LMFDB - Embedded newform 342.2.u.d.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			253.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	342.253
Dual form			342.2.u.d.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(0.0812519 + 0.460802i) q^{5} +(2.20574 - 3.82045i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(0.0812519 + 0.460802i) q^{5} +(2.20574 - 3.82045i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.358441 - 0.300767i) q^{10} +(-2.76604 - 4.79093i) q^{11} +(-5.62449 + 2.04715i) q^{13} +(0.766044 + 4.34445i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(3.33022 - 2.79439i) q^{17} +(4.34002 + 0.405223i) q^{19} +0.467911 q^{20} +(5.19846 + 1.89209i) q^{22} +(0.549163 - 3.11446i) q^{23} +(4.49273 - 1.63522i) q^{25} +(2.99273 - 5.18355i) q^{26} +(-3.37939 - 2.83564i) q^{28} +(1.15657 + 0.970481i) q^{29} +(1.09240 - 1.89209i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.754900 + 4.28125i) q^{34} +(1.93969 + 0.705990i) q^{35} -2.75877 q^{37} +(-3.58512 + 2.47929i) q^{38} +(-0.358441 + 0.300767i) q^{40} +(-1.84002 - 0.669713i) q^{41} +(0.624485 + 3.54163i) q^{43} +(-5.19846 + 1.89209i) q^{44} +(1.58125 + 2.73881i) q^{46} +(7.08512 + 5.94512i) q^{47} +(-6.23055 - 10.7916i) q^{49} +(-2.39053 + 4.14052i) q^{50} +(1.03936 + 5.89452i) q^{52} +(0.464508 - 2.63435i) q^{53} +(1.98293 - 1.66387i) q^{55} +4.41147 q^{56} -1.50980 q^{58} +(-1.01707 + 0.853427i) q^{59} +(-1.15270 + 6.53731i) q^{61} +(0.379385 + 2.15160i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.40033 - 2.42544i) q^{65} +(-1.90760 - 1.60067i) q^{67} +(-2.17365 - 3.76487i) q^{68} +(-1.93969 + 0.705990i) q^{70} +(1.31908 + 7.48086i) q^{71} +(-2.97431 - 1.08256i) q^{73} +(2.11334 - 1.77330i) q^{74} +(1.15270 - 4.20372i) q^{76} -24.4047 q^{77} +(-1.18732 - 0.432149i) q^{79} +(0.0812519 - 0.460802i) q^{80} +(1.84002 - 0.669713i) q^{82} +(-8.96838 + 15.5337i) q^{83} +(1.55825 + 1.30753i) q^{85} +(-2.75490 - 2.31164i) q^{86} +(2.76604 - 4.79093i) q^{88} +(11.7280 - 4.26865i) q^{89} +(-4.58512 + 26.0035i) q^{91} +(-2.97178 - 1.08164i) q^{92} -9.24897 q^{94} +(0.165907 + 2.03282i) q^{95} +(-6.36618 + 5.34186i) q^{97} +(11.7096 + 4.26195i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 12 q^{11} - 21 q^{13} - 3 q^{17} + 6 q^{19} + 12 q^{20} + 3 q^{22} + 15 q^{23} + 9 q^{25} - 9 q^{28} - 15 q^{29} + 3 q^{31} - 6 q^{34} + 6 q^{35} + 6 q^{37} + 6 q^{40} + 9 q^{41} - 9 q^{43} - 3 q^{44} + 12 q^{46} + 21 q^{47} + 3 q^{50} + 15 q^{52} - 30 q^{53} - 9 q^{55} + 6 q^{56} - 12 q^{58} - 27 q^{59} - 9 q^{61} - 9 q^{62} - 3 q^{64} + 6 q^{65} - 15 q^{67} - 12 q^{68} - 6 q^{70} - 9 q^{71} + 12 q^{73} + 6 q^{74} + 9 q^{76} - 42 q^{77} + 15 q^{79} + 3 q^{80} - 9 q^{82} + 3 q^{83} - 36 q^{85} - 18 q^{86} + 12 q^{88} + 48 q^{89} - 6 q^{91} - 3 q^{92} - 30 q^{94} + 48 q^{95} + 18 q^{97} + 36 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 12 * q^11 - 21 * q^13 - 3 * q^17 + 6 * q^19 + 12 * q^20 + 3 * q^22 + 15 * q^23 + 9 * q^25 - 9 * q^28 - 15 * q^29 + 3 * q^31 - 6 * q^34 + 6 * q^35 + 6 * q^37 + 6 * q^40 + 9 * q^41 - 9 * q^43 - 3 * q^44 + 12 * q^46 + 21 * q^47 + 3 * q^50 + 15 * q^52 - 30 * q^53 - 9 * q^55 + 6 * q^56 - 12 * q^58 - 27 * q^59 - 9 * q^61 - 9 * q^62 - 3 * q^64 + 6 * q^65 - 15 * q^67 - 12 * q^68 - 6 * q^70 - 9 * q^71 + 12 * q^73 + 6 * q^74 + 9 * q^76 - 42 * q^77 + 15 * q^79 + 3 * q^80 - 9 * q^82 + 3 * q^83 - 36 * q^85 - 18 * q^86 + 12 * q^88 + 48 * q^89 - 6 * q^91 - 3 * q^92 - 30 * q^94 + 48 * q^95 + 18 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.0812519	+	0.460802i	0.0363370	+	0.206077i	0.997571	−	0.0696565i	$-0.0221903\pi$
$5$	0.0812519	+	0.460802i	0.0363370	+	0.206077i	−0.961234	+	0.275734i	$0.911079\pi$
$6$		0			0
$7$	2.20574	−	3.82045i	0.833690	−	1.44399i	−0.0614021	−	0.998113i	$-0.519557\pi$
$7$	2.20574	−	3.82045i	0.833690	−	1.44399i	0.895092	−	0.445881i	$-0.147109\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	−0.358441	−	0.300767i	−0.113349	−	0.0951110i
$11$	−2.76604	−	4.79093i	−0.833994	−	1.44452i	−0.894847	−	0.446373i	$-0.852716\pi$
$11$	−2.76604	−	4.79093i	−0.833994	−	1.44452i	0.0608533	−	0.998147i	$-0.480618\pi$
$12$		0			0
$13$	−5.62449	+	2.04715i	−1.55995	+	0.567776i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−5.62449	+	2.04715i	−1.55995	+	0.567776i	−0.589226	+	0.807968i	$0.700567\pi$
$14$	0.766044	+	4.34445i	0.204734	+	1.16110i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.33022	−	2.79439i	0.807698	−	0.677739i	−0.142360	−	0.989815i	$-0.545469\pi$
$17$	3.33022	−	2.79439i	0.807698	−	0.677739i	0.950057	+	0.312076i	$0.101024\pi$
$18$		0			0
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$	0.467911			0.104628
$21$		0			0
$22$	5.19846	+	1.89209i	1.10832	+	0.403394i
$23$	0.549163	−	3.11446i	0.114508	−	0.649409i	−0.872484	−	0.488643i	$-0.837492\pi$
$23$	0.549163	−	3.11446i	0.114508	−	0.649409i	0.986992	−	0.160767i	$-0.0513967\pi$
$24$		0			0
$25$	4.49273	−	1.63522i	0.898545	−	0.327044i
$26$	2.99273	−	5.18355i	0.586922	−	1.01658i
$27$		0			0
$28$	−3.37939	−	2.83564i	−0.638644	−	0.535886i
$29$	1.15657	+	0.970481i	0.214770	+	0.180214i	0.743826	−	0.668374i	$-0.233009\pi$
$29$	1.15657	+	0.970481i	0.214770	+	0.180214i	−0.529055	+	0.848587i	$0.677454\pi$
$30$		0			0
$31$	1.09240	−	1.89209i	0.196200	−	0.339829i	−0.751093	−	0.660196i	$-0.770473\pi$
$31$	1.09240	−	1.89209i	0.196200	−	0.339829i	0.947293	+	0.320368i	$0.103806\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$		0			0
$34$	−0.754900	+	4.28125i	−0.129464	+	0.734229i
$35$	1.93969	+	0.705990i	0.327868	+	0.119334i
$36$		0			0
$37$	−2.75877			−0.453539			−0.226770	−	0.973948i	$-0.572816\pi$
$37$	−2.75877			−0.453539			−0.226770	+	0.973948i	$0.572816\pi$
$38$	−3.58512	+	2.47929i	−0.581584	+	0.402195i
$39$		0			0
$40$	−0.358441	+	0.300767i	−0.0566745	+	0.0475555i
$41$	−1.84002	−	0.669713i	−0.287363	−	0.104592i	0.194317	−	0.980939i	$-0.437751\pi$
$41$	−1.84002	−	0.669713i	−0.287363	−	0.104592i	−0.481680	+	0.876347i	$0.659973\pi$
$42$		0			0
$43$	0.624485	+	3.54163i	0.0952331	+	0.540094i	0.994676	+	0.103055i	$0.0328617\pi$
$43$	0.624485	+	3.54163i	0.0952331	+	0.540094i	−0.899443	+	0.437039i	$0.856027\pi$
$44$	−5.19846	+	1.89209i	−0.783698	+	0.285243i
$45$		0			0
$46$	1.58125	+	2.73881i	0.233143	+	0.403815i
$47$	7.08512	+	5.94512i	1.03347	+	0.867185i	0.991260	−	0.131923i	$-0.0421153\pi$
$47$	7.08512	+	5.94512i	1.03347	+	0.867185i	0.0422114	+	0.999109i	$0.486560\pi$
$48$		0			0
$49$	−6.23055	−	10.7916i	−0.890079	−	1.54166i
$50$	−2.39053	+	4.14052i	−0.338072	+	0.585558i
$51$		0			0
$52$	1.03936	+	5.89452i	0.144134	+	0.817423i
$53$	0.464508	−	2.63435i	0.0638050	−	0.361856i	−0.936143	−	0.351621i	$-0.885631\pi$
$53$	0.464508	−	2.63435i	0.0638050	−	0.361856i	0.999948	−	0.0102357i	$-0.00325817\pi$
$54$		0			0
$55$	1.98293	−	1.66387i	0.267378	−	0.224357i
$56$	4.41147			0.589508
$57$		0			0
$58$	−1.50980			−0.198246
$59$	−1.01707	+	0.853427i	−0.132412	+	0.111107i	−0.706588	−	0.707625i	$-0.749767\pi$
$59$	−1.01707	+	0.853427i	−0.132412	+	0.111107i	0.574177	+	0.818731i	$0.305322\pi$
$60$		0			0
$61$	−1.15270	+	6.53731i	−0.147589	+	0.837016i	0.817664	+	0.575696i	$0.195269\pi$
$61$	−1.15270	+	6.53731i	−0.147589	+	0.837016i	−0.965252	+	0.261320i	$0.915842\pi$
$62$	0.379385	+	2.15160i	0.0481820	+	0.273254i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.40033	−	2.42544i	−0.173690	−	0.300839i
$66$		0			0
$67$	−1.90760	−	1.60067i	−0.233051	−	0.195553i	0.518782	−	0.854907i	$-0.326386\pi$
$67$	−1.90760	−	1.60067i	−0.233051	−	0.195553i	−0.751833	+	0.659354i	$0.770830\pi$
$68$	−2.17365	−	3.76487i	−0.263594	−	0.456557i
$69$		0			0
$70$	−1.93969	+	0.705990i	−0.231838	+	0.0843820i
$71$	1.31908	+	7.48086i	0.156546	+	0.887815i	0.957359	+	0.288901i	$0.0932898\pi$
$71$	1.31908	+	7.48086i	0.156546	+	0.887815i	−0.800813	+	0.598914i	$0.795599\pi$
$72$		0			0
$73$	−2.97431	−	1.08256i	−0.348116	−	0.126704i	0.162043	−	0.986784i	$-0.448192\pi$
$73$	−2.97431	−	1.08256i	−0.348116	−	0.126704i	−0.510160	+	0.860080i	$0.670414\pi$
$74$	2.11334	−	1.77330i	0.245671	−	0.206142i
$75$		0			0
$76$	1.15270	−	4.20372i	0.132224	−	0.482200i
$77$	−24.4047			−2.78117
$78$		0			0
$79$	−1.18732	−	0.432149i	−0.133584	−	0.0486205i	0.274363	−	0.961626i	$-0.411533\pi$
$79$	−1.18732	−	0.432149i	−0.133584	−	0.0486205i	−0.407947	+	0.913006i	$0.633755\pi$
$80$	0.0812519	−	0.460802i	0.00908424	−	0.0515193i
$81$		0			0
$82$	1.84002	−	0.669713i	0.203196	−	0.0739575i
$83$	−8.96838	+	15.5337i	−0.984407	+	1.70504i	−0.339867	+	0.940474i	$0.610382\pi$
$83$	−8.96838	+	15.5337i	−0.984407	+	1.70504i	−0.644541	+	0.764570i	$0.722951\pi$
$84$		0			0
$85$	1.55825	+	1.30753i	0.169016	+	0.141821i
$86$	−2.75490	−	2.31164i	−0.297069	−	0.249270i
$87$		0			0
$88$	2.76604	−	4.79093i	0.294861	−	0.510715i
$89$	11.7280	−	4.26865i	1.24317	−	0.452476i	0.365081	−	0.930976i	$-0.381041\pi$
$89$	11.7280	−	4.26865i	1.24317	−	0.452476i	0.878088	+	0.478500i	$0.158819\pi$
$90$		0			0
$91$	−4.58512	+	26.0035i	−0.480651	+	2.72591i
$92$	−2.97178	−	1.08164i	−0.309830	−	0.112769i
$93$		0			0
$94$	−9.24897			−0.953958
$95$	0.165907	+	2.03282i	0.0170217	+	0.208563i
$96$		0			0
$97$	−6.36618	+	5.34186i	−0.646388	+	0.542384i	−0.905972	−	0.423337i	$-0.860859\pi$
$97$	−6.36618	+	5.34186i	−0.646388	+	0.542384i	0.259585	+	0.965720i	$0.416414\pi$
$98$	11.7096	+	4.26195i	1.18285	+	0.430522i
$99$		0			0
$100$	−0.830222	−	4.70842i	−0.0830222	−	0.470842i
$101$	1.16637	−	0.424525i	0.116059	−	0.0422419i	−0.283338	−	0.959020i	$-0.591442\pi$
$101$	1.16637	−	0.424525i	0.116059	−	0.0422419i	0.399397	+	0.916778i	$0.369220\pi$
$102$		0			0
$103$	−1.69207	−	2.93075i	−0.166724	−	0.288775i	0.770542	−	0.637389i	$-0.219986\pi$
$103$	−1.69207	−	2.93075i	−0.166724	−	0.288775i	−0.937266	+	0.348614i	$0.886652\pi$
$104$	−4.58512	−	3.84737i	−0.449608	−	0.377266i
$105$		0			0
$106$	1.33750	+	2.31661i	0.129909	+	0.225009i
$107$	7.90807	−	13.6972i	0.764502	−	1.32416i	−0.176007	−	0.984389i	$-0.556318\pi$
$107$	7.90807	−	13.6972i	0.764502	−	1.32416i	0.940509	−	0.339768i	$-0.110348\pi$
$108$		0			0
$109$	−1.00980	−	5.72686i	−0.0967213	−	0.548534i	−0.994206	−	0.107489i	$-0.965719\pi$
$109$	−1.00980	−	5.72686i	−0.0967213	−	0.548534i	0.897485	−	0.441045i	$-0.145392\pi$
$110$	−0.449493	+	2.54920i	−0.0428575	+	0.243057i
$111$		0			0
$112$	−3.37939	+	2.83564i	−0.319322	+	0.267943i
$113$	−12.1361			−1.14167			−0.570834	−	0.821066i	$-0.693380\pi$
$113$	−12.1361			−1.14167			−0.570834	+	0.821066i	$0.693380\pi$
$114$		0			0
$115$	1.47977			0.137989
$116$	1.15657	−	0.970481i	0.107385	−	0.0901069i
$117$		0			0
$118$	0.230552	−	1.30753i	0.0212240	−	0.120367i
$119$	−3.33022	−	18.8866i	−0.305281	−	1.73133i
$120$		0			0
$121$	−9.80200	+	16.9776i	−0.891091	+	1.54342i
$122$	−3.31908	−	5.74881i	−0.300495	−	0.520473i
$123$		0			0
$124$	−1.67365	−	1.40436i	−0.150298	−	0.126115i
$125$	2.28833	+	3.96351i	0.204675	+	0.354507i
$126$		0			0
$127$	−0.426022	+	0.155059i	−0.0378033	+	0.0137593i	−0.360853	−	0.932623i	$-0.617514\pi$
$127$	−0.426022	+	0.155059i	−0.0378033	+	0.0137593i	0.323049	+	0.946382i	$0.395292\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$		0			0
$130$	2.63176	+	0.957882i	0.230821	+	0.0840118i
$131$	8.27972	−	6.94751i	0.723402	−	0.607006i	−0.204922	−	0.978778i	$-0.565694\pi$
$131$	8.27972	−	6.94751i	0.723402	−	0.607006i	0.928324	+	0.371772i	$0.121250\pi$
$132$		0			0
$133$	11.1211	−	15.6870i	0.964320	−	1.36024i
$134$	2.49020			0.215120
$135$		0			0
$136$	4.08512	+	1.48686i	0.350296	+	0.127497i
$137$	−1.90508	+	10.8042i	−0.162762	+	0.923068i	0.788580	+	0.614932i	$0.210816\pi$
$137$	−1.90508	+	10.8042i	−0.162762	+	0.923068i	−0.951342	+	0.308136i	$0.900295\pi$
$138$		0			0
$139$	12.6493	−	4.60397i	1.07290	−	0.390504i	0.255639	−	0.966772i	$-0.417714\pi$
$139$	12.6493	−	4.60397i	1.07290	−	0.390504i	0.817260	+	0.576269i	$0.195492\pi$
$140$	1.03209	−	1.78763i	0.0872274	−	0.151082i
$141$		0			0
$142$	−5.81908	−	4.88279i	−0.488326	−	0.409754i
$143$	25.3653	+	21.2840i	2.12115	+	1.77986i
$144$		0			0
$145$	−0.353226	+	0.611806i	−0.0293338	+	0.0508077i
$146$	2.97431	−	1.08256i	0.246155	−	0.0895933i
$147$		0			0
$148$	−0.479055	+	2.71686i	−0.0393781	+	0.223324i
$149$	7.69594	+	2.80109i	0.630476	+	0.229474i	0.637438	−	0.770501i	$-0.279994\pi$
$149$	7.69594	+	2.80109i	0.630476	+	0.229474i	−0.00696263	+	0.999976i	$0.502216\pi$
$150$		0			0
$151$	21.1411			1.72044			0.860221	−	0.509921i	$-0.170325\pi$
$151$	21.1411			1.72044			0.860221	+	0.509921i	$0.170325\pi$
$152$	1.81908	+	3.96118i	0.147547	+	0.321294i
$153$		0			0
$154$	18.6951	−	15.6870i	1.50649	−	1.26410i
$155$	0.960637	+	0.349643i	0.0771602	+	0.0280840i
$156$		0			0
$157$	3.41013	+	19.3398i	0.272158	+	1.54348i	0.747847	+	0.663871i	$0.231088\pi$
$157$	3.41013	+	19.3398i	0.272158	+	1.54348i	−0.475689	+	0.879614i	$0.657801\pi$
$158$	1.18732	−	0.432149i	0.0944580	−	0.0343799i
$159$		0			0
$160$	0.233956	+	0.405223i	0.0184958	+	0.0320357i
$161$	−10.6873	−	8.96773i	−0.842279	−	0.706756i
$162$		0			0
$163$	−2.27584	−	3.94188i	−0.178258	−	0.308752i	0.763026	−	0.646368i	$-0.223713\pi$
$163$	−2.27584	−	3.94188i	−0.178258	−	0.308752i	−0.941284	+	0.337616i	$0.890379\pi$
$164$	−0.979055	+	1.69577i	−0.0764514	+	0.132418i
$165$		0			0
$166$	−3.11468	−	17.6643i	−0.241746	−	1.37101i
$167$	−3.32383	+	18.8504i	−0.257205	+	1.45868i	0.533142	+	0.846026i	$0.321011\pi$
$167$	−3.32383	+	18.8504i	−0.257205	+	1.45868i	−0.790348	+	0.612658i	$0.790100\pi$
$168$		0			0
$169$	17.4855	−	14.6720i	1.34503	−	1.12862i
$170$	−2.03415			−0.156012
$171$		0			0
$172$	3.59627			0.274213
$173$	−4.25284	+	3.56856i	−0.323337	+	0.271312i	−0.789979	−	0.613134i	$-0.789908\pi$
$173$	−4.25284	+	3.56856i	−0.323337	+	0.271312i	0.466641	+	0.884447i	$0.345464\pi$
$174$		0			0
$175$	3.66250	−	20.7711i	0.276859	−	1.57015i
$176$	0.960637	+	5.44804i	0.0724107	+	0.410662i
$177$		0			0
$178$	−6.24035	+	10.8086i	−0.467734	+	0.810139i
$179$	−4.17499	−	7.23130i	−0.312054	−	0.540493i	0.666753	−	0.745279i	$-0.267684\pi$
$179$	−4.17499	−	7.23130i	−0.312054	−	0.540493i	−0.978807	+	0.204786i	$0.934350\pi$
$180$		0			0
$181$	−9.64337	−	8.09175i	−0.716786	−	0.601455i	0.209708	−	0.977764i	$-0.432749\pi$
$181$	−9.64337	−	8.09175i	−0.716786	−	0.601455i	−0.926494	+	0.376309i	$0.877193\pi$
$182$	−13.2023	−	22.8671i	−0.978622	−	1.69502i
$183$		0			0
$184$	2.97178	−	1.08164i	0.219083	−	0.0797396i
$185$	−0.224155	−	1.27125i	−0.0164802	−	0.0934640i
$186$		0			0
$187$	−22.5993	−	8.22546i	−1.65262	−	0.601505i
$188$	7.08512	−	5.94512i	0.516736	−	0.433593i
$189$		0			0
$190$	−1.43376	−	1.45059i	−0.104016	−	0.105237i
$191$	6.71688			0.486016			0.243008	−	0.970024i	$-0.421866\pi$
$191$	6.71688			0.486016			0.243008	+	0.970024i	$0.421866\pi$
$192$		0			0
$193$	11.7763	+	4.28623i	0.847677	+	0.308529i	0.729093	−	0.684415i	$-0.239942\pi$
$193$	11.7763	+	4.28623i	0.847677	+	0.308529i	0.118584	+	0.992944i	$0.462164\pi$
$194$	1.44310	−	8.18421i	0.103608	−	0.587592i
$195$		0			0
$196$	−11.7096	+	4.26195i	−0.836401	+	0.304425i
$197$	−2.03596	+	3.52638i	−0.145056	+	0.251245i	−0.929394	−	0.369089i	$-0.879670\pi$
$197$	−2.03596	+	3.52638i	−0.145056	+	0.251245i	0.784338	+	0.620334i	$0.213003\pi$
$198$		0			0
$199$	−5.48158	−	4.59959i	−0.388579	−	0.326057i	0.427480	−	0.904025i	$-0.359401\pi$
$199$	−5.48158	−	4.59959i	−0.388579	−	0.326057i	−0.816059	+	0.577968i	$0.803846\pi$
$200$	3.66250	+	3.07321i	0.258978	+	0.217308i
$201$		0			0
$202$	−0.620615	+	1.07494i	−0.0436663	+	0.0756323i
$203$	6.25877	−	2.27801i	0.439280	−	0.159885i
$204$		0			0
$205$	0.159100	−	0.902302i	0.0111120	−	0.0630195i
$206$	3.18004	+	1.15744i	0.221564	+	0.0806428i
$207$		0			0
$208$	5.98545			0.415016
$209$	−10.0633	−	21.9136i	−0.696093	−	1.51580i
$210$		0			0
$211$	−2.03209	+	1.70513i	−0.139895	+	0.117386i	−0.710050	−	0.704151i	$-0.751328\pi$
$211$	−2.03209	+	1.70513i	−0.139895	+	0.117386i	0.570155	+	0.821537i	$0.306883\pi$
$212$	−2.51367	−	0.914901i	−0.172640	−	0.0628357i
$213$		0			0
$214$	2.74644	+	15.5759i	0.187743	+	1.06474i
$215$	−1.58125	+	0.575529i	−0.107840	+	0.0392507i
$216$		0			0
$217$	−4.81908	−	8.34689i	−0.327140	−	0.566624i
$218$	4.45471	+	3.73794i	0.301711	+	0.253165i
$219$		0			0
$220$	−1.29426	−	2.24173i	−0.0872592	−	0.151137i
$221$	−13.0103	+	22.5344i	−0.875165	+	1.51583i
$222$		0			0
$223$	2.42246	+	13.7384i	0.162220	+	0.919993i	0.951885	+	0.306456i	$0.0991431\pi$
$223$	2.42246	+	13.7384i	0.162220	+	0.919993i	−0.789665	+	0.613538i	$0.789746\pi$
$224$	0.766044	−	4.34445i	0.0511835	−	0.290276i
$225$		0			0
$226$	9.29679	−	7.80093i	0.618413	−	0.518910i
$227$	23.6117			1.56717			0.783583	−	0.621287i	$-0.213390\pi$
$227$	23.6117			1.56717			0.783583	+	0.621287i	$0.213390\pi$
$228$		0			0
$229$	8.61081			0.569019			0.284509	−	0.958673i	$-0.408169\pi$
$229$	8.61081			0.569019			0.284509	+	0.958673i	$0.408169\pi$
$230$	−1.13357	+	0.951178i	−0.0747454	+	0.0627188i
$231$		0			0
$232$	−0.262174	+	1.48686i	−0.0172126	+	0.0976173i
$233$	2.68139	+	15.2069i	0.175664	+	0.996238i	0.937375	+	0.348322i	$0.113248\pi$
$233$	2.68139	+	15.2069i	0.175664	+	0.996238i	−0.761711	+	0.647916i	$0.775641\pi$
$234$		0			0
$235$	−2.16385	+	3.74789i	−0.141154	+	0.244486i
$236$	0.663848	+	1.14982i	0.0432128	+	0.0748468i
$237$		0			0
$238$	14.6912	+	12.3274i	0.952288	+	0.799065i
$239$	3.87939	+	6.71929i	0.250937	+	0.434635i	0.963784	−	0.266684i	$-0.0859281\pi$
$239$	3.87939	+	6.71929i	0.250937	+	0.434635i	−0.712847	+	0.701319i	$0.752595\pi$
$240$		0			0
$241$	12.4846	−	4.54401i	0.804202	−	0.292706i	0.0929755	−	0.995668i	$-0.470362\pi$
$241$	12.4846	−	4.54401i	0.804202	−	0.292706i	0.711227	+	0.702963i	$0.248140\pi$
$242$	−3.40420	−	19.3062i	−0.218830	−	1.24105i
$243$		0			0
$244$	6.23783	+	2.27038i	0.399336	+	0.145346i
$245$	4.46657	−	3.74789i	0.285358	−	0.239444i
$246$		0			0
$247$	−25.2399	+	6.60549i	−1.60598	+	0.420297i
$248$	2.18479			0.138734
$249$		0			0
$250$	−4.30066	−	1.56531i	−0.271998	−	0.0989990i
$251$	3.06506	−	17.3828i	0.193465	−	1.09719i	−0.721124	−	0.692806i	$-0.756374\pi$
$251$	3.06506	−	17.3828i	0.193465	−	1.09719i	0.914588	−	0.404386i	$-0.132515\pi$
$252$		0			0
$253$	−16.4402	+	5.98373i	−1.03358	+	0.376194i
$254$	0.226682	−	0.392624i	0.0142233	−	0.0246354i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−6.05303	−	5.07910i	−0.377578	−	0.316825i	0.434173	−	0.900830i	$-0.357041\pi$
$257$	−6.05303	−	5.07910i	−0.377578	−	0.316825i	−0.811751	+	0.584004i	$0.801485\pi$
$258$		0			0
$259$	−6.08512	+	10.5397i	−0.378111	+	0.654908i
$260$	−2.63176	+	0.957882i	−0.163215	+	0.0594053i
$261$		0			0
$262$	−1.87686	+	10.6442i	−0.115953	+	0.657601i
$263$	−23.8405	−	8.67723i	−1.47007	−	0.535061i	−0.521949	−	0.852977i	$-0.674795\pi$
$263$	−23.8405	−	8.67723i	−1.47007	−	0.535061i	−0.948119	+	0.317916i	$0.897017\pi$
$264$		0			0
$265$	1.25166			0.0768888
$266$	1.56418	+	19.1654i	0.0959059	+	1.17511i
$267$		0			0
$268$	−1.90760	+	1.60067i	−0.116525	+	0.0977765i
$269$	18.9538	+	6.89863i	1.15564	+	0.420617i	0.847536	−	0.530737i	$-0.178085\pi$
$269$	18.9538	+	6.89863i	1.15564	+	0.420617i	0.308099	+	0.951354i	$0.400307\pi$
$270$		0			0
$271$	3.56165	+	20.1991i	0.216355	+	1.22701i	0.878540	+	0.477669i	$0.158518\pi$
$271$	3.56165	+	20.1991i	0.216355	+	1.22701i	−0.662185	+	0.749341i	$0.730371\pi$
$272$	−4.08512	+	1.48686i	−0.247697	+	0.0901543i
$273$		0			0
$274$	−5.48545	−	9.50108i	−0.331388	−	0.573981i
$275$	−20.2613	−	17.0012i	−1.22180	−	1.02521i
$276$		0			0
$277$	−4.56758	−	7.91128i	−0.274439	−	0.475343i	0.695554	−	0.718474i	$-0.255159\pi$
$277$	−4.56758	−	7.91128i	−0.274439	−	0.475343i	−0.969994	+	0.243131i	$0.921826\pi$
$278$	−6.73055	+	11.6577i	−0.403672	+	0.699180i
$279$		0			0
$280$	0.358441	+	2.03282i	0.0214209	+	0.121484i
$281$	0.595800	−	3.37895i	0.0355424	−	0.201571i	−0.961866	−	0.273522i	$-0.911811\pi$
$281$	0.595800	−	3.37895i	0.0355424	−	0.201571i	0.997408	+	0.0719508i	$0.0229225\pi$
$282$		0			0
$283$	8.61200	−	7.22632i	0.511930	−	0.429560i	−0.349878	−	0.936795i	$-0.613777\pi$
$283$	8.61200	−	7.22632i	0.511930	−	0.429560i	0.861808	+	0.507235i	$0.169332\pi$
$284$	7.59627			0.450755
$285$		0			0
$286$	−33.1121			−1.95796
$287$	−6.61721	+	5.55250i	−0.390602	+	0.327754i
$288$		0			0
$289$	0.329755	−	1.87014i	0.0193974	−	0.110008i
$290$	−0.122674	−	0.695720i	−0.00720367	−	0.0408541i
$291$		0			0
$292$	−1.58260	+	2.74114i	−0.0926144	+	0.160413i
$293$	−7.26604	−	12.5852i	−0.424487	−	0.735233i	0.571886	−	0.820333i	$-0.306212\pi$
$293$	−7.26604	−	12.5852i	−0.424487	−	0.735233i	−0.996372	+	0.0851007i	$0.972879\pi$
$294$		0			0
$295$	−0.475900	−	0.399328i	−0.0277080	−	0.0232498i
$296$	−1.37939	−	2.38917i	−0.0801751	−	0.138867i
$297$		0			0
$298$	−7.69594	+	2.80109i	−0.445814	+	0.162263i
$299$	3.28699	+	18.6414i	0.190091	+	1.07806i
$300$		0			0
$301$	14.9081	+	5.42609i	0.859287	+	0.312755i
$302$	−16.1951	+	13.5893i	−0.931921	+	0.781975i
$303$		0			0
$304$	−3.93969	−	1.86516i	−0.225957	−	0.106974i
$305$	−3.10607			−0.177853
$306$		0			0
$307$	24.1532	+	8.79104i	1.37849	+	0.501731i	0.921721	−	0.387853i	$-0.126783\pi$
$307$	24.1532	+	8.79104i	1.37849	+	0.501731i	0.456773	+	0.889583i	$0.349005\pi$
$308$	−4.23783	+	24.0339i	−0.241473	+	1.36946i
$309$		0			0
$310$	−0.960637	+	0.349643i	−0.0545605	+	0.0198584i
$311$	2.91875	−	5.05542i	0.165507	−	0.286667i	−0.771328	−	0.636438i	$-0.780407\pi$
$311$	2.91875	−	5.05542i	0.165507	−	0.286667i	0.936835	+	0.349771i	$0.113741\pi$
$312$		0			0
$313$	−12.6480	−	10.6129i	−0.714905	−	0.599876i	0.211066	−	0.977472i	$-0.432307\pi$
$313$	−12.6480	−	10.6129i	−0.714905	−	0.599876i	−0.925971	+	0.377596i	$0.876751\pi$
$314$	−15.0437	−	12.6232i	−0.848965	−	0.712366i
$315$		0			0
$316$	−0.631759	+	1.09424i	−0.0355392	+	0.0615557i
$317$	−25.3243	+	9.21729i	−1.42235	+	0.517695i	−0.934730	−	0.355359i	$-0.884359\pi$
$317$	−25.3243	+	9.21729i	−1.42235	+	0.517695i	−0.487624	+	0.873054i	$0.662136\pi$
$318$		0			0
$319$	1.45037	−	8.22546i	0.0812051	−	0.460537i
$320$	−0.439693	−	0.160035i	−0.0245796	−	0.00894623i
$321$		0			0
$322$	13.9513			0.777476
$323$	15.5856	−	10.7782i	0.867205	−	0.599716i
$324$		0			0
$325$	−21.9217	+	18.3945i	−1.21600	+	1.02034i
$326$	4.27719	+	1.55677i	0.236892	+	0.0862215i
$327$		0			0
$328$	−0.340022	−	1.92836i	−0.0187746	−	0.106476i
$329$	38.3410	−	13.9550i	2.11381	−	0.769362i
$330$		0			0
$331$	−14.2442	−	24.6717i	−0.782933	−	1.35608i	−0.930226	−	0.366987i	$-0.880389\pi$
$331$	−14.2442	−	24.6717i	−0.782933	−	1.35608i	0.147293	−	0.989093i	$-0.452944\pi$
$332$	13.7404	+	11.5295i	0.754100	+	0.632765i
$333$		0			0
$334$	−9.57057	−	16.5767i	−0.523679	−	0.907038i
$335$	0.582596	−	1.00909i	0.0318306	−	0.0551323i
$336$		0			0
$337$	2.89780	+	16.4343i	0.157853	+	0.895231i	0.956131	+	0.292941i	$0.0946339\pi$
$337$	2.89780	+	16.4343i	0.157853	+	0.895231i	−0.798277	+	0.602290i	$0.794255\pi$
$338$	−3.96363	+	22.4789i	−0.215593	+	1.22269i
$339$		0			0
$340$	1.55825	−	1.30753i	0.0845079	−	0.0709105i
$341$	−12.0865			−0.654519
$342$		0			0
$343$	−24.0915			−1.30082
$344$	−2.75490	+	2.31164i	−0.148534	+	0.124635i
$345$		0			0
$346$	0.964041	−	5.46735i	0.0518272	−	0.293926i
$347$	3.25237	+	18.4451i	0.174597	+	0.990186i	0.938608	+	0.344984i	$0.112116\pi$
$347$	3.25237	+	18.4451i	0.174597	+	0.990186i	−0.764012	+	0.645202i	$0.776773\pi$
$348$		0			0
$349$	0.820422	−	1.42101i	0.0439162	−	0.0760651i	−0.843232	−	0.537550i	$-0.819350\pi$
$349$	0.820422	−	1.42101i	0.0439162	−	0.0760651i	0.887148	+	0.461485i	$0.152683\pi$
$350$	10.5458	+	18.2658i	0.563695	+	0.976348i
$351$		0			0
$352$	−4.23783	−	3.55596i	−0.225877	−	0.189533i
$353$	−5.95336	−	10.3115i	−0.316866	−	0.548827i	0.662967	−	0.748649i	$-0.269297\pi$
$353$	−5.95336	−	10.3115i	−0.316866	−	0.548827i	−0.979832	+	0.199822i	$0.935964\pi$
$354$		0			0
$355$	−3.34002	+	1.21567i	−0.177270	+	0.0645210i
$356$	−2.16725	−	12.2911i	−0.114864	−	0.651427i
$357$		0			0
$358$	7.84642	+	2.85586i	0.414696	+	0.150937i
$359$	−1.75877	+	1.47578i	−0.0928244	+	0.0778889i	−0.688019	−	0.725693i	$-0.741519\pi$
$359$	−1.75877	+	1.47578i	−0.0928244	+	0.0778889i	0.595195	+	0.803582i	$0.297075\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$	12.5885			0.661638
$363$		0			0
$364$	24.8123	+	9.03093i	1.30052	+	0.473349i
$365$	0.257178	−	1.45853i	0.0134613	−	0.0763429i
$366$		0			0
$367$	20.1989	−	7.35181i	1.05438	−	0.383761i	0.244063	−	0.969759i	$-0.421520\pi$
$367$	20.1989	−	7.35181i	1.05438	−	0.383761i	0.810312	+	0.585998i	$0.199297\pi$
$368$	−1.58125	+	2.73881i	−0.0824285	+	0.142770i
$369$		0			0
$370$	0.988856	+	0.829748i	0.0514082	+	0.0431366i
$371$	−9.03983	−	7.58532i	−0.469325	−	0.393810i
$372$		0			0
$373$	−13.9907	+	24.2325i	−0.724409	+	1.25471i	0.234807	+	0.972042i	$0.424554\pi$
$373$	−13.9907	+	24.2325i	−0.724409	+	1.25471i	−0.959217	+	0.282672i	$0.908779\pi$
$374$	22.5993	−	8.22546i	1.16858	−	0.425328i
$375$		0			0
$376$	−1.60607	+	9.10846i	−0.0828266	+	0.469733i
$377$	−8.49185	−	3.09078i	−0.437352	−	0.159183i
$378$		0			0
$379$	8.88981			0.456639			0.228320	−	0.973586i	$-0.426677\pi$
$379$	8.88981			0.456639			0.228320	+	0.973586i	$0.426677\pi$
$380$	2.03074	+	0.189608i	0.104175	+	0.00972670i
$381$		0			0
$382$	−5.14543	+	4.31753i	−0.263263	+	0.220904i
$383$	−23.5069	−	8.55580i	−1.20114	−	0.437181i	−0.337521	−	0.941318i	$-0.609588\pi$
$383$	−23.5069	−	8.55580i	−1.20114	−	0.437181i	−0.863624	+	0.504137i	$0.831811\pi$
$384$		0			0
$385$	−1.98293	−	11.2457i	−0.101059	−	0.573136i
$386$	−11.7763	+	4.28623i	−0.599398	+	0.218163i
$387$		0			0
$388$	4.15523	+	7.19707i	0.210950	+	0.365376i
$389$	17.8739	+	14.9980i	0.906244	+	0.760429i	0.971401	−	0.237446i	$-0.0763103\pi$
$389$	17.8739	+	14.9980i	0.906244	+	0.760429i	−0.0651569	+	0.997875i	$0.520755\pi$
$390$		0			0
$391$	−6.87417	−	11.9064i	−0.347642	−	0.602133i
$392$	6.23055	−	10.7916i	0.314690	−	0.545060i
$393$		0			0
$394$	−0.707081	−	4.01006i	−0.0356222	−	0.202024i
$395$	0.102663	−	0.582232i	0.00516555	−	0.0292953i
$396$		0			0
$397$	2.90239	−	2.43539i	0.145667	−	0.122229i	−0.567042	−	0.823689i	$-0.691912\pi$
$397$	2.90239	−	2.43539i	0.145667	−	0.122229i	0.712709	+	0.701460i	$0.247468\pi$
$398$	7.15570			0.358683
$399$		0			0
$400$	−4.78106			−0.239053
$401$	16.7456	−	14.0512i	0.836234	−	0.701683i	−0.120479	−	0.992716i	$-0.538443\pi$
$401$	16.7456	−	14.0512i	0.836234	−	0.701683i	0.956713	+	0.291032i	$0.0939988\pi$
$402$		0			0
$403$	−2.27079	+	12.8783i	−0.113116	+	0.641514i
$404$	−0.215537	−	1.22237i	−0.0107234	−	0.0608153i
$405$		0			0
$406$	−3.33022	+	5.76811i	−0.165276	+	0.286267i
$407$	7.63088	+	13.2171i	0.378249	+	0.655146i
$408$		0			0
$409$	−6.06418	−	5.08845i	−0.299854	−	0.251608i	0.480429	−	0.877033i	$-0.340481\pi$
$409$	−6.06418	−	5.08845i	−0.299854	−	0.251608i	−0.780284	+	0.625426i	$0.784925\pi$
$410$	0.458111	+	0.793471i	0.0226245	+	0.0391868i
$411$		0			0
$412$	−3.18004	+	1.15744i	−0.156670	+	0.0570231i
$413$	1.01707	+	5.76811i	0.0500469	+	0.283830i
$414$		0			0
$415$	−7.88666	−	2.87051i	−0.387141	−	0.140908i
$416$	−4.58512	+	3.84737i	−0.224804	+	0.188633i
$417$		0			0
$418$	21.7947	+	10.3182i	1.06602	+	0.504681i
$419$	−6.22937			−0.304325			−0.152162	−	0.988356i	$-0.548624\pi$
$419$	−6.22937			−0.304325			−0.152162	+	0.988356i	$0.548624\pi$
$420$		0			0
$421$	3.35591	+	1.22145i	0.163557	+	0.0595300i	0.422501	−	0.906362i	$-0.361152\pi$
$421$	3.35591	+	1.22145i	0.163557	+	0.0595300i	−0.258944	+	0.965892i	$0.583374\pi$
$422$	0.460637	−	2.61240i	0.0224235	−	0.127170i
$423$		0			0
$424$	2.51367	−	0.914901i	0.122075	−	0.0444315i
$425$	10.3923	−	18.0001i	0.504103	−	0.873131i
$426$		0			0
$427$	22.4329	+	18.8234i	1.08560	+	0.910929i
$428$	−12.1159	−	10.1664i	−0.585643	−	0.491412i
$429$		0			0
$430$	0.841367	−	1.45729i	0.0405743	−	0.0702767i
$431$	−24.2520	+	8.82699i	−1.16818	+	0.425181i	−0.852011	−	0.523523i	$-0.824617\pi$
$431$	−24.2520	+	8.82699i	−1.16818	+	0.425181i	−0.316164	+	0.948704i	$0.602395\pi$
$432$		0			0
$433$	4.53209	−	25.7028i	0.217798	−	1.23520i	−0.658186	−	0.752856i	$-0.728676\pi$
$433$	4.53209	−	25.7028i	0.217798	−	1.23520i	0.875984	−	0.482340i	$-0.160213\pi$
$434$	9.05690	+	3.29644i	0.434745	+	0.158234i
$435$		0			0
$436$	−5.81521			−0.278498
$437$	3.64543	−	13.2943i	0.174385	−	0.635952i
$438$		0			0
$439$	17.3366	−	14.5472i	0.827432	−	0.694298i	−0.127268	−	0.991868i	$-0.540621\pi$
$439$	17.3366	−	14.5472i	0.827432	−	0.694298i	0.954700	+	0.297571i	$0.0961764\pi$
$440$	2.43242	+	0.885328i	0.115961	+	0.0422064i
$441$		0			0
$442$	−4.51842	−	25.6252i	−0.214919	−	1.21887i
$443$	13.5432	−	4.92933i	0.643458	−	0.234200i	0.000379869	−	1.00000i	$-0.499879\pi$
$443$	13.5432	−	4.92933i	0.643458	−	0.234200i	0.643079	+	0.765800i	$0.277657\pi$
$444$		0			0
$445$	2.91993	+	5.05747i	0.138418	+	0.239747i
$446$	−10.6866	−	8.96713i	−0.506025	−	0.424606i
$447$		0			0
$448$	2.20574	+	3.82045i	0.104211	+	0.180499i
$449$	18.1361	−	31.4126i	0.855895	−	1.48245i	−0.0199166	−	0.999802i	$-0.506340\pi$
$449$	18.1361	−	31.4126i	0.855895	−	1.48245i	0.875812	−	0.482653i	$-0.160327\pi$
$450$		0			0
$451$	1.88103	+	10.6679i	0.0885744	+	0.502331i
$452$	−2.10741	+	11.9517i	−0.0991243	+	0.562162i
$453$		0			0
$454$	−18.0876	+	15.1773i	−0.848895	+	0.712308i
$455$	−12.3550			−0.579213
$456$		0			0
$457$	−40.4543			−1.89237			−0.946186	−	0.323623i	$-0.895099\pi$
$457$	−40.4543			−1.89237			−0.946186	+	0.323623i	$0.895099\pi$
$458$	−6.59627	+	5.53492i	−0.308223	+	0.258630i
$459$		0			0
$460$	0.256959	−	1.45729i	0.0119808	−	0.0679465i
$461$	6.81996	+	38.6779i	0.317637	+	1.80141i	0.557037	+	0.830488i	$0.311938\pi$
$461$	6.81996	+	38.6779i	0.317637	+	1.80141i	−0.239400	+	0.970921i	$0.576951\pi$
$462$		0			0
$463$	−10.4167	+	18.0422i	−0.484105	+	0.838494i	−0.999833	−	0.0182582i	$-0.994188\pi$
$463$	−10.4167	+	18.0422i	−0.484105	+	0.838494i	0.515729	+	0.856752i	$0.327521\pi$
$464$	−0.754900	−	1.30753i	−0.0350454	−	0.0607003i
$465$		0			0
$466$	−11.8289	−	9.92561i	−0.547962	−	0.459795i
$467$	−5.96198	−	10.3265i	−0.275888	−	0.477851i	0.694471	−	0.719521i	$-0.255638\pi$
$467$	−5.96198	−	10.3265i	−0.275888	−	0.477851i	−0.970359	+	0.241669i	$0.922305\pi$
$468$		0			0
$469$	−10.3229	+	3.75725i	−0.476669	+	0.173493i
$470$	−0.751497	−	4.26195i	−0.0346639	−	0.196589i
$471$		0			0
$472$	−1.24763	−	0.454099i	−0.0574266	−	0.0209016i
$473$	15.2404	−	12.7882i	0.700752	−	0.588001i
$474$		0			0
$475$	20.1612	−	5.27633i	0.925057	−	0.242095i
$476$	−19.1780			−0.879022
$477$		0			0
$478$	−7.29086	−	2.65366i	−0.333476	−	0.121375i
$479$	1.28564	−	7.29125i	0.0587426	−	0.333146i	−0.941247	−	0.337719i	$-0.890345\pi$
$479$	1.28564	−	7.29125i	0.0587426	−	0.333146i	0.999990	+	0.00457323i	$0.00145571\pi$
$480$		0			0
$481$	15.5167	−	5.64760i	0.707499	−	0.257509i
$482$	−6.64290	+	11.5058i	−0.302576	+	0.524077i
$483$		0			0
$484$	15.0175	+	12.6012i	0.682615	+	0.572782i
$485$	−2.97881	−	2.49952i	−0.135261	−	0.113497i
$486$		0			0
$487$	11.2934	−	19.5607i	0.511752	−	0.886381i	−0.488155	−	0.872757i	$-0.662330\pi$
$487$	11.2934	−	19.5607i	0.511752	−	0.886381i	0.999907	−	0.0136238i	$-0.00433672\pi$
$488$	−6.23783	+	2.27038i	−0.282373	+	0.102775i
$489$		0			0
$490$	−1.01249	+	5.74211i	−0.0457396	+	0.259402i
$491$	15.0680	+	5.48432i	0.680011	+	0.247504i	0.658852	−	0.752272i	$-0.271042\pi$
$491$	15.0680	+	5.48432i	0.680011	+	0.247504i	0.0211590	+	0.999776i	$0.493264\pi$
$492$		0			0
$493$	6.56355			0.295607
$494$	15.0890	−	21.2840i	0.678886	−	0.957613i
$495$		0			0
$496$	−1.67365	+	1.40436i	−0.0751490	+	0.0630575i
$497$	31.4898	+	11.4613i	1.41251	+	0.514112i
$498$		0			0
$499$	−6.09879	−	34.5880i	−0.273019	−	1.54837i	−0.745183	−	0.666860i	$-0.767638\pi$
$499$	−6.09879	−	34.5880i	−0.273019	−	1.54837i	0.472164	−	0.881511i	$-0.343473\pi$
$500$	4.30066	−	1.56531i	0.192331	−	0.0700029i
$501$		0			0
$502$	8.82547	+	15.2862i	0.393900	+	0.682255i
$503$	−30.7395	−	25.7935i	−1.37061	−	1.15007i	−0.972545	−	0.232715i	$-0.925239\pi$
$503$	−30.7395	−	25.7935i	−1.37061	−	1.15007i	−0.398061	−	0.917359i	$-0.630317\pi$
$504$		0			0
$505$	0.290393	+	0.502975i	0.0129223	+	0.0223821i
$506$	8.74763	−	15.1513i	0.388879	−	0.673559i
$507$		0			0
$508$	0.0787257	+	0.446476i	0.00349289	+	0.0198092i
$509$	−0.745100	+	4.22567i	−0.0330260	+	0.187300i	−0.996858	−	0.0792114i	$-0.974760\pi$
$509$	−0.745100	+	4.22567i	−0.0330260	+	0.187300i	0.963832	+	0.266511i	$0.0858709\pi$
$510$		0			0
$511$	−10.6964	+	8.97535i	−0.473181	+	0.397046i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.90167			0.348528
$515$	1.21301	−	1.01784i	0.0534517	−	0.0448513i
$516$		0			0
$517$	8.88490	−	50.3888i	0.390758	−	2.21610i
$518$	−2.11334	−	11.9854i	−0.0928549	−	0.526606i
$519$		0			0
$520$	1.40033	−	2.42544i	0.0614085	−	0.106363i
$521$	4.38532	+	7.59559i	0.192124	+	0.332769i	0.945954	−	0.324301i	$-0.105129\pi$
$521$	4.38532	+	7.59559i	0.192124	+	0.332769i	−0.753830	+	0.657070i	$0.771796\pi$
$522$		0			0
$523$	22.9800	+	19.2825i	1.00484	+	0.843165i	0.987648	−	0.156687i	$-0.0500815\pi$
$523$	22.9800	+	19.2825i	1.00484	+	0.843165i	0.0171965	+	0.999852i	$0.494526\pi$
$524$	−5.40420	−	9.36035i	−0.236084	−	0.408909i
$525$		0			0
$526$	23.8405	−	8.67723i	1.03949	−	0.378345i
$527$	−1.64930	−	9.35365i	−0.0718446	−	0.407451i
$528$		0			0
$529$	12.2147	+	4.44577i	0.531072	+	0.193294i
$530$	−0.958826	+	0.804551i	−0.0416487	+	0.0349474i
$531$		0			0
$532$	−13.5175	−	13.6761i	−0.586060	−	0.592936i
$533$	11.7202			0.507657
$534$		0			0
$535$	6.95424	+	2.53114i	0.300658	+	0.109431i
$536$	0.432419	−	2.45237i	0.0186776	−	0.105926i
$537$		0			0
$538$	−18.9538	+	6.89863i	−0.817158	+	0.297421i
$539$	−34.4680	+	59.7003i	−1.48464	+	2.57147i
$540$		0			0
$541$	3.83544	+	3.21831i	0.164898	+	0.138366i	0.721503	−	0.692411i	$-0.243452\pi$
$541$	3.83544	+	3.21831i	0.164898	+	0.138366i	−0.556605	+	0.830778i	$0.687896\pi$
$542$	−15.7121	−	13.1840i	−0.674894	−	0.566303i
$543$		0			0
$544$	2.17365	−	3.76487i	0.0931944	−	0.161417i
$545$	2.55690	−	0.930637i	0.109526	−	0.0398641i
$546$		0			0
$547$	2.35803	−	13.3731i	0.100822	−	0.571790i	−0.891985	−	0.452065i	$-0.850687\pi$
$547$	2.35803	−	13.3731i	0.100822	−	0.571790i	0.992807	−	0.119725i	$-0.0382014\pi$
$548$	10.3093	+	3.75227i	0.440391	+	0.160289i
$549$		0			0
$550$	26.4492			1.12780
$551$	4.62630	+	4.68058i	0.197087	+	0.199399i
$552$		0			0
$553$	−4.26991	+	3.58288i	−0.181575	+	0.152360i
$554$	8.58424	+	3.12441i	0.364710	+	0.132743i
$555$		0			0
$556$	−2.33750	−	13.2566i	−0.0991319	−	0.562205i
$557$	−22.2961	+	8.11511i	−0.944715	+	0.343848i	−0.768026	−	0.640419i	$-0.778761\pi$
$557$	−22.2961	+	8.11511i	−0.944715	+	0.343848i	−0.176689	+	0.984267i	$0.556539\pi$
$558$		0			0
$559$	−10.7626	−	18.6414i	−0.455211	−	0.788449i
$560$	−1.58125	−	1.32683i	−0.0668201	−	0.0560687i
$561$		0			0
$562$	1.71554	+	2.97140i	0.0723656	+	0.125341i
$563$	−7.37211	+	12.7689i	−0.310697	+	0.538144i	−0.978514	−	0.206183i	$-0.933896\pi$
$563$	−7.37211	+	12.7689i	−0.310697	+	0.538144i	0.667816	+	0.744326i	$0.267229\pi$
$564$		0			0
$565$	−0.986081	−	5.59234i	−0.0414847	−	0.235272i
$566$	−1.95218	+	11.0714i	−0.0820563	+	0.465364i
$567$		0			0
$568$	−5.81908	+	4.88279i	−0.244163	+	0.204877i
$569$	−23.9668			−1.00474			−0.502370	−	0.864653i	$-0.667538\pi$
$569$	−23.9668			−1.00474			−0.502370	+	0.864653i	$0.667538\pi$
$570$		0			0
$571$	−41.0847			−1.71934			−0.859671	−	0.510848i	$-0.829331\pi$
$571$	−41.0847			−1.71934			−0.859671	+	0.510848i	$0.829331\pi$
$572$	25.3653	−	21.2840i	1.06058	−	0.889929i
$573$		0			0
$574$	1.50000	−	8.50692i	0.0626088	−	0.355072i
$575$	−2.62558	−	14.8904i	−0.109494	−	0.620973i
$576$		0			0
$577$	3.72756	−	6.45632i	0.155180	−	0.268780i	−0.777944	−	0.628333i	$-0.783737\pi$
$577$	3.72756	−	6.45632i	0.155180	−	0.268780i	0.933125	+	0.359553i	$0.117071\pi$
$578$	0.949493	+	1.64457i	0.0394937	+	0.0684051i
$579$		0			0
$580$	0.541174	+	0.454099i	0.0224710	+	0.0188554i
$581$	39.5638	+	68.5265i	1.64138	+	2.84296i
$582$		0			0
$583$	−13.9058	+	5.06132i	−0.575921	+	0.209618i
$584$	−0.549630	−	3.11711i	−0.0227438	−	0.128987i
$585$		0			0
$586$	13.6557	+	4.97027i	0.564112	+	0.205320i
$587$	−4.53462	+	3.80499i	−0.187164	+	0.157049i	−0.731555	−	0.681782i	$-0.761205\pi$
$587$	−4.53462	+	3.80499i	−0.187164	+	0.157049i	0.544391	+	0.838831i	$0.316761\pi$
$588$		0			0
$589$	5.50774	−	7.76903i	0.226943	−	0.320117i
$590$	0.621244			0.0255762
$591$		0			0
$592$	2.59240	+	0.943555i	0.106547	+	0.0387799i
$593$	0.870767	−	4.93837i	0.0357581	−	0.202794i	−0.961695	−	0.274122i	$-0.911613\pi$
$593$	0.870767	−	4.93837i	0.0357581	−	0.202794i	0.997453	+	0.0713281i	$0.0227237\pi$
$594$		0			0
$595$	8.43242	−	3.06915i	0.345695	−	0.125823i
$596$	4.09492	−	7.09261i	0.167735	−	0.290525i
$597$		0			0
$598$	−14.5005	−	12.1673i	−0.592968	−	0.497559i
$599$	−3.68164	−	3.08926i	−0.150428	−	0.126224i	0.564468	−	0.825455i	$-0.309081\pi$
$599$	−3.68164	−	3.08926i	−0.150428	−	0.126224i	−0.714896	+	0.699231i	$0.753526\pi$
$600$		0			0
$601$	−4.42468	+	7.66377i	−0.180486	+	0.312612i	−0.942046	−	0.335483i	$-0.891101\pi$
$601$	−4.42468	+	7.66377i	−0.180486	+	0.312612i	0.761560	+	0.648095i	$0.224434\pi$
$602$	−14.9081	+	5.42609i	−0.607608	+	0.221151i
$603$		0			0
$604$	3.67112	−	20.8200i	0.149376	−	0.847152i
$605$	−8.61974	−	3.13733i	−0.350442	−	0.127551i
$606$		0			0
$607$	0.715948			0.0290594			0.0145297	−	0.999894i	$-0.495375\pi$
$607$	0.715948			0.0290594			0.0145297	+	0.999894i	$0.495375\pi$
$608$	4.21688	−	1.10359i	0.171017	−	0.0447565i
$609$		0			0
$610$	2.37939	−	1.99654i	0.0963385	−	0.0808376i
$611$	−52.0207	−	18.9340i	−2.10453	−	0.765987i
$612$		0			0
$613$	4.23870	+	24.0389i	0.171200	+	0.970921i	0.942440	+	0.334377i	$0.108526\pi$
$613$	4.23870	+	24.0389i	0.171200	+	0.970921i	−0.771240	+	0.636545i	$0.780363\pi$
$614$	−24.1532	+	8.79104i	−0.974743	+	0.354777i
$615$		0			0
$616$	−12.2023	−	21.1351i	−0.491646	−	0.851556i
$617$	33.2918	+	27.9351i	1.34028	+	1.12463i	0.981555	+	0.191182i	$0.0612320\pi$
$617$	33.2918	+	27.9351i	1.34028	+	1.12463i	0.358722	+	0.933444i	$0.383212\pi$
$618$		0			0
$619$	−11.8648	−	20.5505i	−0.476888	−	0.825994i	0.522761	−	0.852479i	$-0.324902\pi$
$619$	−11.8648	−	20.5505i	−0.476888	−	0.825994i	−0.999649	+	0.0264848i	$0.991569\pi$
$620$	0.511144	−	0.885328i	0.0205281	−	0.0355556i
$621$		0			0
$622$	1.01367	+	5.74881i	0.0406445	+	0.230506i
$623$	9.56077	−	54.2218i	0.383044	−	2.17235i
$624$		0			0
$625$	16.6721	−	13.9895i	0.666882	−	0.559581i
$626$	16.5107			0.659902
$627$		0			0
$628$	19.6382			0.783648
$629$	−9.18732	+	7.70908i	−0.366322	+	0.307381i
$630$		0			0
$631$	−4.48293	+	25.4239i	−0.178462	+	1.01211i	0.755609	+	0.655023i	$0.227341\pi$
$631$	−4.48293	+	25.4239i	−0.178462	+	1.01211i	−0.934071	+	0.357087i	$0.883770\pi$
$632$	−0.219408	−	1.24432i	−0.00872757	−	0.0494965i
$633$		0			0
$634$	13.4748	−	23.3390i	0.535152	−	0.926910i
$635$	−0.106067	−	0.183713i	−0.00420913	−	0.00729043i
$636$		0			0
$637$	57.1357	+	47.9425i	2.26380	+	1.89955i
$638$	4.17617	+	7.23335i	0.165336	+	0.286371i
$639$		0			0
$640$	0.439693	−	0.160035i	0.0173804	−	0.00632594i
$641$	1.87645	+	10.6419i	0.0741153	+	0.420329i	0.999179	+	0.0405163i	$0.0129003\pi$
$641$	1.87645	+	10.6419i	0.0741153	+	0.420329i	−0.925064	+	0.379812i	$0.875989\pi$
$642$		0			0
$643$	−13.5360	−	4.92669i	−0.533806	−	0.194290i	0.0610309	−	0.998136i	$-0.480561\pi$
$643$	−13.5360	−	4.92669i	−0.533806	−	0.194290i	−0.594837	+	0.803846i	$0.702783\pi$
$644$	−10.6873	+	8.96773i	−0.421139	+	0.353378i
$645$		0			0
$646$	−5.01114	+	18.2748i	−0.197161	+	0.719013i
$647$	24.9463			0.980738			0.490369	−	0.871515i	$-0.336862\pi$
$647$	24.9463			0.980738			0.490369	+	0.871515i	$0.336862\pi$
$648$		0			0
$649$	6.90198	+	2.51211i	0.270926	+	0.0986091i
$650$	4.96926	−	28.1820i	0.194910	−	1.10539i
$651$		0			0
$652$	−4.27719	+	1.55677i	−0.167508	+	0.0609678i
$653$	17.8071	−	30.8427i	0.696844	−	1.20697i	−0.272711	−	0.962096i	$-0.587920\pi$
$653$	17.8071	−	30.8427i	0.696844	−	1.20697i	0.969555	−	0.244873i	$-0.0787463\pi$
$654$		0			0
$655$	3.87417	+	3.25082i	0.151376	+	0.127020i
$656$	1.50000	+	1.25865i	0.0585652	+	0.0491420i
$657$		0			0
$658$	−20.4008	+	35.3352i	−0.795306	+	1.37751i
$659$	−46.0163	+	16.7485i	−1.79254	+	0.652431i	−0.793501	+	0.608569i	$0.791744\pi$
$659$	−46.0163	+	16.7485i	−1.79254	+	0.652431i	−0.999038	+	0.0438619i	$0.986034\pi$
$660$		0			0
$661$	−5.90966	+	33.5154i	−0.229859	+	1.30360i	0.623315	+	0.781971i	$0.285785\pi$
$661$	−5.90966	+	33.5154i	−0.229859	+	1.30360i	−0.853174	+	0.521626i	$0.825326\pi$
$662$	26.7704	+	9.74362i	1.04046	+	0.378697i
$663$		0			0
$664$	−17.9368			−0.696081
$665$	8.13223	+	3.85002i	0.315354	+	0.149297i
$666$		0			0
$667$	3.65767	−	3.06915i	0.141626	−	0.118838i
$668$	17.9868	+	6.54666i	0.695930	+	0.253298i
$669$		0			0
$670$	0.202333	+	1.14749i	0.00781682	+	0.0443314i
$671$	34.5082	−	12.5600i	1.33217	−	0.484872i
$672$		0			0
$673$	14.1493	+	24.5073i	0.545415	+	0.944687i	0.998581	+	0.0532607i	$0.0169614\pi$
$673$	14.1493	+	24.5073i	0.545415	+	0.944687i	−0.453165	+	0.891427i	$0.649705\pi$
$674$	−12.7836	−	10.7267i	−0.492405	−	0.413177i
$675$		0			0
$676$	−11.4128	−	19.7676i	−0.438955	−	0.760292i
$677$	12.5025	−	21.6550i	0.480511	−	0.832270i	−0.519239	−	0.854629i	$-0.673785\pi$
$677$	12.5025	−	21.6550i	0.480511	−	0.832270i	0.999750	+	0.0223595i	$0.00711784\pi$
$678$		0			0
$679$	6.36618	+	36.1044i	0.244312	+	1.38556i
$680$	−0.353226	+	2.00324i	−0.0135456	+	0.0768209i
$681$		0			0
$682$	9.25877	−	7.76903i	0.354537	−	0.297492i
$683$	40.1284			1.53547			0.767734	−	0.640768i	$-0.221384\pi$
$683$	40.1284			1.53547			0.767734	+	0.640768i	$0.221384\pi$
$684$		0			0
$685$	−5.13341			−0.196137
$686$	18.4552	−	15.4857i	0.704622	−	0.591248i
$687$		0			0
$688$	0.624485	−	3.54163i	0.0238083	−	0.135023i
$689$	2.78029	+	15.7678i	0.105921	+	0.600705i
$690$		0			0
$691$	−1.44087	+	2.49567i	−0.0548135	+	0.0949397i	−0.892130	−	0.451778i	$-0.850790\pi$
$691$	−1.44087	+	2.49567i	−0.0548135	+	0.0949397i	0.837317	+	0.546718i	$0.184123\pi$
$692$	2.77584	+	4.80790i	0.105522	+	0.182769i
$693$		0			0
$694$	−14.3478	−	12.0392i	−0.544634	−	0.457002i
$695$	3.14930	+	5.45475i	0.119460	+	0.206910i
$696$		0			0
$697$	−7.99912	+	2.91144i	−0.302988	+	0.110279i
$698$	0.284930	+	1.61592i	0.0107847	+	0.0611633i
$699$		0			0
$700$	−19.8195	−	7.21372i	−0.749108	−	0.272653i
$701$	−11.8491	+	9.94258i	−0.447535	+	0.375526i	−0.838520	−	0.544871i	$-0.816579\pi$
$701$	−11.8491	+	9.94258i	−0.447535	+	0.375526i	0.390985	+	0.920397i	$0.372134\pi$
$702$		0			0
$703$	−11.9731	−	1.11792i	−0.451575	−	0.0421630i
$704$	5.53209			0.208498
$705$		0			0
$706$	11.1887	+	4.07234i	0.421091	+	0.153265i
$707$	0.950837	−	5.39246i	0.0357599	−	0.202804i
$708$		0			0
$709$	−43.8353	+	15.9548i	−1.64627	+	0.599193i	−0.988119	−	0.153692i	$-0.950884\pi$
$709$	−43.8353	+	15.9548i	−1.64627	+	0.599193i	−0.658152	+	0.752885i	$0.728661\pi$
$710$	1.77719	−	3.07818i	0.0666967	−	0.115522i
$711$		0			0
$712$	9.56077	+	8.02244i	0.358305	+	0.300654i
$713$	−5.29292	−	4.44129i	−0.198221	−	0.166327i
$714$		0			0
$715$	−7.74675	+	13.4178i	−0.289712	+	0.501796i
$716$	−7.84642	+	2.85586i	−0.293234	+	0.106729i
$717$		0			0
$718$	0.398681	−	2.26103i	0.0148786	−	0.0843810i
$719$	−10.8020	−	3.93161i	−0.402847	−	0.146624i	0.132647	−	0.991163i	$-0.457652\pi$
$719$	−10.8020	−	3.93161i	−0.402847	−	0.146624i	−0.535494	+	0.844539i	$0.679875\pi$
$720$		0			0
$721$	−14.9290			−0.555986
$722$	−16.5642	+	9.30742i	−0.616455	+	0.346386i
$723$		0			0
$724$	−9.64337	+	8.09175i	−0.358393	+	0.300727i
$725$	6.78312	+	2.46885i	0.251919	+	0.0916909i
$726$		0			0
$727$	3.02687	+	17.1663i	0.112261	+	0.636661i	0.988070	+	0.154004i	$0.0492170\pi$
$727$	3.02687	+	17.1663i	0.112261	+	0.636661i	−0.875810	+	0.482657i	$0.839672\pi$
$728$	−24.8123	+	9.03093i	−0.919604	+	0.334708i
$729$		0			0
$730$	0.740514	+	1.28261i	0.0274077	+	0.0474715i
$731$	11.9764	+	10.0494i	0.442962	+	0.371689i
$732$		0			0
$733$	21.9393	+	38.0000i	0.810346	+	1.40356i	0.912622	+	0.408804i	$0.134054\pi$
$733$	21.9393	+	38.0000i	0.810346	+	1.40356i	−0.102276	+	0.994756i	$0.532613\pi$
$734$	−10.7476	+	18.6154i	−0.396702	+	0.687108i
$735$		0			0
$736$	−0.549163	−	3.11446i	−0.0202424	−	0.114800i
$737$	−2.39218	+	13.5667i	−0.0881170	+	0.499736i
$738$		0			0
$739$	−13.6040	+	11.4151i	−0.500432	+	0.419912i	−0.857747	−	0.514072i	$-0.828136\pi$
$739$	−13.6040	+	11.4151i	−0.500432	+	0.419912i	0.357316	+	0.933984i	$0.383692\pi$
$740$	−1.29086			−0.0474529
$741$		0			0
$742$	11.8007			0.433216
$743$	−7.98751	+	6.70232i	−0.293033	+	0.245884i	−0.777438	−	0.628960i	$-0.783481\pi$
$743$	−7.98751	+	6.70232i	−0.293033	+	0.245884i	0.484404	+	0.874844i	$0.339036\pi$
$744$		0			0
$745$	−0.665441	+	3.77390i	−0.0243799	+	0.138265i
$746$	−4.85891	−	27.5562i	−0.177897	−	1.00891i
$747$		0			0
$748$	−12.0248	+	20.8276i	−0.439671	+	0.761532i
$749$	−34.8862	−	60.4248i	−1.27472	−	2.20787i
$750$		0			0
$751$	−26.0915	−	21.8934i	−0.952093	−	0.798901i	0.0275557	−	0.999620i	$-0.491228\pi$
$751$	−26.0915	−	21.8934i	−0.952093	−	0.798901i	−0.979649	+	0.200719i	$0.935672\pi$
$752$	−4.62449	−	8.00984i	−0.168638	−	0.292089i
$753$		0			0
$754$	8.49185	−	3.09078i	0.309255	−	0.112560i
$755$	1.71776	+	9.74189i	0.0625156	+	0.354544i
$756$		0			0
$757$	−40.6664	−	14.8014i	−1.47805	−	0.537965i	−0.527774	−	0.849385i	$-0.676973\pi$
$757$	−40.6664	−	14.8014i	−1.47805	−	0.537965i	−0.950272	+	0.311420i	$0.899195\pi$
$758$	−6.80999	+	5.71426i	−0.247350	+	0.207551i
$759$		0			0
$760$	−1.67752	+	1.16009i	−0.0608500	+	0.0420809i
$761$	−14.1679			−0.513585			−0.256793	−	0.966467i	$-0.582666\pi$
$761$	−14.1679			−0.513585			−0.256793	+	0.966467i	$0.582666\pi$
$762$		0			0
$763$	−24.1065	−	8.77406i	−0.872715	−	0.317642i
$764$	1.16637	−	6.61484i	0.0421979	−	0.239316i
$765$		0			0
$766$	23.5069	−	8.55580i	0.849338	−	0.309134i
$767$	3.97343	−	6.88218i	0.143472	−	0.248501i
$768$		0			0
$769$	−13.9722	−	11.7241i	−0.503852	−	0.422782i	0.355107	−	0.934825i	$-0.384444\pi$
$769$	−13.9722	−	11.7241i	−0.503852	−	0.422782i	−0.858960	+	0.512043i	$0.828889\pi$
$770$	8.74763	+	7.34013i	0.315243	+	0.264520i
$771$		0			0
$772$	6.26604	−	10.8531i	0.225520	−	0.390612i
$773$	−26.5437	+	9.66112i	−0.954711	+	0.347486i	−0.771959	−	0.635673i	$-0.780723\pi$
$773$	−26.5437	+	9.66112i	−0.954711	+	0.347486i	−0.182752	+	0.983159i	$0.558501\pi$
$774$		0			0
$775$	1.81386	−	10.2869i	0.0651559	−	0.369517i
$776$	−7.80928	−	2.84234i	−0.280337	−	0.102034i
$777$		0			0
$778$	−23.3327			−0.836520
$779$	−7.71436	−	3.65219i	−0.276395	−	0.130853i
$780$		0			0
$781$	32.1917	−	27.0120i	1.15191	−	0.966566i
$782$	12.9192	+	4.70221i	0.461990	+	0.168151i
$783$		0			0
$784$	2.16385	+	12.2718i	0.0772803	+	0.438278i
$785$	−8.63475	+	3.14279i	−0.308188	+	0.112171i
$786$		0			0
$787$	−9.07057	−	15.7107i	−0.323331	−	0.560026i	0.657842	−	0.753156i	$-0.271469\pi$
$787$	−9.07057	−	15.7107i	−0.323331	−	0.560026i	−0.981173	+	0.193130i	$0.938136\pi$
$788$	3.11927	+	2.61738i	0.111119	+	0.0932403i
$789$		0			0
$790$	0.295607	+	0.512007i	0.0105172	+	0.0182164i
$791$	−26.7690	+	46.3653i	−0.951797	+	1.64856i
$792$		0			0
$793$	−6.89945	−	39.1287i	−0.245007	−	1.38950i
$794$	−0.657918	+	3.73124i	−0.0233486	+	0.132417i
$795$		0			0
$796$	−5.48158	+	4.59959i	−0.194290	+	0.163028i
$797$	32.8111			1.16223			0.581114	−	0.813822i	$-0.302617\pi$
$797$	32.8111			1.16223			0.581114	+	0.813822i	$0.302617\pi$
$798$		0			0
$799$	40.2080			1.42246
$800$	3.66250	−	3.07321i	0.129489	−	0.108654i
$801$		0			0
$802$	−3.79591	+	21.5277i	−0.134038	+	0.760169i
$803$	3.04060	+	17.2441i	0.107300	+	0.608531i
$804$		0			0
$805$	3.26399	−	5.65339i	0.115040	−	0.199256i
$806$	−6.53849	−	11.3250i	−0.230308	−	0.398906i
$807$		0			0
$808$	0.950837	+	0.797847i	0.0334503	+	0.0280682i
$809$	−4.67112	−	8.09062i	−0.164228	−	0.284451i	0.772153	−	0.635437i	$-0.219180\pi$
$809$	−4.67112	−	8.09062i	−0.164228	−	0.284451i	−0.936381	+	0.350986i	$0.885847\pi$
$810$		0			0
$811$	14.1027	−	5.13295i	0.495211	−	0.180242i	−0.0823275	−	0.996605i	$-0.526235\pi$
$811$	14.1027	−	5.13295i	0.495211	−	0.180242i	0.577539	+	0.816363i	$0.304013\pi$
$812$	−1.15657	−	6.55926i	−0.0405878	−	0.230185i
$813$		0			0
$814$	−14.3414	−	5.21983i	−0.502665	−	0.182955i
$815$	1.63151	−	1.36900i	0.0571493	−	0.0479540i
$816$		0			0
$817$	1.27513	+	15.6238i	0.0446111	+	0.546608i
$818$	7.91622			0.276784
$819$		0			0
$820$	−0.860967	−	0.313366i	−0.0300663	−	0.0109432i
$821$	−6.34760	+	35.9990i	−0.221533	+	1.25637i	0.647671	+	0.761920i	$0.275743\pi$
$821$	−6.34760	+	35.9990i	−0.221533	+	1.25637i	−0.869203	+	0.494455i	$0.835368\pi$
$822$		0			0
$823$	−21.4595	+	7.81060i	−0.748030	+	0.272261i	−0.687776	−	0.725923i	$-0.741413\pi$
$823$	−21.4595	+	7.81060i	−0.748030	+	0.272261i	−0.0602532	+	0.998183i	$0.519191\pi$
$824$	1.69207	−	2.93075i	0.0589459	−	0.102097i
$825$		0			0
$826$	−4.48680	−	3.76487i	−0.156116	−	0.130997i
$827$	−1.86303	−	1.56326i	−0.0647838	−	0.0543600i	0.609821	−	0.792539i	$-0.291241\pi$
$827$	−1.86303	−	1.56326i	−0.0647838	−	0.0543600i	−0.674605	+	0.738179i	$0.735686\pi$
$828$		0			0
$829$	11.6702	−	20.2135i	0.405324	−	0.702042i	−0.589035	−	0.808108i	$-0.700492\pi$
$829$	11.6702	−	20.2135i	0.405324	−	0.702042i	0.994359	+	0.106065i	$0.0338253\pi$
$830$	7.88666	−	2.87051i	0.273750	−	0.0996368i
$831$		0			0
$832$	1.03936	−	5.89452i	0.0360334	−	0.204356i
$833$	−50.9051	−	18.5280i	−1.76376	−	0.641956i
$834$		0			0
$835$	−8.95636			−0.309947
$836$	−23.3282	+	6.10516i	−0.806821	+	0.211151i
$837$		0			0
$838$	4.77197	−	4.00416i	0.164845	−	0.138321i
$839$	−1.37851	−	0.501736i	−0.0475914	−	0.0173218i	0.318115	−	0.948052i	$-0.396950\pi$
$839$	−1.37851	−	0.501736i	−0.0475914	−	0.0173218i	−0.365706	+	0.930730i	$0.619172\pi$
$840$		0			0
$841$	−4.63997	−	26.3146i	−0.159999	−	0.907399i
$842$	−3.35591	+	1.22145i	−0.115652	+	0.0420940i
$843$		0			0
$844$	1.32635	+	2.29731i	0.0456549	+	0.0790766i
$845$	8.18164	+	6.86521i	0.281457	+	0.236170i
$846$		0			0
$847$	43.2413	+	74.8961i	1.48579	+	2.57346i
$848$	−1.33750	+	2.31661i	−0.0459298	+	0.0795528i
$849$		0			0
$850$	3.60922	+	20.4689i	0.123795	+	0.702078i
$851$	−1.51501	+	8.59208i	−0.0519340	+	0.294533i
$852$		0			0
$853$	−7.15207	+	6.00130i	−0.244882	+	0.205481i	−0.756965	−	0.653456i	$-0.773319\pi$
$853$	−7.15207	+	6.00130i	−0.244882	+	0.205481i	0.512083	+	0.858936i	$0.328874\pi$
$854$	−29.2841			−1.00208
$855$		0			0
$856$	15.8161			0.540585
$857$	−26.6930	+	22.3981i	−0.911816	+	0.765104i	−0.972464	−	0.233055i	$-0.925128\pi$
$857$	−26.6930	+	22.3981i	−0.911816	+	0.765104i	0.0606480	+	0.998159i	$0.480683\pi$
$858$		0			0
$859$	−4.00758	+	22.7281i	−0.136737	+	0.775473i	0.836898	+	0.547359i	$0.184367\pi$
$859$	−4.00758	+	22.7281i	−0.136737	+	0.775473i	−0.973635	+	0.228114i	$0.926744\pi$
$860$	0.292204	+	1.65717i	0.00996406	+	0.0565090i
$861$		0			0
$862$	12.9042	−	22.3507i	0.439519	−	0.761269i
$863$	21.5788	+	37.3755i	0.734550	+	1.27228i	0.954920	+	0.296862i	$0.0959402\pi$
$863$	21.5788	+	37.3755i	0.734550	+	1.27228i	−0.220370	+	0.975416i	$0.570727\pi$
$864$		0			0
$865$	−1.98995	−	1.66977i	−0.0676604	−	0.0567738i
$866$	13.0496	+	22.6026i	0.443444	+	0.768068i
$867$		0			0
$868$	−9.05690	+	3.29644i	−0.307411	+	0.111889i
$869$	1.21378	+	6.88370i	0.0411748	+	0.233514i
$870$		0			0
$871$	14.0061	+	5.09780i	0.474578	+	0.172732i
$872$	4.45471	−	3.73794i	0.150855	−	0.126583i
$873$		0			0
$874$	5.75284	+	12.5273i	0.194593	+	0.423741i
$875$	20.1898			0.682541
$876$		0			0
$877$	−42.1374	−	15.3368i	−1.42288	−	0.517886i	−0.487998	−	0.872845i	$-0.662273\pi$
$877$	−42.1374	−	15.3368i	−1.42288	−	0.517886i	−0.934882	+	0.354959i	$0.884495\pi$
$878$	−3.92989	+	22.2875i	−0.132627	+	0.752168i
$879$		0			0
$880$	−2.43242	+	0.885328i	−0.0819968	+	0.0298444i
$881$	−2.29932	+	3.98253i	−0.0774659	+	0.134175i	−0.902156	−	0.431410i	$-0.858016\pi$
$881$	−2.29932	+	3.98253i	−0.0774659	+	0.134175i	0.824690	+	0.565585i	$0.191350\pi$
$882$		0			0
$883$	−5.53524	−	4.64462i	−0.186276	−	0.156304i	0.544881	−	0.838513i	$-0.316575\pi$
$883$	−5.53524	−	4.64462i	−0.186276	−	0.156304i	−0.731157	+	0.682209i	$0.761019\pi$
$884$	19.9329	+	16.7257i	0.670415	+	0.562545i
$885$		0			0
$886$	−7.20620	+	12.4815i	−0.242097	+	0.419325i
$887$	43.5676	−	15.8573i	1.46286	−	0.532437i	0.516707	−	0.856162i	$-0.327158\pi$
$887$	43.5676	−	15.8573i	1.46286	−	0.532437i	0.946151	+	0.323725i	$0.104935\pi$
$888$		0			0
$889$	−0.347296	+	1.96962i	−0.0116479	+	0.0660588i
$890$	−5.48767	−	1.99735i	−0.183947	−	0.0669513i
$891$		0			0
$892$	13.9504			0.467093
$893$	28.3405	+	28.6730i	0.948378	+	0.959506i
$894$		0			0
$895$	2.99297	−	2.51140i	0.100044	−	0.0839470i
$896$	−4.14543	−	1.50881i	−0.138489	−	0.0504059i
$897$		0			0
$898$	6.29860	+	35.7211i	0.210187	+	1.19203i
$899$	3.09967	−	1.12819i	0.103380	−	0.0376272i
$900$		0			0
$901$	−5.81449	−	10.0710i	−0.193709	−	0.335514i
$902$	−8.29813	−	6.96296i	−0.276298	−	0.231841i
$903$		0			0
$904$	−6.06805	−	10.5102i	−0.201820	−	0.349563i
$905$	2.94516	−	5.10116i	0.0979003	−	0.169568i
$906$		0			0
$907$	−9.44222	−	53.5495i	−0.313524	−	1.77808i	−0.580381	−	0.814345i	$-0.697096\pi$
$907$	−9.44222	−	53.5495i	−0.313524	−	1.77808i	0.266857	−	0.963736i	$-0.414015\pi$
$908$	4.10014	−	23.2530i	0.136068	−	0.771679i
$909$		0			0
$910$	9.46451	−	7.94166i	0.313745	−	0.263264i
$911$	16.8993			0.559899			0.279950	−	0.960015i	$-0.409682\pi$
$911$	16.8993			0.559899			0.279950	+	0.960015i	$0.409682\pi$
$912$		0			0
$913$	99.2277			3.28396
$914$	30.9898	−	26.0035i	1.02505	−	0.860120i
$915$		0			0
$916$	1.49525	−	8.48000i	0.0494045	−	0.280187i
$917$	−8.27972	−	46.9566i	−0.273420	−	1.55064i
$918$		0			0
$919$	3.85100	−	6.67014i	0.127033	−	0.220027i	−0.795493	−	0.605963i	$-0.792788\pi$
$919$	3.85100	−	6.67014i	0.127033	−	0.220027i	0.922526	+	0.385936i	$0.126121\pi$
$920$	0.739885	+	1.28152i	0.0243933	+	0.0422504i
$921$		0			0
$922$	−30.0861	−	25.2452i	−0.990831	−	0.831406i
$923$	−22.7335	−	39.3757i	−0.748284	−	1.29607i
$924$		0			0
$925$	−12.3944	+	4.51119i	−0.407525	+	0.148327i
$926$	−3.61768	−	20.5169i	−0.118884	−	0.674226i
$927$		0			0
$928$	1.41875	+	0.516382i	0.0465727	+	0.0169511i
$929$	13.9010	−	11.6644i	0.456078	−	0.382695i	−0.385607	−	0.922663i	$-0.626008\pi$
$929$	13.9010	−	11.6644i	0.456078	−	0.382695i	0.841686	+	0.539968i	$0.181564\pi$
$930$		0			0
$931$	−22.6677	−	49.3607i	−0.742904	−	1.61773i
$932$	15.4415			0.505803
$933$		0			0
$934$	11.2049	+	4.07824i	0.366634	+	0.133444i
$935$	1.95408	−	11.0821i	0.0639052	−	0.362424i
$936$		0			0
$937$	9.71436	−	3.53574i	0.317354	−	0.115507i	−0.178432	−	0.983952i	$-0.557102\pi$
$937$	9.71436	−	3.53574i	0.317354	−	0.115507i	0.495786	+	0.868445i	$0.334880\pi$
$938$	5.49273	−	9.51368i	0.179344	−	0.310633i
$939$		0			0
$940$	3.31521	+	2.78179i	0.108130	+	0.0907320i
$941$	−34.5808	−	29.0168i	−1.12730	−	0.945920i	−0.128353	−	0.991729i	$-0.540969\pi$
$941$	−34.5808	−	29.0168i	−1.12730	−	0.945920i	−0.998950	+	0.0458088i	$0.985413\pi$
$942$		0			0
$943$	−3.09627	+	5.36289i	−0.100828	+	0.174640i
$944$	1.24763	−	0.454099i	0.0406068	−	0.0147797i
$945$		0			0
$946$	−3.45471	+	19.5926i	−0.112322	+	0.637011i
$947$	−18.9561	−	6.89944i	−0.615989	−	0.224202i	0.0151327	−	0.999885i	$-0.495183\pi$
$947$	−18.9561	−	6.89944i	−0.615989	−	0.224202i	−0.631122	+	0.775684i	$0.717405\pi$
$948$		0			0
$949$	18.9451			0.614984
$950$	−12.0528	+	17.0012i	−0.391044	+	0.551593i
$951$		0			0
$952$	14.6912	−	12.3274i	0.476144	−	0.399532i
$953$	−42.0232	−	15.2952i	−1.36127	−	0.495460i	−0.444820	−	0.895620i	$-0.646732\pi$
$953$	−42.0232	−	15.2952i	−1.36127	−	0.495460i	−0.916445	+	0.400160i	$0.868955\pi$
$954$		0			0
$955$	0.545759	+	3.09516i	0.0176604	+	0.100157i
$956$	7.29086	−	2.65366i	0.235803	−	0.0858254i
$957$		0			0
$958$	3.70187	+	6.41182i	0.119602	+	0.207157i
$959$	37.0749	+	31.1095i	1.19721	+	1.00458i
$960$		0			0
$961$	13.1133	+	22.7130i	0.423011	+	0.732677i
$962$	−8.25624	+	14.3002i	−0.266192	+	0.461058i
$963$		0			0
$964$	−2.30706	−	13.0840i	−0.0743053	−	0.421406i
$965$	−1.01826	+	5.77482i	−0.0327788	+	0.185898i
$966$		0			0
$967$	−8.96270	+	7.52060i	−0.288221	+	0.241846i	−0.775421	−	0.631444i	$-0.782463\pi$
$967$	−8.96270	+	7.52060i	−0.288221	+	0.241846i	0.487201	+	0.873290i	$0.338018\pi$
$968$	−19.6040			−0.630097
$969$		0			0
$970$	3.88856			0.124854
$971$	−27.9786	+	23.4769i	−0.897877	+	0.753409i	−0.969774	−	0.244003i	$-0.921539\pi$
$971$	−27.9786	+	23.4769i	−0.897877	+	0.753409i	0.0718969	+	0.997412i	$0.477095\pi$
$972$		0			0
$973$	10.3118	−	58.4811i	0.330581	−	1.87482i
$974$	3.92215	+	22.2436i	0.125674	+	0.712732i
$975$		0			0
$976$	3.31908	−	5.74881i	0.106241	−	0.184015i
$977$	−25.0219	−	43.3392i	−0.800521	−	1.38654i	−0.919274	−	0.393619i	$-0.871223\pi$
$977$	−25.0219	−	43.3392i	−0.800521	−	1.38654i	0.118753	−	0.992924i	$-0.462110\pi$
$978$		0			0
$979$	−52.8911	−	44.3809i	−1.69041	−	1.41842i
$980$	−2.91534	−	5.04952i	−0.0931273	−	0.161301i
$981$		0			0
$982$	−15.0680	+	5.48432i	−0.480841	+	0.175012i
$983$	−1.71317	−	9.71589i	−0.0546417	−	0.309889i	0.945221	−	0.326430i	$-0.105846\pi$
$983$	−1.71317	−	9.71589i	−0.0546417	−	0.309889i	−0.999863	+	0.0165411i	$0.994735\pi$
$984$		0			0
$985$	−1.79039	−	0.651650i	−0.0570466	−	0.0207633i
$986$	−5.02797	+	4.21897i	−0.160123	+	0.134359i
$987$		0			0
$988$	2.12226	+	26.0035i	0.0675182	+	0.827282i
$989$	11.3732			0.361647
$990$		0			0
$991$	−32.1596	−	11.7051i	−1.02158	−	0.371826i	−0.223712	−	0.974655i	$-0.571818\pi$
$991$	−32.1596	−	11.7051i	−1.02158	−	0.371826i	−0.797870	+	0.602830i	$0.794040\pi$
$992$	0.379385	−	2.15160i	0.0120455	−	0.0683134i
$993$		0			0
$994$	−31.4898	+	11.4613i	−0.998795	+	0.363532i
$995$	1.67412	−	2.89965i	0.0530730	−	0.0919252i
$996$		0			0
$997$	30.4818	+	25.5773i	0.965368	+	0.810040i	0.981818	−	0.189825i	$-0.0607919\pi$
$997$	30.4818	+	25.5773i	0.965368	+	0.810040i	−0.0164497	+	0.999865i	$0.505236\pi$
$998$	26.9047	+	22.5757i	0.851652	+	0.714621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.d.253.1		6
3.2	odd	2		114.2.i.b.25.1	✓	6
12.11	even	2		912.2.bo.c.481.1		6
19.4	even	9		6498.2.a.bo.1.1		3
19.15	odd	18		6498.2.a.bt.1.1		3
19.16	even	9	inner	342.2.u.d.73.1		6
57.23	odd	18		2166.2.a.t.1.3		3
57.35	odd	18		114.2.i.b.73.1	yes	6
57.53	even	18		2166.2.a.n.1.3		3
228.35	even	18		912.2.bo.c.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.25.1	✓	6	3.2	odd	2
114.2.i.b.73.1	yes	6	57.35	odd	18
342.2.u.d.73.1		6	19.16	even	9	inner
342.2.u.d.253.1		6	1.1	even	1	trivial
912.2.bo.c.481.1		6	12.11	even	2
912.2.bo.c.529.1		6	228.35	even	18
2166.2.a.n.1.3		3	57.53	even	18
2166.2.a.t.1.3		3	57.23	odd	18
6498.2.a.bo.1.1		3	19.4	even	9
6498.2.a.bt.1.1		3	19.15	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(0.0812519 + 0.460802i) q^{5} +(2.20574 - 3.82045i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(0.0812519 + 0.460802i) q^{5} +(2.20574 - 3.82045i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.358441 - 0.300767i) q^{10} +(-2.76604 - 4.79093i) q^{11} +(-5.62449 + 2.04715i) q^{13} +(0.766044 + 4.34445i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(3.33022 - 2.79439i) q^{17} +(4.34002 + 0.405223i) q^{19} +0.467911 q^{20} +(5.19846 + 1.89209i) q^{22} +(0.549163 - 3.11446i) q^{23} +(4.49273 - 1.63522i) q^{25} +(2.99273 - 5.18355i) q^{26} +(-3.37939 - 2.83564i) q^{28} +(1.15657 + 0.970481i) q^{29} +(1.09240 - 1.89209i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.754900 + 4.28125i) q^{34} +(1.93969 + 0.705990i) q^{35} -2.75877 q^{37} +(-3.58512 + 2.47929i) q^{38} +(-0.358441 + 0.300767i) q^{40} +(-1.84002 - 0.669713i) q^{41} +(0.624485 + 3.54163i) q^{43} +(-5.19846 + 1.89209i) q^{44} +(1.58125 + 2.73881i) q^{46} +(7.08512 + 5.94512i) q^{47} +(-6.23055 - 10.7916i) q^{49} +(-2.39053 + 4.14052i) q^{50} +(1.03936 + 5.89452i) q^{52} +(0.464508 - 2.63435i) q^{53} +(1.98293 - 1.66387i) q^{55} +4.41147 q^{56} -1.50980 q^{58} +(-1.01707 + 0.853427i) q^{59} +(-1.15270 + 6.53731i) q^{61} +(0.379385 + 2.15160i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.40033 - 2.42544i) q^{65} +(-1.90760 - 1.60067i) q^{67} +(-2.17365 - 3.76487i) q^{68} +(-1.93969 + 0.705990i) q^{70} +(1.31908 + 7.48086i) q^{71} +(-2.97431 - 1.08256i) q^{73} +(2.11334 - 1.77330i) q^{74} +(1.15270 - 4.20372i) q^{76} -24.4047 q^{77} +(-1.18732 - 0.432149i) q^{79} +(0.0812519 - 0.460802i) q^{80} +(1.84002 - 0.669713i) q^{82} +(-8.96838 + 15.5337i) q^{83} +(1.55825 + 1.30753i) q^{85} +(-2.75490 - 2.31164i) q^{86} +(2.76604 - 4.79093i) q^{88} +(11.7280 - 4.26865i) q^{89} +(-4.58512 + 26.0035i) q^{91} +(-2.97178 - 1.08164i) q^{92} -9.24897 q^{94} +(0.165907 + 2.03282i) q^{95} +(-6.36618 + 5.34186i) q^{97} +(11.7096 + 4.26195i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 12 q^{11} - 21 q^{13} - 3 q^{17} + 6 q^{19} + 12 q^{20} + 3 q^{22} + 15 q^{23} + 9 q^{25} - 9 q^{28} - 15 q^{29} + 3 q^{31} - 6 q^{34} + 6 q^{35} + 6 q^{37} + 6 q^{40} + 9 q^{41} - 9 q^{43} - 3 q^{44} + 12 q^{46} + 21 q^{47} + 3 q^{50} + 15 q^{52} - 30 q^{53} - 9 q^{55} + 6 q^{56} - 12 q^{58} - 27 q^{59} - 9 q^{61} - 9 q^{62} - 3 q^{64} + 6 q^{65} - 15 q^{67} - 12 q^{68} - 6 q^{70} - 9 q^{71} + 12 q^{73} + 6 q^{74} + 9 q^{76} - 42 q^{77} + 15 q^{79} + 3 q^{80} - 9 q^{82} + 3 q^{83} - 36 q^{85} - 18 q^{86} + 12 q^{88} + 48 q^{89} - 6 q^{91} - 3 q^{92} - 30 q^{94} + 48 q^{95} + 18 q^{97} + 36 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 12 * q^11 - 21 * q^13 - 3 * q^17 + 6 * q^19 + 12 * q^20 + 3 * q^22 + 15 * q^23 + 9 * q^25 - 9 * q^28 - 15 * q^29 + 3 * q^31 - 6 * q^34 + 6 * q^35 + 6 * q^37 + 6 * q^40 + 9 * q^41 - 9 * q^43 - 3 * q^44 + 12 * q^46 + 21 * q^47 + 3 * q^50 + 15 * q^52 - 30 * q^53 - 9 * q^55 + 6 * q^56 - 12 * q^58 - 27 * q^59 - 9 * q^61 - 9 * q^62 - 3 * q^64 + 6 * q^65 - 15 * q^67 - 12 * q^68 - 6 * q^70 - 9 * q^71 + 12 * q^73 + 6 * q^74 + 9 * q^76 - 42 * q^77 + 15 * q^79 + 3 * q^80 - 9 * q^82 + 3 * q^83 - 36 * q^85 - 18 * q^86 + 12 * q^88 + 48 * q^89 - 6 * q^91 - 3 * q^92 - 30 * q^94 + 48 * q^95 + 18 * q^97 + 36 * q^98

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