LMFDB - Embedded newform 88.2.g.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(43,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("88.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.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:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.10070523904.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{4} + 16 $ x^8 + 6*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.7
Root			$-1.16342 - 0.804019i$ of defining polynomial
Character	$\chi$	$=$	88.43
Dual form			88.2.g.b.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16342 - 0.804019i) q^{2} +0.414214 q^{3} +(0.707107 - 1.87083i) q^{4} +2.64575i q^{5} +(0.481906 - 0.333036i) q^{6} -3.29066 q^{7} +(-0.681517 - 2.74509i) q^{8} -2.82843 q^{9} +(2.12723 + 3.07813i) q^{10} +(2.41421 - 2.27411i) q^{11} +(0.292893 - 0.774923i) q^{12} +1.36303 q^{13} +(-3.82843 + 2.64575i) q^{14} +1.09591i q^{15} +(-3.00000 - 2.64575i) q^{16} +5.49019i q^{17} +(-3.29066 + 2.27411i) q^{18} +2.27411i q^{19} +(4.94975 + 1.87083i) q^{20} -1.36303 q^{21} +(0.980325 - 4.58682i) q^{22} -6.38741i q^{23} +(-0.282294 - 1.13705i) q^{24} -2.00000 q^{25} +(1.58579 - 1.09591i) q^{26} -2.41421 q^{27} +(-2.32685 + 6.15626i) q^{28} +6.58132 q^{29} +(0.881129 + 1.27500i) q^{30} -1.09591i q^{31} +(-5.61750 - 0.666071i) q^{32} +(1.00000 - 0.941967i) q^{33} +(4.41421 + 6.38741i) q^{34} -8.70626i q^{35} +(-2.00000 + 5.29150i) q^{36} +4.83756i q^{37} +(1.82843 + 2.64575i) q^{38} +0.564588 q^{39} +(7.26283 - 1.80313i) q^{40} -10.0384i q^{41} +(-1.58579 + 1.09591i) q^{42} +6.43215i q^{43} +(-2.54736 - 6.12462i) q^{44} -7.48331i q^{45} +(-5.13560 - 7.43126i) q^{46} +(-1.24264 - 1.09591i) q^{48} +3.82843 q^{49} +(-2.32685 + 1.60804i) q^{50} +2.27411i q^{51} +(0.963811 - 2.55000i) q^{52} -7.48331i q^{53} +(-2.80875 + 1.94107i) q^{54} +(6.01673 + 6.38741i) q^{55} +(2.24264 + 9.03316i) q^{56} +0.941967i q^{57} +(7.65685 - 5.29150i) q^{58} +3.24264 q^{59} +(2.05025 + 0.774923i) q^{60} -6.58132 q^{61} +(-0.881129 - 1.27500i) q^{62} +9.30739 q^{63} +(-7.07107 + 3.74166i) q^{64} +3.60625i q^{65} +(0.406064 - 1.89993i) q^{66} -6.07107 q^{67} +(10.2712 + 3.88215i) q^{68} -2.64575i q^{69} +(-7.00000 - 10.1291i) q^{70} +6.38741i q^{71} +(1.92762 + 7.76429i) q^{72} +0.941967i q^{73} +(3.88949 + 5.62813i) q^{74} -0.828427 q^{75} +(4.25447 + 1.60804i) q^{76} +(-7.94435 + 7.48331i) q^{77} +(0.656854 - 0.453939i) q^{78} -9.30739 q^{79} +(7.00000 - 7.93725i) q^{80} +7.48528 q^{81} +(-8.07107 - 11.6789i) q^{82} +4.54822i q^{83} +(-0.963811 + 2.55000i) q^{84} -14.5257 q^{85} +(5.17157 + 7.48331i) q^{86} +2.72607 q^{87} +(-7.88797 - 5.07739i) q^{88} -10.6569 q^{89} +(-6.01673 - 8.70626i) q^{90} -4.48528 q^{91} +(-11.9497 - 4.51658i) q^{92} -0.453939i q^{93} -6.01673 q^{95} +(-2.32685 - 0.275896i) q^{96} +7.48528 q^{97} +(4.45408 - 3.07813i) q^{98} +(-6.82843 + 6.43215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 8 q^{11} + 8 q^{12} - 8 q^{14} - 24 q^{16} + 8 q^{22} - 16 q^{25} + 24 q^{26} - 8 q^{27} + 8 q^{33} + 24 q^{34} - 16 q^{36} - 8 q^{38} - 24 q^{42} + 8 q^{44} + 24 q^{48} + 8 q^{49} - 16 q^{56}+ \cdots - 32 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 8 * q^11 + 8 * q^12 - 8 * q^14 - 24 * q^16 + 8 * q^22 - 16 * q^25 + 24 * q^26 - 8 * q^27 + 8 * q^33 + 24 * q^34 - 16 * q^36 - 8 * q^38 - 24 * q^42 + 8 * q^44 + 24 * q^48 + 8 * q^49 - 16 * q^56 + 16 * q^58 - 8 * q^59 + 56 * q^60 - 40 * q^66 + 8 * q^67 - 56 * q^70 + 16 * q^75 - 40 * q^78 + 56 * q^80 - 8 * q^81 - 8 * q^82 + 64 * q^86 - 16 * q^88 - 40 * q^89 + 32 * q^91 - 56 * q^92 - 8 * q^97 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.16342	−	0.804019i	0.822664	−	0.568527i
$2$	1.16342	−	0.804019i	0.822664	−	0.568527i
$3$	0.414214			0.239146			0.119573	−	0.992825i	$-0.461847\pi$
$3$	0.414214			0.239146			0.119573	+	0.992825i	$0.461847\pi$
$4$	0.707107	−	1.87083i	0.353553	−	0.935414i
$5$			2.64575i			1.18322i	0.806226	+	0.591608i	$0.201507\pi$
$5$			2.64575i			1.18322i	−0.806226	+	0.591608i	$0.798493\pi$
$6$	0.481906	−	0.333036i	0.196737	−	0.135961i
$7$	−3.29066			−1.24375			−0.621876	−	0.783116i	$-0.713629\pi$
$7$	−3.29066			−1.24375			−0.621876	+	0.783116i	$0.713629\pi$
$8$	−0.681517	−	2.74509i	−0.240953	−	0.970537i
$9$	−2.82843			−0.942809
$10$	2.12723	+	3.07813i	0.672691	+	0.973390i
$11$	2.41421	−	2.27411i	0.727913	−	0.685670i
$11$	2.41421	−	2.27411i	0.727913	−	0.685670i
$12$	0.292893	−	0.774923i	0.0845510	−	0.223701i
$13$	1.36303			0.378038			0.189019	−	0.981973i	$-0.439469\pi$
$13$	1.36303			0.378038			0.189019	+	0.981973i	$0.439469\pi$
$14$	−3.82843	+	2.64575i	−1.02319	+	0.707107i
$15$			1.09591i			0.282962i
$16$	−3.00000	−	2.64575i	−0.750000	−	0.661438i
$17$			5.49019i			1.33157i	0.746146	+	0.665783i	$0.231902\pi$
$17$			5.49019i			1.33157i	−0.746146	+	0.665783i	$0.768098\pi$
$18$	−3.29066	+	2.27411i	−0.775615	+	0.536013i
$19$			2.27411i			0.521716i	0.965377	+	0.260858i	$0.0840055\pi$
$19$			2.27411i			0.521716i	−0.965377	+	0.260858i	$0.915994\pi$
$20$	4.94975	+	1.87083i	1.10680	+	0.418330i
$21$	−1.36303			−0.297439
$22$	0.980325	−	4.58682i	0.209006	−	0.977914i
$23$		−	6.38741i		−	1.33187i	−0.746011	−	0.665933i	$-0.768033\pi$
$23$		−	6.38741i		−	1.33187i	0.746011	−	0.665933i	$-0.231967\pi$
$24$	−0.282294	−	1.13705i	−0.0576230	−	0.232100i
$25$	−2.00000			−0.400000
$26$	1.58579	−	1.09591i	0.310998	−	0.214925i
$27$	−2.41421			−0.464616
$28$	−2.32685	+	6.15626i	−0.439733	+	1.16342i
$29$	6.58132			1.22212			0.611060	−	0.791584i	$-0.290743\pi$
$29$	6.58132			1.22212			0.611060	+	0.791584i	$0.290743\pi$
$30$	0.881129	+	1.27500i	0.160871	+	0.232783i
$31$		−	1.09591i		−	0.196831i	−0.995145	−	0.0984153i	$-0.968623\pi$
$31$		−	1.09591i		−	0.196831i	0.995145	−	0.0984153i	$-0.0313773\pi$
$32$	−5.61750	−	0.666071i	−0.993044	−	0.117746i
$33$	1.00000	−	0.941967i	0.174078	−	0.163975i
$34$	4.41421	+	6.38741i	0.757031	+	1.09543i
$35$		−	8.70626i		−	1.47163i
$36$	−2.00000	+	5.29150i	−0.333333	+	0.881917i
$37$			4.83756i			0.795291i	0.917539	+	0.397645i	$0.130173\pi$
$37$			4.83756i			0.795291i	−0.917539	+	0.397645i	$0.869827\pi$
$38$	1.82843	+	2.64575i	0.296610	+	0.429198i
$39$	0.564588			0.0904064
$40$	7.26283	−	1.80313i	1.14835	−	0.285099i
$41$		−	10.0384i		−	1.56774i	−0.620928	−	0.783868i	$-0.713244\pi$
$41$		−	10.0384i		−	1.56774i	0.620928	−	0.783868i	$-0.286756\pi$
$42$	−1.58579	+	1.09591i	−0.244692	+	0.169102i
$43$			6.43215i			0.980894i	0.871471	+	0.490447i	$0.163166\pi$
$43$			6.43215i			0.980894i	−0.871471	+	0.490447i	$0.836834\pi$
$44$	−2.54736	−	6.12462i	−0.384029	−	0.923321i
$45$		−	7.48331i		−	1.11555i
$46$	−5.13560	−	7.43126i	−0.757203	−	1.09568i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−1.24264	−	1.09591i	−0.179360	−	0.158180i
$49$	3.82843			0.546918
$50$	−2.32685	+	1.60804i	−0.329066	+	0.227411i
$51$			2.27411i			0.318439i
$52$	0.963811	−	2.55000i	0.133657	−	0.353622i
$53$		−	7.48331i		−	1.02791i	−0.857816	−	0.513956i	$-0.828179\pi$
$53$		−	7.48331i		−	1.02791i	0.857816	−	0.513956i	$-0.171821\pi$
$54$	−2.80875	+	1.94107i	−0.382223	+	0.264147i
$55$	6.01673	+	6.38741i	0.811295	+	0.861278i
$56$	2.24264	+	9.03316i	0.299685	+	1.20711i
$57$			0.941967i			0.124767i
$58$	7.65685	−	5.29150i	1.00539	−	0.694808i
$59$	3.24264			0.422156			0.211078	−	0.977469i	$-0.432303\pi$
$59$	3.24264			0.422156			0.211078	+	0.977469i	$0.432303\pi$
$60$	2.05025	+	0.774923i	0.264686	+	0.100042i
$61$	−6.58132			−0.842651			−0.421326	−	0.906909i	$-0.638435\pi$
$61$	−6.58132			−0.842651			−0.421326	+	0.906909i	$0.638435\pi$
$62$	−0.881129	−	1.27500i	−0.111904	−	0.161925i
$63$	9.30739			1.17262
$64$	−7.07107	+	3.74166i	−0.883883	+	0.467707i
$65$			3.60625i			0.447300i
$66$	0.406064	−	1.89993i	0.0499830	−	0.233865i
$67$	−6.07107			−0.741699			−0.370849	−	0.928693i	$-0.620933\pi$
$67$	−6.07107			−0.741699			−0.370849	+	0.928693i	$0.620933\pi$
$68$	10.2712	+	3.88215i	1.24557	+	0.470780i
$69$		−	2.64575i		−	0.318511i
$70$	−7.00000	−	10.1291i	−0.836660	−	1.21065i
$71$			6.38741i			0.758046i	0.925387	+	0.379023i	$0.123740\pi$
$71$			6.38741i			0.758046i	−0.925387	+	0.379023i	$0.876260\pi$
$72$	1.92762	+	7.76429i	0.227172	+	0.915031i
$73$			0.941967i			0.110249i	0.998479	+	0.0551244i	$0.0175556\pi$
$73$			0.941967i			0.110249i	−0.998479	+	0.0551244i	$0.982444\pi$
$74$	3.88949	+	5.62813i	0.452144	+	0.654257i
$75$	−0.828427			−0.0956585
$76$	4.25447	+	1.60804i	0.488021	+	0.184455i
$77$	−7.94435	+	7.48331i	−0.905343	+	0.852803i
$78$	0.656854	−	0.453939i	0.0743741	−	0.0513985i
$79$	−9.30739			−1.04716			−0.523581	−	0.851976i	$-0.675404\pi$
$79$	−9.30739			−1.04716			−0.523581	+	0.851976i	$0.675404\pi$
$80$	7.00000	−	7.93725i	0.782624	−	0.887412i
$81$	7.48528			0.831698
$82$	−8.07107	−	11.6789i	−0.891300	−	1.28972i
$83$			4.54822i			0.499232i	0.968345	+	0.249616i	$0.0803044\pi$
$83$			4.54822i			0.499232i	−0.968345	+	0.249616i	$0.919696\pi$
$84$	−0.963811	+	2.55000i	−0.105160	+	0.278228i
$85$	−14.5257			−1.57553
$86$	5.17157	+	7.48331i	0.557665	+	0.806947i
$87$	2.72607			0.292265
$88$	−7.88797	−	5.07739i	−0.840860	−	0.541252i
$89$	−10.6569			−1.12962			−0.564812	−	0.825220i	$-0.691051\pi$
$89$	−10.6569			−1.12962			−0.564812	+	0.825220i	$0.691051\pi$
$90$	−6.01673	−	8.70626i	−0.634219	−	0.917721i
$91$	−4.48528			−0.470185
$92$	−11.9497	−	4.51658i	−1.24585	−	0.470886i
$93$		−	0.453939i		−	0.0470713i
$94$		0			0
$95$	−6.01673			−0.617303
$96$	−2.32685	−	0.275896i	−0.237483	−	0.0281585i
$97$	7.48528			0.760015			0.380008	−	0.924983i	$-0.375921\pi$
$97$	7.48528			0.760015			0.380008	+	0.924983i	$0.375921\pi$
$98$	4.45408	−	3.07813i	0.449930	−	0.310938i
$99$	−6.82843	+	6.43215i	−0.686283	+	0.646456i
$100$	−1.41421	+	3.74166i	−0.141421	+	0.374166i
$101$	17.2517			1.71661			0.858306	−	0.513138i	$-0.171517\pi$
$101$	17.2517			1.71661			0.858306	+	0.513138i	$0.171517\pi$
$102$	1.82843	+	2.64575i	0.181041	+	0.261968i
$103$			18.0663i			1.78013i	0.455836	+	0.890064i	$0.349340\pi$
$103$			18.0663i			1.78013i	−0.455836	+	0.890064i	$0.650660\pi$
$104$	−0.928932	−	3.74166i	−0.0910893	−	0.366900i
$105$		−	3.60625i		−	0.351934i
$106$	−6.01673	−	8.70626i	−0.584396	−	0.845627i
$107$			8.70626i			0.841666i	0.907138	+	0.420833i	$0.138262\pi$
$107$			8.70626i			0.841666i	−0.907138	+	0.420833i	$0.861738\pi$
$108$	−1.70711	+	4.51658i	−0.164266	+	0.434608i
$109$	−2.72607			−0.261110			−0.130555	−	0.991441i	$-0.541676\pi$
$109$	−2.72607			−0.261110			−0.130555	+	0.991441i	$0.541676\pi$
$110$	12.1356	+	2.59370i	1.15708	+	0.247299i
$111$			2.00378i			0.190191i
$112$	9.87197	+	8.70626i	0.932814	+	0.822664i
$113$	6.17157			0.580573			0.290286	−	0.956940i	$-0.406249\pi$
$113$	6.17157			0.580573			0.290286	+	0.956940i	$0.406249\pi$
$114$	0.757359	+	1.09591i	0.0709332	+	0.102641i
$115$	16.8995			1.57589
$116$	4.65369	−	12.3125i	0.432085	−	1.14319i
$117$	−3.85525			−0.356418
$118$	3.77256	−	2.60714i	0.347293	−	0.240007i
$119$		−	18.0663i		−	1.65614i
$120$	3.00836	−	0.746879i	0.274625	−	0.0681804i
$121$	0.656854	−	10.9804i	0.0597140	−	0.998216i
$122$	−7.65685	+	5.29150i	−0.693219	+	0.479070i
$123$		−	4.15804i		−	0.374918i
$124$	−2.05025	−	0.774923i	−0.184118	−	0.0695901i
$125$			7.93725i			0.709930i
$126$	10.8284	−	7.48331i	0.964673	−	0.666667i
$127$	−0.564588			−0.0500990			−0.0250495	−	0.999686i	$-0.507974\pi$
$127$	−0.564588			−0.0500990			−0.0250495	+	0.999686i	$0.507974\pi$
$128$	−5.21828	+	10.0384i	−0.461235	+	0.887278i
$129$			2.66428i			0.234577i
$130$	2.89949	+	4.19560i	0.254303	+	0.367978i
$131$		−	6.82233i		−	0.596070i	−0.954555	−	0.298035i	$-0.903669\pi$
$131$		−	6.82233i		−	0.596070i	0.954555	−	0.298035i	$-0.0963311\pi$
$132$	−1.05515	−	2.53690i	−0.0918392	−	0.220809i
$133$		−	7.48331i		−	0.648886i
$134$	−7.06322	+	4.88125i	−0.610169	+	0.421676i
$135$		−	6.38741i		−	0.549741i
$136$	15.0711	−	3.74166i	1.29233	−	0.320844i
$137$	−8.65685			−0.739605			−0.369802	−	0.929110i	$-0.620575\pi$
$137$	−8.65685			−0.739605			−0.369802	+	0.929110i	$0.620575\pi$
$138$	−2.12723	−	3.07813i	−0.181082	−	0.262028i
$139$		−	19.6866i		−	1.66980i	−0.550403	−	0.834899i	$-0.685526\pi$
$139$		−	19.6866i		−	1.66980i	0.550403	−	0.834899i	$-0.314474\pi$
$140$	−16.2879	−	6.15626i	−1.37658	−	0.520299i
$141$		0			0
$142$	5.13560	+	7.43126i	0.430970	+	0.623617i
$143$	3.29066	−	3.09969i	0.275179	−	0.259209i
$144$	8.48528	+	7.48331i	0.707107	+	0.623610i
$145$			17.4125i			1.44603i
$146$	0.757359	+	1.09591i	0.0626795	+	0.0906978i
$147$	1.58579			0.130793
$148$	9.05025	+	3.42067i	0.743926	+	0.281178i
$149$	21.1070			1.72915			0.864576	−	0.502503i	$-0.167587\pi$
$149$	21.1070			1.72915			0.864576	+	0.502503i	$0.167587\pi$
$150$	−0.963811	+	0.666071i	−0.0786949	+	0.0543845i
$151$	13.1626			1.07116			0.535580	−	0.844485i	$-0.320093\pi$
$151$	13.1626			1.07116			0.535580	+	0.844485i	$0.320093\pi$
$152$	6.24264	−	1.54985i	0.506345	−	0.125709i
$153$		−	15.5286i		−	1.25541i
$154$	−3.22591	+	15.0937i	−0.259951	+	1.21628i
$155$	2.89949			0.232893
$156$	0.399224	−	1.05625i	0.0319635	−	0.0845674i
$157$			0.453939i			0.0362283i	0.999836	+	0.0181141i	$0.00576623\pi$
$157$			0.453939i			0.0362283i	−0.999836	+	0.0181141i	$0.994234\pi$
$158$	−10.8284	+	7.48331i	−0.861463	+	0.595341i
$159$		−	3.09969i		−	0.245821i
$160$	1.76226	−	14.8625i	0.139319	−	1.17499i
$161$			21.0188i			1.65651i
$162$	8.70855	−	6.01831i	0.684208	−	0.472843i
$163$	−12.8284			−1.00480			−0.502400	−	0.864635i	$-0.667549\pi$
$163$	−12.8284			−1.00480			−0.502400	+	0.864635i	$0.667549\pi$
$164$	−18.7801	−	7.09822i	−1.46648	−	0.554278i
$165$	2.49221	+	2.64575i	0.194018	+	0.205971i
$166$	3.65685	+	5.29150i	0.283827	+	0.410700i
$167$	−21.9054			−1.69509			−0.847546	−	0.530721i	$-0.821921\pi$
$167$	−21.9054			−1.69509			−0.847546	+	0.530721i	$0.821921\pi$
$168$	0.928932	+	3.74166i	0.0716687	+	0.288675i
$169$	−11.1421			−0.857087
$170$	−16.8995	+	11.6789i	−1.29613	+	0.895732i
$171$		−	6.43215i		−	0.491879i
$172$	12.0335	+	4.54822i	0.917542	+	0.346798i
$173$	−5.45214			−0.414519			−0.207259	−	0.978286i	$-0.566454\pi$
$173$	−5.45214			−0.414519			−0.207259	+	0.978286i	$0.566454\pi$
$174$	3.17157	−	2.19181i	0.240436	−	0.166161i
$175$	6.58132			0.497501
$176$	−13.2594	+	0.434919i	−0.999462	+	0.0327833i
$177$	1.34315			0.100957
$178$	−12.3984	+	8.56831i	−0.929302	+	0.642222i
$179$	9.72792			0.727099			0.363550	−	0.931575i	$-0.381565\pi$
$179$	9.72792			0.727099			0.363550	+	0.931575i	$0.381565\pi$
$180$	−14.0000	−	5.29150i	−1.04350	−	0.394405i
$181$		−	2.64575i		−	0.196657i	−0.995154	−	0.0983286i	$-0.968650\pi$
$181$		−	2.64575i		−	0.196657i	0.995154	−	0.0983286i	$-0.0313496\pi$
$182$	−5.21828	+	3.60625i	−0.386805	+	0.267313i
$183$	−2.72607			−0.201517
$184$	−17.5340	+	4.35313i	−1.29263	+	0.320917i
$185$	−12.7990			−0.941000
$186$	−0.364976	−	0.528123i	−0.0267613	−	0.0387239i
$187$	12.4853	+	13.2545i	0.913014	+	0.969264i
$188$		0			0
$189$	7.94435			0.577866
$190$	−7.00000	+	4.83756i	−0.507833	+	0.350954i
$191$		−	16.9704i		−	1.22794i	−0.789331	−	0.613968i	$-0.789572\pi$
$191$		−	16.9704i		−	1.22794i	0.789331	−	0.613968i	$-0.210428\pi$
$192$	−2.92893	+	1.54985i	−0.211377	+	0.111850i
$193$		−	12.8643i		−	0.925993i	−0.886360	−	0.462996i	$-0.846774\pi$
$193$		−	12.8643i		−	0.925993i	0.886360	−	0.462996i	$-0.153226\pi$
$194$	8.70855	−	6.01831i	0.625237	−	0.432089i
$195$			1.49376i			0.106970i
$196$	2.70711	−	7.16233i	0.193365	−	0.511595i
$197$	−10.4366			−0.743574			−0.371787	−	0.928318i	$-0.621255\pi$
$197$	−10.4366			−0.743574			−0.371787	+	0.928318i	$0.621255\pi$
$198$	−2.77278	+	12.9735i	−0.197053	+	0.921987i
$199$		−	21.1660i		−	1.50042i	−0.661200	−	0.750209i	$-0.729953\pi$
$199$		−	21.1660i		−	1.50042i	0.661200	−	0.750209i	$-0.270047\pi$
$200$	1.36303	+	5.49019i	0.0963811	+	0.388215i
$201$	−2.51472			−0.177375
$202$	20.0711	−	13.8707i	1.41220	−	0.975941i
$203$	−21.6569			−1.52001
$204$	4.25447	+	1.60804i	0.297872	+	0.112585i
$205$	26.5591			1.85497
$206$	14.5257	+	21.0188i	1.01205	+	1.46445i
$207$			18.0663i			1.25570i
$208$	−4.08910	−	3.60625i	−0.283528	−	0.250049i
$209$	5.17157	+	5.49019i	0.357725	+	0.379764i
$210$	−2.89949	−	4.19560i	−0.200084	−	0.289524i
$211$			9.09644i			0.626225i	0.949716	+	0.313112i	$0.101372\pi$
$211$			9.09644i			0.626225i	−0.949716	+	0.313112i	$0.898628\pi$
$212$	−14.0000	−	5.29150i	−0.961524	−	0.363422i
$213$			2.64575i			0.181284i
$214$	7.00000	+	10.1291i	0.478510	+	0.692409i
$215$	−17.0179			−1.16061
$216$	1.64533	+	6.62724i	0.111950	+	0.450927i
$217$			3.60625i			0.244808i
$218$	−3.17157	+	2.19181i	−0.214806	+	0.148448i
$219$			0.390175i			0.0263656i
$220$	16.2042	−	6.73969i	1.09249	−	0.454390i
$221$			7.48331i			0.503382i
$222$	1.61108	+	2.33125i	0.108129	+	0.156463i
$223$			4.19560i			0.280958i	0.990084	+	0.140479i	$0.0448642\pi$
$223$			4.19560i			0.280958i	−0.990084	+	0.140479i	$0.955136\pi$
$224$	18.4853	+	2.19181i	1.23510	+	0.146447i
$225$	5.65685			0.377124
$226$	7.18015	−	4.96206i	0.477617	−	0.330071i
$227$		−	13.2545i		−	0.879731i	−0.898064	−	0.439865i	$-0.855026\pi$
$227$		−	13.2545i		−	0.879731i	0.898064	−	0.439865i	$-0.144974\pi$
$228$	1.76226	+	0.666071i	0.116708	+	0.0441116i
$229$			10.1291i			0.669348i	0.942334	+	0.334674i	$0.108626\pi$
$229$			10.1291i			0.669348i	−0.942334	+	0.334674i	$0.891374\pi$
$230$	19.6613	−	13.5875i	1.29643	−	0.895934i
$231$	−3.29066	+	3.09969i	−0.216509	+	0.203945i
$232$	−4.48528	−	18.0663i	−0.294473	−	1.18611i
$233$			8.31609i			0.544805i	0.962183	+	0.272402i	$0.0878182\pi$
$233$			8.31609i			0.544805i	−0.962183	+	0.272402i	$0.912182\pi$
$234$	−4.48528	+	3.09969i	−0.293212	+	0.202633i
$235$		0			0
$236$	2.29289	−	6.06643i	0.149255	−	0.394891i
$237$	−3.85525			−0.250425
$238$	−14.5257	−	21.0188i	−0.941559	−	1.36244i
$239$	5.45214			0.352670			0.176335	−	0.984330i	$-0.443576\pi$
$239$	5.45214			0.352670			0.176335	+	0.984330i	$0.443576\pi$
$240$	2.89949	−	3.28772i	0.187162	−	0.212221i
$241$		−	4.54822i		−	0.292977i	−0.989212	−	0.146488i	$-0.953203\pi$
$241$		−	4.54822i		−	0.292977i	0.989212	−	0.146488i	$-0.0467971\pi$
$242$	−8.06423	−	13.3029i	−0.518388	−	0.855145i
$243$	10.3431			0.663513
$244$	−4.65369	+	12.3125i	−0.297922	+	0.788228i
$245$			10.1291i			0.647122i
$246$	−3.34315	−	4.83756i	−0.213151	−	0.308432i
$247$			3.09969i			0.197229i
$248$	−3.00836	+	0.746879i	−0.191031	+	0.0474269i
$249$			1.88393i			0.119389i
$250$	6.38170	+	9.23438i	0.403614	+	0.584034i
$251$	18.4142			1.16229			0.581147	−	0.813798i	$-0.302604\pi$
$251$	18.4142			1.16229			0.581147	+	0.813798i	$0.302604\pi$
$252$	6.58132	−	17.4125i	0.414584	−	1.09689i
$253$	−14.5257	−	15.4206i	−0.913221	−	0.969483i
$254$	−0.656854	+	0.453939i	−0.0412147	+	0.0284827i
$255$	−6.01673			−0.376782
$256$	2.00000	+	15.8745i	0.125000	+	0.992157i
$257$	6.48528			0.404541			0.202270	−	0.979330i	$-0.435168\pi$
$257$	6.48528			0.404541			0.202270	+	0.979330i	$0.435168\pi$
$258$	2.14214	+	3.09969i	0.133364	+	0.192978i
$259$		−	15.9188i		−	0.989144i
$260$	6.74668	+	2.55000i	0.418411	+	0.158145i
$261$	−18.6148			−1.15223
$262$	−5.48528	−	7.93725i	−0.338882	−	0.490365i
$263$	19.1794			1.18265			0.591325	−	0.806433i	$-0.298605\pi$
$263$	19.1794			1.18265			0.591325	+	0.806433i	$0.298605\pi$
$264$	−3.26730	−	2.10313i	−0.201089	−	0.129438i
$265$	19.7990			1.21624
$266$	−6.01673	−	8.70626i	−0.368909	−	0.533815i
$267$	−4.41421			−0.270145
$268$	−4.29289	+	11.3579i	−0.262230	+	0.693796i
$269$			13.6827i			0.834249i	0.908849	+	0.417124i	$0.136962\pi$
$269$			13.6827i			0.834249i	−0.908849	+	0.417124i	$0.863038\pi$
$270$	−5.13560	−	7.43126i	−0.312543	−	0.452252i
$271$	−12.5980			−0.765277			−0.382638	−	0.923898i	$-0.624984\pi$
$271$	−12.5980			−0.765277			−0.382638	+	0.923898i	$0.624984\pi$
$272$	14.5257	−	16.4706i	0.880748	−	0.998674i
$273$	−1.85786			−0.112443
$274$	−10.0716	+	6.96028i	−0.608447	+	0.420486i
$275$	−4.82843	+	4.54822i	−0.291165	+	0.274268i
$276$	−4.94975	−	1.87083i	−0.297940	−	0.112611i
$277$	3.85525			0.231639			0.115820	−	0.993270i	$-0.463051\pi$
$277$	3.85525			0.231639			0.115820	+	0.993270i	$0.463051\pi$
$278$	−15.8284	−	22.9039i	−0.949326	−	1.37368i
$279$			3.09969i			0.185574i
$280$	−23.8995	+	5.93347i	−1.42827	+	0.354593i
$281$		−	6.43215i		−	0.383710i	−0.981423	−	0.191855i	$-0.938550\pi$
$281$		−	6.43215i		−	0.383710i	0.981423	−	0.191855i	$-0.0614503\pi$
$282$		0			0
$283$			1.88393i			0.111988i	0.998431	+	0.0559941i	$0.0178328\pi$
$283$			1.88393i			0.111988i	−0.998431	+	0.0559941i	$0.982167\pi$
$284$	11.9497	+	4.51658i	0.709087	+	0.268010i
$285$	−2.49221			−0.147626
$286$	1.33622	−	6.25200i	0.0790122	−	0.369689i
$287$			33.0329i			1.94987i
$288$	15.8887	+	1.88393i	0.936251	+	0.111012i
$289$	−13.1421			−0.773067
$290$	14.0000	+	20.2581i	0.822108	+	1.18960i
$291$	3.10051			0.181755
$292$	1.76226	+	0.666071i	0.103128	+	0.0389789i
$293$	−14.5257			−0.848598			−0.424299	−	0.905522i	$-0.639480\pi$
$293$	−14.5257			−0.848598			−0.424299	+	0.905522i	$0.639480\pi$
$294$	1.84494	−	1.27500i	0.107599	−	0.0743597i
$295$			8.57922i			0.499502i
$296$	13.2796	−	3.29688i	0.771859	−	0.191627i
$297$	−5.82843	+	5.49019i	−0.338200	+	0.318573i
$298$	24.5563	−	16.9704i	1.42251	−	0.983070i
$299$		−	8.70626i		−	0.503496i
$300$	−0.585786	+	1.54985i	−0.0338204	+	0.0894804i
$301$		−	21.1660i		−	1.21999i
$302$	15.3137	−	10.5830i	0.881205	−	0.608984i
$303$	7.14590			0.410521
$304$	6.01673	−	6.82233i	0.345083	−	0.391287i
$305$		−	17.4125i		−	0.997038i
$306$	−12.4853	−	18.0663i	−0.713736	−	1.03278i
$307$			22.3509i			1.27563i	0.770188	+	0.637817i	$0.220162\pi$
$307$			22.3509i			1.27563i	−0.770188	+	0.637817i	$0.779838\pi$
$308$	8.38250	+	20.1540i	0.477637	+	1.14838i
$309$			7.48331i			0.425711i
$310$	3.37334	−	2.33125i	0.191593	−	0.132406i
$311$			14.9666i			0.848680i	0.905503	+	0.424340i	$0.139494\pi$
$311$			14.9666i			0.848680i	−0.905503	+	0.424340i	$0.860506\pi$
$312$	−0.384776	−	1.54985i	−0.0217837	−	0.0877427i
$313$	7.82843			0.442489			0.221244	−	0.975218i	$-0.428988\pi$
$313$	7.82843			0.442489			0.221244	+	0.975218i	$0.428988\pi$
$314$	0.364976	+	0.528123i	0.0205968	+	0.0298037i
$315$			24.6250i			1.38746i
$316$	−6.58132	+	17.4125i	−0.370228	+	0.979531i
$317$		−	15.4206i		−	0.866105i	−0.901369	−	0.433053i	$-0.857436\pi$
$317$		−	15.4206i		−	0.866105i	0.901369	−	0.433053i	$-0.142564\pi$
$318$	−2.49221	−	3.60625i	−0.139756	−	0.202229i
$319$	15.8887	−	14.9666i	0.889596	−	0.837970i
$320$	−9.89949	−	18.7083i	−0.553399	−	1.04583i
$321$			3.60625i			0.201281i
$322$	16.8995	+	24.4537i	0.941772	+	1.36275i
$323$	−12.4853			−0.694700
$324$	5.29289	−	14.0037i	0.294050	−	0.777982i
$325$	−2.72607			−0.151215
$326$	−14.9249	+	10.3143i	−0.826613	+	0.571256i
$327$	−1.12918			−0.0624435
$328$	−27.5563	+	6.84135i	−1.52154	+	0.377750i
$329$		0			0
$330$	5.02673	+	1.07434i	0.276712	+	0.0591407i
$331$	−18.0711			−0.993276			−0.496638	−	0.867958i	$-0.665432\pi$
$331$	−18.0711			−0.993276			−0.496638	+	0.867958i	$0.665432\pi$
$332$	8.50894	+	3.21608i	0.466989	+	0.176505i
$333$		−	13.6827i		−	0.749807i
$334$	−25.4853	+	17.6124i	−1.39449	+	0.963707i
$335$		−	16.0625i		−	0.877590i
$336$	4.08910	+	3.60625i	0.223079	+	0.196737i
$337$		−	19.1348i		−	1.04234i	−0.853453	−	0.521171i	$-0.825496\pi$
$337$		−	19.1348i		−	1.04234i	0.853453	−	0.521171i	$-0.174504\pi$
$338$	−12.9630	+	8.95849i	−0.705095	+	0.487278i
$339$	2.55635			0.138842
$340$	−10.2712	+	27.1750i	−0.557034	+	1.47377i
$341$	−2.49221	−	2.64575i	−0.134961	−	0.143275i
$342$	−5.17157	−	7.48331i	−0.279647	−	0.404651i
$343$	10.4366			0.563521
$344$	17.6569	−	4.38362i	0.951994	−	0.236349i
$345$	7.00000			0.376867
$346$	−6.34315	+	4.38362i	−0.341010	+	0.235665i
$347$			4.15804i			0.223215i	0.993752	+	0.111608i	$0.0356000\pi$
$347$			4.15804i			0.223215i	−0.993752	+	0.111608i	$0.964400\pi$
$348$	1.92762	−	5.10001i	0.103331	−	0.273389i
$349$	14.5257			0.777541			0.388771	−	0.921335i	$-0.372900\pi$
$349$	14.5257			0.777541			0.388771	+	0.921335i	$0.372900\pi$
$350$	7.65685	−	5.29150i	0.409276	−	0.282843i
$351$	−3.29066			−0.175642
$352$	−15.0766	+	11.1668i	−0.803584	+	0.595191i
$353$	1.82843			0.0973174			0.0486587	−	0.998815i	$-0.484505\pi$
$353$	1.82843			0.0973174			0.0486587	+	0.998815i	$0.484505\pi$
$354$	1.56265	−	1.07991i	0.0830537	−	0.0573968i
$355$	−16.8995			−0.896932
$356$	−7.53553	+	19.9371i	−0.399382	+	1.05667i
$357$		−	7.48331i		−	0.396059i
$358$	11.3177	−	7.82143i	0.598158	−	0.413376i
$359$	3.29066			0.173674			0.0868371	−	0.996223i	$-0.472324\pi$
$359$	3.29066			0.173674			0.0868371	+	0.996223i	$0.472324\pi$
$360$	−20.5424	+	5.10001i	−1.08268	+	0.268794i
$361$	13.8284			0.727812
$362$	−2.12723	−	3.07813i	−0.111805	−	0.161783i
$363$	0.272078	−	4.54822i	0.0142804	−	0.238720i
$364$	−3.17157	+	8.39119i	−0.166236	+	0.439818i
$365$	−2.49221			−0.130448
$366$	−3.17157	+	2.19181i	−0.165781	+	0.114568i
$367$		−	22.2619i		−	1.16206i	−0.813881	−	0.581031i	$-0.802649\pi$
$367$		−	22.2619i		−	1.16206i	0.813881	−	0.581031i	$-0.197351\pi$
$368$	−16.8995	+	19.1622i	−0.880947	+	0.998900i
$369$			28.3929i			1.47808i
$370$	−14.8906	+	10.2906i	−0.774128	+	0.534984i
$371$			24.6250i			1.27847i
$372$	−0.849242	−	0.320983i	−0.0440312	−	0.0166422i
$373$	−0.233860			−0.0121088			−0.00605440	−	0.999982i	$-0.501927\pi$
$373$	−0.233860			−0.0121088			−0.00605440	+	0.999982i	$0.501927\pi$
$374$	25.1825	+	5.38216i	1.30216	+	0.278305i
$375$			3.28772i			0.169777i
$376$		0			0
$377$	8.97056			0.462007
$378$	9.24264	−	6.38741i	0.475390	−	0.328533i
$379$	−16.0711			−0.825515			−0.412758	−	0.910841i	$-0.635434\pi$
$379$	−16.0711			−0.825515			−0.412758	+	0.910841i	$0.635434\pi$
$380$	−4.25447	+	11.2563i	−0.218250	+	0.577434i
$381$	−0.233860			−0.0119810
$382$	−13.6445	−	19.7438i	−0.698115	−	1.01018i
$383$			7.29529i			0.372772i	0.982477	+	0.186386i	$0.0596775\pi$
$383$			7.29529i			0.372772i	−0.982477	+	0.186386i	$0.940323\pi$
$384$	−2.16148	+	4.15804i	−0.110303	+	0.212189i
$385$	−19.7990	−	21.0188i	−1.00905	−	1.07122i
$386$	−10.3431	−	14.9666i	−0.526452	−	0.761781i
$387$		−	18.1929i		−	0.924796i
$388$	5.29289	−	14.0037i	0.268706	−	0.710929i
$389$		−	32.5790i		−	1.65182i	−0.563801	−	0.825911i	$-0.690661\pi$
$389$		−	32.5790i		−	1.65182i	0.563801	−	0.825911i	$-0.309339\pi$
$390$	1.20101	+	1.73787i	0.0608155	+	0.0880006i
$391$	35.0681			1.77347
$392$	−2.60914	−	10.5094i	−0.131781	−	0.530804i
$393$		−	2.82590i		−	0.142548i
$394$	−12.1421	+	8.39119i	−0.611712	+	0.422742i
$395$		−	24.6250i		−	1.23902i
$396$	7.20503	+	17.3230i	0.362066	+	0.870515i
$397$			22.4499i			1.12673i	0.826208	+	0.563365i	$0.190494\pi$
$397$			22.4499i			1.12673i	−0.826208	+	0.563365i	$0.809506\pi$
$398$	−17.0179	−	24.6250i	−0.853029	−	1.23434i
$399$		−	3.09969i		−	0.155179i
$400$	6.00000	+	5.29150i	0.300000	+	0.264575i
$401$	−4.82843			−0.241120			−0.120560	−	0.992706i	$-0.538469\pi$
$401$	−4.82843			−0.241120			−0.120560	+	0.992706i	$0.538469\pi$
$402$	−2.92568	+	2.02188i	−0.145920	+	0.100842i
$403$		−	1.49376i		−	0.0744094i
$404$	12.1988	−	32.2750i	0.606914	−	1.60574i
$405$			19.8042i			0.984078i
$406$	−25.1961	+	17.4125i	−1.25046	+	0.864169i
$407$	11.0011	+	11.6789i	0.545307	+	0.578902i
$408$	6.24264	−	1.54985i	0.309057	−	0.0767288i
$409$		−	1.88393i		−	0.0931545i	−0.998915	−	0.0465773i	$-0.985169\pi$
$409$		−	1.88393i		−	0.0931545i	0.998915	−	0.0465773i	$-0.0148314\pi$
$410$	30.8995	−	21.3540i	1.52602	−	1.05460i
$411$	−3.58579			−0.176874
$412$	33.7990	+	12.7748i	1.66516	+	0.629370i
$413$	−10.6704			−0.525057
$414$	14.5257	+	21.0188i	0.713897	+	1.03302i
$415$	−12.0335			−0.590699
$416$	−7.65685	−	0.907878i	−0.375408	−	0.0445124i
$417$		−	8.15447i		−	0.399326i
$418$	10.4309	+	2.22937i	0.510194	+	0.109042i
$419$	16.1421			0.788595			0.394297	−	0.918983i	$-0.370988\pi$
$419$	16.1421			0.788595			0.394297	+	0.918983i	$0.370988\pi$
$420$	−6.74668	−	2.55000i	−0.329204	−	0.124428i
$421$		−	7.48331i		−	0.364714i	−0.983232	−	0.182357i	$-0.941627\pi$
$421$		−	7.48331i		−	0.364714i	0.983232	−	0.182357i	$-0.0583727\pi$
$422$	7.31371	+	10.5830i	0.356026	+	0.515173i
$423$		0			0
$424$	−20.5424	+	5.10001i	−0.997627	+	0.247678i
$425$		−	10.9804i		−	0.532626i
$426$	2.12723	+	3.07813i	0.103065	+	0.149136i
$427$	21.6569			1.04805
$428$	16.2879	+	6.15626i	0.787307	+	0.297574i
$429$	1.36303	−	1.28393i	0.0658079	−	0.0619889i
$430$	−19.7990	+	13.6827i	−0.954792	+	0.659838i
$431$	2.16148			0.104115			0.0520575	−	0.998644i	$-0.483422\pi$
$431$	2.16148			0.104115			0.0520575	+	0.998644i	$0.483422\pi$
$432$	7.24264	+	6.38741i	0.348462	+	0.307314i
$433$	−17.3431			−0.833458			−0.416729	−	0.909031i	$-0.636824\pi$
$433$	−17.3431			−0.833458			−0.416729	+	0.909031i	$0.636824\pi$
$434$	2.89949	+	4.19560i	0.139180	+	0.201395i
$435$			7.21250i			0.345813i
$436$	−1.92762	+	5.10001i	−0.0923164	+	0.244246i
$437$	14.5257			0.694857
$438$	0.313708	+	0.453939i	0.0149896	+	0.0216901i
$439$	−34.5035			−1.64676			−0.823380	−	0.567490i	$-0.807915\pi$
$439$	−34.5035			−1.64676			−0.823380	+	0.567490i	$0.807915\pi$
$440$	13.4335	−	20.8696i	0.640418	−	0.994919i
$441$	−10.8284			−0.515639
$442$	6.01673	+	8.70626i	0.286187	+	0.414115i
$443$	26.4142			1.25498			0.627489	−	0.778626i	$-0.284083\pi$
$443$	26.4142			1.25498			0.627489	+	0.778626i	$0.284083\pi$
$444$	3.74874	+	1.41689i	0.177907	+	0.0672426i
$445$		−	28.1954i		−	1.33659i
$446$	3.37334	+	4.88125i	0.159732	+	0.231134i
$447$	8.74280			0.413520
$448$	23.2685	−	12.3125i	1.09933	−	0.581712i
$449$	15.9706			0.753697			0.376849	−	0.926275i	$-0.377008\pi$
$449$	15.9706			0.753697			0.376849	+	0.926275i	$0.377008\pi$
$450$	6.58132	−	4.54822i	0.310246	−	0.214405i
$451$	−22.8284	−	24.2349i	−1.07495	−	1.14117i
$452$	4.36396	−	11.5460i	0.205263	−	0.543076i
$453$	5.45214			0.256164
$454$	−10.6569	−	15.4206i	−0.500151	−	0.723723i
$455$		−	11.8669i		−	0.556331i
$456$	2.58579	−	0.641967i	0.121091	−	0.0300629i
$457$			22.7411i			1.06378i	0.846812	+	0.531892i	$0.178519\pi$
$457$			22.7411i			1.06378i	−0.846812	+	0.531892i	$0.821481\pi$
$458$	8.14396	+	11.7844i	0.380542	+	0.550648i
$459$		−	13.2545i		−	0.618666i
$460$	11.9497	−	31.6161i	0.557160	−	1.47411i
$461$	3.85525			0.179557			0.0897783	−	0.995962i	$-0.471384\pi$
$461$	3.85525			0.179557			0.0897783	+	0.995962i	$0.471384\pi$
$462$	−1.33622	+	6.25200i	−0.0621664	+	0.290869i
$463$			22.2619i			1.03460i	0.855804	+	0.517300i	$0.173063\pi$
$463$			22.2619i			1.03460i	−0.855804	+	0.517300i	$0.826937\pi$
$464$	−19.7439	−	17.4125i	−0.916590	−	0.808356i
$465$	1.20101			0.0556955
$466$	6.68629	+	9.67513i	0.309736	+	0.448192i
$467$	36.0711			1.66917			0.834585	−	0.550879i	$-0.185708\pi$
$467$	36.0711			1.66917			0.834585	+	0.550879i	$0.185708\pi$
$468$	−2.72607	+	7.21250i	−0.126013	+	0.333398i
$469$	19.9778			0.922489
$470$		0			0
$471$			0.188028i			0.00866386i
$472$	−2.20992	−	8.90135i	−0.101720	−	0.409718i
$473$	14.6274	+	15.5286i	0.672569	+	0.714005i
$474$	−4.48528	+	3.09969i	−0.206016	+	0.142373i
$475$		−	4.54822i		−	0.208687i
$476$	−33.7990	−	12.7748i	−1.54917	−	0.585533i
$477$			21.1660i			0.969125i
$478$	6.34315	−	4.38362i	0.290129	−	0.200502i
$479$	−27.3576			−1.25000			−0.625000	−	0.780625i	$-0.714901\pi$
$479$	−27.3576			−1.25000			−0.625000	+	0.780625i	$0.714901\pi$
$480$	0.729951	−	6.15626i	0.0333176	−	0.280993i
$481$			6.59377i			0.300650i
$482$	−3.65685	−	5.29150i	−0.166565	−	0.241021i
$483$			8.70626i			0.396149i
$484$	−20.0779	−	8.99316i	−0.912633	−	0.408780i
$485$			19.8042i			0.899262i
$486$	12.0335	−	8.31609i	0.545849	−	0.377225i
$487$		−	26.6455i		−	1.20742i	−0.797202	−	0.603712i	$-0.793688\pi$
$487$		−	26.6455i		−	1.20742i	0.797202	−	0.603712i	$-0.206312\pi$
$488$	4.48528	+	18.0663i	0.203039	+	0.817824i
$489$	−5.31371			−0.240294
$490$	8.14396	+	11.7844i	0.367907	+	0.532364i
$491$			25.7286i			1.16112i	0.814219	+	0.580558i	$0.197166\pi$
$491$			25.7286i			1.16112i	−0.814219	+	0.580558i	$0.802834\pi$
$492$	−7.77899	−	2.94018i	−0.350704	−	0.132554i
$493$			36.1326i			1.62733i
$494$	2.49221	+	3.60625i	0.112130	+	0.162253i
$495$	−17.0179	−	18.0663i	−0.764897	−	0.812021i
$496$	−2.89949	+	3.28772i	−0.130191	+	0.147623i
$497$		−	21.0188i		−	0.942821i
$498$	1.51472	+	2.19181i	0.0678762	+	0.0982175i
$499$	18.4853			0.827515			0.413757	−	0.910387i	$-0.364216\pi$
$499$	18.4853			0.827515			0.413757	+	0.910387i	$0.364216\pi$
$500$	14.8492	+	5.61249i	0.664078	+	0.250998i
$501$	−9.07353			−0.405375
$502$	21.4235	−	14.8054i	0.956179	−	0.660796i
$503$	−3.85525			−0.171897			−0.0859484	−	0.996300i	$-0.527392\pi$
$503$	−3.85525			−0.171897			−0.0859484	+	0.996300i	$0.527392\pi$
$504$	−6.34315	−	25.5496i	−0.282546	−	1.13807i
$505$			45.6438i			2.03112i
$506$	−29.2979	−	6.26174i	−1.30245	−	0.278368i
$507$	−4.61522			−0.204969
$508$	−0.399224	+	1.05625i	−0.0177127	+	0.0468634i
$509$			35.6787i			1.58143i	0.612184	+	0.790715i	$0.290291\pi$
$509$			35.6787i			1.58143i	−0.612184	+	0.790715i	$0.709709\pi$
$510$	−7.00000	+	4.83756i	−0.309965	+	0.214211i
$511$		−	3.09969i		−	0.137122i
$512$	15.0903	+	16.8607i	0.666901	+	0.745146i
$513$		−	5.49019i		−	0.242398i
$514$	7.54513	−	5.21429i	0.332801	−	0.229992i
$515$	−47.7990			−2.10628
$516$	4.98442	+	1.88393i	0.219427	+	0.0829356i
$517$		0			0
$518$	−12.7990	−	18.5203i	−0.562355	−	0.813733i
$519$	−2.25835			−0.0991306
$520$	9.89949	−	2.45772i	0.434122	−	0.107778i
$521$	−20.1127			−0.881153			−0.440577	−	0.897715i	$-0.645226\pi$
$521$	−20.1127			−0.881153			−0.440577	+	0.897715i	$0.645226\pi$
$522$	−21.6569	+	14.9666i	−0.947895	+	0.655072i
$523$			17.0223i			0.744335i	0.928166	+	0.372168i	$0.121385\pi$
$523$			17.0223i			0.744335i	−0.928166	+	0.372168i	$0.878615\pi$
$524$	−12.7634	−	4.82411i	−0.557572	−	0.210742i
$525$	2.72607			0.118975
$526$	22.3137	−	15.4206i	0.972924	−	0.672369i
$527$	6.01673			0.262093
$528$	−5.49221	+	0.180149i	−0.239018	+	0.00783999i
$529$	−17.7990			−0.773869
$530$	23.0346	−	15.9188i	1.00056	−	0.691467i
$531$	−9.17157			−0.398012
$532$	−14.0000	−	5.29150i	−0.606977	−	0.229416i
$533$		−	13.6827i		−	0.592663i
$534$	−5.13560	+	3.54911i	−0.222239	+	0.153585i
$535$	−23.0346			−0.995873
$536$	4.13754	+	16.6656i	0.178714	+	0.719846i
$537$	4.02944			0.173883
$538$	11.0011	+	15.9188i	0.474293	+	0.686307i
$539$	9.24264	−	8.70626i	0.398109	−	0.375005i
$540$	−11.9497	−	4.51658i	−0.514235	−	0.194363i
$541$	−17.2517			−0.741710			−0.370855	−	0.928691i	$-0.620935\pi$
$541$	−17.2517			−0.741710			−0.370855	+	0.928691i	$0.620935\pi$
$542$	−14.6569	+	10.1291i	−0.629566	+	0.435081i
$543$		−	1.09591i		−	0.0470298i
$544$	3.65685	−	30.8411i	0.156786	−	1.32230i
$545$		−	7.21250i		−	0.308950i
$546$	−2.16148	+	1.49376i	−0.0925029	+	0.0639270i
$547$		−	41.2572i		−	1.76403i	−0.471221	−	0.882015i	$-0.656187\pi$
$547$		−	41.2572i		−	1.76403i	0.471221	−	0.882015i	$-0.343813\pi$
$548$	−6.12132	+	16.1955i	−0.261490	+	0.691837i
$549$	18.6148			0.794459
$550$	−1.96065	+	9.17365i	−0.0836024	+	0.391166i
$551$			14.9666i			0.637600i
$552$	−7.26283	+	1.80313i	−0.309127	+	0.0767461i
$553$	30.6274			1.30241
$554$	4.48528	−	3.09969i	0.190561	−	0.131693i
$555$	−5.30152			−0.225037
$556$	−36.8303	−	13.9206i	−1.56195	−	0.590363i
$557$	−23.8331			−1.00984			−0.504919	−	0.863167i	$-0.668478\pi$
$557$	−23.8331			−1.00984			−0.504919	+	0.863167i	$0.668478\pi$
$558$	2.49221	+	3.60625i	0.105504	+	0.152665i
$559$			8.76725i			0.370815i
$560$	−23.0346	+	26.1188i	−0.973390	+	1.10372i
$561$	5.17157	+	5.49019i	0.218344	+	0.231796i
$562$	−5.17157	−	7.48331i	−0.218150	−	0.315665i
$563$			11.7607i			0.495655i	0.968804	+	0.247828i	$0.0797167\pi$
$563$			11.7607i			0.495655i	−0.968804	+	0.247828i	$0.920283\pi$
$564$		0			0
$565$			16.3284i			0.686943i
$566$	1.51472	+	2.19181i	0.0636684	+	0.0921287i
$567$	−24.6315			−1.03443
$568$	17.5340	−	4.35313i	0.735712	−	0.182653i
$569$		−	2.66428i		−	0.111693i	−0.998439	−	0.0558463i	$-0.982214\pi$
$569$		−	2.66428i		−	0.111693i	0.998439	−	0.0558463i	$-0.0177857\pi$
$570$	−2.89949	+	2.00378i	−0.121446	+	0.0839293i
$571$			21.9607i			0.919028i	0.888170	+	0.459514i	$0.151976\pi$
$571$			21.9607i			0.919028i	−0.888170	+	0.459514i	$0.848024\pi$
$572$	−3.47214	−	8.34807i	−0.145178	−	0.349050i
$573$		−	7.02938i		−	0.293656i
$574$	26.5591	+	38.4313i	1.10856	+	1.60409i
$575$			12.7748i			0.532747i
$576$	20.0000	−	10.5830i	0.833333	−	0.440959i
$577$	−31.6274			−1.31667			−0.658333	−	0.752727i	$-0.728738\pi$
$577$	−31.6274			−1.31667			−0.658333	+	0.752727i	$0.728738\pi$
$578$	−15.2899	+	10.5665i	−0.635975	+	0.439510i
$579$		−	5.32857i		−	0.221448i
$580$	32.5758	+	12.3125i	1.35264	+	0.511249i
$581$		−	14.9666i		−	0.620920i
$582$	3.60720	−	2.49287i	0.149523	−	0.103333i
$583$	−17.0179	−	18.0663i	−0.704808	−	0.748231i
$584$	2.58579	−	0.641967i	0.107001	−	0.0265648i
$585$		−	10.2000i		−	0.421719i
$586$	−16.8995	+	11.6789i	−0.698112	+	0.482451i
$587$	−30.2843			−1.24997			−0.624983	−	0.780639i	$-0.714894\pi$
$587$	−30.2843			−1.24997			−0.624983	+	0.780639i	$0.714894\pi$
$588$	1.12132	−	2.96673i	0.0462425	−	0.122346i
$589$	2.49221			0.102690
$590$	6.89786	+	9.98126i	0.283980	+	0.410922i
$591$	−4.32296			−0.177823
$592$	12.7990	−	14.5127i	0.526035	−	0.596468i
$593$		−	1.88393i		−	0.0773639i	−0.999252	−	0.0386819i	$-0.987684\pi$
$593$		−	1.88393i		−	0.0773639i	0.999252	−	0.0386819i	$-0.0123159\pi$
$594$	−2.36671	+	11.0736i	−0.0971074	+	0.454354i
$595$	47.7990			1.95957
$596$	14.9249	−	39.4875i	0.611347	−	1.61747i
$597$		−	8.76725i		−	0.358820i
$598$	−7.00000	−	10.1291i	−0.286251	−	0.414208i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	0.564588	+	2.27411i	0.0230492	+	0.0928401i
$601$			32.7795i			1.33710i	0.743666	+	0.668552i	$0.233085\pi$
$601$			32.7795i			1.33710i	−0.743666	+	0.668552i	$0.766915\pi$
$602$	−17.0179	−	24.6250i	−0.693597	−	1.00364i
$603$	17.1716			0.699281
$604$	9.30739	−	24.6250i	0.378712	−	1.00198i
$605$	29.0513	+	1.73787i	1.18110	+	0.0706546i
$606$	8.31371	−	5.74544i	0.337721	−	0.233393i
$607$	29.0513			1.17916			0.589579	−	0.807711i	$-0.299294\pi$
$607$	29.0513			1.17916			0.589579	+	0.807711i	$0.299294\pi$
$608$	1.51472	−	12.7748i	0.0614300	−	0.518087i
$609$	−8.97056			−0.363506
$610$	−14.0000	−	20.2581i	−0.566843	−	0.820228i
$611$		0			0
$612$	−29.0513	−	10.9804i	−1.17433	−	0.443855i
$613$	26.7930			1.08216			0.541079	−	0.840972i	$-0.318016\pi$
$613$	26.7930			1.08216			0.541079	+	0.840972i	$0.318016\pi$
$614$	17.9706	+	26.0036i	0.725233	+	1.04942i
$615$	11.0011			0.443609
$616$	25.9566	+	16.7080i	1.04582	+	0.673183i
$617$	33.1127			1.33307			0.666534	−	0.745475i	$-0.267777\pi$
$617$	33.1127			1.33307			0.666534	+	0.745475i	$0.267777\pi$
$618$	6.01673	+	8.70626i	0.242028	+	0.350217i
$619$	31.5269			1.26717			0.633587	−	0.773672i	$-0.281582\pi$
$619$	31.5269			1.26717			0.633587	+	0.773672i	$0.281582\pi$
$620$	2.05025	−	5.42446i	0.0823401	−	0.217851i
$621$			15.4206i			0.618806i
$622$	12.0335	+	17.4125i	0.482498	+	0.698179i
$623$	35.0681			1.40497
$624$	−1.69376	−	1.49376i	−0.0678048	−	0.0597982i
$625$	−31.0000			−1.24000
$626$	9.10777	−	6.29420i	0.364020	−	0.251567i
$627$	2.14214	+	2.27411i	0.0855487	+	0.0908192i
$628$	0.849242	+	0.320983i	0.0338885	+	0.0128086i
$629$	−26.5591			−1.05898
$630$	19.7990	+	28.6493i	0.788811	+	1.14142i
$631$			11.6789i			0.464930i	0.972605	+	0.232465i	$0.0746791\pi$
$631$			11.6789i			0.464930i	−0.972605	+	0.232465i	$0.925321\pi$
$632$	6.34315	+	25.5496i	0.252317	+	1.01631i
$633$			3.76787i			0.149759i
$634$	−12.3984	−	17.9406i	−0.492405	−	0.712514i
$635$		−	1.49376i		−	0.0592780i
$636$	−5.79899	−	2.19181i	−0.229945	−	0.0869110i
$637$	5.21828			0.206756
$638$	6.45183	−	30.1873i	0.255430	−	1.19513i
$639$		−	18.0663i		−	0.714693i
$640$	−26.5591	−	13.8063i	−1.04984	−	0.545741i
$641$	−17.8284			−0.704181			−0.352090	−	0.935966i	$-0.614529\pi$
$641$	−17.8284			−0.704181			−0.352090	+	0.935966i	$0.614529\pi$
$642$	2.89949	+	4.19560i	0.114434	+	0.165587i
$643$	0.615224			0.0242621			0.0121310	−	0.999926i	$-0.496138\pi$
$643$	0.615224			0.0242621			0.0121310	+	0.999926i	$0.496138\pi$
$644$	39.3225	+	14.8625i	1.54952	+	0.585665i
$645$	−7.04903			−0.277555
$646$	−14.5257	+	10.0384i	−0.571505	+	0.394956i
$647$		−	23.5459i		−	0.925683i	−0.886441	−	0.462841i	$-0.846830\pi$
$647$		−	23.5459i		−	0.925683i	0.886441	−	0.462841i	$-0.153170\pi$
$648$	−5.10135	−	20.5478i	−0.200400	−	0.807193i
$649$	7.82843	−	7.37412i	0.307293	−	0.289459i
$650$	−3.17157	+	2.19181i	−0.124399	+	0.0859699i
$651$			1.49376i			0.0585450i
$652$	−9.07107	+	23.9998i	−0.355250	+	0.939904i
$653$		−	36.5866i		−	1.43174i	−0.698232	−	0.715872i	$-0.746030\pi$
$653$		−	36.5866i		−	1.43174i	0.698232	−	0.715872i	$-0.253970\pi$
$654$	−1.31371	+	0.907878i	−0.0513701	+	0.0355009i
$655$	18.0502			0.705279
$656$	−26.5591	+	30.1152i	−1.03696	+	1.17580i
$657$		−	2.66428i		−	0.103944i
$658$		0			0
$659$		−	10.9804i		−	0.427735i	−0.976863	−	0.213867i	$-0.931394\pi$
$659$		−	10.9804i		−	0.427735i	0.976863	−	0.213867i	$-0.0686060\pi$
$660$	6.71201	−	2.79167i	0.261264	−	0.108666i
$661$		−	12.3209i		−	0.479227i	−0.970868	−	0.239613i	$-0.922979\pi$
$661$		−	12.3209i		−	0.479227i	0.970868	−	0.239613i	$-0.0770207\pi$
$662$	−21.0243	+	14.5295i	−0.817133	+	0.564704i
$663$			3.09969i			0.120382i
$664$	12.4853	−	3.09969i	0.484523	−	0.120291i
$665$	19.7990			0.767772
$666$	−11.0011	−	15.9188i	−0.426286	−	0.616840i
$667$		−	42.0375i		−	1.62770i
$668$	−15.4895	+	40.9813i	−0.599306	+	1.58561i
$669$			1.73787i			0.0671901i
$670$	−12.9146	−	18.6875i	−0.498934	−	0.721962i
$671$	−15.8887	+	14.9666i	−0.613376	+	0.577780i
$672$	7.65685	+	0.907878i	0.295370	+	0.0350222i
$673$		−	38.2697i		−	1.47519i	−0.675245	−	0.737594i	$-0.735962\pi$
$673$		−	38.2697i		−	1.47519i	0.675245	−	0.737594i	$-0.264038\pi$
$674$	−15.3848	−	22.2619i	−0.592599	−	0.857497i
$675$	4.82843			0.185846
$676$	−7.87868	+	20.8450i	−0.303026	+	0.801732i
$677$	2.49221			0.0957834			0.0478917	−	0.998853i	$-0.484750\pi$
$677$	2.49221			0.0957834			0.0478917	+	0.998853i	$0.484750\pi$
$678$	2.97412	−	2.05535i	0.114220	−	0.0789354i
$679$	−24.6315			−0.945270
$680$	9.89949	+	39.8743i	0.379628	+	1.52911i
$681$		−	5.49019i		−	0.210384i
$682$	−5.02673	−	1.07434i	−0.192483	−	0.0411388i
$683$	−36.4264			−1.39382			−0.696909	−	0.717160i	$-0.745442\pi$
$683$	−36.4264			−1.39382			−0.696909	+	0.717160i	$0.745442\pi$
$684$	−12.0335	−	4.54822i	−0.460111	−	0.173905i
$685$		−	22.9039i		−	0.875112i
$686$	12.1421	−	8.39119i	0.463589	−	0.320377i
$687$			4.19560i			0.160072i
$688$	17.0179	−	19.2965i	0.648800	−	0.735671i
$689$		−	10.2000i		−	0.388590i
$690$	8.14396	−	5.62813i	0.310035	−	0.214259i
$691$	−8.75736			−0.333146			−0.166573	−	0.986029i	$-0.553270\pi$
$691$	−8.75736			−0.333146			−0.166573	+	0.986029i	$0.553270\pi$
$692$	−3.85525	+	10.2000i	−0.146554	+	0.387747i
$693$	22.4700	−	21.1660i	0.853565	−	0.804030i
$694$	3.34315	+	4.83756i	0.126904	+	0.183631i
$695$	52.0859			1.97573
$696$	−1.85786	−	7.48331i	−0.0704222	−	0.283654i
$697$	55.1127			2.08754
$698$	16.8995	−	11.6789i	0.639655	−	0.442053i
$699$			3.44464i			0.130288i
$700$	4.65369	−	12.3125i	0.175893	−	0.465369i
$701$	−26.0914			−0.985459			−0.492729	−	0.870183i	$-0.664001\pi$
$701$	−26.0914			−0.985459			−0.492729	+	0.870183i	$0.664001\pi$
$702$	−3.82843	+	2.64575i	−0.144495	+	0.0998574i
$703$	−11.0011			−0.414916
$704$	−8.56213	+	25.1135i	−0.322697	+	0.946502i
$705$		0			0
$706$	2.12723	−	1.47009i	0.0800595	−	0.0553276i
$707$	−56.7696			−2.13504
$708$	0.949747	−	2.51280i	0.0356937	−	0.0944366i
$709$			46.2617i			1.73739i	0.495343	+	0.868697i	$0.335042\pi$
$709$			46.2617i			1.73739i	−0.495343	+	0.868697i	$0.664958\pi$
$710$	−19.6613	+	13.5875i	−0.737874	+	0.509930i
$711$	26.3253			0.987274
$712$	7.26283	+	29.2541i	0.272186	+	1.09634i
$713$	−7.00000			−0.262152
$714$	−6.01673	−	8.70626i	−0.225170	−	0.325824i
$715$	8.20101	+	8.70626i	0.306700	+	0.325596i
$716$	6.87868	−	18.1993i	0.257068	−	0.680139i
$717$	2.25835			0.0843396
$718$	3.82843	−	2.64575i	0.142876	−	0.0987386i
$719$			5.10347i			0.190327i	0.995462	+	0.0951637i	$0.0303375\pi$
$719$			5.10347i			0.190327i	−0.995462	+	0.0951637i	$0.969663\pi$
$720$	−19.7990	+	22.4499i	−0.737865	+	0.836660i
$721$		−	59.4501i		−	2.21404i
$722$	16.0883	−	11.1183i	0.598745	−	0.413781i
$723$		−	1.88393i		−	0.0700643i
$724$	−4.94975	−	1.87083i	−0.183956	−	0.0695288i
$725$	−13.1626			−0.488848
$726$	−3.34031	−	5.51026i	−0.123971	−	0.204505i
$727$		−	8.57922i		−	0.318186i	−0.987264	−	0.159093i	$-0.949143\pi$
$727$		−	8.57922i		−	0.318186i	0.987264	−	0.159093i	$-0.0508569\pi$
$728$	3.05680	+	12.3125i	0.113292	+	0.456332i
$729$	−18.1716			−0.673021
$730$	−2.89949	+	2.00378i	−0.107315	+	0.0741634i
$731$	−35.3137			−1.30612
$732$	−1.92762	+	5.10001i	−0.0712470	+	0.188502i
$733$	−27.4544			−1.01405			−0.507026	−	0.861931i	$-0.669255\pi$
$733$	−27.4544			−1.01405			−0.507026	+	0.861931i	$0.669255\pi$
$734$	−17.8990	−	25.9000i	−0.660664	−	0.955988i
$735$			4.19560i			0.154757i
$736$	−4.25447	+	35.8813i	−0.156822	+	1.32260i
$737$	−14.6569	+	13.8063i	−0.539892	+	0.508561i
$738$	22.8284	+	33.0329i	0.840326	+	1.21596i
$739$			47.6894i			1.75428i	0.480234	+	0.877141i	$0.340552\pi$
$739$			47.6894i			1.75428i	−0.480234	+	0.877141i	$0.659448\pi$
$740$	−9.05025	+	23.9447i	−0.332694	+	0.880225i
$741$			1.28393i			0.0471665i
$742$	19.7990	+	28.6493i	0.726844	+	1.05175i
$743$	25.1961			0.924355			0.462177	−	0.886788i	$-0.347068\pi$
$743$	25.1961			0.924355			0.462177	+	0.886788i	$0.347068\pi$
$744$	−1.24611	+	0.309367i	−0.0456844	+	0.0113420i
$745$			55.8438i			2.04596i
$746$	−0.272078	+	0.188028i	−0.00996148	+	0.00688419i
$747$		−	12.8643i		−	0.470680i
$748$	33.6253	−	13.9855i	1.22946	−	0.511360i
$749$		−	28.6493i		−	1.04682i
$750$	2.64339	+	3.82501i	0.0965229	+	0.139670i
$751$			7.29529i			0.266209i	0.991102	+	0.133104i	$0.0424946\pi$
$751$			7.29529i			0.266209i	−0.991102	+	0.133104i	$0.957505\pi$
$752$		0			0
$753$	7.62742			0.277959
$754$	10.4366	−	7.21250i	0.380077	−	0.262664i
$755$			34.8250i			1.26741i
$756$	5.61750	−	14.8625i	0.204307	−	0.540545i
$757$		−	28.6493i		−	1.04128i	−0.853777	−	0.520639i	$-0.825694\pi$
$757$		−	28.6493i		−	1.04128i	0.853777	−	0.520639i	$-0.174306\pi$
$758$	−18.6975	+	12.9214i	−0.679122	+	0.469328i
$759$	−6.01673	−	6.38741i	−0.218393	−	0.231848i
$760$	4.10051	+	16.5165i	0.148741	+	0.599116i
$761$		−	7.37412i		−	0.267312i	−0.991028	−	0.133656i	$-0.957328\pi$
$761$		−	7.37412i		−	0.267312i	0.991028	−	0.133656i	$-0.0426717\pi$
$762$	−0.272078	+	0.188028i	−0.00985634	+	0.00681153i
$763$	8.97056			0.324756
$764$	−31.7487	−	11.9999i	−1.14863	−	0.434141i
$765$	41.0848			1.48542
$766$	5.86555	+	8.48751i	0.211931	+	0.306666i
$767$	4.41983			0.159591
$768$	0.828427	+	6.57544i	0.0298933	+	0.237271i
$769$			2.82590i			0.101905i	0.998701	+	0.0509523i	$0.0162256\pi$
$769$			2.82590i			0.101905i	−0.998701	+	0.0509523i	$0.983774\pi$
$770$	−39.9341	−	8.53496i	−1.43912	−	0.307579i
$771$	2.68629			0.0967444
$772$	−24.0669	−	9.09644i	−0.866187	−	0.327388i
$773$			8.76725i			0.315336i	0.987492	+	0.157668i	$0.0503976\pi$
$773$			8.76725i			0.315336i	−0.987492	+	0.157668i	$0.949602\pi$
$774$	−14.6274	−	21.1660i	−0.525772	−	0.760797i
$775$			2.19181i			0.0787322i
$776$	−5.10135	−	20.5478i	−0.183128	−	0.737623i
$777$		−	6.59377i		−	0.236550i
$778$	−26.1941	−	37.9032i	−0.939106	−	1.35889i
$779$	22.8284			0.817913
$780$	2.79457	+	1.05625i	0.100062	+	0.0378197i
$781$	14.5257	+	15.4206i	0.519769	+	0.551791i
$782$	40.7990	−	28.1954i	1.45897	−	1.00826i
$783$	−15.8887			−0.567816
$784$	−11.4853	−	10.1291i	−0.410189	−	0.361752i
$785$	−1.20101			−0.0428659
$786$	−2.27208	−	3.28772i	−0.0810423	−	0.117269i
$787$			32.9411i			1.17422i	0.809506	+	0.587112i	$0.199735\pi$
$787$			32.9411i			1.17422i	−0.809506	+	0.587112i	$0.800265\pi$
$788$	−7.37976	+	19.5250i	−0.262893	+	0.695550i
$789$	7.94435			0.282826
$790$	−19.7990	−	28.6493i	−0.704416	−	1.01930i
$791$	−20.3085			−0.722088
$792$	22.3105	+	14.3610i	0.792771	+	0.510297i
$793$	−8.97056			−0.318554
$794$	18.0502	+	26.1188i	0.640577	+	0.926921i
$795$	8.20101			0.290860
$796$	−39.5980	−	14.9666i	−1.40351	−	0.530478i
$797$		−	44.0699i		−	1.56104i	−0.625133	−	0.780518i	$-0.714955\pi$
$797$		−	44.0699i		−	1.56104i	0.625133	−	0.780518i	$-0.285045\pi$
$798$	−2.49221	−	3.60625i	−0.0882233	−	0.127660i
$799$		0			0
$800$	11.2350	+	1.33214i	0.397218	+	0.0470983i
$801$	30.1421			1.06502
$802$	−5.61750	+	3.88215i	−0.198361	+	0.137083i
$803$	2.14214	+	2.27411i	0.0755943	+	0.0802516i
$804$	−1.77817	+	4.70461i	−0.0627114	+	0.165919i
$805$	−55.6105			−1.96001
$806$	−1.20101	−	1.73787i	−0.0423038	−	0.0612140i
$807$			5.66756i			0.199507i
$808$	−11.7574	−	47.3576i	−0.413622	−	1.66603i
$809$			0.941967i			0.0331178i	0.999863	+	0.0165589i	$0.00527110\pi$
$809$			0.941967i			0.0331178i	−0.999863	+	0.0165589i	$0.994729\pi$
$810$	15.9229	+	23.0407i	0.559475	+	0.809566i
$811$		−	5.65180i		−	0.198462i	−0.995064	−	0.0992308i	$-0.968362\pi$
$811$		−	5.65180i		−	0.198462i	0.995064	−	0.0992308i	$-0.0316382\pi$
$812$	−15.3137	+	40.5163i	−0.537406	+	1.42184i
$813$	−5.21828			−0.183013
$814$	22.1891	+	4.74238i	0.777726	+	0.166220i
$815$		−	33.9408i		−	1.18890i
$816$	6.01673	−	6.82233i	0.210628	−	0.238829i
$817$	−14.6274			−0.511749
$818$	−1.51472	−	2.19181i	−0.0529609	−	0.0766349i
$819$	12.6863			0.443295
$820$	18.7801	−	49.6876i	0.655831	−	1.73517i
$821$	−21.3408			−0.744800			−0.372400	−	0.928072i	$-0.621465\pi$
$821$	−21.3408			−0.744800			−0.372400	+	0.928072i	$0.621465\pi$
$822$	−4.17179	+	2.88304i	−0.145508	+	0.100558i
$823$			35.9446i			1.25295i	0.779441	+	0.626475i	$0.215503\pi$
$823$			35.9446i			1.25295i	−0.779441	+	0.626475i	$0.784497\pi$
$824$	49.5937	−	12.3125i	1.72768	−	0.428927i
$825$	−2.00000	+	1.88393i	−0.0696311	+	0.0655902i
$826$	−12.4142	+	8.57922i	−0.431946	+	0.298509i
$827$			50.7438i			1.76454i	0.470748	+	0.882268i	$0.343984\pi$
$827$			50.7438i			1.76454i	−0.470748	+	0.882268i	$0.656016\pi$
$828$	33.7990	+	12.7748i	1.17460	+	0.443956i
$829$			41.8781i			1.45449i	0.686380	+	0.727243i	$0.259199\pi$
$829$			41.8781i			1.45449i	−0.686380	+	0.727243i	$0.740801\pi$
$830$	−14.0000	+	9.67513i	−0.485947	+	0.335829i
$831$	1.59689			0.0553957
$832$	−9.63811	+	5.10001i	−0.334141	+	0.176811i
$833$			21.0188i			0.728257i
$834$	−6.55635	−	9.48710i	−0.227028	−	0.328511i
$835$		−	57.9563i		−	2.00566i
$836$	13.9281	−	5.79298i	0.481712	−	0.200354i
$837$			2.64575i			0.0914505i
$838$	18.7801	−	12.9786i	0.648749	−	0.448338i
$839$			54.3870i			1.87765i	0.344398	+	0.938824i	$0.388083\pi$
$839$			54.3870i			1.87765i	−0.344398	+	0.938824i	$0.611917\pi$
$840$	−9.89949	+	2.45772i	−0.341565	+	0.0847995i
$841$	14.3137			0.493576
$842$	−6.01673	−	8.70626i	−0.207350	−	0.300038i
$843$		−	2.66428i		−	0.0917628i
$844$	17.0179	+	6.43215i	0.585779	+	0.221404i
$845$		−	29.4793i		−	1.01412i
$846$		0			0
$847$	−2.16148	+	36.1326i	−0.0742694	+	1.24153i
$848$	−19.7990	+	22.4499i	−0.679900	+	0.770934i
$849$			0.780351i			0.0267816i
$850$	−8.82843	−	12.7748i	−0.302813	−	0.438173i
$851$	30.8995			1.05922
$852$	4.94975	+	1.87083i	0.169576	+	0.0640935i
$853$	−58.1027			−1.98940			−0.994699	−	0.102833i	$-0.967209\pi$
$853$	−58.1027			−1.98940			−0.994699	+	0.102833i	$0.967209\pi$
$854$	25.1961	−	17.4125i	0.862192	−	0.595844i
$855$	17.0179			0.581999
$856$	23.8995	−	5.93347i	0.816868	−	0.202802i
$857$		−	21.9607i		−	0.750165i	−0.926992	−	0.375082i	$-0.877614\pi$
$857$		−	21.9607i		−	0.750165i	0.926992	−	0.375082i	$-0.122386\pi$
$858$	0.553479	−	2.58966i	0.0188955	−	0.0884097i
$859$	−49.2426			−1.68014			−0.840069	−	0.542480i	$-0.817485\pi$
$859$	−49.2426			−1.68014			−0.840069	+	0.542480i	$0.817485\pi$
$860$	−12.0335	+	31.8375i	−0.410337	+	1.08565i
$861$			13.6827i			0.466305i
$862$	2.51472	−	1.73787i	0.0856517	−	0.0591922i
$863$			14.9666i			0.509470i	0.967011	+	0.254735i	$0.0819882\pi$
$863$			14.9666i			0.509470i	−0.967011	+	0.254735i	$0.918012\pi$
$864$	13.5619	+	1.60804i	0.461384	+	0.0547066i
$865$		−	14.4250i		−	0.490465i
$866$	−20.1774	+	13.9442i	−0.685657	+	0.473844i
$867$	−5.44365			−0.184876
$868$	6.74668	+	2.55000i	0.228997	+	0.0865528i
$869$	−22.4700	+	21.1660i	−0.762243	+	0.718008i
$870$	5.79899	+	8.39119i	0.196604	+	0.284488i
$871$	−8.27508			−0.280390
$872$	1.85786	+	7.48331i	0.0629152	+	0.253417i
$873$	−21.1716			−0.716549
$874$	16.8995	−	11.6789i	0.571634	−	0.395045i
$875$		−	26.1188i		−	0.882976i
$876$	0.729951	+	0.275896i	0.0246628	+	0.00932165i
$877$	29.2852			0.988891			0.494445	−	0.869209i	$-0.335371\pi$
$877$	29.2852			0.988891			0.494445	+	0.869209i	$0.335371\pi$
$878$	−40.1421	+	27.7414i	−1.35473	+	0.936228i
$879$	−6.01673			−0.202939
$880$	−1.15069	−	35.0810i	−0.0387897	−	1.18258i
$881$	6.51472			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$881$	6.51472			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$882$	−12.5980	+	8.70626i	−0.424198	+	0.293155i
$883$	−4.34315			−0.146158			−0.0730792	−	0.997326i	$-0.523283\pi$
$883$	−4.34315			−0.146158			−0.0730792	+	0.997326i	$0.523283\pi$
$884$	14.0000	+	5.29150i	0.470871	+	0.177972i
$885$			3.55363i			0.119454i
$886$	30.7309	−	21.2375i	1.03243	−	0.713489i
$887$	46.5369			1.56256			0.781279	−	0.624183i	$-0.214568\pi$
$887$	46.5369			1.56256			0.781279	+	0.624183i	$0.214568\pi$
$888$	5.50057	−	1.36561i	0.184587	−	0.0458270i
$889$	1.85786			0.0623108
$890$	−22.6696	−	32.8032i	−0.759888	−	1.09956i
$891$	18.0711	−	17.0223i	0.605404	−	0.570270i
$892$	7.84924	+	2.96673i	0.262812	+	0.0993336i
$893$		0			0
$894$	10.1716	−	7.02938i	0.340188	−	0.235097i
$895$			25.7377i			0.860315i
$896$	17.1716	−	33.0329i	0.573662	−	1.10355i
$897$		−	3.60625i		−	0.120409i
$898$	18.5805	−	12.8406i	0.620040	−	0.428498i
$899$		−	7.21250i		−	0.240550i
$900$	4.00000	−	10.5830i	0.133333	−	0.352767i
$901$	41.0848			1.36873
$902$	−46.0444	−	9.84090i	−1.53311	−	0.327666i
$903$		−	8.76725i		−	0.291756i
$904$	−4.20603	−	16.9415i	−0.139891	−	0.563467i
$905$	7.00000			0.232688
$906$	6.34315	−	4.38362i	0.210737	−	0.145636i
$907$	−33.5147			−1.11284			−0.556419	−	0.830902i	$-0.687825\pi$
$907$	−33.5147			−1.11284			−0.556419	+	0.830902i	$0.687825\pi$
$908$	−24.7969	−	9.37233i	−0.822913	−	0.311032i
$909$	−48.7953			−1.61844
$910$	−9.54124	−	13.8063i	−0.316289	−	0.457673i
$911$		−	44.8999i		−	1.48760i	−0.668402	−	0.743800i	$-0.733022\pi$
$911$		−	44.8999i		−	1.48760i	0.668402	−	0.743800i	$-0.266978\pi$
$912$	2.49221	−	2.82590i	0.0825253	−	0.0935749i
$913$	10.3431	+	10.9804i	0.342308	+	0.363397i
$914$	18.2843	+	26.4575i	0.604790	+	0.875137i
$915$		−	7.21250i		−	0.238438i
$916$	18.9497	+	7.16233i	0.626117	+	0.236650i
$917$			22.4499i			0.741362i
$918$	−10.6569	−	15.4206i	−0.351729	−	0.508955i
$919$	−23.5992			−0.778465			−0.389233	−	0.921139i	$-0.627260\pi$
$919$	−23.5992			−0.778465			−0.389233	+	0.921139i	$0.627260\pi$
$920$	−11.5173	−	46.3907i	−0.379714	−	1.52946i
$921$			9.25805i			0.305063i
$922$	4.48528	−	3.09969i	0.147715	−	0.102083i
$923$			8.70626i			0.286570i
$924$	3.47214	+	8.34807i	0.114225	+	0.274631i
$925$		−	9.67513i		−	0.318116i
$926$	17.8990	+	25.9000i	0.588198	+	0.851128i
$927$		−	51.0993i		−	1.67832i
$928$	−36.9706	−	4.38362i	−1.21362	−	0.143900i
$929$	34.4853			1.13143			0.565713	−	0.824602i	$-0.308601\pi$
$929$	34.4853			1.13143			0.565713	+	0.824602i	$0.308601\pi$
$930$	1.39728	−	0.965635i	0.0458187	−	0.0316644i
$931$			8.70626i			0.285336i
$932$	15.5580	+	5.88036i	0.509618	+	0.192618i
$933$			6.19938i			0.202959i
$934$	41.9659	−	29.0018i	1.37317	−	0.948969i
$935$	−35.0681	+	33.0329i	−1.14685	+	1.08029i
$936$	2.62742	+	10.5830i	0.0858798	+	0.345916i
$937$			21.7991i			0.712146i	0.934458	+	0.356073i	$0.115885\pi$
$937$			21.7991i			0.712146i	−0.934458	+	0.356073i	$0.884115\pi$
$938$	23.2426	−	16.0625i	0.758899	−	0.524460i
$939$	3.24264			0.105820
$940$		0			0
$941$	14.7595			0.481147			0.240573	−	0.970631i	$-0.422665\pi$
$941$	14.7595			0.481147			0.240573	+	0.970631i	$0.422665\pi$
$942$	0.151178	+	0.218756i	0.00492564	+	0.00712745i
$943$	−64.1194			−2.08801
$944$	−9.72792	−	8.57922i	−0.316617	−	0.279230i
$945$			21.0188i			0.683741i
$946$	29.5032	+	6.30560i	0.959230	+	0.205013i
$947$	24.4142			0.793355			0.396678	−	0.917958i	$-0.370163\pi$
$947$	24.4142			0.793355			0.396678	+	0.917958i	$0.370163\pi$
$948$	−2.72607	+	7.21250i	−0.0885386	+	0.234251i
$949$			1.28393i			0.0416783i
$950$	−3.65685	−	5.29150i	−0.118644	−	0.171679i
$951$		−	6.38741i		−	0.207126i
$952$	−49.5937	+	12.3125i	−1.60734	+	0.399051i
$953$		−	36.5474i		−	1.18389i	−0.805980	−	0.591943i	$-0.798361\pi$
$953$		−	36.5474i		−	1.18389i	0.805980	−	0.591943i	$-0.201639\pi$
$954$	17.0179	+	24.6250i	0.550974	+	0.797265i
$955$	44.8995			1.45291
$956$	3.85525	−	10.2000i	0.124688	−	0.329892i
$957$	6.58132	−	6.19938i	0.212744	−	0.200398i
$958$	−31.8284	+	21.9960i	−1.02833	+	0.710659i
$959$	28.4867			0.919885
$960$	−4.10051	−	7.74923i	−0.132343	−	0.250105i
$961$	29.7990			0.961258
$962$	5.30152	+	7.67134i	0.170928	+	0.247334i
$963$		−	24.6250i		−	0.793530i
$964$	−8.50894	−	3.21608i	−0.274054	−	0.103583i
$965$	34.0358			1.09565
$966$	7.00000	+	10.1291i	0.225221	+	0.325897i
$967$	3.85525			0.123976			0.0619882	−	0.998077i	$-0.480256\pi$
$967$	3.85525			0.123976			0.0619882	+	0.998077i	$0.480256\pi$
$968$	−30.5898	+	5.68019i	−0.983193	+	0.182568i
$969$	−5.17157			−0.166135
$970$	15.9229	+	23.0407i	0.511255	+	0.739791i
$971$	32.8406			1.05391			0.526953	−	0.849895i	$-0.323334\pi$
$971$	32.8406			1.05391			0.526953	+	0.849895i	$0.323334\pi$
$972$	7.31371	−	19.3503i	0.234587	−	0.620660i
$973$			64.7820i			2.07681i
$974$	−21.4235	−	31.0000i	−0.686454	−	0.993305i
$975$	−1.12918			−0.0361625
$976$	19.7439	+	17.4125i	0.631988	+	0.557361i
$977$	−45.6274			−1.45975			−0.729875	−	0.683580i	$-0.760422\pi$
$977$	−45.6274			−1.45975			−0.729875	+	0.683580i	$0.760422\pi$
$978$	−6.18209	+	4.27232i	−0.197681	+	0.136614i
$979$	−25.7279	+	24.2349i	−0.822268	+	0.774549i
$980$	18.9497	+	7.16233i	0.605327	+	0.228792i
$981$	7.71049			0.246177
$982$	20.6863	+	29.9333i	0.660126	+	0.955209i
$983$		−	17.8783i		−	0.570229i	−0.958493	−	0.285114i	$-0.907968\pi$
$983$		−	17.8783i		−	0.570229i	0.958493	−	0.285114i	$-0.0920316\pi$
$984$	−11.4142	+	2.83378i	−0.363872	+	0.0903376i
$985$		−	27.6125i		−	0.879809i
$986$	29.0513	+	42.0375i	0.925183	+	1.33875i
$987$		0			0
$988$	5.79899	+	2.19181i	0.184490	+	0.0697308i
$989$	41.0848			1.30642
$990$	−34.3247	−	7.33608i	−1.09091	−	0.233156i
$991$		−	29.9333i		−	0.950861i	−0.879753	−	0.475431i	$-0.842292\pi$
$991$		−	29.9333i		−	0.950861i	0.879753	−	0.475431i	$-0.157708\pi$
$992$	−0.729951	+	6.15626i	−0.0231760	+	0.195461i
$993$	−7.48528			−0.237538
$994$	−16.8995	−	24.4537i	−0.536019	−	0.775625i
$995$	56.0000			1.77532
$996$	3.52452	+	1.33214i	0.111679	+	0.0422105i
$997$	55.6105			1.76120			0.880600	−	0.473860i	$-0.157140\pi$
$997$	55.6105			1.76120			0.880600	+	0.473860i	$0.157140\pi$
$998$	21.5062	−	14.8625i	0.680767	−	0.470465i
$999$		−	11.6789i		−	0.369504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.g.b.43.7	yes	8
3.2	odd	2		792.2.h.g.307.2		8
4.3	odd	2		352.2.g.b.175.4		8
8.3	odd	2	inner	88.2.g.b.43.1	✓	8
8.5	even	2		352.2.g.b.175.1		8
11.2	odd	10		968.2.k.g.403.8		32
11.3	even	5		968.2.k.g.475.4		32
11.4	even	5		968.2.k.g.699.7		32
11.5	even	5		968.2.k.g.723.3		32
11.6	odd	10		968.2.k.g.723.6		32
11.7	odd	10		968.2.k.g.699.2		32
11.8	odd	10		968.2.k.g.475.5		32
11.9	even	5		968.2.k.g.403.1		32
11.10	odd	2	inner	88.2.g.b.43.2	yes	8
12.11	even	2		3168.2.h.g.2287.4		8
16.3	odd	4		2816.2.e.o.2815.7		16
16.5	even	4		2816.2.e.o.2815.6		16
16.11	odd	4		2816.2.e.o.2815.9		16
16.13	even	4		2816.2.e.o.2815.12		16
24.5	odd	2		3168.2.h.g.2287.5		8
24.11	even	2		792.2.h.g.307.8		8
33.32	even	2		792.2.h.g.307.7		8
44.43	even	2		352.2.g.b.175.3		8
88.3	odd	10		968.2.k.g.475.2		32
88.19	even	10		968.2.k.g.475.7		32
88.21	odd	2		352.2.g.b.175.2		8
88.27	odd	10		968.2.k.g.723.8		32
88.35	even	10		968.2.k.g.403.3		32
88.43	even	2	inner	88.2.g.b.43.8	yes	8
88.51	even	10		968.2.k.g.699.4		32
88.59	odd	10		968.2.k.g.699.5		32
88.75	odd	10		968.2.k.g.403.6		32
88.83	even	10		968.2.k.g.723.1		32
132.131	odd	2		3168.2.h.g.2287.1		8
176.21	odd	4		2816.2.e.o.2815.5		16
176.43	even	4		2816.2.e.o.2815.10		16
176.109	odd	4		2816.2.e.o.2815.11		16
176.131	even	4		2816.2.e.o.2815.8		16
264.131	odd	2		792.2.h.g.307.1		8
264.197	even	2		3168.2.h.g.2287.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.g.b.43.1	✓	8	8.3	odd	2	inner
88.2.g.b.43.2	yes	8	11.10	odd	2	inner
88.2.g.b.43.7	yes	8	1.1	even	1	trivial
88.2.g.b.43.8	yes	8	88.43	even	2	inner
352.2.g.b.175.1		8	8.5	even	2
352.2.g.b.175.2		8	88.21	odd	2
352.2.g.b.175.3		8	44.43	even	2
352.2.g.b.175.4		8	4.3	odd	2
792.2.h.g.307.1		8	264.131	odd	2
792.2.h.g.307.2		8	3.2	odd	2
792.2.h.g.307.7		8	33.32	even	2
792.2.h.g.307.8		8	24.11	even	2
968.2.k.g.403.1		32	11.9	even	5
968.2.k.g.403.3		32	88.35	even	10
968.2.k.g.403.6		32	88.75	odd	10
968.2.k.g.403.8		32	11.2	odd	10
968.2.k.g.475.2		32	88.3	odd	10
968.2.k.g.475.4		32	11.3	even	5
968.2.k.g.475.5		32	11.8	odd	10
968.2.k.g.475.7		32	88.19	even	10
968.2.k.g.699.2		32	11.7	odd	10
968.2.k.g.699.4		32	88.51	even	10
968.2.k.g.699.5		32	88.59	odd	10
968.2.k.g.699.7		32	11.4	even	5
968.2.k.g.723.1		32	88.83	even	10
968.2.k.g.723.3		32	11.5	even	5
968.2.k.g.723.6		32	11.6	odd	10
968.2.k.g.723.8		32	88.27	odd	10
2816.2.e.o.2815.5		16	176.21	odd	4
2816.2.e.o.2815.6		16	16.5	even	4
2816.2.e.o.2815.7		16	16.3	odd	4
2816.2.e.o.2815.8		16	176.131	even	4
2816.2.e.o.2815.9		16	16.11	odd	4
2816.2.e.o.2815.10		16	176.43	even	4
2816.2.e.o.2815.11		16	176.109	odd	4
2816.2.e.o.2815.12		16	16.13	even	4
3168.2.h.g.2287.1		8	132.131	odd	2
3168.2.h.g.2287.4		8	12.11	even	2
3168.2.h.g.2287.5		8	24.5	odd	2
3168.2.h.g.2287.8		8	264.197	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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16342 - 0.804019i) q^{2} +0.414214 q^{3} +(0.707107 - 1.87083i) q^{4} +2.64575i q^{5} +(0.481906 - 0.333036i) q^{6} -3.29066 q^{7} +(-0.681517 - 2.74509i) q^{8} -2.82843 q^{9} +(2.12723 + 3.07813i) q^{10} +(2.41421 - 2.27411i) q^{11} +(0.292893 - 0.774923i) q^{12} +1.36303 q^{13} +(-3.82843 + 2.64575i) q^{14} +1.09591i q^{15} +(-3.00000 - 2.64575i) q^{16} +5.49019i q^{17} +(-3.29066 + 2.27411i) q^{18} +2.27411i q^{19} +(4.94975 + 1.87083i) q^{20} -1.36303 q^{21} +(0.980325 - 4.58682i) q^{22} -6.38741i q^{23} +(-0.282294 - 1.13705i) q^{24} -2.00000 q^{25} +(1.58579 - 1.09591i) q^{26} -2.41421 q^{27} +(-2.32685 + 6.15626i) q^{28} +6.58132 q^{29} +(0.881129 + 1.27500i) q^{30} -1.09591i q^{31} +(-5.61750 - 0.666071i) q^{32} +(1.00000 - 0.941967i) q^{33} +(4.41421 + 6.38741i) q^{34} -8.70626i q^{35} +(-2.00000 + 5.29150i) q^{36} +4.83756i q^{37} +(1.82843 + 2.64575i) q^{38} +0.564588 q^{39} +(7.26283 - 1.80313i) q^{40} -10.0384i q^{41} +(-1.58579 + 1.09591i) q^{42} +6.43215i q^{43} +(-2.54736 - 6.12462i) q^{44} -7.48331i q^{45} +(-5.13560 - 7.43126i) q^{46} +(-1.24264 - 1.09591i) q^{48} +3.82843 q^{49} +(-2.32685 + 1.60804i) q^{50} +2.27411i q^{51} +(0.963811 - 2.55000i) q^{52} -7.48331i q^{53} +(-2.80875 + 1.94107i) q^{54} +(6.01673 + 6.38741i) q^{55} +(2.24264 + 9.03316i) q^{56} +0.941967i q^{57} +(7.65685 - 5.29150i) q^{58} +3.24264 q^{59} +(2.05025 + 0.774923i) q^{60} -6.58132 q^{61} +(-0.881129 - 1.27500i) q^{62} +9.30739 q^{63} +(-7.07107 + 3.74166i) q^{64} +3.60625i q^{65} +(0.406064 - 1.89993i) q^{66} -6.07107 q^{67} +(10.2712 + 3.88215i) q^{68} -2.64575i q^{69} +(-7.00000 - 10.1291i) q^{70} +6.38741i q^{71} +(1.92762 + 7.76429i) q^{72} +0.941967i q^{73} +(3.88949 + 5.62813i) q^{74} -0.828427 q^{75} +(4.25447 + 1.60804i) q^{76} +(-7.94435 + 7.48331i) q^{77} +(0.656854 - 0.453939i) q^{78} -9.30739 q^{79} +(7.00000 - 7.93725i) q^{80} +7.48528 q^{81} +(-8.07107 - 11.6789i) q^{82} +4.54822i q^{83} +(-0.963811 + 2.55000i) q^{84} -14.5257 q^{85} +(5.17157 + 7.48331i) q^{86} +2.72607 q^{87} +(-7.88797 - 5.07739i) q^{88} -10.6569 q^{89} +(-6.01673 - 8.70626i) q^{90} -4.48528 q^{91} +(-11.9497 - 4.51658i) q^{92} -0.453939i q^{93} -6.01673 q^{95} +(-2.32685 - 0.275896i) q^{96} +7.48528 q^{97} +(4.45408 - 3.07813i) q^{98} +(-6.82843 + 6.43215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 8 q^{11} + 8 q^{12} - 8 q^{14} - 24 q^{16} + 8 q^{22} - 16 q^{25} + 24 q^{26} - 8 q^{27} + 8 q^{33} + 24 q^{34} - 16 q^{36} - 8 q^{38} - 24 q^{42} + 8 q^{44} + 24 q^{48} + 8 q^{49} - 16 q^{56}+ \cdots - 32 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 8 * q^11 + 8 * q^12 - 8 * q^14 - 24 * q^16 + 8 * q^22 - 16 * q^25 + 24 * q^26 - 8 * q^27 + 8 * q^33 + 24 * q^34 - 16 * q^36 - 8 * q^38 - 24 * q^42 + 8 * q^44 + 24 * q^48 + 8 * q^49 - 16 * q^56 + 16 * q^58 - 8 * q^59 + 56 * q^60 - 40 * q^66 + 8 * q^67 - 56 * q^70 + 16 * q^75 - 40 * q^78 + 56 * q^80 - 8 * q^81 - 8 * q^82 + 64 * q^86 - 16 * q^88 - 40 * q^89 + 32 * q^91 - 56 * q^92 - 8 * q^97 - 32 * q^99

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