LMFDB - Embedded newform 441.2.bg.a.278.1

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			278.1
Character	$\chi$	$=$	441.278
Dual form			441.2.bg.a.395.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45194 + 0.962314i) q^{2} +(3.61984 - 3.35872i) q^{4} +(1.47762 - 1.00742i) q^{5} +(2.09999 + 1.60937i) q^{7} +(-3.35777 + 6.97247i) q^{8} +O(q^{10})$	\(q+(-2.45194 + 0.962314i) q^{2} +(3.61984 - 3.35872i) q^{4} +(1.47762 - 1.00742i) q^{5} +(2.09999 + 1.60937i) q^{7} +(-3.35777 + 6.97247i) q^{8} +(-2.65357 + 3.89208i) q^{10} +(-0.538606 + 3.57342i) q^{11} +(-2.76752 - 2.20702i) q^{13} +(-6.69775 - 1.92522i) q^{14} +(0.785279 - 10.4788i) q^{16} +(2.32943 - 0.718533i) q^{17} +(6.52328 + 3.76622i) q^{19} +(1.96509 - 8.60964i) q^{20} +(-2.11812 - 9.28010i) q^{22} +(1.91813 - 6.21843i) q^{23} +(-0.658247 + 1.67719i) q^{25} +(8.90963 + 2.74826i) q^{26} +(13.0070 - 1.22762i) q^{28} +(4.35647 + 0.994336i) q^{29} +(-5.85986 + 3.38319i) q^{31} +(3.59633 + 11.6590i) q^{32} +(-5.02015 + 4.00344i) q^{34} +(4.72430 + 0.262454i) q^{35} +(-4.18776 - 3.88567i) q^{37} +(-19.6190 - 2.95708i) q^{38} +(2.06274 + 13.6854i) q^{40} +(3.53525 + 1.70249i) q^{41} +(3.05468 - 1.47106i) q^{43} +(10.0524 + 14.7442i) q^{44} +(1.28095 + 17.0930i) q^{46} +(1.81628 + 4.62779i) q^{47} +(1.81988 + 6.75929i) q^{49} -4.74579i q^{50} +(-17.4308 + 1.30625i) q^{52} +(-3.20504 - 3.45421i) q^{53} +(2.80409 + 5.82276i) q^{55} +(-18.2725 + 9.23822i) q^{56} +(-11.6387 + 1.75424i) q^{58} +(9.48163 + 6.46446i) q^{59} +(4.54073 - 4.89374i) q^{61} +(11.1123 - 13.9344i) q^{62} +(-6.93408 - 8.69506i) q^{64} +(-6.31275 - 0.473075i) q^{65} +(6.90681 + 11.9629i) q^{67} +(6.01880 - 10.4249i) q^{68} +(-11.8362 + 3.90274i) q^{70} +(1.21008 - 0.276193i) q^{71} +(8.19697 + 3.21707i) q^{73} +(14.0074 + 5.49749i) q^{74} +(36.2629 - 8.27678i) q^{76} +(-6.88200 + 6.63731i) q^{77} +(5.24053 - 9.07686i) q^{79} +(-9.39628 - 16.2748i) q^{80} +(-10.3066 - 0.772369i) q^{82} +(-8.72515 - 10.9410i) q^{83} +(2.71814 - 3.40844i) q^{85} +(-6.07427 + 6.54650i) q^{86} +(-23.1070 - 15.7541i) q^{88} +(-7.03212 + 1.05992i) q^{89} +(-2.25984 - 9.08866i) q^{91} +(-13.9427 - 28.9522i) q^{92} +(-8.90679 - 9.59923i) q^{94} +(13.4331 - 1.00667i) q^{95} +1.36179i q^{97} +(-10.9668 - 14.8221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$-1$

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 $

$2$	−2.45194	+	0.962314i	−1.73378	+	0.680459i	−0.733782	+	0.679385i	$0.762247\pi$
$2$	−2.45194	+	0.962314i	−1.73378	+	0.680459i	−0.999999	+	0.00107413i	$0.999658\pi$
$3$		0			0
$3$		0			0
$4$	3.61984	−	3.35872i	1.80992	−	1.67936i
$5$	1.47762	−	1.00742i	0.660812	−	0.450534i	−0.185912	−	0.982566i	$-0.559524\pi$
$5$	1.47762	−	1.00742i	0.660812	−	0.450534i	0.846724	+	0.532032i	$0.178572\pi$
$6$		0			0
$7$	2.09999	+	1.60937i	0.793720	+	0.608283i
$7$	2.09999	+	1.60937i	0.793720	+	0.608283i
$8$	−3.35777	+	6.97247i	−1.18715	+	2.46514i
$9$		0			0
$10$	−2.65357	+	3.89208i	−0.839134	+	1.23078i
$11$	−0.538606	+	3.57342i	−0.162396	+	1.07743i	0.748004	+	0.663695i	$0.231013\pi$
$11$	−0.538606	+	3.57342i	−0.162396	+	1.07743i	−0.910399	+	0.413731i	$0.864226\pi$
$12$		0			0
$13$	−2.76752	−	2.20702i	−0.767571	−	0.612118i	0.159415	−	0.987212i	$-0.449039\pi$
$13$	−2.76752	−	2.20702i	−0.767571	−	0.612118i	−0.926987	+	0.375094i	$0.877610\pi$
$14$	−6.69775	−	1.92522i	−1.79005	−	0.514536i
$15$		0			0
$16$	0.785279	−	10.4788i	0.196320	−	2.61970i
$17$	2.32943	−	0.718533i	0.564969	−	0.174270i	0.000902867	−	1.00000i	$-0.499713\pi$
$17$	2.32943	−	0.718533i	0.564969	−	0.174270i	0.564066	+	0.825730i	$0.309236\pi$
$18$		0			0
$19$	6.52328	+	3.76622i	1.49654	+	0.864030i	0.999992	−	0.00397809i	$-0.00126627\pi$
$19$	6.52328	+	3.76622i	1.49654	+	0.864030i	0.496551	+	0.868008i	$0.334600\pi$
$20$	1.96509	−	8.60964i	0.439408	−	1.92517i
$21$		0			0
$22$	−2.11812	−	9.28010i	−0.451585	−	1.97852i
$23$	1.91813	−	6.21843i	0.399958	−	1.29663i	−0.502022	−	0.864855i	$-0.667410\pi$
$23$	1.91813	−	6.21843i	0.399958	−	1.29663i	0.901980	−	0.431778i	$-0.142113\pi$
$24$		0			0
$25$	−0.658247	+	1.67719i	−0.131649	+	0.335437i
$26$	8.90963	+	2.74826i	1.74732	+	0.538977i
$27$		0			0
$28$	13.0070	−	1.22762i	2.45810	−	0.231999i
$29$	4.35647	+	0.994336i	0.808976	+	0.184644i	0.606953	−	0.794737i	$-0.292391\pi$
$29$	4.35647	+	0.994336i	0.808976	+	0.184644i	0.202023	+	0.979381i	$0.435249\pi$
$30$		0			0
$31$	−5.85986	+	3.38319i	−1.05246	+	0.607639i	−0.923337	−	0.383990i	$-0.874550\pi$
$31$	−5.85986	+	3.38319i	−1.05246	+	0.607639i	−0.129124	+	0.991628i	$0.541216\pi$
$32$	3.59633	+	11.6590i	0.635747	+	2.06104i
$33$		0			0
$34$	−5.02015	+	4.00344i	−0.860949	+	0.686584i
$35$	4.72430	+	0.262454i	0.798552	+	0.0443628i
$36$		0			0
$37$	−4.18776	−	3.88567i	−0.688464	−	0.638801i	0.256283	−	0.966602i	$-0.417502\pi$
$37$	−4.18776	−	3.88567i	−0.688464	−	0.638801i	−0.944747	+	0.327801i	$0.893692\pi$
$38$	−19.6190	−	2.95708i	−3.18262	−	0.479702i
$39$		0			0
$40$	2.06274	+	13.6854i	0.326147	+	2.16385i
$41$	3.53525	+	1.70249i	0.552114	+	0.265884i	0.689072	−	0.724693i	$-0.258018\pi$
$41$	3.53525	+	1.70249i	0.552114	+	0.265884i	−0.136958	+	0.990577i	$0.543733\pi$
$42$		0			0
$43$	3.05468	−	1.47106i	0.465834	−	0.224334i	−0.186217	−	0.982509i	$-0.559623\pi$
$43$	3.05468	−	1.47106i	0.465834	−	0.224334i	0.652052	+	0.758175i	$0.273909\pi$
$44$	10.0524	+	14.7442i	1.51546	+	2.22278i
$45$		0			0
$46$	1.28095	+	17.0930i	0.188865	+	2.52023i
$47$	1.81628	+	4.62779i	0.264931	+	0.675033i	0.999996	−	0.00296394i	$-0.000943454\pi$
$47$	1.81628	+	4.62779i	0.264931	+	0.675033i	−0.735065	+	0.677997i	$0.762848\pi$
$48$		0			0
$49$	1.81988	+	6.75929i	0.259983	+	0.965613i
$50$		−	4.74579i		−	0.671157i
$51$		0			0
$52$	−17.4308	+	1.30625i	−2.41721	+	0.181145i
$53$	−3.20504	−	3.45421i	−0.440247	−	0.474473i	0.473479	−	0.880805i	$-0.342998\pi$
$53$	−3.20504	−	3.45421i	−0.440247	−	0.474473i	−0.913725	+	0.406332i	$0.866808\pi$
$54$		0			0
$55$	2.80409	+	5.82276i	0.378104	+	0.785141i
$56$	−18.2725	+	9.23822i	−2.44177	+	1.23451i
$57$		0			0
$58$	−11.6387	+	1.75424i	−1.52823	+	0.230344i
$59$	9.48163	+	6.46446i	1.23440	+	0.841601i	0.991709	−	0.128502i	$-0.0410168\pi$
$59$	9.48163	+	6.46446i	1.23440	+	0.841601i	0.242693	+	0.970103i	$0.421969\pi$
$60$		0			0
$61$	4.54073	−	4.89374i	0.581381	−	0.626580i	−0.372042	−	0.928216i	$-0.621342\pi$
$61$	4.54073	−	4.89374i	0.581381	−	0.626580i	0.953423	+	0.301636i	$0.0975328\pi$
$62$	11.1123	−	13.9344i	1.41126	−	1.76967i
$63$		0			0
$64$	−6.93408	−	8.69506i	−0.866759	−	1.08688i
$65$	−6.31275	−	0.473075i	−0.783000	−	0.0586778i
$66$		0			0
$67$	6.90681	+	11.9629i	0.843801	+	1.46151i	0.886658	+	0.462425i	$0.153020\pi$
$67$	6.90681	+	11.9629i	0.843801	+	1.46151i	−0.0428576	+	0.999081i	$0.513646\pi$
$68$	6.01880	−	10.4249i	0.729887	−	1.26420i
$69$		0			0
$70$	−11.8362	+	3.90274i	−1.41470	+	0.466467i
$71$	1.21008	−	0.276193i	0.143610	−	0.0327781i	−0.150112	−	0.988669i	$-0.547963\pi$
$71$	1.21008	−	0.276193i	0.143610	−	0.0327781i	0.293722	+	0.955891i	$0.405106\pi$
$72$		0			0
$73$	8.19697	+	3.21707i	0.959383	+	0.376530i	0.792790	−	0.609495i	$-0.208628\pi$
$73$	8.19697	+	3.21707i	0.959383	+	0.376530i	0.166594	+	0.986026i	$0.446723\pi$
$74$	14.0074	+	5.49749i	1.62832	+	0.639070i
$75$		0			0
$76$	36.2629	−	8.27678i	4.15964	−	0.949412i
$77$	−6.88200	+	6.63731i	−0.784276	+	0.756392i
$78$		0			0
$79$	5.24053	−	9.07686i	0.589606	−	1.02123i	−0.404678	−	0.914459i	$-0.632616\pi$
$79$	5.24053	−	9.07686i	0.589606	−	1.02123i	0.994284	−	0.106768i	$-0.0340502\pi$
$80$	−9.39628	−	16.2748i	−1.05054	−	1.81958i
$81$		0			0
$82$	−10.3066	−	0.772369i	−1.13817	−	0.0852939i
$83$	−8.72515	−	10.9410i	−0.957710	−	1.20093i	−0.979557	−	0.201169i	$-0.935526\pi$
$83$	−8.72515	−	10.9410i	−0.957710	−	1.20093i	0.0218467	−	0.999761i	$-0.493045\pi$
$84$		0			0
$85$	2.71814	−	3.40844i	0.294824	−	0.369697i
$86$	−6.07427	+	6.54650i	−0.655005	+	0.705927i
$87$		0			0
$88$	−23.1070	−	15.7541i	−2.46322	−	1.67939i
$89$	−7.03212	+	1.05992i	−0.745403	+	0.112351i	−0.510752	−	0.859728i	$-0.670633\pi$
$89$	−7.03212	+	1.05992i	−0.745403	+	0.112351i	−0.234651	+	0.972080i	$0.575395\pi$
$90$		0			0
$91$	−2.25984	−	9.08866i	−0.236896	−	0.952751i
$92$	−13.9427	−	28.9522i	−1.45362	−	3.01848i
$93$		0			0
$94$	−8.90679	−	9.59923i	−0.918665	−	0.990085i
$95$	13.4331	−	1.00667i	1.37821	−	0.103282i
$96$		0			0
$97$			1.36179i			0.138269i	0.997607	+	0.0691347i	$0.0220238\pi$
$97$			1.36179i			0.138269i	−0.997607	+	0.0691347i	$0.977976\pi$
$98$	−10.9668	−	14.8221i	−1.10781	−	1.49725i
$99$		0			0
$100$	3.25045	+	8.28202i	0.325045	+	0.828202i
$101$	0.646268	+	8.62384i	0.0643060	+	0.858104i	0.932336	+	0.361593i	$0.117767\pi$
$101$	0.646268	+	8.62384i	0.0643060	+	0.858104i	−0.868030	+	0.496512i	$0.834614\pi$
$102$		0			0
$103$	−8.38856	−	12.3038i	−0.826550	−	1.21233i	−0.974735	−	0.223366i	$-0.928295\pi$
$103$	−8.38856	−	12.3038i	−0.826550	−	1.21233i	0.148185	−	0.988960i	$-0.452657\pi$
$104$	24.6811	−	11.8858i	2.42018	−	1.16550i
$105$		0			0
$106$	11.1826	+	5.38526i	1.08615	+	0.523063i
$107$	2.23305	+	14.8153i	0.215877	+	1.43225i	0.789811	+	0.613350i	$0.210178\pi$
$107$	2.23305	+	14.8153i	0.215877	+	1.43225i	−0.573934	+	0.818901i	$0.694584\pi$
$108$		0			0
$109$	−15.2528	−	2.29900i	−1.46096	−	0.220204i	−0.630024	−	0.776576i	$-0.716955\pi$
$109$	−15.2528	−	2.29900i	−1.46096	−	0.220204i	−0.830934	+	0.556372i	$0.812193\pi$
$110$	−12.4788	−	11.5786i	−1.18981	−	1.10398i
$111$		0			0
$112$	18.5133	−	20.7416i	1.74934	−	1.95989i
$113$	2.47511	−	1.97383i	0.232838	−	0.185682i	−0.500120	−	0.865956i	$-0.666711\pi$
$113$	2.47511	−	1.97383i	0.232838	−	0.185682i	0.732958	+	0.680274i	$0.238139\pi$
$114$		0			0
$115$	−3.43033	−	11.1209i	−0.319880	−	1.03703i
$116$	19.1094	−	11.0328i	1.77427	−	1.02437i
$117$		0			0
$118$	−29.4692	−	6.72615i	−2.71286	−	0.619192i
$119$	6.04814	+	2.23999i	0.554432	+	0.205339i
$120$		0			0
$121$	−1.96790	−	0.607018i	−0.178900	−	0.0551834i
$122$	−6.42427	+	16.3688i	−0.581626	+	1.48196i
$123$		0			0
$124$	−9.84856	+	31.9283i	−0.884427	+	2.86724i
$125$	2.70675	+	11.8590i	0.242099	+	1.06070i
$126$		0			0
$127$	2.81359	−	12.3271i	0.249666	−	1.09386i	−0.682232	−	0.731136i	$-0.738990\pi$
$127$	2.81359	−	12.3271i	0.249666	−	1.09386i	0.931898	−	0.362722i	$-0.118152\pi$
$128$	4.23644	+	2.44591i	0.374452	+	0.216190i
$129$		0			0
$130$	15.9337	−	4.91490i	1.39748	−	0.431065i
$131$	0.625833	−	8.35116i	0.0546793	−	0.729644i	−0.900734	−	0.434371i	$-0.856971\pi$
$131$	0.625833	−	8.35116i	0.0546793	−	0.729644i	0.955413	−	0.295272i	$-0.0954104\pi$
$132$		0			0
$133$	7.63758	+	18.4073i	0.662262	+	1.59612i
$134$	−28.4472	−	22.6859i	−2.45746	−	1.95976i
$135$		0			0
$136$	−2.81172	+	18.6545i	−0.241103	+	1.59961i
$137$	3.40952	−	5.00085i	0.291295	−	0.427251i	−0.652497	−	0.757791i	$-0.726278\pi$
$137$	3.40952	−	5.00085i	0.291295	−	0.427251i	0.943792	+	0.330540i	$0.107231\pi$
$138$		0			0
$139$	4.97685	−	10.3345i	0.422131	−	0.876565i	−0.576115	−	0.817369i	$-0.695432\pi$
$139$	4.97685	−	10.3345i	0.422131	−	0.876565i	0.998246	−	0.0591961i	$-0.0188537\pi$
$140$	17.9827	−	14.9176i	1.51982	−	1.26076i
$141$		0			0
$142$	−2.70126	+	1.84168i	−0.226684	+	0.154551i
$143$	9.37721	−	8.70078i	0.784162	−	0.727596i
$144$		0			0
$145$	7.43893	−	2.91956i	0.617769	−	0.242457i
$146$	−23.1943			−1.91957
$147$		0			0
$148$	−28.2099			−2.31884
$149$	−11.7419	+	4.60836i	−0.961934	+	0.377531i	−0.793763	−	0.608227i	$-0.791881\pi$
$149$	−11.7419	+	4.60836i	−0.961934	+	0.377531i	−0.168171	+	0.985758i	$0.553786\pi$
$150$		0			0
$151$	1.35780	−	1.25985i	0.110496	−	0.102525i	−0.622990	−	0.782230i	$-0.714082\pi$
$151$	1.35780	−	1.25985i	0.110496	−	0.102525i	0.733486	+	0.679704i	$0.237892\pi$
$152$	−48.1635	+	32.8373i	−3.90658	+	2.66346i
$153$		0			0
$154$	10.4870	−	22.8969i	0.845070	−	1.84509i
$155$	−5.25034	+	10.9024i	−0.421717	+	0.875705i
$156$		0			0
$157$	−5.62320	+	8.24772i	−0.448780	+	0.658240i	−0.982249	−	0.187580i	$-0.939936\pi$
$157$	−5.62320	+	8.24772i	−0.448780	+	0.658240i	0.533469	+	0.845820i	$0.320888\pi$
$158$	−4.11465	+	27.2989i	−0.327344	+	2.17179i
$159$		0			0
$160$	17.0596	+	13.6046i	1.34868	+	1.07553i
$161$	14.0358	−	9.97164i	1.10617	−	0.785876i
$162$		0			0
$163$	0.815078	−	10.8765i	0.0638418	−	0.851910i	−0.869732	−	0.493525i	$-0.835708\pi$
$163$	0.815078	−	10.8765i	0.0638418	−	0.851910i	0.933574	−	0.358386i	$-0.116673\pi$
$164$	18.5153	−	5.71120i	1.44580	−	0.445970i
$165$		0			0
$166$	31.9222	+	18.4303i	2.47764	+	1.43047i
$167$	−4.24385	+	18.5935i	−0.328399	+	1.43881i	0.493784	+	0.869585i	$0.335613\pi$
$167$	−4.24385	+	18.5935i	−0.328399	+	1.43881i	−0.822183	+	0.569224i	$0.807244\pi$
$168$		0			0
$169$	−0.104562	−	0.458117i	−0.00804325	−	0.0352398i
$170$	−3.38472	+	10.9730i	−0.259596	+	0.841590i
$171$		0			0
$172$	6.11659	−	15.5848i	0.466386	−	1.18833i
$173$	−17.0108	−	5.24713i	−1.29330	−	0.398932i	−0.429641	−	0.903000i	$-0.641360\pi$
$173$	−17.0108	−	5.24713i	−1.29330	−	0.398932i	−0.863664	+	0.504068i	$0.831836\pi$
$174$		0			0
$175$	−4.08151	+	2.46271i	−0.308533	+	0.186163i
$176$	37.0222	+	8.45008i	2.79065	+	0.636949i
$177$		0			0
$178$	16.2223	−	9.36597i	1.21592	−	0.702009i
$179$	−4.74524	−	15.3837i	−0.354676	−	1.14983i	−0.940615	−	0.339476i	$-0.889750\pi$
$179$	−4.74524	−	15.3837i	−0.354676	−	1.14983i	0.585939	−	0.810355i	$-0.300726\pi$
$180$		0			0
$181$	−1.22615	+	0.977821i	−0.0911389	+	0.0726809i	−0.667999	−	0.744162i	$-0.732849\pi$
$181$	−1.22615	+	0.977821i	−0.0911389	+	0.0726809i	0.576860	+	0.816843i	$0.304278\pi$
$182$	14.2871	+	20.1102i	1.05903	+	1.49066i
$183$		0			0
$184$	36.9172	+	34.2542i	2.72157	+	2.52525i
$185$	−10.1024	−	1.52270i	−0.742747	−	0.111951i
$186$		0			0
$187$	1.31297	+	8.71101i	0.0960142	+	0.637012i
$188$	22.1181	+	10.6515i	1.61313	+	0.776842i
$189$		0			0
$190$	−31.9684	+	15.3952i	−2.31923	+	1.11688i
$191$	−4.14328	−	6.07708i	−0.299797	−	0.439722i	0.646551	−	0.762871i	$-0.276211\pi$
$191$	−4.14328	−	6.07708i	−0.299797	−	0.439722i	−0.946348	+	0.323149i	$0.895259\pi$
$192$		0			0
$193$	0.156219	+	2.08460i	0.0112449	+	0.150053i	1.00000		0.000508213i	$0.000161769\pi$
$193$	0.156219	+	2.08460i	0.0112449	+	0.150053i	−0.988755	+	0.149545i	$0.952219\pi$
$194$	−1.31047	−	3.33904i	−0.0940866	−	0.239729i
$195$		0			0
$196$	29.2903	+	18.3551i	2.09216	+	1.31108i
$197$		−	6.13583i		−	0.437159i	−0.975819	−	0.218580i	$-0.929858\pi$
$197$		−	6.13583i		−	0.437159i	0.975819	−	0.218580i	$-0.0701424\pi$
$198$		0			0
$199$	−24.1519	+	1.80994i	−1.71209	+	0.128303i	−0.894373	−	0.447322i	$-0.852378\pi$
$199$	−24.1519	+	1.80994i	−1.71209	+	0.128303i	−0.817713	+	0.575625i	$0.804759\pi$
$200$	−9.48389	−	10.2212i	−0.670612	−	0.722748i
$201$		0			0
$202$	−9.88346	−	20.5232i	−0.695398	−	1.44401i
$203$	7.54828	+	9.09924i	0.529785	+	0.638642i
$204$		0			0
$205$	6.93890	−	1.04587i	0.484633	−	0.0730467i
$206$	32.4083	+	22.0956i	2.25799	+	1.53947i
$207$		0			0
$208$	−25.3003	+	27.2672i	−1.75426	+	1.89064i
$209$	−16.9717	+	21.2819i	−1.17396	+	1.47210i
$210$		0			0
$211$	4.19892	+	5.26528i	0.289066	+	0.362477i	0.905068	−	0.425268i	$-0.139820\pi$
$211$	4.19892	+	5.26528i	0.289066	+	0.362477i	−0.616002	+	0.787745i	$0.711249\pi$
$212$	−23.2035	−	1.73886i	−1.59362	−	0.119426i
$213$		0			0
$214$	−19.7323	−	34.1773i	−1.34887	−	2.33631i
$215$	3.03168	−	5.25102i	0.206759	−	0.358117i
$216$		0			0
$217$	−17.7504	−	2.32600i	−1.20498	−	0.157899i
$218$	39.6114	−	9.04104i	2.68282	−	0.612336i
$219$		0			0
$220$	29.7074	+	11.6593i	2.00287	+	0.786070i
$221$	−8.03254	−	3.15254i	−0.540327	−	0.212063i
$222$		0			0
$223$	−7.92276	+	1.80832i	−0.530547	+	0.121094i	−0.479399	−	0.877597i	$-0.659145\pi$
$223$	−7.92276	+	1.80832i	−0.530547	+	0.121094i	−0.0511482	+	0.998691i	$0.516288\pi$
$224$	−11.2114	+	30.2715i	−0.749091	+	2.02260i
$225$		0			0
$226$	−4.16936	+	7.22154i	−0.277342	+	0.480370i
$227$	−1.53188	−	2.65330i	−0.101675	−	0.176106i	0.810700	−	0.585462i	$-0.199087\pi$
$227$	−1.53188	−	2.65330i	−0.101675	−	0.176106i	−0.912375	+	0.409356i	$0.865753\pi$
$228$		0			0
$229$	0.150273	+	0.0112614i	0.00993034	+	0.000744176i	0.0796943	−	0.996819i	$-0.474606\pi$
$229$	0.150273	+	0.0112614i	0.00993034	+	0.000744176i	−0.0697640	+	0.997564i	$0.522225\pi$
$230$	19.1127	+	23.9666i	1.26026	+	1.58031i
$231$		0			0
$232$	−21.5610	+	27.0366i	−1.41555	+	1.77504i
$233$	14.6211	−	15.7578i	0.957860	−	1.03233i	−0.0415891	−	0.999135i	$-0.513242\pi$
$233$	14.6211	−	15.7578i	0.957860	−	1.03233i	0.999449	−	0.0331927i	$-0.0105675\pi$
$234$		0			0
$235$	7.34592	+	5.00836i	0.479195	+	0.326710i
$236$	56.0343	−	8.44582i	3.64753	−	0.549776i
$237$		0			0
$238$	−16.9852	+	0.327903i	−1.10099	+	0.0212548i
$239$	−3.87558	−	8.04773i	−0.250691	−	0.520564i	0.737208	−	0.675666i	$-0.236144\pi$
$239$	−3.87558	−	8.04773i	−0.250691	−	0.520564i	−0.987899	+	0.155102i	$0.950430\pi$
$240$		0			0
$241$	−6.13948	−	6.61679i	−0.395479	−	0.426225i	0.503651	−	0.863907i	$-0.331990\pi$
$241$	−6.13948	−	6.61679i	−0.395479	−	0.426225i	−0.899130	+	0.437683i	$0.855799\pi$
$242$	5.40932	−	0.405372i	0.347724	−	0.0260583i
$243$		0			0
$244$		−	32.9657i		−	2.11041i
$245$	9.49858	+	8.15427i	0.606842	+	0.520957i
$246$		0			0
$247$	−9.74117	−	24.8201i	−0.619816	−	1.57926i
$248$	−3.91317	−	52.2177i	−0.248487	−	3.31582i
$249$		0			0
$250$	−18.0489	−	26.4729i	−1.14151	−	1.67429i
$251$	10.7491	−	5.17648i	0.678476	−	0.326737i	−0.0627146	−	0.998031i	$-0.519976\pi$
$251$	10.7491	−	5.17648i	0.678476	−	0.326737i	0.741191	+	0.671295i	$0.234262\pi$
$252$		0			0
$253$	21.1879	+	10.2036i	1.33207	+	0.641493i
$254$	4.96384	+	32.9330i	0.311459	+	2.06640i
$255$		0			0
$256$	9.25313	+	1.39469i	0.578321	+	0.0871678i
$257$	−9.42230	−	8.74262i	−0.587747	−	0.545349i	0.329251	−	0.944243i	$-0.393204\pi$
$257$	−9.42230	−	8.74262i	−0.587747	−	0.545349i	−0.916997	+	0.398893i	$0.869394\pi$
$258$		0			0
$259$	−2.54077	−	14.8995i	−0.157876	−	0.925810i
$260$	−24.4401	+	19.4903i	−1.51571	+	1.20874i
$261$		0			0
$262$	6.50194	+	21.0788i	0.401691	+	1.30225i
$263$	−1.45825	+	0.841921i	−0.0899196	+	0.0519151i	−0.544286	−	0.838900i	$-0.683199\pi$
$263$	−1.45825	+	0.841921i	−0.0899196	+	0.0519151i	0.454366	+	0.890815i	$0.349866\pi$
$264$		0			0
$265$	−8.21570	−	1.87518i	−0.504686	−	0.115191i
$266$	−36.4405	−	37.7839i	−2.23431	−	2.31668i
$267$		0			0
$268$	65.1818	+	20.1059i	3.98161	+	1.22816i
$269$	−7.64504	+	19.4792i	−0.466126	+	1.18767i	0.483795	+	0.875181i	$0.339258\pi$
$269$	−7.64504	+	19.4792i	−0.466126	+	1.18767i	−0.949921	+	0.312489i	$0.898837\pi$
$270$		0			0
$271$	5.75145	−	18.6458i	0.349376	−	1.13265i	−0.594985	−	0.803737i	$-0.702842\pi$
$271$	5.75145	−	18.6458i	0.349376	−	1.13265i	0.944361	−	0.328912i	$-0.106682\pi$
$272$	−5.70012	−	24.9739i	−0.345621	−	1.51426i
$273$		0			0
$274$	−3.54754	+	15.5428i	−0.214315	+	0.938975i
$275$	−5.63874	−	3.25553i	−0.340029	−	0.196316i
$276$		0			0
$277$	4.17247	−	1.28704i	0.250700	−	0.0773306i	−0.166858	−	0.985981i	$-0.553362\pi$
$277$	4.17247	−	1.28704i	0.250700	−	0.0773306i	0.417558	+	0.908650i	$0.362886\pi$
$278$	−2.25785	+	30.1290i	−0.135417	+	1.80701i
$279$		0			0
$280$	−17.6930	+	32.0588i	−1.05736	+	1.91588i
$281$	−12.6794	−	10.1115i	−0.756389	−	0.603200i	0.167495	−	0.985873i	$-0.446432\pi$
$281$	−12.6794	−	10.1115i	−0.756389	−	0.603200i	−0.923884	+	0.382673i	$0.875004\pi$
$282$		0			0
$283$	−2.67459	+	17.7447i	−0.158988	+	1.05481i	0.756944	+	0.653480i	$0.226692\pi$
$283$	−2.67459	+	17.7447i	−0.158988	+	1.05481i	−0.915932	+	0.401334i	$0.868547\pi$
$284$	3.45264	−	5.06410i	0.204877	−	0.300499i
$285$		0			0
$286$	−14.6194	+	30.3576i	−0.864466	+	1.79508i
$287$	4.68406	+	9.26472i	0.276491	+	0.546879i
$288$		0			0
$289$	−9.13612	+	6.22890i	−0.537419	+	0.366406i
$290$	−15.4302	+	14.3172i	−0.906095	+	0.840734i
$291$		0			0
$292$	40.4770	−	15.8861i	2.36874	−	0.929661i
$293$	−32.9586			−1.92546			−0.962731	−	0.270461i	$-0.912824\pi$
$293$	−32.9586			−1.92546			−0.962731	+	0.270461i	$0.912824\pi$
$294$		0			0
$295$	20.5227			1.19488
$296$	41.1543	−	16.1519i	2.39204	−	0.938808i
$297$		0			0
$298$	24.3557	−	22.5988i	1.41089	−	1.30911i
$299$	−19.0327	+	12.9763i	−1.10069	+	0.750436i
$300$		0			0
$301$	8.78225	+	1.82690i	0.506201	+	0.105301i
$302$	−2.11686	+	4.39571i	−0.121812	+	0.252945i
$303$		0			0
$304$	44.5881	−	65.3987i	2.55730	−	3.75087i
$305$	1.77940	−	11.8055i	0.101888	−	0.675983i
$306$		0			0
$307$	−4.83163	−	3.85309i	−0.275755	−	0.219908i	0.475840	−	0.879532i	$-0.342144\pi$
$307$	−4.83163	−	3.85309i	−0.275755	−	0.219908i	−0.751596	+	0.659624i	$0.770715\pi$
$308$	−2.61886	+	47.1408i	−0.149223	+	2.68609i
$309$		0			0
$310$	2.38192	−	31.7846i	0.135284	−	1.80524i
$311$	8.13363	−	2.50889i	0.461216	−	0.142266i	−0.0554351	−	0.998462i	$-0.517655\pi$
$311$	8.13363	−	2.50889i	0.461216	−	0.142266i	0.516651	+	0.856196i	$0.327178\pi$
$312$		0			0
$313$	−20.3319	−	11.7386i	−1.14923	−	0.663507i	−0.200529	−	0.979688i	$-0.564266\pi$
$313$	−20.3319	−	11.7386i	−1.14923	−	0.663507i	−0.948699	+	0.316181i	$0.897599\pi$
$314$	5.85083	−	25.6342i	0.330182	−	1.44662i
$315$		0			0
$316$	−11.5168	−	50.4583i	−0.647870	−	2.83850i
$317$	1.54066	−	4.99470i	0.0865322	−	0.280530i	−0.901956	−	0.431828i	$-0.857869\pi$
$317$	1.54066	−	4.99470i	0.0865322	−	0.280530i	0.988488	+	0.151297i	$0.0483451\pi$
$318$		0			0
$319$	−5.89959	+	15.0319i	−0.330314	+	0.841626i
$320$	−19.0055	−	5.86244i	−1.06244	−	0.327720i
$321$		0			0
$322$	−24.8190	+	37.9567i	−1.38311	+	2.11524i
$323$	17.9016	+	4.08593i	0.996074	+	0.227347i
$324$		0			0
$325$	5.52329	−	3.18888i	0.306377	−	0.176887i
$326$	8.46806	+	27.4528i	0.469002	+	1.52047i
$327$		0			0
$328$	−23.7411	+	18.9329i	−1.31088	+	1.04540i
$329$	−3.63366	+	12.6414i	−0.200330	+	0.696940i
$330$		0			0
$331$	2.08468	+	1.93430i	0.114584	+	0.106319i	0.735384	−	0.677650i	$-0.237002\pi$
$331$	2.08468	+	1.93430i	0.114584	+	0.106319i	−0.620800	+	0.783969i	$0.713192\pi$
$332$	−68.3315	−	10.2993i	−3.75018	−	0.565248i
$333$		0			0
$334$	−7.48715	−	49.6740i	−0.409679	−	2.71804i
$335$	22.2574	+	10.7186i	1.21605	+	0.585620i
$336$		0			0
$337$	−3.74529	+	1.80364i	−0.204019	+	0.0982503i	−0.533103	−	0.846050i	$-0.678974\pi$
$337$	−3.74529	+	1.80364i	−0.204019	+	0.0982503i	0.329084	+	0.944301i	$0.393260\pi$
$338$	0.697233	+	1.02265i	0.0379245	+	0.0556250i
$339$		0			0
$340$	−1.60877	−	21.4675i	−0.0872476	−	1.16424i
$341$	−8.93339	−	22.7619i	−0.483770	−	1.23263i
$342$		0			0
$343$	−7.05644	+	17.1233i	−0.381012	+	0.924570i
$344$			26.2381i			1.41467i
$345$		0			0
$346$	46.7587	−	3.50408i	2.51376	−	0.188381i
$347$	7.22248	+	7.78398i	0.387723	+	0.417866i	0.896508	−	0.443028i	$-0.146096\pi$
$347$	7.22248	+	7.78398i	0.387723	+	0.417866i	−0.508785	+	0.860894i	$0.669905\pi$
$348$		0			0
$349$	3.07452	+	6.38430i	0.164575	+	0.341744i	0.966905	−	0.255137i	$-0.0821207\pi$
$349$	3.07452	+	6.38430i	0.164575	+	0.341744i	−0.802330	+	0.596881i	$0.796406\pi$
$350$	7.63772	−	9.96610i	0.408253	−	0.532710i
$351$		0			0
$352$	−43.5995	+	6.57156i	−2.32386	+	0.350265i
$353$	−22.5490	−	15.3737i	−1.20016	−	0.818257i	−0.212856	−	0.977084i	$-0.568276\pi$
$353$	−22.5490	−	15.3737i	−1.20016	−	0.818257i	−0.987306	+	0.158827i	$0.949229\pi$
$354$		0			0
$355$	1.50980	−	1.62717i	0.0801316	−	0.0863614i
$356$	−21.8952	+	27.4557i	−1.16044	+	1.45515i
$357$		0			0
$358$	26.4390	+	33.1534i	1.39734	+	1.75221i
$359$	13.5615	+	1.01630i	0.715750	+	0.0536380i	0.427627	−	0.903955i	$-0.359350\pi$
$359$	13.5615	+	1.01630i	0.715750	+	0.0536380i	0.288123	+	0.957593i	$0.406969\pi$
$360$		0			0
$361$	18.8688	+	32.6817i	0.993094	+	1.72009i
$362$	2.06547	−	3.57750i	0.108559	−	0.188029i
$363$		0			0
$364$	−38.7066	−	25.3093i	−2.02878	−	1.32657i
$365$	15.3530	−	3.50422i	0.803612	−	0.183419i
$366$		0			0
$367$	−28.0445	−	11.0066i	−1.46391	−	0.574542i	−0.506235	−	0.862395i	$-0.668963\pi$
$367$	−28.0445	−	11.0066i	−1.46391	−	0.574542i	−0.957675	+	0.287853i	$0.907059\pi$
$368$	−63.6555	−	24.9830i	−3.31827	−	1.30233i
$369$		0			0
$370$	26.2359	−	5.98817i	1.36394	−	0.311310i
$371$	−1.17145	−	12.4119i	−0.0608187	−	0.644393i
$372$		0			0
$373$	−3.76187	+	6.51575i	−0.194782	+	0.337373i	−0.946829	−	0.321737i	$-0.895733\pi$
$373$	−3.76187	+	6.51575i	−0.194782	+	0.337373i	0.752047	+	0.659110i	$0.229067\pi$
$374$	−11.6021	−	20.0954i	−0.599928	−	1.03911i
$375$		0			0
$376$	−38.3658	−	2.87512i	−1.97856	−	0.148273i
$377$	−9.86209	−	12.3667i	−0.507923	−	0.636916i
$378$		0			0
$379$	2.63147	−	3.29975i	0.135169	−	0.169497i	−0.709640	−	0.704564i	$-0.751142\pi$
$379$	2.63147	−	3.29975i	0.135169	−	0.169497i	0.844809	+	0.535067i	$0.179714\pi$
$380$	45.2446	−	48.7621i	2.32100	−	2.50144i
$381$		0			0
$382$	16.0071	+	10.9135i	0.818996	+	0.558382i
$383$	−4.24118	+	0.639255i	−0.216714	+	0.0326644i	−0.256502	−	0.966544i	$-0.582570\pi$
$383$	−4.24118	+	0.639255i	−0.216714	+	0.0326644i	0.0397876	+	0.999208i	$0.487332\pi$
$384$		0			0
$385$	−3.48239	+	16.7405i	−0.177479	+	0.853176i
$386$	−2.38908	−	4.96098i	−0.121601	−	0.252507i
$387$		0			0
$388$	4.57389	+	4.92948i	0.232204	+	0.250257i
$389$	−13.0184	+	0.975597i	−0.660061	+	0.0494647i	−0.400549	−	0.916275i	$-0.631181\pi$
$389$	−13.0184	+	0.975597i	−0.660061	+	0.0494647i	−0.259512	+	0.965740i	$0.583562\pi$
$390$		0			0
$391$		−	15.8636i		−	0.802257i
$392$	−53.2397	−	10.0070i	−2.68901	−	0.505431i
$393$		0			0
$394$	5.90459	+	15.0447i	0.297469	+	0.757939i
$395$	−1.40074	−	18.6916i	−0.0704790	−	0.940477i
$396$		0			0
$397$	18.0630	+	26.4936i	0.906558	+	1.32968i	0.943851	+	0.330372i	$0.107174\pi$
$397$	18.0630	+	26.4936i	0.906558	+	1.32968i	−0.0372929	+	0.999304i	$0.511873\pi$
$398$	57.4773	−	27.6796i	2.88108	−	1.38745i
$399$		0			0
$400$	17.0580	+	8.21471i	0.852901	+	0.410735i
$401$	0.0147931	+	0.0981455i	0.000738730	+	0.00490115i	0.989197	−	0.146591i	$-0.0468302\pi$
$401$	0.0147931	+	0.0981455i	0.000738730	+	0.00490115i	−0.988458	+	0.151492i	$0.951592\pi$
$402$		0			0
$403$	23.6840	+	3.56979i	1.17979	+	0.177824i
$404$	31.3045	+	29.0463i	1.55746	+	1.44511i
$405$		0			0
$406$	−27.2642	−	15.0470i	−1.35310	−	0.746768i
$407$	16.1407	−	12.8718i	0.800064	−	0.638030i
$408$		0			0
$409$	−1.32490	−	4.29523i	−0.0655123	−	0.212386i	0.916898	−	0.399122i	$-0.130685\pi$
$409$	−1.32490	−	4.29523i	−0.0655123	−	0.212386i	−0.982410	+	0.186737i	$0.940209\pi$
$410$	−16.0073	+	9.24181i	−0.790543	+	0.456420i
$411$		0			0
$412$	−71.6902	−	16.3628i	−3.53192	−	0.806139i
$413$	9.50760	+	28.8347i	0.467838	+	1.41886i
$414$		0			0
$415$	−23.9147	−	7.37671i	−1.17393	−	0.362108i
$416$	15.7788	−	40.2037i	0.773618	−	1.97115i
$417$		0			0
$418$	21.1338	−	68.5140i	1.03369	−	3.35113i
$419$	−3.03434	−	13.2943i	−0.148237	−	0.649470i	−0.993375	−	0.114921i	$-0.963339\pi$
$419$	−3.03434	−	13.2943i	−0.148237	−	0.649470i	0.845137	−	0.534549i	$-0.179519\pi$
$420$		0			0
$421$	5.61051	−	24.5813i	0.273440	−	1.19802i	−0.632483	−	0.774574i	$-0.717964\pi$
$421$	5.61051	−	24.5813i	0.273440	−	1.19802i	0.905923	−	0.423443i	$-0.139179\pi$
$422$	−15.3624	−	8.86946i	−0.747828	−	0.431759i
$423$		0			0
$424$	34.8462	−	10.7486i	1.69228	−	0.522000i
$425$	−0.328224	+	4.37985i	−0.0159212	+	0.212454i
$426$		0			0
$427$	17.4113	−	2.96910i	0.842592	−	0.143685i
$428$	57.8439	+	46.1289i	2.79599	+	2.22973i
$429$		0			0
$430$	−2.38035	+	15.7926i	−0.114791	+	0.761587i
$431$	7.62931	−	11.1901i	0.367491	−	0.539010i	−0.597303	−	0.802015i	$-0.703761\pi$
$431$	7.62931	−	11.1901i	0.367491	−	0.539010i	0.964794	+	0.263005i	$0.0847135\pi$
$432$		0			0
$433$	−6.37412	+	13.2360i	−0.306321	+	0.636081i	−0.996128	−	0.0879115i	$-0.971981\pi$
$433$	−6.37412	+	13.2360i	−0.306321	+	0.636081i	0.689808	+	0.723993i	$0.257695\pi$
$434$	45.7612	−	11.3783i	2.19661	−	0.546174i
$435$		0			0
$436$	−62.9346	+	42.9081i	−3.01402	+	2.05492i
$437$	35.9325	−	33.3405i	1.71888	−	1.59489i
$438$		0			0
$439$	−0.572327	+	0.224622i	−0.0273157	+	0.0107206i	−0.378960	−	0.925413i	$-0.623718\pi$
$439$	−0.572327	+	0.224622i	−0.0273157	+	0.0107206i	0.351644	+	0.936134i	$0.385623\pi$
$440$	−50.0145			−2.38435
$441$		0			0
$442$	22.7290			1.08111
$443$	14.0115	−	5.49909i	0.665704	−	0.261270i	−0.00833484	−	0.999965i	$-0.502653\pi$
$443$	14.0115	−	5.49909i	0.665704	−	0.261270i	0.674039	+	0.738696i	$0.264558\pi$
$444$		0			0
$445$	−9.32302	+	8.65049i	−0.441953	+	0.410073i
$446$	17.6859	−	12.0581i	0.837453	−	0.570966i
$447$		0			0
$448$	−0.567938	−	29.4190i	−0.0268326	−	1.38992i
$449$	2.79316	−	5.80005i	0.131817	−	0.273721i	−0.824605	−	0.565709i	$-0.808602\pi$
$449$	2.79316	−	5.80005i	0.131817	−	0.273721i	0.956422	+	0.291988i	$0.0943167\pi$
$450$		0			0
$451$	−7.98781	+	11.7160i	−0.376131	+	0.551683i
$452$	2.32994	−	15.4582i	0.109591	−	0.727091i
$453$		0			0
$454$	6.30940	+	5.03157i	0.296115	+	0.236144i
$455$	−12.4953	−	11.1530i	−0.585790	−	0.522860i
$456$		0			0
$457$	2.37788	−	31.7305i	0.111232	−	1.48429i	−0.610443	−	0.792060i	$-0.709008\pi$
$457$	2.37788	−	31.7305i	0.111232	−	1.48429i	0.721675	−	0.692232i	$-0.243372\pi$
$458$	−0.379298	+	0.116998i	−0.0177234	+	0.00546695i
$459$		0			0
$460$	−49.7691	−	28.7342i	−2.32050	−	1.33974i
$461$	−3.77229	+	16.5275i	−0.175693	+	0.769762i	0.807894	+	0.589328i	$0.200607\pi$
$461$	−3.77229	+	16.5275i	−0.175693	+	0.769762i	−0.983587	+	0.180434i	$0.942250\pi$
$462$		0			0
$463$	5.33414	+	23.3704i	0.247899	+	1.08612i	0.933624	+	0.358255i	$0.116628\pi$
$463$	5.33414	+	23.3704i	0.247899	+	1.08612i	−0.685725	+	0.727860i	$0.740515\pi$
$464$	13.8405	−	44.8698i	0.642529	−	2.08303i
$465$		0			0
$466$	−20.6861	+	52.7072i	−0.958263	+	2.44161i
$467$	−14.6360	−	4.51462i	−0.677275	−	0.208912i	−0.0630118	−	0.998013i	$-0.520071\pi$
$467$	−14.6360	−	4.51462i	−0.677275	−	0.208912i	−0.614263	+	0.789101i	$0.710547\pi$
$468$		0			0
$469$	−4.74855	+	36.2376i	−0.219268	+	1.67330i
$470$	−22.8314	−	5.21111i	−1.05313	−	0.240370i
$471$		0			0
$472$	−76.9104	+	44.4042i	−3.54009	+	2.04387i
$473$	3.61143	+	11.7080i	0.166054	+	0.538333i
$474$		0			0
$475$	−10.6106	+	8.46165i	−0.486846	+	0.388247i
$476$	29.4168	−	12.2056i	1.34832	−	0.559444i
$477$		0			0
$478$	17.2471	+	16.0030i	0.788865	+	0.731960i
$479$	12.0884	+	1.82203i	0.552331	+	0.0832506i	0.419277	−	0.907858i	$-0.362284\pi$
$479$	12.0884	+	1.82203i	0.552331	+	0.0832506i	0.133054	+	0.991109i	$0.457522\pi$
$480$		0			0
$481$	3.01393	+	19.9962i	0.137424	+	0.911746i
$482$	21.4211	+	10.3158i	0.975702	+	0.469873i
$483$		0			0
$484$	−9.16231	+	4.41233i	−0.416468	+	0.200561i
$485$	1.37191	+	2.01222i	0.0622950	+	0.0913700i
$486$		0			0
$487$	−1.41790	−	18.9206i	−0.0642513	−	0.857374i	−0.932483	−	0.361215i	$-0.882362\pi$
$487$	−1.41790	−	18.9206i	−0.0642513	−	0.857374i	0.868231	−	0.496160i	$-0.165257\pi$
$488$	18.8748	+	48.0922i	0.854422	+	2.17703i
$489$		0			0
$490$	−31.1369	−	10.8531i	−1.40662	−	0.490295i
$491$			40.3477i			1.82087i	0.413654	+	0.910434i	$0.364252\pi$
$491$			40.3477i			1.82087i	−0.413654	+	0.910434i	$0.635748\pi$
$492$		0			0
$493$	10.8625	−	0.814034i	0.489224	−	0.0366623i
$494$	47.7695	+	51.4832i	2.14925	+	2.31634i
$495$		0			0
$496$	30.8502	+	64.0611i	1.38522	+	2.87643i
$497$	2.98565	+	1.36746i	0.133925	+	0.0613390i
$498$		0			0
$499$	−4.49533	+	0.677562i	−0.201239	+	0.0303318i	−0.248888	−	0.968532i	$-0.580065\pi$
$499$	−4.49533	+	0.677562i	−0.201239	+	0.0303318i	0.0476494	+	0.998864i	$0.484827\pi$
$500$	49.6292	+	33.8366i	2.21949	+	1.51322i
$501$		0			0
$502$	−21.3747	+	23.0364i	−0.953998	+	1.02817i
$503$	−1.74258	+	2.18513i	−0.0776980	+	0.0974302i	−0.819161	−	0.573563i	$-0.805561\pi$
$503$	−1.74258	+	2.18513i	−0.0776980	+	0.0974302i	0.741463	+	0.670993i	$0.234132\pi$
$504$		0			0
$505$	9.64281	+	12.0917i	0.429099	+	0.538074i
$506$	−61.7705	−	4.62906i	−2.74603	−	0.205787i
$507$		0			0
$508$	−31.2187	−	54.0724i	−1.38511	−	2.39908i
$509$	0.169361	−	0.293342i	0.00750680	−	0.0130022i	−0.862248	−	0.506487i	$-0.830944\pi$
$509$	0.169361	−	0.293342i	0.00750680	−	0.0130022i	0.869754	+	0.493485i	$0.164277\pi$
$510$		0			0
$511$	12.0361	+	19.9477i	0.532445	+	0.882436i
$512$	−33.5686	+	7.66181i	−1.48354	+	0.338607i
$513$		0			0
$514$	31.5160	+	12.3691i	1.39011	+	0.545579i
$515$	−24.7902	−	9.72945i	−1.09239	−	0.428731i
$516$		0			0
$517$	−17.5153	+	3.99775i	−0.770321	+	0.175821i
$518$	20.5678	+	34.0876i	0.903698	+	1.49772i
$519$		0			0
$520$	24.4952	−	42.4270i	1.07419	−	1.86055i
$521$	1.73700	+	3.00857i	0.0760994	+	0.131808i	0.901564	−	0.432646i	$-0.142420\pi$
$521$	1.73700	+	3.00857i	0.0760994	+	0.131808i	−0.825464	+	0.564454i	$0.809087\pi$
$522$		0			0
$523$	16.9196	+	1.26795i	0.739844	+	0.0554436i	0.439320	−	0.898331i	$-0.355219\pi$
$523$	16.9196	+	1.26795i	0.739844	+	0.0554436i	0.300524	+	0.953774i	$0.402839\pi$
$524$	−25.7838	−	32.3319i	−1.12637	−	1.41242i
$525$		0			0
$526$	2.76535	−	3.46763i	0.120575	−	0.151196i
$527$	−11.2192	+	12.0914i	−0.488715	+	0.526709i
$528$		0			0
$529$	−15.9862	−	10.8992i	−0.695050	−	0.473877i
$530$	21.9489	−	3.30826i	0.953399	−	0.143702i
$531$		0			0
$532$	89.4720	+	40.9792i	3.87910	+	1.77667i
$533$	−6.02645	−	12.5141i	−0.261035	−	0.542044i
$534$		0			0
$535$	18.2249	+	19.6418i	0.787932	+	0.849189i
$536$	−106.603	+	7.98877i	−4.60454	+	0.345062i
$537$		0			0
$538$		−	55.1188i		−	2.37634i
$539$	−25.1340	+	2.86261i	−1.08260	+	0.123301i
$540$		0			0
$541$	11.8096	+	30.0905i	0.507736	+	1.29369i	0.923283	+	0.384119i	$0.125495\pi$
$541$	11.8096	+	30.0905i	0.507736	+	1.29369i	−0.415547	+	0.909572i	$0.636410\pi$
$542$	3.84088	+	51.2529i	0.164980	+	2.20150i
$543$		0			0
$544$	16.7547	+	24.5747i	0.718354	+	1.05363i
$545$	−24.8540	+	11.9690i	−1.06463	+	0.512698i
$546$		0			0
$547$	6.87858	+	3.31255i	0.294107	+	0.141634i	0.575119	−	0.818070i	$-0.304956\pi$
$547$	6.87858	+	3.31255i	0.294107	+	0.141634i	−0.281012	+	0.959704i	$0.590670\pi$
$548$	−4.45454	−	29.5539i	−0.190288	−	1.26248i
$549$		0			0
$550$	16.9587	+	2.55611i	0.723121	+	0.108993i
$551$	24.6736	+	22.8937i	1.05113	+	0.975306i
$552$		0			0
$553$	25.6130	−	10.6274i	1.08918	−	0.451921i
$554$	−8.99211	+	7.17096i	−0.382038	+	0.304665i
$555$		0			0
$556$	−16.6954	−	54.1253i	−0.708045	−	2.29542i
$557$	30.3332	−	17.5129i	1.28526	−	0.742044i	0.307454	−	0.951563i	$-0.400523\pi$
$557$	30.3332	−	17.5129i	1.28526	−	0.742044i	0.977805	+	0.209519i	$0.0671898\pi$
$558$		0			0
$559$	−11.7005	−	2.67057i	−0.494880	−	0.112953i
$560$	6.46010	−	49.2990i	0.272989	−	2.08326i
$561$		0			0
$562$	40.8195	+	12.5911i	1.72187	+	0.531125i
$563$	−9.58141	+	24.4130i	−0.403808	+	1.02889i	0.573901	+	0.818924i	$0.305429\pi$
$563$	−9.58141	+	24.4130i	−0.403808	+	1.02889i	−0.977710	+	0.209962i	$0.932666\pi$
$564$		0			0
$565$	1.66878	−	5.41006i	0.0702062	−	0.227603i
$566$	−10.5181	−	46.0827i	−0.442108	−	1.93700i
$567$		0			0
$568$	−2.13742	+	9.36464i	−0.0896841	+	0.392932i
$569$	24.4831	+	14.1353i	1.02638	+	0.592583i	0.915946	−	0.401301i	$-0.131442\pi$
$569$	24.4831	+	14.1353i	1.02638	+	0.592583i	0.110437	+	0.993883i	$0.464775\pi$
$570$		0			0
$571$	−26.3016	+	8.11296i	−1.10069	+	0.339517i	−0.791305	−	0.611421i	$-0.790598\pi$
$571$	−26.3016	+	8.11296i	−1.10069	+	0.339517i	−0.309381	+	0.950938i	$0.600122\pi$
$572$	4.72052	−	62.9909i	0.197375	−	2.63378i
$573$		0			0
$574$	−20.4006	−	18.2090i	−0.851504	−	0.760028i
$575$	9.16686	+	7.31032i	0.382284	+	0.304862i
$576$		0			0
$577$	−1.40499	+	9.32147i	−0.0584903	+	0.388058i	0.940363	+	0.340174i	$0.110486\pi$
$577$	−1.40499	+	9.32147i	−0.0584903	+	0.388058i	−0.998853	+	0.0478841i	$0.984752\pi$
$578$	16.4070	−	24.0647i	0.682443	−	1.00096i
$579$		0			0
$580$	17.1217	−	35.5537i	0.710942	−	1.47629i
$581$	−0.714637	−	37.0179i	−0.0296481	−	1.53576i
$582$		0			0
$583$	14.0696	−	9.59249i	0.582703	−	0.397280i
$584$	−49.9545	+	46.3510i	−2.06713	+	1.91802i
$585$		0			0
$586$	80.8124	−	31.7165i	3.33833	−	1.31020i
$587$	4.59513			0.189661			0.0948306	−	0.995493i	$-0.469769\pi$
$587$	4.59513			0.189661			0.0948306	+	0.995493i	$0.469769\pi$
$588$		0			0
$589$	−50.9673			−2.10007
$590$	−50.3204	+	19.7493i	−2.07166	+	0.813066i
$591$		0			0
$592$	−44.0058	+	40.8314i	−1.80863	+	1.67816i
$593$	21.5535	−	14.6949i	0.885097	−	0.603449i	−0.0331531	−	0.999450i	$-0.510555\pi$
$593$	21.5535	−	14.6949i	0.885097	−	0.603449i	0.918250	+	0.396002i	$0.129603\pi$
$594$		0			0
$595$	11.1935	−	2.78320i	0.458888	−	0.114100i
$596$	−27.0256	+	56.1193i	−1.10701	+	2.29874i
$597$		0			0
$598$	34.1797	−	50.1324i	1.39771	−	2.05007i
$599$	4.85200	−	32.1909i	0.198247	−	1.31528i	−0.639316	−	0.768944i	$-0.720782\pi$
$599$	4.85200	−	32.1909i	0.198247	−	1.31528i	0.837563	−	0.546341i	$-0.183980\pi$
$600$		0			0
$601$	1.15697	+	0.922654i	0.0471938	+	0.0376358i	0.646803	−	0.762657i	$-0.276106\pi$
$601$	1.15697	+	0.922654i	0.0471938	+	0.0376358i	−0.599609	+	0.800293i	$0.704677\pi$
$602$	−23.2916	+	3.97185i	−0.949294	+	0.161880i
$603$		0			0
$604$	0.683520	−	9.12094i	0.0278120	−	0.371126i
$605$	−3.51934	+	1.08557i	−0.143081	+	0.0441348i
$606$		0			0
$607$	16.0586	+	9.27142i	0.651797	+	0.376315i	0.789144	−	0.614208i	$-0.210524\pi$
$607$	16.0586	+	9.27142i	0.651797	+	0.376315i	−0.137347	+	0.990523i	$0.543858\pi$
$608$	−20.4505	+	89.5995i	−0.829377	+	3.63374i
$609$		0			0
$610$	6.99767	+	30.6588i	0.283327	+	1.24134i
$611$	5.18707	−	16.8161i	0.209846	−	0.680305i
$612$		0			0
$613$	9.73929	−	24.8153i	0.393366	−	1.00228i	−0.587781	−	0.809020i	$-0.699998\pi$
$613$	9.73929	−	24.8153i	0.393366	−	1.00228i	0.981147	−	0.193261i	$-0.0619063\pi$
$614$	15.5547	+	4.79800i	0.627738	+	0.193631i
$615$		0			0
$616$	−23.1703	−	70.2711i	−0.933559	−	2.83130i
$617$	−26.1918	−	5.97810i	−1.05444	−	0.240669i	−0.340043	−	0.940410i	$-0.610442\pi$
$617$	−26.1918	−	5.97810i	−1.05444	−	0.240669i	−0.714397	+	0.699741i	$0.753299\pi$
$618$		0			0
$619$	1.76710	−	1.02024i	0.0710259	−	0.0410068i	−0.464066	−	0.885800i	$-0.653610\pi$
$619$	1.76710	−	1.02024i	0.0710259	−	0.0410068i	0.535092	+	0.844794i	$0.320277\pi$
$620$	17.6129	+	57.0995i	0.707350	+	2.29317i
$621$		0			0
$622$	−17.5288	+	13.9788i	−0.702842	+	0.560497i
$623$	−16.4732	−	9.09143i	−0.659983	−	0.364241i
$624$		0			0
$625$	9.34282	+	8.66887i	0.373713	+	0.346755i
$626$	61.1488	+	9.21670i	2.44400	+	0.368374i
$627$		0			0
$628$	7.34671	+	48.7422i	0.293166	+	1.94503i
$629$	−12.5471	−	6.04235i	−0.500284	−	0.240924i
$630$		0			0
$631$	−3.10135	+	1.49353i	−0.123463	+	0.0594565i	−0.494595	−	0.869123i	$-0.664684\pi$
$631$	−3.10135	+	1.49353i	−0.123463	+	0.0594565i	0.371133	+	0.928580i	$0.378969\pi$
$632$	45.6917	+	67.0174i	1.81752	+	2.66581i
$633$		0			0
$634$	1.02887	+	13.7293i	0.0408616	+	0.545260i
$635$	−8.26125	−	21.0493i	−0.327838	−	0.835317i
$636$		0			0
$637$	9.88134	−	22.7230i	0.391513	−	0.900317i
$638$		−	42.5346i		−	1.68396i
$639$		0			0
$640$	8.72392	−	0.653768i	0.344843	−	0.0258424i
$641$	−10.0345	−	10.8146i	−0.396340	−	0.427153i	0.503079	−	0.864240i	$-0.332200\pi$
$641$	−10.0345	−	10.8146i	−0.396340	−	0.427153i	−0.899419	+	0.437088i	$0.856010\pi$
$642$		0			0
$643$	12.4660	+	25.8858i	0.491609	+	1.02084i	0.988245	+	0.152878i	$0.0488542\pi$
$643$	12.4660	+	25.8858i	0.491609	+	1.02084i	−0.496636	+	0.867959i	$0.665432\pi$
$644$	17.3153	−	83.2381i	0.682320	−	3.28004i
$645$		0			0
$646$	−47.8257	+	7.20856i	−1.88168	+	0.283617i
$647$	14.3926	+	9.81273i	0.565833	+	0.385778i	0.812183	−	0.583403i	$-0.198279\pi$
$647$	14.3926	+	9.81273i	0.565833	+	0.385778i	−0.246350	+	0.969181i	$0.579231\pi$
$648$		0			0
$649$	−28.2071	+	30.4000i	−1.10722	+	1.19330i
$650$	−10.4741	+	13.1341i	−0.410827	+	0.515161i
$651$		0			0
$652$	−33.5806	−	42.1087i	−1.31512	−	1.64910i
$653$	−16.6668	−	1.24900i	−0.652220	−	0.0488772i	−0.255489	−	0.966812i	$-0.582237\pi$
$653$	−16.6668	−	1.24900i	−0.652220	−	0.0488772i	−0.396731	+	0.917935i	$0.629856\pi$
$654$		0			0
$655$	−7.48842	−	12.9703i	−0.292597	−	0.506792i
$656$	20.6162	−	35.7084i	0.804929	−	1.39418i
$657$		0			0
$658$	−3.25545	−	34.4925i	−0.126911	−	1.34466i
$659$	34.9386	−	7.97450i	1.36101	−	0.310643i	0.521162	−	0.853458i	$-0.325499\pi$
$659$	34.9386	−	7.97450i	1.36101	−	0.310643i	0.839852	+	0.542815i	$0.182642\pi$
$660$		0			0
$661$	−43.5575	−	17.0950i	−1.69419	−	0.664920i	−0.695620	−	0.718410i	$-0.744870\pi$
$661$	−43.5575	−	17.0950i	−1.69419	−	0.664920i	−0.998568	+	0.0534897i	$0.982966\pi$
$662$	−6.97291	−	2.73666i	−0.271010	−	0.106363i
$663$		0			0
$664$	105.583	−	24.0986i	4.09741	−	0.935207i
$665$	29.8295	+	19.5048i	1.15674	+	0.756363i
$666$		0			0
$667$	14.5395	−	25.1831i	0.562971	−	0.975095i
$668$	47.0884	+	81.5595i	1.82190	+	3.15563i
$669$		0			0
$670$	−64.8884	−	4.86272i	−2.50686	−	0.187863i
$671$	15.0417	+	18.8617i	0.580679	+	0.728149i
$672$		0			0
$673$	21.7277	−	27.2457i	0.837542	−	1.05024i	−0.160459	−	0.987043i	$-0.551297\pi$
$673$	21.7277	−	27.2457i	0.837542	−	1.05024i	0.998001	−	0.0632019i	$-0.0201312\pi$
$674$	7.44754	−	8.02654i	0.286869	−	0.309171i
$675$		0			0
$676$	−1.91719	−	1.30712i	−0.0737380	−	0.0502737i
$677$	−24.5223	+	3.69615i	−0.942470	+	0.142054i	−0.602264	−	0.798297i	$-0.705735\pi$
$677$	−24.5223	+	3.69615i	−0.942470	+	0.142054i	−0.340205	+	0.940351i	$0.610497\pi$
$678$		0			0
$679$	−2.19163	+	2.85975i	−0.0841069	+	0.109747i
$680$	14.6384	+	30.3969i	0.561356	+	1.16567i
$681$		0			0
$682$	43.8082	+	47.2140i	1.67750	+	1.80792i
$683$	−16.4540	+	1.23306i	−0.629596	+	0.0471817i	−0.385707	−	0.922622i	$-0.626042\pi$
$683$	−16.4540	+	1.23306i	−0.629596	+	0.0471817i	−0.243889	+	0.969803i	$0.578423\pi$
$684$		0			0
$685$		−	10.8242i		−	0.413571i
$686$	0.823972	−	48.7757i	0.0314594	−	1.86227i
$687$		0			0
$688$	−13.0162	−	33.1646i	−0.496236	−	1.26439i
$689$	1.24649	+	16.6332i	0.0474873	+	0.633675i
$690$		0			0
$691$	1.14649	+	1.68159i	0.0436146	+	0.0639709i	0.847427	−	0.530912i	$-0.178151\pi$
$691$	1.14649	+	1.68159i	0.0436146	+	0.0639709i	−0.803812	+	0.594883i	$0.797198\pi$
$692$	−79.1999	+	38.1407i	−3.01073	+	1.44989i
$693$		0			0
$694$	−25.1997	−	12.1355i	−0.956568	−	0.460659i
$695$	−3.05737	−	20.2843i	−0.115973	−	0.769429i
$696$		0			0
$697$	9.45841	+	1.42563i	0.358263	+	0.0539994i
$698$	−13.6822	−	12.6953i	−0.517880	−	0.480522i
$699$		0			0
$700$	−6.50289	+	22.6233i	−0.245786	+	0.855080i
$701$	24.4713	−	19.5152i	0.924267	−	0.737079i	−0.0407762	−	0.999168i	$-0.512983\pi$
$701$	24.4713	−	19.5152i	0.924267	−	0.737079i	0.965044	+	0.262090i	$0.0844116\pi$
$702$		0			0
$703$	−12.6836	−	41.1194i	−0.478373	−	1.55085i
$704$	34.8058	−	20.0951i	1.31179	−	0.757364i
$705$		0			0
$706$	70.0830	+	15.9960i	2.63761	+	0.602017i
$707$	−12.5218	+	19.1500i	−0.470929	+	0.720211i
$708$		0			0
$709$	−17.2167	−	5.31064i	−0.646586	−	0.199445i	−0.0459197	−	0.998945i	$-0.514622\pi$
$709$	−17.2167	−	5.31064i	−0.646586	−	0.199445i	−0.600666	+	0.799500i	$0.705098\pi$
$710$	−2.13607	+	5.44262i	−0.0801654	+	0.204258i
$711$		0			0
$712$	16.2219	−	52.5902i	0.607943	−	1.97090i
$713$	9.79815	+	42.9285i	0.366944	+	1.60769i
$714$		0			0
$715$	5.09058	−	22.3033i	0.190377	−	0.834095i
$716$	−68.8466	−	39.7486i	−2.57292	−	1.48548i
$717$		0			0
$718$	−34.2300	+	10.5586i	−1.27745	+	0.394042i
$719$	−1.58598	+	21.1634i	−0.0591471	+	0.789263i	0.886222	+	0.463261i	$0.153321\pi$
$719$	−1.58598	+	21.1634i	−0.0591471	+	0.789263i	−0.945369	+	0.326002i	$0.894298\pi$
$720$		0			0
$721$	2.18539	−	39.3380i	0.0813880	−	1.46502i
$722$	−77.7151	−	61.9758i	−2.89226	−	2.30650i
$723$		0			0
$724$	−1.15424	+	7.65786i	−0.0428968	+	0.284602i
$725$	−4.53532	+	6.65209i	−0.168437	+	0.247052i
$726$		0			0
$727$	−3.87602	+	8.04863i	−0.143753	+	0.298507i	−0.960397	−	0.278635i	$-0.910118\pi$
$727$	−3.87602	+	8.04863i	−0.143753	+	0.298507i	0.816644	+	0.577142i	$0.195832\pi$
$728$	70.9585	+	14.7609i	2.62990	+	0.547076i
$729$		0			0
$730$	−34.2724	+	23.3665i	−1.26848	+	0.864834i
$731$	6.05865	−	5.62160i	0.224087	−	0.207923i
$732$		0			0
$733$	−10.5663	+	4.14695i	−0.390274	+	0.153171i	−0.552360	−	0.833605i	$-0.686273\pi$
$733$	−10.5663	+	4.14695i	−0.390274	+	0.153171i	0.162087	+	0.986777i	$0.448178\pi$
$734$	79.3552			2.92905
$735$		0			0
$736$	79.3989			2.92668
$737$	−46.4686	+	18.2376i	−1.71169	+	0.671790i
$738$		0			0
$739$	−16.4690	+	15.2810i	−0.605823	+	0.562121i	−0.922298	−	0.386479i	$-0.873691\pi$
$739$	−16.4690	+	15.2810i	−0.605823	+	0.562121i	0.316475	+	0.948601i	$0.397501\pi$
$740$	−41.6836	+	28.4194i	−1.53232	+	1.04472i
$741$		0			0
$742$	14.8165	+	29.3059i	0.543930	+	1.07585i
$743$	15.4681	−	32.1198i	0.567468	−	1.17836i	−0.397890	−	0.917433i	$-0.630257\pi$
$743$	15.4681	−	32.1198i	0.567468	−	1.17836i	0.965358	−	0.260927i	$-0.0840283\pi$
$744$		0			0
$745$	−12.7075	+	18.6385i	−0.465567	+	0.682861i
$746$	2.95367	−	19.5963i	0.108142	−	0.717472i
$747$		0			0
$748$	34.0106	+	27.1226i	1.24355	+	0.991700i
$749$	−19.1539	+	34.7058i	−0.699868	+	1.26812i
$750$		0			0
$751$	2.28540	−	30.4966i	0.0833955	−	1.11283i	−0.785838	−	0.618433i	$-0.787768\pi$
$751$	2.28540	−	30.4966i	0.0833955	−	1.11283i	0.869233	−	0.494402i	$-0.164613\pi$
$752$	49.9201	−	15.3983i	1.82040	−	0.561519i
$753$		0			0
$754$	36.0818	+	20.8319i	1.31402	+	0.758652i
$755$	0.737105	−	3.22947i	0.0268260	−	0.117532i
$756$		0			0
$757$	−4.69912	−	20.5882i	−0.170793	−	0.748291i	−0.985674	−	0.168663i	$-0.946055\pi$
$757$	−4.69912	−	20.5882i	−0.170793	−	0.748291i	0.814881	−	0.579628i	$-0.196802\pi$
$758$	−3.27679	+	10.6231i	−0.119018	+	0.385848i
$759$		0			0
$760$	−38.0863	+	97.0422i	−1.38153	+	3.52009i
$761$	−21.1016	−	6.50898i	−0.764932	−	0.235950i	−0.112350	−	0.993669i	$-0.535838\pi$
$761$	−21.1016	−	6.50898i	−0.764932	−	0.235950i	−0.652582	+	0.757718i	$0.726314\pi$
$762$		0			0
$763$	−28.3308	−	29.3753i	−1.02565	−	1.06346i
$764$	−35.4093	−	8.08194i	−1.28106	−	0.292394i
$765$		0			0
$766$	9.78395	−	5.64876i	0.353508	−	0.204098i
$767$	−11.9734	−	38.8167i	−0.432333	−	1.40159i
$768$		0			0
$769$	28.0841	−	22.3963i	1.01274	−	0.807632i	0.0313193	−	0.999509i	$-0.490029\pi$
$769$	28.0841	−	22.3963i	1.01274	−	0.807632i	0.981419	+	0.191878i	$0.0614577\pi$
$770$	−7.57104	−	44.3979i	−0.272841	−	1.59999i
$771$		0			0
$772$	7.56710	+	7.02124i	0.272346	+	0.252700i
$773$	−17.7403	−	2.67391i	−0.638072	−	0.0961740i	−0.177964	−	0.984037i	$-0.556951\pi$
$773$	−17.7403	−	2.67391i	−0.638072	−	0.0961740i	−0.460108	+	0.887863i	$0.652189\pi$
$774$		0			0
$775$	−1.81700	−	12.0550i	−0.0652687	−	0.433030i
$776$	−9.49508	−	4.57259i	−0.340853	−	0.164146i
$777$		0			0
$778$	30.9816	−	14.9199i	1.11074	−	0.534906i
$779$	16.6495	+	24.4203i	0.596531	+	0.874950i
$780$		0			0
$781$	0.335196	+	4.47288i	0.0119943	+	0.160052i
$782$	15.2658	+	38.8966i	0.545903	+	1.39094i
$783$		0			0
$784$	72.2585	−	13.7623i	2.58066	−	0.491511i
$785$			17.8520i			0.637164i
$786$		0			0
$787$	15.8280	−	1.18614i	0.564206	−	0.0422814i	0.210426	−	0.977610i	$-0.432515\pi$
$787$	15.8280	−	1.18614i	0.564206	−	0.0422814i	0.353780	+	0.935329i	$0.384896\pi$
$788$	−20.6085	−	22.2107i	−0.734149	−	0.791224i
$789$		0			0
$790$	21.4217	+	44.4827i	0.762151	+	1.58262i
$791$	8.37430	−	0.161667i	0.297756	−	0.00574823i
$792$		0			0
$793$	−23.3672	+	3.52203i	−0.829792	+	0.125071i
$794$	−69.7846	−	47.5784i	−2.47656	−	1.68849i
$795$		0			0
$796$	−81.3472	+	87.6714i	−2.88327	+	3.10743i
$797$	25.6062	−	32.1091i	0.907017	−	1.13736i	−0.0830193	−	0.996548i	$-0.526456\pi$
$797$	25.6062	−	32.1091i	0.907017	−	1.13736i	0.990036	−	0.140815i	$-0.0449723\pi$
$798$		0			0
$799$	7.55610	+	9.47505i	0.267316	+	0.335203i
$800$	−21.9216	−	1.64279i	−0.775045	−	0.0580816i
$801$		0			0
$802$	−0.130718	−	0.226411i	−0.00461583	−	0.00799485i
$803$	−15.9109	+	27.5585i	−0.561483	+	0.972517i
$804$		0			0
$805$	10.6939	−	28.8743i	0.376910	−	1.01769i
$806$	−61.5070	+	14.0386i	−2.16649	+	0.494488i
$807$		0			0
$808$	−62.2995	−	24.4508i	−2.19169	−	0.860175i
$809$	31.1093	+	12.2095i	1.09375	+	0.429264i	0.842520	−	0.538665i	$-0.181071\pi$
$809$	31.1093	+	12.2095i	1.09375	+	0.429264i	0.251226	+	0.967928i	$0.419166\pi$
$810$		0			0
$811$	34.7913	−	7.94090i	1.22169	−	0.278843i	0.437417	−	0.899259i	$-0.355893\pi$
$811$	34.7913	−	7.94090i	1.22169	−	0.278843i	0.784273	+	0.620416i	$0.213036\pi$
$812$	57.8854	+	7.58526i	2.03138	+	0.266191i
$813$		0			0
$814$	−27.1893	+	47.0932i	−0.952983	+	1.65061i
$815$	−9.75284	−	16.8924i	−0.341627	−	0.591715i
$816$		0			0
$817$	25.4669	+	1.90848i	0.890972	+	0.0667692i
$818$	7.38195	+	9.25667i	0.258104	+	0.323652i
$819$		0			0
$820$	21.6049	−	27.0917i	0.754477	−	0.946084i
$821$	−6.25502	+	6.74131i	−0.218302	+	0.235273i	−0.832702	−	0.553721i	$-0.813207\pi$
$821$	−6.25502	+	6.74131i	−0.218302	+	0.235273i	0.614401	+	0.788994i	$0.289398\pi$
$822$		0			0
$823$	16.1956	+	11.0419i	0.564542	+	0.384898i	0.811698	−	0.584078i	$-0.198544\pi$
$823$	16.1956	+	11.0419i	0.564542	+	0.384898i	−0.247156	+	0.968976i	$0.579496\pi$
$824$	113.954	−	17.1759i	3.96979	−	0.598350i
$825$		0			0
$826$	−51.0601	−	61.5515i	−1.77661	−	2.14165i
$827$	10.6728	+	22.1623i	0.371130	+	0.770659i	0.999976	−	0.00687070i	$-0.00218703\pi$
$827$	10.6728	+	22.1623i	0.371130	+	0.770659i	−0.628847	+	0.777529i	$0.716473\pi$
$828$		0			0
$829$	−7.97493	−	8.59493i	−0.276981	−	0.298514i	0.579206	−	0.815182i	$-0.303363\pi$
$829$	−7.97493	−	8.59493i	−0.276981	−	0.298514i	−0.856186	+	0.516667i	$0.827172\pi$
$830$	65.7360	−	4.92624i	2.28173	−	0.170992i
$831$		0			0
$832$			39.3674i			1.36482i
$833$	9.09606	+	14.4376i	0.315160	+	0.500234i
$834$		0			0
$835$	12.4608	+	31.7495i	0.431222	+	1.09874i
$836$	10.0449	+	134.040i	0.347412	+	4.63589i
$837$		0			0
$838$	20.2333	+	29.6769i	0.698949	+	1.02517i
$839$	25.3212	−	12.1941i	0.874185	−	0.420985i	0.0576879	−	0.998335i	$-0.481627\pi$
$839$	25.3212	−	12.1941i	0.874185	−	0.420985i	0.816497	+	0.577349i	$0.195913\pi$
$840$		0			0
$841$	−8.13797	−	3.91904i	−0.280620	−	0.135139i
$842$	9.89828	+	65.6708i	0.341117	+	2.26316i
$843$		0			0
$844$	32.8841	+	4.95648i	1.13192	+	0.170609i
$845$	−0.616022	−	0.571585i	−0.0211918	−	0.0196631i
$846$		0			0
$847$	−3.15566	−	4.44180i	−0.108430	−	0.152622i
$848$	−38.7129	+	30.8725i	−1.32941	+	1.06017i
$849$		0			0
$850$	−3.41001	−	11.0550i	−0.116962	−	0.379182i
$851$	−32.1955	+	18.5881i	−1.10365	+	0.637191i
$852$		0			0
$853$	39.2497	+	8.95850i	1.34389	+	0.306733i	0.833170	−	0.553017i	$-0.186523\pi$
$853$	39.2497	+	8.95850i	1.34389	+	0.306733i	0.510715	+	0.859750i	$0.329381\pi$
$854$	−39.8342	+	24.0352i	−1.36310	+	0.822467i
$855$		0			0
$856$	−110.797	−	34.1765i	−3.78698	−	1.16813i
$857$	6.10723	−	15.5610i	0.208619	−	0.531553i	−0.787817	−	0.615910i	$-0.788789\pi$
$857$	6.10723	−	15.5610i	0.208619	−	0.531553i	0.996436	+	0.0843574i	$0.0268837\pi$
$858$		0			0
$859$	−8.77908	+	28.4611i	−0.299538	+	0.971079i	0.673256	+	0.739409i	$0.264895\pi$
$859$	−8.77908	+	28.4611i	−0.299538	+	0.971079i	−0.972794	+	0.231670i	$0.925581\pi$
$860$	−6.66253	−	29.1905i	−0.227190	−	0.995387i
$861$		0			0
$862$	−7.93816	+	34.7793i	−0.270375	+	1.18459i
$863$	20.2279	+	11.6786i	0.688567	+	0.397544i	0.803075	−	0.595878i	$-0.203196\pi$
$863$	20.2279	+	11.6786i	0.688567	+	0.397544i	−0.114508	+	0.993422i	$0.536529\pi$
$864$		0			0
$865$	−30.4215	+	9.38380i	−1.03436	+	0.319059i
$866$	2.89175	−	38.5877i	0.0982657	−	1.31126i
$867$		0			0
$868$	−72.0661	+	51.1990i	−2.44608	+	1.73781i
$869$	29.6128	+	23.6154i	1.00455	+	0.801099i
$870$		0			0
$871$	7.28776	−	48.3511i	0.246936	−	1.63832i
$872$	67.2452	−	98.6306i	2.27721	−	3.34005i
$873$		0			0
$874$	−56.0202	+	116.327i	−1.89491	+	3.93482i
$875$	−13.4014	+	29.2600i	−0.453050	+	0.989167i
$876$		0			0
$877$	−29.2279	+	19.9272i	−0.986956	+	0.672895i	−0.945288	−	0.326237i	$-0.894219\pi$
$877$	−29.2279	+	19.9272i	−0.986956	+	0.672895i	−0.0416675	+	0.999132i	$0.513267\pi$
$878$	1.18715	−	1.10152i	0.0400645	−	0.0371744i
$879$		0			0
$880$	63.2176	−	24.8111i	2.13107	−	0.836382i
$881$	−35.5266			−1.19692			−0.598460	−	0.801153i	$-0.704221\pi$
$881$	−35.5266			−1.19692			−0.598460	+	0.801153i	$0.704221\pi$
$882$		0			0
$883$	−31.8523			−1.07191			−0.535957	−	0.844245i	$-0.680049\pi$
$883$	−31.8523			−1.07191			−0.535957	+	0.844245i	$0.680049\pi$
$884$	−39.6651	+	15.5674i	−1.33408	+	0.523588i
$885$		0			0
$886$	−29.0634	+	26.9669i	−0.976403	+	0.905969i
$887$	−19.9137	+	13.5769i	−0.668637	+	0.455869i	−0.849465	−	0.527646i	$-0.823075\pi$
$887$	−19.9137	+	13.5769i	−0.668637	+	0.455869i	0.180827	+	0.983515i	$0.442123\pi$
$888$		0			0
$889$	25.7474	−	21.3587i	0.863540	−	0.716349i
$890$	14.5350	−	30.1821i	0.487213	−	1.01171i
$891$		0			0
$892$	−22.6055	+	33.1562i	−0.756888	+	1.11015i
$893$	−5.58121	+	37.0289i	−0.186768	+	1.23912i
$894$		0			0
$895$	−22.5096	−	17.9508i	−0.752412	−	0.600029i
$896$	4.96010	+	11.9544i	0.165705	+	0.399367i
$897$		0			0
$898$	−1.26717	+	16.9093i	−0.0422861	+	0.564269i
$899$	−28.8923	+	8.91210i	−0.963613	+	0.297235i
$900$		0			0
$901$	−9.94788	−	5.74341i	−0.331412	−	0.191341i
$902$	8.31117	−	36.4136i	0.276732	−	1.21244i
$903$		0			0
$904$	5.45166	+	23.8853i	0.181319	+	0.794412i
$905$	−0.826702	+	2.68010i	−0.0274805	+	0.0890896i
$906$		0			0
$907$	0.128781	−	0.328130i	0.00427612	−	0.0108954i	−0.928720	−	0.370782i	$-0.879090\pi$
$907$	0.128781	−	0.328130i	0.00427612	−	0.0108954i	0.932996	+	0.359887i	$0.117185\pi$
$908$	−14.4569	−	4.45936i	−0.479769	−	0.147989i
$909$		0			0
$910$	41.3705	+	15.3220i	1.37142	+	0.507918i
$911$	−43.2101	−	9.86243i	−1.43161	−	0.326757i	−0.564734	−	0.825273i	$-0.691021\pi$
$911$	−43.2101	−	9.86243i	−1.43161	−	0.326757i	−0.866881	+	0.498516i	$0.833879\pi$
$912$		0			0
$913$	43.7961	−	25.2857i	1.44944	−	0.836835i
$914$	24.7044	+	80.0896i	0.817148	+	2.64913i
$915$		0			0
$916$	0.581790	−	0.463962i	0.0192229	−	0.0153297i
$917$	14.7543	−	16.5301i	0.487230	−	0.545873i
$918$		0			0
$919$	3.93331	+	3.64958i	0.129748	+	0.120389i	0.742378	−	0.669981i	$-0.233698\pi$
$919$	3.93331	+	3.64958i	0.129748	+	0.120389i	−0.612630	+	0.790370i	$0.709888\pi$
$920$	89.0581	+	13.4234i	2.93616	+	0.442555i
$921$		0			0
$922$	−6.65522	−	44.1545i	−0.219178	−	1.45415i
$923$	−3.95848	−	1.90630i	−0.130295	−	0.0627468i
$924$		0			0
$925$	9.27357	−	4.46592i	0.304913	−	0.146838i
$926$	−35.5687	−	52.1697i	−1.16886	−	1.71440i
$927$		0			0
$928$	4.07432	+	54.3680i	0.133746	+	1.78472i
$929$	2.43805	+	6.21206i	0.0799900	+	0.203811i	0.965274	−	0.261240i	$-0.0841313\pi$
$929$	2.43805	+	6.21206i	0.0799900	+	0.203811i	−0.885284	+	0.465051i	$0.846036\pi$
$930$		0			0
$931$	−13.5853	+	50.9468i	−0.445242	+	1.66971i
$932$		−	106.149i		−	3.47703i
$933$		0			0
$934$	40.2311	−	3.01491i	1.31640	−	0.0986508i
$935$	10.7158	+	11.5488i	0.350443	+	0.377688i
$936$		0			0
$937$	6.62343	+	13.7537i	0.216378	+	0.449314i	0.980699	−	0.195522i	$-0.0626401\pi$
$937$	6.62343	+	13.7537i	0.216378	+	0.449314i	−0.764321	+	0.644836i	$0.776926\pi$
$938$	−23.2288	−	93.4219i	−0.758448	−	3.05033i
$939$		0			0
$940$	43.4128	−	6.54343i	1.41597	−	0.213423i
$941$	30.6168	+	20.8742i	0.998078	+	0.680478i	0.948001	−	0.318267i	$-0.103101\pi$
$941$	30.6168	+	20.8742i	0.998078	+	0.680478i	0.0500769	+	0.998745i	$0.484053\pi$
$942$		0			0
$943$	17.3679	−	18.7181i	0.565576	−	0.609546i
$944$	75.1857	−	94.2798i	2.44708	−	3.06855i
$945$		0			0
$946$	−20.1217	−	25.2319i	−0.654214	−	0.820359i
$947$	56.6172	+	4.24287i	1.83981	+	0.137875i	0.948754	−	0.316015i	$-0.102345\pi$
$947$	56.6172	+	4.24287i	1.83981	+	0.137875i	0.891058	+	0.453890i	$0.149964\pi$
$948$		0			0
$949$	−15.5851	−	26.9942i	−0.505914	−	0.876269i
$950$	17.8737	−	30.9581i	0.579899	−	1.00441i
$951$		0			0
$952$	−35.9265	+	34.6492i	−1.16439	+	1.12299i
$953$	−53.1943	+	12.1413i	−1.72313	+	0.393294i	−0.965709	−	0.259628i	$-0.916400\pi$
$953$	−53.1943	+	12.1413i	−1.72313	+	0.393294i	−0.757425	+	0.652922i	$0.773543\pi$
$954$		0			0
$955$	−12.2444	−	4.80557i	−0.396220	−	0.155505i
$956$	−41.0591	−	16.1145i	−1.32795	−	0.521180i
$957$		0			0
$958$	−31.3933	+	7.16531i	−1.01427	+	0.231501i
$959$	15.2081	−	5.01455i	0.491096	−	0.161928i
$960$		0			0
$961$	7.39194	−	12.8032i	0.238450	−	0.413007i
$962$	−26.6326	−	46.1290i	−0.858668	−	1.48726i
$963$		0			0
$964$	−44.4479	−	3.33091i	−1.43157	−	0.107281i
$965$	2.33091	+	2.92287i	0.0750348	+	0.0940906i
$966$		0			0
$967$	10.4506	−	13.1046i	0.336068	−	0.421416i	−0.584869	−	0.811128i	$-0.698854\pi$
$967$	10.4506	−	13.1046i	0.336068	−	0.421416i	0.920937	+	0.389712i	$0.127425\pi$
$968$	10.8402	−	11.6829i	0.348416	−	0.375504i
$969$		0			0
$970$	−5.30021	−	3.61362i	−0.170180	−	0.116026i
$971$	38.1097	−	5.74411i	1.22300	−	0.184337i	0.494373	−	0.869250i	$-0.335398\pi$
$971$	38.1097	−	5.74411i	1.22300	−	0.184337i	0.728625	+	0.684913i	$0.240160\pi$
$972$		0			0
$973$	27.0834	−	13.6928i	0.868254	−	0.438972i
$974$	21.6842	+	45.0277i	0.694806	+	1.44278i
$975$		0			0
$976$	−47.7149	−	51.4245i	−1.52732	−	1.64606i
$977$	34.9164	−	2.61662i	1.11707	−	0.0837132i	0.496629	−	0.867963i	$-0.334571\pi$
$977$	34.9164	−	2.61662i	1.11707	−	0.0837132i	0.620445	+	0.784250i	$0.286952\pi$
$978$		0			0
$979$		−	25.6996i		−	0.821362i
$980$	61.7713	−	2.38590i	1.97321	−	0.0762148i
$981$		0			0
$982$	−38.8272	−	98.9301i	−1.23903	−	3.15699i
$983$	−3.86606	−	51.5890i	−0.123308	−	1.64543i	−0.625172	−	0.780487i	$-0.714971\pi$
$983$	−3.86606	−	51.5890i	−0.123308	−	1.64543i	0.501864	−	0.864946i	$-0.332648\pi$
$984$		0			0
$985$	−6.18138	−	9.06642i	−0.196955	−	0.288880i
$986$	−25.8509	+	12.4491i	−0.823260	+	0.396461i
$987$		0			0
$988$	−118.625	−	57.1270i	−3.77398	−	1.81745i
$989$	−3.28838	−	21.8170i	−0.104565	−	0.693740i
$990$		0			0
$991$	−17.1473	−	2.58455i	−0.544703	−	0.0821008i	−0.129074	−	0.991635i	$-0.541201\pi$
$991$	−17.1473	−	2.58455i	−0.544703	−	0.0821008i	−0.415629	+	0.909534i	$0.636439\pi$
$992$	−60.5186	−	56.1530i	−1.92147	−	1.78286i
$993$		0			0
$994$	−8.63654	−	0.479795i	−0.273935	−	0.0152182i
$995$	−33.8640	+	27.0057i	−1.07356	+	0.856137i
$996$		0			0
$997$	10.0927	+	32.7198i	0.319640	+	1.03625i	0.962732	+	0.270457i	$0.0871749\pi$
$997$	10.0927	+	32.7198i	0.319640	+	1.03625i	−0.643092	+	0.765789i	$0.722349\pi$
$998$	10.3702	−	5.98726i	0.328264	−	0.189523i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.278.1	✓	216
3.2	odd	2	inner	441.2.bg.a.278.18	yes	216
49.3	odd	42	inner	441.2.bg.a.395.18	yes	216
147.101	even	42	inner	441.2.bg.a.395.1	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.1	✓	216	1.1	even	1	trivial
441.2.bg.a.278.18	yes	216	3.2	odd	2	inner
441.2.bg.a.395.1	yes	216	147.101	even	42	inner
441.2.bg.a.395.18	yes	216	49.3	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)

\(f(q)\)	\(=\)	\(q+(-2.45194 + 0.962314i) q^{2} +(3.61984 - 3.35872i) q^{4} +(1.47762 - 1.00742i) q^{5} +(2.09999 + 1.60937i) q^{7} +(-3.35777 + 6.97247i) q^{8} +O(q^{10})\)	\(q+(-2.45194 + 0.962314i) q^{2} +(3.61984 - 3.35872i) q^{4} +(1.47762 - 1.00742i) q^{5} +(2.09999 + 1.60937i) q^{7} +(-3.35777 + 6.97247i) q^{8} +(-2.65357 + 3.89208i) q^{10} +(-0.538606 + 3.57342i) q^{11} +(-2.76752 - 2.20702i) q^{13} +(-6.69775 - 1.92522i) q^{14} +(0.785279 - 10.4788i) q^{16} +(2.32943 - 0.718533i) q^{17} +(6.52328 + 3.76622i) q^{19} +(1.96509 - 8.60964i) q^{20} +(-2.11812 - 9.28010i) q^{22} +(1.91813 - 6.21843i) q^{23} +(-0.658247 + 1.67719i) q^{25} +(8.90963 + 2.74826i) q^{26} +(13.0070 - 1.22762i) q^{28} +(4.35647 + 0.994336i) q^{29} +(-5.85986 + 3.38319i) q^{31} +(3.59633 + 11.6590i) q^{32} +(-5.02015 + 4.00344i) q^{34} +(4.72430 + 0.262454i) q^{35} +(-4.18776 - 3.88567i) q^{37} +(-19.6190 - 2.95708i) q^{38} +(2.06274 + 13.6854i) q^{40} +(3.53525 + 1.70249i) q^{41} +(3.05468 - 1.47106i) q^{43} +(10.0524 + 14.7442i) q^{44} +(1.28095 + 17.0930i) q^{46} +(1.81628 + 4.62779i) q^{47} +(1.81988 + 6.75929i) q^{49} -4.74579i q^{50} +(-17.4308 + 1.30625i) q^{52} +(-3.20504 - 3.45421i) q^{53} +(2.80409 + 5.82276i) q^{55} +(-18.2725 + 9.23822i) q^{56} +(-11.6387 + 1.75424i) q^{58} +(9.48163 + 6.46446i) q^{59} +(4.54073 - 4.89374i) q^{61} +(11.1123 - 13.9344i) q^{62} +(-6.93408 - 8.69506i) q^{64} +(-6.31275 - 0.473075i) q^{65} +(6.90681 + 11.9629i) q^{67} +(6.01880 - 10.4249i) q^{68} +(-11.8362 + 3.90274i) q^{70} +(1.21008 - 0.276193i) q^{71} +(8.19697 + 3.21707i) q^{73} +(14.0074 + 5.49749i) q^{74} +(36.2629 - 8.27678i) q^{76} +(-6.88200 + 6.63731i) q^{77} +(5.24053 - 9.07686i) q^{79} +(-9.39628 - 16.2748i) q^{80} +(-10.3066 - 0.772369i) q^{82} +(-8.72515 - 10.9410i) q^{83} +(2.71814 - 3.40844i) q^{85} +(-6.07427 + 6.54650i) q^{86} +(-23.1070 - 15.7541i) q^{88} +(-7.03212 + 1.05992i) q^{89} +(-2.25984 - 9.08866i) q^{91} +(-13.9427 - 28.9522i) q^{92} +(-8.90679 - 9.59923i) q^{94} +(13.4331 - 1.00667i) q^{95} +1.36179i q^{97} +(-10.9668 - 14.8221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 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

Modular forms

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