LMFDB - Embedded newform 342.2.u.f.73.1

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 237x^{8} + 1312x^{6} + 5283x^{4} + 11049x^{2} + 16129 $ x^12 + 18x^10 + 237x^8 + 1312x^6 + 5283x^4 + 11049*x^2 + 16129
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$0.925476 + 1.60297i$ of defining polynomial
Character	$\chi$	$=$	342.73
Dual form			342.2.u.f.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.318787 + 1.80793i) q^{5} +(0.425476 + 0.736946i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.318787 + 1.80793i) q^{5} +(0.425476 + 0.736946i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.40632 + 1.18004i) q^{10} +(-1.64693 + 2.85257i) q^{11} +(0.464002 + 0.168883i) q^{13} +(-0.147766 + 0.838024i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.06143 + 0.890650i) q^{17} +(2.39726 - 3.64049i) q^{19} -1.83582 q^{20} +(-3.09521 + 1.12657i) q^{22} +(0.631658 + 3.58231i) q^{23} +(1.53147 + 0.557409i) q^{25} +(0.246890 + 0.427626i) q^{26} +(-0.651867 + 0.546981i) q^{28} +(-1.72511 + 1.44754i) q^{29} +(-3.40906 - 5.90467i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.240608 + 1.36455i) q^{34} +(-1.46798 + 0.534303i) q^{35} +4.72214 q^{37} +(4.17647 - 1.24785i) q^{38} +(-1.40632 - 1.18004i) q^{40} +(5.89726 - 2.14643i) q^{41} +(0.414432 - 2.35036i) q^{43} +(-3.09521 - 1.12657i) q^{44} +(-1.81879 + 3.15023i) q^{46} +(1.19510 - 1.00281i) q^{47} +(3.13794 - 5.43507i) q^{49} +(0.814878 + 1.41141i) q^{50} +(-0.0857441 + 0.486279i) q^{52} +(-2.31071 - 13.1047i) q^{53} +(-4.63222 - 3.88690i) q^{55} -0.850952 q^{56} -2.25197 q^{58} +(2.03001 + 1.70338i) q^{59} +(1.55932 + 8.84332i) q^{61} +(1.18396 - 6.71455i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.453247 + 0.785046i) q^{65} +(-6.56239 + 5.50650i) q^{67} +(-0.692802 + 1.19997i) q^{68} +(-1.46798 - 0.534303i) q^{70} +(1.87624 - 10.6407i) q^{71} +(3.85055 - 1.40148i) q^{73} +(3.61737 + 3.03533i) q^{74} +(4.00146 + 1.72867i) q^{76} -2.80291 q^{77} +(0.480486 - 0.174883i) q^{79} +(-0.318787 - 1.80793i) q^{80} +(5.89726 + 2.14643i) q^{82} +(-6.62628 - 11.4770i) q^{83} +(-1.94861 + 1.63507i) q^{85} +(1.82826 - 1.53409i) q^{86} +(-1.64693 - 2.85257i) q^{88} +(-7.29938 - 2.65676i) q^{89} +(0.0729641 + 0.413800i) q^{91} +(-3.41820 + 1.24412i) q^{92} +1.56009 q^{94} +(5.81754 + 5.49462i) q^{95} +(13.3209 + 11.1776i) q^{97} +(5.89740 - 2.14648i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8	$ 12 q - 6 q^{7} - 6 q^{8} - 6 q^{11} + 6 q^{17} - 12 q^{19} + 12 q^{20} - 12 q^{23} - 18 q^{25} - 12 q^{26} + 6 q^{31} + 6 q^{34} - 12 q^{35} + 24 q^{37} + 18 q^{38} + 30 q^{41} + 36 q^{43} - 18 q^{46} - 24 q^{47} - 18 q^{50} - 12 q^{53} - 36 q^{55} + 12 q^{56} - 12 q^{58} + 42 q^{59} - 24 q^{61} - 12 q^{62} - 6 q^{64} + 12 q^{65} - 48 q^{67} - 12 q^{68} - 12 q^{70} - 18 q^{71} - 24 q^{73} + 24 q^{74} - 6 q^{76} + 60 q^{77} + 12 q^{79} + 30 q^{82} - 42 q^{83} + 84 q^{85} - 18 q^{86} - 6 q^{88} - 36 q^{89} + 66 q^{91} + 6 q^{92} + 60 q^{94} + 90 q^{95} + 12 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 - 6 * q^11 + 6 * q^17 - 12 * q^19 + 12 * q^20 - 12 * q^23 - 18 * q^25 - 12 * q^26 + 6 * q^31 + 6 * q^34 - 12 * q^35 + 24 * q^37 + 18 * q^38 + 30 * q^41 + 36 * q^43 - 18 * q^46 - 24 * q^47 - 18 * q^50 - 12 * q^53 - 36 * q^55 + 12 * q^56 - 12 * q^58 + 42 * q^59 - 24 * q^61 - 12 * q^62 - 6 * q^64 + 12 * q^65 - 48 * q^67 - 12 * q^68 - 12 * q^70 - 18 * q^71 - 24 * q^73 + 24 * q^74 - 6 * q^76 + 60 * q^77 + 12 * q^79 + 30 * q^82 - 42 * q^83 + 84 * q^85 - 18 * q^86 - 6 * q^88 - 36 * q^89 + 66 * q^91 + 6 * q^92 + 60 * q^94 + 90 * q^95 + 12 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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
$5$	−0.318787	+	1.80793i	−0.142566	+	0.808532i	0.826723	+	0.562609i	$0.190202\pi$
$5$	−0.318787	+	1.80793i	−0.142566	+	0.808532i	−0.969289	+	0.245923i	$0.920909\pi$
$6$		0			0
$7$	0.425476	+	0.736946i	0.160815	+	0.278539i	0.935161	−	0.354223i	$-0.115254\pi$
$7$	0.425476	+	0.736946i	0.160815	+	0.278539i	−0.774346	+	0.632762i	$0.781921\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$		0			0
$10$	−1.40632	+	1.18004i	−0.444718	+	0.373163i
$11$	−1.64693	+	2.85257i	−0.496568	+	0.860081i	−0.999992	−	0.00395854i	$-0.998740\pi$
$11$	−1.64693	+	2.85257i	−0.496568	+	0.860081i	0.503424	+	0.864039i	$0.332073\pi$
$12$		0			0
$13$	0.464002	+	0.168883i	0.128691	+	0.0468397i	0.405563	−	0.914067i	$-0.367076\pi$
$13$	0.464002	+	0.168883i	0.128691	+	0.0468397i	−0.276872	+	0.960907i	$0.589298\pi$
$14$	−0.147766	+	0.838024i	−0.0394922	+	0.223971i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.06143	+	0.890650i	0.257436	+	0.216014i	0.762366	−	0.647146i	$-0.224037\pi$
$17$	1.06143	+	0.890650i	0.257436	+	0.216014i	−0.504931	+	0.863160i	$0.668482\pi$
$18$		0			0
$19$	2.39726	−	3.64049i	0.549969	−	0.835185i
$19$	2.39726	−	3.64049i	0.549969	−	0.835185i
$20$	−1.83582			−0.410502
$21$		0			0
$22$	−3.09521	+	1.12657i	−0.659902	+	0.240185i
$23$	0.631658	+	3.58231i	0.131710	+	0.746964i	0.977095	+	0.212806i	$0.0682601\pi$
$23$	0.631658	+	3.58231i	0.131710	+	0.746964i	−0.845385	+	0.534158i	$0.820629\pi$
$24$		0			0
$25$	1.53147	+	0.557409i	0.306294	+	0.111482i
$26$	0.246890	+	0.427626i	0.0484192	+	0.0838644i
$27$		0			0
$28$	−0.651867	+	0.546981i	−0.123191	+	0.103370i
$29$	−1.72511	+	1.44754i	−0.320345	+	0.268801i	−0.788752	−	0.614712i	$-0.789272\pi$
$29$	−1.72511	+	1.44754i	−0.320345	+	0.268801i	0.468407	+	0.883513i	$0.344828\pi$
$30$		0			0
$31$	−3.40906	−	5.90467i	−0.612286	−	1.06051i	−0.990854	−	0.134937i	$-0.956917\pi$
$31$	−3.40906	−	5.90467i	−0.612286	−	1.06051i	0.378568	−	0.925573i	$-0.376417\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$		0			0
$34$	0.240608	+	1.36455i	0.0412639	+	0.234019i
$35$	−1.46798	+	0.534303i	−0.248135	+	0.0903136i
$36$		0			0
$37$	4.72214			0.776314			0.388157	−	0.921593i	$-0.373112\pi$
$37$	4.72214			0.776314			0.388157	+	0.921593i	$0.373112\pi$
$38$	4.17647	−	1.24785i	0.677512	−	0.202428i
$39$		0			0
$40$	−1.40632	−	1.18004i	−0.222359	−	0.186581i
$41$	5.89726	−	2.14643i	0.920997	−	0.335215i	0.162362	−	0.986731i	$-0.448089\pi$
$41$	5.89726	−	2.14643i	0.920997	−	0.335215i	0.758635	+	0.651516i	$0.225867\pi$
$42$		0			0
$43$	0.414432	−	2.35036i	0.0632004	−	0.358427i	−0.936764	−	0.349962i	$-0.886194\pi$
$43$	0.414432	−	2.35036i	0.0632004	−	0.358427i	0.999964	−	0.00846480i	$-0.00269446\pi$
$44$	−3.09521	−	1.12657i	−0.466621	−	0.169836i
$45$		0			0
$46$	−1.81879	+	3.15023i	−0.268166	+	0.464476i
$47$	1.19510	−	1.00281i	0.174323	−	0.146275i	−0.551452	−	0.834207i	$-0.685926\pi$
$47$	1.19510	−	1.00281i	0.174323	−	0.146275i	0.725775	+	0.687932i	$0.241481\pi$
$48$		0			0
$49$	3.13794	−	5.43507i	0.448277	−	0.776439i
$50$	0.814878	+	1.41141i	0.115241	+	0.199604i
$51$		0			0
$52$	−0.0857441	+	0.486279i	−0.0118906	+	0.0674347i
$53$	−2.31071	−	13.1047i	−0.317401	−	1.80007i	−0.558432	−	0.829551i	$-0.688597\pi$
$53$	−2.31071	−	13.1047i	−0.317401	−	1.80007i	0.241031	−	0.970517i	$-0.422514\pi$
$54$		0			0
$55$	−4.63222	−	3.88690i	−0.624609	−	0.524109i
$56$	−0.850952			−0.113713
$57$		0			0
$58$	−2.25197			−0.295698
$59$	2.03001	+	1.70338i	0.264285	+	0.221761i	0.765294	−	0.643681i	$-0.222593\pi$
$59$	2.03001	+	1.70338i	0.264285	+	0.221761i	−0.501010	+	0.865442i	$0.667038\pi$
$60$		0			0
$61$	1.55932	+	8.84332i	0.199650	+	1.13227i	0.905639	+	0.424049i	$0.139391\pi$
$61$	1.55932	+	8.84332i	0.199650	+	1.13227i	−0.705989	+	0.708222i	$0.749497\pi$
$62$	1.18396	−	6.71455i	0.150363	−	0.852748i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.453247	+	0.785046i	−0.0562183	+	0.0973730i
$66$		0			0
$67$	−6.56239	+	5.50650i	−0.801723	+	0.672726i	−0.948617	−	0.316427i	$-0.897517\pi$
$67$	−6.56239	+	5.50650i	−0.801723	+	0.672726i	0.146894	+	0.989152i	$0.453072\pi$
$68$	−0.692802	+	1.19997i	−0.0840146	+	0.145518i
$69$		0			0
$70$	−1.46798	−	0.534303i	−0.175458	−	0.0638614i
$71$	1.87624	−	10.6407i	0.222668	−	1.26282i	−0.644424	−	0.764668i	$-0.722903\pi$
$71$	1.87624	−	10.6407i	0.222668	−	1.26282i	0.867092	−	0.498147i	$-0.165986\pi$
$72$		0			0
$73$	3.85055	−	1.40148i	0.450672	−	0.164031i	−0.106705	−	0.994291i	$-0.534030\pi$
$73$	3.85055	−	1.40148i	0.450672	−	0.164031i	0.557377	+	0.830259i	$0.311808\pi$
$74$	3.61737	+	3.03533i	0.420510	+	0.352850i
$75$		0			0
$76$	4.00146	+	1.72867i	0.458999	+	0.198292i
$77$	−2.80291			−0.319422
$78$		0			0
$79$	0.480486	−	0.174883i	0.0540589	−	0.0196758i	−0.314849	−	0.949142i	$-0.601954\pi$
$79$	0.480486	−	0.174883i	0.0540589	−	0.0196758i	0.368908	+	0.929466i	$0.379732\pi$
$80$	−0.318787	−	1.80793i	−0.0356415	−	0.202133i
$81$		0			0
$82$	5.89726	+	2.14643i	0.651243	+	0.237033i
$83$	−6.62628	−	11.4770i	−0.727328	−	1.25977i	−0.958008	−	0.286740i	$-0.907428\pi$
$83$	−6.62628	−	11.4770i	−0.727328	−	1.25977i	0.230680	−	0.973030i	$-0.425905\pi$
$84$		0			0
$85$	−1.94861	+	1.63507i	−0.211356	+	0.177349i
$86$	1.82826	−	1.53409i	0.197146	−	0.165425i
$87$		0			0
$88$	−1.64693	−	2.85257i	−0.175563	−	0.304084i
$89$	−7.29938	−	2.65676i	−0.773733	−	0.281616i	−0.0751759	−	0.997170i	$-0.523952\pi$
$89$	−7.29938	−	2.65676i	−0.773733	−	0.281616i	−0.698557	+	0.715555i	$0.746174\pi$
$90$		0			0
$91$	0.0729641	+	0.413800i	0.00764871	+	0.0433780i
$92$	−3.41820	+	1.24412i	−0.356372	+	0.129709i
$93$		0			0
$94$	1.56009			0.160911
$95$	5.81754	+	5.49462i	0.596867	+	0.563736i
$96$		0			0
$97$	13.3209	+	11.1776i	1.35254	+	1.13491i	0.978210	+	0.207616i	$0.0665706\pi$
$97$	13.3209	+	11.1776i	1.35254	+	1.13491i	0.374327	+	0.927297i	$0.377874\pi$
$98$	5.89740	−	2.14648i	0.595727	−	0.216827i
$99$		0			0
$100$	−0.283004	+	1.60500i	−0.0283004	+	0.160500i
$101$	5.65216	+	2.05722i	0.562411	+	0.204701i	0.607552	−	0.794280i	$-0.292152\pi$
$101$	5.65216	+	2.05722i	0.562411	+	0.204701i	−0.0451411	+	0.998981i	$0.514374\pi$
$102$		0			0
$103$	0.0827516	−	0.143330i	0.00815376	−	0.0141227i	−0.861920	−	0.507045i	$-0.830738\pi$
$103$	0.0827516	−	0.143330i	0.00815376	−	0.0141227i	0.870073	+	0.492922i	$0.164071\pi$
$104$	−0.378258	+	0.317396i	−0.0370912	+	0.0311232i
$105$		0			0
$106$	6.65343	−	11.5241i	0.646238	−	1.11932i
$107$	−6.42161	−	11.1226i	−0.620800	−	1.07526i	−0.989337	−	0.145644i	$-0.953474\pi$
$107$	−6.42161	−	11.1226i	−0.620800	−	1.07526i	0.368537	−	0.929613i	$-0.379859\pi$
$108$		0			0
$109$	−1.54061	+	8.73721i	−0.147563	+	0.836873i	0.817710	+	0.575631i	$0.195243\pi$
$109$	−1.54061	+	8.73721i	−0.147563	+	0.836873i	−0.965273	+	0.261243i	$0.915868\pi$
$110$	−1.05004	−	5.95507i	−0.100117	−	0.567794i
$111$		0			0
$112$	−0.651867	−	0.546981i	−0.0615956	−	0.0516849i
$113$	12.3830			1.16489			0.582446	−	0.812870i	$-0.302096\pi$
$113$	12.3830			1.16489			0.582446	+	0.812870i	$0.302096\pi$
$114$		0			0
$115$	−6.67794			−0.622721
$116$	−1.72511	−	1.44754i	−0.160172	−	0.134401i
$117$		0			0
$118$	0.460166	+	2.60973i	0.0423617	+	0.240245i
$119$	−0.204746	+	1.16117i	−0.0187690	+	0.106444i
$120$		0			0
$121$	0.0752474	+	0.130332i	0.00684068	+	0.0118484i
$122$	−4.48987	+	7.77668i	−0.406494	+	0.704068i
$123$		0			0
$124$	5.22299	−	4.38261i	0.469038	−	0.393570i
$125$	−6.08553	+	10.5404i	−0.544306	+	0.942766i
$126$		0			0
$127$	−11.0698	−	4.02908i	−0.982287	−	0.357523i	−0.199558	−	0.979886i	$-0.563951\pi$
$127$	−11.0698	−	4.02908i	−0.982287	−	0.357523i	−0.782729	+	0.622363i	$0.786173\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$		0			0
$130$	−0.851825	+	0.310039i	−0.0747100	+	0.0271922i
$131$	14.4010	+	12.0838i	1.25822	+	1.05577i	0.995870	+	0.0907961i	$0.0289412\pi$
$131$	14.4010	+	12.0838i	1.25822	+	1.05577i	0.262348	+	0.964973i	$0.415503\pi$
$132$		0			0
$133$	3.70282	+	0.217709i	0.321075	+	0.0188777i
$134$	−8.56659			−0.740041
$135$		0			0
$136$	−1.30204	+	0.473905i	−0.111649	+	0.0406370i
$137$	2.34967	+	13.3256i	0.200746	+	1.13849i	0.903995	+	0.427542i	$0.140621\pi$
$137$	2.34967	+	13.3256i	0.200746	+	1.13849i	−0.703250	+	0.710943i	$0.748268\pi$
$138$		0			0
$139$	−17.8020	−	6.47941i	−1.50995	−	0.549576i	−0.551334	−	0.834284i	$-0.685881\pi$
$139$	−17.8020	−	6.47941i	−1.50995	−	0.549576i	−0.958614	+	0.284708i	$0.908103\pi$
$140$	−0.781098	−	1.35290i	−0.0660148	−	0.114341i
$141$		0			0
$142$	8.27698	−	6.94521i	0.694588	−	0.582829i
$143$	−1.24593	+	1.04546i	−0.104190	+	0.0874255i
$144$		0			0
$145$	−2.06711	−	3.58034i	−0.171664	−	0.297331i
$146$	3.85055	+	1.40148i	0.318674	+	0.115988i
$147$		0			0
$148$	0.819990	+	4.65040i	0.0674028	+	0.382260i
$149$	−14.2772	+	5.19648i	−1.16964	+	0.425713i	−0.852530	−	0.522678i	$-0.824933\pi$
$149$	−14.2772	+	5.19648i	−1.16964	+	0.425713i	−0.317105	+	0.948390i	$0.602711\pi$
$150$		0			0
$151$	−3.70848			−0.301792			−0.150896	−	0.988550i	$-0.548216\pi$
$151$	−3.70848			−0.301792			−0.150896	+	0.988550i	$0.548216\pi$
$152$	1.95413	+	3.89633i	0.158501	+	0.316034i
$153$		0			0
$154$	−2.14716	−	1.80168i	−0.173023	−	0.145183i
$155$	11.7620	−	4.28102i	0.944748	−	0.343860i
$156$		0			0
$157$	−2.73648	+	15.5193i	−0.218395	+	1.23858i	0.656523	+	0.754306i	$0.272026\pi$
$157$	−2.73648	+	15.5193i	−0.218395	+	1.23858i	−0.874918	+	0.484272i	$0.839085\pi$
$158$	0.480486	+	0.174883i	0.0382254	+	0.0139129i
$159$		0			0
$160$	0.917911	−	1.58987i	0.0725673	−	0.125690i
$161$	−2.37121	+	1.98968i	−0.186878	+	0.156809i
$162$		0			0
$163$	4.19734	−	7.27000i	0.328761	−	0.569430i	−0.653506	−	0.756922i	$-0.726702\pi$
$163$	4.19734	−	7.27000i	0.328761	−	0.569430i	0.982266	+	0.187492i	$0.0600357\pi$
$164$	3.13787	+	5.43494i	0.245026	+	0.424398i
$165$		0			0
$166$	2.30128	−	13.0512i	0.178614	−	1.01297i
$167$	−0.666871	−	3.78201i	−0.0516040	−	0.292661i	0.948074	−	0.318051i	$-0.103028\pi$
$167$	−0.666871	−	3.78201i	−0.0516040	−	0.292661i	−0.999678	+	0.0253900i	$0.991917\pi$
$168$		0			0
$169$	−9.77180	−	8.19952i	−0.751677	−	0.630732i
$170$	−2.54372			−0.195095
$171$		0			0
$172$	2.38662			0.181978
$173$	3.70984	+	3.11292i	0.282054	+	0.236671i	0.772828	−	0.634616i	$-0.218842\pi$
$173$	3.70984	+	3.11292i	0.282054	+	0.236671i	−0.490774	+	0.871287i	$0.663286\pi$
$174$		0			0
$175$	0.240823	+	1.36577i	0.0182045	+	0.103243i
$176$	0.571973	−	3.24382i	0.0431141	−	0.244512i
$177$		0			0
$178$	−3.88392	−	6.72714i	−0.291112	−	0.504221i
$179$	−12.2886	+	21.2844i	−0.918491	+	1.59087i	−0.116782	+	0.993158i	$0.537258\pi$
$179$	−12.2886	+	21.2844i	−0.918491	+	1.59087i	−0.801709	+	0.597715i	$0.796076\pi$
$180$		0			0
$181$	−9.28442	+	7.79056i	−0.690106	+	0.579067i	−0.918940	−	0.394398i	$-0.870953\pi$
$181$	−9.28442	+	7.79056i	−0.690106	+	0.579067i	0.228834	+	0.973465i	$0.426509\pi$
$182$	−0.210092	+	0.363889i	−0.0155730	+	0.0269733i
$183$		0			0
$184$	−3.41820	−	1.24412i	−0.251993	−	0.0917180i
$185$	−1.50536	+	8.53730i	−0.110676	+	0.627675i
$186$		0			0
$187$	−4.28874	+	1.56098i	−0.313624	+	0.114150i
$188$	1.19510	+	1.00281i	0.0871616	+	0.0731373i
$189$		0			0
$190$	0.924622	+	7.94857i	0.0670791	+	0.576650i
$191$	−20.2083			−1.46222			−0.731112	−	0.682258i	$-0.760998\pi$
$191$	−20.2083			−1.46222			−0.731112	+	0.682258i	$0.760998\pi$
$192$		0			0
$193$	13.7482	−	5.00392i	0.989614	−	0.360190i	0.204043	−	0.978962i	$-0.434592\pi$
$193$	13.7482	−	5.00392i	0.989614	−	0.360190i	0.785571	+	0.618772i	$0.212369\pi$
$194$	3.01961	+	17.1251i	0.216796	+	1.22951i
$195$		0			0
$196$	5.89740	+	2.14648i	0.421243	+	0.153320i
$197$	−9.47773	−	16.4159i	−0.675261	−	1.16959i	−0.976393	−	0.216003i	$-0.930698\pi$
$197$	−9.47773	−	16.4159i	−0.675261	−	1.16959i	0.301132	−	0.953582i	$-0.402636\pi$
$198$		0			0
$199$	6.03692	−	5.06557i	0.427946	−	0.359089i	−0.403230	−	0.915099i	$-0.632113\pi$
$199$	6.03692	−	5.06557i	0.427946	−	0.359089i	0.831176	+	0.556010i	$0.187668\pi$
$200$	−1.24847	+	1.04759i	−0.0882798	+	0.0740756i
$201$		0			0
$202$	3.00745	+	5.20906i	0.211604	+	0.366508i
$203$	−1.80075	−	0.655419i	−0.126388	−	0.0460014i
$204$		0			0
$205$	2.00062	+	11.3461i	0.139730	+	0.792446i
$206$	0.155522	−	0.0566054i	0.0108357	−	0.00394389i
$207$		0			0
$208$	−0.493780			−0.0342375
$209$	6.43662	+	12.8340i	0.445230	+	0.887744i
$210$		0			0
$211$	0.535882	+	0.449659i	0.0368917	+	0.0309558i	0.661047	−	0.750344i	$-0.270112\pi$
$211$	0.535882	+	0.449659i	0.0368917	+	0.0309558i	−0.624155	+	0.781300i	$0.714557\pi$
$212$	12.5044	−	4.55121i	0.858802	−	0.312579i
$213$		0			0
$214$	2.23020	−	12.6481i	0.152453	−	0.864606i
$215$	4.11718	+	1.49853i	0.280789	+	0.102199i
$216$		0			0
$217$	2.90095	−	5.02459i	0.196929	−	0.341091i
$218$	−6.79634	+	5.70281i	−0.460306	+	0.386243i
$219$		0			0
$220$	3.02347	−	5.23680i	0.203842	−	0.353065i
$221$	0.342092	+	0.592521i	0.0230116	+	0.0398573i
$222$		0			0
$223$	−2.62922	+	14.9110i	−0.176066	+	0.998517i	0.760841	+	0.648938i	$0.224787\pi$
$223$	−2.62922	+	14.9110i	−0.176066	+	0.998517i	−0.936907	+	0.349579i	$0.886325\pi$
$224$	−0.147766	−	0.838024i	−0.00987304	−	0.0559928i
$225$		0			0
$226$	9.48590	+	7.95962i	0.630993	+	0.529466i
$227$	17.0328			1.13051			0.565253	−	0.824917i	$-0.308778\pi$
$227$	17.0328			1.13051			0.565253	+	0.824917i	$0.308778\pi$
$228$		0			0
$229$	12.9202			0.853790			0.426895	−	0.904301i	$-0.359607\pi$
$229$	12.9202			0.853790			0.426895	+	0.904301i	$0.359607\pi$
$230$	−5.11560	−	4.29250i	−0.337313	−	0.283039i
$231$		0			0
$232$	−0.391050	−	2.21776i	−0.0256737	−	0.145603i
$233$	4.52454	−	25.6599i	0.296412	−	1.68104i	−0.364994	−	0.931010i	$-0.618929\pi$
$233$	4.52454	−	25.6599i	0.296412	−	1.68104i	0.661406	−	0.750028i	$-0.269960\pi$
$234$		0			0
$235$	1.43203	+	2.48034i	0.0934151	+	0.161800i
$236$	−1.32499	+	2.29496i	−0.0862498	+	0.149389i
$237$		0			0
$238$	−0.903230	+	0.757900i	−0.0585477	+	0.0491273i
$239$	−13.0578	+	22.6168i	−0.844641	+	1.46296i	0.0412918	+	0.999147i	$0.486853\pi$
$239$	−13.0578	+	22.6168i	−0.844641	+	1.46296i	−0.885933	+	0.463814i	$0.846481\pi$
$240$		0			0
$241$	−4.62593	−	1.68370i	−0.297983	−	0.108457i	0.188702	−	0.982034i	$-0.439572\pi$
$241$	−4.62593	−	1.68370i	−0.297983	−	0.108457i	−0.486685	+	0.873578i	$0.661794\pi$
$242$	−0.0261332	+	0.148208i	−0.00167990	+	0.00952720i
$243$		0			0
$244$	−8.43820	+	3.07125i	−0.540200	+	0.196617i
$245$	8.82591	+	7.40582i	0.563867	+	0.473140i
$246$		0			0
$247$	1.72715	−	1.28434i	0.109896	−	0.0817205i
$248$	6.81813			0.432952
$249$		0			0
$250$	−11.4371	+	4.16275i	−0.723343	+	0.263275i
$251$	−1.19432	−	6.77335i	−0.0753851	−	0.427530i	−0.999020	−	0.0442569i	$-0.985908\pi$
$251$	−1.19432	−	6.77335i	−0.0753851	−	0.427530i	0.923635	−	0.383273i	$-0.125203\pi$
$252$		0			0
$253$	−11.2591	−	4.09797i	−0.707852	−	0.257637i
$254$	−5.89013	−	10.2020i	−0.369579	−	0.640130i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−1.41720	+	1.18917i	−0.0884024	+	0.0741784i	−0.685918	−	0.727679i	$-0.740599\pi$
$257$	−1.41720	+	1.18917i	−0.0884024	+	0.0741784i	0.597515	+	0.801857i	$0.296155\pi$
$258$		0			0
$259$	2.00915	+	3.47996i	0.124843	+	0.216234i
$260$	−0.851825	−	0.310039i	−0.0528279	−	0.0192278i
$261$		0			0
$262$	3.26443	+	18.5135i	0.201677	+	1.14377i
$263$	8.72514	−	3.17569i	0.538015	−	0.195821i	−0.0586985	−	0.998276i	$-0.518695\pi$
$263$	8.72514	−	3.17569i	0.538015	−	0.195821i	0.596714	+	0.802454i	$0.296473\pi$
$264$		0			0
$265$	24.4290			1.50066
$266$	2.69658	+	2.54690i	0.165338	+	0.156160i
$267$		0			0
$268$	−6.56239	−	5.50650i	−0.400862	−	0.336363i
$269$	20.5799	−	7.49047i	1.25478	−	0.456702i	0.372764	−	0.927926i	$-0.378410\pi$
$269$	20.5799	−	7.49047i	1.25478	−	0.456702i	0.882013	+	0.471224i	$0.156188\pi$
$270$		0			0
$271$	0.958450	−	5.43564i	0.0582217	−	0.330192i	−0.941760	−	0.336286i	$-0.890829\pi$
$271$	0.958450	−	5.43564i	0.0582217	−	0.330192i	0.999981	+	0.00609486i	$0.00194007\pi$
$272$	−1.30204	−	0.473905i	−0.0789479	−	0.0287347i
$273$		0			0
$274$	−6.76560	+	11.7184i	−0.408725	+	0.707932i
$275$	−4.11227	+	3.45060i	−0.247979	+	0.208079i
$276$		0			0
$277$	−16.2448	+	28.1368i	−0.976056	+	1.69058i	−0.299651	+	0.954049i	$0.596870\pi$
$277$	−16.2448	+	28.1368i	−0.976056	+	1.69058i	−0.676405	+	0.736530i	$0.736463\pi$
$278$	−9.47226	−	16.4064i	−0.568109	−	0.983993i
$279$		0			0
$280$	0.271273	−	1.53846i	0.0162116	−	0.0919407i
$281$	−4.79977	−	27.2209i	−0.286331	−	1.62386i	−0.700494	−	0.713659i	$-0.747037\pi$
$281$	−4.79977	−	27.2209i	−0.286331	−	1.62386i	0.414163	−	0.910203i	$-0.364074\pi$
$282$		0			0
$283$	−8.57314	−	7.19372i	−0.509620	−	0.427622i	0.351375	−	0.936235i	$-0.385714\pi$
$283$	−8.57314	−	7.19372i	−0.509620	−	0.427622i	−0.860995	+	0.508613i	$0.830159\pi$
$284$	10.8048			0.641148
$285$		0			0
$286$	−1.62644			−0.0961736
$287$	4.09094	+	3.43271i	0.241481	+	0.202626i
$288$		0			0
$289$	−2.61863	−	14.8510i	−0.154037	−	0.873588i
$290$	0.717899	−	4.07141i	0.0421565	−	0.239081i
$291$		0			0
$292$	2.04883	+	3.54868i	0.119899	+	0.207671i
$293$	6.30300	−	10.9171i	0.368225	−	0.637785i	−0.621063	−	0.783761i	$-0.713299\pi$
$293$	6.30300	−	10.9171i	0.368225	−	0.637785i	0.989288	+	0.145976i	$0.0466322\pi$
$294$		0			0
$295$	−3.72674	+	3.12710i	−0.216979	+	0.182067i
$296$	−2.36107	+	4.08949i	−0.137234	+	0.237697i
$297$		0			0
$298$	−14.2772	−	5.19648i	−0.827057	−	0.301024i
$299$	−0.311900	+	1.76888i	−0.0180377	+	0.102297i
$300$		0			0
$301$	1.90842	−	0.694608i	0.110000	−	0.0400366i
$302$	−2.84086	−	2.38377i	−0.163473	−	0.137170i
$303$		0			0
$304$	−1.00756	+	4.24085i	−0.0577878	+	0.243229i
$305$	−16.4852			−0.943941
$306$		0			0
$307$	27.9464	−	10.1716i	1.59498	−	0.580527i	0.616591	−	0.787283i	$-0.288513\pi$
$307$	27.9464	−	10.1716i	1.59498	−	0.580527i	0.978392	+	0.206757i	$0.0662908\pi$
$308$	−0.486721	−	2.76033i	−0.0277335	−	0.157285i
$309$		0			0
$310$	11.7620	+	4.28102i	0.668038	+	0.243146i
$311$	−11.7886	−	20.4185i	−0.668470	−	1.15782i	−0.978332	−	0.207043i	$-0.933616\pi$
$311$	−11.7886	−	20.4185i	−0.668470	−	1.15782i	0.309862	−	0.950782i	$-0.399717\pi$
$312$		0			0
$313$	17.4587	−	14.6496i	0.986824	−	0.828044i	0.00171930	−	0.999999i	$-0.499453\pi$
$313$	17.4587	−	14.6496i	0.986824	−	0.828044i	0.985105	+	0.171955i	$0.0550083\pi$
$314$	−12.0719	+	10.1295i	−0.681257	+	0.571642i
$315$		0			0
$316$	0.255661	+	0.442819i	0.0143821	+	0.0249105i
$317$	−11.9824	−	4.36122i	−0.672996	−	0.244951i	−0.0171588	−	0.999853i	$-0.505462\pi$
$317$	−11.9824	−	4.36122i	−0.672996	−	0.244951i	−0.655837	+	0.754902i	$0.727684\pi$
$318$		0			0
$319$	−1.28806	−	7.30498i	−0.0721178	−	0.409000i
$320$	1.72511	−	0.627888i	0.0964365	−	0.0351000i
$321$		0			0
$322$	−3.09540			−0.172500
$323$	5.78693	−	1.72903i	0.321994	−	0.0962055i
$324$		0			0
$325$	0.616468	+	0.517278i	0.0341955	+	0.0286934i
$326$	7.88841	−	2.87115i	0.436899	−	0.159018i
$327$		0			0
$328$	−1.08977	+	6.18039i	−0.0601724	+	0.341255i
$329$	1.24750	+	0.454053i	0.0687770	+	0.0250328i
$330$		0			0
$331$	1.58384	−	2.74329i	0.0870558	−	0.150785i	−0.819210	−	0.573494i	$-0.805587\pi$
$331$	1.58384	−	2.74329i	0.0870558	−	0.150785i	0.906265	+	0.422709i	$0.138921\pi$
$332$	10.1520	−	8.51858i	0.557166	−	0.467518i
$333$		0			0
$334$	1.92018	−	3.32585i	0.105068	−	0.181982i
$335$	−7.86337	−	13.6198i	−0.429622	−	0.744127i
$336$		0			0
$337$	1.71555	−	9.72937i	0.0934520	−	0.529992i	−0.901759	−	0.432240i	$-0.857723\pi$
$337$	1.71555	−	9.72937i	0.0934520	−	0.529992i	0.995211	−	0.0977528i	$-0.0311654\pi$
$338$	−2.21509	−	12.5624i	−0.120485	−	0.683304i
$339$		0			0
$340$	−1.94861	−	1.63507i	−0.105678	−	0.0886744i
$341$	22.4580			1.21617
$342$		0			0
$343$	11.2971			0.609988
$344$	1.82826	+	1.53409i	0.0985731	+	0.0827126i
$345$		0			0
$346$	0.840952	+	4.76928i	0.0452099	+	0.256398i
$347$	2.51433	−	14.2595i	0.134976	−	0.765488i	−0.839900	−	0.542741i	$-0.817387\pi$
$347$	2.51433	−	14.2595i	0.134976	−	0.765488i	0.974876	−	0.222747i	$-0.0715023\pi$
$348$		0			0
$349$	−1.80380	−	3.12427i	−0.0965552	−	0.167239i	0.813701	−	0.581283i	$-0.197449\pi$
$349$	−1.80380	−	3.12427i	−0.0965552	−	0.167239i	−0.910257	+	0.414045i	$0.864116\pi$
$350$	−0.693422	+	1.20104i	−0.0370650	+	0.0641984i
$351$		0			0
$352$	2.52324	−	2.11725i	0.134489	−	0.112850i
$353$	−2.01297	+	3.48657i	−0.107140	+	0.185572i	−0.914610	−	0.404336i	$-0.867503\pi$
$353$	−2.01297	+	3.48657i	−0.107140	+	0.185572i	0.807471	+	0.589908i	$0.200836\pi$
$354$		0			0
$355$	18.6395	+	6.78422i	0.989282	+	0.360069i
$356$	1.34887	−	7.64983i	0.0714900	−	0.405440i
$357$		0			0
$358$	−23.0949	+	8.40587i	−1.22061	+	0.444264i
$359$	−3.79911	−	3.18783i	−0.200509	−	0.168247i	0.537004	−	0.843579i	$-0.319556\pi$
$359$	−3.79911	−	3.18783i	−0.200509	−	0.168247i	−0.737514	+	0.675332i	$0.764000\pi$
$360$		0			0
$361$	−7.50631	−	17.4544i	−0.395069	−	0.918651i
$362$	−12.1200			−0.637011
$363$		0			0
$364$	−0.394843	+	0.143711i	−0.0206954	+	0.00753251i
$365$	1.30628	+	7.40830i	0.0683740	+	0.387768i
$366$		0			0
$367$	−23.3202	−	8.48786i	−1.21730	−	0.443063i	−0.348073	−	0.937468i	$-0.613164\pi$
$367$	−23.3202	−	8.48786i	−1.21730	−	0.443063i	−0.869232	+	0.494405i	$0.835386\pi$
$368$	−1.81879	−	3.15023i	−0.0948108	−	0.164217i
$369$		0			0
$370$	−6.64084	+	5.57233i	−0.345241	+	0.289692i
$371$	8.67430	−	7.27860i	0.450347	−	0.377886i
$372$		0			0
$373$	0.271862	+	0.470879i	0.0140765	+	0.0243812i	0.872978	−	0.487760i	$-0.162186\pi$
$373$	0.271862	+	0.470879i	0.0140765	+	0.0243812i	−0.858901	+	0.512141i	$0.828852\pi$
$374$	−4.28874	−	1.56098i	−0.221766	−	0.0807161i
$375$		0			0
$376$	0.270907	+	1.53639i	0.0139710	+	0.0792333i
$377$	−1.04492	+	0.380319i	−0.0538160	+	0.0195874i
$378$		0			0
$379$	−2.73521			−0.140498			−0.0702492	−	0.997529i	$-0.522379\pi$
$379$	−2.73521			−0.140498			−0.0702492	+	0.997529i	$0.522379\pi$
$380$	−4.40094	+	6.68329i	−0.225763	+	0.342846i
$381$		0			0
$382$	−15.4805	−	12.9897i	−0.792050	−	0.664609i
$383$	32.1559	−	11.7038i	1.64309	−	0.598036i	0.655515	−	0.755182i	$-0.272452\pi$
$383$	32.1559	−	11.7038i	1.64309	−	0.598036i	0.987575	+	0.157146i	$0.0502294\pi$
$384$		0			0
$385$	0.893533	−	5.06748i	0.0455387	−	0.258263i
$386$	13.7482	+	5.00392i	0.699763	+	0.254693i
$387$		0			0
$388$	−8.69463	+	15.0595i	−0.441403	+	0.764532i
$389$	−15.8300	+	13.2829i	−0.802610	+	0.673470i	−0.948832	−	0.315782i	$-0.897733\pi$
$389$	−15.8300	+	13.2829i	−0.802610	+	0.673470i	0.146221	+	0.989252i	$0.453289\pi$
$390$		0			0
$391$	−2.52012	+	4.36498i	−0.127448	+	0.220746i
$392$	3.13794	+	5.43507i	0.158490	+	0.274513i
$393$		0			0
$394$	3.29158	−	18.6675i	0.165828	−	0.940455i
$395$	0.163003	+	0.924437i	0.00820158	+	0.0465135i
$396$		0			0
$397$	−3.02469	−	2.53802i	−0.151805	−	0.127379i	0.563722	−	0.825965i	$-0.309369\pi$
$397$	−3.02469	−	2.53802i	−0.151805	−	0.127379i	−0.715527	+	0.698585i	$0.753813\pi$
$398$	7.88063			0.395020
$399$		0			0
$400$	−1.62976			−0.0814878
$401$	−14.7172	−	12.3492i	−0.734944	−	0.616692i	0.196530	−	0.980498i	$-0.437033\pi$
$401$	−14.7172	−	12.3492i	−0.734944	−	0.616692i	−0.931475	+	0.363806i	$0.881477\pi$
$402$		0			0
$403$	−0.584614	−	3.31551i	−0.0291217	−	0.165157i
$404$	−1.04448	+	5.92353i	−0.0519647	+	0.294706i
$405$		0			0
$406$	−0.958159	−	1.65958i	−0.0475526	−	0.0823635i
$407$	−7.77702	+	13.4702i	−0.385493	+	0.667693i
$408$		0			0
$409$	−1.83816	+	1.54240i	−0.0908909	+	0.0762665i	−0.687101	−	0.726562i	$-0.741117\pi$
$409$	−1.83816	+	1.54240i	−0.0908909	+	0.0762665i	0.596210	+	0.802829i	$0.296673\pi$
$410$	−5.76056	+	9.97759i	−0.284494	+	0.492758i
$411$		0			0
$412$	0.155522	+	0.0566054i	0.00766202	+	0.00278875i
$413$	−0.391579	+	2.22075i	−0.0192683	+	0.109276i
$414$		0			0
$415$	22.8621	−	8.32112i	1.12226	−	0.408468i
$416$	−0.378258	−	0.317396i	−0.0185456	−	0.0155616i
$417$		0			0
$418$	−3.31878	+	13.9688i	−0.162327	+	0.683235i
$419$	−29.0694			−1.42013			−0.710066	−	0.704135i	$-0.751335\pi$
$419$	−29.0694			−1.42013			−0.710066	+	0.704135i	$0.751335\pi$
$420$		0			0
$421$	−20.0777	+	7.30770i	−0.978529	+	0.356156i	−0.781268	−	0.624195i	$-0.785427\pi$
$421$	−20.0777	+	7.30770i	−0.978529	+	0.356156i	−0.197261	+	0.980351i	$0.563205\pi$
$422$	0.121475	+	0.688917i	0.00591330	+	0.0335360i
$423$		0			0
$424$	12.5044	+	4.55121i	0.607265	+	0.221026i
$425$	1.12910	+	1.95566i	0.0547693	+	0.0948633i
$426$		0			0
$427$	−5.85360	+	4.91175i	−0.283275	+	0.237696i
$428$	9.83847	−	8.25546i	0.475561	−	0.399043i
$429$		0			0
$430$	2.19071	+	3.79441i	0.105645	+	0.182983i
$431$	19.1193	+	6.95886i	0.920944	+	0.335196i	0.758614	−	0.651540i	$-0.225877\pi$
$431$	19.1193	+	6.95886i	0.920944	+	0.335196i	0.162330	+	0.986737i	$0.448099\pi$
$432$		0			0
$433$	−6.03917	−	34.2499i	−0.290224	−	1.64594i	−0.686004	−	0.727598i	$-0.740637\pi$
$433$	−6.03917	−	34.2499i	−0.290224	−	1.64594i	0.395780	−	0.918345i	$-0.370474\pi$
$434$	5.45200	−	1.98437i	0.261704	−	0.0952526i
$435$		0			0
$436$	−8.87200			−0.424892
$437$	14.5556	+	6.28818i	0.696289	+	0.300804i
$438$		0			0
$439$	16.4994	+	13.8446i	0.787473	+	0.660769i	0.945119	−	0.326727i	$-0.105946\pi$
$439$	16.4994	+	13.8446i	0.787473	+	0.660769i	−0.157645	+	0.987496i	$0.550390\pi$
$440$	5.68226	−	2.06818i	0.270891	−	0.0985964i
$441$		0			0
$442$	−0.118807	+	0.673790i	−0.00565109	+	0.0320489i
$443$	−14.2595	−	5.19003i	−0.677489	−	0.246586i	−0.0197202	−	0.999806i	$-0.506278\pi$
$443$	−14.2595	−	5.19003i	−0.677489	−	0.246586i	−0.657769	+	0.753220i	$0.728500\pi$
$444$		0			0
$445$	7.13018	−	12.3498i	0.338003	−	0.585439i
$446$	−11.5987	+	9.73249i	−0.549216	+	0.460847i
$447$		0			0
$448$	0.425476	−	0.736946i	0.0201018	−	0.0348174i
$449$	8.26581	+	14.3168i	0.390088	+	0.675652i	0.992461	−	0.122563i	$-0.0391114\pi$
$449$	8.26581	+	14.3168i	0.390088	+	0.675652i	−0.602373	+	0.798215i	$0.705778\pi$
$450$		0			0
$451$	−3.58955	+	20.3573i	−0.169025	+	0.958589i
$452$	2.15028	+	12.1948i	0.101141	+	0.573597i
$453$		0			0
$454$	13.0479	+	10.9485i	0.612367	+	0.513837i
$455$	−0.771382			−0.0361629
$456$		0			0
$457$	0.605508			0.0283245			0.0141622	−	0.999900i	$-0.495492\pi$
$457$	0.605508			0.0283245			0.0141622	+	0.999900i	$0.495492\pi$
$458$	9.89744	+	8.30493i	0.462477	+	0.388064i
$459$		0			0
$460$	−1.15961	−	6.57649i	−0.0540672	−	0.306630i
$461$	2.48270	−	14.0801i	0.115631	−	0.655775i	−0.870805	−	0.491628i	$-0.836402\pi$
$461$	2.48270	−	14.0801i	0.115631	−	0.655775i	0.986436	−	0.164147i	$-0.0524871\pi$
$462$		0			0
$463$	5.36374	+	9.29026i	0.249274	+	0.431755i	0.963325	−	0.268339i	$-0.0864747\pi$
$463$	5.36374	+	9.29026i	0.249274	+	0.431755i	−0.714051	+	0.700094i	$0.753141\pi$
$464$	1.12598	−	1.95026i	0.0522725	−	0.0905387i
$465$		0			0
$466$	19.9599	−	16.7483i	0.924623	−	0.775851i
$467$	−9.33085	+	16.1615i	−0.431780	+	0.747865i	−0.997027	−	0.0770567i	$-0.975448\pi$
$467$	−9.33085	+	16.1615i	−0.431780	+	0.747865i	0.565246	+	0.824922i	$0.308781\pi$
$468$		0			0
$469$	−6.85013	−	2.49324i	−0.316310	−	0.115127i
$470$	−0.497337	+	2.82054i	−0.0229405	+	0.130102i
$471$		0			0
$472$	−2.49017	+	0.906349i	−0.114620	+	0.0417181i
$473$	6.02202	+	5.05308i	0.276893	+	0.232341i
$474$		0			0
$475$	5.70057	−	4.23904i	0.261560	−	0.194501i
$476$	−1.17908			−0.0540432
$477$		0			0
$478$	−24.5407	+	8.93208i	−1.12247	+	0.408544i
$479$	5.76837	+	32.7140i	0.263563	+	1.49474i	0.773095	+	0.634290i	$0.218708\pi$
$479$	5.76837	+	32.7140i	0.263563	+	1.49474i	−0.509532	+	0.860452i	$0.670181\pi$
$480$		0			0
$481$	2.19108	+	0.797488i	0.0999046	+	0.0363623i
$482$	−2.46141	−	4.26328i	−0.112114	−	0.194187i
$483$		0			0
$484$	−0.115286	+	0.0967362i	−0.00524026	+	0.00439710i
$485$	−24.4549	+	20.5201i	−1.11044	+	0.931769i
$486$		0			0
$487$	15.3045	+	26.5081i	0.693511	+	1.20120i	0.970680	+	0.240375i	$0.0772704\pi$
$487$	15.3045	+	26.5081i	0.693511	+	1.20120i	−0.277169	+	0.960821i	$0.589396\pi$
$488$	−8.43820	−	3.07125i	−0.381979	−	0.139029i
$489$		0			0
$490$	2.00067	+	11.3464i	0.0903811	+	0.512577i
$491$	−3.92851	+	1.42986i	−0.177291	+	0.0645287i	−0.429141	−	0.903238i	$-0.641183\pi$
$491$	−3.92851	+	1.42986i	−0.177291	+	0.0645287i	0.251849	+	0.967766i	$0.418961\pi$
$492$		0			0
$493$	−3.12034			−0.140533
$494$	2.14863	+	0.126330i	0.0966714	+	0.00568383i
$495$		0			0
$496$	5.22299	+	4.38261i	0.234519	+	0.196785i
$497$	8.63989	−	3.14466i	0.387552	−	0.141057i
$498$		0			0
$499$	−2.25750	+	12.8029i	−0.101060	+	0.573138i	0.891661	+	0.452703i	$0.149540\pi$
$499$	−2.25750	+	12.8029i	−0.101060	+	0.573138i	−0.992721	+	0.120435i	$0.961571\pi$
$500$	−11.4371	−	4.16275i	−0.511480	−	0.186164i
$501$		0			0
$502$	3.43892	−	5.95638i	0.153486	−	0.265846i
$503$	8.29245	−	6.95819i	0.369742	−	0.310250i	−0.438917	−	0.898527i	$-0.644638\pi$
$503$	8.29245	−	6.95819i	0.369742	−	0.310250i	0.808660	+	0.588277i	$0.200193\pi$
$504$		0			0
$505$	−5.52115	+	9.56291i	−0.245688	+	0.425544i
$506$	−5.99083	−	10.3764i	−0.266325	−	0.461288i
$507$		0			0
$508$	2.04562	−	11.6013i	0.0907597	−	0.514724i
$509$	2.08167	+	11.8057i	0.0922684	+	0.523280i	0.995550	+	0.0942324i	$0.0300397\pi$
$509$	2.08167	+	11.8057i	0.0922684	+	0.523280i	−0.903282	+	0.429048i	$0.858849\pi$
$510$		0			0
$511$	2.67113	+	2.24135i	0.118164	+	0.0991513i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−1.85002			−0.0816009
$515$	0.232751	+	0.195301i	0.0102562	+	0.00860599i
$516$		0			0
$517$	0.892330	+	5.06065i	0.0392446	+	0.222567i
$518$	−0.697772	+	3.95726i	−0.0306583	+	0.173872i
$519$		0			0
$520$	−0.453247	−	0.785046i	−0.0198762	−	0.0344266i
$521$	−19.7922	+	34.2811i	−0.867112	+	1.50188i	−0.00217681	+	0.999998i	$0.500693\pi$
$521$	−19.7922	+	34.2811i	−0.867112	+	1.50188i	−0.864935	+	0.501884i	$0.832640\pi$
$522$		0			0
$523$	10.4462	−	8.76542i	0.456781	−	0.383285i	−0.385164	−	0.922848i	$-0.625855\pi$
$523$	10.4462	−	8.76542i	0.456781	−	0.383285i	0.841945	+	0.539563i	$0.181411\pi$
$524$	−9.39955	+	16.2805i	−0.410621	+	0.711217i
$525$		0			0
$526$	8.72514	+	3.17569i	0.380434	+	0.138467i
$527$	1.64049	−	9.30371i	0.0714611	−	0.405276i
$528$		0			0
$529$	9.17897	−	3.34087i	0.399085	−	0.145255i
$530$	18.7137	+	15.7027i	0.812872	+	0.682080i
$531$		0			0
$532$	0.428586	+	3.68437i	0.0185816	+	0.159738i
$533$	3.09883			0.134225
$534$		0			0
$535$	22.1559	−	8.06410i	0.957885	−	0.348642i
$536$	−1.48757	−	8.43644i	−0.0642534	−	0.364399i
$537$		0			0
$538$	20.5799	+	7.49047i	0.887262	+	0.322937i
$539$	10.3359	+	17.9024i	0.445200	+	0.771109i
$540$		0			0
$541$	−33.6562	+	28.2409i	−1.44699	+	1.21417i	−0.512257	+	0.858832i	$0.671190\pi$
$541$	−33.6562	+	28.2409i	−1.44699	+	1.21417i	−0.934737	+	0.355340i	$0.884365\pi$
$542$	4.22818	−	3.54786i	0.181616	−	0.152394i
$543$		0			0
$544$	−0.692802	−	1.19997i	−0.0297037	−	0.0514482i
$545$	−15.3052	−	5.57062i	−0.655601	−	0.238619i
$546$		0			0
$547$	−0.972903	−	5.51761i	−0.0415983	−	0.235916i	0.956919	−	0.290356i	$-0.0937737\pi$
$547$	−0.972903	−	5.51761i	−0.0415983	−	0.235916i	−0.998517	+	0.0544401i	$0.982663\pi$
$548$	−12.7152	+	4.62794i	−0.543165	+	0.197696i
$549$		0			0
$550$	−5.36819			−0.228900
$551$	1.13422	+	9.75036i	0.0483192	+	0.415379i
$552$		0			0
$553$	0.333314	+	0.279684i	0.0141740	+	0.0118934i
$554$	−30.5303	+	11.1121i	−1.29711	+	0.472108i
$555$		0			0
$556$	3.28968	−	18.6567i	0.139514	−	0.791221i
$557$	35.2279	+	12.8219i	1.49266	+	0.543282i	0.954147	−	0.299338i	$-0.0967659\pi$
$557$	35.2279	+	12.8219i	1.49266	+	0.543282i	0.538508	+	0.842620i	$0.318988\pi$
$558$		0			0
$559$	0.589233	−	1.02058i	0.0249219	−	0.0431660i
$560$	1.19671	−	1.00416i	0.0505703	−	0.0424335i
$561$		0			0
$562$	13.8204	−	23.9376i	0.582978	−	1.00975i
$563$	−0.786588	−	1.36241i	−0.0331507	−	0.0574188i	0.848974	−	0.528435i	$-0.177221\pi$
$563$	−0.786588	−	1.36241i	−0.0331507	−	0.0574188i	−0.882125	+	0.471016i	$0.843887\pi$
$564$		0			0
$565$	−3.94753	+	22.3876i	−0.166074	+	0.941852i
$566$	−1.94337	−	11.0214i	−0.0816860	−	0.463265i
$567$		0			0
$568$	8.27698	+	6.94521i	0.347294	+	0.291414i
$569$	−23.7454			−0.995457			−0.497729	−	0.867333i	$-0.665832\pi$
$569$	−23.7454			−0.995457			−0.497729	+	0.867333i	$0.665832\pi$
$570$		0			0
$571$	−17.0880			−0.715110			−0.357555	−	0.933892i	$-0.616389\pi$
$571$	−17.0880			−0.715110			−0.357555	+	0.933892i	$0.616389\pi$
$572$	−1.24593	−	1.04546i	−0.0520948	−	0.0437128i
$573$		0			0
$574$	0.927341	+	5.25921i	0.0387065	+	0.219515i
$575$	−1.02945	+	5.83829i	−0.0429310	+	0.243474i
$576$		0			0
$577$	−9.02192	−	15.6264i	−0.375587	−	0.650537i	0.614827	−	0.788662i	$-0.289226\pi$
$577$	−9.02192	−	15.6264i	−0.375587	−	0.650537i	−0.990415	+	0.138125i	$0.955892\pi$
$578$	7.54005	−	13.0597i	0.313625	−	0.543214i
$579$		0			0
$580$	3.16699	−	2.65742i	0.131502	−	0.110343i
$581$	5.63864	−	9.76641i	0.233930	−	0.405179i
$582$		0			0
$583$	41.1876	+	14.9910i	1.70581	+	0.620866i
$584$	−0.711552	+	4.03541i	−0.0294442	+	0.166987i
$585$		0			0
$586$	11.8458	−	4.31151i	0.489344	−	0.178107i
$587$	1.20843	+	1.01399i	0.0498771	+	0.0418519i	0.667385	−	0.744712i	$-0.267413\pi$
$587$	1.20843	+	1.01399i	0.0498771	+	0.0418519i	−0.617508	+	0.786564i	$0.711858\pi$
$588$		0			0
$589$	−29.6683	−	1.74436i	−1.22246	−	0.0718751i
$590$	−4.86491			−0.200285
$591$		0			0
$592$	−4.43736	+	1.61507i	−0.182374	+	0.0663788i
$593$	−0.401996	−	2.27983i	−0.0165080	−	0.0936215i	0.975441	−	0.220263i	$-0.0706914\pi$
$593$	−0.401996	−	2.27983i	−0.0165080	−	0.0936215i	−0.991949	+	0.126641i	$0.959580\pi$
$594$		0			0
$595$	−2.03405	−	0.740332i	−0.0833878	−	0.0303507i
$596$	−7.59675	−	13.1580i	−0.311175	−	0.538971i
$597$		0			0
$598$	−1.37594	+	1.15455i	−0.0562664	+	0.0472131i
$599$	3.53882	−	2.96942i	0.144592	−	0.121327i	−0.567623	−	0.823289i	$-0.692137\pi$
$599$	3.53882	−	2.96942i	0.144592	−	0.121327i	0.712215	+	0.701962i	$0.247692\pi$
$600$		0			0
$601$	−18.6076	−	32.2293i	−0.759019	−	1.31466i	−0.943351	−	0.331795i	$-0.892346\pi$
$601$	−18.6076	−	32.2293i	−0.759019	−	1.31466i	0.184333	−	0.982864i	$-0.440988\pi$
$602$	1.90842	+	0.694608i	0.0777814	+	0.0283101i
$603$		0			0
$604$	−0.643971	−	3.65214i	−0.0262028	−	0.148604i
$605$	−0.259620	+	0.0944940i	−0.0105551	+	0.00384173i
$606$		0			0
$607$	−38.7882			−1.57437			−0.787183	−	0.616720i	$-0.788461\pi$
$607$	−38.7882			−1.57437			−0.787183	+	0.616720i	$0.788461\pi$
$608$	−3.49781	+	2.60103i	−0.141855	+	0.105486i
$609$		0			0
$610$	−12.6284	−	10.5965i	−0.511309	−	0.429039i
$611$	0.723886	−	0.263473i	0.0292853	−	0.0106590i
$612$		0			0
$613$	−5.74411	+	32.5765i	−0.232002	+	1.31575i	0.616833	+	0.787094i	$0.288415\pi$
$613$	−5.74411	+	32.5765i	−0.232002	+	1.31575i	−0.848835	+	0.528657i	$0.822696\pi$
$614$	27.9464	+	10.1716i	1.12782	+	0.410494i
$615$		0			0
$616$	1.40146	−	2.42740i	0.0564663	−	0.0978025i
$617$	−1.31244	+	1.10127i	−0.0528370	+	0.0443355i	−0.668824	−	0.743421i	$-0.733202\pi$
$617$	−1.31244	+	1.10127i	−0.0528370	+	0.0443355i	0.615987	+	0.787756i	$0.288757\pi$
$618$		0			0
$619$	−14.0194	+	24.2823i	−0.563486	+	0.975987i	0.433703	+	0.901056i	$0.357207\pi$
$619$	−14.0194	+	24.2823i	−0.563486	+	0.975987i	−0.997189	+	0.0749305i	$0.976126\pi$
$620$	6.25844	+	10.8399i	0.251345	+	0.435342i
$621$		0			0
$622$	4.09414	−	23.2190i	0.164160	−	0.930997i
$623$	−1.14782	−	6.50963i	−0.0459866	−	0.260803i
$624$		0			0
$625$	−10.8741	−	9.12444i	−0.434964	−	0.364978i
$626$	22.7907			0.910900
$627$		0			0
$628$	−15.7587			−0.628842
$629$	5.01224	+	4.20577i	0.199851	+	0.167695i
$630$		0			0
$631$	1.14023	+	6.46656i	0.0453918	+	0.257430i	0.999056	−	0.0434438i	$-0.0138330\pi$
$631$	1.14023	+	6.46656i	0.0453918	+	0.257430i	−0.953664	+	0.300873i	$0.902722\pi$
$632$	−0.0887903	+	0.503555i	−0.00353189	+	0.0200303i
$633$		0			0
$634$	−6.37568	−	11.0430i	−0.253211	−	0.438574i
$635$	10.8132	−	18.7291i	0.429110	−	0.743240i
$636$		0			0
$637$	2.37390	−	1.99194i	0.0940574	−	0.0789235i
$638$	3.70883	−	6.42389i	0.146834	−	0.254324i
$639$		0			0
$640$	1.72511	+	0.627888i	0.0681909	+	0.0248195i
$641$	2.08964	−	11.8509i	0.0825357	−	0.468083i	−0.915326	−	0.402715i	$-0.868067\pi$
$641$	2.08964	−	11.8509i	0.0825357	−	0.468083i	0.997861	−	0.0653683i	$-0.0208222\pi$
$642$		0			0
$643$	27.4445	−	9.98899i	1.08231	−	0.393927i	0.261541	−	0.965192i	$-0.415769\pi$
$643$	27.4445	−	9.98899i	1.08231	−	0.393927i	0.820766	+	0.571265i	$0.193547\pi$
$644$	−2.37121	−	1.98968i	−0.0934389	−	0.0784046i
$645$		0			0
$646$	5.54444	+	2.39526i	0.218143	+	0.0942402i
$647$	8.90424			0.350062			0.175031	−	0.984563i	$-0.443997\pi$
$647$	8.90424			0.350062			0.175031	+	0.984563i	$0.443997\pi$
$648$		0			0
$649$	−8.20228	+	2.98539i	−0.321968	+	0.117187i
$650$	0.139742	+	0.792516i	0.00548113	+	0.0310850i
$651$		0			0
$652$	7.88841	+	2.87115i	0.308934	+	0.112443i
$653$	−15.4522	−	26.7639i	−0.604690	−	1.04735i	−0.992100	−	0.125446i	$-0.959964\pi$
$653$	−15.4522	−	26.7639i	−0.604690	−	1.04735i	0.387410	−	0.921907i	$-0.373370\pi$
$654$		0			0
$655$	−26.4376	+	22.1838i	−1.03300	+	0.866792i
$656$	−4.80749	+	4.03396i	−0.187701	+	0.157500i
$657$		0			0
$658$	0.663782	+	1.14970i	0.0258769	+	0.0448201i
$659$	−6.91436	−	2.51662i	−0.269345	−	0.0980336i	0.203817	−	0.979009i	$-0.434665\pi$
$659$	−6.91436	−	2.51662i	−0.269345	−	0.0980336i	−0.473162	+	0.880975i	$0.656888\pi$
$660$		0			0
$661$	−6.96137	−	39.4799i	−0.270766	−	1.53559i	−0.752098	−	0.659051i	$-0.770958\pi$
$661$	−6.96137	−	39.4799i	−0.270766	−	1.53559i	0.481332	−	0.876538i	$-0.340153\pi$
$662$	2.97665	−	1.08341i	0.115691	−	0.0421080i
$663$		0			0
$664$	13.2526			0.514299
$665$	−1.57401	+	6.62504i	−0.0610376	+	0.256908i
$666$		0			0
$667$	−6.27521	−	5.26553i	−0.242977	−	0.203882i
$668$	3.60876	−	1.31348i	0.139627	−	0.0508201i
$669$		0			0
$670$	2.73092	−	15.4878i	0.105505	−	0.598346i
$671$	−27.7942	−	10.1163i	−1.07298	−	0.390534i
$672$		0			0
$673$	17.2630	−	29.9003i	0.665438	−	1.15257i	−0.313728	−	0.949513i	$-0.601578\pi$
$673$	17.2630	−	29.9003i	0.665438	−	1.15257i	0.979166	−	0.203060i	$-0.0650886\pi$
$674$	7.56810	−	6.35039i	0.291512	−	0.244608i
$675$		0			0
$676$	6.37809	−	11.0472i	0.245311	−	0.424891i
$677$	2.29275	+	3.97116i	0.0881176	+	0.152624i	0.906715	−	0.421743i	$-0.138582\pi$
$677$	2.29275	+	3.97116i	0.0881176	+	0.152624i	−0.818598	+	0.574367i	$0.805248\pi$
$678$		0			0
$679$	−2.56954	+	14.5726i	−0.0986101	+	0.559246i
$680$	−0.441713	−	2.50508i	−0.0169389	−	0.0960654i
$681$		0			0
$682$	17.2038	+	14.4357i	0.658767	+	0.552771i
$683$	1.71380			0.0655766			0.0327883	−	0.999462i	$-0.489561\pi$
$683$	1.71380			0.0655766			0.0327883	+	0.999462i	$0.489561\pi$
$684$		0			0
$685$	−24.8409			−0.949121
$686$	8.65411	+	7.26166i	0.330415	+	0.277251i
$687$		0			0
$688$	0.414432	+	2.35036i	0.0158001	+	0.0896067i
$689$	1.14098	−	6.47084i	0.0434680	−	0.246519i
$690$		0			0
$691$	19.7082	+	34.1355i	0.749734	+	1.29858i	0.947950	+	0.318419i	$0.103152\pi$
$691$	19.7082	+	34.1355i	0.749734	+	1.29858i	−0.198217	+	0.980158i	$0.563515\pi$
$692$	−2.42142	+	4.19403i	−0.0920487	+	0.159433i
$693$		0			0
$694$	11.0919	−	9.30720i	0.421042	−	0.353296i
$695$	17.3894	−	30.1193i	0.659617	−	1.14249i
$696$		0			0
$697$	8.17127	+	2.97410i	0.309509	+	0.112652i
$698$	0.626453	−	3.55279i	0.0237116	−	0.134475i
$699$		0			0
$700$	−1.30321	+	0.474328i	−0.0492566	+	0.0179279i
$701$	−9.88950	−	8.29828i	−0.373521	−	0.313422i	0.436631	−	0.899641i	$-0.356171\pi$
$701$	−9.88950	−	8.29828i	−0.373521	−	0.313422i	−0.810153	+	0.586219i	$0.800616\pi$
$702$		0			0
$703$	11.3202	−	17.1909i	0.426948	−	0.648366i
$704$	3.29386			0.124142
$705$		0			0
$706$	−3.78315	+	1.37696i	−0.142381	+	0.0518224i
$707$	0.888800	+	5.04063i	0.0334268	+	0.189573i
$708$		0			0
$709$	−4.95651	−	1.80402i	−0.186146	−	0.0677515i	0.247265	−	0.968948i	$-0.420468\pi$
$709$	−4.95651	−	1.80402i	−0.186146	−	0.0677515i	−0.433411	+	0.901196i	$0.642690\pi$
$710$	9.91787	+	17.1783i	0.372211	+	0.644688i
$711$		0			0
$712$	5.95051	−	4.99307i	0.223005	−	0.187123i
$713$	18.9990	−	15.9421i	0.711519	−	0.597035i
$714$		0			0
$715$	−1.49293	−	2.58583i	−0.0558324	−	0.0967046i
$716$	−23.0949	−	8.40587i	−0.863099	−	0.314142i
$717$		0			0
$718$	−0.861188	−	4.88404i	−0.0321393	−	0.182271i
$719$	−5.98107	+	2.17693i	−0.223056	+	0.0811858i	−0.451131	−	0.892458i	$-0.648979\pi$
$719$	−5.98107	+	2.17693i	−0.223056	+	0.0811858i	0.228075	+	0.973644i	$0.426757\pi$
$720$		0			0
$721$	0.140835			0.00524498
$722$	5.46929	−	18.1958i	0.203546	−	0.677177i
$723$		0			0
$724$	−9.28442	−	7.79056i	−0.345053	−	0.289534i
$725$	−3.44882	+	1.25527i	−0.128086	+	0.0466195i
$726$		0			0
$727$	7.47318	−	42.3825i	0.277165	−	1.57188i	−0.454835	−	0.890576i	$-0.650302\pi$
$727$	7.47318	−	42.3825i	0.277165	−	1.57188i	0.732000	−	0.681304i	$-0.238587\pi$
$728$	−0.394843	−	0.143711i	−0.0146339	−	0.00532629i
$729$		0			0
$730$	−3.76129	+	6.51475i	−0.139212	+	0.241122i
$731$	2.53324	−	2.12564i	0.0936954	−	0.0786198i
$732$		0			0
$733$	−18.2604	+	31.6280i	−0.674464	+	1.16821i	0.302161	+	0.953257i	$0.402292\pi$
$733$	−18.2604	+	31.6280i	−0.674464	+	1.16821i	−0.976625	+	0.214950i	$0.931041\pi$
$734$	−12.4084	−	21.4920i	−0.458003	−	0.793285i
$735$		0			0
$736$	0.631658	−	3.58231i	0.0232832	−	0.132046i
$737$	−4.89985	−	27.7885i	−0.180488	−	1.02360i
$738$		0			0
$739$	25.1129	+	21.0722i	0.923794	+	0.775155i	0.974693	−	0.223549i	$-0.0717642\pi$
$739$	25.1129	+	21.0722i	0.923794	+	0.775155i	−0.0508988	+	0.998704i	$0.516209\pi$
$740$	−8.66900			−0.318679
$741$		0			0
$742$	11.3235			0.415698
$743$	−29.9769	−	25.1536i	−1.09974	−	0.922795i	−0.102337	−	0.994750i	$-0.532632\pi$
$743$	−29.9769	−	25.1536i	−1.09974	−	0.922795i	−0.997408	+	0.0719543i	$0.977076\pi$
$744$		0			0
$745$	−4.84349	−	27.4688i	−0.177452	−	1.00638i
$746$	−0.0944168	+	0.535464i	−0.00345684	+	0.0196047i
$747$		0			0
$748$	−2.28199	−	3.95253i	−0.0834379	−	0.144519i
$749$	5.46448	−	9.46475i	0.199668	−	0.345835i
$750$		0			0
$751$	−19.8836	+	16.6843i	−0.725563	+	0.608819i	−0.928918	−	0.370286i	$-0.879260\pi$
$751$	−19.8836	+	16.6843i	−0.725563	+	0.608819i	0.203355	+	0.979105i	$0.434815\pi$
$752$	−0.780046	+	1.35108i	−0.0284454	+	0.0492688i
$753$		0			0
$754$	−1.04492	−	0.380319i	−0.0380537	−	0.0138504i
$755$	1.18222	−	6.70469i	0.0430253	−	0.244009i
$756$		0			0
$757$	−10.4791	+	3.81407i	−0.380869	+	0.138625i	−0.525358	−	0.850882i	$-0.676068\pi$
$757$	−10.4791	+	3.81407i	−0.380869	+	0.138625i	0.144489	+	0.989506i	$0.453846\pi$
$758$	−2.09529	−	1.75816i	−0.0761045	−	0.0638593i
$759$		0			0
$760$	−7.66725	+	2.29083i	−0.278120	+	0.0830971i
$761$	42.5374			1.54198			0.770991	−	0.636846i	$-0.219761\pi$
$761$	42.5374			1.54198			0.770991	+	0.636846i	$0.219761\pi$
$762$		0			0
$763$	−7.09434	+	2.58213i	−0.256832	+	0.0934793i
$764$	−3.50914	−	19.9013i	−0.126956	−	0.720004i
$765$		0			0
$766$	32.1559	+	11.7038i	1.16184	+	0.422875i
$767$	0.654256	+	1.13320i	0.0236238	+	0.0409177i
$768$		0			0
$769$	2.42581	−	2.03550i	0.0874771	−	0.0734020i	−0.598000	−	0.801496i	$-0.704038\pi$
$769$	2.42581	−	2.03550i	0.0874771	−	0.0734020i	0.685478	+	0.728094i	$0.259593\pi$
$770$	3.94180	−	3.30756i	0.142053	−	0.119196i
$771$		0			0
$772$	7.31524	+	12.6704i	0.263281	+	0.456017i
$773$	31.8571	+	11.5950i	1.14582	+	0.417045i	0.844012	−	0.536324i	$-0.180187\pi$
$773$	31.8571	+	11.5950i	1.14582	+	0.417045i	0.301808	+	0.953369i	$0.402410\pi$
$774$		0			0
$775$	−1.92956	−	10.9431i	−0.0693118	−	0.393087i
$776$	−16.3406	+	5.94748i	−0.586592	+	0.213502i
$777$		0			0
$778$	−20.6645			−0.740859
$779$	6.32320	−	26.6144i	0.226552	−	0.953561i
$780$		0			0
$781$	27.2632	+	22.8765i	0.975554	+	0.818587i
$782$	−4.73628	+	1.72386i	−0.169369	+	0.0616452i
$783$		0			0
$784$	−1.08980	+	6.18054i	−0.0389213	+	0.220733i
$785$	−27.1856	−	9.89473i	−0.970294	−	0.353158i
$786$		0			0
$787$	−8.26214	+	14.3104i	−0.294513	+	0.510112i	−0.974872	−	0.222768i	$-0.928491\pi$
$787$	−8.26214	+	14.3104i	−0.294513	+	0.510112i	0.680358	+	0.732880i	$0.261824\pi$
$788$	14.5207	−	12.1843i	0.517280	−	0.434049i
$789$		0			0
$790$	−0.469349	+	0.812936i	−0.0166987	+	0.0289230i
$791$	5.26865	+	9.12557i	0.187332	+	0.324468i
$792$		0			0
$793$	−0.769960	+	4.36666i	−0.0273421	+	0.155065i
$794$	−0.685642	−	3.88847i	−0.0243325	−	0.137997i
$795$		0			0
$796$	6.03692	+	5.06557i	0.213973	+	0.179544i
$797$	−44.2751			−1.56830			−0.784152	−	0.620569i	$-0.786902\pi$
$797$	−44.2751			−1.56830			−0.784152	+	0.620569i	$0.786902\pi$
$798$		0			0
$799$	2.16167			0.0764744
$800$	−1.24847	−	1.04759i	−0.0441399	−	0.0370378i
$801$		0			0
$802$	−3.33613	−	18.9201i	−0.117803	−	0.668093i
$803$	−2.34375	+	13.2921i	−0.0827093	+	0.469067i
$804$		0			0
$805$	−2.84130	−	4.92128i	−0.100143	−	0.173452i
$806$	1.68333	−	2.91561i	0.0592927	−	0.102698i
$807$		0			0
$808$	−4.60768	+	3.86631i	−0.162098	+	0.136016i
$809$	−0.439437	+	0.761127i	−0.0154498	+	0.0267598i	−0.873647	−	0.486560i	$-0.838251\pi$
$809$	−0.439437	+	0.761127i	−0.0154498	+	0.0267598i	0.858197	+	0.513320i	$0.171585\pi$
$810$		0			0
$811$	21.2662	+	7.74026i	0.746756	+	0.271797i	0.687240	−	0.726430i	$-0.258822\pi$
$811$	21.2662	+	7.74026i	0.746756	+	0.271797i	0.0595162	+	0.998227i	$0.481044\pi$
$812$	0.332765	−	1.88720i	0.0116778	−	0.0662279i
$813$		0			0
$814$	−14.6160	+	5.31980i	−0.512291	+	0.186459i
$815$	11.8056	+	9.90608i	0.413532	+	0.346995i
$816$		0			0
$817$	−7.56297	−	7.14316i	−0.264595	−	0.249908i
$818$	−2.39954			−0.0838980
$819$		0			0
$820$	−10.8263	+	3.94046i	−0.378071	+	0.137607i
$821$	−6.03179	−	34.2080i	−0.210511	−	1.19387i	−0.888528	−	0.458822i	$-0.848272\pi$
$821$	−6.03179	−	34.2080i	−0.210511	−	1.19387i	0.678017	−	0.735046i	$-0.262839\pi$
$822$		0			0
$823$	1.83830	+	0.669088i	0.0640792	+	0.0233229i	0.373861	−	0.927485i	$-0.378034\pi$
$823$	1.83830	+	0.669088i	0.0640792	+	0.0233229i	−0.309782	+	0.950808i	$0.600256\pi$
$824$	0.0827516	+	0.143330i	0.00288279	+	0.00499313i
$825$		0			0
$826$	−1.72744	+	1.44949i	−0.0601053	+	0.0504343i
$827$	5.29969	−	4.44697i	0.184288	−	0.154636i	−0.545976	−	0.837801i	$-0.683841\pi$
$827$	5.29969	−	4.44697i	0.184288	−	0.154636i	0.730265	+	0.683164i	$0.239397\pi$
$828$		0			0
$829$	−6.14317	−	10.6403i	−0.213361	−	0.369552i	0.739403	−	0.673263i	$-0.235108\pi$
$829$	−6.14317	−	10.6403i	−0.213361	−	0.369552i	−0.952764	+	0.303711i	$0.901774\pi$
$830$	22.8621	+	8.32112i	0.793555	+	0.288830i
$831$		0			0
$832$	−0.0857441	−	0.486279i	−0.00297264	−	0.0168587i
$833$	8.17146	−	2.97417i	0.283124	−	0.103049i
$834$		0			0
$835$	7.05022			0.243983
$836$	−11.5213	+	8.56743i	−0.398472	+	0.296311i
$837$		0			0
$838$	−22.2684	−	18.6854i	−0.769251	−	0.645478i
$839$	−14.5631	+	5.30052i	−0.502772	+	0.182994i	−0.580941	−	0.813946i	$-0.697315\pi$
$839$	−14.5631	+	5.30052i	−0.502772	+	0.182994i	0.0781681	+	0.996940i	$0.475093\pi$
$840$		0			0
$841$	−4.15516	+	23.5651i	−0.143281	+	0.812590i
$842$	−20.0777	−	7.30770i	−0.691925	−	0.251840i
$843$		0			0
$844$	−0.349772	+	0.605824i	−0.0120397	+	0.0208533i
$845$	17.9393	−	15.0529i	0.617130	−	0.517834i
$846$		0			0
$847$	−0.0640319	+	0.110907i	−0.00220016	+	0.00381079i
$848$	6.65343	+	11.5241i	0.228480	+	0.395738i
$849$		0			0
$850$	−0.392132	+	2.22389i	−0.0134500	+	0.0762788i
$851$	2.98278	+	16.9162i	0.102248	+	0.579879i
$852$		0			0
$853$	16.9049	+	14.1849i	0.578813	+	0.485682i	0.884557	−	0.466432i	$-0.154461\pi$
$853$	16.9049	+	14.1849i	0.578813	+	0.485682i	−0.305744	+	0.952114i	$0.598905\pi$
$854$	−7.64133			−0.261481
$855$		0			0
$856$	12.8432			0.438972
$857$	20.8911	+	17.5297i	0.713627	+	0.598804i	0.925614	−	0.378468i	$-0.123549\pi$
$857$	20.8911	+	17.5297i	0.713627	+	0.598804i	−0.211987	+	0.977272i	$0.567994\pi$
$858$		0			0
$859$	4.37678	+	24.8219i	0.149334	+	0.846914i	0.963785	+	0.266682i	$0.0859272\pi$
$859$	4.37678	+	24.8219i	0.149334	+	0.846914i	−0.814451	+	0.580232i	$0.802962\pi$
$860$	−0.760824	+	4.31485i	−0.0259439	+	0.147135i
$861$		0			0
$862$	10.1732	+	17.6204i	0.346499	+	0.600155i
$863$	−13.8776	+	24.0368i	−0.472400	+	0.818221i	−0.999501	−	0.0315818i	$-0.989946\pi$
$863$	−13.8776	+	24.0368i	−0.472400	+	0.818221i	0.527101	+	0.849803i	$0.323279\pi$
$864$		0			0
$865$	−6.81060	+	5.71477i	−0.231567	+	0.194308i
$866$	17.3891	−	30.1188i	0.590906	−	1.02348i
$867$		0			0
$868$	5.45200	+	1.98437i	0.185053	+	0.0673538i
$869$	−0.292463	+	1.65864i	−0.00992111	+	0.0562654i
$870$		0			0
$871$	−3.97491	+	1.44675i	−0.134685	+	0.0490213i
$872$	−6.79634	−	5.70281i	−0.230153	−	0.193122i
$873$		0			0
$874$	7.10828	+	14.1732i	0.240441	+	0.479415i
$875$	−10.3570			−0.350130
$876$		0			0
$877$	11.7800	−	4.28756i	0.397782	−	0.144781i	−0.135381	−	0.990794i	$-0.543226\pi$
$877$	11.7800	−	4.28756i	0.397782	−	0.144781i	0.533162	+	0.846013i	$0.321003\pi$
$878$	3.74011	+	21.2112i	0.126223	+	0.715844i
$879$		0			0
$880$	5.68226	+	2.06818i	0.191549	+	0.0697182i
$881$	28.2494	+	48.9295i	0.951748	+	1.64848i	0.741641	+	0.670797i	$0.234048\pi$
$881$	28.2494	+	48.9295i	0.951748	+	1.64848i	0.210107	+	0.977678i	$0.432619\pi$
$882$		0			0
$883$	14.1279	−	11.8547i	0.475442	−	0.398943i	−0.373333	−	0.927697i	$-0.621785\pi$
$883$	14.1279	−	11.8547i	0.475442	−	0.398943i	0.848775	+	0.528754i	$0.177341\pi$
$884$	−0.524116	+	0.439785i	−0.0176279	+	0.0147916i
$885$		0			0
$886$	−7.58732	−	13.1416i	−0.254901	−	0.441502i
$887$	11.6097	+	4.22560i	0.389817	+	0.141882i	0.529490	−	0.848316i	$-0.322383\pi$
$887$	11.6097	+	4.22560i	0.389817	+	0.141882i	−0.139674	+	0.990198i	$0.544605\pi$
$888$		0			0
$889$	−1.74072	−	9.87213i	−0.0583820	−	0.331101i
$890$	13.4004	−	4.87733i	0.449181	−	0.163489i
$891$		0			0
$892$	−15.1411			−0.506960
$893$	−0.785749	−	6.75474i	−0.0262941	−	0.226039i
$894$		0			0
$895$	−34.5634	−	29.0021i	−1.15533	−	0.969433i
$896$	0.799633	−	0.291043i	0.0267139	−	0.00972305i
$897$		0			0
$898$	−2.87068	+	16.2805i	−0.0957960	+	0.543286i
$899$	14.4282	+	5.25145i	0.481209	+	0.175146i
$900$		0			0
$901$	9.21902	−	15.9678i	0.307130	−	0.531965i
$902$	−15.8352	+	13.2873i	−0.527254	+	0.442419i
$903$		0			0
$904$	−6.19148	+	10.7240i	−0.205926	+	0.356674i
$905$	−11.1250	−	19.2691i	−0.369809	−	0.640528i
$906$		0			0
$907$	1.57989	−	8.96001i	0.0524594	−	0.297512i	−0.947278	−	0.320412i	$-0.896179\pi$
$907$	1.57989	−	8.96001i	0.0524594	−	0.297512i	0.999738	+	0.0228997i	$0.00728984\pi$
$908$	2.95771	+	16.7740i	0.0981552	+	0.556666i
$909$		0			0
$910$	−0.590913	−	0.495835i	−0.0195886	−	0.0164368i
$911$	5.50145			0.182271			0.0911355	−	0.995839i	$-0.470950\pi$
$911$	5.50145			0.182271			0.0911355	+	0.995839i	$0.470950\pi$
$912$		0			0
$913$	43.6520			1.44467
$914$	0.463846	+	0.389213i	0.0153427	+	0.0128740i
$915$		0			0
$916$	2.24357	+	12.7239i	0.0741295	+	0.420409i
$917$	−2.77787	+	15.7541i	−0.0917335	+	0.520246i
$918$		0			0
$919$	23.2195	+	40.2174i	0.765941	+	1.32665i	0.939748	+	0.341869i	$0.111060\pi$
$919$	23.2195	+	40.2174i	0.765941	+	1.32665i	−0.173807	+	0.984780i	$0.555607\pi$
$920$	3.33897	−	5.78327i	0.110083	−	0.190669i
$921$		0			0
$922$	10.9524	−	9.19013i	0.360697	−	0.302661i
$923$	2.66761	−	4.62043i	0.0878053	−	0.152083i
$924$		0			0
$925$	7.23181	+	2.63216i	0.237780	+	0.0865450i
$926$	−1.86281	+	10.5645i	−0.0612156	+	0.347171i
$927$		0			0
$928$	2.11616	−	0.770219i	0.0694663	−	0.0252837i
$929$	−6.57462	−	5.51676i	−0.215706	−	0.180999i	0.528532	−	0.848914i	$-0.322743\pi$
$929$	−6.57462	−	5.51676i	−0.215706	−	0.180999i	−0.744238	+	0.667914i	$0.767187\pi$
$930$		0			0
$931$	−12.2639	−	24.4529i	−0.401932	−	0.801412i
$932$	26.0558			0.853485
$933$		0			0
$934$	−17.5363	+	6.38268i	−0.573804	+	0.208848i
$935$	−1.45494	−	8.25138i	−0.0475816	−	0.269849i
$936$		0			0
$937$	−1.45128	−	0.528223i	−0.0474113	−	0.0172563i	0.318206	−	0.948022i	$-0.396920\pi$
$937$	−1.45128	−	0.528223i	−0.0474113	−	0.0172563i	−0.365617	+	0.930765i	$0.619142\pi$
$938$	−3.64488	−	6.31311i	−0.119009	−	0.206130i
$939$		0			0
$940$	−2.19399	+	1.84098i	−0.0715601	+	0.0600461i
$941$	−14.9610	+	12.5538i	−0.487715	+	0.409242i	−0.853207	−	0.521573i	$-0.825345\pi$
$941$	−14.9610	+	12.5538i	−0.487715	+	0.409242i	0.365491	+	0.930815i	$0.380901\pi$
$942$		0			0
$943$	11.4142	+	19.7700i	0.371698	+	0.643800i
$944$	−2.49017	−	0.906349i	−0.0810483	−	0.0294992i
$945$		0			0
$946$	1.36508	+	7.74176i	0.0443826	+	0.251706i
$947$	−5.74365	+	2.09052i	−0.186644	+	0.0679328i	−0.433651	−	0.901081i	$-0.642775\pi$
$947$	−5.74365	+	2.09052i	−0.186644	+	0.0679328i	0.247007	+	0.969014i	$0.420553\pi$
$948$		0			0
$949$	2.02335			0.0656806
$950$	7.09169	+	0.416959i	0.230085	+	0.0135279i
$951$		0			0
$952$	−0.903230	−	0.757900i	−0.0292738	−	0.0245637i
$953$	−37.7175	+	13.7280i	−1.22179	+	0.444695i	−0.870778	−	0.491676i	$-0.836384\pi$
$953$	−37.7175	+	13.7280i	−1.22179	+	0.444695i	−0.351011	+	0.936371i	$0.614162\pi$
$954$		0			0
$955$	6.44216	−	36.5353i	0.208463	−	1.18225i
$956$	−24.5407	−	8.93208i	−0.793703	−	0.288884i
$957$		0			0
$958$	−16.6093	+	28.7682i	−0.536624	+	0.929459i
$959$	−8.82054	+	7.40131i	−0.284830	+	0.239001i
$960$		0			0
$961$	−7.74344	+	13.4120i	−0.249788	+	0.432646i
$962$	1.16585	+	2.01931i	0.0375885	+	0.0651052i
$963$		0			0
$964$	0.854838	−	4.84803i	0.0275325	−	0.156144i
$965$	4.66401	+	26.4509i	0.150140	+	0.851486i
$966$		0			0
$967$	−18.9495	−	15.9006i	−0.609376	−	0.511327i	0.285068	−	0.958507i	$-0.407984\pi$
$967$	−18.9495	−	15.9006i	−0.609376	−	0.511327i	−0.894444	+	0.447180i	$0.852428\pi$
$968$	−0.150495			−0.00483709
$969$		0			0
$970$	−31.9236			−1.02500
$971$	31.9088	+	26.7747i	1.02400	+	0.859240i	0.990125	−	0.140186i	$-0.0447700\pi$
$971$	31.9088	+	26.7747i	1.02400	+	0.859240i	0.0338773	+	0.999426i	$0.489214\pi$
$972$		0			0
$973$	−2.79936	−	15.8760i	−0.0897434	−	0.508960i
$974$	−5.31518	+	30.1439i	−0.170309	+	0.965872i
$975$		0			0
$976$	−4.48987	−	7.77668i	−0.143717	−	0.248926i
$977$	18.5791	−	32.1799i	0.594398	−	1.02953i	−0.399234	−	0.916849i	$-0.630724\pi$
$977$	18.5791	−	32.1799i	0.594398	−	1.02953i	0.993632	−	0.112678i	$-0.0359428\pi$
$978$		0			0
$979$	19.6001	−	16.4465i	0.626423	−	0.525631i
$980$	−5.76070	+	9.97783i	−0.184019	+	0.318730i
$981$		0			0
$982$	−3.92851	−	1.42986i	−0.125364	−	0.0456287i
$983$	−5.76922	+	32.7189i	−0.184010	+	1.04357i	0.743212	+	0.669056i	$0.233301\pi$
$983$	−5.76922	+	32.7189i	−0.184010	+	1.04357i	−0.927221	+	0.374514i	$0.877810\pi$
$984$		0			0
$985$	32.7002	−	11.9019i	1.04192	−	0.379227i
$986$	−2.39032	−	2.00572i	−0.0761233	−	0.0638750i
$987$		0			0
$988$	1.56474	+	1.47789i	0.0497811	+	0.0470178i
$989$	8.68151			0.276056
$990$		0			0
$991$	29.3334	−	10.6765i	0.931807	−	0.339150i	0.168882	−	0.985636i	$-0.445984\pi$
$991$	29.3334	−	10.6765i	0.931807	−	0.339150i	0.762926	+	0.646486i	$0.223762\pi$
$992$	1.18396	+	6.71455i	0.0375906	+	0.213187i
$993$		0			0
$994$	8.63989	+	3.14466i	0.274041	+	0.0997427i
$995$	7.23372	+	12.5292i	0.229324	+	0.397201i
$996$		0			0
$997$	8.48758	−	7.12193i	0.268804	−	0.225554i	−0.498415	−	0.866939i	$-0.666084\pi$
$997$	8.48758	−	7.12193i	0.268804	−	0.225554i	0.767219	+	0.641385i	$0.221640\pi$
$998$	−9.95891	+	8.35652i	−0.315244	+	0.264521i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.f.73.1	✓	12
3.2	odd	2		342.2.u.g.73.2	yes	12
19.5	even	9		6498.2.a.ce.1.2		6
19.6	even	9	inner	342.2.u.f.253.1	yes	12
19.14	odd	18		6498.2.a.cc.1.2		6
57.5	odd	18		6498.2.a.cb.1.5		6
57.14	even	18		6498.2.a.cd.1.5		6
57.44	odd	18		342.2.u.g.253.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.u.f.73.1	✓	12	1.1	even	1	trivial
342.2.u.f.253.1	yes	12	19.6	even	9	inner
342.2.u.g.73.2	yes	12	3.2	odd	2
342.2.u.g.253.2	yes	12	57.44	odd	18
6498.2.a.cb.1.5		6	57.5	odd	18
6498.2.a.cc.1.2		6	19.14	odd	18
6498.2.a.cd.1.5		6	57.14	even	18
6498.2.a.ce.1.2		6	19.5	even	9

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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.318787 + 1.80793i) q^{5} +(0.425476 + 0.736946i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.318787 + 1.80793i) q^{5} +(0.425476 + 0.736946i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.40632 + 1.18004i) q^{10} +(-1.64693 + 2.85257i) q^{11} +(0.464002 + 0.168883i) q^{13} +(-0.147766 + 0.838024i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.06143 + 0.890650i) q^{17} +(2.39726 - 3.64049i) q^{19} -1.83582 q^{20} +(-3.09521 + 1.12657i) q^{22} +(0.631658 + 3.58231i) q^{23} +(1.53147 + 0.557409i) q^{25} +(0.246890 + 0.427626i) q^{26} +(-0.651867 + 0.546981i) q^{28} +(-1.72511 + 1.44754i) q^{29} +(-3.40906 - 5.90467i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.240608 + 1.36455i) q^{34} +(-1.46798 + 0.534303i) q^{35} +4.72214 q^{37} +(4.17647 - 1.24785i) q^{38} +(-1.40632 - 1.18004i) q^{40} +(5.89726 - 2.14643i) q^{41} +(0.414432 - 2.35036i) q^{43} +(-3.09521 - 1.12657i) q^{44} +(-1.81879 + 3.15023i) q^{46} +(1.19510 - 1.00281i) q^{47} +(3.13794 - 5.43507i) q^{49} +(0.814878 + 1.41141i) q^{50} +(-0.0857441 + 0.486279i) q^{52} +(-2.31071 - 13.1047i) q^{53} +(-4.63222 - 3.88690i) q^{55} -0.850952 q^{56} -2.25197 q^{58} +(2.03001 + 1.70338i) q^{59} +(1.55932 + 8.84332i) q^{61} +(1.18396 - 6.71455i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.453247 + 0.785046i) q^{65} +(-6.56239 + 5.50650i) q^{67} +(-0.692802 + 1.19997i) q^{68} +(-1.46798 - 0.534303i) q^{70} +(1.87624 - 10.6407i) q^{71} +(3.85055 - 1.40148i) q^{73} +(3.61737 + 3.03533i) q^{74} +(4.00146 + 1.72867i) q^{76} -2.80291 q^{77} +(0.480486 - 0.174883i) q^{79} +(-0.318787 - 1.80793i) q^{80} +(5.89726 + 2.14643i) q^{82} +(-6.62628 - 11.4770i) q^{83} +(-1.94861 + 1.63507i) q^{85} +(1.82826 - 1.53409i) q^{86} +(-1.64693 - 2.85257i) q^{88} +(-7.29938 - 2.65676i) q^{89} +(0.0729641 + 0.413800i) q^{91} +(-3.41820 + 1.24412i) q^{92} +1.56009 q^{94} +(5.81754 + 5.49462i) q^{95} +(13.3209 + 11.1776i) q^{97} +(5.89740 - 2.14648i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8	\( 12 q - 6 q^{7} - 6 q^{8} - 6 q^{11} + 6 q^{17} - 12 q^{19} + 12 q^{20} - 12 q^{23} - 18 q^{25} - 12 q^{26} + 6 q^{31} + 6 q^{34} - 12 q^{35} + 24 q^{37} + 18 q^{38} + 30 q^{41} + 36 q^{43} - 18 q^{46} - 24 q^{47} - 18 q^{50} - 12 q^{53} - 36 q^{55} + 12 q^{56} - 12 q^{58} + 42 q^{59} - 24 q^{61} - 12 q^{62} - 6 q^{64} + 12 q^{65} - 48 q^{67} - 12 q^{68} - 12 q^{70} - 18 q^{71} - 24 q^{73} + 24 q^{74} - 6 q^{76} + 60 q^{77} + 12 q^{79} + 30 q^{82} - 42 q^{83} + 84 q^{85} - 18 q^{86} - 6 q^{88} - 36 q^{89} + 66 q^{91} + 6 q^{92} + 60 q^{94} + 90 q^{95} + 12 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 - 6 * q^11 + 6 * q^17 - 12 * q^19 + 12 * q^20 - 12 * q^23 - 18 * q^25 - 12 * q^26 + 6 * q^31 + 6 * q^34 - 12 * q^35 + 24 * q^37 + 18 * q^38 + 30 * q^41 + 36 * q^43 - 18 * q^46 - 24 * q^47 - 18 * q^50 - 12 * q^53 - 36 * q^55 + 12 * q^56 - 12 * q^58 + 42 * q^59 - 24 * q^61 - 12 * q^62 - 6 * q^64 + 12 * q^65 - 48 * q^67 - 12 * q^68 - 12 * q^70 - 18 * q^71 - 24 * q^73 + 24 * q^74 - 6 * q^76 + 60 * q^77 + 12 * q^79 + 30 * q^82 - 42 * q^83 + 84 * q^85 - 18 * q^86 - 6 * q^88 - 36 * q^89 + 66 * q^91 + 6 * q^92 + 60 * q^94 + 90 * q^95 + 12 * q^97 + 24 * q^98

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