LMFDB - Embedded newform 441.2.bg.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	441.17
Dual form			441.2.bg.a.26.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51461 + 0.113504i) q^{2} +(0.303503 - 0.0457458i) q^{4} +(2.45092 - 2.27412i) q^{5} +(1.78982 + 1.94847i) q^{7} +(2.50706 - 0.572220i) q^{8} +O(q^{10})$	\(q+(-1.51461 + 0.113504i) q^{2} +(0.303503 - 0.0457458i) q^{4} +(2.45092 - 2.27412i) q^{5} +(1.78982 + 1.94847i) q^{7} +(2.50706 - 0.572220i) q^{8} +(-3.45407 + 3.72260i) q^{10} +(0.256186 + 0.375756i) q^{11} +(-1.47524 + 3.06337i) q^{13} +(-2.93205 - 2.74802i) q^{14} +(-4.31886 + 1.33219i) q^{16} +(-1.83192 - 4.66766i) q^{17} +(3.96050 - 2.28660i) q^{19} +(0.639832 - 0.802323i) q^{20} +(-0.430673 - 0.540047i) q^{22} +(0.552433 + 0.216814i) q^{23} +(0.461731 - 6.16138i) q^{25} +(1.88671 - 4.80726i) q^{26} +(0.632352 + 0.509490i) q^{28} +(5.06540 + 4.03952i) q^{29} +(3.57497 + 2.06401i) q^{31} +(1.60264 - 0.628991i) q^{32} +(3.30445 + 6.86176i) q^{34} +(8.81778 + 0.705270i) q^{35} +(6.92679 + 1.04405i) q^{37} +(-5.73909 + 3.91284i) q^{38} +(4.84330 - 7.10382i) q^{40} +(-1.61152 - 7.06051i) q^{41} +(1.37951 - 6.04402i) q^{43} +(0.0949427 + 0.102324i) q^{44} +(-0.861331 - 0.265685i) q^{46} +(0.826898 + 11.0342i) q^{47} +(-0.593070 + 6.97483i) q^{49} +9.38450i q^{50} +(-0.307605 + 0.997230i) q^{52} +(-0.382386 - 2.53696i) q^{53} +(1.48241 + 0.338350i) q^{55} +(5.60214 + 3.86076i) q^{56} +(-8.13062 - 5.54336i) q^{58} +(-5.68865 - 5.27829i) q^{59} +(0.642183 - 4.26060i) q^{61} +(-5.64897 - 2.72040i) q^{62} +(5.78815 - 2.78743i) q^{64} +(3.35078 + 10.8630i) q^{65} +(6.53077 - 11.3116i) q^{67} +(-0.769520 - 1.33285i) q^{68} +(-13.4356 - 0.0673540i) q^{70} +(7.61059 - 6.06925i) q^{71} +(-12.4186 - 0.930644i) q^{73} +(-10.6099 - 0.795103i) q^{74} +(1.09742 - 0.875167i) q^{76} +(-0.273622 + 1.17171i) q^{77} +(6.44302 + 11.1596i) q^{79} +(-7.55562 + 13.0867i) q^{80} +(3.24222 + 10.5110i) q^{82} +(3.67219 - 1.76843i) q^{83} +(-15.1047 - 7.27405i) q^{85} +(-1.40340 + 9.31093i) q^{86} +(0.857289 + 0.795448i) q^{88} +(-12.7943 - 8.72299i) q^{89} +(-8.60931 + 2.60843i) q^{91} +(0.177584 + 0.0405323i) q^{92} +(-2.50486 - 16.6187i) q^{94} +(4.50688 - 14.6109i) q^{95} +6.73267i q^{97} +(0.106596 - 10.6315i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{25}{42}\right)$	$-1$

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 $

$2$	−1.51461	+	0.113504i	−1.07099	+	0.0802598i	−0.598537	−	0.801095i	$-0.704251\pi$
$2$	−1.51461	+	0.113504i	−1.07099	+	0.0802598i	−0.472455	+	0.881355i	$0.656632\pi$
$3$		0			0
$3$		0			0
$4$	0.303503	−	0.0457458i	0.151752	−	0.0228729i
$5$	2.45092	−	2.27412i	1.09609	−	1.01702i	0.0963203	−	0.995350i	$-0.469293\pi$
$5$	2.45092	−	2.27412i	1.09609	−	1.01702i	0.999765	−	0.0216683i	$-0.00689778\pi$
$6$		0			0
$7$	1.78982	+	1.94847i	0.676489	+	0.736452i
$7$	1.78982	+	1.94847i	0.676489	+	0.736452i
$8$	2.50706	−	0.572220i	0.886379	−	0.202310i
$9$		0			0
$10$	−3.45407	+	3.72260i	−1.09227	+	1.17719i
$11$	0.256186	+	0.375756i	0.0772431	+	0.113295i	0.862916	−	0.505347i	$-0.168636\pi$
$11$	0.256186	+	0.375756i	0.0772431	+	0.113295i	−0.785673	+	0.618642i	$0.787683\pi$
$12$		0			0
$13$	−1.47524	+	3.06337i	−0.409158	+	0.849626i	0.589951	+	0.807439i	$0.299147\pi$
$13$	−1.47524	+	3.06337i	−0.409158	+	0.849626i	−0.999110	+	0.0421874i	$0.986567\pi$
$14$	−2.93205	−	2.74802i	−0.783622	−	0.734440i
$15$		0			0
$16$	−4.31886	+	1.33219i	−1.07972	+	0.333048i
$17$	−1.83192	−	4.66766i	−0.444306	−	1.13207i	−0.961158	−	0.275999i	$-0.910992\pi$
$17$	−1.83192	−	4.66766i	−0.444306	−	1.13207i	0.516852	−	0.856075i	$-0.327104\pi$
$18$		0			0
$19$	3.96050	−	2.28660i	0.908602	−	0.524582i	0.0286210	−	0.999590i	$-0.490888\pi$
$19$	3.96050	−	2.28660i	0.908602	−	0.524582i	0.879981	+	0.475009i	$0.157555\pi$
$20$	0.639832	−	0.802323i	0.143071	−	0.179405i
$21$		0			0
$22$	−0.430673	−	0.540047i	−0.0918198	−	0.115138i
$23$	0.552433	+	0.216814i	0.115190	+	0.0452088i	0.422236	−	0.906486i	$-0.361245\pi$
$23$	0.552433	+	0.216814i	0.115190	+	0.0452088i	−0.307046	+	0.951695i	$0.599341\pi$
$24$		0			0
$25$	0.461731	−	6.16138i	0.0923463	−	1.23228i
$26$	1.88671	−	4.80726i	0.370015	−	0.942782i
$27$		0			0
$28$	0.632352	+	0.509490i	0.119503	+	0.0962846i
$29$	5.06540	+	4.03952i	0.940621	+	0.750121i	0.968376	−	0.249494i	$-0.0802644\pi$
$29$	5.06540	+	4.03952i	0.940621	+	0.750121i	−0.0277549	+	0.999615i	$0.508836\pi$
$30$		0			0
$31$	3.57497	+	2.06401i	0.642084	+	0.370707i	0.785417	−	0.618967i	$-0.212449\pi$
$31$	3.57497	+	2.06401i	0.642084	+	0.370707i	−0.143333	+	0.989675i	$0.545782\pi$
$32$	1.60264	−	0.628991i	0.283310	−	0.111191i
$33$		0			0
$34$	3.30445	+	6.86176i	0.566708	+	1.17678i
$35$	8.81778	+	0.705270i	1.49048	+	0.119212i
$36$		0			0
$37$	6.92679	+	1.04405i	1.13876	+	0.171640i	0.691233	−	0.722632i	$-0.257068\pi$
$37$	6.92679	+	1.04405i	1.13876	+	0.171640i	0.447525	+	0.894272i	$0.352306\pi$
$38$	−5.73909	+	3.91284i	−0.931003	+	0.634747i
$39$		0			0
$40$	4.84330	−	7.10382i	0.765794	−	1.12321i
$41$	−1.61152	−	7.06051i	−0.251676	−	1.10267i	−0.929900	−	0.367811i	$-0.880107\pi$
$41$	−1.61152	−	7.06051i	−0.251676	−	1.10267i	0.678224	−	0.734855i	$-0.262750\pi$
$42$		0			0
$43$	1.37951	−	6.04402i	0.210373	−	0.921705i	−0.753941	−	0.656943i	$-0.771849\pi$
$43$	1.37951	−	6.04402i	0.210373	−	0.921705i	0.964314	−	0.264762i	$-0.0852935\pi$
$44$	0.0949427	+	0.102324i	0.0143131	+	0.0154259i
$45$		0			0
$46$	−0.861331	−	0.265685i	−0.126996	−	0.0391732i
$47$	0.826898	+	11.0342i	0.120616	+	1.60950i	0.649198	+	0.760620i	$0.275105\pi$
$47$	0.826898	+	11.0342i	0.120616	+	1.60950i	−0.528582	+	0.848882i	$0.677276\pi$
$48$		0			0
$49$	−0.593070	+	6.97483i	−0.0847243	+	0.996404i
$50$			9.38450i			1.32717i
$51$		0			0
$52$	−0.307605	+	0.997230i	−0.0426571	+	0.138291i
$53$	−0.382386	−	2.53696i	−0.0525247	−	0.348479i	−0.999621	−	0.0275292i	$-0.991236\pi$
$53$	−0.382386	−	2.53696i	−0.0525247	−	0.348479i	0.947096	−	0.320950i	$-0.104002\pi$
$54$		0			0
$55$	1.48241	+	0.338350i	0.199888	+	0.0456231i
$56$	5.60214	+	3.86076i	0.748618	+	0.515915i
$57$		0			0
$58$	−8.13062	−	5.54336i	−1.06760	−	0.727879i
$59$	−5.68865	−	5.27829i	−0.740599	−	0.687175i	0.216712	−	0.976236i	$-0.430467\pi$
$59$	−5.68865	−	5.27829i	−0.740599	−	0.687175i	−0.957311	+	0.289060i	$0.906657\pi$
$60$		0			0
$61$	0.642183	−	4.26060i	0.0822231	−	0.545514i	−0.909357	−	0.416017i	$-0.863426\pi$
$61$	0.642183	−	4.26060i	0.0822231	−	0.545514i	0.991580	−	0.129497i	$-0.0413363\pi$
$62$	−5.64897	−	2.72040i	−0.717420	−	0.345491i
$63$		0			0
$64$	5.78815	−	2.78743i	0.723519	−	0.348428i
$65$	3.35078	+	10.8630i	0.415613	+	1.34738i
$66$		0			0
$67$	6.53077	−	11.3116i	0.797861	−	1.38194i	−0.123146	−	0.992389i	$-0.539298\pi$
$67$	6.53077	−	11.3116i	0.797861	−	1.38194i	0.921007	−	0.389547i	$-0.127368\pi$
$68$	−0.769520	−	1.33285i	−0.0933180	−	0.161631i
$69$		0			0
$70$	−13.4356	−	0.0673540i	−1.60586	−	0.00805034i
$71$	7.61059	−	6.06925i	0.903211	−	0.720287i	−0.0573503	−	0.998354i	$-0.518265\pi$
$71$	7.61059	−	6.06925i	0.903211	−	0.720287i	0.960562	+	0.278067i	$0.0896938\pi$
$72$		0			0
$73$	−12.4186	−	0.930644i	−1.45348	−	0.108924i	−0.675571	−	0.737295i	$-0.736103\pi$
$73$	−12.4186	−	0.930644i	−1.45348	−	0.108924i	−0.777913	+	0.628371i	$0.783722\pi$
$74$	−10.6099	−	0.795103i	−1.23338	−	0.0924288i
$75$		0			0
$76$	1.09742	−	0.875167i	0.125883	−	0.100389i
$77$	−0.273622	+	1.17171i	−0.0311821	+	0.133529i
$78$		0			0
$79$	6.44302	+	11.1596i	0.724896	+	1.25556i	0.959017	+	0.283349i	$0.0914456\pi$
$79$	6.44302	+	11.1596i	0.724896	+	1.25556i	−0.234121	+	0.972208i	$0.575221\pi$
$80$	−7.55562	+	13.0867i	−0.844744	+	1.46314i
$81$		0			0
$82$	3.24222	+	10.5110i	0.358043	+	1.16075i
$83$	3.67219	−	1.76843i	0.403075	−	0.194111i	−0.221352	−	0.975194i	$-0.571047\pi$
$83$	3.67219	−	1.76843i	0.403075	−	0.194111i	0.624427	+	0.781083i	$0.285333\pi$
$84$		0			0
$85$	−15.1047	−	7.27405i	−1.63834	−	0.788982i
$86$	−1.40340	+	9.31093i	−0.151332	+	1.00402i
$87$		0			0
$88$	0.857289	+	0.795448i	0.0913873	+	0.0847950i
$89$	−12.7943	−	8.72299i	−1.35619	−	0.924635i	−0.356238	−	0.934395i	$-0.615941\pi$
$89$	−12.7943	−	8.72299i	−1.35619	−	0.924635i	−0.999952	+	0.00976074i	$0.996893\pi$
$90$		0			0
$91$	−8.60931	+	2.60843i	−0.902501	+	0.273437i
$92$	0.177584	+	0.0405323i	0.0185144	+	0.00422578i
$93$		0			0
$94$	−2.50486	−	16.6187i	−0.258357	−	1.71408i
$95$	4.50688	−	14.6109i	0.462396	−	1.49905i
$96$		0			0
$97$			6.73267i			0.683599i	0.939773	+	0.341800i	$0.111036\pi$
$97$			6.73267i			0.683599i	−0.939773	+	0.341800i	$0.888964\pi$
$98$	0.106596	−	10.6315i	0.0107678	−	1.07394i
$99$		0			0
$100$	−0.141720	−	1.89112i	−0.0141720	−	0.189112i
$101$	−3.25407	−	1.00375i	−0.323792	−	0.0998766i	0.128598	−	0.991697i	$-0.458952\pi$
$101$	−3.25407	−	1.00375i	−0.323792	−	0.0998766i	−0.452390	+	0.891820i	$0.649428\pi$
$102$		0			0
$103$	4.08241	+	4.39979i	0.402252	+	0.433524i	0.901397	−	0.432994i	$-0.142543\pi$
$103$	4.08241	+	4.39979i	0.402252	+	0.433524i	−0.499145	+	0.866519i	$0.666352\pi$
$104$	−1.94560	+	8.52421i	−0.190781	+	0.835868i
$105$		0			0
$106$	0.867123	+	3.79911i	0.0842224	+	0.369002i
$107$	−7.84595	+	11.5079i	−0.758497	+	1.11251i	0.231694	+	0.972789i	$0.425573\pi$
$107$	−7.84595	+	11.5079i	−0.758497	+	1.11251i	−0.990191	+	0.139722i	$0.955379\pi$
$108$		0			0
$109$	−12.2333	+	8.34052i	−1.17174	+	0.798877i	−0.983082	−	0.183166i	$-0.941365\pi$
$109$	−12.2333	+	8.34052i	−1.17174	+	0.798877i	−0.188656	+	0.982043i	$0.560413\pi$
$110$	−2.28368	−	0.344209i	−0.217740	−	0.0328190i
$111$		0			0
$112$	−10.3257	−	6.03078i	−0.975690	−	0.569855i
$113$	0.372935	+	0.774408i	0.0350828	+	0.0728502i	0.917774	−	0.397104i	$-0.129985\pi$
$113$	0.372935	+	0.774408i	0.0350828	+	0.0728502i	−0.882691	+	0.469954i	$0.844270\pi$
$114$		0			0
$115$	1.84703	−	0.724906i	0.172237	−	0.0675979i
$116$	1.72216	+	0.994288i	0.159898	+	0.0923173i
$117$		0			0
$118$	9.21520	+	7.34888i	0.848328	+	0.676519i
$119$	5.81598	−	11.9237i	0.533150	−	1.09305i
$120$		0			0
$121$	3.94319	−	10.0471i	0.358472	−	0.913371i
$122$	−0.489060	+	6.52605i	−0.0442774	+	0.590841i
$123$		0			0
$124$	1.17944	+	0.462894i	0.105916	+	0.0415692i
$125$	−2.45703	−	3.08101i	−0.219763	−	0.275574i
$126$		0			0
$127$	−13.6862	+	17.1619i	−1.21445	+	1.52287i	−0.429812	+	0.902918i	$0.641420\pi$
$127$	−13.6862	+	17.1619i	−1.21445	+	1.52287i	−0.784638	+	0.619954i	$0.787151\pi$
$128$	−11.4324	+	6.60050i	−1.01049	+	0.583408i
$129$		0			0
$130$	−6.30813	−	16.0728i	−0.553259	−	1.40968i
$131$	−1.06249	+	0.327734i	−0.0928300	+	0.0286342i	−0.340822	−	0.940128i	$-0.610705\pi$
$131$	−1.06249	+	0.327734i	−0.0928300	+	0.0286342i	0.247992	+	0.968762i	$0.420229\pi$
$132$		0			0
$133$	11.5440	+	3.62432i	1.00099	+	0.314268i
$134$	−8.60766	+	17.8740i	−0.743589	+	1.54408i
$135$		0			0
$136$	−7.26366	−	10.6538i	−0.622853	−	0.913558i
$137$	−14.9928	+	16.1584i	−1.28092	+	1.38050i	−0.393643	+	0.919263i	$0.628786\pi$
$137$	−14.9928	+	16.1584i	−1.28092	+	1.38050i	−0.887276	+	0.461239i	$0.847405\pi$
$138$		0			0
$139$	5.26859	−	1.20252i	0.446876	−	0.101996i	0.00683968	−	0.999977i	$-0.497823\pi$
$139$	5.26859	−	1.20252i	0.446876	−	0.101996i	0.440036	+	0.897980i	$0.354966\pi$
$140$	2.70849	−	0.189324i	0.228909	−	0.0160008i
$141$		0			0
$142$	−10.8382	+	10.0564i	−0.909522	+	0.843913i
$143$	−1.52902	+	0.230462i	−0.127863	+	0.0192722i
$144$		0			0
$145$	21.6013	−	1.61879i	1.79389	−	0.134433i
$146$	18.9150			1.56541
$147$		0			0
$148$	2.15007			0.176734
$149$	−10.2597	+	0.768856i	−0.840505	+	0.0629872i	−0.488022	−	0.872831i	$-0.662282\pi$
$149$	−10.2597	+	0.768856i	−0.840505	+	0.0629872i	−0.352483	+	0.935818i	$0.614662\pi$
$150$		0			0
$151$	−4.61651	+	0.695827i	−0.375686	+	0.0566256i	−0.334172	−	0.942512i	$-0.608456\pi$
$151$	−4.61651	+	0.695827i	−0.375686	+	0.0566256i	−0.0415148	+	0.999138i	$0.513218\pi$
$152$	8.62078	−	7.99891i	0.699237	−	0.648798i
$153$		0			0
$154$	0.281437	−	1.80574i	0.0226788	−	0.145511i
$155$	13.4558	−	3.07120i	1.08080	−	0.246684i
$156$		0			0
$157$	−8.56079	+	9.22634i	−0.683226	+	0.736342i	−0.975502	−	0.219992i	$-0.929397\pi$
$157$	−8.56079	+	9.22634i	−0.683226	+	0.736342i	0.292276	+	0.956334i	$0.405587\pi$
$158$	−11.0253	−	16.1712i	−0.877129	−	1.28651i
$159$		0			0
$160$	2.49755	−	5.18622i	0.197449	−	0.410007i
$161$	0.566301	+	1.46446i	0.0446308	+	0.115415i
$162$		0			0
$163$	11.0794	−	3.41754i	0.867805	−	0.267682i	0.171286	−	0.985221i	$-0.445208\pi$
$163$	11.0794	−	3.41754i	0.867805	−	0.267682i	0.696518	+	0.717539i	$0.254731\pi$
$164$	−0.812089	−	2.06917i	−0.0634135	−	0.161575i
$165$		0			0
$166$	−5.36121	+	3.09530i	−0.416111	+	0.240242i
$167$	10.0279	−	12.5746i	0.775981	−	0.973049i	−0.224018	−	0.974585i	$-0.571917\pi$
$167$	10.0279	−	12.5746i	0.775981	−	0.973049i	0.999999	+	0.00153601i	$0.000488927\pi$
$168$		0			0
$169$	0.897465	+	1.12539i	0.0690357	+	0.0865681i
$170$	23.7034	+	9.30291i	1.81797	+	0.713500i
$171$		0			0
$172$	0.142197	−	1.89749i	0.0108424	−	0.144682i
$173$	−1.37461	+	3.50245i	−0.104510	+	0.266286i	−0.973558	−	0.228442i	$-0.926637\pi$
$173$	−1.37461	+	3.50245i	−0.104510	+	0.266286i	0.869048	+	0.494728i	$0.164732\pi$
$174$		0			0
$175$	12.8317	−	10.1281i	0.969983	−	0.765612i
$176$	−1.60701	−	1.28155i	−0.121133	−	0.0966005i
$177$		0			0
$178$	20.3684	+	11.7597i	1.52668	+	0.881429i
$179$	−0.524798	+	0.205968i	−0.0392252	+	0.0153948i	−0.384873	−	0.922970i	$-0.625755\pi$
$179$	−0.524798	+	0.205968i	−0.0392252	+	0.0153948i	0.345647	+	0.938365i	$0.387659\pi$
$180$		0			0
$181$	0.115515	+	0.239868i	0.00858613	+	0.0178293i	0.905218	−	0.424948i	$-0.139708\pi$
$181$	0.115515	+	0.239868i	0.00858613	+	0.0178293i	−0.896632	+	0.442777i	$0.853993\pi$
$182$	12.7437	−	4.92795i	0.944625	−	0.365284i
$183$		0			0
$184$	1.50905	+	0.227452i	0.111248	+	0.0167680i
$185$	19.3513	−	13.1935i	1.42274	−	0.970006i
$186$		0			0
$187$	1.28459	−	1.88415i	0.0939384	−	0.137782i
$188$	0.755734	+	3.31109i	0.0551176	+	0.241486i
$189$		0			0
$190$	−5.16777	+	22.6415i	−0.374909	+	1.64258i
$191$	−14.7495	−	15.8962i	−1.06724	−	1.15021i	−0.988174	−	0.153338i	$-0.950998\pi$
$191$	−14.7495	−	15.8962i	−1.06724	−	1.15021i	−0.0790628	−	0.996870i	$-0.525193\pi$
$192$		0			0
$193$	−9.50394	−	2.93158i	−0.684109	−	0.211020i	−0.0668302	−	0.997764i	$-0.521289\pi$
$193$	−9.50394	−	2.93158i	−0.684109	−	0.211020i	−0.617278	+	0.786745i	$0.711765\pi$
$194$	−0.764188	−	10.1974i	−0.0548655	−	0.732130i
$195$		0			0
$196$	0.139070	+	2.14402i	0.00993360	+	0.153144i
$197$			17.3347i			1.23505i	0.786552	+	0.617525i	$0.211864\pi$
$197$			17.3347i			1.23505i	−0.786552	+	0.617525i	$0.788136\pi$
$198$		0			0
$199$	2.67587	−	8.67495i	0.189687	−	0.614951i	−0.809910	−	0.586555i	$-0.800484\pi$
$199$	2.67587	−	8.67495i	0.189687	−	0.614951i	0.999597	−	0.0283960i	$-0.00903994\pi$
$200$	−2.36807	−	15.7111i	−0.167448	−	1.11095i
$201$		0			0
$202$	5.04258	+	1.15094i	0.354795	+	0.0809796i
$203$	1.19528	+	17.0998i	0.0838923	+	1.20017i
$204$		0			0
$205$	−20.0062	−	13.6400i	−1.39729	−	0.952657i
$206$	−6.68266	−	6.20060i	−0.465603	−	0.432017i
$207$		0			0
$208$	2.29036	−	15.1956i	0.158808	−	1.05362i
$209$	1.87383	+	0.902389i	0.129616	+	0.0624196i
$210$		0			0
$211$	−5.42338	+	2.61176i	−0.373361	+	0.179801i	−0.611148	−	0.791516i	$-0.709292\pi$
$211$	−5.42338	+	2.61176i	−0.373361	+	0.179801i	0.237788	+	0.971317i	$0.423578\pi$
$212$	−0.232111	−	0.752485i	−0.0159414	−	0.0516809i
$213$		0			0
$214$	10.5774	−	18.3206i	0.723054	−	1.25237i
$215$	−10.3638	−	17.9506i	−0.706804	−	1.22422i
$216$		0			0
$217$	2.37690	+	10.6599i	0.161355	+	0.723644i
$218$	17.5820	−	14.0212i	1.19080	−	0.949635i
$219$		0			0
$220$	0.465394	+	0.0348765i	0.0313769	+	0.00235137i
$221$	17.0013	+	1.27407i	1.14363	+	0.0857033i
$222$		0			0
$223$	6.55082	−	5.22410i	0.438675	−	0.349832i	−0.379114	−	0.925350i	$-0.623771\pi$
$223$	6.55082	−	5.22410i	0.438675	−	0.349832i	0.817789	+	0.575518i	$0.195200\pi$
$224$	4.09402	+	1.99692i	0.273543	+	0.133425i
$225$		0			0
$226$	−0.652751	−	1.13060i	−0.0434203	−	0.0752062i
$227$	−6.90448	+	11.9589i	−0.458266	+	0.793740i	−0.998869	−	0.0475372i	$-0.984863\pi$
$227$	−6.90448	+	11.9589i	−0.458266	+	0.793740i	0.540603	+	0.841278i	$0.318196\pi$
$228$		0			0
$229$	0.551823	+	1.78897i	0.0364655	+	0.118218i	0.971976	−	0.235082i	$-0.0755357\pi$
$229$	0.551823	+	1.78897i	0.0364655	+	0.118218i	−0.935510	+	0.353300i	$0.885060\pi$
$230$	−2.71525	+	1.30760i	−0.179039	+	0.0862204i
$231$		0			0
$232$	15.0107	+	7.22880i	0.985504	+	0.474594i
$233$	−2.01150	+	13.3454i	−0.131778	+	0.874288i	0.821068	+	0.570831i	$0.193379\pi$
$233$	−2.01150	+	13.3454i	−0.131778	+	0.874288i	−0.952845	+	0.303457i	$0.901859\pi$
$234$		0			0
$235$	27.1198	+	25.1635i	1.76910	+	1.64148i
$236$	−1.96798	−	1.34175i	−0.128105	−	0.0873404i
$237$		0			0
$238$	−7.45555	+	18.7199i	−0.483272	+	1.21343i
$239$	−12.3845	−	2.82669i	−0.801088	−	0.182843i	−0.197671	−	0.980268i	$-0.563338\pi$
$239$	−12.3845	−	2.82669i	−0.801088	−	0.182843i	−0.603418	+	0.797425i	$0.706195\pi$
$240$		0			0
$241$	−4.34345	−	28.8169i	−0.279786	−	1.85626i	−0.481008	−	0.876716i	$-0.659729\pi$
$241$	−4.34345	−	28.8169i	−0.279786	−	1.85626i	0.201221	−	0.979546i	$-0.435509\pi$
$242$	−4.83201	+	15.6650i	−0.310614	+	1.00698i
$243$		0			0
$244$		−	1.32249i		−	0.0846634i
$245$	14.4081	+	18.4435i	0.920497	+	1.17831i
$246$		0			0
$247$	1.16200	+	15.5058i	0.0739361	+	0.986609i
$248$	10.1437	+	3.12893i	0.644127	+	0.198687i
$249$		0			0
$250$	4.07115	+	4.38766i	0.257482	+	0.277500i
$251$	4.18920	−	18.3541i	0.264420	−	1.15850i	−0.651980	−	0.758236i	$-0.726061\pi$
$251$	4.18920	−	18.3541i	0.264420	−	1.15850i	0.916400	−	0.400264i	$-0.131081\pi$
$252$		0			0
$253$	0.0600565	+	0.263125i	0.00377572	+	0.0165425i
$254$	18.7813	−	27.5471i	1.17844	−	1.72846i
$255$		0			0
$256$	5.95036	−	4.05689i	0.371897	−	0.253555i
$257$	18.4814	+	2.78563i	1.15284	+	0.173763i	0.697520	−	0.716565i	$-0.254287\pi$
$257$	18.4814	+	2.78563i	1.15284	+	0.173763i	0.455320	+	0.890328i	$0.349525\pi$
$258$		0			0
$259$	10.3634	+	15.3653i	0.643953	+	0.954754i
$260$	1.51391	+	3.14366i	0.0938886	+	0.194962i
$261$		0			0
$262$	1.57206	−	0.616987i	0.0971220	−	0.0381176i
$263$	−1.45415	−	0.839555i	−0.0896669	−	0.0517692i	0.454496	−	0.890749i	$-0.349819\pi$
$263$	−1.45415	−	0.839555i	−0.0896669	−	0.0517692i	−0.544163	+	0.838980i	$0.683153\pi$
$264$		0			0
$265$	−6.70656	−	5.34831i	−0.411981	−	0.328544i
$266$	−17.8960	−	4.17914i	−1.09727	−	0.256240i
$267$		0			0
$268$	1.46465	−	3.73187i	0.0894679	−	0.227960i
$269$	−1.27168	+	16.9694i	−0.0775356	+	1.03464i	0.813755	+	0.581208i	$0.197420\pi$
$269$	−1.27168	+	16.9694i	−0.0775356	+	1.03464i	−0.891291	+	0.453432i	$0.850199\pi$
$270$		0			0
$271$	−20.9283	−	8.21373i	−1.27130	−	0.498949i	−0.368748	−	0.929529i	$-0.620214\pi$
$271$	−20.9283	−	8.21373i	−1.27130	−	0.498949i	−0.902552	+	0.430580i	$0.858309\pi$
$272$	14.1300	+	17.7185i	0.856759	+	1.07434i
$273$		0			0
$274$	20.8742	−	26.1754i	1.26106	−	1.58131i
$275$	2.43347	−	1.40496i	0.146743	−	0.0847224i
$276$		0			0
$277$	8.53528	+	21.7475i	0.512835	+	1.30668i	0.919494	+	0.393103i	$0.128598\pi$
$277$	8.53528	+	21.7475i	0.512835	+	1.30668i	−0.406659	+	0.913580i	$0.633306\pi$
$278$	−7.84337	+	2.41936i	−0.470414	+	0.145104i
$279$		0			0
$280$	22.5102	−	3.27755i	1.34524	−	0.195871i
$281$	−0.344766	+	0.715914i	−0.0205670	+	0.0427078i	−0.910999	−	0.412408i	$-0.864688\pi$
$281$	−0.344766	+	0.715914i	−0.0205670	+	0.0427078i	0.890432	+	0.455116i	$0.150402\pi$
$282$		0			0
$283$	0.917602	+	1.34587i	0.0545457	+	0.0800039i	0.852543	−	0.522658i	$-0.175059\pi$
$283$	0.917602	+	1.34587i	0.0545457	+	0.0800039i	−0.797997	+	0.602661i	$0.794107\pi$
$284$	2.03220	−	2.19019i	0.120589	−	0.129964i
$285$		0			0
$286$	2.28971	−	0.522611i	0.135393	−	0.0309027i
$287$	10.8729	−	15.7771i	0.641805	−	0.931290i
$288$		0			0
$289$	−5.96921	+	5.53862i	−0.351130	+	0.325801i
$290$	−32.5338	+	4.90368i	−1.91045	+	0.287954i
$291$		0			0
$292$	−3.81165	+	0.285644i	−0.223060	+	0.0167160i
$293$	−10.2940			−0.601383			−0.300691	−	0.953721i	$-0.597217\pi$
$293$	−10.2940			−0.601383			−0.300691	+	0.953721i	$0.597217\pi$
$294$		0			0
$295$	−25.9459			−1.51063
$296$	17.9633	−	1.34616i	1.04410	−	0.0782441i
$297$		0			0
$298$	15.4522	−	2.32904i	0.895119	−	0.134917i
$299$	−1.47915	+	1.37245i	−0.0855416	+	0.0793710i
$300$		0			0
$301$	14.2457	−	8.12980i	0.821107	−	0.468594i
$302$	6.91324	−	1.57790i	0.397812	−	0.0907981i
$303$		0			0
$304$	−14.0587	+	15.1517i	−0.806321	+	0.869007i
$305$	−8.11520	−	11.9028i	−0.464675	−	0.681553i
$306$		0			0
$307$	−2.32561	+	4.82917i	−0.132729	+	0.275615i	−0.956732	−	0.290971i	$-0.906022\pi$
$307$	−2.32561	+	4.82917i	−0.132729	+	0.275615i	0.824003	+	0.566586i	$0.191736\pi$
$308$	−0.0294444	+	0.368135i	−0.00167775	+	0.0209764i
$309$		0			0
$310$	−20.0317	+	6.17896i	−1.13772	+	0.350941i
$311$	−2.85520	−	7.27493i	−0.161903	−	0.412523i	0.826783	−	0.562521i	$-0.190169\pi$
$311$	−2.85520	−	7.27493i	−0.161903	−	0.412523i	−0.988686	+	0.149998i	$0.952073\pi$
$312$		0			0
$313$	−27.8263	+	16.0655i	−1.57284	+	0.908078i	−0.577018	+	0.816732i	$0.695784\pi$
$313$	−27.8263	+	16.0655i	−1.57284	+	0.908078i	−0.995819	+	0.0913464i	$0.970883\pi$
$314$	11.9190	−	14.9460i	0.672631	−	0.843452i
$315$		0			0
$316$	2.46598	+	3.09225i	0.138722	+	0.173952i
$317$	0.420736	+	0.165127i	0.0236309	+	0.00927444i	0.377127	−	0.926162i	$-0.376912\pi$
$317$	0.420736	+	0.165127i	0.0236309	+	0.00927444i	−0.353496	+	0.935436i	$0.615007\pi$
$318$		0			0
$319$	−0.220190	+	2.93823i	−0.0123283	+	0.164509i
$320$	7.84735	−	19.9947i	0.438680	−	1.11774i
$321$		0			0
$322$	−1.02395	−	2.15381i	−0.0570625	−	0.120027i
$323$	−17.9284	−	14.2974i	−0.997562	−	0.795529i
$324$		0			0
$325$	18.1934	+	10.5040i	1.00919	+	0.582656i
$326$	−16.3931	+	6.43381i	−0.907928	+	0.356336i
$327$		0			0
$328$	−8.08033	−	16.7790i	−0.446161	−	0.926464i
$329$	−20.0198	+	21.3604i	−1.10373	+	1.17764i
$330$		0			0
$331$	−24.5446	−	3.69950i	−1.34909	−	0.203343i	−0.565566	−	0.824703i	$-0.691342\pi$
$331$	−24.5446	−	3.69950i	−1.34909	−	0.203343i	−0.783525	+	0.621360i	$0.786580\pi$
$332$	1.03362	−	0.704712i	0.0567274	−	0.0386761i
$333$		0			0
$334$	−13.7611	+	20.1838i	−0.752972	+	1.10441i
$335$	−9.71762	−	42.5757i	−0.530930	−	2.32616i
$336$		0			0
$337$	0.745035	−	3.26421i	0.0405847	−	0.177813i	−0.950573	−	0.310500i	$-0.899503\pi$
$337$	0.745035	−	3.26421i	0.0405847	−	0.177813i	0.991158	+	0.132687i	$0.0423606\pi$
$338$	−1.48705	−	1.60266i	−0.0808847	−	0.0871729i
$339$		0			0
$340$	−4.91709	−	1.51672i	−0.266667	−	0.0822558i
$341$	0.140294	+	1.87209i	0.00759733	+	0.101379i
$342$		0			0
$343$	−14.6517	+	11.3281i	−0.791120	+	0.611662i
$344$		−	15.9421i		−	0.859540i
$345$		0			0
$346$	1.68446	−	5.46087i	0.0905570	−	0.293578i
$347$	2.57224	+	17.0657i	0.138085	+	0.916134i	0.945376	+	0.325981i	$0.105694\pi$
$347$	2.57224	+	17.0657i	0.138085	+	0.916134i	−0.807291	+	0.590153i	$0.799067\pi$
$348$		0			0
$349$	−15.3411	−	3.50150i	−0.821190	−	0.187431i	−0.208771	−	0.977965i	$-0.566946\pi$
$349$	−15.3411	−	3.50150i	−0.821190	−	0.187431i	−0.612419	+	0.790533i	$0.709803\pi$
$350$	−18.2854	+	16.7966i	−0.977397	+	0.897815i
$351$		0			0
$352$	0.646923	+	0.441065i	0.0344811	+	0.0235088i
$353$	−1.02165	−	0.947953i	−0.0543770	−	0.0504545i	0.652516	−	0.757775i	$-0.273713\pi$
$353$	−1.02165	−	0.947953i	−0.0543770	−	0.0504545i	−0.706893	+	0.707320i	$0.749904\pi$
$354$		0			0
$355$	4.85076	−	32.1827i	0.257451	−	1.70808i
$356$	−4.28214	−	2.06217i	−0.226953	−	0.109295i
$357$		0			0
$358$	0.771487	−	0.371528i	0.0407743	−	0.0196359i
$359$	−2.83914	−	9.20425i	−0.149844	−	0.485782i	0.849266	−	0.527965i	$-0.177045\pi$
$359$	−2.83914	−	9.20425i	−0.149844	−	0.485782i	−0.999110	+	0.0421834i	$0.986569\pi$
$360$		0			0
$361$	0.957064	−	1.65768i	0.0503718	−	0.0872465i
$362$	−0.202186	−	0.350196i	−0.0106266	−	0.0184059i
$363$		0			0
$364$	−2.49363	+	1.18551i	−0.130702	+	0.0621374i
$365$	−32.5534	+	25.9604i	−1.70392	+	1.35883i
$366$		0			0
$367$	−6.56616	−	0.492066i	−0.342751	−	0.0256856i	−0.0977571	−	0.995210i	$-0.531167\pi$
$367$	−6.56616	−	0.492066i	−0.342751	−	0.0256856i	−0.244994	+	0.969525i	$0.578786\pi$
$368$	−2.67472	−	0.200442i	−0.139429	−	0.0104488i
$369$		0			0
$370$	−27.8122	+	22.1795i	−1.44589	+	1.15306i
$371$	4.25879	−	5.28578i	0.221106	−	0.274424i
$372$		0			0
$373$	−14.8418	−	25.7067i	−0.768477	−	1.33104i	−0.938388	−	0.345582i	$-0.887681\pi$
$373$	−14.8418	−	25.7067i	−0.768477	−	1.33104i	0.169911	−	0.985459i	$-0.445652\pi$
$374$	−1.73179	+	2.99956i	−0.0895490	+	0.155103i
$375$		0			0
$376$	8.38706	+	27.1902i	0.432530	+	1.40223i
$377$	−19.8472	+	9.55793i	−1.02219	+	0.492258i
$378$		0			0
$379$	−13.1813	−	6.34776i	−0.677076	−	0.326063i	0.0635515	−	0.997979i	$-0.479757\pi$
$379$	−13.1813	−	6.34776i	−0.677076	−	0.326063i	−0.740627	+	0.671916i	$0.765472\pi$
$380$	0.699464	−	4.64064i	0.0358818	−	0.238060i
$381$		0			0
$382$	24.1441	+	22.4024i	1.23532	+	1.14621i
$383$	16.6811	+	11.3730i	0.852362	+	0.581131i	0.908780	−	0.417277i	$-0.137015\pi$
$383$	16.6811	+	11.3730i	0.852362	+	0.581131i	−0.0564173	+	0.998407i	$0.517968\pi$
$384$		0			0
$385$	1.99398	+	3.49402i	0.101623	+	0.178072i
$386$	14.7275	+	3.36146i	0.749611	+	0.171094i
$387$		0			0
$388$	0.307991	+	2.04339i	0.0156359	+	0.103737i
$389$	−7.59636	+	24.6268i	−0.385151	+	1.24863i	0.530855	+	0.847463i	$0.321871\pi$
$389$	−7.59636	+	24.6268i	−0.385151	+	1.24863i	−0.916005	+	0.401166i	$0.868605\pi$
$390$		0			0
$391$		−	2.97575i		−	0.150490i
$392$	2.50427	+	17.8257i	0.126485	+	0.900332i
$393$		0			0
$394$	−1.96757	−	26.2554i	−0.0991248	−	1.32273i
$395$	41.1697	+	12.6992i	2.07147	+	0.638965i
$396$		0			0
$397$	−23.9107	−	25.7696i	−1.20004	−	1.29334i	−0.945251	−	0.326344i	$-0.894183\pi$
$397$	−23.9107	−	25.7696i	−1.20004	−	1.29334i	−0.254793	−	0.966996i	$-0.582007\pi$
$398$	−3.06825	+	13.4429i	−0.153798	+	0.673832i
$399$		0			0
$400$	6.21398	+	27.2252i	0.310699	+	1.36126i
$401$	1.68881	−	2.47703i	0.0843351	−	0.123697i	−0.781753	−	0.623588i	$-0.785674\pi$
$401$	1.68881	−	2.47703i	0.0843351	−	0.123697i	0.866088	+	0.499891i	$0.166627\pi$
$402$		0			0
$403$	−11.5968	+	7.90655i	−0.577677	+	0.393853i
$404$	−1.03354	−	0.155781i	−0.0514204	−	0.00775038i
$405$		0			0
$406$	−3.75129	−	25.7639i	−0.186173	−	1.27864i
$407$	1.38224	+	2.87026i	0.0685152	+	0.142273i
$408$		0			0
$409$	35.5547	−	13.9542i	1.75807	−	0.689991i	0.758818	−	0.651303i	$-0.225777\pi$
$409$	35.5547	−	13.9542i	1.75807	−	0.689991i	0.999251	−	0.0386882i	$-0.0123179\pi$
$410$	31.8498	+	18.3885i	1.57295	+	0.908142i
$411$		0			0
$412$	1.44030	+	1.14860i	0.0709584	+	0.0565874i
$413$	0.102926	−	20.5314i	0.00506466	−	1.01028i
$414$		0			0
$415$	4.97861	−	12.6853i	0.244390	−	0.622697i
$416$	−0.437453	+	5.83741i	−0.0214479	+	0.286202i
$417$		0			0
$418$	−2.94055	−	1.15408i	−0.143827	−	0.0564480i
$419$	9.91799	+	12.4368i	0.484526	+	0.607576i	0.962661	−	0.270710i	$-0.0872585\pi$
$419$	9.91799	+	12.4368i	0.484526	+	0.607576i	−0.478135	+	0.878286i	$0.658687\pi$
$420$		0			0
$421$	19.8667	−	24.9121i	0.968244	−	1.21414i	−0.00855054	−	0.999963i	$-0.502722\pi$
$421$	19.8667	−	24.9121i	0.968244	−	1.21414i	0.976795	−	0.214177i	$-0.0687068\pi$
$422$	7.91786	−	4.57138i	0.385435	−	0.222531i
$423$		0			0
$424$	−2.41036	−	6.14151i	−0.117058	−	0.298258i
$425$	−29.6050	+	9.13195i	−1.43606	+	0.442965i
$426$		0			0
$427$	9.45105	−	6.37445i	0.457368	−	0.308481i
$428$	−1.85484	+	3.85161i	−0.0896569	+	0.186174i
$429$		0			0
$430$	17.7346	+	26.0119i	0.855238	+	1.25440i
$431$	−23.9682	+	25.8316i	−1.15451	+	1.24426i	−0.189547	+	0.981872i	$0.560702\pi$
$431$	−23.9682	+	25.8316i	−1.15451	+	1.24426i	−0.964961	+	0.262393i	$0.915488\pi$
$432$		0			0
$433$	13.9280	−	3.17899i	0.669339	−	0.152772i	0.125670	−	0.992072i	$-0.459892\pi$
$433$	13.9280	−	3.17899i	0.669339	−	0.152772i	0.543669	+	0.839300i	$0.317035\pi$
$434$	−4.81003	−	15.8759i	−0.230889	−	0.762066i
$435$		0			0
$436$	−3.33130	+	3.09100i	−0.159541	+	0.148032i
$437$	2.68368	−	0.404500i	0.128378	−	0.0193498i
$438$		0			0
$439$	33.8648	−	2.53782i	1.61628	−	0.121123i	0.764358	−	0.644792i	$-0.223056\pi$
$439$	33.8648	−	2.53782i	1.61628	−	0.121123i	0.851922	+	0.523668i	$0.175437\pi$
$440$	3.91010			0.186406
$441$		0			0
$442$	−25.8950			−1.23170
$443$	−20.0957	+	1.50596i	−0.954775	+	0.0715505i	−0.542998	−	0.839734i	$-0.682711\pi$
$443$	−20.0957	+	1.50596i	−0.954775	+	0.0715505i	−0.411777	+	0.911284i	$0.635092\pi$
$444$		0			0
$445$	−51.1949	+	7.71639i	−2.42687	+	0.365792i
$446$	−9.32898	+	8.65603i	−0.441740	+	0.409875i
$447$		0			0
$448$	15.7910	+	6.28904i	0.746053	+	0.297129i
$449$	15.7616	−	3.59749i	0.743837	−	0.169776i	0.166226	−	0.986088i	$-0.446842\pi$
$449$	15.7616	−	3.59749i	0.743837	−	0.169776i	0.577612	+	0.816312i	$0.303985\pi$
$450$		0			0
$451$	2.24018	−	2.41434i	0.105486	−	0.113687i
$452$	0.148613	+	0.217975i	0.00699017	+	0.0102527i
$453$		0			0
$454$	9.10021	−	18.8968i	0.427094	−	0.886870i
$455$	−15.1689	+	25.9717i	−0.711127	+	1.21757i
$456$		0			0
$457$	24.5828	−	7.58280i	1.14994	−	0.354708i	0.339541	−	0.940591i	$-0.389728\pi$
$457$	24.5828	−	7.58280i	1.14994	−	0.354708i	0.810396	+	0.585883i	$0.199252\pi$
$458$	−1.03885	−	2.64696i	−0.0485425	−	0.123684i
$459$		0			0
$460$	0.527419	−	0.304505i	0.0245910	−	0.0141976i
$461$	−13.3218	+	16.7049i	−0.620456	+	0.778027i	−0.988409	−	0.151818i	$-0.951487\pi$
$461$	−13.3218	+	16.7049i	−0.620456	+	0.778027i	0.367953	+	0.929844i	$0.380059\pi$
$462$		0			0
$463$	8.63070	+	10.8226i	0.401102	+	0.502967i	0.940833	−	0.338871i	$-0.110045\pi$
$463$	8.63070	+	10.8226i	0.401102	+	0.502967i	−0.539730	+	0.841838i	$0.681474\pi$
$464$	−27.2582	−	10.6980i	−1.26543	−	0.496644i
$465$		0			0
$466$	1.53187	−	20.4414i	0.0709627	−	0.946932i
$467$	−2.26608	+	5.77389i	−0.104862	+	0.267184i	−0.973669	−	0.227967i	$-0.926792\pi$
$467$	−2.26608	+	5.77389i	−0.104862	+	0.267184i	0.868807	+	0.495151i	$0.164887\pi$
$468$		0			0
$469$	33.7293	−	7.52080i	1.55747	−	0.347278i
$470$	−43.9321	−	35.0347i	−2.02644	−	1.61603i
$471$		0			0
$472$	−17.2821	−	9.97783i	−0.795474	−	0.459267i
$473$	2.62449	−	1.03004i	0.120674	−	0.0473612i
$474$		0			0
$475$	−12.2599	−	25.4579i	−0.562523	−	1.16809i
$476$	1.21971	−	3.88495i	0.0559053	−	0.178066i
$477$		0			0
$478$	19.0786	+	2.87563i	0.872634	+	0.131528i
$479$	21.8347	−	14.8866i	0.997651	−	0.680187i	0.0497530	−	0.998762i	$-0.484157\pi$
$479$	21.8347	−	14.8866i	0.997651	−	0.680187i	0.947898	+	0.318575i	$0.103204\pi$
$480$		0			0
$481$	−13.4170	+	19.6791i	−0.611762	+	0.897291i
$482$	9.84950	+	43.1535i	0.448632	+	1.96559i
$483$		0			0
$484$	0.737160	−	3.22971i	0.0335073	−	0.146805i
$485$	15.3109	+	16.5013i	0.695233	+	0.749283i
$486$		0			0
$487$	25.4499	+	7.85026i	1.15325	+	0.355729i	0.811665	−	0.584123i	$-0.198561\pi$
$487$	25.4499	+	7.85026i	1.15325	+	0.355729i	0.341581	+	0.939852i	$0.389038\pi$
$488$	−0.828012	−	11.0491i	−0.0374823	−	0.500167i
$489$		0			0
$490$	−23.9160	−	26.2993i	−1.08042	−	1.18808i
$491$			28.3337i			1.27868i	0.768924	+	0.639340i	$0.220792\pi$
$491$			28.3337i			1.27868i	−0.768924	+	0.639340i	$0.779208\pi$
$492$		0			0
$493$	9.57570	−	31.0436i	0.431268	−	1.39814i
$494$	−3.51995	−	23.3533i	−0.158370	−	1.05072i
$495$		0			0
$496$	−18.1895	−	4.15163i	−0.816731	−	0.186414i
$497$	25.4474	+	3.96614i	1.14147	+	0.177906i
$498$		0			0
$499$	16.2203	+	11.0588i	0.726120	+	0.495060i	0.869082	−	0.494668i	$-0.164710\pi$
$499$	16.2203	+	11.0588i	0.726120	+	0.495060i	−0.142962	+	0.989728i	$0.545663\pi$
$500$	−0.886659	−	0.822699i	−0.0396526	−	0.0367922i
$501$		0			0
$502$	−4.26174	+	28.2748i	−0.190211	+	1.26197i
$503$	8.63742	+	4.15956i	0.385124	+	0.185466i	0.616420	−	0.787418i	$-0.288582\pi$
$503$	8.63742	+	4.15956i	0.385124	+	0.185466i	−0.231296	+	0.972883i	$0.574297\pi$
$504$		0			0
$505$	−10.2581	+	4.94005i	−0.456480	+	0.219829i
$506$	−0.120828	−	0.391715i	−0.00537147	−	0.0174139i
$507$		0			0
$508$	−3.36871	+	5.83478i	−0.149462	+	0.258876i
$509$	−5.34547	−	9.25862i	−0.236934	−	0.410381i	0.722899	−	0.690953i	$-0.242809\pi$
$509$	−5.34547	−	9.25862i	−0.236934	−	0.410381i	−0.959833	+	0.280572i	$0.909476\pi$
$510$		0			0
$511$	−20.4137	−	25.8629i	−0.903050	−	1.14411i
$512$	12.0899	−	9.64139i	0.534304	−	0.426093i
$513$		0			0
$514$	−28.3084	−	2.12142i	−1.24863	−	0.0935717i
$515$	20.0113	+	1.49964i	0.881805	+	0.0660821i
$516$		0			0
$517$	−3.93433	+	3.13752i	−0.173032	+	0.137988i
$518$	−17.4406	−	22.0962i	−0.766297	−	0.970850i
$519$		0			0
$520$	14.6166	+	25.3167i	0.640980	+	1.11021i
$521$	14.0613	−	24.3549i	0.616037	−	1.06701i	−0.374165	−	0.927362i	$-0.622071\pi$
$521$	14.0613	−	24.3549i	0.616037	−	1.06701i	0.990202	−	0.139645i	$-0.0445961\pi$
$522$		0			0
$523$	−8.05898	−	26.1266i	−0.352395	−	1.14244i	−0.942245	−	0.334923i	$-0.891290\pi$
$523$	−8.05898	−	26.1266i	−0.352395	−	1.14244i	0.589851	−	0.807512i	$-0.299187\pi$
$524$	−0.307476	+	0.148073i	−0.0134322	+	0.00646859i
$525$		0			0
$526$	2.29777	+	1.10655i	0.100188	+	0.0482478i
$527$	3.08503	−	20.4678i	0.134386	−	0.891593i
$528$		0			0
$529$	−16.6020	−	15.4044i	−0.721827	−	0.669758i
$530$	10.7649	+	7.33938i	0.467597	+	0.318802i
$531$		0			0
$532$	3.66943	+	0.571905i	0.159090	+	0.0247952i
$533$	24.0063	+	5.47929i	1.03983	+	0.237334i
$534$		0			0
$535$	6.94056	+	46.0476i	0.300067	+	1.99081i
$536$	9.90029	−	32.0959i	0.427627	−	1.38633i
$537$		0			0
$538$		−	25.8463i		−	1.11431i
$539$	−2.77277	+	1.56401i	−0.119432	+	0.0673665i
$540$		0			0
$541$	2.31494	+	30.8907i	0.0995268	+	1.32809i	0.793711	+	0.608296i	$0.208146\pi$
$541$	2.31494	+	30.8907i	0.0995268	+	1.32809i	−0.694184	+	0.719798i	$0.744235\pi$
$542$	32.6305	+	10.0652i	1.40160	+	0.432336i
$543$		0			0
$544$	−5.87183	−	6.32833i	−0.251753	−	0.271325i
$545$	−11.0155	+	48.2620i	−0.471852	+	2.06732i
$546$		0			0
$547$	7.22069	+	31.6359i	0.308734	+	1.35265i	0.856554	+	0.516057i	$0.172601\pi$
$547$	7.22069	+	31.6359i	0.308734	+	1.35265i	−0.547820	+	0.836596i	$0.684542\pi$
$548$	−3.81118	+	5.58998i	−0.162806	+	0.238792i
$549$		0			0
$550$	−3.52629	+	2.40418i	−0.150361	+	0.102515i
$551$	29.2983	+	4.41601i	1.24815	+	0.188128i
$552$		0			0
$553$	−10.2124	+	32.5278i	−0.434273	+	1.38322i
$554$	−15.3961	−	31.9703i	−0.654117	−	1.35829i
$555$		0			0
$556$	1.54402	−	0.605985i	0.0654812	−	0.0256995i
$557$	8.45989	+	4.88432i	0.358457	+	0.206955i	0.668404	−	0.743799i	$-0.266978\pi$
$557$	8.45989	+	4.88432i	0.358457	+	0.206955i	−0.309947	+	0.950754i	$0.600311\pi$
$558$		0			0
$559$	16.4800	+	13.1423i	0.697029	+	0.555862i
$560$	−39.0223	+	8.70101i	−1.64899	+	0.367685i
$561$		0			0
$562$	0.440927	−	1.12346i	0.0185994	−	0.0473905i
$563$	0.336953	−	4.49632i	0.0142009	−	0.189497i	−0.985592	−	0.169141i	$-0.945901\pi$
$563$	0.336953	−	4.49632i	0.0142009	−	0.189497i	0.999793	−	0.0203566i	$-0.00648017\pi$
$564$		0			0
$565$	2.67513	+	1.04991i	0.112544	+	0.0441702i
$566$	−1.54257	−	1.93432i	−0.0648392	−	0.0813057i
$567$		0			0
$568$	15.6073	−	19.5709i	0.654866	−	0.821176i
$569$	1.49353	−	0.862289i	0.0626120	−	0.0361490i	−0.468367	−	0.883534i	$-0.655158\pi$
$569$	1.49353	−	0.862289i	0.0626120	−	0.0361490i	0.530979	+	0.847385i	$0.321824\pi$
$570$		0			0
$571$	7.34879	+	18.7244i	0.307537	+	0.783593i	0.998175	+	0.0603913i	$0.0192349\pi$
$571$	7.34879	+	18.7244i	0.307537	+	0.783593i	−0.690637	+	0.723201i	$0.742670\pi$
$572$	−0.453519	+	0.139892i	−0.0189626	+	0.00584919i
$573$		0			0
$574$	−14.6774	+	25.1302i	−0.612623	+	1.04892i
$575$	1.59095	−	3.30364i	0.0663471	−	0.137771i
$576$		0			0
$577$	−20.6629	−	30.3069i	−0.860208	−	1.26169i	−0.963680	−	0.267061i	$-0.913947\pi$
$577$	−20.6629	−	30.3069i	−0.860208	−	1.26169i	0.103471	−	0.994632i	$-0.467005\pi$
$578$	8.41238	−	9.06639i	0.349909	−	0.377112i
$579$		0			0
$580$	6.48201	−	1.47948i	0.269151	−	0.0614319i
$581$	10.0183	+	3.98997i	0.415629	+	0.165532i
$582$		0			0
$583$	0.855318	−	0.793619i	0.0354237	−	0.0328684i
$584$	−31.6666	+	4.77298i	−1.31037	+	0.197507i
$585$		0			0
$586$	15.5914	−	1.16842i	0.644076	−	0.0482668i
$587$	2.20136			0.0908599			0.0454299	−	0.998968i	$-0.485534\pi$
$587$	2.20136			0.0908599			0.0454299	+	0.998968i	$0.485534\pi$
$588$		0			0
$589$	18.8783			0.777865
$590$	39.2980	−	2.94498i	1.61787	−	0.121243i
$591$		0			0
$592$	−31.3067	+	4.71873i	−1.28670	+	0.193939i
$593$	−18.3140	+	16.9929i	−0.752065	+	0.697815i	−0.959898	−	0.280350i	$-0.909550\pi$
$593$	−18.3140	+	16.9929i	−0.752065	+	0.697815i	0.207833	+	0.978164i	$0.433359\pi$
$594$		0			0
$595$	−12.8615	−	42.4504i	−0.527270	−	1.74029i
$596$	−3.07867	+	0.702687i	−0.126107	+	0.0287832i
$597$		0			0
$598$	2.08456	−	2.24662i	0.0852441	−	0.0918713i
$599$	−0.00222033	−	0.00325663i	−9.07203e−5	−	0.000133062i	0.826193	−	0.563387i	$-0.190502\pi$
$599$	−0.00222033	−	0.00325663i	−9.07203e−5	−	0.000133062i	−0.826284	+	0.563254i	$0.809549\pi$
$600$		0			0
$601$	11.8282	−	24.5616i	0.482483	−	1.00189i	−0.507625	−	0.861578i	$-0.669476\pi$
$601$	11.8282	−	24.5616i	0.482483	−	1.00189i	0.990108	−	0.140309i	$-0.0448094\pi$
$602$	−20.6539	+	13.9304i	−0.841790	+	0.567762i
$603$		0			0
$604$	−1.36930	+	0.422372i	−0.0557159	+	0.0171861i
$605$	−13.1839	−	33.5919i	−0.536000	−	1.36571i
$606$		0			0
$607$	−18.0984	+	10.4491i	−0.734591	+	0.424116i	−0.820099	−	0.572221i	$-0.806082\pi$
$607$	−18.0984	+	10.4491i	−0.734591	+	0.424116i	0.0855083	+	0.996337i	$0.472749\pi$
$608$	4.90903	−	6.15573i	0.199087	−	0.249648i
$609$		0			0
$610$	13.6424	+	17.1070i	0.552364	+	0.692643i
$611$	−35.0217	−	13.7450i	−1.41683	−	0.556063i
$612$		0			0
$613$	0.0253873	−	0.338770i	0.00102538	−	0.0136828i	−0.996668	−	0.0815697i	$-0.974007\pi$
$613$	0.0253873	−	0.338770i	0.00102538	−	0.0136828i	0.997693	+	0.0678869i	$0.0216257\pi$
$614$	2.97426	−	7.57829i	0.120031	−	0.305835i
$615$		0			0
$616$	−0.0155111	+	3.09411i	−0.000624962	+	0.124665i
$617$	−30.4007	−	24.2438i	−1.22389	−	0.976017i	−0.999999	−	0.00140190i	$-0.999554\pi$
$617$	−30.4007	−	24.2438i	−1.22389	−	0.976017i	−0.223887	−	0.974615i	$-0.571875\pi$
$618$		0			0
$619$	23.2444	+	13.4201i	0.934270	+	0.539401i	0.888160	−	0.459535i	$-0.151984\pi$
$619$	23.2444	+	13.4201i	0.934270	+	0.539401i	0.0461107	+	0.998936i	$0.485317\pi$
$620$	3.94338	−	1.54766i	0.158370	−	0.0621557i
$621$		0			0
$622$	5.15025	+	10.6946i	0.206506	+	0.428815i
$623$	−5.90300	−	40.5418i	−0.236499	−	1.62427i
$624$		0			0
$625$	17.5196	+	2.64066i	0.700785	+	0.105626i
$626$	40.3226	−	27.4915i	1.61161	−	1.09878i
$627$		0			0
$628$	−2.17616	+	3.19185i	−0.0868384	+	0.127369i
$629$	−7.81609	−	34.2445i	−0.311648	−	1.36542i
$630$		0			0
$631$	4.74242	−	20.7779i	0.188793	−	0.827155i	−0.788461	−	0.615084i	$-0.789122\pi$
$631$	4.74242	−	20.7779i	0.188793	−	0.827155i	0.977254	−	0.212071i	$-0.0680209\pi$
$632$	22.5388	+	24.2910i	0.896545	+	0.966245i
$633$		0			0
$634$	−0.655994	−	0.202347i	−0.0260529	−	0.00803624i
$635$	5.48457	+	73.1865i	0.217648	+	2.90432i
$636$		0			0
$637$	−20.4916	−	12.1064i	−0.811906	−	0.479671i
$638$		−	4.47527i		−	0.177177i
$639$		0			0
$640$	−13.0096	+	42.1760i	−0.514249	+	1.66715i
$641$	−1.58922	−	10.5438i	−0.0627704	−	0.416454i	−0.998043	−	0.0625269i	$-0.980084\pi$
$641$	−1.58922	−	10.5438i	−0.0627704	−	0.416454i	0.935273	−	0.353927i	$-0.115154\pi$
$642$		0			0
$643$	12.8477	+	2.93240i	0.506663	+	0.115642i	0.468209	−	0.883618i	$-0.344900\pi$
$643$	12.8477	+	2.93240i	0.506663	+	0.115642i	0.0384541	+	0.999260i	$0.487757\pi$
$644$	0.238867	+	0.418562i	0.00941268	+	0.0164936i
$645$		0			0
$646$	28.7774	+	19.6201i	1.13223	+	0.771942i
$647$	7.12315	+	6.60932i	0.280040	+	0.259839i	0.807670	−	0.589635i	$-0.200729\pi$
$647$	7.12315	+	6.60932i	0.280040	+	0.259839i	−0.527629	+	0.849475i	$0.676919\pi$
$648$		0			0
$649$	0.525998	−	3.48977i	0.0206472	−	0.136986i
$650$	−28.7482	−	13.8444i	−1.12760	−	0.543022i
$651$		0			0
$652$	3.20630	−	1.54407i	0.125568	−	0.0604705i
$653$	−10.6920	−	34.6625i	−0.418408	−	1.35645i	−0.882355	−	0.470584i	$-0.844043\pi$
$653$	−10.6920	−	34.6625i	−0.418408	−	1.35645i	0.463947	−	0.885863i	$-0.346433\pi$
$654$		0			0
$655$	−1.85877	+	3.21948i	−0.0726280	+	0.125795i
$656$	16.3659	+	28.3465i	0.638980	+	1.10675i
$657$		0			0
$658$	27.8977	−	34.6251i	1.08757	−	1.34983i
$659$	4.94415	−	3.94283i	0.192597	−	0.153591i	−0.522444	−	0.852674i	$-0.674980\pi$
$659$	4.94415	−	3.94283i	0.192597	−	0.153591i	0.715041	+	0.699083i	$0.246408\pi$
$660$		0			0
$661$	−5.09530	−	0.381840i	−0.198184	−	0.0148519i	−0.0247319	−	0.999694i	$-0.507873\pi$
$661$	−5.09530	−	0.381840i	−0.198184	−	0.0148519i	−0.173452	+	0.984842i	$0.555492\pi$
$662$	37.5954	+	2.81738i	1.46119	+	0.109501i
$663$		0			0
$664$	8.19446	−	6.53486i	0.318007	−	0.253602i
$665$	36.5355	−	17.3695i	1.41679	−	0.673560i
$666$		0			0
$667$	1.92247	+	3.32981i	0.0744383	+	0.128931i
$668$	2.46826	−	4.27516i	0.0954999	−	0.165411i
$669$		0			0
$670$	19.5510	+	63.3826i	0.755319	+	2.44868i
$671$	1.76547	−	0.850204i	0.0681551	−	0.0328218i
$672$		0			0
$673$	−16.7480	−	8.06542i	−0.645588	−	0.310899i	0.0822868	−	0.996609i	$-0.473778\pi$
$673$	−16.7480	−	8.06542i	−0.645588	−	0.310899i	−0.727875	+	0.685710i	$0.759492\pi$
$674$	−0.757936	+	5.02858i	−0.0291946	+	0.193694i
$675$		0			0
$676$	0.323865	+	0.300503i	0.0124564	+	0.0115578i
$677$	−2.75285	−	1.87686i	−0.105801	−	0.0721338i	0.509264	−	0.860610i	$-0.329918\pi$
$677$	−2.75285	−	1.87686i	−0.105801	−	0.0721338i	−0.615065	+	0.788477i	$0.710870\pi$
$678$		0			0
$679$	−13.1184	+	12.0503i	−0.503438	+	0.462448i
$680$	−42.0308	−	9.59325i	−1.61181	−	0.367884i
$681$		0			0
$682$	−0.424981	−	2.81956i	−0.0162734	−	0.107967i
$683$	7.47571	−	24.2357i	0.286050	−	0.927352i	−0.692513	−	0.721405i	$-0.743497\pi$
$683$	7.47571	−	24.2357i	0.286050	−	0.927352i	0.978563	−	0.205946i	$-0.0660273\pi$
$684$		0			0
$685$			73.6983i			2.81587i
$686$	20.9059	−	18.8208i	0.798191	−	0.718580i
$687$		0			0
$688$	2.09389	+	27.9411i	0.0798289	+	1.06524i
$689$	8.33577	+	2.57124i	0.317568	+	0.0979566i
$690$		0			0
$691$	0.0258112	+	0.0278179i	0.000981905	+	0.00105824i	0.733543	−	0.679643i	$-0.237865\pi$
$691$	0.0258112	+	0.0278179i	0.000981905	+	0.00105824i	−0.732561	+	0.680702i	$0.761675\pi$
$692$	−0.256977	+	1.12589i	−0.00976878	+	0.0427998i
$693$		0			0
$694$	−5.83297	−	25.5559i	−0.221417	−	0.970089i
$695$	10.1782	−	14.9287i	0.386082	−	0.566278i
$696$		0			0
$697$	−30.0039	+	20.4563i	−1.13648	+	0.774838i
$698$	23.6332	+	3.56214i	0.894531	+	0.134829i
$699$		0			0
$700$	3.43114	−	3.66091i	0.129685	−	0.138369i
$701$	−10.1880	−	21.1557i	−0.384797	−	0.799038i	−0.999944	−	0.0106259i	$-0.996618\pi$
$701$	−10.1880	−	21.1557i	−0.384797	−	0.799038i	0.615147	−	0.788412i	$-0.289097\pi$
$702$		0			0
$703$	29.8209	−	11.7038i	1.12472	−	0.441419i
$704$	2.53024	+	1.46083i	0.0953619	+	0.0550572i
$705$		0			0
$706$	1.65500	+	1.31982i	0.0622868	+	0.0496721i
$707$	−3.86843	−	8.13698i	−0.145487	−	0.306023i
$708$		0			0
$709$	−9.12235	+	23.2434i	−0.342597	+	0.872923i	0.650910	+	0.759155i	$0.274387\pi$
$709$	−9.12235	+	23.2434i	−0.342597	+	0.872923i	−0.993507	+	0.113769i	$0.963708\pi$
$710$	−3.69414	+	49.2948i	−0.138638	+	1.85000i
$711$		0			0
$712$	−37.0674	−	14.5479i	−1.38916	−	0.545206i
$713$	1.52743	+	1.91533i	0.0572025	+	0.0717297i
$714$		0			0
$715$	−3.22340	+	4.04202i	−0.120548	+	0.151163i
$716$	−0.149856	+	0.0865193i	−0.00560037	+	0.00323338i
$717$		0			0
$718$	5.34491	+	13.6186i	0.199470	+	0.508242i
$719$	−29.0552	+	8.96234i	−1.08358	+	0.334239i	−0.784588	−	0.620018i	$-0.787125\pi$
$719$	−29.0552	+	8.96234i	−1.08358	+	0.334239i	−0.298988	+	0.954257i	$0.596649\pi$
$720$		0			0
$721$	−1.26607	+	15.8293i	−0.0471510	+	0.589514i
$722$	−1.26143	+	2.61938i	−0.0469454	+	0.0974832i
$723$		0			0
$724$	0.0460320	+	0.0675166i	0.00171077	+	0.00250923i
$725$	27.2279	−	29.3447i	1.01122	−	1.08983i
$726$		0			0
$727$	4.44453	−	1.01443i	0.164838	−	0.0376233i	−0.139305	−	0.990250i	$-0.544487\pi$
$727$	4.44453	−	1.01443i	0.164838	−	0.0376233i	0.304144	+	0.952626i	$0.401630\pi$
$728$	−20.0914	+	11.4659i	−0.744638	+	0.424954i
$729$		0			0
$730$	46.3591	−	43.0149i	1.71583	−	1.59205i
$731$	−30.7386	+	4.63310i	−1.13691	+	0.171361i
$732$		0			0
$733$	9.60481	−	0.719781i	0.354762	−	0.0265857i	0.103843	−	0.994594i	$-0.466886\pi$
$733$	9.60481	−	0.719781i	0.354762	−	0.0265857i	0.250919	+	0.968008i	$0.419267\pi$
$734$	10.0010			0.369145
$735$		0			0
$736$	1.02173			0.0376614
$737$	5.92351	−	0.443906i	0.218195	−	0.0163515i
$738$		0			0
$739$	−19.2401	+	2.89998i	−0.707760	+	0.106678i	−0.493051	−	0.870000i	$-0.664118\pi$
$739$	−19.2401	+	2.89998i	−0.707760	+	0.106678i	−0.214709	+	0.976678i	$0.568880\pi$
$740$	5.26964	−	4.88952i	0.193716	−	0.179742i
$741$		0			0
$742$	−5.85046	+	8.48930i	−0.214777	+	0.311652i
$743$	19.2649	−	4.39708i	0.706759	−	0.161313i	0.145991	−	0.989286i	$-0.453363\pi$
$743$	19.2649	−	4.39708i	0.706759	−	0.161313i	0.560768	+	0.827973i	$0.310506\pi$
$744$		0			0
$745$	−23.3972	+	25.2162i	−0.857206	+	0.923849i
$746$	25.3973	+	37.2510i	0.929862	+	1.36386i
$747$		0			0
$748$	0.303685	−	0.630609i	0.0111038	−	0.0230574i
$749$	−36.4657	+	5.30950i	−1.33243	+	0.194005i
$750$		0			0
$751$	20.5569	−	6.34095i	0.750130	−	0.231385i	0.103964	−	0.994581i	$-0.466847\pi$
$751$	20.5569	−	6.34095i	0.750130	−	0.231385i	0.646167	+	0.763196i	$0.276371\pi$
$752$	−18.2709	−	46.5535i	−0.666272	−	1.69763i
$753$		0			0
$754$	28.9760	−	16.7293i	1.05524	−	0.609245i
$755$	−9.73231	+	12.2039i	−0.354195	+	0.444147i
$756$		0			0
$757$	−5.60578	−	7.02942i	−0.203746	−	0.255489i	0.669452	−	0.742855i	$-0.266529\pi$
$757$	−5.60578	−	7.02942i	−0.203746	−	0.255489i	−0.873197	+	0.487367i	$0.837958\pi$
$758$	20.6850	+	8.11826i	0.751313	+	0.294868i
$759$		0			0
$760$	2.93834	−	39.2094i	0.106585	−	1.42228i
$761$	1.93240	−	4.92367i	0.0700494	−	0.178483i	−0.891561	−	0.452900i	$-0.850390\pi$
$761$	1.93240	−	4.92367i	0.0700494	−	0.178483i	0.961611	+	0.274417i	$0.0884848\pi$
$762$		0			0
$763$	−38.1467	−	8.90816i	−1.38100	−	0.322497i
$764$	−5.20371	−	4.14982i	−0.188264	−	0.150135i
$765$		0			0
$766$	−26.5562	−	15.3322i	−0.959515	−	0.553976i
$767$	24.5615	−	9.63968i	0.886864	−	0.348069i
$768$		0			0
$769$	−6.16694	−	12.8058i	−0.222385	−	0.461788i	0.759688	−	0.650288i	$-0.225352\pi$
$769$	−6.16694	−	12.8058i	−0.222385	−	0.461788i	−0.982073	+	0.188500i	$0.939637\pi$
$770$	−3.41670	−	5.06575i	−0.123129	−	0.182557i
$771$		0			0
$772$	−3.01859	−	0.454979i	−0.108641	−	0.0163750i
$773$	5.49361	−	3.74548i	0.197591	−	0.134716i	−0.460483	−	0.887669i	$-0.652324\pi$
$773$	5.49361	−	3.74548i	0.197591	−	0.134716i	0.658074	+	0.752953i	$0.271371\pi$
$774$		0			0
$775$	14.3678	−	21.0737i	0.516107	−	0.756991i
$776$	3.85257	+	16.8792i	0.138299	+	0.605928i
$777$		0			0
$778$	8.71029	−	38.1623i	0.312279	−	1.36818i
$779$	−22.5270	−	24.2783i	−0.807112	−	0.869860i
$780$		0			0
$781$	4.23029	+	1.30487i	0.151372	+	0.0466920i
$782$	0.337761	+	4.50711i	0.0120783	+	0.161174i
$783$		0			0
$784$	−6.73043	−	30.9134i	−0.240372	−	1.10405i
$785$			42.0813i			1.50195i
$786$		0			0
$787$	−14.8659	+	48.1939i	−0.529911	+	1.71793i	0.153733	+	0.988112i	$0.450871\pi$
$787$	−14.8659	+	48.1939i	−0.529911	+	1.71793i	−0.683643	+	0.729816i	$0.739606\pi$
$788$	0.792991	+	5.26115i	0.0282491	+	0.187421i
$789$		0			0
$790$	−63.7975	−	14.5614i	−2.26981	−	0.518070i
$791$	−0.841423	+	2.11271i	−0.0299176	+	0.0751192i
$792$		0			0
$793$	12.1044	+	8.25266i	0.429841	+	0.293061i
$794$	39.1404	+	36.3170i	1.38904	+	1.28884i
$795$		0			0
$796$	0.415293	−	2.75529i	0.0147197	−	0.0976585i
$797$	−38.8300	−	18.6996i	−1.37543	−	0.662372i	−0.407410	−	0.913245i	$-0.633568\pi$
$797$	−38.8300	−	18.6996i	−1.37543	−	0.662372i	−0.968020	+	0.250873i	$0.919282\pi$
$798$		0			0
$799$	49.9890	−	24.0734i	1.76848	−	0.851657i
$800$	−3.13546	−	10.1649i	−0.110855	−	0.359384i
$801$		0			0
$802$	−2.27674	+	3.94342i	−0.0803944	+	0.139247i
$803$	−2.83177	−	4.90478i	−0.0999311	−	0.173086i
$804$		0			0
$805$	4.71832	+	2.30143i	0.166299	+	0.0811148i
$806$	16.6672	−	13.2916i	0.587077	−	0.468178i
$807$		0			0
$808$	−8.73250	−	0.654411i	−0.307208	−	0.0230221i
$809$	−2.27859	−	0.170757i	−0.0801111	−	0.00600350i	0.0346142	−	0.999401i	$-0.488980\pi$
$809$	−2.27859	−	0.170757i	−0.0801111	−	0.00600350i	−0.114725	+	0.993397i	$0.536599\pi$
$810$		0			0
$811$	−18.3618	+	14.6430i	−0.644769	+	0.514186i	−0.890401	−	0.455177i	$-0.849576\pi$
$811$	−18.3618	+	14.6430i	−0.644769	+	0.514186i	0.245632	+	0.969363i	$0.421005\pi$
$812$	1.14502	+	5.13517i	0.0401822	+	0.180209i
$813$		0			0
$814$	−2.41935	−	4.19043i	−0.0847981	−	0.146875i
$815$	19.3828	−	33.5720i	0.678950	−	1.17598i
$816$		0			0
$817$	−8.35670	−	27.0918i	−0.292364	−	0.947821i
$818$	−52.2678	+	25.1708i	−1.82750	+	0.880077i
$819$		0			0
$820$	−6.69591	−	3.22458i	−0.233831	−	0.112607i
$821$	2.62702	−	17.4291i	0.0916837	−	0.608281i	−0.895054	−	0.445958i	$-0.852863\pi$
$821$	2.62702	−	17.4291i	0.0916837	−	0.608281i	0.986738	−	0.162323i	$-0.0518988\pi$
$822$		0			0
$823$	18.5497	+	17.2116i	0.646603	+	0.599959i	0.933750	−	0.357927i	$-0.116516\pi$
$823$	18.5497	+	17.2116i	0.646603	+	0.599959i	−0.287147	+	0.957887i	$0.592707\pi$
$824$	12.7525	+	8.69450i	0.444254	+	0.302887i
$825$		0			0
$826$	2.17451	+	31.1087i	0.0756608	+	1.08241i
$827$	31.3143	+	7.14728i	1.08890	+	0.248535i	0.729041	−	0.684470i	$-0.239966\pi$
$827$	31.3143	+	7.14728i	1.08890	+	0.248535i	0.359863	+	0.933005i	$0.382823\pi$
$828$		0			0
$829$	5.86763	+	38.9292i	0.203791	+	1.35207i	0.823537	+	0.567263i	$0.191998\pi$
$829$	5.86763	+	38.9292i	0.203791	+	1.35207i	−0.619746	+	0.784803i	$0.712764\pi$
$830$	−6.10083	+	19.7784i	−0.211763	+	0.686518i
$831$		0			0
$832$			21.8434i			0.757283i
$833$	33.6426	−	10.0091i	1.16565	−	0.346794i
$834$		0			0
$835$	−4.01856	−	53.6239i	−0.139068	−	1.85573i
$836$	0.609995	+	0.188158i	0.0210971	+	0.00650760i
$837$		0			0
$838$	−16.4335	−	17.7111i	−0.567687	−	0.611821i
$839$	2.09788	−	9.19142i	0.0724269	−	0.317323i	−0.925717	−	0.378216i	$-0.876538\pi$
$839$	2.09788	−	9.19142i	0.0724269	−	0.317323i	0.998144	+	0.0608930i	$0.0193948\pi$
$840$		0			0
$841$	2.88744	+	12.6507i	0.0995668	+	0.436231i
$842$	−27.2627	+	39.9871i	−0.939536	+	1.37805i
$843$		0			0
$844$	−1.52654	+	1.04077i	−0.0525455	+	0.0358249i
$845$	4.75888	+	0.717286i	0.163710	+	0.0246754i
$846$		0			0
$847$	26.6341	−	10.2993i	0.915157	−	0.353889i
$848$	5.03119	+	10.4474i	0.172772	+	0.358765i
$849$		0			0
$850$	43.8036	−	17.1917i	1.50245	−	0.589669i
$851$	3.60023	+	2.07859i	0.123414	+	0.0712532i
$852$		0			0
$853$	6.58157	+	5.24863i	0.225349	+	0.179710i	0.729655	−	0.683815i	$-0.239680\pi$
$853$	6.58157	+	5.24863i	0.225349	+	0.179710i	−0.504307	+	0.863525i	$0.668252\pi$
$854$	−13.5911	+	10.7276i	−0.465079	+	0.367089i
$855$		0			0
$856$	−13.0852	+	33.3406i	−0.447243	+	1.13956i
$857$	2.21371	−	29.5398i	0.0756187	−	1.00906i	−0.822344	−	0.568991i	$-0.807334\pi$
$857$	2.21371	−	29.5398i	0.0756187	−	1.00906i	0.897963	−	0.440071i	$-0.145047\pi$
$858$		0			0
$859$	11.5663	+	4.53944i	0.394637	+	0.154884i	0.554358	−	0.832279i	$-0.312964\pi$
$859$	11.5663	+	4.53944i	0.394637	+	0.154884i	−0.159720	+	0.987162i	$0.551059\pi$
$860$	−3.96661	−	4.97397i	−0.135260	−	0.169611i
$861$		0			0
$862$	33.3705	−	41.8453i	1.13661	−	1.42526i
$863$	−5.52021	+	3.18709i	−0.187910	+	0.108490i	−0.591004	−	0.806669i	$-0.701268\pi$
$863$	−5.52021	+	3.18709i	−0.187910	+	0.108490i	0.403094	+	0.915159i	$0.367935\pi$
$864$		0			0
$865$	4.59594	+	11.7103i	0.156267	+	0.398161i
$866$	−20.7347	+	6.39582i	−0.704595	+	0.217339i
$867$		0			0
$868$	1.20905	+	3.12659i	0.0410377	+	0.106124i
$869$	−2.54269	+	5.27995i	−0.0862549	+	0.179110i
$870$		0			0
$871$	25.0172	+	36.6936i	0.847677	+	1.24331i
$872$	−25.8970	+	27.9103i	−0.876982	+	0.945162i
$873$		0			0
$874$	−4.01882	+	0.917269i	−0.135939	+	0.0310271i
$875$	1.60562	−	10.3019i	0.0542799	−	0.348268i
$876$		0			0
$877$	19.1954	−	17.8107i	0.648181	−	0.601424i	−0.285997	−	0.958230i	$-0.592325\pi$
$877$	19.1954	−	17.8107i	0.648181	−	0.601424i	0.934178	+	0.356806i	$0.116134\pi$
$878$	−51.0040	+	7.68762i	−1.72130	+	0.259445i
$879$		0			0
$880$	−6.85306	+	0.513566i	−0.231017	+	0.0173123i
$881$	1.70212			0.0573458			0.0286729	−	0.999589i	$-0.490872\pi$
$881$	1.70212			0.0573458			0.0286729	+	0.999589i	$0.490872\pi$
$882$		0			0
$883$	−26.7332			−0.899645			−0.449823	−	0.893118i	$-0.648513\pi$
$883$	−26.7332			−0.899645			−0.449823	+	0.893118i	$0.648513\pi$
$884$	5.21823	−	0.391053i	0.175508	−	0.0131525i
$885$		0			0
$886$	30.2662	−	4.56190i	1.01681	−	0.153260i
$887$	19.2175	−	17.8313i	0.645261	−	0.598715i	−0.288123	−	0.957593i	$-0.593031\pi$
$887$	19.2175	−	17.8313i	0.645261	−	0.598715i	0.933384	+	0.358878i	$0.116841\pi$
$888$		0			0
$889$	−57.9352	+	4.04969i	−1.94309	+	0.135822i
$890$	76.6645	−	17.4982i	2.56980	−	0.586540i
$891$		0			0
$892$	1.74921	−	1.88520i	0.0585680	−	0.0631213i
$893$	28.5057	+	41.8102i	0.953907	+	1.39912i
$894$		0			0
$895$	−0.817842	+	1.69827i	−0.0273374	+	0.0567668i
$896$	−33.3229	−	10.4620i	−1.11324	−	0.349510i
$897$		0			0
$898$	−23.4644	+	7.23781i	−0.783018	+	0.241529i
$899$	9.77105	+	24.8962i	0.325883	+	0.830335i
$900$		0			0
$901$	−11.1412	+	6.43236i	−0.371166	+	0.214293i
$902$	−3.11897	+	3.91106i	−0.103850	+	0.130224i
$903$		0			0
$904$	1.37810	+	1.72809i	0.0458350	+	0.0574753i
$905$	0.828607	+	0.325204i	0.0275438	+	0.0108102i
$906$		0			0
$907$	3.58238	−	47.8036i	0.118951	−	1.58729i	−0.544297	−	0.838892i	$-0.683204\pi$
$907$	3.58238	−	47.8036i	0.118951	−	1.58729i	0.663248	−	0.748399i	$-0.269177\pi$
$908$	−1.54846	+	3.94542i	−0.0513876	+	0.130933i
$909$		0			0
$910$	20.0270	−	41.0587i	0.663889	−	1.36108i
$911$	24.4587	+	19.5051i	0.810351	+	0.646234i	0.938406	−	0.345533i	$-0.112302\pi$
$911$	24.4587	+	19.5051i	0.810351	+	0.646234i	−0.128055	+	0.991767i	$0.540873\pi$
$912$		0			0
$913$	1.60526	+	0.926800i	0.0531265	+	0.0306726i
$914$	−36.3728	+	14.2753i	−1.20310	+	0.472183i
$915$		0			0
$916$	0.249318	+	0.517714i	0.00823770	+	0.0171058i
$917$	−2.54024	−	1.48364i	−0.0838862	−	0.0489941i
$918$		0			0
$919$	3.22700	+	0.486393i	0.106449	+	0.0160446i	0.202051	−	0.979375i	$-0.435239\pi$
$919$	3.22700	+	0.486393i	0.106449	+	0.0160446i	−0.0956017	+	0.995420i	$0.530478\pi$
$920$	4.21581	−	2.87429i	0.138991	−	0.0947625i
$921$		0			0
$922$	18.2812	−	26.8136i	0.602059	−	0.883058i
$923$	7.36489	+	32.2677i	0.242418	+	1.06210i
$924$		0			0
$925$	9.63108	−	42.1965i	0.316668	−	1.38741i
$926$	−14.3006	−	15.4123i	−0.469946	−	0.506481i
$927$		0			0
$928$	10.6589	+	3.28782i	0.349894	+	0.107928i
$929$	1.44918	+	19.3379i	0.0475459	+	0.634456i	0.969173	+	0.246380i	$0.0792412\pi$
$929$	1.44918	+	19.3379i	0.0475459	+	0.634456i	−0.921627	+	0.388076i	$0.873140\pi$
$930$		0			0
$931$	13.5998	+	28.9800i	0.445715	+	0.949780i
$932$			4.14240i			0.135689i
$933$		0			0
$934$	2.77687	−	9.00240i	0.0908621	−	0.294568i
$935$	−1.13635	−	7.53921i	−0.0371627	−	0.246558i
$936$		0			0
$937$	8.92050	+	2.03605i	0.291420	+	0.0665147i	0.365732	−	0.930720i	$-0.380819\pi$
$937$	8.92050	+	2.03605i	0.291420	+	0.0665147i	−0.0743117	+	0.997235i	$0.523676\pi$
$938$	−50.2331	+	15.2195i	−1.64017	+	0.496935i
$939$		0			0
$940$	9.38207	+	6.39658i	0.306009	+	0.208634i
$941$	−6.27578	−	5.82308i	−0.204585	−	0.189827i	0.571226	−	0.820793i	$-0.306468\pi$
$941$	−6.27578	−	5.82308i	−0.204585	−	0.189827i	−0.775810	+	0.630966i	$0.782659\pi$
$942$		0			0
$943$	0.640563	−	4.24986i	0.0208596	−	0.138394i
$944$	31.6002	+	15.2178i	1.02850	+	0.495299i
$945$		0			0
$946$	−3.85817	+	1.85800i	−0.125440	+	0.0604087i
$947$	16.4525	+	53.3376i	0.534633	+	1.73324i	0.669921	+	0.742432i	$0.266328\pi$
$947$	16.4525	+	53.3376i	0.534633	+	1.73324i	−0.135288	+	0.990806i	$0.543196\pi$
$948$		0			0
$949$	21.1713	−	36.6698i	0.687250	−	1.19035i
$950$	21.4586	+	37.1674i	0.696208	+	1.20587i
$951$		0			0
$952$	7.75801	−	33.2215i	0.251438	−	1.07671i
$953$	20.5356	−	16.3766i	0.665214	−	0.530490i	−0.231649	−	0.972799i	$-0.574412\pi$
$953$	20.5356	−	16.3766i	0.665214	−	0.530490i	0.896863	+	0.442309i	$0.145841\pi$
$954$		0			0
$955$	−72.2998	−	5.41812i	−2.33957	−	0.175326i
$956$	−3.88806	−	0.291369i	−0.125749	−	0.00942356i
$957$		0			0
$958$	−31.3813	+	25.0258i	−1.01388	+	0.808546i
$959$	−58.3185	−	0.292357i	−1.88320	−	0.00944071i
$960$		0			0
$961$	−6.97972	−	12.0892i	−0.225152	−	0.389975i
$962$	18.0879	−	31.3291i	0.583176	−	1.01009i
$963$		0			0
$964$	−2.63651	−	8.54734i	−0.0849162	−	0.275291i
$965$	−29.9602	+	14.4281i	−0.964452	+	0.464456i
$966$		0			0
$967$	−10.9623	−	5.27917i	−0.352524	−	0.169767i	0.249238	−	0.968442i	$-0.419820\pi$
$967$	−10.9623	−	5.27917i	−0.352524	−	0.169767i	−0.601762	+	0.798676i	$0.705534\pi$
$968$	4.13667	−	27.4450i	0.132958	−	0.882115i
$969$		0			0
$970$	−25.0631	−	23.2551i	−0.804727	−	0.746677i
$971$	−18.9651	−	12.9302i	−0.608619	−	0.414949i	0.219412	−	0.975632i	$-0.429586\pi$
$971$	−18.9651	−	12.9302i	−0.608619	−	0.414949i	−0.828030	+	0.560683i	$0.810539\pi$
$972$		0			0
$973$	11.7729	+	8.11338i	0.377422	+	0.260103i
$974$	−39.4378	−	9.00142i	−1.26367	−	0.288424i
$975$		0			0
$976$	2.90245	+	19.2565i	0.0929050	+	0.616384i
$977$	−18.0079	+	58.3802i	−0.576124	+	1.86775i	−0.0855829	+	0.996331i	$0.527275\pi$
$977$	−18.0079	+	58.3802i	−0.576124	+	1.86775i	−0.490541	+	0.871418i	$0.663201\pi$
$978$		0			0
$979$		−	7.04224i		−	0.225071i
$980$	5.21661	+	4.93855i	0.166638	+	0.157756i
$981$		0			0
$982$	−3.21600	−	42.9145i	−0.102627	−	1.36946i
$983$	−19.1495	−	5.90685i	−0.610775	−	0.188399i	−0.0260901	−	0.999660i	$-0.508306\pi$
$983$	−19.1495	−	5.90685i	−0.610775	−	0.188399i	−0.584685	+	0.811260i	$0.698782\pi$
$984$		0			0
$985$	39.4213	+	42.4861i	1.25607	+	1.35372i
$986$	−10.9799	+	48.1059i	−0.349670	+	1.53201i
$987$		0			0
$988$	1.06199	+	4.65290i	0.0337865	+	0.148028i
$989$	2.07251	−	3.03982i	0.0659021	−	0.0966607i
$990$		0			0
$991$	27.3692	−	18.6600i	0.869413	−	0.592756i	−0.0443444	−	0.999016i	$-0.514120\pi$
$991$	27.3692	−	18.6600i	0.869413	−	0.592756i	0.913757	+	0.406261i	$0.133167\pi$
$992$	7.02765	+	1.05925i	0.223128	+	0.0336312i
$993$		0			0
$994$	−38.9930	−	3.11877i	−1.23678	−	0.0989215i
$995$	−13.1696	−	27.3469i	−0.417503	−	0.866954i
$996$		0			0
$997$	12.4180	−	4.87369i	0.393281	−	0.154351i	−0.160456	−	0.987043i	$-0.551297\pi$
$997$	12.4180	−	4.87369i	0.393281	−	0.154351i	0.553737	+	0.832692i	$0.313201\pi$
$998$	−25.8227	−	14.9087i	−0.817402	−	0.471927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.17.5	✓	216
3.2	odd	2	inner	441.2.bg.a.17.14	yes	216
49.26	odd	42	inner	441.2.bg.a.26.14	yes	216
147.26	even	42	inner	441.2.bg.a.26.5	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.17.5	✓	216	1.1	even	1	trivial
441.2.bg.a.17.14	yes	216	3.2	odd	2	inner
441.2.bg.a.26.5	yes	216	147.26	even	42	inner
441.2.bg.a.26.14	yes	216	49.26	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51461 + 0.113504i) q^{2} +(0.303503 - 0.0457458i) q^{4} +(2.45092 - 2.27412i) q^{5} +(1.78982 + 1.94847i) q^{7} +(2.50706 - 0.572220i) q^{8} +O(q^{10})\)	\(q+(-1.51461 + 0.113504i) q^{2} +(0.303503 - 0.0457458i) q^{4} +(2.45092 - 2.27412i) q^{5} +(1.78982 + 1.94847i) q^{7} +(2.50706 - 0.572220i) q^{8} +(-3.45407 + 3.72260i) q^{10} +(0.256186 + 0.375756i) q^{11} +(-1.47524 + 3.06337i) q^{13} +(-2.93205 - 2.74802i) q^{14} +(-4.31886 + 1.33219i) q^{16} +(-1.83192 - 4.66766i) q^{17} +(3.96050 - 2.28660i) q^{19} +(0.639832 - 0.802323i) q^{20} +(-0.430673 - 0.540047i) q^{22} +(0.552433 + 0.216814i) q^{23} +(0.461731 - 6.16138i) q^{25} +(1.88671 - 4.80726i) q^{26} +(0.632352 + 0.509490i) q^{28} +(5.06540 + 4.03952i) q^{29} +(3.57497 + 2.06401i) q^{31} +(1.60264 - 0.628991i) q^{32} +(3.30445 + 6.86176i) q^{34} +(8.81778 + 0.705270i) q^{35} +(6.92679 + 1.04405i) q^{37} +(-5.73909 + 3.91284i) q^{38} +(4.84330 - 7.10382i) q^{40} +(-1.61152 - 7.06051i) q^{41} +(1.37951 - 6.04402i) q^{43} +(0.0949427 + 0.102324i) q^{44} +(-0.861331 - 0.265685i) q^{46} +(0.826898 + 11.0342i) q^{47} +(-0.593070 + 6.97483i) q^{49} +9.38450i q^{50} +(-0.307605 + 0.997230i) q^{52} +(-0.382386 - 2.53696i) q^{53} +(1.48241 + 0.338350i) q^{55} +(5.60214 + 3.86076i) q^{56} +(-8.13062 - 5.54336i) q^{58} +(-5.68865 - 5.27829i) q^{59} +(0.642183 - 4.26060i) q^{61} +(-5.64897 - 2.72040i) q^{62} +(5.78815 - 2.78743i) q^{64} +(3.35078 + 10.8630i) q^{65} +(6.53077 - 11.3116i) q^{67} +(-0.769520 - 1.33285i) q^{68} +(-13.4356 - 0.0673540i) q^{70} +(7.61059 - 6.06925i) q^{71} +(-12.4186 - 0.930644i) q^{73} +(-10.6099 - 0.795103i) q^{74} +(1.09742 - 0.875167i) q^{76} +(-0.273622 + 1.17171i) q^{77} +(6.44302 + 11.1596i) q^{79} +(-7.55562 + 13.0867i) q^{80} +(3.24222 + 10.5110i) q^{82} +(3.67219 - 1.76843i) q^{83} +(-15.1047 - 7.27405i) q^{85} +(-1.40340 + 9.31093i) q^{86} +(0.857289 + 0.795448i) q^{88} +(-12.7943 - 8.72299i) q^{89} +(-8.60931 + 2.60843i) q^{91} +(0.177584 + 0.0405323i) q^{92} +(-2.50486 - 16.6187i) q^{94} +(4.50688 - 14.6109i) q^{95} +6.73267i q^{97} +(0.106596 - 10.6315i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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