LMFDB - Embedded newform 525.2.i.h.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(151,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.10423593216.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.758290 - 1.31340i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.h.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25829 + 2.17942i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.16659 - 3.75264i) q^{4} -2.51658 q^{6} +(2.29673 - 1.31340i) q^{7} +5.87162 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.489068 - 0.847090i) q^{11} +(2.16659 - 3.75264i) q^{12} +5.14977 q^{13} +(-0.0275122 + 6.65819i) q^{14} +(-3.05502 + 5.29146i) q^{16} +(2.07488 + 3.59380i) q^{17} +(-1.25829 - 2.17942i) q^{18} +(1.15001 - 1.99187i) q^{19} +(2.28580 + 1.33233i) q^{21} +2.46156 q^{22} +(-2.53644 + 4.39324i) q^{23} +(2.93581 + 5.08497i) q^{24} +(-6.47990 + 11.2235i) q^{26} -1.00000 q^{27} +(-9.90478 - 5.77323i) q^{28} +5.92664 q^{29} +(-0.316594 - 0.548357i) q^{31} +(-1.81659 - 3.14643i) q^{32} +(0.489068 - 0.847090i) q^{33} -10.4432 q^{34} +4.33317 q^{36} +(-4.52751 + 7.84188i) q^{37} +(2.89408 + 5.01270i) q^{38} +(2.57488 + 4.45983i) q^{39} +2.65505 q^{41} +(-5.77992 + 3.30527i) q^{42} +0.344947 q^{43} +(-2.11922 + 3.67059i) q^{44} +(-6.38315 - 11.0559i) q^{46} +(2.11922 - 3.67059i) q^{47} -6.11005 q^{48} +(3.54998 - 6.03305i) q^{49} +(-2.07488 + 3.59380i) q^{51} +(-11.1574 - 19.3252i) q^{52} +(-3.81659 - 6.61053i) q^{53} +(1.25829 - 2.17942i) q^{54} +(13.4855 - 7.71176i) q^{56} +2.30001 q^{57} +(-7.45743 + 12.9167i) q^{58} +(-0.908297 - 1.57322i) q^{59} +(-0.328128 + 0.568335i) q^{61} +1.59347 q^{62} +(-0.0109324 + 2.64573i) q^{63} -3.07689 q^{64} +(1.23078 + 2.13177i) q^{66} +(4.62991 + 8.01924i) q^{67} +(8.99083 - 15.5726i) q^{68} -5.07288 q^{69} -5.49351 q^{71} +(-2.93581 + 5.08497i) q^{72} +(-2.68905 - 4.65758i) q^{73} +(-11.3938 - 19.7347i) q^{74} -9.96636 q^{76} +(-2.23582 - 1.30320i) q^{77} -12.9598 q^{78} +(5.44346 - 9.42835i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.34083 + 5.78648i) q^{82} +6.62663 q^{83} +(0.0473719 - 11.4644i) q^{84} +(-0.434043 + 0.751785i) q^{86} +(2.96332 + 5.13262i) q^{87} +(-2.87162 - 4.97379i) q^{88} +(-8.15542 + 14.1256i) q^{89} +(11.8277 - 6.76369i) q^{91} +21.9817 q^{92} +(0.316594 - 0.548357i) q^{93} +(5.33317 + 9.23733i) q^{94} +(1.81659 - 3.14643i) q^{96} -1.53844 q^{97} +(8.68165 + 15.3282i) q^{98} +0.978135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 4 q^{13} + 12 q^{14} - 2 q^{17} - 2 q^{18} + 12 q^{19} - 2 q^{21} + 28 q^{22} - 10 q^{23} + 6 q^{24} - 6 q^{26} - 8 q^{27}+ \cdots - 20 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9 + 4 * q^12 + 4 * q^13 + 12 * q^14 - 2 * q^17 - 2 * q^18 + 12 * q^19 - 2 * q^21 + 28 * q^22 - 10 * q^23 + 6 * q^24 - 6 * q^26 - 8 * q^27 - 12 * q^28 - 12 * q^29 + 8 * q^31 - 4 * q^32 - 8 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 + 2 * q^39 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 10 * q^44 - 16 * q^46 + 10 * q^47 + 20 * q^49 + 2 * q^51 - 34 * q^52 - 20 * q^53 + 2 * q^54 + 42 * q^56 + 24 * q^57 - 10 * q^58 - 2 * q^59 + 8 * q^61 - 20 * q^62 - 4 * q^63 - 8 * q^64 + 14 * q^66 - 6 * q^67 + 30 * q^68 - 20 * q^69 - 28 * q^71 - 6 * q^72 - 12 * q^73 - 20 * q^74 - 32 * q^76 - 6 * q^77 - 12 * q^78 + 8 * q^79 - 4 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 - 24 * q^86 - 6 * q^87 + 12 * q^88 - 8 * q^89 + 4 * q^91 + 92 * q^92 - 8 * q^93 + 16 * q^94 + 4 * q^96 - 4 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.25829	+	2.17942i	−0.889745	+	1.54108i	−0.0495691	+	0.998771i	$0.515785\pi$
$2$	−1.25829	+	2.17942i	−0.889745	+	1.54108i	−0.840176	+	0.542313i	$0.817549\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.16659	−	3.75264i	−1.08329	−	1.87632i
$5$		0			0
$5$		0			0
$6$	−2.51658			−1.02739
$7$	2.29673	−	1.31340i	0.868084	−	0.496417i
$7$	2.29673	−	1.31340i	0.868084	−	0.496417i
$8$	5.87162			2.07593
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.489068	−	0.847090i	−0.147459	−	0.255407i	0.782828	−	0.622238i	$-0.213776\pi$
$11$	−0.489068	−	0.847090i	−0.147459	−	0.255407i	−0.930288	+	0.366830i	$0.880443\pi$
$12$	2.16659	−	3.75264i	0.625440	−	1.08329i
$13$	5.14977			1.42829			0.714144	−	0.699998i	$-0.246816\pi$
$13$	5.14977			1.42829			0.714144	+	0.699998i	$0.246816\pi$
$14$	−0.0275122	+	6.65819i	−0.00735294	+	1.77948i
$15$		0			0
$16$	−3.05502	+	5.29146i	−0.763756	+	1.32286i
$17$	2.07488	+	3.59380i	0.503233	+	0.871626i	0.999993	+	0.00373753i	$0.00118970\pi$
$17$	2.07488	+	3.59380i	0.503233	+	0.871626i	−0.496760	+	0.867888i	$0.665477\pi$
$18$	−1.25829	−	2.17942i	−0.296582	−	0.513695i
$19$	1.15001	−	1.99187i	0.263830	−	0.456967i	−0.703427	−	0.710768i	$-0.748348\pi$
$19$	1.15001	−	1.99187i	0.263830	−	0.456967i	0.967256	+	0.253801i	$0.0816810\pi$
$20$		0			0
$21$	2.28580	+	1.33233i	0.498803	+	0.290739i
$22$	2.46156			0.524805
$23$	−2.53644	+	4.39324i	−0.528884	+	0.916054i	0.470548	+	0.882374i	$0.344056\pi$
$23$	−2.53644	+	4.39324i	−0.528884	+	0.916054i	−0.999433	+	0.0336802i	$0.989277\pi$
$24$	2.93581	+	5.08497i	0.599270	+	1.03797i
$25$		0			0
$26$	−6.47990	+	11.2235i	−1.27081	+	2.20111i
$27$	−1.00000			−0.192450
$28$	−9.90478	−	5.77323i	−1.87183	−	1.09104i
$29$	5.92664			1.10055			0.550275	−	0.834983i	$-0.314523\pi$
$29$	5.92664			1.10055			0.550275	+	0.834983i	$0.314523\pi$
$30$		0			0
$31$	−0.316594	−	0.548357i	−0.0568620	−	0.0984879i	0.836193	−	0.548435i	$-0.184776\pi$
$31$	−0.316594	−	0.548357i	−0.0568620	−	0.0984879i	−0.893055	+	0.449947i	$0.851443\pi$
$32$	−1.81659	−	3.14643i	−0.321132	−	0.556216i
$33$	0.489068	−	0.847090i	0.0851357	−	0.147459i
$34$	−10.4432			−1.79100
$35$		0			0
$36$	4.33317			0.722196
$37$	−4.52751	+	7.84188i	−0.744318	+	1.28920i	0.206194	+	0.978511i	$0.433892\pi$
$37$	−4.52751	+	7.84188i	−0.744318	+	1.28920i	−0.950513	+	0.310686i	$0.899441\pi$
$38$	2.89408	+	5.01270i	0.469483	+	0.813168i
$39$	2.57488	+	4.45983i	0.412311	+	0.714144i
$40$		0			0
$41$	2.65505			0.414650			0.207325	−	0.978272i	$-0.433524\pi$
$41$	2.65505			0.414650			0.207325	+	0.978272i	$0.433524\pi$
$42$	−5.77992	+	3.30527i	−0.891860	+	0.510014i
$43$	0.344947			0.0526039			0.0263020	−	0.999654i	$-0.491627\pi$
$43$	0.344947			0.0526039			0.0263020	+	0.999654i	$0.491627\pi$
$44$	−2.11922	+	3.67059i	−0.319484	+	0.553362i
$45$		0			0
$46$	−6.38315	−	11.0559i	−0.941144	−	1.63011i
$47$	2.11922	−	3.67059i	0.309119	−	0.535410i	−0.669051	−	0.743217i	$-0.733299\pi$
$47$	2.11922	−	3.67059i	0.309119	−	0.535410i	0.978170	+	0.207806i	$0.0666324\pi$
$48$	−6.11005			−0.881910
$49$	3.54998	−	6.03305i	0.507140	−	0.861864i
$50$		0			0
$51$	−2.07488	+	3.59380i	−0.290542	+	0.503233i
$52$	−11.1574	−	19.3252i	−1.54726	−	2.67993i
$53$	−3.81659	−	6.61053i	−0.524250	−	0.908027i	−0.999601	−	0.0282311i	$-0.991013\pi$
$53$	−3.81659	−	6.61053i	−0.524250	−	0.908027i	0.475352	−	0.879796i	$-0.342321\pi$
$54$	1.25829	−	2.17942i	0.171232	−	0.296582i
$55$		0			0
$56$	13.4855	−	7.71176i	1.80208	−	1.03053i
$57$	2.30001			0.304644
$58$	−7.45743	+	12.9167i	−0.979209	+	1.69604i
$59$	−0.908297	−	1.57322i	−0.118250	−	0.204815i	0.800824	−	0.598900i	$-0.204395\pi$
$59$	−0.908297	−	1.57322i	−0.118250	−	0.204815i	−0.919074	+	0.394084i	$0.871062\pi$
$60$		0			0
$61$	−0.328128	+	0.568335i	−0.0420125	+	0.0727678i	−0.886267	−	0.463175i	$-0.846710\pi$
$61$	−0.328128	+	0.568335i	−0.0420125	+	0.0727678i	0.844255	+	0.535942i	$0.180044\pi$
$62$	1.59347			0.202371
$63$	−0.0109324	+	2.64573i	−0.00137735	+	0.333330i
$64$	−3.07689			−0.384611
$65$		0			0
$66$	1.23078	+	2.13177i	0.151498	+	0.262403i
$67$	4.62991	+	8.01924i	0.565633	+	0.979706i	0.996990	+	0.0775244i	$0.0247016\pi$
$67$	4.62991	+	8.01924i	0.565633	+	0.979706i	−0.431357	+	0.902181i	$0.641965\pi$
$68$	8.99083	−	15.5726i	1.09030	−	1.88845i
$69$	−5.07288			−0.610703
$70$		0			0
$71$	−5.49351			−0.651960			−0.325980	−	0.945377i	$-0.605694\pi$
$71$	−5.49351			−0.651960			−0.325980	+	0.945377i	$0.605694\pi$
$72$	−2.93581	+	5.08497i	−0.345988	+	0.599270i
$73$	−2.68905	−	4.65758i	−0.314730	−	0.545128i	0.664650	−	0.747155i	$-0.268581\pi$
$73$	−2.68905	−	4.65758i	−0.314730	−	0.545128i	−0.979380	+	0.202027i	$0.935247\pi$
$74$	−11.3938	−	19.7347i	−1.32451	−	2.29411i
$75$		0			0
$76$	−9.96636			−1.14322
$77$	−2.23582	−	1.30320i	−0.254796	−	0.148514i
$78$	−12.9598			−1.46741
$79$	5.44346	−	9.42835i	0.612437	−	1.06077i	−0.378391	−	0.925646i	$-0.623523\pi$
$79$	5.44346	−	9.42835i	0.612437	−	1.06077i	0.990828	−	0.135127i	$-0.0431441\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.34083	+	5.78648i	−0.368933	+	0.639010i
$83$	6.62663			0.727367			0.363683	−	0.931523i	$-0.381519\pi$
$83$	6.62663			0.727367			0.363683	+	0.931523i	$0.381519\pi$
$84$	0.0473719	−	11.4644i	0.00516870	−	1.25087i
$85$		0			0
$86$	−0.434043	+	0.751785i	−0.0468041	+	0.0810671i
$87$	2.96332	+	5.13262i	0.317701	+	0.550275i
$88$	−2.87162	−	4.97379i	−0.306116	−	0.530208i
$89$	−8.15542	+	14.1256i	−0.864472	+	1.49731i	0.00309785	+	0.999995i	$0.499014\pi$
$89$	−8.15542	+	14.1256i	−0.864472	+	1.49731i	−0.867570	+	0.497315i	$0.834319\pi$
$90$		0			0
$91$	11.8277	−	6.76369i	1.23987	−	0.709027i
$92$	21.9817			2.29175
$93$	0.316594	−	0.548357i	0.0328293	−	0.0568620i
$94$	5.33317	+	9.23733i	0.550075	+	0.952758i
$95$		0			0
$96$	1.81659	−	3.14643i	0.185405	−	0.321132i
$97$	−1.53844			−0.156205			−0.0781027	−	0.996945i	$-0.524886\pi$
$97$	−1.53844			−0.156205			−0.0781027	+	0.996945i	$0.524886\pi$
$98$	8.68165	+	15.3282i	0.876979	+	1.54838i
$99$	0.978135			0.0983063
$100$		0			0
$101$	2.75805	+	4.77708i	0.274436	+	0.475338i	0.969993	−	0.243134i	$-0.0781754\pi$
$101$	2.75805	+	4.77708i	0.274436	+	0.475338i	−0.695556	+	0.718471i	$0.744842\pi$
$102$	−5.22161	−	9.04410i	−0.517017	−	0.895499i
$103$	−8.26066	+	14.3079i	−0.813947	+	1.40980i	0.0961349	+	0.995368i	$0.469352\pi$
$103$	−8.26066	+	14.3079i	−0.813947	+	1.40980i	−0.910082	+	0.414429i	$0.863981\pi$
$104$	30.2375			2.96503
$105$		0			0
$106$	19.2095			1.86579
$107$	1.19410	−	2.06824i	0.115438	−	0.199944i	−0.802517	−	0.596630i	$-0.796506\pi$
$107$	1.19410	−	2.06824i	0.115438	−	0.199944i	0.917955	+	0.396685i	$0.129840\pi$
$108$	2.16659	+	3.75264i	0.208480	+	0.361098i
$109$	9.05479	+	15.6833i	0.867291	+	1.50219i	0.864754	+	0.502196i	$0.167474\pi$
$109$	9.05479	+	15.6833i	0.867291	+	1.50219i	0.00253705	+	0.999997i	$0.499192\pi$
$110$		0			0
$111$	−9.05502			−0.859465
$112$	−0.0667973	+	16.1655i	−0.00631176	+	1.52750i
$113$	4.04373			0.380402			0.190201	−	0.981745i	$-0.439086\pi$
$113$	4.04373			0.380402			0.190201	+	0.981745i	$0.439086\pi$
$114$	−2.89408	+	5.01270i	−0.271056	+	0.469483i
$115$		0			0
$116$	−12.8406	−	22.2405i	−1.19222	−	2.06498i
$117$	−2.57488	+	4.45983i	−0.238048	+	0.412311i
$118$	4.57160			0.420850
$119$	9.48555	+	5.52887i	0.869539	+	0.506831i
$120$		0			0
$121$	5.02163	−	8.69771i	0.456511	−	0.790701i
$122$	−0.825761	−	1.43026i	−0.0747608	−	0.129490i
$123$	1.32753	+	2.29934i	0.119699	+	0.207325i
$124$	−1.37186	+	2.37613i	−0.123196	+	0.213383i
$125$		0			0
$126$	−5.75240	−	3.35292i	−0.512465	−	0.298702i
$127$	6.85023			0.607860			0.303930	−	0.952694i	$-0.401701\pi$
$127$	6.85023			0.607860			0.303930	+	0.952694i	$0.401701\pi$
$128$	7.50481	−	12.9987i	0.663337	−	1.14893i
$129$	0.172473	+	0.298733i	0.0151854	+	0.0263020i
$130$		0			0
$131$	2.01270	−	3.48610i	0.175850	−	0.304582i	−0.764605	−	0.644499i	$-0.777066\pi$
$131$	2.01270	−	3.48610i	0.175850	−	0.304582i	0.940455	+	0.339918i	$0.110399\pi$
$132$	−4.23843			−0.368908
$133$	0.0251446	−	6.08521i	0.00218031	−	0.527655i
$134$	−23.3031			−2.01308
$135$		0			0
$136$	12.1829	+	21.1014i	1.04468	+	1.80943i
$137$	−5.61594	−	9.72709i	−0.479802	−	0.831041i	0.519930	−	0.854209i	$-0.325958\pi$
$137$	−5.61594	−	9.72709i	−0.479802	−	0.831041i	−0.999732	+	0.0231680i	$0.992625\pi$
$138$	6.38315	−	11.0559i	0.543370	−	0.941144i
$139$	−4.98991			−0.423238			−0.211619	−	0.977352i	$-0.567874\pi$
$139$	−4.98991			−0.423238			−0.211619	+	0.977352i	$0.567874\pi$
$140$		0			0
$141$	4.23843			0.356940
$142$	6.91243	−	11.9727i	0.580078	−	1.00473i
$143$	−2.51858	−	4.36232i	−0.210615	−	0.364795i
$144$	−3.05502	−	5.29146i	−0.254585	−	0.440955i
$145$		0			0
$146$	13.5344			1.12012
$147$	6.99976	+	0.0578482i	0.577331	+	0.00477124i
$148$	39.2370			3.22526
$149$	7.24712	−	12.5524i	0.593707	−	1.02833i	−0.400021	−	0.916506i	$-0.630997\pi$
$149$	7.24712	−	12.5524i	0.593707	−	1.02833i	0.993728	−	0.111825i	$-0.0356695\pi$
$150$		0			0
$151$	−3.94346	−	6.83028i	−0.320914	−	0.555840i	0.659763	−	0.751474i	$-0.270657\pi$
$151$	−3.94346	−	6.83028i	−0.320914	−	0.555840i	−0.980677	+	0.195634i	$0.937324\pi$
$152$	6.75240	−	11.6955i	0.547692	−	0.948631i
$153$	−4.14977			−0.335489
$154$	5.65354	−	3.23300i	0.455575	−	0.260522i
$155$		0			0
$156$	11.1574	−	19.3252i	0.893309	−	1.54726i
$157$	−3.27815	−	5.67792i	−0.261625	−	0.453147i	0.705049	−	0.709159i	$-0.250925\pi$
$157$	−3.27815	−	5.67792i	−0.261625	−	0.453147i	−0.966674	+	0.256011i	$0.917592\pi$
$158$	13.6989	+	23.7272i	1.08983	+	1.88763i
$159$	3.81659	−	6.61053i	0.302676	−	0.524250i
$160$		0			0
$161$	−0.0554586	+	13.4215i	−0.00437075	+	1.05776i
$162$	2.51658			0.197721
$163$	6.12790	−	10.6138i	0.479974	−	0.831340i	−0.519762	−	0.854311i	$-0.673979\pi$
$163$	6.12790	−	10.6138i	0.479974	−	0.831340i	0.999736	+	0.0229712i	$0.00731260\pi$
$164$	−5.75240	−	9.96346i	−0.449187	−	0.778015i
$165$		0			0
$166$	−8.33822	+	14.4422i	−0.647171	+	1.12093i
$167$	−2.13239			−0.165009			−0.0825047	−	0.996591i	$-0.526292\pi$
$167$	−2.13239			−0.165009			−0.0825047	+	0.996591i	$0.526292\pi$
$168$	13.4214	+	7.82295i	1.03548	+	0.603553i
$169$	13.5201			1.04001
$170$		0			0
$171$	1.15001	+	1.99187i	0.0879432	+	0.152322i
$172$	−0.747358	−	1.29446i	−0.0569855	−	0.0987017i
$173$	−5.77427	+	10.0013i	−0.439009	+	0.760387i	−0.997613	−	0.0690479i	$-0.978004\pi$
$173$	−5.77427	+	10.0013i	−0.439009	+	0.760387i	0.558604	+	0.829435i	$0.311337\pi$
$174$	−14.9149			−1.13069
$175$		0			0
$176$	5.97645			0.450492
$177$	0.908297	−	1.57322i	0.0682718	−	0.118250i
$178$	−20.5238	−	35.5482i	−1.53832	−	2.66445i
$179$	−4.44978	−	7.70725i	−0.332592	−	0.576067i	0.650427	−	0.759569i	$-0.274590\pi$
$179$	−4.44978	−	7.70725i	−0.332592	−	0.576067i	−0.983019	+	0.183502i	$0.941257\pi$
$180$		0			0
$181$	−3.17940			−0.236323			−0.118161	−	0.992994i	$-0.537700\pi$
$181$	−3.17940			−0.236323			−0.118161	+	0.992994i	$0.537700\pi$
$182$	−0.141681	+	34.2881i	−0.0105021	+	2.54160i
$183$	−0.656256			−0.0485119
$184$	−14.8930	+	25.7954i	−1.09793	+	1.90167i
$185$		0			0
$186$	0.796734	+	1.37998i	0.0584194	+	0.101185i
$187$	2.02952	−	3.51523i	0.148413	−	0.257059i
$188$	−18.3659			−1.33947
$189$	−2.29673	+	1.31340i	−0.167063	+	0.0955355i
$190$		0			0
$191$	0.311309	−	0.539203i	0.0225255	−	0.0390154i	−0.854543	−	0.519381i	$-0.826163\pi$
$191$	0.311309	−	0.539203i	0.0225255	−	0.0390154i	0.877068	+	0.480365i	$0.159496\pi$
$192$	−1.53844	−	2.66466i	−0.111028	−	0.192306i
$193$	7.59383	+	13.1529i	0.546616	+	0.946767i	0.998503	+	0.0546916i	$0.0174176\pi$
$193$	7.59383	+	13.1529i	0.546616	+	0.946767i	−0.451887	+	0.892075i	$0.649249\pi$
$194$	1.93581	−	3.35292i	0.138983	−	0.240726i
$195$		0			0
$196$	−30.3312	−	0.250666i	−2.16651	−	0.0179047i
$197$	−23.9410			−1.70573			−0.852863	−	0.522136i	$-0.825136\pi$
$197$	−23.9410			−1.70573			−0.852863	+	0.522136i	$0.825136\pi$
$198$	−1.23078	+	2.13177i	−0.0874676	+	0.151498i
$199$	−6.97662	−	12.0839i	−0.494560	−	0.856602i	0.505421	−	0.862873i	$-0.331337\pi$
$199$	−6.97662	−	12.0839i	−0.494560	−	0.856602i	−0.999980	+	0.00627071i	$0.998004\pi$
$200$		0			0
$201$	−4.62991	+	8.01924i	−0.326569	+	0.565633i
$202$	−13.8817			−0.976714
$203$	13.6119	−	7.78403i	0.955370	−	0.546332i
$204$	17.9817			1.25897
$205$		0			0
$206$	−20.7886	−	36.0069i	−1.44841	−	2.50872i
$207$	−2.53644	−	4.39324i	−0.176295	−	0.305351i
$208$	−15.7327	+	27.2498i	−1.09086	+	1.88943i
$209$	−2.24973			−0.155617
$210$		0			0
$211$	4.82315			0.332040			0.166020	−	0.986122i	$-0.446908\pi$
$211$	4.82315			0.332040			0.166020	+	0.986122i	$0.446908\pi$
$212$	−16.5380	+	28.6446i	−1.13583	+	1.96732i
$213$	−2.74676	−	4.75752i	−0.188205	−	0.325980i
$214$	3.00505	+	5.20489i	0.205421	+	0.355799i
$215$		0			0
$216$	−5.87162			−0.399513
$217$	−1.44734	−	0.843617i	−0.0982521	−	0.0572685i
$218$	−45.5742			−3.08667
$219$	2.68905	−	4.65758i	0.181709	−	0.314730i
$220$		0			0
$221$	10.6852	+	18.5073i	0.718762	+	1.24493i
$222$	11.3938	−	19.7347i	0.764705	−	1.32451i
$223$	−15.8227			−1.05956			−0.529782	−	0.848134i	$-0.677726\pi$
$223$	−15.8227			−1.05956			−0.529782	+	0.848134i	$0.677726\pi$
$224$	−8.30475	−	4.84061i	−0.554884	−	0.323427i
$225$		0			0
$226$	−5.08818	+	8.81299i	−0.338461	+	0.586232i
$227$	−10.8492	−	18.7913i	−0.720084	−	1.24722i	−0.960966	−	0.276667i	$-0.910770\pi$
$227$	−10.8492	−	18.7913i	−0.720084	−	1.24722i	0.240882	−	0.970554i	$-0.422563\pi$
$228$	−4.98318	−	8.63112i	−0.330019	−	0.571610i
$229$	1.03844	−	1.79864i	0.0686223	−	0.118857i	−0.829673	−	0.558250i	$-0.811473\pi$
$229$	1.03844	−	1.79864i	0.0686223	−	0.118857i	0.898295	+	0.439393i	$0.144806\pi$
$230$		0			0
$231$	0.0106933	−	2.58788i	0.000703570	−	0.170270i
$232$	34.7990			2.28467
$233$	−3.37951	+	5.85348i	−0.221399	+	0.383474i	−0.955233	−	0.295854i	$-0.904396\pi$
$233$	−3.37951	+	5.85348i	−0.221399	+	0.383474i	0.733834	+	0.679329i	$0.237729\pi$
$234$	−6.47990	−	11.2235i	−0.423604	−	0.733704i
$235$		0			0
$236$	−3.93581	+	6.81702i	−0.256199	+	0.443750i
$237$	10.8869			0.707182
$238$	−23.9853	+	13.7161i	−1.55474	+	0.889082i
$239$	−2.90478			−0.187894			−0.0939472	−	0.995577i	$-0.529949\pi$
$239$	−2.90478			−0.187894			−0.0939472	+	0.995577i	$0.529949\pi$
$240$		0			0
$241$	4.44875	+	7.70546i	0.286569	+	0.496352i	0.972988	−	0.230854i	$-0.0741519\pi$
$241$	4.44875	+	7.70546i	0.286569	+	0.496352i	−0.686419	+	0.727206i	$0.740819\pi$
$242$	12.6373	+	21.8885i	0.812358	+	1.40705i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.84367			0.182047
$245$		0			0
$246$	−6.68165			−0.426007
$247$	5.92227	−	10.2577i	0.376825	−	0.652680i
$248$	−1.85892	−	3.21974i	−0.118042	−	0.204454i
$249$	3.31331	+	5.73883i	0.209973	+	0.363683i
$250$		0			0
$251$	−21.1747			−1.33653			−0.668267	−	0.743921i	$-0.732964\pi$
$251$	−21.1747			−1.33653			−0.668267	+	0.743921i	$0.732964\pi$
$252$	9.95215	−	5.69118i	0.626927	−	0.358510i
$253$	4.96196			0.311956
$254$	−8.61958	+	14.9295i	−0.540840	+	0.936763i
$255$		0			0
$256$	15.8096	+	27.3830i	0.988097	+	1.71143i
$257$	3.11721	−	5.39917i	0.194446	−	0.336791i	−0.752273	−	0.658852i	$-0.771042\pi$
$257$	3.11721	−	5.39917i	0.194446	−	0.336791i	0.946719	+	0.322061i	$0.104376\pi$
$258$	−0.868086			−0.0540447
$259$	−0.0989929	+	23.9571i	−0.00615112	+	1.48862i
$260$		0			0
$261$	−2.96332	+	5.13262i	−0.183425	+	0.317701i
$262$	5.06512	+	8.77304i	0.312924	+	0.542000i
$263$	−14.0240	−	24.2903i	−0.864756	−	1.49780i	−0.867289	−	0.497805i	$-0.834139\pi$
$263$	−14.0240	−	24.2903i	−0.864756	−	1.49780i	0.00253231	−	0.999997i	$-0.499194\pi$
$264$	2.87162	−	4.97379i	0.176736	−	0.306116i
$265$		0			0
$266$	13.2306	+	7.71176i	0.811221	+	0.472839i
$267$	−16.3108			−0.998207
$268$	20.0622	−	34.7487i	1.22549	−	2.12262i
$269$	−3.70915	−	6.42444i	−0.226151	−	0.391705i	0.730513	−	0.682899i	$-0.239281\pi$
$269$	−3.70915	−	6.42444i	−0.226151	−	0.391705i	−0.956664	+	0.291194i	$0.905948\pi$
$270$		0			0
$271$	15.6058	−	27.0300i	0.947985	−	1.64196i	0.198323	−	0.980137i	$-0.436450\pi$
$271$	15.6058	−	27.0300i	0.947985	−	1.64196i	0.749662	−	0.661821i	$-0.230216\pi$
$272$	−25.3553			−1.53739
$273$	11.7714	+	6.86120i	0.712435	+	0.415259i
$274$	28.2659			1.70761
$275$		0			0
$276$	10.9908	+	19.0367i	0.661570	+	1.14587i
$277$	−6.22629	−	10.7843i	−0.374102	−	0.647963i	0.616090	−	0.787675i	$-0.288716\pi$
$277$	−6.22629	−	10.7843i	−0.374102	−	0.647963i	−0.990192	+	0.139712i	$0.955382\pi$
$278$	6.27875	−	10.8751i	0.376574	−	0.652246i
$279$	0.633188			0.0379080
$280$		0			0
$281$	−0.0409225			−0.00244123			−0.00122061	−	0.999999i	$-0.500389\pi$
$281$	−0.0409225			−0.00244123			−0.00122061	+	0.999999i	$0.500389\pi$
$282$	−5.33317	+	9.23733i	−0.317586	+	0.550075i
$283$	5.42100	+	9.38944i	0.322245	+	0.558144i	0.980951	−	0.194256i	$-0.0622293\pi$
$283$	5.42100	+	9.38944i	0.322245	+	0.558144i	−0.658706	+	0.752400i	$0.728896\pi$
$284$	11.9022	+	20.6152i	0.706264	+	1.22329i
$285$		0			0
$286$	12.6764			0.749574
$287$	6.09795	−	3.48714i	0.359951	−	0.205839i
$288$	3.63319			0.214088
$289$	−0.110288	+	0.191024i	−0.00648752	+	0.0112367i
$290$		0			0
$291$	−0.769222	−	1.33233i	−0.0450926	−	0.0781027i
$292$	−11.6521	+	20.1821i	−0.681890	+	1.18107i
$293$	−29.6455			−1.73191			−0.865953	−	0.500125i	$-0.833287\pi$
$293$	−29.6455			−1.73191			−0.865953	+	0.500125i	$0.833287\pi$
$294$	−8.93380	+	15.1826i	−0.521030	+	0.885470i
$295$		0			0
$296$	−26.5838	+	46.0445i	−1.54515	+	2.67628i
$297$	0.489068	+	0.847090i	0.0283786	+	0.0491531i
$298$	18.2380	+	31.5891i	1.05650	+	1.82991i
$299$	−13.0621	+	22.6242i	−0.755399	+	1.30839i
$300$		0			0
$301$	0.792252	−	0.453052i	0.0456646	−	0.0261135i
$302$	19.8481			1.14213
$303$	−2.75805	+	4.77708i	−0.158446	+	0.274436i
$304$	7.02660	+	12.1704i	0.403003	+	0.698022i
$305$		0			0
$306$	5.22161	−	9.04410i	0.298500	−	0.517017i
$307$	−31.6055			−1.80382			−0.901910	−	0.431923i	$-0.857835\pi$
$307$	−31.6055			−1.80382			−0.901910	+	0.431923i	$0.857835\pi$
$308$	−0.0463361	+	11.2137i	−0.00264024	+	0.638962i
$309$	−16.5213			−0.939865
$310$		0			0
$311$	−11.0851	−	19.2000i	−0.628581	−	1.08873i	−0.987837	−	0.155495i	$-0.950303\pi$
$311$	−11.0851	−	19.2000i	−0.628581	−	1.08873i	0.359256	−	0.933239i	$-0.383031\pi$
$312$	15.1187	+	26.1864i	0.855930	+	1.48251i
$313$	3.44286	−	5.96321i	0.194602	−	0.337060i	−0.752168	−	0.658971i	$-0.770992\pi$
$313$	3.44286	−	5.96321i	0.194602	−	0.337060i	0.946770	+	0.321911i	$0.104325\pi$
$314$	16.4995			0.931118
$315$		0			0
$316$	−47.1749			−2.65380
$317$	6.41935	−	11.1186i	0.360547	−	0.624485i	−0.627504	−	0.778613i	$-0.715923\pi$
$317$	6.41935	−	11.1186i	0.360547	−	0.624485i	0.988051	+	0.154128i	$0.0492568\pi$
$318$	9.60476	+	16.6359i	0.538608	+	0.932897i
$319$	−2.89853	−	5.02040i	−0.162286	−	0.281088i
$320$		0			0
$321$	2.38820			0.133296
$322$	−29.1812	−	17.0090i	−1.62621	−	0.947872i
$323$	9.54453			0.531072
$324$	−2.16659	+	3.75264i	−0.120366	+	0.208480i
$325$		0			0
$326$	15.4214	+	26.7106i	0.854110	+	1.47936i
$327$	−9.05479	+	15.6833i	−0.500731	+	0.867291i
$328$	15.5895			0.860784
$329$	0.0463361	−	11.2137i	0.00255459	−	0.618233i
$330$		0			0
$331$	4.26678	−	7.39028i	0.234524	−	0.406207i	−0.724611	−	0.689159i	$-0.757980\pi$
$331$	4.26678	−	7.39028i	0.234524	−	0.406207i	0.959134	+	0.282952i	$0.0913137\pi$
$332$	−14.3572	−	24.8673i	−0.787952	−	1.36477i
$333$	−4.52751	−	7.84188i	−0.248106	−	0.429732i
$334$	2.68317	−	4.64738i	0.146816	−	0.254293i
$335$		0			0
$336$	−14.0332	+	8.02492i	−0.765572	+	0.437795i
$337$	29.1131			1.58589			0.792946	−	0.609292i	$-0.208546\pi$
$337$	29.1131			1.58589			0.792946	+	0.609292i	$0.208546\pi$
$338$	−17.0122	+	29.4660i	−0.925343	+	1.60274i
$339$	2.02186	+	3.50197i	0.109813	+	0.190201i
$340$		0			0
$341$	−0.309672	+	0.536367i	−0.0167697	+	0.0290459i
$342$	−5.78817			−0.312988
$343$	0.229575	−	18.5188i	0.0123959	−	0.999923i
$344$	2.02540			0.109202
$345$		0			0
$346$	−14.5314	−	25.1691i	−0.781213	−	1.35310i
$347$	−6.72137	−	11.6418i	−0.360822	−	0.624962i	0.627274	−	0.778798i	$-0.284171\pi$
$347$	−6.72137	−	11.6418i	−0.360822	−	0.624962i	−0.988096	+	0.153836i	$0.950837\pi$
$348$	12.8406	−	22.2405i	0.688328	−	1.19222i
$349$	−24.7397			−1.32429			−0.662144	−	0.749377i	$-0.730353\pi$
$349$	−24.7397			−1.32429			−0.662144	+	0.749377i	$0.730353\pi$
$350$		0			0
$351$	−5.14977			−0.274874
$352$	−1.77687	+	3.07764i	−0.0947077	+	0.164039i
$353$	8.37751	+	14.5103i	0.445890	+	0.772303i	0.998114	−	0.0613923i	$-0.0195541\pi$
$353$	8.37751	+	14.5103i	0.445890	+	0.772303i	−0.552224	+	0.833696i	$0.686221\pi$
$354$	2.28580	+	3.95913i	0.121489	+	0.210425i
$355$		0			0
$356$	70.6777			3.74591
$357$	−0.0453668	+	10.9792i	−0.00240107	+	0.581079i
$358$	22.3965			1.18369
$359$	16.2462	−	28.1393i	0.857442	−	1.48513i	−0.0169190	−	0.999857i	$-0.505386\pi$
$359$	16.2462	−	28.1393i	0.857442	−	1.48513i	0.874361	−	0.485276i	$-0.161281\pi$
$360$		0			0
$361$	6.85497	+	11.8732i	0.360788	+	0.624903i
$362$	4.00060	−	6.92925i	0.210267	−	0.364193i
$363$	10.0433			0.527134
$364$	−51.0073	−	29.7308i	−2.67351	−	1.55832i
$365$		0			0
$366$	0.825761	−	1.43026i	0.0431632	−	0.0747608i
$367$	11.9809	+	20.7516i	0.625400	+	1.08322i	0.988463	+	0.151460i	$0.0483974\pi$
$367$	11.9809	+	20.7516i	0.625400	+	1.08322i	−0.363064	+	0.931764i	$0.618269\pi$
$368$	−15.4978	−	26.8429i	−0.807877	−	1.39928i
$369$	−1.32753	+	2.29934i	−0.0691083	+	0.119699i
$370$		0			0
$371$	−17.4480	−	10.1699i	−0.905853	−	0.527997i
$372$	−2.74372			−0.142255
$373$	−5.53771	+	9.59160i	−0.286732	+	0.496634i	−0.973028	−	0.230688i	$-0.925902\pi$
$373$	−5.53771	+	9.59160i	−0.286732	+	0.496634i	0.686296	+	0.727323i	$0.259236\pi$
$374$	5.10744	+	8.84635i	0.264100	+	0.457434i
$375$		0			0
$376$	12.4432	−	21.5523i	0.641710	−	1.11147i
$377$	30.5208			1.57190
$378$	0.0275122	−	6.65819i	0.00141507	−	0.342460i
$379$	−32.7423			−1.68186			−0.840929	−	0.541145i	$-0.817991\pi$
$379$	−32.7423			−1.68186			−0.840929	+	0.541145i	$0.817991\pi$
$380$		0			0
$381$	3.42512	+	5.93247i	0.175474	+	0.303930i
$382$	0.783435	+	1.35695i	0.0400840	+	0.0694275i
$383$	11.6262	−	20.1371i	0.594069	−	1.02896i	−0.399609	−	0.916686i	$-0.630854\pi$
$383$	11.6262	−	20.1371i	0.594069	−	1.02896i	0.993678	−	0.112271i	$-0.0358125\pi$
$384$	15.0096			0.765956
$385$		0			0
$386$	−38.2210			−1.94540
$387$	−0.172473	+	0.298733i	−0.00876732	+	0.0151854i
$388$	3.33317	+	5.77323i	0.169216	+	0.293091i
$389$	18.8131	+	32.5852i	0.953861	+	1.65214i	0.736954	+	0.675943i	$0.236263\pi$
$389$	18.8131	+	32.5852i	0.953861	+	1.65214i	0.216907	+	0.976192i	$0.430403\pi$
$390$		0			0
$391$	−21.0513			−1.06461
$392$	20.8441	−	35.4237i	1.05279	−	1.78917i
$393$	4.02540			0.203054
$394$	30.1247	−	52.1775i	1.51766	−	2.62867i
$395$		0			0
$396$	−2.11922	−	3.67059i	−0.106495	−	0.184454i
$397$	0.0287870	−	0.0498605i	0.00144478	−	0.00250243i	−0.865302	−	0.501251i	$-0.832873\pi$
$397$	0.0287870	−	0.0498605i	0.00144478	−	0.00250243i	0.866747	+	0.498748i	$0.166207\pi$
$398$	35.1144			1.76013
$399$	5.28252	−	3.02083i	0.264457	−	0.151231i
$400$		0			0
$401$	4.53797	−	7.85999i	0.226615	−	0.392509i	−0.730188	−	0.683247i	$-0.760567\pi$
$401$	4.53797	−	7.85999i	0.226615	−	0.392509i	0.956803	+	0.290738i	$0.0939007\pi$
$402$	−11.6515	−	20.1810i	−0.581126	−	1.00654i
$403$	−1.63039	−	2.82391i	−0.0812153	−	0.140669i
$404$	11.9511	−	20.6999i	0.594590	−	1.02986i
$405$		0			0
$406$	−0.163055	+	39.4607i	−0.00809228	+	1.95840i
$407$	8.85704			0.439027
$408$	−12.1829	+	21.1014i	−0.603145	+	1.04468i
$409$	−8.30602	−	14.3865i	−0.410706	−	0.711364i	0.584261	−	0.811566i	$-0.301385\pi$
$409$	−8.30602	−	14.3865i	−0.410706	−	0.711364i	−0.994967	+	0.100202i	$0.968051\pi$
$410$		0			0
$411$	5.61594	−	9.72709i	0.277014	−	0.479802i
$412$	71.5897			3.52697
$413$	−4.15237	−	2.42031i	−0.204325	−	0.119096i
$414$	12.7663			0.627430
$415$		0			0
$416$	−9.35504	−	16.2034i	−0.458669	−	0.794437i
$417$	−2.49495	−	4.32139i	−0.122178	−	0.211619i
$418$	2.83081	−	4.90310i	0.138459	−	0.239818i
$419$	−29.8759			−1.45953			−0.729766	−	0.683697i	$-0.760371\pi$
$419$	−29.8759			−1.45953			−0.729766	+	0.683697i	$0.760371\pi$
$420$		0			0
$421$	−19.3201			−0.941602			−0.470801	−	0.882239i	$-0.656035\pi$
$421$	−19.3201			−0.941602			−0.470801	+	0.882239i	$0.656035\pi$
$422$	−6.06893	+	10.5117i	−0.295431	+	0.511701i
$423$	2.11922	+	3.67059i	0.103040	+	0.178470i
$424$	−22.4096	−	38.8145i	−1.08831	−	1.88500i
$425$		0			0
$426$	13.8249			0.669817
$427$	−0.00717444	+	1.73628i	−0.000347195	+	0.0840243i
$428$	−10.3485			−0.500213
$429$	2.51858	−	4.36232i	0.121598	−	0.210615i
$430$		0			0
$431$	10.9981	+	19.0493i	0.529761	+	0.917572i	0.999397	+	0.0347127i	$0.0110516\pi$
$431$	10.9981	+	19.0493i	0.529761	+	0.917572i	−0.469637	+	0.882860i	$0.655615\pi$
$432$	3.05502	−	5.29146i	0.146985	−	0.254585i
$433$	−2.72706			−0.131054			−0.0655272	−	0.997851i	$-0.520873\pi$
$433$	−2.72706			−0.131054			−0.0655272	+	0.997851i	$0.520873\pi$
$434$	3.65978	−	2.09286i	0.175675	−	0.100460i
$435$		0			0
$436$	39.2360	−	67.9587i	1.87906	−	3.25463i
$437$	5.83385	+	10.1045i	0.279071	+	0.483365i
$438$	6.76722	+	11.7212i	0.323350	+	0.560059i
$439$	3.77183	−	6.53300i	0.180020	−	0.311803i	−0.761867	−	0.647733i	$-0.775717\pi$
$439$	3.77183	−	6.53300i	0.180020	−	0.311803i	0.941887	+	0.335930i	$0.109051\pi$
$440$		0			0
$441$	3.44978	+	6.09089i	0.164275	+	0.290043i
$442$	−53.7802			−2.55806
$443$	5.21917	−	9.03987i	0.247970	−	0.429497i	−0.714992	−	0.699132i	$-0.753570\pi$
$443$	5.21917	−	9.03987i	0.247970	−	0.429497i	0.962963	+	0.269635i	$0.0869031\pi$
$444$	19.6185	+	33.9802i	0.931053	+	1.61263i
$445$		0			0
$446$	19.9095	−	34.4843i	0.942743	−	1.63288i
$447$	14.4942			0.685554
$448$	−7.06680	+	4.04118i	−0.333875	+	0.190928i
$449$	−1.73107			−0.0816944			−0.0408472	−	0.999165i	$-0.513006\pi$
$449$	−1.73107			−0.0816944			−0.0408472	+	0.999165i	$0.513006\pi$
$450$		0			0
$451$	−1.29850	−	2.24907i	−0.0611440	−	0.105905i
$452$	−8.76109	−	15.1747i	−0.412087	−	0.713756i
$453$	3.94346	−	6.83028i	0.185280	−	0.320914i
$454$	54.6055			2.56276
$455$		0			0
$456$	13.5048			0.632421
$457$	−15.4307	+	26.7268i	−0.721819	+	1.25023i	0.238452	+	0.971154i	$0.423360\pi$
$457$	−15.4307	+	26.7268i	−0.721819	+	1.25023i	−0.960270	+	0.279072i	$0.909973\pi$
$458$	2.61333	+	4.52642i	0.122113	+	0.211506i
$459$	−2.07488	−	3.59380i	−0.0968473	−	0.167744i
$460$		0			0
$461$	10.7294			0.499718			0.249859	−	0.968282i	$-0.419616\pi$
$461$	10.7294			0.499718			0.249859	+	0.968282i	$0.419616\pi$
$462$	5.62663	+	3.27961i	0.261774	+	0.152581i
$463$	11.1060			0.516141			0.258071	−	0.966126i	$-0.416913\pi$
$463$	11.1060			0.516141			0.258071	+	0.966126i	$0.416913\pi$
$464$	−18.1060	+	31.3606i	−0.840552	+	1.45588i
$465$		0			0
$466$	−8.50481	−	14.7308i	−0.393978	−	0.682389i
$467$	−13.7947	+	23.8932i	−0.638344	+	1.10564i	0.347452	+	0.937698i	$0.387047\pi$
$467$	−13.7947	+	23.8932i	−0.638344	+	1.10564i	−0.985796	+	0.167946i	$0.946286\pi$
$468$	22.3148			1.03150
$469$	21.1661	+	12.3372i	0.977360	+	0.569677i
$470$		0			0
$471$	3.27815	−	5.67792i	0.151049	−	0.261625i
$472$	−5.33317	−	9.23733i	−0.245479	−	0.425182i
$473$	−0.168702	−	0.292201i	−0.00775694	−	0.0134354i
$474$	−13.6989	+	23.7272i	−0.629212	+	1.08983i
$475$		0			0
$476$	0.196582	−	47.5746i	0.00901034	−	2.18058i
$477$	7.63319			0.349500
$478$	3.65505	−	6.33074i	0.167178	−	0.289561i
$479$	5.00869	+	8.67530i	0.228853	+	0.396385i	0.957468	−	0.288538i	$-0.0931692\pi$
$479$	5.00869	+	8.67530i	0.228853	+	0.396385i	−0.728616	+	0.684923i	$0.759836\pi$
$480$		0			0
$481$	−23.3156	+	40.3839i	−1.06310	+	1.84135i
$482$	−22.3913			−1.01989
$483$	−11.6511	+	6.66270i	−0.530141	+	0.303163i
$484$	−43.5192			−1.97814
$485$		0			0
$486$	1.25829	+	2.17942i	0.0570772	+	0.0988606i
$487$	15.3671	+	26.6165i	0.696348	+	1.20611i	0.969724	+	0.244203i	$0.0785264\pi$
$487$	15.3671	+	26.6165i	0.696348	+	1.20611i	−0.273376	+	0.961907i	$0.588140\pi$
$488$	−1.92664	+	3.33704i	−0.0872150	+	0.151061i
$489$	12.2558			0.554227
$490$		0			0
$491$	4.14054			0.186860			0.0934301	−	0.995626i	$-0.470217\pi$
$491$	4.14054			0.186860			0.0934301	+	0.995626i	$0.470217\pi$
$492$	5.75240	−	9.96346i	0.259338	−	0.449187i
$493$	12.2971	+	21.2992i	0.553833	+	0.959268i
$494$	14.9039	+	25.8143i	0.670557	+	1.16144i
$495$		0			0
$496$	3.86881			0.173715
$497$	−12.6171	+	7.21516i	−0.565956	+	0.323644i
$498$	−16.6764			−0.747289
$499$	0.774139	−	1.34085i	0.0346552	−	0.0600246i	−0.848178	−	0.529712i	$-0.822300\pi$
$499$	0.774139	−	1.34085i	0.0346552	−	0.0600246i	0.882833	+	0.469687i	$0.155633\pi$
$500$		0			0
$501$	−1.06620	−	1.84671i	−0.0476341	−	0.0825047i
$502$	26.6439	−	46.1486i	1.18918	−	2.05971i
$503$	15.1658			0.676210			0.338105	−	0.941108i	$-0.390214\pi$
$503$	15.1658			0.676210			0.338105	+	0.941108i	$0.390214\pi$
$504$	−0.0641907	+	15.5347i	−0.00285928	+	0.691971i
$505$		0			0
$506$	−6.24359	+	10.8142i	−0.277561	+	0.480750i
$507$	6.76006	+	11.7088i	0.300225	+	0.520004i
$508$	−14.8416	−	25.7064i	−0.658491	−	1.14054i
$509$	10.2327	−	17.7236i	0.453558	−	0.785586i	−0.545046	−	0.838406i	$-0.683488\pi$
$509$	10.2327	−	17.7236i	0.453558	−	0.785586i	0.998604	+	0.0528204i	$0.0168211\pi$
$510$		0			0
$511$	−12.2933	−	7.16542i	−0.543823	−	0.316980i
$512$	−49.5528			−2.18994
$513$	−1.15001	+	1.99187i	−0.0507741	+	0.0879432i
$514$	7.84471	+	13.5874i	0.346015	+	0.599316i
$515$		0			0
$516$	0.747358	−	1.29446i	0.0329006	−	0.0569855i
$517$	−4.14576			−0.182330
$518$	−52.0882	−	30.3608i	−2.28862	−	1.33398i
$519$	−11.5485			−0.506924
$520$		0			0
$521$	−1.37337	−	2.37875i	−0.0601685	−	0.104215i	0.834372	−	0.551202i	$-0.185830\pi$
$521$	−1.37337	−	2.37875i	−0.0601685	−	0.104215i	−0.894541	+	0.446987i	$0.852497\pi$
$522$	−7.45743	−	12.9167i	−0.326403	−	0.565347i
$523$	−19.9335	+	34.5258i	−0.871629	+	1.50971i	−0.0113184	+	0.999936i	$0.503603\pi$
$523$	−19.9335	+	34.5258i	−0.871629	+	1.50971i	−0.860311	+	0.509770i	$0.829731\pi$
$524$	−17.4427			−0.761990
$525$		0			0
$526$	70.5850			3.07765
$527$	1.31379	−	2.27556i	0.0572297	−	0.0991247i
$528$	2.98823	+	5.17576i	0.130046	+	0.225246i
$529$	−1.36705	−	2.36780i	−0.0594370	−	0.102948i
$530$		0			0
$531$	1.81659			0.0788335
$532$	−22.8901	+	13.0898i	−0.992411	+	0.567514i
$533$	13.6729			0.592239
$534$	20.5238	−	35.5482i	0.888150	−	1.53832i
$535$		0			0
$536$	27.1851	+	47.0859i	1.17422	+	2.03380i
$537$	4.44978	−	7.70725i	0.192022	−	0.332592i
$538$	18.6688			0.804867
$539$	−6.84671	−	0.0565834i	−0.294909	−	0.00243722i
$540$		0			0
$541$	−13.2493	+	22.9485i	−0.569633	+	0.986633i	0.426969	+	0.904266i	$0.359581\pi$
$541$	−13.2493	+	22.9485i	−0.569633	+	0.986633i	−0.996602	+	0.0823667i	$0.973752\pi$
$542$	39.2732	+	68.0232i	1.68693	+	2.92185i
$543$	−1.58970	−	2.75344i	−0.0682205	−	0.118161i
$544$	7.53844	−	13.0570i	0.323208	−	0.559813i
$545$		0			0
$546$	−29.7652	+	17.0214i	−1.27383	+	0.728447i
$547$	12.9090			0.551950			0.275975	−	0.961165i	$-0.410999\pi$
$547$	12.9090			0.551950			0.275975	+	0.961165i	$0.410999\pi$
$548$	−24.3348	+	42.1492i	−1.03953	+	1.80052i
$549$	−0.328128	−	0.568335i	−0.0140042	−	0.0242559i
$550$		0			0
$551$	6.81568	−	11.8051i	0.290358	−	0.502914i
$552$	−29.7860			−1.26778
$553$	0.119020	−	28.8038i	0.00506124	−	1.22486i
$554$	31.3379			1.33142
$555$		0			0
$556$	10.8111	+	18.7253i	0.458492	+	0.794131i
$557$	−3.59254	−	6.22247i	−0.152221	−	0.263654i	0.779823	−	0.626000i	$-0.215309\pi$
$557$	−3.59254	−	6.22247i	−0.152221	−	0.263654i	−0.932044	+	0.362346i	$0.881976\pi$
$558$	−0.796734	+	1.37998i	−0.0337285	+	0.0584194i
$559$	1.77640			0.0751336
$560$		0			0
$561$	4.05903			0.171373
$562$	0.0514923	−	0.0891873i	0.00217207	−	0.00376214i
$563$	−1.19350	−	2.06720i	−0.0502999	−	0.0871220i	0.839779	−	0.542928i	$-0.182684\pi$
$563$	−1.19350	−	2.06720i	−0.0502999	−	0.0871220i	−0.890079	+	0.455806i	$0.849351\pi$
$564$	−9.18293	−	15.9053i	−0.386671	−	0.669734i
$565$		0			0
$566$	−27.2847			−1.14686
$567$	−2.28580	−	1.33233i	−0.0959947	−	0.0559527i
$568$	−32.2558			−1.35342
$569$	−14.9271	+	25.8545i	−0.625776	+	1.08388i	0.362615	+	0.931939i	$0.381884\pi$
$569$	−14.9271	+	25.8545i	−0.625776	+	1.08388i	−0.988390	+	0.151936i	$0.951449\pi$
$570$		0			0
$571$	9.73170	+	16.8558i	0.407259	+	0.705393i	0.994582	−	0.103960i	$-0.0331513\pi$
$571$	9.73170	+	16.8558i	0.407259	+	0.705393i	−0.587322	+	0.809353i	$0.699818\pi$
$572$	−10.9135	+	18.9027i	−0.456315	+	0.790361i
$573$	0.622618			0.0260103
$574$	−0.0730463	+	17.6778i	−0.00304889	+	0.737859i
$575$		0			0
$576$	1.53844	−	2.66466i	0.0641019	−	0.111028i
$577$	−1.98094	−	3.43108i	−0.0824675	−	0.142838i	0.821842	−	0.569716i	$-0.192947\pi$
$577$	−1.98094	−	3.43108i	−0.0824675	−	0.142838i	−0.904309	+	0.426878i	$0.859613\pi$
$578$	−0.277548	−	0.480727i	−0.0115445	−	0.0199956i
$579$	−7.59383	+	13.1529i	−0.315589	+	0.546616i
$580$		0			0
$581$	15.2196	−	8.70339i	0.631416	−	0.361078i
$582$	3.87162			0.160484
$583$	−3.73315	+	6.46600i	−0.154611	+	0.267794i
$584$	−15.7891	−	27.3475i	−0.653357	−	1.13165i
$585$		0			0
$586$	37.3026	−	64.6100i	1.54096	−	2.66901i
$587$	−13.9419			−0.575446			−0.287723	−	0.957714i	$-0.592898\pi$
$587$	−13.9419			−0.575446			−0.287723	+	0.957714i	$0.592898\pi$
$588$	−14.9485	−	26.3929i	−0.616466	−	1.08843i
$589$	−1.45634			−0.0600075
$590$		0			0
$591$	−11.9705	−	20.7335i	−0.492400	−	0.852863i
$592$	−27.6633	−	47.9143i	−1.13696	−	1.96926i
$593$	−19.2486	+	33.3396i	−0.790447	+	1.36909i	0.135243	+	0.990812i	$0.456818\pi$
$593$	−19.2486	+	33.3396i	−0.790447	+	1.36909i	−0.925690	+	0.378282i	$0.876515\pi$
$594$	−2.46156			−0.100999
$595$		0			0
$596$	−62.8061			−2.57264
$597$	6.97662	−	12.0839i	0.285534	−	0.494560i
$598$	−32.8718	−	56.9356i	−1.34423	−	2.32827i
$599$	−8.74985	−	15.1552i	−0.357509	−	0.619224i	0.630035	−	0.776567i	$-0.283041\pi$
$599$	−8.74985	−	15.1552i	−0.357509	−	0.619224i	−0.987544	+	0.157343i	$0.949707\pi$
$600$		0			0
$601$	34.5192			1.40807			0.704033	−	0.710167i	$-0.251381\pi$
$601$	34.5192			1.40807			0.704033	+	0.710167i	$0.251381\pi$
$602$	−0.00949025	+	2.29672i	−0.000386794	+	0.0936074i
$603$	−9.25982			−0.377089
$604$	−17.0877	+	29.5968i	−0.695289	+	1.20428i
$605$		0			0
$606$	−6.94086	−	12.0219i	−0.281953	−	0.488357i
$607$	5.45780	−	9.45318i	0.221525	−	0.383693i	−0.733746	−	0.679424i	$-0.762230\pi$
$607$	5.45780	−	9.45318i	0.221525	−	0.383693i	0.955271	+	0.295731i	$0.0955632\pi$
$608$	−8.35639			−0.338896
$609$	13.5471	+	7.89626i	0.548958	+	0.319972i
$610$		0			0
$611$	10.9135	−	18.9027i	0.441512	−	0.764721i
$612$	8.99083	+	15.5726i	0.363433	+	0.629484i
$613$	−13.0587	−	22.6183i	−0.527435	−	0.913543i	−0.999489	−	0.0319739i	$-0.989821\pi$
$613$	−13.0587	−	22.6183i	−0.527435	−	0.913543i	0.472054	−	0.881570i	$-0.343513\pi$
$614$	39.7689	−	68.8817i	1.60494	−	2.77984i
$615$		0			0
$616$	−13.1279	−	7.65190i	−0.528938	−	0.308304i
$617$	−11.6689			−0.469772			−0.234886	−	0.972023i	$-0.575472\pi$
$617$	−11.6689			−0.469772			−0.234886	+	0.972023i	$0.575472\pi$
$618$	20.7886	−	36.0069i	0.836240	−	1.44841i
$619$	0.411816	+	0.713286i	0.0165523	+	0.0286694i	0.874183	−	0.485597i	$-0.161398\pi$
$619$	0.411816	+	0.713286i	0.0165523	+	0.0286694i	−0.857631	+	0.514266i	$0.828064\pi$
$620$		0			0
$621$	2.53644	−	4.39324i	0.101784	−	0.176295i
$622$	55.7933			2.23711
$623$	−0.178316	+	43.1540i	−0.00714408	+	1.72893i
$624$	−31.4653			−1.25962
$625$		0			0
$626$	8.66423	+	15.0069i	0.346292	+	0.599796i
$627$	−1.12486	−	1.94832i	−0.0449227	−	0.0778084i
$628$	−14.2048	+	24.6034i	−0.566833	+	0.981783i
$629$	−37.5763			−1.49826
$630$		0			0
$631$	−20.5920			−0.819755			−0.409877	−	0.912141i	$-0.634429\pi$
$631$	−20.5920			−0.819755			−0.409877	+	0.912141i	$0.634429\pi$
$632$	31.9619	−	55.3597i	1.27138	−	2.20209i
$633$	2.41158	+	4.17697i	0.0958516	+	0.166020i
$634$	16.1548	+	27.9810i	0.641590	+	1.11127i
$635$		0			0
$636$	−33.0759			−1.31155
$637$	18.2816	−	31.0688i	0.724342	−	1.23099i
$638$	14.5888			0.577575
$639$	2.74676	−	4.75752i	0.108660	−	0.188205i
$640$		0			0
$641$	−14.8371	−	25.6986i	−0.586029	−	1.01503i	−0.994746	−	0.102371i	$-0.967357\pi$
$641$	−14.8371	−	25.6986i	−0.586029	−	1.01503i	0.408717	−	0.912661i	$-0.365976\pi$
$642$	−3.00505	+	5.20489i	−0.118600	+	0.205421i
$643$	−11.1286			−0.438870			−0.219435	−	0.975627i	$-0.570421\pi$
$643$	−11.1286			−0.438870			−0.219435	+	0.975627i	$0.570421\pi$
$644$	50.4861	−	28.8706i	1.98943	−	1.13766i
$645$		0			0
$646$	−12.0098	+	20.8016i	−0.472519	+	0.818426i
$647$	−5.46168	−	9.45991i	−0.214721	−	0.371907i	0.738465	−	0.674291i	$-0.235551\pi$
$647$	−5.46168	−	9.45991i	−0.214721	−	0.371907i	−0.953186	+	0.302384i	$0.902217\pi$
$648$	−2.93581	−	5.08497i	−0.115329	−	0.199757i
$649$	−0.888437	+	1.53882i	−0.0348742	+	0.0604039i
$650$		0			0
$651$	0.00692225	−	1.67524i	0.000271304	−	0.0656580i
$652$	−53.1065			−2.07981
$653$	−3.58538	+	6.21006i	−0.140307	+	0.243019i	−0.927612	−	0.373545i	$-0.878142\pi$
$653$	−3.58538	+	6.21006i	−0.140307	+	0.243019i	0.787305	+	0.616563i	$0.211476\pi$
$654$	−22.7871	−	39.4684i	−0.891046	−	1.54334i
$655$		0			0
$656$	−8.11125	+	14.0491i	−0.316691	+	0.548525i
$657$	5.37811			0.209820
$658$	24.3812	+	14.2111i	0.950477	+	0.554007i
$659$	14.1232			0.550161			0.275080	−	0.961421i	$-0.411296\pi$
$659$	14.1232			0.550161			0.275080	+	0.961421i	$0.411296\pi$
$660$		0			0
$661$	−14.4608	−	25.0469i	−0.562461	−	0.974212i	−0.997281	−	0.0736941i	$-0.976521\pi$
$661$	−14.4608	−	25.0469i	−0.562461	−	0.974212i	0.434819	−	0.900518i	$-0.356812\pi$
$662$	10.7377	+	18.5982i	0.417333	+	0.722841i
$663$	−10.6852	+	18.5073i	−0.414978	+	0.718762i
$664$	38.9090			1.50996
$665$		0			0
$666$	22.7877			0.883005
$667$	−15.0326	+	26.0372i	−0.582063	+	1.00816i
$668$	4.62001	+	8.00210i	0.178754	+	0.309610i
$669$	−7.91134	−	13.7028i	−0.305870	−	0.529782i
$670$		0			0
$671$	0.641907			0.0247806
$672$	0.0397194	−	9.61243i	0.00153221	−	0.370808i
$673$	14.4081			0.555392			0.277696	−	0.960669i	$-0.410429\pi$
$673$	14.4081			0.555392			0.277696	+	0.960669i	$0.410429\pi$
$674$	−36.6327	+	63.4497i	−1.41104	+	2.44399i
$675$		0			0
$676$	−29.2925	−	50.7361i	−1.12663	−	1.95139i
$677$	−15.0683	+	26.0991i	−0.579123	+	1.00307i	0.416457	+	0.909155i	$0.363271\pi$
$677$	−15.0683	+	26.0991i	−0.579123	+	1.00307i	−0.995580	+	0.0939148i	$0.970062\pi$
$678$	−10.1764			−0.390821
$679$	−3.53340	+	2.02059i	−0.135599	+	0.0775430i
$680$		0			0
$681$	10.8492	−	18.7913i	0.415740	−	0.720084i
$682$	−0.779314	−	1.34981i	−0.0298415	−	0.0516870i
$683$	−7.75842	−	13.4380i	−0.296868	−	0.514190i	0.678550	−	0.734554i	$-0.262609\pi$
$683$	−7.75842	−	13.4380i	−0.296868	−	0.514190i	−0.975418	+	0.220364i	$0.929275\pi$
$684$	4.98318	−	8.63112i	0.190537	−	0.330019i
$685$		0			0
$686$	40.0715	+	23.8024i	1.52994	+	0.908780i
$687$	2.07689			0.0792383
$688$	−1.05382	+	1.82527i	−0.0401766	+	0.0695878i
$689$	−19.6546	−	34.0427i	−0.748780	−	1.29692i
$690$		0			0
$691$	−22.8917	+	39.6496i	−0.870842	+	1.50834i	−0.00971588	+	0.999953i	$0.503093\pi$
$691$	−22.8917	+	39.6496i	−0.870842	+	1.50834i	−0.861127	+	0.508391i	$0.830241\pi$
$692$	50.0418			1.90230
$693$	2.24652	−	1.28468i	0.0853381	−	0.0488009i
$694$	33.8297			1.28416
$695$		0			0
$696$	17.3995	+	30.1368i	0.659526	+	1.14233i
$697$	5.50893	+	9.54174i	0.208666	+	0.361419i
$698$	31.1298	−	53.9183i	1.17828	−	2.04084i
$699$	−6.75902			−0.255650
$700$		0			0
$701$	24.0419			0.908050			0.454025	−	0.890989i	$-0.349988\pi$
$701$	24.0419			0.908050			0.454025	+	0.890989i	$0.349988\pi$
$702$	6.47990	−	11.2235i	0.244568	−	0.423604i
$703$	10.4133	+	18.0364i	0.392747	+	0.680257i
$704$	1.50481	+	2.60640i	0.0567145	+	0.0982325i
$705$		0			0
$706$	−42.1653			−1.58691
$707$	12.6087	+	7.34928i	0.474200	+	0.276398i
$708$	−7.87162			−0.295834
$709$	−9.19854	+	15.9323i	−0.345459	+	0.598352i	−0.985437	−	0.170041i	$-0.945610\pi$
$709$	−9.19854	+	15.9323i	−0.345459	+	0.598352i	0.639978	+	0.768393i	$0.278943\pi$
$710$		0			0
$711$	5.44346	+	9.42835i	0.204146	+	0.353591i
$712$	−47.8855	+	82.9401i	−1.79458	+	3.10831i
$713$	3.21209			0.120294
$714$	−23.8711	−	13.9138i	−0.893355	−	0.520712i
$715$		0			0
$716$	−19.2817	+	33.3969i	−0.720590	+	1.24810i
$717$	−1.45239	−	2.51561i	−0.0542405	−	0.0939472i
$718$	40.8849	+	70.8147i	1.52581	+	2.64278i
$719$	8.12275	−	14.0690i	0.302927	−	0.524686i	−0.673870	−	0.738850i	$-0.735369\pi$
$719$	8.12275	−	14.0690i	0.302927	−	0.524686i	0.976798	+	0.214164i	$0.0687027\pi$
$720$		0			0
$721$	−0.180617	+	43.7109i	−0.00672654	+	1.62788i
$722$	−34.5021			−1.28404
$723$	−4.44875	+	7.70546i	−0.165451	+	0.286569i
$724$	6.88844	+	11.9311i	0.256007	+	0.443417i
$725$		0			0
$726$	−12.6373	+	21.8885i	−0.469015	+	0.812358i
$727$	−42.6977			−1.58357			−0.791785	−	0.610800i	$-0.790848\pi$
$727$	−42.6977			−1.58357			−0.791785	+	0.610800i	$0.790848\pi$
$728$	69.4474	−	39.7138i	2.57389	−	1.47189i
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.715725	+	1.23967i	0.0264720	+	0.0458509i
$732$	1.42184	+	2.46269i	0.0525526	+	0.0910237i
$733$	23.3560	−	40.4538i	0.862674	−	1.49420i	−0.00666408	−	0.999978i	$-0.502121\pi$
$733$	23.3560	−	40.4538i	0.862674	−	1.49420i	0.869338	−	0.494218i	$-0.164545\pi$
$734$	−60.3020			−2.22579
$735$		0			0
$736$	18.4307			0.679366
$737$	4.52868	−	7.84390i	0.166816	−	0.288934i
$738$	−3.34083	−	5.78648i	−0.122978	−	0.213003i
$739$	−3.52410	−	6.10393i	−0.129636	−	0.224537i	0.793899	−	0.608049i	$-0.208048\pi$
$739$	−3.52410	−	6.10393i	−0.129636	−	0.224537i	−0.923536	+	0.383513i	$0.874714\pi$
$740$		0			0
$741$	11.8445			0.435120
$742$	44.1192	−	25.2297i	1.61967	−	0.926212i
$743$	−8.55510			−0.313856			−0.156928	−	0.987610i	$-0.550159\pi$
$743$	−8.55510			−0.313856			−0.156928	+	0.987610i	$0.550159\pi$
$744$	1.85892	−	3.21974i	0.0681513	−	0.118042i
$745$		0			0
$746$	−13.9361	−	24.1380i	−0.510237	−	0.883756i
$747$	−3.31331	+	5.73883i	−0.121228	+	0.209973i
$748$	−17.5885			−0.643099
$749$	0.0261087	−	6.31853i	0.000953990	−	0.230874i
$750$		0			0
$751$	1.48823	−	2.57768i	0.0543062	−	0.0940611i	−0.837594	−	0.546293i	$-0.816039\pi$
$751$	1.48823	−	2.57768i	0.0543062	−	0.0940611i	0.891901	+	0.452232i	$0.149372\pi$
$752$	12.9485	+	22.4275i	0.472183	+	0.817846i
$753$	−10.5873	−	18.3378i	−0.385824	−	0.668267i
$754$	−38.4041	+	66.5178i	−1.39859	+	2.42243i
$755$		0			0
$756$	9.90478	+	5.77323i	0.360233	+	0.209970i
$757$	43.6750			1.58740			0.793698	−	0.608313i	$-0.208153\pi$
$757$	43.6750			1.58740			0.793698	+	0.608313i	$0.208153\pi$
$758$	41.1993	−	71.3592i	1.49643	−	2.59188i
$759$	2.48098	+	4.29718i	0.0900539	+	0.155978i
$760$		0			0
$761$	−13.3628	+	23.1451i	−0.484402	+	0.839008i	−0.999839	−	0.0179187i	$-0.994296\pi$
$761$	−13.3628	+	23.1451i	−0.484402	+	0.839008i	0.515438	+	0.856927i	$0.327629\pi$
$762$	−17.2392			−0.624509
$763$	41.3949	+	24.1280i	1.49860	+	0.873491i
$764$	−2.69791			−0.0976071
$765$		0			0
$766$	29.2581	+	50.6766i	1.05714	+	1.83102i
$767$	−4.67752	−	8.10170i	−0.168895	−	0.292535i
$768$	−15.8096	+	27.3830i	−0.570478	+	0.988097i
$769$	−4.04661			−0.145925			−0.0729623	−	0.997335i	$-0.523245\pi$
$769$	−4.04661			−0.145925			−0.0729623	+	0.997335i	$0.523245\pi$
$770$		0			0
$771$	6.23442			0.224527
$772$	32.9054	−	56.9938i	1.18429	−	2.05125i
$773$	−3.15553	−	5.46553i	−0.113496	−	0.196581i	0.803681	−	0.595060i	$-0.202872\pi$
$773$	−3.15553	−	5.46553i	−0.113496	−	0.196581i	−0.917178	+	0.398478i	$0.869538\pi$
$774$	−0.434043	−	0.751785i	−0.0156014	−	0.0270224i
$775$		0			0
$776$	−9.03316			−0.324272
$777$	−20.7970	+	11.8928i	−0.746088	+	0.426653i
$778$	−94.6892			−3.39477
$779$	3.05333	−	5.28852i	0.109397	−	0.189481i
$780$		0			0
$781$	2.68670	+	4.65350i	0.0961376	+	0.166515i
$782$	26.4886	−	45.8796i	0.947230	−	1.64065i
$783$	−5.92664			−0.211801
$784$	21.0783	+	37.2157i	0.752798	+	1.32913i
$785$		0			0
$786$	−5.06512	+	8.77304i	−0.180667	+	0.312924i
$787$	−14.9877	−	25.9595i	−0.534256	−	0.925358i	−0.999199	−	0.0400174i	$-0.987259\pi$
$787$	−14.9877	−	25.9595i	−0.534256	−	0.925358i	0.464943	−	0.885340i	$-0.346075\pi$
$788$	51.8702	+	89.8419i	1.84780	+	3.20048i
$789$	14.0240	−	24.2903i	0.499267	−	0.864756i
$790$		0			0
$791$	9.28737	−	5.31102i	0.330221	−	0.188838i
$792$	5.74324			0.204077
$793$	−1.68978	+	2.92679i	−0.0600060	+	0.103933i
$794$	0.0724448	+	0.125478i	0.00257097	+	0.00445305i
$795$		0			0
$796$	−30.2309	+	52.3615i	−1.07151	+	1.85590i
$797$	0.676527			0.0239638			0.0119819	−	0.999928i	$-0.496186\pi$
$797$	0.676527			0.0239638			0.0119819	+	0.999928i	$0.496186\pi$
$798$	−0.0632784	+	15.3139i	−0.00224003	+	0.542107i
$799$	17.5885			0.622236
$800$		0			0
$801$	−8.15542	−	14.1256i	−0.288157	−	0.499103i
$802$	11.4202	+	19.7803i	0.403260	+	0.698466i
$803$	−2.63026	+	4.55574i	−0.0928198	+	0.160769i
$804$	40.1244			1.41508
$805$		0			0
$806$	8.20600			0.289044
$807$	3.70915	−	6.42444i	0.130568	−	0.226151i
$808$	16.1942	+	28.0492i	0.569711	+	0.986768i
$809$	25.0612	+	43.4072i	0.881104	+	1.52612i	0.850115	+	0.526596i	$0.176532\pi$
$809$	25.0612	+	43.4072i	0.881104	+	1.52612i	0.0309881	+	0.999520i	$0.490135\pi$
$810$		0			0
$811$	−36.4884			−1.28128			−0.640641	−	0.767841i	$-0.721331\pi$
$811$	−36.4884			−1.28128			−0.640641	+	0.767841i	$0.721331\pi$
$812$	−58.7021	−	34.2159i	−2.06004	−	1.20074i
$813$	31.2116			1.09464
$814$	−11.1447	+	19.3032i	−0.390622	+	0.676578i
$815$		0			0
$816$	−12.6776	−	21.9583i	−0.443806	−	0.768695i
$817$	0.396691	−	0.687090i	0.0138785	−	0.0240382i
$818$	41.8055			1.46170
$819$	−0.0562992	+	13.6249i	−0.00196725	+	0.476092i
$820$		0			0
$821$	−19.3654	+	33.5419i	−0.675858	+	1.17062i	0.300359	+	0.953826i	$0.402893\pi$
$821$	−19.3654	+	33.5419i	−0.675858	+	1.17062i	−0.976217	+	0.216794i	$0.930440\pi$
$822$	14.1329	+	24.4790i	0.492943	+	0.853803i
$823$	−10.4906	−	18.1702i	−0.365679	−	0.633375i	0.623206	−	0.782058i	$-0.285830\pi$
$823$	−10.4906	−	18.1702i	−0.365679	−	0.633375i	−0.988885	+	0.148683i	$0.952497\pi$
$824$	−48.5034	+	84.0104i	−1.68970	+	2.92664i
$825$		0			0
$826$	10.4998	−	6.00433i	0.365333	−	0.208917i
$827$	37.8114			1.31483			0.657416	−	0.753528i	$-0.271650\pi$
$827$	37.8114			1.31483			0.657416	+	0.753528i	$0.271650\pi$
$828$	−10.9908	+	19.0367i	−0.381958	+	0.661570i
$829$	26.6591	+	46.1749i	0.925908	+	1.60372i	0.790095	+	0.612985i	$0.210031\pi$
$829$	26.6591	+	46.1749i	0.925908	+	1.60372i	0.135813	+	0.990734i	$0.456635\pi$
$830$		0			0
$831$	6.22629	−	10.7843i	0.215988	−	0.374102i
$832$	−15.8453			−0.549336
$833$	29.0474	+	0.240057i	1.00643	+	0.00831747i
$834$	12.5575			0.434831
$835$		0			0
$836$	4.87423	+	8.44241i	0.168579	+	0.291987i
$837$	0.316594	+	0.548357i	0.0109431	+	0.0189540i
$838$	37.5925	−	65.1121i	1.29861	−	2.24926i
$839$	52.6452			1.81752			0.908758	−	0.417324i	$-0.137032\pi$
$839$	52.6452			1.81752			0.908758	+	0.417324i	$0.137032\pi$
$840$		0			0
$841$	6.12510			0.211210
$842$	24.3102	−	42.1066i	0.837786	−	1.45109i
$843$	−0.0204612	−	0.0354399i	−0.000704722	−	0.00122061i
$844$	−10.4498	−	18.0996i	−0.359696	−	0.623012i
$845$		0			0
$846$	−10.6663			−0.366717
$847$	0.109797	−	26.5717i	0.00377266	−	0.913015i
$848$	46.6392			1.60160
$849$	−5.42100	+	9.38944i	−0.186048	+	0.322245i
$850$		0			0
$851$	−22.9675	−	39.7809i	−0.787316	−	1.36367i
$852$	−11.9022	+	20.6152i	−0.407762	+	0.706264i
$853$	−5.01225			−0.171616			−0.0858081	−	0.996312i	$-0.527347\pi$
$853$	−5.01225			−0.171616			−0.0858081	+	0.996312i	$0.527347\pi$
$854$	−3.77505	−	2.20037i	−0.129180	−	0.0752953i
$855$		0			0
$856$	7.01129	−	12.1439i	0.239641	−	0.415071i
$857$	19.2106	+	33.2737i	0.656222	+	1.13661i	0.981586	+	0.191021i	$0.0611798\pi$
$857$	19.2106	+	33.2737i	0.656222	+	1.13661i	−0.325364	+	0.945589i	$0.605487\pi$
$858$	6.33822	+	10.9781i	0.216383	+	0.374787i
$859$	−11.6709	+	20.2146i	−0.398207	+	0.689714i	−0.993505	−	0.113791i	$-0.963701\pi$
$859$	−11.6709	+	20.2146i	−0.398207	+	0.689714i	0.595298	+	0.803505i	$0.297034\pi$
$860$		0			0
$861$	6.06893	+	3.53741i	0.206828	+	0.120555i
$862$	−55.3553			−1.88541
$863$	27.1879	−	47.0908i	0.925486	−	1.60299i	0.134707	−	0.990885i	$-0.456991\pi$
$863$	27.1879	−	47.0908i	0.925486	−	1.60299i	0.790778	−	0.612103i	$-0.209676\pi$
$864$	1.81659	+	3.14643i	0.0618018	+	0.107044i
$865$		0			0
$866$	3.43144	−	5.94342i	0.116605	−	0.201966i
$867$	−0.220576			−0.00749114
$868$	−0.0299953	+	7.25913i	−0.00101811	+	0.246391i
$869$	−10.6489			−0.361239
$870$		0			0
$871$	23.8430	+	41.2972i	0.807888	+	1.39930i
$872$	53.1662	+	92.0866i	1.80044	+	3.11845i
$873$	0.769222	−	1.33233i	0.0260342	−	0.0450926i
$874$	−29.3627			−0.993208
$875$		0			0
$876$	−23.3043			−0.787378
$877$	−14.2279	+	24.6434i	−0.480441	+	0.832148i	−0.999748	−	0.0224397i	$-0.992857\pi$
$877$	−14.2279	+	24.6434i	−0.480441	+	0.832148i	0.519307	+	0.854587i	$0.326190\pi$
$878$	9.49211	+	16.4408i	0.320343	+	0.554851i
$879$	−14.8227	−	25.6737i	−0.499958	−	0.865953i
$880$		0			0
$881$	−6.50466			−0.219148			−0.109574	−	0.993979i	$-0.534949\pi$
$881$	−6.50466			−0.219148			−0.109574	+	0.993979i	$0.534949\pi$
$882$	−17.6155	−	0.145580i	−0.593143	−	0.00490192i
$883$	−34.7640			−1.16990			−0.584951	−	0.811069i	$-0.698886\pi$
$883$	−34.7640			−1.16990			−0.584951	+	0.811069i	$0.698886\pi$
$884$	46.3007	−	80.1952i	1.55726	−	2.69726i
$885$		0			0
$886$	13.1345	+	22.7496i	0.441261	+	0.764286i
$887$	14.6770	−	25.4214i	0.492807	−	0.853566i	−0.507159	−	0.861853i	$-0.669304\pi$
$887$	14.6770	−	25.4214i	0.492807	−	0.853566i	0.999966	+	0.00828615i	$0.00263759\pi$
$888$	−53.1676			−1.78419
$889$	15.7332	−	8.99707i	0.527673	−	0.301752i
$890$		0			0
$891$	−0.489068	+	0.847090i	−0.0163844	+	0.0283786i
$892$	34.2812	+	59.3768i	1.14782	+	1.98808i
$893$	−4.87423	−	8.44241i	−0.163110	−	0.282514i
$894$	−18.2380	+	31.5891i	−0.609968	+	1.05650i
$895$		0			0
$896$	0.164091	−	39.7114i	0.00548189	−	1.32666i
$897$	−26.1242			−0.872260
$898$	2.17819	−	3.77274i	0.0726872	−	0.125898i
$899$	−1.87634	−	3.24992i	−0.0625795	−	0.108391i
$900$		0			0
$901$	15.8380	−	27.4322i	0.527640	−	0.913899i
$902$	6.53556			0.217610
$903$	0.788480	+	0.459584i	0.0262390	+	0.0152940i
$904$	23.7432			0.789688
$905$		0			0
$906$	9.92404	+	17.1889i	0.329704	+	0.571064i
$907$	18.1436	+	31.4256i	0.602447	+	1.04347i	0.992449	+	0.122655i	$0.0391410\pi$
$907$	18.1436	+	31.4256i	0.602447	+	1.04347i	−0.390002	+	0.920814i	$0.627526\pi$
$908$	−47.0113	+	81.4259i	−1.56012	+	2.70221i
$909$	−5.51610			−0.182958
$910$		0			0
$911$	51.6732			1.71201			0.856004	−	0.516968i	$-0.172940\pi$
$911$	51.6732			1.71201			0.856004	+	0.516968i	$0.172940\pi$
$912$	−7.02660	+	12.1704i	−0.232674	+	0.403003i
$913$	−3.24087	−	5.61335i	−0.107257	−	0.185775i
$914$	−38.8326	−	67.2601i	−1.28447	−	2.22477i
$915$		0			0
$916$	−8.99952			−0.297353
$917$	0.0440071	−	10.6501i	0.00145324	−	0.351698i
$918$	10.4432			0.344678
$919$	20.5188	−	35.5397i	0.676854	−	1.17235i	−0.299069	−	0.954231i	$-0.596676\pi$
$919$	20.5188	−	35.5397i	0.676854	−	1.17235i	0.975923	−	0.218114i	$-0.0699905\pi$
$920$		0			0
$921$	−15.8027	−	27.3712i	−0.520718	−	0.901910i
$922$	−13.5007	+	23.3839i	−0.444621	+	0.770107i
$923$	−28.2903			−0.931187
$924$	−9.73455	+	5.56674i	−0.320243	+	0.183132i
$925$		0			0
$926$	−13.9746	+	24.2047i	−0.459234	+	0.795417i
$927$	−8.26066	−	14.3079i	−0.271316	−	0.469932i
$928$	−10.7663	−	18.6478i	−0.353421	−	0.612144i
$929$	1.49260	−	2.58526i	0.0489706	−	0.0848196i	−0.840501	−	0.541810i	$-0.817739\pi$
$929$	1.49260	−	2.58526i	0.0489706	−	0.0848196i	0.889472	+	0.456990i	$0.151073\pi$
$930$		0			0
$931$	−7.93455	−	14.0091i	−0.260044	−	0.459131i
$932$	29.2880			0.959361
$933$	11.0851	−	19.2000i	0.362911	−	0.628581i
$934$	−34.7155	−	60.1291i	−1.13593	−	1.96748i
$935$		0			0
$936$	−15.1187	+	26.1864i	−0.494171	+	0.855930i
$937$	−26.1169			−0.853201			−0.426601	−	0.904440i	$-0.640289\pi$
$937$	−26.1169			−0.853201			−0.426601	+	0.904440i	$0.640289\pi$
$938$	−53.5210	+	30.6062i	−1.74752	+	0.999327i
$939$	6.88572			0.224707
$940$		0			0
$941$	−5.10580	−	8.84351i	−0.166444	−	0.288290i	0.770723	−	0.637171i	$-0.219895\pi$
$941$	−5.10580	−	8.84351i	−0.166444	−	0.288290i	−0.937167	+	0.348880i	$0.886562\pi$
$942$	8.24973	+	14.2889i	0.268791	+	0.465559i
$943$	−6.73438	+	11.6643i	−0.219302	+	0.379842i
$944$	11.0995			0.361257
$945$		0			0
$946$	0.849106			0.0276068
$947$	23.2722	−	40.3086i	0.756245	−	1.30985i	−0.188509	−	0.982072i	$-0.560365\pi$
$947$	23.2722	−	40.3086i	0.756245	−	1.30985i	0.944753	−	0.327783i	$-0.106301\pi$
$948$	−23.5875	−	40.8547i	−0.766085	−	1.32690i
$949$	−13.8480	−	23.9854i	−0.449525	−	0.778600i
$950$		0			0
$951$	12.8387			0.416324
$952$	55.6955	+	32.4634i	1.80510	+	1.05215i
$953$	−30.6348			−0.992358			−0.496179	−	0.868220i	$-0.665264\pi$
$953$	−30.6348			−0.992358			−0.496179	+	0.868220i	$0.665264\pi$
$954$	−9.60476	+	16.6359i	−0.310966	+	0.538608i
$955$		0			0
$956$	6.29345	+	10.9006i	0.203545	+	0.352550i
$957$	2.89853	−	5.02040i	0.0936961	−	0.162286i
$958$	−25.2095			−0.814483
$959$	−25.6738	−	14.9646i	−0.829051	−	0.483232i
$960$		0			0
$961$	15.2995	−	26.4996i	0.493533	−	0.854825i
$962$	−58.6757	−	101.629i	−1.89178	−	3.27666i
$963$	1.19410	+	2.06824i	0.0384793	+	0.0666481i
$964$	19.2772	−	33.3891i	0.620877	−	1.07539i
$965$		0			0
$966$	0.139566	−	33.7762i	0.00449046	−	1.08673i
$967$	−57.4401			−1.84715			−0.923575	−	0.383419i	$-0.874747\pi$
$967$	−57.4401			−1.84715			−0.923575	+	0.383419i	$0.874747\pi$
$968$	29.4851	−	51.0696i	0.947686	−	1.64144i
$969$	4.77226	+	8.26580i	0.153307	+	0.265536i
$970$		0			0
$971$	−24.0908	+	41.7265i	−0.773110	+	1.33907i	0.162740	+	0.986669i	$0.447967\pi$
$971$	−24.0908	+	41.7265i	−0.773110	+	1.33907i	−0.935850	+	0.352397i	$0.885367\pi$
$972$	−4.33317			−0.138987
$973$	−11.4605	+	6.55373i	−0.367407	+	0.210103i
$974$	−77.3449			−2.47829
$975$		0			0
$976$	−2.00488	−	3.47255i	−0.0641746	−	0.111154i
$977$	−6.87617	−	11.9099i	−0.219988	−	0.381031i	0.734816	−	0.678267i	$-0.237269\pi$
$977$	−6.87617	−	11.9099i	−0.219988	−	0.381031i	−0.954804	+	0.297236i	$0.903935\pi$
$978$	−15.4214	+	26.7106i	−0.493121	+	0.854110i
$979$	15.9542			0.509898
$980$		0			0
$981$	−18.1096			−0.578194
$982$	−5.21001	+	9.02399i	−0.166258	+	0.287967i
$983$	−19.0972	−	33.0773i	−0.609106	−	1.05500i	−0.991388	−	0.130957i	$-0.958195\pi$
$983$	−19.0972	−	33.0773i	−0.609106	−	1.05500i	0.382282	−	0.924046i	$-0.375138\pi$
$984$	7.79473	+	13.5009i	0.248487	+	0.430392i
$985$		0			0
$986$	−61.8933			−1.97108
$987$	9.73455	−	5.56674i	0.309854	−	0.177191i
$988$	−51.3245			−1.63285
$989$	−0.874937	+	1.51544i	−0.0278214	+	0.0481880i
$990$		0			0
$991$	−19.7600	−	34.2253i	−0.627697	−	1.08720i	−0.988013	−	0.154372i	$-0.950665\pi$
$991$	−19.7600	−	34.2253i	−0.627697	−	1.08720i	0.360316	−	0.932830i	$-0.382669\pi$
$992$	−1.15025	+	1.99228i	−0.0365204	+	0.0632551i
$993$	8.53357			0.270805
$994$	0.151139	−	36.5768i	0.00479382	−	1.16015i
$995$		0			0
$996$	14.3572	−	24.8673i	0.454924	−	0.787952i
$997$	5.76448	+	9.98438i	0.182563	+	0.316208i	0.942753	−	0.333493i	$-0.108227\pi$
$997$	5.76448	+	9.98438i	0.182563	+	0.316208i	−0.760190	+	0.649701i	$0.774894\pi$
$998$	1.94818	+	3.37435i	0.0616687	+	0.106813i
$999$	4.52751	−	7.84188i	0.143244	−	0.248106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.h.226.1		8
5.2	odd	4		105.2.q.a.79.1	yes	16
5.3	odd	4		105.2.q.a.79.8	yes	16
5.4	even	2		525.2.i.k.226.4		8
7.2	even	3		3675.2.a.bz.1.4		4
7.4	even	3	inner	525.2.i.h.151.1		8
7.5	odd	6		3675.2.a.cb.1.4		4
15.2	even	4		315.2.bf.b.289.8		16
15.8	even	4		315.2.bf.b.289.1		16
20.3	even	4		1680.2.di.d.289.5		16
20.7	even	4		1680.2.di.d.289.4		16
35.2	odd	12		735.2.d.d.589.8		8
35.3	even	12		735.2.q.g.214.1		16
35.4	even	6		525.2.i.k.151.4		8
35.9	even	6		3675.2.a.bp.1.1		4
35.12	even	12		735.2.d.e.589.8		8
35.13	even	4		735.2.q.g.79.8		16
35.17	even	12		735.2.q.g.214.8		16
35.18	odd	12		105.2.q.a.4.1	✓	16
35.19	odd	6		3675.2.a.bn.1.1		4
35.23	odd	12		735.2.d.d.589.1		8
35.27	even	4		735.2.q.g.79.1		16
35.32	odd	12		105.2.q.a.4.8	yes	16
35.33	even	12		735.2.d.e.589.1		8
105.2	even	12		2205.2.d.s.1324.1		8
105.23	even	12		2205.2.d.s.1324.8		8
105.32	even	12		315.2.bf.b.109.1		16
105.47	odd	12		2205.2.d.o.1324.1		8
105.53	even	12		315.2.bf.b.109.8		16
105.68	odd	12		2205.2.d.o.1324.8		8
140.67	even	12		1680.2.di.d.529.5		16
140.123	even	12		1680.2.di.d.529.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	35.18	odd	12
105.2.q.a.4.8	yes	16	35.32	odd	12
105.2.q.a.79.1	yes	16	5.2	odd	4
105.2.q.a.79.8	yes	16	5.3	odd	4
315.2.bf.b.109.1		16	105.32	even	12
315.2.bf.b.109.8		16	105.53	even	12
315.2.bf.b.289.1		16	15.8	even	4
315.2.bf.b.289.8		16	15.2	even	4
525.2.i.h.151.1		8	7.4	even	3	inner
525.2.i.h.226.1		8	1.1	even	1	trivial
525.2.i.k.151.4		8	35.4	even	6
525.2.i.k.226.4		8	5.4	even	2
735.2.d.d.589.1		8	35.23	odd	12
735.2.d.d.589.8		8	35.2	odd	12
735.2.d.e.589.1		8	35.33	even	12
735.2.d.e.589.8		8	35.12	even	12
735.2.q.g.79.1		16	35.27	even	4
735.2.q.g.79.8		16	35.13	even	4
735.2.q.g.214.1		16	35.3	even	12
735.2.q.g.214.8		16	35.17	even	12
1680.2.di.d.289.4		16	20.7	even	4
1680.2.di.d.289.5		16	20.3	even	4
1680.2.di.d.529.4		16	140.123	even	12
1680.2.di.d.529.5		16	140.67	even	12
2205.2.d.o.1324.1		8	105.47	odd	12
2205.2.d.o.1324.8		8	105.68	odd	12
2205.2.d.s.1324.1		8	105.2	even	12
2205.2.d.s.1324.8		8	105.23	even	12
3675.2.a.bn.1.1		4	35.19	odd	6
3675.2.a.bp.1.1		4	35.9	even	6
3675.2.a.bz.1.4		4	7.2	even	3
3675.2.a.cb.1.4		4	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25829 + 2.17942i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.16659 - 3.75264i) q^{4} -2.51658 q^{6} +(2.29673 - 1.31340i) q^{7} +5.87162 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.489068 - 0.847090i) q^{11} +(2.16659 - 3.75264i) q^{12} +5.14977 q^{13} +(-0.0275122 + 6.65819i) q^{14} +(-3.05502 + 5.29146i) q^{16} +(2.07488 + 3.59380i) q^{17} +(-1.25829 - 2.17942i) q^{18} +(1.15001 - 1.99187i) q^{19} +(2.28580 + 1.33233i) q^{21} +2.46156 q^{22} +(-2.53644 + 4.39324i) q^{23} +(2.93581 + 5.08497i) q^{24} +(-6.47990 + 11.2235i) q^{26} -1.00000 q^{27} +(-9.90478 - 5.77323i) q^{28} +5.92664 q^{29} +(-0.316594 - 0.548357i) q^{31} +(-1.81659 - 3.14643i) q^{32} +(0.489068 - 0.847090i) q^{33} -10.4432 q^{34} +4.33317 q^{36} +(-4.52751 + 7.84188i) q^{37} +(2.89408 + 5.01270i) q^{38} +(2.57488 + 4.45983i) q^{39} +2.65505 q^{41} +(-5.77992 + 3.30527i) q^{42} +0.344947 q^{43} +(-2.11922 + 3.67059i) q^{44} +(-6.38315 - 11.0559i) q^{46} +(2.11922 - 3.67059i) q^{47} -6.11005 q^{48} +(3.54998 - 6.03305i) q^{49} +(-2.07488 + 3.59380i) q^{51} +(-11.1574 - 19.3252i) q^{52} +(-3.81659 - 6.61053i) q^{53} +(1.25829 - 2.17942i) q^{54} +(13.4855 - 7.71176i) q^{56} +2.30001 q^{57} +(-7.45743 + 12.9167i) q^{58} +(-0.908297 - 1.57322i) q^{59} +(-0.328128 + 0.568335i) q^{61} +1.59347 q^{62} +(-0.0109324 + 2.64573i) q^{63} -3.07689 q^{64} +(1.23078 + 2.13177i) q^{66} +(4.62991 + 8.01924i) q^{67} +(8.99083 - 15.5726i) q^{68} -5.07288 q^{69} -5.49351 q^{71} +(-2.93581 + 5.08497i) q^{72} +(-2.68905 - 4.65758i) q^{73} +(-11.3938 - 19.7347i) q^{74} -9.96636 q^{76} +(-2.23582 - 1.30320i) q^{77} -12.9598 q^{78} +(5.44346 - 9.42835i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.34083 + 5.78648i) q^{82} +6.62663 q^{83} +(0.0473719 - 11.4644i) q^{84} +(-0.434043 + 0.751785i) q^{86} +(2.96332 + 5.13262i) q^{87} +(-2.87162 - 4.97379i) q^{88} +(-8.15542 + 14.1256i) q^{89} +(11.8277 - 6.76369i) q^{91} +21.9817 q^{92} +(0.316594 - 0.548357i) q^{93} +(5.33317 + 9.23733i) q^{94} +(1.81659 - 3.14643i) q^{96} -1.53844 q^{97} +(8.68165 + 15.3282i) q^{98} +0.978135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 4 q^{13} + 12 q^{14} - 2 q^{17} - 2 q^{18} + 12 q^{19} - 2 q^{21} + 28 q^{22} - 10 q^{23} + 6 q^{24} - 6 q^{26} - 8 q^{27}+ \cdots - 20 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9 + 4 * q^12 + 4 * q^13 + 12 * q^14 - 2 * q^17 - 2 * q^18 + 12 * q^19 - 2 * q^21 + 28 * q^22 - 10 * q^23 + 6 * q^24 - 6 * q^26 - 8 * q^27 - 12 * q^28 - 12 * q^29 + 8 * q^31 - 4 * q^32 - 8 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 + 2 * q^39 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 10 * q^44 - 16 * q^46 + 10 * q^47 + 20 * q^49 + 2 * q^51 - 34 * q^52 - 20 * q^53 + 2 * q^54 + 42 * q^56 + 24 * q^57 - 10 * q^58 - 2 * q^59 + 8 * q^61 - 20 * q^62 - 4 * q^63 - 8 * q^64 + 14 * q^66 - 6 * q^67 + 30 * q^68 - 20 * q^69 - 28 * q^71 - 6 * q^72 - 12 * q^73 - 20 * q^74 - 32 * q^76 - 6 * q^77 - 12 * q^78 + 8 * q^79 - 4 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 - 24 * q^86 - 6 * q^87 + 12 * q^88 - 8 * q^89 + 4 * q^91 + 92 * q^92 - 8 * q^93 + 16 * q^94 + 4 * q^96 - 4 * q^97 - 20 * q^98

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