LMFDB - Embedded newform 864.2.bn.a.611.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			611.24
Character	$\chi$	$=$	864.611
Dual form			864.2.bn.a.683.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.200844 - 1.39988i) q^{2} +(-1.91932 - 0.562314i) q^{4} +(0.202788 - 1.54033i) q^{5} +(1.17766 - 4.39511i) q^{7} +(-1.17266 + 2.57388i) q^{8} +O(q^{10})$	\(q+(0.200844 - 1.39988i) q^{2} +(-1.91932 - 0.562314i) q^{4} +(0.202788 - 1.54033i) q^{5} +(1.17766 - 4.39511i) q^{7} +(-1.17266 + 2.57388i) q^{8} +(-2.11554 - 0.593244i) q^{10} +(-3.93681 - 3.02082i) q^{11} +(0.682021 + 0.888828i) q^{13} +(-5.91609 - 2.53132i) q^{14} +(3.36761 + 2.15853i) q^{16} +4.08402 q^{17} +(2.37867 + 0.985278i) q^{19} +(-1.25536 + 2.84235i) q^{20} +(-5.01947 + 4.90434i) q^{22} +(-5.35870 + 1.43586i) q^{23} +(2.49815 + 0.669376i) q^{25} +(1.38123 - 0.776232i) q^{26} +(-4.73175 + 7.77341i) q^{28} +(-9.39407 + 1.23675i) q^{29} +(-0.512694 - 0.296004i) q^{31} +(3.69804 - 4.28071i) q^{32} +(0.820250 - 5.71713i) q^{34} +(-6.53108 - 2.70526i) q^{35} +(-1.95073 - 4.70947i) q^{37} +(1.85701 - 3.13197i) q^{38} +(3.72682 + 2.32823i) q^{40} +(1.25344 + 4.67789i) q^{41} +(1.63054 - 2.12496i) q^{43} +(5.85736 + 8.01165i) q^{44} +(0.933768 + 7.78992i) q^{46} +(2.20325 - 1.27205i) q^{47} +(-11.8679 - 6.85192i) q^{49} +(1.43878 - 3.36266i) q^{50} +(-0.809219 - 2.08946i) q^{52} +(-2.74153 - 6.61863i) q^{53} +(-5.45138 + 5.45138i) q^{55} +(9.93149 + 8.18512i) q^{56} +(-0.155437 + 13.3990i) q^{58} +(0.630820 + 0.0830490i) q^{59} +(1.61659 + 12.2792i) q^{61} +(-0.517341 + 0.658259i) q^{62} +(-5.24975 - 6.03656i) q^{64} +(1.50739 - 0.870292i) q^{65} +(-5.85104 - 7.62523i) q^{67} +(-7.83855 - 2.29650i) q^{68} +(-5.09877 + 8.59939i) q^{70} +(-1.64564 + 1.64564i) q^{71} +(-0.361810 - 0.361810i) q^{73} +(-6.98448 + 1.78491i) q^{74} +(-4.01141 - 3.22863i) q^{76} +(-17.9131 + 13.7452i) q^{77} +(-3.24123 - 5.61397i) q^{79} +(4.00774 - 4.74949i) q^{80} +(6.80022 - 0.815134i) q^{82} +(12.0094 - 1.58106i) q^{83} +(0.828189 - 6.29072i) q^{85} +(-2.64720 - 2.70934i) q^{86} +(12.3918 - 6.59050i) q^{88} +(2.45638 + 2.45638i) q^{89} +(4.70968 - 1.95082i) q^{91} +(11.0925 + 0.257395i) q^{92} +(-1.33820 - 3.33977i) q^{94} +(2.00002 - 3.46413i) q^{95} +(8.51749 + 14.7527i) q^{97} +(-11.9755 + 15.2374i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.200844	−	1.39988i	0.142018	−	0.989864i
$2$	0.200844	−	1.39988i	0.142018	−	0.989864i
$3$		0			0
$3$		0			0
$4$	−1.91932	−	0.562314i	−0.959662	−	0.281157i
$5$	0.202788	−	1.54033i	0.0906895	−	0.688855i	−0.884350	−	0.466824i	$-0.845398\pi$
$5$	0.202788	−	1.54033i	0.0906895	−	0.688855i	0.975040	−	0.222031i	$-0.0712686\pi$
$6$		0			0
$7$	1.17766	−	4.39511i	0.445116	−	1.66119i	−0.270516	−	0.962716i	$-0.587194\pi$
$7$	1.17766	−	4.39511i	0.445116	−	1.66119i	0.715631	−	0.698478i	$-0.246139\pi$
$8$	−1.17266	+	2.57388i	−0.414597	+	0.910005i
$9$		0			0
$10$	−2.11554	−	0.593244i	−0.668993	−	0.187600i
$11$	−3.93681	−	3.02082i	−1.18699	−	0.910811i	−0.189521	−	0.981877i	$-0.560693\pi$
$11$	−3.93681	−	3.02082i	−1.18699	−	0.910811i	−0.997472	+	0.0710656i	$0.977360\pi$
$12$		0			0
$13$	0.682021	+	0.888828i	0.189159	+	0.246516i	0.878299	−	0.478111i	$-0.158678\pi$
$13$	0.682021	+	0.888828i	0.189159	+	0.246516i	−0.689141	+	0.724628i	$0.742012\pi$
$14$	−5.91609	−	2.53132i	−1.58114	−	0.676523i
$15$		0			0
$16$	3.36761	+	2.15853i	0.841901	+	0.539632i
$17$	4.08402			0.990519			0.495260	−	0.868745i	$-0.335073\pi$
$17$	4.08402			0.990519			0.495260	+	0.868745i	$0.335073\pi$
$18$		0			0
$19$	2.37867	+	0.985278i	0.545705	+	0.226038i	0.638466	−	0.769650i	$-0.279569\pi$
$19$	2.37867	+	0.985278i	0.545705	+	0.226038i	−0.0927611	+	0.995688i	$0.529569\pi$
$20$	−1.25536	+	2.84235i	−0.280708	+	0.635570i
$21$		0			0
$22$	−5.01947	+	4.90434i	−1.07015	+	1.04561i
$23$	−5.35870	+	1.43586i	−1.11737	+	0.299397i	−0.769817	−	0.638264i	$-0.779653\pi$
$23$	−5.35870	+	1.43586i	−1.11737	+	0.299397i	−0.347549	+	0.937662i	$0.612986\pi$
$24$		0			0
$25$	2.49815	+	0.669376i	0.499629	+	0.133875i
$26$	1.38123	−	0.776232i	0.270882	−	0.152232i
$27$		0			0
$28$	−4.73175	+	7.77341i	−0.894217	+	1.46904i
$29$	−9.39407	+	1.23675i	−1.74444	+	0.229659i	−0.934276	−	0.356551i	$-0.883953\pi$
$29$	−9.39407	+	1.23675i	−1.74444	+	0.229659i	−0.810159	+	0.586210i	$0.800619\pi$
$30$		0			0
$31$	−0.512694	−	0.296004i	−0.0920825	−	0.0531639i	0.453252	−	0.891383i	$-0.350264\pi$
$31$	−0.512694	−	0.296004i	−0.0920825	−	0.0531639i	−0.545334	+	0.838219i	$0.683597\pi$
$32$	3.69804	−	4.28071i	0.653727	−	0.756730i
$33$		0			0
$34$	0.820250	−	5.71713i	0.140672	−	0.980480i
$35$	−6.53108	−	2.70526i	−1.10395	−	0.457273i
$36$		0			0
$37$	−1.95073	−	4.70947i	−0.320698	−	0.774233i	−0.999214	−	0.0396471i	$-0.987377\pi$
$37$	−1.95073	−	4.70947i	−0.320698	−	0.774233i	0.678516	−	0.734586i	$-0.262623\pi$
$38$	1.85701	−	3.13197i	0.301247	−	0.508072i
$39$		0			0
$40$	3.72682	+	2.32823i	0.589262	+	0.368125i
$41$	1.25344	+	4.67789i	0.195754	+	0.730563i	0.992070	+	0.125683i	$0.0401123\pi$
$41$	1.25344	+	4.67789i	0.195754	+	0.730563i	−0.796317	+	0.604880i	$0.793221\pi$
$42$		0			0
$43$	1.63054	−	2.12496i	0.248654	−	0.324053i	−0.652305	−	0.757957i	$-0.726198\pi$
$43$	1.63054	−	2.12496i	0.248654	−	0.324053i	0.900959	+	0.433904i	$0.142864\pi$
$44$	5.85736	+	8.01165i	0.883030	+	1.20780i
$45$		0			0
$46$	0.933768	+	7.78992i	0.137677	+	1.14856i
$47$	2.20325	−	1.27205i	0.321377	−	0.185547i	−0.330629	−	0.943761i	$-0.607261\pi$
$47$	2.20325	−	1.27205i	0.321377	−	0.185547i	0.652006	+	0.758214i	$0.273928\pi$
$48$		0			0
$49$	−11.8679	−	6.85192i	−1.69541	−	0.978846i
$50$	1.43878	−	3.36266i	0.203475	−	0.475552i
$51$		0			0
$52$	−0.809219	−	2.08946i	−0.112219	−	0.289756i
$53$	−2.74153	−	6.61863i	−0.376578	−	0.909139i	−0.992602	−	0.121412i	$-0.961258\pi$
$53$	−2.74153	−	6.61863i	−0.376578	−	0.909139i	0.616024	−	0.787727i	$-0.288742\pi$
$54$		0			0
$55$	−5.45138	+	5.45138i	−0.735064	+	0.735064i
$56$	9.93149	+	8.18512i	1.32715	+	1.09378i
$57$		0			0
$58$	−0.155437	+	13.3990i	−0.0204099	+	1.75937i
$59$	0.630820	+	0.0830490i	0.0821257	+	0.0108121i	0.171477	−	0.985188i	$-0.445146\pi$
$59$	0.630820	+	0.0830490i	0.0821257	+	0.0108121i	−0.0893513	+	0.996000i	$0.528479\pi$
$60$		0			0
$61$	1.61659	+	12.2792i	0.206983	+	1.57219i	0.707658	+	0.706556i	$0.249752\pi$
$61$	1.61659	+	12.2792i	0.206983	+	1.57219i	−0.500675	+	0.865636i	$0.666915\pi$
$62$	−0.517341	+	0.658259i	−0.0657024	+	0.0835990i
$63$		0			0
$64$	−5.24975	−	6.03656i	−0.656219	−	0.754570i
$65$	1.50739	−	0.870292i	0.186969	−	0.107946i
$66$		0			0
$67$	−5.85104	−	7.62523i	−0.714819	−	0.931570i	0.284816	−	0.958582i	$-0.408067\pi$
$67$	−5.85104	−	7.62523i	−0.714819	−	0.931570i	−0.999635	+	0.0270123i	$0.991401\pi$
$68$	−7.83855	−	2.29650i	−0.950564	−	0.278492i
$69$		0			0
$70$	−5.09877	+	8.59939i	−0.609419	+	1.02782i
$71$	−1.64564	+	1.64564i	−0.195301	+	0.195301i	−0.797982	−	0.602681i	$-0.794099\pi$
$71$	−1.64564	+	1.64564i	−0.195301	+	0.195301i	0.602681	+	0.797982i	$0.294099\pi$
$72$		0			0
$73$	−0.361810	−	0.361810i	−0.0423466	−	0.0423466i	0.685616	−	0.727963i	$-0.259533\pi$
$73$	−0.361810	−	0.361810i	−0.0423466	−	0.0423466i	−0.727963	+	0.685616i	$0.759533\pi$
$74$	−6.98448	+	1.78491i	−0.811930	+	0.207492i
$75$		0			0
$76$	−4.01141	−	3.22863i	−0.460140	−	0.370349i
$77$	−17.9131	+	13.7452i	−2.04138	+	1.56641i
$78$		0			0
$79$	−3.24123	−	5.61397i	−0.364667	−	0.631622i	0.624056	−	0.781380i	$-0.285484\pi$
$79$	−3.24123	−	5.61397i	−0.364667	−	0.631622i	−0.988723	+	0.149758i	$0.952150\pi$
$80$	4.00774	−	4.74949i	0.448079	−	0.531009i
$81$		0			0
$82$	6.80022	−	0.815134i	0.750959	−	0.0900165i
$83$	12.0094	−	1.58106i	1.31820	−	0.173544i	0.561593	−	0.827414i	$-0.310189\pi$
$83$	12.0094	−	1.58106i	1.31820	−	0.173544i	0.756607	+	0.653870i	$0.226856\pi$
$84$		0			0
$85$	0.828189	−	6.29072i	0.0898297	−	0.682324i
$86$	−2.64720	−	2.70934i	−0.285455	−	0.292155i
$87$		0			0
$88$	12.3918	−	6.59050i	1.32097	−	0.702550i
$89$	2.45638	+	2.45638i	0.260376	+	0.260376i	0.825207	−	0.564831i	$-0.191059\pi$
$89$	2.45638	+	2.45638i	0.260376	+	0.260376i	−0.564831	+	0.825207i	$0.691059\pi$
$90$		0			0
$91$	4.70968	−	1.95082i	0.493709	−	0.204501i
$92$	11.0925	+	0.257395i	1.15647	+	0.0268353i
$93$		0			0
$94$	−1.33820	−	3.33977i	−0.138025	−	0.344471i
$95$	2.00002	−	3.46413i	0.205197	−	0.355412i
$96$		0			0
$97$	8.51749	+	14.7527i	0.864820	+	1.49791i	0.867225	+	0.497916i	$0.165901\pi$
$97$	8.51749	+	14.7527i	0.864820	+	1.49791i	−0.00240483	+	0.999997i	$0.500765\pi$
$98$	−11.9755	+	15.2374i	−1.20970	+	1.53921i
$99$		0			0
$100$	−4.41835	−	2.68949i	−0.441835	−	0.268949i
$101$	−3.20048	−	2.45582i	−0.318460	−	0.244363i	0.437144	−	0.899391i	$-0.355990\pi$
$101$	−3.20048	−	2.45582i	−0.318460	−	0.244363i	−0.755604	+	0.655028i	$0.772657\pi$
$102$		0			0
$103$	15.3404	−	4.11044i	1.51153	−	0.405013i	0.594587	−	0.804031i	$-0.297316\pi$
$103$	15.3404	−	4.11044i	1.51153	−	0.405013i	0.916943	+	0.399018i	$0.130649\pi$
$104$	−3.08752	+	0.713154i	−0.302756	+	0.0699305i
$105$		0			0
$106$	−9.81591	+	2.50850i	−0.953405	+	0.243647i
$107$	2.60587	−	1.07939i	0.251919	−	0.104348i	−0.253150	−	0.967427i	$-0.581467\pi$
$107$	2.60587	−	1.07939i	0.251919	−	0.104348i	0.505070	+	0.863079i	$0.331467\pi$
$108$		0			0
$109$	−0.946606	+	2.28531i	−0.0906684	+	0.218893i	−0.962708	−	0.270542i	$-0.912797\pi$
$109$	−0.946606	+	2.28531i	−0.0906684	+	0.218893i	0.872040	+	0.489435i	$0.162797\pi$
$110$	6.53640	+	8.72616i	0.623221	+	0.832006i
$111$		0			0
$112$	13.4529	−	12.2590i	1.27118	−	1.15836i
$113$	8.13956	−	14.0981i	0.765705	−	1.32624i	−0.174167	−	0.984716i	$-0.555723\pi$
$113$	8.13956	−	14.0981i	0.765705	−	1.32624i	0.939873	−	0.341525i	$-0.110943\pi$
$114$		0			0
$115$	1.12501	+	8.54533i	0.104908	+	0.796856i
$116$	18.7257	+	2.90869i	1.73864	+	0.270065i
$117$		0			0
$118$	0.242955	−	0.866392i	0.0223658	−	0.0797578i
$119$	4.80960	−	17.9497i	0.440896	−	1.64544i
$120$		0			0
$121$	3.52610	+	13.1596i	0.320554	+	1.19633i
$122$	17.5141	+	0.203175i	1.58565	+	0.0183946i
$123$		0			0
$124$	0.817578	+	0.856422i	0.0734207	+	0.0769090i
$125$	4.51037	−	10.8890i	0.403420	−	0.973942i
$126$		0			0
$127$		−	21.9679i		−	1.94934i	−0.223651	−	0.974669i	$-0.571798\pi$
$127$		−	21.9679i		−	1.94934i	0.223651	−	0.974669i	$-0.428202\pi$
$128$	−9.50484	+	6.13661i	−0.840117	+	0.542405i
$129$		0			0
$130$	−0.915554	−	2.28496i	−0.0802994	−	0.200404i
$131$	2.58818	−	1.98598i	0.226130	−	0.173516i	−0.489482	−	0.872013i	$-0.662814\pi$
$131$	2.58818	−	1.98598i	0.226130	−	0.173516i	0.715613	+	0.698497i	$0.246148\pi$
$132$		0			0
$133$	7.13168	−	9.29419i	0.618395	−	0.805908i
$134$	−11.8495	+	6.65927i	−1.02364	+	0.575274i
$135$		0			0
$136$	−4.78915	+	10.5118i	−0.410666	+	0.901378i
$137$	3.35747	+	0.899631i	0.286848	+	0.0768606i	0.399374	−	0.916788i	$-0.369228\pi$
$137$	3.35747	+	0.899631i	0.286848	+	0.0768606i	−0.112526	+	0.993649i	$0.535894\pi$
$138$		0			0
$139$	−16.1894	−	2.13138i	−1.37317	−	0.180781i	−0.592423	−	0.805627i	$-0.701828\pi$
$139$	−16.1894	−	2.13138i	−1.37317	−	0.180781i	−0.780748	+	0.624846i	$0.785162\pi$
$140$	11.0140	+	8.86479i	0.930857	+	0.749212i
$141$		0			0
$142$	1.97318	+	2.63421i	0.165586	+	0.221058i
$143$		−	5.55941i		−	0.464901i
$144$		0			0
$145$			14.7207i			1.22249i
$146$	−0.579157	+	0.433823i	−0.0479314	+	0.0359034i
$147$		0			0
$148$	1.09587	+	10.1359i	0.0900802	+	0.833168i
$149$	9.88347	+	1.30118i	0.809685	+	0.106597i	0.523991	−	0.851724i	$-0.324443\pi$
$149$	9.88347	+	1.30118i	0.809685	+	0.106597i	0.285694	+	0.958321i	$0.407776\pi$
$150$		0			0
$151$	−4.32703	−	1.15942i	−0.352129	−	0.0943526i	0.0784188	−	0.996921i	$-0.475013\pi$
$151$	−4.32703	−	1.15942i	−0.352129	−	0.0943526i	−0.430548	+	0.902568i	$0.641680\pi$
$152$	−5.32536	+	4.96703i	−0.431944	+	0.402880i
$153$		0			0
$154$	15.6439	+	27.8368i	1.26062	+	2.24315i
$155$	−0.559911	+	0.729690i	−0.0449731	+	0.0586101i
$156$		0			0
$157$	6.14501	−	4.71523i	0.490425	−	0.376317i	−0.333741	−	0.942665i	$-0.608311\pi$
$157$	6.14501	−	4.71523i	0.490425	−	0.376317i	0.824166	+	0.566348i	$0.191644\pi$
$158$	−8.50987	+	3.40980i	−0.677009	+	0.271269i
$159$		0			0
$160$	−5.84378	−	6.56426i	−0.461991	−	0.518951i
$161$			25.2430i			1.98943i
$162$		0			0
$163$	−4.51520	+	10.9007i	−0.353658	+	0.853806i	0.642504	+	0.766282i	$0.277895\pi$
$163$	−4.51520	+	10.9007i	−0.353658	+	0.853806i	−0.996162	+	0.0875240i	$0.972105\pi$
$164$	0.224694	−	9.68321i	0.0175456	−	0.756131i
$165$		0			0
$166$	0.198711	−	17.1292i	0.0154229	−	1.32949i
$167$	−0.234682	−	0.875847i	−0.0181603	−	0.0677751i	0.956251	−	0.292547i	$-0.0945029\pi$
$167$	−0.234682	−	0.875847i	−0.0181603	−	0.0677751i	−0.974411	+	0.224772i	$0.927836\pi$
$168$		0			0
$169$	3.03979	−	11.3446i	0.233830	−	0.872664i
$170$	−8.63991	−	2.42282i	−0.662651	−	0.185822i
$171$		0			0
$172$	−4.32442	+	3.16160i	−0.329734	+	0.241070i
$173$	−0.137639	−	1.04547i	−0.0104645	−	0.0794859i	0.985416	−	0.170164i	$-0.0544298\pi$
$173$	−0.137639	−	1.04547i	−0.0104645	−	0.0794859i	−0.995880	+	0.0906783i	$0.971096\pi$
$174$		0			0
$175$	5.88396	−	10.1913i	0.444785	−	0.770391i
$176$	−6.73710	−	18.6706i	−0.507828	−	1.40735i
$177$		0			0
$178$	3.93199	−	2.94529i	0.294715	−	0.220759i
$179$	8.10504	−	19.5673i	0.605799	−	1.46253i	−0.261730	−	0.965141i	$-0.584293\pi$
$179$	8.10504	−	19.5673i	0.605799	−	1.46253i	0.867529	−	0.497387i	$-0.165707\pi$
$180$		0			0
$181$	4.74472	−	1.96533i	0.352672	−	0.146082i	−0.199312	−	0.979936i	$-0.563871\pi$
$181$	4.74472	−	1.96533i	0.352672	−	0.146082i	0.551984	+	0.833854i	$0.313871\pi$
$182$	−1.78499	−	6.98480i	−0.132313	−	0.517748i
$183$		0			0
$184$	2.58818	−	15.4764i	0.190803	−	1.14094i
$185$	−7.64971	+	2.04973i	−0.562418	+	0.150699i
$186$		0			0
$187$	−16.0780	−	12.3371i	−1.17574	−	0.902176i
$188$	−4.94404	+	1.20255i	−0.360581	+	0.0877050i
$189$		0			0
$190$	−4.44767	−	3.49553i	−0.322668	−	0.253592i
$191$	−2.81155	−	4.86975i	−0.203437	−	0.352363i	0.746197	−	0.665725i	$-0.231878\pi$
$191$	−2.81155	−	4.86975i	−0.203437	−	0.352363i	−0.949634	+	0.313363i	$0.898544\pi$
$192$		0			0
$193$	0.551350	−	0.954966i	0.0396870	−	0.0687399i	−0.845500	−	0.533976i	$-0.820697\pi$
$193$	0.551350	−	0.954966i	0.0396870	−	0.0687399i	0.885187	+	0.465236i	$0.154031\pi$
$194$	22.3627	−	8.96047i	1.60555	−	0.643324i
$195$		0			0
$196$	18.9254	+	19.8245i	1.35181	+	1.41604i
$197$	7.02701	−	2.91068i	0.500653	−	0.207377i	−0.118042	−	0.993009i	$-0.537662\pi$
$197$	7.02701	−	2.91068i	0.500653	−	0.207377i	0.618695	+	0.785631i	$0.287662\pi$
$198$		0			0
$199$	1.84792	+	1.84792i	0.130996	+	0.130996i	0.769565	−	0.638569i	$-0.220473\pi$
$199$	1.84792	+	1.84792i	0.130996	+	0.130996i	−0.638569	+	0.769565i	$0.720473\pi$
$200$	−4.65236	+	5.64499i	−0.328972	+	0.399161i
$201$		0			0
$202$	−4.08065	+	3.98705i	−0.287113	+	0.280528i
$203$	−5.62741	+	42.7444i	−0.394967	+	3.00007i
$204$		0			0
$205$	7.45966	−	0.982082i	0.521005	−	0.0685916i
$206$	−2.67310	−	22.3002i	−0.186243	−	1.55373i
$207$		0			0
$208$	0.378221	+	4.46538i	0.0262249	+	0.309619i
$209$	−6.38803	−	11.0644i	−0.441869	−	0.765340i
$210$		0			0
$211$	0.862538	−	0.661849i	0.0593796	−	0.0455635i	−0.578645	−	0.815579i	$-0.696418\pi$
$211$	0.862538	−	0.661849i	0.0593796	−	0.0455635i	0.638025	+	0.770016i	$0.279752\pi$
$212$	1.54013	+	14.2449i	0.105776	+	0.978344i
$213$		0			0
$214$	−0.987640	−	3.86470i	−0.0675137	−	0.264185i
$215$	−2.94247	−	2.94247i	−0.200675	−	0.200675i
$216$		0			0
$217$	−1.90475	+	1.90475i	−0.129303	+	0.129303i
$218$	3.00904	+	1.78412i	0.203798	+	0.120836i
$219$		0			0
$220$	13.5284	−	7.39758i	0.912082	−	0.498745i
$221$	2.78539	+	3.62999i	0.187365	+	0.244179i
$222$		0			0
$223$	5.00046	−	2.88701i	0.334855	−	0.193329i	−0.323139	−	0.946351i	$-0.604738\pi$
$223$	5.00046	−	2.88701i	0.334855	−	0.193329i	0.657995	+	0.753023i	$0.271405\pi$
$224$	−14.4591	−	21.2945i	−0.966092	−	1.42280i
$225$		0			0
$226$	−18.1009	−	14.2259i	−1.20405	−	0.946294i
$227$	0.802907	+	6.09868i	0.0532908	+	0.404784i	0.997212	+	0.0746142i	$0.0237725\pi$
$227$	0.802907	+	6.09868i	0.0532908	+	0.404784i	−0.943922	+	0.330169i	$0.892894\pi$
$228$		0			0
$229$	−14.7068	−	1.93618i	−0.971851	−	0.127947i	−0.372152	−	0.928172i	$-0.621380\pi$
$229$	−14.7068	−	1.93618i	−0.971851	−	0.127947i	−0.599700	+	0.800225i	$0.704713\pi$
$230$	12.1884	+	0.141393i	0.803678	+	0.00932321i
$231$		0			0
$232$	7.83276	−	25.6295i	0.514246	−	1.68266i
$233$	−14.8047	+	14.8047i	−0.969888	+	0.969888i	−0.999560	−	0.0296721i	$-0.990554\pi$
$233$	−14.8047	+	14.8047i	−0.969888	+	0.969888i	0.0296721	+	0.999560i	$0.490554\pi$
$234$		0			0
$235$	−1.51258	−	3.65168i	−0.0986695	−	0.238209i
$236$	−1.16405	−	0.514117i	−0.0757730	−	0.0334662i
$237$		0			0
$238$	−24.1614	−	10.3379i	−1.56615	−	0.670110i
$239$	−5.86397	−	3.38557i	−0.379309	−	0.218994i	0.298209	−	0.954501i	$-0.403611\pi$
$239$	−5.86397	−	3.38557i	−0.379309	−	0.218994i	−0.677518	+	0.735507i	$0.736944\pi$
$240$		0			0
$241$	25.0688	−	14.4735i	1.61482	−	0.932318i	0.626592	−	0.779348i	$-0.284449\pi$
$241$	25.0688	−	14.4735i	1.61482	−	0.932318i	0.988231	−	0.152970i	$-0.0488839\pi$
$242$	19.1300	−	2.29309i	1.22972	−	0.147406i
$243$		0			0
$244$	3.80202	−	24.4768i	0.243399	−	1.56697i
$245$	−12.9609	+	16.8909i	−0.828039	+	1.07912i
$246$		0			0
$247$	0.746563	+	2.78621i	0.0475027	+	0.177282i
$248$	1.36309	−	0.972503i	0.0865565	−	0.0617540i
$249$		0			0
$250$	−14.3374	−	8.50096i	−0.906777	−	0.537648i
$251$	−1.10999	−	2.67976i	−0.0700622	−	0.169145i	0.884969	−	0.465649i	$-0.154179\pi$
$251$	−1.10999	−	2.67976i	−0.0700622	−	0.169145i	−0.955032	+	0.296504i	$0.904179\pi$
$252$		0			0
$253$	25.4337	+	10.5350i	1.59900	+	0.662327i
$254$	−30.7524	−	4.41212i	−1.92958	−	0.276841i
$255$		0			0
$256$	6.68153	+	14.5381i	0.417596	+	0.908633i
$257$	19.8010	+	11.4321i	1.23515	+	0.713115i	0.968099	−	0.250567i	$-0.0806170\pi$
$257$	19.8010	+	11.4321i	1.23515	+	0.713115i	0.267052	+	0.963682i	$0.413950\pi$
$258$		0			0
$259$	−22.9959	+	3.02747i	−1.42890	+	0.188118i
$260$	−3.38255	+	0.822745i	−0.209777	+	0.0510245i
$261$		0			0
$262$	−2.26031	−	4.02201i	−0.139643	−	0.248481i
$263$	−0.590968	−	0.158349i	−0.0364407	−	0.00976425i	0.240553	−	0.970636i	$-0.422671\pi$
$263$	−0.590968	−	0.158349i	−0.0364407	−	0.00976425i	−0.276993	+	0.960872i	$0.589338\pi$
$264$		0			0
$265$	−10.7508	+	2.88067i	−0.660417	+	0.176958i
$266$	−11.5784	−	11.8502i	−0.709916	−	0.726581i
$267$		0			0
$268$	6.94227	+	17.9254i	0.424067	+	1.09497i
$269$	1.42907	+	0.591941i	0.0871321	+	0.0360913i	0.425824	−	0.904806i	$-0.359984\pi$
$269$	1.42907	+	0.591941i	0.0871321	+	0.0360913i	−0.338692	+	0.940897i	$0.609984\pi$
$270$		0			0
$271$	12.8060			0.777912			0.388956	−	0.921256i	$-0.372836\pi$
$271$	12.8060			0.777912			0.388956	+	0.921256i	$0.372836\pi$
$272$	13.7534	+	8.81546i	0.833920	+	0.534516i
$273$		0			0
$274$	1.93370	−	4.51936i	0.116819	−	0.273025i
$275$	−7.81266	−	10.1817i	−0.471121	−	0.613977i
$276$		0			0
$277$	−8.33871	−	6.39852i	−0.501025	−	0.384450i	0.327103	−	0.944989i	$-0.393927\pi$
$277$	−8.33871	−	6.39852i	−0.501025	−	0.384450i	−0.828128	+	0.560539i	$0.810594\pi$
$278$	−6.23523	+	22.2352i	−0.373964	+	1.33358i
$279$		0			0
$280$	14.6217	−	13.6379i	0.873816	−	0.815020i
$281$	−2.09852	+	7.83178i	−0.125187	+	0.467205i	−0.999846	−	0.0175337i	$-0.994419\pi$
$281$	−2.09852	+	7.83178i	−0.125187	+	0.467205i	0.874659	+	0.484738i	$0.161085\pi$
$282$		0			0
$283$	−1.51058	+	11.4740i	−0.0897947	+	0.682059i	0.886049	+	0.463591i	$0.153439\pi$
$283$	−1.51058	+	11.4740i	−0.0897947	+	0.682059i	−0.975844	+	0.218468i	$0.929894\pi$
$284$	4.08388	−	2.23315i	0.242334	−	0.132513i
$285$		0			0
$286$	−7.78250	−	1.11657i	−0.460189	−	0.0660243i
$287$	22.0359			1.30074
$288$		0			0
$289$	−0.320814			−0.0188714
$290$	20.6073	+	2.95657i	1.21010	+	0.173616i
$291$		0			0
$292$	0.490979	+	0.897881i	0.0287324	+	0.0525445i
$293$	−0.378280	+	2.87332i	−0.0220993	+	0.167861i	−0.998936	−	0.0461271i	$-0.985312\pi$
$293$	−0.378280	+	2.87332i	−0.0220993	+	0.167861i	0.976836	+	0.213988i	$0.0686454\pi$
$294$		0			0
$295$	0.255845	−	0.954827i	0.0148959	−	0.0555922i
$296$	14.4092	+	0.501649i	0.837516	+	0.0291577i
$297$		0			0
$298$	3.80653	−	13.5743i	0.220507	−	0.786340i
$299$	−4.93098	−	3.78368i	−0.285166	−	0.218816i
$300$		0			0
$301$	−7.41918	−	9.66887i	−0.427635	−	0.557304i
$302$	−2.49211	+	5.82446i	−0.143405	+	0.335160i
$303$		0			0
$304$	5.88368	+	8.45246i	0.337452	+	0.484782i
$305$	19.2418			1.10178
$306$		0			0
$307$	−25.8180	−	10.6941i	−1.47351	−	0.610347i	−0.505852	−	0.862620i	$-0.668822\pi$
$307$	−25.8180	−	10.6941i	−1.47351	−	0.610347i	−0.967656	+	0.252273i	$0.918822\pi$
$308$	42.1101	−	16.3087i	2.39944	−	0.929272i
$309$		0			0
$310$	0.909023	+	0.930361i	0.0516290	+	0.0528410i
$311$	32.4549	−	8.69628i	1.84035	−	0.493121i	0.841465	−	0.540311i	$-0.181694\pi$
$311$	32.4549	−	8.69628i	1.84035	−	0.493121i	0.998886	+	0.0471908i	$0.0150269\pi$
$312$		0			0
$313$	−11.2593	−	3.01691i	−0.636412	−	0.170526i	−0.0738342	−	0.997271i	$-0.523524\pi$
$313$	−11.2593	−	3.01691i	−0.636412	−	0.170526i	−0.562578	+	0.826745i	$0.690190\pi$
$314$	−5.36657	−	9.54930i	−0.302853	−	0.538898i
$315$		0			0
$316$	3.06415	+	12.5976i	0.172372	+	0.708672i
$317$	−25.9981	+	3.42271i	−1.46020	+	0.192239i	−0.818406	−	0.574640i	$-0.805142\pi$
$317$	−25.9981	+	3.42271i	−1.46020	+	0.192239i	−0.641792	+	0.766879i	$0.721809\pi$
$318$		0			0
$319$	40.7187	+	23.5089i	2.27981	+	1.31625i
$320$	−10.3629	+	6.86219i	−0.579302	+	0.383608i
$321$		0			0
$322$	35.3372	+	5.06991i	1.96926	+	0.282535i
$323$	9.71454	+	4.02389i	0.540531	+	0.223895i
$324$		0			0
$325$	1.10883	+	2.67695i	0.0615068	+	0.148491i
$326$	14.3528	+	8.51007i	0.794926	+	0.471329i
$327$		0			0
$328$	−13.5102	−	2.25936i	−0.745975	−	0.124752i
$329$	−2.99609	−	11.1816i	−0.165180	−	0.616460i
$330$		0			0
$331$	−20.5227	+	26.7458i	−1.12803	+	1.47008i	−0.265477	+	0.964117i	$0.585529\pi$
$331$	−20.5227	+	26.7458i	−1.12803	+	1.47008i	−0.862555	+	0.505963i	$0.831137\pi$
$332$	−23.9389	−	3.71847i	−1.31382	−	0.204078i
$333$		0			0
$334$	−1.27321	+	0.152619i	−0.0696672	+	0.00835092i
$335$	−12.9319	+	7.46621i	−0.706543	+	0.407923i
$336$		0			0
$337$	2.73282	+	1.57779i	0.148866	+	0.0859478i	0.572583	−	0.819847i	$-0.305942\pi$
$337$	2.73282	+	1.57779i	0.148866	+	0.0859478i	−0.423717	+	0.905795i	$0.639275\pi$
$338$	−15.2706	−	6.53383i	−0.830611	−	0.355394i
$339$		0			0
$340$	−5.12692	+	11.6082i	−0.278046	+	0.629544i
$341$	1.12420	+	2.71407i	0.0608790	+	0.146975i
$342$		0			0
$343$	−21.5692	+	21.5692i	−1.16463	+	1.16463i
$344$	3.55733	+	6.68866i	0.191798	+	0.360628i
$345$		0			0
$346$	−1.49118	−	0.0172987i	−0.0801664	−	0.000929985i
$347$	25.4794	+	3.35443i	1.36781	+	0.180075i	0.778404	−	0.627764i	$-0.216030\pi$
$347$	25.4794	+	3.35443i	1.36781	+	0.180075i	0.589403	+	0.807839i	$0.299363\pi$
$348$		0			0
$349$	−1.58498	−	12.0391i	−0.0848420	−	0.644439i	−0.980044	−	0.198779i	$-0.936302\pi$
$349$	−1.58498	−	12.0391i	−0.0848420	−	0.644439i	0.895202	−	0.445660i	$-0.147031\pi$
$350$	−13.0849	−	10.2837i	−0.699415	−	0.549687i
$351$		0			0
$352$	−27.4897	+	5.68124i	−1.46521	+	0.302811i
$353$	3.33343	−	1.92456i	0.177421	−	0.102434i	−0.408660	−	0.912687i	$-0.634004\pi$
$353$	3.33343	−	1.92456i	0.177421	−	0.102434i	0.586080	+	0.810253i	$0.300670\pi$
$354$		0			0
$355$	2.20111	+	2.86854i	0.116823	+	0.152246i
$356$	−3.33333	−	6.09585i	−0.176666	−	0.323080i
$357$		0			0
$358$	−25.7640	−	15.2760i	−1.36167	−	0.807364i
$359$	14.3336	−	14.3336i	0.756497	−	0.756497i	−0.219186	−	0.975683i	$-0.570340\pi$
$359$	14.3336	−	14.3336i	0.756497	−	0.756497i	0.975683	+	0.219186i	$0.0703402\pi$
$360$		0			0
$361$	−8.74772	−	8.74772i	−0.460406	−	0.460406i
$362$	−1.79827	−	7.03676i	−0.0945151	−	0.369844i
$363$		0			0
$364$	−10.1364	+	1.09592i	−0.531291	+	0.0574419i
$365$	−0.630676	+	0.483935i	−0.0330111	+	0.0253303i
$366$		0			0
$367$	4.67472	+	8.09686i	0.244019	+	0.422652i	0.961855	−	0.273559i	$-0.0882009\pi$
$367$	4.67472	+	8.09686i	0.244019	+	0.422652i	−0.717837	+	0.696212i	$0.754868\pi$
$368$	−21.1453	−	6.73149i	−1.10228	−	0.350903i
$369$		0			0
$370$	1.33298	+	11.1203i	0.0692984	+	0.578119i
$371$	−32.3182	+	4.25477i	−1.67788	+	0.220897i
$372$		0			0
$373$	−0.741285	+	5.63062i	−0.0383823	+	0.291542i	0.961479	+	0.274879i	$0.0886377\pi$
$373$	−0.741285	+	5.63062i	−0.0383823	+	0.291542i	−0.999861	+	0.0166635i	$0.994696\pi$
$374$	−20.4996	+	20.0294i	−1.06001	+	1.03570i
$375$		0			0
$376$	0.690445	+	7.16258i	0.0356070	+	0.369382i
$377$	−7.50622	−	7.50622i	−0.386590	−	0.386590i
$378$		0			0
$379$	21.3058	−	8.82516i	1.09441	−	0.453318i	0.238865	−	0.971053i	$-0.423225\pi$
$379$	21.3058	−	8.82516i	1.09441	−	0.453318i	0.855541	+	0.517735i	$0.173225\pi$
$380$	−5.78661	+	5.52415i	−0.296847	+	0.283383i
$381$		0			0
$382$	−7.38175	+	2.95777i	−0.377683	+	0.151333i
$383$	11.6397	−	20.1606i	0.594762	−	1.03016i	−0.398818	−	0.917030i	$-0.630580\pi$
$383$	11.6397	−	20.1606i	0.594762	−	1.03016i	0.993580	−	0.113128i	$-0.0360871\pi$
$384$		0			0
$385$	17.5395	+	30.3793i	0.893896	+	1.54827i
$386$	−1.22610	−	0.963622i	−0.0624069	−	0.0490471i
$387$		0			0
$388$	−8.05215	−	33.1048i	−0.408786	−	1.68064i
$389$	2.18552	+	1.67701i	0.110810	+	0.0850275i	0.662680	−	0.748903i	$-0.269419\pi$
$389$	2.18552	+	1.67701i	0.110810	+	0.0850275i	−0.551870	+	0.833930i	$0.686086\pi$
$390$		0			0
$391$	−21.8850	+	5.86407i	−1.10677	+	0.296559i
$392$	31.5530	−	22.5116i	1.59367	−	1.13701i
$393$		0			0
$394$	−2.66327	−	10.4216i	−0.134174	−	0.525030i
$395$	−9.30464	+	3.85411i	−0.468167	+	0.193921i
$396$		0			0
$397$	−7.43673	+	17.9539i	−0.373239	+	0.901078i	0.619958	+	0.784635i	$0.287149\pi$
$397$	−7.43673	+	17.9539i	−0.373239	+	0.901078i	−0.993197	+	0.116444i	$0.962851\pi$
$398$	2.95802	−	2.21573i	0.148272	−	0.111064i
$399$		0			0
$400$	6.96790	+	7.64651i	0.348395	+	0.382325i
$401$	−10.3222	+	17.8787i	−0.515468	+	0.892817i	0.484370	+	0.874863i	$0.339049\pi$
$401$	−10.3222	+	17.8787i	−0.515468	+	0.892817i	−0.999839	+	0.0179544i	$0.994285\pi$
$402$		0			0
$403$	−0.0865717	−	0.657577i	−0.00431244	−	0.0327563i
$404$	4.76182	+	6.51319i	0.236909	+	0.324043i
$405$		0			0
$406$	58.7068	+	16.4626i	2.91357	+	0.817027i
$407$	−6.54683	+	24.4331i	−0.324514	+	1.21110i
$408$		0			0
$409$	4.93596	+	18.4213i	0.244068	+	0.910873i	0.973850	+	0.227193i	$0.0729549\pi$
$409$	4.93596	+	18.4213i	0.244068	+	0.910873i	−0.729782	+	0.683680i	$0.760378\pi$
$410$	0.123430	−	10.6399i	0.00609576	−	0.525465i
$411$		0			0
$412$	−31.7545	−	0.736846i	−1.56443	−	0.0363018i
$413$	1.10790	−	2.67472i	0.0545164	−	0.131614i
$414$		0			0
$415$		−	18.8190i		−	0.923787i
$416$	6.32696	+	0.367381i	0.310205	+	0.0180123i
$417$		0			0
$418$	−16.7718	+	6.72025i	−0.820336	+	0.328698i
$419$	−23.1211	+	17.7415i	−1.12954	+	0.866728i	−0.992306	−	0.123811i	$-0.960488\pi$
$419$	−23.1211	+	17.7415i	−1.12954	+	0.866728i	−0.137236	+	0.990538i	$0.543822\pi$
$420$		0			0
$421$	16.3019	−	21.2451i	0.794506	−	1.03542i	−0.203900	−	0.978992i	$-0.565362\pi$
$421$	16.3019	−	21.2451i	0.794506	−	1.03542i	0.998407	−	0.0564291i	$-0.0179715\pi$
$422$	−0.753273	−	1.34038i	−0.0366687	−	0.0652485i
$423$		0			0
$424$	20.2505	+	0.705011i	0.983450	+	0.0342383i
$425$	10.2025	+	2.73374i	0.494892	+	0.132606i
$426$		0			0
$427$	55.8722	+	7.35571i	2.70385	+	0.355968i
$428$	−5.60847	+	0.606375i	−0.271096	+	0.0293102i
$429$		0			0
$430$	−4.71009	+	3.52813i	−0.227141	+	0.170142i
$431$			0.846314i			0.0407655i	0.999792	+	0.0203828i	$0.00648848\pi$
$431$			0.846314i			0.0407655i	−0.999792	+	0.0203828i	$0.993512\pi$
$432$		0			0
$433$			35.1194i			1.68773i	0.536554	+	0.843866i	$0.319726\pi$
$433$			35.1194i			1.68773i	−0.536554	+	0.843866i	$0.680274\pi$
$434$	2.28386	+	3.04898i	0.109629	+	0.146356i
$435$		0			0
$436$	3.10191	−	3.85396i	0.148554	−	0.184571i
$437$	−14.1613	−	1.86437i	−0.677428	−	0.0891851i
$438$		0			0
$439$	−6.15039	−	1.64799i	−0.293542	−	0.0786544i	0.109043	−	0.994037i	$-0.465221\pi$
$439$	−6.15039	−	1.64799i	−0.293542	−	0.0786544i	−0.402585	+	0.915383i	$0.631888\pi$
$440$	−7.63863	−	20.4238i	−0.364157	−	0.973668i
$441$		0			0
$442$	5.64097	−	3.17014i	0.268314	−	0.150788i
$443$	12.2314	−	15.9403i	0.581132	−	0.757346i	−0.406583	−	0.913614i	$-0.633280\pi$
$443$	12.2314	−	15.9403i	0.581132	−	0.757346i	0.987715	+	0.156268i	$0.0499463\pi$
$444$		0			0
$445$	4.28176	−	3.28551i	0.202975	−	0.155748i
$446$	−3.03716	−	7.57987i	−0.143814	−	0.358917i
$447$		0			0
$448$	−32.7138	+	15.9642i	−1.54558	+	0.754236i
$449$			2.52101i			0.118974i	0.998229	+	0.0594870i	$0.0189465\pi$
$449$			2.52101i			0.118974i	−0.998229	+	0.0594870i	$0.981054\pi$
$450$		0			0
$451$	9.19651	−	22.2023i	0.433047	−	1.04547i
$452$	−23.5500	+	22.4819i	−1.10770	+	1.05746i
$453$		0			0
$454$	8.69867	+	0.100911i	0.408249	+	0.00473597i
$455$	−2.04983	−	7.65005i	−0.0960973	−	0.358640i
$456$		0			0
$457$	−5.70405	+	21.2878i	−0.266824	+	0.995801i	0.694300	+	0.719686i	$0.255714\pi$
$457$	−5.70405	+	21.2878i	−0.266824	+	0.995801i	−0.961124	+	0.276116i	$0.910953\pi$
$458$	−5.66419	+	20.1988i	−0.264670	+	0.943830i
$459$		0			0
$460$	2.64589	−	17.0339i	0.123365	−	0.794208i
$461$	0.0909258	+	0.690650i	0.00423484	+	0.0321668i	0.993432	−	0.114426i	$-0.0365028\pi$
$461$	0.0909258	+	0.690650i	0.00423484	+	0.0321668i	−0.989197	+	0.146592i	$0.953169\pi$
$462$		0			0
$463$	−7.41183	+	12.8377i	−0.344457	+	0.596617i	−0.985255	−	0.171092i	$-0.945270\pi$
$463$	−7.41183	+	12.8377i	−0.344457	+	0.596617i	0.640798	+	0.767710i	$0.278604\pi$
$464$	−34.3051	−	16.1125i	−1.59257	−	0.748002i
$465$		0			0
$466$	17.7513	+	23.6982i	0.822315	+	1.09780i
$467$	0.222565	−	0.537320i	0.0102991	−	0.0248642i	−0.918646	−	0.395081i	$-0.870717\pi$
$467$	0.222565	−	0.537320i	0.0102991	−	0.0248642i	0.928945	+	0.370217i	$0.120717\pi$
$468$		0			0
$469$	−40.4042	+	16.7360i	−1.86569	+	0.772796i
$470$	−5.41570	+	1.38401i	−0.249808	+	0.0638394i
$471$		0			0
$472$	−0.953493	+	1.52627i	−0.0438881	+	0.0702522i
$473$	−12.8382	+	3.43999i	−0.590302	+	0.158171i
$474$		0			0
$475$	5.28275	+	4.05360i	0.242389	+	0.185992i
$476$	−19.3245	+	31.7467i	−0.885739	+	1.45511i
$477$		0			0
$478$	−5.91713	+	7.52888i	−0.270643	+	0.344363i
$479$	18.1501	+	31.4369i	0.829300	+	1.43639i	0.898588	+	0.438793i	$0.144594\pi$
$479$	18.1501	+	31.4369i	0.829300	+	1.43639i	−0.0692877	+	0.997597i	$0.522073\pi$
$480$		0			0
$481$	2.85547	−	4.94582i	0.130198	−	0.225510i
$482$	−15.2262	−	38.0002i	−0.693534	−	1.73086i
$483$		0			0
$484$	0.632097	−	27.2403i	0.0287317	−	1.23819i
$485$	24.4513	−	10.1280i	1.11027	−	0.459891i
$486$		0			0
$487$	5.14815	+	5.14815i	0.233285	+	0.233285i	0.814062	−	0.580777i	$-0.197251\pi$
$487$	5.14815	+	5.14815i	0.233285	+	0.233285i	−0.580777	+	0.814062i	$0.697251\pi$
$488$	−33.5009	−	10.2384i	−1.51652	−	0.463470i
$489$		0			0
$490$	21.0421	+	21.5361i	0.950587	+	0.972901i
$491$	−2.81970	+	21.4178i	−0.127251	+	0.966570i	0.802052	+	0.597254i	$0.203741\pi$
$491$	−2.81970	+	21.4178i	−0.127251	+	0.966570i	−0.929304	+	0.369316i	$0.879592\pi$
$492$		0			0
$493$	−38.3655	+	5.05092i	−1.72790	+	0.227482i
$494$	4.05030	−	0.485505i	0.182232	−	0.0218439i
$495$		0			0
$496$	−1.08762	−	2.10349i	−0.0488355	−	0.0944494i
$497$	5.29475	+	9.17077i	0.237502	+	0.411365i
$498$		0			0
$499$	−26.8946	+	20.6370i	−1.20397	+	0.923838i	−0.998496	−	0.0548242i	$-0.982540\pi$
$499$	−26.8946	+	20.6370i	−1.20397	+	0.923838i	−0.205474	+	0.978663i	$0.565873\pi$
$500$	−14.7799	+	18.3633i	−0.660977	+	0.821230i
$501$		0			0
$502$	−3.97428	+	1.01564i	−0.177381	+	0.0453304i
$503$	−8.18706	−	8.18706i	−0.365043	−	0.365043i	0.500623	−	0.865666i	$-0.333104\pi$
$503$	−8.18706	−	8.18706i	−0.365043	−	0.365043i	−0.865666	+	0.500623i	$0.833104\pi$
$504$		0			0
$505$	−4.43178	+	4.43178i	−0.197212	+	0.197212i
$506$	19.8559	−	33.4882i	0.882701	−	1.48873i
$507$		0			0
$508$	−12.3529	+	42.1636i	−0.548071	+	1.87071i
$509$	12.6432	+	16.4770i	0.560401	+	0.730328i	0.984519	−	0.175278i	$-0.0560826\pi$
$509$	12.6432	+	16.4770i	0.560401	+	0.730328i	−0.424118	+	0.905607i	$0.639416\pi$
$510$		0			0
$511$	−2.01628	+	1.16410i	−0.0891951	+	0.0514968i
$512$	21.6936	−	6.43344i	0.958729	−	0.284321i
$513$		0			0
$514$	19.9805	−	25.4229i	0.881301	−	1.12136i
$515$	−3.22058	−	24.4627i	−0.141916	−	1.07796i
$516$		0			0
$517$	−12.5164	−	1.64781i	−0.550471	−	0.0724708i
$518$	−0.380498	+	32.7996i	−0.0167181	+	1.44113i
$519$		0			0
$520$	0.472380	+	4.90040i	0.0207152	+	0.214897i
$521$	20.7314	−	20.7314i	0.908261	−	0.908261i	−0.0878707	−	0.996132i	$-0.528006\pi$
$521$	20.7314	−	20.7314i	0.908261	−	0.908261i	0.996132	+	0.0878707i	$0.0280062\pi$
$522$		0			0
$523$	−5.99966	−	14.4845i	−0.262347	−	0.633361i	0.736736	−	0.676181i	$-0.236366\pi$
$523$	−5.99966	−	14.4845i	−0.262347	−	0.633361i	−0.999083	+	0.0428191i	$0.986366\pi$
$524$	−6.08430	+	2.35637i	−0.265794	+	0.102938i
$525$		0			0
$526$	−0.340362	+	0.795481i	−0.0148405	+	0.0346846i
$527$	−2.09385	−	1.20888i	−0.0912095	−	0.0526598i
$528$		0			0
$529$	6.73541	−	3.88869i	0.292844	−	0.169073i
$530$	1.87336	+	15.6284i	0.0813734	+	0.678854i
$531$		0			0
$532$	−18.9143	+	13.8283i	−0.820037	+	0.599533i
$533$	−3.30297	+	4.30451i	−0.143067	+	0.186449i
$534$		0			0
$535$	−1.13417	−	4.23278i	−0.0490345	−	0.182999i
$536$	26.4877	−	6.11813i	1.14409	−	0.264263i
$537$		0			0
$538$	1.11567	−	1.88164i	0.0480998	−	0.0811233i
$539$	26.0231	+	62.8254i	1.12090	+	2.70608i
$540$		0			0
$541$	−4.63048	−	1.91801i	−0.199080	−	0.0824617i	0.280916	−	0.959732i	$-0.409362\pi$
$541$	−4.63048	−	1.91801i	−0.199080	−	0.0824617i	−0.479996	+	0.877271i	$0.659362\pi$
$542$	2.57202	−	17.9269i	0.110478	−	0.770027i
$543$		0			0
$544$	15.1028	−	17.4825i	0.647529	−	0.749556i
$545$	3.32816	+	1.92152i	0.142563	+	0.0823087i
$546$		0			0
$547$	32.3265	−	4.25586i	1.38218	−	0.181968i	0.597501	−	0.801868i	$-0.296160\pi$
$547$	32.3265	−	4.25586i	1.38218	−	0.181968i	0.784680	+	0.619901i	$0.212827\pi$
$548$	−5.93819	−	3.61463i	−0.253667	−	0.154410i
$549$		0			0
$550$	−15.8222	+	8.89185i	−0.674661	+	0.379150i
$551$	−23.5640	−	6.31395i	−1.00386	−	0.268983i
$552$		0			0
$553$	−28.4911	+	7.63417i	−1.21156	+	0.324638i
$554$	−10.6319	+	10.3881i	−0.451708	+	0.441348i
$555$		0			0
$556$	29.8743	+	13.1944i	1.26695	+	0.559566i
$557$	−29.0633	−	12.0384i	−1.23145	−	0.510083i	−0.330418	−	0.943835i	$-0.607190\pi$
$557$	−29.0633	−	12.0384i	−1.23145	−	0.510083i	−0.901033	+	0.433751i	$0.857190\pi$
$558$		0			0
$559$	3.00078			0.126920
$560$	−16.1547	−	23.2078i	−0.682662	−	0.980707i
$561$		0			0
$562$	10.5421	+	4.51064i	0.444690	+	0.190270i
$563$	−0.193257	−	0.251857i	−0.00814479	−	0.0106145i	0.789263	−	0.614055i	$-0.210463\pi$
$563$	−0.193257	−	0.251857i	−0.00814479	−	0.0106145i	−0.797408	+	0.603441i	$0.793796\pi$
$564$		0			0
$565$	−20.0651	−	15.3965i	−0.844146	−	0.647736i
$566$	15.7588	+	4.41911i	0.662393	+	0.185749i
$567$		0			0
$568$	−2.30591	−	6.16546i	−0.0967540	−	0.258697i
$569$	11.4624	−	42.7781i	0.480527	−	1.79335i	−0.118881	−	0.992909i	$-0.537931\pi$
$569$	11.4624	−	42.7781i	0.480527	−	1.79335i	0.599408	−	0.800444i	$-0.295403\pi$
$570$		0			0
$571$	−0.837628	+	6.36242i	−0.0350537	+	0.266259i	0.964939	+	0.262474i	$0.0845383\pi$
$571$	−0.837628	+	6.36242i	−0.0350537	+	0.266259i	−0.999993	+	0.00378539i	$0.998795\pi$
$572$	−3.12613	+	10.6703i	−0.130710	+	0.446148i
$573$		0			0
$574$	4.42578	−	30.8477i	0.184729	−	1.28756i
$575$	−14.3480			−0.598351
$576$		0			0
$577$	6.71403			0.279509			0.139754	−	0.990186i	$-0.455369\pi$
$577$	6.71403			0.279509			0.139754	+	0.990186i	$0.455369\pi$
$578$	−0.0644335	+	0.449101i	−0.00268008	+	0.0186801i
$579$		0			0
$580$	8.27768	−	28.2539i	0.343712	−	1.17318i
$581$	7.19407	−	54.6444i	0.298460	−	2.26703i
$582$		0			0
$583$	−9.20083	+	34.3380i	−0.381059	+	1.42213i
$584$	1.35553	−	0.506978i	0.0560924	−	0.0209789i
$585$		0			0
$586$	3.94633	+	1.10663i	0.163021	+	0.0457147i
$587$	8.36957	+	6.42220i	0.345449	+	0.265072i	0.766883	−	0.641787i	$-0.221806\pi$
$587$	8.36957	+	6.42220i	0.345449	+	0.265072i	−0.421434	+	0.906859i	$0.638473\pi$
$588$		0			0
$589$	−0.927884	−	1.20924i	−0.0382328	−	0.0498260i
$590$	−1.28526	−	0.549923i	−0.0529132	−	0.0226400i
$591$		0			0
$592$	3.59624	−	20.0703i	0.147805	−	0.824886i
$593$	13.6954			0.562403			0.281202	−	0.959649i	$-0.409267\pi$
$593$	13.6954			0.562403			0.281202	+	0.959649i	$0.409267\pi$
$594$		0			0
$595$	−26.6730	−	11.0483i	−1.09349	−	0.452938i
$596$	−18.2379	−	8.05501i	−0.747053	−	0.329946i
$597$		0			0
$598$	−6.28705	+	6.14285i	−0.257096	+	0.251200i
$599$	−39.5590	+	10.5998i	−1.61634	+	0.433096i	−0.949923	−	0.312485i	$-0.898839\pi$
$599$	−39.5590	+	10.5998i	−1.61634	+	0.433096i	−0.666415	+	0.745581i	$0.732172\pi$
$600$		0			0
$601$	22.5982	+	6.05516i	0.921798	+	0.246995i	0.688354	−	0.725375i	$-0.258334\pi$
$601$	22.5982	+	6.05516i	0.921798	+	0.246995i	0.233444	+	0.972370i	$0.425000\pi$
$602$	−15.0253	+	8.44403i	−0.612387	+	0.344153i
$603$		0			0
$604$	7.65301	+	4.65846i	0.311397	+	0.189550i
$605$	20.9851	−	2.76274i	0.853166	−	0.112321i
$606$		0			0
$607$	−16.3379	−	9.43267i	−0.663133	−	0.382860i	0.130337	−	0.991470i	$-0.458394\pi$
$607$	−16.3379	−	9.43267i	−0.663133	−	0.382860i	−0.793470	+	0.608610i	$0.791728\pi$
$608$	13.0141	−	6.53882i	0.527792	−	0.265184i
$609$		0			0
$610$	3.86460	−	26.9362i	0.156473	−	1.09062i
$611$	2.63329	+	1.09075i	0.106532	+	0.0441269i
$612$		0			0
$613$	−9.88791	−	23.8715i	−0.399369	−	0.964162i	−0.987816	−	0.155626i	$-0.950260\pi$
$613$	−9.88791	−	23.8715i	−0.399369	−	0.964162i	0.588447	−	0.808536i	$-0.299740\pi$
$614$	−20.1559	+	33.9942i	−0.813426	+	1.37189i
$615$		0			0
$616$	−14.3726	−	62.2245i	−0.579089	−	2.50710i
$617$	−0.271173	−	1.01203i	−0.0109170	−	0.0407428i	0.960252	−	0.279133i	$-0.0900470\pi$
$617$	−0.271173	−	1.01203i	−0.0109170	−	0.0407428i	−0.971169	+	0.238390i	$0.923380\pi$
$618$		0			0
$619$	−4.92501	+	6.41840i	−0.197953	+	0.257977i	−0.881774	−	0.471673i	$-0.843650\pi$
$619$	−4.92501	+	6.41840i	−0.197953	+	0.257977i	0.683821	+	0.729650i	$0.260317\pi$
$620$	1.48496	−	1.08567i	0.0596376	−	0.0436014i
$621$		0			0
$622$	−5.65536	−	47.1796i	−0.226759	−	1.89173i
$623$	13.6889	−	7.90327i	0.548433	−	0.316638i
$624$		0			0
$625$	−4.65908	−	2.68992i	−0.186363	−	0.107597i
$626$	−6.48467	+	15.1557i	−0.259180	+	0.605743i
$627$		0			0
$628$	−14.4457	+	5.59463i	−0.576446	+	0.223250i
$629$	−7.96680	−	19.2336i	−0.317657	−	0.766892i
$630$		0			0
$631$	−2.84039	+	2.84039i	−0.113074	+	0.113074i	−0.761380	−	0.648306i	$-0.775478\pi$
$631$	−2.84039	+	2.84039i	−0.113074	+	0.113074i	0.648306	+	0.761380i	$0.275478\pi$
$632$	18.2506	−	1.75928i	0.725969	−	0.0699806i
$633$		0			0
$634$	−0.430172	+	37.0816i	−0.0170843	+	1.47270i
$635$	−33.8378	−	4.45483i	−1.34281	−	0.176784i
$636$		0			0
$637$	−2.00397	−	15.2217i	−0.0794002	−	0.603104i
$638$	41.0878	−	52.2796i	1.62668	−	2.06977i
$639$		0			0
$640$	7.52492	+	15.8850i	0.297449	+	0.627909i
$641$	18.8927	−	10.9077i	0.746215	−	0.430828i	−0.0781094	−	0.996945i	$-0.524888\pi$
$641$	18.8927	−	10.9077i	0.746215	−	0.430828i	0.824325	+	0.566117i	$0.191555\pi$
$642$		0			0
$643$	1.96897	+	2.56601i	0.0776485	+	0.101193i	0.830563	−	0.556925i	$-0.188019\pi$
$643$	1.96897	+	2.56601i	0.0776485	+	0.101193i	−0.752914	+	0.658119i	$0.771352\pi$
$644$	14.1945	−	48.4495i	0.559342	−	1.90918i
$645$		0			0
$646$	7.58407	−	12.7910i	0.298391	−	0.503255i
$647$	−16.3835	+	16.3835i	−0.644101	+	0.644101i	−0.951561	−	0.307460i	$-0.900521\pi$
$647$	−16.3835	+	16.3835i	−0.644101	+	0.644101i	0.307460	+	0.951561i	$0.400521\pi$
$648$		0			0
$649$	−2.23254	−	2.23254i	−0.0876349	−	0.0876349i
$650$	3.97011	−	1.01458i	0.155720	−	0.0397950i
$651$		0			0
$652$	14.7957	−	18.3829i	0.579446	−	0.719932i
$653$	19.1626	−	14.7040i	0.749890	−	0.575411i	−0.161540	−	0.986866i	$-0.551646\pi$
$653$	19.1626	−	14.7040i	0.749890	−	0.575411i	0.911430	+	0.411456i	$0.134979\pi$
$654$		0			0
$655$	−2.53421	−	4.38938i	−0.0990197	−	0.171507i
$656$	−5.87627	+	18.4589i	−0.229430	+	0.720697i
$657$		0			0
$658$	−16.2546	+	1.94842i	−0.633670	+	0.0759572i
$659$	7.02331	−	0.924636i	0.273589	−	0.0360187i	0.00751688	−	0.999972i	$-0.497607\pi$
$659$	7.02331	−	0.924636i	0.273589	−	0.0360187i	0.266072	+	0.963953i	$0.414274\pi$
$660$		0			0
$661$	5.03887	−	38.2740i	0.195989	−	1.48869i	−0.556922	−	0.830565i	$-0.688018\pi$
$661$	5.03887	−	38.2740i	0.195989	−	1.48869i	0.752911	−	0.658122i	$-0.228649\pi$
$662$	33.3190	+	34.1011i	1.29498	+	1.32538i
$663$		0			0
$664$	−10.0134	+	32.7648i	−0.388595	+	1.27152i
$665$	−12.8699	−	12.8699i	−0.499072	−	0.499072i
$666$		0			0
$667$	48.5642	−	20.1160i	1.88041	−	0.778893i
$668$	−0.0420697	+	1.81300i	−0.00162773	+	0.0701470i
$669$		0			0
$670$	7.85451	+	19.6026i	0.303446	+	0.757314i
$671$	30.7291	−	53.2243i	1.18628	−	2.05470i
$672$		0			0
$673$	−4.86626	−	8.42860i	−0.187580	−	0.324899i	0.756863	−	0.653574i	$-0.226731\pi$
$673$	−4.86626	−	8.42860i	−0.187580	−	0.324899i	−0.944443	+	0.328675i	$0.893398\pi$
$674$	2.75759	−	3.50872i	0.106218	−	0.135151i
$675$		0			0
$676$	−12.2136	+	20.0647i	−0.469753	+	0.771720i
$677$	21.1827	+	16.2540i	0.814116	+	0.624693i	0.929581	−	0.368618i	$-0.120169\pi$
$677$	21.1827	+	16.2540i	0.814116	+	0.624693i	−0.115465	+	0.993312i	$0.536836\pi$
$678$		0			0
$679$	74.8706	−	20.0615i	2.87327	−	0.769890i
$680$	15.2204	+	9.50851i	0.583675	+	0.364635i
$681$		0			0
$682$	4.02515	−	1.02864i	0.154131	−	0.0393888i
$683$	−13.9691	+	5.78620i	−0.534513	+	0.221403i	−0.633579	−	0.773678i	$-0.718415\pi$
$683$	−13.9691	+	5.78620i	−0.534513	+	0.221403i	0.0990653	+	0.995081i	$0.468415\pi$
$684$		0			0
$685$	2.06658	−	4.98916i	0.0789599	−	0.190626i
$686$	25.8623	+	34.5264i	0.987426	+	1.31822i
$687$		0			0
$688$	10.0778	−	3.63646i	0.384212	−	0.138639i
$689$	4.01304	−	6.95080i	0.152885	−	0.264804i
$690$		0			0
$691$	−4.39444	−	33.3791i	−0.167172	−	1.26980i	−0.845075	−	0.534648i	$-0.820444\pi$
$691$	−4.39444	−	33.3791i	−0.167172	−	1.26980i	0.677902	−	0.735152i	$-0.262889\pi$
$692$	−0.323711	+	2.08400i	−0.0123056	+	0.0792218i
$693$		0			0
$694$	9.81318	−	34.9944i	0.372503	−	1.32837i
$695$	−6.56604	+	24.5048i	−0.249064	+	0.929520i
$696$		0			0
$697$	5.11905	+	19.1046i	0.193898	+	0.723637i
$698$	−17.1716	−	0.199203i	−0.649956	−	0.00753994i
$699$		0			0
$700$	−17.0239	+	16.2518i	−0.643445	+	0.614260i
$701$	−8.97900	+	21.6772i	−0.339132	+	0.818737i	0.658667	+	0.752434i	$0.271120\pi$
$701$	−8.97900	+	21.6772i	−0.339132	+	0.818737i	−0.997800	+	0.0663032i	$0.978880\pi$
$702$		0			0
$703$		−	13.1243i		−	0.494993i
$704$	2.43191	+	39.6233i	0.0916559	+	1.49336i
$705$		0			0
$706$	−2.02465	−	5.05293i	−0.0761986	−	0.190170i
$707$	−14.5627	+	11.1743i	−0.547686	+	0.420254i
$708$		0			0
$709$	−18.2360	+	23.7656i	−0.684868	+	0.892537i	−0.998371	−	0.0570496i	$-0.981831\pi$
$709$	−18.2360	+	23.7656i	−0.684868	+	0.892537i	0.313503	+	0.949587i	$0.398497\pi$
$710$	4.45769	−	2.50516i	0.167294	−	0.0940168i
$711$		0			0
$712$	−9.20294	+	3.44195i	−0.344895	+	0.128993i
$713$	3.17239	+	0.850040i	0.118807	+	0.0318343i
$714$		0			0
$715$	−8.56330	−	1.12738i	−0.320249	−	0.0421616i
$716$	−26.5592	+	32.9984i	−0.992562	+	1.23321i
$717$		0			0
$718$	−17.1865	−	22.9441i	−0.641393	−	0.856265i
$719$			40.2309i			1.50036i	0.661234	+	0.750180i	$0.270033\pi$
$719$			40.2309i			1.50036i	−0.661234	+	0.750180i	$0.729967\pi$
$720$		0			0
$721$		−	72.2632i		−	2.69122i
$722$	−14.0027	+	10.4888i	−0.521126	+	0.390354i
$723$		0			0
$724$	−10.2118	+	1.10407i	−0.379518	+	0.0410326i
$725$	−24.2956	−	3.19858i	−0.902317	−	0.118792i
$726$		0			0
$727$	−14.5365	−	3.89504i	−0.539129	−	0.144459i	−0.0210282	−	0.999779i	$-0.506694\pi$
$727$	−14.5365	−	3.89504i	−0.539129	−	0.144459i	−0.518100	+	0.855320i	$0.673361\pi$
$728$	−0.501671	+	14.4098i	−0.0185932	+	0.534063i
$729$		0			0
$730$	0.550783	+	0.980065i	0.0203854	+	0.0362738i
$731$	6.65914	−	8.67836i	0.246297	−	0.320981i
$732$		0			0
$733$	1.04651	−	0.803017i	0.0386538	−	0.0296601i	−0.589254	−	0.807948i	$-0.700578\pi$
$733$	1.04651	−	0.803017i	0.0386538	−	0.0296601i	0.627908	+	0.778288i	$0.283912\pi$
$734$	12.2735	−	4.91784i	0.453024	−	0.181521i
$735$		0			0
$736$	−13.6702	+	28.2489i	−0.503890	+	1.04127i
$737$			47.6940i			1.75683i
$738$		0			0
$739$	−11.4907	+	27.7409i	−0.422691	+	1.02047i	0.558860	+	0.829262i	$0.311239\pi$
$739$	−11.4907	+	27.7409i	−0.422691	+	1.02047i	−0.981550	+	0.191204i	$0.938761\pi$
$740$	15.8349	+	0.367440i	0.582101	+	0.0135074i
$741$		0			0
$742$	−0.534746	+	46.0961i	−0.0196312	+	1.69224i
$743$	−1.46392	−	5.46342i	−0.0537060	−	0.200433i	0.933860	−	0.357639i	$-0.116418\pi$
$743$	−1.46392	−	5.46342i	−0.0537060	−	0.200433i	−0.987566	+	0.157206i	$0.949751\pi$
$744$		0			0
$745$	4.00849	−	14.9599i	0.146860	−	0.548089i
$746$	7.73330	+	2.16858i	0.283136	+	0.0793975i
$747$		0			0
$748$	23.9215	+	32.7197i	0.874658	+	1.19635i
$749$	−1.67518	−	12.7243i	−0.0612097	−	0.464934i
$750$		0			0
$751$	−26.9412	+	46.6635i	−0.983099	+	1.70278i	−0.333001	+	0.942927i	$0.608061\pi$
$751$	−26.9412	+	46.6635i	−0.983099	+	1.70278i	−0.650098	+	0.759850i	$0.725272\pi$
$752$	10.1654	+	0.472021i	0.370695	+	0.0172128i
$753$		0			0
$754$	−12.0154	+	9.00022i	−0.437574	+	0.327769i
$755$	−2.66336	+	6.42992i	−0.0969296	+	0.234009i
$756$		0			0
$757$	34.5808	−	14.3238i	1.25686	−	0.520609i	0.347916	−	0.937526i	$-0.386889\pi$
$757$	34.5808	−	14.3238i	1.25686	−	0.520609i	0.908945	+	0.416917i	$0.136889\pi$
$758$	−8.07501	−	31.5981i	−0.293298	−	1.14769i
$759$		0			0
$760$	6.57093	+	9.21004i	0.238353	+	0.334083i
$761$	20.7070	−	5.54843i	0.750629	−	0.201130i	0.136832	−	0.990594i	$-0.456308\pi$
$761$	20.7070	−	5.54843i	0.750629	−	0.201130i	0.613797	+	0.789464i	$0.289641\pi$
$762$		0			0
$763$	8.92939	+	6.85176i	0.323266	+	0.248050i
$764$	2.65795	+	10.9276i	0.0961612	+	0.395347i
$765$		0			0
$766$	−25.8846	−	20.3433i	−0.935250	−	0.735035i
$767$	0.356416	+	0.617331i	0.0128695	+	0.0222905i
$768$		0			0
$769$	23.0680	−	39.9550i	0.831854	−	1.44081i	−0.0647118	−	0.997904i	$-0.520613\pi$
$769$	23.0680	−	39.9550i	0.831854	−	1.44081i	0.896566	−	0.442910i	$-0.146054\pi$
$770$	46.0501	−	18.4517i	1.65953	−	0.664953i
$771$		0			0
$772$	−1.59521	+	1.52286i	−0.0574128	+	0.0548088i
$773$	3.48172	−	1.44218i	0.125229	−	0.0518715i	−0.319189	−	0.947691i	$-0.603411\pi$
$773$	3.48172	−	1.44218i	0.125229	−	0.0518715i	0.444418	+	0.895820i	$0.353411\pi$
$774$		0			0
$775$	−1.08265	−	1.08265i	−0.0388898	−	0.0388898i
$776$	−47.9599	+	4.62315i	−1.72166	+	0.165961i
$777$		0			0
$778$	2.78655	−	2.72264i	0.0999027	−	0.0976114i
$779$	−1.62751	+	12.3621i	−0.0583115	+	0.442920i
$780$		0			0
$781$	11.4497	−	1.50739i	0.409704	−	0.0539386i
$782$	3.81352	+	31.8142i	0.136371	+	1.13767i
$783$		0			0
$784$	−25.1763	−	48.6917i	−0.899153	−	1.73899i
$785$	−6.01686	−	10.4215i	−0.214751	−	0.371960i
$786$		0			0
$787$	2.96828	−	2.27764i	0.105808	−	0.0811893i	−0.554502	−	0.832182i	$-0.687091\pi$
$787$	2.96828	−	2.27764i	0.105808	−	0.0811893i	0.660310	+	0.750993i	$0.270425\pi$
$788$	−15.1238	+	1.63515i	−0.538764	+	0.0582499i
$789$		0			0
$790$	3.52650	+	13.7994i	0.125467	+	0.490962i
$791$	−52.3771	−	52.3771i	−1.86232	−	1.86232i
$792$		0			0
$793$	−9.81155	+	9.81155i	−0.348418	+	0.348418i
$794$	23.6396	+	14.0164i	0.838938	+	0.497425i
$795$		0			0
$796$	−2.50765	−	4.58588i	−0.0888813	−	0.162542i
$797$	17.8536	+	23.2672i	0.632406	+	0.824168i	0.994138	−	0.108114i	$-0.0344813\pi$
$797$	17.8536	+	23.2672i	0.632406	+	0.824168i	−0.361732	+	0.932282i	$0.617815\pi$
$798$		0			0
$799$	8.99811	−	5.19506i	0.318330	−	0.183788i
$800$	12.1037	−	8.21847i	0.427929	−	0.290567i
$801$		0			0
$802$	22.9548	+	18.0407i	0.810562	+	0.637040i
$803$	0.331414	+	2.51734i	0.0116953	+	0.0888349i
$804$		0			0
$805$	38.8825	+	5.11898i	1.37043	+	0.180420i
$806$	−0.937916	−	0.0108805i	−0.0330367	−	0.000383248i
$807$		0			0
$808$	10.0741	−	5.35784i	0.354404	−	0.188488i
$809$	14.3467	−	14.3467i	0.504404	−	0.504404i	−0.408400	−	0.912803i	$-0.633913\pi$
$809$	14.3467	−	14.3467i	0.504404	−	0.504404i	0.912803	+	0.408400i	$0.133913\pi$
$810$		0			0
$811$	13.2334	+	31.9483i	0.464688	+	1.12186i	0.966451	+	0.256851i	$0.0826848\pi$
$811$	13.2334	+	31.9483i	0.464688	+	1.12186i	−0.501763	+	0.865005i	$0.667315\pi$
$812$	34.8366	−	78.8760i	1.22253	−	2.76800i
$813$		0			0
$814$	32.8885	+	14.0720i	1.15274	+	0.493223i
$815$	15.8750	+	9.16541i	0.556075	+	0.321050i
$816$		0			0
$817$	5.97219	−	3.44804i	0.208940	−	0.120632i
$818$	26.7789	−	3.20995i	0.936303	−	0.112233i
$819$		0			0
$820$	−14.8697	−	2.30974i	−0.519274	−	0.0806596i
$821$	17.1807	−	22.3903i	0.599609	−	0.781426i	−0.390668	−	0.920532i	$-0.627756\pi$
$821$	17.1807	−	22.3903i	0.599609	−	0.781426i	0.990278	+	0.139105i	$0.0444227\pi$
$822$		0			0
$823$	5.54918	+	20.7098i	0.193432	+	0.721899i	0.992667	+	0.120880i	$0.0385717\pi$
$823$	5.54918	+	20.7098i	0.193432	+	0.721899i	−0.799235	+	0.601019i	$0.794762\pi$
$824$	−7.40918	+	44.3044i	−0.258111	+	1.54342i
$825$		0			0
$826$	−3.52176	−	2.08813i	−0.122538	−	0.0726554i
$827$	1.83537	+	4.43098i	0.0638222	+	0.154080i	0.952573	−	0.304310i	$-0.0984260\pi$
$827$	1.83537	+	4.43098i	0.0638222	+	0.154080i	−0.888751	+	0.458391i	$0.848426\pi$
$828$		0			0
$829$	31.7765	+	13.1623i	1.10364	+	0.457144i	0.858744	−	0.512405i	$-0.171245\pi$
$829$	31.7765	+	13.1623i	1.10364	+	0.457144i	0.244899	+	0.969549i	$0.421245\pi$
$830$	−26.3443	−	3.77968i	−0.914424	−	0.131194i
$831$		0			0
$832$	1.78502	−	8.78319i	0.0618844	−	0.304502i
$833$	−48.4686	−	27.9834i	−1.67934	−	0.969566i
$834$		0			0
$835$	−1.39668	+	0.183876i	−0.0483341	+	0.00636331i
$836$	6.03903	+	24.8282i	0.208864	+	0.858702i
$837$		0			0
$838$	20.1922	+	35.9301i	0.697527	+	1.24118i
$839$	6.05695	+	1.62295i	0.209109	+	0.0560306i	0.361853	−	0.932235i	$-0.382144\pi$
$839$	6.05695	+	1.62295i	0.209109	+	0.0560306i	−0.152744	+	0.988266i	$0.548811\pi$
$840$		0			0
$841$	58.7072	−	15.7305i	2.02439	−	0.542432i
$842$	−26.4664	−	27.0876i	−0.912092	−	0.933502i
$843$		0			0
$844$	−2.02766	+	0.785284i	−0.0697948	+	0.0270306i
$845$	−16.8580	−	6.98282i	−0.579933	−	0.240216i
$846$		0			0
$847$	61.9903			2.13001
$848$	5.05411	−	28.2066i	0.173559	−	0.968619i
$849$		0			0
$850$	5.87601	−	13.7332i	0.201546	−	0.471044i
$851$	17.2155	+	22.4357i	0.590140	+	0.769086i
$852$		0			0
$853$	36.9971	+	28.3888i	1.26675	+	0.972015i	0.999966	+	0.00826028i	$0.00262936\pi$
$853$	36.9971	+	28.3888i	1.26675	+	0.972015i	0.266789	+	0.963755i	$0.414037\pi$
$854$	21.5187	−	76.7370i	0.736355	−	2.62589i
$855$		0			0
$856$	−0.277575	+	7.97297i	−0.00948733	+	0.272510i
$857$	2.61101	−	9.74444i	0.0891906	−	0.332864i	−0.906884	−	0.421380i	$-0.861546\pi$
$857$	2.61101	−	9.74444i	0.0891906	−	0.332864i	0.996075	+	0.0885163i	$0.0282125\pi$
$858$		0			0
$859$	2.34801	−	17.8349i	0.0801131	−	0.608520i	−0.903548	−	0.428488i	$-0.859047\pi$
$859$	2.34801	−	17.8349i	0.0801131	−	0.608520i	0.983661	−	0.180032i	$-0.0576201\pi$
$860$	3.99296	+	7.30215i	0.136159	+	0.249001i
$861$		0			0
$862$	1.18474	+	0.169977i	0.0403523	+	0.00578944i
$863$	−0.213637			−0.00727230			−0.00363615	−	0.999993i	$-0.501157\pi$
$863$	−0.213637			−0.00727230			−0.00363615	+	0.999993i	$0.501157\pi$
$864$		0			0
$865$	−1.63828			−0.0557033
$866$	49.1629	+	7.05352i	1.67062	+	0.239688i
$867$		0			0
$868$	4.72690	−	2.58476i	0.160441	−	0.0877326i
$869$	−4.19870	+	31.8923i	−0.142431	+	1.08187i
$870$		0			0
$871$	2.78698	−	10.4011i	0.0944331	−	0.352429i
$872$	−4.77208	−	5.11634i	−0.161603	−	0.173261i
$873$		0			0
$874$	−5.45411	+	19.4497i	−0.184488	+	0.657896i
$875$	−42.5466	−	32.6471i	−1.43834	−	1.10368i
$876$		0			0
$877$	−19.6882	−	25.6581i	−0.664823	−	0.866414i	0.332225	−	0.943200i	$-0.392201\pi$
$877$	−19.6882	−	25.6581i	−0.664823	−	0.866414i	−0.997048	+	0.0767862i	$0.975534\pi$
$878$	−3.54226	+	8.27881i	−0.119545	+	0.279396i
$879$		0			0
$880$	−30.1251	+	6.59115i	−1.01552	+	0.222188i
$881$	−40.2583			−1.35634			−0.678168	−	0.734907i	$-0.737226\pi$
$881$	−40.2583			−1.35634			−0.678168	+	0.734907i	$0.737226\pi$
$882$		0			0
$883$	25.3073	+	10.4826i	0.851660	+	0.352769i	0.765440	−	0.643507i	$-0.222521\pi$
$883$	25.3073	+	10.4826i	0.851660	+	0.352769i	0.0862196	+	0.996276i	$0.472521\pi$
$884$	−3.30486	−	8.53338i	−0.111155	−	0.287009i
$885$		0			0
$886$	−19.8579	−	20.3240i	−0.667138	−	0.682799i
$887$	1.77186	−	0.474768i	0.0594931	−	0.0159411i	−0.228950	−	0.973438i	$-0.573529\pi$
$887$	1.77186	−	0.474768i	0.0594931	−	0.0159411i	0.288443	+	0.957497i	$0.406862\pi$
$888$		0			0
$889$	−96.5514	−	25.8709i	−3.23823	−	0.867681i
$890$	−3.73935	−	6.65382i	−0.125343	−	0.223036i
$891$		0			0
$892$	−11.2209	+	2.72929i	−0.375704	+	0.0913833i
$893$	6.49413	−	0.854969i	0.217318	−	0.0286104i
$894$		0			0
$895$	−28.4964	−	16.4524i	−0.952530	−	0.549944i
$896$	15.7775	+	49.0016i	0.527091	+	1.63703i
$897$		0			0
$898$	3.52912	+	0.506330i	0.117768	+	0.0168965i
$899$	5.18237	+	2.14661i	0.172842	+	0.0715933i
$900$		0			0
$901$	−11.1964	−	27.0306i	−0.373008	−	0.900520i
$902$	−29.2335	−	17.3332i	−0.973371	−	0.577133i
$903$		0			0
$904$	26.7420	+	37.4825i	0.889427	+	1.24665i
$905$	−2.06507	−	7.70696i	−0.0686454	−	0.256188i
$906$		0			0
$907$	−34.7536	+	45.2918i	−1.15397	+	1.50389i	−0.324026	+	0.946048i	$0.605036\pi$
$907$	−34.7536	+	45.2918i	−1.15397	+	1.50389i	−0.829948	+	0.557840i	$0.811630\pi$
$908$	1.88834	−	12.1568i	0.0626667	−	0.403438i
$909$		0			0
$910$	−11.1208	+	1.33304i	−0.368652	+	0.0441899i
$911$	3.88028	−	2.24028i	0.128559	−	0.0742237i	−0.434341	−	0.900748i	$-0.643019\pi$
$911$	3.88028	−	2.24028i	0.128559	−	0.0742237i	0.562900	+	0.826525i	$0.309685\pi$
$912$		0			0
$913$	−52.0547	−	30.0538i	−1.72276	−	0.994635i
$914$	28.6547	+	12.2605i	0.947814	+	0.405541i
$915$		0			0
$916$	27.1383	+	11.9860i	0.896675	+	0.396028i
$917$	−5.68059	−	13.7142i	−0.187590	−	0.452881i
$918$		0			0
$919$	12.8420	−	12.8420i	0.423620	−	0.423620i	−0.462828	−	0.886448i	$-0.653165\pi$
$919$	12.8420	−	12.8420i	0.423620	−	0.423620i	0.886448	+	0.462828i	$0.153165\pi$
$920$	−23.3139	−	7.12508i	−0.768637	−	0.234907i
$921$		0			0
$922$	0.985089	+	0.0114277i	0.0324422	+	0.000376351i
$923$	−2.58505	−	0.340329i	−0.0850880	−	0.0112020i
$924$		0			0
$925$	−1.72079	−	13.0707i	−0.0565793	−	0.429763i
$926$	16.4826	+	12.9540i	0.541651	+	0.425696i
$927$		0			0
$928$	−29.4455	+	44.7869i	−0.966594	+	1.47020i
$929$	37.2662	−	21.5156i	1.22266	−	0.705905i	0.257178	−	0.966364i	$-0.417207\pi$
$929$	37.2662	−	21.5156i	1.22266	−	0.705905i	0.965485	+	0.260459i	$0.0838739\pi$
$930$		0			0
$931$	−21.4787	−	27.9916i	−0.703938	−	0.917389i
$932$	36.7399	−	20.0901i	1.20345	−	0.658073i
$933$		0			0
$934$	−0.707482	−	0.419482i	−0.0231495	−	0.0137259i
$935$	−22.2635	+	22.2635i	−0.728096	+	0.728096i
$936$		0			0
$937$	30.0408	+	30.0408i	0.981392	+	0.981392i	0.999830	−	0.0184383i	$-0.00586941\pi$
$937$	30.0408	+	30.0408i	0.981392	+	0.981392i	−0.0184383	+	0.999830i	$0.505869\pi$
$938$	15.3134	+	59.9224i	0.500001	+	1.95654i
$939$		0			0
$940$	0.849729	+	7.85930i	0.0277151	+	0.256342i
$941$	−17.0028	+	13.0467i	−0.554276	+	0.425311i	−0.847548	−	0.530718i	$-0.821922\pi$
$941$	−17.0028	+	13.0467i	−0.554276	+	0.425311i	0.293273	+	0.956029i	$0.405256\pi$
$942$		0			0
$943$	−13.4336	−	23.2676i	−0.437458	−	0.757699i
$944$	1.94509	+	1.64132i	0.0633072	+	0.0534203i
$945$		0			0
$946$	2.23709	+	18.6629i	0.0727342	+	0.606782i
$947$	12.8489	−	1.69158i	0.417532	−	0.0549691i	0.0811661	−	0.996701i	$-0.474136\pi$
$947$	12.8489	−	1.69158i	0.417532	−	0.0549691i	0.336366	+	0.941732i	$0.390802\pi$
$948$		0			0
$949$	0.0748245	−	0.568349i	0.00242891	−	0.0184494i
$950$	6.73555	−	6.58107i	0.218530	−	0.213518i
$951$		0			0
$952$	40.5604	+	33.4282i	1.31457	+	1.08341i
$953$	−17.4567	−	17.4567i	−0.565477	−	0.565477i	0.365381	−	0.930858i	$-0.380939\pi$
$953$	−17.4567	−	17.4567i	−0.565477	−	0.565477i	−0.930858	+	0.365381i	$0.880939\pi$
$954$		0			0
$955$	−8.07116	+	3.34318i	−0.261176	+	0.108183i
$956$	9.35111	+	9.79539i	0.302436	+	0.316806i
$957$		0			0
$958$	47.6533	−	19.0941i	1.53961	−	0.616901i
$959$	7.90794	−	13.6970i	0.255361	−	0.442298i
$960$		0			0
$961$	−15.3248	−	26.5433i	−0.494347	−	0.856234i
$962$	−6.35005	−	4.99065i	−0.204734	−	0.160905i
$963$		0			0
$964$	−56.2537	+	13.6827i	−1.81181	+	0.440691i
$965$	−1.35915	−	1.04291i	−0.0437527	−	0.0335726i
$966$		0			0
$967$	−43.2077	+	11.5775i	−1.38947	+	0.372306i	−0.874550	−	0.484935i	$-0.838843\pi$
$967$	−43.2077	+	11.5775i	−1.38947	+	0.372306i	−0.514915	+	0.857241i	$0.672177\pi$
$968$	−38.0061	−	6.35590i	−1.22156	−	0.204286i
$969$		0			0
$970$	−9.26715	−	36.2630i	−0.297550	−	1.16433i
$971$	35.1496	−	14.5595i	1.12801	−	0.467235i	0.260903	−	0.965365i	$-0.415980\pi$
$971$	35.1496	−	14.5595i	1.12801	−	0.467235i	0.867103	+	0.498130i	$0.165980\pi$
$972$		0			0
$973$	−28.4334	+	68.6443i	−0.911532	+	2.20063i
$974$	8.24076	−	6.17282i	0.264051	−	0.197790i
$975$		0			0
$976$	−21.0610	+	44.8410i	−0.674145	+	1.43532i
$977$	3.00365	−	5.20247i	0.0960952	−	0.166442i	−0.813970	−	0.580907i	$-0.802698\pi$
$977$	3.00365	−	5.20247i	0.0960952	−	0.166442i	0.910065	+	0.414465i	$0.136031\pi$
$978$		0			0
$979$	−2.25002	−	17.0906i	−0.0719109	−	0.546218i
$980$	34.3741	−	25.1311i	1.09804	−	0.802782i
$981$		0			0
$982$	29.4160	+	8.24887i	0.938701	+	0.263232i
$983$	−7.48681	+	27.9412i	−0.238792	+	0.891184i	0.737611	+	0.675226i	$0.235954\pi$
$983$	−7.48681	+	27.9412i	−0.238792	+	0.891184i	−0.976403	+	0.215958i	$0.930713\pi$
$984$		0			0
$985$	−3.05841	−	11.4141i	−0.0974490	−	0.363685i
$986$	−0.634807	+	54.7216i	−0.0202164	+	1.74269i
$987$		0			0
$988$	0.133831	−	5.76744i	0.00425772	−	0.183487i
$989$	−5.68642	+	13.7282i	−0.180818	+	0.436532i
$990$		0			0
$991$		−	36.4148i		−	1.15675i	−0.815770	−	0.578377i	$-0.803686\pi$
$991$		−	36.4148i		−	1.15675i	0.815770	−	0.578377i	$-0.196314\pi$
$992$	−3.16307	+	1.10006i	−0.100428	+	0.0349270i
$993$		0			0
$994$	13.9014	−	5.57011i	0.440925	−	0.176673i
$995$	3.22114	−	2.47167i	0.102117	−	0.0783572i
$996$		0			0
$997$	−23.8237	+	31.0476i	−0.754503	+	0.983288i	0.245400	+	0.969422i	$0.421081\pi$
$997$	−23.8237	+	31.0476i	−0.754503	+	0.983288i	−0.999904	+	0.0138661i	$0.995586\pi$
$998$	23.4877	+	41.7941i	0.743489	+	1.32297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.611.24		368
3.2	odd	2		288.2.bf.a.131.23	yes	368
9.2	odd	6	inner	864.2.bn.a.35.40		368
9.7	even	3		288.2.bf.a.227.7	yes	368
32.11	odd	8	inner	864.2.bn.a.395.40		368
96.11	even	8		288.2.bf.a.203.7	yes	368
288.11	even	24	inner	864.2.bn.a.683.24		368
288.43	odd	24		288.2.bf.a.11.23	✓	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.23	✓	368	288.43	odd	24
288.2.bf.a.131.23	yes	368	3.2	odd	2
288.2.bf.a.203.7	yes	368	96.11	even	8
288.2.bf.a.227.7	yes	368	9.7	even	3
864.2.bn.a.35.40		368	9.2	odd	6	inner
864.2.bn.a.395.40		368	32.11	odd	8	inner
864.2.bn.a.611.24		368	1.1	even	1	trivial
864.2.bn.a.683.24		368	288.11	even	24	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.200844 - 1.39988i) q^{2} +(-1.91932 - 0.562314i) q^{4} +(0.202788 - 1.54033i) q^{5} +(1.17766 - 4.39511i) q^{7} +(-1.17266 + 2.57388i) q^{8} +O(q^{10})\)	\(q+(0.200844 - 1.39988i) q^{2} +(-1.91932 - 0.562314i) q^{4} +(0.202788 - 1.54033i) q^{5} +(1.17766 - 4.39511i) q^{7} +(-1.17266 + 2.57388i) q^{8} +(-2.11554 - 0.593244i) q^{10} +(-3.93681 - 3.02082i) q^{11} +(0.682021 + 0.888828i) q^{13} +(-5.91609 - 2.53132i) q^{14} +(3.36761 + 2.15853i) q^{16} +4.08402 q^{17} +(2.37867 + 0.985278i) q^{19} +(-1.25536 + 2.84235i) q^{20} +(-5.01947 + 4.90434i) q^{22} +(-5.35870 + 1.43586i) q^{23} +(2.49815 + 0.669376i) q^{25} +(1.38123 - 0.776232i) q^{26} +(-4.73175 + 7.77341i) q^{28} +(-9.39407 + 1.23675i) q^{29} +(-0.512694 - 0.296004i) q^{31} +(3.69804 - 4.28071i) q^{32} +(0.820250 - 5.71713i) q^{34} +(-6.53108 - 2.70526i) q^{35} +(-1.95073 - 4.70947i) q^{37} +(1.85701 - 3.13197i) q^{38} +(3.72682 + 2.32823i) q^{40} +(1.25344 + 4.67789i) q^{41} +(1.63054 - 2.12496i) q^{43} +(5.85736 + 8.01165i) q^{44} +(0.933768 + 7.78992i) q^{46} +(2.20325 - 1.27205i) q^{47} +(-11.8679 - 6.85192i) q^{49} +(1.43878 - 3.36266i) q^{50} +(-0.809219 - 2.08946i) q^{52} +(-2.74153 - 6.61863i) q^{53} +(-5.45138 + 5.45138i) q^{55} +(9.93149 + 8.18512i) q^{56} +(-0.155437 + 13.3990i) q^{58} +(0.630820 + 0.0830490i) q^{59} +(1.61659 + 12.2792i) q^{61} +(-0.517341 + 0.658259i) q^{62} +(-5.24975 - 6.03656i) q^{64} +(1.50739 - 0.870292i) q^{65} +(-5.85104 - 7.62523i) q^{67} +(-7.83855 - 2.29650i) q^{68} +(-5.09877 + 8.59939i) q^{70} +(-1.64564 + 1.64564i) q^{71} +(-0.361810 - 0.361810i) q^{73} +(-6.98448 + 1.78491i) q^{74} +(-4.01141 - 3.22863i) q^{76} +(-17.9131 + 13.7452i) q^{77} +(-3.24123 - 5.61397i) q^{79} +(4.00774 - 4.74949i) q^{80} +(6.80022 - 0.815134i) q^{82} +(12.0094 - 1.58106i) q^{83} +(0.828189 - 6.29072i) q^{85} +(-2.64720 - 2.70934i) q^{86} +(12.3918 - 6.59050i) q^{88} +(2.45638 + 2.45638i) q^{89} +(4.70968 - 1.95082i) q^{91} +(11.0925 + 0.257395i) q^{92} +(-1.33820 - 3.33977i) q^{94} +(2.00002 - 3.46413i) q^{95} +(8.51749 + 14.7527i) q^{97} +(-11.9755 + 15.2374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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