LMFDB - Embedded newform 432.2.y.e.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05869 - 0.937649i) q^{2} +(0.241628 + 1.98535i) q^{4} +(0.491749 - 0.131764i) q^{5} +(-2.40518 + 1.38863i) q^{7} +(1.60575 - 2.32842i) q^{8} +O(q^{10})$	\(q+(-1.05869 - 0.937649i) q^{2} +(0.241628 + 1.98535i) q^{4} +(0.491749 - 0.131764i) q^{5} +(-2.40518 + 1.38863i) q^{7} +(1.60575 - 2.32842i) q^{8} +(-0.644156 - 0.321592i) q^{10} +(-1.06358 + 3.96934i) q^{11} +(-0.596329 - 2.22553i) q^{13} +(3.84837 + 0.785091i) q^{14} +(-3.88323 + 0.959433i) q^{16} -2.87908 q^{17} +(-3.48018 + 3.48018i) q^{19} +(0.380418 + 0.944457i) q^{20} +(4.84784 - 3.20501i) q^{22} +(3.85945 + 2.22826i) q^{23} +(-4.10567 + 2.37041i) q^{25} +(-1.45544 + 2.91528i) q^{26} +(-3.33808 - 4.43959i) q^{28} +(-5.88383 - 1.57657i) q^{29} +(-1.28296 + 2.22216i) q^{31} +(5.01073 + 2.62537i) q^{32} +(3.04804 + 2.69956i) q^{34} +(-0.999773 + 0.999773i) q^{35} +(7.64112 + 7.64112i) q^{37} +(6.94761 - 0.421227i) q^{38} +(0.482826 - 1.35658i) q^{40} +(-4.84731 - 2.79860i) q^{41} +(0.911456 - 3.40160i) q^{43} +(-8.13752 - 1.15248i) q^{44} +(-1.99662 - 5.97783i) q^{46} +(4.94233 + 8.56037i) q^{47} +(0.356586 - 0.617625i) q^{49} +(6.56923 + 1.34016i) q^{50} +(4.27437 - 1.72167i) q^{52} +(2.86564 + 2.86564i) q^{53} +2.09206i q^{55} +(-0.628805 + 7.83007i) q^{56} +(4.75085 + 7.18605i) q^{58} +(-2.15652 + 0.577838i) q^{59} +(4.79709 + 1.28538i) q^{61} +(3.44186 - 1.14960i) q^{62} +(-2.84311 - 7.47775i) q^{64} +(-0.586489 - 1.01583i) q^{65} +(3.96319 + 14.7908i) q^{67} +(-0.695666 - 5.71597i) q^{68} +(1.99588 - 0.121008i) q^{70} -13.2447i q^{71} -11.3768i q^{73} +(-0.924850 - 15.2542i) q^{74} +(-7.75029 - 6.06847i) q^{76} +(-2.95384 - 11.0239i) q^{77} +(-1.56750 - 2.71499i) q^{79} +(-1.78316 + 0.983470i) q^{80} +(2.50768 + 7.50791i) q^{82} +(-11.0286 - 2.95510i) q^{83} +(-1.41578 + 0.379358i) q^{85} +(-4.15445 + 2.74660i) q^{86} +(7.53445 + 8.85025i) q^{88} -2.37475i q^{89} +(4.52472 + 4.52472i) q^{91} +(-3.49132 + 8.20078i) q^{92} +(2.79425 - 13.6969i) q^{94} +(-1.25282 + 2.16994i) q^{95} +(-5.04313 - 8.73496i) q^{97} +(-0.956628 + 0.319518i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05869	−	0.937649i	−0.748603	−	0.663018i
$2$	−1.05869	−	0.937649i	−0.748603	−	0.663018i
$3$		0			0
$3$		0			0
$4$	0.241628	+	1.98535i	0.120814	+	0.992675i
$5$	0.491749	−	0.131764i	0.219917	−	0.0589266i	−0.147178	−	0.989110i	$-0.547019\pi$
$5$	0.491749	−	0.131764i	0.219917	−	0.0589266i	0.367095	+	0.930183i	$0.380352\pi$
$6$		0			0
$7$	−2.40518	+	1.38863i	−0.909072	+	0.524853i	−0.880132	−	0.474728i	$-0.842546\pi$
$7$	−2.40518	+	1.38863i	−0.909072	+	0.524853i	−0.0289393	+	0.999581i	$0.509213\pi$
$8$	1.60575	−	2.32842i	0.567720	−	0.823222i
$9$		0			0
$10$	−0.644156	−	0.321592i	−0.203700	−	0.101696i
$11$	−1.06358	+	3.96934i	−0.320682	+	1.19680i	0.597900	+	0.801570i	$0.296002\pi$
$11$	−1.06358	+	3.96934i	−0.320682	+	1.19680i	−0.918582	+	0.395230i	$0.870665\pi$
$12$		0			0
$13$	−0.596329	−	2.22553i	−0.165392	−	0.617251i	−0.997990	−	0.0633733i	$-0.979814\pi$
$13$	−0.596329	−	2.22553i	−0.165392	−	0.617251i	0.832598	−	0.553878i	$-0.186853\pi$
$14$	3.84837	+	0.785091i	1.02852	+	0.209824i
$15$		0			0
$16$	−3.88323	+	0.959433i	−0.970808	+	0.239858i
$17$	−2.87908			−0.698279			−0.349139	−	0.937071i	$-0.613526\pi$
$17$	−2.87908			−0.698279			−0.349139	+	0.937071i	$0.613526\pi$
$18$		0			0
$19$	−3.48018	+	3.48018i	−0.798409	+	0.798409i	−0.982845	−	0.184436i	$-0.940954\pi$
$19$	−3.48018	+	3.48018i	−0.798409	+	0.798409i	0.184436	+	0.982845i	$0.440954\pi$
$20$	0.380418	+	0.944457i	0.0850640	+	0.211187i
$21$		0			0
$22$	4.84784	−	3.20501i	1.03356	−	0.683311i
$23$	3.85945	+	2.22826i	0.804752	+	0.464624i	0.845130	−	0.534561i	$-0.179523\pi$
$23$	3.85945	+	2.22826i	0.804752	+	0.464624i	−0.0403783	+	0.999184i	$0.512856\pi$
$24$		0			0
$25$	−4.10567	+	2.37041i	−0.821134	+	0.474082i
$26$	−1.45544	+	2.91528i	−0.285436	+	0.571734i
$27$		0			0
$28$	−3.33808	−	4.43959i	−0.630837	−	0.839003i
$29$	−5.88383	−	1.57657i	−1.09260	−	0.292761i	−0.332852	−	0.942979i	$-0.608011\pi$
$29$	−5.88383	−	1.57657i	−1.09260	−	0.292761i	−0.759748	+	0.650218i	$0.774677\pi$
$30$		0			0
$31$	−1.28296	+	2.22216i	−0.230427	+	0.399112i	−0.957934	−	0.286989i	$-0.907346\pi$
$31$	−1.28296	+	2.22216i	−0.230427	+	0.399112i	0.727507	+	0.686101i	$0.240679\pi$
$32$	5.01073	+	2.62537i	0.885780	+	0.464104i
$33$		0			0
$34$	3.04804	+	2.69956i	0.522734	+	0.462971i
$35$	−0.999773	+	0.999773i	−0.168993	+	0.168993i
$36$		0			0
$37$	7.64112	+	7.64112i	1.25619	+	1.25619i	0.952896	+	0.303297i	$0.0980873\pi$
$37$	7.64112	+	7.64112i	1.25619	+	1.25619i	0.303297	+	0.952896i	$0.401913\pi$
$38$	6.94761	−	0.421227i	1.12705	−	0.0683321i
$39$		0			0
$40$	0.482826	−	1.35658i	0.0763416	−	0.214494i
$41$	−4.84731	−	2.79860i	−0.757023	−	0.437067i	0.0712028	−	0.997462i	$-0.477316\pi$
$41$	−4.84731	−	2.79860i	−0.757023	−	0.437067i	−0.828226	+	0.560394i	$0.810650\pi$
$42$		0			0
$43$	0.911456	−	3.40160i	0.138996	−	0.518739i	−0.860954	−	0.508683i	$-0.830132\pi$
$43$	0.911456	−	3.40160i	0.138996	−	0.518739i	0.999949	−	0.0100559i	$-0.00320096\pi$
$44$	−8.13752	−	1.15248i	−1.22678	−	0.173742i
$45$		0			0
$46$	−1.99662	−	5.97783i	−0.294386	−	0.881384i
$47$	4.94233	+	8.56037i	0.720913	+	1.24866i	0.960634	+	0.277817i	$0.0896108\pi$
$47$	4.94233	+	8.56037i	0.720913	+	1.24866i	−0.239721	+	0.970842i	$0.577056\pi$
$48$		0			0
$49$	0.356586	−	0.617625i	0.0509409	−	0.0882322i
$50$	6.56923	+	1.34016i	0.929029	+	0.189527i
$51$		0			0
$52$	4.27437	−	1.72167i	0.592748	−	0.238753i
$53$	2.86564	+	2.86564i	0.393626	+	0.393626i	0.875978	−	0.482352i	$-0.160217\pi$
$53$	2.86564	+	2.86564i	0.393626	+	0.393626i	−0.482352	+	0.875978i	$0.660217\pi$
$54$		0			0
$55$			2.09206i			0.282093i
$56$	−0.628805	+	7.83007i	−0.0840276	+	1.04634i
$57$		0			0
$58$	4.75085	+	7.18605i	0.623818	+	0.943575i
$59$	−2.15652	+	0.577838i	−0.280755	+	0.0752281i	−0.396449	−	0.918057i	$-0.629758\pi$
$59$	−2.15652	+	0.577838i	−0.280755	+	0.0752281i	0.115694	+	0.993285i	$0.463091\pi$
$60$		0			0
$61$	4.79709	+	1.28538i	0.614204	+	0.164575i	0.552491	−	0.833519i	$-0.313677\pi$
$61$	4.79709	+	1.28538i	0.614204	+	0.164575i	0.0617124	+	0.998094i	$0.480344\pi$
$62$	3.44186	−	1.14960i	0.437117	−	0.145999i
$63$		0			0
$64$	−2.84311	−	7.47775i	−0.355389	−	0.934719i
$65$	−0.586489	−	1.01583i	−0.0727450	−	0.125998i
$66$		0			0
$67$	3.96319	+	14.7908i	0.484181	+	1.80699i	0.583721	+	0.811955i	$0.301596\pi$
$67$	3.96319	+	14.7908i	0.484181	+	1.80699i	−0.0995397	+	0.995034i	$0.531737\pi$
$68$	−0.695666	−	5.71597i	−0.0843619	−	0.693164i
$69$		0			0
$70$	1.99588	−	0.121008i	0.238553	−	0.0144633i
$71$		−	13.2447i		−	1.57186i	−0.618317	−	0.785929i	$-0.712185\pi$
$71$		−	13.2447i		−	1.57186i	0.618317	−	0.785929i	$-0.287815\pi$
$72$		0			0
$73$		−	11.3768i		−	1.33155i	−0.746152	−	0.665776i	$-0.768101\pi$
$73$		−	11.3768i		−	1.33155i	0.746152	−	0.665776i	$-0.231899\pi$
$74$	−0.924850	−	15.2542i	−0.107512	−	1.77327i
$75$		0			0
$76$	−7.75029	−	6.06847i	−0.889020	−	0.696102i
$77$	−2.95384	−	11.0239i	−0.336621	−	1.25629i
$78$		0			0
$79$	−1.56750	−	2.71499i	−0.176358	−	0.305460i	0.764273	−	0.644893i	$-0.223098\pi$
$79$	−1.56750	−	2.71499i	−0.176358	−	0.305460i	−0.940630	+	0.339433i	$0.889765\pi$
$80$	−1.78316	+	0.983470i	−0.199363	+	0.109955i
$81$		0			0
$82$	2.50768	+	7.50791i	0.276926	+	0.829110i
$83$	−11.0286	−	2.95510i	−1.21055	−	0.324365i	−0.403569	−	0.914949i	$-0.632231\pi$
$83$	−11.0286	−	2.95510i	−1.21055	−	0.324365i	−0.806976	+	0.590584i	$0.798897\pi$
$84$		0			0
$85$	−1.41578	+	0.379358i	−0.153563	+	0.0411472i
$86$	−4.15445	+	2.74660i	−0.447986	+	0.296173i
$87$		0			0
$88$	7.53445	+	8.85025i	0.803175	+	0.943440i
$89$		−	2.37475i		−	0.251723i	−0.992048	−	0.125862i	$-0.959830\pi$
$89$		−	2.37475i		−	0.251723i	0.992048	−	0.125862i	$-0.0401696\pi$
$90$		0			0
$91$	4.52472	+	4.52472i	0.474319	+	0.474319i
$92$	−3.49132	+	8.20078i	−0.363995	+	0.854990i
$93$		0			0
$94$	2.79425	−	13.6969i	0.288205	−	1.41273i
$95$	−1.25282	+	2.16994i	−0.128536	+	0.222631i
$96$		0			0
$97$	−5.04313	−	8.73496i	−0.512052	−	0.886900i	−0.999902	−	0.0139730i	$-0.995552\pi$
$97$	−5.04313	−	8.73496i	−0.512052	−	0.886900i	0.487850	−	0.872927i	$-0.337781\pi$
$98$	−0.956628	+	0.319518i	−0.0966340	+	0.0322762i
$99$		0			0
$100$	−5.69814	−	7.57844i	−0.569814	−	0.757844i
$101$	−1.55666	+	5.80953i	−0.154893	+	0.578070i	0.844221	+	0.535995i	$0.180063\pi$
$101$	−1.55666	+	5.80953i	−0.154893	+	0.578070i	−0.999114	+	0.0420749i	$0.986603\pi$
$102$		0			0
$103$	−11.7431	−	6.77986i	−1.15708	−	0.668039i	−0.206476	−	0.978452i	$-0.566200\pi$
$103$	−11.7431	−	6.77986i	−1.15708	−	0.668039i	−0.950602	+	0.310412i	$0.899533\pi$
$104$	−6.13953	−	2.18515i	−0.602031	−	0.214271i
$105$		0			0
$106$	−0.346845	−	5.72077i	−0.0336886	−	0.555651i
$107$	−2.81971	−	2.81971i	−0.272592	−	0.272592i	0.557551	−	0.830143i	$-0.311741\pi$
$107$	−2.81971	−	2.81971i	−0.272592	−	0.272592i	−0.830143	+	0.557551i	$0.811741\pi$
$108$		0			0
$109$	3.20455	−	3.20455i	0.306940	−	0.306940i	−0.536781	−	0.843721i	$-0.680360\pi$
$109$	3.20455	−	3.20455i	0.306940	−	0.306940i	0.843721	+	0.536781i	$0.180360\pi$
$110$	1.96162	−	2.21483i	0.187033	−	0.211176i
$111$		0			0
$112$	8.00756	−	7.69998i	0.756644	−	0.727580i
$113$	5.07913	−	8.79731i	0.477804	−	0.827581i	−0.521872	−	0.853024i	$-0.674766\pi$
$113$	5.07913	−	8.79731i	0.477804	−	0.827581i	0.999676	+	0.0254424i	$0.00809945\pi$
$114$		0			0
$115$	2.19149	+	0.587207i	0.204357	+	0.0547573i
$116$	1.70834	−	12.0624i	0.158615	−	1.11997i
$117$		0			0
$118$	2.82489	+	1.41031i	0.260052	+	0.129830i
$119$	6.92469	−	3.99797i	0.634785	−	0.366493i
$120$		0			0
$121$	−5.09817	−	2.94343i	−0.463470	−	0.267584i
$122$	−3.87337	−	5.85879i	−0.350679	−	0.530430i
$123$		0			0
$124$	−4.72177	−	2.01020i	−0.424027	−	0.180521i
$125$	−3.50655	+	3.50655i	−0.313636	+	0.313636i
$126$		0			0
$127$	7.32268			0.649783			0.324892	−	0.945751i	$-0.394672\pi$
$127$	7.32268			0.649783			0.324892	+	0.945751i	$0.394672\pi$
$128$	−4.00155	+	10.5824i	−0.353690	+	0.935363i
$129$		0			0
$130$	−0.331584	+	1.62536i	−0.0290818	+	0.142554i
$131$	5.31322	+	19.8292i	0.464218	+	1.73249i	0.659468	+	0.751733i	$0.270782\pi$
$131$	5.31322	+	19.8292i	0.464218	+	1.73249i	−0.195250	+	0.980754i	$0.562552\pi$
$132$		0			0
$133$	3.53777	−	13.2031i	0.306764	−	1.14486i
$134$	9.67284	−	19.3749i	0.835606	−	1.67374i
$135$		0			0
$136$	−4.62309	+	6.70371i	−0.396427	+	0.574838i
$137$	10.0888	−	5.82479i	0.861947	−	0.497646i	−0.00271649	−	0.999996i	$-0.500865\pi$
$137$	10.0888	−	5.82479i	0.861947	−	0.497646i	0.864664	+	0.502351i	$0.167531\pi$
$138$		0			0
$139$	−11.5413	+	3.09248i	−0.978918	+	0.262300i	−0.712589	−	0.701582i	$-0.752478\pi$
$139$	−11.5413	+	3.09248i	−0.978918	+	0.262300i	−0.266329	+	0.963882i	$0.585811\pi$
$140$	−2.22647	−	1.74333i	−0.188171	−	0.147338i
$141$		0			0
$142$	−12.4189	+	14.0220i	−1.04217	+	1.17670i
$143$	9.46813			0.791765
$144$		0			0
$145$	−3.10110			−0.257533
$146$	−10.6674	+	12.0444i	−0.882843	+	0.996804i
$147$		0			0
$148$	−13.3240	+	17.0166i	−1.09523	+	1.39876i
$149$	−1.01009	+	0.270654i	−0.0827502	+	0.0221728i	−0.299957	−	0.953953i	$-0.596972\pi$
$149$	−1.01009	+	0.270654i	−0.0827502	+	0.0221728i	0.217206	+	0.976126i	$0.430306\pi$
$150$		0			0
$151$	11.0495	−	6.37943i	0.899195	−	0.519150i	0.0222559	−	0.999752i	$-0.492915\pi$
$151$	11.0495	−	6.37943i	0.899195	−	0.519150i	0.876939	+	0.480602i	$0.159582\pi$
$152$	2.51502	+	13.6917i	0.203995	+	1.11054i
$153$		0			0
$154$	−7.20935	+	14.4405i	−0.580946	+	1.16365i
$155$	−0.338097	+	1.26179i	−0.0271566	+	0.101350i
$156$		0			0
$157$	−2.95544	−	11.0299i	−0.235870	−	0.880279i	−0.977755	−	0.209751i	$-0.932735\pi$
$157$	−2.95544	−	11.0299i	−0.235870	−	0.880279i	0.741885	−	0.670527i	$-0.233932\pi$
$158$	−0.886219	+	4.34409i	−0.0705038	+	0.345597i
$159$		0			0
$160$	2.80995	+	0.630791i	0.222146	+	0.0498684i
$161$	−12.3769			−0.975436
$162$		0			0
$163$	−4.61842	+	4.61842i	−0.361742	+	0.361742i	−0.864454	−	0.502712i	$-0.832336\pi$
$163$	−4.61842	+	4.61842i	−0.361742	+	0.361742i	0.502712	+	0.864454i	$0.332336\pi$
$164$	4.38495	−	10.2998i	0.342407	−	0.804282i
$165$		0			0
$166$	8.90496	+	13.4695i	0.691159	+	1.04543i
$167$	6.85336	+	3.95679i	0.530329	+	0.306186i	0.741150	−	0.671339i	$-0.234280\pi$
$167$	6.85336	+	3.95679i	0.530329	+	0.306186i	−0.210821	+	0.977525i	$0.567614\pi$
$168$		0			0
$169$	6.66095	−	3.84570i	0.512381	−	0.295823i
$170$	1.85457	+	0.925888i	0.142239	+	0.0710123i
$171$		0			0
$172$	6.97360	+	0.987637i	0.531732	+	0.0753066i
$173$	20.9267	+	5.60729i	1.59103	+	0.426315i	0.942317	−	0.334721i	$-0.108642\pi$
$173$	20.9267	+	5.60729i	1.59103	+	0.426315i	0.648711	+	0.761035i	$0.275309\pi$
$174$		0			0
$175$	6.58325	−	11.4025i	0.497647	−	0.861949i
$176$	0.321817	−	16.4343i	0.0242578	−	1.23878i
$177$		0			0
$178$	−2.22669	+	2.51412i	−0.166897	+	0.188441i
$179$	−4.24438	+	4.24438i	−0.317240	+	0.317240i	−0.847706	−	0.530466i	$-0.822017\pi$
$179$	−4.24438	+	4.24438i	−0.317240	+	0.317240i	0.530466	+	0.847706i	$0.322017\pi$
$180$		0			0
$181$	10.0752	+	10.0752i	0.748886	+	0.748886i	0.974270	−	0.225384i	$-0.0723638\pi$
$181$	10.0752	+	10.0752i	0.748886	+	0.748886i	−0.225384	+	0.974270i	$0.572364\pi$
$182$	−0.547653	−	9.03285i	−0.0405948	−	0.669559i
$183$		0			0
$184$	11.3857	−	5.40841i	0.839362	−	0.398713i
$185$	4.76434	+	2.75069i	0.350281	+	0.202235i
$186$		0			0
$187$	3.06213	−	11.4280i	0.223925	−	0.835700i
$188$	−15.8011	+	11.8807i	−1.15242	+	0.866488i
$189$		0			0
$190$	3.36098	−	1.12258i	0.243831	−	0.0814407i
$191$	−5.46820	−	9.47119i	−0.395665	−	0.685312i	0.597521	−	0.801853i	$-0.296152\pi$
$191$	−5.46820	−	9.47119i	−0.395665	−	0.685312i	−0.993186	+	0.116542i	$0.962819\pi$
$192$		0			0
$193$	−9.82326	+	17.0144i	−0.707094	+	1.22472i	0.258837	+	0.965921i	$0.416661\pi$
$193$	−9.82326	+	17.0144i	−0.707094	+	1.22472i	−0.965931	+	0.258801i	$0.916673\pi$
$194$	−2.85124	+	13.9763i	−0.204707	+	1.00344i
$195$		0			0
$196$	1.31236	+	0.558713i	0.0937402	+	0.0399080i
$197$	17.9489	+	17.9489i	1.27881	+	1.27881i	0.941336	+	0.337472i	$0.109572\pi$
$197$	17.9489	+	17.9489i	1.27881	+	1.27881i	0.337472	+	0.941336i	$0.390428\pi$
$198$		0			0
$199$		−	10.7912i		−	0.764966i	−0.923963	−	0.382483i	$-0.875069\pi$
$199$		−	10.7912i		−	0.764966i	0.923963	−	0.382483i	$-0.124931\pi$
$200$	−1.07338	+	13.3660i	−0.0758994	+	0.945121i
$201$		0			0
$202$	7.09531	−	4.69086i	0.499225	−	0.330048i
$203$	16.3409	−	4.37854i	1.14691	−	0.307313i
$204$		0			0
$205$	−2.75242	−	0.737508i	−0.192237	−	0.0515098i
$206$	6.07507	+	18.1886i	0.423270	+	1.26726i
$207$		0			0
$208$	4.45093	+	8.07011i	0.308617	+	0.559562i
$209$	−10.1126	−	17.5155i	−0.699501	−	1.21157i
$210$		0			0
$211$	2.28982	+	8.54571i	0.157637	+	0.588311i	0.998865	+	0.0476299i	$0.0151668\pi$
$211$	2.28982	+	8.54571i	0.157637	+	0.588311i	−0.841228	+	0.540681i	$0.818167\pi$
$212$	−4.99688	+	6.38172i	−0.343187	+	0.438298i
$213$		0			0
$214$	0.341287	+	5.62909i	0.0233299	+	0.384797i
$215$		−	1.79283i		−	0.122270i
$216$		0			0
$217$		−	7.12625i		−	0.483762i
$218$	−6.39735	+	0.387865i	−0.433283	+	0.0262696i
$219$		0			0
$220$	−4.15347	+	0.505501i	−0.280027	+	0.0340809i
$221$	1.71688	+	6.40747i	0.115490	+	0.431013i
$222$		0			0
$223$	7.53363	+	13.0486i	0.504489	+	0.873800i	0.999987	+	0.00519105i	$0.00165237\pi$
$223$	7.53363	+	13.0486i	0.504489	+	0.873800i	−0.495498	+	0.868609i	$0.665014\pi$
$224$	−15.6974	+	0.643567i	−1.04882	+	0.0430001i
$225$		0			0
$226$	−13.6260	+	4.55114i	−0.906387	+	0.302737i
$227$	−5.94741	−	1.59360i	−0.394743	−	0.105771i	0.0559866	−	0.998432i	$-0.482170\pi$
$227$	−5.94741	−	1.59360i	−0.394743	−	0.105771i	−0.450730	+	0.892660i	$0.648836\pi$
$228$		0			0
$229$	4.03435	−	1.08100i	0.266597	−	0.0714345i	−0.123044	−	0.992401i	$-0.539266\pi$
$229$	4.03435	−	1.08100i	0.266597	−	0.0714345i	0.389641	+	0.920967i	$0.372599\pi$
$230$	−1.76950	−	2.67651i	−0.116677	−	0.176484i
$231$		0			0
$232$	−13.1189	+	11.1685i	−0.861297	+	0.733245i
$233$			1.71937i			0.112640i	0.998413	+	0.0563200i	$0.0179367\pi$
$233$			1.71937i			0.112640i	−0.998413	+	0.0563200i	$0.982063\pi$
$234$		0			0
$235$	3.55834	+	3.55834i	0.232120	+	0.232120i
$236$	−1.66829	−	4.14183i	−0.108596	−	0.269610i
$237$		0			0
$238$	−11.0798	−	2.26034i	−0.718194	−	0.146516i
$239$	−4.99586	+	8.65308i	−0.323155	+	0.559721i	−0.981137	−	0.193312i	$-0.938077\pi$
$239$	−4.99586	+	8.65308i	−0.323155	+	0.559721i	0.657982	+	0.753034i	$0.271410\pi$
$240$		0			0
$241$	10.9017	+	18.8822i	0.702238	+	1.21631i	0.967679	+	0.252184i	$0.0811489\pi$
$241$	10.9017	+	18.8822i	0.702238	+	1.21631i	−0.265442	+	0.964127i	$0.585518\pi$
$242$	2.63745	+	7.89645i	0.169542	+	0.507603i
$243$		0			0
$244$	−1.39281	+	9.83448i	−0.0891655	+	0.629588i
$245$	0.0939703	−	0.350702i	0.00600354	−	0.0224055i
$246$		0			0
$247$	9.82059	+	5.66992i	0.624869	+	0.360768i
$248$	3.11400	+	6.55553i	0.197739	+	0.416276i
$249$		0			0
$250$	7.00025	−	0.424419i	0.442735	−	0.0268426i
$251$	−0.351987	−	0.351987i	−0.0222172	−	0.0222172i	0.695911	−	0.718128i	$-0.255001\pi$
$251$	−0.351987	−	0.351987i	−0.0222172	−	0.0222172i	−0.718128	+	0.695911i	$0.755001\pi$
$252$		0			0
$253$	−12.9495	+	12.9495i	−0.814131	+	0.814131i
$254$	−7.75242	−	6.86611i	−0.486430	−	0.430818i
$255$		0			0
$256$	14.1590	−	7.45140i	0.884936	−	0.465713i
$257$	−5.69516	+	9.86431i	−0.355254	+	0.615319i	−0.987161	−	0.159726i	$-0.948939\pi$
$257$	−5.69516	+	9.86431i	−0.355254	+	0.615319i	0.631907	+	0.775044i	$0.282272\pi$
$258$		0			0
$259$	−28.9889	−	7.76756i	−1.80129	−	0.482653i
$260$	1.87506	−	1.40984i	0.116286	−	0.0874345i
$261$		0			0
$262$	12.9678	−	25.9748i	0.801154	−	1.60473i
$263$	−4.43754	+	2.56201i	−0.273630	+	0.157980i	−0.630536	−	0.776160i	$-0.717165\pi$
$263$	−4.43754	+	2.56201i	−0.273630	+	0.157980i	0.356906	+	0.934140i	$0.383832\pi$
$264$		0			0
$265$	1.78676	+	1.03159i	0.109760	+	0.0633700i
$266$	−16.1253	+	10.6608i	−0.988706	+	0.653655i
$267$		0			0
$268$	−28.4074	+	11.4422i	−1.73526	+	0.698944i
$269$	−8.67269	+	8.67269i	−0.528784	+	0.528784i	−0.920210	−	0.391426i	$-0.871982\pi$
$269$	−8.67269	+	8.67269i	−0.528784	+	0.528784i	0.391426	+	0.920210i	$0.371982\pi$
$270$		0			0
$271$	−19.6128			−1.19139			−0.595696	−	0.803210i	$-0.703124\pi$
$271$	−19.6128			−1.19139			−0.595696	+	0.803210i	$0.703124\pi$
$272$	11.1801	−	2.76228i	0.677894	−	0.167488i
$273$		0			0
$274$	−16.1425	−	3.29317i	−0.975205	−	0.198948i
$275$	−5.04225	−	18.8179i	−0.304059	−	1.13476i
$276$		0			0
$277$	4.36219	−	16.2799i	0.262099	−	0.978165i	−0.701904	−	0.712272i	$-0.747666\pi$
$277$	4.36219	−	16.2799i	0.262099	−	0.978165i	0.964002	−	0.265893i	$-0.0856669\pi$
$278$	15.1182	+	7.54771i	0.906732	+	0.452682i
$279$		0			0
$280$	0.722505	+	3.93328i	0.0431780	+	0.235059i
$281$	14.0437	−	8.10816i	0.837780	−	0.483692i	−0.0187292	−	0.999825i	$-0.505962\pi$
$281$	14.0437	−	8.10816i	0.837780	−	0.483692i	0.856509	+	0.516132i	$0.172629\pi$
$282$		0			0
$283$	−0.905572	+	0.242647i	−0.0538307	+	0.0144239i	−0.285634	−	0.958339i	$-0.592204\pi$
$283$	−0.905572	+	0.242647i	−0.0538307	+	0.0144239i	0.231803	+	0.972763i	$0.425537\pi$
$284$	26.2954	−	3.20029i	1.56034	−	0.189903i
$285$		0			0
$286$	−10.0238	−	8.87778i	−0.592718	−	0.524954i
$287$	15.5449			0.917584
$288$		0			0
$289$	−8.71092			−0.512407
$290$	3.28309	+	2.90775i	0.192790	+	0.170749i
$291$		0			0
$292$	22.5869	−	2.74895i	1.32180	−	0.160870i
$293$	−9.76797	+	2.61732i	−0.570651	+	0.152905i	−0.532595	−	0.846370i	$-0.678783\pi$
$293$	−9.76797	+	2.61732i	−0.570651	+	0.152905i	−0.0380557	+	0.999276i	$0.512116\pi$
$294$		0			0
$295$	−0.984330	+	0.568303i	−0.0573099	+	0.0330879i
$296$	30.0615	−	5.52200i	1.74729	−	0.320960i
$297$		0			0
$298$	1.32315	+	0.660577i	0.0766481	+	0.0382662i
$299$	2.65755	−	9.91811i	0.153690	−	0.573579i
$300$		0			0
$301$	2.53135	+	9.44713i	0.145905	+	0.544524i
$302$	−17.6796	−	3.60674i	−1.01735	−	0.207545i
$303$		0			0
$304$	10.1754	−	16.8534i	0.583597	−	0.966607i
$305$	2.52833			0.144772
$306$		0			0
$307$	16.1653	−	16.1653i	0.922603	−	0.922603i	−0.0746101	−	0.997213i	$-0.523771\pi$
$307$	16.1653	−	16.1653i	0.922603	−	0.922603i	0.997213	+	0.0746101i	$0.0237712\pi$
$308$	21.1725	−	8.52809i	1.20642	−	0.485933i
$309$		0			0
$310$	1.54106	−	1.01883i	0.0875262	−	0.0578654i
$311$	−11.8457	−	6.83912i	−0.671708	−	0.387811i	0.125015	−	0.992155i	$-0.460102\pi$
$311$	−11.8457	−	6.83912i	−0.671708	−	0.387811i	−0.796724	+	0.604344i	$0.793435\pi$
$312$		0			0
$313$	−22.5829	+	13.0383i	−1.27646	+	0.736966i	−0.976196	−	0.216890i	$-0.930409\pi$
$313$	−22.5829	+	13.0383i	−1.27646	+	0.736966i	−0.300266	+	0.953855i	$0.597075\pi$
$314$	−7.21326	+	14.4483i	−0.407068	+	0.815366i
$315$		0			0
$316$	5.01145	−	3.76806i	0.281916	−	0.211970i
$317$	14.9639	+	4.00957i	0.840457	+	0.225200i	0.653270	−	0.757125i	$-0.273396\pi$
$317$	14.9639	+	4.00957i	0.840457	+	0.225200i	0.187187	+	0.982324i	$0.440063\pi$
$318$		0			0
$319$	12.5159	−	21.6781i	0.700753	−	1.21374i
$320$	−2.38339	−	3.30256i	−0.133236	−	0.184619i
$321$		0			0
$322$	13.1032	+	11.6052i	0.730215	+	0.646732i
$323$	10.0197	−	10.0197i	0.557512	−	0.557512i
$324$		0			0
$325$	7.72375	+	7.72375i	0.428437	+	0.428437i
$326$	9.21991	−	0.558995i	0.510643	−	0.0309599i
$327$		0			0
$328$	−14.2999	+	6.79274i	−0.789580	+	0.375066i
$329$	−23.7744	−	13.7261i	−1.31072	−	0.756747i
$330$		0			0
$331$	−2.82670	+	10.5494i	−0.155370	+	0.579847i	0.843704	+	0.536809i	$0.180370\pi$
$331$	−2.82670	+	10.5494i	−0.155370	+	0.579847i	−0.999073	+	0.0430383i	$0.986296\pi$
$332$	3.20210	−	22.6097i	0.175738	−	1.24087i
$333$		0			0
$334$	−3.54547	−	10.6150i	−0.194000	−	0.580829i
$335$	3.89779	+	6.75118i	0.212959	+	0.368856i
$336$		0			0
$337$	−2.81502	+	4.87577i	−0.153344	+	0.265600i	−0.932455	−	0.361287i	$-0.882338\pi$
$337$	−2.81502	+	4.87577i	−0.153344	+	0.265600i	0.779111	+	0.626886i	$0.215671\pi$
$338$	−10.6578	−	2.17425i	−0.579706	−	0.118264i
$339$		0			0
$340$	−1.09525	−	2.71916i	−0.0593984	−	0.147467i
$341$	−7.45597	−	7.45597i	−0.403763	−	0.403763i
$342$		0			0
$343$		−	17.4602i		−	0.942760i
$344$	−6.45679	−	7.58439i	−0.348127	−	0.408923i
$345$		0			0
$346$	−16.8971	−	25.5583i	−0.908395	−	1.37402i
$347$	−1.40004	+	0.375139i	−0.0751579	+	0.0201385i	−0.296202	−	0.955125i	$-0.595720\pi$
$347$	−1.40004	+	0.375139i	−0.0751579	+	0.0201385i	0.221044	+	0.975264i	$0.429054\pi$
$348$		0			0
$349$	4.05103	+	1.08547i	0.216847	+	0.0581039i	0.365607	−	0.930769i	$-0.380861\pi$
$349$	4.05103	+	1.08547i	0.216847	+	0.0581039i	−0.148760	+	0.988873i	$0.547528\pi$
$350$	−17.6611	+	5.89890i	−0.944028	+	0.315309i
$351$		0			0
$352$	−15.7503	+	17.0970i	−0.839494	+	0.911273i
$353$	5.70555	+	9.88230i	0.303676	+	0.525982i	0.976966	−	0.213397i	$-0.0684527\pi$
$353$	5.70555	+	9.88230i	0.303676	+	0.525982i	−0.673290	+	0.739379i	$0.735119\pi$
$354$		0			0
$355$	−1.74517	−	6.51307i	−0.0926242	−	0.345678i
$356$	4.71472	−	0.573808i	0.249880	−	0.0304117i
$357$		0			0
$358$	8.47320	−	0.513722i	0.447822	−	0.0271511i
$359$			1.05572i			0.0557189i	0.999612	+	0.0278594i	$0.00886909\pi$
$359$			1.05572i			0.0557189i	−0.999612	+	0.0278594i	$0.991131\pi$
$360$		0			0
$361$		−	5.22336i		−	0.274914i
$362$	−1.21946	−	20.1135i	−0.0640936	−	1.05714i
$363$		0			0
$364$	−7.88985	+	10.0764i	−0.413540	+	0.528149i
$365$	−1.49905	−	5.59452i	−0.0784638	−	0.292831i
$366$		0			0
$367$	4.67503	+	8.09739i	0.244035	+	0.422680i	0.961860	−	0.273543i	$-0.0881956\pi$
$367$	4.67503	+	8.09739i	0.244035	+	0.422680i	−0.717825	+	0.696223i	$0.754862\pi$
$368$	−17.1250	−	4.94995i	−0.892703	−	0.258034i
$369$		0			0
$370$	−2.46475	−	7.37940i	−0.128136	−	0.383637i
$371$	−10.8717	−	2.91306i	−0.564430	−	0.151239i
$372$		0			0
$373$	5.80682	−	1.55593i	0.300666	−	0.0805631i	−0.105332	−	0.994437i	$-0.533591\pi$
$373$	5.80682	−	1.55593i	0.300666	−	0.0805631i	0.405998	+	0.913874i	$0.366924\pi$
$374$	−13.9573	+	9.22748i	−0.721716	+	0.477142i
$375$		0			0
$376$	27.8683	+	2.23801i	1.43720	+	0.115416i
$377$			14.0348i			0.722828i
$378$		0			0
$379$	6.35334	+	6.35334i	0.326349	+	0.326349i	0.851196	−	0.524847i	$-0.175878\pi$
$379$	6.35334	+	6.35334i	0.326349	+	0.326349i	−0.524847	+	0.851196i	$0.675878\pi$
$380$	−4.61081	−	1.96296i	−0.236529	−	0.100698i
$381$		0			0
$382$	−3.09156	+	15.1543i	−0.158178	+	0.775360i
$383$	10.8961	−	18.8725i	0.556762	−	0.964341i	−0.441002	−	0.897506i	$-0.645377\pi$
$383$	10.8961	−	18.8725i	0.556762	−	0.964341i	0.997764	−	0.0668344i	$-0.0212899\pi$
$384$		0			0
$385$	−2.90510	−	5.03178i	−0.148058	−	0.256443i
$386$	26.3533	−	8.80210i	1.34135	−	0.448015i
$387$		0			0
$388$	16.1234	−	12.1230i	0.818541	−	0.615452i
$389$	1.30926	−	4.88623i	0.0663822	−	0.247742i	−0.924759	−	0.380553i	$-0.875734\pi$
$389$	1.30926	−	4.88623i	0.0663822	−	0.247742i	0.991141	+	0.132811i	$0.0424004\pi$
$390$		0			0
$391$	−11.1117	−	6.41532i	−0.561941	−	0.324437i
$392$	−0.865503	−	1.82204i	−0.0437145	−	0.0920268i
$393$		0			0
$394$	−2.17246	−	35.8320i	−0.109447	−	1.80519i
$395$	−1.12855	−	1.12855i	−0.0567837	−	0.0567837i
$396$		0			0
$397$	2.11018	−	2.11018i	0.105907	−	0.105907i	−0.652168	−	0.758075i	$-0.726140\pi$
$397$	2.11018	−	2.11018i	0.105907	−	0.105907i	0.758075	+	0.652168i	$0.226140\pi$
$398$	−10.1183	+	11.4245i	−0.507186	+	0.572656i
$399$		0			0
$400$	13.6690	−	13.1440i	0.683451	−	0.657199i
$401$	−4.22120	+	7.31133i	−0.210797	+	0.365110i	−0.951964	−	0.306210i	$-0.900939\pi$
$401$	−4.22120	+	7.31133i	−0.210797	+	0.365110i	0.741168	+	0.671320i	$0.234272\pi$
$402$		0			0
$403$	5.71055	+	1.53014i	0.284463	+	0.0762216i
$404$	−11.9101	−	1.68677i	−0.592549	−	0.0839198i
$405$		0			0
$406$	−21.4054	−	10.6866i	−1.06233	−	0.530365i
$407$	−38.4572	+	22.2032i	−1.90625	+	1.10057i
$408$		0			0
$409$	34.4821	+	19.9082i	1.70503	+	0.984399i	0.940490	+	0.339822i	$0.110367\pi$
$409$	34.4821	+	19.9082i	1.70503	+	0.984399i	0.764539	+	0.644577i	$0.222967\pi$
$410$	2.22242	+	3.36159i	0.109757	+	0.166017i
$411$		0			0
$412$	10.6229	−	24.9523i	0.523355	−	1.22931i
$413$	4.38441	−	4.38441i	0.215743	−	0.215743i
$414$		0			0
$415$	−5.81268			−0.285333
$416$	2.85480	−	12.7171i	0.139968	−	0.623508i
$417$		0			0
$418$	−5.71735	+	28.0254i	−0.279645	+	1.37077i
$419$	1.69652	+	6.33148i	0.0828802	+	0.309313i	0.994904	−	0.100823i	$-0.0321477\pi$
$419$	1.69652	+	6.33148i	0.0828802	+	0.309313i	−0.912024	+	0.410137i	$0.865481\pi$
$420$		0			0
$421$	−8.71468	+	32.5236i	−0.424727	+	1.58510i	0.339790	+	0.940501i	$0.389644\pi$
$421$	−8.71468	+	32.5236i	−0.424727	+	1.58510i	−0.764518	+	0.644603i	$0.777023\pi$
$422$	5.58869	−	11.1943i	0.272053	−	0.544928i
$423$		0			0
$424$	11.2739	−	2.07091i	0.547511	−	0.100572i
$425$	11.8205	−	6.82459i	0.573380	−	0.331041i
$426$		0			0
$427$	−13.3228	+	3.56982i	−0.644733	+	0.172756i
$428$	4.91680	−	6.27944i	0.237662	−	0.303528i
$429$		0			0
$430$	−1.68105	+	1.89804i	−0.0810673	+	0.0915318i
$431$	−19.0914			−0.919602			−0.459801	−	0.888022i	$-0.652079\pi$
$431$	−19.0914			−0.919602			−0.459801	+	0.888022i	$0.652079\pi$
$432$		0			0
$433$	−4.98594			−0.239609			−0.119805	−	0.992797i	$-0.538227\pi$
$433$	−4.98594			−0.239609			−0.119805	+	0.992797i	$0.538227\pi$
$434$	−6.68192	+	7.54446i	−0.320743	+	0.362146i
$435$		0			0
$436$	7.13646	+	5.58784i	0.341774	+	0.267609i
$437$	−21.1863	+	5.67687i	−1.01348	+	0.271561i
$438$		0			0
$439$	−11.1893	+	6.46017i	−0.534038	+	0.308327i	−0.742659	−	0.669670i	$-0.766436\pi$
$439$	−11.1893	+	6.46017i	−0.534038	+	0.308327i	0.208621	+	0.977997i	$0.433102\pi$
$440$	4.87120	+	3.35933i	0.232226	+	0.160150i
$441$		0			0
$442$	4.19033	−	8.39332i	0.199314	−	0.399230i
$443$	−3.84803	+	14.3610i	−0.182825	+	0.682314i	0.812260	+	0.583295i	$0.198237\pi$
$443$	−3.84803	+	14.3610i	−0.182825	+	0.682314i	−0.995086	+	0.0990185i	$0.968430\pi$
$444$		0			0
$445$	−0.312907	−	1.16778i	−0.0148332	−	0.0553583i
$446$	4.25929	−	20.8783i	0.201683	−	0.988615i
$447$		0			0
$448$	17.2220	+	14.0373i	0.813663	+	0.663200i
$449$	3.60684			0.170217			0.0851086	−	0.996372i	$-0.472876\pi$
$449$	3.60684			0.170217			0.0851086	+	0.996372i	$0.472876\pi$
$450$		0			0
$451$	16.2641	−	16.2641i	0.765846	−	0.765846i
$452$	18.6930	+	7.95817i	0.879245	+	0.374321i
$453$		0			0
$454$	4.80219	+	7.26371i	0.225378	+	0.340903i
$455$	2.82122	+	1.62883i	0.132261	+	0.0763608i
$456$		0			0
$457$	−4.13238	+	2.38583i	−0.193304	+	0.111604i	−0.593529	−	0.804813i	$-0.702266\pi$
$457$	−4.13238	+	2.38583i	−0.193304	+	0.111604i	0.400224	+	0.916417i	$0.368932\pi$
$458$	−5.28470	−	2.63836i	−0.246938	−	0.123283i
$459$		0			0
$460$	−0.636287	+	4.49276i	−0.0296670	+	0.209476i
$461$	−22.7740	−	6.10228i	−1.06069	−	0.284212i	−0.314029	−	0.949413i	$-0.601679\pi$
$461$	−22.7740	−	6.10228i	−1.06069	−	0.284212i	−0.746664	+	0.665202i	$0.768345\pi$
$462$		0			0
$463$	15.9602	−	27.6439i	0.741735	−	1.28472i	−0.209970	−	0.977708i	$-0.567337\pi$
$463$	15.9602	−	27.6439i	0.741735	−	1.28472i	0.951705	−	0.307014i	$-0.0993299\pi$
$464$	24.3609	+	0.477035i	1.13093	+	0.0221458i
$465$		0			0
$466$	1.61217	−	1.82028i	0.0746824	−	0.0843227i
$467$	−7.26104	+	7.26104i	−0.336001	+	0.336001i	−0.854860	−	0.518859i	$-0.826357\pi$
$467$	−7.26104	+	7.26104i	−0.336001	+	0.336001i	0.518859	+	0.854860i	$0.326357\pi$
$468$		0			0
$469$	−30.0712	−	30.0712i	−1.38856	−	1.38856i
$470$	−0.430687	−	7.10363i	−0.0198661	−	0.327666i
$471$		0			0
$472$	−2.11739	+	5.94916i	−0.0974608	+	0.273832i
$473$	12.5327	+	7.23576i	0.576254	+	0.332700i
$474$		0			0
$475$	6.03903	−	22.5380i	0.277090	−	1.03411i
$476$	9.61057	+	12.7819i	0.440500	+	0.585858i
$477$		0			0
$478$	13.4026	−	4.47653i	0.613020	−	0.204752i
$479$	−13.4733	−	23.3364i	−0.615609	−	1.06627i	−0.990277	−	0.139107i	$-0.955577\pi$
$479$	−13.4733	−	23.3364i	−0.615609	−	1.06627i	0.374669	−	0.927159i	$-0.377756\pi$
$480$		0			0
$481$	12.4489	−	21.5622i	0.567622	−	0.983151i
$482$	6.16348	−	30.2123i	0.280739	−	1.37613i
$483$		0			0
$484$	4.61187	−	10.8329i	0.209631	−	0.492403i
$485$	−3.63091	−	3.63091i	−0.164871	−	0.164871i
$486$		0			0
$487$			33.3405i			1.51080i	0.655264	+	0.755400i	$0.272558\pi$
$487$			33.3405i			1.51080i	−0.655264	+	0.755400i	$0.727442\pi$
$488$	10.6958	−	9.10565i	0.484178	−	0.412193i
$489$		0			0
$490$	−0.428320	+	0.283172i	−0.0193495	+	0.0127924i
$491$	−22.4169	+	6.00659i	−1.01166	+	0.271074i	−0.726323	−	0.687353i	$-0.758772\pi$
$491$	−22.4169	+	6.00659i	−1.01166	+	0.271074i	−0.285338	+	0.958427i	$0.592106\pi$
$492$		0			0
$493$	16.9400	+	4.53906i	0.762939	+	0.204429i
$494$	−5.08052	−	15.2109i	−0.228583	−	0.684372i
$495$		0			0
$496$	2.85004	−	9.86008i	0.127970	−	0.442731i
$497$	18.3920	+	31.8559i	0.824994	+	1.42893i
$498$		0			0
$499$	4.03564	+	15.0612i	0.180660	+	0.674233i	0.995518	+	0.0945722i	$0.0301483\pi$
$499$	4.03564	+	15.0612i	0.180660	+	0.674233i	−0.814858	+	0.579661i	$0.803185\pi$
$500$	−7.80902	−	6.11446i	−0.349230	−	0.273447i
$501$		0			0
$502$	0.0426030	+	0.702683i	0.00190147	+	0.0313623i
$503$		−	26.2715i		−	1.17139i	−0.810533	−	0.585693i	$-0.800822\pi$
$503$		−	26.2715i		−	1.17139i	0.810533	−	0.585693i	$-0.199178\pi$
$504$		0			0
$505$			3.06194i			0.136255i
$506$	25.8516	−	1.56736i	1.14924	−	0.0696777i
$507$		0			0
$508$	1.76937	+	14.5381i	0.0785029	+	0.645023i
$509$	7.08716	+	26.4496i	0.314133	+	1.17236i	0.924794	+	0.380468i	$0.124237\pi$
$509$	7.08716	+	26.4496i	0.314133	+	1.17236i	−0.610661	+	0.791892i	$0.709096\pi$
$510$		0			0
$511$	15.7981	+	27.3632i	0.698869	+	1.21048i
$512$	−21.9767	−	5.38746i	−0.971242	−	0.238094i
$513$		0			0
$514$	15.2786	−	5.10313i	0.673912	−	0.225090i
$515$	−6.66798	−	1.78668i	−0.293826	−	0.0787305i
$516$		0			0
$517$	−39.2356	+	10.5131i	−1.72558	+	0.462368i
$518$	23.4069	+	35.4049i	1.02844	+	1.55560i
$519$		0			0
$520$	−3.30704	−	0.265576i	−0.145023	−	0.0116463i
$521$			13.9069i			0.609272i	0.952469	+	0.304636i	$0.0985348\pi$
$521$			13.9069i			0.609272i	−0.952469	+	0.304636i	$0.901465\pi$
$522$		0			0
$523$	14.8539	+	14.8539i	0.649517	+	0.649517i	0.952876	−	0.303359i	$-0.0981082\pi$
$523$	14.8539	+	14.8539i	0.649517	+	0.649517i	−0.303359	+	0.952876i	$0.598108\pi$
$524$	−38.0841	+	15.3399i	−1.66371	+	0.670127i
$525$		0			0
$526$	7.10022	+	1.44849i	0.309584	+	0.0631570i
$527$	3.69375	−	6.39777i	0.160902	−	0.278691i
$528$		0			0
$529$	−1.56975	−	2.71888i	−0.0682499	−	0.118212i
$530$	−0.924352	−	2.76749i	−0.0401513	−	0.120212i
$531$		0			0
$532$	27.0677	+	3.83347i	1.17353	+	0.166202i
$533$	−3.33777	+	12.4567i	−0.144575	+	0.539561i
$534$		0			0
$535$	−1.75813	−	1.01506i	−0.0760105	−	0.0438847i
$536$	40.8032	+	14.5225i	1.76243	+	0.627274i
$537$		0			0
$538$	17.3136	−	1.04971i	0.746442	−	0.0452561i
$539$	2.07230	+	2.07230i	0.0892605	+	0.0892605i
$540$		0			0
$541$	−30.6206	+	30.6206i	−1.31648	+	1.31648i	−0.399939	+	0.916542i	$0.630969\pi$
$541$	−30.6206	+	30.6206i	−1.31648	+	1.31648i	−0.916542	+	0.399939i	$0.869031\pi$
$542$	20.7638	+	18.3899i	0.891879	+	0.789914i
$543$		0			0
$544$	−14.4263	−	7.55864i	−0.618522	−	0.324074i
$545$	1.15359	−	1.99808i	0.0494144	−	0.0855882i
$546$		0			0
$547$	0.751802	+	0.201445i	0.0321447	+	0.00861315i	0.274856	−	0.961486i	$-0.411370\pi$
$547$	0.751802	+	0.201445i	0.0321447	+	0.00861315i	−0.242711	+	0.970099i	$0.578037\pi$
$548$	14.0020	+	18.6224i	0.598136	+	0.795511i
$549$		0			0
$550$	−12.3065	+	24.6501i	−0.524749	+	1.05108i
$551$	25.9635	−	14.9901i	1.10608	−	0.638598i
$552$		0			0
$553$	7.54023	+	4.35336i	0.320643	+	0.185124i
$554$	−19.8830	+	13.1451i	−0.844749	+	0.558482i
$555$		0			0
$556$	−8.92835	−	22.1663i	−0.378646	−	0.940058i
$557$	15.1991	−	15.1991i	0.644006	−	0.644006i	−0.307532	−	0.951538i	$-0.599503\pi$
$557$	15.1991	−	15.1991i	0.644006	−	0.644006i	0.951538	+	0.307532i	$0.0995030\pi$
$558$		0			0
$559$	−8.11390			−0.343181
$560$	2.92314	−	4.84157i	0.123525	−	0.204594i
$561$		0			0
$562$	−22.4705	−	4.58412i	−0.947862	−	0.193369i
$563$	−2.92996	−	10.9348i	−0.123483	−	0.460846i	0.876298	−	0.481770i	$-0.160006\pi$
$563$	−2.92996	−	10.9348i	−0.123483	−	0.460846i	−0.999781	+	0.0209240i	$0.993339\pi$
$564$		0			0
$565$	1.33849	−	4.99532i	0.0563107	−	0.210155i
$566$	1.18623	+	0.592222i	0.0498611	+	0.0248929i
$567$		0			0
$568$	−30.8393	−	21.2677i	−1.29399	−	0.892374i
$569$	−38.8985	+	22.4581i	−1.63071	+	0.941491i	−0.646835	+	0.762630i	$0.723908\pi$
$569$	−38.8985	+	22.4581i	−1.63071	+	0.941491i	−0.983874	+	0.178861i	$0.942759\pi$
$570$		0			0
$571$	22.0647	−	5.91221i	0.923378	−	0.247418i	0.234349	−	0.972152i	$-0.424704\pi$
$571$	22.0647	−	5.91221i	0.923378	−	0.247418i	0.689029	+	0.724734i	$0.258037\pi$
$572$	2.28777	+	18.7976i	0.0956563	+	0.785965i
$573$		0			0
$574$	−16.4571	−	14.5756i	−0.686907	−	0.608375i
$575$	−21.1275			−0.881079
$576$		0			0
$577$	−13.2304			−0.550790			−0.275395	−	0.961331i	$-0.588809\pi$
$577$	−13.2304			−0.550790			−0.275395	+	0.961331i	$0.588809\pi$
$578$	9.22212	+	8.16779i	0.383590	+	0.339735i
$579$		0			0
$580$	−0.749314	−	6.15677i	−0.0311136	−	0.255646i
$581$	30.6293	−	8.20709i	1.27072	−	0.340487i
$582$		0			0
$583$	−14.4225	+	8.32685i	−0.597320	+	0.344863i
$584$	−26.4900	−	18.2683i	−1.09616	−	0.755948i
$585$		0			0
$586$	12.7953	+	6.38801i	0.528570	+	0.263886i
$587$	0.899168	−	3.35574i	0.0371126	−	0.138506i	−0.944884	−	0.327406i	$-0.893825\pi$
$587$	0.899168	−	3.35574i	0.0371126	−	0.138506i	0.981996	+	0.188900i	$0.0604922\pi$
$588$		0			0
$589$	−3.26857	−	12.1985i	−0.134679	−	0.502630i
$590$	1.57496	+	0.321302i	0.0648402	+	0.0132278i
$591$		0			0
$592$	−37.0034	−	22.3411i	−1.52083	−	0.918214i
$593$	43.3013			1.77817			0.889086	−	0.457740i	$-0.151341\pi$
$593$	43.3013			1.77817			0.889086	+	0.457740i	$0.151341\pi$
$594$		0			0
$595$	2.87842	−	2.87842i	0.118004	−	0.118004i
$596$	−0.781410	−	1.93999i	−0.0320078	−	0.0794652i
$597$		0			0
$598$	−12.1132	+	8.00830i	−0.495346	+	0.327484i
$599$	15.9727	+	9.22187i	0.652629	+	0.376795i	0.789463	−	0.613799i	$-0.210359\pi$
$599$	15.9727	+	9.22187i	0.652629	+	0.376795i	−0.136834	+	0.990594i	$0.543693\pi$
$600$		0			0
$601$	−17.7246	+	10.2333i	−0.723003	+	0.417426i	−0.815857	−	0.578254i	$-0.803734\pi$
$601$	−17.7246	+	10.2333i	−0.723003	+	0.417426i	0.0928541	+	0.995680i	$0.470401\pi$
$602$	6.17819	−	12.3751i	0.251804	−	0.504370i
$603$		0			0
$604$	15.3353	+	20.3957i	0.623983	+	0.829888i
$605$	−2.89486	−	0.775674i	−0.117693	−	0.0315357i
$606$		0			0
$607$	−8.07865	+	13.9926i	−0.327902	+	0.567944i	−0.982095	−	0.188384i	$-0.939675\pi$
$607$	−8.07865	+	13.9926i	−0.327902	+	0.567944i	0.654193	+	0.756328i	$0.273008\pi$
$608$	−26.5750	+	8.30149i	−1.07776	+	0.336670i
$609$		0			0
$610$	−2.67670	−	2.37069i	−0.108377	−	0.0959863i
$611$	16.1041	−	16.1041i	0.651503	−	0.651503i
$612$		0			0
$613$	22.2010	+	22.2010i	0.896689	+	0.896689i	0.995142	−	0.0984526i	$-0.0313893\pi$
$613$	22.2010	+	22.2010i	0.896689	+	0.896689i	−0.0984526	+	0.995142i	$0.531389\pi$
$614$	−32.2714	+	1.95658i	−1.30237	+	0.0789613i
$615$		0			0
$616$	−30.4114	−	10.8239i	−1.22531	−	0.436105i
$617$	−0.887087	−	0.512160i	−0.0357128	−	0.0206188i	0.482037	−	0.876151i	$-0.339897\pi$
$617$	−0.887087	−	0.512160i	−0.0357128	−	0.0206188i	−0.517750	+	0.855532i	$0.673230\pi$
$618$		0			0
$619$	−2.14654	+	8.01100i	−0.0862768	+	0.321989i	−0.995553	−	0.0942040i	$-0.969969\pi$
$619$	−2.14654	+	8.01100i	−0.0862768	+	0.321989i	0.909276	+	0.416193i	$0.136636\pi$
$620$	−2.58680	−	0.366355i	−0.103888	−	0.0147132i
$621$		0			0
$622$	6.12817	+	18.3476i	0.245717	+	0.735671i
$623$	3.29766	+	5.71171i	0.132118	+	0.228835i
$624$		0			0
$625$	10.5897	−	18.3420i	0.423590	−	0.733679i
$626$	36.1335	+	7.37145i	1.44419	+	0.294622i
$627$		0			0
$628$	21.1840	−	8.53272i	0.845335	−	0.340492i
$629$	−21.9994	−	21.9994i	−0.877172	−	0.877172i
$630$		0			0
$631$			17.1003i			0.680750i	0.940290	+	0.340375i	$0.110554\pi$
$631$			17.1003i			0.680750i	−0.940290	+	0.340375i	$0.889446\pi$
$632$	−8.83867	−	0.709802i	−0.351583	−	0.0282344i
$633$		0			0
$634$	−12.0825	−	18.2758i	−0.479857	−	0.725823i
$635$	3.60092	−	0.964865i	0.142898	−	0.0382895i
$636$		0			0
$637$	−1.58719	−	0.425285i	−0.0628866	−	0.0168504i
$638$	−33.5768	+	11.2148i	−1.32932	+	0.443998i
$639$		0			0
$640$	−0.573378	+	5.73116i	−0.0226648	+	0.226544i
$641$	4.96926	+	8.60701i	0.196274	+	0.339956i	0.947317	−	0.320296i	$-0.103783\pi$
$641$	4.96926	+	8.60701i	0.196274	+	0.339956i	−0.751044	+	0.660253i	$0.770449\pi$
$642$		0			0
$643$	−8.95763	−	33.4303i	−0.353254	−	1.31836i	−0.882667	−	0.469999i	$-0.844254\pi$
$643$	−8.95763	−	33.4303i	−0.353254	−	1.31836i	0.529413	−	0.848364i	$-0.322412\pi$
$644$	−2.99061	−	24.5725i	−0.117846	−	0.968291i
$645$		0			0
$646$	−20.0027	+	1.21275i	−0.786996	+	0.0477148i
$647$			41.6750i			1.63841i	0.573498	+	0.819207i	$0.305586\pi$
$647$			41.6750i			1.63841i	−0.573498	+	0.819207i	$0.694414\pi$
$648$		0			0
$649$		−	9.17454i		−	0.360132i
$650$	−0.934852	−	15.4192i	−0.0366679	−	0.604790i
$651$		0			0
$652$	−10.2851	−	8.05324i	−0.402796	−	0.315389i
$653$	−10.9418	−	40.8352i	−0.428184	−	1.59800i	−0.756871	−	0.653565i	$-0.773273\pi$
$653$	−10.9418	−	40.8352i	−0.428184	−	1.59800i	0.328687	−	0.944439i	$-0.393394\pi$
$654$		0			0
$655$	5.22555	+	9.05091i	0.204179	+	0.353648i
$656$	21.5083	+	6.21693i	0.839758	+	0.242730i
$657$		0			0
$658$	12.2993	+	36.8237i	0.479476	+	1.43554i
$659$	25.4089	+	6.80828i	0.989789	+	0.265213i	0.717162	−	0.696907i	$-0.245441\pi$
$659$	25.4089	+	6.80828i	0.989789	+	0.265213i	0.272627	+	0.962120i	$0.412108\pi$
$660$		0			0
$661$	−12.8649	+	3.44715i	−0.500388	+	0.134079i	−0.500180	−	0.865921i	$-0.666733\pi$
$661$	−12.8649	+	3.44715i	−0.500388	+	0.134079i	−0.000208061		1.00000i	$0.500066\pi$
$662$	12.8842	−	8.51803i	0.500759	−	0.331063i
$663$		0			0
$664$	−24.5899	+	20.9341i	−0.954275	+	0.812399i
$665$		−	6.95879i		−	0.269850i
$666$		0			0
$667$	−19.1954	−	19.1954i	−0.743247	−	0.743247i
$668$	−6.19965	+	14.5624i	−0.239872	+	0.563436i
$669$		0			0
$670$	2.20370	−	10.8021i	0.0851363	−	0.417323i
$671$	−10.2042	+	17.6742i	−0.393928	+	0.682303i
$672$		0			0
$673$	−6.35961	−	11.0152i	−0.245145	−	0.424604i	0.717027	−	0.697045i	$-0.245502\pi$
$673$	−6.35961	−	11.0152i	−0.245145	−	0.424604i	−0.962172	+	0.272441i	$0.912169\pi$
$674$	7.55198	−	2.52239i	0.290891	−	0.0971590i
$675$		0			0
$676$	9.24454	+	12.2951i	0.355559	+	0.472888i
$677$	11.3408	−	42.3243i	0.435861	−	1.62665i	−0.303137	−	0.952947i	$-0.598034\pi$
$677$	11.3408	−	42.3243i	0.435861	−	1.62665i	0.738998	−	0.673708i	$-0.235299\pi$
$678$		0			0
$679$	24.2592	+	14.0061i	0.930984	+	0.537504i
$680$	−1.39009	+	3.90570i	−0.0533077	+	0.149777i
$681$		0			0
$682$	0.902440	+	14.8846i	0.0345562	+	0.569961i
$683$	−4.22715	−	4.22715i	−0.161748	−	0.161748i	0.621593	−	0.783340i	$-0.286486\pi$
$683$	−4.22715	−	4.22715i	−0.161748	−	0.161748i	−0.783340	+	0.621593i	$0.786486\pi$
$684$		0			0
$685$	4.19368	−	4.19368i	0.160232	−	0.160232i
$686$	−16.3715	+	18.4848i	−0.625067	+	0.705753i
$687$		0			0
$688$	−0.275787	+	14.0837i	−0.0105143	+	0.536936i
$689$	4.66870	−	8.08643i	0.177863	−	0.308069i
$690$		0			0
$691$	−3.57753	−	0.958595i	−0.136096	−	0.0364667i	0.190128	−	0.981759i	$-0.439110\pi$
$691$	−3.57753	−	0.958595i	−0.136096	−	0.0364667i	−0.326224	+	0.945293i	$0.605776\pi$
$692$	−6.07596	+	42.9017i	−0.230973	+	1.63088i
$693$		0			0
$694$	1.83395	+	0.915589i	0.0696156	+	0.0347553i
$695$	−5.26794	+	3.04145i	−0.199824	+	0.115369i
$696$		0			0
$697$	13.9558	+	8.05738i	0.528613	+	0.305195i
$698$	−3.27098	−	4.94762i	−0.123808	−	0.187270i
$699$		0			0
$700$	24.2287	+	10.3149i	0.915758	+	0.389866i
$701$	−22.6596	+	22.6596i	−0.855842	+	0.855842i	−0.990845	−	0.135003i	$-0.956896\pi$
$701$	−22.6596	+	22.6596i	−0.855842	+	0.855842i	0.135003	+	0.990845i	$0.456896\pi$
$702$		0			0
$703$	−53.1850			−2.00591
$704$	32.7056	−	3.33207i	1.23264	−	0.125582i
$705$		0			0
$706$	3.22575	−	15.8121i	0.121403	−	0.595094i
$707$	−4.32325	−	16.1346i	−0.162592	−	0.606803i
$708$		0			0
$709$	5.72683	−	21.3728i	0.215076	−	0.802673i	−0.771064	−	0.636757i	$-0.780275\pi$
$709$	5.72683	−	21.3728i	0.215076	−	0.802673i	0.986140	−	0.165916i	$-0.0530580\pi$
$710$	−4.25939	+	8.53165i	−0.159852	+	0.320187i
$711$		0			0
$712$	−5.52943	−	3.81327i	−0.207224	−	0.142908i
$713$	−9.90308	+	5.71755i	−0.370873	+	0.214124i
$714$		0			0
$715$	4.65595	−	1.24756i	0.174122	−	0.0466560i
$716$	−9.45214	−	7.40101i	−0.353243	−	0.276589i
$717$		0			0
$718$	0.989897	−	1.11768i	0.0369426	−	0.0417114i
$719$	−8.65067			−0.322616			−0.161308	−	0.986904i	$-0.551571\pi$
$719$	−8.65067			−0.322616			−0.161308	+	0.986904i	$0.551571\pi$
$720$		0			0
$721$	37.6589			1.40249
$722$	−4.89768	+	5.52989i	−0.182273	+	0.205801i
$723$		0			0
$724$	−17.5684	+	22.4373i	−0.652924	+	0.833876i
$725$	27.8942	−	7.47422i	1.03596	−	0.277586i
$726$		0			0
$727$	2.70356	−	1.56090i	0.100269	−	0.0578905i	−0.449027	−	0.893518i	$-0.648229\pi$
$727$	2.70356	−	1.56090i	0.100269	−	0.0578905i	0.549296	+	0.835628i	$0.314896\pi$
$728$	17.8010	−	3.26987i	0.659750	−	0.121190i
$729$		0			0
$730$	−3.65868	+	7.32842i	−0.135414	+	0.271237i
$731$	−2.62415	+	9.79347i	−0.0970578	+	0.362225i
$732$		0			0
$733$	−0.888818	−	3.31711i	−0.0328292	−	0.122520i	0.947567	−	0.319558i	$-0.103534\pi$
$733$	−0.888818	−	3.31711i	−0.0328292	−	0.122520i	−0.980396	+	0.197038i	$0.936868\pi$
$734$	2.64313	−	12.9561i	0.0975596	−	0.478219i
$735$		0			0
$736$	13.4887	+	21.2977i	0.497199	+	0.785043i
$737$	−62.9250			−2.31787
$738$		0			0
$739$	11.1765	−	11.1765i	0.411133	−	0.411133i	−0.471000	−	0.882133i	$-0.656107\pi$
$739$	11.1765	−	11.1765i	0.411133	−	0.411133i	0.882133	+	0.471000i	$0.156107\pi$
$740$	−4.30989	+	10.1235i	−0.158435	+	0.372148i
$741$		0			0
$742$	8.77826	+	13.2778i	0.322260	+	0.487445i
$743$	8.55561	+	4.93958i	0.313875	+	0.181216i	0.648659	−	0.761079i	$-0.275330\pi$
$743$	8.55561	+	4.93958i	0.313875	+	0.181216i	−0.334784	+	0.942295i	$0.608663\pi$
$744$		0			0
$745$	−0.461051	+	0.266188i	−0.0168916	+	0.00975237i
$746$	−7.60651	−	3.79751i	−0.278494	−	0.139037i
$747$		0			0
$748$	23.4285	+	3.31807i	0.856632	+	0.121321i
$749$	10.6974	+	2.86637i	0.390876	+	0.104735i
$750$		0			0
$751$	−23.4223	+	40.5685i	−0.854690	+	1.48037i	0.0222416	+	0.999753i	$0.492920\pi$
$751$	−23.4223	+	40.5685i	−0.854690	+	1.48037i	−0.876932	+	0.480615i	$0.840414\pi$
$752$	−27.4053	−	28.5001i	−0.999370	−	1.03929i
$753$		0			0
$754$	13.1597	−	14.8584i	0.479248	−	0.541112i
$755$	4.59300	−	4.59300i	0.167156	−	0.167156i
$756$		0			0
$757$	−14.0064	−	14.0064i	−0.509071	−	0.509071i	0.405170	−	0.914241i	$-0.367212\pi$
$757$	−14.0064	−	14.0064i	−0.509071	−	0.509071i	−0.914241	+	0.405170i	$0.867212\pi$
$758$	−0.768983	−	12.6834i	−0.0279307	−	0.460682i
$759$		0			0
$760$	3.04083	+	6.40147i	0.110302	+	0.232206i
$761$	24.1008	+	13.9146i	0.873655	+	0.504405i	0.868561	−	0.495582i	$-0.165045\pi$
$761$	24.1008	+	13.9146i	0.873655	+	0.504405i	0.00509371	+	0.999987i	$0.498379\pi$
$762$		0			0
$763$	−3.25757	+	12.1574i	−0.117932	+	0.440129i
$764$	17.4824	−	13.1448i	0.632490	−	0.475562i
$765$		0			0
$766$	−29.2313	+	9.76338i	−1.05617	+	0.352765i
$767$	2.57199	+	4.45482i	0.0928693	+	0.160854i
$768$		0			0
$769$	8.70836	−	15.0833i	0.314031	−	0.543918i	−0.665200	−	0.746666i	$-0.731654\pi$
$769$	8.70836	−	15.0833i	0.314031	−	0.543918i	0.979231	+	0.202747i	$0.0649869\pi$
$770$	−1.64246	+	8.05103i	−0.0591901	+	0.290139i
$771$		0			0
$772$	−36.1531	−	15.3915i	−1.30118	−	0.553951i
$773$	−2.74550	−	2.74550i	−0.0987489	−	0.0987489i	0.656006	−	0.754755i	$-0.272244\pi$
$773$	−2.74550	−	2.74550i	−0.0987489	−	0.0987489i	−0.754755	+	0.656006i	$0.772244\pi$
$774$		0			0
$775$		−	12.1646i		−	0.436966i
$776$	−28.4367	−	2.28365i	−1.02082	−	0.0819783i
$777$		0			0
$778$	−5.96767	+	3.94535i	−0.213951	+	0.141448i
$779$	26.6092	−	7.12991i	0.953373	−	0.255455i
$780$		0			0
$781$	52.5727	+	14.0868i	1.88120	+	0.504066i
$782$	5.74843	+	17.2106i	0.205563	+	0.615451i
$783$		0			0
$784$	−0.792136	+	2.74050i	−0.0282906	+	0.0978751i
$785$	−2.90667	−	5.03451i	−0.103744	−	0.179689i
$786$		0			0
$787$	0.187023	+	0.697981i	0.00666666	+	0.0248803i	0.969179	−	0.246357i	$-0.0792337\pi$
$787$	0.187023	+	0.697981i	0.00666666	+	0.0248803i	−0.962512	+	0.271238i	$0.912567\pi$
$788$	−31.2979	+	39.9719i	−1.11494	+	1.42394i
$789$		0			0
$790$	0.136596	+	2.25297i	0.00485986	+	0.0801572i
$791$			28.2121i			1.00311i
$792$		0			0
$793$		−	11.4426i		−	0.406337i
$794$	−4.21263	+	0.255408i	−0.149501	+	0.00906409i
$795$		0			0
$796$	21.4243	−	2.60745i	0.759363	−	0.0924186i
$797$	4.56209	+	17.0260i	0.161598	+	0.603090i	0.998450	+	0.0556613i	$0.0177267\pi$
$797$	4.56209	+	17.0260i	0.161598	+	0.603090i	−0.836852	+	0.547429i	$0.815607\pi$
$798$		0			0
$799$	−14.2294	−	24.6460i	−0.503398	−	0.871912i
$800$	−26.7956	+	1.09858i	−0.947368	+	0.0388406i
$801$		0			0
$802$	11.3244	−	3.78239i	0.399878	−	0.133561i
$803$	45.1583	+	12.1001i	1.59360	+	0.427004i
$804$		0			0
$805$	−6.08633	+	1.63083i	−0.214515	+	0.0574791i
$806$	−4.61095	−	6.97443i	−0.162414	−	0.245664i
$807$		0			0
$808$	11.0274	+	12.9532i	0.387944	+	0.455693i
$809$		−	34.5309i		−	1.21404i	−0.794685	−	0.607022i	$-0.792364\pi$
$809$		−	34.5309i		−	1.21404i	0.794685	−	0.607022i	$-0.207636\pi$
$810$		0			0
$811$	−21.6237	−	21.6237i	−0.759310	−	0.759310i	0.216887	−	0.976197i	$-0.430410\pi$
$811$	−21.6237	−	21.6237i	−0.759310	−	0.759310i	−0.976197	+	0.216887i	$0.930410\pi$
$812$	12.6414	+	31.3845i	0.443624	+	1.10138i
$813$		0			0
$814$	61.5329	+	12.5531i	2.15673	+	0.439985i
$815$	−1.66256	+	2.87964i	−0.0582371	+	0.100870i
$816$		0			0
$817$	8.66616	+	15.0102i	0.303191	+	0.525142i
$818$	−17.8387	−	53.4086i	−0.623716	−	1.86739i
$819$		0			0
$820$	0.799150	−	5.64271i	0.0279075	−	0.197052i
$821$	2.88421	−	10.7640i	0.100660	−	0.375667i	−0.897157	−	0.441712i	$-0.854371\pi$
$821$	2.88421	−	10.7640i	0.100660	−	0.375667i	0.997817	+	0.0660446i	$0.0210380\pi$
$822$		0			0
$823$	22.0500	+	12.7306i	0.768616	+	0.443760i	0.832381	−	0.554205i	$-0.186977\pi$
$823$	22.0500	+	12.7306i	0.768616	+	0.443760i	−0.0637649	+	0.997965i	$0.520311\pi$
$824$	−34.6428	+	16.4560i	−1.20684	+	0.573273i
$825$		0			0
$826$	−8.75275	+	0.530672i	−0.304547	+	0.0184644i
$827$	15.8750	+	15.8750i	0.552029	+	0.552029i	0.927026	−	0.374997i	$-0.122356\pi$
$827$	15.8750	+	15.8750i	0.552029	+	0.552029i	−0.374997	+	0.927026i	$0.622356\pi$
$828$		0			0
$829$	28.3270	−	28.3270i	0.983836	−	0.983836i	−0.0160352	−	0.999871i	$-0.505104\pi$
$829$	28.3270	−	28.3270i	0.983836	−	0.983836i	0.999871	+	0.0160352i	$0.00510438\pi$
$830$	6.15380	+	5.45025i	0.213601	+	0.189181i
$831$		0			0
$832$	−14.9465	+	10.7866i	−0.518178	+	0.373959i
$833$	−1.02664	+	1.77819i	−0.0355709	+	0.0616106i
$834$		0			0
$835$	3.89150	+	1.04272i	0.134671	+	0.0360849i
$836$	32.3309	−	24.3092i	1.11819	−	0.840752i
$837$		0			0
$838$	4.14063	−	8.29378i	0.143036	−	0.286504i
$839$	17.2154	−	9.93933i	0.594342	−	0.343144i	−0.172470	−	0.985015i	$-0.555175\pi$
$839$	17.2154	−	9.93933i	0.594342	−	0.343144i	0.766813	+	0.641871i	$0.221842\pi$
$840$		0			0
$841$	7.01912	+	4.05249i	0.242039	+	0.139741i
$842$	39.7218	−	26.2610i	1.36890	−	0.905012i
$843$		0			0
$844$	−16.4129	+	6.61097i	−0.564957	+	0.227559i
$845$	2.76879	−	2.76879i	0.0952494	−	0.0952494i
$846$		0			0
$847$	16.3493			0.561769
$848$	−13.8773	−	8.37855i	−0.476550	−	0.287721i
$849$		0			0
$850$	−18.9133	−	3.85843i	−0.648721	−	0.132343i
$851$	12.4642	+	46.5169i	0.427266	+	1.59458i
$852$		0			0
$853$	6.83749	−	25.5178i	0.234111	−	0.873715i	−0.744436	−	0.667693i	$-0.767282\pi$
$853$	6.83749	−	25.5178i	0.234111	−	0.873715i	0.978548	−	0.206021i	$-0.0660516\pi$
$854$	17.4518	+	8.71275i	0.597190	+	0.298144i
$855$		0			0
$856$	−11.0932	+	2.03772i	−0.379159	+	0.0696478i
$857$	−6.38473	+	3.68622i	−0.218098	+	0.125919i	−0.605069	−	0.796173i	$-0.706855\pi$
$857$	−6.38473	+	3.68622i	−0.218098	+	0.125919i	0.386971	+	0.922092i	$0.373521\pi$
$858$		0			0
$859$	−24.1370	+	6.46749i	−0.823544	+	0.220668i	−0.645895	−	0.763426i	$-0.723516\pi$
$859$	−24.1370	+	6.46749i	−0.823544	+	0.220668i	−0.177649	+	0.984094i	$0.556849\pi$
$860$	3.55940	−	0.433199i	0.121375	−	0.0147720i
$861$		0			0
$862$	20.2118	+	17.9011i	0.688417	+	0.609713i
$863$	22.7407			0.774104			0.387052	−	0.922058i	$-0.373493\pi$
$863$	22.7407			0.774104			0.387052	+	0.922058i	$0.373493\pi$
$864$		0			0
$865$	11.0295			0.375015
$866$	5.27855	+	4.67507i	0.179372	+	0.158865i
$867$		0			0
$868$	14.1481	−	1.72190i	0.480218	−	0.0584452i
$869$	12.4439	−	3.33433i	0.422130	−	0.113109i
$870$		0			0
$871$	30.5541	−	17.6404i	1.03529	−	0.597723i
$872$	−2.31583	−	12.6073i	−0.0784238	−	0.426936i
$873$		0			0
$874$	27.7526	+	13.8553i	0.938745	+	0.468664i
$875$	3.56458	−	13.3032i	0.120505	−	0.449730i
$876$		0			0
$877$	−5.79980	−	21.6451i	−0.195845	−	0.730905i	−0.992046	−	0.125873i	$-0.959827\pi$
$877$	−5.79980	−	21.6451i	−0.195845	−	0.730905i	0.796201	−	0.605032i	$-0.206840\pi$
$878$	17.9034	+	3.65239i	0.604209	+	0.123262i
$879$		0			0
$880$	−2.00719	−	8.12396i	−0.0676624	−	0.273859i
$881$	55.9231			1.88410			0.942048	−	0.335477i	$-0.108898\pi$
$881$	55.9231			1.88410			0.942048	+	0.335477i	$0.108898\pi$
$882$		0			0
$883$	−7.12196	+	7.12196i	−0.239673	+	0.239673i	−0.816715	−	0.577042i	$-0.804207\pi$
$883$	−7.12196	+	7.12196i	−0.239673	+	0.239673i	0.577042	+	0.816715i	$0.304207\pi$
$884$	−12.3062	+	4.95683i	−0.413903	+	0.166716i
$885$		0			0
$886$	17.5395	−	11.5957i	0.589250	−	0.389566i
$887$	1.13549	+	0.655576i	0.0381260	+	0.0220121i	0.518942	−	0.854810i	$-0.326326\pi$
$887$	1.13549	+	0.655576i	0.0381260	+	0.0220121i	−0.480816	+	0.876822i	$0.659659\pi$
$888$		0			0
$889$	−17.6124	+	10.1685i	−0.590699	+	0.341040i
$890$	−0.763702	+	1.52971i	−0.0255993	+	0.0512761i
$891$		0			0
$892$	−24.0857	+	18.1098i	−0.806450	+	0.606361i
$893$	−46.9919	−	12.5914i	−1.57252	−	0.421357i
$894$		0			0
$895$	−1.52791	+	2.64642i	−0.0510725	+	0.0884602i
$896$	−5.07063	−	31.0093i	−0.169398	−	1.03595i
$897$		0			0
$898$	−3.81850	−	3.38195i	−0.127425	−	0.112857i
$899$	11.0521	−	11.0521i	0.368609	−	0.368609i
$900$		0			0
$901$	−8.25040	−	8.25040i	−0.274861	−	0.274861i
$902$	−32.4686	+	1.96854i	−1.08108	+	0.0655452i
$903$		0			0
$904$	−12.3280	−	25.9527i	−0.410024	−	0.863173i
$905$	6.28204	+	3.62693i	0.208822	+	0.120563i
$906$		0			0
$907$	4.81582	−	17.9729i	0.159907	−	0.596780i	−0.838728	−	0.544550i	$-0.816700\pi$
$907$	4.81582	−	17.9729i	0.159907	−	0.596780i	0.998635	−	0.0522300i	$-0.0166329\pi$
$908$	1.72680	−	12.1927i	0.0573058	−	0.404631i
$909$		0			0
$910$	−1.45951	−	4.36973i	−0.0483823	−	0.144855i
$911$	−1.56545	−	2.71143i	−0.0518656	−	0.0898338i	0.838927	−	0.544244i	$-0.183183\pi$
$911$	−1.56545	−	2.71143i	−0.0518656	−	0.0898338i	−0.890793	+	0.454410i	$0.849850\pi$
$912$		0			0
$913$	23.4596	−	40.6332i	0.776400	−	1.34476i
$914$	6.61196	+	1.34888i	0.218704	+	0.0446169i
$915$		0			0
$916$	3.12098	+	7.74839i	0.103120	+	0.256014i
$917$	−40.3147	−	40.3147i	−1.33131	−	1.33131i
$918$		0			0
$919$		−	20.2458i		−	0.667847i	−0.942600	−	0.333924i	$-0.891627\pi$
$919$		−	20.2458i		−	0.667847i	0.942600	−	0.333924i	$-0.108373\pi$
$920$	4.88626	−	4.15980i	0.161095	−	0.137145i
$921$		0			0
$922$	18.3887	+	27.8144i	0.605600	+	0.916020i
$923$	−29.4765	+	7.89820i	−0.970231	+	0.259973i
$924$		0			0
$925$	−49.4845	−	13.2593i	−1.62704	−	0.435964i
$926$	−42.8172	+	14.3011i	−1.40706	+	0.469964i
$927$		0			0
$928$	−25.3432	−	23.3470i	−0.831931	−	0.766402i
$929$	−7.78745	−	13.4883i	−0.255498	−	0.442535i	0.709533	−	0.704672i	$-0.248906\pi$
$929$	−7.78745	−	13.4883i	−0.255498	−	0.442535i	−0.965031	+	0.262137i	$0.915573\pi$
$930$		0			0
$931$	0.908464	+	3.39043i	0.0297737	+	0.111117i
$932$	−3.41356	+	0.415449i	−0.111815	+	0.0136085i
$933$		0			0
$934$	14.4955	−	0.878847i	0.474306	−	0.0287568i
$935$		−	6.02320i		−	0.196980i
$936$		0			0
$937$		−	40.1896i		−	1.31294i	−0.754354	−	0.656468i	$-0.772050\pi$
$937$		−	40.1896i		−	1.31294i	0.754354	−	0.656468i	$-0.227950\pi$
$938$	3.63969	+	60.0321i	0.118840	+	1.96012i
$939$		0			0
$940$	−6.20475	+	7.92434i	−0.202377	+	0.258463i
$941$	−0.547985	−	2.04511i	−0.0178638	−	0.0666686i	0.956419	−	0.291999i	$-0.0943205\pi$
$941$	−0.547985	−	2.04511i	−0.0178638	−	0.0666686i	−0.974282	+	0.225331i	$0.927654\pi$
$942$		0			0
$943$	−12.4720	−	21.6021i	−0.406144	−	0.703462i
$944$	7.81988	−	4.31292i	0.254515	−	0.140374i
$945$		0			0
$946$	−6.48358	−	19.4117i	−0.210799	−	0.631128i
$947$	46.7422	+	12.5245i	1.51892	+	0.406993i	0.919386	−	0.393358i	$-0.128687\pi$
$947$	46.7422	+	12.5245i	1.51892	+	0.406993i	0.599532	+	0.800350i	$0.295353\pi$
$948$		0			0
$949$	−25.3194	+	6.78431i	−0.821902	+	0.220228i
$950$	−27.5261	+	18.1981i	−0.893065	+	0.590425i
$951$		0			0
$952$	1.81038	−	22.5434i	0.0586747	−	0.730635i
$953$			41.3167i			1.33838i	0.743091	+	0.669190i	$0.233359\pi$
$953$			41.3167i			1.33838i	−0.743091	+	0.669190i	$0.766641\pi$
$954$		0			0
$955$	−3.93694	−	3.93694i	−0.127396	−	0.127396i
$956$	−18.3865	−	7.82770i	−0.594663	−	0.253166i
$957$		0			0
$958$	−7.61738	+	37.3390i	−0.246107	+	1.20637i
$959$	−16.1770	+	28.0193i	−0.522381	+	0.904791i
$960$		0			0
$961$	12.2080	+	21.1449i	0.393807	+	0.682093i
$962$	−33.3973	+	11.1548i	−1.07677	+	0.359646i
$963$		0			0
$964$	−34.8537	+	26.2061i	−1.12256	+	0.844041i
$965$	−2.58870	+	9.66116i	−0.0833332	+	0.311004i
$966$		0			0
$967$	15.5967	+	9.00476i	0.501556	+	0.289574i	0.729356	−	0.684134i	$-0.239820\pi$
$967$	15.5967	+	9.00476i	0.501556	+	0.289574i	−0.227800	+	0.973708i	$0.573153\pi$
$968$	−15.0399	+	7.14427i	−0.483402	+	0.229625i
$969$		0			0
$970$	0.439470	+	7.24850i	0.0141105	+	0.232735i
$971$	−26.1482	−	26.1482i	−0.839134	−	0.839134i	0.149611	−	0.988745i	$-0.452198\pi$
$971$	−26.1482	−	26.1482i	−0.839134	−	0.839134i	−0.988745	+	0.149611i	$0.952198\pi$
$972$		0			0
$973$	23.4645	−	23.4645i	0.752238	−	0.752238i
$974$	31.2617	−	35.2970i	1.00169	−	1.13099i
$975$		0			0
$976$	−19.8614	−	0.388927i	−0.635749	−	0.0124492i
$977$	9.85534	−	17.0699i	0.315300	−	0.546116i	−0.664201	−	0.747554i	$-0.731228\pi$
$977$	9.85534	−	17.0699i	0.315300	−	0.546116i	0.979501	+	0.201438i	$0.0645615\pi$
$978$		0			0
$979$	9.42621	+	2.52574i	0.301263	+	0.0807231i
$980$	0.718972	+	0.101824i	0.0229667	+	0.00325266i
$981$		0			0
$982$	29.3645	+	14.6601i	0.937059	+	0.467823i
$983$	−5.03257	+	2.90556i	−0.160514	+	0.0926729i	−0.578105	−	0.815962i	$-0.696208\pi$
$983$	−5.03257	+	2.90556i	−0.160514	+	0.0926729i	0.417591	+	0.908635i	$0.362874\pi$
$984$		0			0
$985$	11.1914	+	6.46135i	0.356587	+	0.205876i
$986$	−13.6781	−	20.6892i	−0.435598	−	0.658878i
$987$		0			0
$988$	−8.88385	+	20.8673i	−0.282633	+	0.663878i
$989$	11.0974	−	11.0974i	0.352876	−	0.352876i
$990$		0			0
$991$	−28.5729			−0.907648			−0.453824	−	0.891091i	$-0.649940\pi$
$991$	−28.5729			−0.907648			−0.453824	+	0.891091i	$0.649940\pi$
$992$	−12.2626	+	7.76639i	−0.389337	+	0.246583i
$993$		0			0
$994$	10.3983	−	50.9706i	0.329814	−	1.61669i
$995$	−1.42189	−	5.30655i	−0.0450768	−	0.168229i
$996$		0			0
$997$	−6.86935	+	25.6368i	−0.217555	+	0.811925i	0.767697	+	0.640813i	$0.221403\pi$
$997$	−6.86935	+	25.6368i	−0.217555	+	0.811925i	−0.985252	+	0.171112i	$0.945264\pi$
$998$	9.84967	−	19.7291i	0.311786	−	0.624514i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.5		72
3.2	odd	2		144.2.x.e.85.14	yes	72
4.3	odd	2		1728.2.bc.e.1009.11		72
9.2	odd	6		144.2.x.e.133.9	yes	72
9.7	even	3	inner	432.2.y.e.181.10		72
12.11	even	2		576.2.bb.e.49.3		72
16.3	odd	4		1728.2.bc.e.145.8		72
16.13	even	4	inner	432.2.y.e.253.10		72
36.7	odd	6		1728.2.bc.e.1585.8		72
36.11	even	6		576.2.bb.e.241.7		72
48.29	odd	4		144.2.x.e.13.9	✓	72
48.35	even	4		576.2.bb.e.337.7		72
144.29	odd	12		144.2.x.e.61.14	yes	72
144.61	even	12	inner	432.2.y.e.397.5		72
144.83	even	12		576.2.bb.e.529.3		72
144.115	odd	12		1728.2.bc.e.721.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.9	✓	72	48.29	odd	4
144.2.x.e.61.14	yes	72	144.29	odd	12
144.2.x.e.85.14	yes	72	3.2	odd	2
144.2.x.e.133.9	yes	72	9.2	odd	6
432.2.y.e.37.5		72	1.1	even	1	trivial
432.2.y.e.181.10		72	9.7	even	3	inner
432.2.y.e.253.10		72	16.13	even	4	inner
432.2.y.e.397.5		72	144.61	even	12	inner
576.2.bb.e.49.3		72	12.11	even	2
576.2.bb.e.241.7		72	36.11	even	6
576.2.bb.e.337.7		72	48.35	even	4
576.2.bb.e.529.3		72	144.83	even	12
1728.2.bc.e.145.8		72	16.3	odd	4
1728.2.bc.e.721.11		72	144.115	odd	12
1728.2.bc.e.1009.11		72	4.3	odd	2
1728.2.bc.e.1585.8		72	36.7	odd	6

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05869 - 0.937649i) q^{2} +(0.241628 + 1.98535i) q^{4} +(0.491749 - 0.131764i) q^{5} +(-2.40518 + 1.38863i) q^{7} +(1.60575 - 2.32842i) q^{8} +O(q^{10})\)	\(q+(-1.05869 - 0.937649i) q^{2} +(0.241628 + 1.98535i) q^{4} +(0.491749 - 0.131764i) q^{5} +(-2.40518 + 1.38863i) q^{7} +(1.60575 - 2.32842i) q^{8} +(-0.644156 - 0.321592i) q^{10} +(-1.06358 + 3.96934i) q^{11} +(-0.596329 - 2.22553i) q^{13} +(3.84837 + 0.785091i) q^{14} +(-3.88323 + 0.959433i) q^{16} -2.87908 q^{17} +(-3.48018 + 3.48018i) q^{19} +(0.380418 + 0.944457i) q^{20} +(4.84784 - 3.20501i) q^{22} +(3.85945 + 2.22826i) q^{23} +(-4.10567 + 2.37041i) q^{25} +(-1.45544 + 2.91528i) q^{26} +(-3.33808 - 4.43959i) q^{28} +(-5.88383 - 1.57657i) q^{29} +(-1.28296 + 2.22216i) q^{31} +(5.01073 + 2.62537i) q^{32} +(3.04804 + 2.69956i) q^{34} +(-0.999773 + 0.999773i) q^{35} +(7.64112 + 7.64112i) q^{37} +(6.94761 - 0.421227i) q^{38} +(0.482826 - 1.35658i) q^{40} +(-4.84731 - 2.79860i) q^{41} +(0.911456 - 3.40160i) q^{43} +(-8.13752 - 1.15248i) q^{44} +(-1.99662 - 5.97783i) q^{46} +(4.94233 + 8.56037i) q^{47} +(0.356586 - 0.617625i) q^{49} +(6.56923 + 1.34016i) q^{50} +(4.27437 - 1.72167i) q^{52} +(2.86564 + 2.86564i) q^{53} +2.09206i q^{55} +(-0.628805 + 7.83007i) q^{56} +(4.75085 + 7.18605i) q^{58} +(-2.15652 + 0.577838i) q^{59} +(4.79709 + 1.28538i) q^{61} +(3.44186 - 1.14960i) q^{62} +(-2.84311 - 7.47775i) q^{64} +(-0.586489 - 1.01583i) q^{65} +(3.96319 + 14.7908i) q^{67} +(-0.695666 - 5.71597i) q^{68} +(1.99588 - 0.121008i) q^{70} -13.2447i q^{71} -11.3768i q^{73} +(-0.924850 - 15.2542i) q^{74} +(-7.75029 - 6.06847i) q^{76} +(-2.95384 - 11.0239i) q^{77} +(-1.56750 - 2.71499i) q^{79} +(-1.78316 + 0.983470i) q^{80} +(2.50768 + 7.50791i) q^{82} +(-11.0286 - 2.95510i) q^{83} +(-1.41578 + 0.379358i) q^{85} +(-4.15445 + 2.74660i) q^{86} +(7.53445 + 8.85025i) q^{88} -2.37475i q^{89} +(4.52472 + 4.52472i) q^{91} +(-3.49132 + 8.20078i) q^{92} +(2.79425 - 13.6969i) q^{94} +(-1.25282 + 2.16994i) q^{95} +(-5.04313 - 8.73496i) q^{97} +(-0.956628 + 0.319518i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

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