896i	0.322614	+	0.648687i
$586$		−	70.9764i		−	2.93201i
$587$	5.48913			0.226560			0.113280	−	0.993563i	$-0.463864\pi$
$587$	5.48913			0.226560			0.113280	+	0.993563i	$0.463864\pi$
$588$	19.3723	+	49.3446i	0.798899	+	2.03494i
$589$	12.0000			0.494451
$590$		−	6.92820i		−	0.285230i
$591$	−8.86141	−	37.7176i	−0.364510	−	1.55149i
$592$	30.2337			1.24260
$593$	1.37228			0.0563528			0.0281764	−	0.999603i	$-0.491030\pi$
$593$	1.37228			0.0563528			0.0281764	+	0.999603i	$0.491030\pi$
$594$	8.00000	−	6.63325i	0.328244	−	0.272166i
$595$	2.74456	+	2.37686i	0.112516	+	0.0974418i
$596$			44.1485i			1.80839i
$597$	5.13859	+	21.8719i	0.210309	+	0.895155i
$598$			27.7128i			1.13326i
$599$			1.78695i			0.0730129i	0.999333	+	0.0365065i	$0.0116230\pi$
$599$			1.78695i			0.0730129i	−0.999333	+	0.0365065i	$0.988377\pi$
$600$	−2.37228	−	10.0974i	−0.0968480	−	0.412223i
$601$		−	2.17448i		−	0.0886989i	−0.999016	−	0.0443495i	$-0.985878\pi$
$601$		−	2.17448i		−	0.0886989i	0.999016	−	0.0443495i	$-0.0141215\pi$
$602$	29.4891	−	34.0511i	1.20189	−	1.38782i
$603$	−18.1168	+	9.01011i	−0.737775	+	0.366920i
$604$	−14.7446			−0.599948
$605$	−10.3723			−0.421693
$606$	−6.00000	−	25.5383i	−0.243733	−	1.03742i
$607$		−	20.9870i		−	0.851836i	−0.904762	−	0.425918i	$-0.859951\pi$
$607$		−	20.9870i		−	0.851836i	0.904762	−	0.425918i	$-0.140049\pi$
$608$	14.2337			0.577252
$609$	9.05842	−	17.2742i	0.367066	−	0.699987i
$610$	17.4891			0.708114
$611$		−	43.0612i		−	1.74207i
$612$	−16.1168	+	8.01544i	−0.651485	+	0.324005i
$613$	−4.51087			−0.182193			−0.0910963	−	0.995842i	$-0.529037\pi$
$613$	−4.51087			−0.182193			−0.0910963	+	0.995842i	$0.529037\pi$
$614$	18.0000			0.726421
$615$	10.1168	−	2.37686i	0.407951	−	0.0958443i
$616$	−9.48913	−	8.21782i	−0.382328	−	0.331106i
$617$		−	37.8102i		−	1.52218i	−0.648646	−	0.761090i	$-0.724665\pi$
$617$		−	37.8102i		−	1.52218i	0.648646	−	0.761090i	$-0.275335\pi$
$618$	−69.0951	+	16.2333i	−2.77941	+	0.652998i
$619$			1.28962i			0.0518342i	0.999664	+	0.0259171i	$0.00825060\pi$
$619$			1.28962i			0.0518342i	−0.999664	+	0.0259171i	$0.991749\pi$
$620$		−	15.1460i		−	0.608279i
$621$	6.23369	+	7.51811i	0.250149	+	0.301691i
$622$			51.0767i			2.04799i
$623$	6.51087	+	5.63858i	0.260853	+	0.225905i
$624$	14.7446	+	62.7586i	0.590255	+	2.51235i
$625$	1.00000			0.0400000
$626$	61.7228			2.46694
$627$	−4.62772	+	1.08724i	−0.184813	+	0.0434202i
$628$		0			0
$629$	6.51087			0.259606
$630$	5.00000	−	19.4024i	0.199205	−	0.773011i
$631$	−5.88316			−0.234205			−0.117102	−	0.993120i	$-0.537361\pi$
$631$	−5.88316			−0.234205			−0.117102	+	0.993120i	$0.537361\pi$
$632$			20.1947i			0.803302i
$633$	−10.3139	+	2.42315i	−0.409939	+	0.0963115i
$634$	21.4891			0.853442
$635$	−10.7446			−0.426385
$636$	14.7446	+	62.7586i	0.584660	+	2.48854i
$637$	40.4674	−	5.84096i	1.60338	−	0.231427i
$638$			8.51278i			0.337024i
$639$	−18.1168	−	36.4280i	−0.716691	−	1.44107i
$640$			14.2063i			0.561552i
$641$			29.7021i			1.17316i	0.809890	+	0.586582i	$0.199527\pi$
$641$			29.7021i			1.17316i	−0.809890	+	0.586582i	$0.800473\pi$
$642$	28.2337	−	6.63325i	1.11429	−	0.261793i
$643$		−	39.5971i		−	1.56156i	−0.624807	−	0.780779i	$-0.714822\pi$
$643$		−	39.5971i		−	1.56156i	0.624807	−	0.780779i	$-0.285178\pi$
$644$	14.2337	−	16.4356i	0.560886	−	0.647655i
$645$	−11.3723	+	2.67181i	−0.447783	+	0.105203i
$646$	12.0000			0.472134
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	42.9783	+	32.5214i	1.68835	+	1.27756i
$649$			2.17448i			0.0853559i
$650$	−14.7446			−0.578329
$651$	7.37228	−	14.0588i	0.288942	−	0.551007i
$652$	−34.9783			−1.36985
$653$		−	33.0564i		−	1.29360i	−0.762660	−	0.646799i	$-0.776107\pi$
$653$		−	33.0564i		−	1.29360i	0.762660	−	0.646799i	$-0.223893\pi$
$654$	0.116844	+	0.497333i	0.00456896	+	0.0194473i
$655$	−17.4891			−0.683357
$656$	38.2337			1.49277
$657$	−9.25544	−	18.6101i	−0.361089	−	0.726050i
$658$	−32.2337	+	37.2203i	−1.25660	+	1.45100i
$659$			20.3971i			0.794558i	0.917698	+	0.397279i	$0.130045\pi$
$659$			20.3971i			0.794558i	−0.917698	+	0.397279i	$0.869955\pi$
$660$	1.37228	+	5.84096i	0.0534160	+	0.227359i
$661$			6.92820i			0.269476i	0.990881	+	0.134738i	$0.0430193\pi$
$661$			6.92820i			0.269476i	−0.990881	+	0.134738i	$0.956981\pi$
$662$			10.0974i			0.392445i
$663$	3.17527	+	13.5152i	0.123317	+	0.524886i
$664$		−	32.8713i		−	1.27565i
$665$	−6.00000	+	6.92820i	−0.232670	+	0.268664i
$666$	−16.0000	−	32.1716i	−0.619987	−	1.24662i
$667$	−8.00000			−0.309761
$668$	−96.7011			−3.74148
$669$	8.31386	+	35.3870i	0.321432	+	1.36814i
$670$		−	17.0256i		−	0.657755i
$671$	−5.48913			−0.211905
$672$	8.74456	−	16.6757i	0.337329	−	0.643279i
$673$	22.2337			0.857046			0.428523	−	0.903531i	$-0.359034\pi$
$673$	22.2337			0.857046			0.428523	+	0.903531i	$0.359034\pi$
$674$			46.0280i			1.77293i
$675$	−4.00000	+	3.31662i	−0.153960	+	0.127657i
$676$	92.3288			3.55111
$677$	−21.6060			−0.830385			−0.415192	−	0.909734i	$-0.636286\pi$
$677$	−21.6060			−0.830385			−0.415192	+	0.909734i	$0.636286\pi$
$678$	42.9783	−	10.0974i	1.65057	−	0.387786i
$679$	1.88316	−	2.17448i	0.0722689	−	0.0834489i
$680$		−	8.21782i		−	0.315139i
$681$	−26.3139	+	6.18220i	−1.00835	+	0.236903i
$682$			6.92820i			0.265295i
$683$			51.7764i			1.98117i	0.136906	+	0.990584i	$0.456284\pi$
$683$			51.7764i			1.98117i	−0.136906	+	0.990584i	$0.543716\pi$
$684$	−20.2337	−	40.6844i	−0.773654	−	1.55561i
$685$		−	13.2665i		−	0.506887i
$686$	−39.3505	−	25.2434i	−1.50241	−	0.963797i
$687$	−1.88316	−	8.01544i	−0.0718469	−	0.305808i
$688$	−42.9783			−1.63853
$689$	49.7228			1.89429
$690$	−8.00000	+	1.87953i	−0.304555	+	0.0715524i
$691$			38.5099i			1.46498i	0.680775	+	0.732492i	$0.261643\pi$
$691$			38.5099i			1.46498i	−0.680775	+	0.732492i	$0.738357\pi$
$692$	70.4674			2.67877
$693$	−1.56930	+	6.08963i	−0.0596127	+	0.231326i
$694$	−46.2337			−1.75501
$695$		−	1.28962i		−	0.0489181i
$696$	−42.9783	+	10.0974i	−1.62909	+	0.382739i
$697$	8.23369			0.311873
$698$	−12.0000			−0.454207
$699$	−1.48913	−	6.33830i	−0.0563239	−	0.239736i
$700$	8.74456	+	7.57301i	0.330513	+	0.286233i
$701$		−	45.8256i		−	1.73081i	−0.501074	−	0.865405i	$-0.667061\pi$
$701$		−	45.8256i		−	1.73081i	0.501074	−	0.865405i	$-0.332939\pi$
$702$	58.9783	−	48.9022i	2.22599	−	1.84569i
$703$			16.4356i			0.619882i
$704$		−	1.87953i		−	0.0708374i
$705$	12.4307	−	2.92048i	0.468167	−	0.109992i
$706$			19.8997i			0.748937i
$707$	12.0000	+	10.3923i	0.451306	+	0.390843i
$708$	−20.2337	+	4.75372i	−0.760429	+	0.178656i
$709$	24.1168			0.905727			0.452864	−	0.891580i	$-0.350402\pi$
$709$	24.1168			0.905727			0.452864	+	0.891580i	$0.350402\pi$
$710$	34.2337			1.28477
$711$	9.05842	−	4.50506i	0.339717	−	0.168953i
$712$		−	19.4950i		−	0.730606i
$713$	−6.51087			−0.243834
$714$	7.37228	−	14.0588i	0.275901	−	0.526137i
$715$	4.62772			0.173067
$716$			29.0024i			1.08387i
$717$	−6.19702	−	26.3769i	−0.231432	−	0.985064i
$718$	24.7446			0.923459
$719$	−40.4674			−1.50918			−0.754589	−	0.656197i	$-0.772164\pi$
$719$	−40.4674			−1.50918			−0.754589	+	0.656197i	$0.772164\pi$
$720$	−17.1168	+	8.51278i	−0.637907	+	0.317252i
$721$	28.1168	−	32.4665i	1.04713	−	1.20912i
$722$		−	17.6704i		−	0.657623i
$723$	9.25544	+	39.3947i	0.344213	+	1.46511i
$724$		−	81.3687i		−	3.02404i
$725$		−	4.25639i		−	0.158078i
$726$	10.3723	+	44.1485i	0.384951	+	1.63850i
$727$		−	3.46410i		−	0.128476i	−0.997935	−	0.0642382i	$-0.979538\pi$
$727$		−	3.46410i		−	0.128476i	0.997935	−	0.0642382i	$-0.0204617\pi$
$728$	−69.9565	−	60.5841i	−2.59276	−	2.24540i
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	17.4891			0.647302
$731$	−9.25544			−0.342325
$732$	−12.0000	−	51.0767i	−0.443533	−	1.88785i
$733$			10.1899i			0.376373i	0.982133	+	0.188187i	$0.0602610\pi$
$733$			10.1899i			0.376373i	−0.982133	+	0.188187i	$0.939739\pi$
$734$	−63.9565			−2.36068
$735$	4.43070	+	11.2858i	0.163429	+	0.416282i
$736$	−7.72281			−0.284667
$737$			5.34363i			0.196835i
$738$	−20.2337	−	40.6844i	−0.744812	−	1.49761i
$739$	−8.62772			−0.317376			−0.158688	−	0.987329i	$-0.550726\pi$
$739$	−8.62772			−0.317376			−0.158688	+	0.987329i	$0.550726\pi$
$740$	20.7446			0.762585
$741$	−34.1168	+	8.01544i	−1.25331	+	0.294455i
$742$	−42.9783	−	37.2203i	−1.57778	−	1.36640i
$743$		−	36.9253i		−	1.35466i	−0.735680	−	0.677329i	$-0.763137\pi$
$743$		−	36.9253i		−	1.35466i	0.735680	−	0.677329i	$-0.236863\pi$
$744$	−34.9783	+	8.21782i	−1.28236	+	0.301280i
$745$			10.0974i			0.369938i
$746$			62.4636i			2.28696i
$747$	−14.7446	+	7.33296i	−0.539475	+	0.268299i
$748$			4.75372i			0.173813i
$749$	−11.4891	+	13.2665i	−0.419804	+	0.484747i
$750$	−1.00000	−	4.25639i	−0.0365148	−	0.155421i
$751$	−22.3505			−0.815582			−0.407791	−	0.913075i	$-0.633701\pi$
$751$	−22.3505			−0.815582			−0.407791	+	0.913075i	$0.633701\pi$
$752$	46.9783			1.71312
$753$	29.4891	−	6.92820i	1.07464	−	0.252478i
$754$			62.7586i			2.28553i
$755$	−3.37228			−0.122730
$756$	−60.0951	−	1.28962i	−2.18564	−	0.0469030i
$757$	−54.2337			−1.97116			−0.985578	−	0.169219i	$-0.945875\pi$
$757$	−54.2337			−1.97116			−0.985578	+	0.169219i	$0.945875\pi$
$758$		−	3.75906i		−	0.136535i
$759$	2.51087	−	0.589907i	0.0911390	−	0.0214123i
$760$	20.7446			0.752484
$761$	26.2337			0.950970			0.475485	−	0.879724i	$-0.342273\pi$
$761$	26.2337			0.950970			0.475485	+	0.879724i	$0.342273\pi$
$762$	10.7446	+	45.7330i	0.389234	+	1.65673i
$763$	−0.233688	−	0.202380i	−0.00846007	−	0.00732664i
$764$		−	68.3972i		−	2.47452i
$765$	−3.68614	+	1.83324i	−0.133273	+	0.0662810i
$766$		−	44.1485i		−	1.59515i
$767$			16.0309i			0.578842i
$768$	52.4674	−	12.3267i	1.89325	−	0.444803i
$769$		−	21.1894i		−	0.764108i	−0.924140	−	0.382054i	$-0.875217\pi$
$769$		−	21.1894i		−	0.764108i	0.924140	−	0.382054i	$-0.124783\pi$
$770$	−4.00000	−	3.46410i	−0.144150	−	0.124838i
$771$	39.6060	−	9.30506i	1.42637	−	0.335114i
$772$	−97.2119			−3.49873
$773$	46.6277			1.67708			0.838541	−	0.544838i	$-0.183409\pi$
$773$	46.6277			1.67708			0.838541	+	0.544838i	$0.183409\pi$
$774$	22.7446	+	45.7330i	0.817536	+	1.64384i
$775$		−	3.46410i		−	0.124434i
$776$	−6.51087			−0.233727
$777$	19.2554	+	10.0974i	0.690785	+	0.362240i
$778$	−34.7446			−1.24565
$779$			20.7846i			0.744686i
$780$	10.1168	+	43.0612i	0.362241	+	1.54184i
$781$	−10.7446			−0.384471
$782$	−6.51087			−0.232828
$783$	14.1168	+	17.0256i	0.504495	+	0.608444i
$784$	6.37228	+	44.1485i	0.227581	+	1.57673i
$785$		0			0
$786$	17.4891	+	74.4405i	0.623816	+	2.65521i
$787$			46.5253i			1.65845i	0.558916	+	0.829224i	$0.311217\pi$
$787$			46.5253i			1.65845i	−0.558916	+	0.829224i	$0.688783\pi$
$788$		−	97.8044i		−	3.48414i
$789$	5.37228	+	22.8665i	0.191258	+	0.814070i
$790$			8.51278i			0.302871i
$791$	−17.4891	+	20.1947i	−0.621842	+	0.718041i
$792$	12.7446	−	6.33830i	0.452858	−	0.225222i
$793$	−40.4674			−1.43704
$794$	−9.25544			−0.328463
$795$	3.37228	+	14.3537i	0.119602	+	0.509075i
$796$			56.7152i			2.01022i
$797$	42.8614			1.51823			0.759114	−	0.650957i	$-0.225632\pi$
$797$	42.8614			1.51823			0.759114	+	0.650957i	$0.225632\pi$
$798$	35.4891	+	18.6101i	1.25630	+	0.658791i
$799$	10.1168			0.357908
$800$		−	4.10891i		−	0.145272i
$801$	−8.74456	+	4.34896i	−0.308974	+	0.153663i
$802$	6.74456			0.238159
$803$	−5.48913			−0.193707
$804$	−49.7228	+	11.6819i	−1.75359	+	0.411990i
$805$	3.25544	−	3.75906i	0.114739	−	0.132489i
$806$			51.0767i			1.79910i
$807$	−14.7446	+	3.46410i	−0.519033	+	0.121942i
$808$		−	35.9306i		−	1.26404i
$809$		−	36.7229i		−	1.29111i	−0.763714	−	0.645555i	$-0.776626\pi$
$809$		−	36.7229i		−	1.29111i	0.763714	−	0.645555i	$-0.223374\pi$
$810$	18.1168	+	13.7089i	0.636561	+	0.481683i
$811$			1.28962i			0.0452847i	0.999744	+	0.0226423i	$0.00720790\pi$
$811$			1.28962i			0.0452847i	−0.999744	+	0.0226423i	$0.992792\pi$
$812$	32.2337	−	37.2203i	1.13118	−	1.30617i
$813$	6.00000	+	25.5383i	0.210429	+	0.895668i
$814$	−9.48913			−0.332594
$815$	−8.00000			−0.280228
$816$	−14.7446	+	3.46410i	−0.516163	+	0.121268i
$817$		−	23.3639i		−	0.817398i
$818$	88.4674			3.09319
$819$	−11.5693	+	44.8945i	−0.404264	+	1.56874i
$820$	26.2337			0.916120
$821$			11.7745i			0.410933i	0.978664	+	0.205466i	$0.0658711\pi$
$821$			11.7745i			0.410933i	−0.978664	+	0.205466i	$0.934129\pi$
$822$	−56.4674	+	13.2665i	−1.96953	+	0.462722i
$823$	−48.2337			−1.68132			−0.840660	−	0.541563i	$-0.817833\pi$
$823$	−48.2337			−1.68132			−0.840660	+	0.541563i	$0.817833\pi$
$824$	−97.2119			−3.38654
$825$	0.313859	+	1.33591i	0.0109272	+	0.0465103i
$826$	12.0000	−	13.8564i	0.417533	−	0.482126i
$827$		−	18.3152i		−	0.636881i	−0.947943	−	0.318441i	$-0.896841\pi$
$827$		−	18.3152i		−	0.636881i	0.947943	−	0.318441i	$-0.103159\pi$
$828$	10.9783	+	22.0742i	0.381521	+	0.767133i
$829$		−	32.4665i		−	1.12761i	−0.825908	−	0.563805i	$-0.809337\pi$
$829$		−	32.4665i		−	1.12761i	0.825908	−	0.563805i	$-0.190663\pi$
$830$		−	13.8564i		−	0.480963i
$831$	10.5109	−	2.46943i	0.364618	−	0.0856637i
$832$		−	13.8564i		−	0.480384i
$833$	1.37228	+	9.50744i	0.0475467	+	0.329413i
$834$	−5.48913	+	1.28962i	−0.190073	+	0.0446559i
$835$	−22.1168			−0.765385
$836$	−12.0000			−0.415029
$837$	11.4891	+	13.8564i	0.397122	+	0.478947i
$838$		−	6.92820i		−	0.239331i
$839$	53.4891			1.84665			0.923325	−	0.384020i	$-0.125461\pi$
$839$	53.4891			1.84665			0.923325	+	0.384020i	$0.125461\pi$
$840$	12.7446	−	24.3036i	0.439729	−	0.838554i
$841$	10.8832			0.375281
$842$			64.6381i			2.22758i
$843$	−1.91983	−	8.17154i	−0.0661224	−	0.281443i
$844$	−26.7446			−0.920586
$845$	21.1168			0.726442
$846$	−24.8614	−	49.9894i	−0.854753	−	1.71867i
$847$	−20.7446	−	17.9653i	−0.712792	−	0.617296i
$848$			54.2458i			1.86281i
$849$	−3.68614	−	15.6896i	−0.126508	−	0.538467i
$850$		−	3.46410i		−	0.118818i
$851$		−	8.91754i		−	0.305689i
$852$	−23.4891	−	99.9788i	−0.804724	−	3.42522i
$853$			46.7277i			1.59993i	0.600049	+	0.799963i	$0.295148\pi$
$853$			46.7277i			1.59993i	−0.600049	+	0.799963i	$0.704852\pi$
$854$	34.9783	+	30.2921i	1.19693	+	1.03657i
$855$	−4.62772	−	9.30506i	−0.158265	−	0.318226i
$856$	39.7228			1.35770
$857$	22.4674			0.767471			0.383735	−	0.923443i	$-0.374637\pi$
$857$	22.4674			0.767471			0.383735	+	0.923443i	$0.374637\pi$
$858$	−4.62772	−	19.6974i	−0.157988	−	0.672457i
$859$		−	45.4381i		−	1.55033i	−0.631760	−	0.775164i	$-0.717667\pi$
$859$		−	45.4381i		−	1.55033i	0.631760	−	0.775164i	$-0.282333\pi$
$860$	−29.4891			−1.00557
$861$	24.3505	+	12.7692i	0.829864	+	0.435172i
$862$	79.9565			2.72333
$863$			28.0078i			0.953395i	0.879067	+	0.476698i	$0.158166\pi$
$863$			28.0078i			0.953395i	−0.879067	+	0.476698i	$0.841834\pi$
$864$	13.6277	+	16.4356i	0.463624	+	0.559152i
$865$	16.1168			0.547989
$866$	6.51087			0.221249
$867$	25.4891	−	5.98844i	0.865656	−	0.203378i
$868$	26.2337	−	30.2921i	0.890429	−	1.02818i
$869$		−	2.67181i		−	0.0906351i
$870$	−18.1168	+	4.25639i	−0.614219	+	0.144305i
$871$			39.3947i			1.33484i
$872$			0.699713i			0.0236953i
$873$	1.45245	+	2.92048i	0.0491581	+	0.0988433i
$874$		−	16.4356i		−	0.555944i
$875$	2.00000	+	1.73205i	0.0676123	+	0.0585540i
$876$	−12.0000	−	51.0767i	−0.405442	−	1.72572i
$877$	30.4674			1.02881			0.514405	−	0.857547i	$-0.328013\pi$
$877$	30.4674			1.02881			0.514405	+	0.857547i	$0.328013\pi$
$878$	−3.25544			−0.109866
$879$	−47.4090	+	11.1383i	−1.59906	+	0.375686i
$880$			5.04868i			0.170191i
$881$	2.23369			0.0752549			0.0376274	−	0.999292i	$-0.488020\pi$
$881$	2.23369			0.0752549			0.0376274	+	0.999292i	$0.488020\pi$
$882$	43.6060	−	30.1446i	1.46829	−	1.01502i
$883$	26.5109			0.892162			0.446081	−	0.894993i	$-0.352819\pi$
$883$	26.5109			0.892162			0.446081	+	0.894993i	$0.352819\pi$
$884$			35.0458i			1.17872i
$885$	−4.62772	+	1.08724i	−0.155559	+	0.0365472i
$886$	−16.7446			−0.562545
$887$	−41.4891			−1.39307			−0.696534	−	0.717524i	$-0.745276\pi$
$887$	−41.4891			−1.39307			−0.696534	+	0.717524i	$0.745276\pi$
$888$	−11.2554	−	47.9075i	−0.377708	−	1.60767i
$889$	−21.4891	−	18.6101i	−0.720722	−	0.624164i
$890$		−	8.21782i		−	0.275462i
$891$	−5.68614	−	4.30268i	−0.190493	−	0.144145i
$892$			91.7610i			3.07239i
$893$			25.5383i			0.854608i
$894$	42.9783	−	10.0974i	1.43741	−	0.337706i
$895$			6.63325i			0.221725i
$896$	−24.6060	+	28.4125i	−0.822028	+	0.949196i
$897$	18.5109	−	4.34896i	0.618060	−	0.145208i
$898$	71.2119			2.37637
$899$	−14.7446			−0.491759
$900$	−11.7446	+	5.84096i	−0.391485	+	0.194699i
$901$			11.6819i			0.389181i
$902$	−12.0000			−0.399556
$903$	−27.3723	−	14.3537i	−0.910892	−	0.477663i
$904$	60.4674			2.01112
$905$		−	18.6101i		−	0.618622i
$906$	3.37228	+	14.3537i	0.112037	+	0.476871i
$907$	8.00000			0.265636			0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000			0.265636			0.132818	+	0.991140i	$0.457597\pi$
$908$	−68.2337			−2.26441
$909$	−16.1168	+	8.01544i	−0.534562	+	0.265855i
$910$	−29.4891	−	25.5383i	−0.977555	−	0.846587i
$911$			23.6588i			0.783851i	0.919997	+	0.391926i	$0.128191\pi$
$911$			23.6588i			0.783851i	−0.919997	+	0.391926i	$0.871809\pi$
$912$	−8.74456	−	37.2203i	−0.289561	−	1.23249i
$913$			4.34896i			0.143930i
$914$			83.2482i			2.75361i
$915$	−2.74456	−	11.6819i	−0.0907324	−	0.386193i
$916$		−	20.7846i		−	0.686743i
$917$	−34.9783	−	30.2921i	−1.15508	−	1.00033i
$918$	11.4891	+	13.8564i	0.379198	+	0.457330i
$919$	−11.3723			−0.375137			−0.187568	−	0.982252i	$-0.560061\pi$
$919$	−11.3723			−0.375137			−0.187568	+	0.982252i	$0.560061\pi$
$920$	−11.2554			−0.371081
$921$	−2.82473	−	12.0232i	−0.0930782	−	0.396177i
$922$		−	22.0742i		−	0.726976i
$923$	−79.2119			−2.60729
$924$	−7.37228	+	14.0588i	−0.242530	+	0.462500i
$925$	4.74456			0.156000
$926$		−	92.0560i		−	3.02515i
$927$	21.6861	+	43.6048i	0.712266	+	1.43217i
$928$	−17.4891			−0.574109
$929$	−7.02175			−0.230376			−0.115188	−	0.993344i	$-0.536747\pi$
$929$	−7.02175			−0.230376			−0.115188	+	0.993344i	$0.536747\pi$
$930$	−14.7446	+	3.46410i	−0.483493	+	0.113592i
$931$	−24.0000	+	3.46410i	−0.786568	+	0.113531i
$932$		−	16.4356i		−	0.538368i
$933$	34.1168	−	8.01544i	1.11694	−	0.262414i
$934$		−	35.0458i		−	1.14673i
$935$			1.08724i			0.0355566i
$936$	93.9565	−	46.7277i	3.07106	−	1.52734i
$937$			49.9894i			1.63308i	0.577287	+	0.816542i	$0.304112\pi$
$937$			49.9894i			1.63308i	−0.577287	+	0.816542i	$0.695888\pi$
$938$	29.4891	−	34.0511i	0.962854	−	1.11181i
$939$	−9.68614	−	41.2280i	−0.316095	−	1.34542i
$940$	32.2337			1.05135
$941$	27.2554			0.888502			0.444251	−	0.895902i	$-0.353470\pi$
$941$	27.2554			0.888502			0.444251	+	0.895902i	$0.353470\pi$
$942$		0			0
$943$		−	11.2772i		−	0.367235i
$944$	−17.4891			−0.569223
$945$	−13.7446	−	0.294954i	−0.447111	−	0.00959484i
$946$	13.4891			0.438569
$947$		−	48.2025i		−	1.56637i	−0.621789	−	0.783185i	$-0.713594\pi$
$947$		−	48.2025i		−	1.56637i	0.621789	−	0.783185i	$-0.286406\pi$
$948$	24.8614	−	5.84096i	0.807461	−	0.189706i
$949$	−40.4674			−1.31363
$950$	8.74456			0.283711
$951$	−3.37228	−	14.3537i	−0.109354	−	0.465452i
$952$	14.2337	−	16.4356i	0.461316	−	0.532682i
$953$			38.8048i			1.25701i	0.777805	+	0.628506i	$0.216333\pi$
$953$			38.8048i			1.25701i	−0.777805	+	0.628506i	$0.783667\pi$
$954$	57.7228	−	28.7075i	1.86885	−	0.929439i
$955$		−	15.6434i		−	0.506207i
$956$		−	68.3972i		−	2.21212i
$957$	5.68614	−	1.33591i	0.183807	−	0.0431838i
$958$			46.7277i			1.50970i
$959$	22.9783	−	26.5330i	0.742006	−	0.856795i
$960$	4.00000	−	0.939764i	0.129099	−	0.0303307i
$961$	19.0000			0.612903
$962$	−69.9565			−2.25549
$963$	−8.86141	−	17.8178i	−0.285555	−	0.574172i
$964$			102.153i			3.29014i
$965$	−22.2337			−0.715728
$966$	−19.2554	−	10.0974i	−0.619534	−	0.324877i
$967$	−24.2337			−0.779303			−0.389651	−	0.920962i	$-0.627405\pi$
$967$	−24.2337			−0.779303			−0.389651	+	0.920962i	$0.627405\pi$
$968$			62.1138i			1.99641i
$969$	−1.88316	−	8.01544i	−0.0604957	−	0.257493i
$970$	−2.74456			−0.0881226
$971$	43.2119			1.38674			0.693369	−	0.720583i	$-0.256126\pi$
$971$	43.2119			1.38674			0.693369	+	0.720583i	$0.256126\pi$
$972$	27.6060	−	62.3162i	0.885462	−	1.99879i
$973$	2.23369	−	2.57924i	0.0716087	−	0.0826867i
$974$		−	36.6303i		−	1.17371i
$975$	2.31386	+	9.84868i	0.0741028	+	0.315410i
$976$		−	44.1485i		−	1.41316i
$977$			38.8048i			1.24148i	0.784018	+	0.620738i	$0.213167\pi$
$977$			38.8048i			1.24148i	−0.784018	+	0.620738i	$0.786833\pi$
$978$	8.00000	+	34.0511i	0.255812	+	1.08883i
$979$			2.57924i			0.0824329i
$980$	4.37228	+	30.2921i	0.139667	+	0.967644i
$981$	0.313859	−	0.156093i	0.0100208	−	0.00498366i
$982$	27.4891			0.877213
$983$	−11.1386			−0.355266			−0.177633	−	0.984097i	$-0.556844\pi$
$983$	−11.1386			−0.355266			−0.177633	+	0.984097i	$0.556844\pi$
$984$	−14.2337	−	60.5841i	−0.453753	−	1.93135i
$985$		−	22.3692i		−	0.712741i
$986$	−14.7446			−0.469563
$987$	29.9198	+	15.6896i	0.952359	+	0.499407i
$988$	−88.4674			−2.81452
$989$			12.6766i			0.403092i
$990$	5.37228	−	2.67181i	0.170742	−	0.0849158i
$991$	2.51087			0.0797606			0.0398803	−	0.999204i	$-0.487302\pi$
$991$	2.51087			0.0797606			0.0398803	+	0.999204i	$0.487302\pi$
$992$	−14.2337			−0.451920
$993$	6.74456	−	1.58457i	0.214032	−	0.0502849i
$994$	68.4674	+	59.2945i	2.17165	+	1.88071i
$995$			12.9715i			0.411226i
$996$	−40.4674	+	9.50744i	−1.28226	+	0.301255i
$997$			21.8719i			0.692688i	0.938107	+	0.346344i	$0.112577\pi$
$997$			21.8719i			0.692688i	−0.938107	+	0.346344i	$0.887423\pi$
$998$			26.1282i			0.827075i
$999$	−18.9783	+	15.7359i	−0.600445	+	0.497863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.b.c.41.1	✓	4
3.2	odd	2		105.2.b.d.41.4	yes	4
4.3	odd	2		1680.2.f.h.881.3		4
5.2	odd	4		525.2.g.e.524.8		8
5.3	odd	4		525.2.g.e.524.1		8
5.4	even	2		525.2.b.g.251.4		4
7.2	even	3		735.2.s.h.521.1		4
7.3	odd	6		735.2.s.j.656.2		4
7.4	even	3		735.2.s.i.656.2		4
7.5	odd	6		735.2.s.g.521.1		4
7.6	odd	2		105.2.b.d.41.1	yes	4
12.11	even	2		1680.2.f.g.881.1		4
15.2	even	4		525.2.g.d.524.1		8
15.8	even	4		525.2.g.d.524.8		8
15.14	odd	2		525.2.b.e.251.1		4
21.2	odd	6		735.2.s.j.521.2		4
21.5	even	6		735.2.s.i.521.2		4
21.11	odd	6		735.2.s.g.656.1		4
21.17	even	6		735.2.s.h.656.1		4
21.20	even	2	inner	105.2.b.c.41.4	yes	4
28.27	even	2		1680.2.f.g.881.2		4
35.13	even	4		525.2.g.d.524.2		8
35.27	even	4		525.2.g.d.524.7		8
35.34	odd	2		525.2.b.e.251.4		4
84.83	odd	2		1680.2.f.h.881.4		4
105.62	odd	4		525.2.g.e.524.2		8
105.83	odd	4		525.2.g.e.524.7		8
105.104	even	2		525.2.b.g.251.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.1	✓	4	1.1	even	1	trivial
105.2.b.c.41.4	yes	4	21.20	even	2	inner
105.2.b.d.41.1	yes	4	7.6	odd	2
105.2.b.d.41.4	yes	4	3.2	odd	2
525.2.b.e.251.1		4	15.14	odd	2
525.2.b.e.251.4		4	35.34	odd	2
525.2.b.g.251.1		4	105.104	even	2
525.2.b.g.251.4		4	5.4	even	2
525.2.g.d.524.1		8	15.2	even	4
525.2.g.d.524.2		8	35.13	even	4
525.2.g.d.524.7		8	35.27	even	4
525.2.g.d.524.8		8	15.8	even	4
525.2.g.e.524.1		8	5.3	odd	4
525.2.g.e.524.2		8	105.62	odd	4
525.2.g.e.524.7		8	105.83	odd	4
525.2.g.e.524.8		8	5.2	odd	4
735.2.s.g.521.1		4	7.5	odd	6
735.2.s.g.656.1		4	21.11	odd	6
735.2.s.h.521.1		4	7.2	even	3
735.2.s.h.656.1		4	21.17	even	6
735.2.s.i.521.2		4	21.5	even	6
735.2.s.i.656.2		4	7.4	even	3
735.2.s.j.521.2		4	21.2	odd	6
735.2.s.j.656.2		4	7.3	odd	6
1680.2.f.g.881.1		4	12.11	even	2
1680.2.f.g.881.2		4	28.27	even	2
1680.2.f.h.881.3		4	4.3	odd	2
1680.2.f.h.881.4		4	84.83	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52434i q^{2} +(-1.68614 + 0.396143i) q^{3} -4.37228 q^{4} -1.00000 q^{5} +(1.00000 + 4.25639i) q^{6} +(-2.00000 - 1.73205i) q^{7} +5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q-2.52434i q^{2} +(-1.68614 + 0.396143i) q^{3} -4.37228 q^{4} -1.00000 q^{5} +(1.00000 + 4.25639i) q^{6} +(-2.00000 - 1.73205i) q^{7} +5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} +2.52434i q^{10} -0.792287i q^{11} +(7.37228 - 1.73205i) q^{12} -5.84096i q^{13} +(-4.37228 + 5.04868i) q^{14} +(1.68614 - 0.396143i) q^{15} +6.37228 q^{16} +1.37228 q^{17} +(-3.37228 - 6.78073i) q^{18} +3.46410i q^{19} +4.37228 q^{20} +(4.05842 + 2.12819i) q^{21} -2.00000 q^{22} -1.87953i q^{23} +(-2.37228 - 10.0974i) q^{24} +1.00000 q^{25} -14.7446 q^{26} +(-4.00000 + 3.31662i) q^{27} +(8.74456 + 7.57301i) q^{28} -4.25639i q^{29} +(-1.00000 - 4.25639i) q^{30} -3.46410i q^{31} -4.10891i q^{32} +(0.313859 + 1.33591i) q^{33} -3.46410i q^{34} +(2.00000 + 1.73205i) q^{35} +(-11.7446 + 5.84096i) q^{36} +4.74456 q^{37} +8.74456 q^{38} +(2.31386 + 9.84868i) q^{39} -5.98844i q^{40} +6.00000 q^{41} +(5.37228 - 10.2448i) q^{42} -6.74456 q^{43} +3.46410i q^{44} +(-2.68614 + 1.33591i) q^{45} -4.74456 q^{46} +7.37228 q^{47} +(-10.7446 + 2.52434i) q^{48} +(1.00000 + 6.92820i) q^{49} -2.52434i q^{50} +(-2.31386 + 0.543620i) q^{51} +25.5383i q^{52} +8.51278i q^{53} +(8.37228 + 10.0974i) q^{54} +0.792287i q^{55} +(10.3723 - 11.9769i) q^{56} +(-1.37228 - 5.84096i) q^{57} -10.7446 q^{58} -2.74456 q^{59} +(-7.37228 + 1.73205i) q^{60} -6.92820i q^{61} -8.74456 q^{62} +(-7.68614 - 1.98072i) q^{63} +2.37228 q^{64} +5.84096i q^{65} +(3.37228 - 0.792287i) q^{66} -6.74456 q^{67} -6.00000 q^{68} +(0.744563 + 3.16915i) q^{69} +(4.37228 - 5.04868i) q^{70} -13.5615i q^{71} +(8.00000 + 16.0858i) q^{72} -6.92820i q^{73} -11.9769i q^{74} +(-1.68614 + 0.396143i) q^{75} -15.1460i q^{76} +(-1.37228 + 1.58457i) q^{77} +(24.8614 - 5.84096i) q^{78} +3.37228 q^{79} -6.37228 q^{80} +(5.43070 - 7.17687i) q^{81} -15.1460i q^{82} -5.48913 q^{83} +(-17.7446 - 9.30506i) q^{84} -1.37228 q^{85} +17.0256i q^{86} +(1.68614 + 7.17687i) q^{87} +4.74456 q^{88} -3.25544 q^{89} +(3.37228 + 6.78073i) q^{90} +(-10.1168 + 11.6819i) q^{91} +8.21782i q^{92} +(1.37228 + 5.84096i) q^{93} -18.6101i q^{94} -3.46410i q^{95} +(1.62772 + 6.92820i) q^{96} +1.08724i q^{97} +(17.4891 - 2.52434i) q^{98} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 6 q^{4} - 4 q^{5} + 4 q^{6} - 8 q^{7} + 5 q^{9}+O(q^{10}) \) 4 * q - q^3 - 6 * q^4 - 4 * q^5 + 4 * q^6 - 8 * q^7 + 5 * q^9	\( 4 q - q^{3} - 6 q^{4} - 4 q^{5} + 4 q^{6} - 8 q^{7} + 5 q^{9} + 18 q^{12} - 6 q^{14} + q^{15} + 14 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{20} - q^{21} - 8 q^{22} + 2 q^{24} + 4 q^{25} - 36 q^{26} - 16 q^{27} + 12 q^{28} - 4 q^{30} + 7 q^{33} + 8 q^{35} - 24 q^{36} - 4 q^{37} + 12 q^{38} + 15 q^{39} + 24 q^{41} + 10 q^{42} - 4 q^{43} - 5 q^{45} + 4 q^{46} + 18 q^{47} - 20 q^{48} + 4 q^{49} - 15 q^{51} + 22 q^{54} + 30 q^{56} + 6 q^{57} - 20 q^{58} + 12 q^{59} - 18 q^{60} - 12 q^{62} - 25 q^{63} - 2 q^{64} + 2 q^{66} - 4 q^{67} - 24 q^{68} - 20 q^{69} + 6 q^{70} + 32 q^{72} - q^{75} + 6 q^{77} + 42 q^{78} + 2 q^{79} - 14 q^{80} - 7 q^{81} + 24 q^{83} - 48 q^{84} + 6 q^{85} + q^{87} - 4 q^{88} - 36 q^{89} + 2 q^{90} - 6 q^{91} - 6 q^{93} + 18 q^{96} + 24 q^{98} + 13 q^{99}+O(q^{100}) \) 4 * q - q^3 - 6 * q^4 - 4 * q^5 + 4 * q^6 - 8 * q^7 + 5 * q^9 + 18 * q^12 - 6 * q^14 + q^15 + 14 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^20 - q^21 - 8 * q^22 + 2 * q^24 + 4 * q^25 - 36 * q^26 - 16 * q^27 + 12 * q^28 - 4 * q^30 + 7 * q^33 + 8 * q^35 - 24 * q^36 - 4 * q^37 + 12 * q^38 + 15 * q^39 + 24 * q^41 + 10 * q^42 - 4 * q^43 - 5 * q^45 + 4 * q^46 + 18 * q^47 - 20 * q^48 + 4 * q^49 - 15 * q^51 + 22 * q^54 + 30 * q^56 + 6 * q^57 - 20 * q^58 + 12 * q^59 - 18 * q^60 - 12 * q^62 - 25 * q^63 - 2 * q^64 + 2 * q^66 - 4 * q^67 - 24 * q^68 - 20 * q^69 + 6 * q^70 + 32 * q^72 - q^75 + 6 * q^77 + 42 * q^78 + 2 * q^79 - 14 * q^80 - 7 * q^81 + 24 * q^83 - 48 * q^84 + 6 * q^85 + q^87 - 4 * q^88 - 36 * q^89 + 2 * q^90 - 6 * q^91 - 6 * q^93 + 18 * q^96 + 24 * q^98 + 13 * q^99

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