LMFDB - Embedded newform 351.2.ba.a.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(71,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("351.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	351.89
Dual form			351.2.ba.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841634 - 0.841634i) q^{2} +0.583303i q^{4} +(2.77680 + 0.744040i) q^{5} +(-1.42554 - 0.381973i) q^{7} +(2.17420 + 2.17420i) q^{8} +O(q^{10})$	\(q+(0.841634 - 0.841634i) q^{2} +0.583303i q^{4} +(2.77680 + 0.744040i) q^{5} +(-1.42554 - 0.381973i) q^{7} +(2.17420 + 2.17420i) q^{8} +(2.96326 - 1.71084i) q^{10} +(1.23230 + 1.23230i) q^{11} +(-3.60363 + 0.117561i) q^{13} +(-1.52127 + 0.878303i) q^{14} +2.49315 q^{16} +(-0.939625 + 1.62748i) q^{17} +(4.34907 - 1.16533i) q^{19} +(-0.434001 + 1.61971i) q^{20} +2.07429 q^{22} +(2.82588 - 4.89457i) q^{23} +(2.82688 + 1.63210i) q^{25} +(-2.93400 + 3.13189i) q^{26} +(0.222806 - 0.831522i) q^{28} -6.70089i q^{29} +(0.676611 - 2.52515i) q^{31} +(-2.25007 + 2.25007i) q^{32} +(0.578921 + 2.16056i) q^{34} +(-3.67424 - 2.12132i) q^{35} +(-11.1775 - 2.99499i) q^{37} +(2.67955 - 4.64111i) q^{38} +(4.41961 + 7.65499i) q^{40} +(-0.168067 - 0.627234i) q^{41} +(1.78065 - 1.02806i) q^{43} +(-0.718802 + 0.718802i) q^{44} +(-1.74108 - 6.49779i) q^{46} +(-2.31288 + 0.619735i) q^{47} +(-4.17591 - 2.41096i) q^{49} +(3.75283 - 1.00557i) q^{50} +(-0.0685738 - 2.10201i) q^{52} +11.5633i q^{53} +(2.50496 + 4.33872i) q^{55} +(-2.26892 - 3.92989i) q^{56} +(-5.63970 - 5.63970i) q^{58} +(9.15908 + 9.15908i) q^{59} +(-5.24278 - 9.08077i) q^{61} +(-1.55579 - 2.69471i) q^{62} +8.77378i q^{64} +(-10.0940 - 2.35481i) q^{65} +(3.50643 - 0.939544i) q^{67} +(-0.949313 - 0.548086i) q^{68} +(-4.87774 + 1.30699i) q^{70} +(-2.99663 - 11.1836i) q^{71} +(-8.97423 + 8.97423i) q^{73} +(-11.9280 + 6.88665i) q^{74} +(0.679740 + 2.53683i) q^{76} +(-1.28599 - 2.22739i) q^{77} +(-4.85927 + 8.41651i) q^{79} +(6.92298 + 1.85501i) q^{80} +(-0.669352 - 0.386451i) q^{82} +(-0.712145 - 2.65776i) q^{83} +(-3.82006 + 3.82006i) q^{85} +(0.633407 - 2.36391i) q^{86} +5.35851i q^{88} +(1.57286 - 5.86998i) q^{89} +(5.18203 + 1.20890i) q^{91} +(2.85501 + 1.64834i) q^{92} +(-1.42501 + 2.46819i) q^{94} +12.9435 q^{95} +(-1.35706 + 5.06463i) q^{97} +(-5.54374 + 1.48544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8}+O(q^{10}) $ 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8	$ 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35} - 6 q^{37} - 36 q^{38} - 12 q^{40} - 18 q^{41} - 30 q^{43} - 12 q^{44} - 12 q^{46} + 36 q^{47} - 6 q^{49} + 60 q^{50} + 56 q^{52} - 4 q^{55} + 6 q^{56} + 50 q^{58} + 6 q^{59} + 2 q^{61} - 18 q^{62} - 72 q^{65} + 26 q^{67} - 42 q^{68} - 16 q^{70} + 48 q^{71} - 22 q^{73} - 30 q^{74} + 6 q^{76} - 72 q^{77} + 8 q^{79} + 54 q^{80} - 12 q^{82} - 54 q^{83} - 24 q^{85} + 54 q^{86} - 16 q^{91} - 120 q^{92} + 26 q^{94} + 12 q^{95} - 24 q^{97} - 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8 - 12 * q^10 + 6 * q^11 - 2 * q^13 + 12 * q^14 - 28 * q^16 - 4 * q^19 + 18 * q^20 - 4 * q^22 + 6 * q^23 + 48 * q^26 - 18 * q^31 - 54 * q^32 + 6 * q^34 - 6 * q^35 - 6 * q^37 - 36 * q^38 - 12 * q^40 - 18 * q^41 - 30 * q^43 - 12 * q^44 - 12 * q^46 + 36 * q^47 - 6 * q^49 + 60 * q^50 + 56 * q^52 - 4 * q^55 + 6 * q^56 + 50 * q^58 + 6 * q^59 + 2 * q^61 - 18 * q^62 - 72 * q^65 + 26 * q^67 - 42 * q^68 - 16 * q^70 + 48 * q^71 - 22 * q^73 - 30 * q^74 + 6 * q^76 - 72 * q^77 + 8 * q^79 + 54 * q^80 - 12 * q^82 - 54 * q^83 - 24 * q^85 + 54 * q^86 - 16 * q^91 - 120 * q^92 + 26 * q^94 + 12 * q^95 - 24 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.841634	−	0.841634i	0.595125	−	0.595125i	−0.343886	−	0.939011i	$-0.611743\pi$
$2$	0.841634	−	0.841634i	0.595125	−	0.595125i	0.939011	+	0.343886i	$0.111743\pi$
$3$		0			0
$3$		0			0
$4$			0.583303i			0.291651i
$5$	2.77680	+	0.744040i	1.24182	+	0.332745i	0.819172	−	0.573548i	$-0.194433\pi$
$5$	2.77680	+	0.744040i	1.24182	+	0.332745i	0.422650	+	0.906293i	$0.361100\pi$
$6$		0			0
$7$	−1.42554	−	0.381973i	−0.538804	−	0.144372i	−0.0208532	−	0.999783i	$-0.506638\pi$
$7$	−1.42554	−	0.381973i	−0.538804	−	0.144372i	−0.517951	+	0.855410i	$0.673305\pi$
$8$	2.17420	+	2.17420i	0.768695	+	0.768695i
$9$		0			0
$10$	2.96326	−	1.71084i	0.937065	−	0.541014i
$11$	1.23230	+	1.23230i	0.371552	+	0.371552i	0.868042	−	0.496491i	$-0.165378\pi$
$11$	1.23230	+	1.23230i	0.371552	+	0.371552i	−0.496491	+	0.868042i	$0.665378\pi$
$12$		0			0
$13$	−3.60363	+	0.117561i	−0.999468	+	0.0326056i
$13$	−3.60363	+	0.117561i	−0.999468	+	0.0326056i
$14$	−1.52127	+	0.878303i	−0.406575	+	0.234736i
$15$		0			0
$16$	2.49315			0.623288
$17$	−0.939625	+	1.62748i	−0.227893	+	0.394722i	−0.957183	−	0.289482i	$-0.906517\pi$
$17$	−0.939625	+	1.62748i	−0.227893	+	0.394722i	0.729291	+	0.684204i	$0.239850\pi$
$18$		0			0
$19$	4.34907	−	1.16533i	0.997745	−	0.267345i	0.277245	−	0.960799i	$-0.410579\pi$
$19$	4.34907	−	1.16533i	0.997745	−	0.267345i	0.720501	+	0.693454i	$0.243912\pi$
$20$	−0.434001	+	1.61971i	−0.0970455	+	0.362179i
$21$		0			0
$22$	2.07429			0.442240
$23$	2.82588	−	4.89457i	0.589237	−	1.02059i	−0.405096	−	0.914274i	$-0.632762\pi$
$23$	2.82588	−	4.89457i	0.589237	−	1.02059i	0.994333	−	0.106314i	$-0.0339048\pi$
$24$		0			0
$25$	2.82688	+	1.63210i	0.565376	+	0.326420i
$26$	−2.93400	+	3.13189i	−0.575405	+	0.614213i
$27$		0			0
$28$	0.222806	−	0.831522i	0.0421063	−	0.157143i
$29$		−	6.70089i		−	1.24432i	−0.782888	−	0.622162i	$-0.786254\pi$
$29$		−	6.70089i		−	1.24432i	0.782888	−	0.622162i	$-0.213746\pi$
$30$		0			0
$31$	0.676611	−	2.52515i	0.121523	−	0.453530i	−0.878169	−	0.478350i	$-0.841235\pi$
$31$	0.676611	−	2.52515i	0.121523	−	0.453530i	0.999692	+	0.0248208i	$0.00790153\pi$
$32$	−2.25007	+	2.25007i	−0.397760	+	0.397760i
$33$		0			0
$34$	0.578921	+	2.16056i	0.0992842	+	0.370534i
$35$	−3.67424	−	2.12132i	−0.621059	−	0.358569i
$36$		0			0
$37$	−11.1775	−	2.99499i	−1.83756	−	0.492374i	−0.838912	−	0.544267i	$-0.816808\pi$
$37$	−11.1775	−	2.99499i	−1.83756	−	0.492374i	−0.998653	+	0.0518927i	$0.983475\pi$
$38$	2.67955	−	4.64111i	0.434680	−	0.752888i
$39$		0			0
$40$	4.41961	+	7.65499i	0.698802	+	1.21036i
$41$	−0.168067	−	0.627234i	−0.0262476	−	0.0979574i	0.951559	−	0.307465i	$-0.0994806\pi$
$41$	−0.168067	−	0.627234i	−0.0262476	−	0.0979574i	−0.977807	+	0.209507i	$0.932814\pi$
$42$		0			0
$43$	1.78065	−	1.02806i	0.271547	−	0.156778i	−0.358044	−	0.933705i	$-0.616556\pi$
$43$	1.78065	−	1.02806i	0.271547	−	0.156778i	0.629590	+	0.776927i	$0.283223\pi$
$44$	−0.718802	+	0.718802i	−0.108364	+	0.108364i
$45$		0			0
$46$	−1.74108	−	6.49779i	−0.256708	−	0.958048i
$47$	−2.31288	+	0.619735i	−0.337369	+	0.0903977i	−0.423526	−	0.905884i	$-0.639208\pi$
$47$	−2.31288	+	0.619735i	−0.337369	+	0.0903977i	0.0861575	+	0.996282i	$0.472541\pi$
$48$		0			0
$49$	−4.17591	−	2.41096i	−0.596559	−	0.344424i
$50$	3.75283	−	1.00557i	0.530730	−	0.142209i
$51$		0			0
$52$	−0.0685738	−	2.10201i	−0.00950947	−	0.291496i
$53$			11.5633i			1.58834i	0.607698	+	0.794168i	$0.292093\pi$
$53$			11.5633i			1.58834i	−0.607698	+	0.794168i	$0.707907\pi$
$54$		0			0
$55$	2.50496	+	4.33872i	0.337769	+	0.585033i
$56$	−2.26892	−	3.92989i	−0.303198	−	0.525154i
$57$		0			0
$58$	−5.63970	−	5.63970i	−0.740529	−	0.740529i
$59$	9.15908	+	9.15908i	1.19241	+	1.19241i	0.976388	+	0.216023i	$0.0693086\pi$
$59$	9.15908	+	9.15908i	1.19241	+	1.19241i	0.216023	+	0.976388i	$0.430691\pi$
$60$		0			0
$61$	−5.24278	−	9.08077i	−0.671269	−	1.16267i	−0.977544	−	0.210730i	$-0.932416\pi$
$61$	−5.24278	−	9.08077i	−0.671269	−	1.16267i	0.306275	−	0.951943i	$-0.400917\pi$
$62$	−1.55579	−	2.69471i	−0.197586	−	0.342228i
$63$		0			0
$64$			8.77378i			1.09672i
$65$	−10.0940	−	2.35481i	−1.25201	−	0.292078i
$66$		0			0
$67$	3.50643	−	0.939544i	0.428378	−	0.114784i	−0.0381866	−	0.999271i	$-0.512158\pi$
$67$	3.50643	−	0.939544i	0.428378	−	0.114784i	0.466565	+	0.884487i	$0.345491\pi$
$68$	−0.949313	−	0.548086i	−0.115121	−	0.0664652i
$69$		0			0
$70$	−4.87774	+	1.30699i	−0.583001	+	0.156215i
$71$	−2.99663	−	11.1836i	−0.355635	−	1.32725i	−0.879684	−	0.475559i	$-0.842246\pi$
$71$	−2.99663	−	11.1836i	−0.355635	−	1.32725i	0.524049	−	0.851688i	$-0.324421\pi$
$72$		0			0
$73$	−8.97423	+	8.97423i	−1.05035	+	1.05035i	−0.0516906	+	0.998663i	$0.516461\pi$
$73$	−8.97423	+	8.97423i	−1.05035	+	1.05035i	−0.998663	+	0.0516906i	$0.983539\pi$
$74$	−11.9280	+	6.88665i	−1.38661	+	0.800557i
$75$		0			0
$76$	0.679740	+	2.53683i	0.0779716	+	0.290994i
$77$	−1.28599	−	2.22739i	−0.146552	−	0.253835i
$78$		0			0
$79$	−4.85927	+	8.41651i	−0.546711	+	0.946931i	0.451786	+	0.892126i	$0.350787\pi$
$79$	−4.85927	+	8.41651i	−0.546711	+	0.946931i	−0.998497	+	0.0548048i	$0.982546\pi$
$80$	6.92298	+	1.85501i	0.774012	+	0.207396i
$81$		0			0
$82$	−0.669352	−	0.386451i	−0.0739176	−	0.0426763i
$83$	−0.712145	−	2.65776i	−0.0781681	−	0.291727i	0.915765	−	0.401715i	$-0.131586\pi$
$83$	−0.712145	−	2.65776i	−0.0781681	−	0.291727i	−0.993933	+	0.109987i	$0.964919\pi$
$84$		0			0
$85$	−3.82006	+	3.82006i	−0.414344	+	0.414344i
$86$	0.633407	−	2.36391i	0.0683020	−	0.254907i
$87$		0			0
$88$			5.35851i			0.571219i
$89$	1.57286	−	5.86998i	0.166722	−	0.622217i	−0.831092	−	0.556135i	$-0.812284\pi$
$89$	1.57286	−	5.86998i	0.166722	−	0.622217i	0.997814	−	0.0660814i	$-0.0210497\pi$
$90$		0			0
$91$	5.18203	+	1.20890i	0.543225	+	0.126727i
$92$	2.85501	+	1.64834i	0.297656	+	0.171852i
$93$		0			0
$94$	−1.42501	+	2.46819i	−0.146979	+	0.254575i
$95$	12.9435			1.32798
$96$		0			0
$97$	−1.35706	+	5.06463i	−0.137789	+	0.514235i	0.862182	+	0.506599i	$0.169097\pi$
$97$	−1.35706	+	5.06463i	−0.137789	+	0.514235i	−0.999971	+	0.00763623i	$0.997569\pi$
$98$	−5.54374	+	1.48544i	−0.560003	+	0.150052i
$99$		0			0
$100$	−0.952008	+	1.64893i	−0.0952008	+	0.164893i
$101$	3.02851			0.301348			0.150674	−	0.988584i	$-0.451856\pi$
$101$	3.02851			0.301348			0.150674	+	0.988584i	$0.451856\pi$
$102$		0			0
$103$	15.9431	−	9.20475i	1.57092	−	0.906971i	0.574864	−	0.818249i	$-0.305055\pi$
$103$	15.9431	−	9.20475i	1.57092	−	0.906971i	0.996056	−	0.0887220i	$-0.0282783\pi$
$104$	−8.09061	−	7.57941i	−0.793350	−	0.743222i
$105$		0			0
$106$	9.73204	+	9.73204i	0.945259	+	0.945259i
$107$	−3.97340	+	2.29404i	−0.384123	+	0.221774i	−0.679611	−	0.733573i	$-0.737851\pi$
$107$	−3.97340	+	2.29404i	−0.384123	+	0.221774i	0.295487	+	0.955347i	$0.404518\pi$
$108$		0			0
$109$	0.138592	+	0.138592i	0.0132747	+	0.0132747i	0.713713	−	0.700438i	$-0.247012\pi$
$109$	0.138592	+	0.138592i	0.0132747	+	0.0132747i	−0.700438	+	0.713713i	$0.747012\pi$
$110$	5.75988	+	1.54335i	0.549183	+	0.147153i
$111$		0			0
$112$	−3.55409	−	0.952316i	−0.335830	−	0.0899854i
$113$			7.46794i			0.702524i	0.936277	+	0.351262i	$0.114247\pi$
$113$			7.46794i			0.702524i	−0.936277	+	0.351262i	$0.885753\pi$
$114$		0			0
$115$	11.4887	−	11.4887i	1.07132	−	1.07132i
$116$	3.90865			0.362909
$117$		0			0
$118$	15.4172			1.41927
$119$	1.96113	−	1.96113i	0.179776	−	0.179776i
$120$		0			0
$121$		−	7.96289i		−	0.723899i
$122$	−12.0552	−	3.23018i	−1.09143	−	0.292447i
$123$		0			0
$124$	1.47292	+	0.394669i	0.132273	+	0.0354423i
$125$	−3.52846	−	3.52846i	−0.315595	−	0.315595i
$126$		0			0
$127$	−9.37062	+	5.41013i	−0.831508	+	0.480071i	−0.854369	−	0.519667i	$-0.826056\pi$
$127$	−9.37062	+	5.41013i	−0.831508	+	0.480071i	0.0228608	+	0.999739i	$0.492723\pi$
$128$	2.88417	+	2.88417i	0.254927	+	0.254927i
$129$		0			0
$130$	−10.4774	+	6.51360i	−0.918926	+	0.571280i
$131$	−6.84566	+	3.95234i	−0.598108	+	0.345318i	−0.768297	−	0.640094i	$-0.778896\pi$
$131$	−6.84566	+	3.95234i	−0.598108	+	0.345318i	0.170189	+	0.985411i	$0.445562\pi$
$132$		0			0
$133$	−6.64490			−0.576186
$134$	2.16038	−	3.74188i	0.186628	−	0.323249i
$135$		0			0
$136$	−5.58139	+	1.49553i	−0.478600	+	0.128241i
$137$	2.19061	−	8.17545i	0.187156	−	0.698476i	−0.807003	−	0.590548i	$-0.798912\pi$
$137$	2.19061	−	8.17545i	0.187156	−	0.698476i	0.994159	−	0.107928i	$-0.0344216\pi$
$138$		0			0
$139$	0.469919			0.0398580			0.0199290	−	0.999801i	$-0.493656\pi$
$139$	0.469919			0.0398580			0.0199290	+	0.999801i	$0.493656\pi$
$140$	1.23737	−	2.14319i	0.104577	−	0.181133i
$141$		0			0
$142$	−11.9346	−	6.89042i	−1.00153	−	0.578231i
$143$	−4.58562	−	4.29588i	−0.383469	−	0.359239i
$144$		0			0
$145$	4.98574	−	18.6070i	0.414043	−	1.54523i
$146$			15.1060i			1.25018i
$147$		0			0
$148$	1.74699	−	6.51985i	0.143602	−	0.535928i
$149$	3.83653	−	3.83653i	0.314301	−	0.314301i	−0.532272	−	0.846573i	$-0.678662\pi$
$149$	3.83653	−	3.83653i	0.314301	−	0.314301i	0.846573	+	0.532272i	$0.178662\pi$
$150$		0			0
$151$	−5.12016	−	19.1087i	−0.416673	−	1.55504i	−0.781462	−	0.623953i	$-0.785525\pi$
$151$	−5.12016	−	19.1087i	−0.416673	−	1.55504i	0.364789	−	0.931090i	$-0.381141\pi$
$152$	11.9894	+	6.92208i	0.972468	+	0.561455i
$153$		0			0
$154$	−2.95698	−	0.792321i	−0.238280	−	0.0638470i
$155$	3.75762	−	6.50839i	0.301819	−	0.522767i
$156$		0			0
$157$	11.5326	+	19.9750i	0.920401	+	1.59418i	0.798796	+	0.601602i	$0.205471\pi$
$157$	11.5326	+	19.9750i	0.920401	+	1.59418i	0.121605	+	0.992579i	$0.461196\pi$
$158$	2.99389	+	11.1734i	0.238181	+	0.888904i
$159$		0			0
$160$	−7.92213	+	4.57384i	−0.626300	+	0.361594i
$161$	−5.89800	+	5.89800i	−0.464827	+	0.464827i
$162$		0			0
$163$	1.15428	+	4.30782i	0.0904100	+	0.337415i	0.996284	−	0.0861334i	$-0.0274511\pi$
$163$	1.15428	+	4.30782i	0.0904100	+	0.337415i	−0.905874	+	0.423548i	$0.860784\pi$
$164$	0.365867	−	0.0980338i	0.0285694	−	0.00765515i
$165$		0			0
$166$	−2.83623	−	1.63750i	−0.220134	−	0.127095i
$167$	−0.344237	+	0.0922379i	−0.0266378	+	0.00713759i	−0.272113	−	0.962265i	$-0.587723\pi$
$167$	−0.344237	+	0.0922379i	−0.0266378	+	0.00713759i	0.245476	+	0.969403i	$0.421056\pi$
$168$		0			0
$169$	12.9724	−	0.847295i	0.997874	−	0.0651766i
$170$			6.43019i			0.493173i
$171$		0			0
$172$	0.599670	+	1.03866i	0.0457244	+	0.0791970i
$173$	5.94881	+	10.3036i	0.452280	+	0.783371i	0.998527	−	0.0542525i	$-0.0172776\pi$
$173$	5.94881	+	10.3036i	0.452280	+	0.783371i	−0.546248	+	0.837624i	$0.683944\pi$
$174$		0			0
$175$	−3.40641	−	3.40641i	−0.257501	−	0.257501i
$176$	3.07230	+	3.07230i	0.231584	+	0.231584i
$177$		0			0
$178$	−3.61661	−	6.26415i	−0.271076	−	0.469518i
$179$	2.92970	+	5.07439i	0.218976	+	0.379278i	0.954495	−	0.298226i	$-0.0963950\pi$
$179$	2.92970	+	5.07439i	0.218976	+	0.379278i	−0.735519	+	0.677504i	$0.763062\pi$
$180$		0			0
$181$		−	8.29778i		−	0.616769i	−0.951262	−	0.308384i	$-0.900212\pi$
$181$		−	8.29778i		−	0.616769i	0.951262	−	0.308384i	$-0.0997883\pi$
$182$	5.37883	−	3.34393i	0.398705	−	0.247868i
$183$		0			0
$184$	16.7858	−	4.49773i	1.23746	−	0.331577i
$185$	−28.8092	−	16.6330i	−2.11809	−	1.22288i
$186$		0			0
$187$	−3.16344	+	0.847640i	−0.231333	+	0.0619856i
$188$	−0.361493	−	1.34911i	−0.0263646	−	0.0983940i
$189$		0			0
$190$	10.8937	−	10.8937i	0.790314	−	0.790314i
$191$	6.20085	−	3.58006i	0.448678	−	0.259044i	−0.258594	−	0.965986i	$-0.583259\pi$
$191$	6.20085	−	3.58006i	0.448678	−	0.259044i	0.707272	+	0.706942i	$0.249926\pi$
$192$		0			0
$193$	−0.709019	−	2.64609i	−0.0510363	−	0.190470i	0.935701	−	0.352793i	$-0.114768\pi$
$193$	−0.709019	−	2.64609i	−0.0510363	−	0.190470i	−0.986738	+	0.162323i	$0.948101\pi$
$194$	3.12041	+	5.40471i	0.224033	+	0.388036i
$195$		0			0
$196$	1.40632	−	2.43582i	0.100452	−	0.173987i
$197$	23.1428	+	6.20110i	1.64886	+	0.441810i	0.959292	−	0.282414i	$-0.0911353\pi$
$197$	23.1428	+	6.20110i	1.64886	+	0.441810i	0.689564	+	0.724224i	$0.257802\pi$
$198$		0			0
$199$	8.08608	+	4.66850i	0.573207	+	0.330941i	0.758429	−	0.651755i	$-0.225967\pi$
$199$	8.08608	+	4.66850i	0.573207	+	0.330941i	−0.185222	+	0.982697i	$0.559300\pi$
$200$	2.59768	+	9.69469i	0.183684	+	0.685518i
$201$		0			0
$202$	2.54890	−	2.54890i	0.179340	−	0.179340i
$203$	−2.55956	+	9.55240i	−0.179646	+	0.670447i
$204$		0			0
$205$		−	1.86675i		−	0.130379i
$206$	5.67122	−	21.1653i	0.395133	−	1.47466i
$207$		0			0
$208$	−8.98441	+	0.293098i	−0.622957	+	0.0203227i
$209$	6.79538	+	3.92332i	0.470046	+	0.271381i
$210$		0			0
$211$	−2.60557	+	4.51298i	−0.179375	+	0.310687i	−0.941667	−	0.336547i	$-0.890741\pi$
$211$	−2.60557	+	4.51298i	−0.179375	+	0.310687i	0.762292	+	0.647234i	$0.224074\pi$
$212$	−6.74488			−0.463240
$213$		0			0
$214$	−1.41341	+	5.27490i	−0.0966184	+	0.360585i
$215$	5.70942	−	1.52984i	0.389379	−	0.104334i
$216$		0			0
$217$	−1.92907	+	3.34125i	−0.130954	+	0.226819i
$218$	0.233287			0.0158002
$219$		0			0
$220$	−2.53079	+	1.46115i	−0.170626	+	0.0985107i
$221$	3.19474	−	5.97530i	0.214901	−	0.401942i
$222$		0			0
$223$	4.83926	+	4.83926i	0.324061	+	0.324061i	0.850323	−	0.526262i	$-0.176407\pi$
$223$	4.83926	+	4.83926i	0.324061	+	0.324061i	−0.526262	+	0.850323i	$0.676407\pi$
$224$	4.06703	−	2.34810i	0.271740	−	0.156889i
$225$		0			0
$226$	6.28527	+	6.28527i	0.418090	+	0.418090i
$227$	12.3360	+	3.30542i	0.818769	+	0.219389i	0.643808	−	0.765187i	$-0.277353\pi$
$227$	12.3360	+	3.30542i	0.818769	+	0.219389i	0.174961	+	0.984575i	$0.444020\pi$
$228$		0			0
$229$	17.6101	+	4.71861i	1.16371	+	0.311815i	0.788446	−	0.615104i	$-0.210886\pi$
$229$	17.6101	+	4.71861i	1.16371	+	0.311815i	0.375263	+	0.926919i	$0.377553\pi$
$230$		−	19.3385i		−	1.27514i
$231$		0			0
$232$	14.5691	−	14.5691i	0.956506	−	0.956506i
$233$	−4.27048			−0.279769			−0.139884	−	0.990168i	$-0.544673\pi$
$233$	−4.27048			−0.279769			−0.139884	+	0.990168i	$0.544673\pi$
$234$		0			0
$235$	−6.88351			−0.449031
$236$	−5.34252	+	5.34252i	−0.347768	+	0.347768i
$237$		0			0
$238$		−	3.30110i		−	0.213979i
$239$	1.08816	+	0.291572i	0.0703874	+	0.0188603i	0.293841	−	0.955854i	$-0.405066\pi$
$239$	1.08816	+	0.291572i	0.0703874	+	0.0188603i	−0.223453	+	0.974715i	$0.571733\pi$
$240$		0			0
$241$	8.52710	+	2.28483i	0.549279	+	0.147179i	0.522776	−	0.852470i	$-0.324896\pi$
$241$	8.52710	+	2.28483i	0.549279	+	0.147179i	0.0265026	+	0.999649i	$0.491563\pi$
$242$	−6.70184	−	6.70184i	−0.430811	−	0.430811i
$243$		0			0
$244$	5.29684	−	3.05813i	0.339095	−	0.195777i
$245$	−9.80181	−	9.80181i	−0.626215	−	0.626215i
$246$		0			0
$247$	−15.5355	+	4.71071i	−0.988498	+	0.299735i
$248$	6.96125	−	4.01908i	0.442040	−	0.255212i
$249$		0			0
$250$	−5.93935			−0.375638
$251$	−8.72352	+	15.1096i	−0.550624	+	0.953708i	0.447606	+	0.894231i	$0.352277\pi$
$251$	−8.72352	+	15.1096i	−0.550624	+	0.953708i	−0.998230	+	0.0594773i	$0.981057\pi$
$252$		0			0
$253$	9.51388	−	2.54924i	0.598133	−	0.160269i
$254$	−3.33328	+	12.4400i	−0.209149	+	0.780554i
$255$		0			0
$256$	−12.6927			−0.793295
$257$	−1.62517	+	2.81488i	−0.101376	+	0.175588i	−0.912252	−	0.409630i	$-0.865658\pi$
$257$	−1.62517	+	2.81488i	−0.101376	+	0.175588i	0.810876	+	0.585218i	$0.198991\pi$
$258$		0			0
$259$	14.7899	+	8.53897i	0.919002	+	0.530586i
$260$	1.37356	−	5.88788i	0.0851849	−	0.365151i
$261$		0			0
$262$	−2.43511	+	9.08797i	−0.150442	+	0.561457i
$263$			18.0770i			1.11467i	0.830286	+	0.557337i	$0.188177\pi$
$263$			18.0770i			1.11467i	−0.830286	+	0.557337i	$0.811823\pi$
$264$		0			0
$265$	−8.60353	+	32.1088i	−0.528511	+	1.97243i
$266$	−5.59258	+	5.59258i	−0.342903	+	0.342903i
$267$		0			0
$268$	0.548039	+	2.04531i	0.0334768	+	0.124937i
$269$	0.992035	+	0.572752i	0.0604854	+	0.0349213i	0.529938	−	0.848037i	$-0.322215\pi$
$269$	0.992035	+	0.572752i	0.0604854	+	0.0349213i	−0.469452	+	0.882958i	$0.655549\pi$
$270$		0			0
$271$	−8.64641	−	2.31680i	−0.525232	−	0.140736i	−0.0135464	−	0.999908i	$-0.504312\pi$
$271$	−8.64641	−	2.31680i	−0.525232	−	0.140736i	−0.511686	+	0.859173i	$0.670979\pi$
$272$	−2.34263	+	4.05755i	−0.142043	+	0.246025i
$273$		0			0
$274$	−5.03705	−	8.72443i	−0.304299	−	0.527062i
$275$	1.47232	+	5.49478i	0.0887844	+	0.331348i
$276$		0			0
$277$	−22.2593	+	12.8514i	−1.33743	+	0.772165i	−0.986426	−	0.164209i	$-0.947493\pi$
$277$	−22.2593	+	12.8514i	−1.33743	+	0.772165i	−0.351003	+	0.936374i	$0.614159\pi$
$278$	0.395500	−	0.395500i	0.0237205	−	0.0237205i
$279$		0			0
$280$	−3.37634	−	12.6007i	−0.201775	−	0.753035i
$281$	−0.868838	+	0.232804i	−0.0518305	+	0.0138879i	−0.284641	−	0.958634i	$-0.591874\pi$
$281$	−0.868838	+	0.232804i	−0.0518305	+	0.0138879i	0.232811	+	0.972522i	$0.425208\pi$
$282$		0			0
$283$	−15.7574	−	9.09752i	−0.936678	−	0.540791i	−0.0477608	−	0.998859i	$-0.515209\pi$
$283$	−15.7574	−	9.09752i	−0.936678	−	0.540791i	−0.888917	+	0.458067i	$0.848542\pi$
$284$	6.52341	−	1.74794i	0.387093	−	0.103721i
$285$		0			0
$286$	−7.47497	+	0.243856i	−0.442004	+	0.0144195i
$287$			0.958344i			0.0565693i
$288$		0			0
$289$	6.73421	+	11.6640i	0.396130	+	0.686117i
$290$	−11.4641	−	19.8565i	−0.673198	−	1.16601i
$291$		0			0
$292$	−5.23469	−	5.23469i	−0.306337	−	0.306337i
$293$	3.24724	+	3.24724i	0.189706	+	0.189706i	0.795569	−	0.605863i	$-0.207172\pi$
$293$	3.24724	+	3.24724i	0.189706	+	0.189706i	−0.605863	+	0.795569i	$0.707172\pi$
$294$		0			0
$295$	18.6182	+	32.2476i	1.08399	+	1.87753i
$296$	−17.7903	−	30.8137i	−1.03404	−	1.79101i
$297$		0			0
$298$		−	6.45792i		−	0.374097i
$299$	−9.60803	+	17.9704i	−0.555646	+	1.03926i
$300$		0			0
$301$	−2.93108	+	0.785381i	−0.168945	+	0.0452686i
$302$	−20.3918	−	11.7732i	−1.17342	−	0.677474i
$303$		0			0
$304$	10.8429	−	2.90535i	0.621883	−	0.166633i
$305$	−7.80168	−	29.1163i	−0.446723	−	1.66719i
$306$		0			0
$307$	3.93098	−	3.93098i	0.224353	−	0.224353i	−0.585976	−	0.810329i	$-0.699289\pi$
$307$	3.93098	−	3.93098i	0.224353	−	0.224353i	0.810329	+	0.585976i	$0.199289\pi$
$308$	1.29925	−	0.750119i	0.0740314	−	0.0427420i
$309$		0			0
$310$	−2.31514	−	8.64023i	−0.131491	−	0.490732i
$311$	10.9466	+	18.9600i	0.620724	+	1.07513i	0.989351	+	0.145548i	$0.0464945\pi$
$311$	10.9466	+	18.9600i	0.620724	+	1.07513i	−0.368627	+	0.929577i	$0.620172\pi$
$312$		0			0
$313$	−3.78444	+	6.55485i	−0.213909	+	0.370502i	−0.952935	−	0.303176i	$-0.901953\pi$
$313$	−3.78444	+	6.55485i	−0.213909	+	0.370502i	0.739025	+	0.673678i	$0.235286\pi$
$314$	26.5179	+	7.10545i	1.49649	+	0.400984i
$315$		0			0
$316$	−4.90937	−	2.83443i	−0.276174	−	0.159449i
$317$	−7.64018	−	28.5136i	−0.429116	−	1.60148i	−0.754768	−	0.655992i	$-0.772251\pi$
$317$	−7.64018	−	28.5136i	−0.429116	−	1.60148i	0.325653	−	0.945489i	$-0.394416\pi$
$318$		0			0
$319$	8.25749	−	8.25749i	0.462331	−	0.462331i
$320$	−6.52805	+	24.3630i	−0.364929	+	1.36193i
$321$		0			0
$322$			9.92792i			0.553261i
$323$	−2.18995	+	8.17300i	−0.121852	+	0.454758i
$324$		0			0
$325$	−10.3789	−	5.54916i	−0.575718	−	0.307812i
$326$	4.59709	+	2.65413i	0.254609	+	0.146999i
$327$		0			0
$328$	0.998319	−	1.72914i	0.0551230	−	0.0954758i
$329$	3.53383			0.194826
$330$		0			0
$331$	4.98513	−	18.6048i	0.274008	−	1.02261i	−0.682496	−	0.730890i	$-0.739105\pi$
$331$	4.98513	−	18.6048i	0.274008	−	1.02261i	0.956503	−	0.291721i	$-0.0942280\pi$
$332$	1.55028	−	0.415396i	0.0850827	−	0.0227978i
$333$		0			0
$334$	−0.212091	+	0.367352i	−0.0116051	+	0.0201006i
$335$	10.4357			0.570163
$336$		0			0
$337$	−15.6291	+	9.02348i	−0.851373	+	0.491541i	−0.861114	−	0.508412i	$-0.830233\pi$
$337$	−15.6291	+	9.02348i	−0.851373	+	0.491541i	0.00974077	+	0.999953i	$0.496899\pi$
$338$	10.2049	−	11.6311i	0.555072	−	0.632648i
$339$		0			0
$340$	−2.22825	−	2.22825i	−0.120844	−	0.120844i
$341$	3.94552	−	2.27794i	0.213662	−	0.123358i
$342$		0			0
$343$	12.3370	+	12.3370i	0.666135	+	0.666135i
$344$	6.10669	+	1.63628i	0.329251	+	0.0882224i
$345$		0			0
$346$	13.6786	+	3.66518i	0.735367	+	0.197041i
$347$		−	25.1292i		−	1.34901i	−0.738272	−	0.674503i	$-0.764358\pi$
$347$		−	25.1292i		−	1.34901i	0.738272	−	0.674503i	$-0.235642\pi$
$348$		0			0
$349$	−16.5014	+	16.5014i	−0.883300	+	0.883300i	−0.993868	−	0.110569i	$-0.964733\pi$
$349$	−16.5014	+	16.5014i	−0.883300	+	0.883300i	0.110569	+	0.993868i	$0.464733\pi$
$350$	−5.73391			−0.306490
$351$		0			0
$352$	−5.54551			−0.295577
$353$	−14.1500	+	14.1500i	−0.753127	+	0.753127i	−0.975061	−	0.221935i	$-0.928763\pi$
$353$	−14.1500	+	14.1500i	−0.753127	+	0.753127i	0.221935	+	0.975061i	$0.428763\pi$
$354$		0			0
$355$		−	33.2841i		−	1.76654i
$356$	3.42398	+	0.917452i	0.181470	+	0.0486248i
$357$		0			0
$358$	6.73652	+	1.80504i	0.356036	+	0.0953996i
$359$	1.97346	+	1.97346i	0.104155	+	0.104155i	0.757264	−	0.653109i	$-0.226536\pi$
$359$	1.97346	+	1.97346i	0.104155	+	0.104155i	−0.653109	+	0.757264i	$0.726536\pi$
$360$		0			0
$361$	1.10195	−	0.636209i	0.0579972	−	0.0334847i
$362$	−6.98370	−	6.98370i	−0.367055	−	0.367055i
$363$		0			0
$364$	−0.705155	+	3.02269i	−0.0369602	+	0.158432i
$365$	−31.5968	+	18.2424i	−1.65385	+	0.954852i
$366$		0			0
$367$	−32.9892			−1.72202			−0.861011	−	0.508587i	$-0.830168\pi$
$367$	−32.9892			−1.72202			−0.861011	+	0.508587i	$0.830168\pi$
$368$	7.04535	−	12.2029i	0.367264	−	0.636120i
$369$		0			0
$370$	−38.2457	+	10.2479i	−1.98830	+	0.532763i
$371$	4.41685	−	16.4839i	0.229311	−	0.855802i
$372$		0			0
$373$	−4.70461			−0.243596			−0.121798	−	0.992555i	$-0.538866\pi$
$373$	−4.70461			−0.243596			−0.121798	+	0.992555i	$0.538866\pi$
$374$	−1.94905	+	3.37586i	−0.100783	+	0.174562i
$375$		0			0
$376$	−6.37609	−	3.68124i	−0.328822	−	0.189845i
$377$	0.787765	+	24.1476i	0.0405720	+	1.24366i
$378$		0			0
$379$	5.09903	−	19.0299i	0.261920	−	0.977498i	−0.702189	−	0.711991i	$-0.747794\pi$
$379$	5.09903	−	19.0299i	0.261920	−	0.977498i	0.964109	−	0.265507i	$-0.0855394\pi$
$380$			7.55000i			0.387307i
$381$		0			0
$382$	2.20574	−	8.23195i	0.112856	−	0.421183i
$383$	−4.04582	+	4.04582i	−0.206732	+	0.206732i	−0.802877	−	0.596145i	$-0.796698\pi$
$383$	−4.04582	+	4.04582i	−0.206732	+	0.206732i	0.596145	+	0.802877i	$0.296698\pi$
$384$		0			0
$385$	−1.91365	−	7.14185i	−0.0975287	−	0.363982i
$386$	−2.82378	−	1.63031i	−0.143727	−	0.0829806i
$387$		0			0
$388$	−2.95421	−	0.791578i	−0.149977	−	0.0401863i
$389$	−8.59884	+	14.8936i	−0.435978	+	0.755137i	−0.997375	−	0.0724102i	$-0.976931\pi$
$389$	−8.59884	+	14.8936i	−0.435978	+	0.755137i	0.561397	+	0.827547i	$0.310264\pi$
$390$		0			0
$391$	5.31054	+	9.19812i	0.268565	+	0.465169i
$392$	−3.83735	−	14.3212i	−0.193815	−	0.723328i
$393$		0			0
$394$	24.6968	−	14.2587i	1.24421	−	0.718344i
$395$	−19.7554	+	19.7554i	−0.994004	+	0.994004i
$396$		0			0
$397$	−0.701121	−	2.61662i	−0.0351882	−	0.131324i	0.946097	−	0.323882i	$-0.104988\pi$
$397$	−0.701121	−	2.61662i	−0.0351882	−	0.131324i	−0.981286	+	0.192558i	$0.938322\pi$
$398$	10.7347	−	2.87635i	0.538082	−	0.144179i
$399$		0			0
$400$	7.04784	+	4.06907i	0.352392	+	0.203454i
$401$	−7.48577	+	2.00581i	−0.373822	+	0.100165i	−0.440838	−	0.897587i	$-0.645319\pi$
$401$	−7.48577	+	2.00581i	−0.373822	+	0.100165i	0.0670163	+	0.997752i	$0.478652\pi$
$402$		0			0
$403$	−2.14140	+	9.17925i	−0.106671	+	0.457251i
$404$			1.76654i			0.0878886i
$405$		0			0
$406$	5.88542	+	10.1938i	0.292088	+	0.505912i
$407$	−10.0832	−	17.4647i	−0.499808	−	0.865692i
$408$		0			0
$409$	−5.60298	−	5.60298i	−0.277050	−	0.277050i	0.554880	−	0.831930i	$-0.312764\pi$
$409$	−5.60298	−	5.60298i	−0.277050	−	0.277050i	−0.831930	+	0.554880i	$0.812764\pi$
$410$	−1.57112	−	1.57112i	−0.0775921	−	0.0775921i
$411$		0			0
$412$	5.36916	+	9.29965i	0.264519	+	0.458161i
$413$	−9.55813	−	16.5552i	−0.470325	−	0.814627i
$414$		0			0
$415$		−	7.90993i		−	0.388283i
$416$	7.84391	−	8.37295i	0.384579	−	0.410518i
$417$		0			0
$418$	9.02123	−	2.41723i	0.441243	−	0.118231i
$419$	26.4028	+	15.2436i	1.28986	+	0.744700i	0.978629	−	0.205634i	$-0.0659257\pi$
$419$	26.4028	+	15.2436i	1.28986	+	0.744700i	0.311230	+	0.950335i	$0.399259\pi$
$420$		0			0
$421$	−7.53981	+	2.02029i	−0.367468	+	0.0984628i	−0.437828	−	0.899059i	$-0.644252\pi$
$421$	−7.53981	+	2.02029i	−0.367468	+	0.0984628i	0.0703596	+	0.997522i	$0.477585\pi$
$422$	1.60534	+	5.99122i	0.0781469	+	0.291648i
$423$		0			0
$424$	−25.1408	+	25.1408i	−1.22095	+	1.22095i
$425$	−5.31241	+	3.06712i	−0.257690	+	0.148777i
$426$		0			0
$427$	4.00520	+	14.9476i	0.193825	+	0.723365i
$428$	−1.33812	−	2.31770i	−0.0646806	−	0.112030i
$429$		0			0
$430$	3.51769	−	6.09281i	0.169638	−	0.293821i
$431$	−30.9395	−	8.29022i	−1.49030	−	0.399326i	−0.580465	−	0.814285i	$-0.697129\pi$
$431$	−30.9395	−	8.29022i	−1.49030	−	0.399326i	−0.909840	+	0.414960i	$0.863796\pi$
$432$		0			0
$433$	19.6303	+	11.3335i	0.943371	+	0.544655i	0.891015	−	0.453973i	$-0.149994\pi$
$433$	19.6303	+	11.3335i	0.943371	+	0.544655i	0.0523555	+	0.998629i	$0.483327\pi$
$434$	1.18854	+	4.43569i	0.0570517	+	0.212920i
$435$		0			0
$436$	−0.0808408	+	0.0808408i	−0.00387157	+	0.00387157i
$437$	6.58617	−	24.5799i	0.315059	−	1.17582i
$438$		0			0
$439$		−	32.3810i		−	1.54546i	−0.634735	−	0.772730i	$-0.718891\pi$
$439$		−	32.3810i		−	1.54546i	0.634735	−	0.772730i	$-0.281109\pi$
$440$	−3.98695	+	14.8795i	−0.190070	+	0.709352i
$441$		0			0
$442$	−2.34022	−	7.71782i	−0.111313	−	0.367099i
$443$	−21.0067	−	12.1282i	−0.998059	−	0.576230i	−0.0903854	−	0.995907i	$-0.528810\pi$
$443$	−21.0067	−	12.1282i	−0.998059	−	0.576230i	−0.907673	+	0.419677i	$0.862143\pi$
$444$		0			0
$445$	8.73501	−	15.1295i	0.414079	−	0.717206i
$446$	8.14578			0.385714
$447$		0			0
$448$	3.35134	−	12.5074i	0.158336	−	0.590918i
$449$	10.4048	−	2.78796i	0.491032	−	0.131572i	−0.00480262	−	0.999988i	$-0.501529\pi$
$449$	10.4048	−	2.78796i	0.491032	−	0.131572i	0.495835	+	0.868417i	$0.334862\pi$
$450$		0			0
$451$	0.565830	−	0.980046i	0.0266439	−	0.0461486i
$452$	−4.35607			−0.204892
$453$		0			0
$454$	13.1644	−	7.60045i	0.617834	−	0.356707i
$455$	13.4900	+	7.21252i	0.632420	+	0.338128i
$456$		0			0
$457$	−17.0357	−	17.0357i	−0.796895	−	0.796895i	0.185710	−	0.982605i	$-0.440541\pi$
$457$	−17.0357	−	17.0357i	−0.796895	−	0.796895i	−0.982605	+	0.185710i	$0.940541\pi$
$458$	18.7926	−	10.8499i	0.878122	−	0.506984i
$459$		0			0
$460$	6.70136	+	6.70136i	0.312453	+	0.312453i
$461$	−2.85339	−	0.764563i	−0.132896	−	0.0356092i	0.191758	−	0.981442i	$-0.438581\pi$
$461$	−2.85339	−	0.764563i	−0.132896	−	0.0356092i	−0.324654	+	0.945833i	$0.605248\pi$
$462$		0			0
$463$	1.79433	+	0.480789i	0.0833896	+	0.0223442i	0.300273	−	0.953853i	$-0.402922\pi$
$463$	1.79433	+	0.480789i	0.0833896	+	0.0223442i	−0.216883	+	0.976198i	$0.569589\pi$
$464$		−	16.7064i		−	0.775573i
$465$		0			0
$466$	−3.59419	+	3.59419i	−0.166497	+	0.166497i
$467$	16.0374			0.742122			0.371061	−	0.928608i	$-0.378994\pi$
$467$	16.0374			0.742122			0.371061	+	0.928608i	$0.378994\pi$
$468$		0			0
$469$	−5.35743			−0.247383
$470$	−5.79340	+	5.79340i	−0.267230	+	0.267230i
$471$		0			0
$472$			39.8273i			1.83320i
$473$	3.46117	+	0.927416i	0.159145	+	0.0426427i
$474$		0			0
$475$	14.1962	+	3.80387i	0.651368	+	0.174533i
$476$	1.14393	+	1.14393i	0.0524320	+	0.0524320i
$477$		0			0
$478$	1.16123	−	0.670438i	0.0531136	−	0.0306651i
$479$	26.1930	+	26.1930i	1.19679	+	1.19679i	0.975123	+	0.221664i	$0.0711489\pi$
$479$	26.1930	+	26.1930i	1.19679	+	1.19679i	0.221664	+	0.975123i	$0.428851\pi$
$480$		0			0
$481$	40.6316	+	9.47883i	1.85264	+	0.432197i
$482$	9.09969	−	5.25371i	0.414480	−	0.239300i
$483$		0			0
$484$	4.64477			0.211126
$485$	−7.53657	+	13.0537i	−0.342218	+	0.592739i
$486$		0			0
$487$	19.5635	−	5.24201i	0.886505	−	0.237538i	0.213293	−	0.976988i	$-0.431581\pi$
$487$	19.5635	−	5.24201i	0.886505	−	0.237538i	0.673212	+	0.739450i	$0.264914\pi$
$488$	8.34453	−	31.1422i	0.377739	−	1.40974i
$489$		0			0
$490$	−16.4991			−0.745352
$491$	−5.66933	+	9.81958i	−0.255854	+	0.443151i	−0.965127	−	0.261782i	$-0.915690\pi$
$491$	−5.66933	+	9.81958i	−0.255854	+	0.443151i	0.709273	+	0.704933i	$0.249023\pi$
$492$		0			0
$493$	10.9056	+	6.29633i	0.491162	+	0.283572i
$494$	−9.11049	+	17.0399i	−0.409900	+	0.766660i
$495$		0			0
$496$	1.68689	−	6.29557i	0.0757438	−	0.282680i
$497$			17.0873i			0.766469i
$498$		0			0
$499$	−1.32264	+	4.93618i	−0.0592097	+	0.220974i	−0.989191	−	0.146634i	$-0.953156\pi$
$499$	−1.32264	+	4.93618i	−0.0592097	+	0.220974i	0.929981	+	0.367607i	$0.119823\pi$
$500$	2.05816	−	2.05816i	0.0920438	−	0.0920438i
$501$		0			0
$502$	5.37473	+	20.0588i	0.239886	+	0.895266i
$503$	16.1644	+	9.33251i	0.720734	+	0.416116i	0.815023	−	0.579429i	$-0.196724\pi$
$503$	16.1644	+	9.33251i	0.720734	+	0.416116i	−0.0942889	+	0.995545i	$0.530058\pi$
$504$		0			0
$505$	8.40956	+	2.25333i	0.374220	+	0.100272i
$506$	5.86169	−	10.1527i	0.260584	−	0.451344i
$507$		0			0
$508$	−3.15574	−	5.46591i	−0.140013	−	0.242510i
$509$	−0.836359	−	3.12134i	−0.0370710	−	0.138351i	0.944910	−	0.327330i	$-0.106149\pi$
$509$	−0.836359	−	3.12134i	−0.0370710	−	0.138351i	−0.981981	+	0.188979i	$0.939482\pi$
$510$		0			0
$511$	16.2210	−	9.36522i	0.717576	−	0.414293i
$512$	−16.4510	+	16.4510i	−0.727037	+	0.727037i
$513$		0			0
$514$	1.00130	+	3.73691i	0.0441655	+	0.164828i
$515$	51.1195	−	13.6974i	2.25259	−	0.603580i
$516$		0			0
$517$	−3.61386	−	2.08646i	−0.158937	−	0.0917625i
$518$	19.6344	−	5.26103i	0.862687	−	0.231156i
$519$		0			0
$520$	−16.8266	−	27.0662i	−0.737895	−	1.18693i
$521$			21.9128i			0.960018i	0.877263	+	0.480009i	$0.159367\pi$
$521$			21.9128i			0.960018i	−0.877263	+	0.480009i	$0.840633\pi$
$522$		0			0
$523$	9.66002	+	16.7316i	0.422403	+	0.731624i	0.996174	−	0.0873922i	$-0.0278533\pi$
$523$	9.66002	+	16.7316i	0.422403	+	0.731624i	−0.573771	+	0.819016i	$0.694520\pi$
$524$	−2.30541	−	3.99309i	−0.100712	−	0.174439i
$525$		0			0
$526$	15.2142	+	15.2142i	0.663371	+	0.663371i
$527$	3.47386	+	3.47386i	0.151324	+	0.151324i
$528$		0			0
$529$	−4.47119	−	7.74433i	−0.194400	−	0.336710i
$530$	19.7829	+	34.2649i	0.859313	+	1.48837i
$531$		0			0
$532$		−	3.87599i		−	0.168046i
$533$	0.679389	+	2.24056i	0.0294276	+	0.0970495i
$534$		0			0
$535$	−12.7402	+	3.41372i	−0.550807	+	0.147588i
$536$	9.66641	+	5.58091i	0.417525	+	0.241058i
$537$		0			0
$538$	1.31698	−	0.352883i	0.0567790	−	0.0152139i
$539$	−2.17494	−	8.11699i	−0.0936814	−	0.349624i
$540$		0			0
$541$	−1.88126	+	1.88126i	−0.0808815	+	0.0808815i	−0.746390	−	0.665509i	$-0.768215\pi$
$541$	−1.88126	+	1.88126i	−0.0808815	+	0.0808815i	0.665509	+	0.746390i	$0.268215\pi$
$542$	−9.22702	+	5.32722i	−0.396334	+	0.228824i
$543$		0			0
$544$	−1.54772	−	5.77617i	−0.0663579	−	0.247651i
$545$	0.281723	+	0.487958i	0.0120677	+	0.0209018i
$546$		0			0
$547$	14.0438	−	24.3246i	0.600469	−	1.04004i	−0.392281	−	0.919846i	$-0.628314\pi$
$547$	14.0438	−	24.3246i	0.600469	−	1.04004i	0.992750	−	0.120198i	$-0.0383529\pi$
$548$	4.76876	+	1.27779i	0.203711	+	0.0545843i
$549$		0			0
$550$	5.86376	+	3.38544i	0.250031	+	0.144356i
$551$	−7.80876	−	29.1427i	−0.332664	−	1.24152i
$552$		0			0
$553$	10.1420	−	10.1420i	0.431280	−	0.431280i
$554$	−7.91798	+	29.5503i	−0.336403	+	1.25547i
$555$		0			0
$556$			0.274105i			0.0116246i
$557$	3.91190	−	14.5994i	0.165753	−	0.618597i	−0.832190	−	0.554490i	$-0.812913\pi$
$557$	3.91190	−	14.5994i	0.165753	−	0.618597i	0.997943	−	0.0641073i	$-0.0204200\pi$
$558$		0			0
$559$	−6.29595	+	3.91408i	−0.266290	+	0.165548i
$560$	−9.16043	−	5.28878i	−0.387099	−	0.223492i
$561$		0			0
$562$	−0.535308	+	0.927180i	−0.0225806	+	0.0391107i
$563$	25.4105			1.07093			0.535463	−	0.844558i	$-0.320137\pi$
$563$	25.4105			1.07093			0.535463	+	0.844558i	$0.320137\pi$
$564$		0			0
$565$	−5.55645	+	20.7369i	−0.233762	+	0.872410i
$566$	−20.9187	+	5.60516i	−0.879280	+	0.235602i
$567$		0			0
$568$	17.8000	−	30.8306i	0.746873	−	1.29362i
$569$	−25.0364			−1.04958			−0.524789	−	0.851232i	$-0.675856\pi$
$569$	−25.0364			−1.04958			−0.524789	+	0.851232i	$0.675856\pi$
$570$		0			0
$571$	−23.2909	+	13.4470i	−0.974693	+	0.562739i	−0.900664	−	0.434517i	$-0.856919\pi$
$571$	−23.2909	+	13.4470i	−0.974693	+	0.562739i	−0.0740294	+	0.997256i	$0.523586\pi$
$572$	2.50580	−	2.67480i	0.104773	−	0.111839i
$573$		0			0
$574$	0.806576	+	0.806576i	0.0336658	+	0.0336658i
$575$	15.9768	−	9.22423i	0.666280	−	0.384677i
$576$		0			0
$577$	−12.8490	−	12.8490i	−0.534912	−	0.534912i	0.387118	−	0.922030i	$-0.373470\pi$
$577$	−12.8490	−	12.8490i	−0.534912	−	0.534912i	−0.922030	+	0.387118i	$0.873470\pi$
$578$	15.4846	+	4.14907i	0.644073	+	0.172579i
$579$		0			0
$580$	10.8535	+	2.90819i	0.450668	+	0.120756i
$581$			4.06077i			0.168469i
$582$		0			0
$583$	−14.2494	+	14.2494i	−0.590149	+	0.590149i
$584$	−39.0235			−1.61480
$585$		0			0
$586$	5.46598			0.225797
$587$	10.0666	−	10.0666i	0.415495	−	0.415495i	−0.468153	−	0.883648i	$-0.655080\pi$
$587$	10.0666	−	10.0666i	0.415495	−	0.415495i	0.883648	+	0.468153i	$0.155080\pi$
$588$		0			0
$589$		−	11.7705i		−	0.484996i
$590$	42.8104	+	11.4710i	1.76248	+	0.472255i
$591$		0			0
$592$	−27.8671	−	7.46698i	−1.14533	−	0.306891i
$593$	14.8629	+	14.8629i	0.610345	+	0.610345i	0.943036	−	0.332691i	$-0.107957\pi$
$593$	14.8629	+	14.8629i	0.610345	+	0.610345i	−0.332691	+	0.943036i	$0.607957\pi$
$594$		0			0
$595$	6.90481	−	3.98649i	0.283070	−	0.163430i
$596$	2.23786	+	2.23786i	0.0916664	+	0.0916664i
$597$		0			0
$598$	7.03810	+	23.2110i	0.287809	+	0.949168i
$599$	29.6012	−	17.0903i	1.20947	−	0.698289i	0.246828	−	0.969059i	$-0.420612\pi$
$599$	29.6012	−	17.0903i	1.20947	−	0.698289i	0.962644	+	0.270770i	$0.0872783\pi$
$600$		0			0
$601$	8.94270			0.364780			0.182390	−	0.983226i	$-0.441617\pi$
$601$	8.94270			0.364780			0.182390	+	0.983226i	$0.441617\pi$
$602$	−1.80590	+	3.12790i	−0.0736028	+	0.127484i
$603$		0			0
$604$	11.1462	−	2.98660i	0.453531	−	0.121523i
$605$	5.92471	−	22.1113i	0.240874	−	0.898953i
$606$		0			0
$607$	9.16628			0.372048			0.186024	−	0.982545i	$-0.440440\pi$
$607$	9.16628			0.372048			0.186024	+	0.982545i	$0.440440\pi$
$608$	−7.16364	+	12.4078i	−0.290524	+	0.503202i
$609$		0			0
$610$	−31.0714	−	17.9391i	−1.25805	−	0.726333i
$611$	8.26193	−	2.50520i	0.334242	−	0.101350i
$612$		0			0
$613$	−0.197913	+	0.738622i	−0.00799364	+	0.0298327i	−0.969807	−	0.243872i	$-0.921582\pi$
$613$	−0.197913	+	0.738622i	−0.00799364	+	0.0298327i	0.961814	+	0.273705i	$0.0882490\pi$
$614$		−	6.61690i		−	0.267037i
$615$		0			0
$616$	2.04680	−	7.63878i	0.0824681	−	0.307775i
$617$	−11.7973	+	11.7973i	−0.474940	+	0.474940i	−0.903509	−	0.428569i	$-0.859018\pi$
$617$	−11.7973	+	11.7973i	−0.474940	+	0.474940i	0.428569	+	0.903509i	$0.359018\pi$
$618$		0			0
$619$	−0.995076	−	3.71367i	−0.0399955	−	0.149265i	0.943041	−	0.332678i	$-0.107952\pi$
$619$	−0.995076	−	3.71367i	−0.0399955	−	0.149265i	−0.983036	+	0.183413i	$0.941286\pi$
$620$	3.79636	+	2.19183i	0.152466	+	0.0880261i
$621$		0			0
$622$	25.1704	+	6.74440i	1.00924	+	0.270426i
$623$	−4.48434	+	7.76711i	−0.179661	+	0.311183i
$624$		0			0
$625$	−15.3330	−	26.5575i	−0.613320	−	1.06230i
$626$	2.33167	+	8.70190i	0.0931922	+	0.347798i
$627$		0			0
$628$	−11.6515	+	6.72699i	−0.464945	+	0.268436i
$629$	15.3769	−	15.3769i	0.613118	−	0.613118i
$630$		0			0
$631$	3.46710	+	12.9394i	0.138023	+	0.515110i	0.999967	+	0.00810607i	$0.00258027\pi$
$631$	3.46710	+	12.9394i	0.138023	+	0.515110i	−0.861944	+	0.507004i	$0.830753\pi$
$632$	−28.8642	+	7.73413i	−1.14815	+	0.307647i
$633$		0			0
$634$	−30.4282	−	17.5678i	−1.20846	−	0.697705i
$635$	−30.0457	+	8.05071i	−1.19233	+	0.319483i
$636$		0			0
$637$	15.3319	+	8.19731i	0.607472	+	0.324789i
$638$		−	13.8996i		−	0.550290i
$639$		0			0
$640$	5.86282	+	10.1547i	0.231748	+	0.401400i
$641$	12.7444	+	22.0740i	0.503375	+	0.871870i	0.999992	+	0.00390095i	$0.00124172\pi$
$641$	12.7444	+	22.0740i	0.503375	+	0.871870i	−0.496618	+	0.867969i	$0.665425\pi$
$642$		0			0
$643$	−3.94884	−	3.94884i	−0.155727	−	0.155727i	0.624943	−	0.780670i	$-0.285122\pi$
$643$	−3.94884	−	3.94884i	−0.155727	−	0.155727i	−0.780670	+	0.624943i	$0.785122\pi$
$644$	−3.44032	−	3.44032i	−0.135568	−	0.135568i
$645$		0			0
$646$	5.03554	+	8.72181i	0.198121	+	0.343155i
$647$	−1.23117	−	2.13245i	−0.0484024	−	0.0838354i	0.840809	−	0.541332i	$-0.182080\pi$
$647$	−1.23117	−	2.13245i	−0.0484024	−	0.0838354i	−0.889212	+	0.457496i	$0.848746\pi$
$648$		0			0
$649$			22.5734i			0.886085i
$650$	−13.4056	+	4.06488i	−0.525811	+	0.159438i
$651$		0			0
$652$	−2.51276	+	0.673293i	−0.0984075	+	0.0263682i
$653$	−27.7948	−	16.0473i	−1.08769	−	0.627981i	−0.154733	−	0.987956i	$-0.549452\pi$
$653$	−27.7948	−	16.0473i	−1.08769	−	0.627981i	−0.932962	+	0.359975i	$0.882785\pi$
$654$		0			0
$655$	−21.9497	+	5.88141i	−0.857646	+	0.229806i
$656$	−0.419016	−	1.56379i	−0.0163598	−	0.0610557i
$657$		0			0
$658$	2.97419	−	2.97419i	0.115946	−	0.115946i
$659$	−4.60604	+	2.65930i	−0.179426	+	0.103591i	−0.587023	−	0.809570i	$-0.699700\pi$
$659$	−4.60604	+	2.65930i	−0.179426	+	0.103591i	0.407597	+	0.913162i	$0.366367\pi$
$660$		0			0
$661$	−5.92362	−	22.1073i	−0.230402	−	0.859872i	−0.980168	−	0.198169i	$-0.936500\pi$
$661$	−5.92362	−	22.1073i	−0.230402	−	0.859872i	0.749766	−	0.661703i	$-0.230166\pi$
$662$	−11.4628	−	19.8541i	−0.445513	−	0.771651i
$663$		0			0
$664$	4.23015	−	7.32684i	0.164162	−	0.284337i
$665$	−18.4516	−	4.94408i	−0.715520	−	0.191723i
$666$		0			0
$667$	−32.7980	−	18.9359i	−1.26994	−	0.733202i
$668$	−0.0538026	−	0.200794i	−0.00208169	−	0.00776896i
$669$		0			0
$670$	8.78304	−	8.78304i	0.339318	−	0.339318i
$671$	4.72954	−	17.6509i	0.182582	−	0.681404i
$672$		0			0
$673$			28.4168i			1.09539i	0.836679	+	0.547693i	$0.184494\pi$
$673$			28.4168i			1.09539i	−0.836679	+	0.547693i	$0.815506\pi$
$674$	−5.55954	+	20.7485i	−0.214146	+	0.799202i
$675$		0			0
$676$	0.494230	+	7.56681i	0.0190088	+	0.291031i
$677$	−19.5004	−	11.2586i	−0.749461	−	0.432701i	0.0760383	−	0.997105i	$-0.475773\pi$
$677$	−19.5004	−	11.2586i	−0.749461	−	0.432701i	−0.825499	+	0.564404i	$0.809106\pi$
$678$		0			0
$679$	3.86910	−	6.70147i	0.148482	−	0.257179i
$680$	−16.6111			−0.637007
$681$		0			0
$682$	1.40349	−	5.23788i	0.0537422	−	0.200569i
$683$	−38.9958	+	10.4489i	−1.49213	+	0.399816i	−0.910457	−	0.413604i	$-0.864270\pi$
$683$	−38.9958	+	10.4489i	−1.49213	+	0.399816i	−0.581677	+	0.813420i	$0.697603\pi$
$684$		0			0
$685$	12.1657	−	21.0717i	0.464829	−	0.805107i
$686$	20.7665			0.792868
$687$		0			0
$688$	4.43943	−	2.56311i	0.169252	−	0.0977176i
$689$	−1.35939	−	41.6698i	−0.0517887	−	1.58749i
$690$		0			0
$691$	23.7637	+	23.7637i	0.904015	+	0.904015i	0.995781	−	0.0917661i	$-0.0292512\pi$
$691$	23.7637	+	23.7637i	0.904015	+	0.904015i	−0.0917661	+	0.995781i	$0.529251\pi$
$692$	−6.01014	+	3.46996i	−0.228471	+	0.131908i
$693$		0			0
$694$	−21.1496	−	21.1496i	−0.802828	−	0.802828i
$695$	1.30487	+	0.349639i	0.0494965	+	0.0132625i
$696$		0			0
$697$	1.17873	+	0.315840i	0.0446476	+	0.0119633i
$698$			27.7763i			1.05135i
$699$		0			0
$700$	1.98697	−	1.98697i	0.0751004	−	0.0751004i
$701$	34.8493			1.31624			0.658120	−	0.752913i	$-0.271352\pi$
$701$	34.8493			1.31624			0.658120	+	0.752913i	$0.271352\pi$
$702$		0			0
$703$	−52.1018			−1.96506
$704$	−10.8119	+	10.8119i	−0.407489	+	0.407489i
$705$		0			0
$706$			23.8182i			0.896410i
$707$	−4.31727	−	1.15681i	−0.162367	−	0.0435062i
$708$		0			0
$709$	8.53384	+	2.28664i	0.320495	+	0.0858764i	0.415480	−	0.909602i	$-0.363614\pi$
$709$	8.53384	+	2.28664i	0.320495	+	0.0858764i	−0.0949849	+	0.995479i	$0.530280\pi$
$710$	−28.0131	−	28.0131i	−1.05131	−	1.05131i
$711$		0			0
$712$	16.1822	−	9.34279i	0.606453	−	0.350136i
$713$	−10.4475	−	10.4475i	−0.391261	−	0.391261i
$714$		0			0
$715$	−9.53702	−	15.3407i	−0.356664	−	0.573708i
$716$	−2.95991	+	1.70890i	−0.110617	+	0.0638647i
$717$		0			0
$718$	3.32187			0.123971
$719$	−12.4677	+	21.5947i	−0.464966	+	0.805345i	−0.999200	−	0.0399915i	$-0.987267\pi$
$719$	−12.4677	+	21.5947i	−0.464966	+	0.805345i	0.534234	+	0.845337i	$0.320600\pi$
$720$		0			0
$721$	−26.2435	+	7.03193i	−0.977359	+	0.261883i
$722$	0.391981	−	1.46289i	0.0145880	−	0.0544432i
$723$		0			0
$724$	4.84012			0.179882
$725$	10.9365	−	18.9426i	0.406172	−	0.703511i
$726$		0			0
$727$	15.7972	+	9.12055i	0.585888	+	0.338262i	0.763470	−	0.645844i	$-0.223494\pi$
$727$	15.7972	+	9.12055i	0.585888	+	0.338262i	−0.177582	+	0.984106i	$0.556828\pi$
$728$	8.63837	+	13.8951i	0.320159	+	0.514989i
$729$		0			0
$730$	−11.2395	+	41.9464i	−0.415993	+	1.55251i
$731$			3.86396i			0.142914i
$732$		0			0
$733$	5.98357	−	22.3310i	0.221008	−	0.824814i	−0.762956	−	0.646450i	$-0.776253\pi$
$733$	5.98357	−	22.3310i	0.221008	−	0.824814i	0.983965	−	0.178364i	$-0.0570805\pi$
$734$	−27.7648	+	27.7648i	−1.02482	+	1.02482i
$735$		0			0
$736$	4.65469	+	17.3715i	0.171574	+	0.640324i
$737$	5.47876	+	3.16316i	0.201813	+	0.116517i
$738$		0			0
$739$	11.4323	+	3.06326i	0.420542	+	0.112684i	0.462883	−	0.886419i	$-0.346815\pi$
$739$	11.4323	+	3.06326i	0.420542	+	0.112684i	−0.0423409	+	0.999103i	$0.513482\pi$
$740$	9.70206	−	16.8045i	0.356655	−	0.617745i
$741$		0			0
$742$	−10.1560	−	17.5908i	−0.372840	−	0.645778i
$743$	−11.3842	−	42.4865i	−0.417647	−	1.55868i	−0.779474	−	0.626434i	$-0.784514\pi$
$743$	−11.3842	−	42.4865i	−0.417647	−	1.55868i	0.361827	−	0.932245i	$-0.382153\pi$
$744$		0			0
$745$	13.5078	−	7.79874i	0.494888	−	0.285724i
$746$	−3.95957	+	3.95957i	−0.144970	+	0.144970i
$747$		0			0
$748$	−0.494431	−	1.84524i	−0.0180782	−	0.0674687i
$749$	6.54051	−	1.75252i	0.238985	−	0.0640358i
$750$		0			0
$751$	32.0454	+	18.5014i	1.16935	+	0.675126i	0.953528	−	0.301306i	$-0.0974225\pi$
$751$	32.0454	+	18.5014i	1.16935	+	0.675126i	0.215825	+	0.976432i	$0.430756\pi$
$752$	−5.76637	+	1.54509i	−0.210278	+	0.0563438i
$753$		0			0
$754$	20.9864	+	19.6604i	0.764281	+	0.715990i
$755$		−	56.8706i		−	2.06973i
$756$		0			0
$757$	−23.2842	−	40.3294i	−0.846278	−	1.46580i	−0.884507	−	0.466527i	$-0.845505\pi$
$757$	−23.2842	−	40.3294i	−0.846278	−	1.46580i	0.0382287	−	0.999269i	$-0.487828\pi$
$758$	−11.7247	−	20.3077i	−0.425859	−	0.737609i
$759$		0			0
$760$	28.1418	+	28.1418i	1.02081	+	1.02081i
$761$	21.4108	+	21.4108i	0.776142	+	0.776142i	0.979172	−	0.203031i	$-0.0650792\pi$
$761$	21.4108	+	21.4108i	0.776142	+	0.776142i	−0.203031	+	0.979172i	$0.565079\pi$
$762$		0			0
$763$	−0.144630	−	0.250506i	−0.00523595	−	0.00906893i
$764$	2.08826	+	3.61697i	0.0755506	+	0.130857i
$765$		0			0
$766$			6.81020i			0.246062i
$767$	−34.0827	−	31.9292i	−1.23066	−	1.15290i
$768$		0			0
$769$	−50.7997	+	13.6117i	−1.83188	+	0.490852i	−0.998121	−	0.0612700i	$-0.980485\pi$
$769$	−50.7997	+	13.6117i	−1.83188	+	0.490852i	−0.833763	+	0.552122i	$0.813818\pi$
$770$	−7.62142	−	4.40023i	−0.274657	−	0.158573i
$771$		0			0
$772$	1.54347	−	0.413573i	0.0555508	−	0.0148848i
$773$	−5.09988	−	19.0330i	−0.183430	−	0.684570i	−0.994961	−	0.100261i	$-0.968032\pi$
$773$	−5.09988	−	19.0330i	−0.183430	−	0.684570i	0.811531	−	0.584309i	$-0.198634\pi$
$774$		0			0
$775$	6.03398	−	6.03398i	0.216747	−	0.216747i
$776$	−13.9620	+	8.06097i	−0.501207	+	0.289372i
$777$		0			0
$778$	5.29791	+	19.7721i	0.189939	+	0.708863i
$779$	−1.46187	−	2.53203i	−0.0523769	−	0.0907194i
$780$		0			0
$781$	10.0888	−	17.4742i	0.361004	−	0.625277i
$782$	12.2110	+	3.27192i	0.436664	+	0.117004i
$783$		0			0
$784$	−10.4112	−	6.01090i	−0.371828	−	0.214675i
$785$	17.1614	+	64.0473i	0.612517	+	2.28595i
$786$		0			0
$787$	−7.17503	+	7.17503i	−0.255762	+	0.255762i	−0.823328	−	0.567566i	$-0.807885\pi$
$787$	−7.17503	+	7.17503i	−0.255762	+	0.255762i	0.567566	+	0.823328i	$0.307885\pi$
$788$	−3.61712	+	13.4993i	−0.128854	+	0.480891i
$789$		0			0
$790$			33.2537i			1.18311i
$791$	2.85255	−	10.6459i	0.101425	−	0.378523i
$792$		0			0
$793$	19.9606	+	32.1074i	0.708822	+	1.14017i
$794$	−2.79232	−	1.61215i	−0.0990958	−	0.0572130i
$795$		0			0
$796$	−2.72315	+	4.71663i	−0.0965195	+	0.167177i
$797$	41.2377			1.46072			0.730358	−	0.683065i	$-0.239353\pi$
$797$	41.2377			1.46072			0.730358	+	0.683065i	$0.239353\pi$
$798$		0			0
$799$	1.16464	−	4.34649i	0.0412019	−	0.153768i
$800$	−10.0330	+	2.68834i	−0.354720	+	0.0950471i
$801$		0			0
$802$	−4.61213	+	7.98844i	−0.162860	+	0.282082i
$803$	−22.1178			−0.780521
$804$		0			0
$805$	−20.7659	+	11.9892i	−0.731902	+	0.422564i
$806$	5.92330	+	9.52785i	0.208639	+	0.335604i
$807$		0			0
$808$	6.58458	+	6.58458i	0.231645	+	0.231645i
$809$	22.9401	−	13.2445i	0.806532	−	0.465651i	−0.0392184	−	0.999231i	$-0.512487\pi$
$809$	22.9401	−	13.2445i	0.806532	−	0.465651i	0.845750	+	0.533579i	$0.179153\pi$
$810$		0			0
$811$	−27.7759	−	27.7759i	−0.975343	−	0.975343i	0.0243602	−	0.999703i	$-0.492245\pi$
$811$	−27.7759	−	27.7759i	−0.975343	−	0.975343i	−0.999703	+	0.0243602i	$0.992245\pi$
$812$	−5.57194	−	1.49300i	−0.195537	−	0.0523939i
$813$		0			0
$814$	−23.1853	−	6.21248i	−0.812644	−	0.217747i
$815$			12.8208i			0.449092i
$816$		0			0
$817$	6.54615	−	6.54615i	0.229021	−	0.229021i
$818$	−9.43133			−0.329759
$819$		0			0
$820$	1.08888			0.0380253
$821$	20.0159	−	20.0159i	0.698561	−	0.698561i	−0.265539	−	0.964100i	$-0.585550\pi$
$821$	20.0159	−	20.0159i	0.698561	−	0.698561i	0.964100	+	0.265539i	$0.0855501\pi$
$822$		0			0
$823$			3.18802i			0.111127i	0.998455	+	0.0555636i	$0.0176956\pi$
$823$			3.18802i			0.111127i	−0.998455	+	0.0555636i	$0.982304\pi$
$824$	54.6764	+	14.6505i	1.90474	+	0.510374i
$825$		0			0
$826$	−21.9779	−	5.88895i	−0.764707	−	0.204903i
$827$	−40.4226	−	40.4226i	−1.40563	−	1.40563i	−0.780603	−	0.625027i	$-0.785088\pi$
$827$	−40.4226	−	40.4226i	−1.40563	−	1.40563i	−0.625027	−	0.780603i	$-0.714912\pi$
$828$		0			0
$829$	0.372721	−	0.215190i	0.0129451	−	0.00747387i	−0.493513	−	0.869738i	$-0.664288\pi$
$829$	0.372721	−	0.215190i	0.0129451	−	0.00747387i	0.506459	+	0.862264i	$0.330954\pi$
$830$	−6.65727	−	6.65727i	−0.231077	−	0.231077i
$831$		0			0
$832$	−1.03146	−	31.6175i	−0.0357593	−	1.09614i
$833$	7.84759	−	4.53081i	0.271903	−	0.156983i
$834$		0			0
$835$	−1.02450			−0.0354544
$836$	−2.28848	+	3.96376i	−0.0791488	+	0.137090i
$837$		0			0
$838$	35.0510	−	9.39190i	1.21082	−	0.324438i
$839$	−1.25045	+	4.66673i	−0.0431702	+	0.161113i	−0.984146	−	0.177361i	$-0.943244\pi$
$839$	−1.25045	+	4.66673i	−0.0431702	+	0.161113i	0.940976	+	0.338474i	$0.109911\pi$
$840$		0			0
$841$	−15.9020			−0.548345
$842$	−4.64542	+	8.04611i	−0.160092	+	0.277287i
$843$		0			0
$844$	−2.63244	−	1.51984i	−0.0906122	−	0.0523150i
$845$	36.6520	+	7.29919i	1.26087	+	0.251100i
$846$		0			0
$847$	−3.04160	+	11.3514i	−0.104511	+	0.390040i
$848$			28.8290i			0.989991i
$849$		0			0
$850$	−1.88971	+	7.05251i	−0.0648166	+	0.241899i
$851$	−46.2454	+	46.2454i	−1.58527	+	1.58527i
$852$		0			0
$853$	−11.5603	−	43.1437i	−0.395818	−	1.47721i	−0.820383	−	0.571815i	$-0.806240\pi$
$853$	−11.5603	−	43.1437i	−0.395818	−	1.47721i	0.424565	−	0.905397i	$-0.360427\pi$
$854$	15.9513	+	9.20951i	0.545843	+	0.315143i
$855$		0			0
$856$	−13.6267	−	3.65125i	−0.465750	−	0.124797i
$857$	−25.1388	+	43.5417i	−0.858725	+	1.48736i	0.0144207	+	0.999896i	$0.495410\pi$
$857$	−25.1388	+	43.5417i	−0.858725	+	1.48736i	−0.873146	+	0.487459i	$0.837924\pi$
$858$		0			0
$859$	25.1679	+	43.5920i	0.858717	+	1.48734i	0.873153	+	0.487445i	$0.162071\pi$
$859$	25.1679	+	43.5920i	0.858717	+	1.48734i	−0.0144366	+	0.999896i	$0.504595\pi$
$860$	0.892357	+	3.33032i	0.0304291	+	0.113563i
$861$		0			0
$862$	−33.0171	+	19.0624i	−1.12457	+	0.649269i
$863$	29.3689	−	29.3689i	0.999728	−	0.999728i	−0.000272025	−	1.00000i	$-0.500087\pi$
$863$	29.3689	−	29.3689i	0.999728	−	0.999728i	1.00000		0.000272025i	$8.65883e-5\pi$
$864$		0			0
$865$	8.85231	+	33.0373i	0.300988	+	1.12330i
$866$	26.0602	−	6.98281i	0.885562	−	0.237286i
$867$		0			0
$868$	−1.94896	−	1.12523i	−0.0661521	−	0.0381929i
$869$	−16.3597	+	4.38357i	−0.554965	+	0.148702i
$870$		0			0
$871$	−12.5254	+	3.79799i	−0.424408	+	0.128690i
$872$			0.602650i			0.0204083i
$873$		0			0
$874$	−15.1442	−	26.2304i	−0.512259	−	0.887258i
$875$	3.68219	+	6.37775i	0.124481	+	0.215607i
$876$		0			0
$877$	−12.4238	−	12.4238i	−0.419523	−	0.419523i	0.465516	−	0.885039i	$-0.345869\pi$
$877$	−12.4238	−	12.4238i	−0.419523	−	0.419523i	−0.885039	+	0.465516i	$0.845869\pi$
$878$	−27.2529	−	27.2529i	−0.919742	−	0.919742i
$879$		0			0
$880$	6.24525	+	10.8171i	0.210527	+	0.364644i
$881$	11.7668	+	20.3807i	0.396434	+	0.686644i	0.993283	−	0.115710i	$-0.0369142\pi$
$881$	11.7668	+	20.3807i	0.396434	+	0.686644i	−0.596849	+	0.802354i	$0.703581\pi$
$882$		0			0
$883$			5.09275i			0.171385i	0.996322	+	0.0856923i	$0.0273102\pi$
$883$			5.09275i			0.171385i	−0.996322	+	0.0856923i	$0.972690\pi$
$884$	3.48541	+	1.86350i	0.117227	+	0.0626763i
$885$		0			0
$886$	−27.8875	+	7.47243i	−0.936899	+	0.251041i
$887$	−11.4511	−	6.61127i	−0.384489	−	0.221985i	0.295281	−	0.955411i	$-0.404587\pi$
$887$	−11.4511	−	6.61127i	−0.384489	−	0.221985i	−0.679769	+	0.733426i	$0.737920\pi$
$888$		0			0
$889$	15.4247	−	4.13304i	0.517329	−	0.138618i
$890$	−5.38181	−	20.0852i	−0.180399	−	0.673256i
$891$		0			0
$892$	−2.82276	+	2.82276i	−0.0945129	+	0.0945129i
$893$	−9.33670	+	5.39054i	−0.312441	+	0.180388i
$894$		0			0
$895$	4.35963	+	16.2704i	0.145726	+	0.543858i
$896$	−3.00983	−	5.21318i	−0.100551	−	0.174160i
$897$		0			0
$898$	6.41059	−	11.1035i	0.213924	−	0.370528i
$899$	−16.9207	−	4.53390i	−0.564338	−	0.151214i
$900$		0			0
$901$	−18.8190	−	10.8651i	−0.626951	−	0.361970i
$902$	−0.348619	−	1.30106i	−0.0116077	−	0.0433207i
$903$		0			0
$904$	−16.2368	+	16.2368i	−0.540027	+	0.540027i
$905$	6.17388	−	23.0412i	0.205227	−	0.765917i
$906$		0			0
$907$		−	9.89130i		−	0.328435i	−0.986424	−	0.164218i	$-0.947490\pi$
$907$		−	9.89130i		−	0.328435i	0.986424	−	0.164218i	$-0.0525099\pi$
$908$	−1.92806	+	7.19562i	−0.0639850	+	0.238795i
$909$		0			0
$910$	17.4239	−	5.28333i	0.577598	−	0.175141i
$911$	10.2559	+	5.92123i	0.339792	+	0.196179i	0.660180	−	0.751107i	$-0.270480\pi$
$911$	10.2559	+	5.92123i	0.339792	+	0.196179i	−0.320388	+	0.947286i	$0.603813\pi$
$912$		0			0
$913$	2.39758	−	4.15273i	0.0793483	−	0.137435i
$914$	−28.6756			−0.948504
$915$		0			0
$916$	−2.75238	+	10.2720i	−0.0909412	+	0.339397i
$917$	11.2685	−	3.01937i	0.372117	−	0.0997085i
$918$		0			0
$919$	−1.00599	+	1.74243i	−0.0331846	+	0.0574775i	−0.882141	−	0.470986i	$-0.843898\pi$
$919$	−1.00599	+	1.74243i	−0.0331846	+	0.0574775i	0.848956	+	0.528463i	$0.177232\pi$
$920$	49.9572			1.64704
$921$		0			0
$922$	−3.04499	+	1.75803i	−0.100281	+	0.0578975i
$923$	12.1135	+	39.9492i	0.398721	+	1.31495i
$924$		0			0
$925$	−26.7092	−	26.7092i	−0.878194	−	0.878194i
$926$	1.91482	−	1.10552i	0.0629248	−	0.0363297i
$927$		0			0
$928$	15.0775	+	15.0775i	0.494943	+	0.494943i
$929$	40.2389	+	10.7820i	1.32019	+	0.353745i	0.849051	−	0.528311i	$-0.177175\pi$
$929$	40.2389	+	10.7820i	1.32019	+	0.353745i	0.471144	+	0.882056i	$0.343841\pi$
$930$		0			0
$931$	−20.9709	−	5.61914i	−0.687294	−	0.184160i
$932$		−	2.49098i		−	0.0815949i
$933$		0			0
$934$	13.4976	−	13.4976i	0.441656	−	0.441656i
$935$	−9.41490			−0.307900
$936$		0			0
$937$	47.9819			1.56750			0.783750	−	0.621077i	$-0.213304\pi$
$937$	47.9819			1.56750			0.783750	+	0.621077i	$0.213304\pi$
$938$	−4.50900	+	4.50900i	−0.147224	+	0.147224i
$939$		0			0
$940$		−	4.01517i		−	0.130960i
$941$	−23.7536	−	6.36477i	−0.774346	−	0.207485i	−0.150056	−	0.988678i	$-0.547945\pi$
$941$	−23.7536	−	6.36477i	−0.774346	−	0.207485i	−0.624291	+	0.781192i	$0.714612\pi$
$942$		0			0
$943$	−3.54497	−	0.949873i	−0.115440	−	0.0309321i
$944$	22.8350	+	22.8350i	0.743216	+	0.743216i
$945$		0			0
$946$	3.69358	−	2.13249i	0.120089	−	0.0693332i
$947$	29.5660	+	29.5660i	0.960767	+	0.960767i	0.999259	−	0.0384921i	$-0.0122554\pi$
$947$	29.5660	+	29.5660i	0.960767	+	0.960767i	−0.0384921	+	0.999259i	$0.512255\pi$
$948$		0			0
$949$	31.2848	−	33.3949i	1.01555	−	1.08404i
$950$	15.1495	−	8.74657i	0.491515	−	0.283776i
$951$		0			0
$952$	8.52775			0.276386
$953$	3.67150	−	6.35923i	0.118932	−	0.205996i	−0.800413	−	0.599449i	$-0.795386\pi$
$953$	3.67150	−	6.35923i	0.118932	−	0.205996i	0.919345	+	0.393453i	$0.128720\pi$
$954$		0			0
$955$	19.8822	−	5.32742i	0.643373	−	0.172391i
$956$	−0.170075	+	0.634729i	−0.00550062	+	0.0205286i
$957$		0			0
$958$	44.0898			1.42448
$959$	−6.24560	+	10.8177i	−0.201681	+	0.349321i
$960$		0			0
$961$	20.9282	+	12.0829i	0.675104	+	0.389772i
$962$	42.1747	−	26.2193i	1.35977	−	0.845343i
$963$		0			0
$964$	−1.33275	+	4.97388i	−0.0429249	+	0.160198i
$965$		−	7.87520i		−	0.253512i
$966$		0			0
$967$	6.78898	−	25.3368i	0.218319	−	0.814778i	−0.766653	−	0.642062i	$-0.778079\pi$
$967$	6.78898	−	25.3368i	0.218319	−	0.814778i	0.984972	−	0.172716i	$-0.0552542\pi$
$968$	17.3129	−	17.3129i	0.556457	−	0.556457i
$969$		0			0
$970$	4.64343	+	17.3295i	0.149091	+	0.556417i
$971$	11.1860	+	6.45823i	0.358975	+	0.207255i	0.668631	−	0.743594i	$-0.266880\pi$
$971$	11.1860	+	6.45823i	0.358975	+	0.207255i	−0.309656	+	0.950849i	$0.600214\pi$
$972$		0			0
$973$	−0.669888	−	0.179496i	−0.0214756	−	0.00575438i
$974$	12.0534	−	20.8771i	0.386217	−	0.668947i
$975$		0			0
$976$	−13.0711	−	22.6397i	−0.418394	−	0.724680i
$977$	−8.97618	−	33.4996i	−0.287174	−	1.07175i	−0.947236	−	0.320536i	$-0.896137\pi$
$977$	−8.97618	−	33.4996i	−0.287174	−	1.07175i	0.660063	−	0.751210i	$-0.270530\pi$
$978$		0			0
$979$	9.17179	−	5.29533i	0.293132	−	0.169240i
$980$	5.71742	−	5.71742i	0.182636	−	0.182636i
$981$		0			0
$982$	3.49299	+	13.0360i	0.111466	+	0.415996i
$983$	−27.3813	+	7.33678i	−0.873326	+	0.234007i	−0.667526	−	0.744587i	$-0.732647\pi$
$983$	−27.3813	+	7.33678i	−0.873326	+	0.234007i	−0.205801	+	0.978594i	$0.565980\pi$
$984$		0			0
$985$	59.6490	+	34.4384i	1.90058	+	1.09730i
$986$	14.4777	−	3.87929i	0.461064	−	0.123542i
$987$		0			0
$988$	−2.74777	−	9.06188i	−0.0874181	−	0.288297i
$989$		−	11.6207i		−	0.369516i
$990$		0			0
$991$	0.249119	+	0.431486i	0.00791352	+	0.0137066i	0.869955	−	0.493131i	$-0.164148\pi$
$991$	0.249119	+	0.431486i	0.00791352	+	0.0137066i	−0.862042	+	0.506838i	$0.830814\pi$
$992$	4.15933	+	7.20418i	0.132059	+	0.228733i
$993$		0			0
$994$	14.3812	+	14.3812i	0.456145	+	0.456145i
$995$	18.9798	+	18.9798i	0.601702	+	0.601702i
$996$		0			0
$997$	−19.9952	−	34.6328i	−0.633255	−	1.09683i	−0.986882	−	0.161444i	$-0.948385\pi$
$997$	−19.9952	−	34.6328i	−0.633255	−	1.09683i	0.353626	−	0.935387i	$-0.384948\pi$
$998$	3.04127	+	5.26764i	0.0962698	+	0.166744i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.ba.a.89.9		48
3.2	odd	2		117.2.x.a.11.4	✓	48
9.4	even	3		117.2.bc.a.50.9	yes	48
9.5	odd	6		351.2.bf.a.206.4		48
13.6	odd	12		351.2.bf.a.305.4		48
39.32	even	12		117.2.bc.a.110.9	yes	48
117.32	even	12	inner	351.2.ba.a.71.9		48
117.58	odd	12		117.2.x.a.32.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.4	✓	48	3.2	odd	2
117.2.x.a.32.4	yes	48	117.58	odd	12
117.2.bc.a.50.9	yes	48	9.4	even	3
117.2.bc.a.110.9	yes	48	39.32	even	12
351.2.ba.a.71.9		48	117.32	even	12	inner
351.2.ba.a.89.9		48	1.1	even	1	trivial
351.2.bf.a.206.4		48	9.5	odd	6
351.2.bf.a.305.4		48	13.6	odd	12

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.841634 - 0.841634i) q^{2} +0.583303i q^{4} +(2.77680 + 0.744040i) q^{5} +(-1.42554 - 0.381973i) q^{7} +(2.17420 + 2.17420i) q^{8} +O(q^{10})\)	\(q+(0.841634 - 0.841634i) q^{2} +0.583303i q^{4} +(2.77680 + 0.744040i) q^{5} +(-1.42554 - 0.381973i) q^{7} +(2.17420 + 2.17420i) q^{8} +(2.96326 - 1.71084i) q^{10} +(1.23230 + 1.23230i) q^{11} +(-3.60363 + 0.117561i) q^{13} +(-1.52127 + 0.878303i) q^{14} +2.49315 q^{16} +(-0.939625 + 1.62748i) q^{17} +(4.34907 - 1.16533i) q^{19} +(-0.434001 + 1.61971i) q^{20} +2.07429 q^{22} +(2.82588 - 4.89457i) q^{23} +(2.82688 + 1.63210i) q^{25} +(-2.93400 + 3.13189i) q^{26} +(0.222806 - 0.831522i) q^{28} -6.70089i q^{29} +(0.676611 - 2.52515i) q^{31} +(-2.25007 + 2.25007i) q^{32} +(0.578921 + 2.16056i) q^{34} +(-3.67424 - 2.12132i) q^{35} +(-11.1775 - 2.99499i) q^{37} +(2.67955 - 4.64111i) q^{38} +(4.41961 + 7.65499i) q^{40} +(-0.168067 - 0.627234i) q^{41} +(1.78065 - 1.02806i) q^{43} +(-0.718802 + 0.718802i) q^{44} +(-1.74108 - 6.49779i) q^{46} +(-2.31288 + 0.619735i) q^{47} +(-4.17591 - 2.41096i) q^{49} +(3.75283 - 1.00557i) q^{50} +(-0.0685738 - 2.10201i) q^{52} +11.5633i q^{53} +(2.50496 + 4.33872i) q^{55} +(-2.26892 - 3.92989i) q^{56} +(-5.63970 - 5.63970i) q^{58} +(9.15908 + 9.15908i) q^{59} +(-5.24278 - 9.08077i) q^{61} +(-1.55579 - 2.69471i) q^{62} +8.77378i q^{64} +(-10.0940 - 2.35481i) q^{65} +(3.50643 - 0.939544i) q^{67} +(-0.949313 - 0.548086i) q^{68} +(-4.87774 + 1.30699i) q^{70} +(-2.99663 - 11.1836i) q^{71} +(-8.97423 + 8.97423i) q^{73} +(-11.9280 + 6.88665i) q^{74} +(0.679740 + 2.53683i) q^{76} +(-1.28599 - 2.22739i) q^{77} +(-4.85927 + 8.41651i) q^{79} +(6.92298 + 1.85501i) q^{80} +(-0.669352 - 0.386451i) q^{82} +(-0.712145 - 2.65776i) q^{83} +(-3.82006 + 3.82006i) q^{85} +(0.633407 - 2.36391i) q^{86} +5.35851i q^{88} +(1.57286 - 5.86998i) q^{89} +(5.18203 + 1.20890i) q^{91} +(2.85501 + 1.64834i) q^{92} +(-1.42501 + 2.46819i) q^{94} +12.9435 q^{95} +(-1.35706 + 5.06463i) q^{97} +(-5.54374 + 1.48544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8}+O(q^{10}) \) 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8	\( 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35} - 6 q^{37} - 36 q^{38} - 12 q^{40} - 18 q^{41} - 30 q^{43} - 12 q^{44} - 12 q^{46} + 36 q^{47} - 6 q^{49} + 60 q^{50} + 56 q^{52} - 4 q^{55} + 6 q^{56} + 50 q^{58} + 6 q^{59} + 2 q^{61} - 18 q^{62} - 72 q^{65} + 26 q^{67} - 42 q^{68} - 16 q^{70} + 48 q^{71} - 22 q^{73} - 30 q^{74} + 6 q^{76} - 72 q^{77} + 8 q^{79} + 54 q^{80} - 12 q^{82} - 54 q^{83} - 24 q^{85} + 54 q^{86} - 16 q^{91} - 120 q^{92} + 26 q^{94} + 12 q^{95} - 24 q^{97} - 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8 - 12 * q^10 + 6 * q^11 - 2 * q^13 + 12 * q^14 - 28 * q^16 - 4 * q^19 + 18 * q^20 - 4 * q^22 + 6 * q^23 + 48 * q^26 - 18 * q^31 - 54 * q^32 + 6 * q^34 - 6 * q^35 - 6 * q^37 - 36 * q^38 - 12 * q^40 - 18 * q^41 - 30 * q^43 - 12 * q^44 - 12 * q^46 + 36 * q^47 - 6 * q^49 + 60 * q^50 + 56 * q^52 - 4 * q^55 + 6 * q^56 + 50 * q^58 + 6 * q^59 + 2 * q^61 - 18 * q^62 - 72 * q^65 + 26 * q^67 - 42 * q^68 - 16 * q^70 + 48 * q^71 - 22 * q^73 - 30 * q^74 + 6 * q^76 - 72 * q^77 + 8 * q^79 + 54 * q^80 - 12 * q^82 - 54 * q^83 - 24 * q^85 + 54 * q^86 - 16 * q^91 - 120 * q^92 + 26 * q^94 + 12 * q^95 - 24 * q^97 - 36 * q^98

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