LMFDB - Embedded newform 56.3.g.b.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(43,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("56.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.g (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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.8
Root			$1.85837 - 0.739226i$ of defining polynomial
Character	$\chi$	$=$	56.43
Dual form			56.3.g.b.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85837 + 0.739226i) q^{2} +0.0974366 q^{3} +(2.90709 + 2.74751i) q^{4} -3.46547i q^{5} +(0.181073 + 0.0720276i) q^{6} +2.64575i q^{7} +(3.37142 + 7.25490i) q^{8} -8.99051 q^{9} +O(q^{10})$	\(q+(1.85837 + 0.739226i) q^{2} +0.0974366 q^{3} +(2.90709 + 2.74751i) q^{4} -3.46547i q^{5} +(0.181073 + 0.0720276i) q^{6} +2.64575i q^{7} +(3.37142 + 7.25490i) q^{8} -8.99051 q^{9} +(2.56177 - 6.44013i) q^{10} -2.92866 q^{11} +(0.283257 + 0.267708i) q^{12} -19.1586i q^{13} +(-1.95581 + 4.91679i) q^{14} -0.337664i q^{15} +(0.902343 + 15.9745i) q^{16} -14.3897 q^{17} +(-16.7077 - 6.64602i) q^{18} +8.09744 q^{19} +(9.52143 - 10.0744i) q^{20} +0.257793i q^{21} +(-5.44254 - 2.16494i) q^{22} +16.7598i q^{23} +(0.328500 + 0.706892i) q^{24} +12.9905 q^{25} +(14.1625 - 35.6038i) q^{26} -1.75293 q^{27} +(-7.26924 + 7.69144i) q^{28} -27.1649i q^{29} +(0.249610 - 0.627505i) q^{30} +44.8923i q^{31} +(-10.1319 + 30.3537i) q^{32} -0.285359 q^{33} +(-26.7415 - 10.6373i) q^{34} +9.16878 q^{35} +(-26.1362 - 24.7015i) q^{36} +39.5687i q^{37} +(15.0480 + 5.98584i) q^{38} -1.86675i q^{39} +(25.1416 - 11.6836i) q^{40} +45.8766 q^{41} +(-0.190567 + 0.479075i) q^{42} +61.0334 q^{43} +(-8.51388 - 8.04653i) q^{44} +31.1563i q^{45} +(-12.3893 + 31.1459i) q^{46} -46.2793i q^{47} +(0.0879212 + 1.55650i) q^{48} -7.00000 q^{49} +(24.1412 + 9.60292i) q^{50} -1.40209 q^{51} +(52.6385 - 55.6957i) q^{52} +9.69424i q^{53} +(-3.25760 - 1.29581i) q^{54} +10.1492i q^{55} +(-19.1947 + 8.91994i) q^{56} +0.788986 q^{57} +(20.0810 - 50.4825i) q^{58} -114.554 q^{59} +(0.927735 - 0.981619i) q^{60} -7.48032i q^{61} +(-33.1855 + 83.4265i) q^{62} -23.7866i q^{63} +(-41.2671 + 48.9186i) q^{64} -66.3935 q^{65} +(-0.530302 - 0.210944i) q^{66} -12.0590 q^{67} +(-41.8323 - 39.5360i) q^{68} +1.63302i q^{69} +(17.0390 + 6.77780i) q^{70} -129.187i q^{71} +(-30.3108 - 65.2252i) q^{72} -18.2854 q^{73} +(-29.2502 + 73.5334i) q^{74} +1.26575 q^{75} +(23.5400 + 22.2478i) q^{76} -7.74851i q^{77} +(1.37995 - 3.46911i) q^{78} -42.6168i q^{79} +(55.3593 - 3.12704i) q^{80} +80.7438 q^{81} +(85.2558 + 33.9132i) q^{82} -109.670 q^{83} +(-0.708289 + 0.749427i) q^{84} +49.8673i q^{85} +(113.423 + 45.1174i) q^{86} -2.64685i q^{87} +(-9.87374 - 21.2471i) q^{88} -80.9162 q^{89} +(-23.0316 + 57.9001i) q^{90} +50.6889 q^{91} +(-46.0478 + 48.7223i) q^{92} +4.37415i q^{93} +(34.2109 - 86.0041i) q^{94} -28.0614i q^{95} +(-0.987218 + 2.95756i) q^{96} +162.086 q^{97} +(-13.0086 - 5.17458i) q^{98} +26.3301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) $ 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9	$ 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9} + 16 q^{10} - 32 q^{11} + 30 q^{12} + 7 q^{14} - 71 q^{16} - 80 q^{17} - 29 q^{18} + 56 q^{19} - 108 q^{20} + 66 q^{22} + 22 q^{24} - 16 q^{25} + 24 q^{26} - 32 q^{27} + 7 q^{28} + 96 q^{30} - 19 q^{32} + 32 q^{33} + 74 q^{34} + 56 q^{35} - 33 q^{36} - 14 q^{38} + 84 q^{40} + 128 q^{41} - 98 q^{42} + 50 q^{44} - 152 q^{46} + 134 q^{48} - 56 q^{49} + 33 q^{50} - 368 q^{51} + 132 q^{52} - 228 q^{54} - 49 q^{56} + 56 q^{57} + 24 q^{58} + 104 q^{59} + 192 q^{60} + 120 q^{62} - 55 q^{64} - 72 q^{65} - 276 q^{66} + 304 q^{67} - 190 q^{68} + 56 q^{70} - 209 q^{72} - 112 q^{73} + 8 q^{74} + 72 q^{75} + 70 q^{76} - 304 q^{78} + 124 q^{80} + 48 q^{81} + 450 q^{82} + 72 q^{83} + 42 q^{84} + 210 q^{86} - 486 q^{88} - 512 q^{89} - 184 q^{90} - 56 q^{91} - 472 q^{92} + 472 q^{94} + 558 q^{96} + 64 q^{97} - 7 q^{98} + 256 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9 + 16 * q^10 - 32 * q^11 + 30 * q^12 + 7 * q^14 - 71 * q^16 - 80 * q^17 - 29 * q^18 + 56 * q^19 - 108 * q^20 + 66 * q^22 + 22 * q^24 - 16 * q^25 + 24 * q^26 - 32 * q^27 + 7 * q^28 + 96 * q^30 - 19 * q^32 + 32 * q^33 + 74 * q^34 + 56 * q^35 - 33 * q^36 - 14 * q^38 + 84 * q^40 + 128 * q^41 - 98 * q^42 + 50 * q^44 - 152 * q^46 + 134 * q^48 - 56 * q^49 + 33 * q^50 - 368 * q^51 + 132 * q^52 - 228 * q^54 - 49 * q^56 + 56 * q^57 + 24 * q^58 + 104 * q^59 + 192 * q^60 + 120 * q^62 - 55 * q^64 - 72 * q^65 - 276 * q^66 + 304 * q^67 - 190 * q^68 + 56 * q^70 - 209 * q^72 - 112 * q^73 + 8 * q^74 + 72 * q^75 + 70 * q^76 - 304 * q^78 + 124 * q^80 + 48 * q^81 + 450 * q^82 + 72 * q^83 + 42 * q^84 + 210 * q^86 - 486 * q^88 - 512 * q^89 - 184 * q^90 - 56 * q^91 - 472 * q^92 + 472 * q^94 + 558 * q^96 + 64 * q^97 - 7 * q^98 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.85837	+	0.739226i	0.929186	+	0.369613i
$2$	1.85837	+	0.739226i	0.929186	+	0.369613i
$3$	0.0974366			0.0324789			0.0162394	−	0.999868i	$-0.494831\pi$
$3$	0.0974366			0.0324789			0.0162394	+	0.999868i	$0.494831\pi$
$4$	2.90709	+	2.74751i	0.726772	+	0.686878i
$5$		−	3.46547i		−	0.693094i	−0.938033	−	0.346547i	$-0.887354\pi$
$5$		−	3.46547i		−	0.693094i	0.938033	−	0.346547i	$-0.112646\pi$
$6$	0.181073	+	0.0720276i	0.0301789	+	0.0120046i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	3.37142	+	7.25490i	0.421428	+	0.906862i
$9$	−8.99051			−0.998945
$10$	2.56177	−	6.44013i	0.256177	−	0.644013i
$11$	−2.92866			−0.266242			−0.133121	−	0.991100i	$-0.542500\pi$
$11$	−2.92866			−0.266242			−0.133121	+	0.991100i	$0.542500\pi$
$12$	0.283257	+	0.267708i	0.0236047	+	0.0223090i
$13$		−	19.1586i		−	1.47374i	−0.676036	−	0.736869i	$-0.736304\pi$
$13$		−	19.1586i		−	1.47374i	0.676036	−	0.736869i	$-0.263696\pi$
$14$	−1.95581	+	4.91679i	−0.139701	+	0.351199i
$15$		−	0.337664i		−	0.0225109i
$16$	0.902343	+	15.9745i	0.0563964	+	0.998408i
$17$	−14.3897			−0.846456			−0.423228	−	0.906023i	$-0.639103\pi$
$17$	−14.3897			−0.846456			−0.423228	+	0.906023i	$0.639103\pi$
$18$	−16.7077	−	6.64602i	−0.928206	−	0.369223i
$19$	8.09744			0.426181			0.213090	−	0.977032i	$-0.431647\pi$
$19$	8.09744			0.426181			0.213090	+	0.977032i	$0.431647\pi$
$20$	9.52143	−	10.0744i	0.476071	−	0.503722i
$21$			0.257793i			0.0122759i
$22$	−5.44254	−	2.16494i	−0.247388	−	0.0984064i
$23$			16.7598i			0.728687i	0.931265	+	0.364344i	$0.118707\pi$
$23$			16.7598i			0.728687i	−0.931265	+	0.364344i	$0.881293\pi$
$24$	0.328500	+	0.706892i	0.0136875	+	0.0294538i
$25$	12.9905			0.519620
$26$	14.1625	−	35.6038i	0.544713	−	1.36938i
$27$	−1.75293			−0.0649234
$28$	−7.26924	+	7.69144i	−0.259616	+	0.274694i
$29$		−	27.1649i		−	0.936720i	−0.883538	−	0.468360i	$-0.844845\pi$
$29$		−	27.1649i		−	0.936720i	0.883538	−	0.468360i	$-0.155155\pi$
$30$	0.249610	−	0.627505i	0.00832032	−	0.0209168i
$31$			44.8923i			1.44814i	0.689728	+	0.724069i	$0.257730\pi$
$31$			44.8923i			1.44814i	−0.689728	+	0.724069i	$0.742270\pi$
$32$	−10.1319	+	30.3537i	−0.316622	+	0.948552i
$33$	−0.285359			−0.00864723
$34$	−26.7415	−	10.6373i	−0.786515	−	0.312861i
$35$	9.16878			0.261965
$36$	−26.1362	−	24.7015i	−0.726006	−	0.686154i
$37$			39.5687i			1.06943i	0.845034	+	0.534713i	$0.179580\pi$
$37$			39.5687i			1.06943i	−0.845034	+	0.534713i	$0.820420\pi$
$38$	15.0480	+	5.98584i	0.396001	+	0.157522i
$39$		−	1.86675i		−	0.0478653i
$40$	25.1416	−	11.6836i	0.628541	−	0.292089i
$41$	45.8766			1.11894			0.559471	−	0.828850i	$-0.311004\pi$
$41$	45.8766			1.11894			0.559471	+	0.828850i	$0.311004\pi$
$42$	−0.190567	+	0.479075i	−0.00453731	+	0.0114065i
$43$	61.0334			1.41938			0.709690	−	0.704514i	$-0.248835\pi$
$43$	61.0334			1.41938			0.709690	+	0.704514i	$0.248835\pi$
$44$	−8.51388	−	8.04653i	−0.193497	−	0.182876i
$45$			31.1563i			0.692363i
$46$	−12.3893	+	31.1459i	−0.269332	+	0.677086i
$47$		−	46.2793i		−	0.984666i	−0.870407	−	0.492333i	$-0.836144\pi$
$47$		−	46.2793i		−	0.984666i	0.870407	−	0.492333i	$-0.163856\pi$
$48$	0.0879212	+	1.55650i	0.00183169	+	0.0324272i
$49$	−7.00000			−0.142857
$50$	24.1412	+	9.60292i	0.482824	+	0.192058i
$51$	−1.40209			−0.0274919
$52$	52.6385	−	55.6957i	1.01228	−	1.07107i
$53$			9.69424i			0.182910i	0.995809	+	0.0914551i	$0.0291518\pi$
$53$			9.69424i			0.182910i	−0.995809	+	0.0914551i	$0.970848\pi$
$54$	−3.25760	−	1.29581i	−0.0603259	−	0.0239965i
$55$			10.1492i			0.184531i
$56$	−19.1947	+	8.91994i	−0.342762	+	0.159285i
$57$	0.788986			0.0138419
$58$	20.0810	−	50.4825i	0.346224	−	0.870387i
$59$	−114.554			−1.94159			−0.970796	−	0.239907i	$-0.922883\pi$
$59$	−114.554			−1.94159			−0.970796	+	0.239907i	$0.922883\pi$
$60$	0.927735	−	0.981619i	0.0154623	−	0.0163603i
$61$		−	7.48032i		−	0.122628i	−0.998119	−	0.0613141i	$-0.980471\pi$
$61$		−	7.48032i		−	0.122628i	0.998119	−	0.0613141i	$-0.0195291\pi$
$62$	−33.1855	+	83.4265i	−0.535251	+	1.34559i
$63$		−	23.7866i		−	0.377566i
$64$	−41.2671	+	48.9186i	−0.644798	+	0.764353i
$65$	−66.3935			−1.02144
$66$	−0.530302	−	0.210944i	−0.00803488	−	0.00319613i
$67$	−12.0590			−0.179985			−0.0899925	−	0.995942i	$-0.528684\pi$
$67$	−12.0590			−0.179985			−0.0899925	+	0.995942i	$0.528684\pi$
$68$	−41.8323	−	39.5360i	−0.615181	−	0.581412i
$69$			1.63302i			0.0236669i
$70$	17.0390	+	6.77780i	0.243414	+	0.0968257i
$71$		−	129.187i		−	1.81953i	−0.415124	−	0.909765i	$-0.636262\pi$
$71$		−	129.187i		−	1.81953i	0.415124	−	0.909765i	$-0.363738\pi$
$72$	−30.3108	−	65.2252i	−0.420983	−	0.905905i
$73$	−18.2854			−0.250484			−0.125242	−	0.992126i	$-0.539971\pi$
$73$	−18.2854			−0.250484			−0.125242	+	0.992126i	$0.539971\pi$
$74$	−29.2502	+	73.5334i	−0.395273	+	0.993695i
$75$	1.26575			0.0168767
$76$	23.5400	+	22.2478i	0.309737	+	0.292734i
$77$		−	7.74851i		−	0.100630i
$78$	1.37995	−	3.46911i	0.0176916	−	0.0444758i
$79$		−	42.6168i		−	0.539454i	−0.962937	−	0.269727i	$-0.913067\pi$
$79$		−	42.6168i		−	0.539454i	0.962937	−	0.269727i	$-0.0869334\pi$
$80$	55.3593	−	3.12704i	0.691991	−	0.0390880i
$81$	80.7438			0.996836
$82$	85.2558	+	33.9132i	1.03971	+	0.413576i
$83$	−109.670			−1.32133			−0.660663	−	0.750683i	$-0.729725\pi$
$83$	−109.670			−1.32133			−0.660663	+	0.750683i	$0.729725\pi$
$84$	−0.708289	+	0.749427i	−0.00843202	+	0.00892175i
$85$			49.8673i			0.586674i
$86$	113.423	+	45.1174i	1.31887	+	0.524622i
$87$		−	2.64685i		−	0.0304236i
$88$	−9.87374	−	21.2471i	−0.112202	−	0.241445i
$89$	−80.9162			−0.909170			−0.454585	−	0.890703i	$-0.650212\pi$
$89$	−80.9162			−0.909170			−0.454585	+	0.890703i	$0.650212\pi$
$90$	−23.0316	+	57.9001i	−0.255906	+	0.643334i
$91$	50.6889			0.557020
$92$	−46.0478	+	48.7223i	−0.500519	+	0.529590i
$93$			4.37415i			0.0470339i
$94$	34.2109	−	86.0041i	0.363945	−	0.914937i
$95$		−	28.0614i		−	0.295384i
$96$	−0.987218	+	2.95756i	−0.0102835	+	0.0308079i
$97$	162.086			1.67099			0.835495	−	0.549498i	$-0.185181\pi$
$97$	162.086			1.67099			0.835495	+	0.549498i	$0.185181\pi$
$98$	−13.0086	−	5.17458i	−0.132741	−	0.0528019i
$99$	26.3301			0.265961
$100$	37.7646	+	35.6916i	0.377646	+	0.356916i
$101$			106.827i			1.05769i	0.848717	+	0.528847i	$0.177375\pi$
$101$			106.827i			1.05769i	−0.848717	+	0.528847i	$0.822625\pi$
$102$	−2.60560	−	1.03646i	−0.0255451	−	0.0101614i
$103$			126.626i			1.22938i	0.788768	+	0.614691i	$0.210719\pi$
$103$			126.626i			1.22938i	−0.788768	+	0.614691i	$0.789281\pi$
$104$	138.994	−	64.5916i	1.33648	−	0.621074i
$105$	0.893374			0.00850832
$106$	−7.16623	+	18.0155i	−0.0676060	+	0.169958i
$107$	87.0191			0.813263			0.406632	−	0.913592i	$-0.366703\pi$
$107$	87.0191			0.813263			0.406632	+	0.913592i	$0.366703\pi$
$108$	−5.09593	−	4.81621i	−0.0471846	−	0.0445945i
$109$		−	189.921i		−	1.74240i	−0.490930	−	0.871199i	$-0.663343\pi$
$109$		−	189.921i		−	1.74240i	0.490930	−	0.871199i	$-0.336657\pi$
$110$	−7.50254	+	18.8610i	−0.0682050	+	0.171463i
$111$			3.85544i			0.0347337i
$112$	−42.2646	+	2.38737i	−0.377363	+	0.0213158i
$113$	−40.1848			−0.355617			−0.177809	−	0.984065i	$-0.556901\pi$
$113$	−40.1848			−0.355617			−0.177809	+	0.984065i	$0.556901\pi$
$114$	1.46623	+	0.583239i	0.0128617	+	0.00511613i
$115$	58.0806			0.505049
$116$	74.6359	−	78.9708i	0.643413	−	0.680783i
$117$			172.245i			1.47218i
$118$	−212.884	−	84.6812i	−1.80410	−	0.717638i
$119$		−	38.0717i		−	0.319930i
$120$	2.44971	−	1.13841i	0.0204143	−	0.00948672i
$121$	−112.423			−0.929115
$122$	5.52964	−	13.9012i	0.0453249	−	0.113944i
$123$	4.47006			0.0363420
$124$	−123.342	+	130.506i	−0.994695	+	1.05247i
$125$		−	131.655i		−	1.05324i
$126$	17.5837	−	44.2044i	0.139553	−	0.350829i
$127$			153.657i			1.20989i	0.796266	+	0.604947i	$0.206806\pi$
$127$			153.657i			1.20989i	−0.796266	+	0.604947i	$0.793194\pi$
$128$	−112.851	+	60.4033i	−0.881652	+	0.471901i
$129$	5.94688			0.0460999
$130$	−123.384	−	49.0798i	−0.949107	−	0.377537i
$131$	61.8649			0.472251			0.236126	−	0.971723i	$-0.424122\pi$
$131$	61.8649			0.472251			0.236126	+	0.971723i	$0.424122\pi$
$132$	−0.829563	−	0.784026i	−0.00628457	−	0.00593959i
$133$			21.4238i			0.161081i
$134$	−22.4101	−	8.91433i	−0.167240	−	0.0665248i
$135$			6.07474i			0.0449981i
$136$	−48.5139	−	104.396i	−0.356720	−	0.767619i
$137$	105.943			0.773307			0.386653	−	0.922225i	$-0.373631\pi$
$137$	105.943			0.773307			0.386653	+	0.922225i	$0.373631\pi$
$138$	−1.20717	+	3.03475i	−0.00874760	+	0.0219910i
$139$	−185.384			−1.33370			−0.666848	−	0.745194i	$-0.732357\pi$
$139$	−185.384			−1.33370			−0.666848	+	0.745194i	$0.732357\pi$
$140$	26.6545	+	25.1913i	0.190389	+	0.179938i
$141$		−	4.50930i		−	0.0319808i
$142$	95.4981	−	240.077i	0.672522	−	1.69068i
$143$			56.1090i			0.392371i
$144$	−8.11252	−	143.619i	−0.0563369	−	0.997355i
$145$	−94.1392			−0.649236
$146$	−33.9810	−	13.5170i	−0.232747	−	0.0925823i
$147$	−0.682056			−0.00463984
$148$	−108.716	+	115.030i	−0.734565	+	0.777229i
$149$			47.4096i			0.318185i	0.987264	+	0.159093i	$0.0508568\pi$
$149$			47.4096i			0.318185i	−0.987264	+	0.159093i	$0.949143\pi$
$150$	2.35223	+	0.935675i	0.0156816	+	0.00623784i
$151$			114.576i			0.758780i	0.925237	+	0.379390i	$0.123866\pi$
$151$			114.576i			0.758780i	−0.925237	+	0.379390i	$0.876134\pi$
$152$	27.2999	+	58.7461i	0.179604	+	0.386487i
$153$	129.371			0.845563
$154$	5.72790	−	14.3996i	0.0371941	−	0.0935039i
$155$	155.573			1.00370
$156$	5.12891	−	5.42680i	0.0328776	−	0.0347872i
$157$		−	294.095i		−	1.87322i	−0.350378	−	0.936608i	$-0.613947\pi$
$157$		−	294.095i		−	1.87322i	0.350378	−	0.936608i	$-0.386053\pi$
$158$	31.5035	−	79.1979i	0.199389	−	0.501253i
$159$			0.944573i			0.00594071i
$160$	105.190	+	35.1118i	0.657436	+	0.219449i
$161$	−44.3423			−0.275418
$162$	150.052	+	59.6879i	0.926246	+	0.368444i
$163$	171.021			1.04921			0.524603	−	0.851347i	$-0.324214\pi$
$163$	171.021			1.04921			0.524603	+	0.851347i	$0.324214\pi$
$164$	133.367	+	126.047i	0.813216	+	0.768577i
$165$			0.988902i			0.00599335i
$166$	−203.808	−	81.0709i	−1.22776	−	0.488379i
$167$			120.657i			0.722499i	0.932469	+	0.361249i	$0.117650\pi$
$167$			120.657i			0.722499i	−0.932469	+	0.361249i	$0.882350\pi$
$168$	−1.87026	+	0.869128i	−0.0111325	+	0.00517338i
$169$	−198.052			−1.17190
$170$	−36.8632	+	92.6719i	−0.216842	+	0.545129i
$171$	−72.8001			−0.425731
$172$	177.429	+	167.690i	1.03157	+	0.974942i
$173$		−	108.339i		−	0.626236i	−0.949714	−	0.313118i	$-0.898626\pi$
$173$		−	108.339i		−	0.626236i	0.949714	−	0.313118i	$-0.101374\pi$
$174$	1.95662	−	4.91884i	0.0112450	−	0.0282692i
$175$			34.3696i			0.196398i
$176$	−2.64266	−	46.7840i	−0.0150151	−	0.265818i
$177$	−11.1617			−0.0630607
$178$	−150.372	−	59.8153i	−0.844788	−	0.336041i
$179$	−161.438			−0.901886			−0.450943	−	0.892553i	$-0.648912\pi$
$179$	−161.438			−0.901886			−0.450943	+	0.892553i	$0.648912\pi$
$180$	−85.6025	+	90.5743i	−0.475569	+	0.503191i
$181$		−	7.14696i		−	0.0394860i	−0.999805	−	0.0197430i	$-0.993715\pi$
$181$		−	7.14696i		−	0.0394860i	0.999805	−	0.0197430i	$-0.00628479\pi$
$182$	94.1987	+	37.4705i	0.517575	+	0.205882i
$183$		−	0.728856i		−	0.00398282i
$184$	−121.591	+	56.5043i	−0.660819	+	0.307089i
$185$	137.124			0.741212
$186$	−3.23348	+	8.12879i	−0.0173843	+	0.0437032i
$187$	42.1427			0.225362
$188$	127.153	−	134.538i	0.676346	−	0.715628i
$189$		−	4.63782i		−	0.0245388i
$190$	20.7437	−	52.1486i	0.109178	−	0.274466i
$191$		−	73.2983i		−	0.383761i	−0.981418	−	0.191880i	$-0.938541\pi$
$191$		−	73.2983i		−	0.383761i	0.981418	−	0.191880i	$-0.0614586\pi$
$192$	−4.02092	+	4.76646i	−0.0209423	+	0.0248253i
$193$	−85.0705			−0.440780			−0.220390	−	0.975412i	$-0.570733\pi$
$193$	−85.0705			−0.440780			−0.220390	+	0.975412i	$0.570733\pi$
$194$	301.216	+	119.818i	1.55266	+	0.617620i
$195$	−6.46916			−0.0331752
$196$	−20.3496	−	19.2326i	−0.103825	−	0.0981255i
$197$			140.460i			0.712996i	0.934296	+	0.356498i	$0.116029\pi$
$197$			140.460i			0.712996i	−0.934296	+	0.356498i	$0.883971\pi$
$198$	48.9312	+	19.4639i	0.247127	+	0.0983026i
$199$		−	143.082i		−	0.719006i	−0.933144	−	0.359503i	$-0.882946\pi$
$199$		−	143.082i		−	0.719006i	0.933144	−	0.359503i	$-0.117054\pi$
$200$	43.7965	+	94.2448i	0.218982	+	0.471224i
$201$	−1.17499			−0.00584571
$202$	−78.9694	+	198.524i	−0.390937	+	0.982794i
$203$	71.8715			0.354047
$204$	−4.07599	−	3.85225i	−0.0199804	−	0.0188836i
$205$		−	158.984i		−	0.775532i
$206$	−93.6055	+	235.319i	−0.454396	+	1.14232i
$207$		−	150.679i		−	0.727919i
$208$	306.050	−	17.2876i	1.47139	−	0.0831135i
$209$	−23.7146			−0.113467
$210$	1.66022	+	0.660405i	0.00790581	+	0.00314479i
$211$	−111.955			−0.530591			−0.265295	−	0.964167i	$-0.585469\pi$
$211$	−111.955			−0.530591			−0.265295	+	0.964167i	$0.585469\pi$
$212$	−26.6350	+	28.1820i	−0.125637	+	0.132934i
$213$		−	12.5875i		−	0.0590962i
$214$	161.714	+	64.3268i	0.755672	+	0.300593i
$215$		−	211.509i		−	0.983765i
$216$	−5.90987	−	12.7173i	−0.0273605	−	0.0588766i
$217$	−118.774			−0.547345
$218$	140.395	−	352.944i	0.644013	−	1.61901i
$219$	−1.78166			−0.00813545
$220$	−27.8850	+	29.5046i	−0.126750	+	0.134112i
$221$			275.687i			1.24745i
$222$	−2.85004	+	7.16484i	−0.0128380	+	0.0322741i
$223$			311.438i			1.39658i	0.715814	+	0.698291i	$0.246056\pi$
$223$			311.438i			1.39658i	−0.715814	+	0.698291i	$0.753944\pi$
$224$	−80.3082	−	26.8065i	−0.358519	−	0.119672i
$225$	−116.791			−0.519072
$226$	−74.6782	−	29.7056i	−0.330435	−	0.131441i
$227$	74.3581			0.327569			0.163784	−	0.986496i	$-0.447630\pi$
$227$	74.3581			0.327569			0.163784	+	0.986496i	$0.447630\pi$
$228$	2.29365	+	2.16775i	0.0100599	+	0.00950768i
$229$		−	78.2710i		−	0.341795i	−0.985289	−	0.170897i	$-0.945333\pi$
$229$		−	78.2710i		−	0.341795i	0.985289	−	0.170897i	$-0.0546667\pi$
$230$	107.935	+	42.9347i	0.469284	+	0.186673i
$231$		−	0.754988i		−	0.00326835i
$232$	197.078	−	91.5842i	0.849476	−	0.394760i
$233$	93.0573			0.399388			0.199694	−	0.979858i	$-0.436005\pi$
$233$	93.0573			0.399388			0.199694	+	0.979858i	$0.436005\pi$
$234$	−127.328	+	320.096i	−0.544138	+	1.36793i
$235$	−160.380			−0.682466
$236$	−333.019	−	314.738i	−1.41110	−	1.33364i
$237$		−	4.15244i		−	0.0175208i
$238$	28.1436	−	70.7513i	0.118250	−	0.297275i
$239$		−	291.605i		−	1.22011i	−0.792361	−	0.610053i	$-0.791148\pi$
$239$		−	291.605i		−	1.22011i	0.792361	−	0.610053i	$-0.208852\pi$
$240$	5.39402	−	0.304688i	0.0224751	−	0.00126953i
$241$	223.748			0.928413			0.464207	−	0.885727i	$-0.346340\pi$
$241$	223.748			0.928413			0.464207	+	0.885727i	$0.346340\pi$
$242$	−208.924	−	83.1060i	−0.863321	−	0.343413i
$243$	23.6438			0.0972996
$244$	20.5523	−	21.7459i	0.0842306	−	0.0891227i
$245$			24.2583i			0.0990135i
$246$	8.30703	+	3.30438i	0.0337684	+	0.0134325i
$247$		−	155.135i		−	0.628079i
$248$	−325.689	+	151.351i	−1.31326	+	0.610285i
$249$	−10.6859			−0.0429151
$250$	97.3228	−	244.664i	0.389291	−	0.978656i
$251$	−310.605			−1.23747			−0.618734	−	0.785600i	$-0.712354\pi$
$251$	−310.605			−1.23747			−0.618734	+	0.785600i	$0.712354\pi$
$252$	65.3541	−	69.1499i	0.259342	−	0.274404i
$253$		−	49.0838i		−	0.194007i
$254$	−113.587	+	285.551i	−0.447193	+	1.12422i
$255$			4.85889i			0.0190545i
$256$	−254.372	+	28.8290i	−0.993639	+	0.112613i
$257$	175.472			0.682769			0.341385	−	0.939924i	$-0.389104\pi$
$257$	175.472			0.682769			0.341385	+	0.939924i	$0.389104\pi$
$258$	11.0515	+	4.39609i	0.0428353	+	0.0170391i
$259$	−104.689			−0.404205
$260$	−193.012	−	182.417i	−0.742354	−	0.701604i
$261$			244.226i			0.935732i
$262$	114.968	+	45.7321i	0.438809	+	0.174550i
$263$			312.127i			1.18680i	0.804910	+	0.593398i	$0.202214\pi$
$263$			312.127i			1.18680i	−0.804910	+	0.593398i	$0.797786\pi$
$264$	−0.962064	−	2.07025i	−0.00364418	−	0.00784185i
$265$	33.5951			0.126774
$266$	−15.8370	+	39.8134i	−0.0595377	+	0.149674i
$267$	−7.88419			−0.0295288
$268$	−35.0566	−	33.1323i	−0.130808	−	0.123628i
$269$			142.817i			0.530918i	0.964122	+	0.265459i	$0.0855234\pi$
$269$			142.817i			0.530918i	−0.964122	+	0.265459i	$0.914477\pi$
$270$	−4.49061	+	11.2891i	−0.0166319	+	0.0418116i
$271$		−	266.117i		−	0.981982i	−0.871165	−	0.490991i	$-0.836635\pi$
$271$		−	266.117i		−	0.981982i	0.871165	−	0.490991i	$-0.163365\pi$
$272$	−12.9845	−	229.870i	−0.0477371	−	0.845108i
$273$	4.93895			0.0180914
$274$	196.882	+	78.3158i	0.718546	+	0.285824i
$275$	−38.0448			−0.138345
$276$	−4.48674	+	4.74733i	−0.0162563	+	0.0172005i
$277$			366.740i			1.32397i	0.749516	+	0.661986i	$0.230286\pi$
$277$			366.740i			1.32397i	−0.749516	+	0.661986i	$0.769714\pi$
$278$	−344.512	−	137.040i	−1.23925	−	0.492951i
$279$		−	403.604i		−	1.44661i
$280$	30.9118	+	66.5185i	0.110399	+	0.237566i
$281$	147.977			0.526607			0.263303	−	0.964713i	$-0.415188\pi$
$281$	147.977			0.526607			0.263303	+	0.964713i	$0.415188\pi$
$282$	3.33339	−	8.37995i	0.0118205	−	0.0297161i
$283$	327.739			1.15809			0.579043	−	0.815297i	$-0.303426\pi$
$283$	327.739			1.15809			0.579043	+	0.815297i	$0.303426\pi$
$284$	354.942	−	375.557i	1.24980	−	1.32238i
$285$		−	2.73421i		−	0.00959372i
$286$	−41.4772	+	104.271i	−0.145025	+	0.364585i
$287$			121.378i			0.422920i
$288$	91.0909	−	272.895i	0.316288	−	0.947551i
$289$	−81.9352			−0.283513
$290$	−174.946	−	69.5901i	−0.603260	−	0.239966i
$291$	15.7931			0.0542718
$292$	−53.1572	−	50.2393i	−0.182045	−	0.172052i
$293$			259.881i			0.886966i	0.896283	+	0.443483i	$0.146257\pi$
$293$			259.881i			0.886966i	−0.896283	+	0.443483i	$0.853743\pi$
$294$	−1.26751	−	0.504193i	−0.00431127	−	0.00171494i
$295$			396.983i			1.34571i
$296$	−287.067	+	133.403i	−0.969821	+	0.450685i
$297$	5.13375			0.0172853
$298$	−35.0464	+	88.1046i	−0.117605	+	0.295653i
$299$	321.094			1.07389
$300$	3.67965	+	3.47767i	0.0122655	+	0.0115922i
$301$			161.479i			0.536475i
$302$	−84.6974	+	212.924i	−0.280455	+	0.705047i
$303$			10.4089i			0.0343527i
$304$	7.30666	+	129.353i	0.0240351	+	0.425503i
$305$	−25.9228			−0.0849929
$306$	240.420	+	95.6345i	0.785685	+	0.312531i
$307$	290.462			0.946131			0.473065	−	0.881027i	$-0.343147\pi$
$307$	290.462			0.946131			0.473065	+	0.881027i	$0.343147\pi$
$308$	21.2891	−	22.5256i	0.0691205	−	0.0731351i
$309$			12.3380i			0.0399289i
$310$	289.112	+	115.004i	0.932620	+	0.370979i
$311$		−	74.9081i		−	0.240862i	−0.992722	−	0.120431i	$-0.961572\pi$
$311$		−	74.9081i		−	0.240862i	0.992722	−	0.120431i	$-0.0384276\pi$
$312$	13.5431	−	6.29359i	0.0434072	−	0.0201718i
$313$	284.507			0.908969			0.454485	−	0.890755i	$-0.349823\pi$
$313$	284.507			0.908969			0.454485	+	0.890755i	$0.349823\pi$
$314$	217.403	−	546.538i	0.692365	−	1.74057i
$315$	−82.4319			−0.261689
$316$	117.090	−	123.891i	0.370539	−	0.392060i
$317$			12.2631i			0.0386850i	0.999813	+	0.0193425i	$0.00615729\pi$
$317$			12.2631i			0.0386850i	−0.999813	+	0.0193425i	$0.993843\pi$
$318$	−0.698253	+	1.75537i	−0.00219576	+	0.00552003i
$319$			79.5567i			0.249394i
$320$	169.526	+	143.010i	0.529769	+	0.446906i
$321$	8.47885			0.0264139
$322$	−82.4044	−	32.7790i	−0.255914	−	0.101798i
$323$	−116.520			−0.360743
$324$	234.729	+	221.845i	0.724473	+	0.684705i
$325$		−	248.880i		−	0.765784i
$326$	317.820	+	126.423i	0.974908	+	0.387800i
$327$		−	18.5053i		−	0.0565911i
$328$	154.669	+	332.830i	0.471553	+	1.01473i
$329$	122.443			0.372169
$330$	−0.731022	+	1.83775i	−0.00221522	+	0.00556893i
$331$	194.466			0.587510			0.293755	−	0.955881i	$-0.405095\pi$
$331$	194.466			0.587510			0.293755	+	0.955881i	$0.405095\pi$
$332$	−318.821	−	301.320i	−0.960303	−	0.907590i
$333$		−	355.743i		−	1.06830i
$334$	−89.1930	+	224.226i	−0.267045	+	0.671336i
$335$			41.7901i			0.124747i
$336$	−4.11812	+	0.232618i	−0.0122563	+	0.000692314i
$337$	0.596077			0.00176877			0.000884387	−	1.00000i	$-0.499718\pi$
$337$	0.596077			0.00176877			0.000884387		1.00000i	$0.499718\pi$
$338$	−368.053	−	146.405i	−1.08892	−	0.433150i
$339$	−3.91547			−0.0115500
$340$	−137.011	+	144.969i	−0.402973	+	0.426378i
$341$		−	131.474i		−	0.385555i
$342$	−135.290	−	53.8157i	−0.395583	−	0.157356i
$343$		−	18.5203i		−	0.0539949i
$344$	205.769	+	442.791i	0.598166	+	1.28718i
$345$	5.65918			0.0164034
$346$	80.0869	−	201.334i	0.231465	−	0.581890i
$347$	−204.867			−0.590394			−0.295197	−	0.955436i	$-0.595385\pi$
$347$	−204.867			−0.590394			−0.295197	+	0.955436i	$0.595385\pi$
$348$	7.27226	−	7.69464i	0.0208973	−	0.0221110i
$349$		−	128.396i		−	0.367898i	−0.982936	−	0.183949i	$-0.941112\pi$
$349$		−	128.396i		−	0.367898i	0.982936	−	0.183949i	$-0.0588882\pi$
$350$	−25.4069	+	63.8716i	−0.0725913	+	0.182490i
$351$			33.5837i			0.0956801i
$352$	29.6729	−	88.8956i	0.0842980	−	0.252544i
$353$	−190.841			−0.540627			−0.270314	−	0.962772i	$-0.587127\pi$
$353$	−190.841			−0.540627			−0.270314	+	0.962772i	$0.587127\pi$
$354$	−20.7427	−	8.25105i	−0.0585951	−	0.0233080i
$355$	−447.692			−1.26111
$356$	−235.231	−	222.318i	−0.660760	−	0.624489i
$357$		−	3.70957i		−	0.0103910i
$358$	−300.011	−	119.339i	−0.838020	−	0.333349i
$359$			215.704i			0.600847i	0.953806	+	0.300424i	$0.0971281\pi$
$359$			215.704i			0.600847i	−0.953806	+	0.300424i	$0.902872\pi$
$360$	−226.036	+	105.041i	−0.627878	+	0.291781i
$361$	−295.432			−0.818370
$362$	5.28322	−	13.2817i	0.0145945	−	0.0366898i
$363$	−10.9541			−0.0301766
$364$	147.357	+	139.268i	0.404827	+	0.382605i
$365$			63.3674i			0.173609i
$366$	0.538789	−	1.35449i	0.00147210	−	0.00370078i
$367$		−	454.789i		−	1.23921i	−0.784915	−	0.619604i	$-0.787293\pi$
$367$		−	454.789i		−	1.23921i	0.784915	−	0.619604i	$-0.212707\pi$
$368$	−267.730	+	15.1231i	−0.727527	+	0.0410954i
$369$	−412.454			−1.11776
$370$	254.828	+	101.366i	0.688724	+	0.273962i
$371$	−25.6485			−0.0691335
$372$	−12.0180	+	12.7160i	−0.0323065	+	0.0341829i
$373$		−	360.748i		−	0.967153i	−0.875302	−	0.483576i	$-0.839338\pi$
$373$		−	360.748i		−	0.967153i	0.875302	−	0.483576i	$-0.160662\pi$
$374$	78.3168	+	31.1530i	0.209403	+	0.0832967i
$375$		−	12.8280i		−	0.0342080i
$376$	335.751	−	156.027i	0.892956	−	0.414965i
$377$	−520.441			−1.38048
$378$	3.42840	−	8.61880i	0.00906984	−	0.0228011i
$379$	−268.427			−0.708250			−0.354125	−	0.935198i	$-0.615221\pi$
$379$	−268.427			−0.708250			−0.354125	+	0.935198i	$0.615221\pi$
$380$	77.0992	−	81.5771i	0.202893	−	0.214677i
$381$			14.9718i			0.0392960i
$382$	54.1840	−	136.215i	0.141843	−	0.356585i
$383$			581.532i			1.51836i	0.650881	+	0.759180i	$0.274400\pi$
$383$			581.532i			1.51836i	−0.650881	+	0.759180i	$0.725600\pi$
$384$	−10.9959	+	5.88549i	−0.0286350	+	0.0153268i
$385$	−26.8522			−0.0697461
$386$	−158.093	−	62.8863i	−0.409566	−	0.162918i
$387$	−548.721			−1.41788
$388$	471.199	+	445.334i	1.21443	+	1.14777i
$389$		−	512.278i		−	1.31691i	−0.752620	−	0.658455i	$-0.771210\pi$
$389$		−	512.278i		−	1.31691i	0.752620	−	0.658455i	$-0.228790\pi$
$390$	−12.0221	−	4.78217i	−0.0308259	−	0.0122620i
$391$		−	241.169i		−	0.616801i
$392$	−23.5999	−	50.7843i	−0.0602039	−	0.129552i
$393$	6.02790			0.0153382
$394$	−103.832	+	261.027i	−0.263532	+	0.662505i
$395$	−147.687			−0.373892
$396$	76.5441	+	72.3424i	0.193293	+	0.182683i
$397$		−	81.3250i		−	0.204849i	−0.994741	−	0.102424i	$-0.967340\pi$
$397$		−	81.3250i		−	0.204849i	0.994741	−	0.102424i	$-0.0326600\pi$
$398$	105.770	−	265.900i	0.265754	−	0.668090i
$399$			2.08746i			0.00523173i
$400$	11.7219	+	207.517i	0.0293047	+	0.518793i
$401$	527.441			1.31531			0.657657	−	0.753318i	$-0.271548\pi$
$401$	527.441			1.31531			0.657657	+	0.753318i	$0.271548\pi$
$402$	−2.18356	−	0.868581i	−0.00543175	−	0.00216065i
$403$	860.073			2.13418
$404$	−293.509	+	310.556i	−0.726507	+	0.768703i
$405$		−	279.815i		−	0.690902i
$406$	133.564	+	53.1293i	0.328975	+	0.130860i
$407$		−	115.883i		−	0.284726i
$408$	−4.72703	−	10.1720i	−0.0115858	−	0.0249314i
$409$	−58.6727			−0.143454			−0.0717270	−	0.997424i	$-0.522851\pi$
$409$	−58.6727			−0.143454			−0.0717270	+	0.997424i	$0.522851\pi$
$410$	117.525	−	295.452i	0.286647	−	0.720614i
$411$	10.3227			0.0251161
$412$	−347.908	+	368.114i	−0.844436	+	0.893481i
$413$		−	303.081i		−	0.733853i
$414$	111.386	−	280.018i	0.269048	−	0.676372i
$415$			380.058i			0.915803i
$416$	581.533	+	194.113i	1.39792	+	0.466618i
$417$	−18.0632			−0.0433169
$418$	−44.0706	−	17.5305i	−0.105432	−	0.0419389i
$419$	760.704			1.81552			0.907761	−	0.419487i	$-0.137790\pi$
$419$	760.704			1.81552			0.907761	+	0.419487i	$0.137790\pi$
$420$	2.59712	+	2.45456i	0.00618362	+	0.00584418i
$421$		−	46.2918i		−	0.109957i	−0.998488	−	0.0549784i	$-0.982491\pi$
$421$		−	46.2918i		−	0.109957i	0.998488	−	0.0549784i	$-0.0175090\pi$
$422$	−208.053	−	82.7598i	−0.493017	−	0.196113i
$423$			416.074i			0.983627i
$424$	−70.3307	+	32.6834i	−0.165874	+	0.0770834i
$425$	−186.930			−0.439835
$426$	9.30501	−	23.3922i	0.0218427	−	0.0549114i
$427$	19.7911			0.0463491
$428$	252.972	+	239.086i	0.591057	+	0.558613i
$429$			5.46707i			0.0127437i
$430$	156.353	−	393.063i	0.363612	−	0.914100i
$431$		−	336.176i		−	0.779991i	−0.920817	−	0.389996i	$-0.872477\pi$
$431$		−	336.176i		−	0.779991i	0.920817	−	0.389996i	$-0.127523\pi$
$432$	−1.58175	−	28.0023i	−0.00366145	−	0.0648201i
$433$	−372.694			−0.860725			−0.430363	−	0.902656i	$-0.641614\pi$
$433$	−372.694			−0.860725			−0.430363	+	0.902656i	$0.641614\pi$
$434$	−220.726	−	87.8007i	−0.508585	−	0.202306i
$435$	−9.17260			−0.0210864
$436$	521.811	−	552.118i	1.19682	−	1.26633i
$437$			135.711i			0.310553i
$438$	−3.31099	−	1.31705i	−0.00755934	−	0.00300697i
$439$			397.478i			0.905418i	0.891658	+	0.452709i	$0.149542\pi$
$439$			397.478i			0.905418i	−0.891658	+	0.452709i	$0.850458\pi$
$440$	−73.6313	+	34.2172i	−0.167344	+	0.0777663i
$441$	62.9335			0.142706
$442$	−203.795	+	512.329i	−0.461075	+	1.15912i
$443$	273.530			0.617450			0.308725	−	0.951151i	$-0.400098\pi$
$443$	273.530			0.617450			0.308725	+	0.951151i	$0.400098\pi$
$444$	−10.5929	+	11.2081i	−0.0238578	+	0.0252435i
$445$			280.413i			0.630141i
$446$	−230.223	+	578.767i	−0.516195	+	1.29768i
$447$			4.61943i			0.0103343i
$448$	−129.426	−	109.182i	−0.288898	−	0.243711i
$449$	428.702			0.954792			0.477396	−	0.878688i	$-0.341581\pi$
$449$	428.702			0.954792			0.477396	+	0.878688i	$0.341581\pi$
$450$	−217.041	−	86.3351i	−0.482314	−	0.191856i
$451$	−134.357			−0.297909
$452$	−116.821	−	110.408i	−0.258453	−	0.244266i
$453$			11.1639i			0.0246443i
$454$	138.185	+	54.9674i	0.304372	+	0.121074i
$455$		−	175.661i		−	0.386068i
$456$	2.66000	+	5.72401i	0.00583334	+	0.0125527i
$457$	10.0500			0.0219913			0.0109956	−	0.999940i	$-0.496500\pi$
$457$	10.0500			0.0219913			0.0109956	+	0.999940i	$0.496500\pi$
$458$	57.8600	−	145.457i	0.126332	−	0.317591i
$459$	25.2243			0.0549548
$460$	168.846	+	159.577i	0.367056	+	0.346907i
$461$			825.802i			1.79133i	0.444732	+	0.895664i	$0.353299\pi$
$461$			825.802i			1.79133i	−0.444732	+	0.895664i	$0.646701\pi$
$462$	0.558107	−	1.40305i	0.00120802	−	0.00303690i
$463$			114.707i			0.247748i	0.992298	+	0.123874i	$0.0395318\pi$
$463$			114.707i			0.247748i	−0.992298	+	0.123874i	$0.960468\pi$
$464$	433.946	−	24.5120i	0.935229	−	0.0528277i
$465$	15.1585			0.0325989
$466$	172.935	+	68.7904i	0.371105	+	0.147619i
$467$	−201.727			−0.431964			−0.215982	−	0.976397i	$-0.569295\pi$
$467$	−201.727			−0.431964			−0.215982	+	0.976397i	$0.569295\pi$
$468$	−473.247	+	500.733i	−1.01121	+	1.06994i
$469$		−	31.9051i		−	0.0680280i
$470$	−298.045	−	118.557i	−0.634138	−	0.252248i
$471$		−	28.6556i		−	0.0608399i
$472$	−386.209	−	831.077i	−0.818240	−	1.76076i
$473$	−178.746			−0.377899
$474$	3.06959	−	7.71677i	0.00647593	−	0.0162801i
$475$	105.190			0.221452
$476$	104.602	−	110.678i	0.219753	−	0.232516i
$477$		−	87.1561i		−	0.182717i
$478$	215.562	−	541.911i	0.450967	−	1.13371i
$479$			597.538i			1.24747i	0.781636	+	0.623735i	$0.214385\pi$
$479$			597.538i			1.24747i	−0.781636	+	0.623735i	$0.785615\pi$
$480$	10.2493	+	3.42118i	0.0213528	+	0.00712745i
$481$	758.081			1.57605
$482$	415.806	+	165.400i	0.862668	+	0.343154i
$483$	−4.32056			−0.00894526
$484$	−326.824	−	308.884i	−0.675255	−	0.638189i
$485$		−	561.705i		−	1.15815i
$486$	43.9389	+	17.4781i	0.0904094	+	0.0359632i
$487$		−	345.125i		−	0.708675i	−0.935118	−	0.354337i	$-0.884706\pi$
$487$		−	345.125i		−	0.708675i	0.935118	−	0.354337i	$-0.115294\pi$
$488$	54.2689	−	25.2193i	0.111207	−	0.0516789i
$489$	16.6637			0.0340770
$490$	−17.9324	+	45.0809i	−0.0365967	+	0.0920019i
$491$	373.498			0.760689			0.380344	−	0.924845i	$-0.375805\pi$
$491$	373.498			0.760689			0.380344	+	0.924845i	$0.375805\pi$
$492$	12.9949	+	12.2816i	0.0264123	+	0.0249625i
$493$			390.896i			0.792892i
$494$	114.680	−	288.299i	0.232146	−	0.583602i
$495$		−	91.2464i		−	0.184336i
$496$	−717.133	+	40.5082i	−1.44583	+	0.0816698i
$497$	341.796			0.687718
$498$	−19.8583	−	7.89927i	−0.0398761	−	0.0158620i
$499$	−850.317			−1.70404			−0.852021	−	0.523508i	$-0.824623\pi$
$499$	−850.317			−1.70404			−0.852021	+	0.523508i	$0.824623\pi$
$500$	361.724	−	382.733i	0.723448	−	0.765466i
$501$			11.7564i			0.0234659i
$502$	−577.219	−	229.607i	−1.14984	−	0.457384i
$503$			459.256i			0.913033i	0.889715	+	0.456517i	$0.150903\pi$
$503$			459.256i			0.913033i	−0.889715	+	0.456517i	$0.849097\pi$
$504$	172.570	−	80.1948i	0.342400	−	0.159117i
$505$	370.206			0.733082
$506$	36.2840	−	91.2159i	0.0717075	−	0.180269i
$507$	−19.2975			−0.0380620
$508$	−422.174	+	446.694i	−0.831050	+	0.879318i
$509$			673.910i			1.32399i	0.749509	+	0.661994i	$0.230290\pi$
$509$			673.910i			1.32399i	−0.749509	+	0.661994i	$0.769710\pi$
$510$	−3.59182	+	9.02963i	−0.00704279	+	0.0177052i
$511$		−	48.3785i		−	0.0946742i
$512$	−494.028	−	134.463i	−0.964898	−	0.262623i
$513$	−14.1943			−0.0276691
$514$	326.092	+	129.713i	0.634419	+	0.252360i
$515$	438.820			0.852078
$516$	17.2881	+	16.3391i	0.0335041	+	0.0316650i
$517$			135.536i			0.262159i
$518$	−194.551	−	77.3888i	−0.375581	−	0.149399i
$519$		−	10.5562i		−	0.0203394i
$520$	−223.841	−	481.678i	−0.430463	−	0.926304i
$521$	−486.473			−0.933729			−0.466864	−	0.884329i	$-0.654616\pi$
$521$	−486.473			−0.933729			−0.466864	+	0.884329i	$0.654616\pi$
$522$	−180.538	+	453.863i	−0.345859	+	0.869469i
$523$	−680.087			−1.30036			−0.650179	−	0.759781i	$-0.725306\pi$
$523$	−680.087			−1.30036			−0.650179	+	0.759781i	$0.725306\pi$
$524$	179.847	+	169.975i	0.343219	+	0.324379i
$525$			3.34886i			0.00637878i
$526$	−230.732	+	580.048i	−0.438655	+	1.10275i
$527$		−	645.988i		−	1.22578i
$528$	−0.257491	−	4.55847i	−0.000487673	−	0.00863347i
$529$	248.109			0.469015
$530$	62.4322	+	24.8344i	0.117797	+	0.0468573i
$531$	1029.90			1.93954
$532$	−58.8622	+	62.2809i	−0.110643	+	0.117069i
$533$		−	878.931i		−	1.64903i
$534$	−14.6518	−	5.82820i	−0.0274378	−	0.0109142i
$535$		−	301.562i		−	0.563668i
$536$	−40.6559	−	87.4868i	−0.0758507	−	0.163222i
$537$	−15.7299			−0.0292922
$538$	−105.574	+	265.407i	−0.196234	+	0.493321i
$539$	20.5006			0.0380346
$540$	−16.6904	+	17.6598i	−0.0309082	+	0.0327034i
$541$			794.999i			1.46950i	0.678339	+	0.734749i	$0.262700\pi$
$541$			794.999i			1.46950i	−0.678339	+	0.734749i	$0.737300\pi$
$542$	196.721	−	494.544i	0.362953	−	0.912444i
$543$		−	0.696375i		−	0.00128246i
$544$	145.796	−	436.781i	0.268006	−	0.802907i
$545$	−658.167			−1.20765
$546$	9.17840	+	3.65100i	0.0168103	+	0.00668681i
$547$	−736.752			−1.34690			−0.673448	−	0.739235i	$-0.735187\pi$
$547$	−736.752			−1.34690			−0.673448	+	0.739235i	$0.735187\pi$
$548$	307.986	+	291.080i	0.562018	+	0.531168i
$549$			67.2518i			0.122499i
$550$	−70.7013	−	28.1237i	−0.128548	−	0.0511340i
$551$		−	219.966i		−	0.399212i
$552$	−11.8474	+	5.50559i	−0.0214626	+	0.00997389i
$553$	112.754			0.203894
$554$	−271.104	+	681.540i	−0.489357	+	1.23022i
$555$	13.3609			0.0240737
$556$	−538.927	−	509.344i	−0.969294	−	0.916087i
$557$			415.758i			0.746423i	0.927746	+	0.373212i	$0.121743\pi$
$557$			415.758i			0.746423i	−0.927746	+	0.373212i	$0.878257\pi$
$558$	298.355	−	750.047i	0.534686	−	1.34417i
$559$		−	1169.31i		−	2.09179i
$560$	8.27338	+	146.467i	0.0147739	+	0.261548i
$561$	4.10624			0.00731950
$562$	274.995	+	109.388i	0.489316	+	0.194641i
$563$	−96.4996			−0.171402			−0.0857012	−	0.996321i	$-0.527313\pi$
$563$	−96.4996			−0.171402			−0.0857012	+	0.996321i	$0.527313\pi$
$564$	12.3893	−	13.1089i	0.0219669	−	0.0232428i
$565$			139.259i			0.246476i
$566$	609.060	+	242.273i	1.07608	+	0.428044i
$567$			213.628i			0.376769i
$568$	937.235	−	435.542i	1.65006	−	0.766800i
$569$	347.953			0.611517			0.305759	−	0.952109i	$-0.401090\pi$
$569$	347.953			0.611517			0.305759	+	0.952109i	$0.401090\pi$
$570$	2.02120	−	5.08118i	0.00354596	−	0.00891435i
$571$	−13.7251			−0.0240370			−0.0120185	−	0.999928i	$-0.503826\pi$
$571$	−13.7251			−0.0240370			−0.0120185	+	0.999928i	$0.503826\pi$
$572$	−154.160	+	163.114i	−0.269511	+	0.285164i
$573$		−	7.14193i		−	0.0124641i
$574$	−89.7259	+	225.566i	−0.156317	+	0.392972i
$575$			217.718i			0.378641i
$576$	371.012	−	439.803i	0.644118	−	0.763547i
$577$	−827.320			−1.43383			−0.716915	−	0.697161i	$-0.754446\pi$
$577$	−827.320			−1.43383			−0.716915	+	0.697161i	$0.754446\pi$
$578$	−152.266	−	60.5686i	−0.263436	−	0.104790i
$579$	−8.28898			−0.0143160
$580$	−273.671	−	258.649i	−0.471847	−	0.445946i
$581$		−	290.160i		−	0.499414i
$582$	29.3495	+	11.6747i	0.0504286	+	0.0200596i
$583$		−	28.3911i		−	0.0486983i
$584$	−61.6476	−	132.658i	−0.105561	−	0.227155i
$585$	596.912			1.02036
$586$	−192.111	+	482.955i	−0.327834	+	0.824156i
$587$	−675.987			−1.15160			−0.575798	−	0.817592i	$-0.695308\pi$
$587$	−675.987			−1.15160			−0.575798	+	0.817592i	$0.695308\pi$
$588$	−1.98280	−	1.87396i	−0.00337211	−	0.00318700i
$589$			363.512i			0.617169i
$590$	−293.460	+	737.743i	−0.497391	+	1.25041i
$591$			13.6860i			0.0231573i
$592$	−632.092	+	35.7046i	−1.06772	+	0.0603118i
$593$	−414.116			−0.698341			−0.349171	−	0.937059i	$-0.613537\pi$
$593$	−414.116			−0.698341			−0.349171	+	0.937059i	$0.613537\pi$
$594$	9.54041	+	3.79500i	0.0160613	+	0.00638889i
$595$	−131.936			−0.221742
$596$	−130.258	+	137.824i	−0.218554	+	0.231248i
$597$		−	13.9414i		−	0.0233525i
$598$	596.712	+	237.361i	0.997847	+	0.396925i
$599$		−	723.303i		−	1.20752i	−0.797167	−	0.603759i	$-0.793669\pi$
$599$		−	723.303i		−	1.20752i	0.797167	−	0.603759i	$-0.206331\pi$
$600$	4.26738	+	9.18289i	0.00711229	+	0.0153048i
$601$	68.7503			0.114393			0.0571966	−	0.998363i	$-0.481784\pi$
$601$	68.7503			0.114393			0.0571966	+	0.998363i	$0.481784\pi$
$602$	−119.370	+	300.088i	−0.198288	+	0.498485i
$603$	108.416			0.179795
$604$	−314.798	+	333.082i	−0.521189	+	0.551460i
$605$			389.599i			0.643965i
$606$	−7.69450	+	19.3435i	−0.0126972	+	0.0319200i
$607$		−	141.263i		−	0.232724i	−0.993207	−	0.116362i	$-0.962877\pi$
$607$		−	141.263i		−	0.232724i	0.993207	−	0.116362i	$-0.0371232\pi$
$608$	−82.0424	+	245.787i	−0.134938	+	0.404255i
$609$	7.00292			0.0114990
$610$	−48.1742	−	19.1628i	−0.0789742	−	0.0314145i
$611$	−886.646			−1.45114
$612$	376.093	+	355.449i	0.614532	+	0.580799i
$613$		−	96.7370i		−	0.157809i	−0.996882	−	0.0789046i	$-0.974858\pi$
$613$		−	96.7370i		−	0.157809i	0.996882	−	0.0789046i	$-0.0251422\pi$
$614$	539.787	+	214.717i	0.879131	+	0.349702i
$615$		−	15.4909i		−	0.0251884i
$616$	56.2146	−	26.1235i	0.0912575	−	0.0424082i
$617$	580.418			0.940709			0.470355	−	0.882478i	$-0.344126\pi$
$617$	580.418			0.940709			0.470355	+	0.882478i	$0.344126\pi$
$618$	−9.12060	+	22.9287i	−0.0147582	+	0.0371014i
$619$	157.945			0.255161			0.127581	−	0.991828i	$-0.459279\pi$
$619$	157.945			0.255161			0.127581	+	0.991828i	$0.459279\pi$
$620$	452.264	+	427.439i	0.729459	+	0.689417i
$621$		−	29.3788i		−	0.0473089i
$622$	55.3740	−	139.207i	0.0890257	−	0.223806i
$623$		−	214.084i		−	0.343634i
$624$	29.8204	−	1.68445i	0.0477891	−	0.00269943i
$625$	−131.484			−0.210375
$626$	528.720	+	210.315i	0.844601	+	0.335967i
$627$	−2.31067			−0.00368528
$628$	808.030	−	854.961i	1.28667	−	1.36140i
$629$		−	569.384i		−	0.905221i
$630$	−153.189	−	60.9358i	−0.243157	−	0.0967235i
$631$		−	771.793i		−	1.22313i	−0.791195	−	0.611564i	$-0.790541\pi$
$631$		−	771.793i		−	1.22313i	0.791195	−	0.611564i	$-0.209459\pi$
$632$	309.181	−	143.679i	0.489210	−	0.227341i
$633$	−10.9085			−0.0172330
$634$	−9.06523	+	22.7895i	−0.0142985	+	0.0359455i
$635$	532.493			0.838571
$636$	−2.59523	+	2.74596i	−0.00408055	+	0.00431755i
$637$			134.110i			0.210534i
$638$	−58.8104	+	147.846i	−0.0921793	+	0.231733i
$639$			1161.45i			1.81761i
$640$	209.326	+	391.083i	0.327072	+	0.611068i
$641$	−586.903			−0.915605			−0.457802	−	0.889054i	$-0.651363\pi$
$641$	−586.903			−0.915605			−0.457802	+	0.889054i	$0.651363\pi$
$642$	15.7568	+	6.26778i	0.0245434	+	0.00976290i
$643$	865.328			1.34577			0.672883	−	0.739749i	$-0.265056\pi$
$643$	865.328			1.34577			0.672883	+	0.739749i	$0.265056\pi$
$644$	−128.907	−	121.831i	−0.200166	−	0.189179i
$645$		−	20.6087i		−	0.0319515i
$646$	−216.538	−	86.1347i	−0.335197	−	0.133335i
$647$			132.883i			0.205383i	0.994713	+	0.102691i	$0.0327454\pi$
$647$			132.883i			0.205383i	−0.994713	+	0.102691i	$0.967255\pi$
$648$	272.221	+	585.788i	0.420094	+	0.903993i
$649$	335.489			0.516933
$650$	183.978	−	462.511i	0.283044	−	0.711555i
$651$	−11.5729			−0.0177771
$652$	497.173	+	469.882i	0.762535	+	0.720677i
$653$		−	364.309i		−	0.557900i	−0.960306	−	0.278950i	$-0.910014\pi$
$653$		−	364.309i		−	0.557900i	0.960306	−	0.278950i	$-0.0899865\pi$
$654$	13.6796	−	34.3897i	0.0209168	−	0.0525836i
$655$		−	214.391i		−	0.327315i
$656$	41.3964	+	732.858i	0.0631043	+	1.11716i
$657$	164.395			0.250220
$658$	227.546	+	90.5134i	0.345814	+	0.137558i
$659$	−18.8972			−0.0286756			−0.0143378	−	0.999897i	$-0.504564\pi$
$659$	−18.8972			−0.0286756			−0.0143378	+	0.999897i	$0.504564\pi$
$660$	−2.71702	+	2.87483i	−0.00411670	+	0.00435580i
$661$			339.106i			0.513019i	0.966542	+	0.256510i	$0.0825725\pi$
$661$			339.106i			0.513019i	−0.966542	+	0.256510i	$0.917427\pi$
$662$	361.390	+	143.754i	0.545906	+	0.217151i
$663$			26.8620i			0.0405159i
$664$	−369.744	−	795.645i	−0.556843	−	1.19826i
$665$	74.2436			0.111644
$666$	262.974	−	661.102i	0.394856	−	0.992646i
$667$	455.278			0.682576
$668$	−331.508	+	350.762i	−0.496269	+	0.525092i
$669$			30.3454i			0.0453594i
$670$	−30.8923	+	77.6616i	−0.0461080	+	0.115913i
$671$			21.9073i			0.0326487i
$672$	−7.82496	−	2.61193i	−0.0116443	−	0.00388680i
$673$	674.869			1.00278			0.501389	−	0.865222i	$-0.332823\pi$
$673$	674.869			1.00278			0.501389	+	0.865222i	$0.332823\pi$
$674$	1.10773	+	0.440635i	0.00164352	+	0.000653762i
$675$	−22.7715			−0.0337355
$676$	−575.754	−	544.149i	−0.851706	−	0.804954i
$677$		−	988.747i		−	1.46048i	−0.683189	−	0.730242i	$-0.739407\pi$
$677$		−	988.747i		−	1.46048i	0.683189	−	0.730242i	$-0.260593\pi$
$678$	−7.27639	−	2.89441i	−0.0107321	−	0.00426905i
$679$			428.839i			0.631575i
$680$	−361.782	+	168.123i	−0.532032	+	0.247240i
$681$	7.24520			0.0106391
$682$	97.1892	−	244.328i	0.142506	−	0.358252i
$683$	−518.125			−0.758602			−0.379301	−	0.925273i	$-0.623835\pi$
$683$	−518.125			−0.758602			−0.379301	+	0.925273i	$0.623835\pi$
$684$	−211.636	−	200.019i	−0.309410	−	0.292426i
$685$		−	367.143i		−	0.535975i
$686$	13.6907	−	34.4175i	0.0199572	−	0.0501713i
$687$		−	7.62646i		−	0.0111011i
$688$	55.0730	+	974.980i	0.0800480	+	1.41712i
$689$	185.728			0.269562
$690$	10.5169	+	4.18341i	0.0152418	+	0.00606291i
$691$	−617.021			−0.892940			−0.446470	−	0.894799i	$-0.647319\pi$
$691$	−617.021			−0.892940			−0.446470	+	0.894799i	$0.647319\pi$
$692$	297.662	−	314.951i	0.430148	−	0.455131i
$693$			69.6630i			0.100524i
$694$	−380.718	−	151.443i	−0.548585	−	0.218217i
$695$			642.442i			0.924377i
$696$	19.2026	−	8.92365i	0.0275900	−	0.0128213i
$697$	−660.153			−0.947135
$698$	94.9140	−	238.608i	0.135980	−	0.341846i
$699$	9.06718			0.0129717
$700$	−94.4311	+	99.9157i	−0.134902	+	0.142737i
$701$		−	97.6954i		−	0.139366i	−0.997569	−	0.0696829i	$-0.977801\pi$
$701$		−	97.6954i		−	0.139366i	0.997569	−	0.0696829i	$-0.0221987\pi$
$702$	−24.8260	+	62.4110i	−0.0353646	+	0.0889046i
$703$			320.405i			0.455768i
$704$	120.857	−	143.266i	0.171672	−	0.203503i
$705$	−15.6268			−0.0221657
$706$	−354.654	−	141.075i	−0.502343	−	0.199823i
$707$	−282.638			−0.399771
$708$	−32.4482	−	30.6670i	−0.0458308	−	0.0433150i
$709$			1249.74i			1.76269i	0.472476	+	0.881343i	$0.343360\pi$
$709$			1249.74i			1.76269i	−0.472476	+	0.881343i	$0.656640\pi$
$710$	−831.979	−	330.946i	−1.17180	−	0.466121i
$711$			383.147i			0.538885i
$712$	−272.802	−	587.038i	−0.383149	−	0.824492i
$713$	−752.386			−1.05524
$714$	2.74221	−	6.89377i	0.00384064	−	0.00965514i
$715$	194.444			0.271950
$716$	−469.314	−	443.552i	−0.655466	−	0.619486i
$717$		−	28.4130i		−	0.0396277i
$718$	−159.454	+	400.859i	−0.222081	+	0.558299i
$719$		−	424.744i		−	0.590743i	−0.955382	−	0.295372i	$-0.904557\pi$
$719$		−	424.744i		−	0.590743i	0.955382	−	0.295372i	$-0.0954435\pi$
$720$	−497.708	+	28.1137i	−0.691261	+	0.0390468i
$721$	−335.022			−0.464663
$722$	−549.022	−	218.391i	−0.760418	−	0.302480i
$723$	21.8012			0.0301538
$724$	19.6364	−	20.7768i	0.0271220	−	0.0286973i
$725$		−	352.886i		−	0.486739i
$726$	−20.3568	−	8.09756i	−0.0280397	−	0.0111537i
$727$		−	79.1445i		−	0.108865i	−0.998517	−	0.0544323i	$-0.982665\pi$
$727$		−	79.1445i		−	0.108865i	0.998517	−	0.0544323i	$-0.0173349\pi$
$728$	170.893	+	367.742i	0.234744	+	0.505141i
$729$	−724.390			−0.993676
$730$	−46.8428	+	117.760i	−0.0641683	+	0.161315i
$731$	−878.255			−1.20144
$732$	2.00254	−	2.11885i	0.00273571	−	0.00289460i
$733$		−	663.766i		−	0.905548i	−0.891625	−	0.452774i	$-0.850434\pi$
$733$		−	663.766i		−	0.905548i	0.891625	−	0.452774i	$-0.149566\pi$
$734$	336.192	−	845.167i	0.458027	−	1.15145i
$735$			2.36365i			0.00321584i
$736$	−508.721	−	169.809i	−0.691198	−	0.230718i
$737$	35.3167			0.0479196
$738$	−766.493	−	304.897i	−1.03861	−	0.413139i
$739$	832.112			1.12600			0.562998	−	0.826458i	$-0.309648\pi$
$739$	832.112			1.12600			0.562998	+	0.826458i	$0.309648\pi$
$740$	398.633	+	376.751i	0.538693	+	0.509123i
$741$		−	15.1159i		−	0.0203993i
$742$	−47.6645	−	18.9601i	−0.0642379	−	0.0255527i
$743$			283.217i			0.381180i	0.981670	+	0.190590i	$0.0610401\pi$
$743$			283.217i			0.381180i	−0.981670	+	0.190590i	$0.938960\pi$
$744$	−31.7340	+	14.7471i	−0.0426532	+	0.0198214i
$745$	164.297			0.220532
$746$	266.674	−	670.404i	0.357472	−	0.898665i
$747$	985.989			1.31993
$748$	122.513	+	115.788i	0.163787	+	0.154796i
$749$			230.231i			0.307385i
$750$	9.48280	−	23.8392i	0.0126437	−	0.0317856i
$751$		−	374.981i		−	0.499309i	−0.968335	−	0.249654i	$-0.919683\pi$
$751$		−	374.981i		−	0.499309i	0.968335	−	0.249654i	$-0.0803170\pi$
$752$	739.290	−	41.7598i	0.983099	−	0.0555316i
$753$	−30.2642			−0.0401916
$754$	−967.173	−	384.723i	−1.28272	−	0.510243i
$755$	397.059			0.525906
$756$	12.7425	−	13.4826i	0.0168551	−	0.0178341i
$757$		−	63.0951i		−	0.0833488i	−0.999131	−	0.0416744i	$-0.986731\pi$
$757$		−	63.0951i		−	0.0833488i	0.999131	−	0.0416744i	$-0.0132692\pi$
$758$	−498.837	−	198.428i	−0.658096	−	0.261779i
$759$		−	4.78255i		−	0.00630113i
$760$	203.583	−	94.6069i	0.267872	−	0.124483i
$761$	467.505			0.614330			0.307165	−	0.951656i	$-0.400620\pi$
$761$	467.505			0.614330			0.307165	+	0.951656i	$0.400620\pi$
$762$	−11.0675	+	27.8231i	−0.0145243	+	0.0365133i
$763$	502.485			0.658564
$764$	201.388	−	213.085i	0.263597	−	0.278907i
$765$		−	448.332i		−	0.586055i
$766$	−429.884	+	1080.70i	−0.561206	+	1.41084i
$767$			2194.69i			2.86140i
$768$	−24.7851	+	2.80900i	−0.0322723	+	0.00365755i
$769$	900.573			1.17110			0.585548	−	0.810638i	$-0.300879\pi$
$769$	900.573			1.17110			0.585548	+	0.810638i	$0.300879\pi$
$770$	−49.9014	−	19.8499i	−0.0648070	−	0.0257790i
$771$	17.0974			0.0221756
$772$	−247.308	−	233.732i	−0.320347	−	0.302762i
$773$		−	1222.76i		−	1.58184i	−0.611920	−	0.790919i	$-0.709603\pi$
$773$		−	1222.76i		−	1.58184i	0.611920	−	0.790919i	$-0.290397\pi$
$774$	−1019.73	−	405.629i	−1.31748	−	0.524068i
$775$			583.173i			0.752482i
$776$	546.460	+	1175.92i	0.704201	+	1.51536i
$777$	−10.2005			−0.0131281
$778$	378.689	−	952.003i	0.486747	−	1.22365i
$779$	371.483			0.476872
$780$	−18.8064	−	17.7741i	−0.0241108	−	0.0227873i
$781$			378.344i			0.484435i
$782$	178.279	−	448.182i	0.227978	−	0.573123i
$783$			47.6182i			0.0608151i
$784$	−6.31640	−	111.822i	−0.00805663	−	0.142630i
$785$	−1019.18			−1.29832
$786$	11.2021	+	4.45598i	0.0142520	+	0.00566919i
$787$	862.942			1.09650			0.548248	−	0.836316i	$-0.315295\pi$
$787$	862.942			1.09650			0.548248	+	0.836316i	$0.315295\pi$
$788$	−385.916	+	408.330i	−0.489741	+	0.518186i
$789$			30.4126i			0.0385457i
$790$	−274.458	−	109.174i	−0.347415	−	0.138195i
$791$		−	106.319i		−	0.134411i
$792$	88.7700	+	191.022i	0.112083	+	0.241190i
$793$	−143.312			−0.180722
$794$	60.1175	−	151.132i	0.0757148	−	0.190343i
$795$	3.27339			0.00411747
$796$	393.120	−	415.953i	0.493869	−	0.522554i
$797$			1078.34i			1.35300i	0.736442	+	0.676500i	$0.236504\pi$
$797$			1078.34i			1.35300i	−0.736442	+	0.676500i	$0.763496\pi$
$798$	−1.54311	+	3.87928i	−0.00193372	+	0.00486125i
$799$			665.947i			0.833476i
$800$	−131.619	+	394.309i	−0.164523	+	0.492887i
$801$	727.477			0.908211
$802$	980.180	+	389.898i	1.22217	+	0.486157i
$803$	53.5516			0.0666894
$804$	−3.41579	−	3.22829i	−0.00424850	−	0.00401529i
$805$			153.667i			0.190891i
$806$	1598.33	+	635.788i	1.98305	+	0.788819i
$807$			13.9156i			0.0172436i
$808$	−775.020	+	360.159i	−0.959183	+	0.445741i
$809$	333.388			0.412099			0.206050	−	0.978542i	$-0.433939\pi$
$809$	333.388			0.412099			0.206050	+	0.978542i	$0.433939\pi$
$810$	206.847	−	520.001i	0.255366	−	0.641976i
$811$	−1246.04			−1.53642			−0.768211	−	0.640197i	$-0.778853\pi$
$811$	−1246.04			−1.53642			−0.768211	+	0.640197i	$0.778853\pi$
$812$	208.937	+	197.468i	0.257312	+	0.243187i
$813$		−	25.9295i		−	0.0318936i
$814$	85.6640	−	215.354i	0.105238	−	0.264563i
$815$		−	592.667i		−	0.727199i
$816$	−1.26516	−	22.3977i	−0.00155045	−	0.0274482i
$817$	494.214			0.604913
$818$	−109.036	−	43.3724i	−0.133295	−	0.0530224i
$819$	−455.719			−0.556433
$820$	436.811	−	462.181i	0.532696	−	0.563636i
$821$		−	1458.68i		−	1.77671i	−0.459162	−	0.888353i	$-0.651850\pi$
$821$		−	1458.68i		−	1.77671i	0.459162	−	0.888353i	$-0.348150\pi$
$822$	19.1835	+	7.63083i	0.0233375	+	0.00928324i
$823$		−	464.047i		−	0.563848i	−0.959437	−	0.281924i	$-0.909027\pi$
$823$		−	464.047i		−	0.563848i	0.959437	−	0.281924i	$-0.0909725\pi$
$824$	−918.661	+	426.911i	−1.11488	+	0.518095i
$825$	−3.70695			−0.00449328
$826$	224.045	−	563.237i	0.271241	−	0.681885i
$827$	1077.41			1.30279			0.651394	−	0.758739i	$-0.274184\pi$
$827$	1077.41			1.30279			0.651394	+	0.758739i	$0.274184\pi$
$828$	413.993	−	438.038i	0.499991	−	0.529031i
$829$			35.9354i			0.0433479i	0.999765	+	0.0216740i	$0.00689958\pi$
$829$			35.9354i			0.0433479i	−0.999765	+	0.0216740i	$0.993100\pi$
$830$	−280.949	+	706.290i	−0.338493	+	0.850951i
$831$			35.7339i			0.0430011i
$832$	937.211	+	790.619i	1.12646	+	0.950263i
$833$	100.728			0.120922
$834$	−33.5681	−	13.3528i	−0.0402495	−	0.0160105i
$835$	418.134			0.500760
$836$	−68.9406	−	65.1563i	−0.0824648	−	0.0779381i
$837$		−	78.6932i		−	0.0940181i
$838$	1413.67	+	562.332i	1.68696	+	0.671041i
$839$			734.676i			0.875656i	0.899059	+	0.437828i	$0.144252\pi$
$839$			734.676i			0.875656i	−0.899059	+	0.437828i	$0.855748\pi$
$840$	3.01194	+	6.48134i	0.00358564	+	0.00771588i
$841$	103.069			0.122555
$842$	34.2201	−	86.0274i	0.0406415	−	0.102170i
$843$	14.4183			0.0171036
$844$	−325.462	−	307.597i	−0.385619	−	0.364451i
$845$			686.342i			0.812239i
$846$	−307.573	+	773.221i	−0.363561	+	0.913972i
$847$		−	297.443i		−	0.351173i
$848$	−154.861	+	8.74753i	−0.182619	+	0.0103155i
$849$	31.9337			0.0376133
$850$	−347.386	−	138.184i	−0.408689	−	0.162569i
$851$	−663.164			−0.779276
$852$	34.5843	−	36.5930i	0.0405919	−	0.0429495i
$853$			402.566i			0.471942i	0.971760	+	0.235971i	$0.0758270\pi$
$853$			402.566i			0.471942i	−0.971760	+	0.235971i	$0.924173\pi$
$854$	36.7791	+	14.6301i	0.0430669	+	0.0171312i
$855$			252.287i			0.295072i
$856$	293.378	+	631.315i	0.342731	+	0.737517i
$857$	552.003			0.644110			0.322055	−	0.946721i	$-0.395626\pi$
$857$	552.003			0.644110			0.322055	+	0.946721i	$0.395626\pi$
$858$	−4.04140	+	10.1598i	−0.00471025	+	0.0118413i
$859$	−330.117			−0.384303			−0.192152	−	0.981365i	$-0.561547\pi$
$859$	−330.117			−0.384303			−0.192152	+	0.981365i	$0.561547\pi$
$860$	581.125	−	614.877i	0.675727	−	0.714973i
$861$			11.8267i			0.0137360i
$862$	248.510	−	624.740i	0.288295	−	0.724757i
$863$		−	1116.67i		−	1.29394i	−0.762516	−	0.646969i	$-0.776036\pi$
$863$		−	1116.67i		−	1.29394i	0.762516	−	0.646969i	$-0.223964\pi$
$864$	17.7605	−	53.2079i	0.0205562	−	0.0615833i
$865$	−375.445			−0.434041
$866$	−692.604	−	275.505i	−0.799774	−	0.318135i
$867$	−7.98348			−0.00920817
$868$	−345.286	−	326.333i	−0.397795	−	0.375959i
$869$			124.810i			0.143625i
$870$	−17.0461	−	6.78062i	−0.0195932	−	0.00779382i
$871$			231.033i			0.265251i
$872$	1377.86	−	640.305i	1.58011	−	0.734294i
$873$	−1457.24			−1.66923
$874$	−100.321	+	252.202i	−0.114784	+	0.288561i
$875$	348.326			0.398087
$876$	−5.17945	−	4.89514i	−0.00591262	−	0.00558806i
$877$			0.747441i			0.000852270i	1.00000		0.000426135i	$0.000135643\pi$
$877$			0.747441i			0.000852270i	−1.00000		0.000426135i	$0.999864\pi$
$878$	−293.826	+	738.662i	−0.334654	+	0.841301i
$879$			25.3219i			0.0288076i
$880$	−162.129	+	9.15805i	−0.184237	+	0.0104069i
$881$	−247.826			−0.281301			−0.140650	−	0.990059i	$-0.544919\pi$
$881$	−247.826			−0.281301			−0.140650	+	0.990059i	$0.544919\pi$
$882$	116.954	+	46.5221i	0.132601	+	0.0527462i
$883$	−1613.74			−1.82757			−0.913784	−	0.406200i	$-0.866854\pi$
$883$	−1613.74			−1.82757			−0.913784	+	0.406200i	$0.866854\pi$
$884$	−757.454	+	801.448i	−0.856849	+	0.906615i
$885$			38.6807i			0.0437070i
$886$	508.321	+	202.201i	0.573726	+	0.228217i
$887$		−	1110.59i		−	1.25207i	−0.779795	−	0.626034i	$-0.784677\pi$
$887$		−	1110.59i		−	1.25207i	0.779795	−	0.626034i	$-0.215323\pi$
$888$	−27.9708	+	12.9983i	−0.0314987	+	0.0146377i
$889$	−406.537			−0.457297
$890$	−207.288	+	521.111i	−0.232908	+	0.585518i
$891$	−236.471			−0.265400
$892$	−855.680	+	905.378i	−0.959282	+	1.01500i
$893$		−	374.744i		−	0.419646i
$894$	−3.41480	+	8.58461i	−0.00381969	+	0.00960247i
$895$			559.458i			0.625092i
$896$	−159.812	−	298.577i	−0.178362	−	0.333233i
$897$	31.2863			0.0348788
$898$	796.687	+	316.907i	0.887179	+	0.352904i
$899$	1219.49			1.35650
$900$	−339.523	−	320.885i	−0.377247	−	0.356539i
$901$		−	139.498i		−	0.154825i
$902$	−249.685	−	99.3202i	−0.276813	−	0.110111i
$903$			15.7340i			0.0174241i
$904$	−135.480	−	291.536i	−0.149867	−	0.322496i
$905$	−24.7676			−0.0273675
$906$	−8.25262	+	20.7466i	−0.00910885	+	0.0228991i
$907$	−518.009			−0.571123			−0.285562	−	0.958360i	$-0.592180\pi$
$907$	−518.009			−0.571123			−0.285562	+	0.958360i	$0.592180\pi$
$908$	216.166	+	204.300i	0.238068	+	0.225000i
$909$		−	960.430i		−	1.05658i
$910$	129.853	−	326.443i	0.142696	−	0.358729i
$911$		−	1065.61i		−	1.16972i	−0.811135	−	0.584860i	$-0.801150\pi$
$911$		−	1065.61i		−	1.16972i	0.811135	−	0.584860i	$-0.198850\pi$
$912$	0.711936	+	12.6037i	0.000780632	+	0.0138198i
$913$	321.186			0.351792
$914$	18.6767	+	7.42923i	0.0204340	+	0.00812826i
$915$	−2.52583			−0.00276047
$916$	215.051	−	227.541i	0.234772	−	0.248407i
$917$			163.679i			0.178494i
$918$	46.8761	+	18.6464i	0.0510632	+	0.0203120i
$919$		−	1183.66i		−	1.28799i	−0.765030	−	0.643994i	$-0.777276\pi$
$919$		−	1183.66i		−	1.28799i	0.765030	−	0.643994i	$-0.222724\pi$
$920$	195.814	+	421.369i	0.212842	+	0.458010i
$921$	28.3016			0.0307292
$922$	−610.454	+	1534.65i	−0.662098	+	1.66448i
$923$	−2475.03			−2.68151
$924$	2.07434	−	2.19482i	0.00224496	−	0.00237534i
$925$			514.018i			0.555695i
$926$	−84.7946	+	213.169i	−0.0915708	+	0.230204i
$927$		−	1138.43i		−	1.22809i
$928$	824.554	+	275.232i	0.888528	+	0.296586i
$929$	−379.019			−0.407986			−0.203993	−	0.978972i	$-0.565392\pi$
$929$	−379.019			−0.407986			−0.203993	+	0.978972i	$0.565392\pi$
$930$	28.1701	+	11.2055i	0.0302904	+	0.0120490i
$931$	−56.6821			−0.0608830
$932$	270.526	+	255.676i	0.290264	+	0.274331i
$933$		−	7.29878i		−	0.00782292i
$934$	−374.884	−	149.122i	−0.401375	−	0.159660i
$935$		−	146.044i		−	0.156197i
$936$	−1249.62	+	580.712i	−1.33507	+	0.620418i
$937$	1316.09			1.40458			0.702289	−	0.711892i	$-0.252161\pi$
$937$	1316.09			1.40458			0.702289	+	0.711892i	$0.252161\pi$
$938$	23.5851	−	59.2916i	0.0251440	−	0.0632106i
$939$	27.7214			0.0295223
$940$	−466.238	−	440.645i	−0.495998	−	0.468771i
$941$		−	497.031i		−	0.528194i	−0.964496	−	0.264097i	$-0.914926\pi$
$941$		−	497.031i		−	0.528194i	0.964496	−	0.264097i	$-0.0850739\pi$
$942$	21.1830	−	53.2528i	0.0224872	−	0.0565316i
$943$			768.883i			0.815359i
$944$	−103.367	−	1829.95i	−0.109499	−	1.93850i
$945$	−16.0723			−0.0170077
$946$	−332.176	−	132.134i	−0.351138	−	0.139676i
$947$	808.487			0.853735			0.426867	−	0.904314i	$-0.359617\pi$
$947$	808.487			0.853735			0.426867	+	0.904314i	$0.359617\pi$
$948$	11.4089	−	12.0715i	0.0120347	−	0.0127337i
$949$			350.322i			0.369148i
$950$	195.482	+	77.7590i	0.205770	+	0.0818516i
$951$			1.19488i			0.00125644i
$952$	276.206	−	128.356i	0.290133	−	0.134827i
$953$	−1345.58			−1.41194			−0.705969	−	0.708243i	$-0.749488\pi$
$953$	−1345.58			−1.41194			−0.705969	+	0.708243i	$0.749488\pi$
$954$	64.4281	−	161.968i	0.0675347	−	0.169778i
$955$	−254.013			−0.265982
$956$	801.190	−	847.723i	0.838064	−	0.886740i
$957$			7.75173i			0.00810004i
$958$	−441.715	+	1110.45i	−0.461081	+	1.15913i
$959$			280.299i			0.292283i
$960$	16.5180	+	13.9344i	0.0172063	+	0.0145150i
$961$	−1054.32			−1.09710
$962$	1408.80	+	560.393i	1.46444	+	0.582529i
$963$	−782.346			−0.812405
$964$	650.454	+	614.749i	0.674745	+	0.637707i
$965$			294.809i			0.305502i
$966$	−8.02920	−	3.19387i	−0.00831181	−	0.00330628i
$967$		−	140.279i		−	0.145066i	−0.997366	−	0.0725330i	$-0.976892\pi$
$967$		−	140.279i		−	0.145066i	0.997366	−	0.0725330i	$-0.0231083\pi$
$968$	−379.025	−	815.617i	−0.391555	−	0.842579i
$969$	−11.3533			−0.0117165
$970$	415.227	−	1043.86i	0.428069	−	1.07614i
$971$	1438.67			1.48164			0.740820	−	0.671704i	$-0.234437\pi$
$971$	1438.67			1.48164			0.740820	+	0.671704i	$0.234437\pi$
$972$	68.7346	+	64.9616i	0.0707146	+	0.0668330i
$973$		−	490.479i		−	0.504090i
$974$	255.125	−	641.370i	0.261935	−	0.658491i
$975$		−	24.2500i		−	0.0248718i
$976$	119.495	−	6.74981i	0.122433	−	0.00691579i
$977$	902.190			0.923428			0.461714	−	0.887029i	$-0.347235\pi$
$977$	902.190			0.923428			0.461714	+	0.887029i	$0.347235\pi$
$978$	30.9673	+	12.3182i	0.0316639	+	0.0125953i
$979$	236.976			0.242059
$980$	−66.6500	+	70.5211i	−0.0680102	+	0.0719603i
$981$			1707.49i			1.74056i
$982$	694.098	+	276.100i	0.706821	+	0.281160i
$983$		−	503.193i		−	0.511896i	−0.966691	−	0.255948i	$-0.917612\pi$
$983$		−	503.193i		−	0.511896i	0.966691	−	0.255948i	$-0.0823875\pi$
$984$	15.0705	+	32.4298i	0.0153155	+	0.0329571i
$985$	486.761			0.494173
$986$	−288.960	+	726.430i	−0.293063	+	0.736744i
$987$	11.9305			0.0120876
$988$	426.237	−	450.993i	0.431414	−	0.456470i
$989$			1022.91i			1.03428i
$990$	67.4517	−	169.570i	0.0681330	−	0.171282i
$991$		−	906.322i		−	0.914553i	−0.889325	−	0.457277i	$-0.848825\pi$
$991$		−	906.322i		−	0.914553i	0.889325	−	0.457277i	$-0.151175\pi$
$992$	−1362.64	−	454.844i	−1.37363	−	0.458512i
$993$	18.9481			0.0190816
$994$	635.183	+	252.664i	0.639017	+	0.254189i
$995$	−495.847			−0.498339
$996$	−31.0648	−	29.3596i	−0.0311895	−	0.0294775i
$997$			608.625i			0.610457i	0.952279	+	0.305228i	$0.0987328\pi$
$997$			608.625i			0.610457i	−0.952279	+	0.305228i	$0.901267\pi$
$998$	−1580.20	−	628.576i	−1.58337	−	0.629836i
$999$		−	69.3613i		−	0.0694308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.g.b.43.8	yes	8
3.2	odd	2		504.3.g.b.379.1		8
4.3	odd	2		224.3.g.b.15.3		8
7.2	even	3		392.3.k.o.67.4		16
7.3	odd	6		392.3.k.n.275.2		16
7.4	even	3		392.3.k.o.275.2		16
7.5	odd	6		392.3.k.n.67.4		16
7.6	odd	2		392.3.g.m.99.8		8
8.3	odd	2	inner	56.3.g.b.43.7	✓	8
8.5	even	2		224.3.g.b.15.4		8
12.11	even	2		2016.3.g.b.1135.5		8
16.3	odd	4		1792.3.d.j.1023.7		16
16.5	even	4		1792.3.d.j.1023.8		16
16.11	odd	4		1792.3.d.j.1023.10		16
16.13	even	4		1792.3.d.j.1023.9		16
24.5	odd	2		2016.3.g.b.1135.4		8
24.11	even	2		504.3.g.b.379.2		8
28.27	even	2		1568.3.g.m.687.6		8
56.3	even	6		392.3.k.n.275.4		16
56.11	odd	6		392.3.k.o.275.4		16
56.13	odd	2		1568.3.g.m.687.5		8
56.19	even	6		392.3.k.n.67.2		16
56.27	even	2		392.3.g.m.99.7		8
56.51	odd	6		392.3.k.o.67.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.7	✓	8	8.3	odd	2	inner
56.3.g.b.43.8	yes	8	1.1	even	1	trivial
224.3.g.b.15.3		8	4.3	odd	2
224.3.g.b.15.4		8	8.5	even	2
392.3.g.m.99.7		8	56.27	even	2
392.3.g.m.99.8		8	7.6	odd	2
392.3.k.n.67.2		16	56.19	even	6
392.3.k.n.67.4		16	7.5	odd	6
392.3.k.n.275.2		16	7.3	odd	6
392.3.k.n.275.4		16	56.3	even	6
392.3.k.o.67.2		16	56.51	odd	6
392.3.k.o.67.4		16	7.2	even	3
392.3.k.o.275.2		16	7.4	even	3
392.3.k.o.275.4		16	56.11	odd	6
504.3.g.b.379.1		8	3.2	odd	2
504.3.g.b.379.2		8	24.11	even	2
1568.3.g.m.687.5		8	56.13	odd	2
1568.3.g.m.687.6		8	28.27	even	2
1792.3.d.j.1023.7		16	16.3	odd	4
1792.3.d.j.1023.8		16	16.5	even	4
1792.3.d.j.1023.9		16	16.13	even	4
1792.3.d.j.1023.10		16	16.11	odd	4
2016.3.g.b.1135.4		8	24.5	odd	2
2016.3.g.b.1135.5		8	12.11	even	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85837 + 0.739226i) q^{2} +0.0974366 q^{3} +(2.90709 + 2.74751i) q^{4} -3.46547i q^{5} +(0.181073 + 0.0720276i) q^{6} +2.64575i q^{7} +(3.37142 + 7.25490i) q^{8} -8.99051 q^{9} +O(q^{10})\)	\(q+(1.85837 + 0.739226i) q^{2} +0.0974366 q^{3} +(2.90709 + 2.74751i) q^{4} -3.46547i q^{5} +(0.181073 + 0.0720276i) q^{6} +2.64575i q^{7} +(3.37142 + 7.25490i) q^{8} -8.99051 q^{9} +(2.56177 - 6.44013i) q^{10} -2.92866 q^{11} +(0.283257 + 0.267708i) q^{12} -19.1586i q^{13} +(-1.95581 + 4.91679i) q^{14} -0.337664i q^{15} +(0.902343 + 15.9745i) q^{16} -14.3897 q^{17} +(-16.7077 - 6.64602i) q^{18} +8.09744 q^{19} +(9.52143 - 10.0744i) q^{20} +0.257793i q^{21} +(-5.44254 - 2.16494i) q^{22} +16.7598i q^{23} +(0.328500 + 0.706892i) q^{24} +12.9905 q^{25} +(14.1625 - 35.6038i) q^{26} -1.75293 q^{27} +(-7.26924 + 7.69144i) q^{28} -27.1649i q^{29} +(0.249610 - 0.627505i) q^{30} +44.8923i q^{31} +(-10.1319 + 30.3537i) q^{32} -0.285359 q^{33} +(-26.7415 - 10.6373i) q^{34} +9.16878 q^{35} +(-26.1362 - 24.7015i) q^{36} +39.5687i q^{37} +(15.0480 + 5.98584i) q^{38} -1.86675i q^{39} +(25.1416 - 11.6836i) q^{40} +45.8766 q^{41} +(-0.190567 + 0.479075i) q^{42} +61.0334 q^{43} +(-8.51388 - 8.04653i) q^{44} +31.1563i q^{45} +(-12.3893 + 31.1459i) q^{46} -46.2793i q^{47} +(0.0879212 + 1.55650i) q^{48} -7.00000 q^{49} +(24.1412 + 9.60292i) q^{50} -1.40209 q^{51} +(52.6385 - 55.6957i) q^{52} +9.69424i q^{53} +(-3.25760 - 1.29581i) q^{54} +10.1492i q^{55} +(-19.1947 + 8.91994i) q^{56} +0.788986 q^{57} +(20.0810 - 50.4825i) q^{58} -114.554 q^{59} +(0.927735 - 0.981619i) q^{60} -7.48032i q^{61} +(-33.1855 + 83.4265i) q^{62} -23.7866i q^{63} +(-41.2671 + 48.9186i) q^{64} -66.3935 q^{65} +(-0.530302 - 0.210944i) q^{66} -12.0590 q^{67} +(-41.8323 - 39.5360i) q^{68} +1.63302i q^{69} +(17.0390 + 6.77780i) q^{70} -129.187i q^{71} +(-30.3108 - 65.2252i) q^{72} -18.2854 q^{73} +(-29.2502 + 73.5334i) q^{74} +1.26575 q^{75} +(23.5400 + 22.2478i) q^{76} -7.74851i q^{77} +(1.37995 - 3.46911i) q^{78} -42.6168i q^{79} +(55.3593 - 3.12704i) q^{80} +80.7438 q^{81} +(85.2558 + 33.9132i) q^{82} -109.670 q^{83} +(-0.708289 + 0.749427i) q^{84} +49.8673i q^{85} +(113.423 + 45.1174i) q^{86} -2.64685i q^{87} +(-9.87374 - 21.2471i) q^{88} -80.9162 q^{89} +(-23.0316 + 57.9001i) q^{90} +50.6889 q^{91} +(-46.0478 + 48.7223i) q^{92} +4.37415i q^{93} +(34.2109 - 86.0041i) q^{94} -28.0614i q^{95} +(-0.987218 + 2.95756i) q^{96} +162.086 q^{97} +(-13.0086 - 5.17458i) q^{98} +26.3301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) \) 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9	\( 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9} + 16 q^{10} - 32 q^{11} + 30 q^{12} + 7 q^{14} - 71 q^{16} - 80 q^{17} - 29 q^{18} + 56 q^{19} - 108 q^{20} + 66 q^{22} + 22 q^{24} - 16 q^{25} + 24 q^{26} - 32 q^{27} + 7 q^{28} + 96 q^{30} - 19 q^{32} + 32 q^{33} + 74 q^{34} + 56 q^{35} - 33 q^{36} - 14 q^{38} + 84 q^{40} + 128 q^{41} - 98 q^{42} + 50 q^{44} - 152 q^{46} + 134 q^{48} - 56 q^{49} + 33 q^{50} - 368 q^{51} + 132 q^{52} - 228 q^{54} - 49 q^{56} + 56 q^{57} + 24 q^{58} + 104 q^{59} + 192 q^{60} + 120 q^{62} - 55 q^{64} - 72 q^{65} - 276 q^{66} + 304 q^{67} - 190 q^{68} + 56 q^{70} - 209 q^{72} - 112 q^{73} + 8 q^{74} + 72 q^{75} + 70 q^{76} - 304 q^{78} + 124 q^{80} + 48 q^{81} + 450 q^{82} + 72 q^{83} + 42 q^{84} + 210 q^{86} - 486 q^{88} - 512 q^{89} - 184 q^{90} - 56 q^{91} - 472 q^{92} + 472 q^{94} + 558 q^{96} + 64 q^{97} - 7 q^{98} + 256 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9 + 16 * q^10 - 32 * q^11 + 30 * q^12 + 7 * q^14 - 71 * q^16 - 80 * q^17 - 29 * q^18 + 56 * q^19 - 108 * q^20 + 66 * q^22 + 22 * q^24 - 16 * q^25 + 24 * q^26 - 32 * q^27 + 7 * q^28 + 96 * q^30 - 19 * q^32 + 32 * q^33 + 74 * q^34 + 56 * q^35 - 33 * q^36 - 14 * q^38 + 84 * q^40 + 128 * q^41 - 98 * q^42 + 50 * q^44 - 152 * q^46 + 134 * q^48 - 56 * q^49 + 33 * q^50 - 368 * q^51 + 132 * q^52 - 228 * q^54 - 49 * q^56 + 56 * q^57 + 24 * q^58 + 104 * q^59 + 192 * q^60 + 120 * q^62 - 55 * q^64 - 72 * q^65 - 276 * q^66 + 304 * q^67 - 190 * q^68 + 56 * q^70 - 209 * q^72 - 112 * q^73 + 8 * q^74 + 72 * q^75 + 70 * q^76 - 304 * q^78 + 124 * q^80 + 48 * q^81 + 450 * q^82 + 72 * q^83 + 42 * q^84 + 210 * q^86 - 486 * q^88 - 512 * q^89 - 184 * q^90 - 56 * q^91 - 472 * q^92 + 472 * q^94 + 558 * q^96 + 64 * q^97 - 7 * q^98 + 256 * q^99

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