LMFDB - Embedded newform 864.2.bn.a.683.24

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			683.24
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.24

$q$-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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

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

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	0.975040	+	0.222031i	$0.0712686\pi$
$5$	0.202788	+	1.54033i	0.0906895	+	0.688855i	−0.884350	+	0.466824i	$0.845398\pi$
$6$		0			0
$7$	1.17766	+	4.39511i	0.445116	+	1.66119i	0.715631	+	0.698478i	$0.246139\pi$
$7$	1.17766	+	4.39511i	0.445116	+	1.66119i	−0.270516	+	0.962716i	$0.587194\pi$
$8$	−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	−0.997472	−	0.0710656i	$-0.977360\pi$
$11$	−3.93681	+	3.02082i	−1.18699	+	0.910811i	−0.189521	+	0.981877i	$0.560693\pi$
$12$		0			0
$13$	0.682021	−	0.888828i	0.189159	−	0.246516i	−0.689141	−	0.724628i	$-0.742012\pi$
$13$	0.682021	−	0.888828i	0.189159	−	0.246516i	0.878299	+	0.478111i	$0.158678\pi$
$14$	−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	−0.0927611	−	0.995688i	$-0.529569\pi$
$19$	2.37867	−	0.985278i	0.545705	−	0.226038i	0.638466	+	0.769650i	$0.279569\pi$
$20$	−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	−0.347549	−	0.937662i	$-0.612986\pi$
$23$	−5.35870	−	1.43586i	−1.11737	−	0.299397i	−0.769817	+	0.638264i	$0.779653\pi$
$24$		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	−0.810159	−	0.586210i	$-0.800619\pi$
$29$	−9.39407	−	1.23675i	−1.74444	−	0.229659i	−0.934276	+	0.356551i	$0.883953\pi$
$30$		0			0
$31$	−0.512694	+	0.296004i	−0.0920825	+	0.0531639i	−0.545334	−	0.838219i	$-0.683597\pi$
$31$	−0.512694	+	0.296004i	−0.0920825	+	0.0531639i	0.453252	+	0.891383i	$0.350264\pi$
$32$	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	0.678516	+	0.734586i	$0.262623\pi$
$37$	−1.95073	+	4.70947i	−0.320698	+	0.774233i	−0.999214	+	0.0396471i	$0.987377\pi$
$38$	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	−0.796317	−	0.604880i	$-0.793221\pi$
$41$	1.25344	−	4.67789i	0.195754	−	0.730563i	0.992070	−	0.125683i	$-0.0401123\pi$
$42$		0			0
$43$	1.63054	+	2.12496i	0.248654	+	0.324053i	0.900959	−	0.433904i	$-0.142864\pi$
$43$	1.63054	+	2.12496i	0.248654	+	0.324053i	−0.652305	+	0.757957i	$0.726198\pi$
$44$	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	0.652006	−	0.758214i	$-0.273928\pi$
$47$	2.20325	+	1.27205i	0.321377	+	0.185547i	−0.330629	+	0.943761i	$0.607261\pi$
$48$		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	0.616024	+	0.787727i	$0.288742\pi$
$53$	−2.74153	+	6.61863i	−0.376578	+	0.909139i	−0.992602	+	0.121412i	$0.961258\pi$
$54$		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	−0.0893513	−	0.996000i	$-0.528479\pi$
$59$	0.630820	−	0.0830490i	0.0821257	−	0.0108121i	0.171477	+	0.985188i	$0.445146\pi$
$60$		0			0
$61$	1.61659	−	12.2792i	0.206983	−	1.57219i	−0.500675	−	0.865636i	$-0.666915\pi$
$61$	1.61659	−	12.2792i	0.206983	−	1.57219i	0.707658	−	0.706556i	$-0.249752\pi$
$62$	−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	−0.999635	−	0.0270123i	$-0.991401\pi$
$67$	−5.85104	+	7.62523i	−0.714819	+	0.931570i	0.284816	+	0.958582i	$0.408067\pi$
$68$	−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	0.602681	−	0.797982i	$-0.294099\pi$
$71$	−1.64564	−	1.64564i	−0.195301	−	0.195301i	−0.797982	+	0.602681i	$0.794099\pi$
$72$		0			0
$73$	−0.361810	+	0.361810i	−0.0423466	+	0.0423466i	−0.727963	−	0.685616i	$-0.759533\pi$
$73$	−0.361810	+	0.361810i	−0.0423466	+	0.0423466i	0.685616	+	0.727963i	$0.259533\pi$
$74$	−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	−0.988723	−	0.149758i	$-0.952150\pi$
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	0.624056	+	0.781380i	$0.285484\pi$
$80$	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	0.756607	−	0.653870i	$-0.226856\pi$
$83$	12.0094	+	1.58106i	1.31820	+	0.173544i	0.561593	+	0.827414i	$0.310189\pi$
$84$		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	−0.564831	−	0.825207i	$-0.691059\pi$
$89$	2.45638	−	2.45638i	0.260376	−	0.260376i	0.825207	+	0.564831i	$0.191059\pi$
$90$		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	−0.00240483	−	0.999997i	$-0.500765\pi$
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	0.867225	−	0.497916i	$-0.165901\pi$
$98$	−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	−0.755604	−	0.655028i	$-0.772657\pi$
$101$	−3.20048	+	2.45582i	−0.318460	+	0.244363i	0.437144	+	0.899391i	$0.355990\pi$
$102$		0			0
$103$	15.3404	+	4.11044i	1.51153	+	0.405013i	0.916943	−	0.399018i	$-0.130649\pi$
$103$	15.3404	+	4.11044i	1.51153	+	0.405013i	0.594587	+	0.804031i	$0.297316\pi$
$104$	−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	0.505070	−	0.863079i	$-0.331467\pi$
$107$	2.60587	+	1.07939i	0.251919	+	0.104348i	−0.253150	+	0.967427i	$0.581467\pi$
$108$		0			0
$109$	−0.946606	−	2.28531i	−0.0906684	−	0.218893i	0.872040	−	0.489435i	$-0.162797\pi$
$109$	−0.946606	−	2.28531i	−0.0906684	−	0.218893i	−0.962708	+	0.270542i	$0.912797\pi$
$110$	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	0.939873	+	0.341525i	$0.110943\pi$
$113$	8.13956	+	14.0981i	0.765705	+	1.32624i	−0.174167	+	0.984716i	$0.555723\pi$
$114$		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	$0.428202\pi$
$127$			21.9679i			1.94934i	−0.223651	+	0.974669i	$0.571798\pi$
$128$	−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	0.715613	−	0.698497i	$-0.246148\pi$
$131$	2.58818	+	1.98598i	0.226130	+	0.173516i	−0.489482	+	0.872013i	$0.662814\pi$
$132$		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	−0.112526	−	0.993649i	$-0.535894\pi$
$137$	3.35747	−	0.899631i	0.286848	−	0.0768606i	0.399374	+	0.916788i	$0.369228\pi$
$138$		0			0
$139$	−16.1894	+	2.13138i	−1.37317	+	0.180781i	−0.780748	−	0.624846i	$-0.785162\pi$
$139$	−16.1894	+	2.13138i	−1.37317	+	0.180781i	−0.592423	+	0.805627i	$0.701828\pi$
$140$	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	0.285694	−	0.958321i	$-0.407776\pi$
$149$	9.88347	−	1.30118i	0.809685	−	0.106597i	0.523991	+	0.851724i	$0.324443\pi$
$150$		0			0
$151$	−4.32703	+	1.15942i	−0.352129	+	0.0943526i	−0.430548	−	0.902568i	$-0.641680\pi$
$151$	−4.32703	+	1.15942i	−0.352129	+	0.0943526i	0.0784188	+	0.996921i	$0.475013\pi$
$152$	−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	0.824166	−	0.566348i	$-0.191644\pi$
$157$	6.14501	+	4.71523i	0.490425	+	0.376317i	−0.333741	+	0.942665i	$0.608311\pi$
$158$	−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	−0.996162	−	0.0875240i	$-0.972105\pi$
$163$	−4.51520	−	10.9007i	−0.353658	−	0.853806i	0.642504	−	0.766282i	$-0.277895\pi$
$164$	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	−0.974411	−	0.224772i	$-0.927836\pi$
$167$	−0.234682	+	0.875847i	−0.0181603	+	0.0677751i	0.956251	+	0.292547i	$0.0945029\pi$
$168$		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	−0.995880	−	0.0906783i	$-0.971096\pi$
$173$	−0.137639	+	1.04547i	−0.0104645	+	0.0794859i	0.985416	+	0.170164i	$0.0544298\pi$
$174$		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	0.867529	+	0.497387i	$0.165707\pi$
$179$	8.10504	+	19.5673i	0.605799	+	1.46253i	−0.261730	+	0.965141i	$0.584293\pi$
$180$		0			0
$181$	4.74472	+	1.96533i	0.352672	+	0.146082i	0.551984	−	0.833854i	$-0.313871\pi$
$181$	4.74472	+	1.96533i	0.352672	+	0.146082i	−0.199312	+	0.979936i	$0.563871\pi$
$182$	−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	−0.949634	−	0.313363i	$-0.898544\pi$
$191$	−2.81155	+	4.86975i	−0.203437	+	0.352363i	0.746197	+	0.665725i	$0.231878\pi$
$192$		0			0
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	0.885187	−	0.465236i	$-0.154031\pi$
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	−0.845500	+	0.533976i	$0.820697\pi$
$194$	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	0.618695	−	0.785631i	$-0.287662\pi$
$197$	7.02701	+	2.91068i	0.500653	+	0.207377i	−0.118042	+	0.993009i	$0.537662\pi$
$198$		0			0
$199$	1.84792	−	1.84792i	0.130996	−	0.130996i	−0.638569	−	0.769565i	$-0.720473\pi$
$199$	1.84792	−	1.84792i	0.130996	−	0.130996i	0.769565	+	0.638569i	$0.220473\pi$
$200$	−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	0.638025	−	0.770016i	$-0.279752\pi$
$211$	0.862538	+	0.661849i	0.0593796	+	0.0455635i	−0.578645	+	0.815579i	$0.696418\pi$
$212$	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	0.657995	−	0.753023i	$-0.271405\pi$
$223$	5.00046	+	2.88701i	0.334855	+	0.193329i	−0.323139	+	0.946351i	$0.604738\pi$
$224$	−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	−0.943922	−	0.330169i	$-0.892894\pi$
$227$	0.802907	−	6.09868i	0.0532908	−	0.404784i	0.997212	−	0.0746142i	$-0.0237725\pi$
$228$		0			0
$229$	−14.7068	+	1.93618i	−0.971851	+	0.127947i	−0.599700	−	0.800225i	$-0.704713\pi$
$229$	−14.7068	+	1.93618i	−0.971851	+	0.127947i	−0.372152	+	0.928172i	$0.621380\pi$
$230$	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	0.0296721	−	0.999560i	$-0.490554\pi$
$233$	−14.8047	−	14.8047i	−0.969888	−	0.969888i	−0.999560	+	0.0296721i	$0.990554\pi$
$234$		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	−0.677518	−	0.735507i	$-0.736944\pi$
$239$	−5.86397	+	3.38557i	−0.379309	+	0.218994i	0.298209	+	0.954501i	$0.403611\pi$
$240$		0			0
$241$	25.0688	+	14.4735i	1.61482	+	0.932318i	0.988231	+	0.152970i	$0.0488839\pi$
$241$	25.0688	+	14.4735i	1.61482	+	0.932318i	0.626592	+	0.779348i	$0.284449\pi$
$242$	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	−0.955032	−	0.296504i	$-0.904179\pi$
$251$	−1.10999	+	2.67976i	−0.0700622	+	0.169145i	0.884969	+	0.465649i	$0.154179\pi$
$252$		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	0.267052	−	0.963682i	$-0.413950\pi$
$257$	19.8010	−	11.4321i	1.23515	−	0.713115i	0.968099	+	0.250567i	$0.0806170\pi$
$258$		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	−0.276993	−	0.960872i	$-0.589338\pi$
$263$	−0.590968	+	0.158349i	−0.0364407	+	0.00976425i	0.240553	+	0.970636i	$0.422671\pi$
$264$		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	−0.338692	−	0.940897i	$-0.609984\pi$
$269$	1.42907	−	0.591941i	0.0871321	−	0.0360913i	0.425824	+	0.904806i	$0.359984\pi$
$270$		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	−0.828128	−	0.560539i	$-0.810594\pi$
$277$	−8.33871	+	6.39852i	−0.501025	+	0.384450i	0.327103	+	0.944989i	$0.393927\pi$
$278$	−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	0.874659	−	0.484738i	$-0.161085\pi$
$281$	−2.09852	−	7.83178i	−0.125187	−	0.467205i	−0.999846	+	0.0175337i	$0.994419\pi$
$282$		0			0
$283$	−1.51058	−	11.4740i	−0.0897947	−	0.682059i	−0.975844	−	0.218468i	$-0.929894\pi$
$283$	−1.51058	−	11.4740i	−0.0897947	−	0.682059i	0.886049	−	0.463591i	$-0.153439\pi$
$284$	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	0.976836	−	0.213988i	$-0.0686454\pi$
$293$	−0.378280	−	2.87332i	−0.0220993	−	0.167861i	−0.998936	+	0.0461271i	$0.985312\pi$
$294$		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	−0.967656	−	0.252273i	$-0.918822\pi$
$307$	−25.8180	+	10.6941i	−1.47351	+	0.610347i	−0.505852	+	0.862620i	$0.668822\pi$
$308$	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	0.998886	−	0.0471908i	$-0.0150269\pi$
$311$	32.4549	+	8.69628i	1.84035	+	0.493121i	0.841465	+	0.540311i	$0.181694\pi$
$312$		0			0
$313$	−11.2593	+	3.01691i	−0.636412	+	0.170526i	−0.562578	−	0.826745i	$-0.690190\pi$
$313$	−11.2593	+	3.01691i	−0.636412	+	0.170526i	−0.0738342	+	0.997271i	$0.523524\pi$
$314$	−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	−0.641792	−	0.766879i	$-0.721809\pi$
$317$	−25.9981	−	3.42271i	−1.46020	−	0.192239i	−0.818406	+	0.574640i	$0.805142\pi$
$318$		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	−0.862555	−	0.505963i	$-0.831137\pi$
$331$	−20.5227	−	26.7458i	−1.12803	−	1.47008i	−0.265477	−	0.964117i	$-0.585529\pi$
$332$	−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	−0.423717	−	0.905795i	$-0.639275\pi$
$337$	2.73282	−	1.57779i	0.148866	−	0.0859478i	0.572583	+	0.819847i	$0.305942\pi$
$338$	−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	0.589403	−	0.807839i	$-0.299363\pi$
$347$	25.4794	−	3.35443i	1.36781	−	0.180075i	0.778404	+	0.627764i	$0.216030\pi$
$348$		0			0
$349$	−1.58498	+	12.0391i	−0.0848420	+	0.644439i	0.895202	+	0.445660i	$0.147031\pi$
$349$	−1.58498	+	12.0391i	−0.0848420	+	0.644439i	−0.980044	+	0.198779i	$0.936302\pi$
$350$	−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	0.586080	−	0.810253i	$-0.300670\pi$
$353$	3.33343	+	1.92456i	0.177421	+	0.102434i	−0.408660	+	0.912687i	$0.634004\pi$
$354$		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	0.975683	−	0.219186i	$-0.0703402\pi$
$359$	14.3336	+	14.3336i	0.756497	+	0.756497i	−0.219186	+	0.975683i	$0.570340\pi$
$360$		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	−0.717837	−	0.696212i	$-0.754868\pi$
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	0.961855	+	0.273559i	$0.0882009\pi$
$368$	−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	−0.999861	−	0.0166635i	$-0.994696\pi$
$373$	−0.741285	−	5.63062i	−0.0383823	−	0.291542i	0.961479	−	0.274879i	$-0.0886377\pi$
$374$	−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	0.855541	−	0.517735i	$-0.173225\pi$
$379$	21.3058	+	8.82516i	1.09441	+	0.453318i	0.238865	+	0.971053i	$0.423225\pi$
$380$	−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	0.993580	+	0.113128i	$0.0360871\pi$
$383$	11.6397	+	20.1606i	0.594762	+	1.03016i	−0.398818	+	0.917030i	$0.630580\pi$
$384$		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	−0.551870	−	0.833930i	$-0.686086\pi$
$389$	2.18552	−	1.67701i	0.110810	−	0.0850275i	0.662680	+	0.748903i	$0.269419\pi$
$390$		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	−0.993197	−	0.116444i	$-0.962851\pi$
$397$	−7.43673	−	17.9539i	−0.373239	−	0.901078i	0.619958	−	0.784635i	$-0.287149\pi$
$398$	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	−0.999839	−	0.0179544i	$-0.994285\pi$
$401$	−10.3222	−	17.8787i	−0.515468	−	0.892817i	0.484370	−	0.874863i	$-0.339049\pi$
$402$		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	−0.729782	−	0.683680i	$-0.760378\pi$
$409$	4.93596	−	18.4213i	0.244068	−	0.910873i	0.973850	−	0.227193i	$-0.0729549\pi$
$410$	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	−0.137236	−	0.990538i	$-0.543822\pi$
$419$	−23.1211	−	17.7415i	−1.12954	−	0.866728i	−0.992306	+	0.123811i	$0.960488\pi$
$420$		0			0
$421$	16.3019	+	21.2451i	0.794506	+	1.03542i	0.998407	+	0.0564291i	$0.0179715\pi$
$421$	16.3019	+	21.2451i	0.794506	+	1.03542i	−0.203900	+	0.978992i	$0.565362\pi$
$422$	−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	$-0.993512\pi$
$431$		−	0.846314i		−	0.0407655i	0.999792	−	0.0203828i	$-0.00648848\pi$
$432$		0			0
$433$		−	35.1194i		−	1.68773i	−0.536554	−	0.843866i	$-0.680274\pi$
$433$		−	35.1194i		−	1.68773i	0.536554	−	0.843866i	$-0.319726\pi$
$434$	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	−0.402585	−	0.915383i	$-0.631888\pi$
$439$	−6.15039	+	1.64799i	−0.293542	+	0.0786544i	0.109043	+	0.994037i	$0.465221\pi$
$440$	−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	0.987715	−	0.156268i	$-0.0499463\pi$
$443$	12.2314	+	15.9403i	0.581132	+	0.757346i	−0.406583	+	0.913614i	$0.633280\pi$
$444$		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	$-0.981054\pi$
$449$		−	2.52101i		−	0.118974i	0.998229	−	0.0594870i	$-0.0189465\pi$
$450$		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	−0.961124	−	0.276116i	$-0.910953\pi$
$457$	−5.70405	−	21.2878i	−0.266824	−	0.995801i	0.694300	−	0.719686i	$-0.255714\pi$
$458$	−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	−0.989197	−	0.146592i	$-0.953169\pi$
$461$	0.0909258	−	0.690650i	0.00423484	−	0.0321668i	0.993432	+	0.114426i	$0.0365028\pi$
$462$		0			0
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	0.640798	−	0.767710i	$-0.278604\pi$
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	−0.985255	+	0.171092i	$0.945270\pi$
$464$	−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	0.928945	−	0.370217i	$-0.120717\pi$
$467$	0.222565	+	0.537320i	0.0102991	+	0.0248642i	−0.918646	+	0.395081i	$0.870717\pi$
$468$		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	−0.0692877	−	0.997597i	$-0.522073\pi$
$479$	18.1501	−	31.4369i	0.829300	−	1.43639i	0.898588	−	0.438793i	$-0.144594\pi$
$480$		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	−0.580777	−	0.814062i	$-0.697251\pi$
$487$	5.14815	−	5.14815i	0.233285	−	0.233285i	0.814062	+	0.580777i	$0.197251\pi$
$488$	−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	−0.929304	−	0.369316i	$-0.879592\pi$
$491$	−2.81970	−	21.4178i	−0.127251	−	0.966570i	0.802052	−	0.597254i	$-0.203741\pi$
$492$		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	−0.205474	−	0.978663i	$-0.565873\pi$
$499$	−26.8946	−	20.6370i	−1.20397	−	0.923838i	−0.998496	+	0.0548242i	$0.982540\pi$
$500$	−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	−0.865666	−	0.500623i	$-0.833104\pi$
$503$	−8.18706	+	8.18706i	−0.365043	+	0.365043i	0.500623	+	0.865666i	$0.333104\pi$
$504$		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	−0.424118	−	0.905607i	$-0.639416\pi$
$509$	12.6432	−	16.4770i	0.560401	−	0.730328i	0.984519	+	0.175278i	$0.0560826\pi$
$510$		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	0.996132	−	0.0878707i	$-0.0280062\pi$
$521$	20.7314	+	20.7314i	0.908261	+	0.908261i	−0.0878707	+	0.996132i	$0.528006\pi$
$522$		0			0
$523$	−5.99966	+	14.4845i	−0.262347	+	0.633361i	−0.999083	−	0.0428191i	$-0.986366\pi$
$523$	−5.99966	+	14.4845i	−0.262347	+	0.633361i	0.736736	+	0.676181i	$0.236366\pi$
$524$	−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	−0.479996	−	0.877271i	$-0.659362\pi$
$541$	−4.63048	+	1.91801i	−0.199080	+	0.0824617i	0.280916	+	0.959732i	$0.409362\pi$
$542$	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	0.784680	−	0.619901i	$-0.212827\pi$
$547$	32.3265	+	4.25586i	1.38218	+	0.181968i	0.597501	+	0.801868i	$0.296160\pi$
$548$	−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	−0.901033	−	0.433751i	$-0.857190\pi$
$557$	−29.0633	+	12.0384i	−1.23145	+	0.510083i	−0.330418	+	0.943835i	$0.607190\pi$
$558$		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	−0.797408	−	0.603441i	$-0.793796\pi$
$563$	−0.193257	+	0.251857i	−0.00814479	+	0.0106145i	0.789263	+	0.614055i	$0.210463\pi$
$564$		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	0.599408	+	0.800444i	$0.295403\pi$
$569$	11.4624	+	42.7781i	0.480527	+	1.79335i	−0.118881	+	0.992909i	$0.537931\pi$
$570$		0			0
$571$	−0.837628	−	6.36242i	−0.0350537	−	0.266259i	−0.999993	−	0.00378539i	$-0.998795\pi$
$571$	−0.837628	−	6.36242i	−0.0350537	−	0.266259i	0.964939	−	0.262474i	$-0.0845383\pi$
$572$	−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	−0.421434	−	0.906859i	$-0.638473\pi$
$587$	8.36957	−	6.42220i	0.345449	−	0.265072i	0.766883	+	0.641787i	$0.221806\pi$
$588$		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	−0.666415	−	0.745581i	$-0.732172\pi$
$599$	−39.5590	−	10.5998i	−1.61634	−	0.433096i	−0.949923	+	0.312485i	$0.898839\pi$
$600$		0			0
$601$	22.5982	−	6.05516i	0.921798	−	0.246995i	0.233444	−	0.972370i	$-0.425000\pi$
$601$	22.5982	−	6.05516i	0.921798	−	0.246995i	0.688354	+	0.725375i	$0.258334\pi$
$602$	−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	−0.793470	−	0.608610i	$-0.791728\pi$
$607$	−16.3379	+	9.43267i	−0.663133	+	0.382860i	0.130337	+	0.991470i	$0.458394\pi$
$608$	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	0.588447	+	0.808536i	$0.299740\pi$
$613$	−9.88791	+	23.8715i	−0.399369	+	0.964162i	−0.987816	+	0.155626i	$0.950260\pi$
$614$	−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	−0.971169	−	0.238390i	$-0.923380\pi$
$617$	−0.271173	+	1.01203i	−0.0109170	+	0.0407428i	0.960252	+	0.279133i	$0.0900470\pi$
$618$		0			0
$619$	−4.92501	−	6.41840i	−0.197953	−	0.257977i	0.683821	−	0.729650i	$-0.260317\pi$
$619$	−4.92501	−	6.41840i	−0.197953	−	0.257977i	−0.881774	+	0.471673i	$0.843650\pi$
$620$	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	0.648306	−	0.761380i	$-0.275478\pi$
$631$	−2.84039	−	2.84039i	−0.113074	−	0.113074i	−0.761380	+	0.648306i	$0.775478\pi$
$632$	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	0.824325	−	0.566117i	$-0.191555\pi$
$641$	18.8927	+	10.9077i	0.746215	+	0.430828i	−0.0781094	+	0.996945i	$0.524888\pi$
$642$		0			0
$643$	1.96897	−	2.56601i	0.0776485	−	0.101193i	−0.752914	−	0.658119i	$-0.771352\pi$
$643$	1.96897	−	2.56601i	0.0776485	−	0.101193i	0.830563	+	0.556925i	$0.188019\pi$
$644$	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	0.307460	−	0.951561i	$-0.400521\pi$
$647$	−16.3835	−	16.3835i	−0.644101	−	0.644101i	−0.951561	+	0.307460i	$0.900521\pi$
$648$		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	0.911430	−	0.411456i	$-0.134979\pi$
$653$	19.1626	+	14.7040i	0.749890	+	0.575411i	−0.161540	+	0.986866i	$0.551646\pi$
$654$		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	0.266072	−	0.963953i	$-0.414274\pi$
$659$	7.02331	+	0.924636i	0.273589	+	0.0360187i	0.00751688	+	0.999972i	$0.497607\pi$
$660$		0			0
$661$	5.03887	+	38.2740i	0.195989	+	1.48869i	0.752911	+	0.658122i	$0.228649\pi$
$661$	5.03887	+	38.2740i	0.195989	+	1.48869i	−0.556922	+	0.830565i	$0.688018\pi$
$662$	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	−0.944443	−	0.328675i	$-0.893398\pi$
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	0.756863	+	0.653574i	$0.226731\pi$
$674$	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	−0.115465	−	0.993312i	$-0.536836\pi$
$677$	21.1827	−	16.2540i	0.814116	−	0.624693i	0.929581	+	0.368618i	$0.120169\pi$
$678$		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	0.0990653	−	0.995081i	$-0.468415\pi$
$683$	−13.9691	−	5.78620i	−0.534513	−	0.221403i	−0.633579	+	0.773678i	$0.718415\pi$
$684$		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	0.677902	+	0.735152i	$0.262889\pi$
$691$	−4.39444	+	33.3791i	−0.167172	+	1.26980i	−0.845075	+	0.534648i	$0.820444\pi$
$692$	−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	−0.997800	−	0.0663032i	$-0.978880\pi$
$701$	−8.97900	−	21.6772i	−0.339132	−	0.818737i	0.658667	−	0.752434i	$-0.271120\pi$
$702$		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	0.313503	−	0.949587i	$-0.398497\pi$
$709$	−18.2360	−	23.7656i	−0.684868	−	0.892537i	−0.998371	+	0.0570496i	$0.981831\pi$
$710$	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	$-0.729967\pi$
$719$		−	40.2309i		−	1.50036i	0.661234	−	0.750180i	$-0.270033\pi$
$720$		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	−0.518100	−	0.855320i	$-0.673361\pi$
$727$	−14.5365	+	3.89504i	−0.539129	+	0.144459i	−0.0210282	+	0.999779i	$0.506694\pi$
$728$	−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	0.627908	−	0.778288i	$-0.283912\pi$
$733$	1.04651	+	0.803017i	0.0386538	+	0.0296601i	−0.589254	+	0.807948i	$0.700578\pi$
$734$	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	−0.981550	−	0.191204i	$-0.938761\pi$
$739$	−11.4907	−	27.7409i	−0.422691	−	1.02047i	0.558860	−	0.829262i	$-0.311239\pi$
$740$	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	−0.987566	−	0.157206i	$-0.949751\pi$
$743$	−1.46392	+	5.46342i	−0.0537060	+	0.200433i	0.933860	+	0.357639i	$0.116418\pi$
$744$		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	−0.650098	−	0.759850i	$-0.725272\pi$
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.333001	−	0.942927i	$-0.608061\pi$
$752$	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	0.908945	−	0.416917i	$-0.136889\pi$
$757$	34.5808	+	14.3238i	1.25686	+	0.520609i	0.347916	+	0.937526i	$0.386889\pi$
$758$	−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	0.613797	−	0.789464i	$-0.289641\pi$
$761$	20.7070	+	5.54843i	0.750629	+	0.201130i	0.136832	+	0.990594i	$0.456308\pi$
$762$		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	0.896566	+	0.442910i	$0.146054\pi$
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	−0.0647118	+	0.997904i	$0.520613\pi$
$770$	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	0.444418	−	0.895820i	$-0.353411\pi$
$773$	3.48172	+	1.44218i	0.125229	+	0.0518715i	−0.319189	+	0.947691i	$0.603411\pi$
$774$		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	0.660310	−	0.750993i	$-0.270425\pi$
$787$	2.96828	+	2.27764i	0.105808	+	0.0811893i	−0.554502	+	0.832182i	$0.687091\pi$
$788$	−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	−0.361732	−	0.932282i	$-0.617815\pi$
$797$	17.8536	−	23.2672i	0.632406	−	0.824168i	0.994138	+	0.108114i	$0.0344813\pi$
$798$		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	0.912803	−	0.408400i	$-0.133913\pi$
$809$	14.3467	+	14.3467i	0.504404	+	0.504404i	−0.408400	+	0.912803i	$0.633913\pi$
$810$		0			0
$811$	13.2334	−	31.9483i	0.464688	−	1.12186i	−0.501763	−	0.865005i	$-0.667315\pi$
$811$	13.2334	−	31.9483i	0.464688	−	1.12186i	0.966451	−	0.256851i	$-0.0826848\pi$
$812$	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	0.990278	−	0.139105i	$-0.0444227\pi$
$821$	17.1807	+	22.3903i	0.599609	+	0.781426i	−0.390668	+	0.920532i	$0.627756\pi$
$822$		0			0
$823$	5.54918	−	20.7098i	0.193432	−	0.721899i	−0.799235	−	0.601019i	$-0.794762\pi$
$823$	5.54918	−	20.7098i	0.193432	−	0.721899i	0.992667	−	0.120880i	$-0.0385717\pi$
$824$	−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	−0.888751	−	0.458391i	$-0.848426\pi$
$827$	1.83537	−	4.43098i	0.0638222	−	0.154080i	0.952573	+	0.304310i	$0.0984260\pi$
$828$		0			0
$829$	31.7765	−	13.1623i	1.10364	−	0.457144i	0.244899	−	0.969549i	$-0.421245\pi$
$829$	31.7765	−	13.1623i	1.10364	−	0.457144i	0.858744	+	0.512405i	$0.171245\pi$
$830$	−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	−0.152744	−	0.988266i	$-0.548811\pi$
$839$	6.05695	−	1.62295i	0.209109	−	0.0560306i	0.361853	+	0.932235i	$0.382144\pi$
$840$		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	0.266789	−	0.963755i	$-0.414037\pi$
$853$	36.9971	−	28.3888i	1.26675	−	0.972015i	0.999966	−	0.00826028i	$-0.00262936\pi$
$854$	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	0.996075	−	0.0885163i	$-0.0282125\pi$
$857$	2.61101	+	9.74444i	0.0891906	+	0.332864i	−0.906884	+	0.421380i	$0.861546\pi$
$858$		0			0
$859$	2.34801	+	17.8349i	0.0801131	+	0.608520i	0.983661	+	0.180032i	$0.0576201\pi$
$859$	2.34801	+	17.8349i	0.0801131	+	0.608520i	−0.903548	+	0.428488i	$0.859047\pi$
$860$	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	−0.997048	−	0.0767862i	$-0.975534\pi$
$877$	−19.6882	+	25.6581i	−0.664823	+	0.866414i	0.332225	+	0.943200i	$0.392201\pi$
$878$	−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	0.0862196	−	0.996276i	$-0.472521\pi$
$883$	25.3073	−	10.4826i	0.851660	−	0.352769i	0.765440	+	0.643507i	$0.222521\pi$
$884$	−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	0.288443	−	0.957497i	$-0.406862\pi$
$887$	1.77186	+	0.474768i	0.0594931	+	0.0159411i	−0.228950	+	0.973438i	$0.573529\pi$
$888$		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	−0.829948	−	0.557840i	$-0.811630\pi$
$907$	−34.7536	−	45.2918i	−1.15397	−	1.50389i	−0.324026	−	0.946048i	$-0.605036\pi$
$908$	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	0.562900	−	0.826525i	$-0.309685\pi$
$911$	3.88028	+	2.24028i	0.128559	+	0.0742237i	−0.434341	+	0.900748i	$0.643019\pi$
$912$		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	0.886448	−	0.462828i	$-0.153165\pi$
$919$	12.8420	+	12.8420i	0.423620	+	0.423620i	−0.462828	+	0.886448i	$0.653165\pi$
$920$	−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	0.965485	−	0.260459i	$-0.0838739\pi$
$929$	37.2662	+	21.5156i	1.22266	+	0.705905i	0.257178	+	0.966364i	$0.417207\pi$
$930$		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	−0.0184383	−	0.999830i	$-0.505869\pi$
$937$	30.0408	−	30.0408i	0.981392	−	0.981392i	0.999830	+	0.0184383i	$0.00586941\pi$
$938$	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	0.293273	−	0.956029i	$-0.405256\pi$
$941$	−17.0028	−	13.0467i	−0.554276	−	0.425311i	−0.847548	+	0.530718i	$0.821922\pi$
$942$		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	0.336366	−	0.941732i	$-0.390802\pi$
$947$	12.8489	+	1.69158i	0.417532	+	0.0549691i	0.0811661	+	0.996701i	$0.474136\pi$
$948$		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	−0.930858	−	0.365381i	$-0.880939\pi$
$953$	−17.4567	+	17.4567i	−0.565477	+	0.565477i	0.365381	+	0.930858i	$0.380939\pi$
$954$		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	−0.514915	−	0.857241i	$-0.672177\pi$
$967$	−43.2077	−	11.5775i	−1.38947	−	0.372306i	−0.874550	+	0.484935i	$0.838843\pi$
$968$	−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	0.867103	−	0.498130i	$-0.165980\pi$
$971$	35.1496	+	14.5595i	1.12801	+	0.467235i	0.260903	+	0.965365i	$0.415980\pi$
$972$		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	0.910065	−	0.414465i	$-0.136031\pi$
$977$	3.00365	+	5.20247i	0.0960952	+	0.166442i	−0.813970	+	0.580907i	$0.802698\pi$
$978$		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	−0.976403	−	0.215958i	$-0.930713\pi$
$983$	−7.48681	−	27.9412i	−0.238792	−	0.891184i	0.737611	−	0.675226i	$-0.235954\pi$
$984$		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	$0.196314\pi$
$991$			36.4148i			1.15675i	−0.815770	+	0.578377i	$0.803686\pi$
$992$	−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	−0.999904	−	0.0138661i	$-0.995586\pi$
$997$	−23.8237	−	31.0476i	−0.754503	−	0.983288i	0.245400	−	0.969422i	$-0.421081\pi$
$998$	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.683.24		368
3.2	odd	2		288.2.bf.a.11.23	✓	368
9.4	even	3		288.2.bf.a.203.7	yes	368
9.5	odd	6	inner	864.2.bn.a.395.40		368
32.3	odd	8	inner	864.2.bn.a.35.40		368
96.35	even	8		288.2.bf.a.227.7	yes	368
288.67	odd	24		288.2.bf.a.131.23	yes	368
288.131	even	24	inner	864.2.bn.a.611.24		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.23	✓	368	3.2	odd	2
288.2.bf.a.131.23	yes	368	288.67	odd	24
288.2.bf.a.203.7	yes	368	9.4	even	3
288.2.bf.a.227.7	yes	368	96.35	even	8
864.2.bn.a.35.40		368	32.3	odd	8	inner
864.2.bn.a.395.40		368	9.5	odd	6	inner
864.2.bn.a.611.24		368	288.131	even	24	inner
864.2.bn.a.683.24		368	1.1	even	1	trivial

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

L-functions

Modular forms

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